Joomla and vBulletin Integration

Hi,
I have a customized user registration and user login form on my Joomla site using chronoform.
I like to use vBulletin as my website forum because they have the capability to make a standalone mobile app for the forum. But I need to know if I can integrate them using chronoform.
I know how to save user's information to multiple databases during registration and profile update using chronoform. That way user's profile will be in sync in both databases. I'm planning to use the same host/server for both platforms.
My question is, how can I set up the user login so that when my users log in to Joomla, they automatically log in to vBulletin too and also the logout process? Is this something that can be done easily or has anyone done it before?
Is there anything else that I need to figure out for this integration to work smoothly?

That seems like something to ask the vBulletin people or a Google search. Not really within the scope of this forum.

My question is, how can I set up the user login so that when my users log in to Joomla, they automatically log in to vBulletin too

Find the PHP code needed for that and use it in a PHP block in the form maybe