# Anti-derivative of a trig equation

1. May 17, 2012

### togame

1. The problem statement, all variables and given/known data
I just need to find the anti-derivative of this equation:
$\int x(sin^2(3x)cos(3x))dx$

2. Relevant equations
$sin^2(x)+cos^2(x)=1$

3. The attempt at a solution
I'm not really sure where to start here. I tried to do a substitution first but couldn't make it work. So then I tried to put sin^2 in terms of cos^2 but that didn't seem to help me out any more. Anyone have an idea of how to tackle this problem? Thanks in advance!

2. May 17, 2012

### Curious3141

Integrate by parts, with u = x, dv = $\sin^2(3x)\cos(3x)dx$.

To integrate $\sin^2(3x)\cos(3x)dx$, use the substitution $y = \sin(3x)$

3. May 17, 2012

### togame

Thank you very much. I didn't see the ability to do another substitution right off hand.