Find the Integral sec(x)tan(x)

Problem

(∫_^)(sec(x)*tan(x)*d(x))

Solution

1. Identify the integrand as a standard trigonometric derivative.

2. Recall the differentiation rule for the secant function, which states that the derivative of sec(x) with respect to x is sec(x)*tan(x)

3. Apply the fundamental theorem of calculus to determine that the antiderivative of sec(x)*tan(x) is sec(x)

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

Final Answer

(∫_^)(sec(x)*tan(x)*d(x))=sec(x)+C

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