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Goodwill and Acquired Intangible Assets - Schedule of Goodwill and Acquired Intangible Assets (Details) - USD ($) $ in Thousands | Sep. 30, 2020 | Sep. 30, 2019 | Sep. 30, 2018
--- | --- | --- | ---
Goodwill (not amortized) | $ 1,625,786 | $ 1,238,179 | $ 1,182,457
Intangible assets with finite lives (amortized), Gross Carrying Amount | 911,809 | 778,968 |
Intangible assets with finite lives (amortized), Accumulated Amortization | 674,239 | 609,019 |
Intangible assets with finite lives (amortized), Net Book Value | 237,570 | 169,949 |
Intangible Assets, Net (Including Goodwill) | 1,863,356 | 1,408,128 |
Purchased Software |  |  |
Intangible assets with finite lives (amortized), Gross Carrying Amount | 443,275 | 377,359 |
Intangible assets with finite lives (amortized), Accumulated Amortization | 309,124 | 278,144 |
Intangible assets with finite lives (amortized), Net Book Value | 134,151 | 99,215 |
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 | 418,953 | 355,931 |
Intangible assets with finite lives (amortized), Accumulated Amortization | 322,092 | 288,828 |
Intangible assets with finite lives (amortized), Net Book Value | 96,861 | 67,103 |
Trademarks |  |  |
Intangible assets with finite lives (amortized), Gross Carrying Amount | 22,687 | 18,891 |
Intangible assets with finite lives (amortized), Accumulated Amortization | 16,129 | 15,260 |
Intangible assets with finite lives (amortized), Net Book Value | 6,558 | 3,631 |
Other |  |  |
Intangible assets with finite lives (amortized), Gross Carrying Amount | 4,017 | 3,910 |
Intangible assets with finite lives (amortized), Accumulated Amortization | 4,017 | 3,910 |
Intangible assets with finite lives (amortized), Net Book Value | $ 0 | $ 0 |

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