Here is a nice easy to produce kernel crash of V 13.1 for those to like to collect these things:
ClearAll[x];
integrand=((x^4-2*x^3+3*x^2-6*x)*Exp[x^2/3]*Log[(x-2)/(5*x)]^2+6*x*Exp[x^2/3]*Log[(x-2)/(5*x)])/(6*x-12);
Integrate[integrand, x]
(*after about 2 minutes, you'll hear a beep and kernel quit*)
report to WRI. It seems this existed also in V 13.0.1. I do not know about earlier releases.
ClearAll[x];
integrand=((x^4-2*x^3+3*x^2-6*x)*Exp[x^2/3]*Log[(x-2)/(5*x)]^2+6*x*Exp[x^2/3]*Log[(x-2)/(5*x)])/(6*x-12);
Integrate[integrand, x]
(*after about 2 minutes, you'll hear a beep and kernel quit*)
report to WRI. It seems this existed also in V 13.0.1. I do not know about earlier releases.