Primitive of x cubed over x squared minus a squared squared

Theorem

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

for $x^2 > a^2$.