These are the test cases from the MIT Integration Bee.
==========================================================================
diff --git a/changelog b/changelog
index 8f37ad8..83cda96 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,4 @@
+20080523 tpd src/input/danzwill2.input MIT integration tests
20080511 tpd src/input/schaum34.input post-mortem fixes
20080508 tpd src/input/schaum18.input ignore gensyms
20080508 tpd src/input/schaum17.input ignore gensyms
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet
index fdf2fff..9bd57b6 100644
--- a/src/input/Makefile.pamphlet
+++ b/src/input/Makefile.pamphlet
@@ -300,7 +300,8 @@ REGRES= algaggr.regress algbrbf.regress algfacob.regress
alist.regress \
constant.regress contfrac.regress contfrc.regress \
curl.regress cwmmt.regress \
cycles1.regress cycles.regress cyfactor.regress \
- danzwill.regress decimal.regress defintef.regress defintrf.regress \
+ danzwill.regress danzwill2.regress \
+ decimal.regress defintef.regress defintrf.regress \
derham.regress dfloat.regress dhtri.regress divisor.regress \
dmp.regress dpol.regress e1.regress ei.regress \
easter.regress efi.regress \
@@ -542,7 +543,8 @@ FILES= ${OUT}/algaggr.input ${OUT}/algbrbf.input
${OUT}/algfacob.input \
${OUT}/cycles.input ${OUT}/cycles1.input ${OUT}/cycloid.input \
${OUT}/cycloid2.input \
${OUT}/cycloid3.input ${OUT}/cyfactor.input ${OUT}/damped.input \
- ${OUT}/danzwill.input ${OUT}/decimal.input ${OUT}/defs.input \
+ ${OUT}/danzwill.input ${OUT}/danzwill2.input \
+ ${OUT}/decimal.input ${OUT}/defs.input \
${OUT}/defintef.input ${OUT}/defintrf.input ${OUT}/derham.input \
${OUT}/de2re.input \
${OUT}/dfloat.input ${OUT}/dhtri.input ${OUT}/divisor.input \
@@ -768,6 +770,7 @@ DOCFILES= \
${DOC}/d02raf.input.dvi ${DOC}/d03edf.input.dvi \
${DOC}/d03eef.input.dvi ${DOC}/d03faf.input.dvi \
${DOC}/damped.input.dvi ${DOC}/danzwill.input.dvi \
+ ${DOC}/danzwill2.input.dvi \
${DOC}/de2re.input.dvi ${DOC}/decimal.input.dvi \
${DOC}/defintef.input.dvi ${DOC}/defintrf.input.dvi \
${DOC}/defs.input.dvi ${DOC}/derham.input.dvi \
diff --git a/src/input/danzwill2.input.pamphlet
b/src/input/danzwill2.input.pamphlet
new file mode 100644
index 0000000..d17eddb
--- /dev/null
+++ b/src/input/danzwill2.input.pamphlet
@@ -0,0 +1,605 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/input danzwill2.input}
+\author{Timothy Daly}
+\maketitle
+\begin{abstract}
+Problems from the MIT Integration Bee
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+<<*>>=
+)spool danzwill2.output
+)set message test on
+)set message auto off
+)clear all
+)set break resume
+
+--S 1 of 17
+i1:= integrate(e^(1991*x),x)
+--R
+--R
+--R 1991x log(e)
+--R %e
+--R (1) --------------
+--R 1991log(e)
+--R Type: Union(Expression
Integer,...)
+--E 1
+
+--S 2 of 17
+i2:= integrate((sin(x)-cos(x))^2,x)
+--R
+--R
+--R 2
+--R (2) cos(x) + x
+--R Type: Union(Expression
Integer,...)
+--E 2
+
+--S 3 of 17
+i3:= integrate(log(x),x)
+--R
+--R
+--R (3) x log(x) - x
+--R Type: Union(Expression
Integer,...)
+--E 3
+
+--S 4 of 17
+i4:= integrate(1/(%pi*x),x)
+--R
+--R
+--R log(x)
+--R (4) ------
+--R %pi
+--R Type: Union(Expression
Integer,...)
