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: 22

Answer

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

Work Step by Step

\[\begin{gathered} \int_{}^{} {\frac{4}{{{x^3}}}dx} \hfill \\ Write\,\,\frac{1}{{{x^3}}}\,\,as\,\,{x^{ - 3}} \hfill \\ \int_{}^{} {4{x^{ - 3}}dx} \hfill \\ Use\,\,the\,\,power\,\,rule \hfill \\ \int_{}^{} {{x^n}dx} = \frac{{{x^{n + 1}}}}{{n + 1}} + C \hfill \\ Then \hfill \\ \int_{}^{} {4{x^{ - 3}}dx} = 4\,\left( {\frac{{{x^{ - 3 + 1}}}}{{ - 3 + 1}}} \right) + C \hfill \\ Simplifying \hfill \\ 4\,\left( {\frac{{{x^{ - 2}}}}{{ - 2}}} \right) + C \hfill \\ - 2{x^{ - 2}} + C \hfill \\ - \frac{2}{{{x^2}}} + C \hfill \\ \end{gathered} \]
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