Question

Need to find equations that cannot be solved analytically. How do you do that someone said have one cube term

Answer 1

Search for Galois theory.

It has indeed been rigorously proven that some polynomial equations/integrals/DE's can't be analytically solved. But the proof of this is by all means not easy.



Read this for the integrals: http://en.wikipedia.org/wiki/Liouville%27s_theorem_%28differential_algebra%29

Answer 2

polynomials with degree 5 or greater cannot generally be solved analytically. there is no general solution using surds, and 4 arithmetic operations