How do you find the antiderivative of e^x(1-(e^-x)sec^2x) dx?

1 Answer
Nov 15, 2017

int e^x(1-e^(-x)sec^2x) dx = e^x-tanx+C

Explanation:

Simplify the expression:

e^x(1-e^(-x)sec^2x) = e^x -sec^2x

then using the linearity of the integral:

int e^x(1-e^(-x)sec^2x) dx = int e^xdx -int sec^2xdx

Both terms are standard integrals:

int e^xdx = e^x+c_1

int sec^2xdx = tanx +c_2

and then:

int e^x(1-e^(-x)sec^2x) dx = e^x-tanx+C