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Goodwill and Intangible Assets (Tables) | 3 Months Ended
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Dec. 31, 2023
Goodwill and Intangible Assets Disclosure [Abstract] |
Schedule of Goodwill and Acquired Intangible Assets | Goodwill and acquired intangible assets consisted of the following:
(in thousands) |  | December 31, 2023 |  |  | September 30, 2023 |
|  | Gross Carrying Amount |  |  | Accumulated Amortization |  |  | Net Book Value |  |  | Gross Carrying Amount |  |  | Accumulated Amortization |  |  | Net Book Value |
Goodwill (not amortized) |  |  |  |  |  |  |  | $ | 3,458,463 |  |  |  |  |  |  |  |  | $ | 3,358,511 |
Intangible assets with finite lives (amortized): |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Purchased software |  | $ | 629,554 |  |  | $ | 406,952 |  |  | $ | 222,602 |  |  | $ | 615,915 |  |  | $ | 395,109 |  |  | $ | 220,806 |
Capitalized software |  |  | 22,877 |  |  |  | 22,877 |  |  |  | — |  |  |  | 22,877 |  |  |  | 22,877 |  |  |  | — |
Customer lists and relationships |  |  | 1,140,213 |  |  |  | 427,224 |  |  |  | 712,989 |  |  |  | 1,116,117 |  |  |  | 413,125 |  |  |  | 702,992 |
Trademarks and trade names |  |  | 37,892 |  |  |  | 20,113 |  |  |  | 17,779 |  |  |  | 36,851 |  |  |  | 19,400 |  |  |  | 17,451 |
Other |  |  | 3,928 |  |  |  | 3,928 |  |  |  | — |  |  |  | 3,867 |  |  |  | 3,867 |  |  |  | — |
Total intangible assets with finite lives |  | $ | 1,834,464 |  |  | $ | 881,094 |  |  | $ | 953,370 |  |  | $ | 1,795,627 |  |  | $ | 854,378 |  |  | $ | 941,249 |
Total goodwill and acquired intangible assets |  |  |  |  |  |  |  | $ | 4,411,833 |  |  |  |  |  |  |  |  | $ | 4,299,760 |
Schedule of Changes in Goodwill by Reportable Segments | Changes in Goodwill were as follows:
(in thousands) |  |
Balance, October 1, 2023 | $ | 3,358,511 |
Acquisitions |  | 77,118 |
Foreign currency translation adjustment |  | 22,834 |
Balance, December 31, 2023 | $ | 3,458,463 |
Schedule of Aggregate Amortization Expense for Intangible Assets with Finite Lives | The aggregate amortization expense for intangible assets with finite lives is classified in our Consolidated Statements of Operations as follows:
(in thousands) |  | Three months ended |
|  | December 31, 2023 |  |  | December 31, 2022 |
Amortization of acquired intangible assets |  | $ | 10,363 |  |  | $ | 8,026 |
Cost of revenue |  |  | 9,566 |  |  |  | 6,142 |
Total amortization expense |  | $ | 19,929 |  |  | $ | 14,168 |

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