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: 7

Answer

$\frac{x^{3}}{3}+\ln|x+2|+C$

Work Step by Step

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