Answer
\[\frac{{\,{{\left( {\log x} \right)}^2}}}{2}\ln 10 + C\]
Work Step by Step
\[\begin{gathered}
\int_{}^{} {\frac{{\log x}}{x}dx} \hfill \\
Let\,\,u = \log x\,\,,\,\,So\,\,That \hfill \\
du = \frac{1}{{\ln 10\,\left( x \right)}}dx \hfill \\
Then \hfill \\
\int_{}^{} {\frac{{\log x}}{x}dx} = \,\,\ln 10\int_{}^{} {\log x\,\left( {\frac{1}{{x\log \,10}}} \right)dx} \hfill \\
= \ln 10\int_{}^{} {udu} \hfill \\
Integrating\, \hfill \\
= \frac{{{u^2}}}{2}\ln 10 + C \hfill \\
Substituting\,\,u = \log x\,\,gives \hfill \\
\frac{{\,{{\left( {\log x} \right)}^2}}}{2}\ln 10 + C \hfill \\
\end{gathered} \]
