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+20081122 tpd src/axiom-website put website under change control
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diff --git a/src/axiom-website/CATS/index.html b/src/axiom-website/CATS/index.html
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+&lt;html&gt;
+ &lt;head&gt;
+  &lt;title&gt;
+   (CATS) Computer Algebra Test Suite
+  &lt;/title&gt;
+ &lt;/head&gt;
+ &lt;body&gt;
+This work is part of the Computer Algebra Test Suite (CATS).
+These files show the results that Axiom computes given the
+set of integrals listed in 
+&lt;pre&gt;
+  Spiegel, Murray R. 
+  Mathematical Handbook of Formulas and Tables
+  Schaum's Outline Series McGraw-Hill 1968 
+&lt;/pre&gt;
+&lt;p&gt;
+Each integral is computed by Axiom and compared against the
+published result.
+&lt;p&gt;
+Each Axiom result is differenced from the published result 
+and reduced to a constant (usually 0). 
+&lt;p&gt;
+
+
+  Schaums 14.59-14.83&amp;nbsp
+  &lt;a href="schaum1.input.pamphlet"&gt;source&lt;/a&gt;
+  &lt;a href="schaum1.input.pdf"&gt;pdf&lt;/a&gt;&lt;br/&gt;
+  Schaums 14.84-14.104&amp;nbsp
+  &lt;a href="schaum2.input.pamphlet"&gt;source&lt;/a&gt;
+  &lt;a href="schaum2.input.pdf"&gt;pdf&lt;/a&gt;&lt;br/&gt;
+  Schaums 14.104-14.112&amp;nbsp
+  &lt;a href="schaum3.input.pamphlet"&gt;source&lt;/a&gt;
+  &lt;a href="schaum3.input.pdf"&gt;pdf&lt;/a&gt;&lt;br/&gt;
+  Schaums 14.113-.119&amp;nbsp
+  &lt;a href="schaum4.input.pamphlet"&gt;source&lt;/a&gt;
+  &lt;a href="schaum4.input.pdf"&gt;pdf&lt;/a&gt;&lt;br/&gt;
+  Schaums 14.120-14.124&amp;nbsp
+  &lt;a href="schaum5.input.pamphlet"&gt;source&lt;/a&gt;
+  &lt;a href="schaum5.input.pdf"&gt;pdf&lt;/a&gt;&lt;br/&gt;
+  Schaums 14.125-14.143&amp;nbsp
+  &lt;a href="schaum6.input.pamphlet"&gt;source&lt;/a&gt;
+  &lt;a href="schaum6.input.pdf"&gt;pdf&lt;/a&gt;&lt;br/&gt;
+  Schaums 14.144-14.162&amp;nbsp
+  &lt;a href="schaum7.input.pamphlet"&gt;source&lt;/a&gt;
+  &lt;a href="schaum7.input.pdf"&gt;pdf&lt;/a&gt;&lt;br/&gt;
+  Schaums 14.163-14.181&amp;nbsp
+  &lt;a href="schaum8.input.pamphlet"&gt;source&lt;/a&gt;
+  &lt;a href="schaum8.input.pdf"&gt;pdf&lt;/a&gt;&lt;br/&gt;
+  Schaums 14.182-14.209&amp;nbsp
+  &lt;a href="schaum9.input.pamphlet"&gt;source&lt;/a&gt;
+  &lt;a href="schaum9.input.pdf"&gt;pdf&lt;/a&gt;&lt;br/&gt;
+  Schaums 14.210-14.236&amp;nbsp
+  &lt;a href="schaum10.input.pamphlet"&gt;source&lt;/a&gt;
+  &lt;a href="schaum10.input.pdf"&gt;pdf&lt;/a&gt;&lt;br/&gt;
+  Schaums 14.237-14.264&amp;nbsp
+  &lt;a href="schaum11.input.pamphlet"&gt;source&lt;/a&gt;
+  &lt;a href="schaum11.input.pdf"&gt;pdf&lt;/a&gt;&lt;br/&gt;
+  Schaums 14.265-14.279&amp;nbsp
+  &lt;a href="schaum12.input.pamphlet"&gt;source&lt;/a&gt;
+  &lt;a href="schaum12.input.pdf"&gt;pdf&lt;/a&gt;&lt;br/&gt;
+  Schaums 14.280-14.298&amp;nbsp
+  &lt;a href="schaum13.input.pamphlet"&gt;source&lt;/a&gt;
+  &lt;a href="schaum13.input.pdf"&gt;pdf&lt;/a&gt;&lt;br/&gt;
+  Schaums 14.299-14.310&amp;nbsp
+  &lt;a href="schaum14.input.pamphlet"&gt;source&lt;/a&gt;
+  &lt;a href="schaum14.input.pdf"&gt;pdf&lt;/a&gt;&lt;br/&gt;
+  Schaums 14.311-14.324&amp;nbsp
+  &lt;a href="schaum15.input.pamphlet"&gt;source&lt;/a&gt;
+  &lt;a href="schaum15.input.pdf"&gt;pdf&lt;/a&gt;&lt;br/&gt;
+  Schaums 14.325-14.338&amp;nbsp
+  &lt;a href="schaum16.input.pamphlet"&gt;source&lt;/a&gt;
+  &lt;a href="schaum16.input.pdf"&gt;pdf&lt;/a&gt;&lt;br/&gt;
+  Schaums 14.339-14.368&amp;nbsp
+  &lt;a href="schaum17.input.pamphlet"&gt;source&lt;/a&gt;
+  &lt;a href="schaum17.input.pdf"&gt;pdf&lt;/a&gt;&lt;br/&gt;
+  Schaums 14.369-14.398&amp;nbsp
+  &lt;a href="schaum18.input.pamphlet"&gt;source&lt;/a&gt;
+  &lt;a href="schaum18.input.pdf"&gt;pdf&lt;/a&gt;&lt;br/&gt;
+  Schaums 14.399-14.428&amp;nbsp
+  &lt;a href="schaum19.input.pamphlet"&gt;source&lt;/a&gt;
+  &lt;a href="schaum19.input.pdf"&gt;pdf&lt;/a&gt;&lt;br/&gt;
+  Schaums 14.429-14.439&amp;nbsp
+  &lt;a href="schaum20.input.pamphlet"&gt;source&lt;/a&gt;
+  &lt;a href="schaum20.input.pdf"&gt;pdf&lt;/a&gt;&lt;br/&gt;
+  Schaums 14.440-14.450&amp;nbsp
+  &lt;a href="schaum21.input.pamphlet"&gt;source&lt;/a&gt;
+  &lt;a href="schaum21.input.pdf"&gt;pdf&lt;/a&gt;&lt;br/&gt;
+  Schaums 14.451-14.460&amp;nbsp
+  &lt;a href="schaum22.input.pamphlet"&gt;source&lt;/a&gt;
+  &lt;a href="schaum22.input.pdf"&gt;pdf&lt;/a&gt;&lt;br/&gt;
+  Schaums 14.461-14.470&amp;nbsp
+  &lt;a href="schaum23.input.pamphlet"&gt;source&lt;/a&gt;
+  &lt;a href="schaum23.input.pdf"&gt;pdf&lt;/a&gt;&lt;br/&gt;
+  Schaums 14.471-14.508&amp;nbsp
+  &lt;a href="schaum24.input.pamphlet"&gt;source&lt;/a&gt;
+  &lt;a href="schaum24.input.pdf"&gt;pdf&lt;/a&gt;&lt;br/&gt;
+  Schaums 14.509-14.524&amp;nbsp
+  &lt;a href="schaum25.input.pamphlet"&gt;source&lt;/a&gt;
+  &lt;a href="schaum25.input.pdf"&gt;pdf&lt;/a&gt;&lt;br/&gt;
+  Schaums 14.525-14.539&amp;nbsp
+  &lt;a href="schaum26.input.pamphlet"&gt;source&lt;/a&gt;
+  &lt;a href="schaum26.input.pdf"&gt;pdf&lt;/a&gt;&lt;br/&gt;
+  Schaums 14.540-14.561&amp;nbsp
+  &lt;a href="schaum27.input.pamphlet"&gt;source&lt;/a&gt;
+  &lt;a href="schaum27.input.pdf"&gt;pdf&lt;/a&gt;&lt;br/&gt;
+  Schaums 14.562-14.589&amp;nbsp
+  &lt;a href="schaum28.input.pamphlet"&gt;source&lt;/a&gt;
+  &lt;a href="schaum28.input.pdf"&gt;pdf&lt;/a&gt;&lt;br/&gt;
+  Schaums 14.590-14.603&amp;nbsp
+  &lt;a href="schaum29.input.pamphlet"&gt;source&lt;/a&gt;
+  &lt;a href="schaum29.input.pdf"&gt;pdf&lt;/a&gt;&lt;br/&gt;
+  Schaums 14.604-14.614&amp;nbsp
+  &lt;a href="schaum30.input.pamphlet"&gt;source&lt;/a&gt;
+  &lt;a href="schaum30.input.pdf"&gt;pdf&lt;/a&gt;&lt;br/&gt;
+  Schaums 14.615-14.625&amp;nbsp
+  &lt;a href="schaum31.input.pamphlet"&gt;source&lt;/a&gt;
+  &lt;a href="schaum31.input.pdf"&gt;pdf&lt;/a&gt;&lt;br/&gt;
+  Schaums 14.626-14.635&amp;nbsp
+  &lt;a href="schaum32.input.pamphlet"&gt;source&lt;/a&gt;
+  &lt;a href="schaum32.input.pdf"&gt;pdf&lt;/a&gt;&lt;br/&gt;
+  Schaums 14.636-14.645&amp;nbsp
+  &lt;a href="schaum33.input.pamphlet"&gt;source&lt;/a&gt;
+  &lt;a href="schaum33.input.pdf"&gt;pdf&lt;/a&gt;&lt;br/&gt;
+  Schaums 14.646-14.677&amp;nbsp
+  &lt;a href="schaum34.input.pamphlet"&gt;source&lt;/a&gt;
+  &lt;a href="schaum34.input.pdf"&gt;pdf&lt;/a&gt;&lt;br/&gt;
+ &lt;/body&gt;
+&lt;/html&gt;
\ No newline at end of file
diff --git a/src/axiom-website/CATS/schaum1.input.pamphlet b/src/axiom-website/CATS/schaum1.input.pamphlet
new file mode 100644
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--- /dev/null
+++ b/src/axiom-website/CATS/schaum1.input.pamphlet
@@ -0,0 +1,1430 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum1.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.59~~~~~$\displaystyle
+\int{\frac{dx}{ax+b}}$}
+$$\int{\frac{1}{ax+b}}=
+\frac{1}{a}~\ln(ax+b)
+$$
+&lt;&lt;*&gt;&gt;=
+)spool schaum1.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1
+aa:=integrate(1/(a*x+b),x)
+--R
+--R        log(a x + b)
+--R   (1)  ------------
+--R              a
+--R                                          Type: Union(Expression Integer,...)
+--E 1
+
+--S 2
+bb:=1/a*log(a*x+b)
+--R
+--R        log(a x + b)
+--R   (2)  ------------
+--R              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3      14:59 Schaums and Axiom agree
+cc:=bb-aa
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+\section{\cite{1}:14.60~~~~~$\displaystyle
+\int{\frac{x~dx}{ax+b}}$}
+$$\int{\frac{x}{ax+b}}=
+\frac{x}{a}-\frac{b}{a^2}~\ln(ax+b)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 4
+aa:=integrate(x/(a*x+b),x)
+--R 
+--R
+--R        - b log(a x + b) + a x
+--R   (1)  ----------------------
+--R                   2
+--R                  a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 5
+bb:=x/a-b/a^2*log(a*x+b)
+--R
+--R        - b log(a x + b) + a x
+--R   (2)  ----------------------
+--R                   2
+--R                  a
+--R                                                     Type: Expression Integer
+--E
+
+--S 6      14:60 Schaums and Axiom agree
+cc:=bb-aa
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.61~~~~~$\displaystyle
+\int{\frac{x^2~dx}{ax+b}}$}
+$$\int{\frac{x^2}{ax+b}}=
+\frac{(ax+b)^2}{2a^3}-\frac{2b(ax+b)}{a^3}+\frac{b^2}{a^3}~\ln(ax+b)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 7
+aa:=integrate(x^2/(a*x+b),x)
+--R
+--R          2                2 2
+--R        2b log(a x + b) + a x  - 2a b x
+--R   (1)  -------------------------------
+--R                        3
+--R                      2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 8
+bb:=(a*x+b)^2/(2*a^3)-(2*b*(a*x+b))/a^3+b^2/a^3*log(a*x+b)
+--R
+--R          2                2 2              2
+--R        2b log(a x + b) + a x  - 2a b x - 3b
+--R   (2)  -------------------------------------
+--R                           3
+--R                         2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 9
+cc:=bb-aa
+--R
+--R            2
+--R          3b
+--R   (3)  - ---
+--R            3
+--R          2a
+--R                                                     Type: Expression Integer
+--E
+@
+This factor is constant with respect to $x$ as shown by taking the
+derivative. It is a constant of integration.
+&lt;&lt;*&gt;&gt;=
+--S 10     14:61 Schaums and Axiom differ by a constant
+differentiate(cc,x)
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
+@
+\section{\cite{1}:14.62~~~~~$\displaystyle
+\int{\frac{x^3~dx}{ax+b}}$}
+$$\int{\frac{x^3}{ax+b}}=
+\frac{(ax+b)^3}{3a^4}-\frac{3b(ax+b)^2}{2a^4}+
+\frac{3b^2(ax+b)}{a^4}-\frac{b^3}{a^4}~\ln(ax+b)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 11
+aa:=integrate(x^3/(a*x+b),x)
+--R
+--R            3                 3 3     2   2       2
+--R        - 6b log(a x + b) + 2a x  - 3a b x  + 6a b x
+--R   (1)  --------------------------------------------
+--R                               4
+--R                             6a
+--R                                          Type: Union(Expression Integer,...)
+--E
+@
+and the book expression is:
+&lt;&lt;*&gt;&gt;=
+--S 12
+bb:=(a*x+b)^3/(3*a^4)-(3*b*(a*x+b)^2)/(2*a^4)+(3*b^2*(a*x+b))/a^4-(b^3/a^4)*log(a*x+b)
+--R
+--R            3                 3 3     2   2       2       3
+--R        - 6b log(a x + b) + 2a x  - 3a b x  + 6a b x + 11b
+--R   (2)  ---------------------------------------------------
+--R                                  4
+--R                                6a
+--R                                                     Type: Expression Integer
+--E 
+@
+
+The difference is a constant with respect to x:
+&lt;&lt;*&gt;&gt;=
+--S 13
+cc:=aa-bb
+--R
+--R             3
+--R          11b
+--R   (3)  - ----
+--R             4
+--R           6a
+--R                                                     Type: Expression Integer
+--E 
+@
+
+If we differentiate each expression we see that this is the integration
+constant.
+&lt;&lt;*&gt;&gt;=
+--S 14     14:62 Schaums and Axiom differ by a constant
+dd:=D(cc,x)
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E 
+@
+
+\section{\cite{1}:14.63~~~~~$\displaystyle
+\int{\frac{dx}{x~(ax+b)}}$}
+$$\int{\frac{1}{x~(ax+b)}}=
+\frac{1}{b}~\ln\left(\frac{x}{ax+b}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 15
+aa:=integrate(1/(x*(a*x+b)),x)
+--R
+--R        - log(a x + b) + log(x)
+--R   (1)  -----------------------
+--R                   b
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 16
+bb:=1/b*log(x/(a*x+b))
+--R
+--R               x
+--R        log(-------)
+--R            a x + b
+--R   (2)  ------------
+--R              b
+--R                                                     Type: Expression Integer
+--E
+
+--S 17
+cc:=aa-bb
+--R
+--R                                         x
+--R        - log(a x + b) + log(x) - log(-------)
+--R                                      a x + b
+--R   (3)  --------------------------------------
+--R                           b
+--R                                                     Type: Expression Integer
+--E
+@
+but we know that $$\log(a)-\log(b)=\log(\frac{a}{b})$$
+
+We can express this fact as a rule:
+&lt;&lt;*&gt;&gt;=
+--S 18
+logdiv:=rule(log(a)-log(b) == log(a/b))
+--R
+--R                                      a
+--I   (4)  - log(b) + log(a) + %I == log(-) + %I
+--R                                      b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E 
+@
+and use this rule to rewrite the logs into divisions:
+&lt;&lt;*&gt;&gt;=
+--S 19     14:63 Schaums and Axiom agree
+dd:=logdiv cc
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
+@
+so we can see the equivalence directly.
+
+\section{\cite{1}:14.64~~~~~$\displaystyle
+\int{\frac{dx}{x^2~(ax+b)}}$}
+$$\int{\frac{1}{x^2~(ax+b)}}=
+-\frac{1}{bx}+\frac{a}{b^2}~\ln\left(\frac{ax+b}{x}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 20
+aa:=integrate(1/(x^2*(a*x+b)),x)
+--R
+--R        a x log(a x + b) - a x log(x) - b
+--R   (1)  ---------------------------------
+--R                        2
+--R                       b x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+The original form given in the book expands to:
+&lt;&lt;*&gt;&gt;=
+--S 21
+bb:=-1/(b*x)+a/b^2*log((a*x+b)/x)
+--R
+--R                a x + b
+--R        a x log(-------) - b
+--R                   x
+--R   (2)  --------------------
+--R                  2
+--R                 b x
+--R                                                     Type: Expression Integer
+--E 
+
+--S 22
+cc:=aa-bb
+--R
+--R                                          a x + b
+--R        a log(a x + b) - a log(x) - a log(-------)
+--R                                             x
+--R   (3)  ------------------------------------------
+--R                             2
+--R                            b
+--R                                                     Type: Expression Integer
+--E
+@
+
+We can define the following rule to expand log forms:
+&lt;&lt;*&gt;&gt;=
+--S 23
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E 
+@
+and apply it to the difference
+&lt;&lt;*&gt;&gt;=
+--S 24     14:64 Schaums and Axiom agree
+divlog cc
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.65~~~~~$\displaystyle
+\int{\frac{dx}{x^3~(ax+b)}}$}
+$$\int{\frac{1}{x^3~(ax+b)}}=
+\frac{2ax-b}{2b^2x^2}+\frac{a^2}{b^3}~\ln\left(\frac{x}{ax+b}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+--S 25
+aa:=integrate(1/(x^3*(a*x+b)),x)
+--R
+--R            2 2                 2 2                   2
+--R        - 2a x log(a x + b) + 2a x log(x) + 2a b x - b
+--R   (1)  -----------------------------------------------
+--R                               3 2
+--R                             2b x
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 26
+bb:=(2*a*x-b)/(2*b^2*x^2)+a^2/b^3*log(x/(a*x+b))
+--R
+--R          2 2       x                 2
+--R        2a x log(-------) + 2a b x - b
+--R                 a x + b
+--R   (2)  -------------------------------
+--R                       3 2
+--R                     2b x
+--R                                                     Type: Expression Integer
+--E
+
+--S 27
+cc:=aa-bb
+--R
+--R           2                2          2       x
+--R        - a log(a x + b) + a log(x) - a log(-------)
+--R                                            a x + b
+--R   (3)  --------------------------------------------
+--R                              3
+--R                             b
+--R                                                     Type: Expression Integer
+--E
+
+--S 28
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 29     14:65 Schaums and Axiom agree
+dd:=divlog cc
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E 
+@
+
+\section{\cite{1}:14.66~~~~~$\displaystyle
+\int{\frac{dx}{(ax+b)^2}}$}
+$$\int{\frac{1}{(ax+b)^2}}=
+\frac{-1}{a~(ax+b)}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 30
+aa:=integrate(1/(a*x+b)^2,x)
+--R
+--R              1
+--R   (1)  - ---------
+--R           2
+--R          a x + a b
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 31
+bb:=-1/(a*(a*x+b))
+--R
+--R              1
+--R   (2)  - ---------
+--R           2
+--R          a x + a b
+--R                                            Type: Fraction Polynomial Integer
+--E
+
+--S 32     14:66 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.67~~~~~$\displaystyle
+\int{\frac{x~dx}{(ax+b)^2}}$}
+$$\int{\frac{x}{(ax+b)^2}}=
+\frac{b}{a^2~(ax+b)}+\frac{1}{a^2}~\ln(ax+b)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 33
+aa:=integrate(x/(a*x+b)^2,x)
+--R
+--R        (a x + b)log(a x + b) + b
+--R   (1)  -------------------------
+--R                 3     2
+--R                a x + a b
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 34
+bb:=b/(a^2*(a*x+b))+1/a^2*log(a*x+b)
+--R
+--R        (a x + b)log(a x + b) + b
+--R   (2)  -------------------------
+--R                 3     2
+--R                a x + a b
+--R                                                     Type: Expression Integer
+--E
+
+--S 35     14:67 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.68~~~~~$\displaystyle
+\int{\frac{x^2~dx}{(ax+b)^2}}$}
+$$\int{\frac{x^2}{(ax+b)^2}}=
+\frac{ax+b}{a^3}-\frac{b^2}{a^3~(ax+b)}
+-\frac{2b}{a^3}~\ln(ax+b)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 36
+aa:=integrate(x^2/(a*x+b)^2,x)
+--R
+--R                      2                 2 2            2
+--R        (- 2a b x - 2b )log(a x + b) + a x  + a b x - b
+--R   (1)  ------------------------------------------------
+--R                             4     3
+--R                            a x + a b
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+and the book expression expands into
+&lt;&lt;*&gt;&gt;=
+--S 37
+bb:=(a*x+b)/a^3-b^2/(a^3*(a*x+b))-((2*b)/a^3)*log(a*x+b)
+--R
+--R                      2                 2 2
+--R        (- 2a b x - 2b )log(a x + b) + a x  + 2a b x
+--R   (2)  --------------------------------------------
+--R                           4     3
+--R                          a x + a b
+--R                                                     Type: Expression Integer
+--E 
+@
+
+These two expressions differ by the constant
+&lt;&lt;*&gt;&gt;=
+--S 38
+cc:=aa-bb
+--R
+--R           b
+--R   (3)  - --
+--R           3
+--R          a
+--R                                                     Type: Expression Integer
+--E 
+@
+
+That this expression is constant can be shown by differentiation:
+&lt;&lt;*&gt;&gt;=
+--S 39     14:68 Schaums and Axiom differ by a constant
+D(cc,x)
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E 
+@
+
+\section{\cite{1}:14.69~~~~~$\displaystyle
+\int{\frac{x^3~dx}{(ax+b)^2}}$}
+$$\int{\frac{x^3}{(ax+b)^2}}=
+\frac{(ax+b)^2}{2a^4}-\frac{3b(ax+b)}{a^4}+\frac{b^3}{a^4(ax+b)}
++\frac{3b^2}{a^4}~\ln(ax+b)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 40
+aa:=integrate(x^3/(a*x+b)^2,x)
+--R
+--R             2      3                 3 3     2   2       2      3
+--R        (6a b x + 6b )log(a x + b) + a x  - 3a b x  - 4a b x + 2b
+--R   (1)  ----------------------------------------------------------
+--R                                  5      4
+--R                                2a x + 2a b
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 41
+bb:=(a*x+b)^2/(2*a^4)-(3*b*(a*x+b))/a^4+b^3/(a^4*(a*x+b))+(3*b^2/a^4)*log(a*x+b)
+--R
+--R             2      3                 3 3     2   2       2      3
+--R        (6a b x + 6b )log(a x + b) + a x  - 3a b x  - 9a b x - 3b
+--R   (2)  ----------------------------------------------------------
+--R                                  5      4
+--R                                2a x + 2a b
+--R                                                     Type: Expression Integer
+--E
+
+--S 42
+cc:=aa-bb
+--R
+--R          2
+--R        5b
+--R   (3)  ---
+--R          4
+--R        2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 43     14:69 Schaums and Axiom differ by a constant
+dd:=D(cc,x)
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
+@
+\section{\cite{1}:14.70~~~~~$\displaystyle
+\int{\frac{dx}{x~(ax+b)^2}}$}
+$$\int{\frac{1}{x~(ax+b)^2}}=
+\frac{1}{b~(ax+b)}+\frac{1}{b^2}~\ln\left(\frac{x}{ax+b}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 44
+aa:=integrate(1/(x*(a*x+b)^2),x)
+--R
+--R        (- a x - b)log(a x + b) + (a x + b)log(x) + b
+--R   (1)  ---------------------------------------------
+--R                             2     3
+--R                          a b x + b
+--R                                          Type: Union(Expression Integer,...)
+--E
+@
+and the book says:
+&lt;&lt;*&gt;&gt;=
+--S 45
+bb:=(1/(b*(a*x+b))+(1/b^2)*log(x/(a*x+b)))
+--R
+--R                        x
+--R        (a x + b)log(-------) + b
+--R                     a x + b
+--R   (2)  -------------------------
+--R                   2     3
+--R                a b x + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 46
+cc:=aa-bb
+--R
+--R                                         x
+--R        - log(a x + b) + log(x) - log(-------)
+--R                                      a x + b
+--R   (3)  --------------------------------------
+--R                           2
+--R                          b
+--R                                                     Type: Expression Integer
+--E
+@
+So we look at the divlog rule again:
+&lt;&lt;*&gt;&gt;=
+--S 47
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+@
+
+we apply it:
+&lt;&lt;*&gt;&gt;=
+--S 48     14:70 Schaums and Axiom agree
+dd:=divlog cc
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.71~~~~~$\displaystyle
+\int{\frac{dx}{x^2~(ax+b)^2}}$}
+$$\int{\frac{1}{x^2~(ax+b)^2}}=
+\frac{-a}{b^2~(ax+b)}-\frac{1}{b^2~x}+
+\frac{2a}{b^3}~\ln\left(\frac{ax+b}{x}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 49
+aa:=integrate(1/(x^2*(a*x+b)^2),x)
+--R
+--R           2 2                              2 2                             2
+--R        (2a x  + 2a b x)log(a x + b) + (- 2a x  - 2a b x)log(x) - 2a b x - b
+--R   (1)  ---------------------------------------------------------------------
+--R                                        3 2    4
+--R                                     a b x  + b x
+--R                                          Type: Union(Expression Integer,...)
+--E
+@
+and the book says:
+&lt;&lt;*&gt;&gt;=
+--S 50
+bb:=(-a/(b^2*(a*x+b)))-(1/(b^2*x))+((2*a)/b^3)*log((a*x+b)/x)
+--R
+--R           2 2              a x + b              2
+--R        (2a x  + 2a b x)log(-------) - 2a b x - b
+--R                               x
+--R   (2)  ------------------------------------------
+--R                          3 2    4
+--R                       a b x  + b x
+--R                                                     Type: Expression Integer
+--E
+
+--S 51
+cc:=aa-bb
+--R
+--R                                             a x + b
+--R        2a log(a x + b) - 2a log(x) - 2a log(-------)
+--R                                                x
+--R   (3)  ---------------------------------------------
+--R                               3
+--R                              b
+--R                                                     Type: Expression Integer
+--E
+@
+which calls for our divlog rule:
+&lt;&lt;*&gt;&gt;=
+--S 52
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+@
+which we use to transform the result:
+&lt;&lt;*&gt;&gt;=
+--S 53     14:71 Schaums and Axiom agree
+dd:=divlog cc
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
+@
+\section{\cite{1}:14.72~~~~~$\displaystyle
+\int{\frac{dx}{x^3~(ax+b)^2}}$}
+$$\int{\frac{1}{x^3~(ax+b)^2}}=
+-\frac{(ax+b)^2}{2b^4x^2}+\frac{3a(ax+b)}{b^4x}-
+\frac{a^3x}{b^4(ax+b)}-\frac{3a^2}{b^4}~\ln\left(\frac{ax+b}{x}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 54
+aa:=integrate(1/(x^3*(a*x+b)^2),x)
+--R
+--R   (1)
+--R            3 3     2   2                   3 3     2   2            2   2
+--R       (- 6a x  - 6a b x )log(a x + b) + (6a x  + 6a b x )log(x) + 6a b x
+--R     + 
+--R           2     3
+--R       3a b x - b
+--R  /
+--R         4 3     5 2
+--R     2a b x  + 2b x
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 55
+bb:=-(a*x+b)^2/(2*b^4*x^2)+(3*a*(a*x+b))/(b^4*x)-(a^3*x)/(b^4*(a*x+b))-((3*a^2)/b^4)*log((a*x+b)/x)
+--R
+--R             3 3     2   2     a x + b      3 3     2   2       2     3
+--R        (- 6a x  - 6a b x )log(-------) + 3a x  + 9a b x  + 3a b x - b
+--R                                  x
+--R   (2)  ---------------------------------------------------------------
+--R                                    4 3     5 2
+--R                                2a b x  + 2b x
+--R                                                     Type: Expression Integer
+--E
+
+--S 56
+cc:=aa-bb
+--R
+--R            2                 2           2    a x + b      2
+--R        - 6a log(a x + b) + 6a log(x) + 6a log(-------) - 3a
+--R                                                  x
+--R   (3)  -----------------------------------------------------
+--R                                   4
+--R                                 2b
+--R                                                     Type: Expression Integer
+--E
+
+--S 57
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 58
+dd:=divlog cc
+--R
+--R            2
+--R          3a
+--R   (5)  - ---
+--R            4
+--R          2b
+--R                                                     Type: Expression Integer
+--E
+
+--S 59     14:72 Schaums and Axiom differ by a constant
+ee:=D(dd,x)
+--R
+--R   (6)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.73~~~~~$\displaystyle
+\int{\frac{dx}{(ax+b)^3}}$}
+$$\int{\frac{1}{(ax+b)^3}}=
+\frac{-1}{2a(ax+b)^2}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 60
+aa:=integrate(1/(a*x+b)^3,x)
+--R
+--R                     1
+--R   (1)  - ----------------------
+--R            3 2     2          2
+--R          2a x  + 4a b x + 2a b
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 61
+bb:=-1/(2*(a*x+b)^2)
+--R
+--R                    1
+--R   (2)  - --------------------
+--R            2 2              2
+--R          2a x  + 4a b x + 2b
+--R                                            Type: Fraction Polynomial Integer
+--E
+
+--S 62
+cc:=aa-bb
+--R
+--R                 a - 1
+--R   (3)  ----------------------
+--R          3 2     2          2
+--R        2a x  + 4a b x + 2a b
+--R                                                     Type: Expression Integer
+--E
+
+--S 63
+dd:=aa/bb
+--R
+--R        1
+--R   (4)  -
+--R        a
+--R                                                     Type: Expression Integer
+--E
+
+--S 64     14:73 Schaums and Axiom differ by a constant
+ee:=D(dd,x)
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.74~~~~~$\displaystyle
+\int{\frac{x~dx}{(ax+b)^3}}$}
+$$\int{\frac{x}{(ax+b)^3}}=
+\frac{-1}{a^2(ax+b)}+\frac{b}{2a^2(ax+b)^2}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 65
+aa:=integrate(x/(a*x+b)^3,x)
+--R
+--R              - 2a x - b
+--R   (1)  ----------------------
+--R          4 2     3        2 2
+--R        2a x  + 4a b x + 2a b
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 66
+bb:=-1/(a^2*(a*x+b))+b/(2*a^2*(a*x+b)^2)
+--R
+--R              - 2a x - b
+--R   (2)  ----------------------
+--R          4 2     3        2 2
+--R        2a x  + 4a b x + 2a b
+--R                                            Type: Fraction Polynomial Integer
+--E
+
+--S 67     14:74 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.75~~~~~$\displaystyle
+\int{\frac{x^2~dx}{(ax+b)^3}}$}
+$$\int{\frac{x^2}{(ax+b)^3}}=
+\frac{2b}{a^3(ax+b)}-\frac{b^2}{2a^3(ax+b)^2}+
+\frac{1}{a^3}~\ln(ax+b)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 68
+aa:=integrate(x^2/(a*x+b)^3,x)
+--R
+--R           2 2              2                           2
+--R        (2a x  + 4a b x + 2b )log(a x + b) + 4a b x + 3b
+--R   (1)  -------------------------------------------------
+--R                        5 2     4        3 2
+--R                      2a x  + 4a b x + 2a b
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 69
+bb:=(2*b)/(a^3*(a*x+b))-(b^2)/(2*a^3*(a*x+b)^2)+1/a^3*log(a*x+b)
+--R
+--R           2 2              2                           2
+--R        (2a x  + 4a b x + 2b )log(a x + b) + 4a b x + 3b
+--R   (2)  -------------------------------------------------
+--R                        5 2     4        3 2
+--R                      2a x  + 4a b x + 2a b
+--R                                                     Type: Expression Integer
+--E
+
+--S 70     14:75 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.76~~~~~$\displaystyle
+\int{\frac{x^3~dx}{(ax+b)^3}}$}
+$$\int{\frac{x^3}{(ax+b)^3}}=
+\frac{x}{a^3}-\frac{3b^2}{a^4(ax+b)}+\frac{b^3}{2a^4(ax+b)^2}-
+\frac{3b}{a^4}~\ln(ax+b)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+--S 71
+aa:=integrate(x^3/(a*x+b)^3,x)
+--R
+--R   (1)
+--R        2   2        2      3                  3 3     2   2       2      3
+--R   (- 6a b x  - 12a b x - 6b )log(a x + b) + 2a x  + 4a b x  - 4a b x - 5b
+--R   ------------------------------------------------------------------------
+--R                              6 2     5        4 2
+--R                            2a x  + 4a b x + 2a b
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 72
+bb:=(x/a^3)-(3*b^2)/(a^4*(a*x+b))+b^3/(2*a^4*(a*x+b)^2)-(3*b)/a^4*log(a*x+b)
+--R
+--R   (2)
+--R        2   2        2      3                  3 3     2   2       2      3
+--R   (- 6a b x  - 12a b x - 6b )log(a x + b) + 2a x  + 4a b x  - 4a b x - 5b
+--R   ------------------------------------------------------------------------
+--R                              6 2     5        4 2
+--R                            2a x  + 4a b x + 2a b
+--R                                                     Type: Expression Integer
+--E
+
+--S 73     14:76 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.77~~~~~$\displaystyle
+\int{\frac{dx}{x(ax+b)^3}}$}
+$$\int{\frac{1}{x(ax+b)^3}}=
+\frac{3}{2b(ax+b)^2}+\frac{2ax}{2b^2(ax+b)^2}-
+\frac{1}{b^3}*\ln\left(\frac{ax+b}{x}\right)
+$$
+
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 74
+aa:=integrate(1/(x*(a*x+b)^3),x)
+--R
+--R   (1)
+--R            2 2              2                   2 2              2
+--R       (- 2a x  - 4a b x - 2b )log(a x + b) + (2a x  + 4a b x + 2b )log(x)
+--R     + 
+--R                  2
+--R       2a b x + 3b
+--R  /
+--R       2 3 2       4      5
+--R     2a b x  + 4a b x + 2b
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 75
+bb:=(a^2*x^2)/(2*b^3*(a*x+b)^2)-(2*a*x)/(b^3*(a*x+b))-(1/b^3)*log((a*x+b)/x)
+--R
+--R             2 2              2     a x + b      2 2
+--R        (- 2a x  - 4a b x - 2b )log(-------) - 3a x  - 4a b x
+--R                                       x
+--R   (2)  -----------------------------------------------------
+--R                          2 3 2       4      5
+--R                        2a b x  + 4a b x + 2b
+--R                                                     Type: Expression Integer
+--E
+
+--S 76
+cc:=aa-bb
+--R
+--R                                         a x + b
+--R        - 2log(a x + b) + 2log(x) + 2log(-------) + 3
+--R                                            x
+--R   (3)  ---------------------------------------------
+--R                               3
+--R                             2b
+--R                                                     Type: Expression Integer
+--E
+
+--S 77
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 78
+dd:=divlog cc
+--R
+--R         3
+--R   (5)  ---
+--R          3
+--R        2b
+--R                                                     Type: Expression Integer
+--E
+
+--S 79     14:77 Schaums and Axiom differ by a constant
+ee:=D(dd,x)
+--R
+--R   (6)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.78~~~~~$\displaystyle
+\int{\frac{dx}{x^2(ax+b)^3}}$}
+$$\int{\frac{1}{x^2(ax+b)^3}}=
+\frac{-a}{2b^2(ax+b)^2}-\frac{2a}{b^3(ax+b)}-
+\frac{1}{b^3x}+\frac{3a}{b^4}~\ln\left(\frac{ax+b}{x}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 80
+aa:=integrate(1/(x^2*(a*x+b)^3),x)
+--R
+--R   (1)
+--R          3 3      2   2       2
+--R       (6a x  + 12a b x  + 6a b x)log(a x + b)
+--R     + 
+--R            3 3      2   2       2             2   2       2      3
+--R       (- 6a x  - 12a b x  - 6a b x)log(x) - 6a b x  - 9a b x - 2b
+--R  /
+--R       2 4 3       5 2     6
+--R     2a b x  + 4a b x  + 2b x
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 81
+bb:=-a/(2*b^2*(a*x+b)^2)-(2*a)/(b^3*(a*x+b))-1/(b^3*x)+((3*a)/b^4)*log((a*x+b)/x)
+--R
+--R           3 3      2   2       2      a x + b      2   2       2      3
+--R        (6a x  + 12a b x  + 6a b x)log(-------) - 6a b x  - 9a b x - 2b
+--R                                          x
+--R   (2)  ----------------------------------------------------------------
+--R                              2 4 3       5 2     6
+--R                            2a b x  + 4a b x  + 2b x
+--R                                                     Type: Expression Integer
+--E
+
+--S 82
+cc:=aa-bb
+--R
+--R                                             a x + b
+--R        3a log(a x + b) - 3a log(x) - 3a log(-------)
+--R                                                x
+--R   (3)  ---------------------------------------------
+--R                               4
+--R                              b
+--R                                                     Type: Expression Integer
+--E
+
+--S 83
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 84     14:78 Schaums and Axiom agree
+dd:=divlog cc
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.79~~~~~$\displaystyle
+\int{\frac{dx}{x^3(ax+b)^3}}$}
+$$\int{\frac{1}{x^3(ax+b)^3}}=
+-\frac{1}{2bx^2(ax+b)^2}+
+\frac{2a}{b^2x(ax+b)^2}+
+\frac{9a^2}{b^3(ax+b)^2}+
+\frac{6a^3x}{b^4(ax+b)^2}-
+\frac{6a^2}{b^5}~\ln\left(\frac{ax+b}{x}\right)$$
+
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 85
+aa:=integrate(1/(x^3*(a*x+b)^3),x)
+--R
+--R   (1)
+--R             4 4      3   3      2 2 2
+--R       (- 12a x  - 24a b x  - 12a b x )log(a x + b)
+--R     + 
+--R           4 4      3   3      2 2 2             3   3      2 2 2       3     4
+--R       (12a x  + 24a b x  + 12a b x )log(x) + 12a b x  + 18a b x  + 4a b x - b
+--R  /
+--R       2 5 4       6 3     7 2
+--R     2a b x  + 4a b x  + 2b x
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 86
+bb:=-1/(2*b*x^2*(a*x+b)^2)_
+    +(2*a)/(b^2*x*(a*x+b)^2)_
+    +(9*a^2)/(b^3*(a*x+b)^2)_
+    +(6*a^3*x)/(b^4*(a*x+b)^2)_
+    +(-6*a^2)/b^5*log((a*x+b)/x)
+--R
+--R   (2)
+--R             4 4      3   3      2 2 2     a x + b       3   3      2 2 2
+--R       (- 12a x  - 24a b x  - 12a b x )log(-------) + 12a b x  + 18a b x
+--R                                              x
+--R     + 
+--R           3     4
+--R       4a b x - b
+--R  /
+--R       2 5 4       6 3     7 2
+--R     2a b x  + 4a b x  + 2b x
+--R                                                     Type: Expression Integer
+--E
+
+--S 87
+cc:=aa-bb
+--R
+--R            2                 2           2    a x + b
+--R        - 6a log(a x + b) + 6a log(x) + 6a log(-------)
+--R                                                  x
+--R   (3)  -----------------------------------------------
+--R                                5
+--R                               b
+--R                                                     Type: Expression Integer
+--E
+
+--S 88
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 89     14:79 Schaums and Axiom agree
+dd:=divlog cc
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.80~~~~~$\displaystyle
+\int{(ax+b)^n~dx}$}
+$$\int{(ax+b)^n}=
+\frac{(ax+b)^{n+1}}{(n+1)a}{\rm\ provided\ }n \ne -1
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+--S 90
+aa:=integrate((a*x+b)^n,x)
+--R
+--R                   n log(a x + b)
+--R        (a x + b)%e
+--R   (1)  -------------------------
+--R                 a n + a
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 91
+bb:=(a*x+b)^(n+1)/((n+1)*a)
+--R
+--R                 n + 1
+--R        (a x + b)
+--R   (2)  --------------
+--R            a n + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 92
+cc:=aa-bb
+--R
+--R                   n log(a x + b)            n + 1
+--R        (a x + b)%e               - (a x + b)
+--R   (3)  ------------------------------------------
+--R                          a n + a
+--R                                                     Type: Expression Integer
+--E
+@
+This messy formula can be simplified using the explog rule:
+&lt;&lt;*&gt;&gt;=
+--S 93
+explog:=rule(%e^(n*log(x)) == x^n)
+--R
+--R          n log(x)     n
+--R   (4)  %e         == x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 94
+dd:=explog cc
+--R
+--R                   n + 1                     n
+--R        - (a x + b)      + (a x + b)(a x + b)
+--R   (5)  --------------------------------------
+--R                        a n + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 95     14:80 Schaums and Axiom agree
+ee:=complexNormalize dd
+--R
+--R   (6)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.81~~~~~$\displaystyle
+\int{x(ax+b)^n~dx}$}
+$$\int{x(ax+b)^n}=
+\frac{(ax+b)^{n+2}}{(n+2)a^2}-\frac{b(ax+b)^{n+1}}{(n+1)a^2}
+{\rm\ provided\ }n \ne -1,-2
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+--S 96
+aa:=integrate(x*(a*x+b)^n,x)
+--R
+--R           2     2  2              2   n log(a x + b)
+--R        ((a n + a )x  + a b n x - b )%e
+--R   (1)  ---------------------------------------------
+--R                       2 2     2      2
+--R                      a n  + 3a n + 2a
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 97
+bb:=((a*x+b)^(n+2))/((n+2)*a^2)-(b*(a*x+b)^(n+1))/((n+1)*a^2)
+--R
+--R                        n + 2                        n + 1
+--R        (n + 1)(a x + b)      + (- b n - 2b)(a x + b)
+--R   (2)  --------------------------------------------------
+--R                          2 2     2      2
+--R                         a n  + 3a n + 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 98
+cc:=aa-bb
+--R
+--R   (3)
+--R          2     2  2              2   n log(a x + b)                     n + 2
+--R       ((a n + a )x  + a b n x - b )%e               + (- n - 1)(a x + b)
+--R     + 
+--R                          n + 1
+--R       (b n + 2b)(a x + b)
+--R  /
+--R      2 2     2      2
+--R     a n  + 3a n + 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 99
+explog:=rule(%e^(n*log(x)) == x^n)
+--R
+--R          n log(x)     n
+--R   (4)  %e         == x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 100
+dd:=explog cc
+--R
+--R   (5)
+--R                         n + 2                      n + 1
+--R       (- n - 1)(a x + b)      + (b n + 2b)(a x + b)
+--R     + 
+--R          2     2  2              2          n
+--R       ((a n + a )x  + a b n x - b )(a x + b)
+--R  /
+--R      2 2     2      2
+--R     a n  + 3a n + 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 101
+ee:=complexNormalize dd
+--R
+--R   (6)  0
+--R                                                     Type: Expression Integer
+--E
+@
+\section{\cite{1}:14.82~~~~~$\displaystyle
+\int{x^2(ax+b)^n~dx}$}
+$$\int{x^2(ax+b)^n}=
+\frac{(ax+b)^{n+2}}{(n+3)a^3}-
+\frac{2b(ax+b)^{n+2}}{(n+2)a^3}+
+\frac{b^2(ax+b)^{n+1}}{(n+1)a^3}
+{\rm\ provided\ }n \ne -1,-2,-3
+$$
+
+&lt;&lt;*&gt;&gt;=
+)clear all
+--S 102
+aa:=integrate(x^2*(a*x+b)^n,x)
+--R
+--R   (1)
+--R      3 2     3      3  3     2   2    2     2       2        3   n log(a x + b)
+--R   ((a n  + 3a n + 2a )x  + (a b n  + a b n)x  - 2a b n x + 2b )%e
+--R   -----------------------------------------------------------------------------
+--R                              3 3     3 2      3      3
+--R                             a n  + 6a n  + 11a n + 6a
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 103
+bb:=(a*x+b)^(n+3)/((n+3)*a^3)-(2*b*(a*x+b)^(n+2))/((n+2)*a^3)+(b^2*(a*x+b)^(n+1))/((n+1)*a^3)
+--R
+--R   (2)
+--R         2                   n + 3          2                      n + 2
+--R       (n  + 3n + 2)(a x + b)      + (- 2b n  - 8b n - 6b)(a x + b)
+--R     + 
+--R         2 2     2      2          n + 1
+--R       (b n  + 5b n + 6b )(a x + b)
+--R  /
+--R      3 3     3 2      3      3
+--R     a n  + 6a n  + 11a n + 6a
+--R                                                     Type: Expression Integer
+--E
+
+--S 104
+cc:=aa-bb
+--R
+--R   (3)
+--R            3 2     3      3  3     2   2    2     2       2        3
+--R         ((a n  + 3a n + 2a )x  + (a b n  + a b n)x  - 2a b n x + 2b )
+--R      *
+--R           n log(a x + b)
+--R         %e
+--R     + 
+--R           2                   n + 3        2                      n + 2
+--R       (- n  - 3n - 2)(a x + b)      + (2b n  + 8b n + 6b)(a x + b)
+--R     + 
+--R           2 2     2      2          n + 1
+--R       (- b n  - 5b n - 6b )(a x + b)
+--R  /
+--R      3 3     3 2      3      3
+--R     a n  + 6a n  + 11a n + 6a
+--R                                                     Type: Expression Integer
+--E
+
+--S 105
+explog:=rule(%e^(n*log(x)) == x^n)
+--R
+--R          n log(x)     n
+--R   (4)  %e         == x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 106
+dd:=explog cc
+--R
+--R   (5)
+--R           2                   n + 3        2                      n + 2
+--R       (- n  - 3n - 2)(a x + b)      + (2b n  + 8b n + 6b)(a x + b)
+--R     + 
+--R           2 2     2      2          n + 1
+--R       (- b n  - 5b n - 6b )(a x + b)
+--R     + 
+--R          3 2     3      3  3     2   2    2     2       2        3          n
+--R       ((a n  + 3a n + 2a )x  + (a b n  + a b n)x  - 2a b n x + 2b )(a x + b)
+--R  /
+--R      3 3     3 2      3      3
+--R     a n  + 6a n  + 11a n + 6a
+--R                                                     Type: Expression Integer
+--E
+
+--S 107    14:82 Schaums and Axiom agree
+ee:=complexNormalize dd
+--R
+--R   (6)  0
+--R                                                     Type: Expression Integer
+--E
+@
+\section{\cite{1}:14.83~~~~~$\displaystyle
+\int{x^m(ax+b)^n}~dx$}
+$$\int{x^m(ax+b)^n}
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{x^{m+1}(ax+b)^n}{m+n+1}
++\frac{nb}{m+n+1}\int{x^m(ax+b)^{n-1}}\\
+\\
+\displaystyle
+\frac{x^{m+1}(ax+b)^{n+1}}{(m+n+1)a}
+-\frac{mb}{(m+n+1)a}\int{x^{m-1}(ax+b)^n}\\
+\\
+\displaystyle
+\frac{-x^{m+1}(ax+b)^{n+1}}{(n+1)b}
++\frac{m+n+2}{(n+1)b}\int{x^m(ax+b)^{n+1}}\\
+\end{array}
+\right.
+$$
+
+&lt;&lt;*&gt;&gt;=
+--S 108    14:83 Axiom cannot do this integration
+aa:=integrate(x^m*(a*x+b)^n,x)
+--R
+--R           x
+--R         ++    m          n
+--I   (1)   |   %U (b + %U a) d%U
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 pp60-61
+\end{thebibliography}
+\end{document}
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+138372
+%%EOF
diff --git a/src/axiom-website/CATS/schaum10.input.pamphlet b/src/axiom-website/CATS/schaum10.input.pamphlet
new file mode 100644
index 0000000..6149cc0
--- /dev/null
+++ b/src/axiom-website/CATS/schaum10.input.pamphlet
@@ -0,0 +1,2310 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum10.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.210~~~~~$\displaystyle\int{\frac{dx}{\sqrt{x^2-a^2}}}$}
+$$\int{\frac{1}{\sqrt{x^2-a^2}}}=\ln\left(x+\sqrt{x^2-a^2}\right)$$
+&lt;&lt;*&gt;&gt;=
+)spool schaum10.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1
+aa:=integrate(1/(sqrt(x^2-a^2)),x)
+--R 
+--R
+--R               +-------+
+--R               | 2    2
+--R   (1)  - log(\|x  - a   - x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 2
+bb:=log(x+sqrt(x^2-a^2))
+--R
+--R             +-------+
+--R             | 2    2
+--R   (2)  log(\|x  - a   + x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 3
+cc:=aa-bb
+--R
+--R               +-------+             +-------+
+--R               | 2    2              | 2    2
+--R   (3)  - log(\|x  - a   + x) - log(\|x  - a   - x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 4
+logmul1:=rule(c*log(a)+c*log(b) == c*log(a*b))
+--R
+--I   (4)  c log(b) + c log(a) + %I == c log(a b) + %I
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 5      14:210 Schaums and Axiom differ by a constant
+dd:=logmul1 cc
+--R
+--R                 2
+--R   (5)  - log(- a )
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.xxx~~~~~$\displaystyle\int{\frac{x~dx}{\sqrt{x^2-a^2}}}$}
+$$\int{\frac{x}{\sqrt{x^2-a^2}}}=\sqrt{x^2-a^2}$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 6
+aa:=integrate(x/(sqrt(x^2-a^2)),x)
+--R 
+--R
+--R            +-------+
+--R            | 2    2     2    2
+--R        - x\|x  - a   + x  - a
+--R   (1)  -----------------------
+--R              +-------+
+--R              | 2    2
+--R             \|x  - a   - x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 7
+bb:=sqrt(x^2-a^2)
+--R
+--R         +-------+
+--R         | 2    2
+--R   (2)  \|x  - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 8      14:xxx Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.211~~~~~$\displaystyle
+\int{\frac{x^2~dx}{\sqrt{x^2-a^2}}}$}
+$$\int{\frac{x^2}{\sqrt{x^2-a^2}}}=
+\frac{x\sqrt{x^2-a^2}}{2}+\frac{a^2}{2}\ln\left(x+\sqrt{x^2-a^2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 9
+aa:=integrate(x^2/sqrt(x^2-a^2),x)
+--R 
+--R
+--R   (1)
+--R               +-------+                   +-------+
+--R            2  | 2    2      2 2    4      | 2    2
+--R       (- 2a x\|x  - a   + 2a x  - a )log(\|x  - a   - x)
+--R     + 
+--R                     +-------+
+--R            3    2   | 2    2      4     2 2
+--R       (- 2x  + a x)\|x  - a   + 2x  - 2a x
+--R  /
+--R        +-------+
+--R        | 2    2      2     2
+--R     4x\|x  - a   - 4x  + 2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 10
+bb:=(x*sqrt(x^2-a^2))/2+a^2/2*log(x+sqrt(x^2-a^2))
+--R
+--R               +-------+          +-------+
+--R         2     | 2    2           | 2    2
+--R        a log(\|x  - a   + x) + x\|x  - a
+--R   (2)  -----------------------------------
+--R                         2
+--R                                                     Type: Expression Integer
+--E
+
+--S 11     
+cc:=aa-bb
+--R
+--R                 +-------+               +-------+
+--R           2     | 2    2          2     | 2    2
+--R        - a log(\|x  - a   + x) - a log(\|x  - a   - x)
+--R   (3)  -----------------------------------------------
+--R                               2
+--R                                                     Type: Expression Integer
+--E
+
+--S 12     14:211 Schaums and Axiom differ by a constant
+dd:=complexNormalize cc
+--R
+--R           2       2
+--R          a log(- a )
+--R   (4)  - -----------
+--R               2
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.212~~~~~$\displaystyle
+\int{\frac{x^3~dx}{\sqrt{x^2-a^2}}}$}
+$$\int{\frac{x^3}{\sqrt{x^2-a^2}}}=
+\frac{(x^2-a^2)^{3/2}}{3}+a^2\sqrt{x^2-a^2}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 13
+aa:=integrate(x^3/sqrt(x^2-a^2),x)
+--R 
+--R
+--R                               +-------+
+--R             5     2 3     4   | 2    2      6     2 4     4 2     6
+--R        (- 4x  - 5a x  + 6a x)\|x  - a   + 4x  + 3a x  - 9a x  + 2a
+--R   (1)  ------------------------------------------------------------
+--R                                 +-------+
+--R                        2     2  | 2    2       3     2
+--R                    (12x  - 3a )\|x  - a   - 12x  + 9a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 14
+bb:=(x^2-a^2)^(3/2)/3+a^2*sqrt(x^2-a^2)
+--R
+--R                   +-------+
+--R          2     2  | 2    2
+--R        (x  + 2a )\|x  - a
+--R   (2)  --------------------
+--R                  3
+--R                                                     Type: Expression Integer
+--E
+
+--S 15     14:212 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.213~~~~~$\displaystyle\int{\frac{dx}{x\sqrt{x^2-a^2}}}$}
+$$\int{\frac{1}{x\sqrt{x^2-a^2}}}=
+\frac{1}{a}\sec^{-1}\left|\frac{x}{a}\right|
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 16
+aa:=integrate(1/(x*sqrt(x^2-a^2)),x)
+--R 
+--R
+--R               +-------+
+--R               | 2    2
+--R              \|x  - a   - x
+--R        2atan(--------------)
+--R                     a
+--R   (1)  ---------------------
+--R                  a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 17
+bb:=1/a*asec(x/a)
+--R
+--R             x
+--R        asec(-)
+--R             a
+--R   (2)  -------
+--R           a
+--R                                                     Type: Expression Integer
+--E
+
+--S 18
+cc:=aa-bb
+--R
+--R               +-------+
+--R               | 2    2
+--R              \|x  - a   - x         x
+--R        2atan(--------------) - asec(-)
+--R                     a               a
+--R   (3)  -------------------------------
+--R                       a
+--R                                                     Type: Expression Integer
+--E
+
+--S 19
+asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x))
+--R
+--R                             +------+
+--R                             | 2
+--R                             |x  - 1
+--R                           x |------  + %i
+--R                             |   2
+--R                            \|  x
+--R                   2%i log(---------------) + %pi
+--R                                  x
+--R   (4)  asec(x) == ------------------------------
+--R                                  2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 20
+dd:=asecrule cc
+--R
+--R                    +-------+
+--R                    | 2    2
+--R                    |x  - a
+--R                  x |-------  + %i a           +-------+
+--R                    |    2                     | 2    2
+--R                   \|   x                     \|x  - a   - x
+--R        - 2%i log(------------------) + 4atan(--------------) - %pi
+--R                           x                         a
+--R   (5)  -----------------------------------------------------------
+--R                                     2a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 21
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (6)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 22
+ee:=atanrule dd
+--R
+--R                    +-------+
+--R                    | 2    2
+--R                    |x  - a
+--R                  x |-------  + %i a               +-------+
+--R                    |    2                         | 2    2
+--R                   \|   x                       - \|x  - a   + x + %i a
+--R        - 2%i log(------------------) - 2%i log(-----------------------) - %pi
+--R                           x                      +-------+
+--R                                                  | 2    2
+--R                                                 \|x  - a   - x + %i a
+--R   (7)  ----------------------------------------------------------------------
+--R                                          2a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 23
+ff:=expandLog ee
+--R
+--R   (8)
+--R                +-------+                        +-------+
+--R                | 2    2                         | 2    2
+--R       2%i log(\|x  - a   - x + %i a) - 2%i log(\|x  - a   - x - %i a)
+--R     + 
+--R                   +-------+
+--R                   | 2    2
+--R                   |x  - a
+--R       - 2%i log(x |-------  + %i a) + 2%i log(x) - 2%i log(- 1) - %pi
+--R                   |    2
+--R                  \|   x
+--R  /
+--R     2a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 24
+gg:=rootSimp ff
+--R
+--R   (9)
+--R                  +-------+                    +-------+
+--R                  | 2    2                     | 2    2
+--R       - 2%i log(\|x  - a   + %i a) + 2%i log(\|x  - a   - x + %i a)
+--R     + 
+--R                  +-------+
+--R                  | 2    2
+--R       - 2%i log(\|x  - a   - x - %i a) + 2%i log(x) - 2%i log(- 1) - %pi
+--R  /
+--R     2a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 25     14:213 Schaums and Axiom differ by a constant
+hh:=complexNormalize gg
+--R
+--R           %pi
+--R   (10)  - ---
+--R            2a
+--R                                             Type: Expression Complex Integer
+--E
+@
+
+\section{\cite{1}:14.214~~~~~$\displaystyle
+\int{\frac{dx}{x^2\sqrt{x^2-a^2}}}$}
+$$\int{\frac{1}{x^2\sqrt{x^2-a^2}}}=
+\frac{\sqrt{x^2-a^2}}{a^2x}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 26
+aa:=integrate(1/(x^2*sqrt(x^2-a^2)),x)
+--R 
+--R
+--R                  1
+--R   (1)  - ----------------
+--R            +-------+
+--R            | 2    2     2
+--R          x\|x  - a   - x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 27
+bb:=sqrt(x^2-a^2)/(a^2*x)
+--R
+--R         +-------+
+--R         | 2    2
+--R        \|x  - a
+--R   (2)  ----------
+--R             2
+--R            a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 28     14:214 Schaums and Axiom differ by a constant
+cc:=aa-bb
+--R
+--R         1
+--R   (3)  --
+--R         2
+--R        a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.215~~~~~$\displaystyle\int{\frac{dx}{x^3\sqrt{x^2-a^2}}}$}
+$$\int{\frac{1}{x^3\sqrt{x^2-a^2}}}=
+-\frac{\sqrt{x^2-a^2}}{2a^2x^2}+\frac{1}{2a^3}
+\sec^{-1}\left|\frac{x}{a}\right|
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 29
+aa:=integrate(1/(x^3*sqrt(x^2-a^2)),x)
+--R 
+--R
+--R   (1)
+--R                                          +-------+
+--R            +-------+                     | 2    2
+--R          3 | 2    2      4     2 2      \|x  - a   - x
+--R       (4x \|x  - a   - 4x  + 2a x )atan(--------------)
+--R                                                a
+--R     + 
+--R                      +-------+
+--R              2    3  | 2    2        3     3
+--R       (- 2a x  + a )\|x  - a   + 2a x  - 2a x
+--R  /
+--R           +-------+
+--R       3 3 | 2    2      3 4     5 2
+--R     4a x \|x  - a   - 4a x  + 2a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 30
+bb:=sqrt(x^2-a^2)/(2*a^2*x^2)+1/(2*a^3)*asec(x/a)
+--R
+--R          +-------+
+--R          | 2    2     2     x
+--R        a\|x  - a   + x asec(-)
+--R                             a
+--R   (2)  -----------------------
+--R                   3 2
+--R                 2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 31
+cc:=aa-bb
+--R 
+--R
+--R               +-------+
+--R               | 2    2
+--R              \|x  - a   - x         x
+--R        2atan(--------------) - asec(-)
+--R                     a               a
+--R   (3)  -------------------------------
+--R                        3
+--R                      2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 32
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (4)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 33
+dd:=atanrule cc
+--R
+--R                    +-------+
+--R                    | 2    2
+--R                 - \|x  - a   + x + %i a         x
+--R        - %i log(-----------------------) - asec(-)
+--R                   +-------+                     a
+--R                   | 2    2
+--R                  \|x  - a   - x + %i a
+--R   (5)  -------------------------------------------
+--R                              3
+--R                            2a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 34
+asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x))
+--R
+--R                             +------+
+--R                             | 2
+--R                             |x  - 1
+--R                           x |------  + %i
+--R                             |   2
+--R                            \|  x
+--R                   2%i log(---------------) + %pi
+--R                                  x
+--R   (6)  asec(x) == ------------------------------
+--R                                  2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 35
+ee:=asecrule dd
+--R
+--R                    +-------+
+--R                    | 2    2
+--R                    |x  - a
+--R                  x |-------  + %i a               +-------+
+--R                    |    2                         | 2    2
+--R                   \|   x                       - \|x  - a   + x + %i a
+--R        - 2%i log(------------------) - 2%i log(-----------------------) - %pi
+--R                           x                      +-------+
+--R                                                  | 2    2
+--R                                                 \|x  - a   - x + %i a
+--R   (7)  ----------------------------------------------------------------------
+--R                                            3
+--R                                          4a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 36
+ff:=expandLog ee
+--R
+--R   (8)
+--R                +-------+                        +-------+
+--R                | 2    2                         | 2    2
+--R       2%i log(\|x  - a   - x + %i a) - 2%i log(\|x  - a   - x - %i a)
+--R     + 
+--R                   +-------+
+--R                   | 2    2
+--R                   |x  - a
+--R       - 2%i log(x |-------  + %i a) + 2%i log(x) - 2%i log(- 1) - %pi
+--R                   |    2
+--R                  \|   x
+--R  /
+--R       3
+--R     4a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 37
+gg:=rootSimp ff
+--R
+--R   (9)
+--R                  +-------+                    +-------+
+--R                  | 2    2                     | 2    2
+--R       - 2%i log(\|x  - a   + %i a) + 2%i log(\|x  - a   - x + %i a)
+--R     + 
+--R                  +-------+
+--R                  | 2    2
+--R       - 2%i log(\|x  - a   - x - %i a) + 2%i log(x) - 2%i log(- 1) - %pi
+--R  /
+--R       3
+--R     4a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 38     14:215 Schaums and Axiom differ by a constant
+hh:=complexNormalize gg
+--R
+--R           %pi
+--R   (10)  - ---
+--R             3
+--R           4a
+--R                                             Type: Expression Complex Integer
+--E
+
+@
+
+\section{\cite{1}:14.216~~~~~$\displaystyle\int{\sqrt{x^2-a^2}}~dx$}
+$$\int{\sqrt{x^2-a^2}}=
+\frac{x\sqrt{x^2-a^2}}{2}-\frac{a^2}{2}\ln\left(x+\sqrt{x^2-a^2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 39
+aa:=integrate(sqrt(x^2-a^2),x)
+--R 
+--R
+--R   (1)
+--R             +-------+                   +-------+
+--R          2  | 2    2      2 2    4      | 2    2
+--R       (2a x\|x  - a   - 2a x  + a )log(\|x  - a   - x)
+--R     + 
+--R                     +-------+
+--R            3    2   | 2    2      4     2 2
+--R       (- 2x  + a x)\|x  - a   + 2x  - 2a x
+--R  /
+--R        +-------+
+--R        | 2    2      2     2
+--R     4x\|x  - a   - 4x  + 2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 40
+bb:=(x*sqrt(x^2-a^2))/2-a^2/2*log(x+sqrt(x^2-a^2))
+--R
+--R                 +-------+          +-------+
+--R           2     | 2    2           | 2    2
+--R        - a log(\|x  - a   + x) + x\|x  - a
+--R   (2)  -------------------------------------
+--R                          2
+--R                                                     Type: Expression Integer
+--E
+
+--S 41
+cc:=aa-bb
+--R
+--R               +-------+               +-------+
+--R         2     | 2    2          2     | 2    2
+--R        a log(\|x  - a   + x) + a log(\|x  - a   - x)
+--R   (3)  ---------------------------------------------
+--R                              2
+--R                                                     Type: Expression Integer
+--E
+
+--S 42     14:216 Schaums and Axiom differ by a constant 
+dd:=complexNormalize cc
+--R
+--R         2       2
+--R        a log(- a )
+--R   (4)  -----------
+--R             2
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.217~~~~~$\displaystyle\int{x\sqrt{x^2-a^2}}~dx$}
+$$\int{x\sqrt{x^2-a^2}}=
+\frac{(x^2-a^2)^{3/2}}{3}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 43
+aa:=integrate(x*sqrt(x^2-a^2),x)
+--R 
+--R
+--R                               +-------+
+--R             5     2 3     4   | 2    2      6     2 4     4 2    6
+--R        (- 4x  + 7a x  - 3a x)\|x  - a   + 4x  - 9a x  + 6a x  - a
+--R   (1)  -----------------------------------------------------------
+--R                                 +-------+
+--R                        2     2  | 2    2       3     2
+--R                    (12x  - 3a )\|x  - a   - 12x  + 9a x
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 44
+bb:=(x^2-a^2)^(3/2)/3
+--R
+--R                  +-------+
+--R          2    2  | 2    2
+--R        (x  - a )\|x  - a
+--R   (2)  -------------------
+--R                 3
+--R                                                     Type: Expression Integer
+--E
+
+--S 45     14:217 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.218~~~~~$\displaystyle
+\int{x^2\sqrt{x^2-a^2}}~dx$}
+$$\int{x^2\sqrt{x^2-a^2}}=
+\frac{x(x^2-a^2)^{3/2}}{4}+\frac{a^2x\sqrt{x^2-a^2}}{8}-
+\frac{a^4}{8}\ln\left(x+\sqrt{x^2-a^2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 46
+aa:=integrate(x^2*sqrt(x^2-a^2),x)
+--R 
+--R
+--R   (1)
+--R                       +-------+                           +-------+
+--R           4 3     6   | 2    2      4 4     6 2    8      | 2    2
+--R       ((8a x  - 4a x)\|x  - a   - 8a x  + 8a x  - a )log(\|x  - a   - x)
+--R     + 
+--R                                      +-------+
+--R           7      2 5      4 3    6   | 2    2       8      2 6      4 4     6 2
+--R     (- 16x  + 24a x  - 10a x  + a x)\|x  - a   + 16x  - 32a x  + 20a x  - 4a x
+--R  /
+--R                    +-------+
+--R         3      2   | 2    2       4      2 2     4
+--R     (64x  - 32a x)\|x  - a   - 64x  + 64a x  - 8a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 47
+bb:=(x*(x^2-a^2)^(3/2))/4+(a^2*x*sqrt(x^2-a^2))/8-a^4/8*log(x+sqrt(x^2-a^2))
+--R
+--R                 +-------+                    +-------+
+--R           4     | 2    2            3    2   | 2    2
+--R        - a log(\|x  - a   + x) + (2x  - a x)\|x  - a
+--R   (2)  -----------------------------------------------
+--R                               8
+--R                                                     Type: Expression Integer
+--E
+
+--S 48     
+cc:=aa-bb
+--R
+--R               +-------+               +-------+
+--R         4     | 2    2          4     | 2    2
+--R        a log(\|x  - a   + x) + a log(\|x  - a   - x)
+--R   (3)  ---------------------------------------------
+--R                              8
+--R                                                     Type: Expression Integer
+--E
+
+--S 49     14:218 Schaums and Axiom differ by a constant
+dd:=complexNormalize cc
+--R
+--R         4       2
+--R        a log(- a )
+--R   (4)  -----------
+--R             8
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.219~~~~~$\displaystyle
+\int{x^3\sqrt{x^2-a^2}}~dx$}
+$$\int{x^3\sqrt{x^2-a^2}}=
+\frac{(x^2-a^2)^{5/2}}{5}+\frac{a^2(x^2-a^2)^{3/2}}{3}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 50
+aa:=integrate(x^3*sqrt(x^2-a^2),x)
+--R 
+--R
+--R   (1)
+--R                                                  +-------+
+--R             9      2 7     4 5      6 3      8   | 2    2       10       2 8
+--R       (- 48x  + 76a x  - 3a x  - 35a x  + 10a x)\|x  - a   + 48x   - 100a x
+--R     + 
+--R          4 6      6 4      8 2     10
+--R       35a x  + 40a x  - 25a x  + 2a
+--R  /
+--R                              +-------+
+--R          4       2 2      4  | 2    2        5       2 3      4
+--R     (240x  - 180a x  + 15a )\|x  - a   - 240x  + 300a x  - 75a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 51
+bb:=(x^2-a^2)^(5/2)/5+(a^2*(x^2-a^2)^(3/2))/3
+--R
+--R                           +-------+
+--R           4    2 2     4  | 2    2
+--R        (3x  - a x  - 2a )\|x  - a
+--R   (2)  ----------------------------
+--R                     15
+--R                                                     Type: Expression Integer
+--E
+
+--S 52     14:219 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.220~~~~~$\displaystyle
+\int{\frac{\sqrt{x^2-a^2}}{x}}~dx$}
+$$\int{\frac{\sqrt{x^2-a^2}}{x}}=
+\sqrt{x^2-a^2}-a\sec^{-1}\left|\frac{x}{a}\right|
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 53
+aa:=integrate(sqrt(x^2-a^2)/x,x)
+--R 
+--R
+--R                                     +-------+
+--R              +-------+              | 2    2           +-------+
+--R              | 2    2              \|x  - a   - x      | 2    2     2    2
+--R        (- 2a\|x  - a   + 2a x)atan(--------------) - x\|x  - a   + x  - a
+--R                                           a
+--R   (1)  -------------------------------------------------------------------
+--R                                    +-------+
+--R                                    | 2    2
+--R                                   \|x  - a   - x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 54
+bb:=sqrt(x^2-a^2)-a*asec(x/a)
+--R
+--R         +-------+
+--R         | 2    2           x
+--R   (2)  \|x  - a   - a asec(-)
+--R                            a
+--R                                                     Type: Expression Integer
+--E
+
+--S 55
+cc:=aa-bb
+--R
+--R                   +-------+
+--R                   | 2    2
+--R                  \|x  - a   - x           x
+--R   (3)  - 2a atan(--------------) + a asec(-)
+--R                         a                 a
+--R                                                     Type: Expression Integer
+--E
+
+--S 56
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (4)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 57
+dd:=atanrule cc
+--R
+--R                    +-------+
+--R                    | 2    2
+--R                 - \|x  - a   + x + %i a           x
+--R   (5)  %i a log(-----------------------) + a asec(-)
+--R                   +-------+                       a
+--R                   | 2    2
+--R                  \|x  - a   - x + %i a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 58
+asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x))
+--R
+--R                             +------+
+--R                             | 2
+--R                             |x  - 1
+--R                           x |------  + %i
+--R                             |   2
+--R                            \|  x
+--R                   2%i log(---------------) + %pi
+--R                                  x
+--R   (6)  asec(x) == ------------------------------
+--R                                  2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 59
+ee:=asecrule dd
+--R
+--R   (7)
+--R               +-------+
+--R               | 2    2
+--R               |x  - a
+--R             x |-------  + %i a                 +-------+
+--R               |    2                           | 2    2
+--R              \|   x                         - \|x  - a   + x + %i a
+--R   2%i a log(------------------) + 2%i a log(-----------------------) + a %pi
+--R                      x                        +-------+
+--R                                               | 2    2
+--R                                              \|x  - a   - x + %i a
+--R   --------------------------------------------------------------------------
+--R                                        2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 60
+ff:=expandLog ee
+--R
+--R   (8)
+--R                    +-------+                          +-------+
+--R                    | 2    2                           | 2    2
+--R       - 2%i a log(\|x  - a   - x + %i a) + 2%i a log(\|x  - a   - x - %i a)
+--R     + 
+--R                   +-------+
+--R                   | 2    2
+--R                   |x  - a
+--R       2%i a log(x |-------  + %i a) - 2%i a log(x) + 2%i a log(- 1) + a %pi
+--R                   |    2
+--R                  \|   x
+--R  /
+--R     2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 61
+gg:=rootSimp ff
+--R
+--R   (9)
+--R                  +-------+                      +-------+
+--R                  | 2    2                       | 2    2
+--R       2%i a log(\|x  - a   + %i a) - 2%i a log(\|x  - a   - x + %i a)
+--R     + 
+--R                  +-------+
+--R                  | 2    2
+--R       2%i a log(\|x  - a   - x - %i a) - 2%i a log(x) + 2%i a log(- 1) + a %pi
+--R  /
+--R     2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 62     14:220 Schaums and Axiom differ by a constant
+hh:=complexNormalize gg
+--R
+--R         a %pi
+--R   (10)  -----
+--R           2
+--R                                             Type: Expression Complex Integer
+--E
+@
+
+\section{\cite{1}:14.221~~~~~$\displaystyle
+\int{\frac{\sqrt{x^2-a^2}}{x^2}}~dx$}
+$$\int{\frac{\sqrt{x^2-a^2}}{x^2}}=
+-\frac{\sqrt{x^2-a^2}}{x}+\ln\left(x+\sqrt{x^2-a^2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 63
+aa:=integrate(sqrt(x^2-a^2)/x^2,x)
+--R 
+--R
+--R             +-------+           +-------+
+--R             | 2    2     2      | 2    2          2
+--R        (- x\|x  - a   + x )log(\|x  - a   - x) + a
+--R   (1)  --------------------------------------------
+--R                        +-------+
+--R                        | 2    2     2
+--R                      x\|x  - a   - x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 64
+bb:=-sqrt(x^2-a^2)/x+log(x+sqrt(x^2-a^2))
+--R
+--R               +-------+         +-------+
+--R               | 2    2          | 2    2
+--R        x log(\|x  - a   + x) - \|x  - a
+--R   (2)  ----------------------------------
+--R                         x
+--R                                                     Type: Expression Integer
+--E
+
+--S 65
+cc:=aa-bb
+--R
+--R               +-------+             +-------+
+--R               | 2    2              | 2    2
+--R   (3)  - log(\|x  - a   + x) - log(\|x  - a   - x) - 1
+--R                                                     Type: Expression Integer
+--E
+
+--S 66     14:221 Schaums and Axiom differ by a constant
+dd:=complexNormalize cc
+--R
+--R                 2
+--R   (4)  - log(- a ) - 1
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.222~~~~~$\displaystyle
+\int{\frac{\sqrt{x^2-a^2}}{x^3}}~dx$}
+$$\int{\frac{\sqrt{x^2-a^2}}{x^3}}=
+-\frac{\sqrt{x^2-a^2}}{2x^2}+\frac{1}{2a}
+\sec^{-1}\left|\frac{x}{a}\right|
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 67
+aa:=integrate(sqrt(x^2-a^2)/x^3,x)
+--R 
+--R
+--R   (1)
+--R                                          +-------+
+--R            +-------+                     | 2    2
+--R          3 | 2    2      4     2 2      \|x  - a   - x
+--R       (4x \|x  - a   - 4x  + 2a x )atan(--------------)
+--R                                                a
+--R     + 
+--R                    +-------+
+--R            2    3  | 2    2        3     3
+--R       (2a x  - a )\|x  - a   - 2a x  + 2a x
+--R  /
+--R           +-------+
+--R         3 | 2    2        4     3 2
+--R     4a x \|x  - a   - 4a x  + 2a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 68
+bb:=-sqrt(x^2-a^2)/(2*x^2)+1/(2*a)*asec(x/a)
+--R
+--R            +-------+
+--R            | 2    2     2     x
+--R        - a\|x  - a   + x asec(-)
+--R                               a
+--R   (2)  -------------------------
+--R                      2
+--R                  2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 69
+cc:=aa-bb
+--R
+--R               +-------+
+--R               | 2    2
+--R              \|x  - a   - x         x
+--R        2atan(--------------) - asec(-)
+--R                     a               a
+--R   (3)  -------------------------------
+--R                       2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 70
+asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x))
+--R
+--R                             +------+
+--R                             | 2
+--R                             |x  - 1
+--R                           x |------  + %i
+--R                             |   2
+--R                            \|  x
+--R                   2%i log(---------------) + %pi
+--R                                  x
+--R   (4)  asec(x) == ------------------------------
+--R                                  2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 71
+dd:=asecrule cc
+--R
+--R                    +-------+
+--R                    | 2    2
+--R                    |x  - a
+--R                  x |-------  + %i a           +-------+
+--R                    |    2                     | 2    2
+--R                   \|   x                     \|x  - a   - x
+--R        - 2%i log(------------------) + 4atan(--------------) - %pi
+--R                           x                         a
+--R   (5)  -----------------------------------------------------------
+--R                                     4a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 72
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (6)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 73
+ee:=atanrule dd
+--R
+--R                    +-------+
+--R                    | 2    2
+--R                    |x  - a
+--R                  x |-------  + %i a               +-------+
+--R                    |    2                         | 2    2
+--R                   \|   x                       - \|x  - a   + x + %i a
+--R        - 2%i log(------------------) - 2%i log(-----------------------) - %pi
+--R                           x                      +-------+
+--R                                                  | 2    2
+--R                                                 \|x  - a   - x + %i a
+--R   (7)  ----------------------------------------------------------------------
+--R                                          4a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 74
+ff:=expandLog ee
+--R
+--R   (8)
+--R                +-------+                        +-------+
+--R                | 2    2                         | 2    2
+--R       2%i log(\|x  - a   - x + %i a) - 2%i log(\|x  - a   - x - %i a)
+--R     + 
+--R                   +-------+
+--R                   | 2    2
+--R                   |x  - a
+--R       - 2%i log(x |-------  + %i a) + 2%i log(x) - 2%i log(- 1) - %pi
+--R                   |    2
+--R                  \|   x
+--R  /
+--R     4a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 75
+gg:=rootSimp ff
+--R
+--R   (9)
+--R                  +-------+                    +-------+
+--R                  | 2    2                     | 2    2
+--R       - 2%i log(\|x  - a   + %i a) + 2%i log(\|x  - a   - x + %i a)
+--R     + 
+--R                  +-------+
+--R                  | 2    2
+--R       - 2%i log(\|x  - a   - x - %i a) + 2%i log(x) - 2%i log(- 1) - %pi
+--R  /
+--R     4a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 76     14:222 Schaums and Axiom differ by a constant
+hh:=complexNormalize gg
+--R
+--R           %pi
+--R   (10)  - ---
+--R            4a
+--R                                             Type: Expression Complex Integer
+--E
+@
+
+\section{\cite{1}:14.223~~~~~$\displaystyle\int{\frac{dx}{(x^2-a^2)^{3/2}}}$}
+$$\int{\frac{1}{(x^2-a^2)^{3/2}}}=
+-\frac{x}{a^2\sqrt{x^2-a^2}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 77
+aa:=integrate(1/(x^2-a^2)^(3/2),x)
+--R 
+--R
+--R                    1
+--R   (1)  - ---------------------
+--R            +-------+
+--R            | 2    2     2    2
+--R          x\|x  - a   - x  + a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 78
+bb:=-x/(a^2*sqrt(x^2-a^2))
+--R
+--R                x
+--R   (2)  - ------------
+--R             +-------+
+--R           2 | 2    2
+--R          a \|x  - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 79     14:223 Schaums and Axiom differ by a constant
+cc:=aa-bb
+--R
+--R           1
+--R   (3)  - --
+--R           2
+--R          a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.224~~~~~$\displaystyle
+\int{\frac{x~dx}{(x^2-a^2)^{3/2}}}$}
+$$\int{\frac{x}{(x^2-a^2)^{3/2}}}=
+\frac{-1}{\sqrt{x^2-a^2}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 80
+aa:=integrate(x/(x^2-a^2)^(3/2),x)
+--R 
+--R
+--R             +-------+
+--R             | 2    2
+--R            \|x  - a   - x
+--R   (1)  ---------------------
+--R          +-------+
+--R          | 2    2     2    2
+--R        x\|x  - a   - x  + a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 81
+bb:=-1/sqrt(x^2-a^2)
+--R
+--R               1
+--R   (2)  - ----------
+--R           +-------+
+--R           | 2    2
+--R          \|x  - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 82     14:224 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.225~~~~~$\displaystyle
+\int{\frac{x^2dx}{(x^2-a^2)^{3/2}}}$}
+$$\int{\frac{x^2}{(x^2-a^2)^{3/2}}}=
+\frac{-x}{\sqrt{x^2-a^2}}+\ln\left(x+\sqrt{x^2-a^2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 83
+aa:=integrate(x^2/(x^2-a^2)^(3/2),x)
+--R 
+--R
+--R             +-------+                +-------+
+--R             | 2    2     2    2      | 2    2          2
+--R        (- x\|x  - a   + x  - a )log(\|x  - a   - x) - a
+--R   (1)  -------------------------------------------------
+--R                        +-------+
+--R                        | 2    2     2    2
+--R                      x\|x  - a   - x  + a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 84
+bb:=-x/sqrt(x^2-a^2)+log(x+sqrt(x^2-a^2))
+--R
+--R         +-------+     +-------+
+--R         | 2    2      | 2    2
+--R        \|x  - a  log(\|x  - a   + x) - x
+--R   (2)  ---------------------------------
+--R                     +-------+
+--R                     | 2    2
+--R                    \|x  - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 85     
+cc:=aa-bb
+--R
+--R               +-------+             +-------+
+--R               | 2    2              | 2    2
+--R   (3)  - log(\|x  - a   + x) - log(\|x  - a   - x) - 1
+--R                                                     Type: Expression Integer
+--E
+
+--S 86     14:225 Schaums and Axiom differ by a constant
+dd:=complexNormalize cc
+--R
+--R                 2
+--R   (4)  - log(- a ) - 1
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.226~~~~~$\displaystyle
+\int{\frac{x^3dx}{(x^2-a^2)^{3/2}}}$}
+$$\int{\frac{x^3}{(x^2-a^2)^{3/2}}}=
+\sqrt{x^2-a^2}-\frac{a^2}{\sqrt{x^2-a^2}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 87
+aa:=integrate(x^3/(x^2-a^2)^(3/2),x)
+--R 
+--R
+--R                       +-------+
+--R             3     2   | 2    2      4     2 2     4
+--R        (- 2x  + 4a x)\|x  - a   + 2x  - 5a x  + 2a
+--R   (1)  --------------------------------------------
+--R                         +-------+
+--R                 2    2  | 2    2      3     2
+--R              (2x  - a )\|x  - a   - 2x  + 2a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 88
+bb:=sqrt(x^2-a^2)-a^2/sqrt(x^2-a^2)
+--R
+--R          2     2
+--R         x  - 2a
+--R   (2)  ----------
+--R         +-------+
+--R         | 2    2
+--R        \|x  - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 89     14:226 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.227~~~~~$\displaystyle
+\int{\frac{dx}{x(x^2-a^2)^{3/2}}}$}
+$$\int{\frac{1}{x(x^2-a^2)^{3/2}}}=
+\frac{-1}{a^2\sqrt{x^2-a^2}}-
+\frac{1}{a^3}\sec^{-1}\left|\frac{x}{a}\right|
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 90
+aa:=integrate(1/(x*(x^2-a^2)^(3/2)),x)
+--R 
+--R
+--R                                          +-------+
+--R              +-------+                   | 2    2           +-------+
+--R              | 2    2      2     2      \|x  - a   - x      | 2    2
+--R        (- 2x\|x  - a   + 2x  - 2a )atan(--------------) + a\|x  - a   - a x
+--R                                                a
+--R   (1)  --------------------------------------------------------------------
+--R                                  +-------+
+--R                               3  | 2    2     3 2    5
+--R                              a x\|x  - a   - a x  + a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 91
+bb:=-1/(a^2*sqrt(x^2-a^2))-1/a^3*asec(x/a)
+--R
+--R                  +-------+
+--R               x  | 2    2
+--R        - asec(-)\|x  - a   - a
+--R               a
+--R   (2)  -----------------------
+--R                 +-------+
+--R               3 | 2    2
+--R              a \|x  - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 92
+cc:=aa-bb
+--R
+--R                 +-------+
+--R                 | 2    2
+--R                \|x  - a   - x         x
+--R        - 2atan(--------------) + asec(-)
+--R                       a               a
+--R   (3)  ---------------------------------
+--R                         3
+--R                        a
+--R                                                     Type: Expression Integer
+--E
+
+--S 93
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (4)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 94
+dd:=atanrule cc
+--R
+--R                  +-------+
+--R                  | 2    2
+--R               - \|x  - a   + x + %i a         x
+--R        %i log(-----------------------) + asec(-)
+--R                 +-------+                     a
+--R                 | 2    2
+--R                \|x  - a   - x + %i a
+--R   (5)  -----------------------------------------
+--R                             3
+--R                            a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 95
+asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x))
+--R
+--R                             +------+
+--R                             | 2
+--R                             |x  - 1
+--R                           x |------  + %i
+--R                             |   2
+--R                            \|  x
+--R                   2%i log(---------------) + %pi
+--R                                  x
+--R   (6)  asec(x) == ------------------------------
+--R                                  2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 96
+ee:=asecrule dd
+--R
+--R                  +-------+
+--R                  | 2    2
+--R                  |x  - a
+--R                x |-------  + %i a               +-------+
+--R                  |    2                         | 2    2
+--R                 \|   x                       - \|x  - a   + x + %i a
+--R        2%i log(------------------) + 2%i log(-----------------------) + %pi
+--R                         x                      +-------+
+--R                                                | 2    2
+--R                                               \|x  - a   - x + %i a
+--R   (7)  --------------------------------------------------------------------
+--R                                           3
+--R                                         2a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 97
+ff:=expandLog ee
+--R
+--R   (8)
+--R                  +-------+                        +-------+
+--R                  | 2    2                         | 2    2
+--R       - 2%i log(\|x  - a   - x + %i a) + 2%i log(\|x  - a   - x - %i a)
+--R     + 
+--R                 +-------+
+--R                 | 2    2
+--R                 |x  - a
+--R       2%i log(x |-------  + %i a) - 2%i log(x) + 2%i log(- 1) + %pi
+--R                 |    2
+--R                \|   x
+--R  /
+--R       3
+--R     2a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 98
+gg:=rootSimp ff
+--R
+--R   (9)
+--R                +-------+                    +-------+
+--R                | 2    2                     | 2    2
+--R       2%i log(\|x  - a   + %i a) - 2%i log(\|x  - a   - x + %i a)
+--R     + 
+--R                +-------+
+--R                | 2    2
+--R       2%i log(\|x  - a   - x - %i a) - 2%i log(x) + 2%i log(- 1) + %pi
+--R  /
+--R       3
+--R     2a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 99     14:227 Schaums and Axiom differ by a constant
+hh:=complexNormalize gg
+--R
+--R         %pi
+--R   (10)  ---
+--R           3
+--R         2a
+--R                                             Type: Expression Complex Integer
+--E
+
+@
+
+\section{\cite{1}:14.228~~~~~$\displaystyle
+\int{\frac{dx}{x^2(x^2-a^2)^{3/2}}}$}
+$$\int{\frac{1}{x^2(x^2-a^2)^{3/2}}}=
+-\frac{\sqrt{x^2-a^2}}{a^4x}-\frac{x}{a^4\sqrt{x^2-a^2}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 100
+aa:=integrate(1/(x^2*(x^2-a^2)^(3/2)),x)
+--R 
+--R
+--R                           1
+--R   (1)  - -----------------------------------
+--R                      +-------+
+--R             3    2   | 2    2      4     2 2
+--R          (2x  - a x)\|x  - a   - 2x  + 2a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 101
+bb:=-sqrt(x^2-a^2)/(a^4*x)-x/(a^4*sqrt(x^2-a^2))
+--R
+--R              2    2
+--R          - 2x  + a
+--R   (2)  -------------
+--R            +-------+
+--R         4  | 2    2
+--R        a x\|x  - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 102    14:228 Schaums and Axiom differ by a constant
+cc:=aa-bb
+--R
+--R           2
+--R   (3)  - --
+--R           4
+--R          a
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.229~~~~~$\displaystyle
+\int{\frac{dx}{x^3(x^2-a^2)^{3/2}}}$}
+$$\int{\frac{1}{x^3(x^2-a^2)^{3/2}}}=
+\frac{1}{2a^2x^2\sqrt{x^2-a^2}}-
+\frac{3}{2a^4\sqrt{x^2-a^2}}-
+\frac{3}{2a^5}\sec^{-1}\left|\frac{x}{a}\right|
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 103
+aa:=integrate(1/(x^3*(x^2-a^2)^(3/2)),x)
+--R 
+--R
+--R   (1)
+--R                                                                  +-------+
+--R                          +-------+                               | 2    2
+--R              5      2 3  | 2    2       6      2 4     4 2      \|x  - a   - x
+--R       ((- 24x  + 18a x )\|x  - a   + 24x  - 30a x  + 6a x )atan(--------------)
+--R                                                                        a
+--R     + 
+--R                             +-------+
+--R             4     3 2    5  | 2    2         5      3 3     5
+--R       (12a x  - 7a x  + a )\|x  - a   - 12a x  + 13a x  - 3a x
+--R  /
+--R                     +-------+
+--R        5 5     7 3  | 2    2      5 6      7 4     9 2
+--R     (8a x  - 6a x )\|x  - a   - 8a x  + 10a x  - 2a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 104
+bb:=1/(2*a^2*x^2*sqrt(x^2-a^2))-3/(2*a^4*sqrt(x^2-a^2))-3/(2*a^5)*asec(x/a)
+--R
+--R                     +-------+
+--R            2     x  | 2    2        2    3
+--R        - 3x asec(-)\|x  - a   - 3a x  + a
+--R                  a
+--R   (2)  -----------------------------------
+--R                        +-------+
+--R                    5 2 | 2    2
+--R                  2a x \|x  - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 105
+cc:=aa-bb
+--R
+--R                 +-------+
+--R                 | 2    2
+--R                \|x  - a   - x          x
+--R        - 6atan(--------------) + 3asec(-)
+--R                       a                a
+--R   (3)  ----------------------------------
+--R                          5
+--R                        2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 106
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (4)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 107
+dd:=atanrule cc
+--R
+--R                   +-------+
+--R                   | 2    2
+--R                - \|x  - a   + x + %i a          x
+--R        3%i log(-----------------------) + 3asec(-)
+--R                  +-------+                      a
+--R                  | 2    2
+--R                 \|x  - a   - x + %i a
+--R   (5)  -------------------------------------------
+--R                              5
+--R                            2a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 108
+asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x))
+--R
+--R                             +------+
+--R                             | 2
+--R                             |x  - 1
+--R                           x |------  + %i
+--R                             |   2
+--R                            \|  x
+--R                   2%i log(---------------) + %pi
+--R                                  x
+--R   (6)  asec(x) == ------------------------------
+--R                                  2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 109
+ee:=asecrule dd
+--R
+--R                  +-------+
+--R                  | 2    2
+--R                  |x  - a
+--R                x |-------  + %i a               +-------+
+--R                  |    2                         | 2    2
+--R                 \|   x                       - \|x  - a   + x + %i a
+--R        6%i log(------------------) + 6%i log(-----------------------) + 3%pi
+--R                         x                      +-------+
+--R                                                | 2    2
+--R                                               \|x  - a   - x + %i a
+--R   (7)  ---------------------------------------------------------------------
+--R                                           5
+--R                                         4a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 110
+ff:=expandLog ee
+--R
+--R   (8)
+--R                  +-------+                        +-------+
+--R                  | 2    2                         | 2    2
+--R       - 6%i log(\|x  - a   - x + %i a) + 6%i log(\|x  - a   - x - %i a)
+--R     + 
+--R                 +-------+
+--R                 | 2    2
+--R                 |x  - a
+--R       6%i log(x |-------  + %i a) - 6%i log(x) + 6%i log(- 1) + 3%pi
+--R                 |    2
+--R                \|   x
+--R  /
+--R       5
+--R     4a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 111
+gg:=rootSimp ff
+--R
+--R   (9)
+--R                +-------+                    +-------+
+--R                | 2    2                     | 2    2
+--R       6%i log(\|x  - a   + %i a) - 6%i log(\|x  - a   - x + %i a)
+--R     + 
+--R                +-------+
+--R                | 2    2
+--R       6%i log(\|x  - a   - x - %i a) - 6%i log(x) + 6%i log(- 1) + 3%pi
+--R  /
+--R       5
+--R     4a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 112    14:229 Schaums and Axiom differ by a constant
+hh:=complexNormalize gg
+--R
+--R         3%pi
+--R   (10)  ----
+--R            5
+--R          4a
+--R                                             Type: Expression Complex Integer
+--E
+@
+\section{\cite{1}:14.230~~~~~$\displaystyle\int{(x^2-a^2)^{3/2}}~dx$}
+$$\int{(x^2-a^2)^{3/2}}=
+\frac{x(x^2-a^2)^{3/2}}{4}-\frac{3a^2x\sqrt{x^2-a^2}}{8}+
+\frac{3}{8}a^4\ln\left(x+\sqrt{x^2-a^2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 113
+aa:=integrate((x^2-a^2)^(3/2),x)
+--R 
+--R
+--R   (1)
+--R                           +-------+                              +-------+
+--R              4 3      6   | 2    2       4 4      6 2     8      | 2    2
+--R       ((- 24a x  + 12a x)\|x  - a   + 24a x  - 24a x  + 3a )log(\|x  - a   - x)
+--R     + 
+--R                                         +-------+
+--R             7      2 5      4 3     6   | 2    2       8      2 6      4 4
+--R       (- 16x  + 56a x  - 42a x  + 5a x)\|x  - a   + 16x  - 64a x  + 68a x
+--R     + 
+--R            6 2
+--R       - 20a x
+--R  /
+--R                    +-------+
+--R         3      2   | 2    2       4      2 2     4
+--R     (64x  - 32a x)\|x  - a   - 64x  + 64a x  - 8a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 114
+bb:=(x*(x^2-a^2)^(3/2))/4-(3*a^2*x*sqrt(x^2-a^2))/8+3/8*a^4*log(x+sqrt(x^2-a^2))
+--R
+--R                +-------+                     +-------+
+--R          4     | 2    2            3     2   | 2    2
+--R        3a log(\|x  - a   + x) + (2x  - 5a x)\|x  - a
+--R   (2)  -----------------------------------------------
+--R                               8
+--R                                                     Type: Expression Integer
+--E
+
+--S 115
+cc:=aa-bb
+--R
+--R                  +-------+                +-------+
+--R            4     | 2    2           4     | 2    2
+--R        - 3a log(\|x  - a   + x) - 3a log(\|x  - a   - x)
+--R   (3)  -------------------------------------------------
+--R                                8
+--R                                                     Type: Expression Integer
+--E
+
+--S 116    14:230 Schaums and Axiom differ by a constant
+dd:=complexNormalize cc
+--R
+--R            4       2
+--R          3a log(- a )
+--R   (4)  - ------------
+--R                8
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.231~~~~~$\displaystyle\int{x(x^2-a^2)^{3/2}}~dx$}
+$$\int{x(x^2-a^2)^{3/2}}=\frac{(x^2-a^2)^{5/2}}{5}$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 117
+aa:=integrate(x*(x^2-a^2)^(3/2),x)
+--R 
+--R
+--R   (1)
+--R                                                  +-------+
+--R             9      2 7      4 5      6 3     8   | 2    2       10      2 8
+--R       (- 16x  + 52a x  - 61a x  + 30a x  - 5a x)\|x  - a   + 16x   - 60a x
+--R     + 
+--R          4 6      6 4      8 2    10
+--R       85a x  - 55a x  + 15a x  - a
+--R  /
+--R                           +-------+
+--R         4      2 2     4  | 2    2       5       2 3      4
+--R     (80x  - 60a x  + 5a )\|x  - a   - 80x  + 100a x  - 25a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 118
+bb:=(x^2-a^2)^(5/2)/5
+--R
+--R                          +-------+
+--R          4     2 2    4  | 2    2
+--R        (x  - 2a x  + a )\|x  - a
+--R   (2)  ---------------------------
+--R                     5
+--R                                                     Type: Expression Integer
+--E
+
+--S 119    14:231 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.232~~~~~$\displaystyle\int{x^2(x^2-a^2)^{3/2}}~dx$}
+$$\int{x^2(x^2-a^2)^{3/2}}=
+\frac{x(x^2-a^2)^{5/2}}{6}+\frac{a^2x(x^2-a^2)^{3/2}}{24}-
+\frac{a^4x\sqrt{x^2-a^2}}{16}+
+\frac{a^6}{16}\ln\left(x+\sqrt{x^2-a^2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 120
+aa:=integrate(x^2*(x^2-a^2)^(3/2),x)
+--R 
+--R
+--R   (1)
+--R                                        +-------+
+--R                 6 5      8 3      10   | 2    2       6 6       8 4      10 2
+--R           (- 96a x  + 96a x  - 18a  x)\|x  - a   + 96a x  - 144a x  + 54a  x
+--R         + 
+--R               12
+--R           - 3a
+--R      *
+--R              +-------+
+--R              | 2    2
+--R         log(\|x  - a   - x)
+--R     + 
+--R                                                                 +-------+
+--R              11       2 9       4 7       6 5      8 3     10   | 2    2
+--R       (- 256x   + 832a x  - 912a x  + 404a x  - 68a x  + 3a  x)\|x  - a
+--R     + 
+--R           12       2 10        4 8       6 6       8 4      10 2
+--R       256x   - 960a x   + 1296a x  - 772a x  + 198a x  - 18a  x
+--R  /
+--R                                  +-------+
+--R           5        2 3       4   | 2    2         6        2 4       4 2      6
+--R     (1536x  - 1536a x  + 288a x)\|x  - a   - 1536x  + 2304a x  - 864a x  + 48a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 121
+bb:=(x*(x^2-a^2)^(5/2))/6+(a^2*x*(x^2-a^2)^(3/2))/24-(a^4*x*sqrt(x^2-a^2))/16+a^6/16*log(x+sqrt(x^2-a^2))
+--R
+--R                +-------+                              +-------+
+--R          6     | 2    2            5      2 3     4   | 2    2
+--R        3a log(\|x  - a   + x) + (8x  - 14a x  + 3a x)\|x  - a
+--R   (2)  --------------------------------------------------------
+--R                                   48
+--R                                                     Type: Expression Integer
+--E
+
+--S 122
+cc:=aa-bb
+--R
+--R                 +-------+               +-------+
+--R           6     | 2    2          6     | 2    2
+--R        - a log(\|x  - a   + x) - a log(\|x  - a   - x)
+--R   (3)  -----------------------------------------------
+--R                               16
+--R                                                     Type: Expression Integer
+--E
+
+--S 123    14:232 Schaums and Axiom differ by a constant
+dd:=complexNormalize cc
+--R
+--R           6       2
+--R          a log(- a )
+--R   (4)  - -----------
+--R               16
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.233~~~~~$\displaystyle\int{x^3(x^2-a^2)^{3/2}}~dx$}
+$$\int{x^3(x^2-a^2)^{3/2}}=
+\frac{(x^2-a^2)^{7/2}}{7}+\frac{a^2(x^2-a^2)^{5/2}}{5}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 124
+aa:=integrate(x^3*(x^2-a^2)^(3/2),x)
+--R 
+--R
+--R   (1)
+--R                   13        2 11        4 9       6 7       8 5       10 3
+--R             - 320x   + 1072a x   - 1240a x  + 467a x  + 112a x  - 105a  x
+--R           + 
+--R                12
+--R             14a  x
+--R      *
+--R          +-------+
+--R          | 2    2
+--R         \|x  - a
+--R     + 
+--R           14        2 12        4 10       6 8      8 6       10 4      12 2
+--R       320x   - 1232a x   + 1736a x   - 973a x  + 21a x  + 175a  x  - 49a  x
+--R     + 
+--R         14
+--R       2a
+--R  /
+--R                                            +-------+
+--R             6        2 4       4 2      6  | 2    2         7        2 5
+--R       (2240x  - 2800a x  + 840a x  - 35a )\|x  - a   - 2240x  + 3920a x
+--R     + 
+--R              4 3       6
+--R       - 1960a x  + 245a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 125
+bb:=(x^2-a^2)^(7/2)/7+(a^2*(x^2-a^2)^(5/2))/5
+--R
+--R                                   +-------+
+--R           6     2 4    4 2     6  | 2    2
+--R        (5x  - 8a x  + a x  + 2a )\|x  - a
+--R   (2)  ------------------------------------
+--R                         35
+--R                                                     Type: Expression Integer
+--E
+
+--S 126    14:233 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.234~~~~~$\displaystyle
+\int{\frac{(x^2-a^2)^{3/2}}{x}}~dx$}
+$$\int{\frac{(x^2-a^2)^{3/2}}{x}}=
+\frac{(x^2-a^2)^{3/2}}{3}-a^2\sqrt{x^2-a^2}+
+a^3\sec^{-1}\left|\frac{x}{a}\right|
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 127
+aa:=integrate((x^2-a^2)^(3/2)/x,x)
+--R 
+--R
+--R   (1)
+--R                                                        +-------+
+--R                       +-------+                        | 2    2
+--R            3 2     5  | 2    2       3 3      5       \|x  - a   - x
+--R       ((24a x  - 6a )\|x  - a   - 24a x  + 18a x)atan(--------------)
+--R                                                              a
+--R     + 
+--R                                +-------+
+--R            5      2 3      4   | 2    2      6      2 4      4 2     6
+--R       (- 4x  + 19a x  - 12a x)\|x  - a   + 4x  - 21a x  + 21a x  - 4a
+--R  /
+--R                  +-------+
+--R         2     2  | 2    2       3     2
+--R     (12x  - 3a )\|x  - a   - 12x  + 9a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 128
+bb:=(x^2-a^2)^(3/2)/3-a^2*sqrt(x^2-a^2)+a^3*asec(x/a)
+--R
+--R                   +-------+
+--R          2     2  | 2    2      3     x
+--R        (x  - 4a )\|x  - a   + 3a asec(-)
+--R                                       a
+--R   (2)  ---------------------------------
+--R                        3
+--R                                                     Type: Expression Integer
+--E
+
+--S 129
+cc:=aa-bb
+--R
+--R                 +-------+
+--R                 | 2    2
+--R          3     \|x  - a   - x     3     x
+--R   (3)  2a atan(--------------) - a asec(-)
+--R                       a                 a
+--R                                                     Type: Expression Integer
+--E
+
+--S 130
+asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x))
+--R
+--R                             +------+
+--R                             | 2
+--R                             |x  - 1
+--R                           x |------  + %i
+--R                             |   2
+--R                            \|  x
+--R                   2%i log(---------------) + %pi
+--R                                  x
+--R   (4)  asec(x) == ------------------------------
+--R                                  2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 131
+dd:=asecrule cc
+--R
+--R                      +-------+
+--R                      | 2    2
+--R                      |x  - a
+--R                    x |-------  + %i a             +-------+
+--R                      |    2                       | 2    2
+--R               3     \|   x                 3     \|x  - a   - x     3
+--R        - 2%i a log(------------------) + 4a atan(--------------) - a %pi
+--R                             x                           a
+--R   (5)  -----------------------------------------------------------------
+--R                                        2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 132
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (6)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 133
+ee:=atanrule dd
+--R
+--R   (7)
+--R                 +-------+
+--R                 | 2    2
+--R                 |x  - a
+--R               x |-------  + %i a                 +-------+
+--R                 |    2                           | 2    2
+--R          3     \|   x                    3    - \|x  - a   + x + %i a     3
+--R   - 2%i a log(------------------) - 2%i a log(-----------------------) - a %pi
+--R                        x                        +-------+
+--R                                                 | 2    2
+--R                                                \|x  - a   - x + %i a
+--R   ----------------------------------------------------------------------------
+--R                                         2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 134
+ff:=expandLog ee
+--R
+--R   (8)
+--R                  +-------+                          +-------+
+--R            3     | 2    2                     3     | 2    2
+--R       2%i a log(\|x  - a   - x + %i a) - 2%i a log(\|x  - a   - x - %i a)
+--R     + 
+--R                     +-------+
+--R                     | 2    2
+--R              3      |x  - a                  3              3            3
+--R       - 2%i a log(x |-------  + %i a) + 2%i a log(x) - 2%i a log(- 1) - a %pi
+--R                     |    2
+--R                    \|   x
+--R  /
+--R     2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 135
+gg:=rootSimp ff
+--R
+--R   (9)
+--R                    +-------+                      +-------+
+--R              3     | 2    2                 3     | 2    2
+--R       - 2%i a log(\|x  - a   + %i a) + 2%i a log(\|x  - a   - x + %i a)
+--R     + 
+--R                  +-------+
+--R            3     | 2    2                     3              3            3
+--R     - 2%i a log(\|x  - a   - x - %i a) + 2%i a log(x) - 2%i a log(- 1) - a %pi
+--R  /
+--R     2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 136    14:234 Schaums and Axiom differ by a constant
+hh:=complexNormalize gg
+--R
+--R            3
+--R           a %pi
+--R   (10)  - -----
+--R             2
+--R                                             Type: Expression Complex Integer
+--E
+@
+
+\section{\cite{1}:14.235~~~~~$\displaystyle
+\int{\frac{(x^2-a^2)^{3/2}}{x^2}}~dx$}
+$$\int{\frac{(x^2-a^2)^{3/2}}{x^2}}=
+-\frac{(x^2-a^2)^{3/2}}{x}+\frac{3x\sqrt{x^2-a^2}}{2}-
+\frac{3}{2}a^2\ln\left(x+\sqrt{x^2-a^2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 137
+aa:=integrate((x^2-a^2)^{3/2}/x^2,x)
+--R 
+--R
+--R   (1)
+--R                        +-------+                       +-------+
+--R            2 3     4   | 2    2       2 4     4 2      | 2    2
+--R       ((12a x  - 3a x)\|x  - a   - 12a x  + 9a x )log(\|x  - a   - x)
+--R     + 
+--R                              +-------+
+--R            5     2 3     4   | 2    2      6     2 4     4 2     6
+--R       (- 4x  + 3a x  + 4a x)\|x  - a   + 4x  - 5a x  - 3a x  + 2a
+--R  /
+--R                  +-------+
+--R        3     2   | 2    2      4     2 2
+--R     (8x  - 2a x)\|x  - a   - 8x  + 6a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 138
+bb:=-(x^2-a^2)^(3/2)/x+3*x*sqrt(x^2-a^2)/2-3/2*a^2*log(x+sqrt(x^2-a^2))
+--R
+--R                    +-------+                   +-------+
+--R            2       | 2    2           2     2  | 2    2
+--R        - 3a x log(\|x  - a   + x) + (x  + 2a )\|x  - a
+--R   (2)  -------------------------------------------------
+--R                                2x
+--R                                                     Type: Expression Integer
+--E
+
+--S 139
+cc:=aa-bb
+--R
+--R                +-------+                +-------+
+--R          2     | 2    2           2     | 2    2           2
+--R        3a log(\|x  - a   + x) + 3a log(\|x  - a   - x) + 2a
+--R   (3)  -----------------------------------------------------
+--R                                  2
+--R                                                     Type: Expression Integer
+--E
+
+--S 140    14:235 Schaums and Axiom differ by a constant
+dd:=complexNormalize cc
+--R
+--R          2       2      2
+--R        3a log(- a ) + 2a
+--R   (4)  ------------------
+--R                 2
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.236~~~~~$\displaystyle
+\int{\frac{(x^2-a^2)^{3/2}}{x^3}}~dx$}
+$$\int{\frac{(x^2-a^2)^{3/2}}{x^3}}=
+-\frac{(x^2-a^2)^{3/2}}{2x^2}+\frac{3}{2}\sqrt{x^2-a^2}-
+\frac{3}{2}a\sec^{-1}\left|\frac{x}{a}\right|
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 141
+aa:=integrate((x^2-a^2)^(3/2)/x^3,x)
+--R 
+--R
+--R   (1)
+--R                                                             +-------+
+--R                           +-------+                         | 2    2
+--R                4     3 2  | 2    2         5      3 3      \|x  - a   - x
+--R       ((- 24a x  + 6a x )\|x  - a   + 24a x  - 18a x )atan(--------------)
+--R                                                                   a
+--R     + 
+--R                              +-------+
+--R            5     2 3     4   | 2    2      6     2 4     4 2    6
+--R       (- 8x  + 2a x  + 3a x)\|x  - a   + 8x  - 6a x  - 3a x  + a
+--R  /
+--R                   +-------+
+--R        4     2 2  | 2    2      5     2 3
+--R     (8x  - 2a x )\|x  - a   - 8x  + 6a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 142
+bb:=-(x^2-a^2)^(3/2)/(2*x^2)+(3*sqrt(x^2-a^2))/2-3/2*a*asec(x/a)
+--R
+--R                   +-------+
+--R           2    2  | 2    2        2     x
+--R        (2x  + a )\|x  - a   - 3a x asec(-)
+--R                                         a
+--R   (2)  -----------------------------------
+--R                          2
+--R                        2x
+--R                                                     Type: Expression Integer
+--E
+
+--S 143
+cc:=aa-bb
+--R
+--R                   +-------+
+--R                   | 2    2
+--R                  \|x  - a   - x            x
+--R        - 6a atan(--------------) + 3a asec(-)
+--R                         a                  a
+--R   (3)  --------------------------------------
+--R                           2
+--R                                                     Type: Expression Integer
+--E
+
+--S 144
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (4)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 145
+dd:=atanrule cc
+--R
+--R                     +-------+
+--R                     | 2    2
+--R                  - \|x  - a   + x + %i a            x
+--R        3%i a log(-----------------------) + 3a asec(-)
+--R                    +-------+                        a
+--R                    | 2    2
+--R                   \|x  - a   - x + %i a
+--R   (5)  -----------------------------------------------
+--R                               2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 146
+asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x))
+--R
+--R                             +------+
+--R                             | 2
+--R                             |x  - 1
+--R                           x |------  + %i
+--R                             |   2
+--R                            \|  x
+--R                   2%i log(---------------) + %pi
+--R                                  x
+--R   (6)  asec(x) == ------------------------------
+--R                                  2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 147
+ee:=asecrule dd
+--R
+--R   (7)
+--R               +-------+
+--R               | 2    2
+--R               |x  - a
+--R             x |-------  + %i a                 +-------+
+--R               |    2                           | 2    2
+--R              \|   x                         - \|x  - a   + x + %i a
+--R   6%i a log(------------------) + 6%i a log(-----------------------) + 3a %pi
+--R                      x                        +-------+
+--R                                               | 2    2
+--R                                              \|x  - a   - x + %i a
+--R   ---------------------------------------------------------------------------
+--R                                        4
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 148
+ff:=expandLog ee
+--R
+--R   (8)
+--R                    +-------+                          +-------+
+--R                    | 2    2                           | 2    2
+--R       - 6%i a log(\|x  - a   - x + %i a) + 6%i a log(\|x  - a   - x - %i a)
+--R     + 
+--R                   +-------+
+--R                   | 2    2
+--R                   |x  - a
+--R       6%i a log(x |-------  + %i a) - 6%i a log(x) + 6%i a log(- 1) + 3a %pi
+--R                   |    2
+--R                  \|   x
+--R  /
+--R     4
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 149
+gg:=rootSimp ff
+--R
+--R   (9)
+--R                  +-------+                      +-------+
+--R                  | 2    2                       | 2    2
+--R       6%i a log(\|x  - a   + %i a) - 6%i a log(\|x  - a   - x + %i a)
+--R     + 
+--R                +-------+
+--R                | 2    2
+--R     6%i a log(\|x  - a   - x - %i a) - 6%i a log(x) + 6%i a log(- 1) + 3a %pi
+--R  /
+--R     4
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 150    14:236 Schaums and Axiom differ by a constant
+hh:=complexNormalize gg
+--R
+--R         3a %pi
+--R   (10)  ------
+--R            4
+--R                                             Type: Expression Complex Integer
+--E
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 pp68-69
+\end{thebibliography}
+\end{document}
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diff --git a/src/axiom-website/CATS/schaum11.input.pamphlet b/src/axiom-website/CATS/schaum11.input.pamphlet
new file mode 100644
index 0000000..fc3117e
--- /dev/null
+++ b/src/axiom-website/CATS/schaum11.input.pamphlet
@@ -0,0 +1,2522 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum11.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.237~~~~~$\displaystyle\int{\frac{dx}{\sqrt{a^2-x^2}}}$}
+$$\int{\frac{1}{\sqrt{a^2-x^2}}}=\ln\left(x+\sqrt{a^2-x^2}\right)$$
+&lt;&lt;*&gt;&gt;=
+)spool schaum11.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1
+aa:=integrate(1/(sqrt(a^2-x^2)),x)
+--R 
+--R
+--R                 +---------+
+--R                 |   2    2
+--R                \|- x  + a   - a
+--R   (1)  - 2atan(----------------)
+--R                        x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 2
+bb:=asin(x/a)
+--R
+--R             x
+--R   (2)  asin(-)
+--R             a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3
+cc:=aa-bb
+--R
+--R                 +---------+
+--R                 |   2    2
+--R                \|- x  + a   - a         x
+--R   (3)  - 2atan(----------------) - asin(-)
+--R                        x                a
+--R                                                     Type: Expression Integer
+--E
+
+--S 4
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (4)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 5
+dd:=atanrule cc
+--R
+--R                  +---------+
+--R                  |   2    2
+--R               - \|- x  + a   + %i x + a         x
+--R   (5)  %i log(-------------------------) - asin(-)
+--R                 +---------+                     a
+--R                 |   2    2
+--R                \|- x  + a   + %i x - a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 6
+asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2)))
+--R
+--R                           +--------+
+--R                           |   2
+--R   (6)  asin(x) == %i log(\|- x  + 1  - %i x)
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 7
+ee:=asinrule dd
+--R
+--R                   +---------+
+--R                   |   2    2
+--R                   |- x  + a
+--R                 a |---------  - %i x              +---------+
+--R                   |     2                         |   2    2
+--R                  \|    a                       - \|- x  + a   + %i x + a
+--R   (7)  - %i log(--------------------) + %i log(-------------------------)
+--R                           a                      +---------+
+--R                                                  |   2    2
+--R                                                 \|- x  + a   + %i x - a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 8
+ff:=rootSimp ee
+--R
+--R                    +-------+                     +-------+
+--R                    | 2    2                      | 2    2
+--R                 %i\|x  - a   - %i x           - \|x  - a   + x - %i a
+--R   (8)  - %i log(-------------------) + %i log(-----------------------)
+--R                          a                      +-------+
+--R                                                 | 2    2
+--R                                                \|x  - a   + x + %i a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 9      14:238 Schaums and Axiom agree
+gg:=complexNormalize ff
+--R
+--R   (9)  0
+--R                                             Type: Expression Complex Integer
+--E
+
+@
+
+\section{\cite{1}:14.238~~~~~$\displaystyle\int{\frac{x~dx}{\sqrt{a^2-x^2}}}$}
+$$\int{\frac{x}{\sqrt{a^2-x^2}}}=\sqrt{a^2-x^2}$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 10
+aa:=integrate(x/(sqrt(a^2-x^2)),x)
+--R 
+--R
+--R                2
+--R               x
+--R   (1)  ----------------
+--R         +---------+
+--R         |   2    2
+--R        \|- x  + a   - a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 11
+bb:=-sqrt(a^2-x^2)
+--R
+--R           +---------+
+--R           |   2    2
+--R   (2)  - \|- x  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 12     14:238 Schaums and Axiom differ by a constant
+cc:=aa-bb
+--R
+--R   (3)  - a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.239~~~~~$\displaystyle
+\int{\frac{x^2~dx}{\sqrt{a^2-x^2}}}$}
+$$\int{\frac{x^2}{\sqrt{a^2-x^2}}}=
+\frac{x\sqrt{a^2-x^2}}{2}+\frac{a^2}{2}\ln\left(x+\sqrt{a^2-x^2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 13
+aa:=integrate(x^2/sqrt(a^2-x^2),x)
+--R 
+--R
+--R   (1)
+--R                                              +---------+
+--R              +---------+                     |   2    2
+--R            3 |   2    2      2 2     4      \|- x  + a   - a
+--R       (- 4a \|- x  + a   - 2a x  + 4a )atan(----------------)
+--R                                                     x
+--R     + 
+--R                     +---------+
+--R           3     2   |   2    2        3     3
+--R       (- x  + 2a x)\|- x  + a   + 2a x  - 2a x
+--R  /
+--R        +---------+
+--R        |   2    2      2     2
+--R     4a\|- x  + a   + 2x  - 4a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 14
+bb:=-(x*sqrt(a^2-x^2))/2+a^2/2*asin(x/a)
+--R
+--R            +---------+
+--R            |   2    2     2     x
+--R        - x\|- x  + a   + a asin(-)
+--R                                 a
+--R   (2)  ---------------------------
+--R                     2
+--R                                                     Type: Expression Integer
+--E
+
+--S 15
+cc:=aa-bb
+--R
+--R                   +---------+
+--R                   |   2    2
+--R            2     \|- x  + a   - a     2     x
+--R        - 2a atan(----------------) - a asin(-)
+--R                          x                  a
+--R   (3)  ---------------------------------------
+--R                           2
+--R                                                     Type: Expression Integer
+--E
+
+--S 16
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (4)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 17
+dd:=atanrule cc
+--R
+--R                    +---------+
+--R                    |   2    2
+--R            2    - \|- x  + a   + %i x + a     2     x
+--R        %i a log(-------------------------) - a asin(-)
+--R                   +---------+                       a
+--R                   |   2    2
+--R                  \|- x  + a   + %i x - a
+--R   (5)  -----------------------------------------------
+--R                               2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 18
+asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2)))
+--R
+--R                           +--------+
+--R                           |   2
+--R   (6)  asin(x) == %i log(\|- x  + 1  - %i x)
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 19
+ee:=asinrule dd
+--R
+--R                     +---------+
+--R                     |   2    2
+--R                     |- x  + a
+--R                   a |---------  - %i x                +---------+
+--R                     |     2                           |   2    2
+--R              2     \|    a                    2    - \|- x  + a   + %i x + a
+--R        - %i a log(--------------------) + %i a log(-------------------------)
+--R                             a                        +---------+
+--R                                                      |   2    2
+--R                                                     \|- x  + a   + %i x - a
+--R   (7)  ----------------------------------------------------------------------
+--R                                           2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 20
+ff:=expandLog ee
+--R
+--R   (8)
+--R                    +---------+
+--R                    |   2    2                      +---------+
+--R             2      |- x  + a                 2     |   2    2
+--R       - %i a log(a |---------  - %i x) - %i a log(\|- x  + a   + %i x - a)
+--R                    |     2
+--R                   \|    a
+--R     + 
+--R                 +---------+
+--R           2     |   2    2                    2             2
+--R       %i a log(\|- x  + a   - %i x - a) + %i a log(a) + %i a log(- 1)
+--R  /
+--R     2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 21
+gg:=rootSimp ff
+--R
+--R   (9)
+--R                     +-------+                           +-------+
+--R             2       | 2    2                    2       | 2    2
+--R       - %i a log(%i\|x  - a   + %i x - a) - %i a log(%i\|x  - a   - %i x)
+--R     + 
+--R                   +-------+
+--R           2       | 2    2                    2             2
+--R       %i a log(%i\|x  - a   - %i x - a) + %i a log(a) + %i a log(- 1)
+--R  /
+--R     2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 22     14:239 Schaums and Axiom agree
+hh:=complexNormalize gg
+--R
+--R   (10)  0
+--R                                             Type: Expression Complex Integer
+--E
+
+@
+
+\section{\cite{1}:14.240~~~~~$\displaystyle
+\int{\frac{x^3~dx}{\sqrt{a^2-x^2}}}$}
+$$\int{\frac{x^3}{\sqrt{a^2-x^2}}}=
+\frac{(a^2-x^2)^{3/2}}{3}+a^2\sqrt{a^2-x^2}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 23
+aa:=integrate(x^3/sqrt(a^2-x^2),x)
+--R 
+--R
+--R                   +---------+
+--R                 4 |   2    2     6     2 4
+--R             3a x \|- x  + a   + x  - 3a x
+--R   (1)  ---------------------------------------
+--R                     +---------+
+--R           2      2  |   2    2        2      3
+--R        (3x  - 12a )\|- x  + a   - 9a x  + 12a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 24
+bb:=(a^2-x^2)^(3/2)/3-a^2*sqrt(a^2-x^2)
+--R
+--R                     +---------+
+--R            2     2  |   2    2
+--R        (- x  - 2a )\|- x  + a
+--R   (2)  ------------------------
+--R                    3
+--R                                                     Type: Expression Integer
+--E
+
+--S 25     14:240 Schaums and Axiom differ by a constant
+cc:=aa-bb
+--R
+--R            3
+--R          2a
+--R   (3)  - ---
+--R           3
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.241~~~~~$\displaystyle\int{\frac{dx}{x\sqrt{a^2-x^2}}}$}
+$$\int{\frac{1}{x\sqrt{a^2-x^2}}}=
+\frac{1}{a}\sec^{-1}\left|\frac{x}{a}\right|
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 26
+aa:=integrate(1/(x*sqrt(a^2-x^2)),x)
+--R 
+--R
+--R             +---------+
+--R             |   2    2
+--R            \|- x  + a   - a
+--R        log(----------------)
+--R                    x
+--R   (1)  ---------------------
+--R                  a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 27
+bb:=-1/a*log((a+sqrt(a^2-x^2))/x)
+--R
+--R               +---------+
+--R               |   2    2
+--R              \|- x  + a   + a
+--R          log(----------------)
+--R                      x
+--R   (2)  - ---------------------
+--R                    a
+--R                                                     Type: Expression Integer
+--E
+
+--S 28
+cc:=aa-bb
+--R
+--R             +---------+             +---------+
+--R             |   2    2              |   2    2
+--R            \|- x  + a   + a        \|- x  + a   - a
+--R        log(----------------) + log(----------------)
+--R                    x                       x
+--R   (3)  ---------------------------------------------
+--R                              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 29
+dd:=expandLog cc
+--R
+--R             +---------+             +---------+
+--R             |   2    2              |   2    2
+--R        log(\|- x  + a   + a) + log(\|- x  + a   - a) - 2log(x)
+--R   (4)  -------------------------------------------------------
+--R                                   a
+--R                                                     Type: Expression Integer
+--E
+
+--S 30
+ee:=complexNormalize dd
+--R
+--R                  x
+--R          2log(-------)
+--R                +----+
+--R                |   2
+--R               \|- x
+--R   (5)  - -------------
+--R                a
+--R                                                     Type: Expression Integer
+--E
+
+--S 31     14:241 Schaums and Axiom differ by a constant
+ff:=rootSimp ee
+--R
+--R              +---+
+--R        2log(\|- 1 )
+--R   (6)  ------------
+--R              a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.242~~~~~$\displaystyle
+\int{\frac{dx}{x^2\sqrt{a^2-x^2}}}$}
+$$\int{\frac{1}{x^2\sqrt{a^2-x^2}}}=
+\frac{\sqrt{a^2-x^2}}{a^2x}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 32
+aa:=integrate(1/(x^2*sqrt(a^2-x^2)),x)
+--R 
+--R
+--R          +---------+
+--R          |   2    2     2    2
+--R        a\|- x  + a   + x  - a
+--R   (1)  -----------------------
+--R             +---------+
+--R          2  |   2    2     3
+--R         a x\|- x  + a   - a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 33
+bb:=-sqrt(a^2-x^2)/(a^2*x)
+--R
+--R           +---------+
+--R           |   2    2
+--R          \|- x  + a
+--R   (2)  - ------------
+--R                2
+--R               a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 34     14:242 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.243~~~~~$\displaystyle\int{\frac{dx}{x^3\sqrt{a^2-x^2}}}$}
+$$\int{\frac{1}{x^3\sqrt{a^2-x^2}}}=
+-\frac{\sqrt{a^2-x^2}}{2a^2x^2}+\frac{1}{2a^3}
+\sec^{-1}\left|\frac{x}{a}\right|
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 35
+aa:=integrate(1/(x^3*sqrt(a^2-x^2)),x)
+--R 
+--R
+--R   (1)
+--R                                            +---------+
+--R              +---------+                   |   2    2
+--R            2 |   2    2     4     2 2     \|- x  + a   - a
+--R       (2a x \|- x  + a   + x  - 2a x )log(----------------)
+--R                                                   x
+--R     + 
+--R                      +---------+
+--R             2     3  |   2    2      2 2     4
+--R       (- a x  + 2a )\|- x  + a   + 2a x  - 2a
+--R  /
+--R           +---------+
+--R       4 2 |   2    2      3 4     5 2
+--R     4a x \|- x  + a   + 2a x  - 4a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 36
+bb:=-sqrt(a^2-x^2)/(2*a^2*x^2)-1/(2*a^3)*log((a+sqrt(a^2-x^2))/x)
+--R
+--R                 +---------+
+--R                 |   2    2           +---------+
+--R           2    \|- x  + a   + a      |   2    2
+--R        - x log(----------------) - a\|- x  + a
+--R                        x
+--R   (2)  -----------------------------------------
+--R                            3 2
+--R                          2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 37
+cc:=aa-bb
+--R
+--R             +---------+             +---------+
+--R             |   2    2              |   2    2
+--R            \|- x  + a   + a        \|- x  + a   - a
+--R        log(----------------) + log(----------------)
+--R                    x                       x
+--R   (3)  ---------------------------------------------
+--R                               3
+--R                             2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 38
+dd:=expandLog cc
+--R
+--R             +---------+             +---------+
+--R             |   2    2              |   2    2
+--R        log(\|- x  + a   + a) + log(\|- x  + a   - a) - 2log(x)
+--R   (4)  -------------------------------------------------------
+--R                                    3
+--R                                  2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 39
+ee:=complexNormalize dd
+--R
+--R                 x
+--R          log(-------)
+--R               +----+
+--R               |   2
+--R              \|- x
+--R   (5)  - ------------
+--R                3
+--R               a
+--R                                                     Type: Expression Integer
+--E 
+
+--S 40     14:243 Schaums and Axiom differ by a constant
+ff:=rootSimp ee
+--R
+--R             +---+
+--R        log(\|- 1 )
+--R   (6)  -----------
+--R              3
+--R             a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.244~~~~~$\displaystyle\int{\sqrt{a^2-x^2}}~dx$}
+$$\int{\sqrt{a^2-x^2}}=
+\frac{x\sqrt{a^2-x^2}}{2}-\frac{a^2}{2}\ln\left(x+\sqrt{a^2-x^2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 41
+aa:=integrate(sqrt(a^2-x^2),x)
+--R 
+--R
+--R   (1)
+--R                                              +---------+
+--R              +---------+                     |   2    2
+--R            3 |   2    2      2 2     4      \|- x  + a   - a
+--R       (- 4a \|- x  + a   - 2a x  + 4a )atan(----------------)
+--R                                                     x
+--R     + 
+--R                   +---------+
+--R         3     2   |   2    2        3     3
+--R       (x  - 2a x)\|- x  + a   - 2a x  + 2a x
+--R  /
+--R        +---------+
+--R        |   2    2      2     2
+--R     4a\|- x  + a   + 2x  - 4a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 42
+bb:=(x*sqrt(a^2-x^2))/2+a^2/2*asin(x/a)
+--R
+--R          +---------+
+--R          |   2    2     2     x
+--R        x\|- x  + a   + a asin(-)
+--R                               a
+--R   (2)  -------------------------
+--R                    2
+--R                                                     Type: Expression Integer
+--E
+
+--S 43
+cc:=aa-bb
+--R
+--R                   +---------+
+--R                   |   2    2
+--R            2     \|- x  + a   - a     2     x
+--R        - 2a atan(----------------) - a asin(-)
+--R                          x                  a
+--R   (3)  ---------------------------------------
+--R                           2
+--R                                                     Type: Expression Integer
+--E
+
+--S 44
+asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2)))
+--R
+--R                           +--------+
+--R                           |   2
+--R   (4)  asin(x) == %i log(\|- x  + 1  - %i x)
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 45
+dd:=asinrule cc
+--R
+--R                     +---------+
+--R                     |   2    2
+--R                     |- x  + a
+--R                   a |---------  - %i x             +---------+
+--R                     |     2                        |   2    2
+--R              2     \|    a                  2     \|- x  + a   - a
+--R        - %i a log(--------------------) - 2a atan(----------------)
+--R                             a                             x
+--R   (5)  ------------------------------------------------------------
+--R                                      2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 46
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (6)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 47
+ee:=atanrule dd
+--R
+--R                     +---------+
+--R                     |   2    2
+--R                     |- x  + a
+--R                   a |---------  - %i x                +---------+
+--R                     |     2                           |   2    2
+--R              2     \|    a                    2    - \|- x  + a   + %i x + a
+--R        - %i a log(--------------------) + %i a log(-------------------------)
+--R                             a                        +---------+
+--R                                                      |   2    2
+--R                                                     \|- x  + a   + %i x - a
+--R   (7)  ----------------------------------------------------------------------
+--R                                           2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 48
+ff:=expandLog ee
+--R
+--R   (8)
+--R                    +---------+
+--R                    |   2    2                      +---------+
+--R             2      |- x  + a                 2     |   2    2
+--R       - %i a log(a |---------  - %i x) - %i a log(\|- x  + a   + %i x - a)
+--R                    |     2
+--R                   \|    a
+--R     + 
+--R                 +---------+
+--R           2     |   2    2                    2             2
+--R       %i a log(\|- x  + a   - %i x - a) + %i a log(a) + %i a log(- 1)
+--R  /
+--R     2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 49
+gg:=rootSimp ff
+--R
+--R   (9)
+--R                     +-------+                           +-------+
+--R             2       | 2    2                    2       | 2    2
+--R       - %i a log(%i\|x  - a   + %i x - a) - %i a log(%i\|x  - a   - %i x)
+--R     + 
+--R                   +-------+
+--R           2       | 2    2                    2             2
+--R       %i a log(%i\|x  - a   - %i x - a) + %i a log(a) + %i a log(- 1)
+--R  /
+--R     2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 50     14:244 Schaums and Axiom agree
+hh:=complexNormalize gg
+--R
+--R   (10)  0
+--R                                             Type: Expression Complex Integer
+--E
+@
+
+\section{\cite{1}:14.245~~~~~$\displaystyle\int{x\sqrt{a^2-x^2}}~dx$}
+$$\int{x\sqrt{a^2-x^2}}=
+\frac{(a^2-x^2)^{3/2}}{3}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 51
+aa:=integrate(x*sqrt(a^2-x^2),x)
+--R 
+--R
+--R                          +---------+
+--R               4     3 2  |   2    2     6     2 4     4 2
+--R        (- 3a x  + 6a x )\|- x  + a   - x  + 6a x  - 6a x
+--R   (1)  --------------------------------------------------
+--R                           +---------+
+--R                 2      2  |   2    2        2      3
+--R              (3x  - 12a )\|- x  + a   - 9a x  + 12a
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 52
+bb:=-(a^2-x^2)^(3/2)/3
+--R
+--R                  +---------+
+--R          2    2  |   2    2
+--R        (x  - a )\|- x  + a
+--R   (2)  ---------------------
+--R                  3
+--R                                                     Type: Expression Integer
+--E
+
+--S 53     14:245 Schaums and Axiom differ by a constant
+cc:=aa-bb
+--R
+--R           3
+--R          a
+--R   (3)  - --
+--R           3
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.246~~~~~$\displaystyle
+\int{x^2\sqrt{a^2-x^2}}~dx$}
+$$\int{x^2\sqrt{a^2-x^2}}=
+\frac{x(a^2-x^2)^{3/2}}{4}+\frac{a^2x\sqrt{a^2-x^2}}{8}-
+\frac{a^4}{8}\ln\left(x+\sqrt{a^2-x^2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 54
+aa:=integrate(x^2*sqrt(a^2-x^2),x)
+--R 
+--R
+--R   (1)
+--R                           +---------+
+--R               5 2      7  |   2    2      4 4      6 2      8
+--R         ((- 8a x  + 16a )\|- x  + a   - 2a x  + 16a x  - 16a )
+--R      *
+--R               +---------+
+--R               |   2    2
+--R              \|- x  + a   - a
+--R         atan(----------------)
+--R                      x
+--R     + 
+--R                                    +---------+
+--R        7      2 5      4 3     6   |   2    2        7      3 5      5 3     7
+--R     (2x  - 17a x  + 24a x  - 8a x)\|- x  + a   - 8a x  + 28a x  - 28a x  + 8a x
+--R  /
+--R                     +---------+
+--R           2      3  |   2    2      4      2 2      4
+--R     (32a x  - 64a )\|- x  + a   + 8x  - 64a x  + 64a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 55
+bb:=-(x*(a^2-x^2)^(3/2))/4+(a^2*x*sqrt(a^2-x^2))/8+a^4/8*asin(x/a)
+--R
+--R                    +---------+
+--R           3    2   |   2    2     4     x
+--R        (2x  - a x)\|- x  + a   + a asin(-)
+--R                                         a
+--R   (2)  -----------------------------------
+--R                         8
+--R                                                     Type: Expression Integer
+--E
+
+--S 56
+cc:=aa-bb
+--R
+--R                   +---------+
+--R                   |   2    2
+--R            4     \|- x  + a   - a     4     x
+--R        - 2a atan(----------------) - a asin(-)
+--R                          x                  a
+--R   (3)  ---------------------------------------
+--R                           8
+--R                                                     Type: Expression Integer
+--E
+
+--S 57
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (4)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 58
+dd:=atanrule cc
+--R
+--R                    +---------+
+--R                    |   2    2
+--R            4    - \|- x  + a   + %i x + a     4     x
+--R        %i a log(-------------------------) - a asin(-)
+--R                   +---------+                       a
+--R                   |   2    2
+--R                  \|- x  + a   + %i x - a
+--R   (5)  -----------------------------------------------
+--R                               8
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 59
+asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2)))
+--R
+--R                           +--------+
+--R                           |   2
+--R   (6)  asin(x) == %i log(\|- x  + 1  - %i x)
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 60
+ee:=asinrule dd
+--R
+--R                     +---------+
+--R                     |   2    2
+--R                     |- x  + a
+--R                   a |---------  - %i x                +---------+
+--R                     |     2                           |   2    2
+--R              4     \|    a                    4    - \|- x  + a   + %i x + a
+--R        - %i a log(--------------------) + %i a log(-------------------------)
+--R                             a                        +---------+
+--R                                                      |   2    2
+--R                                                     \|- x  + a   + %i x - a
+--R   (7)  ----------------------------------------------------------------------
+--R                                           8
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 61
+ff:=expandLog ee
+--R
+--R   (8)
+--R                    +---------+
+--R                    |   2    2                      +---------+
+--R             4      |- x  + a                 4     |   2    2
+--R       - %i a log(a |---------  - %i x) - %i a log(\|- x  + a   + %i x - a)
+--R                    |     2
+--R                   \|    a
+--R     + 
+--R                 +---------+
+--R           4     |   2    2                    4             4
+--R       %i a log(\|- x  + a   - %i x - a) + %i a log(a) + %i a log(- 1)
+--R  /
+--R     8
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 62
+gg:=rootSimp ff
+--R
+--R   (9)
+--R                     +-------+                           +-------+
+--R             4       | 2    2                    4       | 2    2
+--R       - %i a log(%i\|x  - a   + %i x - a) - %i a log(%i\|x  - a   - %i x)
+--R     + 
+--R                   +-------+
+--R           4       | 2    2                    4             4
+--R       %i a log(%i\|x  - a   - %i x - a) + %i a log(a) + %i a log(- 1)
+--R  /
+--R     8
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 63     14:246 Schaums and Axiom agree
+hh:=complexNormalize gg
+--R
+--R   (10)  0
+--R                                             Type: Expression Complex Integer
+--E
+@
+
+\section{\cite{1}:14.247~~~~~$\displaystyle
+\int{x^3\sqrt{a^2-x^2}}~dx$}
+$$\int{x^3\sqrt{a^2-x^2}}=
+\frac{(a^2-x^2)^{5/2}}{5}+\frac{a^2(a^2-x^2)^{3/2}}{3}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 64
+aa:=integrate(x^3*sqrt(a^2-x^2),x)
+--R 
+--R
+--R   (1)
+--R                                +---------+
+--R           8      3 6      5 4  |   2    2      10      2 8      4 6      6 4
+--R   (- 15a x  + 65a x  - 60a x )\|- x  + a   - 3x   + 40a x  - 95a x  + 60a x
+--R   --------------------------------------------------------------------------
+--R                                  +---------+
+--R             4       2 2       4  |   2    2         4       3 2       5
+--R         (15x  - 180a x  + 240a )\|- x  + a   - 75a x  + 300a x  - 240a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 65
+bb:=(a^2-x^2)^(5/2)/5-(a^2*(a^2-x^2)^(3/2))/3
+--R
+--R                           +---------+
+--R           4    2 2     4  |   2    2
+--R        (3x  - a x  - 2a )\|- x  + a
+--R   (2)  ------------------------------
+--R                      15
+--R                                                     Type: Expression Integer
+--E 
+
+--S 66     14:247 Schaums and Axiom differ by a constant
+cc:=aa-bb
+--R
+--R            5
+--R          2a
+--R   (3)  - ---
+--R           15
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.248~~~~~$\displaystyle
+\int{\frac{\sqrt{a^2-x^2}}{x}}~dx$}
+$$\int{\frac{\sqrt{a^2-x^2}}{x}}=
+\sqrt{a^2-x^2}-a\sec^{-1}\left|\frac{x}{a}\right|
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 67
+aa:=integrate(sqrt(a^2-x^2)/x,x)
+--R 
+--R
+--R                                 +---------+
+--R           +---------+           |   2    2
+--R           |   2    2     2     \|- x  + a   - a     2
+--R        (a\|- x  + a   - a )log(----------------) - x
+--R                                        x
+--R   (1)  ----------------------------------------------
+--R                        +---------+
+--R                        |   2    2
+--R                       \|- x  + a   - a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 68
+bb:=sqrt(a^2-x^2)-a*log((a+sqrt(a^2-x^2))/x)
+--R
+--R                 +---------+
+--R                 |   2    2          +---------+
+--R                \|- x  + a   + a     |   2    2
+--R   (2)  - a log(----------------) + \|- x  + a
+--R                        x
+--R                                                     Type: Expression Integer
+--E
+
+--S 69
+cc:=aa-bb
+--R
+--R               +---------+               +---------+
+--R               |   2    2                |   2    2
+--R              \|- x  + a   + a          \|- x  + a   - a
+--R   (3)  a log(----------------) + a log(----------------) + a
+--R                      x                         x
+--R                                                     Type: Expression Integer
+--E
+
+--S 70
+dd:=expandLog cc
+--R
+--R               +---------+               +---------+
+--R               |   2    2                |   2    2
+--R   (4)  a log(\|- x  + a   + a) + a log(\|- x  + a   - a) - 2a log(x) + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 71
+ee:=complexNormalize dd
+--R
+--R                    x
+--R   (5)  - 2a log(-------) + a
+--R                  +----+
+--R                  |   2
+--R                 \|- x
+--R                                                     Type: Expression Integer
+--E
+
+--S 72     14:248 Schaums and Axiom differ by a constant
+ff:=rootSimp ee
+--R
+--R                +---+
+--R   (6)  2a log(\|- 1 ) + a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.249~~~~~$\displaystyle
+\int{\frac{\sqrt{a^2-x^2}}{x^2}}~dx$}
+$$\int{\frac{\sqrt{a^2-x^2}}{x^2}}=
+-\frac{\sqrt{a^2-x^2}}{x}+\ln\left(x+\sqrt{a^2-x^2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 73
+aa:=integrate(sqrt(a^2-x^2)/x^2,x)
+--R 
+--R
+--R   (1)
+--R                                +---------+
+--R       +---------+              |   2    2           +---------+
+--R       |   2    2              \|- x  + a   - a      |   2    2     2    2
+--R   (2x\|- x  + a   - 2a x)atan(----------------) + a\|- x  + a   + x  - a
+--R                                       x
+--R   -----------------------------------------------------------------------
+--R                               +---------+
+--R                               |   2    2
+--R                             x\|- x  + a   - a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 74
+bb:=-sqrt(a^2-x^2)/x-asin(x/a)
+--R
+--R           +---------+
+--R           |   2    2           x
+--R        - \|- x  + a   - x asin(-)
+--R                                a
+--R   (2)  --------------------------
+--R                     x
+--R                                                     Type: Expression Integer
+--E
+
+--S 75
+cc:=aa-bb
+--R
+--R               +---------+
+--R               |   2    2
+--R              \|- x  + a   - a         x
+--R   (3)  2atan(----------------) + asin(-)
+--R                      x                a
+--R                                                     Type: Expression Integer
+--E
+
+--S 76
+asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2)))
+--R
+--R                           +--------+
+--R                           |   2
+--R   (4)  asin(x) == %i log(\|- x  + 1  - %i x)
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 77
+dd:=asinrule cc
+--R
+--R                 +---------+
+--R                 |   2    2
+--R                 |- x  + a
+--R               a |---------  - %i x           +---------+
+--R                 |     2                      |   2    2
+--R                \|    a                      \|- x  + a   - a
+--R   (5)  %i log(--------------------) + 2atan(----------------)
+--R                         a                           x
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 78
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (6)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 79
+ee:=atanrule dd
+--R
+--R                 +---------+
+--R                 |   2    2
+--R                 |- x  + a
+--R               a |---------  - %i x              +---------+
+--R                 |     2                         |   2    2
+--R                \|    a                       - \|- x  + a   + %i x + a
+--R   (7)  %i log(--------------------) - %i log(-------------------------)
+--R                         a                      +---------+
+--R                                                |   2    2
+--R                                               \|- x  + a   + %i x - a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 80
+ff:=expandLog ee
+--R
+--R   (8)
+--R              +---------+
+--R              |   2    2                    +---------+
+--R              |- x  + a                     |   2    2
+--R     %i log(a |---------  - %i x) + %i log(\|- x  + a   + %i x - a)
+--R              |     2
+--R             \|    a
+--R   + 
+--R               +---------+
+--R               |   2    2
+--R     - %i log(\|- x  + a   - %i x - a) - %i log(a) - %i log(- 1)
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 81
+gg:=rootSimp ff
+--R
+--R   (9)
+--R               +-------+                         +-------+
+--R               | 2    2                          | 2    2
+--R     %i log(%i\|x  - a   + %i x - a) + %i log(%i\|x  - a   - %i x)
+--R   + 
+--R                 +-------+
+--R                 | 2    2
+--R     - %i log(%i\|x  - a   - %i x - a) - %i log(a) - %i log(- 1)
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 82     14:249 Schaums and Axiom agree
+hh:=complexNormalize gg
+--R
+--R   (10)  0
+--R                                             Type: Expression Complex Integer
+--E
+@
+
+\section{\cite{1}:14.250~~~~~$\displaystyle
+\int{\frac{\sqrt{a^2-x^2}}{x^3}}~dx$}
+$$\int{\frac{\sqrt{a^2-x^2}}{x^3}}=
+-\frac{\sqrt{a^2-x^2}}{2x^2}+\frac{1}{2a}
+\sec^{-1}\left|\frac{x}{a}\right|
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 83
+aa:=integrate(sqrt(a^2-x^2)/x^3,x)
+--R 
+--R
+--R   (1)
+--R                                              +---------+
+--R                +---------+                   |   2    2
+--R              2 |   2    2     4     2 2     \|- x  + a   - a
+--R       (- 2a x \|- x  + a   - x  + 2a x )log(----------------)
+--R                                                     x
+--R     + 
+--R                      +---------+
+--R             2     3  |   2    2      2 2     4
+--R       (- a x  + 2a )\|- x  + a   + 2a x  - 2a
+--R  /
+--R           +---------+
+--R       2 2 |   2    2        4     3 2
+--R     4a x \|- x  + a   + 2a x  - 4a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 84
+bb:=-sqrt(a^2-x^2)/(2*x^2)+1/(2*a)*log((a+sqrt(a^2-x^2))/x)
+--R
+--R               +---------+
+--R               |   2    2           +---------+
+--R         2    \|- x  + a   + a      |   2    2
+--R        x log(----------------) - a\|- x  + a
+--R                      x
+--R   (2)  ---------------------------------------
+--R                             2
+--R                         2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 85
+cc:=aa-bb
+--R
+--R               +---------+             +---------+
+--R               |   2    2              |   2    2
+--R              \|- x  + a   + a        \|- x  + a   - a
+--R        - log(----------------) - log(----------------)
+--R                      x                       x
+--R   (3)  -----------------------------------------------
+--R                               2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 86
+dd:=expandLog cc
+--R
+--R               +---------+             +---------+
+--R               |   2    2              |   2    2
+--R        - log(\|- x  + a   + a) - log(\|- x  + a   - a) + 2log(x)
+--R   (4)  ---------------------------------------------------------
+--R                                    2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 87
+ee:=complexNormalize dd
+--R
+--R               x
+--R        log(-------)
+--R             +----+
+--R             |   2
+--R            \|- x
+--R   (5)  ------------
+--R              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 88     14:250 Schaums and Axiom differ by a constant
+ff:=rootSimp ee
+--R
+--R               +---+
+--R          log(\|- 1 )
+--R   (6)  - -----------
+--R               a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.251~~~~~$\displaystyle\int{\frac{dx}{(a^2-x^2)^{3/2}}}$}
+$$\int{\frac{1}{(a^2-x^2)^{3/2}}}=
+-\frac{x}{a^2\sqrt{a^2-x^2}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 89
+aa:=integrate(1/(a^2-x^2)^(3/2),x)
+--R 
+--R
+--R               +---------+
+--R               |   2    2
+--R           - x\|- x  + a   + a x
+--R   (1)  --------------------------
+--R           +---------+
+--R         3 |   2    2     2 2    4
+--R        a \|- x  + a   + a x  - a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 90
+bb:=x/(a^2*sqrt(a^2-x^2))
+--R
+--R               x
+--R   (2)  --------------
+--R           +---------+
+--R         2 |   2    2
+--R        a \|- x  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 91     14:251 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.252~~~~~$\displaystyle
+\int{\frac{x~dx}{(a^2-x^2)^{3/2}}}$}
+$$\int{\frac{x}{(a^2-x^2)^{3/2}}}=
+\frac{-1}{\sqrt{a^2-x^2}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 92
+aa:=integrate(x/(a^2-x^2)^(3/2),x)
+--R 
+--R
+--R                     2
+--R                    x
+--R   (1)  --------------------------
+--R           +---------+
+--R         2 |   2    2       2    3
+--R        a \|- x  + a   + a x  - a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 93
+bb:=1/sqrt(a^2-x^2)
+--R
+--R              1
+--R   (2)  ------------
+--R         +---------+
+--R         |   2    2
+--R        \|- x  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 94     14:252 Schaums and Axiom differ by a constant
+cc:=aa-bb
+--R
+--R        1
+--R   (3)  -
+--R        a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.253~~~~~$\displaystyle
+\int{\frac{x^2dx}{(a^2-x^2)^{3/2}}}$}
+$$\int{\frac{x^2}{(a^2-x^2)^{3/2}}}=
+\frac{-x}{\sqrt{a^2-x^2}}+\ln\left(x+\sqrt{a^2-x^2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 95
+aa:=integrate(x^2/(a^2-x^2)^(3/2),x)
+--R 
+--R
+--R   (1)
+--R                                     +---------+
+--R       +---------+                   |   2    2           +---------+
+--R       |   2    2      2     2      \|- x  + a   - a      |   2    2
+--R   (2a\|- x  + a   + 2x  - 2a )atan(----------------) - x\|- x  + a   + a x
+--R                                            x
+--R   ------------------------------------------------------------------------
+--R                              +---------+
+--R                              |   2    2     2    2
+--R                            a\|- x  + a   + x  - a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 96
+bb:=x/sqrt(a^2-x^2)-asin(x/a)
+--R
+--R                  +---------+
+--R               x  |   2    2
+--R        - asin(-)\|- x  + a   + x
+--R               a
+--R   (2)  -------------------------
+--R                +---------+
+--R                |   2    2
+--R               \|- x  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 97
+cc:=aa-bb
+--R
+--R               +---------+
+--R               |   2    2
+--R              \|- x  + a   - a         x
+--R   (3)  2atan(----------------) + asin(-)
+--R                      x                a
+--R                                                     Type: Expression Integer
+--E
+
+--S 98
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (4)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 99
+dd:=atanrule cc
+--R
+--R                    +---------+
+--R                    |   2    2
+--R                 - \|- x  + a   + %i x + a         x
+--R   (5)  - %i log(-------------------------) + asin(-)
+--R                   +---------+                     a
+--R                   |   2    2
+--R                  \|- x  + a   + %i x - a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 100
+asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2)))
+--R
+--R                           +--------+
+--R                           |   2
+--R   (6)  asin(x) == %i log(\|- x  + 1  - %i x)
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 101
+ee:=asinrule dd
+--R
+--R                 +---------+
+--R                 |   2    2
+--R                 |- x  + a
+--R               a |---------  - %i x              +---------+
+--R                 |     2                         |   2    2
+--R                \|    a                       - \|- x  + a   + %i x + a
+--R   (7)  %i log(--------------------) - %i log(-------------------------)
+--R                         a                      +---------+
+--R                                                |   2    2
+--R                                               \|- x  + a   + %i x - a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 102
+ff:=expandLog ee
+--R
+--R   (8)
+--R              +---------+
+--R              |   2    2                    +---------+
+--R              |- x  + a                     |   2    2
+--R     %i log(a |---------  - %i x) + %i log(\|- x  + a   + %i x - a)
+--R              |     2
+--R             \|    a
+--R   + 
+--R               +---------+
+--R               |   2    2
+--R     - %i log(\|- x  + a   - %i x - a) - %i log(a) - %i log(- 1)
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 103
+gg:=rootSimp ff
+--R
+--R   (9)
+--R               +-------+                         +-------+
+--R               | 2    2                          | 2    2
+--R     %i log(%i\|x  - a   + %i x - a) + %i log(%i\|x  - a   - %i x)
+--R   + 
+--R                 +-------+
+--R                 | 2    2
+--R     - %i log(%i\|x  - a   - %i x - a) - %i log(a) - %i log(- 1)
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 104    14:253 Schaums and Axiom agree
+hh:=complexNormalize gg
+--R
+--R   (10)  0
+--R                                             Type: Expression Complex Integer
+--E
+@
+
+\section{\cite{1}:14.254~~~~~$\displaystyle
+\int{\frac{x^3dx}{(a^2-x^2)^{3/2}}}$}
+$$\int{\frac{x^3}{(a^2-x^2)^{3/2}}}=
+\sqrt{a^2-x^2}-\frac{a^2}{\sqrt{a^2-x^2}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 105
+aa:=integrate(x^3/(a^2-x^2)^(3/2),x)
+--R 
+--R
+--R                            4
+--R                           x
+--R   (1)  - ------------------------------------
+--R                     +---------+
+--R            2     2  |   2    2        2     3
+--R          (x  - 2a )\|- x  + a   - 2a x  + 2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 106
+bb:=sqrt(a^2-x^2)+a^2/sqrt(a^2-x^2)
+--R
+--R            2     2
+--R         - x  + 2a
+--R   (2)  ------------
+--R         +---------+
+--R         |   2    2
+--R        \|- x  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 107    14:254 Schaums and Axiom differ by a constant
+cc:=aa-bb
+--R
+--R   (3)  2a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.255~~~~~$\displaystyle
+\int{\frac{dx}{x(a^2-x^2)^{3/2}}}$}
+$$\int{\frac{1}{x(a^2-x^2)^{3/2}}}=
+\frac{-1}{a^2\sqrt{a^2-x^2}}-
+\frac{1}{a^3}\sec^{-1}\left|\frac{x}{a}\right|
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 108
+aa:=integrate(1/(x*(a^2-x^2)^(3/2)),x)
+--R 
+--R
+--R                                      +---------+
+--R           +---------+                |   2    2
+--R           |   2    2     2    2     \|- x  + a   - a     2
+--R        (a\|- x  + a   + x  - a )log(----------------) + x
+--R                                             x
+--R   (1)  ---------------------------------------------------
+--R                        +---------+
+--R                      4 |   2    2     3 2    5
+--R                     a \|- x  + a   + a x  - a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 109
+bb:=1/(a^2*sqrt(a^2-x^2))-1/a^3*log((a+sqrt(a^2-x^2))/x)
+--R
+--R                           +---------+
+--R           +---------+     |   2    2
+--R           |   2    2     \|- x  + a   + a
+--R        - \|- x  + a  log(----------------) + a
+--R                                  x
+--R   (2)  ---------------------------------------
+--R                        +---------+
+--R                      3 |   2    2
+--R                     a \|- x  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 110
+cc:=aa-bb
+--R
+--R             +---------+             +---------+
+--R             |   2    2              |   2    2
+--R            \|- x  + a   + a        \|- x  + a   - a
+--R        log(----------------) + log(----------------) + 1
+--R                    x                       x
+--R   (3)  -------------------------------------------------
+--R                                 3
+--R                                a
+--R                                                     Type: Expression Integer
+--E
+
+--S 111
+dd:=expandLog cc
+--R
+--R             +---------+             +---------+
+--R             |   2    2              |   2    2
+--R        log(\|- x  + a   + a) + log(\|- x  + a   - a) - 2log(x) + 1
+--R   (4)  -----------------------------------------------------------
+--R                                      3
+--R                                     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 112
+ee:=complexNormalize dd
+--R
+--R                  x
+--R        - 2log(-------) + 1
+--R                +----+
+--R                |   2
+--R               \|- x
+--R   (5)  -------------------
+--R                  3
+--R                 a
+--R                                                     Type: Expression Integer
+--E
+
+--S 113    14:255 Schaums and Axiom differ by a constant
+ff:=rootSimp ee
+--R
+--R              +---+
+--R        2log(\|- 1 ) + 1
+--R   (6)  ----------------
+--R                3
+--R               a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.256~~~~~$\displaystyle
+\int{\frac{dx}{x^2(a^2-x^2)^{3/2}}}$}
+$$\int{\frac{1}{x^2(a^2-x^2)^{3/2}}}=
+-\frac{\sqrt{a^2-x^2}}{a^4x}-\frac{x}{a^4\sqrt{a^2-x^2}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 114
+aa:=integrate(1/(x^2*(a^2-x^2)^(3/2)),x)
+--R 
+--R
+--R                      +---------+
+--R             2     3  |   2    2      4     2 2     4
+--R        (4a x  - 2a )\|- x  + a   + 2x  - 5a x  + 2a
+--R   (1)  ---------------------------------------------
+--R                         +---------+
+--R             4 3     6   |   2    2      5 3     7
+--R           (a x  - 2a x)\|- x  + a   - 2a x  + 2a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 115
+bb:=-sqrt(a^2-x^2)/(a^4*x)+x/(a^4*sqrt(a^2-x^2))
+--R
+--R              2    2
+--R            2x  - a
+--R   (2)  ---------------
+--R            +---------+
+--R         4  |   2    2
+--R        a x\|- x  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 116    14:256 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.257~~~~~$\displaystyle
+\int{\frac{dx}{x^3(a^2-x^2)^{3/2}}}$}
+$$\int{\frac{1}{x^3(a^2-x^2)^{3/2}}}=
+\frac{1}{2a^2x^2\sqrt{a^2-x^2}}-
+\frac{3}{2a^4\sqrt{a^2-x^2}}-
+\frac{3}{2a^5}\sec^{-1}\left|\frac{x}{a}\right|
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 117
+aa:=integrate(1/(x^3*(a^2-x^2)^(3/2)),x)
+--R 
+--R
+--R   (1)
+--R                           +---------+
+--R               4      3 2  |   2    2      6      2 4      4 2
+--R         ((9a x  - 12a x )\|- x  + a   + 3x  - 15a x  + 12a x )
+--R      *
+--R              +---------+
+--R              |   2    2
+--R             \|- x  + a   - a
+--R         log(----------------)
+--R                     x
+--R     + 
+--R                             +---------+
+--R            4     3 2     5  |   2    2      6    2 4     4 2     6
+--R       (3a x  + 5a x  - 4a )\|- x  + a   + 2x  - a x  - 7a x  + 4a
+--R  /
+--R                     +---------+
+--R        6 4     8 2  |   2    2      5 6      7 4     9 2
+--R     (6a x  - 8a x )\|- x  + a   + 2a x  - 10a x  + 8a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 118
+bb:=-1/(2*a^2*x^2*sqrt(a^2-x^2))+3/(2*a^4*sqrt(a^2-x^2))-3/(2*a^5)*log((a+sqrt(a^2-x^2))/x)
+--R
+--R                              +---------+
+--R              +---------+     |   2    2
+--R            2 |   2    2     \|- x  + a   + a        2    3
+--R        - 3x \|- x  + a  log(----------------) + 3a x  - a
+--R                                     x
+--R   (2)  ---------------------------------------------------
+--R                               +---------+
+--R                           5 2 |   2    2
+--R                         2a x \|- x  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 119
+cc:=aa-bb
+--R
+--R              +---------+              +---------+
+--R              |   2    2               |   2    2
+--R             \|- x  + a   + a         \|- x  + a   - a
+--R        3log(----------------) + 3log(----------------) + 2
+--R                     x                        x
+--R   (3)  ---------------------------------------------------
+--R                                  5
+--R                                2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 120
+dd:=expandLog cc
+--R
+--R              +---------+              +---------+
+--R              |   2    2               |   2    2
+--R        3log(\|- x  + a   + a) + 3log(\|- x  + a   - a) - 6log(x) + 2
+--R   (4)  -------------------------------------------------------------
+--R                                       5
+--R                                     2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 121
+ee:=complexNormalize dd
+--R
+--R                  x
+--R        - 3log(-------) + 1
+--R                +----+
+--R                |   2
+--R               \|- x
+--R   (5)  -------------------
+--R                  5
+--R                 a
+--R                                                     Type: Expression Integer
+--E
+
+--S 122    14:257 Schaums and Axiom differ by a constant
+ff:=rootSimp ee
+--R
+--R              +---+
+--R        3log(\|- 1 ) + 1
+--R   (6)  ----------------
+--R                5
+--R               a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.258~~~~~$\displaystyle\int{(a^2-x^2)^{3/2}}~dx$}
+$$\int{(a^2-x^2)^{3/2}}=
+\frac{x(a^2-x^2)^{3/2}}{4}-\frac{3a^2x\sqrt{a^2-x^2}}{8}+
+\frac{3}{8}a^4\ln\left(x+\sqrt{a^2-x^2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 123
+aa:=integrate((a^2-x^2)^(3/2),x)
+--R 
+--R
+--R   (1)
+--R                            +---------+
+--R                5 2      7  |   2    2      4 4      6 2      8
+--R         ((- 24a x  + 48a )\|- x  + a   - 6a x  + 48a x  - 48a )
+--R      *
+--R               +---------+
+--R               |   2    2
+--R              \|- x  + a   - a
+--R         atan(----------------)
+--R                      x
+--R     + 
+--R                                         +---------+
+--R            7      2 5      4 3      6   |   2    2        7      3 5      5 3
+--R       (- 2x  + 21a x  - 56a x  + 40a x)\|- x  + a   + 8a x  - 44a x  + 76a x
+--R     + 
+--R            7
+--R       - 40a x
+--R  /
+--R                     +---------+
+--R           2      3  |   2    2      4      2 2      4
+--R     (32a x  - 64a )\|- x  + a   + 8x  - 64a x  + 64a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 124
+bb:=(x*(a^2-x^2)^(3/2))/4+(3*a^2*x*sqrt(a^2-x^2))/8+3/8*a^4*asin(x/a)
+--R
+--R                       +---------+
+--R             3     2   |   2    2      4     x
+--R        (- 2x  + 5a x)\|- x  + a   + 3a asin(-)
+--R                                             a
+--R   (2)  ---------------------------------------
+--R                           8
+--R                                                     Type: Expression Integer
+--E
+
+--S 125
+cc:=aa-bb
+--R
+--R                   +---------+
+--R                   |   2    2
+--R            4     \|- x  + a   - a      4     x
+--R        - 6a atan(----------------) - 3a asin(-)
+--R                          x                   a
+--R   (3)  ----------------------------------------
+--R                            8
+--R                                                     Type: Expression Integer
+--E
+
+--S 126
+asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2)))
+--R
+--R                           +--------+
+--R                           |   2
+--R   (4)  asin(x) == %i log(\|- x  + 1  - %i x)
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E 
+
+--S 127
+ee:=asinrule cc
+--R
+--R                      +---------+
+--R                      |   2    2
+--R                      |- x  + a
+--R                    a |---------  - %i x             +---------+
+--R                      |     2                        |   2    2
+--R               4     \|    a                  4     \|- x  + a   - a
+--R        - 3%i a log(--------------------) - 6a atan(----------------)
+--R                              a                             x
+--R   (5)  -------------------------------------------------------------
+--R                                      8
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 128
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (6)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 129
+ff:=atanrule ee
+--R
+--R   (7)
+--R                 +---------+
+--R                 |   2    2
+--R                 |- x  + a
+--R               a |---------  - %i x                 +---------+
+--R                 |     2                            |   2    2
+--R          4     \|    a                     4    - \|- x  + a   + %i x + a
+--R   - 3%i a log(--------------------) + 3%i a log(-------------------------)
+--R                         a                         +---------+
+--R                                                   |   2    2
+--R                                                  \|- x  + a   + %i x - a
+--R   ------------------------------------------------------------------------
+--R                                       8
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 130
+gg:=expandLog ff
+--R
+--R   (8)
+--R                     +---------+
+--R                     |   2    2                       +---------+
+--R              4      |- x  + a                  4     |   2    2
+--R       - 3%i a log(a |---------  - %i x) - 3%i a log(\|- x  + a   + %i x - a)
+--R                     |     2
+--R                    \|    a
+--R     + 
+--R                  +---------+
+--R            4     |   2    2                     4              4
+--R       3%i a log(\|- x  + a   - %i x - a) + 3%i a log(a) + 3%i a log(- 1)
+--R  /
+--R     8
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 131
+hh:=rootSimp gg
+--R
+--R   (9)
+--R                      +-------+                            +-------+
+--R              4       | 2    2                     4       | 2    2
+--R       - 3%i a log(%i\|x  - a   + %i x - a) - 3%i a log(%i\|x  - a   - %i x)
+--R     + 
+--R                    +-------+
+--R            4       | 2    2                     4              4
+--R       3%i a log(%i\|x  - a   - %i x - a) + 3%i a log(a) + 3%i a log(- 1)
+--R  /
+--R     8
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 132    14:258 Schaums and Axiom agree
+ii:=complexNormalize hh
+--R
+--R   (10)  0
+--R                                             Type: Expression Complex Integer
+--E
+@
+
+\section{\cite{1}:14.259~~~~~$\displaystyle\int{x(a^2-x^2)^{3/2}}~dx$}
+$$\int{x(a^2-x^2)^{3/2}}=\frac{(a^2-x^2)^{5/2}}{5}$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 133
+aa:=integrate(x*(a^2-x^2)^(3/2),x)
+--R 
+--R
+--R   (1)
+--R                                          +---------+
+--R            8      3 6      5 4      7 2  |   2    2     10      2 8      4 6
+--R       (5a x  - 30a x  + 60a x  - 40a x )\|- x  + a   + x   - 15a x  + 55a x
+--R     + 
+--R            6 4      8 2
+--R       - 80a x  + 40a x
+--R  /
+--R                           +---------+
+--R        4      2 2      4  |   2    2         4       3 2      5
+--R     (5x  - 60a x  + 80a )\|- x  + a   - 25a x  + 100a x  - 80a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 134
+bb:=-(a^2-x^2)^(5/2)/5
+--R
+--R                            +---------+
+--R            4     2 2    4  |   2    2
+--R        (- x  + 2a x  - a )\|- x  + a
+--R   (2)  -------------------------------
+--R                       5
+--R                                                     Type: Expression Integer
+--E
+
+--S 135    14:259 Schaums and Axiom differ by a constant
+cc:=aa-bb
+--R
+--R           5
+--R          a
+--R   (3)  - --
+--R           5
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.260~~~~~$\displaystyle\int{x^2(a^2-x^2)^{3/2}}~dx$}
+$$\int{x^2(a^2-x^2)^{3/2}}=
+\frac{x(a^2-x^2)^{5/2}}{6}+\frac{a^2x(a^2-x^2)^{3/2}}{24}-
+\frac{a^4x\sqrt{a^2-x^2}}{16}+
+\frac{a^6}{16}\ln\left(x+\sqrt{a^2-x^2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 136
+aa:=integrate(x^2*(a^2-x^2)^(3/2),x)
+--R 
+--R
+--R   (1)
+--R                                         +---------+
+--R                 7 4       9 2       11  |   2    2      6 6       8 4
+--R           (- 36a x  + 192a x  - 192a  )\|- x  + a   - 6a x  + 108a x
+--R         + 
+--R                 10 2       12
+--R           - 288a  x  + 192a
+--R      *
+--R               +---------+
+--R               |   2    2
+--R              \|- x  + a   - a
+--R         atan(----------------)
+--R                      x
+--R     + 
+--R                                                                 +---------+
+--R            11       2 9       4 7       6 5       8 3      10   |   2    2
+--R       (- 8x   + 158a x  - 639a x  + 982a x  - 592a x  + 96a  x)\|- x  + a
+--R     + 
+--R            11       3 9        5 7        7 5       9 3      11
+--R       48a x   - 388a x  + 1062a x  - 1266a x  + 640a x  - 96a  x
+--R  /
+--R                                     +---------+
+--R              4        3 2        5  |   2    2       6       2 4        4 2
+--R       (288a x  - 1536a x  + 1536a )\|- x  + a   + 48x  - 864a x  + 2304a x
+--R     + 
+--R              6
+--R       - 1536a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 137
+bb:=-(x*(a^2-x^2)^(5/2))/6+(a^2*x*(a^2-x^2)^(3/2))/24+(a^4*x*sqrt(a^2-x^2))/16+a^6/16*asin(x/a)
+--R
+--R                                +---------+
+--R             5      2 3     4   |   2    2      6     x
+--R        (- 8x  + 14a x  - 3a x)\|- x  + a   + 3a asin(-)
+--R                                                      a
+--R   (2)  ------------------------------------------------
+--R                               48
+--R                                                     Type: Expression Integer
+--E
+
+--S 138
+cc:=aa-bb
+--R
+--R                   +---------+
+--R                   |   2    2
+--R            6     \|- x  + a   - a     6     x
+--R        - 2a atan(----------------) - a asin(-)
+--R                          x                  a
+--R   (3)  ---------------------------------------
+--R                           16
+--R                                                     Type: Expression Integer
+--E 
+
+--S 139
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (4)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 140
+dd:=atanrule cc
+--R
+--R                    +---------+
+--R                    |   2    2
+--R            6    - \|- x  + a   + %i x + a     6     x
+--R        %i a log(-------------------------) - a asin(-)
+--R                   +---------+                       a
+--R                   |   2    2
+--R                  \|- x  + a   + %i x - a
+--R   (5)  -----------------------------------------------
+--R                               16
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 141
+asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2)))
+--R
+--R                           +--------+
+--R                           |   2
+--R   (6)  asin(x) == %i log(\|- x  + 1  - %i x)
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 142
+ee:=asinrule dd
+--R
+--R                     +---------+
+--R                     |   2    2
+--R                     |- x  + a
+--R                   a |---------  - %i x                +---------+
+--R                     |     2                           |   2    2
+--R              6     \|    a                    6    - \|- x  + a   + %i x + a
+--R        - %i a log(--------------------) + %i a log(-------------------------)
+--R                             a                        +---------+
+--R                                                      |   2    2
+--R                                                     \|- x  + a   + %i x - a
+--R   (7)  ----------------------------------------------------------------------
+--R                                          16
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 143
+ff:=expandLog ee
+--R
+--R   (8)
+--R                    +---------+
+--R                    |   2    2                      +---------+
+--R             6      |- x  + a                 6     |   2    2
+--R       - %i a log(a |---------  - %i x) - %i a log(\|- x  + a   + %i x - a)
+--R                    |     2
+--R                   \|    a
+--R     + 
+--R                 +---------+
+--R           6     |   2    2                    6             6
+--R       %i a log(\|- x  + a   - %i x - a) + %i a log(a) + %i a log(- 1)
+--R  /
+--R     16
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 144
+gg:=rootSimp ff
+--R
+--R   (9)
+--R                     +-------+                           +-------+
+--R             6       | 2    2                    6       | 2    2
+--R       - %i a log(%i\|x  - a   + %i x - a) - %i a log(%i\|x  - a   - %i x)
+--R     + 
+--R                   +-------+
+--R           6       | 2    2                    6             6
+--R       %i a log(%i\|x  - a   - %i x - a) + %i a log(a) + %i a log(- 1)
+--R  /
+--R     16
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 145    14:260 Schaums and Axiom agree
+hh:=complexNormalize gg
+--R
+--R   (10)  0
+--R                                             Type: Expression Complex Integer
+--E
+@
+
+\section{\cite{1}:14.261~~~~~$\displaystyle\int{x^3(a^2-x^2)^{3/2}}~dx$}
+$$\int{x^3(a^2-x^2)^{3/2}}=
+\frac{(a^2-x^2)^{7/2}}{7}+\frac{a^2(a^2-x^2)^{5/2}}{5}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 146
+aa:=integrate(x^3*(a^2-x^2)^(3/2),x)
+--R 
+--R
+--R   (1)
+--R                                                            +---------+
+--R             12       3 10        5 8        7 6       9 4  |   2    2      14
+--R       (35a x   - 336a x   + 1015a x  - 1260a x  + 560a x )\|- x  + a   + 5x
+--R     + 
+--R             2 12       4 10        6 8        8 6       10 4
+--R       - 133a x   + 721a x   - 1575a x  + 1540a x  - 560a  x
+--R  /
+--R                                            +---------+
+--R           6       2 4        4 2        6  |   2    2          6        3 4
+--R       (35x  - 840a x  + 2800a x  - 2240a )\|- x  + a   - 245a x  + 1960a x
+--R     + 
+--R              5 2        7
+--R       - 3920a x  + 2240a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 147
+bb:=(a^2-x^2)^(7/2)/7-(a^2*(a^2-x^2)^(5/2))/5
+--R
+--R                                     +---------+
+--R             6     2 4    4 2     6  |   2    2
+--R        (- 5x  + 8a x  - a x  - 2a )\|- x  + a
+--R   (2)  ----------------------------------------
+--R                           35
+--R                                                     Type: Expression Integer
+--E
+
+--S 148    14:261 Schaums and Axiom differ by a constant
+cc:=aa-bb
+--R
+--R            7
+--R          2a
+--R   (3)  - ---
+--R           35
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.262~~~~~$\displaystyle
+\int{\frac{(a^2-x^2)^{3/2}}{x}}~dx$}
+$$\int{\frac{(a^2-x^2)^{3/2}}{x}}=
+\frac{(a^2-x^2)^{3/2}}{3}-a^2\sqrt{a^2-x^2}+
+a^3\sec^{-1}\left|\frac{x}{a}\right|
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 149
+aa:=integrate((a^2-x^2)^(3/2)/x,x)
+--R 
+--R
+--R   (1)
+--R                                                       +---------+
+--R                       +---------+                     |   2    2
+--R           3 2      5  |   2    2      4 2      6     \|- x  + a   - a
+--R       ((3a x  - 12a )\|- x  + a   - 9a x  + 12a )log(----------------)
+--R                                                              x
+--R     + 
+--R                        +---------+
+--R            4      3 2  |   2    2     6     2 4      4 2
+--R       (3a x  - 12a x )\|- x  + a   + x  - 9a x  + 12a x
+--R  /
+--R                  +---------+
+--R        2      2  |   2    2        2      3
+--R     (3x  - 12a )\|- x  + a   - 9a x  + 12a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 150
+bb:=(a^2-x^2)^(3/2)/3+a^2*sqrt(a^2-x^2)-a^3*log((a+sqrt(a^2-x^2))/x)
+--R
+--R                  +---------+
+--R                  |   2    2                      +---------+
+--R            3    \|- x  + a   + a        2     2  |   2    2
+--R        - 3a log(----------------) + (- x  + 4a )\|- x  + a
+--R                         x
+--R   (2)  -----------------------------------------------------
+--R                                  3
+--R                                                     Type: Expression Integer
+--E
+
+--S 151
+cc:=aa-bb
+--R
+--R                +---------+                +---------+
+--R                |   2    2                 |   2    2
+--R          3    \|- x  + a   + a      3    \|- x  + a   - a      3
+--R        3a log(----------------) + 3a log(----------------) + 4a
+--R                       x                          x
+--R   (3)  ---------------------------------------------------------
+--R                                    3
+--R                                                     Type: Expression Integer
+--E
+
+--S 152
+dd:=expandLog cc
+--R
+--R                +---------+                +---------+
+--R          3     |   2    2           3     |   2    2           3           3
+--R        3a log(\|- x  + a   + a) + 3a log(\|- x  + a   - a) - 6a log(x) + 4a
+--R   (4)  ---------------------------------------------------------------------
+--R                                          3
+--R                                                     Type: Expression Integer
+--E
+
+--S 153
+ee:=complexNormalize dd
+--R
+--R            3       x         3
+--R        - 6a log(-------) + 4a
+--R                  +----+
+--R                  |   2
+--R                 \|- x
+--R   (5)  -----------------------
+--R                   3
+--R                                                     Type: Expression Integer
+--E
+
+--S 154    14:262 Schaums and Axiom differ by a constant
+ff:=rootSimp ee
+--R
+--R          3     +---+      3
+--R        6a log(\|- 1 ) + 4a
+--R   (6)  --------------------
+--R                  3
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.263~~~~~$\displaystyle
+\int{\frac{(a^2-x^2)^{3/2}}{x^2}}~dx$}
+$$\int{\frac{(a^2-x^2)^{3/2}}{x^2}}=
+-\frac{(a^2-x^2)^{3/2}}{x}+\frac{3x\sqrt{a^2-x^2}}{2}-
+\frac{3}{2}a^2\ln\left(x+\sqrt{a^2-x^2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 155
+aa:=integrate((a^2-x^2)^{3/2}/x^2,x)
+--R 
+--R
+--R   (1)
+--R                                                           +---------+
+--R                        +---------+                        |   2    2
+--R           2 3      4   |   2    2       3 3      5       \|- x  + a   - a
+--R       ((6a x  - 24a x)\|- x  + a   - 18a x  + 24a x)atan(----------------)
+--R                                                                  x
+--R     + 
+--R                             +---------+
+--R            4     3 2     5  |   2    2     6     2 4     4 2     6
+--R       (3a x  + 2a x  - 8a )\|- x  + a   + x  - 3a x  - 6a x  + 8a
+--R  /
+--R                  +---------+
+--R        3     2   |   2    2        3     3
+--R     (2x  - 8a x)\|- x  + a   - 6a x  + 8a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 156
+bb:=-(a^2-x^2)^(3/2)/x-(3*x*sqrt(a^2-x^2))/2-3/2*a^2*asin(x/a)
+--R
+--R                     +---------+
+--R            2     2  |   2    2      2       x
+--R        (- x  - 2a )\|- x  + a   - 3a x asin(-)
+--R                                             a
+--R   (2)  ---------------------------------------
+--R                           2x
+--R                                                     Type: Expression Integer
+--E
+
+--S 157
+cc:=aa-bb
+--R
+--R                 +---------+
+--R                 |   2    2
+--R          2     \|- x  + a   - a      2     x
+--R        6a atan(----------------) + 3a asin(-)
+--R                        x                   a
+--R   (3)  --------------------------------------
+--R                           2
+--R                                                     Type: Expression Integer
+--E
+
+--S 158
+asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2)))
+--R
+--R                           +--------+
+--R                           |   2
+--R   (4)  asin(x) == %i log(\|- x  + 1  - %i x)
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 159
+dd:=asinrule cc
+--R
+--R                    +---------+
+--R                    |   2    2
+--R                    |- x  + a
+--R                  a |---------  - %i x             +---------+
+--R                    |     2                        |   2    2
+--R             2     \|    a                  2     \|- x  + a   - a
+--R        3%i a log(--------------------) + 6a atan(----------------)
+--R                            a                             x
+--R   (5)  -----------------------------------------------------------
+--R                                     2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 160
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (6)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 161
+ee:=atanrule dd
+--R
+--R                    +---------+
+--R                    |   2    2
+--R                    |- x  + a
+--R                  a |---------  - %i x                 +---------+
+--R                    |     2                            |   2    2
+--R             2     \|    a                     2    - \|- x  + a   + %i x + a
+--R        3%i a log(--------------------) - 3%i a log(-------------------------)
+--R                            a                         +---------+
+--R                                                      |   2    2
+--R                                                     \|- x  + a   + %i x - a
+--R   (7)  ----------------------------------------------------------------------
+--R                                           2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 162
+ff:=expandLog ee
+--R
+--R   (8)
+--R                   +---------+
+--R                   |   2    2                       +---------+
+--R            2      |- x  + a                  2     |   2    2
+--R       3%i a log(a |---------  - %i x) + 3%i a log(\|- x  + a   + %i x - a)
+--R                   |     2
+--R                  \|    a
+--R     + 
+--R                    +---------+
+--R              2     |   2    2                     2              2
+--R       - 3%i a log(\|- x  + a   - %i x - a) - 3%i a log(a) - 3%i a log(- 1)
+--R  /
+--R     2
+--R                                             Type: Expression Complex Integer
+--E 
+
+--S 163
+gg:=rootSimp ff
+--R
+--R   (9)
+--R                    +-------+                            +-------+
+--R            2       | 2    2                     2       | 2    2
+--R       3%i a log(%i\|x  - a   + %i x - a) + 3%i a log(%i\|x  - a   - %i x)
+--R     + 
+--R                      +-------+
+--R              2       | 2    2                     2              2
+--R       - 3%i a log(%i\|x  - a   - %i x - a) - 3%i a log(a) - 3%i a log(- 1)
+--R  /
+--R     2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 164    14:263 Schaums and Axiom agree
+hh:=complexNormalize gg
+--R
+--R   (10)  0
+--R                                             Type: Expression Complex Integer
+--E
+@
+
+\section{\cite{1}:14.264~~~~~$\displaystyle
+\int{\frac{(a^2-x^2)^{3/2}}{x^3}}~dx$}
+$$\int{\frac{(a^2-x^2)^{3/2}}{x^3}}=
+-\frac{(a^2-x^2)^{3/2}}{2x^2}+\frac{3}{2}\sqrt{a^2-x^2}-
+\frac{3}{2}a\sec^{-1}\left|\frac{x}{a}\right|
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 165
+aa:=integrate((a^2-x^2)^(3/2)/x^3,x)
+--R 
+--R
+--R   (1)
+--R                                                             +---------+
+--R                           +---------+                       |   2    2
+--R               4      3 2  |   2    2      2 4      4 2     \|- x  + a   - a
+--R       ((- 3a x  + 12a x )\|- x  + a   + 9a x  - 12a x )log(----------------)
+--R                                                                    x
+--R     + 
+--R                             +---------+
+--R            4     3 2     5  |   2    2      6     2 4     4 2     6
+--R       (4a x  + 3a x  - 4a )\|- x  + a   + 2x  - 3a x  - 5a x  + 4a
+--R  /
+--R                   +---------+
+--R        4     2 2  |   2    2        4     3 2
+--R     (2x  - 8a x )\|- x  + a   - 6a x  + 8a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 166
+bb:=-(a^2-x^2)^(3/2)/(2*x^2)-(3*sqrt(a^2-x^2))/2+3/2*a*log((a+sqrt(a^2-x^2))/x)
+--R
+--R                  +---------+
+--R                  |   2    2                      +---------+
+--R            2    \|- x  + a   + a         2    2  |   2    2
+--R        3a x log(----------------) + (- 2x  - a )\|- x  + a
+--R                         x
+--R   (2)  -----------------------------------------------------
+--R                                   2
+--R                                 2x
+--R                                                     Type: Expression Integer
+--E
+
+--S 167
+cc:=aa-bb
+--R
+--R                  +---------+                +---------+
+--R                  |   2    2                 |   2    2
+--R                 \|- x  + a   + a           \|- x  + a   - a
+--R        - 3a log(----------------) - 3a log(----------------) - 2a
+--R                         x                          x
+--R   (3)  ----------------------------------------------------------
+--R                                     2
+--R                                                     Type: Expression Integer
+--E
+
+--S 168
+dd:=expandLog cc
+--R
+--R                  +---------+                +---------+
+--R                  |   2    2                 |   2    2
+--R        - 3a log(\|- x  + a   + a) - 3a log(\|- x  + a   - a) + 6a log(x) - 2a
+--R   (4)  ----------------------------------------------------------------------
+--R                                           2
+--R                                                     Type: Expression Integer
+--E
+
+--S 169
+ee:=complexNormalize dd
+--R
+--R                  x
+--R   (5)  3a log(-------) - a
+--R                +----+
+--R                |   2
+--R               \|- x
+--R                                                     Type: Expression Integer
+--E
+
+--S 170    14:264 Schaums and Axiom differ by a constant
+ff:=rootSimp ee
+--R
+--R                  +---+
+--R   (6)  - 3a log(\|- 1 ) - a
+--R                                                     Type: Expression Integer
+--E
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 pp68-69
+\end{thebibliography}
+\end{document}
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diff --git a/src/axiom-website/CATS/schaum12.input.pamphlet b/src/axiom-website/CATS/schaum12.input.pamphlet
new file mode 100644
index 0000000..7d5d77a
--- /dev/null
+++ b/src/axiom-website/CATS/schaum12.input.pamphlet
@@ -0,0 +1,2870 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum12.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.265~~~~~$\displaystyle
+\int{\frac{dx}{ax^2+bx+c}}$}
+$$\int{\frac{1}{ax^2+bx+c}}=
+\left\{
+\begin{array}{l}
+\displaystyle\frac{2}{\sqrt{4ac-b^2}}\tan^{-1}\frac{2ax+b}{\sqrt{4ac-b^2}}\\
+\displaystyle\frac{1}{\sqrt{b^2-4ac}}\ln\left(
+\frac{2ax+b-\sqrt{b^2-4ac}}{2ax+b+\sqrt{b^2-4ac}}\right)
+\end{array}
+\right.
+$$
+&lt;&lt;*&gt;&gt;=
+)spool schaum12.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1
+aa:=integrate(1/(a*x^2+b*x+c),x)
+--R
+--R   (1)
+--R   [
+--R       log
+--R                                           +-----------+
+--R                 2 2                    2  |          2       2        2
+--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R            + 
+--R                        3
+--R              4a b c - b
+--R         /
+--R               2
+--R            a x  + b x + c
+--R    /
+--R        +-----------+
+--R        |          2
+--R       \|- 4a c + b
+--R     ,
+--R                     +---------+
+--R                     |        2
+--R          (2a x + b)\|4a c - b
+--R    2atan(----------------------)
+--R                         2
+--R                 4a c - b
+--R    -----------------------------]
+--R              +---------+
+--R              |        2
+--R             \|4a c - b
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 2
+bb1:=2/sqrt(4*a*c-b^2)*atan((2*a*x+b)/sqrt(4*a*c-b^2))
+--R 
+--R
+--R                2a x + b
+--R        2atan(------------)
+--R               +---------+
+--R               |        2
+--R              \|4a c - b
+--R   (2)  -------------------
+--R             +---------+
+--R             |        2
+--R            \|4a c - b
+--R                                                     Type: Expression Integer
+--E
+
+--S 3
+bb2:=1/sqrt(b^2-4*a*c)*log((2*a*x+b-sqrt(b^2-4*a*c))/(2*a*x+b+sqrt(b^2-4*a*c)))
+--R 
+--R
+--R               +-----------+
+--R               |          2
+--R            - \|- 4a c + b   + 2a x + b
+--R        log(---------------------------)
+--R              +-----------+
+--R              |          2
+--R             \|- 4a c + b   + 2a x + b
+--R   (3)  --------------------------------
+--R                  +-----------+
+--R                  |          2
+--R                 \|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 4
+cc1:=aa.1-bb1
+--R
+--R   (4)
+--R          +---------+
+--R          |        2
+--R         \|4a c - b
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2       2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R              + 
+--R                          3
+--R                4a b c - b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R           +-----------+
+--R           |          2        2a x + b
+--R       - 2\|- 4a c + b  atan(------------)
+--R                              +---------+
+--R                              |        2
+--R                             \|4a c - b
+--R  /
+--R      +-----------+ +---------+
+--R      |          2  |        2
+--R     \|- 4a c + b  \|4a c - b
+--R                                                     Type: Expression Integer
+--E
+
+--S 5
+cc2:=aa.1-bb2
+--R
+--R   (5)
+--R       log
+--R                                           +-----------+
+--R                 2 2                    2  |          2       2        2
+--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R            + 
+--R                        3
+--R              4a b c - b
+--R         /
+--R               2
+--R            a x  + b x + c
+--R     + 
+--R                +-----------+
+--R                |          2
+--R             - \|- 4a c + b   + 2a x + b
+--R       - log(---------------------------)
+--R               +-----------+
+--R               |          2
+--R              \|- 4a c + b   + 2a x + b
+--R  /
+--R      +-----------+
+--R      |          2
+--R     \|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 6
+cc3:=aa.2-bb1
+--R
+--R                         +---------+
+--R                         |        2
+--R              (2a x + b)\|4a c - b              2a x + b
+--R        2atan(----------------------) - 2atan(------------)
+--R                             2                 +---------+
+--R                     4a c - b                  |        2
+--R                                              \|4a c - b
+--R   (6)  ---------------------------------------------------
+--R                             +---------+
+--R                             |        2
+--R                            \|4a c - b
+--R                                                     Type: Expression Integer
+--E
+
+--S 7
+cc4:=aa.2-bb2
+--R
+--R   (7)
+--R                            +-----------+
+--R          +---------+       |          2
+--R          |        2     - \|- 4a c + b   + 2a x + b
+--R       - \|4a c - b  log(---------------------------)
+--R                           +-----------+
+--R                           |          2
+--R                          \|- 4a c + b   + 2a x + b
+--R     + 
+--R                                      +---------+
+--R         +-----------+                |        2
+--R         |          2      (2a x + b)\|4a c - b
+--R       2\|- 4a c + b  atan(----------------------)
+--R                                          2
+--R                                  4a c - b
+--R  /
+--R      +-----------+ +---------+
+--R      |          2  |        2
+--R     \|- 4a c + b  \|4a c - b
+--R                                                     Type: Expression Integer
+--E
+
+--S 8
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (8)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 9
+dd3:=atanrule cc3
+--R
+--R   (9)
+--R               +---------+
+--R               |        2
+--R              \|4a c - b   + 2%i a x + %i b
+--R       %i log(-----------------------------)
+--R               +---------+
+--R               |        2
+--R              \|4a c - b   - 2%i a x - %i b
+--R     + 
+--R                             +---------+
+--R                             |        2                  2
+--R                (- 2a x - b)\|4a c - b   + 4%i a c - %i b
+--R       - %i log(------------------------------------------)
+--R                            +---------+
+--R                            |        2                  2
+--R                 (2a x + b)\|4a c - b   + 4%i a c - %i b
+--R  /
+--R      +---------+
+--R      |        2
+--R     \|4a c - b
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 10
+ee3:=expandLog dd3
+--R
+--R   (10)
+--R                         +---------+
+--R                         |        2                  2
+--R       %i log((2a x + b)\|4a c - b   + 4%i a c - %i b )
+--R     + 
+--R                           +---------+
+--R                           |        2                  2
+--R       - %i log((2a x + b)\|4a c - b   - 4%i a c + %i b )
+--R     + 
+--R               +---------+
+--R               |        2
+--R       %i log(\|4a c - b   + 2%i a x + %i b)
+--R     + 
+--R                 +---------+
+--R                 |        2
+--R       - %i log(\|4a c - b   - 2%i a x - %i b) - %i log(- 1)
+--R  /
+--R      +---------+
+--R      |        2
+--R     \|4a c - b
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 11     14:265 Schaums and Axiom agree
+ff3:=complexNormalize ee3
+--R
+--R   (11)  0
+--R                                             Type: Expression Complex Integer
+--E
+@
+
+\section{\cite{1}:14.266~~~~~$\displaystyle
+\int{\frac{x~dx}{ax^2+bx+c}}$}
+$$\int{\frac{x}{ax^2+bx+c}}=
+\frac{1}{2a}\ln(ax^2+bx+c)-\frac{b}{2a}\int{\frac{1}{ax^2+bx+c}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 12
+aa:=integrate(x/(a*x^2+b*x+c),x)
+--R
+--R   (1)
+--R   [
+--R           b
+--R        *
+--R           log
+--R                                               +-----------+
+--R                     2 2                    2  |          2         2        2
+--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R                + 
+--R                              3
+--R                  - 4a b c + b
+--R             /
+--R                   2
+--R                a x  + b x + c
+--R       + 
+--R                             +-----------+
+--R                2            |          2
+--R         log(a x  + b x + c)\|- 4a c + b
+--R    /
+--R          +-----------+
+--R          |          2
+--R       2a\|- 4a c + b
+--R     ,
+--R                         +---------+
+--R                         |        2                         +---------+
+--R              (2a x + b)\|4a c - b             2            |        2
+--R    - 2b atan(----------------------) + log(a x  + b x + c)\|4a c - b
+--R                             2
+--R                     4a c - b
+--R    -------------------------------------------------------------------]
+--R                                  +---------+
+--R                                  |        2
+--R                               2a\|4a c - b
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+
+--S 13
+t1:=integrate(1/(a*x^2+b*x+c),x)
+--R 
+--R
+--R   (2)
+--R   [
+--R       log
+--R                                           +-----------+
+--R                 2 2                    2  |          2       2        2
+--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R            + 
+--R                        3
+--R              4a b c - b
+--R         /
+--R               2
+--R            a x  + b x + c
+--R    /
+--R        +-----------+
+--R        |          2
+--R       \|- 4a c + b
+--R     ,
+--R                     +---------+
+--R                     |        2
+--R          (2a x + b)\|4a c - b
+--R    2atan(----------------------)
+--R                         2
+--R                 4a c - b
+--R    -----------------------------]
+--R              +---------+
+--R              |        2
+--R             \|4a c - b
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 14
+bb1:=1/(2*a)*log(a*x^2+b*x+c)-b/(2*a)*t1.1
+--R 
+--R
+--R   (3)
+--R       -
+--R            b
+--R         *
+--R            log
+--R                                                +-----------+
+--R                      2 2                    2  |          2       2        2
+--R                   (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R                 + 
+--R                             3
+--R                   4a b c - b
+--R              /
+--R                    2
+--R                 a x  + b x + c
+--R     + 
+--R                           +-----------+
+--R              2            |          2
+--R       log(a x  + b x + c)\|- 4a c + b
+--R  /
+--R        +-----------+
+--R        |          2
+--R     2a\|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 15
+bb2:=1/(2*a)*log(a*x^2+b*x+c)-b/(2*a)*t1.2
+--R 
+--R
+--R                             +---------+
+--R                             |        2                         +---------+
+--R                  (2a x + b)\|4a c - b             2            |        2
+--R        - 2b atan(----------------------) + log(a x  + b x + c)\|4a c - b
+--R                                 2
+--R                         4a c - b
+--R   (4)  -------------------------------------------------------------------
+--R                                      +---------+
+--R                                      |        2
+--R                                   2a\|4a c - b
+--R                                                     Type: Expression Integer
+--E
+
+--S 16
+cc1:=aa.1-bb1
+--R
+--R   (5)
+--R         b
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2       2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R              + 
+--R                          3
+--R                4a b c - b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R         b
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2         2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R              + 
+--R                            3
+--R                - 4a b c + b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R  /
+--R        +-----------+
+--R        |          2
+--R     2a\|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 17
+cc2:=aa.2-bb1
+--R
+--R   (6)
+--R           +---------+
+--R           |        2
+--R         b\|4a c - b
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2       2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R              + 
+--R                          3
+--R                4a b c - b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R                                         +---------+
+--R            +-----------+                |        2
+--R            |          2      (2a x + b)\|4a c - b
+--R       - 2b\|- 4a c + b  atan(----------------------)
+--R                                             2
+--R                                     4a c - b
+--R  /
+--R        +-----------+ +---------+
+--R        |          2  |        2
+--R     2a\|- 4a c + b  \|4a c - b
+--R                                                     Type: Expression Integer
+--E
+
+--S 18
+cc3:=aa.2-bb1
+--R
+--R   (7)
+--R           +---------+
+--R           |        2
+--R         b\|4a c - b
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2       2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R              + 
+--R                          3
+--R                4a b c - b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R                                         +---------+
+--R            +-----------+                |        2
+--R            |          2      (2a x + b)\|4a c - b
+--R       - 2b\|- 4a c + b  atan(----------------------)
+--R                                             2
+--R                                     4a c - b
+--R  /
+--R        +-----------+ +---------+
+--R        |          2  |        2
+--R     2a\|- 4a c + b  \|4a c - b
+--R                                                     Type: Expression Integer
+--E
+
+--S 19     14:266 Schaums and Axiom agree
+cc4:=aa.2-bb2
+--R
+--R   (8)  0
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.267~~~~~$\displaystyle
+\int{\frac{x^2dx}{ax^2+bx+c}}$}
+$$\int{\frac{x^2}{ax^2+bx+c}}=
+\frac{x}{a}-\frac{b}{2a^2}\ln(ax^2+bx+c)+\frac{b^2-2ac}{2a^2}
+\int{\frac{1}{ax^2+bx+c}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 20
+aa:=integrate(x^2/(a*x^2+b*x+c),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R                    2
+--R           (2a c - b )
+--R        *
+--R           log
+--R                                               +-----------+
+--R                     2 2                    2  |          2         2        2
+--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R                + 
+--R                              3
+--R                  - 4a b c + b
+--R             /
+--R                   2
+--R                a x  + b x + c
+--R       + 
+--R                                          +-----------+
+--R                     2                    |          2
+--R         (- b log(a x  + b x + c) + 2a x)\|- 4a c + b
+--R    /
+--R           +-----------+
+--R         2 |          2
+--R       2a \|- 4a c + b
+--R     ,
+--R
+--R                                       +---------+
+--R                                       |        2
+--R                     2      (2a x + b)\|4a c - b
+--R         (- 4a c + 2b )atan(----------------------)
+--R                                           2
+--R                                   4a c - b
+--R       + 
+--R                                          +---------+
+--R                     2                    |        2
+--R         (- b log(a x  + b x + c) + 2a x)\|4a c - b
+--R    /
+--R           +---------+
+--R         2 |        2
+--R       2a \|4a c - b
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+
+--S 21
+t1:=integrate(1/(a*x^2+b*x+c),x)
+--R 
+--R
+--R   (2)
+--R   [
+--R       log
+--R                                           +-----------+
+--R                 2 2                    2  |          2       2        2
+--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R            + 
+--R                        3
+--R              4a b c - b
+--R         /
+--R               2
+--R            a x  + b x + c
+--R    /
+--R        +-----------+
+--R        |          2
+--R       \|- 4a c + b
+--R     ,
+--R                     +---------+
+--R                     |        2
+--R          (2a x + b)\|4a c - b
+--R    2atan(----------------------)
+--R                         2
+--R                 4a c - b
+--R    -----------------------------]
+--R              +---------+
+--R              |        2
+--R             \|4a c - b
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 22
+bb1:=x/a-b/(2*a^2)*log(a*x^2+b*x+c)+(b^2-2*a*c)/(2*a^2)*t1.1
+--R 
+--R
+--R   (3)
+--R                    2
+--R         (- 2a c + b )
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2       2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R              + 
+--R                          3
+--R                4a b c - b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R                                        +-----------+
+--R                   2                    |          2
+--R       (- b log(a x  + b x + c) + 2a x)\|- 4a c + b
+--R  /
+--R         +-----------+
+--R       2 |          2
+--R     2a \|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 23
+bb2:=x/a-b/(2*a^2)*log(a*x^2+b*x+c)+(b^2-2*a*c)/(2*a^2)*t1.2
+--R 
+--R
+--R   (4)
+--R                                     +---------+
+--R                                     |        2
+--R                   2      (2a x + b)\|4a c - b
+--R       (- 4a c + 2b )atan(----------------------)
+--R                                         2
+--R                                 4a c - b
+--R     + 
+--R                                        +---------+
+--R                   2                    |        2
+--R       (- b log(a x  + b x + c) + 2a x)\|4a c - b
+--R  /
+--R         +---------+
+--R       2 |        2
+--R     2a \|4a c - b
+--R                                                     Type: Expression Integer
+--E
+
+--S 24
+cc1:=bb1-aa.1
+--R
+--R   (5)
+--R                    2
+--R         (- 2a c + b )
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2       2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R              + 
+--R                          3
+--R                4a b c - b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R                    2
+--R         (- 2a c + b )
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2         2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R              + 
+--R                            3
+--R                - 4a b c + b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R  /
+--R         +-----------+
+--R       2 |          2
+--R     2a \|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 25     14:267 Schaums and Axiom differ by a constant
+dd1:=complexNormalize cc1
+--R
+--R                   2          3      2 2
+--R        (- 2a c + b )log(- 16a c + 4a b )
+--R   (6)  ---------------------------------
+--R                    +-----------+
+--R                  2 |          2
+--R                2a \|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.268~~~~~$\displaystyle
+\int{\frac{x^m~dx}{ax^2+bx+c}}$}
+$$\int{\frac{x^m}{ax^2+bx+c}}=
+\frac{x^{m-1}}{(m-1)a}-\frac{c}{a}\int{\frac{x^{m-2}}{ax^2+bx+c}}-
+\frac{b}{a}\int{\frac{x^{m-1}}{ax^2+bx+c}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 26     14:268 Axiom cannot compute this integral
+aa:=integrate(x^m/(a*x^2+b*x+c),x)
+--R 
+--R
+--R           x         m
+--I         ++        %N
+--I   (1)   |   --------------- d%N
+--R        ++                2
+--I             c + %N b + %N a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+@
+
+\section{\cite{1}:14.269~~~~~$\displaystyle
+\int{\frac{dx}{x(ax^2+bx+c)}}$}
+$$\int{\frac{1}{x(ax^2+bx+c)}}=
+\frac{1}{2c}\ln\left(\frac{x^2}{ax^2+bx+c}\right)-
+\frac{b}{2c}\int{\frac{1}{ax^2+bx+c}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 27
+aa:=integrate(1/(x*(a*x^2+b*x+c)),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R           b
+--R        *
+--R           log
+--R                                               +-----------+
+--R                     2 2                    2  |          2         2        2
+--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R                + 
+--R                              3
+--R                  - 4a b c + b
+--R             /
+--R                   2
+--R                a x  + b x + c
+--R       + 
+--R                                           +-----------+
+--R                   2                       |          2
+--R         (- log(a x  + b x + c) + 2log(x))\|- 4a c + b
+--R    /
+--R          +-----------+
+--R          |          2
+--R       2c\|- 4a c + b
+--R     ,
+--R
+--R                              +---------+
+--R                              |        2
+--R                   (2a x + b)\|4a c - b
+--R         - 2b atan(----------------------)
+--R                                  2
+--R                          4a c - b
+--R       + 
+--R                                           +---------+
+--R                   2                       |        2
+--R         (- log(a x  + b x + c) + 2log(x))\|4a c - b
+--R    /
+--R          +---------+
+--R          |        2
+--R       2c\|4a c - b
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+
+--S 28
+t1:=integrate(1/(a*x^2+b*x+c),x)
+--R 
+--R
+--R   (2)
+--R   [
+--R       log
+--R                                           +-----------+
+--R                 2 2                    2  |          2       2        2
+--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R            + 
+--R                        3
+--R              4a b c - b
+--R         /
+--R               2
+--R            a x  + b x + c
+--R    /
+--R        +-----------+
+--R        |          2
+--R       \|- 4a c + b
+--R     ,
+--R                     +---------+
+--R                     |        2
+--R          (2a x + b)\|4a c - b
+--R    2atan(----------------------)
+--R                         2
+--R                 4a c - b
+--R    -----------------------------]
+--R              +---------+
+--R              |        2
+--R             \|4a c - b
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 29
+bb1:=1/(2*c)*log(x^2/(a*x^2+b*x+c))-b/(2*c)*t1.1
+--R 
+--R
+--R   (3)
+--R       -
+--R            b
+--R         *
+--R            log
+--R                                                +-----------+
+--R                      2 2                    2  |          2       2        2
+--R                   (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R                 + 
+--R                             3
+--R                   4a b c - b
+--R              /
+--R                    2
+--R                 a x  + b x + c
+--R     + 
+--R                  2        +-----------+
+--R                 x         |          2
+--R       log(--------------)\|- 4a c + b
+--R              2
+--R           a x  + b x + c
+--R  /
+--R        +-----------+
+--R        |          2
+--R     2c\|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 30
+bb2:=1/(2*c)*log(x^2/(a*x^2+b*x+c))-b/(2*c)*t1.2
+--R 
+--R
+--R                             +---------+
+--R                             |        2                2        +---------+
+--R                  (2a x + b)\|4a c - b                x         |        2
+--R        - 2b atan(----------------------) + log(--------------)\|4a c - b
+--R                                 2                 2
+--R                         4a c - b               a x  + b x + c
+--R   (4)  -------------------------------------------------------------------
+--R                                      +---------+
+--R                                      |        2
+--R                                   2c\|4a c - b
+--R                                                     Type: Expression Integer
+--E
+
+--S 31
+cc1:=bb1-aa.1
+--R
+--R   (5)
+--R       -
+--R            b
+--R         *
+--R            log
+--R                                                +-----------+
+--R                      2 2                    2  |          2       2        2
+--R                   (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R                 + 
+--R                             3
+--R                   4a b c - b
+--R              /
+--R                    2
+--R                 a x  + b x + c
+--R     + 
+--R       -
+--R            b
+--R         *
+--R            log
+--R                                                +-----------+
+--R                      2 2                    2  |          2
+--R                   (2a x  + 2a b x - 2a c + b )\|- 4a c + b
+--R                 + 
+--R                        2        2               3
+--R                   (- 8a c + 2a b )x - 4a b c + b
+--R              /
+--R                    2
+--R                 a x  + b x + c
+--R     + 
+--R                                                   2         +-----------+
+--R               2                                  x          |          2
+--R       (log(a x  + b x + c) - 2log(x) + log(--------------))\|- 4a c + b
+--R                                               2
+--R                                            a x  + b x + c
+--R  /
+--R        +-----------+
+--R        |          2
+--R     2c\|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 32
+dd1:=expandLog cc1
+--R
+--R   (6)
+--R       -
+--R            b
+--R         *
+--R            log
+--R                                              +-----------+
+--R                    2 2                    2  |          2       2        2
+--R                 (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R               + 
+--R                           3
+--R                 4a b c - b
+--R     + 
+--R       -
+--R            b
+--R         *
+--R            log
+--R                                              +-----------+
+--R                    2 2                    2  |          2         2        2
+--R                 (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R               + 
+--R                             3
+--R                 - 4a b c + b
+--R     + 
+--R                 2
+--R       2b log(a x  + b x + c)
+--R  /
+--R        +-----------+
+--R        |          2
+--R     2c\|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 33     14:269 Schaums and Axiom differ by a constant
+ee1:=complexNormalize dd1
+--R
+--R                     3      2 2
+--R          b log(- 16a c + 4a b )
+--R   (7)  - ----------------------
+--R                +-----------+
+--R                |          2
+--R             2c\|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.270~~~~~$\displaystyle
+\int{\frac{dx}{x^2(ax^2+bx+c)}}$}
+$$\int{\frac{1}{x^2(ax^2+bx+c)}}=
+\frac{b}{2c^2}\ln\left(\frac{ax^2+bx+c}{x^2}\right)-\frac{1}{cx}+
+\frac{b^2-2ac}{2c^2}\int{\frac{1}{ax^2+bx+c}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 34
+aa:=integrate(1/(x^2*(a*x^2+b*x+c)),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R                    2
+--R           (2a c - b )x
+--R        *
+--R           log
+--R                                               +-----------+
+--R                     2 2                    2  |          2         2        2
+--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R                + 
+--R                              3
+--R                  - 4a b c + b
+--R             /
+--R                   2
+--R                a x  + b x + c
+--R       + 
+--R                                                      +-----------+
+--R                     2                                |          2
+--R         (b x log(a x  + b x + c) - 2b x log(x) - 2c)\|- 4a c + b
+--R    /
+--R            +-----------+
+--R         2  |          2
+--R       2c x\|- 4a c + b
+--R     ,
+--R
+--R                                         +---------+
+--R                                         |        2
+--R                     2        (2a x + b)\|4a c - b
+--R         (- 4a c + 2b )x atan(----------------------)
+--R                                             2
+--R                                     4a c - b
+--R       + 
+--R                                                      +---------+
+--R                     2                                |        2
+--R         (b x log(a x  + b x + c) - 2b x log(x) - 2c)\|4a c - b
+--R    /
+--R            +---------+
+--R         2  |        2
+--R       2c x\|4a c - b
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+
+--S 35
+t1:=integrate(1/(a*x^2+b*x+c),x)
+--R 
+--R
+--R   (2)
+--R   [
+--R       log
+--R                                           +-----------+
+--R                 2 2                    2  |          2       2        2
+--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R            + 
+--R                        3
+--R              4a b c - b
+--R         /
+--R               2
+--R            a x  + b x + c
+--R    /
+--R        +-----------+
+--R        |          2
+--R       \|- 4a c + b
+--R     ,
+--R                     +---------+
+--R                     |        2
+--R          (2a x + b)\|4a c - b
+--R    2atan(----------------------)
+--R                         2
+--R                 4a c - b
+--R    -----------------------------]
+--R              +---------+
+--R              |        2
+--R             \|4a c - b
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 36
+bb1:=b/(2*c^2)*log((a*x^2+b*x+c)/x^2)-1/(c*x)+(b^2-2*a*c)/(2*c^2)*t1.1
+--R 
+--R
+--R   (3)
+--R                    2
+--R         (- 2a c + b )x
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2       2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R              + 
+--R                          3
+--R                4a b c - b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R                   2                  +-----------+
+--R                a x  + b x + c        |          2
+--R       (b x log(--------------) - 2c)\|- 4a c + b
+--R                       2
+--R                      x
+--R  /
+--R          +-----------+
+--R       2  |          2
+--R     2c x\|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 37
+bb2:=b/(2*c^2)*log((a*x^2+b*x+c)/x^2)-1/(c*x)+(b^2-2*a*c)/(2*c^2)*t1.2
+--R 
+--R
+--R   (4)
+--R                                       +---------+
+--R                                       |        2
+--R                   2        (2a x + b)\|4a c - b
+--R       (- 4a c + 2b )x atan(----------------------)
+--R                                           2
+--R                                   4a c - b
+--R     + 
+--R                   2                  +---------+
+--R                a x  + b x + c        |        2
+--R       (b x log(--------------) - 2c)\|4a c - b
+--R                       2
+--R                      x
+--R  /
+--R          +---------+
+--R       2  |        2
+--R     2c x\|4a c - b
+--R                                                     Type: Expression Integer
+--E
+
+--S 38
+cc1:=bb1-aa.1
+--R
+--R   (5)
+--R                    2
+--R         (- 2a c + b )
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2       2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R              + 
+--R                          3
+--R                4a b c - b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R                    2
+--R         (- 2a c + b )
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2         2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R              + 
+--R                            3
+--R                - 4a b c + b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R                                                     2             +-----------+
+--R                 2                                a x  + b x + c   |          2
+--R     (- b log(a x  + b x + c) + 2b log(x) + b log(--------------))\|- 4a c + b
+--R                                                         2
+--R                                                        x
+--R  /
+--R         +-----------+
+--R       2 |          2
+--R     2c \|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 39
+dd1:=expandLog cc1
+--R
+--R   (6)
+--R                    2
+--R         (- 2a c + b )
+--R      *
+--R         log
+--R                                           +-----------+
+--R                 2 2                    2  |          2       2        2
+--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R            + 
+--R                        3
+--R              4a b c - b
+--R     + 
+--R                    2
+--R         (- 2a c + b )
+--R      *
+--R         log
+--R                                           +-----------+
+--R                 2 2                    2  |          2         2        2
+--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R            + 
+--R                          3
+--R              - 4a b c + b
+--R     + 
+--R                 2        2
+--R       (4a c - 2b )log(a x  + b x + c)
+--R  /
+--R         +-----------+
+--R       2 |          2
+--R     2c \|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 40     14:270 Schaums and Axiom differ by a constant
+ee1:=complexNormalize dd1
+--R
+--R                   2          3      2 2
+--R        (- 2a c + b )log(- 16a c + 4a b )
+--R   (7)  ---------------------------------
+--R                    +-----------+
+--R                  2 |          2
+--R                2c \|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.271~~~~~$\displaystyle
+\int{\frac{dx}{x^n(ax^2+bx+c)}}$}
+$$\int{\frac{1}{x^n(ax^2+bx+c)}}=
+-\frac{1}{(n-1)cx^{n-1}}-
+\frac{b}{c}\int{\frac{1}{x^{n-1}(ax^2+bx+c)}}-
+\frac{a}{c}\int{\frac{1}{x^{x-2}(ax^2+bx+c)}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 41     14:271 Axiom cannot compute this integral
+aa:=integrate(1/(x^n*(a*x^2+b*x+c)),x)
+--R 
+--R
+--R           x
+--R         ++            1
+--I   (1)   |   -------------------- d%N
+--R        ++                 2    n
+--I             (c + %N b + %N a)%N
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+@
+
+\section{\cite{1}:14.272~~~~~$\displaystyle
+\int{\frac{dx}{(ax^2+bx+c)^2}}$}
+$$\int{\frac{1}{(ax^2+bx+c)^2}}=
+\frac{2xa+b}{(4ac-b^2)(ax^2+bx+c)}+
+\frac{2a}{4ac-b^2}\int{\frac{1}{ax^2+bx+c}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 42
+aa:=integrate(1/(a*x^2+b*x+c)^2,x)
+--R 
+--R
+--R   (1)
+--R   [
+--R              2 2
+--R           (2a x  + 2a b x + 2a c)
+--R        *
+--R           log
+--R                                               +-----------+
+--R                     2 2                    2  |          2       2        2
+--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R                + 
+--R                            3
+--R                  4a b c - b
+--R             /
+--R                   2
+--R                a x  + b x + c
+--R       + 
+--R                    +-----------+
+--R                    |          2
+--R         (2a x + b)\|- 4a c + b
+--R    /
+--R                                                        +-----------+
+--R           2       2  2              3         2    2   |          2
+--R       ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|- 4a c + b
+--R     ,
+--R                                           +---------+
+--R                                           |        2                +---------+
+--R       2 2                      (2a x + b)\|4a c - b                 |        2
+--R    (4a x  + 4a b x + 4a c)atan(----------------------) + (2a x + b)\|4a c - b
+--R                                               2
+--R                                       4a c - b
+--R    ----------------------------------------------------------------------------
+--R                                                             +---------+
+--R                2       2  2              3         2    2   |        2
+--R            ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|4a c - b
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+
+--S 43
+t1:=integrate(1/(a*x^2+b*x+c),x)
+--R 
+--R
+--R   (2)
+--R   [
+--R       log
+--R                                           +-----------+
+--R                 2 2                    2  |          2       2        2
+--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R            + 
+--R                        3
+--R              4a b c - b
+--R         /
+--R               2
+--R            a x  + b x + c
+--R    /
+--R        +-----------+
+--R        |          2
+--R       \|- 4a c + b
+--R     ,
+--R                     +---------+
+--R                     |        2
+--R          (2a x + b)\|4a c - b
+--R    2atan(----------------------)
+--R                         2
+--R                 4a c - b
+--R    -----------------------------]
+--R              +---------+
+--R              |        2
+--R             \|4a c - b
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 44
+bb1:=(2*a*x+b)/((4*a*c-b^2)*(a*x^2+b*x+c))+(2*a)/(4*a*c-b^2)*t1.1
+--R
+--R   (3)
+--R            2 2
+--R         (2a x  + 2a b x + 2a c)
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2       2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R              + 
+--R                          3
+--R                4a b c - b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R                  +-----------+
+--R                  |          2
+--R       (2a x + b)\|- 4a c + b
+--R  /
+--R                                                      +-----------+
+--R         2       2  2              3         2    2   |          2
+--R     ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 45
+bb2:=(2*a*x+b)/((4*a*c-b^2)*(a*x^2+b*x+c))+(2*a)/(4*a*c-b^2)*t1.2
+--R
+--R   (4)
+--R                                          +---------+
+--R                                          |        2                +---------+
+--R      2 2                      (2a x + b)\|4a c - b                 |        2
+--R   (4a x  + 4a b x + 4a c)atan(----------------------) + (2a x + b)\|4a c - b
+--R                                              2
+--R                                      4a c - b
+--R   ----------------------------------------------------------------------------
+--R                                                            +---------+
+--R               2       2  2              3         2    2   |        2
+--R           ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|4a c - b
+--R                                                     Type: Expression Integer
+--E
+
+--S 46
+cc1:=aa.1-bb1
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
+
+--S 47
+cc2:=aa.2-bb1
+--R
+--R   (6)
+--R       -
+--R               +---------+
+--R               |        2
+--R            2a\|4a c - b
+--R         *
+--R            log
+--R                                                +-----------+
+--R                      2 2                    2  |          2       2        2
+--R                   (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R                 + 
+--R                             3
+--R                   4a b c - b
+--R              /
+--R                    2
+--R                 a x  + b x + c
+--R     + 
+--R                                       +---------+
+--R          +-----------+                |        2
+--R          |          2      (2a x + b)\|4a c - b
+--R       4a\|- 4a c + b  atan(----------------------)
+--R                                           2
+--R                                   4a c - b
+--R  /
+--R                 +-----------+ +---------+
+--R              2  |          2  |        2
+--R     (4a c - b )\|- 4a c + b  \|4a c - b
+--R                                                     Type: Expression Integer
+--E
+
+--S 48
+cc3:=aa.1-bb2
+--R
+--R   (7)
+--R            +---------+
+--R            |        2
+--R         2a\|4a c - b
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2       2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R              + 
+--R                          3
+--R                4a b c - b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R                                         +---------+
+--R            +-----------+                |        2
+--R            |          2      (2a x + b)\|4a c - b
+--R       - 4a\|- 4a c + b  atan(----------------------)
+--R                                             2
+--R                                     4a c - b
+--R  /
+--R                 +-----------+ +---------+
+--R              2  |          2  |        2
+--R     (4a c - b )\|- 4a c + b  \|4a c - b
+--R                                                     Type: Expression Integer
+--E
+
+--S 49     14:272 Schaums and Axiom agree
+cc4:=aa.2-bb2
+--R
+--R   (8)  0
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.273~~~~~$\displaystyle
+\int{\frac{x~dx}{(ax^2+bx+c)^2}}$}
+$$\int{\frac{x}{(ax^2+bx+c)^2}}=
+-\frac{bx+2c}{(4ac-b^2)(ax^2+bx+c)}-
+\frac{b}{4ac-b^2}\int{\frac{1}{ax^2+bx+c}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 50
+aa:=integrate(x/(a*x^2+b*x+c)^2,x)
+--R 
+--R
+--R   (1)
+--R   [
+--R                 2    2
+--R           (a b x  + b x + b c)
+--R        *
+--R           log
+--R                                               +-----------+
+--R                     2 2                    2  |          2         2        2
+--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R                + 
+--R                              3
+--R                  - 4a b c + b
+--R             /
+--R                   2
+--R                a x  + b x + c
+--R       + 
+--R                      +-----------+
+--R                      |          2
+--R         (- b x - 2c)\|- 4a c + b
+--R    /
+--R                                                        +-----------+
+--R           2       2  2              3         2    2   |          2
+--R       ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|- 4a c + b
+--R     ,
+--R
+--R                                                  +---------+
+--R                                                  |        2
+--R                  2     2              (2a x + b)\|4a c - b
+--R         (- 2a b x  - 2b x - 2b c)atan(----------------------)
+--R                                                      2
+--R                                              4a c - b
+--R       + 
+--R                      +---------+
+--R                      |        2
+--R         (- b x - 2c)\|4a c - b
+--R    /
+--R                                                        +---------+
+--R           2       2  2              3         2    2   |        2
+--R       ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|4a c - b
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 51
+t1:=integrate(1/(a*x^2+b*x+c),x)
+--R 
+--R
+--R   (2)
+--R   [
+--R       log
+--R                                           +-----------+
+--R                 2 2                    2  |          2       2        2
+--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R            + 
+--R                        3
+--R              4a b c - b
+--R         /
+--R               2
+--R            a x  + b x + c
+--R    /
+--R        +-----------+
+--R        |          2
+--R       \|- 4a c + b
+--R     ,
+--R                     +---------+
+--R                     |        2
+--R          (2a x + b)\|4a c - b
+--R    2atan(----------------------)
+--R                         2
+--R                 4a c - b
+--R    -----------------------------]
+--R              +---------+
+--R              |        2
+--R             \|4a c - b
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 52
+bb1:=-(b*x+2*c)/((4*a*c-b^2)*(a*x^2+b*x+c))-b/(4*a*c-b^2)*t1.1
+--R 
+--R
+--R   (3)
+--R                 2    2
+--R         (- a b x  - b x - b c)
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2       2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R              + 
+--R                          3
+--R                4a b c - b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R                    +-----------+
+--R                    |          2
+--R       (- b x - 2c)\|- 4a c + b
+--R  /
+--R                                                      +-----------+
+--R         2       2  2              3         2    2   |          2
+--R     ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 53
+bb2:=-(b*x+2*c)/((4*a*c-b^2)*(a*x^2+b*x+c))-b/(4*a*c-b^2)*t1.2
+--R 
+--R
+--R   (4)
+--R                                                +---------+
+--R                                                |        2
+--R                2     2              (2a x + b)\|4a c - b
+--R       (- 2a b x  - 2b x - 2b c)atan(----------------------)
+--R                                                    2
+--R                                            4a c - b
+--R     + 
+--R                    +---------+
+--R                    |        2
+--R       (- b x - 2c)\|4a c - b
+--R  /
+--R                                                      +---------+
+--R         2       2  2              3         2    2   |        2
+--R     ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|4a c - b
+--R                                                     Type: Expression Integer
+--E
+
+--S 54
+cc1:=bb1-aa.1
+--R
+--R   (5)
+--R       -
+--R            b
+--R         *
+--R            log
+--R                                                +-----------+
+--R                      2 2                    2  |          2       2        2
+--R                   (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R                 + 
+--R                             3
+--R                   4a b c - b
+--R              /
+--R                    2
+--R                 a x  + b x + c
+--R     + 
+--R       -
+--R            b
+--R         *
+--R            log
+--R                                                +-----------+
+--R                      2 2                    2  |          2
+--R                   (2a x  + 2a b x - 2a c + b )\|- 4a c + b
+--R                 + 
+--R                        2        2               3
+--R                   (- 8a c + 2a b )x - 4a b c + b
+--R              /
+--R                    2
+--R                 a x  + b x + c
+--R  /
+--R                 +-----------+
+--R              2  |          2
+--R     (4a c - b )\|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 55
+dd1:=expandLog cc1
+--R
+--R   (6)
+--R       -
+--R            b
+--R         *
+--R            log
+--R                                              +-----------+
+--R                    2 2                    2  |          2       2        2
+--R                 (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R               + 
+--R                           3
+--R                 4a b c - b
+--R     + 
+--R       -
+--R            b
+--R         *
+--R            log
+--R                                              +-----------+
+--R                    2 2                    2  |          2         2        2
+--R                 (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R               + 
+--R                             3
+--R                 - 4a b c + b
+--R     + 
+--R                 2
+--R       2b log(a x  + b x + c)
+--R  /
+--R                 +-----------+
+--R              2  |          2
+--R     (4a c - b )\|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 56     14:273 Schaums and Axiom differ by a constant
+ee1:=complexNormalize dd1
+--R
+--R                       3      2 2
+--R            b log(- 16a c + 4a b )
+--R   (7)  - -------------------------
+--R                      +-----------+
+--R                   2  |          2
+--R          (4a c - b )\|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.274~~~~~$\displaystyle
+\int{\frac{x^2~dx}{(ax^2+bx+c)^2}}$}
+$$\int{\frac{x^2}{(ax^2+bx+c)^2}}=
+\frac{(b^2-2ac)x+bc}{a(4ac-b^2)(ax^2+bx+c)}+
+\frac{2c}{4ac-b^2}\int{\frac{1}{ax^2+bx+c}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 57
+aa:=integrate(x^2/(a*x^2+b*x+c)^2,x)
+--R 
+--R
+--R   (1)
+--R   [
+--R              2   2                  2
+--R           (2a c x  + 2a b c x + 2a c )
+--R        *
+--R           log
+--R                                               +-----------+
+--R                     2 2                    2  |          2       2        2
+--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R                + 
+--R                            3
+--R                  4a b c - b
+--R             /
+--R                   2
+--R                a x  + b x + c
+--R       + 
+--R                                +-----------+
+--R                     2          |          2
+--R         ((- 2a c + b )x + b c)\|- 4a c + b
+--R    /
+--R                                                            +-----------+
+--R           3     2 2  2      2         3       2 2      2   |          2
+--R       ((4a c - a b )x  + (4a b c - a b )x + 4a c  - a b c)\|- 4a c + b
+--R     ,
+--R
+--R                                                     +---------+
+--R                                                     |        2
+--R            2   2                  2      (2a x + b)\|4a c - b
+--R         (4a c x  + 4a b c x + 4a c )atan(----------------------)
+--R                                                         2
+--R                                                 4a c - b
+--R       + 
+--R                                +---------+
+--R                     2          |        2
+--R         ((- 2a c + b )x + b c)\|4a c - b
+--R    /
+--R                                                            +---------+
+--R           3     2 2  2      2         3       2 2      2   |        2
+--R       ((4a c - a b )x  + (4a b c - a b )x + 4a c  - a b c)\|4a c - b
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+
+--S 58
+t1:=integrate(1/(a*x^2+b*x+c),x)
+--R 
+--R
+--R   (2)
+--R   [
+--R       log
+--R                                           +-----------+
+--R                 2 2                    2  |          2       2        2
+--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R            + 
+--R                        3
+--R              4a b c - b
+--R         /
+--R               2
+--R            a x  + b x + c
+--R    /
+--R        +-----------+
+--R        |          2
+--R       \|- 4a c + b
+--R     ,
+--R                     +---------+
+--R                     |        2
+--R          (2a x + b)\|4a c - b
+--R    2atan(----------------------)
+--R                         2
+--R                 4a c - b
+--R    -----------------------------]
+--R              +---------+
+--R              |        2
+--R             \|4a c - b
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 59
+bb1:=((b^2-2*a*c)*x+b*c)/(a*(4*a*c-b^2)*(a*x^2+b*x+c))+(2*c)/(4*a*c-b^2)*t1.1
+--R
+--R   (3)
+--R            2   2                  2
+--R         (2a c x  + 2a b c x + 2a c )
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2       2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R              + 
+--R                          3
+--R                4a b c - b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R                              +-----------+
+--R                   2          |          2
+--R       ((- 2a c + b )x + b c)\|- 4a c + b
+--R  /
+--R                                                          +-----------+
+--R         3     2 2  2      2         3       2 2      2   |          2
+--R     ((4a c - a b )x  + (4a b c - a b )x + 4a c  - a b c)\|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 60
+bb2:=((b^2-2*a*c)*x+b*c)/(a*(4*a*c-b^2)*(a*x^2+b*x+c))+(2*c)/(4*a*c-b^2)*t1.2
+--R
+--R   (4)
+--R                                                   +---------+
+--R                                                   |        2
+--R          2   2                  2      (2a x + b)\|4a c - b
+--R       (4a c x  + 4a b c x + 4a c )atan(----------------------)
+--R                                                       2
+--R                                               4a c - b
+--R     + 
+--R                              +---------+
+--R                   2          |        2
+--R       ((- 2a c + b )x + b c)\|4a c - b
+--R  /
+--R                                                          +---------+
+--R         3     2 2  2      2         3       2 2      2   |        2
+--R     ((4a c - a b )x  + (4a b c - a b )x + 4a c  - a b c)\|4a c - b
+--R                                                     Type: Expression Integer
+--E
+
+--S 61     14:274 Schaums and Axiom agree
+cc1:=aa.1-bb1
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.275~~~~~$\displaystyle
+\int{\frac{x^m~dx}{(ax^2+bx+c)^n}}$}
+$$
+\begin{array}{lr}
+\displaystyle\int{\frac{x^m}{(ax^2+bx+c)^n}}=
+&amp;\displaystyle-\frac{x^{m-1}}{(2n-m-1)a(ax^2+bx+c)^{n-1}}\\
+&amp;\\
+&amp;\displaystyle+\frac{(m-1)c}{(2n-m-1)a}\int{\frac{x^{m-2}}{(ax^2+bx+2)^n}}\\
+&amp;\\
+&amp;\displaystyle-\frac{(n-m)b}{(2n-m-1)a}\int{\frac{x^{m-1}}{(ax^2+bx+c)^n}}
+\end{array}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 62     14:275 Axiom cannot compute this integral
+aa:=integrate(x^m/(a*x^2+b*x+c)^n,x)
+--R 
+--R
+--R           x           m
+--I         ++          %N
+--I   (1)   |   ------------------ d%N
+--R        ++                 2  n
+--I             (c + %N b + %N a)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+@
+
+\section{\cite{1}:14.276~~~~~$\displaystyle
+\int{\frac{x^{2n-1}~dx}{(ax^2+bx+c)^n}}$}
+$$\begin{array}{lr}
+\displaystyle\int{\frac{x^{2n-1}}{(ax^2+bx+c)^n}}=
+&amp;\displaystyle\frac{1}{a}\int{\frac{x^{2n-3}}{(ax^2+bx+c)^{n-1}}}\\
+&amp;\\
+&amp;\displaystyle-\frac{c}{a}\int{\frac{x^{2n-3}}{(ax^2+bx+c)^n}}\\
+&amp;\\
+&amp;\displaystyle-\frac{b}{a}\int{\frac{x^{2n-2}}{(ax^2+bx+c)^n}}
+\end{array}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 63     14:276 Axiom cannot compute this integral
+aa:=integrate(x^(2*n-1)/(a*x^2+b*x+c)^n,x)
+--R 
+--R
+--R           x        2n - 1
+--I         ++       %N
+--I   (1)   |   ------------------ d%N
+--R        ++                 2  n
+--I             (c + %N b + %N a)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+@
+
+\section{\cite{1}:14.277~~~~~$\displaystyle
+\int{\frac{dx}{x(ax^2+bx+c)^2}}$}
+$$\begin{array}{lr}
+\displaystyle\int{\frac{1}{x(ax^2+bx+c)^2}}=
+&amp;\displaystyle\frac{1}{2c(ax^2+bx+2)}\\
+&amp;\\
+&amp;\displaystyle-\frac{b}{2c}\int{\frac{1}{(ax^2+bx+c)^2}}\\
+&amp;\\
+&amp;\displaystyle+\frac{1}{c}\int{\frac{1}{x(ax^2+bx+c)}}
+\end{array}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 64
+aa:=integrate(1/(x*(a*x^2+b*x+c)^2),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R               2         3  2        2     4           2    3
+--R           ((6a b c - a b )x  + (6a b c - b )x + 6a b c  - b c)
+--R        *
+--R           log
+--R                                               +-----------+
+--R                     2 2                    2  |          2         2        2
+--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R                + 
+--R                              3
+--R                  - 4a b c + b
+--R             /
+--R                   2
+--R                a x  + b x + c
+--R       + 
+--R                     2       2  2                3         2    2
+--R               ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
+--R            *
+--R                      2
+--R               log(a x  + b x + c)
+--R           + 
+--R                 2        2  2               3         2     2
+--R             ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x)
+--R           + 
+--R                              2     2
+--R             - 2a b c x + 4a c  - 2b c
+--R        *
+--R            +-----------+
+--R            |          2
+--R           \|- 4a c + b
+--R    /
+--R                                                                  +-----------+
+--R           2 3       2 2  2          3     3 2         4     2 3  |          2
+--R       ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|- 4a c + b
+--R     ,
+--R
+--R                  2          3  2           2      4            2     3
+--R           ((- 12a b c + 2a b )x  + (- 12a b c + 2b )x - 12a b c  + 2b c)
+--R        *
+--R                           +---------+
+--R                           |        2
+--R                (2a x + b)\|4a c - b
+--R           atan(----------------------)
+--R                               2
+--R                       4a c - b
+--R       + 
+--R                     2       2  2                3         2    2
+--R               ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
+--R            *
+--R                      2
+--R               log(a x  + b x + c)
+--R           + 
+--R                 2        2  2               3         2     2
+--R             ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x)
+--R           + 
+--R                              2     2
+--R             - 2a b c x + 4a c  - 2b c
+--R        *
+--R            +---------+
+--R            |        2
+--R           \|4a c - b
+--R    /
+--R                                                                  +---------+
+--R           2 3       2 2  2          3     3 2         4     2 3  |        2
+--R       ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|4a c - b
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+
+--S 65
+t1:=integrate(1/(a*x^2+b*x+c)^2,x)
+--R 
+--R
+--R   (2)
+--R   [
+--R              2 2
+--R           (2a x  + 2a b x + 2a c)
+--R        *
+--R           log
+--R                                               +-----------+
+--R                     2 2                    2  |          2       2        2
+--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R                + 
+--R                            3
+--R                  4a b c - b
+--R             /
+--R                   2
+--R                a x  + b x + c
+--R       + 
+--R                    +-----------+
+--R                    |          2
+--R         (2a x + b)\|- 4a c + b
+--R    /
+--R                                                        +-----------+
+--R           2       2  2              3         2    2   |          2
+--R       ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|- 4a c + b
+--R     ,
+--R                                           +---------+
+--R                                           |        2                +---------+
+--R       2 2                      (2a x + b)\|4a c - b                 |        2
+--R    (4a x  + 4a b x + 4a c)atan(----------------------) + (2a x + b)\|4a c - b
+--R                                               2
+--R                                       4a c - b
+--R    ----------------------------------------------------------------------------
+--R                                                             +---------+
+--R                2       2  2              3         2    2   |        2
+--R            ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|4a c - b
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 66
+t2:=integrate(1/(x*(a*x^2+b*x+c)),x)
+--R 
+--R
+--R   (3)
+--R   [
+--R           b
+--R        *
+--R           log
+--R                                               +-----------+
+--R                     2 2                    2  |          2         2        2
+--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R                + 
+--R                              3
+--R                  - 4a b c + b
+--R             /
+--R                   2
+--R                a x  + b x + c
+--R       + 
+--R                                           +-----------+
+--R                   2                       |          2
+--R         (- log(a x  + b x + c) + 2log(x))\|- 4a c + b
+--R    /
+--R          +-----------+
+--R          |          2
+--R       2c\|- 4a c + b
+--R     ,
+--R
+--R                              +---------+
+--R                              |        2
+--R                   (2a x + b)\|4a c - b
+--R         - 2b atan(----------------------)
+--R                                  2
+--R                          4a c - b
+--R       + 
+--R                                           +---------+
+--R                   2                       |        2
+--R         (- log(a x  + b x + c) + 2log(x))\|4a c - b
+--R    /
+--R          +---------+
+--R          |        2
+--R       2c\|4a c - b
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 67
+bb1:=1/(2*c*(a*x^2+b*x+c))-b/(2*c)*t1.1+1/c*t2.1
+--R 
+--R
+--R   (4)
+--R              2     2       2            2
+--R         (- 2a b c x  - 2a b c x - 2a b c )
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2       2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R              + 
+--R                          3
+--R                4a b c - b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R             2         3  2        2     4           2    3
+--R         ((4a b c - a b )x  + (4a b c - b )x + 4a b c  - b c)
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2         2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R              + 
+--R                            3
+--R                - 4a b c + b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R                   2       2  2                3         2    2
+--R             ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
+--R          *
+--R                    2
+--R             log(a x  + b x + c)
+--R         + 
+--R               2        2  2               3         2     2
+--R           ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x) - 2a b c x
+--R         + 
+--R               2     2
+--R           4a c  - 2b c
+--R      *
+--R          +-----------+
+--R          |          2
+--R         \|- 4a c + b
+--R  /
+--R                                                                +-----------+
+--R         2 3       2 2  2          3     3 2         4     2 3  |          2
+--R     ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 68
+bb2:=1/(2*c*(a*x^2+b*x+c))-b/(2*c)*t1.2+1/c*t2.1
+--R 
+--R
+--R   (5)
+--R                                                              +---------+
+--R             2         3  2        2     4           2    3   |        2
+--R         ((4a b c - a b )x  + (4a b c - b )x + 4a b c  - b c)\|4a c - b
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2         2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R              + 
+--R                            3
+--R                - 4a b c + b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R                                            +-----------+
+--R              2     2       2            2  |          2
+--R         (- 4a b c x  - 4a b c x - 4a b c )\|- 4a c + b
+--R      *
+--R                         +---------+
+--R                         |        2
+--R              (2a x + b)\|4a c - b
+--R         atan(----------------------)
+--R                             2
+--R                     4a c - b
+--R     + 
+--R                   2       2  2                3         2    2
+--R             ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
+--R          *
+--R                    2
+--R             log(a x  + b x + c)
+--R         + 
+--R               2        2  2               3         2     2
+--R           ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x) - 2a b c x
+--R         + 
+--R               2     2
+--R           4a c  - 2b c
+--R      *
+--R          +-----------+ +---------+
+--R          |          2  |        2
+--R         \|- 4a c + b  \|4a c - b
+--R  /
+--R                                                                  +-----------+
+--R           2 3       2 2  2          3     3 2         4     2 3  |          2
+--R       ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|- 4a c + b
+--R    *
+--R        +---------+
+--R        |        2
+--R       \|4a c - b
+--R                                                     Type: Expression Integer
+--E
+
+--S 69
+bb3:=1/(2*c*(a*x^2+b*x+c))-b/(2*c)*t1.1+1/c*t2.2
+--R 
+--R
+--R   (6)
+--R                                            +---------+
+--R              2     2       2            2  |        2
+--R         (- 2a b c x  - 2a b c x - 2a b c )\|4a c - b
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2       2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R              + 
+--R                          3
+--R                4a b c - b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R               2          3  2          2      4           2     3
+--R         ((- 8a b c + 2a b )x  + (- 8a b c + 2b )x - 8a b c  + 2b c)
+--R      *
+--R                                       +---------+
+--R          +-----------+                |        2
+--R          |          2      (2a x + b)\|4a c - b
+--R         \|- 4a c + b  atan(----------------------)
+--R                                           2
+--R                                   4a c - b
+--R     + 
+--R                   2       2  2                3         2    2
+--R             ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
+--R          *
+--R                    2
+--R             log(a x  + b x + c)
+--R         + 
+--R               2        2  2               3         2     2
+--R           ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x) - 2a b c x
+--R         + 
+--R               2     2
+--R           4a c  - 2b c
+--R      *
+--R          +-----------+ +---------+
+--R          |          2  |        2
+--R         \|- 4a c + b  \|4a c - b
+--R  /
+--R                                                                  +-----------+
+--R           2 3       2 2  2          3     3 2         4     2 3  |          2
+--R       ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|- 4a c + b
+--R    *
+--R        +---------+
+--R        |        2
+--R       \|4a c - b
+--R                                                     Type: Expression Integer
+--E
+
+--S 70
+bb4:=1/(2*c*(a*x^2+b*x+c))-b/(2*c)*t1.2+1/c*t2.2
+--R 
+--R
+--R   (7)
+--R                2          3  2           2      4            2     3
+--R         ((- 12a b c + 2a b )x  + (- 12a b c + 2b )x - 12a b c  + 2b c)
+--R      *
+--R                         +---------+
+--R                         |        2
+--R              (2a x + b)\|4a c - b
+--R         atan(----------------------)
+--R                             2
+--R                     4a c - b
+--R     + 
+--R                   2       2  2                3         2    2
+--R             ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
+--R          *
+--R                    2
+--R             log(a x  + b x + c)
+--R         + 
+--R               2        2  2               3         2     2
+--R           ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x) - 2a b c x
+--R         + 
+--R               2     2
+--R           4a c  - 2b c
+--R      *
+--R          +---------+
+--R          |        2
+--R         \|4a c - b
+--R  /
+--R                                                                +---------+
+--R         2 3       2 2  2          3     3 2         4     2 3  |        2
+--R     ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|4a c - b
+--R                                                     Type: Expression Integer
+--E
+
+--S 71
+cc1:=aa.1-bb1
+--R
+--R   (8)
+--R         a b
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2       2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R              + 
+--R                          3
+--R                4a b c - b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R         a b
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2         2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R              + 
+--R                            3
+--R                - 4a b c + b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R  /
+--R                   +-----------+
+--R          2    2   |          2
+--R     (4a c  - b c)\|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 72
+dd1:=expandLog cc1
+--R
+--R   (9)
+--R         a b
+--R      *
+--R         log
+--R                                           +-----------+
+--R                 2 2                    2  |          2       2        2
+--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R            + 
+--R                        3
+--R              4a b c - b
+--R     + 
+--R         a b
+--R      *
+--R         log
+--R                                           +-----------+
+--R                 2 2                    2  |          2         2        2
+--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R            + 
+--R                          3
+--R              - 4a b c + b
+--R     + 
+--R                     2
+--R       - 2a b log(a x  + b x + c)
+--R  /
+--R                   +-----------+
+--R          2    2   |          2
+--R     (4a c  - b c)\|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 73     14:277 Schaums and Axiom differ by a constant
+ee1:=complexNormalize dd1
+--R
+--R                        3      2 2
+--R           a b log(- 16a c + 4a b )
+--R   (10)  ---------------------------
+--R                       +-----------+
+--R              2    2   |          2
+--R         (4a c  - b c)\|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.278~~~~~$\displaystyle
+\int{\frac{dx}{x^2(ax^2+bx+c)^2}}$}
+$$\begin{array}{lr}
+\displaystyle\int{\frac{1}{x^2(ax^2+bx+c)^2}}=
+&amp;\displaystyle-\frac{1}{cx(ax^2+bx+c)}\\
+&amp;\\
+&amp;\displaystyle-\frac{3a}{c}\int{\frac{1}{(ax^2+bx+c)^2}}\\
+&amp;\\
+&amp;\displaystyle-\frac{2b}{c}\int{\frac{1}{x(ax^2+bx+c)^2}}
+\end{array}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 74
+aa:=integrate(1/(x^2*(a*x^2+b*x+c)^2),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R                3 2     2 2       4  3      2   2       3     5  2
+--R             (6a c  - 6a b c + a b )x  + (6a b c  - 6a b c + b )x
+--R           + 
+--R                2 3       2 2    4
+--R             (6a c  - 6a b c  + b c)x
+--R        *
+--R           log
+--R                                               +-----------+
+--R                     2 2                    2  |          2         2        2
+--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R                + 
+--R                              3
+--R                  - 4a b c + b
+--R             /
+--R                   2
+--R                a x  + b x + c
+--R       + 
+--R                   2         3  3        2     4  2          2    3
+--R               ((4a b c - a b )x  + (4a b c - b )x  + (4a b c  - b c)x)
+--R            *
+--R                      2
+--R               log(a x  + b x + c)
+--R           + 
+--R                     2          3  3          2      4  2            2     3
+--R               ((- 8a b c + 2a b )x  + (- 8a b c + 2b )x  + (- 8a b c  + 2b c)x)
+--R            *
+--R               log(x)
+--R           + 
+--R                  2 2       2   2            2     3          3    2 2
+--R             (- 6a c  + 2a b c)x  + (- 7a b c  + 2b c)x - 4a c  + b c
+--R        *
+--R            +-----------+
+--R            |          2
+--R           \|- 4a c + b
+--R    /
+--R                                                                   +-----------+
+--R           2 4      2 3  3          4    3 3  2        5    2 4    |          2
+--R       ((4a c  - a b c )x  + (4a b c  - b c )x  + (4a c  - b c )x)\|- 4a c + b
+--R     ,
+--R
+--R                   3 2      2 2        4  3         2   2        3      5  2
+--R             (- 12a c  + 12a b c - 2a b )x  + (- 12a b c  + 12a b c - 2b )x
+--R           + 
+--R                   2 3        2 2     4
+--R             (- 12a c  + 12a b c  - 2b c)x
+--R        *
+--R                           +---------+
+--R                           |        2
+--R                (2a x + b)\|4a c - b
+--R           atan(----------------------)
+--R                               2
+--R                       4a c - b
+--R       + 
+--R                   2         3  3        2     4  2          2    3
+--R               ((4a b c - a b )x  + (4a b c - b )x  + (4a b c  - b c)x)
+--R            *
+--R                      2
+--R               log(a x  + b x + c)
+--R           + 
+--R                     2          3  3          2      4  2            2     3
+--R               ((- 8a b c + 2a b )x  + (- 8a b c + 2b )x  + (- 8a b c  + 2b c)x)
+--R            *
+--R               log(x)
+--R           + 
+--R                  2 2       2   2            2     3          3    2 2
+--R             (- 6a c  + 2a b c)x  + (- 7a b c  + 2b c)x - 4a c  + b c
+--R        *
+--R            +---------+
+--R            |        2
+--R           \|4a c - b
+--R    /
+--R                                                                   +---------+
+--R           2 4      2 3  3          4    3 3  2        5    2 4    |        2
+--R       ((4a c  - a b c )x  + (4a b c  - b c )x  + (4a c  - b c )x)\|4a c - b
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+
+--S 75
+t1:=integrate(1/(a*x^2+b*x+c)^2,x)
+--R 
+--R
+--R   (2)
+--R   [
+--R              2 2
+--R           (2a x  + 2a b x + 2a c)
+--R        *
+--R           log
+--R                                               +-----------+
+--R                     2 2                    2  |          2       2        2
+--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R                + 
+--R                            3
+--R                  4a b c - b
+--R             /
+--R                   2
+--R                a x  + b x + c
+--R       + 
+--R                    +-----------+
+--R                    |          2
+--R         (2a x + b)\|- 4a c + b
+--R    /
+--R                                                        +-----------+
+--R           2       2  2              3         2    2   |          2
+--R       ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|- 4a c + b
+--R     ,
+--R                                           +---------+
+--R                                           |        2                +---------+
+--R       2 2                      (2a x + b)\|4a c - b                 |        2
+--R    (4a x  + 4a b x + 4a c)atan(----------------------) + (2a x + b)\|4a c - b
+--R                                               2
+--R                                       4a c - b
+--R    ----------------------------------------------------------------------------
+--R                                                             +---------+
+--R                2       2  2              3         2    2   |        2
+--R            ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|4a c - b
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 76
+t2:=integrate(1/(x*(a*x^2+b*x+c)^2),x)
+--R 
+--R
+--R   (3)
+--R   [
+--R               2         3  2        2     4           2    3
+--R           ((6a b c - a b )x  + (6a b c - b )x + 6a b c  - b c)
+--R        *
+--R           log
+--R                                               +-----------+
+--R                     2 2                    2  |          2         2        2
+--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R                + 
+--R                              3
+--R                  - 4a b c + b
+--R             /
+--R                   2
+--R                a x  + b x + c
+--R       + 
+--R                     2       2  2                3         2    2
+--R               ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
+--R            *
+--R                      2
+--R               log(a x  + b x + c)
+--R           + 
+--R                 2        2  2               3         2     2
+--R             ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x)
+--R           + 
+--R                              2     2
+--R             - 2a b c x + 4a c  - 2b c
+--R        *
+--R            +-----------+
+--R            |          2
+--R           \|- 4a c + b
+--R    /
+--R                                                                  +-----------+
+--R           2 3       2 2  2          3     3 2         4     2 3  |          2
+--R       ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|- 4a c + b
+--R     ,
+--R
+--R                  2          3  2           2      4            2     3
+--R           ((- 12a b c + 2a b )x  + (- 12a b c + 2b )x - 12a b c  + 2b c)
+--R        *
+--R                           +---------+
+--R                           |        2
+--R                (2a x + b)\|4a c - b
+--R           atan(----------------------)
+--R                               2
+--R                       4a c - b
+--R       + 
+--R                     2       2  2                3         2    2
+--R               ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
+--R            *
+--R                      2
+--R               log(a x  + b x + c)
+--R           + 
+--R                 2        2  2               3         2     2
+--R             ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x)
+--R           + 
+--R                              2     2
+--R             - 2a b c x + 4a c  - 2b c
+--R        *
+--R            +---------+
+--R            |        2
+--R           \|4a c - b
+--R    /
+--R                                                                  +---------+
+--R           2 3       2 2  2          3     3 2         4     2 3  |        2
+--R       ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|4a c - b
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 77
+bb1:=-1/(c*x*(a*x^2+b*x+c))-((3*a)/c)*t1.1-(2*b)/c*t2.1
+--R 
+--R
+--R   (4)
+--R              3 2 3     2   2 2     2 3
+--R         (- 6a c x  - 6a b c x  - 6a c x)
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2       2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R              + 
+--R                          3
+--R                4a b c - b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R               2 2       4  3          3     5  2          2 2    4
+--R         ((- 6a b c + a b )x  + (- 6a b c + b )x  + (- 6a b c  + b c)x)
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2         2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R              + 
+--R                            3
+--R                - 4a b c + b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R                 2         3  3        2     4  2          2    3
+--R             ((4a b c - a b )x  + (4a b c - b )x  + (4a b c  - b c)x)
+--R          *
+--R                    2
+--R             log(a x  + b x + c)
+--R         + 
+--R                   2          3  3          2      4  2            2     3
+--R             ((- 8a b c + 2a b )x  + (- 8a b c + 2b )x  + (- 8a b c  + 2b c)x)
+--R          *
+--R             log(x)
+--R         + 
+--R                2 2       2   2            2     3          3    2 2
+--R           (- 6a c  + 2a b c)x  + (- 7a b c  + 2b c)x - 4a c  + b c
+--R      *
+--R          +-----------+
+--R          |          2
+--R         \|- 4a c + b
+--R  /
+--R                                                                 +-----------+
+--R         2 4      2 3  3          4    3 3  2        5    2 4    |          2
+--R     ((4a c  - a b c )x  + (4a b c  - b c )x  + (4a c  - b c )x)\|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 78
+bb2:=-1/(c*x*(a*x^2+b*x+c))-((3*a)/c)*t1.2-(2*b)/c*t2.1
+--R 
+--R
+--R   (5)
+--R               2 2       4  3          3     5  2          2 2    4
+--R         ((- 6a b c + a b )x  + (- 6a b c + b )x  + (- 6a b c  + b c)x)
+--R      *
+--R          +---------+
+--R          |        2
+--R         \|4a c - b
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2         2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R              + 
+--R                            3
+--R                - 4a b c + b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R                                             +-----------+
+--R               3 2 3      2   2 2      2 3   |          2
+--R         (- 12a c x  - 12a b c x  - 12a c x)\|- 4a c + b
+--R      *
+--R                         +---------+
+--R                         |        2
+--R              (2a x + b)\|4a c - b
+--R         atan(----------------------)
+--R                             2
+--R                     4a c - b
+--R     + 
+--R                 2         3  3        2     4  2          2    3
+--R             ((4a b c - a b )x  + (4a b c - b )x  + (4a b c  - b c)x)
+--R          *
+--R                    2
+--R             log(a x  + b x + c)
+--R         + 
+--R                   2          3  3          2      4  2            2     3
+--R             ((- 8a b c + 2a b )x  + (- 8a b c + 2b )x  + (- 8a b c  + 2b c)x)
+--R          *
+--R             log(x)
+--R         + 
+--R                2 2       2   2            2     3          3    2 2
+--R           (- 6a c  + 2a b c)x  + (- 7a b c  + 2b c)x - 4a c  + b c
+--R      *
+--R          +-----------+ +---------+
+--R          |          2  |        2
+--R         \|- 4a c + b  \|4a c - b
+--R  /
+--R                                                                   +-----------+
+--R           2 4      2 3  3          4    3 3  2        5    2 4    |          2
+--R       ((4a c  - a b c )x  + (4a b c  - b c )x  + (4a c  - b c )x)\|- 4a c + b
+--R    *
+--R        +---------+
+--R        |        2
+--R       \|4a c - b
+--R                                                     Type: Expression Integer
+--E
+
+--S 79
+bb3:=-1/(c*x*(a*x^2+b*x+c))-((3*a)/c)*t1.1-(2*b)/c*t2.2
+--R 
+--R
+--R   (6)
+--R                                          +---------+
+--R              3 2 3     2   2 2     2 3   |        2
+--R         (- 6a c x  - 6a b c x  - 6a c x)\|4a c - b
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2       2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R              + 
+--R                          3
+--R                4a b c - b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R              2 2        4  3         3      5  2         2 2     4
+--R         ((12a b c - 2a b )x  + (12a b c - 2b )x  + (12a b c  - 2b c)x)
+--R      *
+--R                                       +---------+
+--R          +-----------+                |        2
+--R          |          2      (2a x + b)\|4a c - b
+--R         \|- 4a c + b  atan(----------------------)
+--R                                           2
+--R                                   4a c - b
+--R     + 
+--R                 2         3  3        2     4  2          2    3
+--R             ((4a b c - a b )x  + (4a b c - b )x  + (4a b c  - b c)x)
+--R          *
+--R                    2
+--R             log(a x  + b x + c)
+--R         + 
+--R                   2          3  3          2      4  2            2     3
+--R             ((- 8a b c + 2a b )x  + (- 8a b c + 2b )x  + (- 8a b c  + 2b c)x)
+--R          *
+--R             log(x)
+--R         + 
+--R                2 2       2   2            2     3          3    2 2
+--R           (- 6a c  + 2a b c)x  + (- 7a b c  + 2b c)x - 4a c  + b c
+--R      *
+--R          +-----------+ +---------+
+--R          |          2  |        2
+--R         \|- 4a c + b  \|4a c - b
+--R  /
+--R                                                                   +-----------+
+--R           2 4      2 3  3          4    3 3  2        5    2 4    |          2
+--R       ((4a c  - a b c )x  + (4a b c  - b c )x  + (4a c  - b c )x)\|- 4a c + b
+--R    *
+--R        +---------+
+--R        |        2
+--R       \|4a c - b
+--R                                                     Type: Expression Integer
+--E
+
+--S 80
+bb4:=-1/(c*x*(a*x^2+b*x+c))-((3*a)/c)*t1.2-(2*b)/c*t2.2
+--R 
+--R
+--R   (7)
+--R                 3 2      2 2        4  3         2   2        3      5  2
+--R           (- 12a c  + 12a b c - 2a b )x  + (- 12a b c  + 12a b c - 2b )x
+--R         + 
+--R                 2 3        2 2     4
+--R           (- 12a c  + 12a b c  - 2b c)x
+--R      *
+--R                         +---------+
+--R                         |        2
+--R              (2a x + b)\|4a c - b
+--R         atan(----------------------)
+--R                             2
+--R                     4a c - b
+--R     + 
+--R                 2         3  3        2     4  2          2    3
+--R             ((4a b c - a b )x  + (4a b c - b )x  + (4a b c  - b c)x)
+--R          *
+--R                    2
+--R             log(a x  + b x + c)
+--R         + 
+--R                   2          3  3          2      4  2            2     3
+--R             ((- 8a b c + 2a b )x  + (- 8a b c + 2b )x  + (- 8a b c  + 2b c)x)
+--R          *
+--R             log(x)
+--R         + 
+--R                2 2       2   2            2     3          3    2 2
+--R           (- 6a c  + 2a b c)x  + (- 7a b c  + 2b c)x - 4a c  + b c
+--R      *
+--R          +---------+
+--R          |        2
+--R         \|4a c - b
+--R  /
+--R                                                                 +---------+
+--R         2 4      2 3  3          4    3 3  2        5    2 4    |        2
+--R     ((4a c  - a b c )x  + (4a b c  - b c )x  + (4a c  - b c )x)\|4a c - b
+--R                                                     Type: Expression Integer
+--E
+
+--S 81
+cc1:=aa.1-bb1
+--R
+--R   (8)
+--R           2
+--R         6a
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2       2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R              + 
+--R                          3
+--R                4a b c - b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R           2
+--R         6a
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2         2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R              + 
+--R                            3
+--R                - 4a b c + b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R  /
+--R                   +-----------+
+--R          2    2   |          2
+--R     (4a c  - b c)\|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 82
+dd1:=expandLog cc1
+--R
+--R   (9)
+--R           2
+--R         6a
+--R      *
+--R         log
+--R                                           +-----------+
+--R                 2 2                    2  |          2       2        2
+--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R            + 
+--R                        3
+--R              4a b c - b
+--R     + 
+--R           2
+--R         6a
+--R      *
+--R         log
+--R                                           +-----------+
+--R                 2 2                    2  |          2         2        2
+--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R            + 
+--R                          3
+--R              - 4a b c + b
+--R     + 
+--R            2       2
+--R       - 12a log(a x  + b x + c)
+--R  /
+--R                   +-----------+
+--R          2    2   |          2
+--R     (4a c  - b c)\|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 83     14:278 Schaums and Axiom differ by a constant
+ee1:=complexNormalize dd1
+--R
+--R             2         3      2 2
+--R           6a log(- 16a c + 4a b )
+--R   (10)  ---------------------------
+--R                       +-----------+
+--R              2    2   |          2
+--R         (4a c  - b c)\|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.279~~~~~$\displaystyle
+\int{\frac{dx}{x^m(ax^2+bx+c)^n}}$}
+$$\begin{array}{lr}
+\displaystyle\int{\frac{1}{x^m(ax^2+bx+c)^n}}=
+&amp;\displaystyle-\frac{1}{(m-1)cx^{m-1}(ax^2+bx+c)^{n-1}}\\
+&amp;\\
+&amp;\displaystyle-\frac{(m+2n-3)a}{(m-1)c}\int{\frac{1}{x^{m-2}(ax^2+bx+c)^n}}\\
+&amp;\\
+&amp;\displaystyle-\frac{(m+n-2)b}{(m-1)c}\int{\frac{1}{x^{m-1}(ax^2+bx+c)^n}}
+\end{array}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 84     14:279 Axiom cannot compute this integral
+aa:=integrate(1/(x^m*(a*x^2+b*x+c)^n),x)
+--R 
+--R
+--R           x
+--R         ++            1
+--I   (1)   |   --------------------- d%N
+--R        ++     m              2  n
+--I             %N (c + %N b + %N a)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 p71
+\end{thebibliography}
+\end{document}
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diff --git a/src/axiom-website/CATS/schaum13.input.pamphlet b/src/axiom-website/CATS/schaum13.input.pamphlet
new file mode 100644
index 0000000..678e41c
--- /dev/null
+++ b/src/axiom-website/CATS/schaum13.input.pamphlet
@@ -0,0 +1,5196 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum13.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.280~~~~~$\displaystyle
+\int{\frac{dx}{\sqrt{ax^2+bx+c}}}$}
+$$\int{\frac{1}{\sqrt{ax^2+bx+c}}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{1}{\sqrt{a}}\ln\left(2\sqrt{a}\sqrt{ax^2+bx+c}+2ax+b\right)\\
+\\
+\displaystyle
+-\frac{1}{\sqrt{-a}}\sin{-1}\left(\frac{2ax+b}{\sqrt{b^2-4ac}}\right)\\
+\\
+\displaystyle
+\frac{1}{\sqrt{a}}\sinh^{-1}\left(\frac{2ax+b}{\sqrt{4ac-b^2}}\right)
+\end{array}
+\right.
