Question

\[\int\frac{\log \left( \log x \right)}{x} dx\]

Answer 1

\[\int\frac{\log \left( \log x \right)}{x}dx\]
`  "Taking log  log x as the first function and   "1/x "as the second function" . `
\[ = \text{ log }\log x\int\frac{1}{x}dx - \int\left\{ \frac{d}{dx} \text{ log }\left( \log x \right)\int\frac{1}{x}dx \right\}dx\]
\[ = \log x . \text{ log }\left( \log x \right) - \int\frac{1}{x \log x}\left( \log x \right)dx\]
\[ = \log x . \text{ log }\left( \log x \right) - \int\frac{1}{x}dx\]
\[ = \log x . \text{ log }\left( \log x \right) - \log x + C\]