Primitive of x over x squared minus a squared squared

Theorem

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

for $x^2 > a^2$.

Proof
Let: