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mapleIntegrandsSolutions.m
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mapleIntegrandsSolutions.m
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(*
results = Timing[ int[#, x, "RationalUndeterminedOnly" -> True] ] & /@ mapleIntegrands;
Count[results, ans_ /; FreeQ[ans, IntegrateAlgebraic]]/Length[mapleIntegrands] // N
results[[All,2]]
*)
mapleIntegrandSolutions = {
(2*ArcTan[Sqrt[-3 + x^3]/Sqrt[3]])/(3*Sqrt[3]),
(Sqrt[2]*ArcTan[Sqrt[-2 + x^3]/Sqrt[2]])/3, Defer[IntegrateAlgebraic][
(1 + x)/((-2 + x)*Sqrt[-2 + x^3]), x], (2*ArcTan[Sqrt[-1 + x^3]])/3,
(2*Sqrt[-1 + x^3])/3, Defer[IntegrateAlgebraic][
(-1 + x)/((2 + x)*Sqrt[-1 + x^3]), x], (-2*ArcTanh[Sqrt[1 + x^3]])/3,
(2*Sqrt[1 + x^3])/3, Defer[IntegrateAlgebraic][
(1 + x)/((-2 + x)*Sqrt[1 + x^3]), x],
-(Sqrt[2]*ArcTanh[Sqrt[2 + x^3]/Sqrt[2]])/3,
Defer[IntegrateAlgebraic][(-1 + x)/((2 + x)*Sqrt[2 + x^3]), x],
(-2*ArcTanh[Sqrt[3 + x^3]/Sqrt[3]])/(3*Sqrt[3]),
Defer[IntegrateAlgebraic][x/((2 + x)*Sqrt[-1 - 2*x + x^3]), x],
Defer[IntegrateAlgebraic][(2 + x)/(x*Sqrt[-1 - 2*x + x^3]), x],
Defer[IntegrateAlgebraic][(-2 + x)/(x*Sqrt[1 - 2*x + x^3]), x],
Defer[IntegrateAlgebraic][x/((-2 + x)*Sqrt[1 - 2*x + x^3]), x],
Defer[IntegrateAlgebraic][(-3 + x)/((1 + x)*Sqrt[-2 + x + x^3]), x],
Defer[IntegrateAlgebraic][(1 + x)/((-3 + x)*Sqrt[-2 + x + x^3]), x],
Defer[IntegrateAlgebraic][(-1 + x)/((3 + x)*Sqrt[2 + x + x^3]), x],
Defer[IntegrateAlgebraic][(3 + x)/((-1 + x)*Sqrt[2 + x + x^3]), x],
(-2*ArcTanh[(Sqrt[3]*x)/Sqrt[-1 + 3*x + x^3]])/Sqrt[3],
(2*ArcTan[Sqrt[1 + 3*x + x^3]/(Sqrt[3]*x)])/Sqrt[3],
Defer[IntegrateAlgebraic][(-3 + x)/((-1 + x)*Sqrt[2 + x - 3*x^2 + x^3]), x],
Defer[IntegrateAlgebraic][(-1 + x)/((-3 + x)*Sqrt[2 + x - 3*x^2 + x^3]), x],
Defer[IntegrateAlgebraic][1/((-1 + x)*Sqrt[-3 + 3*x - 3*x^2 + x^3]), x],
Defer[IntegrateAlgebraic][x/((-3 + x)*Sqrt[-3 + 3*x - 3*x^2 + x^3]), x],
Defer[IntegrateAlgebraic][1/((-1 + x)*Sqrt[-2 + 3*x - 3*x^2 + x^3]), x],
Defer[IntegrateAlgebraic][(-2 + x)/((1 + x)*Sqrt[-2 + 3*x - 3*x^2 + x^3]),
x], Defer[IntegrateAlgebraic][1/((-1 + x)*Sqrt[1 + 3*x - 3*x^2 + x^3]), x],
Sqrt[2/3]*ArcTan[Sqrt[1 + 3*x - 3*x^2 + x^3]/(Sqrt[6]*x)],
Defer[IntegrateAlgebraic][1/((-1 + x)*Sqrt[2 + 3*x - 3*x^2 + x^3]), x],
Defer[IntegrateAlgebraic][1/((-1 + x)*Sqrt[3 + 3*x - 3*x^2 + x^3]), x],
Defer[IntegrateAlgebraic][(-3 + x)/(x*Sqrt[1 - 2*x^2 + x^3]), x],
Defer[IntegrateAlgebraic][(-1 + 2*x)/((-2 + x)*Sqrt[1 - 2*x^2 + x^3]), x],
Defer[IntegrateAlgebraic][(1 + 2*x)/((-2 + x)*Sqrt[2 - 2*x^2 + x^3]), x],
Defer[IntegrateAlgebraic][x/((-3 + x)*Sqrt[1 - x - 2*x^2 + x^3]), x],
Defer[IntegrateAlgebraic][(-2 + x)/(x*Sqrt[-1 + 2*x - 2*x^2 + x^3]), x],
Defer[IntegrateAlgebraic][x/((-2 + x)*Sqrt[-1 + 2*x - 2*x^2 + x^3]), x],
-2*ArcTanh[x/Sqrt[-1 + 3*x - 2*x^2 + x^3]],
(2*ArcTan[Sqrt[1 + 3*x - 2*x^2 + x^3]/(Sqrt[5]*x)])/Sqrt[5],
Defer[IntegrateAlgebraic][(3 + x)/(x*Sqrt[-1 - 2*x - x^2 + x^3]), x],
Defer[IntegrateAlgebraic][(-1 + x)/((2 + x)*Sqrt[1 - 2*x - x^2 + x^3]), x],
Defer[IntegrateAlgebraic][(-3 + 2*x)/((1 + x)*Sqrt[-1 - x - x^2 + x^3]), x],
Defer[IntegrateAlgebraic][(1 + x)/((-2 + x)*Sqrt[-3 + 2*x - x^2 + x^3]), x],
Defer[IntegrateAlgebraic][(-3 + x)/(x*Sqrt[-1 + 2*x - x^2 + x^3]), x],
Defer[IntegrateAlgebraic][(-3 + x)/((1 + x)*Sqrt[-3 + 3*x - x^2 + x^3]), x],
Defer[IntegrateAlgebraic][(1 + x)/((-3 + x)*Sqrt[-3 + 3*x - x^2 + x^3]), x],
-(Sqrt[2]*ArcTanh[(Sqrt[2]*x)/Sqrt[-1 + 3*x - x^2 + x^3]]),
ArcTan[Sqrt[1 + 3*x - x^2 + x^3]/(2*x)], Defer[IntegrateAlgebraic][
(1 + x)/((-2 + x)*Sqrt[-1 - 2*x + x^2 + x^3]), x],
Defer[IntegrateAlgebraic][(-3 + x)/(x*Sqrt[1 - 2*x + x^2 + x^3]), x],
Defer[IntegrateAlgebraic][(3 + 2*x)/((-1 + x)*Sqrt[1 - x + x^2 + x^3]), x],
