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

Theorem

 * $\displaystyle \int \frac {\mathrm d x} {x^3 \left({\sqrt {x^2 - a^2} }\right)^3} = \frac 1 {2 a^2 x^2 \sqrt {x^2 - a^2} } - \frac 3 {2 a^4 \sqrt {x^2 - a^2} } + \frac 3 {2 a^5} \operatorname{arcsec} \left\vert{\frac x a}\right\vert + C$

Also see

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