diff --git a/changelog b/changelog
index 366d13f..fcc6814 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,4 @@
+20080505 tpd src/input/schaum24.input branch-cut analysis
 20080505 tpd src/input/schaum23.input post-mortem fixes
 20080505 tpd src/input/schaum22.input post-mortem fixes
 20080505 tpd src/input/schaum21.input post-mortem fixes
diff --git a/src/input/schaum24.input.pamphlet b/src/input/schaum24.input.pamphlet
index 24b4527..71f28d5 100644
--- a/src/input/schaum24.input.pamphlet
+++ b/src/input/schaum24.input.pamphlet
@@ -95,7 +95,7 @@ bb:=(x^2/2-a^2/4)*asin(x/a)+(x*sqrt(a^2-x^2))/4
 --R                                                     Type: Expression Integer
 --E
 
---S 6      14:472 Axiom cannot simplify this expression
+--S 6
 cc:=aa-bb
 --R
 --R                            +---------+
@@ -108,6 +108,145 @@ cc:=aa-bb
 --R                                   8
 --R                                                     Type: Expression Integer
 --E
+
+@
+Here we try to understand why we cannot find a simplification
+that makes these two expressions equal. If the expressions were
+equal then we could use them as functions, substitute floating
+point values and expect the same numeric results. So we try that here.
+<<*>>=
+)clear all
+@
+This is the initial integrand.
+<<*>>=
+--S 7
+t1:=x*asin(x/a)
+--R
+--R               x
+--R   (1)  x asin(-)
+--R               a
+--R                                                     Type: Expression Integer
+--E
+@
+This is the integral result provided by Axiom.
+<<*>>=
+--S 8
+t2:=integrate(t1,x)
+--R
+--R                            +---------+
+--R                            |   2    2        +---------+
+--R             2    2      2x\|- x  + a         |   2    2
+--R        (- 2x  + a )atan(--------------) + 2x\|- x  + a
+--R                              2    2
+--R                            2x  - a
+--R   (2)  -------------------------------------------------
+--R                                8
+--R                                          Type: Union(Expression Integer,...)
+--E
+@
+This is the derivative of the integral computed by Axiom
+<<*>>=
+--S 9
+t3:=D(t2,x)
+--R
+--R                    +---------+
+--R                    |   2    2
+--R                 2x\|- x  + a
+--R          x atan(--------------)
+--R                      2    2
+--R                    2x  - a
+--R   (3)  - ----------------------
+--R                     2
+--R                                                     Type: Expression Integer
+--E
+@
+This is the integral result provided by Schaums
+<<*>>=
+--S 10
+t4:=(x^2/2-a^2/4)*asin(x/a)+(x*sqrt(a^2-x^2))/4
+--R
+--R          +---------+
+--R          |   2    2       2    2      x
+--R        x\|- x  + a   + (2x  - a )asin(-)
+--R                                       a
+--R   (4)  ---------------------------------
+--R                        4
+--R                                                     Type: Expression Integer
+--E
+@
+This is the derivative of the integral of the original function
+according to Schaums.
+<<*>>=
+--S 11
+t5:=D(t4,x)
+--R
+--R   (5)
+--R                                           +---------+
+--R                 +---------+               |   2    2               +---------+
+--R              x  |   2    2        2    3  |- x  + a        2    2  |   2    2
+--R   (4a x asin(-)\|- x  + a   - 2a x  + a ) |---------  + (2x  - a )\|- x  + a
+--R              a                            |     2
+--R                                          \|    a
+--R   ----------------------------------------------------------------------------
+--R                                           +---------+
+--R                               +---------+ |   2    2
+--R                               |   2    2  |- x  + a
+--R                            4a\|- x  + a   |---------
+--R                                           |     2
+--R                                          \|    a
+--R                                                     Type: Expression Integer
+--E
+@
+Now we create a function for computing the integrand's values.
+<<*>>=
+--S 12
+f:=makeFloatFunction(t1,x,a)
+--I   Compiling function %BF with type (DoubleFloat,DoubleFloat) -> 
+--R      DoubleFloat 
+--R
+--I   (6)  theMap(MKBCFUNC;binaryFunction;SM;2!0,120)
+--R                             Type: ((DoubleFloat,DoubleFloat) -> DoubleFloat)
+--E
+@
+Now we create a function for computing Axiom's values for its integrand.
+<<*>>=
+--S 13
+axiom:=makeFloatFunction(t3,x,a)
+--I   Compiling function %BJ with type (DoubleFloat,DoubleFloat) -> 
+--R      DoubleFloat 
+--R
+--I   (7)  theMap(MKBCFUNC;binaryFunction;SM;2!0,996)
+--R                             Type: ((DoubleFloat,DoubleFloat) -> DoubleFloat)
+--E
+@
+Now we create a function for computing Schams values for its integrand.
+<<*>>=
+--S 14
+schaums:=makeFloatFunction(t5,x,a)
+--I   Compiling function %BK with type (DoubleFloat,DoubleFloat) -> 
+--R      DoubleFloat 
+--R
+--I   (8)  theMap(MKBCFUNC;binaryFunction;SM;2!0,62)
+--R                             Type: ((DoubleFloat,DoubleFloat) -> DoubleFloat)
+--E
+@
+And now we compute the floating point values for each function
+and compare the results. As can be clearly seen, the Axiom result
+lies on a different branch cut from the Schaums result and the
+functions are only equal within the branch cut range. This is a
+generic problem with all of the inverse functions that are
+multi-valued.
+<<*>>=
+--S 15     14:472 Schaums and Axiom agree (modulo branch cuts)
+[ [f(i::Float,i::Float+1.0::Float)::Float,axiom(i::Float,i::Float+1.0::Float)::Float,schaums(i::Float,i::Float+1.0::Float)::Float] for i in 1..4]
+--R
+--R   (9)
+--R   [[0.5235987755 9829892668,0.5235987755 9829892668,0.5235987755 9829881566],
+--R    [1.4594553124 539326738,1.4594553124 539326738,1.4594553124 539324518],
+--R    [2.5441862369 444430136,- 2.1682027434 402466604,2.5441862369 444430136],
+--R    [3.7091808720 064496363,- 2.5740044351 731374839,3.7091808720 064500804]]
+--R                                                        Type: List List Float
+--E
 @
 
 \section{\cite{1}:14.473~~~~~$\displaystyle
@@ -118,7 +257,7 @@ $$
 <<*>>=
 )clear all
 
---S 7
+--S 16
 aa:=integrate(x^2*asin(x/a),x)
 --R 
 --R
@@ -133,7 +272,7 @@ aa:=integrate(x^2*asin(x/a),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 8
+--S 17
 bb:=x^3/3*asin(x/a)+((x^2+2*a^2)*sqrt(a^2-x^2))/9
 --R
 --R                   +---------+
@@ -145,7 +284,7 @@ bb:=x^3/3*asin(x/a)+((x^2+2*a^2)*sqrt(a^2-x^2))/9
 --R                                                     Type: Expression Integer
 --E
 
---S 9      14:473 Axiom cannot simplify this expression
+--S 18     14:473 Axiom cannot simplify this expression
 cc:=aa-bb
 --R
 --R                    +---------+
@@ -170,7 +309,7 @@ $$
 <<*>>=
 )clear all
 
---S 10     14:474 Axiom cannot compute this integral
+--S 19     14:474 Axiom cannot compute this integral
 aa:=integrate(asin(x/a)/x,x)
 --R 
 --R
@@ -192,7 +331,7 @@ $$
 <<*>>=
 )clear all
 
---S 11
+--S 20
 aa:=integrate(asin(x/a)/x^2,x)
 --R 
 --R
@@ -208,7 +347,7 @@ aa:=integrate(asin(x/a)/x^2,x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 12
+--S 21
 bb:=-asin(x/a)/x-1/a*log((a+sqrt(a^2-x^2))/x)
 --R
 --R                 +---------+
@@ -221,7 +360,7 @@ bb:=-asin(x/a)/x-1/a*log((a+sqrt(a^2-x^2))/x)
 --R                                                     Type: Expression Integer
 --E
 
---S 13     14:475 Axiom cannot simplify this expression
+--S 22     14:475 Axiom cannot simplify this expression
 cc:=aa-bb
 --R
 --R   (3)
@@ -249,7 +388,7 @@ $$
 <<*>>=
 )clear all
 
---S 14
+--S 23
 aa:=integrate(asin(x/a)^2,x)
 --R 
 --R
@@ -264,7 +403,7 @@ aa:=integrate(asin(x/a)^2,x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 15
+--S 24
 bb:=x*asin(x/a)^2-2*x+2*sqrt(a^2-x^2)*asin(x/a)
 --R
 --R                 +---------+
@@ -274,7 +413,7 @@ bb:=x*asin(x/a)^2-2*x+2*sqrt(a^2-x^2)*asin(x/a)
 --R                                                     Type: Expression Integer
 --E
 
---S 16     14:476 Axiom cannot simplify this expression
+--S 25     14:476 Axiom cannot simplify this expression
 cc:=aa-bb
 --R
 --R   (3)
@@ -303,7 +442,7 @@ $$
 <<*>>=
 )clear all
 
---S 17
+--S 26
 aa:=integrate(acos(x/a),x)
 --R 
 --R
@@ -318,7 +457,7 @@ aa:=integrate(acos(x/a),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 18
+--S 27
 bb:=x*acos(x/a)-sqrt(a^2-x^2)
 --R
 --R           +---------+
@@ -328,7 +467,7 @@ bb:=x*acos(x/a)-sqrt(a^2-x^2)
 --R                                                     Type: Expression Integer
 --E
 
---S 19     14:477 Axiom cannot simplify this expression
+--S 28     14:477 Axiom cannot simplify this expression
 cc:=aa-bb
 --R
 --R                  +---------+
@@ -352,7 +491,7 @@ $$
 <<*>>=
 )clear all
 
---S 20
+--S 29
 aa:=integrate(x*acos(x/a),x)
 --R 
 --R
@@ -367,7 +506,7 @@ aa:=integrate(x*acos(x/a),x)
 --R                                          Type: Union(Expression Integer,...)
 --E
 
---S 21
+--S 30
 bb:=(x^2/2-a^2/4)*acos(x/a)-(x*sqrt(a^2-x^2))/4
 --R
 --R            +---------+
@@ -379,7 +518,7 @@ bb:=(x^2/2-a^2/4)*acos(x/a)-(x*sqrt(a^2-x^2))/4
 --R                                                     Type: Expression Integer
 --E
 
