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[Axiom-developer] 20080330.01.tpd.patch (CATS integration regression tes
|
From: |
daly |
|
Subject: |
[Axiom-developer] 20080330.01.tpd.patch (CATS integration regression testing) |
|
Date: |
Mon, 31 Mar 2008 00:08:49 -0600 |
More files for integration testing. These are an initial checkin of
the raw files. More CATS work needs to be done on each one.
Tim
========================================================================
diff --git a/changelog b/changelog
index c467da5..6b98774 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,14 @@
+20080330 tpd src/input/Makefile add integration regression testing
+20080330 tpd src/input/schaum11.input integrals of sqrt(a^2-x^2)
+20080330 tpd src/input/schaum10.input integrals of sqrt(x^2-a^2)
+20080330 tpd src/input/schaum9.input integrals of sqrt(x^2+a^2)
+20080330 tpd src/input/schaum8.input integrals of a^2-x^2, x^2<a^2
+20080330 tpd src/input/schaum7.input integrals of x^2-a^2, x^2>a^2
+20080330 tpd src/input/schaum6.input make regression testing uniform
+20080330 tpd src/input/schaum5.input make regression testing uniform
+20080330 tpd src/input/schaum4.input make regression testing uniform
+20080330 tpd src/input/schaum3.input make regression testing uniform
+20080330 tpd src/input/schaum2.input make regression testing uniform
20080328 tpd src/input/Makefile add integration regression testing
20080328 tpd src/input/schaum6.input integrals of x^2+a^2
20080328 tpd src/input/schaum5.input integrals of sqrt(ax+b) and sqrt(px+q)
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet
index d4caed2..a1382e4 100644
--- a/src/input/Makefile.pamphlet
+++ b/src/input/Makefile.pamphlet
@@ -356,7 +356,8 @@ REGRES= algaggr.regress algbrbf.regress algfacob.regress
alist.regress \
realclos.regress reclos.regress repa6.regress robidoux.regress \
roman.regress roots.regress ruleset.regress rules.regress \
schaum1.regress schaum2.regress schaum3.regress schaum4.regress \
- schaum5.regress schaum6.regress \
+ schaum5.regress schaum6.regress schaum7.regress schaum8.regress \
+ schaum9.regress schaum10.regress schaum11.regress \
scherk.regress scope.regress seccsc.regress \
segbind.regress seg.regress \
series2.regress series.regress sersolve.regress set.regress \
@@ -630,7 +631,9 @@ FILES= ${OUT}/algaggr.input ${OUT}/algbrbf.input
${OUT}/algfacob.input \
${OUT}/robidoux.input ${OUT}/roman.input ${OUT}/roots.input \
${OUT}/ruleset.input ${OUT}/rules.input ${OUT}/schaum1.input \
${OUT}/schaum2.input ${OUT}/schaum3.input ${OUT}/schaum4.input \
- ${OUT}/schaum5.input ${OUT}/schaum6.input \
+ ${OUT}/schaum5.input ${OUT}/schaum6.input ${OUT}/schaum7.input \
+ ${OUT}/schaum8.input ${OUT}/schaum9.input ${OUT}/schaum10.input \
+ ${OUT}/schaum11.input \
${OUT}/saddle.input \
${OUT}/scherk.input ${OUT}/scope.input ${OUT}/seccsc.input \
${OUT}/segbind.input ${OUT}/seg.input ${OUT}/series2.input \
@@ -932,6 +935,9 @@ DOCFILES= \
${DOC}/schaum1.input.dvi ${DOC}/schaum2.input.dvi \
${DOC}/schaum3.input.dvi ${DOC}/schaum4.input.dvi \
${DOC}/schaum5.input.dvi ${DOC}/schaum6.input.dvi \
+ ${DOC}/schaum7.input.dvi ${DOC}/schaum8.input.dvi \
+ ${DOC}/schaum9.input.dvi ${DOC}/schaum10.input.dvi \
+ ${DOC}/schaum11.input.dvi \
${DOC}/s01eaf.input.dvi ${DOC}/s13aaf.input.dvi \
${DOC}/s13acf.input.dvi ${DOC}/s13adf.input.dvi \
${DOC}/s14aaf.input.dvi ${DOC}/s14abf.input.dvi \
diff --git a/src/input/schaum10.input.pamphlet
b/src/input/schaum10.input.pamphlet
new file mode 100644
index 0000000..8582086
--- /dev/null
+++ b/src/input/schaum10.input.pamphlet
@@ -0,0 +1,757 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum10.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.210~~~~~$\displaystyle\int{\frac{dx}{\sqrt{x^2-a^2}}}$}
+$$\int{\frac{1}{\sqrt{x^2-a^2}}}=\ln\left(x+\sqrt{x^2-a^2}\right)$$
+<<*>>=
+)spool schaum10.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 28
+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
+@
+
+\section{\cite{1}:14.xxx~~~~~$\displaystyle\int{\frac{x~dx}{\sqrt{x^2-a^2}}}$}
+$$\int{\frac{x}{\sqrt{x^2-a^2}}}=\sqrt{x^2-a^2}$$
+<<*>>=
+)clear all
+
+--S 2 of 28
+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
+@
+
+\section{\cite{1}:14.211~~~~~$\displaystyle
+\int{\frac{x^2~dx}{\sqrt{x^2-a^2}}}$}
+$$\int{\frac{x^2}{\sqrt{x^2-a^2}}}=
+\frac{x\sqrt{x^2-a^2}}{2}+\frac{a^2}{2}\ln\left(x+\sqrt{x^2-a^2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 3 of 28
+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
+@
+
+\section{\cite{1}:14.212~~~~~$\displaystyle
+\int{\frac{x^3~dx}{\sqrt{x^2-a^2}}}$}
+$$\int{\frac{x^3}{\sqrt{x^2-a^2}}}=
+\frac{(x^2-a^2)^{3/2}}{3}+a^2\sqrt{x^2-a^2}
+$$
+<<*>>=
+)clear all
+
+--S 4 of 28
+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
+@
+
+\section{\cite{1}:14.213~~~~~$\displaystyle\int{\frac{dx}{x\sqrt{x^2-a^2}}}$}
+$$\int{\frac{1}{x\sqrt{x^2-a^2}}}=
+\frac{1}{a}\sec^{-1}\left|\frac{x}{a}\right|
+$$
+<<*>>=
+)clear all
+
+--S 5 of 28
+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
+@
+
+\section{\cite{1}:14.214~~~~~$\displaystyle
+\int{\frac{dx}{x^2\sqrt{x^2-a^2}}}$}
+$$\int{\frac{1}{x^2\sqrt{x^2-a^2}}}=
+\frac{\sqrt{x^2-a^2}}{a^2x}
+$$
+<<*>>=
+)clear all
+
+--S 6 of 28
+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
+@
+
+\section{\cite{1}:14.215~~~~~$\displaystyle\int{\frac{dx}{x^3\sqrt{x^2-a^2}}}$}
+$$\int{\frac{1}{x^3\sqrt{x^2-a^2}}}=
+-\frac{\sqrt{x^2-a^2}}{2a^2x^2}+\frac{1}{2a^3}
+\sec^{-1}\left|\frac{x}{a}\right|
+$$
+<<*>>=
+)clear all
+
+--S 7 of 28
+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
+@
+
+\section{\cite{1}:14.216~~~~~$\displaystyle\int{\sqrt{x^2-a^2}}~dx$}
+$$\int{\sqrt{x^2-a^2}}=
+\frac{x\sqrt{x^2-a^2}}{2}-\frac{a^2}{2}\ln\left(x+\sqrt{x^2-a^2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 8 of 28
+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
+@
+
+\section{\cite{1}:14.217~~~~~$\displaystyle\int{x\sqrt{x^2-a^2}}~dx$}
+$$\int{x\sqrt{x^2-a^2}}=
+\frac{(x^2-a^2)^{3/2}}{3}
+$$
+<<*>>=
+)clear all
+
+--S 9 of 28
+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
+@
+
+\section{\cite{1}:14.218~~~~~$\displaystyle
+\int{x^2\sqrt{x^2-a^2}}~dx$}
+$$\int{x^2\sqrt{x^2-a^2}}=
+\frac{x(x^2-a^2)^{3/2}}{4}+\frac{a^2x\sqrt{x^2-a^2}}{8}-
+\frac{a^4}{8}\ln\left(x+\sqrt{x^2-a^2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 10 of 28
+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
+@
+
+\section{\cite{1}:14.219~~~~~$\displaystyle
+\int{x^3\sqrt{x^2-a^2}}~dx$}
+$$\int{x^3\sqrt{x^2-a^2}}=
+\frac{(x^2-a^2)^{5/2}}{5}+\frac{a^2(x^2-a^2)^{3/2}}{3}
+$$
+<<*>>=
+)clear all
+
+--S 11 of 28
+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
+@
+
+\section{\cite{1}:14.220~~~~~$\displaystyle
+\int{\frac{\sqrt{x^2-a^2}}{x}}~dx$}
+$$\int{\frac{\sqrt{x^2-a^2}}{x}}=
+\sqrt{x^2-a^2}-a\sec^{-1}\left|\frac{x}{a}\right|
+$$
+<<*>>=
+)clear all
+
+--S 12 of 28
+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
+@
+
+\section{\cite{1}:14.221~~~~~$\displaystyle
+\int{\frac{\sqrt{x^2-a^2}}{x^2}}~dx$}
+$$\int{\frac{\sqrt{x^2-a^2}}{x^2}}=
