Definition:Inverse Hyperbolic Sine/Real/Definition 2

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

where:
 * $\sqrt{x^2 + 1}$ denotes the positive square root of $x^2 + 1$
 * $\ln$ denotes the natural logarithm of a (strictly) positive real number.

Also see

 * Derivation of Real Hyperbolic Arcsine from Inverse Hyperbolic Sine Multifunction