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Goodwill and Intangible Assets (Tables) | 3 Months Ended
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Dec. 31, 2024
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, 2024 |  |  | September 30, 2024 |
|  | Gross Carrying Amount |  |  | Accumulated Amortization |  |  | Net Book Value |  |  | Gross Carrying Amount |  |  | Accumulated Amortization |  |  | Net Book Value |
Goodwill (not amortized) |  |  |  |  |  |  |  | $ | 3,423,420 |  |  |  |  |  |  |  |  | $ | 3,461,891 |
Intangible assets with finite lives (amortized): |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Purchased software |  | $ | 628,414 |  |  | $ | 440,693 |  |  | $ | 187,721 |  |  | $ | 634,439 |  |  | $ | 436,471 |  |  | $ | 197,968 |
Capitalized software |  |  | 22,877 |  |  |  | 22,877 |  |  |  | — |  |  |  | 22,877 |  |  |  | 22,877 |  |  |  | — |
Customer lists and relationships |  |  | 1,129,789 |  |  |  | 460,818 |  |  |  | 668,971 |  |  |  | 1,141,086 |  |  |  | 457,718 |  |  |  | 683,368 |
Trademarks and trade names |  |  | 37,565 |  |  |  | 22,149 |  |  |  | 15,416 |  |  |  | 37,961 |  |  |  | 21,821 |  |  |  | 16,140 |
Other |  |  | 3,839 |  |  |  | 3,839 |  |  |  | — |  |  |  | 3,941 |  |  |  | 3,941 |  |  |  | — |
Total intangible assets with finite lives |  | $ | 1,822,484 |  |  | $ | 950,376 |  |  | $ | 872,108 |  |  | $ | 1,840,304 |  |  | $ | 942,828 |  |  | $ | 897,476 |
Total goodwill and acquired intangible assets |  |  |  |  |  |  |  | $ | 4,295,528 |  |  |  |  |  |  |  |  | $ | 4,359,367 |
Schedule of Changes in Goodwill by Reportable Segments | Changes in Goodwill were as follows:
(in thousands) |  |
Balance, October 1, 2024 | $ | 3,461,891 |
Foreign currency translation adjustment |  | (38,471 | )
Balance, December 31, 2024 | $ | 3,423,420 |
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, 2024 |  |  | December 31, 2023 |
Amortization of acquired intangible assets |  | $ | 11,440 |  |  | $ | 10,363 |
Cost of revenue |  |  | 8,300 |  |  |  | 9,566 |
Total amortization expense |  | $ | 19,740 |  |  | $ | 19,929 |

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