Primitive of Reciprocal of a squared minus x squared squared

Theorem

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

for $x^2 < a^2$.

Also see

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