1. The problem statement, all variables and given/known data the function is Exp[-w^2]/w^2, how to solve the Fourier transform analytically with Residue theorem? It is better if there is more general results. Mathematica can solve it analytically, but I need a human-soluable way. 2. Relevant equations 3. The attempt at a solution My attempt follows the Fresnel integral, but there is still something wrong.