For high-level bdd integration testing, iafonov is correct. cucumber and related things (selenium, capybara) work fine. If you do not need such human-readable tests, there is also a steak stone (https://github.com/cavalle/steak). I have not used it, but it seems reasonable.
If you need more unit test as behavior for js, then I suggest Jasmine. I used it and it worked great for me. I especially liked how close it is to rspec syntax.
Perhaps if you post the problems you have, we can help with this?
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