+-\frac{\sqrt{x^2-a^2}}{x}+\ln\left(x+\sqrt{x^2-a^2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 13 of 28
+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
+@
+
+\section{\cite{1}:14.222~~~~~$\displaystyle
+\int{\frac{\sqrt{x^2-a^2}}{x^3}}~dx$}
+$$\int{\frac{\sqrt{x^2-a^2}}{x^3}}=
+-\frac{\sqrt{x^2-a^2}}{2x^2}+\frac{1}{2a}
+\sec^{-1}\left|\frac{x}{a}\right|
+$$
+<<*>>=
+)clear all
+
+--S 14 of 28
+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
+@
+
+\section{\cite{1}:14.223~~~~~$\displaystyle\int{\frac{dx}{(x^2-a^2)^{3/2}}}$}
+$$\int{\frac{1}{(x^2-a^2)^{3/2}}}=
+-\frac{x}{a^2\sqrt{x^2-a^2}}
+$$
+<<*>>=
+)clear all
+
+--S 15 of 28
+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
+@
+
+\section{\cite{1}:14.224~~~~~$\displaystyle
+\int{\frac{x~dx}{(x^2-a^2)^{3/2}}}$}
+$$\int{\frac{x}{(x^2-a^2)^{3/2}}}=
+\frac{-1}{\sqrt{x^2-a^2}}
+$$
+<<*>>=
+)clear all
+
+--S 16 of 28
+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
+@
+
+\section{\cite{1}:14.225~~~~~$\displaystyle
+\int{\frac{x^2dx}{(x^2-a^2)^{3/2}}}$}
+$$\int{\frac{x^2}{(x^2-a^2)^{3/2}}}=
+\frac{-x}{\sqrt{x^2-a^2}}+\ln\left(x+\sqrt{x^2-a^2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 17 of 28
+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
+@
+
+\section{\cite{1}:14.226~~~~~$\displaystyle
+\int{\frac{x^3dx}{(x^2-a^2)^{3/2}}}$}
+$$\int{\frac{x^3}{(x^2-a^2)^{3/2}}}=
+\sqrt{x^2-a^2}-\frac{a^2}{\sqrt{x^2-a^2}}
+$$
+<<*>>=
+)clear all
+
+--S 18 of 28
+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
+@
+
+\section{\cite{1}:14.227~~~~~$\displaystyle
+\int{\frac{dx}{x(x^2-a^2)^{3/2}}}$}
+$$\int{\frac{1}{x(x^2-a^2)^{3/2}}}=
+\frac{-1}{a^2\sqrt{x^2-a^2}}-
+\frac{1}{a^3}\sec^{-1}\left|\frac{x}{a}\right|
+$$
+<<*>>=
+)clear all
+
+--S 19 of 28
+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
+@
+
+\section{\cite{1}:14.228~~~~~$\displaystyle
+\int{\frac{dx}{x^2(x^2-a^2)^{3/2}}}$}
+$$\int{\frac{1}{x^2(x^2-a^2)^{3/2}}}=
+-\frac{\sqrt{x^2-a^2}}{a^4x}-\frac{x}{a^4\sqrt{x^2-a^2}}
+$$
+<<*>>=
+)clear all
+
+--S 20 of 28
+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
+@
+
+\section{\cite{1}:14.229~~~~~$\displaystyle
+\int{\frac{dx}{x^3(x^2-a^2)^{3/2}}}$}
+$$\int{\frac{1}{x^3(x^2-a^2)^{3/2}}}=
+\frac{1}{2a^2x^2\sqrt{x^2-a^2}}-
+\frac{3}{2a^4\sqrt{x^2-a^2}}-
+\frac{3}{2a^5}\sec^{-1}\left|\frac{x}{a}\right|
+$$
+<<*>>=
+)clear all
+
+--S 21 of 28
+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
+@
+
+\section{\cite{1}:14.230~~~~~$\displaystyle\int{(x^2-a^2)^{3/2}}~dx$}
+$$\int{(x^2-a^2)^{3/2}}=
+\frac{x(x^2-a^2)^{3/2}}{4}-\frac{3a^2x\sqrt{x^2-a^2}}{8}+
+\frac{3}{8}a^4\ln\left(x+\sqrt{x^2-a^2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 22 of 28
+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
+@
+
+\section{\cite{1}:14.231~~~~~$\displaystyle\int{x(x^2-a^2)^{3/2}}~dx$}
+$$\int{x(x^2-a^2)^{3/2}}=\frac{(x^2-a^2)^{5/2}}{5}$$
+<<*>>=
+)clear all
+
+--S 23 of 28
+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
+@
+
+\section{\cite{1}:14.232~~~~~$\displaystyle\int{x^2(x^2-a^2)^{3/2}}~dx$}
+$$\int{x^2(x^2-a^2)^{3/2}}=
+\frac{x(x^2-a^2)^{5/2}}{6}+\frac{a^2x(x^2-a^2)^{3/2}}{24}-
+\frac{a^4x\sqrt{x^2-a^2}}{16}+
+\frac{a^6}{16}\ln\left(x+\sqrt{x^2-a^2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 24 of 28
+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
+@
+
+\section{\cite{1}:14.233~~~~~$\displaystyle\int{x^3(x^2-a^2)^{3/2}}~dx$}
+$$\int{x^3(x^2-a^2)^{3/2}}=
+\frac{(x^2-a^2)^{7/2}}{7}+\frac{a^2(x^2-a^2)^{5/2}}{5}
+$$
+<<*>>=
+)clear all
+
+--S 25 of 28
+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
+@
+
+\section{\cite{1}:14.234~~~~~$\displaystyle
+\int{\frac{(x^2-a^2)^{3/2}}{x}}~dx$}
+$$\int{\frac{(x^2-a^2)^{3/2}}{x}}=
+\frac{(x^2-a^2)^{3/2}}{3}-a^2\sqrt{x^2-a^2}+
+a^3\sec^{-1}\left|\frac{x}{a}\right|
+$$
+<<*>>=
+)clear all
+
+--S 26 of 28
+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
+@
+
+\section{\cite{1}:14.235~~~~~$\displaystyle
+\int{\frac{(x^2-a^2)^{3/2}}{x^2}}~dx$}
+$$\int{\frac{(x^2-a^2)^{3/2}}{x^2}}=
+-\frac{(x^2-a^2)^{3/2}}{x}+\frac{3x\sqrt{x^2-a^2}}{2}-
+\frac{3}{2}a^2\ln\left(x+\sqrt{x^2-a^2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 27 of 28
+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
+@
+
+\section{\cite{1}:14.236~~~~~$\displaystyle
+\int{\frac{(x^2-a^2)^{3/2}}{x^3}}~dx$}
+$$\int{\frac{(x^2-a^2)^{3/2}}{x^3}}=
+-\frac{(x^2-a^2)^{3/2}}{2x^2}+\frac{3}{2}\sqrt{x^2-a^2}-
+\frac{3}{2}a\sec^{-1}\left|\frac{x}{a}\right|
+$$
+<<*>>=
+)clear all
+
+--S 28 of 28
+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
+
+)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}
diff --git a/src/input/schaum11.input.pamphlet
b/src/input/schaum11.input.pamphlet
new file mode 100644
index 0000000..6cd59a6
--- /dev/null
+++ b/src/input/schaum11.input.pamphlet
@@ -0,0 +1,783 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum11.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.237~~~~~$\displaystyle\int{\frac{dx}{\sqrt{a^2-x^2}}}$}
+$$\int{\frac{1}{\sqrt{a^2-x^2}}}=\ln\left(x+\sqrt{a^2-x^2}\right)$$
+<<*>>=
+)spool schaum11.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 28
+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
+@
+
+\section{\cite{1}:14.238~~~~~$\displaystyle\int{\frac{x~dx}{\sqrt{a^2-x^2}}}$}
+$$\int{\frac{x}{\sqrt{a^2-x^2}}}=\sqrt{a^2-x^2}$$
+<<*>>=
+)clear all
+
+--S 2 of 28
+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
+@
+
+\section{\cite{1}:14.239~~~~~$\displaystyle
+\int{\frac{x^2~dx}{\sqrt{a^2-x^2}}}$}
+$$\int{\frac{x^2}{\sqrt{a^2-x^2}}}=
+\frac{x\sqrt{a^2-x^2}}{2}+\frac{a^2}{2}\ln\left(x+\sqrt{a^2-x^2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 3 of 28
+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
+@
+
+\section{\cite{1}:14.240~~~~~$\displaystyle
+\int{\frac{x^3~dx}{\sqrt{a^2-x^2}}}$}
+$$\int{\frac{x^3}{\sqrt{a^2-x^2}}}=
+\frac{(a^2-x^2)^{3/2}}{3}+a^2\sqrt{a^2-x^2}
+$$
+<<*>>=
+)clear all
+
+--S 4 of 28
+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
+@
+
+\section{\cite{1}:14.241~~~~~$\displaystyle\int{\frac{dx}{x\sqrt{a^2-x^2}}}$}
+$$\int{\frac{1}{x\sqrt{a^2-x^2}}}=
+\frac{1}{a}\sec^{-1}\left|\frac{x}{a}\right|
+$$
+<<*>>=
+)clear all
+
+--S 5 of 28
+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
+@
+
+\section{\cite{1}:14.242~~~~~$\displaystyle
+\int{\frac{dx}{x^2\sqrt{a^2-x^2}}}$}
+$$\int{\frac{1}{x^2\sqrt{a^2-x^2}}}=
+\frac{\sqrt{a^2-x^2}}{a^2x}
+$$
+<<*>>=
+)clear all
+
+--S 6 of 28
+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
+@
+
+\section{\cite{1}:14.243~~~~~$\displaystyle\int{\frac{dx}{x^3\sqrt{a^2-x^2}}}$}
+$$\int{\frac{1}{x^3\sqrt{a^2-x^2}}}=
+-\frac{\sqrt{a^2-x^2}}{2a^2x^2}+\frac{1}{2a^3}
+\sec^{-1}\left|\frac{x}{a}\right|
+$$
+<<*>>=
+)clear all
+
+--S 7 of 28
+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
+@
+
+\section{\cite{1}:14.244~~~~~$\displaystyle\int{\sqrt{a^2-x^2}}~dx$}
+$$\int{\sqrt{a^2-x^2}}=
+\frac{x\sqrt{a^2-x^2}}{2}-\frac{a^2}{2}\ln\left(x+\sqrt{a^2-x^2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 8 of 28
+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
+@
+
+\section{\cite{1}:14.245~~~~~$\displaystyle\int{x\sqrt{a^2-x^2}}~dx$}
