Answer
$\frac{1}{2}\ln|1+e^{2x}|+C$
Work Step by Step
$\int \frac{e^{2x}}{1+e^{2x}}dx$
let $1+e^{2x}=u$
$2e^{2x}=dx=du$
$\int \frac{e^{2x}}{1+e^{2x}}dx$
$=\frac{1}{2} \int \frac{1}{u}du$
$=\frac{1}{2}\ln|u|+C$
$=\frac{1}{2}\ln|1+e^{2x}|+C$
Calculus 10th Edition
by Larson, Ron; Edwards, Bruce H.
Published by
Brooks Cole
ISBN 10:
1-28505-709-0
ISBN 13:
978-1-28505-709-5
Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.4 Exercises - Page 354: 100
Update this answer!
You can help us out by revising, improving and updating this answer.
Update this answerAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.
