reported to WRI. [CASE:3960295]
I run the CAS integration tests which contains 15000 integrals over number of Mathematica versions.
I found that the average leaf size of the anti-derivatives blows up after version 9. Here is diagram
To find the integrals which cause this increase in leaf size, I picked those in version 11.2 which had leaf size of at least 5 times as large as in version 9.0. I found 260 such integrals. Many have much larger ratio than 5. some have ratio of 50 times as large and 100 times as large.
The question is, why did this happen after version 9? Is there a common cause among these 260 integrals? I will give one such example, and link to the report which contain list of the 260 integrals and also the zip file of the raw test files obtained from Rubi web site.
First integral
command: Integrate[Tan[x]/Sqrt[1 + Sec[x]^3],x]
Version 11.2 leaf size: 37353
Version 9 leaf size: 296
Ratio of version 11.2 leaf size to verion 9: 126
Version 11.2
Integrate[Tan[x]/Sqrt[1+Sec[x]^3],x]
(*output too large to post*)
In version 9
The report in PDF and HTML can be found here
Appendix
Here is partial part of the list. Too long to post here in full.
Command used: Integrate[Tan[x]/Sqrt[1 + Sec[x]^3],x]
Version 11.2 leaf size: 37353.
Version 9 leaf size: 296.
Ratio of version 11.2 leaf size to verion 9 leaf size: 126
Command used: Integrate[ArcTan[Sqrt[-1 + Sec[x]]]*Sin[x],x]
Version 11.2 leaf size: 6968.
Version 9 leaf size: 1043.
Ratio of version 11.2 leaf size to verion 9 leaf size: 7
Command used: Integrate[(1 + x^2)/((1 - x^2)*Sqrt[1 + x^4]),x]
Version 11.2 leaf size: 269.
Version 9 leaf size: 36.
Ratio of version 11.2 leaf size to verion 9 leaf size: 7
Command used: Integrate[(1 - x^2)/((1 + x^2)*Sqrt[1 + x^4]),x]
Version 11.2 leaf size: 266.
Version 9 leaf size: 40.
Ratio of version 11.2 leaf size to verion 9 leaf size: 7
Command used: Integrate[(1 - x^2)/((1 + x^2)*Sqrt[1 + x^4]),x]
Version 11.2 leaf size: 266.
Version 9 leaf size: 40.
Ratio of version 11.2 leaf size to verion 9 leaf size: 7
Command used: Integrate[(1 + x^2)/((1 - x^2)*Sqrt[1 + x^4]),x]
Version 11.2 leaf size: 269.
Version 9 leaf size: 36.
Ratio of version 11.2 leaf size to verion 9 leaf size: 7
Command used: Integrate[(1 - x^2)/((1 + x^2)*Sqrt[1 + x^2 + x^4]),x]
Version 11.2 leaf size: 567.
Version 9 leaf size: 94.
Ratio of version 11.2 leaf size to verion 9 leaf size: 6
Command used: Integrate[(Sqrt[Cos[x]*Sin[x]^3] - 2*Sin[2*x])/(-Sqrt[Cos[x]^3*Sin[x]] + Sqrt[Tan[x]]),x]
Version 11.2 leaf size: 68457.
Version 9 leaf size: 2051.
Ratio of version 11.2 leaf size to verion 9 leaf size: 33
Command used: Integrate[(Cosh[x]*(-Cosh[2*x] + Tanh[x]))/(Sqrt[Sinh[2*x]]*(Sinh[x]^2 + Sinh[2*x])),x]
Version 11.2 leaf size: 5173.
Version 9 leaf size: 490.
Ratio of version 11.2 leaf size to verion 9 leaf size: 11
Command used: Integrate[Sqrt[1 + p*x^2 - x^4]/(1 + x^4),x]
Version 11.2 leaf size: 10200.
Version 9 leaf size: 322.
Ratio of version 11.2 leaf size to verion 9 leaf size: 32
Command used: Integrate[Sqrt[e + f*x^2]/((a + b*x^2)*(c + d*x^2)^(7/2)),x]
Version 11.2 leaf size: 12924.
Version 9 leaf size: 577.
Ratio of version 11.2 leaf size to verion 9 leaf size: 22
Command used: Integrate[(Sqrt[c + d*x^2]*(e + f*x^2)^(3/2))/(a + b*x^2),x]
Version 11.2 leaf size: 11662.
Version 9 leaf size: 739.
Ratio of version 11.2 leaf size to verion 9 leaf size: 16
Command used: Integrate[(Sqrt[2 + d*x^2]*Sqrt[3 + f*x^2])/(a + b*x^2),x]
Version 11.2 leaf size: 7470.
