Evaluate: $$ \int_0^2\int_0^{2-x}(x+y)^2 e^{2y\over x+y}dy dx. $$
My attempt: I've changed the order and got this as $$ \int_{y=0}^2\int_{x=0}^{2-y}(x+y)^2 e^{2y\over x+y}dy dx. $$ and then substituted ${2y\over x+y}=t$ so the integral becomes $$ 8\int_{y=0}^2\int_{t=y}^{2}e^t t^{-4}\,dt\,y^3 dy $$ from here it's becoming very absurd. Please help me to solve easily from here onward, any other short cut will be very benefited. Thanks in advance.