Goodwill and Intangible Assets - Net - Summary of Finite-Lived Intangible Assets (Detail) - USD ($) $ in Thousands	12 Months Ended
	Sep. 30, 2022	Sep. 30, 2021
Finite Lived Intangible Assets [Line Items]
Gross Carrying Value	$ 720,068	$ 670,886
Accumulated Amortization	(474,233)	(428,314)
Net Carrying Value	$ 245,835	242,572
Minimum [Member]
Finite Lived Intangible Assets [Line Items]
Lives in Years	3 years
Maximum [Member]
Finite Lived Intangible Assets [Line Items]
Lives in Years	20 years
Propriety knowledge [Member]
Finite Lived Intangible Assets [Line Items]
Gross Carrying Value	$ 300,400	289,300
Accumulated Amortization	(236,024)	(216,283)
Net Carrying Value	$ 64,376	$ 73,017
Propriety knowledge [Member] | Minimum [Member]
Finite Lived Intangible Assets [Line Items]
Lives in Years	10 years	10 years
Propriety knowledge [Member] | Maximum [Member]
Finite Lived Intangible Assets [Line Items]
Lives in Years	15 years	15 years
Trademarks [Member]
Finite Lived Intangible Assets [Line Items]
Gross Carrying Value	$ 230,240	$ 223,840
Accumulated Amortization	(151,259)	(139,631)
Net Carrying Value	$ 78,981	$ 84,209
Trademarks [Member] | Minimum [Member]
Finite Lived Intangible Assets [Line Items]
Lives in Years	5 years	5 years
Trademarks [Member] | Maximum [Member]
Finite Lived Intangible Assets [Line Items]
Lives in Years	20 years	20 years
Customer Relationships [Member]
Finite Lived Intangible Assets [Line Items]
Gross Carrying Value	$ 176,852	$ 146,670
Accumulated Amortization	(78,015)	(64,412)
Net Carrying Value	$ 98,837	$ 82,258
Customer Relationships [Member] | Minimum [Member]
Finite Lived Intangible Assets [Line Items]
Lives in Years	12 years	15 years
Customer Relationships [Member] | Maximum [Member]
Finite Lived Intangible Assets [Line Items]
Lives in Years	19 years	19 years
Patents [Member]
Finite Lived Intangible Assets [Line Items]
Lives in Years		10 years
Gross Carrying Value	$ 8,500	$ 7,000
Accumulated Amortization	(4,950)	(4,105)
Net Carrying Value	$ 3,550	2,895
Patents [Member] | Minimum [Member]
Finite Lived Intangible Assets [Line Items]
Lives in Years	9 years
Patents [Member] | Maximum [Member]
Finite Lived Intangible Assets [Line Items]
Lives in Years	10 years
Other intangible [Member]
Finite Lived Intangible Assets [Line Items]
Gross Carrying Value	$ 4,076	4,076
Accumulated Amortization	(3,985)	(3,883)
Net Carrying Value	$ 91	$ 193
Other intangible [Member] | Minimum [Member]
Finite Lived Intangible Assets [Line Items]
Lives in Years	3 years	3 years
Other intangible [Member] | Maximum [Member]
Finite Lived Intangible Assets [Line Items]
Lives in Years	15 years	15 years