Primitive of x squared over x squared minus a squared

Theorem

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

for $x^2 > a^2$.

Proof
Let: