Now this is certainly a puzzling matter. At first I assumed it would be easy to figure out the amount of experience required to level. I glanced at a couple of levels in particular 97,98, and 99. The respective experiences required for the level were 5860, 5979, and 6099. So I thought perhaps it's very simple 97 to 98 increased the required experience by 119 and 98 to 99 increased the required experience by 120 and I reasoned that each level might just increase the increase by 1. But this doesn't hold completely and actually fails quite quickly because the experience required from 99 to 100 increases by 122 (not by 121 if it were to follow the pattern).
Then I tried fitting a function to a level vs experience required plot, but that just turned out to be too complicated and actually failed quite miserably at numbers outside the known numbers.
Now, I have a little bit more accurate method. First I'll sum it up in a simple formula:
Experience Required=(2.21+0.6n)n Where n=level you are trying to find experience required for
Now you might be wondering where did the 0.6 (or you might not care, but I'm telling you anyway). Well what I did to find this was take the experience required and divided it by the level, then I noticed that after each level this ratio increases on average by 0.6.
This formula doesn't work for level 1, but I believe GREE may have just changed level 1 to 5 experience just for the aethetics. There's no way to know for sure how well this works for lower levels but I do have one peice of small evidence that supports this formula. As DinoKev pointed out to me the battle experience appears to be equal to the experience to next level with the last digit removed. (e.g. Level 58 requires 2147xp and gives 214xp from battle) At level 9 battles give 6xp, and my formula gives a required xp of 68 (rounded).
Anyway, this is the best formula I could come up with and I'm content with the results based on current data.
If you would like to find out a bunch of levels then I suggest you put it in a spreadsheet, or you can ask for a copy of mine if you want. I just don't plan on putting the numbers in wiki page because they are not actual recorded numbers, and don't want to give false info, even if it's just off for smaller levels.