Definition:Inverse Hyperbolic Sine/Real/Definition 2

Definition
The principal branch of the real inverse hyperbolic sine function is defined as:
 * $\operatorname{arcsinh} \left({x}\right) := \ln \left({x + \sqrt{x^2 + 1} }\right)$

Also see

 * Derivation of Real Arcsine from Inverse Hyperbolic Sine Multifunction