Revenue from Contracts with Customers - Additional Information (Details) - USD ($)	3 Months Ended
	Dec. 31, 2021	Dec. 31, 2020	Sep. 30, 2021
Revenue from External Customer [Line Items]
Contract with customer, asset, expected to be transferred to receivables within the next 12 months and therefore	$ 8,400,000
Contract with customer, asset, reclassified to receivable	5,100,000
Contract with customer, asset, increase in contract assets related to revenue recognized	5,400,000
Impairments of the contract cost asset	0	$ 0
Deferred revenue, revenue recognized	222,000,000.0
Deferred revenue, additions	205,400,000
Short term and long term accounts receivable	683,800,000		$ 744,600,000
Refund liability	40,100,000		40,300,000
Allowance for doubtful accounts receivable	300,000		300,000
Amortization expense related to costs to obtain a contract with a customer	11,600,000	$ 10,400,000
Deferred revenue	481,070,000		497,677,000
Revenue, remaining performance obligation, amount	1,621,400,000
Unrecorded
Revenue from External Customer [Line Items]
Revenue, remaining performance obligation, amount	1,140,300,000
Other Current Assets
Revenue from External Customer [Line Items]
Capitalized contract cost, net	41,600,000		40,200,000
Other Assets
Revenue from External Customer [Line Items]
Capitalized contract cost, net	$ 80,700,000		$ 81,100,000