Calculus: Early Transcendentals 8th Edition

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 507: 14


$$\int ln(1+x^{2})dx=x\,ln(1+x^{2})-2x+2arctan\,x+C$$

Work Step by Step

$$\int ln(1+x^{2})dx=x\,ln(1+x^{2})-\int \frac{2x^{2}}{1+x^{2}}dx$$ $$=x\,ln(1+x^{2})-\int (2-\frac{2}{1+x^{2}})dx$$ $$=x\,ln(1+x^{2})-2x+2arctan\,x+C$$
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