What is ∫ sec^2(x) dx equal to?

The integral of sec²(x) dx is directly related to the derivative of the tangent function. The derivative of tan(x) is sec²(x), which means that when integrating sec²(x), we essentially reverse this operation. Thus, the integral ∫ sec²(x) dx results in tan(x) plus a constant of integration, C.

This relationship arises from the fundamental connection between differentiation and integration in calculus. Since sec²(x) is the derivative of tan(x), integrating sec²(x) naturally leads to tan(x) as the result.

Other choices provided—cot(x), sin(x), and csc(x)—do not relate to the function sec²(x) in the context of integration. Therefore, they would not yield correct results when integrated, which further underscores why tan(x) + C is the correct outcome for this integral. This clear relationship between the functions through their derivatives is central to solving integration problems involving trigonometric functions.