Updates:
Labels: Integration
Comment #1 on issue 1388 by asmeurer: integrate(exp(-x)*x**n, x) fails
http://code.google.com/p/sympy/issues/detail?id=1388
The solutions to integrals with symbolic powers are not easy to compute.
The solution here is (according to Maple)
int(x**n/exp(x), x);
/ 1 \ (1/2 n) /1 1 1 \
exp|- - x| x WhittakerM|- n, - n + -, x|
\ 2 / \2 2 2 /
-----------------------------------------------
1 + n
This WhittakerM function can also be written in terms of the hypergeometric
function, so maybe the way (and only way) to do things like this will be to
use a MeijerG based definite integration and to do something like
integrate(exp(-t)*t**n, (t, 0, x))
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