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: 7

Answer

\[ = -\dfrac{1}{3} (x^2+2x-4)^{-3}+C \]

Work Step by Step

In order to integrate this function, we have to use an «u» substitution. Choose an u, derivate it: $ u = x^2+2x-4$ $ du = 2x+2$ Then substitute: \[ = \int \dfrac{du}{u^4} = \int u^{-4} \] Then integrate \[ = -\dfrac{1}{3} u^{-3}+C \] And undo the substitution: \[ = \boxed{-\dfrac{1}{3} (x^2+2x-4)^{-3}+C} \]
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