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
$\int{\frac{x^{3}+2x^{2}+1}{x+2}}dx$ = $\int(x^{2}+\frac{1}{x+2})dx$ = $\frac{x^{3}}{3}+\ln|x+2|+C$
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: 7
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