Swede here. I just want to add that the picture is even more complicated than that. In the past decade, Sweden has made a conscious effort to encourage people who are victims of rape to report the offense, because it's known that many rapes go unreported. The government has funded multi-million campaigns on a regular basis encouraging openness to increase the amount of victims that actually file a report. As a result it's hard to tell whether the increase in reported rapes means the actual number has gone up, or that a larger % of victims decide to report it. Or possibly a combination of both. When Swedish rape statistics, or crime statistics in general are reported by foreign media and foreign people I always feel like the numbers are simplified, taken with little or no context and often used to reach conclusions that simply aren't warranted. I'm not suggesting the number of rapes hasn't increased, I'm simply saying that we can't infer this from the information at hand. If you want to know more, I suggest you read this:
http://www.government.se/articles/2017/02/facts-about-migration-and-crime-in-sweden/
Also, since most Americans I've encountered who talk about these statistics are concerned about the migrant situation, I just wanna add that I'm extremely critical of the way Sweden has dealt with this issue. So I'm not making this point to somehow justify or defend my country. The government has made many critical mistakes, but the notion that Sweden has become the "rape capital of Europe" is unwarranted at best, and ridiculous at worst.