Defer[IntegrateAlgebraic][(3 + x)/(x*Sqrt[1 + 2*x + x^2 + x^3]), x],
Defer[IntegrateAlgebraic][(1 + x)/((-2 + 2*x + x^2)*
Sqrt[2 + 2*x + x^2 + x^3]), x], Defer[IntegrateAlgebraic][
(-1 + x)/((2 + x)*Sqrt[3 + 2*x + x^2 + x^3]), x],
-ArcTanh[(2*x)/Sqrt[-1 + 3*x + x^2 + x^3]],
Sqrt[2]*ArcTan[Sqrt[1 + 3*x + x^2 + x^3]/(Sqrt[2]*x)],
Defer[IntegrateAlgebraic][(-1 + x)/((3 + x)*Sqrt[3 + 3*x + x^2 + x^3]), x],
Defer[IntegrateAlgebraic][(3 + x)/((-1 + x)*Sqrt[3 + 3*x + x^2 + x^3]), x],
Defer[IntegrateAlgebraic][(-1 + 2*x)/((2 + x)*Sqrt[-2 + 2*x^2 + x^3]), x],
Defer[IntegrateAlgebraic][(3 + x)/(x*Sqrt[-1 + 2*x^2 + x^3]), x],
Defer[IntegrateAlgebraic][(1 + 2*x)/((2 + x)*Sqrt[-1 + 2*x^2 + x^3]), x],
Defer[IntegrateAlgebraic][x/((3 + x)*Sqrt[-1 - x + 2*x^2 + x^3]), x],
Defer[IntegrateAlgebraic][x/((2 + x)*Sqrt[1 + 2*x + 2*x^2 + x^3]), x],
Defer[IntegrateAlgebraic][(2 + x)/(x*Sqrt[1 + 2*x + 2*x^2 + x^3]), x],
(-2*ArcTanh[(Sqrt[5]*x)/Sqrt[-1 + 3*x + 2*x^2 + x^3]])/Sqrt[5],
2*ArcTan[Sqrt[1 + 3*x + 2*x^2 + x^3]/x], Defer[IntegrateAlgebraic][
(1 + x)/((3 + x)*Sqrt[-2 + x + 3*x^2 + x^3]), x],
Defer[IntegrateAlgebraic][(3 + x)/((1 + x)*Sqrt[-2 + x + 3*x^2 + x^3]), x],
Defer[IntegrateAlgebraic][1/((1 + x)*Sqrt[-3 + 3*x + 3*x^2 + x^3]), x],
Defer[IntegrateAlgebraic][1/((1 + x)*Sqrt[-2 + 3*x + 3*x^2 + x^3]), x],
Defer[IntegrateAlgebraic][1/((1 + x)*Sqrt[-1 + 3*x + 3*x^2 + x^3]), x],
-(Sqrt[2/3]*ArcTanh[(Sqrt[6]*x)/Sqrt[-1 + 3*x + 3*x^2 + x^3]]),
Defer[IntegrateAlgebraic][1/((1 + x)*Sqrt[2 + 3*x + 3*x^2 + x^3]), x],
Defer[IntegrateAlgebraic][(2 + x)/((-1 + x)*Sqrt[2 + 3*x + 3*x^2 + x^3]),
x], Defer[IntegrateAlgebraic][1/((1 + x)*Sqrt[3 + 3*x + 3*x^2 + x^3]), x],
Defer[IntegrateAlgebraic][x/((3 + x)*Sqrt[3 + 3*x + 3*x^2 + x^3]), x],
Log[x^2 + Sqrt[-3 + x^4]]/2, ArcTan[Sqrt[-2 + x^4]/Sqrt[2]]/(2*Sqrt[2]),
Log[x^2 + Sqrt[-2 + x^4]]/2, ArcTan[Sqrt[-1 + x^4]]/2,
Log[x^2 + Sqrt[-1 + x^4]]/2, Sqrt[-1 + x^4]/(2 + 2*x^2),
-ArcTanh[Sqrt[1 + x^4]]/2, Log[x^2 + Sqrt[1 + x^4]]/2,
-(Sqrt[2]*ArcTanh[(Sqrt[2]*x)/(1 + 2*x + x^2 + Sqrt[1 + x^4])]),
-(Sqrt[2]*ArcTanh[(Sqrt[2]*x)/(1 - 2*x + x^2 + Sqrt[1 + x^4])]),
-(ArcTanh[(-1 + x^2 + Sqrt[1 + x^4])/Sqrt[2]]/Sqrt[2]),
-(ArcTan[(Sqrt[2]*x)/Sqrt[1 + x^4]]/Sqrt[2]),
Defer[IntegrateAlgebraic][(1 + x^2)/((-1 + x)*Sqrt[1 + x^4]), x],
Defer[IntegrateAlgebraic][(1 + x^2)/((1 + x)*Sqrt[1 + x^4]), x],
Defer[IntegrateAlgebraic][(1 + x^2)/(x*(1 + x)*Sqrt[1 + x^4]), x],
(-2*ArcTanh[(Sqrt[3]*x)/(-1 - x + x^2 + Sqrt[1 + x^4])])/Sqrt[3],
-2*ArcTan[x/(1 - x + x^2 + Sqrt[1 + x^4])],
-ArcTanh[(Sqrt[2]*x)/(1 - 2*x + x^2 + Sqrt[1 + x^4])]/(2*Sqrt[2]) -
(3*ArcTanh[(Sqrt[2]*x)/(1 + 2*x + x^2 + Sqrt[1 + x^4])])/(2*Sqrt[2]),
-(ArcTan[(Sqrt[2]*x)/Sqrt[1 + x^4]]/Sqrt[2]) -
ArcTanh[(2*Sqrt[2]*x^2)/(1 + 2*x^2 + x^4 + (-1 + x^2)*Sqrt[1 + x^4])]/
(2*Sqrt[2]), -2*ArcTan[x/(1 + x + x^2 + Sqrt[1 + x^4])],
(-3*ArcTanh[(Sqrt[2]*x)/(1 - 2*x + x^2 + Sqrt[1 + x^4])])/(2*Sqrt[2]) -
ArcTanh[(Sqrt[2]*x)/(1 + 2*x + x^2 + Sqrt[1 + x^4])]/(2*Sqrt[2]),
-ArcTanh[Sqrt[2 + x^4]/Sqrt[2]]/(2*Sqrt[2]), Log[x^2 + Sqrt[2 + x^4]]/2,
Log[x^2 + Sqrt[3 + x^4]]/2, ArcTan[(-x^2 + Sqrt[-3 - 3*x^2 + x^4])/Sqrt[3]]/
Sqrt[3], -Log[3 - 2*x^2 + 2*Sqrt[-3 - 3*x^2 + x^4]]/2,
-Log[3 - 2*x^2 + 2*Sqrt[-2 - 3*x^2 + x^4]]/2,
-Log[3 - 2*x^2 + 2*Sqrt[-1 - 3*x^2 + x^4]]/2,
-2*ArcTan[x/(1 + 2*x + x^2 + Sqrt[1 - 3*x^2 + x^4])],
-2*ArcTan[x/(1 - 2*x + x^2 + Sqrt[1 - 3*x^2 + x^4])],
Defer[IntegrateAlgebraic][1/((-1 + x)*Sqrt[3 - 3*x^2 + x^4]), x],
-Log[3 - 2*x^2 + 2*Sqrt[3 - 3*x^2 + x^4]]/2,
-Log[1 - x^2 + Sqrt[-2 - 2*x^2 + x^4]]/2,
-Log[1 - x^2 + Sqrt[-1 - 2*x^2 + x^4]]/2,
-(ArcTanh[(-x^2 + Sqrt[2 - 2*x^2 + x^4])/Sqrt[2]]/Sqrt[2]),
-(ArcTanh[(-x^2 + Sqrt[2 - 2*x^2 + x^4])/Sqrt[2]]/Sqrt[2]) -
(3*Log[1 - x^2 + Sqrt[2 - 2*x^2 + x^4]])/2,
