Primitive of x over a squared minus x squared

Theorem

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

for $x^2 < a^2$.

Proof
Let:

Also see

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