Updates:
Labels: Assumptions
Comment #2 on issue 3647 by [email protected]: Require explicit
assumptions when integrating.
http://code.google.com/p/sympy/issues/detail?id=3647
By the way, there's some discussion of this in the source code for the
risch algorithm (which is what should be doing both those integrals). In
general, do differentiate between elementary and non-elementary integrals,
we have to determine if some expression is rational (which Piecewise can't
even represent yet). I believe most of it is in prde.py.
A more general case is also difficult if you want to solve. For example,
for integrate(exp((some_complicated_expression)*x), x), do you want to
split out all the different cases where some_complicated_expression = 0, if
you can?
And finally, it's not easy to find every possible instance of when you
divide by something, especially if it's in some intermediate step. In
general, it could happen anywhere. And it can be complicated. For example,
it happens a ton of times when using Matrix.rref.
Another case is just integrate(x**n, x).
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