Primitive of Reciprocal of x squared minus a squared/Logarithm Form 2/Proof 1

Proof
Let $x > a$.

Then:

Let $x < -a$.

Let $z = -x$.

Then:
 * $\d x = -\d z$

and we then have:

The result follows.

Also see

 * Primitive of $\dfrac 1 {a^2 - x^2}$: Logarithm Form: Proof 1