Income Taxes - Reconciliation Between Federal Statutory Income Tax Rate and Effective Tax Rate (Details) - USD ($) $ in Thousands	12 Months Ended
	Sep. 30, 2020	Sep. 30, 2019	Sep. 30, 2018
Income Tax Disclosure [Abstract]
Effective Income Tax Rate Reconciliation, at Federal Statutory Income Tax Rate, Percent	21.00%	21.00%	24.50%
Income tax provision at U.S. federal statutory rate	$ 53,970	$ 45,375	$ 38,495
State income taxes, net of U.S. federal benefit	4,619	4,194	2,755
Foreign tax rate differential	493	839	(649)
Research credits	(5,868)	(5,761)	(3,486)
Domestic production deduction	0	0	(2,421)
Amended returns/audit settlements/statute expirations	(1,085)	(2,268)	(2,349)
Foreign	7,513	11,177	4,040
Valuation allowance	5,332	(333)	1,907
Foreign tax credit and tax withholding	2,086	(464)	1,320
Excess tax benefits relating to stock-based compensation	(45,086)	(24,891)	(22,253)
Tax effect of the Tax Act	0	0	16,719
GILTI, FDII and BEAT	5,050	1,931	0
Other	(6,435)	(5,851)	(3,628)
Total provision	$ 20,589	$ 23,948	$ 30,450