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

Theorem

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

Proof
Let:

Also see

 * Primitive of Reciprocal of x by Root of x squared plus a squared
 * Primitive of Reciprocal of x by Root of a squared minus x squared