Comment #2 on issue 3852 by [email protected]: Multiple integrals with
piecewise should be smarter
http://code.google.com/p/sympy/issues/detail?id=3852
First the integral over x is tried. It is passed to trigintegrate, but the
y is factored out, as it is independent of x. Trigintegrate returns a
Piecewise; it doesn't know that the y in the denominator will be cancelled
by a y prefactor since it never sees that prefactor. You can check this by
calling the integral over x directly.
integrate(y*cos(x*y), x)
// x for y = 0\
|| |
y*|<sin(x*y) |
||-------- otherwise|
\\ y /
Only after piecewise_fold is called do we get the redundant Piecewise.
piecewise_fold(_)
/ x*y for y = 0
<
\sin(x*y) otherwise
The logic to collapse the above Piecewise to simply sin(x*y) would need to
be in the Piecewise constructor or in piecewise_fold.
I can't answer your remaining queries as I don't know what a "double
indefinite integral" is.
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