Find the Antiderivative sec(x)^2

Problem

(∫_^)(sec2(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 sec2(x)

3. Apply the fundamental theorem of calculus which states that if d(tan(x))/d(x)=sec2(x) then the antiderivative of sec2(x) is tan(x)

4. 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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