Convergence of $\int_{0}^{+\infty} \frac{x}{1+e^x}\,dx$ Does this integral converge to any particular value?
$$\int_{0}^{+\infty} \frac{x}{1+e^x}\,dx$$
If the answer is yes, how should I calculate its value? 
I tried to use convergence tests but I failed due to the complexity of the integral itself.

Comparison test:
$$\frac x{1+e^x}\le\frac x{e^x}\;$$
and you can directly do integration by parts in the rightmost function to check it converges.
