In mathematics, the Chebyshev integral, named after Pafnuty Chebyshev, is
∫ x p ( 1 − x ) q d x = B ( x ; 1 + p , 1 + q ) , {\displaystyle \int x^{p}(1-x)^{q}\,dx=B(x;1+p,1+q),}
where B ( x ; a , b ) {\displaystyle B(x;a,b)} is an incomplete beta function.
References Weisstein, Eric W. "Chebyshev Integral". MathWorld.