Acts 13:32-37

Acts 13:32-37. And we declare unto you glad tidings, how that the promise which was made unto the fathers. God hath fulfilled the same unto us their children, in that he hath raised up Jesus again: as it is also written in the second Psalm, Thou art my Son, this day have I begotten thee. And as concerning that he raised him up from the dead, now no more to return to corruption, he said on this wise, I will give you the sure mercies of David. Wherefore he saith also in another psalm, Thou shalt not suffer thine Holy one to see corruption. For David, after he had served his own generation by the will of God, fell on sleep, and was laid unto his fathers, and saw corruption; But he, whom God raised again, saw no corruption.

So that David was not speaking of himself, but he was speaking of another and higher David, his greater Son, the Son of God, begotten of the Father.