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

Theorem

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

for $x^2 > a^2$.

Also see

 * Primitive of $\dfrac 1 {x^3 \left({a^2 - x^2}\right)}$