Compute ∫ sec^2(x) dx.

To find the integral of sec²(x) with respect to x, we can utilize a fundamental result from calculus. The integral of sec²(x) is directly related to the derivative of a well-known trigonometric function.

The derivative of the tangent function, tan(x), is sec²(x). This relationship indicates that when we integrate sec²(x), we are essentially reversing the differentiation process. Therefore, the integral can be expressed as:

∫ sec²(x) dx = tan(x) + C

Here, C represents the constant of integration, which is included because the integral of a function is not unique; it can differ by a constant.

This matches perfectly with the answer option that states tan(x) + C, confirming its correctness. Understanding this fundamental relationship between differentiation and integration of trigonometric functions is crucial for solving such integral problems effectively.