How do you integrate e^(tanx) * sec^2(x) dx?

1 Answer
Jul 12, 2016

int e^(tan x) sec^(2)(x) dx = e^(tan x) + C

Explanation:

We can use a simple u-substitution to evaluate this integral.

Given int e^(tan x) sec^(2)(x) dx

Note that sec^2(x) is the derivative of tan x, thus we can use

u = tan x -> du = sec^(2)(x) dx

Since

int e^(u) du = e^(u) + C

We only have to substitute u back into our result to get

int e^(tan x) sec^(2)(x) dx = e^(tan x) + C