Revenue from Contracts with Customers - Additional Information (Details) - USD ($)	3 Months Ended		6 Months Ended
	Mar. 31, 2022	Mar. 31, 2021	Mar. 31, 2022	Mar. 31, 2021	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	$ 11,500,000		$ 11,500,000
Contract with customer, asset, reclassified to receivable			6,800,000
Contract with customer, asset, increase in contract assets related to revenue recognized			10,100,000
Impairments of the contract cost asset	0	$ 0	0	$ 0
Deferred revenue, revenue recognized			357,900,000
Deferred revenue, additions			394,900,000
Short term and long term accounts receivable	726,900,000		726,900,000		$ 744,600,000
Refund liability	36,200,000		36,200,000		40,300,000
Allowance for doubtful accounts receivable	700,000		700,000		300,000
Amortization expense related to costs to obtain a contract with a customer	12,700,000	$ 11,000,000.0	24,300,000	$ 21,400,000
Deferred revenue	534,681,000		534,681,000		497,677,000
Revenue, remaining performance obligation, amount	1,554,100,000		1,554,100,000
Unrecorded
Revenue from External Customer [Line Items]
Revenue, remaining performance obligation, amount	1,019,400,000		1,019,400,000
Other Current Assets
Revenue from External Customer [Line Items]
Capitalized contract cost, net	40,600,000		40,600,000		40,200,000
Other Assets
Revenue from External Customer [Line Items]
Capitalized contract cost, net	$ 78,000,000.0		$ 78,000,000.0		$ 81,100,000