Is the word incluir the same in Brazilian and European Portuguese?

Yes

The only difference between "incluir" in Brazilian and Continental Portuguese is pronunciation. In Brazilian Portuguese, vowels are generally more "open" and clearly articulated, even in unstressed syllables. In Continental Portuguese, there is a heavy "vowel reduction," where unstressed vowels are often swallowed or pronounced very shortly, making the word sound more "closed" or clipped. The spelling, meaning, and grammatical conjugation are identical in both dialects.

Brazilian Portuguese Examples

1. Você pode incluir o café no meu pedido? (Can you include the coffee in my order?)
2. Eu vou incluir meu nome na lista. (I'm going to include my name on the list.)
3. Não esqueça de incluir o imposto no preço. (Don't forget to include the tax in the price.)
4. Eles querem incluir mais pessoas no projeto. (They want to include more people in the project.)
5. O hotel vai incluir o café da manhã no valor da diária. (The hotel will include breakfast in the daily rate.)

Continental Portuguese Examples

1. Podes incluir o café na minha encomenda? (Can you include the coffee in my order?)
2. Vou incluir o meu nome na lista. (I'm going to include my name on the list.)
3. Não te esqueças de incluir o imposto no preço. (Don't forget to include the tax in the price.)
4. Eles querem incluir mais pessoas no projeto. (They want to include more people in the project.)
5. O hotel vai incluir o pequeno-almoço no valor da diária. (The hotel will include breakfast in the daily rate.)