I was doing my differential equations homework. I had to solve y'' -4y = (e^(2x))/x.(adsbygoogle = window.adsbygoogle || []).push({});

While doing this I ran into an integral[tex]\int\frac{e^{4x}}{4x}dx[/tex]. 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 ?

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

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