Intangible Assets - Identifiable Intangible Assets (Details) - USD ($) $ in Thousands	6 Months Ended
	Feb. 28, 2023	Aug. 31, 2022
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	$ 2,153,653	$ 2,134,480
Accumulated amortization	283,879	238,571
Net carrying amount	$ 1,869,774	1,895,909
ABA business process
Finite-Lived Intangible Assets [Line Items]
Estimated useful life	36 years
Gross carrying amount	$ 1,583,000	1,583,000
Accumulated amortization	43,972	21,986
Net carrying amount	1,539,028	1,561,014
Client relationships
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	263,825	263,163
Accumulated amortization	62,102	55,405
Net carrying amount	201,723	207,758
Software technology
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	123,463	122,363
Accumulated amortization	101,985	96,567
Net carrying amount	21,478	25,796
Developed technology
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	96,981	80,956
Accumulated amortization	41,654	33,676
Net carrying amount	$ 55,327	47,280
Acquired databases
Finite-Lived Intangible Assets [Line Items]
Estimated useful life	15 years
Gross carrying amount	$ 46,000	46,000
Accumulated amortization	3,067	1,533
Net carrying amount	42,933	44,467
Data content
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	33,625	32,305
Accumulated amortization	26,704	24,973
Net carrying amount	$ 6,921	7,332
Client relationships
Finite-Lived Intangible Assets [Line Items]
Estimated useful life	15 years
Gross carrying amount	$ 6,759	6,693
Accumulated amortization	4,395	4,431
Net carrying amount	$ 2,364	$ 2,262
Minimum | Client relationships
Finite-Lived Intangible Assets [Line Items]
Estimated useful life	11 years
Minimum | Software technology
Finite-Lived Intangible Assets [Line Items]
Estimated useful life	2 years
Minimum | Developed technology
Finite-Lived Intangible Assets [Line Items]
Estimated useful life	3 years
Minimum | Data content
Finite-Lived Intangible Assets [Line Items]
Estimated useful life	7 years
Maximum | Client relationships
Finite-Lived Intangible Assets [Line Items]
Estimated useful life	26 years
Maximum | Software technology
Finite-Lived Intangible Assets [Line Items]
Estimated useful life	9 years
Maximum | Developed technology
Finite-Lived Intangible Assets [Line Items]
Estimated useful life	5 years
Maximum | Data content
Finite-Lived Intangible Assets [Line Items]
Estimated useful life	20 years