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

Theorem

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

for $x^2 < a^2$.

Also see

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