In solving the integral
I misread it as
After a while of failing to solve this, I realized my mistake. How would I go about solving the second integral?
On first glance I thought it could be integration by parts, but since there are no $\cos(2x)$ or $\sin(3x)$ terms that seems like the wrong approach. I thought of using the $\sin(x)\cos(y) = \dots$ and $\sin(x)\sin(y) = \dots$ identities, but that didn't pan out either.