Evaluate the integral I=∫01xn(1−x)m dxI = \int_{0}^{1} x^n (1-x)^m \, dxI=∫01xn(1−x)mdx where n,m>0n, m > 0n,m>0.
n!m!(n+m)!\frac{n! m!}{(n+m)!}(n+m)!n!m!
n!m!(n+m+1)!\frac{n! m!}{(n+m+1)!}(n+m+1)!n!m!
(n+m)!n!m!\frac{(n+m)!}{n! m!}n!m!(n+m)!
n!m!(n+m+2)!\frac{n! m!}{(n+m+2)!}(n+m+2)!n!m!