Đáp án:

• Xét  \( \int \frac{1}{\ln{x}} \, dx \)

• Đặt  \( \begin{cases} u = \frac{1}{\ln{x}} \\ dv = dx \end{cases} \quad \Rightarrow \quad \begin{cases} du = -\frac{1}{x \ln^2{x}} dx \\ v = x \end{cases} \)

• \( \int \frac{1}{\ln{x}} \, dx =  \frac{x}{\ln{x}} + \int \frac{1}{\ln^2{x}} \, dx \)

• \( \Rightarrow \int \left( \frac{1}{\ln{x}} - \frac{1}{\ln^2{x}} \right) dx = \frac{x}{\ln{x}} + C \)