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Goodwill and Acquired Intangible Assets - Schedule of Goodwill and Acquired Intangible Assets (Details) - USD ($) $ in Thousands | Sep. 30, 2021 | Sep. 30, 2020 | Sep. 30, 2019
--- | --- | --- | ---
Goodwill (not amortized) | $ 2,191,887 | $ 1,625,786 | $ 1,238,179
Intangible assets with finite lives (amortized), Gross Carrying Amount | 1,112,070 | 911,809 |
Intangible assets with finite lives (amortized), Accumulated Amortization | 733,103 | 674,239 |
Intangible assets with finite lives (amortized), Net Book Value | 378,967 | 237,570 |
Intangible assets | 2,570,854 | 1,863,356 |
Intangible Assets, Net (Including Goodwill) | 2,570,854 | 1,863,356 |
Purchased Software |  |  |
Intangible assets with finite lives (amortized), Gross Carrying Amount | 483,771 | 443,275 |
Intangible assets with finite lives (amortized), Accumulated Amortization | 338,542 | 309,124 |
Intangible assets with finite lives (amortized), Net Book Value | 145,229 | 134,151 |
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 | 574,516 | 418,953 |
Intangible assets with finite lives (amortized), Accumulated Amortization | 350,648 | 322,092 |
Intangible assets with finite lives (amortized), Net Book Value | 223,868 | 96,861 |
Trademarks |  |  |
Intangible assets with finite lives (amortized), Gross Carrying Amount | 26,906 | 22,687 |
Intangible assets with finite lives (amortized), Accumulated Amortization | 17,036 | 16,129 |
Intangible assets with finite lives (amortized), Net Book Value | 9,870 | 6,558 |
Other |  |  |
Intangible assets with finite lives (amortized), Gross Carrying Amount | 4,000 | 4,017 |
Intangible assets with finite lives (amortized), Accumulated Amortization | 4,000 | 4,017 |
Intangible assets with finite lives (amortized), Net Book Value | $ 0 | $ 0 |

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