Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 7 - Integration - 7.2 Substitution - 7.2 Exercises: 5

Answer

\[ =-\dfrac{(2m+1)^{-2}}{2} +C \]

Work Step by Step

In order to integrate this function, we have to use a «u» substitution. But first rewrite the function: \[ \int 2(2m+1)^{-3} dm \] Choose an u, derivate it: $ u = 2m+1 $ $ du = 2dm$ Then substitute: \[ =\int u^{-3} du \] Then integrate \[ =\dfrac{u^{-2}}{-2}+C \] And undo the substitution: \[ =-\dfrac{(2m+1)^{-2}}{2} +C \]
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