Income Taxes - Differences between the U.S. statutory rate and the aggregate income tax provision (Details) - USD ($)	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
Income Tax Disclosure [Abstract]
First $1M of officer compensation									$ 1,000,000
Income tax provision (benefit) at U.S. Federal statutory rate									61,900,000	$ (9,000,000.0)	$ (188,400,000)
State income tax benefit, net of the U.S. Federal benefit									(5,300,000)	(11,400,000)	(21,900,000)
Foreign income taxed at rates different from the U.S. statutory rate including GILTI									(41,200,000)	117,800,000	(53,300,000)
Valuation allowance adjustment									65,300,000	18,800,000	(82,500,000)
Transition tax and revisions due to subsequent regulations									9,600,000	(16,000,000.0)	408,400,000
Tax effect of non-deductible stock-based compensation									24,900,000	7,600,000	20,700,000
Stock compensation windfall / shortfall									(22,400,000)	(39,400,000)	(67,700,000)
Research and development tax credit benefit									(19,800,000)	(23,500,000)	(11,300,000)
Closure of income tax audits and changes in uncertain tax positions									(2,000,000.0)	(12,700,000)	1,200,000
Tax effect of officer compensation in excess of $1.0 million									3,400,000	5,000,000.0	2,200,000
Non-deductible expenses									5,400,000	1,500,000	2,100,000
Other									500,000	(600,000)	100,000
Income tax expense	$ (8,500,000)	$ 29,700,000	$ 26,300,000	$ 32,800,000	$ (31,700,000)	$ 35,200,000	$ 16,000,000.0	$ 18,600,000	$ 80,300,000	$ 38,100,000	$ 9,600,000