+$$
+&lt;&lt;*&gt;&gt;=
+)spool schaum13.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1
+aa:=integrate(1/sqrt(a*x^2+b*x+c),x)
+--R
+--R   (1)
+--R   [
+--R       log
+--R                                 +--------------+
+--R                 +-+ +-+         |   2                   +-+
+--R              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R            + 
+--R                     2             +-+
+--R              (- 2a x  - b x - 2c)\|a
+--R         /
+--R                  +--------------+
+--R              +-+ |   2
+--R            2\|c \|a x  + b x + c  - b x - 2c
+--R    /
+--R        +-+
+--R       \|a
+--R     ,
+--R                 +--------------+
+--R           +---+ |   2               +---+ +-+
+--R          \|- a \|a x  + b x + c  - \|- a \|c
+--R    2atan(------------------------------------)
+--R                           a x
+--R    -------------------------------------------]
+--R                        +---+
+--R                       \|- a
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+
+--S 2
+bb1:=1/sqrt(a)*log(2*sqrt(a)*sqrt(a*x^2+b*x+c)+2*a*x+b)
+--R
+--R                  +--------------+
+--R              +-+ |   2
+--R        log(2\|a \|a x  + b x + c  + 2a x + b)
+--R   (2)  --------------------------------------
+--R                          +-+
+--R                         \|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3
+bb2:=-1/sqrt(-a)*asin((2*a*x+b)/sqrt(b^2-4*a*c))
+--R
+--R                  2a x + b
+--R          asin(--------------)
+--R                +-----------+
+--R                |          2
+--R               \|- 4a c + b
+--R   (3)  - --------------------
+--R                  +---+
+--R                 \|- a
+--R                                                     Type: Expression Integer
+--E
+
+--S 4
+bb3:=1/sqrt(a)*asinh((2*a*x+b)/sqrt(4*a*c-b^2))
+--R
+--R                2a x + b
+--R        asinh(------------)
+--R               +---------+
+--R               |        2
+--R              \|4a c - b
+--R   (4)  -------------------
+--R                 +-+
+--R                \|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 5
+cc1:=bb1-aa.1
+--R
+--R   (5)
+--R                 +--------------+
+--R             +-+ |   2
+--R       log(2\|a \|a x  + b x + c  + 2a x + b)
+--R     + 
+--R       -
+--R          log
+--R                                    +--------------+
+--R                    +-+ +-+         |   2                   +-+
+--R                 (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R               + 
+--R                        2             +-+
+--R                 (- 2a x  - b x - 2c)\|a
+--R            /
+--R                     +--------------+
+--R                 +-+ |   2
+--R               2\|c \|a x  + b x + c  - b x - 2c
+--R  /
+--R      +-+
+--R     \|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 6
+cc2:=bb1-aa.2
+--R
+--R   (6)
+--R                       +--------------+
+--R        +---+      +-+ |   2
+--R       \|- a log(2\|a \|a x  + b x + c  + 2a x + b)
+--R     + 
+--R                          +--------------+
+--R                    +---+ |   2               +---+ +-+
+--R           +-+     \|- a \|a x  + b x + c  - \|- a \|c
+--R       - 2\|a atan(------------------------------------)
+--R                                    a x
+--R  /
+--R      +---+ +-+
+--R     \|- a \|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 7
+cc3:=bb2-aa.1
+--R
+--R   (7)
+--R       -
+--R             +---+
+--R            \|- a
+--R         *
+--R            log
+--R                                      +--------------+
+--R                      +-+ +-+         |   2                   +-+
+--R                   (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R                 + 
+--R                          2             +-+
+--R                   (- 2a x  - b x - 2c)\|a
+--R              /
+--R                       +--------------+
+--R                   +-+ |   2
+--R                 2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R          +-+        2a x + b
+--R       - \|a asin(--------------)
+--R                   +-----------+
+--R                   |          2
+--R                  \|- 4a c + b
+--R  /
+--R      +---+ +-+
+--R     \|- a \|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 8
+cc4:=bb2-aa.2
+--R
+--R                       +--------------+
+--R                 +---+ |   2               +---+ +-+
+--R                \|- a \|a x  + b x + c  - \|- a \|c             2a x + b
+--R        - 2atan(------------------------------------) - asin(--------------)
+--R                                 a x                          +-----------+
+--R                                                              |          2
+--R                                                             \|- 4a c + b
+--R   (8)  --------------------------------------------------------------------
+--R                                        +---+
+--R                                       \|- a
+--R                                                     Type: Expression Integer
+--E
+
+--S 9
+cc5:=bb3-aa.1
+--R
+--R   (9)
+--R       -
+--R          log
+--R                                    +--------------+
+--R                    +-+ +-+         |   2                   +-+
+--R                 (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R               + 
+--R                        2             +-+
+--R                 (- 2a x  - b x - 2c)\|a
+--R            /
+--R                     +--------------+
+--R                 +-+ |   2
+--R               2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R               2a x + b
+--R       asinh(------------)
+--R              +---------+
+--R              |        2
+--R             \|4a c - b
+--R  /
+--R      +-+
+--R     \|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 10
+cc6:=bb3-aa.2
+--R
+--R   (10)
+--R                      +--------------+
+--R                +---+ |   2               +---+ +-+
+--R       +-+     \|- a \|a x  + b x + c  - \|- a \|c      +---+        2a x + b
+--R   - 2\|a atan(------------------------------------) + \|- a asinh(------------)
+--R                                a x                                 +---------+
+--R                                                                    |        2
+--R                                                                   \|4a c - b
+--R   -----------------------------------------------------------------------------
+--R                                      +---+ +-+
+--R                                     \|- a \|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 11
+dd1:=simplifyLog cc1
+--R
+--R   (11)
+--R     log
+--R                                                  +--------------+
+--R                         +-+                 +-+  |   2
+--R            ((4a x + 2b)\|c  + (- 2b x - 4c)\|a )\|a x  + b x + c
+--R          + 
+--R                 2              +-+ +-+         2              2
+--R            (4a x  + 4b x + 4c)\|a \|c  - 2a b x  + (- 4a c - b )x - 2b c
+--R       /
+--R                               +--------------+
+--R               +-+ +-+         |   2                   +-+
+--R            (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R          + 
+--R                   2             +-+
+--R            (- 2a x  - b x - 2c)\|a
+--R  /
+--R      +-+
+--R     \|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 12     14:280 Schaums and Axiom differ by a constant
+ee1:=ratDenom dd1
+--R
+--R                      +-+     +-+
+--R          +-+    - 2a\|c  + b\|a
+--R         \|a log(----------------)
+--R                         a
+--R   (12)  -------------------------
+--R                     a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.281~~~~~$\displaystyle
+\int{\frac{x~dx}{\sqrt{ax^2+bx+c}}}$}
+$$\int{\frac{x}{\sqrt{ax^2+bx+c}}}=
+\frac{\sqrt{ax^2+bx+c}}{a}-\frac{b}{2a}\int{\frac{1}{\sqrt{ax^2+bx+c}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 11
+aa:=integrate(x/sqrt(a*x^2+b*x+c),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R                   +--------------+
+--R               +-+ |   2               2
+--R           (2b\|c \|a x  + b x + c  - b x - 2b c)
+--R        *
+--R           log
+--R                                     +--------------+
+--R                     +-+ +-+         |   2                   +-+
+--R                  (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
+--R                + 
+--R                         2             +-+
+--R                  (- 2a x  - b x - 2c)\|a
+--R             /
+--R                      +--------------+
+--R                  +-+ |   2
+--R                2\|c \|a x  + b x + c  - b x - 2c
+--R       + 
+--R                    +--------------+
+--R                +-+ |   2                   2         +-+ +-+
+--R         - 2b x\|a \|a x  + b x + c  + (4a x  + 2b x)\|a \|c
+--R    /
+--R                  +--------------+
+--R          +-+ +-+ |   2                                +-+
+--R       4a\|a \|c \|a x  + b x + c  + (- 2a b x - 4a c)\|a
+--R     ,
+--R
+--R                     +--------------+
+--R                 +-+ |   2               2
+--R           (- 2b\|c \|a x  + b x + c  + b x + 2b c)
+--R        *
+--R                       +--------------+
+--R                 +---+ |   2               +---+ +-+
+--R                \|- a \|a x  + b x + c  - \|- a \|c
+--R           atan(------------------------------------)
+--R                                 a x
+--R       + 
+--R                     +--------------+
+--R               +---+ |   2                   2        +---+ +-+
+--R         - b x\|- a \|a x  + b x + c  + (2a x  + b x)\|- a \|c
+--R    /
+--R                    +--------------+
+--R          +---+ +-+ |   2                               +---+
+--R       2a\|- a \|c \|a x  + b x + c  + (- a b x - 2a c)\|- a
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+
+--S 12
+t1:=integrate(1/sqrt(a*x^2+b*x+c),x)
+--R
+--R   (2)
+--R   [
+--R       log
+--R                                 +--------------+
+--R                 +-+ +-+         |   2                   +-+
+--R              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R            + 
+--R                     2             +-+
+--R              (- 2a x  - b x - 2c)\|a
+--R         /
+--R                  +--------------+
+--R              +-+ |   2
+--R            2\|c \|a x  + b x + c  - b x - 2c
+--R    /
+--R        +-+
+--R       \|a
+--R     ,
+--R                 +--------------+
+--R           +---+ |   2               +---+ +-+
+--R          \|- a \|a x  + b x + c  - \|- a \|c
+--R    2atan(------------------------------------)
+--R                           a x
+--R    -------------------------------------------]
+--R                        +---+
+--R                       \|- a
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 13
+bb1:=sqrt(a*x^2+b*x+c)/a-b/(2*a)*t1.1
+--R
+--R   (3)
+--R       -
+--R            b
+--R         *
+--R            log
+--R                                      +--------------+
+--R                      +-+ +-+         |   2                   +-+
+--R                   (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R                 + 
+--R                          2             +-+
+--R                   (- 2a x  - b x - 2c)\|a
+--R              /
+--R                       +--------------+
+--R                   +-+ |   2
+--R                 2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R             +--------------+
+--R         +-+ |   2
+--R       2\|a \|a x  + b x + c
+--R  /
+--R        +-+
+--R     2a\|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 14
+bb2:=sqrt(a*x^2+b*x+c)/a-b/(2*a)*t1.2
+--R
+--R   (4)
+--R                   +--------------+
+--R             +---+ |   2               +---+ +-+           +--------------+
+--R            \|- a \|a x  + b x + c  - \|- a \|c      +---+ |   2
+--R   - b atan(------------------------------------) + \|- a \|a x  + b x + c
+--R                             a x
+--R   ------------------------------------------------------------------------
+--R                                      +---+
+--R                                    a\|- a
+--R                                                     Type: Expression Integer
+--E
+
+--S 15
+cc1:=bb1-aa.1
+--R
+--R   (5)
+--R                   +--------------+
+--R               +-+ |   2               2
+--R         (- 2b\|c \|a x  + b x + c  + b x + 2b c)
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                   +--------------+
+--R               +-+ |   2               2
+--R         (- 2b\|c \|a x  + b x + c  + b x + 2b c)
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                +--------------+
+--R            +-+ |   2                          +-+ +-+
+--R       - 4c\|a \|a x  + b x + c  + (2b x + 4c)\|a \|c
+--R  /
+--R                +--------------+
+--R        +-+ +-+ |   2                                +-+
+--R     4a\|a \|c \|a x  + b x + c  + (- 2a b x - 4a c)\|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 16
+cc2:=bb1-aa.2
+--R
+--R   (6)
+--R                         +--------------+
+--R               +---+ +-+ |   2                2          +---+
+--R         (- 2b\|- a \|c \|a x  + b x + c  + (b x + 2b c)\|- a )
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                     +--------------+
+--R             +-+ +-+ |   2                   2          +-+
+--R         (4b\|a \|c \|a x  + b x + c  + (- 2b x - 4b c)\|a )
+--R      *
+--R                     +--------------+
+--R               +---+ |   2               +---+ +-+
+--R              \|- a \|a x  + b x + c  - \|- a \|c
+--R         atan(------------------------------------)
+--R                               a x
+--R     + 
+--R                      +--------------+
+--R            +---+ +-+ |   2                          +---+ +-+ +-+
+--R       - 4c\|- a \|a \|a x  + b x + c  + (2b x + 4c)\|- a \|a \|c
+--R  /
+--R                      +--------------+
+--R        +---+ +-+ +-+ |   2                                +---+ +-+
+--R     4a\|- a \|a \|c \|a x  + b x + c  + (- 2a b x - 4a c)\|- a \|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 17
+cc3:=bb2-aa.1
+--R
+--R   (7)
+--R                         +--------------+
+--R               +---+ +-+ |   2                2          +---+
+--R         (- 2b\|- a \|c \|a x  + b x + c  + (b x + 2b c)\|- a )
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                       +--------------+
+--R               +-+ +-+ |   2                 2          +-+
+--R         (- 4b\|a \|c \|a x  + b x + c  + (2b x + 4b c)\|a )
+--R      *
+--R                     +--------------+
+--R               +---+ |   2               +---+ +-+
+--R              \|- a \|a x  + b x + c  - \|- a \|c
+--R         atan(------------------------------------)
+--R                               a x
+--R     + 
+--R                      +--------------+
+--R            +---+ +-+ |   2                          +---+ +-+ +-+
+--R       - 4c\|- a \|a \|a x  + b x + c  + (2b x + 4c)\|- a \|a \|c
+--R  /
+--R                      +--------------+
+--R        +---+ +-+ +-+ |   2                                +---+ +-+
+--R     4a\|- a \|a \|c \|a x  + b x + c  + (- 2a b x - 4a c)\|- a \|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 18
+cc4:=bb2-aa.2
+--R
+--R             +--------------+
+--R             |   2                         +-+
+--R        - 2c\|a x  + b x + c  + (b x + 2c)\|c
+--R   (8)  --------------------------------------
+--R               +--------------+
+--R           +-+ |   2
+--R        2a\|c \|a x  + b x + c  - a b x - 2a c
+--R                                                     Type: Expression Integer
+--E
+
+--S 19     14:281 Schaums and Axiom differ by a constant
+dd1:=ratDenom cc4
+--R
+--R           +-+
+--R          \|c
+--R   (9)  - ----
+--R            a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.282~~~~~$\displaystyle
+\int{\frac{x^2dx}{\sqrt{ax^2+bx+c}}}$}
+$$\int{\frac{x^2}{\sqrt{ax^2+bx+c}}}=
+\frac{2ax-3b}{4a^2}\sqrt{ax^2+bx+c}+\frac{3b^2-4ac}{8a^2}
+\int{\frac{1}{\sqrt{ax^2+bx+c}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 19
+aa:=integrate(x^2/sqrt(a*x^2+b*x+c),x)
+--R
+--R   (1)
+--R   [
+--R                                                      +--------------+
+--R                            3          2      2   +-+ |   2
+--R             ((16a b c - 12b )x + 32a c  - 24b c)\|c \|a x  + b x + c
+--R           + 
+--R                 2 2       2      4  2             2      3           3      2 2
+--R           (- 16a c  + 8a b c + 3b )x  + (- 32a b c  + 24b c)x - 32a c  + 24b c
+--R        *
+--R           log
+--R                                     +--------------+
+--R                     +-+ +-+         |   2                   +-+
+--R                  (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
+--R                + 
+--R                         2             +-+
+--R                  (- 2a x  - b x - 2c)\|a
+--R             /
+--R                      +--------------+
+--R                  +-+ |   2
+--R                2\|c \|a x  + b x + c  - b x - 2c
+--R       + 
+--R                  2        2  3                 3  2           2      2     +-+
+--R           ((- 16a c - 4a b )x  + (- 8a b c + 6b )x  + (- 32a c  + 24b c)x)\|a
+--R        *
+--R            +--------------+
+--R            |   2
+--R           \|a x  + b x + c
+--R       + 
+--R                  2   4       2        2  3                 3  2
+--R               16a b x  + (32a c - 8a b )x  + (24a b c - 18b )x
+--R             + 
+--R                     2      2
+--R               (32a c  - 24b c)x
+--R        *
+--R            +-+ +-+
+--R           \|a \|c
+--R    /
+--R                                   +--------------+
+--R             2         2   +-+ +-+ |   2
+--R         (32a b x + 64a c)\|a \|c \|a x  + b x + c
+--R       + 
+--R                3      2 2  2      2           2 2  +-+
+--R         ((- 32a c - 8a b )x  - 64a b c x - 64a c )\|a
+--R     ,
+--R
+--R                                                        +--------------+
+--R                              3          2      2   +-+ |   2
+--R             ((- 16a b c + 12b )x - 32a c  + 24b c)\|c \|a x  + b x + c
+--R           + 
+--R                 2 2       2      4  2           2      3           3      2 2
+--R             (16a c  - 8a b c - 3b )x  + (32a b c  - 24b c)x + 32a c  - 24b c
+--R        *
+--R                       +--------------+
+--R                 +---+ |   2               +---+ +-+
+--R                \|- a \|a x  + b x + c  - \|- a \|c
+--R           atan(------------------------------------)
+--R                                 a x
+--R       + 
+--R                 2        2  3                 3  2           2      2     +---+
+--R           ((- 8a c - 2a b )x  + (- 4a b c + 3b )x  + (- 16a c  + 12b c)x)\|- a
+--R        *
+--R            +--------------+
+--R            |   2
+--R           \|a x  + b x + c
+--R       + 
+--R              2   4       2        2  3                3  2         2      2
+--R           (8a b x  + (16a c - 4a b )x  + (12a b c - 9b )x  + (16a c  - 12b c)x)
+--R        *
+--R            +---+ +-+
+--R           \|- a \|c
+--R    /
+--R                                     +--------------+
+--R             2         2   +---+ +-+ |   2
+--R         (16a b x + 32a c)\|- a \|c \|a x  + b x + c
+--R       + 
+--R                3      2 2  2      2           2 2  +---+
+--R         ((- 16a c - 4a b )x  - 32a b c x - 32a c )\|- a
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 20
+t1:=integrate(1/sqrt(a*x^2+b*x+c),x)
+--R
+--R   (2)
+--R   [
+--R       log
+--R                                 +--------------+
+--R                 +-+ +-+         |   2                   +-+
+--R              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R            + 
+--R                     2             +-+
+--R              (- 2a x  - b x - 2c)\|a
+--R         /
+--R                  +--------------+
+--R              +-+ |   2
+--R            2\|c \|a x  + b x + c  - b x - 2c
+--R    /
+--R        +-+
+--R       \|a
+--R     ,
+--R                 +--------------+
+--R           +---+ |   2               +---+ +-+
+--R          \|- a \|a x  + b x + c  - \|- a \|c
+--R    2atan(------------------------------------)
+--R                           a x
+--R    -------------------------------------------]
+--R                        +---+
+--R                       \|- a
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 21
+bb1:=(2*a*x-3*b)/(4*a^2)*sqrt(a*x^2+b*x+c)+(3*b^2-4*a*c)/(8*a^2)*t1.1
+--R
+--R   (3)
+--R                     2
+--R         (- 4a c + 3b )
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                       +--------------+
+--R                   +-+ |   2
+--R       (4a x - 6b)\|a \|a x  + b x + c
+--R  /
+--R       2 +-+
+--R     8a \|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 22
+bb2:=(2*a*x-3*b)/(4*a^2)*sqrt(a*x^2+b*x+c)+(3*b^2-4*a*c)/(8*a^2)*t1.2
+--R
+--R   (4)
+--R                                 +--------------+
+--R                           +---+ |   2               +---+ +-+
+--R                   2      \|- a \|a x  + b x + c  - \|- a \|c
+--R       (- 4a c + 3b )atan(------------------------------------)
+--R                                           a x
+--R     + 
+--R                         +--------------+
+--R                   +---+ |   2
+--R       (2a x - 3b)\|- a \|a x  + b x + c
+--R  /
+--R       2 +---+
+--R     4a \|- a
+--R                                                     Type: Expression Integer
+--E
+
+--S 23
+cc1:=aa.1-bb1
+--R
+--R   (5)
+--R                                                    +--------------+
+--R                          3          2      2   +-+ |   2
+--R           ((16a b c - 12b )x + 32a c  - 24b c)\|c \|a x  + b x + c
+--R         + 
+--R               2 2       2      4  2             2      3           3      2 2
+--R         (- 16a c  + 8a b c + 3b )x  + (- 32a b c  + 24b c)x - 32a c  + 24b c
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                                                    +--------------+
+--R                          3          2      2   +-+ |   2
+--R           ((16a b c - 12b )x + 32a c  - 24b c)\|c \|a x  + b x + c
+--R         + 
+--R               2 2       2      4  2             2      3           3      2 2
+--R         (- 16a c  + 8a b c + 3b )x  + (- 32a b c  + 24b c)x - 32a c  + 24b c
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                                +--------------+
+--R             2           2  +-+ |   2
+--R       (- 24b c x - 48b c )\|a \|a x  + b x + c
+--R     + 
+--R                     3  2      2           2  +-+ +-+
+--R       ((24a b c + 6b )x  + 48b c x + 48b c )\|a \|c
+--R  /
+--R                                 +--------------+
+--R           2         2   +-+ +-+ |   2
+--R       (32a b x + 64a c)\|a \|c \|a x  + b x + c
+--R     + 
+--R              3      2 2  2      2           2 2  +-+
+--R       ((- 32a c - 8a b )x  - 64a b c x - 64a c )\|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 24
+cc2:=aa.2-bb1
+--R
+--R   (6)
+--R                                                          +--------------+
+--R                          3          2      2   +---+ +-+ |   2
+--R           ((16a b c - 12b )x + 32a c  - 24b c)\|- a \|c \|a x  + b x + c
+--R         + 
+--R                     2 2       2      4  2             2      3           3
+--R               (- 16a c  + 8a b c + 3b )x  + (- 32a b c  + 24b c)x - 32a c
+--R             + 
+--R                  2 2
+--R               24b c
+--R          *
+--R              +---+
+--R             \|- a
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                                                          +--------------+
+--R                            3          2      2   +-+ +-+ |   2
+--R           ((- 32a b c + 24b )x - 64a c  + 48b c)\|a \|c \|a x  + b x + c
+--R         + 
+--R                     2 2        2      4  2           2      3           3
+--R                 (32a c  - 16a b c - 6b )x  + (64a b c  - 48b c)x + 64a c
+--R               + 
+--R                      2 2
+--R                 - 48b c
+--R          *
+--R              +-+
+--R             \|a
+--R      *
+--R                     +--------------+
+--R               +---+ |   2               +---+ +-+
+--R              \|- a \|a x  + b x + c  - \|- a \|c
+--R         atan(------------------------------------)
+--R                               a x
+--R     + 
+--R                                      +--------------+
+--R             2           2  +---+ +-+ |   2
+--R       (- 24b c x - 48b c )\|- a \|a \|a x  + b x + c
+--R     + 
+--R                     3  2      2           2  +---+ +-+ +-+
+--R       ((24a b c + 6b )x  + 48b c x + 48b c )\|- a \|a \|c
+--R  /
+--R                                       +--------------+
+--R           2         2   +---+ +-+ +-+ |   2
+--R       (32a b x + 64a c)\|- a \|a \|c \|a x  + b x + c
+--R     + 
+--R              3      2 2  2      2           2 2  +---+ +-+
+--R       ((- 32a c - 8a b )x  - 64a b c x - 64a c )\|- a \|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 25
+cc3:=aa.2-bb1
+--R
+--R   (7)
+--R                                                          +--------------+
+--R                          3          2      2   +---+ +-+ |   2
+--R           ((16a b c - 12b )x + 32a c  - 24b c)\|- a \|c \|a x  + b x + c
+--R         + 
+--R                     2 2       2      4  2             2      3           3
+--R               (- 16a c  + 8a b c + 3b )x  + (- 32a b c  + 24b c)x - 32a c
+--R             + 
+--R                  2 2
+--R               24b c
+--R          *
+--R              +---+
+--R             \|- a
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                                                          +--------------+
+--R                            3          2      2   +-+ +-+ |   2
+--R           ((- 32a b c + 24b )x - 64a c  + 48b c)\|a \|c \|a x  + b x + c
+--R         + 
+--R                     2 2        2      4  2           2      3           3
+--R                 (32a c  - 16a b c - 6b )x  + (64a b c  - 48b c)x + 64a c
+--R               + 
+--R                      2 2
+--R                 - 48b c
+--R          *
+--R              +-+
+--R             \|a
+--R      *
+--R                     +--------------+
+--R               +---+ |   2               +---+ +-+
+--R              \|- a \|a x  + b x + c  - \|- a \|c
+--R         atan(------------------------------------)
+--R                               a x
+--R     + 
+--R                                      +--------------+
+--R             2           2  +---+ +-+ |   2
+--R       (- 24b c x - 48b c )\|- a \|a \|a x  + b x + c
+--R     + 
+--R                     3  2      2           2  +---+ +-+ +-+
+--R       ((24a b c + 6b )x  + 48b c x + 48b c )\|- a \|a \|c
+--R  /
+--R                                       +--------------+
+--R           2         2   +---+ +-+ +-+ |   2
+--R       (32a b x + 64a c)\|- a \|a \|c \|a x  + b x + c
+--R     + 
+--R              3      2 2  2      2           2 2  +---+ +-+
+--R       ((- 32a c - 8a b )x  - 64a b c x - 64a c )\|- a \|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 26
+cc4:=aa.2-bb2
+--R
+--R   (8)
+--R                            +--------------+
+--R             2           2  |   2
+--R       (- 12b c x - 24b c )\|a x  + b x + c
+--R     + 
+--R                     3  2      2           2  +-+
+--R       ((12a b c + 3b )x  + 24b c x + 24b c )\|c
+--R  /
+--R                             +--------------+
+--R           2         2   +-+ |   2                    3      2 2  2      2
+--R       (16a b x + 32a c)\|c \|a x  + b x + c  + (- 16a c - 4a b )x  - 32a b c x
+--R     + 
+--R            2 2
+--R       - 32a c
+--R                                                     Type: Expression Integer
+--E
+
+--S 27     14:282 Schaums and Axiom differ by a constant
+dd4:=ratDenom cc4
+--R
+--R             +-+
+--R          3b\|c
+--R   (9)  - ------
+--R              2
+--R            4a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.283~~~~~$\displaystyle
+\int{\frac{dx}{x\sqrt{ax^2+bx+c}}}$}
+$$\int{\frac{1}{x\sqrt{ax^2+bx+c}}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+-\frac{1}{\sqrt{c}}
+\ln\left(\frac{2\sqrt{c}{\sqrt{ax^2+bx+c}}+bx+2c}{x}\right)\\
+\\
+\displaystyle
+\frac{1}{\sqrt{-c}}\sin^{-1}\left(\frac{bx+2c}{|x|\sqrt{b^2-4ac}}\right)\\
+\\
+\displaystyle
+-\frac{1}{\sqrt{c}}\sinh^{-1}\left(\frac{bx+2c}{|x|\sqrt{4ac-b^2}}\right)
+\end{array}
+\right.
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 27
+aa:=integrate(1/(x*sqrt(a*x^2+b*x+c)),x)
+--R
+--R                  +--------------+
+--R              +-+ |   2
+--R            2\|c \|a x  + b x + c  - b x - 2c
+--R        log(---------------------------------)
+--R                            x
+--R   (1)  --------------------------------------
+--R                          +-+
+--R                         \|c
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 28
+bb1:=-1/sqrt(c)*log((2*sqrt(c)*sqrt(a*x^2+b*x+c)+b*x+2*c)/x)
+--R
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  + b x + 2c
+--R          log(---------------------------------)
+--R                              x
+--R   (2)  - --------------------------------------
+--R                            +-+
+--R                           \|c
+--R                                                     Type: Expression Integer
+--E
+
+--S 29
+bb2:=1/sqrt(-c)*asin((b*x+2*c)/(x*sqrt(b^2-4*a*c)))
+--R
+--R                 b x + 2c
+--R        asin(---------------)
+--R               +-----------+
+--R               |          2
+--R             x\|- 4a c + b
+--R   (3)  ---------------------
+--R                 +---+
+--R                \|- c
+--R                                                     Type: Expression Integer
+--E
+
+--S 30
+bb3:=-1/sqrt(c)*asinh((b*x+2*c)/(x*sqrt(4*a*c-b^2)))
+--R
+--R                   b x + 2c
+--R          asinh(-------------)
+--R                  +---------+
+--R                  |        2
+--R                x\|4a c - b
+--R   (4)  - --------------------
+--R                   +-+
+--R                  \|c
+--R                                                     Type: Expression Integer
+--E
+
+--S 31
+cc1:=aa-bb1
+--R
+--R   (5)
+--R                 +--------------+
+--R             +-+ |   2
+--R           2\|c \|a x  + b x + c  + b x + 2c
+--R       log(---------------------------------)
+--R                           x
+--R     + 
+--R                 +--------------+
+--R             +-+ |   2
+--R           2\|c \|a x  + b x + c  - b x - 2c
+--R       log(---------------------------------)
+--R                           x
+--R  /
+--R      +-+
+--R     \|c
+--R                                                     Type: Expression Integer
+--E
+
+--S 32
+cc2:=aa-bb2
+--R
+--R   (6)
+--R                   +--------------+
+--R               +-+ |   2
+--R    +---+    2\|c \|a x  + b x + c  - b x - 2c     +-+         b x + 2c
+--R   \|- c log(---------------------------------) - \|c asin(---------------)
+--R                             x                               +-----------+
+--R                                                             |          2
+--R                                                           x\|- 4a c + b
+--R   ------------------------------------------------------------------------
+--R                                   +---+ +-+
+--R                                  \|- c \|c
+--R                                                     Type: Expression Integer
+--E
+
+--S 33
+cc3:=aa-bb3
+--R
+--R                  +--------------+
+--R              +-+ |   2
+--R            2\|c \|a x  + b x + c  - b x - 2c             b x + 2c
+--R        log(---------------------------------) + asinh(-------------)
+--R                            x                            +---------+
+--R                                                         |        2
+--R                                                       x\|4a c - b
+--R   (7)  -------------------------------------------------------------
+--R                                      +-+
+--R                                     \|c
+--R                                                     Type: Expression Integer
+--E
+
+--S 34
+dd1:=expandLog cc1
+--R
+--R   (8)
+--R                 +--------------+
+--R             +-+ |   2
+--R       log(2\|c \|a x  + b x + c  + b x + 2c)
+--R     + 
+--R                 +--------------+
+--R             +-+ |   2
+--R       log(2\|c \|a x  + b x + c  - b x - 2c) - 2log(x)
+--R  /
+--R      +-+
+--R     \|c
+--R                                                     Type: Expression Integer
+--E
+
+--S 35
+ee1:=ratDenom dd1
+--R
+--R   (9)
+--R                     +--------------+
+--R        +-+      +-+ |   2
+--R       \|c log(2\|c \|a x  + b x + c  + b x + 2c)
+--R     + 
+--R                     +--------------+
+--R        +-+      +-+ |   2                                  +-+
+--R       \|c log(2\|c \|a x  + b x + c  - b x - 2c) - 2log(x)\|c
+--R  /
+--R     c
+--R                                                     Type: Expression Integer
+--E
+
+--S 36     14:283 Schaums and Axiom differ by a constant
+ff1:=complexNormalize ee1
+--R
+--R                     2  +-+
+--R         log(4a c - b )\|c
+--R   (10)  ------------------
+--R                  c
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.284~~~~~$\displaystyle
+\int{\frac{dx}{x^2\sqrt{ax^2+bx+c}}}$}
+$$\int{\frac{1}{x^2\sqrt{ax^2+bx+c}}}=
+-\frac{\sqrt{ax^2+bx+c}}{cx}-\frac{b}{2c}\int{\frac{1}{x\sqrt{ax^2+bx+c}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 37
+aa:=integrate(1/(x^2*sqrt(a*x^2+b*x+c)),x)
+--R
+--R   (1)
+--R                     +--------------+
+--R                 +-+ |   2                2 2
+--R         (- 4b x\|c \|a x  + b x + c  + 2b x  + 4b c x)
+--R      *
+--R                +--------------+
+--R                |   2                           +-+
+--R             2c\|a x  + b x + c  + (- b x - 2c)\|c
+--R         log(--------------------------------------)
+--R                              2c x
+--R     + 
+--R                       +--------------+
+--R                   +-+ |   2                         2  2              2
+--R       (2b x + 8c)\|c \|a x  + b x + c  + (- 8a c + b )x  - 6b c x - 8c
+--R  /
+--R          +--------------+
+--R       2  |   2                       2     2   +-+
+--R     8c x\|a x  + b x + c  + (- 4b c x  - 8c x)\|c
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 38
+t1:=integrate(1/(x*sqrt(a*x^2+b*x+c)),x)
+--R
+--R                  +--------------+
+--R              +-+ |   2
+--R            2\|c \|a x  + b x + c  - b x - 2c
+--R        log(---------------------------------)
+--R                            x
+--R   (2)  --------------------------------------
+--R                          +-+
+--R                         \|c
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 39
+bb:=-sqrt(a*x^2+b*x+c)/(c*x)-b/(2*c)*t1
+--R
+--R                        +--------------+
+--R                    +-+ |   2                                +--------------+
+--R                  2\|c \|a x  + b x + c  - b x - 2c      +-+ |   2
+--R        - b x log(---------------------------------) - 2\|c \|a x  + b x + c
+--R                                  x
+--R   (3)  ---------------------------------------------------------------------
+--R                                            +-+
+--R                                       2c x\|c
+--R                                                     Type: Expression Integer
+--E
+
+--S 40
+cc:=aa-bb
+--R
+--R   (4)
+--R               +--------------+
+--R               |   2                   2          +-+
+--R         (4b c\|a x  + b x + c  + (- 2b x - 4b c)\|c )
+--R      *
+--R                   +--------------+
+--R               +-+ |   2
+--R             2\|c \|a x  + b x + c  - b x - 2c
+--R         log(---------------------------------)
+--R                             x
+--R     + 
+--R                 +--------------+
+--R                 |   2                 2          +-+
+--R         (- 4b c\|a x  + b x + c  + (2b x + 4b c)\|c )
+--R      *
+--R                +--------------+
+--R                |   2                           +-+
+--R             2c\|a x  + b x + c  + (- b x - 2c)\|c
+--R         log(--------------------------------------)
+--R                              2c x
+--R     + 
+--R              +--------------+
+--R              |   2                2          +-+
+--R       - 2b c\|a x  + b x + c  + (b x + 2b c)\|c
+--R  /
+--R             +--------------+
+--R       2 +-+ |   2                  2      3
+--R     8c \|c \|a x  + b x + c  - 4b c x - 8c
+--R                                                     Type: Expression Integer
+--E
+
+--S 41
+dd:=expandLog cc
+--R
+--R   (5)
+--R               +--------------+
+--R               |   2                   2          +-+
+--R         (4b c\|a x  + b x + c  + (- 2b x - 4b c)\|c )
+--R      *
+--R                   +--------------+
+--R               +-+ |   2
+--R         log(2\|c \|a x  + b x + c  - b x - 2c)
+--R     + 
+--R                 +--------------+
+--R                 |   2                 2          +-+
+--R         (- 4b c\|a x  + b x + c  + (2b x + 4b c)\|c )
+--R      *
+--R                +--------------+
+--R                |   2                           +-+
+--R         log(2c\|a x  + b x + c  + (- b x - 2c)\|c )
+--R     + 
+--R                                          +--------------+
+--R                                          |   2
+--R       (4b c log(c) + 4b c log(2) - 2b c)\|a x  + b x + c
+--R     + 
+--R             2                       2                   2          +-+
+--R       ((- 2b x - 4b c)log(c) + (- 2b x - 4b c)log(2) + b x + 2b c)\|c
+--R  /
+--R             +--------------+
+--R       2 +-+ |   2                  2      3
+--R     8c \|c \|a x  + b x + c  - 4b c x - 8c
+--R                                                     Type: Expression Integer
+--E
+
+--S 42
+ee:=ratDenom dd
+--R
+--R   (6)
+--R                       +--------------+
+--R          +-+      +-+ |   2
+--R       2b\|c log(2\|c \|a x  + b x + c  - b x - 2c)
+--R     + 
+--R                      +--------------+
+--R            +-+       |   2                           +-+
+--R       - 2b\|c log(2c\|a x  + b x + c  + (- b x - 2c)\|c )
+--R     + 
+--R                                   +-+
+--R       (2b log(c) + 2b log(2) - b)\|c
+--R  /
+--R       2
+--R     4c
+--R                                                     Type: Expression Integer
+--E
+
+--S 43     14:284 Schaums and Axiom differ by a constant
+ff:=complexNormalize ee
+--R
+--R                                   +-+
+--R        (b log(c) + 2b log(2) - b)\|c
+--R   (7)  ------------------------------
+--R                        2
+--R                      4c
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.285~~~~~$\displaystyle
+\int{\sqrt{ax^2+bx+c}}~dx$}
+$$\int{\sqrt{ax^2+bx+c}}=
+\frac{(2ax+b)\sqrt{ax^2+bx+c}}{4a}+
+\frac{4ac-b^2}{8a}\int{\frac{1}{\sqrt{ax^2+bx+c}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 44
+aa:=integrate(sqrt(a*x^2+b*x+c),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R                                                    +--------------+
+--R                           3          2     2   +-+ |   2
+--R             ((16a b c - 4b )x + 32a c  - 8b c)\|c \|a x  + b x + c
+--R           + 
+--R                   2 2    4  2             2     3           3     2 2
+--R             (- 16a c  + b )x  + (- 32a b c  + 8b c)x - 32a c  + 8b c
+--R        *
+--R           log
+--R                                     +--------------+
+--R                     +-+ +-+         |   2                   +-+
+--R                  (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R                + 
+--R                         2             +-+
+--R                  (- 2a x  - b x - 2c)\|a
+--R             /
+--R                      +--------------+
+--R                  +-+ |   2
+--R                2\|c \|a x  + b x + c  - b x - 2c
+--R       + 
+--R                  2        2  3                  3  2           2     2     +-+
+--R           ((- 16a c - 4a b )x  + (- 40a b c - 2b )x  + (- 32a c  - 8b c)x)\|a
+--R        *
+--R            +--------------+
+--R            |   2
+--R           \|a x  + b x + c
+--R       + 
+--R                  2   4       2         2  3                3  2
+--R               16a b x  + (32a c + 24a b )x  + (56a b c + 6b )x
+--R             + 
+--R                     2     2
+--R               (32a c  + 8b c)x
+--R        *
+--R            +-+ +-+
+--R           \|a \|c
+--R    /
+--R                                   +--------------+
+--R                           +-+ +-+ |   2
+--R         (32a b x + 64a c)\|a \|c \|a x  + b x + c
+--R       + 
+--R                2        2  2                    2  +-+
+--R         ((- 32a c - 8a b )x  - 64a b c x - 64a c )\|a
+--R     ,
+--R
+--R                                                    +--------------+
+--R                           3          2     2   +-+ |   2
+--R             ((16a b c - 4b )x + 32a c  - 8b c)\|c \|a x  + b x + c
+--R           + 
+--R                   2 2    4  2             2     3           3     2 2
+--R             (- 16a c  + b )x  + (- 32a b c  + 8b c)x - 32a c  + 8b c
+--R        *
+--R                       +--------------+
+--R                 +---+ |   2               +---+ +-+
+--R                \|- a \|a x  + b x + c  - \|- a \|c
+--R           atan(------------------------------------)
+--R                                 a x
+--R       + 
+--R                 2        2  3                 3  2           2     2     +---+
+--R           ((- 8a c - 2a b )x  + (- 20a b c - b )x  + (- 16a c  - 4b c)x)\|- a
+--R        *
+--R            +--------------+
+--R            |   2
+--R           \|a x  + b x + c
+--R       + 
+--R              2   4       2         2  3                3  2         2     2
+--R           (8a b x  + (16a c + 12a b )x  + (28a b c + 3b )x  + (16a c  + 4b c)x)
+--R        *
+--R            +---+ +-+
+--R           \|- a \|c
+--R    /
+--R                                     +--------------+
+--R                           +---+ +-+ |   2
+--R         (16a b x + 32a c)\|- a \|c \|a x  + b x + c
+--R       + 
+--R                2        2  2                    2  +---+
+--R         ((- 16a c - 4a b )x  - 32a b c x - 32a c )\|- a
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+
+--S 45
+t1:=integrate(1/sqrt(a*x^2+b*x+c),x)
+--R
+--R   (2)
+--R   [
+--R       log
+--R                                 +--------------+
+--R                 +-+ +-+         |   2                   +-+
+--R              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R            + 
+--R                     2             +-+
+--R              (- 2a x  - b x - 2c)\|a
+--R         /
+--R                  +--------------+
+--R              +-+ |   2
+--R            2\|c \|a x  + b x + c  - b x - 2c
+--R    /
+--R        +-+
+--R       \|a
+--R     ,
+--R                 +--------------+
+--R           +---+ |   2               +---+ +-+
+--R          \|- a \|a x  + b x + c  - \|- a \|c
+--R    2atan(------------------------------------)
+--R                           a x
+--R    -------------------------------------------]
+--R                        +---+
+--R                       \|- a
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 46
+bb1:=((2*a*x+b)*sqrt(a*x^2+b*x+c))/(4*a)+(4*a*c-b^2)/(8*a)*t1.1
+--R
+--R   (3)
+--R                  2
+--R         (4a c - b )
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                       +--------------+
+--R                   +-+ |   2
+--R       (4a x + 2b)\|a \|a x  + b x + c
+--R  /
+--R        +-+
+--R     8a\|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 47
+bb2:=((2*a*x+b)*sqrt(a*x^2+b*x+c))/(4*a)+(4*a*c-b^2)/(8*a)*t1.2
+--R
+--R   (4)
+--R                              +--------------+
+--R                        +---+ |   2               +---+ +-+
+--R                2      \|- a \|a x  + b x + c  - \|- a \|c
+--R       (4a c - b )atan(------------------------------------)
+--R                                        a x
+--R     + 
+--R                        +--------------+
+--R                  +---+ |   2
+--R       (2a x + b)\|- a \|a x  + b x + c
+--R  /
+--R        +---+
+--R     4a\|- a
+--R                                                     Type: Expression Integer
+--E
+
+--S 48
+cc1:=aa.1-bb1
+--R
+--R   (5)
+--R                        +--------------+
+--R          2          2  |   2
+--R       (4b c x + 8b c )\|a x  + b x + c
+--R     + 
+--R                     3  2     2          2  +-+
+--R       ((- 4a b c - b )x  - 8b c x - 8b c )\|c
+--R  /
+--R                             +--------------+
+--R                         +-+ |   2                    2        2  2
+--R       (16a b x + 32a c)\|c \|a x  + b x + c  + (- 16a c - 4a b )x  - 32a b c x
+--R     + 
+--R              2
+--R       - 32a c
+--R                                                     Type: Expression Integer
+--E
+
+--S 49
+cc2:=aa.2-bb1
+--R
+--R   (6)
+--R                                                          +--------------+
+--R                           3          2     2   +---+ +-+ |   2
+--R           ((- 16a b c + 4b )x - 32a c  + 8b c)\|- a \|c \|a x  + b x + c
+--R         + 
+--R                2 2    4  2           2     3           3     2 2  +---+
+--R           ((16a c  - b )x  + (32a b c  - 8b c)x + 32a c  - 8b c )\|- a
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                                                       +--------------+
+--R                         3          2      2   +-+ +-+ |   2
+--R           ((32a b c - 8b )x + 64a c  - 16b c)\|a \|c \|a x  + b x + c
+--R         + 
+--R                  2 2     4  2             2      3           3      2 2  +-+
+--R           ((- 32a c  + 2b )x  + (- 64a b c  + 16b c)x - 64a c  + 16b c )\|a
+--R      *
+--R                     +--------------+
+--R               +---+ |   2               +---+ +-+
+--R              \|- a \|a x  + b x + c  - \|- a \|c
+--R         atan(------------------------------------)
+--R                               a x
+--R     + 
+--R                                   +--------------+
+--R          2           2  +---+ +-+ |   2
+--R       (8b c x + 16b c )\|- a \|a \|a x  + b x + c
+--R     + 
+--R                      3  2      2           2  +---+ +-+ +-+
+--R       ((- 8a b c - 2b )x  - 16b c x - 16b c )\|- a \|a \|c
+--R  /
+--R                                       +--------------+
+--R                         +---+ +-+ +-+ |   2
+--R       (32a b x + 64a c)\|- a \|a \|c \|a x  + b x + c
+--R     + 
+--R              2        2  2                    2  +---+ +-+
+--R       ((- 32a c - 8a b )x  - 64a b c x - 64a c )\|- a \|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 50
+cc3:=aa.1-bb2
+--R
+--R   (7)
+--R                                                        +--------------+
+--R                         3          2     2   +---+ +-+ |   2
+--R           ((16a b c - 4b )x + 32a c  - 8b c)\|- a \|c \|a x  + b x + c
+--R         + 
+--R                  2 2    4  2             2     3           3     2 2  +---+
+--R           ((- 16a c  + b )x  + (- 32a b c  + 8b c)x - 32a c  + 8b c )\|- a
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                                                         +--------------+
+--R                           3          2      2   +-+ +-+ |   2
+--R           ((- 32a b c + 8b )x - 64a c  + 16b c)\|a \|c \|a x  + b x + c
+--R         + 
+--R                2 2     4  2           2      3           3      2 2  +-+
+--R           ((32a c  - 2b )x  + (64a b c  - 16b c)x + 64a c  - 16b c )\|a
+--R      *
+--R                     +--------------+
+--R               +---+ |   2               +---+ +-+
+--R              \|- a \|a x  + b x + c  - \|- a \|c
+--R         atan(------------------------------------)
+--R                               a x
+--R     + 
+--R                                   +--------------+
+--R          2           2  +---+ +-+ |   2
+--R       (8b c x + 16b c )\|- a \|a \|a x  + b x + c
+--R     + 
+--R                      3  2      2           2  +---+ +-+ +-+
+--R       ((- 8a b c - 2b )x  - 16b c x - 16b c )\|- a \|a \|c
+--R  /
+--R                                       +--------------+
+--R                         +---+ +-+ +-+ |   2
+--R       (32a b x + 64a c)\|- a \|a \|c \|a x  + b x + c
+--R     + 
+--R              2        2  2                    2  +---+ +-+
+--R       ((- 32a c - 8a b )x  - 64a b c x - 64a c )\|- a \|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 51
+cc4:=aa.2-bb2
+--R
+--R   (8)
+--R                        +--------------+
+--R          2          2  |   2
+--R       (4b c x + 8b c )\|a x  + b x + c
+--R     + 
+--R                     3  2     2          2  +-+
+--R       ((- 4a b c - b )x  - 8b c x - 8b c )\|c
+--R  /
+--R                             +--------------+
+--R                         +-+ |   2                    2        2  2
+--R       (16a b x + 32a c)\|c \|a x  + b x + c  + (- 16a c - 4a b )x  - 32a b c x
+--R     + 
+--R              2
+--R       - 32a c
+--R                                                     Type: Expression Integer
+--E
+
+--S 52     14:285 Schaums and Axiom differ by a constant
+dd4:=ratDenom cc4
+--R
+--R          +-+
+--R        b\|c
+--R   (9)  -----
+--R          4a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.286~~~~~$\displaystyle
+\int{x\sqrt{ax^2+bx+c}}~dx$}
+$$
+\begin{array}{rl}
+\displaystyle
+\int{x\sqrt{ax^2+bx+c}}=&amp;\displaystyle\frac{(ax^2+bx+c)^{3/2}}{3a}\\
+&amp;\\
+&amp;\displaystyle-\frac{b(2ax+b)}{8a^2}\sqrt{ax^2+bx+c}\\
+&amp;\\
+&amp;\displaystyle-\frac{b(4ac-b^2)}{16a^2}\int{\frac{1}{\sqrt{ax^2+bx+c}}}
+\end{array}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 53
+aa:=integrate(x*sqrt(a*x^2+b*x+c),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R                     2   2        3       5  2          2 2      4
+--R                 (96a b c  + 48a b c - 18b )x  + (384a b c  - 96b c)x
+--R               + 
+--R                         3      3 2
+--R                 384a b c  - 96b c
+--R            *
+--R                    +--------------+
+--R                +-+ |   2
+--R               \|c \|a x  + b x + c
+--R           + 
+--R                    2 2 2        4      6  3
+--R             (- 144a b c  + 24a b c + 3b )x
+--R           + 
+--R                    2   3         3 2      5   2            2 3       4 2
+--R             (- 288a b c  - 144a b c  + 54b c)x  + (- 576a b c  + 144b c )x
+--R           + 
+--R                       4      3 3
+--R             - 384a b c  + 96b c
+--R        *
+--R           log
+--R                                     +--------------+
+--R                     +-+ +-+         |   2                   +-+
+--R                  (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
+--R                + 
+--R                         2             +-+
+--R                  (- 2a x  - b x - 2c)\|a
+--R             /
+--R                      +--------------+
+--R                  +-+ |   2
+--R                2\|c \|a x  + b x + c  - b x - 2c
+--R       + 
+--R                    3         2 3  5          3 2       2 2        4  4
+--R             (- 192a b c - 16a b )x  + (- 384a c  - 336a b c - 4a b )x
+--R           + 
+--R                     2   2        3      5  3
+--R             (- 1056a b c  - 16a b c + 6b )x
+--R           + 
+--R                    2 3         2 2      4   2              3      3 2
+--R             (- 768a c  - 288a b c  + 72b c)x  + (- 384a b c  + 96b c )x
+--R        *
+--R                +--------------+
+--R            +-+ |   2
+--R           \|a \|a x  + b x + c
+--R       + 
+--R                  4       3 2  6        3          2 3  5
+--R             (128a c + 96a b )x  + (672a b c + 120a b )x
+--R           + 
+--R                  3 2       2 2         4  4         2   2        3       5  3
+--R             (768a c  + 816a b c - 12a b )x  + (1632a b c  + 64a b c - 30b )x
+--R           + 
+--R                  2 3         2 2       4   2            3      3 2
+--R             (768a c  + 480a b c  - 120b c)x  + (384a b c  - 96b c )x
+--R        *
+--R            +-+ +-+
+--R           \|a \|c
+--R    /
+--R                 3        2 2  2        2             2 2  +-+ +-+
+--R           ((384a c + 288a b )x  + 1536a b c x + 1536a c )\|a \|c
+--R        *
+--R            +--------------+
+--R            |   2
+--R           \|a x  + b x + c
+--R       + 
+--R                    3         2 3  3           3 2       2 2   2        2   2
+--R             (- 576a b c - 48a b )x  + (- 1152a c  - 864a b c)x  - 2304a b c x
+--R           + 
+--R                    2 3
+--R             - 1536a c
+--R        *
+--R            +-+
+--R           \|a
+--R     ,
+--R
+--R                       2   2        3       5  2            2 2      4
+--R                 (- 96a b c  - 48a b c + 18b )x  + (- 384a b c  + 96b c)x
+--R               + 
+--R                           3      3 2
+--R                 - 384a b c  + 96b c
+--R            *
+--R                    +--------------+
+--R                +-+ |   2
+--R               \|c \|a x  + b x + c
+--R           + 
+--R                  2 2 2        4      6  3        2   3         3 2      5   2
+--R             (144a b c  - 24a b c - 3b )x  + (288a b c  + 144a b c  - 54b c)x
+--R           + 
+--R                    2 3       4 2             4      3 3
+--R             (576a b c  - 144b c )x + 384a b c  - 96b c
+--R        *
+--R                       +--------------+
+--R                 +---+ |   2               +---+ +-+
+--R                \|- a \|a x  + b x + c  - \|- a \|c
+--R           atan(------------------------------------)
+--R                                 a x
+--R       + 
+--R                   3        2 3  5          3 2       2 2        4  4
+--R             (- 96a b c - 8a b )x  + (- 192a c  - 168a b c - 2a b )x
+--R           + 
+--R                    2   2       3      5  3          2 3         2 2      4   2
+--R             (- 528a b c  - 8a b c + 3b )x  + (- 384a c  - 144a b c  + 36b c)x
+--R           + 
+--R                        3      3 2
+--R             (- 192a b c  + 48b c )x
+--R        *
+--R                  +--------------+
+--R            +---+ |   2
+--R           \|- a \|a x  + b x + c
+--R       + 
+--R                 4       3 2  6        3         2 3  5
+--R             (64a c + 48a b )x  + (336a b c + 60a b )x
+--R           + 
+--R                  3 2       2 2        4  4        2   2        3       5  3
+--R             (384a c  + 408a b c - 6a b )x  + (816a b c  + 32a b c - 15b )x
+--R           + 
+--R                  2 3         2 2      4   2            3      3 2
+--R             (384a c  + 240a b c  - 60b c)x  + (192a b c  - 48b c )x
+--R        *
+--R            +---+ +-+
+--R           \|- a \|c
+--R    /
+--R                 3        2 2  2       2            2 2  +---+ +-+
+--R           ((192a c + 144a b )x  + 768a b c x + 768a c )\|- a \|c
+--R        *
+--R            +--------------+
+--R            |   2
+--R           \|a x  + b x + c
+--R       + 
+--R                    3         2 3  3          3 2       2 2   2        2   2
+--R             (- 288a b c - 24a b )x  + (- 576a c  - 432a b c)x  - 1152a b c x
+--R           + 
+--R                   2 3
+--R             - 768a c
+--R        *
+--R            +---+
+--R           \|- a
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+
+--S 54
+t1:=integrate(1/sqrt(a*x^2+b*x+c),x)
+--R
+--R   (2)
+--R   [
+--R       log
+--R                                 +--------------+
+--R                 +-+ +-+         |   2                   +-+
+--R              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R            + 
+--R                     2             +-+
+--R              (- 2a x  - b x - 2c)\|a
+--R         /
+--R                  +--------------+
+--R              +-+ |   2
+--R            2\|c \|a x  + b x + c  - b x - 2c
+--R    /
+--R        +-+
+--R       \|a
+--R     ,
+--R                 +--------------+
+--R           +---+ |   2               +---+ +-+
+--R          \|- a \|a x  + b x + c  - \|- a \|c
+--R    2atan(------------------------------------)
+--R                           a x
+--R    -------------------------------------------]
+--R                        +---+
+--R                       \|- a
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 55
+bb1:=(a*x^2+b*x+c)^(3/2)/(3*a)-(b*(2*a*x+b))/(8*a^2)*sqrt(a*x^2+b*x+c)-(b*(4*a*c-b^2))/(16*a^2)*t1.1
+--R
+--R   (3)
+--R                        3
+--R         (- 12a b c + 3b )
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                                           +--------------+
+--R           2 2                      2  +-+ |   2
+--R       (16a x  + 4a b x + 16a c - 6b )\|a \|a x  + b x + c
+--R  /
+--R        2 +-+
+--R     48a \|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 56
+bb2:=(a*x^2+b*x+c)^(3/2)/(3*a)-(b*(2*a*x+b))/(8*a^2)*sqrt(a*x^2+b*x+c)-(b*(4*a*c-b^2))/(16*a^2)*t1.2
+--R
+--R   (4)
+--R                                    +--------------+
+--R                              +---+ |   2               +---+ +-+
+--R                      3      \|- a \|a x  + b x + c  - \|- a \|c
+--R       (- 12a b c + 3b )atan(------------------------------------)
+--R                                              a x
+--R     + 
+--R                                           +--------------+
+--R          2 2                     2  +---+ |   2
+--R       (8a x  + 2a b x + 8a c - 3b )\|- a \|a x  + b x + c
+--R  /
+--R        2 +---+
+--R     24a \|- a
+--R                                                     Type: Expression Integer
+--E
+
+--S 57
+cc1:=aa.1-bb1
+--R
+--R   (5)
+--R                   2   2        3       5  2          2 2      4              3
+--R               (96a b c  + 48a b c - 18b )x  + (384a b c  - 96b c)x + 384a b c
+--R             + 
+--R                    3 2
+--R               - 96b c
+--R          *
+--R                  +--------------+
+--R              +-+ |   2
+--R             \|c \|a x  + b x + c
+--R         + 
+--R                  2 2 2        4      6  3          2   3         3 2      5   2
+--R           (- 144a b c  + 24a b c + 3b )x  + (- 288a b c  - 144a b c  + 54b c)x
+--R         + 
+--R                    2 3       4 2             4      3 3
+--R           (- 576a b c  + 144b c )x - 384a b c  + 96b c
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                   2   2        3       5  2          2 2      4              3
+--R               (96a b c  + 48a b c - 18b )x  + (384a b c  - 96b c)x + 384a b c
+--R             + 
+--R                    3 2
+--R               - 96b c
+--R          *
+--R                  +--------------+
+--R              +-+ |   2
+--R             \|c \|a x  + b x + c
+--R         + 
+--R                  2 2 2        4      6  3          2   3         3 2      5   2
+--R           (- 144a b c  + 24a b c + 3b )x  + (- 288a b c  - 144a b c  + 54b c)x
+--R         + 
+--R                    2 3       4 2             4      3 3
+--R           (- 576a b c  + 144b c )x - 384a b c  + 96b c
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                2 3        2 2      4   2            3       3 2           4
+--R           (128a c  + 48a b c  - 36b c)x  + (512a b c  - 192b c )x + 512a c
+--R         + 
+--R                 2 3
+--R           - 192b c
+--R      *
+--R              +--------------+
+--R          +-+ |   2
+--R         \|a \|a x  + b x + c
+--R     + 
+--R                  2   2        3      5  3          2 3         2 2       4   2
+--R           (- 192a b c  + 56a b c + 6b )x  + (- 384a c  - 144a b c  + 108b c)x
+--R         + 
+--R                      3       3 2           4       2 3
+--R           (- 768a b c  + 288b c )x - 512a c  + 192b c
+--R      *
+--R          +-+ +-+
+--R         \|a \|c
+--R  /
+--R                                                               +--------------+
+--R             3        2 2  2        2             2 2  +-+ +-+ |   2
+--R       ((384a c + 288a b )x  + 1536a b c x + 1536a c )\|a \|c \|a x  + b x + c
+--R     + 
+--R                  3         2 3  3           3 2       2 2   2        2   2
+--R           (- 576a b c - 48a b )x  + (- 1152a c  - 864a b c)x  - 2304a b c x
+--R         + 
+--R                  2 3
+--R           - 1536a c
+--R      *
+--R          +-+
+--R         \|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 58
+cc2:=aa.2-bb1
+--R
+--R   (6)
+--R                   2   2        3       5  2          2 2      4              3
+--R               (96a b c  + 48a b c - 18b )x  + (384a b c  - 96b c)x + 384a b c
+--R             + 
+--R                    3 2
+--R               - 96b c
+--R          *
+--R                        +--------------+
+--R              +---+ +-+ |   2
+--R             \|- a \|c \|a x  + b x + c
+--R         + 
+--R                      2 2 2        4      6  3
+--R               (- 144a b c  + 24a b c + 3b )x
+--R             + 
+--R                      2   3         3 2      5   2            2 3       4 2
+--R               (- 288a b c  - 144a b c  + 54b c)x  + (- 576a b c  + 144b c )x
+--R             + 
+--R                         4      3 3
+--R               - 384a b c  + 96b c
+--R          *
+--R              +---+
+--R             \|- a
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                      2   2        3       5  2            2 2       4
+--R               (- 192a b c  - 96a b c + 36b )x  + (- 768a b c  + 192b c)x
+--R             + 
+--R                         3       3 2
+--R               - 768a b c  + 192b c
+--R          *
+--R                      +--------------+
+--R              +-+ +-+ |   2
+--R             \|a \|c \|a x  + b x + c
+--R         + 
+--R                    2 2 2        4      6  3
+--R               (288a b c  - 48a b c - 6b )x
+--R             + 
+--R                    2   3         3 2       5   2           2 3       4 2
+--R               (576a b c  + 288a b c  - 108b c)x  + (1152a b c  - 288b c )x
+--R             + 
+--R                       4       3 3
+--R               768a b c  - 192b c
+--R          *
+--R              +-+
+--R             \|a
+--R      *
+--R                     +--------------+
+--R               +---+ |   2               +---+ +-+
+--R              \|- a \|a x  + b x + c  - \|- a \|c
+--R         atan(------------------------------------)
+--R                               a x
+--R     + 
+--R                2 3        2 2      4   2            3       3 2           4
+--R           (128a c  + 48a b c  - 36b c)x  + (512a b c  - 192b c )x + 512a c
+--R         + 
+--R                 2 3
+--R           - 192b c
+--R      *
+--R                    +--------------+
+--R          +---+ +-+ |   2
+--R         \|- a \|a \|a x  + b x + c
+--R     + 
+--R                  2   2        3      5  3          2 3         2 2       4   2
+--R           (- 192a b c  + 56a b c + 6b )x  + (- 384a c  - 144a b c  + 108b c)x
+--R         + 
+--R                      3       3 2           4       2 3
+--R           (- 768a b c  + 288b c )x - 512a c  + 192b c
+--R      *
+--R          +---+ +-+ +-+
+--R         \|- a \|a \|c
+--R  /
+--R               3        2 2  2        2             2 2  +---+ +-+ +-+
+--R         ((384a c + 288a b )x  + 1536a b c x + 1536a c )\|- a \|a \|c
+--R      *
+--R          +--------------+
+--R          |   2
+--R         \|a x  + b x + c
+--R     + 
+--R                  3         2 3  3           3 2       2 2   2        2   2
+--R           (- 576a b c - 48a b )x  + (- 1152a c  - 864a b c)x  - 2304a b c x
+--R         + 
+--R                  2 3
+--R           - 1536a c
+--R      *
+--R          +---+ +-+
+--R         \|- a \|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 59
+cc3:=aa.1-bb2
+--R
+--R   (7)
+--R                   2   2        3       5  2          2 2      4              3
+--R               (96a b c  + 48a b c - 18b )x  + (384a b c  - 96b c)x + 384a b c
+--R             + 
+--R                    3 2
+--R               - 96b c
+--R          *
+--R                        +--------------+
+--R              +---+ +-+ |   2
+--R             \|- a \|c \|a x  + b x + c
+--R         + 
+--R                      2 2 2        4      6  3
+--R               (- 144a b c  + 24a b c + 3b )x
+--R             + 
+--R                      2   3         3 2      5   2            2 3       4 2
+--R               (- 288a b c  - 144a b c  + 54b c)x  + (- 576a b c  + 144b c )x
+--R             + 
+--R                         4      3 3
+--R               - 384a b c  + 96b c
+--R          *
+--R              +---+
+--R             \|- a
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                    2   2        3       5  2          2 2       4
+--R               (192a b c  + 96a b c - 36b )x  + (768a b c  - 192b c)x
+--R             + 
+--R                       3       3 2
+--R               768a b c  - 192b c
+--R          *
+--R                      +--------------+
+--R              +-+ +-+ |   2
+--R             \|a \|c \|a x  + b x + c
+--R         + 
+--R                      2 2 2        4      6  3
+--R               (- 288a b c  + 48a b c + 6b )x
+--R             + 
+--R                      2   3         3 2       5   2             2 3       4 2
+--R               (- 576a b c  - 288a b c  + 108b c)x  + (- 1152a b c  + 288b c )x
+--R             + 
+--R                         4       3 3
+--R               - 768a b c  + 192b c
+--R          *
+--R              +-+
+--R             \|a
+--R      *
+--R                     +--------------+
+--R               +---+ |   2               +---+ +-+
+--R              \|- a \|a x  + b x + c  - \|- a \|c
+--R         atan(------------------------------------)
+--R                               a x
+--R     + 
+--R                2 3        2 2      4   2            3       3 2           4
+--R           (128a c  + 48a b c  - 36b c)x  + (512a b c  - 192b c )x + 512a c
+--R         + 
+--R                 2 3
+--R           - 192b c
+--R      *
+--R                    +--------------+
+--R          +---+ +-+ |   2
+--R         \|- a \|a \|a x  + b x + c
+--R     + 
+--R                  2   2        3      5  3          2 3         2 2       4   2
+--R           (- 192a b c  + 56a b c + 6b )x  + (- 384a c  - 144a b c  + 108b c)x
+--R         + 
+--R                      3       3 2           4       2 3
+--R           (- 768a b c  + 288b c )x - 512a c  + 192b c
+--R      *
+--R          +---+ +-+ +-+
+--R         \|- a \|a \|c
+--R  /
+--R               3        2 2  2        2             2 2  +---+ +-+ +-+
+--R         ((384a c + 288a b )x  + 1536a b c x + 1536a c )\|- a \|a \|c
+--R      *
+--R          +--------------+
+--R          |   2
+--R         \|a x  + b x + c
+--R     + 
+--R                  3         2 3  3           3 2       2 2   2        2   2
+--R           (- 576a b c - 48a b )x  + (- 1152a c  - 864a b c)x  - 2304a b c x
+--R         + 
+--R                  2 3
+--R           - 1536a c
+--R      *
+--R          +---+ +-+
+--R         \|- a \|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 60
+cc4:=aa.2-bb2
+--R
+--R   (8)
+--R               2 3        2 2      4   2            3      3 2           4
+--R           (64a c  + 24a b c  - 18b c)x  + (256a b c  - 96b c )x + 256a c
+--R         + 
+--R                2 3
+--R           - 96b c
+--R      *
+--R          +--------------+
+--R          |   2
+--R         \|a x  + b x + c
+--R     + 
+--R                 2   2        3      5  3          2 3        2 2      4   2
+--R           (- 96a b c  + 28a b c + 3b )x  + (- 192a c  - 72a b c  + 54b c)x
+--R         + 
+--R                      3       3 2           4      2 3
+--R           (- 384a b c  + 144b c )x - 256a c  + 96b c
+--R      *
+--R          +-+
+--R         \|c
+--R  /
+--R                                                         +--------------+
+--R             3        2 2  2       2            2 2  +-+ |   2
+--R       ((192a c + 144a b )x  + 768a b c x + 768a c )\|c \|a x  + b x + c
+--R     + 
+--R            3         2 3  3          3 2       2 2   2        2   2        2 3
+--R     (- 288a b c - 24a b )x  + (- 576a c  - 432a b c)x  - 1152a b c x - 768a c
+--R                                                     Type: Expression Integer
+--E
+
+--S 61     14:286 Schaums and Axiom differ by a constant
+dd4:=ratDenom cc4
+--R
+--R                  2  +-+
+--R        (8a c - 3b )\|c
+--R   (9)  ----------------
+--R                 2
+--R              24a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.287~~~~~$\displaystyle
+\int{x^2\sqrt{ax^2+bx+c}}~dx$}
+$$\int{x^2\sqrt{ax^2+bx+c}}=
+\frac{6ax-5b}{24a^2}(ax^2+bx+c)^{3/2}+
+\frac{5b^2-4ac}{16a^2}\int{\sqrt{ax^2+bx+c}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 62
+aa:=integrate(x^2*sqrt(a*x^2+b*x+c),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R                       3   3        2 3 2        5        7  3
+--R                 (1536a b c  - 1920a b c  - 96a b c + 120b )x
+--R               + 
+--R                       3 4       2 2 3          4 2        6   2
+--R                 (3072a c  - 768a b c  - 4800a b c  + 1200b c)x
+--R               + 
+--R                       2   4           3 3        5 2          2 5          2 4
+--R                 (9216a b c  - 13824a b c  + 2880b c )x + 6144a c  - 9216a b c
+--R               + 
+--R                      4 3
+--R                 1920b c
+--R            *
+--R                    +--------------+
+--R                +-+ |   2
+--R               \|c \|a x  + b x + c
+--R           + 
+--R                    4 4        2 4 2         6       8  4
+--R             (- 768a c  + 1440a b c  - 288a b c - 15b )x
+--R           + 
+--R                     3   4        2 3 3         5 2       7   3
+--R             (- 6144a b c  + 7680a b c  + 384a b c  - 480b c)x
+--R           + 
+--R                     3 5        2 2 4          4 3        6 2  2
+--R             (- 6144a c  + 1536a b c  + 9600a b c  - 2400b c )x
+--R           + 
+--R                      2   5           3 4        5 3          2 6          2 5
+--R             (- 12288a b c  + 18432a b c  - 3840b c )x - 6144a c  + 9216a b c
+--R           + 
+--R                    4 4
+--R             - 1920b c
+--R        *
+--R           log
+--R                                     +--------------+
+--R                     +-+ +-+         |   2                   +-+
+--R                  (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
+--R                + 
+--R                         2             +-+
+--R                  (- 2a x  - b x - 2c)\|a
+--R             /
+--R                      +--------------+
+--R                  +-+ |   2
+--R                2\|c \|a x  + b x + c  - b x - 2c
+--R       + 
+--R                     5 2        4 2       3 4  7
+--R             (- 1536a c  - 2304a b c - 96a b )x
+--R           + 
+--R                      4   2        3 3       2 5  6
+--R             (- 12544a b c  - 3456a b c - 16a b )x
+--R           + 
+--R                      4 3         3 2 2      2 4         6  5
+--R             (- 13056a c  - 18240a b c  - 80a b c + 20a b )x
+--R           + 
+--R                      3   3       2 3 2        5       7  4
+--R             (- 31104a b c  + 480a b c  + 24a b c - 30b )x
+--R           + 
+--R                      3 4       2 2 3          4 2       6   3
+--R             (- 18432a c  + 768a b c  + 2816a b c  - 720b c)x
+--R           + 
+--R                     2   4           3 3        5 2  2
+--R             (- 7680a b c  + 11520a b c  - 2400b c )x
+--R           + 
+--R                     2 5          2 4        4 3
+--R             (- 6144a c  + 9216a b c  - 1920b c )x
+--R        *
+--R                +--------------+
+--R            +-+ |   2
+--R           \|a \|a x  + b x + c
+--R       + 
+--R                   5          4 3  8         5 2         4 2        3 4  7
+--R             (3072a b c + 768a b )x  + (6144a c  + 11264a b c + 896a b )x
+--R           + 
+--R                    4   2        3 3       2 5  6
+--R             (30208a b c  + 9984a b c - 32a b )x
+--R           + 
+--R                    4 3         3 2 2       2 4         6  5
+--R             (21504a c  + 31488a b c  - 320a b c + 80a b )x
+--R           + 
+--R                    3   3        2 3 2         5        7  4
+--R             (42624a b c  - 4896a b c  + 152a b c + 210b )x
+--R           + 
+--R                    3 4        2 2 3          4 2        6   3
+--R             (21504a c  - 2304a b c  - 6464a b c  + 1680b c)x
+--R           + 
+--R                    2   4           3 3        5 2  2
+--R             (10752a b c  - 16128a b c  + 3360b c )x
+--R           + 
+--R                   2 5          2 4        4 3
+--R             (6144a c  - 9216a b c  + 1920b c )x
+--R        *
+--R            +-+ +-+
+--R           \|a \|c
+--R    /
+--R                    4           3 3  3          4 2         3 2   2
+--R             (12288a b c + 3072a b )x  + (24576a c  + 30720a b c)x
+--R           + 
+--R                   3   2          3 3
+--R             73728a b c x + 49152a c
+--R        *
+--R                    +--------------+
+--R            +-+ +-+ |   2
+--R           \|a \|c \|a x  + b x + c
+--R       + 
+--R                     5 2        4 2        3 4  4
+--R             (- 6144a c  - 9216a b c - 384a b )x
+--R           + 
+--R                      4   2         3 3   3            4 3         3 2 2  2
+--R             (- 49152a b c  - 12288a b c)x  + (- 49152a c  - 61440a b c )x
+--R           + 
+--R                     3   3          3 4
+--R             - 98304a b c x - 49152a c
+--R        *
+--R            +-+
+--R           \|a
+--R     ,
+--R
+--R                         3   3        2 3 2        5        7  3
+--R                 (- 1536a b c  + 1920a b c  + 96a b c - 120b )x
+--R               + 
+--R                         3 4       2 2 3          4 2        6   2
+--R                 (- 3072a c  + 768a b c  + 4800a b c  - 1200b c)x
+--R               + 
+--R                         2   4           3 3        5 2          2 5
+--R                 (- 9216a b c  + 13824a b c  - 2880b c )x - 6144a c
+--R               + 
+--R                        2 4        4 3
+--R                 9216a b c  - 1920b c
+--R            *
+--R                    +--------------+
+--R                +-+ |   2
+--R               \|c \|a x  + b x + c
+--R           + 
+--R                  4 4        2 4 2         6       8  4
+--R             (768a c  - 1440a b c  + 288a b c + 15b )x
+--R           + 
+--R                   3   4        2 3 3         5 2       7   3
+--R             (6144a b c  - 7680a b c  - 384a b c  + 480b c)x
+--R           + 
+--R                   3 5        2 2 4          4 3        6 2  2
+--R             (6144a c  - 1536a b c  - 9600a b c  + 2400b c )x
+--R           + 
+--R                    2   5           3 4        5 3          2 6          2 5
+--R             (12288a b c  - 18432a b c  + 3840b c )x + 6144a c  - 9216a b c
+--R           + 
+--R                  4 4
+--R             1920b c
+--R        *
+--R                       +--------------+
+--R                 +---+ |   2               +---+ +-+
+--R                \|- a \|a x  + b x + c  - \|- a \|c
+--R           atan(------------------------------------)
+--R                                 a x
+--R       + 
+--R                    5 2        4 2       3 4  7
+--R             (- 768a c  - 1152a b c - 48a b )x
+--R           + 
+--R                     4   2        3 3      2 5  6
+--R             (- 6272a b c  - 1728a b c - 8a b )x
+--R           + 
+--R                     4 3        3 2 2      2 4         6  5
+--R             (- 6528a c  - 9120a b c  - 40a b c + 10a b )x
+--R           + 
+--R                      3   3       2 3 2        5       7  4
+--R             (- 15552a b c  + 240a b c  + 12a b c - 15b )x
+--R           + 
+--R                     3 4       2 2 3          4 2       6   3
+--R             (- 9216a c  + 384a b c  + 1408a b c  - 360b c)x
+--R           + 
+--R                     2   4          3 3        5 2  2
+--R             (- 3840a b c  + 5760a b c  - 1200b c )x
+--R           + 
+--R                     2 5          2 4       4 3
+--R             (- 3072a c  + 4608a b c  - 960b c )x
+--R        *
+--R                  +--------------+
+--R            +---+ |   2
+--R           \|- a \|a x  + b x + c
+--R       + 
+--R                   5          4 3  8         5 2        4 2        3 4  7
+--R             (1536a b c + 384a b )x  + (3072a c  + 5632a b c + 448a b )x
+--R           + 
+--R                    4   2        3 3       2 5  6
+--R             (15104a b c  + 4992a b c - 16a b )x
+--R           + 
+--R                    4 3         3 2 2       2 4         6  5
+--R             (10752a c  + 15744a b c  - 160a b c + 40a b )x
+--R           + 
+--R                    3   3        2 3 2        5        7  4
+--R             (21312a b c  - 2448a b c  + 76a b c + 105b )x
+--R           + 
+--R                    3 4        2 2 3          4 2       6   3
+--R             (10752a c  - 1152a b c  - 3232a b c  + 840b c)x
+--R           + 
+--R                   2   4          3 3        5 2  2
+--R             (5376a b c  - 8064a b c  + 1680b c )x
+--R           + 
+--R                   2 5          2 4       4 3
+--R             (3072a c  - 4608a b c  + 960b c )x
+--R        *
+--R            +---+ +-+
+--R           \|- a \|c
+--R    /
+--R                   4           3 3  3          4 2         3 2   2
+--R             (6144a b c + 1536a b )x  + (12288a c  + 15360a b c)x
+--R           + 
+--R                   3   2          3 3
+--R             36864a b c x + 24576a c
+--R        *
+--R                      +--------------+
+--R            +---+ +-+ |   2
+--R           \|- a \|c \|a x  + b x + c
+--R       + 
+--R                     5 2        4 2        3 4  4
+--R             (- 3072a c  - 4608a b c - 192a b )x
+--R           + 
+--R                      4   2        3 3   3            4 3         3 2 2  2
+--R             (- 24576a b c  - 6144a b c)x  + (- 24576a c  - 30720a b c )x
+--R           + 
+--R                     3   3          3 4
+--R             - 49152a b c x - 24576a c
+--R        *
+--R            +---+
+--R           \|- a
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 63
+t1:=integrate(sqrt(a*x^2+b*x+c),x)
+--R
+--R   (2)
+--R   [
+--R                                                    +--------------+
+--R                           3          2     2   +-+ |   2
+--R             ((16a b c - 4b )x + 32a c  - 8b c)\|c \|a x  + b x + c
+--R           + 
+--R                   2 2    4  2             2     3           3     2 2
+--R             (- 16a c  + b )x  + (- 32a b c  + 8b c)x - 32a c  + 8b c
+--R        *
+--R           log
+--R                                     +--------------+
+--R                     +-+ +-+         |   2                   +-+
+--R                  (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R                + 
+--R                         2             +-+
+--R                  (- 2a x  - b x - 2c)\|a
+--R             /
+--R                      +--------------+
+--R                  +-+ |   2
+--R                2\|c \|a x  + b x + c  - b x - 2c
+--R       + 
+--R                  2        2  3                  3  2           2     2     +-+
+--R           ((- 16a c - 4a b )x  + (- 40a b c - 2b )x  + (- 32a c  - 8b c)x)\|a
+--R        *
+--R            +--------------+
+--R            |   2
+--R           \|a x  + b x + c
+--R       + 
+--R                  2   4       2         2  3                3  2
+--R               16a b x  + (32a c + 24a b )x  + (56a b c + 6b )x
+--R             + 
+--R                     2     2
+--R               (32a c  + 8b c)x
+--R        *
+--R            +-+ +-+
+--R           \|a \|c
+--R    /
+--R                                   +--------------+
+--R                           +-+ +-+ |   2
+--R         (32a b x + 64a c)\|a \|c \|a x  + b x + c
+--R       + 
+--R                2        2  2                    2  +-+
+--R         ((- 32a c - 8a b )x  - 64a b c x - 64a c )\|a
+--R     ,
+--R
+--R                                                    +--------------+
+--R                           3          2     2   +-+ |   2
+--R             ((16a b c - 4b )x + 32a c  - 8b c)\|c \|a x  + b x + c
+--R           + 
+--R                   2 2    4  2             2     3           3     2 2
+--R             (- 16a c  + b )x  + (- 32a b c  + 8b c)x - 32a c  + 8b c
+--R        *
+--R                       +--------------+
+--R                 +---+ |   2               +---+ +-+
+--R                \|- a \|a x  + b x + c  - \|- a \|c
+--R           atan(------------------------------------)
+--R                                 a x
+--R       + 
+--R                 2        2  3                 3  2           2     2     +---+
+--R           ((- 8a c - 2a b )x  + (- 20a b c - b )x  + (- 16a c  - 4b c)x)\|- a
+--R        *
+--R            +--------------+
+--R            |   2
+--R           \|a x  + b x + c
+--R       + 
+--R              2   4       2         2  3                3  2         2     2
+--R           (8a b x  + (16a c + 12a b )x  + (28a b c + 3b )x  + (16a c  + 4b c)x)
+--R        *
+--R            +---+ +-+
+--R           \|- a \|c
+--R    /
+--R                                     +--------------+
+--R                           +---+ +-+ |   2
+--R         (16a b x + 32a c)\|- a \|c \|a x  + b x + c
+--R       + 
+--R                2        2  2                    2  +---+
+--R         ((- 16a c - 4a b )x  - 32a b c x - 32a c )\|- a
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 64
+bb1:=(6*a*x-5*b)/(24*a^2)*(a*x^2+b*x+c)^(3/2)+(5*b^2-4*a*c)/(16*a^2)*t1.1
+--R
+--R   (3)
+--R                     2   2         3       5         2 3         2 2       4
+--R             ((- 192a b c  + 288a b c - 60b )x - 384a c  + 576a b c  - 120b c)
+--R          *
+--R                  +--------------+
+--R              +-+ |   2
+--R             \|c \|a x  + b x + c
+--R         + 
+--R                3 3       2 2 2        4       6  2
+--R           (192a c  - 240a b c  - 12a b c + 15b )x
+--R         + 
+--R                2   3         3 2       5          2 4         2 3       4 2
+--R           (384a b c  - 576a b c  + 120b c)x + 384a c  - 576a b c  + 120b c
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                  4       3 2  5          3         2 3  4
+--R           (- 384a c - 96a b )x  + (- 832a b c - 16a b )x
+--R         + 
+--R                  3 2      2 2         4  3         2   2         3       5  2
+--R           (- 960a c  - 96a b c + 20a b )x  + (- 96a b c  + 144a b c - 30b )x
+--R         + 
+--R                  2 3         2 2       4              3
+--R           (- 384a c  + 896a b c  - 120b c)x + 640a b c
+--R      *
+--R              +--------------+
+--R          +-+ |   2
+--R         \|a \|a x  + b x + c
+--R     + 
+--R               4   6        4        3 2  5         3         2 3  4
+--R           384a b x  + (768a c + 448a b )x  + (1472a b c - 16a b )x
+--R         + 
+--R                 3 2       2 2         4  3         2   2         3       5  2
+--R           (1152a c  - 192a b c + 40a b )x  + (- 32a b c  - 512a b c + 90b )x
+--R         + 
+--R                2 3          2 2       4              3
+--R           (384a c  - 1216a b c  + 120b c)x - 640a b c
+--R      *
+--R          +-+ +-+
+--R         \|a \|c
+--R  /
+--R                                     +--------------+
+--R             3           3   +-+ +-+ |   2
+--R       (1536a b x + 3072a c)\|a \|c \|a x  + b x + c
+--R     + 
+--R                4        3 2  2        3             3 2  +-+
+--R       ((- 1536a c - 384a b )x  - 3072a b c x - 3072a c )\|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 65
+bb2:=(6*a*x-5*b)/(24*a^2)*(a*x^2+b*x+c)^(3/2)+(5*b^2-4*a*c)/(16*a^2)*t1.2
+--R
+--R   (4)
+--R                     2   2         3       5         2 3         2 2       4
+--R             ((- 192a b c  + 288a b c - 60b )x - 384a c  + 576a b c  - 120b c)
+--R          *
+--R                  +--------------+
+--R              +-+ |   2
+--R             \|c \|a x  + b x + c
+--R         + 
+--R                3 3       2 2 2        4       6  2
+--R           (192a c  - 240a b c  - 12a b c + 15b )x
+--R         + 
+--R                2   3         3 2       5          2 4         2 3       4 2
+--R           (384a b c  - 576a b c  + 120b c)x + 384a c  - 576a b c  + 120b c
+--R      *
+--R                     +--------------+
+--R               +---+ |   2               +---+ +-+
+--R              \|- a \|a x  + b x + c  - \|- a \|c
+--R         atan(------------------------------------)
+--R                               a x
+--R     + 
+--R                  4       3 2  5          3        2 3  4
+--R           (- 192a c - 48a b )x  + (- 416a b c - 8a b )x
+--R         + 
+--R                  3 2      2 2         4  3         2   2        3       5  2
+--R           (- 480a c  - 48a b c + 10a b )x  + (- 48a b c  + 72a b c - 15b )x
+--R         + 
+--R                  2 3         2 2      4              3
+--R           (- 192a c  + 448a b c  - 60b c)x + 320a b c
+--R      *
+--R                +--------------+
+--R          +---+ |   2
+--R         \|- a \|a x  + b x + c
+--R     + 
+--R               4   6        4        3 2  5        3        2 3  4
+--R           192a b x  + (384a c + 224a b )x  + (736a b c - 8a b )x
+--R         + 
+--R                3 2      2 2         4  3         2   2         3       5  2
+--R           (576a c  - 96a b c + 20a b )x  + (- 16a b c  - 256a b c + 45b )x
+--R         + 
+--R                2 3         2 2      4              3
+--R           (192a c  - 608a b c  + 60b c)x - 320a b c
+--R      *
+--R          +---+ +-+
+--R         \|- a \|c
+--R  /
+--R                                      +--------------+
+--R            3           3   +---+ +-+ |   2
+--R       (768a b x + 1536a c)\|- a \|c \|a x  + b x + c
+--R     + 
+--R               4        3 2  2        3             3 2  +---+
+--R       ((- 768a c - 192a b )x  - 1536a b c x - 1536a c )\|- a
+--R                                                     Type: Expression Integer
+--E
+
+--S 66
+cc1:=aa.1-bb1
+--R
+--R   (5)
+--R                     4   4        3 3 3        2 5 2          7        9  5
+--R               (9216a b c  - 6144a b c  - 8064a b c  + 1536a b c + 180b )x
+--R             + 
+--R                      4 5         3 2 4         2 4 3        8   4
+--R               (18432a c  + 36864a b c  - 77568a b c  + 4200b c)x
+--R             + 
+--R                       3   5          2 3 4           5 3         7 2  3
+--R               (147456a b c  - 135168a b c  - 82944a b c  + 26880b c )x
+--R             + 
+--R                      3 6         2 2 5            4 4         6 3  2
+--R               (98304a c  + 73728a b c  - 301056a b c  + 69120b c )x
+--R             + 
+--R                       2   6            3 5         5 4           2 7
+--R               (245760a b c  - 368640a b c  + 76800b c )x + 98304a c
+--R             + 
+--R                          2 6         4 5
+--R               - 147456a b c  + 30720b c
+--R          *
+--R                  +--------------+
+--R              +-+ |   2
+--R             \|c \|a x  + b x + c
+--R         + 
+--R                      5 5        4 2 4         3 4 3       2 6 2         8
+--R               - 3072a c  - 6912a b c  + 13440a b c  + 672a b c  - 828a b c
+--R             + 
+--R                    10
+--R               - 15b
+--R          *
+--R              6
+--R             x
+--R         + 
+--R                    4   5         3 3 4         2 5 3          7 2        9   5
+--R           (- 55296a b c  + 36864a b c  + 48384a b c  - 9216a b c  - 1080b c)x
+--R         + 
+--R                    4 6          3 2 5          2 4 4         8 2  4
+--R           (- 55296a c  - 110592a b c  + 232704a b c  - 12600b c )x
+--R         + 
+--R                     3   6          2 3 5            5 4         7 3  3
+--R           (- 294912a b c  + 270336a b c  + 165888a b c  - 53760b c )x
+--R         + 
+--R                     3 7          2 2 6            4 5          6 4  2
+--R           (- 147456a c  - 110592a b c  + 451584a b c  - 103680b c )x
+--R         + 
+--R                     2   7            3 6         5 5           2 8
+--R           (- 294912a b c  + 442368a b c  - 92160b c )x - 98304a c
+--R         + 
+--R                    2 7         4 6
+--R           147456a b c  - 30720b c
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                     4   4        3 3 3        2 5 2          7        9  5
+--R               (9216a b c  - 6144a b c  - 8064a b c  + 1536a b c + 180b )x
+--R             + 
+--R                      4 5         3 2 4         2 4 3        8   4
+--R               (18432a c  + 36864a b c  - 77568a b c  + 4200b c)x
+--R             + 
+--R                       3   5          2 3 4           5 3         7 2  3
+--R               (147456a b c  - 135168a b c  - 82944a b c  + 26880b c )x
+--R             + 
+--R                      3 6         2 2 5            4 4         6 3  2
+--R               (98304a c  + 73728a b c  - 301056a b c  + 69120b c )x
+--R             + 
+--R                       2   6            3 5         5 4           2 7
+--R               (245760a b c  - 368640a b c  + 76800b c )x + 98304a c
+--R             + 
+--R                          2 6         4 5
+--R               - 147456a b c  + 30720b c
+--R          *
+--R                  +--------------+
+--R              +-+ |   2
+--R             \|c \|a x  + b x + c
+--R         + 
+--R                      5 5        4 2 4         3 4 3       2 6 2         8
+--R               - 3072a c  - 6912a b c  + 13440a b c  + 672a b c  - 828a b c
+--R             + 
+--R                    10
+--R               - 15b
+--R          *
+--R              6
+--R             x
+--R         + 
+--R                    4   5         3 3 4         2 5 3          7 2        9   5
+--R           (- 55296a b c  + 36864a b c  + 48384a b c  - 9216a b c  - 1080b c)x
+--R         + 
+--R                    4 6          3 2 5          2 4 4         8 2  4
+--R           (- 55296a c  - 110592a b c  + 232704a b c  - 12600b c )x
+--R         + 
+--R                     3   6          2 3 5            5 4         7 3  3
+--R           (- 294912a b c  + 270336a b c  + 165888a b c  - 53760b c )x
+--R         + 
+--R                     3 7          2 2 6            4 5          6 4  2
+--R           (- 147456a c  - 110592a b c  + 451584a b c  - 103680b c )x
+--R         + 
+--R                     2   7            3 6         5 5           2 8
+--R           (- 294912a b c  + 442368a b c  - 92160b c )x - 98304a c
+--R         + 
+--R                    2 7         4 6
+--R           147456a b c  - 30720b c
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                    3 2 4         2 4 3         6 2  5
+--R           (- 15360a b c  - 12800a b c  - 960a b c )x
+--R         + 
+--R                    3   5          2 3 4           5 3  4
+--R           (- 30720a b c  - 107520a b c  - 22400a b c )x
+--R         + 
+--R                     2 2 5            4 4  3             2   6            3 5  2
+--R           (- 245760a b c  - 143360a b c )x  + (- 163840a b c  - 368640a b c )x
+--R         + 
+--R                      2 6               7
+--R           - 409600a b c x - 163840a b c
+--R      *
+--R              +--------------+
+--R          +-+ |   2
+--R         \|a \|a x  + b x + c
+--R     + 
+--R                 4   4         3 3 3        2 5 2        7   6
+--R           (5120a b c  + 19200a b c  + 4800a b c  + 80a b c)x
+--R         + 
+--R                  3 2 4         2 4 3          6 2  5
+--R           (92160a b c  + 76800a b c  + 5760a b c )x
+--R         + 
+--R                  3   5          2 3 4           5 3  4
+--R           (92160a b c  + 322560a b c  + 67200a b c )x
+--R         + 
+--R                   2 2 5            4 4  3           2   6            3 5  2
+--R           (491520a b c  + 286720a b c )x  + (245760a b c  + 552960a b c )x
+--R         + 
+--R                    2 6               7
+--R           491520a b c x + 163840a b c
+--R      *
+--R          +-+ +-+
+--R         \|a \|c
+--R  /
+--R                  5   2         4 3         3 5  5
+--R           (73728a b c  + 61440a b c + 4608a b )x
+--R         + 
+--R                   5 3          4 2 2          3 4   4
+--R           (147456a c  + 516096a b c  + 107520a b c)x
+--R         + 
+--R                    4   3          3 3 2  3           4 4           3 2 3  2
+--R           (1179648a b c  + 688128a b c )x  + (786432a c  + 1769472a b c )x
+--R         + 
+--R                   3   4           3 5
+--R           1966080a b c x + 786432a c
+--R      *
+--R                  +--------------+
+--R          +-+ +-+ |   2
+--R         \|a \|c \|a x  + b x + c
+--R     + 
+--R                    6 3         5 2 2         4 4        3 6  6
+--R           (- 24576a c  - 92160a b c  - 23040a b c - 384a b )x
+--R         + 
+--R                     5   3          4 3 2         3 5   5
+--R           (- 442368a b c  - 368640a b c  - 27648a b c)x
+--R         + 
+--R                     5 4           4 2 3          3 4 2  4
+--R           (- 442368a c  - 1548288a b c  - 322560a b c )x
+--R         + 
+--R                      4   4           3 3 3  3
+--R           (- 2359296a b c  - 1376256a b c )x
+--R         + 
+--R                      4 5           3 2 4  2           3   5           3 6
+--R           (- 1179648a c  - 2654208a b c )x  - 2359296a b c x - 786432a c
+--R      *
+--R          +-+
+--R         \|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 67
+cc2:=aa.2-bb1
+--R
+--R   (6)
+--R                     4   4        3 3 3        2 5 2          7        9  5
+--R               (9216a b c  - 6144a b c  - 8064a b c  + 1536a b c + 180b )x
+--R             + 
+--R                      4 5         3 2 4         2 4 3        8   4
+--R               (18432a c  + 36864a b c  - 77568a b c  + 4200b c)x
+--R             + 
+--R                       3   5          2 3 4           5 3         7 2  3
+--R               (147456a b c  - 135168a b c  - 82944a b c  + 26880b c )x
+--R             + 
+--R                      3 6         2 2 5            4 4         6 3  2
+--R               (98304a c  + 73728a b c  - 301056a b c  + 69120b c )x
+--R             + 
+--R                       2   6            3 5         5 4           2 7
+--R               (245760a b c  - 368640a b c  + 76800b c )x + 98304a c
+--R             + 
+--R                          2 6         4 5
+--R               - 147456a b c  + 30720b c
+--R          *
+--R                        +--------------+
+--R              +---+ +-+ |   2
+--R             \|- a \|c \|a x  + b x + c
+--R         + 
+--R                          5 5        4 2 4         3 4 3       2 6 2         8
+--R                   - 3072a c  - 6912a b c  + 13440a b c  + 672a b c  - 828a b c
+--R                 + 
+--R                        10
+--R                   - 15b
+--R              *
+--R                  6
+--R                 x
+--R             + 
+--R                           4   5         3 3 4         2 5 3          7 2
+--R                   - 55296a b c  + 36864a b c  + 48384a b c  - 9216a b c
+--R                 + 
+--R                          9
+--R                   - 1080b c
+--R              *
+--R                  5
+--R                 x
+--R             + 
+--R                        4 6          3 2 5          2 4 4         8 2  4
+--R               (- 55296a c  - 110592a b c  + 232704a b c  - 12600b c )x
+--R             + 
+--R                         3   6          2 3 5            5 4         7 3  3
+--R               (- 294912a b c  + 270336a b c  + 165888a b c  - 53760b c )x
+--R             + 
+--R                         3 7          2 2 6            4 5          6 4  2
+--R               (- 147456a c  - 110592a b c  + 451584a b c  - 103680b c )x
+--R             + 
+--R                         2   7            3 6         5 5           2 8
+--R               (- 294912a b c  + 442368a b c  - 92160b c )x - 98304a c
+--R             + 
+--R                        2 7         4 6
+--R               147456a b c  - 30720b c
+--R          *
+--R              +---+
+--R             \|- a
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                        4   4         3 3 3         2 5 2          7        9  5
+--R               (- 18432a b c  + 12288a b c  + 16128a b c  - 3072a b c - 360b )x
+--R             + 
+--R                        4 5         3 2 4          2 4 3        8   4
+--R               (- 36864a c  - 73728a b c  + 155136a b c  - 8400b c)x
+--R             + 
+--R                         3   5          2 3 4            5 3         7 2  3
+--R               (- 294912a b c  + 270336a b c  + 165888a b c  - 53760b c )x
+--R             + 
+--R                         3 6          2 2 5            4 4          6 3  2
+--R               (- 196608a c  - 147456a b c  + 602112a b c  - 138240b c )x
+--R             + 
+--R                         2   6            3 5          5 4            2 7
+--R               (- 491520a b c  + 737280a b c  - 153600b c )x - 196608a c
+--R             + 
+--R                        2 6         4 5
+--R               294912a b c  - 61440b c
+--R          *
+--R                      +--------------+
+--R              +-+ +-+ |   2
+--R             \|a \|c \|a x  + b x + c
+--R         + 
+--R                        5 5         4 2 4         3 4 3        2 6 2          8
+--R                   6144a c  + 13824a b c  - 26880a b c  - 1344a b c  + 1656a b c
+--R                 + 
+--R                      10
+--R                   30b
+--R              *
+--R                  6
+--R                 x
+--R             + 
+--R                          4   5         3 3 4         2 5 3           7 2
+--R                   110592a b c  - 73728a b c  - 96768a b c  + 18432a b c
+--R                 + 
+--R                        9
+--R                   2160b c
+--R              *
+--R                  5
+--R                 x
+--R             + 
+--R                       4 6          3 2 5          2 4 4         8 2  4
+--R               (110592a c  + 221184a b c  - 465408a b c  + 25200b c )x
+--R             + 
+--R                       3   6          2 3 5            5 4          7 3  3
+--R               (589824a b c  - 540672a b c  - 331776a b c  + 107520b c )x
+--R             + 
+--R                       3 7          2 2 6            4 5          6 4  2
+--R               (294912a c  + 221184a b c  - 903168a b c  + 207360b c )x
+--R             + 
+--R                       2   7            3 6          5 5            2 8
+--R               (589824a b c  - 884736a b c  + 184320b c )x + 196608a c
+--R             + 
+--R                          2 7         4 6
+--R               - 294912a b c  + 61440b c
+--R          *
+--R              +-+
+--R             \|a
+--R      *
+--R                     +--------------+
+--R               +---+ |   2               +---+ +-+
+--R              \|- a \|a x  + b x + c  - \|- a \|c
+--R         atan(------------------------------------)
+--R                               a x
+--R     + 
+--R                    3 2 4         2 4 3         6 2  5
+--R           (- 15360a b c  - 12800a b c  - 960a b c )x
+--R         + 
+--R                    3   5          2 3 4           5 3  4
+--R           (- 30720a b c  - 107520a b c  - 22400a b c )x
+--R         + 
+--R                     2 2 5            4 4  3             2   6            3 5  2
+--R           (- 245760a b c  - 143360a b c )x  + (- 163840a b c  - 368640a b c )x
+--R         + 
+--R                      2 6               7
+--R           - 409600a b c x - 163840a b c
+--R      *
+--R                    +--------------+
+--R          +---+ +-+ |   2
+--R         \|- a \|a \|a x  + b x + c
+--R     + 
+--R                 4   4         3 3 3        2 5 2        7   6
+--R           (5120a b c  + 19200a b c  + 4800a b c  + 80a b c)x
+--R         + 
+--R                  3 2 4         2 4 3          6 2  5
+--R           (92160a b c  + 76800a b c  + 5760a b c )x
+--R         + 
+--R                  3   5          2 3 4           5 3  4
+--R           (92160a b c  + 322560a b c  + 67200a b c )x
+--R         + 
+--R                   2 2 5            4 4  3           2   6            3 5  2
+--R           (491520a b c  + 286720a b c )x  + (245760a b c  + 552960a b c )x
+--R         + 
+--R                    2 6               7
+--R           491520a b c x + 163840a b c
+--R      *
+--R          +---+ +-+ +-+
+--R         \|- a \|a \|c
+--R  /
+--R                  5   2         4 3         3 5  5
+--R           (73728a b c  + 61440a b c + 4608a b )x
+--R         + 
+--R                   5 3          4 2 2          3 4   4
+--R           (147456a c  + 516096a b c  + 107520a b c)x
+--R         + 
+--R                    4   3          3 3 2  3           4 4           3 2 3  2
+--R           (1179648a b c  + 688128a b c )x  + (786432a c  + 1769472a b c )x
+--R         + 
+--R                   3   4           3 5
+--R           1966080a b c x + 786432a c
+--R      *
+--R                        +--------------+
+--R          +---+ +-+ +-+ |   2
+--R         \|- a \|a \|c \|a x  + b x + c
+--R     + 
+--R                    6 3         5 2 2         4 4        3 6  6
+--R           (- 24576a c  - 92160a b c  - 23040a b c - 384a b )x
+--R         + 
+--R                     5   3          4 3 2         3 5   5
+--R           (- 442368a b c  - 368640a b c  - 27648a b c)x
+--R         + 
+--R                     5 4           4 2 3          3 4 2  4
+--R           (- 442368a c  - 1548288a b c  - 322560a b c )x
+--R         + 
+--R                      4   4           3 3 3  3
+--R           (- 2359296a b c  - 1376256a b c )x
+--R         + 
+--R                      4 5           3 2 4  2           3   5           3 6
+--R           (- 1179648a c  - 2654208a b c )x  - 2359296a b c x - 786432a c
+--R      *
+--R          +---+ +-+
+--R         \|- a \|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 68
+cc3:=aa.1-bb2
+--R
+--R   (7)
+--R                     4   4        3 3 3        2 5 2          7        9  5
+--R               (9216a b c  - 6144a b c  - 8064a b c  + 1536a b c + 180b )x
+--R             + 
+--R                      4 5         3 2 4         2 4 3        8   4
+--R               (18432a c  + 36864a b c  - 77568a b c  + 4200b c)x
+--R             + 
+--R                       3   5          2 3 4           5 3         7 2  3
+--R               (147456a b c  - 135168a b c  - 82944a b c  + 26880b c )x
+--R             + 
+--R                      3 6         2 2 5            4 4         6 3  2
+--R               (98304a c  + 73728a b c  - 301056a b c  + 69120b c )x
+--R             + 
+--R                       2   6            3 5         5 4           2 7
+--R               (245760a b c  - 368640a b c  + 76800b c )x + 98304a c
+--R             + 
+--R                          2 6         4 5
+--R               - 147456a b c  + 30720b c
+--R          *
+--R                        +--------------+
+--R              +---+ +-+ |   2
+--R             \|- a \|c \|a x  + b x + c
+--R         + 
+--R                          5 5        4 2 4         3 4 3       2 6 2         8
+--R                   - 3072a c  - 6912a b c  + 13440a b c  + 672a b c  - 828a b c
+--R                 + 
+--R                        10
+--R                   - 15b
+--R              *
+--R                  6
+--R                 x
+--R             + 
+--R                           4   5         3 3 4         2 5 3          7 2
+--R                   - 55296a b c  + 36864a b c  + 48384a b c  - 9216a b c
+--R                 + 
+--R                          9
+--R                   - 1080b c
+--R              *
+--R                  5
+--R                 x
+--R             + 
+--R                        4 6          3 2 5          2 4 4         8 2  4
+--R               (- 55296a c  - 110592a b c  + 232704a b c  - 12600b c )x
+--R             + 
+--R                         3   6          2 3 5            5 4         7 3  3
+--R               (- 294912a b c  + 270336a b c  + 165888a b c  - 53760b c )x
+--R             + 
+--R                         3 7          2 2 6            4 5          6 4  2
+--R               (- 147456a c  - 110592a b c  + 451584a b c  - 103680b c )x
+--R             + 
+--R                         2   7            3 6         5 5           2 8
+--R               (- 294912a b c  + 442368a b c  - 92160b c )x - 98304a c
+--R             + 
+--R                        2 7         4 6
+--R               147456a b c  - 30720b c
+--R          *
+--R              +---+
+--R             \|- a
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                      4   4         3 3 3         2 5 2          7        9  5
+--R               (18432a b c  - 12288a b c  - 16128a b c  + 3072a b c + 360b )x
+--R             + 
+--R                      4 5         3 2 4          2 4 3        8   4
+--R               (36864a c  + 73728a b c  - 155136a b c  + 8400b c)x
+--R             + 
+--R                       3   5          2 3 4            5 3         7 2  3
+--R               (294912a b c  - 270336a b c  - 165888a b c  + 53760b c )x
+--R             + 
+--R                       3 6          2 2 5            4 4          6 3  2
+--R               (196608a c  + 147456a b c  - 602112a b c  + 138240b c )x
+--R             + 
+--R                       2   6            3 5          5 4            2 7
+--R               (491520a b c  - 737280a b c  + 153600b c )x + 196608a c
+--R             + 
+--R                          2 6         4 5
+--R               - 294912a b c  + 61440b c
+--R          *
+--R                      +--------------+
+--R              +-+ +-+ |   2
+--R             \|a \|c \|a x  + b x + c
+--R         + 
+--R                          5 5         4 2 4         3 4 3        2 6 2
+--R                   - 6144a c  - 13824a b c  + 26880a b c  + 1344a b c
+--R                 + 
+--R                            8       10
+--R                   - 1656a b c - 30b
+--R              *
+--R                  6
+--R                 x
+--R             + 
+--R                            4   5         3 3 4         2 5 3           7 2
+--R                   - 110592a b c  + 73728a b c  + 96768a b c  - 18432a b c
+--R                 + 
+--R                          9
+--R                   - 2160b c
+--R              *
+--R                  5
+--R                 x
+--R             + 
+--R                         4 6          3 2 5          2 4 4         8 2  4
+--R               (- 110592a c  - 221184a b c  + 465408a b c  - 25200b c )x
+--R             + 
+--R                         3   6          2 3 5            5 4          7 3  3
+--R               (- 589824a b c  + 540672a b c  + 331776a b c  - 107520b c )x
+--R             + 
+--R                         3 7          2 2 6            4 5          6 4  2
+--R               (- 294912a c  - 221184a b c  + 903168a b c  - 207360b c )x
+--R             + 
+--R                         2   7            3 6          5 5            2 8
+--R               (- 589824a b c  + 884736a b c  - 184320b c )x - 196608a c
+--R             + 
+--R                        2 7         4 6
+--R               294912a b c  - 61440b c
+--R          *
+--R              +-+
+--R             \|a
+--R      *
+--R                     +--------------+
+--R               +---+ |   2               +---+ +-+
+--R              \|- a \|a x  + b x + c  - \|- a \|c
+--R         atan(------------------------------------)
+--R                               a x
+--R     + 
+--R                    3 2 4         2 4 3         6 2  5
+--R           (- 15360a b c  - 12800a b c  - 960a b c )x
+--R         + 
+--R                    3   5          2 3 4           5 3  4
+--R           (- 30720a b c  - 107520a b c  - 22400a b c )x
+--R         + 
+--R                     2 2 5            4 4  3             2   6            3 5  2
+--R           (- 245760a b c  - 143360a b c )x  + (- 163840a b c  - 368640a b c )x
+--R         + 
+--R                      2 6               7
+--R           - 409600a b c x - 163840a b c
+--R      *
+--R                    +--------------+
+--R          +---+ +-+ |   2
+--R         \|- a \|a \|a x  + b x + c
+--R     + 
+--R                 4   4         3 3 3        2 5 2        7   6
+--R           (5120a b c  + 19200a b c  + 4800a b c  + 80a b c)x
+--R         + 
+--R                  3 2 4         2 4 3          6 2  5
+--R           (92160a b c  + 76800a b c  + 5760a b c )x
+--R         + 
+--R                  3   5          2 3 4           5 3  4
+--R           (92160a b c  + 322560a b c  + 67200a b c )x
+--R         + 
+--R                   2 2 5            4 4  3           2   6            3 5  2
+--R           (491520a b c  + 286720a b c )x  + (245760a b c  + 552960a b c )x
+--R         + 
+--R                    2 6               7
+--R           491520a b c x + 163840a b c
+--R      *
+--R          +---+ +-+ +-+
+--R         \|- a \|a \|c
+--R  /
+--R                  5   2         4 3         3 5  5
+--R           (73728a b c  + 61440a b c + 4608a b )x
+--R         + 
+--R                   5 3          4 2 2          3 4   4
+--R           (147456a c  + 516096a b c  + 107520a b c)x
+--R         + 
+--R                    4   3          3 3 2  3           4 4           3 2 3  2
+--R           (1179648a b c  + 688128a b c )x  + (786432a c  + 1769472a b c )x
+--R         + 
+--R                   3   4           3 5
+--R           1966080a b c x + 786432a c
+--R      *
+--R                        +--------------+
+--R          +---+ +-+ +-+ |   2
+--R         \|- a \|a \|c \|a x  + b x + c
+--R     + 
+--R                    6 3         5 2 2         4 4        3 6  6
+--R           (- 24576a c  - 92160a b c  - 23040a b c - 384a b )x
+--R         + 
+--R                     5   3          4 3 2         3 5   5
+--R           (- 442368a b c  - 368640a b c  - 27648a b c)x
+--R         + 
+--R                     5 4           4 2 3          3 4 2  4
+--R           (- 442368a c  - 1548288a b c  - 322560a b c )x
+--R         + 
+--R                      4   4           3 3 3  3
+--R           (- 2359296a b c  - 1376256a b c )x
+--R         + 
+--R                      4 5           3 2 4  2           3   5           3 6
+--R           (- 1179648a c  - 2654208a b c )x  - 2359296a b c x - 786432a c
+--R      *
+--R          +---+ +-+
+--R         \|- a \|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 69
+cc4:=aa.2-bb2
+--R
+--R   (8)
+--R                  2 2 4         4 3      6 2  5
+--R           (- 960a b c  - 800a b c  - 60b c )x
+--R         + 
+--R                   2   5          3 4        5 3  4
+--R           (- 1920a b c  - 6720a b c  - 1400b c )x
+--R         + 
+--R                      2 5        4 4  3                6         3 5  2
+--R           (- 15360a b c  - 8960b c )x  + (- 10240a b c  - 23040b c )x
+--R         + 
+--R                   2 6            7
+--R           - 25600b c x - 10240b c
+--R      *
+--R          +--------------+
+--R          |   2
+--R         \|a x  + b x + c
+--R     + 
+--R                3   4        2 3 3         5 2     7   6
+--R           (320a b c  + 1200a b c  + 300a b c  + 5b c)x
+--R         + 
+--R                 2 2 4          4 3       6 2  5
+--R           (5760a b c  + 4800a b c  + 360b c )x
+--R         + 
+--R                 2   5           3 4        5 3  4            2 5         4 4  3
+--R           (5760a b c  + 20160a b c  + 4200b c )x  + (30720a b c  + 17920b c )x
+--R         + 
+--R                      6         3 5  2         2 6            7
+--R           (15360a b c  + 34560b c )x  + 30720b c x + 10240b c
+--R      *
+--R          +-+
+--R         \|c
+--R  /
+--R                 4   2        3 3        2 5  5
+--R           (4608a b c  + 3840a b c + 288a b )x
+--R         + 
+--R                 4 3         3 2 2        2 4   4
+--R           (9216a c  + 32256a b c  + 6720a b c)x
+--R         + 
+--R                  3   3         2 3 2  3          3 4          2 2 3  2
+--R           (73728a b c  + 43008a b c )x  + (49152a c  + 110592a b c )x
+--R         + 
+--R                  2   4          2 5
+--R           122880a b c x + 49152a c
+--R      *
+--R              +--------------+
+--R          +-+ |   2
+--R         \|c \|a x  + b x + c
+--R     + 
+--R               5 3        4 2 2        3 4       2 6  6
+--R       (- 1536a c  - 5760a b c  - 1440a b c - 24a b )x
+--R     + 
+--R                4   3         3 3 2        2 5   5
+--R       (- 27648a b c  - 23040a b c  - 1728a b c)x
+--R     + 
+--R                4 4         3 2 3         2 4 2  4
+--R       (- 27648a c  - 96768a b c  - 20160a b c )x
+--R     + 
+--R                 3   4         2 3 3  3            3 5          2 2 4  2
+--R       (- 147456a b c  - 86016a b c )x  + (- 73728a c  - 165888a b c )x
+--R     + 
+--R                2   5          2 6
+--R       - 147456a b c x - 49152a c
+--R                                                     Type: Expression Integer
+--E
+
+--S 70     14:287 Schaums and Axiom differ by a constant
+dd4:=ratDenom cc4
+--R
+--R               +-+
+--R          5b c\|c
+--R   (9)  - --------
+--R               2
+--R            24a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.288~~~~~$\displaystyle
+\int{\frac{\sqrt{ax^2+bx+c}}{x}}~dx$}
+$$\int{\frac{\sqrt{ax^2+bx+c}}{x}}=
+\sqrt{ax^2+bx+c}+\frac{b}{2}\int{\frac{1}{\sqrt{ax^2+bx+c}}}
++c\int{\frac{1}{x\sqrt{ax^2+bx+c}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 71
+aa:=integrate(sqrt(a*x^2+b*x+c)/x,x)
+--R 
+--R
+--R   (1)
+--R   [
+--R                   +--------------+
+--R               +-+ |   2                            +-+ +-+
+--R           (4c\|a \|a x  + b x + c  + (- 2b x - 4c)\|a \|c )
+--R        *
+--R                     +--------------+
+--R                 +-+ |   2
+--R               2\|c \|a x  + b x + c  - b x - 2c
+--R           log(---------------------------------)
+--R                                +-+
+--R                             2x\|c
+--R       + 
+--R                   +--------------+
+--R               +-+ |   2               2
+--R           (2b\|c \|a x  + b x + c  - b x - 2b c)
+--R        *
+--R           log
+--R                              2           +-+          2              2  +-+
+--R                    ((- 2a b x  - 8a c x)\|c  + (4a c x  + 4b c x + 8c )\|a )
+--R                 *
+--R                     +--------------+
+--R                     |   2
+--R                    \|a x  + b x + c
+--R                + 
+--R                           3              2  2              2  +-+ +-+     2   3
+--R                  (- 2a b x  + (- 8a c - b )x  - 8b c x - 8c )\|a \|c  + 4a c x
+--R                + 
+--R                          2       2
+--R                  6a b c x  + 8a c x
+--R             /
+--R                                 +--------------+
+--R                              2  |   2
+--R                  (4b c x + 8c )\|a x  + b x + c
+--R                + 
+--R                              2  2              2  +-+
+--R                  ((- 4a c - b )x  - 8b c x - 8c )\|c
+--R       + 
+--R                    +--------------+
+--R                +-+ |   2                   2         +-+ +-+
+--R         - 2b x\|a \|a x  + b x + c  + (4a x  + 2b x)\|a \|c
+--R    /
+--R                 +--------------+
+--R         +-+ +-+ |   2                            +-+
+--R       4\|a \|c \|a x  + b x + c  + (- 2b x - 4c)\|a
+--R     ,
+--R
+--R                     +--------------+
+--R               +---+ |   2                           +---+ +-+
+--R           (2c\|- a \|a x  + b x + c  + (- b x - 2c)\|- a \|c )
+--R        *
+--R                     +--------------+
+--R                 +-+ |   2
+--R               2\|c \|a x  + b x + c  - b x - 2c
+--R           log(---------------------------------)
+--R                                +-+
+--R                             2x\|c
+--R       + 
+--R                   +--------------+
+--R               +-+ |   2               2
+--R           (2b\|c \|a x  + b x + c  - b x - 2b c)
+--R        *
+--R                           +--------------+
+--R                 +---+ +-+ |   2                +---+
+--R                \|- a \|c \|a x  + b x + c  - c\|- a
+--R           atan(-------------------------------------)
+--R                                   +-+
+--R                               a x\|c
+--R       + 
+--R                     +--------------+
+--R               +---+ |   2                   2        +---+ +-+
+--R         - b x\|- a \|a x  + b x + c  + (2a x  + b x)\|- a \|c
+--R    /
+--R                   +--------------+
+--R         +---+ +-+ |   2                           +---+
+--R       2\|- a \|c \|a x  + b x + c  + (- b x - 2c)\|- a
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 72
+t1:=integrate(1/sqrt(a*x^2+b*x+c),x)
+--R
+--R   (2)
+--R   [
+--R       log
+--R                                 +--------------+
+--R                 +-+ +-+         |   2                   +-+
+--R              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R            + 
+--R                     2             +-+
+--R              (- 2a x  - b x - 2c)\|a
+--R         /
+--R                  +--------------+
+--R              +-+ |   2
+--R            2\|c \|a x  + b x + c  - b x - 2c
+--R    /
+--R        +-+
+--R       \|a
+--R     ,
+--R                 +--------------+
+--R           +---+ |   2               +---+ +-+
+--R          \|- a \|a x  + b x + c  - \|- a \|c
+--R    2atan(------------------------------------)
+--R                           a x
+--R    -------------------------------------------]
+--R                        +---+
+--R                       \|- a
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 73
+t2:=integrate(1/(x*sqrt(a*x^2+b*x+c)),x)
+--R
+--R                  +--------------+
+--R              +-+ |   2
+--R            2\|c \|a x  + b x + c  - b x - 2c
+--R        log(---------------------------------)
+--R                            x
+--R   (3)  --------------------------------------
+--R                          +-+
+--R                         \|c
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 74
+bb1:=sqrt(a*x^2+b*x+c)+b/2*t1.1+c*t2
+--R
+--R   (4)
+--R                       +--------------+
+--R                   +-+ |   2
+--R          +-+    2\|c \|a x  + b x + c  - b x - 2c
+--R       2c\|a log(---------------------------------)
+--R                                 x
+--R     + 
+--R           +-+
+--R         b\|c
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                 +--------------+
+--R         +-+ +-+ |   2
+--R       2\|a \|c \|a x  + b x + c
+--R  /
+--R       +-+ +-+
+--R     2\|a \|c
+--R                                                     Type: Expression Integer
+--E
+
+--S 75
+bb2:=sqrt(a*x^2+b*x+c)+b/2*t1.2+c*t2
+--R
+--R   (5)
+--R                        +--------------+
+--R                    +-+ |   2
+--R         +---+    2\|c \|a x  + b x + c  - b x - 2c
+--R       c\|- a log(---------------------------------)
+--R                                  x
+--R     + 
+--R                        +--------------+
+--R                  +---+ |   2               +---+ +-+
+--R         +-+     \|- a \|a x  + b x + c  - \|- a \|c
+--R       b\|c atan(------------------------------------)
+--R                                  a x
+--R     + 
+--R                  +--------------+
+--R        +---+ +-+ |   2
+--R       \|- a \|c \|a x  + b x + c
+--R  /
+--R      +---+ +-+
+--R     \|- a \|c
+--R                                                     Type: Expression Integer
+--E
+
+--S 76
+cc1:=aa.1-bb1
+--R
+--R   (6)
+--R                         +--------------+
+--R                     +-+ |   2
+--R            +-+    2\|c \|a x  + b x + c  - b x - 2c
+--R       - 2c\|a log(---------------------------------)
+--R                                   x
+--R     + 
+--R                       +--------------+
+--R                   +-+ |   2
+--R          +-+    2\|c \|a x  + b x + c  - b x - 2c
+--R       2c\|a log(---------------------------------)
+--R                                  +-+
+--R                               2x\|c
+--R     + 
+--R       -
+--R              +-+
+--R            b\|c
+--R         *
+--R            log
+--R                                      +--------------+
+--R                      +-+ +-+         |   2                   +-+
+--R                   (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R                 + 
+--R                          2             +-+
+--R                   (- 2a x  - b x - 2c)\|a
+--R              /
+--R                       +--------------+
+--R                   +-+ |   2
+--R                 2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R           +-+
+--R         b\|c
+--R      *
+--R         log
+--R                            2           +-+          2              2  +-+
+--R                  ((- 2a b x  - 8a c x)\|c  + (4a c x  + 4b c x + 8c )\|a )
+--R               *
+--R                   +--------------+
+--R                   |   2
+--R                  \|a x  + b x + c
+--R              + 
+--R                         3              2  2              2  +-+ +-+     2   3
+--R                (- 2a b x  + (- 8a c - b )x  - 8b c x - 8c )\|a \|c  + 4a c x
+--R              + 
+--R                        2       2
+--R                6a b c x  + 8a c x
+--R           /
+--R                               +--------------+
+--R                            2  |   2
+--R                (4b c x + 8c )\|a x  + b x + c
+--R              + 
+--R                            2  2              2  +-+
+--R                ((- 4a c - b )x  - 8b c x - 8c )\|c
+--R     + 
+--R          +-+
+--R       2c\|a
+--R  /
+--R       +-+ +-+
+--R     2\|a \|c
+--R                                                     Type: Expression Integer
+--E
+
+--S 77
+cc2:=aa.2-bb1
+--R
+--R   (7)
+--R                               +--------------+
+--R                           +-+ |   2
+--R            +---+ +-+    2\|c \|a x  + b x + c  - b x - 2c
+--R       - 2c\|- a \|a log(---------------------------------)
+--R                                         x
+--R     + 
+--R                             +--------------+
+--R                         +-+ |   2
+--R          +---+ +-+    2\|c \|a x  + b x + c  - b x - 2c
+--R       2c\|- a \|a log(---------------------------------)
+--R                                        +-+
+--R                                     2x\|c
+--R     + 
+--R       -
+--R              +---+ +-+
+--R            b\|- a \|c
+--R         *
+--R            log
+--R                                      +--------------+
+--R                      +-+ +-+         |   2                   +-+
+--R                   (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R                 + 
+--R                          2             +-+
+--R                   (- 2a x  - b x - 2c)\|a
+--R              /
+--R                       +--------------+
+--R                   +-+ |   2
+--R                 2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                                 +--------------+
+--R                       +---+ +-+ |   2                +---+
+--R          +-+ +-+     \|- a \|c \|a x  + b x + c  - c\|- a        +---+ +-+
+--R       2b\|a \|c atan(-------------------------------------) + 2c\|- a \|a
+--R                                         +-+
+--R                                     a x\|c
+--R  /
+--R       +---+ +-+ +-+
+--R     2\|- a \|a \|c
+--R                                                     Type: Expression Integer
+--E
+
+--S 78
+cc3:=aa.1-bb2
+--R
+--R   (8)
+--R                               +--------------+
+--R                           +-+ |   2
+--R            +---+ +-+    2\|c \|a x  + b x + c  - b x - 2c
+--R       - 2c\|- a \|a log(---------------------------------)
+--R                                         x
+--R     + 
+--R                             +--------------+
+--R                         +-+ |   2
+--R          +---+ +-+    2\|c \|a x  + b x + c  - b x - 2c
+--R       2c\|- a \|a log(---------------------------------)
+--R                                        +-+
+--R                                     2x\|c
+--R     + 
+--R           +---+ +-+
+--R         b\|- a \|c
+--R      *
+--R         log
+--R                            2           +-+          2              2  +-+
+--R                  ((- 2a b x  - 8a c x)\|c  + (4a c x  + 4b c x + 8c )\|a )
+--R               *
+--R                   +--------------+
+--R                   |   2
+--R                  \|a x  + b x + c
+--R              + 
+--R                         3              2  2              2  +-+ +-+     2   3
+--R                (- 2a b x  + (- 8a c - b )x  - 8b c x - 8c )\|a \|c  + 4a c x
+--R              + 
+--R                        2       2
+--R                6a b c x  + 8a c x
+--R           /
+--R                               +--------------+
+--R                            2  |   2
+--R                (4b c x + 8c )\|a x  + b x + c
+--R              + 
+--R                            2  2              2  +-+
+--R                ((- 4a c - b )x  - 8b c x - 8c )\|c
+--R     + 
+--R                               +--------------+
+--R                         +---+ |   2               +---+ +-+
+--R            +-+ +-+     \|- a \|a x  + b x + c  - \|- a \|c        +---+ +-+
+--R       - 2b\|a \|c atan(------------------------------------) + 2c\|- a \|a
+--R                                         a x
+--R  /
+--R       +---+ +-+ +-+
+--R     2\|- a \|a \|c
+--R                                                     Type: Expression Integer
+--E
+
+--S 79
+cc4:=aa.2-bb2
+--R
+--R   (9)
+--R                          +--------------+
+--R                      +-+ |   2
+--R           +---+    2\|c \|a x  + b x + c  - b x - 2c
+--R       - c\|- a log(---------------------------------)
+--R                                    x
+--R     + 
+--R                        +--------------+
+--R                    +-+ |   2
+--R         +---+    2\|c \|a x  + b x + c  - b x - 2c
+--R       c\|- a log(---------------------------------)
+--R                                   +-+
+--R                                2x\|c
+--R     + 
+--R                            +--------------+
+--R                  +---+ +-+ |   2                +---+
+--R         +-+     \|- a \|c \|a x  + b x + c  - c\|- a
+--R       b\|c atan(-------------------------------------)
+--R                                    +-+
+--R                                a x\|c
+--R     + 
+--R                          +--------------+
+--R                    +---+ |   2               +---+ +-+
+--R           +-+     \|- a \|a x  + b x + c  - \|- a \|c       +---+
+--R       - b\|c atan(------------------------------------) + c\|- a
+--R                                    a x
+--R  /
+--R      +---+ +-+
+--R     \|- a \|c
+--R                                                     Type: Expression Integer
+--E
+
+--S 80
+dd4:=ratDenom cc4
+--R
+--R   (10)
+--R                     +--------------+
+--R                 +-+ |   2
+--R        +-+    2\|c \|a x  + b x + c  - b x - 2c
+--R     - \|c log(---------------------------------)
+--R                               x
+--R   + 
+--R                +--------------+
+--R                |   2                           +-+
+--R      +-+    2c\|a x  + b x + c  + (- b x - 2c)\|c      +-+
+--R     \|c log(--------------------------------------) + \|c
+--R                              2c x
+--R                                                     Type: Expression Integer
+--E
+
+--S 81
+ee4:=expandLog dd4
+--R
+--R   (11)
+--R                     +--------------+
+--R        +-+      +-+ |   2
+--R     - \|c log(2\|c \|a x  + b x + c  - b x - 2c)
+--R   + 
+--R              +--------------+
+--R    +-+       |   2                           +-+                            +-+
+--R   \|c log(2c\|a x  + b x + c  + (- b x - 2c)\|c ) + (- log(c) - log(2) + 1)\|c
+--R                                                     Type: Expression Integer
+--E
+
+--S 82     14:288 Schaums and Axiom differ by a constant
+ff4:=complexNormalize ee4
+--R
+--R                                  +-+
+--R         (- log(c) - 2log(2) + 2)\|c
+--R   (12)  ----------------------------
+--R                       2
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.289~~~~~$\displaystyle
+\int{\frac{\sqrt{ax^2+bx+c}}{x^2}}~dx$}
+$$\int{\frac{\sqrt{ax^2+bx+c}}{x^2}}=
+-\frac{\sqrt{ax^2+bx+c}}{x^2}
++a\int{\frac{1}{\sqrt{ax^2+bx+c}}}
++\frac{b}{2}\int{\frac{1}{x\sqrt{ax^2+bx+c}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 83
+aa:=integrate(sqrt(a*x^2+b*x+c)/x^2,x)
+--R 
+--R
+--R   (1)
+--R   [
+--R                     +--------------+
+--R                 +-+ |   2                2 2
+--R           (4b x\|c \|a x  + b x + c  - 2b x  - 4b c x)
+--R        *
+--R                  +--------------+
+--R                  |   2                           +-+
+--R               2c\|a x  + b x + c  + (- b x - 2c)\|c
+--R           log(--------------------------------------)
+--R                                2c x
+--R       + 
+--R                     +--------------+
+--R                 +-+ |   2                     2         +-+ +-+
+--R           (8c x\|a \|a x  + b x + c  + (- 4b x  - 8c x)\|a \|c )
+--R        *
+--R                              +--------------+
+--R                +-+      +-+  |   2                 +-+ +-+       2
+--R             (2\|c  - 2x\|a )\|a x  + b x + c  + 2x\|a \|c  - 2a x  - b x - 2c
+--R         log(-----------------------------------------------------------------)
+--R                                   +--------------+
+--R                               +-+ |   2
+--R                             2\|c \|a x  + b x + c  - b x - 2c
+--R       + 
+--R                         +--------------+
+--R                     +-+ |   2                         2  2              2
+--R         (2b x + 8c)\|c \|a x  + b x + c  + (- 8a c + b )x  - 6b c x - 8c
+--R    /
+--R            +--------------+
+--R            |   2                     2         +-+
+--R       8c x\|a x  + b x + c  + (- 4b x  - 8c x)\|c
+--R     ,
+--R
+--R                     +--------------+
+--R                 +-+ |   2                2 2
+--R           (4b x\|c \|a x  + b x + c  - 2b x  - 4b c x)
+--R        *
+--R                  +--------------+
+--R                  |   2                           +-+
+--R               2c\|a x  + b x + c  + (- b x - 2c)\|c
+--R           log(--------------------------------------)
+--R                                2c x
+--R       + 
+--R                        +--------------+
+--R                  +---+ |   2                     2          +---+ +-+
+--R           (16c x\|- a \|a x  + b x + c  + (- 8b x  - 16c x)\|- a \|c )
+--R        *
+--R                 +--------------+
+--R                 |   2               +-+
+--R                \|a x  + b x + c  - \|c
+--R           atan(------------------------)
+--R                           +---+
+--R                         x\|- a
+--R       + 
+--R                         +--------------+
+--R                     +-+ |   2                         2  2              2
+--R         (2b x + 8c)\|c \|a x  + b x + c  + (- 8a c + b )x  - 6b c x - 8c
+--R    /
+--R            +--------------+
+--R            |   2                     2         +-+
+--R       8c x\|a x  + b x + c  + (- 4b x  - 8c x)\|c
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 84
+t1:=integrate(1/sqrt(a*x^2+b*x+c),x)
+--R
+--R   (2)
+--R   [
+--R       log
+--R                                 +--------------+
+--R                 +-+ +-+         |   2                   +-+
+--R              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R            + 
+--R                     2             +-+
+--R              (- 2a x  - b x - 2c)\|a
+--R         /
+--R                  +--------------+
+--R              +-+ |   2
+--R            2\|c \|a x  + b x + c  - b x - 2c
+--R    /
+--R        +-+
+--R       \|a
+--R     ,
+--R                 +--------------+
+--R           +---+ |   2               +---+ +-+
+--R          \|- a \|a x  + b x + c  - \|- a \|c
+--R    2atan(------------------------------------)
+--R                           a x
+--R    -------------------------------------------]
+--R                        +---+
+--R                       \|- a
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 85
+t2:=integrate(1/(x*sqrt(a*x^2+b*x+c)),x)
+--R
+--R                  +--------------+
+--R              +-+ |   2
+--R            2\|c \|a x  + b x + c  - b x - 2c
+--R        log(---------------------------------)
+--R                            x
+--R   (3)  --------------------------------------
+--R                          +-+
+--R                         \|c
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 86
+bb1:=-sqrt(a*x^2+b*x+c)/x+a*t1.1+b/2*t2
+--R
+--R   (4)
+--R                        +--------------+
+--R                    +-+ |   2
+--R           +-+    2\|c \|a x  + b x + c  - b x - 2c
+--R       b x\|a log(---------------------------------)
+--R                                  x
+--R     + 
+--R              +-+
+--R         2a x\|c
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                   +--------------+
+--R           +-+ +-+ |   2
+--R       - 2\|a \|c \|a x  + b x + c
+--R  /
+--R        +-+ +-+
+--R     2x\|a \|c
+--R                                                     Type: Expression Integer
+--E
+
+--S 87
+bb2:=-sqrt(a*x^2+b*x+c)/x+a*t1.2+b/2*t2
+--R
+--R   (5)
+--R                          +--------------+
+--R                      +-+ |   2
+--R           +---+    2\|c \|a x  + b x + c  - b x - 2c
+--R       b x\|- a log(---------------------------------)
+--R                                    x
+--R     + 
+--R                           +--------------+
+--R                     +---+ |   2               +---+ +-+
+--R            +-+     \|- a \|a x  + b x + c  - \|- a \|c
+--R       4a x\|c atan(------------------------------------)
+--R                                     a x
+--R     + 
+--R                     +--------------+
+--R           +---+ +-+ |   2
+--R       - 2\|- a \|c \|a x  + b x + c
+--R  /
+--R        +---+ +-+
+--R     2x\|- a \|c
+--R                                                     Type: Expression Integer
+--E
+
+--S 88
+cc1:=aa.1-bb1
+--R
+--R   (6)
+--R                     +--------------+
+--R                 +-+ |   2                 2          +-+ +-+
+--R         (- 4b c\|a \|a x  + b x + c  + (2b x + 4b c)\|a \|c )
+--R      *
+--R                   +--------------+
+--R               +-+ |   2
+--R             2\|c \|a x  + b x + c  - b x - 2c
+--R         log(---------------------------------)
+--R                             x
+--R     + 
+--R                   +--------------+
+--R               +-+ |   2                   2          +-+ +-+
+--R         (4b c\|a \|a x  + b x + c  + (- 2b x - 4b c)\|a \|c )
+--R      *
+--R                +--------------+
+--R                |   2                           +-+
+--R             2c\|a x  + b x + c  + (- b x - 2c)\|c
+--R         log(--------------------------------------)
+--R                              2c x
+--R     + 
+--R                     +--------------+
+--R                 +-+ |   2                             2
+--R         (- 8a c\|c \|a x  + b x + c  + 4a b c x + 8a c )
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                   +--------------+
+--R               +-+ |   2                             2
+--R         (8a c\|c \|a x  + b x + c  - 4a b c x - 8a c )
+--R      *
+--R                              +--------------+
+--R                +-+      +-+  |   2                 +-+ +-+       2
+--R             (2\|c  - 2x\|a )\|a x  + b x + c  + 2x\|a \|c  - 2a x  - b x - 2c
+--R         log(-----------------------------------------------------------------)
+--R                                   +--------------+
+--R                               +-+ |   2
+--R                             2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                  +--------------+
+--R              +-+ |   2                2          +-+ +-+
+--R       - 2b c\|a \|a x  + b x + c  + (b x + 2b c)\|a \|c
+--R  /
+--R                +--------------+
+--R        +-+ +-+ |   2                            2  +-+
+--R     8c\|a \|c \|a x  + b x + c  + (- 4b c x - 8c )\|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 89
+cc2:=aa.2-bb1
+--R
+--R   (7)
+--R                     +--------------+
+--R                 +-+ |   2                 2          +-+ +-+
+--R         (- 4b c\|a \|a x  + b x + c  + (2b x + 4b c)\|a \|c )
+--R      *
+--R                   +--------------+
+--R               +-+ |   2
+--R             2\|c \|a x  + b x + c  - b x - 2c
+--R         log(---------------------------------)
+--R                             x
+--R     + 
+--R                   +--------------+
+--R               +-+ |   2                   2          +-+ +-+
+--R         (4b c\|a \|a x  + b x + c  + (- 2b x - 4b c)\|a \|c )
+--R      *
+--R                +--------------+
+--R                |   2                           +-+
+--R             2c\|a x  + b x + c  + (- b x - 2c)\|c
+--R         log(--------------------------------------)
+--R                              2c x
+--R     + 
+--R                     +--------------+
+--R                 +-+ |   2                             2
+--R         (- 8a c\|c \|a x  + b x + c  + 4a b c x + 8a c )
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                            +--------------+
+--R              +---+ +-+ +-+ |   2                             2  +---+ +-+
+--R         (16c\|- a \|a \|c \|a x  + b x + c  + (- 8b c x - 16c )\|- a \|a )
+--R      *
+--R               +--------------+
+--R               |   2               +-+
+--R              \|a x  + b x + c  - \|c
+--R         atan(------------------------)
+--R                         +---+
+--R                       x\|- a
+--R     + 
+--R                  +--------------+
+--R              +-+ |   2                2          +-+ +-+
+--R       - 2b c\|a \|a x  + b x + c  + (b x + 2b c)\|a \|c
+--R  /
+--R                +--------------+
+--R        +-+ +-+ |   2                            2  +-+
+--R     8c\|a \|c \|a x  + b x + c  + (- 4b c x - 8c )\|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 90
+cc3:=aa.1-bb2
+--R
+--R   (8)
+--R                       +--------------+
+--R                 +---+ |   2                 2          +---+ +-+
+--R         (- 4b c\|- a \|a x  + b x + c  + (2b x + 4b c)\|- a \|c )
+--R      *
+--R                   +--------------+
+--R               +-+ |   2
+--R             2\|c \|a x  + b x + c  - b x - 2c
+--R         log(---------------------------------)
+--R                             x
+--R     + 
+--R                     +--------------+
+--R               +---+ |   2                   2          +---+ +-+
+--R         (4b c\|- a \|a x  + b x + c  + (- 2b x - 4b c)\|- a \|c )
+--R      *
+--R                +--------------+
+--R                |   2                           +-+
+--R             2c\|a x  + b x + c  + (- b x - 2c)\|c
+--R         log(--------------------------------------)
+--R                              2c x
+--R     + 
+--R                           +--------------+
+--R             +---+ +-+ +-+ |   2                            2  +---+ +-+
+--R         (8c\|- a \|a \|c \|a x  + b x + c  + (- 4b c x - 8c )\|- a \|a )
+--R      *
+--R                              +--------------+
+--R                +-+      +-+  |   2                 +-+ +-+       2
+--R             (2\|c  - 2x\|a )\|a x  + b x + c  + 2x\|a \|c  - 2a x  - b x - 2c
+--R         log(-----------------------------------------------------------------)
+--R                                   +--------------+
+--R                               +-+ |   2
+--R                             2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                      +--------------+
+--R                  +-+ |   2                              2
+--R         (- 16a c\|c \|a x  + b x + c  + 8a b c x + 16a c )
+--R      *
+--R                     +--------------+
+--R               +---+ |   2               +---+ +-+
+--R              \|- a \|a x  + b x + c  - \|- a \|c
+--R         atan(------------------------------------)
+--R                               a x
+--R     + 
+--R                    +--------------+
+--R              +---+ |   2                2          +---+ +-+
+--R       - 2b c\|- a \|a x  + b x + c  + (b x + 2b c)\|- a \|c
+--R  /
+--R                  +--------------+
+--R        +---+ +-+ |   2                            2  +---+
+--R     8c\|- a \|c \|a x  + b x + c  + (- 4b c x - 8c )\|- a
+--R                                                     Type: Expression Integer
+--E
+
+--S 91
+cc4:=aa.2-bb2
+--R
+--R   (9)
+--R                       +--------------+
+--R                 +---+ |   2                 2          +---+ +-+
+--R         (- 4b c\|- a \|a x  + b x + c  + (2b x + 4b c)\|- a \|c )
+--R      *
+--R                   +--------------+
+--R               +-+ |   2
+--R             2\|c \|a x  + b x + c  - b x - 2c
+--R         log(---------------------------------)
+--R                             x
+--R     + 
+--R                     +--------------+
+--R               +---+ |   2                   2          +---+ +-+
+--R         (4b c\|- a \|a x  + b x + c  + (- 2b x - 4b c)\|- a \|c )
+--R      *
+--R                +--------------+
+--R                |   2                           +-+
+--R             2c\|a x  + b x + c  + (- b x - 2c)\|c
+--R         log(--------------------------------------)
+--R                              2c x
+--R     + 
+--R                      +--------------+
+--R                  +-+ |   2                              2
+--R         (- 16a c\|c \|a x  + b x + c  + 8a b c x + 16a c )
+--R      *
+--R                     +--------------+
+--R               +---+ |   2               +---+ +-+
+--R              \|- a \|a x  + b x + c  - \|- a \|c
+--R         atan(------------------------------------)
+--R                               a x
+--R     + 
+--R                      +--------------+
+--R                  +-+ |   2                              2
+--R         (- 16a c\|c \|a x  + b x + c  + 8a b c x + 16a c )
+--R      *
+--R               +--------------+
+--R               |   2               +-+
+--R              \|a x  + b x + c  - \|c
+--R         atan(------------------------)
+--R                         +---+
+--R                       x\|- a
+--R     + 
+--R                    +--------------+
+--R              +---+ |   2                2          +---+ +-+
+--R       - 2b c\|- a \|a x  + b x + c  + (b x + 2b c)\|- a \|c
+--R  /
+--R                  +--------------+
+--R        +---+ +-+ |   2                            2  +---+
+--R     8c\|- a \|c \|a x  + b x + c  + (- 4b c x - 8c )\|- a
+--R                                                     Type: Expression Integer
+--E
+
+--S 92
+dd4:=ratDenom cc4
+--R
+--R   (10)
+--R                         +--------------+
+--R                     +-+ |   2
+--R            +-+    2\|c \|a x  + b x + c  - b x - 2c
+--R       - 2b\|c log(---------------------------------)
+--R                                   x
+--R     + 
+--R                    +--------------+
+--R                    |   2                           +-+
+--R          +-+    2c\|a x  + b x + c  + (- b x - 2c)\|c       +-+
+--R       2b\|c log(--------------------------------------) - b\|c
+--R                                  2c x
+--R  /
+--R     4c
+--R                                                     Type: Expression Integer
+--E
+
+--S 93
+ee4:=expandLog dd4
+--R
+--R   (11)
+--R                         +--------------+
+--R            +-+      +-+ |   2
+--R       - 2b\|c log(2\|c \|a x  + b x + c  - b x - 2c)
+--R     + 
+--R                    +--------------+
+--R          +-+       |   2                           +-+
+--R       2b\|c log(2c\|a x  + b x + c  + (- b x - 2c)\|c )
+--R     + 
+--R                                     +-+
+--R       (- 2b log(c) - 2b log(2) - b)\|c
+--R  /
+--R     4c
+--R                                                     Type: Expression Integer
+--E
+
+--S 94     14:289 Schaums and Axiom differ by a constant
+ff4:=complexNormalize ee4
+--R
+--R                                      +-+
+--R         (- b log(c) - 2b log(2) - b)\|c
+--R   (12)  --------------------------------
+--R                        4c
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.290~~~~~$\displaystyle
+\int{\frac{dx}{(ax^2+bx+c)^{3/2}}}$}
+$$
+\int{\frac{1}{(ax^2+bx+c)^{3/2}}}=
+\frac{2(2ax+b)}{(4ac-b^2)\sqrt{ax^2+bx+c}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 95
+aa:=integrate(1/(a*x^2+b*x+c)^(3/2),x)
+--R 
+--R
+--R                          +--------------+
+--R                          |   2                 +-+
+--R                     - 2x\|a x  + b x + c  + 2x\|c
+--R   (1)  --------------------------------------------------------
+--R                       +--------------+
+--R                   +-+ |   2                    2              2
+--R        (b x + 2c)\|c \|a x  + b x + c  - 2a c x  - 2b c x - 2c
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 96
+bb:=(2*(2*a*x+b))/((4*a*c-b^2)*sqrt(a*x^2+b*x+c))
+--R
+--R                  4a x + 2b
+--R   (2)  ----------------------------
+--R                    +--------------+
+--R                 2  |   2
+--R        (4a c - b )\|a x  + b x + c
+--R                                                     Type: Expression Integer
+--E
+
+--S 97
+cc:=aa-bb
+--R
+--R   (3)
+--R                           +--------------+
+--R                       +-+ |   2                2
+--R                    4b\|c \|a x  + b x + c  - 2b x - 4b c
+--R   -----------------------------------------------------------------------
+--R                  +--------------+
+--R        2     2   |   2                            3         2     2   +-+
+--R   (8a c  - 2b c)\|a x  + b x + c  + ((- 4a b c + b )x - 8a c  + 2b c)\|c
+--R                                                     Type: Expression Integer
+--E
+
+--S 98     14:290 Schaums and Axiom differ by a constant
+dd:=ratDenom cc
+--R
+--R              +-+
+--R           2b\|c
+--R   (4)  -----------
+--R            2    2
+--R        4a c  - b c
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.291~~~~~$\displaystyle
+\int{\frac{x~dx}{(ax^2+bx+c)^{3/2}}}$}
+$$\int{\frac{x}{(ax^2+bx+c)^{3/2}}}=
+\frac{2(bx+2c)}{(b^2-4ac)\sqrt{ax^2+bx+c}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 99
+aa:=integrate(x/(a*x^2+b*x+c)^(3/2),x)
+--R 
+--R
+--R                                   2 +-+
+--R                                 2x \|c
+--R   (1)  --------------------------------------------------------
+--R                       +--------------+
+--R                   +-+ |   2                    2              2
+--R        (b x + 2c)\|c \|a x  + b x + c  - 2a c x  - 2b c x - 2c
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 100
+bb:=(2*(b*x+2*c))/((b^2-4*a*c)*sqrt(a*x^2+b*x+c))
+--R
+--R                 - 2b x - 4c
+--R   (2)  ----------------------------
+--R                    +--------------+
+--R                 2  |   2
+--R        (4a c - b )\|a x  + b x + c
+--R                                                     Type: Expression Integer
+--E
+
+--S 101
+cc:=aa-bb
+--R
+--R   (3)
+--R                            +--------------+
+--R                        +-+ |   2                         2
+--R                   - 8c\|c \|a x  + b x + c  + 4b c x + 8c
+--R   -----------------------------------------------------------------------
+--R                  +--------------+
+--R        2     2   |   2                            3         2     2   +-+
+--R   (8a c  - 2b c)\|a x  + b x + c  + ((- 4a b c + b )x - 8a c  + 2b c)\|c
+--R                                                     Type: Expression Integer
+--E
+
+--S 102    14:291 Schaums and Axiom differ by a constant
+dd:=ratDenom cc
+--R
+--R              +-+
+--R            4\|c
+--R   (4)  - ---------
+--R                  2
+--R          4a c - b
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.292~~~~~$\displaystyle
+\int{\frac{x^2~dx}{(ax^2+bx+c)^{3/2}}}$}
+$$\int{\frac{x^2}{(ax^2+bx+c)^{3/2}}}=
+\frac{(2b^2-4ac)x+2bc}{a(4ac-b^2)\sqrt{ax^2+bx+c}}
++\frac{1}{a}\int{\frac{1}{\sqrt{ax^2+bx+c}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 103
+aa:=integrate(x^2/(a*x^2+b*x+c)^(3/2),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R                           +--------------+
+--R                       +-+ |   2                    2              2
+--R           ((b x + 2c)\|c \|a x  + b x + c  - 2a c x  - 2b c x - 2c )
+--R        *
+--R           log
+--R                                     +--------------+
+--R                     +-+ +-+         |   2                   +-+
+--R                  (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R                + 
+--R                         2             +-+
+--R                  (- 2a x  - b x - 2c)\|a
+--R             /
+--R                      +--------------+
+--R                  +-+ |   2
+--R                2\|c \|a x  + b x + c  - b x - 2c
+--R       + 
+--R                  +--------------+
+--R              +-+ |   2                     2         +-+ +-+
+--R         2c x\|a \|a x  + b x + c  + (- 2b x  - 2c x)\|a \|c
+--R    /
+--R                                +--------------+
+--R                        +-+ +-+ |   2
+--R         (a b x + 2a c)\|a \|c \|a x  + b x + c
+--R       + 
+--R              2   2                  2  +-+
+--R         (- 2a c x  - 2a b c x - 2a c )\|a
+--R     ,
+--R
+--R                            +--------------+
+--R                        +-+ |   2                    2              2
+--R           ((2b x + 4c)\|c \|a x  + b x + c  - 4a c x  - 4b c x - 4c )
+--R        *
+--R                       +--------------+
+--R                 +---+ |   2               +---+ +-+
+--R                \|- a \|a x  + b x + c  - \|- a \|c
+--R           atan(------------------------------------)
+--R                                 a x
+--R       + 
+--R                    +--------------+
+--R              +---+ |   2                     2         +---+ +-+
+--R         2c x\|- a \|a x  + b x + c  + (- 2b x  - 2c x)\|- a \|c
+--R    /
+--R                                  +--------------+
+--R                        +---+ +-+ |   2
+--R         (a b x + 2a c)\|- a \|c \|a x  + b x + c
+--R       + 
+--R              2   2                  2  +---+
+--R         (- 2a c x  - 2a b c x - 2a c )\|- a
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+
+--S 104
+t1:=integrate(1/sqrt(a*x^2+b*x+c),x)
+--R
+--R   (2)
+--R   [
+--R       log
+--R                                 +--------------+
+--R                 +-+ +-+         |   2                   +-+
+--R              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R            + 
+--R                     2             +-+
+--R              (- 2a x  - b x - 2c)\|a
+--R         /
+--R                  +--------------+
+--R              +-+ |   2
+--R            2\|c \|a x  + b x + c  - b x - 2c
+--R    /
+--R        +-+
+--R       \|a
+--R     ,
+--R                 +--------------+
+--R           +---+ |   2               +---+ +-+
+--R          \|- a \|a x  + b x + c  - \|- a \|c
+--R    2atan(------------------------------------)
+--R                           a x
+--R    -------------------------------------------]
+--R                        +---+
+--R                       \|- a
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 105
+bb1:=((2*b^2-4*a*c)*x+2*b*c)/(a*(4*a*c-b^2)*sqrt(a*x^2+b*x+c))+1/a*t1.1
+--R
+--R   (3)
+--R                     +--------------+
+--R                  2  |   2
+--R         (4a c - b )\|a x  + b x + c
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                    2           +-+
+--R       ((- 4a c + 2b )x + 2b c)\|a
+--R  /
+--R                       +--------------+
+--R        2       2  +-+ |   2
+--R     (4a c - a b )\|a \|a x  + b x + c
+--R                                                     Type: Expression Integer
+--E
+
+--S 106
+bb2:=((2*b^2-4*a*c)*x+2*b*c)/(a*(4*a*c-b^2)*sqrt(a*x^2+b*x+c))+1/a*t1.2
+--R
+--R   (4)
+--R                                                +--------------+
+--R                    +--------------+      +---+ |   2               +---+ +-+
+--R                 2  |   2                \|- a \|a x  + b x + c  - \|- a \|c
+--R       (8a c - 2b )\|a x  + b x + c atan(------------------------------------)
+--R                                                          a x
+--R     + 
+--R                    2           +---+
+--R       ((- 4a c + 2b )x + 2b c)\|- a
+--R  /
+--R                         +--------------+
+--R        2       2  +---+ |   2
+--R     (4a c - a b )\|- a \|a x  + b x + c
+--R                                                     Type: Expression Integer
+--E
+
+--S 107
+cc1:=aa.1-bb1
+--R
+--R   (5)
+--R                              +--------------+
+--R                          +-+ |   2                2          2
+--R                     4b c\|c \|a x  + b x + c  - 2b c x - 4b c
+--R   -----------------------------------------------------------------------------
+--R                    +--------------+
+--R      2 2       2   |   2                    2         3       2 2       2   +-+
+--R   (8a c  - 2a b c)\|a x  + b x + c  + ((- 4a b c + a b )x - 8a c  + 2a b c)\|c
+--R                                                     Type: Expression Integer
+--E
+
+--S 108
+cc2:=aa.2-bb1
+--R
+--R   (6)
+--R                                  +--------------+
+--R                  2     2   +---+ |   2
+--R           (- 8a c  + 2b c)\|- a \|a x  + b x + c
+--R         + 
+--R                       3         2     2   +---+ +-+
+--R           ((4a b c - b )x + 8a c  - 2b c)\|- a \|c
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                               +--------------+
+--R                 2     2   +-+ |   2
+--R           (16a c  - 4b c)\|a \|a x  + b x + c
+--R         + 
+--R                          3          2     2   +-+ +-+
+--R           ((- 8a b c + 2b )x - 16a c  + 4b c)\|a \|c
+--R      *
+--R                     +--------------+
+--R               +---+ |   2               +---+ +-+
+--R              \|- a \|a x  + b x + c  - \|- a \|c
+--R         atan(------------------------------------)
+--R                               a x
+--R     + 
+--R                          +--------------+
+--R            +---+ +-+ +-+ |   2                   2          2  +---+ +-+
+--R       4b c\|- a \|a \|c \|a x  + b x + c  + (- 2b c x - 4b c )\|- a \|a
+--R  /
+--R                                  +--------------+
+--R          2 2       2   +---+ +-+ |   2
+--R       (8a c  - 2a b c)\|- a \|a \|a x  + b x + c
+--R     + 
+--R             2         3       2 2       2   +---+ +-+ +-+
+--R       ((- 4a b c + a b )x - 8a c  + 2a b c)\|- a \|a \|c
+--R                                                     Type: Expression Integer
+--E
+
+--S 109
+cc3:=aa.1-bb2
+--R
+--R   (7)
+--R                                +--------------+
+--R                2     2   +---+ |   2
+--R           (8a c  - 2b c)\|- a \|a x  + b x + c
+--R         + 
+--R                         3         2     2   +---+ +-+
+--R           ((- 4a b c + b )x - 8a c  + 2b c)\|- a \|c
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                                 +--------------+
+--R                   2     2   +-+ |   2
+--R           (- 16a c  + 4b c)\|a \|a x  + b x + c
+--R         + 
+--R                        3          2     2   +-+ +-+
+--R           ((8a b c - 2b )x + 16a c  - 4b c)\|a \|c
+--R      *
+--R                     +--------------+
+--R               +---+ |   2               +---+ +-+
+--R              \|- a \|a x  + b x + c  - \|- a \|c
+--R         atan(------------------------------------)
+--R                               a x
+--R     + 
+--R                          +--------------+
+--R            +---+ +-+ +-+ |   2                   2          2  +---+ +-+
+--R       4b c\|- a \|a \|c \|a x  + b x + c  + (- 2b c x - 4b c )\|- a \|a
+--R  /
+--R                                  +--------------+
+--R          2 2       2   +---+ +-+ |   2
+--R       (8a c  - 2a b c)\|- a \|a \|a x  + b x + c
+--R     + 
+--R             2         3       2 2       2   +---+ +-+ +-+
+--R       ((- 4a b c + a b )x - 8a c  + 2a b c)\|- a \|a \|c
+--R                                                     Type: Expression Integer
+--E
+
+--S 110
+cc4:=aa.2-bb2
+--R
+--R   (8)
+--R                              +--------------+
+--R                          +-+ |   2                2          2
+--R                     4b c\|c \|a x  + b x + c  - 2b c x - 4b c
+--R   -----------------------------------------------------------------------------
+--R                    +--------------+
+--R      2 2       2   |   2                    2         3       2 2       2   +-+
+--R   (8a c  - 2a b c)\|a x  + b x + c  + ((- 4a b c + a b )x - 8a c  + 2a b c)\|c
+--R                                                     Type: Expression Integer
+--E
+
+--S 111    14:292 Schaums and Axiom differ by a constant
+dd4:=ratDenom cc4
+--R
+--R              +-+
+--R           2b\|c
+--R   (9)  -----------
+--R          2       2
+--R        4a c - a b
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.293~~~~~$\displaystyle
+\int{\frac{dx}{x(ax^2+bx+c)^{3/2}}}$}
+$$\int{\frac{1}{x(ax^2+bx+c)^{3/2}}}=
+\frac{1}{c\sqrt{ax^2+bx+c}}
++\frac{1}{c}\int{\frac{1}{x\sqrt{ax^2+bx+c}}}
+-\frac{b}{2c}\int{\frac{1}{(ax^2+bx+c)^{3/2}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 112
+aa:=integrate(1/(x*(a*x^2+b*x+c)^(3/2)),x)
+--R 
+--R
+--R   (1)
+--R                     +--------------+
+--R                     |   2                     2              +-+
+--R         ((b x + 2c)\|a x  + b x + c  + (- 2a x  - 2b x - 2c)\|c )
+--R      *
+--R                   +--------------+
+--R               +-+ |   2
+--R             2\|c \|a x  + b x + c  - b x - 2c
+--R         log(---------------------------------)
+--R                              +-+
+--R                           2x\|c
+--R     + 
+--R            +--------------+
+--R            |   2                     2         +-+
+--R       2b x\|a x  + b x + c  + (- 2a x  - 2b x)\|c
+--R  /
+--R                       +--------------+
+--R                2  +-+ |   2                  2 2       2      3
+--R     (b c x + 2c )\|c \|a x  + b x + c  - 2a c x  - 2b c x - 2c
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 113
+t1:=integrate(1/(x*sqrt(a*x^2+b*x+c)),x)
+--R
+--R                  +--------------+
+--R              +-+ |   2
+--R            2\|c \|a x  + b x + c  - b x - 2c
+--R        log(---------------------------------)
+--R                            x
+--R   (2)  --------------------------------------
+--R                          +-+
+--R                         \|c
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 114
+t2:=integrate(1/(a*x^2+b*x+c)^(3/2),x)
+--R
+--R                          +--------------+
+--R                          |   2                 +-+
+--R                     - 2x\|a x  + b x + c  + 2x\|c
+--R   (3)  --------------------------------------------------------
+--R                       +--------------+
+--R                   +-+ |   2                    2              2
+--R        (b x + 2c)\|c \|a x  + b x + c  - 2a c x  - 2b c x - 2c
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 115
+bb:=1/(c*sqrt(a*x^2+b*x+c))+1/c*t1-b/(2*c)*t2
+--R
+--R   (4)
+--R                                    +--------------+
+--R                  2              2  |   2
+--R           (2a c x  + 2b c x + 2c )\|a x  + b x + c
+--R         + 
+--R                   3              2  2              2  +-+
+--R           (- a b x  + (- 2a c - b )x  - 3b c x - 2c )\|c
+--R      *
+--R                   +--------------+
+--R               +-+ |   2
+--R             2\|c \|a x  + b x + c  - b x - 2c
+--R         log(---------------------------------)
+--R                             x
+--R     + 
+--R             +--------------+
+--R           2 |   2                      3            2  2             2  +-+
+--R       - 2c \|a x  + b x + c  + (- a b x  + (2a c - b )x  + b c x + 2c )\|c
+--R  /
+--R                                    +--------------+
+--R            2 2       2      3  +-+ |   2                   2 3
+--R       (2a c x  + 2b c x + 2c )\|c \|a x  + b x + c  - a b c x
+--R     + 
+--R              3    2 2  2       3      4
+--R       (- 2a c  - b c )x  - 3b c x - 2c
+--R                                                     Type: Expression Integer
+--E
+
+--S 116
+cc:=aa-bb
+--R
+--R   (5)
+--R                                            +--------------+
+--R                       2  2              2  |   2
+--R           ((- 4a c - b )x  - 8b c x - 8c )\|a x  + b x + c
+--R         + 
+--R                  3             2  2               2  +-+
+--R           (4a b x  + (8a c + 4b )x  + 12b c x + 8c )\|c
+--R      *
+--R                   +--------------+
+--R               +-+ |   2
+--R             2\|c \|a x  + b x + c  - b x - 2c
+--R         log(---------------------------------)
+--R                             x
+--R     + 
+--R                                          +--------------+
+--R                     2  2              2  |   2
+--R           ((4a c + b )x  + 8b c x + 8c )\|a x  + b x + c
+--R         + 
+--R                    3               2  2               2  +-+
+--R           (- 4a b x  + (- 8a c - 4b )x  - 12b c x - 8c )\|c
+--R      *
+--R                   +--------------+
+--R               +-+ |   2
+--R             2\|c \|a x  + b x + c  - b x - 2c
+--R         log(---------------------------------)
+--R                              +-+
+--R                           2x\|c
+--R     + 
+--R                                      +--------------+
+--R                 2  2              2  |   2
+--R       ((4a c + b )x  + 8b c x + 8c )\|a x  + b x + c
+--R     + 
+--R                3               2  2               2  +-+
+--R       (- 4a b x  + (- 8a c - 4b )x  - 12b c x - 8c )\|c
+--R  /
+--R                                            +--------------+
+--R             2    2   2       2      3  +-+ |   2                    2 3
+--R       ((4a c  + b c)x  + 8b c x + 8c )\|c \|a x  + b x + c  - 4a b c x
+--R     + 
+--R              3     2 2  2        3      4
+--R       (- 8a c  - 4b c )x  - 12b c x - 8c
+--R                                                     Type: Expression Integer
+--E
+
+--S 117
+dd:=ratDenom cc
+--R
+--R   (6)
+--R                       +--------------+
+--R                   +-+ |   2
+--R          +-+    2\|c \|a x  + b x + c  - b x - 2c
+--R       - \|c log(---------------------------------)
+--R                                 x
+--R     + 
+--R                  +--------------+
+--R                  |   2                           +-+
+--R        +-+    2c\|a x  + b x + c  + (- b x - 2c)\|c      +-+
+--R       \|c log(--------------------------------------) + \|c
+--R                                2c x
+--R  /
+--R      2
+--R     c
+--R                                                     Type: Expression Integer
+--E
+
+--S 118
+ee:=expandLog dd
+--R
+--R   (7)
+--R                       +--------------+
+--R          +-+      +-+ |   2
+--R       - \|c log(2\|c \|a x  + b x + c  - b x - 2c)
+--R     + 
+--R                  +--------------+
+--R        +-+       |   2                           +-+
+--R       \|c log(2c\|a x  + b x + c  + (- b x - 2c)\|c )
+--R     + 
+--R                               +-+
+--R       (- log(c) - log(2) + 1)\|c
+--R  /
+--R      2
+--R     c
+--R                                                     Type: Expression Integer
+--E
+
+--S 119    14:293 Schaums and Axiom differ by a constant
+ff:=complexNormalize ee
+--R
+--R                                 +-+
+--R        (- log(c) - 2log(2) + 2)\|c
+--R   (8)  ----------------------------
+--R                       2
+--R                     2c
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.294~~~~~$\displaystyle
+\int{\frac{dx}{x^2(ax^2+bx+c)^{3/2}}}$}
+$$\begin{array}{rl}
+\displaystyle\int{\frac{1}{x^2(ax^2+bx+c)^{3/2}}}=
+&amp;\displaystyle-\frac{ax^2+bx+c}{c^2x\sqrt{ax^2+bx+c}}\\
+&amp;\\
+&amp;\displaystyle+\frac{b^2-2ac}{2c^2}\int{\frac{1}{(ax^2+bx+c)^{3/2}}}\\
+&amp;\\
+&amp;\displaystyle-\frac{3b}{2c^2}\int{\frac{1}{x\sqrt{ax^2+bx+c}}}
+\end{array}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 120
+aa:=integrate(1/(x^2*(a*x^2+b*x+c)^(3/2)),x)
+--R 
+--R
+--R   (1)
+--R                                                          +--------------+
+--R                           3  3      2   2        2   +-+ |   2
+--R           ((- 24a b c - 6b )x  - 48b c x  - 48b c x)\|c \|a x  + b x + c
+--R         + 
+--R                2   4           2      3   3      2 2 2        3
+--R           24a b c x  + (48a b c  + 24b c)x  + 72b c x  + 48b c x
+--R      *
+--R                   +--------------+
+--R               +-+ |   2
+--R             2\|c \|a x  + b x + c  - b x - 2c
+--R         log(---------------------------------)
+--R                              +-+
+--R                           2x\|c
+--R     + 
+--R                      3  3         2      2   2        2       3  +-+
+--R         ((4a b c - 9b )x  + (64a c  - 24b c)x  + 40b c x + 32c )\|c
+--R      *
+--R          +--------------+
+--R          |   2
+--R         \|a x  + b x + c
+--R     + 
+--R             2 2        2   4             2      3   3           3     2 2  2
+--R       (- 32a c  + 24a b c)x  + (- 48a b c  + 24b c)x  + (- 80a c  + 8b c )x
+--R     + 
+--R              3       4
+--R       - 56b c x - 32c
+--R  /
+--R                                               +--------------+
+--R              4     2 3  3        4 2      5   |   2
+--R       ((16a c  + 4b c )x  + 32b c x  + 32c x)\|a x  + b x + c
+--R     + 
+--R                 3 4           4      2 3  3        4 2      5   +-+
+--R       (- 16a b c x  + (- 32a c  - 16b c )x  - 48b c x  - 32c x)\|c
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 121
+t1:=integrate(1/(a*x^2+b*x+c)^(3/2),x)
+--R
+--R                          +--------------+
+--R                          |   2                 +-+
+--R                     - 2x\|a x  + b x + c  + 2x\|c
+--R   (2)  --------------------------------------------------------
+--R                       +--------------+
+--R                   +-+ |   2                    2              2
+--R        (b x + 2c)\|c \|a x  + b x + c  - 2a c x  - 2b c x - 2c
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 122
+t2:=integrate(1/(x*sqrt(a*x^2+b*x+c)),x)
+--R
+--R                  +--------------+
+--R              +-+ |   2
+--R            2\|c \|a x  + b x + c  - b x - 2c
+--R        log(---------------------------------)
+--R                            x
+--R   (3)  --------------------------------------
+--R                          +-+
+--R                         \|c
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 123
+bb:=-(a*x^2+2*b*x+c)/(c^2*x*sqrt(a*x^2+b*x+c))+(b^2-2*a*c)/(2*c^2)*t1-(3*b)/(2*c^2)*t2
+--R
+--R   (4)
+--R                                            +--------------+
+--R                      3     2   2       2   |   2
+--R           (- 6a b c x  - 6b c x  - 6b c x)\|a x  + b x + c
+--R         + 
+--R                2 4               3  3     2   2       2   +-+
+--R           (3a b x  + (6a b c + 3b )x  + 9b c x  + 6b c x)\|c
+--R      *
+--R                   +--------------+
+--R               +-+ |   2
+--R             2\|c \|a x  + b x + c  - b x - 2c
+--R         log(---------------------------------)
+--R                             x
+--R     + 
+--R                                                      +--------------+
+--R                3        2     2   2        2      3  |   2
+--R       (2a b c x  + (8a c  + 2b c)x  + 10b c x + 4c )\|a x  + b x + c
+--R     + 
+--R                2        2  4                  3  3           2     2   2
+--R           (- 8a c + 2a b )x  + (- 16a b c + 2b )x  + (- 12a c  - 6b c)x
+--R         + 
+--R                  2      3
+--R           - 12b c x - 4c
+--R      *
+--R          +-+
+--R         \|c
+--R  /
+--R                                      +--------------+
+--R            3 3       3 2     4   +-+ |   2                    3 4
+--R       (4a c x  + 4b c x  + 4c x)\|c \|a x  + b x + c  - 2a b c x
+--R     + 
+--R              4     2 3  3       4 2     5
+--R       (- 4a c  - 2b c )x  - 6b c x  - 4c x
+--R                                                     Type: Expression Integer
+--E
+
+--S 124
+cc:=aa-bb
+--R
+--R   (5)
+--R                    2      4  3            2       3   2       2 2          3
+--R             ((72a b c + 6b )x  + (144a b c  + 108b c)x  + 288b c x + 192b c )
+--R          *
+--R                  +--------------+
+--R              +-+ |   2
+--R             \|c \|a x  + b x + c
+--R         + 
+--R                 2   2        3   4            2 2      4   3
+--R           (- 48a b c  - 36a b c)x  + (- 240a b c  - 36b c)x
+--R         + 
+--R                      3       3 2  2       2 3          4
+--R           (- 240a b c  - 228b c )x  - 384b c x - 192b c
+--R      *
+--R                   +--------------+
+--R               +-+ |   2
+--R             2\|c \|a x  + b x + c  - b x - 2c
+--R         log(---------------------------------)
+--R                             x
+--R     + 
+--R                         2      4  3              2       3   2       2 2
+--R                 (- 72a b c - 6b )x  + (- 144a b c  - 108b c)x  - 288b c x
+--R               + 
+--R                         3
+--R                 - 192b c
+--R          *
+--R                  +--------------+
+--R              +-+ |   2
+--R             \|c \|a x  + b x + c
+--R         + 
+--R               2   2        3   4          2 2      4   3
+--R           (48a b c  + 36a b c)x  + (240a b c  + 36b c)x
+--R         + 
+--R                    3       3 2  2       2 3          4
+--R           (240a b c  + 228b c )x  + 384b c x + 192b c
+--R      *
+--R                   +--------------+
+--R               +-+ |   2
+--R             2\|c \|a x  + b x + c  - b x - 2c
+--R         log(---------------------------------)
+--R                              +-+
+--R                           2x\|c
+--R     + 
+--R                  2      4  3              2      3   2       2 2          3
+--R         ((- 60a b c - 5b )x  + (- 120a b c  - 90b c)x  - 240b c x - 160b c )
+--R      *
+--R              +--------------+
+--R          +-+ |   2
+--R         \|c \|a x  + b x + c
+--R     + 
+--R           2   2        3   4          2 2      4   3            3       3 2  2
+--R       (40a b c  + 30a b c)x  + (200a b c  + 30b c)x  + (200a b c  + 190b c )x
+--R     + 
+--R           2 3          4
+--R       320b c x + 160b c
+--R  /
+--R                  4     3 3  3         5      2 4  2         5        6
+--R         ((48a b c  + 4b c )x  + (96a c  + 72b c )x  + 192b c x + 128c )
+--R      *
+--R          +--------------+
+--R          |   2
+--R         \|a x  + b x + c
+--R     + 
+--R                 2 4        2 3  4              4      3 3  3
+--R           (- 32a c  - 24a b c )x  + (- 160a b c  - 24b c )x
+--R         + 
+--R                    5       2 4  2         5        6
+--R           (- 160a c  - 152b c )x  - 256b c x - 128c
+--R      *
+--R          +-+
+--R         \|c
+--R                                                     Type: Expression Integer
+--E
+
+--S 125
+dd:=ratDenom cc
+--R
+--R   (6)
+--R                       +--------------+
+--R                   +-+ |   2
+--R          +-+    2\|c \|a x  + b x + c  - b x - 2c
+--R       6b\|c log(---------------------------------)
+--R                                 x
+--R     + 
+--R                      +--------------+
+--R                      |   2                           +-+
+--R            +-+    2c\|a x  + b x + c  + (- b x - 2c)\|c        +-+
+--R       - 6b\|c log(--------------------------------------) - 5b\|c
+--R                                    2c x
+--R  /
+--R       3
+--R     4c
+--R                                                     Type: Expression Integer
+--E
+
+--S 126
+ee:=expandLog dd
+--R
+--R   (7)
+--R                       +--------------+
+--R          +-+      +-+ |   2
+--R       6b\|c log(2\|c \|a x  + b x + c  - b x - 2c)
+--R     + 
+--R                      +--------------+
+--R            +-+       |   2                           +-+
+--R       - 6b\|c log(2c\|a x  + b x + c  + (- b x - 2c)\|c )
+--R     + 
+--R                                    +-+
+--R       (6b log(c) + 6b log(2) - 5b)\|c
+--R  /
+--R       3
+--R     4c
+--R                                                     Type: Expression Integer
+--E
+
+--S 127    14:294 Schaums and Axiom differ by a constant
+ff:=complexNormalize ee
+--R
+--R                                     +-+
+--R        (3b log(c) + 6b log(2) - 5b)\|c
+--R   (8)  --------------------------------
+--R                         3
+--R                       4c
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.295~~~~~$\displaystyle
+\int{(ax^2+bx+c)^{n+1/2}}~dx$}
+$$\begin{array}{rl}
+\displaystyle\int{(ax^2+bx+c)^{n+1/2}}=
+&amp;\displaystyle\frac{(2ax+b)(ax^2+bx+c)^{n+1/2}}{4a(n+1)}\\
+&amp;\\
+&amp;\displaystyle+\frac{(2n+1)(4ac-b^2)}{8a(n+1)}
+\int{(ax^2+bx+c)^{n-1/2}}
+\end{array}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 128    14:295 Axiom cannot compute this integral
+aa:=integrate((a*x^2+b*x+c)^(n+1/2),x)
+--R 
+--R
+--R                              2n + 1
+--R           x                  ------
+--R         ++                2     2
+--I   (1)   |   (c + %N b + %N a)      d%N
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.296~~~~~$\displaystyle
+\int{x(ax^2+bx+c)^{n+1/2}}~dx$}
+$$\int{x(ax^2+bx+c)^{n+1/2}}=
+\frac{(ax^2+bx+c)^{n+3/2}}{a(2n+3)}-
+\frac{b}{2a}\int{(ax^2+bx+c)^{n+1/2}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 129    14:296 Axiom cannot compute this integral
+aa:=integrate(x*(a*x^2+b*x+c)^(n+1/2),x)
+--R 
+--R
+--R                                 2n + 1
+--R           x                     ------
+--R         ++                   2     2
+--I   (1)   |   %N (c + %N b + %N a)      d%N
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.297~~~~~$\displaystyle
+\int{\frac{dx}{(ax^2+bx+c)^{n+1/2}}}$}
+$$\begin{array}{rl}
+\displaystyle\int{\frac{1}{(ax^2+bx+c)^{n+1/2}}}=
+&amp;\displaystyle\frac{2(2ax+b)}{(2n-1)(4ac-b^2)(ax^2+bx+c)^{n-1/2}}\\
+&amp;\\
+&amp;\displaystyle
++\frac{8a(n-1)}{(2n-1)(4ac-b^2)}\int{\frac{1}{(ax^2+bx+c)^{n-1/2}}}
+\end{array}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 130    14:297 Axiom cannot compute this integral
+aa:=integrate(1/(a*x^2+b*x+c)^(n+1/2),x)
+--R 
+--R
+--R           x
+--R         ++             1
+--I   (1)   |   ----------------------- d%N
+--R        ++                    2n + 1
+--R                              ------
+--R                           2     2
+--I             (c + %N b + %N a)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.298~~~~~$\displaystyle
+\int{\frac{dx}{x(ax^2+bx+c)^{n+1/2}}}$}
+$$\begin{array}{rl}
+\displaystyle\int{\frac{1}{x(ax^2+bx+c)^{n+1/2}}}=
+&amp;\displaystyle\frac{1}{(2n-1)c(ax^2+bx+c)^{n-1/2}}\\
+&amp;\\
+&amp;\displaystyle
++\frac{1}{c}\int{\frac{1}{x(ax^2+bx+c)^{n-1/2}}}\\
+&amp;\\
+&amp;\displaystyle
+-\frac{b}{2c}\int{\frac{1}{(ax^2+bx+c)^{n+1/2}}}
+\end{array}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 131    14:298 Axiom cannot compute this integral
+aa:=integrate(1/(x*(a*x^2+b*x+c)^(n+1/2)),x)
+--R 
+--R
+--R           x
+--R         ++               1
+--I   (1)   |   -------------------------- d%N
+--R        ++                       2n + 1
+--R                                 ------
+--R                              2     2
+--I             %N (c + %N b + %N a)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 pp72-73
+\end{thebibliography}
+\end{document}
diff --git a/src/axiom-website/CATS/schaum13.input.pdf b/src/axiom-website/CATS/schaum13.input.pdf
new file mode 100644
index 0000000..91d46bd
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+++ b/src/axiom-website/CATS/schaum13.input.pdf
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diff --git a/src/axiom-website/CATS/schaum14.input.pamphlet b/src/axiom-website/CATS/schaum14.input.pamphlet
new file mode 100644
index 0000000..3452b30
--- /dev/null
+++ b/src/axiom-website/CATS/schaum14.input.pamphlet
@@ -0,0 +1,621 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum14.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.299~~~~~$\displaystyle
+\int{\frac{dx}{x^3+a^3}}$}
+$$\int{\frac{1}{x^3+a^3}}=
+\frac{1}{6a^2}\ln\frac{(x+a)^2}{x^2-ax+a^2}
++\frac{1}{a^2\sqrt{3}}\tan^{-1}\frac{2x-a}{a\sqrt{3}}
+$$
+&lt;&lt;*&gt;&gt;=
+)spool schaum14.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1
+aa:=integrate(1/(x^3+a^3),x)
+--R 
+--R
+--R                                                                    +-+
+--R           +-+     2          2      +-+                   (2x - a)\|3
+--R        - \|3 log(x  - a x + a ) + 2\|3 log(x + a) + 6atan(------------)
+--R                                                                3a
+--R   (1)  ----------------------------------------------------------------
+--R                                       2 +-+
+--R                                     6a \|3
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 2
+bb:=1/(6*a^2)*log((x+a)^2/(x^2-a*x+a^2))+1/(a^2*sqrt(3))*atan((2*x-a)/(a*sqrt(3)))
+--R
+--R             2           2                       +-+
+--R            x  + 2a x + a       +-+     (2x - a)\|3
+--R        log(--------------) + 2\|3 atan(------------)
+--R              2          2                   3a
+--R             x  - a x + a
+--R   (2)  ---------------------------------------------
+--R                               2
+--R                             6a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3
+cc:=aa-bb
+--R
+--R                                                  2           2
+--R               2          2                      x  + 2a x + a
+--R        - log(x  - a x + a ) + 2log(x + a) - log(--------------)
+--R                                                   2          2
+--R                                                  x  - a x + a
+--R   (3)  --------------------------------------------------------
+--R                                     2
+--R                                   6a
+--R                                                     Type: Expression Integer
+--E
+
+--S 4      14:299 Schaums and Axiom agree
+dd:=expandLog cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.300~~~~~$\displaystyle
+\int{\frac{x~dx}{x^3+a^3}}$}
+$$\int{\frac{x}{x^3+a^3}}=
+\frac{1}{6a}\ln\frac{x^2-ax+a^2}{(x+a)^2}
++\frac{1}{a\sqrt{3}}\tan^{-1}\frac{2x-a}{a\sqrt{3}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 5
+aa:=integrate(x/(x^3+a^3),x)
+--R 
+--R
+--R                                                                  +-+
+--R         +-+     2          2      +-+                   (2x - a)\|3
+--R        \|3 log(x  - a x + a ) - 2\|3 log(x + a) + 6atan(------------)
+--R                                                              3a
+--R   (1)  --------------------------------------------------------------
+--R                                       +-+
+--R                                    6a\|3
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 6
+bb:=1/(6*a)*log((x^2-a*x+a^2)/(x+a)^2)+1/(a*sqrt(3))*atan((2*x-a)/(a*sqrt(3)))
+--R
+--R              2          2                       +-+
+--R             x  - a x + a       +-+     (2x - a)\|3
+--R        log(--------------) + 2\|3 atan(------------)
+--R             2           2                   3a
+--R            x  + 2a x + a
+--R   (2)  ---------------------------------------------
+--R                              6a
+--R                                                     Type: Expression Integer
+--E
+
+--S 7
+cc:=aa-bb
+--R
+--R                                                 2          2
+--R             2          2                       x  - a x + a
+--R        log(x  - a x + a ) - 2log(x + a) - log(--------------)
+--R                                                2           2
+--R                                               x  + 2a x + a
+--R   (3)  ------------------------------------------------------
+--R                                  6a
+--R                                                     Type: Expression Integer
+--E
+
+--S 8      14:300 Schaums and Axiom agree
+dd:=expandLog cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.301~~~~~$\displaystyle
+\int{\frac{x^2~dx}{x^3+a^3}}$}
+$$\int{\frac{x^2}{x^3+a^3}}=
+\frac{1}{3}\ln(x^3+a^3)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 9
+aa:=integrate(x^2/(x^3+a^3),x)
+--R 
+--R
+--R             3    3
+--R        log(x  + a )
+--R   (1)  ------------
+--R              3
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 10
+bb:=1/3*log(x^3+a^3)
+--R
+--R             3    3
+--R        log(x  + a )
+--R   (2)  ------------
+--R              3
+--R                                                     Type: Expression Integer
+--E
+
+--S 11     14:301 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.302~~~~~$\displaystyle
+\int{\frac{dx}{x(x^3+a^3)}}$}
+$$\int{\frac{1}{x(x^3+a^3)}}=
+\frac{1}{3a^3}\ln\left(\frac{x^3}{x^3+a^3}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 12
+aa:=integrate(1/(x*(x^3+a^3)),x)
+--R 
+--R
+--R               3    3
+--R        - log(x  + a ) + 3log(x)
+--R   (1)  ------------------------
+--R                     3
+--R                   3a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 13
+bb:=1/(3*a^3)*log(x^3/(x^3+a^3))
+--R
+--R                3
+--R               x
+--R        log(-------)
+--R             3    3
+--R            x  + a
+--R   (2)  ------------
+--R               3
+--R             3a
+--R                                                     Type: Expression Integer
+--E
+
+--S 14
+cc:=aa-bb
+--R
+--R                                           3
+--R               3    3                     x
+--R        - log(x  + a ) + 3log(x) - log(-------)
+--R                                        3    3
+--R                                       x  + a
+--R   (3)  ---------------------------------------
+--R                            3
+--R                          3a
+--R                                                     Type: Expression Integer
+--E
+
+--S 15     14:302 Schaums and Axiom agree
+dd:=expandLog cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.303~~~~~$\displaystyle
+\int{\frac{dx}{x^2(x^3+a^3)}}~dx$}
+$$\int{\frac{1}{x^2(x^3+a^3)}}=
+-\frac{1}{a^3x}-\frac{1}{6a^4}\ln\frac{x^2-ax+a^2}{(x+a)^2}
+-\frac{1}{a^4\sqrt{3}}\tan^{-1}\frac{2x-a}{a\sqrt{3}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 15
+aa:=integrate(1/(x^2*(x^3+a^3)),x)
+--R 
+--R
+--R   (1)
+--R                                                                   +-+
+--R       +-+     2          2       +-+                     (2x - a)\|3        +-+
+--R   - x\|3 log(x  - a x + a ) + 2x\|3 log(x + a) - 6x atan(------------) - 6a\|3
+--R                                                               3a
+--R   -----------------------------------------------------------------------------
+--R                                        4  +-+
+--R                                      6a x\|3
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 16
+bb:=-1/(a^3*x)-1/(6*a^4)*log((x^2-a*x+a^2)/(x+a)^2)-1/(a^4*sqrt(3))*atan((2*x-a)/(a*sqrt(3)))
+--R
+--R                  2          2                        +-+
+--R                 x  - a x + a        +-+     (2x - a)\|3
+--R        - x log(--------------) - 2x\|3 atan(------------) - 6a
+--R                 2           2                    3a
+--R                x  + 2a x + a
+--R   (2)  -------------------------------------------------------
+--R                                    4
+--R                                  6a x
+--R                                                     Type: Expression Integer
+--E 
+
+--S 17
+cc:=aa-bb
+--R
+--R                                                   2          2
+--R               2          2                       x  - a x + a
+--R        - log(x  - a x + a ) + 2log(x + a) + log(--------------)
+--R                                                  2           2
+--R                                                 x  + 2a x + a
+--R   (3)  --------------------------------------------------------
+--R                                     4
+--R                                   6a
+--R                                                     Type: Expression Integer
+--E
+
+--S 18     14:303 Schaums and Axiom agree
+dd:=expandLog cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.304~~~~~$\displaystyle
+\int{\frac{dx}{(x^3+a^3)^2}}$}
+$$\int{\frac{1}{(x^3+a^3)^2}}=
+\frac{x}{3a^3(x^3+a^3)}
++\frac{1}{9a^5}\ln\frac{(x+a)^2}{x^2-ax+a^2}
++\frac{2}{3a^5\sqrt{3}}\tan^{-1}\frac{2x-a}{a\sqrt{3}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 19
+aa:=integrate(1/(x^3+a^3)^2,x)
+--R 
+--R
+--R   (1)
+--R           3    3  +-+     2          2       3     3  +-+
+--R       (- x  - a )\|3 log(x  - a x + a ) + (2x  + 2a )\|3 log(x + a)
+--R     + 
+--R                                +-+
+--R          3     3      (2x - a)\|3       2  +-+
+--R       (6x  + 6a )atan(------------) + 3a x\|3
+--R                            3a
+--R  /
+--R        5 3     8  +-+
+--R     (9a x  + 9a )\|3
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 20
+bb:=x/(3*a^3*(x^3+a^3))+1/(9*a^5)*log((x+a)^2/(x^2-a*x+a^2))+2/(3*a^5*sqrt(3))*atan((2*x-a)/(a*sqrt(3)))
+--R
+--R   (2)
+--R                 2           2                                 +-+
+--R     3    3     x  + 2a x + a        3     3  +-+     (2x - a)\|3       2
+--R   (x  + a )log(--------------) + (2x  + 2a )\|3 atan(------------) + 3a x
+--R                  2          2                             3a
+--R                 x  - a x + a
+--R   -----------------------------------------------------------------------
+--R                                   5 3     8
+--R                                 9a x  + 9a
+--R                                                     Type: Expression Integer
+--E
+
+--S 21
+cc:=aa-bb
+--R
+--R                                                  2           2
+--R               2          2                      x  + 2a x + a
+--R        - log(x  - a x + a ) + 2log(x + a) - log(--------------)
+--R                                                   2          2
+--R                                                  x  - a x + a
+--R   (3)  --------------------------------------------------------
+--R                                     5
+--R                                   9a
+--R                                                     Type: Expression Integer
+--E
+
+--S 22     14:304 Schaums and Axiom agree
+dd:=expandLog cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.305~~~~~$\displaystyle
+\int{\frac{x~dx}{(x^3+a^3)^2}}$}
+$$\int{\frac{x}{(x^3+a^3)^2}}=
+\frac{x^2}{3a^3(x^3+a^3)}
++\frac{1}{18a^4}\ln\frac{x^2-ax+a^2}{(x+a)^2}
++\frac{1}{3a^4\sqrt{3}}\tan^{-1}\frac{2x-a}{a\sqrt{3}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 23
+aa:=integrate(x/(x^3+a^3)^2,x)
+--R 
+--R
+--R   (1)
+--R         3    3  +-+     2          2         3     3  +-+
+--R       (x  + a )\|3 log(x  - a x + a ) + (- 2x  - 2a )\|3 log(x + a)
+--R     + 
+--R                                +-+
+--R          3     3      (2x - a)\|3         2 +-+
+--R       (6x  + 6a )atan(------------) + 6a x \|3
+--R                            3a
+--R  /
+--R         4 3      7  +-+
+--R     (18a x  + 18a )\|3
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 24
+bb:=x^2/(3*a^3*(x^3+a^3))+1/(18*a^4)*log((x^2-a*x+a^2)/(x+a)^2)+1/(3*a^4*sqrt(3))*atan((2*x-a)/(a*sqrt(3)))
+--R
+--R   (2)
+--R                  2          2                                 +-+
+--R     3    3      x  - a x + a        3     3  +-+     (2x - a)\|3         2
+--R   (x  + a )log(--------------) + (2x  + 2a )\|3 atan(------------) + 6a x
+--R                 2           2                             3a
+--R                x  + 2a x + a
+--R   ------------------------------------------------------------------------
+--R                                    4 3      7
+--R                                 18a x  + 18a
+--R                                                     Type: Expression Integer
+--E
+
+--S 25
+cc:=aa-bb
+--R
+--R                                                 2          2
+--R             2          2                       x  - a x + a
+--R        log(x  - a x + a ) - 2log(x + a) - log(--------------)
+--R                                                2           2
+--R                                               x  + 2a x + a
+--R   (3)  ------------------------------------------------------
+--R                                    4
+--R                                 18a
+--R                                                     Type: Expression Integer
+--E
+
+--S 26     14:305 Schaums and Axiom agree
+dd:=expandLog cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.306~~~~~$\displaystyle
+\int{\frac{x^2~dx}{(x^3+a^3)^2}}$}
+$$\int{\frac{x^2}{(x^3+a^3)^2}}=
+-\frac{1}{3(x^3+a^3)}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 27
+aa:=integrate(x^2/(x^3+a^3)^2,x)
+--R 
+--R
+--R              1
+--R   (1)  - ---------
+--R            3     3
+--R          3x  + 3a
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 28
+bb:=-1/(3*(x^3+a^3))
+--R
+--R              1
+--R   (2)  - ---------
+--R            3     3
+--R          3x  + 3a
+--R                                            Type: Fraction Polynomial Integer
+--E 
+
+--S 29     14:306 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.307~~~~~$\displaystyle
+\int{\frac{dx}{x(x^3+a^3)^2}}$}
+$$\int{\frac{1}{x(x^3+a^3)^2}}=
+\frac{1}{3a^3(x^3+a^3)}+\frac{1}{3a^6}\ln\left(\frac{x^3}{x^3+a^3}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 30
+aa:=integrate(1/(x*(x^3+a^3)^2),x)
+--R 
+--R
+--R            3    3      3    3       3     3           3
+--R        (- x  - a )log(x  + a ) + (3x  + 3a )log(x) + a
+--R   (1)  ------------------------------------------------
+--R                             6 3     9
+--R                           3a x  + 3a
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 31
+bb:=1/(3*a^3*(x^3+a^3))+1/(3*a^6)*log(x^3/(x^3+a^3))
+--R
+--R                         3
+--R          3    3        x        3
+--R        (x  + a )log(-------) + a
+--R                      3    3
+--R                     x  + a
+--R   (2)  --------------------------
+--R                  6 3     9
+--R                3a x  + 3a
+--R                                                     Type: Expression Integer
+--E
+
+--S 32
+cc:=aa-bb
+--R
+--R                                           3
+--R               3    3                     x
+--R        - log(x  + a ) + 3log(x) - log(-------)
+--R                                        3    3
+--R                                       x  + a
+--R   (3)  ---------------------------------------
+--R                            6
+--R                          3a
+--R                                                     Type: Expression Integer
+--E
+
+--S 33     14:307 Schaums and Axiom agree
+dd:=expandLog cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.308~~~~~$\displaystyle
+\int{\frac{dx}{x^2(x^3+a^3)^2}}~dx$}
+$$\int{\frac{1}{x^2(x^3+a^3)^2}}=
+-\frac{1}{a^6x}-\frac{x^2}{3a^6(x^3+a^3)}
+-\frac{4}{3a^6}\int{\frac{x}{x^3+a^3}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 34
+aa:=integrate(1/(x^2*(x^3+a^3)^2),x)
+--R 
+--R
+--R   (1)
+--R            4     3   +-+     2          2       4     3   +-+
+--R       (- 2x  - 2a x)\|3 log(x  - a x + a ) + (4x  + 4a x)\|3 log(x + a)
+--R     + 
+--R                                     +-+
+--R             4      3       (2x - a)\|3             3     4  +-+
+--R       (- 12x  - 12a x)atan(------------) + (- 12a x  - 9a )\|3
+--R                                 3a
+--R  /
+--R        7 4     10   +-+
+--R     (9a x  + 9a  x)\|3
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 35
+t1:=integrate(x/(x^3+a^3),x)
+--R
+--R                                                                  +-+
+--R         +-+     2          2      +-+                   (2x - a)\|3
+--R        \|3 log(x  - a x + a ) - 2\|3 log(x + a) + 6atan(------------)
+--R                                                              3a
+--R   (2)  --------------------------------------------------------------
+--R                                       +-+
+--R                                    6a\|3
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 36
+bb:=-1/(a^6*x)-x^2/(3*a^6*(x^3+a^3))-4/(3*a^6)*t1
+--R
+--R   (3)
+--R            4     3   +-+     2          2       4     3   +-+
+--R       (- 2x  - 2a x)\|3 log(x  - a x + a ) + (4x  + 4a x)\|3 log(x + a)
+--R     + 
+--R                                     +-+
+--R             4      3       (2x - a)\|3             3     4  +-+
+--R       (- 12x  - 12a x)atan(------------) + (- 12a x  - 9a )\|3
+--R                                 3a
+--R  /
+--R        7 4     10   +-+
+--R     (9a x  + 9a  x)\|3
+--R                                                     Type: Expression Integer
+--E 
+
+--S 37     14:308 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.309~~~~~$\displaystyle
+\int{\frac{x^m~dx}{x^3+a^3}}$}
+$$\int{\frac{x^m}{x^3+a^3}}=
+\frac{x^{m-2}}{m-2}-a^3\int{\frac{x^{m-3}}{x^3+a^3}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 38     14:309 Axiom cannot compute this integral
+aa:=integrate(x^m/(x^3+a^3),x)
+--R 
+--R
+--R           x      m
+--I         ++     %L
+--I   (1)   |   -------- d%L
+--R        ++    3     3
+--I             a  + %L
+--R                                          Type: Union(Expression Integer,...)
+--E
+@
+
+\section{\cite{1}:14.310~~~~~$\displaystyle
+\int{\frac{dx}{x^n(x^3+a^3)}}$}
+$$\int{\frac{1}{x^n(x^3+a^3)}}=
+\frac{-1}{a^3(n-1)x^{n-1}}-\frac{1}{a^3}\int{\frac{1}{x^{n-3}(x^3+a^3)}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 39     14:310 Axiom cannot compute this integral
+aa:=integrate(1/(x^n*(x^3+a^3)),x)
+--R 
+--R
+--R           x
+--R         ++        1
+--I   (1)   |   ------------- d%L
+--R        ++     3     3   n
+--I             (a  + %L )%L
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 p73
+\end{thebibliography}
+\end{document}
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diff --git a/src/axiom-website/CATS/schaum15.input.pamphlet b/src/axiom-website/CATS/schaum15.input.pamphlet
new file mode 100644
index 0000000..0c01fbb
--- /dev/null
+++ b/src/axiom-website/CATS/schaum15.input.pamphlet
@@ -0,0 +1,1332 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum15.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.311~~~~~$\displaystyle
+\int{\frac{dx}{x^4+a^4}}$}
+$$\int{\frac{1}{x^4+a^4}}=
+\frac{1}{4a^3\sqrt{2}}
+\ln\left(\frac{x^2+ax\sqrt{2}+a^2}{x^2-ax\sqrt{2}+a^2}\right)
+-\frac{1}{2a^3\sqrt{2}}\tan^{-1}\frac{ax\sqrt{2}}{x^2-a^2}
+$$
+&lt;&lt;*&gt;&gt;=
+)spool schaum15.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1
+aa:=integrate(1/(x^4+a^4),x)
+--R 
+--R
+--R   (1)
+--R        +------+          +------+2            +------+
+--R        |   1          8  |   1        4  +-+  |   1      2
+--R        |------ log(16a   |------  + 4a x\|2   |------ + x )
+--R       4|    12          4|    12             4|    12
+--R       \|256a            \|256a               \|256a
+--R     + 
+--R          +------+          +------+2            +------+
+--R          |   1          8  |   1        4  +-+  |   1      2
+--R       -  |------ log(16a   |------  - 4a x\|2   |------ + x )
+--R         4|    12          4|    12             4|    12
+--R         \|256a            \|256a               \|256a
+--R     + 
+--R                              +------+                               +------+
+--R                           4  |   1                               4  |   1
+--R                         4a   |------                           4a   |------
+--R        +------+             4|    12          +------+             4|    12
+--R        |   1                \|256a            |   1                \|256a
+--R     2  |------ atan(-------------------- - 2  |------ atan(--------------------)
+--R       4|    12           +------+            4|    12           +------+
+--R       \|256a          4  |   1       +-+     \|256a          4  |   1       +-+
+--R                     4a   |------ - x\|2                    4a   |------ + x\|2
+--R                         4|    12                               4|    12
+--R                         \|256a                                 \|256a
+--R  /
+--R      +-+
+--R     \|2
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 2
+bb:=1/(4*a^3*sqrt(2))*log((x^2+a*x*sqrt(2)+a^2)/(x^2-a*x*sqrt(2)+a^2))-1/(2*a^3*sqrt(2))*atan((a*x*sqrt(2))/(x^2-a^2))
+--R
+--R                      +-+    2    2                  +-+
+--R         +-+    - a x\|2  - x  - a       +-+     a x\|2
+--R        \|2 log(-------------------) - 2\|2 atan(-------)
+--R                     +-+    2    2                2    2
+--R                 a x\|2  - x  - a                x  - a
+--R   (2)  -------------------------------------------------
+--R                                 3
+--R                               8a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3
+cc:=aa-bb
+--R
+--R   (3)
+--R            +------+          +------+2            +------+
+--R         3  |   1          8  |   1        4  +-+  |   1      2
+--R       4a   |------ log(16a   |------  + 4a x\|2   |------ + x )
+--R           4|    12          4|    12             4|    12
+--R           \|256a            \|256a               \|256a
+--R     + 
+--R              +------+          +------+2            +------+
+--R           3  |   1          8  |   1        4  +-+  |   1      2
+--R       - 4a   |------ log(16a   |------  - 4a x\|2   |------ + x )
+--R             4|    12          4|    12             4|    12
+--R             \|256a            \|256a               \|256a
+--R     + 
+--R                                  +------+
+--R                               4  |   1
+--R                             4a   |------
+--R            +------+             4|    12
+--R         3  |   1                \|256a
+--R       8a   |------ atan(--------------------)
+--R           4|    12           +------+
+--R           \|256a          4  |   1       +-+
+--R                         4a   |------ - x\|2
+--R                             4|    12
+--R                             \|256a
+--R     + 
+--R                                    +------+
+--R                                 4  |   1
+--R                               4a   |------
+--R              +------+             4|    12                 +-+    2    2
+--R           3  |   1                \|256a             - a x\|2  - x  - a
+--R       - 8a   |------ atan(-------------------- - log(-------------------)
+--R             4|    12           +------+                   +-+    2    2
+--R             \|256a          4  |   1       +-+        a x\|2  - x  - a
+--R                           4a   |------ + x\|2
+--R                               4|    12
+--R                               \|256a
+--R     + 
+--R                 +-+
+--R             a x\|2
+--R       2atan(-------)
+--R              2    2
+--R             x  - a
+--R  /
+--R       3 +-+
+--R     4a \|2
+--R                                                     Type: Expression Integer
+--E
+
+--S 4
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (4)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 5
+dd:=atanrule cc
+--R
+--R   (5)
+--R            +------+          +------+2            +------+
+--R         3  |   1          8  |   1        4  +-+  |   1      2
+--R       4a   |------ log(16a   |------  + 4a x\|2   |------ + x )
+--R           4|    12          4|    12             4|    12
+--R           \|256a            \|256a               \|256a
+--R     + 
+--R              +------+          +------+2            +------+
+--R           3  |   1          8  |   1        4  +-+  |   1      2
+--R       - 4a   |------ log(16a   |------  - 4a x\|2   |------ + x )
+--R             4|    12          4|    12             4|    12
+--R             \|256a            \|256a               \|256a
+--R     + 
+--R                                          +------+
+--R                                       4  |   1          +-+
+--R                           (- 4 + 4%i)a   |------ + %i x\|2
+--R               +------+                  4|    12
+--R            3  |   1                     \|256a
+--R       4%i a   |------ log(---------------------------------)
+--R              4|    12                   +------+
+--R              \|256a                  4  |   1          +-+
+--R                            (4 + 4%i)a   |------ + %i x\|2
+--R                                        4|    12
+--R                                        \|256a
+--R     + 
+--R                                            +------+
+--R                                         4  |   1          +-+
+--R                             (- 4 + 4%i)a   |------ - %i x\|2
+--R                 +------+                  4|    12
+--R              3  |   1                     \|256a
+--R       - 4%i a   |------ log(---------------------------------)
+--R                4|    12                   +------+
+--R                \|256a                  4  |   1          +-+
+--R                              (4 + 4%i)a   |------ - %i x\|2
+--R                                          4|    12
+--R                                          \|256a
+--R     + 
+--R                      +-+       2       2              +-+    2    2
+--R                - a x\|2  + %i x  - %i a         - a x\|2  - x  - a
+--R       - %i log(-------------------------) - log(-------------------)
+--R                     +-+       2       2              +-+    2    2
+--R                 a x\|2  + %i x  - %i a           a x\|2  - x  - a
+--R  /
+--R       3 +-+
+--R     4a \|2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 6
+ee:=rootSimp dd
+--R
+--R   (6)
+--R                                         +-+
+--R               +-+    2    2           x\|2  + (1 + %i)a
+--R       log(a x\|2  + x  + a ) + %i log(-----------------)
+--R                                         +-+
+--R                                       x\|2  + (1 - %i)a
+--R     + 
+--R                  +-+                               +-+       2       2
+--R                x\|2  + (- 1 - %i)a           - a x\|2  + %i x  - %i a
+--R       - %i log(-------------------) - %i log(-------------------------)
+--R                  +-+                              +-+       2       2
+--R                x\|2  + (- 1 + %i)a            a x\|2  + %i x  - %i a
+--R     + 
+--R                   +-+    2    2
+--R             - a x\|2  - x  - a               +-+    2    2
+--R       - log(-------------------) - log(- a x\|2  + x  + a )
+--R                  +-+    2    2
+--R              a x\|2  - x  - a
+--R  /
+--R       3 +-+
+--R     4a \|2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 7
+ff:=expandLog ee
+--R
+--R   (7)
+--R                  +-+       2       2               +-+       2       2
+--R       %i log(a x\|2  + %i x  - %i a ) - %i log(a x\|2  - %i x  + %i a )
+--R     + 
+--R                +-+                         +-+
+--R       %i log(x\|2  + (1 + %i)a) - %i log(x\|2  + (1 - %i)a)
+--R     + 
+--R                +-+                           +-+
+--R       %i log(x\|2  + (- 1 + %i)a) - %i log(x\|2  + (- 1 - %i)a)
+--R     + 
+--R       (- 2 - %i)log(- 1)
+--R  /
+--R       3 +-+
+--R     4a \|2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 8
+gg:=complexNormalize ff
+--R
+--R               %i             %i
+--R        %i log(--) - %i log(- --) + (- 2 - %i)log(- 1)
+--R                2              2
+--R   (8)  ----------------------------------------------
+--R                              3 +-+
+--R                            4a \|2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 9      14:311 Schaums and Axiom differ by a constant
+hh:=expandLog gg
+--R
+--R        %i log(%i) - %i log(- %i) + (- 2 - %i)log(- 1)
+--R   (9)  ----------------------------------------------
+--R                              3 +-+
+--R                            4a \|2
+--R                                             Type: Expression Complex Integer
+--E
+@
+
+\section{\cite{1}:14.312~~~~~$\displaystyle
+\int{\frac{x~dx}{x^4+a^4}}$}
+$$\int{\frac{x}{x^4+a^4}}=
+\frac{1}{2a^2}\tan^{-1}\frac{x^2}{a^2}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 10
+aa:=integrate(x/(x^4+a^4),x)
+--R 
+--R
+--R              2
+--R             x
+--R        atan(--)
+--R              2
+--R             a
+--R   (1)  --------
+--R             2
+--R           2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 11
+bb:=1/(2*a^2)*atan(x^2/a^2)
+--R
+--R              2
+--R             x
+--R        atan(--)
+--R              2
+--R             a
+--R   (2)  --------
+--R             2
+--R           2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 12     14:312 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.313~~~~~$\displaystyle
+\int{\frac{x^2~dx}{x^4+a^4}}$}
+$$\int{\frac{x^2}{x^4+a^4}}=
+\frac{1}{4a\sqrt{2}}
+\ln\left(\frac{x^2-ax\sqrt{2}+a^2}{x^2+ax\sqrt{2}+a^2}\right)
+-\frac{1}{2a\sqrt{2}}\tan^{-1}\frac{ax\sqrt{2}}{x^2-a^2}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 13
+aa:=integrate(x^2/(x^4+a^4),x)
+--R 
+--R
+--R   (1)
+--R          +-----+               +-----+3        +-----+2
+--R          |  1          4  +-+  |  1         4  |  1       2
+--R       -  |----- log(64a x\|2   |-----  + 16a   |-----  + x )
+--R         4|    4               4|    4         4|    4
+--R         \|256a                \|256a          \|256a
+--R     + 
+--R        +-----+                 +-----+3        +-----+2
+--R        |  1            4  +-+  |  1         4  |  1       2
+--R        |----- log(- 64a x\|2   |-----  + 16a   |-----  + x )
+--R       4|    4                 4|    4         4|    4
+--R       \|256a                  \|256a          \|256a
+--R     + 
+--R                              +-----+3                               +-----+3
+--R                           4  |  1                                4  |  1
+--R                        64a   |-----                           64a   |-----
+--R        +-----+              4|    4           +-----+              4|    4
+--R        |  1                 \|256a            |  1                 \|256a
+--R     2  |----- atan(--------------------- - 2  |----- atan(---------------------)
+--R       4|    4            +-----+3            4|    4            +-----+3
+--R       \|256a          4  |  1        +-+     \|256a          4  |  1        +-+
+--R                    64a   |-----  - x\|2                   64a   |-----  + x\|2
+--R                         4|    4                                4|    4
+--R                         \|256a                                 \|256a
+--R  /
+--R      +-+
+--R     \|2
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 14
+bb:=1/(4*a*sqrt(2))*log((x^2-a*x*sqrt(2)+a^2)/(x^2+a*x*sqrt(2)+a^2))-1/(2*a*sqrt(2))*atan((a*x*sqrt(2))/(x^2-a^2))
+--R
+--R                      +-+    2    2                  +-+
+--R         +-+    - a x\|2  + x  + a       +-+     a x\|2
+--R        \|2 log(-------------------) - 2\|2 atan(-------)
+--R                     +-+    2    2                2    2
+--R                 a x\|2  + x  + a                x  - a
+--R   (2)  -------------------------------------------------
+--R                                8a
+--R                                                     Type: Expression Integer
+--E
+
+--S 15
+cc:=aa-bb
+--R
+--R   (3)
+--R             +-----+               +-----+3        +-----+2
+--R             |  1          4  +-+  |  1         4  |  1       2
+--R       - 4a  |----- log(64a x\|2   |-----  + 16a   |-----  + x )
+--R            4|    4               4|    4         4|    4
+--R            \|256a                \|256a          \|256a
+--R     + 
+--R           +-----+                 +-----+3        +-----+2
+--R           |  1            4  +-+  |  1         4  |  1       2
+--R       4a  |----- log(- 64a x\|2   |-----  + 16a   |-----  + x )
+--R          4|    4                 4|    4         4|    4
+--R          \|256a                  \|256a          \|256a
+--R     + 
+--R                                 +-----+3
+--R                              4  |  1
+--R                           64a   |-----
+--R           +-----+              4|    4
+--R           |  1                 \|256a
+--R       8a  |----- atan(---------------------)
+--R          4|    4            +-----+3
+--R          \|256a          4  |  1        +-+
+--R                       64a   |-----  - x\|2
+--R                            4|    4
+--R                            \|256a
+--R     + 
+--R                                   +-----+3
+--R                                4  |  1
+--R                             64a   |-----
+--R             +-----+              4|    4                  +-+    2    2
+--R             |  1                 \|256a             - a x\|2  + x  + a
+--R       - 8a  |----- atan(--------------------- - log(-------------------)
+--R            4|    4            +-----+3                   +-+    2    2
+--R            \|256a          4  |  1        +-+        a x\|2  + x  + a
+--R                         64a   |-----  + x\|2
+--R                              4|    4
+--R                              \|256a
+--R     + 
+--R                 +-+
+--R             a x\|2
+--R       2atan(-------)
+--R              2    2
+--R             x  - a
+--R  /
+--R        +-+
+--R     4a\|2
+--R                                                     Type: Expression Integer
+--E
+
+--S 16
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (4)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 17
+dd:=atanrule cc
+--R
+--R   (5)
+--R             +-----+               +-----+3        +-----+2
+--R             |  1          4  +-+  |  1         4  |  1       2
+--R       - 4a  |----- log(64a x\|2   |-----  + 16a   |-----  + x )
+--R            4|    4               4|    4         4|    4
+--R            \|256a                \|256a          \|256a
+--R     + 
+--R                                          +-----+3
+--R                                       4  |  1           +-+
+--R                         (- 64 + 64%i)a   |-----  + %i x\|2
+--R              +-----+                    4|    4
+--R              |  1                       \|256a
+--R       4%i a  |----- log(-----------------------------------)
+--R             4|    4                     +-----+3
+--R             \|256a                   4  |  1           +-+
+--R                          (64 + 64%i)a   |-----  + %i x\|2
+--R                                        4|    4
+--R                                        \|256a
+--R     + 
+--R                                            +-----+3
+--R                                         4  |  1           +-+
+--R                           (- 64 + 64%i)a   |-----  - %i x\|2
+--R                +-----+                    4|    4
+--R                |  1                       \|256a
+--R       - 4%i a  |----- log(-----------------------------------)
+--R               4|    4                     +-----+3
+--R               \|256a                   4  |  1           +-+
+--R                            (64 + 64%i)a   |-----  - %i x\|2
+--R                                          4|    4
+--R                                          \|256a
+--R     + 
+--R           +-----+                 +-----+3        +-----+2
+--R           |  1            4  +-+  |  1         4  |  1       2
+--R       4a  |----- log(- 64a x\|2   |-----  + 16a   |-----  + x )
+--R          4|    4                 4|    4         4|    4
+--R          \|256a                  \|256a          \|256a
+--R     + 
+--R                   +-+    2    2                 +-+       2       2
+--R             - a x\|2  + x  + a            - a x\|2  + %i x  - %i a
+--R       - log(-------------------) - %i log(-------------------------)
+--R                  +-+    2    2                 +-+       2       2
+--R              a x\|2  + x  + a              a x\|2  + %i x  - %i a
+--R  /
+--R        +-+
+--R     4a\|2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 18
+ee:=expandLog dd
+--R
+--R   (6)
+--R             +-----+               +-----+3        +-----+2
+--R             |  1          4  +-+  |  1         4  |  1       2
+--R       - 4a  |----- log(64a x\|2   |-----  + 16a   |-----  + x )
+--R            4|    4               4|    4         4|    4
+--R            \|256a                \|256a          \|256a
+--R     + 
+--R           +-----+               +-----+3        +-----+2
+--R           |  1          4  +-+  |  1         4  |  1       2
+--R       4a  |----- log(64a x\|2   |-----  - 16a   |-----  - x )
+--R          4|    4               4|    4         4|    4
+--R          \|256a                \|256a          \|256a
+--R     + 
+--R              +-----+                   +-----+3
+--R              |  1                   4  |  1        +-+
+--R       4%i a  |----- log((64 + 64%i)a   |-----  + x\|2 )
+--R             4|    4                   4|    4
+--R             \|256a                    \|256a
+--R     + 
+--R                +-----+                   +-----+3
+--R                |  1                   4  |  1           +-+
+--R       - 4%i a  |----- log((64 + 64%i)a   |-----  + %i x\|2 )
+--R               4|    4                   4|    4
+--R               \|256a                    \|256a
+--R     + 
+--R              +-----+                   +-----+3
+--R              |  1                   4  |  1           +-+
+--R       4%i a  |----- log((64 + 64%i)a   |-----  - %i x\|2 )
+--R             4|    4                   4|    4
+--R             \|256a                    \|256a
+--R     + 
+--R                +-----+                   +-----+3                       +-----+
+--R                |  1                   4  |  1        +-+                |  1
+--R       - 4%i a  |----- log((64 + 64%i)a   |-----  - x\|2  + 4a log(- 1)  |-----
+--R               4|    4                   4|    4                        4|    4
+--R               \|256a                    \|256a                         \|256a
+--R     + 
+--R               +-+    2    2               +-+       2       2
+--R       log(a x\|2  + x  + a ) + %i log(a x\|2  + %i x  - %i a )
+--R     + 
+--R                    +-+       2       2            +-+    2    2
+--R       - %i log(a x\|2  - %i x  + %i a ) - log(a x\|2  - x  - a )
+--R     + 
+--R       (- 1 - %i)log(- 1)
+--R  /
+--R        +-+
+--R     4a\|2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 19
+ff:=rootSimp ee
+--R
+--R   (7)
+--R                  +-+       2       2               +-+       2       2
+--R       %i log(a x\|2  + %i x  - %i a ) - %i log(a x\|2  - %i x  + %i a )
+--R     + 
+--R                +-+                            +-+
+--R       %i log(x\|2  + (1 + %i)a) - %i log(%i x\|2  + (1 + %i)a)
+--R     + 
+--R                   +-+                           +-+
+--R     %i log(- %i x\|2  + (1 + %i)a) - %i log(- x\|2  + (1 + %i)a) - %i log(- 1)
+--R  /
+--R        +-+
+--R     4a\|2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 20     14:313 Schaums and Axiom differ by a constant
+gg:=complexNormalize ff
+--R
+--R        %i log(2) - %i log(- 1) - %i log(- 2)
+--R   (8)  -------------------------------------
+--R                           +-+
+--R                        4a\|2
+--R                                             Type: Expression Complex Integer
+--E
+@
+
+\section{\cite{1}:14.314~~~~~$\displaystyle
+\int{\frac{x^3~dx}{x^4+a^4}}$}
+$$\int{\frac{x^3}{x^4+a^4}}=
+\frac{1}{4}\ln(x^4+a^4)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 21
+aa:=integrate(x^3/(x^4+a^4),x)
+--R 
+--R
+--R             4    4
+--R        log(x  + a )
+--R   (1)  ------------
+--R              4
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 22
+bb:=1/4*log(x^4+a^4)
+--R
+--R             4    4
+--R        log(x  + a )
+--R   (2)  ------------
+--R              4
+--R                                                     Type: Expression Integer
+--E 
+
+--S 23     14:314 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.315~~~~~$\displaystyle
+\int{\frac{dx}{x(x^4+a^4)}}~dx$}
+$$\int{\frac{1}{x(x^4+a^4)}}=
+\frac{1}{4a^4}\ln\left(\frac{x^4}{x^4+a^4}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 24
+aa:=integrate(1/(x*(x^4+a^4)),x)
+--R 
+--R
+--R               4    4
+--R        - log(x  + a ) + 4log(x)
+--R   (1)  ------------------------
+--R                     4
+--R                   4a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 25
+bb:=1/(4*a^4)*log(x^4/(x^4+a^4))
+--R
+--R                4
+--R               x
+--R        log(-------)
+--R             4    4
+--R            x  + a
+--R   (2)  ------------
+--R               4
+--R             4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 26
+cc:=aa-bb
+--R
+--R                                           4
+--R               4    4                     x
+--R        - log(x  + a ) + 4log(x) - log(-------)
+--R                                        4    4
+--R                                       x  + a
+--R   (3)  ---------------------------------------
+--R                            4
+--R                          4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 27     14:315 Schaums and Axiom agree
+dd:=expandLog cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.316~~~~~$\displaystyle
+\int{\frac{dx}{x^2(x^4+a^4)}}$}
+$$\int{\frac{1}{x^2(x^4+a^4)}}=
+-\frac{1}{a^4x}-\frac{1}{4a^5\sqrt{2}}
+\ln\left(\frac{x^2-ax\sqrt{2}+a^2}{x^2+ax\sqrt{2}+a^2}\right)
++\frac{1}{2a^5\sqrt{2}}\tan^{-1}\frac{ax\sqrt{2}}{x^2-a^2}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 28
+aa:=integrate(1/(x^2*(x^4+a^4)),x)
+--R 
+--R
+--R   (1)
+--R            +------+                +------+3         +------+2
+--R        4   |   1          16  +-+  |   1         12  |   1       2
+--R       a x  |------ log(64a  x\|2   |------  + 16a    |------  + x )
+--R           4|    20                4|    20          4|    20
+--R           \|256a                  \|256a            \|256a
+--R     + 
+--R              +------+                  +------+3         +------+2
+--R          4   |   1            16  +-+  |   1         12  |   1       2
+--R       - a x  |------ log(- 64a  x\|2   |------  + 16a    |------  + x )
+--R             4|    20                  4|    20          4|    20
+--R             \|256a                    \|256a            \|256a
+--R     + 
+--R                                       +------+3
+--R                                   16  |   1
+--R                                64a    |------
+--R               +------+               4|    20
+--R           4   |   1                  \|256a
+--R       - 2a x  |------ atan(-----------------------)
+--R              4|    20             +------+3
+--R              \|256a           16  |   1        +-+
+--R                            64a    |------  - x\|2
+--R                                  4|    20
+--R                                  \|256a
+--R     + 
+--R                                     +------+3
+--R                                 16  |   1
+--R                              64a    |------
+--R             +------+               4|    20
+--R         4   |   1                  \|256a           +-+
+--R       2a x  |------ atan(----------------------- - \|2
+--R            4|    20             +------+3
+--R            \|256a           16  |   1        +-+
+--R                          64a    |------  + x\|2
+--R                                4|    20
+--R                                \|256a
+--R  /
+--R      4  +-+
+--R     a x\|2
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 29
+bb:=-1/(a^4*x)-1/(4*a^5*sqrt(2))*log((x^2-a*x*sqrt(2)+a^2)/(x^2+a*x*sqrt(2)+a^2))+1/(2*a^5*sqrt(2))*atan((a*x*sqrt(2))/(x^2-a^2))
+--R
+--R                         +-+    2    2                   +-+
+--R            +-+    - a x\|2  + x  + a        +-+     a x\|2
+--R        - x\|2 log(-------------------) + 2x\|2 atan(-------) - 8a
+--R                        +-+    2    2                 2    2
+--R                    a x\|2  + x  + a                 x  - a
+--R   (2)  ----------------------------------------------------------
+--R                                     5
+--R                                   8a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 30
+cc:=aa-bb
+--R
+--R   (3)
+--R            +------+                +------+3         +------+2
+--R         5  |   1          16  +-+  |   1         12  |   1       2
+--R       4a   |------ log(64a  x\|2   |------  + 16a    |------  + x )
+--R           4|    20                4|    20          4|    20
+--R           \|256a                  \|256a            \|256a
+--R     + 
+--R              +------+                  +------+3         +------+2
+--R           5  |   1            16  +-+  |   1         12  |   1       2
+--R       - 4a   |------ log(- 64a  x\|2   |------  + 16a    |------  + x )
+--R             4|    20                  4|    20          4|    20
+--R             \|256a                    \|256a            \|256a
+--R     + 
+--R                                      +------+3
+--R                                  16  |   1
+--R                               64a    |------
+--R              +------+               4|    20
+--R           5  |   1                  \|256a
+--R       - 8a   |------ atan(-----------------------)
+--R             4|    20             +------+3
+--R             \|256a           16  |   1        +-+
+--R                           64a    |------  - x\|2
+--R                                 4|    20
+--R                                 \|256a
+--R     + 
+--R                                    +------+3
+--R                                16  |   1
+--R                             64a    |------
+--R            +------+               4|    20                  +-+    2    2
+--R         5  |   1                  \|256a              - a x\|2  + x  + a
+--R       8a   |------ atan(----------------------- + log(-------------------)
+--R           4|    20             +------+3                   +-+    2    2
+--R           \|256a           16  |   1        +-+        a x\|2  + x  + a
+--R                         64a    |------  + x\|2
+--R                               4|    20
+--R                               \|256a
+--R     + 
+--R                   +-+
+--R               a x\|2
+--R       - 2atan(-------)
+--R                2    2
+--R               x  - a
+--R  /
+--R       5 +-+
+--R     4a \|2
+--R                                                     Type: Expression Integer
+--E
+
+--S 31
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (4)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 32
+dd:=atanrule cc
+--R
+--R   (5)
+--R            +------+                +------+3         +------+2
+--R         5  |   1          16  +-+  |   1         12  |   1       2
+--R       4a   |------ log(64a  x\|2   |------  + 16a    |------  + x )
+--R           4|    20                4|    20          4|    20
+--R           \|256a                  \|256a            \|256a
+--R     + 
+--R                                               +------+3
+--R                                           16  |   1           +-+
+--R                             (- 64 + 64%i)a    |------  + %i x\|2
+--R                 +------+                     4|    20
+--R              5  |   1                        \|256a
+--R       - 4%i a   |------ log(-------------------------------------)
+--R                4|    20                      +------+3
+--R                \|256a                    16  |   1           +-+
+--R                              (64 + 64%i)a    |------  + %i x\|2
+--R                                             4|    20
+--R                                             \|256a
+--R     + 
+--R                                             +------+3
+--R                                         16  |   1           +-+
+--R                           (- 64 + 64%i)a    |------  - %i x\|2
+--R               +------+                     4|    20
+--R            5  |   1                        \|256a
+--R       4%i a   |------ log(-------------------------------------)
+--R              4|    20                      +------+3
+--R              \|256a                    16  |   1           +-+
+--R                            (64 + 64%i)a    |------  - %i x\|2
+--R                                           4|    20
+--R                                           \|256a
+--R     + 
+--R              +------+                  +------+3         +------+2
+--R           5  |   1            16  +-+  |   1         12  |   1       2
+--R       - 4a   |------ log(- 64a  x\|2   |------  + 16a    |------  + x )
+--R             4|    20                  4|    20          4|    20
+--R             \|256a                    \|256a            \|256a
+--R     + 
+--R                 +-+    2    2                 +-+       2       2
+--R           - a x\|2  + x  + a            - a x\|2  + %i x  - %i a
+--R       log(-------------------) + %i log(-------------------------)
+--R                +-+    2    2                 +-+       2       2
+--R            a x\|2  + x  + a              a x\|2  + %i x  - %i a
+--R  /
+--R       5 +-+
+--R     4a \|2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 33
+ee:=expandLog dd
+--R
+--R   (6)
+--R            +------+                +------+3         +------+2
+--R         5  |   1          16  +-+  |   1         12  |   1       2
+--R       4a   |------ log(64a  x\|2   |------  + 16a    |------  + x )
+--R           4|    20                4|    20          4|    20
+--R           \|256a                  \|256a            \|256a
+--R     + 
+--R              +------+                +------+3         +------+2
+--R           5  |   1          16  +-+  |   1         12  |   1       2
+--R       - 4a   |------ log(64a  x\|2   |------  - 16a    |------  - x )
+--R             4|    20                4|    20          4|    20
+--R             \|256a                  \|256a            \|256a
+--R     + 
+--R                 +------+                    +------+3
+--R              5  |   1                   16  |   1        +-+
+--R       - 4%i a   |------ log((64 + 64%i)a    |------  + x\|2 )
+--R                4|    20                    4|    20
+--R                \|256a                      \|256a
+--R     + 
+--R               +------+                    +------+3
+--R            5  |   1                   16  |   1           +-+
+--R       4%i a   |------ log((64 + 64%i)a    |------  + %i x\|2 )
+--R              4|    20                    4|    20
+--R              \|256a                      \|256a
+--R     + 
+--R                 +------+                    +------+3
+--R              5  |   1                   16  |   1           +-+
+--R       - 4%i a   |------ log((64 + 64%i)a    |------  - %i x\|2 )
+--R                4|    20                    4|    20
+--R                \|256a                      \|256a
+--R     + 
+--R               +------+                    +------+3
+--R            5  |   1                   16  |   1        +-+
+--R       4%i a   |------ log((64 + 64%i)a    |------  - x\|2 )
+--R              4|    20                    4|    20
+--R              \|256a                      \|256a
+--R     + 
+--R                      +------+
+--R           5          |   1             +-+    2    2
+--R       - 4a log(- 1)  |------ - log(a x\|2  + x  + a )
+--R                     4|    20
+--R                     \|256a
+--R     + 
+--R                    +-+       2       2               +-+       2       2
+--R       - %i log(a x\|2  + %i x  - %i a ) + %i log(a x\|2  - %i x  + %i a )
+--R     + 
+--R               +-+    2    2
+--R       log(a x\|2  - x  - a ) + (1 + %i)log(- 1)
+--R  /
+--R       5 +-+
+--R     4a \|2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 34
+ff:=rootSimp ee
+--R
+--R   (7)
+--R                    +-+       2       2               +-+       2       2
+--R       - %i log(a x\|2  + %i x  - %i a ) + %i log(a x\|2  - %i x  + %i a )
+--R     + 
+--R                  +-+                            +-+
+--R       - %i log(x\|2  + (1 + %i)a) + %i log(%i x\|2  + (1 + %i)a)
+--R     + 
+--R                       +-+                           +-+
+--R       - %i log(- %i x\|2  + (1 + %i)a) + %i log(- x\|2  + (1 + %i)a)
+--R     + 
+--R       %i log(- 1)
+--R  /
+--R       5 +-+
+--R     4a \|2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 35     14:316 Schaums and Axiom differ by a constant
+gg:=complexNormalize ff
+--R
+--R        - %i log(2) + %i log(- 1) + %i log(- 2)
+--R   (8)  ---------------------------------------
+--R                          5 +-+
+--R                        4a \|2
+--R                                             Type: Expression Complex Integer
+--E
+@
+
+\section{\cite{1}:14.317~~~~~$\displaystyle
+\int{\frac{dx}{x^3(x^4+a^4)}}$}
+$$\int{\frac{1}{x^3(x^4+a^4)}}=
+-\frac{1}{2a^4x^2}-\frac{1}{2a^6}\tan^{-1}\frac{x^2}{a^2}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 36
+aa:=integrate(1/(x^3*(x^4+a^4)),x)
+--R 
+--R
+--R                  2
+--R           2     x      2
+--R        - x atan(--) - a
+--R                  2
+--R                 a
+--R   (1)  -----------------
+--R                6 2
+--R              2a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 37
+bb:=-1/(2*a^4*x^2)-1/(2*a^6)*atan(x^2/a^2)
+--R
+--R                  2
+--R           2     x      2
+--R        - x atan(--) - a
+--R                  2
+--R                 a
+--R   (2)  -----------------
+--R                6 2
+--R              2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 38     14:317 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.318~~~~~$\displaystyle
+\int{\frac{dx}{(x^4-a^4)}}$}
+$$\int{\frac{1}{(x^4-a^4)}}=
+\frac{1}{4a^3}\ln\left(\frac{x-a}{x+a}\right)
+-\frac{1}{2a^3}\tan^{-1}\frac{x}{a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 39
+aa:=integrate(1/(x^4-a^4),x)
+--R 
+--R
+--R                                          x
+--R        - log(x + a) + log(x - a) - 2atan(-)
+--R                                          a
+--R   (1)  ------------------------------------
+--R                           3
+--R                         4a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 40
+bb:=1/(4*a^3)*log((x-a)/(x+a))-1/(2*a^3)*atan(x/a)
+--R
+--R            x - a          x
+--R        log(-----) - 2atan(-)
+--R            x + a          a
+--R   (2)  ---------------------
+--R                   3
+--R                 4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 41
+cc:=aa-bb
+--R
+--R                                        x - a
+--R        - log(x + a) + log(x - a) - log(-----)
+--R                                        x + a
+--R   (3)  --------------------------------------
+--R                            3
+--R                          4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 42     14:318 Schaums and Axiom agree
+dd:=expandLog cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.319~~~~~$\displaystyle
+\int{\frac{x~dx}{(x^4-a^4)}}$}
+$$\int{\frac{x}{(x^4-a^4)}}=
+\frac{1}{4a^2}\ln\left(\frac{x^2-a^2}{x^2+a^2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 43
+aa:=integrate(x/(x^4-a^4),x)
+--R 
+--R
+--R               2    2         2    2
+--R        - log(x  + a ) + log(x  - a )
+--R   (1)  -----------------------------
+--R                       2
+--R                     4a
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 44
+bb:=1/(4*a^2)*log((x^2-a^2)/(x^2+a^2))
+--R
+--R             2    2
+--R            x  - a
+--R        log(-------)
+--R             2    2
+--R            x  + a
+--R   (2)  ------------
+--R               2
+--R             4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 45
+cc:=aa-bb
+--R
+--R                                             2    2
+--R               2    2         2    2        x  - a
+--R        - log(x  + a ) + log(x  - a ) - log(-------)
+--R                                             2    2
+--R                                            x  + a
+--R   (3)  --------------------------------------------
+--R                               2
+--R                             4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 46     14:319 Schaums and Axiom agree
+dd:=expandLog cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.320~~~~~$\displaystyle
+\int{\frac{x^2~dx}{x^4-a^4}}$}
+$$\int{\frac{x^2}{x^4-a^4}}=
+\frac{1}{4a}\ln\left(\frac{x-a}{x+a}\right)
++\frac{1}{2a}\tan^{-1}\frac{x}{a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 47
+aa:=integrate(x^2/(x^4-a^4),x)
+--R 
+--R
+--R                                          x
+--R        - log(x + a) + log(x - a) + 2atan(-)
+--R                                          a
+--R   (1)  ------------------------------------
+--R                         4a
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 48
+bb:=1/(4*a)*log((x-a)/(x+a))+1/(2*a)*atan(x/a)
+--R
+--R            x - a          x
+--R        log(-----) + 2atan(-)
+--R            x + a          a
+--R   (2)  ---------------------
+--R                  4a
+--R                                                     Type: Expression Integer
+--E 
+
+--S 49
+cc:=aa-bb
+--R
+--R                                        x - a
+--R        - log(x + a) + log(x - a) - log(-----)
+--R                                        x + a
+--R   (3)  --------------------------------------
+--R                          4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 50     14:320 Schaums and Axiom agree
+dd:=expandLog cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.321~~~~~$\displaystyle
+\int{\frac{x^3~dx}{x^4-a^4}}$}
+$$\int{\frac{x^3}{x^4-a^4}}=
+\frac{1}{4}\ln(x^4-a^4)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 51
+aa:=integrate(x^3/(x^4-a^4),x)
+--R 
+--R
+--R             4    4
+--R        log(x  - a )
+--R   (1)  ------------
+--R              4
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 52
+bb:=1/4*log(x^4-a^4)
+--R
+--R             4    4
+--R        log(x  - a )
+--R   (2)  ------------
+--R              4
+--R                                                     Type: Expression Integer
+--E
+
+--S 53     14:321 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.322~~~~~$\displaystyle
+\int{\frac{dx}{x(x^4-a^4)}}$}
+$$\int{\frac{1}{x(x^4-a^4)}}=
+\frac{1}{4a^4}\ln\left(\frac{x^4-a^4}{x^4}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 54
+aa:=integrate(1/(x*(x^4-a^4)),x)
+--R 
+--R
+--R             4    4
+--R        log(x  - a ) - 4log(x)
+--R   (1)  ----------------------
+--R                    4
+--R                  4a
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 55
+bb:=1/(4*a^4)*log((x^4-a^4)/x^4)
+--R
+--R             4    4
+--R            x  - a
+--R        log(-------)
+--R                4
+--R               x
+--R   (2)  ------------
+--R               4
+--R             4a
+--R                                                     Type: Expression Integer
+--E 
+
+--S 56
+cc:=aa-bb
+--R
+--R                                      4    4
+--R             4    4                  x  - a
+--R        log(x  - a ) - 4log(x) - log(-------)
+--R                                         4
+--R                                        x
+--R   (3)  -------------------------------------
+--R                           4
+--R                         4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 57     14:322 Schaums and Axiom agree
+dd:=expandLog cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.323~~~~~$\displaystyle
+\int{\frac{dx}{x^2(x^4-a^4)}}$}
+$$\int{\frac{1}{x^2(x^4-a^4)}}=
+\frac{1}{a^4x}+\frac{1}{4a^5}\ln\left(\frac{x-a}{x+a}\right)
++\frac{1}{2a^5}\tan^{-1}\frac{x}{a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 58
+aa:=integrate(1/(x^2*(x^4-a^4)),x)
+--R 
+--R
+--R                                                x
+--R        - x log(x + a) + x log(x - a) + 2x atan(-) + 4a
+--R                                                a
+--R   (1)  -----------------------------------------------
+--R                                5
+--R                              4a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 59
+bb:=1/(a^4*x)+1/(4*a^5)*log((x-a)/(x+a))+1/(2*a^5)*atan(x/a)
+--R
+--R              x - a            x
+--R        x log(-----) + 2x atan(-) + 4a
+--R              x + a            a
+--R   (2)  ------------------------------
+--R                       5
+--R                     4a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 60
+cc:=aa-bb
+--R
+--R                                        x - a
+--R        - log(x + a) + log(x - a) - log(-----)
+--R                                        x + a
+--R   (3)  --------------------------------------
+--R                            5
+--R                          4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 61     14:323 Schaums and Axiom agree
+dd:=expandLog cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.324~~~~~$\displaystyle
+\int{\frac{dx}{x^3(x^4-a^4)}}$}
+$$\int{\frac{1}{x^3(x^4-a^4)}}=
+\frac{1}{2a^4x^2}+\frac{1}{4a^6}\ln\left(\frac{x^2-a^2}{x^2+a^2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 62
+aa:=integrate(1/(x^3*(x^4-a^4)),x)
+--R 
+--R
+--R           2     2    2     2     2    2      2
+--R        - x log(x  + a ) + x log(x  - a ) + 2a
+--R   (1)  ---------------------------------------
+--R                           6 2
+--R                         4a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 63
+bb:=1/(2*a^4*x^2)+1/(4*a^6)*log((x^2-a^2)/(x^2+a^2))
+--R
+--R               2    2
+--R         2    x  - a       2
+--R        x log(-------) + 2a
+--R               2    2
+--R              x  + a
+--R   (2)  --------------------
+--R                  6 2
+--R                4a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 64
+cc:=aa-bb
+--R
+--R                                             2    2
+--R               2    2         2    2        x  - a
+--R        - log(x  + a ) + log(x  - a ) - log(-------)
+--R                                             2    2
+--R                                            x  + a
+--R   (3)  --------------------------------------------
+--R                               6
+--R                             4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 65     14:324 Schaums and Axiom agree
+dd:=expandLog cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 pp73-74
+\end{thebibliography}
+\end{document}
diff --git a/src/axiom-website/CATS/schaum15.input.pdf b/src/axiom-website/CATS/schaum15.input.pdf
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diff --git a/src/axiom-website/CATS/schaum16.input.pamphlet b/src/axiom-website/CATS/schaum16.input.pamphlet
new file mode 100644
index 0000000..caf8bfd
--- /dev/null
+++ b/src/axiom-website/CATS/schaum16.input.pamphlet
@@ -0,0 +1,748 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum16.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.325~~~~~$\displaystyle
+\int{\frac{dx}{x(x^n+a^n)}}$}
+$$\int{\frac{1}{x(x^n+a^n)}}=
+\frac{1}{na^n}\ln\frac{x^n}{x^n+a^n}
+$$
+&lt;&lt;*&gt;&gt;=
+)spool schaum16.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1
+aa:=integrate(1/(x*(x^n+a^n)),x)
+--R
+--R                n log(x)    n
+--R        - log(%e         + a ) + n log(x)
+--R   (1)  ---------------------------------
+--R                          n
+--R                       n a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 2
+bb:=1/(n*a^n)*log(x^n/(x^n+a^n))
+--R
+--R                n
+--R               x
+--R        log(-------)
+--R             n    n
+--R            x  + a
+--R   (2)  ------------
+--R               n
+--R            n a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3
+cc:=aa-bb
+--R
+--R                                         n
+--R                n log(x)    n           x
+--R        - log(%e         + a ) - log(-------) + n log(x)
+--R                                      n    n
+--R                                     x  + a
+--R   (3)  ------------------------------------------------
+--R                                 n
+--R                              n a
+--R                                                     Type: Expression Integer
+--E
+
+--S 4
+dd:=expandLog cc
+--R
+--R                n log(x)    n         n    n         n
+--R        - log(%e         + a ) + log(x  + a ) - log(x ) + n log(x)
+--R   (4)  ----------------------------------------------------------
+--R                                      n
+--R                                   n a
+--R                                                     Type: Expression Integer
+--E
+
+--S 5      14:325 Schaums and Axiom agree
+ee:=complexNormalize dd
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.326~~~~~$\displaystyle
+\int{\frac{x^{n-1}~dx}{x^n+a^n}}$}
+$$\int{\frac{x^{n-1}}{x^n+a^n}}=
+\frac{1}{n}\ln(x^n+a^n)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 8
+aa:=integrate(x^(n-1)/(x^n+a^n),x)
+--R 
+--R
+--R              n log(x)    n
+--R        log(%e         + a )
+--R   (1)  --------------------
+--R                  n
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 9
+bb:=1/n*log(x^n+a^n)
+--R
+--R             n    n
+--R        log(x  + a )
+--R   (2)  ------------
+--R              n
+--R                                                     Type: Expression Integer
+--E
+
+--S 10
+cc:=aa-bb
+--R
+--R              n log(x)    n         n    n
+--R        log(%e         + a ) - log(x  + a )
+--R   (3)  -----------------------------------
+--R                         n
+--R                                                     Type: Expression Integer
+--E
+
+--S 11
+explog:=rule(%e^(n*log(x)) == x^n)
+--R
+--R          n log(x)     n
+--R   (4)  %e         == x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 12     14:326 Schaums and Axiom agree
+dd:=explog cc
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.327~~~~~$\displaystyle
+\int{\frac{x^m~dx}{(x^n+a^n)^r}}$}
+$$\int{\frac{x^m}{(x^n+a^n)^r}}=
+\int{\frac{x^{m-n}}{(x^n+a^n)^{r-1}}}
+-a^n\int{\frac{x^{m-n}}{(x^n+a^n)^r}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 13     14:327 Axiom cannot compute this integral
+aa:=integrate(x^m/(x^n+a^n)^r,x)
+--R 
+--R
+--R           x       m
+--I         ++      %J
+--I   (1)   |   ----------- d%J
+--R        ++     n     n r
+--I             (a  + %J )
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.328~~~~~$\displaystyle
+\int{\frac{dx}{x^m(x^n+a^n)^r}}$}
+$$\int{\frac{1}{x^m(x^n+a^n)^r}}=
+\frac{1}{a^n}\int{\frac{1}{x^m(x^n+a^n)^{r-1}}}
+-\frac{1}{a^n}\int{\frac{1}{x^{m-n}(x^n+a^n)^r}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 14     14:328 Axiom cannot compute this integral
+aa:=integrate(1/(x^m*(x^n+a^n)^r),x)
+--R 
+--R
+--R           x
+--R         ++         1
+--I   (1)   |   -------------- d%J
+--R        ++     m  n     n r
+--I             %J (a  + %J )
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.329~~~~~$\displaystyle
+\int{\frac{dx}{x\sqrt{x^n+a^n}}}$}
+$$\int{\frac{1}{x\sqrt{x^n+a^n}}}=
+\frac{1}{n\sqrt{a^n}}\ln\left(\frac{\sqrt{x^n+a^n}-\sqrt{a^n}}
+{\sqrt{x^n+a^n}+\sqrt{a^n}}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 15
+aa:=integrate(1/(x*sqrt(x^n+a^n)),x)
+--R 
+--R
+--R   (1)
+--R              +---------------+                      +--+
+--R            n |  n log(x)    n       n log(x)     n  | n
+--R        - 2a \|%e         + a   + (%e         + 2a )\|a
+--R    log(-------------------------------------------------)
+--R                              n log(x)
+--R                            %e
+--R   [------------------------------------------------------,
+--R                              +--+
+--R                              | n
+--R                            n\|a
+--R             +----+ +---------------+
+--R             |   n  |  n log(x)    n
+--R            \|- a  \|%e         + a
+--R      2atan(-------------------------)
+--R                         n
+--R                        a
+--R    - --------------------------------]
+--R                    +----+
+--R                    |   n
+--R                  n\|- a
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+
+--S 16
+bb:=1/(n*sqrt(a^n))*log((sqrt(x^n+a^n)-sqrt(a^n))/(sqrt(x^n+a^n)+sqrt(a^n)))
+--R
+--R             +-------+    +--+
+--R             | n    n     | n
+--R            \|x  + a   - \|a
+--R        log(------------------)
+--R             +-------+    +--+
+--R             | n    n     | n
+--R            \|x  + a   + \|a
+--R   (2)  -----------------------
+--R                   +--+
+--R                   | n
+--R                 n\|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 17
+cc1:=aa.1-bb
+--R
+--R   (3)
+--R                 +---------------+                      +--+
+--R               n |  n log(x)    n       n log(x)     n  | n
+--R           - 2a \|%e         + a   + (%e         + 2a )\|a
+--R       log(-------------------------------------------------)
+--R                                 n log(x)
+--R                               %e
+--R     + 
+--R              +-------+    +--+
+--R              | n    n     | n
+--R             \|x  + a   - \|a
+--R       - log(------------------)
+--R              +-------+    +--+
+--R              | n    n     | n
+--R             \|x  + a   + \|a
+--R  /
+--R       +--+
+--R       | n
+--R     n\|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 18
+dd1:=expandLog cc1
+--R
+--R   (4)
+--R               +---------------+                        +--+
+--R             n |  n log(x)    n         n log(x)     n  | n
+--R       log(2a \|%e         + a   + (- %e         - 2a )\|a  )
+--R     + 
+--R            +-------+    +--+         +-------+    +--+
+--R            | n    n     | n          | n    n     | n
+--R       log(\|x  + a   + \|a  ) - log(\|x  + a   - \|a  ) - n log(x) + log(- 1)
+--R  /
+--R       +--+
+--R       | n
+--R     n\|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 19
+explog:=rule(%e^(n*log(x)) == x^n)
+--R
+--R          n log(x)     n
+--R   (5)  %e         == x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 20
+ee1:=explog dd1
+--R
+--R   (6)
+--R               +-------+                +--+         +-------+    +--+
+--R             n | n    n        n     n  | n          | n    n     | n
+--R       log(2a \|x  + a   + (- x  - 2a )\|a  ) + log(\|x  + a   + \|a  )
+--R     + 
+--R              +-------+    +--+
+--R              | n    n     | n
+--R       - log(\|x  + a   - \|a  ) - n log(x) + log(- 1)
+--R  /
+--R       +--+
+--R       | n
+--R     n\|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 21
+ff1:=complexNormalize ee1
+--R
+--R        n log(a) + 4log(- 1)
+--R   (7)  --------------------
+--R              +----------+
+--R              |  n log(a)
+--R           2n\|%e
+--R                                                     Type: Expression Integer
+--E
+
+--S 22     14:329 Schaums and Axiom differ by a constant
+gg1:=explog ff1
+--R
+--R        n log(a) + 4log(- 1)
+--R   (8)  --------------------
+--R                  +--+
+--R                  | n
+--R               2n\|a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.330~~~~~$\displaystyle
+\int{\frac{dx}{x(x^n-a^n)}}$}
+$$\int{\frac{1}{x(x^n-a^n)}}=
+\frac{1}{na^n}\ln\left(\frac{x^n-a^n}{x^n}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 23
+aa:=integrate(1/(x*(x^n-a^n)),x)
+--R 
+--R
+--R              n log(x)    n
+--R        log(%e         - a ) - n log(x)
+--R   (1)  -------------------------------
+--R                         n
+--R                      n a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 24
+bb:=1/(n*a^n)*log((x^n-a^n)/x^n)
+--R
+--R             n    n
+--R            x  - a
+--R        log(-------)
+--R                n
+--R               x
+--R   (2)  ------------
+--R               n
+--R            n a
+--R                                                     Type: Expression Integer
+--E
+
+--S 25
+cc:=aa-bb
+--R
+--R                                    n    n
+--R              n log(x)    n        x  - a
+--R        log(%e         - a ) - log(-------) - n log(x)
+--R                                       n
+--R                                      x
+--R   (3)  ----------------------------------------------
+--R                                n
+--R                             n a
+--R                                                     Type: Expression Integer
+--E
+
+--S 26
+dd:=expandLog cc
+--R
+--R              n log(x)    n         n         n    n
+--R        log(%e         - a ) + log(x ) - log(x  - a ) - n log(x)
+--R   (4)  --------------------------------------------------------
+--R                                     n
+--R                                  n a
+--R                                                     Type: Expression Integer
+--E
+
+--S 27
+explog:=rule(%e^(n*log(x)) == x^n)
+--R
+--R          n log(x)     n
+--R   (5)  %e         == x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 28
+ee:=explog dd
+--R
+--R             n
+--R        log(x ) - n log(x)
+--R   (6)  ------------------
+--R                  n
+--R               n a
+--R                                                     Type: Expression Integer
+--E
+
+--S 29
+logpow:=rule(log(a^n) == n*log(a))
+--R
+--R             n
+--R   (7)  log(a ) == n log(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 30     14:330 Schaums and Axiom agree
+ff:=logpow ee
+--R
+--R   (8)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.331~~~~~$\displaystyle
+\int{\frac{x^{n-1}dx}{x^n-a^n}}$}
+$$\int{\frac{x^{n-1}}{x^n-a^n}}=
+\frac{1}{n}\ln(x^n-a^n)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 31
+aa:=integrate(x^(n-1)/(x^n-a^n),x)
+--R 
+--R
+--R              n log(x)    n
+--R        log(%e         - a )
+--R   (1)  --------------------
+--R                  n
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 32
+bb:=1/n*log(x^n-a^n)
+--R
+--R             n    n
+--R        log(x  - a )
+--R   (2)  ------------
+--R              n
+--R                                                     Type: Expression Integer
+--E
+
+--S 33
+cc:=aa-bb
+--R
+--R              n log(x)    n         n    n
+--R        log(%e         - a ) - log(x  - a )
+--R   (3)  -----------------------------------
+--R                         n
+--R                                                     Type: Expression Integer
+--E
+
+--S 34
+explog:=rule(%e^(n*log(x)) == x^n)
+--R
+--R          n log(x)     n
+--R   (4)  %e         == x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 35     14:331 Schaums and Axiom agree
+dd:=explog cc
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.332~~~~~$\displaystyle
+\int{\frac{x^m~dx}{(x^n-a^n)^r}}$}
+$$\int{\frac{x^m}{(x^n-a^n)^r}}=
+a^n\int{\frac{x^{m-n}}{(x^n-a^n)^r}}
++\int{\frac{x^{m-n}}{(x^n-a^n)^{r-1}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 36     14:332 Axiom cannot compute this integral
+aa:=integrate(x^m/(x^n-a^n)^r,x)
+--R 
+--R
+--R           x        m
+--I         ++       %J
+--I   (1)   |   ------------- d%J
+--R        ++       n     n r
+--I             (- a  + %J )
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.333~~~~~$\displaystyle
+\int{\frac{dx}{x^m(x^n-a^n)^r}}$}
+$$\int{\frac{1}{x^m(x^n-a^n)^r}}=
+\frac{1}{a^n}\int{\frac{1}{x^{m-n}(x^n-a^n)^r}}
+-\frac{1}{a^n}\int{\frac{1}{x^m(x^n-a^n)^{r-1}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 37     14:333 Axiom cannot compute this integral
+aa:=integrate(1/(x^m*(x^n-a^n)^r),x)
+--R 
+--R
+--R           x
+--R         ++          1
+--I   (1)   |   ---------------- d%J
+--R        ++     m    n     n r
+--I             %J (- a  + %J )
+--R                                          Type: Union(Expression Integer,...)
+--E
+@
+
+\section{\cite{1}:14.334~~~~~$\displaystyle
+\int{\frac{dx}{x\sqrt{x^n-a^n}}}$}
+$$\int{\frac{1}{x\sqrt{x^n-a^n}}}=
+\frac{2}{n\sqrt{a^n}}\cos^{-1}\sqrt{\frac{a^n}{x^n}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 38
+aa:=integrate(1/(x*sqrt(x^n-a^n)),x)
+--R 
+--R
+--R   (1)
+--R            +---------------+                      +----+
+--R          n |  n log(x)    n       n log(x)     n  |   n
+--R        2a \|%e         - a   + (%e         - 2a )\|- a
+--R    log(-------------------------------------------------)
+--R                              n log(x)
+--R                            %e
+--R   [------------------------------------------------------,
+--R                             +----+
+--R                             |   n
+--R                           n\|- a
+--R           +--+ +---------------+
+--R           | n  |  n log(x)    n
+--R          \|a  \|%e         - a
+--R    2atan(-----------------------)
+--R                      n
+--R                     a
+--R    ------------------------------]
+--R                  +--+
+--R                  | n
+--R                n\|a
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+
+--S 39
+bb:=2/(n*sqrt(a^n))*acos(sqrt(a^n/x^n))
+--R
+--R               +--+
+--R               | n
+--R               |a
+--R        2acos( |-- )
+--R               | n
+--R              \|x
+--R   (2)  ------------
+--R             +--+
+--R             | n
+--R           n\|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 40
+cc1:=aa.1-bb
+--R
+--R   (3)
+--R                    +---------------+                      +----+
+--R        +--+      n |  n log(x)    n       n log(x)     n  |   n
+--R        | n     2a \|%e         - a   + (%e         - 2a )\|- a
+--R       \|a  log(-------------------------------------------------)
+--R                                      n log(x)
+--R                                    %e
+--R     + 
+--R                       +--+
+--R           +----+      | n
+--R           |   n       |a
+--R       - 2\|- a  acos( |-- )
+--R                       | n
+--R                      \|x
+--R  /
+--R       +----+ +--+
+--R       |   n  | n
+--R     n\|- a  \|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 41     14:334 Axiom cannot simplify this expression
+cc2:=aa.2-bb
+--R
+--R               +--+ +---------------+           +--+
+--R               | n  |  n log(x)    n            | n
+--R              \|a  \|%e         - a             |a
+--R        2atan(-----------------------) - 2acos( |-- )
+--R                          n                     | n
+--R                         a                     \|x
+--R   (4)  ---------------------------------------------
+--R                              +--+
+--R                              | n
+--R                            n\|a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.335~~~~~$\displaystyle
+\int{\frac{x^{p-1}~dx}{x^{2m}+a^{2m}}}$ provided $0&lt;p\le 2m$}
+$$\begin{array}{rl}
+\displaystyle\int{\frac{x^{p-1}}{x^{2m}+a^{2m}}}=
+&amp;\displaystyle\frac{1}{ma^{2m-p}}\sum_{k=1}^m{\sin\frac{(2k-1)p\pi}{2m}
+\tan^{-1}\left(\frac{x+a\cos\left((2k-1)\pi/2m\right)}
+{a\sin\left((2k-1)\pi/2m\right)}\right)}\\
+&amp;\\
+&amp;\displaystyle-\frac{1}{2ma^{2m-p}}\sum_{k=1}^m{\cos\frac{(2k-1)p\pi}{2m}
+\ln\left(x^2+2ax\cos\frac{(2k-1)\pi}{2m}+a^2\right)}
+\end{array}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 42     14:335 Axiom cannot compute this integral
+aa:=integrate(x^(p-1)/(x^(2*m)+a^(2*m)),x)
+--R 
+--R
+--R           x     p - 1
+--I         ++    %J
+--I   (1)   |   ---------- d%J
+--R        ++    2m     2m
+--I             a   + %J
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.336~~~~~$\displaystyle
+\int{\frac{x^{p-1}dx}{x^{2m}-a^{2m}}}$ provided $0&lt;p\le 2m$}
+$$\begin{array}{rl}
+\displaystyle
+\int{\frac{x^{p-1}}{x^{2m}-a^{2m}}}=
+&amp;\displaystyle\frac{1}{2ma^{2m-p}}\sum_{k=1}^{m-1}\cos\frac{kp\pi}{m}
+\ln\left(x^2-2ax\cos\frac{k\pi}{m}+a^2\right)\\
+&amp;\\
+&amp;\displaystyle-\frac{1}{ma^{2m-p}}\sum_{k=1}^{m-1}\sin\frac{kp\pi}{m}
+\tan^{-1}\left(\frac{x-a\cos(k\pi/m)}{a\sin(k\pi/m)}\right)\\
+&amp;\\
+&amp;\displaystyle+\frac{1}{2ma^{2m-p}}\left(\ln(x-a)+(-1)^p\ln(x+a)\right)
+\end{array}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 43     14:336 Axiom cannot compute this integral
+aa:=integrate(x^(p-1)/(x^(2*m)-a^(2*m)),x)
+--R 
+--R
+--R           x       p - 1
+--I         ++      %J
+--I   (1)   |   - ---------- d%J
+--R        ++      2m     2m
+--I               a   - %J
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.337~~~~~$\displaystyle
+\int{\frac{x^{p-1}~dx}{x^{2m+1}+a^{2m+1}}}$ provided $0&lt;p\le 2m+1$}
+$$\begin{array}{rl}
+\displaystyle\int{\frac{x^{p-1}}{x^{2m+1}+a^{2m+1}}}=&amp;\hbox{\hskip 6.5cm}
+\end{array}
+$$
+$$\begin{array}{rl}
+\hbox{\hskip 1cm}&amp;\displaystyle
+\frac{2(-1)^{p-1}}{(2m+1)a^{2m-p+1}}\sum_{k=1}^m{\sin\frac{2kp\pi}{2m+1}
+\tan^{-1}\left(\frac{x+a\cos\left(2k\pi/(2m+1)\right)}
+{a\sin\left(2k\pi/(2m+1)\right)}\right)}\\
+&amp;\displaystyle
+-\frac{(-1)^{p-1}}{(2m+1)a^{2m-p+1}}\sum_{k=1}^m{\cos\frac{2kp\pi}{2m+1}
+\ln\left(x^2+2ax\cos\frac{2k\pi}{2m+1}+a^2\right)}\\
+&amp;\\
+&amp;\displaystyle+\frac{(-1)^{p-1}\ln(x+a)}{(2m+1)a^{2m-p+1}}
+\end{array}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 44     14:337 Axiom cannot compute this integral
+aa:=integrate(x^(p-1)/(x^(2*m+1)+a^(2*m+1)),x)
+--R 
+--R
+--R           x         p - 1
+--I         ++        %J
+--I   (1)   |   ------------------ d%J
+--R        ++    2m + 1     2m + 1
+--I             a       + %J
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.338~~~~~$\displaystyle
+\int{\frac{x^{p-1}~dx}{x^{2m+1}-a^{2m+1}}}$ provided $0&lt;p\le 2m+1$}
+$$\begin{array}{rl}
+\displaystyle\int{\frac{x^{p-1}}{x^{2m+1}-a^{2m+1}}}=&amp;\hbox{\hskip 6cm}
+\end{array}
+$$
+$$\begin{array}{rl}
+\hbox{\hskip 1cm}&amp;\displaystyle
+\frac{2}{(2m+1)a^{2m-p+1}}\sum_{k=1}^m{\sin\frac{2kp\pi}{2m+1}
+\tan^{-1}\left(\frac{x-a\cos\left(2kp\pi/(2m+1)\right)}
+{a\sin\left(2k\pi/(2m+1)\right)}\right)}\\
+&amp;\\
+&amp;\hbox{\hskip 1cm}\displaystyle
++\frac{1}{(2m+1)a^{2m-p+1}}\sum_{k=1}^m{\cos\frac{2kp\pi}{2m+1}
+\ln\left(x^2-2ax\cos\frac{2k\pi}{2m+1}+a^2\right)}\\
+&amp;\\
+&amp;\hbox{\hskip 1cm}\displaystyle
++\frac{\ln(x-a)}{(2m+1)a^{2m-p+1}}
+\end{array}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 45     14:338 Axiom cannot compute this integral
+aa:=integrate(x^(p-1)/(x^(2*m+1)-a^(2*m+1)),x)
+--R 
+--R
+--R           x           p - 1
+--I         ++          %J
+--I   (1)   |   - ------------------ d%J
+--R        ++      2m + 1     2m + 1
+--I               a       - %J
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 pp74-75
+\end{thebibliography}
+\end{document}
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diff --git a/src/axiom-website/CATS/schaum17.input.pamphlet b/src/axiom-website/CATS/schaum17.input.pamphlet
new file mode 100644
index 0000000..6939c30
--- /dev/null
+++ b/src/axiom-website/CATS/schaum17.input.pamphlet
@@ -0,0 +1,3077 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum17.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.339~~~~~$\displaystyle
+\int{\sin ax ~dx}$}
+$$\int{\sin ax}=
+-\frac{\cos{ax}}{a}
+$$
+&lt;&lt;*&gt;&gt;=
+)spool schaum17.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1
+aa:=integrate(sin(a*x),x)
+--R 
+--R
+--R          cos(a x)
+--R   (1)  - --------
+--R              a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 2
+bb:=-cos(a*x)/a
+--R
+--R          cos(a x)
+--R   (2)  - --------
+--R              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3      14:339 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.340~~~~~$\displaystyle
+\int{x\sin{ax}~dx}$}
+$$\int{x\sin{ax}}=
+\frac{\sin{ax}}{a^2}-\frac{x\cos{ax}}{a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 4
+aa:=integrate(x*sin(a*x),x)
+--R 
+--R
+--R        sin(a x) - a x cos(a x)
+--R   (1)  -----------------------
+--R                    2
+--R                   a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 5
+bb:=sin(a*x)/a^2-(x*cos(a*x))/a
+--R
+--R        sin(a x) - a x cos(a x)
+--R   (2)  -----------------------
+--R                    2
+--R                   a
+--R                                                     Type: Expression Integer
+--E
+
+--S 6      14:340 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.341~~~~~$\displaystyle
+\int{x^2\sin{ax}~dx}$}
+$$\int{x^2\sin{ax}}=
+\frac{2x}{a^2}\sin{ax}+\left(\frac{2}{a^3}-\frac{x^2}{a}\right)\cos{ax}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 7
+aa:=integrate(x^2*sin(a*x),x)
+--R 
+--R
+--R                            2 2
+--R        2a x sin(a x) + (- a x  + 2)cos(a x)
+--R   (1)  ------------------------------------
+--R                          3
+--R                         a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 8
+bb:=(2*x)/a^2*sin(a*x)+(2/a^3-x^2/a)*cos(a*x)
+--R
+--R                            2 2
+--R        2a x sin(a x) + (- a x  + 2)cos(a x)
+--R   (2)  ------------------------------------
+--R                          3
+--R                         a
+--R                                                     Type: Expression Integer
+--E
+
+--S 9      14:341 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.342~~~~~$\displaystyle
+\int{x^3\sin{ax}~dx}$}
+$$\int{x^3\sin{ax}}=
+\left(\frac{3x^2}{a^2}-\frac{6}{a^4}\right)\sin{ax}
++\left(\frac{6x}{a^3}-\frac{x^3}{a}\right)\cos{ax}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 10
+aa:=integrate(x^3*sin(a*x),x)
+--R 
+--R
+--R           2 2                    3 3
+--R        (3a x  - 6)sin(a x) + (- a x  + 6a x)cos(a x)
+--R   (1)  ---------------------------------------------
+--R                               4
+--R                              a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 11
+bb:=((3*x^2)/a^2-6/a^4)*sin(a*x)+(6*x/a^3-x^3/a)*cos(a*x)
+--R
+--R           2 2                    3 3
+--R        (3a x  - 6)sin(a x) + (- a x  + 6a x)cos(a x)
+--R   (2)  ---------------------------------------------
+--R                               4
+--R                              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 12     14:342 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.343~~~~~$\displaystyle
+\int{\frac{\sin{ax}}{x}}~dx$}
+$$\int{\frac{\sin{ax}}{x}}=
+ax-\frac{(ax)^3}{3\cdot 3!}+\frac{(ax)^5}{5\cdot 5!}-\cdots
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 13     14:343 Schaums and Axiom agree by definition
+aa:=integrate(sin(x)/x,x)
+--R 
+--R
+--R   (1)  Si(x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.344~~~~~$\displaystyle
+\int{\frac{\sin{ax}}{x^2}}~dx$}
+$$\int{\frac{\sin{ax}}{x^2}}=
+-\frac{\sin{ax}}{x}+a\int{\frac{\cos{ax}}{x}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 14     14:344 Axiom cannot compute this integral
+aa:=integrate(sin(a*x)/x^2,x)
+--R 
+--R
+--R           x
+--I         ++  sin(%I a)
+--I   (1)   |   --------- d%I
+--R        ++        2
+--I                %I
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.345~~~~~$\displaystyle
+\int{\frac{dx}{\sin{ax}}}$}
+$$\int{\frac{1}{\sin{ax}}}=
+\frac{1}{a}\ln(\csc{ax}-\cot{ax})=
+\frac{1}{a}\ln\tan\frac{ax}{2}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 15
+aa:=integrate(1/sin(a*x),x)
+--R 
+--R
+--R              sin(a x)
+--R        log(------------)
+--R            cos(a x) + 1
+--R   (1)  -----------------
+--R                a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 16
+bb:=1/a*log(tan((a*x)/2))
+--R
+--R                a x
+--R        log(tan(---))
+--R                 2
+--R   (2)  -------------
+--R              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 17
+cc:=aa-bb
+--R
+--R                  a x           sin(a x)
+--R        - log(tan(---)) + log(------------)
+--R                   2          cos(a x) + 1
+--R   (3)  -----------------------------------
+--R                         a
+--R                                                     Type: Expression Integer
+--E
+
+--S 18     14:345 Schaums and Axiom agree
+dd:=complexNormalize cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.346~~~~~$\displaystyle
+\int{\frac{x~dx}{\sin{ax}}}$}
+$$\int{\frac{x}{\sin{ax}}}=
+\frac{1}{a^2}\left\{
+ax+\frac{(ax)^3}{18}+\frac{7(ax)^5}{1800}+\cdots+
+\frac{2(2^{2n-1}-1)B_n(ax)^{2n+1}}{(2n+1)!}+\cdots\right\}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 19     14:346 Axiom cannot compute this integral
+aa:=integrate(x/sin(a*x),x)
+--R 
+--R
+--R           x
+--I         ++      %I
+--I   (1)   |   --------- d%I
+--I        ++   sin(%I a)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.347~~~~~$\displaystyle
+\int{\sin^2{ax}}~dx$}
+$$\int{\sin^2{ax}}=
+\frac{x}{2}-\frac{\sin{2ax}}{4a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 20
+aa:=integrate(sin(a*x)^2,x)
+--R 
+--R
+--R        - cos(a x)sin(a x) + a x
+--R   (1)  ------------------------
+--R                   2a
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 21
+bb:=x/2-sin(2*a*x)/(4*a)
+--R
+--R        - sin(2a x) + 2a x
+--R   (2)  ------------------
+--R                4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 22
+cc:=aa-bb
+--R
+--R        sin(2a x) - 2cos(a x)sin(a x)
+--R   (3)  -----------------------------
+--R                      4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 23     14:347 Schaums and Axiom agreee
+dd:=complexNormalize cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.348~~~~~$\displaystyle
+\int{x\sin^2{ax}}~dx$}
+$$\int{x\sin^2{ax}}=
+\frac{x^2}{4}-\frac{x\sin{2ax}}{4a}-\frac{\cos{2ax}}{8a^2}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 24
+aa:=integrate(x*sin(a*x)^2,x)
+--R 
+--R
+--R                                          2    2 2
+--R        - 2a x cos(a x)sin(a x) - cos(a x)  + a x
+--R   (1)  ------------------------------------------
+--R                              2
+--R                            4a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 25
+bb:=x^2/4-(x*sin(2*a*x))/(4*a)-cos(2*a*x)/(8*a^2)
+--R
+--R                                         2 2
+--R        - 2a x sin(2a x) - cos(2a x) + 2a x
+--R   (2)  ------------------------------------
+--R                           2
+--R                         8a
+--R                                                     Type: Expression Integer
+--E
+
+--S 26
+cc:=aa-bb
+--R
+--R                                                                      2
+--R        2a x sin(2a x) - 4a x cos(a x)sin(a x) + cos(2a x) - 2cos(a x)
+--R   (3)  ---------------------------------------------------------------
+--R                                        2
+--R                                      8a
+--R                                                     Type: Expression Integer
+--E
+
+--S 27     14:348 Schaums and Axiom differ by a constant
+dd:=complexNormalize cc
+--R
+--R           1
+--R   (4)  - ---
+--R            2
+--R          8a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.349~~~~~$\displaystyle
+\int{\sin^3{ax}}~dx$}
+$$\int{\sin^3{ax}}=
+-\frac{\cos{ax}}{a}+\frac{\cos^3{ax}}{3a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 28
+aa:=integrate(sin(a*x)^3,x)
+--R 
+--R
+--R                3
+--R        cos(a x)  - 3cos(a x)
+--R   (1)  ---------------------
+--R                  3a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 29
+bb:=-cos(a*x)/a+cos(a*x)^3/(3*a)
+--R
+--R                3
+--R        cos(a x)  - 3cos(a x)
+--R   (2)  ---------------------
+--R                  3a
+--R                                                     Type: Expression Integer
+--E
+
+--S 30     14:349 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.350~~~~~$\displaystyle
+\int{\sin^4{ax}}~dx$}
+$$\int{\sin^4{ax}}=
+\frac{3x}{8}-\frac{\sin{2ax}}{4a}+\frac{\sin{4ax}}{32a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 31
+aa:=integrate(sin(a*x)^4,x)
+--R 
+--R
+--R                  3
+--R        (2cos(a x)  - 5cos(a x))sin(a x) + 3a x
+--R   (1)  ---------------------------------------
+--R                           8a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 32
+bb:=(3*x)/8-sin(2*a*x)/(4*a)+sin(4*a*x)/(32*a)
+--R
+--R        sin(4a x) - 8sin(2a x) + 12a x
+--R   (2)  ------------------------------
+--R                      32a
+--R                                                     Type: Expression Integer
+--E
+
+--S 33
+cc:=aa-bb
+--R
+--R                                             3
+--R        - sin(4a x) + 8sin(2a x) + (8cos(a x)  - 20cos(a x))sin(a x)
+--R   (3)  ------------------------------------------------------------
+--R                                     32a
+--R                                                     Type: Expression Integer
+--E
+
+--S 34     14:350 Schaums and Axiom agree
+dd:=complexNormalize cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.351~~~~~$\displaystyle
+\int{\frac{dx}{\sin^2{ax}}}$}
+$$\int{\frac{1}{\sin^2{ax}}}=
+-\frac{1}{a}\cot{ax}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 35
+aa:=integrate(1/sin(a*x)^2,x)
+--R 
+--R
+--R           cos(a x)
+--R   (1)  - ----------
+--R          a sin(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 36
+bb:=-1/a*cot(a*x)
+--R
+--R          cot(a x)
+--R   (2)  - --------
+--R              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 37
+cc:=aa-bb
+--R
+--R        cot(a x)sin(a x) - cos(a x)
+--R   (3)  ---------------------------
+--R                 a sin(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 38     14:351 Schaums and Axiom agree
+dd:=complexNormalize cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.352~~~~~$\displaystyle
+\int{\frac{dx}{\sin^3{ax}}}$}
+$$\int{\frac{1}{\sin^3{ax}}}=
+-\frac{\cos{ax}}{2a\sin^2{ax}}+\frac{1}{2a}\ln\tan\frac{ax}{2}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 39
+aa:=integrate(1/sin(a*x)^3,x)
+--R 
+--R
+--R                 2           sin(a x)
+--R        (cos(a x)  - 1)log(------------) + cos(a x)
+--R                           cos(a x) + 1
+--R   (1)  -------------------------------------------
+--R                                2
+--R                     2a cos(a x)  - 2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 40
+bb:=-cos(a*x)/(2*a*sin(a*x)^2)+1/(2*a)*log(tan((a*x)/2))
+--R
+--R                2        a x
+--R        sin(a x) log(tan(---)) - cos(a x)
+--R                          2
+--R   (2)  ---------------------------------
+--R                              2
+--R                   2a sin(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 41
+cc:=aa-bb
+--R
+--R   (3)
+--R                  2             2        a x
+--R       (- cos(a x)  + 1)sin(a x) log(tan(---))
+--R                                          2
+--R     + 
+--R                2             2      sin(a x)                      2           3
+--R       (cos(a x)  - 1)sin(a x) log(------------) + cos(a x)sin(a x)  + cos(a x)
+--R                                   cos(a x) + 1
+--R     + 
+--R       - cos(a x)
+--R  /
+--R                 2              2
+--R     (2a cos(a x)  - 2a)sin(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 42
+dd:=expandLog cc
+--R
+--R   (4)
+--R                  2             2        a x
+--R       (- cos(a x)  + 1)sin(a x) log(tan(---))
+--R                                          2
+--R     + 
+--R                2             2
+--R       (cos(a x)  - 1)sin(a x) log(sin(a x))
+--R     + 
+--R                  2             2                                    2
+--R       (- cos(a x)  + 1)sin(a x) log(cos(a x) + 1) + cos(a x)sin(a x)
+--R     + 
+--R               3
+--R       cos(a x)  - cos(a x)
+--R  /
+--R                 2              2
+--R     (2a cos(a x)  - 2a)sin(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 43     14:352 Schaums and Axiom agree
+ee:=complexNormalize dd
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.353~~~~~$\displaystyle
+\int{\sin{px}\sin{qx}}~dx$}
+$$\int{\sin{px}\sin{qx}}=
+\frac{\sin{(p-q)x}}{2(p-q)}-\frac{\sin{(p+q)x}}{2(p+q)}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 44
+aa:=integrate(sin(p*x)*sin(q*x),x)
+--R 
+--R
+--R        p cos(p x)sin(q x) - q cos(q x)sin(p x)
+--R   (1)  ---------------------------------------
+--R                         2    2
+--R                        q  - p
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 45
+bb:=sin((p-q)*x)/(2*(p-q))-sin((p+q)*x)/(2*(p+q))
+--R
+--R        (- q + p)sin((q + p)x) + (q + p)sin((q - p)x)
+--R   (2)  ---------------------------------------------
+--R                            2     2
+--R                          2q  - 2p
+--R                                                     Type: Expression Integer
+--E 
+
+--S 46
+cc:=aa-bb
+--R
+--R   (3)
+--R       (q - p)sin((q + p)x) + 2p cos(p x)sin(q x) + (- q - p)sin((q - p)x)
+--R     + 
+--R       - 2q cos(q x)sin(p x)
+--R  /
+--R       2     2
+--R     2q  - 2p
+--R                                                     Type: Expression Integer
+--E
+
+--S 47     14:353 Schams and Axiom agree
+dd:=complexNormalize cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.354~~~~~$\displaystyle
+\int{\frac{dx}{1-\sin{ax}}}$}
+$$\int{\frac{1}{1-\sin{ax}}}=
+\frac{1}{a}\tan\left(\frac{\pi}{4}+\frac{ax}{2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 48
+aa:=integrate(1/(1-sin(a*x)),x)
+--R 
+--R
+--R              - 2cos(a x) - 2
+--R   (1)  ---------------------------
+--R        a sin(a x) - a cos(a x) - a
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 49
+bb:=1/a*tan(%pi/4+(a*x)/2)
+--R
+--R            2a x + %pi
+--R        tan(----------)
+--R                 4
+--R   (2)  ---------------
+--R               a
+--R                                                     Type: Expression Integer
+--E 
+
+--S 50
+cc:=aa-bb
+--R
+--R                                       2a x + %pi
+--R        (- sin(a x) + cos(a x) + 1)tan(----------) - 2cos(a x) - 2
+--R                                            4
+--R   (3)  ----------------------------------------------------------
+--R                        a sin(a x) - a cos(a x) - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 51     14:354 Schaums and Axiom differ by a constant
+dd:=complexNormalize cc
+--R
+--R        1
+--R   (4)  -
+--R        a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.355~~~~~$\displaystyle
+\int{\frac{x~dx}{1-\sin{ax}}}$}
+$$\int{\frac{x}{1-\sin{ax}}}=
+\frac{x}{a}\tan\left(\frac{\pi}{4}+\frac{ax}{2}\right)
++\frac{2}{a^2}\ln~\sin\left(\frac{\pi}{4}-\frac{ax}{2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 52
+aa:=integrate(x/(1-sin(ax)),x)
+--R 
+--R
+--R                2
+--R               x
+--R   (1)  - ------------
+--R          2sin(ax) - 2
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 53
+bb:=x/a*tan(%pi/4+(a*x)/2)+2/a^2*log(sin(%pi/4-(a*x)/2))
+--R
+--R                   2a x - %pi             2a x + %pi
+--R        2log(- sin(----------)) + a x tan(----------)
+--R                        4                      4
+--R   (2)  ---------------------------------------------
+--R                               2
+--R                              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 54     14:355 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R                                 2a x - %pi
+--R       (- 4sin(ax) + 4)log(- sin(----------))
+--R                                      4
+--R     + 
+--R                                  2a x + %pi     2 2
+--R       (- 2a x sin(ax) + 2a x)tan(----------) - a x
+--R                                       4
+--R  /
+--R       2            2
+--R     2a sin(ax) - 2a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.356~~~~~$\displaystyle
+\int{\frac{dx}{1+\sin{ax}}}$}
+$$\int{\frac{1}{1+\sin{ax}}}=
+-\frac{1}{a}\tan\left(\frac{\pi}{4}-\frac{ax}{2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 55
+aa:=integrate(1/(1+sin(ax)),x)
+--R 
+--R
+--R             x
+--R   (1)  -----------
+--R        sin(ax) + 1
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 56
+bb:=-1/a*tan(%pi/4-(a*x)/2)
+--R
+--R            2a x - %pi
+--R        tan(----------)
+--R                 4
+--R   (2)  ---------------
+--R               a
+--R                                                     Type: Expression Integer
+--E
+
+--S 57
+cc:=aa-bb
+--R
+--R                           2a x - %pi
+--R        (- sin(ax) - 1)tan(----------) + a x
+--R                                4
+--R   (3)  ------------------------------------
+--R                    a sin(ax) + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 58
+tanrule:=rule(tan(a/b) == sin(a)/cos(b))
+--R
+--R            a     sin(a)
+--R   (4)  tan(-) == ------
+--R            b     cos(b)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 59     14:356 Axiom cannot simplify this expression
+dd:=tanrule cc
+--R
+--R        (- sin(ax) - 1)sin(2a x - %pi) + a x cos(4)
+--R   (5)  -------------------------------------------
+--R                 a cos(4)sin(ax) + a cos(4)
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.357~~~~~$\displaystyle
+\int{\frac{x~dx}{1+\sin{ax}}}$}
+$$\int{\frac{x}{1+\sin{ax}}}=
+-\frac{x}{a}\tan\left(\frac{\pi}{4}-\frac{ax}{2}\right)
++\frac{2}{a^2}\ln~\sin\left(\frac{\pi}{4}+\frac{ax}{2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 60
+aa:=integrate(x/(1+sin(a*x)),x)
+--R 
+--R
+--R   (1)
+--R                                      sin(a x) + cos(a x) + 1
+--R       (2sin(a x) + 2cos(a x) + 2)log(-----------------------)
+--R                                            cos(a x) + 1
+--R     + 
+--R                                            2
+--R       (- sin(a x) - cos(a x) - 1)log(------------) + a x sin(a x)
+--R                                      cos(a x) + 1
+--R     + 
+--R       - a x cos(a x) - a x
+--R  /
+--R      2            2            2
+--R     a sin(a x) + a cos(a x) + a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 61
+bb:=-x/a*tan(%pi/4-(a*x)/2)+2/a^2*log(sin(%pi/4+(a*x)/2))
+--R
+--R                 2a x + %pi             2a x - %pi
+--R        2log(sin(----------)) + a x tan(----------)
+--R                      4                      4
+--R   (2)  -------------------------------------------
+--R                              2
+--R                             a
+--R                                                     Type: Expression Integer
+--E
+
+--S 62     14:257 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R                                      sin(a x) + cos(a x) + 1
+--R       (2sin(a x) + 2cos(a x) + 2)log(-----------------------)
+--R                                            cos(a x) + 1
+--R     + 
+--R                                            2a x + %pi
+--R       (- 2sin(a x) - 2cos(a x) - 2)log(sin(----------))
+--R                                                 4
+--R     + 
+--R                                            2
+--R       (- sin(a x) - cos(a x) - 1)log(------------)
+--R                                      cos(a x) + 1
+--R     + 
+--R                                                2a x - %pi
+--R       (- a x sin(a x) - a x cos(a x) - a x)tan(----------) + a x sin(a x)
+--R                                                     4
+--R     + 
+--R       - a x cos(a x) - a x
+--R  /
+--R      2            2            2
+--R     a sin(a x) + a cos(a x) + a
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.358~~~~~$\displaystyle
+\int{\frac{dx}{(1-\sin{ax})^2}}$}
+$$\int{\frac{1}{(1-\sin{ax})^2}}=
+\frac{1}{2a}\tan\left(\frac{\pi}{4}+\frac{ax}{2}\right)
++\frac{1}{6a}\tan^3\left(\frac{\pi}{4}+\frac{ax}{2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 63
+aa:=integrate(1/(1-sin(a*x))^2,x)
+--R
+--R                                               2
+--R             (3cos(a x) + 3)sin(a x) + cos(a x)  - 4cos(a x) - 5
+--R   (1)  ------------------------------------------------------------
+--R                                                2
+--R        (3a cos(a x) + 6a)sin(a x) + 3a cos(a x)  - 3a cos(a x) - 6a
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 64
+bb:=1/(2*a)*tan(%pi/4+(a*x)/2)+1/(6*a)*tan(%pi/4+(a*x)/2)^3
+--R
+--R            2a x + %pi 3        2a x + %pi
+--R        tan(----------)  + 3tan(----------)
+--R                 4                   4
+--R   (2)  -----------------------------------
+--R                         6a
+--R                                                     Type: Expression Integer
+--E 
+
+--S 65
+cc:=aa-bb
+--R
+--R   (3)
+--R                                           2                    2a x + %pi 3
+--R       ((- cos(a x) - 2)sin(a x) - cos(a x)  + cos(a x) + 2)tan(----------)
+--R                                                                     4
+--R     + 
+--R                                             2                     2a x + %pi
+--R       ((- 3cos(a x) - 6)sin(a x) - 3cos(a x)  + 3cos(a x) + 6)tan(----------)
+--R                                                                        4
+--R     + 
+--R                                          2
+--R       (6cos(a x) + 6)sin(a x) + 2cos(a x)  - 8cos(a x) - 10
+--R  /
+--R                                              2
+--R     (6a cos(a x) + 12a)sin(a x) + 6a cos(a x)  - 6a cos(a x) - 12a
+--R                                                     Type: Expression Integer
+--E
+
+--S 66
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (4)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 67
+dd:=tanrule cc
+--R
+--R   (5)
+--R                               2a x + %pi 3
+--R           (- cos(a x) - 2)sin(----------)
+--R                                    4
+--R         + 
+--R                   2a x + %pi 2                2a x + %pi 2     2a x + %pi
+--R           (- 3cos(----------) cos(a x) - 6cos(----------) )sin(----------)
+--R                        4                           4                4
+--R         + 
+--R                2a x + %pi 3                2a x + %pi 3
+--R           6cos(----------) cos(a x) + 6cos(----------)
+--R                     4                           4
+--R      *
+--R         sin(a x)
+--R     + 
+--R                  2                    2a x + %pi 3
+--R       (- cos(a x)  + cos(a x) + 2)sin(----------)
+--R                                            4
+--R     + 
+--R                  2a x + %pi 2        2        2a x + %pi 2
+--R           - 3cos(----------) cos(a x)  + 3cos(----------) cos(a x)
+--R                       4                            4
+--R         + 
+--R                2a x + %pi 2
+--R           6cos(----------)
+--R                     4
+--R      *
+--R             2a x + %pi
+--R         sin(----------)
+--R                  4
+--R     + 
+--R          2a x + %pi 3        2        2a x + %pi 3                 2a x + %pi 3
+--R     2cos(----------) cos(a x)  - 8cos(----------) cos(a x) - 10cos(----------)
+--R               4                            4                            4
+--R  /
+--R               2a x + %pi 3                   2a x + %pi 3
+--R       (6a cos(----------) cos(a x) + 12a cos(----------) )sin(a x)
+--R                    4                              4
+--R     + 
+--R              2a x + %pi 3        2          2a x + %pi 3
+--R       6a cos(----------) cos(a x)  - 6a cos(----------) cos(a x)
+--R                   4                              4
+--R     + 
+--R                 2a x + %pi 3
+--R       - 12a cos(----------)
+--R                      4
+--R                                                     Type: Expression Integer
+--E
+
+--S 68
+sindiffrule2:=rule(sin((a-b)/4) == sin(a/4)*cos(b/4)-cos(a/4)*sin(b/4))
+--R
+--R                 b - a              a     b           b     a
+--I   (6)  - %K sin(-----) == - %K cos(-)sin(-) + %K cos(-)sin(-)
+--R                   4                4     4           4     4
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 69
+ee:=sindiffrule2 dd
+--R
+--R   (7)
+--R                               2a x + %pi 3
+--R           (- cos(a x) - 2)sin(----------)
+--R                                    4
+--R         + 
+--R                   2a x + %pi 2                2a x + %pi 2     2a x + %pi
+--R           (- 3cos(----------) cos(a x) - 6cos(----------) )sin(----------)
+--R                        4                           4                4
+--R         + 
+--R                2a x + %pi 3                2a x + %pi 3
+--R           6cos(----------) cos(a x) + 6cos(----------)
+--R                     4                           4
+--R      *
+--R         sin(a x)
+--R     + 
+--R                  2                    2a x + %pi 3
+--R       (- cos(a x)  + cos(a x) + 2)sin(----------)
+--R                                            4
+--R     + 
+--R                  2a x + %pi 2        2        2a x + %pi 2
+--R           - 3cos(----------) cos(a x)  + 3cos(----------) cos(a x)
+--R                       4                            4
+--R         + 
+--R                2a x + %pi 2
+--R           6cos(----------)
+--R                     4
+--R      *
+--R             2a x + %pi
+--R         sin(----------)
+--R                  4
+--R     + 
+--R          2a x + %pi 3        2        2a x + %pi 3                 2a x + %pi 3
+--R     2cos(----------) cos(a x)  - 8cos(----------) cos(a x) - 10cos(----------)
+--R               4                            4                            4
+--R  /
+--R               2a x + %pi 3                   2a x + %pi 3
+--R       (6a cos(----------) cos(a x) + 12a cos(----------) )sin(a x)
+--R                    4                              4
+--R     + 
+--R              2a x + %pi 3        2          2a x + %pi 3
+--R       6a cos(----------) cos(a x)  - 6a cos(----------) cos(a x)
+--R                   4                              4
+--R     + 
+--R                 2a x + %pi 3
+--R       - 12a cos(----------)
+--R                      4
+--R                                                     Type: Expression Integer
+--E
+
+--S 70
+sincuberule:=rule(sin(a)^3 == 3/4*sin(a)-1/4*sin(3*a))
+--R
+--R              3    - sin(3a) + 3sin(a)
+--R   (8)  sin(a)  == -------------------
+--R                            4
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 71
+ff:=sincuberule ee
+--R
+--R   (9)
+--R                                         2                    6a x + 3%pi
+--R       ((cos(a x) + 2)sin(a x) + cos(a x)  - cos(a x) - 2)sin(-----------)
+--R                                                                   4
+--R     + 
+--R                       2a x + %pi 2                      2a x + %pi 2
+--R             ((- 12cos(----------)  - 3)cos(a x) - 24cos(----------)  - 6)
+--R                            4                                 4
+--R          *
+--R                 2a x + %pi
+--R             sin(----------)
+--R                      4
+--R         + 
+--R                 2a x + %pi 3                 2a x + %pi 3
+--R           24cos(----------) cos(a x) + 24cos(----------)
+--R                      4                            4
+--R      *
+--R         sin(a x)
+--R     + 
+--R                    2a x + %pi 2             2
+--R           (- 12cos(----------)  - 3)cos(a x)
+--R                         4
+--R         + 
+--R                  2a x + %pi 2                      2a x + %pi 2
+--R           (12cos(----------)  + 3)cos(a x) + 24cos(----------)  + 6
+--R                       4                                 4
+--R      *
+--R             2a x + %pi
+--R         sin(----------)
+--R                  4
+--R     + 
+--R            2a x + %pi 3        2         2a x + %pi 3
+--R       8cos(----------) cos(a x)  - 32cos(----------) cos(a x)
+--R                 4                             4
+--R     + 
+--R               2a x + %pi 3
+--R       - 40cos(----------)
+--R                    4
+--R  /
+--R                2a x + %pi 3                   2a x + %pi 3
+--R       (24a cos(----------) cos(a x) + 48a cos(----------) )sin(a x)
+--R                     4                              4
+--R     + 
+--R               2a x + %pi 3        2           2a x + %pi 3
+--R       24a cos(----------) cos(a x)  - 24a cos(----------) cos(a x)
+--R                    4                               4
+--R     + 
+--R                 2a x + %pi 3
+--R       - 48a cos(----------)
+--R                      4
+--R                                                     Type: Expression Integer
+--E
+
+--S 72     14:358 Schaums and Axiom differ by a constant
+complexNormalize %
+--R
+--R          2
+--R   (10)  --
+--R         3a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.359~~~~~$\displaystyle
+\int{\frac{dx}{(1+\sin{ax})^2}}$}
+$$\int{\frac{1}{(1+\sin{ax})^2}}=
+-\frac{1}{2a}\tan\left(\frac{\pi}{4}-\frac{ax}{2}\right)
+-\frac{1}{6a}\tan^3\left(\frac{\pi}{4}-\frac{ax}{2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 73
+aa:=integrate(1/(1+sin(a*x))^2,x)
+--R
+--R                                                2
+--R            (- 3cos(a x) - 3)sin(a x) + cos(a x)  - 4cos(a x) - 5
+--R   (1)  ------------------------------------------------------------
+--R                                                2
+--R        (3a cos(a x) + 6a)sin(a x) - 3a cos(a x)  + 3a cos(a x) + 6a
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 74
+bb:=-1/(2*a)*tan(%pi/4-(a*x)/2)-1/(6*a)*tan(%pi/4-(a*x)/2)^3
+--R
+--R            2a x - %pi 3        2a x - %pi
+--R        tan(----------)  + 3tan(----------)
+--R                 4                   4
+--R   (2)  -----------------------------------
+--R                         6a
+--R                                                     Type: Expression Integer
+--E 
+
+--S 75
+cc:=aa-bb
+--R
+--R   (3)
+--R                                           2                    2a x - %pi 3
+--R       ((- cos(a x) - 2)sin(a x) + cos(a x)  - cos(a x) - 2)tan(----------)
+--R                                                                     4
+--R     + 
+--R                                             2                     2a x - %pi
+--R       ((- 3cos(a x) - 6)sin(a x) + 3cos(a x)  - 3cos(a x) - 6)tan(----------)
+--R                                                                        4
+--R     + 
+--R                                            2
+--R       (- 6cos(a x) - 6)sin(a x) + 2cos(a x)  - 8cos(a x) - 10
+--R  /
+--R                                              2
+--R     (6a cos(a x) + 12a)sin(a x) - 6a cos(a x)  + 6a cos(a x) + 12a
+--R                                                     Type: Expression Integer
+--E
+
+--S 76
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (4)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 77
+dd:=tanrule cc
+--R
+--R   (5)
+--R                               2a x - %pi 3
+--R           (- cos(a x) - 2)sin(----------)
+--R                                    4
+--R         + 
+--R                   2a x - %pi 2                2a x - %pi 2     2a x - %pi
+--R           (- 3cos(----------) cos(a x) - 6cos(----------) )sin(----------)
+--R                        4                           4                4
+--R         + 
+--R                  2a x - %pi 3                2a x - %pi 3
+--R           - 6cos(----------) cos(a x) - 6cos(----------)
+--R                       4                           4
+--R      *
+--R         sin(a x)
+--R     + 
+--R                2                    2a x - %pi 3
+--R       (cos(a x)  - cos(a x) - 2)sin(----------)
+--R                                          4
+--R     + 
+--R                2a x - %pi 2        2        2a x - %pi 2
+--R           3cos(----------) cos(a x)  - 3cos(----------) cos(a x)
+--R                     4                            4
+--R         + 
+--R                  2a x - %pi 2
+--R           - 6cos(----------)
+--R                       4
+--R      *
+--R             2a x - %pi
+--R         sin(----------)
+--R                  4
+--R     + 
+--R          2a x - %pi 3        2        2a x - %pi 3                 2a x - %pi 3
+--R     2cos(----------) cos(a x)  - 8cos(----------) cos(a x) - 10cos(----------)
+--R               4                            4                            4
+--R  /
+--R               2a x - %pi 3                   2a x - %pi 3
+--R       (6a cos(----------) cos(a x) + 12a cos(----------) )sin(a x)
+--R                    4                              4
+--R     + 
+--R                2a x - %pi 3        2          2a x - %pi 3
+--R       - 6a cos(----------) cos(a x)  + 6a cos(----------) cos(a x)
+--R                     4                              4
+--R     + 
+--R               2a x - %pi 3
+--R       12a cos(----------)
+--R                    4
+--R                                                     Type: Expression Integer
+--E
+
+--S 78
+sindiffrule2:=rule(sin((a-b)/4) == sin(a/4)*cos(b/4)-cos(a/4)*sin(b/4))
+--R 
+--R
+--I                 b - a              a     b           b     a
+--I   (6)  - %U sin(-----) == - %U cos(-)sin(-) + %U cos(-)sin(-)
+--I                   4                4     4           4     4
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 79
+ee:=sindiffrule2 dd
+--R
+--R   (7)
+--R                +-+    2a x - %pi 2             +-+    2a x - %pi 2     a x
+--R           (- 3\|2 cos(----------) cos(a x) - 6\|2 cos(----------) )sin(---)
+--R                            4                               4            2
+--R         + 
+--R                                2a x - %pi 3
+--R           (- 2cos(a x) - 4)sin(----------)
+--R                                     4
+--R         + 
+--R              +-+    2a x - %pi 2    a x          2a x - %pi 3
+--R           (3\|2 cos(----------) cos(---) - 12cos(----------) )cos(a x)
+--R                          4           2                4
+--R         + 
+--R             +-+    2a x - %pi 2    a x          2a x - %pi 3
+--R           6\|2 cos(----------) cos(---) - 12cos(----------)
+--R                         4           2                4
+--R      *
+--R         sin(a x)
+--R     + 
+--R            +-+    2a x - %pi 2             +-+    2a x - %pi 2     a x
+--R       (- 3\|2 cos(----------) cos(a x) - 6\|2 cos(----------) )sin(---)
+--R                        4                               4            2
+--R     + 
+--R                 2                     2a x - %pi 3
+--R       (2cos(a x)  - 2cos(a x) - 4)sin(----------)
+--R                                            4
+--R     + 
+--R            2a x - %pi 2        2    2a x - %pi         2a x - %pi 3        2
+--R       6cos(----------) cos(a x) sin(----------) + 4cos(----------) cos(a x)
+--R                 4                        4                  4
+--R     + 
+--R          +-+    2a x - %pi 2    a x          2a x - %pi 3
+--R       (3\|2 cos(----------) cos(---) - 16cos(----------) )cos(a x)
+--R                      4           2                4
+--R     + 
+--R         +-+    2a x - %pi 2    a x          2a x - %pi 3
+--R       6\|2 cos(----------) cos(---) - 20cos(----------)
+--R                     4           2                4
+--R  /
+--R                2a x - %pi 3                   2a x - %pi 3
+--R       (12a cos(----------) cos(a x) + 24a cos(----------) )sin(a x)
+--R                     4                              4
+--R     + 
+--R                 2a x - %pi 3        2           2a x - %pi 3
+--R       - 12a cos(----------) cos(a x)  + 12a cos(----------) cos(a x)
+--R                      4                               4
+--R     + 
+--R               2a x - %pi 3
+--R       24a cos(----------)
+--R                    4
+--R                                                     Type: Expression Integer
+--E
+
+--S 80
+sincuberule:=rule(sin(a)^3 == 3/4*sin(a)-1/4*sin(3*a))
+--R
+--R              3    - sin(3a) + 3sin(a)
+--R   (8)  sin(a)  == -------------------
+--R                            4
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 81
+ff:=sincuberule ee
+--R
+--R   (9)
+--R                                         2                    6a x - 3%pi
+--R       ((cos(a x) + 2)sin(a x) - cos(a x)  + cos(a x) + 2)sin(-----------)
+--R                                                                   4
+--R     + 
+--R                +-+    2a x - %pi 2              +-+    2a x - %pi 2     a x
+--R           (- 6\|2 cos(----------) cos(a x) - 12\|2 cos(----------) )sin(---)
+--R                            4                                4            2
+--R         + 
+--R                                2a x - %pi
+--R           (- 3cos(a x) - 6)sin(----------)
+--R                                     4
+--R         + 
+--R              +-+    2a x - %pi 2    a x          2a x - %pi 3
+--R           (6\|2 cos(----------) cos(---) - 24cos(----------) )cos(a x)
+--R                          4           2                4
+--R         + 
+--R              +-+    2a x - %pi 2    a x          2a x - %pi 3
+--R           12\|2 cos(----------) cos(---) - 24cos(----------)
+--R                          4           2                4
+--R      *
+--R         sin(a x)
+--R     + 
+--R            +-+    2a x - %pi 2              +-+    2a x - %pi 2     a x
+--R       (- 6\|2 cos(----------) cos(a x) - 12\|2 cos(----------) )sin(---)
+--R                        4                                4            2
+--R     + 
+--R               2a x - %pi 2             2                     2a x - %pi
+--R       ((12cos(----------)  + 3)cos(a x)  - 3cos(a x) - 6)sin(----------)
+--R                    4                                              4
+--R     + 
+--R            2a x - %pi 3        2
+--R       8cos(----------) cos(a x)
+--R                 4
+--R     + 
+--R          +-+    2a x - %pi 2    a x          2a x - %pi 3
+--R       (6\|2 cos(----------) cos(---) - 32cos(----------) )cos(a x)
+--R                      4           2                4
+--R     + 
+--R          +-+    2a x - %pi 2    a x          2a x - %pi 3
+--R       12\|2 cos(----------) cos(---) - 40cos(----------)
+--R                      4           2                4
+--R  /
+--R                2a x - %pi 3                   2a x - %pi 3
+--R       (24a cos(----------) cos(a x) + 48a cos(----------) )sin(a x)
+--R                     4                              4
+--R     + 
+--R                 2a x - %pi 3        2           2a x - %pi 3
+--R       - 24a cos(----------) cos(a x)  + 24a cos(----------) cos(a x)
+--R                      4                               4
+--R     + 
+--R               2a x - %pi 3
+--R       48a cos(----------)
+--R                    4
+--R                                                     Type: Expression Integer
+--E
+
+--S 82     14:359 Schaums and Axiom differ by a constant
+complexNormalize %
+--R
+--R            2
+--R   (10)  - --
+--R           3a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.360~~~~~$\displaystyle
+\int{\frac{dx}{p+q\sin{ax}}}$}
+$$\int{\frac{1}{p+q\sin{ax}}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{2}{a\sqrt{p^2-q^q}}
+\tan^{-1}\frac{p\tan{\frac{1}{2}ax}+q}{\sqrt{p^2-q^2}}\\
+\\
+\displaystyle
+\frac{1}{a\sqrt{q^2-p^2}}\ln\left(\frac{p\tan{\frac{1}{2}ax}+q-\sqrt{q^2-p^2}}
+{p\tan{\frac{1}{2}ax}+q+\sqrt{q^2-p^2}}\right)
+\end{array}
+\right.
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 83
+aa:=integrate(1/(p+q*sin(a*x)),x)
+--R
+--R   (1)
+--R   [
+--R       log
+--R                                                      +-------+
+--R                                2    2             2  | 2    2
+--R              (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
+--R            + 
+--R                    2    3                3    2              3    2
+--R              (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
+--R         /
+--R            q sin(a x) + p
+--R    /
+--R         +-------+
+--R         | 2    2
+--R       a\|q  - p
+--R     ,
+--R                                          +---------+
+--R                                          |   2    2
+--R            (p sin(a x) + q cos(a x) + q)\|- q  + p
+--R      2atan(-----------------------------------------)
+--R                     2    2             2    2
+--R                   (q  - p )cos(a x) + q  - p
+--R    - ------------------------------------------------]
+--R                          +---------+
+--R                          |   2    2
+--R                        a\|- q  + p
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+
+--S 84
+bb1:=2/(a*sqrt(p^2-q^2))*atan((p*tan(a*x/2)+q)/sqrt(p^2-q^2))
+--R
+--R                    a x
+--R              p tan(---) + q
+--R                     2
+--R        2atan(--------------)
+--R                +---------+
+--R                |   2    2
+--R               \|- q  + p
+--R   (2)  ---------------------
+--R              +---------+
+--R              |   2    2
+--R            a\|- q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 85
+bb2:=1/(a*sqrt(q^2-p^2))*log((p*tan((a*x)/2)+q-sqrt(q^2-p^2))/(p*tan((a*x)/2)+q+sqrt(q^2-p^2)))
+--R
+--R               +-------+
+--R               | 2    2          a x
+--R            - \|q  - p   + p tan(---) + q
+--R                                  2
+--R        log(-----------------------------)
+--R              +-------+
+--R              | 2    2          a x
+--R             \|q  - p   + p tan(---) + q
+--R                                 2
+--R   (3)  ----------------------------------
+--R                      +-------+
+--R                      | 2    2
+--R                    a\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 86
+cc1:=aa.1-bb1
+--R
+--R   (4)
+--R          +---------+
+--R          |   2    2
+--R         \|- q  + p
+--R      *
+--R         log
+--R                                                        +-------+
+--R                                  2    2             2  | 2    2
+--R                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
+--R              + 
+--R                      2    3                3    2              3    2
+--R                (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
+--R           /
+--R              q sin(a x) + p
+--R     + 
+--R                               a x
+--R           +-------+     p tan(---) + q
+--R           | 2    2             2
+--R       - 2\|q  - p  atan(--------------)
+--R                           +---------+
+--R                           |   2    2
+--R                          \|- q  + p
+--R  /
+--R       +---------+ +-------+
+--R       |   2    2  | 2    2
+--R     a\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 87
+cc2:=aa.2-bb1
+--R
+--R   (5)
+--R                                         +---------+                a x
+--R                                         |   2    2           p tan(---) + q
+--R           (p sin(a x) + q cos(a x) + q)\|- q  + p                   2
+--R   - 2atan(-----------------------------------------) - 2atan(--------------)
+--R                    2    2             2    2                   +---------+
+--R                  (q  - p )cos(a x) + q  - p                    |   2    2
+--R                                                               \|- q  + p
+--R   --------------------------------------------------------------------------
+--R                                    +---------+
+--R                                    |   2    2
+--R                                  a\|- q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 88
+cc3:=aa.1-bb2
+--R
+--R   (6)
+--R       log
+--R                                                      +-------+
+--R                                2    2             2  | 2    2
+--R              (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
+--R            + 
+--R                    2    3                3    2              3    2
+--R              (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
+--R         /
+--R            q sin(a x) + p
+--R     + 
+--R                +-------+
+--R                | 2    2          a x
+--R             - \|q  - p   + p tan(---) + q
+--R                                   2
+--R       - log(-----------------------------)
+--R               +-------+
+--R               | 2    2          a x
+--R              \|q  - p   + p tan(---) + q
+--R                                  2
+--R  /
+--R       +-------+
+--R       | 2    2
+--R     a\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 89
+cc4:=aa.2-bb2
+--R
+--R   (7)
+--R                            +-------+
+--R                            | 2    2          a x
+--R          +---------+    - \|q  - p   + p tan(---) + q
+--R          |   2    2                           2
+--R       - \|- q  + p  log(-----------------------------)
+--R                           +-------+
+--R                           | 2    2          a x
+--R                          \|q  - p   + p tan(---) + q
+--R                                              2
+--R     + 
+--R                                                       +---------+
+--R           +-------+                                   |   2    2
+--R           | 2    2      (p sin(a x) + q cos(a x) + q)\|- q  + p
+--R       - 2\|q  - p  atan(-----------------------------------------)
+--R                                  2    2             2    2
+--R                                (q  - p )cos(a x) + q  - p
+--R  /
+--R       +---------+ +-------+
+--R       |   2    2  | 2    2
+--R     a\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 90
+dd2:=ratDenom cc2
+--R
+--R   (8)
+--R                                            +---------+
+--R                                  a x       |   2    2
+--R           +---------+     (p tan(---) + q)\|- q  + p
+--R           |   2    2              2
+--R       - 2\|- q  + p  atan(----------------------------)
+--R                                       2    2
+--R                                      q  - p
+--R     + 
+--R                                                       +---------+
+--R         +---------+                                   |   2    2
+--R         |   2    2      (p sin(a x) + q cos(a x) + q)\|- q  + p
+--R       2\|- q  + p  atan(-----------------------------------------)
+--R                                  2    2             2    2
+--R                                (q  - p )cos(a x) + q  - p
+--R  /
+--R        2      2
+--R     a q  - a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 91
+atanrule2:=rule(atan(x) == 1/2*%i*(log(1-%i*x)-log(1+%i*x)))
+--R
+--R                     1                    1
+--R   (9)  atan(x) == - - %i log(%i x + 1) + - %i log(- %i x + 1)
+--R                     2                    2
+--RType: RewriteRule(Integer,Complex Fraction Integer,Expression Complex Fraction Integer)
+--E
+
+--S 92
+ee2:=atanrule2 dd2
+--R
+--R   (10)
+--R                                                  +---------+
+--R                                   1              |   2    2     2    2
+--R          +---------+    (%i p tan(- a x) + %i q)\|- q  + p   + q  - p
+--R          |   2    2               2
+--R       %i\|- q  + p  log(----------------------------------------------)
+--R                                              2    2
+--R                                             q  - p
+--R     + 
+--R       -
+--R               +---------+
+--R               |   2    2
+--R            %i\|- q  + p
+--R         *
+--R            log
+--R                                                          +---------+
+--R                                                          |   2    2
+--R                   (%i p sin(a x) + %i q cos(a x) + %i q)\|- q  + p
+--R                 + 
+--R                     2    2             2    2
+--R                   (q  - p )cos(a x) + q  - p
+--R              /
+--R                   2    2             2    2
+--R                 (q  - p )cos(a x) + q  - p
+--R     + 
+--R            +---------+
+--R            |   2    2
+--R         %i\|- q  + p
+--R      *
+--R         log
+--R                                                         +---------+
+--R                                                         |   2    2
+--R                (- %i p sin(a x) - %i q cos(a x) - %i q)\|- q  + p
+--R              + 
+--R                  2    2             2    2
+--R                (q  - p )cos(a x) + q  - p
+--R           /
+--R                2    2             2    2
+--R              (q  - p )cos(a x) + q  - p
+--R     + 
+--R                                                      +---------+
+--R                                       1              |   2    2     2    2
+--R            +---------+    (- %i p tan(- a x) - %i q)\|- q  + p   + q  - p
+--R            |   2    2                 2
+--R       - %i\|- q  + p  log(------------------------------------------------)
+--R                                                 2    2
+--R                                                q  - p
+--R  /
+--R        2      2
+--R     a q  - a p
+--R                                    Type: Expression Complex Fraction Integer
+--E
+
+--S 93
+ff2:=expandLog ee2
+--R
+--R   (11)
+--R            +---------+                       +---------+
+--R            |   2    2            1           |   2    2        2       2
+--R       - %i\|- q  + p  log((p tan(- a x) + q)\|- q  + p   + %i q  - %i p )
+--R                                  2
+--R     + 
+--R          +---------+                       +---------+
+--R          |   2    2            1           |   2    2        2       2
+--R       %i\|- q  + p  log((p tan(- a x) + q)\|- q  + p   - %i q  + %i p )
+--R                                2
+--R     + 
+--R            +---------+
+--R            |   2    2
+--R         %i\|- q  + p
+--R      *
+--R         log
+--R                                            +---------+
+--R                                            |   2    2
+--R              (p sin(a x) + q cos(a x) + q)\|- q  + p
+--R            + 
+--R                   2       2                2       2
+--R              (%i q  - %i p )cos(a x) + %i q  - %i p
+--R     + 
+--R       -
+--R               +---------+
+--R               |   2    2
+--R            %i\|- q  + p
+--R         *
+--R            log
+--R                                               +---------+
+--R                                               |   2    2
+--R                 (p sin(a x) + q cos(a x) + q)\|- q  + p
+--R               + 
+--R                        2       2                2       2
+--R                 (- %i q  + %i p )cos(a x) - %i q  + %i p
+--R  /
+--R        2      2
+--R     a q  - a p
+--R                                    Type: Expression Complex Fraction Integer
+--E
+
+--S 94
+gg2:=numer(ff2)/denom(ff2)
+--R
+--R   (12)
+--R            +---------+                       +---------+
+--R            |   2    2            1           |   2    2        2       2
+--R       - %i\|- q  + p  log((p tan(- a x) + q)\|- q  + p   + %i q  - %i p )
+--R                                  2
+--R     + 
+--R          +---------+                       +---------+
+--R          |   2    2            1           |   2    2        2       2
+--R       %i\|- q  + p  log((p tan(- a x) + q)\|- q  + p   - %i q  + %i p )
+--R                                2
+--R     + 
+--R            +---------+
+--R            |   2    2
+--R         %i\|- q  + p
+--R      *
+--R         log
+--R                                            +---------+
+--R                                            |   2    2
+--R              (p sin(a x) + q cos(a x) + q)\|- q  + p
+--R            + 
+--R                   2       2                2       2
+--R              (%i q  - %i p )cos(a x) + %i q  - %i p
+--R     + 
+--R       -
+--R               +---------+
+--R               |   2    2
+--R            %i\|- q  + p
+--R         *
+--R            log
+--R                                               +---------+
+--R                                               |   2    2
+--R                 (p sin(a x) + q cos(a x) + q)\|- q  + p
+--R               + 
+--R                        2       2                2       2
+--R                 (- %i q  + %i p )cos(a x) - %i q  + %i p
+--R  /
+--R        2      2
+--R     a q  - a p
+--RType: Fraction SparseMultivariatePolynomial(Complex Fraction Integer,Kernel Expression Complex Fraction Integer)
+--E
+
+--S 95
+hh2:=gg2::Expression Complex Fraction Integer
+--R
+--R   (13)
+--R            +---------+                       +---------+
+--R            |   2    2            1           |   2    2        2       2
+--R       - %i\|- q  + p  log((p tan(- a x) + q)\|- q  + p   + %i q  - %i p )
+--R                                  2
+--R     + 
+--R          +---------+                       +---------+
+--R          |   2    2            1           |   2    2        2       2
+--R       %i\|- q  + p  log((p tan(- a x) + q)\|- q  + p   - %i q  + %i p )
+--R                                2
+--R     + 
+--R            +---------+
+--R            |   2    2
+--R         %i\|- q  + p
+--R      *
+--R         log
+--R                                            +---------+
+--R                                            |   2    2
+--R              (p sin(a x) + q cos(a x) + q)\|- q  + p
+--R            + 
+--R                   2       2                2       2
+--R              (%i q  - %i p )cos(a x) + %i q  - %i p
+--R     + 
+--R       -
+--R               +---------+
+--R               |   2    2
+--R            %i\|- q  + p
+--R         *
+--R            log
+--R                                               +---------+
+--R                                               |   2    2
+--R                 (p sin(a x) + q cos(a x) + q)\|- q  + p
+--R               + 
+--R                        2       2                2       2
+--R                 (- %i q  + %i p )cos(a x) - %i q  + %i p
+--R  /
+--R        2      2
+--R     a q  - a p
+--R                                    Type: Expression Complex Fraction Integer
+--E
+
+--S 96     14:360 Schaums and Axiom agree
+complexNormalize hh2
+--R
+--R   (14)  0
+--R                                    Type: Expression Complex Fraction Integer
+--E
+@
+
+\section{\cite{1}:14.361~~~~~$\displaystyle
+\int{\frac{dx}{(p+q\sin{ax})^2}}$}
+$$\int{\frac{1}{(p+q\sin{ax})^2}}=
+\frac{q\cos{ax}}{a(p^2-q^2)(p+q\sin{ax})}
++\frac{p}{p^2-q^2}\int{\frac{1}{p+q\sin{ax}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 97
+aa:=integrate(1/(p+q*sin(a*x))^2,x)
+--R 
+--R
+--R   (1)
+--R   [
+--R             2              3
+--R           (p q sin(a x) + p )
+--R        *
+--R           log
+--R                                                          +-------+
+--R                                    2    2             2  | 2    2
+--R                  (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
+--R                + 
+--R                      2    3              3    2              3    2
+--R                  (p q  - p )sin(a x) + (q  - p q)cos(a x) + q  - p q
+--R             /
+--R                q sin(a x) + p
+--R       + 
+--R                                             +-------+
+--R             2                               | 2    2
+--R         (- q sin(a x) - p q cos(a x) - p q)\|q  - p
+--R    /
+--R                                                  +-------+
+--R              3      3                2 2      4  | 2    2
+--R       ((a p q  - a p q)sin(a x) + a p q  - a p )\|q  - p
+--R     ,
+--R
+--R                                                                 +---------+
+--R                                                                 |   2    2
+--R            2               3      (p sin(a x) + q cos(a x) + q)\|- q  + p
+--R         (2p q sin(a x) + 2p )atan(-----------------------------------------)
+--R                                            2    2             2    2
+--R                                          (q  - p )cos(a x) + q  - p
+--R       + 
+--R                                             +---------+
+--R             2                               |   2    2
+--R         (- q sin(a x) - p q cos(a x) - p q)\|- q  + p
+--R    /
+--R                                                  +---------+
+--R              3      3                2 2      4  |   2    2
+--R       ((a p q  - a p q)sin(a x) + a p q  - a p )\|- q  + p
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+
+--S 98
+t1:=integrate(1/(p+q*sin(a*x)),x)
+--R
+--R   (2)
+--R   [
+--R       log
+--R                                                      +-------+
+--R                                2    2             2  | 2    2
+--R              (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
+--R            + 
+--R                    2    3                3    2              3    2
+--R              (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
+--R         /
+--R            q sin(a x) + p
+--R    /
+--R         +-------+
+--R         | 2    2
+--R       a\|q  - p
+--R     ,
+--R                                          +---------+
+--R                                          |   2    2
+--R            (p sin(a x) + q cos(a x) + q)\|- q  + p
+--R      2atan(-----------------------------------------)
+--R                     2    2             2    2
+--R                   (q  - p )cos(a x) + q  - p
+--R    - ------------------------------------------------]
+--R                          +---------+
+--R                          |   2    2
+--R                        a\|- q  + p
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 99
+bb1:=(q*cos(a*x))/(a*(p^2-q^2)*(p+q*sin(a*x)))+p/(p^2-q^2)*t1.1
+--R
+--R   (3)
+--R                            2
+--R         (- p q sin(a x) - p )
+--R      *
+--R         log
+--R                                                        +-------+
+--R                                  2    2             2  | 2    2
+--R                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
+--R              + 
+--R                      2    3                3    2              3    2
+--R                (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
+--R           /
+--R              q sin(a x) + p
+--R     + 
+--R                    +-------+
+--R                    | 2    2
+--R       - q cos(a x)\|q  - p
+--R  /
+--R                                              +-------+
+--R          3      2                  2      3  | 2    2
+--R     ((a q  - a p q)sin(a x) + a p q  - a p )\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 100
+bb2:=(q*cos(a*x))/(a*(p^2-q^2)*(p+q*sin(a*x)))+p/(p^2-q^2)*t1.2
+--R
+--R   (4)
+--R                                                               +---------+
+--R                                                               |   2    2
+--R                          2      (p sin(a x) + q cos(a x) + q)\|- q  + p
+--R       (2p q sin(a x) + 2p )atan(-----------------------------------------)
+--R                                          2    2             2    2
+--R                                        (q  - p )cos(a x) + q  - p
+--R     + 
+--R                    +---------+
+--R                    |   2    2
+--R       - q cos(a x)\|- q  + p
+--R  /
+--R                                              +---------+
+--R          3      2                  2      3  |   2    2
+--R     ((a q  - a p q)sin(a x) + a p q  - a p )\|- q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 101
+cc1:=aa.1-bb1
+--R
+--R   (5)
+--R          2
+--R         p
+--R      *
+--R         log
+--R                                                        +-------+
+--R                                  2    2             2  | 2    2
+--R                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
+--R              + 
+--R                    2    3              3    2              3    2
+--R                (p q  - p )sin(a x) + (q  - p q)cos(a x) + q  - p q
+--R           /
+--R              q sin(a x) + p
+--R     + 
+--R          2
+--R         p
+--R      *
+--R         log
+--R                                                        +-------+
+--R                                  2    2             2  | 2    2
+--R                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
+--R              + 
+--R                      2    3                3    2              3    2
+--R                (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
+--R           /
+--R              q sin(a x) + p
+--R     + 
+--R           +-------+
+--R           | 2    2
+--R       - q\|q  - p
+--R  /
+--R                     +-------+
+--R           2      3  | 2    2
+--R     (a p q  - a p )\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 102
+cc2:=aa.2-bb1
+--R
+--R   (6)
+--R            +---------+
+--R          2 |   2    2
+--R         p \|- q  + p
+--R      *
+--R         log
+--R                                                        +-------+
+--R                                  2    2             2  | 2    2
+--R                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
+--R              + 
+--R                      2    3                3    2              3    2
+--R                (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
+--R           /
+--R              q sin(a x) + p
+--R     + 
+--R                                                       +---------+
+--R           +-------+                                   |   2    2
+--R         2 | 2    2      (p sin(a x) + q cos(a x) + q)\|- q  + p
+--R       2p \|q  - p  atan(-----------------------------------------)
+--R                                  2    2             2    2
+--R                                (q  - p )cos(a x) + q  - p
+--R     + 
+--R           +---------+ +-------+
+--R           |   2    2  | 2    2
+--R       - q\|- q  + p  \|q  - p
+--R  /
+--R                     +---------+ +-------+
+--R           2      3  |   2    2  | 2    2
+--R     (a p q  - a p )\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 103
+cc3:=aa.1-bb2
+--R
+--R   (7)
+--R            +---------+
+--R          2 |   2    2
+--R         p \|- q  + p
+--R      *
+--R         log
+--R                                                        +-------+
+--R                                  2    2             2  | 2    2
+--R                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
+--R              + 
+--R                    2    3              3    2              3    2
+--R                (p q  - p )sin(a x) + (q  - p q)cos(a x) + q  - p q
+--R           /
+--R              q sin(a x) + p
+--R     + 
+--R                                                         +---------+
+--R             +-------+                                   |   2    2
+--R           2 | 2    2      (p sin(a x) + q cos(a x) + q)\|- q  + p
+--R       - 2p \|q  - p  atan(-----------------------------------------)
+--R                                    2    2             2    2
+--R                                  (q  - p )cos(a x) + q  - p
+--R     + 
+--R           +---------+ +-------+
+--R           |   2    2  | 2    2
+--R       - q\|- q  + p  \|q  - p
+--R  /
+--R                     +---------+ +-------+
+--R           2      3  |   2    2  | 2    2
+--R     (a p q  - a p )\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 104    14:361 Schaums and Axiom differ by a constant
+cc4:=aa.2-bb2
+--R
+--R                q
+--R   (8)  - -------------
+--R               2      3
+--R          a p q  - a p
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.362~~~~~$\displaystyle
+\int{\frac{dx}{p^2+q^2\sin^2{ax}}}$}
+$$\int{\frac{1}{p^2+q^2\sin^2{ax}}}=
+\frac{1}{ap\sqrt{p^2+q^2}}\tan^{-1}\frac{\sqrt{p^2+q^2}\tan{ax}}{p}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 105
+aa:=integrate(1/(p^2+q^2*sin(a*x)^2),x)
+--R
+--R   (1)
+--R                             +-------+
+--R                             | 2    2
+--R                  p sin(a x)\|q  + p
+--R       atan(-------------------------------)
+--R               2     2              2     2
+--R            (2q  + 2p )cos(a x) + 2q  + 2p
+--R     + 
+--R                 2    2              2     2
+--R             ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)
+--R       atan(-----------------------------------------)
+--R                                            +-------+
+--R                       2                    | 2    2
+--R            (p cos(a x)  + 2p cos(a x) + p)\|q  + p
+--R  /
+--R         +-------+
+--R         | 2    2
+--R     a p\|q  + p
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 106
+bb:=1/(a*p*sqrt(p^2+q^2))*atan((sqrt(p^2+q^2)*tan(a*x))/p)
+--R
+--R                      +-------+
+--R                      | 2    2
+--R             tan(a x)\|q  + p
+--R        atan(------------------)
+--R                      p
+--R   (2)  ------------------------
+--R                  +-------+
+--R                  | 2    2
+--R              a p\|q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 107
+cc:=aa-bb
+--R
+--R   (3)
+--R                       +-------+                          +-------+
+--R                       | 2    2                           | 2    2
+--R              tan(a x)\|q  + p                 p sin(a x)\|q  + p
+--R       - atan(------------------) + atan(-------------------------------)
+--R                       p                    2     2              2     2
+--R                                         (2q  + 2p )cos(a x) + 2q  + 2p
+--R     + 
+--R                 2    2              2     2
+--R             ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)
+--R       atan(-----------------------------------------)
+--R                                            +-------+
+--R                       2                    | 2    2
+--R            (p cos(a x)  + 2p cos(a x) + p)\|q  + p
+--R  /
+--R         +-------+
+--R         | 2    2
+--R     a p\|q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 108
+dd:=ratDenom cc
+--R
+--R   (4)
+--R                                 +-------+
+--R          +-------+              | 2    2
+--R          | 2    2      tan(a x)\|q  + p
+--R       - \|q  + p  atan(------------------)
+--R                                 p
+--R     + 
+--R                                                                  +-------+
+--R        +-------+            2    2              2     2          | 2    2
+--R        | 2    2         ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)\|q  + p
+--R       \|q  + p  atan(--------------------------------------------------------)
+--R                          2    3         2        2     3               2    3
+--R                      (p q  + p )cos(a x)  + (2p q  + 2p )cos(a x) + p q  + p
+--R     + 
+--R                                       +-------+
+--R        +-------+                      | 2    2
+--R        | 2    2            p sin(a x)\|q  + p
+--R       \|q  + p  atan(-------------------------------)
+--R                         2     2              2     2
+--R                      (2q  + 2p )cos(a x) + 2q  + 2p
+--R  /
+--R          2      3
+--R     a p q  + a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 109
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (5)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 110
+ee:=atanrule dd
+--R
+--R   (6)
+--R       -
+--R               +-------+
+--R               | 2    2
+--R            %i\|q  + p
+--R         *
+--R            log
+--R                                +-------+
+--R                                | 2    2          2        2                 2
+--R                   - p sin(a x)\|q  + p   + (2%i q  + 2%i p )cos(a x) + 2%i q
+--R                 + 
+--R                        2
+--R                   2%i p
+--R              /
+--R                              +-------+
+--R                              | 2    2          2        2                 2
+--R                   p sin(a x)\|q  + p   + (2%i q  + 2%i p )cos(a x) + 2%i q
+--R                 + 
+--R                        2
+--R                   2%i p
+--R     + 
+--R       -
+--R               +-------+
+--R               | 2    2
+--R            %i\|q  + p
+--R         *
+--R            log
+--R                                                              +-------+
+--R                         2    2              2     2          | 2    2
+--R                   ((- 2q  - p )cos(a x) - 2q  - 2p )sin(a x)\|q  + p
+--R                 + 
+--R                          2       3         2           2        3
+--R                   (%i p q  + %i p )cos(a x)  + (2%i p q  + 2%i p )cos(a x)
+--R                 + 
+--R                         2       3
+--R                   %i p q  + %i p
+--R              /
+--R                                                            +-------+
+--R                       2    2              2     2          | 2    2
+--R                   ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)\|q  + p
+--R                 + 
+--R                          2       3         2           2        3
+--R                   (%i p q  + %i p )cos(a x)  + (2%i p q  + 2%i p )cos(a x)
+--R                 + 
+--R                         2       3
+--R                   %i p q  + %i p
+--R     + 
+--R                                  +-------+
+--R          +-------+               | 2    2
+--R          | 2    2     - tan(a x)\|q  + p   + %i p
+--R       %i\|q  + p  log(---------------------------)
+--R                                 +-------+
+--R                                 | 2    2
+--R                        tan(a x)\|q  + p   + %i p
+--R  /
+--R           2       3
+--R     2a p q  + 2a p
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 111
+ff:=expandLog ee
+--R
+--R   (7)
+--R            +-------+             +-------+
+--R            | 2    2              | 2    2
+--R       - %i\|q  + p  log(tan(a x)\|q  + p   + %i p)
+--R     + 
+--R          +-------+             +-------+
+--R          | 2    2              | 2    2
+--R       %i\|q  + p  log(tan(a x)\|q  + p   - %i p)
+--R     + 
+--R            +-------+
+--R            | 2    2
+--R         %i\|q  + p
+--R      *
+--R         log
+--R                                                       +-------+
+--R                  2    2              2     2          | 2    2
+--R              ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)\|q  + p
+--R            + 
+--R                     2       3         2           2        3                  2
+--R              (%i p q  + %i p )cos(a x)  + (2%i p q  + 2%i p )cos(a x) + %i p q
+--R            + 
+--R                  3
+--R              %i p
+--R     + 
+--R       -
+--R               +-------+
+--R               | 2    2
+--R            %i\|q  + p
+--R         *
+--R            log
+--R                                                          +-------+
+--R                     2    2              2     2          | 2    2
+--R                 ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)\|q  + p
+--R               + 
+--R                          2       3         2             2        3
+--R                 (- %i p q  - %i p )cos(a x)  + (- 2%i p q  - 2%i p )cos(a x)
+--R               + 
+--R                         2       3
+--R                 - %i p q  - %i p
+--R     + 
+--R            +-------+
+--R            | 2    2
+--R         %i\|q  + p
+--R      *
+--R                      +-------+
+--R                      | 2    2          2        2                 2        2
+--R       log(p sin(a x)\|q  + p   + (2%i q  + 2%i p )cos(a x) + 2%i q  + 2%i p )
+--R     + 
+--R       -
+--R               +-------+
+--R               | 2    2
+--R            %i\|q  + p
+--R         *
+--R            log
+--R                            +-------+
+--R                            | 2    2            2        2                 2
+--R                 p sin(a x)\|q  + p   + (- 2%i q  - 2%i p )cos(a x) - 2%i q
+--R               + 
+--R                        2
+--R                 - 2%i p
+--R     + 
+--R                     +-------+
+--R                     | 2    2
+--R       - %i log(- 1)\|q  + p
+--R  /
+--R           2       3
+--R     2a p q  + 2a p
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 112
+tanrule2:RewriteRule(INT,COMPLEX(INT),EXPR(COMPLEX(INT))):=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (8)  tan(a) == ------
+--R                  cos(a)
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 113
+gg:=tanrule2 ff
+--R
+--R   (9)
+--R            +-------+
+--R            | 2    2
+--R         %i\|q  + p
+--R      *
+--R         log
+--R                                                       +-------+
+--R                  2    2              2     2          | 2    2
+--R              ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)\|q  + p
+--R            + 
+--R                     2       3         2           2        3                  2
+--R              (%i p q  + %i p )cos(a x)  + (2%i p q  + 2%i p )cos(a x) + %i p q
+--R            + 
+--R                  3
+--R              %i p
+--R     + 
+--R       -
+--R               +-------+
+--R               | 2    2
+--R            %i\|q  + p
+--R         *
+--R            log
+--R                                                          +-------+
+--R                     2    2              2     2          | 2    2
+--R                 ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)\|q  + p
+--R               + 
+--R                          2       3         2             2        3
+--R                 (- %i p q  - %i p )cos(a x)  + (- 2%i p q  - 2%i p )cos(a x)
+--R               + 
+--R                         2       3
+--R                 - %i p q  - %i p
+--R     + 
+--R            +-------+
+--R            | 2    2
+--R         %i\|q  + p
+--R      *
+--R                      +-------+
+--R                      | 2    2          2        2                 2        2
+--R       log(p sin(a x)\|q  + p   + (2%i q  + 2%i p )cos(a x) + 2%i q  + 2%i p )
+--R     + 
+--R       -
+--R               +-------+
+--R               | 2    2
+--R            %i\|q  + p
+--R         *
+--R            log
+--R                            +-------+
+--R                            | 2    2            2        2                 2
+--R                 p sin(a x)\|q  + p   + (- 2%i q  - 2%i p )cos(a x) - 2%i q
+--R               + 
+--R                        2
+--R                 - 2%i p
+--R     + 
+--R                                  +-------+
+--R            +-------+             | 2    2
+--R            | 2    2     sin(a x)\|q  + p   + %i p cos(a x)
+--R       - %i\|q  + p  log(----------------------------------)
+--R                                      cos(a x)
+--R     + 
+--R                              +-------+
+--R        +-------+             | 2    2                                 +-------+
+--R        | 2    2     sin(a x)\|q  + p   - %i p cos(a x)                | 2    2
+--R     %i\|q  + p  log(----------------------------------) - %i log(- 1)\|q  + p
+--R                                  cos(a x)
+--R  /
+--R           2       3
+--R     2a p q  + 2a p
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 114
+hh:=expandLog gg
+--R
+--R   (10)
+--R            +-------+
+--R            | 2    2
+--R         %i\|q  + p
+--R      *
+--R         log
+--R                                                       +-------+
+--R                  2    2              2     2          | 2    2
+--R              ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)\|q  + p
+--R            + 
+--R                     2       3         2           2        3                  2
+--R              (%i p q  + %i p )cos(a x)  + (2%i p q  + 2%i p )cos(a x) + %i p q
+--R            + 
+--R                  3
+--R              %i p
+--R     + 
+--R       -
+--R               +-------+
+--R               | 2    2
+--R            %i\|q  + p
+--R         *
+--R            log
+--R                                                          +-------+
+--R                     2    2              2     2          | 2    2
+--R                 ((2q  + p )cos(a x) + 2q  + 2p )sin(a x)\|q  + p
+--R               + 
+--R                          2       3         2             2        3
+--R                 (- %i p q  - %i p )cos(a x)  + (- 2%i p q  - 2%i p )cos(a x)
+--R               + 
+--R                         2       3
+--R                 - %i p q  - %i p
+--R     + 
+--R            +-------+
+--R            | 2    2
+--R         %i\|q  + p
+--R      *
+--R                      +-------+
+--R                      | 2    2          2        2                 2        2
+--R       log(p sin(a x)\|q  + p   + (2%i q  + 2%i p )cos(a x) + 2%i q  + 2%i p )
+--R     + 
+--R       -
+--R               +-------+
+--R               | 2    2
+--R            %i\|q  + p
+--R         *
+--R            log
+--R                            +-------+
+--R                            | 2    2            2        2                 2
+--R                 p sin(a x)\|q  + p   + (- 2%i q  - 2%i p )cos(a x) - 2%i q
+--R               + 
+--R                        2
+--R                 - 2%i p
+--R     + 
+--R            +-------+             +-------+
+--R            | 2    2              | 2    2
+--R       - %i\|q  + p  log(sin(a x)\|q  + p   + %i p cos(a x))
+--R     + 
+--R        +-------+             +-------+                                +-------+
+--R        | 2    2              | 2    2                                 | 2    2
+--R     %i\|q  + p  log(sin(a x)\|q  + p   - %i p cos(a x)) - %i log(- 1)\|q  + p
+--R  /
+--R           2       3
+--R     2a p q  + 2a p
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 115    14:362 Schaums and Axiom differ by a constant
+ii:=complexNormalize hh
+--R
+--R                                                   +-------+
+--R                                                   | 2    2
+--R         (%i log(%i) - %i log(- %i) - %i log(- 1))\|q  + p
+--R   (11)  ---------------------------------------------------
+--R                                 2       3
+--R                           2a p q  + 2a p
+--R                                             Type: Expression Complex Integer
+--E
+@
+
+\section{\cite{1}:14.363~~~~~$\displaystyle
+\int{\frac{dx}{p^2-q^2\sin^2{ax}}}$}
+$$\int{\frac{1}{p^2-q^2\sin^2{ax}}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{1}{ap\sqrt{p^2-q^2}}\tan^{-1}\frac{\sqrt{p^2-q^2}\tan{ax}}{p}\\
+\\
+\displaystyle
+\frac{1}{2ap\sqrt{q^2-p^2}}\ln\left(\frac{\sqrt{q^2-p^2}\tan{ax}+p}
+{\sqrt{q^2-p^2}\tan{ax}-p}\right)
+\end{array}
+\right.
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 116
+aa:=integrate(1/(p^2-q^2*sin(a*x)^2),x)
+--R
+--R   (1)
+--R   [
+--R       log
+--R                                                +-------+
+--R                   2     2         2    2    2  | 2    2
+--R              ((- q  + 2p )cos(a x)  + q  - p )\|q  - p
+--R            + 
+--R                   2     3
+--R              (2p q  - 2p )cos(a x)sin(a x)
+--R         /
+--R             2        2    2    2
+--R            q cos(a x)  - q  + p
+--R    /
+--R            +-------+
+--R            | 2    2
+--R       2a p\|q  - p
+--R     ,
+--R
+--R                                +---------+
+--R                                |   2    2
+--R                     p sin(a x)\|- q  + p
+--R         - atan(-------------------------------)
+--R                   2     2              2     2
+--R                (2q  - 2p )cos(a x) + 2q  - 2p
+--R       + 
+--R                      2    2              2     2
+--R                  ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)
+--R         - atan(-------------------------------------------)
+--R                                                +---------+
+--R                           2                    |   2    2
+--R                (p cos(a x)  + 2p cos(a x) + p)\|- q  + p
+--R    /
+--R           +---------+
+--R           |   2    2
+--R       a p\|- q  + p
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+
+--S 117
+bb1:=1/(a*p*sqrt(p^2-q^2))*atan((sqrt(p^2-q^2)*tan(a*x))/p)
+--R
+--R                      +---------+
+--R                      |   2    2
+--R             tan(a x)\|- q  + p
+--R        atan(--------------------)
+--R                       p
+--R   (2)  --------------------------
+--R                  +---------+
+--R                  |   2    2
+--R              a p\|- q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 118
+bb2:=1/(2*a*p*sqrt(q^2-p^2))*log((sqrt(q^2-p^2)*tan(a*x)+p)/(sqrt(q^2-p^2)*tan(a*x)-p))
+--R
+--R                     +-------+
+--R                     | 2    2
+--R            tan(a x)\|q  - p   + p
+--R        log(----------------------)
+--R                     +-------+
+--R                     | 2    2
+--R            tan(a x)\|q  - p   - p
+--R   (3)  ---------------------------
+--R                    +-------+
+--R                    | 2    2
+--R               2a p\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 119
+cc1:=aa.1-bb1
+--R
+--R   (4)
+--R          +---------+
+--R          |   2    2
+--R         \|- q  + p
+--R      *
+--R         log
+--R                                                  +-------+
+--R                     2     2         2    2    2  | 2    2
+--R                ((- q  + 2p )cos(a x)  + q  - p )\|q  - p
+--R              + 
+--R                     2     3
+--R                (2p q  - 2p )cos(a x)sin(a x)
+--R           /
+--R               2        2    2    2
+--R              q cos(a x)  - q  + p
+--R     + 
+--R                                  +---------+
+--R           +-------+              |   2    2
+--R           | 2    2      tan(a x)\|- q  + p
+--R       - 2\|q  - p  atan(--------------------)
+--R                                   p
+--R  /
+--R          +---------+ +-------+
+--R          |   2    2  | 2    2
+--R     2a p\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 120
+cc2:=aa.2-bb1
+--R
+--R   (5)
+--R                       +---------+                         +---------+
+--R                       |   2    2                          |   2    2
+--R              tan(a x)\|- q  + p                p sin(a x)\|- q  + p
+--R       - atan(--------------------) - atan(-------------------------------)
+--R                        p                     2     2              2     2
+--R                                           (2q  - 2p )cos(a x) + 2q  - 2p
+--R     + 
+--R                    2    2              2     2
+--R                ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)
+--R       - atan(-------------------------------------------)
+--R                                              +---------+
+--R                         2                    |   2    2
+--R              (p cos(a x)  + 2p cos(a x) + p)\|- q  + p
+--R  /
+--R         +---------+
+--R         |   2    2
+--R     a p\|- q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 121
+cc3:=aa.1-bb2
+--R
+--R   (6)
+--R                      +-------+
+--R                      | 2    2
+--R             tan(a x)\|q  - p   + p
+--R       - log(----------------------)
+--R                      +-------+
+--R                      | 2    2
+--R             tan(a x)\|q  - p   - p
+--R     + 
+--R       log
+--R                                                +-------+
+--R                   2     2         2    2    2  | 2    2
+--R              ((- q  + 2p )cos(a x)  + q  - p )\|q  - p
+--R            + 
+--R                   2     3
+--R              (2p q  - 2p )cos(a x)sin(a x)
+--R         /
+--R             2        2    2    2
+--R            q cos(a x)  - q  + p
+--R  /
+--R          +-------+
+--R          | 2    2
+--R     2a p\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 122
+cc4:=aa.2-bb2
+--R
+--R   (7)
+--R                                  +-------+
+--R          +---------+             | 2    2
+--R          |   2    2     tan(a x)\|q  - p   + p
+--R       - \|- q  + p  log(----------------------)
+--R                                  +-------+
+--R                                  | 2    2
+--R                         tan(a x)\|q  - p   - p
+--R     + 
+--R                                         +---------+
+--R           +-------+                     |   2    2
+--R           | 2    2           p sin(a x)\|- q  + p
+--R       - 2\|q  - p  atan(-------------------------------)
+--R                            2     2              2     2
+--R                         (2q  - 2p )cos(a x) + 2q  - 2p
+--R     + 
+--R           +-------+           2    2              2     2
+--R           | 2    2        ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)
+--R       - 2\|q  - p  atan(-------------------------------------------)
+--R                                                         +---------+
+--R                                    2                    |   2    2
+--R                         (p cos(a x)  + 2p cos(a x) + p)\|- q  + p
+--R  /
+--R          +---------+ +-------+
+--R          |   2    2  | 2    2
+--R     2a p\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 123
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (8)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 124
+dd2:=tanrule cc2
+--R
+--R   (9)
+--R                       +---------+                         +---------+
+--R                       |   2    2                          |   2    2
+--R              sin(a x)\|- q  + p                p sin(a x)\|- q  + p
+--R       - atan(--------------------) - atan(-------------------------------)
+--R                   p cos(a x)                 2     2              2     2
+--R                                           (2q  - 2p )cos(a x) + 2q  - 2p
+--R     + 
+--R                    2    2              2     2
+--R                ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)
+--R       - atan(-------------------------------------------)
+--R                                              +---------+
+--R                         2                    |   2    2
+--R              (p cos(a x)  + 2p cos(a x) + p)\|- q  + p
+--R  /
+--R         +---------+
+--R         |   2    2
+--R     a p\|- q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 125
+ee2:=ratDenom dd2
+--R
+--R   (10)
+--R       -
+--R             +---------+
+--R             |   2    2
+--R            \|- q  + p
+--R         *
+--R                                                            +---------+
+--R                       2    2              2     2          |   2    2
+--R                   ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)\|- q  + p
+--R            atan(--------------------------------------------------------)
+--R                     2    3         2        2     3               2    3
+--R                 (p q  - p )cos(a x)  + (2p q  - 2p )cos(a x) + p q  - p
+--R     + 
+--R                                 +---------+
+--R        +---------+              |   2    2
+--R        |   2    2      sin(a x)\|- q  + p
+--R       \|- q  + p  atan(--------------------)
+--R                             p cos(a x)
+--R     + 
+--R                                        +---------+
+--R        +---------+                     |   2    2
+--R        |   2    2           p sin(a x)\|- q  + p
+--R       \|- q  + p  atan(-------------------------------)
+--R                           2     2              2     2
+--R                        (2q  - 2p )cos(a x) + 2q  - 2p
+--R  /
+--R          2      3
+--R     a p q  - a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 126
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                             - x + %i
+--R                      %i log(--------)
+--R                              x + %i
+--R   (11)  atan(x) == - ----------------
+--R                              2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 127
+ff2:=atanrule ee2
+--R
+--R   (12)
+--R       -
+--R               +---------+
+--R               |   2    2
+--R            %i\|- q  + p
+--R         *
+--R            log
+--R                                +---------+
+--R                                |   2    2          2        2                 2
+--R                   - p sin(a x)\|- q  + p   + (2%i q  - 2%i p )cos(a x) + 2%i q
+--R                 + 
+--R                          2
+--R                   - 2%i p
+--R              /
+--R                              +---------+
+--R                              |   2    2          2        2                 2
+--R                   p sin(a x)\|- q  + p   + (2%i q  - 2%i p )cos(a x) + 2%i q
+--R                 + 
+--R                          2
+--R                   - 2%i p
+--R     + 
+--R                                      +---------+
+--R            +---------+               |   2    2
+--R            |   2    2     - sin(a x)\|- q  + p   + %i p cos(a x)
+--R       - %i\|- q  + p  log(--------------------------------------)
+--R                                     +---------+
+--R                                     |   2    2
+--R                            sin(a x)\|- q  + p   + %i p cos(a x)
+--R     + 
+--R            +---------+
+--R            |   2    2
+--R         %i\|- q  + p
+--R      *
+--R         log
+--R                                                           +---------+
+--R                      2    2              2     2          |   2    2
+--R                ((- 2q  + p )cos(a x) - 2q  + 2p )sin(a x)\|- q  + p
+--R              + 
+--R                       2       3         2           2        3
+--R                (%i p q  - %i p )cos(a x)  + (2%i p q  - 2%i p )cos(a x)
+--R              + 
+--R                      2       3
+--R                %i p q  - %i p
+--R           /
+--R                                                         +---------+
+--R                    2    2              2     2          |   2    2
+--R                ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)\|- q  + p
+--R              + 
+--R                       2       3         2           2        3
+--R                (%i p q  - %i p )cos(a x)  + (2%i p q  - 2%i p )cos(a x)
+--R              + 
+--R                      2       3
+--R                %i p q  - %i p
+--R  /
+--R           2       3
+--R     2a p q  - 2a p
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 128
+gg2:=expandLog ff2
+--R
+--R   (13)
+--R       -
+--R               +---------+
+--R               |   2    2
+--R            %i\|- q  + p
+--R         *
+--R            log
+--R                                                          +---------+
+--R                     2    2              2     2          |   2    2
+--R                 ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)\|- q  + p
+--R               + 
+--R                        2       3         2           2        3
+--R                 (%i p q  - %i p )cos(a x)  + (2%i p q  - 2%i p )cos(a x)
+--R               + 
+--R                       2       3
+--R                 %i p q  - %i p
+--R     + 
+--R            +---------+
+--R            |   2    2
+--R         %i\|- q  + p
+--R      *
+--R         log
+--R                                                       +---------+
+--R                  2    2              2     2          |   2    2
+--R              ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)\|- q  + p
+--R            + 
+--R                       2       3         2             2        3
+--R              (- %i p q  + %i p )cos(a x)  + (- 2%i p q  + 2%i p )cos(a x)
+--R            + 
+--R                      2       3
+--R              - %i p q  + %i p
+--R     + 
+--R            +---------+
+--R            |   2    2
+--R         %i\|- q  + p
+--R      *
+--R                      +---------+
+--R                      |   2    2          2        2                 2        2
+--R       log(p sin(a x)\|- q  + p   + (2%i q  - 2%i p )cos(a x) + 2%i q  - 2%i p )
+--R     + 
+--R       -
+--R               +---------+
+--R               |   2    2
+--R            %i\|- q  + p
+--R         *
+--R            log
+--R                            +---------+
+--R                            |   2    2            2        2                 2
+--R                 p sin(a x)\|- q  + p   + (- 2%i q  + 2%i p )cos(a x) - 2%i q
+--R               + 
+--R                      2
+--R                 2%i p
+--R     + 
+--R          +---------+             +---------+
+--R          |   2    2              |   2    2
+--R       %i\|- q  + p  log(sin(a x)\|- q  + p   + %i p cos(a x))
+--R     + 
+--R            +---------+             +---------+
+--R            |   2    2              |   2    2
+--R       - %i\|- q  + p  log(sin(a x)\|- q  + p   - %i p cos(a x))
+--R     + 
+--R                     +---------+
+--R                     |   2    2
+--R       - %i log(- 1)\|- q  + p
+--R  /
+--R           2       3
+--R     2a p q  - 2a p
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 129
+rootrule4a:RewriteRule(INT,COMPLEX(INT),EXPR(COMPLEX(INT))):=rule(sqrt(p^2-q^2)==sqrt(p-q)*sqrt(q+p))
+--R
+--R          +---------+
+--R          |   2    2      +-------+ +-----+
+--R   (14)  \|- q  + p   == \|- q + p \|q + p
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 130
+hh2:=rootrule4a gg2
+--R
+--R   (15)
+--R       -
+--R               +-------+ +-----+
+--R            %i\|- q + p \|q + p
+--R         *
+--R            log
+--R                     2    2              2     2          +-------+ +-----+
+--R                 ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)\|- q + p \|q + p
+--R               + 
+--R                        2       3         2           2        3
+--R                 (%i p q  - %i p )cos(a x)  + (2%i p q  - 2%i p )cos(a x)
+--R               + 
+--R                       2       3
+--R                 %i p q  - %i p
+--R     + 
+--R            +-------+ +-----+
+--R         %i\|- q + p \|q + p
+--R      *
+--R         log
+--R                  2    2              2     2          +-------+ +-----+
+--R              ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)\|- q + p \|q + p
+--R            + 
+--R                       2       3         2             2        3
+--R              (- %i p q  + %i p )cos(a x)  + (- 2%i p q  + 2%i p )cos(a x)
+--R            + 
+--R                      2       3
+--R              - %i p q  + %i p
+--R     + 
+--R            +-------+ +-----+
+--R         %i\|- q + p \|q + p
+--R      *
+--R         log
+--R                         +-------+ +-----+         2        2                 2
+--R              p sin(a x)\|- q + p \|q + p  + (2%i q  - 2%i p )cos(a x) + 2%i q
+--R            + 
+--R                     2
+--R              - 2%i p
+--R     + 
+--R       -
+--R               +-------+ +-----+
+--R            %i\|- q + p \|q + p
+--R         *
+--R            log
+--R                            +-------+ +-----+           2        2
+--R                 p sin(a x)\|- q + p \|q + p  + (- 2%i q  + 2%i p )cos(a x)
+--R               + 
+--R                        2        2
+--R                 - 2%i q  + 2%i p
+--R     + 
+--R          +-------+ +-----+             +-------+ +-----+
+--R       %i\|- q + p \|q + p log(sin(a x)\|- q + p \|q + p  + %i p cos(a x))
+--R     + 
+--R            +-------+ +-----+             +-------+ +-----+
+--R       - %i\|- q + p \|q + p log(sin(a x)\|- q + p \|q + p  - %i p cos(a x))
+--R     + 
+--R                     +-------+ +-----+
+--R       - %i log(- 1)\|- q + p \|q + p
+--R  /
+--R           2       3
+--R     2a p q  - 2a p
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 131    14:363 Schaums and Axiom differ by a constant
+ii2:=complexNormalize hh2
+--R
+--R                                                   +-------+ +-----+
+--R         (%i log(%i) - %i log(- %i) - %i log(- 1))\|- q + p \|q + p
+--R   (16)  -----------------------------------------------------------
+--R                                     2       3
+--R                               2a p q  - 2a p
+--R                                             Type: Expression Complex Integer
+--E
+@
+
+\section{\cite{1}:14.364~~~~~$\displaystyle
+\int{x^m\sin{ax}}~dx$}
+$$\int{x^m\sin{ax}}=
+-\frac{x^m\cos{ax}}{a}+\frac{mx^{m-1}\sin{ax}}{a^2}
+-\frac{m(m-1)}{a^2}\int{x^{m-2}\sin{ax}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 132    14:364 Axiom cannot compute this integral
+aa:=integrate(x^m*sin(a*x),x)
+--R 
+--R
+--R           x
+--R         ++             m
+--I   (1)   |   sin(%I a)%I d%I
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.365~~~~~$\displaystyle
+\int{\frac{\sin{ax}}{x^n}}~dx$}
+$$\int{\frac{\sin{ax}}{x^n}}=
+-\frac{\sin{ax}}{(n-1)x^{n-1}}+\frac{a}{n-1}\int{\frac{\cos{ax}}{x^{n-1}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 133    14:365 Axiom cannot compute this integral
+aa:=integrate(sin(a*x)/x^n,x)
+--R 
+--R
+--R           x
+--I         ++  sin(%I a)
+--I   (1)   |   --------- d%I
+--R        ++        n
+--I                %I
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.366~~~~~$\displaystyle
+\int{\sin^n{ax}}~dx$}
+$$\int{\sin^n{ax}}=
+-\frac{\sin^{n-1}{ax}\cos{ax}}{an}+\frac{n-1}{n}\int{\sin^{n-2}{ax}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 134    14:366 Axiom cannot compute this integral
+aa:=integrate(sin(a*x)^n,x)
+--R 
+--R
+--R           x
+--R         ++           n
+--I   (1)   |   sin(%I a) d%I
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.367~~~~~$\displaystyle
+\int{\frac{1}{\sin^n{ax}}}~dx$}
+$$\int{\frac{1}{\sin^n{ax}}}=
+\frac{-\cos{ax}}{a(n-1)\sin^{n-1}{ax}}
++\frac{n-2}{n-1}\int{\frac{1}{\sin^{n-2}{ax}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 135    14:367 Axiom cannot compute this integral
+aa:=integrate(1/(sin(a*x))^n,x)
+--R 
+--R
+--R           x
+--R         ++       1
+--I   (1)   |   ---------- d%I
+--R        ++            n
+--I             sin(%I a)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.368~~~~~$\displaystyle
+\int{\frac{x~dx}{sin^n{ax}}}$}
+$$\int{\frac{x}{sin^n{ax}}}=
+\frac{-x\cos{ax}}{a(n-1)\sin^{n-1}{ax}}
+-\frac{1}{a^2(n-1)(n-2)\sin^{n-2}{ax}}
++\frac{n-2}{n-1}\int{\frac{x}{\sin^{n-2}{ax}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 136    14:368 Axiom cannot compute this integral
+aa:=integrate(x/sin(a*x)^n,x)
+--R 
+--R
+--R           x
+--I         ++      %I
+--I   (1)   |   ---------- d%I
+--R        ++            n
+--I             sin(%I a)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 pp75-76
+\end{thebibliography}
+\end{document}
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+173128
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diff --git a/src/axiom-website/CATS/schaum18.input.pamphlet b/src/axiom-website/CATS/schaum18.input.pamphlet
new file mode 100644
index 0000000..62de8d7
--- /dev/null
+++ b/src/axiom-website/CATS/schaum18.input.pamphlet
@@ -0,0 +1,2310 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum18.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.369~~~~~$\displaystyle
+\int{\cos ax ~dx}$}
+$$\int{\cos ax}=
+\frac{\sin{ax}}{a}
+$$
+&lt;&lt;*&gt;&gt;=
+)spool schaum18.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1
+aa:=integrate(cos(a*x),x)
+--R 
+--R
+--R        sin(a x)
+--R   (1)  --------
+--R            a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 2
+bb:=sin(a*x)/a
+--R
+--R        sin(a x)
+--R   (2)  --------
+--R            a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3      14:369 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.370~~~~~$\displaystyle
+\int{x\cos{ax}~dx}$}
+$$\int{x\cos{ax}}=
+\frac{\cos{ax}}{a^2}+\frac{x\sin{ax}}{a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 4
+aa:=integrate(x*cos(a*x),x)
+--R 
+--R
+--R        a x sin(a x) + cos(a x)
+--R   (1)  -----------------------
+--R                    2
+--R                   a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 5
+bb:=cos(a*x)/a^2+(x*sin(a*x))/a
+--R
+--R        a x sin(a x) + cos(a x)
+--R   (2)  -----------------------
+--R                    2
+--R                   a
+--R                                                     Type: Expression Integer
+--E
+
+--S 6      14:370 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.371~~~~~$\displaystyle
+\int{x^2\cos{ax}~dx}$}
+$$\int{x^2\cos{ax}}=
+\frac{2x}{a^2}\cos{ax}+\left(\frac{x^2}{a}-\frac{2}{a^3}\right)\sin{ax}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 7
+aa:=integrate(x^2*cos(a*x),x)
+--R 
+--R
+--R          2 2
+--R        (a x  - 2)sin(a x) + 2a x cos(a x)
+--R   (1)  ----------------------------------
+--R                         3
+--R                        a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 8
+bb:=(2*x)/a^2*cos(a*x)+(x^2/a-2/a^3)*sin(a*x)
+--R
+--R          2 2
+--R        (a x  - 2)sin(a x) + 2a x cos(a x)
+--R   (2)  ----------------------------------
+--R                         3
+--R                        a
+--R                                                     Type: Expression Integer
+--E
+
+--S 9      14:371 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.372~~~~~$\displaystyle
+\int{x^3\cos{ax}~dx}$}
+$$\int{x^3\cos{ax}}=
+\left(\frac{3x^2}{a^2}-\frac{6}{a^4}\right)\cos{ax}
++\left(\frac{x^3}{a}-\frac{6x}{a^3}\right)\sin{ax}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 10
+aa:=integrate(x^3*cos(a*x),x)
+--R 
+--R
+--R          3 3                      2 2
+--R        (a x  - 6a x)sin(a x) + (3a x  - 6)cos(a x)
+--R   (1)  -------------------------------------------
+--R                              4
+--R                             a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 11
+bb:=((3*x^2)/a^2-6/a^4)*cos(a*x)+(x^3/a-(6*x)/a^3)*sin(a*x)
+--R
+--R          3 3                      2 2
+--R        (a x  - 6a x)sin(a x) + (3a x  - 6)cos(a x)
+--R   (2)  -------------------------------------------
+--R                              4
+--R                             a
+--R                                                     Type: Expression Integer
+--E
+
+--S 12     14:372 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.373~~~~~$\displaystyle
+\int{\frac{\cos{ax}}{x}}~dx$}
+$$\int{\frac{\cos{ax}}{x}}=
+\ln{x}-\frac{(ax)^2}{2\cdot 2!}+\frac{(ax)^4}{4\cdot 4!}
+-\frac{(ax)^6}{6\cdot 6!}+\cdots
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 13     14:373 Schaums and Axiom agree by definition
+aa:=integrate(cos(x)/x,x)
+--R 
+--R
+--R   (1)  Ci(x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.374~~~~~$\displaystyle
+\int{\frac{\cos{ax}}{x^2}}~dx$}
+$$\int{\frac{\cos{ax}}{x^2}}=
+-\frac{\cos{ax}}{x}-a\int{\frac{\sin{ax}}{x}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 14     14:374 Axiom cannot compute this integral
+aa:=integrate(cos(a*x)/x^2,x)
+--R 
+--R
+--R           x
+--I         ++  cos(%I a)
+--I   (1)   |   --------- d%I
+--R        ++        2
+--I                %I
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.375~~~~~$\displaystyle
+\int{\frac{dx}{\cos{ax}}}$}
+$$\int{\frac{1}{\cos{ax}}}=
+\frac{1}{a}\ln(\sec{ax}-\tan{ax})=
+\frac{1}{a}\ln\tan\left(\frac{\pi}{4}+\frac{ax}{2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 15
+aa:=integrate(1/cos(a*x),x)
+--R 
+--R
+--R            sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
+--R        log(-----------------------) - log(-----------------------)
+--R                  cos(a x) + 1                   cos(a x) + 1
+--R   (1)  -----------------------------------------------------------
+--R                                     a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 16
+bb1:=1/a*log(sec(a*x)+tan(a*x))
+--R
+--R        log(tan(a x) + sec(a x))
+--R   (2)  ------------------------
+--R                    a
+--R                                                     Type: Expression Integer
+--E
+
+--S 17
+bb2:=1/a*log(tan(%pi/4+(a*x)/2))
+--R
+--R                2a x + %pi
+--R        log(tan(----------))
+--R                     4
+--R   (3)  --------------------
+--R                  a
+--R                                                     Type: Expression Integer
+--E
+
+--S 18
+cc1:=aa-bb1
+--R
+--R   (4)
+--R                                        sin(a x) + cos(a x) + 1
+--R       - log(tan(a x) + sec(a x)) + log(-----------------------)
+--R                                              cos(a x) + 1
+--R     + 
+--R             sin(a x) - cos(a x) - 1
+--R       - log(-----------------------)
+--R                   cos(a x) + 1
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 19
+cc2:=aa-bb2
+--R
+--R   (5)
+--R                 2a x + %pi         sin(a x) + cos(a x) + 1
+--R       - log(tan(----------)) + log(-----------------------)
+--R                      4                   cos(a x) + 1
+--R     + 
+--R             sin(a x) - cos(a x) - 1
+--R       - log(-----------------------)
+--R                   cos(a x) + 1
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 20     14:375 Schaums and Axiom differ by a constant
+complexNormalize cc1
+--R
+--R        log(- 1)
+--R   (6)  --------
+--R            a
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.376~~~~~$\displaystyle
+\int{\frac{x~dx}{\cos{ax}}}$}
+$$\int{\frac{x}{\cos{ax}}}=
+\frac{1}{a^2}\left\{
+\frac{(ax)^2}{2}+\frac{(ax)^4}{8}+\frac{5(ax)^6}{144}+\cdots+
+\frac{E_n(ax)^{2n+2}}{(2n+2)(2n)!}+\cdots
+\right\}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 21     14:376 Axiom cannot compute this integral
+aa:=integrate(x/cos(a*x),x)
+--R 
+--R
+--R           x
+--I         ++      %I
+--I   (1)   |   --------- d%I
+--I        ++   cos(%I a)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.377~~~~~$\displaystyle
+\int{\cos^2{ax}}~dx$}
+$$\int{\cos^2{ax}}=
+\frac{x}{2}+\frac{\sin{2ax}}{4a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 22
+aa:=integrate(cos(a*x)^2,x)
+--R 
+--R
+--R        cos(a x)sin(a x) + a x
+--R   (1)  ----------------------
+--R                  2a
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 23
+bb:=x/2+sin(2*a*x)/(4*a)
+--R
+--R        sin(2a x) + 2a x
+--R   (2)  ----------------
+--R               4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 24
+cc:=aa-bb
+--R
+--R        - sin(2a x) + 2cos(a x)sin(a x)
+--R   (3)  -------------------------------
+--R                       4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 25
+cossinrule:=rule(cos(b)*sin(a) == 1/2*(sin(a-b)+sin(a+b)))
+--R 
+--R
+--I                           %M sin(b + a) - %M sin(b - a)
+--I   (4)  %M cos(b)sin(a) == -----------------------------
+--R                                         2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 26     14:377 Schaums and Axiom agree
+dd:=cossinrule cc
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.378~~~~~$\displaystyle
+\int{x\cos^2{ax}}~dx$}
+$$\int{x\cos^2{ax}}=
+\frac{x^2}{4}+\frac{x\sin{2ax}}{4a}+\frac{\cos{2ax}}{8a^2}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 27
+aa:=integrate(x*cos(a*x)^2,x)
+--R 
+--R
+--R                                        2    2 2
+--R        2a x cos(a x)sin(a x) + cos(a x)  + a x
+--R   (1)  ----------------------------------------
+--R                             2
+--R                           4a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 28
+bb:=x^2/4+(x*sin(2*a*x))/(4*a)+cos(2*a*x)/(8*a^2)
+--R
+--R                                       2 2
+--R        2a x sin(2a x) + cos(2a x) + 2a x
+--R   (2)  ----------------------------------
+--R                          2
+--R                        8a
+--R                                                     Type: Expression Integer
+--E
+
+--S 29
+cc:=aa-bb
+--R
+--R                                                                        2
+--R        - 2a x sin(2a x) + 4a x cos(a x)sin(a x) - cos(2a x) + 2cos(a x)
+--R   (3)  -----------------------------------------------------------------
+--R                                         2
+--R                                       8a
+--R                                                     Type: Expression Integer
+--E
+
+--S 30
+cossinrule:=rule(cos(b)*sin(a) == 1/2*(sin(a-b)+sin(a+b)))
+--R 
+--R
+--I                           %N sin(b + a) - %N sin(b - a)
+--I   (4)  %N cos(b)sin(a) == -----------------------------
+--R                                         2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 31
+dd:=cossinrule cc
+--R
+--R                               2
+--R        - cos(2a x) + 2cos(a x)
+--R   (5)  ------------------------
+--R                     2
+--R                   8a
+--R                                                     Type: Expression Integer
+--E
+
+--S 32
+coscosrule:=rule(cos(a)*cos(b) == 1/2*(cos(a-b)+cos(a+b)))
+--R 
+--R
+--I                           %O cos(b + a) + %O cos(b - a)
+--I   (6)  %O cos(a)cos(b) == -----------------------------
+--I                                         2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 33
+ee:=coscosrule dd
+--R
+--R                               2
+--R        - cos(2a x) + 2cos(a x)
+--R   (7)  ------------------------
+--R                     2
+--R                   8a
+--R                                                     Type: Expression Integer
+--E
+
+--S 34
+cossqrrule1:=rule(cos(a)^2 == 1/2+1/2*cos(2*a))
+--R
+--R              2    cos(2a) + 1
+--R   (8)  cos(a)  == -----------
+--R                        2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 35     14:378 Schaums and Axiom differ by a constant
+ff:=cossqrrule1 ee
+--R
+--R         1
+--R   (9)  ---
+--R          2
+--R        8a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.379~~~~~$\displaystyle
+\int{\cos^3{ax}}~dx$}
+$$\int{\cos^3{ax}}=
+\frac{\sin{ax}}{a}-\frac{\sin^3{ax}}{3a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 36
+aa:=integrate(cos(a*x)^3,x)
+--R 
+--R
+--R                 2
+--R        (cos(a x)  + 2)sin(a x)
+--R   (1)  -----------------------
+--R                   3a
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 37
+bb:=sin(a*x)/a-sin(a*x)^3/(3*a)
+--R
+--R                  3
+--R        - sin(a x)  + 3sin(a x)
+--R   (2)  -----------------------
+--R                   3a
+--R                                                     Type: Expression Integer
+--E 
+
+--S 38
+cc:=aa-bb
+--R
+--R                3            2
+--R        sin(a x)  + (cos(a x)  - 1)sin(a x)
+--R   (3)  -----------------------------------
+--R                         3a
+--R                                                     Type: Expression Integer
+--E
+
+--S 39
+cossqrrule:=rule(cos(a)^2 == 1-sin(a)^2)
+--R
+--R              2            2
+--R   (4)  cos(a)  == - sin(a)  + 1
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 40     14:379 Schaums and Axiom agree
+dd:=cossqrrule cc
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.380~~~~~$\displaystyle
+\int{\cos^4{ax}}~dx$}
+$$\int{\cos^4{ax}}=
+\frac{3x}{8}+\frac{\sin{2ax}}{4a}+\frac{\sin{4ax}}{32a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 41
+aa:=integrate(cos(a*x)^4,x)
+--R 
+--R
+--R                  3
+--R        (2cos(a x)  + 3cos(a x))sin(a x) + 3a x
+--R   (1)  ---------------------------------------
+--R                           8a
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 42
+bb:=(3*x)/8+sin(2*a*x)/(4*a)+sin(4*a*x)/(32*a)
+--R
+--R        sin(4a x) + 8sin(2a x) + 12a x
+--R   (2)  ------------------------------
+--R                      32a
+--R                                                     Type: Expression Integer
+--E 
+
+--S 43
+cc:=aa-bb
+--R
+--R                                             3
+--R        - sin(4a x) - 8sin(2a x) + (8cos(a x)  + 12cos(a x))sin(a x)
+--R   (3)  ------------------------------------------------------------
+--R                                     32a
+--R                                                     Type: Expression Integer
+--E
+
+--S 44     14:380 Schaums and Axiom agree
+complexNormalize cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.381~~~~~$\displaystyle
+\int{\frac{dx}{\cos^2{ax}}}$}
+$$\int{\frac{1}{\cos^2{ax}}}=
+\frac{\tan{ax}}{a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 45
+aa:=integrate(1/cos(a*x)^2,x)
+--R 
+--R
+--R         sin(a x)
+--R   (1)  ----------
+--R        a cos(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 46
+bb:=tan(a*x)/a
+--R
+--R        tan(a x)
+--R   (2)  --------
+--R            a
+--R                                                     Type: Expression Integer
+--E 
+
+--S 47
+cc:=aa-bb
+--R
+--R        - cos(a x)tan(a x) + sin(a x)
+--R   (3)  -----------------------------
+--R                  a cos(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 48
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (4)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 49     14:381 Schaums and Axiom agree
+dd:=tanrule cc
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.382~~~~~$\displaystyle
+\int{\frac{dx}{\cos^3{ax}}}$}
+$$\int{\frac{1}{\cos^3{ax}}}=
+\frac{\sin{ax}}{2a\cos^2{ax}}
++\frac{1}{2a}\ln\tan\left(\frac{\pi}{4}+\frac{ax}{2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 50
+aa:=integrate(1/cos(a*x)^3,x)
+--R 
+--R
+--R   (1)
+--R               2    sin(a x) + cos(a x) + 1
+--R       cos(a x) log(-----------------------)
+--R                          cos(a x) + 1
+--R     + 
+--R                 2    sin(a x) - cos(a x) - 1
+--R       - cos(a x) log(-----------------------) + sin(a x)
+--R                            cos(a x) + 1
+--R  /
+--R                2
+--R     2a cos(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 51
+bb:=sin(a*x)/(2*a*cos(a*x)^2)+1/(2*a)*log(tan(%pi/4+(a*x)/2))
+--R
+--R                2        2a x + %pi
+--R        cos(a x) log(tan(----------)) + sin(a x)
+--R                              4
+--R   (2)  ----------------------------------------
+--R                                 2
+--R                      2a cos(a x)
+--R                                                     Type: Expression Integer
+--E 
+
+--S 52
+cc:=aa-bb
+--R
+--R   (3)
+--R                 2a x + %pi         sin(a x) + cos(a x) + 1
+--R       - log(tan(----------)) + log(-----------------------)
+--R                      4                   cos(a x) + 1
+--R     + 
+--R             sin(a x) - cos(a x) - 1
+--R       - log(-----------------------)
+--R                   cos(a x) + 1
+--R  /
+--R     2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 53     14:382 Schaums and Axiom differ by a constant
+complexNormalize cc
+--R
+--R        log(- 1)
+--R   (4)  --------
+--R           2a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.383~~~~~$\displaystyle
+\int{\cos{px}\cos{qx}}~dx$}
+$$\int{\cos{ax}\cos{px}}=
+\frac{\sin{(a-p)x}}{2(a-p)}+\frac{\sin{(a+p)x}}{2(a+p)}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 54
+aa:=integrate(cos(a*x)*cos(p*x),x)
+--R
+--R        p cos(a x)sin(p x) - a cos(p x)sin(a x)
+--R   (1)  ---------------------------------------
+--R                         2    2
+--R                        p  - a
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 55
+bb:=(sin((a-p)*x))/(2*(a-p))+(sin((a+p)*x))/(2*(a+p))
+--R
+--R        (p - a)sin((p + a)x) + (p + a)sin((p - a)x)
+--R   (2)  -------------------------------------------
+--R                           2     2
+--R                         2p  - 2a
+--R                                                     Type: Expression Integer
+--E 
+
+--S 56
+cc:=aa-bb
+--R
+--R   (3)
+--R       (- p + a)sin((p + a)x) + 2p cos(a x)sin(p x) + (- p - a)sin((p - a)x)
+--R     + 
+--R       - 2a cos(p x)sin(a x)
+--R  /
+--R       2     2
+--R     2p  - 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 57     14:383 Schaums and Axiom agree
+complexNormalize cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.384~~~~~$\displaystyle
+\int{\frac{dx}{1-\cos{ax}}}$}
+$$\int{\frac{1}{1-\cos{ax}}}=
+-\frac{1}{a}\cot\frac{ax}{2}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 58
+aa:=integrate(1/(1-cos(a*x)),x)
+--R 
+--R
+--R        - cos(a x) - 1
+--R   (1)  --------------
+--R          a sin(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 59
+bb:=-1/a*cot((a*x)/2)
+--R
+--R              a x
+--R          cot(---)
+--R               2
+--R   (2)  - --------
+--R              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 60
+cc:=aa-bb
+--R
+--R            a x
+--R        cot(---)sin(a x) - cos(a x) - 1
+--R             2
+--R   (3)  -------------------------------
+--R                   a sin(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 61     14:384 Schaums and Axiom agree
+dd:=complexNormalize cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.385~~~~~$\displaystyle
+\int{\frac{x~dx}{1-\cos{ax}}}$}
+$$\int{\frac{x}{1-\cos{ax}}}=
+-\frac{x}{a}\cot\frac{ax}{2}
++\frac{2}{a^2}\ln~\sin\frac{ax}{2}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 62
+aa:=integrate(x/(1-cos(a*x)),x)
+--R
+--R   (1)
+--R                  sin(a x)                        2
+--R   2sin(a x)log(------------) - sin(a x)log(------------) - a x cos(a x) - a x
+--R                cos(a x) + 1                cos(a x) + 1
+--R   ---------------------------------------------------------------------------
+--R                                     2
+--R                                    a sin(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 63
+bb:=-x/a*cot((a*x)/2)+2/a^2*log(sin((a*x)/2))
+--R
+--R                 a x             a x
+--R        2log(sin(---)) - a x cot(---)
+--R                  2               2
+--R   (2)  -----------------------------
+--R                       2
+--R                      a
+--R                                                     Type: Expression Integer
+--E
+
+--S 64
+cc:=aa-bb
+--R
+--R   (3)
+--R                      sin(a x)                       a x
+--R       2sin(a x)log(------------) - 2sin(a x)log(sin(---))
+--R                    cos(a x) + 1                      2
+--R     + 
+--R                           2                 a x
+--R       - sin(a x)log(------------) + a x cot(---)sin(a x) - a x cos(a x) - a x
+--R                     cos(a x) + 1             2
+--R  /
+--R      2
+--R     a sin(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 65
+cotrule:=rule(cot(a) == cos(a)/sin(a))
+--R
+--R                  cos(a)
+--R   (4)  cot(a) == ------
+--R                  sin(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 66
+dd:=cotrule cc
+--R
+--R   (5)
+--R            a x               sin(a x)           a x                 a x
+--R       2sin(---)sin(a x)log(------------) - 2sin(---)sin(a x)log(sin(---))
+--R             2              cos(a x) + 1          2                   2
+--R     + 
+--R             a x                   2                 a x
+--R       - sin(---)sin(a x)log(------------) + a x cos(---)sin(a x)
+--R              2              cos(a x) + 1             2
+--R     + 
+--R                                 a x
+--R       (- a x cos(a x) - a x)sin(---)
+--R                                  2
+--R  /
+--R      2    a x
+--R     a sin(---)sin(a x)
+--R            2
+--R                                                     Type: Expression Integer
+--E
+
+--S 67
+ee:=expandLog dd
+--R
+--R   (6)
+--R            a x                              a x                 a x
+--R       2sin(---)sin(a x)log(sin(a x)) - 2sin(---)sin(a x)log(sin(---))
+--R             2                                2                   2
+--R     + 
+--R             a x
+--R       - sin(---)sin(a x)log(cos(a x) + 1)
+--R              2
+--R     + 
+--R                  a x            a x                                       a x
+--R     (- log(2)sin(---) + a x cos(---))sin(a x) + (- a x cos(a x) - a x)sin(---)
+--R                   2              2                                         2
+--R  /
+--R      2    a x
+--R     a sin(---)sin(a x)
+--R            2
+--R                                                     Type: Expression Integer
+--E
+
+--S 68     14:385 Schaums and Axiom agree
+complexNormalize ee
+--R
+--R   (7)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.386~~~~~$\displaystyle
+\int{\frac{dx}{1+\cos{ax}}}$}
+$$\int{\frac{1}{1+\cos{ax}}}=
+\frac{1}{a}\tan\frac{ax}{2}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 69
+aa:=integrate(1/(1+cos(a*x)),x)
+--R
+--R           sin(a x)
+--R   (1)  --------------
+--R        a cos(a x) + a
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 70
+bb:=1/a*tan((a*x)/2)
+--R
+--R            a x
+--R        tan(---)
+--R             2
+--R   (2)  --------
+--R            a
+--R                                                     Type: Expression Integer
+--E
+
+--S 71
+cc:=aa-bb
+--R
+--R                            a x
+--R        (- cos(a x) - 1)tan(---) + sin(a x)
+--R                             2
+--R   (3)  -----------------------------------
+--R                   a cos(a x) + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 72     14:386 Schaums and Axiom agree
+complexNormalize cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.387~~~~~$\displaystyle
+\int{\frac{x~dx}{1+\cos{ax}}}$}
+$$\int{\frac{x}{1+\cos{ax}}}=
+\frac{x}{a}\tan\frac{ax}{2}
++\frac{2}{a^2}\ln~\cos\frac{ax}{2}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 73
+aa:=integrate(x/(1+cos(a*x)),x)
+--R 
+--R
+--R                                  2
+--R        (- cos(a x) - 1)log(------------) + a x sin(a x)
+--R                            cos(a x) + 1
+--R   (1)  ------------------------------------------------
+--R                          2            2
+--R                         a cos(a x) + a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 74
+bb:=x/a*tan((a*x)/2)+2/a^2*log(cos((a*x)/2))
+--R
+--R                 a x             a x
+--R        2log(cos(---)) + a x tan(---)
+--R                  2               2
+--R   (2)  -----------------------------
+--R                       2
+--R                      a
+--R                                                     Type: Expression Integer
+--E
+
+--S 75
+cc:=aa-bb
+--R
+--R   (3)
+--R                                a x                               2
+--R       (- 2cos(a x) - 2)log(cos(---)) + (- cos(a x) - 1)log(------------)
+--R                                 2                          cos(a x) + 1
+--R     + 
+--R                                 a x
+--R       (- a x cos(a x) - a x)tan(---) + a x sin(a x)
+--R                                  2
+--R  /
+--R      2            2
+--R     a cos(a x) + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 76
+dd:=expandLog cc
+--R
+--R   (4)
+--R                                                                  a x
+--R       (cos(a x) + 1)log(cos(a x) + 1) + (- 2cos(a x) - 2)log(cos(---))
+--R                                                                   2
+--R     + 
+--R                                 a x
+--R       (- a x cos(a x) - a x)tan(---) + a x sin(a x) - log(2)cos(a x) - log(2)
+--R                                  2
+--R  /
+--R      2            2
+--R     a cos(a x) + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 77     14:387 Schaums and Axiom agree
+complexNormalize dd
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.388~~~~~$\displaystyle
+\int{\frac{dx}{(1-\cos{ax})^2}}$}
+$$\int{\frac{1}{(1-\cos{ax})^2}}=
+-\frac{1}{2a}\cot\frac{ax}{2}
+-\frac{1}{6a}\cot^3\frac{ax}{2}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 78
+aa:=integrate(1/(1-cos(a*x))^2,x)
+--R 
+--R
+--R                  2
+--R        - cos(a x)  + cos(a x) + 2
+--R   (1)  --------------------------
+--R        (3a cos(a x) - 3a)sin(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 79
+bb:=-1/(2*a)*cot((a*x)/2)-1/(6*a)*cot((a*x)/2)^3
+--R
+--R              a x 3        a x
+--R        - cot(---)  - 3cot(---)
+--R               2            2
+--R   (2)  -----------------------
+--R                   6a
+--R                                                     Type: Expression Integer
+--E 
+
+--S 80
+cc:=aa-bb
+--R
+--R   (3)
+--R                          a x 3                      a x                      2
+--R       ((cos(a x) - 1)cot(---)  + (3cos(a x) - 3)cot(---))sin(a x) - 2cos(a x)
+--R                           2                          2
+--R     + 
+--R       2cos(a x) + 4
+--R  /
+--R     (6a cos(a x) - 6a)sin(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 81     14:388 Schaums and Axiom agree
+complexNormalize cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.389~~~~~$\displaystyle
+\int{\frac{dx}{(1+\cos{ax})^2}}$}
+$$\int{\frac{1}{(1+\cos{ax})^2}}=
+\frac{1}{2a}\tan\frac{ax}{2}
++\frac{1}{6a}\tan^3\frac{ax}{2}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 82
+aa:=integrate(1/(1+cos(a*x))^2,x)
+--R 
+--R
+--R             (cos(a x) + 2)sin(a x)
+--R   (1)  -------------------------------
+--R                   2
+--R        3a cos(a x)  + 6a cos(a x) + 3a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 83
+bb:=1/(2*a)*tan((a*x)/2)+1/(6*a)*tan((a*x)/2)^3
+--R
+--R            a x 3        a x
+--R        tan(---)  + 3tan(---)
+--R             2            2
+--R   (2)  ---------------------
+--R                  6a
+--R                                                     Type: Expression Integer
+--E
+
+--S 84
+cc:=aa-bb
+--R
+--R   (3)
+--R                  2                     a x 3
+--R       (- cos(a x)  - 2cos(a x) - 1)tan(---)
+--R                                         2
+--R     + 
+--R                   2                     a x
+--R       (- 3cos(a x)  - 6cos(a x) - 3)tan(---) + (2cos(a x) + 4)sin(a x)
+--R                                          2
+--R  /
+--R                2
+--R     6a cos(a x)  + 12a cos(a x) + 6a
+--R                                                     Type: Expression Integer
+--E
+
+--S 85     14:389 Schaums and Axiom agree
+complexNormalize cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.390~~~~~$\displaystyle
+\int{\frac{dx}{p+q\cos{ax}}}$}
+$$\int{\frac{1}{p+q\cos{ax}}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{2}{a\sqrt{p^2-q^q}}
+\tan^{-1}\sqrt{(p-q)/(p+q)}\tan\frac{1}{2}ax
+\\
+\displaystyle
+\frac{1}{a\sqrt{q^2-p^2}}\ln\left(
+\frac{\tan\frac{1}{2}ax+\sqrt{(q+p)/(q-p)}}
+{\tan\frac{1}{2}ax-\sqrt{(q+p)(q-p)}}\right)
+\end{array}
+\right.
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 86
+aa:=integrate(1/(p+q*cos(a*x)),x)
+--R
+--R   (1)
+--R                           +-------+
+--R                           | 2    2        2    2
+--R        (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
+--R    log(--------------------------------------------------)
+--R                          q cos(a x) + p
+--R   [-------------------------------------------------------,
+--R                            +-------+
+--R                            | 2    2
+--R                          a\|q  - p
+--R                     +---------+
+--R                     |   2    2
+--R            sin(a x)\|- q  + p
+--R    2atan(-----------------------)
+--R          (q + p)cos(a x) + q + p
+--R    ------------------------------]
+--R               +---------+
+--R               |   2    2
+--R             a\|- q  + p
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+
+--S 87
+bb1:=2/(a*sqrt(p^2-q^2))*atan(sqrt((p-q)/(p+q))*tan(1/2*a*x))
+--R 
+--R
+--R                       +-------+
+--R                  a x  |- q + p
+--R        2atan(tan(---) |------- )
+--R                   2  \| q + p
+--R   (2)  -------------------------
+--R                +---------+
+--R                |   2    2
+--R              a\|- q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 88
+bb2:=1/(a*sqrt(q^2-p^2))*log((tan(1/2*a*x)+sqrt((q+p)/(q-p)))/(tan(1/2*a*x)-sqrt((q+p)/(q-p))))
+--R
+--R               +-----+
+--R               |q + p        a x
+--R            -  |-----  - tan(---)
+--R              \|q - p         2
+--R        log(---------------------)
+--R              +-----+
+--R              |q + p        a x
+--R              |-----  - tan(---)
+--R             \|q - p         2
+--R   (3)  --------------------------
+--R                  +-------+
+--R                  | 2    2
+--R                a\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 89
+cc1:=aa.1-bb1
+--R 
+--R
+--R   (4)
+--R                                          +-------+
+--R        +---------+                       | 2    2        2    2
+--R        |   2    2     (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
+--R       \|- q  + p  log(--------------------------------------------------)
+--R                                         q cos(a x) + p
+--R     + 
+--R           +-------+              +-------+
+--R           | 2    2          a x  |- q + p
+--R       - 2\|q  - p  atan(tan(---) |------- )
+--R                              2  \| q + p
+--R  /
+--R       +---------+ +-------+
+--R       |   2    2  | 2    2
+--R     a\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 90
+cc2:=aa.2-bb1
+--R 
+--R
+--R                                                       +---------+
+--R                         +-------+                     |   2    2
+--R                    a x  |- q + p             sin(a x)\|- q  + p
+--R        - 2atan(tan(---) |------- ) + 2atan(-----------------------)
+--R                     2  \| q + p            (q + p)cos(a x) + q + p
+--R   (5)  ------------------------------------------------------------
+--R                                  +---------+
+--R                                  |   2    2
+--R                                a\|- q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 91
+cc3:=aa.1-bb2
+--R
+--R   (6)
+--R                +-----+
+--R                |q + p        a x
+--R             -  |-----  - tan(---)
+--R               \|q - p         2
+--R       - log(---------------------)
+--R               +-----+
+--R               |q + p        a x
+--R               |-----  - tan(---)
+--R              \|q - p         2
+--R     + 
+--R                              +-------+
+--R                              | 2    2        2    2
+--R           (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
+--R       log(--------------------------------------------------)
+--R                             q cos(a x) + p
+--R  /
+--R       +-------+
+--R       | 2    2
+--R     a\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 92     14:390 Axiom cannot simplify these expressions
+cc4:=aa.2-bb2
+--R
+--R   (7)
+--R                            +-----+
+--R                            |q + p        a x
+--R          +---------+    -  |-----  - tan(---)
+--R          |   2    2       \|q - p         2
+--R       - \|- q  + p  log(---------------------)
+--R                           +-----+
+--R                           |q + p        a x
+--R                           |-----  - tan(---)
+--R                          \|q - p         2
+--R     + 
+--R                                  +---------+
+--R         +-------+                |   2    2
+--R         | 2    2        sin(a x)\|- q  + p
+--R       2\|q  - p  atan(-----------------------)
+--R                       (q + p)cos(a x) + q + p
+--R  /
+--R       +---------+ +-------+
+--R       |   2    2  | 2    2
+--R     a\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.391~~~~~$\displaystyle
+\int{\frac{dx}{(p+q\cos{ax})^2}}$}
+$$\int{\frac{1}{(p+q\cos{ax})^2}}=
+\frac{q\sin{ax}}{a(q^2-p^2)(p+q\cos{ax})}
+-\frac{p}{q^2-p^2}\int{\frac{1}{p+q\cos{ax}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 93
+aa:=integrate(1/(p+q*cos(a*x))^2,x)
+--R 
+--R
+--R   (1)
+--R   [
+--R                            2
+--R           (p q cos(a x) + p )
+--R        *
+--R                                  +-------+
+--R                                  | 2    2      2    2
+--R               (- p cos(a x) - q)\|q  - p   + (q  - p )sin(a x)
+--R           log(------------------------------------------------)
+--R                                q cos(a x) + p
+--R       + 
+--R                    +-------+
+--R                    | 2    2
+--R         q sin(a x)\|q  - p
+--R    /
+--R                                                +-------+
+--R            3      2                  2      3  | 2    2
+--R       ((a q  - a p q)cos(a x) + a p q  - a p )\|q  - p
+--R     ,
+--R
+--R                                                +---------+
+--R                                                |   2    2
+--R                              2        sin(a x)\|- q  + p
+--R         (- 2p q cos(a x) - 2p )atan(-----------------------)
+--R                                     (q + p)cos(a x) + q + p
+--R       + 
+--R                    +---------+
+--R                    |   2    2
+--R         q sin(a x)\|- q  + p
+--R    /
+--R                                                +---------+
+--R            3      2                  2      3  |   2    2
+--R       ((a q  - a p q)cos(a x) + a p q  - a p )\|- q  + p
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+
+--S 94
+t1:=integrate(1/(p+q*cos(a*x)),x)
+--R
+--R   (2)
+--R                           +-------+
+--R                           | 2    2        2    2
+--R        (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
+--R    log(--------------------------------------------------)
+--R                          q cos(a x) + p
+--R   [-------------------------------------------------------,
+--R                            +-------+
+--R                            | 2    2
+--R                          a\|q  - p
+--R                     +---------+
+--R                     |   2    2
+--R            sin(a x)\|- q  + p
+--R    2atan(-----------------------)
+--R          (q + p)cos(a x) + q + p
+--R    ------------------------------]
+--R               +---------+
+--R               |   2    2
+--R             a\|- q  + p
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 95
+bb1:=(q*sin(a*x))/(a*(q^2-p^2)*(p+q*cos(a*x)))-p/(q^2-p^2)*t1.1
+--R
+--R   (3)
+--R                            2
+--R         (- p q cos(a x) - p )
+--R      *
+--R                                +-------+
+--R                                | 2    2        2    2
+--R             (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
+--R         log(--------------------------------------------------)
+--R                               q cos(a x) + p
+--R     + 
+--R                  +-------+
+--R                  | 2    2
+--R       q sin(a x)\|q  - p
+--R  /
+--R                                              +-------+
+--R          3      2                  2      3  | 2    2
+--R     ((a q  - a p q)cos(a x) + a p q  - a p )\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 96
+bb2:=(q*sin(a*x))/(a*(q^2-p^2)*(p+q*cos(a*x)))-p/(q^2-p^2)*t1.2
+--R
+--R   (4)
+--R                                          +---------+
+--R                                          |   2    2                 +---------+
+--R                        2        sin(a x)\|- q  + p                  |   2    2
+--R   (- 2p q cos(a x) - 2p )atan(-----------------------) + q sin(a x)\|- q  + p
+--R                               (q + p)cos(a x) + q + p
+--R   -----------------------------------------------------------------------------
+--R                                                         +---------+
+--R                     3      2                  2      3  |   2    2
+--R                ((a q  - a p q)cos(a x) + a p q  - a p )\|- q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 97
+cc1:=aa.1-bb1
+--R
+--R   (5)
+--R                                +-------+
+--R                                | 2    2      2    2
+--R             (- p cos(a x) - q)\|q  - p   + (q  - p )sin(a x)
+--R       p log(------------------------------------------------)
+--R                              q cos(a x) + p
+--R     + 
+--R                                +-------+
+--R                                | 2    2        2    2
+--R             (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
+--R       p log(--------------------------------------------------)
+--R                               q cos(a x) + p
+--R  /
+--R                   +-------+
+--R         2      2  | 2    2
+--R     (a q  - a p )\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 98
+cc2:=aa.2-bb1
+--R
+--R   (6)
+--R                                           +-------+
+--R         +---------+                       | 2    2        2    2
+--R         |   2    2     (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
+--R       p\|- q  + p  log(--------------------------------------------------)
+--R                                          q cos(a x) + p
+--R     + 
+--R                                     +---------+
+--R            +-------+                |   2    2
+--R            | 2    2        sin(a x)\|- q  + p
+--R       - 2p\|q  - p  atan(-----------------------)
+--R                          (q + p)cos(a x) + q + p
+--R  /
+--R                   +---------+ +-------+
+--R         2      2  |   2    2  | 2    2
+--R     (a q  - a p )\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 99
+cc3:=aa.1-bb2
+--R
+--R   (7)
+--R                                           +-------+
+--R         +---------+                       | 2    2      2    2
+--R         |   2    2     (- p cos(a x) - q)\|q  - p   + (q  - p )sin(a x)
+--R       p\|- q  + p  log(------------------------------------------------)
+--R                                         q cos(a x) + p
+--R     + 
+--R                                   +---------+
+--R          +-------+                |   2    2
+--R          | 2    2        sin(a x)\|- q  + p
+--R       2p\|q  - p  atan(-----------------------)
+--R                        (q + p)cos(a x) + q + p
+--R  /
+--R                   +---------+ +-------+
+--R         2      2  |   2    2  | 2    2
+--R     (a q  - a p )\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 100    14:391 Schaums and Axiom agree
+cc4:=aa.2-bb2
+--R
+--R   (8)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.392~~~~~$\displaystyle
+\int{\frac{dx}{p^2+q^2\cos^2{ax}}}$}
+$$\int{\frac{1}{p^2+q^2\cos^2{ax}}}=
+\frac{1}{ap\sqrt{p^2+q^2}}\tan^{-1}\frac{p\tan{ax}}{\sqrt{p^2+q^2}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 101
+aa:=integrate(1/(p^2+q^2*cos(a*x)^2),x)
+--R 
+--R
+--R   (1)
+--R                 +-------+
+--R                 | 2    2                 2    2              2
+--R        sin(a x)\|q  + p               ((q  - p )cos(a x) - 2p )sin(a x)
+--R   atan(------------------) - atan(-----------------------------------------)
+--R         2p cos(a x) + 2p                                          +-------+
+--R                                              2                    | 2    2
+--R                                   (p cos(a x)  + 2p cos(a x) + p)\|q  + p
+--R   --------------------------------------------------------------------------
+--R                                      +-------+
+--R                                      | 2    2
+--R                                  a p\|q  + p
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 102
+bb:=1/(a*p*sqrt(p^2+q^2))*atan((p*tan(a*x))/sqrt(p^2+q^2))
+--R
+--R             p tan(a x)
+--R        atan(----------)
+--R              +-------+
+--R              | 2    2
+--R             \|q  + p
+--R   (2)  ----------------
+--R              +-------+
+--R              | 2    2
+--R          a p\|q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 103
+cc:=aa-bb
+--R
+--R   (3)
+--R                     +-------+
+--R                     | 2    2
+--R            sin(a x)\|q  + p           p tan(a x)
+--R       atan(------------------) - atan(----------)
+--R             2p cos(a x) + 2p           +-------+
+--R                                        | 2    2
+--R                                       \|q  + p
+--R     + 
+--R                     2    2              2
+--R                  ((q  - p )cos(a x) - 2p )sin(a x)
+--R       - atan(-----------------------------------------)
+--R                                              +-------+
+--R                         2                    | 2    2
+--R              (p cos(a x)  + 2p cos(a x) + p)\|q  + p
+--R  /
+--R         +-------+
+--R         | 2    2
+--R     a p\|q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 104
+dd:=ratDenom cc
+--R
+--R   (4)
+--R                                   +-------+
+--R          +-------+                | 2    2
+--R          | 2    2      p tan(a x)\|q  + p
+--R       - \|q  + p  atan(--------------------)
+--R                                2    2
+--R                               q  + p
+--R     + 
+--R       -
+--R             +-------+
+--R             | 2    2
+--R            \|q  + p
+--R         *
+--R                                                          +-------+
+--R                           2    2              2          | 2    2
+--R                        ((q  - p )cos(a x) - 2p )sin(a x)\|q  + p
+--R            atan(--------------------------------------------------------)
+--R                     2    3         2        2     3               2    3
+--R                 (p q  + p )cos(a x)  + (2p q  + 2p )cos(a x) + p q  + p
+--R     + 
+--R                               +-------+
+--R        +-------+              | 2    2
+--R        | 2    2      sin(a x)\|q  + p
+--R       \|q  + p  atan(------------------)
+--R                       2p cos(a x) + 2p
+--R  /
+--R          2      3
+--R     a p q  + a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 105
+atanrule2:=rule(atan(x) == 1/2*%i*(log(1-%i*x)-log(1+%i*x)))
+--R
+--R                     1                    1
+--R   (5)  atan(x) == - - %i log(%i x + 1) + - %i log(- %i x + 1)
+--R                     2                    2
+--RType: RewriteRule(Integer,Complex Fraction Integer,Expression Complex Fraction Integer)
+--E
+
+--S 106
+ee:=atanrule2 dd
+--R
+--R   (6)
+--R                                       +-------+
+--R            +-------+                  | 2    2     2    2
+--R       1    | 2    2     %i p tan(a x)\|q  + p   + q  + p
+--R       - %i\|q  + p  log(---------------------------------)
+--R       2                               2    2
+--R                                      q  + p
+--R     + 
+--R              +-------+
+--R         1    | 2    2
+--R         - %i\|q  + p
+--R         2
+--R      *
+--R         log
+--R                                                           +-------+
+--R                      2       2                 2          | 2    2
+--R                ((%i q  - %i p )cos(a x) - 2%i p )sin(a x)\|q  + p
+--R              + 
+--R                    2    3         2        2     3               2    3
+--R                (p q  + p )cos(a x)  + (2p q  + 2p )cos(a x) + p q  + p
+--R           /
+--R                  2    3         2        2     3               2    3
+--R              (p q  + p )cos(a x)  + (2p q  + 2p )cos(a x) + p q  + p
+--R     + 
+--R                                         +-------+
+--R                           1             | 2    2
+--R              +-------+    - %i sin(a x)\|q  + p   + p cos(a x) + p
+--R         1    | 2    2     2
+--R       - - %i\|q  + p  log(----------------------------------------)
+--R         2                              p cos(a x) + p
+--R     + 
+--R                                         +-------+
+--R                           1             | 2    2
+--R            +-------+    - - %i sin(a x)\|q  + p   + p cos(a x) + p
+--R       1    | 2    2       2
+--R       - %i\|q  + p  log(------------------------------------------)
+--R       2                               p cos(a x) + p
+--R     + 
+--R       -
+--R                 +-------+
+--R            1    | 2    2
+--R            - %i\|q  + p
+--R            2
+--R         *
+--R            log
+--R                                                                +-------+
+--R                           2       2                 2          | 2    2
+--R                   ((- %i q  + %i p )cos(a x) + 2%i p )sin(a x)\|q  + p
+--R                 + 
+--R                       2    3         2        2     3               2    3
+--R                   (p q  + p )cos(a x)  + (2p q  + 2p )cos(a x) + p q  + p
+--R              /
+--R                     2    3         2        2     3               2    3
+--R                 (p q  + p )cos(a x)  + (2p q  + 2p )cos(a x) + p q  + p
+--R     + 
+--R                                           +-------+
+--R              +-------+                    | 2    2     2    2
+--R         1    | 2    2     - %i p tan(a x)\|q  + p   + q  + p
+--R       - - %i\|q  + p  log(-----------------------------------)
+--R         2                                2    2
+--R                                         q  + p
+--R  /
+--R          2      3
+--R     a p q  + a p
+--R                                    Type: Expression Complex Fraction Integer
+--E
+
+--S 107
+ff:=expandLog ee
+--R
+--R   (7)
+--R              +-------+               +-------+
+--R         1    | 2    2                | 2    2        2       2
+--R       - - %i\|q  + p  log(p tan(a x)\|q  + p   + %i q  + %i p )
+--R         2
+--R     + 
+--R            +-------+               +-------+
+--R       1    | 2    2                | 2    2        2       2
+--R       - %i\|q  + p  log(p tan(a x)\|q  + p   - %i q  - %i p )
+--R       2
+--R     + 
+--R       -
+--R                 +-------+
+--R            1    | 2    2
+--R            - %i\|q  + p
+--R            2
+--R         *
+--R            log
+--R                                                   +-------+
+--R                    2    2              2          | 2    2
+--R                 ((q  - p )cos(a x) - 2p )sin(a x)\|q  + p
+--R               + 
+--R                        2       3         2           2        3
+--R                 (%i p q  + %i p )cos(a x)  + (2%i p q  + 2%i p )cos(a x)
+--R               + 
+--R                       2       3
+--R                 %i p q  + %i p
+--R     + 
+--R              +-------+
+--R         1    | 2    2
+--R         - %i\|q  + p
+--R         2
+--R      *
+--R         log
+--R                                                +-------+
+--R                 2    2              2          | 2    2
+--R              ((q  - p )cos(a x) - 2p )sin(a x)\|q  + p
+--R            + 
+--R                       2       3         2             2        3
+--R              (- %i p q  - %i p )cos(a x)  + (- 2%i p q  - 2%i p )cos(a x)
+--R            + 
+--R                      2       3
+--R              - %i p q  - %i p
+--R     + 
+--R            +-------+             +-------+
+--R       1    | 2    2              | 2    2
+--R       - %i\|q  + p  log(sin(a x)\|q  + p   + 2%i p cos(a x) + 2%i p)
+--R       2
+--R     + 
+--R              +-------+             +-------+
+--R         1    | 2    2              | 2    2
+--R       - - %i\|q  + p  log(sin(a x)\|q  + p   - 2%i p cos(a x) - 2%i p)
+--R         2
+--R     + 
+--R                                                                     +-------+
+--R                   1        1       1          1                     | 2    2
+--R     (%i log(%i) - - %i log(- %i) + - %i log(- - %i) - %i log(- %i))\|q  + p
+--R                   2        2       2          2
+--R  /
+--R          2      3
+--R     a p q  + a p
+--R                                    Type: Expression Complex Fraction Integer
+--E
+
+--S 108    14:392 Schaums and Axiom differ by a constant
+complexNormalize ff
+--R
+--R   (8)
+--R                      1        1       1          1
+--R         %i log(%i) - - %i log(- %i) + - %i log(- - %i) - %i log(- %i)
+--R                      2        2       2          2
+--R       + 
+--R           1
+--R         - - %i log(- 1)
+--R           2
+--R    *
+--R        +-------+
+--R        | 2    2
+--R       \|q  + p
+--R  /
+--R          2      3
+--R     a p q  + a p
+--R                                    Type: Expression Complex Fraction Integer
+--E
+
+@
+
+\section{\cite{1}:14.393~~~~~$\displaystyle
+\int{\frac{dx}{p^2-q^2\cos^2{ax}}}$}
+$$\int{\frac{1}{p^2-q^2\cos^2{ax}}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{1}{ap\sqrt{p^2-q^2}}\tan^{-1}\frac{p\tan{ax}}{\sqrt{p^2-q^2}}\\
+\\
+\displaystyle
+\frac{1}{2ap\sqrt{q^2-p^2}}\ln\left(\frac{p\tan{ax}-\sqrt{q^2-p^2}}
+{p\tan{ax}+\sqrt{q^2-p^2}}\right)
+\end{array}
+\right.
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 109
+aa:=integrate(1/(p^2-q^2*cos(a*x)^2),x)
+--R 
+--R
+--R   (1)
+--R                                   +-------+
+--R           2     2         2    2  | 2    2           2     3
+--R        ((q  - 2p )cos(a x)  + p )\|q  - p   + (- 2p q  + 2p )cos(a x)sin(a x)
+--R    log(----------------------------------------------------------------------)
+--R                                    2        2    2
+--R                                   q cos(a x)  - p
+--R   [---------------------------------------------------------------------------,
+--R                                        +-------+
+--R                                        | 2    2
+--R                                   2a p\|q  - p
+--R
+--R                       +---------+
+--R                       |   2    2
+--R              sin(a x)\|- q  + p
+--R         atan(--------------------)
+--R                2p cos(a x) + 2p
+--R       + 
+--R                      2    2              2
+--R                   ((q  + p )cos(a x) + 2p )sin(a x)
+--R         atan(-------------------------------------------)
+--R                                              +---------+
+--R                         2                    |   2    2
+--R              (p cos(a x)  + 2p cos(a x) + p)\|- q  + p
+--R    /
+--R           +---------+
+--R           |   2    2
+--R       a p\|- q  + p
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+
+--S 110
+bb1:=1/(a*p*sqrt(p^2-q^2))*atan((p*tan(a*x))/sqrt(p^2-q^2))
+--R
+--R              p tan(a x)
+--R        atan(------------)
+--R              +---------+
+--R              |   2    2
+--R             \|- q  + p
+--R   (2)  ------------------
+--R              +---------+
+--R              |   2    2
+--R          a p\|- q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 111
+bb2:=1/(2*a*p*sqrt(q^2-p^2))*log((p*tan(a*x)-sqrt(q^2-p^2))/(p*tan(a*x)+sqrt(q^2-p^2)))
+--R
+--R               +-------+
+--R               | 2    2
+--R            - \|q  - p   + p tan(a x)
+--R        log(-------------------------)
+--R              +-------+
+--R              | 2    2
+--R             \|q  - p   + p tan(a x)
+--R   (3)  ------------------------------
+--R                     +-------+
+--R                     | 2    2
+--R                2a p\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 112
+cc1:=aa.1-bb1
+--R
+--R   (4)
+--R          +---------+
+--R          |   2    2
+--R         \|- q  + p
+--R      *
+--R         log
+--R                                           +-------+
+--R                   2     2         2    2  | 2    2
+--R                ((q  - 2p )cos(a x)  + p )\|q  - p
+--R              + 
+--R                       2     3
+--R                (- 2p q  + 2p )cos(a x)sin(a x)
+--R           /
+--R               2        2    2
+--R              q cos(a x)  - p
+--R     + 
+--R           +-------+
+--R           | 2    2       p tan(a x)
+--R       - 2\|q  - p  atan(------------)
+--R                          +---------+
+--R                          |   2    2
+--R                         \|- q  + p
+--R  /
+--R          +---------+ +-------+
+--R          |   2    2  | 2    2
+--R     2a p\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 113
+cc2:=aa.2-bb1
+--R
+--R   (5)
+--R                     +---------+
+--R                     |   2    2
+--R            sin(a x)\|- q  + p            p tan(a x)
+--R       atan(--------------------) - atan(------------)
+--R              2p cos(a x) + 2p            +---------+
+--R                                          |   2    2
+--R                                         \|- q  + p
+--R     + 
+--R                    2    2              2
+--R                 ((q  + p )cos(a x) + 2p )sin(a x)
+--R       atan(-------------------------------------------)
+--R                                            +---------+
+--R                       2                    |   2    2
+--R            (p cos(a x)  + 2p cos(a x) + p)\|- q  + p
+--R  /
+--R         +---------+
+--R         |   2    2
+--R     a p\|- q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 114
+cc3:=aa.1-bb2
+--R
+--R   (6)
+--R       log
+--R                                     +-------+
+--R             2     2         2    2  | 2    2           2     3
+--R          ((q  - 2p )cos(a x)  + p )\|q  - p   + (- 2p q  + 2p )cos(a x)sin(a x)
+--R          ----------------------------------------------------------------------
+--R                                      2        2    2
+--R                                     q cos(a x)  - p
+--R     + 
+--R                +-------+
+--R                | 2    2
+--R             - \|q  - p   + p tan(a x)
+--R       - log(-------------------------)
+--R               +-------+
+--R               | 2    2
+--R              \|q  - p   + p tan(a x)
+--R  /
+--R          +-------+
+--R          | 2    2
+--R     2a p\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 115
+cc4:=aa.2-bb2
+--R
+--R   (7)
+--R                            +-------+
+--R          +---------+       | 2    2
+--R          |   2    2     - \|q  - p   + p tan(a x)
+--R       - \|- q  + p  log(-------------------------)
+--R                           +-------+
+--R                           | 2    2
+--R                          \|q  - p   + p tan(a x)
+--R     + 
+--R                                +---------+
+--R         +-------+              |   2    2
+--R         | 2    2      sin(a x)\|- q  + p
+--R       2\|q  - p  atan(--------------------)
+--R                         2p cos(a x) + 2p
+--R     + 
+--R         +-------+             2    2              2
+--R         | 2    2           ((q  + p )cos(a x) + 2p )sin(a x)
+--R       2\|q  - p  atan(-------------------------------------------)
+--R                                                       +---------+
+--R                                  2                    |   2    2
+--R                       (p cos(a x)  + 2p cos(a x) + p)\|- q  + p
+--R  /
+--R          +---------+ +-------+
+--R          |   2    2  | 2    2
+--R     2a p\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 116
+dd2:=ratDenom cc2
+--R
+--R   (8)
+--R                                     +---------+
+--R          +---------+                |   2    2
+--R          |   2    2      p tan(a x)\|- q  + p
+--R       - \|- q  + p  atan(----------------------)
+--R                                   2    2
+--R                                  q  - p
+--R     + 
+--R          +---------+
+--R          |   2    2
+--R         \|- q  + p
+--R      *
+--R                                                      +---------+
+--R                       2    2              2          |   2    2
+--R                    ((q  + p )cos(a x) + 2p )sin(a x)\|- q  + p
+--R         atan(--------------------------------------------------------)
+--R                  2    3         2        2     3               2    3
+--R              (p q  - p )cos(a x)  + (2p q  - 2p )cos(a x) + p q  - p
+--R     + 
+--R                                   +---------+
+--R          +---------+              |   2    2
+--R          |   2    2      sin(a x)\|- q  + p
+--R       - \|- q  + p  atan(--------------------)
+--R                            2p cos(a x) + 2p
+--R  /
+--R          2      3
+--R     a p q  - a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 117
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (9)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 118
+ee2:=tanrule dd2
+--R
+--R   (10)
+--R          +---------+
+--R          |   2    2
+--R         \|- q  + p
+--R      *
+--R                                                      +---------+
+--R                       2    2              2          |   2    2
+--R                    ((q  + p )cos(a x) + 2p )sin(a x)\|- q  + p
+--R         atan(--------------------------------------------------------)
+--R                  2    3         2        2     3               2    3
+--R              (p q  - p )cos(a x)  + (2p q  - 2p )cos(a x) + p q  - p
+--R     + 
+--R                                   +---------+
+--R          +---------+              |   2    2
+--R          |   2    2      sin(a x)\|- q  + p
+--R       - \|- q  + p  atan(--------------------)
+--R                            2p cos(a x) + 2p
+--R     + 
+--R                                     +---------+
+--R          +---------+                |   2    2
+--R          |   2    2      p sin(a x)\|- q  + p
+--R       - \|- q  + p  atan(----------------------)
+--R                               2    2
+--R                             (q  - p )cos(a x)
+--R  /
+--R          2      3
+--R     a p q  - a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 119
+atanrule2:=rule(atan(x) == 1/2*%i*(log(1-%i*x)-log(1+%i*x)))
+--R
+--R                      1                    1
+--R   (11)  atan(x) == - - %i log(%i x + 1) + - %i log(- %i x + 1)
+--R                      2                    2
+--RType: RewriteRule(Integer,Complex Fraction Integer,Expression Complex Fraction Integer)
+--E
+
+--S 120
+ff2:=atanrule2 ee2
+--R
+--R   (12)
+--R       -
+--R                 +---------+
+--R            1    |   2    2
+--R            - %i\|- q  + p
+--R            2
+--R         *
+--R            log
+--R                                                              +---------+
+--R                         2       2                 2          |   2    2
+--R                   ((%i q  + %i p )cos(a x) + 2%i p )sin(a x)\|- q  + p
+--R                 + 
+--R                       2    3         2        2     3               2    3
+--R                   (p q  - p )cos(a x)  + (2p q  - 2p )cos(a x) + p q  - p
+--R              /
+--R                     2    3         2        2     3               2    3
+--R                 (p q  - p )cos(a x)  + (2p q  - 2p )cos(a x) + p q  - p
+--R     + 
+--R                                         +---------+
+--R                           1             |   2    2
+--R            +---------+    - %i sin(a x)\|- q  + p   + p cos(a x) + p
+--R       1    |   2    2     2
+--R       - %i\|- q  + p  log(------------------------------------------)
+--R       2                                 p cos(a x) + p
+--R     + 
+--R                                         +---------+
+--R            +---------+                  |   2    2      2    2
+--R       1    |   2    2     %i p sin(a x)\|- q  + p   + (q  - p )cos(a x)
+--R       - %i\|- q  + p  log(---------------------------------------------)
+--R       2                                   2    2
+--R                                         (q  - p )cos(a x)
+--R     + 
+--R                                             +---------+
+--R              +---------+                    |   2    2      2    2
+--R         1    |   2    2     - %i p sin(a x)\|- q  + p   + (q  - p )cos(a x)
+--R       - - %i\|- q  + p  log(-----------------------------------------------)
+--R         2                                    2    2
+--R                                            (q  - p )cos(a x)
+--R     + 
+--R                                             +---------+
+--R                               1             |   2    2
+--R              +---------+    - - %i sin(a x)\|- q  + p   + p cos(a x) + p
+--R         1    |   2    2       2
+--R       - - %i\|- q  + p  log(--------------------------------------------)
+--R         2                                  p cos(a x) + p
+--R     + 
+--R              +---------+
+--R         1    |   2    2
+--R         - %i\|- q  + p
+--R         2
+--R      *
+--R         log
+--R                                                             +---------+
+--R                        2       2                 2          |   2    2
+--R                ((- %i q  - %i p )cos(a x) - 2%i p )sin(a x)\|- q  + p
+--R              + 
+--R                    2    3         2        2     3               2    3
+--R                (p q  - p )cos(a x)  + (2p q  - 2p )cos(a x) + p q  - p
+--R           /
+--R                  2    3         2        2     3               2    3
+--R              (p q  - p )cos(a x)  + (2p q  - 2p )cos(a x) + p q  - p
+--R  /
+--R          2      3
+--R     a p q  - a p
+--R                                    Type: Expression Complex Fraction Integer
+--E
+
+--S 121
+gg2:=expandLog ff2
+--R
+--R   (13)
+--R              +---------+
+--R         1    |   2    2
+--R         - %i\|- q  + p
+--R         2
+--R      *
+--R         log
+--R                                                +---------+
+--R                 2    2              2          |   2    2
+--R              ((q  + p )cos(a x) + 2p )sin(a x)\|- q  + p
+--R            + 
+--R                     2       3         2           2        3                  2
+--R              (%i p q  - %i p )cos(a x)  + (2%i p q  - 2%i p )cos(a x) + %i p q
+--R            + 
+--R                    3
+--R              - %i p
+--R     + 
+--R       -
+--R                 +---------+
+--R            1    |   2    2
+--R            - %i\|- q  + p
+--R            2
+--R         *
+--R            log
+--R                                                   +---------+
+--R                    2    2              2          |   2    2
+--R                 ((q  + p )cos(a x) + 2p )sin(a x)\|- q  + p
+--R               + 
+--R                          2       3         2             2        3
+--R                 (- %i p q  + %i p )cos(a x)  + (- 2%i p q  + 2%i p )cos(a x)
+--R               + 
+--R                         2       3
+--R                 - %i p q  + %i p
+--R     + 
+--R              +---------+               +---------+
+--R         1    |   2    2                |   2    2         2       2
+--R       - - %i\|- q  + p  log(p sin(a x)\|- q  + p   + (%i q  - %i p )cos(a x))
+--R         2
+--R     + 
+--R            +---------+               +---------+
+--R       1    |   2    2                |   2    2           2       2
+--R       - %i\|- q  + p  log(p sin(a x)\|- q  + p   + (- %i q  + %i p )cos(a x))
+--R       2
+--R     + 
+--R              +---------+             +---------+
+--R         1    |   2    2              |   2    2
+--R       - - %i\|- q  + p  log(sin(a x)\|- q  + p   + 2%i p cos(a x) + 2%i p)
+--R         2
+--R     + 
+--R            +---------+             +---------+
+--R       1    |   2    2              |   2    2
+--R       - %i\|- q  + p  log(sin(a x)\|- q  + p   - 2%i p cos(a x) - 2%i p)
+--R       2
+--R     + 
+--R                                           +---------+
+--R        1        1       1          1      |   2    2
+--R       (- %i log(- %i) - - %i log(- - %i))\|- q  + p
+--R        2        2       2          2
+--R  /
+--R          2      3
+--R     a p q  - a p
+--R                                    Type: Expression Complex Fraction Integer
+--E
+
+--S 122    14:393 Schaums and Axiom differ by a constant
+hh2:=complexNormalize gg2
+--R
+--R   (14)
+--R          1              1        1       1          1       1
+--R       (- - %i log(%i) + - %i log(- %i) - - %i log(- - %i) + - %i log(- %i))
+--R          2              2        2       2          2       2
+--R    *
+--R        +---------+
+--R        |   2    2
+--R       \|- q  + p
+--R  /
+--R          2      3
+--R     a p q  - a p
+--R                                    Type: Expression Complex Fraction Integer
+--E
+@
+
+\section{\cite{1}:14.394~~~~~$\displaystyle
+\int{x^m\cos{ax}}~dx$}
+$$\int{x^m\cos{ax}}=
+\frac{x^m\sin{ax}}{a}+\frac{mx^{m-1}}{a^2}\cos{ax}
+-\frac{m(m-1)}{a^2}\int{x^{m-2}\cos{ax}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 123    14:394 Axiom cannot compute this integral
+aa:=integrate(x^m*cos(a*x),x)
+--R 
+--R
+--R           x
+--R         ++             m
+--I   (1)   |   cos(%I a)%I d%I
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.395~~~~~$\displaystyle
+\int{\frac{\cos{ax}}{x^n}}~dx$}
+$$\int{\frac{\cos{ax}}{x^n}}=
+-\frac{\cos{ax}}{(n-1)x^{n-1}}-\frac{a}{n-1}\int{\frac{\sin{ax}}{x^{n-1}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 124    14:395 Axiom cannot compute this integral
+aa:=integrate(cos(a*x)/x^n,x)
+--R 
+--R
+--R           x
+--I         ++  cos(%I a)
+--I   (1)   |   --------- d%I
+--R        ++        n
+--I                %I
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.396~~~~~$\displaystyle
+\int{\cos^n{ax}}~dx$}
+$$\int{\cos^n{ax}}=
+\frac{\sin{ax}\cos^{n-1}{ax}}{an}+\frac{n-1}{n}\int{\cos^{n-2}{ax}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 125    14:396 Axiom cannot compute this integral
+aa:=integrate(cos(a*x)^n,x)
+--R 
+--R
+--R           x
+--R         ++           n
+--I   (1)   |   cos(%I a) d%I
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.397~~~~~$\displaystyle
+\int{\frac{1}{\cos^n{ax}}}~dx$}
+$$\int{\frac{1}{\cos^n{ax}}}=
+\frac{\sin{ax}}{a(n-1)\cos^{n-1}{ax}}
++\frac{n-2}{n-1}\int{\frac{1}{\cos^{n-2}{ax}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 126    14:397 Axiom cannot compute this integral
+aa:=integrate(1/(cos(a*x))^n,x)
+--R 
+--R
+--R           x
+--R         ++       1
+--I   (1)   |   ---------- d%I
+--R        ++            n
+--I             cos(%I a)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.398~~~~~$\displaystyle
+\int{\frac{x~dx}{cos^n{ax}}}$}
+$$\int{\frac{x}{cos^n{ax}}}=
+\frac{x\sin{ax}}{a(n-1)\cos^{n-1}{ax}}
+-\frac{1}{a^2(n-1)(n-2)\cos^{n-2}{ax}}
++\frac{n-2}{n-1}\int{\frac{x}{\cos^{n-2}{ax}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 127    14:398 Axiom cannot compute this integral
+aa:=integrate(x/cos(a*x)^n,x)
+--R 
+--R
+--R           x
+--I         ++      %I
+--I   (1)   |   ---------- d%I
+--R        ++            n
+--I             cos(%I a)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 pp77-78
+\end{thebibliography}
+\end{document}
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diff --git a/src/axiom-website/CATS/schaum19.input.pamphlet b/src/axiom-website/CATS/schaum19.input.pamphlet
new file mode 100644
index 0000000..eeb4d9d
--- /dev/null
+++ b/src/axiom-website/CATS/schaum19.input.pamphlet
@@ -0,0 +1,2781 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum19.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.399~~~~~$\displaystyle
+\int{\sin{ax}\cos{ax}}~dx$}
+$$\int{\sin{ax}\cos{ax}}=
+\frac{\sin^2{ax}}{2a}
+$$
+&lt;&lt;*&gt;&gt;=
+)spool schaum19.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1
+aa:=integrate(sin(a*x)*cos(a*x),x)
+--R 
+--R
+--R                  2
+--R          cos(a x)
+--R   (1)  - ---------
+--R              2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 2
+bb:=sin(a*x)^2/(2*a)
+--R
+--R                2
+--R        sin(a x)
+--R   (2)  ---------
+--R            2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3
+cc:=aa-bb
+--R
+--R                  2           2
+--R        - sin(a x)  - cos(a x)
+--R   (3)  -----------------------
+--R                   2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 4
+cossqrrule:=rule(cos(a)^2 == 1-sin(a)^2)
+--R
+--R              2            2
+--R   (4)  cos(a)  == - sin(a)  + 1
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 5      14:399 Schaums and Axiom differ by a constant
+dd:=cossqrrule cc
+--R
+--R           1
+--R   (5)  - --
+--R          2a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.400~~~~~$\displaystyle
+\int{\sin{px}\cos{qx}}~dx$}
+$$\int{\sin{px}\cos{qx}}=
+-\frac{cos(p-q)x}{2(p-q)}-\frac{cos(p+q)x}{2(p+q)}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 6
+aa:=integrate(sin(p*x)*cos(q*x),x)
+--R 
+--R
+--R        q sin(p x)sin(q x) + p cos(p x)cos(q x)
+--R   (1)  ---------------------------------------
+--R                         2    2
+--R                        q  - p
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 7
+bb:=-cos((p-q)*x)/(2*(p-q))-cos((p+q)*x)/(2*(p+q))
+--R
+--R        (- q + p)cos((q + p)x) + (q + p)cos((q - p)x)
+--R   (2)  ---------------------------------------------
+--R                            2     2
+--R                          2q  - 2p
+--R                                                     Type: Expression Integer
+--E
+
+--S 8
+cc:=aa-bb
+--R
+--R   (3)
+--R       2q sin(p x)sin(q x) + (q - p)cos((q + p)x) + 2p cos(p x)cos(q x)
+--R     + 
+--R       (- q - p)cos((q - p)x)
+--R  /
+--R       2     2
+--R     2q  - 2p
+--R                                                     Type: Expression Integer
+--E
+
+--S 9      14:400 Schaums and Axiom agree
+complexNormalize cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.401~~~~~$\displaystyle
+\int{\sin^n{ax}\cos{ax}}~dx$ provided $n \ne -1$}
+$$\int{\sin^n{ax}\cos{ax}}=
+\frac{\sin^{n+1}{ax}}{(n+1)a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 10
+aa:=integrate(sin(a*x)^n*cos(a*x),x)
+--R 
+--R
+--R                  n log(sin(a x))
+--R        sin(a x)%e
+--R   (1)  -------------------------
+--R                 a n + a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 11
+bb:=sin(a*x)^(n+1)/((n+1)*a)
+--R
+--R                n + 1
+--R        sin(a x)
+--R   (2)  -------------
+--R           a n + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 12
+cc:=aa-bb
+--R
+--R                  n log(sin(a x))           n + 1
+--R        sin(a x)%e                - sin(a x)
+--R   (3)  -----------------------------------------
+--R                         a n + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 13
+explog:=rule(%e^(n*log(x)) == x^n)
+--R
+--R          n log(x)     n
+--R   (4)  %e         == x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 14
+dd:=explog cc
+--R
+--R                  n + 1                   n
+--R        - sin(a x)      + sin(a x)sin(a x)
+--R   (5)  -----------------------------------
+--R                      a n + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 15     14:401 Schaums and Axiom agree
+ee:=complexNormalize dd
+--R
+--R   (6)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.402~~~~~$\displaystyle
+\int{\cos^n{ax}*sin{ax}}~dx$ provided $n \ne -1$}
+$$\int{\cos^n{ax}*sin{ax}}=
+-\frac{\cos^{n+1}{ax}}{(n+1)a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 16
+aa:=integrate(cos(a*x)^n*sin(a*x),x)
+--R 
+--R
+--R                    n log(cos(a x))
+--R          cos(a x)%e
+--R   (1)  - -------------------------
+--R                   a n + a
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 17
+bb:=-cos(a*x)^(n+1)/((n+1)*a)
+--R
+--R                  n + 1
+--R          cos(a x)
+--R   (2)  - -------------
+--R             a n + a
+--R                                                     Type: Expression Integer
+--E 
+
+--S 18
+cc:=aa-bb
+--R
+--R                    n log(cos(a x))           n + 1
+--R        - cos(a x)%e                + cos(a x)
+--R   (3)  -------------------------------------------
+--R                          a n + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 19
+explog:=rule(%e^(n*log(x)) == x^n)
+--R
+--R          n log(x)     n
+--R   (4)  %e         == x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 20
+dd:=explog cc
+--R
+--R                n + 1                   n
+--R        cos(a x)      - cos(a x)cos(a x)
+--R   (5)  ---------------------------------
+--R                     a n + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 21     14:402 Schaums and Axiom agree
+ee:=complexNormalize dd
+--R
+--R   (6)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.403~~~~~$\displaystyle
+\int{\sin^2{ax}\cos^2{ax}}$}
+$$\int{\sin^2{ax}\cos^2{ax}}=
+\frac{x}{8}-\frac{\sin{4ax}}{32a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 22
+aa:=integrate(sin(a*x)^2*cos(a*x)^2,x)
+--R 
+--R
+--R                    3
+--R        (- 2cos(a x)  + cos(a x))sin(a x) + a x
+--R   (1)  ---------------------------------------
+--R                           8a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 23
+bb:=x/8-sin(4*a*x)/(32*a)
+--R
+--R        - sin(4a x) + 4a x
+--R   (2)  ------------------
+--R                32a
+--R                                                     Type: Expression Integer
+--E
+
+--S 24
+cc:=aa-bb
+--R
+--R                                3
+--R        sin(4a x) + (- 8cos(a x)  + 4cos(a x))sin(a x)
+--R   (3)  ----------------------------------------------
+--R                              32a
+--R                                                     Type: Expression Integer
+--E
+
+--S 25     14:403 Schaums and Axiom agree
+dd:=complexNormalize cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.404~~~~~$\displaystyle
+\int{\frac{dx}{\sin{ax}\cos{ax}}}$}
+$$\int{\frac{1}{\sin{ax}\cos{ax}}}=
+\frac{1}{a}\ln~\tan{ax}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 26
+aa:=integrate(1/(sin(a*x)*cos(a*x)),x)
+--R 
+--R
+--R              sin(a x)              2cos(a x)
+--R        log(------------) - log(- ------------)
+--R            cos(a x) + 1          cos(a x) + 1
+--R   (1)  ---------------------------------------
+--R                           a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 27
+bb:=1/a*log(tan(a*x))
+--R
+--R        log(tan(a x))
+--R   (2)  -------------
+--R              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 28
+cc:=aa-bb
+--R
+--R                                sin(a x)              2cos(a x)
+--R        - log(tan(a x)) + log(------------) - log(- ------------)
+--R                              cos(a x) + 1          cos(a x) + 1
+--R   (3)  ---------------------------------------------------------
+--R                                    a
+--R                                                     Type: Expression Integer
+--E
+
+--S 29
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (4)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 30
+dd:=tanrule cc
+--R
+--R              sin(a x)          sin(a x)              2cos(a x)
+--R        - log(--------) + log(------------) - log(- ------------)
+--R              cos(a x)        cos(a x) + 1          cos(a x) + 1
+--R   (5)  ---------------------------------------------------------
+--R                                    a
+--R                                                     Type: Expression Integer
+--E
+
+--S 31     14:404 Schaums and Axiom differ by a constant
+ee:=expandLog dd
+--R
+--R          log(- 2)
+--R   (6)  - --------
+--R              a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.405~~~~~$\displaystyle
+\int{\frac{dx}{\sin^2{ax}\cos{ax}}}$}
+$$\int{\frac{1}{\sin^2{ax}\cos{ax}}}=
+\frac{1}{a}\ln~\tan\left(\frac{\pi}{4}+\frac{ax}{2}\right)-\frac{1}{a\sin{ax}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 32
+aa:=integrate(1/(sin(a*x)^2*cos(a*x)),x)
+--R 
+--R
+--R   (1)
+--R                   sin(a x) + cos(a x) + 1
+--R       sin(a x)log(-----------------------)
+--R                         cos(a x) + 1
+--R     + 
+--R                     sin(a x) - cos(a x) - 1
+--R       - sin(a x)log(-----------------------) - 1
+--R                           cos(a x) + 1
+--R  /
+--R     a sin(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 33
+bb:=1/a*log(tan(%pi/4+(a*x)/2))-1/(a*sin(a*x))
+--R
+--R                        2a x + %pi
+--R        sin(a x)log(tan(----------)) - 1
+--R                             4
+--R   (2)  --------------------------------
+--R                   a sin(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 34
+cc:=aa-bb
+--R
+--R   (3)
+--R                 2a x + %pi         sin(a x) + cos(a x) + 1
+--R       - log(tan(----------)) + log(-----------------------)
+--R                      4                   cos(a x) + 1
+--R     + 
+--R             sin(a x) - cos(a x) - 1
+--R       - log(-----------------------)
+--R                   cos(a x) + 1
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 35
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (4)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 36
+dd:=tanrule cc
+--R
+--R   (5)
+--R           sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
+--R       log(-----------------------) - log(-----------------------)
+--R                 cos(a x) + 1                   cos(a x) + 1
+--R     + 
+--R                 2a x + %pi
+--R             sin(----------)
+--R                      4
+--R       - log(---------------)
+--R                 2a x + %pi
+--R             cos(----------)
+--R                      4
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 37
+ee:=expandLog dd
+--R
+--R   (6)
+--R       log(sin(a x) + cos(a x) + 1) - log(sin(a x) - cos(a x) - 1)
+--R     + 
+--R                 2a x + %pi             2a x + %pi
+--R       - log(sin(----------)) + log(cos(----------))
+--R                      4                      4
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 38     14:405 Schaums and Axiom differ by a constant
+ff:=complexNormalize %
+--R
+--R        log(- 1)
+--R   (7)  --------
+--R            a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.406~~~~~$\displaystyle
+\int{\frac{dx}{\sin{ax}\cos^2{ax}}}$}
+$$\int{\frac{1}{\sin{ax}\cos^2{ax}}}=
+\frac{1}{a}\ln~\tan\frac{ax}{2}+\frac{1}{a\cos{ax}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 39
+aa:=integrate(1/(sin(a*x)*cos(a*x)^2),x)
+--R 
+--R
+--R                      sin(a x)
+--R        cos(a x)log(------------) + cos(a x) + 1
+--R                    cos(a x) + 1
+--R   (1)  ----------------------------------------
+--R                       a cos(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 40
+bb:=1/a*log(tan((a*x)/2))+1/(a*cos(a*x))
+--R
+--R                        a x
+--R        cos(a x)log(tan(---)) + 1
+--R                         2
+--R   (2)  -------------------------
+--R                a cos(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 41
+cc:=aa-bb
+--R
+--R                  a x           sin(a x)
+--R        - log(tan(---)) + log(------------) + 1
+--R                   2          cos(a x) + 1
+--R   (3)  ---------------------------------------
+--R                           a
+--R                                                     Type: Expression Integer
+--E
+
+--S 42
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (4)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 43
+dd:=tanrule cc
+--R
+--R                                    a x
+--R                                sin(---)
+--R              sin(a x)               2
+--R        log(------------) - log(--------) + 1
+--R            cos(a x) + 1            a x
+--R                                cos(---)
+--R                                     2
+--R   (5)  -------------------------------------
+--R                          a
+--R                                                     Type: Expression Integer
+--E
+
+--S 44
+ee:=expandLog dd
+--R
+--R                                a x                                 a x
+--R        log(sin(a x)) - log(sin(---)) - log(cos(a x) + 1) + log(cos(---)) + 1
+--R                                 2                                   2
+--R   (6)  ---------------------------------------------------------------------
+--R                                          a
+--R                                                     Type: Expression Integer
+--E
+
+--S 45     14:406 Schaums and Axiom differ by a constant
+ff:=complexNormalize ee
+--R
+--R        1
+--R   (7)  -
+--R        a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.407~~~~~$\displaystyle
+\int{\frac{dx}{\sin^2{ax}\cos^2{ax}}}$}
+$$\int{\frac{1}{\sin^2{ax}\cos^2{ax}}}=
+-\frac{2\cot{2ax}}{a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 46
+aa:=integrate(1/(sin(a*x)^2*cos(a*x)^2),x)
+--R 
+--R
+--R                    2
+--R         - 2cos(a x)  + 1
+--R   (1)  ------------------
+--R        a cos(a x)sin(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 47
+bb:=-(2*cot(2*a*x))/a
+--R
+--R          2cot(2a x)
+--R   (2)  - ----------
+--R               a
+--R                                                     Type: Expression Integer
+--E
+
+--S 48
+cc:=aa-bb
+--R
+--R                                              2
+--R        2cos(a x)cot(2a x)sin(a x) - 2cos(a x)  + 1
+--R   (3)  -------------------------------------------
+--R                     a cos(a x)sin(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 49
+cotrule:=rule(cot(a) == cos(a)/sin(a))
+--R
+--R                  cos(a)
+--R   (4)  cot(a) == ------
+--R                  sin(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 50
+dd:=cotrule cc
+--R
+--R                    2
+--R        (- 2cos(a x)  + 1)sin(2a x) + 2cos(a x)cos(2a x)sin(a x)
+--R   (5)  --------------------------------------------------------
+--R                       a cos(a x)sin(a x)sin(2a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 51     14:407 Schaums and Axiom agree
+ee:=complexNormalize dd
+--R
+--R   (6)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.408~~~~~$\displaystyle
+\int{\frac{\sin^2{ax}}{\cos{ax}}}~dx$}
+$$\int{\frac{\sin^2{ax}}{\cos{ax}}}=
+-\frac{\sin{ax}}{a}+\frac{1}{a}\ln~\tan\left(\frac{ax}{2}+\frac{\pi}{4}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 52
+aa:=integrate(sin(a*x)^2/cos(a*x),x)
+--R 
+--R
+--R            sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
+--R        log(-----------------------) - log(-----------------------) - sin(a x)
+--R                  cos(a x) + 1                   cos(a x) + 1
+--R   (1)  ----------------------------------------------------------------------
+--R                                           a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 53
+bb:=-sin(a*x)/a+1/a*log(tan((a*x)/2+%pi/4))
+--R
+--R                2a x + %pi
+--R        log(tan(----------)) - sin(a x)
+--R                     4
+--R   (2)  -------------------------------
+--R                       a
+--R                                                     Type: Expression Integer
+--E
+
+--S 54
+cc:=aa-bb
+--R
+--R   (3)
+--R                 2a x + %pi         sin(a x) + cos(a x) + 1
+--R       - log(tan(----------)) + log(-----------------------)
+--R                      4                   cos(a x) + 1
+--R     + 
+--R             sin(a x) - cos(a x) - 1
+--R       - log(-----------------------)
+--R                   cos(a x) + 1
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 55
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (4)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 56
+dd:=tanrule cc
+--R
+--R   (5)
+--R           sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
+--R       log(-----------------------) - log(-----------------------)
+--R                 cos(a x) + 1                   cos(a x) + 1
+--R     + 
+--R                 2a x + %pi
+--R             sin(----------)
+--R                      4
+--R       - log(---------------)
+--R                 2a x + %pi
+--R             cos(----------)
+--R                      4
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 57
+ee:=expandLog dd
+--R
+--R   (6)
+--R       log(sin(a x) + cos(a x) + 1) - log(sin(a x) - cos(a x) - 1)
+--R     + 
+--R                 2a x + %pi             2a x + %pi
+--R       - log(sin(----------)) + log(cos(----------))
+--R                      4                      4
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 58     14:408 Schaums and Axiom differ by a constant
+ff:=complexNormalize ee
+--R
+--R        log(- 1)
+--R   (7)  --------
+--R            a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.409~~~~~$\displaystyle
+\int{\frac{\cos^2{ax}}{\sin{ax}}}~dx$}
+$$\int{\frac{\cos^2{ax}}{\sin{ax}}}=
+\frac{\cos{ax}}{a}+\frac{1}{a}\ln~\tan{\frac{ax}{2}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 59
+aa:=integrate(cos(a*x)^2/sin(a*x),x)
+--R 
+--R
+--R              sin(a x)
+--R        log(------------) + cos(a x)
+--R            cos(a x) + 1
+--R   (1)  ----------------------------
+--R                      a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 60
+bb:=cos(a*x)/a+1/a*log(tan((a*x)/2))
+--R
+--R                a x
+--R        log(tan(---)) + cos(a x)
+--R                 2
+--R   (2)  ------------------------
+--R                    a
+--R                                                     Type: Expression Integer
+--E
+
+--S 61
+cc:=aa-bb
+--R
+--R                  a x           sin(a x)
+--R        - log(tan(---)) + log(------------)
+--R                   2          cos(a x) + 1
+--R   (3)  -----------------------------------
+--R                         a
+--R                                                     Type: Expression Integer
+--E
+
+--S 62
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (4)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 63
+dd:=tanrule cc
+--R
+--R                                    a x
+--R                                sin(---)
+--R              sin(a x)               2
+--R        log(------------) - log(--------)
+--R            cos(a x) + 1            a x
+--R                                cos(---)
+--R                                     2
+--R   (5)  ---------------------------------
+--R                        a
+--R                                                     Type: Expression Integer
+--E
+
+--S 64
+ee:=expandLog dd
+--R
+--R                                a x                                 a x
+--R        log(sin(a x)) - log(sin(---)) - log(cos(a x) + 1) + log(cos(---))
+--R                                 2                                   2
+--R   (6)  -----------------------------------------------------------------
+--R                                        a
+--R                                                     Type: Expression Integer
+--E
+
+--S 65     14:409 Schaums and Axiom agree
+ff:=complexNormalize ee
+--R
+--R   (7)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.410~~~~~$\displaystyle
+\int{\frac{dx}{\cos{ax}(1\pm\sin{ax})}}$}
+$$\int{\frac{1}{\cos{ax}(1\pm\sin{ax})}}=
+\mp\frac{1}{2a(1\pm\sin{ax})}
++\frac{1}{2a}\ln~\tan\left(\frac{ax}{2}+\frac{\pi}{4}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 66
+aa:=integrate(1/(cos(a*x)*(1+sin(a*x))),x)
+--R 
+--R
+--R   (1)
+--R                         sin(a x) + cos(a x) + 1
+--R       (sin(a x) + 1)log(-----------------------)
+--R                               cos(a x) + 1
+--R     + 
+--R                           sin(a x) - cos(a x) - 1
+--R       (- sin(a x) - 1)log(-----------------------) + sin(a x)
+--R                                 cos(a x) + 1
+--R  /
+--R     2a sin(a x) + 2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 67
+bb:=-1/(2*a*(1+sin(a*x)))+1/(2*a)*log(tan((a*x)/2+%pi/4))
+--R
+--R                              2a x + %pi
+--R        (sin(a x) + 1)log(tan(----------)) - 1
+--R                                   4
+--R   (2)  --------------------------------------
+--R                   2a sin(a x) + 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 68
+cc:=aa-bb
+--R
+--R   (3)
+--R                 2a x + %pi         sin(a x) + cos(a x) + 1
+--R       - log(tan(----------)) + log(-----------------------)
+--R                      4                   cos(a x) + 1
+--R     + 
+--R             sin(a x) - cos(a x) - 1
+--R       - log(-----------------------) + 1
+--R                   cos(a x) + 1
+--R  /
+--R     2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 69
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (4)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 70
+dd:=tanrule cc
+--R
+--R   (5)
+--R           sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
+--R       log(-----------------------) - log(-----------------------)
+--R                 cos(a x) + 1                   cos(a x) + 1
+--R     + 
+--R                 2a x + %pi
+--R             sin(----------)
+--R                      4
+--R       - log(---------------) + 1
+--R                 2a x + %pi
+--R             cos(----------)
+--R                      4
+--R  /
+--R     2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 71
+ee:=expandLog dd
+--R
+--R   (6)
+--R       log(sin(a x) + cos(a x) + 1) - log(sin(a x) - cos(a x) - 1)
+--R     + 
+--R                 2a x + %pi             2a x + %pi
+--R       - log(sin(----------)) + log(cos(----------)) + 1
+--R                      4                      4
+--R  /
+--R     2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 72
+ff:=complexNormalize ee
+--R
+--R        log(- 1) + 1
+--R   (7)  ------------
+--R             2a
+--R                                                     Type: Expression Integer
+--E
+
+)clear all 
+
+--S 73
+aa:=integrate(1/(cos(a*x)*(1-sin(a*x))),x)
+--R 
+--R
+--R   (1)
+--R                         sin(a x) + cos(a x) + 1
+--R       (sin(a x) - 1)log(-----------------------)
+--R                               cos(a x) + 1
+--R     + 
+--R                           sin(a x) - cos(a x) - 1
+--R       (- sin(a x) + 1)log(-----------------------) - sin(a x)
+--R                                 cos(a x) + 1
+--R  /
+--R     2a sin(a x) - 2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 74
+bb:=1/(2*a*(1-sin(a*x)))+1/(2*a)*log(tan((a*x)/2+%pi/4))
+--R
+--R                              2a x + %pi
+--R        (sin(a x) - 1)log(tan(----------)) - 1
+--R                                   4
+--R   (2)  --------------------------------------
+--R                   2a sin(a x) - 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 75
+cc:=aa-bb
+--R
+--R   (3)
+--R                 2a x + %pi         sin(a x) + cos(a x) + 1
+--R       - log(tan(----------)) + log(-----------------------)
+--R                      4                   cos(a x) + 1
+--R     + 
+--R             sin(a x) - cos(a x) - 1
+--R       - log(-----------------------) - 1
+--R                   cos(a x) + 1
+--R  /
+--R     2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 76
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (4)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 77
+dd:=tanrule cc
+--R
+--R   (5)
+--R           sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
+--R       log(-----------------------) - log(-----------------------)
+--R                 cos(a x) + 1                   cos(a x) + 1
+--R     + 
+--R                 2a x + %pi
+--R             sin(----------)
+--R                      4
+--R       - log(---------------) - 1
+--R                 2a x + %pi
+--R             cos(----------)
+--R                      4
+--R  /
+--R     2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 78
+ee:=expandLog dd
+--R
+--R   (6)
+--R       log(sin(a x) + cos(a x) + 1) - log(sin(a x) - cos(a x) - 1)
+--R     + 
+--R                 2a x + %pi             2a x + %pi
+--R       - log(sin(----------)) + log(cos(----------)) - 1
+--R                      4                      4
+--R  /
+--R     2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 79     14:410 Schaums and Axiom differ by a constant
+ff:=complexNormalize ee
+--R
+--R        log(- 1) - 1
+--R   (7)  ------------
+--R             2a
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.411~~~~~$\displaystyle
+\int{\frac{dx}{\sin{ax}(1\pm\cos{ax})}}$}
+$$\int{\frac{1}{\sin{ax}(1\pm\cos{ax})}}=
+\pm\frac{1}{2a(1\pm\cos{ax})}+\frac{1}{2a}\ln~\tan\frac{ax}{2}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 80
+aa:=integrate(1/(sin(a*x)*(1+cos(a*x))),x)
+--R 
+--R
+--R                             sin(a x)
+--R        (2cos(a x) + 2)log(------------) - cos(a x) + 1
+--R                           cos(a x) + 1
+--R   (1)  -----------------------------------------------
+--R                        4a cos(a x) + 4a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 81
+bb:=1/(2*a*(1+cos(a*x)))+1/(2*a)*log(tan((a*x)/2))
+--R
+--R                              a x
+--R        (cos(a x) + 1)log(tan(---)) + 1
+--R                               2
+--R   (2)  -------------------------------
+--R                2a cos(a x) + 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 82
+cc:=aa-bb
+--R
+--R                   a x            sin(a x)
+--R        - 2log(tan(---)) + 2log(------------) - 1
+--R                    2           cos(a x) + 1
+--R   (3)  -----------------------------------------
+--R                            4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 83
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (4)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 84
+dd:=tanrule cc
+--R
+--R                                      a x
+--R                                  sin(---)
+--R               sin(a x)                2
+--R        2log(------------) - 2log(--------) - 1
+--R             cos(a x) + 1             a x
+--R                                  cos(---)
+--R                                       2
+--R   (5)  ---------------------------------------
+--R                           4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 85
+ee:=expandLog dd
+--R
+--R   (6)
+--R                             a x                                   a x
+--R   2log(sin(a x)) - 2log(sin(---)) - 2log(cos(a x) + 1) + 2log(cos(---)) - 1
+--R                              2                                     2
+--R   -------------------------------------------------------------------------
+--R                                       4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 86
+ff:=complexNormalize ee
+--R
+--R           1
+--R   (7)  - --
+--R          4a
+--R                                                     Type: Expression Integer
+--E
+
+)clear all
+
+--S 87
+aa:=integrate(1/(sin(a*x)*(1-cos(a*x))),x)
+--R 
+--R
+--R                             sin(a x)
+--R        (2cos(a x) - 2)log(------------) + cos(a x) + 1
+--R                           cos(a x) + 1
+--R   (1)  -----------------------------------------------
+--R                        4a cos(a x) - 4a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 88
+bb:=-1/(2*a*(1-cos(a*x)))+1/(2*a)*log(tan((a*x)/2))
+--R
+--R                              a x
+--R        (cos(a x) - 1)log(tan(---)) + 1
+--R                               2
+--R   (2)  -------------------------------
+--R                2a cos(a x) - 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 89
+cc:=aa-bb
+--R
+--R                   a x            sin(a x)
+--R        - 2log(tan(---)) + 2log(------------) + 1
+--R                    2           cos(a x) + 1
+--R   (3)  -----------------------------------------
+--R                            4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 90
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (4)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 91
+dd:=tanrule cc
+--R
+--R                                      a x
+--R                                  sin(---)
+--R               sin(a x)                2
+--R        2log(------------) - 2log(--------) + 1
+--R             cos(a x) + 1             a x
+--R                                  cos(---)
+--R                                       2
+--R   (5)  ---------------------------------------
+--R                           4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 92
+ee:=expandLog dd
+--R
+--R   (6)
+--R                             a x                                   a x
+--R   2log(sin(a x)) - 2log(sin(---)) - 2log(cos(a x) + 1) + 2log(cos(---)) + 1
+--R                              2                                     2
+--R   -------------------------------------------------------------------------
+--R                                       4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 93     14:411 Schaums and Axiom differ by a constant
+ff:=complexNormalize ee
+--R
+--R         1
+--R   (7)  --
+--R        4a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.412~~~~~$\displaystyle
+\int{\frac{dx}{\sin{ax}\pm\cos{ax}}}$}
+$$\int{\frac{1}{\sin{ax}\pm\cos{ax}}}=
+\frac{1}{a\sqrt{2}}\ln~\tan\left(\frac{ax}{2}\pm\frac{\pi}{8}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 94
+aa:=integrate(1/(sin(a*x)+cos(a*x)),x)
+--R 
+--R
+--R                    +-+                  +-+                 +-+
+--R         +-+    (- \|2  + 1)sin(a x) + (\|2  - 1)cos(a x) + \|2  - 2
+--R        \|2 log(----------------------------------------------------)
+--R                                 sin(a x) + cos(a x)
+--R   (1)  -------------------------------------------------------------
+--R                                      2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 95
+bb:=1/(a*sqrt(2))*log(tan((a*x)/2+%pi/8))
+--R
+--R         +-+        4a x + %pi
+--R        \|2 log(tan(----------))
+--R                         8
+--R   (2)  ------------------------
+--R                   2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 96
+cc:=aa-bb
+--R
+--R   (3)
+--R          +-+        4a x + %pi
+--R       - \|2 log(tan(----------))
+--R                          8
+--R     + 
+--R                   +-+                  +-+                 +-+
+--R        +-+    (- \|2  + 1)sin(a x) + (\|2  - 1)cos(a x) + \|2  - 2
+--R       \|2 log(----------------------------------------------------)
+--R                                sin(a x) + cos(a x)
+--R  /
+--R     2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 97
+complexNormalize cc
+--R
+--R                 +-+
+--R         +-+    \|2  - 2
+--R        \|2 log(--------)
+--R                   +-+
+--R                  \|2
+--R   (4)  -----------------
+--R                2a
+--R                                                     Type: Expression Integer
+--E
+
+)clear all
+
+--S 98
+aa:=integrate(1/(sin(a*x)-cos(a*x)),x)
+--R 
+--R
+--R                    +-+                    +-+                 +-+
+--R         +-+    (- \|2  + 1)sin(a x) + (- \|2  + 1)cos(a x) - \|2  + 2
+--R        \|2 log(------------------------------------------------------)
+--R                                  sin(a x) - cos(a x)
+--R   (1)  ---------------------------------------------------------------
+--R                                       2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 99
+bb:=1/(a*sqrt(2))*log(tan((a*x)/2-%pi/8))
+--R
+--R         +-+        4a x - %pi
+--R        \|2 log(tan(----------))
+--R                         8
+--R   (2)  ------------------------
+--R                   2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 100
+cc:=aa-bb
+--R
+--R   (3)
+--R          +-+        4a x - %pi
+--R       - \|2 log(tan(----------))
+--R                          8
+--R     + 
+--R                   +-+                    +-+                 +-+
+--R        +-+    (- \|2  + 1)sin(a x) + (- \|2  + 1)cos(a x) - \|2  + 2
+--R       \|2 log(------------------------------------------------------)
+--R                                 sin(a x) - cos(a x)
+--R  /
+--R     2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 101    14:412 Schaums and Axiom differ by a constant
+complexNormalize cc
+--R
+--R         +-+     +-+
+--R        \|2 log(\|2  - 1)
+--R   (4)  -----------------
+--R                2a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.413~~~~~$\displaystyle
+\int{\frac{\sin{ax}~dx}{\sin{ax}\pm\cos{ax}}}$}
+$$\int{\frac{\sin{ax}}{\sin{ax}\pm\cos{ax}}}=
+\frac{x}{2}\mp\frac{1}{2a}\ln(\sin{ax}\pm\cos{ax})
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 102
+aa:=integrate(sin(a*x)/(sin(a*x)+cos(a*x)),x)
+--R 
+--R
+--R                  2             - 2sin(a x) - 2cos(a x)
+--R        log(------------) - log(-----------------------) + a x
+--R            cos(a x) + 1              cos(a x) + 1
+--R   (1)  ------------------------------------------------------
+--R                                  2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 103
+bb:=x/2-1/(2*a)*log(sin(a*x)+cos(a*x))
+--R
+--R        - log(sin(a x) + cos(a x)) + a x
+--R   (2)  --------------------------------
+--R                       2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 104
+cc:=aa-bb
+--R
+--R   (3)
+--R                                        2             - 2sin(a x) - 2cos(a x)
+--R   log(sin(a x) + cos(a x)) + log(------------) - log(-----------------------)
+--R                                  cos(a x) + 1              cos(a x) + 1
+--R   ---------------------------------------------------------------------------
+--R                                        2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 105
+dd:=expandLog cc
+--R
+--R        log(sin(a x) + cos(a x)) - log(- sin(a x) - cos(a x))
+--R   (4)  -----------------------------------------------------
+--R                                  2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 106
+ee:=complexNormalize dd
+--R
+--R        log(- 1)
+--R   (5)  --------
+--R           2a
+--R                                                     Type: Expression Integer
+--E
+
+)clear all 
+
+--S 107
+aa:=integrate(sin(a*x)/(sin(a*x)-cos(a*x)),x)
+--R 
+--R
+--R            2sin(a x) - 2cos(a x)              2
+--R        log(---------------------) - log(------------) + a x
+--R                 cos(a x) + 1            cos(a x) + 1
+--R   (1)  ----------------------------------------------------
+--R                                 2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 108
+bb:=x/2+1/(2*a)*log(sin(a*x)-cos(a*x))
+--R
+--R        log(sin(a x) - cos(a x)) + a x
+--R   (2)  ------------------------------
+--R                      2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 109
+cc:=aa-bb
+--R
+--R   (3)
+--R                                    2sin(a x) - 2cos(a x)              2
+--R   - log(sin(a x) - cos(a x)) + log(---------------------) - log(------------)
+--R                                         cos(a x) + 1            cos(a x) + 1
+--R   ---------------------------------------------------------------------------
+--R                                        2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 110    14:413 Schaums and Axiom agree
+dd:=expandLog cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.414~~~~~$\displaystyle
+\int{\frac{cos{ax}~dx}{\sin{ax}\pm{\cos{ax}}}}$}
+$$\int{\frac{cos{ax}}{\sin{ax}\pm{\cos{ax}}}}=
+\pm\frac{x}{2}+\frac{1}{2a}\ln(sin{ax}\pm\cos{ax})
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 111
+aa:=integrate(cos(a*x)/(sin(a*x)+cos(a*x)),x)
+--R 
+--R
+--R                    2             - 2sin(a x) - 2cos(a x)
+--R        - log(------------) + log(-----------------------) + a x
+--R              cos(a x) + 1              cos(a x) + 1
+--R   (1)  --------------------------------------------------------
+--R                                   2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 112
+bb:=x/2+1/(2*a)*log(sin(a*x)+cos(a*x))
+--R
+--R        log(sin(a x) + cos(a x)) + a x
+--R   (2)  ------------------------------
+--R                      2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 113
+cc:=aa-bb
+--R
+--R   (3)
+--R                                          2             - 2sin(a x) - 2cos(a x)
+--R   - log(sin(a x) + cos(a x)) - log(------------) + log(-----------------------)
+--R                                    cos(a x) + 1              cos(a x) + 1
+--R   -----------------------------------------------------------------------------
+--R                                         2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 114
+dd:=expandLog cc
+--R
+--R        - log(sin(a x) + cos(a x)) + log(- sin(a x) - cos(a x))
+--R   (4)  -------------------------------------------------------
+--R                                   2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 115
+ee:=complexNormalize dd
+--R
+--R          log(- 1)
+--R   (5)  - --------
+--R             2a
+--R                                                     Type: Expression Integer
+--E
+
+)clear all
+
+--S 116
+aa:=integrate(cos(a*x)/(sin(a*x)-cos(a*x)),x)
+--R 
+--R
+--R            2sin(a x) - 2cos(a x)              2
+--R        log(---------------------) - log(------------) - a x
+--R                 cos(a x) + 1            cos(a x) + 1
+--R   (1)  ----------------------------------------------------
+--R                                 2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 117
+bb:=-x/2+1/(2*a)*log(sin(a*x)-cos(a*x))
+--R
+--R        log(sin(a x) - cos(a x)) - a x
+--R   (2)  ------------------------------
+--R                      2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 118
+cc:=aa-bb
+--R
+--R   (3)
+--R                                    2sin(a x) - 2cos(a x)              2
+--R   - log(sin(a x) - cos(a x)) + log(---------------------) - log(------------)
+--R                                         cos(a x) + 1            cos(a x) + 1
+--R   ---------------------------------------------------------------------------
+--R                                        2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 119    14:414 Schaums and Axiom agree
+dd:=expandLog cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.415~~~~~$\displaystyle
+\int{\frac{\sin{ax}~dx}{p+q\cos{ax}}}$}
+$$\int{\frac{\sin{ax}}{p+q\cos{ax}}}=
+-\frac{1}{aq}\ln(p+q\cos{ax})
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 120
+aa:=integrate(sin(a*x)/(p+q*cos(a*x)),x)
+--R 
+--R
+--R                  2             - 2q cos(a x) - 2p
+--R        log(------------) - log(------------------)
+--R            cos(a x) + 1           cos(a x) + 1
+--R   (1)  -------------------------------------------
+--R                            a q
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 121
+bb:=-1/(a*q)*log(p+q*cos(a*x))
+--R
+--R          log(q cos(a x) + p)
+--R   (2)  - -------------------
+--R                  a q
+--R                                                     Type: Expression Integer
+--E
+
+--S 122
+cc:=aa-bb
+--R
+--R                                        2             - 2q cos(a x) - 2p
+--R        log(q cos(a x) + p) + log(------------) - log(------------------)
+--R                                  cos(a x) + 1           cos(a x) + 1
+--R   (3)  -----------------------------------------------------------------
+--R                                       a q
+--R                                                     Type: Expression Integer
+--E
+
+--S 123
+dd:=expandLog cc
+--R
+--R        log(q cos(a x) + p) - log(- q cos(a x) - p)
+--R   (4)  -------------------------------------------
+--R                            a q
+--R                                                     Type: Expression Integer
+--E
+
+--S 124    14:415 Schaums and Axiom differ by a constant
+ee:=complexNormalize dd
+--R
+--R        log(- 1)
+--R   (5)  --------
+--R           a q
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.416~~~~~$\displaystyle
+\int{\frac{\cos{ax}~dx}{p+q\sin{ax}}}$}
+$$\int{\frac{\cos{ax}}{p+q\sin{ax}}}=
+\frac{1}{aq}\ln(p+q\sin{ax})
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 125
+aa:=integrate(cos(a*x)/(p+q*sin(a*x)),x)
+--R 
+--R
+--R            2q sin(a x) + 2p              2
+--R        log(----------------) - log(------------)
+--R              cos(a x) + 1          cos(a x) + 1
+--R   (1)  -----------------------------------------
+--R                           a q
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 126
+bb:=1/(a*q)*log(p+q*sin(a*x))
+--R
+--R        log(q sin(a x) + p)
+--R   (2)  -------------------
+--R                a q
+--R                                                     Type: Expression Integer
+--E
+
+--S 127
+cc:=aa-bb
+--R
+--R                                    2q sin(a x) + 2p              2
+--R        - log(q sin(a x) + p) + log(----------------) - log(------------)
+--R                                      cos(a x) + 1          cos(a x) + 1
+--R   (3)  -----------------------------------------------------------------
+--R                                       a q
+--R                                                     Type: Expression Integer
+--E
+
+--S 128    14:416 Schaums and Axiom agree
+dd:=expandLog cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.417~~~~~$\displaystyle
+\int{\frac{\sin{ax}~dx}{(p+q\cos{ax})^n}}$}
+$$\int{\frac{\sin{ax}}{(p+q\cos{ax})^n}}=
+\frac{1}{aq(n-1)(p+q\cos{ax})^{n-1}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 129
+aa:=integrate(sin(a*x)/(p+q*cos(a*x))^n,x)
+--R 
+--R
+--R                  q cos(a x) + p
+--R   (1)  ----------------------------------
+--R                     n log(q cos(a x) + p)
+--R        (a n - a)q %e
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 130
+bb:=1/(a*q*(n-1)*(p+q*cos(a*x))^(n-1))
+--R
+--R                        1
+--R   (2)  --------------------------------
+--R                                   n - 1
+--R        (a n - a)q (q cos(a x) + p)
+--R                                                     Type: Expression Integer
+--E
+
+--S 131
+cc:=aa-bb
+--R
+--R            n log(q cos(a x) + p)                                   n - 1
+--R        - %e                      + (q cos(a x) + p)(q cos(a x) + p)
+--R   (3)  -----------------------------------------------------------------
+--R                                        n - 1  n log(q cos(a x) + p)
+--R             (a n - a)q (q cos(a x) + p)     %e
+--R                                                     Type: Expression Integer
+--E
+
+--S 132
+explog:=rule(%e^(n*log(x)) == x^n)
+--R
+--R          n log(x)     n
+--R   (4)  %e         == x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 133
+dd:=explog cc
+--R
+--R                          n                                   n - 1
+--R        - (q cos(a x) + p)  + (q cos(a x) + p)(q cos(a x) + p)
+--R   (5)  -----------------------------------------------------------
+--R                                        n - 1                n
+--R             (a n - a)q (q cos(a x) + p)     (q cos(a x) + p)
+--R                                                     Type: Expression Integer
+--E
+
+--S 134    14:417 Schaums and Axiom agree
+ee:=complexNormalize dd
+--R
+--R   (6)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.418~~~~~$\displaystyle
+\int{\frac{\cos{ax}~dx}{(p+q\sin{ax})^n}}$}
+$$\int{\frac{\cos{ax}}{(p+q\sin{ax})^n}}=
+\frac{-1}{aq(n-1)(p+q\sin{ax})^{n-1}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 135
+aa:=integrate(cos(a*x)/(p+q*sin(a*x))^n,x)
+--R 
+--R
+--R                 - q sin(a x) - p
+--R   (1)  ----------------------------------
+--R                     n log(q sin(a x) + p)
+--R        (a n - a)q %e
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 136
+bb:=-1/(a*q*(n-1)*(p+q*sin(a*x))^(n-1))
+--R
+--R                          1
+--R   (2)  - --------------------------------
+--R                                     n - 1
+--R          (a n - a)q (q sin(a x) + p)
+--R                                                     Type: Expression Integer
+--E
+
+--S 137
+cc:=aa-bb
+--R
+--R          n log(q sin(a x) + p)                                     n - 1
+--R        %e                      + (- q sin(a x) - p)(q sin(a x) + p)
+--R   (3)  -----------------------------------------------------------------
+--R                                        n - 1  n log(q sin(a x) + p)
+--R             (a n - a)q (q sin(a x) + p)     %e
+--R                                                     Type: Expression Integer
+--E
+
+--S 138
+explog:=rule(%e^(n*log(x)) == x^n)
+--R
+--R          n log(x)     n
+--R   (4)  %e         == x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 139
+dd:=explog cc
+--R
+--R                        n                                     n - 1
+--R        (q sin(a x) + p)  + (- q sin(a x) - p)(q sin(a x) + p)
+--R   (5)  -----------------------------------------------------------
+--R                                        n - 1                n
+--R             (a n - a)q (q sin(a x) + p)     (q sin(a x) + p)
+--R                                                     Type: Expression Integer
+--E
+
+--S 140    14:418 Schaums and Axiom agree
+ee:=complexNormalize dd
+--R
+--R   (6)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.419~~~~~$\displaystyle
+\int{\frac{dx}{p\sin{ax}+q\cos{ax}}}$}
+$$\int{\frac{1}{p\sin{ax}+q\cos{ax}}}=
+\frac{1}{a\sqrt{p^2+q^2}}\ln~\tan\left(\frac{ax+\tan^{-1}(q/p)}{2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 141
+aa:=integrate(1/(p*sin(a*x)+q*cos(a*x)),x)
+--R 
+--R
+--R   (1)
+--R     log
+--R                                                  +-------+
+--R                             2            2    2  | 2    2
+--R            (p q sin(a x) - p cos(a x) - q  - p )\|q  + p
+--R          + 
+--R                3    2                 2    3               2    3
+--R            (- q  - p q)sin(a x) + (p q  + p )cos(a x) + p q  + p
+--R       /
+--R          p sin(a x) + q cos(a x)
+--R  /
+--R       +-------+
+--R       | 2    2
+--R     a\|q  + p
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 142
+bb:=1/(a*sqrt(p^2+q^2))*log(tan((a*x+atan(q/p))/2))
+--R
+--R                     q
+--R                atan(-) + a x
+--R                     p
+--R        log(tan(-------------))
+--R                      2
+--R   (2)  -----------------------
+--R                +-------+
+--R                | 2    2
+--R              a\|q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 143
+cc:=aa-bb
+--R
+--R   (3)
+--R                      q
+--R                 atan(-) + a x
+--R                      p
+--R       - log(tan(-------------))
+--R                       2
+--R     + 
+--R       log
+--R                                                    +-------+
+--R                               2            2    2  | 2    2
+--R              (p q sin(a x) - p cos(a x) - q  - p )\|q  + p
+--R            + 
+--R                  3    2                 2    3               2    3
+--R              (- q  - p q)sin(a x) + (p q  + p )cos(a x) + p q  + p
+--R         /
+--R            p sin(a x) + q cos(a x)
+--R  /
+--R       +-------+
+--R       | 2    2
+--R     a\|q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 144
+dd:=normalize cc
+--R
+--R                            +-------+
+--R                            | 2    2     2     2
+--R                       - 2p\|q  + p   + q  + 2p
+--R          log(------------------------------------------)
+--R                            +-------+
+--R                   2     3  | 2    2     4     2 2     4
+--R              (3p q  + 4p )\|q  + p   - q  - 5p q  - 4p
+--R   (4)  - -----------------------------------------------
+--R                              +-------+
+--R                              | 2    2
+--R                            a\|q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 145    14:419 Schaums and Axiom differ by a constant
+ee:=ratDenom dd
+--R
+--R                            +-------+
+--R           +-------+        | 2    2     2    2
+--R           | 2    2     - p\|q  + p   - q  - p
+--R          \|q  + p  log(-----------------------)
+--R                                4    2 2
+--R                               q  + p q
+--R   (5)  - --------------------------------------
+--R                           2      2
+--R                        a q  + a p
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.420~~~~~$\displaystyle
+\int{\frac{dx}{p\sin{ax}+q\cos{ax}+r}}$}
+$$\int{\frac{1}{p\sin{ax}+q\cos{ax}+r}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{2}{a\sqrt{r^2-p^2-q^q}}
+\tan^{-1}\left(\frac{p+(r-q)\tan(ax/2)}{\sqrt{r^2-p^2-a^2}}\right)\\
+\\
+\displaystyle
+\frac{1}{a\sqrt{p^2+q^2-r^2}}\ln\left(
+\frac{p-\sqrt{p^2+q^2-r^2}+(r-q)\tan{(ax/2)}}
+{p+\sqrt{p^2+q^2-r^2}+(r-q)\tan{(ax/2)}}\right)
+\end{array}
+\right.
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 146
+aa:=integrate(1/(p*sin(a*x)+q*cos(a*x)+r),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R       log
+--R                                              2          2                   2
+--R                    (p r - p q)sin(a x) + (- r  + q r + p )cos(a x) - q r + q
+--R                  + 
+--R                     2
+--R                    p
+--R             *
+--R                 +--------------+
+--R                 |   2    2    2
+--R                \|- r  + q  + p
+--R            + 
+--R                3      2       2    2      3    2
+--R              (r  - q r  + (- q  - p )r + q  + p q)sin(a x)
+--R            + 
+--R                  2      2    3               2      2    3
+--R              (p r  - p q  - p )cos(a x) + p r  - p q  - p
+--R         /
+--R            p sin(a x) + q cos(a x) + r
+--R    /
+--R         +--------------+
+--R         |   2    2    2
+--R       a\|- r  + q  + p
+--R     ,
+--R                                             +------------+
+--R                                             | 2    2    2
+--R          ((r - q)sin(a x) + p cos(a x) + p)\|r  - q  - p
+--R    2atan(-------------------------------------------------)
+--R                  2    2    2             2    2    2
+--R                (r  - q  - p )cos(a x) + r  - q  - p
+--R    --------------------------------------------------------]
+--R                          +------------+
+--R                          | 2    2    2
+--R                        a\|r  - q  - p
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+
+--S 147
+bb1:=2/(a*sqrt(r^2-p^2-q^2))*atan((p+(r-q)*tan((a*x)/2))/sqrt(r^2-p^2-q^2))
+--R
+--R                         a x
+--R              (r - q)tan(---) + p
+--R                          2
+--R        2atan(-------------------)
+--R                 +------------+
+--R                 | 2    2    2
+--R                \|r  - q  - p
+--R   (2)  --------------------------
+--R               +------------+
+--R               | 2    2    2
+--R             a\|r  - q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 148
+bb2:=1/(a*sqrt(p^2+q^2-r^2))*log((p-sqrt(p^2+q^2-r^2)+(r-q)*tan((a*x)/2))/(p+sqrt(p^2+q^2-r^2)+(r-q)*tan((a*x)/2)))
+--R
+--R               +--------------+
+--R               |   2    2    2               a x
+--R            - \|- r  + q  + p   + (r - q)tan(---) + p
+--R                                              2
+--R        log(-----------------------------------------)
+--R              +--------------+
+--R              |   2    2    2               a x
+--R             \|- r  + q  + p   + (r - q)tan(---) + p
+--R                                             2
+--R   (3)  ----------------------------------------------
+--R                        +--------------+
+--R                        |   2    2    2
+--R                      a\|- r  + q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 149
+cc1:=aa.1-bb1
+--R
+--R   (4)
+--R          +------------+
+--R          | 2    2    2
+--R         \|r  - q  - p
+--R      *
+--R         log
+--R                                              2          2                   2
+--R                    (p r - p q)sin(a x) + (- r  + q r + p )cos(a x) - q r + q
+--R                  + 
+--R                     2
+--R                    p
+--R               *
+--R                   +--------------+
+--R                   |   2    2    2
+--R                  \|- r  + q  + p
+--R              + 
+--R                  3      2       2    2      3    2
+--R                (r  - q r  + (- q  - p )r + q  + p q)sin(a x)
+--R              + 
+--R                    2      2    3               2      2    3
+--R                (p r  - p q  - p )cos(a x) + p r  - p q  - p
+--R           /
+--R              p sin(a x) + q cos(a x) + r
+--R     + 
+--R                                           a x
+--R           +--------------+     (r - q)tan(---) + p
+--R           |   2    2    2                  2
+--R       - 2\|- r  + q  + p  atan(-------------------)
+--R                                   +------------+
+--R                                   | 2    2    2
+--R                                  \|r  - q  - p
+--R  /
+--R       +--------------+ +------------+
+--R       |   2    2    2  | 2    2    2
+--R     a\|- r  + q  + p  \|r  - q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 150
+cc2:=aa.2-bb1
+--R
+--R   (5)
+--R                                                +------------+
+--R                                                | 2    2    2
+--R             ((r - q)sin(a x) + p cos(a x) + p)\|r  - q  - p
+--R       2atan(-------------------------------------------------)
+--R                     2    2    2             2    2    2
+--R                   (r  - q  - p )cos(a x) + r  - q  - p
+--R     + 
+--R                          a x
+--R               (r - q)tan(---) + p
+--R                           2
+--R       - 2atan(-------------------)
+--R                  +------------+
+--R                  | 2    2    2
+--R                 \|r  - q  - p
+--R  /
+--R       +------------+
+--R       | 2    2    2
+--R     a\|r  - q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 151
+cc3:=aa.1-bb2
+--R
+--R   (6)
+--R       log
+--R                                              2          2                   2
+--R                    (p r - p q)sin(a x) + (- r  + q r + p )cos(a x) - q r + q
+--R                  + 
+--R                     2
+--R                    p
+--R             *
+--R                 +--------------+
+--R                 |   2    2    2
+--R                \|- r  + q  + p
+--R            + 
+--R                3      2       2    2      3    2
+--R              (r  - q r  + (- q  - p )r + q  + p q)sin(a x)
+--R            + 
+--R                  2      2    3               2      2    3
+--R              (p r  - p q  - p )cos(a x) + p r  - p q  - p
+--R         /
+--R            p sin(a x) + q cos(a x) + r
+--R     + 
+--R                +--------------+
+--R                |   2    2    2               a x
+--R             - \|- r  + q  + p   + (r - q)tan(---) + p
+--R                                               2
+--R       - log(-----------------------------------------)
+--R               +--------------+
+--R               |   2    2    2               a x
+--R              \|- r  + q  + p   + (r - q)tan(---) + p
+--R                                              2
+--R  /
+--R       +--------------+
+--R       |   2    2    2
+--R     a\|- r  + q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 152
+cc4:=aa.2-bb2
+--R
+--R   (7)
+--R                               +--------------+
+--R                               |   2    2    2               a x
+--R          +------------+    - \|- r  + q  + p   + (r - q)tan(---) + p
+--R          | 2    2    2                                       2
+--R       - \|r  - q  - p  log(-----------------------------------------)
+--R                              +--------------+
+--R                              |   2    2    2               a x
+--R                             \|- r  + q  + p   + (r - q)tan(---) + p
+--R                                                             2
+--R     + 
+--R                                                               +------------+
+--R       +--------------+                                        | 2    2    2
+--R       |   2    2    2      ((r - q)sin(a x) + p cos(a x) + p)\|r  - q  - p
+--R     2\|- r  + q  + p  atan(-------------------------------------------------)
+--R                                    2    2    2             2    2    2
+--R                                  (r  - q  - p )cos(a x) + r  - q  - p
+--R  /
+--R       +--------------+ +------------+
+--R       |   2    2    2  | 2    2    2
+--R     a\|- r  + q  + p  \|r  - q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 153    14:420 Schaums and Axiom agree
+dd2:=normalize cc2
+--R
+--R   (8)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.421~~~~~$\displaystyle
+\int{\frac{dx}{p\sin{ax}+q(1+\cos{ax})}}$}
+$$\int{\frac{1}{p\sin{ax}+q(1+\cos{ax})}}=
+\frac{1}{ap}\ln\left(q+p\tan{\frac{ax}{2}}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 154
+aa:=integrate(1/(p*sin(a*x)+q*(1+cos(a*x))),x)
+--R 
+--R
+--R            p sin(a x) + q cos(a x) + q
+--R        log(---------------------------)
+--R                    cos(a x) + 1
+--R   (1)  --------------------------------
+--R                       a p
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 155
+bb:=1/(a*p)*log(q+p*tan((a*x)/2))
+--R
+--R                  a x
+--R        log(p tan(---) + q)
+--R                   2
+--R   (2)  -------------------
+--R                a p
+--R                                                     Type: Expression Integer
+--E 
+
+--S 156
+cc:=aa-bb
+--R
+--R                    a x             p sin(a x) + q cos(a x) + q
+--R        - log(p tan(---) + q) + log(---------------------------)
+--R                     2                      cos(a x) + 1
+--R   (3)  --------------------------------------------------------
+--R                                   a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 157
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (4)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 158
+dd:=tanrule cc
+--R
+--R                                                     a x          a x
+--R                                               p sin(---) + q cos(---)
+--R            p sin(a x) + q cos(a x) + q               2            2
+--R        log(---------------------------) - log(-----------------------)
+--R                    cos(a x) + 1                           a x
+--R                                                       cos(---)
+--R                                                            2
+--R   (5)  ---------------------------------------------------------------
+--R                                      a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 159
+ee:=expandLog dd
+--R
+--R   (6)
+--R                                                    a x          a x
+--R       log(p sin(a x) + q cos(a x) + q) - log(p sin(---) + q cos(---))
+--R                                                     2            2
+--R     + 
+--R                                     a x
+--R       - log(cos(a x) + 1) + log(cos(---))
+--R                                      2
+--R  /
+--R     a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 160    14:421 Schaums and Axiom agree
+ff:=complexNormalize ee
+--R
+--R   (7)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.422~~~~~$\displaystyle
+\int{\frac{dx}{p\sin{ax}+q\cos{ax}\pm\sqrt{p^2+q^2}}}$}
+$$\int{\frac{1}{p\sin{ax}+q\cos{ax}\pm\sqrt{p^2+q^2}}}=
+\frac{-1}{a\sqrt{p^2+q^2}}
+\tan\left(\frac{\pi}{4}\mp\frac{ax+\tan^{-1}{(q/p)}}{2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 161
+aa:=integrate(1/(p*sin(a*x)+q*cos(a*x)+sqrt(p^2+q^2)),x)
+--R 
+--R
+--R   (1)
+--R                                                                 +-------+
+--R            5      2 3      4                5      2 3      4   | 2    2
+--R       ((64q  + 64p q  + 12p q)cos(a x) + 64q  + 64p q  + 12p q)\|q  + p
+--R     + 
+--R             6      2 4      4 2     6               6      2 4      4 2     6
+--R       (- 64q  - 96p q  - 36p q  - 2p )cos(a x) - 64q  - 96p q  - 36p q  - 2p
+--R  /
+--R                 6        2 4        4 2      6
+--R           (64a q  + 80a p q  + 24a p q  + a p )sin(a x)
+--R         + 
+--R                   5        3 3       5                    5        3 3       5
+--R         (- 32a p q  - 32a p q  - 6a p q)cos(a x) - 32a p q  - 32a p q  - 6a p q
+--R      *
+--R          +-------+
+--R          | 2    2
+--R         \|q  + p
+--R     + 
+--R               7         2 5        4 3       6
+--R       (- 64a q  - 112a p q  - 56a p q  - 7a p q)sin(a x)
+--R     + 
+--R               6        3 4        5 2      7                   6        3 4
+--R       (32a p q  + 48a p q  + 18a p q  + a p )cos(a x) + 32a p q  + 48a p q
+--R     + 
+--R            5 2      7
+--R       18a p q  + a p
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 162
+bb:=-1/(a*sqrt(p^2+q^2))*tan(%pi/4-(a*x+atan(q/p))/2)
+--R
+--R                  q
+--R            2atan(-) + 2a x - %pi
+--R                  p
+--R        tan(---------------------)
+--R                      4
+--R   (2)  --------------------------
+--R                  +-------+
+--R                  | 2    2
+--R                a\|q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 163
+cc:=aa-bb
+--R
+--R   (3)
+--R                   6      2 4      4 2    6
+--R               (64q  + 80p q  + 24p q  + p )sin(a x)
+--R             + 
+--R                       5      3 3     5                  5      3 3     5
+--R               (- 32p q  - 32p q  - 6p q)cos(a x) - 32p q  - 32p q  - 6p q
+--R          *
+--R              +-------+
+--R              | 2    2
+--R             \|q  + p
+--R         + 
+--R                 7       2 5      4 3     6
+--R           (- 64q  - 112p q  - 56p q  - 7p q)sin(a x)
+--R         + 
+--R               6      3 4      5 2    7                 6      3 4      5 2    7
+--R         (32p q  + 48p q  + 18p q  + p )cos(a x) + 32p q  + 48p q  + 18p q  + p
+--R      *
+--R                   q
+--R             2atan(-) + 2a x - %pi
+--R                   p
+--R         tan(---------------------)
+--R                       4
+--R     + 
+--R              6      2 4      4 2     6               6      2 4      4 2     6
+--R         ((64q  + 96p q  + 36p q  + 2p )cos(a x) + 64q  + 96p q  + 36p q  + 2p )
+--R      *
+--R          +-------+
+--R          | 2    2
+--R         \|q  + p
+--R     + 
+--R             7       2 5      4 3      6                7       2 5      4 3
+--R       (- 64q  - 128p q  - 76p q  - 12p q)cos(a x) - 64q  - 128p q  - 76p q
+--R     + 
+--R            6
+--R       - 12p q
+--R  /
+--R                 7         2 5        4 3       6
+--R           (64a q  + 112a p q  + 56a p q  + 7a p q)sin(a x)
+--R         + 
+--R                     6        3 4        5 2      7                   6
+--R           (- 32a p q  - 48a p q  - 18a p q  - a p )cos(a x) - 32a p q
+--R         + 
+--R                  3 4        5 2      7
+--R           - 48a p q  - 18a p q  - a p
+--R      *
+--R          +-------+
+--R          | 2    2
+--R         \|q  + p
+--R     + 
+--R               8         2 6         4 4        6 2      8
+--R       (- 64a q  - 144a p q  - 104a p q  - 25a p q  - a p )sin(a x)
+--R     + 
+--R               7        3 5        5 3       7                    7        3 5
+--R       (32a p q  + 64a p q  + 38a p q  + 6a p q)cos(a x) + 32a p q  + 64a p q
+--R     + 
+--R            5 3       7
+--R       38a p q  + 6a p q
+--R                                                     Type: Expression Integer
+--E
+
+--S 164
+dd:=normalize cc
+--R
+--R   (4)
+--R                                                                  +-------+
+--R               6      2 5      3 4      4 3      5 2     6     7  | 2    2
+--R       (- 32p q  - 16p q  - 48p q  - 20p q  - 18p q  - 5p q - p )\|q  + p
+--R     + 
+--R            7      2 6      3 5      4 4      5 3      6 2     7     8
+--R       32p q  + 16p q  + 64p q  + 28p q  + 38p q  + 13p q  + 6p q + p
+--R  /
+--R                8          7         2 6        3 5         4 4        5 3
+--R           64a q  + 32a p q  + 144a p q  + 64a p q  + 104a p q  + 38a p q
+--R         + 
+--R                6 2       7       8
+--R           25a p q  + 6a p q + a p
+--R      *
+--R          +-------+
+--R          | 2    2
+--R         \|q  + p
+--R     + 
+--R              9          8         2 7        3 6         4 5        5 4
+--R       - 64a q  - 32a p q  - 176a p q  - 80a p q  - 168a p q  - 66a p q
+--R     + 
+--R              6 3        7 2       8       9
+--R       - 63a p q  - 19a p q  - 7a p q - a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 165
+ee:=ratDenom dd
+--R
+--R            +-------+
+--R            | 2    2     2    2
+--R        - q\|q  + p   - q  - p
+--R   (5)  -----------------------
+--R                  2      3
+--R             a p q  + a p
+--R                                                     Type: Expression Integer
+--E
+
+)clear all
+
+--S 166
+aa:=integrate(1/(p*sin(a*x)+q*cos(a*x)-sqrt(p^2+q^2)),x)
+--R 
+--R
+--R   (1)
+--R                                                                 +-------+
+--R            5      2 3      4                5      2 3      4   | 2    2
+--R       ((64q  + 64p q  + 12p q)cos(a x) + 64q  + 64p q  + 12p q)\|q  + p
+--R     + 
+--R           6      2 4      4 2     6               6      2 4      4 2     6
+--R       (64q  + 96p q  + 36p q  + 2p )cos(a x) + 64q  + 96p q  + 36p q  + 2p
+--R  /
+--R                 6        2 4        4 2      6
+--R           (64a q  + 80a p q  + 24a p q  + a p )sin(a x)
+--R         + 
+--R                   5        3 3       5                    5        3 3       5
+--R         (- 32a p q  - 32a p q  - 6a p q)cos(a x) - 32a p q  - 32a p q  - 6a p q
+--R      *
+--R          +-------+
+--R          | 2    2
+--R         \|q  + p
+--R     + 
+--R             7         2 5        4 3       6
+--R       (64a q  + 112a p q  + 56a p q  + 7a p q)sin(a x)
+--R     + 
+--R                 6        3 4        5 2      7                   6        3 4
+--R       (- 32a p q  - 48a p q  - 18a p q  - a p )cos(a x) - 32a p q  - 48a p q
+--R     + 
+--R              5 2      7
+--R       - 18a p q  - a p
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 167
+bb:=-1/(a*sqrt(p^2+q^2))*tan(%pi/4+(a*x+atan(q/p))/2)
+--R
+--R                    q
+--R              2atan(-) + 2a x + %pi
+--R                    p
+--R          tan(---------------------)
+--R                        4
+--R   (2)  - --------------------------
+--R                    +-------+
+--R                    | 2    2
+--R                  a\|q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 168
+cc:=aa-bb
+--R
+--R   (3)
+--R                   6      2 4      4 2    6
+--R               (64q  + 80p q  + 24p q  + p )sin(a x)
+--R             + 
+--R                       5      3 3     5                  5      3 3     5
+--R               (- 32p q  - 32p q  - 6p q)cos(a x) - 32p q  - 32p q  - 6p q
+--R          *
+--R              +-------+
+--R              | 2    2
+--R             \|q  + p
+--R         + 
+--R               7       2 5      4 3     6
+--R           (64q  + 112p q  + 56p q  + 7p q)sin(a x)
+--R         + 
+--R                   6      3 4      5 2    7                 6      3 4      5 2
+--R           (- 32p q  - 48p q  - 18p q  - p )cos(a x) - 32p q  - 48p q  - 18p q
+--R         + 
+--R              7
+--R           - p
+--R      *
+--R                   q
+--R             2atan(-) + 2a x + %pi
+--R                   p
+--R         tan(---------------------)
+--R                       4
+--R     + 
+--R              6      2 4      4 2     6               6      2 4      4 2     6
+--R         ((64q  + 96p q  + 36p q  + 2p )cos(a x) + 64q  + 96p q  + 36p q  + 2p )
+--R      *
+--R          +-------+
+--R          | 2    2
+--R         \|q  + p
+--R     + 
+--R         7       2 5      4 3      6                7       2 5      4 3      6
+--R     (64q  + 128p q  + 76p q  + 12p q)cos(a x) + 64q  + 128p q  + 76p q  + 12p q
+--R  /
+--R                 7         2 5        4 3       6
+--R           (64a q  + 112a p q  + 56a p q  + 7a p q)sin(a x)
+--R         + 
+--R                     6        3 4        5 2      7                   6
+--R           (- 32a p q  - 48a p q  - 18a p q  - a p )cos(a x) - 32a p q
+--R         + 
+--R                  3 4        5 2      7
+--R           - 48a p q  - 18a p q  - a p
+--R      *
+--R          +-------+
+--R          | 2    2
+--R         \|q  + p
+--R     + 
+--R             8         2 6         4 4        6 2      8
+--R       (64a q  + 144a p q  + 104a p q  + 25a p q  + a p )sin(a x)
+--R     + 
+--R                 7        3 5        5 3       7                    7        3 5
+--R       (- 32a p q  - 64a p q  - 38a p q  - 6a p q)cos(a x) - 32a p q  - 64a p q
+--R     + 
+--R              5 3       7
+--R       - 38a p q  - 6a p q
+--R                                                     Type: Expression Integer
+--E
+
+--S 169
+dd:=normalize cc
+--R
+--R   (4)
+--R                                                                  +-------+
+--R               6      2 5      3 4      4 3      5 2     6     7  | 2    2
+--R       (- 32p q  + 16p q  - 48p q  + 20p q  - 18p q  + 5p q - p )\|q  + p
+--R     + 
+--R              7      2 6      3 5      4 4      5 3      6 2     7     8
+--R       - 32p q  + 16p q  - 64p q  + 28p q  - 38p q  + 13p q  - 6p q + p
+--R  /
+--R                8          7         2 6        3 5         4 4        5 3
+--R           64a q  - 32a p q  + 144a p q  - 64a p q  + 104a p q  - 38a p q
+--R         + 
+--R                6 2       7       8
+--R           25a p q  - 6a p q + a p
+--R      *
+--R          +-------+
+--R          | 2    2
+--R         \|q  + p
+--R     + 
+--R            9          8         2 7        3 6         4 5        5 4
+--R       64a q  - 32a p q  + 176a p q  - 80a p q  + 168a p q  - 66a p q
+--R     + 
+--R            6 3        7 2       8       9
+--R       63a p q  - 19a p q  + 7a p q - a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 170    14:422 Schaums and Axiom differ by a constant
+ee:=ratDenom dd
+--R
+--R          +-------+
+--R          | 2    2     2    2
+--R        q\|q  + p   - q  - p
+--R   (5)  ---------------------
+--R                 2      3
+--R            a p q  + a p
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.423~~~~~$\displaystyle
+\int{\frac{dx}{p^2\sin^2{ax}+q^2\cos^2{ax}}}$}
+$$\int{\frac{1}{p^2\sin^2{ax}+q^2\cos^2{ax}}}=
+\frac{1}{apq}\tan^{-1}\left(\frac{p\tan{ax}}{q}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 171
+aa:=integrate(1/(p^2*sin(a*x)^2+q^2*cos(a*x)^2),x)
+--R 
+--R
+--R                   2     2              2
+--R                ((q  - 2p )cos(a x) - 2p )sin(a x)            q sin(a x)
+--R        - atan(-----------------------------------) + atan(----------------)
+--R                           2                               2p cos(a x) + 2p
+--R               p q cos(a x)  + 2p q cos(a x) + p q
+--R   (1)  --------------------------------------------------------------------
+--R                                        a p q
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 172
+bb:=1/(a*p*q)*atan((p*tan(a*x))/q)
+--R
+--R             p tan(a x)
+--R        atan(----------)
+--R                  q
+--R   (2)  ----------------
+--R              a p q
+--R                                                     Type: Expression Integer
+--E
+
+--S 173
+cc:=aa-bb
+--R
+--R   (3)
+--R                                     2     2              2
+--R              p tan(a x)          ((q  - 2p )cos(a x) - 2p )sin(a x)
+--R       - atan(----------) - atan(-----------------------------------)
+--R                   q                         2
+--R                                 p q cos(a x)  + 2p q cos(a x) + p q
+--R     + 
+--R               q sin(a x)
+--R       atan(----------------)
+--R            2p cos(a x) + 2p
+--R  /
+--R     a p q
+--R                                                     Type: Expression Integer
+--E
+
+--S 174    14:423 Schaums and Axiom agree
+dd:=normalize cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
+
+
+@
+
+\section{\cite{1}:14.424~~~~~$\displaystyle
+\int{\frac{dx}{p^2\sin^2{ax}-q^2\cos^2{ax}}}$}
+$$\int{\frac{1}{p^2\sin^2{ax}-q^2\cos^2{ax}}}=
+\frac{1}{2apq}\ln\left(\frac{p\tan{ax}-q}{p\tan{ax}+q}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 175
+aa:=integrate(1/(p^2*sin(a*x)^2-q^2*cos(a*x)^2),x)
+--R 
+--R
+--R            2p sin(a x) - 2q cos(a x)        - 2p sin(a x) - 2q cos(a x)
+--R        log(-------------------------) - log(---------------------------)
+--R                   cos(a x) + 1                      cos(a x) + 1
+--R   (1)  -----------------------------------------------------------------
+--R                                      2a p q
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 176
+bb:=1/(2*a*p*q)*log((p*tan(a*x)-q)/(p*tan(a*x)+q))
+--R
+--R            p tan(a x) - q
+--R        log(--------------)
+--R            p tan(a x) + q
+--R   (2)  -------------------
+--R               2a p q
+--R                                                     Type: Expression Integer
+--E 
+
+--S 177
+cc:=aa-bb
+--R
+--R   (3)
+--R           2p sin(a x) - 2q cos(a x)        p tan(a x) - q
+--R       log(-------------------------) - log(--------------)
+--R                  cos(a x) + 1              p tan(a x) + q
+--R     + 
+--R             - 2p sin(a x) - 2q cos(a x)
+--R       - log(---------------------------)
+--R                     cos(a x) + 1
+--R  /
+--R     2a p q
+--R                                                     Type: Expression Integer
+--E
+
+--S 178
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (4)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 179
+dd:=tanrule cc
+--R
+--R   (5)
+--R           2p sin(a x) - 2q cos(a x)        p sin(a x) - q cos(a x)
+--R       log(-------------------------) - log(-----------------------)
+--R                  cos(a x) + 1              p sin(a x) + q cos(a x)
+--R     + 
+--R             - 2p sin(a x) - 2q cos(a x)
+--R       - log(---------------------------)
+--R                     cos(a x) + 1
+--R  /
+--R     2a p q
+--R                                                     Type: Expression Integer
+--E
+
+--S 180
+ee:=expandLog dd
+--R
+--R        log(p sin(a x) + q cos(a x)) - log(- p sin(a x) - q cos(a x))
+--R   (6)  -------------------------------------------------------------
+--R                                    2a p q
+--R                                                     Type: Expression Integer
+--E
+
+--S 181    14:424 Schaums and Axiom differ by a constant
+ff:=complexNormalize ee
+--R
+--R        log(- 1)
+--R   (7)  --------
+--R         2a p q
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.425~~~~~$\displaystyle
+\int{\sin^m{ax}\cos^n{ax}}~dx$}
+$$\int{\sin^m{ax}\cos^n{ax}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+-\frac{\sin^{m-1}{ax}\cos^{n+1}ax}{a(m+n)}
++\frac{m-1}{m+n}\int{\sin^{m-2}{ax}\cos^n{ax}}\\
+\\
+\displaystyle
+\frac{\sin^{m+1}{ax}\cos^{n-1}{ax}}{a(m+n)}
++\frac{n-1}{m+n}\int{\sin^m{ax}\cos^{n-2}{ax}}
+\end{array}
+\right.
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 182    14:425 Axiom cannot compute this integral
+aa:=integrate(sin(a*x)^m*cos(a*x)^n,x)
+--R 
+--R
+--R           x
+--R         ++           n         m
+--I   (1)   |   cos(%H a) sin(%H a) d%H
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.426~~~~~$\displaystyle
+\int{\frac{\sin^m{ax}}{\cos^n{ax}}}~dx$}
+$$\int{\frac{\sin^m{ax}}{\cos^n{ax}}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{\sin^{m-1}{ax}}{a(n-1)\cos^{n-1}{ax}}
+-\frac{m-1}{n-1}\int{\frac{\sin^{m-2}{ax}}{\cos^{n-2}{ax}}}\\
+\\
+\displaystyle
+\frac{\sin^{m+1}{ax}}{a(n-1)\cos^{n-1}{ax}}
+-\frac{m-n+2}{n-1}\int{\frac{\sin^m{ax}}{\cos^{n-2}{ax}}}\\
+\\
+\displaystyle
+\frac{-\sin^{m-1}{ax}}{a(m-n)\cos^{n-1}{ax}}
++\frac{m-1}{m-n}\int{\frac{\sin^{m-2}{ax}}{\cos^n{ax}}}
+\end{array}
+\right.
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 183    14:426 Axiom cannot compute this integral
+aa:=integrate(sin(a*x)^m/cos(a*x)^n,x)
+--R 
+--R
+--R           x          m
+--I         ++  sin(%H a)
+--I   (1)   |   ---------- d%H
+--R        ++            n
+--I             cos(%H a)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.427~~~~~$\displaystyle
+\int{\frac{\cos^m{ax}}{\sin^n{ax}}}~dx$}
+$$\int{\frac{\cos^m{ax}}{\sin^n{ax}}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{-\cos^{m-1}{ax}}{a(n-1)\sin^{n-1}{ax}}
+-\frac{m-1}{n-1}\int{\frac{\cos^{m-2}{ax}}{\sin^{n-2}{ax}}}\\
+\\
+\displaystyle
+\frac{-\cos^{m+1}{ax}}{a(n-1)\sin^{n-1}{ax}}
+-\frac{m-n+2}{n-1}\int{\frac{\cos^m{ax}}{\sin^{n-2}{ax}}}\\
+\\
+\displaystyle
+\frac{\cos^{m-1}{ax}}{a(m-n)\sin^{n-1}{ax}}
++\frac{m-1}{m-n}\int{\frac{\cos^{m-2}{ax}}{\sin^n{ax}}}
+\end{array}
+\right.
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 184    14:427 Axiom cannot compute this integral
+aa:=integrate(cos(a*x)^m/sin(a*x)^n,x)
+--R 
+--R
+--R           x          m
+--I         ++  cos(%H a)
+--I   (1)   |   ---------- d%H
+--R        ++            n
+--I             sin(%H a)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.428~~~~~$\displaystyle
+\int{\frac{dx}{\sin^m{ax}\cos^n{ax}}}$}
+$$\int{\frac{1}{\sin^m{ax}\cos^n{ax}}}
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{1}{a(n-1)\sin^{m-1}{ax}\cos^{n-1}{ax}}
++\frac{m+n-2}{n-1}\int{\frac{1}{\sin^m{ax}\cos^{n-2}{ax}}}\\
+\\
+\displaystyle
+\frac{-1}{a(m-1)\sin^{m-1}{ax}\cos^{n-1}{ax}}
++\frac{m+n-2}{m-1}\int{\frac{1}{\sin^{m-2}{ax}\cos^n{ax}}}
+\end{array}
+\right.
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 185    14:428 Axiom cannot compute this integral
+aa:=integrate(1/(sin(a*x)^m*cos(a*x)^n),x)
+--R 
+--R
+--R           x
+--R         ++            1
+--I   (1)   |   -------------------- d%H
+--R        ++            n         m
+--I             cos(%H a) sin(%H a)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 pp78-80
+\end{thebibliography}
+\end{document}
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diff --git a/src/axiom-website/CATS/schaum2.input.pamphlet b/src/axiom-website/CATS/schaum2.input.pamphlet
new file mode 100644
index 0000000..7a4ef98
--- /dev/null
+++ b/src/axiom-website/CATS/schaum2.input.pamphlet
@@ -0,0 +1,1549 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum2.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.84~~~~~$\displaystyle
+\int{\frac{dx}{\sqrt{ax+b}}}$}
+$$\int{\frac{1}{\sqrt{ax+b}}}=
+\frac{2\sqrt{ax+b}}{a}
+$$
+&lt;&lt;*&gt;&gt;=
+)spool schaum2.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1
+aa:=integrate(1/sqrt(a*x+b),x)
+--R 
+--R
+--R          +-------+
+--R        2\|a x + b
+--R   (1)  -----------
+--R             a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 2
+bb:=(2*sqrt(a*x+b))/a
+--R 
+--R
+--R          +-------+
+--R        2\|a x + b
+--R   (2)  -----------
+--R             a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3      14:84 Schaums and Axiom agree
+cc:=aa-bb
+--R 
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.85~~~~~$\displaystyle
+\int{\frac{x~dx}{\sqrt{ax+b}}}$}
+$$\int{\frac{x}{\sqrt{ax+b}}}=
+\frac{2(ax-2b)}{3a^2}\sqrt{ax+b}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 4
+aa:=integrate(x/sqrt(a*x+b),x)
+--R 
+--R
+--R                    +-------+
+--R        (2a x - 4b)\|a x + b
+--R   (1)  ---------------------
+--R                   2
+--R                 3a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 5
+bb:=(2*(a*x-2*b))/(3*a^2)*sqrt(a*x+b)
+--R 
+--R
+--R                    +-------+
+--R        (2a x - 4b)\|a x + b
+--R   (2)  ---------------------
+--R                   2
+--R                 3a
+--R                                                     Type: Expression Integer
+--E
+
+--S 6      14:85 Schaums and Axiom agree
+cc:=aa-bb
+--R 
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.86~~~~~$\displaystyle
+\int{\frac{x^2~dx}{\sqrt{ax+b}}}$}
+$$\int{\frac{x}{\sqrt{ax+b}}}=
+\frac{2(3a^2x^2-4abx+8b^2)}{15a^2}\sqrt{ax+b}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 7
+aa:=integrate(x^2/sqrt(a*x+b),x)
+--R 
+--R
+--R           2 2               2  +-------+
+--R        (6a x  - 8a b x + 16b )\|a x + b
+--R   (1)  ---------------------------------
+--R                          3
+--R                       15a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 8
+bb:=(2*(3*a^2*x^2-4*a*b*x+8*b^2))/(15*a^3)*sqrt(a*x+b)
+--R 
+--R
+--R           2 2               2  +-------+
+--R        (6a x  - 8a b x + 16b )\|a x + b
+--R   (2)  ---------------------------------
+--R                          3
+--R                       15a
+--R                                                     Type: Expression Integer
+--E
+
+--S 9      14:86 Schaums and Axiom agree
+cc:=aa-bb
+--R 
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.87~~~~~$\displaystyle
+\int{\frac{dx}{x\sqrt{ax+b}}}$}
+$$\int{\frac{1}{x\sqrt{ax+b}}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{1}{\sqrt{b}}~\ln
+\left(\frac{\sqrt{ax+b}-\sqrt{b}}{\sqrt{ax+b}+\sqrt{b}}\right)\\
+\displaystyle
+\frac{2}{\sqrt{-b}}~\tan^{-1}\sqrt{\frac{ax+b}{-b}}
+\end{array}
+\right.
+$$
+
+Note: the first answer assumes $b &gt; 0$ and the second assumes $b &lt; 0$.
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 10
+aa:=integrate(1/(x*sqrt(a*x+b)),x)
+--R 
+--R
+--R                  +-------+              +-+           +---+ +-------+
+--R             - 2b\|a x + b  + (a x + 2b)\|b           \|- b \|a x + b
+--R         log(-------------------------------)   2atan(----------------)
+--R                            x                                 b
+--R   (1)  [------------------------------------,- -----------------------]
+--R                          +-+                             +---+
+--R                         \|b                             \|- b
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+@
+Cleary Spiegel's first answer assumes $b &gt; 0$:
+&lt;&lt;*&gt;&gt;=
+--S 11
+bb1:=1/sqrt(b)*log((sqrt(a*x+b)-sqrt(b))/(sqrt(a*x+b)+sqrt(b)))
+--R 
+--R
+--R             +-------+    +-+
+--R            \|a x + b  - \|b
+--R        log(-----------------)
+--R             +-------+    +-+
+--R            \|a x + b  + \|b
+--R   (2)  ----------------------
+--R                  +-+
+--R                 \|b
+--R                                                     Type: Expression Integer
+--E
+@
+So we try the difference of the two results
+&lt;&lt;*&gt;&gt;=
+--S 12
+cc11:=aa.1-bb1
+--R
+--R               +-------+    +-+             +-------+              +-+
+--R              \|a x + b  - \|b         - 2b\|a x + b  + (a x + 2b)\|b
+--R        - log(-----------------) + log(-------------------------------)
+--R               +-------+    +-+                       x
+--R              \|a x + b  + \|b
+--R   (3)  ---------------------------------------------------------------
+--R                                       +-+
+--R                                      \|b
+--R                                                     Type: Expression Integer
+--E
+@
+But the results don't simplify to 0. So we try some other tricks.
+
+Since both functions are of the form log(f(x))/sqrt(b) we extract
+the f(x) from each. First we get the function from Axiom's first answer:
+&lt;&lt;*&gt;&gt;=
+--S 13
+ff:=exp(aa.1*sqrt(b))
+--R
+--R             +-------+              +-+
+--R        - 2b\|a x + b  + (a x + 2b)\|b
+--R   (4)  -------------------------------
+--R                       x
+--R                                                     Type: Expression Integer
+--E
+@
+and we get the same form from Spiegel's answer
+&lt;&lt;*&gt;&gt;=
+--S 14
+gg:=exp(bb1*sqrt(b))
+--R
+--R         +-------+    +-+
+--R        \|a x + b  - \|b
+--R   (5)  -----------------
+--R         +-------+    +-+
+--R        \|a x + b  + \|b
+--R                                                     Type: Expression Integer
+--E
+@
+We can change Spiegel's form into Axiom's form because they differ by
+the constant a*sqrt(b). To see this we multiply the numerator and
+denominator by $1 == (sqrt(a*x+b) - sqrt(b))/(sqrt(a*x+b) - sqrt(b))$.
+
+First we multiply the numerator by $(sqrt(a*x+b) - sqrt(b))$
+&lt;&lt;*&gt;&gt;=
+--S 15
+gg1:=gg*(sqrt(a*x+b) - sqrt(b))
+--R
+--R            +-+ +-------+
+--R        - 2\|b \|a x + b  + a x + 2b
+--R   (6)  ----------------------------
+--R               +-------+    +-+
+--R              \|a x + b  + \|b
+--R                                                     Type: Expression Integer
+--E
+@
+Now we multiply the denominator by $(sqrt(a*x+b) - sqrt(b))$
+&lt;&lt;*&gt;&gt;=
+--S 16
+gg2:=gg1/(sqrt(a*x+b) - sqrt(b))
+--R
+--R            +-+ +-------+
+--R        - 2\|b \|a x + b  + a x + 2b
+--R   (7)  ----------------------------
+--R                     a x
+--R                                                     Type: Expression Integer
+--E
+@
+and now we multiply by the integration constant $a*sqrt(b)$
+&lt;&lt;*&gt;&gt;=
+--S 17
+gg3:=gg2*(a*sqrt(b))
+--R
+--R             +-------+              +-+
+--R        - 2b\|a x + b  + (a x + 2b)\|b
+--R   (8)  -------------------------------
+--R                       x
+--R                                                     Type: Expression Integer
+--E
+@
+and when we difference this with ff, the Axiom answer we get:
+&lt;&lt;*&gt;&gt;=
+--S 18     14:87a Schaums and Axiom differ by a constant
+ff-gg3
+--R
+--R   (9)  0
+--R                                                     Type: Expression Integer
+--E
+@
+So the constant of integration difference is $a*sqrt(b)$
+
+Now we look at the second equations. We difference Axiom's second answer
+from Spiegel's answer:
+&lt;&lt;*&gt;&gt;=
+--S 19
+t1:=aa.2-bb1
+--R
+--R                      +-------+    +-+               +---+ +-------+
+--R            +---+    \|a x + b  - \|b       +-+     \|- b \|a x + b
+--R         - \|- b log(-----------------) - 2\|b atan(----------------)
+--R                      +-------+    +-+                      b
+--R                     \|a x + b  + \|b
+--R   (10)  ------------------------------------------------------------
+--R                                   +---+ +-+
+--R                                  \|- b \|b
+--R                                                     Type: Expression Integer
+--E
+@
+and again they do not simplify to zero. But we can show that both answers
+differ by a constant because the derivative is zero:
+&lt;&lt;*&gt;&gt;=
+--S 20
+D(t1,x)
+--R
+--R   (11)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+Rather than find the constant this time we will differentiate both
+answers and compare them with the original equation.
+&lt;&lt;*&gt;&gt;=
+--S 21
+target:=1/(x*sqrt(a*x+b))
+--R
+--R              1
+--R   (12)  -----------
+--R           +-------+
+--R         x\|a x + b
+--R                                                     Type: Expression Integer
+--E
+@
+and we select the second Axiom solution
+&lt;&lt;*&gt;&gt;=
+--S 22
+aa2:=aa.2
+--R
+--R                  +---+ +-------+
+--R                 \|- b \|a x + b
+--R           2atan(----------------)
+--R                         b
+--R   (13)  - -----------------------
+--R                     +---+
+--R                    \|- b
+--R                                                     Type: Expression Integer
+--E
+@
+take its derivative
+&lt;&lt;*&gt;&gt;=
+--S 23
+ad2:=D(aa2,x)
+--R
+--R              1
+--R   (14)  -----------
+--R           +-------+
+--R         x\|a x + b
+--R                                                     Type: Expression Integer
+--E
+@
+When we take the difference of Axiom's input and the derivative of the
+output we see:
+&lt;&lt;*&gt;&gt;=
+--S 24
+ad2-target
+--R
+--R   (15)  0
+--R                                                     Type: Expression Integer
+--E
+@
+Thus the original equation and Axiom's derivative of the integral are equal.
+
+Now we do the same with Spiegel's answer. We take the derivative of his
+answer.
+&lt;&lt;*&gt;&gt;=
+--S 25
+ab1:=D(bb1,x)
+--R
+--R                +-------+    +-+
+--R               \|a x + b  + \|b
+--R   (16)  ----------------------------
+--R           +-+ +-------+      2
+--R         x\|b \|a x + b  + a x  + b x
+--R                                                     Type: Expression Integer
+--E
+@
+and we difference it from the original equation
+&lt;&lt;*&gt;&gt;=
+--S 26     14:87b Schaums and Axiom differ by a constant
+ab1-target
+--R
+--R   (17)  0
+--R                                                     Type: Expression Integer
+--E
+@
+Thus the original equation and Spiegel's derivative of the integral are equal.
+
+So we can conclude that both second answers are correct although they differ
+by a constant of integration.
+
+\section{\cite{1}:14.88~~~~~$\displaystyle
+\int{\frac{dx}{x^2\sqrt{ax+b}}}$}
+$$\int{\frac{1}{x^2\sqrt{ax+b}}}=
+-\frac{\sqrt{ax+b}}{bx}-\frac{a}{2b}~\int{\frac{1}{x\sqrt{ax+b}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 27
+aa:=integrate(1/(x^2*sqrt(a*x+b)),x)
+--R 
+--R
+--R   (1)
+--R               +-------+              +-+
+--R            2b\|a x + b  + (a x + 2b)\|b       +-+ +-------+
+--R    a x log(-----------------------------) - 2\|b \|a x + b
+--R                          x
+--R   [--------------------------------------------------------,
+--R                                 +-+
+--R                            2b x\|b
+--R              +---+ +-------+
+--R             \|- b \|a x + b      +---+ +-------+
+--R    a x atan(----------------) - \|- b \|a x + b
+--R                     b
+--R    ---------------------------------------------]
+--R                          +---+
+--R                      b x\|- b
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+@
+
+In order to write down the book answer we need to first take the
+integral which has two results
+&lt;&lt;*&gt;&gt;=
+--S 28
+dd:=integrate(1/(x*sqrt(a*x+b)),x)
+--R 
+--R
+--R                  +-------+              +-+           +---+ +-------+
+--R             - 2b\|a x + b  + (a x + 2b)\|b           \|- b \|a x + b
+--R         log(-------------------------------)   2atan(----------------)
+--R                            x                                 b
+--R   (2)  [------------------------------------,- -----------------------]
+--R                          +-+                             +---+
+--R                         \|b                             \|- b
+--R                                     Type: Union(List Expression Integer,...)
+--E
+@
+and derive two results for the book answer. The first result assumes
+$b &gt; 0$
+&lt;&lt;*&gt;&gt;=
+--S 29
+bb1:=-sqrt(a*x+b)/(b*x)-a/(2*b)*dd.1
+--R 
+--R
+--R                       +-------+              +-+
+--R                  - 2b\|a x + b  + (a x + 2b)\|b       +-+ +-------+
+--R        - a x log(-------------------------------) - 2\|b \|a x + b
+--R                                 x
+--R   (3)  ------------------------------------------------------------
+--R                                       +-+
+--R                                  2b x\|b
+--R                                                     Type: Expression Integer
+--E
+@
+and the second result assumes $b &lt; 0$.
+&lt;&lt;*&gt;&gt;=
+--S 30
+bb2:=-sqrt(a*x+b)/(b*x)-a/(2*b)*dd.2
+--R 
+--R
+--R                  +---+ +-------+
+--R                 \|- b \|a x + b      +---+ +-------+
+--R        a x atan(----------------) - \|- b \|a x + b
+--R                         b
+--R   (4)  ---------------------------------------------
+--R                              +---+
+--R                          b x\|- b
+--R                                                     Type: Expression Integer
+--E
+@
+
+So we compute the difference of Axiom's first result with Spiegel's
+first result
+&lt;&lt;*&gt;&gt;=
+--S 31
+cc11:=bb1-aa.1
+--R
+--R   (5)
+--R                  +-------+              +-+
+--R               2b\|a x + b  + (a x + 2b)\|b
+--R       - a log(-----------------------------)
+--R                             x
+--R     + 
+--R                    +-------+              +-+
+--R               - 2b\|a x + b  + (a x + 2b)\|b
+--R       - a log(-------------------------------)
+--R                              x
+--R  /
+--R        +-+
+--R     2b\|b
+--R                                                     Type: Expression Integer
+--E
+@
+we compute its derivative
+&lt;&lt;*&gt;&gt;=
+--S 32
+D(cc11,x)
+--R
+--R   (6)  0
+--R                                                     Type: Expression Integer
+--E
+@
+and we can see that the answers differ by a constant, the constant of
+integration. So Axiom's first answer should differentiate back to the target
+equation.
+&lt;&lt;*&gt;&gt;=
+--S 33
+target:=1/(x^2*sqrt(a*x+b))
+--R
+--R              1
+--R   (7)  ------------
+--R         2 +-------+
+--R        x \|a x + b
+--R                                                     Type: Expression Integer
+--E
+@
+We differentiate Axiom's first answer
+&lt;&lt;*&gt;&gt;=
+--S 34
+ad1:=D(aa.1,x)
+--R
+--R                             +-+ +-------+              2
+--R                  (a x + 2b)\|b \|a x + b  + 2a b x + 2b
+--R   (8)  ----------------------------------------------------------
+--R               3     2 2  +-------+     2 4         3     2 2  +-+
+--R        (2a b x  + 2b x )\|a x + b  + (a x  + 3a b x  + 2b x )\|b
+--R                                                     Type: Expression Integer
+--E
+@
+and subtract it from the target equation
+&lt;&lt;*&gt;&gt;=
+--S 35
+ad1-target
+--R
+--R   (9)  0
+--R                                                     Type: Expression Integer
+--E
+@
+and now we do the same with first Spiegel's answer:
+&lt;&lt;*&gt;&gt;=
+--S 36
+bd1:=D(bb1,x)
+--R
+--R                                +-+ +-------+              2
+--R                   (- a x - 2b)\|b \|a x + b  + 2a b x + 2b
+--R   (10)  ------------------------------------------------------------
+--R                3     2 2  +-------+       2 4         3     2 2  +-+
+--R         (2a b x  + 2b x )\|a x + b  + (- a x  - 3a b x  - 2b x )\|b
+--R                                                     Type: Expression Integer
+--E
+@
+and we subtract it from the target
+&lt;&lt;*&gt;&gt;=
+--S 37     
+bd1-target
+--R
+--R   (11)  0
+--R                                                     Type: Expression Integer
+--E
+@
+so we know that the two first answers are both correct and that their
+integrals differ by a constant.
+
+Now we look at the second answers. We difference the answers and can
+see immediately that they are equal.
+&lt;&lt;*&gt;&gt;=
+--S 38     14:88 Schaums and Axiom differ by a constant
+cc22:=bb2-aa.2
+--R 
+--R
+--R   (12)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.89~~~~~$\displaystyle
+\int{\sqrt{ax+b}~dx}$}
+$$\int{\sqrt{ax+b}}=
+\frac{2\sqrt{(ax+b)^3}}{3a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 39
+aa:=integrate(sqrt(a*x+b),x)
+--R 
+--R
+--R                    +-------+
+--R        (2a x + 2b)\|a x + b
+--R   (1)  ---------------------
+--R                  3a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+&lt;&lt;*&gt;&gt;=
+--S 40
+bb:=(2*sqrt((a*x+b)^3))/(3*a)
+--R 
+--R
+--R          +----------------------------+
+--R          | 3 3     2   2       2     3
+--R        2\|a x  + 3a b x  + 3a b x + b
+--R   (2)  --------------------------------
+--R                       3a
+--R                                                     Type: Expression Integer
+--E
+@
+&lt;&lt;*&gt;&gt;=
+--S 41
+cc:=aa-bb
+--R
+--R            +----------------------------+
+--R            | 3 3     2   2       2     3                +-------+
+--R        - 2\|a x  + 3a b x  + 3a b x + b   + (2a x + 2b)\|a x + b
+--R   (3)  ----------------------------------------------------------
+--R                                    3a
+--R                                                     Type: Expression Integer
+--E
+@
+Since this didn't simplify we could check each answer using the derivative
+&lt;&lt;*&gt;&gt;=
+--S 42
+target:=sqrt(a*x+b)
+--R
+--R         +-------+
+--R   (4)  \|a x + b
+--R                                                     Type: Expression Integer
+--E
+@
+We take the derivative of Axiom's answer
+&lt;&lt;*&gt;&gt;=
+--S 43
+t1:=D(aa,x)
+--R
+--R          a x + b
+--R   (5)  ----------
+--R         +-------+
+--R        \|a x + b
+--R                                                     Type: Expression Integer
+--E
+@
+And we subtract the target from the derivative of Axiom's answer
+&lt;&lt;*&gt;&gt;=
+--S 44
+t1-target
+--R
+--R   (6)  0
+--R                                                     Type: Expression Integer
+--E
+@
+So they are equal. Now we do the same with Spiegel's answer
+&lt;&lt;*&gt;&gt;=
+--S 45
+t2:=D(bb,x)
+--R
+--R                2 2             2
+--R               a x  + 2a b x + b
+--R   (7)  -------------------------------
+--R         +----------------------------+
+--R         | 3 3     2   2       2     3
+--R        \|a x  + 3a b x  + 3a b x + b
+--R                                                     Type: Expression Integer
+--E
+@
+The numerator is
+&lt;&lt;*&gt;&gt;=
+--S 46
+nn:=(a*x+b)^2
+--R
+--R         2 2             2
+--R   (8)  a x  + 2a b x + b
+--R                                                     Type: Polynomial Integer
+--E
+@
+&lt;&lt;*&gt;&gt;=
+--S 47
+mm:=(a*x+b)^3
+--R
+--R         3 3     2   2       2     3
+--R   (9)  a x  + 3a b x  + 3a b x + b
+--R                                                     Type: Polynomial Integer
+--E
+@
+which expands to Spiegel's version.
+&lt;&lt;*&gt;&gt;=
+--S 48     14:89 Schaums and Axiom differ by a constant
+result=nn/sqrt(mm)
+--R
+--R                         2 2             2
+--R                        a x  + 2a b x + b
+--R   (10)  result= -------------------------------
+--R                  +----------------------------+
+--R                  | 3 3     2   2       2     3
+--R                 \|a x  + 3a b x  + 3a b x + b
+--R                                            Type: Equation Expression Integer
+--E
+@
+and this reduces to $\sqrt{ax+b}$
+
+\section{\cite{1}:14.90~~~~~$\displaystyle
+\int{x\sqrt{ax+b}~dx}$}
+$$\int{x\sqrt{ax+b}}=
+\frac{2(3ax-2b)}{15a^2}~\sqrt{(ax+b)^3}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 49
+aa:=integrate(x*sqrt(a*x+b),x)
+--R 
+--R
+--R           2 2              2  +-------+
+--R        (6a x  + 2a b x - 4b )\|a x + b
+--R   (1)  --------------------------------
+--R                         2
+--R                      15a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 50
+bb:=(2*(3*a*x-2*b))/(15*a^2)*sqrt((a*x+b)^3)
+--R 
+--R
+--R                    +----------------------------+
+--R                    | 3 3     2   2       2     3
+--R        (6a x - 4b)\|a x  + 3a b x  + 3a b x + b
+--R   (2)  ------------------------------------------
+--R                              2
+--R                           15a
+--R                                                     Type: Expression Integer
+--E
+
+--S 51
+cc:=aa-bb
+--R
+--R   (3)
+--R                     +----------------------------+
+--R                     | 3 3     2   2       2     3
+--R       (- 6a x + 4b)\|a x  + 3a b x  + 3a b x + b
+--R     + 
+--R          2 2              2  +-------+
+--R       (6a x  + 2a b x - 4b )\|a x + b
+--R  /
+--R        2
+--R     15a
+--R                                                     Type: Expression Integer
+--E
+
+--S 52     14:90 Schaums and Axiom agree
+dd:=rootSimp cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.91~~~~~$\displaystyle
+\int{x^2\sqrt{ax+b}~dx}$}
+$$\int{x^2\sqrt{ax+b}}=
+\frac{2(15a^2x^2-12abx+8b^2)}{105a^2}~\sqrt{(a+bx)^3}
+$$
+Note: the sqrt term is almost certainly $\sqrt{(ax+b)}$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 53
+aa:=integrate(x^2*sqrt(a*x+b),x)
+--R 
+--R
+--R            3 3     2   2       2       3  +-------+
+--R        (30a x  + 6a b x  - 8a b x + 16b )\|a x + b
+--R   (1)  --------------------------------------------
+--R                                3
+--R                            105a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 54
+bb:=(2*(15*a^2*x^2-12*a*b*x+8*b^2))/(105*a^3)*sqrt((a+b*x)^3)
+--R 
+--R
+--R                                  +----------------------------+
+--R            2 2                2  | 3 3       2 2     2       3
+--R        (30a x  - 24a b x + 16b )\|b x  + 3a b x  + 3a b x + a
+--R   (2)  --------------------------------------------------------
+--R                                      3
+--R                                  105a
+--R                                                     Type: Expression Integer
+--E
+
+--S 55     14:91 Axiom cannot simplify this expression. Schaums typo?
+cc:=aa-bb
+--R
+--R   (3)
+--R                                   +----------------------------+
+--R             2 2                2  | 3 3       2 2     2       3
+--R       (- 30a x  + 24a b x - 16b )\|b x  + 3a b x  + 3a b x + a
+--R     + 
+--R           3 3     2   2       2       3  +-------+
+--R       (30a x  + 6a b x  - 8a b x + 16b )\|a x + b
+--R  /
+--R         3
+--R     105a
+--R                                                     Type: Expression Integer
+--E
+
+@
+Notice that if we factor the numerator of 'aa' we get an expression that
+differs from schaums on by the order of the variables in the square root.
+(We can square the term (a*x+b) and drag it under the square root to get
+the cubic term). It appears that Schaums has a typo.
+&lt;&lt;*&gt;&gt;=
+--S 56
+factor numer aa
+--R
+--R                      2 2               2  +-------+
+--R   (4)  2(a x + b)(15a x  - 12a b x + 8b )\|a x + b
+--RType: Factored SparseMultivariatePolynomial(Integer,Kernel Expression Integer)
+--E
+@
+
+\section{\cite{1}:14.92~~~~~$\displaystyle
+\int{\frac{\sqrt{ax+b}}{x}~dx}$}
+$$\int{\frac{\sqrt{ax+b}}{x}}=
+2\sqrt{ax+b}+b~\int{\frac{1}{x\sqrt{ax+b}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 57
+aa:=integrate(sqrt(a*x+b)/x,x)
+--R 
+--R
+--R   (1)
+--R                +-+ +-------+
+--R     +-+    - 2\|b \|a x + b  + a x + 2b      +-------+
+--R   [\|b log(----------------------------) + 2\|a x + b ,
+--R                          x
+--R                   +-------+
+--R        +---+     \|a x + b       +-------+
+--R    - 2\|- b atan(----------) + 2\|a x + b ]
+--R                     +---+
+--R                    \|- b
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+
+--S 58
+dd:=integrate(1/(x*sqrt(a*x+b)),x)
+--R 
+--R
+--R                  +-------+              +-+           +---+ +-------+
+--R             - 2b\|a x + b  + (a x + 2b)\|b           \|- b \|a x + b
+--R         log(-------------------------------)   2atan(----------------)
+--R                            x                                 b
+--R   (2)  [------------------------------------,- -----------------------]
+--R                          +-+                             +---+
+--R                         \|b                             \|- b
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 59
+bb1:=2*sqrt(a*x+b)+b*dd.1
+--R 
+--R
+--R                   +-------+              +-+
+--R              - 2b\|a x + b  + (a x + 2b)\|b       +-+ +-------+
+--R        b log(-------------------------------) + 2\|b \|a x + b
+--R                             x
+--R   (3)  --------------------------------------------------------
+--R                                   +-+
+--R                                  \|b
+--R                                                     Type: Expression Integer
+--E
+
+--S 60
+bb2:=2*sqrt(a*x+b)+b*dd.2
+--R 
+--R
+--R                   +---+ +-------+
+--R                  \|- b \|a x + b       +---+ +-------+
+--R        - 2b atan(----------------) + 2\|- b \|a x + b
+--R                          b
+--R   (4)  -----------------------------------------------
+--R                              +---+
+--R                             \|- b
+--R                                                     Type: Expression Integer
+--E
+
+--S 61
+cc11:=bb1-aa.1
+--R 
+--R
+--R   (5)
+--R              +-------+              +-+              +-+ +-------+
+--R         - 2b\|a x + b  + (a x + 2b)\|b           - 2\|b \|a x + b  + a x + 2b
+--R   b log(-------------------------------) - b log(----------------------------)
+--R                        x                                       x
+--R   ----------------------------------------------------------------------------
+--R                                        +-+
+--R                                       \|b
+--R                                                     Type: Expression Integer
+--E
+
+--S 62
+cc12:=bb1-aa.2
+--R 
+--R
+--R                   +-------+              +-+                     +-------+
+--R              - 2b\|a x + b  + (a x + 2b)\|b       +---+ +-+     \|a x + b
+--R        b log(-------------------------------) + 2\|- b \|b atan(----------)
+--R                             x                                      +---+
+--R                                                                   \|- b
+--R   (6)  --------------------------------------------------------------------
+--R                                         +-+
+--R                                        \|b
+--R                                                     Type: Expression Integer
+--E
+
+--S 63
+cc21:=bb2-aa.1
+--R 
+--R
+--R   (7)
+--R                       +-+ +-------+                        +---+ +-------+
+--R      +---+ +-+    - 2\|b \|a x + b  + a x + 2b            \|- b \|a x + b
+--R   - \|- b \|b log(----------------------------) - 2b atan(----------------)
+--R                                 x                                 b
+--R   -------------------------------------------------------------------------
+--R                                      +---+
+--R                                     \|- b
+--R                                                     Type: Expression Integer
+--E
+
+--S 64
+cc22:=bb2-aa.2
+--R 
+--R
+--R                   +---+ +-------+             +-------+
+--R                  \|- b \|a x + b             \|a x + b
+--R        - 2b atan(----------------) - 2b atan(----------)
+--R                          b                      +---+
+--R                                                \|- b
+--R   (8)  -------------------------------------------------
+--R                               +---+
+--R                              \|- b
+--R                                                     Type: Expression Integer
+--E
+
+--S 65     14:92 Schaums and Axiom agree
+dd22:=ratDenom cc22
+--R
+--R   (9)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.93~~~~~$\displaystyle
+\int{\frac{\sqrt{ax+b}}{x^2}~dx}$}
+$$\int{\frac{\sqrt{ax+b}}{x^2}}=
+-\frac{\sqrt{ax+b}}{x}+\frac{a}{2}~\int{\frac{1}{x\sqrt{ax+b}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 65
+aa:=integrate(sqrt(a*x+b)/x^2,x)
+--R 
+--R
+--R   (1)
+--R                 +-------+              +-+
+--R            - 2b\|a x + b  + (a x + 2b)\|b       +-+ +-------+
+--R    a x log(-------------------------------) - 2\|b \|a x + b
+--R                           x
+--R   [----------------------------------------------------------,
+--R                                 +-+
+--R                              2x\|b
+--R                +---+ +-------+
+--R               \|- b \|a x + b      +---+ +-------+
+--R    - a x atan(----------------) - \|- b \|a x + b
+--R                       b
+--R    -----------------------------------------------]
+--R                          +---+
+--R                        x\|- b
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+
+--S 66
+dd:=integrate(1/(x*sqrt(a*x+b)),x)
+--R 
+--R
+--R                  +-------+              +-+           +---+ +-------+
+--R             - 2b\|a x + b  + (a x + 2b)\|b           \|- b \|a x + b
+--R         log(-------------------------------)   2atan(----------------)
+--R                            x                                 b
+--R   (2)  [------------------------------------,- -----------------------]
+--R                          +-+                             +---+
+--R                         \|b                             \|- b
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 67
+bb1:=-sqrt(a*x+b)/x+a/2*dd.1
+--R 
+--R
+--R                     +-------+              +-+
+--R                - 2b\|a x + b  + (a x + 2b)\|b       +-+ +-------+
+--R        a x log(-------------------------------) - 2\|b \|a x + b
+--R                               x
+--R   (3)  ----------------------------------------------------------
+--R                                     +-+
+--R                                  2x\|b
+--R                                                     Type: Expression Integer
+--E
+
+--S 68
+bb2:=-sqrt(a*x+b)/x+a/2*dd.2
+--R 
+--R
+--R                    +---+ +-------+
+--R                   \|- b \|a x + b      +---+ +-------+
+--R        - a x atan(----------------) - \|- b \|a x + b
+--R                           b
+--R   (4)  -----------------------------------------------
+--R                              +---+
+--R                            x\|- b
+--R                                                     Type: Expression Integer
+--E
+
+--S 69
+cc11:=bb1-aa.1
+--R 
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
+
+--S 70
+cc21:=bb-aa.1
+--R 
+--R
+--R   (6)
+--R                  +-------+              +-+
+--R             - 2b\|a x + b  + (a x + 2b)\|b       +-+ +-------+         +-+
+--R   - a x log(-------------------------------) + 2\|b \|a x + b  + 2bb x\|b
+--R                            x
+--R   ------------------------------------------------------------------------
+--R                                       +-+
+--R                                    2x\|b
+--R                                                     Type: Expression Integer
+--E
+
+--S 71
+cc12:=bb1-aa.2
+--R 
+--R
+--R   (7)
+--R                   +-------+              +-+                +---+ +-------+
+--R     +---+    - 2b\|a x + b  + (a x + 2b)\|b        +-+     \|- b \|a x + b
+--R   a\|- b log(-------------------------------) + 2a\|b atan(----------------)
+--R                             x                                      b
+--R   --------------------------------------------------------------------------
+--R                                     +---+ +-+
+--R                                   2\|- b \|b
+--R                                                     Type: Expression Integer
+--E
+
+--S 72     14:93 Schaums and Axiom agree
+cc22:=bb2-aa.2
+--R 
+--R
+--R   (8)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.94~~~~~$\displaystyle
+\int{\frac{x^m}{\sqrt{ax+b}}~dx}$}
+$$\int{\frac{x^m}{\sqrt{ax+b}}}=
+\frac{2x^m\sqrt{ax+b}}{(2m+1)a}-\frac{2mb}{(2m+1)a}
+~\int{\frac{x^{m-1}}{\sqrt{ax+b}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 73     14:94 Axiom cannot do this integral
+aa:=integrate(x^m/sqrt(a*x+b),x)
+--R 
+--R
+--R           x       m
+--I         ++      %L
+--I   (1)   |   ----------- d%L
+--R        ++    +--------+
+--I             \|b + %L a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.95~~~~~$\displaystyle
+\int{\frac{dx}{x^m\sqrt{ax+b}}}$}
+$$\int{\frac{1}{x^m\sqrt{ax+b}}}=
+-\frac{\sqrt{ax+b}}{(m-1)bx^{m-1}}-\frac{(2m-3)a}{(2m-2)b}
+~\int{\frac{1}{x^{m-1}\sqrt{ax+b}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 74     14:95 Axiom cannot do this integral
+aa:=integrate(1/(x^m*sqrt(a*x+b)),x)
+--R 
+--R
+--R           x
+--R         ++         1
+--I   (1)   |   -------------- d%L
+--R        ++     m +--------+
+--I             %L \|b + %L a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.96~~~~~$\displaystyle
+\int{x^m\sqrt{ax+b}~dx}$}
+$$\int{x^m\sqrt{ax+b}}=
+\frac{2x^m}{(2m+3)a}(ax+b)^{3/2}
+-\frac{2mb}{(2m+3)a}~\int{x^{m-1}\sqrt{ax+b}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 75     14:96 Axiom cannot do this integral
+aa:=integrate(x^m*sqrt(a*x+b),x)
+--R 
+--R
+--R           x
+--R         ++    m +--------+
+--I   (1)   |   %L \|b + %L a d%L
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.97~~~~~$\displaystyle
+\int{\frac{\sqrt{ax+b}}{x^m}~dx}$}
+$$\int{\frac{\sqrt{ax+b}}{x^m}}=
+-\frac{\sqrt{ax+b}}{(m-1)x^{m-1}}
++\frac{a}{2(m-1)}~\int{\frac{1}{x^{m-1}\sqrt{ax+b}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 76     14:97 Axiom cannot do this integral
+aa:=integrate(sqrt(a*x+b)/x^m,x)
+--R 
+--R
+--R           x  +--------+
+--I         ++  \|b + %L a
+--I   (1)   |   ----------- d%L
+--R        ++         m
+--I                 %L
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.98~~~~~$\displaystyle
+\int{\frac{\sqrt{ax+b}}{x^m}~dx}$}
+$$\int{\frac{\sqrt{ax+b}}{x^m}}=
+\frac{-(ax+b)^{3/2}}{(m-1)bx^{m-1}}
+-\frac{(2m-5)a}{(2m-2)b}~\int{\frac{\sqrt{ax+b}}{x^{m-1}}}
+$$
+Note: 14.98 is the same as 14.97
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 77     14:98 Axiom cannot do this integral
+aa:=integrate(sqrt(a*x+b)/x^m,x)
+--R 
+--R
+--R           x  +--------+
+--I         ++  \|b + %L a
+--I   (1)   |   ----------- d%L
+--R        ++         m
+--I                 %L
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.99~~~~~$\displaystyle
+\int{(ax+b)^{m/2}~dx}$}
+$$\int{(ax+b)^{m/2}}=
+\frac{2(ax+b)^{(m+2)/2}}{a(m+2)}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 78
+aa:=integrate((a*x+b)^(m/2),x)
+--R 
+--R
+--R                     m log(a x + b)
+--R                     --------------
+--R                            2
+--R        (2a x + 2b)%e
+--R   (1)  ---------------------------
+--R                  a m + 2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 79
+bb:=(2*(a*x+b)^((m+2)/2))/(a*(m+2))
+--R 
+--R
+--R                  m + 2
+--R                  -----
+--R                    2
+--R        2(a x + b)
+--R   (2)  ---------------
+--R            a m + 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 80
+cc:=aa-bb
+--R 
+--R
+--R                     m log(a x + b)             m + 2
+--R                     --------------             -----
+--R                            2                     2
+--R        (2a x + 2b)%e               - 2(a x + b)
+--R   (3)  ---------------------------------------------
+--R                           a m + 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 81
+explog:=rule(%e^(n*log(x)) == x^n)
+--R
+--R          n log(x)     n
+--R   (4)  %e         == x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 82
+dd:=explog cc
+--R
+--R                    m + 2                       m
+--R                    -----                       -
+--R                      2                         2
+--R        - 2(a x + b)      + (2a x + 2b)(a x + b)
+--R   (5)  -----------------------------------------
+--R                         a m + 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 83     14:99 Schaums and Axiom agree
+ee:=complexNormalize dd
+--R
+--R   (6)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.100~~~~~$\displaystyle
+\int{x(ax+b)^{m/2}~dx}$}
+$$\int{x(ax+b)^{m/2}}=
+\frac{2(ax+b)^{(m+4)/2}}{a^2(m+4)}
+-\frac{2b(ax+b)^{(m+2)/2}}{a^2(m+2)}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 84
+aa:=integrate(x*(a*x+b)^(m/2),x)
+--R 
+--R
+--R                                           m log(a x + b)
+--R                                           --------------
+--R            2      2  2                2          2
+--R        ((2a m + 4a )x  + 2a b m x - 4b )%e
+--R   (1)  -------------------------------------------------
+--R                         2 2     2      2
+--R                        a m  + 6a m + 8a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 85
+bb:=(2*(a*x+b)^((m+4)/2))/(a^2*(m+4))-(2*b*(a*x+b)^((m+2)/2))/(a^2*(m+2))
+--R 
+--R
+--R                         m + 4                         m + 2
+--R                         -----                         -----
+--R                           2                             2
+--R        (2m + 4)(a x + b)      + (- 2b m - 8b)(a x + b)
+--R   (2)  ----------------------------------------------------
+--R                           2 2     2      2
+--R                          a m  + 6a m + 8a
+--R                                                     Type: Expression Integer
+--E
+
+--S 86
+cc:=aa-bb
+--R 
+--R
+--R   (3)
+--R                                          m log(a x + b)
+--R                                          --------------
+--R           2      2  2                2          2
+--R       ((2a m + 4a )x  + 2a b m x - 4b )%e
+--R     + 
+--R                          m + 4                       m + 2
+--R                          -----                       -----
+--R                            2                           2
+--R       (- 2m - 4)(a x + b)      + (2b m + 8b)(a x + b)
+--R  /
+--R      2 2     2      2
+--R     a m  + 6a m + 8a
+--R                                                     Type: Expression Integer
+--E
+
+--S 87
+explog:=rule(%e^(n*log(x)) == x^n)
+--R
+--R          n log(x)     n
+--R   (4)  %e         == x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 88
+dd:=explog cc
+--R
+--R   (5)
+--R                          m + 4                       m + 2
+--R                          -----                       -----
+--R                            2                           2
+--R       (- 2m - 4)(a x + b)      + (2b m + 8b)(a x + b)
+--R     + 
+--R                                                 m
+--R                                                 -
+--R           2      2  2                2          2
+--R       ((2a m + 4a )x  + 2a b m x - 4b )(a x + b)
+--R  /
+--R      2 2     2      2
+--R     a m  + 6a m + 8a
+--R                                                     Type: Expression Integer
+--E
+
+--S 89     14:100 Schaums and Axiom agree
+ee:=complexNormalize dd
+--R
+--R   (6)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.101~~~~~$\displaystyle
+\int{x^2(ax+b)^{m/2}~dx}$}
+$$\int{x^2(ax+b)^{m/2}}=
+\frac{2(ax+b)^{(m+6)/2}}{a^3(m+6)}
+-\frac{4b(ax+b)^{(m+4)/2}}{a^3(m+4)}
++\frac{2b^2(ax+b)^{(m+2)/2}}{a^3(m+2)}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 90
+aa:=integrate(x^2*(a*x+b)^(m/2),x)
+--R 
+--R
+--R   (1)
+--R           3 2      3       3  3      2   2     2     2       2         3
+--R       ((2a m  + 12a m + 16a )x  + (2a b m  + 4a b m)x  - 8a b m x + 16b )
+--R    *
+--R         m log(a x + b)
+--R         --------------
+--R                2
+--R       %e
+--R  /
+--R      3 3      3 2      3       3
+--R     a m  + 12a m  + 44a m + 48a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 91
+bb:=(2*(a*x+b)^((m+6)/2))/(a^3*(m+6))-_
+      (4*b*(a*x+b)^((m+4)/2))/(a^3*(m+4))+_
+        (2*b^2*(a*x+b)^((m+2)/2))/(a^3*(m+2))
+--R 
+--R
+--R   (2)
+--R                                m + 6                                   m + 4
+--R                                -----                                   -----
+--R          2                       2            2                          2
+--R       (2m  + 12m + 16)(a x + b)      + (- 4b m  - 32b m - 48b)(a x + b)
+--R     + 
+--R                                      m + 2
+--R                                      -----
+--R          2 2      2       2            2
+--R       (2b m  + 20b m + 48b )(a x + b)
+--R  /
+--R      3 3      3 2      3       3
+--R     a m  + 12a m  + 44a m + 48a
+--R                                                     Type: Expression Integer
+--E
+
+--S 92
+cc:=aa-bb
+--R 
+--R
+--R   (3)
+--R             3 2      3       3  3      2   2     2     2       2         3
+--R         ((2a m  + 12a m + 16a )x  + (2a b m  + 4a b m)x  - 8a b m x + 16b )
+--R      *
+--R           m log(a x + b)
+--R           --------------
+--R                  2
+--R         %e
+--R     + 
+--R                                  m + 6                                 m + 4
+--R                                  -----                                 -----
+--R            2                       2          2                          2
+--R       (- 2m  - 12m - 16)(a x + b)      + (4b m  + 32b m + 48b)(a x + b)
+--R     + 
+--R                                        m + 2
+--R                                        -----
+--R            2 2      2       2            2
+--R       (- 2b m  - 20b m - 48b )(a x + b)
+--R  /
+--R      3 3      3 2      3       3
+--R     a m  + 12a m  + 44a m + 48a
+--R                                                     Type: Expression Integer
+--E
+
+--S 93
+explog:=rule(%e^(n*log(x)) == x^n)
+--R
+--R          n log(x)     n
+--R   (4)  %e         == x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 94
+dd:=explog cc
+--R
+--R   (5)
+--R                                  m + 6                                 m + 4
+--R                                  -----                                 -----
+--R            2                       2          2                          2
+--R       (- 2m  - 12m - 16)(a x + b)      + (4b m  + 32b m + 48b)(a x + b)
+--R     + 
+--R                                        m + 2
+--R                                        -----
+--R            2 2      2       2            2
+--R       (- 2b m  - 20b m - 48b )(a x + b)
+--R     + 
+--R             3 2      3       3  3      2   2     2     2       2         3
+--R         ((2a m  + 12a m + 16a )x  + (2a b m  + 4a b m)x  - 8a b m x + 16b )
+--R      *
+--R                  m
+--R                  -
+--R                  2
+--R         (a x + b)
+--R  /
+--R      3 3      3 2      3       3
+--R     a m  + 12a m  + 44a m + 48a
+--R                                                     Type: Expression Integer
+--E
+
+--S 95     14:101 Schaums and Axiom agree
+ee:=complexNormalize dd
+--R
+--R   (6)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.102~~~~~$\displaystyle
+\int{\frac{(ax+b)^{m/2}}{x}~dx}$}
+$$\int{\frac{(ax+b)^{m/2}}{x}}=
+\frac{2(ax+b)^{m/2}}{m}
++b~\int{\frac{(ax+b)^{(m-2)/2}}{x}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 96     14:102 Axiom cannot do this integral
+aa:=integrate((a*x+b)^(m/2)/x,x)
+--R 
+--R
+--R                       m
+--R                       -
+--R           x           2
+--I         ++  (b + %L a)
+--I   (1)   |   ----------- d%L
+--I        ++        %L
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+\section{\cite{1}:14.103~~~~~$\displaystyle
+\int{\frac{(ax+b)^{m/2}}{x^2}~dx}$}
+$$\int{\frac{(ax+b)^{m/2}}{x^2}}=
+-\frac{(ax+b)^{(m+2)/2}}{bx}
++\frac{ma}{2b}~\int{\frac{(ax+b)^{m/2}}{x}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 97     14:103 Axiom cannot do this integral
+aa:=integrate((a*x+b)^(m/2)/x^2,x)
+--R 
+--R
+--R                       m
+--R                       -
+--R           x           2
+--I         ++  (b + %L a)
+--I   (1)   |   ----------- d%L
+--R        ++         2
+--I                 %L
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+\section{\cite{1}:14.104~~~~~$\displaystyle
+\int{\frac{dx}{x(ax+b)^{m/2}}}$}
+$$\int{\frac{1}{x(ax+b)^{m/2}}}=
+\frac{2}{(m-2)b(ax+b)^{(m-2)/2}}
++\frac{1}{b}~\int{\frac{1}{x(ax+b)^{(m-2)/2}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 98     14:104 Axiom cannot do this integral
+aa:=integrate(1/(x*(a*x+b)^(m/2)),x)
+--R 
+--R
+--R           x
+--R         ++         1
+--I   (1)   |   -------------- d%L
+--R        ++                m
+--R                          -
+--R                          2
+--I             %L (b + %L a)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 pp61-62
+\end{thebibliography}
+\end{document}
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diff --git a/src/axiom-website/CATS/schaum20.input.pamphlet b/src/axiom-website/CATS/schaum20.input.pamphlet
new file mode 100644
index 0000000..e6981a6
--- /dev/null
+++ b/src/axiom-website/CATS/schaum20.input.pamphlet
@@ -0,0 +1,688 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum20.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.429~~~~~$\displaystyle
+\int{\tan{ax}}~dx$}
+$$\int{\tan{ax}}=
+-\frac{1}{a}\ln~\cos{ax}=
+\frac{1}{a}\ln~\sec{ax}
+$$
+&lt;&lt;*&gt;&gt;=
+)spool schaum20.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1
+aa:=integrate(tan(a*x),x)
+--R 
+--R
+--R                    2
+--R        log(tan(a x)  + 1)
+--R   (1)  ------------------
+--R                2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 2
+bb1:=-1/a*log(cos(a*x))
+--R
+--R          log(cos(a x))
+--R   (2)  - -------------
+--R                a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3
+bb2:=1/a*log(sec(a*x))
+--R
+--R        log(sec(a x))
+--R   (3)  -------------
+--R              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 4
+cc1:=aa-bb1
+--R
+--R                    2
+--R        log(tan(a x)  + 1) + 2log(cos(a x))
+--R   (4)  -----------------------------------
+--R                         2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 5
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (5)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 6
+dd1:=tanrule cc1
+--R
+--R                    2           2
+--R            sin(a x)  + cos(a x)
+--R        log(---------------------) + 2log(cos(a x))
+--R                          2
+--R                  cos(a x)
+--R   (6)  -------------------------------------------
+--R                             2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 7
+ee1:=expandLog dd1
+--R
+--R                    2           2
+--R        log(sin(a x)  + cos(a x) )
+--R   (7)  --------------------------
+--R                    2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 8
+sincossqrrule:=rule(sin(a)^2+cos(a)^2 == 1)
+--R
+--R              2         2
+--I   (8)  sin(a)  + cos(a)  + %K == %K + 1
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 9      14:429 Schaums and Axiom agree
+ff1:=sincossqrrule ee1
+--R
+--R   (9)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.430~~~~~$\displaystyle
+\int{\tan^2{ax}}~dx$}
+$$\int{\tan^2{ax}}=
+\frac{\tan{ax}}{x}-x
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 10
+aa:=integrate(tan(a*x)^2,x)
+--R 
+--R
+--R        tan(a x) - a x
+--R   (1)  --------------
+--R               a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 11
+bb:=tan(a*x)/a-x
+--R
+--R        tan(a x) - a x
+--R   (2)  --------------
+--R               a
+--R                                                     Type: Expression Integer
+--E
+
+--S 12     14:430 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.431~~~~~$\displaystyle
+\int{\tan^3{ax}}~dx$}
+$$\int{\tan^3{ax}}=
+\frac{\tan^2{ax}}{2a}+\frac{1}{a}\ln~\cos{ax}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 13
+aa:=integrate(tan(a*x)^3,x)
+--R 
+--R
+--R                      2                2
+--R        - log(tan(a x)  + 1) + tan(a x)
+--R   (1)  --------------------------------
+--R                       2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 14
+bb:=tan(a*x)^2/(2*a)+1/a*log(cos(a*x))
+--R
+--R                                 2
+--R        2log(cos(a x)) + tan(a x)
+--R   (2)  --------------------------
+--R                    2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 15
+cc:=aa-bb
+--R
+--R                      2
+--R        - log(tan(a x)  + 1) - 2log(cos(a x))
+--R   (3)  -------------------------------------
+--R                          2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 16
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (4)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 17
+dd:=tanrule cc
+--R
+--R                      2           2
+--R              sin(a x)  + cos(a x)
+--R        - log(---------------------) - 2log(cos(a x))
+--R                            2
+--R                    cos(a x)
+--R   (5)  ---------------------------------------------
+--R                              2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 18
+ee:=expandLog dd
+--R
+--R                      2           2
+--R          log(sin(a x)  + cos(a x) )
+--R   (6)  - --------------------------
+--R                      2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 19
+sincossqrrule:=rule(sin(a)^2+cos(a)^2 == 1)
+--R
+--R              2         2
+--I   (7)  sin(a)  + cos(a)  + %L == %L + 1
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 20     14:431 Schaums and Axiom agree
+ff:=sincossqrrule ee
+--R
+--R   (8)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.432~~~~~$\displaystyle
+\int{\tan^n{ax}\sec^2{ax}}~dx$}
+$$\int{\tan^n{ax}\sec^2{ax}}=
+\frac{\tan^{n+1}{ax}}{(n+1)a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 21
+aa:=integrate(tan(a*x)^n*sec(a*x)^2,x)
+--R 
+--R
+--R                        sin(a x)
+--R                  n log(--------)
+--R                        cos(a x)
+--R        sin(a x)%e
+--R   (1)  -------------------------
+--R            (a n + a)cos(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 22
+bb:=tan(a*x)^(n+1)/((n+1)*a)
+--R
+--R                n + 1
+--R        tan(a x)
+--R   (2)  -------------
+--R           a n + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 23
+cc:=aa-bb
+--R
+--R                        sin(a x)
+--R                  n log(--------)
+--R                        cos(a x)                    n + 1
+--R        sin(a x)%e                - cos(a x)tan(a x)
+--R   (3)  -------------------------------------------------
+--R                        (a n + a)cos(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 24
+explog:=rule(%e^(n*log(x)) == x^n)
+--R
+--R          n log(x)     n
+--R   (4)  %e         == x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 25
+dd:=explog cc
+--R
+--R                          n + 1            sin(a x) n
+--R        - cos(a x)tan(a x)      + sin(a x)(--------)
+--R                                           cos(a x)
+--R   (5)  ---------------------------------------------
+--R                      (a n + a)cos(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 26
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (6)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 27
+ee:=tanrule dd
+--R
+--R                   sin(a x) n + 1            sin(a x) n
+--R        - cos(a x)(--------)      + sin(a x)(--------)
+--R                   cos(a x)                  cos(a x)
+--R   (7)  -----------------------------------------------
+--R                       (a n + a)cos(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 28     14:432 Schaums and Axiom agree
+ff:=complexNormalize ee
+--R
+--R   (8)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.433~~~~~$\displaystyle
+\int{\frac{\sec^2{ax}}{\tan{ax}}}~dx$}
+$$\int{\frac{\sec^2{ax}}{\tan{ax}}}=
+\frac{1}{a}\ln~\tan{ax}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 29
+aa:=integrate(sec(a*x)^2/tan(a*x),x)
+--R 
+--R
+--R              sin(a x)              2cos(a x)
+--R        log(------------) - log(- ------------)
+--R            cos(a x) + 1          cos(a x) + 1
+--R   (1)  ---------------------------------------
+--R                           a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 30
+bb:=1/a*log(tan(a*x))
+--R
+--R        log(tan(a x))
+--R   (2)  -------------
+--R              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 31
+cc:=aa-bb
+--R
+--R                                sin(a x)              2cos(a x)
+--R        - log(tan(a x)) + log(------------) - log(- ------------)
+--R                              cos(a x) + 1          cos(a x) + 1
+--R   (3)  ---------------------------------------------------------
+--R                                    a
+--R                                                     Type: Expression Integer
+--E
+
+--S 32
+dd:=expandLog cc
+--R
+--R        - log(tan(a x)) + log(sin(a x)) - log(cos(a x)) - log(- 2)
+--R   (4)  ----------------------------------------------------------
+--R                                     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 33     14:433 Schaums and Axiom differ by a constant
+ee:=complexNormalize dd
+--R
+--R          log(- 2)
+--R   (5)  - --------
+--R              a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.434~~~~~$\displaystyle
+\int{\frac{dx}{\tan{ax}}}~dx$}
+$$\int{\frac{1}{\tan{ax}}}=
+\frac{1}{a}\ln~\sin{ax}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 34
+aa:=integrate(1/tan(a*x),x)
+--R 
+--R
+--R                      2
+--R        - log(tan(a x)  + 1) + 2log(tan(a x))
+--R   (1)  -------------------------------------
+--R                          2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 35
+bb:=1/a*log(sin(a*x))
+--R
+--R        log(sin(a x))
+--R   (2)  -------------
+--R              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 36
+cc:=aa-bb
+--R
+--R                      2
+--R        - log(tan(a x)  + 1) + 2log(tan(a x)) - 2log(sin(a x))
+--R   (3)  ------------------------------------------------------
+--R                                  2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 37
+complexNormalize cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.435~~~~~$\displaystyle
+\int{x\tan{ax}}~dx$}
+$$\int{x\tan{ax}}=
+\frac{1}{a^2}\left\{\frac{(ax)^3}{3}+\frac{(ax)^5}{15}+\frac{2(ax)^7}{105}
++\cdots+\frac{2^{2n}(2^{2n}-1)B_n(ax)^{2n+1}}{(2n+1)!}+\cdots\right\}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 38     14:435 Axiom cannot compute this integral
+aa:=integrate(x*tan(a*x),x)
+--R 
+--R
+--R           x
+--R         ++
+--I   (1)   |   %I tan(%I a)d%I
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.436~~~~~$\displaystyle
+\int{\frac{\tan{ax}}{x}}~dx$}
+$$\int{\frac{\tan{ax}}{x}}=
+ax+\frac{(ax)^3}{9}+\frac{2(ax)^5}{75}+\cdots
++\frac{2^{2n}(2^{2n}-1)B_n(ax)^{2n-1}}{(2n-1)(2n)!}+\cdots
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 39     14:436 Axiom cannot compute this integral
+aa:=integrate(tan(a*x)/x,x)
+--R 
+--R
+--R           x
+--I         ++  tan(%I a)
+--I   (1)   |   --------- d%I
+--I        ++       %I
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.437~~~~~$\displaystyle
+\int{x\tan^2{ax}}~dx$}
+$$\int{x\tan^2{ax}}=
+\frac{x\tan{ax}}{a}+\frac{1}{a^2}\ln~\cos{ax}-\frac{x^2}{2}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 40
+aa:=integrate(x*tan(a*x)^2,x)
+--R 
+--R
+--R                      2                         2 2
+--R        - log(tan(a x)  + 1) + 2a x tan(a x) - a x
+--R   (1)  -------------------------------------------
+--R                              2
+--R                            2a
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 41
+bb:=(x*tan(a*x))/a+1/a^2*log(cos(a*x))-x^2/2
+--R
+--R                                          2 2
+--R        2log(cos(a x)) + 2a x tan(a x) - a x
+--R   (2)  -------------------------------------
+--R                           2
+--R                         2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 42
+cc:=aa-bb
+--R
+--R                      2
+--R        - log(tan(a x)  + 1) - 2log(cos(a x))
+--R   (3)  -------------------------------------
+--R                           2
+--R                         2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 43
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (4)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 44
+dd:=tanrule cc
+--R
+--R                      2           2
+--R              sin(a x)  + cos(a x)
+--R        - log(---------------------) - 2log(cos(a x))
+--R                            2
+--R                    cos(a x)
+--R   (5)  ---------------------------------------------
+--R                               2
+--R                             2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 45
+ee:=expandLog dd
+--R
+--R                      2           2
+--R          log(sin(a x)  + cos(a x) )
+--R   (6)  - --------------------------
+--R                        2
+--R                      2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 46
+sincossqrrule:=rule(sin(a)^2+cos(a)^2 == 1)
+--R
+--R              2         2
+--I   (7)  sin(a)  + cos(a)  + %R == %R + 1
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 47     14:437 Schaums and Axiom agree
+ff:=sincossqrrule ee
+--R
+--R   (8)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.438~~~~~$\displaystyle
+\int{\frac{dx}{p+q\tan{ax}}}~dx$}
+$$\int{\frac{1}{p+q\tan{ax}}}=
+\frac{px}{p^2+q^2}+\frac{q}{a(p^2+q^2)}\ln(q\sin{ax}+p\cos{ax})
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 48
+aa:=integrate(1/(p+q*tan(a*x)),x)
+--R 
+--R
+--R                        2
+--R        - q log(tan(a x)  + 1) + 2q log(q tan(a x) + p) + 2a p x
+--R   (1)  --------------------------------------------------------
+--R                                  2       2
+--R                              2a q  + 2a p
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 49
+bb:=(p*x)/(p^2+q^2)+q/(a*(p^2+q^2))*log(q*sin(a*x)+p*cos(a*x))
+--R
+--R        q log(q sin(a x) + p cos(a x)) + a p x
+--R   (2)  --------------------------------------
+--R                         2      2
+--R                      a q  + a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 50
+cc:=aa-bb
+--R
+--R   (3)
+--R                       2
+--R       - q log(tan(a x)  + 1) + 2q log(q tan(a x) + p)
+--R     + 
+--R       - 2q log(q sin(a x) + p cos(a x))
+--R  /
+--R         2       2
+--R     2a q  + 2a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 51
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (4)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 52
+dd:=tanrule cc
+--R
+--R   (5)
+--R                       2           2
+--R               sin(a x)  + cos(a x)
+--R       - q log(---------------------) - 2q log(q sin(a x) + p cos(a x))
+--R                             2
+--R                     cos(a x)
+--R     + 
+--R              q sin(a x) + p cos(a x)
+--R       2q log(-----------------------)
+--R                      cos(a x)
+--R  /
+--R         2       2
+--R     2a q  + 2a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 53
+ee:=expandLog dd
+--R
+--R                        2           2
+--R          q log(sin(a x)  + cos(a x) )
+--R   (6)  - ----------------------------
+--R                      2       2
+--R                  2a q  + 2a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 54
+sincossqrrule:=rule(sin(a)^2+cos(a)^2 == 1)
+--R
+--R              2         2
+--I   (7)  sin(a)  + cos(a)  + %S == %S + 1
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 55     14:438 Schaums and Axiom agree
+ff:=sincossqrrule ee
+--R
+--R   (8)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.439~~~~~$\displaystyle
+\int{\tan^n{ax}}~dx$}
+$$\int{\tan^n{ax}}=
+\frac{\tan^{n-1}{ax}}{(n-1)a}-\int{\tan^{n-2}{ax}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 56     14:439 Axiom cannot compute this integral
+aa:=integrate(tan(a*x)^n,x)
+--R 
+--R
+--R           x
+--R         ++           n
+--I   (1)   |   tan(%I a) d%I
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 p80
+\end{thebibliography}
+\end{document}
diff --git a/src/axiom-website/CATS/schaum20.input.pdf b/src/axiom-website/CATS/schaum20.input.pdf
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diff --git a/src/axiom-website/CATS/schaum21.input.pamphlet b/src/axiom-website/CATS/schaum21.input.pamphlet
new file mode 100644
index 0000000..2c24de5
--- /dev/null
+++ b/src/axiom-website/CATS/schaum21.input.pamphlet
@@ -0,0 +1,720 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum21.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.440~~~~~$\displaystyle
+\int{\cot{ax}}~dx$}
+$$\int{\cot{ax}}=
+\frac{1}{a}\ln\sin{ax}
+$$
+&lt;&lt;*&gt;&gt;=
+)spool schaum21.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1
+aa:=integrate(cot(a*x),x)
+--R 
+--R
+--R               sin(2a x)                2
+--R        2log(-------------) - log(-------------)
+--R             cos(2a x) + 1        cos(2a x) + 1
+--R   (1)  ----------------------------------------
+--R                           2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 2
+bb:=1/a*log(sin(a*x))
+--R
+--R        log(sin(a x))
+--R   (2)  -------------
+--R              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3
+cc:=aa-bb
+--R
+--R               sin(2a x)                                 2
+--R        2log(-------------) - 2log(sin(a x)) - log(-------------)
+--R             cos(2a x) + 1                         cos(2a x) + 1
+--R   (3)  ---------------------------------------------------------
+--R                                    2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 4
+dd:=expandLog cc
+--R
+--R        2log(sin(2a x)) - 2log(sin(a x)) - log(cos(2a x) + 1) - log(2)
+--R   (4)  --------------------------------------------------------------
+--R                                      2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 5      14:440 Schaums and Axiom agree
+ee:=complexNormalize dd
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.441~~~~~$\displaystyle
+\int{\cot^2{ax}}~dx$}
+$$\int{\cot^2{ax}}=
+-\frac{\cot{ax}}{a}-x
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 6
+aa:=integrate(cot(a*x)^2,x)
+--R 
+--R
+--R        - a x sin(2a x) - cos(2a x) - 1
+--R   (1)  -------------------------------
+--R                  a sin(2a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 7
+bb:=-cot(a*x)/a-x
+--R
+--R        - cot(a x) - a x
+--R   (2)  ----------------
+--R                a
+--R                                                     Type: Expression Integer
+--E
+
+--S 8
+cc:=aa-bb
+--R
+--R        cot(a x)sin(2a x) - cos(2a x) - 1
+--R   (3)  ---------------------------------
+--R                   a sin(2a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 9
+cotrule:=rule(cot(a) == cos(a)/sin(a))
+--R
+--R                  cos(a)
+--R   (4)  cot(a) == ------
+--R                  sin(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 10
+dd:=cotrule cc
+--R
+--R        cos(a x)sin(2a x) + (- cos(2a x) - 1)sin(a x)
+--R   (5)  ---------------------------------------------
+--R                     a sin(a x)sin(2a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 11     14:441 Schaums and Axiom agree
+ee:=complexNormalize dd
+--R
+--R   (6)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.442~~~~~$\displaystyle
+\int{\cot^3{ax}}~dx$}
+$$\int{\cot^3{ax}}=
+-\frac{\cot^2{ax}}{2a}-\frac{1}{a}\ln\sin{ax}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 12
+aa:=integrate(cot(a*x)^3,x)
+--R 
+--R
+--R   (1)
+--R                               sin(2a x)                               2
+--R       (- 2cos(2a x) + 2)log(-------------) + (cos(2a x) - 1)log(-------------)
+--R                             cos(2a x) + 1                       cos(2a x) + 1
+--R     + 
+--R       cos(2a x) + 1
+--R  /
+--R     2a cos(2a x) - 2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 13
+bb:=-cot(a*x)^2/(2*a)-1/a*log(sin(a*x))
+--R
+--R                                   2
+--R        - 2log(sin(a x)) - cot(a x)
+--R   (2)  ----------------------------
+--R                     2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 14
+cc:=aa-bb
+--R
+--R   (3)
+--R                               sin(2a x)
+--R       (- 2cos(2a x) + 2)log(-------------) + (2cos(2a x) - 2)log(sin(a x))
+--R                             cos(2a x) + 1
+--R     + 
+--R                                2                                 2
+--R       (cos(2a x) - 1)log(-------------) + (cos(2a x) - 1)cot(a x)  + cos(2a x)
+--R                          cos(2a x) + 1
+--R     + 
+--R       1
+--R  /
+--R     2a cos(2a x) - 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 15
+cotrule:=rule(cot(a) == cos(a)/sin(a))
+--R
+--R                  cos(a)
+--R   (4)  cot(a) == ------
+--R                  sin(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 16
+dd:=cotrule cc
+--R
+--R   (5)
+--R                                 2      sin(2a x)
+--R       (- 2cos(2a x) + 2)sin(a x) log(-------------)
+--R                                      cos(2a x) + 1
+--R     + 
+--R                               2
+--R       (2cos(2a x) - 2)sin(a x) log(sin(a x))
+--R     + 
+--R                              2          2                                 2
+--R       (cos(2a x) - 1)sin(a x) log(-------------) + (cos(2a x) + 1)sin(a x)
+--R                                   cos(2a x) + 1
+--R     + 
+--R               2                    2
+--R       cos(a x) cos(2a x) - cos(a x)
+--R  /
+--R                                2
+--R     (2a cos(2a x) - 2a)sin(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 17
+ee:=expandLog dd
+--R
+--R   (6)
+--R                                 2
+--R       (- 2cos(2a x) + 2)sin(a x) log(sin(2a x))
+--R     + 
+--R                               2
+--R       (2cos(2a x) - 2)sin(a x) log(sin(a x))
+--R     + 
+--R                              2
+--R       (cos(2a x) - 1)sin(a x) log(cos(2a x) + 1)
+--R     + 
+--R                                                   2           2
+--R       ((log(2) + 1)cos(2a x) - log(2) + 1)sin(a x)  + cos(a x) cos(2a x)
+--R     + 
+--R                 2
+--R       - cos(a x)
+--R  /
+--R                                2
+--R     (2a cos(2a x) - 2a)sin(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 18     14:442 Schaums and Axiom agree
+ff:=complexNormalize ee
+--R
+--R   (7)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.443~~~~~$\displaystyle
+\int{\cot^n{ax}\csc^2{ax}}~dx$}
+$$\int{\cot^n{ax}\csc^2{ax}}=
+-\frac{\cot^{n+1}{ax}}{(n+1)a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 19
+aa:=integrate(cot(a*x)^n*csc(a*x)^2,x)
+--R 
+--R
+--R                          cos(a x)
+--R                    n log(--------)
+--R                          sin(a x)
+--R          cos(a x)%e
+--R   (1)  - -------------------------
+--R              (a n + a)sin(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 20
+bb:=-cot(a*x)^(n+1)/((n+1)*a)
+--R
+--R                  n + 1
+--R          cot(a x)
+--R   (2)  - -------------
+--R             a n + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 21
+cc:=aa-bb
+--R
+--R                          cos(a x)
+--R                    n log(--------)
+--R                          sin(a x)                    n + 1
+--R        - cos(a x)%e                + sin(a x)cot(a x)
+--R   (3)  ---------------------------------------------------
+--R                         (a n + a)sin(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 22
+explog:=rule(%e^(n*log(x)) == x^n)
+--R
+--R          n log(x)     n
+--R   (4)  %e         == x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 23
+dd:=explog cc
+--R
+--R                        n + 1            cos(a x) n
+--R        sin(a x)cot(a x)      - cos(a x)(--------)
+--R                                         sin(a x)
+--R   (5)  -------------------------------------------
+--R                     (a n + a)sin(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 24
+cotrule:=rule(cot(a) == cos(a)/sin(a))
+--R
+--R                  cos(a)
+--R   (6)  cot(a) == ------
+--R                  sin(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 25
+ee:=cotrule dd
+--R
+--R                 cos(a x) n + 1            cos(a x) n
+--R        sin(a x)(--------)      - cos(a x)(--------)
+--R                 sin(a x)                  sin(a x)
+--R   (7)  ---------------------------------------------
+--R                      (a n + a)sin(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 26     14:443 Schaums and Axiom agree
+ff:=complexNormalize ee
+--R
+--R   (8)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.444~~~~~$\displaystyle
+\int{\frac{\csc^2{ax}}{\cot{ax}}}~dx$}
+$$\int{\frac{\csc^2{ax}}{\cot{ax}}}=
+-\frac{1}{a}\ln\cot{ax}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 27
+aa:=integrate(csc(a*x)^2/cot(a*x),x)
+--R 
+--R
+--R              sin(a x)              2cos(a x)
+--R        log(------------) - log(- ------------)
+--R            cos(a x) + 1          cos(a x) + 1
+--R   (1)  ---------------------------------------
+--R                           a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 28
+bb:=-1/a*log(cot(a*x))
+--R
+--R          log(cot(a x))
+--R   (2)  - -------------
+--R                a
+--R                                                     Type: Expression Integer
+--E
+
+--S 29
+cc:=aa-bb
+--R
+--R              sin(a x)                              2cos(a x)
+--R        log(------------) + log(cot(a x)) - log(- ------------)
+--R            cos(a x) + 1                          cos(a x) + 1
+--R   (3)  -------------------------------------------------------
+--R                                   a
+--R                                                     Type: Expression Integer
+--E
+
+--S 30
+cotrule:=rule(cot(a) == cos(a)/sin(a))
+--R
+--R                  cos(a)
+--R   (4)  cot(a) == ------
+--R                  sin(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 31
+dd:=cotrule cc
+--R
+--R              sin(a x)          cos(a x)            2cos(a x)
+--R        log(------------) + log(--------) - log(- ------------)
+--R            cos(a x) + 1        sin(a x)          cos(a x) + 1
+--R   (5)  -------------------------------------------------------
+--R                                   a
+--R                                                     Type: Expression Integer
+--E
+
+--S 32     14:444 Schaums and Axiom differ by a constant
+ee:=expandLog dd
+--R
+--R          log(- 2)
+--R   (6)  - --------
+--R              a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.445~~~~~$\displaystyle
+\int{\frac{dx}{\cot{ax}}}~dx$}
+$$\int{\frac{1}{\cot{ax}}}=
+-\frac{1}{a}\ln\cos{ax}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 33
+aa:=integrate(1/cot(a*x),x)
+--R 
+--R
+--R                  2
+--R        log(-------------)
+--R            cos(2a x) + 1
+--R   (1)  ------------------
+--R                2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 34
+bb:=-1/a*log(cos(a*x))
+--R
+--R          log(cos(a x))
+--R   (2)  - -------------
+--R                a
+--R                                                     Type: Expression Integer
+--E
+
+--S 35
+cc:=aa-bb
+--R
+--R                                   2
+--R        2log(cos(a x)) + log(-------------)
+--R                             cos(2a x) + 1
+--R   (3)  -----------------------------------
+--R                         2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 36
+dd:=expandLog cc
+--R
+--R        - log(cos(2a x) + 1) + 2log(cos(a x)) + log(2)
+--R   (4)  ----------------------------------------------
+--R                              2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 37     14:445 Schaums and Axiom agree
+ee:=complexNormalize dd
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.446~~~~~$\displaystyle
+\int{x\cot{ax}}~dx$}
+$$\int{x\cot{ax}}=
+\frac{1}{a^2}\left\{ax
+-\frac{(ax)^3}{9}-\frac{(ax)^5}{225}
+-\cdots-\frac{2^{2n}B_n(ax)^{2n+1}}{(2n+1)!}-\cdots\right\}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 38     14:446 Axiom cannot compute this integral
+aa:=integrate(x*cot(a*x),x)
+--R 
+--R
+--R           x
+--R         ++
+--I   (1)   |   %I cot(%I a)d%I
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.447~~~~~$\displaystyle
+\int{\frac{\cot{ax}}{x}}~dx$}
+$$\int{\frac{\cot{ax}}{x}}=
+-\frac{1}{ax}-\frac{ax}{3}-\frac{(ax)^3}{135}-\cdots
+-\frac{2^{2n}B_n(ax)^{2n-1}}{(2n-1)(2n)!}-\cdots
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 39     14:447 Axiom cannot compute this integral
+aa:=integrate(cot(a*x)/x,x)
+--R 
+--R
+--R           x
+--I         ++  cot(%I a)
+--I   (1)   |   --------- d%I
+--I        ++       %I
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.448~~~~~$\displaystyle
+\int{x\cot^2{ax}}~dx$}
+$$\int{x\cot^2{ax}}=
+-\frac{x\cot{ax}}{a}+\frac{1}{a^2}\ln\sin{ax}-\frac{x^2}{2}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 40
+aa:=integrate(x*cot(a*x)^2,x)
+--R 
+--R
+--R   (1)
+--R                       sin(2a x)                         2
+--R       2sin(2a x)log(-------------) - sin(2a x)log(-------------)
+--R                     cos(2a x) + 1                 cos(2a x) + 1
+--R     + 
+--R          2 2
+--R       - a x sin(2a x) - 2a x cos(2a x) - 2a x
+--R  /
+--R       2
+--R     2a sin(2a x)
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 41
+bb:=-(x*cot(a*x))/a+1/a^2*log(sin(a*x))-x^2/2
+--R
+--R                                          2 2
+--R        2log(sin(a x)) - 2a x cot(a x) - a x
+--R   (2)  -------------------------------------
+--R                           2
+--R                         2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 42
+cc:=aa-bb
+--R
+--R   (3)
+--R                       sin(2a x)
+--R       2sin(2a x)log(-------------) - 2sin(2a x)log(sin(a x))
+--R                     cos(2a x) + 1
+--R     + 
+--R                            2
+--R       - sin(2a x)log(-------------) + 2a x cot(a x)sin(2a x) - 2a x cos(2a x)
+--R                      cos(2a x) + 1
+--R     + 
+--R       - 2a x
+--R  /
+--R       2
+--R     2a sin(2a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 43
+dd:=expandLog cc
+--R
+--R   (4)
+--R       2sin(2a x)log(sin(2a x)) - 2sin(2a x)log(sin(a x))
+--R     + 
+--R       - sin(2a x)log(cos(2a x) + 1) + (2a x cot(a x) - log(2))sin(2a x)
+--R     + 
+--R       - 2a x cos(2a x) - 2a x
+--R  /
+--R       2
+--R     2a sin(2a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 44     14:448 Schaums and Axiom agree
+ee:=complexNormalize dd
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.449~~~~~$\displaystyle
+\int{\frac{dx}{p+q\cot{ax}}}~dx$}
+$$\int{\frac{1}{p+q\cot{ax}}}=
+\frac{px}{p^2+q^2}-\frac{q}{a(p^2+q^2)}\ln(p\sin{ax}+q\cos{ax})
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 45
+aa:=integrate(1/(p+q*cot(a*x)),x)
+--R 
+--R
+--R   (1)
+--R            p sin(2a x) + q cos(2a x) + q                2
+--R   - 2q log(-----------------------------) + q log(-------------) + 2a p x
+--R                    cos(2a x) + 1                  cos(2a x) + 1
+--R   -----------------------------------------------------------------------
+--R                                    2       2
+--R                                2a q  + 2a p
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 46
+bb:=(p*x)/(p^2+q^2)-q/(a*(p^2+q^2))*log(p*sin(a*x)+q*cos(a*x))
+--R
+--R        - q log(p sin(a x) + q cos(a x)) + a p x
+--R   (2)  ----------------------------------------
+--R                          2      2
+--R                       a q  + a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 47
+cc:=aa-bb
+--R
+--R   (3)
+--R                p sin(2a x) + q cos(2a x) + q
+--R       - 2q log(-----------------------------) + 2q log(p sin(a x) + q cos(a x))
+--R                        cos(2a x) + 1
+--R     + 
+--R                   2
+--R       q log(-------------)
+--R             cos(2a x) + 1
+--R  /
+--R         2       2
+--R     2a q  + 2a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 48
+sindblrule:=rule(sin(2*a) == 2*sin(a)*cos(a))
+--R
+--R   (4)  sin(2a) == 2cos(a)sin(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 49
+dd:=sindblrule cc
+--R
+--R   (5)
+--R       2q log(p sin(a x) + q cos(a x))
+--R     + 
+--R                2p cos(a x)sin(a x) + q cos(2a x) + q                2
+--R       - 2q log(-------------------------------------) + q log(-------------)
+--R                            cos(2a x) + 1                      cos(2a x) + 1
+--R  /
+--R         2       2
+--R     2a q  + 2a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 50
+cosdblrule:=rule(cos(2*a) == 2*cos(a)^2-1)
+--R
+--R                          2
+--R   (6)  cos(2a) == 2cos(a)  - 1
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 51
+ee:=cosdblrule dd
+--R
+--R   (7)
+--R                                                p sin(a x) + q cos(a x)
+--R       2q log(p sin(a x) + q cos(a x)) - 2q log(-----------------------)
+--R                                                        cos(a x)
+--R     + 
+--R                 1
+--R       q log(---------)
+--R                     2
+--R             cos(a x)
+--R  /
+--R         2       2
+--R     2a q  + 2a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 52     14:449 Schaums and Axiom agree
+ff:=expandLog %
+--R
+--R   (8)  0
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.450~~~~~$\displaystyle
+\int{\cot^n{ax}}~dx$}
+$$\int{\cot^n{ax}}=
+-\frac{\cot^{n-1}{ax}}{(n-1)a}-\int{\cos^{n-2}{ax}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 53     14:450 Axiom cannot compute this integral
+aa:=integrate(cot(a*x)^n,x)
+--R 
+--R
+--R           x
+--R         ++           n
+--I   (1)   |   cot(%I a) d%I
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 p81
+\end{thebibliography}
+\end{document}
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diff --git a/src/axiom-website/CATS/schaum22.input.pamphlet b/src/axiom-website/CATS/schaum22.input.pamphlet
new file mode 100644
index 0000000..42fad96
--- /dev/null
+++ b/src/axiom-website/CATS/schaum22.input.pamphlet
@@ -0,0 +1,796 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum22.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.451~~~~~$\displaystyle
+\int{\sec{ax}}~dx$}
+$$\int{\sec{ax}}=
+\frac{1}{a}\ln(\sec{ax}+\tan{ax})=
+\frac{1}{a}\ln\tan\left(\frac{ax}{2}+\frac{\pi}{4}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)spool schaum22.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1
+aa:=integrate(sec(a*x),x)
+--R 
+--R
+--R            sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
+--R        log(-----------------------) - log(-----------------------)
+--R                  cos(a x) + 1                   cos(a x) + 1
+--R   (1)  -----------------------------------------------------------
+--R                                     a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 2
+bb1:=1/a*log(sec(a*x)+tan(a*x))
+--R
+--R        log(tan(a x) + sec(a x))
+--R   (2)  ------------------------
+--R                    a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3
+bb2:=1/a*log(tan((a*x)/2+%pi/4))
+--R
+--R                2a x + %pi
+--R        log(tan(----------))
+--R                     4
+--R   (3)  --------------------
+--R                  a
+--R                                                     Type: Expression Integer
+--E
+
+--S 4
+cc1:=aa-bb1
+--R
+--R   (4)
+--R                                        sin(a x) + cos(a x) + 1
+--R       - log(tan(a x) + sec(a x)) + log(-----------------------)
+--R                                              cos(a x) + 1
+--R     + 
+--R             sin(a x) - cos(a x) - 1
+--R       - log(-----------------------)
+--R                   cos(a x) + 1
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 5
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (5)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 6
+dd1:=tanrule cc1
+--R
+--R   (6)
+--R             sin(a x) + cos(a x)sec(a x)        sin(a x) + cos(a x) + 1
+--R       - log(---------------------------) + log(-----------------------)
+--R                       cos(a x)                       cos(a x) + 1
+--R     + 
+--R             sin(a x) - cos(a x) - 1
+--R       - log(-----------------------)
+--R                   cos(a x) + 1
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 7
+secrule:=rule(sec(a) == 1/cos(a))
+--R
+--R                     1
+--R   (7)  sec(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 8
+ee1:=secrule dd1
+--R
+--R   (8)
+--R             sin(a x) + 1        sin(a x) + cos(a x) + 1
+--R       - log(------------) + log(-----------------------)
+--R               cos(a x)                cos(a x) + 1
+--R     + 
+--R             sin(a x) - cos(a x) - 1
+--R       - log(-----------------------)
+--R                   cos(a x) + 1
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 9
+ff1:=expandLog ee1
+--R
+--R   (9)
+--R       log(sin(a x) + cos(a x) + 1) - log(sin(a x) + 1)
+--R     + 
+--R       - log(sin(a x) - cos(a x) - 1) + log(cos(a x))
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 10
+gg1:=complexNormalize ff1
+--R
+--R         log(- 1)
+--R   (10)  --------
+--R             a
+--R                                                     Type: Expression Integer
+--E
+
+--S 11
+cc2:=aa-bb2
+--R
+--R   (11)
+--R                 2a x + %pi         sin(a x) + cos(a x) + 1
+--R       - log(tan(----------)) + log(-----------------------)
+--R                      4                   cos(a x) + 1
+--R     + 
+--R             sin(a x) - cos(a x) - 1
+--R       - log(-----------------------)
+--R                   cos(a x) + 1
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 12
+dd2:=tanrule cc2
+--R
+--R   (12)
+--R           sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
+--R       log(-----------------------) - log(-----------------------)
+--R                 cos(a x) + 1                   cos(a x) + 1
+--R     + 
+--R                 2a x + %pi
+--R             sin(----------)
+--R                      4
+--R       - log(---------------)
+--R                 2a x + %pi
+--R             cos(----------)
+--R                      4
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 13
+ee2:=expandLog dd2
+--R
+--R   (13)
+--R       log(sin(a x) + cos(a x) + 1) - log(sin(a x) - cos(a x) - 1)
+--R     + 
+--R                 2a x + %pi             2a x + %pi
+--R       - log(sin(----------)) + log(cos(----------))
+--R                      4                      4
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 14     14:451 Schaums and Axiom differ by a constant
+ff2:=complexNormalize ee2
+--R
+--R         log(- 1)
+--R   (14)  --------
+--R             a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.452~~~~~$\displaystyle
+\int{\sec^2{ax}}~dx$}
+$$\int{\sec^2{ax}}=
+\frac{\tan{ax}}{a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 15
+aa:=integrate(sec(a*x)^2,x)
+--R 
+--R
+--R         sin(a x)
+--R   (1)  ----------
+--R        a cos(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 16
+bb:=tan(a*x)/a
+--R
+--R        tan(a x)
+--R   (2)  --------
+--R            a
+--R                                                     Type: Expression Integer
+--E
+
+--S 17
+cc:=aa-bb
+--R
+--R        - cos(a x)tan(a x) + sin(a x)
+--R   (3)  -----------------------------
+--R                  a cos(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 18
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (4)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 19     14:452 Schaums and Axiom agree
+dd:=tanrule cc
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.453~~~~~$\displaystyle
+\int{\sec^3{ax}}~dx$}
+$$\int{\sec^3{ax}}=
+\frac{\sec{ax}\tan{ax}}{2a}+\frac{1}{2a}\ln(\sec{ax}+\tan{ax})
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 20
+aa:=integrate(sec(a*x)^3,x)
+--R 
+--R
+--R   (1)
+--R               2    sin(a x) + cos(a x) + 1
+--R       cos(a x) log(-----------------------)
+--R                          cos(a x) + 1
+--R     + 
+--R                 2    sin(a x) - cos(a x) - 1
+--R       - cos(a x) log(-----------------------) + sin(a x)
+--R                            cos(a x) + 1
+--R  /
+--R                2
+--R     2a cos(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 21
+bb:=(sec(a*x)*tan(a*x))/(2*a)+1/(2*a)*log(sec(a*x)+tan(a*x))
+--R
+--R        log(tan(a x) + sec(a x)) + sec(a x)tan(a x)
+--R   (2)  -------------------------------------------
+--R                             2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 22
+cc:=aa-bb
+--R
+--R   (3)
+--R                 2
+--R       - cos(a x) log(tan(a x) + sec(a x))
+--R     + 
+--R               2    sin(a x) + cos(a x) + 1
+--R       cos(a x) log(-----------------------)
+--R                          cos(a x) + 1
+--R     + 
+--R                 2    sin(a x) - cos(a x) - 1            2
+--R       - cos(a x) log(-----------------------) - cos(a x) sec(a x)tan(a x)
+--R                            cos(a x) + 1
+--R     + 
+--R       sin(a x)
+--R  /
+--R                2
+--R     2a cos(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 23
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (4)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 24
+dd:=tanrule cc
+--R
+--R   (5)
+--R                 2    sin(a x) + cos(a x)sec(a x)
+--R       - cos(a x) log(---------------------------)
+--R                                cos(a x)
+--R     + 
+--R               2    sin(a x) + cos(a x) + 1
+--R       cos(a x) log(-----------------------)
+--R                          cos(a x) + 1
+--R     + 
+--R               2    sin(a x) - cos(a x) - 1
+--R     - cos(a x) log(-----------------------) + (- cos(a x)sec(a x) + 1)sin(a x)
+--R                          cos(a x) + 1
+--R  /
+--R                2
+--R     2a cos(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 25
+secrule:=rule(sec(a) == 1/cos(a))
+--R
+--R                     1
+--R   (6)  sec(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 26
+ee:=secrule dd
+--R
+--R   (7)
+--R             sin(a x) + 1        sin(a x) + cos(a x) + 1
+--R       - log(------------) + log(-----------------------)
+--R               cos(a x)                cos(a x) + 1
+--R     + 
+--R             sin(a x) - cos(a x) - 1
+--R       - log(-----------------------)
+--R                   cos(a x) + 1
+--R  /
+--R     2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 27
+ff:=expandLog ee
+--R
+--R   (8)
+--R       log(sin(a x) + cos(a x) + 1) - log(sin(a x) + 1)
+--R     + 
+--R       - log(sin(a x) - cos(a x) - 1) + log(cos(a x))
+--R  /
+--R     2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 28     14:453 Schaums and Axiom differ by a constant
+gg:=complexNormalize ff
+--R
+--R        log(- 1)
+--R   (9)  --------
+--R           2a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.454~~~~~$\displaystyle
+\int{\sec^n{ax}\tan{ax}}~dx$}
+$$\int{\sec^n{ax}\tan{ax}}=
+\frac{\sec^n{ax}}{na}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 29
+aa:=integrate(sec(a*x)^n*tan(a*x),x)
+--R
+--R                    1
+--R          n log(---------)
+--R                        2
+--R                cos(a x)
+--R          ----------------
+--R                  2
+--R        %e
+--R   (1)  ------------------
+--R                a n
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 30
+bb:=sec(a*x)^n/(n*a)
+--R
+--R                n
+--R        sec(a x)
+--R   (2)  ---------
+--R           a n
+--R                                                     Type: Expression Integer
+--E
+
+--S 31
+cc:=aa-bb
+--R
+--R                    1
+--R          n log(---------)
+--R                        2
+--R                cos(a x)
+--R          ----------------
+--R                  2                  n
+--R        %e                 - sec(a x)
+--R   (3)  ------------------------------
+--R                      a n
+--R                                                     Type: Expression Integer
+--E
+
+--S 32     14:454 Schaums and Axiom agree
+normalize cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.455~~~~~$\displaystyle
+\int{\frac{dx}{\sec{ax}}}~dx$}
+$$\int{\frac{1}{\sec{ax}}}=
+\frac{\sin{ax}}{a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 33
+aa:=integrate(1/sec(a*x),x)
+--R 
+--R
+--R        sin(a x)
+--R   (1)  --------
+--R            a
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 34
+bb:=sin(a*x)/a
+--R
+--R        sin(a x)
+--R   (2)  --------
+--R            a
+--R                                                     Type: Expression Integer
+--E 
+
+--S 35     14:455 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.456~~~~~$\displaystyle
+\int{x\sec{ax}}~dx$}
+$$\int{x\sec{ax}}=
+\frac{1}{a^2}\left\{\frac{(ax)^2}{2}+\frac{(ax)^4}{8}+\frac{5(ax)^6}{144}
++\cdots+\frac{E_n(ax)^{2n+2}}{(2n+2)(2n)!}+\cdots\right\}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 36     14:456 Axiom cannot compute this integral
+aa:=integrate(x*sec(a*x),x)
+--R 
+--R
+--R           x
+--R         ++
+--I   (1)   |   %N sec(%N a)d%N
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.457~~~~~$\displaystyle
+\int{\frac{\sec{ax}}{x}}~dx$}
+$$\int{\frac{\sec{ax}}{x}}=
+\ln{x}+\frac{(ax)^2}{4}+\frac{5(ax)^4}{96}+\frac{61(ax)^6}{4320}
++\cdots+\frac{E_n(ax)^{2n}}{(2n)(2n)!}+\cdots
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 37     14:457 Axiom cannot compute this integral
+aa:=integrate(sec(a*x)/x,x)
+--R 
+--R
+--R           x
+--I         ++  sec(%N a)
+--I   (1)   |   --------- d%N
+--I        ++       %N
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.458~~~~~$\displaystyle
+\int{x\sec^2{ax}}~dx$}
+$$\int{x\sec^2{ax}}=
+\frac{x}{a}\tan{ax}+\frac{1}{a^2}\ln\cos{ax}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 38
+aa:=integrate(x*sec(a*x)^2,x)
+--R 
+--R
+--R   (1)
+--R                       2                         2cos(a x)
+--R   - cos(a x)log(------------) + cos(a x)log(- ------------) + a x sin(a x)
+--R                 cos(a x) + 1                  cos(a x) + 1
+--R   ------------------------------------------------------------------------
+--R                                   2
+--R                                  a cos(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 39
+bb:=x/a*tan(a*x)+1/a^2*log(cos(a*x))
+--R
+--R        log(cos(a x)) + a x tan(a x)
+--R   (2)  ----------------------------
+--R                      2
+--R                     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 40
+cc:=aa-bb
+--R
+--R   (3)
+--R                                                   2
+--R       - cos(a x)log(cos(a x)) - cos(a x)log(------------)
+--R                                             cos(a x) + 1
+--R     + 
+--R                       2cos(a x)
+--R       cos(a x)log(- ------------) - a x cos(a x)tan(a x) + a x sin(a x)
+--R                     cos(a x) + 1
+--R  /
+--R      2
+--R     a cos(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 41
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (4)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 42
+dd:=tanrule cc
+--R
+--R                                    2                 2cos(a x)
+--R        - log(cos(a x)) - log(------------) + log(- ------------)
+--R                              cos(a x) + 1          cos(a x) + 1
+--R   (5)  ---------------------------------------------------------
+--R                                     2
+--R                                    a
+--R                                                     Type: Expression Integer
+--E
+
+--S 43     14:458 Schaums and Axiom differ by a constant
+ee:=expandLog dd
+--R
+--R        - log(2) + log(- 2)
+--R   (6)  -------------------
+--R                  2
+--R                 a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.459~~~~~$\displaystyle
+\int{\frac{dx}{q+p\sec{ax}}}~dx$}
+$$\int{\frac{1}{q+p\sec{ax}}}=
+\frac{x}{q}-\frac{p}{q}\int{\frac{dx}{p+q\cos{ax}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 44
+aa:=integrate(1/(q+p*sec(a*x)),x)
+--R 
+--R
+--R   (1)
+--R                             +-------+
+--R                             | 2    2      2    2                 +-------+
+--R          (- p cos(a x) - q)\|q  - p   + (q  - p )sin(a x)        | 2    2
+--R    p log(------------------------------------------------) + a x\|q  - p
+--R                           q cos(a x) + p
+--R   [-----------------------------------------------------------------------,
+--R                                     +-------+
+--R                                     | 2    2
+--R                                 a q\|q  - p
+--R                         +---------+
+--R                         |   2    2          +---------+
+--R                sin(a x)\|- q  + p           |   2    2
+--R    - 2p atan(-----------------------) + a x\|- q  + p
+--R              (q + p)cos(a x) + q + p
+--R    ----------------------------------------------------]
+--R                           +---------+
+--R                           |   2    2
+--R                       a q\|- q  + p
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 45
+t1:=integrate(1/(p+q*cos(a*x)),x)
+--R
+--R   (2)
+--R                           +-------+
+--R                           | 2    2        2    2
+--R        (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
+--R    log(--------------------------------------------------)
+--R                          q cos(a x) + p
+--R   [-------------------------------------------------------,
+--R                            +-------+
+--R                            | 2    2
+--R                          a\|q  - p
+--R                     +---------+
+--R                     |   2    2
+--R            sin(a x)\|- q  + p
+--R    2atan(-----------------------)
+--R          (q + p)cos(a x) + q + p
+--R    ------------------------------]
+--R               +---------+
+--R               |   2    2
+--R             a\|- q  + p
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+
+--S 46
+bb1:=x/q-p/q*t1.1
+--R
+--R   (3)
+--R                              +-------+
+--R                              | 2    2        2    2                 +-------+
+--R           (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)        | 2    2
+--R   - p log(--------------------------------------------------) + a x\|q  - p
+--R                             q cos(a x) + p
+--R   ---------------------------------------------------------------------------
+--R                                      +-------+
+--R                                      | 2    2
+--R                                  a q\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 47
+bb2:=x/q-p/q*t1.2
+--R
+--R                             +---------+
+--R                             |   2    2          +---------+
+--R                    sin(a x)\|- q  + p           |   2    2
+--R        - 2p atan(-----------------------) + a x\|- q  + p
+--R                  (q + p)cos(a x) + q + p
+--R   (4)  ----------------------------------------------------
+--R                               +---------+
+--R                               |   2    2
+--R                           a q\|- q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 48
+cc1:=aa.1-bb1
+--R
+--R   (5)
+--R                                +-------+
+--R                                | 2    2      2    2
+--R             (- p cos(a x) - q)\|q  - p   + (q  - p )sin(a x)
+--R       p log(------------------------------------------------)
+--R                              q cos(a x) + p
+--R     + 
+--R                                +-------+
+--R                                | 2    2        2    2
+--R             (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
+--R       p log(--------------------------------------------------)
+--R                               q cos(a x) + p
+--R  /
+--R         +-------+
+--R         | 2    2
+--R     a q\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 49
+cc2:=aa.1-bb2
+--R
+--R   (6)
+--R                                           +-------+
+--R         +---------+                       | 2    2      2    2
+--R         |   2    2     (- p cos(a x) - q)\|q  - p   + (q  - p )sin(a x)
+--R       p\|- q  + p  log(------------------------------------------------)
+--R                                         q cos(a x) + p
+--R     + 
+--R                                   +---------+
+--R          +-------+                |   2    2
+--R          | 2    2        sin(a x)\|- q  + p
+--R       2p\|q  - p  atan(-----------------------)
+--R                        (q + p)cos(a x) + q + p
+--R  /
+--R         +---------+ +-------+
+--R         |   2    2  | 2    2
+--R     a q\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 50
+cc3:=aa.2-bb1
+--R
+--R   (7)
+--R                                           +-------+
+--R         +---------+                       | 2    2        2    2
+--R         |   2    2     (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
+--R       p\|- q  + p  log(--------------------------------------------------)
+--R                                          q cos(a x) + p
+--R     + 
+--R                                     +---------+
+--R            +-------+                |   2    2
+--R            | 2    2        sin(a x)\|- q  + p
+--R       - 2p\|q  - p  atan(-----------------------)
+--R                          (q + p)cos(a x) + q + p
+--R  /
+--R         +---------+ +-------+
+--R         |   2    2  | 2    2
+--R     a q\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 51     14:459 Schaums and Axiom agree
+cc4:=aa.2-bb2
+--R
+--R   (8)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.460~~~~~$\displaystyle
+\int{\sec^n{ax}}~dx$}
+$$\int{\sec^n{ax}}=
+\frac{\sec^{n-2}{ax}\tan{ax}}{a(n-1)}
++\frac{n-2}{n-1}\int{\sec^{n-2}{ax}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 52     14:460 Axiom cannot compute this integral
+aa:=integrate(sec(a*x)^n,x)
+--R 
+--R
+--R           x
+--R         ++           n
+--I   (1)   |   sec(%N a) d%N
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 pp81-82
+\end{thebibliography}
+\end{document}
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diff --git a/src/axiom-website/CATS/schaum23.input.pamphlet b/src/axiom-website/CATS/schaum23.input.pamphlet
new file mode 100644
index 0000000..96485e2
--- /dev/null
+++ b/src/axiom-website/CATS/schaum23.input.pamphlet
@@ -0,0 +1,875 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum23.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.461~~~~~$\displaystyle
+\int{\csc{ax}}~dx$}
+$$\int{\csc{ax}}=
+\frac{1}{a}\ln(\csc{ax}-\cot{ax})=
+\frac{1}{a}\ln\tan{\frac{ax}{2}}
+$$
+&lt;&lt;*&gt;&gt;=
+)spool schaum23.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1
+aa:=integrate(csc(a*x),x)
+--R 
+--R
+--R              sin(a x)
+--R        log(------------)
+--R            cos(a x) + 1
+--R   (1)  -----------------
+--R                a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 2
+bb1:=1/a*log(csc(a*x)-cot(a*x))
+--R
+--R        log(csc(a x) - cot(a x))
+--R   (2)  ------------------------
+--R                    a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3
+bb2:=1/a*log(tan((a*x)/2))
+--R
+--R                a x
+--R        log(tan(---))
+--R                 2
+--R   (3)  -------------
+--R              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 4
+cc1:=aa-bb1
+--R
+--R              sin(a x)
+--R        log(------------) - log(csc(a x) - cot(a x))
+--R            cos(a x) + 1
+--R   (4)  --------------------------------------------
+--R                              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 5
+cotrule:=rule(cot(a) == cos(a)/sin(a))
+--R
+--R                  cos(a)
+--R   (5)  cot(a) == ------
+--R                  sin(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 6
+dd1:=cotrule cc1
+--R
+--R              sin(a x)          csc(a x)sin(a x) - cos(a x)
+--R        log(------------) - log(---------------------------)
+--R            cos(a x) + 1                  sin(a x)
+--R   (6)  ----------------------------------------------------
+--R                                  a
+--R                                                     Type: Expression Integer
+--E
+
+--S 7
+cscrule:=rule(csc(a) == 1/sin(a))
+--R
+--R                     1
+--R   (7)  csc(a) == ------
+--R                  sin(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 8
+ee1:=cscrule dd1
+--R
+--R              sin(a x)          - cos(a x) + 1
+--R        log(------------) - log(--------------)
+--R            cos(a x) + 1           sin(a x)
+--R   (8)  ---------------------------------------
+--R                           a
+--R                                                     Type: Expression Integer
+--E
+
+--S 9
+ff1:=expandLog ee1
+--R
+--R        2log(sin(a x)) - log(cos(a x) + 1) - log(cos(a x) - 1) - log(- 1)
+--R   (9)  -----------------------------------------------------------------
+--R                                        a
+--R                                                     Type: Expression Integer
+--E
+
+--S 10
+gg1:=complexNormalize ff1
+--R
+--R           2log(- 1)
+--R   (10)  - ---------
+--R               a
+--R                                                     Type: Expression Integer
+--E
+
+--S 11
+cc2:=aa-bb2
+--R
+--R                   a x           sin(a x)
+--R         - log(tan(---)) + log(------------)
+--R                    2          cos(a x) + 1
+--R   (11)  -----------------------------------
+--R                          a
+--R                                                     Type: Expression Integer
+--E
+
+--S 12
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                   sin(a)
+--R   (12)  tan(a) == ------
+--R                   cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 13
+dd2:=tanrule cc2
+--R
+--R                                     a x
+--R                                 sin(---)
+--R               sin(a x)               2
+--R         log(------------) - log(--------)
+--R             cos(a x) + 1            a x
+--R                                 cos(---)
+--R                                      2
+--R   (13)  ---------------------------------
+--R                         a
+--R                                                     Type: Expression Integer
+--E
+
+--S 14
+ee2:=expandLog dd2
+--R
+--R                                 a x                                 a x
+--R         log(sin(a x)) - log(sin(---)) - log(cos(a x) + 1) + log(cos(---))
+--R                                  2                                   2
+--R   (14)  -----------------------------------------------------------------
+--R                                         a
+--R                                                     Type: Expression Integer
+--E
+
+--S 15     14:461 Schaums and Axiom agree
+ff2:=complexNormalize ee2
+--R
+--R   (15)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.462~~~~~$\displaystyle
+\int{\csc^2{ax}}~dx$}
+$$\int{\csc^2{ax}}=
+-\frac{\cot{ax}}{a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 16
+aa:=integrate(csc(a*x)^2,x)
+--R 
+--R
+--R           cos(a x)
+--R   (1)  - ----------
+--R          a sin(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 17
+bb:=-cot(a*x)/a
+--R
+--R          cot(a x)
+--R   (2)  - --------
+--R              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 18
+cc:=aa-bb
+--R
+--R        cot(a x)sin(a x) - cos(a x)
+--R   (3)  ---------------------------
+--R                 a sin(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 19
+cotrule:=rule(cot(a) == cos(a)/sin(a))
+--R
+--R                  cos(a)
+--R   (4)  cot(a) == ------
+--R                  sin(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 20     14:462 Schaums and Axiom agree
+dd:=cotrule cc
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.463~~~~~$\displaystyle
+\int{\csc^3{ax}}~dx$}
+$$\int{\csc^3{ax}}=
+-\frac{\csc{ax}\cot{ax}}{2a}+\frac{1}{2a}\ln\tan{\frac{ax}{2}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 21
+aa:=integrate(csc(a*x)^3,x)
+--R 
+--R
+--R                 2           sin(a x)
+--R        (cos(a x)  - 1)log(------------) + cos(a x)
+--R                           cos(a x) + 1
+--R   (1)  -------------------------------------------
+--R                                2
+--R                     2a cos(a x)  - 2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 22
+bb:=-(csc(a*x)*cot(a*x))/(2*a)+1/(2*a)*log(tan((a*x)/2))
+--R
+--R                a x
+--R        log(tan(---)) - cot(a x)csc(a x)
+--R                 2
+--R   (2)  --------------------------------
+--R                       2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 23
+cc:=aa-bb
+--R
+--R   (3)
+--R                  2             a x              2           sin(a x)
+--R       (- cos(a x)  + 1)log(tan(---)) + (cos(a x)  - 1)log(------------)
+--R                                 2                         cos(a x) + 1
+--R     + 
+--R                2
+--R       (cos(a x)  - 1)cot(a x)csc(a x) + cos(a x)
+--R  /
+--R                2
+--R     2a cos(a x)  - 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 24
+cotrule:=rule(cot(a) == cos(a)/sin(a))
+--R
+--R                  cos(a)
+--R   (4)  cot(a) == ------
+--R                  sin(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 25
+dd:=cotrule cc
+--R
+--R   (5)
+--R                  2                     a x
+--R       (- cos(a x)  + 1)sin(a x)log(tan(---))
+--R                                         2
+--R     + 
+--R                2                   sin(a x)
+--R       (cos(a x)  - 1)sin(a x)log(------------) + cos(a x)sin(a x)
+--R                                  cos(a x) + 1
+--R     + 
+--R                3
+--R       (cos(a x)  - cos(a x))csc(a x)
+--R  /
+--R                 2
+--R     (2a cos(a x)  - 2a)sin(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 26
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (6)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 27
+ee:=tanrule dd
+--R
+--R   (7)
+--R                2                   sin(a x)
+--R       (cos(a x)  - 1)sin(a x)log(------------)
+--R                                  cos(a x) + 1
+--R     + 
+--R                                        a x
+--R                                    sin(---)
+--R                  2                      2
+--R       (- cos(a x)  + 1)sin(a x)log(--------) + cos(a x)sin(a x)
+--R                                        a x
+--R                                    cos(---)
+--R                                         2
+--R     + 
+--R                3
+--R       (cos(a x)  - cos(a x))csc(a x)
+--R  /
+--R                 2
+--R     (2a cos(a x)  - 2a)sin(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 28
+cscrule:=rule(csc(a) == 1/sin(a))
+--R
+--R                     1
+--R   (8)  csc(a) == ------
+--R                  sin(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 29
+ff:=cscrule ee
+--R
+--R   (9)
+--R                2             2      sin(a x)
+--R       (cos(a x)  - 1)sin(a x) log(------------)
+--R                                   cos(a x) + 1
+--R     + 
+--R                                         a x
+--R                                     sin(---)
+--R                  2             2         2                      2           3
+--R       (- cos(a x)  + 1)sin(a x) log(--------) + cos(a x)sin(a x)  + cos(a x)
+--R                                         a x
+--R                                     cos(---)
+--R                                          2
+--R     + 
+--R       - cos(a x)
+--R  /
+--R                 2              2
+--R     (2a cos(a x)  - 2a)sin(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 30
+gg:=expandLog ff
+--R
+--R   (10)
+--R                2             2
+--R       (cos(a x)  - 1)sin(a x) log(sin(a x))
+--R     + 
+--R                  2             2        a x
+--R       (- cos(a x)  + 1)sin(a x) log(sin(---))
+--R                                          2
+--R     + 
+--R                  2             2
+--R       (- cos(a x)  + 1)sin(a x) log(cos(a x) + 1)
+--R     + 
+--R                2             2        a x                     2           3
+--R       (cos(a x)  - 1)sin(a x) log(cos(---)) + cos(a x)sin(a x)  + cos(a x)
+--R                                        2
+--R     + 
+--R       - cos(a x)
+--R  /
+--R                 2              2
+--R     (2a cos(a x)  - 2a)sin(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 31     14:463 Schaums and Axiom agree
+hh:=complexNormalize gg
+--R
+--R   (11)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.464~~~~~$\displaystyle
+\int{\csc^n{ax}\cot{ax}}~dx$}
+$$\int{\csc^n{ax}\cot{ax}}=
+-\frac{csc^n{ax}}{na}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 32
+aa:=integrate(csc(a*x)^n*cot(a*x),x)
+--R 
+--R
+--R                          1
+--R            n log(- -------------)
+--R                            2
+--R                    cos(a x)  - 1
+--R            ----------------------
+--R                       2
+--R          %e
+--R   (1)  - ------------------------
+--R                     a n
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 33
+bb:=-csc(a*x)^n/(n*a)
+--R
+--R                  n
+--R          csc(a x)
+--R   (2)  - ---------
+--R             a n
+--R                                                     Type: Expression Integer
+--E
+
+--S 34
+cc:=aa-bb
+--R
+--R                          1
+--R            n log(- -------------)
+--R                            2
+--R                    cos(a x)  - 1
+--R            ----------------------
+--R                       2                     n
+--R        - %e                       + csc(a x)
+--R   (3)  --------------------------------------
+--R                          a n
+--R                                                     Type: Expression Integer
+--E
+
+--S 35     14:464 Schaums and Axiom agree
+normalize cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.465~~~~~$\displaystyle
+\int{\frac{dx}{\csc{ax}}}~dx$}
+$$\int{\frac{1}{\csc{ax}}}=
+-\frac{\cos{ax}}{a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 36
+aa:=integrate(1/csc(a*x),x)
+--R 
+--R
+--R          cos(a x)
+--R   (1)  - --------
+--R              a
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 37
+bb:=-cos(a*x)/a
+--R
+--R          cos(a x)
+--R   (2)  - --------
+--R              a
+--R                                                     Type: Expression Integer
+--E 
+
+--S 38     14:465 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.466~~~~~$\displaystyle
+\int{x\csc{ax}}~dx$}
+$$\int{x\csc{ax}}=
+\frac{1}{a^2}\left\{ax+\frac{(ax)^3}{18}+\frac{7(ax)^5}{1800}
++\cdots+\frac{2(2^{2n-1}-1)B_n(ax)^{2n+1}}{(2n+1)!}+\cdots\right\}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 39     14:466 Axiom cannot compute this integral
+aa:=integrate(x*csc(a*x),x)
+--R 
+--R
+--R           x
+--R         ++
+--I   (1)   |   %H csc(%H a)d%H
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.467~~~~~$\displaystyle
+\int{\frac{\csc{ax}}{x}}~dx$}
+$$\int{\frac{\csc{ax}}{x}}=
+-\frac{1}{ax}+\frac{(ax)}{6}+\frac{7(ax)^3}{1800}
++\cdots+\frac{2(2^{2n-1}-1)B_n(ax)^{2n-1}}{(2n-1)(2n)!}+\cdots
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 40     14:467 Axiom cannot compute this integral
+aa:=integrate(csc(a*x)/x,x)
+--R 
+--R
+--R           x
+--I         ++  csc(%H a)
+--I   (1)   |   --------- d%H
+--I        ++       %H
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.468~~~~~$\displaystyle
+\int{x\csc^2{ax}}~dx$}
+$$\int{x\csc^2{ax}}=
+-\frac{x\cot{ax}}{a}+\frac{1}{a^2}\ln\sin{ax}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 41
+aa:=integrate(x*csc(a*x)^2,x)
+--R 
+--R
+--R                      sin(a x)                        2
+--R        sin(a x)log(------------) - sin(a x)log(------------) - a x cos(a x)
+--R                    cos(a x) + 1                cos(a x) + 1
+--R   (1)  --------------------------------------------------------------------
+--R                                      2
+--R                                     a sin(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 42
+bb:=-(x*cot(a*x))/a+1/a^2*log(sin(a*x))
+--R
+--R        log(sin(a x)) - a x cot(a x)
+--R   (2)  ----------------------------
+--R                      2
+--R                     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 43
+cc:=aa-bb
+--R
+--R   (3)
+--R                                               sin(a x)
+--R       - sin(a x)log(sin(a x)) + sin(a x)log(------------)
+--R                                             cos(a x) + 1
+--R     + 
+--R                           2
+--R       - sin(a x)log(------------) + a x cot(a x)sin(a x) - a x cos(a x)
+--R                     cos(a x) + 1
+--R  /
+--R      2
+--R     a sin(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 44
+cotrule:=rule(cot(a) == cos(a)/sin(a))
+--R
+--R                  cos(a)
+--R   (4)  cot(a) == ------
+--R                  sin(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 45
+dd:=cotrule cc
+--R
+--R                                sin(a x)                2
+--R        - log(sin(a x)) + log(------------) - log(------------)
+--R                              cos(a x) + 1        cos(a x) + 1
+--R   (5)  -------------------------------------------------------
+--R                                    2
+--R                                   a
+--R                                                     Type: Expression Integer
+--E
+
+--S 46     14:468 Schaums and Axiom differ by a constant
+ee:=expandLog dd
+--R
+--R          log(2)
+--R   (6)  - ------
+--R             2
+--R            a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.469~~~~~$\displaystyle
+\int{\frac{dx}{q+p\csc{ax}}}~dx$}
+$$\int{\frac{1}{q+p\csc{ax}}}=
+\frac{x}{q}-\frac{p}{q}\int{\frac{1}{p+q\sin{ax}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 47
+aa:=integrate(1/(q+p*csc(a*x)),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R           p
+--R        *
+--R           log
+--R                                                          +-------+
+--R                                    2    2             2  | 2    2
+--R                  (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
+--R                + 
+--R                      2    3              3    2              3    2
+--R                  (p q  - p )sin(a x) + (q  - p q)cos(a x) + q  - p q
+--R             /
+--R                q sin(a x) + p
+--R       + 
+--R             +-------+
+--R             | 2    2
+--R         a x\|q  - p
+--R    /
+--R           +-------+
+--R           | 2    2
+--R       a q\|q  - p
+--R     ,
+--R                                          +---------+
+--R                                          |   2    2         +---------+
+--R            (p sin(a x) + q cos(a x) + q)\|- q  + p          |   2    2
+--R    2p atan(-----------------------------------------) + a x\|- q  + p
+--R                     2    2             2    2
+--R                   (q  - p )cos(a x) + q  - p
+--R    --------------------------------------------------------------------]
+--R                                   +---------+
+--R                                   |   2    2
+--R                               a q\|- q  + p
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+
+--S 48
+t1:=integrate(1/(p+q*sin(a*x)),x)
+--R
+--R   (2)
+--R   [
+--R       log
+--R                                                      +-------+
+--R                                2    2             2  | 2    2
+--R              (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
+--R            + 
+--R                    2    3                3    2              3    2
+--R              (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
+--R         /
+--R            q sin(a x) + p
+--R    /
+--R         +-------+
+--R         | 2    2
+--R       a\|q  - p
+--R     ,
+--R                                          +---------+
+--R                                          |   2    2
+--R            (p sin(a x) + q cos(a x) + q)\|- q  + p
+--R      2atan(-----------------------------------------)
+--R                     2    2             2    2
+--R                   (q  - p )cos(a x) + q  - p
+--R    - ------------------------------------------------]
+--R                          +---------+
+--R                          |   2    2
+--R                        a\|- q  + p
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 49
+bb1:=x/q-p/q*t1.1
+--R
+--R   (3)
+--R       -
+--R            p
+--R         *
+--R            log
+--R                                                           +-------+
+--R                                     2    2             2  | 2    2
+--R                   (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
+--R                 + 
+--R                         2    3                3    2              3    2
+--R                   (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
+--R              /
+--R                 q sin(a x) + p
+--R     + 
+--R           +-------+
+--R           | 2    2
+--R       a x\|q  - p
+--R  /
+--R         +-------+
+--R         | 2    2
+--R     a q\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 50
+bb2:=x/q-p/q*t1.2
+--R
+--R                                              +---------+
+--R                                              |   2    2         +---------+
+--R                (p sin(a x) + q cos(a x) + q)\|- q  + p          |   2    2
+--R        2p atan(-----------------------------------------) + a x\|- q  + p
+--R                         2    2             2    2
+--R                       (q  - p )cos(a x) + q  - p
+--R   (4)  --------------------------------------------------------------------
+--R                                       +---------+
+--R                                       |   2    2
+--R                                   a q\|- q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 51
+cc1:=aa.1-bb1
+--R
+--R   (5)
+--R         p
+--R      *
+--R         log
+--R                                                        +-------+
+--R                                  2    2             2  | 2    2
+--R                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
+--R              + 
+--R                    2    3              3    2              3    2
+--R                (p q  - p )sin(a x) + (q  - p q)cos(a x) + q  - p q
+--R           /
+--R              q sin(a x) + p
+--R     + 
+--R         p
+--R      *
+--R         log
+--R                                                        +-------+
+--R                                  2    2             2  | 2    2
+--R                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
+--R              + 
+--R                      2    3                3    2              3    2
+--R                (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
+--R           /
+--R              q sin(a x) + p
+--R  /
+--R         +-------+
+--R         | 2    2
+--R     a q\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 52
+cc2:=aa.2-bb1
+--R
+--R   (6)
+--R           +---------+
+--R           |   2    2
+--R         p\|- q  + p
+--R      *
+--R         log
+--R                                                        +-------+
+--R                                  2    2             2  | 2    2
+--R                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
+--R              + 
+--R                      2    3                3    2              3    2
+--R                (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
+--R           /
+--R              q sin(a x) + p
+--R     + 
+--R                                                      +---------+
+--R          +-------+                                   |   2    2
+--R          | 2    2      (p sin(a x) + q cos(a x) + q)\|- q  + p
+--R       2p\|q  - p  atan(-----------------------------------------)
+--R                                 2    2             2    2
+--R                               (q  - p )cos(a x) + q  - p
+--R  /
+--R         +---------+ +-------+
+--R         |   2    2  | 2    2
+--R     a q\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 53
+cc3:=aa.1-bb2
+--R
+--R   (7)
+--R           +---------+
+--R           |   2    2
+--R         p\|- q  + p
+--R      *
+--R         log
+--R                                                        +-------+
+--R                                  2    2             2  | 2    2
+--R                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
+--R              + 
+--R                    2    3              3    2              3    2
+--R                (p q  - p )sin(a x) + (q  - p q)cos(a x) + q  - p q
+--R           /
+--R              q sin(a x) + p
+--R     + 
+--R                                                        +---------+
+--R            +-------+                                   |   2    2
+--R            | 2    2      (p sin(a x) + q cos(a x) + q)\|- q  + p
+--R       - 2p\|q  - p  atan(-----------------------------------------)
+--R                                   2    2             2    2
+--R                                 (q  - p )cos(a x) + q  - p
+--R  /
+--R         +---------+ +-------+
+--R         |   2    2  | 2    2
+--R     a q\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 54     14:469 Schaums and Axiom agree
+cc4:=aa.2-bb2
+--R
+--R   (8)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.470~~~~~$\displaystyle
+\int{\csc^n{ax}}~dx$}
+$$\int{\csc^n{ax}}=
+-\frac{\csc^{n-2}{ax}\cot{ax}}{a(n-1)}
++\frac{n-2}{n-1}\int{\csc^{n-2}{ax}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 55     14:470 Axiom cannot compute this integral
+aa:=integrate(csc(a*x)^n,x)
+--R 
+--R
+--R           x
+--R         ++           n
+--I   (1)   |   csc(%H a) d%H
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 p82
+\end{thebibliography}
+\end{document}
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diff --git a/src/axiom-website/CATS/schaum24.input.pamphlet b/src/axiom-website/CATS/schaum24.input.pamphlet
new file mode 100644
index 0000000..71f28d5
--- /dev/null
+++ b/src/axiom-website/CATS/schaum24.input.pamphlet
@@ -0,0 +1,2555 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum24.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.471~~~~~$\displaystyle
+\int{\sin^{-1}{\frac{x}{a}}}~dx$}
+$$\int{\sin^{-1}{\frac{x}{a}}}=
+x\sin^{-1}{\frac{x}{a}}+\sqrt{a^2-x^2}
+$$
+&lt;&lt;*&gt;&gt;=
+)spool schaum24.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1
+aa:=integrate(asin(x/a),x)
+--R 
+--R
+--R                    +---------+
+--R                    |   2    2       +---------+
+--R                 2x\|- x  + a        |   2    2
+--R        - x atan(--------------) + 2\|- x  + a
+--R                      2    2
+--R                    2x  - a
+--R   (1)  ----------------------------------------
+--R                            2
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 2
+bb:=s+asin(x/a)+sqrt(a^2-x^2)
+--R
+--R         +---------+
+--R         |   2    2         x
+--R   (2)  \|- x  + a   + asin(-) + s
+--R                            a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3      14:471 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R                    +---------+
+--R                    |   2    2
+--R                 2x\|- x  + a            x
+--R        - x atan(--------------) - 2asin(-) - 2s
+--R                      2    2             a
+--R                    2x  - a
+--R   (3)  ----------------------------------------
+--R                            2
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.472~~~~~$\displaystyle
+\int{x\sin^{-1}{\frac{x}{a}}}~dx$}
+$$\int{x\sin^{-1}{\frac{x}{a}}}=
+\left(\frac{x^2}{2}-\frac{a^2}{4}\right)\sin^{-1}{\frac{x}{a}}
++\frac{x\sqrt{a^2-x^2}}{4}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 4
+aa:=integrate(x*asin(x/a),x)
+--R 
+--R
+--R                            +---------+
+--R                            |   2    2        +---------+
+--R             2    2      2x\|- x  + a         |   2    2
+--R        (- 2x  + a )atan(--------------) + 2x\|- x  + a
+--R                              2    2
+--R                            2x  - a
+--R   (1)  -------------------------------------------------
+--R                                8
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 5
+bb:=(x^2/2-a^2/4)*asin(x/a)+(x*sqrt(a^2-x^2))/4
+--R
+--R          +---------+
+--R          |   2    2       2    2      x
+--R        x\|- x  + a   + (2x  - a )asin(-)
+--R                                       a
+--R   (2)  ---------------------------------
+--R                        4
+--R                                                     Type: Expression Integer
+--E
+
+--S 6
+cc:=aa-bb
+--R
+--R                            +---------+
+--R                            |   2    2
+--R             2    2      2x\|- x  + a           2     2      x
+--R        (- 2x  + a )atan(--------------) + (- 4x  + 2a )asin(-)
+--R                              2    2                         a
+--R                            2x  - a
+--R   (3)  -------------------------------------------------------
+--R                                   8
+--R                                                     Type: Expression Integer
+--E
+
+@
+Here we try to understand why we cannot find a simplification
+that makes these two expressions equal. If the expressions were
+equal then we could use them as functions, substitute floating
+point values and expect the same numeric results. So we try that here.
+&lt;&lt;*&gt;&gt;=
+)clear all
+@
+This is the initial integrand.
+&lt;&lt;*&gt;&gt;=
+--S 7
+t1:=x*asin(x/a)
+--R
+--R               x
+--R   (1)  x asin(-)
+--R               a
+--R                                                     Type: Expression Integer
+--E
+@
+This is the integral result provided by Axiom.
+&lt;&lt;*&gt;&gt;=
+--S 8
+t2:=integrate(t1,x)
+--R
+--R                            +---------+
+--R                            |   2    2        +---------+
+--R             2    2      2x\|- x  + a         |   2    2
+--R        (- 2x  + a )atan(--------------) + 2x\|- x  + a
+--R                              2    2
+--R                            2x  - a
+--R   (2)  -------------------------------------------------
+--R                                8
+--R                                          Type: Union(Expression Integer,...)
+--E
+@
+This is the derivative of the integral computed by Axiom
+&lt;&lt;*&gt;&gt;=
+--S 9
+t3:=D(t2,x)
+--R
+--R                    +---------+
+--R                    |   2    2
+--R                 2x\|- x  + a
+--R          x atan(--------------)
+--R                      2    2
+--R                    2x  - a
+--R   (3)  - ----------------------
+--R                     2
+--R                                                     Type: Expression Integer
+--E
+@
+This is the integral result provided by Schaums
+&lt;&lt;*&gt;&gt;=
+--S 10
+t4:=(x^2/2-a^2/4)*asin(x/a)+(x*sqrt(a^2-x^2))/4
+--R
+--R          +---------+
+--R          |   2    2       2    2      x
+--R        x\|- x  + a   + (2x  - a )asin(-)
+--R                                       a
+--R   (4)  ---------------------------------
+--R                        4
+--R                                                     Type: Expression Integer
+--E
+@
+This is the derivative of the integral of the original function
+according to Schaums.
+&lt;&lt;*&gt;&gt;=
+--S 11
+t5:=D(t4,x)
+--R
+--R   (5)
+--R                                           +---------+
+--R                 +---------+               |   2    2               +---------+
+--R              x  |   2    2        2    3  |- x  + a        2    2  |   2    2
+--R   (4a x asin(-)\|- x  + a   - 2a x  + a ) |---------  + (2x  - a )\|- x  + a
+--R              a                            |     2
+--R                                          \|    a
+--R   ----------------------------------------------------------------------------
+--R                                           +---------+
+--R                               +---------+ |   2    2
+--R                               |   2    2  |- x  + a
+--R                            4a\|- x  + a   |---------
+--R                                           |     2
+--R                                          \|    a
+--R                                                     Type: Expression Integer
+--E
+@
+Now we create a function for computing the integrand's values.
+&lt;&lt;*&gt;&gt;=
+--S 12
+f:=makeFloatFunction(t1,x,a)
+--I   Compiling function %BF with type (DoubleFloat,DoubleFloat) -&gt; 
+--R      DoubleFloat 
+--R
+--I   (6)  theMap(MKBCFUNC;binaryFunction;SM;2!0,120)
+--R                             Type: ((DoubleFloat,DoubleFloat) -&gt; DoubleFloat)
+--E
+@
+Now we create a function for computing Axiom's values for its integrand.
+&lt;&lt;*&gt;&gt;=
+--S 13
+axiom:=makeFloatFunction(t3,x,a)
+--I   Compiling function %BJ with type (DoubleFloat,DoubleFloat) -&gt; 
+--R      DoubleFloat 
+--R
+--I   (7)  theMap(MKBCFUNC;binaryFunction;SM;2!0,996)
+--R                             Type: ((DoubleFloat,DoubleFloat) -&gt; DoubleFloat)
+--E
+@
+Now we create a function for computing Schams values for its integrand.
+&lt;&lt;*&gt;&gt;=
+--S 14
+schaums:=makeFloatFunction(t5,x,a)
+--I   Compiling function %BK with type (DoubleFloat,DoubleFloat) -&gt; 
+--R      DoubleFloat 
+--R
+--I   (8)  theMap(MKBCFUNC;binaryFunction;SM;2!0,62)
+--R                             Type: ((DoubleFloat,DoubleFloat) -&gt; DoubleFloat)
+--E
+@
+And now we compute the floating point values for each function
+and compare the results. As can be clearly seen, the Axiom result
+lies on a different branch cut from the Schaums result and the
+functions are only equal within the branch cut range. This is a
+generic problem with all of the inverse functions that are
+multi-valued.
+&lt;&lt;*&gt;&gt;=
+--S 15     14:472 Schaums and Axiom agree (modulo branch cuts)
+[ [f(i::Float,i::Float+1.0::Float)::Float,axiom(i::Float,i::Float+1.0::Float)::Float,schaums(i::Float,i::Float+1.0::Float)::Float] for i in 1..4]
+--R
+--R   (9)
+--R   [[0.5235987755 9829892668,0.5235987755 9829892668,0.5235987755 9829881566],
+--R    [1.4594553124 539326738,1.4594553124 539326738,1.4594553124 539324518],
+--R    [2.5441862369 444430136,- 2.1682027434 402466604,2.5441862369 444430136],
+--R    [3.7091808720 064496363,- 2.5740044351 731374839,3.7091808720 064500804]]
+--R                                                        Type: List List Float
+--E
+@
+
+\section{\cite{1}:14.473~~~~~$\displaystyle
+\int{x^2\sin^{-1}\frac{x}{a}}~dx$}
+$$\int{x^2\sin^{-1}\frac{x}{a}}=
+\frac{x^3}{3}\sin^{-1}\frac{x}{a}+\frac{(x^2+2a^2)\sqrt{a^2-x^2}}{9}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 16
+aa:=integrate(x^2*asin(x/a),x)
+--R 
+--R
+--R                     +---------+
+--R                     |   2    2                 +---------+
+--R            3     2x\|- x  + a         2     2  |   2    2
+--R        - 3x atan(--------------) + (2x  + 4a )\|- x  + a
+--R                       2    2
+--R                     2x  - a
+--R   (1)  ---------------------------------------------------
+--R                                 18
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 17
+bb:=x^3/3*asin(x/a)+((x^2+2*a^2)*sqrt(a^2-x^2))/9
+--R
+--R                   +---------+
+--R          2     2  |   2    2      3     x
+--R        (x  + 2a )\|- x  + a   + 3x asin(-)
+--R                                         a
+--R   (2)  -----------------------------------
+--R                         9
+--R                                                     Type: Expression Integer
+--E
+
+--S 18     14:473 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R                    +---------+
+--R                    |   2    2
+--R           3     2x\|- x  + a        3     x
+--R        - x atan(--------------) - 2x asin(-)
+--R                      2    2               a
+--R                    2x  - a
+--R   (3)  -------------------------------------
+--R                          6
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.474~~~~~$\displaystyle
+\int{\frac{\sin^{-1}(x/a)}{x}}~dx$}
+$$\int{\frac{\sin^{-1}(x/a)}{x}}=
+\frac{x}{a}+\frac{(x/a)^3}{2\cdot 3\cdot 3}
++\frac{1\cdot 3(x/a)^5}{2\cdot 4\cdot 5\cdot 5}
++\frac{1\cdot 3\cdot 5(x/a)^7}{2\cdot 4\cdot 6\cdot 7\cdot 7}+\cdots
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 19     14:474 Axiom cannot compute this integral
+aa:=integrate(asin(x/a)/x,x)
+--R 
+--R
+--I                  %H
+--R           x asin(--)
+--R         ++        a
+--I   (1)   |   -------- d%H
+--I        ++      %H
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.475~~~~~$\displaystyle
+\int{\frac{\sin^{-1}{(x/a)}}{x^2}}~dx$}
+$$\int{\frac{\sin^{-1}{(x/a)}}{x^2}}=
+-\frac{\sin^{-1}(x/a)}{x}
+-\frac{1}{a}\ln\left(\frac{a+\sqrt{a^2-x^2}}{x}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 20
+aa:=integrate(asin(x/a)/x^2,x)
+--R 
+--R
+--R   (1)
+--R                                                                   +---------+
+--R            +---------+               +---------+                  |   2    2
+--R            |   2    2                |   2    2                2x\|- x  + a
+--R   - x log(\|- x  + a   + a) + x log(\|- x  + a   - a) + a atan(--------------)
+--R                                                                     2    2
+--R                                                                   2x  - a
+--R   ----------------------------------------------------------------------------
+--R                                       2a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 21
+bb:=-asin(x/a)/x-1/a*log((a+sqrt(a^2-x^2))/x)
+--R
+--R                 +---------+
+--R                 |   2    2
+--R                \|- x  + a   + a           x
+--R        - x log(----------------) - a asin(-)
+--R                        x                  a
+--R   (2)  -------------------------------------
+--R                         a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 22     14:475 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R                +---------+               +---------+
+--R                |   2    2                |   2    2
+--R       - x log(\|- x  + a   + a) + x log(\|- x  + a   - a)
+--R     + 
+--R               +---------+                  +---------+
+--R               |   2    2                   |   2    2
+--R              \|- x  + a   + a           2x\|- x  + a              x
+--R       2x log(----------------) + a atan(--------------) + 2a asin(-)
+--R                      x                       2    2               a
+--R                                            2x  - a
+--R  /
+--R     2a x
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.476~~~~~$\displaystyle
+\int{\left(sin^{-1}\frac{x}{a}\right)^2}~dx$}
+$$\int{\left(sin^{-1}\frac{x}{a}\right)^2}=
+x\left(\sin^{-1}\frac{x}{a}\right)^2-2x+2\sqrt{a^2-x^2}\sin^{-1}\frac{x}{a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 23
+aa:=integrate(asin(x/a)^2,x)
+--R 
+--R
+--R                  +---------+ 2                        +---------+
+--R                  |   2    2        +---------+        |   2    2
+--R               2x\|- x  + a         |   2    2      2x\|- x  + a
+--R        x atan(--------------)  - 4\|- x  + a  atan(--------------) - 8x
+--R                    2    2                               2    2
+--R                  2x  - a                              2x  - a
+--R   (1)  ----------------------------------------------------------------
+--R                                        4
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 24
+bb:=x*asin(x/a)^2-2*x+2*sqrt(a^2-x^2)*asin(x/a)
+--R
+--R                 +---------+
+--R              x  |   2    2           x 2
+--R   (2)  2asin(-)\|- x  + a   + x asin(-)  - 2x
+--R              a                       a
+--R                                                     Type: Expression Integer
+--E
+
+--S 25     14:476 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R                 +---------+ 2                        +---------+
+--R                 |   2    2        +---------+        |   2    2
+--R              2x\|- x  + a         |   2    2      2x\|- x  + a
+--R       x atan(--------------)  - 4\|- x  + a  atan(--------------)
+--R                   2    2                               2    2
+--R                 2x  - a                              2x  - a
+--R     + 
+--R                  +---------+
+--R               x  |   2    2            x 2
+--R       - 8asin(-)\|- x  + a   - 4x asin(-)
+--R               a                        a
+--R  /
+--R     4
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.477~~~~~$\displaystyle
+\int{\cos^{-1}\frac{x}{a}}~dx$}
+$$\int{\cos^{-1}\frac{x}{a}}=
+x\cos^{-1}\frac{x}{a}-\sqrt{a^2-x^2}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 26
+aa:=integrate(acos(x/a),x)
+--R 
+--R
+--R                  +---------+
+--R                  |   2    2       +---------+
+--R               2x\|- x  + a        |   2    2
+--R        x atan(--------------) - 2\|- x  + a
+--R                    2    2
+--R                  2x  - a
+--R   (1)  --------------------------------------
+--R                           2
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 27
+bb:=x*acos(x/a)-sqrt(a^2-x^2)
+--R
+--R           +---------+
+--R           |   2    2           x
+--R   (2)  - \|- x  + a   + x acos(-)
+--R                                a
+--R                                                     Type: Expression Integer
+--E
+
+--S 28     14:477 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R                  +---------+
+--R                  |   2    2
+--R               2x\|- x  + a              x
+--R        x atan(--------------) - 2x acos(-)
+--R                    2    2               a
+--R                  2x  - a
+--R   (3)  -----------------------------------
+--R                         2
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.478~~~~~$\displaystyle
+\int{x\cos^{-1}\frac{x}{a}}~dx$}
+$$\int{x\cos^{-1}\frac{x}{a}}=
+\left(\frac{x^2}{2}-\frac{a^2}{4}\right)\cos^{-1}\frac{x}{a}
+-\frac{x\sqrt{a^2-x^2}}{4}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 29
+aa:=integrate(x*acos(x/a),x)
+--R 
+--R
+--R                          +---------+
+--R                          |   2    2        +---------+
+--R           2    2      2x\|- x  + a         |   2    2
+--R        (2x  - a )atan(--------------) - 2x\|- x  + a
+--R                            2    2
+--R                          2x  - a
+--R   (1)  -----------------------------------------------
+--R                               8
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 30
+bb:=(x^2/2-a^2/4)*acos(x/a)-(x*sqrt(a^2-x^2))/4
+--R
+--R            +---------+
+--R            |   2    2       2    2      x
+--R        - x\|- x  + a   + (2x  - a )acos(-)
+--R                                         a
+--R   (2)  -----------------------------------
+--R                         4
+--R                                                     Type: Expression Integer
+--E
+
+--S 31     14:478 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R                          +---------+
+--R                          |   2    2
+--R           2    2      2x\|- x  + a           2     2      x
+--R        (2x  - a )atan(--------------) + (- 4x  + 2a )acos(-)
+--R                            2    2                         a
+--R                          2x  - a
+--R   (3)  -----------------------------------------------------
+--R                                  8
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.479~~~~~$\displaystyle
+\int{x^2\cos^{-1}\frac{x}{a}}~dx$}
+$$\int{x^2\cos^{-1}\frac{x}{a}}=
+\frac{x^3}{3}\cos^{-1}\frac{x}{a}-\frac{(x^2+2a^2)\sqrt{a^2-x^2}}{9}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 32
+aa:=integrate(x^2*acos(x/a),x)
+--R 
+--R
+--R                   +---------+
+--R                   |   2    2                   +---------+
+--R          3     2x\|- x  + a           2     2  |   2    2
+--R        3x atan(--------------) + (- 2x  - 4a )\|- x  + a
+--R                     2    2
+--R                   2x  - a
+--R   (1)  ---------------------------------------------------
+--R                                 18
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 33
+bb:=x^3/3*acos(x/a)-((x^2+2*a^2)*sqrt(a^2-x^2))/9
+--R
+--R                     +---------+
+--R            2     2  |   2    2      3     x
+--R        (- x  - 2a )\|- x  + a   + 3x acos(-)
+--R                                           a
+--R   (2)  -------------------------------------
+--R                          9
+--R                                                     Type: Expression Integer
+--E
+
+--S 34     14:479 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R                  +---------+
+--R                  |   2    2
+--R         3     2x\|- x  + a        3     x
+--R        x atan(--------------) - 2x acos(-)
+--R                    2    2               a
+--R                  2x  - a
+--R   (3)  -----------------------------------
+--R                         6
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.480~~~~~$\displaystyle
+\int{\frac{\cos^{-1}(x/a)}{x}}~dx$}
+$$\int{\frac{\cos^{-1}(x/a)}{x}}=
+\frac{x}{2}\ln{x}-\int{\frac{\sin^{-1}(x/a)}{x}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 35     14:480 Axiom cannot compute this integral
+aa:=integrate(acos(x/a)/x,x)
+--R 
+--R
+--I                  %H
+--R           x acos(--)
+--R         ++        a
+--I   (1)   |   -------- d%H
+--I        ++      %H
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.481~~~~~$\displaystyle
+\int{\frac{\cos^{-1}(x/a)}{x^2}}~dx$}
+$$\int{\frac{\cos^{-1}(x/a)}{x^2}}=
+-\frac{\cos^{-1}(x/a)}{x}+\frac{1}{a}\ln\left(\frac{a+\sqrt{a^2-x^2}}{x}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 36
+aa:=integrate(acos(x/a)/x^2,x)
+--R 
+--R
+--R   (1)
+--R                                                                 +---------+
+--R          +---------+               +---------+                  |   2    2
+--R          |   2    2                |   2    2                2x\|- x  + a
+--R   x log(\|- x  + a   + a) - x log(\|- x  + a   - a) - a atan(--------------)
+--R                                                                   2    2
+--R                                                                 2x  - a
+--R   --------------------------------------------------------------------------
+--R                                      2a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 37
+bb:=-acos(x/a)/x+1/a*log((a+sqrt(a^2-x^2))/x)
+--R
+--R               +---------+
+--R               |   2    2
+--R              \|- x  + a   + a           x
+--R        x log(----------------) - a acos(-)
+--R                      x                  a
+--R   (2)  -----------------------------------
+--R                        a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 38     14:481 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R              +---------+               +---------+
+--R              |   2    2                |   2    2
+--R       x log(\|- x  + a   + a) - x log(\|- x  + a   - a)
+--R     + 
+--R                 +---------+                  +---------+
+--R                 |   2    2                   |   2    2
+--R                \|- x  + a   + a           2x\|- x  + a              x
+--R       - 2x log(----------------) - a atan(--------------) + 2a acos(-)
+--R                        x                       2    2               a
+--R                                              2x  - a
+--R  /
+--R     2a x
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.482~~~~~$\displaystyle
+\int{\left(\cos^{-1}\frac{x}{a}\right)^2}~dx$}
+$$\int{\left(\cos^{-1}\frac{x}{a}\right)^2}=
+x\left(\cos^{-1}\frac{x}{a}\right)^2-2x-2\sqrt{a^2-x^2}\cos^{-1}\frac{x}{a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 39
+aa:=integrate(acos(x/a)^2,x)
+--R 
+--R
+--R                  +---------+ 2                        +---------+
+--R                  |   2    2        +---------+        |   2    2
+--R               2x\|- x  + a         |   2    2      2x\|- x  + a
+--R        x atan(--------------)  - 4\|- x  + a  atan(--------------) - 8x
+--R                    2    2                               2    2
+--R                  2x  - a                              2x  - a
+--R   (1)  ----------------------------------------------------------------
+--R                                        4
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 40
+bb:=x*acos(x/a)^2-2*x-2*sqrt(a^2-x^2)*acos(x/a)
+--R
+--R                   +---------+
+--R                x  |   2    2           x 2
+--R   (2)  - 2acos(-)\|- x  + a   + x acos(-)  - 2x
+--R                a                       a
+--R                                                     Type: Expression Integer
+--E
+
+--S 41     14:482 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R                 +---------+ 2                        +---------+
+--R                 |   2    2        +---------+        |   2    2
+--R              2x\|- x  + a         |   2    2      2x\|- x  + a
+--R       x atan(--------------)  - 4\|- x  + a  atan(--------------)
+--R                   2    2                               2    2
+--R                 2x  - a                              2x  - a
+--R     + 
+--R                +---------+
+--R             x  |   2    2            x 2
+--R       8acos(-)\|- x  + a   - 4x acos(-)
+--R             a                        a
+--R  /
+--R     4
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.483~~~~~$\displaystyle
+\int{\tan^{-1}\frac{x}{a}}~dx$}
+$$\int{\tan^{-1}\frac{x}{a}}=
+x\tan^{-1}\frac{x}{a}-\frac{a}{2}\ln(x^2+a^2)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 42
+aa:=integrate(atan(x/a),x)
+--R 
+--R
+--R                 2    2             2a x
+--R        - a log(x  + a ) - x atan(-------)
+--R                                   2    2
+--R                                  x  - a
+--R   (1)  ----------------------------------
+--R                         2
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 43
+bb:=x*atan(x/a)-a/2*log(x^2+a^2)
+--R
+--R                 2    2            x
+--R        - a log(x  + a ) + 2x atan(-)
+--R                                   a
+--R   (2)  -----------------------------
+--R                      2
+--R                                                     Type: Expression Integer
+--E
+
+--S 44
+cc:=aa-bb
+--R
+--R                  x             2a x
+--R        - 2x atan(-) - x atan(-------)
+--R                  a            2    2
+--R                              x  - a
+--R   (3)  ------------------------------
+--R                       2
+--R                                                     Type: Expression Integer
+--E
+
+--S 45
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (4)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 46
+dd:=atanrule cc
+--R
+--R                  2              2
+--R                 x  + 2%i a x - a               - x + %i a
+--R        %i x log(-----------------) + 2%i x log(----------)
+--R                  2              2               x + %i a
+--R                 x  - 2%i a x - a
+--R   (5)  ---------------------------------------------------
+--R                                 4
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 47     14:483 SCHAUMS AND AXIOM DIFFER? (BRANCH CUTS?)
+ee:=expandLog dd
+--R
+--R        %i x log(- 1)
+--R   (6)  -------------
+--R              2
+--R                                             Type: Expression Complex Integer
+--E
+@
+
+\section{\cite{1}:14.484~~~~~$\displaystyle
+\int{x\tan^{-1}\frac{x}{a}}~dx$}
+$$\int{x\tan^{-1}\frac{x}{a}}=
+\frac{1}{2}(x^2+a^2)\tan^{-1}\frac{x}{a}-\frac{ax}{2}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 48     14:484 Axiom cannot compute this integral
+aa:=integrate(x*tan(x/a),x)
+--R 
+--R
+--R           x
+--I         ++         %H
+--I   (1)   |   %H tan(--)d%H
+--R        ++           a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.485~~~~~$\displaystyle
+\int{x^2\tan^{-1}\frac{x}{a}}~dx$}
+$$\int{x^2\tan^{-1}\frac{x}{a}}=
+\frac{x^3}{3}\tan^{-1}\frac{x}{a}-\frac{ax^2}{6}+\frac{a^3}{6}\ln(x^2+a^2)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 49
+aa:=integrate(x^2*atan(x/a),x)
+--R 
+--R
+--R         3     2    2     3       2a x        2
+--R        a log(x  + a ) - x atan(-------) - a x
+--R                                 2    2
+--R                                x  - a
+--R   (1)  ---------------------------------------
+--R                           6
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 50
+bb:=x^3/2*atan(x/a)-(a*x^2)/6+a^3/6*log(x^2+a^2)
+--R
+--R         3     2    2      3     x       2
+--R        a log(x  + a ) + 3x atan(-) - a x
+--R                                 a
+--R   (2)  ----------------------------------
+--R                         6
+--R                                                     Type: Expression Integer
+--E
+
+--S 51     14:485 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R            3     x     3       2a x
+--R        - 3x atan(-) - x atan(-------)
+--R                  a            2    2
+--R                              x  - a
+--R   (3)  ------------------------------
+--R                       6
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.486~~~~~$\displaystyle
+\int{\frac{\tan^{-1}(x/a)}{x}}~dx$}
+$$\int{\frac{\tan^{-1}(x/a)}{x}}=
+\frac{x}{a}-\frac{(x/a)^3}{3^2}+\frac{(x/a)^5}{5^2}-\frac{(x/a)^7}{7^2}+\cdots
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 52     14:486 Axiom cannot compute this integral
+aa:=integrate(atan(x/a)/x,x)
+--R 
+--R
+--I                  %H
+--R           x atan(--)
+--R         ++        a
+--I   (1)   |   -------- d%H
+--I        ++      %H
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.487~~~~~$\displaystyle
+\int{\frac{\tan^{-1}(x/a)}{x^2}}~dx$}
+$$\int{\frac{\tan^{-1}(x/a)}{x^2}}=
+-\frac{1}{x}\tan^{-1}\frac{x}{a}
+-\frac{1}{2a}\ln\left(\frac{x^2+a^2}{x^2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 53
+aa:=integrate(atan(x/a)/x^2,x)
+--R 
+--R
+--R                 2    2                         2a x
+--R        - x log(x  + a ) + 2x log(x) + a atan(-------)
+--R                                               2    2
+--R                                              x  - a
+--R   (1)  ----------------------------------------------
+--R                             2a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 54
+bb:=-1/x*atan(x/a)-1/(2*a)*log((x^2+a^2)/x^2)
+--R
+--R                 2    2
+--R                x  + a             x
+--R        - x log(-------) - 2a atan(-)
+--R                    2              a
+--R                   x
+--R   (2)  -----------------------------
+--R                     2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 55
+cc:=aa-bb
+--R
+--R   (3)
+--R                                         2    2
+--R            2    2                      x  + a             x             2a x
+--R   - x log(x  + a ) + 2x log(x) + x log(-------) + 2a atan(-) + a atan(-------)
+--R                                            2              a            2    2
+--R                                           x                           x  - a
+--R   ----------------------------------------------------------------------------
+--R                                       2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 56
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (4)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 57
+dd:=atanrule cc
+--R
+--R   (5)
+--R                                                 2              2
+--R                 2    2                         x  + 2%i a x - a
+--R       - 2x log(x  + a ) + 4x log(x) - %i a log(-----------------)
+--R                                                 2              2
+--R                                                x  - 2%i a x - a
+--R     + 
+--R               2    2
+--R              x  + a               - x + %i a
+--R       2x log(-------) - 2%i a log(----------)
+--R                  2                 x + %i a
+--R                 x
+--R  /
+--R     4a x
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 58     14:487 SCHAUMS AND AXIOM DIFFER? (branch cuts?)
+ee:=expandLog dd
+--R
+--R          %i log(- 1)
+--R   (6)  - -----------
+--R               2x
+--R                                             Type: Expression Complex Integer
+--E
+@
+
+\section{\cite{1}:14.488~~~~~$\displaystyle
+\int{\cot^{-1}\frac{x}{a}}~dx$}
+$$\int{\cot^{-1}\frac{x}{a}}=
+x\cot^{-1}\frac{x}{a}+\frac{a}{2}\ln(x^2+a^2)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 59
+aa:=integrate(acot(x/a),x)
+--R 
+--R
+--R               2    2             2a x
+--R        a log(x  + a ) + x atan(-------)
+--R                                 2    2
+--R                                x  - a
+--R   (1)  --------------------------------
+--R                        2
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 60
+bb:=x*acot(x/a)+a/2*log(x^2+a^2)
+--R
+--R               2    2            x
+--R        a log(x  + a ) + 2x acot(-)
+--R                                 a
+--R   (2)  ---------------------------
+--R                     2
+--R                                                     Type: Expression Integer
+--E 
+
+--S 61
+cc:=aa-bb
+--R
+--R                 2a x             x
+--R        x atan(-------) - 2x acot(-)
+--R                2    2            a
+--R               x  - a
+--R   (3)  ----------------------------
+--R                      2
+--R                                                     Type: Expression Integer
+--E
+
+--S 62
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (4)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 63
+dd:=atanrule cc
+--R
+--R                    2              2
+--R                   x  + 2%i a x - a             x
+--R        - %i x log(-----------------) - 4x acot(-)
+--R                    2              2            a
+--R                   x  - 2%i a x - a
+--R   (5)  ------------------------------------------
+--R                             4
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 64
+acotrule:=rule(acot(x) == -%i/2*log((%i*x-1)/(%i*x+1)))
+--R
+--R                            x + %i
+--R                     %i log(------)
+--R                            x - %i
+--R   (6)  acot(x) == - --------------
+--R                            2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 65
+ee:=acotrule dd
+--R
+--R                    2              2
+--R                   x  + 2%i a x - a               x + %i a
+--R        - %i x log(-----------------) + 2%i x log(--------)
+--R                    2              2              x - %i a
+--R                   x  - 2%i a x - a
+--R   (7)  ---------------------------------------------------
+--R                                 4
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 66     14:488 Axiom and Schaums agree
+ff:=expandLog %
+--R
+--R   (8)  0
+--R                                             Type: Expression Complex Integer
+--E
+@
+
+\section{\cite{1}:14.489~~~~~$\displaystyle
+\int{x\cot^{-1}\frac{x}{a}}~dx$}
+$$\int{x\cot^{-1}\frac{x}{a}}=
+\frac{1}{2}(x^2+a^2)\cot^{-1}\frac{x}{a}+\frac{ax}{2}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 67
+aa:=integrate(x*acot(x/a),x)
+--R 
+--R
+--R          2    2        2a x
+--R        (x  + a )atan(-------) + 2a x
+--R                       2    2
+--R                      x  - a
+--R   (1)  -----------------------------
+--R                      4
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 68
+bb:=1/2*(x^2+a^2)*acot(x/a)+(a*x)/2
+--R
+--R          2    2      x
+--R        (x  + a )acot(-) + a x
+--R                      a
+--R   (2)  ----------------------
+--R                   2
+--R                                                     Type: Expression Integer
+--E
+
+--S 69
+cc:=aa-bb
+--R
+--R          2    2        2a x          2     2      x
+--R        (x  + a )atan(-------) + (- 2x  - 2a )acot(-)
+--R                       2    2                      a
+--R                      x  - a
+--R   (3)  ---------------------------------------------
+--R                              4
+--R                                                     Type: Expression Integer
+--E
+
+--S 70
+acotrule:=rule(acot(x) == -%i/2*log((%i*x-1)/(%i*x+1)))
+--R
+--R                            x + %i
+--R                     %i log(------)
+--R                            x - %i
+--R   (4)  acot(x) == - --------------
+--R                            2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 71
+dd:=acotrule cc
+--R
+--R             2       2     x + %i a      2    2        2a x
+--R        (%i x  + %i a )log(--------) + (x  + a )atan(-------)
+--R                           x - %i a                   2    2
+--R                                                     x  - a
+--R   (5)  -----------------------------------------------------
+--R                                  4
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 72
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (6)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 73
+ee:=atanrule dd
+--R
+--R   (7)
+--R                         2              2
+--R          2       2     x  + 2%i a x - a           2        2     x + %i a
+--R   (- %i x  - %i a )log(-----------------) + (2%i x  + 2%i a )log(--------)
+--R                         2              2                         x - %i a
+--R                        x  - 2%i a x - a
+--R   ------------------------------------------------------------------------
+--R                                       8
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 74     14:489 Axiom and Schaums agree
+ff:=expandLog ee
+--R
+--R   (8)  0
+--R                                             Type: Expression Complex Integer
+--E
+@
+
+\section{\cite{1}:14.490~~~~~$\displaystyle
+\int{x^2\cot^{-1}\frac{x}{a}}~dx$}
+$$\int{x^2\cot^{-1}\frac{x}{a}}=
+\frac{x^3}{3}\cot^{-1}\frac{x}{a}+\frac{ax^2}{6}-\frac{a^3}{6}\ln(x^2+a^2)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 75
+aa:=integrate(x^2*acot(x/a),x)
+--R 
+--R
+--R           3     2    2     3       2a x        2
+--R        - a log(x  + a ) + x atan(-------) + a x
+--R                                   2    2
+--R                                  x  - a
+--R   (1)  -----------------------------------------
+--R                            6
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 76
+bb:=x^3/3*acot(x/a)+(a*x^2)/6-a^3/6*log(x^2+a^2)
+--R
+--R           3     2    2      3     x       2
+--R        - a log(x  + a ) + 2x acot(-) + a x
+--R                                   a
+--R   (2)  ------------------------------------
+--R                          6
+--R                                                     Type: Expression Integer
+--E 
+
+--S 77
+cc:=aa-bb
+--R
+--R         3       2a x       3     x
+--R        x atan(-------) - 2x acot(-)
+--R                2    2            a
+--R               x  - a
+--R   (3)  ----------------------------
+--R                      6
+--R                                                     Type: Expression Integer
+--E
+
+--S 78
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (4)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 79
+dd:=atanrule cc
+--R
+--R                    2              2
+--R              3    x  + 2%i a x - a       3     x
+--R        - %i x log(-----------------) - 4x acot(-)
+--R                    2              2            a
+--R                   x  - 2%i a x - a
+--R   (5)  ------------------------------------------
+--R                            12
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 80
+acotrule:=rule(acot(x) == -%i/2*log((%i*x-1)/(%i*x+1)))
+--R
+--R                            x + %i
+--R                     %i log(------)
+--R                            x - %i
+--R   (6)  acot(x) == - --------------
+--R                            2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 81
+ee:=acotrule dd
+--R
+--R                    2              2
+--R              3    x  + 2%i a x - a          3    x + %i a
+--R        - %i x log(-----------------) + 2%i x log(--------)
+--R                    2              2              x - %i a
+--R                   x  - 2%i a x - a
+--R   (7)  ---------------------------------------------------
+--R                                 12
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 82     14:490 Axiom and Schaums agree
+ff:=expandLog ee
+--R
+--R   (8)  0
+--R                                             Type: Expression Complex Integer
+--E
+@
+
+\section{\cite{1}:14.491~~~~~$\displaystyle
+\int{\frac{\cot^{-1}(x/a)}{x}}~dx$}
+$$\int{\frac{\cot^{-1}(x/a)}{x}}=
+\frac{\pi}{2}\ln{x}-\int{\frac{\tan^{-1}(x/a)}{x}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 83     14:491 Axiom cannot compute this integral
+aa:=integrate(acot(x/a)/x,x)
+--R 
+--R
+--I                  %H
+--R           x acot(--)
+--R         ++        a
+--I   (1)   |   -------- d%H
+--I        ++      %H
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.492~~~~~$\displaystyle
+\int{\frac{\cot^{-1}(x/a)}{x^2}}~dx$}
+$$\int{\frac{\cot^{-1}(x/a)}{x^2}}=
+-\frac{cot^{-1}(x/a)}{x}+\frac{1}{2a}\ln\left(\frac{x^2+a^2}{x^2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 84
+aa:=integrate(acot(x/a)/x^2,x)
+--R 
+--R
+--R               2    2                         2a x
+--R        x log(x  + a ) - 2x log(x) - a atan(-------)
+--R                                             2    2
+--R                                            x  - a
+--R   (1)  --------------------------------------------
+--R                            2a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 85
+bb:=-acot(x/a)/x+1/(2*a)*log((x^2+a^2)/x^2)
+--R
+--R               2    2
+--R              x  + a             x
+--R        x log(-------) - 2a acot(-)
+--R                  2              a
+--R                 x
+--R   (2)  ---------------------------
+--R                    2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 86
+cc:=aa-bb
+--R
+--R   (3)
+--R                                       2    2
+--R          2    2                      x  + a              2a x             x
+--R   x log(x  + a ) - 2x log(x) - x log(-------) - a atan(-------) + 2a acot(-)
+--R                                          2              2    2            a
+--R                                         x              x  - a
+--R   --------------------------------------------------------------------------
+--R                                      2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 87
+acotrule:=rule(acot(x) == -%i/2*log((%i*x-1)/(%i*x+1)))
+--R
+--R                            x + %i
+--R                     %i log(------)
+--R                            x - %i
+--R   (4)  acot(x) == - --------------
+--R                            2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 88
+dd:=acotrule cc
+--R
+--R   (5)
+--R                                                                2    2
+--R              2    2                         x + %i a          x  + a
+--R       x log(x  + a ) - 2x log(x) - %i a log(--------) - x log(-------)
+--R                                             x - %i a              2
+--R                                                                  x
+--R     + 
+--R                  2a x
+--R       - a atan(-------)
+--R                 2    2
+--R                x  - a
+--R  /
+--R     2a x
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 89
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (6)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 90
+ee:=atanrule dd
+--R
+--R   (7)
+--R                                               2              2
+--R               2    2                         x  + 2%i a x - a
+--R       2x log(x  + a ) - 4x log(x) + %i a log(-----------------)
+--R                                               2              2
+--R                                              x  - 2%i a x - a
+--R     + 
+--R                                       2    2
+--R                   x + %i a           x  + a
+--R       - 2%i a log(--------) - 2x log(-------)
+--R                   x - %i a               2
+--R                                         x
+--R  /
+--R     4a x
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 91     14:492 Schaums and Axiom agree
+ff:=expandLog ee
+--R
+--R   (8)  0
+--R                                             Type: Expression Complex Integer
+--E
+@
+
+\section{\cite{1}:14.493~~~~~$\displaystyle
+\int{\sec^{-1}\frac{x}{a}}~dx$}
+$$\int{\sec^{-1}\frac{x}{a}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+x\sec^{-1}\frac{x}{a}-a\ln(x+\sqrt{x^2-a^2}) 
+{\rm \ if\ }0 &lt; \sec^{-1}\frac{x}{a} &lt; \frac{\pi}{2}\\
+\\
+\displaystyle
+x\sec^{-1}\frac{x}{a}+a\ln(x+\sqrt{x^2-a^2})
+{\rm \ if\ }\frac{\pi}{2} &lt; \sec^{-1}\frac{x}{a} &lt; \pi
+\end{array}
+\right.
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 92
+aa:=integrate(asec(x/a),x)
+--R 
+--R
+--R   (1)
+--R                          +---------+              +---------+
+--R                      +-+ |   2    2               |   2    2
+--R           +-+     2x\|2 \|- x  + a             2a\|- x  + a
+--R       - a\|2 atan(------------------) + x atan(--------------)
+--R                          2     2                      2
+--R                        3x  - 2a                      x
+--R     + 
+--R                       x
+--R       - 2a atan(------------)
+--R                  +---------+
+--R                  |   2    2
+--R                 \|- x  + a
+--R  /
+--R     2
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 93
+bb1:=x*asec(x/a)-a*log(x+sqrt(x^2-a^2))
+--R
+--R                 +-------+
+--R                 | 2    2                x
+--R   (2)  - a log(\|x  - a   + x) + x asec(-)
+--R                                         a
+--R                                                     Type: Expression Integer
+--E
+
+--S 94
+bb2:=x*asec(x/a)+a*log(x+sqrt(x^2-a^2))
+--R
+--R               +-------+
+--R               | 2    2                x
+--R   (3)  a log(\|x  - a   + x) + x asec(-)
+--R                                       a
+--R                                                     Type: Expression Integer
+--E
+
+--S 95
+cc1:=aa-bb1
+--R
+--R   (4)
+--R                                                 +---------+
+--R               +-------+                     +-+ |   2    2
+--R               | 2    2           +-+     2x\|2 \|- x  + a
+--R       2a log(\|x  - a   + x) - a\|2 atan(------------------)
+--R                                                 2     2
+--R                                               3x  - 2a
+--R     + 
+--R                 +---------+
+--R                 |   2    2
+--R              2a\|- x  + a                    x                 x
+--R       x atan(--------------) - 2a atan(------------) - 2x asec(-)
+--R                     2                   +---------+            a
+--R                    x                    |   2    2
+--R                                        \|- x  + a
+--R  /
+--R     2
+--R                                                     Type: Expression Integer
+--E
+
+--S 96     14:493 Axiom cannot simplify these expressions
+cc2:=aa-bb2
+--R
+--R   (5)
+--R                                                   +---------+
+--R                 +-------+                     +-+ |   2    2
+--R                 | 2    2           +-+     2x\|2 \|- x  + a
+--R       - 2a log(\|x  - a   + x) - a\|2 atan(------------------)
+--R                                                   2     2
+--R                                                 3x  - 2a
+--R     + 
+--R                 +---------+
+--R                 |   2    2
+--R              2a\|- x  + a                    x                 x
+--R       x atan(--------------) - 2a atan(------------) - 2x asec(-)
+--R                     2                   +---------+            a
+--R                    x                    |   2    2
+--R                                        \|- x  + a
+--R  /
+--R     2
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.494~~~~~$\displaystyle
+\int{x\sec^{-1}\frac{x}{a}}~dx$}
+$$\int{x\sec^{-1}\frac{x}{a}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{x^2}{2}\sec^{-1}\frac{x}{a}-\frac{a\sqrt{x^2-a^2}}{2}
+{\rm \ if\ }0 &lt; \sec^{-1}\frac{x}{a} &lt; \frac{\pi}{2}\\
+\\
+\displaystyle
+\frac{x^2}{2}\sec^{-1}\frac{x}{a}+\frac{a\sqrt{x^2-a^2}}{2}
+{\rm \ if\ }\frac{\pi}{2} &lt; \sec^{-1}\frac{x}{a} &lt; \pi
+\end{array}
+\right.
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 97
+aa:=integrate(x*asec(x/a),x)
+--R 
+--R
+--R                          +---------+
+--R                          |   2    2        +---------+
+--R          2     2      2a\|- x  + a         |   2    2
+--R        (x  - 2a )atan(--------------) + 2a\|- x  + a
+--R                              2
+--R                             x
+--R   (1)  -----------------------------------------------
+--R                               4
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 98
+bb1:=x^2/2*asec(x/a)-(a*sqrt(x^2-a^2))/2
+--R
+--R            +-------+
+--R            | 2    2     2     x
+--R        - a\|x  - a   + x asec(-)
+--R                               a
+--R   (2)  -------------------------
+--R                    2
+--R                                                     Type: Expression Integer
+--E
+
+--S 99
+bb2:=x^2/2*asec(x/a)+(a*sqrt(x^2-a^2))/2
+--R
+--R          +-------+
+--R          | 2    2     2     x
+--R        a\|x  - a   + x asec(-)
+--R                             a
+--R   (3)  -----------------------
+--R                   2
+--R                                                     Type: Expression Integer
+--E
+
+--S 100
+cc1:=aa-bb1
+--R
+--R   (4)
+--R                     +---------+
+--R                     |   2    2        +-------+      +---------+
+--R     2     2      2a\|- x  + a         | 2    2       |   2    2      2     x
+--R   (x  - 2a )atan(--------------) + 2a\|x  - a   + 2a\|- x  + a   - 2x asec(-)
+--R                         2                                                  a
+--R                        x
+--R   ---------------------------------------------------------------------------
+--R                                        4
+--R                                                     Type: Expression Integer
+--E
+
+--S 101    14:494 Axiom cannot simplify these expressions
+cc2:=aa-bb2
+--R
+--R   (5)
+--R                     +---------+
+--R                     |   2    2        +-------+      +---------+
+--R     2     2      2a\|- x  + a         | 2    2       |   2    2      2     x
+--R   (x  - 2a )atan(--------------) - 2a\|x  - a   + 2a\|- x  + a   - 2x asec(-)
+--R                         2                                                  a
+--R                        x
+--R   ---------------------------------------------------------------------------
+--R                                        4
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.495~~~~~$\displaystyle
+\int{x^2\sec^{-1}\frac{x}{a}}~dx$}
+$$\int{x^2\sec^{-1}\frac{x}{a}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{x^3}{3}\sec^{-1}\frac{x}{a}-\frac{ax\sqrt{x^2-a^2}}{6}
+-\frac{a^3}{6}\ln(x+\sqrt{x^2-a^2})\\
+\\
+\displaystyle
+\hbox{\hskip 3cm}{\rm \ if\ }0 &lt; \sec^{-1}\frac{x}{a} &lt; \frac{\pi}{2}\\
+\\
+\displaystyle
+\frac{x^3}{3}\sec^{-1}\frac{x}{a}+\frac{ax\sqrt{x^2-a^2}}{6}
++\frac{a^3}{6}\ln(x+\sqrt{x^2-a^2})\\
+\\
+\displaystyle
+\hbox{\hskip 3cm}
+{\rm \ if\ }\frac{\pi}{2} &lt; \sec^{-1}\frac{x}{a} &lt; \pi\\
+\end{array}
+\right.
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 102
+aa:=integrate(x^2*asec(x/a),x)
+--R 
+--R
+--R   (1)
+--R                            +---------+              +---------+
+--R                        +-+ |   2    2               |   2    2
+--R           3 +-+     2x\|2 \|- x  + a       3     2a\|- x  + a
+--R       - 2a \|2 atan(------------------) + x atan(--------------)
+--R                            2     2                      2
+--R                          3x  - 2a                      x
+--R     + 
+--R                                     +---------+
+--R           3           x             |   2    2
+--R       - 5a atan(------------) + a x\|- x  + a
+--R                  +---------+
+--R                  |   2    2
+--R                 \|- x  + a
+--R  /
+--R     6
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 103
+bb1:=x^3/3*asec(x/a)-(a*x*sqrt(x^2-a^2))/6-a^3/6*log(x+sqrt(x^2-a^2))
+--R
+--R                 +-------+            +-------+
+--R           3     | 2    2             | 2    2      3     x
+--R        - a log(\|x  - a   + x) - a x\|x  - a   + 2x asec(-)
+--R                                                          a
+--R   (2)  ----------------------------------------------------
+--R                                  6
+--R                                                     Type: Expression Integer
+--E
+
+--S 104
+bb2:=x^3/3*asec(x/a)+(a*x*sqrt(x^2-a^2))/6+a^3/6*log(x+sqrt(x^2-a^2))
+--R
+--R               +-------+            +-------+
+--R         3     | 2    2             | 2    2      3     x
+--R        a log(\|x  - a   + x) + a x\|x  - a   + 2x asec(-)
+--R                                                        a
+--R   (3)  --------------------------------------------------
+--R                                 6
+--R                                                     Type: Expression Integer
+--E
+
+--S 105
+cc1:=aa-bb1
+--R
+--R   (4)
+--R                                                  +---------+
+--R              +-------+                       +-+ |   2    2
+--R        3     | 2    2           3 +-+     2x\|2 \|- x  + a
+--R       a log(\|x  - a   + x) - 2a \|2 atan(------------------)
+--R                                                  2     2
+--R                                                3x  - 2a
+--R     + 
+--R                 +---------+
+--R                 |   2    2                                 +-------+
+--R        3     2a\|- x  + a        3           x             | 2    2
+--R       x atan(--------------) - 5a atan(------------) + a x\|x  - a
+--R                     2                   +---------+
+--R                    x                    |   2    2
+--R                                        \|- x  + a
+--R     + 
+--R           +---------+
+--R           |   2    2      3     x
+--R       a x\|- x  + a   - 2x asec(-)
+--R                                 a
+--R  /
+--R     6
+--R                                                     Type: Expression Integer
+--E
+
+--S 106     14:495 Axiom cannot simplify these expressions
+cc2:=aa-bb2
+--R
+--R   (5)
+--R                                                    +---------+
+--R                +-------+                       +-+ |   2    2
+--R          3     | 2    2           3 +-+     2x\|2 \|- x  + a
+--R       - a log(\|x  - a   + x) - 2a \|2 atan(------------------)
+--R                                                    2     2
+--R                                                  3x  - 2a
+--R     + 
+--R                 +---------+
+--R                 |   2    2                                 +-------+
+--R        3     2a\|- x  + a        3           x             | 2    2
+--R       x atan(--------------) - 5a atan(------------) - a x\|x  - a
+--R                     2                   +---------+
+--R                    x                    |   2    2
+--R                                        \|- x  + a
+--R     + 
+--R           +---------+
+--R           |   2    2      3     x
+--R       a x\|- x  + a   - 2x asec(-)
+--R                                 a
+--R  /
+--R     6
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.496~~~~~$\displaystyle
+\int{\frac{\sec^{-1}(x/a)}{x}}~dx$}
+$$\int{\frac{\sec^{-1}(x/a)}{x}}=
+\frac{\pi}{2}\ln{x}+\frac{a}{x}+\frac{(a/x)^3}{2\cdot 3\cdot 3}
++\frac{1\cdot 3(a/x)^5}{2\cdot 4\cdot 5\cdot 5}
++\frac{1\cdot 3\cdot 5(a/x)^7}{2\cdot 4\cdot 6\cdot 7\cdot 7}+\cdots
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 107    14:496 Axiom cannot compute this integral
+aa:=integrate(asec(x/a)/x,x)
+--R 
+--R
+--I                  %H
+--R           x asec(--)
+--R         ++        a
+--I   (1)   |   -------- d%H
+--I        ++      %H
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.497~~~~~$\displaystyle
+\int{\frac{\sec^{-1}(x/a)}{x^2}}~dx$}
+$$\int{\frac{\sec^{-1}(x/a)}{x^2}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+-\frac{\sec^{-1}(x/a)}{x}+\frac{\sqrt{x^2-a^2}}{ax}
+{\rm \ if\ }0 &lt; \sec^{-1}\frac{x}{a} &lt; \frac{\pi}{2}\\
+\\
+\displaystyle
+-\frac{\sec^{-1}(x/a)}{x}-\frac{\sqrt{x^2-a^2}}{ax}
+{\rm \ if\ }\frac{\pi}{2} &lt; \sec^{-1}\frac{x}{a} &lt; \pi\\
+\end{array}
+\right.
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 108
+aa:=integrate(asec(x/a)/x^2,x)
+--R 
+--R
+--R                      +---------+                 +---------+
+--R                  +-+ |   2    2                  |   2    2
+--R               2x\|2 \|- x  + a        +-+     2a\|- x  + a
+--R        x atan(------------------) - a\|2 atan(--------------)
+--R                      2     2                         2
+--R                    3x  - 2a                         x
+--R   (1)  ------------------------------------------------------
+--R                                    +-+
+--R                               2a x\|2
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 109
+bb1:=-asec(x/a)/x+sqrt(x^2-a^2)/(a*x)
+--R
+--R         +-------+
+--R         | 2    2           x
+--R        \|x  - a   - a asec(-)
+--R                            a
+--R   (2)  ----------------------
+--R                  a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 110
+bb2:=-asec(x/a)/x-sqrt(x^2-a^2)/(a*x)
+--R
+--R           +-------+
+--R           | 2    2           x
+--R        - \|x  - a   - a asec(-)
+--R                              a
+--R   (3)  ------------------------
+--R                   a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 111
+cc1:=aa-bb1
+--R
+--R   (4)
+--R                     +---------+                 +---------+
+--R                 +-+ |   2    2                  |   2    2           +-------+
+--R              2x\|2 \|- x  + a        +-+     2a\|- x  + a        +-+ | 2    2
+--R       x atan(------------------) - a\|2 atan(--------------) - 2\|2 \|x  - a
+--R                     2     2                         2
+--R                   3x  - 2a                         x
+--R     + 
+--R          +-+     x
+--R       2a\|2 asec(-)
+--R                  a
+--R  /
+--R          +-+
+--R     2a x\|2
+--R                                                     Type: Expression Integer
+--E
+
+--S 112    14:497 Axiom cannot simplify these expressions
+cc2:=aa-bb2
+--R
+--R   (5)
+--R                     +---------+                 +---------+
+--R                 +-+ |   2    2                  |   2    2           +-------+
+--R              2x\|2 \|- x  + a        +-+     2a\|- x  + a        +-+ | 2    2
+--R       x atan(------------------) - a\|2 atan(--------------) + 2\|2 \|x  - a
+--R                     2     2                         2
+--R                   3x  - 2a                         x
+--R     + 
+--R          +-+     x
+--R       2a\|2 asec(-)
+--R                  a
+--R  /
+--R          +-+
+--R     2a x\|2
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.498~~~~~$\displaystyle
+\int{\csc^{-1}\frac{x}{a}}~dx$}
+$$\int{\csc^{-1}\frac{x}{a}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+x\csc^{-1}\frac{x}{a}+a\ln(x+\sqrt{x^2-a^2})
+{\rm \ if\ }0 &lt; \csc^{-1}\frac{x}{a} &lt; \frac{\pi}{2}\\
+\\
+\displaystyle
+x\csc^{-1}\frac{x}{a}-a\ln(x+\sqrt{x^2-a^2})
+{\rm \ if\ }-\frac{\pi}{2} &lt; \csc^{-1}\frac{x}{a} &lt; 0\\
+\end{array}
+\right.
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 113
+aa:=integrate(acsc(x/a),x)
+--R 
+--R
+--R   (1)
+--R                        +---------+              +---------+
+--R                    +-+ |   2    2               |   2    2
+--R         +-+     2x\|2 \|- x  + a             2a\|- x  + a
+--R       a\|2 atan(------------------) - x atan(--------------)
+--R                        2     2                      2
+--R                      3x  - 2a                      x
+--R     + 
+--R                     x
+--R       2a atan(------------)
+--R                +---------+
+--R                |   2    2
+--R               \|- x  + a
+--R  /
+--R     2
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 114
+bb1:=x*acsc(x/a)+a*log(x+sqrt(x^2-a^2))
+--R
+--R               +-------+
+--R               | 2    2                x
+--R   (2)  a log(\|x  - a   + x) + x acsc(-)
+--R                                       a
+--R                                                     Type: Expression Integer
+--E
+
+--S 115
+bb2:=x*acsc(x/a)-a*log(x+sqrt(x^2-a^2))
+--R
+--R                 +-------+
+--R                 | 2    2                x
+--R   (3)  - a log(\|x  - a   + x) + x acsc(-)
+--R                                         a
+--R                                                     Type: Expression Integer
+--E
+
+--S 116
+cc1:=aa-bb1
+--R
+--R   (4)
+--R                                                   +---------+
+--R                 +-------+                     +-+ |   2    2
+--R                 | 2    2           +-+     2x\|2 \|- x  + a
+--R       - 2a log(\|x  - a   + x) + a\|2 atan(------------------)
+--R                                                   2     2
+--R                                                 3x  - 2a
+--R     + 
+--R                   +---------+
+--R                   |   2    2
+--R                2a\|- x  + a                    x                 x
+--R       - x atan(--------------) + 2a atan(------------) - 2x acsc(-)
+--R                       2                   +---------+            a
+--R                      x                    |   2    2
+--R                                          \|- x  + a
+--R  /
+--R     2
+--R                                                     Type: Expression Integer
+--E
+
+--S 117    14:498 Axiom cannot simplify these expressions
+cc2:=aa-bb2
+--R
+--R   (5)
+--R                                                 +---------+
+--R               +-------+                     +-+ |   2    2
+--R               | 2    2           +-+     2x\|2 \|- x  + a
+--R       2a log(\|x  - a   + x) + a\|2 atan(------------------)
+--R                                                 2     2
+--R                                               3x  - 2a
+--R     + 
+--R                   +---------+
+--R                   |   2    2
+--R                2a\|- x  + a                    x                 x
+--R       - x atan(--------------) + 2a atan(------------) - 2x acsc(-)
+--R                       2                   +---------+            a
+--R                      x                    |   2    2
+--R                                          \|- x  + a
+--R  /
+--R     2
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.499~~~~~$\displaystyle
+\int{x\csc^{-1}\frac{x}{a}}~dx$}
+$$\int{x\csc^{-1}\frac{x}{a}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{x^2}{2}\csc^{-1}\frac{x}{a}+\frac{a\sqrt{x^2-a^2}}{2}
+{\rm \ if\ }0 &lt; \csc^{-1}\frac{x}{a} &lt; \frac{\pi}{2}\\
+\\
+\displaystyle
+\frac{x^2}{2}\csc^{-1}\frac{x}{a}-\frac{a\sqrt{x^2-a^2}}{2}
+{\rm \ if\ }-\frac{\pi}{2} &lt; \csc^{-1}\frac{x}{a} &lt; 0\\
+\end{array}
+\right.
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 118
+aa:=integrate(x*acsc(x/a),x)
+--R 
+--R
+--R                            +---------+
+--R                            |   2    2        +---------+
+--R            2     2      2a\|- x  + a         |   2    2
+--R        (- x  + 2a )atan(--------------) - 2a\|- x  + a
+--R                                2
+--R                               x
+--R   (1)  -------------------------------------------------
+--R                                4
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 119
+bb1:=x^2/2*acsc(x/a)+(a*sqrt(x^2-a^2))/2
+--R
+--R          +-------+
+--R          | 2    2     2     x
+--R        a\|x  - a   + x acsc(-)
+--R                             a
+--R   (2)  -----------------------
+--R                   2
+--R                                                     Type: Expression Integer
+--E
+
+--S 120
+bb2:=x^2/2*acsc(x/a)-(a*sqrt(x^2-a^2))/2
+--R
+--R            +-------+
+--R            | 2    2     2     x
+--R        - a\|x  - a   + x acsc(-)
+--R                               a
+--R   (3)  -------------------------
+--R                    2
+--R                                                     Type: Expression Integer
+--E
+
+--S 121
+cc1:=aa-bb1
+--R
+--R   (4)
+--R                       +---------+
+--R                       |   2    2        +-------+      +---------+
+--R       2     2      2a\|- x  + a         | 2    2       |   2    2      2     x
+--R   (- x  + 2a )atan(--------------) - 2a\|x  - a   - 2a\|- x  + a   - 2x acsc(-)
+--R                           2                                                  a
+--R                          x
+--R   -----------------------------------------------------------------------------
+--R                                         4
+--R                                                     Type: Expression Integer
+--E
+
+--S 122    14:499 Axiom cannot simplify these expressions
+cc2:=aa-bb2
+--R
+--R   (5)
+--R                       +---------+
+--R                       |   2    2        +-------+      +---------+
+--R       2     2      2a\|- x  + a         | 2    2       |   2    2      2     x
+--R   (- x  + 2a )atan(--------------) + 2a\|x  - a   - 2a\|- x  + a   - 2x acsc(-)
+--R                           2                                                  a
+--R                          x
+--R   -----------------------------------------------------------------------------
+--R                                         4
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.500~~~~~$\displaystyle
+\int{x^2\csc^{-1}\frac{x}{a}}~dx$}
+$$\int{x^2\csc^{-1}\frac{x}{a}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{x^3}{3}\csc^{-1}\frac{x}{a}+\frac{ax\sqrt{x^2-a^2}}{6}
++\frac{a^3}{6}\ln(x+\sqrt{x^2-a^2})\\
+\\
+\displaystyle
+\hbox{\hskip 3cm}{\rm \ if\ }0 &lt; \csc^{-1}\frac{x}{a} &lt; \frac{\pi}{2}\\
+\\
+\displaystyle
+\frac{x^3}{3}\sec^{-1}\frac{x}{a}-\frac{ax\sqrt{x^2-a^2}}{6}
+-\frac{a^3}{6}\ln(x+\sqrt{x^2-a^2})\\
+\\
+\displaystyle
+\hbox{\hskip 3cm}
+{\rm \ if\ }-\frac{\pi}{2} &lt; \csc^{-1}\frac{x}{a} &lt; 0\\
+\end{array}
+\right.
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 123
+aa:=integrate(x^2*acsc(x/a),x)
+--R 
+--R
+--R   (1)
+--R                          +---------+              +---------+
+--R                      +-+ |   2    2               |   2    2
+--R         3 +-+     2x\|2 \|- x  + a       3     2a\|- x  + a
+--R       2a \|2 atan(------------------) - x atan(--------------)
+--R                          2     2                      2
+--R                        3x  - 2a                      x
+--R     + 
+--R                                   +---------+
+--R         3           x             |   2    2
+--R       5a atan(------------) - a x\|- x  + a
+--R                +---------+
+--R                |   2    2
+--R               \|- x  + a
+--R  /
+--R     6
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 124
+bb1:=x^3/3*acsc(x/a)+(a*x*sqrt(x^2-a^2))/6+a^3/6*log(x+sqrt(x^2-a^2))
+--R
+--R               +-------+            +-------+
+--R         3     | 2    2             | 2    2      3     x
+--R        a log(\|x  - a   + x) + a x\|x  - a   + 2x acsc(-)
+--R                                                        a
+--R   (2)  --------------------------------------------------
+--R                                 6
+--R                                                     Type: Expression Integer
+--E
+
+--S 125
+bb2:=x^3/3*acsc(x/a)-(a*x*sqrt(x^2-a^2))/6-a^3/6*log(x+sqrt(x^2-a^2))
+--R
+--R                 +-------+            +-------+
+--R           3     | 2    2             | 2    2      3     x
+--R        - a log(\|x  - a   + x) - a x\|x  - a   + 2x acsc(-)
+--R                                                          a
+--R   (3)  ----------------------------------------------------
+--R                                  6
+--R                                                     Type: Expression Integer
+--E
+
+--S 126
+cc1:=aa-bb1
+--R
+--R   (4)
+--R                                                    +---------+
+--R                +-------+                       +-+ |   2    2
+--R          3     | 2    2           3 +-+     2x\|2 \|- x  + a
+--R       - a log(\|x  - a   + x) + 2a \|2 atan(------------------)
+--R                                                    2     2
+--R                                                  3x  - 2a
+--R     + 
+--R                   +---------+
+--R                   |   2    2                                 +-------+
+--R          3     2a\|- x  + a        3           x             | 2    2
+--R       - x atan(--------------) + 5a atan(------------) - a x\|x  - a
+--R                       2                   +---------+
+--R                      x                    |   2    2
+--R                                          \|- x  + a
+--R     + 
+--R             +---------+
+--R             |   2    2      3     x
+--R       - a x\|- x  + a   - 2x acsc(-)
+--R                                   a
+--R  /
+--R     6
+--R                                                     Type: Expression Integer
+--E
+
+--S 127    14:500 Axiom cannot simplify this expression
+cc2:=aa-bb2
+--R
+--R   (5)
+--R                                                  +---------+
+--R              +-------+                       +-+ |   2    2
+--R        3     | 2    2           3 +-+     2x\|2 \|- x  + a
+--R       a log(\|x  - a   + x) + 2a \|2 atan(------------------)
+--R                                                  2     2
+--R                                                3x  - 2a
+--R     + 
+--R                   +---------+
+--R                   |   2    2                                 +-------+
+--R          3     2a\|- x  + a        3           x             | 2    2
+--R       - x atan(--------------) + 5a atan(------------) + a x\|x  - a
+--R                       2                   +---------+
+--R                      x                    |   2    2
+--R                                          \|- x  + a
+--R     + 
+--R             +---------+
+--R             |   2    2      3     x
+--R       - a x\|- x  + a   - 2x acsc(-)
+--R                                   a
+--R  /
+--R     6
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.501~~~~~$\displaystyle
+\int{\frac{\csc^{-1}(x/a)}{x}}~dx$}
+$$\int{\frac{\csc^{-1}(x/a)}{x}}=
+-\left(\frac{a}{x}+\frac{(a/x)^3}{2\cdot 3\cdot 3}
++\frac{1\cdot 3(a/x)^5}{2\cdot 4\cdot 5\cdot 5}
++\frac{1\cdot 3\cdot 5(a/x)^7}{2\cdot 4\cdot 6\cdot 7\cdot 7}+\cdots\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 128    14:501 Axiom cannot compute this integral
+aa:=integrate(acsc(x/a)/x,x)
+--R 
+--R
+--I                  %H
+--R           x acsc(--)
+--R         ++        a
+--I   (1)   |   -------- d%H
+--I        ++      %H
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.502~~~~~$\displaystyle
+\int{\frac{\csc^{-1}(x/a)}{x^2}}~dx$}
+$$\int{\frac{\csc^{-1}(x/a)}{x^2}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+-\frac{csc^{-1}(x/a)}{x}-\frac{\sqrt{x^2-a^2}}{ax}
+{\rm \ if\ }0 &lt; \csc^{-1}\frac{x}{a} &lt; \frac{\pi}{2}\\
+\\
+\displaystyle
+-\frac{csc^{-1}(x/a)}{x}+\frac{\sqrt{x^2-a^2}}{ax}
+{\rm \ if\ }-\frac{\pi}{2} &lt; \csc^{-1}\frac{x}{a} &lt; 0\\
+\end{array}
+\right.
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 129
+aa:=integrate(acsc(x/a)/x^2,x)
+--R 
+--R
+--R                        +---------+                 +---------+
+--R                    +-+ |   2    2                  |   2    2
+--R                 2x\|2 \|- x  + a        +-+     2a\|- x  + a
+--R        - x atan(------------------) + a\|2 atan(--------------)
+--R                        2     2                         2
+--R                      3x  - 2a                         x
+--R   (1)  --------------------------------------------------------
+--R                                     +-+
+--R                                2a x\|2
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 130
+bb1:=-acsc(x/a)/x-sqrt(x^2-a^2)/(a*x)
+--R
+--R           +-------+
+--R           | 2    2           x
+--R        - \|x  - a   - a acsc(-)
+--R                              a
+--R   (2)  ------------------------
+--R                   a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 131
+bb2:=-acsc(x/a)/x+sqrt(x^2-a^2)/(a*x)
+--R
+--R         +-------+
+--R         | 2    2           x
+--R        \|x  - a   - a acsc(-)
+--R                            a
+--R   (3)  ----------------------
+--R                  a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 132
+cc1:=aa-bb1
+--R
+--R   (4)
+--R                       +---------+                 +---------+
+--R                   +-+ |   2    2                  |   2    2
+--R                2x\|2 \|- x  + a        +-+     2a\|- x  + a
+--R       - x atan(------------------) + a\|2 atan(--------------)
+--R                       2     2                         2
+--R                     3x  - 2a                         x
+--R     + 
+--R             +-------+
+--R         +-+ | 2    2       +-+     x
+--R       2\|2 \|x  - a   + 2a\|2 acsc(-)
+--R                                    a
+--R  /
+--R          +-+
+--R     2a x\|2
+--R                                                     Type: Expression Integer
+--E
+
+--S 133    14:502 Axiom cannot simplify this expression
+cc2:=aa-bb2
+--R
+--R   (5)
+--R                       +---------+                 +---------+
+--R                   +-+ |   2    2                  |   2    2
+--R                2x\|2 \|- x  + a        +-+     2a\|- x  + a
+--R       - x atan(------------------) + a\|2 atan(--------------)
+--R                       2     2                         2
+--R                     3x  - 2a                         x
+--R     + 
+--R               +-------+
+--R           +-+ | 2    2       +-+     x
+--R       - 2\|2 \|x  - a   + 2a\|2 acsc(-)
+--R                                      a
+--R  /
+--R          +-+
+--R     2a x\|2
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.503~~~~~$\displaystyle
+\int{x^m\sin^{-1}\frac{x}{a}}~dx$}
+$$\int{x^m\sin^{-1}\frac{x}{a}}=
+\frac{x^{m+1}}{m+1}\sin^{-1}\frac{x}{a}-\frac{1}{m+1}\int{\frac{x^{m+1}}{\sqrt{a^2-x^2}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 134    14:503 Axiom cannot compute this integral
+aa:=integrate(x^m*asin(x/a),x)
+--R 
+--R
+--R           x
+--I         ++       %H   m
+--I   (1)   |   asin(--)%H d%H
+--R        ++         a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.504~~~~~$\displaystyle
+\int{x^m\cos^{-1}\frac{x}{a}}~dx$}
+$$\int{x^m\cos^{-1}\frac{x}{a}}=
+\frac{x^{m+1}}{m+1}\cos^{-1}\frac{x}{a}+\frac{1}{m+1}\int{\frac{x^{m+1}}{\sqrt{a^2-x^2}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 135    14:504 Axiom cannot compute this integral
+aa:=integrate(x^m*acos(x/a),x)
+--R 
+--R
+--R           x
+--I         ++       %H   m
+--I   (1)   |   acos(--)%H d%H
+--R        ++         a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.505~~~~~$\displaystyle
+\int{x^m\tan^{-1}\frac{x}{a}}~dx$}
+$$\int{x^m\tan^{-1}\frac{x}{a}}=
+\frac{x^{m_1}}{m+1}\tan^{-1}\frac{x}{a}
+-\frac{a}{m+1}\int{\frac{x^{m+1}}{x^2+a^2}}
+$$
+This appears to be an interesting integral. Axiom found a closed
+form solution to the problem. However, the t1 integral below does
+not have a closed form solution. Note that we did not return a
+result for the prior two integrals, nor for the next integral. They
+have the same form but are expressed in terms of asin, acos, and acot.
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 136
+aa:=integrate(x*m*atan(x/a),x)
+--R 
+--R
+--R              2    2         2a x
+--R        (- m x  - a m)atan(-------) - 2a m x
+--R                            2    2
+--R                           x  - a
+--R   (1)  ------------------------------------
+--R                          4
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 137
+t1:=integrate(x^(m+1)/(x^2+a^2),x)
+--E
+@
+Since we cannot get a closed form version of the prior integral
+we proceed to try to prove that Axiom got a correct answer. We
+do this by computing the derivate of 'aa' above and finding the
+difference from the original formula.
+
+So first we generate the derivative:
+&lt;&lt;*&gt;&gt;=
+
+--S 138
+bb:=D(aa,x)
+--R
+--R                     2a x
+--R          m x atan(-------)
+--R                    2    2
+--R                   x  - a
+--R   (3)  - -----------------
+--R                  2
+--R                                                     Type: Expression Integer
+--E
+@
+Then we input the original expression
+&lt;&lt;*&gt;&gt;=
+--S 139
+aa1:=x*m*atan(x/a)
+--R
+--R                 x
+--R   (4)  m x atan(-)
+--R                 a
+--R                                                     Type: Expression Integer
+--E
+@
+Now we take their difference
+&lt;&lt;*&gt;&gt;=
+--S 140
+dd:=aa1-bb
+--R
+--R                  x               2a x
+--R        2m x atan(-) + m x atan(-------)
+--R                  a              2    2
+--R                                x  - a
+--R   (5)  --------------------------------
+--R                        2
+--R                                                     Type: Expression Integer
+--E
+@
+Now we input the atan transformation
+&lt;&lt;*&gt;&gt;=
+--S 141
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (6)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+@
+And apply the transformation to the difference
+&lt;&lt;*&gt;&gt;=
+--S 142
+ee:=atanrule dd
+--R
+--R                      2              2
+--R                     x  + 2%i a x - a                 - x + %i a
+--R        - %i m x log(-----------------) - 2%i m x log(----------)
+--R                      2              2                 x + %i a
+--R                     x  - 2%i a x - a
+--R   (7)  ---------------------------------------------------------
+--R                                    4
+--R                                             Type: Expression Complex Integer
+--E
+@
+And now we simplify
+&lt;&lt;*&gt;&gt;=
+--S 143    14:505 SCHAUMS AND AXIOM DISAGREE? (branch cuts?)
+ff:=expandLog ee
+--R
+--R          %i m x log(- 1)
+--R   (8)  - ---------------
+--R                 2
+--R                                             Type: Expression Complex Integer
+--E
+@
+And we get the surprising result that they are not equal.
+In fact, they differ by a complex value depending on x.
+Likely there is a branch-cut issue lurking somewhere.
+
+\section{\cite{1}:14.506~~~~~$\displaystyle
+\int{x^m\cot^{-1}\frac{x}{a}}~dx$}
+$$\int{x^m\cot^{-1}\frac{x}{a}}=
+\frac{x^{m+1}}{m+1}\cot^{-1}\frac{x}{a}
++\frac{a}{m+1}\int{\frac{x^{m+1}}{x^2+a^2}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 144    14:506 Axiom cannot compute this integral
+aa:=integrate(x^m*acot(x/a),x)
+--R 
+--R
+--R           x
+--I         ++       %H   m
+--I   (1)   |   acot(--)%H d%H
+--R        ++         a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.507~~~~~$\displaystyle
+\int{x^m\sec^{-1}\frac{x}{a}}~dx$}
+$$\int{x^m\sec^{-1}\frac{x}{a}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{x^{m+1}\sec^{-1}(x/a)}{m+1}-\frac{a}{m+1}\int{\frac{x^m}{\sqrt{x^2-a^2}}}
+{\rm \ if\ }0 &lt; \sec^{-1}\frac{x}{a} &lt; \frac{\pi}{2}\\
+\\
+\displaystyle
+\frac{x^{m+1}\sec^{-1}(x/a)}{m+1}+\frac{a}{m+1}\int{\frac{x^m}{\sqrt{x^2-a^2}}}
+{\rm \ if\ }\frac{\pi}{2} &lt; \sec^{-1}\frac{x}{a} &lt; \pi\\
+\end{array}
+\right.
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 145    14:507 Axiom cannot compute this integral
+aa:=integrate(x^m*asec(x/a),x)
+--R 
+--R
+--R           x
+--I         ++       %H   m
+--I   (1)   |   asec(--)%H d%H
+--R        ++         a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.508~~~~~$\displaystyle
+\int{x^m\csc^{-1}\frac{x}{a}}~dx$}
+$$\int{x^m\csc^{-1}\frac{x}{a}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{x^{m+1}\csc^{-1}(x/a)}{m+1}+\frac{a}{m+1}\int{\frac{x^m}{\sqrt{x^2-a^2}}}
+{\rm \ if\ }0 &lt; \csc^{-1}\frac{x}{a} &lt; \frac{\pi}{2}\\
+\\
+\displaystyle
+\frac{x^{m+1}\csc^{-1}(x/a)}{m+1}-\frac{a}{m+1}\int{\frac{x^m}{\sqrt{x^2-a^2}}}
+{\rm \ if\ }-\frac{\pi}{2} &lt; \csc^{-1}\frac{x}{a} &lt; 0\\
+\end{array}
+\right.
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 146    14:508 Axiom cannot compute this integral
+aa:=integrate(x^m*acsc(x/a),x)
+--R 
+--R
+--R           x
+--I         ++       %H   m
+--I   (1)   |   acsc(--)%H d%H
+--R        ++         a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 pp82-84
+\end{thebibliography}
+\end{document}
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diff --git a/src/axiom-website/CATS/schaum25.input.pamphlet b/src/axiom-website/CATS/schaum25.input.pamphlet
new file mode 100644
index 0000000..0a55f34
--- /dev/null
+++ b/src/axiom-website/CATS/schaum25.input.pamphlet
@@ -0,0 +1,618 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum25.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.509~~~~~$\displaystyle
+\int{e^{ax}}~dx$}
+$$\int{e^{ax}}=
+\frac{e^{ax}}{a}
+$$
+&lt;&lt;*&gt;&gt;=
+)spool schaum25.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1
+aa:=integrate(%e^(a*x),x)
+--R
+--R          a x
+--R        %e
+--R   (1)  -----
+--R          a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 2
+bb:=%e^(a*x)/a
+--R
+--R          a x
+--R        %e
+--R   (2)  -----
+--R          a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3      14:509 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.510~~~~~$\displaystyle
+\int{xe^{ax}}~dx$}
+$$\int{xe^{ax}}=
+\frac{e^{ax}}{x}\left(x-\frac{1}{a}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 4
+aa:=integrate(x*%e^(a*x),x)
+--R
+--R                   a x
+--R        (a x - 1)%e
+--R   (1)  --------------
+--R               2
+--R              a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 5
+bb:=%e^(a*x)/a*(x-1/a)
+--R
+--R                   a x
+--R        (a x - 1)%e
+--R   (2)  --------------
+--R               2
+--R              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 6      14:510 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.511~~~~~$\displaystyle
+\int{x^2e^{ax}}~dx$}
+$$\int{x^2e^{ax}}=
+\frac{e^{ax}}{x}\left(x^2-\frac{2x}{a}+\frac{2}{a^2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 7
+aa:=integrate(x^2*%e^(a*x),x)
+--R
+--R          2 2              a x
+--R        (a x  - 2a x + 2)%e
+--R   (1)  ----------------------
+--R                   3
+--R                  a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 8
+bb:=%e^(a*x)/a*(x^2-(2*x)/a+2/a^2)
+--R
+--R          2 2              a x
+--R        (a x  - 2a x + 2)%e
+--R   (2)  ----------------------
+--R                   3
+--R                  a
+--R                                                     Type: Expression Integer
+--E
+
+--S 9      14:511 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.512~~~~~$\displaystyle
+\int{x^ne^{ax}}~dx$}
+$$\begin{array}{rl}
+\displaystyle\int{x^ne^{ax}}=&amp;
+\displaystyle
+\frac{x^ne^{ax}}{a}-\frac{n}{a}\int{x^{n-1}e^{ax}}\\
+\\
+&amp;\displaystyle
+=\frac{e^{ax}}{x}\left(x^n-\frac{nx^{n-1}}{a}+\frac{n(n-1)x^{n-2}}{a^2}
+-\cdots \frac{(-1)^nn!}{a^n}\right)
+\\
+&amp;\hbox{\hskip 5cm}{\rm\ if\ }n={\rm positive integer}
+\end{array}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 10     14:512 Axiom cannot compute this integral
+aa:=integrate(x^n*%e^(a*x),x)
+--R
+--R           x
+--I         ++    %I a  n
+--I   (1)   |   %e    %I d%I
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+@
+
+\section{\cite{1}:14.513~~~~~$\displaystyle
+\int{\frac{e^{ax}}{x}}~dx$}
+$$\int{\frac{e^{ax}}{x}}=
+\ln{x}+\frac{ax}{1\cdot 1!}+\frac{(ax)^2}{2\cdot 2!}
++\frac{(ax)^3}{3\cdot 3!}+\cdots
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 11     14:513 Schaums and Axiom agree by definition
+aa:=integrate(%e^(a*x)/x,x)
+--R
+--R   (1)  Ei(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.514~~~~~$\displaystyle
+\int{\frac{e^{ax}}{x^n}}~dx$}
+$$\int{\frac{e^{ax}}{x^n}}=
+\frac{-e^{ax}}{(n-1)x^{n-1}}+\frac{a}{n-1}\int{\frac{e^{ax}}{x^{n-1}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 12     14:514 Axiom cannot compute this integral
+aa:=integrate(%e^(a*x)/x^n,x)
+--R
+--I           x   %I a
+--R         ++  %e
+--I   (1)   |   ------ d%I
+--R        ++       n
+--I               %I
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.515~~~~~$\displaystyle
+\int{\frac{dx}{p+qe^{ax}}}~dx$}
+$$\int{\frac{1}{p+qe^{ax}}}=
+\frac{x}{p}-\frac{1}{ap}\ln(p+qe^{ax})
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 13
+aa:=integrate(1/(p+q*%e^(a*x)),x)
+--R
+--R                  a x
+--R        - log(q %e    + p) + a x
+--R   (1)  ------------------------
+--R                   a p
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 14
+bb:=x/p-1/(a*p)*log(p+q*%e^(a*x))
+--R
+--R                  a x
+--R        - log(q %e    + p) + a x
+--R   (2)  ------------------------
+--R                   a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 15     14:515 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.516~~~~~$\displaystyle
+\int{\frac{dx}{(p+qe^{ax})^2}}~dx$}
+$$\int{\frac{dx}{(p+qe^{ax})^2}}=
+\frac{x}{p^2}+\frac{1}{ap(p+qe^{ax})}-\frac{1}{ap^2}\ln(p+qe^{ax})
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 16
+aa:=integrate(1/(p+q*%e^(a*x))^2,x)
+--R
+--R               a x             a x                a x
+--R        (- q %e    - p)log(q %e    + p) + a q x %e    + a p x + p
+--R   (1)  ---------------------------------------------------------
+--R                               2    a x      3
+--R                            a p q %e    + a p
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 17
+bb:=x/p^2+1/(a*p*(p+q*%e^(a*x)))-1/(a*p^2)*log(p+q*%e^(a*x))
+--R
+--R               a x             a x                a x
+--R        (- q %e    - p)log(q %e    + p) + a q x %e    + a p x + p
+--R   (2)  ---------------------------------------------------------
+--R                               2    a x      3
+--R                            a p q %e    + a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 18     14:516 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.517~~~~~$\displaystyle
+\int{\frac{dx}{pe^{ax}+qe^{ax}}}~dx$}
+$$\int{\frac{dx}{pe^{ax}+qe^{ax}}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{1}{a\sqrt{pq}}\tan^{-1}\left(\sqrt{\frac{p}{q}}e^{ax}\right)\\
+\\
+\displaystyle
+\frac{1}{2a\sqrt{-pq}}
+\ln\left(\frac{e^{ax}-\sqrt{-q/p}}{e^{ax}+\sqrt{-q/p}}\right)
+\end{array}
+\right.
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 19
+aa:=integrate(1/(p*%e^(a*x)+q*%e^-(a*x)),x)
+--R
+--R                   a x 2      +-----+          a x
+--R             (p (%e   )  - q)\|- p q  + 2p q %e            a x +---+
+--R         log(-------------------------------------)      %e   \|p q
+--R                              a x 2                 atan(-----------)
+--R                         p (%e   )  + q                       q
+--R   (1)  [------------------------------------------,-----------------]
+--R                            +-----+                        +---+
+--R                         2a\|- p q                       a\|p q
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+
+--S 20
+bb1:=1/(a*sqrt(p*q))*atan(sqrt(p/q)*%e^(a*x))
+--R
+--R                   +-+
+--R               a x |p
+--R        atan(%e    |- )
+--R                  \|q
+--R   (2)  ---------------
+--R              +---+
+--R            a\|p q
+--R                                                     Type: Expression Integer
+--E
+
+--S 21
+bb2:=1/(2*a*sqrt(-p*q))*log((%e^(a*x)-sqrt(-q/p))/(%e^(a*x)+sqrt(-q/p)))
+--R
+--R               +---+
+--R               |  q      a x
+--R            -  |- -  + %e
+--R              \|  p
+--R        log(----------------)
+--R              +---+
+--R              |  q      a x
+--R              |- -  + %e
+--R             \|  p
+--R   (3)  ---------------------
+--R                 +-----+
+--R              2a\|- p q
+--R                                                     Type: Expression Integer
+--E
+
+--S 22
+cc1:=aa.1-bb1
+--R
+--R   (4)
+--R                   a x 2      +-----+          a x                        +-+
+--R    +---+    (p (%e   )  - q)\|- p q  + 2p q %e         +-----+       a x |p
+--R   \|p q log(-------------------------------------) - 2\|- p q atan(%e    |- )
+--R                              a x 2                                      \|q
+--R                         p (%e   )  + q
+--R   ---------------------------------------------------------------------------
+--R                                    +-----+ +---+
+--R                                 2a\|- p q \|p q
+--R                                                     Type: Expression Integer
+--E
+
+--S 23
+cc2:=aa.2-bb1
+--R
+--R               a x +---+               +-+
+--R             %e   \|p q            a x |p
+--R        atan(-----------) - atan(%e    |- )
+--R                  q                   \|q
+--R   (5)  -----------------------------------
+--R                        +---+
+--R                      a\|p q
+--R                                                     Type: Expression Integer
+--E
+
+--S 24
+cc3:=aa.1-bb2
+--R
+--R                                                            +---+
+--R                                                            |  q      a x
+--R                  a x 2      +-----+          a x        -  |- -  + %e
+--R            (p (%e   )  - q)\|- p q  + 2p q %e             \|  p
+--R        log(-------------------------------------) - log(----------------)
+--R                             a x 2                         +---+
+--R                        p (%e   )  + q                     |  q      a x
+--R                                                           |- -  + %e
+--R                                                          \|  p
+--R   (6)  ------------------------------------------------------------------
+--R                                       +-----+
+--R                                    2a\|- p q
+--R                                                     Type: Expression Integer
+--E
+
+--S 25     14:517 Axiom cannot simplify these expressions
+cc4:=aa.2-bb2
+--R
+--R                       +---+
+--R                       |  q      a x
+--R                    -  |- -  + %e                       a x +---+
+--R           +---+      \|  p               +-----+     %e   \|p q
+--R        - \|p q log(----------------) + 2\|- p q atan(-----------)
+--R                      +---+                                q
+--R                      |  q      a x
+--R                      |- -  + %e
+--R                     \|  p
+--R   (7)  ----------------------------------------------------------
+--R                                +-----+ +---+
+--R                             2a\|- p q \|p q
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.518~~~~~$\displaystyle
+\int{e^{ax}\sin{bx}}~dx$}
+$$\int{e^{ax}\sin{bx}}=
+\frac{e^{ax}(a\sin{bx}-b\cos{bx})}{a^2+b^2}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 26
+aa:=integrate(%e^(a*x)*sin(b*x),x)
+--R
+--R            a x                       a x
+--R        a %e   sin(b x) - b cos(b x)%e
+--R   (1)  ---------------------------------
+--R                      2    2
+--R                     b  + a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 27
+bb:=((%e^(a*x))*(a*sin(b*x)-b*cos(b*x)))/(a^2+b^2)
+--R
+--R            a x                       a x
+--R        a %e   sin(b x) - b cos(b x)%e
+--R   (2)  ---------------------------------
+--R                      2    2
+--R                     b  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 28     14:518 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.519~~~~~$\displaystyle
+\int{e^{ax}\cos{bx}}~dx$}
+$$\int{e^{ax}\cos{bx}}=
+\frac{e^{ax}(a\cos{bx}-b\sin{bx})}{a^2+b^2}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 29
+aa:=integrate(%e^(a*x)*cos(b*x),x)
+--R
+--R            a x                       a x
+--R        b %e   sin(b x) + a cos(b x)%e
+--R   (1)  ---------------------------------
+--R                      2    2
+--R                     b  + a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 30
+bb:=((%e^(a*x))*(a*cos(b*x)+b*sin(b*x)))/(a^2+b^2)
+--R
+--R            a x                       a x
+--R        b %e   sin(b x) + a cos(b x)%e
+--R   (2)  ---------------------------------
+--R                      2    2
+--R                     b  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 31     14:519 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.520~~~~~$\displaystyle
+\int{xe^{ax}\sin{bx}}~dx$}
+$$\int{xe^{ax}\sin{bx}}=
+\frac{xe^{ax}(a\sin{bx}-b\cos{bx})}{a^2+b^2}
+-\frac{e^{ax}\left((a^2-b^2)\sin{bx}-2ab\cos{bx}\right)}{(a^2+b^2)^2}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 32
+aa:=integrate(x*%e^(a*x)*sin(b*x),x)
+--R
+--R   (1)
+--R        2    3      2    2   a x                3    2                     a x
+--R   ((a b  + a )x + b  - a )%e   sin(b x) + ((- b  - a b)x + 2a b)cos(b x)%e
+--R   ---------------------------------------------------------------------------
+--R                                  4     2 2    4
+--R                                 b  + 2a b  + a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 33
+bb:=(x*%e^(a*x)*(a*sin(b*x)-b*cos(b*x)))/(a^2+b^2)-(%e^(a*x)*((a^2-b^2)*sin(b*x)-2*a*b*cos(b*x)))/(a^2+b^2)^2
+--R
+--R   (2)
+--R        2    3      2    2   a x                3    2                     a x
+--R   ((a b  + a )x + b  - a )%e   sin(b x) + ((- b  - a b)x + 2a b)cos(b x)%e
+--R   ---------------------------------------------------------------------------
+--R                                  4     2 2    4
+--R                                 b  + 2a b  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 34     14:520 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.521~~~~~$\displaystyle
+\int{xe^{ax}\cos{bx}}~dx$}
+$$\int{xe^{ax}\cos{bx}}=
+\frac{xe^{ax}(a\cos{bx}-b\sin{bx})}{a^2+b^2}
+-\frac{e^{ax}\left((a^2-b^2)\cos{bx}-2ab\sin{bx}\right)}{(a^2+b^2)^2}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 35
+aa:=integrate(x*%e^(a*x)*cos(b*x),x)
+--R
+--R   (1)
+--R      3    2             a x                2    3      2    2           a x
+--R   ((b  + a b)x - 2a b)%e   sin(b x) + ((a b  + a )x + b  - a )cos(b x)%e
+--R   -------------------------------------------------------------------------
+--R                                 4     2 2    4
+--R                                b  + 2a b  + a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 36
+bb:=(x*%e^(a*x)*(a*cos(b*x)+b*sin(b*x)))/(a^2+b^2)-(%e^(a*x)*((a^2-b^2)*cos(b*x)+2*a*b*sin(b*x)))/(a^2+b^2)^2
+--R
+--R   (2)
+--R      3    2             a x                2    3      2    2           a x
+--R   ((b  + a b)x - 2a b)%e   sin(b x) + ((a b  + a )x + b  - a )cos(b x)%e
+--R   -------------------------------------------------------------------------
+--R                                 4     2 2    4
+--R                                b  + 2a b  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 37     14:521 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.522~~~~~$\displaystyle
+\int{e^{ax}\ln{x}}~dx$}
+$$\int{e^{ax}\ln{x}}=
+\frac{e^{ax}\ln{x}}{a}-\frac{1}{a}\int{\frac{e^{ax}}{x}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 38     14:522 Schaums and Axiom agree by definition
+aa:=integrate(%e^(a*x)*log(x),x)
+--R
+--R          a x
+--R        %e   log(x) - Ei(a x)
+--R   (1)  ---------------------
+--R                  a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.523~~~~~$\displaystyle
+\int{e^{ax}\sin^n{bx}}~dx$}
+$$\int{e^{ax}\sin^n{bx}}=
+\frac{e^{ax}\sin^{n-1}{bx}}{a^2+n^2b^2}(a\sin{bx}-nb\cos{bx})
++\frac{n(n-1)b^2}{a^2+n^2b^2}\int{e^{ax}\sin^{n-2}{bx}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 39     14:523 Axiom cannot compute this integral
+aa:=integrate(%e^(a*x)*sin(b*x)^n,x)
+--R
+--R           x
+--I         ++    %I a         n
+--I   (1)   |   %e    sin(%I b) d%I
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.524~~~~~$\displaystyle
+\int{e^{ax}\cos^n{bx}}~dx$}
+$$\int{e^{ax}\cos^n{bx}}=
+\frac{e^{ax}\cos^{n-1}{bx}}{a^2+n^2b^2}(a\cos{bx}-nb\sin{bx})
++\frac{n(n-1)b^2}{a^2+n^2b^2}\int{e^{ax}\cos^{n-2}{bx}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 40     14:524 Axiom cannot compute this integral
+aa:=integrate(%e^(a*x)*cos(b*x)^n,x)
+--R
+--R           x
+--I         ++    %I a         n
+--I   (1)   |   %e    cos(%I b) d%I
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 p85
+\end{thebibliography}
+\end{document}
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diff --git a/src/axiom-website/CATS/schaum26.input.pamphlet b/src/axiom-website/CATS/schaum26.input.pamphlet
new file mode 100644
index 0000000..9bdeec5
--- /dev/null
+++ b/src/axiom-website/CATS/schaum26.input.pamphlet
@@ -0,0 +1,552 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum26.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.525~~~~~$\displaystyle
+\int{ln x}~dx$}
+$$\int{ln x}=
+x\ln{x}-x
+$$
+&lt;&lt;*&gt;&gt;=
+)spool schaum26.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1
+aa:=integrate(log(x),x)
+--R 
+--R
+--R   (1)  x log(x) - x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 2
+bb:=x*log(x)-x
+--R
+--R   (2)  x log(x) - x
+--R                                                     Type: Expression Integer
+--E
+
+--S 3      14:525 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.526~~~~~$\displaystyle
+\int{x\ln{x}}~dx$}
+$$\int{x\ln{x}}=
+\frac{x^2}{2}\left(\ln{x}-\frac{1}{2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 4
+aa:=integrate(x*log(x),x)
+--R 
+--R
+--R          2          2
+--R        2x log(x) - x
+--R   (1)  --------------
+--R               4
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 5
+bb:=x^2/2*(log(x)-1/2)
+--R
+--R          2          2
+--R        2x log(x) - x
+--R   (2)  --------------
+--R               4
+--R                                                     Type: Expression Integer
+--E 
+
+--S 6      14:526 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.527~~~~~$\displaystyle
+\int{x^m\ln{x}}~dx$}
+$$\int{x^m\ln{x}}=
+\frac{x^{m+1}}{m+1}\left(\ln{x}-\frac{1}{m+1}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 7
+aa:=integrate(x^m*log(x),x)
+--R 
+--R
+--R                               m log(x)
+--R        ((m + 1)x log(x) - x)%e
+--R   (1)  -------------------------------
+--R                   2
+--R                  m  + 2m + 1
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 8
+bb:=x^(m+1)/(m+1)*(log(x)-1/(m+1))
+--R
+--R                            m + 1
+--R        ((m + 1)log(x) - 1)x
+--R   (2)  -------------------------
+--R                2
+--R               m  + 2m + 1
+--R                                                     Type: Expression Integer
+--E
+
+--S 9
+cc:=aa-bb
+--R
+--R                               m log(x)                         m + 1
+--R        ((m + 1)x log(x) - x)%e         + ((- m - 1)log(x) + 1)x
+--R   (3)  -------------------------------------------------------------
+--R                                  2
+--R                                 m  + 2m + 1
+--R                                                     Type: Expression Integer
+--E
+
+--S 10
+explog:=rule(%e^(n*log(x)) == x^n)
+--R
+--R          n log(x)     n
+--R   (4)  %e         == x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 11
+dd:=explog cc
+--R
+--R                              m + 1                         m
+--R        ((- m - 1)log(x) + 1)x      + ((m + 1)x log(x) - x)x
+--R   (5)  -----------------------------------------------------
+--R                              2
+--R                             m  + 2m + 1
+--R                                                     Type: Expression Integer
+--E
+
+--S 12     14:527 Schaums and Axiom agree
+ee:=complexNormalize dd
+--R
+--R   (6)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.528~~~~~$\displaystyle
+\int{\frac{\ln{x}}{x}}~dx$}
+$$\int{\frac{\ln{x}}{x}}=
+\frac{1}{2}\ln^2{x}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 13
+aa:=integrate(log(x)/x,x)
+--R 
+--R
+--R              2
+--R        log(x)
+--R   (1)  -------
+--R           2
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 14
+bb:=1/2*log(x)^2
+--R
+--R              2
+--R        log(x)
+--R   (2)  -------
+--R           2
+--R                                                     Type: Expression Integer
+--E 
+
+--S 15     14:528 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.529~~~~~$\displaystyle
+\int{\frac{\ln{x}}{x^2}}~dx$}
+$$\int{\frac{\ln{x}}{x^2}}=
+-\frac{\ln{x}}{x}-\frac{1}{x}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 16
+aa:=integrate(log(x)/x^2,x)
+--R 
+--R
+--R        - log(x) - 1
+--R   (1)  ------------
+--R              x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 17
+bb:=-log(x)/x-1/x
+--R
+--R        - log(x) - 1
+--R   (2)  ------------
+--R              x
+--R                                                     Type: Expression Integer
+--E
+
+--S 18     14:529 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.530~~~~~$\displaystyle
+\int{\ln^2{x}}~dx$}
+$$\int{\ln^2{x}}=
+x\ln^2{x}-2x\ln{x}+2x
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 19
+aa:=integrate(log(x)^2,x)
+--R 
+--R
+--R                2
+--R   (1)  x log(x)  - 2x log(x) + 2x
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 20
+bb:=x*log(x)^2-2*x*log(x)+2*x
+--R
+--R                2
+--R   (2)  x log(x)  - 2x log(x) + 2x
+--R                                                     Type: Expression Integer
+--E 
+
+--S 21     14:530 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.531~~~~~$\displaystyle
+\int{\frac{\ln^n{x}}{x}}~dx$}
+$$\int{\frac{\ln^n{x}}{x}}=
+\frac{ln^{n+1}{x}}{n+1}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 22
+aa:=integrate(log(x)^n/x,x)
+--R 
+--R
+--R                n log(log(x))
+--R        log(x)%e
+--R   (1)  ---------------------
+--R                n + 1
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 23
+bb:=log(x)^(n+1)/(n+1)
+--R
+--R              n + 1
+--R        log(x)
+--R   (2)  -----------
+--R           n + 1
+--R                                                     Type: Expression Integer
+--E 
+
+--S 24
+cc:=aa-bb
+--R
+--R                n log(log(x))         n + 1
+--R        log(x)%e              - log(x)
+--R   (3)  -----------------------------------
+--R                       n + 1
+--R                                                     Type: Expression Integer
+--E
+
+--S 25
+explog:=rule(%e^(n*log(x)) == x^n)
+--R
+--R          n log(x)     n
+--R   (4)  %e         == x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 26
+dd:=explog cc
+--R
+--R                n + 1               n
+--R        - log(x)      + log(x)log(x)
+--R   (5)  -----------------------------
+--R                    n + 1
+--R                                                     Type: Expression Integer
+--E
+
+--S 27     14:531 Schaums and Axiom agree
+ee:=complexNormalize dd
+--R
+--R   (6)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.532~~~~~$\displaystyle
+\int{\frac{dx}{x\ln{x}}}$}
+$$\int{\frac{1}{x\ln{x}}}=
+\ln(\ln{x})
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 28
+aa:=integrate(1/(x*log(x)),x)
+--R 
+--R
+--R   (1)  log(log(x))
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 29
+bb:=log(log(x))
+--R
+--R   (2)  log(log(x))
+--R                                                     Type: Expression Integer
+--E
+
+--S 30     14:532 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.533~~~~~$\displaystyle
+\int{\frac{dx}{\ln{x}}}$}
+$$\int{\frac{1}{\ln{x}}}=
+\ln(\ln{x})+\ln{x}+\frac{\ln^2{x}}{2\cdot 2!}
++\frac{\ln^3{x}}{3\cdot 3!}+\cdots
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 31     14:533 Schaums and Axiom agree by definition
+aa:=integrate(1/log(x),x)
+--R 
+--R
+--R   (1)  li(x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.534~~~~~$\displaystyle
+\int{\frac{x^m}{\ln{x}}}~dx$}
+$$\int{\frac{x^m}{\ln{x}}}=
+\ln(\ln{x})+(m+1)\ln{x}+\frac{(m+1)^2\ln^2{x}}{2\cdot 2!}
++\frac{(m+1)^3\ln^3{x}}{3\cdot 3!}+\cdots
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 32     14:534 Axiom cannot compute this integral
+aa:=integrate(x^m/log(x),x)
+--R 
+--R
+--R           x     m
+--I         ++    %I
+--I   (1)   |   ------- d%I
+--I        ++   log(%I)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.535~~~~~$\displaystyle
+\int{\ln^n{x}}~dx$}
+$$\int{\ln^n{x}}=
+x\ln^n{x}-n\int{\ln^{n-1}{x}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 33     14:535 Axiom cannot compute this integral
+aa:=integrate(log(x)^n,x)
+--R 
+--R
+--R           x
+--R         ++         n
+--I   (1)   |   log(%I) d%I
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.536~~~~~$\displaystyle
+\int{x^m\ln^n{x}}~dx$}
+$$\int{x^m\ln^n{x}}=
+\frac{x^{m+1}\ln^n{x}}{m+1}-\frac{n}{m+1}\int{x^m\ln^{n-1}{x}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 34     14:536 Axiom cannot compute this integral
+aa:=integrate(x^m*log(x)^n,x)
+--R 
+--R
+--R           x
+--R         ++    m       n
+--I   (1)   |   %I log(%I) d%I
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.537~~~~~$\displaystyle
+\int{\ln{(x^2+a^2)}}~dx$}
+$$\int{\ln{(x^2+a^2)}}=
+x\ln(x^2+a^2)-2x+2a\tan^{-1}\frac{x}{a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 35
+aa:=integrate(log(x^2+a^2),x)
+--R 
+--R
+--R               2    2            x
+--R   (1)  x log(x  + a ) + 2a atan(-) - 2x
+--R                                 a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 36
+bb:=x*log(x^2+a^2)-2*x+2*a*atan(x/a)
+--R
+--R               2    2            x
+--R   (2)  x log(x  + a ) + 2a atan(-) - 2x
+--R                                 a
+--R                                                     Type: Expression Integer
+--E
+
+--S 37     14:537 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.538~~~~~$\displaystyle
+\int{\ln(x^2-a^2)}~dx$}
+$$\int{\ln(x^2-a^2)}=
+x\ln(x^2-a^2)-2x+a\ln\left(\frac{x+a}{x-a}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 38
+aa:=integrate(log(x^2-a^2),x)
+--R 
+--R
+--R               2    2
+--R   (1)  x log(x  - a ) + a log(x + a) - a log(x - a) - 2x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 39
+bb:=x*log(x^2-a^2)-2*x+a*log((x+a)/(x-a))
+--R
+--R               2    2          x + a
+--R   (2)  x log(x  - a ) + a log(-----) - 2x
+--R                               x - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 40
+cc:=aa-bb
+--R
+--R                                            x + a
+--R   (3)  a log(x + a) - a log(x - a) - a log(-----)
+--R                                            x - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 41     14:538 Schaums and Axiom agree
+dd:=expandLog cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.539~~~~~$\displaystyle
+\int{x^m\ln(x^2\pm a^2)}~dx$}
+$$\int{x^m\ln(x^2\pm a^2)}=
+\frac{x^{m-1}\ln(x^2\pm a^2)}{m+1}
+-\frac{2}{m+1}\int{\frac{x^{m+2}}{x^2\pm a^2}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 42
+aa:=integrate(x^m*log(x^2+a^2),x)
+--R 
+--R
+--R           x
+--R         ++       2     2   m
+--I   (1)   |   log(a  + %I )%I d%I
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+)clear all
+
+--S 43     14:539 Axiom cannot compute this integral
+aa:=integrate(x^m*log(x^2-a^2),x)
+--R 
+--R
+--R           x
+--R         ++         2     2   m
+--I   (1)   |   log(- a  + %I )%I d%I
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 p86
+\end{thebibliography}
+\end{document}
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diff --git a/src/axiom-website/CATS/schaum27.input.pamphlet b/src/axiom-website/CATS/schaum27.input.pamphlet
new file mode 100644
index 0000000..68d33a3
--- /dev/null
+++ b/src/axiom-website/CATS/schaum27.input.pamphlet
@@ -0,0 +1,1571 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum27.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.540~~~~~$\displaystyle
+\int{\sinh{ax}}~dx$}
+$$\int{\sinh{ax}}=
+\frac{\cosh{ax}}{a}
+$$
+&lt;&lt;*&gt;&gt;=
+)spool schaum27.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1
+aa:=integrate(sinh(a*x),x)
+--R
+--R        cosh(a x)
+--R   (1)  ---------
+--R            a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 2
+bb:=cosh(a*x)/a
+--R
+--R        cosh(a x)
+--R   (2)  ---------
+--R            a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3      14:540 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.541~~~~~$\displaystyle
+\int{x\sinh{ax}}~dx$}
+$$\int{x\sinh{ax}}=
+\frac{x*\cosh{ax}}{a}-\frac{\sinh{ax}}{a^2}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 4
+aa:=integrate(x*sinh(a*x),x)
+--R 
+--R
+--R        - sinh(a x) + a x cosh(a x)
+--R   (1)  ---------------------------
+--R                      2
+--R                     a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 5
+bb:=(x*cosh(a*x))/a-sinh(a*x)/a^2
+--R
+--R        - sinh(a x) + a x cosh(a x)
+--R   (2)  ---------------------------
+--R                      2
+--R                     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 6      14:541 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.542~~~~~$\displaystyle
+\int{x^2\sinh{ax}}~dx$}
+$$\int{x^2\sinh{ax}}=
+\left(\frac{x^2}{a}+\frac{2}{a^3}\right)\cosh{ax}-\frac{2x}{a^2}\sinh{ax}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 7
+aa:=integrate(x^2*sinh(a*x),x)
+--R 
+--R
+--R                             2 2
+--R        - 2a x sinh(a x) + (a x  + 2)cosh(a x)
+--R   (1)  --------------------------------------
+--R                           3
+--R                          a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 8
+bb:=(x^2/a+2/a^3)*cosh(a*x)-(2*x)/a^2*sinh(a*x)
+--R
+--R                             2 2
+--R        - 2a x sinh(a x) + (a x  + 2)cosh(a x)
+--R   (2)  --------------------------------------
+--R                           3
+--R                          a
+--R                                                     Type: Expression Integer
+--E
+
+--S 9      14:542 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.543~~~~~$\displaystyle
+\int{\frac{\sinh{ax}}{x}}~dx$}
+$$\int{\frac{\sinh{ax}}{x}}=
+ax+\frac{(ax)^3}{3\cdot 3!}+\frac{(ax)^5}{5\cdot 5!}+\cdots
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 10     14:543 Axiom cannot compute this integral
+aa:=integrate(sinh(a*x)/x,x)
+--R 
+--R
+--R           x
+--I         ++  sinh(%N a)
+--I   (1)   |   ---------- d%N
+--I        ++       %N
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.544~~~~~$\displaystyle
+\int{\frac{\sinh{ax}}{x^2}}~dx$}
+$$\int{\frac{\sinh{ax}}{x^2}}=
+-\frac{\sinh{ax}}{x}+\int{\frac{\cosh{ax}}{x}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 11     14:544 Axiom cannot compute this integral
+aa:=integrate(sinh(a*x)/x^2,x)
+--R 
+--R
+--R           x
+--I         ++  sinh(%N a)
+--I   (1)   |   ---------- d%N
+--R        ++         2
+--I                 %N
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.545~~~~~$\displaystyle
+\int{\frac{dx}{\sinh{ax}}}~dx$}
+$$\int{\frac{1}{\sinh{ax}}}=
+\frac{1}{a}\ln\tanh{\frac{ax}{2}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 12
+aa:=integrate(1/sinh(a*x),x)
+--R 
+--R
+--R        - log(sinh(a x) + cosh(a x) + 1) + log(sinh(a x) + cosh(a x) - 1)
+--R   (1)  -----------------------------------------------------------------
+--R                                        a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 13
+bb:=1/a*log(tanh(a*x)/2)
+--R
+--R            tanh(a x)
+--R        log(---------)
+--R                2
+--R   (2)  --------------
+--R               a
+--R                                                     Type: Expression Integer
+--E
+
+--S 14     14:545 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R             tanh(a x)
+--R       - log(---------) - log(sinh(a x) + cosh(a x) + 1)
+--R                 2
+--R     + 
+--R       log(sinh(a x) + cosh(a x) - 1)
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.546~~~~~$\displaystyle
+\int{\frac{x~dx}{\sinh{ax}}}~dx$}
+$$\int{\frac{x}{\sinh{ax}}}=
+\frac{1}{a^2}\left\{ax-\frac{(ax)^3}{18}+\frac{7(ax)^5}{1800}-\cdots
++\frac{2(-1)^n(2^{2n-1})B_n(ax)^{2n+1}}{(2n+1)!}+\cdots\right\}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 15     14:546 Axiom cannot compute this integral
+aa:=integrate(x/sinh(a*x),x)
+--R 
+--R
+--R           x
+--I         ++      %N
+--I   (1)   |   ---------- d%N
+--I        ++   sinh(%N a)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.547~~~~~$\displaystyle
+\int{\sinh^2{ax}}~dx$}
+$$\int{\sinh^2{ax}}=
+\frac{\sinh{ax}\cosh{ax}}{2a}-\frac{x}{2}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 16
+aa:=integrate(sinh(a*x)^2,x)
+--R 
+--R
+--R        cosh(a x)sinh(a x) - a x
+--R   (1)  ------------------------
+--R                   2a
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 17
+bb:=(sinh(a*x)*cosh(a*x))/(2*a)-x/2
+--R
+--R        cosh(a x)sinh(a x) - a x
+--R   (2)  ------------------------
+--R                   2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 18     14:547 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.548~~~~~$\displaystyle
+\int{x\sinh^2{ax}}~dx$}
+$$\int{x\sinh^2{ax}}=
+\frac{x*\sinh{2ax}}{4a}-\frac{\cosh{2ax}}{8a^2}-\frac{x^2}{4}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 19
+aa:=integrate(x*sinh(a*x)^2,x)
+--R 
+--R
+--R                   2                                      2     2 2
+--R        - sinh(a x)  + 4a x cosh(a x)sinh(a x) - cosh(a x)  - 2a x
+--R   (1)  -----------------------------------------------------------
+--R                                      2
+--R                                    8a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 20
+bb:=(x*sinh(2*a*x))/(4*a)-cosh(2*a*x)/(8*a^2)-x^2/4
+--R
+--R                                         2 2
+--R        2a x sinh(2a x) - cosh(2a x) - 2a x
+--R   (2)  ------------------------------------
+--R                           2
+--R                         8a
+--R                                                     Type: Expression Integer
+--E
+
+--S 21
+cc:=aa-bb
+--R
+--R   (3)
+--R                                    2
+--R       - 2a x sinh(2a x) - sinh(a x)  + 4a x cosh(a x)sinh(a x) + cosh(2a x)
+--R     + 
+--R                  2
+--R       - cosh(a x)
+--R  /
+--R       2
+--R     8a
+--R                                                     Type: Expression Integer
+--E
+
+--S 22
+sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
+--R
+--R               2    cosh(2x) - 1
+--R   (4)  sinh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 23
+dd:=sinhsqrrule cc
+--R
+--R   (5)
+--R                                                                        2
+--R   - 4a x sinh(2a x) + 8a x cosh(a x)sinh(a x) + cosh(2a x) - 2cosh(a x)  + 1
+--R   --------------------------------------------------------------------------
+--R                                         2
+--R                                      16a
+--R                                                     Type: Expression Integer
+--E
+
+--S 24
+coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
+--R
+--R               2    cosh(2x) + 1
+--R   (6)  cosh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 25
+ee:=coshsqrrule dd
+--R
+--R        - x sinh(2a x) + 2x cosh(a x)sinh(a x)
+--R   (7)  --------------------------------------
+--R                          4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 26
+sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
+--R
+--I                             %K sinh(y + x) - %K sinh(y - x)
+--I   (8)  %K cosh(y)sinh(x) == -------------------------------
+--R                                            2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 27     14:548 Schaums and Axiom agree
+ff:=sinhcoshrule ee
+--R
+--R   (9)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.549~~~~~$\displaystyle
+\int{\frac{dx}{\sinh^2{ax}}}~dx$}
+$$\int{\frac{1}{\sinh^2{ax}}}=
+-\frac{\coth{ax}}{a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 28
+aa:=integrate(1/sinh(a*x)^2,x)
+--R 
+--R
+--R                                     2
+--R   (1)  - -------------------------------------------------------
+--R                     2                                      2
+--R          a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 29
+bb:=-coth(a*x)/a
+--R
+--R          coth(a x)
+--R   (2)  - ---------
+--R              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 30
+cc:=aa-bb
+--R
+--R   (3)
+--R                         2
+--R       coth(a x)sinh(a x)  + 2cosh(a x)coth(a x)sinh(a x)
+--R     + 
+--R                 2
+--R       (cosh(a x)  - 1)coth(a x) - 2
+--R  /
+--R                2                                      2
+--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 31
+sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
+--R
+--R               2    cosh(2x) - 1
+--R   (4)  sinh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 32
+dd:=sinhsqrrule cc
+--R
+--R   (5)
+--R                                                          2
+--R   4cosh(a x)coth(a x)sinh(a x) + (cosh(2a x) + 2cosh(a x)  - 3)coth(a x) - 4
+--R   --------------------------------------------------------------------------
+--R                                                               2
+--R            4a cosh(a x)sinh(a x) + a cosh(2a x) + 2a cosh(a x)  - 3a
+--R                                                     Type: Expression Integer
+--E
+
+--S 33
+coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
+--R
+--R               2    cosh(2x) + 1
+--R   (6)  cosh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 34
+ee:=coshsqrrule dd
+--R
+--R        2cosh(a x)coth(a x)sinh(a x) + (cosh(2a x) - 1)coth(a x) - 2
+--R   (7)  ------------------------------------------------------------
+--R                  2a cosh(a x)sinh(a x) + a cosh(2a x) - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 35
+sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
+--I                             %B sinh(y + x) - %B sinh(y - x)
+--I   (8)  %B cosh(y)sinh(x) == -------------------------------
+--R                                            2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 36
+ff:=sinhcoshrule ee
+--R
+--R        coth(a x)sinh(2a x) + (cosh(2a x) - 1)coth(a x) - 2
+--R   (9)  ---------------------------------------------------
+--R                  a sinh(2a x) + a cosh(2a x) - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 37
+cothrule:=rule(coth(x) == cosh(x)/sinh(x))
+--R
+--R                    cosh(x)
+--R   (10)  coth(x) == -------
+--R                    sinh(x)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 38
+gg:=cothrule ff
+--R
+--R         cosh(a x)sinh(2a x) - 2sinh(a x) + cosh(a x)cosh(2a x) - cosh(a x)
+--R   (11)  ------------------------------------------------------------------
+--R                 a sinh(a x)sinh(2a x) + (a cosh(2a x) - a)sinh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 39
+hh:=sinhcoshrule gg
+--R
+--R         sinh(3a x) - 3sinh(a x) + 2cosh(a x)cosh(2a x) - 2cosh(a x)
+--R   (12)  -----------------------------------------------------------
+--R             a sinh(3a x) + 2a sinh(a x)sinh(2a x) - 3a sinh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 40
+sinhsinhrule:=rule(sinh(x)*sinh(y)==1/2*(cosh(x+y)-cosh(x-y)))
+--R
+--I                              %M cosh(y + x) - %M cosh(y - x)
+--I   (13)  %M sinh(x)sinh(y) == -------------------------------
+--R                                             2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 41
+ii:=sinhsinhrule gg
+--R
+--R         2cosh(a x)sinh(2a x) - 4sinh(a x) + 2cosh(a x)cosh(2a x) - 2cosh(a x)
+--R   (14)  ---------------------------------------------------------------------
+--R               (2a cosh(2a x) - 2a)sinh(a x) + a cosh(3a x) - a cosh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 42
+coshcoshrule:=rule(cosh(x)*cosh(y)==1/2*(cosh(x+y)+cosh(x-y)))
+--R
+--I                              %N cosh(y + x) + %N cosh(y - x)
+--I   (15)  %N cosh(x)cosh(y) == -------------------------------
+--R                                             2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 43
+jj:=coshcoshrule ii
+--R
+--R         2cosh(a x)sinh(2a x) - 4sinh(a x) + cosh(3a x) - cosh(a x)
+--R   (16)  ----------------------------------------------------------
+--R         (2a cosh(2a x) - 2a)sinh(a x) + a cosh(3a x) - a cosh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 44     14:549 Schaums and Axiom differ by a constant
+kk:=sinhcoshrule jj
+--R
+--R         1
+--R   (17)  -
+--R         a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.550~~~~~$\displaystyle
+\int{\sinh{ax}\sinh{px}}~dx$}
+$$\int{\sinh{ax}\sinh{px}}=
+\frac{\sinh(a+p)x}{2(a+p)}-\frac{\sinh(a-p)x}{2(a-p)}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 45
+aa:=integrate(sinh(a*x)*sinh(p*x),x)
+--R 
+--R
+--R        a cosh(a x)sinh(p x) - p cosh(p x)sinh(a x)
+--R   (1)  -------------------------------------------
+--R          2    2          2       2    2          2
+--R        (p  - a )sinh(a x)  + (- p  + a )cosh(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 46
+bb:=(sinh(a+p)*x)/(2*(a+p))-(sinh(a-p)*x)/(2*(a-p))
+--R
+--R        (p - a)x sinh(p + a) + (- p - a)x sinh(p - a)
+--R   (2)  ---------------------------------------------
+--R                            2     2
+--R                          2p  - 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 47     14:550 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R       2a cosh(a x)sinh(p x)
+--R     + 
+--R                                                               2
+--R       ((- p + a)x sinh(p + a) + (p + a)x sinh(p - a))sinh(a x)
+--R     + 
+--R                                                   2
+--R       - 2p cosh(p x)sinh(a x) + (p - a)x cosh(a x) sinh(p + a)
+--R     + 
+--R                           2
+--R       (- p - a)x cosh(a x) sinh(p - a)
+--R  /
+--R        2     2          2        2     2          2
+--R     (2p  - 2a )sinh(a x)  + (- 2p  + 2a )cosh(a x)
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.551~~~~~$\displaystyle
+\int{\sinh{ax}\sin{px}}~dx$}
+$$\int{\sinh{ax}\sin{px}}=
+\frac{a\cosh{ax}\sin{px}-p\sinh{ax}\cos{px}}{a^2+p^2}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 48
+aa:=integrate(sinh(a*x)*sin(p*x),x)
+--R 
+--R
+--R   (1)
+--R                                         2
+--R       (a sin(p x) - p cos(p x))sinh(a x)
+--R     + 
+--R       (2a cosh(a x)sin(p x) - 2p cos(p x)cosh(a x))sinh(a x)
+--R     + 
+--R                   2                                   2
+--R       (a cosh(a x)  + a)sin(p x) - p cos(p x)cosh(a x)  + p cos(p x)
+--R  /
+--R        2     2                2     2
+--R     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 49
+bb:=(a*cosh(a*x)*sin(p*x)-p*sinh(a*x)*cos(p*x))/(a^2+p^2)
+--R
+--R        - p cos(p x)sinh(a x) + a cosh(a x)sin(p x)
+--R   (2)  -------------------------------------------
+--R                           2    2
+--R                          p  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 50
+cc:=aa-bb
+--R
+--R   (3)
+--R                                         2                 2
+--R       (a sin(p x) + p cos(p x))sinh(a x)  + (- a cosh(a x)  + a)sin(p x)
+--R     + 
+--R                            2
+--R       - p cos(p x)cosh(a x)  + p cos(p x)
+--R  /
+--R        2     2                2     2
+--R     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 51
+sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
+--R
+--R               2    cosh(2x) - 1
+--R   (4)  sinh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 52
+dd:=sinhsqrrule cc
+--R
+--R   (5)
+--R                                   2
+--R       (a cosh(2a x) - 2a cosh(a x)  + a)sin(p x) + p cos(p x)cosh(2a x)
+--R     + 
+--R                             2
+--R       - 2p cos(p x)cosh(a x)  + p cos(p x)
+--R  /
+--R        2     2                2     2
+--R     (4p  + 4a )sinh(a x) + (4p  + 4a )cosh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 53
+coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
+--R
+--R               2    cosh(2x) + 1
+--R   (6)  cosh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 54     14:551 Schaums and Axiom agree
+ee:=coshsqrrule dd
+--R
+--R   (7)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.552~~~~~$\displaystyle
+\int{\sinh{ax}\cos{px}}~dx$}
+$$\int{\sinh{ax}\cos{px}}=
+\frac{a\cosh{ax}\cos{px}+p\sinh{ax}\sin{px}}{a^2+p^2}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 55
+aa:=integrate(sinh(a*x)*cos(p*x),x)
+--R 
+--R
+--R   (1)
+--R                                         2
+--R       (p sin(p x) + a cos(p x))sinh(a x)
+--R     + 
+--R       (2p cosh(a x)sin(p x) + 2a cos(p x)cosh(a x))sinh(a x)
+--R     + 
+--R                   2                                   2
+--R       (p cosh(a x)  - p)sin(p x) + a cos(p x)cosh(a x)  + a cos(p x)
+--R  /
+--R        2     2                2     2
+--R     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 56
+bb:=(a*cosh(a*x)*cos(p*x)+p*sinh(a*x)*sin(p*x))/(a^2+p^2)
+--R
+--R        p sin(p x)sinh(a x) + a cos(p x)cosh(a x)
+--R   (2)  -----------------------------------------
+--R                          2    2
+--R                         p  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 57
+cc:=aa-bb
+--R
+--R   (3)
+--R                                           2               2
+--R       (- p sin(p x) + a cos(p x))sinh(a x)  + (p cosh(a x)  - p)sin(p x)
+--R     + 
+--R                            2
+--R       - a cos(p x)cosh(a x)  + a cos(p x)
+--R  /
+--R        2     2                2     2
+--R     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 58
+sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
+--R
+--R               2    cosh(2x) - 1
+--R   (4)  sinh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 59
+dd:=sinhsqrrule cc
+--R
+--R   (5)
+--R                                     2
+--R       (- p cosh(2a x) + 2p cosh(a x)  - p)sin(p x) + a cos(p x)cosh(2a x)
+--R     + 
+--R                             2
+--R       - 2a cos(p x)cosh(a x)  + a cos(p x)
+--R  /
+--R        2     2                2     2
+--R     (4p  + 4a )sinh(a x) + (4p  + 4a )cosh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 60
+coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
+--R
+--R               2    cosh(2x) + 1
+--R   (6)  cosh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 61     14:552 Schaums and Axiom agree
+ee:=coshsqrrule dd
+--R
+--R   (7)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.553~~~~~$\displaystyle
+\int{\frac{dx}{p+q\sinh{ax}}}~dx$}
+$$\int{\frac{1}{p+q\sinh{ax}}}=
+\frac{1}{a\sqrt{p^2+q^2}}
+\ln\left(\frac{qe^{ax}+p-\sqrt{p^2+q^2}}{qe^{ax}+p+\sqrt{p^2+q^2}}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 62
+aa:=integrate(1/(p+q*sinh(a*x)),x)
+--R 
+--R
+--R   (1)
+--R     log
+--R                 2         2      2                              2         2
+--R                q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R              + 
+--R                                  2     2
+--R                2p q cosh(a x) + q  + 2p
+--R           *
+--R               +-------+
+--R               | 2    2
+--R              \|q  + p
+--R          + 
+--R                 3     2                   3     2                  2     3
+--R            (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
+--R       /
+--R                       2                                             2
+--R            q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R          + 
+--R            2p cosh(a x) - q
+--R  /
+--R       +-------+
+--R       | 2    2
+--R     a\|q  + p
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 63
+bb:=1/(a*sqrt(p^2+q^2))*log((q*%e^(a*x)+p-sqrt(p^2+q^2))/(q*%e^(a*x)+p+sqrt(p^2+q^2)))
+--R
+--R               +-------+
+--R               | 2    2        a x
+--R            - \|q  + p   + q %e    + p
+--R        log(--------------------------)
+--R              +-------+
+--R              | 2    2        a x
+--R             \|q  + p   + q %e    + p
+--R   (2)  -------------------------------
+--R                    +-------+
+--R                    | 2    2
+--R                  a\|q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 64     14:553 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R       log
+--R                   2         2      2                              2         2
+--R                  q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R                + 
+--R                                    2     2
+--R                  2p q cosh(a x) + q  + 2p
+--R             *
+--R                 +-------+
+--R                 | 2    2
+--R                \|q  + p
+--R            + 
+--R                   3     2                   3     2                  2     3
+--R              (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
+--R         /
+--R                         2                                             2
+--R              q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R            + 
+--R              2p cosh(a x) - q
+--R     + 
+--R                +-------+
+--R                | 2    2        a x
+--R             - \|q  + p   + q %e    + p
+--R       - log(--------------------------)
+--R               +-------+
+--R               | 2    2        a x
+--R              \|q  + p   + q %e    + p
+--R  /
+--R       +-------+
+--R       | 2    2
+--R     a\|q  + p
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.554~~~~~$\displaystyle
+\int{\frac{dx}{(p+q\sinh{ax})^2}}~dx$}
+$$\int{\frac{1}{(p+q\sinh{ax})^2}}=
+\frac{-q\cosh{ax}}{a(p^2+q^2)(p+q\sinh{ax})}
++\frac{p}{p^2+q^2}\int{\frac{1}{p+q\sinh{ax}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 65
+aa:=integrate(1/(p*q*sinh(a*x))^2,x)
+--R 
+--R
+--R   (1)
+--R                                         2
+--R   - ------------------------------------------------------------------------
+--R        2 2         2       2 2                        2 2         2      2 2
+--R     a p q sinh(a x)  + 2a p q cosh(a x)sinh(a x) + a p q cosh(a x)  - a p q
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 66
+t1:=integrate(1/(p+q*sinh(a*x)),x)
+--R
+--R   (2)
+--R     log
+--R                 2         2      2                              2         2
+--R                q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R              + 
+--R                                  2     2
+--R                2p q cosh(a x) + q  + 2p
+--R           *
+--R               +-------+
+--R               | 2    2
+--R              \|q  + p
+--R          + 
+--R                 3     2                   3     2                  2     3
+--R            (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
+--R       /
+--R                       2                                             2
+--R            q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R          + 
+--R            2p cosh(a x) - q
+--R  /
+--R       +-------+
+--R       | 2    2
+--R     a\|q  + p
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 67
+bb:=(-q*cosh(a*x))/(a*(p^2+q^2)*(p+q*sinh(a*x)))+p/(p^2+q^2)*t1
+--R
+--R   (3)
+--R                           2
+--R         (p q sinh(a x) + p )
+--R      *
+--R         log
+--R                     2         2      2                              2         2
+--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R                  + 
+--R                                      2     2
+--R                    2p q cosh(a x) + q  + 2p
+--R               *
+--R                   +-------+
+--R                   | 2    2
+--R                  \|q  + p
+--R              + 
+--R                     3     2                   3     2                  2     3
+--R                (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
+--R           /
+--R                           2                                             2
+--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R              + 
+--R                2p cosh(a x) - q
+--R     + 
+--R                     +-------+
+--R                     | 2    2
+--R       - q cosh(a x)\|q  + p
+--R  /
+--R                                               +-------+
+--R          3      2                   2      3  | 2    2
+--R     ((a q  + a p q)sinh(a x) + a p q  + a p )\|q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 68     14:554 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (4)
+--R              3 3         3        3 3             4 2          2
+--R           - p q sinh(a x)  + (- 2p q cosh(a x) - p q )sinh(a x)
+--R         + 
+--R               3 3         2     4 2             3 3              4 2         2
+--R           (- p q cosh(a x)  - 2p q cosh(a x) + p q )sinh(a x) - p q cosh(a x)
+--R         + 
+--R            4 2
+--R           p q
+--R      *
+--R         log
+--R                     2         2      2                              2         2
+--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R                  + 
+--R                                      2     2
+--R                    2p q cosh(a x) + q  + 2p
+--R               *
+--R                   +-------+
+--R                   | 2    2
+--R                  \|q  + p
+--R              + 
+--R                     3     2                   3     2                  2     3
+--R                (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
+--R           /
+--R                           2                                             2
+--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R              + 
+--R                2p cosh(a x) - q
+--R     + 
+--R            2 3                  2      2 3         2     3     2
+--R           p q cosh(a x)sinh(a x)  + (2p q cosh(a x)  - 2q  - 2p q)sinh(a x)
+--R         + 
+--R            2 3         3    2 3                2     3
+--R           p q cosh(a x)  - p q cosh(a x) - 2p q  - 2p
+--R      *
+--R          +-------+
+--R          | 2    2
+--R         \|q  + p
+--R  /
+--R             2 5      4 3          3
+--R         (a p q  + a p q )sinh(a x)
+--R       + 
+--R               2 5       4 3                3 4      5 2          2
+--R         ((2a p q  + 2a p q )cosh(a x) + a p q  + a p q )sinh(a x)
+--R       + 
+--R                 2 5      4 3          2        3 4       5 2                2 5
+--R             (a p q  + a p q )cosh(a x)  + (2a p q  + 2a p q )cosh(a x) - a p q
+--R           + 
+--R                  4 3
+--R             - a p q
+--R        *
+--R           sinh(a x)
+--R       + 
+--R             3 4      5 2          2      3 4      5 2
+--R         (a p q  + a p q )cosh(a x)  - a p q  - a p q
+--R    *
+--R        +-------+
+--R        | 2    2
+--R       \|q  + p
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.555~~~~~$\displaystyle
+\int{\frac{dx}{p^2+q^2\sinh^2{ax}}}$}
+$$\int{\frac{1}{p^2+q^2\sinh^2{ax}}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{1}{ap\sqrt{q^2-p^2}}\tan^{-1}\frac{\sqrt{q^2-p^2}\tanh{ax}}{p}\\
+\\
+\displaystyle
+\frac{1}{2ap\sqrt{p^2-q^2}}\ln\left(\frac{p+\sqrt{p^2-q^2}\tanh{ax}}
+{p-\sqrt{p^2-q^2}\tanh{ax}}\right)
+\end{array}
+\right.
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 69
+aa:=integrate(1/(p^2+q^2*sinh(a*x)^2),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R       log
+--R                   4         4     4                  3
+--R                  q sinh(a x)  + 4q cosh(a x)sinh(a x)
+--R                + 
+--R                     4         2     4     2 2          2
+--R                  (6q cosh(a x)  - 2q  + 4p q )sinh(a x)
+--R                + 
+--R                     4         3        4     2 2
+--R                  (4q cosh(a x)  + (- 4q  + 8p q )cosh(a x))sinh(a x)
+--R                + 
+--R                   4         4        4     2 2          2    4     2 2     4
+--R                  q cosh(a x)  + (- 2q  + 4p q )cosh(a x)  + q  - 8p q  + 8p
+--R             *
+--R                 +---------+
+--R                 |   2    2
+--R                \|- q  + p
+--R            + 
+--R                   4     3 2          2        4     3 2
+--R              (4p q  - 4p q )sinh(a x)  + (8p q  - 8p q )cosh(a x)sinh(a x)
+--R            + 
+--R                   4     3 2          2       4      3 2     5
+--R              (4p q  - 4p q )cosh(a x)  - 4p q  + 12p q  - 8p
+--R         /
+--R               2         4     2                  3
+--R              q sinh(a x)  + 4q cosh(a x)sinh(a x)
+--R            + 
+--R                 2         2     2     2          2
+--R              (6q cosh(a x)  - 2q  + 4p )sinh(a x)
+--R            + 
+--R                 2         3        2     2                        2         4
+--R              (4q cosh(a x)  + (- 4q  + 8p )cosh(a x))sinh(a x) + q cosh(a x)
+--R            + 
+--R                   2     2          2    2
+--R              (- 2q  + 4p )cosh(a x)  + q
+--R    /
+--R            +---------+
+--R            |   2    2
+--R       2a p\|- q  + p
+--R     ,
+--R
+--R       atan
+--R                2         2     2                      2         2    2     2
+--R              (q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  - q  + 2p )
+--R           *
+--R               +-------+
+--R               | 2    2
+--R              \|q  - p
+--R         /
+--R                2     3
+--R            2p q  - 2p
+--R    /
+--R           +-------+
+--R           | 2    2
+--R       a p\|q  - p
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+
+--S 70
+bb1:=1/(a*p*sqrt(q^2-p^2))*atan((sqrt(q^2-p^2)*tanh(a*x))/p)
+--R
+--R                       +-------+
+--R                       | 2    2
+--R             tanh(a x)\|q  - p
+--R        atan(-------------------)
+--R                      p
+--R   (2)  -------------------------
+--R                  +-------+
+--R                  | 2    2
+--R              a p\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 71
+bb2:=1/(2*a*p*sqrt(p^2-q^2))*log((p+sqrt(p^2-q^2)*tanh(a*x))/(p-sqrt(p^2-q^2)*tanh(a*x)))
+--R
+--R                        +---------+
+--R                        |   2    2
+--R            - tanh(a x)\|- q  + p   - p
+--R        log(---------------------------)
+--R                       +---------+
+--R                       |   2    2
+--R             tanh(a x)\|- q  + p   - p
+--R   (3)  --------------------------------
+--R                     +---------+
+--R                     |   2    2
+--R                2a p\|- q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 72
+cc1:=aa.1-bb1
+--R
+--R   (4)
+--R          +-------+
+--R          | 2    2
+--R         \|q  - p
+--R      *
+--R         log
+--R                     4         4     4                  3
+--R                    q sinh(a x)  + 4q cosh(a x)sinh(a x)
+--R                  + 
+--R                       4         2     4     2 2          2
+--R                    (6q cosh(a x)  - 2q  + 4p q )sinh(a x)
+--R                  + 
+--R                       4         3        4     2 2
+--R                    (4q cosh(a x)  + (- 4q  + 8p q )cosh(a x))sinh(a x)
+--R                  + 
+--R                     4         4        4     2 2          2    4     2 2     4
+--R                    q cosh(a x)  + (- 2q  + 4p q )cosh(a x)  + q  - 8p q  + 8p
+--R               *
+--R                   +---------+
+--R                   |   2    2
+--R                  \|- q  + p
+--R              + 
+--R                     4     3 2          2        4     3 2
+--R                (4p q  - 4p q )sinh(a x)  + (8p q  - 8p q )cosh(a x)sinh(a x)
+--R              + 
+--R                     4     3 2          2       4      3 2     5
+--R                (4p q  - 4p q )cosh(a x)  - 4p q  + 12p q  - 8p
+--R           /
+--R                 2         4     2                  3
+--R                q sinh(a x)  + 4q cosh(a x)sinh(a x)
+--R              + 
+--R                   2         2     2     2          2
+--R                (6q cosh(a x)  - 2q  + 4p )sinh(a x)
+--R              + 
+--R                   2         3        2     2                        2         4
+--R                (4q cosh(a x)  + (- 4q  + 8p )cosh(a x))sinh(a x) + q cosh(a x)
+--R              + 
+--R                     2     2          2    2
+--R                (- 2q  + 4p )cosh(a x)  + q
+--R     + 
+--R                                     +-------+
+--R           +---------+               | 2    2
+--R           |   2    2      tanh(a x)\|q  - p
+--R       - 2\|- q  + p  atan(-------------------)
+--R                                    p
+--R  /
+--R          +---------+ +-------+
+--R          |   2    2  | 2    2
+--R     2a p\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 73
+cc2:=aa.2-bb1
+--R
+--R   (5)
+--R                        +-------+
+--R                        | 2    2
+--R              tanh(a x)\|q  - p
+--R       - atan(-------------------)
+--R                       p
+--R     + 
+--R       atan
+--R                2         2     2                      2         2    2     2
+--R              (q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  - q  + 2p )
+--R           *
+--R               +-------+
+--R               | 2    2
+--R              \|q  - p
+--R         /
+--R                2     3
+--R            2p q  - 2p
+--R  /
+--R         +-------+
+--R         | 2    2
+--R     a p\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 74
+cc3:=aa.2-bb1
+--R
+--R   (6)
+--R                        +-------+
+--R                        | 2    2
+--R              tanh(a x)\|q  - p
+--R       - atan(-------------------)
+--R                       p
+--R     + 
+--R       atan
+--R                2         2     2                      2         2    2     2
+--R              (q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  - q  + 2p )
+--R           *
+--R               +-------+
+--R               | 2    2
+--R              \|q  - p
+--R         /
+--R                2     3
+--R            2p q  - 2p
+--R  /
+--R         +-------+
+--R         | 2    2
+--R     a p\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 75     14:555 Axiom cannot simplify this expression
+cc4:=aa.2-bb2
+--R
+--R   (7)
+--R                                   +---------+
+--R          +-------+                |   2    2
+--R          | 2    2     - tanh(a x)\|- q  + p   - p
+--R       - \|q  - p  log(---------------------------)
+--R                                  +---------+
+--R                                  |   2    2
+--R                        tanh(a x)\|- q  + p   - p
+--R     + 
+--R           +---------+
+--R           |   2    2
+--R         2\|- q  + p
+--R      *
+--R         atan
+--R                  2         2     2                      2         2    2     2
+--R                (q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  - q  + 2p )
+--R             *
+--R                 +-------+
+--R                 | 2    2
+--R                \|q  - p
+--R           /
+--R                  2     3
+--R              2p q  - 2p
+--R  /
+--R          +---------+ +-------+
+--R          |   2    2  | 2    2
+--R     2a p\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.556~~~~~$\displaystyle
+\int{\frac{dx}{p^2-q^2\sinh^2{ax}}}~dx$}
+$$\int{\frac{1}{p^2-q^2\sinh^2{ax}}}=
+\frac{1}{2ap\sqrt{p^2+q^2}}\ln\left(\frac{p+\sqrt{p^2+q^2}\tanh{ax}}
+{p-\sqrt{p^2+q^2}\tanh{ax}}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 76
+aa:=integrate(1/(p^2+q^2*sinh(a*x)^2),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R       log
+--R                   4         4     4                  3
+--R                  q sinh(a x)  + 4q cosh(a x)sinh(a x)
+--R                + 
+--R                     4         2     4     2 2          2
+--R                  (6q cosh(a x)  - 2q  + 4p q )sinh(a x)
+--R                + 
+--R                     4         3        4     2 2
+--R                  (4q cosh(a x)  + (- 4q  + 8p q )cosh(a x))sinh(a x)
+--R                + 
+--R                   4         4        4     2 2          2    4     2 2     4
+--R                  q cosh(a x)  + (- 2q  + 4p q )cosh(a x)  + q  - 8p q  + 8p
+--R             *
+--R                 +---------+
+--R                 |   2    2
+--R                \|- q  + p
+--R            + 
+--R                   4     3 2          2        4     3 2
+--R              (4p q  - 4p q )sinh(a x)  + (8p q  - 8p q )cosh(a x)sinh(a x)
+--R            + 
+--R                   4     3 2          2       4      3 2     5
+--R              (4p q  - 4p q )cosh(a x)  - 4p q  + 12p q  - 8p
+--R         /
+--R               2         4     2                  3
+--R              q sinh(a x)  + 4q cosh(a x)sinh(a x)
+--R            + 
+--R                 2         2     2     2          2
+--R              (6q cosh(a x)  - 2q  + 4p )sinh(a x)
+--R            + 
+--R                 2         3        2     2                        2         4
+--R              (4q cosh(a x)  + (- 4q  + 8p )cosh(a x))sinh(a x) + q cosh(a x)
+--R            + 
+--R                   2     2          2    2
+--R              (- 2q  + 4p )cosh(a x)  + q
+--R    /
+--R            +---------+
+--R            |   2    2
+--R       2a p\|- q  + p
+--R     ,
+--R
+--R       atan
+--R                2         2     2                      2         2    2     2
+--R              (q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  - q  + 2p )
+--R           *
+--R               +-------+
+--R               | 2    2
+--R              \|q  - p
+--R         /
+--R                2     3
+--R            2p q  - 2p
+--R    /
+--R           +-------+
+--R           | 2    2
+--R       a p\|q  - p
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+
+--S 77
+bb:=1/(2*a*p*sqrt(p^2+q^2))*log((p+sqrt(p^2+q^2)*tanh(a*x))/(p-sqrt(p^2+q^2)*tanh(a*x)))
+--R
+--R                        +-------+
+--R                        | 2    2
+--R            - tanh(a x)\|q  + p   - p
+--R        log(-------------------------)
+--R                       +-------+
+--R                       | 2    2
+--R             tanh(a x)\|q  + p   - p
+--R   (2)  ------------------------------
+--R                     +-------+
+--R                     | 2    2
+--R                2a p\|q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 78
+cc1:=aa.1-bb
+--R
+--R   (3)
+--R          +-------+
+--R          | 2    2
+--R         \|q  + p
+--R      *
+--R         log
+--R                     4         4     4                  3
+--R                    q sinh(a x)  + 4q cosh(a x)sinh(a x)
+--R                  + 
+--R                       4         2     4     2 2          2
+--R                    (6q cosh(a x)  - 2q  + 4p q )sinh(a x)
+--R                  + 
+--R                       4         3        4     2 2
+--R                    (4q cosh(a x)  + (- 4q  + 8p q )cosh(a x))sinh(a x)
+--R                  + 
+--R                     4         4        4     2 2          2    4     2 2     4
+--R                    q cosh(a x)  + (- 2q  + 4p q )cosh(a x)  + q  - 8p q  + 8p
+--R               *
+--R                   +---------+
+--R                   |   2    2
+--R                  \|- q  + p
+--R              + 
+--R                     4     3 2          2        4     3 2
+--R                (4p q  - 4p q )sinh(a x)  + (8p q  - 8p q )cosh(a x)sinh(a x)
+--R              + 
+--R                     4     3 2          2       4      3 2     5
+--R                (4p q  - 4p q )cosh(a x)  - 4p q  + 12p q  - 8p
+--R           /
+--R                 2         4     2                  3
+--R                q sinh(a x)  + 4q cosh(a x)sinh(a x)
+--R              + 
+--R                   2         2     2     2          2
+--R                (6q cosh(a x)  - 2q  + 4p )sinh(a x)
+--R              + 
+--R                   2         3        2     2                        2         4
+--R                (4q cosh(a x)  + (- 4q  + 8p )cosh(a x))sinh(a x) + q cosh(a x)
+--R              + 
+--R                     2     2          2    2
+--R                (- 2q  + 4p )cosh(a x)  + q
+--R     + 
+--R                                     +-------+
+--R          +---------+                | 2    2
+--R          |   2    2     - tanh(a x)\|q  + p   - p
+--R       - \|- q  + p  log(-------------------------)
+--R                                    +-------+
+--R                                    | 2    2
+--R                          tanh(a x)\|q  + p   - p
+--R  /
+--R          +---------+ +-------+
+--R          |   2    2  | 2    2
+--R     2a p\|- q  + p  \|q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 79     14:556 Axiom cannot simplify this expression
+cc2:=aa.2-bb
+--R
+--R   (4)
+--R                                   +-------+
+--R          +-------+                | 2    2
+--R          | 2    2     - tanh(a x)\|q  + p   - p
+--R       - \|q  - p  log(-------------------------)
+--R                                  +-------+
+--R                                  | 2    2
+--R                        tanh(a x)\|q  + p   - p
+--R     + 
+--R           +-------+
+--R           | 2    2
+--R         2\|q  + p
+--R      *
+--R         atan
+--R                  2         2     2                      2         2    2     2
+--R                (q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  - q  + 2p )
+--R             *
+--R                 +-------+
+--R                 | 2    2
+--R                \|q  - p
+--R           /
+--R                  2     3
+--R              2p q  - 2p
+--R  /
+--R          +-------+ +-------+
+--R          | 2    2  | 2    2
+--R     2a p\|q  - p  \|q  + p
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.557~~~~~$\displaystyle
+\int{x^m\sinh{ax}}~dx$}
+$$\int{x^m\sinh{ax}}=
+\frac{x^m\cosh{ax}}{a}-\frac{m}{a}\int{x^{m-1}\cosh{ax}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 80     14:557 Axiom cannot compute this integral
+aa:=integrate(x^m*sinh(a*x),x)
+--R 
+--R
+--R           x
+--R         ++              m
+--I   (1)   |   sinh(%N a)%N d%N
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.558~~~~~$\displaystyle
+\int{\sinh^n}~dx$}
+$$\int{\sinh^n}=
+\frac{\sinh^{n-1}{ax}\cosh{ax}}{an}-\frac{n-1}{n}\int{\sinh^{n-2}{ax}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 81     14:558 Axiom cannot compute this integral
+aa:=integrate(sinh(a*x)^n,x)
+--R 
+--R
+--R           x
+--R         ++            n
+--I   (1)   |   sinh(%N a) d%N
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.559~~~~~$\displaystyle
+\int{\frac{\sinh{ax}}{x^n}}~dx$}
+$$\int{\frac{\sinh{ax}}{x^n}}=
+\frac{-\sinh{ax}}{(n-1)x^{n-1}}+\frac{a}{n-1}\int{\frac{\cosh{ax}}{n^{n-1}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 82     14:559 Axiom cannot compute this integral
+aa:=integrate(sinh(a*x)/x^n,x)
+--R
+--R           x
+--I         ++  sinh(%T a)
+--I   (3)   |   ---------- d%T
+--R        ++         n
+--I                 %T
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+@
+
+\section{\cite{1}:14.560~~~~~$\displaystyle
+\int{\frac{dx}{\sinh^n{ax}}}~dx$}
+$$\int{\frac{1}{\sinh^n{ax}}}=
+\frac{-\cosh{ax}}{a(n-1)\sinh^{n-1}{ax}}
+-\frac{n-2}{n-1}\int{\frac{1}{\sinh^{n-2}{ax}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 83     14:560 Axiom cannot compute this integral
+aa:=integrate(1/sinh(a*x)^n,x)
+--R 
+--R
+--R           x
+--R         ++       1
+--I   (1)   |   ----------- d%N
+--R        ++             n
+--I             sinh(%N a)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.561~~~~~$\displaystyle
+\int{\frac{x~dx}{\sinh^n{ax}}}~dx$}
+$$\int{\frac{x}{\sinh^n{ax}}}=
+\frac{-x\cosh{ax}}{a(n-1)\sinh^{n-1}{ax}}
+-\frac{1}{a^2(n-1)(n-2)\sinh^{n-2}{ax}}
+-\frac{n-2}{n-1}\int{\frac{x}{\sinh^{n-2}{ax}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 84     14:561 Axiom cannot compute this integral
+aa:=integrate(x/sinh(a*x)^n,x)
+--R 
+--R
+--R           x
+--I         ++       %N
+--I   (1)   |   ----------- d%N
+--R        ++             n
+--I             sinh(%N a)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 p86
+\end{thebibliography}
+\end{document}
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diff --git a/src/axiom-website/CATS/schaum28.input.pamphlet b/src/axiom-website/CATS/schaum28.input.pamphlet
new file mode 100644
index 0000000..49efb0e
--- /dev/null
+++ b/src/axiom-website/CATS/schaum28.input.pamphlet
@@ -0,0 +1,2854 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum28.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.562~~~~~$\displaystyle
+\int{\cosh{ax}}~dx$}
+$$\int{\cosh{ax}}=
+\frac{\sinh{ax}}{a}
+$$
+&lt;&lt;*&gt;&gt;=
+)spool schaum28.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1
+aa:=integrate(cosh(a*x),x)
+--R 
+--R
+--R        sinh(a x)
+--R   (1)  ---------
+--R            a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 2
+bb:=sinh(a*x)/a
+--R
+--R        sinh(a x)
+--R   (2)  ---------
+--R            a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3      14:562 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.563~~~~~$\displaystyle
+\int{x\cosh{ax}}~dx$}
+$$\int{x\cosh{ax}}=
+\frac{x\sinh{ax}}{a}-\frac{\cosh{ax}}{a^2}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 4
+aa:=integrate(x*cosh(a*x),x)
+--R 
+--R
+--R        a x sinh(a x) - cosh(a x)
+--R   (1)  -------------------------
+--R                     2
+--R                    a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 5
+bb:=(x*sinh(a*x))/a-cosh(a*x)/a^2
+--R
+--R        a x sinh(a x) - cosh(a x)
+--R   (2)  -------------------------
+--R                     2
+--R                    a
+--R                                                     Type: Expression Integer
+--E
+
+--S 6      14:563 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.564~~~~~$\displaystyle
+\int{x^2\cosh{ax}}~dx$}
+$$\int{x^2\cosh{ax}}=
+-\frac{2x\cosh{ax}}{a^2}+\left(\frac{x^2}{a}+\frac{2}{a^3}\right)\sinh{ax}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 7
+aa:=integrate(x^2*cosh(a*x),x)
+--R 
+--R
+--R          2 2
+--R        (a x  + 2)sinh(a x) - 2a x cosh(a x)
+--R   (1)  ------------------------------------
+--R                          3
+--R                         a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 8
+bb:=-(2*x*cosh(a*x))/a^2+(x^2/a+2/a^3)*sinh(a*x)
+--R
+--R          2 2
+--R        (a x  + 2)sinh(a x) - 2a x cosh(a x)
+--R   (2)  ------------------------------------
+--R                          3
+--R                         a
+--R                                                     Type: Expression Integer
+--E
+
+--S 9      14:564 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.565~~~~~$\displaystyle
+\int{\frac{\cosh{ax}}{x}}~dx$}
+$$\int{\frac{\cosh{ax}}{x}}=
+\ln{x}+\frac{(ax)^2}{2\cdot 2!}
++\frac{(ax)^4}{4\cdot 4!}
++\frac{(ax)^6}{6\cdot 6!}+\cdots
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 10     14:565 Axiom cannot compute this integral
+aa:=integrate(cosh(a*x)/x,x)
+--R 
+--R
+--R           x
+--I         ++  cosh(%N a)
+--I   (1)   |   ---------- d%N
+--I        ++       %N
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.566~~~~~$\displaystyle
+\int{\frac{\cosh{ax}}{x^2}}~dx$}
+$$\int{\frac{\cosh{ax}}{x^2}}=
+-\frac{\cosh{ax}}{x}+a\int{\frac{\sinh{ax}}{a}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 11     14:566 Axiom cannot compute this integral
+aa:=integrate(cosh(a*x)/x^2,x)
+--R 
+--R
+--R           x
+--I         ++  cosh(%N a)
+--I   (1)   |   ---------- d%N
+--R        ++         2
+--I                 %N
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.567~~~~~$\displaystyle
+\int{\frac{dx}{\cosh{ax}}}~dx$}
+$$\int{\frac{1}{\cosh{ax}}}=
+\frac{2}{a}\tan^{-1}e^{ax}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 12
+aa:=integrate(1/cosh(a*x),x)
+--R 
+--R
+--R        2atan(sinh(a x) + cosh(a x))
+--R   (1)  ----------------------------
+--R                      a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 13
+bb:=2/a*atan(%e^(a*x))
+--R
+--R                a x
+--R        2atan(%e   )
+--R   (2)  ------------
+--R              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 14
+cc:=aa-bb
+--R
+--R                                               a x
+--R        2atan(sinh(a x) + cosh(a x)) - 2atan(%e   )
+--R   (3)  -------------------------------------------
+--R                             a
+--R                                                     Type: Expression Integer
+--E
+
+--S 15     14:567 Schaums and Axiom agree
+dd:=complexNormalize cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.568~~~~~$\displaystyle
+\int{\frac{x~dx}{\cosh{ax}}}~dx$}
+$$\int{\frac{x}{\cosh{ax}}}=
+\frac{1}{a^2}\left\{\frac{(ax)^2}{2}-\frac{(ax)^4}{8}+\frac{5(ax)^6}{144}
++\cdots+\frac{(-1)^nE_n(ax)^{2n+2}}{(2n+2)(2n)!}+\cdots\right\}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 16     14:568 Axiom cannot compute this integral
+aa:=integrate(x/cosh(a*x),x)
+--R 
+--R
+--R           x
+--I         ++      %N
+--I   (1)   |   ---------- d%N
+--I        ++   cosh(%N a)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.569~~~~~$\displaystyle
+\int{\cosh^2{ax}}~dx$}
+$$\int{\cosh^2{ax}}=
+\frac{x}{2}+\frac{\sinh{ax}\cosh{ax}}{2a}
+$$
+Note that the Schaums print edition (1968 printing 3) has a typo:
+$$\int{\cosh^2{ax}}=
+\frac{x}{2}+\frac{\sinh{ax}\cosh{ax}}{2}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 17
+aa:=integrate(cosh(a*x)^2,x)
+--R 
+--R
+--R        cosh(a x)sinh(a x) + a x
+--R   (1)  ------------------------
+--R                   2a
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 18
+bb:=x/2+(sinh(a*x)*cosh(a*x))/(2*a)
+--R
+--R        cosh(a x)sinh(a x) + a x
+--R   (2)  ------------------------
+--R                   2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 19     14:569 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.570~~~~~$\displaystyle
+\int{x\cosh^2{ax}}~dx$}
+$$\int{x\cosh^2{ax}}=
+\frac{x^2}{4}+\frac{x\sinh{2ax}}{4a}-\frac{\cosh{2ax}}{8a^2}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 20
+aa:=integrate(x*cosh(a*x)^2,x)
+--R 
+--R
+--R                   2                                      2     2 2
+--R        - sinh(a x)  + 4a x cosh(a x)sinh(a x) - cosh(a x)  + 2a x
+--R   (1)  -----------------------------------------------------------
+--R                                      2
+--R                                    8a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 21
+bb:=x^2/4+(x*sinh(2*a*x))/(4*a)-cosh(2*a*x)/(8*a^2)
+--R
+--R                                         2 2
+--R        2a x sinh(2a x) - cosh(2a x) + 2a x
+--R   (2)  ------------------------------------
+--R                           2
+--R                         8a
+--R                                                     Type: Expression Integer
+--E
+
+--S 22
+cc:=aa-bb
+--R
+--R   (3)
+--R                                    2
+--R       - 2a x sinh(2a x) - sinh(a x)  + 4a x cosh(a x)sinh(a x) + cosh(2a x)
+--R     + 
+--R                  2
+--R       - cosh(a x)
+--R  /
+--R       2
+--R     8a
+--R                                                     Type: Expression Integer
+--E
+
+--S 23
+sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
+--R
+--R               2    cosh(2x) - 1
+--R   (4)  sinh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 24
+dd:=sinhsqrrule cc
+--R
+--R   (5)
+--R                                                                        2
+--R   - 4a x sinh(2a x) + 8a x cosh(a x)sinh(a x) + cosh(2a x) - 2cosh(a x)  + 1
+--R   --------------------------------------------------------------------------
+--R                                         2
+--R                                      16a
+--R                                                     Type: Expression Integer
+--E
+
+--S 25
+coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
+--R
+--R               2    cosh(2x) + 1
+--R   (6)  cosh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 26
+ee:=coshsqrrule dd
+--R
+--R        - x sinh(2a x) + 2x cosh(a x)sinh(a x)
+--R   (7)  --------------------------------------
+--R                          4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 27
+sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
+--R
+--I                             %S sinh(y + x) - %S sinh(y - x)
+--I   (8)  %S cosh(y)sinh(x) == -------------------------------
+--R                                            2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 28     14:570 Schaums and Axiom agree
+ff:=sinhcoshrule ee
+--R
+--R   (9)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.571~~~~~$\displaystyle
+\int{\frac{dx}{\cosh^2{ax}}}~dx$}
+$$\int{\frac{1}{\cosh^2{ax}}}=
+\frac{\tanh{ax}}{a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 29
+aa:=integrate(1/cosh(a*x)^2,x)
+--R 
+--R
+--R                                     2
+--R   (1)  - -------------------------------------------------------
+--R                     2                                      2
+--R          a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 30
+bb:=tanh(a*x)/a
+--R
+--R        tanh(a x)
+--R   (2)  ---------
+--R            a
+--R                                                     Type: Expression Integer
+--E
+
+--S 31
+cc:=aa-bb
+--R
+--R                    2                                  2
+--R        (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)tanh(a x) - 2
+--R   (3)  ------------------------------------------------------------------
+--R                         2                                      2
+--R              a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 32     14:571 Schaums and Axiom differ by a constant
+dd:=complexNormalize cc
+--R
+--R          1
+--R   (4)  - -
+--R          a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.572~~~~~$\displaystyle
+\int{\cosh{ax}\cosh{px}}~dx$}
+$$\int{\cosh{ax}\cosh{px}}=
+\frac{\sinh(a-p)x}{2(a-p)}+\frac{\sinh(a+p)x}{2(a+p)}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 33 
+aa:=integrate(cosh(a*x)*cosh(p*x),x)
+--R 
+--R
+--R        - p cosh(a x)sinh(p x) + a cosh(p x)sinh(a x)
+--R   (1)  ---------------------------------------------
+--R           2    2          2       2    2          2
+--R         (p  - a )sinh(a x)  + (- p  + a )cosh(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 34
+bb:=(sinh(a-p)*x)/(2*(a-p))+(sinh(a+p)*x)/(2*(a+p))
+--R
+--R        (p - a)x sinh(p + a) + (p + a)x sinh(p - a)
+--R   (2)  -------------------------------------------
+--R                           2     2
+--R                         2p  - 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 35
+cc:=aa-bb
+--R
+--R   (3)
+--R       - 2p cosh(a x)sinh(p x)
+--R     + 
+--R                                                                 2
+--R       ((- p + a)x sinh(p + a) + (- p - a)x sinh(p - a))sinh(a x)
+--R     + 
+--R                                                 2
+--R       2a cosh(p x)sinh(a x) + (p - a)x cosh(a x) sinh(p + a)
+--R     + 
+--R                         2
+--R       (p + a)x cosh(a x) sinh(p - a)
+--R  /
+--R        2     2          2        2     2          2
+--R     (2p  - 2a )sinh(a x)  + (- 2p  + 2a )cosh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 36
+sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
+--R
+--R               2    cosh(2x) - 1
+--R   (4)  sinh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 37
+dd:=sinhsqrrule cc
+--R
+--R   (5)
+--R       - 4p cosh(a x)sinh(p x) + 4a cosh(p x)sinh(a x)
+--R     + 
+--R                                                    2
+--R       ((- p + a)x cosh(2a x) + (2p - 2a)x cosh(a x)  + (p - a)x)sinh(p + a)
+--R     + 
+--R                                                    2
+--R       ((- p - a)x cosh(2a x) + (2p + 2a)x cosh(a x)  + (p + a)x)sinh(p - a)
+--R  /
+--R        2     2                   2     2          2     2     2
+--R     (2p  - 2a )cosh(2a x) + (- 4p  + 4a )cosh(a x)  - 2p  + 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 38
+coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
+--R
+--R               2    cosh(2x) + 1
+--R   (6)  cosh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 39
+ee:=coshsqrrule dd
+--R
+--R   (7)
+--R       2p cosh(a x)sinh(p x) - 2a cosh(p x)sinh(a x) + (- p + a)x sinh(p + a)
+--R     + 
+--R       (- p - a)x sinh(p - a)
+--R  /
+--R       2     2
+--R     2p  - 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 40
+sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
+--R
+--I                             %V sinh(y + x) - %V sinh(y - x)
+--I   (8)  %V cosh(y)sinh(x) == -------------------------------
+--R                                            2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 41     14:572 Axiom cannot simplify this expression
+ff:=sinhcoshrule ee
+--R
+--R   (9)
+--R       (p - a)sinh((p + a)x) + (p + a)sinh((p - a)x) + (- p + a)x sinh(p + a)
+--R     + 
+--R       (- p - a)x sinh(p - a)
+--R  /
+--R       2     2
+--R     2p  - 2a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.573~~~~~$\displaystyle
+\int{\cosh{ax}\sin{px}}~dx$}
+$$\int{\cosh{ax}\sin{px}}=
+\frac{a\sinh{ax}\sin{px}-p\cosh{ax}\cos{px}}{a^2+p^2}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 42
+aa:=integrate(cosh(a*x)*sin(p*x),x)
+--R 
+--R
+--R   (1)
+--R                                         2
+--R       (a sin(p x) - p cos(p x))sinh(a x)
+--R     + 
+--R       (2a cosh(a x)sin(p x) - 2p cos(p x)cosh(a x))sinh(a x)
+--R     + 
+--R                   2                                   2
+--R       (a cosh(a x)  - a)sin(p x) - p cos(p x)cosh(a x)  - p cos(p x)
+--R  /
+--R        2     2                2     2
+--R     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 43
+bb:=(a*sinh(a*x)*sin(p*x)-p*cosh(a*x)*cos(p*x))/(a^2+p^2)
+--R
+--R        a sin(p x)sinh(a x) - p cos(p x)cosh(a x)
+--R   (2)  -----------------------------------------
+--R                          2    2
+--R                         p  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 44
+cc:=aa-bb
+--R
+--R   (3)
+--R                                           2               2
+--R       (- a sin(p x) - p cos(p x))sinh(a x)  + (a cosh(a x)  - a)sin(p x)
+--R     + 
+--R                          2
+--R       p cos(p x)cosh(a x)  - p cos(p x)
+--R  /
+--R        2     2                2     2
+--R     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 45
+coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
+--R
+--R               2    cosh(2x) + 1
+--R   (4)  cosh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 46
+dd:=coshsqrrule cc
+--R
+--R   (5)
+--R                                             2
+--R       (- 2a sin(p x) - 2p cos(p x))sinh(a x)  + (a cosh(2a x) - a)sin(p x)
+--R     + 
+--R       p cos(p x)cosh(2a x) - p cos(p x)
+--R  /
+--R        2     2                2     2
+--R     (4p  + 4a )sinh(a x) + (4p  + 4a )cosh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 47
+sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
+--R
+--R               2    cosh(2x) - 1
+--R   (6)  sinh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 48     14:573 Schaums and Axiom agree
+ee:=sinhsqrrule dd
+--R
+--R   (7)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.574~~~~~$\displaystyle
+\int{\cosh{ax}\cos{px}}~dx$}
+$$\int{\cosh{ax}\cos{px}}=
+\frac{a\sinh{ax}\cos{px}+p\cosh{ax}\sin{px}}{a^2+p^2}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 49
+aa:=integrate(cosh(a*x)*cos(p*x),x)
+--R 
+--R
+--R   (1)
+--R                                         2
+--R       (p sin(p x) + a cos(p x))sinh(a x)
+--R     + 
+--R       (2p cosh(a x)sin(p x) + 2a cos(p x)cosh(a x))sinh(a x)
+--R     + 
+--R                   2                                   2
+--R       (p cosh(a x)  + p)sin(p x) + a cos(p x)cosh(a x)  - a cos(p x)
+--R  /
+--R        2     2                2     2
+--R     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 50
+bb:=(a*sinh(a*x)*cos(p*x)+p*cosh(a*x)*sin(p*x))/(a^2+p^2)
+--R
+--R        a cos(p x)sinh(a x) + p cosh(a x)sin(p x)
+--R   (2)  -----------------------------------------
+--R                          2    2
+--R                         p  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 51
+cc:=aa-bb
+--R
+--R   (3)
+--R                                         2                 2
+--R       (p sin(p x) - a cos(p x))sinh(a x)  + (- p cosh(a x)  + p)sin(p x)
+--R     + 
+--R                          2
+--R       a cos(p x)cosh(a x)  - a cos(p x)
+--R  /
+--R        2     2                2     2
+--R     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 52
+coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
+--R
+--R               2    cosh(2x) + 1
+--R   (4)  cosh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 53
+dd:=coshsqrrule cc
+--R
+--R   (5)
+--R                                           2
+--R       (2p sin(p x) - 2a cos(p x))sinh(a x)  + (- p cosh(2a x) + p)sin(p x)
+--R     + 
+--R       a cos(p x)cosh(2a x) - a cos(p x)
+--R  /
+--R        2     2                2     2
+--R     (4p  + 4a )sinh(a x) + (4p  + 4a )cosh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 54
+sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
+--R
+--R               2    cosh(2x) - 1
+--R   (6)  sinh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 55     14:574 Schaums and Axiom agree
+ee:=sinhsqrrule dd
+--R
+--R   (7)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.575~~~~~$\displaystyle
+\int{\frac{dx}{\cosh{ax}+1}}$}
+$$\int{\frac{1}{\cosh{ax}+1}}=
+\frac{1}{a}\tanh{\frac{ax}{2}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 56
+aa:=integrate(1/(cosh(a*x)+1),x)
+--R 
+--R
+--R                        2
+--R   (1)  - -----------------------------
+--R          a sinh(a x) + a cosh(a x) + a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 57
+bb:=1/a*tanh((a*x)/2)
+--R
+--R             a x
+--R        tanh(---)
+--R              2
+--R   (2)  ---------
+--R            a
+--R                                                     Type: Expression Integer
+--E
+
+--S 58
+cc:=aa-bb
+--R
+--R                                          a x
+--R        (- sinh(a x) - cosh(a x) - 1)tanh(---) - 2
+--R                                           2
+--R   (3)  ------------------------------------------
+--R               a sinh(a x) + a cosh(a x) + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 59
+tanhrule:=rule(tanh(x) == sinh(x)/cosh(x))
+--R
+--R                   sinh(x)
+--R   (4)  tanh(x) == -------
+--R                   cosh(x)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 60
+dd:=tanhrule cc
+--R
+--R               a x                                   a x          a x
+--R        - sinh(---)sinh(a x) + (- cosh(a x) - 1)sinh(---) - 2cosh(---)
+--R                2                                     2            2
+--R   (5)  --------------------------------------------------------------
+--R                  a x                    a x                    a x
+--R           a cosh(---)sinh(a x) + a cosh(---)cosh(a x) + a cosh(---)
+--R                   2                      2                      2
+--R                                                     Type: Expression Integer
+--E
+
+--S 61
+sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
+--R
+--I                              %BC sinh(y + x) - %BC sinh(y - x)
+--I   (6)  %BC cosh(y)sinh(x) == -------------------------------
+--R                                              2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 62
+ee:=sinhcoshrule dd
+--R
+--R                  3a x          a x                  a x          a x
+--R           - sinh(----) - 2sinh(---)sinh(a x) - sinh(---) - 4cosh(---)
+--R                    2            2                    2            2
+--R   (7)  -----------------------------------------------------------------
+--R               3a x           a x            a x                     a x
+--R        a sinh(----) + a sinh(---) + 2a cosh(---)cosh(a x) + 2a cosh(---)
+--R                 2             2              2                       2
+--R                                                     Type: Expression Integer
+--E
+
+--S 63
+sinhsinhrule:=rule(sinh(x)*sinh(y)==1/2*(cosh(x+y)-cosh(x-y)))
+--R
+--I                              %BD sinh(y + x) - %BD sinh(y - x)
+--I   (8)  %BD cosh(y)sinh(x) == -------------------------------
+--R                                              2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 64
+ff:=sinhsinhrule ee
+--R
+--R                       3a x         a x         3a x          a x
+--R                - sinh(----) - sinh(---) - cosh(----) - 3cosh(---)
+--R                         2           2            2            2
+--R   (9)  -----------------------------------------------------------------
+--R               3a x           a x            a x                     a x
+--R        a sinh(----) + a sinh(---) + 2a cosh(---)cosh(a x) + 2a cosh(---)
+--R                 2             2              2                       2
+--R                                                     Type: Expression Integer
+--E
+
+--S 65
+coshcoshrule:=rule(cosh(x)*cosh(y)==1/2*(cosh(x+y)+cosh(x-y)))
+--R
+--I                               %BC cosh(y + x) + %BC cosh(y - x)
+--I   (10)  %BC cosh(x)cosh(y) == ---------------------------------
+--R                                               2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 66     14:575 Schaums and Axiom differ by a constant
+gg:=coshcoshrule ff
+--R
+--R           1
+--R   (11)  - -
+--R           a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.576~~~~~$\displaystyle
+\int{\frac{dx}{\cosh{ax}-1}}$}
+$$\int{\frac{1}{\cosh{ax}-1}}=
+-\frac{1}{a}\coth{\frac{ax}{2}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 67
+aa:=integrate(1/(cosh(a*x)-1),x)
+--R 
+--R
+--R                        2
+--R   (1)  - -----------------------------
+--R          a sinh(a x) + a cosh(a x) - a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 68
+bb:=-1/a*coth((a*x)/2)
+--R
+--R               a x
+--R          coth(---)
+--R                2
+--R   (2)  - ---------
+--R              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 69
+cc:=aa-bb
+--R
+--R             a x                                 a x
+--R        coth(---)sinh(a x) + (cosh(a x) - 1)coth(---) - 2
+--R              2                                   2
+--R   (3)  -------------------------------------------------
+--R                  a sinh(a x) + a cosh(a x) - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 70
+cothrule:=rule(coth(x) == cosh(x)/sinh(x))
+--R
+--R                   cosh(x)
+--R   (4)  coth(x) == -------
+--R                   sinh(x)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 71
+dd:=cothrule cc
+--R
+--R             a x                   a x         a x                  a x
+--R        cosh(---)sinh(a x) - 2sinh(---) + cosh(---)cosh(a x) - cosh(---)
+--R              2                     2           2                    2
+--R   (5)  ----------------------------------------------------------------
+--R                       a x                                   a x
+--R                a sinh(---)sinh(a x) + (a cosh(a x) - a)sinh(---)
+--R                        2                                     2
+--R                                                     Type: Expression Integer
+--E
+
+--S 72
+sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
+--R
+--I                              %BD sinh(y + x) - %BD sinh(y - x)
+--I   (6)  %BD cosh(y)sinh(x) == ---------------------------------
+--R                                              2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 73
+ee:=sinhcoshrule dd
+--R
+--R             3a x          a x          a x                   a x
+--R        sinh(----) - 3sinh(---) + 2cosh(---)cosh(a x) - 2cosh(---)
+--R               2            2            2                     2
+--R   (7)  ----------------------------------------------------------
+--R                   3a x            a x                     a x
+--R            a sinh(----) + 2a sinh(---)sinh(a x) - 3a sinh(---)
+--R                     2              2                       2
+--R                                                     Type: Expression Integer
+--E
+
+--S 74
+sinhsinhrule:=rule(sinh(x)*sinh(y)==1/2*(cosh(x+y)-cosh(x-y)))
+--R
+--I                              %BE cosh(y + x) - %BE cosh(y - x)
+--I   (8)  %BE sinh(x)sinh(y) == ---------------------------------
+--R                                              2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 75
+ff:=sinhsinhrule ee
+--R
+--R             3a x          a x          a x                   a x
+--R        sinh(----) - 3sinh(---) + 2cosh(---)cosh(a x) - 2cosh(---)
+--R               2            2            2                     2
+--R   (9)  ----------------------------------------------------------
+--R                3a x            a x           3a x           a x
+--R         a sinh(----) - 3a sinh(---) + a cosh(----) - a cosh(---)
+--R                  2              2              2             2
+--R                                                     Type: Expression Integer
+--E
+
+--S 76
+coshcoshrule:=rule(cosh(x)*cosh(y)==1/2*(cosh(x+y)+cosh(x-y)))
+--R
+--I                               %BF cosh(y + x) + %BF cosh(y - x)
+--I   (10)  %BF cosh(x)cosh(y) == ---------------------------------
+--R                                               2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 77     14:576 Schaums and Axiom differ by a constant
+gg:=coshcoshrule ff
+--R
+--R         1
+--R   (11)  -
+--R         a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.577~~~~~$\displaystyle
+\int{\frac{x~dx}{\cosh{ax}+1}}~dx$}
+$$\int{\frac{x}{\cosh{ax}+1}}=
+\frac{x}{a}\tanh\frac{ax}{2}-\frac{2}{a^2}\ln\cosh\frac{ax}{2}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 78
+aa:=integrate(x/(cosh(a*x)+1),x)
+--R 
+--R
+--R   (1)
+--R       (- 2sinh(a x) - 2cosh(a x) - 2)log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R       2a x sinh(a x) + 2a x cosh(a x)
+--R  /
+--R      2             2             2
+--R     a sinh(a x) + a cosh(a x) + a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 79
+bb:=x/a*tanh((a*x)/2)-2/a^2*log(cosh((a*x)/2))
+--R
+--R                    a x              a x
+--R        - 2log(cosh(---)) + a x tanh(---)
+--R                     2                2
+--R   (2)  ---------------------------------
+--R                         2
+--R                        a
+--R                                                     Type: Expression Integer
+--E
+
+--S 80
+cc:=aa-bb
+--R
+--R   (3)
+--R       (- 2sinh(a x) - 2cosh(a x) - 2)log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R                                             a x
+--R       (2sinh(a x) + 2cosh(a x) + 2)log(cosh(---))
+--R                                              2
+--R     + 
+--R                                                   a x
+--R       (- a x sinh(a x) - a x cosh(a x) - a x)tanh(---) + 2a x sinh(a x)
+--R                                                    2
+--R     + 
+--R       2a x cosh(a x)
+--R  /
+--R      2             2             2
+--R     a sinh(a x) + a cosh(a x) + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 81
+tanhrule:=rule(tanh(x) == sinh(x)/cosh(x))
+--R
+--R                   sinh(x)
+--R   (4)  tanh(x) == -------
+--R                   cosh(x)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 82
+dd:=tanhrule cc
+--R
+--R   (5)
+--R                  a x                   a x                   a x
+--R         (- 2cosh(---)sinh(a x) - 2cosh(---)cosh(a x) - 2cosh(---))
+--R                   2                     2                     2
+--R      *
+--R         log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R              a x                   a x                   a x           a x
+--R       (2cosh(---)sinh(a x) + 2cosh(---)cosh(a x) + 2cosh(---))log(cosh(---))
+--R               2                     2                     2             2
+--R     + 
+--R                   a x              a x
+--R       (- a x sinh(---) + 2a x cosh(---))sinh(a x)
+--R                    2                2
+--R     + 
+--R                                   a x              a x
+--R       (- a x cosh(a x) - a x)sinh(---) + 2a x cosh(---)cosh(a x)
+--R                                    2                2
+--R  /
+--R      2     a x              2     a x              2     a x
+--R     a cosh(---)sinh(a x) + a cosh(---)cosh(a x) + a cosh(---)
+--R             2                      2                      2
+--R                                                     Type: Expression Integer
+--E
+
+--S 83
+coshcoshrule:=rule(cosh(x)*cosh(y)==1/2*(cosh(x+y)+cosh(x-y)))
+--R
+--I                              %BG cosh(y + x) + %BG cosh(y - x)
+--I   (6)  %BG cosh(x)cosh(y) == ---------------------------------
+--R                                              2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 84
+ee:=coshcoshrule dd
+--R
+--R   (7)
+--R                  a x                   3a x          a x
+--R         (- 4cosh(---)sinh(a x) - 2cosh(----) - 6cosh(---))
+--R                   2                      2            2
+--R      *
+--R         log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R              a x                   3a x          a x           a x
+--R       (4cosh(---)sinh(a x) + 2cosh(----) + 6cosh(---))log(cosh(---))
+--R               2                      2            2             2
+--R     + 
+--R                    a x              a x
+--R       (- 2a x sinh(---) + 4a x cosh(---))sinh(a x)
+--R                     2                2
+--R     + 
+--R                                     a x              3a x              a x
+--R       (- 2a x cosh(a x) - 2a x)sinh(---) + 2a x cosh(----) + 2a x cosh(---)
+--R                                      2                 2                2
+--R  /
+--R       2     a x              2     3a x      2     a x
+--R     2a cosh(---)sinh(a x) + a cosh(----) + 3a cosh(---)
+--R              2                       2              2
+--R                                                     Type: Expression Integer
+--E
+
+--S 85
+sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
+--R
+--I                              %BH sinh(y + x) - %BH sinh(y - x)
+--I   (8)  %BH cosh(y)sinh(x) == ---------------------------------
+--R                                              2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 86
+ff:=sinhcoshrule ee
+--R
+--R   (9)
+--R                  3a x          a x          3a x          a x
+--R         (- 2sinh(----) - 2sinh(---) - 2cosh(----) - 6cosh(---))
+--R                    2            2             2            2
+--R      *
+--R         log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R              3a x          a x          3a x          a x           a x
+--R       (2sinh(----) + 2sinh(---) + 2cosh(----) + 6cosh(---))log(cosh(---))
+--R                2            2             2            2             2
+--R     + 
+--R                3a x              a x                      a x
+--R       a x sinh(----) - 2a x sinh(---)sinh(a x) + a x sinh(---)
+--R                  2                2                        2
+--R     + 
+--R                 3a x              a x
+--R       2a x cosh(----) + 2a x cosh(---)
+--R                   2                2
+--R  /
+--R      2     3a x     2     a x     2     3a x      2     a x
+--R     a sinh(----) + a sinh(---) + a cosh(----) + 3a cosh(---)
+--R              2             2              2              2
+--R                                                     Type: Expression Integer
+--E
+
+--S 87
+sinhsinhrule:=rule(sinh(x)*sinh(y)==1/2*(cosh(x+y)-cosh(x-y)))
+--R
+--I                               %BI cosh(y + x) - %BI cosh(y - x)
+--I   (10)  %BI sinh(x)sinh(y) == ---------------------------------
+--R                                               2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 88
+gg:=sinhsinhrule ff
+--R
+--R                                                       a x
+--R         - 2log(sinh(a x) + cosh(a x) + 1) + 2log(cosh(---)) + a x
+--R                                                        2
+--R   (11)  ---------------------------------------------------------
+--R                                      2
+--R                                     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 89     14:577 Schaums and Axiom differ by a constant
+complexNormalize gg
+--R
+--R           2log(2)
+--R   (12)  - -------
+--R               2
+--R              a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.578~~~~~$\displaystyle
+\int{\frac{x~dx}{\cosh{ax}-1}}$}
+$$\int{\frac{x}{\cosh{ax}-1}}
+-\frac{x}{a}\coth\frac{ax}{2}+\frac{2}{a^2}\ln\sinh\frac{ax}{2}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 90
+aa:=integrate(x/(cosh(a*x)-1),x)
+--R 
+--R
+--R   (1)
+--R       (2sinh(a x) + 2cosh(a x) - 2)log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R       - 2a x sinh(a x) - 2a x cosh(a x)
+--R  /
+--R      2             2             2
+--R     a sinh(a x) + a cosh(a x) - a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 91
+bb:=-x/a*coth((a*x)/2)+2/a^2*log(sinh((a*x)/2))
+--R
+--R                  a x              a x
+--R        2log(sinh(---)) - a x coth(---)
+--R                   2                2
+--R   (2)  -------------------------------
+--R                        2
+--R                       a
+--R                                                     Type: Expression Integer
+--E
+
+--S 92
+cc:=aa-bb
+--R
+--R   (3)
+--R       (2sinh(a x) + 2cosh(a x) - 2)log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R                                               a x
+--R       (- 2sinh(a x) - 2cosh(a x) + 2)log(sinh(---))
+--R                                                2
+--R     + 
+--R                 a x                                               a x
+--R       (a x coth(---) - 2a x)sinh(a x) + (a x cosh(a x) - a x)coth(---)
+--R                  2                                                 2
+--R     + 
+--R       - 2a x cosh(a x)
+--R  /
+--R      2             2             2
+--R     a sinh(a x) + a cosh(a x) - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 93
+cothrule:=rule(coth(x) == cosh(x)/sinh(x))
+--R
+--R                   cosh(x)
+--R   (4)  coth(x) == -------
+--R                   sinh(x)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 94
+dd:=cothrule cc
+--R
+--R   (5)
+--R                a x                                  a x
+--R         (2sinh(---)sinh(a x) + (2cosh(a x) - 2)sinh(---))
+--R                 2                                    2
+--R      *
+--R         log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R                a x                                    a x           a x
+--R       (- 2sinh(---)sinh(a x) + (- 2cosh(a x) + 2)sinh(---))log(sinh(---))
+--R                 2                                      2             2
+--R     + 
+--R                    a x             a x                                 a x
+--R       (- 2a x sinh(---) + a x cosh(---))sinh(a x) - 2a x cosh(a x)sinh(---)
+--R                     2               2                                   2
+--R     + 
+--R                a x                      a x
+--R       a x cosh(---)cosh(a x) - a x cosh(---)
+--R                 2                        2
+--R  /
+--R      2     a x               2             2      a x
+--R     a sinh(---)sinh(a x) + (a cosh(a x) - a )sinh(---)
+--R             2                                      2
+--R                                                     Type: Expression Integer
+--E
+
+--S 95
+sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
+--R
+--I                              %BJ sinh(y + x) - %BJ sinh(y - x)
+--I   (6)  %BJ cosh(y)sinh(x) == ---------------------------------
+--R                                              2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 96
+ee:=sinhcoshrule dd
+--R
+--R   (7)
+--R                3a x          a x                   a x
+--R         (2sinh(----) + 4sinh(---)sinh(a x) - 6sinh(---))
+--R                  2            2                     2
+--R      *
+--R         log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R                3a x          a x                   a x           a x
+--R       (- 2sinh(----) - 4sinh(---)sinh(a x) + 6sinh(---))log(sinh(---))
+--R                  2            2                     2             2
+--R     + 
+--R                  3a x              a x                       a x
+--R       - a x sinh(----) - 4a x sinh(---)sinh(a x) + 3a x sinh(---)
+--R                    2                2                         2
+--R     + 
+--R                 a x                       a x
+--R       2a x cosh(---)cosh(a x) - 2a x cosh(---)
+--R                  2                         2
+--R  /
+--R      2     3a x      2     a x               2     a x
+--R     a sinh(----) + 2a sinh(---)sinh(a x) - 3a sinh(---)
+--R              2              2                       2
+--R                                                     Type: Expression Integer
+--E
+
+--S 97
+sinhsinhrule:=rule(sinh(x)*sinh(y)==1/2*(cosh(x+y)-cosh(x-y)))
+--R
+--I                              %BK cosh(y + x) - %BK cosh(y - x)
+--I   (8)  %BK sinh(x)sinh(y) == ---------------------------------
+--R                                              2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 98
+ff:=sinhsinhrule ee
+--R
+--R   (9)
+--R                3a x          a x          3a x          a x
+--R         (2sinh(----) - 6sinh(---) + 2cosh(----) - 2cosh(---))
+--R                  2            2             2            2
+--R      *
+--R         log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R                3a x          a x          3a x          a x           a x
+--R       (- 2sinh(----) + 6sinh(---) - 2cosh(----) + 2cosh(---))log(sinh(---))
+--R                  2            2             2            2             2
+--R     + 
+--R                  3a x              a x              3a x
+--R       - a x sinh(----) + 3a x sinh(---) - 2a x cosh(----)
+--R                    2                2                 2
+--R     + 
+--R                 a x
+--R       2a x cosh(---)cosh(a x)
+--R                  2
+--R  /
+--R      2     3a x      2     a x     2     3a x     2     a x
+--R     a sinh(----) - 3a sinh(---) + a cosh(----) - a cosh(---)
+--R              2              2              2             2
+--R                                                     Type: Expression Integer
+--E
+
+--S 99
+coshcoshrule:=rule(cosh(x)*cosh(y)==1/2*(cosh(x+y)+cosh(x-y)))
+--R
+--I                               %BL cosh(y + x) + %BL cosh(y - x)
+--I   (10)  %BL cosh(x)cosh(y) == ---------------------------------
+--R                                               2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 100
+gg:=coshcoshrule ff
+--R
+--R                                                     a x
+--R         2log(sinh(a x) + cosh(a x) - 1) - 2log(sinh(---)) - a x
+--R                                                      2
+--R   (11)  -------------------------------------------------------
+--R                                     2
+--R                                    a
+--R                                                     Type: Expression Integer
+--E
+
+--S 101    14:578 Schaums and Axiom differ by a constant
+hh:=complexNormalize gg
+--R
+--R         2log(2)
+--R   (12)  -------
+--R             2
+--R            a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.579~~~~~$\displaystyle
+\int{\frac{dx}{(\cosh{ax}+1)^2}}$}
+$$\int{\frac{1}{(\cosh{ax}+1)^2}}=
+\frac{1}{2a}\tanh{\frac{ax}{2}}-\frac{1}{6a}\tanh^3{\frac{ax}{2}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 102
+aa:=integrate(1/(cosh(a*x)+1)^2,x)
+--R 
+--R
+--R   (1)
+--R     - 6sinh(a x) - 6cosh(a x) - 2
+--R  /
+--R                   3                               2
+--R       3a sinh(a x)  + (9a cosh(a x) + 9a)sinh(a x)
+--R     + 
+--R                    2                                              3
+--R       (9a cosh(a x)  + 18a cosh(a x) + 9a)sinh(a x) + 3a cosh(a x)
+--R     + 
+--R                   2
+--R       9a cosh(a x)  + 9a cosh(a x) + 3a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 103
+bb:=1/(2*a)*tanh((a*x)/2)-1/(6*a)*tanh((a*x)/2)^3
+--R
+--R               a x 3         a x
+--R        - tanh(---)  + 3tanh(---)
+--R                2             2
+--R   (2)  -------------------------
+--R                    6a
+--R                                                     Type: Expression Integer
+--E
+
+--S 104    14:579 Axiom cannot compute this integral
+cc:=aa-bb
+--R
+--R   (3)
+--R                    3                            2
+--R           sinh(a x)  + (3cosh(a x) + 3)sinh(a x)
+--R         + 
+--R                      2                                       3             2
+--R           (3cosh(a x)  + 6cosh(a x) + 3)sinh(a x) + cosh(a x)  + 3cosh(a x)
+--R         + 
+--R           3cosh(a x) + 1
+--R      *
+--R              a x 3
+--R         tanh(---)
+--R               2
+--R     + 
+--R                       3                              2
+--R           - 3sinh(a x)  + (- 9cosh(a x) - 9)sinh(a x)
+--R         + 
+--R                        2                                         3
+--R           (- 9cosh(a x)  - 18cosh(a x) - 9)sinh(a x) - 3cosh(a x)
+--R         + 
+--R                       2
+--R           - 9cosh(a x)  - 9cosh(a x) - 3
+--R      *
+--R              a x
+--R         tanh(---)
+--R               2
+--R     + 
+--R       - 12sinh(a x) - 12cosh(a x) - 4
+--R  /
+--R                   3                                 2
+--R       6a sinh(a x)  + (18a cosh(a x) + 18a)sinh(a x)
+--R     + 
+--R                     2                                               3
+--R       (18a cosh(a x)  + 36a cosh(a x) + 18a)sinh(a x) + 6a cosh(a x)
+--R     + 
+--R                    2
+--R       18a cosh(a x)  + 18a cosh(a x) + 6a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.580~~~~~$\displaystyle
+\int{\frac{dx}{(\cosh{ax}-1)^2}}$}
+$$\int{\frac{1}{(\cosh{ax}-1)^2}}=
+\frac{1}{2a}\coth{\frac{ax}{2}}-\frac{1}{6a}\coth^3{\frac{ax}{2}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 105
+aa:=integrate(1/(cosh(a*x)-1)^2,x)
+--R 
+--R
+--R   (1)
+--R     - 6sinh(a x) - 6cosh(a x) + 2
+--R  /
+--R                   3                               2
+--R       3a sinh(a x)  + (9a cosh(a x) - 9a)sinh(a x)
+--R     + 
+--R                    2                                              3
+--R       (9a cosh(a x)  - 18a cosh(a x) + 9a)sinh(a x) + 3a cosh(a x)
+--R     + 
+--R                     2
+--R       - 9a cosh(a x)  + 9a cosh(a x) - 3a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 106
+bb:=1/(2*a)*coth((a*x)/2)-1/(6*a)*coth((a*x)/2)^3
+--R
+--R               a x 3         a x
+--R        - coth(---)  + 3coth(---)
+--R                2             2
+--R   (2)  -------------------------
+--R                    6a
+--R                                                     Type: Expression Integer
+--E
+
+--S 107    14:580 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R             a x 3         a x           3
+--R       (coth(---)  - 3coth(---))sinh(a x)
+--R              2             2
+--R     + 
+--R                             a x 3                          a x           2
+--R       ((3cosh(a x) - 3)coth(---)  + (- 9cosh(a x) + 9)coth(---))sinh(a x)
+--R                              2                              2
+--R     + 
+--R                      2                       a x 3
+--R           (3cosh(a x)  - 6cosh(a x) + 3)coth(---)
+--R                                               2
+--R         + 
+--R                        2                        a x
+--R           (- 9cosh(a x)  + 18cosh(a x) - 9)coth(---) - 12
+--R                                                  2
+--R      *
+--R         sinh(a x)
+--R     + 
+--R                 3             2                       a x 3
+--R       (cosh(a x)  - 3cosh(a x)  + 3cosh(a x) - 1)coth(---)
+--R                                                        2
+--R     + 
+--R                  3             2                       a x
+--R     (- 3cosh(a x)  + 9cosh(a x)  - 9cosh(a x) + 3)coth(---) - 12cosh(a x) + 4
+--R                                                         2
+--R  /
+--R                   3                                 2
+--R       6a sinh(a x)  + (18a cosh(a x) - 18a)sinh(a x)
+--R     + 
+--R                     2                                               3
+--R       (18a cosh(a x)  - 36a cosh(a x) + 18a)sinh(a x) + 6a cosh(a x)
+--R     + 
+--R                      2
+--R       - 18a cosh(a x)  + 18a cosh(a x) - 6a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.581~~~~~$\displaystyle
+\int{\frac{dx}{p+q\cosh{ax}}}$}
+$$\int{\frac{1}{p+q\cosh{ax}}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{2}{a\sqrt{q^2-p^2}}\tan^{-1}\frac{qe^{ax}+p}{\sqrt{q^2-p^2}}\\
+\\
+\displaystyle
+\frac{1}{a\sqrt{p^2-a^2}}\ln\left(\frac{qe^{ax}+p-\sqrt{p^2-q^2}}
+{qe^{ax}+p+\sqrt{p^2-q^2}}\right)
+\end{array}
+\right.
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 108
+aa:=integrate(1/(p+q*cosh(a*x)),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R       log
+--R                   2         2      2                              2         2
+--R                  q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R                + 
+--R                                    2     2
+--R                  2p q cosh(a x) - q  + 2p
+--R             *
+--R                 +---------+
+--R                 |   2    2
+--R                \|- q  + p
+--R            + 
+--R                 3     2                 3     2                  2     3
+--R              (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
+--R         /
+--R                         2                                             2
+--R              q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R            + 
+--R              2p cosh(a x) + q
+--R    /
+--R         +---------+
+--R         |   2    2
+--R       a\|- q  + p
+--R     ,
+--R                                          +-------+
+--R                                          | 2    2
+--R          (q sinh(a x) + q cosh(a x) + p)\|q  - p
+--R    2atan(-----------------------------------------)
+--R                            2    2
+--R                           q  - p
+--R    ------------------------------------------------]
+--R                         +-------+
+--R                         | 2    2
+--R                       a\|q  - p
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+
+--S 109
+bb1:=2/(a*sqrt(q^2-p^2))*atan((q*%e^(a*x)+p)/sqrt(q^2-p^2))
+--R
+--R                  a x
+--R              q %e    + p
+--R        2atan(-----------)
+--R                +-------+
+--R                | 2    2
+--R               \|q  - p
+--R   (2)  ------------------
+--R              +-------+
+--R              | 2    2
+--R            a\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 110
+bb2:=1/(a*sqrt(p^2-q^2))*log((q*%e^(a*x)+p-sqrt(p^2-q^2))/(q*%e^(a*x)+p+sqrt(p^2-q^2)))
+--R
+--R               +---------+
+--R               |   2    2        a x
+--R            - \|- q  + p   + q %e    + p
+--R        log(----------------------------)
+--R              +---------+
+--R              |   2    2        a x
+--R             \|- q  + p   + q %e    + p
+--R   (3)  ---------------------------------
+--R                    +---------+
+--R                    |   2    2
+--R                  a\|- q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 111
+cc1:=aa.1-bb1
+--R
+--R   (4)
+--R          +-------+
+--R          | 2    2
+--R         \|q  - p
+--R      *
+--R         log
+--R                     2         2      2                              2         2
+--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R                  + 
+--R                                      2     2
+--R                    2p q cosh(a x) - q  + 2p
+--R               *
+--R                   +---------+
+--R                   |   2    2
+--R                  \|- q  + p
+--R              + 
+--R                   3     2                 3     2                  2     3
+--R                (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
+--R           /
+--R                           2                                             2
+--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R              + 
+--R                2p cosh(a x) + q
+--R     + 
+--R           +---------+         a x
+--R           |   2    2      q %e    + p
+--R       - 2\|- q  + p  atan(-----------)
+--R                             +-------+
+--R                             | 2    2
+--R                            \|q  - p
+--R  /
+--R       +---------+ +-------+
+--R       |   2    2  | 2    2
+--R     a\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 112
+cc2:=aa.2-bb1
+--R
+--R                                              +-------+
+--R                                              | 2    2               a x
+--R              (q sinh(a x) + q cosh(a x) + p)\|q  - p            q %e    + p
+--R        2atan(-----------------------------------------) - 2atan(-----------)
+--R                                2    2                             +-------+
+--R                               q  - p                              | 2    2
+--R                                                                  \|q  - p
+--R   (5)  ---------------------------------------------------------------------
+--R                                       +-------+
+--R                                       | 2    2
+--R                                     a\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 113
+cc3:=aa.1-bb2
+--R
+--R   (6)
+--R       log
+--R                   2         2      2                              2         2
+--R                  q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R                + 
+--R                                    2     2
+--R                  2p q cosh(a x) - q  + 2p
+--R             *
+--R                 +---------+
+--R                 |   2    2
+--R                \|- q  + p
+--R            + 
+--R                 3     2                 3     2                  2     3
+--R              (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
+--R         /
+--R                         2                                             2
+--R              q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R            + 
+--R              2p cosh(a x) + q
+--R     + 
+--R                +---------+
+--R                |   2    2        a x
+--R             - \|- q  + p   + q %e    + p
+--R       - log(----------------------------)
+--R               +---------+
+--R               |   2    2        a x
+--R              \|- q  + p   + q %e    + p
+--R  /
+--R       +---------+
+--R       |   2    2
+--R     a\|- q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 114    14:581 Axiom cannot simplify this expression
+cc4:=aa.2-bb2
+--R
+--R   (7)
+--R                          +---------+
+--R          +-------+       |   2    2        a x
+--R          | 2    2     - \|- q  + p   + q %e    + p
+--R       - \|q  - p  log(----------------------------)
+--R                         +---------+
+--R                         |   2    2        a x
+--R                        \|- q  + p   + q %e    + p
+--R     + 
+--R                                                         +-------+
+--R         +---------+                                     | 2    2
+--R         |   2    2      (q sinh(a x) + q cosh(a x) + p)\|q  - p
+--R       2\|- q  + p  atan(-----------------------------------------)
+--R                                           2    2
+--R                                          q  - p
+--R  /
+--R       +---------+ +-------+
+--R       |   2    2  | 2    2
+--R     a\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.582~~~~~$\displaystyle
+\int{\frac{dx}{(p+q\cosh{ax})^2}}~dx$}
+$$\int{\frac{1}{(p+q\cosh{ax})^2}}=
+\frac{q\sinh{ax}}{a(q^2-p^2)(p+q\cosh{ax})}
+-\frac{p}{q^2-p^2}\int{\frac{1}{p+q\cosh{ax}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 115
+aa:=integrate(1/(p+q*cosh(a*x))^2,x)
+--R 
+--R
+--R   (1)
+--R   [
+--R                          2                       2                          2
+--R             p q sinh(a x)  + (2p q cosh(a x) + 2p )sinh(a x) + p q cosh(a x)
+--R           + 
+--R               2
+--R             2p cosh(a x) + p q
+--R        *
+--R           log
+--R                       2         2      2
+--R                      q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x)
+--R                    + 
+--R                       2         2                     2     2
+--R                      q cosh(a x)  + 2p q cosh(a x) - q  + 2p
+--R                 *
+--R                     +---------+
+--R                     |   2    2
+--R                    \|- q  + p
+--R                + 
+--R                     3     2                   3     2                  2     3
+--R                (- 2q  + 2p q)sinh(a x) + (- 2q  + 2p q)cosh(a x) - 2p q  + 2p
+--R             /
+--R                             2                                             2
+--R                  q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R                + 
+--R                  2p cosh(a x) + q
+--R       + 
+--R                                              +---------+
+--R                                              |   2    2
+--R         (- 2p sinh(a x) - 2p cosh(a x) - 2q)\|- q  + p
+--R    /
+--R               3      2           2
+--R           (a q  - a p q)sinh(a x)
+--R         + 
+--R                 3       2                    2       3
+--R           ((2a q  - 2a p q)cosh(a x) + 2a p q  - 2a p )sinh(a x)
+--R         + 
+--R               3      2           2          2       3                3      2
+--R           (a q  - a p q)cosh(a x)  + (2a p q  - 2a p )cosh(a x) + a q  - a p q
+--R      *
+--R          +---------+
+--R          |   2    2
+--R         \|- q  + p
+--R     ,
+--R
+--R                             2                         2
+--R             - 2p q sinh(a x)  + (- 4p q cosh(a x) - 4p )sinh(a x)
+--R           + 
+--R                             2     2
+--R             - 2p q cosh(a x)  - 4p cosh(a x) - 2p q
+--R        *
+--R                                                +-------+
+--R                                                | 2    2
+--R                (q sinh(a x) + q cosh(a x) + p)\|q  - p
+--R           atan(-----------------------------------------)
+--R                                  2    2
+--R                                 q  - p
+--R       + 
+--R                                              +-------+
+--R                                              | 2    2
+--R         (- 2p sinh(a x) - 2p cosh(a x) - 2q)\|q  - p
+--R    /
+--R               3      2           2
+--R           (a q  - a p q)sinh(a x)
+--R         + 
+--R                 3       2                    2       3
+--R           ((2a q  - 2a p q)cosh(a x) + 2a p q  - 2a p )sinh(a x)
+--R         + 
+--R               3      2           2          2       3                3      2
+--R           (a q  - a p q)cosh(a x)  + (2a p q  - 2a p )cosh(a x) + a q  - a p q
+--R      *
+--R          +-------+
+--R          | 2    2
+--R         \|q  - p
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+
+--S 116
+t1:=integrate(1/(p+q*cosh(a*x)),x)
+--R
+--R   (2)
+--R   [
+--R       log
+--R                   2         2      2                              2         2
+--R                  q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R                + 
+--R                                    2     2
+--R                  2p q cosh(a x) - q  + 2p
+--R             *
+--R                 +---------+
+--R                 |   2    2
+--R                \|- q  + p
+--R            + 
+--R                 3     2                 3     2                  2     3
+--R              (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
+--R         /
+--R                         2                                             2
+--R              q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R            + 
+--R              2p cosh(a x) + q
+--R    /
+--R         +---------+
+--R         |   2    2
+--R       a\|- q  + p
+--R     ,
+--R                                          +-------+
+--R                                          | 2    2
+--R          (q sinh(a x) + q cosh(a x) + p)\|q  - p
+--R    2atan(-----------------------------------------)
+--R                            2    2
+--R                           q  - p
+--R    ------------------------------------------------]
+--R                         +-------+
+--R                         | 2    2
+--R                       a\|q  - p
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 117
+bb1:=(q*sinh(a*x))/(a*(q^2-p^2)*(p+q*cosh(a*x)))-p/(q^2-p^2)*t1.1
+--R
+--R   (3)
+--R                             2
+--R         (- p q cosh(a x) - p )
+--R      *
+--R         log
+--R                     2         2      2                              2         2
+--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R                  + 
+--R                                      2     2
+--R                    2p q cosh(a x) - q  + 2p
+--R               *
+--R                   +---------+
+--R                   |   2    2
+--R                  \|- q  + p
+--R              + 
+--R                   3     2                 3     2                  2     3
+--R                (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
+--R           /
+--R                           2                                             2
+--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R              + 
+--R                2p cosh(a x) + q
+--R     + 
+--R                   +---------+
+--R                   |   2    2
+--R       q sinh(a x)\|- q  + p
+--R  /
+--R                                               +---------+
+--R          3      2                   2      3  |   2    2
+--R     ((a q  - a p q)cosh(a x) + a p q  - a p )\|- q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 118
+bb2:=(q*sinh(a*x))/(a*(q^2-p^2)*(p+q*cosh(a*x)))-p/(q^2-p^2)*t1.2
+--R
+--R   (4)
+--R                                                                    +-------+
+--R                                                                    | 2    2
+--R                             2      (q sinh(a x) + q cosh(a x) + p)\|q  - p
+--R       (- 2p q cosh(a x) - 2p )atan(-----------------------------------------)
+--R                                                      2    2
+--R                                                     q  - p
+--R     + 
+--R                   +-------+
+--R                   | 2    2
+--R       q sinh(a x)\|q  - p
+--R  /
+--R                                               +-------+
+--R          3      2                   2      3  | 2    2
+--R     ((a q  - a p q)cosh(a x) + a p q  - a p )\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 119
+cc1:=aa.1-bb1
+--R
+--R   (5)
+--R               2             2           2
+--R           (p q cosh(a x) + p q)sinh(a x)
+--R         + 
+--R                2         2     2                3                2         3
+--R           (2p q cosh(a x)  + 4p q cosh(a x) + 2p )sinh(a x) + p q cosh(a x)
+--R         + 
+--R             2           2       2     3              2
+--R           3p q cosh(a x)  + (p q  + 2p )cosh(a x) + p q
+--R      *
+--R         log
+--R                     2         2      2                              2         2
+--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R                  + 
+--R                                      2     2
+--R                    2p q cosh(a x) - q  + 2p
+--R               *
+--R                   +---------+
+--R                   |   2    2
+--R                  \|- q  + p
+--R              + 
+--R                   3     2                 3     2                  2     3
+--R                (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
+--R           /
+--R                           2                                             2
+--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R              + 
+--R                2p cosh(a x) + q
+--R     + 
+--R               2             2           2
+--R           (p q cosh(a x) + p q)sinh(a x)
+--R         + 
+--R                2         2     2                3                2         3
+--R           (2p q cosh(a x)  + 4p q cosh(a x) + 2p )sinh(a x) + p q cosh(a x)
+--R         + 
+--R             2           2       2     3              2
+--R           3p q cosh(a x)  + (p q  + 2p )cosh(a x) + p q
+--R      *
+--R         log
+--R                     2         2      2                              2         2
+--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R                  + 
+--R                                      2     2
+--R                    2p q cosh(a x) - q  + 2p
+--R               *
+--R                   +---------+
+--R                   |   2    2
+--R                  \|- q  + p
+--R              + 
+--R                     3     2                   3     2                  2     3
+--R                (- 2q  + 2p q)sinh(a x) + (- 2q  + 2p q)cosh(a x) - 2p q  + 2p
+--R           /
+--R                           2                                             2
+--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R              + 
+--R                2p cosh(a x) + q
+--R     + 
+--R              2         3        2                          2
+--R           - q sinh(a x)  + (- 2q cosh(a x) - 2p q)sinh(a x)
+--R         + 
+--R               2         2                     2     2
+--R           (- q cosh(a x)  - 4p q cosh(a x) - q  - 2p )sinh(a x)
+--R         + 
+--R                           2        2     2
+--R           - 2p q cosh(a x)  + (- 2q  - 2p )cosh(a x) - 2p q
+--R      *
+--R          +---------+
+--R          |   2    2
+--R         \|- q  + p
+--R  /
+--R              4      2 2                  3      3           2
+--R         ((a q  - a p q )cosh(a x) + a p q  - a p q)sinh(a x)
+--R       + 
+--R                  4       2 2          2          3       3                  2 2
+--R             (2a q  - 2a p q )cosh(a x)  + (4a p q  - 4a p q)cosh(a x) + 2a p q
+--R           + 
+--R                   4
+--R             - 2a p
+--R        *
+--R           sinh(a x)
+--R       + 
+--R             4      2 2          3          3       3           2
+--R         (a q  - a p q )cosh(a x)  + (3a p q  - 3a p q)cosh(a x)
+--R       + 
+--R             4      2 2       4                  3      3
+--R         (a q  + a p q  - 2a p )cosh(a x) + a p q  - a p q
+--R    *
+--R        +---------+
+--R        |   2    2
+--R       \|- q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 120
+cc2:=aa.2-bb1
+--R
+--R   (6)
+--R               2             2           2
+--R           (p q cosh(a x) + p q)sinh(a x)
+--R         + 
+--R                2         2     2                3                2         3
+--R           (2p q cosh(a x)  + 4p q cosh(a x) + 2p )sinh(a x) + p q cosh(a x)
+--R         + 
+--R             2           2       2     3              2
+--R           3p q cosh(a x)  + (p q  + 2p )cosh(a x) + p q
+--R      *
+--R          +-------+
+--R          | 2    2
+--R         \|q  - p
+--R      *
+--R         log
+--R                     2         2      2                              2         2
+--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R                  + 
+--R                                      2     2
+--R                    2p q cosh(a x) - q  + 2p
+--R               *
+--R                   +---------+
+--R                   |   2    2
+--R                  \|- q  + p
+--R              + 
+--R                   3     2                 3     2                  2     3
+--R                (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
+--R           /
+--R                           2                                             2
+--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R              + 
+--R                2p cosh(a x) + q
+--R     + 
+--R                  2              2           2
+--R           (- 2p q cosh(a x) - 2p q)sinh(a x)
+--R         + 
+--R                  2         2     2                3                 2         3
+--R           (- 4p q cosh(a x)  - 8p q cosh(a x) - 4p )sinh(a x) - 2p q cosh(a x)
+--R         + 
+--R               2           2          2     3               2
+--R           - 6p q cosh(a x)  + (- 2p q  - 4p )cosh(a x) - 2p q
+--R      *
+--R                                                          +-------+
+--R          +---------+                                     | 2    2
+--R          |   2    2      (q sinh(a x) + q cosh(a x) + p)\|q  - p
+--R         \|- q  + p  atan(-----------------------------------------)
+--R                                            2    2
+--R                                           q  - p
+--R     + 
+--R              2         3        2                          2
+--R           - q sinh(a x)  + (- 2q cosh(a x) - 2p q)sinh(a x)
+--R         + 
+--R               2         2                     2     2
+--R           (- q cosh(a x)  - 4p q cosh(a x) - q  - 2p )sinh(a x)
+--R         + 
+--R                           2        2     2
+--R           - 2p q cosh(a x)  + (- 2q  - 2p )cosh(a x) - 2p q
+--R      *
+--R          +---------+ +-------+
+--R          |   2    2  | 2    2
+--R         \|- q  + p  \|q  - p
+--R  /
+--R              4      2 2                  3      3           2
+--R         ((a q  - a p q )cosh(a x) + a p q  - a p q)sinh(a x)
+--R       + 
+--R                  4       2 2          2          3       3                  2 2
+--R             (2a q  - 2a p q )cosh(a x)  + (4a p q  - 4a p q)cosh(a x) + 2a p q
+--R           + 
+--R                   4
+--R             - 2a p
+--R        *
+--R           sinh(a x)
+--R       + 
+--R             4      2 2          3          3       3           2
+--R         (a q  - a p q )cosh(a x)  + (3a p q  - 3a p q)cosh(a x)
+--R       + 
+--R             4      2 2       4                  3      3
+--R         (a q  + a p q  - 2a p )cosh(a x) + a p q  - a p q
+--R    *
+--R        +---------+ +-------+
+--R        |   2    2  | 2    2
+--R       \|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 121
+cc3:=aa.1-bb2
+--R
+--R   (7)
+--R               2             2           2
+--R           (p q cosh(a x) + p q)sinh(a x)
+--R         + 
+--R                2         2     2                3                2         3
+--R           (2p q cosh(a x)  + 4p q cosh(a x) + 2p )sinh(a x) + p q cosh(a x)
+--R         + 
+--R             2           2       2     3              2
+--R           3p q cosh(a x)  + (p q  + 2p )cosh(a x) + p q
+--R      *
+--R          +-------+
+--R          | 2    2
+--R         \|q  - p
+--R      *
+--R         log
+--R                     2         2      2                              2         2
+--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R                  + 
+--R                                      2     2
+--R                    2p q cosh(a x) - q  + 2p
+--R               *
+--R                   +---------+
+--R                   |   2    2
+--R                  \|- q  + p
+--R              + 
+--R                     3     2                   3     2                  2     3
+--R                (- 2q  + 2p q)sinh(a x) + (- 2q  + 2p q)cosh(a x) - 2p q  + 2p
+--R           /
+--R                           2                                             2
+--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R              + 
+--R                2p cosh(a x) + q
+--R     + 
+--R                2              2           2
+--R           (2p q cosh(a x) + 2p q)sinh(a x)
+--R         + 
+--R                2         2     2                3                 2         3
+--R           (4p q cosh(a x)  + 8p q cosh(a x) + 4p )sinh(a x) + 2p q cosh(a x)
+--R         + 
+--R             2           2        2     3               2
+--R           6p q cosh(a x)  + (2p q  + 4p )cosh(a x) + 2p q
+--R      *
+--R                                                          +-------+
+--R          +---------+                                     | 2    2
+--R          |   2    2      (q sinh(a x) + q cosh(a x) + p)\|q  - p
+--R         \|- q  + p  atan(-----------------------------------------)
+--R                                            2    2
+--R                                           q  - p
+--R     + 
+--R              2         3        2                          2
+--R           - q sinh(a x)  + (- 2q cosh(a x) - 2p q)sinh(a x)
+--R         + 
+--R               2         2                     2     2
+--R           (- q cosh(a x)  - 4p q cosh(a x) - q  - 2p )sinh(a x)
+--R         + 
+--R                           2        2     2
+--R           - 2p q cosh(a x)  + (- 2q  - 2p )cosh(a x) - 2p q
+--R      *
+--R          +---------+ +-------+
+--R          |   2    2  | 2    2
+--R         \|- q  + p  \|q  - p
+--R  /
+--R              4      2 2                  3      3           2
+--R         ((a q  - a p q )cosh(a x) + a p q  - a p q)sinh(a x)
+--R       + 
+--R                  4       2 2          2          3       3                  2 2
+--R             (2a q  - 2a p q )cosh(a x)  + (4a p q  - 4a p q)cosh(a x) + 2a p q
+--R           + 
+--R                   4
+--R             - 2a p
+--R        *
+--R           sinh(a x)
+--R       + 
+--R             4      2 2          3          3       3           2
+--R         (a q  - a p q )cosh(a x)  + (3a p q  - 3a p q)cosh(a x)
+--R       + 
+--R             4      2 2       4                  3      3
+--R         (a q  + a p q  - 2a p )cosh(a x) + a p q  - a p q
+--R    *
+--R        +---------+ +-------+
+--R        |   2    2  | 2    2
+--R       \|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 122    14:582 Axiom cannot simplify this expression
+cc4:=aa.2-bb2
+--R
+--R   (8)
+--R          2         3        2                          2
+--R       - q sinh(a x)  + (- 2q cosh(a x) - 2p q)sinh(a x)
+--R     + 
+--R           2         2                     2     2                           2
+--R       (- q cosh(a x)  - 4p q cosh(a x) - q  - 2p )sinh(a x) - 2p q cosh(a x)
+--R     + 
+--R            2     2
+--R       (- 2q  - 2p )cosh(a x) - 2p q
+--R  /
+--R            4      2 2                  3      3           2
+--R       ((a q  - a p q )cosh(a x) + a p q  - a p q)sinh(a x)
+--R     + 
+--R                4       2 2          2          3       3                  2 2
+--R           (2a q  - 2a p q )cosh(a x)  + (4a p q  - 4a p q)cosh(a x) + 2a p q
+--R         + 
+--R                 4
+--R           - 2a p
+--R      *
+--R         sinh(a x)
+--R     + 
+--R           4      2 2          3          3       3           2
+--R       (a q  - a p q )cosh(a x)  + (3a p q  - 3a p q)cosh(a x)
+--R     + 
+--R           4      2 2       4                  3      3
+--R       (a q  + a p q  - 2a p )cosh(a x) + a p q  - a p q
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.583~~~~~$\displaystyle
+\int{\frac{dx}{p^2-q^2\cosh^2{ax}}}$}
+$$\int{\frac{1}{p^2-q^2\cosh^2{ax}}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{1}{2ap\sqrt{p^2-q^2}}\ln\left(\frac{p\tanh{ax}+\sqrt{p^2-q^2}}
+{p\tanh{ax}-\sqrt{p^2-q^2}}\right)\\
+\\
+\displaystyle
+\frac{1}{ap\sqrt{q^2-p^2}}\tan^{-1}\frac{p\tanh{ax}}{\sqrt{q^2-p^2}}\\
+\end{array}
+\right.
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 123
+aa:=integrate(1/(p^2-q^2*cosh(a*x)^2),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R       log
+--R                   4         4     4                  3
+--R                  q sinh(a x)  + 4q cosh(a x)sinh(a x)
+--R                + 
+--R                     4         2     4     2 2          2
+--R                  (6q cosh(a x)  + 2q  - 4p q )sinh(a x)
+--R                + 
+--R                     4         3      4     2 2
+--R                  (4q cosh(a x)  + (4q  - 8p q )cosh(a x))sinh(a x)
+--R                + 
+--R                   4         4      4     2 2          2    4     2 2     4
+--R                  q cosh(a x)  + (2q  - 4p q )cosh(a x)  + q  - 8p q  + 8p
+--R             *
+--R                 +---------+
+--R                 |   2    2
+--R                \|- q  + p
+--R            + 
+--R                     4     3 2          2          4     3 2
+--R              (- 4p q  + 4p q )sinh(a x)  + (- 8p q  + 8p q )cosh(a x)sinh(a x)
+--R            + 
+--R                     4     3 2          2       4      3 2     5
+--R              (- 4p q  + 4p q )cosh(a x)  - 4p q  + 12p q  - 8p
+--R         /
+--R               2         4     2                  3
+--R              q sinh(a x)  + 4q cosh(a x)sinh(a x)
+--R            + 
+--R                 2         2     2     2          2
+--R              (6q cosh(a x)  + 2q  - 4p )sinh(a x)
+--R            + 
+--R                 2         3      2     2                        2         4
+--R              (4q cosh(a x)  + (4q  - 8p )cosh(a x))sinh(a x) + q cosh(a x)
+--R            + 
+--R                 2     2          2    2
+--R              (2q  - 4p )cosh(a x)  + q
+--R    /
+--R            +---------+
+--R            |   2    2
+--R       2a p\|- q  + p
+--R     ,
+--R
+--R     -
+--R          atan
+--R                      2         2     2                      2         2    2
+--R                     q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  + q
+--R                   + 
+--R                         2
+--R                     - 2p
+--R              *
+--R                  +-------+
+--R                  | 2    2
+--R                 \|q  - p
+--R            /
+--R                   2     3
+--R               2p q  - 2p
+--R       /
+--R              +-------+
+--R              | 2    2
+--R          a p\|q  - p
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+
+--S 124
+bb1:=1/(2*a*p*sqrt(p^2-q^2))*log((p*tanh(a*x)+sqrt(p^2-q^2))/(p*tanh(a*x)-sqrt(p^2-q^2)))
+--R
+--R               +---------+
+--R               |   2    2
+--R            - \|- q  + p   - p tanh(a x)
+--R        log(----------------------------)
+--R              +---------+
+--R              |   2    2
+--R             \|- q  + p   - p tanh(a x)
+--R   (2)  ---------------------------------
+--R                      +---------+
+--R                      |   2    2
+--R                 2a p\|- q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 125
+bb2:=-1/(a*p*sqrt(q^2-p^2))*atan((p*tanh(a*x))/sqrt(q^2-p^2))
+--R
+--R               p tanh(a x)
+--R          atan(-----------)
+--R                 +-------+
+--R                 | 2    2
+--R                \|q  - p
+--R   (3)  - -----------------
+--R                +-------+
+--R                | 2    2
+--R            a p\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 126
+cc1:=aa.1-bb1
+--R
+--R   (4)
+--R       log
+--R                   4         4     4                  3
+--R                  q sinh(a x)  + 4q cosh(a x)sinh(a x)
+--R                + 
+--R                     4         2     4     2 2          2
+--R                  (6q cosh(a x)  + 2q  - 4p q )sinh(a x)
+--R                + 
+--R                     4         3      4     2 2
+--R                  (4q cosh(a x)  + (4q  - 8p q )cosh(a x))sinh(a x)
+--R                + 
+--R                   4         4      4     2 2          2    4     2 2     4
+--R                  q cosh(a x)  + (2q  - 4p q )cosh(a x)  + q  - 8p q  + 8p
+--R             *
+--R                 +---------+
+--R                 |   2    2
+--R                \|- q  + p
+--R            + 
+--R                     4     3 2          2          4     3 2
+--R              (- 4p q  + 4p q )sinh(a x)  + (- 8p q  + 8p q )cosh(a x)sinh(a x)
+--R            + 
+--R                     4     3 2          2       4      3 2     5
+--R              (- 4p q  + 4p q )cosh(a x)  - 4p q  + 12p q  - 8p
+--R         /
+--R               2         4     2                  3
+--R              q sinh(a x)  + 4q cosh(a x)sinh(a x)
+--R            + 
+--R                 2         2     2     2          2
+--R              (6q cosh(a x)  + 2q  - 4p )sinh(a x)
+--R            + 
+--R                 2         3      2     2                        2         4
+--R              (4q cosh(a x)  + (4q  - 8p )cosh(a x))sinh(a x) + q cosh(a x)
+--R            + 
+--R                 2     2          2    2
+--R              (2q  - 4p )cosh(a x)  + q
+--R     + 
+--R                +---------+
+--R                |   2    2
+--R             - \|- q  + p   - p tanh(a x)
+--R       - log(----------------------------)
+--R               +---------+
+--R               |   2    2
+--R              \|- q  + p   - p tanh(a x)
+--R  /
+--R          +---------+
+--R          |   2    2
+--R     2a p\|- q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 127
+cc2:=aa.2-bb1
+--R
+--R   (5)
+--R                          +---------+
+--R          +-------+       |   2    2
+--R          | 2    2     - \|- q  + p   - p tanh(a x)
+--R       - \|q  - p  log(----------------------------)
+--R                         +---------+
+--R                         |   2    2
+--R                        \|- q  + p   - p tanh(a x)
+--R     + 
+--R       -
+--R              +---------+
+--R              |   2    2
+--R            2\|- q  + p
+--R         *
+--R            atan
+--R                      2         2     2                      2         2    2
+--R                     q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  + q
+--R                   + 
+--R                         2
+--R                     - 2p
+--R                *
+--R                    +-------+
+--R                    | 2    2
+--R                   \|q  - p
+--R              /
+--R                     2     3
+--R                 2p q  - 2p
+--R  /
+--R          +---------+ +-------+
+--R          |   2    2  | 2    2
+--R     2a p\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 128
+cc3:=aa.1-bb2
+--R
+--R   (6)
+--R          +-------+
+--R          | 2    2
+--R         \|q  - p
+--R      *
+--R         log
+--R                     4         4     4                  3
+--R                    q sinh(a x)  + 4q cosh(a x)sinh(a x)
+--R                  + 
+--R                       4         2     4     2 2          2
+--R                    (6q cosh(a x)  + 2q  - 4p q )sinh(a x)
+--R                  + 
+--R                       4         3      4     2 2
+--R                    (4q cosh(a x)  + (4q  - 8p q )cosh(a x))sinh(a x)
+--R                  + 
+--R                     4         4      4     2 2          2    4     2 2     4
+--R                    q cosh(a x)  + (2q  - 4p q )cosh(a x)  + q  - 8p q  + 8p
+--R               *
+--R                   +---------+
+--R                   |   2    2
+--R                  \|- q  + p
+--R              + 
+--R                       4     3 2          2
+--R                (- 4p q  + 4p q )sinh(a x)
+--R              + 
+--R                       4     3 2
+--R                (- 8p q  + 8p q )cosh(a x)sinh(a x)
+--R              + 
+--R                       4     3 2          2       4      3 2     5
+--R                (- 4p q  + 4p q )cosh(a x)  - 4p q  + 12p q  - 8p
+--R           /
+--R                 2         4     2                  3
+--R                q sinh(a x)  + 4q cosh(a x)sinh(a x)
+--R              + 
+--R                   2         2     2     2          2
+--R                (6q cosh(a x)  + 2q  - 4p )sinh(a x)
+--R              + 
+--R                   2         3      2     2                        2         4
+--R                (4q cosh(a x)  + (4q  - 8p )cosh(a x))sinh(a x) + q cosh(a x)
+--R              + 
+--R                   2     2          2    2
+--R                (2q  - 4p )cosh(a x)  + q
+--R     + 
+--R         +---------+
+--R         |   2    2      p tanh(a x)
+--R       2\|- q  + p  atan(-----------)
+--R                           +-------+
+--R                           | 2    2
+--R                          \|q  - p
+--R  /
+--R          +---------+ +-------+
+--R          |   2    2  | 2    2
+--R     2a p\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 129    14:583 Axiom cannot simplify this expression
+cc4:=aa.2-bb2
+--R
+--R   (7)
+--R       -
+--R          atan
+--R                      2         2     2                      2         2    2
+--R                     q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  + q
+--R                   + 
+--R                         2
+--R                     - 2p
+--R              *
+--R                  +-------+
+--R                  | 2    2
+--R                 \|q  - p
+--R            /
+--R                   2     3
+--R               2p q  - 2p
+--R     + 
+--R            p tanh(a x)
+--R       atan(-----------)
+--R              +-------+
+--R              | 2    2
+--R             \|q  - p
+--R  /
+--R         +-------+
+--R         | 2    2
+--R     a p\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.584~~~~~$\displaystyle
+\int{\frac{dx}{p^2+q^2\cosh^2{ax}}}$}
+$$\int{\frac{1}{p^2+q^2\cosh^2{ax}}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{1}{2ap\sqrt{p^2+q^2}}\ln\left(\frac{p\tanh{ax}+\sqrt{p^2+q^2}}
+{p\tanh{ax}-\sqrt{p^2+q^2}}\right)\\
+\\
+\displaystyle
+\frac{1}{ap\sqrt{p^2+q^2}}\tan^{-1}\frac{p\tanh{ax}}{\sqrt{p^2+q^2}}\\
+\end{array}
+\right.
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 130
+aa:=integrate(1/(p^2+q^2*cosh(a*x)^2),x)
+--R 
+--R
+--R   (1)
+--R     log
+--R                 4         4     4                  3
+--R                q sinh(a x)  + 4q cosh(a x)sinh(a x)
+--R              + 
+--R                   4         2     4     2 2          2
+--R                (6q cosh(a x)  + 2q  + 4p q )sinh(a x)
+--R              + 
+--R                   4         3      4     2 2                        4         4
+--R                (4q cosh(a x)  + (4q  + 8p q )cosh(a x))sinh(a x) + q cosh(a x)
+--R              + 
+--R                   4     2 2          2    4     2 2     4
+--R                (2q  + 4p q )cosh(a x)  + q  + 8p q  + 8p
+--R           *
+--R               +-------+
+--R               | 2    2
+--R              \|q  + p
+--R          + 
+--R                   4     3 2          2          4     3 2
+--R            (- 4p q  - 4p q )sinh(a x)  + (- 8p q  - 8p q )cosh(a x)sinh(a x)
+--R          + 
+--R                   4     3 2          2       4      3 2     5
+--R            (- 4p q  - 4p q )cosh(a x)  - 4p q  - 12p q  - 8p
+--R       /
+--R             2         4     2                  3
+--R            q sinh(a x)  + 4q cosh(a x)sinh(a x)
+--R          + 
+--R               2         2     2     2          2
+--R            (6q cosh(a x)  + 2q  + 4p )sinh(a x)
+--R          + 
+--R               2         3      2     2                        2         4
+--R            (4q cosh(a x)  + (4q  + 8p )cosh(a x))sinh(a x) + q cosh(a x)
+--R          + 
+--R               2     2          2    2
+--R            (2q  + 4p )cosh(a x)  + q
+--R  /
+--R          +-------+
+--R          | 2    2
+--R     2a p\|q  + p
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 131
+bb1:=1/(2*a*p*sqrt(p^2+q^2))*log((p*tanh(a*x)+sqrt(p^2+q^2))/(p*tanh(a*x)-sqrt(p^2+q^2)))
+--R
+--R               +-------+
+--R               | 2    2
+--R            - \|q  + p   - p tanh(a x)
+--R        log(--------------------------)
+--R              +-------+
+--R              | 2    2
+--R             \|q  + p   - p tanh(a x)
+--R   (2)  -------------------------------
+--R                      +-------+
+--R                      | 2    2
+--R                 2a p\|q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 132
+bb2:=1/(a*p*sqrt(p^2+q^2))*atan((p*tanh(a*x))/sqrt(p^2+q^2))
+--R
+--R             p tanh(a x)
+--R        atan(-----------)
+--R               +-------+
+--R               | 2    2
+--R              \|q  + p
+--R   (3)  -----------------
+--R              +-------+
+--R              | 2    2
+--R          a p\|q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 133
+cc1:=aa-bb1
+--R
+--R   (4)
+--R       log
+--R                   4         4     4                  3
+--R                  q sinh(a x)  + 4q cosh(a x)sinh(a x)
+--R                + 
+--R                     4         2     4     2 2          2
+--R                  (6q cosh(a x)  + 2q  + 4p q )sinh(a x)
+--R                + 
+--R                     4         3      4     2 2
+--R                  (4q cosh(a x)  + (4q  + 8p q )cosh(a x))sinh(a x)
+--R                + 
+--R                   4         4      4     2 2          2    4     2 2     4
+--R                  q cosh(a x)  + (2q  + 4p q )cosh(a x)  + q  + 8p q  + 8p
+--R             *
+--R                 +-------+
+--R                 | 2    2
+--R                \|q  + p
+--R            + 
+--R                     4     3 2          2          4     3 2
+--R              (- 4p q  - 4p q )sinh(a x)  + (- 8p q  - 8p q )cosh(a x)sinh(a x)
+--R            + 
+--R                     4     3 2          2       4      3 2     5
+--R              (- 4p q  - 4p q )cosh(a x)  - 4p q  - 12p q  - 8p
+--R         /
+--R               2         4     2                  3
+--R              q sinh(a x)  + 4q cosh(a x)sinh(a x)
+--R            + 
+--R                 2         2     2     2          2
+--R              (6q cosh(a x)  + 2q  + 4p )sinh(a x)
+--R            + 
+--R                 2         3      2     2                        2         4
+--R              (4q cosh(a x)  + (4q  + 8p )cosh(a x))sinh(a x) + q cosh(a x)
+--R            + 
+--R                 2     2          2    2
+--R              (2q  + 4p )cosh(a x)  + q
+--R     + 
+--R                +-------+
+--R                | 2    2
+--R             - \|q  + p   - p tanh(a x)
+--R       - log(--------------------------)
+--R               +-------+
+--R               | 2    2
+--R              \|q  + p   - p tanh(a x)
+--R  /
+--R          +-------+
+--R          | 2    2
+--R     2a p\|q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 134    14:584 Axiom cannot simplify this expression
+cc2:=aa-bb2
+--R
+--R   (5)
+--R       log
+--R                   4         4     4                  3
+--R                  q sinh(a x)  + 4q cosh(a x)sinh(a x)
+--R                + 
+--R                     4         2     4     2 2          2
+--R                  (6q cosh(a x)  + 2q  + 4p q )sinh(a x)
+--R                + 
+--R                     4         3      4     2 2
+--R                  (4q cosh(a x)  + (4q  + 8p q )cosh(a x))sinh(a x)
+--R                + 
+--R                   4         4      4     2 2          2    4     2 2     4
+--R                  q cosh(a x)  + (2q  + 4p q )cosh(a x)  + q  + 8p q  + 8p
+--R             *
+--R                 +-------+
+--R                 | 2    2
+--R                \|q  + p
+--R            + 
+--R                     4     3 2          2          4     3 2
+--R              (- 4p q  - 4p q )sinh(a x)  + (- 8p q  - 8p q )cosh(a x)sinh(a x)
+--R            + 
+--R                     4     3 2          2       4      3 2     5
+--R              (- 4p q  - 4p q )cosh(a x)  - 4p q  - 12p q  - 8p
+--R         /
+--R               2         4     2                  3
+--R              q sinh(a x)  + 4q cosh(a x)sinh(a x)
+--R            + 
+--R                 2         2     2     2          2
+--R              (6q cosh(a x)  + 2q  + 4p )sinh(a x)
+--R            + 
+--R                 2         3      2     2                        2         4
+--R              (4q cosh(a x)  + (4q  + 8p )cosh(a x))sinh(a x) + q cosh(a x)
+--R            + 
+--R                 2     2          2    2
+--R              (2q  + 4p )cosh(a x)  + q
+--R     + 
+--R               p tanh(a x)
+--R       - 2atan(-----------)
+--R                 +-------+
+--R                 | 2    2
+--R                \|q  + p
+--R  /
+--R          +-------+
+--R          | 2    2
+--R     2a p\|q  + p
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.585~~~~~$\displaystyle
+\int{x^m\cosh{ax}}~dx$}
+$$\int{x^m\cosh{ax}}=
+\frac{x^m\sinh{ax}}{a}-\frac{m}{a}\int{x^{m-1}\sinh{ax}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 135    14:585 Axiom cannot compute this integral
+aa:=integrate(x^m*cosh(a*x),x)
+--R 
+--R
+--R           x
+--R         ++              m
+--I   (1)   |   cosh(%N a)%N d%N
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.586~~~~~$\displaystyle
+\int{\cosh^n{ax}}~dx$}
+$$\int{\cosh^n{ax}}=
+\frac{\cosh^{n-1}{ax}\sinh{ax}}{an}+\frac{n-1}{n}\int{\cosh^{n-2}{ax}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 136    14:586 Axiom cannot compute this integral
+aa:=integrate(cosh(a*x)^n,x)
+--R 
+--R
+--R           x
+--R         ++            n
+--I   (1)   |   cosh(%N a) d%N
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.587~~~~~$\displaystyle
+\int{\frac{\cosh{ax}}{x^n}}~dx$}
+$$\int{\frac{\cosh{ax}}{x^n}}=
+\frac{-\cosh{ax}}{(n-1)x^{n-1}}
++\frac{a}{n-1}\int{\frac{\sinh{ax}}{x^{n-1}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 137    14:587 Axiom cannot compute this integral
+aa:=integrate(cosh(a*x)/x^n,x)
+--R 
+--R
+--R           x
+--I         ++  cosh(%N a)
+--I   (1)   |   ---------- d%N
+--R        ++         n
+--I                 %N
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.588~~~~~$\displaystyle
+\int{\frac{dx}{\cosh^n{ax}}}~dx$}
+$$\int{\frac{1}{\cosh^n{ax}}}=
+\frac{\sinh{ax}}{a(n-1)\cosh^{n-1}{ax}}
++\frac{n-2}{n-1}\int{\frac{1}{\cosh^{n-2}{ax}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 138    14:588 Axiom cannot compute this integral
+aa:=integrate(1/cosh(a*x)^n,x)
+--R 
+--R
+--R           x
+--R         ++       1
+--I   (1)   |   ----------- d%N
+--R        ++             n
+--I             cosh(%N a)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.589~~~~~$\displaystyle
+\int{\frac{x}{\cosh^n{ax}}}~dx$}
+$$\int{\frac{x}{\cosh^n{ax}}}=
+\frac{x\sinh{ax}}{a(n-1)\cosh^{n-1}{ax}}
++\frac{1}{(n-1)(n-2)a^2\cosh^{n-2}{ax}}
++\frac{n-2}{n-1}\int{\frac{x}{\cosh^{n-2}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 139    14:589 Axiom cannot compute this integral
+aa:=integrate(1/cosh(a*x)^n,x)
+--R 
+--R
+--R           x
+--R         ++       1
+--I   (1)   |   ----------- d%N
+--R        ++             n
+--I             cosh(%N a)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 pp88-89
+\end{thebibliography}
+\end{document}
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diff --git a/src/axiom-website/CATS/schaum29.input.pamphlet b/src/axiom-website/CATS/schaum29.input.pamphlet
new file mode 100644
index 0000000..9c79630
--- /dev/null
+++ b/src/axiom-website/CATS/schaum29.input.pamphlet
@@ -0,0 +1,1431 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum29.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.590~~~~~$\displaystyle
+\int{\sinh{ax}\cosh{ax}}~dx$}
+$$\int{\sinh{ax}\cosh{ax}}=
+\frac{\sinh^2{ax}}{2a}
+$$
+&lt;&lt;*&gt;&gt;=
+)spool schaum29.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1
+aa:=integrate(sinh(a*x)*cosh(a*x),x)
+--R 
+--R
+--R                 2            2
+--R        sinh(a x)  + cosh(a x)
+--R   (1)  -----------------------
+--R                   4a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 2
+bb:=sinh(a*x)^2/(2*a)
+--R
+--R                 2
+--R        sinh(a x)
+--R   (2)  ----------
+--R            2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3
+cc:=aa-bb
+--R
+--R                   2            2
+--R        - sinh(a x)  + cosh(a x)
+--R   (3)  -------------------------
+--R                    4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 4
+sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
+--R
+--R               2    cosh(2x) - 1
+--R   (4)  sinh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 5
+dd:=sinhsqrrule cc
+--R
+--R                                 2
+--R        - cosh(2a x) + 2cosh(a x)  + 1
+--R   (5)  ------------------------------
+--R                      8a
+--R                                                     Type: Expression Integer
+--E
+
+--S 6
+coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
+--R
+--R               2    cosh(2x) + 1
+--R   (6)  cosh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 7      14:590 Schaums and Axiom differ by a constant
+ee:=coshsqrrule dd
+--R
+--R         1
+--R   (7)  --
+--R        4a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.591~~~~~$\displaystyle
+\int{\sinh{px}\cosh{qx}}~dx$}
+$$\int{\sinh{px}\cosh{qx}}=
+\frac{\cosh(p+q)x}{2(p+q)}+\frac{\cosh(p-q)x}{2(p-q)}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 8
+aa:=integrate(sinh(p*x)*cosh(q*x),x)
+--R 
+--R
+--R        - q sinh(p x)sinh(q x) + p cosh(p x)cosh(q x)
+--R   (1)  ---------------------------------------------
+--R           2    2          2       2    2          2
+--R         (q  - p )sinh(p x)  + (- q  + p )cosh(p x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 9
+bb:=(cosh(p+q)*x)/(2*(p+q))+(cosh(p-q)*x)/(2*(p-q))
+--R
+--R        (q - p)x cosh(q + p) + (- q - p)x cosh(q - p)
+--R   (2)  ---------------------------------------------
+--R                            2     2
+--R                          2q  - 2p
+--R                                                     Type: Expression Integer
+--E
+
+--S 10     14:591 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R       - 2q sinh(p x)sinh(q x)
+--R     + 
+--R                                                               2
+--R       ((- q + p)x cosh(q + p) + (q + p)x cosh(q - p))sinh(p x)
+--R     + 
+--R       2p cosh(p x)cosh(q x)
+--R     + 
+--R                                                               2
+--R       ((q - p)x cosh(q + p) + (- q - p)x cosh(q - p))cosh(p x)
+--R  /
+--R        2     2          2        2     2          2
+--R     (2q  - 2p )sinh(p x)  + (- 2q  + 2p )cosh(p x)
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.592~~~~~$\displaystyle
+\int{\sinh^n{ax}\cosh{ax}}~dx$}
+$$\int{\sinh^n{ax}\cosh{ax}}=
+\frac{\sinh^{n+1}{ax}}{(n+1)a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 11
+aa:=integrate(sinh(a*x)^n*cosh(a*x),x)
+--R 
+--R
+--R        - sinh(a x)sinh(n log(sinh(a x))) - sinh(a x)cosh(n log(sinh(a x)))
+--R   (1)  -------------------------------------------------------------------
+--R                                      2                       2
+--R                    (a n + a)sinh(a x)  + (- a n - a)cosh(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 12
+bb:=sinh(a*x)/((n+1)*a)
+--R
+--R        sinh(a x)
+--R   (2)  ---------
+--R         a n + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 13     14:592 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R       - sinh(a x)sinh(n log(sinh(a x))) - sinh(a x)cosh(n log(sinh(a x)))
+--R     + 
+--R                  3            2
+--R       - sinh(a x)  + cosh(a x) sinh(a x)
+--R  /
+--R                       2                       2
+--R     (a n + a)sinh(a x)  + (- a n - a)cosh(a x)
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.593~~~~~$\displaystyle
+\int{\cosh^n{ax}\sinh{ax}}~dx$}
+$$\int{\cosh^n{ax}\sinh{ax}}=
+\frac{\cosh^{n+1}{ax}}{(n+1)a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 14
+aa:=integrate(cosh(a*x)^n*sinh(a*x),x)
+--R 
+--R
+--R        - cosh(a x)sinh(n log(cosh(a x))) - cosh(a x)cosh(n log(cosh(a x)))
+--R   (1)  -------------------------------------------------------------------
+--R                                      2                       2
+--R                    (a n + a)sinh(a x)  + (- a n - a)cosh(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 15
+bb:=cosh(a*x)^(n+1)/((n+1)*a)
+--R
+--R                 n + 1
+--R        cosh(a x)
+--R   (2)  --------------
+--R            a n + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 16     14:593 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R       - cosh(a x)sinh(n log(cosh(a x))) - cosh(a x)cosh(n log(cosh(a x)))
+--R     + 
+--R                   2            2          n + 1
+--R       (- sinh(a x)  + cosh(a x) )cosh(a x)
+--R  /
+--R                       2                       2
+--R     (a n + a)sinh(a x)  + (- a n - a)cosh(a x)
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.594~~~~~$\displaystyle
+\int{\sinh^2{ax}\cosh^2{ax}}~dx$}
+$$\int{\sinh^2{ax}\cosh^2{ax}}=
+\frac{\sinh{4ax}}{32a}-\frac{x}{8}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 17
+aa:=integrate(sinh(a*x)^2*cosh(a*x)^2,x)
+--R 
+--R
+--R                          3            3
+--R        cosh(a x)sinh(a x)  + cosh(a x) sinh(a x) - a x
+--R   (1)  -----------------------------------------------
+--R                               8a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 18
+bb:=sinh(4*a*x)/(32*a)-x/8
+--R
+--R        sinh(4a x) - 4a x
+--R   (2)  -----------------
+--R               32a
+--R                                                     Type: Expression Integer
+--E
+
+--S 19     14:594 Schaums and Axiom agree
+cc:=complexNormalize(aa-bb)
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.595~~~~~$\displaystyle
+\int{\frac{dx}{\sinh{ax}\cosh{ax}}}$}
+$$\int{\frac{1}{\sinh{ax}\cosh{ax}}}=
+\frac{1}{a}\ln\tanh{ax}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 20
+aa:=integrate(1/(sinh(a*x)*cosh(a*x)),x)
+--R 
+--R
+--R                      2cosh(a x)                     2sinh(a x)
+--R        - log(- ---------------------) + log(- ---------------------)
+--R                sinh(a x) - cosh(a x)          sinh(a x) - cosh(a x)
+--R   (1)  -------------------------------------------------------------
+--R                                      a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 21
+bb:=1/a*log(tanh(a*x))
+--R
+--R        log(tanh(a x))
+--R   (2)  --------------
+--R               a
+--R                                                     Type: Expression Integer
+--E
+
+--S 22
+cc:=aa-bb
+--R
+--R   (3)
+--R                                      2cosh(a x)
+--R       - log(tanh(a x)) - log(- ---------------------)
+--R                                sinh(a x) - cosh(a x)
+--R     + 
+--R                   2sinh(a x)
+--R       log(- ---------------------)
+--R             sinh(a x) - cosh(a x)
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 23
+dd:=expandLog cc
+--R
+--R        - log(tanh(a x)) + log(sinh(a x)) - log(cosh(a x))
+--R   (4)  --------------------------------------------------
+--R                                 a
+--R                                                     Type: Expression Integer
+--E
+
+--S 24
+tanhrule:=rule(tanh(x) == sinh(x)/cosh(x))
+--R
+--R                   sinh(x)
+--R   (5)  tanh(x) == -------
+--R                   cosh(x)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 25
+ee:=tanhrule dd
+--R
+--R                             sinh(a x)
+--R        log(sinh(a x)) - log(---------) - log(cosh(a x))
+--R                             cosh(a x)
+--R   (6)  ------------------------------------------------
+--R                                a
+--R                                                     Type: Expression Integer
+--E
+
+--S 26     14:595 Schaums and Axiom agree
+ff:=expandLog ee
+--R
+--R   (7)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.596~~~~~$\displaystyle
+\int{\frac{dx}{\sinh^2{ax}\cosh{ax}}}$}
+$$\int{\frac{1}{\sinh^2{ax}\cosh{ax}}}=
+-\frac{1}{a}\tan^{-1}\sinh{ax}-\frac{{\rm csch~}{ax}}{a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 27
+aa:=integrate(1/(sinh(a*x)^2*cosh(a*x)),x)
+--R
+--R   (1)
+--R                      2                                   2
+--R         (- 2sinh(a x)  - 4cosh(a x)sinh(a x) - 2cosh(a x)  + 2)
+--R      *
+--R         atan(sinh(a x) + cosh(a x))
+--R     + 
+--R       - 2sinh(a x) - 2cosh(a x)
+--R  /
+--R                2                                      2
+--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 28
+bb:=-1/a*atan(sinh(a*x)-csch(a*x))/a
+--R
+--R          atan(sinh(a x) - csch(a x))
+--R   (2)  - ---------------------------
+--R                        2
+--R                       a
+--R                                                     Type: Expression Integer
+--E
+
+--S 29     14:596 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R                        2                                       2
+--R         (- 2a sinh(a x)  - 4a cosh(a x)sinh(a x) - 2a cosh(a x)  + 2a)
+--R      *
+--R         atan(sinh(a x) + cosh(a x))
+--R     + 
+--R                   2                                  2
+--R         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1)
+--R      *
+--R         atan(sinh(a x) - csch(a x))
+--R     + 
+--R       - 2a sinh(a x) - 2a cosh(a x)
+--R  /
+--R      2         2     2                      2         2    2
+--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.597~~~~~$\displaystyle
+\int{\frac{dx}{\sinh{ax}\cosh^2{ax}}}$}
+$$\int{\frac{1}{\sinh{ax}\cosh^2{ax}}}=
+\frac{{\rm sech~}{ax}}{a}+\frac{1}{a}\ln\tanh{\frac{ax}{2}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 30
+aa:=integrate(1/(sinh(a*x)*cosh(a*x)^2),x)
+--R 
+--R
+--R   (1)
+--R                     2                                  2
+--R         (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)
+--R      *
+--R         log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R                   2                                  2
+--R         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1)
+--R      *
+--R         log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R       2sinh(a x) + 2cosh(a x)
+--R  /
+--R                2                                      2
+--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 31
+bb:=sech(a*x)/a+1/a*log(tanh((a*x)/2))
+--R
+--R                 a x
+--R        log(tanh(---)) + sech(a x)
+--R                  2
+--R   (2)  --------------------------
+--R                     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 32
+cc:=aa-bb
+--R
+--R   (3)
+--R                   2                                  2              a x
+--R       (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)log(tanh(---))
+--R                                                                      2
+--R     + 
+--R                     2                                  2
+--R         (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)
+--R      *
+--R         log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R                   2                                  2
+--R         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1)
+--R      *
+--R         log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R                           2
+--R       - sech(a x)sinh(a x)  + (- 2cosh(a x)sech(a x) + 2)sinh(a x)
+--R     + 
+--R                   2
+--R       (- cosh(a x)  - 1)sech(a x) + 2cosh(a x)
+--R  /
+--R                2                                      2
+--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 33
+sechrule:=rule(sech(x) == 1/cosh(x))
+--R
+--R                      1
+--R   (4)  sech(x) == -------
+--R                   cosh(x)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 34
+dd:=sechrule cc
+--R
+--R   (5)
+--R                              2             2                     3
+--R         (- cosh(a x)sinh(a x)  - 2cosh(a x) sinh(a x) - cosh(a x)  - cosh(a x))
+--R      *
+--R                  a x
+--R         log(tanh(---))
+--R                   2
+--R     + 
+--R                              2             2                     3
+--R         (- cosh(a x)sinh(a x)  - 2cosh(a x) sinh(a x) - cosh(a x)  - cosh(a x))
+--R      *
+--R         log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R                            2             2                     3
+--R         (cosh(a x)sinh(a x)  + 2cosh(a x) sinh(a x) + cosh(a x)  + cosh(a x))
+--R      *
+--R         log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R                  2            2
+--R       - sinh(a x)  + cosh(a x)  - 1
+--R  /
+--R                         2               2                       3
+--R     a cosh(a x)sinh(a x)  + 2a cosh(a x) sinh(a x) + a cosh(a x)  + a cosh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 35
+tanhrule:=rule(tanh(x) == sinh(x)/cosh(x))
+--R
+--R                   sinh(x)
+--R   (6)  tanh(x) == -------
+--R                   cosh(x)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 36
+ee:=tanhrule dd
+--R
+--R   (7)
+--R                              2             2                     3
+--R         (- cosh(a x)sinh(a x)  - 2cosh(a x) sinh(a x) - cosh(a x)  - cosh(a x))
+--R      *
+--R         log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R                            2             2                     3
+--R         (cosh(a x)sinh(a x)  + 2cosh(a x) sinh(a x) + cosh(a x)  + cosh(a x))
+--R      *
+--R         log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R                              2             2                     3
+--R         (- cosh(a x)sinh(a x)  - 2cosh(a x) sinh(a x) - cosh(a x)  - cosh(a x))
+--R      *
+--R                  a x
+--R             sinh(---)
+--R                   2
+--R         log(---------)
+--R                  a x
+--R             cosh(---)
+--R                   2
+--R     + 
+--R                  2            2
+--R       - sinh(a x)  + cosh(a x)  - 1
+--R  /
+--R                         2               2                       3
+--R     a cosh(a x)sinh(a x)  + 2a cosh(a x) sinh(a x) + a cosh(a x)  + a cosh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 37
+coshcuberule:=rule(cosh(x)^3 == 1/4*cosh(3*x)-3/4*cosh(x))
+--R
+--R               3    cosh(3x) - 3cosh(x)
+--R   (8)  cosh(x)  == -------------------
+--R                             4
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 38
+ff:=coshcuberule ee
+--R
+--R   (9)
+--R                                  2             2
+--R             - 4cosh(a x)sinh(a x)  - 8cosh(a x) sinh(a x) - cosh(3a x)
+--R           + 
+--R             - cosh(a x)
+--R      *
+--R         log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R                             2             2
+--R         (4cosh(a x)sinh(a x)  + 8cosh(a x) sinh(a x) + cosh(3a x) + cosh(a x))
+--R      *
+--R         log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R                                  2             2
+--R             - 4cosh(a x)sinh(a x)  - 8cosh(a x) sinh(a x) - cosh(3a x)
+--R           + 
+--R             - cosh(a x)
+--R      *
+--R                  a x
+--R             sinh(---)
+--R                   2
+--R         log(---------)
+--R                  a x
+--R             cosh(---)
+--R                   2
+--R     + 
+--R                   2             2
+--R       - 4sinh(a x)  + 4cosh(a x)  - 4
+--R  /
+--R                            2               2
+--R       4a cosh(a x)sinh(a x)  + 8a cosh(a x) sinh(a x) + a cosh(3a x)
+--R     + 
+--R       a cosh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 39
+coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
+--R
+--R                2    cosh(2x) + 1
+--R   (10)  cosh(x)  == ------------
+--R                           2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 40
+gg:=coshsqrrule ff
+--R
+--R   (11)
+--R                                2
+--R           - 4cosh(a x)sinh(a x)  + (- 4cosh(2a x) - 4)sinh(a x) - cosh(3a x)
+--R         + 
+--R           - cosh(a x)
+--R      *
+--R         log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R                              2
+--R           4cosh(a x)sinh(a x)  + (4cosh(2a x) + 4)sinh(a x) + cosh(3a x)
+--R         + 
+--R           cosh(a x)
+--R      *
+--R         log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R                                2
+--R           - 4cosh(a x)sinh(a x)  + (- 4cosh(2a x) - 4)sinh(a x) - cosh(3a x)
+--R         + 
+--R           - cosh(a x)
+--R      *
+--R                  a x
+--R             sinh(---)
+--R                   2
+--R         log(---------)
+--R                  a x
+--R             cosh(---)
+--R                   2
+--R     + 
+--R                   2
+--R       - 4sinh(a x)  + 2cosh(2a x) - 2
+--R  /
+--R                            2
+--R       4a cosh(a x)sinh(a x)  + (4a cosh(2a x) + 4a)sinh(a x) + a cosh(3a x)
+--R     + 
+--R       a cosh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 41
+sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
+--R
+--R                2    cosh(2x) - 1
+--R   (12)  sinh(x)  == ------------
+--R                           2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 42
+hh:=sinhsqrrule gg
+--R
+--R   (13)
+--R       - log(sinh(a x) + cosh(a x) + 1) + log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R                  a x
+--R             sinh(---)
+--R                   2
+--R       - log(---------)
+--R                  a x
+--R             cosh(---)
+--R                   2
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 43
+ii:=expandLog hh
+--R
+--R   (14)
+--R       - log(sinh(a x) + cosh(a x) + 1) + log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R                  a x              a x
+--R       - log(sinh(---)) + log(cosh(---))
+--R                   2                2
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 44     14:597 Schaums and Axiom agree
+jj:=complexNormalize ii
+--R
+--R   (15)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.598~~~~~$\displaystyle
+\int{\frac{dx}{\sinh^2{ax}\cosh^2{ax}}}$}
+$$\int{\frac{1}{\sinh^2{ax}\cosh^2{ax}}}=
+-\frac{2\coth{2ax}}{a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 45
+aa:=integrate(1/(sinh(a*x)^2*cosh(a*x)^2),x)
+--R 
+--R
+--R   (1)
+--R   -
+--R        4
+--R     /
+--R                     4                        3               2         2
+--R          a sinh(a x)  + 4a cosh(a x)sinh(a x)  + 6a cosh(a x) sinh(a x)
+--R        + 
+--R                      3                       4
+--R          4a cosh(a x) sinh(a x) + a cosh(a x)  - a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 46
+bb:=-(2*coth(2*a*x))/a
+--R
+--R          2coth(2a x)
+--R   (2)  - -----------
+--R               a
+--R                                                     Type: Expression Integer
+--E
+
+--S 47     14:598 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R                           4                                3
+--R       2coth(2a x)sinh(a x)  + 8cosh(a x)coth(2a x)sinh(a x)
+--R     + 
+--R                  2                   2             3
+--R       12cosh(a x) coth(2a x)sinh(a x)  + 8cosh(a x) coth(2a x)sinh(a x)
+--R     + 
+--R                  4
+--R       (2cosh(a x)  - 2)coth(2a x) - 4
+--R  /
+--R                  4                        3               2         2
+--R       a sinh(a x)  + 4a cosh(a x)sinh(a x)  + 6a cosh(a x) sinh(a x)
+--R     + 
+--R                   3                       4
+--R       4a cosh(a x) sinh(a x) + a cosh(a x)  - a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.599~~~~~$\displaystyle
+\int{\frac{\sinh^2{ax}}{\cosh{ax}}}~dx$}
+$$\int{\frac{\sinh^2{ax}}{\cosh{ax}}}~dx=
+\frac{\sinh{ax}}{a}-\frac{1}{a}\tan^{-1}\sinh{ax}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 48
+aa:=integrate(sinh(a*x)^2/cosh(a*x),x)
+--R 
+--R
+--R   (1)
+--R                                                                         2
+--R       (- 4sinh(a x) - 4cosh(a x))atan(sinh(a x) + cosh(a x)) + sinh(a x)
+--R     + 
+--R                                      2
+--R       2cosh(a x)sinh(a x) + cosh(a x)  - 1
+--R  /
+--R     2a sinh(a x) + 2a cosh(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 49
+bb:=sinh(a*x)/a-1/a*atan(sinh(a*x))
+--R
+--R        - atan(sinh(a x)) + sinh(a x)
+--R   (2)  -----------------------------
+--R                      a
+--R                                                     Type: Expression Integer
+--E
+
+--S 50     14:599 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R       (- 4sinh(a x) - 4cosh(a x))atan(sinh(a x) + cosh(a x))
+--R     + 
+--R                                                           2            2
+--R       (2sinh(a x) + 2cosh(a x))atan(sinh(a x)) - sinh(a x)  + cosh(a x)  - 1
+--R  /
+--R     2a sinh(a x) + 2a cosh(a x)
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.600~~~~~$\displaystyle
+\int{\frac{\cosh^2{ax}}{\sinh{ax}}}~dx$}
+$$\int{\frac{\cosh^2{ax}}{\sinh{ax}}}=
+\frac{\cosh{ax}}{a}+\frac{1}{a}\ln\tanh{\frac{ax}{2}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 51
+aa:=integrate(cosh(a*x)^2/sinh(a*x),x)
+--R 
+--R
+--R   (1)
+--R       (- 2sinh(a x) - 2cosh(a x))log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R                                                                          2
+--R       (2sinh(a x) + 2cosh(a x))log(sinh(a x) + cosh(a x) - 1) + sinh(a x)
+--R     + 
+--R                                      2
+--R       2cosh(a x)sinh(a x) + cosh(a x)  + 1
+--R  /
+--R     2a sinh(a x) + 2a cosh(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 52
+bb:=cosh(a*x)/a+1/a*log(tanh((a*x)/2))
+--R
+--R                 a x
+--R        log(tanh(---)) + cosh(a x)
+--R                  2
+--R   (2)  --------------------------
+--R                     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 53     14:600 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R                                           a x
+--R       (- 2sinh(a x) - 2cosh(a x))log(tanh(---))
+--R                                            2
+--R     + 
+--R       (- 2sinh(a x) - 2cosh(a x))log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R                                                                          2
+--R       (2sinh(a x) + 2cosh(a x))log(sinh(a x) + cosh(a x) - 1) + sinh(a x)
+--R     + 
+--R                  2
+--R       - cosh(a x)  + 1
+--R  /
+--R     2a sinh(a x) + 2a cosh(a x)
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.601~~~~~$\displaystyle
+\int{\frac{dx}{\cosh{ax}(1+\sinh{ax})}}$}
+$$\int{\frac{1}{\cosh{ax}(1+\sinh{ax})}}=
+\frac{1}{2a}\ln\left(\frac{1+\sinh{ax}}{\cosh{ax}}\right)
++\frac{1}{a}\tan^{-1}{e^{ax}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 54
+aa:=integrate(1/(cosh(a*x)*(1+sinh(a*x))),x)
+--R 
+--R
+--R   (1)
+--R                     2cosh(a x)                - 2sinh(a x) - 2
+--R       - log(- ---------------------) + log(---------------------)
+--R               sinh(a x) - cosh(a x)        sinh(a x) - cosh(a x)
+--R     + 
+--R       2atan(sinh(a x) + cosh(a x))
+--R  /
+--R     2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 55
+bb:=1/(2*a)*log((1+sinh(a*x))/cosh(a*x))+1/a*atan(%e^(a*x))
+--R
+--R            sinh(a x) + 1            a x
+--R        log(-------------) + 2atan(%e   )
+--R              cosh(a x)
+--R   (2)  ---------------------------------
+--R                        2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 56
+cc:=aa-bb
+--R
+--R   (3)
+--R             sinh(a x) + 1                2cosh(a x)
+--R       - log(-------------) - log(- ---------------------)
+--R               cosh(a x)            sinh(a x) - cosh(a x)
+--R     + 
+--R              - 2sinh(a x) - 2                                             a x
+--R       log(---------------------) + 2atan(sinh(a x) + cosh(a x)) - 2atan(%e   )
+--R           sinh(a x) - cosh(a x)
+--R  /
+--R     2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 57
+dd:=expandLog cc
+--R
+--R                                             a x
+--R        atan(sinh(a x) + cosh(a x)) - atan(%e   )
+--R   (4)  -----------------------------------------
+--R                            a
+--R                                                     Type: Expression Integer
+--E
+
+--S 58
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (5)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 59
+ee:=atanrule dd
+--R
+--R                   a x
+--R               - %e    + %i           - sinh(a x) - cosh(a x) + %i
+--R        %i log(------------) - %i log(----------------------------)
+--R                  a x                  sinh(a x) + cosh(a x) + %i
+--R                %e    + %i
+--R   (6)  -----------------------------------------------------------
+--R                                     2a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 60
+ff:=expandLog ee
+--R
+--R   (7)
+--R       %i log(sinh(a x) + cosh(a x) + %i) - %i log(sinh(a x) + cosh(a x) - %i)
+--R     + 
+--R                  a x                  a x
+--R       - %i log(%e    + %i) + %i log(%e    - %i)
+--R  /
+--R     2a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 61     14:601 Schaums and Axiom agree
+gg:=complexNormalize ff
+--R
+--R   (8)  0
+--R                                             Type: Expression Complex Integer
+--E
+@
+
+\section{\cite{1}:14.602~~~~~$\displaystyle
+\int{\frac{dx}{\sinh{ax}(\cosh{ax}+1)}}$}
+$$\int{\frac{1}{\sinh{ax}(\cosh{ax}+1)}}=
+\frac{1}{2a}\ln\tanh\frac{ax}{2}+\frac{1}{2a(\cosh{ax}+1)}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 62
+aa:=integrate(1/(sinh(a*x)*(cosh(a*x)+1)),x)
+--R 
+--R
+--R   (1)
+--R                      2                                          2
+--R           - sinh(a x)  + (- 2cosh(a x) - 2)sinh(a x) - cosh(a x)  - 2cosh(a x)
+--R         + 
+--R           - 1
+--R      *
+--R         log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R                   2                                        2
+--R         (sinh(a x)  + (2cosh(a x) + 2)sinh(a x) + cosh(a x)  + 2cosh(a x) + 1)
+--R      *
+--R         log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R       2sinh(a x) + 2cosh(a x)
+--R  /
+--R                   2                                              2
+--R       2a sinh(a x)  + (4a cosh(a x) + 4a)sinh(a x) + 2a cosh(a x)
+--R     + 
+--R       4a cosh(a x) + 2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 63
+bb:=1/(2*a)*log(tanh((a*x)/2))+1/(2*a*(cosh(a*x)+1))
+--R
+--R                                a x
+--R        (cosh(a x) + 1)log(tanh(---)) + 1
+--R                                 2
+--R   (2)  ---------------------------------
+--R                2a cosh(a x) + 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 64
+cc:=aa-bb
+--R
+--R   (3)
+--R                                     2
+--R           (- cosh(a x) - 1)sinh(a x)
+--R         + 
+--R                        2                                       3             2
+--R           (- 2cosh(a x)  - 4cosh(a x) - 2)sinh(a x) - cosh(a x)  - 3cosh(a x)
+--R         + 
+--R           - 3cosh(a x) - 1
+--R      *
+--R                  a x
+--R         log(tanh(---))
+--R                   2
+--R     + 
+--R                                     2
+--R           (- cosh(a x) - 1)sinh(a x)
+--R         + 
+--R                        2                                       3             2
+--R           (- 2cosh(a x)  - 4cosh(a x) - 2)sinh(a x) - cosh(a x)  - 3cosh(a x)
+--R         + 
+--R           - 3cosh(a x) - 1
+--R      *
+--R         log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R                                   2              2
+--R           (cosh(a x) + 1)sinh(a x)  + (2cosh(a x)  + 4cosh(a x) + 2)sinh(a x)
+--R         + 
+--R                    3             2
+--R           cosh(a x)  + 3cosh(a x)  + 3cosh(a x) + 1
+--R      *
+--R         log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R                  2            2
+--R       - sinh(a x)  + cosh(a x)  - 1
+--R  /
+--R                                   2
+--R       (2a cosh(a x) + 2a)sinh(a x)
+--R     + 
+--R                    2                                             3
+--R       (4a cosh(a x)  + 8a cosh(a x) + 4a)sinh(a x) + 2a cosh(a x)
+--R     + 
+--R                   2
+--R       6a cosh(a x)  + 6a cosh(a x) + 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 65
+coshcuberule:=rule(cosh(x)^3 == 1/4*cosh(3*x)-3/4*cosh(x))
+--R
+--R               3    cosh(3x) - 3cosh(x)
+--R   (4)  cosh(x)  == -------------------
+--R                             4
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 66
+dd:=coshcuberule cc
+--R
+--R   (5)
+--R                                      2
+--R           (- 4cosh(a x) - 4)sinh(a x)
+--R         + 
+--R                        2
+--R           (- 8cosh(a x)  - 16cosh(a x) - 8)sinh(a x) - cosh(3a x)
+--R         + 
+--R                        2
+--R           - 12cosh(a x)  - 9cosh(a x) - 4
+--R      *
+--R                  a x
+--R         log(tanh(---))
+--R                   2
+--R     + 
+--R                                      2
+--R           (- 4cosh(a x) - 4)sinh(a x)
+--R         + 
+--R                        2
+--R           (- 8cosh(a x)  - 16cosh(a x) - 8)sinh(a x) - cosh(3a x)
+--R         + 
+--R                        2
+--R           - 12cosh(a x)  - 9cosh(a x) - 4
+--R      *
+--R         log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R                                    2              2
+--R           (4cosh(a x) + 4)sinh(a x)  + (8cosh(a x)  + 16cosh(a x) + 8)sinh(a x)
+--R         + 
+--R                                   2
+--R           cosh(3a x) + 12cosh(a x)  + 9cosh(a x) + 4
+--R      *
+--R         log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R                   2             2
+--R       - 4sinh(a x)  + 4cosh(a x)  - 4
+--R  /
+--R                                   2
+--R       (8a cosh(a x) + 8a)sinh(a x)
+--R     + 
+--R                     2
+--R       (16a cosh(a x)  + 32a cosh(a x) + 16a)sinh(a x) + 2a cosh(3a x)
+--R     + 
+--R                    2
+--R       24a cosh(a x)  + 18a cosh(a x) + 8a
+--R                                                     Type: Expression Integer
+--E
+
+--S 67
+sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
+--R
+--R               2    cosh(2x) - 1
+--R   (6)  sinh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 68
+ee:=sinhsqrrule dd
+--R
+--R   (7)
+--R                        2
+--R           (- 8cosh(a x)  - 16cosh(a x) - 8)sinh(a x) - cosh(3a x)
+--R         + 
+--R                                                     2
+--R           (- 2cosh(a x) - 2)cosh(2a x) - 12cosh(a x)  - 7cosh(a x) - 2
+--R      *
+--R                  a x
+--R         log(tanh(---))
+--R                   2
+--R     + 
+--R                        2
+--R           (- 8cosh(a x)  - 16cosh(a x) - 8)sinh(a x) - cosh(3a x)
+--R         + 
+--R                                                     2
+--R           (- 2cosh(a x) - 2)cosh(2a x) - 12cosh(a x)  - 7cosh(a x) - 2
+--R      *
+--R         log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R                      2
+--R           (8cosh(a x)  + 16cosh(a x) + 8)sinh(a x) + cosh(3a x)
+--R         + 
+--R                                                   2
+--R           (2cosh(a x) + 2)cosh(2a x) + 12cosh(a x)  + 7cosh(a x) + 2
+--R      *
+--R         log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R                                 2
+--R       - 2cosh(2a x) + 4cosh(a x)  - 2
+--R  /
+--R                     2
+--R       (16a cosh(a x)  + 32a cosh(a x) + 16a)sinh(a x) + 2a cosh(3a x)
+--R     + 
+--R                                                    2
+--R       (4a cosh(a x) + 4a)cosh(2a x) + 24a cosh(a x)  + 14a cosh(a x) + 4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 69
+coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
+--R
+--R               2    cosh(2x) + 1
+--R   (8)  cosh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 70
+ff:=coshsqrrule ee
+--R
+--R   (9)
+--R                  a x
+--R       - log(tanh(---)) - log(sinh(a x) + cosh(a x) + 1)
+--R                   2
+--R     + 
+--R       log(sinh(a x) + cosh(a x) - 1)
+--R  /
+--R     2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 71     14:602 Schaums and Axiom agree
+gg:=complexNormalize ff
+--R
+--R   (10)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.603~~~~~$\displaystyle
+\int{\frac{dx}{\sinh{ax}(\cosh{ax}-1)}}$}
+$$\int{\frac{1}{\sinh{ax}(\cosh{ax}-1)}}=
+-\frac{1}{2a}\ln\tanh\frac{ax}{2}-\frac{1}{2a(cosh{ax}-1)}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 72
+aa:=integrate(1/(sinh(a*x)*(cosh(a*x)-1)),x)
+--R 
+--R
+--R   (1)
+--R                   2                                        2
+--R         (sinh(a x)  + (2cosh(a x) - 2)sinh(a x) + cosh(a x)  - 2cosh(a x) + 1)
+--R      *
+--R         log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R                      2                                          2
+--R           - sinh(a x)  + (- 2cosh(a x) + 2)sinh(a x) - cosh(a x)  + 2cosh(a x)
+--R         + 
+--R           - 1
+--R      *
+--R         log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R       - 2sinh(a x) - 2cosh(a x)
+--R  /
+--R                   2                                              2
+--R       2a sinh(a x)  + (4a cosh(a x) - 4a)sinh(a x) + 2a cosh(a x)
+--R     + 
+--R       - 4a cosh(a x) + 2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 73
+bb:=-1/(2*a)*log(tanh((a*x)/2))-1/(2*a*(cosh(a*x)-1))
+--R
+--R                                  a x
+--R        (- cosh(a x) + 1)log(tanh(---)) - 1
+--R                                   2
+--R   (2)  -----------------------------------
+--R                 2a cosh(a x) - 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 74
+cc:=aa-bb
+--R
+--R   (3)
+--R                                   2              2
+--R           (cosh(a x) - 1)sinh(a x)  + (2cosh(a x)  - 4cosh(a x) + 2)sinh(a x)
+--R         + 
+--R                    3             2
+--R           cosh(a x)  - 3cosh(a x)  + 3cosh(a x) - 1
+--R      *
+--R                  a x
+--R         log(tanh(---))
+--R                   2
+--R     + 
+--R                                   2              2
+--R           (cosh(a x) - 1)sinh(a x)  + (2cosh(a x)  - 4cosh(a x) + 2)sinh(a x)
+--R         + 
+--R                    3             2
+--R           cosh(a x)  - 3cosh(a x)  + 3cosh(a x) - 1
+--R      *
+--R         log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R                                     2
+--R           (- cosh(a x) + 1)sinh(a x)
+--R         + 
+--R                        2                                       3             2
+--R           (- 2cosh(a x)  + 4cosh(a x) - 2)sinh(a x) - cosh(a x)  + 3cosh(a x)
+--R         + 
+--R           - 3cosh(a x) + 1
+--R      *
+--R         log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R                2            2
+--R       sinh(a x)  - cosh(a x)  + 1
+--R  /
+--R                                   2
+--R       (2a cosh(a x) - 2a)sinh(a x)
+--R     + 
+--R                    2                                             3
+--R       (4a cosh(a x)  - 8a cosh(a x) + 4a)sinh(a x) + 2a cosh(a x)
+--R     + 
+--R                     2
+--R       - 6a cosh(a x)  + 6a cosh(a x) - 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 75
+coshcuberule:=rule(cosh(x)^3 == 1/4*cosh(3*x)-3/4*cosh(x))
+--R
+--R               3    cosh(3x) - 3cosh(x)
+--R   (4)  cosh(x)  == -------------------
+--R                             4
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 76
+dd:=coshcuberule cc
+--R
+--R   (5)
+--R                                    2              2
+--R           (4cosh(a x) - 4)sinh(a x)  + (8cosh(a x)  - 16cosh(a x) + 8)sinh(a x)
+--R         + 
+--R                                   2
+--R           cosh(3a x) - 12cosh(a x)  + 9cosh(a x) - 4
+--R      *
+--R                  a x
+--R         log(tanh(---))
+--R                   2
+--R     + 
+--R                                    2              2
+--R           (4cosh(a x) - 4)sinh(a x)  + (8cosh(a x)  - 16cosh(a x) + 8)sinh(a x)
+--R         + 
+--R                                   2
+--R           cosh(3a x) - 12cosh(a x)  + 9cosh(a x) - 4
+--R      *
+--R         log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R                                      2
+--R           (- 4cosh(a x) + 4)sinh(a x)
+--R         + 
+--R                        2
+--R           (- 8cosh(a x)  + 16cosh(a x) - 8)sinh(a x) - cosh(3a x)
+--R         + 
+--R                      2
+--R           12cosh(a x)  - 9cosh(a x) + 4
+--R      *
+--R         log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R                 2             2
+--R       4sinh(a x)  - 4cosh(a x)  + 4
+--R  /
+--R                                   2
+--R       (8a cosh(a x) - 8a)sinh(a x)
+--R     + 
+--R                     2
+--R       (16a cosh(a x)  - 32a cosh(a x) + 16a)sinh(a x) + 2a cosh(3a x)
+--R     + 
+--R                      2
+--R       - 24a cosh(a x)  + 18a cosh(a x) - 8a
+--R                                                     Type: Expression Integer
+--E
+
+--S 77
+sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
+--R
+--R               2    cosh(2x) - 1
+--R   (6)  sinh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 78
+ee:=sinhsqrrule dd
+--R
+--R   (7)
+--R                      2
+--R           (8cosh(a x)  - 16cosh(a x) + 8)sinh(a x) + cosh(3a x)
+--R         + 
+--R                                                   2
+--R           (2cosh(a x) - 2)cosh(2a x) - 12cosh(a x)  + 7cosh(a x) - 2
+--R      *
+--R                  a x
+--R         log(tanh(---))
+--R                   2
+--R     + 
+--R                      2
+--R           (8cosh(a x)  - 16cosh(a x) + 8)sinh(a x) + cosh(3a x)
+--R         + 
+--R                                                   2
+--R           (2cosh(a x) - 2)cosh(2a x) - 12cosh(a x)  + 7cosh(a x) - 2
+--R      *
+--R         log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R                        2
+--R           (- 8cosh(a x)  + 16cosh(a x) - 8)sinh(a x) - cosh(3a x)
+--R         + 
+--R                                                     2
+--R           (- 2cosh(a x) + 2)cosh(2a x) + 12cosh(a x)  - 7cosh(a x) + 2
+--R      *
+--R         log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R                               2
+--R       2cosh(2a x) - 4cosh(a x)  + 2
+--R  /
+--R                     2
+--R       (16a cosh(a x)  - 32a cosh(a x) + 16a)sinh(a x) + 2a cosh(3a x)
+--R     + 
+--R                                                    2
+--R       (4a cosh(a x) - 4a)cosh(2a x) - 24a cosh(a x)  + 14a cosh(a x) - 4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 79
+coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
+--R
+--R               2    cosh(2x) + 1
+--R   (8)  cosh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 80
+ff:=coshsqrrule ee
+--R
+--R   (9)
+--R                a x
+--R       log(tanh(---)) + log(sinh(a x) + cosh(a x) + 1)
+--R                 2
+--R     + 
+--R       - log(sinh(a x) + cosh(a x) - 1)
+--R  /
+--R     2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 81     14:603 Schaums and Axiom agree
+gg:=complexNormalize ff
+--R
+--R   (10)  0
+--R                                                     Type: Expression Integer
+--E
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 pp89-90
+\end{thebibliography}
+\end{document}
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diff --git a/src/axiom-website/CATS/schaum3.input.pamphlet b/src/axiom-website/CATS/schaum3.input.pamphlet
new file mode 100644
index 0000000..bed98c8
--- /dev/null
+++ b/src/axiom-website/CATS/schaum3.input.pamphlet
@@ -0,0 +1,398 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum3.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.105~~~~~$\displaystyle\int{\frac{dx}{(ax+b)(px+q)}}$}
+$$\int{\frac{1}{(ax+b)(px+q)}}=
+\frac{1}{bp-aq}~\ln\left(\frac{px+q}{ax+b}\right)$$
+&lt;&lt;*&gt;&gt;=
+)spool schaum3.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1
+aa:=integrate(1/((a*x+b)*(p*x+q)),x)
+--R 
+--R
+--R        - log(p x + q) + log(a x + b)
+--R   (1)  -----------------------------
+--R                  a q - b p
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 2
+bb:=1/(b*p-a*q)*log((p*x+q)/(a*x+b))
+--R 
+--R
+--R              p x + q
+--R          log(-------)
+--R              a x + b
+--R   (2)  - ------------
+--R            a q - b p
+--R                                                     Type: Expression Integer
+--E
+
+--S 3
+cc:=aa-bb
+--R 
+--R
+--R                                            p x + q
+--R        - log(p x + q) + log(a x + b) + log(-------)
+--R                                            a x + b
+--R   (3)  --------------------------------------------
+--R                          a q - b p
+--R                                                     Type: Expression Integer
+--E
+
+--S 4
+logdiv:=rule(log(a)-log(b) == log(a/b))
+--R
+--R                                      a
+--I   (4)  - log(b) + log(a) + %I == log(-) + %I
+--R                                      b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 5
+dd:=logdiv cc
+--R
+--R                              1
+--R        log(a x + b) + log(-------)
+--R                           a x + b
+--R   (5)  ---------------------------
+--R                 a q - b p
+--R                                                     Type: Expression Integer
+--E
+
+--S 6
+logmul:=rule(log(a)+log(b) == log(a*b))
+--R
+--I   (6)  log(b) + log(a) + %J == log(a b) + %J
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 7      14:105 Schaums and Axiom agree
+ee:=logmul dd
+--R
+--R   (7)  0
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.106~~~~~$\displaystyle\int{\frac{x~dx}{(ax+b)(px+q)}}$}
+$$\int{\frac{x}{(ax+b)(px+q)}}=
+\frac{1}{bp-aq}\left\{\frac{b}{a}~\ln(ax+b)-\frac{q}{p}~\ln(px+q)\right\}$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 8
+aa:=integrate(x/((a*x+b)*(p*x+q)),x)
+--R 
+--R
+--R        a q log(p x + q) - b p log(a x + b)
+--R   (1)  -----------------------------------
+--R                    2           2
+--R                   a p q - a b p
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 9
+bb:=1/(b*p-a*q)*(b/a*log(a*x+b)-q/p*log(p*x+q))
+--R 
+--R
+--R        a q log(p x + q) - b p log(a x + b)
+--R   (2)  -----------------------------------
+--R                    2           2
+--R                   a p q - a b p
+--R                                                     Type: Expression Integer
+--E
+
+--S 10     14:106 Schaums and Axiom agree
+cc:=aa-bb
+--R 
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.107~~~~~$\displaystyle\int{\frac{dx}{(ax+b)^2(px+q)}}$}
+$$\int{\frac{1}{(ax+b)^2(px+q)}}=
+\frac{1}{bp-aq}
+\left\{\frac{1}{ax+b}+
+\frac{p}{bp-aq}~\ln\left(\frac{px+q}{ax+b}\right)\right\}$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 11
+aa:=integrate(1/((a*x+b)^2*(p*x+q)),x)
+--R 
+--R
+--R        (a p x + b p)log(p x + q) + (- a p x - b p)log(a x + b) - a q + b p
+--R   (1)  -------------------------------------------------------------------
+--R                 3 2     2           2 2      2   2       2       3 2
+--R               (a q  - 2a b p q + a b p )x + a b q  - 2a b p q + b p
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 12
+bb:=1/(b*p-a*q)*(1/(a*x+b)+p/(b*p-a*q)*log((p*x+q)/(a*x+b)))
+--R 
+--R
+--R                                  p x + q
+--R                 (a p x + b p)log(-------) - a q + b p
+--R                                  a x + b
+--R   (2)  ------------------------------------------------------
+--R          3 2     2           2 2      2   2       2       3 2
+--R        (a q  - 2a b p q + a b p )x + a b q  - 2a b p q + b p
+--R                                                     Type: Expression Integer
+--E
+
+--S 13
+cc:=aa-bb
+--R 
+--R
+--R                                                p x + q
+--R        p log(p x + q) - p log(a x + b) - p log(-------)
+--R                                                a x + b
+--R   (3)  ------------------------------------------------
+--R                      2 2               2 2
+--R                     a q  - 2a b p q + b p
+--R                                                     Type: Expression Integer
+--E
+
+--S 14
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 15     14:107 Schaums and Axiom agree
+dd:=divlog cc
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.108~~~~~$\displaystyle\int{\frac{x~dx}{(ax+b)^2(px+q)}}$}
+$$\int{\frac{x}{(ax+b)^2(px+q)}}=
+\frac{1}{bp-aq}
+\left\{\frac{q}{bp-aq}
+~\ln\left(\frac{ax+b}{px+q}\right)-\frac{b}{a(ax+b)}\right\}$$
+
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 16
+aa:=integrate(x/((a*x+b)^2*(p*x+q)),x)
+--R 
+--R
+--R   (1)
+--R       2                             2                                    2
+--R   (- a q x - a b q)log(p x + q) + (a q x + a b q)log(a x + b) + a b q - b p
+--R   -------------------------------------------------------------------------
+--R              4 2     3         2 2 2      3   2     2 2         3 2
+--R            (a q  - 2a b p q + a b p )x + a b q  - 2a b p q + a b p
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 17
+bb:=1/(b*p-a*q)*(q/(b*p-a*q)*log((a*x+b)/(p*x+q))-b/(a*(a*x+b)))
+--R 
+--R
+--R                  2                a x + b             2
+--R                (a q x + a b q)log(-------) + a b q - b p
+--R                                   p x + q
+--R   (2)  --------------------------------------------------------
+--R          4 2     3         2 2 2      3   2     2 2         3 2
+--R        (a q  - 2a b p q + a b p )x + a b q  - 2a b p q + a b p
+--R                                                     Type: Expression Integer
+--E
+
+--S 18
+cc:=aa-bb
+--R 
+--R
+--R                                                  a x + b
+--R        - q log(p x + q) + q log(a x + b) - q log(-------)
+--R                                                  p x + q
+--R   (3)  --------------------------------------------------
+--R                       2 2               2 2
+--R                      a q  - 2a b p q + b p
+--R                                                     Type: Expression Integer
+--E
+
+--S 19
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 20     14:108 Schaums and Axiom agree
+dd:=divlog cc
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.109~~~~~$\displaystyle
+\int{\frac{x^2~dx}{(ax+b)^2(px+q)}}$}
+$$\int{\frac{x^2}{(ax+b)^2(px+q)}}=$$
+$$\frac{b^2}{(bp-aq)a^2(ax+b)}+\frac{1}{(bp-aq)^2}
+\left\{\frac{q^2}{p}~\ln(px+q)+\frac{b(bp-2aq)}{a^2}~\ln(ax+b)\right\}$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 21
+aa:=integrate(x^2/((a*x+b)^2*(p*x+q)),x)
+--R 
+--R
+--R   (1)
+--R         3 2     2   2
+--R       (a q x + a b q )log(p x + q)
+--R     + 
+--R             2           2 2         2       3 2                   2       3 2
+--R       ((- 2a b p q + a b p )x - 2a b p q + b p )log(a x + b) - a b p q + b p
+--R  /
+--R       5   2     4   2     3 2 3      4     2     3 2 2     2 3 3
+--R     (a p q  - 2a b p q + a b p )x + a b p q  - 2a b p q + a b p
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 22
+bb:=b^2/((b*p-a*q)*a^2*(a*x+b))+_
+     1/(b*p-a*q)^2*(q^2/p*log(p*x+q)+((b*(b*p-2*a*q))/a^2)*log(a*x+b))
+--R 
+--R
+--R   (2)
+--R         3 2     2   2
+--R       (a q x + a b q )log(p x + q)
+--R     + 
+--R             2           2 2         2       3 2                   2       3 2
+--R       ((- 2a b p q + a b p )x - 2a b p q + b p )log(a x + b) - a b p q + b p
+--R  /
+--R       5   2     4   2     3 2 3      4     2     3 2 2     2 3 3
+--R     (a p q  - 2a b p q + a b p )x + a b p q  - 2a b p q + a b p
+--R                                                     Type: Expression Integer
+--E
+
+--S 23     14:109 Schaums and Axiom agree
+cc:=aa-bb
+--R 
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.110~~~~~$\displaystyle\int{\frac{dx}{(ax+b)^m(px+q)^n}}$}
+$$\int{\frac{1}{(ax+b)^m(px+q)^n}}=$$
+$$\frac{-1}{(n-1)(bp-aq)}
+\left\{\frac{1}{(ax+b)^{m-1}(px+q)^{n-1}}+
+a(m+n-2)~\int{\frac{1}{(ax+b)^m(px+q)^{n-1}}}\right\}$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 24     14:110 Axiom cannot do this integral
+aa:=integrate(1/((a*x+b)^m*(p*x+q)^n),x)
+--R 
+--R
+--R           x
+--R         ++             1
+--I   (1)   |   ---------------------- d%L
+--R        ++             m          n
+--I             (b + %L a) (q + %L p)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+@
+\section{\cite{1}:14.111~~~~~$\displaystyle\int{\frac{ax+b}{px+q}~dx}$}
+$$\int{\frac{ax+b}{px+q}}=\frac{ax}{p}+\frac{bp-aq}{p^2}~\ln(px+q)$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 25
+aa:=integrate((a*x+b)/(p*x+q),x)
+--R 
+--R
+--R        (- a q + b p)log(p x + q) + a p x
+--R   (1)  ---------------------------------
+--R                         2
+--R                        p
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 26
+bb:=(a*x)/p+(b*p-a*q)/p^2*log(p*x+q)
+--R 
+--R
+--R        (- a q + b p)log(p x + q) + a p x
+--R   (2)  ---------------------------------
+--R                         2
+--R                        p
+--R                                                     Type: Expression Integer
+--E
+
+--S 27     14:111 Schaums and Axiom agree
+cc:=aa-bb
+--R 
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.112~~~~~$\displaystyle\int{\frac{(ax+b)^m}{(px+q)^n}~dx}$}
+$$\int{\frac{(ax+b)^m}{(px+q)^n}}=\left\{
+\begin{array}{c}
+\frac{-1}{(n-1)(bp-aq)}
+\left\{\frac{(ax+b)^{m+1}}{(px+q)^{n-1}}+(n-m-2)a
+\int{\frac{(ax+b)^m}{(px+q)^{n-1}}}\right\}\\
+\frac{-1}{(n-m-1)p}+\left\{\frac{(ax+b)^m}{(px+q)^{n-1}}+m(bp-aq)
+\int{\frac{(ax+b)^{m-1}}{(px+q)^n}}\right\}\\
+\frac{-1}{(n-1)p}\left\{\frac{(ax+b)^m}{(px+q)^{n-1}}-ma
+\int{\frac{(ax+b)^{m-1}}{(px+q)^{n-1}}}\right\}
+\end{array}
+\right.$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 28     14:112 Axiom cannot do this integral
+aa:=integrate((a*x+b)^m/(p*x+q)^n,x)
+--R 
+--R
+--R           x           m
+--I         ++  (b + %L a)
+--I   (1)   |   ----------- d%L
+--R        ++             n
+--I             (q + %L p)
+--R                                          Type: Union(Expression Integer,...)
+--E
+&lt;&lt;*&gt;&gt;=
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 pp62-63
+\end{thebibliography}
+\end{document}
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diff --git a/src/axiom-website/CATS/schaum30.input.pamphlet b/src/axiom-website/CATS/schaum30.input.pamphlet
new file mode 100644
index 0000000..5df48bc
--- /dev/null
+++ b/src/axiom-website/CATS/schaum30.input.pamphlet
@@ -0,0 +1,744 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum30.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.604~~~~~$\displaystyle
+\int{\tanh{ax}}~dx$}
+$$\int{\tanh{ax}}=
+\frac{1}{a}\ln\cosh{ax}
+$$
+&lt;&lt;*&gt;&gt;=
+)spool schaum30.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1
+aa:=integrate(tanh(a*x),x)
+--R 
+--R
+--R                    2cosh(a x)
+--R        log(- ---------------------) - a x
+--R              sinh(a x) - cosh(a x)
+--R   (1)  ----------------------------------
+--R                         a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 2
+bb:=1/a*log(cosh(a*x))
+--R
+--R        log(cosh(a x))
+--R   (2)  --------------
+--R               a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3
+cc:=aa-bb
+--R
+--R                                       2cosh(a x)
+--R        - log(cosh(a x)) + log(- ---------------------) - a x
+--R                                 sinh(a x) - cosh(a x)
+--R   (3)  -----------------------------------------------------
+--R                                  a
+--R                                                     Type: Expression Integer
+--E
+
+--S 4
+dd:=expandLog cc
+--R
+--R        - log(sinh(a x) - cosh(a x)) + log(- 2) - a x
+--R   (4)  ---------------------------------------------
+--R                              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 5      14:604 Schaums and Axiom differ by a constant
+ee:=complexNormalize dd
+--R
+--R        - log(- 1) + log(- 2)
+--R   (5)  ---------------------
+--R                  a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.605~~~~~$\displaystyle
+\int{\tanh^2{ax}}~dx$}
+$$\int{\tanh^2{ax}}=
+x-\frac{\tanh{ax}}{a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 6
+aa:=integrate(tanh(a*x)^2,x)
+--R 
+--R
+--R        - sinh(a x) + (a x + 1)cosh(a x)
+--R   (1)  --------------------------------
+--R                   a cosh(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 7
+bb:=x-tanh(a*x)/a
+--R
+--R        - tanh(a x) + a x
+--R   (2)  -----------------
+--R                a
+--R                                                     Type: Expression Integer
+--E
+
+--S 8
+cc:=aa-bb
+--R
+--R        cosh(a x)tanh(a x) - sinh(a x) + cosh(a x)
+--R   (3)  ------------------------------------------
+--R                        a cosh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 9
+tanhrule:=rule(tanh(x) == sinh(x)/cosh(x))
+--R
+--R                   sinh(x)
+--R   (4)  tanh(x) == -------
+--R                   cosh(x)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 10     14:605 Schaums and Axiom differ by a constant
+dd:=tanhrule cc
+--R
+--R        1
+--R   (5)  -
+--R        a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.606~~~~~$\displaystyle
+\int{\tanh^3{ax}}~dx$}
+$$\int{\tanh^3{ax}}=
+\frac{1}{a}\ln\cosh{ax}-\frac{\tanh^2{ax}}{2a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 11
+aa:=integrate(tanh(a*x)^3,x)
+--R 
+--R
+--R   (1)
+--R                    4                      3              2              2
+--R           sinh(a x)  + 4cosh(a x)sinh(a x)  + (6cosh(a x)  + 2)sinh(a x)
+--R         + 
+--R                      3                                   4             2
+--R           (4cosh(a x)  + 4cosh(a x))sinh(a x) + cosh(a x)  + 2cosh(a x)  + 1
+--R      *
+--R                     2cosh(a x)
+--R         log(- ---------------------)
+--R               sinh(a x) - cosh(a x)
+--R     + 
+--R                      4                          3
+--R       - a x sinh(a x)  - 4a x cosh(a x)sinh(a x)
+--R     + 
+--R                        2                     2
+--R       (- 6a x cosh(a x)  - 2a x + 2)sinh(a x)
+--R     + 
+--R                        3                                                  4
+--R       (- 4a x cosh(a x)  + (- 4a x + 4)cosh(a x))sinh(a x) - a x cosh(a x)
+--R     + 
+--R                            2
+--R       (- 2a x + 2)cosh(a x)  - a x
+--R  /
+--R                  4                        3                2               2
+--R       a sinh(a x)  + 4a cosh(a x)sinh(a x)  + (6a cosh(a x)  + 2a)sinh(a x)
+--R     + 
+--R                  3                                       4               2
+--R     (4a cosh(a x)  + 4a cosh(a x))sinh(a x) + a cosh(a x)  + 2a cosh(a x)  + a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 12
+bb:=1/a*log(cosh(a*x))-tanh(a*x)^2/(2*a)
+--R
+--R                                   2
+--R        2log(cosh(a x)) - tanh(a x)
+--R   (2)  ----------------------------
+--R                     2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 13     14:606 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R                       4                      3                 2              2
+--R           - 2sinh(a x)  - 8cosh(a x)sinh(a x)  + (- 12cosh(a x)  - 4)sinh(a x)
+--R         + 
+--R                      3                                    4             2
+--R         (- 8cosh(a x)  - 8cosh(a x))sinh(a x) - 2cosh(a x)  - 4cosh(a x)  - 2
+--R      *
+--R         log(cosh(a x))
+--R     + 
+--R                     4                      3               2              2
+--R           2sinh(a x)  + 8cosh(a x)sinh(a x)  + (12cosh(a x)  + 4)sinh(a x)
+--R         + 
+--R                      3                                    4             2
+--R           (8cosh(a x)  + 8cosh(a x))sinh(a x) + 2cosh(a x)  + 4cosh(a x)  + 2
+--R      *
+--R                     2cosh(a x)
+--R         log(- ---------------------)
+--R               sinh(a x) - cosh(a x)
+--R     + 
+--R                    4                      3              2              2
+--R           sinh(a x)  + 4cosh(a x)sinh(a x)  + (6cosh(a x)  + 2)sinh(a x)
+--R         + 
+--R                      3                                   4             2
+--R           (4cosh(a x)  + 4cosh(a x))sinh(a x) + cosh(a x)  + 2cosh(a x)  + 1
+--R      *
+--R                  2
+--R         tanh(a x)
+--R     + 
+--R                       4                          3
+--R       - 2a x sinh(a x)  - 8a x cosh(a x)sinh(a x)
+--R     + 
+--R                         2                     2
+--R       (- 12a x cosh(a x)  - 4a x + 4)sinh(a x)
+--R     + 
+--R                        3                                                   4
+--R       (- 8a x cosh(a x)  + (- 8a x + 8)cosh(a x))sinh(a x) - 2a x cosh(a x)
+--R     + 
+--R                            2
+--R       (- 4a x + 4)cosh(a x)  - 2a x
+--R  /
+--R                   4                        3                 2               2
+--R       2a sinh(a x)  + 8a cosh(a x)sinh(a x)  + (12a cosh(a x)  + 4a)sinh(a x)
+--R     + 
+--R                    3                                        4               2
+--R       (8a cosh(a x)  + 8a cosh(a x))sinh(a x) + 2a cosh(a x)  + 4a cosh(a x)
+--R     + 
+--R       2a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.607~~~~~$\displaystyle
+\int{\tanh^n{ax}{{\rm ~sech}^2{ax}}}~dx$}
+$$\int{\tanh^n{ax}{{\rm ~sech}^2{ax}}}=
+\frac{\tanh^{n+1}{ax}}{(n+1)a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 14
+aa:=integrate(tanh(a*x)^n*sech(a*x)^2,x)
+--R 
+--R
+--R                            sinh(a x)                         sinh(a x)
+--R        sinh(a x)sinh(n log(---------)) + sinh(a x)cosh(n log(---------))
+--R                            cosh(a x)                         cosh(a x)
+--R   (1)  -----------------------------------------------------------------
+--R                                (a n + a)cosh(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 15
+bb:=tanh(a*x)^(n+1)/((n+1)*a)
+--R
+--R                 n + 1
+--R        tanh(a x)
+--R   (2)  --------------
+--R            a n + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 16     14:607 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R                           sinh(a x)                         sinh(a x)
+--R       sinh(a x)sinh(n log(---------)) + sinh(a x)cosh(n log(---------))
+--R                           cosh(a x)                         cosh(a x)
+--R     + 
+--R                           n + 1
+--R       - cosh(a x)tanh(a x)
+--R  /
+--R     (a n + a)cosh(a x)
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.608~~~~~$\displaystyle
+\int{\frac{{\rm sech}^2{ax}}{\tanh{ax}}}~dx$}
+$$\int{\frac{{\rm sech}^2{ax}}{\tanh{ax}}}=
+\frac{1}{a}\ln\tanh{ax}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 17
+aa:=integrate(sech(a*x)^2/tanh(a*x),x)
+--R 
+--R
+--R                      2cosh(a x)                     2sinh(a x)
+--R        - log(- ---------------------) + log(- ---------------------)
+--R                sinh(a x) - cosh(a x)          sinh(a x) - cosh(a x)
+--R   (1)  -------------------------------------------------------------
+--R                                      a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 18
+bb:=1/a*log(tanh(a*x))
+--R
+--R        log(tanh(a x))
+--R   (2)  --------------
+--R               a
+--R                                                     Type: Expression Integer
+--E
+
+--S 19
+cc:=aa-bb
+--R
+--R   (3)
+--R                                      2cosh(a x)
+--R       - log(tanh(a x)) - log(- ---------------------)
+--R                                sinh(a x) - cosh(a x)
+--R     + 
+--R                   2sinh(a x)
+--R       log(- ---------------------)
+--R             sinh(a x) - cosh(a x)
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 20
+tanhrule:=rule(tanh(x) == sinh(x)/cosh(x))
+--R
+--R                   sinh(x)
+--R   (4)  tanh(x) == -------
+--R                   cosh(x)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 21
+dd:=tanhrule cc
+--R
+--R   (5)
+--R             sinh(a x)                2cosh(a x)
+--R       - log(---------) - log(- ---------------------)
+--R             cosh(a x)          sinh(a x) - cosh(a x)
+--R     + 
+--R                   2sinh(a x)
+--R       log(- ---------------------)
+--R             sinh(a x) - cosh(a x)
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 22     14:608 Schaums and Axiom agree
+ee:=expandLog dd
+--R
+--R   (6)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.609~~~~~$\displaystyle
+\int{\frac{dx}{\tanh{ax}}}~dx$}
+$$\int{\frac{1}{\tanh{ax}}}=
+\frac{1}{a}\ln\sinh{ax}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 23
+aa:=integrate(1/tanh(a*x),x)
+--R 
+--R
+--R                    2sinh(a x)
+--R        log(- ---------------------) - a x
+--R              sinh(a x) - cosh(a x)
+--R   (1)  ----------------------------------
+--R                         a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 24
+bb:=1/a*log(sinh(a*x))
+--R
+--R        log(sinh(a x))
+--R   (2)  --------------
+--R               a
+--R                                                     Type: Expression Integer
+--E
+
+--S 25
+cc:=aa-bb
+--R
+--R                                       2sinh(a x)
+--R        - log(sinh(a x)) + log(- ---------------------) - a x
+--R                                 sinh(a x) - cosh(a x)
+--R   (3)  -----------------------------------------------------
+--R                                  a
+--R                                                     Type: Expression Integer
+--E
+
+--S 26
+dd:=expandLog cc
+--R
+--R        - log(sinh(a x) - cosh(a x)) + log(- 2) - a x
+--R   (4)  ---------------------------------------------
+--R                              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 27     14:609 Schaums and Axiom differ by a constant
+ee:=complexNormalize dd
+--R
+--R        - log(- 1) + log(- 2)
+--R   (5)  ---------------------
+--R                  a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.610~~~~~$\displaystyle
+\int{x\tanh{ax}}~dx$}
+$$\int{x\tanh{ax}}=
+\frac{1}{a^2}\left\{
+\frac{(ax)^3}{3}-\frac{(ax)^5}{15}+\frac{2(ax)^7}{105}-\cdots
+\frac{(-1)^{n-1}2^{2n}(2^{2n}-1)B_n(ax)^{2n+1}}{(2n+1)!}+\cdots\right\}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 28     14:610 Axiom cannot compute this integral
+aa:=integrate(x*tanh(a*x),x)
+--R 
+--R
+--R           x
+--R         ++
+--I   (1)   |   %O tanh(%O a)d%O
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.611~~~~~$\displaystyle
+\int{x\tanh^2{ax}}~dx$}
+$$\int{x\tanh^2{ax}}=
+\frac{x^2}{2}-\frac{x\tanh{ax}}{a}+\frac{1}{a^2}\ln\cosh{ax}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 29
+aa:=integrate(x*tanh(a*x)^2,x)
+--R 
+--R
+--R   (1)
+--R                    2                                   2
+--R         (2sinh(a x)  + 4cosh(a x)sinh(a x) + 2cosh(a x)  + 2)
+--R      *
+--R                     2cosh(a x)
+--R         log(- ---------------------)
+--R               sinh(a x) - cosh(a x)
+--R     + 
+--R         2 2                 2      2 2
+--R       (a x  - 4a x)sinh(a x)  + (2a x  - 8a x)cosh(a x)sinh(a x)
+--R     + 
+--R         2 2                 2    2 2
+--R       (a x  - 4a x)cosh(a x)  + a x
+--R  /
+--R       2         2     2                       2         2     2
+--R     2a sinh(a x)  + 4a cosh(a x)sinh(a x) + 2a cosh(a x)  + 2a
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 30
+bb:=x^2/2-(x*tanh(a*x))/a+1/a^2*log(cosh(a*x))
+--R
+--R                                            2 2
+--R        2log(cosh(a x)) - 2a x tanh(a x) + a x
+--R   (2)  ---------------------------------------
+--R                            2
+--R                          2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 31
+cc:=aa-bb
+--R
+--R   (3)
+--R                   2                                  2
+--R       (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)log(cosh(a x))
+--R     + 
+--R                   2                                  2
+--R         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1)
+--R      *
+--R                     2cosh(a x)
+--R         log(- ---------------------)
+--R               sinh(a x) - cosh(a x)
+--R     + 
+--R                       2                                          2
+--R         (a x sinh(a x)  + 2a x cosh(a x)sinh(a x) + a x cosh(a x)  + a x)
+--R      *
+--R         tanh(a x)
+--R     + 
+--R                       2                                           2
+--R       - 2a x sinh(a x)  - 4a x cosh(a x)sinh(a x) - 2a x cosh(a x)
+--R  /
+--R      2         2     2                      2         2    2
+--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 32
+sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
+--R
+--R               2    cosh(2x) - 1
+--R   (4)  sinh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 33
+dd:=sinhsqrrule cc
+--R
+--R   (5)
+--R                                                       2
+--R       (- 4cosh(a x)sinh(a x) - cosh(2a x) - 2cosh(a x)  - 1)log(cosh(a x))
+--R     + 
+--R                                                       2
+--R         (4cosh(a x)sinh(a x) + cosh(2a x) + 2cosh(a x)  + 1)
+--R      *
+--R                     2cosh(a x)
+--R         log(- ---------------------)
+--R               sinh(a x) - cosh(a x)
+--R     + 
+--R                                                                   2
+--R         (4a x cosh(a x)sinh(a x) + a x cosh(2a x) + 2a x cosh(a x)  + a x)
+--R      *
+--R         tanh(a x)
+--R     + 
+--R                                                                   2
+--R       - 8a x cosh(a x)sinh(a x) - 2a x cosh(2a x) - 4a x cosh(a x)  + 2a x
+--R  /
+--R       2                      2               2         2    2
+--R     4a cosh(a x)sinh(a x) + a cosh(2a x) + 2a cosh(a x)  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 34
+coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
+--R
+--R               2    cosh(2x) + 1
+--R   (6)  cosh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 35
+ee:=coshsqrrule dd
+--R
+--R   (7)
+--R       (- 2cosh(a x)sinh(a x) - cosh(2a x) - 1)log(cosh(a x))
+--R     + 
+--R                                                         2cosh(a x)
+--R       (2cosh(a x)sinh(a x) + cosh(2a x) + 1)log(- ---------------------)
+--R                                                   sinh(a x) - cosh(a x)
+--R     + 
+--R       (2a x cosh(a x)sinh(a x) + a x cosh(2a x) + a x)tanh(a x)
+--R     + 
+--R       - 4a x cosh(a x)sinh(a x) - 2a x cosh(2a x)
+--R  /
+--R       2                      2              2
+--R     2a cosh(a x)sinh(a x) + a cosh(2a x) + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 36
+ff:=expandLog ee
+--R
+--R   (8)
+--R       (- 2cosh(a x)sinh(a x) - cosh(2a x) - 1)log(sinh(a x) - cosh(a x))
+--R     + 
+--R       (2a x cosh(a x)sinh(a x) + a x cosh(2a x) + a x)tanh(a x)
+--R     + 
+--R       (2log(- 2) - 4a x)cosh(a x)sinh(a x) + (log(- 2) - 2a x)cosh(2a x)
+--R     + 
+--R       log(- 2)
+--R  /
+--R       2                      2              2
+--R     2a cosh(a x)sinh(a x) + a cosh(2a x) + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 37
+sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
+--R
+--I                             %N sinh(y + x) - %N sinh(y - x)
+--I   (9)  %N cosh(y)sinh(x) == -------------------------------
+--R                                            2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 38
+gg:=sinhcoshrule ff
+--R
+--R   (10)
+--R       (- sinh(2a x) - cosh(2a x) - 1)log(sinh(a x) - cosh(a x))
+--R     + 
+--R       (a x sinh(2a x) + a x cosh(2a x) + a x)tanh(a x)
+--R     + 
+--R       (log(- 2) - 2a x)sinh(2a x) + (log(- 2) - 2a x)cosh(2a x) + log(- 2)
+--R  /
+--R      2              2              2
+--R     a sinh(2a x) + a cosh(2a x) + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 39     14:611 Schaums and Axiom differ by a constant
+hh:=complexNormalize gg
+--R
+--R         - log(- 1) + log(- 2)
+--R   (11)  ---------------------
+--R                    2
+--R                   a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.612~~~~~$\displaystyle
+\int{\frac{\tanh{ax}}{x}}~dx$}
+$$\int{\frac{\tanh{ax}}{x}}=
+ax-\frac{(ax)^3}{9}+\frac{2(ax)^5}{75}-\cdots
+\frac{(-1)^{n-1}2^{2n}(2^{2n}-1)B_n(ax)^{2n-1}}{(2n-1)(2n)!}+\cdots
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 40     14:612 Axiom cannot compute this integral
+aa:=integrate(tanh(a*x)/x,x)
+--R 
+--R
+--R           x
+--I         ++  tanh(%O a)
+--I   (1)   |   ---------- d%O
+--I        ++       %O
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.613~~~~~$\displaystyle
+\int{\frac{dx}{p+q\tanh{ax}}}~dx$}
+$$\int{\frac{1}{p+q\tanh{ax}}}=
+\frac{px}{p^2-q^2}-\frac{q}{a(p^2-q^2)}\ln(q\sinh{ax}+p\cosh{ax})
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 41
+aa:=integrate(1/(p+q*tanh(a*x)),x)
+--R 
+--R
+--R              - 2q sinh(a x) - 2p cosh(a x)
+--R        q log(-----------------------------) + (- a q - a p)x
+--R                  sinh(a x) - cosh(a x)
+--R   (1)  -----------------------------------------------------
+--R                                2      2
+--R                             a q  - a p
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 42
+bb:=(p*x)/(p^2-q^2)-q/(a*(p^2-q^2))*log(q*sinh(a*x)+p*cosh(a*x))
+--R
+--R        q log(q sinh(a x) + p cosh(a x)) - a p x
+--R   (2)  ----------------------------------------
+--R                          2      2
+--R                       a q  - a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 43
+cc:=aa-bb
+--R
+--R   (3)
+--R                                                  - 2q sinh(a x) - 2p cosh(a x)
+--R       - q log(q sinh(a x) + p cosh(a x)) + q log(-----------------------------)
+--R                                                      sinh(a x) - cosh(a x)
+--R     + 
+--R       - a q x
+--R  /
+--R        2      2
+--R     a q  - a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 44
+dd:=expandLog cc
+--R
+--R   (4)
+--R       - q log(q sinh(a x) + p cosh(a x)) - q log(sinh(a x) - cosh(a x))
+--R     + 
+--R       q log(- q sinh(a x) - p cosh(a x)) + q log(2) - a q x
+--R  /
+--R        2      2
+--R     a q  - a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 45     14:613 Schaums and Axiom differ by a constant
+ee:=complexNormalize dd
+--R
+--R        q log(2) - 2q log(- 1)
+--R   (5)  ----------------------
+--R                 2      2
+--R              a q  - a p
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.614~~~~~$\displaystyle
+\int{\tanh^n{ax}}~dx$}
+$$\int{\tanh^n{ax}}=
+\frac{-\tanh^{n-1}{ax}}{a(n-1)}+\int{\tanh^{n-2}{ax}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 46     14:614 Axiom cannot compute this integral
+aa:=integrate(tanh(a*x)^n,x)
+--R 
+--R
+--R           x
+--R         ++            n
+--I   (1)   |   tanh(%O a) d%O
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 pp89-90
+\end{thebibliography}
+\end{document}
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diff --git a/src/axiom-website/CATS/schaum31.input.pamphlet b/src/axiom-website/CATS/schaum31.input.pamphlet
new file mode 100644
index 0000000..343aa2a
--- /dev/null
+++ b/src/axiom-website/CATS/schaum31.input.pamphlet
@@ -0,0 +1,735 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum31.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.615~~~~~$\displaystyle
+\int{\coth{ax}}~dx$}
+$$\int{\coth{ax}}=
+\frac{1}{a}\ln\sinh{ax}
+$$
+&lt;&lt;*&gt;&gt;=
+)spool schaum31.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1
+aa:=integrate(coth(a*x),x)
+--R 
+--R
+--R                    2sinh(a x)
+--R        log(- ---------------------) - a x
+--R              sinh(a x) - cosh(a x)
+--R   (1)  ----------------------------------
+--R                         a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 2
+bb:=1/a*log(sinh(a*x))
+--R
+--R        log(sinh(a x))
+--R   (2)  --------------
+--R               a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3
+cc:=aa-bb
+--R
+--R                                       2sinh(a x)
+--R        - log(sinh(a x)) + log(- ---------------------) - a x
+--R                                 sinh(a x) - cosh(a x)
+--R   (3)  -----------------------------------------------------
+--R                                  a
+--R                                                     Type: Expression Integer
+--E
+
+--S 4
+dd:=expandLog cc
+--R
+--R        - log(sinh(a x) - cosh(a x)) + log(- 2) - a x
+--R   (4)  ---------------------------------------------
+--R                              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 5      14:615 Schaums and Axiom differ by a constant
+ee:=complexNormalize dd
+--R
+--R        - log(- 1) + log(- 2)
+--R   (5)  ---------------------
+--R                  a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.616~~~~~$\displaystyle
+\int{\coth^2{ax}}~dx$}
+$$\int{\coth^2{ax}}=
+x-\frac{\coth{ax}}{a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 6
+aa:=integrate(coth(a*x)^2,x)
+--R 
+--R
+--R        (a x + 1)sinh(a x) - cosh(a x)
+--R   (1)  ------------------------------
+--R                  a sinh(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 7
+bb:=x-coth(a*x)/a
+--R
+--R        - coth(a x) + a x
+--R   (2)  -----------------
+--R                a
+--R                                                     Type: Expression Integer
+--E
+
+--S 8
+cc:=aa-bb
+--R
+--R        (coth(a x) + 1)sinh(a x) - cosh(a x)
+--R   (3)  ------------------------------------
+--R                     a sinh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 9      14:616 Schaums and Axiom differ by a constant
+dd:=complexNormalize cc
+--R
+--R        1
+--R   (4)  -
+--R        a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.617~~~~~$\displaystyle
+\int{\coth^3{ax}}~dx$}
+$$\int{\coth^3{ax}}=
+\frac{1}{a}\ln\sinh{ax}-\frac{\coth^2{ax}}{2a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 10
+aa:=integrate(coth(a*x)^3,x)
+--R 
+--R
+--R   (1)
+--R                    4                      3              2              2
+--R           sinh(a x)  + 4cosh(a x)sinh(a x)  + (6cosh(a x)  - 2)sinh(a x)
+--R         + 
+--R                      3                                   4             2
+--R           (4cosh(a x)  - 4cosh(a x))sinh(a x) + cosh(a x)  - 2cosh(a x)  + 1
+--R      *
+--R                     2sinh(a x)
+--R         log(- ---------------------)
+--R               sinh(a x) - cosh(a x)
+--R     + 
+--R                      4                          3
+--R       - a x sinh(a x)  - 4a x cosh(a x)sinh(a x)
+--R     + 
+--R                        2                     2
+--R       (- 6a x cosh(a x)  + 2a x - 2)sinh(a x)
+--R     + 
+--R                        3                                                4
+--R       (- 4a x cosh(a x)  + (4a x - 4)cosh(a x))sinh(a x) - a x cosh(a x)
+--R     + 
+--R                          2
+--R       (2a x - 2)cosh(a x)  - a x
+--R  /
+--R                  4                        3                2               2
+--R       a sinh(a x)  + 4a cosh(a x)sinh(a x)  + (6a cosh(a x)  - 2a)sinh(a x)
+--R     + 
+--R                  3                                       4               2
+--R     (4a cosh(a x)  - 4a cosh(a x))sinh(a x) + a cosh(a x)  - 2a cosh(a x)  + a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 11
+bb:=1/a*log(sinh(a*x)-coth(a*x)^2)/(2*a)
+--R
+--R                                 2
+--R        log(sinh(a x) - coth(a x) )
+--R   (2)  ---------------------------
+--R                      2
+--R                    2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 12     14:617 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R                      4                      3                2              2
+--R           - sinh(a x)  - 4cosh(a x)sinh(a x)  + (- 6cosh(a x)  + 2)sinh(a x)
+--R         + 
+--R                        3                                   4             2
+--R           (- 4cosh(a x)  + 4cosh(a x))sinh(a x) - cosh(a x)  + 2cosh(a x)  - 1
+--R      *
+--R                                  2
+--R         log(sinh(a x) - coth(a x) )
+--R     + 
+--R                       4                        3
+--R           2a sinh(a x)  + 8a cosh(a x)sinh(a x)
+--R         + 
+--R                         2               2
+--R           (12a cosh(a x)  - 4a)sinh(a x)
+--R         + 
+--R                        3                                        4
+--R           (8a cosh(a x)  - 8a cosh(a x))sinh(a x) + 2a cosh(a x)
+--R         + 
+--R                         2
+--R           - 4a cosh(a x)  + 2a
+--R      *
+--R                     2sinh(a x)
+--R         log(- ---------------------)
+--R               sinh(a x) - cosh(a x)
+--R     + 
+--R           2           4     2                    3
+--R       - 2a x sinh(a x)  - 8a x cosh(a x)sinh(a x)
+--R     + 
+--R             2           2     2                2
+--R       (- 12a x cosh(a x)  + 4a x - 4a)sinh(a x)
+--R     + 
+--R            2           3      2                               2           4
+--R       (- 8a x cosh(a x)  + (8a x - 8a)cosh(a x))sinh(a x) - 2a x cosh(a x)
+--R     + 
+--R          2                2     2
+--R       (4a x - 4a)cosh(a x)  - 2a x
+--R  /
+--R         2         4     2                  3       2         2     2          2
+--R       2a sinh(a x)  + 8a cosh(a x)sinh(a x)  + (12a cosh(a x)  - 4a )sinh(a x)
+--R     + 
+--R          2         3     2                        2         4     2         2
+--R       (8a cosh(a x)  - 8a cosh(a x))sinh(a x) + 2a cosh(a x)  - 4a cosh(a x)
+--R     + 
+--R         2
+--R       2a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.618~~~~~$\displaystyle
+\int{\coth^n{ax}{{\rm ~csch}^2{ax}}}~dx$}
+$$\int{\coth^n{ax}{{\rm ~csch}^2{ax}}}=
+-\frac{\coth^{n+1}{ax}}{(n+1)a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 13
+aa:=integrate(coth(a*x)^n*csch(a*x)^2,x)
+--R 
+--R
+--R                              cosh(a x)                         cosh(a x)
+--R        - cosh(a x)sinh(n log(---------)) - cosh(a x)cosh(n log(---------))
+--R                              sinh(a x)                         sinh(a x)
+--R   (1)  -------------------------------------------------------------------
+--R                                 (a n + a)sinh(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 14
+bb:=-coth(a*x)^(n+1)/((n+1)*a)
+--R
+--R                   n + 1
+--R          coth(a x)
+--R   (2)  - --------------
+--R              a n + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 15
+cc:=aa-bb
+--R
+--R   (3)
+--R                             cosh(a x)                         cosh(a x)
+--R       - cosh(a x)sinh(n log(---------)) - cosh(a x)cosh(n log(---------))
+--R                             sinh(a x)                         sinh(a x)
+--R     + 
+--R                         n + 1
+--R       sinh(a x)coth(a x)
+--R  /
+--R     (a n + a)sinh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 16
+dd:=expandLog cc
+--R
+--R   (4)
+--R       cosh(a x)sinh(n log(sinh(a x)) - n log(cosh(a x)))
+--R     + 
+--R       - cosh(a x)cosh(n log(sinh(a x)) - n log(cosh(a x)))
+--R     + 
+--R                         n + 1
+--R       sinh(a x)coth(a x)
+--R  /
+--R     (a n + a)sinh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 17     14:618 Schaums and Axiom agree
+ee:=complexNormalize dd
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.619~~~~~$\displaystyle
+\int{\frac{{\rm csch}^2{ax}}{\coth{ax}}}~dx$}
+$$\int{\frac{{\rm csch}^2{ax}}{\coth{ax}}}=
+-\frac{1}{a}\ln\coth{ax}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 18
+aa:=integrate(csch(a*x)^2/coth(a*x),x)
+--R 
+--R
+--R                      2cosh(a x)                     2sinh(a x)
+--R        - log(- ---------------------) + log(- ---------------------)
+--R                sinh(a x) - cosh(a x)          sinh(a x) - cosh(a x)
+--R   (1)  -------------------------------------------------------------
+--R                                      a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 19
+bb:=-1/a*log(coth(a*x))
+--R
+--R          log(coth(a x))
+--R   (2)  - --------------
+--R                 a
+--R                                                     Type: Expression Integer
+--E
+
+--S 20
+cc:=aa-bb
+--R
+--R   (3)
+--R                                2cosh(a x)                     2sinh(a x)
+--R   log(coth(a x)) - log(- ---------------------) + log(- ---------------------)
+--R                          sinh(a x) - cosh(a x)          sinh(a x) - cosh(a x)
+--R   ----------------------------------------------------------------------------
+--R                                         a
+--R                                                     Type: Expression Integer
+--E
+
+--S 21
+dd:=expandLog cc
+--R
+--R        log(sinh(a x)) + log(coth(a x)) - log(cosh(a x))
+--R   (4)  ------------------------------------------------
+--R                                a
+--R                                                     Type: Expression Integer
+--E
+
+--S 22     14:619 Schaums and Axiom agree
+ee:=complexNormalize dd
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.620~~~~~$\displaystyle
+\int{\frac{dx}{\coth{ax}}}~dx$}
+$$\int{\frac{1}{\coth{ax}}}=
+\frac{1}{a}\ln\cosh{ax}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 23
+aa:=integrate(1/coth(a*x),x)
+--R 
+--R
+--R                    2cosh(a x)
+--R        log(- ---------------------) - a x
+--R              sinh(a x) - cosh(a x)
+--R   (1)  ----------------------------------
+--R                         a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 24
+bb:=1/a*log(cosh(a*x))
+--R
+--R        log(cosh(a x))
+--R   (2)  --------------
+--R               a
+--R                                                     Type: Expression Integer
+--E
+
+--S 25
+cc:=aa-bb
+--R
+--R                                       2cosh(a x)
+--R        - log(cosh(a x)) + log(- ---------------------) - a x
+--R                                 sinh(a x) - cosh(a x)
+--R   (3)  -----------------------------------------------------
+--R                                  a
+--R                                                     Type: Expression Integer
+--E
+
+--S 26
+dd:=expandLog cc
+--R
+--R        - log(sinh(a x) - cosh(a x)) + log(- 2) - a x
+--R   (4)  ---------------------------------------------
+--R                              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 27     14:620 Schaums and Axiom differ by a constant
+ee:=complexNormalize dd
+--R
+--R        - log(- 1) + log(- 2)
+--R   (5)  ---------------------
+--R                  a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.621~~~~~$\displaystyle
+\int{x\coth{ax}}~dx$}
+$$\int{x\coth{ax}}=
+\frac{1}{a^2}\left\{
+ax+\frac{(ax)^3}{9}-\frac{(ax)^5}{225}+\cdots
+\frac{(-1)^{n-1}2^{2n}B_n(ax)^{2n+1}}{(2n+1)!}+\cdots\right\}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 28     14:621 Axiom cannot compute this integral
+aa:=integrate(x*coth(a*x),x)
+--R 
+--R
+--R           x
+--R         ++
+--I   (1)   |   %O coth(%O a)d%O
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.622~~~~~$\displaystyle
+\int{x\coth^2{ax}}~dx$}
+$$\int{x\coth^2{ax}}=
+\frac{x^2}{2}-\frac{x\coth{ax}}{a}+\frac{1}{a^2}\ln\sinh{ax}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 29
+aa:=integrate(x*coth(a*x)^2,x)
+--R 
+--R
+--R   (1)
+--R                    2                                   2
+--R         (2sinh(a x)  + 4cosh(a x)sinh(a x) + 2cosh(a x)  - 2)
+--R      *
+--R                     2sinh(a x)
+--R         log(- ---------------------)
+--R               sinh(a x) - cosh(a x)
+--R     + 
+--R         2 2                 2      2 2
+--R       (a x  - 4a x)sinh(a x)  + (2a x  - 8a x)cosh(a x)sinh(a x)
+--R     + 
+--R         2 2                 2    2 2
+--R       (a x  - 4a x)cosh(a x)  - a x
+--R  /
+--R       2         2     2                       2         2     2
+--R     2a sinh(a x)  + 4a cosh(a x)sinh(a x) + 2a cosh(a x)  - 2a
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 30
+bb:=x^2/2-(x*coth(a*x)/a)+1/a^2*log(sinh(a*x))
+--R
+--R                                            2 2
+--R        2log(sinh(a x)) - 2a x coth(a x) + a x
+--R   (2)  ---------------------------------------
+--R                            2
+--R                          2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 31
+cc:=aa-bb
+--R
+--R   (3)
+--R                   2                                  2
+--R       (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  + 1)log(sinh(a x))
+--R     + 
+--R                   2                                  2
+--R         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1)
+--R      *
+--R                     2sinh(a x)
+--R         log(- ---------------------)
+--R               sinh(a x) - cosh(a x)
+--R     + 
+--R                                      2
+--R       (a x coth(a x) - 2a x)sinh(a x)
+--R     + 
+--R       (2a x cosh(a x)coth(a x) - 4a x cosh(a x))sinh(a x)
+--R     + 
+--R                     2                                 2
+--R       (a x cosh(a x)  - a x)coth(a x) - 2a x cosh(a x)
+--R  /
+--R      2         2     2                      2         2    2
+--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 32
+dd:=expandLog cc
+--R
+--R   (4)
+--R                     2                                  2
+--R         (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  + 1)
+--R      *
+--R         log(sinh(a x) - cosh(a x))
+--R     + 
+--R                                                 2
+--R       (a x coth(a x) + log(- 2) - 2a x)sinh(a x)
+--R     + 
+--R       (2a x cosh(a x)coth(a x) + (2log(- 2) - 4a x)cosh(a x))sinh(a x)
+--R     + 
+--R                     2                                             2
+--R       (a x cosh(a x)  - a x)coth(a x) + (log(- 2) - 2a x)cosh(a x)  - log(- 2)
+--R  /
+--R      2         2     2                      2         2    2
+--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 33
+sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
+--R
+--R               2    cosh(2x) - 1
+--R   (5)  sinh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 34
+ee:=sinhsqrrule dd
+--R
+--R   (6)
+--R                                                         2
+--R         (- 4cosh(a x)sinh(a x) - cosh(2a x) - 2cosh(a x)  + 3)
+--R      *
+--R         log(sinh(a x) - cosh(a x))
+--R     + 
+--R       (4a x cosh(a x)coth(a x) + (4log(- 2) - 8a x)cosh(a x))sinh(a x)
+--R     + 
+--R                                       2
+--R       (a x cosh(2a x) + 2a x cosh(a x)  - 3a x)coth(a x)
+--R     + 
+--R                                                                2
+--R       (log(- 2) - 2a x)cosh(2a x) + (2log(- 2) - 4a x)cosh(a x)  - 3log(- 2)
+--R     + 
+--R       2a x
+--R  /
+--R       2                      2               2         2     2
+--R     4a cosh(a x)sinh(a x) + a cosh(2a x) + 2a cosh(a x)  - 3a
+--R                                                     Type: Expression Integer
+--E
+
+--S 35
+coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
+--R
+--R               2    cosh(2x) + 1
+--R   (7)  cosh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 36
+ff:=coshsqrrule ee
+--R
+--R   (8)
+--R       (- 2cosh(a x)sinh(a x) - cosh(2a x) + 1)log(sinh(a x) - cosh(a x))
+--R     + 
+--R       (2a x cosh(a x)coth(a x) + (2log(- 2) - 4a x)cosh(a x))sinh(a x)
+--R     + 
+--R       (a x cosh(2a x) - a x)coth(a x) + (log(- 2) - 2a x)cosh(2a x) - log(- 2)
+--R  /
+--R       2                      2              2
+--R     2a cosh(a x)sinh(a x) + a cosh(2a x) - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 37
+sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
+--R
+--I                             %L sinh(y + x) - %L sinh(y - x)
+--I   (9)  %L cosh(y)sinh(x) == -------------------------------
+--R                                            2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 38
+gg:=sinhcoshrule ff
+--R
+--R   (10)
+--R       (- sinh(2a x) - cosh(2a x) + 1)log(sinh(a x) - cosh(a x))
+--R     + 
+--R       (a x coth(a x) + log(- 2) - 2a x)sinh(2a x)
+--R     + 
+--R       (a x cosh(2a x) - a x)coth(a x) + (log(- 2) - 2a x)cosh(2a x) - log(- 2)
+--R  /
+--R      2              2              2
+--R     a sinh(2a x) + a cosh(2a x) - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 39     14:622 Schaums and Axiom differ by a constant
+hh:=complexNormalize gg
+--R
+--R         - log(- 1) + log(- 2)
+--R   (11)  ---------------------
+--R                    2
+--R                   a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.623~~~~~$\displaystyle
+\int{\frac{\coth{ax}}{x}}~dx$}
+$$\int{\frac{\coth{ax}}{x}}=
+-\frac{1}{ax}+\frac{(ax)}{3}-\frac{(ax)^3}{135}+\cdots
+\frac{(-1)^{n}2^{2n}B_n(ax)^{2n-1}}{(2n-1)(2n)!}+\cdots
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 40     14:623 Axiom cannot compute this integral
+aa:=integrate(coth(a*x)/x,x)
+--R 
+--R
+--R           x
+--I         ++  coth(%O a)
+--I   (1)   |   ---------- d%O
+--I        ++       %O
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.624~~~~~$\displaystyle
+\int{\frac{dx}{p+q\coth{ax}}}~dx$}
+$$\int{\frac{1}{p+q\coth{ax}}}=
+\frac{px}{p^2-q^2}-\frac{q}{a(p^2-q^2)}\ln(p\sinh{ax}+q\cosh{ax})
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 41
+aa:=integrate(1/(p+q*coth(a*x)),x)
+--R 
+--R
+--R              - 2p sinh(a x) - 2q cosh(a x)
+--R        q log(-----------------------------) + (- a q - a p)x
+--R                  sinh(a x) - cosh(a x)
+--R   (1)  -----------------------------------------------------
+--R                                2      2
+--R                             a q  - a p
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 42
+bb:=(p*x)/(p^2-q^2)-q/(a*(p^2-q^2))*log(p*sinh(a*x)+q*cosh(a*x))
+--R
+--R        q log(p sinh(a x) + q cosh(a x)) - a p x
+--R   (2)  ----------------------------------------
+--R                          2      2
+--R                       a q  - a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 43
+cc:=aa-bb
+--R
+--R   (3)
+--R                                                  - 2p sinh(a x) - 2q cosh(a x)
+--R       - q log(p sinh(a x) + q cosh(a x)) + q log(-----------------------------)
+--R                                                      sinh(a x) - cosh(a x)
+--R     + 
+--R       - a q x
+--R  /
+--R        2      2
+--R     a q  - a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 44
+dd:=expandLog cc
+--R
+--R   (4)
+--R       - q log(p sinh(a x) + q cosh(a x)) - q log(sinh(a x) - cosh(a x))
+--R     + 
+--R       q log(- p sinh(a x) - q cosh(a x)) + q log(2) - a q x
+--R  /
+--R        2      2
+--R     a q  - a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 45     14:624 Schaums and Axiom differ by a constant
+ee:=complexNormalize dd
+--R
+--R        q log(2) - 2q log(- 1)
+--R   (5)  ----------------------
+--R                 2      2
+--R              a q  - a p
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.625~~~~~$\displaystyle
+\int{\coth^n{ax}}~dx$}
+$$\int{\coth^n{ax}}=
+-\frac{\coth^{n-1}{ax}}{a(n-1)}+\int{\coth^{n-1}{ax}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 46     14:625 Axiom cannot compute this integral
+aa:=integrate(coth(a*x)^n,x)
+--R 
+--R
+--R           x
+--R         ++            n
+--I   (1)   |   coth(%O a) d%O
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 pp90-91
+\end{thebibliography}
+\end{document}
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diff --git a/src/axiom-website/CATS/schaum32.input.pamphlet b/src/axiom-website/CATS/schaum32.input.pamphlet
new file mode 100644
index 0000000..e5b2409
--- /dev/null
+++ b/src/axiom-website/CATS/schaum32.input.pamphlet
@@ -0,0 +1,999 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum32.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.626~~~~~$\displaystyle
+\int{{\rm sech~}{ax}}~dx$}
+$$\int{{\rm sech~}{ax}}=
+\frac{2}{a}\tanh^{-1}{e^{ax}}
+$$
+&lt;&lt;*&gt;&gt;=
+)spool schaum32.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1
+aa:=integrate(sech(a*x),x)
+--R 
+--R
+--R        2atan(sinh(a x) + cosh(a x))
+--R   (1)  ----------------------------
+--R                      a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 2
+bb:=2/a*atan(%e^(a*x))
+--R
+--R                a x
+--R        2atan(%e   )
+--R   (2)  ------------
+--R              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3
+cc:=aa-bb
+--R
+--R                                               a x
+--R        2atan(sinh(a x) + cosh(a x)) - 2atan(%e   )
+--R   (3)  -------------------------------------------
+--R                             a
+--R                                                     Type: Expression Integer
+--E
+
+--S 4
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (4)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 5
+dd:=atanrule cc
+--R
+--R                   a x
+--R               - %e    + %i           - sinh(a x) - cosh(a x) + %i
+--R        %i log(------------) - %i log(----------------------------)
+--R                  a x                  sinh(a x) + cosh(a x) + %i
+--R                %e    + %i
+--R   (5)  -----------------------------------------------------------
+--R                                     a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 6
+ee:=expandLog dd
+--R
+--R   (6)
+--R       %i log(sinh(a x) + cosh(a x) + %i) - %i log(sinh(a x) + cosh(a x) - %i)
+--R     + 
+--R                  a x                  a x
+--R       - %i log(%e    + %i) + %i log(%e    - %i)
+--R  /
+--R     a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 7      14:626 Schaums and Axiom agree
+ff:=complexNormalize ee
+--R
+--R   (7)  0
+--R                                             Type: Expression Complex Integer
+--E
+@
+
+\section{\cite{1}:14.627~~~~~$\displaystyle
+\int{{\rm sech}^2~{ax}}~dx$}
+$$\int{{\rm sech}^2~{ax}}=
+\frac{\tanh{ax}}{a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 8
+aa:=integrate(sech(a*x)^2,x)
+--R 
+--R
+--R                                     2
+--R   (1)  - -------------------------------------------------------
+--R                     2                                      2
+--R          a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 9
+bb:=tanh(a*x)/a
+--R
+--R        tanh(a x)
+--R   (2)  ---------
+--R            a
+--R                                                     Type: Expression Integer
+--E
+
+--S 10
+cc:=aa-bb
+--R
+--R                    2                                  2
+--R        (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)tanh(a x) - 2
+--R   (3)  ------------------------------------------------------------------
+--R                         2                                      2
+--R              a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 11
+sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
+--R
+--R               2    cosh(2x) - 1
+--R   (4)  sinh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 12
+dd:=sinhsqrrule cc
+--R
+--R                                                        2
+--R        (- 4cosh(a x)sinh(a x) - cosh(2a x) - 2cosh(a x)  - 1)tanh(a x) - 4
+--R   (5)  -------------------------------------------------------------------
+--R                                                                 2
+--R              4a cosh(a x)sinh(a x) + a cosh(2a x) + 2a cosh(a x)  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 13
+coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
+--R
+--R               2    cosh(2x) + 1
+--R   (6)  cosh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 14
+ee:=coshsqrrule dd
+--R
+--R        (- 2cosh(a x)sinh(a x) - cosh(2a x) - 1)tanh(a x) - 2
+--R   (7)  -----------------------------------------------------
+--R               2a cosh(a x)sinh(a x) + a cosh(2a x) + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 15
+sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
+--R
+--I                             %L sinh(y + x) - %L sinh(y - x)
+--I   (8)  %L cosh(y)sinh(x) == -------------------------------
+--R                                            2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 16
+ff:=sinhcoshrule ee
+--R
+--R        (- sinh(2a x) - cosh(2a x) - 1)tanh(a x) - 2
+--R   (9)  --------------------------------------------
+--R               a sinh(2a x) + a cosh(2a x) + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 17     14:627 Schaums and Axiom differ by a constant
+gg:=complexNormalize ff
+--R
+--R           1
+--R   (10)  - -
+--R           a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.628~~~~~$\displaystyle
+\int{{\rm sech}^3~{ax}}~dx$}
+$$\int{{\rm sech}^3~{ax}}=
+\frac{{\rm sech}~{ax}~\tanh{ax}}{2a}+\frac{1}{2a}\tan^{-1}{\rm ~sech~}{ax}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 18
+aa:=integrate(sech(a*x)^3,x)
+--R 
+--R
+--R   (1)
+--R                    4                      3              2              2
+--R           sinh(a x)  + 4cosh(a x)sinh(a x)  + (6cosh(a x)  + 2)sinh(a x)
+--R         + 
+--R                      3                                   4             2
+--R           (4cosh(a x)  + 4cosh(a x))sinh(a x) + cosh(a x)  + 2cosh(a x)  + 1
+--R      *
+--R         atan(sinh(a x) + cosh(a x))
+--R     + 
+--R                3                      2              2
+--R       sinh(a x)  + 3cosh(a x)sinh(a x)  + (3cosh(a x)  - 1)sinh(a x)
+--R     + 
+--R                3
+--R       cosh(a x)  - cosh(a x)
+--R  /
+--R                  4                        3                2               2
+--R       a sinh(a x)  + 4a cosh(a x)sinh(a x)  + (6a cosh(a x)  + 2a)sinh(a x)
+--R     + 
+--R                  3                                       4               2
+--R     (4a cosh(a x)  + 4a cosh(a x))sinh(a x) + a cosh(a x)  + 2a cosh(a x)  + a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 19
+bb:=(sech(a*x)*tanh(a*x))/(2*a)+1/(2*a)*atan(sinh(a*x))
+--R
+--R        atan(sinh(a x)) + sech(a x)tanh(a x)
+--R   (2)  ------------------------------------
+--R                         2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 20     14:628 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R                     4                      3               2              2
+--R           2sinh(a x)  + 8cosh(a x)sinh(a x)  + (12cosh(a x)  + 4)sinh(a x)
+--R         + 
+--R                      3                                    4             2
+--R           (8cosh(a x)  + 8cosh(a x))sinh(a x) + 2cosh(a x)  + 4cosh(a x)  + 2
+--R      *
+--R         atan(sinh(a x) + cosh(a x))
+--R     + 
+--R                      4                      3                2              2
+--R           - sinh(a x)  - 4cosh(a x)sinh(a x)  + (- 6cosh(a x)  - 2)sinh(a x)
+--R         + 
+--R                        3                                   4             2
+--R           (- 4cosh(a x)  - 4cosh(a x))sinh(a x) - cosh(a x)  - 2cosh(a x)  - 1
+--R      *
+--R         atan(sinh(a x))
+--R     + 
+--R                               4                               3
+--R           - sech(a x)sinh(a x)  - 4cosh(a x)sech(a x)sinh(a x)
+--R         + 
+--R                        2                       2
+--R           (- 6cosh(a x)  - 2)sech(a x)sinh(a x)
+--R         + 
+--R                        3
+--R           (- 4cosh(a x)  - 4cosh(a x))sech(a x)sinh(a x)
+--R         + 
+--R                       4             2
+--R           (- cosh(a x)  - 2cosh(a x)  - 1)sech(a x)
+--R      *
+--R         tanh(a x)
+--R     + 
+--R                 3                      2              2
+--R       2sinh(a x)  + 6cosh(a x)sinh(a x)  + (6cosh(a x)  - 2)sinh(a x)
+--R     + 
+--R                 3
+--R       2cosh(a x)  - 2cosh(a x)
+--R  /
+--R                   4                        3                 2               2
+--R       2a sinh(a x)  + 8a cosh(a x)sinh(a x)  + (12a cosh(a x)  + 4a)sinh(a x)
+--R     + 
+--R                    3                                        4               2
+--R       (8a cosh(a x)  + 8a cosh(a x))sinh(a x) + 2a cosh(a x)  + 4a cosh(a x)
+--R     + 
+--R       2a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.629~~~~~$\displaystyle
+\int{{\rm sech}^n~{ax}~{\tanh{ax}}}~dx$}
+$$\int{{\rm sech~}^n{ax}~{\tanh{ax}}}=
+-\frac{{\rm sech~}^{n}{ax}}{na}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 21
+aa:=integrate(sech(a*x)^n*tanh(a*x),x)
+--R 
+--R
+--R   (1)
+--R                                 2sinh(a x) + 2cosh(a x)
+--R       - sinh(n log(-------------------------------------------------))
+--R                             2                                  2
+--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1
+--R     + 
+--R                                 2sinh(a x) + 2cosh(a x)
+--R       - cosh(n log(-------------------------------------------------))
+--R                             2                                  2
+--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1
+--R  /
+--R     a n
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 22
+bb:=-sech(a*x)^n/(n*a)
+--R
+--R                   n
+--R          sech(a x)
+--R   (2)  - ----------
+--R              a n
+--R                                                     Type: Expression Integer
+--E
+
+--S 23
+cc:=aa-bb
+--R
+--R   (3)
+--R                                 2sinh(a x) + 2cosh(a x)
+--R       - sinh(n log(-------------------------------------------------))
+--R                             2                                  2
+--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1
+--R     + 
+--R                                 2sinh(a x) + 2cosh(a x)
+--R       - cosh(n log(-------------------------------------------------))
+--R                             2                                  2
+--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1
+--R     + 
+--R                n
+--R       sech(a x)
+--R  /
+--R     a n
+--R                                                     Type: Expression Integer
+--E
+
+--S 24
+sechrule:=rule(sech(x) == 1/cosh(x))
+--R
+--R                      1
+--R   (4)  sech(x) == -------
+--R                   cosh(x)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 25
+dd:=sechrule cc
+--R
+--R   (5)
+--R                                 2sinh(a x) + 2cosh(a x)
+--R       - sinh(n log(-------------------------------------------------))
+--R                             2                                  2
+--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1
+--R     + 
+--R                                 2sinh(a x) + 2cosh(a x)
+--R       - cosh(n log(-------------------------------------------------))
+--R                             2                                  2
+--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1
+--R     + 
+--R            1     n
+--R       (---------)
+--R        cosh(a x)
+--R  /
+--R     a n
+--R                                                     Type: Expression Integer
+--E
+
+--S 26
+ee:=expandLog dd
+--R
+--R   (6)
+--R       sinh
+--R                           2                                  2
+--R            n log(sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1)
+--R          + 
+--R            - n log(sinh(a x) + cosh(a x)) - n log(2)
+--R     + 
+--R       -
+--R          cosh
+--R                              2                                  2
+--R               n log(sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1)
+--R             + 
+--R               - n log(sinh(a x) + cosh(a x)) - n log(2)
+--R     + 
+--R            1     n
+--R       (---------)
+--R        cosh(a x)
+--R  /
+--R     a n
+--R                                                     Type: Expression Integer
+--E
+
+--S 27     14:629 Schaums and Axiom agree
+ff:=complexNormalize ee
+--R
+--R   (7)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.630~~~~~$\displaystyle
+\int{\frac{dx}{{\rm sech~}{ax}}}~dx$}
+$$\int{\frac{1}{{\rm sech~}{ax}}}=
+\frac{{\rm sech}~{ax}}{a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 28
+aa:=integrate(1/sech(a*x),x)
+--R 
+--R
+--R        sinh(a x)
+--R   (1)  ---------
+--R            a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 29
+bb:=sinh(a*x)/a
+--R
+--R        sinh(a x)
+--R   (2)  ---------
+--R            a
+--R                                                     Type: Expression Integer
+--E
+
+--S 30     14:630 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.631~~~~~$\displaystyle
+\int{x{\rm ~sech~}{ax}}~dx$}
+$$\int{x{\rm ~sech~}{ax}}=
+\frac{1}{a^2}\left\{
+\frac{(ax)^2}{2}-\frac{(ax)^4}{8}+\frac{5(ax)^6}{144}+\cdots
+\frac{(-1)^{n}E_n(ax)^{2n+2}}{(2n+2)(2n)!}+\cdots\right\}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 31     14:631 Axiom cannot compute this integral
+aa:=integrate(x*sech(a*x),x)
+--R 
+--R
+--R           x
+--R         ++
+--I   (1)   |   %O sech(%O a)d%O
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.632~~~~~$\displaystyle
+\int{x~{\rm sech}^2~{ax}}~dx$}
+$$\int{x~{\rm sech}^2~{ax}}=
+\frac{x\tanh{ax}}{a}-\frac{1}{a^2}\ln\cosh{ax}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 32
+aa:=integrate(x*sech(a*x)^2,x)
+--R 
+--R
+--R   (1)
+--R                     2                                  2
+--R         (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)
+--R      *
+--R                     2cosh(a x)
+--R         log(- ---------------------)
+--R               sinh(a x) - cosh(a x)
+--R     + 
+--R                     2                                           2
+--R       2a x sinh(a x)  + 4a x cosh(a x)sinh(a x) + 2a x cosh(a x)
+--R  /
+--R      2         2     2                      2         2    2
+--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 33
+bb:=(x*tanh(a*x))/a-1/a^2*log(cosh(a*x))
+--R
+--R        - log(cosh(a x)) + a x tanh(a x)
+--R   (2)  --------------------------------
+--R                        2
+--R                       a
+--R                                                     Type: Expression Integer
+--E
+
+--S 34
+cc:=aa-bb
+--R
+--R   (3)
+--R                 2                                  2
+--R       (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1)log(cosh(a x))
+--R     + 
+--R                     2                                  2
+--R         (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)
+--R      *
+--R                     2cosh(a x)
+--R         log(- ---------------------)
+--R               sinh(a x) - cosh(a x)
+--R     + 
+--R                         2                                          2
+--R         (- a x sinh(a x)  - 2a x cosh(a x)sinh(a x) - a x cosh(a x)  - a x)
+--R      *
+--R         tanh(a x)
+--R     + 
+--R                     2                                           2
+--R       2a x sinh(a x)  + 4a x cosh(a x)sinh(a x) + 2a x cosh(a x)
+--R  /
+--R      2         2     2                      2         2    2
+--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 35
+dd:=expandLog cc
+--R
+--R   (4)
+--R                   2                                  2
+--R         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1)
+--R      *
+--R         log(sinh(a x) - cosh(a x))
+--R     + 
+--R                         2                                          2
+--R         (- a x sinh(a x)  - 2a x cosh(a x)sinh(a x) - a x cosh(a x)  - a x)
+--R      *
+--R         tanh(a x)
+--R     + 
+--R                                   2
+--R       (- log(- 2) + 2a x)sinh(a x)  + (- 2log(- 2) + 4a x)cosh(a x)sinh(a x)
+--R     + 
+--R                                   2
+--R       (- log(- 2) + 2a x)cosh(a x)  - log(- 2)
+--R  /
+--R      2         2     2                      2         2    2
+--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 36
+sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
+--R
+--R               2    cosh(2x) - 1
+--R   (5)  sinh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 37
+ee:=sinhsqrrule dd
+--R
+--R   (6)
+--R                                                       2
+--R         (4cosh(a x)sinh(a x) + cosh(2a x) + 2cosh(a x)  + 1)
+--R      *
+--R         log(sinh(a x) - cosh(a x))
+--R     + 
+--R                                                                     2
+--R         (- 4a x cosh(a x)sinh(a x) - a x cosh(2a x) - 2a x cosh(a x)  - a x)
+--R      *
+--R         tanh(a x)
+--R     + 
+--R       (- 4log(- 2) + 8a x)cosh(a x)sinh(a x) + (- log(- 2) + 2a x)cosh(2a x)
+--R     + 
+--R                                    2
+--R       (- 2log(- 2) + 4a x)cosh(a x)  - log(- 2) - 2a x
+--R  /
+--R       2                      2               2         2    2
+--R     4a cosh(a x)sinh(a x) + a cosh(2a x) + 2a cosh(a x)  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 38
+coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
+--R
+--R               2    cosh(2x) + 1
+--R   (7)  cosh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 39
+ff:=coshsqrrule ee
+--R
+--R   (8)
+--R       (2cosh(a x)sinh(a x) + cosh(2a x) + 1)log(sinh(a x) - cosh(a x))
+--R     + 
+--R       (- 2a x cosh(a x)sinh(a x) - a x cosh(2a x) - a x)tanh(a x)
+--R     + 
+--R       (- 2log(- 2) + 4a x)cosh(a x)sinh(a x) + (- log(- 2) + 2a x)cosh(2a x)
+--R     + 
+--R       - log(- 2)
+--R  /
+--R       2                      2              2
+--R     2a cosh(a x)sinh(a x) + a cosh(2a x) + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 40
+sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
+--R
+--I                             %P sinh(y + x) - %P sinh(y - x)
+--I   (9)  %P cosh(y)sinh(x) == -------------------------------
+--R                                            2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 41
+gg:=sinhcoshrule ff
+--R
+--R   (10)
+--R       (sinh(2a x) + cosh(2a x) + 1)log(sinh(a x) - cosh(a x))
+--R     + 
+--R       (- a x sinh(2a x) - a x cosh(2a x) - a x)tanh(a x)
+--R     + 
+--R       (- log(- 2) + 2a x)sinh(2a x) + (- log(- 2) + 2a x)cosh(2a x) - log(- 2)
+--R  /
+--R      2              2              2
+--R     a sinh(2a x) + a cosh(2a x) + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 42     14:632 Schaums and Axiom differ by a constant
+hh:=complexNormalize gg
+--R
+--R         log(- 1) - log(- 2)
+--R   (11)  -------------------
+--R                   2
+--R                  a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.633~~~~~$\displaystyle
+\int{\frac{{\rm sech~}{ax}}{x}}~dx$}
+$$\int{\frac{{\rm sech~}{ax}}{x}}=
+\ln{x}-\frac{(ax)^2}{4}+\frac{5(ax)^4}{96}-\frac{61(ax)^6}{4320}+\cdots
+\frac{(-1)^{n}E_n(ax)^{2n}}{2n(2n)!}+\cdots
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 43     14:633 Axiom cannot compute this integral
+aa:=integrate(sech(a*x)/x,x)
+--R 
+--R
+--R           x
+--I         ++  sech(%O a)
+--I   (1)   |   ---------- d%O
+--I        ++       %O
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.634~~~~~$\displaystyle
+\int{\frac{dx}{q+p{\rm ~sech~}{ax}}}~dx$}
+$$\int{\frac{1}{q+p{\rm ~sech~}{ax}}}=
+\frac{x}{q}-\frac{p}{q}\int{\frac{dx}{p+q\cosh{ax}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 44
+aa:=integrate(1/(q+p*sech(a*x)),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R           p
+--R        *
+--R           log
+--R                       2         2      2
+--R                      q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x)
+--R                    + 
+--R                       2         2                     2     2
+--R                      q cosh(a x)  + 2p q cosh(a x) - q  + 2p
+--R                 *
+--R                     +---------+
+--R                     |   2    2
+--R                    \|- q  + p
+--R                + 
+--R                     3     2                   3     2                  2     3
+--R                (- 2q  + 2p q)sinh(a x) + (- 2q  + 2p q)cosh(a x) - 2p q  + 2p
+--R             /
+--R                             2                                             2
+--R                  q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R                + 
+--R                  2p cosh(a x) + q
+--R       + 
+--R             +---------+
+--R             |   2    2
+--R         a x\|- q  + p
+--R    /
+--R           +---------+
+--R           |   2    2
+--R       a q\|- q  + p
+--R     ,
+--R                                              +-------+
+--R                                              | 2    2         +-------+
+--R              (q sinh(a x) + q cosh(a x) + p)\|q  - p          | 2    2
+--R    - 2p atan(-----------------------------------------) + a x\|q  - p
+--R                                2    2
+--R                               q  - p
+--R    --------------------------------------------------------------------]
+--R                                    +-------+
+--R                                    | 2    2
+--R                                a q\|q  - p
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+
+--S 45
+t1:=integrate(1/(p+q*cosh(a*x)),x)
+--R
+--R   (2)
+--R   [
+--R       log
+--R                   2         2      2                              2         2
+--R                  q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R                + 
+--R                                    2     2
+--R                  2p q cosh(a x) - q  + 2p
+--R             *
+--R                 +---------+
+--R                 |   2    2
+--R                \|- q  + p
+--R            + 
+--R                 3     2                 3     2                  2     3
+--R              (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
+--R         /
+--R                         2                                             2
+--R              q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R            + 
+--R              2p cosh(a x) + q
+--R    /
+--R         +---------+
+--R         |   2    2
+--R       a\|- q  + p
+--R     ,
+--R                                          +-------+
+--R                                          | 2    2
+--R          (q sinh(a x) + q cosh(a x) + p)\|q  - p
+--R    2atan(-----------------------------------------)
+--R                            2    2
+--R                           q  - p
+--R    ------------------------------------------------]
+--R                         +-------+
+--R                         | 2    2
+--R                       a\|q  - p
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 46
+bb1:=x/q-p/q*t1.1
+--R
+--R   (3)
+--R       -
+--R            p
+--R         *
+--R            log
+--R                        2         2      2
+--R                       q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x)
+--R                     + 
+--R                        2         2                     2     2
+--R                       q cosh(a x)  + 2p q cosh(a x) - q  + 2p
+--R                  *
+--R                      +---------+
+--R                      |   2    2
+--R                     \|- q  + p
+--R                 + 
+--R                      3     2                 3     2                  2     3
+--R                   (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
+--R              /
+--R                              2                                             2
+--R                   q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R                 + 
+--R                   2p cosh(a x) + q
+--R     + 
+--R           +---------+
+--R           |   2    2
+--R       a x\|- q  + p
+--R  /
+--R         +---------+
+--R         |   2    2
+--R     a q\|- q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 47
+bb2:=x/q-p/q*t1.2
+--R
+--R                                                  +-------+
+--R                                                  | 2    2         +-------+
+--R                  (q sinh(a x) + q cosh(a x) + p)\|q  - p          | 2    2
+--R        - 2p atan(-----------------------------------------) + a x\|q  - p
+--R                                    2    2
+--R                                   q  - p
+--R   (4)  --------------------------------------------------------------------
+--R                                        +-------+
+--R                                        | 2    2
+--R                                    a q\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 48
+cc1:=aa.1-bb1
+--R
+--R   (5)
+--R         p
+--R      *
+--R         log
+--R                     2         2      2                              2         2
+--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R                  + 
+--R                                      2     2
+--R                    2p q cosh(a x) - q  + 2p
+--R               *
+--R                   +---------+
+--R                   |   2    2
+--R                  \|- q  + p
+--R              + 
+--R                   3     2                 3     2                  2     3
+--R                (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
+--R           /
+--R                           2                                             2
+--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R              + 
+--R                2p cosh(a x) + q
+--R     + 
+--R         p
+--R      *
+--R         log
+--R                     2         2      2                              2         2
+--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R                  + 
+--R                                      2     2
+--R                    2p q cosh(a x) - q  + 2p
+--R               *
+--R                   +---------+
+--R                   |   2    2
+--R                  \|- q  + p
+--R              + 
+--R                     3     2                   3     2                  2     3
+--R                (- 2q  + 2p q)sinh(a x) + (- 2q  + 2p q)cosh(a x) - 2p q  + 2p
+--R           /
+--R                           2                                             2
+--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R              + 
+--R                2p cosh(a x) + q
+--R  /
+--R         +---------+
+--R         |   2    2
+--R     a q\|- q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 49
+cc2:=aa.2-bb1
+--R
+--R   (6)
+--R           +-------+
+--R           | 2    2
+--R         p\|q  - p
+--R      *
+--R         log
+--R                     2         2      2                              2         2
+--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R                  + 
+--R                                      2     2
+--R                    2p q cosh(a x) - q  + 2p
+--R               *
+--R                   +---------+
+--R                   |   2    2
+--R                  \|- q  + p
+--R              + 
+--R                   3     2                 3     2                  2     3
+--R                (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
+--R           /
+--R                           2                                             2
+--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R              + 
+--R                2p cosh(a x) + q
+--R     + 
+--R                                                            +-------+
+--R            +---------+                                     | 2    2
+--R            |   2    2      (q sinh(a x) + q cosh(a x) + p)\|q  - p
+--R       - 2p\|- q  + p  atan(-----------------------------------------)
+--R                                              2    2
+--R                                             q  - p
+--R  /
+--R         +---------+ +-------+
+--R         |   2    2  | 2    2
+--R     a q\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 50
+cc3:=aa.1-bb2
+--R
+--R   (7)
+--R           +-------+
+--R           | 2    2
+--R         p\|q  - p
+--R      *
+--R         log
+--R                     2         2      2                              2         2
+--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R                  + 
+--R                                      2     2
+--R                    2p q cosh(a x) - q  + 2p
+--R               *
+--R                   +---------+
+--R                   |   2    2
+--R                  \|- q  + p
+--R              + 
+--R                     3     2                   3     2                  2     3
+--R                (- 2q  + 2p q)sinh(a x) + (- 2q  + 2p q)cosh(a x) - 2p q  + 2p
+--R           /
+--R                           2                                             2
+--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R              + 
+--R                2p cosh(a x) + q
+--R     + 
+--R                                                          +-------+
+--R          +---------+                                     | 2    2
+--R          |   2    2      (q sinh(a x) + q cosh(a x) + p)\|q  - p
+--R       2p\|- q  + p  atan(-----------------------------------------)
+--R                                            2    2
+--R                                           q  - p
+--R  /
+--R         +---------+ +-------+
+--R         |   2    2  | 2    2
+--R     a q\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 51     14:634 Schaums and Axiom agree
+cc4:=aa.2-bb2
+--R
+--R   (8)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.635~~~~~$\displaystyle
+\int{{\rm sech}^n~{ax}}~dx$}
+$$\int{{\rm sech}^n~{ax}}=
+\frac{{\rm sech}^{n-2}~{ax}~\tanh{ax}}{a(n-1)}
++\frac{n-2}{n-1}\int{{\rm sech}^{n-2}~{ax}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 52     14:635 Axiom cannot compute this integral
+aa:=integrate(sech(a*x)^n,x)
+--R 
+--R
+--R           x
+--R         ++            n
+--I   (1)   |   sech(%O a) d%O
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 p91
+\end{thebibliography}
+\end{document}
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diff --git a/src/axiom-website/CATS/schaum33.input.pamphlet b/src/axiom-website/CATS/schaum33.input.pamphlet
new file mode 100644
index 0000000..61506d7
--- /dev/null
+++ b/src/axiom-website/CATS/schaum33.input.pamphlet
@@ -0,0 +1,1021 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum33.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.636~~~~~$\displaystyle
+\int{{\rm csch~}{ax}}~dx$}
+$$\int{{\rm csch~}{ax}}=
+\frac{1}{a}\ln\tanh{\frac{ax}{2}}
+$$
+&lt;&lt;*&gt;&gt;=
+)spool schaum33.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1
+aa:=integrate(csch(a*x),x)
+--R 
+--R
+--R        - log(sinh(a x) + cosh(a x) + 1) + log(sinh(a x) + cosh(a x) - 1)
+--R   (1)  -----------------------------------------------------------------
+--R                                        a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 2
+bb:=1/a*log(tanh((a*x)/2))
+--R
+--R                 a x
+--R        log(tanh(---))
+--R                  2
+--R   (2)  --------------
+--R               a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3
+cc:=aa-bb
+--R
+--R   (3)
+--R                  a x
+--R       - log(tanh(---)) - log(sinh(a x) + cosh(a x) + 1)
+--R                   2
+--R     + 
+--R       log(sinh(a x) + cosh(a x) - 1)
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 4      14:636 Schaums and Axiom agree
+dd:=complexNormalize cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.637~~~~~$\displaystyle
+\int{{\rm csch}^2~{ax}}~dx$}
+$$\int{{\rm csch}^2~{ax}}=
+-\frac{\coth{ax}}{a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 5
+aa:=integrate(csch(a*x)^2,x)
+--R 
+--R
+--R                                     2
+--R   (1)  - -------------------------------------------------------
+--R                     2                                      2
+--R          a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 6
+bb:=-coth(a*x)/a
+--R
+--R          coth(a x)
+--R   (2)  - ---------
+--R              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 7      14:637 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R                         2
+--R       coth(a x)sinh(a x)  + 2cosh(a x)coth(a x)sinh(a x)
+--R     + 
+--R                 2
+--R       (cosh(a x)  - 1)coth(a x) - 2
+--R  /
+--R                2                                      2
+--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.638~~~~~$\displaystyle
+\int{{\rm csch}^3~{ax}}~dx$}
+$$\int{{\rm csch}^3~{ax}}=
+-\frac{{\rm csch~}{ax}\coth{ax}}{2a}-\frac{1}{2a}\ln\tanh\frac{ax}{2}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 8
+aa:=integrate(csch(a*x)^3,x)
+--R 
+--R
+--R   (1)
+--R                    4                      3              2              2
+--R           sinh(a x)  + 4cosh(a x)sinh(a x)  + (6cosh(a x)  - 2)sinh(a x)
+--R         + 
+--R                      3                                   4             2
+--R           (4cosh(a x)  - 4cosh(a x))sinh(a x) + cosh(a x)  - 2cosh(a x)  + 1
+--R      *
+--R         log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R                      4                      3                2              2
+--R           - sinh(a x)  - 4cosh(a x)sinh(a x)  + (- 6cosh(a x)  + 2)sinh(a x)
+--R         + 
+--R                        3                                   4             2
+--R           (- 4cosh(a x)  + 4cosh(a x))sinh(a x) - cosh(a x)  + 2cosh(a x)  - 1
+--R      *
+--R         log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R                   3                      2                2
+--R       - 2sinh(a x)  - 6cosh(a x)sinh(a x)  + (- 6cosh(a x)  - 2)sinh(a x)
+--R     + 
+--R                   3
+--R       - 2cosh(a x)  - 2cosh(a x)
+--R  /
+--R                   4                        3                 2               2
+--R       2a sinh(a x)  + 8a cosh(a x)sinh(a x)  + (12a cosh(a x)  - 4a)sinh(a x)
+--R     + 
+--R                    3                                        4               2
+--R       (8a cosh(a x)  - 8a cosh(a x))sinh(a x) + 2a cosh(a x)  - 4a cosh(a x)
+--R     + 
+--R       2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 9
+bb:=-(csch(a*x)*coth(a*x))/(2*a)-1/(2*a)*log(tanh((a*x)/2))
+--R
+--R                   a x
+--R        - log(tanh(---)) - coth(a x)csch(a x)
+--R                    2
+--R   (2)  -------------------------------------
+--R                          2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 10     14:638 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R                    4                      3              2              2
+--R           sinh(a x)  + 4cosh(a x)sinh(a x)  + (6cosh(a x)  - 2)sinh(a x)
+--R         + 
+--R                      3                                   4             2
+--R           (4cosh(a x)  - 4cosh(a x))sinh(a x) + cosh(a x)  - 2cosh(a x)  + 1
+--R      *
+--R                  a x
+--R         log(tanh(---))
+--R                   2
+--R     + 
+--R                    4                      3              2              2
+--R           sinh(a x)  + 4cosh(a x)sinh(a x)  + (6cosh(a x)  - 2)sinh(a x)
+--R         + 
+--R                      3                                   4             2
+--R           (4cosh(a x)  - 4cosh(a x))sinh(a x) + cosh(a x)  - 2cosh(a x)  + 1
+--R      *
+--R         log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R                      4                      3                2              2
+--R           - sinh(a x)  - 4cosh(a x)sinh(a x)  + (- 6cosh(a x)  + 2)sinh(a x)
+--R         + 
+--R                        3                                   4             2
+--R           (- 4cosh(a x)  + 4cosh(a x))sinh(a x) - cosh(a x)  + 2cosh(a x)  - 1
+--R      *
+--R         log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R                                  4
+--R       coth(a x)csch(a x)sinh(a x)
+--R     + 
+--R                                                  3
+--R       (4cosh(a x)coth(a x)csch(a x) - 2)sinh(a x)
+--R     + 
+--R                   2                                              2
+--R       ((6cosh(a x)  - 2)coth(a x)csch(a x) - 6cosh(a x))sinh(a x)
+--R     + 
+--R                   3                                             2
+--R       ((4cosh(a x)  - 4cosh(a x))coth(a x)csch(a x) - 6cosh(a x)  - 2)sinh(a x)
+--R     + 
+--R               4             2                                    3
+--R     (cosh(a x)  - 2cosh(a x)  + 1)coth(a x)csch(a x) - 2cosh(a x)  - 2cosh(a x)
+--R  /
+--R                   4                        3                 2               2
+--R       2a sinh(a x)  + 8a cosh(a x)sinh(a x)  + (12a cosh(a x)  - 4a)sinh(a x)
+--R     + 
+--R                    3                                        4               2
+--R       (8a cosh(a x)  - 8a cosh(a x))sinh(a x) + 2a cosh(a x)  - 4a cosh(a x)
+--R     + 
+--R       2a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.639~~~~~$\displaystyle
+\int{{\rm csch}^n~{ax}~{\coth{ax}}}~dx$}
+$$\int{{\rm csch~}^n{ax}~{\coth{ax}}}=
+-\frac{{\rm csch~}^{n}{ax}}{na}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 11
+aa:=integrate(csch(a*x)^n*coth(a*x),x)
+--R 
+--R
+--R   (1)
+--R                                 2sinh(a x) + 2cosh(a x)
+--R       - sinh(n log(-------------------------------------------------))
+--R                             2                                  2
+--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1
+--R     + 
+--R                                 2sinh(a x) + 2cosh(a x)
+--R       - cosh(n log(-------------------------------------------------))
+--R                             2                                  2
+--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1
+--R  /
+--R     a n
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 12
+bb:=-csch(a*x)^n/(n*a)
+--R
+--R                   n
+--R          csch(a x)
+--R   (2)  - ----------
+--R              a n
+--R                                                     Type: Expression Integer
+--E
+
+--S 13
+cc:=aa-bb
+--R
+--R   (3)
+--R                                 2sinh(a x) + 2cosh(a x)
+--R       - sinh(n log(-------------------------------------------------))
+--R                             2                                  2
+--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1
+--R     + 
+--R                                 2sinh(a x) + 2cosh(a x)
+--R       - cosh(n log(-------------------------------------------------))
+--R                             2                                  2
+--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1
+--R     + 
+--R                n
+--R       csch(a x)
+--R  /
+--R     a n
+--R                                                     Type: Expression Integer
+--E
+
+--S 14
+cschrule:=rule(csch(x) == 1/sinh(x))
+--R
+--R                      1
+--R   (4)  csch(x) == -------
+--R                   sinh(x)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 15
+dd:=cschrule cc
+--R
+--R   (5)
+--R                                 2sinh(a x) + 2cosh(a x)
+--R       - sinh(n log(-------------------------------------------------))
+--R                             2                                  2
+--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1
+--R     + 
+--R                                 2sinh(a x) + 2cosh(a x)
+--R       - cosh(n log(-------------------------------------------------))
+--R                             2                                  2
+--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1
+--R     + 
+--R            1     n
+--R       (---------)
+--R        sinh(a x)
+--R  /
+--R     a n
+--R                                                     Type: Expression Integer
+--E
+
+--S 16
+ee:=expandLog dd
+--R
+--R   (6)
+--R       sinh
+--R                           2                                  2
+--R            n log(sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1)
+--R          + 
+--R            - n log(sinh(a x) + cosh(a x)) - n log(2)
+--R     + 
+--R       -
+--R          cosh
+--R                              2                                  2
+--R               n log(sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1)
+--R             + 
+--R               - n log(sinh(a x) + cosh(a x)) - n log(2)
+--R     + 
+--R            1     n
+--R       (---------)
+--R        sinh(a x)
+--R  /
+--R     a n
+--R                                                     Type: Expression Integer
+--E
+
+--S 17
+sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
+--R
+--R               2    cosh(2x) - 1
+--R   (7)  sinh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 18
+ff:=sinhsqrrule ee
+--R
+--R   (8)
+--R       sinh
+--R                                                               2
+--R                  4cosh(a x)sinh(a x) + cosh(2a x) + 2cosh(a x)  - 3
+--R            n log(--------------------------------------------------)
+--R                                           2
+--R          + 
+--R            - n log(sinh(a x) + cosh(a x)) - n log(2)
+--R     + 
+--R       -
+--R          cosh
+--R                                                                  2
+--R                     4cosh(a x)sinh(a x) + cosh(2a x) + 2cosh(a x)  - 3
+--R               n log(--------------------------------------------------)
+--R                                              2
+--R             + 
+--R               - n log(sinh(a x) + cosh(a x)) - n log(2)
+--R     + 
+--R            1     n
+--R       (---------)
+--R        sinh(a x)
+--R  /
+--R     a n
+--R                                                     Type: Expression Integer
+--E
+
+--S 19
+coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
+--R
+--R               2    cosh(2x) + 1
+--R   (9)  cosh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 20
+gg:=coshsqrrule ff
+--R
+--R   (10)
+--R       sinh
+--R            n log(2cosh(a x)sinh(a x) + cosh(2a x) - 1)
+--R          + 
+--R            - n log(sinh(a x) + cosh(a x)) - n log(2)
+--R     + 
+--R       -
+--R          cosh
+--R               n log(2cosh(a x)sinh(a x) + cosh(2a x) - 1)
+--R             + 
+--R               - n log(sinh(a x) + cosh(a x)) - n log(2)
+--R     + 
+--R            1     n
+--R       (---------)
+--R        sinh(a x)
+--R  /
+--R     a n
+--R                                                     Type: Expression Integer
+--E
+
+--S 21
+sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
+--R
+--I                              %O sinh(y + x) - %O sinh(y - x)
+--I   (11)  %O cosh(y)sinh(x) == -------------------------------
+--R                                             2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 22
+hh:=sinhcoshrule gg
+--R
+--R   (12)
+--R       sinh
+--R            n log(sinh(2a x) + cosh(2a x) - 1) - n log(sinh(a x) + cosh(a x))
+--R          + 
+--R            - n log(2)
+--R     + 
+--R       -
+--R          cosh
+--R               n log(sinh(2a x) + cosh(2a x) - 1) - n log(sinh(a x) + cosh(a x))
+--R             + 
+--R               - n log(2)
+--R     + 
+--R            1     n
+--R       (---------)
+--R        sinh(a x)
+--R  /
+--R     a n
+--R                                                     Type: Expression Integer
+--E
+
+--S 23     14:639 Schaums and Axiom agree
+ii:=complexNormalize hh
+--R
+--R   (13)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.640~~~~~$\displaystyle
+\int{\frac{dx}{{\rm csch~}{ax}}}~dx$}
+$$\int{\frac{1}{{\rm csch~}{ax}}}=
+\frac{1}{a}{\rm cosh}~{ax}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 24
+aa:=integrate(1/csch(a*x),x)
+--R 
+--R
+--R        cosh(a x)
+--R   (1)  ---------
+--R            a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 25
+bb:=1/a*cosh(a*x)
+--R
+--R        cosh(a x)
+--R   (2)  ---------
+--R            a
+--R                                                     Type: Expression Integer
+--E
+
+--S 26     14:640 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.641~~~~~$\displaystyle
+\int{x{\rm ~csch~}{ax}}~dx$}
+$$\int{x{\rm ~csch~}{ax}}=
+\frac{1}{a^2}\left\{
+ax-\frac{(ax)^3}{18}+\frac{7(ax)^5}{1800}+\cdots+
+\frac{2(-1)^n(2^{2n-1}-1)B_n(ax)^{2n+1}}{(2n+1)!}+\cdots\right\}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 27     14:641 Axiom cannot compute this integral
+aa:=integrate(x*csch(a*x),x)
+--R 
+--R
+--R           x
+--R         ++
+--I   (1)   |   %O csch(%O a)d%O
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.642~~~~~$\displaystyle
+\int{x~{\rm csch}^2~{ax}}~dx$}
+$$\int{x~{\rm csch}^2~{ax}}=
+-\frac{x\coth{ax}}{a}+\frac{1}{a^2}\ln\sinh{ax}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 28
+aa:=integrate(x*csch(a*x)^2,x)
+--R 
+--R
+--R   (1)
+--R                   2                                  2
+--R         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1)
+--R      *
+--R                     2sinh(a x)
+--R         log(- ---------------------)
+--R               sinh(a x) - cosh(a x)
+--R     + 
+--R                       2                                           2
+--R       - 2a x sinh(a x)  - 4a x cosh(a x)sinh(a x) - 2a x cosh(a x)
+--R  /
+--R      2         2     2                      2         2    2
+--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 29
+bb:=-(x*coth(a*x))/a+1/a^2*log(sinh(a*x))
+--R
+--R        log(sinh(a x)) - a x coth(a x)
+--R   (2)  ------------------------------
+--R                       2
+--R                      a
+--R                                                     Type: Expression Integer
+--E
+
+--S 30
+cc:=aa-bb
+--R
+--R   (3)
+--R                   2                                  2
+--R       (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  + 1)log(sinh(a x))
+--R     + 
+--R                   2                                  2
+--R         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1)
+--R      *
+--R                     2sinh(a x)
+--R         log(- ---------------------)
+--R               sinh(a x) - cosh(a x)
+--R     + 
+--R                                      2
+--R       (a x coth(a x) - 2a x)sinh(a x)
+--R     + 
+--R       (2a x cosh(a x)coth(a x) - 4a x cosh(a x))sinh(a x)
+--R     + 
+--R                     2                                 2
+--R       (a x cosh(a x)  - a x)coth(a x) - 2a x cosh(a x)
+--R  /
+--R      2         2     2                      2         2    2
+--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 31
+dd:=expandLog cc
+--R
+--R   (4)
+--R                     2                                  2
+--R         (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  + 1)
+--R      *
+--R         log(sinh(a x) - cosh(a x))
+--R     + 
+--R                                                 2
+--R       (a x coth(a x) + log(- 2) - 2a x)sinh(a x)
+--R     + 
+--R       (2a x cosh(a x)coth(a x) + (2log(- 2) - 4a x)cosh(a x))sinh(a x)
+--R     + 
+--R                     2                                             2
+--R       (a x cosh(a x)  - a x)coth(a x) + (log(- 2) - 2a x)cosh(a x)  - log(- 2)
+--R  /
+--R      2         2     2                      2         2    2
+--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 32
+sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
+--R
+--R               2    cosh(2x) - 1
+--R   (5)  sinh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 33
+ee:=sinhsqrrule dd
+--R
+--R   (6)
+--R                                                         2
+--R         (- 4cosh(a x)sinh(a x) - cosh(2a x) - 2cosh(a x)  + 3)
+--R      *
+--R         log(sinh(a x) - cosh(a x))
+--R     + 
+--R       (4a x cosh(a x)coth(a x) + (4log(- 2) - 8a x)cosh(a x))sinh(a x)
+--R     + 
+--R                                       2
+--R       (a x cosh(2a x) + 2a x cosh(a x)  - 3a x)coth(a x)
+--R     + 
+--R                                                                2
+--R       (log(- 2) - 2a x)cosh(2a x) + (2log(- 2) - 4a x)cosh(a x)  - 3log(- 2)
+--R     + 
+--R       2a x
+--R  /
+--R       2                      2               2         2     2
+--R     4a cosh(a x)sinh(a x) + a cosh(2a x) + 2a cosh(a x)  - 3a
+--R                                                     Type: Expression Integer
+--E
+
+--S 34
+coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
+--R
+--R               2    cosh(2x) + 1
+--R   (7)  cosh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 35
+ff:=coshsqrrule ee
+--R
+--R   (8)
+--R       (- 2cosh(a x)sinh(a x) - cosh(2a x) + 1)log(sinh(a x) - cosh(a x))
+--R     + 
+--R       (2a x cosh(a x)coth(a x) + (2log(- 2) - 4a x)cosh(a x))sinh(a x)
+--R     + 
+--R       (a x cosh(2a x) - a x)coth(a x) + (log(- 2) - 2a x)cosh(2a x) - log(- 2)
+--R  /
+--R       2                      2              2
+--R     2a cosh(a x)sinh(a x) + a cosh(2a x) - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 36
+sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
+--R
+--I                             %P sinh(y + x) - %P sinh(y - x)
+--I   (9)  %P cosh(y)sinh(x) == -------------------------------
+--R                                            2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 37
+gg:=sinhcoshrule ff
+--R
+--R   (10)
+--R       (- sinh(2a x) - cosh(2a x) + 1)log(sinh(a x) - cosh(a x))
+--R     + 
+--R       (a x coth(a x) + log(- 2) - 2a x)sinh(2a x)
+--R     + 
+--R       (a x cosh(2a x) - a x)coth(a x) + (log(- 2) - 2a x)cosh(2a x) - log(- 2)
+--R  /
+--R      2              2              2
+--R     a sinh(2a x) + a cosh(2a x) - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 38     14:642 Schaums and Axiom differ by a constant
+hh:=complexNormalize gg
+--R
+--R         - log(- 1) + log(- 2)
+--R   (11)  ---------------------
+--R                    2
+--R                   a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.643~~~~~$\displaystyle
+\int{\frac{{\rm csch~}{ax}}{x}}~dx$}
+$$\int{\frac{{\rm csch~}{ax}}{x}}=
+-\frac{1}{ax}-\frac{ax}{6}+\frac{7(ax)^3}{1080}+\cdots
+\frac{(-1)^n2(2^{2n-1}-1)B_n(ax)^{2n-1}}{(2n-1)(2n)!}+\cdots
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 39     14:643 Axiom cannot compute this integral
+aa:=integrate(csch(a*x)/x,x)
+--R 
+--R
+--R           x
+--I         ++  csch(%O a)
+--I   (1)   |   ---------- d%O
+--I        ++       %O
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.644~~~~~$\displaystyle
+\int{\frac{dx}{q+p{\rm ~csch~}{ax}}}~dx$}
+$$\int{\frac{1}{q+p{\rm ~csch~}{ax}}}=
+\frac{x}{q}-\frac{p}{q}\int{\frac{dx}{p+q\sinh{ax}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 40
+aa:=integrate(1/(q+p*csch(a*x)),x)
+--R 
+--R
+--R   (1)
+--R         p
+--R      *
+--R         log
+--R                     2         2      2                              2         2
+--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R                  + 
+--R                                      2     2
+--R                    2p q cosh(a x) + q  + 2p
+--R               *
+--R                   +-------+
+--R                   | 2    2
+--R                  \|q  + p
+--R              + 
+--R                   3     2                 3     2                  2     3
+--R                (2q  + 2p q)sinh(a x) + (2q  + 2p q)cosh(a x) + 2p q  + 2p
+--R           /
+--R                           2                                             2
+--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R              + 
+--R                2p cosh(a x) - q
+--R     + 
+--R           +-------+
+--R           | 2    2
+--R       a x\|q  + p
+--R  /
+--R         +-------+
+--R         | 2    2
+--R     a q\|q  + p
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 41
+t1:=integrate(1/(p+q*sinh(a*x)),x)
+--R
+--R   (2)
+--R     log
+--R                 2         2      2                              2         2
+--R                q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R              + 
+--R                                  2     2
+--R                2p q cosh(a x) + q  + 2p
+--R           *
+--R               +-------+
+--R               | 2    2
+--R              \|q  + p
+--R          + 
+--R                 3     2                   3     2                  2     3
+--R            (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
+--R       /
+--R                       2                                             2
+--R            q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R          + 
+--R            2p cosh(a x) - q
+--R  /
+--R       +-------+
+--R       | 2    2
+--R     a\|q  + p
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 42
+bb:=x/q-p/q*t1
+--R
+--R   (3)
+--R       -
+--R            p
+--R         *
+--R            log
+--R                        2         2      2
+--R                       q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x)
+--R                     + 
+--R                        2         2                     2     2
+--R                       q cosh(a x)  + 2p q cosh(a x) + q  + 2p
+--R                  *
+--R                      +-------+
+--R                      | 2    2
+--R                     \|q  + p
+--R                 + 
+--R                      3     2                   3     2                  2     3
+--R                 (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
+--R              /
+--R                              2                                             2
+--R                   q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R                 + 
+--R                   2p cosh(a x) - q
+--R     + 
+--R           +-------+
+--R           | 2    2
+--R       a x\|q  + p
+--R  /
+--R         +-------+
+--R         | 2    2
+--R     a q\|q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 43
+cc:=aa-bb
+--R
+--R   (4)
+--R         p
+--R      *
+--R         log
+--R                     2         2      2                              2         2
+--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R                  + 
+--R                                      2     2
+--R                    2p q cosh(a x) + q  + 2p
+--R               *
+--R                   +-------+
+--R                   | 2    2
+--R                  \|q  + p
+--R              + 
+--R                   3     2                 3     2                  2     3
+--R                (2q  + 2p q)sinh(a x) + (2q  + 2p q)cosh(a x) + 2p q  + 2p
+--R           /
+--R                           2                                             2
+--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R              + 
+--R                2p cosh(a x) - q
+--R     + 
+--R         p
+--R      *
+--R         log
+--R                     2         2      2                              2         2
+--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R                  + 
+--R                                      2     2
+--R                    2p q cosh(a x) + q  + 2p
+--R               *
+--R                   +-------+
+--R                   | 2    2
+--R                  \|q  + p
+--R              + 
+--R                     3     2                   3     2                  2     3
+--R                (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
+--R           /
+--R                           2                                             2
+--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R              + 
+--R                2p cosh(a x) - q
+--R  /
+--R         +-------+
+--R         | 2    2
+--R     a q\|q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 44
+sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
+--R
+--R               2    cosh(2x) - 1
+--R   (5)  sinh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 45
+dd:=sinhsqrrule cc
+--R
+--R   (6)
+--R         p
+--R      *
+--R         log
+--R                       2                              2
+--R                    (4q cosh(a x) + 4p q)sinh(a x) + q cosh(2a x)
+--R                  + 
+--R                      2         2                     2     2
+--R                    2q cosh(a x)  + 4p q cosh(a x) + q  + 4p
+--R               *
+--R                   +-------+
+--R                   | 2    2
+--R                  \|q  + p
+--R              + 
+--R                   3     2                 3     2                  2     3
+--R                (4q  + 4p q)sinh(a x) + (4q  + 4p q)cosh(a x) + 4p q  + 4p
+--R           /
+--R                                                                          2
+--R                (4q cosh(a x) + 4p)sinh(a x) + q cosh(2a x) + 2q cosh(a x)
+--R              + 
+--R                4p cosh(a x) - 3q
+--R     + 
+--R         p
+--R      *
+--R         log
+--R                       2                              2
+--R                    (4q cosh(a x) + 4p q)sinh(a x) + q cosh(2a x)
+--R                  + 
+--R                      2         2                     2     2
+--R                    2q cosh(a x)  + 4p q cosh(a x) + q  + 4p
+--R               *
+--R                   +-------+
+--R                   | 2    2
+--R                  \|q  + p
+--R              + 
+--R                     3     2                   3     2                  2     3
+--R                (- 4q  - 4p q)sinh(a x) + (- 4q  - 4p q)cosh(a x) - 4p q  - 4p
+--R           /
+--R                                                                          2
+--R                (4q cosh(a x) + 4p)sinh(a x) + q cosh(2a x) + 2q cosh(a x)
+--R              + 
+--R                4p cosh(a x) - 3q
+--R  /
+--R         +-------+
+--R         | 2    2
+--R     a q\|q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 46
+coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
+--R
+--R               2    cosh(2x) + 1
+--R   (7)  cosh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 47
+ee:=coshsqrrule dd
+--R
+--R   (8)
+--R         p
+--R      *
+--R         log
+--R                       2                              2
+--R                    (2q cosh(a x) + 2p q)sinh(a x) + q cosh(2a x)
+--R                  + 
+--R                                      2     2
+--R                    2p q cosh(a x) + q  + 2p
+--R               *
+--R                   +-------+
+--R                   | 2    2
+--R                  \|q  + p
+--R              + 
+--R                   3     2                 3     2                  2     3
+--R                (2q  + 2p q)sinh(a x) + (2q  + 2p q)cosh(a x) + 2p q  + 2p
+--R           /
+--R              (2q cosh(a x) + 2p)sinh(a x) + q cosh(2a x) + 2p cosh(a x) - q
+--R     + 
+--R         p
+--R      *
+--R         log
+--R                       2                              2
+--R                    (2q cosh(a x) + 2p q)sinh(a x) + q cosh(2a x)
+--R                  + 
+--R                                      2     2
+--R                    2p q cosh(a x) + q  + 2p
+--R               *
+--R                   +-------+
+--R                   | 2    2
+--R                  \|q  + p
+--R              + 
+--R                     3     2                   3     2                  2     3
+--R                (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
+--R           /
+--R              (2q cosh(a x) + 2p)sinh(a x) + q cosh(2a x) + 2p cosh(a x) - q
+--R  /
+--R         +-------+
+--R         | 2    2
+--R     a q\|q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 48     14:644 Schaums and Axiom differ by a constant
+ff:=complexNormalize ee
+--R
+--R               4    2 2
+--R        p log(q  + p q )
+--R   (9)  ----------------
+--R              +-------+
+--R              | 2    2
+--R          a q\|q  + p
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.645~~~~~$\displaystyle
+\int{{\rm csch}^n~{ax}}~dx$}
+$$\int{{\rm csch}^n~{ax}}=
+\frac{-{\rm csch}^{n-2}~{ax}~\coth{ax}}{a(n-1)}
+-\frac{n-2}{n-1}\int{{\rm csch}^{n-2}~{ax}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 49     14:645 Axiom cannot compute this integral
+aa:=integrate(csch(a*x)^n,x)
+--R 
+--R
+--R           x
+--R         ++            n
+--I   (1)   |   csch(%O a) d%O
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 pp91-92
+\end{thebibliography}
+\end{document}
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diff --git a/src/axiom-website/CATS/schaum34.input.pamphlet b/src/axiom-website/CATS/schaum34.input.pamphlet
new file mode 100644
index 0000000..d61b757
--- /dev/null
+++ b/src/axiom-website/CATS/schaum34.input.pamphlet
@@ -0,0 +1,2492 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum34.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.646~~~~~$\displaystyle
+\int{\sinh^{-1}\frac{x}{a}}~dx$}
+$$\int{\sinh^{-1}\frac{x}{a}}=
+x\sinh^{-1}\frac{x}{a}-\sqrt{x^2+a^2}
+$$
+&lt;&lt;*&gt;&gt;=
+)spool schaum34.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1
+aa:=integrate(asinh(x/a),x)
+--R 
+--R
+--R                               +-------+
+--R           +-------+           | 2    2           +-------+
+--R           | 2    2     2     \|x  + a   + x      | 2    2     2    2
+--R        (x\|x  + a   - x )log(--------------) + x\|x  + a   - x  - a
+--R                                     a
+--R   (1)  -------------------------------------------------------------
+--R                                 +-------+
+--R                                 | 2    2
+--R                                \|x  + a   - x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 2
+bb:=x*asinh(x/a)-sqrt(x^2+a^2)
+--R
+--R           +-------+
+--R           | 2    2            x
+--R   (2)  - \|x  + a   + x asinh(-)
+--R                               a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3
+cc:=aa-bb
+--R
+--R               +-------+
+--R               | 2    2
+--R              \|x  + a   + x            x
+--R   (3)  x log(--------------) - x asinh(-)
+--R                     a                  a
+--R                                                     Type: Expression Integer
+--E
+
+--S 4
+asinhlogrule:=rule(asinh(x) == log(x+sqrt(x^2+1)))
+--R
+--R                         +------+
+--R                         | 2
+--R   (4)  asinh(x) == log(\|x  + 1  + x)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 5
+dd:=asinhlogrule cc
+--R
+--R                                        +-------+
+--R                                        | 2    2
+--R                                        |x  + a
+--R               +-------+              a |-------  + x
+--R               | 2    2                 |    2
+--R              \|x  + a   + x           \|   a
+--R   (5)  x log(--------------) - x log(---------------)
+--R                     a                       a
+--R                                                     Type: Expression Integer
+--E
+
+--S 6
+ee:=expandLog dd
+--R
+--R                                        +-------+
+--R               +-------+                | 2    2
+--R               | 2    2                 |x  + a
+--R   (6)  x log(\|x  + a   + x) - x log(a |-------  + x)
+--R                                        |    2
+--R                                       \|   a
+--R                                                     Type: Expression Integer
+--E
+
+--S 7      14:646 Schaums and Axiom agree
+ff:=rootSimp ee
+--R
+--R   (7)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.647~~~~~$\displaystyle
+\int{x\sinh^{-1}\frac{x}{a}}~dx$}
+$$\int{x\sinh^{-1}\frac{x}{a}}=
+\left(\frac{x^2}{2}+\frac{a^2}{4}\right)\sinh^{-1}\frac{x}{a}
+-\frac{x\sqrt{x^2+a^2}}{4}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 8
+aa:=integrate(x*asinh(x/a),x)
+--R 
+--R
+--R   (1)
+--R                                                       +-------+
+--R                     +-------+                         | 2    2
+--R           3     2   | 2    2      4     2 2    4     \|x  + a   + x
+--R       ((4x  + 2a x)\|x  + a   - 4x  - 4a x  - a )log(--------------)
+--R                                                             a
+--R     + 
+--R                   +-------+
+--R          3    2   | 2    2      4     2 2
+--R       (2x  + a x)\|x  + a   - 2x  - 2a x
+--R  /
+--R        +-------+
+--R        | 2    2      2     2
+--R     8x\|x  + a   - 8x  - 4a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 9
+bb:=(x^2/2+a^2/4)*asinh(x/a)-(x*sqrt(x^2+a^2))/4
+--R
+--R            +-------+
+--R            | 2    2       2    2       x
+--R        - x\|x  + a   + (2x  + a )asinh(-)
+--R                                        a
+--R   (2)  ----------------------------------
+--R                         4
+--R                                                     Type: Expression Integer
+--E
+
+--S 10
+cc:=aa-bb
+--R
+--R                       +-------+
+--R                       | 2    2
+--R           2    2     \|x  + a   + x         2    2       x
+--R        (2x  + a )log(--------------) + (- 2x  - a )asinh(-)
+--R                             a                            a
+--R   (3)  ----------------------------------------------------
+--R                                  4
+--R                                                     Type: Expression Integer
+--E
+
+--S 11
+asinhlogrule:=rule(asinh(x) == log(x+sqrt(x^2+1)))
+--R
+--R                         +------+
+--R                         | 2
+--R   (4)  asinh(x) == log(\|x  + 1  + x)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 12
+dd:=asinhlogrule cc
+--R
+--R                                                          +-------+
+--R                                                          | 2    2
+--R                                                          |x  + a
+--R                       +-------+                        a |-------  + x
+--R                       | 2    2                           |    2
+--R           2    2     \|x  + a   + x         2    2      \|   a
+--R        (2x  + a )log(--------------) + (- 2x  - a )log(---------------)
+--R                             a                                 a
+--R   (5)  ----------------------------------------------------------------
+--R                                        4
+--R                                                     Type: Expression Integer
+--E
+
+--S 13
+ee:=expandLog dd
+--R
+--R                                                          +-------+
+--R                       +-------+                          | 2    2
+--R           2    2      | 2    2              2    2       |x  + a
+--R        (2x  + a )log(\|x  + a   + x) + (- 2x  - a )log(a |-------  + x)
+--R                                                          |    2
+--R                                                         \|   a
+--R   (6)  ----------------------------------------------------------------
+--R                                        4
+--R                                                     Type: Expression Integer
+--E
+
+--S 14     14:647 Schaums and Axiom agree
+ff:=rootSimp ee
+--R
+--R   (7)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.648~~~~~$\displaystyle
+\int{x^2\sinh^{-1}\frac{x}{a}}~dx$}
+$$\int{x^2\sinh^{-1}\frac{x}{a}}=
+\frac{x^3}{3}\sinh^{-1}\frac{x}{a}+\frac{(2a^2-x^2)\sqrt{x^2+a^2}}{9}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 15
+aa:=integrate(x^2*asinh(x/a),x)
+--R 
+--R
+--R   (1)
+--R                                                     +-------+
+--R                       +-------+                     | 2    2
+--R            5     2 3  | 2    2       6     2 4     \|x  + a   + x
+--R       ((12x  + 3a x )\|x  + a   - 12x  - 9a x )log(--------------)
+--R                                                           a
+--R     + 
+--R                            +-------+
+--R          5     2 3     4   | 2    2      6     2 4     4 2     6
+--R       (4x  - 5a x  - 6a x)\|x  + a   - 4x  + 3a x  + 9a x  + 2a
+--R  /
+--R                  +-------+
+--R         2     2  | 2    2       3      2
+--R     (36x  + 9a )\|x  + a   - 36x  - 27a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 16
+bb:=x^3/3*asinh(x/a)+((2*a^2-x^2)*sqrt(x^2+a^2))/9
+--R
+--R                     +-------+
+--R            2     2  | 2    2      3      x
+--R        (- x  + 2a )\|x  + a   + 3x asinh(-)
+--R                                          a
+--R   (2)  ------------------------------------
+--R                          9
+--R                                                     Type: Expression Integer
+--E
+
+--S 17
+cc:=aa-bb
+--R
+--R               +-------+
+--R               | 2    2
+--R         3    \|x  + a   + x     3      x
+--R        x log(--------------) - x asinh(-)
+--R                     a                  a
+--R   (3)  ----------------------------------
+--R                         3
+--R                                                     Type: Expression Integer
+--E
+
+--S 18
+asinhlogrule:=rule(asinh(x) == log(x+sqrt(x^2+1)))
+--R
+--R                         +------+
+--R                         | 2
+--R   (4)  asinh(x) == log(\|x  + 1  + x)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 19
+dd:=asinhlogrule cc
+--R
+--R                                        +-------+
+--R                                        | 2    2
+--R                                        |x  + a
+--R               +-------+              a |-------  + x
+--R               | 2    2                 |    2
+--R         3    \|x  + a   + x     3     \|   a
+--R        x log(--------------) - x log(---------------)
+--R                     a                       a
+--R   (5)  ----------------------------------------------
+--R                               3
+--R                                                     Type: Expression Integer
+--E
+
+--S 20
+ee:=expandLog dd
+--R
+--R                                        +-------+
+--R               +-------+                | 2    2
+--R         3     | 2    2          3      |x  + a
+--R        x log(\|x  + a   + x) - x log(a |-------  + x)
+--R                                        |    2
+--R                                       \|   a
+--R   (6)  ----------------------------------------------
+--R                               3
+--R                                                     Type: Expression Integer
+--E
+
+--S 21     14:648 Schaums and Axiom agree
+ff:=rootSimp ee
+--R
+--R   (7)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.649~~~~~$\displaystyle
+\int{\frac{\sinh^{-1}(x/a)}{x}}~dx$}
+$$\int{\frac{\sinh^{-1}(x/a)}{x}}=
+\left\{
+\begin{array}{lr}
+\displaystyle
+\frac{x}{a}-\frac{(x/a)^3}{2\cdot 3\cdot 3}
++\frac{1\cdot 3(x/a)^5}{2\cdot 4\cdot 5\cdot 5}
+-\frac{1\cdot 3\cdot 5(x/a)^7}{2\cdot 4\cdot 6\cdot 7\cdot 7}+\cdots&amp;
+|x|&lt;a\\
+\\
+\displaystyle
+\frac{\ln^2(2x/a)}{2}-\frac{(a/x)^2}{2\cdot 2\cdot 2}
++\frac{1\cdot 3(a/x)^4}{2\cdot 4\cdot 4\cdot 4}
+-\frac{1\cdot 3\cdot 5(a/x)^6}{2\cdot 4\cdot 6\cdot 6\cdot 6}+\cdots&amp;
+x &gt; a\\
+\\
+\displaystyle
+-\frac{\ln^2(-2x/a)}{2}+\frac{(a/x)^2}{2\cdot 2\cdot 2}
+-\frac{1\cdot 3(a/x)^4}{2\cdot 4\cdot 4\cdot 4}
++\frac{1\cdot 3\cdot 5(a/x)^6}{2\cdot 4\cdot 6\cdot 6\cdot 6}-\cdots&amp;
+x&lt;-a\\
+\end{array}
+\right.
