complex analysis - How to evaluate $int_{-infty}^infty {e^{ax} over 1 +e^x } ; dx$

Given that $0 < a < 1$ how to evaluate by the method of residues

$$\int_{-\infty}^\infty {e^{ax} \over 1 +e^x } \; dx$$

Answer

Substituting $u=e^x$, so that $dx = \dfrac{du}{u}$, the integral becomes

$$\int_0^{\infty} \dfrac{u^{a-1}}{1+u}du$$

How might you solve this? You've tagged the question as homework, so I'll leave it here for now, but if you're still stuck, post in the comments.