An expression of the type
where and are real numbers, while , and are rational numbers. The indefinite integral of a differential binomial,
is reduced to an integral of rational functions if at least one of the numbers , and is an integer. In all other cases, the integral of a differential binomial cannot be expressed by elementary functions (P.L. Chebyshev, 1853).
The statement on the reduction to an integral of rational functions is called the Chebyshev theorem on the integration of binomial differentials.
Differential binomial. L.D. Kudryavtsev (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Differential_binomial&oldid=11396