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Stock-based Compensation Expense (Stock Based Compensation Expense) (Details) - USD ($) $ in Millions | 3 Months Ended
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Apr. 30, 2020 | Apr. 30, 2019
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items] |  |
Stock-based compensation expense related to stock awards and ESPP purchases | $ 98.2 | $ 75.2
Tax benefit | (0.1) | (0.2)
Stock-based compensation expense related to stock awards and ESPP purchases, net of tax | 98.1 | 75.0
Cost of subscription and maintenance revenue |  |
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items] |  |
Stock-based compensation expense related to stock awards and ESPP purchases | 3.7 | 3.6
Cost of other revenue |  |
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items] |  |
Stock-based compensation expense related to stock awards and ESPP purchases | 1.5 | 1.3
Marketing and sales |  |
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items] |  |
Stock-based compensation expense related to stock awards and ESPP purchases | 40.7 | 32.5
Research and development |  |
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items] |  |
Stock-based compensation expense related to stock awards and ESPP purchases | 32.9 | 26.7
General and administrative |  |
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items] |  |
Stock-based compensation expense related to stock awards and ESPP purchases | $ 19.4 | $ 11.1

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