Primitive of Reciprocal of x squared minus a squared

Theorem

 * $\displaystyle \int \frac {\mathrm d x} {x^2 - a^2} = - \frac 1 a \coth^{-1} {\frac x a} + C$

where $x^2 > a^2$.

Proof
Let:

Also see

 * Primitive of Reciprocal of Constant Squared minus Variable Squared for the case $x^2 < a^2$.