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 22     14:649 Axiom cannot compute this integral
+aa:=integrate(asinh(x/a)/x,x)
+--R 
+--R
+--I                   %P
+--R           x asinh(--)
+--R         ++         a
+--I   (1)   |   --------- d%P
+--I        ++       %P
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.650~~~~~$\displaystyle
+\int{\frac{\sinh^{-1}(x/a)}{x^2}}~dx$}
+$$\int{\frac{\sinh^{-1}(x/a)}{x^2}}=
+-\frac{\sinh^{-1}(x/a)}{x}
+-\frac{1}{a}\ln\left(\frac{a+\sqrt{x^2+a^2}}{x}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 23
+aa:=integrate(asinh(x/a)/x^2,x)
+--R 
+--R
+--R   (1)
+--R                +-------+                   +-------+
+--R                | 2    2                    | 2    2
+--R       - x log(\|x  + a   - x + a) + x log(\|x  + a   - x - a)
+--R     + 
+--R                +-------+
+--R                | 2    2
+--R               \|x  + a   + x
+--R       - a log(--------------)
+--R                      a
+--R  /
+--R     a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 24
+bb:=-asinh(x/a)/x-1/a*log((a+sqrt(x^2+a^2))/x)
+--R
+--R                 +-------+
+--R                 | 2    2
+--R                \|x  + a   + a            x
+--R        - x log(--------------) - a asinh(-)
+--R                       x                  a
+--R   (2)  ------------------------------------
+--R                         a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 25
+cc:=aa-bb
+--R
+--R   (3)
+--R                +-------+                   +-------+
+--R                | 2    2                    | 2    2
+--R       - x log(\|x  + a   - x + a) + x log(\|x  + a   - x - a)
+--R     + 
+--R                +-------+               +-------+
+--R                | 2    2                | 2    2
+--R               \|x  + a   + x          \|x  + a   + a            x
+--R       - a log(--------------) + x log(--------------) + a asinh(-)
+--R                      a                       x                  a
+--R  /
+--R     a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 26
+asinhlogrule:=rule(asinh(x) == log(x+sqrt(x^2+1)))
+--R
+--R                         +------+
+--R                         | 2
+--R   (4)  asinh(x) == log(\|x  + 1  + x)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 27
+dd:=asinhlogrule cc
+--R
+--R   (5)
+--R                +-------+                   +-------+
+--R                | 2    2                    | 2    2
+--R       - x log(\|x  + a   - x + a) + x log(\|x  + a   - x - a)
+--R     + 
+--R                                                                 +-------+
+--R                                                                 | 2    2
+--R                                                                 |x  + a
+--R                +-------+               +-------+              a |-------  + x
+--R                | 2    2                | 2    2                 |    2
+--R               \|x  + a   + x          \|x  + a   + a           \|   a
+--R       - a log(--------------) + x log(--------------) + a log(---------------)
+--R                      a                       x                       a
+--R  /
+--R     a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 28
+ee:=expandLog dd
+--R
+--R   (6)
+--R                +-------+               +-------+
+--R                | 2    2                | 2    2
+--R       - a log(\|x  + a   + x) + x log(\|x  + a   + a)
+--R     + 
+--R                +-------+                   +-------+
+--R                | 2    2                    | 2    2
+--R       - x log(\|x  + a   - x + a) + x log(\|x  + a   - x - a)
+--R     + 
+--R               +-------+
+--R               | 2    2
+--R               |x  + a
+--R       a log(a |-------  + x) - x log(x)
+--R               |    2
+--R              \|   a
+--R  /
+--R     a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 29
+ff:=rootSimp ee
+--R
+--R   (7)
+--R            +-------+             +-------+                 +-------+
+--R            | 2    2              | 2    2                  | 2    2
+--R       log(\|x  + a   + a) - log(\|x  + a   - x + a) + log(\|x  + a   - x - a)
+--R     + 
+--R       - log(x)
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 30     14:650 Schaums and Axiom differ by a constant
+gg:=complexNormalize ff
+--R
+--R          log(- 1)
+--R   (8)  - --------
+--R              a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.651~~~~~$\displaystyle
+\int{\cosh^{-1}\frac{x}{a}}~dx$}
+$$\int{\cosh^{-1}\frac{x}{a}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+x\cosh^{-1}(x/a)-\sqrt{x^2-a^2},\quad\cosh^{-1}\frac{x}{a} &gt; 0\\
+\\
+\displaystyle
+x\cosh^{-1}(x/a)+\sqrt{x^2-a^2},\quad\cosh^{-1}\frac{x}{a} &lt; 0\\
+\end{array}
+\right.
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 31
+aa:=integrate(acosh(x/a),x)
+--R 
+--R
+--R                               +-------+
+--R           +-------+           | 2    2           +-------+
+--R           | 2    2     2     \|x  - a   + x      | 2    2     2    2
+--R        (x\|x  - a   - x )log(--------------) + x\|x  - a   - x  + a
+--R                                     a
+--R   (1)  -------------------------------------------------------------
+--R                                 +-------+
+--R                                 | 2    2
+--R                                \|x  - a   - x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 32
+bb1:=x*acosh(x/a)-sqrt(x^2-a^2)
+--R
+--R           +-------+
+--R           | 2    2            x
+--R   (2)  - \|x  - a   + x acosh(-)
+--R                               a
+--R                                                     Type: Expression Integer
+--E
+
+--S 33
+bb2:=x*acosh(x/a)+sqrt(x^2-a^2)
+--R
+--R         +-------+
+--R         | 2    2            x
+--R   (3)  \|x  - a   + x acosh(-)
+--R                             a
+--R                                                     Type: Expression Integer
+--E
+
+--S 34
+cc1:=aa-bb1
+--R
+--R               +-------+
+--R               | 2    2
+--R              \|x  - a   + x            x
+--R   (4)  x log(--------------) - x acosh(-)
+--R                     a                  a
+--R                                                     Type: Expression Integer
+--E
+
+--S 35
+cc2:=aa-bb2
+--R
+--R   (5)
+--R                              +-------+
+--R          +-------+           | 2    2                             +-------+
+--R          | 2    2     2     \|x  - a   + x               x        | 2    2
+--R       (x\|x  - a   - x )log(--------------) + (- x acosh(-) + 2x)\|x  - a
+--R                                    a                     a
+--R     + 
+--R        2      x      2     2
+--R       x acosh(-) - 2x  + 2a
+--R               a
+--R  /
+--R      +-------+
+--R      | 2    2
+--R     \|x  - a   - x
+--R                                                     Type: Expression Integer
+--E
+
+--S 36
+acoshlogrule:=rule(acosh(x) == log(x+sqrt(x^2-1)))
+--R
+--R                         +------+
+--R                         | 2
+--R   (6)  acosh(x) == log(\|x  - 1  + x)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 37
+dd1:=acoshlogrule cc1
+--R
+--R                                        +-------+
+--R                                        | 2    2
+--R                                        |x  - a
+--R               +-------+              a |-------  + x
+--R               | 2    2                 |    2
+--R              \|x  - a   + x           \|   a
+--R   (7)  x log(--------------) - x log(---------------)
+--R                     a                       a
+--R                                                     Type: Expression Integer
+--E
+
+--S 38
+ee1:=expandLog dd1
+--R
+--R                                        +-------+
+--R               +-------+                | 2    2
+--R               | 2    2                 |x  - a
+--R   (8)  x log(\|x  - a   + x) - x log(a |-------  + x)
+--R                                        |    2
+--R                                       \|   a
+--R                                                     Type: Expression Integer
+--E
+
+--S 39     14:651 Schaums and Axiom agree
+ff1:=rootSimp ee1
+--R
+--R   (9)  0
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.652~~~~~$\displaystyle
+\int{x\cosh^{-1}\frac{x}{a}}~dx$}
+$$\int{x\cosh^{-1}\frac{x}{a}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{1}{4}(2x^2-a^2)\cosh^{-1}(x/a)-\frac{1}{4}x\sqrt{x^2-a^2},
+\quad\cosh^{-1}(x/a)&gt;0\\
+\\
+\displaystyle
+\frac{1}{4}(2x^2-a^2)\cosh^{-1}(x/a)+\frac{1}{4}x\sqrt{x^2-a^2},
+\quad\cosh^{-1}(x/a)&lt;0\\
+\end{array}
+\right.
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 40
+aa:=integrate(x*acosh(x/a),x)
+--R 
+--R
+--R   (1)
+--R                                                       +-------+
+--R                     +-------+                         | 2    2
+--R           3     2   | 2    2      4     2 2    4     \|x  - a   + x
+--R       ((4x  - 2a x)\|x  - a   - 4x  + 4a x  - a )log(--------------)
+--R                                                             a
+--R     + 
+--R                   +-------+
+--R          3    2   | 2    2      4     2 2
+--R       (2x  - a x)\|x  - a   - 2x  + 2a x
+--R  /
+--R        +-------+
+--R        | 2    2      2     2
+--R     8x\|x  - a   - 8x  + 4a
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 41
+bb1:=1/4*(2*x^2-a^2)*acosh(x/a)-1/4*x*sqrt(x^2-a^2)
+--R
+--R            +-------+
+--R            | 2    2       2    2       x
+--R        - x\|x  - a   + (2x  - a )acosh(-)
+--R                                        a
+--R   (2)  ----------------------------------
+--R                         4
+--R                                                     Type: Expression Integer
+--E
+
+--S 42
+bb2:=1/4*(2*x^2-a^2)*acosh(x/a)+1/4*x*sqrt(x^2-a^2)
+--R
+--R          +-------+
+--R          | 2    2       2    2       x
+--R        x\|x  - a   + (2x  - a )acosh(-)
+--R                                      a
+--R   (3)  --------------------------------
+--R                        4
+--R                                                     Type: Expression Integer
+--E
+
+--S 43
+cc1:=aa-bb1
+--R
+--R                       +-------+
+--R                       | 2    2
+--R           2    2     \|x  - a   + x         2    2       x
+--R        (2x  - a )log(--------------) + (- 2x  + a )acosh(-)
+--R                             a                            a
+--R   (4)  ----------------------------------------------------
+--R                                  4
+--R                                                     Type: Expression Integer
+--E
+
+--S 44
+cc2:=aa-bb2
+--R
+--R   (5)
+--R                                                       +-------+
+--R                     +-------+                         | 2    2
+--R           3     2   | 2    2      4     2 2    4     \|x  - a   + x
+--R       ((4x  - 2a x)\|x  - a   - 4x  + 4a x  - a )log(--------------)
+--R                                                             a
+--R     + 
+--R                                             +-------+
+--R             3     2        x      3     2   | 2    2
+--R       ((- 4x  + 2a x)acosh(-) + 4x  - 2a x)\|x  - a
+--R                            a
+--R     + 
+--R          4     2 2    4       x      4     2 2
+--R       (4x  - 4a x  + a )acosh(-) - 4x  + 4a x
+--R                               a
+--R  /
+--R        +-------+
+--R        | 2    2      2     2
+--R     8x\|x  - a   - 8x  + 4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 45
+acoshlogrule:=rule(acosh(x) == log(x+sqrt(x^2-1)))
+--R
+--R                         +------+
+--R                         | 2
+--R   (6)  acosh(x) == log(\|x  - 1  + x)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 46
+dd1:=acoshlogrule cc1
+--R
+--R                                                          +-------+
+--R                                                          | 2    2
+--R                                                          |x  - a
+--R                       +-------+                        a |-------  + x
+--R                       | 2    2                           |    2
+--R           2    2     \|x  - a   + x         2    2      \|   a
+--R        (2x  - a )log(--------------) + (- 2x  + a )log(---------------)
+--R                             a                                 a
+--R   (7)  ----------------------------------------------------------------
+--R                                        4
+--R                                                     Type: Expression Integer
+--E
+
+--S 47
+ee1:=expandLog dd1
+--R
+--R                                                          +-------+
+--R                       +-------+                          | 2    2
+--R           2    2      | 2    2              2    2       |x  - a
+--R        (2x  - a )log(\|x  - a   + x) + (- 2x  + a )log(a |-------  + x)
+--R                                                          |    2
+--R                                                         \|   a
+--R   (8)  ----------------------------------------------------------------
+--R                                        4
+--R                                                     Type: Expression Integer
+--E
+
+--S 48     14:652 Schaums and Axiom agree
+ff1:=rootSimp ee1
+--R
+--R   (9)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.653~~~~~$\displaystyle
+\int{x^2\cosh^{-1}\frac{x}{a}}~dx$}
+$$\int{x^2\cosh^{-1}\frac{x}{a}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{1}{3}x^3\cosh^{-1}(x/a)-\frac{1}{9}(x^2+2a^2)\sqrt{x^2-a^2},
+\quad\cosh^{-1}(x/a)&gt;0\\
+\\
+\displaystyle
+\frac{1}{3}x^3\cosh^{-1}(x/a)+\frac{1}{9}(x^2+2a^2)\sqrt{x^2-a^2},
+\quad\cosh^{-1}(x/a)&lt;0\\
+\end{array}
+\right.
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 49
+aa:=integrate(x^2*acosh(x/a),x)
+--R 
+--R
+--R   (1)
+--R                                                     +-------+
+--R                       +-------+                     | 2    2
+--R            5     2 3  | 2    2       6     2 4     \|x  - a   + x
+--R       ((12x  - 3a x )\|x  - a   - 12x  + 9a x )log(--------------)
+--R                                                           a
+--R     + 
+--R                            +-------+
+--R          5     2 3     4   | 2    2      6     2 4     4 2     6
+--R       (4x  + 5a x  - 6a x)\|x  - a   - 4x  - 3a x  + 9a x  - 2a
+--R  /
+--R                  +-------+
+--R         2     2  | 2    2       3      2
+--R     (36x  - 9a )\|x  - a   - 36x  + 27a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 50
+bb1:=1/3*x^3*acosh(x/a)-1/9*(x^2+2*a^2)*sqrt(x^2-a^2)
+--R
+--R                     +-------+
+--R            2     2  | 2    2      3      x
+--R        (- x  - 2a )\|x  - a   + 3x acosh(-)
+--R                                          a
+--R   (2)  ------------------------------------
+--R                          9
+--R                                                     Type: Expression Integer
+--E
+
+--S 51
+bb2:=1/3*x^3*acosh(x/a)+1/9*(x^2+2*a^2)*sqrt(x^2-a^2)
+--R
+--R                   +-------+
+--R          2     2  | 2    2      3      x
+--R        (x  + 2a )\|x  - a   + 3x acosh(-)
+--R                                        a
+--R   (3)  ----------------------------------
+--R                         9
+--R                                                     Type: Expression Integer
+--E
+
+--S 52
+cc1:=aa-bb1
+--R
+--R               +-------+
+--R               | 2    2
+--R         3    \|x  - a   + x     3      x
+--R        x log(--------------) - x acosh(-)
+--R                     a                  a
+--R   (4)  ----------------------------------
+--R                         3
+--R                                                     Type: Expression Integer
+--E
+
+--S 53
+cc2:=aa-bb2
+--R
+--R   (5)
+--R                                                     +-------+
+--R                       +-------+                     | 2    2
+--R            5     2 3  | 2    2       6     2 4     \|x  - a   + x
+--R       ((12x  - 3a x )\|x  - a   - 12x  + 9a x )log(--------------)
+--R                                                           a
+--R     + 
+--R                                                         +-------+
+--R              5     2 3       x      5      2 3      4   | 2    2
+--R       ((- 12x  + 3a x )acosh(-) + 8x  + 10a x  - 12a x)\|x  - a
+--R                              a
+--R     + 
+--R           6     2 4       x      6     2 4      4 2     6
+--R       (12x  - 9a x )acosh(-) - 8x  - 6a x  + 18a x  - 4a
+--R                           a
+--R  /
+--R                  +-------+
+--R         2     2  | 2    2       3      2
+--R     (36x  - 9a )\|x  - a   - 36x  + 27a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 54
+acoshlogrule:=rule(acosh(x) == log(x+sqrt(x^2-1)))
+--R
+--R                         +------+
+--R                         | 2
+--R   (6)  acosh(x) == log(\|x  - 1  + x)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 55
+dd1:=acoshlogrule cc1
+--R
+--R                                        +-------+
+--R                                        | 2    2
+--R                                        |x  - a
+--R               +-------+              a |-------  + x
+--R               | 2    2                 |    2
+--R         3    \|x  - a   + x     3     \|   a
+--R        x log(--------------) - x log(---------------)
+--R                     a                       a
+--R   (7)  ----------------------------------------------
+--R                               3
+--R                                                     Type: Expression Integer
+--E
+
+--S 56
+ee1:=expandLog dd1
+--R
+--R                                        +-------+
+--R               +-------+                | 2    2
+--R         3     | 2    2          3      |x  - a
+--R        x log(\|x  - a   + x) - x log(a |-------  + x)
+--R                                        |    2
+--R                                       \|   a
+--R   (8)  ----------------------------------------------
+--R                               3
+--R                                                     Type: Expression Integer
+--E
+
+--S 57     14:653 Schaums and Axiom agree
+ff1:=rootSimp ee1
+--R
+--R   (9)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.654~~~~~$\displaystyle
+\int{\frac{\cosh^{-1}(x/a)}{x}}~dx$}
+$$\int{\frac{\cosh^{-1}(x/a)}{x}}=
+\begin{array}{l}
+\displaystyle
+\pm\left[\frac{1}{2}\ln^2(2x/a)+\frac{(a/x)^2}{2\cdot 2\cdot 2}
++\frac{1\cdot 3(a/x)^4}{2\cdot 4\cdot 4\cdot 4}
++\frac{1\cdot 3\cdot 5(a/x)^6}{2\cdot 4\cdot 6\cdot 6\cdot 6}+\cdots\right]\\
+\\
+\displaystyle
+\hbox{\hskip 2cm}+{\rm if\ }\cosh^{-1}(x/a)&gt;0,
+\quad -{\rm if\ }\cosh^{-1}(x/a)&lt;0,
+\end{array}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 58     14:654 Axiom cannot compute this integral
+aa:=integrate(acosh(x/a)/x,x)
+--R 
+--R
+--I                   %P
+--R           x acosh(--)
+--R         ++         a
+--I   (1)   |   --------- d%P
+--I        ++       %P
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.655~~~~~$\displaystyle
+\int{\frac{\cosh^{-1}(x/a)}{x^2}}~dx$}
+$$\int{\frac{\cosh^{-1}(x/a)}{x^2}}=
+\begin{array}{l}
+\displaystyle
+-\frac{\cosh^{-1}(x/a)}{x}
+\mp\frac{1}{a}\ln\left(\frac{a+\sqrt{x^2+a^2}}{x}\right)\\
+\\
+\displaystyle
+\hbox{\hskip 1cm}-{\rm if\ }\cosh^{-1}(x/a)&gt;0,
+\quad +{\rm if\ }\cosh^{-1}(x/a)&lt;0,
+\end{array}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 59
+aa:=integrate(acosh(x/a)/x^2,x)
+--R 
+--R
+--R                 +-------+                 +-------+
+--R                 | 2    2                  | 2    2
+--R                \|x  - a   + x            \|x  - a   - x
+--R        - a log(--------------) + 2x atan(--------------)
+--R                       a                         a
+--R   (1)  -------------------------------------------------
+--R                               a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 60
+bb1:=-acosh(x/a)/x-1/a*log((a+sqrt(x^2+a^2))/x)
+--R
+--R                 +-------+
+--R                 | 2    2
+--R                \|x  + a   + a            x
+--R        - x log(--------------) - a acosh(-)
+--R                       x                  a
+--R   (2)  ------------------------------------
+--R                         a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 61
+bb2:=-acosh(x/a)/x+1/a*log((a+sqrt(x^2+a^2))/x)
+--R
+--R               +-------+
+--R               | 2    2
+--R              \|x  + a   + a            x
+--R        x log(--------------) - a acosh(-)
+--R                     x                  a
+--R   (3)  ----------------------------------
+--R                        a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 62
+cc1:=aa-bb1
+--R
+--R   (4)
+--R              +-------+               +-------+                 +-------+
+--R              | 2    2                | 2    2                  | 2    2
+--R             \|x  + a   + a          \|x  - a   + x            \|x  - a   - x
+--R       x log(--------------) - a log(--------------) + 2x atan(--------------)
+--R                    x                       a                         a
+--R     + 
+--R               x
+--R       a acosh(-)
+--R               a
+--R  /
+--R     a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 63     14:655 Axiom cannot simplify these expressions
+cc2:=aa-bb2
+--R
+--R   (5)
+--R                +-------+               +-------+                 +-------+
+--R                | 2    2                | 2    2                  | 2    2
+--R               \|x  + a   + a          \|x  - a   + x            \|x  - a   - x
+--R       - x log(--------------) - a log(--------------) + 2x atan(--------------)
+--R                      x                       a                         a
+--R     + 
+--R               x
+--R       a acosh(-)
+--R               a
+--R  /
+--R     a x
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.656~~~~~$\displaystyle
+\int{\tanh^{-1}\frac{x}{a}}~dx$}
+$$\int{\tanh^{-1}\frac{x}{a}}=
+x\tanh^{-1}\frac{x}{a}+\frac{a}{2}\ln(a^2-x^2)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 64
+aa:=integrate(atanh(x/a),x)
+--R 
+--R
+--R               2    2          - x - a
+--R        a log(x  - a ) + x log(-------)
+--R                                x - a
+--R   (1)  -------------------------------
+--R                       2
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 65
+bb:=x*atanh(x/a)+a/2*log(a^2-x^2)
+--R
+--R                 2    2             x
+--R        a log(- x  + a ) + 2x atanh(-)
+--R                                    a
+--R   (2)  ------------------------------
+--R                       2
+--R                                                     Type: Expression Integer
+--E
+
+--S 66
+cc:=aa-bb
+--R
+--R               2    2          - x - a             2    2             x
+--R        a log(x  - a ) + x log(-------) - a log(- x  + a ) - 2x atanh(-)
+--R                                x - a                                 a
+--R   (3)  ----------------------------------------------------------------
+--R                                        2
+--R                                                     Type: Expression Integer
+--E
+
+--S 67
+atanhrule:=rule(atanh(x) == 1/2*log((1+x)/(1-x)))
+--R
+--R                        - x - 1
+--R                    log(-------)
+--R                         x - 1
+--R   (4)  atanh(x) == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 68
+dd:=atanhrule cc
+--R
+--R               2    2             2    2
+--R        a log(x  - a ) - a log(- x  + a )
+--R   (5)  ---------------------------------
+--R                        2
+--R                                                     Type: Expression Integer
+--E
+
+--S 69     14:656 Schaums and Axiom differ by a constant
+ee:=complexNormalize dd
+--R
+--R        a log(- 1)
+--R   (6)  ----------
+--R             2
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.657~~~~~$\displaystyle
+\int{x*\tanh^{-1}\frac{x}{a}}~dx$}
+$$\int{x*\tanh^{-1}\frac{x}{a}}=
+\frac{ax}{2}+\frac{1}{2}(x^2-a^2)\tanh^{-1}\frac{x}{a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 70
+aa:=integrate(x*atanh(x/a),x)
+--R 
+--R
+--R          2    2     - x - a
+--R        (x  - a )log(-------) + 2a x
+--R                      x - a
+--R   (1)  ----------------------------
+--R                      4
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 71
+bb:=(a*x)/2+1/2*(x^2-a^2)*atanh(x/a)
+--R
+--R          2    2       x
+--R        (x  - a )atanh(-) + a x
+--R                       a
+--R   (2)  -----------------------
+--R                   2
+--R                                                     Type: Expression Integer
+--E
+
+--S 72
+cc:=aa-bb
+--R
+--R          2    2     - x - a         2     2       x
+--R        (x  - a )log(-------) + (- 2x  + 2a )atanh(-)
+--R                      x - a                        a
+--R   (3)  ---------------------------------------------
+--R                              4
+--R                                                     Type: Expression Integer
+--E
+
+--S 73
+atanhrule:=rule(atanh(x) == 1/2*log((1+x)/(1-x)))
+--R
+--R                        - x - 1
+--R                    log(-------)
+--R                         x - 1
+--R   (4)  atanh(x) == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 74     14:657 Schaums and Axiom agree
+dd:=atanhrule cc
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.658~~~~~$\displaystyle
+\int{x^2\tanh^{-1}\frac{x}{a}}~dx$}
+$$\int{x^2\tanh^{-1}\frac{x}{a}}=
+\frac{ax^2}{6}+\frac{x^3}{3}\tanh^{-1}\frac{x}{a}
++\frac{a^3}{6}\ln(a^2-x^2)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 75
+aa:=integrate(x^2*atanh(x/a),x)
+--R 
+--R
+--R         3     2    2     3    - x - a       2
+--R        a log(x  - a ) + x log(-------) + a x
+--R                                x - a
+--R   (1)  --------------------------------------
+--R                           6
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 76
+bb:=(a*x^2)/6+x^3/3*atanh(x/a)+a^3/6*log(a^2-x^2)
+--R
+--R         3       2    2      3      x       2
+--R        a log(- x  + a ) + 2x atanh(-) + a x
+--R                                    a
+--R   (2)  -------------------------------------
+--R                          6
+--R                                                     Type: Expression Integer
+--E
+
+--S 77
+cc:=aa-bb
+--R
+--R         3     2    2     3    - x - a     3       2    2      3      x
+--R        a log(x  - a ) + x log(-------) - a log(- x  + a ) - 2x atanh(-)
+--R                                x - a                                 a
+--R   (3)  ----------------------------------------------------------------
+--R                                        6
+--R                                                     Type: Expression Integer
+--E
+
+--S 78
+atanhrule:=rule(atanh(x) == 1/2*log((1+x)/(1-x)))
+--R
+--R                        - x - 1
+--R                    log(-------)
+--R                         x - 1
+--R   (4)  atanh(x) == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 79
+dd:=atanhrule cc
+--R
+--R         3     2    2     3       2    2
+--R        a log(x  - a ) - a log(- x  + a )
+--R   (5)  ---------------------------------
+--R                        6
+--R                                                     Type: Expression Integer
+--E
+
+--S 80     14:658 Schaums and Axiom differ by a constant
+ee:=complexNormalize dd
+--R
+--R         3
+--R        a log(- 1)
+--R   (6)  ----------
+--R             6
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.659~~~~~$\displaystyle
+\int{\frac{\tanh^{-1}(x/a)}{a}}~dx$}
+$$\int{\frac{\tanh^{-1}(x/a)}{a}}=
+\frac{x}{a}+\frac{(x/a)^3}{3^2}+\frac{(x/a)^5}{5^2}+\cdots
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 81     14:659 Axiom cannot compute this integral
+aa:=integrate(atanh(x/a)/x,x)
+--R 
+--R
+--I                   %P
+--R           x atanh(--)
+--R         ++         a
+--I   (1)   |   --------- d%P
+--I        ++       %P
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.660~~~~~$\displaystyle
+\int{\frac{tanh^{-1}(x/a)}{x^2}}~dx$}
+$$\int{\frac{tanh^{-1}(x/a)}{x^2}}=
+-\frac{\tanh^{-1}(x/a)}{x}+\frac{1}{2a}\ln\left(\frac{x^2}{a^2-x^2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 82
+aa:=integrate(atanh(x/a)/x^2,x)
+--R 
+--R
+--R                 2    2                      - x - a
+--R        - x log(x  - a ) + 2x log(x) - a log(-------)
+--R                                              x - a
+--R   (1)  ---------------------------------------------
+--R                             2a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 83
+bb:=-atanh(x/a)/x+1/(2*a)*log(x^2/(a^2-x^2))
+--R
+--R                    2
+--R                   x                x
+--R        x log(- -------) - 2a atanh(-)
+--R                 2    2             a
+--R                x  - a
+--R   (2)  ------------------------------
+--R                     2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 84
+cc:=aa-bb
+--R
+--R   (3)
+--R                                                  2
+--R                2    2                           x             - x - a
+--R       - x log(x  - a ) + 2x log(x) - x log(- -------) - a log(-------)
+--R                                               2    2           x - a
+--R                                              x  - a
+--R     + 
+--R                x
+--R       2a atanh(-)
+--R                a
+--R  /
+--R     2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 85
+atanhrule:=rule(atanh(x) == 1/2*log((1+x)/(1-x)))
+--R
+--R                        - x - 1
+--R                    log(-------)
+--R                         x - 1
+--R   (4)  atanh(x) == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 86
+dd:=atanhrule cc
+--R
+--R                                             2
+--R               2    2                       x
+--R        - log(x  - a ) + 2log(x) - log(- -------)
+--R                                          2    2
+--R                                         x  - a
+--R   (5)  -----------------------------------------
+--R                            2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 87     14:660 Schaums and Axiom agree
+ee:=expandLog dd
+--R
+--R          log(- 1)
+--R   (6)  - --------
+--R             2a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.661~~~~~$\displaystyle
+\int{\coth^{-1}\frac{x}{a}}~dx$}
+$$\int{\coth^{-1}\frac{x}{a}}=
+x\coth^{-1}{x}+\frac{a}{2}\ln(x^2-a^2)
+$$
+
+Note that it appears there is a typo in Schaums (1968 printing 4). 
+$$\int{\coth^{-1}\frac{x}{a}}=
+x\coth^{-1}{x/a}+\frac{a}{2}\ln(x^2-a^2)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 88
+aa:=integrate(acoth(x/a),x)
+--R 
+--R
+--R               2    2          x + a
+--R        a log(x  - a ) + x log(-----)
+--R                               x - a
+--R   (1)  -----------------------------
+--R                      2
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 89
+bb:=x*acoth(x/a)+a/2*log(x^2-a^2)
+--R
+--R               2    2             x
+--R        a log(x  - a ) + 2x acoth(-)
+--R                                  a
+--R   (2)  ----------------------------
+--R                      2
+--R                                                     Type: Expression Integer
+--E
+
+--S 90
+cc:=aa-bb
+--R
+--R              x + a             x
+--R        x log(-----) - 2x acoth(-)
+--R              x - a             a
+--R   (3)  --------------------------
+--R                     2
+--R                                                     Type: Expression Integer
+--E
+
+--S 91
+acothrule:=rule(acoth(x) == 1/2*log((x+1)/(x-1)))
+--R
+--R                        x + 1
+--R                    log(-----)
+--R                        x - 1
+--R   (4)  acoth(x) == ----------
+--R                         2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 92     14:661 Schaums and Axiom agree
+dd:=acothrule cc
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.662~~~~~$\displaystyle
+\int{x\coth^{-1}\frac{x}{a}}~dx$}
+$$\int{x\coth^{-1}\frac{x}{a}}=
+\frac{ax}{2}+\frac{1}{2}(x^2-a^2)\coth^{-1}\frac{x}{a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 93
+aa:=integrate(x*acoth(x/a),x)
+--R 
+--R
+--R          2    2     x + a
+--R        (x  - a )log(-----) + 2a x
+--R                     x - a
+--R   (1)  --------------------------
+--R                     4
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 94
+bb:=(a*x)/2+1/2*(x^2-a^2)*acoth(x/a)
+--R
+--R          2    2       x
+--R        (x  - a )acoth(-) + a x
+--R                       a
+--R   (2)  -----------------------
+--R                   2
+--R                                                     Type: Expression Integer
+--E
+
+--S 95
+cc:=aa-bb
+--R
+--R          2    2     x + a         2     2       x
+--R        (x  - a )log(-----) + (- 2x  + 2a )acoth(-)
+--R                     x - a                       a
+--R   (3)  -------------------------------------------
+--R                             4
+--R                                                     Type: Expression Integer
+--E
+
+--S 96
+acothrule:=rule(acoth(x) == 1/2*log((x+1)/(x-1)))
+--R
+--R                        x + 1
+--R                    log(-----)
+--R                        x - 1
+--R   (4)  acoth(x) == ----------
+--R                         2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 97     14:662 Schaums and Axiom agree
+dd:=acothrule cc
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.663~~~~~$\displaystyle
+\int{x^2\coth^{-1}\frac{x}{a}}~dx$}
+$$\int{x^2\coth^{-1}\frac{x}{a}}=
+\frac{ax^2}{6}+\frac{x^3}{3}\coth^{-1}\frac{x}{a}
++\frac{a^3}{6}\ln(x^2-a^2)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 98
+aa:=integrate(x^2*acoth(x/a),x)
+--R 
+--R
+--R         3     2    2     3    x + a       2
+--R        a log(x  - a ) + x log(-----) + a x
+--R                               x - a
+--R   (1)  ------------------------------------
+--R                          6
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 99
+bb:=(a*x^2)/6+x^3/3*acoth(x/a)+a^3/6*log(x^2-a^2)
+--R
+--R         3     2    2      3      x       2
+--R        a log(x  - a ) + 2x acoth(-) + a x
+--R                                  a
+--R   (2)  -----------------------------------
+--R                         6
+--R                                                     Type: Expression Integer
+--E
+
+--S 100
+cc:=aa-bb
+--R
+--R         3    x + a      3      x
+--R        x log(-----) - 2x acoth(-)
+--R              x - a             a
+--R   (3)  --------------------------
+--R                     6
+--R                                                     Type: Expression Integer
+--E
+
+--S 101
+acothrule:=rule(acoth(x) == 1/2*log((x+1)/(x-1)))
+--R
+--R                        x + 1
+--R                    log(-----)
+--R                        x - 1
+--R   (4)  acoth(x) == ----------
+--R                         2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 102    14:663 Schaums and Axiom agree
+dd:=acothrule cc
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.664~~~~~$\displaystyle
+\int{\frac{\coth^{-1}(x/a)}{x}}~dx$}
+$$\int{\frac{\coth^{-1}(x/a)}{x}}=
+-\left(\frac{a}{x}+\frac{(a/x)^3}{3^2}+\frac{(a/x)^5}{5^2}+\cdots\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 103    14:664 Axiom cannot compute this integral
+aa:=integrate(acoth(x/a)/x,x)
+--R 
+--R
+--I                   %P
+--R           x acoth(--)
+--R         ++         a
+--I   (1)   |   --------- d%P
+--I        ++       %P
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.665~~~~~$\displaystyle
+\int{\frac{\coth^{-1}(x/a)}{x^2}}~dx$}
+$$\int{\frac{\coth^{-1}(x/a)}{x^2}}=
+-\frac{\coth^{-1}(x/a)}{x}+\frac{1}{2a}\ln\left(\frac{x^2}{x^2-a^2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 104
+aa:=integrate(acoth(x/a)/x^2,x)
+--R 
+--R
+--R                 2    2                      x + a
+--R        - x log(x  - a ) + 2x log(x) - a log(-----)
+--R                                             x - a
+--R   (1)  -------------------------------------------
+--R                            2a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 105
+bb:=-acoth(x/a)/x+1/(2*a)*log(x^2/(x^2-a^2))
+--R
+--R                  2
+--R                 x                x
+--R        x log(-------) - 2a acoth(-)
+--R               2    2             a
+--R              x  - a
+--R   (2)  ----------------------------
+--R                    2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 106
+cc:=aa-bb
+--R
+--R   (3)
+--R                                                           2
+--R            2    2                      x + a             x                x
+--R   - x log(x  - a ) + 2x log(x) - a log(-----) - x log(-------) + 2a acoth(-)
+--R                                        x - a           2    2             a
+--R                                                       x  - a
+--R   --------------------------------------------------------------------------
+--R                                      2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 107
+acothrule:=rule(acoth(x) == 1/2*log((x+1)/(x-1)))
+--R
+--R                        x + 1
+--R                    log(-----)
+--R                        x - 1
+--R   (4)  acoth(x) == ----------
+--R                         2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 108
+dd:=acothrule cc
+--R
+--R                                           2
+--R               2    2                     x
+--R        - log(x  - a ) + 2log(x) - log(-------)
+--R                                        2    2
+--R                                       x  - a
+--R   (5)  ---------------------------------------
+--R                           2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 109    14:665 Schaums and Axiom agree
+ee:=expandLog dd
+--R
+--R   (6)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.666~~~~~$\displaystyle
+\int{{\rm sech}^{-1}\frac{x}{a}}~dx$}
+$$\int{{\rm sech}^{-1}\frac{x}{a}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+x{\rm ~sech}^{-1}(x/a)+a\sin^{-1}(x/a),\quad{\rm sech}^{-1}(x/a)&gt;0\\
+\\
+\displaystyle
+x{\rm ~sech}^{-1}(x/a)-a\sin^{-1}(x/a),\quad{\rm sech}^{-1}(x/a)&lt;0\\
+\end{array}
+\right.
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 110
+aa:=integrate(asech(x/a),x)
+--R 
+--R
+--R               +---------+                 +---------+
+--R               |   2    2                  |   2    2
+--R              \|- x  + a   + a            \|- x  + a   - a
+--R   (1)  x log(----------------) - 2a atan(----------------)
+--R                      x                           x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 111
+bb1:=x*asech(x/a)+a*asin(x/a)
+--R
+--R               x            x
+--R   (2)  a asin(-) + x asech(-)
+--R               a            a
+--R                                                     Type: Expression Integer
+--E
+
+--S 112
+bb2:=x*asech(x/a)-a*asin(x/a)
+--R
+--R                 x            x
+--R   (3)  - a asin(-) + x asech(-)
+--R                 a            a
+--R                                                     Type: Expression Integer
+--E
+
+--S 113
+cc1:=aa-bb1
+--R
+--R   (4)
+--R          +---------+                 +---------+
+--R          |   2    2                  |   2    2
+--R         \|- x  + a   + a            \|- x  + a   - a           x            x
+--R   x log(----------------) - 2a atan(----------------) - a asin(-) - x asech(-)
+--R                 x                           x                  a            a
+--R                                                     Type: Expression Integer
+--E
+
+--S 114
+cc2:=aa-bb2
+--R
+--R   (5)
+--R          +---------+                 +---------+
+--R          |   2    2                  |   2    2
+--R         \|- x  + a   + a            \|- x  + a   - a           x            x
+--R   x log(----------------) - 2a atan(----------------) + a asin(-) - x asech(-)
+--R                 x                           x                  a            a
+--R                                                     Type: Expression Integer
+--E
+
+--S 115
+asechrule:=rule(asech(x) == log(1/x+sqrt(1/x^2-1)))
+--R
+--R                          +--------+
+--R                          |   2
+--R                          |- x  + 1
+--R                        x |--------  + 1
+--R                          |    2
+--R                         \|   x
+--R   (6)  asech(x) == log(----------------)
+--R                                x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 116
+dd1:=asechrule cc1
+--R
+--R   (7)
+--R               +---------+
+--R               |   2    2
+--R               |- x  + a
+--R             x |---------  + a           +---------+
+--R               |     2                   |   2    2
+--R              \|    x                   \|- x  + a   + a
+--R     - x log(-----------------) + x log(----------------)
+--R                     x                          x
+--R   + 
+--R                +---------+
+--R                |   2    2
+--R               \|- x  + a   - a           x
+--R     - 2a atan(----------------) - a asin(-)
+--R                       x                  a
+--R                                                     Type: Expression Integer
+--E
+
+--S 117
+asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2)))
+--R
+--R                           +--------+
+--R                           |   2
+--R   (8)  asin(x) == %i log(\|- x  + 1  - %i x)
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 118
+ee1:=asinrule dd1
+--R
+--R   (9)
+--R               +---------+                   +---------+
+--R               |   2    2                    |   2    2
+--R               |- x  + a                     |- x  + a
+--R             x |---------  + a             a |---------  - %i x
+--R               |     2                       |     2
+--R              \|    x                       \|    a
+--R     - x log(-----------------) - %i a log(--------------------)
+--R                     x                               a
+--R   + 
+--R            +---------+                 +---------+
+--R            |   2    2                  |   2    2
+--R           \|- x  + a   + a            \|- x  + a   - a
+--R     x log(----------------) - 2a atan(----------------)
+--R                   x                           x
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 119
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                             - x + %i
+--R                      %i log(--------)
+--R                              x + %i
+--R   (10)  atan(x) == - ----------------
+--R                              2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 120
+ff1:=atanrule ee1
+--R
+--R   (11)
+--R               +---------+                   +---------+
+--R               |   2    2                    |   2    2
+--R               |- x  + a                     |- x  + a
+--R             x |---------  + a             a |---------  - %i x
+--R               |     2                       |     2
+--R              \|    x                       \|    a
+--R     - x log(-----------------) - %i a log(--------------------)
+--R                     x                               a
+--R   + 
+--R            +---------+                    +---------+
+--R            |   2    2                     |   2    2
+--R           \|- x  + a   + a             - \|- x  + a   + %i x + a
+--R     x log(----------------) + %i a log(-------------------------)
+--R                   x                      +---------+
+--R                                          |   2    2
+--R                                         \|- x  + a   + %i x - a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 121
+gg1:=expandLog ff1
+--R
+--R   (12)
+--R               +---------+                   +---------+
+--R               |   2    2                    |   2    2
+--R               |- x  + a                     |- x  + a
+--R     - x log(x |---------  + a) - %i a log(a |---------  - %i x)
+--R               |     2                       |     2
+--R              \|    x                       \|    a
+--R   + 
+--R                 +---------+                      +---------+
+--R                 |   2    2                       |   2    2
+--R     - %i a log(\|- x  + a   + %i x - a) + x log(\|- x  + a   + a)
+--R   + 
+--R               +---------+
+--R               |   2    2
+--R     %i a log(\|- x  + a   - %i x - a) + %i a log(a) + %i a log(- 1)
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 122
+hh1:=rootSimp gg1
+--R
+--R   (13)
+--R                   +-------+                           +-------+
+--R                   | 2    2                            | 2    2
+--R     - %i a log(%i\|x  - a   + %i x - a) - %i a log(%i\|x  - a   - %i x)
+--R   + 
+--R                 +-------+
+--R                 | 2    2
+--R     %i a log(%i\|x  - a   - %i x - a) + %i a log(a) + %i a log(- 1)
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 123    14:666 Schaums and Axiom agree
+ii1:=complexNormalize hh1
+--R
+--R   (14)  0
+--R                                             Type: Expression Complex Integer
+--E
+
+@
+Note that Axiom has a built-in assumption about the sign of asech(x/a).
+We can see this if we simplify the cc2 value and show that it differs
+by a complex value of x.
+&lt;&lt;*&gt;&gt;=
+--S 124
+dd2:=asechrule cc2
+--R
+--R   (15)
+--R               +---------+
+--R               |   2    2
+--R               |- x  + a
+--R             x |---------  + a           +---------+
+--R               |     2                   |   2    2
+--R              \|    x                   \|- x  + a   + a
+--R     - x log(-----------------) + x log(----------------)
+--R                     x                          x
+--R   + 
+--R                +---------+
+--R                |   2    2
+--R               \|- x  + a   - a           x
+--R     - 2a atan(----------------) + a asin(-)
+--R                       x                  a
+--R                                                     Type: Expression Integer
+--E
+
+--S 125
+ee2:=asinrule dd2
+--R
+--R   (16)
+--R               +---------+                   +---------+
+--R               |   2    2                    |   2    2
+--R               |- x  + a                     |- x  + a
+--R             x |---------  + a             a |---------  - %i x
+--R               |     2                       |     2
+--R              \|    x                       \|    a
+--R     - x log(-----------------) + %i a log(--------------------)
+--R                     x                               a
+--R   + 
+--R            +---------+                 +---------+
+--R            |   2    2                  |   2    2
+--R           \|- x  + a   + a            \|- x  + a   - a
+--R     x log(----------------) - 2a atan(----------------)
+--R                   x                           x
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 126
+ff2:=atanrule ee2
+--R
+--R   (17)
+--R               +---------+                   +---------+
+--R               |   2    2                    |   2    2
+--R               |- x  + a                     |- x  + a
+--R             x |---------  + a             a |---------  - %i x
+--R               |     2                       |     2
+--R              \|    x                       \|    a
+--R     - x log(-----------------) + %i a log(--------------------)
+--R                     x                               a
+--R   + 
+--R            +---------+                    +---------+
+--R            |   2    2                     |   2    2
+--R           \|- x  + a   + a             - \|- x  + a   + %i x + a
+--R     x log(----------------) + %i a log(-------------------------)
+--R                   x                      +---------+
+--R                                          |   2    2
+--R                                         \|- x  + a   + %i x - a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 127
+gg2:=expandLog ff2
+--R
+--R   (18)
+--R               +---------+                   +---------+
+--R               |   2    2                    |   2    2
+--R               |- x  + a                     |- x  + a
+--R     - x log(x |---------  + a) + %i a log(a |---------  - %i x)
+--R               |     2                       |     2
+--R              \|    x                       \|    a
+--R   + 
+--R                 +---------+                      +---------+
+--R                 |   2    2                       |   2    2
+--R     - %i a log(\|- x  + a   + %i x - a) + x log(\|- x  + a   + a)
+--R   + 
+--R               +---------+
+--R               |   2    2
+--R     %i a log(\|- x  + a   - %i x - a) - %i a log(a) + %i a log(- 1)
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 128
+hh2:=rootSimp gg2
+--R
+--R   (19)
+--R                   +-------+                           +-------+
+--R                   | 2    2                            | 2    2
+--R     - %i a log(%i\|x  - a   + %i x - a) + %i a log(%i\|x  - a   - %i x)
+--R   + 
+--R                 +-------+
+--R                 | 2    2
+--R     %i a log(%i\|x  - a   - %i x - a) - %i a log(a) + %i a log(- 1)
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 129
+ii2:=complexNormalize hh2
+--R
+--R                      +-------+
+--R                      | 2    2
+--R   (20)  2%i a log(%i\|x  - a   - %i x) - 2%i a log(a)
+--R                                             Type: Expression Complex Integer
+--E
+
+@
+Thus we can conjecture that solutions that show up with x in only the
+imaginary part do so when the assumption of the sign of an inverse
+function differs.
+
+\section{\cite{1}:14.667~~~~~$\displaystyle
+\int{x{\rm ~sech}^{-1}\frac{x}{a}}~dx$}
+$$\int{x{\rm ~sech}^{-1}\frac{x}{a}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{1}{2}x^2{\rm ~sech}^{-1}(x/a)-\frac{1}{2}a\sqrt{a^2-x^2},
+\quad{\rm sech}^{-1}(x/a)&gt;0\\
+\\
+\displaystyle
+\frac{1}{2}x^2{\rm ~sech}^{-1}(x/a)+\frac{1}{2}a\sqrt{a^2-x^2},
+\quad{\rm sech}^{-1}(x/a)&lt;0\\
+\end{array}
+\right.
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 130
+aa:=integrate(x*asech(x/a),x)
+--R 
+--R
+--R                                    +---------+
+--R            +---------+             |   2    2
+--R          2 |   2    2       2     \|- x  + a   + a       2
+--R        (x \|- x  + a   - a x )log(----------------) + a x
+--R                                           x
+--R   (1)  ---------------------------------------------------
+--R                           +---------+
+--R                           |   2    2
+--R                         2\|- x  + a   - 2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 131
+bb1:=1/2*x^2*asech(x/a)-1/2*a*sqrt(a^2-x^2)
+--R
+--R            +---------+
+--R            |   2    2     2      x
+--R        - a\|- x  + a   + x asech(-)
+--R                                  a
+--R   (2)  ----------------------------
+--R                      2
+--R                                                     Type: Expression Integer
+--E
+
+--S 132
+bb2:=1/2*x^2*asech(x/a)+1/2*a*sqrt(a^2-x^2)
+--R
+--R          +---------+
+--R          |   2    2     2      x
+--R        a\|- x  + a   + x asech(-)
+--R                                a
+--R   (3)  --------------------------
+--R                     2
+--R                                                     Type: Expression Integer
+--E
+
+--S 133
+cc1:=aa-bb1
+--R
+--R               +---------+
+--R               |   2    2
+--R         2    \|- x  + a   + a     2      x     2
+--R        x log(----------------) - x asech(-) - a
+--R                      x                   a
+--R   (4)  -----------------------------------------
+--R                            2
+--R                                                     Type: Expression Integer
+--E
+
+--S 134
+cc2:=aa-bb2
+--R
+--R   (5)
+--R                                   +---------+
+--R           +---------+             |   2    2
+--R         2 |   2    2       2     \|- x  + a   + a
+--R       (x \|- x  + a   - a x )log(----------------)
+--R                                          x
+--R     + 
+--R                           +---------+
+--R           2      x     2  |   2    2       2      x        2    3
+--R       (- x asech(-) + a )\|- x  + a   + a x asech(-) + 2a x  - a
+--R                  a                                a
+--R  /
+--R       +---------+
+--R       |   2    2
+--R     2\|- x  + a   - 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 135
+asechrule:=rule(asech(x) == log(1/x+sqrt(1/x^2-1)))
+--R
+--R                          +--------+
+--R                          |   2
+--R                          |- x  + 1
+--R                        x |--------  + 1
+--R                          |    2
+--R                         \|   x
+--R   (6)  asech(x) == log(----------------)
+--R                                x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 136
+dd1:=asechrule cc1
+--R
+--R                  +---------+
+--R                  |   2    2
+--R                  |- x  + a
+--R                x |---------  + a           +---------+
+--R                  |     2                   |   2    2
+--R           2     \|    x              2    \|- x  + a   + a     2
+--R        - x log(-----------------) + x log(----------------) - a
+--R                        x                          x
+--R   (7)  ---------------------------------------------------------
+--R                                    2
+--R                                                     Type: Expression Integer
+--E
+
+--S 137
+ee1:=expandLog dd1
+--R
+--R                  +---------+
+--R                  |   2    2                +---------+
+--R           2      |- x  + a           2     |   2    2          2
+--R        - x log(x |---------  + a) + x log(\|- x  + a   + a) - a
+--R                  |     2
+--R                 \|    x
+--R   (8)  ---------------------------------------------------------
+--R                                    2
+--R                                                     Type: Expression Integer
+--E
+
+--S 138    14:667 Schaums and Axiom differ by a constant
+ff1:=rootSimp ee1
+--R
+--R           2
+--R          a
+--R   (9)  - --
+--R           2
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.668~~~~~$\displaystyle
+\int{\frac{{\rm sech}^{-1}(x/a)}{x}}~dx$}
+$$\int{\frac{{\rm sech}^{-1}(x/a)}{x}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+-\frac{1}{2}\ln(a/x)\ln(4a/x)-\frac{(x/a)^2}{2\cdot 2\cdot 2}
+-\frac{1\cdot 3(x/a)^4}{2\cdot 4\cdot 4\cdot 4}
+-\cdots,\quad{\rm sech}^{-1}(x/a)&gt;0\\
+\\
+\displaystyle
+\frac{1}{2}\ln(a/x)\ln(4a/x)+\frac{(x/a)^2}{2\cdot 2\cdot 2}
++\frac{1\cdot 3(x/a)^4}{2\cdot 4\cdot 4\cdot 4}
++\cdots,\quad{\rm sech}^{-1}(x/a)&lt;0\\
+\end{array}
+\right.
+$$
+
+This is a interesting result since Axiom gives a closed form 
+solution to the problem but Schaums gives a series solution.
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 139    14:668 Axiom cannot compute this integral
+aa:=integrate(asech(x/a)/x,x)
+--R 
+--R
+--I                   %P
+--R           x asech(--)
+--R         ++         a
+--I   (1)   |   --------- d%P
+--I        ++       %P
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.669~~~~~$\displaystyle
+\int{{\rm csch}^{-1}\frac{x}{a}}~dx$}
+$$\int{{\rm csch}^{-1}\frac{x}{a}}=
+x{\rm ~csch}^{-1}\frac{x}{a}\pm a\sinh^{-1}\frac{x}{a}
+\quad +{\rm if\ }x&gt;0, -{\rm if\ }x&lt;0
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 140
+aa:=integrate(acsch(x/a),x)
+--R 
+--R
+--R                                         +-------+
+--R                 +-------+               | 2    2
+--R                 | 2    2               \|x  + a   + a
+--R   (1)  - a log(\|x  + a   - x) + x log(--------------)
+--R                                               x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 141
+bb1:=x*acsch(x/a)+a*asinh(x/a)
+--R
+--R                x            x
+--R   (2)  a asinh(-) + x acsch(-)
+--R                a            a
+--R                                                     Type: Expression Integer
+--E
+
+--S 142
+bb2:=x*acsch(x/a)-a*asinh(x/a)
+--R
+--R                  x            x
+--R   (3)  - a asinh(-) + x acsch(-)
+--R                  a            a
+--R                                                     Type: Expression Integer
+--E
+
+--S 143
+cc1:=aa-bb1
+--R
+--R   (4)
+--R                                    +-------+
+--R            +-------+               | 2    2
+--R            | 2    2               \|x  + a   + a            x            x
+--R   - a log(\|x  + a   - x) + x log(--------------) - a asinh(-) - x acsch(-)
+--R                                          x                  a            a
+--R                                                     Type: Expression Integer
+--E
+
+--S 144    14:669 Axiom cannot simplify these expressions
+cc2:=aa-bb2
+--R
+--R   (5)
+--R                                    +-------+
+--R            +-------+               | 2    2
+--R            | 2    2               \|x  + a   + a            x            x
+--R   - a log(\|x  + a   - x) + x log(--------------) + a asinh(-) - x acsch(-)
+--R                                          x                  a            a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.670~~~~~$\displaystyle
+\int{x{\rm ~csch}^{-1}\frac{x}{a}}~dx$}
+$$\int{x{\rm ~csch}^{-1}\frac{x}{a}}=
+\frac{x^2}{2}{\rm ~csch}^{-1}\frac{x}{a}\pm \frac{a\sqrt{x^2+a^2}}{2}
+\quad +{\rm if\ }x&gt;0, -{\rm if\ }x&lt;0
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 145
+aa:=integrate(x*acsch(x/a),x)
+--R 
+--R
+--R                                +-------+
+--R            +-------+           | 2    2             +-------+
+--R          2 | 2    2     3     \|x  + a   + a        | 2    2       2    3
+--R        (x \|x  + a   - x )log(--------------) - a x\|x  + a   + a x  + a
+--R                                      x
+--R   (1)  ------------------------------------------------------------------
+--R                                   +-------+
+--R                                   | 2    2
+--R                                 2\|x  + a   - 2x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 146
+bb1:=x^2/2*acsch(x/a)+(a*sqrt(x^2+a^2))/2
+--R
+--R          +-------+
+--R          | 2    2     2      x
+--R        a\|x  + a   + x acsch(-)
+--R                              a
+--R   (2)  ------------------------
+--R                    2
+--R                                                     Type: Expression Integer
+--E
+
+--S 147
+bb2:=x^2/2*acsch(x/a)-(a*sqrt(x^2+a^2))/2
+--R
+--R            +-------+
+--R            | 2    2     2      x
+--R        - a\|x  + a   + x acsch(-)
+--R                                a
+--R   (3)  --------------------------
+--R                     2
+--R                                                     Type: Expression Integer
+--E
+
+--S 148
+cc1:=aa-bb1
+--R
+--R               +-------+
+--R               | 2    2
+--R         2    \|x  + a   + a     2      x
+--R        x log(--------------) - x acsch(-)
+--R                     x                  a
+--R   (4)  ----------------------------------
+--R                         2
+--R                                                     Type: Expression Integer
+--E
+
+--S 149    14:670 Axiom cannot simplify these expressions
+cc2:=aa-bb2
+--R
+--R   (5)
+--R                               +-------+
+--R           +-------+           | 2    2                               +-------+
+--R         2 | 2    2     3     \|x  + a   + a        2      x          | 2    2
+--R       (x \|x  + a   - x )log(--------------) + (- x acsch(-) - 2a x)\|x  + a
+--R                                     x                     a
+--R     + 
+--R        3      x        2     3
+--R       x acsch(-) + 2a x  + 2a
+--R               a
+--R  /
+--R       +-------+
+--R       | 2    2
+--R     2\|x  + a   - 2x
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.671~~~~~$\displaystyle
+\int{\frac{{\rm csch}^{-1}(x/a)}{x}}~dx$}
+$$\int{\frac{{\rm csch}^{-1}(x/a)}{x}}=
+\left\{
+\begin{array}{lr}
+\displaystyle
+\frac{1}{2}\ln(x/a)\ln(4a/x)+\frac{1(x/a)^2}{2\cdot 2\cdot 2}
+-\frac{1\cdot 3(x/a)^4}{2\cdot 4\cdot 4\cdot 4}+\cdots&amp;
+0&lt;x&lt;a\\
+\\
+\displaystyle
+\frac{1}{2}\ln(-x/a)\ln(-x/4a)-\frac{(x/a)^2}{2\cdot 2\cdot 2}
++\frac{1\cdot 3(x/a)^4}{2\cdot 4\cdot 4\cdot 4}-\cdots&amp;
+-a&lt;x&lt;0\\
+\\
+\displaystyle
+-\frac{a}{x}+\frac{(a/x)^3}{2\cdot 3\cdot 3}
+-\frac{1\cdot 3(a/x)^5}{2\cdot 4\cdot 5\cdot 5}+\cdots&amp;
+|x|&gt;a
+\end{array}
+\right.
+$$
+
+Schaums gives 3 different series expansions for this integral
+but Axiom has computed a closed form.
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 150    14:671 Axiom cannot compute this integral
+aa:=integrate(acsch(x/a)/x,x)
+--R 
+--R
+--I                   %P
+--R           x acsch(--)
+--R         ++         a
+--I   (1)   |   --------- d%P
+--I        ++       %P
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+@
+
+\section{\cite{1}:14.672~~~~~$\displaystyle
+\int{x^m\sinh^{-1}\frac{x}{a}}~dx$}
+$$\int{x^m\sinh^{-1}\frac{x}{a}}=
+\frac{x^{m+1}}{m+1}\sinh^{-1}\frac{x}{a}
+-\frac{1}{m+1}\int{\frac{x^{m+1}}{\sqrt{x^2+a^2}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 151    14:672 Axiom cannot compute this integral
+aa:=integrate(x^m*asinh(x/a),x)
+--R 
+--R
+--R           x
+--I         ++        %P   m
+--I   (1)   |   asinh(--)%P d%P
+--R        ++          a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.673~~~~~$\displaystyle
+\int{x^m\cosh^{-1}\frac{x}{a}}~dx$}
+$$\int{x^m\cosh^{-1}\frac{x}{a}}=
+\left\{
+\begin{array}{lr}
+\displaystyle
+\frac{x^{m+1}}{m+1}\cosh^{-1}\frac{x}{a}
+-\frac{1}{m+1}\int{\frac{x^{m+1}}{\sqrt{x^2-a^2}}},&amp;
+\quad\cosh^{-1}(x/a)&gt;0\\
+\\
+\displaystyle
+\frac{x^{m+1}}{m+1}\cosh^{-1}\frac{x}{a}
++\frac{1}{m+1}\int{\frac{x^{m+1}}{\sqrt{x^2-a^2}}},&amp;
+\quad\cosh^{-1}(x/a)&lt;0\\
+\end{array}
+\right.
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 152    14:673 Axiom cannot compute this integral
+aa:=integrate(x^m*acosh(x/a),x)
+--R 
+--R
+--R           x
+--I         ++        %P   m
+--I   (1)   |   acosh(--)%P d%P
+--R        ++          a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.674~~~~~$\displaystyle
+\int{x^m\tanh^{-1}\frac{x}{a}}~dx$}
+$$\int{x^m\tanh^{-1}\frac{x}{a}}=
+\frac{x^{m+1}}{m+1}\tanh^{-1}\frac{x}{a}
+-\frac{a}{m+1}\int{\frac{x^{m+1}}{a^2-x^2}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 153    14:674 Axiom cannot compute this integral
+aa:=integrate(x^m*atanh(x/a),x)
+--R 
+--R
+--R           x
+--I         ++        %P   m
+--I   (1)   |   atanh(--)%P d%P
+--R        ++          a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.675~~~~~$\displaystyle
+\int{x^m\coth^{-1}\frac{x}{a}}~dx$}
+$$\int{x^m\coth^{-1}\frac{x}{a}}=
+\frac{x^{m+1}}{m+1}\coth^{-1}\frac{x}{a}
+-\frac{a}{m+1}\int{\frac{x^{m+1}}{a^2-x^2}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 154    14:675 Axiom cannot compute this integral
+aa:=integrate(x^m*acoth(x/a),x)
+--R 
+--R
+--R           x
+--I         ++        %P   m
+--I   (1)   |   acoth(--)%P d%P
+--R        ++          a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.676~~~~~$\displaystyle
+\int{x^m{\rm ~sech}^{-1}\frac{x}{a}}~dx$}
+$$\int{x^m{\rm ~sech}^{-1}\frac{x}{a}}=
+\left\{
+\begin{array}{lr}
+\displaystyle
+\frac{x^{m+1}}{m+1}{\rm ~sech}^{-1}\frac{x}{a}
++\frac{a}{m+1}\int{\frac{x^m}{\sqrt{a^2-x^2}}}&amp;
+{\rm sech}^{-1}(x/a)&gt;0\\
+\\
+\displaystyle
+\frac{x^{m+1}}{m+1}{\rm ~sech}^{-1}\frac{x}{a}
+-\frac{a}{m+1}\int{\frac{x^m}{\sqrt{a^2-x^2}}}&amp;
+{\rm sech}^{-1}(x/a)&lt;0\\
+\end{array}
+\right.
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 155    14:676 Axiom cannot compute this integral
+aa:=integrate(x^m*asech(x/a),x)
+--R 
+--R
+--R           x
+--I         ++        %P   m
+--I   (1)   |   asech(--)%P d%P
+--R        ++          a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.677~~~~~$\displaystyle
+\int{x^m{\rm ~csch}^{-1}\frac{x}{a}}~dx$}
+$$\int{x^m{\rm ~csch}^{-1}\frac{x}{a}}=
+\frac{x^{m+1}}{m+1}{\rm ~csch}^{-1}\frac{x}{a}
+\pm\frac{a}{m+1}\int{\frac{x^m}{\sqrt{x^2+a^2}}}
+\quad+{\rm if\ }x&gt;0
+~-{\rm if\ }x&lt;0
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 156    14:677 Axiom cannot compute this integral
+aa:=integrate(x^m*acsch(x/a),x)
+--R 
+--R
+--R           x
+--I         ++        %P   m
+--I   (1)   |   acsch(--)%P d%P
+--R        ++          a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 pp92-93
+\end{thebibliography}
+\end{document}
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diff --git a/src/axiom-website/CATS/schaum4.input.pamphlet b/src/axiom-website/CATS/schaum4.input.pamphlet
new file mode 100644
index 0000000..0edbbf9
--- /dev/null
+++ b/src/axiom-website/CATS/schaum4.input.pamphlet
@@ -0,0 +1,525 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum4.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.113~~~~~$\displaystyle\int{\frac{px+q}{\sqrt{ax+b}}}~dx$}
+$$\int{\frac{px+q}{\sqrt{ax+b}}}=
+\frac{2(apx+3aq-2bp)}{3a^2}\sqrt{ax+b}$$
+&lt;&lt;*&gt;&gt;=
+)spool schaum4.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1
+aa:=integrate((p*x+q)/sqrt(a*x+b),x)
+--R 
+--R
+--R                               +-------+
+--R        (2a p x + 6a q - 4b p)\|a x + b
+--R   (1)  --------------------------------
+--R                         2
+--R                       3a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 2
+bb:=(2*(a*p*x+3*a*q-2*b*p))/(3*a^2)*sqrt(a*x+b)
+--R
+--R                               +-------+
+--R        (2a p x + 6a q - 4b p)\|a x + b
+--R   (2)  --------------------------------
+--R                         2
+--R                       3a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3      14:113 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.114~~~~~$\displaystyle
+\int{\frac{dx}{(px+q)\sqrt{ax+b}}}$}
+$$\int{\frac{1}{(px+q)\sqrt{ax+b}}}=
+\left\{
+\begin{array}{l}
+\frac{1}{\sqrt{bp-aq}\sqrt{p}}\ln\left(
+\frac{\sqrt{p(ax+b)}-\sqrt{bp-aq}}{\sqrt{p(ax+b)}+\sqrt{bp-aq}}\right)\\
+\frac{2}{\sqrt{aq-bp}\sqrt{p}}\tan^{-1}\sqrt{\frac{p(ax+b)}{aq-bp}}
+\end{array}
+\right.
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 4
+aa:=integrate(1/((p*x+q)*sqrt(a*x+b)),x)
+--R 
+--R
+--R   (1)
+--R                                                          +--------------+
+--R                      2  +-------+                        |             2
+--R        (2a p q - 2b p )\|a x + b  + (a p x - a q + 2b p)\|- a p q + b p
+--R    log(------------------------------------------------------------------)
+--R                                      p x + q
+--R   [-----------------------------------------------------------------------,
+--R                                +--------------+
+--R                                |             2
+--R                               \|- a p q + b p
+--R           +------------+
+--R           |           2  +-------+
+--R          \|a p q - b p  \|a x + b
+--R    2atan(-------------------------)
+--R                  a q - b p
+--R    --------------------------------]
+--R              +------------+
+--R              |           2
+--R             \|a p q - b p
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+
+--S 5
+aa1:=aa.1
+--R
+--R   (2)
+--R                                                         +--------------+
+--R                     2  +-------+                        |             2
+--R       (2a p q - 2b p )\|a x + b  + (a p x - a q + 2b p)\|- a p q + b p
+--R   log(------------------------------------------------------------------)
+--R                                     p x + q
+--R   -----------------------------------------------------------------------
+--R                               +--------------+
+--R                               |             2
+--R                              \|- a p q + b p
+--R                                                     Type: Expression Integer
+--E
+
+--S 6
+aa2:=aa.2
+--R
+--R               +------------+
+--R               |           2  +-------+
+--R              \|a p q - b p  \|a x + b
+--R        2atan(-------------------------)
+--R                      a q - b p
+--R   (3)  --------------------------------
+--R                  +------------+
+--R                  |           2
+--R                 \|a p q - b p
+--R                                                     Type: Expression Integer
+--E
+
+--S 7
+bb1:=1/sqrt(b*p-a*q)*log((sqrt(p*(a*x+b))-sqrt(b*p-a*q))/(sqrt(p*(a*x+b))+sqrt(b*p-a*q)))
+--R
+--R             +-----------+    +-----------+
+--R            \|a p x + b p  - \|- a q + b p
+--R        log(-------------------------------)
+--R             +-----------+    +-----------+
+--R            \|a p x + b p  + \|- a q + b p
+--R   (4)  ------------------------------------
+--R                    +-----------+
+--R                   \|- a q + b p
+--R                                                     Type: Expression Integer
+--E
+
+--S 8
+bb2:=2/(sqrt(a*q-b*p)*sqrt(p))*atan(sqrt((p*(a*x+b))/(a*q-b*p)))
+--R
+--R               +-----------+
+--R               |a p x + b p
+--R        2atan( |----------- )
+--R              \| a q - b p
+--R   (5)  ---------------------
+--R            +-+ +---------+
+--R           \|p \|a q - b p
+--R                                                     Type: Expression Integer
+--E
+
+--S 9
+cc1:=aa1-bb1
+--R
+--R   (6)
+--R          +-----------+
+--R         \|- a q + b p
+--R      *
+--R                                                             +--------------+
+--R                         2  +-------+                        |             2
+--R           (2a p q - 2b p )\|a x + b  + (a p x - a q + 2b p)\|- a p q + b p
+--R       log(------------------------------------------------------------------)
+--R                                         p x + q
+--R     + 
+--R          +--------------+     +-----------+    +-----------+
+--R          |             2     \|a p x + b p  - \|- a q + b p
+--R       - \|- a p q + b p  log(-------------------------------)
+--R                               +-----------+    +-----------+
+--R                              \|a p x + b p  + \|- a q + b p
+--R  /
+--R      +--------------+
+--R      |             2  +-----------+
+--R     \|- a p q + b p  \|- a q + b p
+--R                                                     Type: Expression Integer
+--E
+
+--S 10
+cc2:=aa1-bb2
+--R
+--R   (7)
+--R          +-+ +---------+
+--R         \|p \|a q - b p
+--R      *
+--R                                                             +--------------+
+--R                         2  +-------+                        |             2
+--R           (2a p q - 2b p )\|a x + b  + (a p x - a q + 2b p)\|- a p q + b p
+--R       log(------------------------------------------------------------------)
+--R                                         p x + q
+--R     + 
+--R           +--------------+      +-----------+
+--R           |             2       |a p x + b p
+--R       - 2\|- a p q + b p  atan( |----------- )
+--R                                \| a q - b p
+--R  /
+--R      +--------------+
+--R      |             2  +-+ +---------+
+--R     \|- a p q + b p  \|p \|a q - b p
+--R                                                     Type: Expression Integer
+--E
+
+--S 11
+cc3:=aa2-bb1
+--R
+--R   (8)
+--R          +------------+     +-----------+    +-----------+
+--R          |           2     \|a p x + b p  - \|- a q + b p
+--R       - \|a p q - b p  log(-------------------------------)
+--R                             +-----------+    +-----------+
+--R                            \|a p x + b p  + \|- a q + b p
+--R     + 
+--R                            +------------+
+--R                            |           2  +-------+
+--R         +-----------+     \|a p q - b p  \|a x + b
+--R       2\|- a q + b p atan(-------------------------)
+--R                                   a q - b p
+--R  /
+--R                    +------------+
+--R      +-----------+ |           2
+--R     \|- a q + b p \|a p q - b p
+--R                                                     Type: Expression Integer
+--E
+
+--S 12     14:114 Axiom cannot simplify these answers
+cc4:=aa2-bb2
+--R
+--R   (9)
+--R                              +------------+
+--R                              |           2  +-------+
+--R         +-+ +---------+     \|a p q - b p  \|a x + b
+--R       2\|p \|a q - b p atan(-------------------------)
+--R                                     a q - b p
+--R     + 
+--R           +------------+      +-----------+
+--R           |           2       |a p x + b p
+--R       - 2\|a p q - b p  atan( |----------- )
+--R                              \| a q - b p
+--R  /
+--R                      +------------+
+--R      +-+ +---------+ |           2
+--R     \|p \|a q - b p \|a p q - b p
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.115~~~~~$\displaystyle\int{\frac{\sqrt{ax+b}}{px+q}}~dx$}
+$$\int{\frac{\sqrt{ax+b}}{px+q}}=
+\left\{
+\begin{array}{l}
+\frac{2\sqrt{ax+b}}{p}+\frac{\sqrt{bp-aq}}{p\sqrt{p}}\ln\left(
+\frac{\sqrt{p(ax+b)}-\sqrt{bp-aq}}{\sqrt{p(ax+b)}+\sqrt{bp-aq}}\right)\\
+\frac{2\sqrt{ax+b}}{p}-\frac{2\sqrt{aq-bp}}{p\sqrt{p}}
+\tan^{-1}\sqrt{\frac{p(ax+b)}{aq-bp}}
+\end{array}
+\right.$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 13
+aa:=integrate(sqrt(a*x+b)/(p*x+q),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R                                +-----------+
+--R                                |- a q + b p  +-------+
+--R          +-----------+    - 2p |----------- \|a x + b  + a p x - a q + 2b p
+--R          |- a q + b p         \|     p
+--R          |----------- log(-------------------------------------------------)
+--R         \|     p                               p x + q
+--R       + 
+--R           +-------+
+--R         2\|a x + b
+--R    /
+--R       p
+--R     ,
+--R         +---------+       +-------+
+--R         |a q - b p       \|a x + b       +-------+
+--R    - 2  |--------- atan(------------ + 2\|a x + b
+--R        \|    p           +---------+
+--R                          |a q - b p
+--R                          |---------
+--R                         \|    p
+--R    -----------------------------------------------]
+--R                           p
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+
+--S 14
+aa1:=aa.1
+--R
+--R   (2)
+--R                              +-----------+
+--R                              |- a q + b p  +-------+
+--R        +-----------+    - 2p |----------- \|a x + b  + a p x - a q + 2b p
+--R        |- a q + b p         \|     p
+--R        |----------- log(-------------------------------------------------)
+--R       \|     p                               p x + q
+--R     + 
+--R         +-------+
+--R       2\|a x + b
+--R  /
+--R     p
+--R                                                     Type: Expression Integer
+--E
+
+--S 15
+aa2:=aa.2
+--R
+--R             +---------+       +-------+
+--R             |a q - b p       \|a x + b       +-------+
+--R        - 2  |--------- atan(------------ + 2\|a x + b
+--R            \|    p           +---------+
+--R                              |a q - b p
+--R                              |---------
+--R                             \|    p
+--R   (3)  -----------------------------------------------
+--R                               p
+--R                                                     Type: Expression Integer
+--E
+
+--S 16
+bb1:=(2*sqrt(a*x+b))/p+sqrt(b*p-a*q)/(p*sqrt(p))*log((sqrt(p*(a*x+b))-sqrt(b*p-a*q))/(sqrt(p*(a*x+b))+sqrt(b*p-a*q)))
+--R
+--R                           +-----------+    +-----------+
+--R         +-----------+    \|a p x + b p  - \|- a q + b p       +-+ +-------+
+--R        \|- a q + b p log(-------------------------------) + 2\|p \|a x + b
+--R                           +-----------+    +-----------+
+--R                          \|a p x + b p  + \|- a q + b p
+--R   (4)  --------------------------------------------------------------------
+--R                                          +-+
+--R                                        p\|p
+--R                                                     Type: Expression Integer
+--E
+
+--S 17
+bb2:=(2*sqrt(a*x+b))/p-(2*sqrt(a*q-b*p))/(p*sqrt(p))*atan(sqrt((p*(a*x+b))/(a*q-b*p)))
+--R
+--R                             +-----------+
+--R            +---------+      |a p x + b p       +-+ +-------+
+--R        - 2\|a q - b p atan( |----------- ) + 2\|p \|a x + b
+--R                            \| a q - b p
+--R   (5)  -----------------------------------------------------
+--R                                  +-+
+--R                                p\|p
+--R                                                     Type: Expression Integer
+--E
+
+--S 18
+cc1:=aa1-bb1
+--R
+--R   (6)
+--R                            +-----------+    +-----------+
+--R          +-----------+    \|a p x + b p  - \|- a q + b p
+--R       - \|- a q + b p log(-------------------------------)
+--R                            +-----------+    +-----------+
+--R                           \|a p x + b p  + \|- a q + b p
+--R     + 
+--R                                  +-----------+
+--R                                  |- a q + b p  +-------+
+--R        +-----------+        - 2p |----------- \|a x + b  + a p x - a q + 2b p
+--R        |- a q + b p  +-+        \|     p
+--R        |----------- \|p log(-------------------------------------------------)
+--R       \|     p                                   p x + q
+--R  /
+--R       +-+
+--R     p\|p
+--R                                                     Type: Expression Integer
+--E
+
+--S 19
+cc2:=aa1-bb2
+--R
+--R   (7)
+--R                                  +-----------+
+--R                                  |- a q + b p  +-------+
+--R        +-----------+        - 2p |----------- \|a x + b  + a p x - a q + 2b p
+--R        |- a q + b p  +-+        \|     p
+--R        |----------- \|p log(-------------------------------------------------)
+--R       \|     p                                   p x + q
+--R     + 
+--R                          +-----------+
+--R         +---------+      |a p x + b p
+--R       2\|a q - b p atan( |----------- )
+--R                         \| a q - b p
+--R  /
+--R       +-+
+--R     p\|p
+--R                                                     Type: Expression Integer
+--E
+
+--S 20
+cc3:=aa2-bb1
+--R
+--R   (8)
+--R                            +-----------+    +-----------+
+--R          +-----------+    \|a p x + b p  - \|- a q + b p
+--R       - \|- a q + b p log(-------------------------------)
+--R                            +-----------+    +-----------+
+--R                           \|a p x + b p  + \|- a q + b p
+--R     + 
+--R               +---------+       +-------+
+--R           +-+ |a q - b p       \|a x + b
+--R       - 2\|p  |--------- atan(------------)
+--R              \|    p           +---------+
+--R                                |a q - b p
+--R                                |---------
+--R                               \|    p
+--R  /
+--R       +-+
+--R     p\|p
+--R                                                     Type: Expression Integer
+--E
+
+--S 21     14:115 Axiom cannot simplify these answers
+cc4:=aa2-bb2
+--R
+--R   (9)
+--R           +---------+       +-------+                        +-----------+
+--R       +-+ |a q - b p       \|a x + b        +---------+      |a p x + b p
+--R   - 2\|p  |--------- atan(------------) + 2\|a q - b p atan( |----------- )
+--R          \|    p           +---------+                      \| a q - b p
+--R                            |a q - b p
+--R                            |---------
+--R                           \|    p
+--R   -------------------------------------------------------------------------
+--R                                       +-+
+--R                                     p\|p
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.116~~~~~$\displaystyle\int{(px+b)^n\sqrt{ax+b}}~dx$}
+$$\int{(px+b)^n\sqrt{ax+b}}=
+\frac{2(px+q)^{n+1}\sqrt{ax+b}}{(2n+3)p}+\frac{bp-aq}{(2n+3)p}
+\int{\frac{(px+q)^n}{\sqrt{ax+b}}}$$
+
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 22     14:116 Axiom cannot compute this integral
+aa:=integrate((p*x+q)^n*sqrt(a*x+b),x)
+--R 
+--R
+--R           x
+--R         ++            n +--------+
+--I   (1)   |   (q + %L p) \|b + %L a d%L
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.117~~~~~$\displaystyle
+\int{\frac{dx}{(px+b)^n\sqrt{ax+b}}}$}
+$$\int{\frac{1}{(px+b)^n\sqrt{ax+b}}}=
+\frac{\sqrt{ax+b}}{(n-1)(aq-bp)(px+q)^{n-1}}+
+\frac{(2n-3)a}{2(n-1)(aq-bp)}
+\int{\frac{1}{(px+q)^{n-1}\sqrt{ax+b}}}$$
+
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 23     14:117 Axiom cannot compute this integral
+aa:=integrate(1/((p*x+q)^n*sqrt(a*x+b)),x)
+--R 
+--R
+--R           x
+--R         ++             1
+--I   (1)   |   ---------------------- d%L
+--R        ++             n +--------+
+--I             (q + %L p) \|b + %L a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.118~~~~~$\displaystyle
+\int{\frac{(px+q)^n}{\sqrt{ax+b}}}~dx$}
+$$\int{\frac{(px+q)^n}{\sqrt{ax+b}}}=
+\frac{2(px+q)^n\sqrt{ax+b}}{(2n+1)a}+
+\frac{2n(aq-bp)}{(2n+1)a}
+\int{\frac{(px+q)^{n-1}}{\sqrt{ax+b}}}$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 24     14:118 Axiom cannot compute this integral
+aa:=integrate((p*x+q)^n/sqrt(a*x+b),x)
+--R 
+--R
+--R           x           n
+--I         ++  (q + %L p)
+--I   (1)   |   ----------- d%L
+--R        ++    +--------+
+--I             \|b + %L a
+--R                                          Type: Union(Expression Integer,...)
+--E
+@
+
+\section{\cite{1}:14.119~~~~~$\displaystyle
+\int{\frac{\sqrt{ax+b}}{(px+q)^n}}~dx$}
+$$\int{\frac{\sqrt{ax+b}}{(px+q)^n}}=
+\frac{-\sqrt{ax+b}}{(n-1)p(px+q)^{n-1}}+
+\frac{a}{2(n-1)p}\int{\frac{1}{(px+q)^{n-1}\sqrt{ax+b}}}$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 25     14:119 Axiom cannot compute this integral
+aa:=integrate(sqrt(a*x+b)/(p*x+q)^n,x)
+--R 
+--R
+--R           x  +--------+
+--I         ++  \|b + %L a
+--I   (1)   |   ----------- d%L
+--R        ++             n
+--I             (q + %L p)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 p63
+\end{thebibliography}
+\end{document}
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diff --git a/src/axiom-website/CATS/schaum5.input.pamphlet b/src/axiom-website/CATS/schaum5.input.pamphlet
new file mode 100644
index 0000000..a5d3fc3
--- /dev/null
+++ b/src/axiom-website/CATS/schaum5.input.pamphlet
@@ -0,0 +1,1667 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum5.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.120~~~~~$\displaystyle
+\int{\frac{dx}{\sqrt{(ax+b)(px+q)}}}$}
+$$\int{\frac{1}{\sqrt{(ax+b)(px+q)}}}=
+\left\{
+\begin{array}{l}
+\frac{2}{\sqrt{ap}}\ln\left(\sqrt{a(px+q)}+\sqrt{p(ax+b)}\right)\\
+\frac{2}{\sqrt{-ap}}\tan^{-1}\sqrt{\frac{-p(ax+b)}{a(px+b)}}
+\end{array}
+\right.$$
+&lt;&lt;*&gt;&gt;=
+)spool schaum5.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1
+aa:=integrate(1/sqrt((a*x+b)*(p*x+q)),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R       log
+--R                                       +---------------------------+
+--R                 +---+ +---+           |     2
+--R              (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
+--R            + 
+--R                     +---+            2                          +---+
+--R              2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
+--R         /
+--R                    +---------------------------+
+--R              +---+ |     2
+--R            2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
+--R    /
+--R        +---+
+--R       \|a p
+--R     ,
+--R                   +---------------------------+
+--R           +-----+ |     2                          +-----+ +---+
+--R          \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
+--R    2atan(-------------------------------------------------------)
+--R                                   a p x
+--R    --------------------------------------------------------------]
+--R                                +-----+
+--R                               \|- a p
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+
+--S 2
+aa1:=aa.1
+--R
+--R   (2)
+--R     log
+--R                                     +---------------------------+
+--R               +---+ +---+           |     2
+--R            (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
+--R          + 
+--R                   +---+            2                          +---+
+--R            2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
+--R       /
+--R                  +---------------------------+
+--R            +---+ |     2
+--R          2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
+--R  /
+--R      +---+
+--R     \|a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 3
+aa2:=aa.2
+--R
+--R                       +---------------------------+
+--R               +-----+ |     2                          +-----+ +---+
+--R              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
+--R        2atan(-------------------------------------------------------)
+--R                                       a p x
+--R   (3)  --------------------------------------------------------------
+--R                                    +-----+
+--R                                   \|- a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 4
+bb1:=2/sqrt(a*p)*log(sqrt(a*(p*x+q))+sqrt(p*(a*x+b)))
+--R
+--R              +-----------+    +-----------+
+--R        2log(\|a p x + a q  + \|a p x + b p )
+--R   (4)  -------------------------------------
+--R                         +---+
+--R                        \|a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 5
+bb2:=2/sqrt(-a*p)*atan(sqrt((-p*(a*x+b))/(a*(p*x+q))))
+--R
+--R               +-------------+
+--R               |- a p x - b p
+--R        2atan( |------------- )
+--R              \| a p x + a q
+--R   (5)  -----------------------
+--R                 +-----+
+--R                \|- a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 6
+cc1:=aa1-bb1
+--R
+--R   (6)
+--R               +-----------+    +-----------+
+--R       - 2log(\|a p x + a q  + \|a p x + b p )
+--R     + 
+--R       log
+--R                                       +---------------------------+
+--R                 +---+ +---+           |     2
+--R              (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
+--R            + 
+--R                     +---+            2                          +---+
+--R              2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
+--R         /
+--R                    +---------------------------+
+--R              +---+ |     2
+--R            2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
+--R  /
+--R      +---+
+--R     \|a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 7
+cc2:=aa1-bb2
+--R
+--R   (7)
+--R          +-----+
+--R         \|- a p
+--R      *
+--R         log
+--R                                         +---------------------------+
+--R                   +---+ +---+           |     2
+--R                (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
+--R              + 
+--R                       +---+            2                          +---+
+--R                2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
+--R           /
+--R                      +---------------------------+
+--R                +---+ |     2
+--R              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
+--R     + 
+--R                      +-------------+
+--R           +---+      |- a p x - b p
+--R       - 2\|a p atan( |------------- )
+--R                     \| a p x + a q
+--R  /
+--R      +-----+ +---+
+--R     \|- a p \|a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 8
+cc3:=aa2-bb1
+--R
+--R   (8)
+--R           +-----+     +-----------+    +-----------+
+--R       - 2\|- a p log(\|a p x + a q  + \|a p x + b p )
+--R     + 
+--R                            +---------------------------+
+--R                    +-----+ |     2                          +-----+ +---+
+--R         +---+     \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
+--R       2\|a p atan(-------------------------------------------------------)
+--R                                            a p x
+--R  /
+--R      +-----+ +---+
+--R     \|- a p \|a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 9      14:120 Axiom cannot simplify these answers
+cc4:=aa2-bb2
+--R
+--R   (9)
+--R                      +---------------------------+
+--R              +-----+ |     2                          +-----+ +---+
+--R             \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
+--R       2atan(-------------------------------------------------------)
+--R                                      a p x
+--R     + 
+--R                +-------------+
+--R                |- a p x - b p
+--R       - 2atan( |------------- )
+--R               \| a p x + a q
+--R  /
+--R      +-----+
+--R     \|- a p
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.121~~~~~$\displaystyle
+\int{\frac{x~dx}{\sqrt{(ax+b)(px+q)}}}$}
+$$\int{\frac{x}{\sqrt{(ax+b)(px+q)}}}=
+\frac{\sqrt{(ax+b)(px+q)}}{ap}-\frac{bp+aq}{2ap}
+\int{\frac{1}{\sqrt{(ax+b)(px+q)}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 10
+aa:=integrate(x/sqrt((a*x+b)*(p*x+q)),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R                                 +---------------------------+
+--R                           +---+ |     2
+--R             (2a q + 2b p)\|b q \|a p x  + (a q + b p)x + b q
+--R           + 
+--R                 2 2               2 2           2     2
+--R             (- a q  - 2a b p q - b p )x - 2a b q  - 2b p q
+--R        *
+--R           log
+--R                                           +---------------------------+
+--R                     +---+ +---+           |     2
+--R                  (2\|a p \|b q  + 2a p x)\|a p x  + (a q + b p)x + b q
+--R                + 
+--R                           +---+            2                          +---+
+--R                  - 2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
+--R             /
+--R                        +---------------------------+
+--R                  +---+ |     2
+--R                2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
+--R       + 
+--R                                +---------------------------+
+--R                          +---+ |     2
+--R         (- 2a q - 2b p)x\|a p \|a p x  + (a q + b p)x + b q
+--R       + 
+--R                2                   +---+ +---+
+--R         (4a p x  + (2a q + 2b p)x)\|a p \|b q
+--R    /
+--R                          +---------------------------+
+--R              +---+ +---+ |     2
+--R         4a p\|a p \|b q \|a p x  + (a q + b p)x + b q
+--R       + 
+--R               2            2               +---+
+--R         ((- 2a p q - 2a b p )x - 4a b p q)\|a p
+--R     ,
+--R
+--R                                   +---------------------------+
+--R                             +---+ |     2
+--R             (- 2a q - 2b p)\|b q \|a p x  + (a q + b p)x + b q
+--R           + 
+--R               2 2               2 2           2     2
+--R             (a q  + 2a b p q + b p )x + 2a b q  + 2b p q
+--R        *
+--R                         +---------------------------+
+--R                 +-----+ |     2                          +-----+ +---+
+--R                \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
+--R           atan(-------------------------------------------------------)
+--R                                         a p x
+--R       + 
+--R                                +---------------------------+
+--R                        +-----+ |     2
+--R         (- a q - b p)x\|- a p \|a p x  + (a q + b p)x + b q
+--R       + 
+--R                2                 +-----+ +---+
+--R         (2a p x  + (a q + b p)x)\|- a p \|b q
+--R    /
+--R                            +---------------------------+
+--R              +-----+ +---+ |     2
+--R         2a p\|- a p \|b q \|a p x  + (a q + b p)x + b q
+--R       + 
+--R              2           2               +-----+
+--R         ((- a p q - a b p )x - 2a b p q)\|- a p
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+
+--S 11
+bb1:=integrate(1/(sqrt(a*x+b)*(p*x+q)),x)
+--R
+--R   (2)
+--R                                                          +--------------+
+--R                      2  +-------+                        |             2
+--R        (2a p q - 2b p )\|a x + b  + (a p x - a q + 2b p)\|- a p q + b p
+--R    log(------------------------------------------------------------------)
+--R                                      p x + q
+--R   [-----------------------------------------------------------------------,
+--R                                +--------------+
+--R                                |             2
+--R                               \|- a p q + b p
+--R           +------------+
+--R           |           2  +-------+
+--R          \|a p q - b p  \|a x + b
+--R    2atan(-------------------------)
+--R                  a q - b p
+--R    --------------------------------]
+--R              +------------+
+--R              |           2
+--R             \|a p q - b p
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 12
+bb2:=sqrt((a*x+b)*(p*x+q))/(a*p)-(b*p+a*q)/(2*a*p)
+--R
+--R          +---------------------------+
+--R          |     2
+--R        2\|a p x  + (a q + b p)x + b q  - a q - b p
+--R   (3)  -------------------------------------------
+--R                            2a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 13
+bb:=bb2*bb1
+--R
+--R   (4)
+--R   [
+--R            +---------------------------+
+--R            |     2
+--R         (2\|a p x  + (a q + b p)x + b q  - a q - b p)
+--R      *
+--R                                                             +--------------+
+--R                         2  +-------+                        |             2
+--R           (2a p q - 2b p )\|a x + b  + (a p x - a q + 2b p)\|- a p q + b p
+--R       log(------------------------------------------------------------------)
+--R                                         p x + q
+--R    /
+--R            +--------------+
+--R            |             2
+--R       2a p\|- a p q + b p
+--R     ,
+--R                                                       +------------+
+--R       +---------------------------+                   |           2  +-------+
+--R       |     2                                        \|a p q - b p  \|a x + b
+--R    (2\|a p x  + (a q + b p)x + b q  - a q - b p)atan(-------------------------)
+--R                                                              a q - b p
+--R    ----------------------------------------------------------------------------
+--R                                     +------------+
+--R                                     |           2
+--R                                 a p\|a p q - b p
+--R     ]
+--R                                              Type: Vector Expression Integer
+--E
+
+--S 14     14:121 Axiom cannot simplify this answer
+cc:=aa-bb
+--R
+--R   (5)
+--R   [
+--R                              +---+ +---+                           +---+
+--R               ((2a q + 2b p)\|a p \|b q  + ((2a q + 2b p)x + 4b q)\|a p )
+--R            *
+--R                +---------------------------+
+--R                |     2
+--R               \|a p x  + (a q + b p)x + b q
+--R           + 
+--R                      2                            +---+ +---+
+--R             (- 4a p x  + (- 4a q - 4b p)x - 4b q)\|a p \|b q
+--R           + 
+--R                  2 2               2 2           2     2     +---+
+--R             ((- a q  - 2a b p q - b p )x - 2a b q  - 2b p q)\|a p
+--R        *
+--R                                                               +--------------+
+--R                           2  +-------+                        |             2
+--R             (2a p q - 2b p )\|a x + b  + (a p x - a q + 2b p)\|- a p q + b p
+--R         log(------------------------------------------------------------------)
+--R                                           p x + q
+--R       + 
+--R                           +--------------+       +---------------------------+
+--R                           |             2  +---+ |     2
+--R             (2a q + 2b p)\|- a p q + b p  \|b q \|a p x  + (a q + b p)x + b q
+--R           + 
+--R                                                              +--------------+
+--R                  2 2               2 2           2     2     |             2
+--R             ((- a q  - 2a b p q - b p )x - 2a b q  - 2b p q)\|- a p q + b p
+--R        *
+--R           log
+--R                                           +---------------------------+
+--R                     +---+ +---+           |     2
+--R                  (2\|a p \|b q  + 2a p x)\|a p x  + (a q + b p)x + b q
+--R                + 
+--R                           +---+            2                          +---+
+--R                  - 2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
+--R             /
+--R                        +---------------------------+
+--R                  +---+ |     2
+--R                2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
+--R       + 
+--R                          +--------------+       +---------------------------+
+--R                          |             2  +---+ |     2
+--R         (- 2a q - 2b p)x\|- a p q + b p  \|a p \|a p x  + (a q + b p)x + b q
+--R       + 
+--R                                    +--------------+
+--R                2                   |             2  +---+ +---+
+--R         (4a p x  + (2a q + 2b p)x)\|- a p q + b p  \|a p \|b q
+--R    /
+--R              +--------------+             +---------------------------+
+--R              |             2  +---+ +---+ |     2
+--R         4a p\|- a p q + b p  \|a p \|b q \|a p x  + (a q + b p)x + b q
+--R       + 
+--R                                            +--------------+
+--R               2            2               |             2  +---+
+--R         ((- 2a p q - 2a b p )x - 4a b p q)\|- a p q + b p  \|a p
+--R     ,
+--R
+--R                                   +------------+ +---------------------------+
+--R                             +---+ |           2  |     2
+--R             (- 2a q - 2b p)\|b q \|a p q - b p  \|a p x  + (a q + b p)x + b q
+--R           + 
+--R                                                            +------------+
+--R                2 2               2 2           2     2     |           2
+--R             ((a q  + 2a b p q + b p )x + 2a b q  + 2b p q)\|a p q - b p
+--R        *
+--R                         +---------------------------+
+--R                 +-----+ |     2                          +-----+ +---+
+--R                \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
+--R           atan(-------------------------------------------------------)
+--R                                         a p x
+--R       + 
+--R                              +-----+ +---+                           +-----+
+--R               ((2a q + 2b p)\|- a p \|b q  + ((2a q + 2b p)x + 4b q)\|- a p )
+--R            *
+--R                +---------------------------+
+--R                |     2
+--R               \|a p x  + (a q + b p)x + b q
+--R           + 
+--R                      2                            +-----+ +---+
+--R             (- 4a p x  + (- 4a q - 4b p)x - 4b q)\|- a p \|b q
+--R           + 
+--R                  2 2               2 2           2     2     +-----+
+--R             ((- a q  - 2a b p q - b p )x - 2a b q  - 2b p q)\|- a p
+--R        *
+--R                 +------------+
+--R                 |           2  +-------+
+--R                \|a p q - b p  \|a x + b
+--R           atan(-------------------------)
+--R                        a q - b p
+--R       + 
+--R                                +------------+ +---------------------------+
+--R                        +-----+ |           2  |     2
+--R         (- a q - b p)x\|- a p \|a p q - b p  \|a p x  + (a q + b p)x + b q
+--R       + 
+--R                                                +------------+
+--R                2                 +-----+ +---+ |           2
+--R         (2a p x  + (a q + b p)x)\|- a p \|b q \|a p q - b p
+--R    /
+--R                            +------------+ +---------------------------+
+--R              +-----+ +---+ |           2  |     2
+--R         2a p\|- a p \|b q \|a p q - b p  \|a p x  + (a q + b p)x + b q
+--R       + 
+--R                                                  +------------+
+--R              2           2               +-----+ |           2
+--R         ((- a p q - a b p )x - 2a b p q)\|- a p \|a p q - b p
+--R     ]
+--R                                              Type: Vector Expression Integer
+--E
+@
+
+\section{\cite{1}:14.122~~~~~$\displaystyle\int{\sqrt{(ax+b)(px+q)}}~dx$}
+$$\int{\sqrt{(ax+b)(px+q)}}=
+\frac{2apx+bp+aq}{4ap}\sqrt{(ax+b)(px+q)}-
+\frac{(bp-aq)^2}{8ap}\int{\frac{1}{\sqrt{(ax+b)(px+q)}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 15
+aa:=integrate(sqrt((a*x+b)*(p*x+q)),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R                    3 3     2     2       2 2      3 3       2   3        2   2
+--R                 (4a q  - 4a b p q  - 4a b p q + 4b p )x + 8a b q  - 16a b p q
+--R               + 
+--R                   3 2
+--R                 8b p q
+--R            *
+--R                      +---------------------------+
+--R                +---+ |     2
+--R               \|b q \|a p x  + (a q + b p)x + b q
+--R           + 
+--R                 4 4     3     3      2 2 2 2       3 3     4 4  2
+--R             (- a q  - 4a b p q  + 10a b p q  - 4a b p q - b p )x
+--R           + 
+--R                  3   4     2 2   3       3 2 2     4 3        2 2 4
+--R             (- 8a b q  + 8a b p q  + 8a b p q  - 8b p q)x - 8a b q
+--R           + 
+--R                  3   3     4 2 2
+--R             16a b p q  - 8b p q
+--R        *
+--R           log
+--R                                           +---------------------------+
+--R                     +---+ +---+           |     2
+--R                  (2\|a p \|b q  + 2a p x)\|a p x  + (a q + b p)x + b q
+--R                + 
+--R                           +---+            2                          +---+
+--R                  - 2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
+--R             /
+--R                        +---------------------------+
+--R                  +---+ |     2
+--R                2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
+--R       + 
+--R                  3   2      2   2        2 3  3
+--R             (- 4a p q  - 24a b p q - 4a b p )x
+--R           + 
+--R                  3 3      2     2        2 2      3 3  2
+--R             (- 2a q  - 46a b p q  - 46a b p q - 2b p )x
+--R           + 
+--R                  2   3        2   2     3 2
+--R             (- 8a b q  - 48a b p q  - 8b p q)x
+--R        *
+--R                  +---------------------------+
+--R            +---+ |     2
+--R           \|a p \|a p x  + (a q + b p)x + b q
+--R       + 
+--R                 3 2       2   3  4       3   2      2   2         2 3  3
+--R             (16a p q + 16a b p )x  + (24a p q  + 80a b p q + 24a b p )x
+--R           + 
+--R                3 3      2     2        2 2      3 3  2
+--R             (6a q  + 74a b p q  + 74a b p q + 6b p )x
+--R           + 
+--R                2   3        2   2     3 2
+--R             (8a b q  + 48a b p q  + 8b p q)x
+--R        *
+--R            +---+ +---+
+--R           \|a p \|b q
+--R    /
+--R                2             2                +---+ +---+
+--R           ((32a p q + 32a b p )x + 64a b p q)\|a p \|b q
+--R        *
+--R            +---------------------------+
+--R            |     2
+--R           \|a p x  + (a q + b p)x + b q
+--R       + 
+--R                  3   2      2   2        2 3  2         2     2        2 2
+--R             (- 8a p q  - 48a b p q - 8a b p )x  + (- 64a b p q  - 64a b p q)x
+--R           + 
+--R                    2   2
+--R             - 64a b p q
+--R        *
+--R            +---+
+--R           \|a p
+--R     ,
+--R
+--R                      3 3     2     2       2 2      3 3       2   3
+--R                 (- 4a q  + 4a b p q  + 4a b p q - 4b p )x - 8a b q
+--R               + 
+--R                      2   2     3 2
+--R                 16a b p q  - 8b p q
+--R            *
+--R                      +---------------------------+
+--R                +---+ |     2
+--R               \|b q \|a p x  + (a q + b p)x + b q
+--R           + 
+--R               4 4     3     3      2 2 2 2       3 3     4 4  2
+--R             (a q  + 4a b p q  - 10a b p q  + 4a b p q + b p )x
+--R           + 
+--R                3   4     2 2   3       3 2 2     4 3        2 2 4        3   3
+--R             (8a b q  - 8a b p q  - 8a b p q  + 8b p q)x + 8a b q  - 16a b p q
+--R           + 
+--R               4 2 2
+--R             8b p q
+--R        *
+--R                         +---------------------------+
+--R                 +-----+ |     2                          +-----+ +---+
+--R                \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
+--R           atan(-------------------------------------------------------)
+--R                                         a p x
+--R       + 
+--R                  3   2      2   2        2 3  3
+--R             (- 2a p q  - 12a b p q - 2a b p )x
+--R           + 
+--R                 3 3      2     2        2 2     3 3  2
+--R             (- a q  - 23a b p q  - 23a b p q - b p )x
+--R           + 
+--R                  2   3        2   2     3 2
+--R             (- 4a b q  - 24a b p q  - 4b p q)x
+--R        *
+--R                    +---------------------------+
+--R            +-----+ |     2
+--R           \|- a p \|a p x  + (a q + b p)x + b q
+--R       + 
+--R                3 2      2   3  4       3   2      2   2         2 3  3
+--R             (8a p q + 8a b p )x  + (12a p q  + 40a b p q + 12a b p )x
+--R           + 
+--R                3 3      2     2        2 2      3 3  2
+--R             (3a q  + 37a b p q  + 37a b p q + 3b p )x
+--R           + 
+--R                2   3        2   2     3 2
+--R             (4a b q  + 24a b p q  + 4b p q)x
+--R        *
+--R            +-----+ +---+
+--R           \|- a p \|b q
+--R    /
+--R                2             2                +-----+ +---+
+--R           ((16a p q + 16a b p )x + 32a b p q)\|- a p \|b q
+--R        *
+--R            +---------------------------+
+--R            |     2
+--R           \|a p x  + (a q + b p)x + b q
+--R       + 
+--R                  3   2      2   2        2 3  2         2     2        2 2
+--R             (- 4a p q  - 24a b p q - 4a b p )x  + (- 32a b p q  - 32a b p q)x
+--R           + 
+--R                    2   2
+--R             - 32a b p q
+--R        *
+--R            +-----+
+--R           \|- a p
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E
+@
+Since there are two parts to the aa variable we split them: 
+&lt;&lt;*&gt;&gt;=
+--S 16
+aa1:=aa.1
+--R
+--R   (2)
+--R                  3 3     2     2       2 2      3 3       2   3        2   2
+--R               (4a q  - 4a b p q  - 4a b p q + 4b p )x + 8a b q  - 16a b p q
+--R             + 
+--R                 3 2
+--R               8b p q
+--R          *
+--R                    +---------------------------+
+--R              +---+ |     2
+--R             \|b q \|a p x  + (a q + b p)x + b q
+--R         + 
+--R               4 4     3     3      2 2 2 2       3 3     4 4  2
+--R           (- a q  - 4a b p q  + 10a b p q  - 4a b p q - b p )x
+--R         + 
+--R                3   4     2 2   3       3 2 2     4 3        2 2 4        3   3
+--R           (- 8a b q  + 8a b p q  + 8a b p q  - 8b p q)x - 8a b q  + 16a b p q
+--R         + 
+--R               4 2 2
+--R           - 8b p q
+--R      *
+--R         log
+--R                                         +---------------------------+
+--R                   +---+ +---+           |     2
+--R                (2\|a p \|b q  + 2a p x)\|a p x  + (a q + b p)x + b q
+--R              + 
+--R                         +---+            2                          +---+
+--R                - 2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
+--R           /
+--R                      +---------------------------+
+--R                +---+ |     2
+--R              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
+--R     + 
+--R                3   2      2   2        2 3  3
+--R           (- 4a p q  - 24a b p q - 4a b p )x
+--R         + 
+--R                3 3      2     2        2 2      3 3  2
+--R           (- 2a q  - 46a b p q  - 46a b p q - 2b p )x
+--R         + 
+--R                2   3        2   2     3 2
+--R           (- 8a b q  - 48a b p q  - 8b p q)x
+--R      *
+--R                +---------------------------+
+--R          +---+ |     2
+--R         \|a p \|a p x  + (a q + b p)x + b q
+--R     + 
+--R               3 2       2   3  4       3   2      2   2         2 3  3
+--R           (16a p q + 16a b p )x  + (24a p q  + 80a b p q + 24a b p )x
+--R         + 
+--R              3 3      2     2        2 2      3 3  2
+--R           (6a q  + 74a b p q  + 74a b p q + 6b p )x
+--R         + 
+--R              2   3        2   2     3 2
+--R           (8a b q  + 48a b p q  + 8b p q)x
+--R      *
+--R          +---+ +---+
+--R         \|a p \|b q
+--R  /
+--R              2             2                +---+ +---+
+--R         ((32a p q + 32a b p )x + 64a b p q)\|a p \|b q
+--R      *
+--R          +---------------------------+
+--R          |     2
+--R         \|a p x  + (a q + b p)x + b q
+--R     + 
+--R                3   2      2   2        2 3  2         2     2        2 2
+--R           (- 8a p q  - 48a b p q - 8a b p )x  + (- 64a b p q  - 64a b p q)x
+--R         + 
+--R                  2   2
+--R           - 64a b p q
+--R      *
+--R          +---+
+--R         \|a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 17
+aa2:=aa.2
+--R
+--R   (3)
+--R                    3 3     2     2       2 2      3 3       2   3        2   2
+--R               (- 4a q  + 4a b p q  + 4a b p q - 4b p )x - 8a b q  + 16a b p q
+--R             + 
+--R                   3 2
+--R               - 8b p q
+--R          *
+--R                    +---------------------------+
+--R              +---+ |     2
+--R             \|b q \|a p x  + (a q + b p)x + b q
+--R         + 
+--R             4 4     3     3      2 2 2 2       3 3     4 4  2
+--R           (a q  + 4a b p q  - 10a b p q  + 4a b p q + b p )x
+--R         + 
+--R              3   4     2 2   3       3 2 2     4 3        2 2 4        3   3
+--R           (8a b q  - 8a b p q  - 8a b p q  + 8b p q)x + 8a b q  - 16a b p q
+--R         + 
+--R             4 2 2
+--R           8b p q
+--R      *
+--R                       +---------------------------+
+--R               +-----+ |     2                          +-----+ +---+
+--R              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
+--R         atan(-------------------------------------------------------)
+--R                                       a p x
+--R     + 
+--R                3   2      2   2        2 3  3
+--R           (- 2a p q  - 12a b p q - 2a b p )x
+--R         + 
+--R               3 3      2     2        2 2     3 3  2
+--R           (- a q  - 23a b p q  - 23a b p q - b p )x
+--R         + 
+--R                2   3        2   2     3 2
+--R           (- 4a b q  - 24a b p q  - 4b p q)x
+--R      *
+--R                  +---------------------------+
+--R          +-----+ |     2
+--R         \|- a p \|a p x  + (a q + b p)x + b q
+--R     + 
+--R              3 2      2   3  4       3   2      2   2         2 3  3
+--R           (8a p q + 8a b p )x  + (12a p q  + 40a b p q + 12a b p )x
+--R         + 
+--R              3 3      2     2        2 2      3 3  2
+--R           (3a q  + 37a b p q  + 37a b p q + 3b p )x
+--R         + 
+--R              2   3        2   2     3 2
+--R           (4a b q  + 24a b p q  + 4b p q)x
+--R      *
+--R          +-----+ +---+
+--R         \|- a p \|b q
+--R  /
+--R              2             2                +-----+ +---+
+--R         ((16a p q + 16a b p )x + 32a b p q)\|- a p \|b q
+--R      *
+--R          +---------------------------+
+--R          |     2
+--R         \|a p x  + (a q + b p)x + b q
+--R     + 
+--R                3   2      2   2        2 3  2         2     2        2 2
+--R           (- 4a p q  - 24a b p q - 4a b p )x  + (- 32a b p q  - 32a b p q)x
+--R         + 
+--R                  2   2
+--R           - 32a b p q
+--R      *
+--R          +-----+
+--R         \|- a p
+--R                                                     Type: Expression Integer
+--E
+@
+We break the books answer into 3 parts, the first term, the coefficient
+of the second term, and the integral.
+&lt;&lt;*&gt;&gt;=
+--S 18
+bba:=((2*a*p*x+b*p+a*q)/(4*a*p))*sqrt((a*x+b)*(p*x+q))
+--R
+--R                             +---------------------------+
+--R                             |     2
+--R        (2a p x + a q + b p)\|a p x  + (a q + b p)x + b q
+--R   (4)  --------------------------------------------------
+--R                               4a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 19
+bbb:=-(b*p-a*q)^2/(8*a*p)
+--R
+--R           2 2               2 2
+--R        - a q  + 2a b p q - b p
+--R   (5)  ------------------------
+--R                  8a p
+--R                                            Type: Fraction Polynomial Integer
+--E
+
+--S 20
+bbc:=integrate(1/sqrt((a*x+b)*(p*x+q)),x)
+--R
+--R   (6)
+--R   [
+--R       log
+--R                                       +---------------------------+
+--R                 +---+ +---+           |     2
+--R              (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
+--R            + 
+--R                     +---+            2                          +---+
+--R              2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
+--R         /
+--R                    +---------------------------+
+--R              +---+ |     2
+--R            2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
+--R    /
+--R        +---+
+--R       \|a p
+--R     ,
+--R                   +---------------------------+
+--R           +-----+ |     2                          +-----+ +---+
+--R          \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
+--R    2atan(-------------------------------------------------------)
+--R                                   a p x
+--R    --------------------------------------------------------------]
+--R                                +-----+
+--R                               \|- a p
+--R                                     Type: Union(List Expression Integer,...)
+--E
+@
+Since the integral has two parts, we break them apart
+&lt;&lt;*&gt;&gt;=
+--S 21
+bbc1:=bbc.1
+--R
+--R   (7)
+--R     log
+--R                                     +---------------------------+
+--R               +---+ +---+           |     2
+--R            (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
+--R          + 
+--R                   +---+            2                          +---+
+--R            2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
+--R       /
+--R                  +---------------------------+
+--R            +---+ |     2
+--R          2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
+--R  /
+--R      +---+
+--R     \|a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 22
+bbc2:=bbc.2
+--R
+--R                       +---------------------------+
+--R               +-----+ |     2                          +-----+ +---+
+--R              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
+--R        2atan(-------------------------------------------------------)
+--R                                       a p x
+--R   (8)  --------------------------------------------------------------
+--R                                    +-----+
+--R                                   \|- a p
+--R                                                     Type: Expression Integer
+--E
+@ 
+And now we construct the two bb answers based on the integral parts
+&lt;&lt;*&gt;&gt;=
+--S 23
+bb1:=bba+bbb*bbc1
+--R
+--R   (9)
+--R             2 2               2 2
+--R         (- a q  + 2a b p q - b p )
+--R      *
+--R         log
+--R                                         +---------------------------+
+--R                   +---+ +---+           |     2
+--R                (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
+--R              + 
+--R                       +---+            2                          +---+
+--R                2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
+--R           /
+--R                      +---------------------------+
+--R                +---+ |     2
+--R              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
+--R     + 
+--R                                    +---------------------------+
+--R                              +---+ |     2
+--R       (4a p x + 2a q + 2b p)\|a p \|a p x  + (a q + b p)x + b q
+--R  /
+--R          +---+
+--R     8a p\|a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 24
+bb2:=bba+bbb*bbc2
+--R
+--R   (10)
+--R             2 2               2 2
+--R         (- a q  + 2a b p q - b p )
+--R      *
+--R                       +---------------------------+
+--R               +-----+ |     2                          +-----+ +---+
+--R              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
+--R         atan(-------------------------------------------------------)
+--R                                       a p x
+--R     + 
+--R                                    +---------------------------+
+--R                            +-----+ |     2
+--R       (2a p x + a q + b p)\|- a p \|a p x  + (a q + b p)x + b q
+--R  /
+--R          +-----+
+--R     4a p\|- a p
+--R                                                     Type: Expression Integer
+--E
+@
+So there are 4 possible combinations that might yield an answer.
+We construct all four.
+&lt;&lt;*&gt;&gt;=
+--S 25
+cc1:=aa1-bb1
+--R
+--R   (11)
+--R                  3 3     2     2       2 2      3 3       2   3        2   2
+--R               (4a q  - 4a b p q  - 4a b p q + 4b p )x + 8a b q  - 16a b p q
+--R             + 
+--R                 3 2
+--R               8b p q
+--R          *
+--R                    +---------------------------+
+--R              +---+ |     2
+--R             \|b q \|a p x  + (a q + b p)x + b q
+--R         + 
+--R               4 4     3     3      2 2 2 2       3 3     4 4  2
+--R           (- a q  - 4a b p q  + 10a b p q  - 4a b p q - b p )x
+--R         + 
+--R                3   4     2 2   3       3 2 2     4 3        2 2 4        3   3
+--R           (- 8a b q  + 8a b p q  + 8a b p q  - 8b p q)x - 8a b q  + 16a b p q
+--R         + 
+--R               4 2 2
+--R           - 8b p q
+--R      *
+--R         log
+--R                                         +---------------------------+
+--R                   +---+ +---+           |     2
+--R                (2\|a p \|b q  + 2a p x)\|a p x  + (a q + b p)x + b q
+--R              + 
+--R                         +---+            2                          +---+
+--R                - 2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
+--R           /
+--R                      +---------------------------+
+--R                +---+ |     2
+--R              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
+--R     + 
+--R                  3 3     2     2       2 2      3 3       2   3        2   2
+--R               (4a q  - 4a b p q  - 4a b p q + 4b p )x + 8a b q  - 16a b p q
+--R             + 
+--R                 3 2
+--R               8b p q
+--R          *
+--R                    +---------------------------+
+--R              +---+ |     2
+--R             \|b q \|a p x  + (a q + b p)x + b q
+--R         + 
+--R               4 4     3     3      2 2 2 2       3 3     4 4  2
+--R           (- a q  - 4a b p q  + 10a b p q  - 4a b p q - b p )x
+--R         + 
+--R                3   4     2 2   3       3 2 2     4 3        2 2 4        3   3
+--R           (- 8a b q  + 8a b p q  + 8a b p q  - 8b p q)x - 8a b q  + 16a b p q
+--R         + 
+--R               4 2 2
+--R           - 8b p q
+--R      *
+--R         log
+--R                                         +---------------------------+
+--R                   +---+ +---+           |     2
+--R                (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
+--R              + 
+--R                       +---+            2                          +---+
+--R                2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
+--R           /
+--R                      +---------------------------+
+--R                +---+ |     2
+--R              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
+--R     + 
+--R             2   3        2   2     3 2           2 3      3   2  +---+
+--R         ((8a b q  + 16a b p q  + 8b p q)x + 16a b q  + 16b p q )\|a p
+--R      *
+--R          +---------------------------+
+--R          |     2
+--R         \|a p x  + (a q + b p)x + b q
+--R     + 
+--R                3 3      2     2        2 2      3 3  2
+--R           (- 2a q  - 14a b p q  - 14a b p q - 2b p )x
+--R         + 
+--R                 2   3        2   2      3 2           2 3      3   2
+--R           (- 16a b q  - 32a b p q  - 16b p q)x - 16a b q  - 16b p q
+--R      *
+--R          +---+ +---+
+--R         \|a p \|b q
+--R  /
+--R              2             2                +---+ +---+
+--R         ((32a p q + 32a b p )x + 64a b p q)\|a p \|b q
+--R      *
+--R          +---------------------------+
+--R          |     2
+--R         \|a p x  + (a q + b p)x + b q
+--R     + 
+--R                3   2      2   2        2 3  2         2     2        2 2
+--R           (- 8a p q  - 48a b p q - 8a b p )x  + (- 64a b p q  - 64a b p q)x
+--R         + 
+--R                  2   2
+--R           - 64a b p q
+--R      *
+--R          +---+
+--R         \|a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 26
+cc2:=aa1-bb2
+--R
+--R   (12)
+--R                  3 3     2     2       2 2      3 3       2   3        2   2
+--R               (4a q  - 4a b p q  - 4a b p q + 4b p )x + 8a b q  - 16a b p q
+--R             + 
+--R                 3 2
+--R               8b p q
+--R          *
+--R                            +---------------------------+
+--R              +-----+ +---+ |     2
+--R             \|- a p \|b q \|a p x  + (a q + b p)x + b q
+--R         + 
+--R                   4 4     3     3      2 2 2 2       3 3     4 4  2
+--R               (- a q  - 4a b p q  + 10a b p q  - 4a b p q - b p )x
+--R             + 
+--R                    3   4     2 2   3       3 2 2     4 3        2 2 4
+--R               (- 8a b q  + 8a b p q  + 8a b p q  - 8b p q)x - 8a b q
+--R             + 
+--R                    3   3     4 2 2
+--R               16a b p q  - 8b p q
+--R          *
+--R              +-----+
+--R             \|- a p
+--R      *
+--R         log
+--R                                         +---------------------------+
+--R                   +---+ +---+           |     2
+--R                (2\|a p \|b q  + 2a p x)\|a p x  + (a q + b p)x + b q
+--R              + 
+--R                         +---+            2                          +---+
+--R                - 2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
+--R           /
+--R                      +---------------------------+
+--R                +---+ |     2
+--R              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
+--R     + 
+--R                  3 3     2     2       2 2      3 3        2   3        2   2
+--R               (8a q  - 8a b p q  - 8a b p q + 8b p )x + 16a b q  - 32a b p q
+--R             + 
+--R                  3 2
+--R               16b p q
+--R          *
+--R                          +---------------------------+
+--R              +---+ +---+ |     2
+--R             \|a p \|b q \|a p x  + (a q + b p)x + b q
+--R         + 
+--R                    4 4     3     3      2 2 2 2       3 3      4 4  2
+--R               (- 2a q  - 8a b p q  + 20a b p q  - 8a b p q - 2b p )x
+--R             + 
+--R                     3   4      2 2   3        3 2 2      4 3         2 2 4
+--R               (- 16a b q  + 16a b p q  + 16a b p q  - 16b p q)x - 16a b q
+--R             + 
+--R                    3   3      4 2 2
+--R               32a b p q  - 16b p q
+--R          *
+--R              +---+
+--R             \|a p
+--R      *
+--R                       +---------------------------+
+--R               +-----+ |     2                          +-----+ +---+
+--R              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
+--R         atan(-------------------------------------------------------)
+--R                                       a p x
+--R     + 
+--R             2   3        2   2     3 2           2 3      3   2  +-----+ +---+
+--R         ((8a b q  + 16a b p q  + 8b p q)x + 16a b q  + 16b p q )\|- a p \|a p
+--R      *
+--R          +---------------------------+
+--R          |     2
+--R         \|a p x  + (a q + b p)x + b q
+--R     + 
+--R                3 3      2     2        2 2      3 3  2
+--R           (- 2a q  - 14a b p q  - 14a b p q - 2b p )x
+--R         + 
+--R                 2   3        2   2      3 2           2 3      3   2
+--R           (- 16a b q  - 32a b p q  - 16b p q)x - 16a b q  - 16b p q
+--R      *
+--R          +-----+ +---+ +---+
+--R         \|- a p \|a p \|b q
+--R  /
+--R              2             2                +-----+ +---+ +---+
+--R         ((32a p q + 32a b p )x + 64a b p q)\|- a p \|a p \|b q
+--R      *
+--R          +---------------------------+
+--R          |     2
+--R         \|a p x  + (a q + b p)x + b q
+--R     + 
+--R                3   2      2   2        2 3  2         2     2        2 2
+--R           (- 8a p q  - 48a b p q - 8a b p )x  + (- 64a b p q  - 64a b p q)x
+--R         + 
+--R                  2   2
+--R           - 64a b p q
+--R      *
+--R          +-----+ +---+
+--R         \|- a p \|a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 27
+cc3:=aa1-bb1
+--R
+--R   (13)
+--R                  3 3     2     2       2 2      3 3       2   3        2   2
+--R               (4a q  - 4a b p q  - 4a b p q + 4b p )x + 8a b q  - 16a b p q
+--R             + 
+--R                 3 2
+--R               8b p q
+--R          *
+--R                    +---------------------------+
+--R              +---+ |     2
+--R             \|b q \|a p x  + (a q + b p)x + b q
+--R         + 
+--R               4 4     3     3      2 2 2 2       3 3     4 4  2
+--R           (- a q  - 4a b p q  + 10a b p q  - 4a b p q - b p )x
+--R         + 
+--R                3   4     2 2   3       3 2 2     4 3        2 2 4        3   3
+--R           (- 8a b q  + 8a b p q  + 8a b p q  - 8b p q)x - 8a b q  + 16a b p q
+--R         + 
+--R               4 2 2
+--R           - 8b p q
+--R      *
+--R         log
+--R                                         +---------------------------+
+--R                   +---+ +---+           |     2
+--R                (2\|a p \|b q  + 2a p x)\|a p x  + (a q + b p)x + b q
+--R              + 
+--R                         +---+            2                          +---+
+--R                - 2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
+--R           /
+--R                      +---------------------------+
+--R                +---+ |     2
+--R              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
+--R     + 
+--R                  3 3     2     2       2 2      3 3       2   3        2   2
+--R               (4a q  - 4a b p q  - 4a b p q + 4b p )x + 8a b q  - 16a b p q
+--R             + 
+--R                 3 2
+--R               8b p q
+--R          *
+--R                    +---------------------------+
+--R              +---+ |     2
+--R             \|b q \|a p x  + (a q + b p)x + b q
+--R         + 
+--R               4 4     3     3      2 2 2 2       3 3     4 4  2
+--R           (- a q  - 4a b p q  + 10a b p q  - 4a b p q - b p )x
+--R         + 
+--R                3   4     2 2   3       3 2 2     4 3        2 2 4        3   3
+--R           (- 8a b q  + 8a b p q  + 8a b p q  - 8b p q)x - 8a b q  + 16a b p q
+--R         + 
+--R               4 2 2
+--R           - 8b p q
+--R      *
+--R         log
+--R                                         +---------------------------+
+--R                   +---+ +---+           |     2
+--R                (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
+--R              + 
+--R                       +---+            2                          +---+
+--R                2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
+--R           /
+--R                      +---------------------------+
+--R                +---+ |     2
+--R              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
+--R     + 
+--R             2   3        2   2     3 2           2 3      3   2  +---+
+--R         ((8a b q  + 16a b p q  + 8b p q)x + 16a b q  + 16b p q )\|a p
+--R      *
+--R          +---------------------------+
+--R          |     2
+--R         \|a p x  + (a q + b p)x + b q
+--R     + 
+--R                3 3      2     2        2 2      3 3  2
+--R           (- 2a q  - 14a b p q  - 14a b p q - 2b p )x
+--R         + 
+--R                 2   3        2   2      3 2           2 3      3   2
+--R           (- 16a b q  - 32a b p q  - 16b p q)x - 16a b q  - 16b p q
+--R      *
+--R          +---+ +---+
+--R         \|a p \|b q
+--R  /
+--R              2             2                +---+ +---+
+--R         ((32a p q + 32a b p )x + 64a b p q)\|a p \|b q
+--R      *
+--R          +---------------------------+
+--R          |     2
+--R         \|a p x  + (a q + b p)x + b q
+--R     + 
+--R                3   2      2   2        2 3  2         2     2        2 2
+--R           (- 8a p q  - 48a b p q - 8a b p )x  + (- 64a b p q  - 64a b p q)x
+--R         + 
+--R                  2   2
+--R           - 64a b p q
+--R      *
+--R          +---+
+--R         \|a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 28     14:122 Axiom cannot simplify this answer
+cc4:=aa2-bb2
+--R
+--R   (14)
+--R             2   3       2   2     3 2          2 3     3   2
+--R         ((4a b q  + 8a b p q  + 4b p q)x + 8a b q  + 8b p q )
+--R      *
+--R          +---------------------------+
+--R          |     2
+--R         \|a p x  + (a q + b p)x + b q
+--R     + 
+--R               3 3     2     2       2 2     3 3  2
+--R           (- a q  - 7a b p q  - 7a b p q - b p )x
+--R         + 
+--R                2   3        2   2     3 2          2 3     3   2
+--R           (- 8a b q  - 16a b p q  - 8b p q)x - 8a b q  - 8b p q
+--R      *
+--R          +---+
+--R         \|b q
+--R  /
+--R                                                 +---------------------------+
+--R            2             2                +---+ |     2
+--R       ((16a p q + 16a b p )x + 32a b p q)\|b q \|a p x  + (a q + b p)x + b q
+--R     + 
+--R            3   2      2   2        2 3  2         2     2        2 2
+--R       (- 4a p q  - 24a b p q - 4a b p )x  + (- 32a b p q  - 32a b p q)x
+--R     + 
+--R              2   2
+--R       - 32a b p q
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.123~~~~~$\displaystyle\int{\sqrt{\frac{px+q}{ax+b}}}~dx$}
+$$\int{\sqrt{\frac{px+q}{ax+b}}}=
+\frac{\sqrt{(ax+b)(px+q)}}{a}+\frac{aq-bp}{2a}
+\int{\frac{1}{\sqrt{(ax+b)(px+q)}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 29
+aa:=integrate(sqrt((p*x+q)/(a*x+b)),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R           (a q - b p)
+--R        *
+--R                                                              +-------+
+--R                                    +---+      2              |p x + q
+--R           log((2a p x + a q + b p)\|a p  + (2a p x + 2a b p) |------- )
+--R                                                             \|a x + b
+--R       + 
+--R                     +-------+
+--R                     |p x + q  +---+
+--R         (2a x + 2b) |------- \|a p
+--R                    \|a x + b
+--R    /
+--R          +---+
+--R       2a\|a p
+--R     ,
+--R                             +-------+
+--R                     +-----+ |p x + q
+--R                    \|- a p  |-------                       +-------+
+--R                            \|a x + b               +-----+ |p x + q
+--R    (a q - b p)atan(------------------) + (a x + b)\|- a p  |-------
+--R                             p                             \|a x + b
+--R    -----------------------------------------------------------------]
+--R                                  +-----+
+--R                                a\|- a p
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+
+--S 30
+aa1:=aa.1
+--R
+--R   (2)
+--R                                                                     +-------+
+--R                                           +---+      2              |p x + q
+--R       (a q - b p)log((2a p x + a q + b p)\|a p  + (2a p x + 2a b p) |------- )
+--R                                                                    \|a x + b
+--R     + 
+--R                   +-------+
+--R                   |p x + q  +---+
+--R       (2a x + 2b) |------- \|a p
+--R                  \|a x + b
+--R  /
+--R        +---+
+--R     2a\|a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 31
+aa2:=aa.2
+--R
+--R                                 +-------+
+--R                         +-----+ |p x + q
+--R                        \|- a p  |-------                       +-------+
+--R                                \|a x + b               +-----+ |p x + q
+--R        (a q - b p)atan(------------------) + (a x + b)\|- a p  |-------
+--R                                 p                             \|a x + b
+--R   (3)  -----------------------------------------------------------------
+--R                                      +-----+
+--R                                    a\|- a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 32
+bba:=sqrt((a*x+b)*(p*x+q))/a
+--R
+--R         +---------------------------+
+--R         |     2
+--R        \|a p x  + (a q + b p)x + b q
+--R   (4)  ------------------------------
+--R                       a
+--R                                                     Type: Expression Integer
+--E
+
+--S 33
+bbb:=(a*q-b*p)/(2*a)
+--R
+--R        a q - b p
+--R   (5)  ---------
+--R            2a
+--R                                            Type: Fraction Polynomial Integer
+--E
+
+--S 34
+bbc:=integrate(1/(sqrt((a*x+b)*(p*x+q))),x)
+--R
+--R   (6)
+--R   [
+--R       log
+--R                                       +---------------------------+
+--R                 +---+ +---+           |     2
+--R              (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
+--R            + 
+--R                     +---+            2                          +---+
+--R              2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
+--R         /
+--R                    +---------------------------+
+--R              +---+ |     2
+--R            2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
+--R    /
+--R        +---+
+--R       \|a p
+--R     ,
+--R                   +---------------------------+
+--R           +-----+ |     2                          +-----+ +---+
+--R          \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
+--R    2atan(-------------------------------------------------------)
+--R                                   a p x
+--R    --------------------------------------------------------------]
+--R                                +-----+
+--R                               \|- a p
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 35
+bbc1:=bbc.1
+--R
+--R   (7)
+--R     log
+--R                                     +---------------------------+
+--R               +---+ +---+           |     2
+--R            (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
+--R          + 
+--R                   +---+            2                          +---+
+--R            2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
+--R       /
+--R                  +---------------------------+
+--R            +---+ |     2
+--R          2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
+--R  /
+--R      +---+
+--R     \|a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 36
+bbc2:=bbc.2
+--R
+--R                       +---------------------------+
+--R               +-----+ |     2                          +-----+ +---+
+--R              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
+--R        2atan(-------------------------------------------------------)
+--R                                       a p x
+--R   (8)  --------------------------------------------------------------
+--R                                    +-----+
+--R                                   \|- a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 37
+bb1:=bba+bbb*bbc1
+--R
+--R   (9)
+--R         (a q - b p)
+--R      *
+--R         log
+--R                                         +---------------------------+
+--R                   +---+ +---+           |     2
+--R                (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
+--R              + 
+--R                       +---+            2                          +---+
+--R                2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
+--R           /
+--R                      +---------------------------+
+--R                +---+ |     2
+--R              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
+--R     + 
+--R               +---------------------------+
+--R         +---+ |     2
+--R       2\|a p \|a p x  + (a q + b p)x + b q
+--R  /
+--R        +---+
+--R     2a\|a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 38
+bb2:=bba+bbb*bbc2
+--R
+--R   (10)
+--R                                +---------------------------+
+--R                        +-----+ |     2                          +-----+ +---+
+--R                       \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
+--R       (a q - b p)atan(-------------------------------------------------------)
+--R                                                a p x
+--R     + 
+--R                +---------------------------+
+--R        +-----+ |     2
+--R       \|- a p \|a p x  + (a q + b p)x + b q
+--R  /
+--R       +-----+
+--R     a\|- a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 39
+cc1:=aa1-bb1
+--R
+--R   (11)
+--R                                                                     +-------+
+--R                                           +---+      2              |p x + q
+--R       (a q - b p)log((2a p x + a q + b p)\|a p  + (2a p x + 2a b p) |------- )
+--R                                                                    \|a x + b
+--R     + 
+--R         (- a q + b p)
+--R      *
+--R         log
+--R                                         +---------------------------+
+--R                   +---+ +---+           |     2
+--R                (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
+--R              + 
+--R                       +---+            2                          +---+
+--R                2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
+--R           /
+--R                      +---------------------------+
+--R                +---+ |     2
+--R              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
+--R     + 
+--R                 +---------------------------+               +-------+
+--R           +---+ |     2                                     |p x + q  +---+
+--R       - 2\|a p \|a p x  + (a q + b p)x + b q  + (2a x + 2b) |------- \|a p
+--R                                                            \|a x + b
+--R  /
+--R        +---+
+--R     2a\|a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 40
+cc2:=aa1-bb2
+--R
+--R   (12)
+--R                     +-----+
+--R         (a q - b p)\|- a p
+--R      *
+--R                                                            +-------+
+--R                                  +---+      2              |p x + q
+--R         log((2a p x + a q + b p)\|a p  + (2a p x + 2a b p) |------- )
+--R                                                           \|a x + b
+--R     + 
+--R                         +---+
+--R         (- 2a q + 2b p)\|a p
+--R      *
+--R                       +---------------------------+
+--R               +-----+ |     2                          +-----+ +---+
+--R              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
+--R         atan(-------------------------------------------------------)
+--R                                       a p x
+--R     + 
+--R                         +---------------------------+
+--R           +-----+ +---+ |     2
+--R       - 2\|- a p \|a p \|a p x  + (a q + b p)x + b q
+--R     + 
+--R                           +-------+
+--R                   +-----+ |p x + q  +---+
+--R       (2a x + 2b)\|- a p  |------- \|a p
+--R                          \|a x + b
+--R  /
+--R        +-----+ +---+
+--R     2a\|- a p \|a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 41
+cc3:=aa2-bb1
+--R
+--R   (13)
+--R                       +-----+
+--R         (- a q + b p)\|- a p
+--R      *
+--R         log
+--R                                         +---------------------------+
+--R                   +---+ +---+           |     2
+--R                (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
+--R              + 
+--R                       +---+            2                          +---+
+--R                2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
+--R           /
+--R                      +---------------------------+
+--R                +---+ |     2
+--R              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
+--R     + 
+--R                                        +-------+
+--R                                +-----+ |p x + q
+--R                               \|- a p  |-------
+--R                     +---+             \|a x + b
+--R       (2a q - 2b p)\|a p atan(------------------)
+--R                                        p
+--R     + 
+--R                         +---------------------------+
+--R           +-----+ +---+ |     2
+--R       - 2\|- a p \|a p \|a p x  + (a q + b p)x + b q
+--R     + 
+--R                           +-------+
+--R                   +-----+ |p x + q  +---+
+--R       (2a x + 2b)\|- a p  |------- \|a p
+--R                          \|a x + b
+--R  /
+--R        +-----+ +---+
+--R     2a\|- a p \|a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 42     14:123 Axiom cannot simplify these results
+cc4:=aa2-bb2
+--R
+--R   (14)
+--R         (- a q + b p)
+--R      *
+--R                       +---------------------------+
+--R               +-----+ |     2                          +-----+ +---+
+--R              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
+--R         atan(-------------------------------------------------------)
+--R                                       a p x
+--R     + 
+--R                                +-------+
+--R                        +-----+ |p x + q
+--R                       \|- a p  |-------
+--R                               \|a x + b
+--R       (a q - b p)atan(------------------)
+--R                                p
+--R     + 
+--R                  +---------------------------+                     +-------+
+--R          +-----+ |     2                                   +-----+ |p x + q
+--R       - \|- a p \|a p x  + (a q + b p)x + b q  + (a x + b)\|- a p  |-------
+--R                                                                   \|a x + b
+--R  /
+--R       +-----+
+--R     a\|- a p
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.124~~~~~$\displaystyle
+\int{\frac{dx}{(px+q)\sqrt{(ax+b)(px+q)}}}~dx$}
+$$\int{\frac{1}{(px+q)\sqrt{(ax+b)(px+q)}}}=
+\frac{2\sqrt{ax+b}}{(aq-bp)\sqrt{px+q}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 43
+aa:=integrate(1/((p*x+q)*sqrt((a*x+b)*(p*x+q))),x)
+--R 
+--R
+--R                                 2x
+--R   (1)  ---------------------------------------------------
+--R          +---------------------------+
+--R          |     2                                     +---+
+--R        q\|a p x  + (a q + b p)x + b q  + (- p x - q)\|b q
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 44
+bb:=(2*sqrt(a*x+b))/((a*q-b*p)*sqrt(p*x+q))
+--R
+--R               +-------+
+--R             2\|a x + b
+--R   (2)  ---------------------
+--R                    +-------+
+--R        (a q - b p)\|p x + q
+--R                                                     Type: Expression Integer
+--E
+
+--S 45     14:124 Axiom cannot simplify this result
+cc:=aa-bb
+--R
+--R   (3)
+--R                      +---------------------------+
+--R            +-------+ |     2                                        +-------+
+--R       - 2q\|a x + b \|a p x  + (a q + b p)x + b q  + (2a q - 2b p)x\|p x + q
+--R     + 
+--R                   +---+ +-------+
+--R       (2p x + 2q)\|b q \|a x + b
+--R  /
+--R                                +---------------------------+
+--R           2          +-------+ |     2
+--R       (a q  - b p q)\|p x + q \|a p x  + (a q + b p)x + b q
+--R     + 
+--R                      2        2          +---+ +-------+
+--R       ((- a p q + b p )x - a q  + b p q)\|b q \|p x + q
+--R                                                     Type: Expression Integer
+--E
+
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 pp63-64
+\end{thebibliography}
+\end{document}
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diff --git a/src/axiom-website/CATS/schaum6.input.pamphlet b/src/axiom-website/CATS/schaum6.input.pamphlet
new file mode 100644
index 0000000..ca2c6aa
--- /dev/null
+++ b/src/axiom-website/CATS/schaum6.input.pamphlet
@@ -0,0 +1,886 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum6.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.125~~~~~$\displaystyle\int{\frac{dx}{x^2+a^2}}$}
+$$\int{\frac{1}{x^2+a^2}}=\frac{1}{a}\tan^{-1}\frac{x}{a}$$
+&lt;&lt;*&gt;&gt;=
+)spool schaum6.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1
+aa:=integrate(1/(x^2+a^2),x)
+--R 
+--R
+--R             x
+--R        atan(-)
+--R             a
+--R   (1)  -------
+--R           a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 2
+bb:=(1/a)*atan(x/a)
+--R
+--R             x
+--R        atan(-)
+--R             a
+--R   (2)  -------
+--R           a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3      14:125 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.126~~~~~$\displaystyle\int{\frac{x~dx}{x^2+a^2}}$}
+$$\int{\frac{x}{x^2+a^2}}=\frac{1}{2}\ln(x^2+a^2)$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 4
+aa:=integrate(x/(x^2+a^2),x)
+--R 
+--R
+--R             2    2
+--R        log(x  + a )
+--R   (1)  ------------
+--R              2
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 5
+bb:=(1/2)*log(x^2+a^2)
+--R
+--R             2    2
+--R        log(x  + a )
+--R   (2)  ------------
+--R              2
+--R                                                     Type: Expression Integer
+--E
+
+--S 6      14:126 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E 
+@
+
+\section{\cite{1}:14.127~~~~~$\displaystyle\int{\frac{x^2~dx}{x^2+a^2}}$}
+$$\int{\frac{x^2}{x^2+a^2}}=x-a\tan^{-1}\frac{x}{a}$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 7
+aa:=integrate(x^2/(x^2+a^2),x)
+--R 
+--R
+--R                 x
+--R   (1)  - a atan(-) + x
+--R                 a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 8
+bb:=x-a*atan(x/a)
+--R
+--R                 x
+--R   (2)  - a atan(-) + x
+--R                 a
+--R                                                     Type: Expression Integer
+--E
+
+--S 9      14:127 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.128~~~~~$\displaystyle\int{\frac{x^3~dx}{x^2+a^2}}$}
+$$\int{\frac{x^3}{x^2+a^2}}=\frac{x^2}{2}-\frac{a^2}{2}\ln(x^2+a^2)$$
+
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 10
+aa:=integrate(x^3/(x^2+a^2),x)
+--R 
+--R
+--R           2     2    2     2
+--R        - a log(x  + a ) + x
+--R   (1)  ---------------------
+--R                  2
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 11
+bb:=x^2/2-a^2/2*log(x^2+a^2)
+--R
+--R           2     2    2     2
+--R        - a log(x  + a ) + x
+--R   (2)  ---------------------
+--R                  2
+--R                                                     Type: Expression Integer
+--E
+
+--S 12     14:128 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.129~~~~~$\displaystyle\int{\frac{dx}{x(x^2+a^2)}}$}
+$$\int{\frac{1}{x(x^2+a^2)}}=
+\frac{1}{2a^2}\ln\left(\frac{x^2}{x^2+a^2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 13
+aa:=integrate(1/(x*(x^2+a^2)),x)
+--R 
+--R
+--R               2    2
+--R        - log(x  + a ) + 2log(x)
+--R   (1)  ------------------------
+--R                     2
+--R                   2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 14
+bb:=1/(2*a^2)*log(x^2/(x^2+a^2))
+--R
+--R                2
+--R               x
+--R        log(-------)
+--R             2    2
+--R            x  + a
+--R   (2)  ------------
+--R               2
+--R             2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 15
+cc:=aa-bb
+--R
+--R                                           2
+--R               2    2                     x
+--R        - log(x  + a ) + 2log(x) - log(-------)
+--R                                        2    2
+--R                                       x  + a
+--R   (3)  ---------------------------------------
+--R                            2
+--R                          2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 16
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 17
+dd:=divlog cc
+--R
+--R               2
+--R        - log(x ) + 2log(x)
+--R   (5)  -------------------
+--R                  2
+--R                2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 18
+logpow:=rule(log(a^n) == n*log(a))
+--R
+--R             n
+--R   (6)  log(a ) == n log(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 19     14:129 Schaums and Axiom agree
+ee:=logpow dd
+--R
+--R   (7)  0
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.130~~~~~$\displaystyle\int{\frac{dx}{x^2(x^2+a^2)}}$}
+$$\int{\frac{1}{x^2(x^2+a^2)}}=
+-\frac{1}{a^2x}-\frac{1}{a^3}\tan^{-1}\frac{x}{a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 20
+aa:=integrate(1/(x^2*(x^2+a^2)),x)
+--R 
+--R
+--R                 x
+--R        - x atan(-) - a
+--R                 a
+--R   (1)  ---------------
+--R               3
+--R              a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 21
+bb:=-1/(a^2*x)-1/a^3*atan(x/a)
+--R
+--R                 x
+--R        - x atan(-) - a
+--R                 a
+--R   (2)  ---------------
+--R               3
+--R              a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 22     14:130 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.131~~~~~$\displaystyle\int{\frac{dx}{x^3(x^2+a^2)}}$}
+$$\int{\frac{1}{x^3(x^2+a^2)}}=
+-\frac{1}{2a^2x^2}-\frac{1}{2a^4}\ln\left(\frac{x^2}{x^2+a^2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 23
+aa:=integrate(1/(x^3*(x^2+a^2)),x)
+--R 
+--R
+--R         2     2    2      2          2
+--R        x log(x  + a ) - 2x log(x) - a
+--R   (1)  -------------------------------
+--R                       4 2
+--R                     2a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 24
+bb:=-1/(2*a^2*x^2)-1/(2*a^4)*log(x^2/(x^2+a^2))
+--R
+--R                    2
+--R           2       x        2
+--R        - x log(-------) - a
+--R                 2    2
+--R                x  + a
+--R   (2)  ---------------------
+--R                  4 2
+--R                2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 25
+cc:=aa-bb
+--R
+--R                                         2
+--R             2    2                     x
+--R        log(x  + a ) - 2log(x) + log(-------)
+--R                                      2    2
+--R                                     x  + a
+--R   (3)  -------------------------------------
+--R                           4
+--R                         2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 26
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 27
+dd:=divlog cc
+--R
+--R             2
+--R        log(x ) - 2log(x)
+--R   (5)  -----------------
+--R                 4
+--R               2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 28
+logpow:=rule(log(a^n) == n*log(a))
+--R
+--R             n
+--R   (6)  log(a ) == n log(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 29     14:131 Schaums and Axiom agree
+ee:=logpow dd
+--R
+--R   (7)  0
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.132~~~~~$\displaystyle\int{\frac{dx}{(x^2+a^2)^2}}$}
+$$\int{\frac{1}{(x^2+a^2)^2}}=
+\frac{x}{2a^2(x^2+a^2)}+\frac{1}{2a^3}\tan^{-1}\frac{x}{a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 30
+aa:=integrate(1/((x^2+a^2)^2),x)
+--R 
+--R
+--R          2    2      x
+--R        (x  + a )atan(-) + a x
+--R                      a
+--R   (1)  ----------------------
+--R                3 2     5
+--R              2a x  + 2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 31
+bb:=x/(2*a^2*(x^2+a^2))+1/(2*a^3)*atan(x/a)
+--R
+--R          2    2      x
+--R        (x  + a )atan(-) + a x
+--R                      a
+--R   (2)  ----------------------
+--R                3 2     5
+--R              2a x  + 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 32     14:132 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.133~~~~~$\displaystyle\int{\frac{x~dx}{(x^2+a^2)^2}}$}
+$$\int{\frac{x}{(x^2+a^2)^2}}=
+\frac{-1}{2(x^2+a^2)}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 33
+aa:=integrate(x/((x^2+a^2)^2),x)
+--R 
+--R
+--R              1
+--R   (1)  - ---------
+--R            2     2
+--R          2x  + 2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 34
+bb:=-1/(2*(x^2+a^2))
+--R
+--R              1
+--R   (2)  - ---------
+--R            2     2
+--R          2x  + 2a
+--R                                            Type: Fraction Polynomial Integer
+--E
+
+--S 35     14:133 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.134~~~~~$\displaystyle\int{\frac{x^2dx}{(x^2+a^2)^2}}$}
+$$\int{\frac{x^2}{(x^2+a^2)^2}}=
+\frac{-x}{2(x^2+a^2)}+\frac{1}{2a}\tan^{-1}\frac{x}{a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 36
+aa:=integrate(x^2/((x^2+a^2)^2),x)
+--R 
+--R
+--R          2    2      x
+--R        (x  + a )atan(-) - a x
+--R                      a
+--R   (1)  ----------------------
+--R                  2     3
+--R              2a x  + 2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 37
+bb:=-x/(2*(x^2+a^2))+1/(2*a)*atan(x/a)
+--R
+--R          2    2      x
+--R        (x  + a )atan(-) - a x
+--R                      a
+--R   (2)  ----------------------
+--R                  2     3
+--R              2a x  + 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 38     14:134 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.135~~~~~$\displaystyle\int{\frac{x^3dx}{(x^2+a^2)^2}}$}
+$$\int{\frac{x^3}{(x^2+a^2)^2}}=
+\frac{a^2}{2(x^2+a^2)}+\frac{1}{2}\ln(x^2+a^2)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 39
+aa:=integrate(x^3/((x^2+a^2)^2),x)
+--R 
+--R
+--R          2    2      2    2     2
+--R        (x  + a )log(x  + a ) + a
+--R   (1)  --------------------------
+--R                   2     2
+--R                 2x  + 2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 40
+bb:=a^2/(2*(x^2+a^2))+1/2*log(x^2+a^2)
+--R
+--R          2    2      2    2     2
+--R        (x  + a )log(x  + a ) + a
+--R   (2)  --------------------------
+--R                   2     2
+--R                 2x  + 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 41     14:135 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.136~~~~~$\displaystyle\int{\frac{dx}{x(x^2+a^2)^2}}$}
+$$\int{\frac{1}{x(x^2+a^2)^2}}=
+\frac{1}{2a^2(x^2+a^2)}+\frac{1}{2a^4}\ln\left(\frac{x^2}{x^2+a^2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 42
+aa:=integrate(1/(x*(x^2+a^2)^2),x)
+--R 
+--R
+--R            2    2      2    2       2     2           2
+--R        (- x  - a )log(x  + a ) + (2x  + 2a )log(x) + a
+--R   (1)  ------------------------------------------------
+--R                             4 2     6
+--R                           2a x  + 2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 43
+bb:=1/(2*a^2*(x^2+a^2))+1/(2*a^4)*log(x^2/(x^2+a^2))
+--R
+--R                         2
+--R          2    2        x        2
+--R        (x  + a )log(-------) + a
+--R                      2    2
+--R                     x  + a
+--R   (2)  --------------------------
+--R                  4 2     6
+--R                2a x  + 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 44
+cc:=aa-bb
+--R
+--R                                           2
+--R               2    2                     x
+--R        - log(x  + a ) + 2log(x) - log(-------)
+--R                                        2    2
+--R                                       x  + a
+--R   (3)  ---------------------------------------
+--R                            4
+--R                          2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 45
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 46
+dd:=divlog cc
+--R
+--R               2
+--R        - log(x ) + 2log(x)
+--R   (5)  -------------------
+--R                  4
+--R                2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 47
+logpow:=rule(log(a^n) == n*log(a))
+--R
+--R             n
+--R   (6)  log(a ) == n log(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 48     14:136 Schaums and Axiom agree
+ee:=logpow dd
+--R
+--R   (7)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.137~~~~~$\displaystyle\int{\frac{dx}{x^2(x^2+a^2)^2}}$}
+$$\int{\frac{1}{x^2(x^2+a^2)^2}}=
+-\frac{1}{a^4x}-\frac{x}{2a^4(x^2+a^2)}-\frac{3}{2a^5}\tan^{-1}\frac{x}{a}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 49
+aa:=integrate(1/(x^2*(x^2+a^2)^2),x)
+--R
+--R             3     2       x        2     3
+--R        (- 3x  - 3a x)atan(-) - 3a x  - 2a
+--R                           a
+--R   (1)  -----------------------------------
+--R                      5 3     7
+--R                    2a x  + 2a x
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 50
+bb:=-1/(a^4*x)-x/(2*a^4*(x^2+a^2))-3/(2*a^5)*atan(x/a)
+--R
+--R             3     2       x        2     3
+--R        (- 3x  - 3a x)atan(-) - 3a x  - 2a
+--R                           a
+--R   (2)  -----------------------------------
+--R                      5 3     7
+--R                    2a x  + 2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 51     14:137 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.138~~~~~$\displaystyle\int{\frac{dx}{x^3(x^2+a^2)^2}}$}
+$$\int{\frac{1}{x^3(x^2+a^2)^2}}=
+-\frac{1}{2a^4x^2}-\frac{1}{2a^4(x^2+a^2)}-
+\frac{1}{a^6}\ln\left(\frac{x^2}{x^2+a^2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 52
+aa:=integrate(1/(x^3*(x^2+a^2)^2),x)
+--R 
+--R
+--R           4     2 2      2    2         4     2 2            2 2    4
+--R        (2x  + 2a x )log(x  + a ) + (- 4x  - 4a x )log(x) - 2a x  - a
+--R   (1)  --------------------------------------------------------------
+--R                                   6 4     8 2
+--R                                 2a x  + 2a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 53
+bb:=-1/(2*a^4*x^2)-1/(2*a^4*(x^2+a^2))-1/a^6*log(x^2/(x^2+a^2))
+--R
+--R                               2
+--R             4     2 2        x         2 2    4
+--R        (- 2x  - 2a x )log(-------) - 2a x  - a
+--R                            2    2
+--R                           x  + a
+--R   (2)  ----------------------------------------
+--R                        6 4     8 2
+--R                      2a x  + 2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 54
+cc:=aa-bb
+--R
+--R                                         2
+--R             2    2                     x
+--R        log(x  + a ) - 2log(x) + log(-------)
+--R                                      2    2
+--R                                     x  + a
+--R   (3)  -------------------------------------
+--R                           6
+--R                          a
+--R                                                     Type: Expression Integer
+--E
+
+--S 55
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 56
+dd:=divlog cc
+--R
+--R             2
+--R        log(x ) - 2log(x)
+--R   (5)  -----------------
+--R                 6
+--R                a
+--R                                                     Type: Expression Integer
+--E
+
+--S 57
+logpow:=rule(log(a^n) == n*log(a))
+--R
+--R             n
+--R   (6)  log(a ) == n log(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 58     14:138 Schaums and Axiom agree
+ee:=logpow dd
+--R
+--R   (7)  0
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.139~~~~~$\displaystyle\int{\frac{dx}{(x^2+a^2)^n}}$}
+$$\int{\frac{1}{(x^2+a^2)^n}}=
+\frac{x}{2(n-1)a^2(x^2+a^2)^{n-1}}+\frac{2n-3}{(2n-2)a^2}
+\int{\frac{1}{(x^2+a^2)^{n-1}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 59     14:139 Axiom cannot do this integral
+aa:=integrate(1/((x^2+a^2)^n),x)
+--R 
+--R
+--R           x
+--R         ++       1
+--I   (1)   |   ----------- d%L
+--R        ++     2     2 n
+--I             (a  + %L )
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.140~~~~~$\displaystyle\int{\frac{x~dx}{(x^2+a^2)^n}}$}
+$$\int{\frac{x}{(x^2+a^2)^n}}=
+\frac{-1}{2(n-1)(x^2+a^2)^{n-1}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 60
+aa:=integrate(x/((x^2+a^2)^n),x)
+--R 
+--R
+--R                   2    2
+--R                - x  - a
+--R   (1)  ------------------------
+--R                         2    2
+--R                  n log(x  + a )
+--R        (2n - 2)%e
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 61
+bb:=-1/(2*(n-1)*(x^2+a^2)^(n-1))
+--R
+--R                     1
+--R   (2)  - ----------------------
+--R                    2    2 n - 1
+--R          (2n - 2)(x  + a )
+--R                                                     Type: Expression Integer
+--E
+
+--S 62
+cc:=aa-bb
+--R
+--R                 2    2
+--R          n log(x  + a )       2    2   2    2 n - 1
+--R        %e               + (- x  - a )(x  + a )
+--R   (3)  --------------------------------------------
+--R                                          2    2
+--R                     2    2 n - 1  n log(x  + a )
+--R           (2n - 2)(x  + a )     %e
+--R                                                     Type: Expression Integer
+--E
+
+--S 63
+explog:=rule(%e^(n*log(x)) == x^n)
+--R
+--R          n log(x)     n
+--R   (4)  %e         == x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 64
+dd:=explog cc
+--R
+--R          2    2 n       2    2   2    2 n - 1
+--R        (x  + a )  + (- x  - a )(x  + a )
+--R   (5)  --------------------------------------
+--R                     2    2 n - 1  2    2 n
+--R           (2n - 2)(x  + a )     (x  + a )
+--R                                                     Type: Expression Integer
+--E
+
+--S 65     14:140 Schaums and Axiom agree
+ee:=complexNormalize dd
+--R
+--R   (6)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.141~~~~~$\displaystyle\int{\frac{dx}{x(x^2+a^2)^n}}$}
+$$\int{\frac{1}{x(x^2+a^2)^n}}=
+\frac{1}{2(n-1)a^2(x^2+a^2)^{n-1}}+\frac{1}{a^2}
+\int{\frac{1}{x(x^2+a^2)^{n-1}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 66     14:141 Axiom cannot do this integral
+aa:=integrate(1/(x*(x^2+a^2)^n),x)
+--R 
+--R
+--R           x
+--R         ++         1
+--I   (1)   |   -------------- d%L
+--R        ++        2     2 n
+--I             %L (a  + %L )
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.142~~~~~$\displaystyle\int{\frac{x^mdx}{(x^2+a^2)^n}}$}
+$$\int{\frac{x^m}{(x^2+a^2)^n}}=
+\int{\frac{x^{m-2}}{(x^2+a^2)^{n-1}}} -
+a^2\int{\frac{x^{m-2}}{(x^2+a^2)^n}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 67     14:142 Axiom cannot do this integral
+aa:=integrate(x^m/((x^2+a^2)^n),x)
+--R 
+--R
+--R           x       m
+--I         ++      %L
+--I   (1)   |   ----------- d%L
+--R        ++     2     2 n
+--I             (a  + %L )
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.143~~~~~$\displaystyle\int{\frac{dx}{x^m(x^2+a^2)^n}}$}
+$$\int{\frac{1}{x^m(x^2+a^2)^n}}=
+\frac{1}{a^2}\int{\frac{1}{x^m(x^2+a^2)^{n-1}}}-
+\frac{1}{a^2}\int{\frac{1}{x^{m-2}(x^2+a^2)^n}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 68     14:143 Axiom cannot do this integral
+aa:=integrate(1/(x^m*(x^2+a^2)^n),x)
+--R 
+--R
+--R           x
+--R         ++         1
+--I   (1)   |   -------------- d%L
+--R        ++     m  2     2 n
+--I             %L (a  + %L )
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 p64
+\end{thebibliography}
+\end{document}
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diff --git a/src/axiom-website/CATS/schaum7.input.pamphlet b/src/axiom-website/CATS/schaum7.input.pamphlet
new file mode 100644
index 0000000..52e0b97
--- /dev/null
+++ b/src/axiom-website/CATS/schaum7.input.pamphlet
@@ -0,0 +1,1009 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum7.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.144~~~~~$\displaystyle\int{\frac{dx}{x^2-a^2}}$}
+$$\int{\frac{1}{x^2-a^2}}=\frac{1}{2a}\ln\left(\frac{x-a}{x+a}\right)$$
+$$\int{\frac{1}{x^2-a^2}}=-\frac{1}{a}\coth^{-1}\frac{x}{a}$$
+&lt;&lt;*&gt;&gt;=
+)spool schaum7.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1
+aa:=integrate(1/(x^2-a^2),x)
+--R 
+--R
+--R        - log(x + a) + log(x - a)
+--R   (1)  -------------------------
+--R                    2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 2
+bb:=1/(2*a)*log((x-a)/(x+a))
+--R
+--R            x - a
+--R        log(-----)
+--R            x + a
+--R   (2)  ----------
+--R            2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3
+cc:=aa-bb
+--R
+--R                                        x - a
+--R        - log(x + a) + log(x - a) - log(-----)
+--R                                        x + a
+--R   (3)  --------------------------------------
+--R                          2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 4
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 5      14:144 Schaums and Axiom agree
+dd:=divlog cc
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.145~~~~~$\displaystyle\int{\frac{x~dx}{x^2-a^2}}$}
+$$\int{\frac{x}{x^2-a^2}}=\frac{1}{2}\ln(x^2-a^2)$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 6
+aa:=integrate(x/(x^2-a^2),x)
+--R 
+--R
+--R             2    2
+--R        log(x  - a )
+--R   (1)  ------------
+--R              2
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 7
+bb:=1/2*log(x^2-a^2)
+--R
+--R             2    2
+--R        log(x  - a )
+--R   (2)  ------------
+--R              2
+--R                                                     Type: Expression Integer
+--E
+
+--S 8      14:145 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.146~~~~~$\displaystyle\int{\frac{x^2~dx}{x^2-a^2}}$}
+$$\int{\frac{x^2}{x^2-a^2}}=x+\frac{a}{2}\ln\left(\frac{x-a}{x+a}\right)$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 9
+aa:=integrate(x^2/(x^2-a^2),x)
+--R 
+--R
+--R        - a log(x + a) + a log(x - a) + 2x
+--R   (1)  ----------------------------------
+--R                         2
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 10
+bb:=x+a/2*log((x-a)/(x+a))
+--R
+--R              x - a
+--R        a log(-----) + 2x
+--R              x + a
+--R   (2)  -----------------
+--R                2
+--R                                                     Type: Expression Integer
+--E
+
+--S 11
+cc:=aa-bb
+--R
+--R                                              x - a
+--R        - a log(x + a) + a log(x - a) - a log(-----)
+--R                                              x + a
+--R   (3)  --------------------------------------------
+--R                              2
+--R                                                     Type: Expression Integer
+--E
+
+--S 12
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 13     14:146 Schaums and Axiom agree
+dd:=divlog cc
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.147~~~~~$\displaystyle\int{\frac{x^3~dx}{x^2-a^2}}$}
+$$\int{\frac{x^3}{x^2-a^2}}=\frac{x^2}{2}+\frac{a^2}{2}\ln(x^2-a^2)$$
+
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 14
+aa:=integrate(x^3/(x^2-a^2),x)
+--R 
+--R
+--R         2     2    2     2
+--R        a log(x  - a ) + x
+--R   (1)  -------------------
+--R                 2
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 15
+bb:=x^2/2+a^2/2*log(x^2-a^2)
+--R
+--R         2     2    2     2
+--R        a log(x  - a ) + x
+--R   (2)  -------------------
+--R                 2
+--R                                                     Type: Expression Integer
+--E
+
+--S 16     14:147 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.148~~~~~$\displaystyle\int{\frac{dx}{x(x^2-a^2)}}$}
+$$\int{\frac{1}{x(x^2-a^2)}}=
+\frac{1}{2a^2}\ln\left(\frac{x^2-a^2}{x^2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 17
+aa:=integrate(1/(x*(x^2-a^2)),x)
+--R 
+--R
+--R             2    2
+--R        log(x  - a ) - 2log(x)
+--R   (1)  ----------------------
+--R                    2
+--R                  2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 18
+bb:=1/(2*a^2)*log((x^2-a^2)/x^2)
+--R
+--R             2    2
+--R            x  - a
+--R        log(-------)
+--R                2
+--R               x
+--R   (2)  ------------
+--R               2
+--R             2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 19
+cc:=aa-bb
+--R
+--R                                      2    2
+--R             2    2                  x  - a
+--R        log(x  - a ) - 2log(x) - log(-------)
+--R                                         2
+--R                                        x
+--R   (3)  -------------------------------------
+--R                           2
+--R                         2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 20
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 21
+dd:=divlog cc
+--R
+--R             2
+--R        log(x ) - 2log(x)
+--R   (5)  -----------------
+--R                 2
+--R               2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 22
+logpow:=rule(log(a^n) == n*log(a))
+--R
+--R             n
+--R   (6)  log(a ) == n log(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 23     14:148 Schaums and Axiom agree
+ee:=logpow dd
+--R
+--R   (7)  0
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.149~~~~~$\displaystyle\int{\frac{dx}{x^2(x^2-a^2)}}$}
+$$\int{\frac{1}{x^2(x^2-a^2)}}=
+\frac{1}{a^2x}+\frac{1}{2a^3}\ln\left(\frac{x-a}{x+a}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 24
+aa:=integrate(1/(x^2*(x^2-a^2)),x)
+--R 
+--R
+--R        - x log(x + a) + x log(x - a) + 2a
+--R   (1)  ----------------------------------
+--R                         3
+--R                       2a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 25
+bb:=1/(a^2*x)+1/(2*a^3)*log((x-a)/(x+a))
+--R
+--R              x - a
+--R        x log(-----) + 2a
+--R              x + a
+--R   (2)  -----------------
+--R                 3
+--R               2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 26
+cc:=aa-bb
+--R
+--R                                        x - a
+--R        - log(x + a) + log(x - a) - log(-----)
+--R                                        x + a
+--R   (3)  --------------------------------------
+--R                            3
+--R                          2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 27
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 28     14:149 Schaums and Axiom agree
+dd:=divlog cc
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.150~~~~~$\displaystyle\int{\frac{dx}{x^3(x^2-a^2)}}$}
+$$\int{\frac{1}{x^3(x^2-a^2)}}=
+\frac{1}{2a^2x^2}-\frac{1}{2a^4}\ln\left(\frac{x^2}{x^2-a^2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 29
+aa:=integrate(1/(x^3*(x^2-a^2)),x)
+--R 
+--R
+--R         2     2    2      2          2
+--R        x log(x  - a ) - 2x log(x) + a
+--R   (1)  -------------------------------
+--R                       4 2
+--R                     2a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 30
+bb:=1/(2*a^2*x^2)-1/(2*a^4)*log(x^2/(x^2-a^2))
+--R
+--R                    2
+--R           2       x        2
+--R        - x log(-------) + a
+--R                 2    2
+--R                x  - a
+--R   (2)  ---------------------
+--R                  4 2
+--R                2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 31
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (3)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 32
+t1:=divlog bb
+--R
+--R           2     2     2     2    2     2
+--R        - x log(x ) + x log(x  - a ) + a
+--R   (4)  ---------------------------------
+--R                        4 2
+--R                      2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 33
+logpow:=rule(log(a^n) == n*log(a))
+--R
+--R             n
+--R   (5)  log(a ) == n log(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 34
+t2:=logpow t1
+--R
+--R         2     2    2      2          2
+--R        x log(x  - a ) - 2x log(x) + a
+--R   (6)  -------------------------------
+--R                       4 2
+--R                     2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 35     14:150 Schaums and Axiom agree
+cc:=aa-t2
+--R
+--R   (7)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.151~~~~~$\displaystyle\int{\frac{dx}{(x^2-a^2)^2}}$}
+$$\int{\frac{1}{(x^2-a^2)^2}}=
+\frac{-x}{2a^2(x^2-a^2)}-\frac{1}{4a^3}\ln\left(\frac{x-a}{x+a}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 36
+aa:=integrate(1/((x^2-a^2)^2),x)
+--R 
+--R
+--R          2    2                  2    2
+--R        (x  - a )log(x + a) + (- x  + a )log(x - a) - 2a x
+--R   (1)  --------------------------------------------------
+--R                              3 2     5
+--R                            4a x  - 4a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 37
+bb:=-x/(2*a^2*(x^2-a^2))-1/(4*a^3)*log((x-a)/(x+a))
+--R
+--R            2    2     x - a
+--R        (- x  + a )log(-----) - 2a x
+--R                       x + a
+--R   (2)  ----------------------------
+--R                   3 2     5
+--R                 4a x  - 4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 38
+cc:=aa-bb
+--R
+--R                                      x - a
+--R        log(x + a) - log(x - a) + log(-----)
+--R                                      x + a
+--R   (3)  ------------------------------------
+--R                           3
+--R                         4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 39
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 40     14:151 Schaums and Axiom agree
+dd:=divlog cc
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.152~~~~~$\displaystyle\int{\frac{x~dx}{(x^2-a^2)^2}}$}
+$$\int{\frac{x}{(x^2-a^2)^2}}=
+\frac{-1}{2(x^2-a^2)}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 41
+aa:=integrate(x/((x^2-a^2)^2),x)
+--R 
+--R
+--R              1
+--R   (1)  - ---------
+--R            2     2
+--R          2x  - 2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 42
+bb:=-1/(2*(x^2-a^2))
+--R
+--R              1
+--R   (2)  - ---------
+--R            2     2
+--R          2x  - 2a
+--R                                            Type: Fraction Polynomial Integer
+--E
+
+--S 43     14:152 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.153~~~~~$\displaystyle\int{\frac{x^2dx}{(x^2-a^2)^2}}$}
+$$\int{\frac{x^2}{(x^2-a^2)^2}}=
+\frac{-x}{2(x^2-a^2)}+\frac{1}{4a}\ln\left(\frac{x-a}{x+a}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 44
+aa:=integrate(x^2/((x^2-a^2)^2),x)
+--R 
+--R
+--R            2    2                2    2
+--R        (- x  + a )log(x + a) + (x  - a )log(x - a) - 2a x
+--R   (1)  --------------------------------------------------
+--R                                2     3
+--R                            4a x  - 4a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 45
+bb:=-x/(2*(x^2-a^2))+1/(4*a)*log((x-a)/(x+a))
+--R
+--R          2    2     x - a
+--R        (x  - a )log(-----) - 2a x
+--R                     x + a
+--R   (2)  --------------------------
+--R                    2     3
+--R                4a x  - 4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 46
+cc:=aa-bb
+--R
+--R                                        x - a
+--R        - log(x + a) + log(x - a) - log(-----)
+--R                                        x + a
+--R   (3)  --------------------------------------
+--R                          4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 47
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 48     14:153 Schaums and Axiom agree
+dd:=divlog cc
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.154~~~~~$\displaystyle\int{\frac{x^3dx}{(x^2-a^2)^2}}$}
+$$\int{\frac{x^3}{(x^2-a^2)^2}}=
+\frac{-a^2}{2(x^2-a^2)}+\frac{1}{2}\ln(x^2-a^2)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 49
+aa:=integrate(x^3/((x^2-a^2)^2),x)
+--R 
+--R
+--R          2    2      2    2     2
+--R        (x  - a )log(x  - a ) - a
+--R   (1)  --------------------------
+--R                   2     2
+--R                 2x  - 2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 50
+bb:=-a^2/(2*(x^2-a^2))+1/2*log(x^2-a^2)
+--R
+--R          2    2      2    2     2
+--R        (x  - a )log(x  - a ) - a
+--R   (2)  --------------------------
+--R                   2     2
+--R                 2x  - 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 51     14:154 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.155~~~~~$\displaystyle\int{\frac{dx}{x(x^2-a^2)^2}}$}
+$$\int{\frac{1}{x(x^2-a^2)^2}}=
+\frac{-1}{2a^2(x^2-a^2)}+\frac{1}{2a^4}\ln\left(\frac{x^2}{x^2-a^2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 52
+aa:=integrate(1/(x*(x^2-a^2)^2),x)
+--R 
+--R
+--R            2    2      2    2       2     2           2
+--R        (- x  + a )log(x  - a ) + (2x  - 2a )log(x) - a
+--R   (1)  ------------------------------------------------
+--R                             4 2     6
+--R                           2a x  - 2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 53
+bb:=-1/(2*a^2*(x^2-a^2))+1/(2*a^4)*log(x^2/(x^2-a^2))
+--R
+--R                         2
+--R          2    2        x        2
+--R        (x  - a )log(-------) - a
+--R                      2    2
+--R                     x  - a
+--R   (2)  --------------------------
+--R                  4 2     6
+--R                2a x  - 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 54
+cc:=aa-bb
+--R
+--R                                           2
+--R               2    2                     x
+--R        - log(x  - a ) + 2log(x) - log(-------)
+--R                                        2    2
+--R                                       x  - a
+--R   (3)  ---------------------------------------
+--R                            4
+--R                          2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 55
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 56
+dd:=divlog cc
+--R
+--R               2
+--R        - log(x ) + 2log(x)
+--R   (5)  -------------------
+--R                  4
+--R                2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 57
+logpow:=rule(log(a^n) == n*log(a))
+--R
+--R             n
+--R   (6)  log(a ) == n log(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 58     14:155 Schaums and Axiom agree
+ee:=logpow dd
+--R
+--R   (7)  0
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.156~~~~~$\displaystyle\int{\frac{dx}{x^2(x^2-a^2)^2}}$}
+$$\int{\frac{1}{x^2(x^2-a^2)^2}}=
+-\frac{1}{a^4x}-\frac{x}{2a^4(x^2-a^2)}-
+\frac{3}{4a^5}\ln\left(\frac{x-a}{x+a}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 59
+aa:=integrate(1/(x^2*(x^2-a^2)^2),x)
+--R
+--R           3     2                    3     2                   2     3
+--R        (3x  - 3a x)log(x + a) + (- 3x  + 3a x)log(x - a) - 6a x  + 4a
+--R   (1)  ---------------------------------------------------------------
+--R                                    5 3     7
+--R                                  4a x  - 4a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 60
+bb:=-1/(a^4*x)-x/(2*a^4*(x^2-a^2))-3/(4*a^5)*log((x-a)/(x+a))
+--R
+--R             3     2      x - a        2     3
+--R        (- 3x  + 3a x)log(-----) - 6a x  + 4a
+--R                          x + a
+--R   (2)  --------------------------------------
+--R                       5 3     7
+--R                     4a x  - 4a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 61
+cc:=aa-bb
+--R
+--R                                         x - a
+--R        3log(x + a) - 3log(x - a) + 3log(-----)
+--R                                         x + a
+--R   (3)  ---------------------------------------
+--R                            5
+--R                          4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 62
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 63     14:156 Schaums and Axiom agree
+dd:=divlog cc
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.157~~~~~$\displaystyle\int{\frac{dx}{x^3(x^2-a^2)^2}}$}
+$$\int{\frac{1}{x^3(x^2-a^2)^2}}=
+-\frac{1}{2a^4x^2}-\frac{1}{2a^4(x^2-a^2)}+
+\frac{1}{a^6}\ln\left(\frac{x^2}{x^2-a^2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 64
+aa:=integrate(1/(x^3*(x^2-a^2)^2),x)
+--R 
+--R
+--R             4     2 2      2    2       4     2 2            2 2    4
+--R        (- 2x  + 2a x )log(x  - a ) + (4x  - 4a x )log(x) - 2a x  + a
+--R   (1)  --------------------------------------------------------------
+--R                                   6 4     8 2
+--R                                 2a x  - 2a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 65
+bb:=-1/(2*a^4*x^2)-1/(2*a^4*(x^2-a^2))+1/a^6*log(x^2/(x^2-a^2))
+--R
+--R                             2
+--R           4     2 2        x         2 2    4
+--R        (2x  - 2a x )log(-------) - 2a x  + a
+--R                          2    2
+--R                         x  - a
+--R   (2)  --------------------------------------
+--R                       6 4     8 2
+--R                     2a x  - 2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 66
+cc:=aa-bb
+--R
+--R                                           2
+--R               2    2                     x
+--R        - log(x  - a ) + 2log(x) - log(-------)
+--R                                        2    2
+--R                                       x  - a
+--R   (3)  ---------------------------------------
+--R                            6
+--R                           a
+--R                                                     Type: Expression Integer
+--E
+
+--S 67
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 68
+dd:=divlog cc
+--R
+--R               2
+--R        - log(x ) + 2log(x)
+--R   (5)  -------------------
+--R                  6
+--R                 a
+--R                                                     Type: Expression Integer
+--E
+
+--S 69
+logpow:=rule(log(a^n) == n*log(a))
+--R
+--R             n
+--R   (6)  log(a ) == n log(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 70     14:157 Schaums and Axiom agree
+ee:=logpow dd
+--R
+--R   (7)  0
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.158~~~~~$\displaystyle\int{\frac{dx}{(x^2-a^2)^n}}$}
+$$\int{\frac{1}{(x^2-a^2)^n}}=
+\frac{-x}{2(n-1)a^2(x^2-a^2)^{n-1}}-
+\frac{2n-3}{(2n-2)a^2}\int{\frac{1}{(x^2-a^2)^{n-1}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 71     14:158 Axiom cannot do this integral
+aa:=integrate(1/((x^2-a^2)^n),x)
+--R 
+--R
+--R           x
+--R         ++        1
+--I   (1)   |   ------------- d%L
+--R        ++       2     2 n
+--I             (- a  + %L )
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.159~~~~~$\displaystyle\int{\frac{x~dx}{(x^2-a^2)^n}}$}
+$$\int{\frac{x}{(x^2-a^2)^n}}=
+\frac{-1}{2(n-1)(x^2-a^2)^{n-1}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 72
+aa:=integrate(x/((x^2-a^2)^n),x)
+--R 
+--R
+--R                   2    2
+--R                - x  + a
+--R   (1)  ------------------------
+--R                         2    2
+--R                  n log(x  - a )
+--R        (2n - 2)%e
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 73
+bb:=-1/(2*(n-1)*(x^2-a^2)^(n-1))
+--R
+--R                     1
+--R   (2)  - ----------------------
+--R                    2    2 n - 1
+--R          (2n - 2)(x  - a )
+--R                                                     Type: Expression Integer
+--E
+
+--S 74
+cc:=aa-bb
+--R
+--R                 2    2
+--R          n log(x  - a )       2    2   2    2 n - 1
+--R        %e               + (- x  + a )(x  - a )
+--R   (3)  --------------------------------------------
+--R                                          2    2
+--R                     2    2 n - 1  n log(x  - a )
+--R           (2n - 2)(x  - a )     %e
+--R                                                     Type: Expression Integer
+--E
+
+--S 75
+explog:=rule(%e^(n*log(x)) == x^n)
+--R
+--R          n log(x)     n
+--R   (4)  %e         == x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 76
+dd:=explog cc
+--R
+--R          2    2 n       2    2   2    2 n - 1
+--R        (x  - a )  + (- x  + a )(x  - a )
+--R   (5)  --------------------------------------
+--R                     2    2 n - 1  2    2 n
+--R           (2n - 2)(x  - a )     (x  - a )
+--R                                                     Type: Expression Integer
+--E
+
+--S 77     14:159 Schaums and Axiom agree
+ee:=complexNormalize dd
+--R
+--R   (6)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.160~~~~~$\displaystyle\int{\frac{dx}{x(x^2-a^2)^n}}$}
+$$\int{\frac{1}{x(x^2-a^2)^n}}=
+\frac{-1}{2(n-1)a^2(x^2-a^2)^{n-1}}-
+\frac{1}{a^2}\int{\frac{1}{x(x^2-a^2)^{n-1}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 78     14:160 Axiom cannot compute this integral
+aa:=integrate(1/(x*(x^2-a^2)^n),x)
+--R 
+--R
+--R           x
+--R         ++          1
+--I   (1)   |   ---------------- d%L
+--R        ++          2     2 n
+--I             %L (- a  + %L )
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.161~~~~~$\displaystyle\int{\frac{x^mdx}{(x^2-a^2)^n}}$}
+$$\int{\frac{x^m}{(x^2-a^2)^n}}=
+\int{\frac{x^{m-2}}{(x^2-a^2)^{n-1}}}+
+a^2\int\frac{x^{m-2}}{(x^2-a^2)^n}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 79     14:161 Axiom cannot compute this integral
+aa:=integrate(x^m/((x^2-a^2)^n),x)
+--R 
+--R
+--R           x        m
+--I         ++       %L
+--I   (1)   |   ------------- d%L
+--R        ++       2     2 n
+--I             (- a  + %L )
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.162~~~~~$\displaystyle\int{\frac{dx}{x^m(x^2-a^2)^n}}$}
+$$\int{\frac{1}{x^m(x^2-a^2)^n}}=
+\frac{1}{a^2}\int{\frac{1}{x^{m-2}(x^2-a^2)^n}}-
+\frac{1}{a^2}\int{\frac{1}{x^m(x^2-a^2)^{n-1}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 80     14:162 Axiom cannot compute this integral
+aa:=integrate(1/(x^m*(x^2-a^2)^n),x)
+--R 
+--R
+--R           x
+--R         ++          1
+--I   (1)   |   ---------------- d%L
+--R        ++       2     2 n  m
+--I             (- a  + %L ) %L
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 p65
+\end{thebibliography}
+\end{document}
diff --git a/src/axiom-website/CATS/schaum7.input.pdf b/src/axiom-website/CATS/schaum7.input.pdf
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diff --git a/src/axiom-website/CATS/schaum8.input.pamphlet b/src/axiom-website/CATS/schaum8.input.pamphlet
new file mode 100644
index 0000000..10d9ef5
--- /dev/null
+++ b/src/axiom-website/CATS/schaum8.input.pamphlet
@@ -0,0 +1,1198 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum8.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.163~~~~~$\displaystyle\int{\frac{dx}{a^2-x^2}}$}
+$$\int{\frac{1}{a^2-x^2}}=\frac{1}{2a}\ln\left(\frac{a-x}{a+x}\right)$$
+$$\int{\frac{1}{a^2-x^2}}=-\frac{1}{a}\coth^{-1}\frac{x}{a}$$
+&lt;&lt;*&gt;&gt;=
+)spool schaum8.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1
+aa:=integrate(1/(a^2-x^2),x)
+--R 
+--R
+--R        log(x + a) - log(x - a)
+--R   (1)  -----------------------
+--R                   2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 2
+bb:=1/(2*a)*log((a+x)/(a-x))
+--R
+--R            - x - a
+--R        log(-------)
+--R             x - a
+--R   (2)  ------------
+--R             2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3
+cc:=aa-bb
+--R
+--R                                      - x - a
+--R        log(x + a) - log(x - a) - log(-------)
+--R                                       x - a
+--R   (3)  --------------------------------------
+--R                          2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 4
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 5      
+dd:=divlog cc
+--R
+--R        log(x + a) - log(- x - a)
+--R   (5)  -------------------------
+--R                    2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 6
+logminus:=rule(log(x + a) - log(- x - a) == log(-1))
+--R
+--I   (6)  log(x + a) - log(- x - a) + %I == log(- 1) + %I
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 7      14:163 Schaums and Axiom differ by a constant
+ee:=logminus dd
+--R
+--R        log(- 1)
+--R   (7)  --------
+--R           2a
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.164~~~~~$\displaystyle\int{\frac{x~dx}{a^2-x^2}}$}
+$$\int{\frac{x}{a^2-x^2}}=-\frac{1}{2}\ln(a^2-x^2)$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 8
+aa:=integrate(x/(a^2-x^2),x)
+--R 
+--R
+--R               2    2
+--R          log(x  - a )
+--R   (1)  - ------------
+--R                2
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 9
+bb:=-1/2*log(a^2-x^2)
+--R
+--R                 2    2
+--R          log(- x  + a )
+--R   (2)  - --------------
+--R                 2
+--R                                                     Type: Expression Integer
+--E
+
+--S 10
+cc:=aa-bb
+--R
+--R               2    2           2    2
+--R        - log(x  - a ) + log(- x  + a )
+--R   (3)  -------------------------------
+--R                       2
+--R                                                     Type: Expression Integer
+--E
+
+--S 11
+logminus1:=rule(-log(x^2-a^2)+log(-x^2+a^2) == log(-1))
+--R
+--R               2    2           2    2
+--I   (4)  - log(x  - a ) + log(- x  + a ) + %H == log(- 1) + %H
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 12     14:164 Schaums and Axiom differ by a constant
+dd:=logminus1 cc
+--R
+--R        log(- 1)
+--R   (5)  --------
+--R            2
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.165~~~~~$\displaystyle\int{\frac{x^2~dx}{a^2-x^2}}$}
+$$\int{\frac{x^2}{a^2-x^2}}=-x+\frac{a}{2}\ln\left(\frac{a+x}{a-x}\right)$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 13
+aa:=integrate(x^2/(a^2-x^2),x)
+--R 
+--R
+--R        a log(x + a) - a log(x - a) - 2x
+--R   (1)  --------------------------------
+--R                        2
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 14
+bb:=-x+a/2*log((a+x)/(a-x))
+--R
+--R              - x - a
+--R        a log(-------) - 2x
+--R               x - a
+--R   (2)  -------------------
+--R                 2
+--R                                                     Type: Expression Integer
+--E
+
+--S 15
+cc:=aa-bb
+--R
+--R                                            - x - a
+--R        a log(x + a) - a log(x - a) - a log(-------)
+--R                                             x - a
+--R   (3)  --------------------------------------------
+--R                              2
+--R                                                     Type: Expression Integer
+--E
+
+--S 16
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 17
+dd:=divlog cc
+--R
+--R        a log(x + a) - a log(- x - a)
+--R   (5)  -----------------------------
+--R                      2
+--R                                                     Type: Expression Integer
+--E
+
+--S 18
+logminusa:=rule(b*log(x + a) - b*log(- x - a) == b*log(-1))
+--R
+--I   (6)  b log(x + a) - b log(- x - a) + %M == b log(- 1) + %M
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 19     14:165 Schaums and Axiom differ by a constant
+ee:=logminusa dd
+--R
+--R        a log(- 1)
+--R   (7)  ----------
+--R             2
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.166~~~~~$\displaystyle\int{\frac{x^3~dx}{a^2-x^2}}$}
+$$\int{\frac{x^3}{a^2-x^2}}=-\frac{x^2}{2}-\frac{a^2}{2}\ln(a^2-x^2)$$
+
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 20
+aa:=integrate(x^3/(a^2-x^2),x)
+--R 
+--R
+--R           2     2    2     2
+--R        - a log(x  - a ) - x
+--R   (1)  ---------------------
+--R                  2
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 21
+bb:=-x^2/2-a^2/2*log(a^2-x^2)
+--R
+--R           2       2    2     2
+--R        - a log(- x  + a ) - x
+--R   (2)  -----------------------
+--R                   2
+--R                                                     Type: Expression Integer
+--E
+
+--S 22
+cc:=aa-bb
+--R
+--R           2     2    2     2       2    2
+--R        - a log(x  - a ) + a log(- x  + a )
+--R   (3)  -----------------------------------
+--R                         2
+--R                                                     Type: Expression Integer
+--E
+
+--S 23
+logminus1b:=rule(-b*log(x^2-a^2)+b*log(-x^2+a^2) == b*log(-1))
+--R
+--R                 2    2             2    2
+--I   (4)  - b log(x  - a ) + b log(- x  + a ) + %N == b log(- 1) + %N
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 24     14:166 Schaums and Axiom differ by a constant
+dd:=logminus1b cc
+--R
+--R         2
+--R        a log(- 1)
+--R   (5)  ----------
+--R             2
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.167~~~~~$\displaystyle\int{\frac{dx}{x(a^2-x^2)}}$}
+$$\int{\frac{1}{x(a^2-x^2)}}=
+\frac{1}{2a^2}\ln\left(\frac{x^2}{a^2-x^2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 25
+aa:=integrate(1/(x*(a^2-x^2)),x)
+--R 
+--R
+--R               2    2
+--R        - log(x  - a ) + 2log(x)
+--R   (1)  ------------------------
+--R                     2
+--R                   2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 26
+bb:=1/(2*a^2)*log(x^2/(a^2-x^2))
+--R
+--R                  2
+--R                 x
+--R        log(- -------)
+--R               2    2
+--R              x  - a
+--R   (2)  --------------
+--R                2
+--R              2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 27
+cc:=aa-bb
+--R
+--R                                             2
+--R               2    2                       x
+--R        - log(x  - a ) + 2log(x) - log(- -------)
+--R                                          2    2
+--R                                         x  - a
+--R   (3)  -----------------------------------------
+--R                             2
+--R                           2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 28
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 29
+dd:=divlog cc
+--R
+--R                         2
+--R        2log(x) - log(- x )
+--R   (5)  -------------------
+--R                  2
+--R                2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 30
+logpowminus:=rule(log(-a^n) == n*log(a)+log(-1))
+--R
+--R               n
+--R   (6)  log(- a ) == n log(a) + log(- 1)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 31     14:167 Schaums and Axiom differ by a constant
+ee:=logpowminus dd
+--R
+--R          log(- 1)
+--R   (7)  - --------
+--R               2
+--R             2a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.168~~~~~$\displaystyle\int{\frac{dx}{x^2(a^2-x^2)}}$}
+$$\int{\frac{1}{x^2(a^2-x^2)}}=
+\frac{1}{a^2x}+\frac{1}{2a^3}\ln\left(\frac{a+x}{a-x}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 32
+aa:=integrate(1/(x^2*(a^2-x^2)),x)
+--R 
+--R
+--R        x log(x + a) - x log(x - a) - 2a
+--R   (1)  --------------------------------
+--R                        3
+--R                      2a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 33
+bb:=-1/(a^2*x)+1/(2*a^3)*log((a+x)/(a-x))
+--R
+--R              - x - a
+--R        x log(-------) - 2a
+--R               x - a
+--R   (2)  -------------------
+--R                  3
+--R                2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 34
+cc:=aa-bb
+--R
+--R                                      - x - a
+--R        log(x + a) - log(x - a) - log(-------)
+--R                                       x - a
+--R   (3)  --------------------------------------
+--R                            3
+--R                          2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 35
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 36
+dd:=divlog cc
+--R
+--R        log(x + a) - log(- x - a)
+--R   (5)  -------------------------
+--R                     3
+--R                   2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 37
+logminus:=rule(log(x + a) - log(- x - a) == log(-1))
+--R
+--I   (6)  log(x + a) - log(- x - a) + %O == log(- 1) + %O
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 38     14:168 Schaums and Axiom differ by a constant
+ee:=logminus dd
+--R
+--R        log(- 1)
+--R   (7)  --------
+--R             3
+--R           2a
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.169~~~~~$\displaystyle\int{\frac{dx}{x^3(a^2-x^2)}}$}
+$$\int{\frac{1}{x^3(a^2-x^2)}}=
+-\frac{1}{2a^2x^2}+\frac{1}{2a^4}\ln\left(\frac{x^2}{a^2-x^2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 39
+aa:=integrate(1/(x^3*(a^2-x^2)),x)
+--R 
+--R
+--R           2     2    2      2          2
+--R        - x log(x  - a ) + 2x log(x) - a
+--R   (1)  ---------------------------------
+--R                        4 2
+--R                      2a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 40
+bb:=-1/(2*a^2*x^2)+1/(2*a^4)*log(x^2/(a^2-x^2))
+--R
+--R                    2
+--R         2         x        2
+--R        x log(- -------) - a
+--R                 2    2
+--R                x  - a
+--R   (2)  ---------------------
+--R                  4 2
+--R                2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 41
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (3)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 42
+bb1:=divlog bb
+--R
+--R           2     2    2     2       2     2
+--R        - x log(x  - a ) + x log(- x ) - a
+--R   (4)  -----------------------------------
+--R                         4 2
+--R                       2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 43
+cc:=aa-bb1
+--R
+--R                         2
+--R        2log(x) - log(- x )
+--R   (5)  -------------------
+--R                  4
+--R                2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 44
+logminuspow:=rule(log(-x^n) == n*log(x)+log(-1))
+--R
+--R               n
+--R   (6)  log(- x ) == n log(x) + log(- 1)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 45     14:169 Schaums and Axiom differ by a constant
+dd:=logminuspow cc
+--R
+--R          log(- 1)
+--R   (7)  - --------
+--R               4
+--R             2a
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.170~~~~~$\displaystyle\int{\frac{dx}{(a^2-x^2)^2}}$}
+$$\int{\frac{1}{(a^2-x^2)^2}}=
+\frac{x}{2a^2(a^2-x^2)}+\frac{1}{4a^3}\ln\left(\frac{a+x}{a-x}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 46
+aa:=integrate(1/((a^2-x^2)^2),x)
+--R 
+--R
+--R          2    2                  2    2
+--R        (x  - a )log(x + a) + (- x  + a )log(x - a) - 2a x
+--R   (1)  --------------------------------------------------
+--R                              3 2     5
+--R                            4a x  - 4a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 47
+bb:=x/(2*a^2*(a^2-x^2))+1/(4*a^3)*log((a+x)/(a-x))
+--R
+--R          2    2     - x - a
+--R        (x  - a )log(-------) - 2a x
+--R                      x - a
+--R   (2)  ----------------------------
+--R                   3 2     5
+--R                 4a x  - 4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 48
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (3)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 49
+bb1:=divlog bb
+--R
+--R            2    2                2    2
+--R        (- x  + a )log(x - a) + (x  - a )log(- x - a) - 2a x
+--R   (4)  ----------------------------------------------------
+--R                               3 2     5
+--R                             4a x  - 4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 50
+cc:=aa-bb1
+--R
+--R        log(x + a) - log(- x - a)
+--R   (5)  -------------------------
+--R                     3
+--R                   4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 51
+logminus:=rule(log(x + a) - log(- x - a) == log(-1))
+--R
+--I   (6)  log(x + a) - log(- x - a) + %P == log(- 1) + %P
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 52     14:170 Schaums and Axiom differ by a constant
+dd:=logminus cc
+--R
+--R        log(- 1)
+--R   (7)  --------
+--R             3
+--R           4a
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.171~~~~~$\displaystyle\int{\frac{x~dx}{(a^2-x^2)^2}}$}
+$$\int{\frac{x}{(a^2-x^2)^2}}=
+\frac{1}{2(a^2-x^2)}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 53
+aa:=integrate(x/((a^2-x^2)^2),x)
+--R 
+--R
+--R              1
+--R   (1)  - ---------
+--R            2     2
+--R          2x  - 2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 54
+bb:=1/(2*(a^2-x^2))
+--R
+--R              1
+--R   (2)  - ---------
+--R            2     2
+--R          2x  - 2a
+--R                                            Type: Fraction Polynomial Integer
+--E
+
+--S 55     14:171 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.172~~~~~$\displaystyle\int{\frac{x^2dx}{(a^2-x^2)^2}}$}
+$$\int{\frac{x^2}{(a^2-x^2)^2}}=
+\frac{x}{2(a^2-x^2)}-\frac{1}{4a}\ln\left(\frac{a+x}{a-x}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 56
+aa:=integrate(x^2/((a^2-x^2)^2),x)
+--R 
+--R
+--R            2    2                2    2
+--R        (- x  + a )log(x + a) + (x  - a )log(x - a) - 2a x
+--R   (1)  --------------------------------------------------
+--R                                2     3
+--R                            4a x  - 4a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 57
+bb:=x/(2*(a^2-x^2))-1/(4*a)*log((a+x)/(a-x))
+--R
+--R            2    2     - x - a
+--R        (- x  + a )log(-------) - 2a x
+--R                        x - a
+--R   (2)  ------------------------------
+--R                      2     3
+--R                  4a x  - 4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 58
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (3)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 59
+bb1:=divlog bb
+--R
+--R          2    2                  2    2
+--R        (x  - a )log(x - a) + (- x  + a )log(- x - a) - 2a x
+--R   (4)  ----------------------------------------------------
+--R                                 2     3
+--R                             4a x  - 4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 60
+cc:=aa-bb1
+--R
+--R        - log(x + a) + log(- x - a)
+--R   (5)  ---------------------------
+--R                     4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 61
+logminus2:=rule(-log(x + a) + log(- x - a) == log(-1))
+--R
+--I   (6)  - log(x + a) + log(- x - a) + %S == log(- 1) + %S
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 62     14:172 Schaums and Axiom differ by a constant
+dd:=logminus2 cc
+--R
+--R        log(- 1)
+--R   (7)  --------
+--R           4a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.173~~~~~$\displaystyle\int{\frac{x^3dx}{(a^2-x^2)^2}}$}
+$$\int{\frac{x^3}{(a^2-x^2)^2}}=
+\frac{a^2}{2(a^2-x^2)}+\frac{1}{2}\ln(a^2-x^2)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 63
+aa:=integrate(x^3/((a^2-x^2)^2),x)
+--R 
+--R
+--R          2    2      2    2     2
+--R        (x  - a )log(x  - a ) - a
+--R   (1)  --------------------------
+--R                   2     2
+--R                 2x  - 2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 64
+bb:=a^2/(2*(a^2-x^2))+1/2*log(a^2-x^2)
+--R
+--R          2    2        2    2     2
+--R        (x  - a )log(- x  + a ) - a
+--R   (2)  ----------------------------
+--R                    2     2
+--R                  2x  - 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 65
+cc:=aa-bb
+--R
+--R             2    2           2    2
+--R        log(x  - a ) - log(- x  + a )
+--R   (3)  -----------------------------
+--R                      2
+--R                                                     Type: Expression Integer
+--E
+
+--S 66
+logminus3:=rule(log(x^2-a^2)-log(-x^2+a^2) == log(-1))
+--R
+--R             2    2           2    2
+--I   (4)  log(x  - a ) - log(- x  + a ) + %T == log(- 1) + %T
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 67     14:173 Schaums and Axiom differ by a constant
+dd:=logminus3 cc
+--R
+--R        log(- 1)
+--R   (5)  --------
+--R            2
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.174~~~~~$\displaystyle\int{\frac{dx}{x(a^2-x^2)^2}}$}
+$$\int{\frac{1}{x(a^2-x^2)^2}}=
+\frac{1}{2a^2(a^2-x^2)}+\frac{1}{2a^4}\ln\left(\frac{x^2}{a^2-x^2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 68
+aa:=integrate(1/(x*(a^2-x^2)^2),x)
+--R 
+--R
+--R            2    2      2    2       2     2           2
+--R        (- x  + a )log(x  - a ) + (2x  - 2a )log(x) - a
+--R   (1)  ------------------------------------------------
+--R                             4 2     6
+--R                           2a x  - 2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 69
+bb:=1/(2*a^2*(a^2-x^2))+1/(2*a^4)*log(x^2/(a^2-x^2))
+--R
+--R                           2
+--R          2    2          x        2
+--R        (x  - a )log(- -------) - a
+--R                        2    2
+--R                       x  - a
+--R   (2)  ----------------------------
+--R                   4 2     6
+--R                 2a x  - 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 70
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (3)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 71
+bb1:=divlog bb
+--R
+--R            2    2      2    2      2    2        2     2
+--R        (- x  + a )log(x  - a ) + (x  - a )log(- x ) - a
+--R   (4)  -------------------------------------------------
+--R                             4 2     6
+--R                           2a x  - 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 72
+cc:=aa-bb1
+--R
+--R                         2
+--R        2log(x) - log(- x )
+--R   (5)  -------------------
+--R                  4
+--R                2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 73
+logpowminus:=rule(log(-a^n) == n*log(a)+log(-1))
+--R
+--R               n
+--R   (6)  log(- a ) == n log(a) + log(- 1)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 74     14:174 Schaums and Axiom differ by a constant
+dd:=logpowminus cc
+--R
+--R          log(- 1)
+--R   (7)  - --------
+--R               4
+--R             2a
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.175~~~~~$\displaystyle\int{\frac{dx}{x^2(a^2-x^2)^2}}$}
+$$\int{\frac{1}{x^2(a^2-x^2)^2}}=
+-\frac{1}{a^4x}+\frac{x}{2a^4(a^2-x^2)}+
+\frac{3}{4a^5}\ln\left(\frac{a+x}{a-x}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 75
+aa:=integrate(1/(x^2*(a^2-x^2)^2),x)
+--R
+--R           3     2                    3     2                   2     3
+--R        (3x  - 3a x)log(x + a) + (- 3x  + 3a x)log(x - a) - 6a x  + 4a
+--R   (1)  ---------------------------------------------------------------
+--R                                    5 3     7
+--R                                  4a x  - 4a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 76
+bb:=-1/(a^4*x)+x/(2*a^4*(a^2-x^2))+3/(4*a^5)*log((a+x)/(a-x))
+--R
+--R           3     2      - x - a        2     3
+--R        (3x  - 3a x)log(-------) - 6a x  + 4a
+--R                         x - a
+--R   (2)  --------------------------------------
+--R                       5 3     7
+--R                     4a x  - 4a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 77
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (3)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 78
+bb1:=divlog bb
+--R
+--R             3     2                  3     2                     2     3
+--R        (- 3x  + 3a x)log(x - a) + (3x  - 3a x)log(- x - a) - 6a x  + 4a
+--R   (4)  -----------------------------------------------------------------
+--R                                     5 3     7
+--R                                   4a x  - 4a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 79
+cc:=aa-bb
+--R
+--R                                         - x - a
+--R        3log(x + a) - 3log(x - a) - 3log(-------)
+--R                                          x - a
+--R   (5)  -----------------------------------------
+--R                             5
+--R                           4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 80
+dd:=divlog cc
+--R
+--R        3log(x + a) - 3log(- x - a)
+--R   (6)  ---------------------------
+--R                      5
+--R                    4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 81
+logminusb:=rule(b*log(x + a) - b*log(- x - a) == b*log(-1))
+--R
+--I   (7)  b log(x + a) - b log(- x - a) + %U == b log(- 1) + %U
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 82     14:175 Schaums and Axiom differ by a constant
+ee:=logminusb dd
+--R
+--R        3log(- 1)
+--R   (8)  ---------
+--R             5
+--R           4a
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.176~~~~~$\displaystyle\int{\frac{dx}{x^3(a^2-x^2)^2}}$}
+$$\int{\frac{1}{x^3(a^2-x^2)^2}}=
+\frac{1}{2a^4x^2}+\frac{1}{2a^4(a^2-x^2)}+
+\frac{1}{a^6}\ln\left(\frac{x^2}{a^2-x^2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 83
+aa:=integrate(1/(x^3*(a^2-x^2)^2),x)
+--R 
+--R
+--R             4     2 2      2    2       4     2 2            2 2    4
+--R        (- 2x  + 2a x )log(x  - a ) + (4x  - 4a x )log(x) - 2a x  + a
+--R   (1)  --------------------------------------------------------------
+--R                                   6 4     8 2
+--R                                 2a x  - 2a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 84
+bb:=-1/(2*a^4*x^2)+1/(2*a^4*(a^2-x^2))+1/a^6*log(x^2/(a^2-x^2))
+--R
+--R                               2
+--R           4     2 2          x         2 2    4
+--R        (2x  - 2a x )log(- -------) - 2a x  + a
+--R                            2    2
+--R                           x  - a
+--R   (2)  ----------------------------------------
+--R                        6 4     8 2
+--R                      2a x  - 2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 85
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (3)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 86
+bb1:=divlog bb
+--R
+--R             4     2 2      2    2       4     2 2        2      2 2    4
+--R        (- 2x  + 2a x )log(x  - a ) + (2x  - 2a x )log(- x ) - 2a x  + a
+--R   (4)  -----------------------------------------------------------------
+--R                                    6 4     8 2
+--R                                  2a x  - 2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 87
+cc:=aa-bb1
+--R
+--R                         2
+--R        2log(x) - log(- x )
+--R   (5)  -------------------
+--R                  6
+--R                 a
+--R                                                     Type: Expression Integer
+--E
+
+--S 88
+logpowminus:=rule(log(-a^n) == n*log(a)+log(-1))
+--R
+--R               n
+--R   (6)  log(- a ) == n log(a) + log(- 1)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 89     14:176 Schaums and Axiom differ by a constant
+dd:=logpowminus cc
+--R
+--R          log(- 1)
+--R   (7)  - --------
+--R              6
+--R             a
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.177~~~~~$\displaystyle\int{\frac{dx}{(a^2-x^2)^n}}$}
+$$\int{\frac{1}{(a^2-x^2)^n}}=
+\frac{x}{2(n-1)a^2(a^2-x^2)^{n-1}}+
+\frac{2n-3}{(2n-2)a^2}\int{\frac{1}{(a^2-x^2)^{n-1}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 90     14:177 Axiom cannot do this integration
+aa:=integrate(1/((a^2-x^2)^n),x)
+--R 
+--R
+--R           x
+--R         ++       1
+--I   (1)   |   ----------- d%L
+--R        ++     2     2 n
+--I             (a  - %L )
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.178~~~~~$\displaystyle\int{\frac{x~dx}{(a^2-x^2)^n}}$}
+$$\int{\frac{x}{(a^2-x^2)^n}}=
+\frac{1}{2(n-1)(a^2-x^2)^{n-1}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 91
+aa:=integrate(x/((a^2-x^2)^n),x)
+--R 
+--R
+--R                    2    2
+--R                 - x  + a
+--R   (1)  --------------------------
+--R                           2    2
+--R                  n log(- x  + a )
+--R        (2n - 2)%e
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 92
+bb:=1/(2*(n-1)*(a^2-x^2)^(n-1))
+--R
+--R                    1
+--R   (2)  ------------------------
+--R                    2    2 n - 1
+--R        (2n - 2)(- x  + a )
+--R                                                     Type: Expression Integer
+--E
+
+--S 93
+cc:=aa-bb
+--R
+--R                     2    2
+--R            n log(- x  + a )       2    2     2    2 n - 1
+--R        - %e                 + (- x  + a )(- x  + a )
+--R   (3)  --------------------------------------------------
+--R                                               2    2
+--R                        2    2 n - 1  n log(- x  + a )
+--R            (2n - 2)(- x  + a )     %e
+--R                                                     Type: Expression Integer
+--E
+
+--S 94
+explog:=rule(%e^(n*log(x)) == x^n)
+--R
+--R          n log(x)     n
+--R   (4)  %e         == x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 95
+dd:=explog cc
+--R
+--R              2    2 n       2    2     2    2 n - 1
+--R        - (- x  + a )  + (- x  + a )(- x  + a )
+--R   (5)  --------------------------------------------
+--R                        2    2 n - 1    2    2 n
+--R            (2n - 2)(- x  + a )     (- x  + a )
+--R                                                     Type: Expression Integer
+--E
+
+--S 96     14:178 Schaums and Axiom agree
+ee:=complexNormalize dd
+--R
+--R   (6)  0
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.179~~~~~$\displaystyle\int{\frac{dx}{x(a^2-x^2)^n}}$}
+$$\int{\frac{1}{x(a^2-x^2)^n}}=
+\frac{1}{2(n-1)a^2(a^2-x^2)^{n-1}}+
+\frac{1}{a^2}\int{\frac{1}{x(a^2-x^2)^{n-1}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 97     14:179 Axiom cannot integrate this expression
+aa:=integrate(1/(x*(a^2-x^2)^n),x)
+--R 
+--R
+--R           x
+--R         ++         1
+--I   (1)   |   -------------- d%L
+--R        ++        2     2 n
+--I             %L (a  - %L )
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.180~~~~~$\displaystyle\int{\frac{x^mdx}{(a^2-x^2)^n}}$}
+$$\int{\frac{x^m}{(a^2-x^2)^n}}=
+a^2\int\frac{x^{m-2}}{(a^2-x^2)^n}-
+\int{\frac{x^{m-2}}{(a^2-x^2)^{n-1}}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 98     14:180 Axiom cannot integrate this expression
+aa:=integrate(x^m/((a^2-x^2)^n),x)
+--R 
+--R
+--R           x       m
+--I         ++      %L
+--I   (1)   |   ----------- d%L
+--R        ++     2     2 n
+--I             (a  - %L )
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.181~~~~~$\displaystyle\int{\frac{dx}{x^m(a^2-x^2)^n}}$}
+$$\int{\frac{1}{x^m(a^2-x^2)^n}}=
+\frac{1}{a^2}\int{\frac{1}{x^m(a^2-x^2)^{n-1}}}+
+\frac{1}{a^2}\int{\frac{1}{x^{m-2}(a^2-x^2)^n}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 99     14:181 Axiom cannot integrate this expression
+aa:=integrate(1/(x^m*(a^2-x^2)^n),x)
+--R 
+--R
+--R           x
+--R         ++         1
+--I   (1)   |   -------------- d%L
+--R        ++     m  2     2 n
+--I             %L (a  - %L )
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 p66
+\end{thebibliography}
+\end{document}
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diff --git a/src/axiom-website/CATS/schaum9.input.pamphlet b/src/axiom-website/CATS/schaum9.input.pamphlet
new file mode 100644
index 0000000..fa7d4f2
--- /dev/null
+++ b/src/axiom-website/CATS/schaum9.input.pamphlet
@@ -0,0 +1,1700 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum9.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.182~~~~~$\displaystyle\int{\frac{dx}{\sqrt{x^2+a^2}}}$}
+$$\int{\frac{1}{\sqrt{x^2+a^2}}}=\ln\left(x+\sqrt{x^2+a^2}\right)$$
+$$\int{\frac{1}{\sqrt{x^2+a^2}}}=\sinh^{-1}\frac{x}{a}$$
+&lt;&lt;*&gt;&gt;=
+)spool schaum9.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1
+aa:=integrate(1/(sqrt(x^2+a^2)),x)
+--R 
+--R
+--R               +-------+
+--R               | 2    2
+--R   (1)  - log(\|x  + a   - x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 2
+bb:=log(x+sqrt(x^2+a^2))
+--R
+--R             +-------+
+--R             | 2    2
+--R   (2)  log(\|x  + a   + x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 3
+cc:=aa-bb
+--R
+--R               +-------+             +-------+
+--R               | 2    2              | 2    2
+--R   (3)  - log(\|x  + a   + x) - log(\|x  + a   - x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 4      14:182 Schaums and Axiom differ by a constant
+dd:=complexNormalize cc
+--R
+--R               2
+--R   (4)  - log(a )
+--R                                                     Type: Expression Integer
+--E
+
+@
+This is equal to $-\log(a^2)$ but Axiom cannot prove it.
