# How to plot: $\int - \frac {W(-\ln x)}{\ln x} dx$? [closed]

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 SchumacherApr 16 at 18:41

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• "This question arises due to a simple mistake such as a trivial syntax error, incorrect capitalization, spelling mistake, or other typographical error and is unlikely to help any future visitors, or else it is easily found in the documentation." – b3m2a1, eyorble, Johu, Henrik Schumacher
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• Is LambertW easily found in the docs? I couldn't find anything about it. – m_goldberg Apr 15 at 2:08
• LambertW is an alias for ProductLog. – Somos Apr 15 at 2:22
• 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) – Carl Lange Apr 16 at 15:49

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]]}]
}
]


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