Midrash su Salmi 51:9

(Ib. b) R. Joshua b. Levi said: "He who mortifies his evil inclination [after he has sinned], and confesses before Heaven, is considered by Scripture as if he glorifies the Holy one, praised be He! in both his world and the world to come, as it is written (Ps. 1, 23) Whose offereth thanksgiving, glorifieth Me." R. Joshua b. Levi said further: "When the Temple was in existence, if one brought a burnt-offering he received the reward for a mere burnt-offering; a meal-offering, he was rewarded for a mere meal-offering; but to him who is humble the Lord accounts it as if he had offered all kinds of sacrifices, as it is said (Ib. 51, 9) Sacrifices of God are a broken spirit. Furthermore, his prayer is never despised, as it is said (Ib.) A broken and a contrite heart, O God, will Thou not despise."

R. Dusthai, of the city of Biri, lectured: "Unto what may be likened the system of David's praver? "Unto a peddler who wanted to sell out his stock little by little. He said before the Holy One, praised be He! (Ps. 19,13-15) 'Sovereign of the Universe, who can guard against errors?' And he was answered, 'They will be forgiven.' (Ib.) 'From secrets (faults) do Thou cleanse me.' 'They will be forgiven.' (Ib.) 'Also from presumptuous sins withhold Thy servants.' 'This will [also] be forgiven.' (Ib.) 'Let them not have dominion over me,' i.e., the Rabbis shall not talk about me. 'This will [also] be allowed to you.' (Ib.) 'Then shall I be blameless,' i.e., my sins shall not be written. And he was answered, 'This is impossible, for, if the Yud which I took away from the name of Sarai complained before me several years, until Joshua came and I added it to his name, as it is said (Num. 13, 16) And Moses called Hoshea; the son of Nun, Joshua, how much more [will there be complaints] if I omit a whole portion of the Torah?' (Ps. 19) Clear from any great transgression, i.e., He said before him: 'Sovereign of the Universe, forgive me the whole sin.' And he was answered, 'It is revealed before Me what Solomon, thy son, will say in his wisdom in the future (Pr. 6, 27-30) Can a man take fire in his bosom, and his clothes not be burnt? Or can one walk upon hot coals, and shall his feet not be scorched? So he that goeth in to his neighbor's wife; whosoever touches her shall not go unpunished.' He then exclaimed, 'If so, then I am lost.' And he was answered: 'Accept affliction upon thyself.' Immediately David accepted affliction upon himself." R. Juda said in the name of Rab: "Six months was David afflicted with leprosy; the Shechina left him, and the Sanhedrin separated themselves from him. He was inflicted with leprosy, as it is written (Ps. 51, 9) Purge me [from sin] with hyssop, etc. The Shechina left him, as it is written (Ib., ib., 14) Restore unto me the gladness of Thy salvation. The Sanhedrin separated themselves from him, as it is written (Ib. 119, 79) Let those that fear Thee return unto me and they that know Thy testimonies. That all this lasted fully six months — when do we learn it? From the following passage (I Kings, 2, 11) And the days that David reigned over Israel were forty years; (Ib. b) In Hebron he reigned thirty-three years over all Israel and Judah. Hence we see that the six months more [which are counted in II Samuel] are not counted [in I Kings], and this was because the six months in which he was inflicted with leprosy were not counted." (Ps. 86, 17) Display on me a sign for good, etc. Thus said David before the Holy One, praised be He! "Sovereign of the universe, forgive me this sin [of Bath Sheba]." "Thou art forgiven," answered the Lord. David then said to the Lord: "Show me a sign while I live." Whereupon He answered, "During thy life I shall not make it known but during the life of Solomon, thy son, I shall make it known." When Solomon had built the Temple he desired to place the ark in the holy of holies, but the gates had become fastened to each other [and they could not be opened]. Solomon then offered twenty-four prayer-songs but was not answered. He then said the prayer (Ps. 24, 9) Raise your heads, O ye gates, and raise up, ye everlasting doors, and let the King of glory enter. Who is the King of glory, the Lord of Hosts, He is the King of glory, Selah (II Chr. 6, l2). Still he was not answered; but as soon as he said O Lord God, turn not away the face of Thy anointed, remember the pious deeds of David Thy servant, he was immediately answered. At that moment the faces of David's enemies turned black like the bottom of a pot and then it was known to all that the Holy One, praised be He! had forgiven David that sin.