I am trying to solve an IVP problem and I seem to be stuck on it because I am getting an integration that seems very complicated and I think I messed up on it, I have my work so far below.

**1. The problem statement, all variables and given/known data**
Find the solution to the IVP

ty^'+7y=2t^2 e^2t, y(1)=7

Is this equation linear? Determine in what interval the solutions exist.

**2. Relevant equations**
**3. The attempt at a solution**
The image has my work so far, as you can see the integration for (t^7)(2te^2t) is a beast and that is why I think I am wrong so far. Here is the integration answer http://www.wolframalpha.com/input/?i=integrate+%28t^7%29%282te^%282t%29%29.