Version 9 leaf size: 134.
Ratio of version 11.2 leaf size to verion 9 leaf size: 56
Command used: Integrate[(Sqrt[c + d*x^2]*Sqrt[e + f*x^2])/(a + b*x^2)^2,x]
Version 11.2 leaf size: 3879.
Version 9 leaf size: 401.
Ratio of version 11.2 leaf size to verion 9 leaf size: 10
Command used: Integrate[1/((a + b*x^2)^2*Sqrt[c - d*x^2]*Sqrt[e + f*x^2]),x]
Version 11.2 leaf size: 7216.
Version 9 leaf size: 773.
Ratio of version 11.2 leaf size to verion 9 leaf size: 9
Command used: Integrate[((e*x)^m*(a + b*x^n)^2*(A + B*x^n))/(c + d*x^n)^3,x]
Version 11.2 leaf size: 1924.
Version 9 leaf size: 345.
Ratio of version 11.2 leaf size to verion 9 leaf size: 6
Command used: Integrate[((b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(d + e*x)^(3/2),x]
Version 11.2 leaf size: 5706.
Version 9 leaf size: 1045.
Ratio of version 11.2 leaf size to verion 9 leaf size: 5
Command used: Integrate[1/(x*(1 + x)^(5/2)*(1 - x + x^2)^(5/2)),x]
Version 11.2 leaf size: 2539.
Version 9 leaf size: 98.
Ratio of version 11.2 leaf size to verion 9 leaf size: 26
Command used: Integrate[Sqrt[2 + 3*x^2 + x^4]/(7 + 5*x^2),x]
Version 11.2 leaf size: 520.
Version 9 leaf size: 90.
Ratio of version 11.2 leaf size to verion 9 leaf size: 6
Command used: Integrate[1/((d + e*x^2)^2*Sqrt[a + b*x^2 - c*x^4]),x]
Version 11.2 leaf size: 10996.
Version 9 leaf size: 1341.
Ratio of version 11.2 leaf size to verion 9 leaf size: 8
Command used: Integrate[Sqrt[a + b*x^2 + c*x^4]/(x^3*(d + e*x^2)),x]
Version 11.2 leaf size: 10848.
Version 9 leaf size: 244.
Ratio of version 11.2 leaf size to verion 9 leaf size: 44
Command used: Integrate[Sqrt[1 + 2*x^2 + 2*x^4]/(x^4*(3 + 2*x^2)),x]
Version 11.2 leaf size: 1546.
Version 9 leaf size: 154.
Ratio of version 11.2 leaf size to verion 9 leaf size: 10
Command used: Integrate[Sqrt[1 + 2*x^2 + 2*x^4]/(x^6*(3 + 2*x^2)),x]
Version 11.2 leaf size: 1650.
Version 9 leaf size: 224.
Ratio of version 11.2 leaf size to verion 9 leaf size: 7
Command used: Integrate[(1 + 2*x^2 + 2*x^4)^(3/2)/(x^2*(3 - 2*x^2)),x]
Version 11.2 leaf size: 1609.
Version 9 leaf size: 213.
Ratio of version 11.2 leaf size to verion 9 leaf size: 8
Command used: Integrate[1/(x*(d + e*x^2)*Sqrt[a + b*x^2 + c*x^4]),x]
Version 11.2 leaf size: 3622.
Version 9 leaf size: 174.
Ratio of version 11.2 leaf size to verion 9 leaf size: 21
Command used: Integrate[x^2/((3 + 2*x^2)*Sqrt[1 + 2*x^2 + 2*x^4]),x]
Version 11.2 leaf size: 1518.
Version 9 leaf size: 99.
Ratio of version 11.2 leaf size to verion 9 leaf size: 15
Command used: Integrate[x^2/((3 + 2*x^2)*(1 + 2*x^2 + 2*x^4)^(3/2)),x]
Version 11.2 leaf size: 1636.
Version 9 leaf size: 199.
Ratio of version 11.2 leaf size to verion 9 leaf size: 8
Command used: Integrate[1/((3 + 2*x^2)*(1 + 2*x^2 + 2*x^4)^(3/2)),x]
Version 11.2 leaf size: 1636.
Version 9 leaf size: 199.
Ratio of version 11.2 leaf size to verion 9 leaf size: 8
Command used: Integrate[Sqrt[1 - x^2]/(x^3*(a + b*x^2 + c*x^4)),x]
Version 11.2 leaf size: 6953.
Version 9 leaf size: 298.
Ratio of version 11.2 leaf size to verion 9 leaf size: 23
Command used: Integrate[(d + e*x^n)*(a + b*x^n + c*x^(2*n))^(3/2),x]
Version 11.2 leaf size: 8312.
