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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

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- Definition Effective Income Tax Rate Reconciliation, Change in Valuation Allowance due to Adoption of Accounting Pronouncement + References No definition available. + Details
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- Definition The portion of the difference between total income tax expense (benefit) as reported in the Income Statement and the expected income tax expense (benefit) computed by applying the domestic federal statutory income tax rates to pretax income from continuing operations attributable to closure of income tax audits and changes in uncertain tax positions. + References No definition available. + Details
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- Definition The amount of income tax expense or benefit for the period computed by applying the domestic federal statutory tax rates to pretax income from continuing operations. + References Reference 1: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 740 -SubTopic 10 -Section 50 -Paragraph 12 -URI http://asc.fasb.org/extlink&oid=84230637&loc=d3e32687-109319 Reference 2: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 235 -SubTopic 10 -Section S99 -Paragraph 1 -Subparagraph (SX 210.4-08(h)(2)) -URI http://asc.fasb.org/extlink&oid=26873400&loc=d3e23780-122690 Reference 3: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 740 -SubTopic 10 -Section 50 -Paragraph 13 -URI http://asc.fasb.org/extlink&oid=84230637&loc=d3e32698-109319 + Details
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