Let $f\left(x\right)$ be a differentiable non-decreasing function such that $\underset{0}{\overset{x}{\int }}\left(f{\left(t\right)}^3\right)dt=\frac{1}{x^2}{\left(\underset{0}{\overset{x}{\int }}f\left(t\right)dt\right)}^3\forall x\in R-\left\{0\right\}$ and $f\left(1\right)=1$. If $\underset{0}{\overset{x}{\int }}f\left(t\right)dt=g\left(x\right)$, then $\frac{x{g}^{\text{'}}\left(x\right)}{g\left(x\right)}$ is