Often don't? Yes. Can never? No. The difficulty depends on where they come from and how old they are when they first arrive, but even the most hopeless looking cases can thrive.

There's an assumption here that being "fully integrated," which is vague in itself, is always a good thing.

There's a difference between "can't" and "shouldn't".

Ideally, people would be able to be fully integrated. In reality, your success will very much be determined by which country you live in. Western countries, while often criticized, are often more open in this regard.

In countries like the far east you could have several generations of history and still never be considered among their peers. In some cases simply having brown hair instead of black will earn you a "foreigner" title.

They will never be integrated, I have seen 2nd 3rd and 4th generation and they still don't integrate.

TL;DR - This depends on how you define 'full integration'.

There are several facets to a person's belonging within a country, and the how we rank these factors will result in varying standards for 'full integration' - such as:

• Whether the immigrant is distinguishable as an immigrant in their new country
• Whether the immigrant establishes a comfortable lifestyle for themselves and feels integrated - this can be difficult to assess, but if we allow this measure to remain subjective, it is easy to imagine that many who feel a particular affinity for their new country would defend their full integration.
• Whether the immigrant attains legal nationality - this is more difficult in some countries than others, making it a highly variable metric. If we choose this definition, first generation immigrants in many countries have easily achieved full integration. Several countries have very simple citizenship processes, while others have strict rules and highly tedious systems. This definition is arguably a superficial one, as it ignores more profound considerations regarding 'belonging' - .e.g., social and emotional factors.
• Whether the immigrant is considered an immigrant by non-immigrants, i.e., whether someone known to be an immigrant is considered an outsider - in this case, the country's inhabitants decide, and the verdict is dependent on how welcoming a country is.
• Whether the immigrant is actively participating in the political processes of the country

This is by no means an exhaustive list. 'Full integration' can be defined by any number of the above and more, and the answer to whether first-generation immigrants can achieve it will decidedly differ. An interesting example can illustrate this:

• Sonia Gandhi is the Italian-born widow of India's 6th Prime Minister, leader of the Indian National Congress. While her Italian descent makes her a first-generation immigrant, her work as an Indian politician and her manner of dressing, for example, easily distinguish her image from her heritage. Some might argue (in tones varying from scorn to admiration, depending on political leanings) that she is 'fully integrated' given her impacts on India's politics and the necessary adoption of Indian culture in the process. Others may choose to claim that she is not fully integrated if the populace still regards her as Italian. A remaining question, is whether she herself feels integrated within the country.

I believe they can’t however It’s not to say they are a negative factor or influence on the country.

Non-integration does not mean non-appreciation

• It isn't an inherently bad thing to not be fully integrated - it is okay to have more than one culture.

• With this perspective, you are able to have strong attachments to multiple cultures without abandoning yourself and losing your identity.

• Greater appreciation of cultures - especially in a country where the first generation immigrant culture is a minority ethnic group.

• When westerners immigrate to other countries, they don't always integrate with the local culture and are not pressured to do so. They are called 'expatriates' as opposed to immigrants and have less burdens to integrate, compared to non-western people immigrating to western countries.

I'm a first-generation immigrant--born in the United States but chose to move to Mexico. I know the history and food as well or better than most Mexicans. My Spanish is sufficient to have conversations about relatively abstract ideas. But I will never be culturally "Mexican" because I can never have the experience of growing up here.