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

Theorem

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

for $x^2 < a^2$.

Also see

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