What is the integral of sec (x)?

Solution:

To integrate this we will multiply and divide sec x with sec x + tan x / sec x + tan x

On multiplying and dividing sec x by sec x + tan x, we get

⇒ ∫ sec(x) × (sec x + tan x) / (sec x + tan x) dx 

⇒ ∫ sec² x + sec x.tan x / (sec x + tan x) dx

Let u = (sec x + tan x)

On differentiating u, we get

du = (sec x.tan x + sec² x) dx

On substituting the values of u and du in the integral, we get

⇒ ∫ du / u

⇒ ln |u| + c

Substitute the value of u = (sec x + tan x), we get

∫ sec x dx = ln |sec x + tan x| + c

Thus, the integral of sec (x) is In |sec x + tan x| + c

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What is the integral of sec (x)?

Summary:

The integral of sec (x) is In |secx + tanx| + c