Item 14:150 Schaums and Axiom DISAGREE BY A
NON-CONSTANT
in schaum7.input.pamphlet is particularly interesting
because
it appears that the derivative of Axiom's answer is the
original
integrand but the derivative of Schaum's answer is not,
implying
that Schaum's has a mistake. This will be verified using
other
systems later.
Axiom is weak in handling certain simplifications. Future
work is
planned to correct this.
Richard Fateman has given me permission to use his TILU
pattern
integration database in Axiom. This should give us much
broader
integration results. TILU has not been tested against
Schaums
but this testing will occur during the merge.
schaum2.input.pamphet
14:150 Schaums and Axiom DISAGREE BY A NON-CONSTANT
\section{\cite{1}:14.150~~~~~$\displaystyle\int{\frac{dx}{x^3(x^2-a^2)}}$}
@@ -124,7 +343,7 @@ $$
<<*>>=
)clear all
---S 7 of 19
+--S 29
aa:=integrate(1/(x^3*(x^2-a^2)),x)
--R
--R
@@ -135,6 +354,73 @@ aa:=integrate(1/(x^3*(x^2-a^2)),x)
--R 2a x
--R Type:
Union(Expression Integer,...)
--E
+
+--S 30
+bb:=1/(2*a^2*x*2)-1/(2*a^4)*log(x^2/(x^2-a^2))
+--R
+--R 2
+--R x 2
+--R - 2x log(-------) + a
+--R 2 2
+--R x - a
+--R (2) ----------------------
+--R 4
+--R 4a x
+--R
Type:
Expression Integer
+--E
+
+--S 31
+cc:=aa-bb
+--R
+--R 2
+--R 2 2 2 2 2 x
2 2
+--R 2x log(x - a ) - 4x log(x) + 2x log(-------)
- a x + 2a
+--R 2 2
+--R x - a
+--R (3)
---------------------------------------------------------
+--R 4 2
+--R 4a x
+--R
Type:
Expression Integer
+--E
+
+--S 32
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R a
+--R (4) log(-) == - log(b) + log(a)
+--R b
+--R Type:
RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 33
+dd:=divlog cc
+--R
+--R 2 2 2 2 2
+--R 2x log(x ) - 4x log(x) - a x + 2a
+--R (5) ----------------------------------
+--R 4 2
+--R 4a x
+--R
Type:
Expression Integer
+--E
+
+--S 34
+logpow:=rule(log(a^n) == n*log(a))
+--R
+--R n
+--R (6) log(a ) == n log(a)
+--R Type:
RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 35 14:150 Schaums and Axiom DISAGREE BY A
NON-CONSTANT
+ee:=logpow dd
+--R
+--R - x + 2
+--R (7) -------
+--R 2 2
+--R 4a x
+--R
Type:
Expression Integer
+--E
+
@