The phrase "engage intensely" is correct and usable in written English.
You can use it when describing a situation where someone is participating or involving themselves deeply in an activity or discussion.
Example: "During the workshop, participants were encouraged to engage intensely with the material to fully grasp the concepts being taught."
Alternatives: "immerse deeply" or "participate fervently."
Mathematicians, when they work, engage in intensely serious play.
President Obama leaves on Saturday for a trip to Asia that will show his commitment to having the United States engage more intensely with countries there.
Science – one of the strongest voices of the environment in governance – must become more active and leave its ivory tower to engage more intensely with other stakeholders.
Unlike our dataset, subjects in DEAP dataset experiment who watched a particular music video for the first time or who had minimal experience with the video would engage so intensely enough in watching the video that they avoided using any recollection memory to associate the music with previous experiences.
As part of their ongoing treatment, these teens must also have periodic physical examinations and engage in intensely private discussions with medical practitioners who may in fact be the most caring and dedicated providers but nevertheless remain unfamiliar adults.
Because feedback giving is an interpersonal activity, extraverted trainers may engage more intensely in feedback giving with a positive effect on frequency and consequential impact.
Third, it has not yet been investigated whether ART would augment the effects of other empirically-evidenced treatments for MDD (possibly because enhanced ER skills might allow patients to engage more intensely in the therapeutic process, [ 31]).
With the field of candidates now down to four and Saturday's primary fast approaching, the candidates engaged in intensely personal verbal combat fittingly set in a sports coliseum.
By this point, I was engaged as intensely as I have ever been with a film - tears in my eyes while hearing those last messages, admiration for the passengers' resolve to go down fighting like the defenders of the Alamo.
The policy proposals come as Mrs. Clinton has been engaged in intensely personal sparring with Donald J. Trump, the presumptive Republican nominee, and could be an effort to turn the page in her campaign a day after the F.B.I. director, James B. Comey, was sharply critical of her "extremely careless" use of a private email address and server.
