1. The problem statement, all variables and given/known data Evaluate ∫e-θcos2θ dθ 2. Relevant equations Integration by parts formula ∫udv = uv -∫vdu 3. The attempt at a solution So in calc II we just started integration by parts and I'm doing one of the assignment problems. I know I need to do the integration by parts twice, but I've hit a loop, or so it seems, which I know isn't right. Maybe someone can see my faults? I set: u = cos(2θ) v = -e-θ du = -2sin(2θ) dθ dv = e-θ dθ So by the formula I got: = [cos(2θ)] [-e-θ] -2∫ [-e-θ] [sin(2θ) dθ] Here I used the second integration by parts: u = sin2θ v = e-θ du = 2cos(2θ) dθ dv = -e-θ dθ Solving by the formula again: = [sin(2θ)] [e-θ] -2∫ [e-θ] [cos(2θ) dθ] I'm not too sure where I've made my algebraic error, or if I'm on the right track and this won't just put my into a loop giving the same equation above? First question I've posted, so hopefully it follows the format ok, if it doesn't, chime in and let me know so I can fix it properly. Thanks in advance everyone!