University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 4 - Practice Exercises - Page 278: 101



Work Step by Step

Since, we know $\int x^{n} dx=\dfrac{x^{n+1}}{n+1}+c$ where $c$ is a constant of proportionality. Substitute $k=r+5 \implies dr =dk$ Now, $\int \dfrac{dr}{(r+5)^2}dt=\int \dfrac{1}{k^2}dk=\int k^{-2} dk$ or, $=\dfrac{k^{-2+1}}{-2+1}+c$ or, $=\dfrac{k^{-1}}{-1}+c$ plug back in: $u=r+5$ Thus, $\dfrac{k^{-1}}{-1}+c=-\dfrac{1}{r+5}+c$
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