"diligently study" is correct and usable in written English.
It can be used to refer to studying with care and intensity. For example, "She diligently studied for her history exam and ended up getting an A".
School systems like Singapore's promise students that if they diligently study the material in their course syllabuses, they will do well on their examinations, Mr. Daro said.
First, diligently study your opponent's success so that you can align your strategy perfectly with what's being practiced by the competition.
"Didi and SoftBank will diligently study local market conditions and policies, and will actively engage with industry practitioners, policymakers and other stakeholders, with the aim of building an open and inclusive platform that will be available to all of Japan's taxi operators," the Chinese firm said in an announcement.
In his early 20's, he diligently studied music in Vienna.
I diligently studied news apps, and even tweeted.
Anyway, back to his disappointing sales figures, which he says he diligently studies.
He trains diligently, studying strategy, technique and spends up to 14 hours a day planning how he can outmanoeuvre the opposition in his chosen discipline.
We see rooms full of diligently studying people sitting at desks, but nobody enters or leaves, and no-one talks to the librarians.
In the East a sterile scholasticism diligently studied Plato and Aristotle, but Epictetus, the stoic from Anatolia, was the preeminent philosopher.
No one among the specialists diligently studying 17th-century Baroque art had thought of researching just how sculptors proceeded when carving their marble statues or creating bronzes.
During the Jets minicamp two weekends ago, McGeoghan worked diligently, studying the nuances of the West Coast offense, implemented by Paul Hackett, the new offensive coordinator who along with the new coach Herman Edwards made a strong first impression on the rookie.
