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Goodwill and Intangible Assets (Tables)
 9 Months Ended
Sep. 30, 2021
Goodwill and Intangible Assets Disclosure [Abstract]  
Intangible Assets (Indefinite-Lived)
Intangible assets are classified as follows:
 September 30, 2021December 31, 2020
(in thousands)Gross
Carrying
Amount		Accumulated
Amortization		Gross
Carrying
Amount		Accumulated
Amortization
Finite-lived intangible assets:
Developed software and core technologies
$887,926 $(409,288)$859,620 $(370,338)
Customer lists194,047 (54,546)288,085 (136,093)
Trade names 175,785 (127,013)175,626 (122,392)
Total$1,257,758 $(590,847)$1,323,331 $(628,823)
Indefinite-lived intangible asset:
Trade name$357 $357 
Intangible Assets (Finite-Lived)
Intangible assets are classified as follows:
 September 30, 2021December 31, 2020
(in thousands)Gross
Carrying
Amount		Accumulated
Amortization		Gross
Carrying
Amount		Accumulated
Amortization
Finite-lived intangible assets:
Developed software and core technologies
$887,926 $(409,288)$859,620 $(370,338)
Customer lists194,047 (54,546)288,085 (136,093)
Trade names 175,785 (127,013)175,626 (122,392)
Total$1,257,758 $(590,847)$1,323,331 $(628,823)
Indefinite-lived intangible asset:
Trade name$357 $357 
Estimated Future Amortization Expense for Intangible Assets
As of September 30, 2021, estimated future amortization expense for the intangible assets reflected above was as follows:
(in thousands) 
Remainder of 2021$18,000 
202278,125 
202380,348 
202479,784 
202577,509 
202675,325 
Thereafter257,820 
Total intangible assets subject to amortization666,911 
Indefinite-lived trade name357 
Other intangible assets, net$667,268 
Changes in Goodwill
The changes in goodwill during the nine months ended September 30, 2021 and 2020 were as follows:
(in thousands)20212020
Beginning balance – January 1$3,038,306 $2,413,280 
Acquisitions and adjustments(1)
79,905 69,598 
Currency translation(16,588)8,712 
Ending balance – September 30$3,101,623 $2,491,590 
(1) In accordance with the accounting for business combinations, we recorded adjustments to goodwill for the effect of changes in the provisional fair values of the assets acquired and liabilities assumed during the measurement period (up to one year from the acquisition date) as we obtained new information about facts and circumstances that existed as of the acquisition date that, if known, would have affected the measurement of the amounts recognized as of that date.