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

Theorem

 * $\ds \int \frac {\d x} {x^3 \paren {\sqrt {x^2 + a^2} }^3} = \frac {-1} {2 a^2 x^2 \sqrt {x^2 + a^2} } - \frac 3 {2 a^4 \sqrt {x^2 + a^2} } + \frac 3 {2 a^5} \map \ln {\frac {a + \sqrt {x^2 + a^2} } x} + C$

Also see

 * Primitive of $\dfrac 1 {x^3 \paren {\sqrt {x^2 - a^2} }^3}$
 * Primitive of $\dfrac 1 {x^3 \paren {\sqrt {a^2 - x^2} }^3}$