alternate integral representation of beta function (2)Substitute x:=11+s, dx=-1(1+s)2ds:∫01xp-1(1-x)q-1𝑑x=∫0∞1(1+s)p+1(s1+s)q-1𝑑s=∫0∞sq-1(1+s)p+q𝑑sSince B(p,q)=B(q,p) this gives:∫0∞sp-1(1+s)p+q𝑑s=Γ(p)Γ(q)Γ(p+q)