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

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    $\begingroup$ Is LambertW easily found in the docs? I couldn't find anything about it. $\endgroup$
    – m_goldberg
    Apr 15, 2019 at 2:08
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    $\begingroup$ LambertW is an alias for ProductLog. $\endgroup$
    – Somos
    Apr 15, 2019 at 2:22
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    $\begingroup$ 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, 2019 at 15:49

2 Answers 2

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Put this all here but this works:

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

ListLinePlot[lambs]

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

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

asdasd

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$\begingroup$ 
 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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