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Requirement
TexMaths makes use of LaTeX program in your system to produce the output on LibreOffice document. So of course to run it you need LaTeX itself. In Ubuntu, it's enough to install texlive-latex-base package with its small dependencies:
$ sudo apt-get install texlive-latex-base
1. Download The Extension
Download the latest TexMaths extension from https://extensions.libreoffice.org/extensions/texmaths-1. At this 17 February 2017, the latest version is 0.42. I can install and run it on LibreOffice 5.2 on Ubuntu 16.10. The LibreOffice extension file format is .oxt.
2. Install The Extension
Visit menu Tools > Extension Manager > click "Add" button > select .oxt file you have downloaded > click "Open" > the extension installed.
3. Restart LibreOffice
Close LibreOffice and start it again.
4. Start Writing Equations
Now you see a new TexMaths toolbar on your window. Start typing LaTeX syntax such as \int_{a}^{b} f (x) d x > highlight the syntax > press the blue pi button on TexMaths toolbar. The result should be like this.
Syntax References
If you need references about writing LaTeX syntax for mathematical expressions, here are good links: