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

Theorem

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

Proof
Let:

Also see

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