Didn't used to or didn't use to? [duplicate]

[1] He didn't use to smoke

[2] He didn't used to smoke.

Only [1] is correct. The uncertainty about which form to use probably arises because the "used to" in [2] is pronounced with a single /t/ and hence is homophonous with the "use to" in [1].

[3] He didn’t use to smoke.

[4] Did he use to smoke”?

The aspectual verb "use" has no present tense, only infinitival and past forms, so although the form "use" appears to be a present tense form, it is in fact the plain (infinitive) form which is only used in negatives and with inversion, as in [3] and [4]. Note that the auxiliary verb "do" requires the verb that follows it to be an infinitive, hence "use", not "used".

There is the added complication that "use" can be a lexical verb or an auxiliary one, though the books tell us that most speakers treat it as a lexical one. I suspect that’s due to the unacceptability for many people of the auxiliary use found in %Smoking usedn’t to be allowed and %Used he to smoke?

Lexical Use (negatives and interrogatives require do-support):

[5] He used to smoke.

[6] He didn’t use to smoke.

[7] Did he use to smoke?

Auxiliary Use (do-support not required):

[8] He used to smoke

[9] %He usedn’t to smoke.

[10] %Used he to smoke?

In this context it should be "use to" rather than "used to" since an infinitive is required (Cf. "I didn't cook it" v. "I didn't *cooked it"). The confusion is understandable though since in other situations (e.g. "I used to cook") the final consonant on "used" is all but identical with the initial consonant of following "to" and so will often be assimilated and/or dropped in speech.