# Chapter 7 - Exponential Functions - 7.3 Logarithms and Their Derivatives - Exercises - Page 343: 108

$1$

#### Work Step by Step

Using the fact that $\frac{u'}{u}=\ln u$, we have $$\int_1^{e} \frac{1}{x}dx =\ln x|_1^{e}=\ln e-\ln 1=1.$$ where used the properties $\ln e=1$ and $\ln 1=0$.

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