Changes

= \abs{x} p \abs{x}^{-1} p \abs{x} - \tfrac{1}{2} \abs{x} ( \laplace \abs{x}^{-1} ) \abs{x}

= \abs{x} p \abs{x}^{-1} p \abs{x} - \tfrac{1}{2} \abs{x} 4 \pi \delta(0) \abs{x}