Maybe a bit ambitious before bed... Still work to be done to get it in terms of a strict quadratic programming problem (remove the "forall"). But this is what it looks like in terms of a_3, b_3, pretty ugly. On the wiki for quadratic programming, this gives Q and c but not sufficient A or b.
![integral of ArcTan[x/a]ArcTan[x/b]/x^2 dx from 0 to infinity](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:wfval2ke6je4eteos4gmokmc/bafkreifdibtzne75vw7qmighkinqwftcd3xevywxpfn35cyhmaeujksaua)
