How to solve this integration: $\int_0^1 \frac{x^{2012}}{1+e^x}dx$ I'm having troubles to solve this integration: $\int_0^1 \frac{x^{2012}}{1+e^x}dx$
I've tried a lot using so many techniques without success. I found $\int_{-1}^1 \frac{x^{2012}}{1+e^x}dx=1/2013$, but I couldn't solve from 0 to 1.
Thanks a lot.

Experimenting with wolfram alpha lead me to: 
$$ \int {x^n \over 1+e^x} = (-1)^{n+1} x^{n+1} + (-1)^n * log(e^x+1)+  \sum_{k = 0}^{n-1} x^{n-i-1} (-1)^n * {n! \over (n-i)!} * Li_{i+2}(-e^x)$$
I got this by trying out small values for n so wolfram alpha manages to do the computations and then generalized it. Can someone verify/correct that?