---S 22     14:478 Axiom cannot simplify this expression
+--S 31     14:478 Axiom cannot simplify this expression
 cc:=aa-bb
 --R
 --R                          +---------+
@@ -402,7 +541,7 @@ $$
 <<*>>=
 )clear all
 
---S 23
+--S 32
 aa:=integrate(x^2*acos(x/a),x)
 --R 
 --R
@@ -417,7 +556,7 @@ aa:=integrate(x^2*acos(x/a),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 24
+--S 33
 bb:=x^3/3*acos(x/a)-((x^2+2*a^2)*sqrt(a^2-x^2))/9
 --R
 --R                     +---------+
@@ -429,7 +568,7 @@ bb:=x^3/3*acos(x/a)-((x^2+2*a^2)*sqrt(a^2-x^2))/9
 --R                                                     Type: Expression Integer
 --E
 
---S 25     14:479 Axiom cannot simplify this expression
+--S 34     14:479 Axiom cannot simplify this expression
 cc:=aa-bb
 --R
 --R                  +---------+
@@ -452,7 +591,7 @@ $$
 <<*>>=
 )clear all
 
---S 26     14:480 Axiom cannot compute this integral
+--S 35     14:480 Axiom cannot compute this integral
 aa:=integrate(acos(x/a)/x,x)
 --R 
 --R
@@ -473,7 +612,7 @@ $$
 <<*>>=
 )clear all
 
---S 27
+--S 36
 aa:=integrate(acos(x/a)/x^2,x)
 --R 
 --R
@@ -489,7 +628,7 @@ aa:=integrate(acos(x/a)/x^2,x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 28
+--S 37
 bb:=-acos(x/a)/x+1/a*log((a+sqrt(a^2-x^2))/x)
 --R
 --R               +---------+
@@ -502,7 +641,7 @@ bb:=-acos(x/a)/x+1/a*log((a+sqrt(a^2-x^2))/x)
 --R                                                     Type: Expression Integer
 --E
 
---S 29     14:481 Axiom cannot simplify this expression
+--S 38     14:481 Axiom cannot simplify this expression
 cc:=aa-bb
 --R
 --R   (3)
@@ -530,7 +669,7 @@ $$
 <<*>>=
 )clear all
 
---S 30
+--S 39
 aa:=integrate(acos(x/a)^2,x)
 --R 
 --R
@@ -545,7 +684,7 @@ aa:=integrate(acos(x/a)^2,x)
 --R                                          Type: Union(Expression Integer,...)
 --E
 
---S 31
+--S 40
 bb:=x*acos(x/a)^2-2*x-2*sqrt(a^2-x^2)*acos(x/a)
 --R
 --R                   +---------+
@@ -555,7 +694,7 @@ bb:=x*acos(x/a)^2-2*x-2*sqrt(a^2-x^2)*acos(x/a)
 --R                                                     Type: Expression Integer
 --E
 
---S 32     14:482 Axiom cannot simplify this expression
+--S 41     14:482 Axiom cannot simplify this expression
 cc:=aa-bb
 --R
 --R   (3)
@@ -584,7 +723,7 @@ $$
 <<*>>=
 )clear all
 
---S 33
+--S 42
 aa:=integrate(atan(x/a),x)
 --R 
 --R
@@ -597,7 +736,7 @@ aa:=integrate(atan(x/a),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 34
+--S 43
 bb:=x*atan(x/a)-a/2*log(x^2+a^2)
 --R
 --R                 2    2            x
@@ -608,7 +747,7 @@ bb:=x*atan(x/a)-a/2*log(x^2+a^2)
 --R                                                     Type: Expression Integer
 --E
 
---S 35
+--S 44
 cc:=aa-bb
 --R
 --R                  x             2a x
@@ -620,7 +759,7 @@ cc:=aa-bb
 --R                                                     Type: Expression Integer
 --E
 
---S 36
+--S 45
 atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 --R
 --R                            - x + %i
@@ -631,7 +770,7 @@ atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 --R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
 --E
 
---S 37
+--S 46
 dd:=atanrule cc
 --R
 --R                  2              2
@@ -644,7 +783,7 @@ dd:=atanrule cc
 --R                                             Type: Expression Complex Integer
 --E
 
---S 38     14:483 SCHAUMS AND AXIOM DIFFER? (BRANCH CUTS?)
+--S 47     14:483 SCHAUMS AND AXIOM DIFFER? (BRANCH CUTS?)
 ee:=expandLog dd
 --R
 --R        %i x log(- 1)
@@ -662,7 +801,7 @@ $$
 <<*>>=
 )clear all
 
---S 39     14:484 Axiom cannot compute this integral
+--S 48     14:484 Axiom cannot compute this integral
 aa:=integrate(x*tan(x/a),x)
 --R 
 --R
@@ -682,7 +821,7 @@ $$
 <<*>>=
 )clear all
 
