Just paste the following code on your functions.php file:
add_shortcode( 'member', 'member_check_shortcode' );
function member_check_shortcode( $atts, $content = null ) {
if ( is_user_logged_in() && !is_null( $content ) && !is_feed() )
return $content;
return '';
}
Once done, you can add the following to your posts to create a portion or text (or any other content) that will be only displayed to registered users:
[member]
This text will be only displayed to registered users.
[/member]