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

Theorem

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

where $\size x > a$.

Proof
Let $\size x > a$.

Let:

Also see

 * Primitive of $\dfrac 1 {a^2 - x^2}$: $\tanh^{-1}$ form for the case $a^2 > x^2$