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Goodwill and Acquired Intangible Assets - Additional Information (Details)
$ in Thousands
12 Months Ended
Sep. 30, 2021
USD ($)
Segment
Sep. 30, 2020
USD ($)
Number of operating segments | Segment 2  
Number of reportable segments | Segment 2  
Intangible assets $ 2,570,854 $ 1,863,356
Estimated aggregate future amortization expense for intangible assets, 2021 57,900  
Estimated aggregate future amortization expense for intangible assets, 2022 49,500  
Estimated aggregate future amortization expense for intangible assets, 2023 40,800  
Estimated aggregate future amortization expense for intangible assets, 2024 34,600  
Estimated aggregate future amortization expense for intangible assets, 2025 31,000  
Estimated aggregate future amortization expense for intangible assets, thereafter 165,200  
Software Products    
Intangible assets 2,525,700 1,818,100
Professional Services    
Intangible assets $ 45,200 $ 45,300