Definition:Real Inverse Hyperbolic Sine/Also known as

Real Inverse Hyperbolic Sine: Also known as
The real inverse hyperbolic sine is also known as the (real) area hyperbolic sine, as it can be used, among other things, for evaluating areas of regions bounded by hyperbolas.

Note that as the real hyperbolic sine $\sinh$ is injective, its inverse is properly a function on its domain.

Hence there is no need to make a separate distinction between branches in the same way as for real inverse hyperbolic cosine and real inverse hyperbolic secant.

Some sources refer to it as hyperbolic arcsine, but this is strictly a misnomer, as there is nothing arc related about an inverse hyperbolic sine.