Updates:
Blockedon: 1397
Comment #5 on issue 1227 by asmeurer: Integration failure
http://code.google.com/p/sympy/issues/detail?id=1227
That's because the way its implemented, it needs to know if R**2 is
positive or negative to know if it should use asin or acosh or whatever
(see around line 205 in risch.py). This isn't so much a gotcha as a
limitation in our implementation of the integration algorithm (ideally, it
would be able to return the algebraic for of the integral, which doesn't
care about sign). But that would require a much more strong integration
algorithm. The fact that heurisch() can do algebraic integrals is mainly
an accident of the form that the algebraic expression happens to take
(algebraic functions can take various equivalent forms, like sqrt(x) ==
x/sqrt(x)). An interim solution would be to implement heuristics for
square root integrals (see issue 1397).
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