+--E 4
+
+--S 5 of 17
+i5:= integrate(%e^(sin(x)^2)*%e^(cos(x)^2),x)
+--R
+--R
+--R (5) x %e
+--R Type: Union(Expression
Integer,...)
+--E 5
+
+--S 6 of 17
+i6:= integrate(1/(x*log(x)),x)
+--R
+--R
+--R (6) log(log(x))
+--R Type: Union(Expression
Integer,...)
+--E 6
+
+--S 7 of 17
+i7:= integrate(x/(x^4+1),x)
+--R
+--R
+--R 2
+--R atan(x )
+--R (7) --------
+--R 2
+--R Type: Union(Expression
Integer,...)
+--E 7
+
+--S 8 of 17
+i8:= integrate((x+1)/(x^2+2*x+2)^(1/3),x)
+--R
+--R
+--R +-----------+2
+--R 3| 2
+--R 3\|x + 2x + 2
+--R (8) ----------------
+--R 4
+--R Type: Union(Expression
Integer,...)
+--E 8
+
+--S 9 of 17
+i9:= integrate(x*%e^x*sin(x),x)
+--R
+--R
+--R x x
+--R x %e sin(x) + (- x + 1)cos(x)%e
+--R (9) --------------------------------
+--R 2
+--R Type: Union(Expression
Integer,...)
+--E 9
+
+--S 10 of 17
+i10:= integrate(%e^(%e^x+x),x)
+--R
+--R
+--R x
+--R %e + x
+--R %e
+--R (10) ---------
+--R x
+--R %e
+--R Type: Union(Expression
Integer,...)
+--E 10
+
+--S 11 of 17
+i11:= integrate(1/(sec(x)+tan(x)*sin(x)),x)
+--R
+--R
+--R (2cos(x) + 3)sin(x) sin(x)
+--R (11) atan(---------------------) - atan(-----------)
+--R 2 2cos(x) + 2
+--R cos(x) + 2cos(x) + 1
+--R Type: Union(Expression
Integer,...)
+--E 11
+
+--S 12 of 17
+i12:= integrate((%e^(5*x)+%e^(7*x))/(%e^x+%e^(-x)),x)
+--R
+--R
+--R x 6
+--R (%e )
+--R (12) ------
+--R 6
+--R Type: Union(Expression
Integer,...)
+--E 12
+
+--S 13 of 17
+i13:= integrate(sqrt(-1+2/(1+3*x)),x)
+--R
+--R
+--R +--------+ +--------+
+--R |- 3x + 1 |- 3x + 1
+--R - 2atan( |-------- ) + (3x + 1) |--------
+--R \| 3x + 1 \| 3x + 1
+--R (13) ------------------------------------------
+--R 3
+--R Type: Union(Expression
Integer,...)
+--E 13
+
+--S 14 of 17
+i14:= integrate(sinh(x)-cosh(x),x)
+--R
+--R
+--R 1
+--R (14) -----------------
+--R sinh(x) + cosh(x)
+--R Type: Union(Expression
Integer,...)
+--E 14
+
+--S 15 of 17
+i15:= integrate((sin(x)*%e^sec(x))/cos(x)^2,x)
+--R
+--R
+--R 1
+--R ------
+--R cos(x)
+--R (15) %e
+--R Type: Union(Expression
Integer,...)
+--E 15
+
+--S 16 of 17
+i16:= integrate((x^2+1)/(x^4-x^2+1),x)
+--R
+--R
+--R 3
+--R (16) atan(x ) + atan(x)
+--R Type: Union(Expression
Integer,...)
+--E 16
+
+--S 17 of 17
+i17:= integrate(1/(%pi*x^2+atan(x)+x^2*atan(x)+%pi),x)
+--R
+--R
+--R 2x 2 2x 2
+--R log(atan(------) - 4%pi atan(------) + 4%pi )
+--R 2 2
+--R x - 1 x - 1
+--R (17) ----------------------------------------------
+--R 2
+--R Type: Union(Expression
Integer,...)
