Solving Complex Integration with Residue Theorem

[hedipaldi]

Homework Statement

use residue theorem to integrate sinh(ax)/sinh(xpi) from -infinity to +infinity, a is between -pi and pi

Homework Equations

residue theorem

3
. The attempt at a solution
i tried rectangular trajection through 0 and ia/pi with the function sinh(az)/sinh(zpi) and some other trajectories but it doesn't really work

 

[HallsofIvy]

The residue theorem applies to integration over closed paths. What closed paths have you used?