Goodwill (Changes in the Carrying Amount of Goodwill) (Details)	3 Months Ended	9 Months Ended
	Oct. 31, 2020 USD ($)	Oct. 31, 2020 USD ($) segment reporting_unit
Goodwill [Roll Forward]
Goodwill gross, beginning of the period		$ 2,594,200,000
Less: accumulated impairment losses, beginning of the period		(149,200,000)
Goodwill net, beginning of the period		2,445,000,000.0
Additions arising from acquisitions during the period		31,400,000
Effect of foreign currency translation, measurement period adjustments, and other		7,800,000
Goodwill net, end of the period	$ 2,484,200,000	$ 2,484,200,000
Number of operating segments | segment		1
Number of reporting units | reporting_unit		1
Goodwill impairment loss	$ 0	$ 0