Find the Integral sec(x)^2

Problem

(∫_^)(sec2(x)*d(x))

Solution

1. Identify the integrand as a standard trigonometric derivative.

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 rule d(tan(x))/d(x)=sec2(x) which implies that 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

Want more problems? Check here!