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1. Download the Extension
Visit the official page here http://elaix.org/download.html and download the current version link. For February 2017, the actual link is http://elaix.org/files/elaix/article/download/eLAIX-4.1.oxt.
2. Install the Extension
Run LibreOffice Writer and go to menu Tools > Extension Manager > click Add > choose the .oxt file you've downloaded > click Open > click Agree to the license (don't worry it's free software, it respects your freedom).
4. Restart Writer
Restart LibreOffice and you should notice the change.
5. What You Get
By installing eLAIX, you get a new toolbar and a new menu. They are both the same, contain all buttons of eLAIX. You should notice the green "Export EPUB Document" button on the left.
Here is the example of my EPUB document being read on Calibre: