Primitive of Power of x over Power of x squared minus a squared

Theorem

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

for $x^2 > a^2$.

Also see

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