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.
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