Hora de ler a documentação. De Instalando o driver e configurando o CLASSPATH :
Once you have extracted the distribution archive, you can install the driver by placing mysql-connector-java-version-bin.jar in your classpath, either by adding the full path to it to your CLASSPATH environment variable, or by directly specifying it with the command line switch -cp when starting the JVM.
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You can set the CLASSPATH environment variable under Unix, Linux, or OS X either locally for a user within their .profile, .login or other login file. You can also set it globally by editing the global /etc/profile file.
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If you are developing servlets or JSPs, and your application server is J2EE-compliant, you can put the driver's .jar file in the WEB-INF/lib subdirectory of your webapp, as this is a standard location for third party class libraries in J2EE web applications.