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Stock-based Compensation Expense (Stock Based Compensation Expense) (Details) - USD ($) $ in Millions | 3 Months Ended | 6 Months Ended
--- | --- | ---
Jul. 31, 2019 | Jul. 31, 2018 | Jul. 31, 2019 | Jul. 31, 2018
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items] |  |  |  |
Stock-based compensation expense related to stock awards and ESPP purchases | $ 88.2 | $ 56.9 | $ 163.4 | $ 111.3
Tax benefit | (0.1) | (0.2) | (0.3) | (0.6)
Stock-based compensation expense related to stock awards and ESPP purchases, net of tax | 88.1 | 56.7 | 163.1 | 110.7
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 | 3.4 | 3.1 | 7.0 | 5.8
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 | 1.4 | 0.9 | 2.7 | 1.7
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 | 36.0 | 25.9 | 68.5 | 49.9
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 | 30.8 | 18.7 | 57.5 | 36.5
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 | $ 16.6 | $ 8.3 | $ 27.7 | $ 17.4

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