There is no legal requirement to keep a digital mileage logbook per se, but it is your responsibility as a company to be able to show how the car has been used in the event of a possible audit by the Swedish Tax Authority.
A digital mileage logbook is the best and easiest proof to provide an overview of all trips, both private and work-related. Let Dina Mil do the hard work of registering the trips, leaving you only having to add notes about the purpose. Maybe you will even discover business trips that you have missed?