How would we plot: $$\int - \frac {W(-\ln x)}{\ln x} dx$$ Where $W$ is the Lambert W function?


closed as off-topic by b3m2a1, eyorble, MarcoB, Johu, Henrik Schumacher Apr 16 at 18:41

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  • 1
    $\begingroup$ Is LambertW easily found in the docs? I couldn't find anything about it. $\endgroup$ – m_goldberg Apr 15 at 2:08
  • 2
    $\begingroup$ LambertW is an alias for ProductLog. $\endgroup$ – Somos Apr 15 at 2:22
  • 1
    $\begingroup$ I don't really know anything about this topic, but isn't this the same as PolyLog? (See the diagram when you search for ReImPlot) $\endgroup$ – Carl Lange Apr 16 at 15:49

Put this all here but this works:

lambs =
    {x, NIntegrate[-LambertW[-Log[y]]/Log[y], {y, .1, x},
      MaxRecursion -> 200]},
    {x, 0, 1.6, .01}


If you take this out to x=10 and plot both the real and imaginary parts:

  Transpose[{lambs[[All, 1]], Im@lambs[[All, 2]]}]


 f[x_] := NIntegrate[-LambertW[-Log[y]]/Log[y], {y, .1, x}]
 Plot[{Re[f[x]], Im[f[x]]}, {x, 0, 10}]

enter image description here


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