Goodwill and Other Intangible Assets - Changes in Carrying Amount of Goodwill (Details) $ in Thousands	6 Months Ended
Mar. 31, 2022 USD ($)
Goodwill And Intangible Assets Disclosure [Abstract]
Balance as of September 30, 2021	$ 1,128,511
Effect of foreign currency translation	(4,950)
Balance as of March 31, 2022	$ 1,123,561

Amount after accumulated impairment loss of an asset representing future economic benefits arising from other assets acquired in a business combination that are not individually identified and separately recognized.

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03(10)(1))
-URI http://asc.fasb.org/extlink&oid=120398452&loc=d3e534808-122878

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 350
-SubTopic 20
-Section 45
-Paragraph 5
-URI http://asc.fasb.org/extlink&oid=120320667&loc=SL49117168-202975

Reference 3: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 852
-SubTopic 10
-Section 55
-Paragraph 10
-URI http://asc.fasb.org/extlink&oid=84165509&loc=d3e56426-112766

Reference 4: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 350
-SubTopic 20
-Section 45
-Paragraph 1
-URI http://asc.fasb.org/extlink&oid=99380562&loc=d3e13770-109266

Name:	us-gaap_Goodwill
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant