This passage is hard for us if we know the story of David... because the scripture makes it clear that he did all of these things! He was guilty of betrayal, of adultery, of conspiracy, of murder! He was a faithless man who killed one of his closest faithful men in order to cover up his own guilt...
In verse 8 David writes "Judge me, O Lord, according to my righteousness, and according to my integrity within me."
These are bold words for a guilty man!! In the end, there are only 2 possible options: either David did not know the character of God, or else he knew something that WE need to understand; something powerful, something fundamental, something wonderful... and this is the truth my beloved! Despite all of his sin, David knew that the Lord forgives and frees those who cry out to Him for mercy. In verse 12 David writes, "If a man does not repent, God will whet his sword"... the stunning implication is this, if a man WILL repent, then God will put away the sword of His fury, the terror of His wrath and the doom of His impending judgment. No matter what you may have done, oh precious child, there is mercy and forgiveness to be found in the person of Jesus Christ! God forgives ALL who repent... and what is more, all who He forgives, He frees!! You will be bound no more to the past you cannot change, but instead called to a glorious future with God as your Father, instead of as your enemy!!