Is -t the Correct Integrating Factor for this Diff Eq?

[jesuslovesu]

[SOLVED] Integrating Factor Diff Eqs

Homework Statement

g ' - g/t = t e^t

I'm trying to solve this, but I seem to have run into a problem, according to my book the integrating factor is 1/t, however I believe that it is -t

Homework Equations

The Attempt at a Solution

e^int(-1/t dt) = e^(-lnt) = -t
That is how I found the solution to all the problems requiring an integrating factor before however this situation seems to be different... Do I have the equation in the right form to find the integrating factor?

 

[Rainbow Child]

$$e^{-\ln t}=e^{\ln t^{-1}}=\frac{1}{t}$$