Income Taxes - Reconciliation Between Federal Statutory Income Tax Rate and Effective Tax Rate (Details) - USD ($) $ in Thousands	12 Months Ended
	Sep. 30, 2019	Sep. 30, 2018	Sep. 30, 2017
Income Tax Disclosure [Abstract]
Effective Income Tax Rate Reconciliation, at Federal Statutory Income Tax Rate, Percent	21.00%	24.50%	35.00%
Income tax provision at U.S. federal statutory rate	$ 45,375	$ 38,495	$ 54,699
State income taxes, net of U.S. federal benefit	4,194	2,755	2,072
Foreign tax rate differential	839	(649)	(4,082)
Intercompany interest	0	0	(477)
Research credits	(5,761)	(3,486)	(2,572)
Domestic production deduction	0	(2,421)	(2,759)
Amended returns/audit settlements/statute expirations	(2,268)	(2,349)	(1,296)
Foreign	11,177	4,040	935
Valuation allowance	(333)	1,907	2,512
Foreign tax credit	(464)	1,320	(1,342)
Excess tax benefits relating to stock-based compensation	(24,891)	(22,253)	(24,746)
Tax effect of the Tax Act	0	16,719	0
Other	(3,920)	(3,628)	(75)
Total provision	$ 23,948	$ 30,450	$ 22,869