Intangible Assets - Identifiable Intangible Assets (Details) - USD ($) $ in Thousands	Feb. 29, 2024	Aug. 31, 2023
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	$ 2,217,169	$ 2,181,243
Accumulated Amortization	356,560	322,041
Total	$ 1,860,609	1,859,202
ABA business process
Finite-Lived Intangible Assets [Line Items]
Estimated Useful Life (years)	36 years
Gross Carrying Amount	$ 1,583,000	1,583,000
Accumulated Amortization	87,944	65,958
Total	1,495,056	1,517,042
Client relationships
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	265,129	265,315
Accumulated Amortization	74,416	68,701
Total	190,713	196,614
Developed technology
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	145,213	109,222
Accumulated Amortization	45,901	45,560
Total	$ 99,312	63,662
Acquired databases
Finite-Lived Intangible Assets [Line Items]
Estimated Useful Life (years)	15 years
Gross Carrying Amount	$ 46,000	46,000
Accumulated Amortization	6,133	4,600
Total	39,867	41,400
Software technology
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	142,368	142,395
Accumulated Amortization	112,798	108,702
Total	29,570	33,693
Data content
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	35,169	35,021
Accumulated Amortization	29,320	28,508
Total	$ 5,849	6,513
Non-compete agreements
Finite-Lived Intangible Assets [Line Items]
Estimated Useful Life (years)	4 years
Gross Carrying Amount	$ 290	290
Accumulated Amortization	48	12
Total	$ 242	$ 278
Minimum | Client relationships
Finite-Lived Intangible Assets [Line Items]
Estimated Useful Life (years)	11 years
Minimum | Developed technology
Finite-Lived Intangible Assets [Line Items]
Estimated Useful Life (years)	3 years
Minimum | Software technology
Finite-Lived Intangible Assets [Line Items]
Estimated Useful Life (years)	2 years
Minimum | Data content
Finite-Lived Intangible Assets [Line Items]
Estimated Useful Life (years)	7 years
Maximum | Client relationships
Finite-Lived Intangible Assets [Line Items]
Estimated Useful Life (years)	26 years
Maximum | Developed technology
Finite-Lived Intangible Assets [Line Items]
Estimated Useful Life (years)	5 years
Maximum | Software technology
Finite-Lived Intangible Assets [Line Items]
Estimated Useful Life (years)	10 years
Maximum | Data content
Finite-Lived Intangible Assets [Line Items]
Estimated Useful Life (years)	20 years