Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 7 - Integration - 7.1 Antiderivatives - 7.1 Exercises: 18

Answer

\[6{x^{5/2}} + \frac{4}{3}{x^{3/2}} + C\]

Work Step by Step

\[\begin{gathered} \int_{}^{} {\,\left( {15x\sqrt x + 2\sqrt x } \right)dx} \hfill \\ Write\,\,\sqrt x \,\,\,as\,\,{x^{1/2}} \hfill \\ \int_{}^{} {\,\left( {15x{x^{1/2}} + 2{x^{1/2}}} \right)dx} \hfill \\ Multiplying \hfill \\ \int_{}^{} {\,\left( {15{x^{3/2}} + 2{x^{1/2}}} \right)dx} \hfill \\ Find\,\,the\,\,antiderivative\,\,\,use\,\,the\,\, \hfill \\ power\,\,\,rule \hfill \\ \int_{}^{} {{x^n}dx} = \frac{{{x^{n + 1}}}}{{n + 1}} + C \hfill \\ 15\,\left( {\frac{{{x^{5/2}}}}{{5/2}}} \right) + 2\,\left( {\frac{{{x^{3/2}}}}{{3/2}}} \right) + C \hfill \\ Simplifying \hfill \\ 6{x^{5/2}} + \frac{4}{3}{x^{3/2}} + C \hfill \\ \end{gathered} \]
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