I know four: Art of Problem Solving, Physic Forum, SOS, and here. You just need to search the sites for complex analysis problems and study the solutions.

Anyway, use:

where is the upper half-disc contour. The big denominator assures you that the integral over the semi-circle component of the contour goes to zero and the integral over the real axis component is twice your integral. There are only two poles in the contour right: and . Now calculate the residues for these poles and use Residue Theorem.