Integral of the Secant Function

In calculus, the integral of the secant function is a standard result that can be derived by several different methods and expressed in a number of equivalent forms related by trigonometric identities. The result is useful for evaluating a range of other trigonometric integrals, including the integral of the secant cubed function, which arises frequently in applications. The definite integral of the secant function starting from zero is also connected to the inverse Gudermannian function, and numerically stable alternative expressions using the inverse hyperbolic sine are used for certain ranges of the argument to avoid loss of precision in computation.