# Exponential integration confused

1. Dec 19, 2014

### JI567

Hi, does anyone know how to integrate e^-x (sin(nπx))? I have tried part integration but that goes on until infinity.... and I am not sure how to use the substitution method....Please help! I have tried taking e^-x as U but then I end up getting the entire cancelled off then...

2. Dec 19, 2014

### Simon Bridge

Do you mean: $$\int e^{-x}\sin n\pi x\; dx$$

There's a trick - as you noticed, integration by parts gets you the original integral back again with some extra terms, so round and round you go.
The trick is this: put $$I = \int e^{-x}\sin n\pi x\; dx$$ ... integrate the RHS by parts, twice only.
When you've done that, you should see the original integral appear again, with a bunch of other stuff.
Replace the integral with "I" and solve the resulting equation for I.

3. Mar 24, 2015