Answer
$x-arctan\,x+C$
Work Step by Step
$$\int \frac{x^{2}}{x^{2}+1}dx=\int \frac{x^{2}+1-1}{x^{2}+1}dx$$
$$=\int (1-\frac{1}{x^{2}+1})dx$$
$$=\int 1dx-\int \frac{1}{x^{2}+1}dx$$
$$=x-arctan\,x+C$$
Thomas' Calculus 13th Edition
by Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0-32187-896-5
ISBN 13:
978-0-32187-896-0
Chapter 8: Techniques of Integration - Section 8.1 - Using Basic Integration Formulas - Exercises 8.1 - Page 448: 2
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