Goodwill and Intangible Assets, Net - Details Regarding Total Definite-Lived Purchased Intangible Assets (Detail) - USD ($) $ in Thousands	Sep. 30, 2024	Sep. 30, 2023
Definite-Lived Intangible Assets [Line Items]
Gross	$ 1,764,172	$ 1,720,716
Accumulated Amortization	(1,603,443)	(1,539,177)
Total	160,729	181,539
Core Technology [Member]
Definite-Lived Intangible Assets [Line Items]
Gross	947,733	939,732
Accumulated Amortization	(898,086)	(875,336)
Total	49,647	64,396
Customer Relationships [Member]
Definite-Lived Intangible Assets [Line Items]
Gross	766,251	732,580
Accumulated Amortization	(658,173)	(619,232)
Total	108,078	113,348
Other [Member]
Definite-Lived Intangible Assets [Line Items]
Gross	50,188	48,404
Accumulated Amortization	(47,184)	(44,609)
Total	$ 3,004	$ 3,795