Primitive of x cubed over x squared minus a squared

Theorem

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

for $x^2 > a^2$.

Proof
Let: