End to end testing a web app that integrates with stripe

I have an express 4.0 web app that integrates with stripe. I can test things by hand, but I'm really curious how I can end-to-end test the entire web app including the payment side.

I have an idea:

1. Launch app
2. Register user
3. Pay for product
4. Check to make sure user can access account

But I can't probe into whether or not I charged them properly and everything is working with the stripe API itself. This is especially important for editing/updating billing information.

What do you guys suggest I do here? I've never had to tackle a problem like this before.

Thank you!