Coulomb’s Law

$\overrightarrow{E}(\overrightarrow{x})=\frac{1}{4\pi {\epsilon }_0}\int \frac{\overrightarrow{x}-{\overrightarrow{x}}^{\prime }}{|\overrightarrow{x}-{\overrightarrow{x}}^{\prime }{|}^3}\rho ({\overrightarrow{x}}^{\prime })d^3{x}^{\prime }=\frac{1}{4\pi {\epsilon }_0}\int \mathrm{\nabla }\frac{-1}{|\overrightarrow{x}-{\overrightarrow{x}}^{\prime }|}\rho ({\overrightarrow{x}}^{\prime })d^3{x}^{\prime }$