Primitive of x cubed over x squared plus a squared

Theorem

 * $\displaystyle \int \frac {x^3 \ \mathrm d x} {x^2 + a^2} = \frac {x^2} 2 - \frac {a^2} 2 \ln \left ({x^2 + a^2}\right) + C$

where $a$ is a non-zero constant.