Primitive of x squared over x squared minus a squared/Inverse Hyperbolic Cotangent Form

Theorem

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

for $x^2 > a^2$.

Proof
Let: