Definite Integration

Let \(\alpha \in (0,1)\) and \(\beta = {\log _e}(1 - \alpha )\). Let \({P_n}(x) = x + {{{x^2}} \over 2} + {{{x^3}} \over 3}\, + \,...\, + \,{{{x^n}} \over n},x \in (0,1)\). Then the integral \(\int\limits_0^\alpha {{{{t^{50}}} \over {1 - t}}dt}\) is equal to