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The phrase "that are integral" is grammatically correct and can be used in written English.
It is commonly used to describe elements or components that are essential or necessary for a certain outcome or function. Example: "Teamwork and good communication are integral to the success of any project."
Exact(57)
Building-integrated photovoltaics (BIPVs), photovoltaic cells and thin-film solar cells that are integral components of a building.
"All of these things that are integral to the cooking they grew up with".
Other terms have shortened periods that are integral submultiples of the fundamental; these are called harmonics.
All three works were performed with the intelligence and emotional refinement that are integral to Zinman's style.
Then other Asian companies piled in, along with the online betting companies that are integral to sport there.
She has been responsible for implementing programmes that are integral not only to Accenture's success but to Accenture's clients' success.
Quinones are abundant, naturally occurring chemicals that are integral to biological processes such as photosynthesis and cellular respiration.
"Slovakia is a technological leader in the automotive, material science, and energy industries, many of the areas that are integral to the Hyperloop system," said Ahlborn.
Similar(3)
She spoke about the risk-taking that is integral to Silicon Valley.
It is the unique boho vibe that is integral to the district's charm.
Ms. Hayes said she had deliberately created shapes that were integral to the lobby's architecture.
More suggestions(15)
that are integrative
that are aspects
that are holistic
that are indispensable
that are complements
that are pivotal
that are essential
that are inalienable
that were an integral part
that form an integral part
that's integral
that is an integral part
which form an integral part
which are integral parts
that are an integral part
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com