Segment and Geographic Information - Segment Results Along with Reconciliation of Segment Profit to Income Before Income Taxes (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Mar. 31, 2021	Mar. 31, 2020	Mar. 31, 2021	Mar. 31, 2020
Segment Reporting Information [Line Items]
Total revenues	$ 346,977	$ 315,924	$ 692,730	$ 677,433
Total segment profit	120,282	95,152	241,533	215,748
Corporate expenses and other, net	(25,723)	(28,671)	(56,838)	(59,119)
Acquisition-related revenues	0	(212)	0	(301)
Stock-based compensation	(34,876)	(32,134)	(69,782)	(62,536)
Amortization of intangible assets	(15,683)	(15,087)	(30,476)	(30,845)
Acquisition-related costs, net	(1,669)	(1,678)	(1,994)	(2,898)
Restructuring and other charges, net	(2,479)	(6,176)	(11,045)	(12,859)
Other expenses, net	(22,295)	(23,805)	(44,584)	(57,474)
Income (loss) before income taxes	17,557	(12,611)	26,814	(10,284)
Operating Segments
Segment Reporting Information [Line Items]
Total segment revenues	346,977	316,136	692,730	677,734
Segment Reconciling Items
Segment Reporting Information [Line Items]
Total revenues	0	(212)	0	(301)
Healthcare
Segment Reporting Information [Line Items]
Total segment revenues	211,892	170,982	411,224	384,792
Total revenues	211,892	170,982	411,224	384,792
Total segment profit	85,226	53,276	160,038	126,990
Enterprise
Segment Reporting Information [Line Items]
Total segment revenues	129,997	137,445	269,149	275,918
Total revenues	129,997	137,233	269,149	275,617
Total segment profit	32,627	38,043	74,095	79,810
Other
Segment Reporting Information [Line Items]
Total segment revenues	5,088	7,709	12,357	17,024
Total revenues	5,088	7,709	12,357	17,024
Total segment profit	$ 2,429	$ 3,833	$ 7,400	$ 8,948