Primitive of Inverse Hyperbolic Cosine Function

Theorem

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

Proof
From Primitive of $\arcosh \dfrac x a$:
 * $\ds \int \arcosh \frac x a \rd x = x \arcosh \dfrac x a - \sqrt {x^2 - a^2} + C$

The result follows by setting $a = 1$.

Also see

 * Primitive of $\arsinh x$
 * Primitive of $\artanh x$
 * Primitive of $\arcoth x$