If you accidentally delete some of your important videos on the iPhone or the iPad, follow these steps to recover them for free.
If your device is running on iOS 8 or newer, then you can firstly check the[b] Recently Deleted Album[/b] in the default Photos app to see the deleted videos are there. (Please note that this feature is only available from iOS 8.x or iOS 9.x)
If there is no videos in the album, it mean you've deleted videos from your device permanently. In this case, you can try some freeware to recover deleted videos from iPhone or iPad for free.
Youtube Guide:

https://www.youtube.com/watch?v=xf4luPKJEoM
There are so many iPhone video recovery tools available in the market. If you don’t want to spend any money on it, Free iPhone Recovery is recommended to you. It is specially designed to recover deleted videos from iPhone, iPad and extract videos from iTunes backup.

Step 1. Run free iPhone Video Recovery, check “Camera Roll”, “Photo Stream” and “App Videos”, then head to the next.
Step 2. Connect your iPhone or iPad to computer. (If you lost your device, directly go to next and select the iTunes backup, or log in your iCloud account.)
Step 3. Star to scan your device or backup, then preview & recover the deleted videos from iPhone or iPad.

If you had your iPhone jailbroken, you can also try PhotoRec which might be difficult to use for you.

Thanks for sharing! And I know there is another software called FonePaw iPhone Data Recover which is a professional recover that can recover kinds of files from iPhone or iPad. Of course, it can recover deleted data from your iPhone and iPad, but not all for free! There is a tutorial about how to recover deleted videos from iPhone or iPad.