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

Theorem

 * $\ds \int \frac {\sqrt {a^2 - x^2} } {x^2} \rd x = \frac {-\sqrt {a^2 - x^2} } x - \arcsin \frac x a + C$

Proof
Let:

Also see

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