Primitive of x by Root of a squared minus x squared

Theorem

 * $\displaystyle \int x \sqrt {a^2 - x^2} \ \mathrm d x = \frac {-\left({\sqrt {a^2 - x^2} }\right)^3} 3 + C$

Proof
Let:

Also see

 * Primitive of $x \sqrt{x^2 + a^2}$
 * Primitive of $x \sqrt{x^2 - a^2}$