`int e^(tan(x)) sec^2(x) dx` Evaluate the indefinite integral.

You need to use the following substitution  `tan x = t` , such that:

`tan x = t=>sec^2 x dx = dt `

`int e^(tan x)*sec^2 x dx = int e^t dt = e^t + c`

Replacing back `tan x` for t yields:

`int e^(tan x)*sec^2 x dx = e^(tan x) + c`

Hence, evaluating the indefinite integral, yields `int e^(tan x)*sec^2 x dx = e^(tan x) + c.`