Evaluate the Integral integral of sec(x)^2 with respect to x

Problem

(∫_^)(sec^2(x)*d(x))

Solution

1. Identify the integrand as the square of the secant function, sec^2(x)

2. Recall the fundamental rules of differentiation for trigonometric functions.

3. Recognize that the derivative of the tangent function is the square of the secant function, expressed as d(tan(x))/d(x)=sec^2(x)

4. Apply the fundamental theorem of calculus, which states that the integral of a derivative is the original function plus a constant of integration.

Final Answer

(∫_^)(sec^2(x)*d(x))=tan(x)+C

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