In Italian an infinitive is connected to another verb with no preposition at all, with the preposition di or with the preposition a. The preposition to use is arbitrary. There is no need to look for a deeper reason, it is just arbitrary. The only thing to know is that in case that the infinitive has the same subject as the infinite verb the infinitive is compulsory and can't be substituted by subordinate clause.
the infinitive as a substitute for a that-clause (finite and infinite verb has the same subject)
Credo di non poterlofare.
incorrect: Credo que possa farlo.
I think (that) I can do it.
The infinitive combined with a verb that requires a preposition
Rifiuto di parlare della mia vita privata.
I refuse to talk about my private live.
Combination if the direct object of the finite verb ist the subject of the infinite verb
Ti prego di non parlarmi più di questa storia.
I beg you not to tell me any more about that story.
We have said before that normally the infinitive is connected with the same preposition as a noun. As always there are some exception to thins rule. It is useful to see as well that a noun sometimes is not combined with the same preposition as a verb.
object without noun, infinitive with di
Questa mattina ho finito il mio romanzo.
This morning I finished my novel.
Questa mattina ho finito di lavorare.
This morning I finished working.
object with a, infinitiv with di
Non credo a lui.
It don' t believe in him.
Non credo di essere capace di farlo.
I don' t think being able to do this.
verbs connecting the infinitive with di
affermare = to claim
Afferma di non essere stato informato di questo avvenimento.
He claims not having been informed about this event.
