integration by parts: integral ( (e^x) (sinx) ) dx

[rooney]

integral((e^x)(sinx)dx)

I tried to integrate by parts, and ended up with (sinx)(e^x)-integral((cosx)(e^x) which I don't know what to do with.

 

[n00blar]

Re: integral by parts

What you want to do here is use integration by parts again:

\(\displaystyle \int {e^x}{sin(x)} dx = {e^x}{sin(x)} - \int {e^x}{cos(x)} dx\)
\(\displaystyle \int {e^x}{cos(x)} dx = {e^x}{cos(x)} + \int {e^x}{sin(x)} dx\)
\(\displaystyle \int {e^x}{sin(x)} dx = {e^x}{sin(x)} - {e^x}{cos(x)} - \int {e^x}{sin(x)} dx\)

The rest is just simple math. =)