I must verify the divergence theorem in the following case :

. And is the surface of the sphere .

My attempt :

.

I calculate the right hand side : .

So 3 times the volume of a sphere with radius , hence the triple integral is worth .

Now comes the problems. I ain't able to calculate .

A normal unit vector to the sphere is .

So the double integral is worth . And I'm stuck here because I have 3 variables ( , and ) but a double integral instead of a triple one.

I know I could solve the problem faster using spherical coordinates, but for the sake of my comprehension let's do it via Cartesian coordinates please.

Do you have any idea how could I continue, in order to reach the ?