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
$\int{\frac{x^{2}+2}{x+3}}dx$ = $\int({x-3+\frac{11}{x+3}})dx$ = $\frac{x^{2}}{2}-3x+11\ln|x+3|+C$
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 - 8.5 The Method of Partial Fractions - Exercises - Page 423: 6
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