1/(xlnx) Step by step if you can please.
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$\displaystyle \displaystyle \int{\frac{1}{x\ln{x}}\,dx} = \int{\frac{1}{\ln{x}}\,\frac{1}{x}\,dx}$. Now make the substitution $\displaystyle \displaystyle u =\ln{x} \implies \frac{du}{dx} = \frac{1}{x}$.
Hint: $\displaystyle \displaystyle \int\frac{1}{x\ln{x}} \;{dx} = \int\frac{(\ln{x})'}{\ln{x}}\;{dx}$.
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