Yes, tapes and/or adhesives are out of the question. You might be able to get a brass hose splice and another length of hose, as well as two hose clamps, then cut the leaking hose back where it's pretty straight, then splice it with the brass and new hose. An auto parts store will likely have the hose, hose clamps, and brass splice that you need. If they don't have the splice, then pick up the hose and clamps and head to a good hardware store for the appropriate splice.
-Rod