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Goodwill and Intangible Assets - Intangible Table by Major Class (Details) - USD ($)
$ in Thousands
Nov. 30, 2022
Aug. 31, 2022
Finite-Lived Intangible Assets [Line Items]    
Gross Carrying Amount $ 3,117,160 $ 2,971,077
Accumulated Amortization (1,087,146) (1,040,269)
Net Carrying Amount 2,030,014 1,930,808
Customer-related    
Finite-Lived Intangible Assets [Line Items]    
Gross Carrying Amount 2,637,724 2,498,001
Accumulated Amortization (872,216) (842,056)
Net Carrying Amount 1,765,508 1,655,945
Technology    
Finite-Lived Intangible Assets [Line Items]    
Gross Carrying Amount 288,708 283,251
Accumulated Amortization (110,107) (96,782)
Net Carrying Amount 178,601 186,469
Patents    
Finite-Lived Intangible Assets [Line Items]    
Gross Carrying Amount 126,385 126,950
Accumulated Amortization (70,784) (70,745)
Net Carrying Amount 55,601 56,205
Other    
Finite-Lived Intangible Assets [Line Items]    
Gross Carrying Amount 64,343 62,875
Accumulated Amortization (34,039) (30,686)
Net Carrying Amount $ 30,304 $ 32,189