# B(x,y)=integral (t^(x-1)+t^(y-1))(1+t)^(-x-y) dt

The following formula holds: $$B(x,y) = \displaystyle\int_0^1 (t^{x-1}+t^{y-1})(1+t)^{-x-y} \mathrm{d}t,$$ where $B$ denotes the beta function.