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Question
\[\int\frac{1}{ x \text{log x } \text{log }\left( \text{log x }\right)} dx\]
Sum
Solution
` Note: "Here, we are considering log x as" log_e x . `
\[\text{Let I }= \int\frac{1}{x \log x \log\left( \log x \right)}dx\]
\[Putting \log\left( \log x \right) = t\]
\[ \Rightarrow \frac{1}{x\log x} = \frac{dt}{dx}\]
\[ \Rightarrow \frac{1}{x \log x}dx = dt\]
\[ \therefore I = \int\frac{dt}{t}\]
\[ = \log\left| t \right| + C\]
\[ = \log\left| \text{log}\left( \ logx \right) \right| + C \left[ \because t = \text{log}\left( \text{log x} \right) \right]\]
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