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

Theorem

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

for $x^2 < a^2$.

Also see

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