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

Theorem

 * $\ds \int \frac {\d x} {x^3 \paren {a^2 - x^2}^2} = \frac {-1} {2 a^4 x^2} + \frac 1 {2 a^4 \paren {a^2 - x^2} } + \frac 1 {a^6} \map \ln {\frac {x^2} {a^2 - x^2} } + C$

for $x^2 < a^2$.

Also see

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