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: 6

Answer

\[ 2(3u-5)^{1/2}+C \]

Work Step by Step

In order to integrate this function, we have to use an «z» substitution. But first let's rewrite the function: \[ \int 3(3u-5)^{-1/2} \] Choose a z, derivate it: $ z = 3u-5$ $ dz = 3du$ Then substitute: \[ =\int z^{-1/2}dz \] Then integrate \[ =2z^{1/2} + C \] And undo the substitution: \[ =\boxed{2(3u-5)^{1/2}+C} \]
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