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, 2023	Sep. 30, 2022	Sep. 30, 2021
Goodwill and Intangible Assets Disclosure [Abstract]
Amortization of acquired intangible assets	$ 40,022	$ 34,970	$ 29,396
Cost of software revenue	35,694	25,578	29,769
Total amortization expense	$ 75,716	$ 60,548	$ 59,165

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.

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Section 45
-Paragraph 28
-Subparagraph (b)
-SubTopic 10
-Topic 230
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482740/230-10-45-28

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 350
-SubTopic 30
-Section 45
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482686/350-30-45-2

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 350
-SubTopic 30
-Section 50
-Paragraph 2
-Subparagraph (a)(2)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482665/350-30-50-2

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