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: 26

Answer

\[ - 4{x^{ - 2.5}} + 4\ln \left| x \right| + C\]

Work Step by Step

\[\begin{gathered} \int_{}^{} {\,\left( {10{x^{ - 3.5}} + 4{x^{ - 1}}} \right)dx} \hfill \\ Use\,\,the\,\,sum\,\,and\,\,difference\,\,rules \hfill \\ \int_{}^{} {10{x^{ - 3.5}}dx + \int_{}^{} {4{x^{ - 1}}dx} } \hfill \\ 10\int_{}^{} {{x^{ - 3.5}}dx} + 4\int_{}^{} {{x^{ - 1}}dx} \hfill \\ \,use\,\,the\,\,power\,\,rule\,\,\,and \hfill \\ \int_{}^{} {\frac{1}{x}dx} = \ln \left| x \right| + C \hfill \\ Then \hfill \\ 10\,\left( {\frac{{{x^{ - 3.5 + 1}}}}{{ - 3.5 + 1}}} \right) + 4\,\left( {\ln \left| x \right|} \right) + C \hfill \\ 10\,\left( {\frac{{{x^{ - 2.5}}}}{{ - 2.5}}} \right) + 4\ln \left| x \right| + C \hfill \\ Simplifying \hfill \\ - 4{x^{ - 2.5}} + 4\ln \left| x \right| + C \hfill \\ \end{gathered} \]
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