How do you get sleeping tablets onto a flight to avoid jetlag?

I am flying from London to Los Angeles in the New Year. I have never flown this far before and really don't want to spend the first few days of my holiday feeling crap. I have been told to drink lots of water and to take sleeping tablets on the flight and sleep as much as I can. But surely if I 'borrow' a few tablets from a friend, how do I convince the customs officials that I am not a drug smuggler, and avoid a painful internal examination?