Is expiation (kaffarah) obligatory, or is repentance (tawbah) sufficient for someone who swore by Allah to do something, while secretly intending not to do it, in order to show people that he would do it?

If someone swears to do something while knowing they will not do it, they have committed the grave sin of prohibited lying, which is considered one of the major sins. If they swear falsely about a future matter, intending not to do it, then expiation is due. However, if they verbally make an exception by saying "Insha'Allah" (if God wills) or something that indicates an exception, then no expiation is due upon breaking the oath. If they swear to a person, they must be truthful to them, and concealing the exception within themselves does not benefit them, except in special cases such as fear of an oppressor. They must also repent from false oaths.