widgets.php not included?

I’m trying to write a plugin to show a sidebar widget, but I’m stumped.

From what I understand, widgets.php is in wp-includes, meaning the widgets.php functions should be available to me. If I add the function:
register_sidebar_widget('Servers','widget_server_widget');
I am told that the function register_sidebar_widget() is not a registered function.
If I add the typical:

if ( !function_exists('register_sidebar_widget') ) {
		include("/home/rage/public_html/wp-includes/widgets.php");
}
register_sidebar_widget('Servers','widget_server_widget');

Then my entire widget configuration in the Presentation tab disappears.

Are the widgets.php functions not available by default, even in 2.2.3, like the documentation says? Or have I just majorly screwed something up somewhere?