Goodwill and Intangible Assets - Schedule of Goodwill and Acquired Intangible Assets (Details) - USD ($) $ in Thousands	Jun. 30, 2021	Sep. 30, 2020
Goodwill (not amortized)	$ 2,197,313	$ 1,625,786
Intangible assets with finite lives (amortized), Gross Carrying Amount	1,115,697	911,809
Intangible assets with finite lives (amortized), Accumulated Amortization	721,015	674,239
Intangible assets with finite lives (amortized), Net Book Value	394,682	237,570
Intangible Assets, Net (Including Goodwill)	2,591,995	1,863,356
Purchased Software
Intangible assets with finite lives (amortized), Gross Carrying Amount	484,810	443,275
Intangible assets with finite lives (amortized), Accumulated Amortization	331,711	309,124
Intangible assets with finite lives (amortized), Net Book Value	153,099	134,151
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	576,985	418,953
Intangible assets with finite lives (amortized), Accumulated Amortization	345,518	322,092
Intangible assets with finite lives (amortized), Net Book Value	231,467	96,861
Trademarks and Trade Names
Intangible assets with finite lives (amortized), Gross Carrying Amount	26,990	22,687
Intangible assets with finite lives (amortized), Accumulated Amortization	16,874	16,129
Intangible assets with finite lives (amortized), Net Book Value	10,116	6,558
Other
Intangible assets with finite lives (amortized), Gross Carrying Amount	4,035	4,017
Intangible assets with finite lives (amortized), Accumulated Amortization	4,035	4,017
Intangible assets with finite lives (amortized), Net Book Value	$ 0	$ 0