\frac{1}{6}\ln \left|\left(\frac{\sqrt[3]{1+\ln ^3x}}{\ln  x}\right)^2+\frac{\sqrt[3]{1+\ln ^3x}}{\ln  x}+1\right|-\frac{1}{3}\ln |\frac{\sqrt[3]{1+\ln ^3x}-\ln  x}{\ln  x}| -\frac{\sqrt{3}}{3}\text{arctan}\left[\frac{1+2 \frac{\sqrt[3]{1+\ln ^3x}}{\ln  x}}{\sqrt{3}}\right]+C