1. The problem statement, all variables and given/known data I need to find the inverse Laplace transform of s/(s^2+a^2), where a is a constant, by the method of residues. I need to prove the part of the contour not actually relating to the desired integral tends to zero as R---> infinity. 2. Relevant equations 3. The attempt at a solution I have calculated the residues, however I am having trouble proving the integral of the contour which isn't the straight line from -R to R vanishes. Any help would be appreciated.