How does Hamlet develop his personal integrity through courage?

Hamlet is an interesting character. For most of the play Hamlet struggles with those two very things. In the beginning of the play Hamlet insinuates that he has more integrity than anyone else. He says the sadness around them is not real, "these are actions that a man might play..." Hamlet's foil is Fortinbras. Hamlet would like to walk up to Claudius and cut his head off; no questions asked and no proof needed. But Hamlet isn't like that; he has too much "integrity". Hamlet is a thinking man so he requires evidence. Hamlet concocts the play "to catch the conscience of the king". His courage stems from his own insecurities about life and death and vengeance. In the end, Hamlet dies seemingly at peace at what he has accomplished. Hamlet, however, is not completely righteous. He uses the fair Ophelia to his advantage and he certainly could have handled his mother differently.