\int \sec(x) dx Evaluate the integral above​

Question

`\int \sec(x) dx`
Evaluate the integral above​

Answer 1

`= \ln( | \sec(x) + \tan(x) | ) + C`

Explanation:

`\int \sec(x) dx`

multiply and divide by sec x + tan x

`= \int ( \sec(x) ( \sec(x) + \tan(x) ) )/( \sec(x) + \tan(x) ) dx`

let u = sec x + tan x

du = (sec x)(sec x + tan x) dx

`= \int (1)/(u) du`

`= \ln( |u| ) + C`

`= \boxed{\color{green} \ln( }`

Answer 2

`&#128075` Hello ! ☺️

Explanation:

∫sec(x)dx =

∫
`(sec(x).(secx + tanx))/(secx + tanx)dx`

∫
`\frac{sec {}^(2) (x) + secxtanx}{secx + tanx}dx`

u = secx + tanx

`du = secx tanx + sec {}^(2)x \: dx`

`∫(1)/(u)du`

∫sec(x)dx= ln |u|

`\boxed{\color{gold} + C}`

`<marquee direction=`