Answer
\[\ln \left| {\ln x} \right| + C\]
Work Step by Step
\[\begin{gathered}
\int_{}^{} {\frac{1}{{x\,\left( {\ln x} \right)}}dx} \hfill \\
Set\,\,u = \ln x\,\,,\,So\,\,that\,\,du = \frac{1}{x}dx \hfill \\
Then \hfill \\
\int_{}^{} {\frac{1}{{x\,\left( {\ln x} \right)}}dx} = \int_{}^{} {\frac{1}{u}du} \hfill \\
Integrating \hfill \\
\ln \left| u \right| + C \hfill \\
Substituting\,\,u = \ln x\,\,gives \hfill \\
\ln \left| {\ln x} \right| + C \hfill \\
\end{gathered} \]
