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

Theorem

 * $\ds \int \frac {\d x} {x^2 \paren {x^2 - a^2} } = \frac 1 {a^2 x} + \frac 1 {2 a^3} \map \ln {\frac {x - a} {x + a} } + C$

for $x^2 > a^2$.

Also see

 * Primitive of $\dfrac 1 {x^2 \paren {a^2 - x^2} }$