You can use QuickTime player to record iPhone/iPad screen, free and easy, no need jailbreak.
1. Plug in iPhone/iPad to computer, launch QuickTime and select menu File->New Movie Recording.
2. On the right of the red circle record button on the video preview screen is a reversed ^ icon. Click on it for a drop down menu allowing you to choose the iPhone/iPad as video source. That's all.
To get better quality video like 4K or HD video, I'd recommend Acethinker iPhone Screen Recorder. Also support stream video recording on iPhone/iPad.