Đáp án:

\( \int_1^4 f(x) \, dx = \int_1^4 \frac{f(2\sqrt{x} - 1)}{\sqrt{x}} \, dx + \int_1^4 \frac{\ln x}{x} \, dx. \)

\({\int_1^4 f(2\sqrt{x} - 1) \, d(2\sqrt{x} - 1)  + \frac{\ln^2 x}{2} }\big|_1^4\)

\(= \int_1^3 f(x) \, dx + \frac{\ln^2 4}{2}\)

\(\Rightarrow \int_3^4 f(x) \, dx = \int_1^4 f(x) \, dx - \int_1^3 f(x) \, dx = 2\ln^2 2  \Rightarrow \boxed{A}\)