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

Theorem

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