# Having trouble finding the Integral

Hello,

I am having trouble getting started with this integral.

$\int sin2x ln(cos2x) dx$

My first thought goes to using integration by parts to solve this but I am still getting stuck. I also know that $sin2x = 2sinxcosx$ but again I'm not seeing how that would help me so I'm back to integration by parts.

My issue is if I set $u = ln(cos2x)$ then I'm having trouble figuring out what $du$ is. I know it's just finding the derivative but I can't for the life of me remember how to do that. Then if I set $dv = sin2x dx$ then $v = - \frac{1}{2} cos2x$

Any help or suggestions would be greatly appreciated.