Primitive of x over x squared minus a squared

Theorem

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

for $x^2 > a^2$.

Proof
Let:

Also see

 * Primitive of x over a squared minus x squared for $x^2 < a^2$.