Inverse hyperbolic sine
= Inverse hyperbolic sine
{title2=$\operatorname{arsinh}x=\ln(x+\sqrt{1+x^2})$}
The real inverse of the <hyperbolic sine> is defined on all real numbers and has <derivative> $1/\sqrt{1+x^2}$. It appears in <arc length> and in <integrals> involving square roots of sums of squares, where a <hyperbolic substitution> can simplify the expression.