# Functions that are not integrable in terms of elementary functions.

by ╔(σ_σ)╝
Tags: elementary, functions, integrable, terms
 P: 850 I was doing my differential equations homework. I had to solve y'' -4y = (e^(2x))/x. While doing this I ran into an integral$$\int\frac{e^{4x}}{4x}dx$$. I tried integrating my times but I couldn't; my guess is that this cannot be integrated in terms of elementary functions but I'm not sure. Is there a theorem or Algorithm for knowing if a function is integrable in terms of elementary functions or not ? If so, can someone tell me the theorem ? And in my case is my function integrable in a finite number of elementary functions ?