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JEE Main & Advanced Sample Paper JEE Main Sample Paper-47

  • question_answer
    If\[{{I}^{r}}\] means \[\log \log ...x,\] the log being repeated/-times, then \[\int{{{\{x\,\log \,x\,{{\log }^{2}}\,(x)...\,{{\log }^{r}}\,(x)\}}^{-1}}dx}\]is equal to

    A)  \[{{\log }^{r+1}}(x)+C\]   

    B)  \[\frac{{{\log }^{(r+1)}}(x)}{r+1}+C\]

    C)  \[{{\log }^{r}}(x)+C\]                    

    D)  None of these

    Correct Answer: A

    Solution :

     Put, \[{{\log }^{r+1}}(x)=t\]          \[\therefore \]    \[dt=\frac{1}{x\cdot \,\log \,(x){{\log }^{2}}(x)...log\,(x)}dx\] \[\therefore \]    \[\int{{{\{x\,(\log \,x)\,{{\log }^{2}}(x)...{{\log }^{r}}(x)\}}^{-1}}dx}\] \[=t+C\] \[={{\log }^{r+1}}(x)+C\]


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