The phrase "accelerate the integration" is correct and usable in written English.
It can be used in contexts where you want to express the idea of speeding up the process of combining or unifying different systems, processes, or entities.
Example: "To improve efficiency, we need to accelerate the integration of our new software with the existing systems."
Alternatives: "speed up the integration" or "hasten the integration".
A common language helps accelerate the integration of separate companies in different regions.
In mid-May his government approved a plan to accelerate the integration process for the second-generation Ethiopians.
The organization's plan challenges the 34 countries with the highest infection rates to rapidly train workers to accelerate the integration of AIDS treatment in their health care programs.
China is eager for such links, expecting that this will stimulate its economy and accelerate the integration of Taiwan and the mainland.
Creating a dollar zone would also be likely to accelerate the integration of Latin American economies with the United States and create trade opportunities for American companies.
One focus for the Americans will be to try to accelerate the integration of Sunni fighters into the Iraqi Army, which is dominated by Shiites.
The Times Company acquired full control of The Herald Tribune in 2003, and has been accelerating the integration of the two papers in recent months.
Ryan has simplified the defensive playbook, giving him more time to explain to Brandon Browner what pass interference means, and perhaps also accelerating the integration of rookies on that side of the ball.
Depending on a company's circumstances, objectives might include aligning everyone around a common set of priorities, solving problems impeding company progress, driving a cultural transformation, or accelerating the integration of a major acquisition.
Recent technological advances in quantitative and cross-linking mass spectrometry, super-resolution fluorescence microscopy and electron microscopy have enormously accelerated the integration of different types of data into coherent structural models.
