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: 14

Answer

\[\frac{1}{3}{e^{{x^3} - 3x}} + C\]

Work Step by Step

\[\begin{gathered} \int_{}^{} {\,\left( {{x^2} - 1} \right){e^{{x^3} - 3x}}dx} \hfill \\ Let\,\,u = {x^3} - 3x \hfill \\ So\,that\,\,du = 3{x^2} - 3 \hfill \\ \,\,\,\,\,\,du = 3\,\left( {{x^2} - 1} \right)dx \hfill \\ Then \hfill \\ \frac{1}{3}\int_{}^{} {3\,\left( {{x^2} - 1} \right){e^{{x^3} - 3x}}dx} \hfill \\ \frac{1}{3}\int_{}^{} {{e^u}du} \hfill \\ Integrating\,\, \hfill \\ \frac{1}{3}{e^u} + C \hfill \\ Substituting\,\,u = {x^3} - 3x\,\,gives \hfill \\ \frac{1}{3}{e^{{x^3} - 3x}} + C \hfill \\ \end{gathered} \]
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