You are here:

Calculus/Calculus 2 indefinite integral

Advertisement


Question
I really need help in evaluating this integral

Evaluate the integral
integrate of (dx)/((e^x)+e^(2x))

Answer
change of variables

let u = e^-x

du/dx = -e^-x

dx = -e^x du

dx = -u^-1 du

S(dx)/((e^x)+e^(2x)) =

S (-u^-1)du / (u^-1 + u^-2) =

-S du/(1+u^-1)  =

-S udu/(u+1) =

-S (1 - 1/(u+1)) du =

S (1/(u+1) - 1) du =

ln(u+1) - u


since u = e^-x , we now have


S(dx)/((e^x)+e^(2x)) = ln(e^-x + 1) - e^-x

The answer is ln(e^-x + 1) - e^-x  

Calculus

All Answers


Answers by Expert:


Ask Experts

Volunteer


Socrates

Expertise

I can answer questions from the standard four semester Calculus sequence. I am not prepared for questions on Tensor Calculus. Everything else is welcome. Derivatives, partial derivatives, ordinary differential equations, single and multiple integrals, change of variable, vector integration (Green`s Theorem, Stokes, and Gauss) and applications.

Experience

Ph.D. in Mathematics and many years teaching Calculus at state universities.

Education/Credentials
B.S. , M.S. , Ph.D.

©2016 About.com. All rights reserved.