MathematicsMedium210×since 2002Q3450Let α∈(0,1)\alpha \in (0,1)α∈(0,1) and β=loge(1−α)\beta = {\log _e}(1 - \alpha )β=loge(1−α). Let Pn(x)=x+x22+x33 + ... + xnn,x∈(0,1){P_n}(x) = x + {{{x^2}} \over 2} + {{{x^3}} \over 3}\, + \,...\, + \,{{{x^n}} \over n},x \in (0,1)Pn(x)=x+2x2+3x3+...+nxn,x∈(0,1). Then the integral ∫0αt501−tdt\int\limits_0^\alpha {{{{t^{50}}} \over {1 - t}}dt}0∫α1−tt50dt is equal toA−(β+P50(α))- \left( {\beta + {P_{50}}\left( \alpha \right)} \right)−(β+P50(α))Bβ−P50(α)\beta - {P_{50}}(\alpha )β−P50(α)CP50(α)−β{P_{50}}(\alpha ) - \betaP50(α)−βDβ+P50−(α)\beta + {P_{50}} - (\alpha )β+P50−(α)Check answerSkip