(x^-2)(y^-2)*((y)+(x^2)(y^2))dx

I assume you want to integrate this with respect to "x"  ??

Simplifying this , first, we have

(y + x^2*y^2) / [(x^2)(y^2)]  =

1/(x^2*y) + 1 =

(1/y)(1/x^2) +1  ........and integrating this, we have

(1/y)∫x^(-2) dx   + ∫ (1) dx =

(1/y) [-x^(-1)] + x  + C  =

x - 1/(xy) + C