[Top][All Lists]
[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]
[Axiom-developer] 20080328.01.tpd.patch (CATS integration regression tes
|
From: |
daly |
|
Subject: |
[Axiom-developer] 20080328.01.tpd.patch (CATS integration regression testing) |
|
Date: |
Sat, 29 Mar 2008 01:03:01 -0600 |
More testing of integration, part of the computer algebra test suite.
Tim
=========================================================================
diff --git a/changelog b/changelog
index f2d93ae..c467da5 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,9 @@
+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)
+20080328 tpd src/input/schaum4.input integrals of sqrt(ax+b) and px+q
+20080328 tpd src/input/schaum3.input integrals of ax+b and px+q
+20080328 tpd src/input/schaum2.input integrals of sqrt(ax+b)
20080325 tpd Makefile VERSION="Axiom (March 2008)"
20080325 tpd src/algebra/axserver.spad set up handling of operations pages
20080325 tpd src/interp/interp-proclaims.lisp case-change display
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet
index 2b626c3..d4caed2 100644
--- a/src/input/Makefile.pamphlet
+++ b/src/input/Makefile.pamphlet
@@ -355,7 +355,8 @@ REGRES= algaggr.regress algbrbf.regress algfacob.regress
alist.regress \
r21bugsbig.regress r21bugs.regress radff.regress radix.regress \
realclos.regress reclos.regress repa6.regress robidoux.regress \
roman.regress roots.regress ruleset.regress rules.regress \
- schaum1.regress \
+ schaum1.regress schaum2.regress schaum3.regress schaum4.regress \
+ schaum5.regress schaum6.regress \
scherk.regress scope.regress seccsc.regress \
segbind.regress seg.regress \
series2.regress series.regress sersolve.regress set.regress \
@@ -628,6 +629,8 @@ FILES= ${OUT}/algaggr.input ${OUT}/algbrbf.input
${OUT}/algfacob.input \
${OUT}/reclos.input ${OUT}/regset.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}/saddle.input \
${OUT}/scherk.input ${OUT}/scope.input ${OUT}/seccsc.input \
${OUT}/segbind.input ${OUT}/seg.input ${OUT}/series2.input \
@@ -926,7 +929,9 @@ DOCFILES= \
${DOC}/robidoux.input.dvi ${DOC}/roman.input.dvi \
${DOC}/romnum.as.dvi ${DOC}/roots.input.dvi \
${DOC}/ruleset.input.dvi ${DOC}/rules.input.dvi \
- ${DOC}/schaum1.input.dvi \
+ ${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}/s01eaf.input.dvi ${DOC}/s13aaf.input.dvi \
${DOC}/s13acf.input.dvi ${DOC}/s13adf.input.dvi \
${DOC}/s14aaf.input.dvi ${DOC}/s14abf.input.dvi \
diff --git a/src/input/schaum2.input.pamphlet b/src/input/schaum2.input.pamphlet
new file mode 100644
index 0000000..cb8e6db
--- /dev/null
+++ b/src/input/schaum2.input.pamphlet
@@ -0,0 +1,1464 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum2.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.84~~~~~$\displaystyle\int{\frac{dx}{\sqrt{ax+b}}}$}
+$$\int{\frac{dx}{\sqrt{ax+b}}}=\frac{2\sqrt{ax+b}}{a}$$
+<<*>>=
+)spool schaum2.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 92
+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 of 92
+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 of 92
+cc:=aa-bb
+--R
+--R
+--R (3) 0
+--R Type: Expression
Integer
+--E
+@
+
+\section{\cite{1}:14.85~~~~~$\displaystyle\int{\frac{x~dx}{\sqrt{ax+b}}}$}
+$$\int{\frac{x~dx}{\sqrt{ax+b}}}=\frac{2(ax-2b)}{3a^2}\sqrt{ax+b}$$
+<<*>>=
+)clear all
+
+--S 4 of 92
+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 of 92
+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 of 92
+cc:=aa-bb
+--R
+--R
+--R (3) 0
+--R Type: Expression
Integer
+--E
+@
+
+\section{\cite{1}:14.86~~~~~$\displaystyle\int{\frac{x^2~dx}{\sqrt{ax+b}}}$}
+$$\int{\frac{x~dx}{\sqrt{ax+b}}}=
+\frac{2(3a^2x^2-4abx+8b^2)}{15a^2}\sqrt{ax+b}$$
+<<*>>=
+)clear all
+
+--S 7 of 92
+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 of 92
+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 of 92
+cc:=aa-bb
+--R
+--R
+--R (3) 0
+--R Type: Expression
Integer
+--E
+@
+
+\section{\cite{1}:14.87~~~~~$\displaystyle\int{\frac{dx}{x\sqrt{ax+b}}}$}
+$$\int{\frac{dx}{x\sqrt{ax+b}}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{1}{\sqrt{b}}~\ln
+\left(\frac{\sqrt{ax+b}-\sqrt{b}}{\sqrt{ax+b}+\sqrt{b}}\right)\\
+\displaystyle
+\frac{2}{\sqrt{-b}}~\tan^{-1}\sqrt{\frac{ax+b}{-b}}
+\end{array}
+\right.$$
+
+Note: the first answer assumes $b > 0$ and the second assumes $b < 0$.
