integration of differential binomial
Theorem. Let , , , , be given real numbers and . The antiderivative
is expressible by of the elementary functions only in the three cases: , ,
In accordance with P. L. Chebyshev (18211894), who has proven this theorem, the expression is called a differential binomial.
It may be worth noting that the differential binomial may be expressed in terms of the incomplete beta function and the hypergeometric function
. Define . Then we have
Chebyshev’s theorem then follows from the theorem on elementary cases of the hypergeometric function.