Find $ \int_0^2 \int_0^2\sqrt{5x^2+5y^2+8xy+1}\hspace{1mm}dy\hspace{1mm}dx$ I need the approximation to four decimals
Not sure how to start or if a closed form solution exists
All Ideas are appreciated

In Maple environment:
[> s:= Int(sqrt(5*x^2+8*x*y+5*y^2+1), x = 0 .. 2);
           /2                          (1/2)   
          |   /   2              2    \        
     s:=  |   \5 x  + 8 x y + 5 y  + 1/      dx
          |
          |                                    
         /0                                    

[> int(s, y = 0 .. 2, numeric);

                                  17.71654322

