A) \[2\log (\log x)+c\]
B) \[\log [\log (\log x)]+c\]
C) \[\log (x\log x)+c\]
D) None of these
Correct Answer: B
Solution :
\[\int_{{}}^{{}}{\frac{dx}{x\log x\,.\,\log (\log x)}}\] Put \[\log x=t,\] then it reduces to \[\int_{{}}^{{}}{\frac{dt}{t\,.\,\log (t)}}\] Again put \[\log t=z,\] then reduces form is \[\int_{{}}^{{}}{\frac{dz}{z}}=\log z=\log [\log (\log x)]+c\].
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