How to solve the indefinite integral $ \int x^2 \sqrt{4 - x^2} \, dx$?

Question

I have tried really hard to do this one but I can not find the right substitution to solve.

$$ \int x^2 \sqrt{4 - x^2} \, dx$$

Answer 1

With $x=2\sin(t)$,

$$\int x^2\sqrt{4-x^2}dx=16\int\sin^2(t)\cos^2(t)dt=4\int\sin^2(2t)dt=2\int(1-\cos(4t))dt.$$