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