I have no idea how to do a problem like this. I know I can't do $u$ substitution because $\tan$ or $\sec$ doesn't cancel out both the $\tan$ and the $\cos$.
$$\int \cos^2 (x) \tan^3 (x) dx$$
$$\int \cos^2 (x) (\sec^2 (x) - 1) \tan (x) dx$$
From here I can't really do anything because no u will cancel out everything.