Goodwill and Intangible Assets, Net - Details Regarding Total Definite-Lived Purchased Intangible Assets (Detail) - USD ($) $ in Thousands	Sep. 30, 2023	Sep. 30, 2022
Definite-Lived Intangible Assets [Line Items]
Gross	$ 1,720,716	$ 1,649,812
Accumulated Amortization	(1,539,177)	(1,471,500)
Total	181,539	178,312
Core Technology [Member]
Definite-Lived Intangible Assets [Line Items]
Gross	939,732	898,448
Accumulated Amortization	(875,336)	(837,404)
Total	64,396	61,044
Customer Relationships [Member]
Definite-Lived Intangible Assets [Line Items]
Gross	732,580	703,824
Accumulated Amortization	(619,232)	(591,119)
Total	113,348	112,705
Other [Member]
Definite-Lived Intangible Assets [Line Items]
Gross	48,404	47,540
Accumulated Amortization	(44,609)	(42,977)
Total	$ 3,795	$ 4,563

Accumulated amount of amortization of assets, excluding financial assets and goodwill, lacking physical substance with a finite life.

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