Calculus: Early Transcendentals (2nd Edition)

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

Chapter 4 - Applications of the Derivative - Review Exercises: 71

Answer

$$ - \frac{1}{x} - \frac{4}{{3{x^{3/2}}}} + C$$

Work Step by Step

$$\eqalign{ & \int {\left( {\frac{1}{{{x^2}}} - \frac{2}{{{x^{5/2}}}}} \right)} dx \cr & {\text{write with negative exponents}} \cr & = \int {\left( {{x^{ - 2}} - 2{x^{ - 5/2}}} \right)} dx \cr & {\text{sum rule}} \cr & = \int {{x^{ - 2}}} dx - \int {2{x^{ - 5/2}}} dx \cr & {\text{integrate by the power rule}} \cr & = \frac{{{x^{ - 1}}}}{{ - 1}} - \frac{{2{x^{ - 3/2}}}}{{3/2}} + C \cr & {\text{simplify}} \cr & = - \frac{1}{x} - \frac{4}{{3{x^{3/2}}}} + C \cr} $$
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