I will freely sacrifice unto thee - The Hebrew words rendered “freely,” mean with “willingness, voluntariness, spontaneousness.” The idea is, that he would do it of a free or willing mind; without constraint or compulsion; voluntarily. The reference is to a free-will or voluntary offering, as distinguished from one, that was prescribed by law. See Exodus 35:29; Exodus 36:3; Leviticus 7:16; Leviticus 22:18; Numbers 15:3; Numbers 29:39. The idea is, that as the result of the divine interposition which he prayed for, he would bring voluntary offerings to God in acknowledgment of his goodness and mercy.
I will praise thy name, O Lord - I will praise thee. See Psalms 52:9.
For it is good - That is, God himself is benevolent; and David says that he would express his sense of God’s goodness by offering him praise.