Indeed, there is no way to know beforehand. And that boils it down to where you and I are probably in disagreement; I don't think that living in Denmark is an inherent right that everyone is born with.
I believe in helping people, but if allowing mass immigration from these countries actually put other people at risk, that's where I draw the line.
It might be harsh, but the Dane born in Denmark has more right to be there than a refugee. So it makes sense that a refugee commiting such a harsh crime gets deported since he obviously has no plans of integrating properly into the society. The Dane is born there, where would you send him if not prison?
This is of course complicated by second generation immigrants who obviously can't be deported to a place they've never been. Technically they are as much a Dane as I am. In that case I would of course not support deportation.
If my brother was homeless I would offer him my home to live in; I wouldn't for a stranger. Being my family member has that privilege.
Now imagine that I DO offer my home to the homeless stranger and he in turn destroys my property. I would throw him out. I probably wouldn't with my brother. Because my brother has more right to be here than the stranger.
I know this is the kind of metaphors that people don't like so I hate to bring it up. But it does have some truth to it.
I disagree, the world would be a much better place with a murderer or a rapist in prison. I don't care much for forgiveness or even punishment. Having him/her locked up means that they aren't a danger to the people around them. Prison is all about the safety of the general population. For some reason many people make it all about the perps instead of the victims.
The unfortunate case you mentioned is not really a question of integration but rather discrimination. Which is of course still a problem some places. And this needs to be addressed obviously. I will point out that often the opposite will also happen because people are too scared of being politically incorrect. I remember a case of a train conductor not being willing to make an immigrant move from his seat (it was booked by someone else) in fear of being "racist".
Have no idea why I distinguished between rape and crime actually :P
And I'm not sure you know exactly how much immigration Sweden has had. Take Malmo for example. 40% of the population has a foreign background, with 30% being born outside of Sweden.
We have a lot of immigrants wanting to immigrate to Denmark going to Malmo because it's so close to Denmark and Sweden's immigration policies are much more lax than ours.
And now look at crime rate comparisons between Malmo and Copenhagen (1 hour away):
http://www.numbeo.com/crime/compare_cities.jsp?country1=Denmark&country2=Sweden&city1=Copenhagen&city2=Malmo
Hell it even has higher crime rates than New York City:
http://www.numbeo.com/crime/compare_cities.jsp?country1=United+States&country2=Sweden&city1=New+York%2C+NY&city2=Malmo
Granted that site might not be 100% accurate, but it's something worth thinking about. And a quick google on Malmo crime will show you that it's not a very safe place to live.
Malmo's got big issues with violence and anti-semitism.
Again this all seems a bit too far fetched to be coincidences, especially considering the state of the countries these people come from.