Multiple integral what am i doing wrong? $$ \iint _d (x-y)^2*{{{e^y}^+}^z} \qquad   d:x-y\ge -1,x-y\le1,x+y\ge1,x+y\le3  $$
i was trying to separate   it to two multiple integral integrals but i cant integrate this integral, i was trying to Integrate  by parts and replacing the variables like so $$ u=x+y \quad du=dx \quad $$ 
and then integrate by parts like so $$ f=u^2\quad df=fu \quad dg=e^u \quad g=e^2 $$
but it dosent work
thanks

It might be more interesting to substitute your variables in a way such that the boundaries become simpler expressions. At first glance you notice that both the integral and the boundary expressions only contain terms of $x+y$ and $x-y$ so you might want to try the substitution: 
$$
x+y = u \\
x-y = v
$$
The boundary conditions then become:
$$
-1\le v \le 1 \\
1 \le u \le 3
$$
and by using the transformation formula for double integrals, the new integral becomes:
$$
\int_{-1}^1dv\int_1^3 v^2 e^u |\left| 
\begin{array}{c c}
\frac{\partial x}{\partial u} & \frac{\partial x}{\partial v} \\ 
\frac{\partial y}{\partial u} & \frac{\partial y}{\partial v}
\end{array}\right|| du =\frac{1}{2}\int_{-1}^1dv\int_1^3 v^2 e^u du
$$
