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

Find $$$\int \frac{\ln\left(1 - z\right)}{z}\, dz$$$.

This integral (Polylogarithm Function) does not have a closed form:

$${\color{red}{\int{\frac{\ln{\left(1 - z \right)}}{z} d z}}} = {\color{red}{\left(- \operatorname{Li}_{2}\left(z\right)\right)}}$$

Therefore,

$$\int{\frac{\ln{\left(1 - z \right)}}{z} d z} = - \operatorname{Li}_{2}\left(z\right)$$

Add the constant of integration:

$$\int{\frac{\ln{\left(1 - z \right)}}{z} d z} = - \operatorname{Li}_{2}\left(z\right)+C$$

$$$\int \frac{\ln\left(1 - z\right)}{z}\, dz = - \operatorname{Li}_{2}\left(z\right) + C$$$A