When withdrawing Monero from Bitfinex, they ask for a 64 character payment ID.
The payment IDs generated by the official wallet are much too short.
Should I be using the integrated address, with no payment ID?
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Sign up to join this communityA payment ID is optional, and determined by whoever you're sending to. If you're sending to yourself, then you do not need a payment ID (or you can make one up as you see fit).
The payment ID is arbitrary data which the recipient can use to associate with a sender: for instance, if you were to sent to Poloniex (instead of your on wallet), then Poloniex would give you a payment ID to use so they can tell an incoming transfer is intended for your Poloniex account, and not anyone else's.
In this case, you can leave the payment ID empty.
Whether you can use an integrated address, I do not know. This depends on whether Bitfinex supports these. It seems likely, but you would have to try (and, if it fails, possibly ask support to recredit your Monero in case this is not automatic).
Long style payment IDs are obsolescent, but most exchanges still use those instead of shorter ones, which are baked directly in a Monero integrated address.
Had the same situation with Bittrex. Gave it a try with a small amount and everything worked fine with a long (64) payment id