Updates:
Status: Accepted
Labels: Integration
Comment #1 on issue 2578 by asmeurer: integrate(sqrt(2+2*sin(x)), x) does
not evaluate
http://code.google.com/p/sympy/issues/detail?id=2578
Actually, integration uses a completely different method from the one that
you learn in calculus. So it's not actually applying any "steps" at all.
This integral is a particularly tricky one for the algorithm to handle
because it is both algebraic (because of the square root) and
transcendental.
The fact is, with the current integration heuristic, you will get different
results with algebraic functions in you rewrite them in different ways,
e.g., moving a square root from the numerator to the denominator.
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