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

Theorem

 * $\displaystyle \int \frac {\mathrm d x} {x \sqrt {x^2 + a^2} } = -\frac 1 a \ln \left({\frac {a + \sqrt {x^2 + a^2} } x}\right) + C$

Also see

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