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: 16

Answer

\[\frac{2}{3}\,{\left( {3{x^2} + x} \right)^{\frac{3}{2}}} + C\]

Work Step by Step

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