Primitive of Root of x squared minus a squared over x

Theorem

 * $\displaystyle \int \frac {\sqrt {x^2 - a^2} } x \rd x = \sqrt {x^2 - a^2} - \frac 1 {2 a} \arcsec \size {\frac x a} + C$

for $\size x \ge a$.

Proof
Let:

Also see

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