Calculus (3rd Edition)

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

Chapter 8 - Techniques of Integration - 8.5 The Method of Partial Fractions - Exercises - Page 423: 8

Answer

$\frac{x^{2}}{2}-\frac{1}{2}\ln(x^{2}+1)+tan^{-1}x+C$

Work Step by Step

long division gives $\frac{x^{3}+1}{x^{2}+1}$ = $x-\frac{x-1}{x^{2}+1}$ so $\int(\frac{x^{3}+1}{x^{2}+1})dx$ = $\int(x-\frac{x}{x^{2}+1}+\frac{1}{x^{2}+1})dx$ = $\frac{x^{2}}{2}-\frac{1}{2}\ln(x^{2}+1)+tan^{-1}x+C$
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