"integral task" is correct and usable in written English.
You can use it to refer to a task that is necessary or crucial in order for something else to succeed. For example, you could say, "The most integral task in launching our new product is finalizing a marketing strategy."
Taking into account that during a clinical career spanning about 40 years, an oncologist, for example, is likely to conduct about 150.000 to 200.000 consultations with patients, communication should be viewed as a core clinical skill and an integral medical task [ 11].
One is simply integral to the task: that, by undertaking this project, America will undoubtedly make itself a continued target for terrorism and for criticism.
In banking, the reduction of the scope and scale of the largest operators is integral to the task of building a reformed onshore capitalism.
With the aid of the Cauchy integral formulae, the task of constructing a complex function which gives the solution of the boundary value problem under consideration is reduced to solving a system of linear algebraic equations.
All these phenomena are taken into account in this paper in order to set up an integral and coherent task flowchart in order to guide the design of spallation sources.
Opinion 1: People will find more new writing on the web; so "book publishers" must start to be native to the web, and see the web as integral to their task of connecting readers and writers; they cannot continue to see the web as some kind of add-on to their marketing departments.
This research shows that external representations are not simply lists of inputs or memory aids but are integral to a task and how it is performed.
Some climate scientists devote part of their time, or just lip service, to advocacy or outreach; the program makes these tasks integral to its scientific mission.
Limiting employers' wage payment obligation only to time spent on tasks "integral and indispensable" to the workers' principal activities may boost the corporate bottom line.
This task is integral to many robotic applications, such as vacuum cleaning robots, painter robots, autonomous underwater vehicles creating image mosaics, demining robots, lawn mowers, automated harvesters, window cleaners and inspection of complex structures, just to name a few.
