Primitive of Root of a squared minus x squared over x

Theorem

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

Proof
Let:

Also see

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