I have the same model laptop, no AppleCare. Battery 1 died a while back, so I bought a second. Thats been replaced 3 times already for free by Apple (had the Service Battery message on the last one that died - bring it in to the Genius bar and they'll test it, and likely give you a new one for free).
The tech was hinting at that they were having issues with Sony-based batteries. The new one I got this time was made by SMP, replacing a bad Sony. Not sure if there's truth to this or not, just what the tech told me.
LOL i had that model once too. My first battery literally expanded from the inside out as if out of pressure until the battery case broke open. The G-bar was baffled and never could figure it out. Oh well applecare just replaced it for free.