Comment #9 on issue 1227 by [email protected]: Integration failure http://code.google.com/p/sympy/issues/detail?id=1227
These cases where integrate() returns a result with nan is due to _eval_interval. It first tries subs, and then if the result is nan, it tries limit(). It can't use limit() directly because that apparently isn't smart enough to just use subs when the limit exists (in particular, it breaks on Piecewise, and possibly elsewhere, I didn't check).
The issue is that it checks if the answer *is* nan, rather than if it contains nan. A simple modification (A.has(nan) instead of A is nan) makes this integral return unevaluated again. This seems less nice than the result returned currently, but the current result is actually nonsensical (because it contains a nan). I've added such a change to https://github.com/sympy/sympy/pull/1643.
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