+<<*>>=
+)clear all
+
+--S 10 of 92
+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 $b > 0$:
+<<*>>=
+--S 11 of 92
+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
+<<*>>=
+--S 12 of 92
+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:
+<<*>>=
+--S 13 of 92
+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
+<<*>>=
+--S 14 of 92
+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 $(sqrt(a*x+b) - sqrt(b))$
+<<*>>=
+--S 15 of 92
+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 $(sqrt(a*x+b) - sqrt(b))$
+<<*>>=
+--S 16 of 92
+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 $a*sqrt(b)$
+<<*>>=
+--S 17 of 92
+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:
+<<*>>=
+--S 18 of 92
+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:
+<<*>>=
+--S 19 of 92
+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:
+<<*>>=
+--S 20 of 92
+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.
+<<*>>=
+--S 21 of 92
+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
+<<*>>=
+--S 22 of 92
+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
+<<*>>=
+--S 23 of 92
+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:
+<<*>>=
+--S 24 of 92
+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.
+<<*>>=
+--S 25 of 92
+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
+<<*>>=
+--S 26 of 92
+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~~~~~$\displaystyle\int{\frac{dx}{x^2\sqrt{ax+b}}}$}
+$$\int{\frac{dx}{x^2\sqrt{ax+b}}}=
+-\frac{\sqrt{ax+b}}{bx}-\frac{a}{2b}~\int{\frac{dx}{x\sqrt{ax+b}}}$$
+<<*>>=
+)clear all
+
+--S 27 of 92
+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
+<<*>>=
+--S 28 of 92
+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
+$b > 0$
+<<*>>=
+--S 29 of 92
+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 $b < 0$.
+<<*>>=
+--S 30 of 92
+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
+<<*>>=
+--S 31 of 92
+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
+<<*>>=
+--S 32 of 92
+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.
+<<*>>=
+--S 33 of 92
+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
+<<*>>=
+--S 34 of 92
+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
+<<*>>=
+--S 35 of 92
+ad1-target
+--R
+--R (9) 0
+--R Type: Expression
Integer
+--E
+@
+and now we do the same with first Spiegel's answer:
+<<*>>=
+--S 36 of 92
+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
+<<*>>=
+--S 37 of 92
+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.
+<<*>>=
+--S 38 of 92
+cc22:=bb2-aa.2
+--R
+--R
+--R (12) 0
+--R Type: Expression
Integer
+--E
+@
+
+\section{\cite{1}:14.89~~~~~$\displaystyle\int{\sqrt{ax+b}~dx}$}
+$$\int{\sqrt{ax+b}~dx}=
+\frac{2\sqrt{(ax+b)^3}}{3a}$$
+<<*>>=
+)clear all
+
+--S 39 of 92
+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
+@
+<<*>>=
+--S 40 of 92
+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
+@
+<<*>>=
+--S 41 of 92
+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
+<<*>>=
+--S 42 of 92
+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
+<<*>>=
+--S 43 of 92
+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
+<<*>>=
+--S 44 of 92
+t1-target
+--R
+--R (6) 0
+--R Type: Expression
Integer
+--E
+@
+So they are equal. Now we do the same with Spiegel's answer
+<<*>>=
+--S 45 of 92
+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
+<<*>>=
+--S 46 of 92
+nn:=(a*x+b)^2
+--R
+--R 2 2 2
+--R (8) a x + 2a b x + b
+--R Type: Polynomial
Integer
+--E
+@
+<<*>>=
+--S 47 of 92
+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.
+<<*>>=
+--S 48 of 92
+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~~~~~$\displaystyle\int{x\sqrt{ax+b}~dx}$}
+$$\int{x\sqrt{ax+b}~dx}=
+\frac{2(3ax-2b)}{15a^2}~\sqrt{(ax+b)^3}$$
+<<*>>=
+)clear all
+
+--S 49 of 92
+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 of 92
+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 of 92
