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

Theorem
For $a > 0$ and $0 < \size x < a$:
 * $\ds \int \frac {\d x} {x \sqrt {a^2 - x^2} } = -\frac 1 a \map \ln {\frac {a + \sqrt {a^2 - x^2} } {\size x} } + C$

Also see

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