Let α ∈(0,1) and β= log_e(1-α). Let P_n(x)=x+x^2/2+x^3/3+…+x^n/n, x ∈(0,1). Then the integral ∫_0^α (t^50)/(1-t) d t is equal to

Let $\displaystyle \alpha \in(0,1)$ and $\displaystyle \beta=\log _e(1-\alpha)$. Let $\displaystyle P_n(x)=x+\frac{x^2}{2}+\frac{x^3}{3}+\ldots+\frac{x^n}{n}, x \in(0,1)$. Then the integral $\displaystyle \int_0^\alpha \frac{t^{50}}{1-t} d t$ is equal to