---S 40
+--S 49
 aa:=integrate(x^2*atan(x/a),x)
 --R 
 --R
@@ -695,7 +834,7 @@ aa:=integrate(x^2*atan(x/a),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 41
+--S 50
 bb:=x^3/2*atan(x/a)-(a*x^2)/6+a^3/6*log(x^2+a^2)
 --R
 --R         3     2    2      3     x       2
@@ -706,7 +845,7 @@ bb:=x^3/2*atan(x/a)-(a*x^2)/6+a^3/6*log(x^2+a^2)
 --R                                                     Type: Expression Integer
 --E
 
---S 42     14:485 Axiom cannot simplify this expression
+--S 51     14:485 Axiom cannot simplify this expression
 cc:=aa-bb
 --R
 --R            3     x     3       2a x
@@ -727,7 +866,7 @@ $$
 <<*>>=
 )clear all
 
---S 43     14:486 Axiom cannot compute this integral
+--S 52     14:486 Axiom cannot compute this integral
 aa:=integrate(atan(x/a)/x,x)
 --R 
 --R
@@ -749,7 +888,7 @@ $$
 <<*>>=
 )clear all
 
---S 44
+--S 53
 aa:=integrate(atan(x/a)/x^2,x)
 --R 
 --R
@@ -762,7 +901,7 @@ aa:=integrate(atan(x/a)/x^2,x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 45
+--S 54
 bb:=-1/x*atan(x/a)-1/(2*a)*log((x^2+a^2)/x^2)
 --R
 --R                 2    2
@@ -775,7 +914,7 @@ bb:=-1/x*atan(x/a)-1/(2*a)*log((x^2+a^2)/x^2)
 --R                                                     Type: Expression Integer
 --E
 
---S 46
+--S 55
 cc:=aa-bb
 --R
 --R   (3)
@@ -789,7 +928,7 @@ cc:=aa-bb
 --R                                                     Type: Expression Integer
 --E
 
---S 47
+--S 56
 atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 --R
 --R                            - x + %i
@@ -800,7 +939,7 @@ atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 --R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
 --E
 
---S 48
+--S 57
 dd:=atanrule cc
 --R
 --R   (5)
@@ -820,7 +959,7 @@ dd:=atanrule cc
 --R                                             Type: Expression Complex Integer
 --E
 
---S 49     14:487 SCHAUMS AND AXIOM DIFFER? (branch cuts?)
+--S 58     14:487 SCHAUMS AND AXIOM DIFFER? (branch cuts?)
 ee:=expandLog dd
 --R
 --R          %i log(- 1)
@@ -838,7 +977,7 @@ $$
 <<*>>=
 )clear all
 
---S 50
+--S 59
 aa:=integrate(acot(x/a),x)
 --R 
 --R
@@ -851,7 +990,7 @@ aa:=integrate(acot(x/a),x)
 --R                                          Type: Union(Expression Integer,...)
 --E
 
---S 51
+--S 60
 bb:=x*acot(x/a)+a/2*log(x^2+a^2)
 --R
 --R               2    2            x
@@ -862,7 +1001,7 @@ bb:=x*acot(x/a)+a/2*log(x^2+a^2)
 --R                                                     Type: Expression Integer
 --E 
 
---S 52
+--S 61
 cc:=aa-bb
 --R
 --R                 2a x             x
@@ -874,7 +1013,7 @@ cc:=aa-bb
 --R                                                     Type: Expression Integer
 --E
 
---S 53
+--S 62
 atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 --R
 --R                            - x + %i
@@ -885,7 +1024,7 @@ atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 --R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
 --E
 
---S 54
+--S 63
 dd:=atanrule cc
 --R
 --R                    2              2
@@ -898,7 +1037,7 @@ dd:=atanrule cc
 --R                                             Type: Expression Complex Integer
 --E
 
---S 55
+--S 64
 acotrule:=rule(acot(x) == -%i/2*log((%i*x-1)/(%i*x+1)))
 --R
 --R                            x + %i
@@ -909,7 +1048,7 @@ acotrule:=rule(acot(x) == -%i/2*log((%i*x-1)/(%i*x+1)))
 --R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
 --E
 
---S 56
+--S 65
 ee:=acotrule dd
 --R
 --R                    2              2
@@ -922,7 +1061,7 @@ ee:=acotrule dd
 --R                                             Type: Expression Complex Integer
 --E
 
---S 57     14:488 Axiom and Schaums agree
+--S 66     14:488 Axiom and Schaums agree
 ff:=expandLog %
 --R
 --R   (8)  0
@@ -938,7 +1077,7 @@ $$
 <<*>>=
 )clear all
 
---S 58
+--S 67
 aa:=integrate(x*acot(x/a),x)
 --R 
 --R
@@ -951,7 +1090,7 @@ aa:=integrate(x*acot(x/a),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 59
+--S 68
 bb:=1/2*(x^2+a^2)*acot(x/a)+(a*x)/2
 --R
 --R          2    2      x
@@ -962,7 +1101,7 @@ bb:=1/2*(x^2+a^2)*acot(x/a)+(a*x)/2
 --R                                                     Type: Expression Integer
 --E
 
---S 60
+--S 69
 cc:=aa-bb
 --R
 --R          2    2        2a x          2     2      x
@@ -974,7 +1113,7 @@ cc:=aa-bb
 --R                                                     Type: Expression Integer
 --E
 
---S 61
+--S 70
 acotrule:=rule(acot(x) == -%i/2*log((%i*x-1)/(%i*x+1)))
 --R
 --R                            x + %i
@@ -985,7 +1124,7 @@ acotrule:=rule(acot(x) == -%i/2*log((%i*x-1)/(%i*x+1)))
 --R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
 --E
 
