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?

Let $y=a^2-x^2$ then $dy=-2xdx$ so 
$$-\frac{1}{2}\int  \sqrt{a^2-x^2} (-2x)dx=-\frac{1}{2}\int  \sqrt{y} dy
=-\frac{1}{3}y^\frac{3}{2}= =-\frac{1}{3}(a^2-x^2)^\frac{3}{2}$$
