What is the integral of the secant function?

The integral of the secant function is the natural logarithm of the absolute value of the secant of x plus the tangent of x, plus a constant. Expressed in mathematical notation, it reads as the integral of sec x dx = ln |sec x + tan x| + C.

The integral of the secant function can be solved by using the integration technique called substitution. The function is rewritten as the integral of the secant of x, times the secant of x plus the tangent of x, over the secant of x plus the tangent of x. Next, u is used to express the secant of x plus the tangent of x, and du is expressed as (sec x tan x + sec2 x) dx.