Possible Duplicate:
How can you prove that a function has no closed form integral?
(Forgive my crude lingo)
Why do some integrals seem to be unsolvable; that is to say the indefinite integral cannot be solved symbolically (or is it analytically(?)). For example, those with the form of a radial distribution function using the Lennard-Jones potential:
$g(r) = \exp(-(r^{-12} - r^{-6}))$
What prevents me from using my standard Calc II knowledge to come up with a continuous expression for $\int{g(r)dr}$?