Answer
$$\int ln(1+x^{2})dx=x\,ln(1+x^{2})-2x+2arctan\,x+C$$
Work Step by Step
$$\int ln(1+x^{2})dx=x\,ln(1+x^{2})-\int \frac{2x^{2}}{1+x^{2}}dx$$
$$=x\,ln(1+x^{2})-\int (2-\frac{2}{1+x^{2}})dx$$
$$=x\,ln(1+x^{2})-2x+2arctan\,x+C$$
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 507: 14
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