Please reason step by step, and put your final answer within \boxed{}.
Given the function $f(x)=({x}^{3}-x)(\frac{1}{2}-\frac{1}{{e}^{x}+1})$, the solution set of the inequality $f\left(x\right)\ln \left(x+2\right)\leqslant 0$ is ______.
user