The problem has nothing to do with gmail integration. The problem is with eclipse
"Unable to execute dex: Java heap space" and "Conversion to Dalvik format failed: Unable to execute dex: Java heap space"
This comes when the eclipse has memory related issues. Try restarting eclipse and/or your system. It should work.
Also you might want to make changes to your eclipse.ini file and increase the ram for eclipse so that this does not happen in the future.
You can do this by following the link:
Increasing heap space in Eclipse: (java.lang.OutOfMemoryError)
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solved Whenever i try for gmail login integration in app every time i run it shows same error [closed]