Q: My BMW X3 2.5l running ruff the hand on mileage jumps when I start it up no check engine light has come on

It is possible that diagnostic trouble codes have set and a mechanic should attempt to retrieve those first using an appropriate scan tool. So long as the engine is mechanically sound (e.g., compression good; no sticky valve problems), typically rough running is due to fuel, ignition, or air induction faults. If you were to request a diagnostic from YourMechanic, the protocol is pretty standard: a certified mechanic will test for ignition, fuel system, air induction and/or engine sensor problems and these possibilities are tested, in a sequence, using a diagnostic "decision tree". Often, the problem is limited and straightforward, that is easily repairable. There is a good chance of that so I recommend that you request a rough running diagnostic and the responding certified mechanic will travel right to your location and get this diagnosed and resolved for you. If you have further questions or concerns, do not hesitate to re-contact YourMechanic.