Goodwill and Intangible Assets - Schedule of Goodwill and Acquired Intangible Assets (Details) - USD ($) $ in Thousands	Jun. 30, 2023	Sep. 30, 2022
Goodwill (not amortized)	$ 3,377,319	$ 2,353,654
Intangible assets with finite lives (amortized), Gross Carrying Amount	1,798,015	1,152,018
Intangible assets with finite lives (amortized), Accumulated Amortization	838,895	769,300
Intangible assets with finite lives (amortized), Net Book Value	959,120	382,718
Intangible Assets, Net (Including Goodwill)	4,336,439	2,736,372
Purchased Software
Intangible assets with finite lives (amortized), Gross Carrying Amount	617,241	502,859
Intangible assets with finite lives (amortized), Accumulated Amortization	386,917	355,857
Intangible assets with finite lives (amortized), Net Book Value	230,324	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	1,116,980	594,970
Intangible assets with finite lives (amortized), Accumulated Amortization	406,177	369,390
Intangible assets with finite lives (amortized), Net Book Value	710,803	225,580
Trademarks and Trade Names
Intangible assets with finite lives (amortized), Gross Carrying Amount	37,005	27,546
Intangible assets with finite lives (amortized), Accumulated Amortization	19,012	17,410
Intangible assets with finite lives (amortized), Net Book Value	17,993	10,136
Other
Intangible assets with finite lives (amortized), Gross Carrying Amount	3,912	3,766
Intangible assets with finite lives (amortized), Accumulated Amortization	3,912	3,766
Intangible assets with finite lives (amortized), Net Book Value	$ 0	$ 0