+--E 17
+
+--S 18 of 18
+i18:= integrate(sec(x)^3,x)
+--R
+--R
+--R (18)
+--R 2 sin(x) + cos(x) + 1 2 sin(x) - cos(x) - 1
+--R cos(x) log(-------------------) - cos(x) log(-------------------) +
sin(x)
+--R cos(x) + 1 cos(x) + 1
+--R
--------------------------------------------------------------------------
+--R 2
+--R 2cos(x)
+--R Type: Union(Expression
Integer,...)
+--E 18
+
+--S 19 of 19
+i19:= integrate(1/(x^2-10*x+26),x)
+--R
+--R
+--R (19) atan(x - 5)
+--R Type: Union(Expression
Integer,...)
+--E 19
+
+--S 20 of 20
+i20:= integrate(1/(x^2-11*x-26),x)
+--R
+--R
+--R - log(x + 2) + log(x - 13)
+--R (20) --------------------------
+--R 15
+--R Type: Union(Expression
Integer,...)
+--E 20
+
+--S 21 of 21
+i21:= integrate(1/(12+13*cos(x)),x)
+--R
+--R
+--R sin(x) + 5cos(x) + 5 sin(x) - 5cos(x) - 5
+--R log(--------------------) - log(--------------------)
+--R cos(x) + 1 cos(x) + 1
+--R (21) -----------------------------------------------------
+--R 5
+--R Type: Union(Expression
Integer,...)
+--E 21
+
+--S 22 of 22
+i22:= integrate((x^3+1)/(x+1),x)
+--R
+--R
+--R 3 2
+--R 2x - 3x + 6x
+--R (22) --------------
+--R 6
+--R Type: Union(Expression
Integer,...)
+--E 22
+
+--S 23 of 23
+i23:= integrate((1-4*x^4)^(-1/2)/(4*x)^(-1),x)
+--R
+--R
+--R +---------+
+--R | 4
+--R \|- 4x + 1 - 1
+--R (23) - 2atan(----------------)
+--R 2
+--R 2x
+--R Type: Union(Expression
Integer,...)
+--E 23
+
+--S 24 of 24
+i24:= integrate(%e^(1991),x)
+--R
+--R
+--R 1991
+--R (24) x %e
+--R Type: Union(Expression
Integer,...)
+--E 24
+
+--S 25 of 25
+i25:= integrate((log(x)+1)*x^x,x)
+--R
+--R
+--R x log(x)
+--R (25) %e
+--R Type: Union(Expression
Integer,...)
+--E 25
+
+--S 26 of 26
+i26:= integrate(cos(2*x)*sin(6*x),x)
+--R
+--R
+--R 4 2
+--R - 2cos(2x) + cos(2x)
+--R (26) ----------------------
+--R 4
+--R Type: Union(Expression
Integer,...)
+--E 26
+
+--S 27 of 27
+i27:= integrate(1/(sqrt(x)*(1+sqrt(x))),x)
+--R
+--R
+--R +-+
+--R (27) 2log(\|x + 1)
+--R Type: Union(Expression
Integer,...)
+--E 27
+
+--S 28 of 28
+i28:= integrate(e^(1/x)*x^(-3),x)
+--R
+--R
+--R log(e)
+--R ------
+--R x
+--R (- log(e) + x)%e
+--R (28) ----------------------
+--R 2
+--R x log(e)
+--R Type: Union(Expression
Integer,...)
+--E 28
+
+--S 29 of 29
+i29:= integrate(sqrt(csc(x)-sin(x)),x)
+--R
+--R
+--R +--------------------------------+
+--R | - 16cos(x) + 16
+--R (29) (- cos(x) - 1) |--------------------------------
+--R 4| 3 2
+--R \|cos(x) + 3cos(x) + 3cos(x) + 1
+--R Type: Union(Expression
Integer,...)
