1. The problem statement, all variables and given/known data How might one proceed to compute the integral depicted in the following image? http://yfrog.com/jdintegralup a is an arbitrary real number. 2. Relevant equations I think the methods of complex analysis can be used. 3. The attempt at a solution This integral, as far as I can tell, does not fall under any of the standard categories of integrals that are calculated using residues. Nevertheless I have a suspicion that residues can be used. Any method is of course fair game! At this point I've just been fiddling with trying to find contours to integrate over, etc., without any luck. Experimentation suggests the answer should be π tanh(aπ/2).