How do I solve the following two integrals over the unit sphere? $$\iint_S \vec{r_0}\otimes\vec{r_0}dS \\ \iint_S \vec{r_0}\otimes\vec{r_0}\otimes\vec{r_0}\otimes\vec{r_0}dS$$ I undestand I should use the divergence theorem somehow but I'm not sure how.
My attempt at the first goes like:
$$\iint_S \vec{r_0}\otimes\vec{r_0}dS=\iint_S d\vec{S}\otimes\vec{r_0}=\iiint\nabla\otimes\vec{r_0}dV$$ And since we were integrating over the unit sphere we can(?) replace $\vec{r_0} \rightarrow \vec{r}$ so: $$=\iiint\nabla\otimes\vec{r}dV=\iiint\hat{\delta}dV=\frac{4}{3}\pi\hat{\delta}$$ However I can't seem to use the same trick for more than two $r$'s multiplied with the tensor product since I get non-constant terms under the integral.
