"an extensive report" is correct and can be used in written English. You can use it when referring to a document that is lengthy and contains a lot of detail. For example, "The team wrote an extensive report on the effects of the new policy.".
The FBI and Department of Homeland Security released an extensive report last week, detailing their evidence that Russia was behind the attacks.
Reporters Without Borders (RSF) published an extensive report into "digital mercenaries" such as Hacking Team, who provide the technical expertise which underpins Snowden-era electronic surveillance.
Editors' Note: June 12 , 2003 Thursday On May 11 The Times published an extensive report about plagiarism and fabrications by Jayson Blair before his resignation as a reporter for The Times a week earlier.
In October, the College Board released an extensive report documenting the gap.
Human Rights Watch is planning to release an extensive report on the killings soon.
Mr. Vines wrote an extensive report on Equatorial Guinea's human rights failings published this summer by Human Rights Watch.
When a Senate committee in Canada issued an extensive report on the country's news media in 2006, it took particular note of the situation in New Brunswick.
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Head Translator and Proofreader @ organictranslations.eu