Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 7 - Integration Techniques - Review Exercises - Page 593: 6

Answer

$$x + \ln \left| {{x^3} + 1} \right| + C$$

Work Step by Step

$$\eqalign{ & \int {\frac{{{x^3} + 3{x^2} + 1}}{{{x^3} + 1}}} dx \cr & {\text{use long division}} \cr & = \int {\left( {1 + \frac{{3{x^2}}}{{{x^3} + 1}}} \right)} dx \cr & {\text{sum rule}} \cr & = \int {dx} + \int {\frac{{3{x^2}}}{{{x^3} + 1}}} dx \cr & {\text{find the antiderivatives}} \cr & = x + \ln \left| {{x^3} + 1} \right| + C \cr} $$
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