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.
Best Answer
$$\int \cos^2 x \tan^3 x\ dx = \int \frac{\sin^3 x}{\cos x}\ dx = \int \frac{1-\cos^2 x}{\cos x}\sin x\ dx$$
$u=\cos x$ substitution