Consider
$$ A = \int_1^{\infty} \int_1^{\infty} f(x,y) \space dx \space dy $$
$$ B = \int_1^{\infty} f(x,y) \space dx $$
$$ C = \int_1^{\infty} f(x,y) \space dy $$
$$ D = \int_1^{\infty} \int_1^{\infty} f(x,y) - f(y,x) \space dx \space dy $$
Where $A,B,C$ converge to a positive real value. $D$ also converges to a real value , but not necc positive. $A$ has a closed form but $B$ , $C$ and $D$ do not.
What are typical solutions for $f(x,y) $ ? And how to find them ?