Based on how well Muslims have integrated all over the world--especially the US and Canada--they are quite capable of assimilating into Western culture. However, whether they will be able to or not in Europe all depends on how willing Europeans themselves are in not only embracing them but helping them integrate into their society. If Europeans continue the practice of pushing immigrants into ghettos, enacting laws that seem hostile to Muslim culture (such as banning religious garb), or antagonizing Muslims with offensive cartoons, there will be less successful integration. However, if Europeans drop these types of practices, Muslims would feel more welcome in Europe and more likely to assimilate.
Yes, it is possible for Muslims to successfully assimilate into European culture; in fact, they do it all the time! There are literally millions of people who have already assimilated into different European cultures. Millions of Muslims live throughout Europe and have assimilated into many different societies. Despite popular news headlines and unfounded beliefs, Muslims are not only immigrants, no; they’re apart of European society’s no less than any other groups. European cultures include Muslims who’re schoolteachers, shop owners, politicians, religious leaders, scientists, journalists, and so much more. Indeed, countless Muslims have assimilated successfully into European culture.
Islamic culture, like most religious cultures, will find it very difficult to smoothly assimilate into advanced culture, and likewise, high society will have a hard time accepting archaic thinking into its populous smoothly. Religious cultures like Islam are not concerned with creating a better world despite our differences, but with getting the world to assimilate to their beliefs.
For Muslims to "successfully assimilate" the European country, does it mean that they have to abandon their religion, beliefs, food, traditions? If that is the question, then I hope they never do. Why should anybody have to assimilate any body's culture? Why should anybody care about what the family next door eats, wears, or what they do in their free time? This is non-sense.