What is integral of sec x?

The integral of sec x is ln|sec(x) + tan(x)| + C, where C is the constant of integration.

∫ sec(x) dx = ln ∣sec(x) + tan(x)∣ + C

The integral of sec(x) with respect to x can be found by recognizing its antiderivative. The antiderivative of sec(x) is ln|sec(x) + tan(x)| + C, where ln represents the natural logarithm, sec(x) is the secant function, tan(x) is the tangent function, and C is the constant of integration.

The process involves finding a function whose derivative is sec(x). The derivative of ln|sec(x) + tan(x)| + C with respect to x is sec(x), confirming that it is indeed the antiderivative of sec(x).

The absolute value ensures that the expression remains valid for all x values, and the constant of integration C accounts for the family of functions that differ by a constant. Thus, ln|sec(x) + tan(x)| + C represents the integral of sec(x) with respect to x.