+
+\section{\cite{1}:14.183~~~~~$\displaystyle\int{\frac{x~dx}{\sqrt{x^2+a^2}}}$}
+$$\int{\frac{x}{\sqrt{x^2+a^2}}}=\sqrt{x^2+a^2}$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 5
+aa:=integrate(x/(sqrt(x^2+a^2)),x)
+--R 
+--R
+--R            +-------+
+--R            | 2    2     2    2
+--R        - x\|x  + a   + x  + a
+--R   (1)  -----------------------
+--R              +-------+
+--R              | 2    2
+--R             \|x  + a   - x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 6
+bb:=sqrt(x^2+a^2)
+--R
+--R         +-------+
+--R         | 2    2
+--R   (2)  \|x  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 7      14:183 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.184~~~~~$\displaystyle
+\int{\frac{x^2~dx}{\sqrt{x^2+a^2}}}$}
+$$\int{\frac{x^2}{\sqrt{x^2+a^2}}}=
+\frac{x\sqrt{x^2+a^2}}{2}-\frac{a^2}{2}\ln\left(x+\sqrt{x^2+a^2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 8
+aa:=integrate(x^2/sqrt(x^2+a^2),x)
+--R 
+--R
+--R   (1)
+--R             +-------+                   +-------+
+--R          2  | 2    2      2 2    4      | 2    2
+--R       (2a x\|x  + a   - 2a x  - a )log(\|x  + a   - x)
+--R     + 
+--R                     +-------+
+--R            3    2   | 2    2      4     2 2
+--R       (- 2x  - a x)\|x  + a   + 2x  + 2a x
+--R  /
+--R        +-------+
+--R        | 2    2      2     2
+--R     4x\|x  + a   - 4x  - 2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 9
+bb:=(x*sqrt(x^2+a^2))/2-a^2/2*log(x+sqrt(x^2+a^2))
+--R
+--R                 +-------+          +-------+
+--R           2     | 2    2           | 2    2
+--R        - a log(\|x  + a   + x) + x\|x  + a
+--R   (2)  -------------------------------------
+--R                          2
+--R                                                     Type: Expression Integer
+--E
+
+--S 10
+cc:=aa-bb
+--R
+--R               +-------+               +-------+
+--R         2     | 2    2          2     | 2    2
+--R        a log(\|x  + a   + x) + a log(\|x  + a   - x)
+--R   (3)  ---------------------------------------------
+--R                              2
+--R                                                     Type: Expression Integer
+--E
+
+--S 11
+logmul1:=rule(c*log(a)+c*log(b) == c*log(a*b))
+--R
+--I   (4)  c log(b) + c log(a) + %K == c log(a b) + %K
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 12     14:184 Schaums and Axiom differ by a constant
+dd:=logmul1 cc
+--R
+--R         2     2
+--R        a log(a )
+--R   (5)  ---------
+--R            2
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.185~~~~~$\displaystyle
+\int{\frac{x^3~dx}{\sqrt{x^2+a^2}}}$}
+$$\int{\frac{x^3}{\sqrt{x^2+a^2}}}=
+\frac{(x^2+a^2)^{3/2}}{3}-a^2\sqrt{x^2+a^2}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 13
+aa:=integrate(x^3/sqrt(x^2+a^2),x)
+--R 
+--R
+--R                               +-------+
+--R             5     2 3     4   | 2    2      6     2 4     4 2     6
+--R        (- 4x  + 5a x  + 6a x)\|x  + a   + 4x  - 3a x  - 9a x  - 2a
+--R   (1)  ------------------------------------------------------------
+--R                                 +-------+
+--R                        2     2  | 2    2       3     2
+--R                    (12x  + 3a )\|x  + a   - 12x  - 9a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 14
+bb:=(x^2+a^2)^(3/2)/3-a^2*sqrt(x^2+a^2)
+--R
+--R                   +-------+
+--R          2     2  | 2    2
+--R        (x  - 2a )\|x  + a
+--R   (2)  --------------------
+--R                  3
+--R                                                     Type: Expression Integer
+--E
+
+--S 15     14:185 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.186~~~~~$\displaystyle\int{\frac{dx}{x\sqrt{x^2+a^2}}}$}
+$$\int{\frac{1}{x\sqrt{x^2+a^2}}}=
+-\frac{1}{a}\ln\left(\frac{a+\sqrt{x^2+a^2}}{x}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 16
+aa:=integrate(1/(x*sqrt(x^2+a^2)),x)
+--R 
+--R
+--R               +-------+                 +-------+
+--R               | 2    2                  | 2    2
+--R        - log(\|x  + a   - x + a) + log(\|x  + a   - x - a)
+--R   (1)  ---------------------------------------------------
+--R                                 a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 17
+bb:=-1/a*log((a+sqrt(x^2+a^2))/x)
+--R
+--R               +-------+
+--R               | 2    2
+--R              \|x  + a   + a
+--R          log(--------------)
+--R                     x
+--R   (2)  - -------------------
+--R                   a
+--R                                                     Type: Expression Integer
+--E
+
+--S 18
+cc:=aa-bb
+--R
+--R   (3)
+--R                                                              +-------+
+--R          +-------+                 +-------+                 | 2    2
+--R          | 2    2                  | 2    2                 \|x  + a   + a
+--R   - log(\|x  + a   - x + a) + log(\|x  + a   - x - a) + log(--------------)
+--R                                                                    x
+--R   -------------------------------------------------------------------------
+--R                                       a
+--R                                                     Type: Expression Integer
+--E
+
+--S 19
+dd:=expandLog cc
+--R
+--R   (4)
+--R            +-------+             +-------+                 +-------+
+--R            | 2    2              | 2    2                  | 2    2
+--R       log(\|x  + a   + a) - log(\|x  + a   - x + a) + log(\|x  + a   - x - a)
+--R     + 
+--R       - log(x)
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 20     14:186 Schaums and Axiom differ by a constant
+ee:=complexNormalize dd
+--R
+--R          log(- 1)
+--R   (5)  - --------
+--R              a
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.187~~~~~$\displaystyle
+\int{\frac{dx}{x^2\sqrt{x^2+a^2}}}$}
+$$\int{\frac{1}{x^2\sqrt{x^2+a^2}}}=
+-\frac{\sqrt{x^2+a^2}}{a^2x}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 21
+aa:=integrate(1/(x^2*sqrt(x^2+a^2)),x)
+--R 
+--R
+--R                  1
+--R   (1)  - ----------------
+--R            +-------+
+--R            | 2    2     2
+--R          x\|x  + a   - x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 22
+bb:=-sqrt(x^2+a^2)/(a^2*x)
+--R
+--R           +-------+
+--R           | 2    2
+--R          \|x  + a
+--R   (2)  - ----------
+--R               2
+--R              a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 23     14:187 Schaums and Axiom differ by a constant
+cc:=aa-bb
+--R
+--R           1
+--R   (3)  - --
+--R           2
+--R          a
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.188~~~~~$\displaystyle\int{\frac{dx}{x^3\sqrt{x^2+a^2}}}$}
+$$\int{\frac{1}{x^3\sqrt{x^2+a^2}}}=
+-\frac{\sqrt{x^2+a^2}}{2a^2x^2}+\frac{1}{2a^3}
+\ln\left(\frac{a+\sqrt{x^2+a^2}}{x}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 24
+aa:=integrate(1/(x^3*sqrt(x^2+a^2)),x)
+--R 
+--R
+--R   (1)
+--R            +-------+                   +-------+
+--R          3 | 2    2      4    2 2      | 2    2
+--R       (2x \|x  + a   - 2x  - a x )log(\|x  + a   - x + a)
+--R     + 
+--R              +-------+                   +-------+
+--R            3 | 2    2      4    2 2      | 2    2
+--R       (- 2x \|x  + a   + 2x  + a x )log(\|x  + a   - x - a)
+--R     + 
+--R                    +-------+
+--R            2    3  | 2    2        3     3
+--R       (2a x  + a )\|x  + a   - 2a x  - 2a x
+--R  /
+--R           +-------+
+--R       3 3 | 2    2      3 4     5 2
+--R     4a x \|x  + a   - 4a x  - 2a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 25
+bb:=-sqrt(x^2+a^2)/(2*a^2*x^2)+1/(2*a^3)*log((a+sqrt(x^2+a^2))/x)
+--R
+--R               +-------+
+--R               | 2    2           +-------+
+--R         2    \|x  + a   + a      | 2    2
+--R        x log(--------------) - a\|x  + a
+--R                     x
+--R   (2)  -----------------------------------
+--R                         3 2
+--R                       2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 26
+cc:=aa-bb
+--R
+--R   (3)
+--R                                                            +-------+
+--R        +-------+                 +-------+                 | 2    2
+--R        | 2    2                  | 2    2                 \|x  + a   + a
+--R   log(\|x  + a   - x + a) - log(\|x  + a   - x - a) - log(--------------)
+--R                                                                  x
+--R   -----------------------------------------------------------------------
+--R                                       3
+--R                                     2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 27
+dd:=expandLog cc
+--R
+--R   (4)
+--R              +-------+             +-------+                 +-------+
+--R              | 2    2              | 2    2                  | 2    2
+--R       - log(\|x  + a   + a) + log(\|x  + a   - x + a) - log(\|x  + a   - x - a)
+--R     + 
+--R       log(x)
+--R  /
+--R       3
+--R     2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 28     14:188 Schaums and Axiom differ by a constant
+ee:=complexNormalize dd
+--R
+--R        log(- 1)
+--R   (5)  --------
+--R             3
+--R           2a
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.189~~~~~$\displaystyle\int{\sqrt{x^2+a^2}}~dx$}
+$$\int{\sqrt{x^2+a^2}}=
+\frac{x\sqrt{x^2+a^2}}{2}+\frac{a^2}{2}\ln\left(x+\sqrt{x^2+a^2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 29
+aa:=integrate(sqrt(x^2+a^2),x)
+--R 
+--R
+--R   (1)
+--R               +-------+                   +-------+
+--R            2  | 2    2      2 2    4      | 2    2
+--R       (- 2a x\|x  + a   + 2a x  + a )log(\|x  + a   - x)
+--R     + 
+--R                     +-------+
+--R            3    2   | 2    2      4     2 2
+--R       (- 2x  - a x)\|x  + a   + 2x  + 2a x
+--R  /
+--R        +-------+
+--R        | 2    2      2     2
+--R     4x\|x  + a   - 4x  - 2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 30
+bb:=(x*sqrt(x^2+a^2))/2+a^2/2*log(x+sqrt(x^2+a^2))
+--R
+--R               +-------+          +-------+
+--R         2     | 2    2           | 2    2
+--R        a log(\|x  + a   + x) + x\|x  + a
+--R   (2)  -----------------------------------
+--R                         2
+--R                                                     Type: Expression Integer
+--E
+
+--S 31
+cc:=aa-bb
+--R
+--R                 +-------+               +-------+
+--R           2     | 2    2          2     | 2    2
+--R        - a log(\|x  + a   + x) - a log(\|x  + a   - x)
+--R   (3)  -----------------------------------------------
+--R                               2
+--R                                                     Type: Expression Integer
+--E
+
+--S 32     14:189 Schaums and Axiom differ by a constant
+dd:=complexNormalize cc
+--R
+--R           2     2
+--R          a log(a )
+--R   (4)  - ---------
+--R              2
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.190~~~~~$\displaystyle\int{x\sqrt{x^2+a^2}}~dx$}
+$$\int{x\sqrt{x^2+a^2}}=
+\frac{(x^2+a^2)^{3/2}}{3}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 33
+aa:=integrate(x*sqrt(x^2+a^2),x)
+--R 
+--R
+--R                               +-------+
+--R             5     2 3     4   | 2    2      6     2 4     4 2    6
+--R        (- 4x  - 7a x  - 3a x)\|x  + a   + 4x  + 9a x  + 6a x  + a
+--R   (1)  -----------------------------------------------------------
+--R                                 +-------+
+--R                        2     2  | 2    2       3     2
+--R                    (12x  + 3a )\|x  + a   - 12x  - 9a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 34
+bb:=(x^2+a^2)^(3/2)/3
+--R
+--R                  +-------+
+--R          2    2  | 2    2
+--R        (x  + a )\|x  + a
+--R   (2)  -------------------
+--R                 3
+--R                                                     Type: Expression Integer
+--E
+
+--S 35     14:190 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.191~~~~~$\displaystyle
+\int{x^2\sqrt{x^2+a^2}}~dx$}
+$$\int{x^2\sqrt{x^2+a^2}}=
+\frac{x(x^2+a^2)^{3/2}}{4}-\frac{a^2x\sqrt{x^2+a^2}}{8}-
+\frac{a^4}{8}\ln\left(x+\sqrt{x^2+a^2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 36
+aa:=integrate(x^2*sqrt(x^2+a^2),x)
+--R 
+--R
+--R   (1)
+--R                       +-------+                           +-------+
+--R           4 3     6   | 2    2      4 4     6 2    8      | 2    2
+--R       ((8a x  + 4a x)\|x  + a   - 8a x  - 8a x  - a )log(\|x  + a   - x)
+--R     + 
+--R                                      +-------+
+--R           7      2 5      4 3    6   | 2    2       8      2 6      4 4     6 2
+--R     (- 16x  - 24a x  - 10a x  - a x)\|x  + a   + 16x  + 32a x  + 20a x  + 4a x
+--R  /
+--R                    +-------+
+--R         3      2   | 2    2       4      2 2     4
+--R     (64x  + 32a x)\|x  + a   - 64x  - 64a x  - 8a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 37
+bb:=(x*(x^2+a^2)^(3/2))/4-(a^2*x*sqrt(x^2+a^2))/8-a^4/8*log(x+sqrt(x^2+a^2))
+--R
+--R                 +-------+                    +-------+
+--R           4     | 2    2            3    2   | 2    2
+--R        - a log(\|x  + a   + x) + (2x  + a x)\|x  + a
+--R   (2)  -----------------------------------------------
+--R                               8
+--R                                                     Type: Expression Integer
+--E
+
+--S 38
+cc:=aa-bb
+--R
+--R               +-------+               +-------+
+--R         4     | 2    2          4     | 2    2
+--R        a log(\|x  + a   + x) + a log(\|x  + a   - x)
+--R   (3)  ---------------------------------------------
+--R                              8
+--R                                                     Type: Expression Integer
+--E
+
+--S 39     14:191 Schaums and Axiom differ by a constant
+dd:=complexNormalize cc
+--R
+--R         4     2
+--R        a log(a )
+--R   (4)  ---------
+--R            8
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.192~~~~~$\displaystyle
+\int{x^3\sqrt{x^2+a^2}}~dx$}
+$$\int{x^3\sqrt{x^2+a^2}}=
+\frac{(x^2+a^2)^{5/2}}{5}-\frac{a^2(x^2+a^2)^{3/2}}{3}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 40
+aa:=integrate(x^3*sqrt(x^2+a^2),x)
+--R 
+--R
+--R   (1)
+--R                                                  +-------+
+--R             9      2 7     4 5      6 3      8   | 2    2       10       2 8
+--R       (- 48x  - 76a x  - 3a x  + 35a x  + 10a x)\|x  + a   + 48x   + 100a x
+--R     + 
+--R          4 6      6 4      8 2     10
+--R       35a x  - 40a x  - 25a x  - 2a
+--R  /
+--R                              +-------+
+--R          4       2 2      4  | 2    2        5       2 3      4
+--R     (240x  + 180a x  + 15a )\|x  + a   - 240x  - 300a x  - 75a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 41
+bb:=(x^2+a^2)^(5/2)/5-(a^2*(x^2+a^2)^(3/2))/3
+--R
+--R                           +-------+
+--R           4    2 2     4  | 2    2
+--R        (3x  + a x  - 2a )\|x  + a
+--R   (2)  ----------------------------
+--R                     15
+--R                                                     Type: Expression Integer
+--E
+
+--S 42     14:192 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.193~~~~~$\displaystyle
+\int{\frac{\sqrt{x^2+a^2}}{x}}~dx$}
+$$\int{\frac{\sqrt{x^2+a^2}}{x}}=
+\sqrt{x^2+a^2}-a\ln\left(\frac{a+\sqrt{x^2+a^2}}{x}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 43
+aa:=integrate(sqrt(x^2+a^2)/x,x)
+--R 
+--R
+--R   (1)
+--R            +-------+            +-------+
+--R            | 2    2             | 2    2
+--R       (- a\|x  + a   + a x)log(\|x  + a   - x + a)
+--R     + 
+--R          +-------+            +-------+              +-------+
+--R          | 2    2             | 2    2               | 2    2     2    2
+--R       (a\|x  + a   - a x)log(\|x  + a   - x - a) - x\|x  + a   + x  + a
+--R  /
+--R      +-------+
+--R      | 2    2
+--R     \|x  + a   - x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 44
+bb:=sqrt(x^2+a^2)-a*log((a+sqrt(x^2+a^2))/x)
+--R
+--R                 +-------+
+--R                 | 2    2          +-------+
+--R                \|x  + a   + a     | 2    2
+--R   (2)  - a log(--------------) + \|x  + a
+--R                       x
+--R                                                     Type: Expression Integer
+--E
+
+--S 45
+cc:=aa-bb
+--R
+--R   (3)
+--R              +-------+                   +-------+
+--R              | 2    2                    | 2    2
+--R     - a log(\|x  + a   - x + a) + a log(\|x  + a   - x - a)
+--R   + 
+--R            +-------+
+--R            | 2    2
+--R           \|x  + a   + a
+--R     a log(--------------)
+--R                  x
+--R                                                     Type: Expression Integer
+--E
+
+--S 46
+dd:=expandLog cc
+--R
+--R   (4)
+--R            +-------+               +-------+
+--R            | 2    2                | 2    2
+--R     a log(\|x  + a   + a) - a log(\|x  + a   - x + a)
+--R   + 
+--R            +-------+
+--R            | 2    2
+--R     a log(\|x  + a   - x - a) - a log(x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 47     14:193 Schaums and Axiom differ by a constant
+ee:=complexNormalize dd
+--R
+--R   (5)  - a log(- 1)
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.194~~~~~$\displaystyle
+\int{\frac{\sqrt{x^2+a^2}}{x^2}}~dx$}
+$$\int{\frac{\sqrt{x^2+a^2}}{x^2}}=
+-\frac{\sqrt{x^2+a^2}}{x}+\ln\left(x+\sqrt{x^2+a^2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 48
+aa:=integrate(sqrt(x^2+a^2)/x^2,x)
+--R 
+--R
+--R             +-------+           +-------+
+--R             | 2    2     2      | 2    2          2
+--R        (- x\|x  + a   + x )log(\|x  + a   - x) - a
+--R   (1)  --------------------------------------------
+--R                        +-------+
+--R                        | 2    2     2
+--R                      x\|x  + a   - x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 49
+bb:=-sqrt(x^2+a^2)/x+log(x+sqrt(x^2+a^2))
+--R
+--R               +-------+         +-------+
+--R               | 2    2          | 2    2
+--R        x log(\|x  + a   + x) - \|x  + a
+--R   (2)  ----------------------------------
+--R                         x
+--R                                                     Type: Expression Integer
+--E
+
+--S 50
+cc:=aa-bb
+--R
+--R               +-------+             +-------+
+--R               | 2    2              | 2    2
+--R   (3)  - log(\|x  + a   + x) - log(\|x  + a   - x) - 1
+--R                                                     Type: Expression Integer
+--E
+
+--S 51     14:194 Schaums and Axiom differ by a constant
+dd:=complexNormalize cc
+--R
+--R               2
+--R   (4)  - log(a ) - 1
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.195~~~~~$\displaystyle
+\int{\frac{\sqrt{x^2+a^2}}{x^3}}~dx$}
+$$\int{\frac{\sqrt{x^2+a^2}}{x^3}}=
+-\frac{\sqrt{x^2+a^2}}{2x^2}-\frac{1}{2a}
+\ln\left(\frac{a+\sqrt{x^2+a^2}}{x}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 52
+aa:=integrate(sqrt(x^2+a^2)/x^3,x)
+--R 
+--R
+--R   (1)
+--R              +-------+                   +-------+
+--R            3 | 2    2      4    2 2      | 2    2
+--R       (- 2x \|x  + a   + 2x  + a x )log(\|x  + a   - x + a)
+--R     + 
+--R            +-------+                   +-------+
+--R          3 | 2    2      4    2 2      | 2    2
+--R       (2x \|x  + a   - 2x  - a x )log(\|x  + a   - x - a)
+--R     + 
+--R                    +-------+
+--R            2    3  | 2    2        3     3
+--R       (2a x  + a )\|x  + a   - 2a x  - 2a x
+--R  /
+--R           +-------+
+--R         3 | 2    2        4     3 2
+--R     4a x \|x  + a   - 4a x  - 2a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 53
+bb:=-sqrt(x^2+a^2)/(2*x^2)-1/(2*a)*log((a+sqrt(x^2+a^2))/x)
+--R
+--R                 +-------+
+--R                 | 2    2           +-------+
+--R           2    \|x  + a   + a      | 2    2
+--R        - x log(--------------) - a\|x  + a
+--R                       x
+--R   (2)  -------------------------------------
+--R                            2
+--R                        2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 54
+cc:=aa-bb
+--R
+--R   (3)
+--R                                                              +-------+
+--R          +-------+                 +-------+                 | 2    2
+--R          | 2    2                  | 2    2                 \|x  + a   + a
+--R   - log(\|x  + a   - x + a) + log(\|x  + a   - x - a) + log(--------------)
+--R                                                                    x
+--R   -------------------------------------------------------------------------
+--R                                       2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 55
+dd:=expandLog cc
+--R
+--R   (4)
+--R            +-------+             +-------+                 +-------+
+--R            | 2    2              | 2    2                  | 2    2
+--R       log(\|x  + a   + a) - log(\|x  + a   - x + a) + log(\|x  + a   - x - a)
+--R     + 
+--R       - log(x)
+--R  /
+--R     2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 56     14:195 Schaums and Axiom differ by a constant
+ee:=complexNormalize dd
+--R
+--R          log(- 1)
+--R   (5)  - --------
+--R             2a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.196~~~~~$\displaystyle\int{\frac{dx}{(x^2+a^2)^{3/2}}}$}
+$$\int{\frac{1}{(x^2+a^2)^{3/2}}}=
+\frac{x}{a^2\sqrt{x^2+a^2}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 57
+aa:=integrate(1/(x^2+a^2)^(3/2),x)
+--R 
+--R
+--R                    1
+--R   (1)  - ---------------------
+--R            +-------+
+--R            | 2    2     2    2
+--R          x\|x  + a   - x  - a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 58
+bb:=x/(a^2*sqrt(x^2+a^2))
+--R
+--R              x
+--R   (2)  ------------
+--R           +-------+
+--R         2 | 2    2
+--R        a \|x  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 59     14:196 Schaums and Axiom differ by a constant
+cc:=aa-bb
+--R
+--R         1
+--R   (3)  --
+--R         2
+--R        a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.197~~~~~$\displaystyle
+\int{\frac{x~dx}{(x^2+a^2)^{3/2}}}$}
+$$\int{\frac{x}{(x^2+a^2)^{3/2}}}=
+\frac{-1}{\sqrt{x^2+a^2}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 60
+aa:=integrate(x/(x^2+a^2)^(3/2),x)
+--R 
+--R
+--R             +-------+
+--R             | 2    2
+--R            \|x  + a   - x
+--R   (1)  ---------------------
+--R          +-------+
+--R          | 2    2     2    2
+--R        x\|x  + a   - x  - a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 61
+bb:=-1/sqrt(x^2+a^2)
+--R
+--R               1
+--R   (2)  - ----------
+--R           +-------+
+--R           | 2    2
+--R          \|x  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 62     14:197 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.198~~~~~$\displaystyle
+\int{\frac{x^2dx}{(x^2+a^2)^{3/2}}}$}
+$$\int{\frac{x^2}{(x^2+a^2)^{3/2}}}=
+\frac{-x}{\sqrt{x^2+a^2}}+\ln\left(x+\sqrt{x^2+a^2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 63
+aa:=integrate(x^2/(x^2+a^2)^(3/2),x)
+--R 
+--R
+--R             +-------+                +-------+
+--R             | 2    2     2    2      | 2    2          2
+--R        (- x\|x  + a   + x  + a )log(\|x  + a   - x) + a
+--R   (1)  -------------------------------------------------
+--R                        +-------+
+--R                        | 2    2     2    2
+--R                      x\|x  + a   - x  - a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 64
+bb:=-x/sqrt(x^2+a^2)+log(x+sqrt(x^2+a^2))
+--R
+--R         +-------+     +-------+
+--R         | 2    2      | 2    2
+--R        \|x  + a  log(\|x  + a   + x) - x
+--R   (2)  ---------------------------------
+--R                     +-------+
+--R                     | 2    2
+--R                    \|x  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 65
+cc:=aa-bb
+--R
+--R               +-------+             +-------+
+--R               | 2    2              | 2    2
+--R   (3)  - log(\|x  + a   + x) - log(\|x  + a   - x) - 1
+--R                                                     Type: Expression Integer
+--E
+
+--S 66     14:198 Schaums and Axiom differ by a constant
+dd:=complexNormalize cc
+--R
+--R               2
+--R   (4)  - log(a ) - 1
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.199~~~~~$\displaystyle
+\int{\frac{x^3dx}{(x^2+a^2)^{3/2}}}$}
+$$\int{\frac{x^3}{(x^2+a^2)^{3/2}}}=
+\sqrt{x^2+a^2}+\frac{a^2}{\sqrt{x^2+a^2}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 67
+aa:=integrate(x^3/(x^2+a^2)^(3/2),x)
+--R 
+--R
+--R                       +-------+
+--R             3     2   | 2    2      4     2 2     4
+--R        (- 2x  - 4a x)\|x  + a   + 2x  + 5a x  + 2a
+--R   (1)  --------------------------------------------
+--R                         +-------+
+--R                 2    2  | 2    2      3     2
+--R              (2x  + a )\|x  + a   - 2x  - 2a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 68
+bb:=sqrt(x^2+a^2)+a^2/sqrt(x^2+a^2)
+--R
+--R          2     2
+--R         x  + 2a
+--R   (2)  ----------
+--R         +-------+
+--R         | 2    2
+--R        \|x  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 69     14:199 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.200~~~~~$\displaystyle
+\int{\frac{dx}{x(x^2+a^2)^{3/2}}}$}
+$$\int{\frac{1}{x(x^2+a^2)^{3/2}}}=
+\frac{1}{a^2\sqrt{x^2+a^2}}-
+\frac{1}{a^3}\ln\left(\frac{a+\sqrt{x^2+a^2}}{x}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 70
+aa:=integrate(1/(x*(x^2+a^2)^(3/2)),x)
+--R 
+--R
+--R   (1)
+--R            +-------+                +-------+
+--R            | 2    2     2    2      | 2    2
+--R       (- x\|x  + a   + x  + a )log(\|x  + a   - x + a)
+--R     + 
+--R          +-------+                +-------+              +-------+
+--R          | 2    2     2    2      | 2    2               | 2    2
+--R       (x\|x  + a   - x  - a )log(\|x  + a   - x - a) - a\|x  + a   + a x
+--R  /
+--R         +-------+
+--R      3  | 2    2     3 2    5
+--R     a x\|x  + a   - a x  - a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 71
+bb:=1/(a^2*sqrt(x^2+a^2))-1/a^3*log((a+sqrt(x^2+a^2))/x)
+--R
+--R                         +-------+
+--R           +-------+     | 2    2
+--R           | 2    2     \|x  + a   + a
+--R        - \|x  + a  log(--------------) + a
+--R                               x
+--R   (2)  -----------------------------------
+--R                       +-------+
+--R                     3 | 2    2
+--R                    a \|x  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 72
+cc:=aa-bb
+--R
+--R   (3)
+--R                                                              +-------+
+--R          +-------+                 +-------+                 | 2    2
+--R          | 2    2                  | 2    2                 \|x  + a   + a
+--R   - log(\|x  + a   - x + a) + log(\|x  + a   - x - a) + log(--------------)
+--R                                                                    x
+--R   -------------------------------------------------------------------------
+--R                                        3
+--R                                       a
+--R                                                     Type: Expression Integer
+--E
+
+--S 73
+dd:=expandLog cc
+--R
+--R   (4)
+--R            +-------+             +-------+                 +-------+
+--R            | 2    2              | 2    2                  | 2    2
+--R       log(\|x  + a   + a) - log(\|x  + a   - x + a) + log(\|x  + a   - x - a)
+--R     + 
+--R       - log(x)
+--R  /
+--R      3
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 74     14:200 Schaums and Axiom differ by a constant
+ee:=complexNormalize dd
+--R
+--R          log(- 1)
+--R   (5)  - --------
+--R              3
+--R             a
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.201~~~~~$\displaystyle
+\int{\frac{dx}{x^2(x^2+a^2)^{3/2}}}$}
+$$\int{\frac{1}{x^2(x^2+a^2)^{3/2}}}=
+-\frac{\sqrt{x^2+a^2}}{a^4x}-\frac{x}{a^4\sqrt{x^2+a^2}}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 75
+aa:=integrate(1/(x^2*(x^2+a^2)^(3/2)),x)
+--R 
+--R
+--R                           1
+--R   (1)  - -----------------------------------
+--R                      +-------+
+--R             3    2   | 2    2      4     2 2
+--R          (2x  + a x)\|x  + a   - 2x  - 2a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 76
+bb:=-sqrt(x^2+a^2)/(a^4*x)-x/(a^4*sqrt(x^2+a^2))
+--R
+--R              2    2
+--R          - 2x  - a
+--R   (2)  -------------
+--R            +-------+
+--R         4  | 2    2
+--R        a x\|x  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 77     14:201 Schaums and Axiom differ by a constant
+cc:=aa-bb
+--R
+--R           2
+--R   (3)  - --
+--R           4
+--R          a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.202~~~~~$\displaystyle
+\int{\frac{dx}{x^3(x^2+a^2)^{3/2}}}$}
+$$\int{\frac{1}{x^3(x^2+a^2)^{3/2}}}=
+\frac{-1}{2a^2x^2\sqrt{x^2+a^2}}-
+\frac{3}{2a^4\sqrt{x^2+a^2}}+
+\frac{3}{2a^5}\ln\left(\frac{a+\sqrt{x^2+a^2}}{x}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 78
+aa:=integrate(1/(x^3*(x^2+a^2)^(3/2)),x)
+--R 
+--R
+--R   (1)
+--R                       +-------+                              +-------+
+--R            5     2 3  | 2    2       6      2 4     4 2      | 2    2
+--R       ((12x  + 9a x )\|x  + a   - 12x  - 15a x  - 3a x )log(\|x  + a   - x + a)
+--R     + 
+--R                           +-------+
+--R                5     2 3  | 2    2       6      2 4     4 2
+--R         ((- 12x  - 9a x )\|x  + a   + 12x  + 15a x  + 3a x )
+--R      *
+--R              +-------+
+--R              | 2    2
+--R         log(\|x  + a   - x - a)
+--R     + 
+--R                             +-------+
+--R             4     3 2    5  | 2    2         5      3 3     5
+--R       (12a x  + 7a x  + a )\|x  + a   - 12a x  - 13a x  - 3a x
+--R  /
+--R                     +-------+
+--R        5 5     7 3  | 2    2      5 6      7 4     9 2
+--R     (8a x  + 6a x )\|x  + a   - 8a x  - 10a x  - 2a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 79
+bb:=-1/(2*a^2*x^2*sqrt(x^2+a^2))-3/(2*a^4*sqrt(x^2+a^2))+3/(2*a^5)*log((a+sqrt(x^2+a^2))/x)
+--R
+--R                          +-------+
+--R            +-------+     | 2    2
+--R          2 | 2    2     \|x  + a   + a        2    3
+--R        3x \|x  + a  log(--------------) - 3a x  - a
+--R                                x
+--R   (2)  ---------------------------------------------
+--R                             +-------+
+--R                         5 2 | 2    2
+--R                       2a x \|x  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 80
+cc:=aa-bb
+--R
+--R   (3)
+--R                                                               +-------+
+--R         +-------+                  +-------+                  | 2    2
+--R         | 2    2                   | 2    2                  \|x  + a   + a
+--R   3log(\|x  + a   - x + a) - 3log(\|x  + a   - x - a) - 3log(--------------)
+--R                                                                     x
+--R   --------------------------------------------------------------------------
+--R                                         5
+--R                                       2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 81
+dd:=expandLog cc
+--R
+--R   (4)
+--R               +-------+              +-------+
+--R               | 2    2               | 2    2
+--R       - 3log(\|x  + a   + a) + 3log(\|x  + a   - x + a)
+--R     + 
+--R               +-------+
+--R               | 2    2
+--R       - 3log(\|x  + a   - x - a) + 3log(x)
+--R  /
+--R       5
+--R     2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 82     14:202 Schaums and Axiom differ by a constant
+ee:=complexNormalize dd
+--R
+--R        3log(- 1)
+--R   (5)  ---------
+--R             5
+--R           2a
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.203~~~~~$\displaystyle\int{(x^2+a^2)^{3/2}}~dx$}
+$$\int{(x^2+a^2)^{3/2}}=
+\frac{x(x^2+a^2)^{3/2}}{4}+\frac{3a^2x\sqrt{x^2+a^2}}{8}+
+\frac{3}{8}a^4\ln\left(x+\sqrt{x^2+a^2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 83
+aa:=integrate((x^2+a^2)^(3/2),x)
+--R
+--R   (1)
+--R                           +-------+                              +-------+
+--R              4 3      6   | 2    2       4 4      6 2     8      | 2    2
+--R       ((- 24a x  - 12a x)\|x  + a   + 24a x  + 24a x  + 3a )log(\|x  + a   - x)
+--R     + 
+--R                                         +-------+
+--R             7      2 5      4 3     6   | 2    2       8      2 6      4 4
+--R       (- 16x  - 56a x  - 42a x  - 5a x)\|x  + a   + 16x  + 64a x  + 68a x
+--R     + 
+--R          6 2
+--R       20a x
+--R  /
+--R                    +-------+
+--R         3      2   | 2    2       4      2 2     4
+--R     (64x  + 32a x)\|x  + a   - 64x  - 64a x  - 8a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 84
+bb:=(x*(x^2+a^2)^(3/2))/4+(3*a^2*x*sqrt(x^2+a^2))/8+3/8*a^4*log(x+sqrt(x^2+a^2))
+--R
+--R                +-------+                     +-------+
+--R          4     | 2    2            3     2   | 2    2
+--R        3a log(\|x  + a   + x) + (2x  + 5a x)\|x  + a
+--R   (2)  -----------------------------------------------
+--R                               8
+--R                                                     Type: Expression Integer
+--E
+
+--S 85
+cc:=aa-bb
+--R
+--R                  +-------+                +-------+
+--R            4     | 2    2           4     | 2    2
+--R        - 3a log(\|x  + a   + x) - 3a log(\|x  + a   - x)
+--R   (3)  -------------------------------------------------
+--R                                8
+--R                                                     Type: Expression Integer
+--E
+
+--S 86     14:203 Schaums and Axiom differ by a constant
+dd:=complexNormalize cc
+--R
+--R            4     2
+--R          3a log(a )
+--R   (4)  - ----------
+--R               8
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.204~~~~~$\displaystyle\int{x(x^2+a^2)^{3/2}}~dx$}
+$$\int{x(x^2+a^2)^{3/2}}=\frac{(x^2+a^2)^{5/2}}{5}$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 87
+aa:=integrate(x*(x^2+a^2)^(3/2),x)
+--R 
+--R
+--R   (1)
+--R                                                  +-------+
+--R             9      2 7      4 5      6 3     8   | 2    2       10      2 8
+--R       (- 16x  - 52a x  - 61a x  - 30a x  - 5a x)\|x  + a   + 16x   + 60a x
+--R     + 
+--R          4 6      6 4      8 2    10
+--R       85a x  + 55a x  + 15a x  + a
+--R  /
+--R                           +-------+
+--R         4      2 2     4  | 2    2       5       2 3      4
+--R     (80x  + 60a x  + 5a )\|x  + a   - 80x  - 100a x  - 25a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 88
+bb:=(x^2+a^2)^(5/2)/5
+--R
+--R                          +-------+
+--R          4     2 2    4  | 2    2
+--R        (x  + 2a x  + a )\|x  + a
+--R   (2)  ---------------------------
+--R                     5
+--R                                                     Type: Expression Integer
+--E
+
+--S 89     14:204 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.205~~~~~$\displaystyle\int{x^2(x^2+a^2)^{3/2}}~dx$}
+$$\int{x^2(x^2+a^2)^{3/2}}=
+\frac{x(x^2+a^2)^{5/2}}{6}-\frac{a^2x(x^2+a^2)^{3/2}}{24}-
+\frac{a^4x\sqrt{x^2+a^2}}{16}-
+\frac{a^6}{16}\ln\left(x+\sqrt{x^2+a^2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 90
+aa:=integrate(x^2*(x^2+a^2)^(3/2),x)
+--R 
+--R
+--R   (1)
+--R                                      +-------+
+--R               6 5      8 3      10   | 2    2       6 6       8 4      10 2
+--R           (96a x  + 96a x  + 18a  x)\|x  + a   - 96a x  - 144a x  - 54a  x
+--R         + 
+--R               12
+--R           - 3a
+--R      *
+--R              +-------+
+--R              | 2    2
+--R         log(\|x  + a   - x)
+--R     + 
+--R                                                                 +-------+
+--R              11       2 9       4 7       6 5      8 3     10   | 2    2
+--R       (- 256x   - 832a x  - 912a x  - 404a x  - 68a x  - 3a  x)\|x  + a
+--R     + 
+--R           12       2 10        4 8       6 6       8 4      10 2
+--R       256x   + 960a x   + 1296a x  + 772a x  + 198a x  + 18a  x
+--R  /
+--R                                  +-------+
+--R           5        2 3       4   | 2    2         6        2 4       4 2      6
+--R     (1536x  + 1536a x  + 288a x)\|x  + a   - 1536x  - 2304a x  - 864a x  - 48a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 91
+bb:=(x*(x^2+a^2)^(5/2))/6-(a^2*x*(x^2+a^2)^(3/2))/24-(a^4*x*sqrt(x^2+a^2))/16-a^6/16*log(x+sqrt(x^2+a^2))
+--R
+--R                  +-------+                              +-------+
+--R            6     | 2    2            5      2 3     4   | 2    2
+--R        - 3a log(\|x  + a   + x) + (8x  + 14a x  + 3a x)\|x  + a
+--R   (2)  ----------------------------------------------------------
+--R                                    48
+--R                                                     Type: Expression Integer
+--E
+
+--S 92
+cc:=aa-bb
+--R
+--R               +-------+               +-------+
+--R         6     | 2    2          6     | 2    2
+--R        a log(\|x  + a   + x) + a log(\|x  + a   - x)
+--R   (3)  ---------------------------------------------
+--R                              16
+--R                                                     Type: Expression Integer
+--E
+
+--S 93     14:205 Schaums and Axiom differ by a constant
+dd:=complexNormalize cc
+--R
+--R         6     2
+--R        a log(a )
+--R   (4)  ---------
+--R            16
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.206~~~~~$\displaystyle\int{x^3(x^2+a^2)^{3/2}}~dx$}
+$$\int{x^3(x^2+a^2)^{3/2}}=
+\frac{(x^2+a^2)^{7/2}}{7}-\frac{a^2(x^2+a^2)^{5/2}}{5}
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 94
+aa:=integrate(x^3*(x^2+a^2)^(3/2),x)
+--R 
+--R
+--R   (1)
+--R                   13        2 11        4 9       6 7       8 5       10 3
+--R             - 320x   - 1072a x   - 1240a x  - 467a x  + 112a x  + 105a  x
+--R           + 
+--R                12
+--R             14a  x
+--R      *
+--R          +-------+
+--R          | 2    2
+--R         \|x  + a
+--R     + 
+--R           14        2 12        4 10       6 8      8 6       10 4      12 2
+--R       320x   + 1232a x   + 1736a x   + 973a x  + 21a x  - 175a  x  - 49a  x
+--R     + 
+--R           14
+--R       - 2a
+--R  /
+--R                                            +-------+
+--R             6        2 4       4 2      6  | 2    2         7        2 5
+--R       (2240x  + 2800a x  + 840a x  + 35a )\|x  + a   - 2240x  - 3920a x
+--R     + 
+--R              4 3       6
+--R       - 1960a x  - 245a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 95
+bb:=(x^2+a^2)^(7/2)/7-(a^2*(x^2+a^2)^(5/2))/5
+--R
+--R                                   +-------+
+--R           6     2 4    4 2     6  | 2    2
+--R        (5x  + 8a x  + a x  - 2a )\|x  + a
+--R   (2)  ------------------------------------
+--R                         35
+--R                                                     Type: Expression Integer
+--E
+
+--S 96     14:206 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.207~~~~~$\displaystyle
+\int{\frac{(x^2+a^2)^{3/2}}{x}}~dx$}
+$$\int{\frac{(x^2+a^2)^{3/2}}{x}}=
+\frac{(x^2+a^2)^{3/2}}{3}+a^2\sqrt{x^2+a^2}-
+a^3\ln\left(\frac{a+\sqrt{x^2+a^2}}{x}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 97
+aa:=integrate((x^2+a^2)^(3/2)/x,x)
+--R 
+--R
+--R   (1)
+--R                         +-------+                      +-------+
+--R              3 2     5  | 2    2       3 3     5       | 2    2
+--R       ((- 12a x  - 3a )\|x  + a   + 12a x  + 9a x)log(\|x  + a   - x + a)
+--R     + 
+--R                       +-------+                      +-------+
+--R            3 2     5  | 2    2       3 3     5       | 2    2
+--R       ((12a x  + 3a )\|x  + a   - 12a x  - 9a x)log(\|x  + a   - x - a)
+--R     + 
+--R                                +-------+
+--R            5      2 3      4   | 2    2      6      2 4      4 2     6
+--R       (- 4x  - 19a x  - 12a x)\|x  + a   + 4x  + 21a x  + 21a x  + 4a
+--R  /
+--R                  +-------+
+--R         2     2  | 2    2       3     2
+--R     (12x  + 3a )\|x  + a   - 12x  - 9a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 98
+bb:=(x^2+a^2)^(3/2)/3+a^2*sqrt(x^2+a^2)-a^3*log((a+sqrt(x^2+a^2))/x)
+--R
+--R                  +-------+
+--R                  | 2    2                    +-------+
+--R            3    \|x  + a   + a      2     2  | 2    2
+--R        - 3a log(--------------) + (x  + 4a )\|x  + a
+--R                        x
+--R   (2)  -----------------------------------------------
+--R                               3
+--R                                                     Type: Expression Integer
+--E
+
+--S 99
+cc:=aa-bb
+--R
+--R   (3)
+--R              +-------+                   +-------+
+--R        3     | 2    2              3     | 2    2
+--R     - a log(\|x  + a   - x + a) + a log(\|x  + a   - x - a)
+--R   + 
+--R            +-------+
+--R            | 2    2
+--R      3    \|x  + a   + a
+--R     a log(--------------)
+--R                  x
+--R                                                     Type: Expression Integer
+--E
+
+--S 100
+dd:=expandLog cc
+--R
+--R   (4)
+--R            +-------+               +-------+
+--R      3     | 2    2          3     | 2    2
+--R     a log(\|x  + a   + a) - a log(\|x  + a   - x + a)
+--R   + 
+--R            +-------+
+--R      3     | 2    2              3
+--R     a log(\|x  + a   - x - a) - a log(x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 101    14:207 Schaums and Axiom differ by a constant
+ee:=complexNormalize dd
+--R
+--R           3
+--R   (5)  - a log(- 1)
+--R                                                     Type: Expression Integer
+--E
+@
+
+\section{\cite{1}:14.208~~~~~$\displaystyle
+\int{\frac{(x^2+a^2)^{3/2}}{x^2}}~dx$}
+$$\int{\frac{(x^2+a^2)^{3/2}}{x^2}}=
+-\frac{(x^2+a^2)^{3/2}}{x}+\frac{3x\sqrt{x^2+a^2}}{2}+
+\frac{3}{2}a^2\ln\left(x+\sqrt{x^2+a^2}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 102
+aa:=integrate((x^2+a^2)^{3/2}/x^2,x)
+--R 
+--R
+--R   (1)
+--R                          +-------+                       +-------+
+--R              2 3     4   | 2    2       2 4     4 2      | 2    2
+--R       ((- 12a x  - 3a x)\|x  + a   + 12a x  + 9a x )log(\|x  + a   - x)
+--R     + 
+--R                              +-------+
+--R            5     2 3     4   | 2    2      6     2 4     4 2     6
+--R       (- 4x  - 3a x  + 4a x)\|x  + a   + 4x  + 5a x  - 3a x  - 2a
+--R  /
+--R                  +-------+
+--R        3     2   | 2    2      4     2 2
+--R     (8x  + 2a x)\|x  + a   - 8x  - 6a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 103
+bb:=-(x^2+a^2)^(3/2)/x+(3*x*sqrt(x^2+a^2))/2+3/2*a^2*log(x+sqrt(x^2+a^2))
+--R
+--R                  +-------+                   +-------+
+--R          2       | 2    2           2     2  | 2    2
+--R        3a x log(\|x  + a   + x) + (x  - 2a )\|x  + a
+--R   (2)  -----------------------------------------------
+--R                               2x
+--R                                                     Type: Expression Integer
+--E
+
+--S 104
+cc:=aa-bb
+--R
+--R                  +-------+                +-------+
+--R            2     | 2    2           2     | 2    2           2
+--R        - 3a log(\|x  + a   + x) - 3a log(\|x  + a   - x) - 2a
+--R   (3)  -------------------------------------------------------
+--R                                   2
+--R                                                     Type: Expression Integer
+--E
+
+--S 105    14:208 Schaums and Axiom differ by a constant
+dd:=complexNormalize cc
+--R
+--R            2     2      2
+--R        - 3a log(a ) - 2a
+--R   (4)  ------------------
+--R                 2
+--R                                                     Type: Expression Integer
+--E
+
+@
+
+\section{\cite{1}:14.209~~~~~$\displaystyle
+\int{\frac{(x^2+a^2)^{3/2}}{x^3}}~dx$}
+$$\int{\frac{(x^2+a^2)^{3/2}}{x^3}}=
+-\frac{(x^2+a^2)^{3/2}}{2x^2}+\frac{3}{2}\sqrt{x^2+a^2}-
+\frac{3}{2}a\ln\left(\frac{a+\sqrt{x^2+a^2}}{x}\right)
+$$
+&lt;&lt;*&gt;&gt;=
+)clear all
+
+--S 106
+aa:=integrate((x^2+a^2)^(3/2)/x^3,x)
+--R 
+--R
+--R   (1)
+--R                           +-------+                       +-------+
+--R                4     3 2  | 2    2         5     3 3      | 2    2
+--R       ((- 12a x  - 3a x )\|x  + a   + 12a x  + 9a x )log(\|x  + a   - x + a)
+--R     + 
+--R                         +-------+                       +-------+
+--R              4     3 2  | 2    2         5     3 3      | 2    2
+--R       ((12a x  + 3a x )\|x  + a   - 12a x  - 9a x )log(\|x  + a   - x - a)
+--R     + 
+--R                              +-------+
+--R            5     2 3     4   | 2    2      6     2 4     4 2    6
+--R       (- 8x  - 2a x  + 3a x)\|x  + a   + 8x  + 6a x  - 3a x  - a
+--R  /
+--R                   +-------+
+--R        4     2 2  | 2    2      5     2 3
+--R     (8x  + 2a x )\|x  + a   - 8x  - 6a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+--S 107
+bb:=-(x^2+a^2)^(3/2)/(2*x^2)+3/2*sqrt(x^2+a^2)-3/2*a*log((a+sqrt(x^2+a^2))/x)
+--R
+--R                    +-------+
+--R                    | 2    2                    +-------+
+--R              2    \|x  + a   + a       2    2  | 2    2
+--R        - 3a x log(--------------) + (2x  - a )\|x  + a
+--R                          x
+--R   (2)  -------------------------------------------------
+--R                                 2
+--R                               2x
+--R                                                     Type: Expression Integer
+--E
+
+--S 108
+cc:=aa-bb
+--R
+--R   (3)
+--R                 +-------+                    +-------+
+--R                 | 2    2                     | 2    2
+--R       - 3a log(\|x  + a   - x + a) + 3a log(\|x  + a   - x - a)
+--R     + 
+--R               +-------+
+--R               | 2    2
+--R              \|x  + a   + a
+--R       3a log(--------------)
+--R                     x
+--R  /
+--R     2
+--R                                                     Type: Expression Integer
+--E
+
+--S 109
+dd:=expandLog cc
+--R
+--R   (4)
+--R               +-------+                +-------+
+--R               | 2    2                 | 2    2
+--R       3a log(\|x  + a   + a) - 3a log(\|x  + a   - x + a)
+--R     + 
+--R               +-------+
+--R               | 2    2
+--R       3a log(\|x  + a   - x - a) - 3a log(x)
+--R  /
+--R     2
+--R                                                     Type: Expression Integer
+--E
+
+--S 110    14:209 Schaums and Axiom differ by a constant
+ee:=complexNormalize dd
+--R
+--R          3a log(- 1)
+--R   (5)  - -----------
+--R               2
+--R                                                     Type: Expression Integer
+--E
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 p67-68
+\end{thebibliography}
+\end{document}
diff --git a/src/axiom-website/CATS/schaum9.input.pdf b/src/axiom-website/CATS/schaum9.input.pdf
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+ &lt;head&gt;
+  &lt;title&gt; 
+   Axiom Journal
+  &lt;/title&gt;
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+ &lt;/body&gt;
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+ &lt;head&gt;
+  &lt;title&gt;
+   Axiom Computer Algebra System
+  &lt;/title&gt;
+   &lt;script type="text/javascript"&gt;
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+  &lt;/script&gt;
+
+ &lt;/head&gt;
+ &lt;body bgcolor="#ffff66"&gt;
+   &lt;div id="head" align="center"&gt; 
+    &lt;a href="http://savannah.nongnu.org/projects/axiom/"&gt;
+     &lt;img src="axiom.png" border="0" alt="Axiom"&gt;
+    &lt;/a&gt;
+    &lt;br&gt;
+    &lt;font size=200%&gt;
+     The Scientific Computation System
+    &lt;/font&gt;
+   &lt;/div&gt;
+   &lt;div align="center"&gt;
+    [
+     &lt;a href="../index.html" title="Home"&gt;
+      Home
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="screenshots.html" title="Screen Shots"&gt;
+      Screenshots
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="faq.html" title="FAQ"&gt;
+      FAQ
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="download.html" 
+        title="Download"&gt;
+      Download
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="documentation.html" title="Documentation"&gt;
+      Documentation
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="currentstate.html" title="Current State"&gt;
+      Current State
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="community.html" title="Community"&gt;
+      Community
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="developers.html" title="Developers"&gt;
+      Developers
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="patches.html" title="Patches"&gt;
+      Patches
+     &lt;/a&gt;
+    ]
+   &lt;/div&gt;
+   &lt;div align="center"&gt;
+    [
+     &lt;a href="bookvol10.2abb.html" title="Abbreviation Graph"&gt;
+      Abbreviation Graph
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="bookvol10.2full.html" title="Full Name Graph"&gt;
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+     &lt;/a&gt;
+    ]
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+  &lt;br&gt;
+  &lt;hr&gt;
+&lt;/head&gt;
+&lt;body bgcolor="#ffff66"&gt;
+&lt;h2&gt;Axiom Abbreviated Category and Domain graph&lt;/h2&gt;	
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+	&lt;a href="#" onclick="SVGscale(0.1);"&gt;0.1&lt;/a&gt; or
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+&lt;/div&gt;
+
+&lt;/body&gt;
+&lt;/html&gt;
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--- /dev/null
+++ b/src/axiom-website/bookvol10.2full.html
@@ -0,0 +1,121 @@
+&lt;html&gt;
+ &lt;head&gt;
+  &lt;title&gt;
+   Axiom Computer Algebra System
+  &lt;/title&gt;
+   &lt;script type="text/javascript"&gt;
+    var W3CDOM = (document.createElement &amp;&amp; document.getElementsByTagName);
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+ &lt;/head&gt;
+ &lt;body bgcolor="#ffff66"&gt;
+   &lt;div id="head" align="center"&gt; 
+    &lt;a href="http://savannah.nongnu.org/projects/axiom/"&gt;
+     &lt;img src="axiom.png" border="0" alt="Axiom"&gt;
+    &lt;/a&gt;
+    &lt;br&gt;
+    &lt;font size=200%&gt;
+     The Scientific Computation System
+    &lt;/font&gt;
+   &lt;/div&gt;
+   &lt;div align="center"&gt;
+    [
+     &lt;a href="../index.html" title="Home"&gt;
+      Home
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="screenshots.html" title="Screen Shots"&gt;
+      Screenshots
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="faq.html" title="FAQ"&gt;
+      FAQ
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="download.html" 
+        title="Download"&gt;
+      Download
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="documentation.html" title="Documentation"&gt;
+      Documentation
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="currentstate.html" title="Current State"&gt;
+      Current State
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="community.html" title="Community"&gt;
+      Community
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="developers.html" title="Developers"&gt;
+      Developers
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="patches.html" title="Patches"&gt;
+      Patches
+     &lt;/a&gt;
+    ]
+   &lt;/div&gt;
+   &lt;div align="center"&gt;
+    [
+     &lt;a href="bookvol10.2abb.html" title="Abbreviation Graph"&gt;
+      Abbreviation Graph
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="bookvol10.2full.html" title="Full Name Graph"&gt;
+      Full Name Graph
+     &lt;/a&gt;
+    ]
+   &lt;/div&gt;
+  &lt;br&gt;
+  &lt;hr&gt;
+&lt;/head&gt;
+&lt;body bgcolor="#ffff66"&gt;
+&lt;h2&gt;Axiom Abbreviated Category and Domain graph&lt;/h2&gt;	
+&lt;div&gt;
+	choose here: 
+	&lt;a href="#" onclick="SVGscale(0.1);"&gt;0.1&lt;/a&gt; or
+	&lt;a href="#" onclick="SVGscale(0.25);"&gt;0.25&lt;/a&gt; or
+	&lt;a href="#" onclick="SVGscale(0.5);"&gt;0.5&lt;/a&gt; or 
+	&lt;a href="#" onclick="SVGscale(1);"&gt;1.0&lt;/a&gt; or 
+	&lt;a href="#" onclick="SVGscale(1.5);"&gt;1.5&lt;/a&gt; or ...
+&lt;/div&gt;
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+&lt;/div&gt;
+
+&lt;/body&gt;
+&lt;/html&gt;
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+&lt;g id="edge224" class="edge"&gt;&lt;title&gt;Ring()&amp;#45;&amp;gt;LeftModule(a:Ring)&lt;/title&gt;
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+&lt;/g&gt;
+&lt;!-- Ring()&amp;#45;&amp;gt;Monoid() --&gt;
+&lt;g id="edge222" class="edge"&gt;&lt;title&gt;Ring()&amp;#45;&amp;gt;Monoid()&lt;/title&gt;
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+&lt;!-- Rng() --&gt;
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+&lt;/a&gt;
+&lt;/g&gt;
+&lt;!-- Ring()&amp;#45;&amp;gt;Rng() --&gt;
+&lt;g id="edge220" class="edge"&gt;&lt;title&gt;Ring()&amp;#45;&amp;gt;Rng()&lt;/title&gt;
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+&lt;g id="edge190" class="edge"&gt;&lt;title&gt;PriorityQueueAggregate(a:Type)&amp;#45;&amp;gt;BagAggregate(a:Type)&lt;/title&gt;
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+&lt;g id="edge194" class="edge"&gt;&lt;title&gt;PriorityQueueAggregate(a:OrderedSet)&amp;#45;&amp;gt;PriorityQueueAggregate(a:SetCategory)&lt;/title&gt;
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+&lt;g id="edge198" class="edge"&gt;&lt;title&gt;QueueAggregate(a:SetCategory)&amp;#45;&amp;gt;QueueAggregate(a:Type)&lt;/title&gt;
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+&lt;!-- RetractableTo(a:Type)&amp;#45;&amp;gt;Category --&gt;
+&lt;g id="edge202" class="edge"&gt;&lt;title&gt;RetractableTo(a:Type)&amp;#45;&amp;gt;Category&lt;/title&gt;
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+&lt;!-- RetractableTo(SetCategory) --&gt;
+&lt;g id="node194" class="node"&gt;&lt;title&gt;RetractableTo(SetCategory)&lt;/title&gt;
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+&lt;!-- RetractableTo(SetCategory)&amp;#45;&amp;gt;RetractableTo(a:Type) --&gt;
+&lt;g id="edge204" class="edge"&gt;&lt;title&gt;RetractableTo(SetCategory)&amp;#45;&amp;gt;RetractableTo(a:Type)&lt;/title&gt;
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+&lt;g id="node196" class="node"&gt;&lt;title&gt;RetractableTo(Symbol)&lt;/title&gt;
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+&lt;g id="edge206" class="edge"&gt;&lt;title&gt;RetractableTo(Symbol)&amp;#45;&amp;gt;RetractableTo(a:Type)&lt;/title&gt;
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+&lt;!-- RetractableTo(Integer)&amp;#45;&amp;gt;RetractableTo(a:Type) --&gt;
+&lt;g id="edge208" class="edge"&gt;&lt;title&gt;RetractableTo(Integer)&amp;#45;&amp;gt;RetractableTo(a:Type)&lt;/title&gt;
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+&lt;!-- RetractableTo(NonNegativeInteger) --&gt;
+&lt;g id="node200" class="node"&gt;&lt;title&gt;RetractableTo(NonNegativeInteger)&lt;/title&gt;
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+&lt;!-- RetractableTo(NonNegativeInteger)&amp;#45;&amp;gt;RetractableTo(a:Type) --&gt;
+&lt;g id="edge210" class="edge"&gt;&lt;title&gt;RetractableTo(NonNegativeInteger)&amp;#45;&amp;gt;RetractableTo(a:Type)&lt;/title&gt;
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+&lt;!-- RetractableTo(Fraction(Integer)) --&gt;
+&lt;g id="node202" class="node"&gt;&lt;title&gt;RetractableTo(Fraction(Integer))&lt;/title&gt;
+&lt;a xlink:href="bookvol10.2.pdf#nameddest=RETRACT" xlink:title="RetractableTo(Fraction(Integer))"&gt;
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+&lt;/a&gt;
+&lt;/g&gt;
+&lt;!-- RetractableTo(Fraction(Integer))&amp;#45;&amp;gt;RetractableTo(a:Type) --&gt;
+&lt;g id="edge212" class="edge"&gt;&lt;title&gt;RetractableTo(Fraction(Integer))&amp;#45;&amp;gt;RetractableTo(a:Type)&lt;/title&gt;
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+&lt;!-- RetractableTo(Float) --&gt;
+&lt;g id="node204" class="node"&gt;&lt;title&gt;RetractableTo(Float)&lt;/title&gt;
+&lt;a xlink:href="bookvol10.2.pdf#nameddest=RETRACT" xlink:title="RetractableTo(Float)"&gt;
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+&lt;text text-anchor="middle" x="9930" y="1161"&gt;RetractableTo(Float)&lt;/text&gt;
+&lt;/a&gt;
+&lt;/g&gt;
+&lt;!-- RetractableTo(Float)&amp;#45;&amp;gt;RetractableTo(a:Type) --&gt;
+&lt;g id="edge214" class="edge"&gt;&lt;title&gt;RetractableTo(Float)&amp;#45;&amp;gt;RetractableTo(a:Type)&lt;/title&gt;
+&lt;path style="fill:none;stroke:black;" d="M9864,1166C9846,1169 9827,1172 9810,1174 9564,1211 9274,1252 9135,1271"/&gt;
+&lt;polygon style="fill:black;stroke:black;" points="9135,1274 9125,1272 9135,1268 9135,1274"/&gt;
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+&lt;!-- RetractableTo(Kernel(ExpressionSpace)) --&gt;
+&lt;g id="node206" class="node"&gt;&lt;title&gt;RetractableTo(Kernel(ExpressionSpace))&lt;/title&gt;
+&lt;a xlink:href="bookvol10.2.pdf#nameddest=RETRACT" xlink:title="RetractableTo(Kernel(ExpressionSpace))"&gt;
+&lt;polygon style="fill:seagreen;stroke:seagreen;" points="10350,1138 10104,1138 10104,1174 10350,1174 10350,1138"/&gt;
+&lt;text text-anchor="middle" x="10227" y="1161"&gt;RetractableTo(Kernel(ExpressionSpace))&lt;/text&gt;
+&lt;/a&gt;
+&lt;/g&gt;
+&lt;!-- RetractableTo(Kernel(ExpressionSpace))&amp;#45;&amp;gt;RetractableTo(a:Type) --&gt;
+&lt;g id="edge216" class="edge"&gt;&lt;title&gt;RetractableTo(Kernel(ExpressionSpace))&amp;#45;&amp;gt;RetractableTo(a:Type)&lt;/title&gt;
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+&lt;polygon style="fill:black;stroke:black;" points="9135,1276 9125,1274 9135,1270 9135,1276"/&gt;
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+&lt;!-- RetractableTo(CommutativeRing) --&gt;
+&lt;g id="node208" class="node"&gt;&lt;title&gt;RetractableTo(CommutativeRing)&lt;/title&gt;
+&lt;a xlink:href="bookvol10.2.pdf#nameddest=RETRACT" xlink:title="RetractableTo(CommutativeRing)"&gt;
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+&lt;/a&gt;
+&lt;/g&gt;
+&lt;!-- RetractableTo(CommutativeRing)&amp;#45;&amp;gt;RetractableTo(a:Type) --&gt;
+&lt;g id="edge218" class="edge"&gt;&lt;title&gt;RetractableTo(CommutativeRing)&amp;#45;&amp;gt;RetractableTo(a:Type)&lt;/title&gt;
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+&lt;polygon style="fill:black;stroke:black;" points="8976,1266 8985,1271 8975,1272 8976,1266"/&gt;
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+&lt;!-- Rng()&amp;#45;&amp;gt;AbelianGroup() --&gt;
+&lt;g id="edge230" class="edge"&gt;&lt;title&gt;Rng()&amp;#45;&amp;gt;AbelianGroup()&lt;/title&gt;
+&lt;path style="fill:none;stroke:black;" d="M4681,286C4727,305 4824,347 4906,382 5004,425 5118,476 5183,504"/&gt;
+&lt;polygon style="fill:black;stroke:black;" points="5184,501 5192,508 5181,507 5184,501"/&gt;
+&lt;/g&gt;
+&lt;!-- Rng()&amp;#45;&amp;gt;SemiGroup() --&gt;
+&lt;g id="edge232" class="edge"&gt;&lt;title&gt;Rng()&amp;#45;&amp;gt;SemiGroup()&lt;/title&gt;
+&lt;path style="fill:none;stroke:black;" d="M4627,292C4595,314 4540,352 4505,376"/&gt;
+&lt;polygon style="fill:black;stroke:black;" points="4506,379 4496,382 4502,374 4506,379"/&gt;
+&lt;/g&gt;
+&lt;!-- RightModule(a:Rng)&amp;#45;&amp;gt;AbelianGroup() --&gt;
+&lt;g id="edge226" class="edge"&gt;&lt;title&gt;RightModule(a:Rng)&amp;#45;&amp;gt;AbelianGroup()&lt;/title&gt;
+&lt;path style="fill:none;stroke:black;" d="M5631,418C5541,442 5383,486 5296,509"/&gt;
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+&lt;!-- StackAggregate(a:SetCategory) --&gt;
+&lt;g id="node227" class="node"&gt;&lt;title&gt;StackAggregate(a:SetCategory)&lt;/title&gt;
+&lt;a xlink:href="bookvol10.2.pdf#nameddest=SKAGG" xlink:title="StackAggregate(a:SetCategory)"&gt;
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+&lt;text text-anchor="middle" x="101" y="657"&gt;StackAggregate(a:SetCategory)&lt;/text&gt;
+&lt;/a&gt;
+&lt;/g&gt;
+&lt;!-- StackAggregate(a:SetCategory)&amp;#45;&amp;gt;StackAggregate(a:Type) --&gt;
+&lt;g id="edge248" class="edge"&gt;&lt;title&gt;StackAggregate(a:SetCategory)&amp;#45;&amp;gt;StackAggregate(a:Type)&lt;/title&gt;
+&lt;path style="fill:none;stroke:black;" d="M143,670C195,693 285,731 341,756"/&gt;
+&lt;polygon style="fill:black;stroke:black;" points="342,753 350,760 339,759 342,753"/&gt;
+&lt;/g&gt;
+&lt;!-- StringAggregate() --&gt;
+&lt;g id="node229" class="node"&gt;&lt;title&gt;StringAggregate()&lt;/title&gt;
+&lt;a xlink:href="bookvol10.2.pdf#nameddest=SRAGG" xlink:title="StringAggregate()"&gt;
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+&lt;text text-anchor="middle" x="2532" y="153"&gt;StringAggregate()&lt;/text&gt;
+&lt;/a&gt;
+&lt;/g&gt;
+&lt;!-- StringAggregate()&amp;#45;&amp;gt;OneDimensionalArrayAggregate(Character) --&gt;
+&lt;g id="edge250" class="edge"&gt;&lt;title&gt;StringAggregate()&amp;#45;&amp;gt;OneDimensionalArrayAggregate(Character)&lt;/title&gt;
+&lt;path style="fill:none;stroke:black;" d="M2531,166C2530,187 2528,221 2526,246"/&gt;
+&lt;polygon style="fill:black;stroke:black;" points="2529,246 2525,256 2523,246 2529,246"/&gt;
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+&lt;!-- UnaryRecursiveAggregate(a:Type)&amp;#45;&amp;gt;RecursiveAggregate(a:Type) --&gt;
+&lt;g id="edge264" class="edge"&gt;&lt;title&gt;UnaryRecursiveAggregate(a:Type)&amp;#45;&amp;gt;RecursiveAggregate(a:Type)&lt;/title&gt;
+&lt;path style="fill:none;stroke:black;" d="M2387,670C2329,693 2229,732 2166,756"/&gt;
+&lt;polygon style="fill:black;stroke:black;" points="2168,759 2157,760 2165,753 2168,759"/&gt;
+&lt;/g&gt;
+&lt;!-- StepThrough() --&gt;
+&lt;g id="node234" class="node"&gt;&lt;title&gt;StepThrough()&lt;/title&gt;
+&lt;a xlink:href="bookvol10.2.pdf#nameddest=STEP" xlink:title="StepThrough()"&gt;
+&lt;polygon style="fill:lightblue;stroke:lightblue;" points="3627,886 3529,886 3529,922 3627,922 3627,886"/&gt;
+&lt;text text-anchor="middle" x="3578" y="909"&gt;StepThrough()&lt;/text&gt;
+&lt;/a&gt;
+&lt;/g&gt;
+&lt;!-- StepThrough()&amp;#45;&amp;gt;SetCategory() --&gt;
+&lt;g id="edge256" class="edge"&gt;&lt;title&gt;StepThrough()&amp;#45;&amp;gt;SetCategory()&lt;/title&gt;
+&lt;path style="fill:none;stroke:black;" d="M3593,922C3611,944 3641,980 3661,1004"/&gt;
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+&lt;/svg&gt;
diff --git a/src/axiom-website/community.html b/src/axiom-website/community.html
new file mode 100644
index 0000000..20314fd
--- /dev/null
+++ b/src/axiom-website/community.html
@@ -0,0 +1,248 @@
+&lt;html&gt;
+ &lt;head&gt;
+  &lt;title&gt;
+   Axiom Computer Algebra System
+  &lt;/title&gt;
+ &lt;/head&gt;
+ &lt;body bgcolor="#ffff66"&gt;
+   &lt;div id="head" align="center"&gt; 
+    &lt;a href="http://savannah.nongnu.org/projects/axiom/"&gt;
+     &lt;img src="axiom.png" border="0" alt="Axiom"&gt;
+    &lt;/a&gt;
+    &lt;br&gt;
+    &lt;font size=200%&gt;
+     The Scientific Computation System
+    &lt;/font&gt;
+   &lt;/div&gt;
+   &lt;div align="center"&gt;
+    [
+     &lt;a href="../index.html" title="Home"&gt;
+      Home
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="screenshots.html" title="Screen Shots"&gt;
+      Screenshots
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="faq.html" title="FAQ"&gt;
+      FAQ
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="download.html" title="Download"&gt;
+      Download
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="documentation.html" title="Documentation"&gt;
+      Documentation
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="currentstate.html" title="Current State"&gt;
+      Current State
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="community.html" title="Community"&gt;
+      Community
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="developers.html" title="Developers"&gt;
+      Developers
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="patches.html" title="Patches"&gt;
+      Patches
+     &lt;/a&gt;
+    ]
+   &lt;/div&gt;
+   &lt;div align="center"&gt;
+    [
+     &lt;a href="bookvol10.2abb.html" title="Abbreviation Graph"&gt;
+      Abbreviation Graph
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="bookvol10.2full.html" title="Full Name Graph"&gt;
+      Full Name Graph
+     &lt;/a&gt;
+    ]
+   &lt;/div&gt;
+  &lt;br&gt;
+  &lt;hr&gt;
+&lt;div id="body"&gt;
+  &lt;h1&gt;Axiom community, mailing lists&lt;/h1&gt;
+
+  &lt;a href="https://savannah.nongnu.org/mail/?group=axiom"&gt;Several
+  mailing lists&lt;/a&gt; are available:
+
+  &lt;dl&gt;
+    &lt;dt&gt;&lt;a href="http://mail.nongnu.org/mailman/listinfo/axiom-mail"&gt;axiom-mail&lt;/a&gt;
+        (&lt;a href="http://mail.nongnu.org/archive/html/axiom-mail"&gt;Archive&lt;/a&gt;)
+    &lt;dd&gt;General discussion on Axiom
+
+    &lt;dt&gt;&lt;a href="http://mail.nongnu.org/mailman/listinfo/axiom-developer"&gt;axiom-developer&lt;/a&gt;
+        (&lt;a href="http://mail.nongnu.org/archive/html/axiom-developer"&gt;Archive&lt;/a&gt;)
+    &lt;dd&gt;When you have issues to compile Axiom, when you have issues with
+    Axiom internals
+
+    &lt;dt&gt;&lt;a href="http://mail.nongnu.org/mailman/listinfo/axiom-legal"&gt;axiom-legal&lt;/a&gt;
+        (&lt;a href="http://mail.nongnu.org/archive/html/axiom-legal"&gt;Archive&lt;/a&gt;)
+    &lt;dd&gt;All legal issues, like license issues
+
+    &lt;dt&gt;&lt;a href="http://mail.nongnu.org/mailman/listinfo/axiom-math"&gt;axiom-math&lt;/a&gt;
+        (&lt;a href="http://mail.nongnu.org/archive/html/axiom-math"&gt;Archive&lt;/a&gt;)
+    &lt;dd&gt;Discussion of math theory and philosophy related to Axiom
+  &lt;/dl&gt;
+
+
+  &lt;h1&gt;Axiom Releases&lt;/h1&gt;
+
+  &lt;p&gt;
+   Axiom is released about every two months on a best-effort basis.
+   The "golden" released sources are maintained in GIT, CVS and ARCH.
+  &lt;/p&gt;
+
+  &lt;p&gt;
+  Axiom release (Git) is hosted on &lt;a
+  href="http://github.com/daly/axiom"&gt;GitHub&lt;/a&gt;.
+  &lt;/p&gt;
+
+  &lt;p&gt;
+  Axiom release (CVS) is hosted on &lt;a
+  href="http://savannah.nongnu.org/cvs/?group=axiom"&gt;Savannah&lt;/a&gt;.
+  &lt;/p&gt;
+
+  &lt;p&gt;
+  Axiom release (CVS) is hosted on &lt;a
+  href="http://sourceforge.net/cvs/?group_id=48359"&gt;Sourceforge&lt;/a&gt;.
+  &lt;/p&gt;
+
+  &lt;p&gt;
+  Axiom release (ARCH) is hosted on &lt;a
+  href="http://arch.axiom-developer.org"&gt;arch.axiom-developer.org&lt;/a&gt;
+  &lt;/p&gt;
+
+
+  &lt;h1&gt;Axiom Development&lt;/h1&gt;
+
+  &lt;p&gt;
+   Axiom is continuously developed and a "silver" version is available.
+   The development sources are maintained in git and SVN.
+  &lt;/p&gt;
+
+  &lt;p&gt;
+  Axiom development (SVN) is hosted on &lt;a
+  href="http://sourceforge.net/svn/?group_id=48359"&gt;Sourceforge&lt;/a&gt;.
+  &lt;/p&gt;
+
+  &lt;p&gt;
+  Axiom development (git) is hosted on &lt;a
+  href="http://git.axiom-developer.org"&gt;git.axiom-developer.org&lt;/a&gt;
+  &lt;/p&gt;
+
+
+  &lt;p&gt;
+  Here is a list of people that have contributed to Axiom (to November, 2008)
+  &lt;pre&gt;
+Cyril Alberga          Roy Adler              Christian Aistleitner
+Richard Anderson       George Andrews         S.J. Atkins
+Henry Baker            Stephen Balzac         Yurij Baransky
+David R. Barton        Gerald Baumgartner     Gilbert Baumslag
+Jay Belanger           David Bindel           Fred Blair
+Vladimir Bondarenko    Mark Botch
+Alexandre Bouyer       Peter A. Broadbery     Martin Brock
+Manuel Bronstein       Florian Bundschuh      Luanne Burns
+William Burge
+Quentin Carpent        Robert Caviness        Bruce Char
+Ondrej Certik          Cheekai Chin           David V. Chudnovsky
+Gregory V. Chudnovsky  Josh Cohen             Christophe Conil
+Don Coppersmith        George Corliss         Robert Corless
+Gary Cornell           Meino Cramer           Claire Di Crescenzo
+David Cyganski
+Timothy Daly Sr.       Timothy Daly Jr.       James H. Davenport
+Didier Deshommes       Michael Dewar
+Jean Della Dora        Gabriel Dos Reis       Claire DiCrescendo
+Sam Dooley             Lionel Ducos           Martin Dunstan
+Brian Dupee            Dominique Duval
+Robert Edwards         Heow Eide-Goodman      Lars Erickson
+Richard Fateman        Bertfried Fauser       Stuart Feldman
+Brian Ford             Albrecht Fortenbacher  George Frances
+Constantine Frangos    Timothy Freeman        Korrinn Fu
+Marc Gaetano           Rudiger Gebauer        Kathy Gerber
+Patricia Gianni        Samantha Goldrich      Holger Gollan
+Teresa Gomez-Diaz      Laureano Gonzalez-Vega Stephen Gortler
+Johannes Grabmeier     Matt Grayson           Klaus Ebbe Grue
+James Griesmer         Vladimir Grinberg      Oswald Gschnitzer
+Jocelyn Guidry
+Steve Hague            Satoshi Hamaguchi      Mike Hansen
+Richard Harke          Vilya Harvey           Martin Hassner
+Arthur S. Hathaway     Dan Hatton             Waldek Hebisch
+Ralf Hemmecke          Henderson              Antoine Hersen
+Gernot Hueber
+Pietro Iglio
+Alejandro Jakubi       Richard Jenks
+Kai Kaminski           Grant Keady            Tony Kennedy
+Paul Kosinski          Klaus Kusche           Bernhard Kutzler
+Larry Lambe            Franz Lehner           Frederic Lehobey
+Michel Levaud          Howard Levy            Liu Xiaojun
+Rudiger Loos           Michael Lucks          Richard Luczak
+Camm Maguire           Francois Maltey        Alasdair McAndrew
+Bob McElrath           Michael McGettrick     Ian Meikle
+David Mentre           Victor S. Miller       Gerard Milmeister
+Mohammed Mobarak       H. Michael Moeller     Michael Monagan
+Marc Moreno-Maza       Scott Morrison         Joel Moses
+Mark Murray
+William Naylor         C. Andrew Neff         John Nelder
+Godfrey Nolan          Arthur Norman          Jinzhong Niu
+Michael O'Connor       Summat Oemrawsingh     Kostas Oikonomou
+Humberto Ortiz-Zuazaga  
+Julian A. Padget       Bill Page              Susan Pelzel
+Michel Petitot         Didier Pinchon         Ayal Pinkus
+Jose Alfredo Portes
+Claude Quitte
+Arthur C. Ralfs        Norman Ramsey          Anatoly Raportirenko
+Michael Richardson     Renaud Rioboo          Jean Rivlin
+Nicolas Robidoux       Simon Robinson         Raymond Rogers
+Michael Rothstein      Martin Rubey
+Philip Santas          Alfred Scheerhorn      William Schelter
+Gerhard Schneider      Martin Schoenert       Marshall Schor
+Frithjof Schulze       Fritz Schwarz          Nick Simicich
+William Sit            Elena Smirnova         Jonathan Steinbach
+Fabio Stumbo           Christine Sundaresan   Robert Sutor
+Moss E. Sweedler       Eugene Surowitz
+Max Tegmark            James Thatcher         Balbir Thomas
+Mike Thomas            Dylan Thurston         Barry Trager
+Themos T. Tsikas
+Gregory Vanuxem
+Bernhard Wall          Stephen Watt           Jaap Weel
+Juergen Weiss          M. Weller              Mark Wegman
+James Wen              Thorsten Werther       Michael Wester
+John M. Wiley          Berhard Will           Clifton J. Williamson
+Stephen Wilson         Shmuel Winograd        Robert Wisbauer
+Sandra Wityak          Waldemar Wiwianka      Knut Wolf
+Clifford Yapp          David Yun
+Vadim Zhytnikov        Richard Zippel         Evelyn Zoernack
+Bruno Zuercher         Dan Zwillinger
+  &lt;/pre&gt;
+  &lt;/p&gt;
+ 
+
+ &lt;/div&gt;
+&lt;/body&gt;
+&lt;/html&gt;
+
diff --git a/src/axiom-website/currentstate.html b/src/axiom-website/currentstate.html
new file mode 100644
index 0000000..cca960f
--- /dev/null
+++ b/src/axiom-website/currentstate.html
@@ -0,0 +1,811 @@
+&lt;HTML&gt;
+ &lt;HEAD&gt;
+  &lt;TITLE&gt;
+   Axiom Website
+  &lt;/TITLE&gt;
+ &lt;/HEAD&gt;
+ &lt;body bgcolor="#ffff66"&gt;
+   &lt;div id="head" align="center"&gt; 
+    &lt;a href="http://savannah.nongnu.org/projects/axiom/"&gt;
+     &lt;img src="axiom.png" border="0" alt="Axiom"&gt;
+    &lt;/a&gt;
+    &lt;br&gt;
+    &lt;font size=200%&gt;
+     The Scientific Computation System
+    &lt;/font&gt;
+   &lt;/div&gt;
+   &lt;div align="center"&gt;
+    [
+     &lt;a href="../index.html" title="Home"&gt;
+      Home
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="screenshots.html" title="Screen Shots"&gt;
+      Screenshots
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="faq.html" title="FAQ"&gt;
+      FAQ
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="download.html" title="Download"&gt;
+      Download
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="documentation.html" title="Documentation"&gt;
+      Documentation
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="currentstate.html" title="Current State"&gt;
+      Current State
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="community.html" title="Community"&gt;
+      Community
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="http://arch.axiom-developer.org/index.html" title="Developers"&gt;
+      Developers
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="patches.html" title="Patches"&gt;
+      Patches
+     &lt;/a&gt;
+    ]
+   &lt;/div&gt;
+   &lt;div align="center"&gt;
+    [
+     &lt;a href="bookvol10.2abb.html" title="Abbreviation Graph"&gt;
+      Abbreviation Graph
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="bookvol10.2full.html" title="Full Name Graph"&gt;
+      Full Name Graph
+     &lt;/a&gt;
+    ]
+   &lt;/div&gt;
+  &lt;br&gt;
+  &lt;hr&gt;
+  &lt;br&gt;
+   This information was last updated on July 23, 2008
+  &lt;br&gt;
+  &lt;PRE&gt;
+
+Axiom was released on March 25, 2008. You can view the 
+&lt;a href="releasenotes.html"&gt;release notes&lt;/a&gt; for each release.
+
+This TODO list represents abbreviated notes to categorize the work directions
+and note progress (completed items have a - prefix). Items are expanded as
+the work thread moves into that subject. There is no priority and no schedule.
+The ratio is (# of completed task per section)/(total completed tasks) and
+is a measure of the ratio of effort between areas. Completed tasks are marked
+with a - in column 1 (+ indicates changes since last update)
+
+There are approximately 285 tasks listed. These tasks are broken into the
+following groups:
+
+ Pristine sources is the main thread of developing Axiom
+ Splits are pieces of work to give away
+ Joins are pieces of work to incorporate or cooperate with
+ New Development is a list of ideas for new directions or needed work
+ Research is a list of ideas that need investigation
+ Community is a list of supporting tasks for the algebra community
+
+**************************************************************************
+PRISTINE SOURCES 
+ Motivation: create a new source tree and slowly migrate original NAG/IBM
+             sources into the tree. This will ensure that only things that
+             are properly required, used and tested get shipped. Further
+             ensure that everything exists under make/cvs control.
+
+ All of the tasks have been completed except
+
+  recover numerics
+  port to Windows
+
+**************************************************************************
+SPLITS 
+ Motivation: several pieces of the system have nothing to do with algebra
+             and either have old technology that needs to be rewritten or
+             common technology that ought to be contributed to other efforts.
+
+
+ FIREFOX BROWSER
+  Motivation: We need a portable, useful front end to Axiom that combines
+  the separate pieces of the Axiom command line, hyperdoc, and graphics
+  into a unified way of working with pamphlet files.
+
+ * Rewrite Hyperdoc Pages
+    This task is to extract the information from the current
+    hyperdoc system and make it available in the browser.
+      rewrite all pages using AJAX
+      add additional pages
+      rearrange the order for clarity
+      dynamically create category/domain/packages pages
+      dynamically create operations pages 
+      allow ASQ style lookups
+
+ * Integrate Graphics
+    This task is to extract the functionality from the graphics
+    and make it work within the browser.
++     collect the graphics into a book volume
+      document the graphics
+      refactor graphics to extract X11 API
+      make API compatible version of graphics for CANVAS element
+      enable dynamic drawing into CANVAS
+      enable popup page with CANVAS and control menu elements
+ 
+ * Write Notebook Front End
+    This task is to make a new, browser-based front end to Axiom.
+      create new API domain to expose history
+      make new context sensitive menus
+      make card/div/Record objects 
+      enable create/destroy/rearrange/import/export of card decks
+      unify card decks and pamphlets
+
+
+ AXIOM TEST SUITE-&gt;COMMON TEST SUITE
+  Motivation: Algebra needs a hand-verified test suite which ought to be
+              shared with other computer algebra systems. Needs a common
+              syntax, could be a driver for previous item.
+   rewrite regression test files with results from MMA, Maple, Maxima
+   reformat files to use a common theory/practice format
+   organize files into a useful taxonomy
+
+
+**************************************************************************
+JOINS 
+ Motivation: there are several CA systems with very interesting features
+             and/or algebra. Axiom needs to import these ideas or find
+             ways to cooperate with these projects.
+
+
+
+
+ GAP-&gt;AXIOM
+  Motivation: GAP has much stronger facilities for manipulating groups.
+              Axiom can do group manipulation but GAP needs to be studied.
+
+
+
+
+ OCTAVE-&gt;AXIOM
+  Motivation: Octave has the capability to be a replacement for the NAG
+              numeric libraries. Either an interface has to be retargetted
+              or the code has to be ported to Aldor or Lisp.
+-  Test rewriting Fortran code into Aldor
++  BLAS converted to pamphlet form
+   BLAS integrated into Axiom
+
+
+
+
+
+ MAGNUS-&gt;AXIOM
+  Motivation: Magnus is strong in infinite group theory. Like GAP it needs
+              to be studied and imported.
+-  Discussion and proposal for work in this area with CCNY
++  Magnus is being rebuilt as a literate program and will eventually be
++  merged with Axiom
+   Rebuild Magnus as a literate program
+   Extract and categorize the magnus algorithms
+   Provide Axiom implementations of the algorithms
+
+
+
+
+
+ ASTRONOMER-&gt;AXIOM
+  Motivation: Internal representation of polynomials that can be scaled to
+              ~250k terms needs to be imported.
+
+This task is dead.
+
+
+
+
+ COMBINAT-&gt;AXIOM
+  Motivation: External basis representation of large polynomials needs to
+              be imported.
+
+This task is dead.
+
+
+
+
+
+ MATHEMATICA-&gt;AXIOM
+  Motivation: Workbooks need to be imported.
+
+This task has changed. Rather than focus on the mathematica workbooks
+we plan to create and use the new Axiom firefox browser as a notebook
+front end similar to Sage.
+
+
+
+
+**************************************************************************
+NEW DEVELOPMENT 
+
+
+
+
+ EXTERNALS DOCUMENTATION
+  Motivation: in order to allow users to use the system we need to collect
+              and organize the documentation and help facilities.
+- The Axiom book was rewritten and is now available as part of the normal
+- distribution. 
+- The Axiom tutorial book was published at Lulu.com
+- The firefox browser was created
++ Additional pages from hyperdoc need firefox rewrites
+  The .dvi files need to be accessible in the firefox hyperdoc
++ )help files are needed for more domains
++ )display operation needs examples for operations 
+
+
+
+ INTERNALS DOCUMENTATION
+  Motivation: in order to allow multiple developers to work on the system
+              the structure of the system needs to be explained.
+-  Directory structure
+-   document shell script
+-   Makefile structure
+-   document how the makefile tree works
+-  Lisp structure
+-   src structure
+-    algebra 
+-   boot
+-    clef
+-    doc
+-    etc
+-   graph
+-    htex
+-    hyper
+-    include
+-    input
+-    interp
+-   install
+-   lib
+-    lsp
+-   noweb
+-    paste
+-    sman
+
+  Motivation: restructure Axiom into literate book volumes
+- Volume 0: Jenks book
+- Volume 1: Tutorial
+  Volume 2: User's Guide
+  Volume 3: Programmer's Guide
++ Volume 4: Developer's Guide
++ Volume 5: Interpreter
+  Volume 6: Axiom Command
++ Volume 7: Hyperdoc
++ Volume 8: Graphics
+  Volume 9: Compiler
+  Volume 10: Algebra
+  Volume 11: Firefox Hyperdoc
+
+
+
+ ALGEGRA DOCUMENTATION
+  LITERATE PROGRAMMING 
+   Motivation: algebra code should be able to include research papers
+               and documentation of design choices, space, time and
+               complexity. Researchers should be encouraged to write
+               literate programs. Literate programs should be easily
+               turned into book sections or chapters. 
+-   seek appropriate tools
+-     tangle, weave
+-     cweb
+-     noweb
+-   seek feedback
+-   create preliminary setup
+-   create example pamphlet (DHMATRIX)
+-     define doc structure
+-     prototype
+-   modify/rewrite noweb
+-     make undefined chunks transparent
+-     example generation
+      test case generation
+-   create booklet example (MATRIX)
++     define booklet structure
++     prototype
+-   integrate into make
+-   integrate into obj/mnt
++   integrate example (DHMATRIX2) into make
++   integrate book example into make
+    write pamphlets for type hierarchy
+      write SetCategory pamphlet
+      integrate into make
+      integrate into test
+    write pamphlets for data structure hierarchy
+      write aggregate pamphlet
+      integrate into make
+      integrate into test
+    create example pamphlet from scratch (PRIMES is in P algorithm)
+      recreate paper in tex
+      write algorithm
+      merge into build
++   create example pamphlet from planarity paper
+      recreate paper in tex
+      write algorithm
+      merge into build
+    create complex pamphlet (Barry Trager's Integration thesis)
+-     recreate thesis in tex
+      factor thesis into booklets
+      factor booklets into pamphlets
+
+
+
+ SINGLE-STEPPING
+  Motivation: Users of algebra should be able to step thru algorithms at
+              some "appropriate" level of detail. Hard to do as most 
+              algebra algorithms differ from hand methods.
+
+
+
+ LIBRARY CLEANUP
+  Motivation: FullyExplicitRingOver needs a better theory basis, etc.
+
+
+
+
+ GCL BUILD
+  Motivation: run on a popular common lisp
+-  Download GCL
+-  Build image in /spad/lsp/gcl
+-  Build Axiom on image
+
+
+
+ CMUCL BUILD
+  Motivation: run on a popular common lisp
+   Download CMUCL sources
+   Build image in /spad/lsp/cmucl
+   Build Axiom on image
+
+
+
+ CCL BUILD
+  Motivation: run on a popular common lisp
+-  Get final CCL sources from Arthur
+-  Build image in /spad/lsp/ccl
+-  Build Axiom on image
+
+This effort is dead.
+              
+**************************************************************************
+RESEARCH 
+
+ AXIOM JOURNAL
+  Motivation: Provide a motivation and place to publish Axiom algorithms
+              in a literate programming style. Journal development will
+              require refereed papers.
+-  Discuss with Community
+   Contact TOMS at ACM
+   Create License for pamphlet submission
+-    This is likely to be the creative commons license
+-  Create Prototype online site (www.nongnu.org/axiom/Journal)
+     Create Journal directory
+     Structure pages similar to Journal
+     Integrate into CVS
+     Allow dynamic referee lists
+   Research online/offline references to Axiom in literature
+   Create citations bibliography
+   Get permission to mirror/host published papers
+-  Give presentation to Univ of Pisa re: literate journal
+-  Worked with ACM to provide electronic ISSAC journal
+
+
+
+ 
++CRYSTAL
++ Motivation: Soon it will be possible to have all prior published math
++             online and locally available. We need to design and build
++             a user interface model that supports researchers in math
++             by providing semantic searches, multi-faceted problem views,
++             real-time problem classification, and an "intensional stance"
++             assistant user interface.
++ Define model of interaction
+  Prototype semantic markup
+  Prototype semantic classification with KROPS
+  Prototype facet viewer
+  Prototype classifier
+  Prototype intensional stance assisant
+
+
+
+
+ COMPLEXITY
+  Motivation: Axiom is fully layered. Research results in the lowest 
+              layers can be leveraged to generate results in higher layers.
+              Use Axiom against itself to create towers of complexity.
+              Insist on complexity results in documentation.
+
+
+
+
+ TEXTBOOK OBJECT
+  Motivation: Axiom interpreter objects don't have a standard name for
+              their parts and do not have a manipulation language for
+              rewriting parts. 
+              idea: have a "tree" primitive for each type
+              idea: define a graph of tree to tree maps that label each 
+                    edge with the transformation applied to the subtree
+
+
+
+
+ TEXTBOOK CONTEXT
+  Motivation: Equations are ambiguous when standing alone. Textbooks provide
+              context in the surrounding text. This is not adequately 
+              captured by the type system. A new approach to this issue
+              is required.
+
+
+
+
+ OPEN PROBLEMS LIST
+  Motivation: Magnus maintains a community agreed-upon list of "open problems"
+              This is an excellent source of PhD work and a good focus
+              mechanism. Create and maintain this.
+
+
+
+
+ PROVISOS
+  Motivation: Assume is a weak, global mechanism for capturing provisos.
+              A new proviso object needs to exist that wraps existing 
+              objects, provides scope for provisos and provides an
+              algebra of provisos based on type (arithmetic, boolean,
+              typed, etc).
+-  Review the literature to extract proviso forms.
+-  Classify proviso forms.
+-  Draft research paper
+   Develop an arithmetic of proviso forms.
+
+
+
+
+ INTERVAL ARITHMETIC
+  Motivation: This is a fundamentally stronger way to represent uncertainty
+              in results. It needs to be lifted from the numeric domain and
+              defined symbolically. It needs to be integrated into the
+              proviso algebra.
+
+   Document interval.as algebra domain
+
+
+
+
++INDEFINITES
++ Motivation: Research needs to be done on how to represent and compute
++             with indefinite objects from domains. An indefinite object
++             has a fixed type (such as Integer) but a non-specified value.
++             Thus it is possible to say that x+1 is of type Indefinite Integer
++             since 1 is an Integer and x is an Indefinite Integer.
++ Submit NSF grant proposal (awarded)
++ Conduct research on indefinites
+   Construct domain examples
+
+
+
+
++WEB ACCESS TO AXIOM
++ Motivation: There are several research efforts to make computer algebra
++             available on the web. Axiom needs to participate and lead.
++ Work with ORCCA
+   rebuild OPENMATH support
+   update to latest OPENMATH standards
++ Work with MathAction
++  integrate automatically running Axiom into web pages
+
+
+
+
+ DOMAIN INTEGRATION
+  Motivation: Axiom would be strongly useful in domains such as robotics.
+              Areas such as backsolving of joint position can be fruitful
+              areas of research. Deep integration in domains (DSP, Vision)
+              needs to be pushed.
++ The Doyen effort is the current direction for this. Axiom will integrate
++ with the rest of the sciences thru this effort.
+
+
+
+
+ SEMI-ANALYTIC SOLUTIONS
+  Motivation: Axiom could provide parallel tasks that would continuously
+              try to extract analytic solutions from incoming data. For
+              example, in vision finding analytic edges to feed to a
+              parallel recognizer algorithm.
+
+
+
+
+ GAMES INTEGRATION
+  Motivation: Axiom can be used to model games in novel ways. For example,
+              flight games with pursuit curves that live in a non-uniform
+              space (planet gravity, changing density across air/water).
+
+
+
+
+ CONSTRAINED MODELS
+  Motivation: Force motion that always remains analytic. Thus the final
+              solution is known to be analytic. For example, constrain
+              intersecting pipes to known boundary conditions. Computational
+              geometry seems the most fruitful area.
+
+
+
+
+ VALIDATION and VERIFICATION
+  Motivation: Algebra systems need a high level of confidence in the results.
+              Hand checking of the results is difficult and expensive. 
+              Automatically substituting results into the original equations
+              could raise confidence. Auditing of boundaries of algebra
+              algorithms. Precondition/Postcondition results for domains.
+              Audited test suites used for regression testing.
+
+
+
+
+ ALGEBRA MANIPULATION LANGUAGE
+  Motivation: Algebra systems have interpreters that embody a lot of 
+              knowledge about the actions available to manipulate equations.
+              This knowledge needs a language. The language needs to be
+              crafted so that it can be added to domains and applied
+              in symbolic form by a generalized simplification routine.
+   Review the literature to extract manipulation sentences.
+   Classify manipulation forms.
+   Draft manipulation paper
+
+
+
+
+ BOYER-MOORE THEOREM PROVER INTEGRATION
+  Motivation: Computational logic is a branch of computer mathematics
+              that is not currently available in Axiom. The Boyer-Moore
+              theorem prover, written in common lisp, provides a good
+              general purpose platform to study the interaction of the
+              theorem proving systems with Axiom
+-  Contact Boyer &amp; Moore
+-  Contact Chandy &amp; Misra
+-  Download ACL2
+   Build ACL2
+   Invoke ACL2 from Axiom
+   Integrate ACL2 into Axiom
+     Use Dijkstra's methods against SetCategory
+   Draft research paper
+
+
+
+
+ MetaPRL THEOREM PROVER Application
+  Motivation: MetaPRL is a Higher-order Logic proof system that is well
+              suited to proving Axiom-style languages. The proofs from
+              this system would give higher confidence levels in the
+              correctness of Axiom's algorithms.
+-  Contact Artimov 
+-   Review nuprl
+-   Review MetaPRL
+-   Construct trial example
+-     Collect all sorting routines in Axiom
+      Model the required subset of Axiom's language 
+      Construct a proof of the sort algorithms
+
+**************************************************************************
+COMMUNITY 
+ 
+ COLLECT AXIOM ALGEBRA DEVELOPERS
+  Motivation: Work in Axiom has continued over the years but has not
+              been integrated. Find this work and integrate it.
+ 
+ COLLECT AXIOM KNOWN BUGS
++ Motivation: Axiom has known bugs. Create a known bug list.
++   Integrate fixes for catdef
++   Integrate fixes for pleqn
+ 
+ TRAIN AXIOM INTERNAL DEVELOPERS
+  Motivation: Many of the subtasks listed above can be split off, done in
+              parallel and lead independently. Find people who are interested,
+              especially external projects (eg work with Gnuplot to enhance
+              it with Axiom's abilities).
+-  Set up cvs on Tenkan
+-  Set up accounts for developers
+-  Import current Axiom tree into CVS
+-  Try system builds on developers machines
+-  Exchange code via CVS
+-  Expand platforms
+-    Cygwin
+-    Mingw
+-    FreeBSD
+
+ SUPPORT FRENCH WORK
+  Motivation: An organized community will help focus new Axiom development.
+-  Lyon conference presentation
+-  Set up OSCAS group
+-  Announce OSCAS group
+-  Moderate OSCAS group
+  This is a dead branch of effort.
+
+ SET UP GOLD REPOSITORIES
+  Motivation: Community needs all the usual tools enabled like bug list,
+              mailing list, cvs, etc.
+- savannah.nongnu.org (CVS)
+- sourceforge.net (CVS)
+- arch.axiom-developer.org (ARCH)
++ github (GIT)
+
+ SET UP SILVER REPOSITORIES
+  Motivation: Expose leading edge work
+- sourceforge.net (SVN)
+- git.axiom-developer.org (GIT)
+  savannah.nongnu.org (GIT)
+
+
+ ROSETTA
+  Motivation: the community needs to see and use the many open source
+              computer algebra systems so they can compare and contrast
+              the various systems. This will help focus the issues of
+              what is currently possible and how hard it is to develop
+              a large, general purpose system. Also useful for teaching.
+-  Build Rosetta CD
+-   collect open source systems
+-   build them on a common subtree
+-   write Rosetta document
+-   write them to CD such that they can be run with installation
+-   distribute CD to conferences, teachers, etc
++  Update Rosetta CD
++   add Axiom
++   fix mistakes
++   add paragraph per table
++   update Rosetta document for Giac
++   update Rosetta document for DoCon
++   update Rosetta document for Macsyma
++   write Meta-Rosetta document to expound on differences
++   integrate systems with browser front-end
++   build broken systems
++    feed back diffs to original projects
++   add new systems
++   find new customers
++ The Rosetta effort is joining with the Quantian effort and the result
++ will be known as Doyen. This work is in process.
+  Build Doyen
+   Create live CD
+   Create standalone MathAction
+   Integrate Axiom into standalone MathAction
+   Build coordination tools between daughter Doyen and mother Doyen site
+
+ AXIOM WEBSITE
+  Motivation: maintain a website so that progress on making
+              Axiom open-source is made visible and the community has
+              a place to discuss issues and ideas (not necessarily
+              related to Axiom but to the community in general).
+-  create website
+-  build interest list
+-  create and maintain update schedule
+
+
+ EXPLORE FUNDING MODELS
+  Motivation: Find creative ways to pay people who work on Axiom. Everybody
+              wants free developers but paid work will motivate development.
+   Academic degree (BA in open source? BA in computer algebra?)
+- Developed an open source lab at City College of NY. Lab is up and running
+- Lab is part of the capstone projects for CS undergrads
+   Grant model by line of code
+-   contact IBM
+-   contact SUN
++   contact NSF
+    contact INRIA
+    contact DARPA 
++   explore other contacts
+   Award Model 
+-   Schelter Award
+-    contact UTexas
+-    contact FSF
+     develop plan
+      define award type and frequency
+      find sponsor organization
+-       Efraim Armendariz &lt;efraim@mail.ma.utexas.edu&gt;
+-       Brad Kuhn &lt;bkuhn@fsf.org&gt;
+      find volunteers to judge award
+    Oscars/Emmy/Tony award model for CA at ISSAC?
+-   Jenks Award
+   Pay for support model
++  Pay for travel model
++   Contact Google
++   Contact IBM
++   Contact SUN
++   Contact Sage
++   Contact NSF  
+
+  &lt;/PRE&gt;
+&lt;hr/&gt;
+Completed, dead, or abandoned tasks
+  &lt;PRE&gt;
+ HYPERTEX-&gt;BROWSER/TEX
+  Motivation: hypertex was pre-browser technology. It should be rewritten
+              to fit into today's technology. At least HTML, possibly XML.
+- This work has forked into two paths. The first path is to recreate the
+- browser from the hypertex sources. The second path is to rebuild the
+- whole effort into a standard browser-based tool. Ultimately this will
+- probably get merged with the Doyen science platform effort 
+- Recreate Hypertex
+- Create standard browser
+-   create standalone browser version
+-   merge into Doyen
+
+
+ ASQ-&gt;JAVADOC/DOC++
+  Motivation: asq is pre-javadoc. It should be rewritten to fit into the
+              browser/tex new world of docs
+- The ASQ tool needs to get redone so that standard html pages get built
+- during system build and made available. They should have a javadoc-like
+- look and feel.
+- Create ASQ-HTML page generator
+
+This task is complete.
+
+
+
+
+ PLOT-&gt;GNUPLOT
+  Motivation: plot has nothing to do with algebra but has some nice features
+              such as data feedback from graph manipulation. These facilities
+              should be moved to Gnuplot and the plot function retargetted.
+  The graphics have been rebuilt and currently work. The graphics can only
+  be run from a file at the moment because the connecting process, called
+  sman, which manages all of the axiom processes is not yet working again.
+  Rebuild sman
+  Connect sman to graphics
+  Connect graphics to gnuplot
+
+This task was abandoned.
+
+
+
+
+The 2D I/O direction has changed. The current plan is to use the
+firefox browser as a universal front-end to Axiom.
+
+ READ-EVAL-PRINT-&gt;TeXmacs
+  Motivation: the time has come for 2d input. TeXmacs provides this. There
+              needs to be a much tighter integration of TeXmacs and Axiom.
+   Connect to TeXmacs community
+-  Build TeXmacs on Linux
+-  Build TexMacs on Cygwin
+   Build TexMacs on Windows
+   pick up the notebook interface ideas from Sage
+
+
+ AXIOM I/O-&gt;COMMON SYNTAX
+  Motivation: Rosetta should not exist. Algebra syntax should standardize.
+              Existing committee work needs feedback from Axiom.
+
+The Rosetta effort is complete.
+
+  &lt;/PRE&gt;
+ &lt;/BODY&gt;
+&lt;/HTML&gt;
+
+
diff --git a/src/axiom-website/developers.html b/src/axiom-website/developers.html
new file mode 100644
index 0000000..baaae86
--- /dev/null
+++ b/src/axiom-website/developers.html
@@ -0,0 +1,263 @@
+&lt;html&gt;
+ &lt;head&gt;
+  &lt;title&gt;
+   Axiom Computer Algebra System
+  &lt;/title&gt;
+ &lt;/head&gt;
+ &lt;body bgcolor="#ffff66"&gt;
+   &lt;div id="head" align="center"&gt; 
+    &lt;a href="http://savannah.nongnu.org/projects/axiom/"&gt;
+     &lt;img src="axiom.png" border="0" alt="Axiom"&gt;
+    &lt;/a&gt;
+    &lt;br&gt;
+    &lt;font size=200%&gt;
+     The Scientific Computation System
+    &lt;/font&gt;
+   &lt;/div&gt;
+   &lt;div align="center"&gt;
+    [
+     &lt;a href="../index.html" title="Home"&gt;
+      Home
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="screenshots.html" title="Screen Shots"&gt;
+      Screenshots
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="faq.html" title="FAQ"&gt;
+      FAQ
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="download.html" title="Download"&gt;
+      Download
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="documentation.html" title="Documentation"&gt;
+      Documentation
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="currentstate.html" title="Current State"&gt;
+      Current State
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="community.html" title="Community"&gt;
+      Community
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="developers.html" title="Developers"&gt;
+      Developers
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="patches.html" title="Patches"&gt;
+      Patches
+     &lt;/a&gt;
+    ]
+   &lt;/div&gt;
+   &lt;div align="center"&gt;
+    [
+     &lt;a href="bookvol10.2abb.html" title="Abbreviation Graph"&gt;
+      Abbreviation Graph
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="bookvol10.2full.html" title="Full Name Graph"&gt;
+      Full Name Graph
+     &lt;/a&gt;
+    ]
+   &lt;/div&gt;
+  &lt;br&gt;
+  &lt;hr&gt;
+&lt;div id="body"&gt;
+  &lt;h1&gt;Axiom Development&lt;/h1&gt;
+
+Axiom development is now hosted on an Arch server 
+running on axiom.developer.org.
+&lt;br&gt;
+&lt;br&gt;
+There is an irc channel where developers can find other developers. It is:
+&lt;br&gt;
+server: irc.freenode.net 
+&lt;br&gt;
+channel:#axiom-developer
+&lt;br&gt;
+&lt;br&gt;
+You only need to do these setup steps once.
+In order to access the arch sources you need to let arch know who
+you are with the command:
+&lt;br&gt;
+&lt;pre&gt;
+  tla my-id "First Last &amp;lt;addy@host.com&amp;gt;"
+&lt;/pre&gt;
+&lt;br&gt;
+Next you need to register an archive:
+&lt;br&gt;
+&lt;pre&gt;
+  tla register-archive arch@axiom-developer.org--axiom http://axiom-developer.org/archive/axiom
+&lt;/pre&gt;
+&lt;br&gt;
+Then set up a default archive
+&lt;br&gt;
+&lt;pre&gt;
+  tla my-default-archive arch@axiom-developer.org--axiom
+&lt;/pre&gt;
+&lt;br&gt;
+&lt;hr&gt;
+In order to get the latest source for the Axiom main line type:
+&lt;br&gt;
+&lt;pre&gt;
+  tla get axiom--main--1
+&lt;/pre&gt;
+&lt;br&gt;
+&lt;hr&gt;
+There are several branches available. Each branch is used to develop
+a particular idea and get a stable, working version before merging
+it back to the main line. The currently available branches are:
+&lt;br&gt;
+&lt;pre&gt;
+axiom--main--1       the main development branch
+     this branch will be mirrored to the CVS on savannah when it
+     is stable and tested. 
+     Currently in &lt;a href="devel.html"&gt;step 4&lt;/a&gt; of development.
+
+axiom--hyperdoc--1   development of hyperdoc
+     NOTE: This branch has been merged and is now dead.
+     this branch contains code for building hyperdoc. 
+
+axiom--BSD--1        port to BSD
+     work with Mark Murray &amp;lt;mark at grondar.org&amp;gt;
+     Currently in &lt;a href="devel.html"&gt;step 1&lt;/a&gt; of development.
+
+axiom--MACOSX--1     port to MACOSX
+     work with Chuck Miller &amp;lt;cfm at ms.unimelb.edu.au&amp;gt;
+     Currently in &lt;a href="devel.html"&gt;step 1&lt;/a&gt; of development.
+
+book--main--1        axiom book
+     work with community to clean up the book for printing
+     Currently in &lt;a href="devel.html"&gt;step 1&lt;/a&gt; of development.
+
+axiom--solaris--1    port to solaris
+     work with Kostas Oikonomou &amp;lt;ko at research.att.com&amp;gt;
+     Currently in &lt;a href="devel.html"&gt;step 1&lt;/a&gt; of development.
+
+axiom--graphics--1   finish graphics integration
+     NOTE: This branch has been merged and is now dead.
+     work on integration, testing of graphics.
+
+axiom--windows--1    port to windows
+     work with &amp;lt; Mike Thomas &amp;lt;mike.thomas at brisbane.paradigmgeo.com&amp;gt;
+     Currently in &lt;a href="devel.html"&gt;step 1&lt;/a&gt; of development.
+
+axiom--language--1   explore axiom language modifications
+     work with Stephen Wilson &amp;lt;wilsons at multiboard.com&amp;gt;
+     Currently in &lt;a href="devel.html"&gt;step 1&lt;/a&gt; of development.
+
+axiom--sbcl--1       port axiom to steel bank common lisp
+     work with Tim Daly Jr. &amp;lt;tim at tenkan.org&amp;gt; and
+               Nate Daly &amp;lt;nate at tenkan.org&amp;gt;
+     Currently in &lt;a href="devel.html"&gt;step 1&lt;/a&gt; of development.
+
+zlc--main--1        add a zero learning curve interface to axiom
+     work with Jinzhong Niu &amp;lt;jniu at gc.cuny.edu&amp;gt;
+               Xaiowei Xu &amp;lt;xuxw at yahoo.com&amp;gt;
+     Currently in &lt;a href="devel.html"&gt;step 1&lt;/a&gt; of development.
+
+axiom--algebra--1    prototype algebra code
+     Currently in &lt;a href="devel.html"&gt;step 1&lt;/a&gt; of development.
+
+axiom--GUI--1    portable GUI interface
+     work with Kai Kaminski (kai.kaminski@gmail.com)
+     Currently in &lt;a href="devel.html"&gt;step 1&lt;/a&gt; of development.
+
+&lt;/pre&gt;
+&lt;br&gt;
+&lt;hr&gt;
+If you need write access to the archive you need to follow these steps:
+&lt;br&gt;
+Create a key by typing:
+&lt;br&gt;
+&lt;pre&gt;
+ssh-keygen -t dsa
+&lt;/pre&gt;
+This will create a file called .ssh/id_dsa.pub. You need to send the
+contents of this file to Tim Daly &amp;lt;daly@idsi.net&amp;gt; 
+so your interactions can be enabled.
+&lt;br&gt;
+In order to access the arch sources you need to let arch know who
+you are with the command:
+&lt;br&gt;
+&lt;pre&gt;
+  tla my-id "First Last &amp;lt;addy@host.com&amp;gt;"
+&lt;/pre&gt;
+&lt;br&gt;
+Next you need to register an archive:
+&lt;br&gt;
+&lt;pre&gt;
+  tla register-archive arch@axiom-developer.org--axiom sftp://arch@axiom-developer.org/home/arch/archive/axiom
+&lt;/pre&gt;
+Notice that you're using sftp rather than http. The sftp function
+uses the secure keys to enable ftp access to the sources. The http
+function is read-only.
+&lt;br&gt;
+Then set up a default archive
+&lt;br&gt;
+&lt;pre&gt;
+  tla my-default-archive arch@axiom-developer.org--axiom
+&lt;/pre&gt;
+&lt;br&gt;
+&lt;hr&gt;
+In order to get the latest source for the Axiom main line type:
+&lt;br&gt;
+&lt;pre&gt;
+  tla get axiom--main--1
+&lt;/pre&gt;
+&lt;br&gt;
+Now you can change the sources. Once you've made changes they need
+to be sent back (commit) to the host. In order to do the commit 
+function in tla you need a log file that summarizes the changes.
+You can create and edit the log file with:
+&lt;br&gt;
+&lt;pre&gt;
+  emacs -nw `tla make-log`
+&lt;/pre&gt;
+&lt;br&gt;
+or for the vi fans
+&lt;pre&gt;
+  vi `tla make-log`
+&lt;/pre&gt;
+Finally you commit the changes with:
+&lt;br&gt;
+&lt;pre&gt;
+  tla commit
+&lt;/pre&gt;
+&lt;hr&gt;
+&lt;br&gt;
+The official website for arch is
+&lt;a href="http://www.gnu.org/software/gnu-arch"&gt;here&lt;/a&gt;
+&lt;br&gt;
+More information on arch is available 
+&lt;a href="http://rubick.com:8002/openacs/arch"&gt;here&lt;/a&gt;
+ &lt;/div&gt;
+ &lt;a href="http://sourceforge.net"&gt;
+  &lt;img src="http://sourceforge.net/sflogo.php?group_id=48359&amp;amp;type=1" 
+       width="88" height="31" border="0" alt="SourceForge.net Logo" /&gt;
+ &lt;/a&gt;
+&lt;/body&gt;
+&lt;/html&gt;
+
diff --git a/src/axiom-website/dhmatrix.spad.pdf b/src/axiom-website/dhmatrix.spad.pdf
new file mode 100644
index 0000000..5fecda9
Binary files /dev/null and b/src/axiom-website/dhmatrix.spad.pdf differ
diff --git a/src/axiom-website/diff.html b/src/axiom-website/diff.html
new file mode 100644
index 0000000..5228d8a
--- /dev/null
+++ b/src/axiom-website/diff.html
@@ -0,0 +1,78 @@
+&lt;html&gt;
+ &lt;head&gt;
+  &lt;title&gt;
+   Submitting patch files
+  &lt;/title&gt;
+ &lt;/head&gt;
+ &lt;body&gt;
+&lt;br&gt;
+&lt;pre&gt;
+In general a patch file is of the form
+
+cd the.dir
+diff -Naur file.pamphlet file.pamphlet.new &gt;the.dir.file.pamphlet.patch
+
+this has several features:
+  * it tells me where the patch is being applied
+  * the Naur options give me context
+  * i can see the impact of a change to multiple files
+
+I read the patches before applying them so be sure to document the
+reasons for the change in the pamphlet file. It may seem trivial
+but remember that I didn't do the initial analysis so I, and others,
+will have to understand after the fact.
+
+In most cases in a pamphlet file if you're changing a few lines
+of code or a whole function it should be documented thus:
+
+
+...
+
+(defun foo ()
+  (list
+    "this is ok code"
+    "this is broken code"
+    "this is also broken"
+    "this is ok"
+  )
+)
+ 
+turns into
+
+\subsection{foo list fix}
+This code used to read:
+\begin{verbatim}
+    "this is broken code"
+    "this is also broken"
+\end{verbatim}
+but clearly the elements of the list are wrong. We are going to
+print this list for the user so we don't want them to know anything
+is broken. Thus we have wonderful new code that will inspire confidence.
+This list is printed with the [[printlist]] function.
+&lt;&lt;foo list fix&gt;&gt;=
+    "this is great code"
+    "this inspires confidence"
+@
+
+
+...
+
+(defun foo ()
+  (list
+    "this is ok code"
+&lt;&lt;foo list fix&gt;&gt;
+    "this is ok"
+  )
+)
+
+and, yes, I do know that this is tedious.
+
+In general, it is also useful to update the pamphlet files with 
+documentation-only changes as you understand what a block of code
+is intended to do. Most of this information has been lost to history
+and the world can leverage your efforts at understanding if you take
+the time to document it. In many ways this is as important as fixing
+the code.
+&lt;/pre&gt;
+&lt;/body&gt;
+&lt;/html&gt;
diff --git a/src/axiom-website/documentation.html b/src/axiom-website/documentation.html
new file mode 100644
index 0000000..a31b83c
--- /dev/null
+++ b/src/axiom-website/documentation.html
@@ -0,0 +1,257 @@
+&lt;html&gt;
+ &lt;head&gt;
+  &lt;title&gt;
+   Axiom Computer Algebra System
+  &lt;/title&gt;
+ &lt;/head&gt;
+ &lt;body bgcolor="#ffff66"&gt;
+   &lt;div id="head" align="center"&gt; 
+    &lt;a href="http://savannah.nongnu.org/projects/axiom/"&gt;
+     &lt;img src="axiom.png" border="0" alt="Axiom"&gt;
+    &lt;/a&gt;
+    &lt;br&gt;
+    &lt;font size=200%&gt;
+     The Scientific Computation System
+    &lt;/font&gt;
+   &lt;/div&gt;
+   &lt;div align="center"&gt;
+    [
+     &lt;a href="../index.html" title="Home"&gt;
+      Home
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="screenshots.html" title="Screen Shots"&gt;
+      Screenshots
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="faq.html" title="FAQ"&gt;
+      FAQ
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="download.html" title="Download"&gt;
+      Download
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="documentation.html" title="Documentation"&gt;
+      Documentation
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="currentstate.html" title="Current State"&gt;
+      Current State
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="community.html" title="Community"&gt;
+      Community
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="developers.html" title="Developers"&gt;
+      Developers
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="patches.html" title="Patches"&gt;
+      Patches
+     &lt;/a&gt;
+    ]
+   &lt;/div&gt;
+   &lt;div align="center"&gt;
+    [
+     &lt;a href="bookvol10.2abb.html" title="Abbreviation Graph"&gt;
+      Abbreviation Graph
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="bookvol10.2full.html" title="Full Name Graph"&gt;
+      Full Name Graph
+     &lt;/a&gt;
+    ]
+   &lt;/div&gt;
+  &lt;br&gt;
+  &lt;hr&gt;
+&lt;div id="body"&gt;
+  &lt;h1&gt; Why Literate Programming?&lt;/h1&gt;
+
+Once a program has been developed and the developers have moved
+on to other tasks it needs to be maintained. The fundamental problem
+is that if you modify code you didn't write, you don't see the big
+picture and you don't understand the reasons why the code is written
+the way it is. Thus changing code without a larger context is almost
+always going to introduce new bugs.
+&lt;/p&gt;
+&lt;p&gt;
+The only way to correctly change code is to deeply understand the
+implications of the change. This requires a deep understanding of
+the code and an awareness of the big picture. Yet the "why" of code
+is rarely ever written down in standard programming practice.
+The goal is only to elaborate the "how" so the machine can perform
+the task. The programmer communicates with the machine.
+&lt;/p&gt;
+&lt;p&gt;
+Literate programming, as used in Axiom, is an attempt to communicate
+with other users, developers, and researchers in addition to the
+machine. The goal is to have the program read like a story so that
+others can understand the rational, the theory, the choices, the
+implications, and the implementation context as well as the "how".
+&lt;/p&gt;
+&lt;p&gt;
+This code is intended to live forever but it is highly probable
+that you will not. Write to communicate with the next person to
+pick up the torch. When you explore code, write down what you learn.
+When you change code, explain why you made your choices. When you 
+write new code explain what others need to know to maintain it.
+&lt;/p&gt;
+
+
+  &lt;h1&gt; User documentation&lt;/h1&gt;
+
+The Axiom system is gradually being documented in a set of volumes.
+These change with every update to the system since they contain the
+actual system source code. The volumes listed here are updated every
+other month when the system is distributed. The current volume set is:
+&lt;ul&gt;
+ &lt;li&gt;
+  &lt;a href="toc.pdf"&gt;Combined Table of Contents&lt;/a&gt;
+ &lt;/li&gt;
+ This is the table of contents from the existing volumes
+ combined into one document for easy reference.
+ &lt;br/&gt;
+ &lt;li&gt;
+  &lt;a href="bookvol0.pdf"&gt;Volume 0: Axiom Jenks and Sutor&lt;/a&gt;
+ &lt;/li&gt;
+ This is the reconstructed Jenks and Sutor volume.
+ &lt;br/&gt;
+ &lt;li&gt;
+  &lt;a href="bookvol1.pdf"&gt;Volume 1: Axiom Tutorial&lt;/a&gt;
+ &lt;/li&gt;
+ This is the tutorial volume ISBN 1-411-66587-X.
+ Hardcopy is available from Amazon.com or Lulu.com
+ &lt;br/&gt;
+ &lt;li&gt;
+  &lt;a href="bookvol2.pdf"&gt;Volume 2: Axiom Users Guide&lt;/a&gt;
+ &lt;/li&gt;
+ This is a more detailed explanation with current information
+ for Axiom users.
+ &lt;br/&gt;
+ &lt;li&gt;
+  &lt;a href="bookvol3.pdf"&gt;Volume 3: Axiom Programmers Guide&lt;/a&gt;
+ &lt;/li&gt;
+ This is information about the language and algebra hierarchy
+ for Spad language programmers.
+ &lt;br/&gt;
+ &lt;li&gt;
+  &lt;a href="bookvol4.pdf"&gt;Volume 4: Axiom Developers Guide&lt;/a&gt;
+ &lt;/li&gt;
+ This is a collection of useful information for developers.
+ &lt;br/&gt;
+ &lt;li&gt;
+  &lt;a href="bookvol5.pdf"&gt;Volume 5: Axiom Interpreter&lt;/a&gt;
+ &lt;/li&gt;
+ This is the source code and explanation for the interpreter.
+ &lt;br/&gt;
+ &lt;li&gt;
+  &lt;a href="bookvol6.pdf"&gt;Volume 6: Axiom Command&lt;/a&gt;
+ &lt;/li&gt;
+ This covers the axiom commands, sman, and some other system
+ related issues.
+ &lt;br/&gt;
+ &lt;li&gt;
+  &lt;a href="bookvol7.pdf"&gt;Volume 7: Axiom Hyperdoc&lt;/a&gt;
+ &lt;/li&gt;
+ This is the source and explanation of the X11 hyperdoc subsystem.
+ &lt;br/&gt;
+ &lt;ul&gt;
+ &lt;li&gt;
+  &lt;a href="bookvol7.1.pdf"&gt;Volume 7.1: Axiom Hyperdoc Pages&lt;/a&gt;
+ &lt;/li&gt;
+ This is the source and pages for Hyperdoc.
+ &lt;/ul&gt;
+ &lt;li&gt;
+  &lt;a href="bookvol8.pdf"&gt;Volume 8: Axiom Graphics&lt;/a&gt;
+ &lt;/li&gt;
+ This is the source and explanation of the X11 graphics subsystem.
+ &lt;br/&gt;
+ &lt;li&gt;
+  &lt;a href="bookvol9.pdf"&gt;Volume 9: Axiom Compiler&lt;/a&gt;
+ &lt;/li&gt;
+ This is the source and explanation of the spad compiler.
+ &lt;br/&gt;
+ &lt;li&gt;
+  &lt;a href="bookvol10.pdf"&gt;Volume 10: Axiom Algebra Implementation&lt;/a&gt;
+ &lt;/li&gt;
+ This is a multi-volume set covering the algebra. The first
+ volume deals with implementation issues.
+ &lt;ul&gt;
+ &lt;li&gt;
+  &lt;a href="bookvol10.1.pdf"&gt;Volume 10.1: Axiom Algebra Theory&lt;/a&gt;
+ &lt;/li&gt;
+ This volume gives background theory for various algebra topics.
+ &lt;li&gt;
+  &lt;a href="bookvol10.2.pdf"&gt;Volume 10.2: Axiom Algebra Categories&lt;/a&gt;
+ &lt;/li&gt;
+ This is the source code for all of the categories.
+ &lt;li&gt;
+  &lt;a href="bookvol10.3.pdf"&gt;Volume 10.3: Axiom Algebra Domains&lt;/a&gt;
+ &lt;/li&gt;
+ This is the source code for all of the domains.
+ &lt;li&gt;
+  &lt;a href="bookvol10.4.pdf"&gt;Volume 10.4: Axiom Algebra Packages&lt;/a&gt;
+ &lt;/li&gt;
+ This is the source code for all of the packages.
+ &lt;/ul&gt;
+ &lt;li&gt;
+  &lt;a href="bookvol11.pdf"&gt;Volume 11: Axiom Browser&lt;/a&gt;
+ &lt;/li&gt;
+ This is the source and explanation of the new Firefox browser
+ front end.
+ &lt;br/&gt;
+ &lt;li&gt;
+  &lt;a href="bookvol12.pdf"&gt;Volume 12: Axiom Crystal&lt;/a&gt;
+ &lt;/li&gt;
+ This is the design documents and internals for the crystal interface.
+ &lt;br/&gt;
+&lt;/ul&gt;
+  
+  &lt;p&gt;
+  Axiom is being reworked to use the Firefox browser as the new
+  front end. &lt;a href="hyperdoc/rootpage.xhtml"&gt;Static pages&lt;/a&gt;
+  from the new hyperdoc show some of the details. These pages 
+  will be "live" in the new Axiom hyperdoc.
+
+  &lt;p&gt;
+  The &lt;a href="dotabb.html"&gt;algebra graph&lt;/a&gt; in its current form is 
+  available. You'll need a reasonably new browser to see the graph.
+  This is a work in progress.
+
+  &lt;p&gt;
+  A first tutorial is available at: &lt;a
+  href="http://www.dcs.st-and.ac.uk/~mnd/documentation/axiom_tutorial/"&gt;
+  http://www.dcs.st-and.ac.uk/~mnd/documentation/axiom_tutorial/ &lt;/a&gt;
+  &lt;/p&gt;
+
+  &lt;p&gt; 
+   The &lt;a href="rosetta.html"&gt;Rosetta&lt;/a&gt; 
+   &lt;a href="rosetta.tex"&gt;(src)&lt;/a&gt; 
+   &lt;a href="rosetta.pdf"&gt;(pdf)&lt;/a&gt; 
+   document is a comparison of nearly equivalent commands between 
+   many different computer algebra systems. 
+  &lt;/p&gt;
+ &lt;/div&gt;
+ &lt;/body&gt;
+&lt;/html&gt;
+
diff --git a/src/axiom-website/dotabb b/src/axiom-website/dotabb
new file mode 100644
index 0000000..4482d7f
--- /dev/null
+++ b/src/axiom-website/dotabb
@@ -0,0 +1,646 @@
+digraph AxiomSept2008 {
+ ranksep=1.25;
+ node [shape=box, color=yellow, style=filled];
+
+"ABELGRP" [color=lightblue,style=filled];
+"ABELGRP" -&gt; "CABMON"
+
+"ABELMON" [color=lightblue,style=filled];
+"ABELMON" -&gt; "ABELSG"
+
+"ABELSG" [color=lightblue,style=filled];
+"ABELSG" -&gt; "SETCAT"
+
+"ACF" [color=lightblue,style=filled];
+"ACF" -&gt; "FIELD"
+"ACF" -&gt; "RADCAT"
+
+"ACPLOT" -&gt; "PPCURVE"
+
+
+"AGG" [color=lightblue,style=filled];
+"AGG" -&gt; "TYPE"
+
+"AHYP" [color=lightblue,style=filled];
+"AHYP" -&gt; "CATEGORY"
+
+"ALAGG" [color=lightblue,style=filled];
+"ALAGG" -&gt; "TBAGG"
+"ALAGG" -&gt; "LSAGG"
+
+"ALGEBRA" [color=lightblue,style=filled];
+"ALGEBRA" -&gt; "RING"
+"ALGEBRA" -&gt; "MODULE"
+
+
+"AMR" [color=lightblue,style=filled];
+"AMR" -&gt; "RING"
+"AMR" -&gt; "BMODULE"
+
+"AN" -&gt; "ES"
+"AN" -&gt; "ACF"
+"AN" -&gt; "RETRACT"
+"AN" -&gt; "LINEXP"
+"AN" -&gt; "REAL"
+"AN" -&gt; "CHARZ"
+"AN" -&gt; "KONVERT"
+"AN" -&gt; "DIFRING"
+
+"ANY" -&gt; "SETCAT"
+
+
+"ARRAY1" -&gt; "A1AGG"
+
+
+"ARRAY2" -&gt; "ARR2CAT"
+"ARRAY2" -&gt; "IIARRAY2"
+
+"ARR2CAT" [color=lightblue,style=filled];
+"ARR2CAT" -&gt; "HOAGG"
+
+"ASTACK" -&gt; "STACK"
+
+"ATRIG" [color=lightblue,style=filled];
+"ATRIG" -&gt; "CATEGORY"
+
+"ATTREG" [color=lightblue,style=filled];
+"ATTREG" -&gt; "CATEGORY"
+
+"A1AGG" [color=lightblue,style=filled];
+"A1AGG" -&gt; "FLAGG"
+
+
+"BASTYPE" [color=lightblue,style=filled];
+"BASTYPE" -&gt; "CATEGORY"
+    
+
+"BGAGG" [color=lightblue,style=filled];
+"BGAGG" -&gt; "HOAGG"
+
+"BITS" -&gt; "BTAGG"
+
+"BMODULE" [color=lightblue,style=filled];
+"BMODULE" -&gt; "LMODULE"
+"BMODULE" -&gt; "RMODULE"
+
+"BOOLEAN" -&gt; "ORDSET"
+"BOOLEAN" -&gt; "FINITE"
+"BOOLEAN" -&gt; "LOGIC"
+"BOOLEAN" -&gt; "KONVERT"
+
+"BRAGG" [color=lightblue,style=filled];
+"BRAGG" -&gt; "RCAGG"
+
+
+"BTAGG" [color=lightblue,style=filled];
+"BTAGG" -&gt; "ORDSET"
+"BTAGG" -&gt; "LOGIC"
+"BTAGG" -&gt; "A1AGG"
+
+"CABMON" [color=lightblue,style=filled];
+"CABMON" -&gt; "ABELMON"
+
+"CARD" -&gt; "ORDSET"
+"CARD" -&gt; "ABELMON"
+"CARD" -&gt; "MONOID"
+"CARD" -&gt; "RETRACT"
+
+"CARTEN" -&gt; "GRALG"
+"CARTEN" -&gt; "GRMOD"
+
+
+"CATEGORY" [color=lightblue,style=filled];
+ 
+"CHARNZ" [color=lightblue,style=filled];
+"CHARNZ" -&gt; "RING"
+
+"CHARZ" [color=lightblue,style=filled];
+"CHARZ" -&gt; "RING"
+
+
+"CLAGG" [color=lightblue,style=filled];
+"CLAGG" -&gt; "HOAGG"
+
+"CLIF" -&gt; "RING"
+"CLIF" -&gt; "ALGEBRA"
+"CLIF" -&gt; "VSPACE"
+
+
+"CFCAT" [color=lightblue,style=filled];
+"CFCAT" -&gt; "CATEGORY" 
+
+
+"COLOR" -&gt; "ABELSG"
+
+
+
+"COMBOPC" [color=lightblue,style=filled];
+"COMBOPC" -&gt; "CFCAT"
+
+"COMRING" [color=lightblue,style=filled];
+"COMRING" -&gt; "RING"
+"COMRING" -&gt; "BMODULE"
+
+"CONTFRAC" -&gt; "ALGEBRA"
+"CONTFRAC" -&gt; "FIELD"
+
+
+
+
+
+"DBASE" -&gt; "SETCAT"
+
+"DEQUEUE" -&gt; "DQAGG"
+
+"DFLOAT" -&gt; "FPS"
+"DFLOAT" -&gt; "DIFRING"
+"DFLOAT" -&gt; "OM"
+"DFLOAT" -&gt; "TRANFUN"
+"DFLOAT" -&gt; "SPFCAT"
+"DFLOAT" -&gt; "KONVERT"
+
+"DIAGG" [color=lightblue,style=filled];
+"DIAGG" -&gt; "DIOPS"
+
+"DIFEXT" [color=lightblue,style=filled];
+"DIFEXT" -&gt; "RING"
+
+"DIFRING" [color=lightblue,style=filled];
+"DIFRING" -&gt; "RING"
+
+"DIOPS" [color=lightblue,style=filled];
+"DIOPS" -&gt; "BGAGG"
+"DIOPS" -&gt; "CLAGG"
+
+"DIVRING" [color=lightblue,style=filled];
+"DIVRING" -&gt; "ENTIRER"
+"DIVRING" -&gt; "ALGEBRA"
+
+"DLAGG" [color=lightblue,style=filled];
+"DLAGG" -&gt; "RCAGG"
+
+"DLIST" -&gt; "LSAGG"
+
+"DQAGG" [color=lightblue,style=filled];
+"DQAGG" -&gt; "SKAGG"
+"DQAGG" -&gt; "QUAGG"
+
+"ELAGG" [color=lightblue,style=filled];
+"ELAGG" -&gt; "LNAGG"
+
+"ELEMFUN" [color=lightblue,style=filled];
+"ELEMFUN" -&gt; "CATEGORY"
+
+"ELTAB" [color=lightblue,style=filled];
+"ELTAB" -&gt; "CATEGORY"
+
+"ELTAGG" [color=lightblue,style=filled];
+"ELTAGG" -&gt; "ELTAB"
+
+"ENTIRER" [color=lightblue,style=filled];
+"ENTIRER" -&gt; "RING"
+"ENTIRER" -&gt; "BMODULE"
+
+"ES" [color=lightblue,style=filled];
+"ES" -&gt; "ORDSET"
+"ES" -&gt; "RETRACT"
+"ES" -&gt; "IEVALAB"
+"ES" -&gt; "EVALAB"
+
+
+
+"EUCDOM" [color=lightblue,style=filled];
+"EUCDOM" -&gt; "PID"
+
+"EVALAB" [color=lightblue,style=filled];
+"EVALAB" -&gt; "IEVALAB"
+
+"FAMR" [color=lightblue,style=filled];
+"FAMR" -&gt; "AMR"
+"FAMR" -&gt; "FRETRCT"
+
+"FARRAY" -&gt; "IFARRAY"
+
+"FFCAT" [color=lightblue,style=filled];
+"FFCAT" -&gt; "MONOGEN"
+
+
+"FIELD" [color=lightblue,style=filled];
+"FIELD" -&gt; "EUCDOM"
+"FIELD" -&gt; "UFD"
+"FIELD" -&gt; "DIVRING"
+
+"FINITE" [color=lightblue,style=filled];
+"FINITE" -&gt; "SETCAT"
+
+"FINRALG" [color=lightblue,style=filled];
+"FINRALG" -&gt; "ALGEBRA"
+
+"FLAGG" [color=lightblue,style=filled];
+"FLAGG" -&gt; "LNAGG"
+
+
+"FLINEXP" [color=lightblue,style=filled];
+"FLINEXP" -&gt; "LINEXP"
+
+"FPATMAB" [color=lightblue,style=filled];
+"FPATMAB" -&gt; "TYPE"
+
+"FPS" [color=lightblue,style=filled];
+"FPS" -&gt; "RNS"
+
+"FRAMALG" [color=lightblue,style=filled];
+"FRAMALG" -&gt; "FINRALG"
+
+"FRETRCT" [color=lightblue,style=filled];
+"FRETRCT" -&gt; "RETRACT"
+
+"FSAGG" [color=lightblue,style=filled];
+"FSAGG" -&gt; "DIAGG"
+"FSAGG" -&gt; "SETAGG"
+
+
+
+"GCDDOM" [color=lightblue,style=filled];
+"GCDDOM" -&gt; "INTDOM"
+
+"GRALG" [color=lightblue,style=filled];
+"GRALG" -&gt; "GRMOD"
+"GRALG" -&gt; "RETRACT"
+
+"GRMOD" [color=lightblue,style=filled];
+"GRMOD" -&gt; "SETCAT"
+
+"GROUP" [color=lightblue,style=filled];
+"GROUP" -&gt; "MONOID"
+
+"HEAP" -&gt; "PRQAGG"
+
+"HOAGG" [color=lightblue,style=filled];
+"HOAGG" -&gt; "AGG"
+
+"HYPCAT" [color=lightblue,style=filled];
+"HYPCAT" -&gt; "CATEGORY"
+
+
+"IAN" -&gt; "ES"
+"IAN" -&gt; "ACF"
+"IAN" -&gt; "RETRACT"
+"IAN" -&gt; "LINEXP"
+"IAN" -&gt; "REAL"
+"IAN" -&gt; "CHARZ"
+"IAN" -&gt; "KONVERT"
+"IAN" -&gt; "DIFRING"
+
+"IARRAY1" -&gt; "A1AGG"
+
+"IARRAY2" -&gt; "ARR2CAT"
+"IARRAY2" -&gt; "IIARRAY2"
+
+"IBITS" -&gt; "BTAGG"
+
+"ICARD" -&gt; "ORDSET"
+
+"IEVALAB" [color=lightblue,style=filled];
+"IEVALAB" -&gt; "CATEGORY"
+
+"IFARRAY" -&gt; "A1AGG"
+"IFARRAY" -&gt; "ELAGG"
+
+"IIARRAY2" -&gt; "ARR2CAT"
+
+
+"INS" [color=lightblue,style=filled];
+"INS" -&gt; "UFD"
+"INS" -&gt; "EUCDOM"
+"INS" -&gt; "OINTDOM"
+"INS" -&gt; "DIFRING"
+"INS" -&gt; "KONVERT"
+"INS" -&gt; "RETRACT"
+"INS" -&gt; "LINEXP"
+"INS" -&gt; "PATMAB"
+"INS" -&gt; "CFCAT"
+"INS" -&gt; "REAL"
+"INS" -&gt; "CHARZ"
+"INS" -&gt; "STEP"
+
+"INT" -&gt; "INS"
+"INT" -&gt; "KONVERT"
+"INT" -&gt; "OM"
+
+"INTDOM" [color=lightblue,style=filled];
+"INTDOM" -&gt; "COMRING"
+"INTDOM" -&gt; "ALGEBRA"
+"INTDOM" -&gt; "ENTIRER"
+
+
+
+"IXAGG" [color=lightblue,style=filled];
+"IXAGG" -&gt; "HOAGG"
+"IXAGG" -&gt; "ELTAGG"
+
+"KDAGG" [color=lightblue,style=filled];
+"KDAGG" -&gt; "DIAGG"
+
+"KOERCE" [color=lightblue,style=filled];
+"KOERCE" -&gt; "CATEGORY"
+
+"KONVERT" [color=lightblue,style=filled];
+"KONVERT" -&gt; "CATEGORY"
+
+"LFCAT" [color=lightblue,style=filled];
+"LFCAT" -&gt; "PRIMCAT"
+"LFCAT" -&gt; "TRANFUN"
+
+"LINEXP" [color=lightblue,style=filled];
+"LINEXP" -&gt; "RING"
+
+"LOGIC" [color=lightblue,style=filled];
+"LOGIC" -&gt; "BASTYPE"
+
+"LMODULE" [color=lightblue,style=filled];
+"LMODULE" -&gt; "ABELGRP"
+
+"LNAGG" [color=lightblue,style=filled];
+"LNAGG" -&gt; "IXAGG"
+"LNAGG" -&gt; "CLAGG"
+
+"LSAGG" [color=lightblue,style=filled];
+"LSAGG" -&gt; "FLAGG"
+"LSAGG" -&gt; "ELAGG"
+
+"MDAGG" [color=lightblue,style=filled];
+"MDAGG" -&gt; "DIOPS"
+
+
+"MODULE" [color=lightblue,style=filled];
+"MODULE" -&gt; "BMODULE"
+
+"MONOID" [color=lightblue,style=filled];
+"MONOID" -&gt; "SGROUP"
+
+"MONOGEN" [color=lightblue,style=filled];
+"MONOGEN" -&gt; "FRAMALG"
+"MONOGEN" -&gt; "COMRING"
+"MONOGEN" -&gt; "KONVERT"
+"MONOGEN" -&gt; "FRETRCT"
+"MONOGEN" -&gt; "FLINEXP"
+
+
+
+"MSETAGG" [color=lightblue,style=filled];
+"MSETAGG" -&gt; "MDAGG"
+"MSETAGG" -&gt; "SETAGG"
+
+
+"MTSCAT" [color=lightblue,style=filled];
+"MTSCAT" -&gt; "PDRING"
+"MTSCAT" -&gt; "PSCAT"
+"MTSCAT" -&gt; "IEVALAB"
+"MTSCAT" -&gt; "EVALAB"
+
+
+"NONE" -&gt; "SETCAT"
+
+
+
+"NNI" -&gt; "OAMONS"
+"NNI" -&gt; "MONOID"
+
+"OAGROUP" [color=lightblue,style=filled];
+"OAGROUP" -&gt; "OCAMON"
+"OAGROUP" -&gt; "ABELGRP"
+
+"OAMON" [color=lightblue,style=filled];
+"OAMON" -&gt; "OASGP"
+"OAMON" -&gt; "ABELMON"
+
+"OAMONS" [color=lightblue,style=filled];
+"OAMONS" -&gt; "OCAMON"
+
+"OASGP" [color=lightblue,style=filled];
+"OASGP" -&gt; "ORDSET"
+"OASGP" -&gt; "ABELMON"
+
+"OCAMON" [color=lightblue,style=filled];
+"OCAMON" -&gt; "OAMON"
+"OCAMON" -&gt; "CABMON"
+
+"OINTDOM" [color=lightblue,style=filled];
+"OINTDOM" -&gt; "INTDOM"
+"OINTDOM" -&gt; "ORDRING"
+
+"OM" [color=lightblue,style=filled];
+"OM" -&gt; "CATEGORY"
+
+"OMSAGG" [color=lightblue,style=filled];
+"OMSAGG" -&gt; "MSETAGG"
+"OMSAGG" -&gt; "PRQAGG"
+
+"ONECOMP" -&gt; "SETCAT"
+"ONECOMP" -&gt; "FRETRCT"
+
+
+
+"ORDCOMP" -&gt; "SETCAT"
+"ORDCOMP" -&gt; "FRETRCT"
+
+
+"ORDFIN" [color=lightblue,style=filled];
+"ORDFIN" -&gt; "ORDSET"
+"ORDFIN" -&gt; "FINITE"
+
+"ORDMON" [color=lightblue,style=filled];
+"ORDMON" -&gt; "ORDSET"
+"ORDMON" -&gt; "MONOID"
+
+"ORDRING" [color=lightblue,style=filled];
+"ORDRING" -&gt; "OAGROUP"
+"ORDRING" -&gt; "RING"
+"ORDRING" -&gt; "MONOID"
+
+"ORDSET" [color=lightblue,style=filled];
+"ORDSET" -&gt; "SETCAT"
+
+"PALETTE" -&gt; "SETCAT"
+
+"PATAB" [color=lightblue,style=filled];
+"PATAB" -&gt; "CATEGORY" 
+
+"PATLRES" -&gt; "SETCAT"
+
+"PATMAB" [color=lightblue,style=filled];
+"PATMAB" -&gt; "SETCAT"
+
+"PATRES" -&gt; "SETCAT"
+
+
+"PATTERN" -&gt; "SETCAT"
+"PATTERN" -&gt; "RETRACT"
+
+
+
+"PDRING" [color=lightblue,style=filled];
+"PDRING" -&gt; "RING"
+
+"PFECAT" [color=lightblue,style=filled];
+"PFECAT" -&gt; "UFD"
+
+"PI" -&gt; "OASGP"
+"PI" -&gt; "MONOID"
+
+"PID" [color=lightblue,style=filled];
+"PID" -&gt; "GCDDOM"
+
+
+
+
+
+
+
+"PRIMARR" -&gt; "A1AGG"
+
+
+"PRIMCAT" [color=lightblue,style=filled];
+"PRIMCAT" -&gt; "CATEGORY"
+
+"PRQAGG" [color=lightblue,style=filled];
+"PRQAGG" -&gt; "BGAGG"
+
+"PSCAT" [color=lightblue,style=filled];
+"PSCAT" -&gt; "AMR"
+
+"RADFF" -&gt; "FFCAT"
+"RADFF" -&gt; "SAE"
+
+
+"REF" -&gt; "TYPE"
+
+"QFORM" -&gt; "ABELGRP"
+
+"QUAGG" [color=lightblue,style=filled];
+"QUAGG" -&gt; "BGAGG"
+
+"QUEUE" -&gt; "QUAGG"
+
+"QEQUAT" -&gt; "KOERCE"
+
+"RCAGG" [color=lightblue,style=filled];
+"RCAGG" -&gt; "HOAGG"
+
+"RADCAT" [color=lightblue,style=filled];
+"RADCAT" -&gt; "CATEGORY"
+
+"REAL" [color=lightblue,style=filled];
+"REAL" -&gt; "KONVERT"
+
+
+"RETRACT" [color=lightblue,style=filled];
+"RETRACT" -&gt; "CATEGORY"
+
+
+"RING" [color=lightblue,style=filled];
+"RING" -&gt; "RNG"
+"RING" -&gt; "MONOID"
+"RING" -&gt; "LMODULE"
+
+"RMODULE" [color=lightblue,style=filled];
+"RMODULE" -&gt; "ABELGRP"
+
+"RNG" [color=lightblue,style=filled];
+"RNG" -&gt; "ABELGRP"
+"RNG" -&gt; "SGROUP"
+
+"RNS" [color=lightblue,style=filled];
+"RNS" -&gt; "FIELD"
+"RNS" -&gt; "ORDRING"
+"RNS" -&gt; "REAL"
+"RNS" -&gt; "RETRACT"
+"RNS" -&gt; "RADCAT"
+"RNS" -&gt; "KONVERT"
+"RNS" -&gt; "PATMAB"
+"RNS" -&gt; "CHARZ"
+
+"ROMAN" -&gt; "INS"
+
+"SAE" -&gt; "MONOGEN"
+
+
+
+"SAOS" -&gt; "ORDSET"
+
+"SETAGG" [color=lightblue,style=filled];
+"SETAGG" -&gt; "SETCAT"
+"SETAGG" -&gt; "CLAGG"
+
+"SETCAT" [color=lightblue,style=filled];
+"SETCAT" -&gt; "BASTYPE"
+"SETCAT" -&gt; "KOERCE"
+
+"SGROUP" [color=lightblue,style=filled];
+"SGROUP" -&gt; "SETCAT"
+
+"SINT" -&gt; "INS"
+"SINT" -&gt; "LOGIC"
+"SINT" -&gt; "OM"
+
+"SKAGG" [color=lightblue,style=filled];
+"SKAGG" -&gt; "BGAGG"
+
+"SRAGG" [color=lightblue,style=filled];
+"SRAGG" -&gt; "A1AGG"
+
+"STACK" -&gt; "SKAGG"
+
+"STAGG" [color=lightblue,style=filled];
+"STAGG" -&gt; "RCAGG"
+"STAGG" -&gt; "LNAGG"
+
+"STEP" [color=lightblue,style=filled];
+"STEP" -&gt; "SETCAT"
+
+"SPFCAT" [color=lightblue,style=filled];
+"SPFCAT" -&gt; "CATEGORY"
+
+
+"TBAGG" [color=lightblue,style=filled];
+"TBAGG" -&gt; "KDAGG"
+"TBAGG" -&gt; "IXAGG"
+
+"TRANFUN" [color=lightblue,style=filled];
+"TRANFUN" -&gt; "TRIGCAT"
+"TRANFUN" -&gt; "ATRIG"
+"TRANFUN" -&gt; "HYPCAT"
+"TRANFUN" -&gt; "AHYP"
+"TRANFUN" -&gt; "ELEMFUN"
+
+"TRIGCAT" [color=lightblue,style=filled];
+"TRIGCAT" -&gt; "CATEGORY"
+
+"TUPLE" -&gt; "PRIMARR"
+
+"TYPE" [color=lightblue,style=filled];
+"TYPE" -&gt; "CATEGORY"
+
+"UFD" [color=lightblue,style=filled];
+"UFD" -&gt; "GCDDOM"
+
+"ULSCAT" [color=lightblue,style=filled];
+"ULSCAT" -&gt; "UPSCAT"
+
+"URAGG" [color=lightblue,style=filled];
+"URAGG" -&gt; "RCAGG"
+
+"UPSCAT" [color=lightblue,style=filled];
+"UPSCAT" -&gt; "PSCAT"
+
+"UPXSCAT" [color=lightblue,style=filled];
+"UPXSCAT" -&gt; "UPSCAT"
+
+"UTSCAT" [color=lightblue,style=filled];
+"UTSCAT" -&gt; "UPSCAT"
+
+"VSPACE" [color=lightblue,style=filled];
+"VSPACE" -&gt; "MODULE"
+
+}
diff --git a/src/axiom-website/dotabb.html b/src/axiom-website/dotabb.html
new file mode 100644
index 0000000..3ce1a05
--- /dev/null
+++ b/src/axiom-website/dotabb.html
@@ -0,0 +1,46 @@
+&lt;html&gt;
+&lt;head&gt;
+&lt;title&gt;Axiom Abbreviated Category and Domain graph&lt;/title&gt;
+&lt;script type="text/javascript"&gt;
+var W3CDOM = (document.createElement &amp;&amp; document.getElementsByTagName);
+window.onload 	= init;
+function init(evt) {
+	SVGscale(0.5);
+}
+function SVGscale(scale) {
+	window.SVGsetDimension(3960*scale, 2312*scale);
+	window.SVGsetScale(scale,scale);	
+	var box 	= document.getElementById('svgid');
+	box.width  	= 3960*scale;
+	box.height 	= 2312*scale;
+}
+&lt;/script&gt;
+
+&lt;/head&gt;
+&lt;body&gt;
+&lt;h1&gt;Axiom Abbreviated Category and Domain graph&lt;/h1&gt;	
+&lt;!--
+&lt;embed src="svg4tom1.svg" width="320" height="240" type="image/svg+xml" id="svgid"&gt;&lt;/embed&gt;
+--&gt;
+
+&lt;div&gt;
+	choose here: 
+	&lt;a href="#" onclick="SVGscale(0.1);"&gt;0.1&lt;/a&gt; or
+	&lt;a href="#" onclick="SVGscale(0.25);"&gt;0.25&lt;/a&gt; or
+	&lt;a href="#" onclick="SVGscale(0.5);"&gt;0.5&lt;/a&gt; or 
+	&lt;a href="#" onclick="SVGscale(1);"&gt;1.0&lt;/a&gt; or 
+	&lt;a href="#" onclick="SVGscale(1.5);"&gt;1.5&lt;/a&gt; or ...
+&lt;/div&gt;
+&lt;!--
+&lt;div&gt;
+&lt;embed src="dotabb.svg" width="3960" height="2312" type="image/svg+xml" id="svgid"&gt;&lt;/embed&gt;
+&lt;/div&gt;
+--&gt;
+&lt;div&gt;
+  &lt;object id='svgid' data="dotabb.svg" type="image/svg+xml" 
+   width="3960" height="2312" wmode="transparent" style="overflow:hidden;" /&gt;
+  &lt;/object&gt;
+&lt;/div&gt;
+
+&lt;/body&gt;
+&lt;/html&gt;
diff --git a/src/axiom-website/dotabb.svg b/src/axiom-website/dotabb.svg
new file mode 100644
index 0000000..daeb754
--- /dev/null
+++ b/src/axiom-website/dotabb.svg
@@ -0,0 +1,2352 @@
+&lt;?xml version="1.0" encoding="UTF-8" standalone="no"?&gt;
+&lt;!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.0//EN"
+ "http://www.w3.org/TR/2001/REC-SVG-20010904/DTD/svg10.dtd" [
+ &lt;!ATTLIST svg xmlns:xlink CDATA #FIXED "http://www.w3.org/1999/xlink"&gt;
+]&gt;
+&lt;!-- Generated by dot version 2.8 (Thu Sep 14 20:34:11 UTC 2006)
+     For user: (root) root --&gt;
+&lt;!-- Title: AxiomSept2008 Pages: 1 --&gt;
+&lt;svg width="3960pt" height="2312pt"
+ viewBox = "0 0 3960 2312"
+ xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"
+ onload="RunScript(evt)"&gt;
+&lt;script type="text/ecmascript"&gt;
+&lt;![CDATA[
+var g_element;
+var SVGDoc;
+var SVGRoot;
+function setDimension(w,h) {
+  SVGDoc.documentElement.setAttribute("width",w);
+  SVGDoc.documentElement.setAttribute("height",h);
+}
+function setScale(sw,sh) {
+  g_element.setAttribute("transform","scale("+sw+" "+sh+")");
+}
+function RunScript(LoadEvent) {
+  top.SVGsetDimension=setDimension;
+  top.SVGsetScale=setScale;
+  SVGDoc=LoadEvent.target.ownerDocument;
+  g_element=SVGDoc.getElementById("graph0");
+}
+]]&gt;
+&lt;/script&gt;
+&lt;g id="graph0" class="graph" style="font-family:Times-Roman;font-size:14.00;"&gt;
+&lt;title&gt;AxiomSept2008&lt;/title&gt;
+&lt;polygon style="fill:white;stroke:white;" points="-2,2314 -2,-2 3962,-2 3962,2314 -2,2314"/&gt;
+&lt;!-- ABELGRP --&gt;
+&lt;g id="node1" class="node"&gt;&lt;title&gt;ABELGRP&lt;/title&gt;
+&lt;polygon style="fill:lightblue;stroke:lightblue;" points="2531,1516 2451,1516 2451,1552 2531,1552 2531,1516"/&gt;
+&lt;text text-anchor="middle" x="2491" y="1539"&gt;ABELGRP&lt;/text&gt;
+&lt;/g&gt;
+&lt;!-- CABMON --&gt;
+&lt;g id="node3" class="node"&gt;&lt;title&gt;CABMON&lt;/title&gt;
+&lt;polygon style="fill:lightblue;stroke:lightblue;" points="2421,1642 2343,1642 2343,1678 2421,1678 2421,1642"/&gt;
+&lt;text text-anchor="middle" x="2382" y="1665"&gt;CABMON&lt;/text&gt;
+&lt;/g&gt;
+&lt;!-- ABELGRP&amp;#45;&amp;gt;CABMON --&gt;
+&lt;g id="edge2" class="edge"&gt;&lt;title&gt;ABELGRP&amp;#45;&amp;gt;CABMON&lt;/title&gt;
+&lt;path style="fill:none;stroke:black;" d="M2475,1552C2456,1574 2426,1610 2405,1634"/&gt;
+&lt;polygon style="fill:black;stroke:black;" points="2407,1637 2398,1642 2402,1632 2407,1637"/&gt;
+&lt;/g&gt;
+&lt;!-- ABELMON --&gt;
+&lt;g id="node4" class="node"&gt;&lt;title&gt;ABELMON&lt;/title&gt;
+&lt;polygon style="fill:lightblue;stroke:lightblue;" points="2339,1768 2253,1768 2253,1804 2339,1804 2339,1768"/&gt;
+&lt;text text-anchor="middle" x="2296" y="1791"&gt;ABELMON&lt;/text&gt;
+&lt;/g&gt;
+&lt;!-- CABMON&amp;#45;&amp;gt;ABELMON --&gt;
+&lt;g id="edge90" class="edge"&gt;&lt;title&gt;CABMON&amp;#45;&amp;gt;ABELMON&lt;/title&gt;
+&lt;path style="fill:none;stroke:black;" d="M2370,1678C2356,1699 2331,1735 2315,1760"/&gt;
+&lt;polygon style="fill:black;stroke:black;" points="2318,1762 2309,1768 2312,1758 2318,1762"/&gt;
+&lt;/g&gt;
+&lt;!-- ABELSG --&gt;
+&lt;g id="node6" class="node"&gt;&lt;title&gt;ABELSG&lt;/title&gt;
+&lt;polygon style="fill:lightblue;stroke:lightblue;" points="2392,1894 2320,1894 2320,1930 2392,1930 2392,1894"/&gt;
+&lt;text text-anchor="middle" x="2356" y="1917"&gt;ABELSG&lt;/text&gt;
+&lt;/g&gt;
+&lt;!-- ABELMON&amp;#45;&amp;gt;ABELSG --&gt;
+&lt;g id="edge4" class="edge"&gt;&lt;title&gt;ABELMON&amp;#45;&amp;gt;ABELSG&lt;/title&gt;
+&lt;path style="fill:none;stroke:black;" d="M2305,1804C2315,1825 2331,1860 2343,1885"/&gt;
+&lt;polygon style="fill:black;stroke:black;" points="2346,1883 2347,1894 2340,1886 2346,1883"/&gt;
+&lt;/g&gt;
+&lt;!-- SETCAT --&gt;
+&lt;g id="node8" class="node"&gt;&lt;title&gt;SETCAT&lt;/title&gt;
+&lt;polygon style="fill:lightblue;stroke:lightblue;" points="2307,2020 2239,2020 2239,2056 2307,2056 2307,2020"/&gt;
+&lt;text text-anchor="middle" x="2273" y="2043"&gt;SETCAT&lt;/text&gt;
+&lt;/g&gt;
+&lt;!-- ABELSG&amp;#45;&amp;gt;SETCAT --&gt;
+&lt;g id="edge6" class="edge"&gt;&lt;title&gt;ABELSG&amp;#45;&amp;gt;SETCAT&lt;/title&gt;
+&lt;path style="fill:none;stroke:black;" d="M2344,1930C2330,1951 2307,1987 2291,2012"/&gt;
+&lt;polygon style="fill:black;stroke:black;" points="2294,2014 2285,2020 2288,2010 2294,2014"/&gt;
+&lt;/g&gt;
+&lt;!-- BASTYPE --&gt;
+&lt;g id="node74" class="node"&gt;&lt;title&gt;BASTYPE&lt;/title&gt;
+&lt;polygon style="fill:lightblue;stroke:lightblue;" points="2312,2146 2234,2146 2234,2182 2312,2182 2312,2146"/&gt;
+&lt;text text-anchor="middle" x="2273" y="2169"&gt;BASTYPE&lt;/text&gt;
+&lt;/g&gt;
+&lt;!-- SETCAT&amp;#45;&amp;gt;BASTYPE --&gt;
+&lt;g id="edge518" class="edge"&gt;&lt;title&gt;SETCAT&amp;#45;&amp;gt;BASTYPE&lt;/title&gt;
+&lt;path style="fill:none;stroke:black;" d="M2273,2056C2273,2077 2273,2111 2273,2136"/&gt;
+&lt;polygon style="fill:black;stroke:black;" points="2277,2136 2273,2146 2270,2136 2277,2136"/&gt;
+&lt;/g&gt;
+&lt;!-- KOERCE --&gt;
+&lt;g id="node285" class="node"&gt;&lt;title&gt;KOERCE&lt;/title&gt;
+&lt;polygon style="fill:lightblue;stroke:lightblue;" points="2820,2146 2748,2146 2748,2182 2820,2182 2820,2146"/&gt;
+&lt;text text-anchor="middle" x="2784" y="2169"&gt;KOERCE&lt;/text&gt;
+&lt;/g&gt;
+&lt;!-- SETCAT&amp;#45;&amp;gt;KOERCE --&gt;
+&lt;g id="edge520" class="edge"&gt;&lt;title&gt;SETCAT&amp;#45;&amp;gt;KOERCE&lt;/title&gt;
+&lt;path style="fill:none;stroke:black;" d="M2307,2046C2397,2068 2636,2128 2738,2153"/&gt;
+&lt;polygon style="fill:black;stroke:black;" points="2739,2150 2748,2155 2738,2156 2739,2150"/&gt;
+&lt;/g&gt;
+&lt;!-- ACF --&gt;
+&lt;g id="node9" class="node"&gt;&lt;title&gt;ACF&lt;/title&gt;
+&lt;polygon style="fill:lightblue;stroke:lightblue;" points="3494,256 3440,256 3440,292 3494,292 3494,256"/&gt;
+&lt;text text-anchor="middle" x="3467" y="279"&gt;ACF&lt;/text&gt;
+&lt;/g&gt;
+&lt;!-- FIELD --&gt;
+&lt;g id="node11" class="node"&gt;&lt;title&gt;FIELD&lt;/title&gt;
+&lt;polygon style="fill:lightblue;stroke:lightblue;" points="3116,382 3060,382 3060,418 3116,418 3116,382"/&gt;
+&lt;text text-anchor="middle" x="3088" y="405"&gt;FIELD&lt;/text&gt;
+&lt;/g&gt;
+&lt;!-- ACF&amp;#45;&amp;gt;FIELD --&gt;
+&lt;g id="edge8" class="edge"&gt;&lt;title&gt;ACF&amp;#45;&amp;gt;FIELD&lt;/title&gt;
+&lt;path style="fill:none;stroke:black;" d="M3440,283C3373,305 3203,362 3126,388"/&gt;
+&lt;polygon style="fill:black;stroke:black;" points="3127,391 3116,391 3125,385 3127,391"/&gt;
+&lt;/g&gt;
+&lt;!-- RADCAT --&gt;
+&lt;g id="node13" class="node"&gt;&lt;title&gt;RADCAT&lt;/title&gt;
+&lt;polygon style="fill:lightblue;stroke:lightblue;" points="3512,382 3440,382 3440,418 3512,418 3512,382"/&gt;
+&lt;text text-anchor="middle" x="3476" y="405"&gt;RADCAT&lt;/text&gt;
+&lt;/g&gt;
+&lt;!-- ACF&amp;#45;&amp;gt;RADCAT --&gt;
+&lt;g id="edge10" class="edge"&gt;&lt;title&gt;ACF&amp;#45;&amp;gt;RADCAT&lt;/title&gt;
+&lt;path style="fill:none;stroke:black;" d="M3468,292C3470,313 3472,347 3474,372"/&gt;
+&lt;polygon style="fill:black;stroke:black;" points="3477,372 3475,382 3471,372 3477,372"/&gt;
+&lt;/g&gt;
+&lt;!-- DIVRING --&gt;
+&lt;g id="node157" class="node"&gt;&lt;title&gt;DIVRING&lt;/title&gt;
+&lt;polygon style="fill:lightblue;stroke:lightblue;" points="2918,886 2842,886 2842,922 2918,922 2918,886"/&gt;
+&lt;text text-anchor="middle" x="2880" y="909"&gt;DIVRING&lt;/text&gt;
+&lt;/g&gt;
+&lt;!-- FIELD&amp;#45;&amp;gt;DIVRING --&gt;
+&lt;g id="edge204" class="edge"&gt;&lt;title&gt;FIELD&amp;#45;&amp;gt;DIVRING&lt;/title&gt;
+&lt;path style="fill:none;stroke:black;" d="M3090,418C3096,478 3108,677 3017,796 2991,831 2950,861 2920,881"/&gt;
+&lt;polygon style="fill:black;stroke:black;" points="2922,884 2912,886 2919,878 2922,884"/&gt;
+&lt;/g&gt;
+&lt;!-- EUCDOM --&gt;
+&lt;g id="node186" class="node"&gt;&lt;title&gt;EUCDOM&lt;/title&gt;
+&lt;polygon style="fill:lightblue;stroke:lightblue;" points="2975,508 2899,508 2899,544 2975,544 2975,508"/&gt;
+&lt;text text-anchor="middle" x="2937" y="531"&gt;EUCDOM&lt;/text&gt;
+&lt;/g&gt;
+&lt;!-- FIELD&amp;#45;&amp;gt;EUCDOM --&gt;
+&lt;g id="edge200" class="edge"&gt;&lt;title&gt;FIELD&amp;#45;&amp;gt;EUCDOM&lt;/title&gt;
+&lt;path style="fill:none;stroke:black;" d="M3066,418C3040,440 2996,477 2967,501"/&gt;
+&lt;polygon style="fill:black;stroke:black;" points="2969,504 2959,508 2964,499 2969,504"/&gt;
+&lt;/g&gt;
+&lt;!-- UFD --&gt;
+&lt;g id="node202" class="node"&gt;&lt;title&gt;UFD&lt;/title&gt;
+&lt;polygon style="fill:lightblue;stroke:lightblue;" points="3047,508 2993,508 2993,544 3047,544 3047,508"/&gt;
+&lt;text text-anchor="middle" x="3020" y="531"&gt;UFD&lt;/text&gt;
+&lt;/g&gt;
+&lt;!-- FIELD&amp;#45;&amp;gt;UFD --&gt;
+&lt;g id="edge202" class="edge"&gt;&lt;title&gt;FIELD&amp;#45;&amp;gt;UFD&lt;/title&gt;
+&lt;path style="fill:none;stroke:black;" d="M3078,418C3067,439 3048,474 3035,499"/&gt;
+&lt;polygon style="fill:black;stroke:black;" points="3038,501 3030,508 3032,498 3038,501"/&gt;
+&lt;/g&gt;
+&lt;!-- CATEGORY --&gt;
+&lt;g id="node22" class="node"&gt;&lt;title&gt;CATEGORY&lt;/title&gt;
+&lt;polygon style="fill:lightblue;stroke:lightblue;" points="3311,2272 3221,2272 3221,2308 3311,2308 3311,2272"/&gt;
+&lt;text text-anchor="middle" x="3266" y="2295"&gt;CATEGORY&lt;/text&gt;
+&lt;/g&gt;
+&lt;!-- RADCAT&amp;#45;&amp;gt;CATEGORY --&gt;
+&lt;g id="edge474" class="edge"&gt;&lt;title&gt;RADCAT&amp;#45;&amp;gt;CATEGORY&lt;/title&gt;
+&lt;path style="fill:none;stroke:black;" d="M3505,418C3561,455 3675,544 3674,652 3674,652 3674,652 3674,1030 3675,1164 3339,2089 3276,2263"/&gt;
+&lt;polygon style="fill:black;stroke:black;" points="3279,2264 3273,2272 3273,2261 3279,2264"/&gt;
+&lt;/g&gt;
+&lt;!-- ACPLOT --&gt;
+&lt;g id="node14" class="node"&gt;&lt;title&gt;ACPLOT&lt;/title&gt;
+&lt;polygon style="fill:yellow;stroke:yellow;" points="3815,4 3745,4 3745,40 3815,40 3815,4"/&gt;
+&lt;text text-anchor="middle" x="3780" y="27"&gt;ACPLOT&lt;/text&gt;
+&lt;/g&gt;
+&lt;!-- PPCURVE --&gt;
+&lt;g id="node16" class="node"&gt;&lt;title&gt;PPCURVE&lt;/title&gt;
+&lt;polygon style="fill:yellow;stroke:yellow;" points="3820,130 3740,130 3740,166 3820,166 3820,130"/&gt;
+&lt;text text-anchor="middle" x="3780" y="153"&gt;PPCURVE&lt;/text&gt;
+&lt;/g&gt;
+&lt;!-- ACPLOT&amp;#45;&amp;gt;PPCURVE --&gt;
+&lt;g id="edge12" class="edge"&gt;&lt;title&gt;ACPLOT&amp;#45;&amp;gt;PPCURVE&lt;/title&gt;
+&lt;path style="fill:none;stroke:black;" d="M3780,40C3780,61 3780,95 3780,120"/&gt;
+&lt;polygon style="fill:black;stroke:black;" points="3784,120 3780,130 3777,120 3784,120"/&gt;
+&lt;/g&gt;
+&lt;!-- AGG --&gt;
+&lt;g id="node17" class="node"&gt;&lt;title&gt;AGG&lt;/title&gt;
+&lt;polygon style="fill:lightblue;stroke:lightblue;" points="1048,2020 994,2020 994,2056 1048,2056 1048,2020"/&gt;
+&lt;text text-anchor="middle" x="1021" y="2043"&gt;AGG&lt;/text&gt;
+&lt;/g&gt;
+&lt;!-- TYPE --&gt;
+&lt;g id="node19" class="node"&gt;&lt;title&gt;TYPE&lt;/title&gt;
+&lt;polygon style="fill:lightblue;stroke:lightblue;" points="1361,2146 1307,2146 1307,2182 1361,2182 1361,2146"/&gt;
+&lt;text text-anchor="middle" x="1334" y="2169"&gt;TYPE&lt;/text&gt;
+&lt;/g&gt;
+&lt;!-- AGG&amp;#45;&amp;gt;TYPE --&gt;
+&lt;g id="edge14" class="edge"&gt;&lt;title&gt;AGG&amp;#45;&amp;gt;TYPE&lt;/title&gt;
+&lt;path style="fill:none;stroke:black;" d="M1048,2049C1104,2072 1234,2124 1298,2149"/&gt;
+&lt;polygon style="fill:black;stroke:black;" points="1299,2146 1307,2153 1296,2152 1299,2146"/&gt;
+&lt;/g&gt;
+&lt;!-- TYPE&amp;#45;&amp;gt;CATEGORY --&gt;
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diff --git a/src/axiom-website/download.html b/src/axiom-website/download.html
new file mode 100644
index 0000000..767259b
--- /dev/null
+++ b/src/axiom-website/download.html
@@ -0,0 +1,1050 @@
+&lt;html&gt;
+ &lt;head&gt;
+  &lt;title&gt;
+   Axiom Computer Algebra System
+  &lt;/title&gt;
+ &lt;/head&gt;
+ &lt;body bgcolor="#ffff66"&gt;
+   &lt;div id="head" align="center"&gt; 
+    &lt;a href="http://savannah.nongnu.org/projects/axiom/"&gt;
+     &lt;img src="axiom.png" border="0" alt="Axiom"&gt;
+    &lt;/a&gt;
+    &lt;br&gt;
+    &lt;font size=200%&gt;
+     The Scientific Computation System
+    &lt;/font&gt;
+   &lt;/div&gt;
+   &lt;div align="center"&gt;
+    [
+     &lt;a href="../index.html" title="Home"&gt;
+      Home
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="screenshots.html" title="Screen Shots"&gt;
+      Screenshots
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="faq.html" title="FAQ"&gt;
+      FAQ
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="download.html" title="Download"&gt;
+      Download
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="documentation.html" title="Documentation"&gt;
+      Documentation
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="currentstate.html" title="Current State"&gt;
+      Current State
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="community.html" title="Community"&gt;
+      Community
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="developers.html" title="Developers"&gt;
+      Developers
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="patches.html" title="Patches"&gt;
+      Patches
+     &lt;/a&gt;
+    ]
+   &lt;/div&gt;
+   &lt;div align="center"&gt;
+    [
+     &lt;a href="bookvol10.2abb.html" title="Abbreviation Graph"&gt;
+      Abbreviation Graph
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="bookvol10.2full.html" title="Full Name Graph"&gt;
+      Full Name Graph
+     &lt;/a&gt;
+    ]
+   &lt;/div&gt;
+  &lt;br&gt;
+  &lt;hr&gt;
+  &lt;h1&gt; Pre-compiled binaries&lt;/h1&gt;
+
+  Axiom has been compiled to run on various platforms. 
+  &lt;br&gt;
+  &lt;br&gt;
+  &lt;hr&gt;
+  &lt;p&gt;
+  This table contains links to various tar-gzipped version of files.
+  In general you need to know the name of the file you download,
+  usually something ending in .tgz (tar-gzip). You also need to know
+  where the file gets untarred, this is referred to as (where) below.
+  When you cd to the (where) location you should see the top level
+  Makefile for Axiom, the changelog, etc.
+  &lt;/p&gt;
+  &lt;p&gt;
+  Axiom builds on various platforms and uses the convention that the last
+  name in the AXIOM shell variable denotes the type of system. This is
+  referred to as the SYSNAME. You need to know which SYSNAME you downloaded.
+  &lt;/p&gt;
+  &lt;p&gt;
+  To use one of these binaries just do:
+&lt;pre&gt;
+  download the binary and untar it.
+  cd axiom
+  export AXIOM=`pwd`/mnt/SYSNAME &lt;= replace SYSNAME with actual name
+  export PATH=$AXIOM/bin:$PATH
+  axiom
+&lt;/pre&gt;
+  &lt;table border="0" cellspacing="2"&gt;
+   &lt;tbody&gt;
+    &lt;tr&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+       SYSNAME&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+       Nov 2007
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+       Jan 2008
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+       Mar 2008
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+       May 2008
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+       July 2008
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+       Sept 2008
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+       Nov 2008
+      &lt;/font&gt;
+     &lt;/td&gt;
+    &lt;/tr&gt;
+
+    &lt;tr&gt;
+     &lt;td align="left"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+       debian
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/silver-jan2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/silver-debian-jan2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-mar2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-debian-mar2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-may2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-debian-may2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-sept2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-debian-sept2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-nov2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-debian-nov2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+    &lt;/tr&gt;
+
+    &lt;tr&gt;
+     &lt;td align="left"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+       Doyen
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/silver-jan2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/silver-doyen-jan2008.iso"&gt;iso&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-mar2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-doyen-mar2008.iso"&gt;iso&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-july2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-doyen-july2008.iso"&gt;iso&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-nov2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+    &lt;/tr&gt;
+
+    &lt;tr&gt;
+     &lt;td align="left"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+       fedora5
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/silver-nov2007-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/silver-fedora5-nov182007-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/silver-jan2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/silver-fedora5-jan2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-mar2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-fedora5-mar2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-may2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-fedora5-may2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-july2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-fedora5-july2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-sept2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-fedora5-sept2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-nov2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-fedora5-nov2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+    &lt;/tr&gt;
+
+    &lt;tr&gt;
+     &lt;td align="left"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+       fedora6
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/silver-nov2007-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/silver-fedora6-nov182007-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/silver-jan2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/silver-fedora6-jan2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-mar2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-fedora6-mar2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-may2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-fedora6-may2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-july2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-fedora6-july2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-sept2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-fedora6-sept2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-nov2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-fedora6-nov2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+    &lt;/tr&gt;
+
+    &lt;tr&gt;
+     &lt;td align="left"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+       fedora7
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/silver-jan2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/silver-fedora7-jan2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-mar2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-fedora7-mar2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-may2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-fedora7-may2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-july2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-fedora7-july2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-sept2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-fedora7-sept2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-nov2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-fedora7-nov2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+    &lt;/tr&gt;
+
+    &lt;tr&gt;
+     &lt;td align="left"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+       fedora8
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/silver-nov2007-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/silver-fedora8-nov182007-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/silver-jan2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/silver-fedora8-jan2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-mar2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-fedora8-mar2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-may2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-fedora8-may2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-july2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-fedora8-july2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-sept2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-fedora8-sept2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-nov2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-fedora8-nov2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+    &lt;/tr&gt;
+
+    &lt;tr&gt;
+     &lt;td align="left"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+       fedora8-64
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-fedora8-64-mar2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-fedora8-64-mar2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-may2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-fedora-64-may2008.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-nov2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+    &lt;/tr&gt;
+
+    &lt;tr&gt;
+     &lt;td align="left"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+       fedora9
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-may2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-fedora9-may2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-july2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-fedora9-july2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-sept2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-fedora9-sept2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-nov2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-fedora9-nov2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+    &lt;/tr&gt;
+
+    &lt;tr&gt;
+     &lt;td align="left"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+       macosxppc
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/silver-jan2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/silver-macosxppc-jan2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-mar2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-macosxppc-mar2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+    &lt;/tr&gt;
+
+    &lt;tr&gt;
+     &lt;td align="left"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+       opensuse
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/silver-jan2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/silver-opensuse-jan2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-mar2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-opensuse-mar2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-may2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-opensuse-may2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-july2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-opensuse-july2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-sept2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-opensuse-sept2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-nov2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+    &lt;/tr&gt;
+
+    &lt;tr&gt;
+     &lt;td align="left"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+       redhat72
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/silver-jan2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/silver-redhat72-jan2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-mar2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-redhat72-mar2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-may2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-redhat72-may2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-july2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-redhat72-july2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-sept2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-redhat72-sept2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-nov2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-redhat72-nov2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+    &lt;/tr&gt;
+
+    &lt;tr&gt;
+     &lt;td align="left"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+       redhat9
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/silver-jan2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/silver-redhat9-jan2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-mar2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-redhat9-mar2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-may2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-redhat9-may2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-july2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-redhat9-july2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-sept2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-redhat9-sept2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-nov2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-redhat9-nov2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+    &lt;/tr&gt;
+
+    &lt;tr&gt;
+     &lt;td align="left"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+       ubuntu
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/silver-jan2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/silver-ubuntu-jan2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-mar2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-ubuntu-mar2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-may2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-ubuntu-may2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-july2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-ubuntu-july2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-sept2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-ubuntu-sept2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-nov2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-ubuntu-nov2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+    &lt;/tr&gt;
+
+    &lt;tr&gt;
+     &lt;td align="left"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+       ubuntu64
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+     &lt;td align="center"&gt;
+      &lt;font face="Helvetica, Arial, sans-serif" size="+1"&gt;
+      &lt;a href="downloads/axiom-ubuntu-nov2008-src.tgz"&gt;src&lt;/a&gt;
+      &lt;a href="downloads/axiom-ubuntu-nov2008-bin.tgz"&gt;bin&lt;/a&gt;
+      &lt;/font&gt;
+     &lt;/td&gt;
+    &lt;/tr&gt;
+
+   &lt;/tbody&gt;
+  &lt;/table&gt;
+
+
+  &lt;h4&gt;Older versions&lt;/h4&gt;
+  &lt;a href="downloads/axiom.fedora1.bin.20041109.tgz"&gt;
+  &lt;b&gt;
+   Fedora Core 1 (binary)
+  &lt;/b&gt;
+  &lt;/a&gt;
+  &lt;br&gt;
+  &lt;a href="downloads/axiom.fedora2.bin.20041109.tgz"&gt;
+  &lt;b&gt;
+   Fedora Core 2 (binary)
+  &lt;/b&gt;
+  &lt;/a&gt;
+  &lt;br&gt;
+  &lt;a href="downloads/axiom.fedora64.bin.20041110.tgz"&gt;
+  &lt;b&gt;
+   Fedora Core 2, AMD 64 bit processor (binary)
+  &lt;/b&gt;
+  &lt;/a&gt;
+  &lt;br&gt;
+
+  &lt;hr&gt;
+&lt;div id="body"&gt;
+  &lt;h1&gt;Source code&lt;/h1&gt;
+&lt;p&gt;
+Axiom source code is maintained in a &lt;b&gt;Gold&lt;/b&gt; and &lt;b&gt;Silver&lt;/b&gt;
+version. The &lt;b&gt;Gold&lt;/b&gt; version is the "released" version. Gold
+versions are released every two months.
+&lt;br/&gt;
+The &lt;b&gt;Silver&lt;/b&gt; version is the current "bleeding edge" that 
+contains changes which will be tested and released into &lt;b&gt;Gold&lt;/b&gt;
+every two months. Unless you need a recent feature or bug fix, or are
+working as a developer, there is no reason to use &lt;b&gt;Silver&lt;/b&gt;
+
+&lt;!--
+  Some snapshots of the current source tree are available in the
+  &lt;a href="http://savannah.nongnu.org/files/?group=axiom"&gt;Download
+  section for Axiom on Savannah&lt;/a&gt;&lt;br/&gt;
+--&gt;
+&lt;h1&gt;GOLD SOURCES&lt;/h1&gt;
+&lt;h2&gt;Tarball&lt;/h2&gt;
+The &lt;b&gt;Gold&lt;/b&gt; (November 2008) release of Axiom is available.
+&lt;br&gt;
+The source code tarball from November, 2008 is
+&lt;a href="downloads/axiom-nov2008-src.tgz"&gt;here&lt;/a&gt;
+
+&lt;pre&gt;
+wget http://axiom.axiom-developer.org/axiom-website/downloads/axiom-july2008-src.tgz
+tar -zxf axiom-july2008-src.tgz
+cd axiom
+export AXIOM=`pwd`/mnt/&lt;SYSNAME&gt; (see table below)
+export PATH=$AXIOM/bin:$PATH
+make
+&lt;/pre&gt;
+
+
+&lt;h2&gt;GIT&lt;/h2&gt;
+You can clone the git repository from GitHub:
+
+&lt;pre&gt;
+git-clone git://github.com/daly/axiom.git
+cd axiom
+export AXIOM=`pwd`/mnt/&lt;SYSNAME&gt; (see table below)
+export PATH=$AXIOM/bin:$PATH
+make
+&lt;/pre&gt;
+
+
+&lt;h2&gt;CVS&lt;/h2&gt;
+  You can also download the source tree from CVS and compile it. To
+  download the code from sourceforge, do:
+
+&lt;pre&gt;
+export CVS_RSH="ssh"
+cvs -z3 -d:pserver:anonymous@axiom.cvs.sourceforge.net:/cvsroot/axiom co -P axiom 
+cd axiom
+export AXIOM=`pwd`/mnt/&lt;SYSNAME&gt; (see table below)
+export PATH=$AXIOM/bin:$PATH
+make
+&lt;/pre&gt;
+
+Or you can download the sourcecode from savannah:
+&lt;pre&gt;
+export CVS_RSH="ssh"
+cvs -z3 -d:pserver:anonymous@cvs.savannah.nongnu.org:/sources/axiom co -P axiom 
+cd axiom
+export AXIOM=`pwd`/mnt/&lt;SYSNAME&gt; (see table below)
+export PATH=$AXIOM/bin:$PATH
+make
+&lt;/pre&gt;
+
+
+  &lt;hr&gt;
+  &lt;h1&gt;Compile notes&lt;/h1&gt;
+   &lt;p&gt;In general, various systems insist on moving critical files
+      around or, worse yet, don't install needed files. These notes
+      show particular details for known systems
+   &lt;/a&gt;
+  &lt;h3&gt;Ubuntu&lt;/h3&gt;
+   &lt;pre&gt;
+echo 0 &gt;/proc/sys/kernel/randomize_va_space
+apt-get install cvs m4 libxpm-dev libxt-dev x-dev libx11-dev libxext-dev gettext git-core texlive gawk
+cvs -z3 -d:pserver:anonymous@axiom.cvs.sourceforge.net:/cvsroot/axiom co -P axiom
+cd axiom
+export AXIOM=`pwd`/mnt/ubuntu
+export PATH=$AXIOM/bin:$PATH
+make
+   &lt;/pre&gt;
+
+  &lt;h3&gt;OpenSuSE&lt;/h3&gt;
+   &lt;pre&gt;
+echo 0 &gt;/proc/sys/kernel/exec_shield
+echo 0 &gt;/proc/sys/kernel/randomize_va_space
+rpm -i texlive-latex-2007-69.noarch.rpm
+cvs -z3 -d:pserver:anonymous@axiom.cvs.sourceforge.net:/cvsroot/axiom co -P axiom
+cd axiom
+export AXIOM=`pwd`/mnt/opensuse
+export PATH=$AXIOM/bin:$PATH
+make
+   &lt;/pre&gt;
+
+  &lt;h3&gt;debian&lt;/h3&gt;
+   &lt;pre&gt;
+You might have to add a line to /etc/apt/sources.list like:
+  deb http://ftp.debian.org/debian etch main contrib
+and then do:
+apt-get update
+
+Next you need to install these packages:
+
+apt-get install gcc libc6-dev build-essential debhelper g++ g++-4.1 gcl 
+apt-get install gettext gs-gpl html2text intltool-debian libgmp3-dev
+apt-get install libgmp3c2 libgmpxx4 libice-dev libxau-dev libxaw-headers
+apt-get install libxaw7-dev libxdmcp-dev libxext-dev libxmu-dev libxmu-headers
+apt-get install libxpm-dev libxt-dev po-debconf x-dev x11proto-core-dev
+apt-get install x11proto-input-dev x11proto-kb-dev x11proto-xext-dev
+apt-get install xtrans-dev libncurses5-dev libreadline5-dev libsm-dev
+apt-get install libstdc++6-4.1-dev libx11-dev gawk
+cvs -z3 -d:pserver:anonymous@axiom.cvs.sourceforge.net:/cvsroot/axiom co -P axiom
+cd axiom
+export AXIOM=`pwd`/mnt/debian
+export PATH=$AXIOM/bin:$PATH
+make
+   &lt;/pre&gt;
+
+  &lt;h3&gt;Mac OSX PPC&lt;/h3&gt;
+The MAC port has a few issues. The known problems are:
+&lt;pre&gt;
+The pseudo-terminals (/dev/pty) don't work so the hyperdoc/graphics fails.
+This is still under study.
+
+The )browse command works but you have to use the latest firefox because
+safari does not seem to know about the http request object.
+
+There is a nasty interaction between CVS and OSX. Apparently CVS won't
+let you delete directories. OSX considers two names that differ only
+by case to be the same thing. Axiom did a global downcase of all
+filenames but CVS doesn't want to delete directories so the uppercase
+ones overwrite the lowercase ones. The fix is to use the sources
+from git rather than from CVS.
+&lt;/pre&gt;
+  &lt;pre&gt;
+install xcode from http://developer.apple.com/tools/download
+download and untar the sources from the apple website.
+
+cd axiom
+export AXIOM=`pwd`/mnt/macosxppc
+export PATH=/sw/bin:$AXIOM/bin:$PATH
+make
+  &lt;/pre&gt;
+
+&lt;!--
+  &lt;h3&gt;Intel Mac OSX &lt;/h3&gt;
+The Intel MAC port has a few issues. The known problems are:
+&lt;pre&gt;
+install xcode from http://developer.apple.com/tools/download
+intall latex from http://www.tug.org/mactex
+
+cd axiom
+export AXIOM=`pwd`/mnt/macosxppc
+export PATH=/sw/bin:$AXIOM/bin:$PATH
+make
+&lt;/pre&gt;
+--&gt;
+
+  &lt;h3&gt;Doyen&lt;/h3&gt;
+&lt;p&gt; The Doyen image was created by Jose Alfredo Portes&lt;/p&gt;
+
+  &lt;hr&gt;
+  &lt;p&gt;
+  The book is included in the binary distribution. To view it type:
+  &lt;br&gt;
+  &lt;b&gt;
+  xdvi (where)/mnt/(SYSNAME)/doc/book.dvi
+  &lt;/b&gt;
+  &lt;/p&gt;
+  &lt;p&gt;
+  The tutorial is also included in the binary distribution. To view it type:
+  &lt;br&gt;
+  &lt;b&gt;
+  xdvi (where)/mnt/(SYSNAME)/doc/bookvol1.dvi
+  &lt;/b&gt;
+  &lt;/p&gt;
+  &lt;hr&gt;
+  Axiom is also available as a pre-compiled package in:
+  &lt;ul&gt;
+   &lt;li&gt; Debian sid: 
+    &lt;a href="http://packages.debian.org/etch/axiom"&gt;
+    http://packages.debian.org/etch/axiom&lt;/a&gt; &lt;/li&gt;
+  &lt;/ul&gt;
+
+
+ &lt;/div&gt;
+In general, you download the binary to a location and then type:
+&lt;pre&gt;
+  tar -zxf binaryname.tgz
+     this creates a directory called "mnt"
+     in "mnt" there is a directory which is the sysname.
+     for instance, you'll see mnt/fedora5 so the sysname is fedora5
+  export AXIOM=`pwd`/mnt/(sysname)
+  export PATH=$AXIOM/bin:$PATH
+  axiom
+&lt;/pre&gt;
+You do not need the source code to run Axiom.
+Everything is in the binary.
+If you do choose to build from the sources you download the source
+and then type:
+&lt;pre&gt;
+  tar -zxf sourcename.tgz
+    this creates a directory called "axiom"
+    the sysname is given in the column head of the following table
+  cd axiom
+  export AXIOM=`pwd`/mnt/(sysname)
+  export PATH=$AXIOM/bin:$PATH
+  make
+&lt;/pre&gt;
+Note that if the make fails on some systems it may be due to the
+security setup. As root you can try:
+&lt;pre&gt;
+ echo 0 &gt;/proc/sys/kernel/exec-shield
+ echo 0 &gt;/proc/sys/kernel/randomize_va_space
+&lt;/pre&gt;
+Both of these settings have caused build problems.
+
+&lt;/body&gt;
+&lt;/html&gt;
+
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+&lt;html&gt;
+ &lt;head&gt;
+  &lt;title&gt;
+   Axiom Computer Algebra System
+  &lt;/title&gt;
+ &lt;/head&gt;
+ &lt;body bgcolor="#ffff66"&gt;
+   &lt;div id="head" align="center"&gt; 
+    &lt;a href="http://savannah.nongnu.org/projects/axiom/"&gt;
+     &lt;img src="axiom.png" border="0" alt="Axiom"&gt;
+    &lt;/a&gt;
+    &lt;br&gt;
+    &lt;font size=200%&gt;
+     The Scientific Computation System
+    &lt;/font&gt;
+   &lt;/div&gt;
+   &lt;div align="center"&gt;
+    [
+     &lt;a href="../index.html" title="Home"&gt;
+      Home
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="screenshots.html" title="Screen Shots"&gt;
+      Screenshots
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="faq.html" title="FAQ"&gt;
+      FAQ
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="download.html" title="Download"&gt;
+      Download
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="documentation.html" title="Documentation"&gt;
+      Documentation
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="currentstate.html" title="Current State"&gt;
+      Current State
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="community.html" title="Community"&gt;
+      Community
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="developers.html" title="Developers"&gt;
+      Developers
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="patches.html" title="Patches"&gt;
+      Patches
+     &lt;/a&gt;
+    ]
+   &lt;/div&gt;
+   &lt;div align="center"&gt;
+    [
+     &lt;a href="bookvol10.2abb.html" title="Abbreviation Graph"&gt;
+      Abbreviation Graph
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="bookvol10.2full.html" title="Full Name Graph"&gt;
+      Full Name Graph
+     &lt;/a&gt;
+    ]
+   &lt;/div&gt;
+  &lt;br&gt;
+  &lt;hr&gt;
+
+&lt;div id="body"&gt;
+  &lt;h1&gt;FAQ&lt;/h1&gt;
+
+  &lt;dl&gt;
+    &lt;dt&gt;
+     &lt;font size=5&gt;
+     What is Axiom license?
+     &lt;/font&gt;
+    &lt;/dt&gt;
+    &lt;dd&gt;
+     Axiom is free software, available under a BSD like license. For
+     more details, please have a look in the &lt;a
+     href="http://savannah.nongnu.org/cgi-bin/viewcvs/axiom/axiom/license/"&gt;licences
+     available in the CVS repository&lt;/a&gt;.
+    &lt;/dd&gt;
+
+    &lt;dt&gt;
+     &lt;font size=5&gt;
+      What is the future of Axiom?
+     &lt;/font&gt;
+    &lt;/dt&gt;
+    &lt;dd&gt;
+
+        Tim Daly is Lead Axiom Developer. He has a &lt;a
+        href="currentstate.html"&gt;fairly detailed agenda for Axiom&lt;/a&gt;.
+
+    &lt;/dd&gt;
+
+    &lt;dt&gt;
+     &lt;font size=5&gt;
+      What is Axiom size?
+     &lt;/font&gt;
+    &lt;/dt&gt;
+    &lt;dd&gt; 
+
+        Axiom is:
+        &lt;ul&gt;
+          &lt;li&gt;92 MB of source code&lt;/li&gt;
+          &lt;li&gt;about 56 MB once compiled&lt;/li&gt;
+          &lt;li&gt;403591 lines for the interpreted in 220 files&lt;/li&gt;
+          &lt;li&gt;255790 lines of algebra in 371 files&lt;/li&gt;
+        &lt;/ul&gt;
+
+    &lt;/dd&gt;
+
+    &lt;dt&gt;
+     &lt;font size=5&gt;
+      On which system is known to run Axiom?
+     &lt;/font&gt;
+    &lt;/dt&gt;
+    &lt;dd&gt; 
+
+        People have compiled and run Axiom on:
+        &lt;ul&gt;
+
+           &lt;li&gt;Debian GNU/Linux 3.0, on i386, Sparc64. On PowerPC
+               architecture, Axiom will &lt;em&gt;not&lt;/em&gt; build because it
+               requires gcc-3.3 (which supports -mlong-calls option,
+               supporting relocs of more tha 24 bits).
+               &lt;/li&gt;
+
+           &lt;li&gt;Debian GNU/Linux sid, on mipsel, ia64, i386, ppc, alpha,
+               and sparc (and &lt;a
+               href="http://buildd.debian.org/build.php?pkg=axiom"&gt;more
+               to come!&lt;/a&gt;)&lt;/li&gt;
+
+           &lt;li&gt;RedHat Linux 7.3 and 9.0 on i386&lt;/li&gt;
+
+           &lt;li&gt;Slackware Linux 8.0.01 on Intel ProLiant ML530
+           2@800MHz&lt;/li&gt;
+
+           &lt;li&gt; Red Hat Linux 8.0 on Intel ProLiant ML530 2@1.0GHz 
+                -- Red Hat Enterprise Linux ES release 2.1 (Panama)&lt;/li&gt;
+
+           &lt;li&gt;SuSE Linux Ent Svr 8.0 on Intel ProLiant DL360 G2
+           2@1.4GHz&lt;/li&gt;
+
+           &lt;li&gt;Red Flag Linux 4.0&lt;/li&gt;
+
+           &lt;li&gt;Microsoft Windows&lt;/li&gt;
+        &lt;/ul&gt;
+
+    &lt;/dd&gt;
+
+    &lt;dt&gt;
+     &lt;font size=5&gt;
+     How do I submit a patch?
+     &lt;/font&gt;
+    &lt;/dt&gt;
+    &lt;dd&gt;
+&lt;pre&gt;
+In general a patch file is of the form
+
+cd the.dir
+diff -Naur file.pamphlet file.pamphlet.new &amp;gt;the.dir.file.pamphlet.patch
+send the patch to the Axiom mailing list 
+&amp;lt;axiom-developer@nongngu.org&amp;gt or
+Tim Daly &amp;lt;daly@axiom-developer.org&amp;gt;
+
+this has several features:
+  * it tells me where the patch is being applied
+  * the Naur options give me context
+  * I can see the impact of a change to multiple files
+
+I read the patches before applying them so be sure to document the
+reasons for the change in the pamphlet file. It may seem trivial
+but remember that I didn't do the initial analysis so I, and others,
+will have to understand after the fact.
+
+In most cases in a pamphlet file if you're changing a few lines
+of code or a whole function it should be documented thus:
+
+
+...
+
+(defun foo ()
+  (list
+    "this is ok code"
+    "this is broken code"
+    "this is also broken"
+    "this is ok"
+  )
+)
+ 
+turns into
+
+\subsection{foo list fix}
+This code used to read:
+\begin{verbatim}
+    "this is broken code"
+    "this is also broken"
+\end{verbatim}
+but clearly the elements of the list are wrong. We are going to
+print this list for the user so we don't want them to know anything
+is broken. Thus we have wonderful new code that will inspire confidence.
+This list is printed with the [[printlist]] function.
+&amp;lt;&amp;lt;foo list fix&amp;gt;&amp;gt;=
+    "this is great code"
+    "this inspires confidence"
+@
+
+
+...
+
+(defun foo ()
+  (list
+    "this is ok code"
+&amp;lt;&amp;lt;foo list fix&amp;gt;&amp;gt;
+    "this is ok"
+  )
+)
+
+and, yes, I do know that this is tedious.
+
+In general, it is also useful to update the pamphlet files with 
+documentation-only changes as you understand what a block of code
+is intended to do. Most of this information has been lost to history
+and the world can leverage your efforts at understanding if you take
+the time to document it. In many ways this is as important as fixing
+the code.
+&lt;/pre&gt;
+  &lt;/dd&gt;
+
+  &lt;/dl&gt;
+ &lt;/div&gt;
+&lt;/body&gt;
+&lt;/html&gt;
+
diff --git a/src/axiom-website/index.html b/src/axiom-website/index.html
new file mode 100644
index 0000000..741592d
--- /dev/null
+++ b/src/axiom-website/index.html
@@ -0,0 +1,214 @@
+&lt;html&gt;
+ &lt;head&gt;
+  &lt;title&gt;
+   Axiom Computer Algebra System
+  &lt;/title&gt;
+ &lt;/head&gt;
+ &lt;body bgcolor="#ffff66"&gt;
+   &lt;div id="head" align="center"&gt; 
+    &lt;a href="http://savannah.nongnu.org/projects/axiom/"&gt;
+     &lt;img src="axiom-website/axiom.png" border="0" alt="Axiom"&gt;
+    &lt;/a&gt;
+    &lt;br&gt;
+    &lt;font size=200%&gt;
+     The Scientific Computation System
+    &lt;/font&gt;
+   &lt;/div&gt;
+   &lt;div align="center"&gt;
+    [
+     &lt;a href="index.html" title="Home"&gt;
+      Home
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="axiom-website/screenshots.html" title="Screen Shots"&gt;
+      Screenshots
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="axiom-website/faq.html" title="FAQ"&gt;
+      FAQ
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="axiom-website/download.html" 
+        title="Download"&gt;
+      Download
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="axiom-website/documentation.html" title="Documentation"&gt;
+      Documentation
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="axiom-website/currentstate.html" title="Current State"&gt;
+      Current State
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="axiom-website/community.html" title="Community"&gt;
+      Community
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="axiom-website/developers.html" title="Developers"&gt;
+      Developers
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="axiom-website/patches.html" title="Patches"&gt;
+      Patches
+     &lt;/a&gt;
+    ]
+   &lt;/div&gt;
+   &lt;div align="center"&gt;
+    [
+     &lt;a href="axiom-website/bookvol10.2abb.html" title="Abbreviation Graph"&gt;
+      Abbreviation Graph
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="axiom-website/bookvol10.2full.html" title="Full Name Graph"&gt;
+      Full Name Graph
+     &lt;/a&gt;
+    ]
+   &lt;/div&gt;
+  &lt;br&gt;
+  &lt;hr&gt;
+DOCUMENTATION:
+&lt;ul&gt;
+ &lt;li&gt;Books
+  &lt;ul&gt;
+   &lt;li&gt;
+    &lt;a href="axiom-website/book.pdf"&gt;
+     Jenks, R.D and Sutor R, "Axiom: The Scientific Computation System"
+    &lt;/a&gt;
+   &lt;/li&gt;
+   &lt;li&gt;
+    &lt;a href="axiom-website/bookvol1.pdf"&gt;
+     Daly, T, "Axiom Volume 1: Tutorial"
+    &lt;/a&gt;
+   &lt;/li&gt;
+  &lt;/ul&gt;
+ &lt;/li&gt;
+ &lt;li&gt;Literate Documents
+  &lt;ul&gt;
+   &lt;li&gt;
+    &lt;a href="axiom-website/dhmatrix.spad.pdf"&gt;dhmatrix.spad.pdf&lt;/a&gt;
+   &lt;/li&gt;
+  &lt;/ul&gt;
+ &lt;/li&gt;
+ &lt;li&gt;Release Notes
+  &lt;ul&gt;
+   &lt;li&gt;
+    &lt;a href="axiom-website/releasenotes.html"&gt;Release Notes&lt;/a&gt;
+   &lt;/li&gt;
+  &lt;/ul&gt;
+ &lt;/li&gt;
+ &lt;li&gt;Blogs
+  &lt;ul&gt;
+   &lt;li&gt;
+    &lt;a href="http://amca01.wordpress.com/2008/05/25/an-introduction-to-axiom-1"&gt;Alasdair's Musings&lt;/a&gt;
+   &lt;/li&gt;
+  &lt;/ul&gt;
+ &lt;/li&gt;
+&lt;/ul&gt;
+
+
+  &lt;div id="body"&gt;
+   &lt;h1&gt;
+    What is Axiom?
+   &lt;/h1&gt;
+   &lt;p&gt;
+   &lt;font size=4&gt;
+  Axiom has been in development since 1971. At that time, it was called
+  Scratchpad. Scratchpad was a large, general purpose computer algebra
+  system that was originally developed by IBM under the direction of
+  Richard Jenks.  The project started in 1971 and evolved slowly.  Barry
+  Trager was key to the technical direction of the project. Scratchpad
+  developed over a 20 year stretch and was basically considered as a
+  research platform for developing new ideas in computational
+  mathematics. In the 1990s, as IBM's fortunes slid, the Scratchpad
+  project was renamed to Axiom, sold to the Numerical Algorithms Group
+  (NAG) in England and became a commercial system.  As part of the
+  Scratchpad project at IBM in Yorktown 
+  &lt;a href="http://daly.axiom-developer.org"&gt;
+  Tim Daly
+  &lt;/a&gt; 
+  worked on all aspects
+  of the system and eventually helped transfer the product to NAG. For a
+  variety of reasons it never became a financial success and NAG
+  withdrew it from the market in October, 2001.
+   &lt;/font&gt;
+   &lt;/p&gt;
+ &lt;p&gt;
+   &lt;font size=4&gt;
+  NAG agreed to release Axiom as free software. The basic motivation was
+  that Axiom represents something different from other programs in a lot
+  of ways. Primarily because of its foundation in mathematics the Axiom
+  system will potentially be useful 30 years from now.  In its current
+  state it represents about 30 years and 300 man-years of research
+  work. To strive to keep such a large collection of knowledge alive
+  seems a worthwhile goal.
+   &lt;/font&gt;
+   &lt;/p&gt;&lt;p&gt;
+   &lt;font size=4&gt;
+  Efforts are underway to extend this software to 
+  &lt;ul&gt;
+  &lt;li&gt; (a) develop a better user interface 
+  &lt;li&gt; (b) make it useful as a teaching tool 
+  &lt;li&gt; (c) develop an algebra server protocol 
+  &lt;li&gt; (d) integrate additional mathematics 
+  &lt;li&gt; (e) rebuild the algebra in a literate programming style 
+  &lt;li&gt; (f) integrate logic programming 
+  &lt;li&gt; (g) develop an Axiom Journal with refereed submissions.
+  &lt;/ul&gt;
+&lt;/p&gt;
+  &lt;/div&gt;
+   &lt;p&gt;
+   &lt;font size=4&gt;
+  Axiom is a general purpose Computer Algebra system. It is useful for
+  research and development of mathematical algorithms. It defines a
+  strongly typed, mathematically correct type hierarchy. It has a
+  programming language and a built-in compiler.
+   &lt;/font&gt;
+   &lt;/p&gt;
+ &lt;p&gt;&lt;font size=4&gt;
+  Axiom development was partially supported by 
+  &lt;a href="http://www.caissny.org"&gt;CAISS&lt;/A&gt;, 
+  the Center for Algorithms and Interactive Scientific Software. 
+  CAISS is a joint effort of the Computer Science and Mathematics
+  Departments of The City College of New York, part of the City
+  University system. Support by CAISS and CCNY is gratefully acknowledged.
+  In particular, the support by 
+  &lt;br&gt;
+  &lt;pre&gt;
+   Matthew Goldstein  CUNY Chancellor
+   Zeev Dagan         CCNY Provost
+   Maria Tamargo      CCNY Dean of Science
+   Joseph Barba       CCNY Dean of Engineering
+   Gilbert Baumslag   CCNY Distinguish Professor, Director of CAISS
+   Douglas Troeger    CCNY Computer Science Chair
+   Ed Grossman        CCNY Mathematics Chair
+  &lt;/pre&gt;
+   &lt;/font&gt;
+   &lt;/p&gt;
+  &lt;a href="http://sourceforge.net"&gt;
+   &lt;img src="http://sourceforge.net/sflogo.php?group_id=48359&amp;amp;type=1" 
+    width="88" height="31" border="0" alt="SourceForge.net Logo" /&gt;
+  &lt;/a&gt;
+   &lt;div id="date" align="right"&gt;&lt;small&gt;Last Update: November 2008&lt;/small&gt;&lt;/div&gt;
+&lt;/body&gt;
+&lt;/html&gt;
+
+
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diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html
new file mode 100644
index 0000000..b717fce
--- /dev/null
+++ b/src/axiom-website/patches.html
@@ -0,0 +1,740 @@
+&lt;html&gt;
+ &lt;head&gt;
+  &lt;title&gt;
+   Axiom Computer Algebra System
+  &lt;/title&gt;
+ &lt;/head&gt;
+ &lt;body bgcolor="#ffff66"&gt;
+   &lt;div id="head" align="center"&gt; 
+    &lt;a href="http://savannah.nongnu.org/projects/axiom/"&gt;
+     &lt;img src="axiom.png" border="0" alt="Axiom"&gt;
+    &lt;/a&gt;
+    &lt;br&gt;
+    &lt;font size=200%&gt;
+     The Scientific Computation System
+    &lt;/font&gt;
+   &lt;/div&gt;
+   &lt;div align="center"&gt;
+    [
+     &lt;a href="../index.html" title="Home"&gt;
+      Home
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="screenshots.html" title="Screen Shots"&gt;
+      Screenshots
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="faq.html" title="FAQ"&gt;
+      FAQ
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="download.html" title="Download"&gt;
+      Download
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="documentation.html" title="Documentation"&gt;
+      Documentation
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="currentstate.html" title="Current State"&gt;
+      Current State
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="community.html" title="Community"&gt;
+      Community
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="developers.html" title="Developers"&gt;
+      Developers
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="patches.html" title="Patches"&gt;
+      Patches
+     &lt;/a&gt;
+    ]
+   &lt;/div&gt;
+   &lt;div align="center"&gt;
+    [
+     &lt;a href="bookvol10.2abb.html" title="Abbreviation Graph"&gt;
+      Abbreviation Graph
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="bookvol10.2full.html" title="Full Name Graph"&gt;
+      Full Name Graph
+     &lt;/a&gt;
+    ]
+   &lt;/div&gt;
+  &lt;br&gt;
+  &lt;hr&gt;
+
+RELEASES
+&lt;ul&gt;
+ &lt;li&gt;&lt;a href="#latest"&gt;Latest&lt;/li&gt;
+ &lt;li&gt;&lt;a href="#20081123"&gt;November 23, 2008&lt;/li&gt;
+ &lt;li&gt;&lt;a href="#20080923"&gt;September 23, 2008&lt;/li&gt;
+ &lt;li&gt;&lt;a href="#20080723"&gt;July 23, 2008&lt;/li&gt;
+ &lt;li&gt;&lt;a href="#20080527"&gt;May 27, 2008&lt;/li&gt;
+ &lt;li&gt;&lt;a href="#20080325"&gt;March 25, 2008&lt;/li&gt;
+ &lt;li&gt;&lt;a href="#20080125"&gt;January 25, 2008&lt;/li&gt;
+ &lt;li&gt;&lt;a href="#20071123"&gt;November 23, 2007&lt;/li&gt;
+&lt;/ul&gt;
+
+  &lt;hr&gt;
+  &lt;h3&gt;November 2007 release&lt;/h3&gt;
+&lt;a name="20071123"/&gt;
+&lt;a href="releasenotes.html#20081123"&gt;November 2007 Release Notes
+&lt;/a&gt;&lt;br/&gt;&lt;br/&gt;
+  &lt;hr&gt;
+&lt;a href="patches/20070721.01.tpd.patch"&gt;20070721.01.tpd.patch&lt;/a&gt;
+update contributor name list&lt;br/&gt;
+&lt;a href="patches/20070721.02.tpd.patch"&gt;20070721.02.tpd.patch&lt;/a&gt;
+make evalSharpOne declare arg specials (Waldek Hebisch)&lt;br/&gt;
+&lt;a href="patches/20070722.01.tpd.patch"&gt;20070722.01.tpd.patch&lt;/a&gt;
+cleanup latex warnings&lt;br/&gt;
+&lt;a href="patches/20070810.01.tpd.patch"&gt;20070810.01.tpd.patch&lt;/a&gt;
+remove metameta&lt;br/&gt;
+&lt;a href="patches/20070811.01.tpd.patch"&gt;20070811.01.tpd.patch&lt;/a&gt;
+add mathml (Arthur Ralfs)&lt;br/&gt;
+&lt;a href="patches/20070811.02.tpd.patch"&gt;20070811.02.tpd.patch&lt;/a&gt;
+remove spurious trace debug calls (Greg Vanuxem)&lt;br/&gt;
+&lt;a href="patches/20070811.03.tpd.patch"&gt;20070811.03.tpd.patch&lt;/a&gt;
+fix digits-by-radix (Steve Wilson)&lt;br/&gt;
+&lt;a href="patches/20070812.01.tpd.patch"&gt;20070812.01.tpd.patch&lt;/a&gt;
+remerge input branch&lt;br/&gt;
+&lt;a href="patches/20070812.02.tpd.patch"&gt;20070812.02.tpd.patch&lt;/a&gt;
+mathml license change&lt;br/&gt;
+&lt;a href="patches/20070812.03.tpd.patch"&gt;20070812.03.tpd.patch&lt;/a&gt;
+newton.spad added&lt;br/&gt;
+&lt;a href="patches/20070819.01.tpd.patch"&gt;20070819.01.tpd.patch&lt;/a&gt;
+move commands into bookvol6&lt;br/&gt;
+&lt;a href="patches/20070821.01.tpd.patch"&gt;20070821.01.tpd.patch&lt;/a&gt;
+remove bookvol6.idx file&lt;br/&gt;
+&lt;a href="patches/20070821.02.tpd.patch"&gt;20070821.02.tpd.patch&lt;/a&gt;
+move axiom command to bookvol6&lt;br/&gt;
+&lt;a href="patches/20070822.01.tpd.patch"&gt;20070822.01.tpd.patch&lt;/a&gt;
+document the axiom command&lt;br/&gt;
+&lt;a href="patches/20070822.02.tpd.patch"&gt;20070822.02.tpd.patch&lt;/a&gt;
+add )help files&lt;br/&gt;
+&lt;a href="patches/20070823.01.tpd.patch"&gt;20070823.01.tpd.patch&lt;/a&gt;
+add )help files&lt;br/&gt;
+&lt;a href="patches/20070824.01.tpd.patch"&gt;20070824.01.tpd.patch&lt;/a&gt;
+add )help documentation to algebra sources&lt;br/&gt;
+&lt;a href="patches/20070826.01.tpd.patch"&gt;20070826.01.tpd.patch&lt;/a&gt;
+add )help files&lt;br/&gt;
+&lt;a href="patches/20070826.02.tpd.patch"&gt;20070826.02.tpd.patch&lt;/a&gt;
+add )help files&lt;br/&gt;
+&lt;a href="patches/20070826.03.tpd.patch"&gt;20070826.03.tpd.patch&lt;/a&gt;
+update VERSION variable&lt;br/&gt;
+&lt;a href="patches/20070901.01.tpd.patch"&gt;20070901.01.tpd.patch&lt;/a&gt;
+add )help files&lt;br/&gt;
+&lt;a href="patches/20070903.01.tpd.patch"&gt;20070903.01.tpd.patch&lt;/a&gt;
+add )help files&lt;br/&gt;
+&lt;a href="patches/20070905.01.tpd.patch"&gt;20070905.01.tpd.patch&lt;/a&gt;
+add )help files&lt;br/&gt;
+&lt;a href="patches/20070906.01.tpd.patch"&gt;20070906.01.tpd.patch&lt;/a&gt;
+add )help files&lt;br/&gt;
+&lt;a href="patches/20070907.01.tpd.patch"&gt;20070907.01.tpd.patch&lt;/a&gt;
+copy axiom command to int&lt;br/&gt;
+&lt;a href="patches/20070907.02.tpd.patch"&gt;20070907.02.tpd.patch&lt;/a&gt;
+make regression respect NOISE variable&lt;br/&gt;
+&lt;a href="patches/20070909.01.tpd.patch"&gt;20070909.01.tpd.patch&lt;/a&gt;
+remove duplicate newton.spad&lt;br/&gt;
+&lt;a href="patches/20070913.01.tpd.patch"&gt;20070913.01.tpd.patch&lt;/a&gt;
+schaum1.input added&lt;br/&gt;
+&lt;a href="patches/20070914.01.tpd.patch"&gt;20070914.01.tpd.patch&lt;/a&gt;
+fix )hd restart (Jose Portes)&lt;br/&gt;
+&lt;a href="patches/20070914.02.tpd.patch"&gt;20070914.02.tpd.patch&lt;/a&gt;
+remove double )spool from regression tests&lt;br/&gt;
+&lt;a href="patches/20070914.03.tpd.patch"&gt;20070914.03.tpd.patch&lt;/a&gt;
+fix bad bracing of )hd command&lt;br/&gt;
+&lt;a href="patches/20070915.01.tpd.patch"&gt;20070915.01.tpd.patch&lt;/a&gt;
+cleanup regression tests&lt;br/&gt;
+&lt;a href="patches/20070915.02.tpd.patch"&gt;20070915.02.tpd.patch&lt;/a&gt;
+100 integrate((z^a+1)^b,z) infinite loop&lt;br/&gt;
+&lt;a href="patches/20070916.01.tpd.patch"&gt;20070916.01.tpd.patch&lt;/a&gt;
+103 solve(z=z,z)&lt;br/&gt;
+&lt;a href="patches/20070921.01.tpd.patch"&gt;20070921.01.tpd.patch&lt;/a&gt;
+101 laplace(log(z),z,w) &lt;br/&gt;
+&lt;a href="patches/20070927.01.tpd.patch"&gt;20070927.01.tpd.patch&lt;/a&gt;
+add pfaffian regression test&lt;br/&gt;
+&lt;a href="patches/20070929.01.tpd.patch"&gt;20070929.01.tpd.patch&lt;/a&gt;
+remove pfaffian regression test&lt;br/&gt;
+&lt;a href="patches/20071003.01.tpd.patch"&gt;20071003.01.tpd.patch&lt;/a&gt;
+add AxiomServer domain&lt;br/&gt;
+&lt;a href="patches/20071004.01.tpd.patch"&gt;20071004.01.tpd.patch&lt;/a&gt;
+kamke0 ODE regression tests&lt;br/&gt;
+&lt;a href="patches/20071004.02.tpd.patch"&gt;20071004.02.tpd.patch&lt;/a&gt;
+kamke1 ODE regression tests&lt;br/&gt;
+&lt;a href="patches/20071005.01.tpd.patch"&gt;20071005.01.tpd.patch&lt;/a&gt;
+kamke2 ODE regression tests&lt;br/&gt;
+&lt;a href="patches/20071005.02.tpd.patch"&gt;20071005.02.tpd.patch&lt;/a&gt;
+kamke3 ODE regression tests&lt;br/&gt;
+&lt;a href="patches/20071005.03.tpd.patch"&gt;20071005.03.tpd.patch&lt;/a&gt;
+kamke4 ODE regression tests&lt;br/&gt;
+&lt;a href="patches/20071005.04.tpd.patch"&gt;20071005.04.tpd.patch&lt;/a&gt;
+kamke5 ODE regression tests&lt;br/&gt;
+&lt;a href="patches/20071006.01.tpd.patch"&gt;20071006.01.tpd.patch&lt;/a&gt;
+kamke6 ODE regression tests&lt;br/&gt;
+&lt;a href="patches/20071006.02.tpd.patch"&gt;20071006.02.tpd.patch&lt;/a&gt;
+kamke7 ODE regression tests&lt;br/&gt;
+&lt;a href="patches/20071013.01.acr.patch"&gt;20071013.01.acr.patch&lt;/a&gt;
+add Arthur Ralfs license&lt;br/&gt;
+&lt;a href="patches/20071014.01.acr.patch"&gt;20071014.01.acr.patch&lt;/a&gt;
+use getContentType(pathvar) in axserver (Arthur Ralfs)&lt;br/&gt;
+&lt;a href="patches/20071020.01.acr.patch"&gt;20071020.01.acr.patch&lt;/a&gt;
+fix axserver to use new return values (Arthur Ralfs)&lt;br/&gt;
+&lt;a href="patches/20071118.01.tpd.patch"&gt;20071118.01.tpd.patch&lt;/a&gt;
+7010 (209), 7011 fix i-output bugs&lt;br/&gt;
+&lt;a href="patches/20071119.01.tpd.patch"&gt;20071119.01.tpd.patch&lt;/a&gt;
+add fedora 6,7,8 stanzas&lt;br/&gt;
+
+  &lt;hr&gt;
+    &lt;h3&gt;January 2008 Release&lt;/h3&gt;
+&lt;a name="20080125"/&gt;
+&lt;a href="releasenotes.html#20080125"&gt;January 2008 Release Notes
+&lt;/a&gt;&lt;br/&gt;&lt;br/&gt;
+  &lt;hr&gt;
+&lt;a href="patches/20071129.01.tpd.patch"&gt;20071129.01.tpd.patch&lt;/a&gt;
+add zips/axiomfonts.tgz for mathml&lt;br/&gt;
+&lt;a href="patches/20071129.02.tpd.patch"&gt;20071129.02.tpd.patch&lt;/a&gt;
+remove some mathml fonts, change instructions&lt;br/&gt;
+&lt;a href="patches/20071205.01.tpd.patch"&gt;20071205.01.tpd.patch&lt;/a&gt;
+7014, 7016 fix continuedFraction mathml&lt;br/&gt;
+&lt;a href="patches/20071206.01.tpd.patch"&gt;20071206.01.tpd.patch&lt;/a&gt;
+7020 find right sourcefile for )show &lt;br/&gt;
+&lt;a href="patches/20071208.01.tpd.patch"&gt;20071208.01.tpd.patch&lt;/a&gt;
+add makeDBPage, getShow to AxiomServer domain&lt;br/&gt;
+&lt;a href="patches/20071215.01.tpd.patch"&gt;20071215.01.tpd.patch&lt;/a&gt;
+rewrite boot code to lisp and add to bookvol5&lt;br/&gt;
+&lt;a href="patches/20071215.02.tpd.patch"&gt;20071215.02.tpd.patch&lt;/a&gt;
+fix Makefile typos for bookvol11 and axbook&lt;br/&gt;
+&lt;a href="patches/20071215.03.gxv.patch"&gt;20071215.03.gxv.patch&lt;/a&gt;
+7023 fix memory leak in makegraph.c (Greg Vanuxem)&lt;br/&gt;
+&lt;a href="patches/20071216.01.tpd.patch"&gt;20071216.01.tpd.patch&lt;/a&gt;
+put Aldor into build process&lt;br/&gt;
+&lt;a href="patches/20071216.02.tpd.patch"&gt;20071216.02.tpd.patch&lt;/a&gt;
+put Aldor into build process&lt;br/&gt;
+&lt;a href="patches/20071216.03.acr.patch"&gt;20071216.03.acr.patch&lt;/a&gt;
+7019 fix F,3 mathml rendering (Arthur Ralfs)&lt;br/&gt;
+&lt;a href="patches/20071217.01.acr.patch"&gt;20071217.01.acr.patch&lt;/a&gt;
+fix hex(10) mathml rendering (Arthur Ralfs)&lt;br/&gt;
+&lt;a href="patches/20071217.02.tpd.patch"&gt;20071217.02.tpd.patch&lt;/a&gt;
+7041, 7042 ignore regression gensyms&lt;br/&gt;
+&lt;a href="patches/20071218.01.acr.patch"&gt;20071218.01.acr.patch&lt;/a&gt;
+fix lastType output (Arthur Ralfs)&lt;br/&gt;
+&lt;a href="patches/20071225.01.sxw.patch"&gt;20071225.01.sxw.patch&lt;/a&gt;
+fix top_level throw target typo (Steve Wilson)&lt;br/&gt;
+&lt;a href="patches/20071228.01.tpd.patch"&gt;20071228.01.tpd.patch&lt;/a&gt;
+create graphics for complex gamma function&lt;br/&gt;
+&lt;a href="patches/20071229.01.jap.patch"&gt;20071229.01.jap.patch&lt;/a&gt;
+fix hardcoded firefox pathnames (Jose Portes)&lt;br/&gt;
+&lt;a href="patches/20071230.01.acr.patch"&gt;20071230.01.acr.patch&lt;/a&gt;
+fix ambiguous mathml output (Arthur Ralfs)&lt;br/&gt;
+&lt;a href="patches/20071230.02.tpd.patch"&gt;20071230.02.tpd.patch&lt;/a&gt;
+update summation.input with new mathml output&lt;br/&gt;
+&lt;a href="patches/20071230.03.tpd.patch"&gt;20071230.03.tpd.patch&lt;/a&gt;
+prevent spurious remake of axbook&lt;br/&gt;
+&lt;a href="patches/20080102.01.tpd.patch"&gt;20080102.01.tpd.patch&lt;/a&gt;
+fix Makefile typo for axbook&lt;br/&gt;
+&lt;a href="patches/20080103.01.tpd.patch"&gt;20080103.01.tpd.patch&lt;/a&gt;
+7090/355 handle besselK&lt;br/&gt;
+&lt;a href="patches/20080104.01.tpd.patch"&gt;20080104.01.tpd.patch&lt;/a&gt;
+function renames in regression files&lt;br/&gt;
+&lt;a href="patches/20080104.02.tpd.patch"&gt;20080104.02.tpd.patch&lt;/a&gt;
+correct authorship of besselk patches&lt;br/&gt;
+&lt;a href="patches/20080106.01.tpd.patch"&gt;20080106.01.tpd.patch&lt;/a&gt;
+revert dgamma change&lt;br/&gt;
+&lt;a href="patches/20080107.01.tpd.patch"&gt;20080107.01.tpd.patch&lt;/a&gt;
+add multiple platforms to Makefile&lt;br/&gt;
+&lt;a href="patches/20080107.02.tpd.patch"&gt;20080107.02.tpd.patch&lt;/a&gt;
+regression test gamma and polygamma&lt;br/&gt;
+&lt;a href="patches/20080107.03.tpd.patch"&gt;20080107.03.tpd.patch&lt;/a&gt;
+regression test besselk&lt;br/&gt;
+&lt;a href="patches/20080116.01.tpd.patch"&gt;20080116.01.tpd.patch&lt;/a&gt;
+regression test special fns against Abramowitz &amp; Stegun&lt;br/&gt;
+&lt;a href="patches/20080119.01.tpd.patch"&gt;20080119.01.tpd.patch&lt;/a&gt;
+add E1 special function&lt;br/&gt;
+&lt;a href="patches/20080119.02.tpd.patch"&gt;20080119.02.tpd.patch&lt;/a&gt;
+add Franz Lehner&lt;br/&gt;
+&lt;a href="patches/20080119.03.tpd.patch"&gt;20080119.03.tpd.patch&lt;/a&gt;
+handle E1(0.0) correctly&lt;br/&gt;
+&lt;a href="patches/20080120.01.gxv.patch"&gt;20080120.01.gxv.patch&lt;/a&gt;
+handle numlock in hyperdoc (Greg Vanuxem)&lt;br/&gt;
+&lt;a href="patches/20080120.02.tpd.patch"&gt;20080120.02.tpd.patch&lt;/a&gt;
+7101/204 fix MoreSystemCommand&lt;br/&gt;
+&lt;a href="patches/20080120.03.tpd.patch"&gt;20080120.03.tpd.patch&lt;/a&gt;
+7102/412 fix equality in TBAGG&lt;br/&gt;
+&lt;a href="patches/20080125.01.tpd.patch"&gt;20080125.01.tpd.patch&lt;/a&gt;
+add En special function&lt;br/&gt;
+&lt;a href="patches/20080125.02.tpd.patch"&gt;20080125.02.tpd.patch&lt;/a&gt;
+change VERSION variable&lt;br/&gt;
+
+  &lt;hr&gt;
+    &lt;h3&gt;March 2008 Release&lt;/h3&gt;
+&lt;a name="20080325"/&gt;
+&lt;a href="releasenotes.html#20080325"&gt;March 2008 Release Notes
+&lt;/a&gt;&lt;br/&gt;&lt;br/&gt;
+  &lt;hr&gt;
+&lt;a href="patches/20080127.01.tpd.patch"&gt;20080127.01.tpd.patch&lt;/a&gt;
+refcard&lt;br/&gt;
+&lt;a href="patches/20080130.01.tpd.patch"&gt;20080130.01.tpd.patch&lt;/a&gt;
+Ei&lt;br/&gt;
+&lt;a href="patches/20080201.01.tpd.patch"&gt;20080201.01.tpd.patch&lt;/a&gt;
+7016 LexTriangularPackage&lt;br/&gt;
+&lt;a href="patches/20080209.01.tpd.patch"&gt;20080209.01.tpd.patch&lt;/a&gt;
+add Exponential Integral to book&lt;br/&gt;
+&lt;a href="patches/20080210.01.tpd.patch"&gt;20080210.01.tpd.patch&lt;/a&gt;
+powerpc-macosx defs patch&lt;br/&gt;
+&lt;a href="patches/20080215.01.tpd.patch"&gt;20080215.01.tpd.patch&lt;/a&gt;
+++E examples&lt;br/&gt;
+&lt;a href="patches/20080216.01.wxh.patch"&gt;20080216.01.wxh.patch&lt;/a&gt;
+hash tables to speed compiles&lt;br/&gt;
+&lt;a href="patches/20080216.02.tpd.patch"&gt;20080216.02.tpd.patch&lt;/a&gt;
+add function examples&lt;br/&gt;
+&lt;a href="patches/20080217.01.wxh.patch"&gt;20080217.01.wxh.patch&lt;/a&gt;
+fix hash tables to speed compiles&lt;br/&gt;
+&lt;a href="patches/20080218.01.tpd.patch"&gt;20080218.01.tpd.patch&lt;/a&gt;
+add function examples&lt;br/&gt;
+&lt;a href="patches/20080218.02.tpd.patch"&gt;20080218.02.tpd.patch&lt;/a&gt;
+add function examples&lt;br/&gt;
+&lt;a href="patches/20080219.01.tpd.patch"&gt;20080219.01.tpd.patch&lt;/a&gt;
+add additional firefox hyperdoc pages&lt;br/&gt;
+&lt;a href="patches/20080220.01.tpd.patch"&gt;20080220.01.tpd.patch&lt;/a&gt;
+add additional firefox hyperdoc pages&lt;br/&gt;
+&lt;a href="patches/20080221.01.tpd.patch"&gt;20080221.01.tpd.patch&lt;/a&gt;
+add additional firefox hyperdoc pages&lt;br/&gt;
+&lt;a href="patches/20080221.02.wxh.patch"&gt;20080221.02.wxh.patch&lt;/a&gt;
+7099 complex gamma function investigation&lt;br/&gt;
+&lt;a href="patches/20080222.01.tpd.patch"&gt;20080222.01.tpd.patch&lt;/a&gt;
+7099 logGamma vs log(Gamma)&lt;br/&gt;
+&lt;a href="patches/20080222.02.tpd.patch"&gt;20080222.02.tpd.patch&lt;/a&gt;
+add additional hyperdoc page translations&lt;br/&gt;
+&lt;a href="patches/20080222.03.tpd.patch"&gt;20080222.03.tpd.patch&lt;/a&gt;
+move hyperdoc bitmaps location&lt;br/&gt;
+&lt;a href="patches/20080229.01.tpd.patch"&gt;20080229.01.tpd.patch&lt;/a&gt;
+add additional hyperdoc page translations&lt;br/&gt;
+&lt;a href="patches/20080301.01.tpd.patch"&gt;20080301.01.tpd.patch&lt;/a&gt;
+add additional hyperdoc page translations&lt;br/&gt;
+&lt;a href="patches/20080302.01.tpd.patch"&gt;20080302.01.tpd.patch&lt;/a&gt;
+add additional hyperdoc page translations&lt;br/&gt;
+&lt;a href="patches/20080303.01.tpd.patch"&gt;20080303.01.tpd.patch&lt;/a&gt;
+add additional hyperdoc page translations&lt;br/&gt;
+&lt;a href="patches/20080304.01.tpd.patch"&gt;20080304.01.tpd.patch&lt;/a&gt;
+add additional hyperdoc page translations&lt;br/&gt;
+&lt;a href="patches/20080305.01.tpd.patch"&gt;20080305.01.tpd.patch&lt;/a&gt;
+add additional hyperdoc page translations&lt;br/&gt;
+&lt;a href="patches/20080312.01.tpd.patch"&gt;20080312.01.tpd.patch&lt;/a&gt;
+BasicSieve, primes, intfact documentation&lt;br/&gt;
+&lt;a href="patches/20080313.01.pab.patch"&gt;20080313.01.pab.patch&lt;/a&gt;
+hashcode for Aldor&lt;br/&gt;
+&lt;a href="patches/20080314.01.wxh.patch"&gt;20080314.01.wxh.patch&lt;/a&gt;
+heugcd fricas rev 256&lt;br/&gt;
+&lt;a href="patches/20080316.01.acr.patch"&gt;20080316.01.acr.patch&lt;/a&gt;
+bug 7113 invisible times&lt;br/&gt;
+&lt;a href="patches/20080316.02.tpd.patch"&gt;20080316.02.tpd.patch&lt;/a&gt;
+CATS verification&lt;br/&gt;
+&lt;a href="patches/20080317.01.tpd.patch"&gt;20080317.01.tpd.patch&lt;/a&gt;
+CATS verification&lt;br/&gt;
+&lt;a href="patches/20080318.01.tpd.patch"&gt;20080318.01.tpd.patch&lt;/a&gt;
+CATS verification&lt;br/&gt;
+&lt;a href="patches/20080323.01.tpd.patch"&gt;20080323.01.tpd.patch&lt;/a&gt;
+add menus to firefox axiom console&lt;br/&gt;
+&lt;a href="patches/20080325.01.tpd.patch"&gt;20080325.01.tpd.patch&lt;/a&gt;
+mathml invisibletimes regression testing&lt;br/&gt;
+&lt;a href="patches/20080325.02.tpd.patch"&gt;20080325.02.tpd.patch&lt;/a&gt;
+move display function to bookvol5&lt;br/&gt;
+&lt;a href="patches/20080325.03.tpd.patch"&gt;20080325.03.tpd.patch&lt;/a&gt;
+handle firefox operations page requests&lt;br/&gt;
+
+  &lt;hr&gt;
+   &lt;h3&gt;May 2008 Release&lt;/h3&gt;
+&lt;a name="20080527"/&gt;
+&lt;a href="releasenotes.html#20080527"&gt;May 2008 Release Notes
+&lt;/a&gt;&lt;br/&gt;&lt;br/&gt;
+  &lt;hr&gt;
+&lt;a href="patches/20080328.01.tpd.patch"&gt;20080328.01.tpd.patch&lt;/a&gt;
+CATS integration regression testing&lt;br/&gt;
+&lt;a href="patches/20080330.01.tpd.patch"&gt;20080330.01.tpd.patch&lt;/a&gt;
+CATS integration regression testing&lt;br/&gt;
+&lt;a href="patches/20080331.01.tpd.patch"&gt;20080331.01.tpd.patch&lt;/a&gt;
+CATS integration regression testing&lt;br/&gt;
+&lt;a href="patches/20080401.01.tpd.patch"&gt;20080401.01.tpd.patch&lt;/a&gt;
+CATS integration regression testing&lt;br/&gt;
+&lt;a href="patches/20080402.01.tpd.patch"&gt;20080402.01.tpd.patch&lt;/a&gt;
+CATS integration regression testing&lt;br/&gt;
+&lt;a href="patches/20080403.01.tpd.patch"&gt;20080403.01.tpd.patch&lt;/a&gt;
+CATS integration regression testing&lt;br/&gt;
+&lt;a href="patches/20080404.01.tpd.patch"&gt;20080404.01.tpd.patch&lt;/a&gt;
+faq 45, faq 46&lt;br/&gt;
+&lt;a href="patches/20080406.01.tpd.patch"&gt;20080406.01.tpd.patch&lt;/a&gt;
+CATS integration regression testing&lt;br/&gt;
+&lt;a href="patches/20080408.01.tpd.patch"&gt;20080408.01.tpd.patch&lt;/a&gt;
+mapleok cleanup&lt;br/&gt;
+&lt;a href="patches/20080409.01.tpd.patch"&gt;20080409.01.tpd.patch&lt;/a&gt;
+CATS integration regression testing&lt;br/&gt;
+&lt;a href="patches/20080409.02.tpd.patch"&gt;20080409.02.tpd.patch&lt;/a&gt;
+add src/doc/toe.gif by Max Tegmark&lt;br/&gt;
+&lt;a href="patches/20080409.03.tpd.patch"&gt;20080409.03.tpd.patch&lt;/a&gt;
+CATS integration regression testing&lt;br/&gt;
+&lt;a href="patches/20080413.01.tpd.patch"&gt;20080413.01.tpd.patch&lt;/a&gt;
+CATS integration regression testing&lt;br/&gt;
+&lt;a href="patches/20080414.01.tpd.patch"&gt;20080414.01.tpd.patch&lt;/a&gt;
+CATS integration test suite&lt;br/&gt;
+&lt;a href="patches/20080415.01.tpd.patch"&gt;20080415.01.tpd.patch&lt;/a&gt;
+CATS Schaums-Axiom equivalence testing (1)&lt;br/&gt;
+&lt;a href="patches/20080416.01.tpd.patch"&gt;20080416.01.tpd.patch&lt;/a&gt;
+CATS Schaums-Axiom equivalence testing (2-7)&lt;br/&gt;
+&lt;a href="patches/20080417.01.tpd.patch"&gt;20080417.01.tpd.patch&lt;/a&gt;
+fixed 14:150&lt;br/&gt;
+&lt;a href="patches/20080417.02.tpd.patch"&gt;20080417.02.tpd.patch&lt;/a&gt;
+CATS Schaums-Axiom equivalence testing (8-10)&lt;br/&gt;
+&lt;a href="patches/20080418.01.tpd.patch"&gt;20080418.01.tpd.patch&lt;/a&gt;
+CATS Schaums-Axiom equivalence testing (1-11)&lt;br/&gt;
+&lt;a href="patches/20080419.01.tpd.patch"&gt;20080419.01.tpd.patch&lt;/a&gt;
+CATS Schaums-Axiom equivalence testing (12)&lt;br/&gt;
+&lt;a href="patches/20080420.01.tpd.patch"&gt;20080420.01.tpd.patch&lt;/a&gt;
+CATS Schaums-Axiom equivalence testing (13)&lt;br/&gt;
+&lt;a href="patches/20080421.01.tpd.patch"&gt;20080421.01.tpd.patch&lt;/a&gt;
+CATS Schaums-Axiom equivalence testing (14-16)&lt;br/&gt;
+&lt;a href="patches/20080423.01.tpd.patch"&gt;20080423.01.tpd.patch&lt;/a&gt;
+CATS Schaums-Axiom equivalence testing (17-22)&lt;br/&gt;
+&lt;a href="patches/20080424.01.tpd.patch"&gt;20080424.01.tpd.patch&lt;/a&gt;
+CATS Schaums-Axiom equivalence testing (23)&lt;br/&gt;
+&lt;a href="patches/20080425.01.tpd.patch"&gt;20080425.01.tpd.patch&lt;/a&gt;
+CATS Schaums-Axiom equivalence testing (24-25)&lt;br/&gt;
+&lt;a href="patches/20080426.01.tpd.patch"&gt;20080426.01.tpd.patch&lt;/a&gt;
+CATS Schaums-Axiom equivalence testing (26-28)&lt;br/&gt;
+&lt;a href="patches/20080427.01.tpd.patch"&gt;20080427.01.tpd.patch&lt;/a&gt;
+CATS Schaums-Axiom equivalence testing (29-34)&lt;br/&gt;
+&lt;a href="patches/20080428.01.tpd.patch"&gt;20080428.01.tpd.patch&lt;/a&gt;
+CATS Schaums-Axiom post-mortem fixex&lt;br/&gt;
+&lt;a href="patches/20080429.01.tpd.patch"&gt;20080429.01.tpd.patch&lt;/a&gt;
+CATS post-mortem typo fixes for schaum12&lt;br/&gt;
+&lt;a href="patches/20080430.01.tpd.patch"&gt;20080430.01.tpd.patch&lt;/a&gt;
+CATS schaum13 post-mortem fixes&lt;br/&gt;
+&lt;a href="patches/20080501.01.tpd.patch"&gt;20080501.01.tpd.patch&lt;/a&gt;
+CATS Schaums-Axiom post-mortem fixes&lt;br/&gt;
+&lt;a href="patches/20080502.01.tpd.patch"&gt;20080502.01.tpd.patch&lt;/a&gt;
+CATS Schaums-Axiom post-mortem fixes&lt;br/&gt;
+&lt;a href="patches/20080504.01.tpd.patch"&gt;20080504.01.tpd.patch&lt;/a&gt;
+CATS Schaums-Axiom post-mortem fixes&lt;br/&gt;
+&lt;a href="patches/20080504.02.tpd.patch"&gt;20080504.02.tpd.patch&lt;/a&gt;
+CATS Schaums-Axiom post-mortem fixes&lt;br/&gt;
+&lt;a href="patches/20080505.01.tpd.patch"&gt;20080505.01.tpd.patch&lt;/a&gt;
+CATS Schaums-Axiom post-mortem fixes&lt;br/&gt;
+&lt;a href="patches/20080505.02.tpd.patch"&gt;20080505.02.tpd.patch&lt;/a&gt;
+CATS Schaums-Axiom branch cut analysis&lt;br/&gt;
+&lt;a href="patches/20080506.01.tpd.patch"&gt;20080506.01.tpd.patch&lt;/a&gt;
+CATS Schaums-Axiom post-mortem fixups&lt;br/&gt;
+&lt;a href="patches/20080508.01.wxh.patch"&gt;20080508.01.wxh.patch&lt;/a&gt;
+intef.spad integrate(asech(x)/x,x) bug&lt;br/&gt;
+&lt;a href="patches/20080508.02.tpd.patch"&gt;20080508.02.tpd.patch&lt;/a&gt;
+ignore gensyms in schaums regression tests&lt;br/&gt;
+&lt;a href="patches/20080511.01.tpd.patch"&gt;20080511.01.tpd.patch&lt;/a&gt;
+CATS Schaums-Axiom post-mortem fixup&lt;br/&gt;
+&lt;a href="patches/20080523.01.tpd.patch"&gt;20080523.01.tpd.patch&lt;/a&gt;
+MIT integration tests&lt;br/&gt;
+&lt;a href="patches/20080526.01.tpd.patch"&gt;20080526.01.tpd.patch&lt;/a&gt;
+add fedora8-64 to Makefile&lt;br/&gt;
+
+  &lt;hr&gt;
+   &lt;h3&gt;July 2008 Release&lt;/h3&gt;
+&lt;a name="20080723"/&gt;
+&lt;a href="releasenotes.html#20080723"&gt;July 2008 Release Notes
+&lt;/a&gt;&lt;br/&gt;&lt;br/&gt;
+  &lt;hr&gt;
+&lt;a href="patches/20080527.01.tpd.patch"&gt;20080527.01.tpd.patch&lt;/a&gt;
+Fedora 9 updates&lt;br/&gt;
+&lt;a href="patches/20080528.01.tpd.patch"&gt;20080528.01.tpd.patch&lt;/a&gt;
+configure/readme rewrite&lt;br/&gt;
+&lt;a href="patches/20080529.01.dxh.patch"&gt;20080529.01.dxh.patch&lt;/a&gt;
+fix hyperdoc on interrupted rebuilds&lt;br/&gt;
+&lt;a href="patches/20080530.01.tpd.patch"&gt;20080530.01.tpd.patch&lt;/a&gt;
+books creation&lt;br/&gt;
+&lt;a href="patches/20080531.01.tpd.patch"&gt;20080531.01.tpd.patch&lt;/a&gt;
+construct book PDFs&lt;br/&gt;
+&lt;a href="patches/20080601.01.tpd.patch"&gt;20080601.01.tpd.patch&lt;/a&gt;
+bookvol8/graphics documentation&lt;br/&gt;
+&lt;a href="patches/20080603.01.tpd.patch"&gt;20080603.01.tpd.patch&lt;/a&gt;
+remove src/graph/view2d&lt;br/&gt;
+&lt;a href="patches/20080604.01.tpd.patch"&gt;20080604.01.tpd.patch&lt;/a&gt;
+bookvol8 extract view3d&lt;br/&gt;
+&lt;a href="patches/20080605.01.tpd.patch"&gt;20080605.01.tpd.patch&lt;/a&gt;
+remove view3d directory and files&lt;br/&gt;
+&lt;a href="patches/20080606.01.tpd.patch"&gt;20080606.01.tpd.patch&lt;/a&gt;
+make viewman from bookvol8&lt;br/&gt;
+&lt;a href="patches/20080606.02.tpd.patch"&gt;20080606.02.tpd.patch&lt;/a&gt;
+remove view&lt;br/&gt;
+&lt;a href="patches/20080606.03.tpd.patch"&gt;20080606.03.tpd.patch&lt;/a&gt;
+correct pathnames in changelog&lt;br/&gt;
+&lt;a href="patches/20080607.01.tpd.patch"&gt;20080607.01.tpd.patch&lt;/a&gt;
+make viewalone from bookvol8&lt;br/&gt;
+&lt;a href="patches/20080607.02.tpd.patch"&gt;20080607.02.tpd.patch&lt;/a&gt;
+Remove src/graph/viewalone directory&lt;br/&gt;
+&lt;a href="patches/20080607.03.tpd.patch"&gt;20080607.03.tpd.patch&lt;/a&gt;
+FAQ 48: Getting Axiom source from git&lt;br/&gt;
+&lt;a href="patches/20080608.01.tpd.patch"&gt;20080608.01.tpd.patch&lt;/a&gt;
+make gdraws from bookvol8&lt;br/&gt;
+&lt;a href="patches/20080608.02.tpd.patch"&gt;20080608.02.tpd.patch&lt;/a&gt;
+remove gdraws directory, use bookvol8&lt;br/&gt;
+&lt;a href="patches/20080608.03.tpd.patch"&gt;20080608.03.tpd.patch&lt;/a&gt;
+remove src/graph, use bookvol8&lt;br/&gt;
+&lt;a href="patches/20080609.01.tpd.patch"&gt;20080609.01.tpd.patch&lt;/a&gt;
+move hypertex into bookvol7&lt;br/&gt;
+&lt;a href="patches/20080609.02.tpd.patch"&gt;20080609.02.tpd.patch&lt;/a&gt;
+remove unused files in src/hyper&lt;br/&gt;
+&lt;a href="patches/20080609.03.tpd.patch"&gt;20080609.03.tpd.patch&lt;/a&gt;
+src/hyper directory removed, use bookvol7&lt;br/&gt;
+&lt;a href="patches/20080610.01.tpd.patch"&gt;20080610.01.tpd.patch&lt;/a&gt;
+build bookvol11&lt;br/&gt;
+&lt;a href="patches/20080610.02.tpd.patch"&gt;20080610.02.tpd.patch&lt;/a&gt;
+stop redundant builds&lt;br/&gt;
+&lt;a href="patches/20080611.01.tpd.patch"&gt;20080611.01.tpd.patch&lt;/a&gt;
+general form updates for books&lt;br/&gt;
+&lt;a href="patches/20080613.01.tpd.patch"&gt;20080613.01.tpd.patch&lt;/a&gt;
+compress viewman.c to a single file&lt;br/&gt;
+&lt;a href="patches/20080614.01.tpd.patch"&gt;20080614.01.tpd.patch&lt;/a&gt;
+compress viewalone to a single C file&lt;br/&gt;
+&lt;a href="patches/20080618.01.tpd.patch"&gt;20080618.01.tpd.patch&lt;/a&gt;
+use dvipdfm for hyperlinking (Anatoly Raportirenko)&lt;br/&gt;
+&lt;a href="patches/20080619.01.tpd.patch"&gt;20080619.01.tpd.patch&lt;/a&gt;
+add Anatoly Raportirenko&lt;br/&gt;
+&lt;a href="patches/20080619.02.tpd.patch"&gt;20080619.02.tpd.patch&lt;/a&gt;
+systematically index chunks&lt;br/&gt;
+&lt;a href="patches/20080619.03.tpd.patch"&gt;20080619.03.tpd.patch&lt;/a&gt;
+add Ralf Hemmecke documentation to ax.boot&lt;br/&gt;
+&lt;a href="patches/20080620.01.wxh.patch"&gt;20080620.01.wxh.patch&lt;/a&gt;
+fix direct product multiply in Monoid&lt;br/&gt;
+&lt;a href="patches/20080621.01.wxh.patch"&gt;20080621.01.wxh.patch&lt;/a&gt;
+default to close on failed read&lt;br/&gt;
+&lt;a href="patches/20080701.01.tpd.patch"&gt;20080701.01.tpd.patch&lt;/a&gt;
+update faq for X11 libs&lt;br/&gt;
+&lt;a href="patches/20080704.01.tpd.patch"&gt;20080704.01.tpd.patch&lt;/a&gt;
+add Samantha Goldrich to credits&lt;br/&gt;
+&lt;a href="patches/20080707.01.tpd.patch"&gt;20080707.01.tpd.patch&lt;/a&gt;
+construct hypertex from bookvol7&lt;br/&gt;
+&lt;a href="patches/20080715.01.tpd.patch"&gt;20080715.01.tpd.patch&lt;/a&gt;
+bookvol7.1 hyperdoc pages&lt;br/&gt;
+&lt;a href="patches/20080715.02.tpd.patch"&gt;20080715.02.tpd.patch&lt;/a&gt;
+remove src/hyper/pages/*.ht&lt;br/&gt;
+&lt;a href="patches/20080715.03.gxv.patch"&gt;20080715.03.gxv.patch&lt;/a&gt;
+mousewheel handling by Greg Vanuxem&lt;br/&gt;
+&lt;a href="patches/20080715.04.tpd.patch"&gt;20080715.04.tpd.patch&lt;/a&gt;
+remove ht.db from bookvol7&lt;br/&gt;
+&lt;a href="patches/20080717.01.tpd.patch"&gt;20080717.01.tpd.patch&lt;/a&gt;
+remove src/graph&lt;br/&gt;
+&lt;a href="patches/20080718.01.tpd.patch"&gt;20080718.01.tpd.patch&lt;/a&gt;
+bookvol7.1 hyperdoc additional documentation&lt;br/&gt;
+&lt;a href="patches/20080719.01.tpd.patch"&gt;20080719.01.tpd.patch&lt;/a&gt;
+bookvol7.1 more documentation&lt;br/&gt;
+&lt;a href="patches/20080720.01.tpd.patch"&gt;20080720.01.tpd.patch&lt;/a&gt;
+bookvol7.1 hyperdoc documentation added&lt;br/&gt;
+&lt;a href="patches/20080721.01.tpd.patch"&gt;20080721.01.tpd.patch&lt;/a&gt;
+bookvol7.1 hyperdoc specific macros&lt;br/&gt;
+&lt;a href="patches/20080722.01.tpd.patch"&gt;20080722.01.tpd.patch&lt;/a&gt;
+change VERSION number&lt;br/&gt;
+
+  &lt;hr&gt;
+   &lt;h3&gt;September 2008 Release&lt;/h3&gt;
+&lt;a name="20080923"/&gt;
+&lt;a href="releasenotes.html#20080923"&gt;September 2008 Release Notes
+&lt;/a&gt;&lt;br/&gt;&lt;br/&gt;
+  &lt;hr&gt;
+&lt;a href="patches/20080724.01.tpd.patch"&gt;20080724.01.tpd.patch&lt;/a&gt;
+document lisp calls from hypertex&lt;br/&gt;
+&lt;a href="patches/20080725.01.tpd.patch"&gt;20080725.01.tpd.patch&lt;/a&gt;
+reflow for line latex overflows&lt;br/&gt;
+&lt;a href="patches/20080727.01.tpd.patch"&gt;20080727.01.tpd.patch&lt;/a&gt;
+update What's New pages&lt;br/&gt;
+&lt;a href="patches/20080728.01.tpd.patch"&gt;20080728.01.tpd.patch&lt;/a&gt;
+expand RootPage-&gt;Topics-&gt;Numbers&lt;br/&gt;
+&lt;a href="patches/20080729.01.tpd.patch"&gt;20080729.01.tpd.patch&lt;/a&gt;
+expand next tree level&lt;br/&gt;
+&lt;a href="patches/20080729.02.tpd.patch"&gt;20080729.02.tpd.patch&lt;/a&gt;
+more hyperdoc pages 1 of 2&lt;br/&gt;
+&lt;a href="patches/20080729.03.tpd.patch"&gt;20080729.03.tpd.patch&lt;/a&gt;
+bookvol7.1 part 2 of 2&lt;br/&gt;
+&lt;a href="patches/20080802.01.tpd.patch"&gt;20080802.01.tpd.patch&lt;/a&gt;
+Build ht.db from bookvol7.1&lt;br/&gt;
+&lt;a href="patches/20080809.01.tpd.patch"&gt;20080809.01.tpd.patch&lt;/a&gt;
+Remove pages directory&lt;br/&gt;
+&lt;a href="patches/20080814.01.tpd.patch"&gt;20080814.01.tpd.patch&lt;/a&gt;
+Use uncompress at build time&lt;br/&gt;
+&lt;a href="patches/20080815.01.tpd.patch"&gt;20080815.01.tpd.patch&lt;/a&gt;
+make firefox pages before input tests&lt;br/&gt;
+&lt;a href="patches/20080816.01.tpd.patch"&gt;20080816.01.tpd.patch&lt;/a&gt;
+comment out long running test&lt;br/&gt;
+&lt;a href="patches/20080816.02.tpd.patch"&gt;20080816.02.tpd.patch&lt;/a&gt;
+add additional regression tests&lt;br/&gt;
+&lt;a href="patches/20080817.01.tpd.patch"&gt;20080817.01.tpd.patch&lt;/a&gt;
+fix uncompress&lt;br/&gt;
+&lt;a href="patches/20080817.02.tpd.patch"&gt;20080817.02.tpd.patch&lt;/a&gt;
+recover function.input&lt;br/&gt;
+&lt;a href="patches/20080817.03.tpd.patch"&gt;20080817.03.tpd.patch&lt;/a&gt;
+exported function documentation&lt;br/&gt;
+&lt;a href="patches/20080818.01.tpd.patch"&gt;20080818.01.tpd.patch&lt;/a&gt;
+demo Axiom type towers (Hemmecke)&lt;br/&gt;
+&lt;a href="patches/20080818.02.tpd.patch"&gt;20080818.02.tpd.patch&lt;/a&gt;
+new input files (Stumbo, Cyganski, Hemmecke)&lt;br/&gt;
+&lt;a href="patches/20080819.01.tpd.patch"&gt;20080819.01.tpd.patch&lt;/a&gt;
+overload.input added (Cyganski)&lt;br/&gt;
+&lt;a href="patches/20080820.01.tpd.patch"&gt;20080820.01.tpd.patch&lt;/a&gt;
+fix typos in latex code&lt;br/&gt;
+&lt;a href="patches/20080821.01.tpd.patch"&gt;20080821.01.tpd.patch&lt;/a&gt;
+add MappingPackage4&lt;br/&gt;
+&lt;a href="patches/20080822.01.tpd.patch"&gt;20080822.01.tpd.patch&lt;/a&gt;
+add linalg,overload regressions&lt;br/&gt;
+&lt;a href="patches/20080823.01.tpd.patch"&gt;20080823.01.tpd.patch&lt;/a&gt;
+UnaryRecursiveAggregate API examples&lt;br/&gt;
+&lt;a href="patches/20080823.02.tpd.patch"&gt;20080823.02.tpd.patch&lt;/a&gt;
+stream API examples&lt;br/&gt;
+&lt;a href="patches/20080823.03.tpd.patch"&gt;20080823.03.tpd.patch&lt;/a&gt;
+++CapitalLetter syntax change&lt;br/&gt;
+&lt;a href="patches/20080824.01.tpd.patch"&gt;20080824.01.tpd.patch&lt;/a&gt;
+use ++X for example lines&lt;br/&gt;
+&lt;a href="patches/20080824.02.tpd.patch"&gt;20080824.02.tpd.patch&lt;/a&gt;
+expose difference between ^ and ** (Xaiojun)&lt;br/&gt;
+&lt;a href="patches/20080827.01.wsp.patch"&gt;20080827.01.wsp.patch&lt;/a&gt;
+replace \over with \frac (Page)&lt;br/&gt;
+&lt;a href="patches/20080828.01.mxr.patch"&gt;20080828.01.mxr.patch&lt;/a&gt;
+add cost to bottomUp output (Page)&lt;br/&gt;
+&lt;a href="patches/20080829.01.tpd.patch"&gt;20080829.01.tpd.patch&lt;/a&gt;
+graphviz dotfile decoration&lt;br/&gt;
+&lt;a href="patches/20080830.01.tpd.patch"&gt;20080830.01.tpd.patch&lt;/a&gt;
+graphviz dotfile decoration&lt;br/&gt;
+&lt;a href="patches/20080831.01.tpd.patch"&gt;20080831.01.tpd.patch&lt;/a&gt;
+graphviz dotfile decoration&lt;br/&gt;
+&lt;a href="patches/20080901.01.tpd.patch"&gt;20080901.01.tpd.patch&lt;/a&gt;
+add start of multivar poly test suite&lt;br/&gt;
+&lt;a href="patches/20080904.01.tst.patch"&gt;20080904.01.tst.patch&lt;/a&gt;
+add reduce example (Tsikas)&lt;br/&gt;
+&lt;a href="patches/20080904.02.tpd.patch"&gt;20080904.02.tpd.patch&lt;/a&gt;
+graphviz dotfile decoration&lt;br/&gt;
+&lt;a href="patches/20080905.01.tpd.patch"&gt;20080905.01.tpd.patch&lt;/a&gt;
+graphviz dotfile decoration&lt;br/&gt;
+&lt;a href="patches/20080906.01.tpd.patch"&gt;20080906.01.tpd.patch&lt;/a&gt;
+move aggcat.spad to bookvol10&lt;br/&gt;
+&lt;a href="patches/20080908.01.tpd.patch"&gt;20080908.01.tpd.patch&lt;/a&gt;
+bookvol10 latex cleanup&lt;br/&gt;
+&lt;a href="patches/20080909.01.tpd.patch"&gt;20080909.01.tpd.patch&lt;/a&gt;
+bookvol0 change \over to \frac&lt;br/&gt;
+&lt;a href="patches/20080911.01.tpd.patch"&gt;20080911.01.tpd.patch&lt;/a&gt;
+bookvol11 fix firefox background image&lt;br/&gt;
+&lt;a href="patches/20080911.02.tpd.patch"&gt;20080911.02.tpd.patch&lt;/a&gt;
+bookvol10 merge coerce.spad&lt;br/&gt;
+&lt;a href="patches/20080912.01.tpd.patch"&gt;20080912.01.tpd.patch&lt;/a&gt;
+split bookvol10 into 10, 10.1..4&lt;br/&gt;
+&lt;a href="patches/20080916.01.tpd.patch"&gt;20080916.01.tpd.patch&lt;/a&gt;
+bookvol10.2 document additional categories&lt;br/&gt;
+&lt;a href="patches/20080917.01.tpd.patch"&gt;20080917.01.tpd.patch&lt;/a&gt;
+bookvol10.2 remove dup function defn in FLAGG&lt;br/&gt;
+&lt;a href="patches/20080917.02.wsp.patch"&gt;20080917.02.wsp.patch&lt;/a&gt;
+mkfunc.spad add parse function&lt;br/&gt;
+&lt;a href="patches/20080918.01.tpd.patch"&gt;20080918.01.tpd.patch&lt;/a&gt;
+bookvol10.2 add BASTYPE, SETCAT, ABELSG&lt;br/&gt;
+&lt;a href="patches/20080918.02.tpd.patch"&gt;20080918.02.tpd.patch&lt;/a&gt;
+bookvol10.2 add FINITE, ORDSET, SGROUP&lt;br/&gt;
+&lt;a href="patches/20080919.01.tpd.patch"&gt;20080919.01.tpd.patch&lt;/a&gt;
+bookvol10.2 add more categories&lt;br/&gt;
+&lt;a href="patches/20080920.01.tpd.patch"&gt;20080920.01.tpd.patch&lt;/a&gt;
+bookvol10.2 add more categories&lt;br/&gt;
+&lt;a href="patches/20080921.01.tpd.patch"&gt;20080921.01.tpd.patch&lt;/a&gt;
+September 2008 release fixups&lt;br/&gt;
+
+  &lt;hr&gt;
+   &lt;h3&gt;November 2008 Release&lt;/h3&gt;
+&lt;a name="20081123"/&gt;
+&lt;a href="releasenotes.html#20081123"&gt;November 2008 Release Notes
+&lt;/a&gt;&lt;br/&gt;&lt;br/&gt;
+  &lt;hr&gt;
+&lt;a href="patches/20080925.01.tpd.patch"&gt;20080925.01.tpd.patch&lt;/a&gt;
+bookvol10.2 new categories added&lt;br/&gt;
+&lt;a href="patches/20080926.01.tpd.patch"&gt;20080926.01.tpd.patch&lt;/a&gt;
+bookvol10.2 new categories, attributes added&lt;br/&gt;
+&lt;a href="patches/20080927.01.tpd.patch"&gt;20080927.01.tpd.patch&lt;/a&gt;
+bookvol10.2 new categories, absorb naalgc&lt;br/&gt;
+&lt;a href="patches/20080928.01.tpd.patch"&gt;20080928.01.tpd.patch&lt;/a&gt;
+bookvol10.2 new categories, absorb trigcat&lt;br/&gt;
+&lt;a href="patches/20080930.01.tpd.patch"&gt;20080930.01.tpd.patch&lt;/a&gt;
+bookvol10.2 move XF, FPC from ffcat.spad&lt;br/&gt;
+&lt;a href="patches/20081001.01.tpd.patch"&gt;20081001.01.tpd.patch&lt;/a&gt;
+bookvol10.2 add more categores&lt;br/&gt;
+&lt;a href="patches/20081002.01.tpd.patch"&gt;20081002.01.tpd.patch&lt;/a&gt;
+bookvol10.2 add more categores&lt;br/&gt;
+&lt;a href="patches/20081003.01.tpd.patch"&gt;20081003.01.tpd.patch&lt;/a&gt;
+bookvol10.2 add POLYCAT&lt;br/&gt;
+&lt;a href="patches/20081004.01.tpd.patch"&gt;20081004.01.tpd.patch&lt;/a&gt;
+bookvol10.2 add UPOLYC, update attributes&lt;br/&gt;
+&lt;a href="patches/20081005.01.tpd.patch"&gt;20081005.01.tpd.patch&lt;/a&gt;
+bookvol10.2 add categories&lt;br/&gt;
+&lt;a href="patches/20081006.01.tpd.patch"&gt;20081006.01.tpd.patch&lt;/a&gt;
+bookvol10.2 add categories&lt;br/&gt;
+&lt;a href="patches/20081007.01.tpd.patch"&gt;20081007.01.tpd.patch&lt;/a&gt;
+bookvol10.2 add categories, update ATTREG&lt;br/&gt;
+&lt;a href="patches/20081008.01.tpd.patch"&gt;20081008.01.tpd.patch&lt;/a&gt;
+bookvol10.2 add ACF, fix MONOGEN, FFCAT&lt;br/&gt;
+&lt;a href="patches/20081023.01.tpd.patch"&gt;20081023.01.tpd.patch&lt;/a&gt;
+bookvol10.2 add categories&lt;br/&gt;
+&lt;a href="patches/20081026.01.tpd.patch"&gt;20081026.01.tpd.patch&lt;/a&gt;
+bookvol10.2 add categories&lt;br/&gt;
+&lt;a href="patches/20081027.01.tpd.patch"&gt;20081027.01.tpd.patch&lt;/a&gt;
+add sae.input regression test&lt;br/&gt;
+&lt;a href="patches/20081029.01.tpd.patch"&gt;20081029.01.tpd.patch&lt;/a&gt;
+bookvol10.2 add categories&lt;br/&gt;
+&lt;a href="patches/20081101.01.tpd.patch"&gt;20081101.01.tpd.patch&lt;/a&gt;
+bookvol10.2 add categories&lt;br/&gt;
+&lt;a href="patches/20081105.01.axj.patch"&gt;20081105.01.axj.patch&lt;/a&gt;
+add reclos2.input&lt;br/&gt;
+&lt;a href="patches/20081106.01.tpd.patch"&gt;20081106.01.tpd.patch&lt;/a&gt;
+remove matcat.spad from src/algebra/Makefile&lt;br/&gt;
+&lt;a href="patches/20081107.01.tpd.patch"&gt;20081107.01.tpd.patch&lt;/a&gt;
+ignore probabilistic results&lt;br/&gt;
+&lt;a href="patches/20081108.01.tpd.patch"&gt;20081108.01.tpd.patch&lt;/a&gt;
+bookvol10.2 add categories&lt;br/&gt;
+&lt;a href="patches/20081109.01.tpd.patch"&gt;20081109.01.tpd.patch&lt;/a&gt;
+bookvol10.2 add categories&lt;br/&gt;
+&lt;a href="patches/20081110.01.tpd.patch"&gt;20081110.01.tpd.patch&lt;/a&gt;
+bookvol10.2 add categories&lt;br/&gt;
+&lt;a href="patches/20081112.01.tpd.patch"&gt;20081112.01.tpd.patch&lt;/a&gt;
+bookvol10.2 add categories&lt;br/&gt;
+&lt;a href="patches/20081114.01.tpd.patch"&gt;20081114.01.tpd.patch&lt;/a&gt;
+bookvol10.3 add dhmatrix&lt;br/&gt;
+&lt;a href="patches/20081115.01.tpd.patch"&gt;20081115.01.tpd.patch&lt;/a&gt;
+bookvol10.2 remove duplicates in export lists&lt;br/&gt;
+&lt;a href="patches/20081116.01.tpd.patch"&gt;20081116.01.tpd.patch&lt;/a&gt;
+rosetta.pamphlet fix magnus URL&lt;br/&gt;
+&lt;a href="patches/20081118.01.tpd.patch"&gt;20081118.01.tpd.patch&lt;/a&gt;
+make parallel test work&lt;br/&gt;
+&lt;a href="patches/20081119.01.tpd.patch"&gt;20081119.01.tpd.patch&lt;/a&gt;
+november 2008 release&lt;br/&gt;
+&lt;a href="patches/20081119.02.tpd.patch"&gt;20081119.02.tpd.patch&lt;/a&gt;
+november 2008 fixups&lt;br/&gt;
+
+  &lt;hr&gt;
+   &lt;h3&gt;January 2009 Release&lt;/h3&gt;
+&lt;a name="latest"/&gt;
+In process, not yet released&lt;br/&gt;&lt;br/&gt;
+  &lt;hr&gt;
+&lt;a href="patches/20081122.02.tpd.patch"&gt;20081122.02.tpd.patch&lt;/a&gt;
+ubuntu64 parallel core support&lt;br/&gt;
+
+ &lt;/body&gt;
+&lt;/html&gt;
\ No newline at end of file
diff --git a/src/axiom-website/releasenotes.html b/src/axiom-website/releasenotes.html
new file mode 100644
index 0000000..fab2ec8
--- /dev/null
+++ b/src/axiom-website/releasenotes.html
@@ -0,0 +1,1280 @@
+&lt;html&gt;
+ &lt;head&gt;
+  &lt;title&gt;
+   Axiom Computer Algebra System
+  &lt;/title&gt;
+ &lt;/head&gt;
+ &lt;body bgcolor="#ffff66"&gt;
+   &lt;div id="head" align="center"&gt; 
+    &lt;a href="http://savannah.nongnu.org/projects/axiom/"&gt;
+     &lt;img src="axiom.png" border="0" alt="Axiom"&gt;
+    &lt;/a&gt;
+    &lt;br&gt;
+    &lt;font size=200%&gt;
+     The Scientific Computation System
+    &lt;/font&gt;
+   &lt;/div&gt;
+   &lt;div align="center"&gt;
+    [
+     &lt;a href="../index.html" title="Home"&gt;
+      Home
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="screenshots.html" title="Screen Shots"&gt;
+      Screenshots
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="faq.html" title="FAQ"&gt;
+      FAQ
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="download.html" title="Download"&gt;
+      Download
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="documentation.html" title="Documentation"&gt;
+      Documentation
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="currentstate.html" title="Current State"&gt;
+      Current State
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="community.html" title="Community"&gt;
+      Community
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="developers.html" title="Developers"&gt;
+      Developers
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="patches.html" title="Patches"&gt;
+      Patches
+     &lt;/a&gt;
+    ]
+   &lt;/div&gt;
+   &lt;div align="center"&gt;
+    [
+     &lt;a href="bookvol10.2abb.html" title="Abbreviation Graph"&gt;
+      Abbreviation Graph
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="bookvol10.2full.html" title="Full Name Graph"&gt;
+      Full Name Graph
+     &lt;/a&gt;
+    ]
+   &lt;/div&gt;
+  &lt;br&gt;
+  &lt;hr&gt;
+
+RELEASES
+&lt;ul&gt;
+ &lt;li&gt;&lt;a href="#20081123"&gt;November 23, 2008&lt;/li&gt;
+ &lt;li&gt;&lt;a href="#20080923"&gt;September 23, 2008&lt;/li&gt;
+ &lt;li&gt;&lt;a href="#20080723"&gt;July 23, 2008&lt;/li&gt;
+ &lt;li&gt;&lt;a href="#20080527"&gt;May 27, 2008&lt;/li&gt;
+ &lt;li&gt;&lt;a href="#20080325"&gt;March 25, 2008&lt;/li&gt;
+ &lt;li&gt;&lt;a href="#20080125"&gt;January 25, 2008&lt;/li&gt;
+ &lt;li&gt;&lt;a href="#20071123"&gt;November 23, 2007&lt;/li&gt;
+&lt;/ul&gt;
+
+&lt;a name="20081123"/&gt;
+&lt;h3&gt;November 23, 2008 Release Notes &lt;/h3&gt;
+&lt;a href="patches.html#20081123"&gt;patch list&lt;/a&gt;
+&lt;pre&gt;
+November 2008 Release Notes
+
+Axiom website
+
+  New patch tracking has been added:
+     * &lt;a href="patches.html"&gt;Patches&lt;/a&gt;
+
+  Volumes have been significantly updated:
+     * &lt;a href="bookvol10.2.pdf"&gt;Book Volume 10.2&lt;/a&gt;
+     * &lt;a href="bookvol10.3.pdf"&gt;Book Volume 10.3&lt;/a&gt;
+
+Book Volume 10.2 Axiom Categories completed
+
+   The effort here is to create fully indexed, cross-referenced,
+   graphical documentation for Axiom categories in a standalone
+   form. This is a "live" literate document which contains the 
+   actual source code used to build the system.