+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
+@
+If we had the terms
+<<*>>=
+--S 52 of 92
+t1:=(3*a*x-2*b)
+--R
+--R (4) 3a x - 2b
+--R Type: Polynomial
Integer
+--E
+@
+<<*>>=
+--S 53 of 92
+t2:=(a*x+b)
+--R
+--R (5) a x + b
+--R Type: Polynomial
Integer
+--E
+@
+We can construct the Axiom result
+<<*>>=
+--S 54 of 92
+2*t1*t2*sqrt(t2)/(15*a^2)
+--R
+--R 2 2 2 +-------+
+--R (6a x + 2a b x - 4b )\|a x + b
+--R (6) --------------------------------
+--R 2
+--R 15a
+--R Type: Expression
Integer
+--E
+@
+and we can construct the Spiegel result
+<<*>>=
+--S 55 of 92
+2*t1*sqrt(t2^3)/(15*a^2)
+--R
+--R +----------------------------+
+--R | 3 3 2 2 2 3
+--R (6a x - 4b)\|a x + 3a b x + 3a b x + b
+--R (7) ------------------------------------------
+--R 2
+--R 15a
+--R Type: Expression
Integer
+--E
+@
+the difference of these two depends on
+<<*>>=
+--S 56 of 92
+t2*sqrt(t2)-sqrt(t2^3)
+--R
+--R +----------------------------+
+--R | 3 3 2 2 2 3 +-------+
+--R (8) - \|a x + 3a b x + 3a b x + b + (a x + b)\|a x + b
+--R Type: Expression
Integer
+--E
+@
+
+\section{\cite{1}:14.91~~~~~$\displaystyle\int{x^2\sqrt{ax+b}~dx}$}
+$$\int{x^2\sqrt{ax+b}~dx}=
+\frac{2(15a^2x^2-12abx+8b^2)}{105a^2}~\sqrt{(a+bx)^3}$$
+Note: the sqrt term is almost certainly $\sqrt{(ax+b)}$
+<<*>>=
+)clear all
+
+--S 57 of 92
+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 58 of 92
+bb:=(2*(15*a^2*x^2-12*a*b*x+8*b^2))/(105*a^2)*sqrt((a*x+b)^3)
+--R
+--R
+--R +----------------------------+
+--R 2 2 2 | 3 3 2 2 2 3
+--R (30a x - 24a b x + 16b )\|a x + 3a b x + 3a b x + b
+--R (2) --------------------------------------------------------
+--R 2
+--R 105a
+--R Type: Expression
Integer
+--E
+@
+<<*>>=
+--S 59 of 92
+cc:=aa-bb
+--R
+--R
+--R (3)
+--R +----------------------------+
+--R 3 2 2 2 | 3 3 2 2 2 3
+--R (- 30a x + 24a b x - 16a b )\|a x + 3a b x + 3a b x + b
+--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
+@
+
+\section{\cite{1}:14.92~~~~~$\displaystyle\int{\frac{\sqrt{ax+b}}{x}~dx}$}
+$$\int{\frac{\sqrt{ax+b}}{x}~dx}=
+2\sqrt{ax+b}+b~\int{\frac{dx}{x\sqrt{ax+b}}}$$
+<<*>>=
+)clear all
+
+--S 60 of 92
+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 61 of 92
+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 62 of 92
+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 63 of 92
+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 64 of 92
+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 65 of 92
+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 66 of 92
+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 67 of 92
+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
+@
+
+\section{\cite{1}:14.93~~~~~$\displaystyle\int{\frac{\sqrt{ax+b}}{x^2}~dx}$}
+$$\int{\frac{\sqrt{ax+b}}{x^2}~dx}=
+-\frac{\sqrt{ax+b}}{x}+\frac{a}{2}~\int{\frac{dx}{x\sqrt{ax+b}}}$$
+<<*>>=
+)clear all
+
+--S 68 of 92
+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 69 of 92
+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 70 of 92
+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 71 of 92
+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 72 of 92
+cc11:=bb1-aa.1
+--R
+--R
+--R (5) 0
+--R Type: Expression
Integer
+--E
+@
+<<*>>=
+--S 73 of 92
+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 74 of 92
+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 75 of 92
+cc22:=bb2-aa.2
+--R
+--R
+--R (8) 0
+--R Type: Expression
Integer
+--E
+@
+
+\section{\cite{1}:14.94~~~~~$\displaystyle\int{\frac{x^m}{\sqrt{ax+b}}~dx}$}
+$$\int{\frac{x^m}{\sqrt{ax+b}}~dx}=
+\frac{2x^m\sqrt{ax+b}}{(2m+1)a}-\frac{2mb}{(2m+1)a}
+~\int{\frac{x^{m-1}}{\sqrt{ax+b}}~dx}$$
+<<*>>=
+)clear all
+
+--S 76 of 92
+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~~~~~$\displaystyle\int{\frac{dx}{x^m\sqrt{ax+b}}}$}
+$$\int{\frac{dx}{x^m\sqrt{ax+b}}}=
+-\frac{\sqrt{ax+b}}{(m-1)bx^{m-1}}-\frac{(2m-3)a}{(2m-2)b}
+~\int{\frac{dx}{x^{m-1}\sqrt{ax+b}}}$$
