Chapter 6 - Exponential, Logarithmic, And Inverse Trigonometric Functions - 6.2 Derivatives And Integrals Involving Logarithmic Functions - Exercises Set 6.2 - Page 426: 64

$=\frac{1}{2}ln|x|+C$

Since $\frac{1}{2x}$ equals $(\frac{1}{2})(\frac{1}{x})$ and $\frac{1}{2}$ is a constant, the constant can be brought outside of the integral. This yields $$\frac{1}{2}\int\frac{dx}{x}=\boxed{\frac{1}{2}ln|x|+C}$$