# Chebyshev theorem on the integration of binomial differentials

From Encyclopedia of Mathematics

The indefinite integral of the binomial differential
$$
x^m (a+bx^n)^p
$$
where $a$ and $b$ are real numbers and $m$, $n$ and $p$ are rational numbers, cannot be expressed in terms of elementary functions for any $m$, $n$ and $p$, except in the case where (at least) one of $p$, $(m+1)/n$ and $p + (m+1)/n$ is an integer. Obtained by P.L. Chebyshev (1853).

#### Comments

See also Differential binomial.

**How to Cite This Entry:**

Chebyshev theorem on the integration of binomial differentials.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Chebyshev_theorem_on_the_integration_of_binomial_differentials&oldid=35531

This article was adapted from an original article by V.I. Bityutskov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article