-(ArcTanh[(-x^2 + Sqrt[3 - 2*x^2 + x^4])/Sqrt[3]]/Sqrt[3]),
-Log[1 - x^2 + Sqrt[3 - 2*x^2 + x^4]]/2, Defer[IntegrateAlgebraic][
x/((-3 + 2*x)*Sqrt[-2 + 3*x - 2*x^2 + x^4]), x],
-Log[1 - 2*x^2 + 2*Sqrt[-3 - x^2 + x^4]]/2,
ArcTan[(-x^2 + Sqrt[-2 - x^2 + x^4])/Sqrt[2]]/Sqrt[2],
-Log[1 - 2*x^2 + 2*Sqrt[-2 - x^2 + x^4]]/2,
-ArcTan[x^2 - Sqrt[-1 - x^2 + x^4]],
-Log[1 - 2*x^2 + 2*Sqrt[-1 - x^2 + x^4]]/2,
ArcTan[1 - x^2 + Sqrt[-1 - x^2 + x^4]],
-ArcTan[x^2 - Sqrt[-1 - x^2 + x^4]] -
Log[1 - 2*x^2 + 2*Sqrt[-1 - x^2 + x^4]]/2, Defer[IntegrateAlgebraic][
(1 - x + x^2)/(x*(1 + x)*Sqrt[-1 - x^2 + x^4]), x],
ArcTanh[x^2 - Sqrt[1 - x^2 + x^4]], -Log[1 - 2*x^2 + 2*Sqrt[1 - x^2 + x^4]]/
2, -2*ArcTanh[x/(1 + 2*x + x^2 + Sqrt[1 - x^2 + x^4])],
-2*ArcTanh[x/(1 - 2*x + x^2 + Sqrt[1 - x^2 + x^4])],
-(ArcTanh[(-1 - x^2 + Sqrt[1 - x^2 + x^4])/Sqrt[3]]/Sqrt[3]),
-(ArcTan[(Sqrt[3]*x)/Sqrt[1 - x^2 + x^4]]/Sqrt[3]),
Defer[IntegrateAlgebraic][(1 + x^2)/((-1 + x)*Sqrt[1 - x^2 + x^4]), x],
ArcTanh[x^2 - Sqrt[1 - x^2 + x^4]] - Log[1 - 2*x^2 + 2*Sqrt[1 - x^2 + x^4]]/
2, Defer[IntegrateAlgebraic][(1 + x^2)/((-1 + x)*x*Sqrt[1 - x^2 + x^4]),
x], Defer[IntegrateAlgebraic][(1 + x^2)/((1 + x)*Sqrt[1 - x^2 + x^4]), x],
Defer[IntegrateAlgebraic][(1 + x^2)/(x*(1 + x)*Sqrt[1 - x^2 + x^4]), x],
-ArcTanh[x/Sqrt[1 - x^2 + x^4]],
-(Sqrt[2]*ArcTanh[(Sqrt[2]*x)/(-1 - x + x^2 + Sqrt[1 - x^2 + x^4])]),
-(ArcTan[(Sqrt[3]*x)/Sqrt[1 - x^2 + x^4]]/Sqrt[3]) +
ArcTanh[(2*Sqrt[3]*x^2)/(1 + 2*x^2 + x^4 + (-1 + x^2)*Sqrt[1 - x^2 + x^4])]/
(2*Sqrt[3]),
-(Sqrt[2]*ArcTan[(Sqrt[2]*x)/(1 - x + x^2 + Sqrt[1 - x^2 + x^4])]),
-(ArcTan[(Sqrt[3]*x)/Sqrt[1 - x^2 + x^4]]/Sqrt[3]) -
ArcTanh[(2*Sqrt[3]*x^2)/(1 + 2*x^2 + x^4 + (-1 + x^2)*Sqrt[1 - x^2 + x^4])]/
(2*Sqrt[3]),
-(Sqrt[2]*ArcTan[(Sqrt[2]*x)/(1 + x + x^2 + Sqrt[1 - x^2 + x^4])]),
(-3*ArcTanh[x/(1 - 2*x + x^2 + Sqrt[1 - x^2 + x^4])])/2 -
ArcTanh[x/(1 + 2*x + x^2 + Sqrt[1 - x^2 + x^4])]/2,
-(ArcTanh[(-x^2 + Sqrt[2 - x^2 + x^4])/Sqrt[2]]/Sqrt[2]),
-Log[1 - 2*x^2 + 2*Sqrt[2 - x^2 + x^4]]/2,
((-2*I)*ArcTan[(Sqrt[15]*x^2)/(4 + 4*x + x^2 -
(4*I)*Sqrt[-1 - 2*x - x^2 + x^4])])/Sqrt[15],
(-2*I)*Log[x] + I*Log[I + I*x + Sqrt[-1 - 2*x - x^2 + x^4]],
(2*I)*Log[x] - I*Log[I - I*x + Sqrt[-1 + 2*x - x^2 + x^4]],
((2*I)*ArcTan[(Sqrt[15]*x^2)/(4 - 4*x + x^2 -
(4*I)*Sqrt[-1 + 2*x - x^2 + x^4])])/Sqrt[15],
ArcTan[(-x^2 + Sqrt[-2 + x^2 + x^4])/Sqrt[2]]/Sqrt[2],
-Log[-1 - 2*x^2 + 2*Sqrt[-2 + x^2 + x^4]]/2,
-ArcTan[x^2 - Sqrt[-1 + x^2 + x^4]],
-Log[-1 - 2*x^2 + 2*Sqrt[-1 + x^2 + x^4]]/2,
Defer[IntegrateAlgebraic][(-1 + 2*x)/((1 + x)*Sqrt[-1 + x^2 + x^4]), x],
Defer[IntegrateAlgebraic][(1 + x + x^2)/((-1 + x)*Sqrt[-1 + x^2 + x^4]), x],
ArcTanh[x^2 - Sqrt[1 + x^2 + x^4]], -Log[-1 - 2*x^2 + 2*Sqrt[1 + x^2 + x^4]]/
2, (-2*ArcTanh[(Sqrt[3]*x)/(1 + 2*x + x^2 + Sqrt[1 + x^2 + x^4])])/Sqrt[3],
(-2*ArcTanh[Sqrt[1 + x^2 + x^4]/(Sqrt[3]*(1 - x + x^2))])/Sqrt[3],
-(ArcTanh[(1 - x^2 + Sqrt[1 + x^2 + x^4])/Sqrt[3]]/Sqrt[3]),
-ArcTan[x/Sqrt[1 + x^2 + x^4]], Defer[IntegrateAlgebraic][
(1 + x^2)/((-1 + x)*Sqrt[1 + x^2 + x^4]), x],
ArcTanh[x^2 - Sqrt[1 + x^2 + x^4]] - Log[-1 - 2*x^2 + 2*Sqrt[1 + x^2 + x^4]]/
2, Defer[IntegrateAlgebraic][(1 + x^2)/((-1 + x)*x*Sqrt[1 + x^2 + x^4]),
x], Defer[IntegrateAlgebraic][(1 + x^2)/((1 + x)*Sqrt[1 + x^2 + x^4]), x],
Defer[IntegrateAlgebraic][(1 + x^2)/(x*(1 + x)*Sqrt[1 + x^2 + x^4]), x],
-(ArcTanh[(Sqrt[3]*x)/Sqrt[1 + x^2 + x^4]]/Sqrt[3]),
ArcTan[(-1 + x^2 + Sqrt[1 + x^2 + x^4])/(3*x)] -
ArcTan[(-1 + x^2 + Sqrt[1 + x^2 + x^4])/x] +
ArcTanh[(2*x^2)/(1 + 2*x^2 + x^4 + (-1 + x^2)*Sqrt[1 + x^2 + x^4])]/2,
-ArcTanh[(2*x)/(-1 + x + x^2 + Sqrt[1 + x^2 + x^4])],
ArcTan[(-1 + x^2 + Sqrt[1 + x^2 + x^4])/(3*x)] -
ArcTan[(-1 + x^2 + Sqrt[1 + x^2 + x^4])/x] -
ArcTanh[(2*x^2)/(1 + 2*x^2 + x^4 + (-1 + x^2)*Sqrt[1 + x^2 + x^4])]/2,