+<<*>>=
+)clear all
+
+--S 77 of 92
+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~~~~~$\displaystyle\int{x^m\sqrt{ax+b}~dx}$}
+$$\int{x^m\sqrt{ax+b}~dx}=
+\frac{2x^m}{(2m+3)a}(ax+b)^{3/2}
+-\frac{2mb}{(2m+3)a}~\int{x^{m-1}\sqrt{ax+b}~dx}$$
+<<*>>=
+)clear all
+
+--S 78 of 92
+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~~~~~$\displaystyle\int{\frac{\sqrt{ax+b}}{x^m}~dx}$}
+$$\int{\frac{\sqrt{ax+b}}{x^m}~dx}=
+-\frac{\sqrt{ax+b}}{(m-1)x^{m-1}}
++\frac{a}{2(m-1)}~\int{\frac{dx}{x^{m-1}\sqrt{ax+b}}}$$
+<<*>>=
+)clear all
+
+--S 79 of 92
+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~~~~~$\displaystyle\int{\frac{\sqrt{ax+b}}{x^m}~dx}$}
+$$\int{\frac{\sqrt{ax+b}}{x^m}~dx}=
+\frac{-(ax+b)^{3/2}}{(m-1)bx^{m-1}}
+-\frac{(2m-5)a}{(2m-2)b}~\int{\frac{\sqrt{ax+b}}{x^{m-1}}~dx}$$
+Note: 14.98 is the same as 14.97
+<<*>>=
+)clear all
+
+--S 80 of 92
+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~~~~~$\displaystyle\int{(ax+b)^{m/2}~dx}$}
+$$\int{(ax+b)^{m/2}~dx}=
+\frac{2(ax+b)^{(m+2)/2}}{a(m+2)}$$
+<<*>>=
+)clear all
+
+--S 81 of 92
+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 82 of 92
+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 83 of 92
+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
+@
+
+\section{\cite{1}:14.100~~~~~$\displaystyle\int{x(ax+b)^{m/2}~dx}$}
+$$\int{x(ax+b)^{m/2}~dx}=
+\frac{2(ax+b)^{(m+4)/2}}{a^2(m+4)}
+-\frac{2b(ax+b)^{(m+2)/2}}{a^2(m+2)}$$
+<<*>>=
+)clear all
+
+--S 84 of 92
+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 of 92
+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 of 92
+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
+@
+
+\section{\cite{1}:14.101~~~~~$\displaystyle\int{x^2(ax+b)^{m/2}~dx}$}
+$$\int{x^2(ax+b)^{m/2}~dx}=
+\frac{2(ax+b)^{(m+6)/2}}{a^3(m+6)}
+-\frac{4b(ax+b)^{(m+4)/2}}{a^3(m+4)}
++\frac{2b^2(ax+b)^{(m+2)/2}}{a^3(m+2)}$$
+<<*>>=
+)clear all
+
+--S 87 of 92
+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 88 of 92
+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 89 of 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
+@
+
+\section{\cite{1}:14.102~~~~~$\displaystyle\int{\frac{(ax+b)^{m/2}}{x}~dx}$}
+$$\int{\frac{(ax+b)^{m/2}}{x}~dx}=
+\frac{2(ax+b)^{m/2}}{m}
++b~\int{\frac{(ax+b)^{(m-2)/2}}{x}~dx}$$
+<<*>>=
+)clear all
+
+--S 90 of 92
+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~~~~~$\displaystyle
+\int{\frac{(ax+b)^{m/2}}{x^2}~dx}$}
+$$\int{\frac{(ax+b)^{m/2}}{x^2}~dx}=
+-\frac{(ax+b)^{(m+2)/2}}{bx}
++\frac{ma}{2b}~\int{\frac{(ax+b)^{m/2}}{x}~dx}$$
+<<*>>=
+)clear all
+
+--S 91 of 92
+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~~~~~$\displaystyle
+\int{\frac{dx}{x(ax+b)^{m/2}}}$}
+$$\int{\frac{dx}{x(ax+b)^{m/2}}}=
+\frac{2}{(m-2)b(ax+b)^{(m-2)/2}}
++\frac{1}{b}~\int{\frac{dx}{x(ax+b)^{(m-2)/2}}}$$
+<<*>>=
+)clear all
+
+--S 92 of 92
+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}
diff --git a/src/input/schaum3.input.pamphlet b/src/input/schaum3.input.pamphlet
new file mode 100644
index 0000000..e273509
--- /dev/null
+++ b/src/input/schaum3.input.pamphlet
@@ -0,0 +1,409 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum3.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.105~~~~~$\displaystyle\int{\frac{dx}{(ax+b)(px+q)}}$}
+$$\int{\frac{dx}{(ax+b)(px+q)}}=
+\frac{1}{bp-aq}~\ln\left(\frac{px+q}{ax+b}\right)$$
+<<*>>=
+)spool schaum3.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 11
+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 of 11
+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 of 11
+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
+@
+
+\section{\cite{1}:14.106~~~~~$\displaystyle\int{\frac{x~dx}{(ax+b)(px+q)}}$}
+$$\int{\frac{x~dx}{(ax+b)(px+q)}}=
+\frac{1}{bp-aq}\left\{\frac{b}{a}~\ln(ax+b)-\frac{q}{p}~\ln(px+q)\right\}$$
+<<*>>=
+)clear all
+
+--S 4 of 11
+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 5 of 11
