Find the Antiderivative f(x)=sec(x)^2

Problem

(∫_^)(sec2(x)*d(x))

Solution

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

2. Recall the basic differentiation rules for trigonometric functions.

3. Recognize that the derivative of the tangent function is the square of the secant function: d(tan(x))/d(x)=sec2(x)

4. Apply the definition of the antiderivative (the indefinite integral), which is the inverse operation of differentiation.

5. Add the constant of integration C to represent the family of all possible antiderivatives.

Final Answer

(∫_^)(sec2(x)*d(x))=tan(x)+C

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