Win 10 makes it very each to capture video streaming on the web with its nifty Game Bar. Activate the Game Bar by pressing the Windows Key + G.
You'll be prompted to open the utility by confirming that you're playing a game.
The controls include options for grabbing a screen shot, and more impressively to record anything happening on screen.
If you click the 'Record from now', the video will begin recording. Be sure to turn off the microphone, and shut down any open windows which may cause extraneous sound.
Game Bar will save the video to a folder located at: C:\Users\[your name]\Videos\Captures
I tested it out today, and Game Bar recorded a 30 minute long webcast posted online without any issues.