According to Google Basic search help
Generally, most punctuation and special characters are ignored, however there is a growing list of punctuation and symbols that are recognized in searches.
How are the symbols not mentioned in that list handled? I thought that the search is the same as if they were replaced by space, but experimenting with some search queries suggest that this is not true. For example, "x^x" integral returns completely different results than "x x" integral. (And the first query gives several results that contain the character ^.)