Primitive of x squared over a squared minus x squared

Theorem

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

for $x^2 < a^2$.

Proof
Let:

{{qed}

Also see

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