$$\int \sin^2 x \cos^3 x dx$$
$$\int (1-\cos^2 x) \cos^3 x dx$$
I know there is a rule in my book (with little explanation) that tells me when I had an odd and an even degree on two trig functions I should split the odd and convert it to an identity but this way seems easier, and I can't get an answer either way.
$$\int \cos^3 dx - \int \cos^ 5 x dx$$
I am not sure where to go from here, I don't know how to get the integral of $\cos^3 x$