Find the Antiderivative sec(x)^2

Problem

(∫_^)(sec^2(x)*d(x))

Solution

1. Identify the standard integral form for the given trigonometric function.

2. Recall the basic differentiation rule where the derivative of tan(x) is sec^2(x)

3. Apply the fundamental theorem of calculus which states that if d(tan(x))/d(x)=sec^2(x) then the antiderivative of sec^2(x) is tan(x)

4. 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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