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

Theorem

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

Proof
Let:

Also see

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