Goodwill and Acquired Intangible Assets - Additional Information (Details) $ in Thousands	12 Months Ended
	Sep. 30, 2020 USD ($) Segment	Sep. 30, 2019 USD ($)
Number of operating segments | Segment	2
Number of reportable segments | Segment	2
Intangible assets	$ 1,863,356	$ 1,408,128
Estimated aggregate future amortization expense for intangible assets, 2021	52,900
Estimated aggregate future amortization expense for intangible assets, 2022	39,100
Estimated aggregate future amortization expense for intangible assets, 2023	29,000
Estimated aggregate future amortization expense for intangible assets, 2024	20,300
Estimated aggregate future amortization expense for intangible assets, 2025	17,300
Estimated aggregate future amortization expense for intangible assets, thereafter	79,000
Software Products
Intangible assets	1,818,100	1,362,400
Professional Services
Intangible assets	$ 45,300	$ 45,700