If you want to check Browsing History on WiFi Router, you the default gateway of the router, a browser, and router's credentials. Check this post to know how to do the same.

Check the router's settings to identify unknown devices. Change your Wi-Fi password to remove unauthorized devices. Use parental controls to regulate access to the device.

Then check the System Log in the firmware for any repeated login failures. In any case, Asus also recommends that you adopt a strong administrative password, good advice for any router.