Here is a list of acts of wanton violence perpetrated by Muslims in a single year, 2004.
I know, I know — these were carried out by "extremists," supposedly a tiny minority among all the "moderate" Muslims. It's true, by definition: as soon as a moderate Muslim heeds the call to annihilate a few infidels, he becomes an extremist, so no taint of the act attaches to all those moderates.
Scroll down the list, please, reading each item. I know it's long, but I don't think you'll be bored. Shocked, probably, but not bored.
Then come back here and tell me Europe, the United States, Canada, and Australia should be inviting Muslims to come and settle so they can be part of the beautiful multi-cultural mosaic. If, that is, you can go through the whole list and the words don't die on your tongue.