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Goodwill and Intangible Assets (Tables) | 6 Months Ended
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Mar. 31, 2021
Goodwill And Intangible Assets Disclosure [Abstract] |
Schedule of Goodwill and Acquired Intangible Assets | Goodwill and acquired intangible assets consisted of the following:
(in thousands) |  | March 31, 2021 |  |  | September 30, 2020 |
|  | Gross Carrying Amount |  |  | Accumulated Amortization |  |  | Net Book Value |  |  | Gross Carrying Amount |  |  | Accumulated Amortization |  |  | Net Book Value |
Goodwill (not amortized) |  |  |  |  |  |  |  |  |  | $ | 2,193,632 |  |  |  |  |  |  |  |  |  |  | $ | 1,625,786 |
Intangible assets with finite lives (amortized): |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Purchased software |  | $ | 484,190 |  |  | $ | 322,869 |  |  | $ | 161,321 |  |  | $ | 443,275 |  |  | $ | 309,124 |  |  | $ | 134,151 |
Capitalized software |  |  | 22,877 |  |  |  | 22,877 |  |  |  | — |  |  |  | 22,877 |  |  |  | 22,877 |  |  |  | — |
Customer lists and relationships |  |  | 575,836 |  |  |  | 337,194 |  |  |  | 238,642 |  |  |  | 418,953 |  |  |  | 322,092 |  |  |  | 96,861 |
Trademarks and trade names |  |  | 26,959 |  |  |  | 16,612 |  |  |  | 10,347 |  |  |  | 22,687 |  |  |  | 16,129 |  |  |  | 6,558 |
Other |  |  | 4,019 |  |  |  | 4,019 |  |  |  | — |  |  |  | 4,017 |  |  |  | 4,017 |  |  |  | — |
Total intangible assets with finite lives |  | $ | 1,113,881 |  |  | $ | 703,571 |  |  | $ | 410,310 |  |  | $ | 911,809 |  |  | $ | 674,239 |  |  | $ | 237,570 |
Total goodwill and acquired intangible assets |  |  |  |  |  |  |  |  |  | $ | 2,603,942 |  |  |  |  |  |  |  |  |  |  | $ | 1,863,356 |
Schedule of Changes in Goodwill by Reportable Segments | Changes in goodwill presented by reportable segments were as follows:
(in thousands) |  | Software Products |  |  | Professional Services |  |  | Total |
Balance, October 1, 2020 |  | $ | 1,583,316 |  |  | $ | 42,470 |  |  | $ | 1,625,786 |
Arena acquisition |  |  | 562,657 |  |  |  | — |  |  |  | 562,657 |
Other acquisitions |  |  | 963 |  |  |  | — |  |  |  | 963 |
Foreign currency translation adjustment |  |  | 4,116 |  |  |  | 110 |  |  |  | 4,226 |
Balance, March 31, 2021 |  | $ | 2,151,052 |  |  | $ | 42,580 |  |  | $ | 2,193,632 |
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 |  |  | Six months ended |
|  | March 31, 2021 |  |  | March 28, 2020 |  |  | March 31, 2021 |  |  | March 28, 2020 |
Amortization of acquired intangible assets |  | $ | 7,650 |  |  | $ | 7,288 |  |  | $ | 14,197 |  |  | $ | 14,065 |
Cost of license revenue |  |  | 7,117 |  |  |  | 6,879 |  |  |  | 13,384 |  |  |  | 13,678 |
Total amortization expense |  | $ | 14,767 |  |  | $ | 14,167 |  |  | $ | 27,581 |  |  | $ | 27,743 |

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