Selected Quarterly Financial Information (Unaudited) (Details) - USD ($) $ / shares in Units, $ in Millions	3 Months Ended								12 Months Ended
	Jan. 31, 2021	Oct. 31, 2020	Jul. 31, 2020	Apr. 30, 2020	Jan. 31, 2020	Oct. 31, 2019	Jul. 31, 2019	Apr. 30, 2019	Jan. 31, 2021	Jan. 31, 2020	Jan. 31, 2019
Quarterly Financial Information Disclosure [Abstract]
Net revenue	$ 1,039.2	$ 952.4	$ 913.1	$ 885.7	$ 899.3	$ 842.7	$ 796.8	$ 735.5	$ 3,790.4	$ 3,274.3	$ 2,569.8
Gross profit	948.6	868.7	832.2	803.8	816.1	763.2	717.3	652.8	3,453.3	2,949.4	2,283.9
Income from operations	184.4	168.0	146.1	130.6	133.8	110.6	73.8	24.8	629.1	343.0	(25.0)
(Provision) benefit for income taxes	740.2	(23.9)	(30.8)	(24.0)	8.5	(29.7)	(26.3)	(32.8)	661.5	(80.3)	(38.1)
Net income (loss)	$ 911.3	$ 132.2	$ 98.2	$ 66.5	$ 131.8	$ 66.7	$ 40.2	$ (24.2)	$ 1,208.2	$ 214.5	$ (80.8)
Basic net (loss) income per share (in dollars per share)	$ 4.15	$ 0.60	$ 0.45	$ 0.30	$ 0.60	$ 0.30	$ 0.18	$ (0.11)	$ 5.51	$ 0.98	$ (0.37)
Diluted net (loss) income per share (in dollars per share)	$ 4.10	$ 0.59	$ 0.44	$ 0.30	$ 0.59	$ 0.30	$ 0.18	$ (0.11)	$ 5.44	$ 0.96	$ (0.37)
Income from operations includes the following items:
Stock-based compensation expense	$ 108.3	$ 97.4	$ 95.9	$ 98.2	$ 105.0	$ 94.0	$ 88.2	$ 75.2	$ 399.8	$ 362.4
Amortization of acquisition related intangibles	17.2	17.2	16.9	17.1	18.0	18.1	18.3	19.0	68.4	73.4
Acquisition related costs	$ 4.7	$ 4.5	$ 3.5	$ 1.9	2.1	2.5	6.0	12.7	14.6	23.3
Restructuring and other exit costs, net					$ 0.0	$ 0.1	$ 0.2	$ 0.2	$ 0.0	$ 0.5	$ 41.9