Evaluate $\int x\sqrt{(a^2 - x^2)}dx$ I need to find $$\int x\sqrt{(a^2 - x^2)}dx$$
I tried putting $x=a cos(t)$ but I ended up getting a very complicated expression, so any tips?

$-\frac{1}{3}(a^2-x^2)^\frac{3}{2}$ is one of the origional function because $\frac{d}{dx}\bigg(-\frac{1}{3}(a^2-x^2)^\frac{3}{2}\bigg)=x\sqrt{a^2-x^2}.$
Why did I come up with it because $\int x\sqrt{a^2-x^2}dx=\int\sqrt{a^2-x^2}d(x^2)=-\frac{1}{3}(a^2-x^2)^\frac{3}{2}$+C.
