Income Taxes - Additional Information (Details) - USD ($) $ in Thousands	12 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2019
Income Tax Disclosure [Line Items]
Income taxes payable	$ 17,300	$ 15,700
Accrued income taxes	5,100	5,000
Prepaid income taxes	25,800	15,400
Income tax payments	55,000	56,000	$ 52,600
Non-cash federal		109,400
State tax benefits		24,800
Foreign tax credits	14,527	36,287
Gross deferred amortization carryforward	118,500
Valuation allowance	22,283	52,085	205,423	$ 177,663
Interest Expense	54,268	50,478	76,428
Penalty expense	0	2,000	0
Interest expense related to income tax accruals	900	700
Accrued tax penalties	0	0	0
Income tax provision upon recognition of unrecognized tax benefit	23,900
Unrecognized tax benefits, increase in valuation allowance upon recognition	5,200
Potential decrease in unrecognized tax benefits	5,000
Charge related to effects of Non US Jurisdiction Tax Matter		37,300
US Income taxes on repatriated foreign earnings		2,900
Stock-based compensation	174,863	177,289	115,149
Tax benefit recognition related to stock based compensation	27,100	39,900	13,400
Provision (benefit) for income taxes	84,017	(85,168)	4,011
Income Tax Expense
Income Tax Disclosure [Line Items]
Interest Expense	200	2,200	300
Domestic Country
Income Tax Disclosure [Line Items]
Net operating loss carryforwards	22,500
Valuation allowance	17,800
Domestic Country | Expire in 2023 to 2036
Income Tax Disclosure [Line Items]
Net operating loss carryforwards	1,600
Credit carryforwards	60,900
Domestic Country | Not Expire
Income Tax Disclosure [Line Items]
Net operating loss carryforwards	20,900
State - Massachusetts
Income Tax Disclosure [Line Items]
Valuation allowance		17,800
State - Massachusetts | Research Tax Credit Carryforward
Income Tax Disclosure [Line Items]
Credit carryforwards	26,100
Foreign Country
Income Tax Disclosure [Line Items]
Net operating loss carryforwards	7,200
Credit carryforwards	$ 14,500
Credit carryforwards expiration	2027
Foreign tax credits	$ 4,000
Valuation allowance	$ 4,500
Foreign Country | Minimum
Income Tax Disclosure [Line Items]
Non-U.S. tax credit carryforwards expiration	2030
Foreign Country | Maximum
Income Tax Disclosure [Line Items]
Non-U.S. tax credit carryforwards expiration	2041
REPUBLIC OF KOREA
Income Tax Disclosure [Line Items]
Charge related to effects of Non US Jurisdiction Tax Matter		34,400
Payment related to effects of Non US jurisdiction tax matter		20,000
Windfall Tax Benefit
Income Tax Disclosure [Line Items]
Provision (benefit) for income taxes	$ 5,200	9,900	$ 1,300
Other Current Liabilities
Income Tax Disclosure [Line Items]
Accrued income taxes	5,600	800
Other Liabilities [Member]
Income Tax Disclosure [Line Items]
Accrued income taxes	$ 6,600	$ 9,900