+$$\int{x\sqrt{a^2-x^2}}=
+\frac{(a^2-x^2)^{3/2}}{3}
+$$
+<<*>>=
+)clear all
+
+--S 9 of 28
+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
+@
+
+\section{\cite{1}:14.246~~~~~$\displaystyle
+\int{x^2\sqrt{a^2-x^2}}~dx$}
+$$\int{x^2\sqrt{a^2-x^2}}=
+\frac{x(a^2-x^2)^{3/2}}{4}+\frac{a^2x\sqrt{a^2-x^2}}{8}-
+\frac{a^4}{8}\ln\left(x+\sqrt{a^2-x^2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 10 of 28
+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
+@
+
+\section{\cite{1}:14.247~~~~~$\displaystyle
+\int{x^3\sqrt{a^2-x^2}}~dx$}
+$$\int{x^3\sqrt{a^2-x^2}}=
+\frac{(a^2-x^2)^{5/2}}{5}+\frac{a^2(a^2-x^2)^{3/2}}{3}
+$$
+<<*>>=
+)clear all
+
+--S 11 of 28
+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
+@
+
+\section{\cite{1}:14.248~~~~~$\displaystyle
+\int{\frac{\sqrt{a^2-x^2}}{x}}~dx$}
+$$\int{\frac{\sqrt{a^2-x^2}}{x}}=
+\sqrt{a^2-x^2}-a\sec^{-1}\left|\frac{x}{a}\right|
+$$
+<<*>>=
+)clear all
+
+--S 12 of 28
+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
+@
+
+\section{\cite{1}:14.249~~~~~$\displaystyle
+\int{\frac{\sqrt{a^2-x^2}}{x^2}}~dx$}
+$$\int{\frac{\sqrt{a^2-x^2}}{x^2}}=
+-\frac{\sqrt{a^2-x^2}}{x}+\ln\left(x+\sqrt{a^2-x^2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 13 of 28
+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
+@
+
+\section{\cite{1}:14.250~~~~~$\displaystyle
+\int{\frac{\sqrt{a^2-x^2}}{x^3}}~dx$}
+$$\int{\frac{\sqrt{a^2-x^2}}{x^3}}=
+-\frac{\sqrt{a^2-x^2}}{2x^2}+\frac{1}{2a}
+\sec^{-1}\left|\frac{x}{a}\right|
+$$
+<<*>>=
+)clear all
+
+--S 14 of 28
+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
+@
+
+\section{\cite{1}:14.251~~~~~$\displaystyle\int{\frac{dx}{(a^2-x^2)^{3/2}}}$}
+$$\int{\frac{1}{(a^2-x^2)^{3/2}}}=
+-\frac{x}{a^2\sqrt{a^2-x^2}}
+$$
+<<*>>=
+)clear all
+
+--S 15 of 28
+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
+@
+
+\section{\cite{1}:14.252~~~~~$\displaystyle
+\int{\frac{x~dx}{(a^2-x^2)^{3/2}}}$}
+$$\int{\frac{x}{(a^2-x^2)^{3/2}}}=
+\frac{-1}{\sqrt{a^2-x^2}}
+$$
+<<*>>=
+)clear all
+
+--S 16 of 28
+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
+@
+
+\section{\cite{1}:14.253~~~~~$\displaystyle
+\int{\frac{x^2dx}{(a^2-x^2)^{3/2}}}$}
+$$\int{\frac{x^2}{(a^2-x^2)^{3/2}}}=
+\frac{-x}{\sqrt{a^2-x^2}}+\ln\left(x+\sqrt{a^2-x^2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 17 of 28
+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
+@
+
+\section{\cite{1}:14.254~~~~~$\displaystyle
+\int{\frac{x^3dx}{(a^2-x^2)^{3/2}}}$}
+$$\int{\frac{x^3}{(a^2-x^2)^{3/2}}}=
+\sqrt{a^2-x^2}-\frac{a^2}{\sqrt{a^2-x^2}}
+$$
+<<*>>=
+)clear all
+
+--S 18 of 28
+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
+@
+
+\section{\cite{1}:14.255~~~~~$\displaystyle
+\int{\frac{dx}{x(a^2-x^2)^{3/2}}}$}
+$$\int{\frac{1}{x(a^2-x^2)^{3/2}}}=
+\frac{-1}{a^2\sqrt{a^2-x^2}}-
+\frac{1}{a^3}\sec^{-1}\left|\frac{x}{a}\right|
+$$
+<<*>>=
+)clear all
+
+--S 19 of 28
+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
+@
+
+\section{\cite{1}:14.256~~~~~$\displaystyle
+\int{\frac{dx}{x^2(a^2-x^2)^{3/2}}}$}
+$$\int{\frac{1}{x^2(a^2-x^2)^{3/2}}}=
+-\frac{\sqrt{a^2-x^2}}{a^4x}-\frac{x}{a^4\sqrt{a^2-x^2}}
+$$
+<<*>>=
+)clear all
+
+--S 20 of 28
+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
+@
+
+\section{\cite{1}:14.257~~~~~$\displaystyle
+\int{\frac{dx}{x^3(a^2-x^2)^{3/2}}}$}
+$$\int{\frac{1}{x^3(a^2-x^2)^{3/2}}}=
+\frac{1}{2a^2x^2\sqrt{a^2-x^2}}-
+\frac{3}{2a^4\sqrt{a^2-x^2}}-
+\frac{3}{2a^5}\sec^{-1}\left|\frac{x}{a}\right|
+$$
+<<*>>=
+)clear all
+
+--S 21 of 28
+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
+@
+
+\section{\cite{1}:14.258~~~~~$\displaystyle\int{(a^2-x^2)^{3/2}}~dx$}
+$$\int{(a^2-x^2)^{3/2}}=
+\frac{x(a^2-x^2)^{3/2}}{4}-\frac{3a^2x\sqrt{a^2-x^2}}{8}+
+\frac{3}{8}a^4\ln\left(x+\sqrt{a^2-x^2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 22 of 28
+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
+@
+
+\section{\cite{1}:14.259~~~~~$\displaystyle\int{x(a^2-x^2)^{3/2}}~dx$}
+$$\int{x(a^2-x^2)^{3/2}}=\frac{(a^2-x^2)^{5/2}}{5}$$
+<<*>>=
+)clear all
+
+--S 23 of 28
+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
+@
+
+\section{\cite{1}:14.260~~~~~$\displaystyle\int{x^2(a^2-x^2)^{3/2}}~dx$}
+$$\int{x^2(a^2-x^2)^{3/2}}=
+\frac{x(a^2-x^2)^{5/2}}{6}+\frac{a^2x(a^2-x^2)^{3/2}}{24}-
+\frac{a^4x\sqrt{a^2-x^2}}{16}+
+\frac{a^6}{16}\ln\left(x+\sqrt{a^2-x^2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 24 of 28
+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
+@
+
+\section{\cite{1}:14.261~~~~~$\displaystyle\int{x^3(a^2-x^2)^{3/2}}~dx$}
+$$\int{x^3(a^2-x^2)^{3/2}}=
+\frac{(a^2-x^2)^{7/2}}{7}+\frac{a^2(a^2-x^2)^{5/2}}{5}
+$$
+<<*>>=
+)clear all
+
+--S 25 of 28
+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
+@
+
+\section{\cite{1}:14.262~~~~~$\displaystyle
+\int{\frac{(a^2-x^2)^{3/2}}{x}}~dx$}
+$$\int{\frac{(a^2-x^2)^{3/2}}{x}}=
+\frac{(a^2-x^2)^{3/2}}{3}-a^2\sqrt{a^2-x^2}+
+a^3\sec^{-1}\left|\frac{x}{a}\right|
+$$
+<<*>>=
+)clear all
+
+--S 26 of 28
+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
+@
+
+\section{\cite{1}:14.263~~~~~$\displaystyle
+\int{\frac{(a^2-x^2)^{3/2}}{x^2}}~dx$}
+$$\int{\frac{(a^2-x^2)^{3/2}}{x^2}}=
+-\frac{(a^2-x^2)^{3/2}}{x}+\frac{3x\sqrt{a^2-x^2}}{2}-
+\frac{3}{2}a^2\ln\left(x+\sqrt{a^2-x^2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 27 of 28
+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
+@
+
+\section{\cite{1}:14.264~~~~~$\displaystyle
+\int{\frac{(a^2-x^2)^{3/2}}{x^3}}~dx$}
+$$\int{\frac{(a^2-x^2)^{3/2}}{x^3}}=
+-\frac{(a^2-x^2)^{3/2}}{2x^2}+\frac{3}{2}\sqrt{a^2-x^2}-
+\frac{3}{2}a\sec^{-1}\left|\frac{x}{a}\right|
+$$
+<<*>>=
+)clear all
+
+--S 28 of 28
+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
+
+)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}
diff --git a/src/input/schaum2.input.pamphlet b/src/input/schaum2.input.pamphlet
index cb8e6db..ba16925 100644
--- a/src/input/schaum2.input.pamphlet
+++ b/src/input/schaum2.input.pamphlet
@@ -8,7 +8,7 @@
\tableofcontents
\eject
\section{\cite{1}:14.84~~~~~$\displaystyle\int{\frac{dx}{\sqrt{ax+b}}}$}
-$$\int{\frac{dx}{\sqrt{ax+b}}}=\frac{2\sqrt{ax+b}}{a}$$
+$$\int{\frac{1}{\sqrt{ax+b}}}=\frac{2\sqrt{ax+b}}{a}$$
<<*>>=
)spool schaum2.output
)set message test on
@@ -49,7 +49,7 @@ cc:=aa-bb
@
\section{\cite{1}:14.85~~~~~$\displaystyle\int{\frac{x~dx}{\sqrt{ax+b}}}$}
-$$\int{\frac{x~dx}{\sqrt{ax+b}}}=\frac{2(ax-2b)}{3a^2}\sqrt{ax+b}$$
+$$\int{\frac{x}{\sqrt{ax+b}}}=\frac{2(ax-2b)}{3a^2}\sqrt{ax+b}$$
<<*>>=
)clear all
@@ -89,7 +89,7 @@ cc:=aa-bb
@
\section{\cite{1}:14.86~~~~~$\displaystyle\int{\frac{x^2~dx}{\sqrt{ax+b}}}$}
-$$\int{\frac{x~dx}{\sqrt{ax+b}}}=
+$$\int{\frac{x}{\sqrt{ax+b}}}=
\frac{2(3a^2x^2-4abx+8b^2)}{15a^2}\sqrt{ax+b}$$
<<*>>=
)clear all
@@ -130,7 +130,7 @@ cc:=aa-bb
@
\section{\cite{1}:14.87~~~~~$\displaystyle\int{\frac{dx}{x\sqrt{ax+b}}}$}
-$$\int{\frac{dx}{x\sqrt{ax+b}}}=
+$$\int{\frac{1}{x\sqrt{ax+b}}}=
\left\{
\begin{array}{l}
\displaystyle
@@ -380,9 +380,9 @@ Thus the original equation and Spiegel's derivative of the
integral are equal.
So we can conclude that both second answers are correct although they differ
by a constant of integration.
