Question

Step by step solution help me pls

Answer 1

Explanation:

Recall that

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

and

`(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.