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

Theorem

 * $\displaystyle \int \frac {\d x} {x \paren {x^2 - a^2}^2} = \frac {-1} {2 a^2 \left({x^2 - a^2}\right)} + \frac 1 {2 a^4} \ln \left({\frac {x^2} {x^2 - a^2} }\right) + C$

for $x^2 > a^2$.

Also see

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