How to integrate$\int \frac{1}{\ln(x)}dx$?

Question

How to integrate $$\int \frac{1}{\ln(x)}dx$$ ? I am trying this question by substituting $\ln(x)=u$. Therefore, $dx=e^{u}du$. So, the above integral will become $$\int \frac{e^{u}}{u}du$$ . Now, I am thinking of applying Integration By Parts. So, according to the rule of ILATE, $\frac{1}{u}=U$ and $e^{u}=V$. So, let $$I=\int\frac{e^{u}}{u}du$$. Therefore, $$I=\frac{e^{u}}{u}+\int \frac{e^{u}}{u^{2}}du$$.(After applying IBP). But I can't understand how to proceed further. Please help me out to integrate the above expression.