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

Theorem

 * $\ds \int \frac {\d x} {x^2 \paren {x^2 - a^2}^2} = \frac {-1} {a^4 x} - \frac x {2 a^4 \paren {x^2 - a^2} } + \frac 3 {4 a^5} \map \ln {\frac {x + a} {x - a} } + C$

for $x^2 > a^2$.

Also see

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