What substitution do I use for simple regions integration?

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Let $G=\{(x,y)\in \mathbb{R}^2 : 4\leq x^2-y^2\leq 5,x\geq 6y,y\geq 0\}$. Calculate $$ \iint _G 4(x^2-y^2)\frac{x-y}{x}\,dA $$

I'm pretty sure I could solve it further but can't seem to get a right substitution.