- \section{\cite{1}:14.88~~~~~$\displaystyle\int{\frac{dx}{x^2\sqrt{ax+b}}}$}
-$$\int{\frac{dx}{x^2\sqrt{ax+b}}}=
--\frac{\sqrt{ax+b}}{bx}-\frac{a}{2b}~\int{\frac{dx}{x\sqrt{ax+b}}}$$
+\section{\cite{1}:14.88~~~~~$\displaystyle\int{\frac{dx}{x^2\sqrt{ax+b}}}$}
+$$\int{\frac{1}{x^2\sqrt{ax+b}}}=
+-\frac{\sqrt{ax+b}}{bx}-\frac{a}{2b}~\int{\frac{1}{x\sqrt{ax+b}}}$$
<<*>>=
)clear all
@@ -565,7 +565,7 @@ cc22:=bb2-aa.2
@
\section{\cite{1}:14.89~~~~~$\displaystyle\int{\sqrt{ax+b}~dx}$}
-$$\int{\sqrt{ax+b}~dx}=
+$$\int{\sqrt{ax+b}}=
\frac{2\sqrt{(ax+b)^3}}{3a}$$
<<*>>=
)clear all
@@ -687,7 +687,7 @@ result=nn/sqrt(mm)
and this reduces to $\sqrt{ax+b}$
\section{\cite{1}:14.90~~~~~$\displaystyle\int{x\sqrt{ax+b}~dx}$}
-$$\int{x\sqrt{ax+b}~dx}=
+$$\int{x\sqrt{ax+b}}=
\frac{2(3ax-2b)}{15a^2}~\sqrt{(ax+b)^3}$$
<<*>>=
)clear all
@@ -792,7 +792,7 @@ t2*sqrt(t2)-sqrt(t2^3)
@
\section{\cite{1}:14.91~~~~~$\displaystyle\int{x^2\sqrt{ax+b}~dx}$}
-$$\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 $\sqrt{(ax+b)}$
<<*>>=
@@ -844,8 +844,8 @@ cc:=aa-bb
@
\section{\cite{1}:14.92~~~~~$\displaystyle\int{\frac{\sqrt{ax+b}}{x}~dx}$}
-$$\int{\frac{\sqrt{ax+b}}{x}~dx}=
-2\sqrt{ax+b}+b~\int{\frac{dx}{x\sqrt{ax+b}}}$$
+$$\int{\frac{\sqrt{ax+b}}{x}}=
+2\sqrt{ax+b}+b~\int{\frac{1}{x\sqrt{ax+b}}}$$
<<*>>=
)clear all
@@ -977,8 +977,8 @@ cc22:=bb2-aa.2
@
\section{\cite{1}:14.93~~~~~$\displaystyle\int{\frac{\sqrt{ax+b}}{x^2}~dx}$}
-$$\int{\frac{\sqrt{ax+b}}{x^2}~dx}=
--\frac{\sqrt{ax+b}}{x}+\frac{a}{2}~\int{\frac{dx}{x\sqrt{ax+b}}}$$
+$$\int{\frac{\sqrt{ax+b}}{x^2}}=
+-\frac{\sqrt{ax+b}}{x}+\frac{a}{2}~\int{\frac{1}{x\sqrt{ax+b}}}$$
<<*>>=
)clear all
@@ -1101,9 +1101,9 @@ cc22:=bb2-aa.2
@
\section{\cite{1}:14.94~~~~~$\displaystyle\int{\frac{x^m}{\sqrt{ax+b}}~dx}$}
-$$\int{\frac{x^m}{\sqrt{ax+b}}~dx}=
+$$\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}}~dx}$$
+~\int{\frac{x^{m-1}}{\sqrt{ax+b}}}$$
<<*>>=
)clear all
@@ -1121,9 +1121,9 @@ aa:=integrate(x^m/sqrt(a*x+b),x)
@
\section{\cite{1}:14.95~~~~~$\displaystyle\int{\frac{dx}{x^m\sqrt{ax+b}}}$}
-$$\int{\frac{dx}{x^m\sqrt{ax+b}}}=
+$$\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{dx}{x^{m-1}\sqrt{ax+b}}}$$
+~\int{\frac{1}{x^{m-1}\sqrt{ax+b}}}$$
<<*>>=
)clear all
@@ -1141,9 +1141,9 @@ aa:=integrate(1/(x^m*sqrt(a*x+b)),x)
@
\section{\cite{1}:14.96~~~~~$\displaystyle\int{x^m\sqrt{ax+b}~dx}$}
-$$\int{x^m\sqrt{ax+b}~dx}=
+$$\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}~dx}$$
+-\frac{2mb}{(2m+3)a}~\int{x^{m-1}\sqrt{ax+b}}$$
<<*>>=
)clear all
@@ -1160,9 +1160,9 @@ aa:=integrate(x^m*sqrt(a*x+b),x)
@
\section{\cite{1}:14.97~~~~~$\displaystyle\int{\frac{\sqrt{ax+b}}{x^m}~dx}$}
-$$\int{\frac{\sqrt{ax+b}}{x^m}~dx}=
+$$\int{\frac{\sqrt{ax+b}}{x^m}}=
-\frac{\sqrt{ax+b}}{(m-1)x^{m-1}}
-+\frac{a}{2(m-1)}~\int{\frac{dx}{x^{m-1}\sqrt{ax+b}}}$$
++\frac{a}{2(m-1)}~\int{\frac{1}{x^{m-1}\sqrt{ax+b}}}$$
<<*>>=
)clear all
@@ -1180,9 +1180,9 @@ aa:=integrate(sqrt(a*x+b)/x^m,x)
@
\section{\cite{1}:14.98~~~~~$\displaystyle\int{\frac{\sqrt{ax+b}}{x^m}~dx}$}
-$$\int{\frac{\sqrt{ax+b}}{x^m}~dx}=
+$$\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}}~dx}$$
+-\frac{(2m-5)a}{(2m-2)b}~\int{\frac{\sqrt{ax+b}}{x^{m-1}}}$$
Note: 14.98 is the same as 14.97
<<*>>=
)clear all
@@ -1201,7 +1201,7 @@ aa:=integrate(sqrt(a*x+b)/x^m,x)
@
\section{\cite{1}:14.99~~~~~$\displaystyle\int{(ax+b)^{m/2}~dx}$}
-$$\int{(ax+b)^{m/2}~dx}=
+$$\int{(ax+b)^{m/2}}=
\frac{2(ax+b)^{(m+2)/2}}{a(m+2)}$$
<<*>>=
)clear all
@@ -1249,7 +1249,7 @@ cc:=aa-bb
@
\section{\cite{1}:14.100~~~~~$\displaystyle\int{x(ax+b)^{m/2}~dx}$}
-$$\int{x(ax+b)^{m/2}~dx}=
+$$\int{x(ax+b)^{m/2}}=
\frac{2(ax+b)^{(m+4)/2}}{a^2(m+4)}
-\frac{2b(ax+b)^{(m+2)/2}}{a^2(m+2)}$$
<<*>>=
@@ -1307,7 +1307,7 @@ cc:=aa-bb
@
\section{\cite{1}:14.101~~~~~$\displaystyle\int{x^2(ax+b)^{m/2}~dx}$}
-$$\int{x^2(ax+b)^{m/2}~dx}=
+$$\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)}$$
@@ -1386,9 +1386,9 @@ cc:=aa-bb
@
\section{\cite{1}:14.102~~~~~$\displaystyle\int{\frac{(ax+b)^{m/2}}{x}~dx}$}
-$$\int{\frac{(ax+b)^{m/2}}{x}~dx}=
+$$\int{\frac{(ax+b)^{m/2}}{x}}=
\frac{2(ax+b)^{m/2}}{m}
-+b~\int{\frac{(ax+b)^{(m-2)/2}}{x}~dx}$$
++b~\int{\frac{(ax+b)^{(m-2)/2}}{x}}$$
<<*>>=
)clear all
@@ -1407,9 +1407,9 @@ aa:=integrate((a*x+b)^(m/2)/x,x)
@
\section{\cite{1}:14.103~~~~~$\displaystyle
\int{\frac{(ax+b)^{m/2}}{x^2}~dx}$}
-$$\int{\frac{(ax+b)^{m/2}}{x^2}~dx}=
+$$\int{\frac{(ax+b)^{m/2}}{x^2}}=
-\frac{(ax+b)^{(m+2)/2}}{bx}
-+\frac{ma}{2b}~\int{\frac{(ax+b)^{m/2}}{x}~dx}$$
++\frac{ma}{2b}~\int{\frac{(ax+b)^{m/2}}{x}}$$
<<*>>=
)clear all
@@ -1429,9 +1429,9 @@ aa:=integrate((a*x+b)^(m/2)/x^2,x)
@
\section{\cite{1}:14.104~~~~~$\displaystyle
\int{\frac{dx}{x(ax+b)^{m/2}}}$}
-$$\int{\frac{dx}{x(ax+b)^{m/2}}}=
+$$\int{\frac{1}{x(ax+b)^{m/2}}}=
\frac{2}{(m-2)b(ax+b)^{(m-2)/2}}
-+\frac{1}{b}~\int{\frac{dx}{x(ax+b)^{(m-2)/2}}}$$
++\frac{1}{b}~\int{\frac{1}{x(ax+b)^{(m-2)/2}}}$$
<<*>>=
)clear all
diff --git a/src/input/schaum3.input.pamphlet b/src/input/schaum3.input.pamphlet
index e273509..e1e030d 100644
--- a/src/input/schaum3.input.pamphlet
+++ b/src/input/schaum3.input.pamphlet
@@ -8,7 +8,7 @@
\tableofcontents
\eject
\section{\cite{1}:14.105~~~~~$\displaystyle\int{\frac{dx}{(ax+b)(px+q)}}$}
-$$\int{\frac{dx}{(ax+b)(px+q)}}=
+$$\int{\frac{1}{(ax+b)(px+q)}}=
\frac{1}{bp-aq}~\ln\left(\frac{px+q}{ax+b}\right)$$
<<*>>=
)spool schaum3.output
@@ -54,7 +54,7 @@ cc:=aa-bb
@
\section{\cite{1}:14.106~~~~~$\displaystyle\int{\frac{x~dx}{(ax+b)(px+q)}}$}
-$$\int{\frac{x~dx}{(ax+b)(px+q)}}=
+$$\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\}$$
<<*>>=
)clear all
@@ -93,7 +93,7 @@ cc:=aa-bb
@
\section{\cite{1}:14.107~~~~~$\displaystyle\int{\frac{dx}{(ax+b)^2(px+q)}}$}
-$$\int{\frac{dx}{(ax+b)^2(px+q)}}=
+$$\int{\frac{1}{(ax+b)^2(px+q)}}=
\frac{1}{bp-aq}
\left\{\frac{1}{ax+b}+
\frac{p}{bp-aq}~\ln\left(\frac{px+q}{ax+b}\right)\right\}$$
@@ -141,7 +141,7 @@ cc:=aa-bb
@
\section{\cite{1}:14.108~~~~~$\displaystyle\int{\frac{x~dx}{(ax+b)^2(px+q)}}$}
-$$\int{\frac{x~dx}{(ax+b)^2(px+q)}}=
+$$\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\}$$
@@ -192,7 +192,7 @@ cc:=aa-bb
\section{\cite{1}:14.109~~~~~$\displaystyle
\int{\frac{x^2~dx}{(ax+b)^2(px+q)}}$}
-$$\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\}$$
<<*>>=
@@ -243,10 +243,10 @@ cc:=aa-bb
@
\section{\cite{1}:14.110~~~~~$\displaystyle\int{\frac{dx}{(ax+b)^m(px+q)^n}}$}
-$$\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{dx}{(ax+b)^m(px+q)^{n-1}}}\right\}$$
+a(m+n-2)~\int{\frac{1}{(ax+b)^m(px+q)^{n-1}}}\right\}$$
<<*>>=
)clear all
@@ -331,7 +331,7 @@ cc:=aa-bb
@
\section{\cite{1}:14.111~~~~~$\displaystyle\int{\frac{ax+b}{px+q}~dx}$}
-$$\int{\frac{ax+b}{px+q}~dx}=\frac{ax}{p}+\frac{bp-aq}{p^2}~\ln(px+q)$$
+$$\int{\frac{ax+b}{px+q}}=\frac{ax}{p}+\frac{bp-aq}{p^2}~\ln(px+q)$$
<<*>>=
)clear all
@@ -369,15 +369,15 @@ cc:=aa-bb
@
\section{\cite{1}:14.112~~~~~$\displaystyle\int{\frac{(ax+b)^m}{(px+q)^n}~dx}$}
-$$\int{\frac{(ax+b)^m}{(px+q)^n}~dx}=\left\{
+$$\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}}}~dx\right\}\\
+\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}}~dx\right\}\\
+\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}}}~dx\right\}
+\int{\frac{(ax+b)^{m-1}}{(px+q)^{n-1}}}\right\}
\end{array}
\right.$$
<<*>>=
diff --git a/src/input/schaum4.input.pamphlet b/src/input/schaum4.input.pamphlet
index b57e857..efd9edc 100644
--- a/src/input/schaum4.input.pamphlet
+++ b/src/input/schaum4.input.pamphlet
@@ -30,8 +30,8 @@ aa:=integrate((p*x+q)/sqrt(a*x+b),x)
@
\section{\cite{1}:14.114~~~~~$\displaystyle
-\int{\frac{dx}{(px+q)\sqrt{ax+b}}}~dx$}
-$$\int{\frac{dx}{(px+q)\sqrt{ax+b}}}=
+\int{\frac{dx}{(px+q)\sqrt{ax+b}}}$}
+$$\int{\frac{1}{(px+q)\sqrt{ax+b}}}=
\left\{
\begin{array}{l}
\frac{1}{\sqrt{bp-aq}\sqrt{p}}\ln\left(
@@ -117,7 +117,7 @@ aa:=integrate(sqrt(a*x+b)/(p*x+q),x)
\section{\cite{1}:14.116~~~~~$\displaystyle\int{(px+b)^n\sqrt{ax+b}}~dx$}
$$\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}}}~dx$$
+\int{\frac{(px+q)^n}{\sqrt{ax+b}}}$$
<<*>>=
)clear all
@@ -136,10 +136,10 @@ aa:=integrate((p*x+q)^n*sqrt(a*x+b),x)
\section{\cite{1}:14.117~~~~~$\displaystyle
\int{\frac{dx}{(px+b)^n\sqrt{ax+b}}}$}
-$$\int{\frac{dx}{(px+b)^n\sqrt{ax+b}}}=
+$$\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{dx}{(px+q)^{n-1}\sqrt{ax+b}}}$$
+\int{\frac{1}{(px+q)^{n-1}\sqrt{ax+b}}}$$
<<*>>=
)clear all
@@ -183,7 +183,7 @@ aa:=integrate((p*x+q)^n/sqrt(a*x+b),x)
\int{\frac{\sqrt{ax+b}}{(px+q)^n}}~dx$}
$$\int{\frac{\sqrt{ax+b}}{(px+q)^n}}=
\frac{-\sqrt{ax+b}}{(n-1)p(px+q)^{n-1}}+
-\frac{a}{2(n-1)p}\int{\frac{dx}{(px+q)^{n-1}\sqrt{ax+b}}}$$
+\frac{a}{2(n-1)p}\int{\frac{1}{(px+q)^{n-1}\sqrt{ax+b}}}$$
<<*>>=
)clear all
diff --git a/src/input/schaum5.input.pamphlet b/src/input/schaum5.input.pamphlet
index a784b92..f8bccc8 100644
--- a/src/input/schaum5.input.pamphlet
+++ b/src/input/schaum5.input.pamphlet
@@ -9,7 +9,7 @@
\eject
\section{\cite{1}:14.120~~~~~$\displaystyle
\int{\frac{dx}{\sqrt{(ax+b)(px+q)}}}$}
-$$\int{\frac{dx}{\sqrt{(ax+b)(px+q)}}}=
+$$\int{\frac{1}{\sqrt{(ax+b)(px+q)}}}=
\left\{
\begin{array}{l}
\frac{2}{\sqrt{ap}}\ln\left(\sqrt{a(px+q)}+\sqrt{p(ax+b)}\right)\\
@@ -57,9 +57,9 @@ aa:=integrate(1/sqrt((a*x+b)*(p*x+q)),x)
\section{\cite{1}:14.121~~~~~$\displaystyle
\int{\frac{x~dx}{\sqrt{(ax+b)(px+q)}}}$}
-$$\int{\frac{x~dx}{\sqrt{(ax+b)(px+q)}}}=
+$$\int{\frac{x}{\sqrt{(ax+b)(px+q)}}}=
\frac{\sqrt{(ax+b)(px+q)}}{ap}-\frac{bp+aq}{2ap}
-\int{\frac{dx}{\sqrt{(ax+b)(px+q)}}}
+\int{\frac{1}{\sqrt{(ax+b)(px+q)}}}
$$
<<*>>=
)clear all
@@ -138,7 +138,7 @@ aa:=integrate(x/sqrt((a*x+b)*(p*x+q)),x)
\section{\cite{1}:14.122~~~~~$\displaystyle\int{\sqrt{(ax+b)(px+q)}}~dx$}
$$\int{\sqrt{(ax+b)(px+q)}}=
\frac{2apx+bp+aq}{4ap}\sqrt{(ax+b)(px+q)}-
-\frac{(bp-aq)^2}{8ap}\int{\frac{dx}{\sqrt{(ax+b)(px+q)}}}
+\frac{(bp-aq)^2}{8ap}\int{\frac{1}{\sqrt{(ax+b)(px+q)}}}
$$
<<*>>=
)clear all
@@ -295,7 +295,7 @@ aa:=integrate(sqrt((a*x+b)*(p*x+q)),x)
\section{\cite{1}:14.123~~~~~$\displaystyle\int{\sqrt{\frac{px+q}{ax+b}}}~dx$}
$$\int{\sqrt{\frac{px+q}{ax+b}}}=
\frac{\sqrt{(ax+b)(px+q)}}{a}+\frac{aq-bp}{2a}
-\int{\frac{dx}{\sqrt{(ax+b)(px+q)}}}
+\int{\frac{1}{\sqrt{(ax+b)(px+q)}}}
$$
<<*>>=
)clear all
@@ -336,7 +336,7 @@ aa:=integrate(sqrt((p*x+q)/(a*x+b)),x)
\section{\cite{1}:14.124~~~~~$\displaystyle
\int{\frac{dx}{(px+q)\sqrt{(ax+b)(px+q)}}}~dx$}
-$$\int{\frac{dx}{(px+q)\sqrt{(ax+b)(px+q)}}}=
+$$\int{\frac{1}{(px+q)\sqrt{(ax+b)(px+q)}}}=
\frac{2\sqrt{ax+b}}{(aq-bp)\sqrt{px+q}}
$$
<<*>>=
diff --git a/src/input/schaum6.input.pamphlet b/src/input/schaum6.input.pamphlet
index 1a4b430..9a08dc6 100644
--- a/src/input/schaum6.input.pamphlet
+++ b/src/input/schaum6.input.pamphlet
@@ -8,7 +8,7 @@
\tableofcontents
\eject
\section{\cite{1}:14.125~~~~~$\displaystyle\int{\frac{dx}{x^2+a^2}}$}
-$$\int{\frac{dx}{x^2+a^2}}=\frac{1}{a}\tan^{-1}\frac{x}{a}$$
+$$\int{\frac{1}{x^2+a^2}}=\frac{1}{a}\tan^{-1}\frac{x}{a}$$
<<*>>=
)spool schaum6.output
)set message test on
@@ -29,7 +29,7 @@ aa:=integrate(1/(x^2+a^2),x)
@
\section{\cite{1}:14.126~~~~~$\displaystyle\int{\frac{x~dx}{x^2+a^2}}$}
-$$\int{\frac{x~dx}{x^2+a^2}}=\frac{1}{2}\ln(x^2+a^2)$$
+$$\int{\frac{x}{x^2+a^2}}=\frac{1}{2}\ln(x^2+a^2)$$
<<*>>=
)clear all
@@ -46,7 +46,7 @@ aa:=integrate(x/(x^2+a^2),x)
@
\section{\cite{1}:14.127~~~~~$\displaystyle\int{\frac{x^2~dx}{x^2+a^2}}$}
-$$\int{\frac{x^2~dx}{x^2+a^2}}=x-a\tan^{-1}\frac{x}{a}$$
+$$\int{\frac{x^2}{x^2+a^2}}=x-a\tan^{-1}\frac{x}{a}$$
<<*>>=
)clear all
@@ -62,7 +62,7 @@ aa:=integrate(x^2/(x^2+a^2),x)
@
\section{\cite{1}:14.128~~~~~$\displaystyle\int{\frac{x^3~dx}{x^2+a^2}}$}
-$$\int{\frac{x^3~dx}{x^2+a^2}}=\frac{x^2}{2}-\frac{a^2}{2}\ln(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)$$
<<*>>=
)clear all
@@ -79,8 +79,8 @@ aa:=integrate(x^3/(x^2+a^2),x)
--E
@
-\section{\cite{1}:14.129~~~~~$\displaystyle\int{\frac{dx}{x(x^2+a^2)}}~dx$}
-$$\int{\frac{dx}{x(x^2+a^2)}}=
+\section{\cite{1}:14.129~~~~~$\displaystyle\int{\frac{dx}{x(x^2+a^2)}}$}
+$$\int{\frac{1}{x(x^2+a^2)}}=
\frac{1}{2a^2}\ln\left(\frac{x^2}{x^2+a^2}\right)
$$
<<*>>=
@@ -99,8 +99,8 @@ aa:=integrate(1/(x*(x^2+a^2)),x)
--E
@
-\section{\cite{1}:14.130~~~~~$\displaystyle\int{\frac{dx}{x^2(x^2+a^2)}}~dx$}
-$$\int{\frac{dx}{x^2(x^2+a^2)}}=
+\section{\cite{1}:14.130~~~~~$\displaystyle\int{\frac{dx}{x^2(x^2+a^2)}}$}
+$$\int{\frac{1}{x^2(x^2+a^2)}}=
-\frac{1}{a^2x}-\frac{1}{a^3}\tan^{-1}\frac{x}{a}
$$
<<*>>=
@@ -120,8 +120,8 @@ aa:=integrate(1/(x^2*(x^2+a^2)),x)
--E
@
-\section{\cite{1}:14.131~~~~~$\displaystyle\int{\frac{dx}{x^3(x^2+a^2)}}~dx$}
-$$\int{\frac{dx}{x^3(x^2+a^2)}}=
+\section{\cite{1}:14.131~~~~~$\displaystyle\int{\frac{dx}{x^3(x^2+a^2)}}$}
+$$\int{\frac{1}{x^3(x^2+a^2)}}=
-\frac{1}{2a^2x^2}-\frac{1}{2a^4}\ln\left(\frac{x^2}{x^2+a^2}\right)
$$
<<*>>=
@@ -140,8 +140,8 @@ aa:=integrate(1/(x^3*(x^2+a^2)),x)
--E
@
-\section{\cite{1}:14.132~~~~~$\displaystyle\int{\frac{dx}{(x^2+a^2)^2}}~dx$}
-$$\int{\frac{dx}{(x^2+a^2)^2}}=
+\section{\cite{1}:14.132~~~~~$\displaystyle\int{\frac{dx}{(x^2+a^2)^2}}$}
+$$\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}
$$
<<*>>=
@@ -161,8 +161,8 @@ aa:=integrate(1/((x^2+a^2)^2),x)
--E
@
-\section{\cite{1}:14.133~~~~~$\displaystyle\int{\frac{x~dx}{(x^2+a^2)^2}}~dx$}
-$$\int{\frac{x~dx}{(x^2+a^2)^2}}=
+\section{\cite{1}:14.133~~~~~$\displaystyle\int{\frac{x~dx}{(x^2+a^2)^2}}$}
+$$\int{\frac{x}{(x^2+a^2)^2}}=
\frac{-1}{2(x^2+a^2)}
$$
<<*>>=
@@ -180,8 +180,8 @@ aa:=integrate(x/((x^2+a^2)^2),x)
--E
@
-\section{\cite{1}:14.134~~~~~$\displaystyle\int{\frac{x^2dx}{(x^2+a^2)^2}}~dx$}
-$$\int{\frac{x^2dx}{(x^2+a^2)^2}}=
+\section{\cite{1}:14.134~~~~~$\displaystyle\int{\frac{x^2dx}{(x^2+a^2)^2}}$}
+$$\int{\frac{x^2}{(x^2+a^2)^2}}=
\frac{-x}{2(x^2+a^2)}+\frac{1}{2a}\tan^{-1}\frac{x}{a}
$$
<<*>>=
@@ -201,8 +201,8 @@ aa:=integrate(x^2/((x^2+a^2)^2),x)
--E
@
-\section{\cite{1}:14.135~~~~~$\displaystyle\int{\frac{x^3dx}{(x^2+a^2)^2}}~dx$}
-$$\int{\frac{x^3dx}{(x^2+a^2)^2}}=
+\section{\cite{1}:14.135~~~~~$\displaystyle\int{\frac{x^3dx}{(x^2+a^2)^2}}$}
+$$\int{\frac{x^3}{(x^2+a^2)^2}}=
\frac{a^2}{2(x^2+a^2)}+\frac{1}{2}\ln(x^2+a^2)
$$
<<*>>=
@@ -221,8 +221,8 @@ aa:=integrate(x^3/((x^2+a^2)^2),x)
--E
@
-\section{\cite{1}:14.136~~~~~$\displaystyle\int{\frac{dx}{x(x^2+a^2)^2}}~dx$}
-$$\int{\frac{dx}{x(x^2+a^2)^2}}=
+\section{\cite{1}:14.136~~~~~$\displaystyle\int{\frac{dx}{x(x^2+a^2)^2}}$}
+$$\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)
$$
<<*>>=
@@ -241,8 +241,8 @@ aa:=integrate(1/(x*(x^2+a^2)^2),x)
--E
@
-\section{\cite{1}:14.137~~~~~$\displaystyle\int{\frac{dx}{x^2(x^2+a^2)^2}}~dx$}
-$$\int{\frac{dx}{x^2(x^2+a^2)^2}}=
+\section{\cite{1}:14.137~~~~~$\displaystyle\int{\frac{dx}{x^2(x^2+a^2)^2}}$}
