Thank you for pointing out this infinite-recursion bug in Rubi 4.3 and earlier versions. A simpler example of the same bug is
Assuming[t>0, Int[Sqrt[(I+1)*(1+t+t^4)], t]]
It occurs when t>0 because Rubi uses algebraic simplification to transform the problem to
Assuming[t>0, Int[Sqrt[I+1]*Sqrt[1+t+t^4], t]]
But then Mathematica simplifies the integrand back to the original one before Rubi has a chance to pull out the constant factor Sqrt[I+1], thereby resulting in a classic case of infinite-recursion.
The just released version 4.4 of Rubi resolves the bug by splitting the factors of the square-root and pulling the resulting constant factor out of the integrand in a single step, yielding the guaranteed simpler problem
Assuming[t>0, Sqrt[I+1]*Int[Sqrt[1+t+t^4], t]]
An executable version of Rubi 4.4 and formatted pdf files of its newly revised rules are available for viewing and/or downloading at