$ sudo apt-get update
$ sudo apt-get install dsyslog-module-mysql 

dsyslog-module-mysql is installed in your system.

Make ensure the dsyslog-module-mysql package were installed using the commands given below,

$ sudo dpkg-query -l | grep dsyslog-module-mysql *

You will get with dsyslog-module-mysql package name, version, architecture and description in a table

dsyslog-module-mysql package basic information: