Primitive of Reciprocal of x by Root of a squared minus x squared/Inverse Hyperbolic Secant Form

Theorem

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

Proof
Let:

Also see

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