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Equity Compensation - Stock Based Compensation Expense (Details) - USD ($) $ in Millions | 3 Months Ended
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Apr. 30, 2021 | Apr. 30, 2020
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items] |  |
Stock-based compensation expense related to stock awards and ESPP purchases | $ 115.8 | $ 98.2
Tax benefit | (16.0) | (0.1)
Stock-based compensation expense related to stock awards and ESPP purchases, net of tax | 99.8 | 98.1
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 | 5.3 | 3.7
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 | 1.8 | 1.5
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 | 48.3 | 40.7
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 | 46.7 | 32.9
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 | $ 13.7 | $ 19.4

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