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: 3

Answer

\[ \dfrac{2}{5}(2x+3)^5 \]

Work Step by Step

In order to integrate this function, we have to use an «u» substitution. Choose an u, derivate it: $u = 2x+3$ $du = 2 dx$ $\dfrac{1}{2}du=dx$ Then and substitute: \[ \dfrac{1}{2} \int 4u^4du \] \[ = 2 \int u^4du\] Then integrate \[ = \dfrac{2}{5} u^5 +C\] And undo the substitution: \[ \dfrac{2}{5}(2x+3)^5 \]
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