Đáp án:

\( I = 2 \int_{1}^{2} \frac{1}{x} dx - \int_{1}^{2} \frac{1}{x^2} dx + \int_{1}^{2} \frac{x f'(x) - f(x)}{x^2} dx \)

\( = 2 \ln x \big|_{1}^{2} + \frac{1}{x} \big|_{1}^{2} + \int_{1}^{2} \left( \frac{f(x)}{x} \right)' dx \)

\( = 2 \ln 2 + \left( \frac{1}{2} - 1 \right) + \left( \frac{f(x)}{x} \right) \big|_{1}^{2} \)

\( = 2 \ln 2 - \frac{1}{2} + \left( \frac{4}{2} - 1 \right) = 2 \ln 2 + \frac{1}{2} \Rightarrow \boxed{C} \)