There 2 ways to add a form in a widget:

PHP hard code integration

In this example i use the free wp plugin Exec-PHP to allow PHP code in widget content.

This is the code i use in the widget content:

<?php w2_contact_form($id_form = 28, $css_theme = 'dark-hive', $css_ui_theme = 'dark-hive'); ?>

$id_form is the id of the form that you want to display.
$css_theme is the CSS theme that you want to use for the form (if you use custom CSS you don’t need to specify teh CSS theme).
$css_ui_theme is UI CSS theme (for UI widget as buttton set, datepicker …) you want to use.

Shortcode

If your theme allow shortcode in widget you can configure the plugin to use WordPress Native Shortcode feature instead smart library loading ( pages selected ).
Just configure the parameter « Load librarys for all page » to « true » in Global Settings tab ( advanced options ).