Residue[2 E^(a z) /((z^2 + 1) (E^(2 a z) + 1)), {z, (Pi I)/(2 a)}]

Uh oh! Wolfram|Alpha doesn't run without JavaScript.

Please enable JavaScript. If you don't know how, you can find instructionshere.Once you've done that, refresh this page to start using Wolfram|Alpha.