A) \[\log (1+\log x)\]
B) \[\log \log (1+\log x)\]
C) \[\log x+\log (\log x)\]
D) None of these
Correct Answer: A
Solution :
\[\int_{{}}^{{}}{\frac{dx}{x+x\,\,\log x}}=\int_{{}}^{{}}{\frac{dx}{x(1+\log x)}}\] Now putting \[1+\log x=t\Rightarrow \frac{1}{x}\,dx=dt,\] it reduces to \[\int_{{}}^{{}}{\frac{dt}{t}}=\log (t)=\log (1+\log x)\].
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