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Homework Statement:
 What's the electrostatic energy associated with two concentric shells with radii ##a## and ##b##, ##b > a##? The outer shell has a charge of ##q##, the inner shell's charge is ##q##
Relevant Equations:

##W = \frac{\epsilon_{0}}{2}\int \vec{E}² d \tau##
##W = \frac{1}{2} \int \rho V d \tau##
I know the energy is ##\frac{q²}{ 8 \pi \epsilon_{0}}( \frac{1}{a}  \frac{1}{b})##, but I can't get this result using the second equation.
What I did:
##W = \frac{1}{2} \int \rho V d \tau ##
##\rho = \frac{q}{ \frac{4}{3} \pi r³}, a < r < b ##
##V = \frac{q}{4 \pi \epsilon_{0} r}##
## W = \frac{ 3 q²} {16 \pi² \epsilon_{0}} \int 4 \pi \frac {r²}{r⁴} dr = \frac{3 q²}{ 8 \pi \epsilon_{0}}( \frac{1}{a}  \frac{1}{b})##
I didn't get rid of that factor of 3, where did I go wrong?
What I did:
##W = \frac{1}{2} \int \rho V d \tau ##
##\rho = \frac{q}{ \frac{4}{3} \pi r³}, a < r < b ##
##V = \frac{q}{4 \pi \epsilon_{0} r}##
## W = \frac{ 3 q²} {16 \pi² \epsilon_{0}} \int 4 \pi \frac {r²}{r⁴} dr = \frac{3 q²}{ 8 \pi \epsilon_{0}}( \frac{1}{a}  \frac{1}{b})##
I didn't get rid of that factor of 3, where did I go wrong?