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Goodwill and Intangible Assets - Schedule of Goodwill and Acquired Intangible Assets (Details) - USD ($) $ in Thousands | Mar. 31, 2023 | Sep. 30, 2022
--- | --- | ---
Goodwill (not amortized) | $ 3,369,041 | $ 2,353,654
Intangible assets with finite lives (amortized), Gross Carrying Amount | 1,796,453 | 1,152,018
Intangible assets with finite lives (amortized), Accumulated Amortization | 817,232 | 769,300
Intangible assets with finite lives (amortized), Net Book Value | 979,221 | 382,718
Intangible Assets, Net (Including Goodwill) | 4,348,262 | 2,736,372
Purchased Software |  |
Intangible assets with finite lives (amortized), Gross Carrying Amount | 616,665 | 502,859
Intangible assets with finite lives (amortized), Accumulated Amortization | 376,637 | 355,857
Intangible assets with finite lives (amortized), Net Book Value | 240,028 | 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 | 1,116,040 | 594,970
Intangible assets with finite lives (amortized), Accumulated Amortization | 395,336 | 369,390
Intangible assets with finite lives (amortized), Net Book Value | 720,704 | 225,580
Trademarks and Trade Names |  |
Intangible assets with finite lives (amortized), Gross Carrying Amount | 36,968 | 27,546
Intangible assets with finite lives (amortized), Accumulated Amortization | 18,479 | 17,410
Intangible assets with finite lives (amortized), Net Book Value | 18,489 | 10,136
Other |  |
Intangible assets with finite lives (amortized), Gross Carrying Amount | 3,903 | 3,766
Intangible assets with finite lives (amortized), Accumulated Amortization | 3,903 | 3,766
Intangible assets with finite lives (amortized), Net Book Value | $ 0 | $ 0

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