+$$\int{\frac{1}{x^2(x^2+a^2)^2}}=
-\frac{1}{a^4x}-\frac{x}{2a^4(x^2+a^2)}-\frac{3}{2a^5}\tan^{-1}\frac{x}{a}
$$
<<*>>=
@@ -262,8 +262,8 @@ aa:=integrate(1/((x^2+a^2)^2),x)
--E
@
-\section{\cite{1}:14.138~~~~~$\displaystyle\int{\frac{dx}{x^3(x^2+a^2)^2}}~dx$}
-$$\int{\frac{dx}{x^3(x^2+a^2)^2}}=
+\section{\cite{1}:14.138~~~~~$\displaystyle\int{\frac{dx}{x^3(x^2+a^2)^2}}$}
+$$\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)
$$
@@ -283,10 +283,10 @@ aa:=integrate(1/(x^3*(x^2+a^2)^2),x)
--E
@
-\section{\cite{1}:14.139~~~~~$\displaystyle\int{\frac{dx}{(x^2+a^2)^n}}~dx$}
-$$\int{\frac{dx}{(x^2+a^2)^n}}=
+\section{\cite{1}:14.139~~~~~$\displaystyle\int{\frac{dx}{(x^2+a^2)^n}}$}
+$$\int{\frac{1}{(x^2+a^2)^n}}=
\frac{x}{2(n-1)a^2(x^2+a^2)^{n-1}}+\frac{2n-3}{(2n-2)a^2}
-\int{\frac{dx}{(x^2+a^2)^{n-1}}}
+\int{\frac{1}{(x^2+a^2)^{n-1}}}
$$
<<*>>=
)clear all
@@ -304,8 +304,8 @@ aa:=integrate(1/((x^2+a^2)^n),x)
--E
@
-\section{\cite{1}:14.140~~~~~$\displaystyle\int{\frac{x~dx}{(x^2+a^2)^n}}~dx$}
-$$\int{\frac{x~dx}{(x^2+a^2)^n}}=
+\section{\cite{1}:14.140~~~~~$\displaystyle\int{\frac{x~dx}{(x^2+a^2)^n}}$}
+$$\int{\frac{x}{(x^2+a^2)^n}}=
\frac{-1}{2(n-1)(x^2+a^2)^{n-1}}
$$
<<*>>=
@@ -325,10 +325,10 @@ aa:=integrate(x/((x^2+a^2)^n),x)
--E
@
-\section{\cite{1}:14.141~~~~~$\displaystyle\int{\frac{dx}{x(x^2+a^2)^n}}~dx$}
-$$\int{\frac{dx}{x(x^2+a^2)^n}}=
+\section{\cite{1}:14.141~~~~~$\displaystyle\int{\frac{dx}{x(x^2+a^2)^n}}$}
+$$\int{\frac{1}{x(x^2+a^2)^n}}=
\frac{1}{2(n-1)a^2(x^2+a^2)^{n-1}}+\frac{1}{a^2}
-\int{\frac{dx}{x(x^2+a^2)^{n-1}}}
+\int{\frac{1}{x(x^2+a^2)^{n-1}}}
$$
<<*>>=
)clear all
@@ -346,10 +346,10 @@ aa:=integrate(1/(x*(x^2+a^2)^n),x)
--E
@
-\section{\cite{1}:14.142~~~~~$\displaystyle\int{\frac{x^mdx}{(x^2+a^2)^n}}~dx$}
-$$\int{\frac{x^mdx}{(x^2+a^2)^n}}=
-\int{\frac{x^{m-2}dx}{(x^2+a^2)^{n-1}}} -
-a^2\int{\frac{x^{m-2}dx}{(x^2+a^2)^n}}
+\section{\cite{1}:14.142~~~~~$\displaystyle\int{\frac{x^mdx}{(x^2+a^2)^n}}$}
+$$\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}}
$$
<<*>>=
)clear all
@@ -367,10 +367,10 @@ aa:=integrate(x^m/((x^2+a^2)^n),x)
--E
@
-\section{\cite{1}:14.143~~~~~$\displaystyle\int{\frac{dx}{x^m(x^2+a^2)^n}}~dx$}
-$$\int{\frac{dx}{x^m(x^2+a^2)^n}}=
-\frac{1}{a^2}\int{\frac{dx}{x^m(x^2+a^2)^{n-1}}}-
-\frac{1}{a^2}\int{\frac{dx}{x^{m-2}(x^2+a^2)^n}}
+\section{\cite{1}:14.143~~~~~$\displaystyle\int{\frac{dx}{x^m(x^2+a^2)^n}}$}
+$$\int{\frac{1}{x^m(x^2+a^2)^n}}=
+\frac{1}{a^2}\int{\frac{1}{x^m(x^2+a^2)^{n-1}}}-
+\frac{1}{a^2}\int{\frac{1}{x^{m-2}(x^2+a^2)^n}}
$$
<<*>>=
)clear all
diff --git a/src/input/schaum7.input.pamphlet b/src/input/schaum7.input.pamphlet
new file mode 100644
index 0000000..9226da0
--- /dev/null
+++ b/src/input/schaum7.input.pamphlet
@@ -0,0 +1,395 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum7.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.144~~~~~$\displaystyle\int{\frac{dx}{x^2-a^2}}$}
+$$\int{\frac{1}{x^2-a^2}}=\frac{1}{2a}\ln\left(\frac{x-a}{x+a}\right)$$
+$$\int{\frac{1}{x^2-a^2}}=-\frac{1}{a}\coth^{-1}\frac{x}{a}$$
+<<*>>=
+)spool schaum7.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 19
+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
+@
+
+\section{\cite{1}:14.145~~~~~$\displaystyle\int{\frac{x~dx}{x^2-a^2}}$}
+$$\int{\frac{x}{x^2-a^2}}=\frac{1}{2}\ln(x^2-a^2)$$
+<<*>>=
+)clear all
+
+--S 2 of 19
+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
+@
+
+\section{\cite{1}:14.146~~~~~$\displaystyle\int{\frac{x^2~dx}{x^2-a^2}}$}
+$$\int{\frac{x^2}{x^2-a^2}}=x+\frac{a}{2}\ln\left(\frac{x-a}{x+a}\right)$$
+<<*>>=
+)clear all
+
+--S 3 of 19
+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
+@
+
+\section{\cite{1}:14.147~~~~~$\displaystyle\int{\frac{x^3~dx}{x^2-a^2}}$}
+$$\int{\frac{x^3}{x^2-a^2}}=\frac{x^2}{2}+\frac{a^2}{2}\ln(x^2-a^2)$$
+
+<<*>>=
+)clear all
+
+--S 4 of 19
+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
+@
+
+\section{\cite{1}:14.148~~~~~$\displaystyle\int{\frac{dx}{x(x^2-a^2)}}$}
+$$\int{\frac{1}{x(x^2-a^2)}}=
+\frac{1}{2a^2}\ln\left(\frac{x^2-a^2}{x^2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 5 of 19
+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
+@
+
+\section{\cite{1}:14.149~~~~~$\displaystyle\int{\frac{dx}{x^2(x^2-a^2)}}$}
+$$\int{\frac{1}{x^2(x^2-a^2)}}=
+\frac{1}{a^2x}+\frac{1}{2a^3}\ln\left(\frac{x-a}{x+a}\right)
+$$
+<<*>>=
+)clear all
+
+--S 6 of 19
+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
+@
+
+\section{\cite{1}:14.150~~~~~$\displaystyle\int{\frac{dx}{x^3(x^2-a^2)}}$}
+$$\int{\frac{1}{x^3(x^2-a^2)}}=
+\frac{1}{2a^2x^2}-\frac{1}{2a^4}\ln\left(\frac{x^2}{x^2-a^2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 7 of 19
+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
+@
+
+\section{\cite{1}:14.151~~~~~$\displaystyle\int{\frac{dx}{(x^2-a^2)^2}}$}
+$$\int{\frac{1}{(x^2-a^2)^2}}=
+\frac{-x}{2a^2(x^2-a^2)}-\frac{1}{4a^3}\ln\left(\frac{x-a}{x+a}\right)
+$$
+<<*>>=
+)clear all
+
+--S 8 of 19
+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
+@
+
+\section{\cite{1}:14.152~~~~~$\displaystyle\int{\frac{x~dx}{(x^2-a^2)^2}}$}
+$$\int{\frac{x}{(x^2-a^2)^2}}=
+\frac{-1}{2(x^2-a^2)}
+$$
+<<*>>=
+)clear all
+
+--S 9 of 19
+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
+@
+
+\section{\cite{1}:14.153~~~~~$\displaystyle\int{\frac{x^2dx}{(x^2-a^2)^2}}$}
+$$\int{\frac{x^2}{(x^2-a^2)^2}}=
+\frac{-x}{2(x^2-a^2)}+\frac{1}{4a}\ln\left(\frac{x-a}{x+a}\right)
+$$
+<<*>>=
+)clear all
+
+--S 10 of 19
+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
+@
+
+\section{\cite{1}:14.154~~~~~$\displaystyle\int{\frac{x^3dx}{(x^2-a^2)^2}}$}
+$$\int{\frac{x^3}{(x^2-a^2)^2}}=
+\frac{-a^2}{2(x^2-a^2)}+\frac{1}{2}\ln(x^2-a^2)
+$$
+<<*>>=
+)clear all
+
+--S 11 of 19
+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
+@
+
+\section{\cite{1}:14.155~~~~~$\displaystyle\int{\frac{dx}{x(x^2-a^2)^2}}$}
+$$\int{\frac{1}{x(x^2-a^2)^2}}=
+\frac{-1}{2a^2(x^2-a^2)}+\frac{1}{2a^4}\ln\left(\frac{x^2}{x^2-a^2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 12 of 19
+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
+@
+
+\section{\cite{1}:14.156~~~~~$\displaystyle\int{\frac{dx}{x^2(x^2-a^2)^2}}$}
+$$\int{\frac{1}{x^2(x^2-a^2)^2}}=
+-\frac{1}{a^4x}-\frac{x}{2a^4(x^2-a^2)}-
+\frac{3}{4a^5}\ln\left(\frac{x-a}{x+a}\right)
+$$
+<<*>>=
+)clear all
+
+--S 13 of 19
+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
+@
+
+\section{\cite{1}:14.157~~~~~$\displaystyle\int{\frac{dx}{x^3(x^2-a^2)^2}}$}
+$$\int{\frac{1}{x^3(x^2-a^2)^2}}=
+-\frac{1}{2a^4x^2}-\frac{1}{2a^4(x^2-a^2)}+
+\frac{1}{a^6}\ln\left(\frac{x^2}{x^2-a^2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 14 of 19
+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
+@
+
+\section{\cite{1}:14.158~~~~~$\displaystyle\int{\frac{dx}{(x^2-a^2)^n}}$}
+$$\int{\frac{1}{(x^2-a^2)^n}}=
+\frac{-x}{2(n-1)a^2(x^2-a^2)^{n-1}}-
+\frac{2n-3}{(2n-2)a^2}\int{\frac{1}{(x^2-a^2)^{n-1}}}
+$$
+<<*>>=
+)clear all
+
+--S 15 of 19
+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~~~~~$\displaystyle\int{\frac{x~dx}{(x^2-a^2)^n}}$}
+$$\int{\frac{x}{(x^2-a^2)^n}}=
+\frac{-1}{2(n-1)(x^2-a^2)^{n-1}}
+$$
+<<*>>=
+)clear all
+
+--S 16 of 19
+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
+@
+
+\section{\cite{1}:14.160~~~~~$\displaystyle\int{\frac{dx}{x(x^2-a^2)^n}}$}
+$$\int{\frac{1}{x(x^2-a^2)^n}}=
