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Comment #5 on issue 790 by asmeurer: risch: PolynimialException when
integrating not-so-trivial exponents
http://code.google.com/p/sympy/issues/detail?id=790
By the way, exact substitution does NOT fix the problem. The problem is
that, once you do exact substitution, it fixes the problem of turning
exp(x) into sqrt(exp(2*x)), but then it no longer turns x into sqrt(x)**2.
We need a special subs that only replaces if the exponent in the new term
is an integer (so it will be a rational function).
By the way, I think such a subs would also be useful for trigsimp(). Isn't
that exactly the same limitation that you want for
(complex_trig_expression).subs(sin(x)**2, 1 - cos(x)**2), i.e., replace
sin(x)**2, but not sin(x), and for sin(x)**3, replace it with sin(x)*(1 -
cos(x)**2)?
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