Please drop this pretense. Nobody invades anything to bring democracy. You can't force democracy on people even if you wanted to. Democracy is so much more than just the elections.
You invade countries because you have geopolitical interests in the area, and want to gain political or economical influence.
It used to be the case that you invaded countries because the territory itself was valuable, but when was the last time you heard invaded people become citizens of the invaders' nation state? These days the cost is calculated and operations carried out are means to an end.
Force necessary to achieve threat elimination and future deterrence work on sovereign adversaries who chose not to play by your rules.
Doesn't matter why they don't like you (rightly or wrongly), if they are a violent adversary you will suffer consequences if you do not stop them.
If the adversary is reasonable, diplomacy is always a preferable option, but not the most common denominator.
Why don't we invade Saudi Arabia, who practices a cruel form of Islam with death-sentences and so on, too? Why don't we abolish them in China or the US? Why don't we focus on Africa or - as a European - Eastern Europe? I am not saying, that ISIS is not bad, I just find the obsession with the Middle East strange, if it is really about their actions that are so horrible, let's stop doing them ourselves first. If you really want to make the world a better place, that should be a much easier goal to achieve.
2. Take their people away from them. Like other forms of extremists, they need young male identiy-seeking misfits, who have nothing going on for them and want easy answers, somebody who gives them orders and to be part of something bigger.
3. Prosecute them like other criminals, too (with police forces).