What is the expiation for someone who swore to divorce his wife with a single divorce due to her anger, then discovered her innocence, and he is regretful and wishes to take her back?

There is no harm in breaking an oath to refrain from divorcing one's wife; rather, it is preferable. This is based on the Prophet's (peace be upon him) saying: "By Allah, if Allah wills, I will not take an oath and then see something else as better than it, except that I will expiate for my oath and do that which is better, or do that which is better and expiate for my oath." Therefore, take your wife back and live with her kindly. Expiate for your oath by feeding ten needy persons or clothing them. If you cannot find them, then fast for three days.