Income Taxes - Provision for Income Taxes (Details) - USD ($) $ in Thousands	3 Months Ended		9 Months Ended
	May 31, 2022	May 31, 2021	May 31, 2022	May 31, 2021
Income Tax Disclosure [Abstract]
Income before income taxes	$ 85,280	$ 114,276	$ 327,166	$ 349,174
Provision for income taxes	$ 10,370	$ 13,597	$ 34,671	$ 50,646
Effective tax rate	12.20%	11.90%	10.60%	14.50%