It's paid, some $33 when I purchased a year or two back. If you're looking for speed while typing up notes, the fastest I've found is the add-on OneNote Gem (Gem for OneNote 2016). Unfortunately, this type of equations is not at all supported by the online, Android or iOS OneNote. The name Microsoft uses is "Math AutoCorrect", and the (limited) configuration is in Options -> Proofing -> AutoCorrect Options -> Math AutoCorrect tab. The best documentation I found is the pdf titled "Unicode Nearly Plain-Text Encoding of Mathematics" (formerly linked to from a somewhat helpful OneNote help page). Try typing this while editing text (what you'll see happening might feel confusing the first time): is pretty quick to learn, but does suffer from very obscure documentation and configuration. The only thing I haven't been able to do are commutative diagrams with too many arrows. It supports most things you'd want: matrices, subscripts, superscripts, blackboard bold, etc. To expand on Joe's answer, while there is no support for actual LaTeX, the LaTeX like language Joe describes is very powerful and convenient. You will need to set up and administer a web server (and most likely a database server as well) in order to use wiki software, but in the long term, and especially if you are serious about having a space to collect your stuff, this is the superior solution. I personally use Confluence, but free alternatives are available (the example that first comes to mind is MediaWiki, which powers Wikipedia, and it has comprehensive LaTeX support). That being said, if you'd like to have a note-taking application together with LaTeX mathematics, I suggest turning to a wiki software that supports advanced typeset mathematics.
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