Redirect not working for complex rewrite rules (.htaccess)

I'm trying to make a redirect from a non-www version of the link to the www one. Its working fine for something like http://mywebsite.com but it fails for a request like http://mywebsite.com/artists/metallica/ or even a complex one. The whole .htaccess file is bellow. Any clues?

Options +FollowSymLinks

RewriteEngine On

RewriteBase / 

RewriteCond %{REQUEST_FILENAME} !-f 

RewriteCond %{REQUEST_URI} !(.*).html

RewriteCond %{REQUEST_URI} !(.*)/$ 

RewriteRule ^(.*)$ http://mywebsite.com/$1/ [L,R=301]

RewriteRule ^artists/([^/-]+)-p([^/]+)/$ /artists.php?l=$1&p=$2 [QSA,L] 

Rewr开发者_如何转开发iteRule ^artists/([^/]+)/$ /artists.php?l=$1 [QSA,L] 

RewriteRule ^submit/$ /submit.php [QSA,L] 

RewriteRule ^users/$ /users.php [QSA,L]  

RewriteCond %{THE_REQUEST} ^.*/index.php 

RewriteRule ^(.*)index.php$ http://www.mywebsite.com/$1 [R=301,L]

Try this rule:

RewriteCond %{HTTP_HOST} !^www\.
RewriteCond %{HTTPS}s ^on(s)|
RewriteRule ^ http%1://www.%{HTTP_HOST}%{REQUEST_URI} [L,R=301]

But make sure that you put this rule in front of those rules that just do an internal rewrite. Otherwise an already internally rewritten rule might get redirected externally.