Error in the integration result

Given the joint p.d.f.:

for -\infty < x, y < \infty

I'm trying to compute the expected value: by the following code:

syms x y
pi = sym('pi'); 
fxy = (1/pi)*exp(-((x-1)^2+2*y*(x-1)+2*y^2)); 
Exy = int(int(x*y*fxy,x,-inf,inf),y,-inf,inf)

However, I got the following solution

I started to wonder if this function is not integrable in the first place. However, the answer was no. I computed the same integral by Wolfram Alpha (no offense...) and got the following result:

Am I doing something wrong in my code? Do you have any idea how to obtian the same result in MATLAB? I appreciate your help.

Answer 1

[Paul]

Expected result after expand() and simplify() of fxy. Don't know why these operations are needed.

syms x y
Pi = sym(pi); %  modified
fxy = (1/Pi)*exp(-((x-1)^2+2*y*(x-1)+2*y^2)); 
Exy = int(int(x*y*simplify(expand(fxy)),x,-inf,inf),y,-inf,inf)

Exy = 

Actually, the simplify() is not needed

syms x y
Pi = sym(pi); % modified 
fxy = (1/Pi)*exp(-((x-1)^2+2*y*(x-1)+2*y^2)); 
Exy = int(int(x*y*expand(fxy),x,-inf,inf),y,-inf,inf)

Exy = 

[Daigo]

I have no idea why we have to expand the polynomial before integration...but I'm glad to know it works in this way. Thanks!