Sqrt[1 + x^2 + x^4]/(1 + x + x^2),
-(Sqrt[3]*ArcTanh[Sqrt[1 + x^2 + x^4]/(Sqrt[3]*(1 - x + x^2))])/2 +
ArcTanh[(Sqrt[3]*Sqrt[1 + x^2 + x^4])/(1 - x + x^2)]/(2*Sqrt[3]),
-Log[-1 - 2*x^2 + 2*Sqrt[2 + x^2 + x^4]]/2,
-(ArcTanh[(-x^2 + Sqrt[3 + x^2 + x^4])/Sqrt[3]]/Sqrt[3]),
-Log[-1 - x^2 + Sqrt[-3 + 2*x^2 + x^4]]/2,
ArcTan[(-x^2 + Sqrt[-2 + 2*x^2 + x^4])/Sqrt[2]]/Sqrt[2],
-Log[-1 - x^2 + Sqrt[-2 + 2*x^2 + x^4]]/2,
-Log[-1 - x^2 + Sqrt[-1 + 2*x^2 + x^4]]/2,
-(ArcTanh[(-x^2 + Sqrt[2 + 2*x^2 + x^4])/Sqrt[2]]/Sqrt[2]),
-Log[-1 - x^2 + Sqrt[2 + 2*x^2 + x^4]]/2,
-(ArcTanh[(-x^2 + Sqrt[3 + 2*x^2 + x^4])/Sqrt[3]]/Sqrt[3]),
-Log[-1 - x^2 + Sqrt[3 + 2*x^2 + x^4]]/2,
ArcTan[(-x^2 + Sqrt[-2 + 3*x^2 + x^4])/Sqrt[2]]/Sqrt[2],
-Log[-3 - 2*x^2 + 2*Sqrt[-2 + 3*x^2 + x^4]]/2,
ArcTanh[x^2 - Sqrt[1 + 3*x^2 + x^4]],
(-2*ArcTanh[(Sqrt[5]*x)/(1 + 2*x + x^2 + Sqrt[1 + 3*x^2 + x^4])])/Sqrt[5],
-(ArcTanh[(-x^2 + Sqrt[2 + 3*x^2 + x^4])/Sqrt[2]]/Sqrt[2]),
-Log[-3 - 2*x^2 + 2*Sqrt[3 + 3*x^2 + x^4]]/2,
(-2*ArcTan[(1 - 2*x + x^2 - Sqrt[1 - 3*x - 3*x^2 - 3*x^3 + x^4])/
(Sqrt[7]*x)])/Sqrt[7], Defer[IntegrateAlgebraic][
1/(x*Sqrt[-2 - 2*x^2 - 3*x^3 + x^4]), x],
Sqrt[2/3]*ArcTanh[Sqrt[1 - 3*x - 2*x^2 - 3*x^3 + x^4]/
(Sqrt[6]*(1 + x + x^2))],
-(Sqrt[2/3]*ArcTan[(1 - 2*x + x^2 - Sqrt[1 - 3*x - 2*x^2 - 3*x^3 + x^4])/
(Sqrt[6]*x)]),
(2*ArcTanh[(Sqrt[7]*x)/(1 + 2*x + x^2 - Sqrt[1 - 3*x - x^2 - 3*x^3 + x^4])])/
Sqrt[7], (-2*ArcTan[(1 - 2*x + x^2 - Sqrt[1 - 3*x - x^2 - 3*x^3 + x^4])/
(Sqrt[5]*x)])/Sqrt[5], Defer[IntegrateAlgebraic][
1/(x*Sqrt[3 + 2*x - x^2 - 3*x^3 + x^4]), x],
(2*ArcTanh[(3*x)/(1 + 2*x + x^2 - Sqrt[1 - 3*x + x^2 - 3*x^3 + x^4])])/3,
(-2*ArcTan[(1 - 2*x + x^2 - Sqrt[1 - 3*x + x^2 - 3*x^3 + x^4])/(Sqrt[3]*x)])/
Sqrt[3], Defer[IntegrateAlgebraic][
1/((-2 + 3*x)*Sqrt[-1 + 2*x + x^2 - 3*x^3 + x^4]), x],
Sqrt[2/5]*ArcTanh[(Sqrt[2/5]*Sqrt[1 - 3*x + 2*x^2 - 3*x^3 + x^4])/
(1 + x^2)],
-2*ArcTan[(1 - 2*x + x^2 - Sqrt[1 - 3*x + 3*x^2 - 3*x^3 + x^4])/x],
-(Sqrt[2]*ArcTan[(1 - 2*x + x^2 - Sqrt[1 - 2*x - 2*x^3 + x^4])/
(Sqrt[2]*x)]), -Log[1 + 2*x - 2*x^2 + 2*Sqrt[-3 + x - 2*x^3 + x^4]],
-Log[1 + 2*x - 2*x^2 + 2*Sqrt[-2 + x - 2*x^3 + x^4]],
-Log[1 + 2*x - 2*x^2 + 2*Sqrt[1 + x - 2*x^3 + x^4]],
(-2*ArcTanh[(-1 + 4*x - 4*x^2 + 4*Sqrt[1 + x - 2*x^3 + x^4])/Sqrt[21]])/
Sqrt[21], -Log[1 + 2*x - 2*x^2 + 2*Sqrt[1 + x - 2*x^3 + x^4]],
(-2*ArcTanh[(-1 + 4*x - 4*x^2 + 4*Sqrt[2 + x - 2*x^3 + x^4])/Sqrt[37]])/
Sqrt[37], Defer[IntegrateAlgebraic][
(3 + x)/((-1 + x)*Sqrt[1 + 2*x - 2*x^3 + x^4]), x],
Defer[IntegrateAlgebraic][x/Sqrt[-3 - 3*x - 3*x^2 - 2*x^3 + x^4], x],
Defer[IntegrateAlgebraic][x/Sqrt[-2 - 2*x - 3*x^2 - 2*x^3 + x^4], x],
(2*ArcTanh[(4 + 4*x + x^2 - Sqrt[-1 - 2*x - 3*x^2 - 2*x^3 + x^4])/
(Sqrt[23]*(1 + x))])/Sqrt[23],
2*ArcTan[(-x^2 + Sqrt[-1 - 2*x - 3*x^2 - 2*x^3 + x^4])/(1 + x)],
(-2*ArcTan[(1 - 2*x + x^2 - Sqrt[1 - 2*x - 3*x^2 - 2*x^3 + x^4])/
(Sqrt[5]*x)])/Sqrt[5], Defer[IntegrateAlgebraic][
x/Sqrt[-1 - x - 3*x^2 - 2*x^3 + x^4], x], Defer[IntegrateAlgebraic][
x/Sqrt[3 + 3*x - 3*x^2 - 2*x^3 + x^4], x], Defer[IntegrateAlgebraic][
(1 + x)/((-2 + x)*Sqrt[3 - 2*x^2 - 2*x^3 + x^4]), x],
Defer[IntegrateAlgebraic][
(2 + x)/((-1 + x)*Sqrt[-3 - 2*x - 2*x^2 - 2*x^3 + x^4]), x],
Defer[IntegrateAlgebraic][
1/((1 + 3*x)*Sqrt[-3 - 2*x - 2*x^2 - 2*x^3 + x^4]), x],
ArcTanh[(2*x)/(1 + 2*x + x^2 - Sqrt[1 - 2*x - 2*x^2 - 2*x^3 + x^4])],
-ArcTan[(1 - 2*x + x^2 - Sqrt[1 - 2*x - 2*x^2 - 2*x^3 + x^4])/(2*x)],
-Log[3 + 2*x - 2*x^2 + 2*Sqrt[-1 + 3*x - 2*x^2 - 2*x^3 + x^4]],
-Log[3 + 2*x - 2*x^2 + 2*Sqrt[1 + 3*x - 2*x^2 - 2*x^3 + x^4]],
(-2*ArcTanh[(-1 + 4*x - 4*x^2 + 4*Sqrt[3 + 3*x - 2*x^2 - 2*x^3 + x^4])/
Sqrt[61]])/Sqrt[61], Defer[IntegrateAlgebraic][
(2 + x)/((-1 + x)*Sqrt[-2 - x^2 - 2*x^3 + x^4]), x],
