Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 7 - Integration Techniques - 7.1 Basic Approaches - 7.1 Exercises: 21

Answer

\[ = x - \ln \left| {x + 1} \right| + C\]

Work Step by Step

\[\begin{gathered} \int_{}^{} {\frac{{dx}}{{{x^{ - 1}} + 1}} = \int_{}^{} {\frac{{xdx}}{{1 + x}}} } \hfill \\ \hfill \\ or \hfill \\ \hfill \\ = \int_{}^{} {\frac{{\,\left( {x + 1} \right) - 1}}{{x + 1}}} dx \hfill \\ \hfill \\ split\,\,the\,\,{\text{integrand}} \hfill \\ \hfill \\ = \int_{}^{} {\,\left( {1 - \frac{1}{{x + 1}}} \right)} dx \hfill \\ \hfill \\ \int_{}^{} {x - \int_{}^{} {\frac{1}{{x + 1}}dx + } } C \hfill \\ \hfill \\ integrate \hfill \\ \hfill \\ = x - \ln \left| {x + 1} \right| + C \hfill \\ \end{gathered} \]
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