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Goodwill and Acquired Intangible Assets - Schedule of Goodwill and Acquired Intangible Assets (Details) - USD ($) $ in Thousands | Sep. 30, 2024 | Sep. 30, 2023 | Sep. 30, 2022
--- | --- | --- | ---
Goodwill (not amortized) | $ 3,461,891 | $ 3,358,511 | $ 2,353,654
Intangible assets with finite lives (amortized), Gross Carrying Amount | 1,840,304 | 1,795,627 |
Intangible assets with finite lives (amortized), Accumulated Amortization | 942,828 | 854,378 |
Intangible assets with finite lives (amortized), Net Book Value | 897,476 | 941,249 |
Intangible Assets, Net (Including Goodwill) | 4,359,367 | 4,299,760 |
Purchased Software |  |  |
Intangible assets with finite lives (amortized), Gross Carrying Amount | 634,439 | 615,915 |
Intangible assets with finite lives (amortized), Accumulated Amortization | 436,471 | 395,109 |
Intangible assets with finite lives (amortized), Net Book Value | 197,968 | 220,806 |
Capitalized Software |  |  |
Intangible assets with finite lives (amortized), Gross Carrying Amount | 22,877 | 22,877 |
Intangible assets with finite lives (amortized), Accumulated Amortization | 22,877 | 22,877 |
Intangible assets with finite lives (amortized), Net Book Value | 0 | 0 |
Customer Lists and Relationships |  |  |
Intangible assets with finite lives (amortized), Gross Carrying Amount | 1,141,086 | 1,116,117 |
Intangible assets with finite lives (amortized), Accumulated Amortization | 457,718 | 413,125 |
Intangible assets with finite lives (amortized), Net Book Value | 683,368 | 702,992 |
Trademarks and Trade Names |  |  |
Intangible assets with finite lives (amortized), Gross Carrying Amount | 37,961 | 36,851 |
Intangible assets with finite lives (amortized), Accumulated Amortization | 21,821 | 19,400 |
Intangible assets with finite lives (amortized), Net Book Value | 16,140 | 17,451 |
Other |  |  |
Intangible assets with finite lives (amortized), Gross Carrying Amount | 3,941 | 3,867 |
Intangible assets with finite lives (amortized), Accumulated Amortization | 3,941 | 3,867 |
Intangible assets with finite lives (amortized), Net Book Value | $ 0 | $ 0 |

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