To maintain a cleaner look of your ThingWorx server access URL, whether for production or convenience reasons, you may look into setting up redirection.
This is a quick example on how to redirect <your.main.url.com> to <your.main.url.com/Thingworx>
Go to the /<apache-tomcat-directory>/webapps/ROOT/ and find the "index.jsp" file. Copy that file for backup purposes and replace with a new one, containing the following:
Please note that once the URL is hit, it will still append the rest of the /Thingworx query in the address bar (i.e keep the "redirected to" address).
You may also utilize this to have your <main.url.com> redirect to one of the mashups. This was the user, with proper permissions in place, may access the mashup directly, bypassing the Composer.