Humming Noise, rear of car

[mcwatts]

Hello,

Okay, so my 2006 X3 3.0i has had a few issues lately, first the leaking valve cover gasket, which I had fixed by the dealership. Also, the car makes a humming noise. It is intermittent and only happens when accelerating (once foot is off accelerator, it stops) at roughly 50 miles per hour and up (highway speeds). The dealer thinks it is either a transfer case failure or a driveshaft failure. They aren't sure, the noise is definitely a deep humming sound, not a whine, like what others have complained about when their transfer cases have failed. Of course, if it is the transfer case, it is a $3,500.00 job on a nine year old car with 148K miles... Or $1,000 for the driveshaft...(I'm fine with that!)I think for some reason it was done before by the previous owner, but of course my records are in the car at the dealer.

Also, the car has "hummed" since I have owned it, and I have driven it in snow and rain it never slides at all, it is great! That is why I am not sure of a transfer case issue.

Any ideas??

Thank you so much, this is stressful!