No, although he was certainly an integral enthusiast, the video does not claim that he was solving them from scratch. Rather, it says he was starting from integrals with known answers and tweaking them slightly to see if he could break the CAS. At that point, although he did apparently try to solve the resulting problems himself, he already knew roughly what the answer would look like (by comparing to the previous answer, and also to the previous solution path.)
Specifically step 5 in my previous post is more work than it sounds, he was doing some calculations by hand, but it's like he's starting 90% of the way there and trying to do the last 10% by hand to fool the CAS. And remember, he can try as many variants of the tweak+10% as he wants until he finds something that works.