Chebyshev theorem on the integration of binomial differentials
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.
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