Updates:
        Status: Invalid

Comment #2 on issue 3298 by [email protected]: integrate / limit does not know the sign of abs() / does nor catch NotImplementedError from limit()
http://code.google.com/p/sympy/issues/detail?id=3298

See the mailing list discussion. This is actually not a bug, because the sign is different depending on if Abs(a) is positive or 0, and the answer is different in the two cases as well (both of the limit and the integral).

If you want a to be strictly positive, it's better to use a = Symbol('a', positive=True).

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