2005 BMW 325xi vibration?

bmw
325

#1

My 2005 BMW 325xi with manual transmission has 134,000 miles on it. It still runs great; but when I drive it for longer distances it develops a vibration, which emerges after about 70 to 80 miles. This vibration occurs only when I am accelerating and goes away completely when I take my foot off of the accelerator. I took it to the BMW dealer service department and they road tested it and couldn’t find anything. Of course they didn’t drive it for 70 miles. I am taking delivery of a new BMW soon and thought I would sell this car to my nephew, but am hesitant without understanding the cause of this vibration.