Đáp án:

• \( I = \int \frac{\ln x - 1}{x^2 (1 - \left( \frac{\ln x}{x} \right)^2)} \, dx\)

• Đặt \( t = \frac{\ln x}{x} \Rightarrow dt = \frac{1 - \ln x}{x^2} \, dx \)

• \( I = -\int \frac{1}{1 - t^2} \, dt = \int \frac{1}{(t - 1)(t + 1)} \, dt \)

   \(= \frac{1}{2} \int \left( \frac{1}{t - 1} - \frac{1}{t + 1} \right) \, dt = \frac{1}{2} \ln \left| \frac{t - 1}{t + 1} \right| + C \)