The following table presents details of our intangible assets which include acquired identifiable intangible assets and capitalized internal-use software costs:


	Weighted- Average Estimated Useful Life (years)	As of June 30, 2025						As of December 31, 2024
		Gross Carrying Amount		Accumulated Amortization		Net Book Value		Gross Carrying Amount		Accumulated Amortization		Net Book Value
		(in thousands)
Intangible assets subject to amortization:
Developed technology	6.3	$	146,855	$	(103,039)	$	43,816	$	146,855	$	(94,193)	$	52,662
Customer relationships	4.3	12,000		(11,667)		333		12,000		(10,363)		1,637
Trade names	5.0	2,619		(2,619)		—		2,619		(2,559)		60
Total acquired intangible assets		$	161,474	$	(117,325)	$	44,149	$	161,474	$	(107,115)	$	54,359
Internal-use software	3.0	76,057		(45,225)		30,832		68,878		(37,518)		31,360
Total intangible assets		$	237,531	$	(162,550)	$	74,981	$	230,352	$	(144,633)	$	85,719

Intangible assets are expensed on a straight-line basis over the useful life of the asset. Amortization expense was $9.0 million and $8.1 million for the three months ended June 30, 2025 and 2024, respectively, and $17.9 million and $16.5 million for the six months ended June 30, 2025 and 2024, respectively.

Estimated future amortization expense of the acquired identifiable intangible assets and completed capitalized internal-use software costs as of June 30, 2025 was as follows (in thousands):

The table above excludes the impact of $9.1 million of capitalized internal-use software costs for projects that have not been completed as of June 30, 2025, and therefore, all the costs associated with these projects have not been incurred.