Chapter 6 - Exponential, Logarithmic, And Inverse Trigonometric Functions - 6.4 Graphs And Applications Involving Logarithmic And Exponential Functions - Exercises Set 6.4 - Page 440: 47

$${f_{avg}} = \frac{1}{{e - 1}}$$

$$\eqalign{ & {\text{The average value of the function is:}} \cr & {f_{avg}} = \frac{1}{{e - 1}}\int_1^e {\frac{1}{x}} dx \cr & {\text{Integrate and evaluate}} \cr & {f_{avg}} = \frac{1}{{e - 1}}\left[ {\ln x} \right]_1^e \cr & {f_{avg}} = \frac{1}{{e - 1}}\left( {\ln e - \ln 1} \right) \cr & {f_{avg}} = \frac{1}{{e - 1}} \cr} $$