Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 5 - The Integral - 5.3 The Indefinite Integral - Exercises: 4

Answer

$\int(9x+15x^{-2})dx=\frac{9}{2}x^2-\frac{15}{x}+C$

Work Step by Step

Antidifferentiating: $\int(9x+15x^{-2})dx =9\times\frac{1}{2}x^2 +15 \times\frac{1}{-1}x^{-1} + C = \frac{9}{2}x^2 - \frac{15}{x} + C$ Checking with differentiation: $(\frac{9}{2}x^2-\frac{15}{x}+C)' = \frac{9}{2} \times2 x-15 \times\frac{-1}{x^2}= 9x + \frac{15}{x^2}$
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