In Definite Integral of square root of polynomial , André Nicolas commented: "So you want to integrate $\sqrt{P(x)}$. If $P(x)$ is a linear or quadratic polynomial, we can integrate in terms of elementary functions. In general, if the degree of $P(x)$ is $\ge 3$, $\sqrt{P(x)}$ does not have an elementary antiderivative except in quite special cases. "
Is this conclusion a theorem? where could I find more details of it?