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

Theorem

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

for $\size x > a$.

Proof
Let:

Also see

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