Loopy integral $\int xe^x\sin(x)$ How to find integral of: $$\int xe^x\sin(x)$$
I know it should be repeated integration by parts, but i do not know how many times i should do this and when to stop.
You had better use the formula $\sin x = \dfrac{e^{ix}-e^{-ix}}{2}$. In this way you obtain an integral like $\int xe^{ax}dx$ and it is easy to reach your goal by integration by parts.

Also, another ways are possible.
Treat x*sinx as first term and e^x as the 2nd term. Then use integration by parts.