Differential calculus: integrate $\frac{1}{x \log^3 (x)}$ I would like a step by step description of how to integrate $$\frac{1}{x \log^3 (x)}$$


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*I know that the answer is - $\frac{1}{2\log^2(x)}$ 

*and that the integral of $\frac{1}{\log^2(x)}$ is $\frac{1}{\log(x)}$

*and that the integral of $\frac{1}{\log(x)}$ is $\log(\log(x))$


But I don't see how these are obtained.

Make the substitution $u=\log x$, then $du=\frac1x\,dx$ and the integral becomes $\int u^{-3}\,du$.
