Updates:
Status: Valid
Labels: Integration Simplify
Comment #1 on issue 3767 by [email protected]: Problem integrate
1/((sin(x)+cos(x)+sqrt(3))**2)
http://code.google.com/p/sympy/issues/detail?id=3767
Yes, unfortunately, one of the algorithms SymPy uses for integration can be
very slow. If you let it run long enough, it will eventually finish. In
general, if it doesn't return within a reasonable amount of time, you can
break it. It is unlikely to give an answer even if you do let if finish.
SymPy will be able to do such integrals once the Risch algorithm is
extended to work with trigonometric integrals. You can actually get an
answer now if you first rewrite the integral in terms of complex
exponentials (integrate(1/((sin(x)+cos(x)+sqrt(3))**2).rewrite(exp), x)),
but the answer will also be in terms of complex exponentials, and we don't
seem to have have good enough simplification algorithms to convert it
entirely back.
By the way, the answer:
http://www.wolframalpha.com/input/?i=integrate+1%2F((sin(x)%2Bcos(x)%2Bsqrt(3))**2)&dataset=
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