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calculus and analysis - Why the Kernel crashes on these integrals in V12?


Reported to WRI, [CASE:4331819]



This is using V12, on windows 10, 64 bit. Note: these integrals work OK on 11.3 on same PC.


enter image description here



Any idea why the Kernel now crashes on these types of integrals?


ClearAll[x,a,b,c,e,d,f,g,n];

(*these from file #40,41*)

Integrate[(1 + x^2)^3/(1 + x^2 + x^4)^(3/2), x];
Integrate[(1 + x^2)^2/(1 + x^2 + x^4)^(3/2), x];
Integrate[(1 + x^2)/(1 + x^2 + x^4)^(3/2), x];
Integrate[(7 + 5*x^2)^3/(2 + 3*x^2 + x^4)^(3/2), x];
Integrate[(7 + 5*x^2)^2/(2 + 3*x^2 + x^4)^(3/2), x];
Integrate[(7 + 5*x^2)/(2 + 3*x^2 + x^4)^(3/2), x];
Integrate[(2 + 3*x^2 + x^4)^(3/2)*(7 + 5*x^2)^3, x];
Integrate[(2 + 3*x^2 + x^4)^(3/2)*(7 + 5*x^2)^2, x];
Integrate[(2 + 3*x^2 + x^4)^(3/2)*(7 + 5*x^2), x];
Integrate[(7+5*x^2)^4/(2+3*x^2+x^4)^(3/2),x];

Integrate[(7+5*x^2)^2/(2+3*x^2+x^4)^(3/2),x];
Integrate[(4+3*x^2+x^4)^(3/2)*(7+5*x^2),x];
Integrate[(d+e*x^2)*(a+b*x^2+c*x^4)^(3/2)/(f*x)^(1/2),x];

(*these from file #42*)
Integrate[(a*g - c*g*x^4)/(a + b*x^2 + c*x^4)^(3/2), x];
Integrate[(a*g+e*x-c*g*x^4)/(a+b*x^2+c*x^4)^(3/2),x];
Integrate[(a*g+f*x^3-c*g*x^4)/(a+b*x^2+c*x^4)^(3/2),x];
Integrate[(a*g+e*x+f*x^3-c*g*x^4)/(a+b*x^2+c*x^4)^(3/2),x];


(*these from file #44*)
Integrate[(A+B*x^2)*(d+e*x^2)/(a+b*x^2+c*x^4)^(3/2),x];
Integrate[(A+B*x^2)/(a+b*x^2+c*x^4)^(3/2),x]

(*these from file #49*)
 Integrate[(-a*h*x^(n/2 - 1) + c*f*x^(n - 1) + c*g*x^(2*n - 1) +c*h*x^((5*n)/2 - 1))/(a + b*x^n + c*x^(2*n))^(3/2), x];
 Integrate[(x^(n/2 - 1)*(-a*h + c*f*x^(n/2) + c*g*x^((3*n)/2)+c*h*x^(2*n)))/(a + b*x^n + c*x^(2*n))^(3/2), x];
 Integrate[((d*x)^(n/2-1)*(-a*h+c*f*x^(n/2)+c*g*x^((3*n)/2)+c*h*x^(2*n)))/(a+b*x^n+c*x^(2*n))^(3/2),x];
(*etc..*)


Mathematica graphics


Mathematica graphics


Mathematica graphics


No problem with V 11.3


Mathematica graphics


Mathematica graphics


Mathematica graphics


Does this happen to others and on other systems or just on windows 10?


It looks like it is the same bug that is causing all these crashes, but I can't be sure.


I am finding that V12 kernel crashes more than V 11.3 kernel and also in strange ways. This makes it very hard to run a long script, when kernel keeps crashing.



ps. I think WRI should have been able to detect these before making a release by running regression tests. I am using Rubi integration test files to find these problems.


pps. I hope I do not get downvoted again for asking about a possible problem in Mathematica like in the last post on that bizarre kernel crash.




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