"What is the integral of secx?" was answered by students like you

Paul Gallegos

Answered question

2023-03-13

What is the integral of

s e c (x)

svikaoeol

Beginner2023-03-14Added 7 answers

Find integration of

\sec (x)

.
To rephrase the integral:

\int \sec x d x = \int \sec x (\frac{\sec x + \tan x}{\sec x + \tan x}) d x \int \sec x d x = \int \frac{\sec^{2} x + \sec x \tan x}{\sec x + \tan x} d x . . . (1)

Take, \sec x + \tan x = t \Rightarrow (\sec x \tan x + \sec^{2} x) d x = d t

.
Add the aforementioned values to the equation

(1)

to find :

\int \sec x d x = \int \frac{d t}{t} \int \sec x d x = \ln | t | + C (∵ \int \frac{d t}{t} = \ln | t |) \int s e c x d x = \ln | (s e c x + \tan x) | + C (Put t = \sec x + \tan x)

Thus, the required integral is

\int s e c x d x = \ln | (s e c x + \tan x) | + C

where

C

is a constant of integration .

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