A) \[1/\,\log \,x\]
B) \[\log \,x\]
C) \[\log \,\,\log \,x\]
D) \[x/\,\log \,x\]
Correct Answer: C
Solution :
We have \[\int{dx/(x\,\log x)=f(x)+\text{constant}}\] ??(i) Let \[\log \,x=t\] \[\Rightarrow \] \[\frac{1}{x}\,\,dx=dt\] \[\therefore \] \[\int{\frac{dx}{x\,\,\log \,x}}=\int{\frac{dt}{t}}=\log (t)+constant\] \[=\log \,(\log x)+\text{constant}\] On comparing with Eq. (i), we get \[f(x)=\log \,(\log x)\]
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