Fragment: On Artaeum has been in my inventory ever since I cleared Bleak Falls Barrow (or whatever its called) way back at the beginning of the game...

Like all quest items you can't drop it.... and I'm cool with that...

I finally got the quest to turn in Fragment: On Artaeum to the Orc at the Mage's college.

The NPC would not take the book in my inventory and instead I was told to retrieve the book from Bleak Falls Barrow.

I returned to the cave, and cleared it all over again and in the chest where the quest marker led... there was no book.

The quest never updated and Now I have a quest stuck in my log, and a book stuck in my inventory.