+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 6 of 11
+cc:=aa-bb
+--R
+--R
+--R (3) 0
+--R Type: Expression
Integer
+--E
+@
+
+\section{\cite{1}:14.107~~~~~$\displaystyle\int{\frac{dx}{(ax+b)^2(px+q)}}$}
+$$\int{\frac{dx}{(ax+b)^2(px+q)}}=
+\frac{1}{bp-aq}
+\left\{\frac{1}{ax+b}+
+\frac{p}{bp-aq}~\ln\left(\frac{px+q}{ax+b}\right)\right\}$$
+<<*>>=
+)clear all
+
+--S 7 of 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 8 of 11
+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 9 of 11
+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
+@
+
+\section{\cite{1}:14.108~~~~~$\displaystyle\int{\frac{x~dx}{(ax+b)^2(px+q)}}$}
+$$\int{\frac{x~dx}{(ax+b)^2(px+q)}}=
+\frac{1}{bp-aq}
+\left\{\frac{q}{bp-aq}
+~\ln\left(\frac{ax+b}{px+q}\right)-\frac{b}{a(ax+b)}\right\}$$
+
+<<*>>=
+)clear all
+
+--S 10 of 11
+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 11 of 11
+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
+@
+<<*>>=
+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
+@
+
+\section{\cite{1}:14.109~~~~~$\displaystyle
+\int{\frac{x^2~dx}{(ax+b)^2(px+q)}}$}
+$$\int{\frac{x^2~dx}{(ax+b)^2(px+q)}}=$$
+$$\frac{b^2}{(bp-aq)a^2(ax+b)}+\frac{1}{(bp-aq)^2}
+\left\{\frac{q^2}{p}~\ln(px+q)+\frac{b(bp-2aq)}{a^2}~\ln(ax+b)\right\}$$
+<<*>>=
+)clear all
+
+--S
+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
+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
+cc:=aa-bb
+--R
+--R
+--R (3) 0
+--R Type: Expression
Integer
+--E
+@
+
+\section{\cite{1}:14.110~~~~~$\displaystyle\int{\frac{dx}{(ax+b)^m(px+q)^n}}$}
+$$\int{\frac{dx}{(ax+b)^m(px+q)^n}}=$$
+$$\frac{-1}{(n-1)(bp-aq)}
+\left\{\frac{1}{(ax+b)^{m-1}(px+q)^{n-1}}+
+a(m+n-2)~\int{\frac{dx}{(ax+b)^m(px+q)^{n-1}}}\right\}$$
+<<*>>=
+)clear all
+
+--S
+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
+@
+<<*>>=
+--S
+dd:=integrate(1/((a*x+b)^m*(p*x+q)^(n-1)),x)
+--R
+--R
+--R x
+--R ++ 1
+--I (2) | -------------------------- d%L
+--R ++ m n - 1
+--I (b + %L a) (q + %L p)
+--R Type: Union(Expression
Integer,...)
+--E
+@
+
+<<*>>=
+--S
+bb:=-1/((n-1)*(b*p-a*q))*(1/((a*x+b)^(m-1)*(p*x+q)^(n-1))+a*(m+n-2)*dd)
+--R
+--R
+--R (3)
+--R m - 1 n - 1
+--R (a n + a m - 2a)(a x + b) (p x + q)
+--R *
+--R x
+--R ++ 1
+--I | -------------------------- d%L
+--R ++ m n - 1
+--I (b + %L a) (q + %L p)
+--R +
+--R 1
+--R /
+--R m - 1 n - 1
+--R ((a n - a)q + (- b n + b)p)(a x + b) (p x + q)
+--R Type: Expression
Integer
+--E
+@
+<<*>>=
+--S
+cc:=aa-bb
+--R
+--R
+--R (4)
+--R m - 1 n - 1
+--R (- a n - a m + 2a)(a x + b) (p x + q)
+--R *
+--R x
+--R ++ 1
+--I | -------------------------- d%L
+--R ++ m n - 1
+--I (b + %L a) (q + %L p)
+--R +
+--R m - 1 n - 1
+--R ((a n - a)q + (- b n + b)p)(a x + b) (p x + q)
+--R *
+--R x
+--R ++ 1
+--I | ---------------------- d%L
+--R ++ m n
+--I (b + %L a) (q + %L p)
+--R +
+--R - 1
+--R /
+--R m - 1 n - 1
+--R ((a n - a)q + (- b n + b)p)(a x + b) (p x + q)
+--R Type: Expression
Integer
+--E
+@
+
+\section{\cite{1}:14.111~~~~~$\displaystyle\int{\frac{ax+b}{px+q}~dx}$}
+$$\int{\frac{ax+b}{px+q}~dx}=\frac{ax}{p}+\frac{bp-aq}{p^2}~\ln(px+q)$$
+<<*>>=
+)clear all
+
+--S
+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
+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
+cc:=aa-bb
+--R
+--R
+--R (3) 0
+--R Type: Expression
Integer
+--E
+@
+
+\section{\cite{1}:14.112~~~~~$\displaystyle\int{\frac{(ax+b)^m}{(px+q)^n}~dx}$}
+$$\int{\frac{(ax+b)^m}{(px+q)^n}~dx}=\left\{
+\begin{array}{c}
+\frac{-1}{(n-1)(bp-aq)}
+\left\{\frac{(ax+b)^{m+1}}{(px+q)^{n-1}}+(n-m-2)a
+\int{\frac{(ax+b)^m}{(px+q)^{n-1}}}~dx\right\}\\
+\frac{-1}{(n-m-1)p}+\left\{\frac{(ax+b)^m}{(px+q)^{n-1}}+m(bp-aq)
+\int{\frac{(ax+b)^{m-1}}{(px+q)^n}}~dx\right\}\\
+\frac{-1}{(n-1)p}\left\{\frac{(ax+b)^m}{(px+q)^{n-1}}-ma
+\int{\frac{(ax+b)^{m-1}}{(px+q)^{n-1}}}~dx\right\}
+\end{array}
+\right.$$
+<<*>>=
+)clear all
+
+--S
+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,...)
