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Inverse hyperbolic secant calculator

This tool evaluates the inverse hyperbolic secant of a number: arsech(x). Enter the argument x below.

x =
Result:
arsech(x) =

Definitions

General

The inverse hyperbolic secant function, in modern notation written as arsech(x) or arcsech(x) or sech^-1x, gives the value t (hyperbolic angle), so that:

The inverse hyperbolic secant function accepts arguments in real interval (0,1], because for all real x. Since the hyperbolic secant is defined through the natural exponential function , its inverse can be defined through the natural logarithm function, using the following formula, for real x, with 0<x≤1:

Properties

The derivative of the inverse hyperbolic secant function is:

The integral of the inverse hyperbolic secant function is given by: