Answer
$$\int \frac{dx}{xlnx-x}= ln\left| lnx -1\right |+C$$
Work Step by Step
$$\int \frac{dx}{xlnx-x}=\int \frac{dx}{x(lnx-1)}$$
$$\int \frac{1}{lnx-1}d(lnx)= ln\left| lnx -1\right |+C$$
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