Answer
$$\int \frac{1}{1+e^{x}}dx=x-ln(e^{x}+1)+C$$
Work Step by Step
$$\int \frac{1}{1+e^{x}}dx=\int \frac{e^{-x}}{e^{-x}+1}dx$$
$$=-\int \frac{1}{e^{-x}+1}d(e^{-x}+1)=-ln(e^{-x}+1)+C$$
$$=-ln(\frac{e^{x}+1}{e^{x}})+C=x-ln(e^{x}+1)+C$$
Calculus: Early Transcendentals 8th Edition
by Stewart, James
Published by
Cengage Learning
ISBN 10:
1285741552
ISBN 13:
978-1-28574-155-0
Chapter 7 - Section 7.5 - Strategy for Integration - 7.5 Exercises - Page 508: 27
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.
