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Stockholders' Equity (Recognized Stock-Based Compensation) (Details) - USD ($)
$ in Thousands
3 Months Ended 9 Months Ended
May 31, 2021
May 31, 2020
May 31, 2021
May 31, 2020
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Stock-based compensation expense $ 18,765 $ 16,882 $ 76,119 $ 62,214
Restricted stock units        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Stock-based compensation expense 15,956 14,299 67,553 54,783
Employee stock purchase plan        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Stock-based compensation expense $ 2,809 $ 2,583 $ 8,566 $ 7,431