1. The problem statement, all variables and given/known data ∫ ex * sin(t-x) dx 2. Relevant equations ∫udv = uv - ∫vdu 3. The attempt at a solution So I know the easiest way to do this is to just use IBP, and when you start with your original equation you can just use some Algebra to get the answer. But I was curious why this approach doesn't work. u = ex, dx = du/ex Now the original equation in terms of u: ∫sin(t-ln(u)) du = -cos(t-ln(u))/(-1/u) + C = ucos(t-ln(u)) + c = ex * cos(t-x) + C I actually went this route on purpose on a quiz because I'm that type of guy who likes to use untraditional ways. Oh well. Any insight would be greatly appreciated!