Chebyshev theorem on the integration of binomial differentials

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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).


See also Differential binomial.

How to Cite This Entry:
Chebyshev theorem on the integration of binomial differentials. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by V.I. Bityutskov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article