Question

\[\int\frac{1}{x \log x} dx\]

Answer 1

\[\text{Here, we are considering }\text{log x  as} \log_e x . \]
\[\text{Let I} = \int\frac{1}{x \log x}dx\]
\[\text{Putting }\log x = t\]
\[ \Rightarrow \frac{1}{x} = \frac{dt}{dx}\]
\[ \Rightarrow \frac{1}{x}dx = dt\]
\[ \therefore I = \int\frac{1}{t}dt\]
\[ = \text{log} \left|  \text{log x} \right| + C\]