1. The problem statement, all variables and given/known data F(t) = sqrt(π/2)e-t for t>0 F(t) = sqrt(π/2)et for t<0 In other words the question asks to solve this integral: 1/sqrt(2π) ∫F(t)eitxdt and show that it equals 1/(1+x2) 2. Relevant equations F(t) = sqrt(π/2)e-t for t>0 F(t) = sqrt(π/2)et for t<0 1/sqrt(2π) ∫F(t)eitxdt 3. The attempt at a solution I want to use complex numbers but these functions are analytic and so I can not do this using residues. A naive approach to integrating with respect to t is straightforward but the limits cause the result to be infinity. How should I approach this properly?