Primitive of x over a squared minus x squared squared

Theorem

 * $\ds \int \frac {x \rd x} {\paren {a^2 - x^2}^2} = \frac 1 {2 \paren {a^2 - x^2} } + C$

for $x^2 < a^2$.

Proof
Let:

Also see

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