Primitive of Root of x squared minus a squared/Inverse Hyperbolic Cosine Form

Theorem

 * $\ds \int \sqrt {x^2 - a^2} \rd x = \frac {x \sqrt {x^2 - a^2} } 2 - \frac {a^2} 2 \cosh^{-1} \frac x a + C$

Proof
Let:

Also:

and:

Thus: