Is it possible to define an assumption for an integral?
Example from Wester test case V8 in Macsyma:
(c27) /* This example involves several symbolic parameters
=> 1/sqrt(b^2 - a^2) log([sqrt(b^2 - a^2) tan(x/2) + a + b]/
[sqrt(b^2 - a^2) tan(x/2) - a - b]) (a^2 <
b^2)
[Gradshteyn and Ryzhik 2.553(3)] */
*assume(b^2 > a^2)$*
Time= 270 msecs
*(c28) integrate(1/(a + b*cos(x)), x)*;
Time= 1070 msecs
(b - a) sin(x) 2 2
-------------- - sqrt(b - a )
cos(x) + 1
log(------------------------------)
(b - a) sin(x) 2 2
-------------- + sqrt(b - a )
cos(x) + 1
(d28) - -----------------------------------
2 2
sqrt(b - a )
(c29) trigsimp(ratsimp(diff(%, x)));
/aquarius/data2/opt/local/macsyma_422/share/trigsimp.so being loaded.
Time= 1740 msecs
1
(d29) ------------
b cos(x) + a
--
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