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

Theorem

 * $\displaystyle \int \frac {x \ \mathrm d x} {\left({\sqrt {x^2 - a^2} }\right)^3} = \frac {-1} {\sqrt {x^2 - a^2} } + C$

Proof
Let:

Also see

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