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**1. Homework Statement**

I'm trying to understand the Variation of Parameters in ODEs and I came up to this following expression which i cannot solve:

[tex]{2\,{e}^{-t}{e}^{-3\,t}\choose {e}^{-t}{e}^{-3\,t}} \int {\,{e}^{t} {e}^{\,t}\choose {e}^{3t}{2e}^{-3\,t}} {10\,\cos \left( t \right) \choose 2\,{e}^{-t}}[/tex]

Can I just integrate each individual component or must I use matrix multiplication first? If anyone could help me I would appreciate it greatly. I'm not sure how to even start on this so I don't have any work to show.