Primitive of Reciprocal of x squared by x squared minus a squared

Theorem

 * $\displaystyle \int \frac {\mathrm d x} {x^2 \left({x^2 - a^2}\right)} = \frac 1 {a^2 x} + \frac 1 {2 a^3} \ln \left({\frac {x - a} {x + a} }\right) + C$

for $x^2 > a^2$.

Also see

 * Primitive of $\dfrac 1 {x^2 \left({a^2 - x^2}\right)}$