'integrate himself' is correct and usable in written English.
It can be used to describe a person who has become part of a group or society. For example: John has worked hard to integrate himself into his new community since he moved to the area last year.
Under the previous management, Huntelaar struggled to integrate himself.
Mr. Wright, for his part, is taking pains to integrate himself into the island's community.
Though nominally working for the StB, Koecher had few official responsibilities and his primary goal was to integrate himself into American society.
And he told me this not that long ago, by the same token, Spock's objective was to overcome the fact that he was half-alien and integrate himself with his human crewmates".
"Joe is not returning because it was not a good fit," General Manager Larry Beinfest said at the time, adding later, "We felt that Joe was not able to integrate himself into the workings of our organization".
Carlo Ancelotti, his coach at Milan, described him as "egocentric" in his autobiography and he was virulently criticised by Paolo Maldini, who said he failed to succeed at San Siro because he did not make the necessary effort to integrate himself into the squad.
Robert saw that he had difficulties integrating himself with the executive team.
Mr. Cammarano had integrated himself into Hoboken's community and seemed to be a devoted family man.
His White House colleagues frequently mention this: the way Mr. Modi so affably and seamlessly integrated himself into the bureaucratic culture.
Unlike most Russians living in New York, Mr. Zakharov was successful in integrating himself into mainstream American life.
But when "normal" modes don't work, he completely integrates himself into his clients' daily routines and becomes the target himself.
