Apache – How to Redirect Port

I know there's a ton of answers to this question out there, but somehow none of them helped me. I have an Ubuntu running 3 webapps, each on different port (8080-8282) – jira, confluence and one more. Now I bought a domain name and bound three subdomains with the IP address of my server, the problem is they all point to the same IP address and to port 80. So I guess I need Apache server now. Now what I want apache to do is to redirect:

• wiki.mydomain.com to http://wiki.mydomain.com:8080
• jira.mydomain.com to http://jira.mydomain.com:8181
• myapp.mydomain.com to http://myapp.mydomain.com:8282

Preferably so it won't show the port. From my understanding I should add some lines to /etc/apache2/httpd.conf, and so I tried (this is literally my whole /etc/apache2/httpd.conf):

RewriteEngine on
RewriteCond %{HTTP_HOST} http://jira.mydomain.com/
RewriteRule ^(.*)$ http://jira.mydomain.com:8181 [L,R]
RewriteCond %{HTTP_HOST} http://wiki.mydomain.com/
RewriteRule ^(.*)$ http://wiki.mydomain.com:8080 [L,R]

But it doesn't work (whenever I try for example wiki.mydomain.com I get the default Apache site). So what am I missing here? (I know that to be able to hide the port number I'll have to use a proxy but first I just want to enable the redirect).