Primitive of Root of x squared minus a squared over x squared

Theorem

 * $\displaystyle \int \frac {\sqrt {x^2 - a^2} } {x^2} \rd x = \frac {-\sqrt {x^2 - a^2} } x + \ln \size {x + \sqrt {x^2 - a^2} } + C$

for $\size x \ge a$.

Proof
Let:

Also see

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