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: 8

Answer

\[ -2(2x^3+7)^{-1/2} +C\]

Work Step by Step

In order to integrate this function, we have to use an «u» substitution. Choose an u, derivate it: $ u=2x^3+7$ $ du = 6x^2dx$ Then substitute: \[ =\int \dfrac{du}{u^{3/2}} = \int u^{-3/2}du \] Then integrate \[ =-2u^{-1/2} +C \] And undo the substitution: \[ =\boxed{-2(2x^3+7)^{-1/2} +C}\]
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