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Goodwill and Intangible Assets, Net (Tables)
 12 Months Ended
Sep. 30, 2022
Goodwill and Intangible Assets, Net [Abstract]  
Details of Total Goodwill
The following table presents details of the Company’s total goodwill:

As of September 30, 2020
    $ 2,578,645  
Goodwill resulting from acquisitions(
1
)
      104,151  
Decrease in goodwill as a result of divestiture(
2
)
      (61,396 ) 
Other
      1,244  
 
 
 
 
 
As of September 30, 2021
    $ 2,622,644  
Goodwill resulting from acquisitions(
3
)
      48,395  
Other
      (8,214 )
 
 
 
 
 
As of September 30, 2022
    $ 2,662,825  
 
 
 
 
 
 
(1)
Mainly relates to the acquisition of Sourced
 Group
. In allocating the total purchase price for Sourced
 
Group
, based on estimated fair values, the Company recorded
 $79,863 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)
Relates to the divestiture of OpenMarket completed on December 31, 2020, see also Note 3. 
(3)
Mainly relates to the acquisitions of DevOps and Roam, see also Note 3. In allocating the total preliminary purchase price for Roam, based on estimated fair values, the Company recorded $24,607 of goodwill, $11,454 of customer relationships to be amortized over approximately five years and $2,299 of core technology to be amortized over two years. In allocating the total preliminary purchase price for DevOps, based on estimated fair values, the Company recorded $23,787 of goodwill, $2,616 of customer relationships to be amortized over approximately five years. 
Details Regarding Total Definite-Lived Purchased Intangible Assets
The following table presents details regarding the Company’s total definite-lived purchased intangible assets:
 
 
  
Gross
 
  
Accumulated
Amortization
 
  
Net
 
September 30, 2022
  
  
  
Core technology
    $ 898,448      $ (837,404 )     $ 61,044  
Customer relationships
      703,824        (591,119 )       112,705  
Other
      47,540        (42,977 )       4,563  
 
 
 
 
 
 
 
 
 
 
 
 
 
Total
    $ 1,649,812      $ (1,471,500 )     $ 178,312  
 
 
 
 
 
 
 
 
 
 
 
 
 
September 30, 2021
                           
Core technology
    $ 896,149      $ (777,419 )     $ 118,730  
Customer relationships
      689,754        (556,716 )       133,038  
Other
      47,540        (40,276 )       7,264  
 
 
 
 
 
 
 
 
 
 
 
 
 
Total
    $ 1,633,443      $ (1,374,411 )     $ 259,032  
 
 
 
 
 
 
 
 
 
 
 
 
 
Estimated Future Amortization Expense
The estimated future amortization expense of definite-lived purchased intangible assets as of September 30, 2022 is as follows:
 
 
  
Amount
 
Fiscal year:
  
2023
    $ 53,213  
2024
      43,721  
2025
      39,759  
2026
      23,334  
2027
      10,893  
Thereafter
      7,392  
 
 
 
 
 
Total
    $ 178,312