Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 5 - Integration - 5.5 Substitution Rule - 5.5 Exercises: 18

Answer

\[\frac{{{e^{{x^2}}}}}{2} + C\]

Work Step by Step

\[\begin{gathered} \int_{}^{} {x{e^{{x^2}}}dx} \hfill \\ \hfill \\ set\,\,the\,\,substitution \hfill \\ \hfill \\ u = {x^2}\,\,\,\,\,\,then\,\,\,\,\,du = 2xdx \hfill \\ \hfill \\ \frac{1}{2}\int_{}^{} {{e^u}du} \hfill \\ \hfill \\ integrate\,\, \hfill \\ \hfill \\ = \frac{{{e^u}}}{2} + C \hfill \\ \hfill \\ replace\,\,u\,\,with\,\,\,u = {x^2} \hfill \\ \hfill \\ \frac{{{e^{{x^2}}}}}{2} + C \hfill \\ \end{gathered} \]
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