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"By investigating" is correct and usable in written English.
It is a subordinating conjunction that introduces a subordinate clause expressing a purpose or result. For example: By investigating the facts, the detective was able to uncover the truth about the crime.
Exact(59)
By investigating the stability of (8) we arrive at Theorem 3.1.
By investigating the WASP using response surface correlation, the factors governing steam injections operations are evaluated.
By investigating the stability of the above equation we arrive at the following theorem.
Alupot was called insane by investigating police officers.
An unhappy suburban mother gains her independence by investigating a murder.
Firstly, it set a benchmark by investigating a complaint made by a group.
He concludes by investigating the future survival of humanity and other intelligent races.
That is what we discover over and over by investigating particular cases.
It allows visitors to perform the role of a detective by investigating crime scenes.
He called on member countries to show "greater institutional responsibility" by investigating and prosecuting their troops.
United has responded, appropriately, by investigating the incident and reaching out to its unhappy flyer.
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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