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Problem/EM-2034 Application of Gauss law to an Integral

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\(\newcommand{\Prime}{{{\,}^\prime}}\)
Approaching the problem of electric field for a uniformly charged sphere in two different ways, find the value of the integral \begin{equation}   \vec{\mathcal E} = \frac{1}{4\pi\epsilon_0} \iiint d^3r\Prime  \frac{(\vec{r}-\vec {r}\Prime) }  {|\vec{r}-\vec{r}\Prime|^3}. \end{equation} where the integral runs over the volume of a sphere of radius \(R\).

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