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The phrase "studies have reported" is correct and can be used in written English.
It can be used when referring to research that has already been conducted and published. For example, "Several studies have reported that students who engage in physical activity improve their academic performance."
Exact(60)
(Other studies have reported lower numbers).
Any number of studies have reported and made recommendations.
Previous studies have reported conflicting results.
However, published studies have reported inconsistent results.
However, individual studies have reported controversial results.
Previous studies have reported lower verbal IQ than nonverbal IQ.
Several studies have reported high job satisfaction among research nurses.
However, several studies have reported genetic variations in iPSC genomes.
Many studies have reported the mechanism underlying umami taste.
Few studies have reported the acoustic characteristics of youth choirs.
Previous studies have reported that the intrathecal (i.t).
More suggestions(16)
studies included reported
education have reported
literature have reported
found have reported
studies identified reported
trial have reported
studies evaluated reported
science have reported
studies established reported
university have reported
studies have shown
studies have bolstered
studies have dismissed
studies have confirmed
studies have produced
studies have suggested
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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