Primitive of x cubed over x squared minus a squared

Theorem

 * $\ds \int \frac {x^3 \rd x} {x^2 - a^2} = \frac {x^2} 2 + \frac {a^2} 2 \map \ln {x^2 - a^2} + C$

for $x^2 > a^2$.

Proof
Let:

Also see

 * Primitive of $\dfrac {x^3} {a^2 - x^2}$