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Goodwill and Other Intangible Assets (Tables)
 12 Months Ended
Dec. 31, 2018
Goodwill and Intangible Assets Disclosure [Abstract]  
Schedule of Goodwill
The changes in the net carrying amount of goodwill for the years ended December 31, are as follows:
 
 
2018
 
2017
Balance as of January 1,
$
401,954

 
$
397,664

 
 
 
 
Goodwill resulting from business combinations
—

 
2,209

 
 
 
 
Foreign currency translation
(1,514
)
 
2,081

 
 
 
 
Balance as of December 31,
$
400,440

 
$
401,954
Schedule of Finite-Lived and Indefinite-Lived Intangible Assets
Other intangible assets consist of the following:
 
December 31, 2018
 
December 31, 2017
 
Weighted Average Amortization Period (Years)
Gross
Carrying
Amount
 
Accumulated
Amortization
 
Gross
Carrying
Amount
 
Accumulated
Amortization
Intangible assets with definite lives:
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Customer and distributor relationships
29
$
214,577

 
$
(97,131
)
 
$
214,685

 
$
(86,137
)
 
 
 
 
 
 


 


Sales representation, marketing and promotional rights
25
149,376

 
(42,000
)
 
149,376

 
(36,000
)
 
 
 
 
 
 
 
 
 
Patents and other intangible assets
14
61,473

 
(44,242
)
 
69,668

 
(42,127
)
 
 
 
 
 
 


 


Developed technology
16
91,965

 
(7,369
)
 
62,283

 
(3,352
)
 
 
 
 
 
 
 
 
 
Intangible assets with indefinite lives:
 
 

 
 

 
 

 
 

 
 
 
 
 
 


 


Trademarks and tradenames
 
86,544

 
—

 
86,544

 
—

 
 
 
 
 
 
 
 
 
 
24
$
603,935

 
$
(190,742
)
 
$
582,556

 
$
(167,616
)
Schedule of Estimated Amortization Expense
The estimated amortization expense related to intangible assets at December 31, 2018 and for each of the five succeeding years is as follows:

 
Amortization included in expense
 
Amortization recorded as a reduction of revenue
 
Total
2019
17,978

 
6,000

 
$
23,978

2020
17,995

 
6,000

 
$
23,995

2021
17,042

 
6,000

 
$
23,042

2022
15,583

 
6,000

 
$
21,583

2023
14,879

 
6,000

 
$
20,879