I am reading Euler original paper about the definition of the Gamma function, there is this formula:
$$\int_0^1 x^{e}(1-x)^{n}dx = \frac{1\cdot2\cdots \cdot n}{(e+1)(e+2)\cdots (e+n+1)}$$
I should expand $\ (1-x)^{n}$ by the binomial theorem, but I can't prove the result.
Could someone please help me?
Thank you