\int {x^{n - 3} \ln \left( {1 - x} \right)dx} = \frac{{x^{n - 2} - 1}}{{n - 2}}\ln \left( {1 - x} \right) - \frac{1}{{n - 2}}\sum\limits_{k = 1}^{n - 2} {\left( \begin{array}{c}
 n - 2 \\ 
 k \\ 
 \end{array} \right)\frac{{\left( {x - 1} \right)^k }}{k}}