Let $\mathbf{n}(x,y,z) $ be the vertical vector on the surface $S$, where $S$ is $$\frac{1}{9}x^{2} + \frac{1}{16}y^{2}+\frac{1}{12}(z-1)^{4} = 1$$ and let $\mathbf{r}=(x,y,z) $. Then calculate $$\int_{S}^{} \frac{r\cdot n}{r^{3}}dS $$
I have hard times trying to understand what this integral is. Is it equal to $\int_{S}^{}\frac{1}{x^{2}+y^{2}+z^{2}}dS$? I tried to use surface integral and I tried to use parameters for this surface but it seems so difficult. I don't think that's the point in this exercise. I think that I have to notice something that I can't find.