sin(wt)cos(nwt) dt
Ooops! Sorry I missed that. Eyes are wearing out from looking at the computer.
Hmmm, my first thought is to try the product to sum conversation for sin(a)cos(b), which looks like:
$\displaystyle \sin(a)\cos(b)=\frac{\sin(a+b)+\sin(a-b)}{2}$
That should split up into things you can integrate separately easily.