Question

Step by step solution help me pls

Answer 1

Step-by-step explanation:

Recall that

$1 + \tan^2 x = \sec^2 x$

and

$\dfrac{d}{dx}(\tan x) = \sec^2 x$

so that

$\displaystyle \int \tan^2 x = \int (\sec^2 x - 1)dx$

$\:\:\:\:\:\:\:\:\:=\int \sec^2 xdx - \int dx$

$\:\:\:\:\:\:\:\:\:=\tan x - x + C$

where C is the constant of integration.