Integration by parts.
Let \(u = lnx\) thus \(du = \frac{dx}{x}\)
Let \(dv = dx\) thus \(v = x\)
\(\int{\ln{x} dx} = x\ln{x} -\int{x\frac{dx}{x}} \)
\(\int{\ln{x} dx} = x\ln{x} - x + C \)