$\int_{1}^{2} \frac{1}{x} d x$

Step 1 ：The integral of \( \frac{1}{x} \) from 1 to 2 is given by the formula \( \int_{1}^{2} \frac{1}{x} dx = \ln(2) - \ln(1) \).

Step 2 ：Calculate the value of \( \ln(2) - \ln(1) \).

Step 3 ：The result is 0.6931471805599453.

Step 4 ：Final Answer: \( \boxed{0.6931471805599453} \)