remove index.php from url only for the client - .htaccess

Question

I know there are some questions like this out there but the solutions are not helpful for me.
I´m using htaccess to redirect to the index.php if the request file isn´t defined (code above).
I´d like to add a code-line that if the user requests for example:
http://www.example.com/test/index.php
he will redirect to
http://www.example.com/test/
but internal it will redirect to the index.php.
Is there a way to extend my code so that it works like I want it to?
# Add Slash
RewriteCond %{REQUEST_URI} !(/$|\.)
RewriteRule (.*) %{REQUEST_URI}/ [R=301,L]
# Redirect to index.php if the following sites were not match
RewriteBase /
RewriteCond %{REQUEST_URI} \.(php|sql|tgz|gz|txt|ttf|TTF|log|txt|ini|html|xml|xhtml|htm)$
RewriteCond %{REQUEST_URI} !^/index.php$
RewriteCond %{REQUEST_URI} !^/phpinfo.php$
RewriteCond %{REQUEST_URI} !^/out.php$
RewriteCond %{REQUEST_URI} !^/sitemap[^0-9]*\.xml$
RewriteCond %{REQUEST_URI} !^/robots.txt$
RewriteRule ^(.*)$ /index.php?dir=$1 [QSA,L]
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_URI} !^/$
RewriteRule ^(.*)$ /index.php?dir=$1 [QSA,L]

Answer 1

Complete code:
DirectoryIndex index.php index.html
Options +FollowSymLinks -MultiViews
# Turn mod_rewrite on
RewriteEngine On
RewriteBase /
# Take off index.php
RewriteCond %{REQUEST_URI} ^(.*/)index\.php$ [NC]
RewriteRule ^ http://%{HTTP_HOST}%1 [R=301,L]
RewriteCond %{REQUEST_FILENAME} !-d
RewriteCond %{REQUEST_URI} \.(php|sql|tgz|gz|txt|ttf|TTF|log|txt|ini|html|xml|xhtml|htm)$
RewriteCond %{REQUEST_URI} !^/((index|phpinfo|out)\.php|robots\.txt|sitemap[^0-9]*\.xml)$
RewriteRule ^(.*)$ /index.php?dir=$1 [QSA,L]
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule ^(.+)$ /index.php?dir=$1 [QSA,L]
# Add Slash for non-files
RewriteCond %{REQUEST_FILENAME} !-f
RewriteRule [^/]$ %{REQUEST_URI}/ [R=301,L]