Separable Equations - Calculus II

I'm working on this problem:
du/dt = 2+2u+t+tu

I tried this:

1 du = (2+2u+t+tu) dt
int du = int (2+2u+t+tu)dt

and then was unsure how to proceed. Can someone point me in the right direction?

write it as

du/dt = u(2+t) + (2+t)
du/dt - u(2+t) = (2+t)
du/dt\cdot e^{2t+t^2/2} - u(2+t)\cdot e^{2t+t^2/2} = (2+t)\cdot e^{2t+t^2/2}
d/dt(u \cdot e^{2t+t^2/2} ) = (2+t)\cdot e^{2t+t^2/2}

integrate with respect to t on both sides, you do the rest.