---S 62
+--S 71
 dd:=acotrule cc
 --R
 --R             2       2     x + %i a      2    2        2a x
@@ -997,7 +1136,7 @@ dd:=acotrule cc
 --R                                             Type: Expression Complex Integer
 --E
 
---S 63
+--S 72
 atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 --R
 --R                            - x + %i
@@ -1008,7 +1147,7 @@ atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 --R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
 --E
 
---S 64
+--S 73
 ee:=atanrule dd
 --R
 --R   (7)
@@ -1022,7 +1161,7 @@ ee:=atanrule dd
 --R                                             Type: Expression Complex Integer
 --E
 
---S 65     14:489 Axiom and Schaums agree
+--S 74     14:489 Axiom and Schaums agree
 ff:=expandLog ee
 --R
 --R   (8)  0
@@ -1038,7 +1177,7 @@ $$
 <<*>>=
 )clear all
 
---S 66
+--S 75
 aa:=integrate(x^2*acot(x/a),x)
 --R 
 --R
@@ -1051,7 +1190,7 @@ aa:=integrate(x^2*acot(x/a),x)
 --R                                          Type: Union(Expression Integer,...)
 --E
 
---S 67
+--S 76
 bb:=x^3/3*acot(x/a)+(a*x^2)/6-a^3/6*log(x^2+a^2)
 --R
 --R           3     2    2      3     x       2
@@ -1062,7 +1201,7 @@ bb:=x^3/3*acot(x/a)+(a*x^2)/6-a^3/6*log(x^2+a^2)
 --R                                                     Type: Expression Integer
 --E 
 
---S 68
+--S 77
 cc:=aa-bb
 --R
 --R         3       2a x       3     x
@@ -1074,7 +1213,7 @@ cc:=aa-bb
 --R                                                     Type: Expression Integer
 --E
 
---S 69
+--S 78
 atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 --R
 --R                            - x + %i
@@ -1085,7 +1224,7 @@ atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 --R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
 --E
 
---S 70
+--S 79
 dd:=atanrule cc
 --R
 --R                    2              2
@@ -1098,7 +1237,7 @@ dd:=atanrule cc
 --R                                             Type: Expression Complex Integer
 --E
 
---S 71
+--S 80
 acotrule:=rule(acot(x) == -%i/2*log((%i*x-1)/(%i*x+1)))
 --R
 --R                            x + %i
@@ -1109,7 +1248,7 @@ acotrule:=rule(acot(x) == -%i/2*log((%i*x-1)/(%i*x+1)))
 --R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
 --E
 
---S 72
+--S 81
 ee:=acotrule dd
 --R
 --R                    2              2
@@ -1122,7 +1261,7 @@ ee:=acotrule dd
 --R                                             Type: Expression Complex Integer
 --E
 
---S 73     14:490 Axiom and Schaums agree
+--S 82     14:490 Axiom and Schaums agree
 ff:=expandLog ee
 --R
 --R   (8)  0
@@ -1138,7 +1277,7 @@ $$
 <<*>>=
 )clear all
 
---S 74     14:491 Axiom cannot compute this integral
+--S 83     14:491 Axiom cannot compute this integral
 aa:=integrate(acot(x/a)/x,x)
 --R 
 --R
@@ -1159,7 +1298,7 @@ $$
 <<*>>=
 )clear all
 
---S 75
+--S 84
 aa:=integrate(acot(x/a)/x^2,x)
 --R 
 --R
@@ -1172,7 +1311,7 @@ aa:=integrate(acot(x/a)/x^2,x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 76
+--S 85
 bb:=-acot(x/a)/x+1/(2*a)*log((x^2+a^2)/x^2)
 --R
 --R               2    2
@@ -1185,7 +1324,7 @@ bb:=-acot(x/a)/x+1/(2*a)*log((x^2+a^2)/x^2)
 --R                                                     Type: Expression Integer
 --E
 
---S 77
+--S 86
 cc:=aa-bb
 --R
 --R   (3)
@@ -1199,7 +1338,7 @@ cc:=aa-bb
 --R                                                     Type: Expression Integer
 --E
 
---S 78
+--S 87
 acotrule:=rule(acot(x) == -%i/2*log((%i*x-1)/(%i*x+1)))
 --R
 --R                            x + %i
@@ -1210,7 +1349,7 @@ acotrule:=rule(acot(x) == -%i/2*log((%i*x-1)/(%i*x+1)))
 --R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
 --E
 
---S 79
+--S 88
 dd:=acotrule cc
 --R
 --R   (5)
@@ -1229,7 +1368,7 @@ dd:=acotrule cc
 --R                                             Type: Expression Complex Integer
 --E
 
---S 80
+--S 89
 atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 --R
 --R                            - x + %i
@@ -1240,7 +1379,7 @@ atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 --R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
 --E
 
---S 81
+--S 90
 ee:=atanrule dd
 --R
 --R   (7)
@@ -1260,7 +1399,7 @@ ee:=atanrule dd
 --R                                             Type: Expression Complex Integer
 --E
 
