Primitive of x over Power of x squared minus a squared

Theorem

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

for $x^2 > a^2$.

Proof
Let: