Hyperbolic inverse sine

Writing functions:

arcsinh(x)

Returns the inverse of that value, which returns the hyperbolic sine, so sinh(arcsinh(x))=x.

The hyperbolic arcsine is a mathematical function that is the inverse of the hyperbolic sine. It is denoted as arcsin(x) and is defined as the natural logarithm of the sum of the argument value and the square root of its square: arcsinh(x) = ln(x + (x^2 + 1)^(1/2)).

The hyperbolic arcsine is used in various fields of mathematics, physics and engineering. It is used, for example, in solving differential equations, in approximating complex functions, and in probability theory.

One of the main properties of this function is its monotonous growth over the entire domain of definition, which makes it convenient in analyzing functions and building mathematical models.

Thus, the hyperbolic arcsine is an important and useful mathematical function that finds application in many fields of science and technology.