Selected Quarterly Financial Information (Unaudited) (Details) - USD ($) $ / shares in Units, $ in Millions	3 Months Ended								12 Months Ended
	Jan. 31, 2020	Oct. 31, 2019	Jul. 31, 2019	Apr. 30, 2019	Jan. 31, 2019	Oct. 31, 2018	Jul. 31, 2018	Apr. 30, 2018	Jan. 31, 2020	Jan. 31, 2019	Jan. 31, 2018
Quarterly Financial Information Disclosure [Abstract]
Net revenue	$ 899.3	$ 842.7	$ 796.8	$ 735.5	$ 737.3	$ 660.9	$ 611.7	$ 559.9	$ 3,274.3	$ 2,569.8	$ 2,056.6
Gross profit	816.1	763.2	717.3	652.8	660.3	588.6	541.9	493.1	2,949.4	2,283.9	1,753.2
Income from operations	133.8	110.6	73.8	24.8	40.3	14.7	(24.7)	(55.3)	343.0	(25.0)	(509.1)
(Provision) benefit for income taxes	8.5	(29.7)	(26.3)	(32.8)	31.7	(35.2)	(16.0)	(18.6)	(80.3)	(38.1)	(9.6)
Net income (loss)	$ 131.8	$ 66.7	$ 40.2	$ (24.2)	$ 64.7	$ (23.7)	$ (39.4)	$ (82.4)	$ 214.5	$ (80.8)	$ (566.9)
Basic net (loss) income per share (in dollars per share)	$ 0.60	$ 0.30	$ 0.18	$ (0.11)	$ 0.30	$ (0.11)	$ (0.18)	$ (0.38)	$ 0.98	$ (0.37)	$ (2.58)
Diluted net (loss) income per share (in dollars per share)	$ 0.59	$ 0.30	$ 0.18	$ (0.11)	$ 0.29	$ (0.11)	$ (0.18)	$ (0.38)	$ 0.96	$ (0.37)	$ (2.58)
(Loss) Income from operations includes the following items:
Stock-based compensation expense	$ 105.0	$ 94.0	$ 88.2	$ 75.2	$ 74.0	$ 64.2	$ 56.9	$ 54.4	$ 362.4	$ 249.5
Amortization of acquisition related intangibles	18.0	18.1	18.3	19.0	11.1	7.8	7.2	7.4	73.4	33.5
CEO transition costs					0.0	0.0	(0.1)	0.0		(0.1)
Acquisition related costs	2.1	2.5	6.0	12.7	11.9	1.8	2.5	0.0	23.3	16.2
Restructuring and other exit costs, net	$ 0.0	$ 0.1	$ 0.2	$ 0.2	$ 1.9	$ 3.7	$ 13.8	$ 22.5	$ 0.5	$ 41.9	$ 94.1