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Goodwill and Acquired Intangible Assets (Tables) | 12 Months Ended
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Sep. 30, 2022
Goodwill and Intangible Assets Disclosure [Abstract] |
Schedule of Goodwill and Acquired Intangible Assets | Goodwill and acquired intangible assets consisted of the following:
(in thousands) |  | September 30, 2022 |  |  | September 30, 2021 |
|  | Gross Carrying Amount |  |  | Accumulated Amortization |  |  | Net Book Value |  |  | Gross Carrying Amount |  |  | Accumulated Amortization |  |  | Net Book Value |
Goodwill (not amortized) |  |  |  |  |  |  |  | $ | 2,353,654 |  |  |  |  |  |  |  |  | $ | 2,191,887 |
Intangible assets with finite lives (amortized)(1): |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Purchased software |  | $ | 502,859 |  |  | $ | 355,857 |  |  | $ | 147,002 |  |  | $ | 483,771 |  |  | $ | 338,542 |  |  | $ | 145,229 |
Capitalized software |  |  | 22,877 |  |  |  | 22,877 |  |  |  | — |  |  |  | 22,877 |  |  |  | 22,877 |  |  |  | — |
Customer lists and relationships |  |  | 594,970 |  |  |  | 369,390 |  |  |  | 225,580 |  |  |  | 574,516 |  |  |  | 350,648 |  |  |  | 223,868 |
Trademarks and trade names |  |  | 27,546 |  |  |  | 17,410 |  |  |  | 10,136 |  |  |  | 26,906 |  |  |  | 17,036 |  |  |  | 9,870 |
Other |  |  | 3,766 |  |  |  | 3,766 |  |  |  | — |  |  |  | 4,000 |  |  |  | 4,000 |  |  |  | — |
|  | $ | 1,152,018 |  |  | $ | 769,300 |  |  | $ | 382,718 |  |  | $ | 1,112,070 |  |  | $ | 733,103 |  |  | $ | 378,967 |
Total goodwill and acquired intangible assets |  |  |  |  |  |  |  | $ | 2,736,372 |  |  |  |  |  |  |  |  | $ | 2,570,854 |
(1) The weighted-average useful lives of purchased software, customer lists and relationships, and trademarks and trade names with a remaining net book value are 11 years, 11 years, and 12 years, respectively.
Schedule of Changes in Goodwill by Reportable Segment | Changes in goodwill presented by reportable segment were as follows:
(in thousands) |  | Software Products |  |  | Professional Services |  |  | Total |
Balance, September 30, 2020 |  | $ | 1,583,316 |  |  | $ | 42,470 |  |  | $ | 1,625,786 |
Arena acquisition |  |  | 563,620 |  |  |  | — |  |  |  | 563,620 |
Other acquisitions |  |  | 181 |  |  |  | 400 |  |  |  | 581 |
Foreign currency translation adjustments |  |  | 1,851 |  |  |  | 49 |  |  |  | 1,900 |
Balance, September 30, 2021 |  | $ | 2,148,968 |  |  | $ | 42,919 |  |  | $ | 2,191,887 |
Intland Software acquisition |  |  | 240,971 |  |  |  | — |  |  |  | 240,971 |
Other acquisitions |  |  | 691 |  |  |  | — |  |  |  | 691 |
Divestiture of business |  |  | — |  |  |  | (32,992 | ) |  |  | (32,992 | )
Foreign currency translation adjustments |  |  | (46,611 | ) |  |  | (292 | ) |  |  | (46,903 | )
Balance, September 30, 2022 |  | $ | 2,344,019 |  |  | $ | 9,635 |  |  | $ | 2,353,654 |
Schedule of Aggregate Amortization Expense for Intangible Assets with Finite Lives | The aggregate amortization expense for intangible assets with finite lives recorded for the years ended September 30, 2022, 2021 and 2020 was reflected in our Consolidated Statements of Operations as follows:
(in thousands) |  | Year ended September 30, |
|  | 2022 |  |  | 2021 |  |  | 2020 |
Amortization of acquired intangible assets |  | $ | 34,970 |  |  | $ | 29,396 |  |  | $ | 28,713 |
Cost of software revenue |  |  | 25,578 |  |  |  | 29,769 |  |  |  | 27,391 |
Total amortization expense |  | $ | 60,548 |  |  | $ | 59,165 |  |  | $ | 56,104 |

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