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

Problem

(∫_^)(sec2(x)*d(x))

Solution

1. Identify the integrand as the square of the secant function, sec2(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)=sec2(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

(∫_^)(sec2(x)*d(x))=tan(x)+C

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