---S 82     14:492 Schaums and Axiom agree
+--S 91     14:492 Schaums and Axiom agree
 ff:=expandLog ee
 --R
 --R   (8)  0
@@ -1286,7 +1425,7 @@ $$
 <<*>>=
 )clear all
 
---S 83
+--S 92
 aa:=integrate(asec(x/a),x)
 --R 
 --R
@@ -1308,7 +1447,7 @@ aa:=integrate(asec(x/a),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 84
+--S 93
 bb1:=x*asec(x/a)-a*log(x+sqrt(x^2-a^2))
 --R
 --R                 +-------+
@@ -1318,7 +1457,7 @@ bb1:=x*asec(x/a)-a*log(x+sqrt(x^2-a^2))
 --R                                                     Type: Expression Integer
 --E
 
---S 85
+--S 94
 bb2:=x*asec(x/a)+a*log(x+sqrt(x^2-a^2))
 --R
 --R               +-------+
@@ -1328,7 +1467,7 @@ bb2:=x*asec(x/a)+a*log(x+sqrt(x^2-a^2))
 --R                                                     Type: Expression Integer
 --E
 
---S 86
+--S 95
 cc1:=aa-bb1
 --R
 --R   (4)
@@ -1351,7 +1490,7 @@ cc1:=aa-bb1
 --R                                                     Type: Expression Integer
 --E
 
---S 87     14:493 Axiom cannot simplify these expressions
+--S 96     14:493 Axiom cannot simplify these expressions
 cc2:=aa-bb2
 --R
 --R   (5)
@@ -1393,7 +1532,7 @@ $$
 <<*>>=
 )clear all
 
---S 88
+--S 97
 aa:=integrate(x*asec(x/a),x)
 --R 
 --R
@@ -1408,7 +1547,7 @@ aa:=integrate(x*asec(x/a),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 89
+--S 98
 bb1:=x^2/2*asec(x/a)-(a*sqrt(x^2-a^2))/2
 --R
 --R            +-------+
@@ -1420,7 +1559,7 @@ bb1:=x^2/2*asec(x/a)-(a*sqrt(x^2-a^2))/2
 --R                                                     Type: Expression Integer
 --E
 
---S 90
+--S 99
 bb2:=x^2/2*asec(x/a)+(a*sqrt(x^2-a^2))/2
 --R
 --R          +-------+
@@ -1432,7 +1571,7 @@ bb2:=x^2/2*asec(x/a)+(a*sqrt(x^2-a^2))/2
 --R                                                     Type: Expression Integer
 --E
 
---S 91
+--S 100
 cc1:=aa-bb1
 --R
 --R   (4)
@@ -1447,7 +1586,7 @@ cc1:=aa-bb1
 --R                                                     Type: Expression Integer
 --E
 
---S 92     14:494 Axiom cannot simplify these expressions
+--S 101    14:494 Axiom cannot simplify these expressions
 cc2:=aa-bb2
 --R
 --R   (5)
@@ -1488,7 +1627,7 @@ $$
 <<*>>=
 )clear all
 
---S 93
+--S 102
 aa:=integrate(x^2*asec(x/a),x)
 --R 
 --R
@@ -1511,7 +1650,7 @@ aa:=integrate(x^2*asec(x/a),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 94
+--S 103
 bb1:=x^3/3*asec(x/a)-(a*x*sqrt(x^2-a^2))/6-a^3/6*log(x+sqrt(x^2-a^2))
 --R
 --R                 +-------+            +-------+
@@ -1523,7 +1662,7 @@ bb1:=x^3/3*asec(x/a)-(a*x*sqrt(x^2-a^2))/6-a^3/6*log(x+sqrt(x^2-a^2))
 --R                                                     Type: Expression Integer
 --E
 
---S 95
+--S 104
 bb2:=x^3/3*asec(x/a)+(a*x*sqrt(x^2-a^2))/6+a^3/6*log(x+sqrt(x^2-a^2))
 --R
 --R               +-------+            +-------+
@@ -1535,7 +1674,7 @@ bb2:=x^3/3*asec(x/a)+(a*x*sqrt(x^2-a^2))/6+a^3/6*log(x+sqrt(x^2-a^2))
 --R                                                     Type: Expression Integer
 --E
 
---S 96
+--S 105
 cc1:=aa-bb1
 --R
 --R   (4)
@@ -1563,7 +1702,7 @@ cc1:=aa-bb1
 --R                                                     Type: Expression Integer
 --E
 
---S 97     14:495 Axiom cannot simplify these expressions
+--S 106     14:495 Axiom cannot simplify these expressions
 cc2:=aa-bb2
 --R
 --R   (5)
@@ -1603,7 +1742,7 @@ $$
 <<*>>=
 )clear all
 
---S 98     14:496 Axiom cannot compute this integral
+--S 107    14:496 Axiom cannot compute this integral
 aa:=integrate(asec(x/a)/x,x)
 --R 
 --R
@@ -1634,7 +1773,7 @@ $$
 <<*>>=
 )clear all
 
---S 99
+--S 108
 aa:=integrate(asec(x/a)/x^2,x)
 --R 
 --R
@@ -1650,7 +1789,7 @@ aa:=integrate(asec(x/a)/x^2,x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 100
+--S 109
 bb1:=-asec(x/a)/x+sqrt(x^2-a^2)/(a*x)
 --R
 --R         +-------+
@@ -1662,7 +1801,7 @@ bb1:=-asec(x/a)/x+sqrt(x^2-a^2)/(a*x)
 --R                                                     Type: Expression Integer
 --E
 
