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

Theorem

 * $\ds \int \frac {\d x} {x^m \paren {a^2 - x^2}^n} = \frac 1 {a^2} \int \frac {\d x} {x^m \paren {a^2 - x^2}^{n - 1} } + \frac 1 {a^2} \int \frac {\d x} {x^{m - 2} \paren {a^2 - x^2}^n}$

for $x^2 < a^2$.

Also see

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