I would have put a small space (\,) between the upright "det" and the matrix. An integral sign is usually followed by a negative small space (\!) and the "dx" is separated by a small space (\,).

Trouble is I'm not sure if these are absolute rules. I'm sure you can find pathological cases where the spacing will be wrong. Maybe the best thing would be to allow the user to modify the spacing easily after the automatic version is made.

I trust you guys have read the TeXBook? Knuth dedicates two chapters to subtleties of mathematical typesetting.