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The phrase "after analysis of your request" is correct and usable in written English.
It can be used when discussing the evaluation or examination of a request made by someone.
Example: "After analysis of your request, we have determined that we can proceed with the project."
Alternatives: "following the review of your request" or "after reviewing your request".
Similar(60)
The review board must arrange a hearing within six weeks of your request (or as soon as possible after that).
Also consider the timing of your request.
Keep track of your request.
Ask your parents to explain their denial of your request.
Look for a summary of your request.
The other player will be informed of your request.
Emphasize the importance of your request in the second paragraph.
Start by writing a one-paragraph description of your request.
If I'm right in my analysis of your manager, though he may find your request a bit surprising, it's unlikely he will take it personally.
But after making your selections, there will be an analysis of your responses.
But after making your selections, there will be an analysis of your responses.\n And don't forget.
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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