(2*ArcTanh[Sqrt[1 - 2*x - x^2 - 2*x^3 + x^4]/(Sqrt[5]*(1 + x + x^2))])/
Sqrt[5], (-2*ArcTan[(1 - 2*x + x^2 - Sqrt[1 - 2*x - x^2 - 2*x^3 + x^4])/
(Sqrt[3]*x)])/Sqrt[3],
(2*ArcTan[(-1 + 4*x - 4*x^2 + 4*Sqrt[-2 + 2*x - x^2 - 2*x^3 + x^4])/
Sqrt[23]])/Sqrt[23],
(2*ArcTan[(-1 + 4*x - 4*x^2 + 4*Sqrt[-1 + 2*x - x^2 - 2*x^3 + x^4])/
Sqrt[7]])/Sqrt[7],
(-2*ArcTanh[(-1 + 4*x - 4*x^2 + 4*Sqrt[3 + 2*x - x^2 - 2*x^3 + x^4])/
Sqrt[57]])/Sqrt[57], Log[-x + x^2 + Sqrt[-2 + x^2 - 2*x^3 + x^4]],
Log[-x + x^2 + Sqrt[1 + x^2 - 2*x^3 + x^4]],
Log[-x + x^2 + Sqrt[2 + x^2 - 2*x^3 + x^4]],
(-2*ArcTanh[(1 - 4*x + 4*x^2 + 4*Sqrt[2 + x^2 - 2*x^3 + x^4])/Sqrt[33]])/
Sqrt[33], -Log[2 - x + x^2 + Sqrt[3 + x^2 - 2*x^3 + x^4]]/7 +
Log[-3 - 2*x + 2*x^2 + 2*Sqrt[3 + x^2 - 2*x^3 + x^4]]/7,
Defer[IntegrateAlgebraic][(-2 + 3*x)/Sqrt[3 - 3*x + x^2 - 2*x^3 + x^4], x],
(2*ArcTanh[(Sqrt[7]*x)/(1 + 2*x + x^2 - Sqrt[1 - 2*x + x^2 - 2*x^3 + x^4])])/
Sqrt[7], -2*ArcTan[(1 - 2*x + x^2 - Sqrt[1 - 2*x + x^2 - 2*x^3 + x^4])/x],
Defer[IntegrateAlgebraic][(-2 + 3*x)/Sqrt[-2 + 2*x + x^2 - 2*x^3 + x^4], x],
Defer[IntegrateAlgebraic][x/((-3 + 2*x)*Sqrt[-2 + 2*x + x^2 - 2*x^3 + x^4]),
x], 2*ArcTan[(-x^2 + Sqrt[-1 + 2*x + x^2 - 2*x^3 + x^4])/(-1 + x)],
(2*ArcTanh[(Sqrt[3]*x)/(-1 - 2*x + x^2 - Sqrt[1 + 2*x + x^2 - 2*x^3 +
x^4])])/Sqrt[3],
(2*ArcTan[(Sqrt[7/5]*Sqrt[-2 - x + 2*x^2 - 2*x^3 + x^4])/(2 - x + x^2)])/
Sqrt[35],
(-2*ArcTanh[(-1 + 4*x - 4*x^2 + 4*Sqrt[1 - x + 2*x^2 - 2*x^3 + x^4])/
Sqrt[13]])/Sqrt[13],
-Log[-1 + 2*x - 2*x^2 + 2*Sqrt[2 - x + 2*x^2 - 2*x^3 + x^4]],
-Log[1 + x - x^2 + Sqrt[2 - 2*x + 3*x^2 - 2*x^3 + x^4]]/5 +
Log[-3 + 2*x - 2*x^2 + 2*Sqrt[2 - 2*x + 3*x^2 - 2*x^3 + x^4]]/5,
-RootSum[8 + 16*#1 + 12*#1^2 + #1^4 & ,
(-Log[x] + Log[1 - x^2 + Sqrt[1 + x - x^3 + x^4] - x*#1] - 2*Log[x]*#1 +
2*Log[1 - x^2 + Sqrt[1 + x - x^3 + x^4] - x*#1]*#1)/
(4 + 6*#1 + #1^3) & ]/2, RootSum[8 + 16*#1 + 12*#1^2 + #1^4 & ,
(2*Log[x] - 2*Log[1 - x^2 + Sqrt[1 + x - x^3 + x^4] - x*#1] -
Log[x]*#1^2 + Log[1 - x^2 + Sqrt[1 + x - x^3 + x^4] - x*#1]*#1^2)/
(4 + 6*#1 + #1^3) & ]/2,
Log[x] - Log[2 + x - 2*x^2 + 2*Sqrt[1 + x - x^3 + x^4]],
Sqrt[2]*ArcTanh[(Sqrt[2]*x)/(-1 + x^2 - Sqrt[1 + x - x^3 + x^4])],
Sqrt[2]*ArcTanh[(Sqrt[2]*x)/(-1 - x + x^2 - Sqrt[1 + x - x^3 + x^4])],
RootSum[8 + 16*#1 + 12*#1^2 + #1^4 & ,
(3*Log[x] - 3*Log[1 - x^2 + Sqrt[1 + x - x^3 + x^4] - x*#1] +
2*Log[x]*#1 - 2*Log[1 - x^2 + Sqrt[1 + x - x^3 + x^4] - x*#1]*#1 -
Log[x]*#1^2 + Log[1 - x^2 + Sqrt[1 + x - x^3 + x^4] - x*#1]*#1^2)/
(4 + 6*#1 + #1^3) & ]/2,
2*ArcTan[(-x^2 + Sqrt[-1 + 2*x - x^3 + x^4])/(-1 + x)],
-2*Log[x] + Log[-2 - 2*x + x^2 + 2*Sqrt[1 + 2*x - x^3 + x^4]],
2*ArcTanh[x/(1 + 2*x + x^2 - Sqrt[1 - x - 3*x^2 - x^3 + x^4])],
Defer[IntegrateAlgebraic][1/(x*Sqrt[1 + 2*x - 3*x^2 - x^3 + x^4]), x],
(2*ArcTanh[(Sqrt[3]*x)/(1 + 2*x + x^2 - Sqrt[1 - x - x^2 - x^3 + x^4])])/
Sqrt[3], -2*ArcTan[(1 - 2*x + x^2 - Sqrt[1 - x - x^2 - x^3 + x^4])/x],
-ArcTan[(1 - 2*x + x^2 - Sqrt[1 - x - x^2 - x^3 + x^4])/x]/2 -
ArcTanh[(Sqrt[3]*x)/(1 + 2*x + x^2 - Sqrt[1 - x - x^2 - x^3 + x^4])]/
(2*Sqrt[3]), Log[x] - Log[-2 + x - 2*x^2 +
2*Sqrt[1 - x - x^2 - x^3 + x^4]],
(-2*ArcTan[(1 + x^2 - Sqrt[1 - x - x^2 - x^3 + x^4])/(Sqrt[3]*x)])/Sqrt[3],
-ArcTan[(1 - 2*x + x^2 - Sqrt[1 - x - x^2 - x^3 + x^4])/x] +
ArcTanh[(Sqrt[3]*x)/(1 + 2*x + x^2 - Sqrt[1 - x - x^2 - x^3 + x^4])]/
Sqrt[3], -ArcTan[(1 - 2*x + x^2 - Sqrt[1 - x - x^2 - x^3 + x^4])/x]/2 +
(Sqrt[3]*ArcTanh[(Sqrt[3]*x)/(1 + 2*x + x^2 -
Sqrt[1 - x - x^2 - x^3 + x^4])])/2,
-2*ArcTan[(1 + x + x^2 - Sqrt[1 - x - x^2 - x^3 + x^4])/x],
(-3*ArcTan[(1 - 2*x + x^2 - Sqrt[1 - x - x^2 - x^3 + x^4])/x])/2 +
ArcTanh[(Sqrt[3]*x)/(1 + 2*x + x^2 - Sqrt[1 - x - x^2 - x^3 + x^4])]/
(2*Sqrt[3]), Log[x] -
Log[2 + x - 2*x^2 + 2*Sqrt[1 + x - x^2 - x^3 + x^4]],
