Integration never works. Why should it? Did the Europeans who came to these shores integrate with the Natives and their lifestyle? No.

The Muslims will never integrate. Why should they?

Cultures are like genes, the strong ones dominate. The Western culture is a weak one, bending backwards before all others to accommodate. In sweet terms it is called "political correctness". In reality it is unwise. 

What makes the West weak is its rampant materialism and wasteful capitalism, and what makes Muslims strong is their frugality - they get more bang for the buck. Islam is efficient. Muslim lifestyle makes them tough - prayers, meditation, fasting, better able to answer to the Primal Question of Existence - Survival, Growth, Evolution.

The Corporate Capitalist West is repeating the same mistakes Muslims made in centuries 7-14 AD after Mohammed died - materialism, colonialism, racism, misogyny, pornography, same-sex unions. The West should learn from debacle of that Islam to reform itself.