1. The problem statement, all variables and given/known data Let x(t) = e-100tu(t) u(t) = 0 for t < 0 u(t) = 1 for t > 0 Evaluate the following integral (from -∞ to ∞): X(ω) = ∫ x(t)e-iωtdt 2. Relevant equations See below. 3. The attempt at a solution I tried to evaluate the integral by splitting it in two parts, since x(t) takes two different values. Keep in mind I'm replacing ∞ with a to evaluate the limit later. from -∞ to 0: X1(ω) = ∫ e-iωtdt X1(ω) = (1/-iω) e-iωt (from -∞ to 0) X1(ω) = (1/-iω)(1 - eiωa) from 0 to ∞: X2(ω) = e-100∫ e-iωtdt X2(ω) = e-100 (1/-iω) e-iωt (from 0 to ∞) X2(ω) = e-100 (1/-iω)(e-iωa - 1) X(ω) = X1(ω) + X2(ω) = (1/-iω)(1 - eiωa) + e-100 (1/-iω)(e-iωa - 1) = (1/-iω) (1 - eiωa + e-100e-iωa - e-100) This is where I'm stuck. The answer is supposed to be X(ω) = 1 / (100 + iω), and I have absolutely no idea how I'm supposed to get there. Would someone mind helping me out?