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: 27

Answer

\[ - \frac{1}{{3x}} + C\]

Work Step by Step

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