Primitive of Reciprocal of x by Root of x squared minus a squared/Arcsecant Form

Theorem

 * $\displaystyle \int \frac {\mathrm d x} {x \sqrt {x^2 - a^2} } = \frac 1 a \operatorname{arcsec} \left\vert{\frac x a}\right\vert + C$

Proof
Let:

Also see

 * Primitive of Reciprocal of $x \sqrt{x^2 + a^2}$
 * Primitive of Reciprocal of $x \sqrt{a^2 - x^2}$