Integrate $ \cos^3x \sin^2 x \ \text{d}x$ $$\int \cos^3x \sin^2 x \ \text{d}x$$
I've simplified it to $\int \cos^3x-\cos^5x \,\mathrm{d}x$ using Pythagorean identities. It this the right way to do it? How do I integrate it from here?

$$
\int \cos^2 x \sin^2 x\ \underbrace{\Big(\cos x\,dx\Big)}_{\text{HINT}} = \int(1-\sin^2 x)\sin^2 x\ \underbrace{\Big(\cos x\,dx\Big)}_{\text{HINT}}
$$
