Income Taxes - 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, 2018	Oct. 31, 2017	Jul. 31, 2017	Apr. 30, 2017	Jan. 31, 2017	Oct. 31, 2016	Jul. 31, 2016	Apr. 30, 2016	Jan. 31, 2018	Jan. 31, 2017	Jan. 31, 2016
Income Tax Disclosure [Abstract]
First $1M of officer compensation									$ 1,000,000,000,000
Income tax provision (benefit) at U.S. Federal statutory rate									(188,400,000)	$ (177,000,000.0)	$ (7,100,000)
State income tax benefit, net of the U.S. Federal benefit									(21,900,000)	(17,300,000)	(7,600,000)
Foreign income taxed at rates different from the U.S. statutory rate									(53,300,000)	22,300,000	(29,400,000)
U.S. valuation allowance									(82,500,000)	233,000,000.0	345,000,000.0
Transition tax									408,400,000	0	0
Increase in attributes due to ASU 2016-9 adoption										(119,400,000)	0
Change in valuation allowance from ASU 2016-9 adoption									0	119,400,000	0
Tax effect of non-deductible stock-based compensation									20,700,000	18,800,000	19,300,000
Stock compensation windfall / shortfall									(67,700,000)	(23,000,000.0)	0
Research and development tax credit benefit									(11,300,000)	(10,300,000)	(9,400,000)
Closure of income tax audits and changes in uncertain tax positions									1,200,000	8,200,000	(4,700,000)
Tax effect of officer compensation in excess of $1.0 million									2,200,000	2,200,000	1,400,000
Non-deductible expenses									2,100,000	2,000,000.0	2,600,000
Other									100,000	(600,000)	100,000
Income tax expense	$ (24,800,000)	$ 8,600,000	$ 17,600,000	$ 8,200,000	$ 5,200,000	$ 13,500,000	$ 25,200,000	$ 14,400,000	$ 9,600,000	$ 58,300,000	$ 310,200,000