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Goodwill and Intangible Assets, Net - Details Regarding Total Definite-Lived Purchased Intangible Assets (Detail) - USD ($) $ in Thousands | Sep. 30, 2020 | Sep. 30, 2019
--- | --- | ---
Definite-Lived Intangible Assets [Line Items] |  |
Gross | $ 1,586,929 | $ 1,414,980
Accumulated Amortization | (1,290,595) | (1,209,818)
Total | 296,334 | 205,162
Core Technology [Member] |  |
Definite-Lived Intangible Assets [Line Items] |  |
Gross | 896,814 | 775,479
Accumulated Amortization | (735,534) | (690,961)
Total | 161,280 | 84,518
Customer Relationships [Member] |  |
Definite-Lived Intangible Assets [Line Items] |  |
Gross | 642,575 | 594,555
Accumulated Amortization | (517,670) | (483,313)
Total | 124,905 | 111,242
Other [Member] |  |
Definite-Lived Intangible Assets [Line Items] |  |
Gross | 47,540 | 44,946
Accumulated Amortization | (37,391) | (35,544)
Total | $ 10,149 | $ 9,402

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