+--E 29
+
+--S 30 of 30
+i30:= integrate((x^2+1)/(x^3-x),x)
+--R
+--R
+--R 2
+--R (30) log(x - 1) - log(x)
+--R Type: Union(Expression
Integer,...)
+--E 30
+
+--S 31 of 31
+i31:= integrate(42^x,x)
+--R
+--R
+--R x log(42)
+--R %e
+--R (31) -----------
+--R log(42)
+--R Type: Union(Expression
Integer,...)
+--E 31
+
+--S 32 of 32
+i32:= integrate(x^5*%e^x,x)
+--R
+--R
+--R 5 4 3 2 x
+--R (32) (x - 5x + 20x - 60x + 120x - 120)%e
+--R Type: Union(Expression
Integer,...)
+--E 32
+
+--S 33 of 33
+i33:= integrate(x*%e^(x^2),x)
+--R
+--R
+--R 2
+--R x
+--R %e
+--R (33) ----
+--R 2
+--R Type: Union(Expression
Integer,...)
+--E 33
+
+--S 34 of 34
+i34:= integrate(1/(x^2+1)^2,x)
+--R
+--R
+--R 2
+--R (x + 1)atan(x) + x
+--R (34) -------------------
+--R 2
+--R 2x + 2
+--R Type: Union(Expression
Integer,...)
+--E 34
+
+--S 35 of 35
+i35:= integrate(1/(%e^x+%e^(-x)),x)
+--R
+--R
+--R x
+--R (35) atan(%e )
+--R Type: Union(Expression
Integer,...)
+--E 35
+
+--S 36 of 36
+i36:= integrate(tan(x)*log(abs(sec(x))),x)
+--R
+--R
+--R +-------+ 2
+--R | 1
+--R log( |------- )
+--R | 2
+--R \|cos(x)
+--R (36) ----------------
+--R 2
+--R Type: Union(Expression
Integer,...)
+--E 36
+
+--S 37 of 37
+i37:= integrate(cos(sin(x))*cos(x),x)
+--R
+--R
+--R (37) sin(sin(x))
+--R Type: Union(Expression
Integer,...)
+--E 37
+
+--S 38 of 38
+i38:= integrate(1/(x^2-9),x)
+--R
+--R
+--R - log(x + 3) + log(x - 3)
+--R (38) -------------------------
+--R 6
+--R Type: Union(Expression
Integer,...)
+--E 38
+
+--S 39 of 39
+i39:= integrate(%pi/sqrt(16-%e^2),x)
+--R
+--R
+--R %pi x
+--R (39) -------------
+--R +----------+
+--R | 2
+--R \|- %e + 16
+--R Type: Union(Expression
Integer,...)
+--E 39
+
+--S 40 of 40
+i40:= integrate(sqrt(tan(x)),x)
+--R
+--R
+--R (40)
+--R +-+
+--R \|2
+--R *
+--R +------+
+--R +-+ +-+ 2 |sin(x)
+--R log((- 2\|2 cos(x)sin(x) - 2\|2 cos(x) ) |------ + 4cos(x)sin(x)
+ 1)
+--R \|cos(x)
+--R +
+--R +------+
+--R |sin(x) +-+ +-+ 2
+-+
+--R 2cos(x)sin(x) |------ - \|2 cos(x)sin(x) + \|2 cos(x) -
\|2
+--R +-+ \|cos(x)
+--R \|2
atan(--------------------------------------------------------------)
+--R +------+
+--R 2 |sin(x) +-+ +-+ 2
+--R 2cos(x) |------ - \|2 cos(x)sin(x) - \|2 cos(x)
+--R \|cos(x)
+--R +
+--R -
+--R +-+
+--R \|2
+--R *
+--R +------+
+--R |sin(x) +-+ +-+ 2
+-+
+--R 4cos(x)sin(x) |------ - 2\|2 cos(x)sin(x) + 2\|2 cos(x) -
\|2
+--R \|cos(x)
+--R
atan(----------------------------------------------------------------)
+--R +------+
+--R 2 |sin(x) +-+ +-+ 2
+-+
+--R 4cos(x) |------ - 2\|2 cos(x)sin(x) - 2\|2 cos(x) + \|2
+--R \|cos(x)
+--R +
+--R +------+
+--R |sin(x) +-+ +-+ 2
+--R 2cos(x)sin(x) |------ - \|2 cos(x)sin(x) + \|2 cos(x)
+--R +-+ \|cos(x)
+--R - \|2 atan(---------------------------------------------------------)
+--R +------+
+--R 2 |sin(x) +-+ +-+ 2 +-+
+--R 2cos(x) |------ - \|2 cos(x)sin(x) - \|2 cos(x) + \|2
+--R \|cos(x)
+--R /
+--R 4
+--R Type: Union(Expression
Integer,...)
