CrunchGear did a tear down of Kindle 2 which is probably similar to the DX and says the battery looks like it's pretty easy to replace yourself if the time comes.
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Most interestingly the battery is actually easy to find and attack, given enough patience. Because this is basically a press-fit case, you need to use annoying iPod opening tools which will definitely void your warranty. However, it does mean you could potentially bybass Amazon’s $60 battery replacement fee if you were so inclined.
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The $109
2 year extended warranty (available in the U.S. only) includes battery replacement.
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One time claim for battery malfunction during second year of coverage
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I'd probably go for the self-install.