An experienced mechanic knows those code by heart.
Did you pull the plug? I've seen individual plugs fail. You can move the coil pack to another location or ohm it with a voltmeter. Compare ohm reading between coil packs. You can do the same for fuel injectors. One cylinder miss fire will cause other cylinders to misfire even though other cylinders may be okay. The P0303 is where I would look the most for troubleshooting. MAF and air intake leaks are very common causes.

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