Answer
$$\int arctan\,x\,dx=arctan\,x-\frac{1}{2}ln(x^{2}+1)+C$$
Work Step by Step
$$\int arctan\,x\,dx=arctan\,x-\int\frac{x}{x^{2}+1}dx$$
$$=arctan\,x-\frac{1}{2}\int \frac{1}{x^{2}+1}d(x^{2}+1)$$
$$=arctan\,x-\frac{1}{2}ln(x^{2}+1)+C$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
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
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