+\frac{-1}{2(n-1)a^2(x^2-a^2)^{n-1}}-
+\frac{1}{a^2}\int{\frac{1}{x(x^2-a^2)^{n-1}}}
+$$
+<<*>>=
+)clear all
+
+--S 17 of 19
+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~~~~~$\displaystyle\int{\frac{x^mdx}{(x^2-a^2)^n}}$}
+$$\int{\frac{x^m}{(x^2-a^2)^n}}=
+\int{\frac{x^{m-2}}{(x^2-a^2)^{n-1}}}+
+a^2\int\frac{x^{m-2}}{(x^2-a^2)^n}
+$$
+<<*>>=
+)clear all
+
+--S 18 of 19
+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~~~~~$\displaystyle\int{\frac{dx}{x^m(x^2-a^2)^n}}$}
+$$\int{\frac{1}{x^m(x^2-a^2)^n}}=
+\frac{1}{a^2}\int{\frac{1}{x^{m-2}(x^2-a^2)^n}}-
+\frac{1}{a^2}\int{\frac{1}{x^m(x^2-a^2)^{n-1}}}
+$$
+<<*>>=
+)clear all
+
+--S 19 of 19
+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/input/schaum8.input.pamphlet b/src/input/schaum8.input.pamphlet
new file mode 100644
index 0000000..a5c0c7e
--- /dev/null
+++ b/src/input/schaum8.input.pamphlet
@@ -0,0 +1,395 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum8.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.163~~~~~$\displaystyle\int{\frac{dx}{a^2-x^2}}$}
+$$\int{\frac{1}{a^2-x^2}}=\frac{1}{2a}\ln\left(\frac{a-x}{a+x}\right)$$
+$$\int{\frac{1}{a^2-x^2}}=-\frac{1}{a}\coth^{-1}\frac{x}{a}$$
+<<*>>=
+)spool schaum8.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 19
+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
+@
+
+\section{\cite{1}:14.164~~~~~$\displaystyle\int{\frac{x~dx}{a^2-x^2}}$}
+$$\int{\frac{x}{a^2-x^2}}=-\frac{1}{2}\ln(a^2-x^2)$$
+<<*>>=
+)clear all
+
+--S 2 of 19
+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
+@
+
+\section{\cite{1}:14.165~~~~~$\displaystyle\int{\frac{x^2~dx}{a^2-x^2}}$}
+$$\int{\frac{x^2}{a^2-x^2}}=-x+\frac{a}{2}\ln\left(\frac{a+x}{a-x}\right)$$
+<<*>>=
+)clear all
+
+--S 3 of 19
+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
+@
+
+\section{\cite{1}:14.166~~~~~$\displaystyle\int{\frac{x^3~dx}{a^2-x^2}}$}
+$$\int{\frac{x^3}{a^2-x^2}}=-\frac{x^2}{2}-\frac{a^2}{2}\ln(a^2-x^2)$$
+
+<<*>>=
+)clear all
+
+--S 4 of 19
+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
+@
+
+\section{\cite{1}:14.167~~~~~$\displaystyle\int{\frac{dx}{x(a^2-x^2)}}$}
+$$\int{\frac{1}{x(a^2-x^2)}}=
+\frac{1}{2a^2}\ln\left(\frac{x^2}{a^2-x^2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 5 of 19
+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
+@
+
+\section{\cite{1}:14.168~~~~~$\displaystyle\int{\frac{dx}{x^2(a^2-x^2)}}$}
+$$\int{\frac{1}{x^2(a^2-x^2)}}=
+\frac{1}{a^2x}+\frac{1}{2a^3}\ln\left(\frac{a+x}{a-x}\right)
+$$
+<<*>>=
+)clear all
+
+--S 6 of 19
+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
+@
+
+\section{\cite{1}:14.169~~~~~$\displaystyle\int{\frac{dx}{x^3(a^2-x^2)}}$}
+$$\int{\frac{1}{x^3(a^2-x^2)}}=
+-\frac{1}{2a^2x^2}+\frac{1}{2a^4}\ln\left(\frac{x^2}{a^2-x^2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 7 of 19
+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
+@
+
+\section{\cite{1}:14.170~~~~~$\displaystyle\int{\frac{dx}{(a^2-x^2)^2}}$}
+$$\int{\frac{1}{(a^2-x^2)^2}}=
+\frac{x}{2a^2(a^2-x^2)}+\frac{1}{4a^3}\ln\left(\frac{a+x}{a-x}\right)
+$$
+<<*>>=
+)clear all
+
+--S 8 of 19
+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
+@
+
+\section{\cite{1}:14.171~~~~~$\displaystyle\int{\frac{x~dx}{(a^2-x^2)^2}}$}
+$$\int{\frac{x}{(a^2-x^2)^2}}=
+\frac{1}{2(a^2-x^2)}
+$$
+<<*>>=
+)clear all
+
+--S 9 of 19
+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
+@
+
+\section{\cite{1}:14.172~~~~~$\displaystyle\int{\frac{x^2dx}{(a^2-x^2)^2}}$}
+$$\int{\frac{x^2}{(a^2-x^2)^2}}=
+\frac{x}{2(a^2-x^2)}-\frac{1}{4a}\ln\left(\frac{a+x}{a-x}\right)
+$$
+<<*>>=
+)clear all
+
+--S 10 of 19
+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
+@
+
+\section{\cite{1}:14.173~~~~~$\displaystyle\int{\frac{x^3dx}{(a^2-x^2)^2}}$}
+$$\int{\frac{x^3}{(a^2-x^2)^2}}=
+\frac{a^2}{2(a^2-x^2)}+\frac{1}{2}\ln(a^2-x^2)
+$$
+<<*>>=
+)clear all
+
+--S 11 of 19
+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
+@
+
+\section{\cite{1}:14.174~~~~~$\displaystyle\int{\frac{dx}{x(a^2-x^2)^2}}$}
+$$\int{\frac{1}{x(a^2-x^2)^2}}=
+\frac{1}{2a^2(a^2-x^2)}+\frac{1}{2a^4}\ln\left(\frac{x^2}{a^2-x^2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 12 of 19
+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
+@
+
+\section{\cite{1}:14.175~~~~~$\displaystyle\int{\frac{dx}{x^2(a^2-x^2)^2}}$}
+$$\int{\frac{1}{x^2(a^2-x^2)^2}}=
+-\frac{1}{a^4x}+\frac{x}{2a^4(a^2-x^2)}+
+\frac{3}{4a^5}\ln\left(\frac{a+x}{a-x}\right)
+$$
+<<*>>=
+)clear all
+
+--S 13 of 19
+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
+@
+
+\section{\cite{1}:14.176~~~~~$\displaystyle\int{\frac{dx}{x^3(a^2-x^2)^2}}$}
+$$\int{\frac{1}{x^3(a^2-x^2)^2}}=
+\frac{1}{2a^4x^2}+\frac{1}{2a^4(a^2-x^2)}+
+\frac{1}{a^6}\ln\left(\frac{x^2}{a^2-x^2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 14 of 19
+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
+@
+
+\section{\cite{1}:14.177~~~~~$\displaystyle\int{\frac{dx}{(a^2-x^2)^n}}$}
+$$\int{\frac{1}{(a^2-x^2)^n}}=
+\frac{x}{2(n-1)a^2(a^2-x^2)^{n-1}}+
+\frac{2n-3}{(2n-2)a^2}\int{\frac{1}{(a^2-x^2)^{n-1}}}
+$$
+<<*>>=
+)clear all
+
+--S 15 of 19
+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~~~~~$\displaystyle\int{\frac{x~dx}{(a^2-x^2)^n}}$}
+$$\int{\frac{x}{(a^2-x^2)^n}}=
+\frac{1}{2(n-1)(a^2-x^2)^{n-1}}
+$$
+<<*>>=
+)clear all
+
+--S 16 of 19
+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
+@
+
+\section{\cite{1}:14.179~~~~~$\displaystyle\int{\frac{dx}{x(a^2-x^2)^n}}$}
+$$\int{\frac{1}{x(a^2-x^2)^n}}=
+\frac{1}{2(n-1)a^2(a^2-x^2)^{n-1}}+
+\frac{1}{a^2}\int{\frac{1}{x(a^2-x^2)^{n-1}}}
+$$
+<<*>>=
+)clear all
+
+--S 17 of 19
+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~~~~~$\displaystyle\int{\frac{x^mdx}{(a^2-x^2)^n}}$}
+$$\int{\frac{x^m}{(a^2-x^2)^n}}=
+a^2\int\frac{x^{m-2}}{(a^2-x^2)^n}-
+\int{\frac{x^{m-2}}{(a^2-x^2)^{n-1}}}
+$$
+<<*>>=
+)clear all
+
+--S 18 of 19
+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~~~~~$\displaystyle\int{\frac{dx}{x^m(a^2-x^2)^n}}$}
+$$\int{\frac{1}{x^m(a^2-x^2)^n}}=
+\frac{1}{a^2}\int{\frac{1}{x^m(a^2-x^2)^{n-1}}}+
+\frac{1}{a^2}\int{\frac{1}{x^{m-2}(a^2-x^2)^n}}
+$$
+<<*>>=
+)clear all
+
+--S 19 of 19
+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}
diff --git a/src/input/schaum9.input.pamphlet b/src/input/schaum9.input.pamphlet
new file mode 100644
index 0000000..6610811
--- /dev/null
+++ b/src/input/schaum9.input.pamphlet
@@ -0,0 +1,776 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum9.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.182~~~~~$\displaystyle\int{\frac{dx}{\sqrt{x^2+a^2}}}$}
+$$\int{\frac{1}{\sqrt{x^2+a^2}}}=\ln\left(x+\sqrt{x^2+a^2}\right)$$
+$$\int{\frac{1}{\sqrt{x^2+a^2}}}=\sinh^{-1}\frac{x}{a}$$
+<<*>>=
+)spool schaum9.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 28
+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
+@
+
+\section{\cite{1}:14.183~~~~~$\displaystyle\int{\frac{x~dx}{\sqrt{x^2+a^2}}}$}
+$$\int{\frac{x}{\sqrt{x^2+a^2}}}=\sqrt{x^2+a^2}$$
+<<*>>=
+)clear all
+
+--S 2 of 28
+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
+@
+
+\section{\cite{1}:14.184~~~~~$\displaystyle
+\int{\frac{x^2~dx}{\sqrt{x^2+a^2}}}$}
+$$\int{\frac{x^2}{\sqrt{x^2+a^2}}}=
+\frac{x\sqrt{x^2+a^2}}{2}-\frac{a^2}{2}\ln\left(x+\sqrt{x^2+a^2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 3 of 28
+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
