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Discover LudwigThe phrase "integral with" is correct and usable in written English.
You can use it when you want to talk about two things that are closely connected and can not exist independently. For example, "The success of this project is integral with the dedication of the team."
Exact(60)
Most notable was the practice of casting cylindrical mounting lugs, called trunnions, integral with the barrel.
Mural, a painting applied to and made integral with the surface of a wall or ceiling.
The shanks of twist drills are either straight or tapered and when not integral with the body are made from low-carbon steel and welded to the body.
involving a Stieltjes integral with a signed measure.
The open impeller design may have vanes cast integral with the hub, usually without side walls.
The viscoelastic force is modeled as a convolution integral with a sum of exponentials kernel.
A power piston is integral with a displacer and a heat regenerator.
The stress intensity factors are evaluated using interaction integral with the domain form.
The controller structure of MT and ES is a proportional integral with a single input.
We give the estimates for the Marcinkiewicz integral with rough variable kernels associated to surfaces.
In the following parts, we introduce the Wiener integral with respect to the Q-fBm.
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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