\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
  1. Find the derivative of \(f(x) = x\ln(x)-x\).
    \(\frac{d}{dx}(x\ln(x)-x)=\)
  2. Hence, find the indefinite integral \(\displaystyle\int \ln(x) \,dx\).
    \(\displaystyle\int \ln(x) \,dx =\)