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: 66

Answer

\[ = \frac{1}{9}\,{\left( {{x^{\frac{3}{2}}} + 8} \right)^6} + C\]

Work Step by Step

\[\begin{gathered} \int_{}^{} {\,{{\left( {{x^{\frac{3}{2}}} + 8} \right)}^5}\sqrt x } dx \hfill \\ \hfill \\ u = {x^{\frac{3}{2}}} + 8\,\,\,\,\,\,then\,\,\,\,du = \frac{3}{2}\sqrt x \,\,dx \hfill \\ \hfill \\ apply\,\,the\,\,\,substitution \hfill \\ \hfill \\ = \frac{2}{3}\int_{}^{} {{u^5}du} \hfill \\ \hfill \\ integrate \hfill \\ \hfill \\ = \frac{1}{9}{u^6} + C \hfill \\ \hfill \\ replace\,\,u\,\,with\,\,u = {x^{\frac{3}{2}}} + 8 \hfill \\ \hfill \\ = \frac{1}{9}\,{\left( {{x^{\frac{3}{2}}} + 8} \right)^6} + C \hfill \\ \end{gathered} \]
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