1. The problem statement, all variables and given/known data Integral of sin(x) sin(x+1) dx from 0 to 2pi. 2. Relevant equations Integration by parts: Integral u dv = uv – Integral v du 3. The attempt at a solution My work has been attached as MyWork.jpg. I, basically, get 0 * integral_I_started_with = something_else instead of nonzero_constant * integral_I_started_with = something_else and, given that I've done this problem a multitude of times and failed (if I remember correctly, always with the same issue) and, I was hoping someone here could point out my mistake. Any input would be greatly appreciated!