7.  Intangible Assets and Goodwill

Intangible Assets, Net

Acquired intangible assets, net consisted of the following as of April 30, 2021 (in thousands):

We record amortization expense associated with acquired developed technology in cost of licenses revenue and cost of maintenance and support revenue, trade names and trademarks in sales and marketing expense, and customer relationships in sales and marketing expense in the condensed consolidated statements of operations. Amortization of acquired intangible assets for the three months ended April 30, 2021 and 2020 was $0.9 million and $0.6 million, respectively.

The expected future amortization expenses related to intangible assets as of April 30, 2021 were as follows (in thousands):

Goodwill

The changes in the carrying amounts of goodwill during the period were as follows (in thousands):