Stockholders' Equity - Accumulated Other Comprehensive Loss (Details) - USD ($) $ in Thousands	May 31, 2022	Feb. 28, 2022	Aug. 31, 2021	May 31, 2021	Feb. 28, 2021	Aug. 31, 2020
Accumulated Other Comprehensive Income (Loss) [Line Items]
Total AOCL	$ 1,267,722	$ 1,215,981	$ 1,016,353	$ 1,031,299	$ 980,468	$ 896,375
Accumulated Other Comprehensive Loss
Accumulated Other Comprehensive Income (Loss) [Line Items]
Total AOCL	(77,134)	$ (55,848)	(38,962)	$ (19,258)	$ (28,496)	$ (39,293)
Accumulated unrealized gains (losses) on cash flow hedges
Accumulated Other Comprehensive Income (Loss) [Line Items]
Total AOCL	3,524		(2,095)
Accumulated foreign currency translation adjustment losses
Accumulated Other Comprehensive Income (Loss) [Line Items]
Total AOCL	$ (80,658)		$ (36,867)