argcosh(x)

Input

cosh^(-1)(x)

Plot

Plot
Plot

Alternate form

log(x + sqrt(x - 1) sqrt(x + 1))

Root

x = 1

Properties as a real function

Domain

{x element R : x>=1}

Range

{y element R : y>=0} (all non-negative real numbers)

Injectivity

injective (one-to-one)

Series expansion at x=-1

(-1)^ceiling(arg(x - 1)/(2 π)) (-i π + i sqrt(2) sqrt(x + 1) + (i (x + 1)^(3/2))/(6 sqrt(2)) + (3 i (x + 1)^(5/2))/(80 sqrt(2)) + (5 i (x + 1)^(7/2))/(448 sqrt(2)) + (35 i (x + 1)^(9/2))/(9216 sqrt(2)) + O((x + 1)^(11/2)))
Big‐O notation »

Derivative

d/dx(cosh^(-1)(x)) = 1/(sqrt(x - 1) sqrt(x + 1))

Indefinite integral

integral cosh^(-1)(x) dx = x cosh^(-1)(x) - sqrt(x - 1) sqrt(x + 1) + constant

Global minimum

min{cosh^(-1)(x)} = 0 at x = 1
POWERED BY THE WOLFRAM LANGUAGE