Sounds exactly like my symptoms for my 3.0i a little over a year ago which turned out to be the ICV.

For your x tho I would probably start by looking at the easier stuff first like the PCV, throttle body, a vacuum leak, spark plugs, coils, intake boots, add some fuel injector cleaner, heck maybe even just sweet talk to your x haha

Hopefully its something easy. GL!

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Current:
2002 X5 3.0i E53 - Max

Previous:
2003 XB9s - Rebeka(missed)
1993 525i E34 - Elizabeth(sold at 83K miles)