# 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?

• Is LambertW easily found in the docs? I couldn't find anything about it. Apr 15, 2019 at 2:08
• LambertW is an alias for ProductLog. Apr 15, 2019 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) Apr 16, 2019 at 15:49

## 2 Answers

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}]