Question

$\int[1+2 tan x (tan x + sec x)]^{\frac{1}{2}}dx$​

Answer 1

I = $\int[1+2 tan x (tan x + sec x)]^{\frac{1}{2}}dx$

$\int(sec x + tan x)dx$

log (sec x + tan x ) + log sec x + c

log(sec² x + sec x tan x ) + c

Answer 2

$\huge\red{Answer}$

Refer to the attachment

HOPE IT HELPS YOU !!