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Goodwill and Acquired Intangible Assets - Schedule of Aggregate Amortization Expense for Intangible Assets with Finite Lives (Details) - USD ($)
$ in Thousands
12 Months Ended
Sep. 30, 2021
Sep. 30, 2020
Sep. 30, 2019
Goodwill And Intangible Assets Disclosure [Abstract]      
Amortization of acquired intangible assets $ 29,396 $ 28,713 $ 23,841
Cost of software revenue 29,769 27,391 27,307
Total amortization expense $ 59,165 $ 56,104 $ 51,148