+--R
+--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 pp62-63
+\end{thebibliography}
+\end{document}
diff --git a/src/input/schaum4.input.pamphlet b/src/input/schaum4.input.pamphlet
new file mode 100644
index 0000000..b57e857
--- /dev/null
+++ b/src/input/schaum4.input.pamphlet
@@ -0,0 +1,212 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum4.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.113~~~~~$\displaystyle\int{\frac{px+q}{\sqrt{ax+b}}}~dx$}
+$$\int{\frac{px+q}{\sqrt{ax+b}}}=
+\frac{2(apx+3aq-2bp)}{3a^2}\sqrt{ax+b}$$
+<<*>>=
+)spool schaum4.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 7
+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
+@
+
+\section{\cite{1}:14.114~~~~~$\displaystyle
+\int{\frac{dx}{(px+q)\sqrt{ax+b}}}~dx$}
+$$\int{\frac{dx}{(px+q)\sqrt{ax+b}}}=
+\left\{
+\begin{array}{l}
+\frac{1}{\sqrt{bp-aq}\sqrt{p}}\ln\left(
+\frac{\sqrt{p(ax+b)}-\sqrt{bp-aq}}{\sqrt{p(ax+b)}+\sqrt{bp-aq}}\right)\\
+\frac{2}{\sqrt{aq-bp}\sqrt{p}}\tan^{-1}\sqrt{\frac{p(ax+b)}{aq-bp}}
+\end{array}
+\right.
+$$
+<<*>>=
+)clear all
+
+--S 2 of 7
+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
+@
+
+\section{\cite{1}:14.115~~~~~$\displaystyle\int{\frac{\sqrt{ax+b}}{px+q}}~dx$}
+$$\int{\frac{\sqrt{ax+b}}{px+q}}=
+\left\{
+\begin{array}{l}
+\frac{2\sqrt{ax+b}}{p}+\frac{\sqrt{bp-aq}}{p\sqrt{p}}\ln\left(
+\frac{\sqrt{p(ax+b)}-\sqrt{bp-aq}}{\sqrt{p(ax+b)}+\sqrt{bp-aq}}\right)\\
+\frac{2\sqrt{ax+b}}{p}-\frac{2\sqrt{aq-bp}}{p\sqrt{p}}
+\tan^{-1}\sqrt{\frac{p(ax+b)}{aq-bp}}
+\end{array}
+\right.$$
+<<*>>=
+)clear all
+
+--S 3 of 7
+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
+@
+
+\section{\cite{1}:14.116~~~~~$\displaystyle\int{(px+b)^n\sqrt{ax+b}}~dx$}
+$$\int{(px+b)^n\sqrt{ax+b}}=
+\frac{2(px+q)^{n+1}\sqrt{ax+b}}{(2n+3)p}+\frac{bp-aq}{(2n+3)p}
+\int{\frac{(px+q)^n}{\sqrt{ax+b}}}~dx$$
+
+<<*>>=
+)clear all
+
+--S 4 of 7
+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~~~~~$\displaystyle
+\int{\frac{dx}{(px+b)^n\sqrt{ax+b}}}$}
+$$\int{\frac{dx}{(px+b)^n\sqrt{ax+b}}}=
+\frac{\sqrt{ax+b}}{(n-1)(aq-bp)(px+q)^{n-1}}+
+\frac{(2n-3)a}{2(n-1)(aq-bp)}
+\int{\frac{dx}{(px+q)^{n-1}\sqrt{ax+b}}}$$
+
+<<*>>=
+)clear all
+
+--S 5 of 7
+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~~~~~$\displaystyle
+\int{\frac{(px+q)^n}{\sqrt{ax+b}}}~dx$}
+$$\int{\frac{(px+q)^n}{\sqrt{ax+b}}}=
+\frac{2(px+q)^n\sqrt{ax+b}}{(2n+1)a}+
+\frac{2n(aq-bp)}{(2n+1)a}
+\int{\frac{(px+q)^{n-1}}{\sqrt{ax+b}}}$$
+<<*>>=
+)clear all
+
+--S 6 of 7
+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~~~~~$\displaystyle
+\int{\frac{\sqrt{ax+b}}{(px+q)^n}}~dx$}
+$$\int{\frac{\sqrt{ax+b}}{(px+q)^n}}=
+\frac{-\sqrt{ax+b}}{(n-1)p(px+q)^{n-1}}+
+\frac{a}{2(n-1)p}\int{\frac{dx}{(px+q)^{n-1}\sqrt{ax+b}}}$$
+<<*>>=
+)clear all
+
+--S 7 of 7
+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}
diff --git a/src/input/schaum5.input.pamphlet b/src/input/schaum5.input.pamphlet
new file mode 100644
index 0000000..a784b92
--- /dev/null
+++ b/src/input/schaum5.input.pamphlet
@@ -0,0 +1,367 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum5.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.120~~~~~$\displaystyle
+\int{\frac{dx}{\sqrt{(ax+b)(px+q)}}}$}
+$$\int{\frac{dx}{\sqrt{(ax+b)(px+q)}}}=
+\left\{
+\begin{array}{l}