2*ArcTanh[x/(-1 - x + x^2 - Sqrt[1 + x - x^2 - x^3 + x^4])],
(2*ArcTanh[(Sqrt[3]*x)/(-1 + x + x^2 - Sqrt[1 + x - x^2 - x^3 + x^4])])/
Sqrt[3], RootSum[5 + 16*#1 + 14*#1^2 + #1^4 & ,
(2*Log[x] - 2*Log[1 - x^2 + Sqrt[1 + x - x^2 - x^3 + x^4] - x*#1] +
2*Log[x]*#1 - 2*Log[1 - x^2 + Sqrt[1 + x - x^2 - x^3 + x^4] - x*#1]*
#1 - Log[x]*#1^2 + Log[1 - x^2 + Sqrt[1 + x - x^2 - x^3 + x^4] - x*#1]*
#1^2)/(4 + 7*#1 + #1^3) & ]/2,
(2*ArcTanh[(Sqrt[5]*x)/(1 + 2*x + x^2 - Sqrt[1 - x + x^2 - x^3 + x^4])])/
Sqrt[5], 2*ArcTanh[x/(1 - 2*x + x^2 - Sqrt[1 - x + x^2 - x^3 + x^4])],
ArcTanh[x/(1 - 2*x + x^2 - Sqrt[1 - x + x^2 - x^3 + x^4])]/2 -
ArcTanh[(Sqrt[5]*x)/(1 + 2*x + x^2 - Sqrt[1 - x + x^2 - x^3 + x^4])]/
(2*Sqrt[5]), Log[x] - Log[-2 + x - 2*x^2 +
2*Sqrt[1 - x + x^2 - x^3 + x^4]],
ArcTanh[x/(1 - 2*x + x^2 - Sqrt[1 - x + x^2 - x^3 + x^4])] +
ArcTanh[(Sqrt[5]*x)/(1 + 2*x + x^2 - Sqrt[1 - x + x^2 - x^3 + x^4])]/
Sqrt[5], -2*ArcTan[(1 - x + x^2 - Sqrt[1 - x + x^2 - x^3 + x^4])/x],
ArcTanh[x/(1 - 2*x + x^2 - Sqrt[1 - x + x^2 - x^3 + x^4])]/2 +
(3*ArcTanh[(Sqrt[5]*x)/(1 + 2*x + x^2 - Sqrt[1 - x + x^2 - x^3 + x^4])])/
(2*Sqrt[5]), 2*ArcTanh[x/(1 + x + x^2 - Sqrt[1 - x + x^2 - x^3 + x^4])],
(3*ArcTanh[x/(1 - 2*x + x^2 - Sqrt[1 - x + x^2 - x^3 + x^4])])/2 +
ArcTanh[(Sqrt[5]*x)/(1 + 2*x + x^2 - Sqrt[1 - x + x^2 - x^3 + x^4])]/
(2*Sqrt[5]), -RootSum[13 + 16*#1 + 10*#1^2 + #1^4 & ,
(-Log[x] + Log[1 - x^2 + Sqrt[1 + x + x^2 - x^3 + x^4] - x*#1] -
2*Log[x]*#1 + 2*Log[1 - x^2 + Sqrt[1 + x + x^2 - x^3 + x^4] - x*#1]*
#1)/(4 + 5*#1 + #1^3) & ]/2,
RootSum[13 + 16*#1 + 10*#1^2 + #1^4 & ,
(3*Log[x] - 3*Log[1 - x^2 + Sqrt[1 + x + x^2 - x^3 + x^4] - x*#1] -
Log[x]*#1^2 + Log[1 - x^2 + Sqrt[1 + x + x^2 - x^3 + x^4] - x*#1]*#1^2)/
(4 + 5*#1 + #1^3) & ]/2,
Log[x] - Log[2 + x - 2*x^2 + 2*Sqrt[1 + x + x^2 - x^3 + x^4]],
(2*ArcTanh[(Sqrt[3]*x)/(-1 + x^2 - Sqrt[1 + x + x^2 - x^3 + x^4])])/Sqrt[3],
RootSum[13 + 16*#1 + 10*#1^2 + #1^4 & ,
(2*Log[x] - 2*Log[1 - x^2 + Sqrt[1 + x + x^2 - x^3 + x^4] - x*#1] -
2*Log[x]*#1 + 2*Log[1 - x^2 + Sqrt[1 + x + x^2 - x^3 + x^4] - x*#1]*
#1 - Log[x]*#1^2 + Log[1 - x^2 + Sqrt[1 + x + x^2 - x^3 + x^4] - x*#1]*
#1^2)/(4 + 5*#1 + #1^3) & ]/2,
(2*ArcTanh[(Sqrt[5]*x)/(-1 + x + x^2 - Sqrt[1 + x + x^2 - x^3 + x^4])])/
Sqrt[5], RootSum[13 + 16*#1 + 10*#1^2 + #1^4 & ,
(4*Log[x] - 4*Log[1 - x^2 + Sqrt[1 + x + x^2 - x^3 + x^4] - x*#1] +
2*Log[x]*#1 - 2*Log[1 - x^2 + Sqrt[1 + x + x^2 - x^3 + x^4] - x*#1]*
#1 - Log[x]*#1^2 + Log[1 - x^2 + Sqrt[1 + x + x^2 - x^3 + x^4] - x*#1]*
#1^2)/(4 + 5*#1 + #1^3) & ]/2,
-2*Log[x] + Log[2 - 2*x + x^2 + 2*Sqrt[1 - 2*x + 2*x^2 - x^3 + x^4]],
Sqrt[2/3]*ArcTanh[(Sqrt[2/3]*Sqrt[1 - x + 2*x^2 - x^3 + x^4])/(1 + x^2)],
-(Sqrt[2]*ArcTanh[(Sqrt[2]*Sqrt[1 - x + 2*x^2 - x^3 + x^4])/(1 + x^2)]),
(2*ArcTanh[(Sqrt[7]*x)/(1 + 2*x + x^2 - Sqrt[1 - x + 3*x^2 - x^3 + x^4])])/
Sqrt[7],
(2*ArcTanh[(Sqrt[3]*x)/(1 - 2*x + x^2 - Sqrt[1 - x + 3*x^2 - x^3 + x^4])])/
Sqrt[3], -2*Log[x] + Log[2 - 2*x - x^2 + 2*Sqrt[1 - 2*x + x^3 + x^4]],
(-2*ArcTanh[(Sqrt[21]*x^2)/(4 - 4*x + x^2 + 4*Sqrt[1 - 2*x + x^3 + x^4])])/
Sqrt[21], -RootSum[8 - 16*#1 + 12*#1^2 + #1^4 & ,
(Log[x] - Log[1 - x^2 + Sqrt[1 - x + x^3 + x^4] - x*#1] - 2*Log[x]*#1 +
2*Log[1 - x^2 + Sqrt[1 - x + x^3 + x^4] - x*#1]*#1)/
(-4 + 6*#1 + #1^3) & ]/2,
Log[x] - Log[2 - x - 2*x^2 + 2*Sqrt[1 - x + x^3 + x^4]],
Sqrt[2]*ArcTanh[(Sqrt[2]*x)/(-1 + x^2 - Sqrt[1 - x + x^3 + x^4])],
ArcTanh[(2*x)/(-1 - x + x^2 - Sqrt[1 - x + x^3 + x^4])],
RootSum[8 - 16*#1 + 12*#1^2 + #1^4 & ,
(Log[x] - Log[1 - x^2 + Sqrt[1 - x + x^3 + x^4] - x*#1] + 2*Log[x]*#1 -
2*Log[1 - x^2 + Sqrt[1 - x + x^3 + x^4] - x*#1]*#1 - Log[x]*#1^2 +
Log[1 - x^2 + Sqrt[1 - x + x^3 + x^4] - x*#1]*#1^2)/
(-4 + 6*#1 + #1^3) & ]/2, Defer[IntegrateAlgebraic][
1/(x*Sqrt[1 - 2*x - 3*x^2 + x^3 + x^4]), x],
