4.  Goodwill and Purchased Intangibles



Goodwill



The carrying value of goodwill at September 30, 2018 and December 31, 2017 was $803,118.  



Intangible assets



The following table presents details of our purchased intangible assets as of September 30, 2018 and December 31, 2017:







The intangible assets are being amortized on a straight-line basis over their estimated useful lives of one to twenty years.



Amortization expense for intangible assets was $9,976 and $10,796 for the three months ended September 30, 2018 and 2017, respectively.



Amortization expense for intangible assets was $31,741 and $32,297 for the nine months ended September 30, 2018 and 2017, respectively.



The estimated future amortization expense of our intangible assets as of September 30, 2018 is as follows: