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Hey. I want to use integrals-math to get from Gauss law in divergence form to the one in integral form. I know you can do it by simply accepting ∇*E dV = ρ/ε => ∫ ∇*E dV= ∫ρ/εdV = Q/ε = ∫E*dA, but I wanna do it another way. I want to begin with ∫∇*E*dV and end up with Q/ε.

So: E = Q*v/(4pi*ε*|r|

Thus,

∫∇*EdV = ∫∇*v*[Q/(4pi*ε*|r|

Q/(4pi*ε)*∫(1 + 1 +1)*|r|

However, I can't seem to solve the integral ∫|r|

So: E = Q*v/(4pi*ε*|r|

^{2}), where v is the directional vector of r: v= D/|r| = [x,y,z]/√(x^{2}+y^{2}+z^{2}).Thus,

∫∇*EdV = ∫∇*v*[Q/(4pi*ε*|r|

^{2})] dV = Q/(4pi*ε)*∫ ∇*D*|r|^{-3}dV =Q/(4pi*ε)*∫(1 + 1 +1)*|r|

^{-3}dV = 3*Q/(4pi*ε)*∫|r|^{-3}dV.However, I can't seem to solve the integral ∫|r|

^{-3}dV using spherical coordinates, as I get that it is infinitely large.. So can you guys assist me? Does perhaps ∫|r|^{-3}dV = |r|^{-3}∫ dV = 4pi/3?
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