+--E 40
+
+--S 41 of 41
+i41:= integrate(sin(x)^(-1),x)
+--R
+--R
+--R sin(x)
+--R (41) log(----------)
+--R cos(x) + 1
+--R Type: Union(Expression
Integer,...)
+--E 41
+
+--S 42 of 42
+i42:= integrate((x^2-2*x+2)/(x^2+1),x)
+--R
+--R
+--R 2
+--R (42) - log(x + 1) + atan(x) + x
+--R Type: Union(Expression
Integer,...)
+--E 42
+
+--S 43 of 43
+i43:= integrate((sin(x)^2*cos(x)^2)/(1+cos(2*x)),x)
+--R
+--R
+--R - cos(x)sin(x) + x
+--R (43) ------------------
+--R 4
+--R Type: Union(Expression
Integer,...)
+--E 43
+
+--S 44 of 44
+i44:= integrate(sqrt(x+x^2*sqrt(x)),x)
+--R
+--R
+--R +----------+
+--R +-+ 2 | 2 +-+
+--R (4\|x + 4x )\|x \|x + x
+--R (44) --------------------------
+--R 9x
+--R Type: Union(Expression
Integer,...)
+--E 44
+
+--S 45 of 45
+i45:= integrate(cos(4*x)*cos(2*x),x)
+--R
+--R
+--R 2
+--R (2cos(2x) + 1)sin(2x)
+--R (45) ----------------------
+--R 6
+--R Type: Union(Expression
Integer,...)
+--E 45
+
+--S 46 of 46
+i46:= integrate(sqrt(x^3-1)/x,x)
+--R
+--R
+--R +------+ +------+
+--R | 3 | 3
+--R - 2atan(\|x - 1 ) + 2\|x - 1
+--R (46) -------------------------------
+--R 3
+--R Type: Union(Expression
Integer,...)
+--E 46
+
+--S 47 of 47
+i47:= integrate((%e^x*(x-2))/x^3,x)
+--R
+--R
+--R x
+--R %e
+--R (47) ---
+--R 2
+--R x
+--R Type: Union(Expression
Integer,...)
+--E 47
+
+--S 48 of 48
+i48:= integrate(cot(x)/log(sin(x)),x)
+--R
+--R
+--R (48) log(log(sin(x)))
+--R Type: Union(Expression
Integer,...)
+--E 48
+
+--S 49 of 49
+i49:= integrate(x*sec(x)^2,x)
+--R
+--R
+--R 2 2cos(x)
+--R - cos(x)log(----------) + cos(x)log(- ----------) + x sin(x)
+--R cos(x) + 1 cos(x) + 1
+--R (49) ------------------------------------------------------------
+--R cos(x)
+--R Type: Union(Expression
Integer,...)
+--E 49
+
+--S 50 of 50
+i50:= integrate(x*sec(x)*(x*tan(x)+2),x)
+--R
+--R
+--R 2
+--R x
+--R (50) ------
+--R cos(x)
+--R Type: Union(Expression
Integer,...)
+--E 50
+)spool
+)lisp (bye)
+
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Zwillinger, Daniel, ``Handbook of Integration'',
+Jones and Bartlett, Boston 1992 ISBN 0-86720-293-9 pp28-29
+\end{thebibliography}
+\end{document}
+
+
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