I am pretty sure that, it costs the same as sending it anywhere else. I looked it up, as long as you do Flat Rate then it should just be the same as shipping it anywhere else.
Someone else just answered back to me on the same question and they said 'Yeah I can ship free to Alaska, I will ship it USPS Flat Rate, it doesn't matter if I ship to Michigan or Up to Alaska, it's the same rates'. Does that help at all?