Answer
$\int_e^6\frac{dx}{xlnx}=ln(ln6)$
Work Step by Step
Consider $lnx=u$ and $\frac{1}{x}dx=du$
Thus, $\int_e^6\frac{dx}{xlnx}=\int_1^{ln6} \frac{du}{u}$
$=|lnu|_1^{ln6}$
$=|ln(ln6)-ln1|$
Hence, $\int_e^6\frac{dx}{xlnx}=ln(ln6)$
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