If you own a bmw you know that transfer case is one very sensitive thing, especially on x3 or e83.
You should replaced every 60 000 km, but this is how it looks on my after 1 year or 15 000 km.
You need 0.7 liter of oil, bmw original oil costs a lot, so alternative is ravenol oil tf-0870.
To change it you don’t need anything except 16mm wrench. First you unscrew bottom drain screw and than fill it up with pump or injection. When it is start to leak from top screw you fill enough oil in it.
After that you must perform adaption with bmw dis or inpa tool. You can purchase it on ebay.