Updates:
Status: Invalid
Comment #1 on issue 2066 by smichr: integration of
c**2*exp(c/x)/(x**3*(1+exp(c/x)**2)) fails
http://code.google.com/p/sympy/issues/detail?id=2066
The answer you obtained from Mathematica was for the integrand:
c**2*exp(c/x)/(x**3*(1 + exp(c/x))**2)
^
not |
V
c**2*exp(c/x)/(x**3*(1 + exp(c/x)**2))
Note the difference (best viewed in monospaced font): (1+exp())**2 vs 1 +
exp()**2
When you enter that, sympy takes a while but eventually (at least in
Aaron's integrate3 branch) gives:
h[13] >>> f = c**2*exp(c/x)/(x**3*(1+exp(c/x))**2)
h[13] >>> integrate(f, x)
c**2*(x*log(1 + exp(c/x))/(x*c**2 + x*c**2*exp(c/x)) + x*exp(c/x)*log(1 +
exp(c/
x))/(x*c**2 + x*c**2*exp(c/x)) - c*exp(c/x)/(x*c**2 + x*c**2*exp(c/x)))
h[14] >>> factor(cancel(_),frac=1)
(x*log(1 + exp(c/x)) + x*exp(c/x)*log(1 + exp(c/x)) - c*exp(c/x))/(x*(1 +
exp(c/
x)))
...
h[16] >>> ratsimp(_)
log(1 + exp(c/x)) - c*exp(c/x)/(x + x*exp(c/x))
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