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: 6

Answer

$\frac{x^{2}}{2}-3x+11\ln|x+3|+C$

Work Step by Step

long division gives us $\frac{x^{2}+2}{x+3}$ = $x-3+\frac{11}{x+3}$ so $\int{\frac{x^{2}+2}{x+3}}dx$ = $\int({x-3+\frac{11}{x+3}})dx$ = $\frac{x^{2}}{2}-3x+11\ln|x+3|+C$
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