What features of elementary functions define a class of functions whose consecutive indefinite integration also gives an elementary function?

Is there a way to check whether a given elementary function has such property?

Take the 2-minute tour
×

MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

What features of elementary functions define a class of functions whose consecutive indefinite integration also gives an elementary function? Is there a way to check whether a given elementary function has such property? |
||||

e.g.$x\mapsto \exp (x^2)$. – Loïc Teyssier May 3 '14 at 8:00