Quarterly Results Of Operations (Unaudited) - Schedule Of Quarterly Results Of Operations (Details) - USD ($) $ / shares in Units, shares in Thousands, $ in Thousands	3 Months Ended									12 Months Ended
	Sep. 30, 2020	Jun. 30, 2020	Mar. 31, 2020	Dec. 31, 2019	Sep. 30, 2019	Jun. 30, 2019	Mar. 31, 2019	Dec. 31, 2018	Sep. 30, 2018	Sep. 30, 2020	Sep. 30, 2019	Sep. 30, 2018
Net revenues	$ 614,816	$ 583,252	$ 583,449	$ 569,305	$ 590,388	$ 563,394	$ 544,895	$ 543,770		$ 2,350,822	$ 2,242,447	$ 2,161,407
Cost of net revenues	111,967	106,040	101,238	88,642	90,918	90,767	88,178	86,714		407,887	356,577	361,481
Gross profit	502,849	477,212	482,211	480,663	499,470	472,627	456,717	457,056		1,942,935	1,885,870	1,799,926
Sales and marketing	220,379	211,808	215,472	195,519	217,554	195,852	170,954	164,259		843,178	748,619	664,135
Research and development	120,300	115,991	109,028	96,005	102,812	116,894	96,314	92,038		441,324	408,058	366,084
General and administrative	63,557	61,792	74,013	59,004	64,390	57,141	46,656	42,543		258,366	210,730	160,382
Restructuring charges	0	0	0	7,800	0	0	0	0	$ 18,400	7,800	0	18,426
Total	404,236	389,591	398,513	358,328	384,756	369,887	313,924	298,840		1,550,668	1,367,407	1,209,027
Income from operations	98,613	87,621	83,698	122,335	114,714	102,740	142,793	158,216		392,267	518,463	590,899
Other income, net	(1,090)	141	(141)	5,220	3,397	4,722	7,434	7,095		4,130	22,648	12,861
Income before income taxes	97,523	87,762	83,557	127,555	118,111	107,462	150,227	165,311		396,397	541,111	603,760
Provision for income taxes	19,860	17,890	22,178	29,028	23,274	21,557	34,140	34,406		88,956	113,377	150,071
Net income	$ 77,663	$ 69,872	$ 61,379	$ 98,527	$ 94,837	$ 85,905	$ 116,087	$ 130,905		$ 307,441	$ 427,734	$ 453,689
Net income per share - basic (USD per share)	$ 1.27	$ 1.15	$ 1.01	$ 1.62	$ 1.57	$ 1.43	$ 1.94	$ 2.17		$ 5.05	$ 7.12	$ 7.41
Weighted average shares - basic (shares)	61,149	60,978	60,869	60,649	60,283	59,981	59,686	60,216		60,911	60,044	61,262
Net income per share - diluted (USD per share)	$ 1.26	$ 1.14	$ 1.00	$ 1.62	$ 1.57	$ 1.43	$ 1.93	$ 2.16		$ 5.01	$ 7.08	$ 7.32
Weighted average shares - diluted (shares)	61,636	61,415	61,084	60,815	60,448	60,196	60,029	60,645		61,378	60,456	62,013
Product [Member]
Net revenues	$ 278,451	$ 253,331	$ 259,538	$ 234,536	$ 264,926	$ 248,929	$ 237,859	$ 233,877		$ 1,025,856	$ 985,591	$ 960,108
Cost of net revenues	62,634	57,437	53,086	42,118	44,693	44,336	43,547	42,410		215,275	174,986	181,061
Service [Member]
Net revenues	336,365	329,921	323,911	334,769	325,462	314,465	307,036	309,893		1,324,966	1,256,856	1,201,299
Cost of net revenues	$ 49,333	$ 48,603	$ 48,152	$ 46,524	$ 46,225	$ 46,431	$ 44,631	$ 44,304		$ 192,612	$ 181,591	$ 180,420