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

Problem

(∫_^)(sec^2(x)*d(x))

Solution

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

(∫_^)(sec^2(x)*d(x))=tan(x)+C

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