How to find anti-derivative of $f(x):=\sin(x)\cos(nx)$.

Question

How to find anti-derivative of $f(x):=\sin(x)\cos(nx)$.

I know the sum-formulas for $\sin(x),\cos(x)$ which I could put to use if $x = nx$, but this is not the case here where $n \in \mathbb N$.

Any suggestions ?

Answer 1

Hint: Use $2 \cos x \sin y = \sin(x + y) - \sin(x - y)$.