Evaluate ∫ sec x ⋅ tan x ⋅ d x

To evaluate the integral ∫ sec x ⋅ tan x ⋅ dx, we can use a straightforward approach based on the properties of derivatives.

Recognizing the Derivative

Recall that the derivative of sec x is sec x ⋅ tan x. This means that the integral of sec x ⋅ tan x is simply sec x itself.

Integration Steps

• Identify the integral: ∫ sec x ⋅ tan x ⋅ dx
• Recognize that the integral is the derivative of sec x.
• Thus, ∫ sec x ⋅ tan x ⋅ dx = sec x + C, where C is the constant of integration.

Final Result

The evaluated integral is: