I'd love to see various ways to solve this integral, please.

$\displaystyle \int_0^{2\pi} \cos^2(mx)\rm{d}x \qquad m\in \mathbb N$

I have thought about using that

$\displaystyle \cos^2(x) = \frac{1+\cos(2x)}{2}$

as I know that $\displaystyle m\in \mathbb N$, but I'm not sure if it is OK. However, I hope someone feels like showing me various ways of doing it.

In advance, thank you for your time and help.