Question about nonelementary integrals

[DivergentSpectrum]

are nonelementary integrals implicit functions?

ie, when we do implicit differentation, we get an explicit function. What if i go the opposite way, and integrate an explicit function to get an implicit antiderivative?

 

[mathman]

You seem to be mixing up two unrelated concepts.

When you get the derivative of an implicit function, at first the expression for the derivative will include both the independent variable and the dependent variable. You may be able to manipulate it to get an explicit expression for the derivative.

When you integrate an explicit function the integral may or may be expressible in terms of elementary functions. Implicit has nothing to do with it.