You can but it is difficult to get to unless you know what you're doing; additionally, it should be registered to the car's computer to prevent down the road issues. I would find a competent independent shop that knows these cars and it will be less expensive.
I somewhat disagree with George T. Removal of the battery is fairly simple. All you have to do is take the tire out of the trunk. And the jack out of its compartment. Remove the plastic under the Jack it just lifts out. That exposes the top of the battery. Disconnect the negative terminal first with a 10 mm wrench. The one in the toolkit in the trunk lid will work.But a socket works faster. Then disconnect the positive cable. Once you have the tire out you'll see the backside of the battery and there's one holddown bracket on the corner. Another 10 mm bolt. Remove the bracket. Slide the battery out. Any import shop with the coding tool can register the battery. Here's a video. They usually charge about 25 or $30 to register the battery. Takes about 15 minutes to register.
I totally agree with RICK and it is very simple to change the battery. The guy in the video used lead-acid battery from walmart, whereas I used AGM battery from advanceautoparts. The OEM for E65/E66 is AGM battery and it costs around $180, compared to $140ish at walmart.
The whole point of this forum, in my opinion, is to learn how to work on your own car and give the least amount of cash to the Stealership. And changing battery is even easier than changing oil except the registration part. If you are familiar with INPA, then it is actually a piece of cake.
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