2*ArcTanh[x/(1 - 2*x + x^2 - Sqrt[1 + x - 3*x^2 + x^3 + x^4])],
-(Sqrt[2]*ArcTan[(1 + 2*x + x^2 - Sqrt[1 + x - 2*x^2 + x^3 + x^4])/
(Sqrt[2]*x)]),
Sqrt[2]*ArcTanh[(Sqrt[2]*x)/(1 - 2*x + x^2 -
Sqrt[1 + x - 2*x^2 + x^3 + x^4])],
2*ArcTan[(-x^2 + Sqrt[-1 + 2*x - 2*x^2 + x^3 + x^4])/(-1 + x)],
(2*ArcTanh[(4 - 4*x + x^2 - Sqrt[-1 + 2*x - 2*x^2 + x^3 + x^4])/
(Sqrt[19]*(-1 + x))])/Sqrt[19], Defer[IntegrateAlgebraic][
(3 + 2*x)/(x*Sqrt[-1 - 2*x - x^2 + x^3 + x^4]), x],
-RootSum[5 - 16*#1 + 14*#1^2 + #1^4 & ,
(Log[x] - Log[1 - x^2 + Sqrt[1 - x - x^2 + x^3 + x^4] - x*#1] -
2*Log[x]*#1 + 2*Log[1 - x^2 + Sqrt[1 - x - x^2 + x^3 + x^4] - x*#1]*
#1)/(-4 + 7*#1 + #1^3) & ]/2,
RootSum[5 - 16*#1 + 14*#1^2 + #1^4 & ,
(Log[x] - Log[1 - x^2 + Sqrt[1 - x - x^2 + x^3 + x^4] - x*#1] -
Log[x]*#1^2 + Log[1 - x^2 + Sqrt[1 - x - x^2 + x^3 + x^4] - x*#1]*#1^2)/
(-4 + 7*#1 + #1^3) & ]/2,
2*ArcTanh[x/(-1 + x^2 - Sqrt[1 - x - x^2 + x^3 + x^4])],
(2*ArcTanh[(Sqrt[3]*x)/(-1 - x + x^2 - Sqrt[1 - x - x^2 + x^3 + x^4])])/
Sqrt[3], -2*ArcTan[(1 + 2*x + x^2 - Sqrt[1 + x - x^2 + x^3 + x^4])/x],
(2*ArcTanh[(Sqrt[3]*x)/(1 - 2*x + x^2 - Sqrt[1 + x - x^2 + x^3 + x^4])])/
Sqrt[3], ArcTan[(1 + 2*x + x^2 - Sqrt[1 + x - x^2 + x^3 + x^4])/x]/2 +
ArcTanh[(Sqrt[3]*x)/(1 - 2*x + x^2 - Sqrt[1 + x - x^2 + x^3 + x^4])]/
(2*Sqrt[3]), (-2*ArcTan[(1 + x^2 - Sqrt[1 + x - x^2 + x^3 + x^4])/
(Sqrt[3]*x)])/Sqrt[3],
-ArcTan[(1 + 2*x + x^2 - Sqrt[1 + x - x^2 + x^3 + x^4])/x] +
ArcTanh[(Sqrt[3]*x)/(1 - 2*x + x^2 - Sqrt[1 + x - x^2 + x^3 + x^4])]/
Sqrt[3], -2*ArcTan[(1 - x + x^2 - Sqrt[1 + x - x^2 + x^3 + x^4])/x],
(-3*ArcTan[(1 + 2*x + x^2 - Sqrt[1 + x - x^2 + x^3 + x^4])/x])/2 +
ArcTanh[(Sqrt[3]*x)/(1 - 2*x + x^2 - Sqrt[1 + x - x^2 + x^3 + x^4])]/
(2*Sqrt[3]), (-2*ArcTan[(1 + x + x^2 - Sqrt[1 + x - x^2 + x^3 + x^4])/
(Sqrt[3]*x)])/Sqrt[3],
-ArcTan[(1 + 2*x + x^2 - Sqrt[1 + x - x^2 + x^3 + x^4])/x]/2 +
(Sqrt[3]*ArcTanh[(Sqrt[3]*x)/(1 - 2*x + x^2 -
Sqrt[1 + x - x^2 + x^3 + x^4])])/2,
-RootSum[13 - 16*#1 + 10*#1^2 + #1^4 & ,
(Log[x] - Log[1 - x^2 + Sqrt[1 - x + x^2 + x^3 + x^4] - x*#1] -
2*Log[x]*#1 + 2*Log[1 - x^2 + Sqrt[1 - x + x^2 + x^3 + x^4] - x*#1]*
#1)/(-4 + 5*#1 + #1^3) & ]/2,
RootSum[13 - 16*#1 + 10*#1^2 + #1^4 & ,
(4*Log[x] - 4*Log[1 - x^2 + Sqrt[1 - x + x^2 + x^3 + x^4] - x*#1] -
2*Log[x]*#1 + 2*Log[1 - x^2 + Sqrt[1 - x + x^2 + x^3 + x^4] - x*#1]*
#1 - Log[x]*#1^2 + Log[1 - x^2 + Sqrt[1 - x + x^2 + x^3 + x^4] - x*#1]*
#1^2)/(-4 + 5*#1 + #1^3) & ]/2,
RootSum[13 - 16*#1 + 10*#1^2 + #1^4 & ,
(2*Log[x] - 2*Log[1 - x^2 + Sqrt[1 - x + x^2 + x^3 + x^4] - x*#1] +
2*Log[x]*#1 - 2*Log[1 - x^2 + Sqrt[1 - x + x^2 + x^3 + x^4] - x*#1]*
#1 - Log[x]*#1^2 + Log[1 - x^2 + Sqrt[1 - x + x^2 + x^3 + x^4] - x*#1]*
#1^2)/(-4 + 5*#1 + #1^3) & ]/2,
2*ArcTanh[x/(1 + 2*x + x^2 - Sqrt[1 + x + x^2 + x^3 + x^4])],
(2*ArcTanh[(Sqrt[5]*x)/(1 - 2*x + x^2 - Sqrt[1 + x + x^2 + x^3 + x^4])])/
Sqrt[5],
ArcTanh[(Sqrt[5]*x)/(1 - 2*x + x^2 - Sqrt[1 + x + x^2 + x^3 + x^4])]/
(2*Sqrt[5]) - ArcTanh[x/(1 + 2*x + x^2 - Sqrt[1 + x + x^2 + x^3 + x^4])]/
2, -2*ArcTan[(1 + x^2 - Sqrt[1 + x + x^2 + x^3 + x^4])/x],
ArcTanh[(Sqrt[5]*x)/(1 - 2*x + x^2 - Sqrt[1 + x + x^2 + x^3 + x^4])]/
(2*Sqrt[5]) +
(3*ArcTanh[x/(1 + 2*x + x^2 - Sqrt[1 + x + x^2 + x^3 + x^4])])/2,
-2*ArcTan[(1 + x + x^2 - Sqrt[1 + x + x^2 + x^3 + x^4])/x],
Defer[IntegrateAlgebraic][(3 + 2*x)/(x*Sqrt[1 + 2*x + x^2 + x^3 + x^4]), x],
Defer[IntegrateAlgebraic][(-1 - 2*x + x^2)/
((-1 + x)*Sqrt[1 - x + 2*x^2 + x^3 + x^4]), x],
Sqrt[2]*ArcTanh[Sqrt[1 + x + 2*x^2 + x^3 + x^4]/(Sqrt[2]*(1 + x + x^2))],
Sqrt[2/3]*ArcTanh[(Sqrt[6]*x)/(1 - 2*x + x^2 -
Sqrt[1 + x + 2*x^2 + x^3 + x^4])],
(2*ArcTanh[(Sqrt[3]*x)/(1 + 2*x + x^2 - Sqrt[1 + x + 3*x^2 + x^3 + x^4])])/
Sqrt[3], Log[-1 + 2*x + 2*x^2 + 2*Sqrt[-2 - x + 2*x^3 + x^4]],
