Answer
\[\ln |\ln x|+C\]
Where $C$ is constant of integration
Work Step by Step
Let \[I=\int\frac{1}{x\ln x}dx\;\;\;...(1)\]
Make a substitution $\;t=\ln x$ ___(2)
\[\Rightarrow dt=\frac{1}{x}dx\]
(1) becomes
\[I=\int\frac{1}{t}dt\]
\[I=\ln |t|+C\]
Where $C$ is constant of integration
Using (2)
\[I=\ln |\ln x|+C\]
Hence \[I=\ln |\ln x|+C\;\;.\]
