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

Yes

The only difference between "investigar" in Brazilian and Continental Portuguese is pronunciation.

In Brazilian Portuguese, the pronunciation is more "open" and syllable-timed. The unstressed vowels are clearly articulated and the rhythm is more melodic. The "e" in "investigar" is clearly heard as a distinct vowel.

In Continental Portuguese, the pronunciation is more "closed" and stress-timed. Unstressed vowels are often reduced, shortened, or even suppressed (devoiced), meaning the "e" in "investigar" may sound almost silent or like a very subtle "schwa" sound, giving the word a more staccato, clipped rhythm.

Brazilian Portuguese Examples:

1. A polícia está investigando o crime. (The police are investigating the crime.)
2. Eu preciso investigar essa informação antes de decidir. (I need to investigate this information before deciding.)
3. Eles estão investigando a causa do incêndio. (They are investigating the cause of the fire.)
4. Nós vamos investigar o que aconteceu ontem. (We are going to investigate what happened yesterday.)
5. Ela está investigando a fundo o assunto. (She is investigating the matter thoroughly.)

Continental Portuguese Examples:

1. A polícia está a investigar o crime. (The police are investigating the crime.)
2. Eu preciso investigar essa informação antes de decidir. (I need to investigate this information before deciding.)
3. Eles estão a investigar a causa do incêndio. (They are investigating the cause of the fire.)
4. Nós vamos investigar o que aconteceu ontem. (We are going to investigate what happened yesterday.)
5. Ela está a investigar o assunto a fundo. (She is investigating the matter thoroughly.)