JEE Math Practice Question

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

1. A.$$ - \left( {\beta + {P_{50}}\left( \alpha \right)} \right)$$
2. B.$$\beta - {P_{50}}(\alpha )$$
3. C.$${P_{50}}(\alpha ) - \beta $$
4. D.$$\beta + {P_{50}} - (\alpha )$$