Browser history locations are as follows
Edge and Internet explorer:
C:\Users\username\AppData\Local\Packages\Microsoft.MicrosoftEdge_\AC\MicrosoftEdge\User\Default\Favorites
C:\Users\username\AppData\Local\Packages\Microsoft.MicrosoftEdge_\AC\MicrosoftEdge\User\Default\Recovery
C:\Users\username\AppData\Local\Packages\Microsoft.MicrosoftEdge_\AC\MicrosoftEdge\User\Default\DataStore
C:\Users\username\AppData\Local\Microsoft\Windows\WebCache
C:\Users\username\AppData\Local\Microsoft\Windows\History
C:\Users\username\AppData\Local\Microsoft\Internet Explorer\IECompatData\
C:\Users\username\AppData\Local\Microsoft\Feeds Cache\
C:\Users\username\AppData\Local\Microsoft\Windows\WebCache\
C:\Users\username\AppData\Local\Microsoft\Windows\Temporary Internet Files\
Chrome:
C:\Users\username\AppData\Local\Google\Chrome\User Data\Default\History
Firefox:
C:\Users\username\AppData\Roaming\Mozilla\Firefox\Profiles\
Locations may change between versions, so you might want to look it up to verify.
If you have a harddrive image, consider dropping it in Autopsy or similar, and use the built-in parsers for extracting the browser history for ease-of-use. If you have live access to the system and it’s OK to inflict changes, use https://www.nirsoft.net/utils/browsing_history_view.html or any of the other Nirsoft browser tools. This can also be used to load and display extracted history files.