(be + to + verb) Grammar

This question destroys my mind so finally I want to know the answer.

All I have to do is + to + verb

or

All I have to do is + verb

Which one is correct, and can't the wrong one be correct informally?

Answer

The second option is the more correct structure.

To explain it as simply as possible, you have to do in the middle of the sentence already. To do is an infinitive verb because the unsuffixed action word do is preceded by the preposition to (which is actually part of the infinitive verb, not just preceding it).

With that, you are now wondering if the verb at the end of the sentence should also be infinitive. It shouldn't simply because the previous infinitive verb, to do, already includes the preposition to, therefore the last verb doesn't need it.

I see this as a simple example of how English tends to reduce repetitive words as much as possible. In your first example, to is found before both verbs. But since that's repetitive, the to can be removed from the second verb and essentially shared from the first verb.