---S 101
+--S 110
 bb2:=-asec(x/a)/x-sqrt(x^2-a^2)/(a*x)
 --R
 --R           +-------+
@@ -1674,7 +1813,7 @@ bb2:=-asec(x/a)/x-sqrt(x^2-a^2)/(a*x)
 --R                                                     Type: Expression Integer
 --E
 
---S 102
+--S 111
 cc1:=aa-bb1
 --R
 --R   (4)
@@ -1694,7 +1833,7 @@ cc1:=aa-bb1
 --R                                                     Type: Expression Integer
 --E
 
---S 103    14:497 Axiom cannot simplify these expressions
+--S 112    14:497 Axiom cannot simplify these expressions
 cc2:=aa-bb2
 --R
 --R   (5)
@@ -1733,7 +1872,7 @@ $$
 <<*>>=
 )clear all
 
---S 104
+--S 113
 aa:=integrate(acsc(x/a),x)
 --R 
 --R
@@ -1755,7 +1894,7 @@ aa:=integrate(acsc(x/a),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 105
+--S 114
 bb1:=x*acsc(x/a)+a*log(x+sqrt(x^2-a^2))
 --R
 --R               +-------+
@@ -1765,7 +1904,7 @@ bb1:=x*acsc(x/a)+a*log(x+sqrt(x^2-a^2))
 --R                                                     Type: Expression Integer
 --E
 
---S 106
+--S 115
 bb2:=x*acsc(x/a)-a*log(x+sqrt(x^2-a^2))
 --R
 --R                 +-------+
@@ -1775,7 +1914,7 @@ bb2:=x*acsc(x/a)-a*log(x+sqrt(x^2-a^2))
 --R                                                     Type: Expression Integer
 --E
 
---S 107
+--S 116
 cc1:=aa-bb1
 --R
 --R   (4)
@@ -1798,7 +1937,7 @@ cc1:=aa-bb1
 --R                                                     Type: Expression Integer
 --E
 
---S 108    14:498 Axiom cannot simplify these expressions
+--S 117    14:498 Axiom cannot simplify these expressions
 cc2:=aa-bb2
 --R
 --R   (5)
@@ -1841,7 +1980,7 @@ $$
 <<*>>=
 )clear all
 
---S 109
+--S 118
 aa:=integrate(x*acsc(x/a),x)
 --R 
 --R
@@ -1856,7 +1995,7 @@ aa:=integrate(x*acsc(x/a),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 110
+--S 119
 bb1:=x^2/2*acsc(x/a)+(a*sqrt(x^2-a^2))/2
 --R
 --R          +-------+
@@ -1868,7 +2007,7 @@ bb1:=x^2/2*acsc(x/a)+(a*sqrt(x^2-a^2))/2
 --R                                                     Type: Expression Integer
 --E
 
---S 111
+--S 120
 bb2:=x^2/2*acsc(x/a)-(a*sqrt(x^2-a^2))/2
 --R
 --R            +-------+
@@ -1880,7 +2019,7 @@ bb2:=x^2/2*acsc(x/a)-(a*sqrt(x^2-a^2))/2
 --R                                                     Type: Expression Integer
 --E
 
---S 112
+--S 121
 cc1:=aa-bb1
 --R
 --R   (4)
@@ -1895,7 +2034,7 @@ cc1:=aa-bb1
 --R                                                     Type: Expression Integer
 --E
 
---S 113    14:499 Axiom cannot simplify these expressions
+--S 122    14:499 Axiom cannot simplify these expressions
 cc2:=aa-bb2
 --R
 --R   (5)
@@ -1936,7 +2075,7 @@ $$
 <<*>>=
 )clear all
 
---S 114
+--S 123
 aa:=integrate(x^2*acsc(x/a),x)
 --R 
 --R
@@ -1959,7 +2098,7 @@ aa:=integrate(x^2*acsc(x/a),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 115
+--S 124
 bb1:=x^3/3*acsc(x/a)+(a*x*sqrt(x^2-a^2))/6+a^3/6*log(x+sqrt(x^2-a^2))
 --R
 --R               +-------+            +-------+
@@ -1971,7 +2110,7 @@ bb1:=x^3/3*acsc(x/a)+(a*x*sqrt(x^2-a^2))/6+a^3/6*log(x+sqrt(x^2-a^2))
 --R                                                     Type: Expression Integer
 --E
 
---S 116
+--S 125
 bb2:=x^3/3*acsc(x/a)-(a*x*sqrt(x^2-a^2))/6-a^3/6*log(x+sqrt(x^2-a^2))
 --R
 --R                 +-------+            +-------+
@@ -1983,7 +2122,7 @@ bb2:=x^3/3*acsc(x/a)-(a*x*sqrt(x^2-a^2))/6-a^3/6*log(x+sqrt(x^2-a^2))
 --R                                                     Type: Expression Integer
 --E
 
---S 117
+--S 126
 cc1:=aa-bb1
 --R
 --R   (4)
@@ -2011,7 +2150,7 @@ cc1:=aa-bb1
 --R                                                     Type: Expression Integer
 --E
 