+\frac{2}{\sqrt{ap}}\ln\left(\sqrt{a(px+q)}+\sqrt{p(ax+b)}\right)\\
+\frac{2}{\sqrt{-ap}}\tan^{-1}\sqrt{\frac{-p(ax+b)}{a(px+b)}}
+\end{array}
+\right.$$
+<<*>>=
+)spool schaum5.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 5
+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
+@
+
+\section{\cite{1}:14.121~~~~~$\displaystyle
+\int{\frac{x~dx}{\sqrt{(ax+b)(px+q)}}}$}
+$$\int{\frac{x~dx}{\sqrt{(ax+b)(px+q)}}}=
+\frac{\sqrt{(ax+b)(px+q)}}{ap}-\frac{bp+aq}{2ap}
+\int{\frac{dx}{\sqrt{(ax+b)(px+q)}}}
+$$
+<<*>>=
+)clear all
+
+--S 2 of 5
+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
+@
+
+\section{\cite{1}:14.122~~~~~$\displaystyle\int{\sqrt{(ax+b)(px+q)}}~dx$}
+$$\int{\sqrt{(ax+b)(px+q)}}=
+\frac{2apx+bp+aq}{4ap}\sqrt{(ax+b)(px+q)}-
+\frac{(bp-aq)^2}{8ap}\int{\frac{dx}{\sqrt{(ax+b)(px+q)}}}
+$$
+<<*>>=
+)clear all
+
+--S 3 of 5
+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
+@
+
+\section{\cite{1}:14.123~~~~~$\displaystyle\int{\sqrt{\frac{px+q}{ax+b}}}~dx$}
+$$\int{\sqrt{\frac{px+q}{ax+b}}}=
+\frac{\sqrt{(ax+b)(px+q)}}{a}+\frac{aq-bp}{2a}
+\int{\frac{dx}{\sqrt{(ax+b)(px+q)}}}
+$$
+<<*>>=
+)clear all
+
+--S 4 of 5
+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
+@
+
+\section{\cite{1}:14.124~~~~~$\displaystyle
+\int{\frac{dx}{(px+q)\sqrt{(ax+b)(px+q)}}}~dx$}
+$$\int{\frac{dx}{(px+q)\sqrt{(ax+b)(px+q)}}}=
+\frac{2\sqrt{ax+b}}{(aq-bp)\sqrt{px+q}}
+$$
+<<*>>=
+)clear all
+
+--S 5 of 5
+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
+
+)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}
diff --git a/src/input/schaum6.input.pamphlet b/src/input/schaum6.input.pamphlet
new file mode 100644
index 0000000..1a4b430
--- /dev/null
+++ b/src/input/schaum6.input.pamphlet
@@ -0,0 +1,400 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum6.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.125~~~~~$\displaystyle\int{\frac{dx}{x^2+a^2}}$}
+$$\int{\frac{dx}{x^2+a^2}}=\frac{1}{a}\tan^{-1}\frac{x}{a}$$
+<<*>>=
+)spool schaum6.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 x
+--R atan(-)
+--R a
+--R (1) -------
+--R a
+--R Type: Union(Expression
Integer,...)
+--E
+@
+
+\section{\cite{1}:14.126~~~~~$\displaystyle\int{\frac{x~dx}{x^2+a^2}}$}
+$$\int{\frac{x~dx}{x^2+a^2}}=\frac{1}{2}\ln(x^2+a^2)$$
+<<*>>=
+)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}:14.127~~~~~$\displaystyle\int{\frac{x^2~dx}{x^2+a^2}}$}
+$$\int{\frac{x^2~dx}{x^2+a^2}}=x-a\tan^{-1}\frac{x}{a}$$
+<<*>>=
+)clear all
+
+--S 3 of 19
+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
+@
+
+\section{\cite{1}:14.128~~~~~$\displaystyle\int{\frac{x^3~dx}{x^2+a^2}}$}
+$$\int{\frac{x^3~dx}{x^2+a^2}}=\frac{x^2}{2}-\frac{a^2}{2}\ln(x^2+a^2)$$
+
+<<*>>=
+)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}:14.129~~~~~$\displaystyle\int{\frac{dx}{x(x^2+a^2)}}~dx$}
+$$\int{\frac{dx}{x(x^2+a^2)}}=
+\frac{1}{2a^2}\ln\left(\frac{x^2}{x^2+a^2}\right)
+$$
+<<*>>=
+)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}:14.130~~~~~$\displaystyle\int{\frac{dx}{x^2(x^2+a^2)}}~dx$}
+$$\int{\frac{dx}{x^2(x^2+a^2)}}=
+-\frac{1}{a^2x}-\frac{1}{a^3}\tan^{-1}\frac{x}{a}
+$$
+<<*>>=
+)clear all
+
+--S 6 of 19
+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
+@
+
+\section{\cite{1}:14.131~~~~~$\displaystyle\int{\frac{dx}{x^3(x^2+a^2)}}~dx$}
+$$\int{\frac{dx}{x^3(x^2+a^2)}}=
