Segment and Geographic Information - Summary of Revenue and Profit Attributable to Our Operating Segments (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Mar. 31, 2022	Mar. 31, 2021	Mar. 31, 2022	Mar. 31, 2021
Segment Reporting Revenue Reconciling Item [Line Items]
Revenue	$ 505,227	$ 461,785	$ 962,948	$ 890,836
Operating costs	93,337	89,448	188,455	176,278
Gross margin	411,890	372,337	774,493	714,558
Sales and marketing	116,408	129,178	241,884	253,903
General and administrative	47,469	60,805	99,409	110,333
Restructuring and other charges, net	(1,562)	469	32,429	716
Intangibles amortization	14,371	14,767	29,348	27,581
Operating income	159,190	101,690	221,368	192,029
Interest and debt premium expense	(12,239)	(12,925)	(25,225)	(24,444)
Other expense, net	(43,385)	(2,408)	(37,201)	(3,821)
Income before income taxes	103,566	86,357	158,942	163,764
Operating Segments
Segment Reporting Revenue Reconciling Item [Line Items]
Revenue	505,227	461,785	962,948	890,836
Operating costs	155,583	142,449	308,594	280,970
Gross margin	349,644	319,336	654,354	609,866
Unallocated
Segment Reporting Revenue Reconciling Item [Line Items]
Sales and marketing	104,962	115,873	217,357	225,599
General and administrative	30,859	31,487	65,036	58,887
Restructuring and other charges, net	(1,562)	469	32,429	716
Intangibles amortization	14,371	14,767	29,348	27,581
Stock-based compensation	37,921	44,740	83,863	90,828
Other unallocated operating expenses	3,903	10,310	4,953	14,226
Software Products | Operating Segments
Segment Reporting Revenue Reconciling Item [Line Items]
Revenue	462,250	421,767	875,843	815,188
Operating costs	121,016	109,310	237,044	214,711
Gross margin	341,234	312,457	638,799	600,477
Professional Services | Operating Segments
Segment Reporting Revenue Reconciling Item [Line Items]
Revenue	42,977	40,018	87,105	75,648
Operating costs	34,567	33,139	71,550	66,259
Gross margin	$ 8,410	$ 6,879	$ 15,555	$ 9,389