I'm kind of stuck in solving this integral problem. I've tried multiple times, but I'm not still not sure what is the correct way of solving.
The problem is to solve
$$\int \sin(4x)(1+\cos(4x)) \mathrm dx$$
I've tried two methods:
The first one is where I didn't distribute $\sin (4x)$, and the second is where I distributed $\sin (4x)$ to turn the function into
$\int \left(\sin(4x)+(\sin(4x)\cos(4x))\right) \mathrm dx$.
I'm not sure if I'm going to use trig. identities, or just straight up integrate by using $u = \cos (4x)$. Can someone help? Thanks in advance.