Version 9 leaf size: 690.
Ratio of version 11.2 leaf size to verion 9 leaf size: 12
Command used: Integrate[(a - c*x^4)/(Sqrt[a + b*x^2 + c*x^4]*(a*d + a*e*x^2 + c*d*x^4)),x]
Version 11.2 leaf size: 26953.
Version 9 leaf size: 419.
Ratio of version 11.2 leaf size to verion 9 leaf size: 64
Command used: Integrate[(a - c*x^4)/((a*e + c*d*x^2)*(d + e*x^2)*Sqrt[a + b*x^2 + c*x^4]),x]
Version 11.2 leaf size: 15438.
Version 9 leaf size: 383.
Ratio of version 11.2 leaf size to verion 9 leaf size: 40
Command used: Integrate[Cos[c + d*x]^6*Sqrt[a + a*Sin[c + d*x]],x]
Version 11.2 leaf size: 995.
Version 9 leaf size: 99.
Ratio of version 11.2 leaf size to verion 9 leaf size: 10
Command used: Integrate[1/((a + b*Sin[e + f*x])^2*(c + d*Sin[e + f*x])^(3/2)),x]
Version 11.2 leaf size: 6518.
Version 9 leaf size: 1057.
Ratio of version 11.2 leaf size to verion 9 leaf size: 6
Command used: Integrate[1/((a + b*Sin[e + f*x])^2*(c + d*Sin[e + f*x])^(5/2)),x]
Version 11.2 leaf size: 6780.
Version 9 leaf size: 1319.
Ratio of version 11.2 leaf size to verion 9 leaf size: 5
Command used: Integrate[(c + d*Sin[e + f*x])^(5/2)/(a + b*Sin[e + f*x])^3,x]
Version 11.2 leaf size: 6610.
Version 9 leaf size: 1149.
Ratio of version 11.2 leaf size to verion 9 leaf size: 6
Command used: Integrate[Sqrt[c + d*Sin[e + f*x]]/(a + b*Sin[e + f*x])^3,x]
Version 11.2 leaf size: 6499.
Version 9 leaf size: 1038.
Ratio of version 11.2 leaf size to verion 9 leaf size: 6
Command used: Integrate[1/((a + b*Sin[e + f*x])^3*(c + d*Sin[e + f*x])^(3/2)),x]
Version 11.2 leaf size: 6779.
Version 9 leaf size: 1318.
Ratio of version 11.2 leaf size to verion 9 leaf size: 5
Command used: Integrate[Cos[c + d*x]*Sin[c + d*x]^n*(a + a*Sin[c + d*x])^4,x]
Version 11.2 leaf size: 457.
Version 9 leaf size: 80.
Ratio of version 11.2 leaf size to verion 9 leaf size: 6
Command used: Integrate[Sqrt[g*Sin[e + f*x]]/(Sqrt[a + a*Sin[e + f*x]]*(c - c*Sin[e + f*x])),x]
Version 11.2 leaf size: 58053.
Version 9 leaf size: 232.
Ratio of version 11.2 leaf size to verion 9 leaf size: 250
Command used: Integrate[1/(Sqrt[g*Sin[e + f*x]]*Sqrt[a + a*Sin[e + f*x]]*(c - c*Sin[e + f*x])),x]
Version 11.2 leaf size: 58056.
Version 9 leaf size: 234.
Ratio of version 11.2 leaf size to verion 9 leaf size: 248
Command used: Integrate[1/(Sqrt[g*Sin[e + f*x]]*Sqrt[a + a*Sin[e + f*x]]*(c + d*Sin[e + f*x])),x]
Version 11.2 leaf size: 663005.
Version 9 leaf size: 99997.
Ratio of version 11.2 leaf size to verion 9 leaf size: 7
Command used: Integrate[Sqrt[3 + 4*Cos[c + d*x]]*Sec[c + d*x]^2,x]
Version 11.2 leaf size: 987.
Version 9 leaf size: 157.
Ratio of version 11.2 leaf size to verion 9 leaf size: 6
Command used: Integrate[Cos[c + d*x]^(3/2)/(a + b*Cos[c + d*x]),x]
Version 11.2 leaf size: 642.
Version 9 leaf size: 84.
Ratio of version 11.2 leaf size to verion 9 leaf size: 8
Command used: Integrate[Cos[c + d*x]^(3/2)/(a + b*Cos[c + d*x])^3,x]
Version 11.2 leaf size: 1390.
Version 9 leaf size: 276.
Ratio of version 11.2 leaf size to verion 9 leaf size: 5
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