As long as your washing machine tub can handle 3.7 cubic feet then you should be able to safely wash your king size comforter in a standard washing machine.
That is as long as you don't put anything else into the washing machine and only wash the king size comforter itself.
If your washing machine is not big enough then it may be best to take your king size comforter to the laundry mat where there's bigger washing machines.