This question is specific only to TeX4ht.
When using MathJax mode in tex4ht, it fails to render the section title which contains $\ln$, but it works for all other symbols I tried so far.
What is so special about $\ln$?
MWE
\documentclass[11pt]{article}%
\usepackage{amsmath}
\begin{document}
This is a document
\section{$\int \arcsin(x) \ln x \,dx$}
test
\section{$\int \arcsin(x) \sqrt x \,dx$}
test
\section{$\int \arcsin(x) \sin x \,dx$}
\end{document}
It must be compiled as follows to see the problem:
make4ht -ulm default foo.tex "htm,1,mathjax"
In the above, the split level is 1. Anything more than 0 is needed to show the problem.
Now the HTML looks like this:

Not using mathjax mode with tex4ht also solves the problem.
Here is the raw HTML generated. Notice that \qopname \relax o{ln}x is generated by tex4ht before mathjax does anything.
<!DOCTYPE html>
<html lang="en-US" xml:lang="en-US" >
<head><title></title>
<meta charset="utf-8" />
<meta name="generator" content="TeX4ht (http://www.tug.org/tex4ht/)" />
<meta name="viewport" content="width=device-width,initial-scale=1" />
<link rel="stylesheet" type="text/css" href="foo.css" />
<meta name="src" content="foo.tex" />
<script type="text/x-mathjax-config"> MathJax.Hub.Config({ 'fast-preview': {disabled: true}, TeX: { extensions: ["color.js","AMSmath.js"], equationNumbers: { autoNumber: "AMS" } }, extensions: ["tex2jax.js"], tex2jax: { inlineMath: [ ["\\\(","\\\)"] ], displayMath: [ ['$$','$$'], ["\\[","\\]"] ], processEscapes: true, processEnvironments: true } }); </script>
<script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/latest.js?config=TeX-AMS-MML_HTMLorMML"></script>
</head><body
>
<!--l. 6--><p class="noindent" >This is a document
</p>
<div class="tableofcontents">
<span class="sectionToc" >1 <a
href="#x1-10001" id="QQ2-1-1">\(\int \arcsin (x) \qopname \relax o{ln}x \,dx\)</a></span>
<br /> <span class="sectionToc" >2 <a
href="#x1-20002" id="QQ2-1-2">\(\int \arcsin (x) \sqrt x \,dx\)</a></span>
<br /> <span class="sectionToc" >3 <a
href="#x1-30003" id="QQ2-1-3">\(\int \arcsin (x) \sin x \,dx\)</a></span>
</div>
<h3 class="sectionHead"><span class="titlemark">1 </span> <a
id="x1-10001"></a>\(\int \arcsin (x) \ln x \,dx\)</h3>
<!--l. 9--><p class="noindent" >test
</p><!--l. 11--><p class="noindent" >
</p>
<h3 class="sectionHead"><span class="titlemark">2 </span> <a
id="x1-20002"></a>\(\int \arcsin (x) \sqrt x \,dx\)</h3>
<!--l. 12--><p class="noindent" >test
</p><!--l. 14--><p class="noindent" >
</p>
<h3 class="sectionHead"><span class="titlemark">3 </span> <a
id="x1-30003"></a>\(\int \arcsin (x) \sin x \,dx\)</h3>
</body>
</html>
Is this a bug in TeX4ht? I will also report this to texh4t bug tracking now and add a link to this post (it easier to explain this here as one can add screen shots).
I am using TeX Live 2019 on Linux.
