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: 4

Answer

\[ = \ln \left| x \right| + C\]

Work Step by Step

\[\begin{gathered} The\,\,restriction\,\,it\,\,is\,\,necessary\,\, \hfill \\ Because\,,\,\,for\,\,n = - 1 \hfill \\ \frac{{{x^{n + 1}}}}{{n + 1}} = \frac{{{x^{ - 1 + 1}}}}{{ - 1 + 1}} = \frac{{{x^0}}}{0} = \frac{1}{0} \hfill \\ and \hfill \\ \int_{}^{} {{x^{ - 1}}dx} = \int_{}^{} {\frac{1}{x}dx} = \ln \left| x \right| + C \hfill \\ \end{gathered} \]
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