The phrase "exert themselves in" is correct and usable in written English
You can use this phrase when referring to someone putting forth a great effort at something, usually some form of physical or mental labor. For example, "The athletes exerted themselves in order to achieve their goals."
Middle-class characters look on as labourers exert themselves in the sunshine.
Its players were talented, but some of them were also known as heavy drinkers who didn't exert themselves in practice.
Characters go hurtling down chutes and crumbling mountainsides or else exert themselves in chaotic battles with masses of roaring, rampaging pixels.
Parents asked one question after another about the offerings, sounding more as though they were evaluating a luxury vacation than preparing themselves to support their kids to exert themselves in a challenging environment.
There follows a bar brawl, if that's not too strong a phrase to denote the sort of fight into which participants mostly exert themselves in making a show of flinging their limbs while being restrained by their more levelheaded friends.
Whereas before, to search something meant you had to through its drawers or folders by hand and inspect things by eye, now it means simply to produce a query and allow the vast computational engines of cloud services to exert themselves in parallel, sifting through petabytes of data and instantly presenting you with your results, ordered and arranged like snacks on a platter.
In that case, the rowers were exerting themselves in synchrony, as a united group.
Tottenham were not over-exerting themselves in pursuit of a fourth goal but did have chances from set-plays.
At Dade's headquarters, the men from Bain — young, nattily dressed Bostonians — exerted themselves in ways big and small as the new owners.
The two 16-year-olds, Isaiah Laurencin in Florida and Don'terio J. Searcy in Georgia, were among five high school students who collapsed after exerting themselves in high temperatures last year and later died.
An early sequence that graphically shows Brüno and his lover exerting themselves in various positions and with the assistance of, among other things, a Champagne bottle, a fire extinguisher and a specially modified exercise machine, derives its humor less from the extremity of their practices than from the assumption that sex between men is inherently weird, gross and comical.
