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

Theorem

 * $\displaystyle \int \frac {\mathrm d x} {x^2 \left({a^2 - x^2}\right)^2} = \frac {-1} {a^4 x} + \frac x {2 a^4 \left({a^2 - x^2}\right)} + \frac 3 {4 a^5} \ln \left({\frac {a + x} {a - x} }\right) + C$

for $x^2 < a^2$.

Also see

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