Primitive of x by Root of a squared minus x squared

Theorem

 * $\ds \int x \sqrt {a^2 - x^2} \rd x = \frac {-\paren {\sqrt {a^2 - x^2} }^3} 3 + C$

Proof
Let:

Also see

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