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