$$x \operatorname{sign}{\left(x + 2 \right)} + \left|{x + 2}\right|$$
2*(x*DiracDelta(2 + x) + sign(2 + x))
$$2 \left(x \delta\left(x + 2\right) + \operatorname{sign}{\left(x + 2 \right)}\right)$$
2*(3*DiracDelta(2 + x) + x*DiracDelta(2 + x, 1))
$$2 \left(x \delta^{\left( 1 \right)}\left( x + 2 \right) + 3 \delta\left(x + 2\right)\right)$$