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

Problem

(∫_^)(sec2(t)*d(t))

Solution

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

2. Recall the basic differentiation rules for trigonometric functions, specifically that the derivative of the tangent function is the square of the secant function.

3. Apply the fundamental rule of integration, which states that d(tan(t))/d(t)=sec2(t)

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

Final Answer

(∫_^)(sec2(t)*d(t))=tan(t)+C

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