Reference request: Source for "Cauchy's Theorem" (?) on integration in elementary functions Buried deep in my notes from a course I took many years ago, I find a reference to the following, which (in my notes) is called "Cauchy's Theorem":

Theorem.  The integral $\int x^p (1-x)^q dx $ can be expressed in terms of elementary functions if and only if one of the following
  holds:
  
  
*
  
*$p\in\mathbb Z$
  
*$q\in\mathbb Z$
  
*$p+q \in\mathbb Z$

Thus, for example, this would imply that $\int x^{1/3}(1-x)^{1/2} dx$ cannot be expressed in elementary functions.
I've been trying to find a source for this theorem but have been coming up empty -- searches for "Cauchy's Integral Theorem" lead to his theorem on line integrals of holomorphic functions in $\mathbb C$, which seems unrelated.  (If it is related, the connection is certainly beyond my comprehension.)
Can anybody provide me with a source for this theorem, or at least a confirmation that it is true and is in fact due to Cauchy?

This is called the differential binomial, and the theorem is due to Chebyshev. You can find this site
http://www2.onu.edu/~m-caragiu.1/bonus_files/CHEBYSHE.pdf
useful, or just google chebyshev differential binomial.
Hope this helps.
