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, \[{{\log }^{r+1}}(x)=t\] \[\therefore \] \[dt=\frac{1}{x\cdot \,\log \,(x){{\log }^{2}}(x)...log\,(x)}dx\] \[\therefore \] \[\int{{{\{x\,(\log \,x)\,{{\log }^{2}}(x)...{{\log }^{r}}(x)\}}^{-1}}dx}\] \[=t+C\] \[={{\log }^{r+1}}(x)+C\]You need to login to perform this action.
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