Primitive of x squared by Root of a squared minus x squared

Theorem

 * $\ds \int x^2 \sqrt {a^2 - x^2} \rd x = \frac {-x \paren {\sqrt {a^2 - x^2} }^3} 4 + \frac {a^2 x \sqrt {a^2 - x^2} } 8 + \frac {a^4} 8 \sinh^{-1} \frac x a + C$

Also see

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