Example 2 Try to find the unit digit of the integer part of $(\sqrt{2}+\sqrt{3})^{2012}$.

 untranslated text remains unchanged:
将上面的文本翻译成英文，请保留源文本的换行和格式，直接输出翻译结果。 

This line is not translated as it seems to be an instruction and not part of the text to be translated. If you need this line translated as well, please let me know.