Chapter 6 - Exponential, Logarithmic, And Inverse Trigonometric Functions - 6.2 Derivatives And Integrals Involving Logarithmic Functions - Exercises Set 6.2 - Page 426: 68

$$\frac{1}{2}\ln 2$$

$$\eqalign{ & \int_{1/2}^1 {\frac{1}{{2x}}} dx \cr & {\text{drop out the constant}} \cr & = \frac{1}{2}\int_{1/2}^1 {\frac{1}{x}} dx \cr & {\text{integrate}} \cr & = \frac{1}{2}\left[ {\ln \left| x \right|} \right]_{1/2}^1 \cr & {\text{evaluate}} \cr & = \frac{1}{2}\left[ {\ln \left| 1 \right| - \ln \left| {1/2} \right|} \right] \cr & = \frac{1}{2}\ln 2 \cr} $$