Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 8 - Techniques of Integration - 8.1 Integration by Parts - Exercises - Page 395: 6


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

Work Step by Step

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