"focus intensively" is correct and can be used in written English.
You should use this phrase when describing an action that requires concentration and focused attention, such as studying, working on a project, etc. For example: "In order to get the project completed in time, it was necessary to focus intensively and stay on task."
We focus intensively on the customer, and our marketing, our operating philosophy, and our performance measures reflect that.
Many of my clients focus intensively (or obsessively) on meetings and presentations they believe can make or break their careers.
By not electing to do everything, we can focus intensively on becoming pre-eminent in what we choose to do.
Succession management systems should focus intensively on linchpin positions jobs that are essential to the long-term health of the organization.
Mr. Abe said the growth strategy would focus intensively on increasing domestic private investment over the next three years, triple infrastructure exports by 2020 and double farm, fisheries and marine exports to 1 trillion yen by the same date.
Stating at the meeting that every high school graduate should be eligible for college without remediation, the district superintendent, Francis DeStefano, said the new school would focus intensively on a few solid academic courses for freshmen and sophomores, with electives and work-study after school.
Lancôme, too, has focused intensively on perfecting their new shade range.
When the Second World War began, there was a new urgency to research poison gases, and the work focussed intensively on mustard gas and similar chemicals.
In recent years, investigators have focused intensively on ways to reactivate cardiomyocyte mitotic activity in both in vitro cell culture systems and in vivo animal models.
The Huntsman campaign has been focusing intensively on New Hampshire for weeks, all but abandoning the three-state strategy that once included South Carolina and Florida.
Several important recent histories of the war and immediate postwar period in the United States have focused intensively on the emperor's responsibility in the war, and on Washington's role in shielding him from judgment.
