Goodwill and Acquired Intangible Assets - Additional Information (Details) $ in Thousands	12 Months Ended
	Sep. 30, 2022 USD ($) Segment	Sep. 30, 2021 USD ($)
Number of operating segments | Segment	2
Number of reportable segments | Segment	2
Intangible assets	$ 2,736,372	$ 2,570,854
Estimated aggregate future amortization expense for intangible assets, 2023	56,400
Estimated aggregate future amortization expense for intangible assets, 2024	48,300
Estimated aggregate future amortization expense for intangible assets, 2025	42,100
Estimated aggregate future amortization expense for intangible assets, 2026	38,700
Estimated aggregate future amortization expense for intangible assets, 2027	36,200
Estimated aggregate future amortization expense for intangible assets, thereafter	161,000
Software Products
Intangible assets	2,725,200	2,525,700
Professional Services
Intangible assets	$ 11,200	$ 45,200