The brief
The X1 had picked up a vibration the owner could feel through the cabin, some odd noises whenever it pulled away or accelerated hard, and one of the engine mounts had a film of oil seeping out of it.
Those three things together point straight at the engine mounts. They are the rubber-and-fluid blocks that hold the engine and gearbox steady and soak up their movement. When one is visibly leaking, the rest are usually the same age and heading the same way, so the smart move is to look at the whole set rather than chase one mount at a time.
The diagnosis
Up on the lift, each mount got a pry-test. The one with the oil film was failing internally, which is what happens when a hydraulic mount loses the damping fluid sealed inside it. The next engine mount had sagged past spec and was no longer holding the engine where it should sit. And the gearbox mount showed clear movement under load.
So every mount in the set was worn out, not just the leaking one. Replacing them piecemeal would have meant going back in soon for the next one, so the call was a full-set replacement in one visit.
The work
The engine and gearbox were taken onto transmission jacks so the weight came off the mounts, then each old mount was removed in turn and a new BMW-spec replacement fitted in its place.
Every fastener was torqued to the manual figures, and before the engine was allowed to load back onto the fresh mounts the workshop checked the drivetrain was sitting square. Get that wrong and the new mounts wear unevenly from day one.
The outcome
The cabin went quiet and smooth. No noises pulling away, no vibration at idle, and nothing leaking from the mounts.
The X1 went home with the engine and gearbox held properly again. For the owner the everyday difference is a car that feels solid and settled rather than buzzy and loose. The longer-term win is that doing the whole set at once means the mounts age together from here, instead of a string of return visits for the next one to give out.