There is a theorem that states that if f(x) and g(x) are rational functions (and g(x) is not a constant) , then can be expressed in terms of a finite number of elementary functions iff there exists a rational function R(x) such that .
So let's take
So I have to show that there does not exist a R(X) such that .
It's a linear first order differential equation with integrating factor
How do I show that R(x) is not rational? Do I have to show that is nonelementary?