Primitive of x cubed over a squared minus x squared squared

Theorem

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

for $x^2 < a^2$.

Also see

 * Primitive of $\dfrac {x^3} {\left({x^2 - a^2}\right)^2}$