$\begin{align}  & \int{\frac{1}{x}{{({{\log }_{e}}x)}^{3}}dx} \\ & \text{Let }u={{\log }_{e}}x \\ & \frac{du}{dx}=\frac{1}{x},\text{  }dx=xdu \\ & \int{\frac{1}{x}{{({{\log }_{e}}x)}^{3}}dx}=\int{\frac{1}{x}{{(u)}^{3}}xdu}=\int{{{u}^{3}}du} \\ & \int{\frac{1}{x}{{({{\log }_{e}}x)}^{3}}dx}=\frac{{{u}^{4}}}{4}+C=\frac{1}{4}{{({{\log }_{e}}x)}^{4}}+C \\\end{align}$