Goodwill and Intangible Assets - Schedule of Goodwill and Acquired Intangible Assets (Details) - USD ($) $ in Thousands	Mar. 31, 2023	Sep. 30, 2022
Goodwill (not amortized)	$ 3,369,041	$ 2,353,654
Intangible assets with finite lives (amortized), Gross Carrying Amount	1,796,453	1,152,018
Intangible assets with finite lives (amortized), Accumulated Amortization	817,232	769,300
Intangible assets with finite lives (amortized), Net Book Value	979,221	382,718
Intangible Assets, Net (Including Goodwill)	4,348,262	2,736,372
Purchased Software
Intangible assets with finite lives (amortized), Gross Carrying Amount	616,665	502,859
Intangible assets with finite lives (amortized), Accumulated Amortization	376,637	355,857
Intangible assets with finite lives (amortized), Net Book Value	240,028	147,002
Capitalized Software
Intangible assets with finite lives (amortized), Gross Carrying Amount	22,877	22,877
Intangible assets with finite lives (amortized), Accumulated Amortization	22,877	22,877
Intangible assets with finite lives (amortized), Net Book Value	0	0
Customer Lists and Relationships
Intangible assets with finite lives (amortized), Gross Carrying Amount	1,116,040	594,970
Intangible assets with finite lives (amortized), Accumulated Amortization	395,336	369,390
Intangible assets with finite lives (amortized), Net Book Value	720,704	225,580
Trademarks and Trade Names
Intangible assets with finite lives (amortized), Gross Carrying Amount	36,968	27,546
Intangible assets with finite lives (amortized), Accumulated Amortization	18,479	17,410
Intangible assets with finite lives (amortized), Net Book Value	18,489	10,136
Other
Intangible assets with finite lives (amortized), Gross Carrying Amount	3,903	3,766
Intangible assets with finite lives (amortized), Accumulated Amortization	3,903	3,766
Intangible assets with finite lives (amortized), Net Book Value	$ 0	$ 0