+@
+
+\section{\cite{1}:14.185~~~~~$\displaystyle
+\int{\frac{x^3~dx}{\sqrt{x^2+a^2}}}$}
+$$\int{\frac{x^3}{\sqrt{x^2+a^2}}}=
+\frac{(x^2+a^2)^{3/2}}{3}-a^2\sqrt{x^2+a^2}
+$$
+<<*>>=
+)clear all
+
+--S 4 of 28
+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
+@
+
+\section{\cite{1}:14.186~~~~~$\displaystyle\int{\frac{dx}{x\sqrt{x^2+a^2}}}$}
+$$\int{\frac{1}{x\sqrt{x^2+a^2}}}=
+-\frac{1}{a}\ln\left(\frac{a+\sqrt{x^2+a^2}}{x}\right)
+$$
+<<*>>=
+)clear all
+
+--S 5 of 28
+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
+@
+
+\section{\cite{1}:14.187~~~~~$\displaystyle
+\int{\frac{dx}{x^2\sqrt{x^2+a^2}}}$}
+$$\int{\frac{1}{x^2\sqrt{x^2+a^2}}}=
+-\frac{\sqrt{x^2+a^2}}{a^2x}
+$$
+<<*>>=
+)clear all
+
+--S 6 of 28
+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
+@
+
+\section{\cite{1}:14.188~~~~~$\displaystyle\int{\frac{dx}{x^3\sqrt{x^2+a^2}}}$}
+$$\int{\frac{1}{x^3\sqrt{x^2+a^2}}}=
+-\frac{\sqrt{x^2+a^2}}{2a^2x^2}+\frac{1}{2a^3}
+\ln\left(\frac{a+\sqrt{x^2+a^2}}{x}\right)
+$$
+<<*>>=
+)clear all
+
+--S 7 of 28
+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
+@
+
+\section{\cite{1}:14.189~~~~~$\displaystyle\int{\sqrt{x^2+a^2}}~dx$}
+$$\int{\sqrt{x^2+a^2}}=
+\frac{x\sqrt{x^2+a^2}}{2}+\frac{a^2}{2}\ln\left(x+\sqrt{x^2+a^2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 8 of 28
+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
+@
+
+\section{\cite{1}:14.190~~~~~$\displaystyle\int{x\sqrt{x^2+a^2}}~dx$}
+$$\int{x\sqrt{x^2+a^2}}=
+\frac{(x^2+a^2)^{3/2}}{3}
+$$
+<<*>>=
+)clear all
+
+--S 9 of 28
+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
+@
+
+\section{\cite{1}:14.191~~~~~$\displaystyle
+\int{x^2\sqrt{x^2+a^2}}~dx$}
+$$\int{x^2\sqrt{x^2+a^2}}=
+\frac{x(x^2+a^2)^{3/2}}{4}-\frac{a^2x\sqrt{x^2+a^2}}{8}-
+\frac{a^4}{8}\ln\left(x+\sqrt{x^2+a^2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 10 of 28
+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
+@
+
+\section{\cite{1}:14.192~~~~~$\displaystyle
+\int{x^3\sqrt{x^2+a^2}}~dx$}
+$$\int{x^3\sqrt{x^2+a^2}}=
+\frac{(x^2+a^2)^{5/2}}{5}-\frac{a^2(x^2+a^2)^{3/2}}{3}
+$$
+<<*>>=
+)clear all
+
+--S 11 of 28
+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
+@
+
+\section{\cite{1}:14.193~~~~~$\displaystyle
+\int{\frac{\sqrt{x^2+a^2}}{x}}~dx$}
+$$\int{\frac{\sqrt{x^2+a^2}}{x}}=
+\sqrt{x^2+a^2}-a\ln\left(\frac{a+\sqrt{x^2+a^2}}{x}\right)
+$$
+<<*>>=
+)clear all
+
+--S 12 of 28
+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
+@
+
+\section{\cite{1}:14.194~~~~~$\displaystyle
+\int{\frac{\sqrt{x^2+a^2}}{x^2}}~dx$}
+$$\int{\frac{\sqrt{x^2+a^2}}{x^2}}=
+-\frac{\sqrt{x^2+a^2}}{x}+\ln\left(x+\sqrt{x^2+a^2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 13 of 28
+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
+@
+
+\section{\cite{1}:14.195~~~~~$\displaystyle
+\int{\frac{\sqrt{x^2+a^2}}{x^3}}~dx$}
+$$\int{\frac{\sqrt{x^2+a^2}}{x^3}}=
+-\frac{\sqrt{x^2+a^2}}{2x^2}-\frac{1}{2a}
+\ln\left(\frac{a+\sqrt{x^2+a^2}}{x}\right)
+$$
+<<*>>=
+)clear all
+
+--S 14 of 28
+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
+@
+
+\section{\cite{1}:14.196~~~~~$\displaystyle\int{\frac{dx}{(x^2+a^2)^{3/2}}}$}
+$$\int{\frac{1}{(x^2+a^2)^{3/2}}}=
+\frac{x}{a^2\sqrt{x^2+a^2}}
+$$
+<<*>>=
+)clear all
+
+--S 15 of 28
+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
+@
+
+\section{\cite{1}:14.197~~~~~$\displaystyle
+\int{\frac{x~dx}{(x^2+a^2)^{3/2}}}$}
+$$\int{\frac{x}{(x^2+a^2)^{3/2}}}=
+\frac{-1}{\sqrt{x^2+a^2}}
+$$
+<<*>>=
+)clear all
+
+--S 16 of 28
+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
+@
+
+\section{\cite{1}:14.198~~~~~$\displaystyle
+\int{\frac{x^2dx}{(x^2+a^2)^{3/2}}}$}
+$$\int{\frac{x^2}{(x^2+a^2)^{3/2}}}=
+\frac{-x}{\sqrt{x^2+a^2}}+\ln\left(x+\sqrt{x^2+a^2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 17 of 28
+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
+@
+
+\section{\cite{1}:14.199~~~~~$\displaystyle
+\int{\frac{x^3dx}{(x^2+a^2)^{3/2}}}$}
+$$\int{\frac{x^3}{(x^2+a^2)^{3/2}}}=
+\sqrt{x^2+a^2}+\frac{a^2}{\sqrt{x^2+a^2}}
+$$
+<<*>>=
+)clear all
+
+--S 18 of 28
+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
+@
+
+\section{\cite{1}:14.200~~~~~$\displaystyle
+\int{\frac{dx}{x(x^2+a^2)^{3/2}}}$}
+$$\int{\frac{1}{x(x^2+a^2)^{3/2}}}=
+\frac{1}{a^2\sqrt{x^2+a^2}}-
+\frac{1}{a^3}\ln\left(\frac{a+\sqrt{x^2+a^2}}{x}\right)
+$$
+<<*>>=
+)clear all
+
+--S 19 of 28
+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
+@
+
+\section{\cite{1}:14.201~~~~~$\displaystyle
+\int{\frac{dx}{x^2(x^2+a^2)^{3/2}}}$}
+$$\int{\frac{1}{x^2(x^2+a^2)^{3/2}}}=
+-\frac{\sqrt{x^2+a^2}}{a^4x}-\frac{x}{a^4\sqrt{x^2+a^2}}
+$$
+<<*>>=
+)clear all
+
+--S 20 of 28
+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
+@
+
+\section{\cite{1}:14.202~~~~~$\displaystyle
+\int{\frac{dx}{x^3(x^2+a^2)^{3/2}}}$}
+$$\int{\frac{1}{x^3(x^2+a^2)^{3/2}}}=
+\frac{-1}{2a^2x^2\sqrt{x^2+a^2}}-
+\frac{3}{2a^4\sqrt{x^2+a^2}}+
+\frac{3}{2a^5}\ln\left(\frac{a+\sqrt{x^2+a^2}}{x}\right)
+$$
+<<*>>=
+)clear all
+
+--S 21 of 28
+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
+@
+
+\section{\cite{1}:14.203~~~~~$\displaystyle\int{(x^2+a^2)^{3/2}}~dx$}
+$$\int{(x^2+a^2)^{3/2}}=
+\frac{x(x^2+a^2)^{3/2}}{4}+\frac{3a^2x\sqrt{x^2+a^2}}{8}+
+\frac{3}{8}a^4\ln\left(x+\sqrt{x^2+a^2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 22 of 28
+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
+@
+
+\section{\cite{1}:14.204~~~~~$\displaystyle\int{x(x^2+a^2)^{3/2}}~dx$}
+$$\int{x(x^2+a^2)^{3/2}}=\frac{(x^2+a^2)^{5/2}}{5}$$
+<<*>>=
+)clear all
+
+--S 23 of 28
+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
+@
+
+\section{\cite{1}:14.205~~~~~$\displaystyle\int{x^2(x^2+a^2)^{3/2}}~dx$}
+$$\int{x^2(x^2+a^2)^{3/2}}=
+\frac{x(x^2+a^2)^{5/2}}{6}-\frac{a^2x(x^2+a^2)^{3/2}}{24}-
+\frac{a^4x\sqrt{x^2+a^2}}{16}-
+\frac{a^6}{16}\ln\left(x+\sqrt{x^2+a^2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 24 of 28
+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
+@
+
+\section{\cite{1}:14.206~~~~~$\displaystyle\int{x^3(x^2+a^2)^{3/2}}~dx$}
+$$\int{x^3(x^2+a^2)^{3/2}}=
+\frac{(x^2+a^2)^{7/2}}{7}-\frac{a^2(x^2+a^2)^{5/2}}{5}
+$$
+<<*>>=
+)clear all
+
+--S 25 of 28
+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
+@
+
+\section{\cite{1}:14.207~~~~~$\displaystyle
+\int{\frac{(x^2+a^2)^{3/2}}{x}}~dx$}
+$$\int{\frac{(x^2+a^2)^{3/2}}{x}}=
+\frac{(x^2+a^2)^{3/2}}{3}+a^2\sqrt{x^2+a^2}-
+a^3\ln\left(\frac{a+\sqrt{x^2+a^2}}{x}\right)
+$$
+<<*>>=
+)clear all
+
+--S 26 of 28
+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
+@
+
+\section{\cite{1}:14.208~~~~~$\displaystyle
+\int{\frac{(x^2+a^2)^{3/2}}{x^2}}~dx$}
+$$\int{\frac{(x^2+a^2)^{3/2}}{x^2}}=
+-\frac{(x^2+a^2)^{3/2}}{x}+\frac{3x\sqrt{x^2+a^2}}{2}+
+\frac{3}{2}a^2\ln\left(x+\sqrt{x^2+a^2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 27 of 28
+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
+@
+
+\section{\cite{1}:14.209~~~~~$\displaystyle
+\int{\frac{(x^2+a^2)^{3/2}}{x^3}}~dx$}
+$$\int{\frac{(x^2+a^2)^{3/2}}{x^3}}=
+-\frac{(x^2+a^2)^{3/2}}{2x^2}+\frac{3}{2}\sqrt{x^2+a^2}-
+\frac{3}{2}a\ln\left(\frac{a+\sqrt{x^2+a^2}}{x}\right)
+$$
+<<*>>=
+)clear all
+
+--S 28 of 28
+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
+
+)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}
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