(2*ArcTan[(1 + 4*x + 4*x^2 + 4*Sqrt[-1 - x + 2*x^3 + x^4])/Sqrt[11]])/
Sqrt[11], Log[-1 + 2*x + 2*x^2 + 2*Sqrt[1 - x + 2*x^3 + x^4]],
(-2*ArcTanh[(1 + 4*x + 4*x^2 + 4*Sqrt[1 - x + 2*x^3 + x^4])/Sqrt[21]])/
Sqrt[21], -(Sqrt[2]*ArcTan[(1 + 2*x + x^2 - Sqrt[1 + 2*x + 2*x^3 + x^4])/
(Sqrt[2]*x)]), Sqrt[2/3]*
ArcTanh[(Sqrt[6]*x)/(1 - 2*x + x^2 - Sqrt[1 + 2*x + 2*x^3 + x^4])],
Defer[IntegrateAlgebraic][(-1 - x + x^2)/
((1 + x^2)*Sqrt[1 + 2*x + 2*x^3 + x^4]), x],
Defer[IntegrateAlgebraic][(1 + x)/((-1 + 2*x + x^2)*
Sqrt[1 + 2*x + 2*x^3 + x^4]), x], Defer[IntegrateAlgebraic][
x/Sqrt[3 - 3*x - 3*x^2 + 2*x^3 + x^4], x], Defer[IntegrateAlgebraic][
x/Sqrt[-2 + 2*x - 3*x^2 + 2*x^3 + x^4], x],
Defer[IntegrateAlgebraic][x/Sqrt[-3 + 3*x - 3*x^2 + 2*x^3 + x^4], x],
(2*ArcTan[(1 + 4*x + 4*x^2 + 4*Sqrt[-3 - 3*x - 2*x^2 + 2*x^3 + x^4])/
Sqrt[35]])/Sqrt[35],
Log[-3 + 2*x + 2*x^2 + 2*Sqrt[-3 - 3*x - 2*x^2 + 2*x^3 + x^4]],
(-2*ArcTanh[(1 + 4*x + 4*x^2 + 4*Sqrt[1 - 3*x - 2*x^2 + 2*x^3 + x^4])/
Sqrt[29]])/Sqrt[29],
(2*ArcTanh[(3*Sqrt[2 - 3*x - 2*x^2 + 2*x^3 + x^4])/
(Sqrt[5]*(-2 + x + x^2))])/(3*Sqrt[5]),
Log[-3 + 2*x + 2*x^2 + 2*Sqrt[2 - 3*x - 2*x^2 + 2*x^3 + x^4]],
Log[-3 + 2*x + 2*x^2 + 2*Sqrt[3 - 3*x - 2*x^2 + 2*x^3 + x^4]],
Log[-1 + x + x^2 + Sqrt[-3 - 2*x - x^2 + 2*x^3 + x^4]],
Log[-1 + x + x^2 + Sqrt[-1 - 2*x - x^2 + 2*x^3 + x^4]],
Log[-1 + x + x^2 + Sqrt[2 - 2*x - x^2 + 2*x^3 + x^4]],
(-2*ArcTan[(Sqrt[3]*Sqrt[1 + 2*x - x^2 + 2*x^3 + x^4])/(1 - x + x^2)])/
Sqrt[3],
(2*ArcTanh[(Sqrt[5]*x)/(1 - 2*x + x^2 - Sqrt[1 + 2*x - x^2 + 2*x^3 + x^4])])/
Sqrt[5], (2*ArcTan[(1 + 4*x + 4*x^2 + 4*Sqrt[-3 + x^2 + 2*x^3 + x^4])/
Sqrt[47]])/Sqrt[47],
(2*ArcTan[(1 + 4*x + 4*x^2 + 4*Sqrt[-2 + x^2 + 2*x^3 + x^4])/Sqrt[31]])/
Sqrt[31], (2*ArcTan[(1 + 4*x + 4*x^2 + 4*Sqrt[-1 + x^2 + 2*x^3 + x^4])/
Sqrt[15]])/Sqrt[15],
(-2*ArcTanh[(1 + 4*x + 4*x^2 + 4*Sqrt[1 + x^2 + 2*x^3 + x^4])/Sqrt[17]])/
Sqrt[17], Log[x + x^2 + Sqrt[2 + x^2 + 2*x^3 + x^4]],
(2*ArcTanh[(4 + 4*x + x^2 - Sqrt[-1 - 2*x + x^2 + 2*x^3 + x^4])/
(Sqrt[7]*(1 + x))])/Sqrt[7],
-2*ArcTan[(1 + 2*x + x^2 - Sqrt[1 + 2*x + x^2 + 2*x^3 + x^4])/x],
(2*ArcTanh[(Sqrt[7]*x)/(1 - 2*x + x^2 - Sqrt[1 + 2*x + x^2 + 2*x^3 + x^4])])/
Sqrt[7], Defer[IntegrateAlgebraic][
(2 + 3*x)/Sqrt[2 + 2*x + x^2 + 2*x^3 + x^4], x],
Defer[IntegrateAlgebraic][(2 + 3*x)/Sqrt[2 + 2*x + x^2 + 2*x^3 + x^4], x],
(2*ArcTan[(1 + 4*x + 4*x^2 + 4*Sqrt[-1 + x + 2*x^2 + 2*x^3 + x^4])/
Sqrt[19]])/Sqrt[19],
Log[1 + 2*x + 2*x^2 + 2*Sqrt[-1 + x + 2*x^2 + 2*x^3 + x^4]],
Log[1 + 2*x + 2*x^2 + 2*Sqrt[1 + x + 2*x^2 + 2*x^3 + x^4]],
Log[1 + 2*x + 2*x^2 + 2*Sqrt[1 + x + 2*x^2 + 2*x^3 + x^4]],
(-2*ArcTanh[(1 + 4*x + 4*x^2 + 4*Sqrt[2 + x + 2*x^2 + 2*x^3 + x^4])/
Sqrt[29]])/Sqrt[29],
ArcTanh[(2*Sqrt[2]*x)/(1 - 2*x + x^2 - Sqrt[1 + 3*x + 3*x^3 + x^4])]/
Sqrt[2], (-2*ArcTan[(1 + 2*x + x^2 - Sqrt[1 + 3*x - 3*x^2 + 3*x^3 + x^4])/
(Sqrt[7]*x)])/Sqrt[7],
-(Sqrt[2/3]*ArcTan[(1 + 2*x + x^2 - Sqrt[1 + 3*x - 2*x^2 + 3*x^3 + x^4])/
(Sqrt[6]*x)]), Defer[IntegrateAlgebraic][
1/(x*Sqrt[3 - 2*x - x^2 + 3*x^3 + x^4]), x],
(-2*ArcTan[(1 + 2*x + x^2 - Sqrt[1 + 3*x + x^2 + 3*x^3 + x^4])/(Sqrt[3]*x)])/
Sqrt[3],
(2*ArcTanh[(3*x)/(1 - 2*x + x^2 - Sqrt[1 + 3*x + x^2 + 3*x^3 + x^4])])/3,
-(Sqrt[2]*ArcTan[(Sqrt[2]*Sqrt[1 + 3*x + 2*x^2 + 3*x^3 + x^4])/(1 + x^2)]),
Sqrt[2/5]*ArcTanh[(Sqrt[10]*x)/(1 - 2*x + x^2 -
Sqrt[1 + 3*x + 2*x^2 + 3*x^3 + x^4])], (2*ArcTan[Sqrt[-1 + x^5]])/5,
(-2*ArcTanh[Sqrt[1 + x^5]])/5, Defer[IntegrateAlgebraic][
(1 + x)/(x*Sqrt[(1 + x)^3*(1 - x + x^2)]), x], ArcTan[Sqrt[-1 + x^6]]/3,
-ArcTanh[Sqrt[1 + x^6]]/3, (-2*ArcTan[x^3 - Sqrt[-1 - x^3 + x^6]])/3,
(2*ArcTanh[x^3 - Sqrt[1 - x^3 + x^6]])/3,
(-2*ArcTan[x^3 - Sqrt[-1 + x^3 + x^6]])/3,
(2*ArcTanh[x^3 - Sqrt[1 + x^3 + x^6]])/3,
(-2*ArcTan[x^3 - Sqrt[-1 + 2*x^3 + x^6]])/3};