+-\frac{1}{2a^2x^2}-\frac{1}{2a^4}\ln\left(\frac{x^2}{x^2+a^2}\right)
+$$
+<<*>>=
+)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}:14.132~~~~~$\displaystyle\int{\frac{dx}{(x^2+a^2)^2}}~dx$}
+$$\int{\frac{dx}{(x^2+a^2)^2}}=
+\frac{x}{2a^2(x^2+a^2)}+\frac{1}{2a^3}\tan^{-1}\frac{x}{a}
+$$
+<<*>>=
+)clear all
+
+--S 8 of 19
+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
+@
+
+\section{\cite{1}:14.133~~~~~$\displaystyle\int{\frac{x~dx}{(x^2+a^2)^2}}~dx$}
+$$\int{\frac{x~dx}{(x^2+a^2)^2}}=
+\frac{-1}{2(x^2+a^2)}
+$$
+<<*>>=
+)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}:14.134~~~~~$\displaystyle\int{\frac{x^2dx}{(x^2+a^2)^2}}~dx$}
+$$\int{\frac{x^2dx}{(x^2+a^2)^2}}=
+\frac{-x}{2(x^2+a^2)}+\frac{1}{2a}\tan^{-1}\frac{x}{a}
+$$
+<<*>>=
+)clear all
+
+--S 10 of 19
+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
+@
+
+\section{\cite{1}:14.135~~~~~$\displaystyle\int{\frac{x^3dx}{(x^2+a^2)^2}}~dx$}
+$$\int{\frac{x^3dx}{(x^2+a^2)^2}}=
+\frac{a^2}{2(x^2+a^2)}+\frac{1}{2}\ln(x^2+a^2)
+$$
+<<*>>=
+)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}:14.136~~~~~$\displaystyle\int{\frac{dx}{x(x^2+a^2)^2}}~dx$}
+$$\int{\frac{dx}{x(x^2+a^2)^2}}=
+\frac{1}{2a^2(x^2+a^2)}+\frac{1}{2a^4}\ln\left(\frac{x^2}{x^2+a^2}\right)
+$$
+<<*>>=
+)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}:14.137~~~~~$\displaystyle\int{\frac{dx}{x^2(x^2+a^2)^2}}~dx$}
+$$\int{\frac{dx}{x^2(x^2+a^2)^2}}=
+-\frac{1}{a^4x}-\frac{x}{2a^4(x^2+a^2)}-\frac{3}{2a^5}\tan^{-1}\frac{x}{a}
+$$
+<<*>>=
+)clear all
+
+--S 13 of 19
+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
+@
+
+\section{\cite{1}:14.138~~~~~$\displaystyle\int{\frac{dx}{x^3(x^2+a^2)^2}}~dx$}
+$$\int{\frac{dx}{x^3(x^2+a^2)^2}}=
+-\frac{1}{2a^4x^2}-\frac{1}{2a^4(x^2+a^2)}-
+\frac{1}{a^6}\ln\left(\frac{x^2}{x^2+a^2}\right)
+$$
+<<*>>=
+)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}:14.139~~~~~$\displaystyle\int{\frac{dx}{(x^2+a^2)^n}}~dx$}
+$$\int{\frac{dx}{(x^2+a^2)^n}}=
+\frac{x}{2(n-1)a^2(x^2+a^2)^{n-1}}+\frac{2n-3}{(2n-2)a^2}
+\int{\frac{dx}{(x^2+a^2)^{n-1}}}
+$$
+<<*>>=
+)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}:14.140~~~~~$\displaystyle\int{\frac{x~dx}{(x^2+a^2)^n}}~dx$}
+$$\int{\frac{x~dx}{(x^2+a^2)^n}}=
+\frac{-1}{2(n-1)(x^2+a^2)^{n-1}}
+$$
+<<*>>=
+)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}:14.141~~~~~$\displaystyle\int{\frac{dx}{x(x^2+a^2)^n}}~dx$}
+$$\int{\frac{dx}{x(x^2+a^2)^n}}=
+\frac{1}{2(n-1)a^2(x^2+a^2)^{n-1}}+\frac{1}{a^2}
+\int{\frac{dx}{x(x^2+a^2)^{n-1}}}
+$$
+<<*>>=
+)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}:14.142~~~~~$\displaystyle\int{\frac{x^mdx}{(x^2+a^2)^n}}~dx$}
+$$\int{\frac{x^mdx}{(x^2+a^2)^n}}=
+\int{\frac{x^{m-2}dx}{(x^2+a^2)^{n-1}}} -
+a^2\int{\frac{x^{m-2}dx}{(x^2+a^2)^n}}
+$$
+<<*>>=
+)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}:14.143~~~~~$\displaystyle\int{\frac{dx}{x^m(x^2+a^2)^n}}~dx$}
+$$\int{\frac{dx}{x^m(x^2+a^2)^n}}=
+\frac{1}{a^2}\int{\frac{dx}{x^m(x^2+a^2)^{n-1}}}-
+\frac{1}{a^2}\int{\frac{dx}{x^{m-2}(x^2+a^2)^n}}
+$$
+<<*>>=
+)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 ++ 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}
| [Prev in Thread] |
Current Thread |
[Next in Thread] |
- [Axiom-developer] 20080328.01.tpd.patch (CATS integration regression testing),
daly <=