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

Theorem

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