I’m going crazy doing “busy work.” Should I ask my boss for more work? Or will that look bad for not keeping busy?

"So you could either be busy every day for the next five weeks ... can be a problem for people's productivity and well-being, workplace experts told BI. The good news is that there are ways ...

I have to submit a daily log and I don’t want to look unproductive. I’m also going crazy doing “busy work.” Should I ask my boss for more work? Or will that look bad for not keeping busy?