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

Theorem

 * $\displaystyle \int x \left({\sqrt {a^2 - x^2} }\right)^3 \ \mathrm d x = \frac {-\left({\sqrt {a^2 - x^2} }\right)^5} 5 + C$

Proof
Let:

Also see

 * Primitive of $x \left({\sqrt {x^2 + a^2} }\right)^3$
 * Primitive of $x \left({\sqrt {x^2 - a^2} }\right)^3$