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

Theorem

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

for $x^2 < a^2$.

Also see

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