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Goodwill and Intangible Assets, Net - Details Regarding Total Definite-Lived Purchased Intangible Assets (Detail) - USD ($)
$ in Thousands
Sep. 30, 2022
Sep. 30, 2021
Definite-Lived Intangible Assets [Line Items]    
Gross $ 1,649,812 $ 1,633,443
Accumulated Amortization (1,471,500) (1,374,411)
Total 178,312 259,032
Core Technology [Member]    
Definite-Lived Intangible Assets [Line Items]    
Gross 898,448 896,149
Accumulated Amortization (837,404) (777,419)
Total 61,044 118,730
Customer Relationships [Member]    
Definite-Lived Intangible Assets [Line Items]    
Gross 703,824 689,754
Accumulated Amortization (591,119) (556,716)
Total 112,705 133,038
Other [Member]    
Definite-Lived Intangible Assets [Line Items]    
Gross 47,540 47,540
Accumulated Amortization (42,977) (40,276)
Total $ 4,563 $ 7,264