David prays for remission of sins, which he confesses fully
To the chief Musician, A Psalm of David, when Nathan the prophet came unto him, after he had gone in to Bathsheba.
7 Purge me with hyssop, and I shall be clean: wash me, and I shall be whiter than snow. 8 Make me to hear joy and gladness; that the bones which thou hast broken may rejoice. 9 Hide thy face from my sins, and blot out all mine iniquities. 10 Create in me a clean heart, O God; and renew a right spirit within me. 11 Cast me not away from thy presence; and take not thy holy spirit from me. 12 Restore unto me the joy of thy salvation; and uphold me with thy free spirit. 13 Then will I teach transgressors thy ways; and sinners shall be converted unto thee.
14 Deliver me from bloodguiltiness, O God, thou God of my salvation: and my tongue shall sing aloud of thy righteousness. 15 O Lord, open thou my lips; and my mouth shall shew forth thy praise. 16 For thou desirest not sacrifice; else would I give it: thou delightest not in burnt offering. 17 The sacrifices of God are a broken spirit: a broken and a contrite heart, O God, thou wilt not despise. 18 Do good in thy good pleasure unto Zion: build thou the walls of Jerusalem. 19 Then shalt thou be pleased with the sacrifices of righteousness, with burnt offering and whole burnt offering: then shall they offer bullocks upon thine altar.
Psalms 51:1-19 (KJV)