+
+   * &lt;a href="bookvol10.2.pdf"&gt;Book Volume 10.2&lt;/a&gt;
+
+Book Volume 10.3 Axiom Domains started
+
+   This volume will contain the Axiom domains.
+
+   * &lt;a href="bookvol10.3.pdf"&gt;Book Volume 10.3&lt;/a&gt;
+
+Rosetta documentation
+
+  * Fix the Magnus URL
+
+Input Files
+
+  * New input files (Jakubi, Maltey, Rubey, Page, Daly}
+     dhmatrix, reclos2
+  * Changed input files (Hebisch, Daly)
+     sae, r20bugs
+
+Build changes
+
+  * Testing is now run in parallel which will significantly
+    speed up the final test phase
+ 
+&lt;/pre&gt;
+
+&lt;a name="20080923"/&gt;
+&lt;h3&gt;September 23, 2008 Release Notes &lt;/h3&gt;
+&lt;a href="patches.html#20080923"&gt;patch list&lt;/a&gt;
+&lt;pre&gt;
+September 2008 Release Notes
+
+
+Axiom website
+   The effort here is to improve the support for offline literate
+   documentation. The primary changes are the inclusion of graphs
+   and additional book volumes.
+
+* &lt;http://axiom-developer.org/axiom-website/documentation.html&gt;
+  Contains the new algebra volumes and subvolumes.
+* &lt;http://axiom-developer.org/axiom-website/bookvol10.2abb.html&gt;
+  Contains a "clickable" graph that indexes into the algebra.
+
+
+
+
+Graphviz, PDF, and HTML integration
+   The effort here is to unify these three technologies in a way
+   that simplifies the user interface and improves documentation
+
+* Graphviz is used if available but not required
+* Algebra graphs are automatically generated at build time
+  from algebra source files
+* Graphviz graphs now properly hyperlink into PDF files allowing
+  any node in a graph to link to any document page
+
+
+
+
+Book volume 0 (Jenks and Sutor)
+
+* &lt;http://axiom-developer.org/axiom-website/bookvol0.pdf&gt;
+* replace \over with \frac
+
+
+
+Book volume 7.1 (Hyperdoc pages)
+   The effort here is to create a literate document that contains
+   all of the "live" pages used in hyperdoc. The PDF is being
+   constructed so that a user can effectively "browse" the static
+   hyperdoc pages, which are included, without a running Axiom.
+
+* &lt;http://axiom-developer.org/axiom-website/bookvol7.1.pdf&gt;
+* The source for all of the pages is now contained in this book.
+* Hyperdoc now fetches the pages directly from the book.
+* The hyper page directory and all files are gone.
+* Some of the static page images are now inside the PDF
+* Pages have href links allowing "in-pdf" navigation of pages
+
+
+
+
+Book volume 10 (Algebra)
+   The effort here is to create a way to describe and deeply
+   document the algebra. This volume was split to better handle
+   the structure of Axiom's information. 
+
+* Split into 5 volumes
+   - 10   Implementation
+   - 10.1 Theory
+   - 10.2 Categories
+   - 10.3 Domains
+   - 10.4 Packages
+
+
+
+
+Book volume 10.2 (Algebra Categories)
+   The effort here is to create fully indexed, cross-referenced,
+   graphical documentation for Axiom categories in a standalone
+   form. This is a "live" literate document which contains the 
+   actual source code used to build the system.
+
+* &lt;http://axiom-developer.org/axiom-website/bookvol10.2.pdf&gt;
+* Contains 60 categories so far
+* Has partial graphs for each category
+* Has list of exported functions 
+* Has information about source of functions
+* Has index cross reference by function and category
+* Has PDF href links so that URLs work:
+   &lt;http://axiom-developer.org/axiom-website/bookvol10.2.pdf#nameddest=AGG&gt;
+* Has forward/backward links between categories
+* Automatically generates "clickable" graphs:
+   &lt;http://axiom-developer.org/axiom-website/bookvol10.2abb.html&gt;
+* Graph clicking automatically opens to the proper source code
+
+
+
+
+New algebra examples (Daly, Tsikas)
+   The effort here is to create "real time" documentation that
+   gives the end user an example of how to construct the proper
+   arguments and call a function. This puts examples into the
+   system so users don't need to consult other documents.
+
+* )d op someop shows examples of function usage
+* about 100 new function examples were added 
+* new comment syntax added to allow automatic API testing
+
+
+
+
+Input Files
+   There is a new effort to automatically extract the algebra
+   examples in order to regression test the user API to the
+   algebra. In addition there is ongoing test work.
+
+* New input files (Hemmecke, Stumbo, Cyganski, Daly)
+     bini, biquat, ifthenelse, liu, overload, sqrt3, typetower
+* Changed input files (Hemmecke, Stumbo, Cyganski, Daly)
+     bern, function, linalg, regset, test, tutchap2
+
+
+
+
+Build changes
+
+* graphics does not depend on compress, done at build time
+* firefox html pages are now built before tests are run
+
+
+
+Algebra changes
+
+* FLAGG (FiniteLinearAggregate) -- removed a duplicate function
+
+
+
+Interpreter changes (Page)
+
+* add cost function to bottomUp output
+
+
+
+ 
+&lt;/pre&gt;
+
+&lt;a name="20080723"/&gt;
+&lt;h3&gt;July 23, 2008 Release Notes &lt;/h3&gt;
+&lt;a href="patches.html#20080723"&gt;patch list&lt;/a&gt;
+&lt;pre&gt;
+The July 2008 release marks the second large-scale change toward a
+literate Axiom distribution. The original change was to make every
+file into a pamphlet document. This second change draws Axiom into
+tighter collections, called books (for obvious reasons). 
+
+There is a new "books" directory which contains 14 books, most of
+which are new:
+
+ bookvol0:  The reconstructed Jenks and Sutor book
+ bookvol1:  The published tutorial volume
+ bookvol2:  Users Guide
+ bookvol3:  Programmers Guide
+ bookvol4:  Developers Guide
+ bookvol5:  Interpreter
+ bookvol6:  Command
+ bookvol7:  Hyperdoc
+ bookvol7.1 Hyperdoc Pages
+ bookvol8:  Graphics
+ bookvol9:  Compiler
+ bookvol10: Algebra
+ bookvol11: Browser
+ bookvol12: Crystal
+
+All of these books now exist. Portions of the current system have
+been moved completely into book form (Graphics and Hyperdoc) so
+the old files have been removed from the src tree. Both Graphics
+and Hyperdoc are now built directly from their book. Work will 
+follow on other parts of the system.
+
+These books are online at:
+&lt;http://axiom.axiom-developer.org/axiom-website/documentation.html&gt;
+
+
+
+
+There is an interesting side-effect of using literate technology.
+Once you combine C and .h files into a single document so that each
+file is a separate chunk it becomes obvious that there is no need for
+local include files. The lines that read:
+   #include "foo.h"
+become
+   &lt;&lt;foo.h&gt;&gt;
+and get expanded inline. Once you do this it also becomes obvious
+that many include files get included multiple times (a clear waste
+of disk I/O and preparser time). Further it becomes clear that there
+is no need for creating tiny .o files since all of the source can
+be combined into one C file using chunks. 
+
+These approaches were used to reduce the compile-time overhead
+for both the graphics and the hyperdoc functions.
+
+
+
+
+In addition to consolidating the source files for Graphics into
+bookvol8 there were several other changes.
+
+  * the functions for graphics, that is, viewman, view2d, view3d
+    and viewalone are now built as single C files. 
+  * the graphics code was reorganized into chapters of related code
+  * there is the beginnings of documentation
+  * there is the beginnings of a test suite based on the 
+    CRC Handbook of Curves and Surfaces
+  * the book is hyperlinked (Bill Page, Frederic Lehobey, Anatoly Raportirenko)
+  * redundant code was eliminated
+  * the code is fully indexed
+  * the src/graph subdirectory is gone
+
+
+
+In addition to consolidating the source files for Hyperdoc into
+bookvol7 there were several other changes.
+
+  * the functions for hyperdoc, that is, spadbuf, ex2ht, htadd, hthits
+    and hypertex are now built as single C files
+  * the hyperdoc code was reorganized into chapters of related code
+  * there is the beginnngs of documentation
+  * redundant code was eliminated
+  * scroll wheel handling was added (Gregory Vanuxem)
+  * the book is hyperlinked (Bill Page, Frederic Lehobey, Anatoly Raportirenko)
+  * the code is fully indexed
+  * )hd now works to start or restart Hyperdoc (Jose Alfredo Portes)
+  * the src/hyper subdirectory is gone
+
+
+
+In addition to consolidating the hyperdoc pages into bookvol7.1
+there were several other changes:
+
+  * the pages are hyperlinked
+  * new latex macros were written to simplify page handling
+  * images of hyperdoc pages were added
+  * forward and backward hyperlinks between pages images works
+    making it possible to "browse" the hyperdoc pages using only
+    the single PDF file (Bill Page, Frederic Lehobey, Anatoly Raportirenko)
+  * the pages are fully indexed
+  * the src/hyper/pages subdirectory is gone
+
+
+
+A combined table of contents PDF is now automatically generated
+which covers all of the volumes. This makes it easier to find the
+topic of interest.
+
+
+In addition there were several other changes.
+
+  * Some fixes were made for different platforms
+       In particular, Fedora9 breaks the build and needs work
+
+  * The configure script was replaced by instructions
+       The standard (export AXIOM) works everywhere so the configure
+       script is useless for guessing.
+
+  * the FAQ was updated about git
+       Since the May 2008 release the primary Gold source code platform
+       is github. The FAQ was updated to reflect this.
+
+  * the FAQ was updated about X11
+       X11 has moved yet again so more notes are needed
+
+  * move axbook to books
+       The hyperlinked version of Jenks is now built from the books dir
+
+  * add Ralf Hemmecke's documentation to ax.boot
+  * add Monoid multiply to DirectProduct (Ralf Hemmecke)
+  * add Monoid multiply regression test
+
+&lt;/pre&gt;
+
+&lt;a name="20080527"/&gt;
+&lt;h3&gt;May 27, 2008 Release Notes &lt;/h3&gt;
+&lt;a href="patches.html#20080527"&gt;patch list&lt;/a&gt;
+&lt;pre&gt;
+
+COMPUTER ALGEBRA TEST SUITE
+
+A large part of the effort for these two months has involved detailed
+test cases of Axiom's integration routines against Schaum's Handbook
+of Mathematical Formulas. Of the 619 integrals, the detailed results are:
+
+419 Schaums and Axiom agree
+137 No closed form solution
+ 60 Cannot simplify
+
+  2 Typos found in Schaums
+  1 Axiom bug
+
+The Axiom bug was in src/algebra/intef.spad.pamphlet. There was a
+fix applied to this code for a previously identified bug but the
+previous fix was incorrect.
+
+In addition, there were
+ src/input/danzwill2.input.pamphlet added for the MIT Integration tests
+ src/inputmapleok.input.pamphlet to fix typos
+ src/input/kamke1.input.pamphlet had ode97 removed due to running time
+ src/input/kamke2.input.pamphlet ode104, ode105 removed for running time
+
+DOCUMENTATION
+	Max Tegmark's 'toe' diagram, src/doc/toe.gif
+
+PORTING
+        GCLOPTS-CUSTRELOC disable-locbfd for MACOSXPPC
+&lt;/pre&gt;
+
+&lt;a name="20080325"/&gt;
+&lt;h3&gt;March 25, 2008 Release Notes &lt;/h3&gt;
+&lt;a href="patches.html#20080325"&gt;patch list&lt;/a&gt;
+&lt;pre&gt;
+Summary: March 2008 release
+
+Axiom is now available at github, a git-based code repository.
+This site will have the Gold version of Axiom, that is, only
+code that changes at each two-month release. To get a clone type:
+
+   git-clone git://github.com/daly/axiom.git
+
+
+USER VISIBLE CHANGES
+
+  One primary focus of this release has been extending the Firefox
+  toward being a full Axiom user interface (as opposed to a simple
+  hyperdoc replacement). The Firefox console page has new, AJAX
+  based, dropdown menus which are planned to be dynamically updated
+  to display available functions for the last computed type. This 
+  should make it much easier to find the applicable functions by
+  category and type. They are currently static in this release.
+
+* Firefox Pages
+
+ o Dropdown menus were added to the Axiom console page
+ o More hyperdoc pages were translated to Firefox/html
+ o Bitmaps and graphics are now properly handled in pages
+ o A minor mathml fix was applied (for invisible times)
+
+* Refcard
+
+ o An Axiom reference card of Axiom commands was created (src/doc/refcard)
+
+* Examples
+
+ o It is often difficult to figure the exact arguments required to call
+   any given function in Axiom. The )display operation command used to
+   only show the available modemaps. This command has now been changed.
+    )display operation foo
+   now shows examples of function calls for foo.
+
+* Help
+
+ o The plot routines have new help files and documentation
+
+PORTING
+
+ o Axiom was ported to MAC-OSX
+
+ o The binary download page now has binaries for 
+   Ubuntu, OpenSUsE, Redhat9, Redhat72, Debian, MACOSX at 
+    &lt;http://axiom.axiom-developer.org/axiom-website/download.html&gt;
+
+ o Binaries for the this release will be available shortly.
+
+
+INTERNALS
+
+* Compiler changes
+ o  hashtables were used to speed up compiles
+
+* Algebra changes
+ o  There are new special functions, Ei,En,Ei1,Ei2,Ei3,Ei4,Ei5,Ei6
+ o  The prime and BasicSieve functions are faster
+ o  The Brent/Pollard algorithm was documented
+ o  Bad gcd reductions are checked (heugcd regression test file added)
+ o  The plot routines have new help files and documentation
+
+* Makefile changes
+ o  Bi-capital SVN copies are no longer made
+
+* Interpreter changes
+ o  Book Volume 5 has new documentation on the display function
+ o  The display function code has been translated and moved to book volume 5
+ o  PI has a higher internal precision
+ o  Mappings are now properly hashed for Aldor
+
+CATS (Computer Algebra Test Suite)
+
+ o The differential equations regression tests are being checked against
+   Mathematica, Maple, and Maxima. This has happended for the kamke2.input
+   regression test file and will happen for the other regression tests.
+
+o  Complex Gamma, logGamma, and log(Gamma) have additional tests and
+   documentation. 
+&lt;/pre&gt;
+
+&lt;a name="20080125"/&gt;
+&lt;h3&gt;January 25, 2008 Release Notes &lt;/h3&gt;
+&lt;a href="patches.html#20080125"&gt;patch list&lt;/a&gt;
+&lt;pre&gt;
+Summary: January 2008 release
+
+There have been two major concentrations of effort in this release.
+
+The first concentration is on the new Firefox Hyperdoc and the
+second concentration was the verification of Axiom against
+published standards.
+
+
+
+
+Firefox Hyperdoc
+
+The Firefox Hyperdoc has been integrated with the rest of the
+interpreter. The new )browse command causes Axiom to listen and
+serve hyperdoc pages on port 8085. 
+
+The interpreter was changed to add the )browse command. As a 
+side-effect new documentation was added to the interpreter
+volume (bookvol5) to explain top-level command handling. In
+addition, lisp and boot code was rewritten as part of the
+literate change.
+
+New sections were added to cover the beginning of the Computer
+Algebra Test Suite (CATS) subsection which brings a focus on
+compliance with published standards.
+
+Arthur Ralf's mathml-enabled version of the Jenks book is fully
+integrated into the Firefox Hyperdoc. Arthur also fixed some
+rendering and ambiguity issues.
+
+  axbook.tgz              fix the user/group settings
+  axserver.spad           fix lastType output re: errors
+  bookvol5                browse and top-level command handling 
+  bookvol11               add standards compliance for gamma
+  gammacomplexinverse.png added
+  gammacomplex.png        added
+  gammareal3.png          added
+  loggamma.png            added
+  mathml.spad             fix ambiguity bug in mathml output
+  mathml.spad             fix hex(10) mathml rendering 
+  mathml.spad             fix F,3 mathml rendering 
+  mathml.spad             remove code to eat %% 
+  psi.png                 added 
+
+
+
+
+Standards Verification
+
+The Computer Algebra Test Suite (CATS) effort checks the results
+that Axiom generates against published results. Axiom has an
+extensive set of regression tests (the KAMKE suite) for ordinary
+differential equations, for integration (the SCHAUM suite), and
+for numeric special functions (the ABRAMOWITZ suite). In addition,
+results have been checked against Mathematica, Maple, and Maxima.
+
+  asinatan.input   regression for the functions asin and atan
+  asinhatanh.input regression for the functions asinh and atanh
+  besselk.input    regression for the function besselK
+  e1.input         regression for the function E1
+  en.input         regression for the function En
+  exp.input        regression for the function exp
+  gamma.input      regression for the function gamma
+  log.input        regression for the functions log
+  pfaffian.input   regression for the function pfaffian
+  seccsc.input     regression for the functions sec and csc
+  sincos.input     regression for the functions sin and cos
+  sinhcosh.input   regression for the functions sinh and cosh
+  tancot.input     regression for the functions tan and cot
+  tanhcoth.input   regression for the functions tanh and coth
+
+
+
+
+New Functions Added
+
+Axiom is missing various special functions found in other computer
+algebra systems. This release adds two new ones, the Exponential
+Integral E1 and the higher order Exponential Integral En.  These have
+been tested against the published results.
+
+  special.spad E1 added
+  special.spad En added
+
+
+
+
+Bugs Fixed
+
+There are 15 bug fixes in this release:
+
+  bug 7015: fix hex(10) mathml rendering
+  bug 7016: remove code to eat %% 
+  bug 7019: fix F,3 mathml rendering 
+  bug 7023: discardGraph free corrected 
+  bug 7042: ignore regression test gensym
+  bug 7045: wrong Makefile for Xpm fix 
+  bug 7052: spurious remake of axbook
+  bug 7054: /home/silver path in bookvol11
+  bug 7057: ambiguity in mathml
+  bug 7089/343: FreeAbelianGroup order 
+  bug 7090/355 handle besselK
+  bug 7093: Function name fix
+  bug 7100/149: numlock in hyperdoc
+  bug 7101/204: MoreSystemCommand unnecessary loading 
+  bug 7102/412: Equality testing in TableAggregate 
+
+
+
+
+Regression test fixes
+
+As changes happen in the system the regression tests are updated
+to reflect the new conditions. Changing the category of PositiveInteger
+caused (a + -bi) to print as (a - bi). New builds raised gensym faults
+which were fixed. And new builds change random numbers so the tests
+that depend on them are marked "ok" despite failures due to randomness.
+The FreeAbelianGroup bug is tested.
+
+  acplot.spad     fix output form of negative numbers
+  calculus2.input fix function names 
+  classtalk.input ignore gensyms
+  collect.input   fix function names 
+  dfloat.input    handle negative number output
+  easter.input    fix function names 
+  elemnum.input   handle negative number output
+  exlap.input     fix function names 
+  exsum.input     fix function names 
+  free.input      added to test bug
+  grpthry.input   mark random generation failures ok
+  grpthry.input   fix function names 
+  ico.input       mark random generation failures ok
+  intg0.input     ignore gensyms
+  is.input        type declare function
+  kamke3.input    mark random generation failures ok
+  knot2.input     fix function names 
+  lodo.spad       ignore regression test gensym 
+  mapleok.input   ignore gensyms
+  mathml.input    handle new mathml sub/sup change
+  ndftip.input    fix missing blank lines
+  pmint.input     rewritten
+  repa6.input     fix function names 
+  r20bugs.input   change spacing
+  sf.spad         fix output form of negative numbers
+  tbagg.input     regression for equality testing in TableAggregate
+
+
+
+
+Algebra file changes
+
+The fundamental change was a supposedly transparent move of
+the category for PositiveInteger. This had the effect of changing
+the output form and broke several regression tests. Some mathml
+issues were fixed. The new functions E1 and En were added. The
+FreeAbelianGroup bug was fixed.
+
+  axserver.spad  fix lastType output re: errors
+  acplot.spad    fix output form of negative numbers
+  combfunc.spad  fix bold font handling
+  integer.spad   category change for PositiveInteger
+  sf.spad fix    output form of negative numbers
+  sf.spad        handle besselK
+  op.spad        handle besselK 
+  combfunc.spad  handle besselK 
+  free.spad      fix FreeAbelianGroup bug 
+  special.spad   add E1
+  special.spad   add En
+  mathml.spad    fix ambiguity bug in mathml output
+  mathml.spad    fix hex(10) mathml rendering 
+  mathml.spad    fix F,3 mathml rendering 
+  mathml.spad    remove code to eat %% 
+
+
+
+Interpreter changes
+
+The primary changes are the addition of bookvol11 for the Firefox
+Hyperdoc and the literate documentation of the top level command
+handling in bookvol5 (the interpreter) along with rewrites of the
+lisp/boot code.
+
+  bootfuns.lisp move $systemCommands to bookvol5
+  bookvol5      browse and top-level command handling
+  bookvol11     added
+  http.lisp     mathObject2String for hex(10) 
+  incl.boot     move incBiteOff to bookvol5
+  intint.lisp   move setCurrentLine to bookvol5
+  int-top.boot  move ncloopCommand, etc. to bookvol5
+  i-syscmd.boot move $SYSCOMMANDS to bookvol5
+  Makefile      wrong Makefile for Xpm fix 
+  makegraph.c   discardGraph free corrected 
+  nci.lisp      move ncloopInclude to bookvol5
+  setq.lisp     move command initialization to bookvol5
+
+
+
+Documentation changes
+
+  bookvol5      explain top level input handling (lisp/boot rewrite)
+  combfunc.spad fix bold font handling
+  axiom.sty     add binom 
+
+
+
+Patches released
+
+  20071129.01.tpd.patch
+  20071129.02.tpd.patch
+  20071205.01.tpd.patch
+  20071206.01.tpd.patch
+  20071208.01.tpd.patch
+  20071215.01.tpd.patch
+  20071215.02.tpd.patch
+  20071215.03.gxv.patch
+  20071216.01.tpd.patch
+  20071216.02.tpd.patch
+  20071216.03.acr.patch
+  20071217.01.acr.patch
+  20071217.02.tpd.patch
+  20071218.01.acr.patch
+  20071225.01.sxw.patch
+  20071228.01.tpd.patch
+  20071229.01.jap.patch
+  20071230.01.acr.patch
+  20071230.02.tpd.patch
+  20071230.03.tpd.patch
+  20080102.01.tpd.patch
+  20080103.01.tpd.patch
+  20080104.01.tpd.patch
+  20080104.02.tpd.patch
+  20080106.01.tpd.patch
+  20080107.01.tpd.patch
+  20080107.02.tpd.patch
+  20080107.03.tpd.patch
+  20080116.01.tpd.patch
+  20080119.01.tpd.patch
+  20080119.02.tpd.patch
+  20080119.03.tpd.patch
+  20080120.01.gxv.patch
+  20080120.02.tpd.patch
+  20080120.03.tpd.patch
+
+
+&lt;/pre&gt;
+
+&lt;a name="20071123"/&gt;
+&lt;h3&gt;November 23, 2007 Release Notes &lt;/h3&gt;
+&lt;a href="patches.html#20071123"&gt;patch list&lt;/a&gt;
+&lt;pre&gt;
+Summary: November 2007 release
+
+All of the golden sources are up to date.
+  savannah.nongnu.org/projects/axiom CVS
+  sourceforge.net/projects/axiom CVS
+  arch@axiom-developer.org ARCH (axiom--main--1--patch-54)
+  git@axiom-developer.org GIT
+  
+
+ADD NEW CREDITS
+  New patches were posted by Arthur and Alfredo so their tlas were
+  added to the changelog
+
+20071001 acr Arthur C. Ralfs &lt;arthur@mathbrane.ca&gt;
+20070914 jap Jose Alfredo Portes &lt;doyenatccny@gmail.com&gt;
+
+
+PORT TO DIFFERENT SYSTEMS
+  As part of the new axiom website there is a binary release page.
+  The stanzas for these supported systems were added.
+
+20071119 tpd Makefile.pamphlet add fedora6,7,8 stanzas
+
+
+NEW Axiom WEBSITE: http://axiom-developer.org STARTED.
+  The new Axiom website (currently at axiom.axiom-developer.org)
+  has been started. It will include the binary release page.
+
+
+REMOVE OLD REGRESSION SYSTEM
+  The previous regression test system was removed. A new combined
+  regression test and help documentation system was built to replace
+  this mechanism.
+
+20070901 tpd src/input/Makefile remove ALGEBRA variable
+20070901 tpd src/algebra/perm.spad remove TEST mechanism
+20070901 tpd src/algebra/view2d.spad remove TEST mechanism
+20070901 tpd src/algebra/fr.spad remove TEST mechanism
+
+
+FIX BOOK DOCUMENTATION
+  Minor typos have been discovered in the book during documentation.
+
+20070905 tpd src/doc/book remove duplicate upperCase, lowerCase typo
+20070903 tpd src/doc/bookvol4 fix typos
+20070902 tpd src/doc/book MultiSet -&gt; Multiset
+20080829 tpd src/doc/book.pamphlet correct typo
+
+
+FIX BUGS
+  Various bugs have been found and fixed.
+
+20071101 tpd src/interp/i-output.boot fix bugs 7010 (209), 7011
+20070920 tpd src/input/Makefile add bug101.input regression test
+20070920 tpd src/input/bug101.input test laplace(log(z),z,w) bug 101
+20070920 wxh src/algebra/laplace.spad fix laplace(log(z),z,w) bug 101
+20070916 tpd src/input/Makefile add bug103.input regression test
+20070916 tpd src/input/bug103.input test solve(z=z,z) bug fix
+20070916 tpd src/algebra/polycat.spad solve(z=z,z) bug fix
+20070916 tpd src/algebra/catdef.spad add zero? to exquo
+20070915 tpd merge bug100 branch
+20070915 tpd src/input/Makefile add bug100.input regression test
+20070915 tpd src/input/bug100.input test integrate((z^a+1)^b,z) infinite loop
+20070915 wxh src/algebra/intef.spad fix integrate((z^a+1)^b,z) infinite loop
+20070915 tpd src/algebra/carten minor edit for regression cleanup
+20070914 wxh src/hyper/hyper fix bad bracing of )hd change
+20070914 tpd src/algebra/fraction.spad remove double )spool command
+20070914 tpd src/algebra/kl.spad remove double )spool command
+20070914 tpd src/algebra/lindep.spad remove double )spool command
+20070914 tpd src/algebra/radix.spad remove double )spool command
+
+
+ENABLE DYNAMIC RESTART OF HYPERDOC
+  Hyperdoc can now be started dynamically or restarted if killed.
+
+20070914 jap adapt changes for )hd restart to Axiom sources
+20070914 wxh src/sman/bookvol6 enable restart of hyperdoc with )hd
+20070914 wxh src/include/sman.h1 enable restart of hyperdoc with )hd
+20070914 wxh src/hyper/hyper enable restart of hyperdoc with )hd
+
+
+SET UP THE NEW FIREFOX BASED HYPERDOC
+  Hyperdoc is going away. A new version of hyperdoc is being built
+  which uses html/javascript/mathml. These files change the interpreter
+  and algebra to support the new hyperdoc machinery.
+
+20071019 acr src/interp/http.lisp use new return values
+20071019 acr src/algebra/axserver.spad use new return values
+20071014 acr src/algebra/axserver.spad use getContentType(pathvar)
+20071013 acr license/license.ralfs license rewrite
+20071013 acr src/interp/http.lisp faster page service
+20071013 acr src/algebra/axserver.spad faster page service
+20071001 tpd src/algebra/exposed.lisp add (|AxiomServer| . AXSERV) to basic
+20071001 tpd src/algebra/Makefile add axserver.spad
+20071001 acr src/algebra/axserver.spad axserver socket connection code
+20071001 tpd src/interp/Makefile add http.lisp
+20071001 acr src/interp/http.lisp axserver socket connection code
+20071001 acr license/license.ralfs added
+
+
+REGRESSION TEST CALCULUS
+  A new regression test suite for calculus is being built. The first
+  of these files has been added to the system.
+
+20070913 tpd src/input/Makefile schaum1.input added
+20070913 tpd src/input/schaum1.input added
+
+
+REGRESSION TEST ORDINARY DIFFERENTIAL EQUATIONS
+  A regression test suite for ordinary differential equations was built. 
+
+20071005 tpd src/input/Makefile kamke7.input regression test added
+20071005 tpd src/input/kamke7.input ODE regression test added
+20071005 tpd src/input/Makefile kamke6.input regression test added
+20071005 tpd src/input/kamke6.input ODE regression test added
+20071005 tpd src/input/Makefile kamke5.input regression test added
+20071005 tpd src/input/kamke5.input ODE regression test added
+20071005 tpd src/input/Makefile kamke4.input regression test added
+20071005 tpd src/input/kamke4.input ODE regression test added
+20071005 tpd src/input/Makefile kamke3.input regression test added
+20071005 tpd src/input/kamke3.input ODE regression test added
+20071004 tpd src/input/Makefile kamke2.input regression test added
+20071004 tpd src/input/kamke2.input ODE regression test added
+20071004 tpd src/input/Makefile kamke1.input regression test added
+20071004 tpd src/input/kamke1.input ODE regression test added
+20071004 tpd src/input/Makefile kamke0.input regression test added
+20071004 tpd src/input/kamke0.input ODE regression test added
+
+
+REGRESSION TEST PFAFFIAN
+  Martin added the pfaffian regression test. It was added and removed
+  due to documentation license issues. New documentation is being written.
+
+20070929 tpd src/input/Makefile pfaffian regression test removed
+20070929 tpd src/input/pfaffian.input regression test removed
+20070927 tpd src/input/Makefile pfaffian regression test added 
+20070927 mxr src/input/pfaffian.input regression test added 
+
+
+ADD PORTIONS OF THE GUESS PACKAGE
+  The newton.spad file is actually part of the fffg.spad file so it
+  was removed. The very top level spad functions in GUESS still do
+  not work properly.
+
+20070909 tpd src/algebra/newton.spad included in fffg.spad
+20070909 tpd src/algebra/Makefile remove newton.spad (duplicate)
+
+
+FIX BUILD PROCESS
+  The build process was not properly suppressing output by default.
+
+20070907 tpd src/algebra/acplot.spad fix PlaneAlgebraicCurvePlot.help NOISE
+20070907 tpd src/algebra/Makefile make regression respect NOISE variable
+20070907 tpd src/input/Makefile make regression respect NOISE variable
+
+
+FIX INSTALL PROCESS
+  The install process had a bug.
+
+20070906 tpd Makefile int/sman/axiom command to target command for install
+20070906 tpd src/sman/Makefile copy axiom command to int
+
+
+ADD ALDOR RELEASE
+  The aldor release has been added to zips. It will soon be part of
+  the build mechanism but separately maintained like GCL.
+
+20070901 tpd zips/aldor.20070901.tgz add pdf documentation
+20070901 tpd zips/aldor.20070901.tgz added
+
+
+ADD )HELP FACILITY
+  The )help facility was recovered. The documentation is now integrated
+  into the spad files and used both for help documentation and algebra
+  regression testing. 
+
+20070902 tpd src/doc/Makefile document how to add help files
+20070902 tpd src/algebra/Makefile document how to add help files
+20070906 tpd merge help files branch
+20070906 tpd src/doc/spadhelp add ZeroDimensionalSolvePackage
+20070906 tpd src/algebra/Makefile add ZeroDimensionalSolvePackage.help 
+20070906 tpd src/algebra/zerodim.spad add ZeroDimensionalSolvePackage.help
+20070906 tpd src/algebra/zerodim.spad ZeroDimensionalSolvePackage.input
+20070906 tpd src/doc/spadhelp add XPolynomialRing
+20070906 tpd src/algebra/Makefile add XPolynomialRing.help 
+20070906 tpd src/algebra/xpoly.spad add XPolynomialRing.help (XPR)
+20070906 tpd src/algebra/xpoly.spad XPolynomialRing.input
+20070906 tpd src/doc/spadhelp add XPolynomial
+20070906 tpd src/algebra/Makefile add XPolynomial.help 
+20070906 tpd src/algebra/xpoly.spad add XPolynomial.help (XPOLY)
+20070906 tpd src/algebra/xpoly.spad XPolynomial.input
+20070906 tpd src/doc/spadhelp add XPBWPolynomial
+20070906 tpd src/algebra/Makefile add XPBWPolynomial.help 
+20070906 tpd src/algebra/xlpoly.spad add XPBWPolynomial.help (XPBWPOLY)
+20070906 tpd src/algebra/xlpoly.spad XPBWPolynomial.input
+20070905 tpd src/doc/spadhelp add WuWenTsunTriangularSet
+20070905 tpd src/algebra/Makefile add WuWenTsunTriangularSet.help 
+20070905 tpd src/algebra/triset.spad add WuWenTsunTriangularSet.help (WUTSET)
+20070905 tpd src/algebra/triset.spad WuWenTsunTriangularSet.input
+20070905 tpd src/doc/spadhelp add Void
+20070905 tpd src/algebra/Makefile add Void.help 
+20070905 tpd src/algebra/void.spad add Void.help (VOID)
+20070905 tpd src/algebra/void.spad Void.input
+20070905 tpd src/doc/spadhelp add Vector
+20070905 tpd src/algebra/Makefile add Vector.help 
+20070905 tpd src/algebra/vector.spad add Vector.help (Vector)
+20070905 tpd src/algebra/vector.spad Vector.input
+20070905 tpd src/doc/spadhelp add UniversalSegment
+20070905 tpd src/algebra/Makefile add UniversalSegment.help 
+20070905 tpd src/algebra/seg.spad add UniversalSegment.help (UNISEG)
+20070905 tpd src/algebra/seg.spad UniversalSegment.input
+20070905 tpd src/doc/spadhelp add UnivariatePolynomial
+20070905 tpd src/algebra/Makefile add UnivariatePolynomial.help 
+20070905 tpd src/algebra/poly.spad add UnivariatePolynomial.help (UP)
+20070905 tpd src/algebra/poly.spad UnivariatePolynomial.input
+20070905 tpd src/doc/spadhelp add TwoDimensionalArray
+20070905 tpd src/algebra/Makefile add TwoDimensionalArray.help 
+20070905 tpd src/algebra/array2.spad add TwoDimensionalArray.help (ARRAY2)
+20070905 tpd src/algebra/array2.spad TwoDimensionalArray.input
+20070905 tpd src/doc/spadhelp add TextFile
+20070905 tpd src/algebra/Makefile add TextFile.help 
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+
+&lt;/pre&gt;
+&lt;/body&gt;
+&lt;/html&gt;
diff --git a/src/axiom-website/rosetta.html b/src/axiom-website/rosetta.html
new file mode 100644
index 0000000..0e0bd55
--- /dev/null
+++ b/src/axiom-website/rosetta.html
@@ -0,0 +1,5781 @@
+&lt;html&gt;
+ &lt;head&gt;
+  &lt;title&gt;
+   Axiom Computer Algebra System
+  &lt;/title&gt;
+ &lt;/head&gt;
+ &lt;body bgcolor="#ffff66"&gt;
+   &lt;div id="head" align="center"&gt; 
+    &lt;a href="http://savannah.nongnu.org/projects/axiom/"&gt;
+     &lt;img src="axiom.png" border="0" alt="Axiom"&gt;
+    &lt;/a&gt;
+    &lt;br&gt;
+    &lt;font size=200%&gt;
+     The Scientific Computation System
+    &lt;/font&gt;
+   &lt;/div&gt;
+   &lt;div align="center"&gt;
+    [
+     &lt;a href="../index.html" title="Home"&gt;
+      Home
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="screenshots.html" title="Screen Shots"&gt;
+      Screenshots
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="faq.html" title="FAQ"&gt;
+      FAQ
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="download.html" title="Download"&gt;
+      Download
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="documentation.html" title="Documentation"&gt;
+      Documentation
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="currentstate.html" title="Current State"&gt;
+      Current State
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="community.html" title="Community"&gt;
+      Community
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="developers.html" title="Developers"&gt;
+      Developers
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="patches.html" title="Patches"&gt;
+      Patches
+     &lt;/a&gt;
+    ]
+   &lt;/div&gt;
+   &lt;div align="center"&gt;
+    [
+     &lt;a href="bookvol10.2abb.html" title="Abbreviation Graph"&gt;
+      Abbreviation Graph
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="bookvol10.2full.html" title="Full Name Graph"&gt;
+      Full Name Graph
+     &lt;/a&gt;
+    ]
+   &lt;/div&gt;
+  &lt;br&gt;
+  &lt;hr&gt;
+  &lt;div id="body"&gt;
+   &lt;h1&gt;
+    Rosetta Stone
+   &lt;/h1&gt;
+   &lt;p&gt;
+   &lt;font size=4&gt;
+The following is a collection of synonyms for various operations in
+the computer algebra systems Axiom, Derive, GAP, DoCon,
+Macsyma, Magnus, Maxima, Maple, Mathematica, MuPAD, Octave,
+Pari, Reduce, Scilab, Sumit and Yacas.  This collection does not
+attempt to be comprehensive, but hopefully it will be useful in giving
+an indication of how to translate between the syntaxes used by the
+different systems in many common situations.  Note that a blank entry
+means either (a) that there may be an exact translation of a
+particular operation for the indicated system, but we don't know what
+it is or (b) there is no exact translation but it may still be
+possible to work around this lack with a related functionality.
+
+While commercial systems are not provided on this CD the intent of the
+Rosetta effort is to make it possible for experienced Computer Algebra
+users to experiment with other systems. Thus the commands for
+commercial systems are included to allow users of those systems to
+translate.
+
+Some of these systems are special purpose and do not support a lot of
+the functionality of the more general purpose systems. Where they do
+support an interpreter the commands are provided.
+
+Originally written by Michael Wester.
+Modified for Rosetta by Timothy Daly, Alexander Hulpke (GAP).
+
+&lt;h3&gt;System availability&lt;/h3&gt;
+
+&lt;table&gt;
+ &lt;tr&gt;
+  &lt;th&gt;System&lt;/th&gt;
+  &lt;th&gt;License&lt;/th&gt;
+  &lt;th&gt;Status (2002)&lt;/th&gt;
+  &lt;th&gt;URL&lt;/th&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Aldor&lt;/td&gt;
+  &lt;td&gt;Non-free&lt;/td&gt;
+  &lt;td&gt;available&lt;/td&gt;
+  &lt;td&gt;http://www.aldor.org&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+ &lt;td&gt;Axiom&lt;/td&gt;
+ &lt;td&gt;ModifiedBSD&lt;/td&gt;
+ &lt;td&gt;available&lt;/td&gt;
+ &lt;td&gt;http://axiom.axiom-developer.org&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+ &lt;td&gt;Derive&lt;/td&gt;
+ &lt;td&gt;commercial&lt;/td&gt;
+ &lt;td&gt;available&lt;/td&gt;
+ &lt;td&gt;http://www.mathware.com&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;open source&lt;/td&gt;
+  &lt;td&gt;available&lt;/td&gt;
+  &lt;td&gt;http://www.haskell.org/docon&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;GPL&lt;/td&gt;
+  &lt;td&gt;Rosetta&lt;/td&gt;
+  &lt;td&gt;http://www.gap-system.org/~gap&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;commercial&lt;/td&gt;
+  &lt;td&gt;dead&lt;/td&gt;
+  &lt;td&gt;unavailable&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;GPL&lt;/td&gt;
+  &lt;td&gt;Rosetta&lt;/td&gt;
+  &lt;td&gt;http://sourceforge.net/projects/magnus&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;GPL&lt;/td&gt;
+  &lt;td&gt;Rosetta&lt;/td&gt;
+  &lt;td&gt;http://www.ma.utexas.edu/maxima.html&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;commercial&lt;/td&gt;
+  &lt;td&gt;available&lt;/td&gt;
+  &lt;td&gt;http://www.maplesoft.com&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;commercial&lt;/td&gt;
+  &lt;td&gt;available&lt;/td&gt;
+  &lt;td&gt;http://www.wolfram.com&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;commercial&lt;/td&gt;
+  &lt;td&gt;available&lt;/td&gt;
+  &lt;td&gt;http://www.mupad.de&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;GPL&lt;/td&gt;
+  &lt;td&gt;Rosetta&lt;/td&gt;
+  &lt;td&gt;http://www.octave.org&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;GPL&lt;/td&gt;
+  &lt;td&gt;Rosetta&lt;/td&gt;
+  &lt;td&gt;http://www.parigp-home.de&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;commercial&lt;/td&gt;
+  &lt;td&gt;available&lt;/td&gt;
+  &lt;td&gt;http://www.zib.de/Symbolik/reduce&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;available&lt;/td&gt;
+  &lt;td&gt;http://www-rocq.inria.fr/scilab&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;available&lt;/td&gt;
+  &lt;td&gt;http://www-sop.inria.fr/cafe/soft-f.html&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;GPL&lt;/td&gt;
+  &lt;td&gt;available&lt;/td&gt;
+  &lt;td&gt;http://yacas.sourceforge.net&lt;/td&gt;
+ &lt;/tr&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+&lt;tr&gt;
+ &lt;th&gt;System&lt;/th&gt;
+ &lt;th&gt;Type&lt;/th&gt;
+ &lt;th&gt;Interpreted or Compiled&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;General Purpose&lt;/td&gt;
+  &lt;td&gt;both&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;General Purpose&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;General Purpose&lt;/td&gt;
+  &lt;td&gt;Interpreted in Haskell&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;Group Theory&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;General Purpose&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;Infinite Group Theory&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;General Purpose&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;General Purpose&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;General Purpose&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;General Purpose&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;Numerical Computing&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;Number Theory&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;General Purpose&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;General Purpose&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;Functional Equations&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;General Purpose&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;h3&gt;Programming and Miscellaneous&lt;/h3&gt;
+
+&lt;table&gt;
+ &lt;tr&gt;
+  &lt;th&gt;System&lt;/th&gt;
+  &lt;th&gt;Unix/Microsoft user initialization file&lt;/th&gt;
+  &lt;th&gt;&lt;/th&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;.axiom.input&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;.gaprc&lt;/td&gt;
+  &lt;td&gt;GAP.RC&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;derive.ini&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;macsyma-init.macsyma&lt;/td&gt;
+  &lt;td&gt;mac-init.mac&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;macsyma-init.macsyma&lt;/td&gt;
+  &lt;td&gt;mac-init.mac&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;.mapleinit&lt;/td&gt;
+  &lt;td&gt;maplev5.ini&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;init.m&lt;/td&gt;
+  &lt;td&gt;init.m&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;.mupadinit&lt;/td&gt;
+  &lt;td&gt;\mupad\bin\userinit.mu&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;.reducerc&lt;/td&gt;
+  &lt;td&gt;reduce.rc&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+ &lt;tr&gt;
+  &lt;th&gt;System&lt;/th&gt;
+  &lt;th&gt;Describe keyword&lt;/th&gt;
+  &lt;th&gt;Find keywords containing pattern&lt;/th&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;)what operations pattern&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;?keyword&lt;/td&gt;
+  &lt;td&gt;??keyword&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;describe("keyword")\$&lt;/td&gt;
+  &lt;td&gt;apropos("pattern");&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;describe("keyword")\$&lt;/td&gt;
+  &lt;td&gt;apropos("pattern");&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;?keyword&lt;/td&gt;
+  &lt;td&gt;?pattern\,\fnm&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;?keyword&lt;/td&gt;
+  &lt;td&gt;?*pattern*&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;?keyword&lt;/td&gt;
+  &lt;td&gt;?*pattern*&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;help -i keyword&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+Only if the pattern is not a keyword and then the matches are simplistic.
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;th&gt;System&lt;/th&gt;
+  &lt;th&gt;Comment&lt;/th&gt;
+  &lt;th&gt;Line Cont.&lt;/th&gt;
+  &lt;th&gt;Prev. Expr.&lt;/th&gt;
+  &lt;th&gt;Case sensitive&lt;/th&gt;
+  &lt;th&gt;Variables assumed&lt;/th&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;-- comment&lt;/td&gt;
+  &lt;td&gt;input _CR input&lt;/td&gt;
+  &lt;td&gt;%&lt;/td&gt;
+  &lt;td&gt;Yes&lt;/td&gt;
+  &lt;td&gt;real&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;"comment"&lt;/td&gt;
+  &lt;td&gt;input CRinput&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;No&lt;/td&gt;
+  &lt;td&gt;real&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;# comment&lt;/td&gt;
+  &lt;td&gt;input\CRinput&lt;/td&gt;
+  &lt;td&gt;last&lt;/td&gt;
+  &lt;td&gt;Yes&lt;/td&gt;
+  &lt;td&gt;no assumption&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;/* comment */&lt;/td&gt;
+  &lt;td&gt;input CR input;&lt;/td&gt;
+  &lt;td&gt;%&lt;/td&gt;
+  &lt;td&gt;No&lt;/td&gt;
+  &lt;td&gt;real&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;/* comment */&lt;/td&gt;
+  &lt;td&gt;input CR input;&lt;/td&gt;
+  &lt;td&gt;%&lt;/td&gt;
+  &lt;td&gt;No&lt;/td&gt;
+  &lt;td&gt;real&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;# comment&lt;/td&gt;
+  &lt;td&gt;input CR input;&lt;/td&gt;
+  &lt;td&gt;%&lt;/td&gt;
+  &lt;td&gt;Yes&lt;/td&gt;
+  &lt;td&gt;complex&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;(* comment *)&lt;/td&gt;
+  &lt;td&gt;input CR input&lt;/td&gt;
+  &lt;td&gt;%&lt;/td&gt;
+  &lt;td&gt;Yes&lt;/td&gt;
+  &lt;td&gt;complex&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;# comment #&lt;/td&gt;
+  &lt;td&gt;input CR input;&lt;/td&gt;
+  &lt;td&gt;%&lt;/td&gt;
+  &lt;td&gt;Yes&lt;/td&gt;
+  &lt;td&gt;complex&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;##&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;Yes&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;% comment&lt;/td&gt;
+  &lt;td&gt;input CR input;&lt;/td&gt;
+  &lt;td&gt;ws&lt;/td&gt;
+  &lt;td&gt;No&lt;/td&gt;
+  &lt;td&gt;complex&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;th&gt;System&lt;/th&gt;
+  &lt;th&gt;Load a file&lt;/th&gt;
+  &lt;th&gt;Time a command&lt;/th&gt;
+  &lt;th&gt;Quit&lt;/th&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;)read "file" )quiet&lt;/td&gt;
+  &lt;td&gt;)set messages time on&lt;/td&gt;
+  &lt;td&gt;)quit&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;[Transfer Load Derive]&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;[Quit]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;Read("file");&lt;/td&gt;
+  &lt;td&gt;time; \h{(also see {\tt Runtime();})}&lt;/td&gt;
+  &lt;td&gt;quit;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;load("file")\$&lt;/td&gt;
+  &lt;td&gt;showtime: all\$&lt;/td&gt;
+  &lt;td&gt;quit();&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;load("file")\$&lt;/td&gt;
+  &lt;td&gt;showtime: all\$&lt;/td&gt;
+  &lt;td&gt;quit();&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;read("file"):&lt;/td&gt;
+  &lt;td&gt;readlib(showtime): on;&lt;/td&gt;
+  &lt;td&gt;quit&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;&lt;&lt; file&lt;/td&gt;
+  &lt;td&gt;Timing[command]&lt;/td&gt;
+  &lt;td&gt;Quit[]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;read("file"):&lt;/td&gt;
+  &lt;td&gt;time(command);&lt;/td&gt;
+  &lt;td&gt;quit&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;load file&lt;/td&gt;
+  &lt;td&gt;tic(); cmd ; toc()&lt;/td&gt;
+  &lt;td&gt;quit \OR\ exit&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;in "file"\$&lt;/td&gt;
+  &lt;td&gt;on time;&lt;/td&gt;
+  &lt;td&gt;quit;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;quit&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\h{Display}&lt;/td&gt;
+  &lt;td&gt;\h{Suppress}&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;\h{output}&lt;/td&gt;
+  &lt;td&gt;\h{output}&lt;/td&gt;
+  &lt;td&gt;\h{Substitution: $f(x, y) \rightarrow f(z, w)$}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;input&lt;/td&gt;
+  &lt;td&gt;input;&lt;/td&gt;
+  &lt;td&gt;subst(f(x, y), [x = z, y = w])&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;input&lt;/td&gt;
+  &lt;td&gt;var:= input&lt;/td&gt;
+  &lt;td&gt;[Manage Substitute]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;input;&lt;/td&gt;
+  &lt;td&gt;input;;&lt;/td&gt;
+  &lt;td&gt;Value(f,[x,y],[z,w]);\fnm&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;input;&lt;/td&gt;
+  &lt;td&gt;input\$&lt;/td&gt;
+  &lt;td&gt;subst([x = z, y = w], f(x, y));&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;input;&lt;/td&gt;
+  &lt;td&gt;input\$&lt;/td&gt;
+  &lt;td&gt;subst([x = z, y = w], f(x, y));&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;input;&lt;/td&gt;
+  &lt;td&gt;input:&lt;/td&gt;
+  &lt;td&gt;subs(\{x = z, y = w\}, f(x, y));&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;input&lt;/td&gt;
+  &lt;td&gt;input;&lt;/td&gt;
+  &lt;td&gt;f[x, y] /. \{x -&gt; z, y -&gt; w\}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;input;&lt;/td&gt;
+  &lt;td&gt;input:&lt;/td&gt;
+  &lt;td&gt;subs(f(x, y), [x = z, y = w]);&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;input&lt;/td&gt;
+  &lt;td&gt;input;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;input;&lt;/td&gt;
+  &lt;td&gt;input\$&lt;/td&gt;
+  &lt;td&gt;sub(\{x = z, y = w\}, f(x, y));&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\h{Set}&lt;/td&gt;
+  &lt;td&gt;\h{List}&lt;/td&gt;
+  &lt;td&gt;\h{Matrix}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;set [1, 2]&lt;/td&gt;
+  &lt;td&gt;[1, 2]&lt;/td&gt;
+  &lt;td&gt;matrix([[1, 2],[3, 4]])&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;\{1, 2\}&lt;/td&gt;
+  &lt;td&gt;[1, 2]&lt;/td&gt;
+  &lt;td&gt;[[1,2], [3,4]]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;Set([1,2])&lt;/td&gt;
+  &lt;td&gt;[1, 2]&lt;/td&gt;
+  &lt;td&gt;[[1,2], [3,4]]\fnm&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;[1, 2]&lt;/td&gt;
+  &lt;td&gt;[1, 2]&lt;/td&gt;
+  &lt;td&gt;matrix([1, 2], [3, 4])&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;[1, 2]&lt;/td&gt;
+  &lt;td&gt;[1, 2]&lt;/td&gt;
+  &lt;td&gt;matrix([1, 2], [3, 4])&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;\{1, 2\}&lt;/td&gt;
+  &lt;td&gt;[1, 2]&lt;/td&gt;
+  &lt;td&gt;matrix([[1, 2], [3, 4]])&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;\{1, 2\}&lt;/td&gt;
+  &lt;td&gt;\{1, 2\}&lt;/td&gt;
+  &lt;td&gt;\{\{1, 2\}, \{3, 4\}\}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;\{1, 2\}&lt;/td&gt;
+  &lt;td&gt;[1, 2]&lt;/td&gt;
+  &lt;td&gt;export(Dom): \q export(linalg):&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;matrix:= ExpressionField(normal)):&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;matrix([[1, 2], [3, 4]])&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;\{1, 2\}&lt;/td&gt;
+  &lt;td&gt;\{1, 2\}&lt;/td&gt;
+  &lt;td&gt;mat((1, 2), (3, 4))&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;list(1,2)&lt;/td&gt;
+  &lt;td&gt;A=[1,2;3,4]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\h{Equation}&lt;/td&gt;
+  &lt;td&gt;\h{List element}&lt;/td&gt;
+  &lt;td&gt;\h{Matrix element}&lt;/td&gt;
+  &lt;td&gt;\h{Length of a list}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;x = 0&lt;/td&gt;
+  &lt;td&gt;l . 2&lt;/td&gt;
+  &lt;td&gt;m(2, 3)&lt;/td&gt;
+  &lt;td&gt;\#l&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;x = 0&lt;/td&gt;
+  &lt;td&gt;l SUB 2&lt;/td&gt;
+  &lt;td&gt;m SUB 2 SUB 3&lt;/td&gt;
+  &lt;td&gt;DIMENSION(l)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;x=0&lt;/td&gt;
+  &lt;td&gt;l[2]&lt;/td&gt;
+  &lt;td&gt;m[2][3]&lt;/td&gt;
+  &lt;td&gt;Length(l)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;x = 0&lt;/td&gt;
+  &lt;td&gt;l[2]&lt;/td&gt;
+  &lt;td&gt;m[2, 3]&lt;/td&gt;
+  &lt;td&gt;length(l)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;x = 0&lt;/td&gt;
+  &lt;td&gt;l[2]&lt;/td&gt;
+  &lt;td&gt;m[2, 3]&lt;/td&gt;
+  &lt;td&gt;length(l)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;x = 0&lt;/td&gt;
+  &lt;td&gt;l[2]&lt;/td&gt;
+  &lt;td&gt;m[2, 3]&lt;/td&gt;
+  &lt;td&gt;nops(l)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;x == 0&lt;/td&gt;
+  &lt;td&gt;l[[2]]&lt;/td&gt;
+  &lt;td&gt;m[[2, 3]]&lt;/td&gt;
+  &lt;td&gt;Length[l]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;x = 0&lt;/td&gt;
+  &lt;td&gt;l[2]&lt;/td&gt;
+  &lt;td&gt;m[2, 3]&lt;/td&gt;
+  &lt;td&gt;nops(l)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;x = 0&lt;/td&gt;
+  &lt;td&gt;part(l, 2)&lt;/td&gt;
+  &lt;td&gt;m(2, 3)&lt;/td&gt;
+  &lt;td&gt;length(l)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;l(2)&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\m{2}{\rm Prepend/append an element to a list}&lt;/td&gt;
+  &lt;td&gt;\h{Append two lists}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;cons(e, l)&lt;/td&gt;
+  &lt;td&gt;concat(l, e)&lt;/td&gt;
+  &lt;td&gt;append(l1, l2)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;APPEND([e], l)&lt;/td&gt;
+  &lt;td&gt;APPEND(l, [e])&lt;/td&gt;
+  &lt;td&gt;APPEND(l1, l2)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;Concatenation([e],l)&lt;/td&gt;
+  &lt;td&gt;Add(l,e)&lt;/td&gt;
+  &lt;td&gt;Append(l1, l2)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;cons(e, l)&lt;/td&gt;
+  &lt;td&gt;endcons(e, l)&lt;/td&gt;
+  &lt;td&gt;append(l1, l2)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;cons(e, l)&lt;/td&gt;
+  &lt;td&gt;endcons(e, l)&lt;/td&gt;
+  &lt;td&gt;append(l1, l2)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;[e, op(l)]&lt;/td&gt;
+  &lt;td&gt;[op(l), e]&lt;/td&gt;
+  &lt;td&gt;[op(l1), op(l2)]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;Prepend[l, e]&lt;/td&gt;
+  &lt;td&gt;Append[l, e]&lt;/td&gt;
+  &lt;td&gt;Join[l1, l2]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;[e, op(l)]&lt;/td&gt;
+  &lt;td&gt;append(l, e)&lt;/td&gt;
+  &lt;td&gt;l1 . l2&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;e . l&lt;/td&gt;
+  &lt;td&gt;append(l, {e})&lt;/td&gt;
+  &lt;td&gt;append(l1, l2)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\h{Matrix column dimension}&lt;/td&gt;
+  &lt;td&gt;\h{Convert a list into a column vector}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;ncols(m)&lt;/td&gt;
+  &lt;td&gt;transpose(matrix([l]))&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;DIMENSION(m SUB 1)&lt;/td&gt;
+  &lt;td&gt;[l]\`{}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;Length(mat[1])&lt;/td&gt;
+  &lt;td&gt;\h{objects are identical}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;mat\_\,ncols(m)&lt;/td&gt;
+  &lt;td&gt;transpose(matrix(l))&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;mat\_\,ncols(m)&lt;/td&gt;
+  &lt;td&gt;transpose(matrix(l))&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;linalg[coldim](m)&lt;/td&gt;
+  &lt;td&gt;linalg[transpose](matrix([l]))&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;Dimensions[m][[2]]&lt;/td&gt;
+  &lt;td&gt;Transpose[\{l\}]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;linalg::ncols(m)&lt;/td&gt;
+  &lt;td&gt;transpose(matrix([l]))\,\fnm&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;load\_\,package(linalg)\$&lt;/td&gt;
+  &lt;td&gt;matrix v(length(l), 1)\$&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;column\_dim(m)&lt;/td&gt;
+  &lt;td&gt;for i:=1:length(l) do&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;\q\q v(i, 1):= part(l, i)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+See the definition of matrix above.
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\h{Convert a column vector into a list}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;[v(i, 1) for i in 1..nrows(v)]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;v\`{} SUB 1&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;\h{objects are identical}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;part(transpose(v), 1)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;part(transpose(v), 1)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;op(convert(linalg[transpose](v), listlist))&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;Flatten[v]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;[op(v)]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;load\_\,package(linalg)\$&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;for i:=1:row\_\,dim(v) collect(v(i, 1))&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\h{True}&lt;/td&gt;
+  &lt;td&gt;\h{False}&lt;/td&gt;
+  &lt;td&gt;\h{And}&lt;/td&gt;
+  &lt;td&gt;\h{Or}&lt;/td&gt;
+  &lt;td&gt;\h{Not}&lt;/td&gt;
+  &lt;td&gt;\h{Equal}&lt;/td&gt;
+  &lt;td&gt;\h{Not equal}
+	&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;true&lt;/td&gt;
+  &lt;td&gt;false&lt;/td&gt;
+  &lt;td&gt;and&lt;/td&gt;
+  &lt;td&gt;or&lt;/td&gt;
+  &lt;td&gt;not&lt;/td&gt;
+  &lt;td&gt;=&lt;/td&gt;
+  &lt;td&gt;=&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;TRUE&lt;/td&gt;
+  &lt;td&gt;FALSE&lt;/td&gt;
+  &lt;td&gt;AND&lt;/td&gt;
+  &lt;td&gt;OR&lt;/td&gt;
+  &lt;td&gt;NOT&lt;/td&gt;
+  &lt;td&gt;=&lt;/td&gt;
+  &lt;td&gt;/=&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;true&lt;/td&gt;
+  &lt;td&gt;false\fnm&lt;/td&gt;
+  &lt;td&gt;and&lt;/td&gt;
+  &lt;td&gt;or&lt;/td&gt;
+  &lt;td&gt;not&lt;/td&gt;
+  &lt;td&gt;=&lt;/td&gt;
+  &lt;td&gt;&lt;&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;true&lt;/td&gt;
+  &lt;td&gt;false&lt;/td&gt;
+  &lt;td&gt;and&lt;/td&gt;
+  &lt;td&gt;or&lt;/td&gt;
+  &lt;td&gt;not&lt;/td&gt;
+  &lt;td&gt;=&lt;/td&gt;
+  &lt;td&gt;\#&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;true&lt;/td&gt;
+  &lt;td&gt;false&lt;/td&gt;
+  &lt;td&gt;and&lt;/td&gt;
+  &lt;td&gt;or&lt;/td&gt;
+  &lt;td&gt;not&lt;/td&gt;
+  &lt;td&gt;=&lt;/td&gt;
+  &lt;td&gt;\#&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;true&lt;/td&gt;
+  &lt;td&gt;false&lt;/td&gt;
+  &lt;td&gt;and&lt;/td&gt;
+  &lt;td&gt;or&lt;/td&gt;
+  &lt;td&gt;not&lt;/td&gt;
+  &lt;td&gt;=&lt;/td&gt;
+  &lt;td&gt;&lt;&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;True&lt;/td&gt;
+  &lt;td&gt;False&lt;/td&gt;
+  &lt;td&gt;\&lt;/td&gt;
+  &lt;td&gt;\&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;||&lt;/td&gt;
+  &lt;td&gt;!&lt;/td&gt;
+  &lt;td&gt;==&lt;/td&gt;
+  &lt;td&gt;!=&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;true&lt;/td&gt;
+  &lt;td&gt;false&lt;/td&gt;
+  &lt;td&gt;and&lt;/td&gt;
+  &lt;td&gt;or&lt;/td&gt;
+  &lt;td&gt;not&lt;/td&gt;
+  &lt;td&gt;=&lt;/td&gt;
+  &lt;td&gt;&lt;&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;t&lt;/td&gt;
+  &lt;td&gt;nil&lt;/td&gt;
+  &lt;td&gt;and&lt;/td&gt;
+  &lt;td&gt;or&lt;/td&gt;
+  &lt;td&gt;not&lt;/td&gt;
+  &lt;td&gt;=&lt;/td&gt;
+  &lt;td&gt;neq&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;\%t&lt;/td&gt;
+  &lt;td&gt;\%f&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\h{If+then+else statements}&lt;/td&gt;
+  &lt;td&gt;\h{Strings (concatenated)}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;if \_ then \_ else if \_ then \_ else \_&lt;/td&gt;
+  &lt;td&gt;concat(["x", "y"])&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;IF(\_, \_, IF(\_, \_, \_))&lt;/td&gt;
+  &lt;td&gt;"xy"&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;if \_ then \_ elif \_ then \_ else \_ fi&lt;/td&gt;
+  &lt;td&gt;Concatenation("x","y")&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;if \_ then \_ else if \_ then \_ else \_&lt;/td&gt;
+  &lt;td&gt;concat("x", "y")&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;if \_ then \_ else if \_ then \_ else \_&lt;/td&gt;
+  &lt;td&gt;concat("x", "y")&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;if \_ then \_ elif \_ then \_ else \_ fi&lt;/td&gt;
+  &lt;td&gt;"x" . "y"&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;If[\_, \_, If[\_, \_, \_]]&lt;/td&gt;
+  &lt;td&gt;"x" &lt;&gt; "y"&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;if \_ then \_ elif \_ then \_ else \_&lt;/td&gt;
+  &lt;td&gt;"x" . "y"&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;\q\q end\_if&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;if \_ then \_ else if \_ then \_ else \_&lt;/td&gt;
+  &lt;td&gt;"xy" \OR\ mkid(x, y)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\h{Simple loop and Block}&lt;/td&gt;
+  &lt;td&gt;\h{Generate the list $[1, 2, \ldots, n]$}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;for i in 1..n repeat ( x; y )&lt;/td&gt;
+  &lt;td&gt;[f(i) for i in 1..n]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;VECTOR([x, y], i, 1, n)&lt;/td&gt;
+  &lt;td&gt;VECTOR(f(i), i, 1, n)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;for i in [1..n] do \_ od;&lt;/td&gt;
+  &lt;td&gt;[1..n] {\rm or} [1,2..n]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;for i:1 thru n do (x, y);&lt;/td&gt;
+  &lt;td&gt;makelist(f(i), i, 1, n);&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;for i:1 thru n do (x, y);&lt;/td&gt;
+  &lt;td&gt;makelist(f(i), i, 1, n);&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;for i from 1 to n do x; y od;&lt;/td&gt;
+  &lt;td&gt;[f(i) \$ i = 1..n];&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;Do[x; y, \{i, 1, n\}]&lt;/td&gt;
+  &lt;td&gt;Table[f[i], \{i, 1, n\}]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;for i from 1 to n do x; y&lt;/td&gt;
+  &lt;td&gt;[f(i) \$ i = 1..n];&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;\q\q end\_for;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;for i:=1:n do &lt;&lt;x; y&gt;&gt;;&lt;/td&gt;
+  &lt;td&gt;for i:=1:n collect f(i);&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;\end{tabular}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;[10pt]
+
+\begin{tabular}{l|l}
+&lt;/td&gt;
+  &lt;td&gt;\h{Complex loop iterating on a list}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;for x in [2, 3, 5] while x**2 &lt; 10 repeat output(x)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;for x in [2, 3, 5] do while x\^{}2&lt;10 do Print(x);od;od;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;for x in [2, 3, 5] while x\^{}2 &lt; 10 do print(x)\$&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;for x in [2, 3, 5] while x\^{}2 &lt; 10 do print(x)\$&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;for x in [2, 3, 5] while x\^{}2 &lt; 10 do print(x) od:&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;For[l = \{2, 3, 5\}, l != \{\} \&lt;/td&gt;
+  &lt;td&gt;\&lt;/td&gt;
+  &lt;td&gt;l[[1]]\^{}2 &lt; 10,&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;\q l = Rest[l], Print[l[[1]]] ]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;for x in [2, 3, 5] do if x\^{}2 &lt; 10 then print(x) end\_if&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;\q end\_for:&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;for each x in \{2, 3, 5\} do if x\^{}2 &lt; 10 then write(x)\$&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\h{\small Assignment}&lt;/td&gt;
+  &lt;td&gt;\h{Function definition}&lt;/td&gt;
+  &lt;td&gt;\h{Clear vars and funs}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;y:= f(x)&lt;/td&gt;
+  &lt;td&gt;f(x, y) == x*y&lt;/td&gt;
+  &lt;td&gt;	{\small\tt )clear properties y f}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;y:= f(x)&lt;/td&gt;
+  &lt;td&gt;f(x, y):= x*y&lt;/td&gt;
+  &lt;td&gt;y:=  f:=&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;y:= f(x);&lt;/td&gt;
+  &lt;td&gt;f:=function(x, y) return x*y; end;&lt;/td&gt;
+  &lt;td&gt;\h{There are
+no symbolic variables}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;y: f(x);&lt;/td&gt;
+  &lt;td&gt;f(x, y):= x*y;&lt;/td&gt;
+  &lt;td&gt;remvalue(y)\$&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;remfunction(f)\$&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;y: f(x);&lt;/td&gt;
+  &lt;td&gt;f(x, y):= x*y;&lt;/td&gt;
+  &lt;td&gt;remvalue(y)\$&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;remfunction(f)\$&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;y:= f(x);&lt;/td&gt;
+  &lt;td&gt;f:= proc(x, y) x*y end;&lt;/td&gt;
+  &lt;td&gt;y:= 'y':  f:= 'f':&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;y = f[x]&lt;/td&gt;
+  &lt;td&gt;f[x\_, y\_\,]:= x*y&lt;/td&gt;
+  &lt;td&gt;Clear[y, f]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;y:= f(x);&lt;/td&gt;
+  &lt;td&gt;f:= proc(x, y)&lt;/td&gt;
+  &lt;td&gt;y:= NIL:  f:= NIL:&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;\q\q begin x*y end\_\,proc;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;y:= f(x);&lt;/td&gt;
+  &lt;td&gt;procedure f(x, y); x*y;&lt;/td&gt;
+  &lt;td&gt;clear y, f;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\h{Function definition with a local variable}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;f(x) == (local n; n:= 2; n*x)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;f:=function(x) local n; n:=2;return n*x; end;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;f(x):= block([n], n: 2, n*x);&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;f(x):= block([n], n: 2, n*x);&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;f:= proc(x) local n; n:= 2; n*x end;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;f[x\_\,]:= Module[\{n\}, n = 2; n*x]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;f:= proc(x) local n; begin n:= 2; n*x end\_\,proc;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;procedure f(x); begin scalar n; n:= 2; return(n*x) end;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\h{Return unevaluated symbol}&lt;/td&gt;
+  &lt;td&gt;\h{Define a function from an expression}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;e:= x*y;\q 'e&lt;/td&gt;
+  &lt;td&gt;function(e, f, x, y)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;e:= x*y\q 'e&lt;/td&gt;
+  &lt;td&gt;f(x, y):== e&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;\h{No unevaluated symbols}\fnm&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;e: x*y\$\q 'e;&lt;/td&gt;
+  &lt;td&gt;define(f(x, y), e);&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;e: x*y\$\q 'e;&lt;/td&gt;
+  &lt;td&gt;define(f(x, y), e);&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;e:= x*y:\q 'e';&lt;/td&gt;
+  &lt;td&gt;f:= unapply(e, x, y);&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;e = x*y;\q HoldForm[e]&lt;/td&gt;
+  &lt;td&gt;f[x\_, y\_\,] = e&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;e:= x*y:\q hold(e);&lt;/td&gt;
+  &lt;td&gt;f:= hold(func)(e, x, y);&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;e:= x*y\$&lt;/td&gt;
+  &lt;td&gt;for all x, y let f(x, y):= e;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+Variables can be assigned to generators of a suitable free
+object, for example x:=X(Rationals,"x"); or 
+f:=FreeGroup(2);x:=f.1;}.
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\h{Fun.\ of an indefinite number of args}&lt;/td&gt;
+  &lt;td&gt;\h{Apply ``+'' to sum a list}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;reduce(+, [1, 2])&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;LST l:= l&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;lst:=function(args) \_ end;&lt;/td&gt;
+  &lt;td&gt;Sum([1,2])&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;lst([l]):= l;&lt;/td&gt;
+  &lt;td&gt;apply("+", [1, 2])&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;lst([l]):= l;&lt;/td&gt;
+  &lt;td&gt;apply("+", [1, 2])&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;lst:=proc() [args[1..nargs]] end;&lt;/td&gt;
+  &lt;td&gt;convert([1, 2], \`{}+\`{})&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;lst[l\_\,\_\,\_\,]:= \{l\}&lt;/td&gt;
+  &lt;td&gt;Apply[Plus, \{1, 2\}]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;lst:= proc(l) begin [args()]&lt;/td&gt;
+  &lt;td&gt;\_\,plus(op([1, 2]))&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;\q\q\q end\_\,proc;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;xapply(+, \{1, 2\})\,\fnm&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+procedure xapply(f, lst); lisp(f . cdr(lst))
+
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\h{Apply a fun.\ to a}&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;\h{list of its args}&lt;/td&gt;
+  &lt;td&gt;\h{Map an anonymous function onto a list}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;reduce(f, l)&lt;/td&gt;
+  &lt;td&gt;map(x +-&gt; x + y, [1, 2])&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;x:= [1, 2]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;VECTOR(x SUB i + y, i, 1, DIMENSION(x))&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;List(l,f)&lt;/td&gt;
+  &lt;td&gt;List([1,2],x-&gt;x+y)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;apply(f, l)&lt;/td&gt;
+  &lt;td&gt;map(lambda([x], x + y), [1, 2])&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;apply(f, l)&lt;/td&gt;
+  &lt;td&gt;map(lambda([x], x + y), [1, 2])&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;f(op(l))&lt;/td&gt;
+  &lt;td&gt;map(x -&gt; x + y, [1, 2])&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;Apply[f, l]&lt;/td&gt;
+  &lt;td&gt;Map[\# + y \&lt;/td&gt;
+  &lt;td&gt;, \{1, 2\}]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;f(op(l))&lt;/td&gt;
+  &lt;td&gt;map([1, 2], func(x + y, x))&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;xapply(f, l)\,\fnm&lt;/td&gt;
+  &lt;td&gt;for each x in \{1, 2\} collect x + y&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\h{Pattern matching: $f(3 y) + f(z y) \rightarrow 3 f(y) + f(z y)$}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;f:= operator('f);&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;( rule f((n | integer?(n)) * x) == n*f(x) )( \_&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;\q\q f(3*y) + f(z*y))&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;matchdeclare(n, integerp, x, true)\$&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;defrule(fnx, f(n*x), n*f(x))\$&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;apply1(f(3*y) + f(z*y), fnx);&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;matchdeclare(n, integerp, x, true)\$&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;defrule(fnx, f(n*x), n*f(x))\$&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;apply1(f(3*y) + f(z*y), fnx);&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;map(proc(q) local m;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;\q\q\q if match(q = f(n*y), y, 'm') and&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;\q\q\q\q\q type(rhs(op(m)), integer) then&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;\q\q\q\q subs(m, n * f(y)) else q fi&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;\q\q end,&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;\q\q f(3*y) + f(z*y));&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;f[3*y] + f[z*y] /. f[n\_Integer * x\_\,] -&gt; n*f[x]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;d:= domain("match"): \q d::FREEVARIABLE:= TRUE:&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;n:= new(d, "n", func(testtype(m, DOM\_INT), m)):&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;x:= new(d, "x", TRUE):&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;map(f(3*y) + f(z*y),&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;\q\q proc(q) local m; begin m:= match(q, f(n*x));&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;\q\q\q if m = FAIL then q&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;\q\q\q else subs(hold("n" * f("x")), m) end\_if&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;\q\q end\_\,proc);&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;operator f;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;f(3*y) + f(z*y)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;\q\q where \{f(n * x) =&gt; n*f(x) when fixp(n)\};&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\h{Define a new infix operator and then use it}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;\h{One can overload existing infix operators for ones own purposes}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;infix("")\$ \q ""(x, y):= sqrt(x\^{}2 + y\^{}2)\$ \q
+	3  4;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;infix("")\$ \q ""(x, y):= sqrt(x\^{}2 + y\^{}2)\$ \q
+	3  4;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;\`{}\&lt;/td&gt;
+  &lt;td&gt;\`{}:= (x, y) -&gt; sqrt(x\^{}2 + y\^{}2): \q 3 \&lt;/td&gt;
+  &lt;td&gt; 4;
+	&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;x\_ $\backslash$[Tilde] y\_:= Sqrt[x\^{}2 + y\^{}2]; \q
+	3 $\backslash$[Tilde] 4&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;tilde:= proc(x, y) begin sqrt(x\^{}2 + y\^{}2) end\_\,proc:&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;\q 3 \&lt;/td&gt;
+  &lt;td&gt;tilde 4;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;infix |\$ \q procedure |(x, y); sqrt(x\^{}2 + y\^{}2)\$ \q
+	3 | 4;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\h{Main expression}&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;\h{operator}&lt;/td&gt;
+  &lt;td&gt;\h{\nth{1} operand}&lt;/td&gt;
+  &lt;td&gt;\h{List of expression operands}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom\fnm&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;kernels(e) . 1&lt;/td&gt;
+  &lt;td&gt;kernels(e)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;{\em various}\fnm&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;\m{3}{\rm There are no formal unevaluated expressions}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;part(e, 0)&lt;/td&gt;
+  &lt;td&gt;part(e, 1)&lt;/td&gt;
+  &lt;td&gt;args(e)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;part(e, 0)&lt;/td&gt;
+  &lt;td&gt;part(e, 1)&lt;/td&gt;
+  &lt;td&gt;args(e)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;op(0, e)&lt;/td&gt;
+  &lt;td&gt;op(1, e)&lt;/td&gt;
+  &lt;td&gt;[op(e)]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;Head[e]&lt;/td&gt;
+  &lt;td&gt;e[[1]]&lt;/td&gt;
+  &lt;td&gt;ReplacePart[e, List, 0]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;op(e, 0)&lt;/td&gt;
+  &lt;td&gt;op(e, 1)&lt;/td&gt;
+  &lt;td&gt;[op(e)]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;part(e, 0)&lt;/td&gt;
+  &lt;td&gt;part(e, 1)&lt;/td&gt;
+  &lt;td&gt;for i:=1:arglength(e)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;\q\q collect part(e, i)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+The following commands work only on expressions that consist of a
+single level (e.g., $x + y + z$ but not $a/b + c/d$).
+TERMS, FACTORS, NUMERATOR, LHS, etc.
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\h{Print text and results}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;output(concat(["sin(", string(0), ") = ",&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;\q string(sin(0))]));&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;"sin(0)" = sin(0)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;Print("There is no sin, but factors(10)= ",Factors(10),
+"$\backslash$n")&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;print("sin(", 0, ") =", sin(0))\$&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;print("sin(", 0, ") =", sin(0))\$&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;printf("sin(\%a) = \%a$\backslash$n", 0, sin(0)):&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;Print[StringForm["sin(\`{}\`{}) = \`{}\`{}", 0, Sin[0]]];&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;print(Unquoted, "sin(".0.")" = sin(0)):&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;write("sin(", 0, ") = ", sin(0))\$&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\h{Generate FORTRAN}&lt;/td&gt;
+  &lt;td&gt;\h{Generate \TeX/\LaTeX}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;outputAsFortran(e)&lt;/td&gt;
+  &lt;td&gt;outputAsTex(e)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;[Transfer Save Fortran]&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;Print(LaTeX(e));&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;fortran(e)\$ \OR gentran(eval(e))\$&lt;/td&gt;
+  &lt;td&gt;tex(e);&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;fortran(e)\$ \OR gentran(eval(e))\$&lt;/td&gt;
+  &lt;td&gt;tex(e);&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;fortran([e]);&lt;/td&gt;
+  &lt;td&gt;latex(e);&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;FortranForm[e]&lt;/td&gt;
+  &lt;td&gt;TexForm[e]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;generate::fortran(e);&lt;/td&gt;
+  &lt;td&gt;generate::TeX(e);&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;on fort; \q e; \q off fort; \OR&lt;/td&gt;
+  &lt;td&gt;load\_\,package(tri)\$&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;load\_\,package(gentran)\$ gentran e;&lt;/td&gt;
+  &lt;td&gt;on TeX; e; off TeX;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\h{Import two space separated columns of integers from {\tt file}}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;[Transfer Load daTa] ({\rm from} file.dat)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;xy: read\_num\_data\_to\_matrix("file", nrows, 2)\$&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;xy: read\_num\_data\_to\_matrix("file", nrows, 2)\$&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;xy:= readdata("file", integer, 2):&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;xy = ReadList["file", Number, RecordLists -&gt; True]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\h{Export two space separated columns of integers to {\tt file}\fnm}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;)set output algebra "file" \q ({\rm creates} file.spout)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;for i in 1..n repeat output( \_&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;\q concat([string(xy(i, 1)), " ", string(xy(i, 2))]) )&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;)set output algebra console&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;xy  [Transfer Print Expressions File]\q({\rm creates} file.prt)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;PrintTo("file");for i in [1..n] do&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;\q AppendTo("file",xy[i][1]," ",xy[i][2],"$\backslash$n");od;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;writefile("file")\$ \q for i:1 thru n do&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;\q print(xy[i, 1], xy[i, 2])\$ \q closefile()\$&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;writefile("file")\$ \q for i:1 thru n do&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;\q print(xy[i, 1], xy[i, 2])\$ \q closefile()\$&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;writedata("file", xy);&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;outfile = OpenWrite["file"];&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;Do[WriteString[outfile,&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;\q xy[[i, 1]], " ", xy[[i, 2]], "$\backslash$n"], \{i, 1, n\}]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;Close[outfile];&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;fprint(Unquoted, Text, "file",&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;\q ("$\backslash$n", xy[i, 1], xy[i, 2]) \$ i = 1..n):&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;out "file"; \q for i:=1:n do&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;\q write(xy(i, 1), " ", xy(i, 2)); \q shut "file";&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;p&gt;
+Some editing of file will be necessary for all systems but
+Maple and Mathematica.
+&lt;/p&gt;
+
+&lt;h3&gt;Mathematics and Graphics&lt;/h3&gt;
+
+Since GAP aims at discrete mathematics, it does not provide much of
+the calculus functionality listed in the following section.
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;$e$&lt;/td&gt;
+  &lt;td&gt;$\pi$&lt;/td&gt;
+  &lt;td&gt;$i$&lt;/td&gt;
+  &lt;td&gt;$+\infty$&lt;/td&gt;
+  &lt;td&gt;$\sqrt{2}$&lt;/td&gt;
+  &lt;td&gt;$2^{1/3}$&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;\%e&lt;/td&gt;
+  &lt;td&gt;\%pi&lt;/td&gt;
+  &lt;td&gt;\%i&lt;/td&gt;
+  &lt;td&gt;\%plusInfinity&lt;/td&gt;
+  &lt;td&gt;sqrt(2)&lt;/td&gt;
+  &lt;td&gt;2**(1/3)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;\#e&lt;/td&gt;
+  &lt;td&gt;pi&lt;/td&gt;
+  &lt;td&gt;\#i&lt;/td&gt;
+  &lt;td&gt;inf&lt;/td&gt;
+  &lt;td&gt;SQRT(2)&lt;/td&gt;
+  &lt;td&gt;2\^{}(1/3)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;E(4)&lt;/td&gt;
+  &lt;td&gt;infinity&lt;/td&gt;
+  &lt;td&gt;ER(2)\fnm&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;\%e&lt;/td&gt;
+  &lt;td&gt;\%pi&lt;/td&gt;
+  &lt;td&gt;\%i&lt;/td&gt;
+  &lt;td&gt;inf&lt;/td&gt;
+  &lt;td&gt;sqrt(2)&lt;/td&gt;
+  &lt;td&gt;2\^{}(1/3)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;\%e&lt;/td&gt;
+  &lt;td&gt;\%pi&lt;/td&gt;
+  &lt;td&gt;\%i&lt;/td&gt;
+  &lt;td&gt;inf&lt;/td&gt;
+  &lt;td&gt;sqrt(2)&lt;/td&gt;
+  &lt;td&gt;2\^{}(1/3)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;exp(1)&lt;/td&gt;
+  &lt;td&gt;Pi&lt;/td&gt;
+  &lt;td&gt;I&lt;/td&gt;
+  &lt;td&gt;infinity&lt;/td&gt;
+  &lt;td&gt;sqrt(2)&lt;/td&gt;
+  &lt;td&gt;2\^{}(1/3)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;E&lt;/td&gt;
+  &lt;td&gt;Pi&lt;/td&gt;
+  &lt;td&gt;I&lt;/td&gt;
+  &lt;td&gt;Infinity&lt;/td&gt;
+  &lt;td&gt;Sqrt[2]&lt;/td&gt;
+  &lt;td&gt;2\^{}(1/3)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;E&lt;/td&gt;
+  &lt;td&gt;PI&lt;/td&gt;
+  &lt;td&gt;I&lt;/td&gt;
+  &lt;td&gt;infinity&lt;/td&gt;
+  &lt;td&gt;sqrt(2)&lt;/td&gt;
+  &lt;td&gt;2\^{}(1/3)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;e&lt;/td&gt;
+  &lt;td&gt;pi&lt;/td&gt;
+  &lt;td&gt;i&lt;/td&gt;
+  &lt;td&gt;infinity&lt;/td&gt;
+  &lt;td&gt;sqrt(2)&lt;/td&gt;
+  &lt;td&gt;2\^{}(1/3)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+&lt;b&gt;ER&lt;/b&gt; represents special cyclotomic numbers and is not a
+root function.}
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\h{Euler's constant}&lt;/td&gt;
+  &lt;td&gt;\h{Natural log}&lt;/td&gt;
+  &lt;td&gt;\h{Arctangent}&lt;/td&gt;
+  &lt;td&gt;$n!$&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;log(x)&lt;/td&gt;
+  &lt;td&gt;atan(x)&lt;/td&gt;
+  &lt;td&gt;factorial(n)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;euler\_\,gamma&lt;/td&gt;
+  &lt;td&gt;LOG(x)&lt;/td&gt;
+  &lt;td&gt;ATAN(x)&lt;/td&gt;
+  &lt;td&gt;n!&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;LogInt(x,base)&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;Factorial(n)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;\%gamma&lt;/td&gt;
+  &lt;td&gt;log(x)&lt;/td&gt;
+  &lt;td&gt;atan(x)&lt;/td&gt;
+  &lt;td&gt;n!&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;\%gamma&lt;/td&gt;
+  &lt;td&gt;log(x)&lt;/td&gt;
+  &lt;td&gt;atan(x)&lt;/td&gt;
+  &lt;td&gt;n!&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;gamma&lt;/td&gt;
+  &lt;td&gt;log(x)&lt;/td&gt;
+  &lt;td&gt;arctan(x)&lt;/td&gt;
+  &lt;td&gt;n!&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;EulerGamma&lt;/td&gt;
+  &lt;td&gt;Log[x]&lt;/td&gt;
+  &lt;td&gt;ArcTan[x]&lt;/td&gt;
+  &lt;td&gt;n!&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;EULER&lt;/td&gt;
+  &lt;td&gt;ln(x)&lt;/td&gt;
+  &lt;td&gt;atan(x)&lt;/td&gt;
+  &lt;td&gt;n!&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;Euler\_\,Gamma&lt;/td&gt;
+  &lt;td&gt;log(x)&lt;/td&gt;
+  &lt;td&gt;atan(x)&lt;/td&gt;
+  &lt;td&gt;factorial(n)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\h{Legendre polynomial}&lt;/td&gt;
+  &lt;td&gt;\h{Chebyshev poly.\ of the \nth{1} kind}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;legendreP(n, x)&lt;/td&gt;
+  &lt;td&gt;chebyshevT(n, x)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;LEGENDRE\_\,P(n, x)&lt;/td&gt;
+  &lt;td&gt;CHEBYCHEV\_\,T(n, x)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;legendre\_\,p(n, x)&lt;/td&gt;
+  &lt;td&gt;chebyshev\_\,t(n, x)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;legendre\_\,p(n, x)&lt;/td&gt;
+  &lt;td&gt;chebyshev\_\,t(n, x)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;orthopoly[P](n, x)&lt;/td&gt;
+  &lt;td&gt;orthopoly[T](n, x)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;LegendreP[n, x]&lt;/td&gt;
+  &lt;td&gt;ChebyshevT[n, x]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;orthpoly::legendre(n, x)&lt;/td&gt;
+  &lt;td&gt;orthpoly::chebyshev1(n, x)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;LegendreP(n, x)&lt;/td&gt;
+  &lt;td&gt;ChebyshevT(n, x)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\h{Fibonacci number}&lt;/td&gt;
+  &lt;td&gt;\h{Elliptic integral of the \nth{1} kind}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;fibonacci(n)&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;FIBONACCI(n)&lt;/td&gt;
+  &lt;td&gt;ELLIPTIC\_\,E(phi, k\^{}2)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;Fibonacci(n)&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;fib(n)&lt;/td&gt;
+  &lt;td&gt;elliptic\_\,e(phi, k\^{}2)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;fib(n)&lt;/td&gt;
+  &lt;td&gt;elliptic\_\,e(phi, k\^{}2)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;combinat[fibonacci](n)&lt;/td&gt;
+  &lt;td&gt;EllipticE(sin(phi), k)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;Fibonacci[n]&lt;/td&gt;
+  &lt;td&gt;EllipticE[phi, k\^{}2]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;numlib::fibonacci(n)&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;EllipticE(phi, k\^{}2)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;$\Gamma(x)$&lt;/td&gt;
+  &lt;td&gt;$\psi(x)$&lt;/td&gt;
+  &lt;td&gt;\h{Cosine integral}&lt;/td&gt;
+  &lt;td&gt;\h{Bessel fun.\ (\nth{1})}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;Gamma(x)&lt;/td&gt;
+  &lt;td&gt;psi(x)&lt;/td&gt;
+  &lt;td&gt;real(Ei(\%i*x))&lt;/td&gt;
+  &lt;td&gt;besselJ(n, x)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;GAMMA(x)&lt;/td&gt;
+  &lt;td&gt;PSI(x)&lt;/td&gt;
+  &lt;td&gt;CI(x)&lt;/td&gt;
+  &lt;td&gt;BESSEL\_\,J(n, x)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;gamma(x)&lt;/td&gt;
+  &lt;td&gt;psi[0](x)&lt;/td&gt;
+  &lt;td&gt;cos\_\,int(x)&lt;/td&gt;
+  &lt;td&gt;bessel\_j[n](x)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;gamma(x)&lt;/td&gt;
+  &lt;td&gt;psi[0](x)&lt;/td&gt;
+  &lt;td&gt;cos\_\,int(x)&lt;/td&gt;
+  &lt;td&gt;bessel\_j[n](x)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;GAMMA(x)&lt;/td&gt;
+  &lt;td&gt;Psi(x)&lt;/td&gt;
+  &lt;td&gt;Ci(x)&lt;/td&gt;
+  &lt;td&gt;BesselJ(n, x)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;Gamma[x]&lt;/td&gt;
+  &lt;td&gt;PolyGamma[x]&lt;/td&gt;
+  &lt;td&gt;CosIntegral[x]&lt;/td&gt;
+  &lt;td&gt;BesselJ[n, x]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;gamma(x)&lt;/td&gt;
+  &lt;td&gt;psi(x)&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;besselJ(n, x)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;Gamma(x)&lt;/td&gt;
+  &lt;td&gt;Psi(x)&lt;/td&gt;
+  &lt;td&gt;Ci(x)&lt;/td&gt;
+  &lt;td&gt;BesselJ(n, x)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\h{Hypergeometric fun.\ ${}_2F_1(a, b; c; x)$}&lt;/td&gt;
+  &lt;td&gt;\h{Dirac delta}&lt;/td&gt;
+  &lt;td&gt;	\h{Unit step fun.}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;GAUSS(a, b, c, x)&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;STEP(x)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;hgfred([a, b], [c], x)&lt;/td&gt;
+  &lt;td&gt;delta(x)&lt;/td&gt;
+  &lt;td&gt;unit\_\,step(x)
+	&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;hgfred([a, b], [c], x)&lt;/td&gt;
+  &lt;td&gt;delta(x)&lt;/td&gt;
+  &lt;td&gt;unit\_\,step(x)
+	&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;hypergeom([a, b], [c], x)&lt;/td&gt;
+  &lt;td&gt;Dirac(x)&lt;/td&gt;
+  &lt;td&gt;Heaviside(x)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;HypergeometricPFQ[\{a,b\},\{c\},x]&lt;/td&gt;
+  &lt;td&gt;	\m{2}{&lt;&lt; Calculus\`{}DiracDelta\`{}}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;dirac(x)&lt;/td&gt;
+  &lt;td&gt;heaviside(x)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;hypergeometric(\{a, b\}, \{c\}, x)&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\h{Define $|x|$ via a piecewise function}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;a(x):= -x*CHI(-inf, x, 0) + x*CHI(0, x, inf)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;a(x):= -x*unit\_\,step(-x) + x*unit\_\,step(x)\$&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;a(x):= -x*unit\_\,step(-x) + x*unit\_\,step(x)\$&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;a:= x -&gt; piecewise(x &lt; 0, -x, x):&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;&lt;&lt; Calculus\`{}DiracDelta\`{}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;a[x\_]:= -x*UnitStep[-x] + x*UnitStep[x]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;a:= proc(x) begin -x*heaviside(-x) + x*heaviside(x)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;\q\q end\_\,proc:&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\h{Assume $x$ is real}&lt;/td&gt;
+  &lt;td&gt;\h{Remove that assumption}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;x :epsilon Real&lt;/td&gt;
+  &lt;td&gt;x:=&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;declare(x, real)\$&lt;/td&gt;
+  &lt;td&gt;remove(x, real)\$&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;declare(x, real)\$&lt;/td&gt;
+  &lt;td&gt;remove(x, real)\$&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;assume(x, real);&lt;/td&gt;
+  &lt;td&gt;x:= 'x':&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;x/: Im[x] = 0;&lt;/td&gt;
+  &lt;td&gt;Clear[x]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;assume(x, Type::RealNum):&lt;/td&gt;
+  &lt;td&gt;unassume(x, Type::RealNum):&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\h{Assume $0 &lt; x \le 1$}&lt;/td&gt;
+  &lt;td&gt;\h{Remove that assumption}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;x :epsilon (0, 1]&lt;/td&gt;
+  &lt;td&gt;x:=&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;assume(x &gt; 0, x &lt;= 1)\$&lt;/td&gt;
+  &lt;td&gt;forget(x &gt; 0, x &lt;= 1)\$&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;assume(x &gt; 0, x &lt;= 1)\$&lt;/td&gt;
+  &lt;td&gt;forget(x &gt; 0, x &lt;= 1)\$&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;assume(x &gt; 0);&lt;/td&gt;
+  &lt;td&gt;x:= 'x':&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;additionally(x &lt;= 1);&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;Assumptions -&gt; 0 &lt; x &lt;= 1\,\fnm&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;assume(x &gt; 0):  assume(x &lt;= 1):&lt;/td&gt;
+  &lt;td&gt;unassume(x):&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+Note: This is an option for {\tt Integrate}.}
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\h{Basic simplification of an expression $e$}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;simplify(e) \OR\ normalize(e) \OR\ complexNormalize(e)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;e&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;e&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;ratsimp(e) \OR\ radcan(e)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;ratsimp(e) \OR\ radcan(e)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;simplify(e)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;Simplify[e] \OR\ FullSimplify[e]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;simplify(e) \OR\ normal(e)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;e&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\h{Use an unknown function}&lt;/td&gt;
+  &lt;td&gt;\h{Numerically evaluate an expr.}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;f:= operator('f); \q f(x)&lt;/td&gt;
+  &lt;td&gt;exp(1) :: Complex Float&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;f(x):=&lt;/td&gt;
+  &lt;td&gt;Precision:= Approximate&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;f(x)&lt;/td&gt;
+  &lt;td&gt;APPROX(EXP(1))&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;Precision:= Exact&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;EvalF(123/456)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;f(x)&lt;/td&gt;
+  &lt;td&gt;sfloat(exp(1));&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;f(x)&lt;/td&gt;
+  &lt;td&gt;sfloat(exp(1));&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;f(x)&lt;/td&gt;
+  &lt;td&gt;evalf(exp(1));&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;f[x]&lt;/td&gt;
+  &lt;td&gt;N[Exp[1]]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;f(x)&lt;/td&gt;
+  &lt;td&gt;float(exp(1));&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;operator f; \q f(x)&lt;/td&gt;
+  &lt;td&gt;on rounded; \q exp(1);&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;off rounded;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;$ n \bmod m$&lt;/td&gt;
+  &lt;td&gt;\h{Solve $e \equiv 0 \bmod m$ for $x$}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;rem(n, m)&lt;/td&gt;
+  &lt;td&gt;solve(e = 0 :: PrimeField(m), x)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;MOD(n, m)&lt;/td&gt;
+  &lt;td&gt;SOLVE\_\,MOD(e = 0, x, m)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;n mod m&lt;/td&gt;
+  &lt;td&gt;\h{solve using finite fields}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;mod(n, m)&lt;/td&gt;
+  &lt;td&gt;modulus: m\$ \q solve(e = 0, x)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;mod(n, m)&lt;/td&gt;
+  &lt;td&gt;modulus: m\$ \q solve(e = 0, x)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;n mod m&lt;/td&gt;
+  &lt;td&gt;msolve(e = 0, m)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;Mod[n, m]&lt;/td&gt;
+  &lt;td&gt;Solve[\{e == 0, Modulus == m\}, x]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;n mod m&lt;/td&gt;
+  &lt;td&gt;solve(poly(e = 0, [x], IntMod(m)), x)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;on modular;&lt;/td&gt;
+  &lt;td&gt;load\_\,package(modsr)\$ \q on modular;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;setmod m\$ \q n&lt;/td&gt;
+  &lt;td&gt;setmod m\$ \q m\_solve(e = 0, x)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\h{Put over common denominator}&lt;/td&gt;
+  &lt;td&gt;\h{Expand into separate fractions}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;a/b + c/d&lt;/td&gt;
+  &lt;td&gt;(a*d + b*c)/(b*d) :: \_&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;\q MPOLY([a], FRAC POLY INT)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;FACTOR(a/b + c/d, Trivial)&lt;/td&gt;
+  &lt;td&gt;EXPAND((a*d + b*c)/(b*d))&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;a/b+c/d&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;xthru(a/b + c/d)&lt;/td&gt;
+  &lt;td&gt;expand((a*d + b*c)/(b*d))&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;xthru(a/b + c/d)&lt;/td&gt;
+  &lt;td&gt;expand((a*d + b*c)/(b*d))&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;normal(a/b + c/d)&lt;/td&gt;
+  &lt;td&gt;expand((a*d + b*c)/(b*d))&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;Together[a/b + c/d]&lt;/td&gt;
+  &lt;td&gt;Apart[(a*d + b*c)/(b*d)]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;normal(a/b + c/d)&lt;/td&gt;
+  &lt;td&gt;expand((a*d + b*c)/(b*d))&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;a/b + c/d&lt;/td&gt;
+  &lt;td&gt;on div;  (a*d + b*c)/(b*d)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\h{Manipulate the root of a polynomial}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;a:= rootOf(x**2 - 2); \q a**2&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;x:=X(Rationals,"x");&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;\q a:=RootOfDefiningPolynomial(AlgebraicExtension(Rationals,x\^{}2-2));
+a\^{}2&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;algebraic:true\$ \q tellrat(a\^{}2 - 2)\$ \q rat(a\^{}2);&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;algebraic:true\$ \q tellrat(a\^{}2 - 2)\$ \q rat(a\^{}2);&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;a:= RootOf(x\^{}2 - 2): \q simplify(a\^{}2);&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;a = Root[\#\^{}2 - 2 \&lt;/td&gt;
+  &lt;td&gt;, 2] \q a\^{}2&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;load\_\,package(arnum)\$ \q defpoly(a\^{}2 - 2); \q a\^{}2;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\h{Noncommutative multiplication}&lt;/td&gt;
+  &lt;td&gt;\h{Solve a pair of equations}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;solve([eqn1, eqn2], [x, y])&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;x :epsilon Nonscalar&lt;/td&gt;
+  &lt;td&gt;SOLVE([eqn1, eqn2], [x, y])&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;y :epsilon Nonscalar&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;x . y&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;*&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;x . y&lt;/td&gt;
+  &lt;td&gt;solve([eqn1, eqn2], [x, y])&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;x . y&lt;/td&gt;
+  &lt;td&gt;solve([eqn1, eqn2], [x, y])&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;x \&lt;/td&gt;
+  &lt;td&gt;* y&lt;/td&gt;
+  &lt;td&gt;solve(\{eqn1, eqn2\}, \{x, y\})&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;x ** y&lt;/td&gt;
+  &lt;td&gt;Solve[\{eqn1, eqn2\}, \{x, y\}]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;solve(\{eqn1, eqn2\}, \{x, y\})&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;operator x, y;&lt;/td&gt;
+  &lt;td&gt;solve(\{eqn1, eqn2\}, \{x, y\})&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;noncom x, y;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;x() * y()&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\m{2}{\rm Decrease/increase angles in trigonometric functions}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;\m{2}{simplify(normalize(sin(2*x)))}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;Trigonometry:= Expand&lt;/td&gt;
+  &lt;td&gt;Trigonometry:= Collect&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;sin(2*x)&lt;/td&gt;
+  &lt;td&gt;2*sin(x)*cos(x)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;trigexpand(sin(2*x))&lt;/td&gt;
+  &lt;td&gt;trigreduce(2*sin(x)*cos(x))&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;trigexpand(sin(2*x))&lt;/td&gt;
+  &lt;td&gt;trigreduce(2*sin(x)*cos(x))&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;expand(sin(2*x))&lt;/td&gt;
+  &lt;td&gt;combine(2*sin(x)*cos(x))&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;TrigExpand[Sin[2*x]]&lt;/td&gt;
+  &lt;td&gt;TrigReduce[2*Sin[x]*Cos[x]]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;expand(sin(2*x))&lt;/td&gt;
+  &lt;td&gt;combine(2*sin(x)*cos(x), sincos)
+	&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;load\_\,package(assist)\$&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;trigexpand(sin(2*x))&lt;/td&gt;
+  &lt;td&gt;trigreduce(2*sin(x)*cos(x))&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\h{Gr\"obner basis}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;groebner([p1, p2, ...])&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;grobner([p1, p2, ...])&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;grobner([p1, p2, ...])&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;Groebner[gbasis]([p1, p2, ...], plex(x1, x2, ...))&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;GroebnerBasis[\{p1, p2, ...\}, \{x1, x2, ...\}]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;groebner::gbasis([p1, p2, ...])&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;load\_\,package(groebner)\$ \q groebner(\{p1, p2, ...\})&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\h{Factorization of $e$ over $i = \sqrt{-1}$}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;factor(e, [rootOf(i**2 + 1)])&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;FACTOR(e, Complex)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;Factors(GaussianIntegers,e)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;gfactor(e); \OR\ factor(e, i\^{}2 + 1);&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;gfactor(e); \OR\ factor(e, i\^{}2 + 1);&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;factor(e, I);&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;Factor[e, Extension -&gt; I]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;QI:= Dom::AlgebraicExtension(Dom::Rational, i\^{}2 + 1);&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;QI::name:= "QI": \q Factor(poly(e, QI));&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;on complex, factor; \q e; \q off complex, factor;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\h{Real part}&lt;/td&gt;
+  &lt;td&gt;\h{Convert a complex expr.\ to rectangular form}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;real(f(z))&lt;/td&gt;
+  &lt;td&gt;complexForm(f(z))&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;RE(f(z))&lt;/td&gt;
+  &lt;td&gt;f(z)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;(f(z)+GaloisCyc(f(z),-1))/2&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;realpart(f(z))&lt;/td&gt;
+  &lt;td&gt;rectform(f(z))&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;realpart(f(z))&lt;/td&gt;
+  &lt;td&gt;rectform(f(z))&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;Re(f(z))&lt;/td&gt;
+  &lt;td&gt;evalc(f(z))&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;Re[f[z]]&lt;/td&gt;
+  &lt;td&gt;ComplexExpand[f[z]]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;Re(f(z))&lt;/td&gt;
+  &lt;td&gt;rectform(f(z))&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;repart(f(z))&lt;/td&gt;
+  &lt;td&gt;repart(f(z)) + i*impart(f(z))&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\h{Matrix addition}&lt;/td&gt;
+  &lt;td&gt;\h{Matrix multiplication}&lt;/td&gt;
+  &lt;td&gt;\h{Matrix transpose}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;A + B&lt;/td&gt;
+  &lt;td&gt;A * B&lt;/td&gt;
+  &lt;td&gt;transpose(A)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;A + B&lt;/td&gt;
+  &lt;td&gt;A . B&lt;/td&gt;
+  &lt;td&gt;A\`{}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;A + B&lt;/td&gt;
+  &lt;td&gt;A * B&lt;/td&gt;
+  &lt;td&gt;TransposedMat(A)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;A + B&lt;/td&gt;
+  &lt;td&gt;A . B&lt;/td&gt;
+  &lt;td&gt;transpose(A)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;A + B&lt;/td&gt;
+  &lt;td&gt;A . B&lt;/td&gt;
+  &lt;td&gt;transpose(A)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;evalm(A + B)&lt;/td&gt;
+  &lt;td&gt;evalm(A \&lt;/td&gt;
+  &lt;td&gt;* B)&lt;/td&gt;
+  &lt;td&gt;linalg[transpose](A)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;A + B&lt;/td&gt;
+  &lt;td&gt;A . B&lt;/td&gt;
+  &lt;td&gt;Transpose[A]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;A + B&lt;/td&gt;
+  &lt;td&gt;A * B&lt;/td&gt;
+  &lt;td&gt;transpose(A)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;A + B&lt;/td&gt;
+  &lt;td&gt;A * B&lt;/td&gt;
+  &lt;td&gt;tp(A)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\h{Solve the matrix equation $A x = b$}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;solve(A, transpose(b)) . 1 . particular :: Matrix \_\_\_&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;SolutionMat(TransposedMat(A),b)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;xx: genvector('x, mat\_nrows(b))\$&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;x: part(matlinsolve(A . xx = b, xx), 1, 2)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;xx: genvector('x, mat\_nrows(b))\$&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;x: part(matlinsolve(A . xx = b, xx), 1, 2)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;x:= linalg[linsolve](A, b)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;x = LinearSolve[A, b]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\h{Sum: $\sum_{i = 1}^n f(i)$}&lt;/td&gt;
+  &lt;td&gt;\h{Product: $\prod_{i = 1}^n f(i)$}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;sum(f(i), i = 1..n)&lt;/td&gt;
+  &lt;td&gt;product(f(i), i = 1..n)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;SUM(f(i), i, 1, n)&lt;/td&gt;
+  &lt;td&gt;PRODUCT(f(i), i, 1, n)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;Sum([1..n],f)&lt;/td&gt;
+  &lt;td&gt;Product([1..n],f)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;closedform(&lt;/td&gt;
+  &lt;td&gt;closedform(&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;\q sum(f(i), i, 1, n))&lt;/td&gt;
+  &lt;td&gt;\q product(f(i), i, 1, n))&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;closedform(&lt;/td&gt;
+  &lt;td&gt;closedform(&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;\q sum(f(i), i, 1, n))&lt;/td&gt;
+  &lt;td&gt;\q product(f(i), i, 1, n))&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;sum(f(i), i = 1..n)&lt;/td&gt;
+  &lt;td&gt;product(f(i), i = 1..n)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;Sum[f[i], \{i, 1, n\}]&lt;/td&gt;
+  &lt;td&gt;Product[f[i], \{i, 1, n\}]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;sum(f(i), i = 1..n)&lt;/td&gt;
+  &lt;td&gt;product(f(i), i = 1..n)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;sum(f(i), i, 1, n)&lt;/td&gt;
+  &lt;td&gt;prod(f(i), i, 1, n)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\h{Limit: $\lim_{x \rightarrow 0-} f(x)$}&lt;/td&gt;
+  &lt;td&gt;\h{Taylor/Laurent/etc.\ series}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;limit(f(x), x = 0, "left")&lt;/td&gt;
+  &lt;td&gt;series(f(x), x = 0, 3)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;LIM(f(x), x, 0, -1)&lt;/td&gt;
+  &lt;td&gt;TAYLOR(f(x), x, 0, 3)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;limit(f(x), x, 0, minus)&lt;/td&gt;
+  &lt;td&gt;taylor(f(x), x, 0, 3)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;limit(f(x), x, 0, minus)&lt;/td&gt;
+  &lt;td&gt;taylor(f(x), x, 0, 3)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;limit(f(x), x = 0, left)&lt;/td&gt;
+  &lt;td&gt;series(f(x), x = 0, 4)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;Limit[f[x], x-&gt;0, Direction-&gt;1]&lt;/td&gt;
+  &lt;td&gt;Series[f[x],\{x, 0, 3\}]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;limit(f(x), x = 0, Left)&lt;/td&gt;
+  &lt;td&gt;series(f(x), x = 0, 4)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;limit!-(f(x), x, 0)&lt;/td&gt;
+  &lt;td&gt;taylor(f(x), x, 0, 3)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\h{Differentiate: $\frac{d^3 f(x, y)}{dx \, dy^2}$}&lt;/td&gt;
+  &lt;td&gt;	\h{Integrate: $\int_0^1 f(x) \, dx$}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;D(f(x, y), [x, y], [1, 2])&lt;/td&gt;
+  &lt;td&gt;integrate(f(x), x = 0..1)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;DIF(DIF(f(x, y), x), y, 2)&lt;/td&gt;
+  &lt;td&gt;INT(f(x), x, 0, 1)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;diff(f(x, y), x, 1, y, 2)&lt;/td&gt;
+  &lt;td&gt;integrate(f(x), x, 0, 1)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;diff(f(x, y), x, 1, y, 2)&lt;/td&gt;
+  &lt;td&gt;integrate(f(x), x, 0, 1)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;diff(f(x, y), x, y\$2)&lt;/td&gt;
+  &lt;td&gt;int(f(x), x = 0..1)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;D[f[x, y], x, \{y, 2\}]&lt;/td&gt;
+  &lt;td&gt;Integrate[f[x], \{x, 0, 1\}]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;diff(f(x, y), x, y\$2)&lt;/td&gt;
+  &lt;td&gt;int(f(x), x = 0..1)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;df(f(x, y), x, y, 2)&lt;/td&gt;
+  &lt;td&gt;int(f(x), x, 0, 1)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\h{Laplace transform}&lt;/td&gt;
+  &lt;td&gt;\h{Inverse Laplace transform}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;laplace(e, t, s)&lt;/td&gt;
+  &lt;td&gt;inverseLaplace(e, s, t)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;LAPLACE(e, t, s)&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;laplace(e, t, s)&lt;/td&gt;
+  &lt;td&gt;ilt(e, s, t)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;laplace(e, t, s)&lt;/td&gt;
+  &lt;td&gt;ilt(e, s, t)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;inttrans[laplace](e,t,s)&lt;/td&gt;
+  &lt;td&gt;inttrans[invlaplace](e,s,t)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;\m{2}{\q &lt;&lt; Calculus\`{}LaplaceTransform\`{}}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;LaplaceTransform[e, t, s]&lt;/td&gt;
+  &lt;td&gt;{\st InverseLaplaceTransform[e,s,t]}
+	&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;transform::laplace(e,t,s)&lt;/td&gt;
+  &lt;td&gt;transform::ilaplace(e, s, t)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;\m{2}{\q load\_\,package(laplace)\$ \q load\_\,package(defint)\$}
+	&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;laplace(e, t, s)&lt;/td&gt;
+  &lt;td&gt;invlap(e, t, s)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\h{Solve an ODE (with the initial condition $y'(0) = 1$)}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;solve(eqn, y, x)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;APPLY\_\,IC(RHS(ODE(eqn, x, y, y\_)), [x, 0], [y, 1])&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;ode\_ibc(ode(eqn, y(x), x), x = 0, diff(y(x), x) = 1)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;ode\_ibc(ode(eqn, y(x), x), x = 0, diff(y(x), x) = 1)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;dsolve(\{eqn, D(y)(0) = 1\}, y(x))&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;DSolve[\{eqn, y'[0] == 1\}, y[x], x]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;solve(ode(\{eqn, D(y)(0) = 1\}, y(x)))&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;odesolve(eqn, y(x), x)&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\h{Define the differential operator $L = D_x + I$ and apply it to $\sin x$}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;DD : LODO(Expression Integer, e +-&gt; D(e, x)) := D();&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;L:= DD + 1; \q L(sin(x))&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;load(opalg)\$ \q L: (diffop(x) - 1)\$ \q L(sin(x));&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;load(opalg)\$ \q L: (diffop(x) - 1)\$ \q L(sin(x));&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;id:= x -&gt; x: \q L:= (D + id): \q L(sin)(x);&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;L = D[\#, x]\&lt;/td&gt;
+  &lt;td&gt;+ Identity; \q Through[L[Sin[x]]]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;L:= (D + id): \q L(sin)(x);&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+&lt;/td&gt;
+  &lt;td&gt;\h{2D plot of two separate curves overlayed}&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;draw(x, x = 0..1); \q draw(acsch(x), x = 0..1);&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;[Plot Overlay]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;plot(x, x, 0, 1)\$ \q plot(acsch(x), x, 0, 1)\$&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;plot(x, x, 0, 1)\$ \q plot(acsch(x), x, 0, 1)\$&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;plot(\{x, arccsch(x)\}, x = 0..1):&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;Plot[\{x, ArcCsch[x]\}, \{x, 0, 1\}];&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;plotfunc(x, acsch(x), x = 0..1):&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;load\_\,package(gnuplot)\$ \q plot(y = x, x = (0 .. 1))\$&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;plot(y = acsch(x), x = (0 .. 1))\$&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;table&gt;
+ &lt;tr&gt;
+  
+  &lt;th&gt;System&lt;/th&gt;
+  &lt;th&gt;Simple 3D plotting&lt;/th&gt;
+ 
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt; &lt;tr&gt;
+  &lt;td&gt;Axiom&lt;/td&gt;
+  &lt;td&gt;draw(abs(x*y), x = 0..1, y = 0..1);&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt; &lt;tr&gt;
+  &lt;td&gt;Derive&lt;/td&gt;
+  &lt;td&gt;[Plot Overlay]&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt; &lt;tr&gt;
+  &lt;td&gt;DoCon&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt; &lt;tr&gt;
+  &lt;td&gt;GAP&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt; &lt;tr&gt;
+  &lt;td&gt;Macsyma&lt;/td&gt;
+  &lt;td&gt;plot3d(abs(x*y), x, 0, 1, y, 0, 1)\$&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt; &lt;tr&gt;
+  &lt;td&gt;Magnus&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt; &lt;tr&gt;
+  &lt;td&gt;Maxima&lt;/td&gt;
+  &lt;td&gt;plot3d(abs(x*y), x, 0, 1, y, 0, 1)\$&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt; &lt;tr&gt;
+  &lt;td&gt;Maple&lt;/td&gt;
+  &lt;td&gt;plot3d(abs(x*y), x = 0..1, y = 0..1):&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt; &lt;tr&gt;
+  &lt;td&gt;Mathematica&lt;/td&gt;
+  &lt;td&gt;Plot3D[Abs[x*y], \{x, 0, 1\}, \{y, 0, 1\}];&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt; &lt;tr&gt;
+  &lt;td&gt;MuPAD&lt;/td&gt;
+  &lt;td&gt;plotfunc(abs(x*y), x = 0..1, y = 0..1):&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt; &lt;tr&gt;
+  &lt;td&gt;Octave&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt; &lt;tr&gt;
+  &lt;td&gt;Pari&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt; &lt;tr&gt;
+  &lt;td&gt;Reduce&lt;/td&gt;
+  &lt;td&gt;load\_\,package(gnuplot)\$&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt; &lt;tr&gt;
+  &lt;td&gt;&lt;/td&gt;
+  &lt;td&gt;plot(z = abs(x*y), x = (0 .. 1), y = (0 .. 1))\$&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt; &lt;tr&gt;
+  &lt;td&gt;Scilab&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt; &lt;tr&gt;
+  &lt;td&gt;Sumit&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt; &lt;tr&gt;
+  &lt;td&gt;Yacas&lt;/td&gt;
+  &lt;td&gt;&lt;/td&gt;
+ &lt;/tr&gt;
+ &lt;tr&gt;
+  &lt;td&gt;
+&lt;/table&gt;
+
+&lt;/body&gt;
+&lt;/html&gt;
+
+
diff --git a/src/axiom-website/rosetta.pdf b/src/axiom-website/rosetta.pdf
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+\documentclass{article}
+\normalsize\baselineskip=12pt
+\parskip=0pt
+\parindent=10pt
+\tolerance=5000
+\pretolerance=5000
+\frenchspacing
+\hangindent=10pt
+\skip\footins=18pt
+\global\textwidth 31pc \global\textheight 47pc
+\headsep 12pt
+\oddsidemargin 0pt
+\evensidemargin 0pt
+%
+\renewcommand{\textfraction}{.1}
+\renewcommand{\floatpagefraction}{.75}
+%
+\catcode`@=11
+\def\ps@plain{\let\@mkboth\@gobbletwo%
+     \let\@oddhead\@empty\def\@oddfoot{\sysdetails}
+     \let\@evenhead\@empty\let\@evenfoot\@oddfoot}
+\def\ps@empty{\let\@mkboth\@gobbletwo%
+     \let\@oddhead\@empty\def\@oddfoot{\sysdetails}
+     \let\@evenhead\@empty\let\@evenfoot\@oddfoot}
+\catcode`@=12
+%
+\def\sysdetails{\parbox{\textwidth}{%
+Based on material originally published in {\sl Computer Algebra Systems: A
+Practical Guide\/} edited by Michael J.\ Wester, John Wiley \&amp; Sons,
+Chichester, United Kingdom, ISBN 0-471-98353-5, xvi+436 pages, 1999.}}
+%
+\pagestyle{plain}
+
+\begin{document}
+%
+% \nth{n} produces 1^{st}, 2^{nd}, 3^{rd}, 4^{th}, etc.
+%
+\def\nth#1{$#1^{\rm \ifcase#1 th\or st\or nd\or rd\else th\fi}$}
+%
+% Abbreviations
+%
+\newcommand{\Axiom}{{\sf Axiom}}
+\newcommand{\Derive}{{\sf Derive}}
+\newcommand{\DoCon}{{\sf DoCon}}
+\newcommand{\GAP}{{\sf GAP}}
+\newcommand{\Gmp}{{\sf Gmp}}
+\newcommand{\Macsyma}{{\sf Macsyma}}
+\newcommand{\Magnus}{{\sf Magnus}}
+\newcommand{\Maxima}{{\sf Maxima}}
+\newcommand{\Maple}{{\sf Maple}}
+\newcommand{\Mathematica}{{\sf Mathematica}}
+\newcommand{\MuPAD}{{\sf MuPAD}}
+\newcommand{\Octave}{{\sf Octave}}
+\newcommand{\Pari}{{\sf Pari}}
+\newcommand{\Reduce}{{\sf Reduce}}
+\newcommand{\Scilab}{{\sf Scilab}}
+\newcommand{\Sumit}{{\sf Sumit}}
+\newcommand{\Yacas}{{\sf Yacas}}
+
+\section{Introduction}
+
+The following is a collection of synonyms for various operations in
+the computer algebra systems \Axiom, \Derive, \GAP, \Gmp, \DoCon,
+\Macsyma, \Magnus, \Maxima, \Maple, \Mathematica, \MuPAD, \Octave,
+\Pari, \Reduce, \Scilab, \Sumit\ and \Yacas.  This collection does not
+attempt to be comprehensive, but hopefully it will be useful in giving
+an indication of how to translate between the syntaxes used by the
+different systems in many common situations.  Note that a blank entry
+means either (a) that there may be an exact translation of a
+particular operation for the indicated system, but we don't know what
+it is or (b) there is no exact translation but it may still be
+possible to work around this lack with a related functionality.
+
+While commercial systems are not provided on this CD the intent of the
+Rosetta effort is to make it possible for experienced Computer Algebra
+users to experiment with other systems. Thus the commands for
+commercial systems are included to allow users of those systems to
+translate.
+
+Some of these systems are special purpose and do not support a lot of
+the functionality of the more general purpose systems. Where they do
+support an interpreter the commands are provided.
+
+Originally written by Michael Wester.
+Modified for Rosetta by Timothy Daly, Alexander Hulpke (GAP).
+
+\section{System availability}
+
+\begin{tabular}{l|lll}
+System &amp; \rm{License} &amp; \rm{Status (May 2002)} &amp; \rm{Web Location} \\
+\hline
+\Axiom       &amp; BSD         &amp; available  &amp; http://www.aldor.org \\
+\Axiom       &amp; open source &amp; pending    &amp; http://home.earthlink.net/~jgg964/axiom.html \\
+\Derive      &amp; commercial  &amp; available  &amp; http://www.mathware.com \\
+\DoCon       &amp; open source &amp; available  &amp; http://www.haskell.org/docon \\
+\GAP         &amp; GPL         &amp; Rosetta    &amp; http://www.gap-system.org/~gap \\
+\Gmp         &amp; GPL         &amp; Rosetta    &amp; http://www.swox.com/gmp \\
+\Macsyma     &amp; commercial  &amp; dead       &amp; unavailable \\
+\Magnus      &amp; GPL         &amp; Rosetta    &amp; http://sourceforge.net/projects/magnus \\
+\Maxima      &amp; GPL         &amp; Rosetta    &amp; http://www.ma.utexas.edu/maxima.html\\
+\Maple       &amp; commercial  &amp; available  &amp; http://www.maplesoft.com \\
+\Mathematica &amp; commercial  &amp; available  &amp; http://www.wolfram.com \\
+\MuPAD       &amp; commercial  &amp; available  &amp; http://www.mupad.de \\
+\Octave      &amp; GPL         &amp; Rosetta    &amp; http://www.octave.org \\
+\Pari        &amp; GPL         &amp; Rosetta    &amp; http://www.parigp-home.de \\
+\Reduce      &amp; commercial  &amp; available  &amp; http://www.zib.de/Symbolik/reduce \\
+\Scilab      &amp; Scilab      &amp; available  &amp; http://www-rocq.inria.fr/scilab \\
+\Sumit       &amp;             &amp; available  &amp; http://www-sop.inria.fr/cafe/soft-f.html \\
+\Yacas       &amp; GPL         &amp; available  &amp; http://yacas.sourceforge.net \\
+\end{tabular} \\[10pt]
+\\
+\begin{tabular}{l|ll}
+System &amp; \rm{Type} &amp; \rm{Interpreted or Compiled}\\
+\hline
+\Axiom       &amp; General Purpose          &amp; both \\
+\Derive      &amp; General Purpose          &amp; \\
+\DoCon       &amp; General Purpose          &amp; Interpreted in Haskell \\
+\GAP         &amp; Group Theory             &amp; \\
+\Gmp         &amp; arb. prec. arithmetic    &amp; \\
+\Macsyma     &amp; General Purpose          &amp; \\
+\Magnus      &amp; Infinite Group Theory    &amp; \\
+\Maxima      &amp; General Purpose          &amp; \\
+\Maple       &amp; General Purpose          &amp; \\
+\Mathematica &amp; General Purpose          &amp; \\
+\MuPAD       &amp; General Purpose          &amp; \\
+\Octave      &amp; Numerical Computing      &amp; \\
+\Pari        &amp; Number Theory            &amp; \\
+\Reduce      &amp; General Purpose          &amp; \\
+\Scilab      &amp; General Purpose          &amp; \\
+\Sumit       &amp; Functional Equations     &amp; \\
+\Yacas       &amp; General Purpose          &amp; \\
+\end{tabular} \\[10pt]
+
+\section{Programming and Miscellaneous}
+
+\begingroup
+\newcommand{\OR}{{\em or }}
+\newcommand{\fnm}{\footnotemark}
+\newcommand{\h}[1]{{\rm #1}}
+\newcommand{\m}[2]{\multicolumn{#1}{l}{#2}}
+\newcommand{\q}{\quad}
+\newcommand{\st}{\small\tt}
+\parindent=0pt
+\hfuzz=1pt
+\begin{tt}
+
+\begin{tabular}{l|ll}
+&amp; \m{2}{\rm Unix/Microsoft user initialization file} \\
+\hline
+\Axiom       &amp; \~{}/axiom.input          &amp; \\
+\GAP         &amp; \~{}/.gaprc               &amp; GAP.RC \\
+\Gmp         &amp;                           &amp; \\
+\DoCon       &amp;                           &amp; \\
+\Derive      &amp;                           &amp; derive.ini   \\
+\Macsyma     &amp; \~{}/macsyma-init.macsyma &amp; mac-init.mac \\
+\Magnus      &amp;                           &amp; \\
+\Maxima      &amp; \~{}/macsyma-init.macsyma &amp; mac-init.mac \\
+\Maple       &amp; \~{}/.mapleinit           &amp; maplev5.ini  \\
+\Mathematica &amp; \~{}/init.m               &amp; init.m       \\
+\MuPAD       &amp; \~{}/.mupadinit           &amp;
+	$\backslash$mupad$\backslash$bin$\backslash$userinit.mu \\
+\Octave      &amp;                           &amp; \\
+\Pari        &amp;                           &amp; \\
+\Reduce      &amp; \~{}/.reducerc            &amp; reduce.rc    \\
+\Scilab      &amp;                           &amp; \\
+\Sumit       &amp;                           &amp; \\
+\Yacas       &amp;                           &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|ll}
+&amp; \h{Describe {\em keyword}} &amp; \h{Find keywords containing {\em pattern}} \\
+\hline
+\Axiom       &amp;                       &amp; )what operations pattern \\
+\Derive      &amp;                       &amp; \\
+\DoCon       &amp;                       &amp; \\
+\GAP         &amp; ?keyword              &amp; ??keyword\\
+\Gmp         &amp;                       &amp; \\
+\Macsyma     &amp; describe("keyword")\$ &amp; apropos("pattern");      \\
+\Magnus      &amp;                       &amp; \\
+\Maxima      &amp; describe("keyword")\$ &amp; apropos("pattern");      \\
+\Maple       &amp; ?keyword              &amp; ?pattern\,\fnm           \\
+\Mathematica &amp; ?keyword              &amp; ?*pattern*               \\
+\MuPAD       &amp; ?keyword              &amp; ?*pattern*               \\
+\Octave      &amp; help -i keyword       &amp; \\
+\Pari        &amp;                       &amp; \\
+\Reduce      &amp;                       &amp; \\
+\Scilab      &amp;                       &amp; \\
+\Sumit       &amp;                       &amp; \\
+\Yacas       &amp;                       &amp; \\
+\end{tabular} \\[10pt]
+
+\footnotetext{Only if the pattern is not a keyword and then the matches are
+simplistic.}
+
+\begin{tabular}{l|l@{ }llll}
+&amp; &amp; &amp; \h{Prev.} &amp; \h{Case} &amp; \h{Variables} \\
+&amp; \h{Comment} &amp; \h{Line continuation} &amp; \h{expr.} &amp; \h{sensitive} &amp; \h{assumed}
+	\\
+\hline
+\Axiom       &amp; -- comment    &amp; input \_&lt;CR&gt;input   &amp; \% &amp; Yes &amp; real    \\
+\Derive      &amp; "comment"     &amp; input \~{}&lt;CR&gt;input &amp;    &amp; No  &amp; real    \\
+\DoCon       &amp;               &amp;                     &amp;    &amp;     &amp; \\
+\GAP         &amp; \# comment    &amp; input$\backslash$&lt;CR&gt;input&amp;last&amp;Yes&amp;no assumption\\
+\Gmp         &amp;               &amp;                     &amp;    &amp;     &amp; \\
+\Macsyma     &amp; /* comment */ &amp; input&lt;CR&gt;input;     &amp; \% &amp; No  &amp; real    \\
+\Magnus      &amp;               &amp;                     &amp;    &amp;     &amp; \\
+\Maxima      &amp; /* comment */ &amp; input&lt;CR&gt;input;     &amp; \% &amp; No  &amp; real    \\
+\Maple       &amp; \# comment    &amp; input&lt;CR&gt;input;     &amp; \% &amp; Yes &amp; complex \\
+\Mathematica &amp; (* comment *) &amp; input&lt;CR&gt;input      &amp; \% &amp; Yes &amp; complex \\
+\MuPAD       &amp; \# comment \# &amp; input&lt;CR&gt;input;     &amp; \% &amp; Yes &amp; complex \\
+\Octave      &amp; \#\#          &amp;                     &amp;    &amp; Yes &amp; \\
+\Pari        &amp;               &amp;                     &amp;    &amp;     &amp; \\
+\Reduce      &amp; \% comment    &amp; input&lt;CR&gt;input;     &amp; ws &amp; No  &amp; complex \\
+\Scilab      &amp;               &amp;                     &amp;    &amp;     &amp; \\
+\Sumit       &amp;               &amp;                     &amp;    &amp;     &amp; \\
+\Yacas       &amp;               &amp;                     &amp;    &amp;     &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|lll}
+&amp; \h{Load a file} &amp; \h{Time a command} &amp; \h{Quit} \\
+\hline
+\Axiom       &amp; )read "file" )quiet    &amp; )set messages time on  &amp; )quit \\
+\Derive      &amp; [Transfer Load Derive] &amp;                        &amp; [Quit] \\
+\DoCon       &amp;                        &amp;                        &amp; \\
+\GAP         &amp; Read("file");          &amp; time; \h{(also see {\tt Runtime();})}&amp;quit;\\
+\Gmp         &amp;                        &amp;                        &amp; \\
+\Macsyma     &amp; load("file")\$         &amp; showtime: all\$        &amp; quit(); \\
+\Magnus      &amp;                        &amp;                        &amp; \\
+\Maxima      &amp; load("file")\$         &amp; showtime: all\$        &amp; quit(); \\
+\Maple       &amp; read("file"):          &amp; readlib(showtime): on; &amp; quit \\
+\Mathematica &amp; @&lt;&lt; file                &amp; Timing[command]        &amp; Quit[] \\
+\MuPAD       &amp; read("file"):          &amp; time(command);         &amp; quit \\
+\Octave      &amp; load file              &amp; tic(); cmd ; toc()     &amp; quit \OR\ exit\\
+\Pari        &amp;                        &amp;                        &amp; \\
+\Reduce      &amp; in "file"\$            &amp; on time;               &amp; quit; \\
+\Scilab      &amp;                        &amp;                        &amp; quit \\
+\Sumit       &amp;                        &amp;                        &amp; \\
+\Yacas       &amp;                        &amp;                        &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|lll}
+&amp; \h{Display} &amp; \h{Suppress} &amp; \\
+&amp; \h{output} &amp; \h{output} &amp; \h{Substitution: $f(x, y) \rightarrow f(z, w)$} \\
+\hline
+\Axiom       &amp; input  &amp; input;      &amp; subst(f(x, y), [x = z, y = w])   \\
+\Derive      &amp; input  &amp; var:= input &amp; [Manage Substitute]              \\
+\DoCon       &amp;        &amp;             &amp; \\
+\GAP         &amp; input; &amp; input;;     &amp; Value(f,[x,y],[z,w]);\fnm         \\
+\Gmp         &amp;        &amp;             &amp; \\
+\Macsyma     &amp; input; &amp; input\$     &amp; subst([x = z, y = w], f(x, y));  \\
+\Magnus      &amp;        &amp;             &amp; \\
+\Maxima      &amp; input; &amp; input\$     &amp; subst([x = z, y = w], f(x, y));  \\
+\Maple       &amp; input; &amp; input:      &amp; subs(\{x = z, y = w\}, f(x, y)); \\
+\Mathematica &amp; input  &amp; input;      &amp; f[x, y] /. \{x -&gt; z, y -&gt; w\}    \\
+\MuPAD       &amp; input; &amp; input:      &amp; subs(f(x, y), [x = z, y = w]);   \\
+\Octave      &amp; input  &amp; input;      &amp; \\
+\Pari        &amp;        &amp;             &amp; \\
+\Reduce      &amp; input; &amp; input\$     &amp; sub(\{x = z, y = w\}, f(x, y));  \\
+\Scilab      &amp;        &amp;             &amp; \\
+\Sumit       &amp;        &amp;             &amp; \\
+\Yacas       &amp;        &amp;             &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|lll}
+&amp; \h{Set} &amp; \h{List} &amp; \h{Matrix} \\
+\hline
+\Axiom       &amp; set [1, 2] &amp; [1, 2]    &amp; matrix(@[[1, 2],[3, 4]])            \\
+\Derive      &amp; \{1, 2\}   &amp; [1, 2]    &amp; @[[1,2], [3,4]]                     \\
+\DoCon       &amp;            &amp;           &amp; \\
+\GAP         &amp; Set([1,2]) &amp; [1, 2]    &amp; @[[1,2], [3,4]]\fnm                 \\
+\Gmp         &amp;            &amp;           &amp; \\
+\Macsyma     &amp; [1, 2]     &amp; [1, 2]    &amp; matrix([1, 2], [3, 4])             \\
+\Magnus      &amp;            &amp;           &amp; \\
+\Maxima      &amp; [1, 2]     &amp; [1, 2]    &amp; matrix([1, 2], [3, 4])             \\
+\Maple       &amp; \{1, 2\}   &amp; [1, 2]    &amp; matrix(@[[1, 2], [3, 4]])           \\
+\Mathematica &amp; \{1, 2\}   &amp; \{1, 2\}  &amp; \{\{1, 2\}, \{3, 4\}\}             \\
+\MuPAD       &amp; \{1, 2\}   &amp; [1, 2]    &amp; export(Dom): \q export(linalg):    \\
+             &amp;            &amp;           &amp; matrix:= ExpressionField(normal)): \\
+             &amp;            &amp;           &amp; matrix(@[[1, 2], [3, 4]])           \\
+\Octave      &amp;            &amp;           &amp; \\
+\Pari        &amp;            &amp;           &amp; \\
+\Reduce      &amp; \{1, 2\}   &amp; \{1, 2\}  &amp; mat((1, 2), (3, 4))                \\
+\Scilab      &amp;            &amp; list(1,2) &amp; A=[1,2;3,4]\\
+\Sumit       &amp;            &amp;           &amp; \\
+\Yacas       &amp;            &amp;           &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|llll}
+&amp; \h{Equation} &amp; \h{List element} &amp; \h{Matrix element} &amp; \h{Length of a list} \\
+\hline
+\Axiom       &amp; x = 0  &amp; l . 2      &amp; m(2, 3)       &amp; \#l          \\
+\Derive      &amp; x = 0  &amp; l SUB 2    &amp; m SUB 2 SUB 3 &amp; DIMENSION(l) \\
+\DoCon       &amp;        &amp;            &amp;               &amp; \\
+\GAP         &amp; x=0    &amp; l[2]       &amp; m[2][3]       &amp; Length(l)    \\
+\Gmp         &amp;        &amp;            &amp;               &amp; \\
+\Macsyma     &amp; x = 0  &amp; l[2]       &amp; m[2, 3]       &amp; length(l)    \\
+\Magnus      &amp;        &amp;            &amp;               &amp; \\
+\Maxima      &amp; x = 0  &amp; l[2]       &amp; m[2, 3]       &amp; length(l)    \\
+\Maple       &amp; x = 0  &amp; l[2]       &amp; m[2, 3]       &amp; nops(l)      \\
+\Mathematica &amp; x == 0 &amp; l@[[2]]     &amp; m@[[2, 3]]     &amp; Length[l]    \\
+\MuPAD       &amp; x = 0  &amp; l[2]       &amp; m[2, 3]       &amp; nops(l)      \\
+\Octave      &amp;        &amp;            &amp;               &amp; \\
+\Pari        &amp;        &amp;            &amp;               &amp; \\
+\Reduce      &amp; x = 0  &amp; part(l, 2) &amp; m(2, 3)       &amp; length(l)    \\
+\Scilab      &amp;        &amp; l(2)       &amp;               &amp; \\
+\Sumit       &amp;        &amp;            &amp;               &amp; \\
+\Yacas       &amp;        &amp;            &amp;               &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|lll}
+&amp; \m{2}{\rm Prepend/append an element to a list} &amp; \h{Append two lists} \\
+\hline
+\Axiom       &amp; cons(e, l)     &amp; concat(l, e)   &amp; append(l1, l2)   \\
+\Derive      &amp; APPEND([e], l) &amp; APPEND(l, [e]) &amp; APPEND(l1, l2)   \\
+\DoCon       &amp;                &amp;                &amp; \\
+\GAP         &amp; Concatenation([e],l) &amp; Add(l,e) &amp; Append(l1, l2)   \\
+\Gmp         &amp;                &amp;                &amp; \\
+\Macsyma     &amp; cons(e, l)     &amp; endcons(e, l)  &amp; append(l1, l2)   \\
+\Magnus      &amp;                &amp;                &amp; \\
+\Maxima      &amp; cons(e, l)     &amp; endcons(e, l)  &amp; append(l1, l2)   \\
+\Maple       &amp; [e, op(l)]     &amp; [op(l), e]     &amp; [op(l1), op(l2)] \\
+\Mathematica &amp; Prepend[l, e]  &amp; Append[l, e]   &amp; Join[l1, l2]     \\
+\MuPAD       &amp; [e, op(l)]     &amp; append(l, e)   &amp; l1 . l2          \\
+\Octave      &amp;                &amp;                &amp; \\
+\Pari        &amp;                &amp;                &amp; \\
+\Reduce      &amp; e . l          &amp; append(l, {e}) &amp; append(l1, l2)   \\
+\Scilab      &amp;                &amp;                &amp; \\
+\Sumit       &amp;                &amp;                &amp; \\
+\Yacas       &amp;                &amp;                &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|ll}
+&amp; \h{Matrix column dimension} &amp; \h{Convert a list into a column vector} \\
+\hline
+\Axiom       &amp; ncols(m)                  &amp; transpose(matrix([l]))         \\
+\Derive      &amp; DIMENSION(m SUB 1)        &amp; [l]\`{}                        \\
+\DoCon       &amp;                           &amp; \\
+\GAP         &amp; Length(mat[1])            &amp; \h{objects are identical}      \\
+\Gmp         &amp;                           &amp; \\
+\Macsyma     &amp; mat\_\,ncols(m)           &amp; transpose(matrix(l))           \\
+\Magnus      &amp;                           &amp; \\
+\Maxima      &amp; mat\_\,ncols(m)           &amp; transpose(matrix(l))           \\
+\Maple       &amp; linalg[coldim](m)         &amp; linalg[transpose](matrix([l])) \\
+\Mathematica &amp; Dimensions[m]@[[2]]        &amp; Transpose[\{l\}]               \\
+\MuPAD       &amp; linalg::ncols(m)          &amp; transpose(matrix([l]))\,\fnm   \\
+\Octave      &amp;                           &amp; \\
+\Pari        &amp;                           &amp; \\
+\Reduce      &amp; load\_\,package(linalg)\$ &amp; matrix v(length(l), 1)\$       \\
+             &amp; column\_dim(m)            &amp; for i:=1:length(l) do          \\
+             &amp;                           &amp; \q\q v(i, 1):= part(l, i)      \\
+\Scilab      &amp;                           &amp; \\
+\Sumit       &amp;                           &amp; \\
+\Yacas       &amp;                           &amp; \\
+\end{tabular} \\[10pt]
+
+\footnotetext{See the definition of {\tt matrix} above.}
+
+\begin{tabular}{l|l}
+&amp; \h{Convert a column vector into a list} \\
+\hline
+\Axiom       &amp; [v(i, 1) for i in 1..nrows(v)]              \\
+\Derive      &amp; v\`{} SUB 1                                 \\
+\DoCon       &amp; \\
+\GAP         &amp; \h{objects are identical}                   \\
+\Gmp         &amp; \\
+\Macsyma     &amp; part(transpose(v), 1)                       \\
+\Magnus      &amp; \\
+\Maxima      &amp; part(transpose(v), 1)                       \\
+\Maple       &amp; op(convert(linalg[transpose](v), listlist)) \\
+\Mathematica &amp; Flatten[v]                                  \\
+\MuPAD       &amp; [op(v)]                                     \\
+\Octave      &amp; \\
+\Pari        &amp; \\
+\Reduce      &amp; load\_\,package(linalg)\$                   \\
+             &amp; for i:=1:row\_\,dim(v) collect(v(i, 1))     \\
+\Scilab      &amp; \\
+\Sumit       &amp; \\
+\Yacas       &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|lllllll}
+&amp; \h{True} &amp; \h{False} &amp; \h{And} &amp; \h{Or} &amp; \h{Not} &amp; \h{Equal} &amp; \h{Not equal}
+	\\
+\hline
+\Axiom       &amp; true &amp; false &amp; and  &amp; or &amp; not &amp; =  &amp; \~{}= \\
+\Derive      &amp; TRUE &amp; FALSE &amp; AND  &amp; OR &amp; NOT &amp; =  &amp; /=    \\
+\DoCon       &amp;      &amp;       &amp;      &amp;    &amp;     &amp;    &amp; \\
+\GAP         &amp; true &amp; false\fnm &amp; and  &amp; or &amp; not &amp; = &amp; &lt;&gt;     \\
+\Gmp         &amp;      &amp;       &amp;      &amp;    &amp;     &amp;    &amp; \\
+\Macsyma     &amp; true &amp; false &amp; and  &amp; or &amp; not &amp; =  &amp; \#    \\
+\Magnus      &amp;      &amp;       &amp;      &amp;    &amp;     &amp;    &amp; \\
+\Maxima      &amp; true &amp; false &amp; and  &amp; or &amp; not &amp; =  &amp; \#    \\
+\Maple       &amp; true &amp; false &amp; and  &amp; or &amp; not &amp; =  &amp; &lt;&gt;    \\
+\Mathematica &amp; True &amp; False &amp; \&amp;\&amp; &amp; || &amp; !   &amp; == &amp; !=    \\
+\MuPAD       &amp; true &amp; false &amp; and  &amp; or &amp; not &amp; =  &amp; &lt;&gt;    \\
+\Octave      &amp;      &amp;       &amp;      &amp;    &amp;     &amp;    &amp; \\
+\Pari        &amp;      &amp;       &amp;      &amp;    &amp;     &amp;    &amp; \\
+\Reduce      &amp; t    &amp; nil   &amp; and  &amp; or &amp; not &amp; =  &amp; neq   \\
+\Scilab      &amp; \%t  &amp; \%f   &amp;      &amp;    &amp;     &amp;    &amp; \\
+\Sumit       &amp;      &amp;       &amp;      &amp;    &amp;     &amp;    &amp; \\
+\Yacas       &amp;      &amp;       &amp;      &amp;    &amp;     &amp;    &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|ll}
+&amp; \h{If+then+else statements} &amp; \h{Strings (concatenated)} \\
+\hline
+\Axiom       &amp; if \_ then \_ else if \_ then \_ else \_ &amp; concat(["x", "y"])  \\
+\Derive      &amp; IF(\_, \_, IF(\_, \_, \_))               &amp; "xy"                \\
+\DoCon       &amp;                                          &amp; \\
+\GAP         &amp; if \_ then \_ elif \_ then \_ else \_ fi &amp; Concatenation("x","y")\\
+\Gmp         &amp;                                          &amp; \\
+\Macsyma     &amp; if \_ then \_ else if \_ then \_ else \_ &amp; concat("x", "y")    \\
+\Magnus      &amp;                                          &amp; \\
+\Maxima      &amp; if \_ then \_ else if \_ then \_ else \_ &amp; concat("x", "y")    \\
+\Maple       &amp; if \_ then \_ elif \_ then \_ else \_ fi &amp; "x" . "y"           \\
+\Mathematica &amp; If[\_, \_, If[\_, \_, \_]]               &amp; "x" &lt;&gt; "y"          \\
+\MuPAD       &amp; if \_ then \_ elif \_ then \_ else \_    &amp; "x" . "y"           \\
+             &amp; \q\q end\_if                             &amp; \\
+\Octave      &amp;                                          &amp; \\
+\Pari        &amp;                                          &amp; \\
+\Reduce      &amp; if \_ then \_ else if \_ then \_ else \_ &amp; "xy" \OR\ mkid(x, y)\\
+\Scilab      &amp;                                          &amp; \\
+\Sumit       &amp;                                          &amp; \\
+\Yacas       &amp;                                          &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|ll}
+&amp; \h{Simple loop and Block} &amp; \h{Generate the list $[1, 2, \ldots, n]$} \\
+\hline
+\Axiom       &amp; for i in 1..n repeat ( x; y )       &amp; [f(i) for i in 1..n]     \\
+\Derive      &amp; VECTOR([x, y], i, 1, n)             &amp; VECTOR(f(i), i, 1, n)    \\
+\DoCon       &amp;                                     &amp; \\
+\GAP         &amp; for i in [1..n] do \_ od;           &amp; [1..n] {\rm or} [1,2..n]\\
+\Gmp         &amp;                                     &amp; \\
+\Macsyma     &amp; for i:1 thru n do (x, y);           &amp; makelist(f(i), i, 1, n); \\
+\Magnus      &amp;                                     &amp; \\
+\Maxima      &amp; for i:1 thru n do (x, y);           &amp; makelist(f(i), i, 1, n); \\
+\Maple       &amp; for i from 1 to n do x; y od;       &amp; [f(i) \$ i = 1..n];      \\
+\Mathematica &amp; Do[x; y, \{i, 1, n\}]               &amp; Table[f[i], \{i, 1, n\}] \\
+\MuPAD       &amp; for i from 1 to n do x; y           &amp; [f(i) \$ i = 1..n];      \\
+             &amp; \q\q end\_for;                      &amp; \\
+\Octave      &amp;                                     &amp; \\
+\Pari        &amp;                                     &amp; \\
+\Reduce      &amp; for i:=1:n do @&lt;&lt;x; y&gt;&gt;;             &amp; for i:=1:n collect f(i); \\
+\Scilab      &amp;                                     &amp; \\
+\Sumit       &amp;                                     &amp; \\
+\Yacas       &amp;                                     &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|l}
+&amp; \h{Complex loop iterating on a list} \\
+\hline
+\Axiom       &amp; for x in [2, 3, 5] while x**2 &lt; 10 repeat output(x)         \\
+\Derive      &amp; \\
+\DoCon       &amp; \\
+\GAP         &amp; for x in [2, 3, 5] do while x\^{}2&lt;10 do Print(x);od;od; \\
+\Gmp         &amp; \\
+\Macsyma     &amp; for x in [2, 3, 5] while x\^{}2 &lt; 10 do print(x)\$          \\
+\Magnus      &amp; \\
+\Maxima      &amp; for x in [2, 3, 5] while x\^{}2 &lt; 10 do print(x)\$          \\
+\Maple       &amp; for x in [2, 3, 5] while x\^{}2 &lt; 10 do print(x) od:        \\
+\Mathematica &amp; For[l = \{2, 3, 5\}, l != \{\} \&amp;\&amp; l@[[1]]\^{}2 &lt; 10,       \\
+             &amp; \q l = Rest[l], Print[l@[[1]]] ]                             \\
+\MuPAD       &amp; for x in [2, 3, 5] do if x\^{}2 &lt; 10 then print(x) end\_if  \\
+             &amp; \q end\_for:                                                \\
+\Octave      &amp; \\
+\Pari        &amp; \\
+\Reduce      &amp; for each x in \{2, 3, 5\} do if x\^{}2 &lt; 10 then write(x)\$ \\
+\Scilab      &amp; \\
+\Sumit       &amp; \\
+\Yacas       &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|lll}
+&amp; \h{\small Assignment} &amp; \h{Function definition} &amp; \h{Clear vars and funs} \\
+\hline
+\Axiom       &amp; y:= f(x)  &amp; f(x, y) == x*y              &amp;
+	{\small\tt )clear properties y f} \\
+\Derive      &amp; y:= f(x)  &amp; f(x, y):= x*y               &amp; y:=  f:=           \\
+\DoCon       &amp;           &amp;                             &amp; \\
+\GAP         &amp; y:= f(x); &amp; f:=function(x, y) return x*y; end; &amp; \h{There are
+no symbolic variables}\\
+\Gmp         &amp;           &amp;                             &amp; \\
+\Macsyma     &amp; y: f(x);  &amp; f(x, y):= x*y;              &amp; remvalue(y)\$      \\
+             &amp;           &amp;                             &amp; remfunction(f)\$   \\
+\Magnus      &amp;           &amp;                             &amp; \\
+\Maxima      &amp; y: f(x);  &amp; f(x, y):= x*y;              &amp; remvalue(y)\$      \\
+             &amp;           &amp;                             &amp; remfunction(f)\$   \\
+\Maple       &amp; y:= f(x); &amp; f:= proc(x, y) x*y end;     &amp; y:= 'y':  f:= 'f': \\
+\Mathematica &amp; y = f[x]  &amp; f[x\_, y\_\,]:= x*y         &amp; Clear[y, f]        \\
+\MuPAD       &amp; y:= f(x); &amp; f:= proc(x, y)              &amp; y:= NIL:  f:= NIL: \\
+             &amp;           &amp; \q\q begin x*y end\_\,proc; &amp; \\
+\Octave      &amp;           &amp;                             &amp; \\
+\Pari        &amp;           &amp;                             &amp; \\
+\Reduce      &amp; y:= f(x); &amp; procedure f(x, y); x*y;     &amp; clear y, f;        \\
+\Scilab      &amp;           &amp;                             &amp; \\
+\Sumit       &amp;           &amp;                             &amp; \\
+\Yacas       &amp;           &amp;                             &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|l}
+&amp; \h{Function definition with a local variable} \\
+\hline
+\Axiom       &amp; f(x) == (local n; n:= 2; n*x)                           \\
+\Derive      &amp; \\
+\DoCon       &amp; \\
+\GAP         &amp; f:=function(x) local n; n:=2;return n*x; end;           \\
+\Gmp         &amp; \\
+\Macsyma     &amp; f(x):= block([n], n: 2, n*x);                           \\
+\Magnus      &amp; \\
+\Maxima      &amp; f(x):= block([n], n: 2, n*x);                           \\
+\Maple       &amp; f:= proc(x) local n; n:= 2; n*x end;                    \\
+\Mathematica &amp; f[x\_\,]:= Module[\{n\}, n = 2; n*x]                    \\
+\MuPAD       &amp; f:= proc(x) local n; begin n:= 2; n*x end\_\,proc;      \\
+\Octave      &amp; \\
+\Pari        &amp; \\
+\Reduce      &amp; procedure f(x); begin scalar n; n:= 2; return(n*x) end; \\
+\Scilab      &amp; \\
+\Sumit       &amp; \\
+\Yacas       &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|ll}
+&amp; \h{Return unevaluated symbol} &amp; \h{Define a function from an expression} \\
+\hline
+\Axiom       &amp; e:= x*y;\q 'e          &amp; function(e, f, x, y)          \\
+\Derive      &amp; e:= x*y\q 'e           &amp; f(x, y):== e                  \\
+\DoCon       &amp;                        &amp; \\
+\GAP         &amp; \h{No unevaluated symbols}\fnm&amp;\\
+\Gmp         &amp;                        &amp; \\
+\Macsyma     &amp; e: x*y\$\q 'e;         &amp; define(f(x, y), e);           \\
+\Magnus      &amp;                        &amp; \\
+\Maxima      &amp; e: x*y\$\q 'e;         &amp; define(f(x, y), e);           \\
+\Maple       &amp; e:= x*y:\q 'e';        &amp; f:= unapply(e, x, y);         \\
+\Mathematica &amp; e = x*y;\q HoldForm[e] &amp; f[x\_, y\_\,] = e             \\
+\MuPAD       &amp; e:= x*y:\q hold(e);    &amp; f:= hold(func)(e, x, y);      \\
+\Octave      &amp;                        &amp; \\
+\Pari        &amp;                        &amp; \\
+\Reduce      &amp; e:= x*y\$              &amp; for all x, y let f(x, y):= e; \\
+\Scilab      &amp;                        &amp; \\
+\Sumit       &amp;                        &amp; \\
+\Yacas       &amp;                        &amp; \\
+\end{tabular} \\[10pt]
+\footnotetext{Variables can be assigned to generators of a suitable free
+object, for example {\tt x:=X(Rationals,"x");} or {\tt
+f:=FreeGroup(2);x:=f.1;}.}
+\addtocounter{footnote}{-1}%
+
+\begin{tabular}{l|ll}
+&amp; \h{Fun.\ of an indefinite number of args} &amp; \h{Apply ``+'' to sum a list} \\
+\hline
+\Axiom       &amp;                                   &amp; reduce(+, [1, 2])          \\
+\Derive      &amp; LST l:= l                         &amp; \\
+\DoCon       &amp;                                   &amp; \\
+\GAP         &amp; lst:=function(args) \_ end;       &amp; Sum([1,2])\\
+\Gmp         &amp;                                   &amp; \\
+\Macsyma     &amp; lst([l]):= l;                     &amp; apply("+", [1, 2])         \\
+\Magnus      &amp;                                   &amp; \\
+\Maxima      &amp; lst([l]):= l;                     &amp; apply("+", [1, 2])         \\
+\Maple       &amp; lst:=proc() [args[1..nargs]] end; &amp; convert([1, 2], \`{}+\`{}) \\
+\Mathematica &amp; lst[l\_\,\_\,\_\,]:= \{l\}        &amp; Apply[Plus, \{1, 2\}]      \\
+\MuPAD       &amp; lst:= proc(l) begin [args()]      &amp; \_\,plus(op([1, 2]))       \\
+             &amp; \q\q\q end\_\,proc;               &amp; \\
+\Octave      &amp;                                   &amp; \\
+\Pari        &amp;                                   &amp; \\
+\Reduce      &amp;                                   &amp; xapply(+, \{1, 2\})\,\fnm  \\
+\Scilab      &amp;                                   &amp; \\
+\Sumit       &amp;                                   &amp; \\
+\Yacas       &amp;                                   &amp; \\
+\end{tabular} \\[10pt]
+
+\footnotetext{\tt procedure xapply(f, lst); lisp(f . cdr(lst))\$}
+\addtocounter{footnote}{-1}%
+
+\begin{tabular}{l|ll}
+&amp; \h{Apply a fun.\ to a} &amp; \\
+&amp; \h{list of its args} &amp; \h{Map an anonymous function onto a list} \\
+\hline
+\Axiom       &amp; reduce(f, l)       &amp; map(x +-&gt; x + y, [1, 2])                \\
+\Derive      &amp;                    &amp; x:= [1, 2]                              \\
+             &amp;                    &amp; VECTOR(x SUB i + y, i, 1, DIMENSION(x)) \\
+\DoCon       &amp;                    &amp; \\
+\GAP         &amp; List(l,f)          &amp; List([1,2],x-&gt;x+y) \\
+\Gmp         &amp;                    &amp; \\
+\Macsyma     &amp; apply(f, l)        &amp; map(lambda([x], x + y), [1, 2])         \\
+\Magnus      &amp;                    &amp; \\
+\Maxima      &amp; apply(f, l)        &amp; map(lambda([x], x + y), [1, 2])         \\
+\Maple       &amp; f(op(l))           &amp; map(x -&gt; x + y, [1, 2])                 \\
+\Mathematica &amp; Apply[f, l]        &amp; Map[\# + y \&amp;, \{1, 2\}]                \\
+\MuPAD       &amp; f(op(l))           &amp; map([1, 2], func(x + y, x))             \\
+\Octave      &amp;                    &amp; \\
+\Pari        &amp;                    &amp; \\
+\Reduce      &amp; xapply(f, l)\,\fnm &amp; for each x in \{1, 2\} collect x + y    \\
+\Scilab      &amp;                    &amp; \\
+\Sumit       &amp;                    &amp; \\
+\Yacas       &amp;                    &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|l}
+&amp; \h{Pattern matching: $f(3 y) + f(z y) \rightarrow 3 f(y) + f(z y)$} \\
+\hline
+\Axiom       &amp; f:= operator('f);                                  \\
+             &amp; ( rule f((n | integer?(n)) * x) == n*f(x) )( \_    \\
+             &amp; \q\q f(3*y) + f(z*y))                              \\
+\Derive      &amp; \\
+\DoCon       &amp; \\
+\GAP         &amp; \\
+\Gmp         &amp; \\
+\Macsyma     &amp; matchdeclare(n, integerp, x, true)\$               \\
+             &amp; defrule(fnx, f(n*x), n*f(x))\$                     \\
+             &amp; apply1(f(3*y) + f(z*y), fnx);                      \\
+\Magnus      &amp; \\
+\Maxima      &amp; matchdeclare(n, integerp, x, true)\$               \\
+             &amp; defrule(fnx, f(n*x), n*f(x))\$                     \\
+             &amp; apply1(f(3*y) + f(z*y), fnx);                      \\
+\Maple       &amp; map(proc(q) local m;                               \\
+             &amp; \q\q\q if match(q = f(n*y), y, 'm') and            \\
+             &amp; \q\q\q\q\q type(rhs(op(m)), integer) then          \\
+             &amp; \q\q\q\q subs(m, n * f(y)) else q fi               \\
+             &amp; \q\q end,                                          \\
+             &amp; \q\q f(3*y) + f(z*y));                             \\
+\Mathematica &amp; f[3*y] + f[z*y] /. f[n\_Integer * x\_\,] -&gt; n*f[x] \\
+\MuPAD       &amp; d:= domain("match"): \q d::FREEVARIABLE:= TRUE:    \\
+             &amp; n:= new(d, "n", func(testtype(m, DOM\_INT), m)):   \\
+             &amp; x:= new(d, "x", TRUE):                             \\
+             &amp; map(f(3*y) + f(z*y),                               \\
+             &amp; \q\q proc(q) local m; begin m:= match(q, f(n*x));  \\
+             &amp; \q\q\q if m = FAIL then q                          \\
+             &amp; \q\q\q else subs(hold("n" * f("x")), m) end\_if    \\
+             &amp; \q\q end\_\,proc);                                 \\
+\Octave      &amp; \\
+\Pari        &amp; \\
+\Reduce      &amp; operator f;                                        \\
+             &amp; f(3*y) + f(z*y)                                    \\
+             &amp; \q\q where \{f(\~{}n * \~{}x) =&gt; n*f(x) when fixp(n)\}; \\
+\Scilab      &amp; \\
+\Sumit       &amp; \\
+\Yacas       &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|l}
+&amp; \h{Define a new infix operator and then use it} \\
+\hline
+\Axiom       &amp; \\
+\Derive      &amp; \\
+\DoCon       &amp; \\
+\GAP     &amp;\h{One can overload existing infix operators for ones own purposes}\\
+\Gmp         &amp; \\
+\Macsyma     &amp; infix("\~{}")\$ \q "\~{}"(x, y):= sqrt(x\^{}2 + y\^{}2)\$ \q
+	3 \~{} 4;               \\
+\Magnus      &amp; \\
+\Maxima      &amp; infix("\~{}")\$ \q "\~{}"(x, y):= sqrt(x\^{}2 + y\^{}2)\$ \q
+	3 \~{} 4;               \\
+\Maple       &amp; \`{}\&amp;\~{}\`{}:= (x, y) -&gt; sqrt(x\^{}2 + y\^{}2): \q 3 \&amp;\~{} 4;
+	\\
+\Mathematica &amp; x\_ $\backslash$[Tilde] y\_:= Sqrt[x\^{}2 + y\^{}2]; \q
+	3 $\backslash$[Tilde] 4 \\
+\MuPAD       &amp; tilde:= proc(x, y) begin sqrt(x\^{}2 + y\^{}2) end\_\,proc: \\
+             &amp; \q 3 \&amp;tilde 4;                                             \\
+\Octave      &amp; \\
+\Pari        &amp; \\
+\Reduce      &amp; infix |\$ \q procedure |(x, y); sqrt(x\^{}2 + y\^{}2)\$ \q
+	3 | 4;                  \\
+\Scilab      &amp; \\
+\Sumit       &amp; \\
+\Yacas       &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|lll}
+&amp; \h{Main expression} &amp; &amp; \\
+&amp; \h{operator} &amp; \h{\nth{1} operand} &amp; \h{List of expression operands} \\
+\hline
+\Axiom\fnm   &amp;            &amp; kernels(e) . 1 &amp; kernels(e)              \\
+\Derive      &amp;            &amp;                &amp; {\em various}\fnm       \\
+\DoCon       &amp;            &amp;                &amp; \\
+\GAP         &amp;\m{3}{\rm There are no formal unevaluated expressions}\\
+\Gmp         &amp;            &amp;                &amp; \\
+\Macsyma     &amp; part(e, 0) &amp; part(e, 1)     &amp; args(e)                 \\
+\Magnus      &amp;            &amp;                &amp; \\
+\Maxima      &amp; part(e, 0) &amp; part(e, 1)     &amp; args(e)                 \\
+\Maple       &amp; op(0, e)   &amp; op(1, e)       &amp; [op(e)]                 \\
+\Mathematica &amp; Head[e]    &amp; e@[[1]]         &amp; ReplacePart[e, List, 0] \\
+\MuPAD       &amp; op(e, 0)   &amp; op(e, 1)       &amp; [op(e)]                 \\
+\Octave      &amp;            &amp;                &amp; \\
+\Pari        &amp;            &amp;                &amp; \\
+\Reduce      &amp; part(e, 0) &amp; part(e, 1)     &amp; for i:=1:arglength(e)   \\
+             &amp;            &amp;                &amp; \q\q collect part(e, i) \\
+\Scilab      &amp;            &amp;                &amp; \\
+\Sumit       &amp;            &amp;                &amp; \\
+\Yacas       &amp;            &amp;                &amp; \\
+\end{tabular} \\[10pt]
+
+\addtocounter{footnote}{-1}%
+\footnotetext{The following commands work only on expressions that consist of a
+single level (e.g., $x + y + z$ but not $a/b + c/d$).}
+\addtocounter{footnote}{-1}%
+\footnotetext{{\tt TERMS}, {\tt FACTORS}, {\tt NUMERATOR}, {\tt LHS}, etc.}
+
+\begin{tabular}{l|l}
+&amp; \h{Print text and results} \\
+\hline
+\Axiom       &amp; output(concat(["sin(", string(0), ") = ",                 \\
+             &amp; \q string(sin(0))]));                                     \\
+\Derive      &amp; "sin(0)" = sin(0)                                         \\
+\DoCon       &amp; \\
+\GAP         &amp; Print("There is no sin, but factors(10)= ",Factors(10),
+"$\backslash$n")\\
+\Gmp         &amp; \\
+\Macsyma     &amp; print("sin(", 0, ") =", sin(0))\$                         \\
+\Magnus      &amp; \\
+\Maxima      &amp; print("sin(", 0, ") =", sin(0))\$                         \\
+\Maple       &amp; printf("sin(\%a) = \%a$\backslash$n", 0, sin(0)):         \\
+\Mathematica &amp; Print[StringForm["sin(\`{}\`{}) = \`{}\`{}", 0, Sin[0]]]; \\
+\MuPAD       &amp; print(Unquoted, "sin(".0.")" = sin(0)):                   \\
+\Octave      &amp; \\
+\Pari        &amp; \\
+\Reduce      &amp; write("sin(", 0, ") = ", sin(0))\$                        \\
+\Scilab      &amp; \\
+\Sumit       &amp; \\
+\Yacas       &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|ll}
+&amp; \h{Generate FORTRAN} &amp; \h{Generate \TeX/\LaTeX} \\
+\hline
+\Axiom       &amp; outputAsFortran(e)                    &amp; outputAsTex(e)      \\
+\Derive      &amp; [Transfer Save Fortran]               &amp; \\
+\DoCon       &amp;                                       &amp; \\
+\GAP         &amp;&amp;Print(LaTeX(e));\\
+\Gmp         &amp;                                       &amp; \\
+\Macsyma     &amp; fortran(e)\$ \OR gentran(eval(e))\$   &amp; tex(e);             \\
+\Magnus      &amp;                                       &amp; \\
+\Maxima      &amp; fortran(e)\$ \OR gentran(eval(e))\$   &amp; tex(e);             \\
+\Maple       &amp; fortran([e]);                         &amp; latex(e);           \\
+\Mathematica &amp; FortranForm[e]                        &amp; TexForm[e]          \\
+\MuPAD       &amp; generate::fortran(e);                 &amp; generate::TeX(e);   \\
+\Octave      &amp;                                       &amp; \\
+\Pari        &amp;                                       &amp; \\
+\Reduce      &amp; on fort; \q e; \q off fort; \OR       &amp; load\_\,package(tri)\$ \\
+             &amp; load\_\,package(gentran)\$ gentran e; &amp; on TeX; e; off TeX; \\
+\Scilab      &amp;                                       &amp; \\
+\Sumit       &amp;                                       &amp; \\
+\Yacas       &amp;                                       &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|l}
+&amp; \h{Import two space separated columns of integers from {\tt file}} \\
+\hline
+\Axiom       &amp; \\
+\Derive      &amp; [Transfer Load daTa] ({\rm from} file.dat)          \\
+\DoCon       &amp; \\
+\GAP         &amp; \\
+\Gmp         &amp; \\
+\Macsyma     &amp; xy: read\_num\_data\_to\_matrix("file", nrows, 2)\$ \\
+\Magnus      &amp; \\
+\Maxima      &amp; xy: read\_num\_data\_to\_matrix("file", nrows, 2)\$ \\
+\Maple       &amp; xy:= readdata("file", integer, 2):                  \\
+\Mathematica &amp; xy = ReadList["file", Number, RecordLists -&gt; True]  \\
+\MuPAD       &amp; \\
+\Octave      &amp; \\
+\Pari        &amp; \\
+\Reduce      &amp; \\
+\Scilab      &amp; \\
+\Sumit       &amp; \\
+\Yacas       &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|l}
+&amp; \h{Export two space separated columns of integers to {\tt file}\fnm} \\
+\hline
+\Axiom       &amp; )set output algebra "file" \q ({\rm creates} file.spout)       \\
+             &amp; for i in 1..n repeat output( \_                                \\
+             &amp; \q concat([string(xy(i, 1)), " ", string(xy(i, 2))]) )         \\
+             &amp; )set output algebra console                                    \\
+\Derive      &amp; xy  [Transfer Print Expressions File]\q({\rm creates} file.prt)\\
+\DoCon       &amp; \\
+\GAP         &amp; PrintTo("file");for i in [1..n] do\\
+             &amp;\q AppendTo("file",xy[i][1]," ",xy[i][2],"$\backslash$n");od;\\
+\Gmp         &amp; \\
+\Macsyma     &amp; writefile("file")\$ \q for i:1 thru n do                       \\
+             &amp; \q print(xy[i, 1], xy[i, 2])\$ \q closefile()\$                \\
+\Magnus      &amp; \\
+\Maxima      &amp; writefile("file")\$ \q for i:1 thru n do                       \\
+             &amp; \q print(xy[i, 1], xy[i, 2])\$ \q closefile()\$                \\
+\Maple       &amp; writedata("file", xy);                                         \\
+\Mathematica &amp; outfile = OpenWrite["file"];                                   \\
+             &amp; Do[WriteString[outfile,                                        \\
+             &amp; \q xy@[[i, 1]], " ", xy@[[i, 2]], "$\backslash$n"], \{i, 1, n\}] \\
+             &amp; Close[outfile];                                                \\
+\MuPAD       &amp; fprint(Unquoted, Text, "file",                                 \\
+             &amp; \q ("$\backslash$n", xy[i, 1], xy[i, 2]) \$ i = 1..n):         \\
+\Octave      &amp; \\
+\Pari        &amp; \\
+\Reduce      &amp; out "file"; \q for i:=1:n do                                   \\
+             &amp; \q write(xy(i, 1), " ", xy(i, 2)); \q shut "file";             \\
+\Scilab      &amp; \\
+\Sumit       &amp; \\
+\Sumit       &amp; \\
+\Yacas       &amp; \\
+\end{tabular} \\[10pt]
+
+\footnotetext{Some editing of {\tt file} will be necessary for all systems but
+\Maple\ and \Mathematica.}
+
+\section{Mathematics and Graphics}
+
+{\rm Since {\GAP} aims at discrete mathematics, it does not provide much of
+the calculus functionality listed in the following section.}
+
+\begin{tabular}{l|llllll}
+&amp; $e$ &amp; $\pi$ &amp; $i$ &amp; $+\infty$ &amp; $\sqrt{2}$ &amp; $2^{1/3}$ \\
+\hline
+\Axiom       &amp; \%e    &amp; \%pi &amp; \%i &amp; \%plusInfinity &amp; sqrt(2) &amp; 2**(1/3)   \\
+\Derive      &amp; \#e    &amp; pi   &amp; \#i &amp; inf            &amp; SQRT(2) &amp; 2\^{}(1/3) \\
+\DoCon       &amp;        &amp;      &amp;     &amp;                &amp;         &amp; \\
+\GAP         &amp;        &amp;      &amp; E(4) &amp; infinity &amp; ER(2)\fnm &amp;\\
+\Gmp         &amp;        &amp;      &amp;     &amp;                &amp;         &amp; \\
+\Macsyma     &amp; \%e    &amp; \%pi &amp; \%i &amp; inf            &amp; sqrt(2) &amp; 2\^{}(1/3) \\
+\Magnus      &amp;        &amp;      &amp;     &amp;                &amp;         &amp; \\
+\Maxima      &amp; \%e    &amp; \%pi &amp; \%i &amp; inf            &amp; sqrt(2) &amp; 2\^{}(1/3) \\
+\Maple       &amp; exp(1) &amp; Pi   &amp; I   &amp; infinity       &amp; sqrt(2) &amp; 2\^{}(1/3) \\
+\Mathematica &amp; E      &amp; Pi   &amp; I   &amp; Infinity       &amp; Sqrt[2] &amp; 2\^{}(1/3) \\
+\MuPAD       &amp; E      &amp; PI   &amp; I   &amp; infinity       &amp; sqrt(2) &amp; 2\^{}(1/3) \\
+\Octave      &amp;        &amp;      &amp;     &amp;                &amp;         &amp; \\
+\Pari        &amp;        &amp;      &amp;     &amp;                &amp;         &amp; \\
+\Reduce      &amp; e      &amp; pi   &amp; i   &amp; infinity       &amp; sqrt(2) &amp; 2\^{}(1/3) \\
+\Scilab      &amp;        &amp;      &amp;     &amp;                &amp;         &amp; \\
+\Sumit       &amp;        &amp;      &amp;     &amp;                &amp;         &amp; \\
+\Yacas       &amp;        &amp;      &amp;     &amp;                &amp;         &amp; \\
+\end{tabular} \\[10pt]
+\footnotetext{{\tt ER} represents special cyclotomic numbers and is not a
+root function.}
+\addtocounter{footnote}{-1}%
+
+\begin{tabular}{l|llll}
+&amp; \h{Euler's constant} &amp; \h{Natural log} &amp; \h{Arctangent} &amp; $n!$ \\
+\hline
+\Axiom       &amp;                &amp; log(x) &amp; atan(x)   &amp; factorial(n) \\
+\Derive      &amp; euler\_\,gamma &amp; LOG(x) &amp; ATAN(x)   &amp; n!           \\
+\DoCon       &amp;                &amp;        &amp;           &amp; \\
+\GAP         &amp;                &amp; LogInt(x,base) &amp;&amp; Factorial(n) \\
+\Gmp         &amp;                &amp;        &amp;           &amp; \\
+\Macsyma     &amp; \%gamma        &amp; log(x) &amp; atan(x)   &amp; n!           \\
+\Magnus      &amp;                &amp;        &amp;           &amp; \\
+\Maxima      &amp; \%gamma        &amp; log(x) &amp; atan(x)   &amp; n!           \\
+\Maple       &amp; gamma          &amp; log(x) &amp; arctan(x) &amp; n!           \\
+\Mathematica &amp; EulerGamma     &amp; Log[x] &amp; ArcTan[x] &amp; n!           \\
+\MuPAD       &amp; EULER          &amp; ln(x)  &amp; atan(x)   &amp; n!           \\
+\Octave      &amp;                &amp;        &amp;           &amp; \\
+\Pari        &amp;                &amp;        &amp;           &amp; \\
+\Reduce      &amp; Euler\_\,Gamma &amp; log(x) &amp; atan(x)   &amp; factorial(n) \\
+\Scilab      &amp;                &amp;        &amp;           &amp; \\
+\Sumit       &amp;                &amp;        &amp;           &amp; \\
+\Yacas       &amp;                &amp;        &amp;           &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|ll}
+&amp; \h{Legendre polynomial} &amp; \h{Chebyshev poly.\ of the \nth{1} kind} \\
+\hline
+\Axiom       &amp; legendreP(n, x)          &amp; chebyshevT(n, x)           \\
+\Derive      &amp; LEGENDRE\_\,P(n, x)      &amp; CHEBYCHEV\_\,T(n, x)       \\
+\DoCon       &amp;                          &amp; \\
+\GAP         &amp;                          &amp; \\
+\Gmp         &amp;                          &amp; \\
+\Macsyma     &amp; legendre\_\,p(n, x)      &amp; chebyshev\_\,t(n, x)       \\
+\Magnus      &amp;                          &amp; \\
+\Maxima      &amp; legendre\_\,p(n, x)      &amp; chebyshev\_\,t(n, x)       \\
+\Maple       &amp; orthopoly[P](n, x)       &amp; orthopoly[T](n, x)         \\
+\Mathematica &amp; LegendreP[n, x]          &amp; ChebyshevT[n, x]           \\
+\MuPAD       &amp; orthpoly::legendre(n, x) &amp; orthpoly::chebyshev1(n, x) \\
+\Octave      &amp;                          &amp; \\
+\Pari        &amp;                          &amp; \\
+\Reduce      &amp; LegendreP(n, x)          &amp; ChebyshevT(n, x)           \\
+\Scilab      &amp;                          &amp; \\
+\Sumit       &amp;                          &amp; \\
+\Yacas       &amp;                          &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|ll}
+&amp; \h{Fibonacci number} &amp; \h{Elliptic integral of the \nth{1} kind} \\
+\hline
+\Axiom       &amp; fibonacci(n)           &amp; \\
+\Derive      &amp; FIBONACCI(n)           &amp; ELLIPTIC\_\,E(phi, k\^{}2) \\
+\DoCon       &amp;                        &amp; \\
+\GAP         &amp; Fibonacci(n)           &amp; \\
+\Gmp         &amp;                        &amp; \\
+\Macsyma     &amp; fib(n)                 &amp; elliptic\_\,e(phi, k\^{}2) \\
+\Magnus      &amp;                        &amp; \\
+\Maxima      &amp; fib(n)                 &amp; elliptic\_\,e(phi, k\^{}2) \\
+\Maple       &amp; combinat[fibonacci](n) &amp; EllipticE(sin(phi), k)     \\
+\Mathematica &amp; Fibonacci[n]           &amp; EllipticE[phi, k\^{}2]     \\
+\MuPAD       &amp; numlib::fibonacci(n)   &amp; \\
+\Octave      &amp;                        &amp; \\
+\Pari        &amp;                        &amp; \\
+\Reduce      &amp;                        &amp; EllipticE(phi, k\^{}2)     \\
+\Scilab      &amp;                        &amp; \\
+\Sumit       &amp;                        &amp; \\
+\Yacas       &amp;                        &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|llll}
+&amp; $\Gamma(x)$ &amp; $\psi(x)$ &amp; \h{Cosine integral} &amp; \h{Bessel fun.\ (\nth{1})} \\
+\hline
+\Axiom       &amp; Gamma(x) &amp; psi(x)       &amp; real(Ei(\%i*x)) &amp; besselJ(n, x)     \\
+\Derive      &amp; GAMMA(x) &amp; PSI(x)       &amp; CI(x)           &amp; BESSEL\_\,J(n, x) \\
+\DoCon       &amp;          &amp;              &amp;                 &amp; \\
+\GAP         &amp;          &amp;              &amp;                 &amp; \\
+\Gmp         &amp;          &amp;              &amp;                 &amp; \\
+\Macsyma     &amp; gamma(x) &amp; psi[0](x)    &amp; cos\_\,int(x)   &amp; bessel\_j[n](x)   \\
+\Magnus      &amp;          &amp;              &amp;                 &amp; \\
+\Maxima      &amp; gamma(x) &amp; psi[0](x)    &amp; cos\_\,int(x)   &amp; bessel\_j[n](x)   \\
+\Maple       &amp; GAMMA(x) &amp; Psi(x)       &amp; Ci(x)           &amp; BesselJ(n, x)     \\
+\Mathematica &amp; Gamma[x] &amp; PolyGamma[x] &amp; CosIntegral[x]  &amp; BesselJ[n, x]     \\
+\MuPAD       &amp; gamma(x) &amp; psi(x)       &amp;                 &amp; besselJ(n, x)     \\
+\Octave      &amp;          &amp;              &amp;                 &amp; \\
+\Pari        &amp;          &amp;              &amp;                 &amp; \\
+\Reduce      &amp; Gamma(x) &amp; Psi(x)       &amp; Ci(x)           &amp; BesselJ(n, x)     \\
+\Scilab      &amp;          &amp;              &amp;                 &amp; \\
+\Sumit       &amp;          &amp;              &amp;                 &amp; \\
+\Yacas       &amp;          &amp;              &amp;                 &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|lll}
+&amp; \h{Hypergeometric fun.\ ${}_2F_1(a, b; c; x)$} &amp; \h{Dirac delta} &amp;
+	\h{Unit step fun.} \\
+\hline
+\Axiom       &amp;                                    &amp;          &amp; \\
+\Derive      &amp; GAUSS(a, b, c, x)                  &amp;          &amp; STEP(x)      \\
+\DoCon       &amp;                                    &amp;          &amp; \\
+\GAP         &amp;                                    &amp;          &amp; \\
+\Gmp         &amp;                                    &amp;          &amp; \\
+\Macsyma     &amp; hgfred([a, b], [c], x)             &amp; delta(x) &amp; unit\_\,step(x)
+	\\
+\Magnus      &amp;                                    &amp;          &amp; \\
+\Maxima      &amp; hgfred([a, b], [c], x)             &amp; delta(x) &amp; unit\_\,step(x)
+	\\
+\Maple       &amp; hypergeom([a, b], [c], x)          &amp; Dirac(x) &amp; Heaviside(x) \\
+\Mathematica &amp; HypergeometricPFQ[\{a,b\},\{c\},x] &amp;
+	\m{2}{@&lt;&lt; Calculus\`{}DiracDelta\`{}} \\
+\MuPAD       &amp;                                    &amp; dirac(x) &amp; heaviside(x) \\
+\Octave      &amp;                                    &amp;          &amp; \\
+\Pari        &amp;                                    &amp;          &amp; \\
+\Reduce      &amp; hypergeometric(\{a, b\}, \{c\}, x) &amp;          &amp; \\
+\Scilab      &amp;                                    &amp;          &amp; \\
+\Sumit       &amp;                                    &amp;          &amp; \\
+\Yacas       &amp;                                    &amp;          &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|l}
+&amp; \h{Define $|x|$ via a piecewise function} \\
+\hline
+\Axiom       &amp; \\
+\Derive      &amp; a(x):= -x*CHI(-inf, x, 0) + x*CHI(0, x, inf)        \\
+\DoCon       &amp; \\
+\GAP         &amp; \\
+\Gmp         &amp; \\
+\Macsyma     &amp; a(x):= -x*unit\_\,step(-x) + x*unit\_\,step(x)\$    \\
+\Magnus      &amp; \\
+\Maxima      &amp; a(x):= -x*unit\_\,step(-x) + x*unit\_\,step(x)\$    \\
+\Maple       &amp; a:= x -&gt; piecewise(x &lt; 0, -x, x):                   \\
+\Mathematica &amp; @&lt;&lt; Calculus\`{}DiracDelta\`{}                       \\
+             &amp; a[x\_]:= -x*UnitStep[-x] + x*UnitStep[x]            \\
+\MuPAD       &amp; a:= proc(x) begin -x*heaviside(-x) + x*heaviside(x) \\
+             &amp; \q\q end\_\,proc:                                   \\
+\Octave      &amp; \\
+\Pari        &amp; \\
+\Reduce      &amp; \\
+\Scilab      &amp; \\
+\Sumit       &amp; \\
+\Yacas       &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|ll}
+&amp; \h{Assume $x$ is real} &amp; \h{Remove that assumption} \\
+\hline
+\Axiom       &amp; &amp; \\
+\Derive      &amp; x :epsilon Real           &amp; x:=                         \\
+\DoCon       &amp;                           &amp; \\
+\GAP         &amp;                           &amp; \\
+\Gmp         &amp;                           &amp; \\
+\Macsyma     &amp; declare(x, real)\$        &amp; remove(x, real)\$           \\
+\Magnus      &amp;                           &amp; \\
+\Maxima      &amp; declare(x, real)\$        &amp; remove(x, real)\$           \\
+\Maple       &amp; assume(x, real);          &amp; x:= 'x':                    \\
+\Mathematica &amp; x/: Im[x] = 0;            &amp; Clear[x]                    \\
+\MuPAD       &amp; assume(x, Type::RealNum): &amp; unassume(x, Type::RealNum): \\
+\Octave      &amp;                           &amp; \\
+\Pari        &amp;                           &amp; \\
+\Reduce      &amp; &amp; \\
+\Scilab      &amp;                           &amp; \\
+\Sumit       &amp;                           &amp; \\
+\Yacas       &amp;                           &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|ll}
+&amp; \h{Assume $0 &lt; x \le 1$} &amp; \h{Remove that assumption} \\
+\hline
+\Axiom       &amp; &amp; \\
+\Derive      &amp; x :epsilon (0, 1]               &amp; x:=                     \\
+\DoCon       &amp;                                 &amp; \\
+\GAP         &amp;                                 &amp; \\
+\Gmp         &amp;                                 &amp; \\
+\Macsyma     &amp; assume(x &gt; 0, x &lt;= 1)\$         &amp; forget(x &gt; 0, x &lt;= 1)\$ \\
+\Magnus      &amp;                                 &amp; \\
+\Maxima      &amp; assume(x &gt; 0, x &lt;= 1)\$         &amp; forget(x &gt; 0, x &lt;= 1)\$ \\
+\Maple       &amp; assume(x &gt; 0);                  &amp; x:= 'x':                \\
+             &amp; additionally(x &lt;= 1);           &amp; \\
+\Mathematica &amp; Assumptions -&gt; 0 &lt; x &lt;= 1\,\fnm &amp; \\
+\MuPAD       &amp; assume(x &gt; 0):  assume(x &lt;= 1): &amp; unassume(x):            \\
+\Octave      &amp;                                 &amp; \\
+\Pari        &amp;                                 &amp; \\
+\Reduce      &amp; &amp; \\
+\Scilab      &amp;                                 &amp; \\
+\Sumit       &amp;                                 &amp; \\
+\Yacas       &amp;                                 &amp; \\
+\end{tabular} \\[10pt]
+
+\footnotetext{This is an option for {\tt Integrate}.}
+
+\begin{tabular}{l|l}
+&amp; \h{Basic simplification of an expression $e$} \\
+\hline
+\Axiom       &amp; simplify(e) \OR\ normalize(e) \OR\ complexNormalize(e) \\
+\Derive      &amp; e                                                      \\
+\DoCon       &amp; \\
+\GAP         &amp; e \\
+\Gmp         &amp; \\
+\Macsyma     &amp; ratsimp(e) \OR\ radcan(e)                              \\
+\Magnus      &amp; \\
+\Maxima      &amp; ratsimp(e) \OR\ radcan(e)                              \\
+\Maple       &amp; simplify(e)                                            \\
+\Mathematica &amp; Simplify[e] \OR\ FullSimplify[e]                       \\
+\MuPAD       &amp; simplify(e) \OR\ normal(e)                             \\
+\Octave      &amp; \\
+\Pari        &amp; \\
+\Reduce      &amp; e                                                      \\
+\Scilab      &amp; \\
+\Sumit       &amp; \\
+\Yacas       &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|ll}
+&amp; \h{Use an unknown function} &amp; \h{Numerically evaluate an expr.} \\
+\hline
+\Axiom       &amp; f:= operator('f); \q f(x) &amp; exp(1) :: Complex Float \\
+\Derive      &amp; f(x):=                    &amp; Precision:= Approximate \\
+             &amp; f(x)                      &amp; APPROX(EXP(1)) \\
+             &amp;                           &amp; Precision:= Exact \\
+\DoCon       &amp;                           &amp; \\
+\GAP         &amp;                           &amp; EvalF(123/456)\\
+\Gmp         &amp;                           &amp; \\
+\Macsyma     &amp; f(x)                      &amp; sfloat(exp(1)); \\
+\Magnus      &amp;                           &amp; \\
+\Maxima      &amp; f(x)                      &amp; sfloat(exp(1)); \\
+\Maple       &amp; f(x)                      &amp; evalf(exp(1)); \\
+\Mathematica &amp; f[x]                      &amp; N[Exp[1]] \\
+\MuPAD       &amp; f(x)                      &amp; float(exp(1)); \\
+\Octave      &amp;                           &amp; \\
+\Pari        &amp;                           &amp; \\
+\Reduce      &amp; operator f; \q f(x)       &amp; on rounded; \q exp(1); \\
+             &amp;                           &amp; off rounded; \\
+\Scilab      &amp;                           &amp; \\
+\Sumit       &amp;                           &amp; \\
+\Yacas       &amp;                           &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|ll}
+&amp; $ n \bmod m$ &amp; \h{Solve $e \equiv 0 \bmod m$ for $x$} \\
+\hline
+\Axiom       &amp; rem(n, m)       &amp; solve(e = 0 :: PrimeField(m), x)        \\
+\Derive      &amp; MOD(n, m)       &amp; SOLVE\_\,MOD(e = 0, x, m)               \\
+\DoCon       &amp;                 &amp; \\
+\GAP         &amp; n mod m         &amp; \h{solve using finite fields}\\
+\Gmp         &amp;                 &amp; \\
+\Macsyma     &amp; mod(n, m)       &amp; modulus: m\$ \q solve(e = 0, x)         \\
+\Magnus      &amp;                 &amp; \\
+\Maxima      &amp; mod(n, m)       &amp; modulus: m\$ \q solve(e = 0, x)         \\
+\Maple       &amp; n mod m         &amp; msolve(e = 0, m)                        \\
+\Mathematica &amp; Mod[n, m]       &amp; Solve[\{e == 0, Modulus == m\}, x]      \\
+\MuPAD       &amp; n mod m         &amp; solve(poly(e = 0, [x], IntMod(m)), x)   \\
+\Octave      &amp;                 &amp; \\
+\Pari        &amp;                 &amp; \\
+\Reduce      &amp; on modular;     &amp; load\_\,package(modsr)\$ \q on modular; \\
+             &amp; setmod m\$ \q n &amp; setmod m\$ \q m\_solve(e = 0, x)        \\
+\Scilab      &amp;                 &amp; \\
+\Sumit       &amp;                 &amp; \\
+\Yacas       &amp;                 &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|ll}
+&amp; \h{Put over common denominator} &amp; \h{Expand into separate fractions} \\
+\hline
+\Axiom       &amp; a/b + c/d                  &amp; (a*d + b*c)/(b*d) :: \_      \\
+             &amp;                            &amp; \q MPOLY([a], FRAC POLY INT) \\
+\Derive      &amp; FACTOR(a/b + c/d, Trivial) &amp; EXPAND((a*d + b*c)/(b*d))    \\
+\DoCon       &amp;                            &amp; \\
+\GAP         &amp; a/b+c/d                    &amp;\\
+\Gmp         &amp;                            &amp; \\
+\Macsyma     &amp; xthru(a/b + c/d)           &amp; expand((a*d + b*c)/(b*d))    \\
+\Magnus      &amp;                            &amp; \\
+\Maxima      &amp; xthru(a/b + c/d)           &amp; expand((a*d + b*c)/(b*d))    \\
+\Maple       &amp; normal(a/b + c/d)          &amp; expand((a*d + b*c)/(b*d))    \\
+\Mathematica &amp; Together[a/b + c/d]        &amp; Apart[(a*d + b*c)/(b*d)]     \\
+\MuPAD       &amp; normal(a/b + c/d)          &amp; expand((a*d + b*c)/(b*d))    \\
+\Octave      &amp;                            &amp; \\
+\Pari        &amp;                            &amp; \\
+\Reduce      &amp; a/b + c/d                  &amp; on div;  (a*d + b*c)/(b*d)   \\
+\Scilab      &amp;                            &amp; \\
+\Sumit       &amp;                            &amp; \\
+\Yacas       &amp;                            &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|l}
+&amp; \h{Manipulate the root of a polynomial} \\
+\hline
+\Axiom       &amp; a:= rootOf(x**2 - 2); \q a**2                               \\
+\Derive      &amp; \\
+\DoCon       &amp; \\
+\GAP         &amp; x:=X(Rationals,"x");\\
+&amp;\q a:=RootOfDefiningPolynomial(AlgebraicExtension(Rationals,x\^{}2-2));
+a\^{}2\\
+\Gmp         &amp; \\
+\Macsyma     &amp; algebraic:true\$ \q tellrat(a\^{}2 - 2)\$ \q rat(a\^{}2);   \\
+\Magnus      &amp; \\
+\Maxima      &amp; algebraic:true\$ \q tellrat(a\^{}2 - 2)\$ \q rat(a\^{}2);   \\
+\Maple       &amp; a:= RootOf(x\^{}2 - 2): \q simplify(a\^{}2);                \\
+\Mathematica &amp; a = Root[\#\^{}2 - 2 \&amp;, 2] \q a\^{}2                       \\
+\MuPAD       &amp; \\
+\Octave      &amp; \\
+\Pari        &amp; \\
+\Reduce      &amp; load\_\,package(arnum)\$ \q defpoly(a\^{}2 - 2); \q a\^{}2; \\
+\Scilab      &amp; \\
+\Sumit       &amp; \\
+\Yacas       &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|ll}
+&amp; \h{Noncommutative multiplication} &amp; \h{Solve a pair of equations} \\
+\hline
+\Axiom       &amp;                      &amp; solve([eqn1, eqn2], [x, y])     \\
+\Derive      &amp; x :epsilon Nonscalar &amp; SOLVE([eqn1, eqn2], [x, y])     \\
+             &amp; y :epsilon Nonscalar &amp; \\
+             &amp; x . y                &amp; \\
+\DoCon       &amp;                      &amp; \\
+\GAP         &amp;*&amp;\\
+\Gmp         &amp;                      &amp; \\
+\Macsyma     &amp; x . y                &amp; solve([eqn1, eqn2], [x, y])     \\
+\Magnus      &amp;                      &amp; \\
+\Maxima      &amp; x . y                &amp; solve([eqn1, eqn2], [x, y])     \\
+\Maple       &amp; x \&amp;* y              &amp; solve(\{eqn1, eqn2\}, \{x, y\}) \\
+\Mathematica &amp; x ** y               &amp; Solve[\{eqn1, eqn2\}, \{x, y\}] \\
+\MuPAD       &amp;                      &amp; solve(\{eqn1, eqn2\}, \{x, y\}) \\
+\Octave      &amp;                      &amp; \\
+\Pari        &amp;                      &amp; \\
+\Reduce      &amp; operator x, y;       &amp; solve(\{eqn1, eqn2\}, \{x, y\}) \\
+             &amp; noncom x, y;         &amp; \\
+             &amp; x() * y()            &amp; \\
+\Scilab      &amp;                      &amp; \\
+\Sumit       &amp;                      &amp; \\
+\Yacas       &amp;                      &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|ll}
+&amp; \m{2}{\rm Decrease/increase angles in trigonometric functions} \\
+\hline
+\Axiom       &amp; \m{2}{simplify(normalize(sin(2*x)))} \\
+\Derive      &amp; Trigonometry:= Expand         &amp; Trigonometry:= Collect      \\
+             &amp; sin(2*x)                      &amp; 2*sin(x)*cos(x)             \\
+\DoCon       &amp;                               &amp; \\
+\GAP         &amp;                               &amp; \\
+\Gmp         &amp;                               &amp; \\
+\Macsyma     &amp; trigexpand(sin(2*x))          &amp; trigreduce(2*sin(x)*cos(x)) \\
+\Magnus      &amp;                               &amp; \\
+\Maxima      &amp; trigexpand(sin(2*x))          &amp; trigreduce(2*sin(x)*cos(x)) \\
+\Maple       &amp; expand(sin(2*x))              &amp; combine(2*sin(x)*cos(x))    \\
+\Mathematica &amp; TrigExpand[Sin[2*x]]          &amp; TrigReduce[2*Sin[x]*Cos[x]] \\
+\MuPAD       &amp; expand(sin(2*x))              &amp; combine(2*sin(x)*cos(x), sincos)
+	\\
+\Octave      &amp;                               &amp; \\
+\Pari        &amp;                               &amp; \\
+\Reduce      &amp; load\_\,package(assist)\$ \\
+             &amp; trigexpand(sin(2*x))          &amp; trigreduce(2*sin(x)*cos(x)) \\
+\Scilab      &amp;                               &amp; \\
+\Sumit       &amp;                               &amp; \\
+\Yacas       &amp;                               &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|l}
+&amp; \h{Gr\"obner basis} \\
+\hline
+\Axiom       &amp; groebner([p1, p2, ...])                                  \\
+\Derive      &amp; \\
+\DoCon       &amp; \\
+\GAP         &amp; \\
+\Gmp         &amp; \\
+\Macsyma     &amp; grobner([p1, p2, ...]) \\
+\Magnus      &amp; \\
+\Maxima      &amp; grobner([p1, p2, ...]) \\
+\Maple       &amp; Groebner[gbasis]([p1, p2, ...], plex(x1, x2, ...))       \\
+\Mathematica &amp; GroebnerBasis[\{p1, p2, ...\}, \{x1, x2, ...\}]          \\
+\MuPAD       &amp; groebner::gbasis([p1, p2, ...])                          \\
+\Octave      &amp; \\
+\Pari        &amp; \\
+\Reduce      &amp; load\_\,package(groebner)\$ \q groebner(\{p1, p2, ...\}) \\
+\Scilab      &amp; \\
+\Sumit       &amp; \\
+\Yacas       &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|l}
+&amp; \h{Factorization of $e$ over $i = \sqrt{-1}$} \\
+\hline
+\Axiom       &amp; factor(e, [rootOf(i**2 + 1)]) \\
+\Derive      &amp; FACTOR(e, Complex) \\
+\DoCon       &amp; \\
+\GAP         &amp; Factors(GaussianIntegers,e)\\
+\Gmp         &amp; \\
+\Macsyma     &amp; gfactor(e); \OR\ factor(e, i\^{}2 + 1); \\
+\Magnus      &amp; \\
+\Maxima      &amp; gfactor(e); \OR\ factor(e, i\^{}2 + 1); \\
+\Maple       &amp; factor(e, I); \\
+\Mathematica &amp; Factor[e, Extension -&gt; I] \\
+\MuPAD       &amp; QI:= Dom::AlgebraicExtension(Dom::Rational, i\^{}2 + 1); \\
+             &amp; QI::name:= "QI": \q Factor(poly(e, QI)); \\
+\Octave      &amp; \\
+\Pari        &amp; \\
+\Reduce      &amp; on complex, factor; \q e; \q off complex, factor; \\
+\Scilab      &amp; \\
+\Sumit       &amp; \\
+\Yacas       &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|ll}
+&amp; \h{Real part} &amp; \h{Convert a complex expr.\ to rectangular form} \\
+\hline
+\Axiom       &amp; real(f(z))     &amp; complexForm(f(z))             \\
+\Derive      &amp; RE(f(z))       &amp; f(z)                          \\
+\DoCon       &amp;                &amp; \\
+\GAP         &amp; (f(z)+GaloisCyc(f(z),-1))/2&amp;\\
+\Gmp         &amp;                &amp; \\
+\Macsyma     &amp; realpart(f(z)) &amp; rectform(f(z))                \\
+\Magnus      &amp;                &amp; \\
+\Maxima      &amp; realpart(f(z)) &amp; rectform(f(z))                \\
+\Maple       &amp; Re(f(z))       &amp; evalc(f(z))                   \\
+\Mathematica &amp; Re[f[z]]       &amp; ComplexExpand[f[z]]           \\
+\MuPAD       &amp; Re(f(z))       &amp; rectform(f(z))                \\
+\Octave      &amp;                &amp; \\
+\Pari        &amp;                &amp; \\
+\Reduce      &amp; repart(f(z))   &amp; repart(f(z)) + i*impart(f(z)) \\
+\Scilab      &amp;                &amp; \\
+\Sumit       &amp;                &amp; \\
+\Yacas       &amp;                &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|lll}
+&amp; \h{Matrix addition} &amp; \h{Matrix multiplication} &amp; \h{Matrix transpose} \\
+\hline
+\Axiom       &amp; A + B        &amp; A * B          &amp; transpose(A)         \\
+\Derive      &amp; A + B        &amp; A . B          &amp; A\`{}                \\
+\DoCon       &amp;              &amp;                &amp; \\
+\GAP         &amp; A + B        &amp; A * B          &amp; TransposedMat(A)\\
+\Gmp         &amp;              &amp;                &amp; \\
+\Macsyma     &amp; A + B        &amp; A . B          &amp; transpose(A)         \\
+\Magnus      &amp;              &amp;                &amp; \\
+\Maxima      &amp; A + B        &amp; A . B          &amp; transpose(A)         \\
+\Maple       &amp; evalm(A + B) &amp; evalm(A \&amp;* B) &amp; linalg[transpose](A) \\
+\Mathematica &amp; A + B        &amp; A . B          &amp; Transpose[A]         \\
+\MuPAD       &amp; A + B        &amp; A * B          &amp; transpose(A)         \\
+\Octave      &amp;              &amp;                &amp; \\
+\Pari        &amp;              &amp;                &amp; \\
+\Reduce      &amp; A + B        &amp; A * B          &amp; tp(A)                \\
+\Scilab      &amp;              &amp;                &amp; \\
+\Sumit       &amp;              &amp;                &amp; \\
+\Yacas       &amp;              &amp;                &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|l}
+&amp; \h{Solve the matrix equation $A x = b$} \\
+\hline
+\Axiom       &amp; solve(A, transpose(b)) . 1 . particular :: Matrix \_\_\_ \\
+\Derive      &amp; \\
+\DoCon       &amp; \\
+\GAP         &amp; SolutionMat(TransposedMat(A),b)\\
+\Gmp         &amp; \\
+\Macsyma     &amp; xx: genvector('x, mat\_nrows(b))\$                       \\
+             &amp; x: part(matlinsolve(A . xx = b, xx), 1, 2)               \\
+\Magnus      &amp; \\
+\Maxima      &amp; xx: genvector('x, mat\_nrows(b))\$                       \\
+             &amp; x: part(matlinsolve(A . xx = b, xx), 1, 2)               \\
+\Maple       &amp; x:= linalg[linsolve](A, b)                               \\
+\Mathematica &amp; x = LinearSolve[A, b]                                    \\
+\MuPAD       &amp; \\
+\Octave      &amp; \\
+\Pari        &amp; \\
+\Reduce      &amp; \\
+\Scilab      &amp; \\
+\Sumit       &amp; \\
+\Yacas       &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|ll}
+&amp; \h{Sum: $\sum_{i = 1}^n f(i)$} &amp; \h{Product: $\prod_{i = 1}^n f(i)$} \\
+\hline
+\Axiom       &amp; sum(f(i), i = 1..n)    &amp; product(f(i), i = 1..n)    \\
+\Derive      &amp; SUM(f(i), i, 1, n)     &amp; PRODUCT(f(i), i, 1, n)     \\
+\DoCon       &amp;                        &amp; \\
+\GAP         &amp; Sum([1..n],f)          &amp; Product([1..n],f)\\
+\Gmp         &amp;                        &amp; \\
+\Macsyma     &amp; closedform(            &amp; closedform(                \\
+             &amp; \q sum(f(i), i, 1, n)) &amp; \q product(f(i), i, 1, n)) \\
+\Magnus      &amp;                        &amp; \\
+\Maxima      &amp; closedform(            &amp; closedform(                \\
+             &amp; \q sum(f(i), i, 1, n)) &amp; \q product(f(i), i, 1, n)) \\
+\Maple       &amp; sum(f(i), i = 1..n)    &amp; product(f(i), i = 1..n)    \\
+\Mathematica &amp; Sum[f[i], \{i, 1, n\}] &amp; Product[f[i], \{i, 1, n\}] \\
+\MuPAD       &amp; sum(f(i), i = 1..n)    &amp; product(f(i), i = 1..n)    \\
+\Octave      &amp;                        &amp; \\
+\Pari        &amp;                        &amp; \\
+\Reduce      &amp; sum(f(i), i, 1, n)     &amp; prod(f(i), i, 1, n)        \\
+\Scilab      &amp;                        &amp; \\
+\Sumit       &amp;                        &amp; \\
+\Yacas       &amp;                        &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|ll}
+&amp; \h{Limit: $\lim_{x \rightarrow 0-} f(x)$} &amp; \h{Taylor/Laurent/etc.\ series} \\
+\hline
+\Axiom       &amp; limit(f(x), x = 0, "left")      &amp; series(f(x), x = 0, 3)   \\
+\Derive      &amp; LIM(f(x), x, 0, -1)             &amp; TAYLOR(f(x), x, 0, 3)    \\
+\DoCon       &amp;                                 &amp; \\
+\GAP         &amp;                                 &amp; \\
+\Gmp         &amp;                                 &amp; \\
+\Macsyma     &amp; limit(f(x), x, 0, minus)        &amp; taylor(f(x), x, 0, 3)    \\
+\Magnus      &amp;                                 &amp; \\
+\Maxima      &amp; limit(f(x), x, 0, minus)        &amp; taylor(f(x), x, 0, 3)    \\
+\Maple       &amp; limit(f(x), x = 0, left)        &amp; series(f(x), x = 0, 4)   \\
+\Mathematica &amp; Limit[f[x], x-&gt;0, Direction-&gt;1] &amp; Series[f[x],\{x, 0, 3\}] \\
+\MuPAD       &amp; limit(f(x), x = 0, Left)        &amp; series(f(x), x = 0, 4)   \\
+\Octave      &amp;                                 &amp; \\
+\Pari        &amp;                                 &amp; \\
+\Reduce      &amp; limit!-(f(x), x, 0)             &amp; taylor(f(x), x, 0, 3)    \\
+\Scilab      &amp;                                 &amp; \\
+\Sumit       &amp;                                 &amp; \\
+\Yacas       &amp;                                 &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|ll}
+&amp; \h{Differentiate: $\frac{d^3 f(x, y)}{dx \, dy^2}$} &amp;
+	\h{Integrate: $\int_0^1 f(x) \, dx$} \\
+\hline
+\Axiom       &amp; D(f(x, y), [x, y], [1, 2]) &amp; integrate(f(x), x = 0..1)    \\
+\Derive      &amp; DIF(DIF(f(x, y), x), y, 2) &amp; INT(f(x), x, 0, 1)           \\
+\DoCon       &amp;                            &amp; \\
+\GAP         &amp;                            &amp; \\
+\Gmp         &amp;                            &amp; \\
+\Macsyma     &amp; diff(f(x, y), x, 1, y, 2)  &amp; integrate(f(x), x, 0, 1)     \\
+\Magnus      &amp;                            &amp; \\
+\Maxima      &amp; diff(f(x, y), x, 1, y, 2)  &amp; integrate(f(x), x, 0, 1)     \\
+\Maple       &amp; diff(f(x, y), x, y\$2)     &amp; int(f(x), x = 0..1)          \\
+\Mathematica &amp; D[f[x, y], x, \{y, 2\}]    &amp; Integrate[f[x], \{x, 0, 1\}] \\
+\MuPAD       &amp; diff(f(x, y), x, y\$2)     &amp; int(f(x), x = 0..1)          \\
+\Octave      &amp;                            &amp; \\
+\Pari        &amp;                            &amp; \\
+\Reduce      &amp; df(f(x, y), x, y, 2)       &amp; int(f(x), x, 0, 1)           \\
+\Scilab      &amp;                            &amp; \\
+\Sumit       &amp;                            &amp; \\
+\Yacas       &amp;                            &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|ll}
+&amp; \h{Laplace transform} &amp; \h{Inverse Laplace transform} \\
+\hline
+\Axiom       &amp; laplace(e, t, s)          &amp; inverseLaplace(e, s, t)        \\
+\Derive      &amp; LAPLACE(e, t, s)          &amp; \\
+\DoCon       &amp;                           &amp; \\
+\GAP         &amp;                           &amp; \\
+\Gmp         &amp;                           &amp; \\
+\Macsyma     &amp; laplace(e, t, s)          &amp; ilt(e, s, t)                   \\
+\Magnus      &amp;                           &amp; \\
+\Maxima      &amp; laplace(e, t, s)          &amp; ilt(e, s, t)                   \\
+\Maple       &amp; inttrans[laplace](e,t,s)  &amp; inttrans[invlaplace](e,s,t)    \\
+\Mathematica &amp; \m{2}{\q @&lt;&lt; Calculus\`{}LaplaceTransform\`{}} \\
+             &amp; LaplaceTransform[e, t, s] &amp; {\st InverseLaplaceTransform[e,s,t]}
+	\\
+\MuPAD       &amp; transform::laplace(e,t,s) &amp; transform::ilaplace(e, s, t)   \\
+\Octave      &amp;                           &amp; \\
+\Pari        &amp;                           &amp; \\
+\Reduce      &amp; \m{2}{\q load\_\,package(laplace)\$ \q load\_\,package(defint)\$}
+	\\
+             &amp; laplace(e, t, s)          &amp; invlap(e, t, s)                \\
+\Scilab      &amp;                           &amp; \\
+\Sumit       &amp;                           &amp; \\
+\Yacas       &amp;                           &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|l}
+&amp; \h{Solve an ODE (with the initial condition $y'(0) = 1$)} \\
+\hline
+\Axiom       &amp; solve(eqn, y, x)                                      \\
+\Derive      &amp; APPLY\_\,IC(RHS(ODE(eqn, x, y, y\_)), [x, 0], [y, 1]) \\
+\DoCon       &amp; \\
+\GAP         &amp; \\
+\Gmp         &amp; \\
+\Macsyma     &amp; ode\_ibc(ode(eqn, y(x), x), x = 0, diff(y(x), x) = 1) \\
+\Magnus      &amp; \\
+\Maxima      &amp; ode\_ibc(ode(eqn, y(x), x), x = 0, diff(y(x), x) = 1) \\
+\Maple       &amp; dsolve(\{eqn, D(y)(0) = 1\}, y(x))                    \\
+\Mathematica &amp; DSolve[\{eqn, y'[0] == 1\}, y[x], x]                  \\
+\MuPAD       &amp; solve(ode(\{eqn, D(y)(0) = 1\}, y(x)))                \\
+\Octave      &amp; \\
+\Pari        &amp; \\
+\Reduce      &amp; odesolve(eqn, y(x), x)                                \\
+\Scilab      &amp; \\
+\Sumit       &amp; \\
+\Yacas       &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|l}
+&amp; \h{Define the differential operator $L = D_x + I$ and apply it to $\sin x$} \\
+\hline
+\Axiom       &amp; DD : LODO(Expression Integer, e +-&gt; D(e, x)) := D(); \\
+             &amp; L:= DD + 1; \q L(sin(x))                             \\
+\Derive      &amp; \\
+\DoCon       &amp; \\
+\GAP         &amp; \\
+\Gmp         &amp; \\
+\Macsyma     &amp; load(opalg)\$ \q L: (diffop(x) - 1)\$ \q L(sin(x));  \\
+\Magnus      &amp; \\
+\Maxima      &amp; load(opalg)\$ \q L: (diffop(x) - 1)\$ \q L(sin(x));  \\
+\Maple       &amp; id:= x -&gt; x: \q L:= (D + id): \q L(sin)(x);          \\
+\Mathematica &amp; L = D[\#, x]\&amp; + Identity; \q Through[L[Sin[x]]]     \\
+\MuPAD       &amp; L:= (D + id): \q L(sin)(x);                          \\
+\Octave      &amp; \\
+\Pari        &amp; \\
+\Reduce      &amp; \\
+\Scilab      &amp; \\
+\Sumit       &amp; \\
+\Yacas       &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|l}
+&amp; \h{2D plot of two separate curves overlayed} \\
+\hline
+\Axiom       &amp; draw(x, x = 0..1); \q draw(acsch(x), x = 0..1);           \\
+\Derive      &amp; [Plot Overlay]                                            \\
+\DoCon       &amp; \\
+\GAP         &amp; \\
+\Gmp         &amp; \\
+\Macsyma     &amp; plot(x, x, 0, 1)\$ \q plot(acsch(x), x, 0, 1)\$           \\
+\Magnus      &amp; \\
+\Maxima      &amp; plot(x, x, 0, 1)\$ \q plot(acsch(x), x, 0, 1)\$           \\
+\Maple       &amp; plot(\{x, arccsch(x)\}, x = 0..1):                        \\
+\Mathematica &amp; Plot[\{x, ArcCsch[x]\}, \{x, 0, 1\}];                     \\
+\MuPAD       &amp; plotfunc(x, acsch(x), x = 0..1):                          \\
+\Octave      &amp; \\
+\Pari        &amp; \\
+\Reduce      &amp; load\_\,package(gnuplot)\$ \q plot(y = x, x = (0 .. 1))\$ \\
+             &amp; plot(y = acsch(x), x = (0 .. 1))\$                        \\
+\Scilab      &amp; \\
+\Sumit       &amp; \\
+\Yacas       &amp; \\
+\end{tabular} \\[10pt]
+
+\begin{tabular}{l|l}
+&amp; \h{Simple 3D plotting} \\
+\hline
+\Axiom       &amp; draw(abs(x*y), x = 0..1, y = 0..1);              \\
+\Derive      &amp; [Plot Overlay]                                   \\
+\DoCon       &amp; \\
+\GAP         &amp; \\
+\Gmp         &amp; \\
+\Macsyma     &amp; plot3d(abs(x*y), x, 0, 1, y, 0, 1)\$             \\
+\Magnus      &amp; \\
+\Maxima      &amp; plot3d(abs(x*y), x, 0, 1, y, 0, 1)\$             \\
+\Maple       &amp; plot3d(abs(x*y), x = 0..1, y = 0..1):            \\
+\Mathematica &amp; Plot3D[Abs[x*y], \{x, 0, 1\}, \{y, 0, 1\}];      \\
+\MuPAD       &amp; plotfunc(abs(x*y), x = 0..1, y = 0..1):          \\
+\Octave      &amp; \\
+\Pari        &amp; \\
+\Reduce      &amp; load\_\,package(gnuplot)\$                       \\
+             &amp; plot(z = abs(x*y), x = (0 .. 1), y = (0 .. 1))\$ \\
+\Scilab      &amp; \\
+\Sumit       &amp; \\
+\Yacas       &amp; \\
+\end{tabular} \\[10pt]
+
+%\begin{tabular}{l|l}
+%&amp; \h{} \\
+%\hline
+%\Axiom       &amp; \\
+%\Derive      &amp; \\
+%\DoCon       &amp; \\
+%\GAP         &amp; \\
+%\Gmp         &amp; \\
+%\Macsyma     &amp; \\
+%\Magnus      &amp; \\
+%\Maxima      &amp; \\
+%\Maple       &amp; \\
+%\Mathematica &amp; \\
+%\MuPAD       &amp; \\
+%\Octave      &amp; \\
+%\Pari        &amp; \\
+%\Reduce      &amp; \\
+%\Scilab      &amp; \\
+%\Sumit       &amp; \\
+%\Yacas       &amp; \\
+%\end{tabular} \\[10pt]
+
+\end{tt}
+\endgroup
+\end{document}
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+&lt;html&gt;
+ &lt;head&gt;
+  &lt;title&gt;
+   Axiom Computer Algebra System
+  &lt;/title&gt;
+ &lt;/head&gt;
+ &lt;body bgcolor="#ffff66"&gt;
+   &lt;div id="head" align="center"&gt; 
+    &lt;a href="http://savannah.nongnu.org/projects/axiom/"&gt;
+     &lt;img src="axiom.png" border="0" alt="Axiom"&gt;
+    &lt;/a&gt;
+    &lt;br&gt;
+    &lt;font size=200%&gt;
+     The Scientific Computation System
+    &lt;/font&gt;
+   &lt;/div&gt;
+   &lt;div align="center"&gt;
+    [
+     &lt;a href="../index.html" title="Home"&gt;
+      Home
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="screenshots.html" title="Screen Shots"&gt;
+      Screenshots
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="faq.html" title="FAQ"&gt;
+      FAQ
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="download.html" title="Download"&gt;
+      Download
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="documentation.html" title="Documentation"&gt;
+      Documentation
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="currentstate.html" title="Current State"&gt;
+      Current State
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="community.html" title="Community"&gt;
+      Community
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="developers.html" title="Developers"&gt;
+      Developers
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="patches.html" title="Patches"&gt;
+      Patches
+     &lt;/a&gt;
+    ]
+   &lt;/div&gt;
+   &lt;div align="center"&gt;
+    [
+     &lt;a href="bookvol10.2abb.html" title="Abbreviation Graph"&gt;
+      Abbreviation Graph
+     &lt;/a&gt;
+    ]
+    &amp;nbsp
+    [
+     &lt;a href="bookvol10.2full.html" title="Full Name Graph"&gt;
+      Full Name Graph
+     &lt;/a&gt;
+    ]
+   &lt;/div&gt;
+  &lt;br&gt;
+  &lt;hr&gt;
+
+&lt;div id="body"&gt;
+
+ &lt;ul&gt;
+
+ &lt;li&gt;
+ &lt;p&gt;
+ &lt;font size=5&gt;
+  Some computations. An important thing: everything is
+  &lt;em&gt;mathematically typed&lt;/em&gt; in Axiom. 
+ &lt;/font&gt;
+ &lt;br&gt;
+  &lt;pre&gt;
+(1) -&gt; 1+1
+
+   (1)  2
+                                                        Type: PositiveInteger
+(2) -&gt; integrate(1/x^(1/3),x)
+
+         3+-+2
+        3\|x
+   (2)  ------
+           2
+                                          Type: Union(Expression Integer,...)
+  &lt;/pre&gt;
+ &lt;/p&gt;
+ &lt;/li&gt;
+
+ &lt;li&gt;
+ &lt;p&gt;
+ &lt;font size=5&gt;
+  Some matrix computations under &lt;a
+ href="http://texmacs.org/"&gt;TeXmacs&lt;/a&gt;. Please notice the hierarchical
+ editing capabilities of TeXmacs. 
+ &lt;/font&gt;
+ &lt;br&gt;
+ &lt;br&gt;
+ &lt;br&gt;
+ &lt;img src="screenshot3.png"&gt; &lt;br/&gt;
+ &lt;/p&gt;
+ &lt;/li&gt;
+
+ &lt;li&gt;
+ &lt;p&gt;
+ &lt;font size=5&gt;
+  Some more complicated computations:
+ &lt;/font&gt;
+ &lt;br&gt;
+ &lt;br&gt;
+ &lt;pre&gt;
+)cl all
+ 
+   All user variables and function definitions have been cleared.
+
+Word := OrderedFreeMonoid(Symbol)
+ 
+
+   (1)  OrderedFreeMonoid Symbol
+                                                                 Type: Domain
+poly:= XPR(Integer,Word)
+ 
+
+   (2)  XPolynomialRing(Integer,OrderedFreeMonoid Symbol)
+                                                                 Type: Domain
+p:poly := 2 * x - 3 * y + 1
+ 
+
+   (3)  1 + 2x - 3y
+                      Type: XPolynomialRing(Integer,OrderedFreeMonoid Symbol)
+q:poly := 2 * x + 1
+ 
+
+   (4)  1 + 2x
+                      Type: XPolynomialRing(Integer,OrderedFreeMonoid Symbol)
+p + q
+ 
+
+   (5)  2 + 4x - 3y
+                      Type: XPolynomialRing(Integer,OrderedFreeMonoid Symbol)
+p * q
+ 
+
+                        2
+   (6)  1 + 4x - 3y + 4x  - 6y x
+                      Type: XPolynomialRing(Integer,OrderedFreeMonoid Symbol)
+(p +q)^2 -p^2 -q^2 - 2*p*q
+ 
+
+   (7)  - 6x y + 6y x
+                      Type: XPolynomialRing(Integer,OrderedFreeMonoid Symbol)
+M := SquareMatrix(2,Fraction Integer)
+ 
+
+   (8)  SquareMatrix(2,Fraction Integer)
+                                                                 Type: Domain
+poly1:= XPR(M,Word)
+ 
+
+   (9)
+   XPolynomialRing(SquareMatrix(2,Fraction Integer),OrderedFreeMonoid Symbol)
+                                                                 Type: Domain
+m1:M := matrix [[i*j**2 for i in 1..2] for j in 1..2]
+ 
+
+         +1  2+
+   (10)  |    |
+         +4  8+
+                                       Type: SquareMatrix(2,Fraction Integer)
+m2:M := m1 - 5/4
+ 
+
+         +  1    +
+         |- -  2 |
+         |  4    |
+   (11)  |       |
+         |     27|
+         | 4   --|
+         +      4+
+                                       Type: SquareMatrix(2,Fraction Integer)
+m3: M := m2**2
+ 
+
+         +129     +
+         |---  13 |
+         | 16     |
+   (12)  |        |
+         |     857|
+         |26   ---|
+         +      16+
+                                       Type: SquareMatrix(2,Fraction Integer)
+pm:poly1   := m1*x + m2*y + m3*z - 2/3
+ 
+
+         +  2     +             +  1    +    +129     +
+         |- -   0 |             |- -  2 |    |---  13 |
+         |  3     |   +1  2+    |  4    |    | 16     |
+   (13)  |        | + |    |x + |       |y + |        |z
+         |       2|   +4  8+    |     27|    |     857|
+         | 0   - -|             | 4   --|    |26   ---|
+         +       3+             +      4+    +      16+
+Type: XPolynomialRing(SquareMatrix(2,Fraction Integer),OrderedFreeMonoid Symbol)
+qm:poly1 := pm - m1*x
+ 
+
+         +  2     +   +  1    +    +129     +
+         |- -   0 |   |- -  2 |    |---  13 |
+         |  3     |   |  4    |    | 16     |
+   (14)  |        | + |       |y + |        |z
+         |       2|   |     27|    |     857|
+         | 0   - -|   | 4   --|    |26   ---|
+         +       3+   +      4+    +      16+
+Type: XPolynomialRing(SquareMatrix(2,Fraction Integer),OrderedFreeMonoid Symbol)
+qm**3
+ 
+
+   (15)
+     +   8      +   +  1  8+    +43   52 +    +  129       +
+     |- --   0  |   |- -  -|    |--   -- |    |- ---  - 26 |
+     |  27      |   |  3  3|    | 4    3 |    |   8        | 2
+     |          | + |      |y + |        |z + |            |y
+     |         8|   |16    |    |104  857|    |         857|
+     | 0    - --|   |--   9|    |---  ---|    |- 52   - ---|
+     +        27+   + 3    +    + 3    12+    +          8 +
+   + 
+     +  3199     831 +      +  3199     831 +      +  103169     6409 +
+     |- ----   - --- |      |- ----   - --- |      |- ------   - ---- |
+     |   32       4  |      |   32       4  |      |    128        4  | 2
+     |               |y z + |               |z y + |                  |z
+     |  831     26467|      |  831     26467|      |   6409     820977|
+     |- ---   - -----|      |- ---   - -----|      | - ----   - ------|
+     +   2        32 +      +   2        32 +      +     2        128 +
+   + 
+     +3199   831 +     +103169   6409 +      +103169   6409 +
+     |----   --- |     |------   ---- |      |------   ---- |
+     | 64     8  | 3   |  256      8  | 2    |  256      8  |
+     |           |y  + |              |y z + |              |y z y
+     |831   26467|     | 6409   820977|      | 6409   820977|
+     |---   -----|     | ----   ------|      | ----   ------|
+     + 4      64 +     +   4      256 +      +   4      256 +
+   + 
+     +3178239   795341 +       +103169   6409 +       +3178239   795341 +
+     |-------   ------ |       |------   ---- |       |-------   ------ |
+     |  1024      128  |   2   |  256      8  |   2   |  1024      128  |
+     |                 |y z  + |              |z y  + |                 |z y z
+     |795341   25447787|       | 6409   820977|       |795341   25447787|
+     |------   --------|       | ----   ------|       |------   --------|
+     +  64       1024  +       +   4      256 +       +  64       1024  +
+   + 
+     +3178239   795341 +      +98625409  12326223 +
+     |-------   ------ |      |--------  -------- |
+     |  1024      128  | 2    |  4096       256   | 3
+     |                 |z y + |                   |z
+     |795341   25447787|      |12326223  788893897|
+     |------   --------|      |--------  ---------|
+     +  64       1024  +      +   128       4096  +
+Type: XPolynomialRing(SquareMatrix(2,Fraction Integer),OrderedFreeMonoid Symbol)
+ &lt;/pre&gt;
+ &lt;/p&gt;
+ &lt;/li&gt;
+
+ &lt;/ul&gt;
+
+&lt;/div&gt;
+&lt;hr&gt;
+ &lt;font size=5&gt;
+Axiom is now running under Windows. This is a screenshot of Axiom
+running on Windows in a TeXmacs window:
+ &lt;/font&gt;
+&lt;br&gt;
+&lt;br&gt;
+&lt;img src="screenshot2.jpg"&gt;
+&lt;br&gt;
+
+&lt;/body&gt;
+&lt;/html&gt;
</pre></body></html>