Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 11 - Infinite Sequences and Series - Review - Exercises - Page 826: 55



Work Step by Step

$\int\frac{e^{x}}{x}dx=\int \frac{1}{x}\Sigma_{n=0}^\infty\frac{x^{n}}{n!}dx=\int \Sigma_{n=0}^\infty\frac{x^{n-1}}{n!}dx$ $\int \Sigma_{n=0}^\infty\frac{x^{n-1}}{n!}dx=\int \frac{1}{x}+\int \Sigma_{n=1}^\infty\frac{x^{n-1}}{n!}dx$ $=C+ln|x|+\Sigma_{n=1}^\infty \int \frac{x^{n-1}}{n!}dx$ $=C+ln|x|+\Sigma_{n=1}^\infty\frac{x^{n}}{n(n!)}$ Hence, $\int\frac{e^{x}}{x}dx=C+ln|x|+\Sigma_{n=1}^\infty\frac{x^{n}}{n(n!)}$
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