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, 2020	Sep. 30, 2019	Sep. 30, 2018
Goodwill And Intangible Assets Disclosure [Abstract]
Amortization of acquired intangible assets	$ 28,713	$ 23,841	$ 31,350
Cost of software revenue	27,391	27,307	26,706
Total amortization expense	$ 56,104	$ 51,148	$ 58,056

The aggregate expense charged against earnings to allocate the cost of intangible assets (nonphysical assets not used in production) in a systematic and rational manner to the periods expected to benefit from such assets. As a noncash expense, this element is added back to net income when calculating cash provided by or used in operations using the indirect method.

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