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

Theorem

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

for $x^2 < a^2$.

Also see

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