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Goodwill and Intangible Assets, Net - Details of Total Goodwill (Detail) - USD ($)
$ in Thousands
 12 Months Ended
Sep. 30, 2021
Sep. 30, 2020
Goodwill and Intangible Assets Disclosure [Abstract]    
Goodwill, Beginning Balance $ 2,578,645 $ 2,462,835
Goodwill resulting from acquisitions 104,151 [1] 118,628 [2]
Decrease in goodwill as a result of divestiture [3] (61,396)  
Other 1,244 (2,818)
Goodwill, Ending Balance $ 2,622,644 $ 2,578,645
[1] Mainly relates to the acquisition of Sourced. In allocating the total preliminary purchase price for Sourced, based on estimated fair values, the Company recorded $80,055 of goodwill, $18,211 of customer relationships to be amortized over approximately seven years and $3,056 of core technology to be amortized over three years.
[2] Mainly relates to the acquisition of Openet. In allocating the total purchase price for Openet, based on estimated fair values, the Company recorded $110,347 of goodwill, $40,409 of customer relationships to be amortized over approximately eight years, $53,614 of core technology to be amortized over five years and $2,594 of trademark to be amortized over two years.
[3] Relates to the divestiture of OpenMarket completed on December 31, 2020, please see also Note 3.