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

Theorem

 * $\displaystyle \int \frac {\d x} {x^2 \paren {\sqrt {x^2 + a^2} }^3} = \frac {-\sqrt {x^2 + a^2} } {a^4 x} - \frac x {a^4 \sqrt {x^2 + a^2} } + C$

Also see

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