---S 118    14:500 Axiom cannot simplify this expression
+--S 127    14:500 Axiom cannot simplify this expression
 cc2:=aa-bb2
 --R
 --R   (5)
@@ -2050,7 +2189,7 @@ $$
 <<*>>=
 )clear all
 
---S 119    14:501 Axiom cannot compute this integral
+--S 128    14:501 Axiom cannot compute this integral
 aa:=integrate(acsc(x/a)/x,x)
 --R 
 --R
@@ -2081,7 +2220,7 @@ $$
 <<*>>=
 )clear all
 
---S 120
+--S 129
 aa:=integrate(acsc(x/a)/x^2,x)
 --R 
 --R
@@ -2097,7 +2236,7 @@ aa:=integrate(acsc(x/a)/x^2,x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 121
+--S 130
 bb1:=-acsc(x/a)/x-sqrt(x^2-a^2)/(a*x)
 --R
 --R           +-------+
@@ -2109,7 +2248,7 @@ bb1:=-acsc(x/a)/x-sqrt(x^2-a^2)/(a*x)
 --R                                                     Type: Expression Integer
 --E
 
---S 122
+--S 131
 bb2:=-acsc(x/a)/x+sqrt(x^2-a^2)/(a*x)
 --R
 --R         +-------+
@@ -2121,7 +2260,7 @@ bb2:=-acsc(x/a)/x+sqrt(x^2-a^2)/(a*x)
 --R                                                     Type: Expression Integer
 --E
 
---S 123
+--S 132
 cc1:=aa-bb1
 --R
 --R   (4)
@@ -2142,7 +2281,7 @@ cc1:=aa-bb1
 --R                                                     Type: Expression Integer
 --E
 
---S 124    14:502 Axiom cannot simplify this expression
+--S 133    14:502 Axiom cannot simplify this expression
 cc2:=aa-bb2
 --R
 --R   (5)
@@ -2172,7 +2311,7 @@ $$
 <<*>>=
 )clear all
 
---S 125    14:503 Axiom cannot compute this integral
+--S 134    14:503 Axiom cannot compute this integral
 aa:=integrate(x^m*asin(x/a),x)
 --R 
 --R
@@ -2192,7 +2331,7 @@ $$
 <<*>>=
 )clear all
 
---S 126    14:504 Axiom cannot compute this integral
+--S 135    14:504 Axiom cannot compute this integral
 aa:=integrate(x^m*acos(x/a),x)
 --R 
 --R
@@ -2218,7 +2357,7 @@ have the same form but are expressed in terms of asin, acos, and acot.
 <<*>>=
 )clear all
 
---S 127
+--S 136
 aa:=integrate(x*m*atan(x/a),x)
 --R 
 --R
@@ -2231,7 +2370,7 @@ aa:=integrate(x*m*atan(x/a),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 128
+--S 137
 t1:=integrate(x^(m+1)/(x^2+a^2),x)
 --E
 @
@@ -2243,7 +2382,7 @@ difference from the original formula.
 So first we generate the derivative:
 <<*>>=
 
---S 129
+--S 138
 bb:=D(aa,x)
 --R
 --R                     2a x
@@ -2257,7 +2396,7 @@ bb:=D(aa,x)
 @
 Then we input the original expression
 <<*>>=
---S 130
+--S 139
 aa1:=x*m*atan(x/a)
 --R
 --R                 x
@@ -2268,7 +2407,7 @@ aa1:=x*m*atan(x/a)
 @
 Now we take their difference
 <<*>>=
---S 131
+--S 140
 dd:=aa1-bb
 --R
 --R                  x               2a x
@@ -2282,7 +2421,7 @@ dd:=aa1-bb
 @
 Now we input the atan transformation
 <<*>>=
---S 132
+--S 141
 atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 --R
 --R                            - x + %i
@@ -2295,7 +2434,7 @@ atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
 @
 And apply the transformation to the difference
 <<*>>=
---S 133
+--S 142
 ee:=atanrule dd
 --R
 --R                      2              2
@@ -2310,7 +2449,7 @@ ee:=atanrule dd
 @
 And now we simplify
 <<*>>=
---S 134    14:505 SCHAUMS AND AXIOM DISAGREE? (branch cuts?)
+--S 143    14:505 SCHAUMS AND AXIOM DISAGREE? (branch cuts?)
 ff:=expandLog ee
 --R
 --R          %i m x log(- 1)
@@ -2332,7 +2471,7 @@ $$
 <<*>>=
 )clear all
 
---S 135    14:506 Axiom cannot compute this integral
+--S 144    14:506 Axiom cannot compute this integral
 aa:=integrate(x^m*acot(x/a),x)
 --R 
 --R
@@ -2362,7 +2501,7 @@ $$
 <<*>>=
 )clear all
 
---S 136    14:507 Axiom cannot compute this integral
+--S 145    14:507 Axiom cannot compute this integral
 aa:=integrate(x^m*asec(x/a),x)
 --R 
 --R
@@ -2392,7 +2531,7 @@ $$
 <<*>>=
 )clear all
 
---S 137    14:508 Axiom cannot compute this integral
+--S 146    14:508 Axiom cannot compute this integral
 aa:=integrate(x^m*acsc(x/a),x)
 --R 
 --R