Primitive of x over Power of a squared minus x squared

Theorem

 * $\displaystyle \int \frac {x \ \mathrm d x} {\left({a^2 - x^2}\right)^n} = \frac 1 {2 \left({n - 1}\right) \left({a^2 - x^2}\right)^{n - 1} }$

for $x^2 < a^2$.

Proof
Let:

Also see

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