# Distances under kelvin transformation

a part of my task is to show that you can express

$$\int\limits_{S_{1/2}(1/2 e_1)} \dfrac{1}{\vert x-z \vert ^n} \ dH(z)$$

as

$$\int\limits_{S_{1/2}(1/2 e_1)} \dfrac{1}{\vert x \vert ^n \vert z \vert ^n \vert \vert z^{*}-x^{*} \vert^n} \ dH(z)$$

where $$x \in B_{1/2}(1/2 e_1)$$ and $$x^{*}= \dfrac{x}{\vert x \vert ^2}$$.

I tried different approaches but didn't success, for example I've tried to transform the integral into an integral over the 1-sphere but I still dont know how to solve the problem. Does anyone have any advices for me?