Integral of $$$\ln\left(1 - x\right) \ln^{2}\left(x + 1\right)$$$

The calculator will find the integral/antiderivative of $$$\ln\left(1 - x\right) \ln^{2}\left(x + 1\right)$$$, with steps shown.

Find $$$\int \ln\left(1 - x\right) \ln^{2}\left(x + 1\right)\, dx$$$.