$\int tan x(\sec x - \tan x) dx =$
Answer & explanation
Correct answer: option 1
$\int tan x(\sec x - \tan x) dx$
$\int \sec x \tan x dx - \int \tan^2 x dx$
as 1 + tan2x = sec2x
so sec2x - 1 = tan2x
= $\sec x - \int (\sec^2x - 1) dx$
so sec x - tan x + x - C