We have two factors. We know to differentiate one (or both)of them and we know how to integrate the other one (or both)of them.
$$ \int udv=uv-\int vdu $$
It is the order to set u into. Often wise, integration by part are attempts to avoid the integration of u.
With “repeat” integrad and a polynomial term
According to LIPET, the two well know form of integration that repeats is trig (sin and cosine) and e^x. Therefore most of the time, the u in tabular method are a polynomial term that will finally end with a 0 as it derivate onwards. (Unsure)
u derivate and dv integrate as they goes down, connect them with diagonals (\). First positive, then negative, then positive…