Primitive of x squared over a squared minus x squared squared

Theorem

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

for $x^2 < a^2$.

Also see

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