Mine developed the same idle shake a few months ago. The SES light set last week for a #3 misfire. Reset and it has gone away. New plugs and coils are going in this week. Mine also needs a front right shaft. The boot is in bad shape. It could tear apart any day. Luckily, I have all four shafts ready to go on. I'll report back which part fixes my vibration.

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'06 X5 3.0i - bought @143,123 miles (12/26/20)