Is Zoom integrated into Slack?

Yes.  To link your accounts, click on the "Apps" link and search for Zoom. Once it pops up, click on it and it will message you with the following instructions:

:wave: Hi @YourSlackName Welcome to the Zoom app on Slack. You can quickly start or join Zoom meetings here. These are the available commands:

/zoom Start a meeting
/zoom meeting [topic] Start a meeting with topic
/zoom join [meeting id/personal link name] Join a meeting using meeting ID/personal link name
/zoom join me Join a meeting using your personal meeting ID
/zoom call [@contact/phone number] Start a phone call with a contact or a phone number
/zoom config Configure your settings for Zoom Meetings in Slack
/zoom logout Logout from Zoom on all your Slack channels and direct messages

At the end of the information you will see an authorization button. If you wish to link your accounts, click "Authorize Zoom" and it will open a Zoom page which will guide you through login and authorization.