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Goodwill and Acquired Intangible Assets - Schedule of Goodwill and Acquired Intangible Assets (Details) - USD ($) $ in Thousands | Sep. 30, 2023 | Sep. 30, 2022 | Sep. 30, 2021
--- | --- | --- | ---
Goodwill (not amortized) | $ 3,358,511 | $ 2,353,654 | $ 2,191,887
Intangible assets with finite lives (amortized), Gross Carrying Amount | 1,795,627 | 1,152,018 |
Intangible assets with finite lives (amortized), Accumulated Amortization | 854,378 | 769,300 |
Intangible assets with finite lives (amortized), Net Book Value | 941,249 | 382,718 |
Intangible Assets, Net (Including Goodwill), Total | 4,299,760 | 2,736,372 |
Purchased Software |  |  |
Intangible assets with finite lives (amortized), Gross Carrying Amount | 615,915 | 502,859 |
Intangible assets with finite lives (amortized), Accumulated Amortization | 395,109 | 355,857 |
Intangible assets with finite lives (amortized), Net Book Value | 220,806 | 147,002 |
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 | 1,116,117 | 594,970 |
Intangible assets with finite lives (amortized), Accumulated Amortization | 413,125 | 369,390 |
Intangible assets with finite lives (amortized), Net Book Value | 702,992 | 225,580 |
Trademarks and Trade Names |  |  |
Intangible assets with finite lives (amortized), Gross Carrying Amount | 36,851 | 27,546 |
Intangible assets with finite lives (amortized), Accumulated Amortization | 19,400 | 17,410 |
Intangible assets with finite lives (amortized), Net Book Value | 17,451 | 10,136 |
Other |  |  |
Intangible assets with finite lives (amortized), Gross Carrying Amount | 3,867 | 3,766 |
Intangible assets with finite lives (amortized), Accumulated Amortization | 3,867 | 3,766 |
Intangible assets with finite lives (amortized), Net Book Value | $ 0 | $ 0 |

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