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Goodwill and Intangible Assets, Net - Details Regarding Total Definite-Lived Purchased Intangible Assets (Detail) - USD ($) $ in Thousands | Sep. 30, 2021 | Sep. 30, 2020
--- | --- | ---
Definite-Lived Intangible Assets [Line Items] |  |
Gross | $ 1,633,443 | $ 1,586,929
Accumulated Amortization | (1,374,411) | (1,290,595)
Total | 259,032 | 296,334
Core Technology [Member] |  |
Definite-Lived Intangible Assets [Line Items] |  |
Gross | 896,149 | 896,814
Accumulated Amortization | (777,419) | (735,534)
Total | 118,730 | 161,280
Customer Relationships [Member] |  |
Definite-Lived Intangible Assets [Line Items] |  |
Gross | 689,754 | 642,575
Accumulated Amortization | (556,716) | (517,670)
Total | 133,038 | 124,905
Other [Member] |  |
Definite-Lived Intangible Assets [Line Items] |  |
Gross | 47,540 | 47,540
Accumulated Amortization | (40,276) | (37,391)
Total | $ 7,264 | $ 10,149

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