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

Theorem

 * $\ds \int x \paren {\sqrt {a^2 - x^2} }^3 \rd x = \frac {-\paren {\sqrt {a^2 - x^2} }^5} 5 + C$

Proof
Let:

Also see

 * Primitive of $x \paren {\sqrt {x^2 + a^2} }^3$
 * Primitive of $x \paren {\sqrt {x^2 - a^2} }^3$