why these integrals fail to evaluate in V 13 compared to V 12.3?

Question

This was also reported to WRI. [CASE:4903465]

I'd like to know why these integrals no longer evaluate in V 13 and timeout after 3 minutes while using the same PC and OS they all evaluate quickly in time using V 12.3.

Is there is a workaround in V 13?

This is on windows 10. 64 GB RAM. These integrals come from Rubi's input test files.

The timeout is there to prevent the script from hanging forever.

Is this a bug in integrate?

I also include at bottom a link to the notebook in V 13 and V 12.3 with the code and output to download.

Clear["Global`*]
timeOut = 3*60;
TimeConstrained[Integrate[Cot[e + f*x]^2*(a + a*Sin[e + f*x])^(1/3), x], timeOut]
TimeConstrained[Integrate[Cot[e + f*x]^4*(a + a*Sin[e + f*x])^(1/3), x], timeOut]
TimeConstrained[Integrate[Csc[c + d*x]^2*(a + a*Sin[c + d*x])^(2/3), x], timeOut]
TimeConstrained[Integrate[Csc[c + d*x]*(a + a*Sin[c + d*x])^(4/3), x], timeOut]
TimeConstrained[Integrate[Csc[c + d*x]^2*(a + a*Sin[c + d*x])^(4/3), x], timeOut]
TimeConstrained[Integrate[Csc[c + d*x]^2/(a + a*Sin[c + d*x])^(1/3), x], timeOut]
TimeConstrained[Integrate[Csc[c + d*x]^2/(a + a*Sin[c + d*x])^(4/3), x], timeOut]
TimeConstrained[Integrate[(d*Sin[e + f*x])^(5/2)/((g*Cos[e + f*x])^(3/2)*(a + b*Sin[e + f*x])), x], timeOut]
TimeConstrained[Integrate[1/((d*Sec[e + f*x])^(5/3)*(a + b*Tan[e + f*x])),x], timeOut]
TimeConstrained[Integrate[1/((d*Sec[e + f*x])^(1/3)*(a + b*Tan[e + f*x])^2),x], timeOut]
TimeConstrained[Integrate[Tan[c + d*x]^(2/3)/Sqrt[a + b*Tan[c + d*x]], x], timeOut]
TimeConstrained[Integrate[1/(Tan[c + d*x]^(4/3)*Sqrt[a + b*Tan[c + d*x]]),x], timeOut]
TimeConstrained[Integrate[(a + a*Sec[c + d*x])^2/Sqrt[e*Sin[c + d*x]], x], timeOut]
TimeConstrained[Integrate[(a + a*Sec[c + d*x])^n*Tan[c + d*x]^(3/2), x], timeOut]

Screen shot

Link to the notebooks is here

Answer 1

I was trying different settings, I found a solution to this problem.

Now they all evaluate in V 13 as they did in V 12.3.

You need to add this setting at the top (this is new in V 13.0)

SetSystemOptions["IntegrateOptions" -> "UseIntegrateAlgebraic" -> False];

The default was True

As an example of one of the above

---

---

IntegrateAlgebraic is very good in solving many integrals that could not be solved easily before and it does it fast, but it looks like there is a small clitch somewhere integrating IntegrateAlgebraic into V 13 Integrate command.

I also noticed I needed to start with Clean kernel when changing the this setting from True to False or vis verse for the new settings to take effect. Not sure why.

The V13 notebook showing they all now evaluate can be downloaded from here.

Answer 2

Whenever you use assumptions, Mathematica V13 computes these integrals.

For example:

I think it's convenient to use assumptions, since the integral has several parameters that could be interpreted as complex by Mathematica.