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

Theorem
For $x \in \R_{\ne 0}$:


 * $\ds \int \frac {\d x} {x \sqrt {x^2 + a^2} } = -\frac 1 a \map \ln {\frac {a + \sqrt {x^2 + a^2} } {\size x} } + C$

Also see

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