Gem files will remain installed in /var/www/discourse/vendor/bundle/ruby/2.5.0/gems/mysql2-0.5.2 for inspection.
Results logged to /var/www/discourse/vendor/bundle/ruby/2.5.0/extensions/x86_64-linux/2.5.0-static/mysql2-0.5.2/gem_make.out
An error occurred while installing mysql2 (0.5.2), and Bundler cannot continue.
Make sure that
gem install mysql2 -v '0.5.2' --source 'https://rubygems.org/'succeeds before bundling.
I found the best way to solve the problem.
I think that you may missing the dev library of mysql:
sudo apt-get install libmysqlclient-dev
On Red Hat/CentOS and other distributions using yum:
sudo yum install mysql-devel
On Mac OS X with Homebrew:
brew install mysql