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I'm sorry to say, but we do not have an integration with CiviCRM. I will forward this to our developers as a feature request. We will update you on this thread as soon as there are any news.
For the meantime, you can check our APP page for the list of CRM that we support: https://apps.jotform.com/category/crm
You can also get your form's full source code to establish the integration there.
If you are familiar with APIs, then you can check JotForm's API to develop an integration to your CiviCRM powered website or system: http://api.jotform.com/
As Civi has its own forms module, I'd guess this is unlikely. Although yours is feature-rich compared to theirs--which is why we would like to stay put.
Charlie has opened up a thread for our developers to look at but please note that it is only something they might "consider" so it's not something we could guarantee but if there's any changes we would let you know about it here.
Also, just to let you know we mainly base our feature requests for new features according to demand and feasibility as in would it benefit everyone or not.