Primitive of x by Root of x squared minus a squared

Theorem

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

for $\size x \ge a$.

Proof
Let:

Also see

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