Primitive of Root of x squared plus a squared over x squared

Theorem

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

Proof
Let:

Also see

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