Integral of $\frac{1}{\ln\left(x\right)}$

Find $\int \frac{1}{\ln\left(x\right)}\, dx$.

This integral (Logarithmic Integral) does not have a closed form:

$${\color{red}{\int{\frac{1}{\ln{\left(x \right)}} d x}}} = {\color{red}{\operatorname{li}{\left(x \right)}}}$$

Therefore,

$$\int{\frac{1}{\ln{\left(x \right)}} d x} = \operatorname{li}{\left(x \right)}$$

Add the constant of integration:

$$\int{\frac{1}{\ln{\left(x \right)}} d x} = \operatorname{li}{\left(x \right)}+C$$

$\int \frac{1}{\ln\left(x\right)}\, dx = \operatorname{li}{\left(x \right)} + C$A