To actively participate in activities in English, you can say "participate actively" or "engage actively". This phrase comes from the verb "participate", which means to take part in something, and the adjective "active", which means involving physical or mental effort to do something. Here are some example sentences and their translations:

I want to participate actively in the discussion. (我想积极参加讨论。)

She always engages actively in the community events. (她总是积极参与社区活动。)

They encouraged everyone to participate actively in the project. (他们鼓励每个人积极参与该项目。)