1,1,15,15,0.0045566,"\int \frac{1}{\sqrt{1-a x}} \, dx","IntegrateAlgebraic[1/Sqrt[1 - a*x],x]","-\frac{2 \sqrt{1-a x}}{a}","-\frac{2 \sqrt{1-a x}}{a}",1,"(-2*Sqrt[1 - a*x])/a","A",1
2,0,0,15,0.0000485,"\int \frac{-2 \log \left(-\sqrt{-1+a x}\right)+\log (-1+a x)}{2 \pi  \sqrt{-1+a x}} \, dx","IntegrateAlgebraic[(-2*Log[-Sqrt[-1 + a*x]] + Log[-1 + a*x])/(2*Pi*Sqrt[-1 + a*x]),x]","\int \frac{-2 \log \left(-\sqrt{-1+a x}\right)+\log (-1+a x)}{2 \pi  \sqrt{-1+a x}} \, dx","-\frac{2 \sqrt{1-a x}}{a}",1,"Could not integrate","F",-1
3,1,71,82,0.3121634,"\int \frac{1}{\left(2 x+\sqrt{1+x^2}\right)^2} \, dx","IntegrateAlgebraic[(2*x + Sqrt[1 + x^2])^(-2),x]","-\frac{4 x}{3 \left(3 x^2-1\right)}+\frac{2 \sqrt{x^2+1}}{3 \left(3 x^2-1\right)}-\frac{2 \tanh ^{-1}\left(\frac{x}{\sqrt{3}}-\frac{\sqrt{x^2+1}}{\sqrt{3}}\right)}{3 \sqrt{3}}","\frac{4 x}{3 \left(1-3 x^2\right)}-\frac{2 \sqrt{x^2+1}}{3 \left(1-3 x^2\right)}+\frac{\tanh ^{-1}\left(\frac{1}{2} \sqrt{3} \sqrt{x^2+1}\right)}{3 \sqrt{3}}-\frac{\tanh ^{-1}\left(\sqrt{3} x\right)}{3 \sqrt{3}}",1,"(-4*x)/(3*(-1 + 3*x^2)) + (2*Sqrt[1 + x^2])/(3*(-1 + 3*x^2)) - (2*ArcTanh[x/Sqrt[3] - Sqrt[1 + x^2]/Sqrt[3]])/(3*Sqrt[3])","A",1
4,1,71,43,0.0839257,"\int \frac{1}{\sqrt{-1+x^2} \left(-4+3 x^2\right)^2} \, dx","IntegrateAlgebraic[1/(Sqrt[-1 + x^2]*(-4 + 3*x^2)^2),x]","-\frac{3 \sqrt{x^2-1} x}{8 \left(3 x^2-4\right)}+\frac{5}{32} \log \left(-x^2+\sqrt{x^2-1} x+2\right)-\frac{5}{32} \log \left(-3 x^2+3 \sqrt{x^2-1} x+2\right)","\frac{3 \sqrt{x^2-1} x}{8 \left(4-3 x^2\right)}+\frac{5}{16} \tanh ^{-1}\left(\frac{x}{2 \sqrt{x^2-1}}\right)",1,"(-3*x*Sqrt[-1 + x^2])/(8*(-4 + 3*x^2)) + (5*Log[2 - x^2 + x*Sqrt[-1 + x^2]])/32 - (5*Log[2 - 3*x^2 + 3*x*Sqrt[-1 + x^2]])/32","A",1
5,1,123,74,0.0719218,"\int \frac{1}{\left(2 \sqrt{x}+\sqrt{1+x}\right)^2} \, dx","IntegrateAlgebraic[(2*Sqrt[x] + Sqrt[1 + x])^(-2),x]","\frac{\sqrt{x} \left(4-4 \sqrt{x+1}\right)}{3 x+\left(6 \sqrt{x+1}-6\right) \sqrt{x}-3 \sqrt{x+1}+3}-\frac{2}{9} \log \left(-\sqrt{x}+\sqrt{x+1}-1\right)-2 \log \left(\sqrt{x}+\sqrt{x+1}-1\right)+\frac{10}{9} \log \left(x+\left(2 \sqrt{x+1}-2\right) \sqrt{x}-\sqrt{x+1}+1\right)","-\frac{4 \sqrt{x} \sqrt{x+1}}{3 (1-3 x)}+\frac{8}{9 (1-3 x)}+\frac{5}{9} \log (1-3 x)-\frac{8}{9} \sinh ^{-1}\left(\sqrt{x}\right)+\frac{10}{9} \tanh ^{-1}\left(\frac{2 \sqrt{x}}{\sqrt{x+1}}\right)",1,"(Sqrt[x]*(4 - 4*Sqrt[1 + x]))/(3 + 3*x - 3*Sqrt[1 + x] + Sqrt[x]*(-6 + 6*Sqrt[1 + x])) - (2*Log[-1 - Sqrt[x] + Sqrt[1 + x]])/9 - 2*Log[-1 + Sqrt[x] + Sqrt[1 + x]] + (10*Log[1 + x - Sqrt[1 + x] + Sqrt[x]*(-2 + 2*Sqrt[1 + x])])/9","A",1
6,1,78,64,0.2521489,"\int \frac{\sqrt{-1+x^2}}{(-i+x)^2} \, dx","IntegrateAlgebraic[Sqrt[-1 + x^2]/(-I + x)^2,x]","\frac{\sqrt{x^2-1}}{-x+i}-\log \left(\sqrt{x^2-1}-x\right)-\sqrt{2} \tanh ^{-1}\left(-\frac{i \sqrt{x^2-1}}{\sqrt{2}}+\frac{i x}{\sqrt{2}}+\frac{1}{\sqrt{2}}\right)","\frac{\sqrt{x^2-1}}{-x+i}-\frac{i \tan ^{-1}\left(\frac{1-i x}{\sqrt{2} \sqrt{x^2-1}}\right)}{\sqrt{2}}+\tanh ^{-1}\left(\frac{x}{\sqrt{x^2-1}}\right)",1,"Sqrt[-1 + x^2]/(I - x) - Sqrt[2]*ArcTanh[1/Sqrt[2] + (I*x)/Sqrt[2] - (I*Sqrt[-1 + x^2])/Sqrt[2]] - Log[-x + Sqrt[-1 + x^2]]","A",1
7,1,64,48,0.1054553,"\int \frac{1}{\sqrt{-1+x^2} \left(1+x^2\right)^2} \, dx","IntegrateAlgebraic[1/(Sqrt[-1 + x^2]*(1 + x^2)^2),x]","\frac{3 \tanh ^{-1}\left(\frac{x^2}{\sqrt{2}}-\frac{\sqrt{x^2-1} x}{\sqrt{2}}+\frac{1}{\sqrt{2}}\right)}{4 \sqrt{2}}-\frac{x \sqrt{x^2-1}}{4 \left(x^2+1\right)}","\frac{3 \tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^2-1}}\right)}{4 \sqrt{2}}-\frac{x \sqrt{x^2-1}}{4 \left(x^2+1\right)}",1,"-1/4*(x*Sqrt[-1 + x^2])/(1 + x^2) + (3*ArcTanh[1/Sqrt[2] + x^2/Sqrt[2] - (x*Sqrt[-1 + x^2])/Sqrt[2]])/(4*Sqrt[2])","A",1
8,1,26,30,0.2825163,"\int \frac{1}{\left(\sqrt{-1+x}+\sqrt{x}\right)^2 \sqrt{-1+x}} \, dx","IntegrateAlgebraic[1/((Sqrt[-1 + x] + Sqrt[x])^2*Sqrt[-1 + x]),x]","\frac{2}{3} \sqrt{x-1} (2 x+1)-\frac{4 x^{3/2}}{3}","-\frac{4 x^{3/2}}{3}+\frac{4}{3} (x-1)^{3/2}+2 \sqrt{x-1}",1,"(-4*x^(3/2))/3 + (2*Sqrt[-1 + x]*(1 + 2*x))/3","A",1
9,1,321,220,9.6039659,"\int \frac{1}{\sqrt{-1+x^2} \left(\sqrt{x}+\sqrt{-1+x^2}\right)^2} \, dx","IntegrateAlgebraic[1/(Sqrt[-1 + x^2]*(Sqrt[x] + Sqrt[-1 + x^2])^2),x]","-\frac{1}{5} \sqrt{2 \sqrt{5}-\frac{22}{5}} \tan ^{-1}\left(\frac{\sqrt{\sqrt{5}-2} \sqrt{x^2-1}}{x+1}\right)+\frac{1}{5} \sqrt{\frac{22}{5}+2 \sqrt{5}} \tanh ^{-1}\left(\frac{\sqrt{2+\sqrt{5}} \sqrt{x^2-1}}{x+1}\right)+\frac{4 x^{3/2}-4 \sqrt{x^2-1} x+2 \sqrt{x^2-1}-2 \sqrt{x}}{5 \left(x^2-x-1\right)}-\frac{4}{5} \sqrt{\frac{2}{5 \sqrt{5}-5}} \tan ^{-1}\left(\sqrt{\frac{1}{2}+\frac{\sqrt{5}}{2}} \sqrt{x}\right)+\frac{2}{5} \sqrt{\frac{2}{\sqrt{5}-1}} \tan ^{-1}\left(\sqrt{\frac{1}{2}+\frac{\sqrt{5}}{2}} \sqrt{x}\right)-\frac{4}{5} \sqrt{\frac{2}{5+5 \sqrt{5}}} \tanh ^{-1}\left(\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}} \sqrt{x}\right)-\frac{2}{5} \sqrt{\frac{2}{1+\sqrt{5}}} \tanh ^{-1}\left(\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}} \sqrt{x}\right)","\frac{2-4 x}{5 \left(\sqrt{x^2-1}+\sqrt{x}\right)}-\frac{1}{50} \sqrt{50 \sqrt{5}-110} \tan ^{-1}\left(\frac{\sqrt{2 \sqrt{5}-2} \sqrt{x^2-1}}{2-\left(1-\sqrt{5}\right) x}\right)-\frac{1}{50} \sqrt{110+50 \sqrt{5}} \tanh ^{-1}\left(\frac{\sqrt{2+2 \sqrt{5}} \sqrt{x^2-1}}{-\sqrt{5} x-x+2}\right)+\frac{1}{25} \sqrt{50 \sqrt{5}-110} \tan ^{-1}\left(\frac{1}{2} \sqrt{2+2 \sqrt{5}} \sqrt{x}\right)-\frac{1}{25} \sqrt{110+50 \sqrt{5}} \tanh ^{-1}\left(\frac{1}{2} \sqrt{2 \sqrt{5}-2} \sqrt{x}\right)",1,"(-2*Sqrt[x] + 4*x^(3/2) + 2*Sqrt[-1 + x^2] - 4*x*Sqrt[-1 + x^2])/(5*(-1 - x + x^2)) + (2*Sqrt[2/(-1 + Sqrt[5])]*ArcTan[Sqrt[1/2 + Sqrt[5]/2]*Sqrt[x]])/5 - (4*Sqrt[2/(-5 + 5*Sqrt[5])]*ArcTan[Sqrt[1/2 + Sqrt[5]/2]*Sqrt[x]])/5 - (Sqrt[-22/5 + 2*Sqrt[5]]*ArcTan[(Sqrt[-2 + Sqrt[5]]*Sqrt[-1 + x^2])/(1 + x)])/5 - (2*Sqrt[2/(1 + Sqrt[5])]*ArcTanh[Sqrt[-1/2 + Sqrt[5]/2]*Sqrt[x]])/5 - (4*Sqrt[2/(5 + 5*Sqrt[5])]*ArcTanh[Sqrt[-1/2 + Sqrt[5]/2]*Sqrt[x]])/5 + (Sqrt[22/5 + 2*Sqrt[5]]*ArcTanh[(Sqrt[2 + Sqrt[5]]*Sqrt[-1 + x^2])/(1 + x)])/5","A",0
10,1,321,220,5.4924456,"\int \frac{\left(\sqrt{x}-\sqrt{-1+x^2}\right)^2}{\left(1+x-x^2\right)^2 \sqrt{-1+x^2}} \, dx","IntegrateAlgebraic[(Sqrt[x] - Sqrt[-1 + x^2])^2/((1 + x - x^2)^2*Sqrt[-1 + x^2]),x]","-\frac{1}{5} \sqrt{2 \sqrt{5}-\frac{22}{5}} \tan ^{-1}\left(\frac{\sqrt{\sqrt{5}-2} \sqrt{x^2-1}}{x+1}\right)+\frac{1}{5} \sqrt{\frac{22}{5}+2 \sqrt{5}} \tanh ^{-1}\left(\frac{\sqrt{2+\sqrt{5}} \sqrt{x^2-1}}{x+1}\right)+\frac{4 x^{3/2}-4 \sqrt{x^2-1} x+2 \sqrt{x^2-1}-2 \sqrt{x}}{5 \left(x^2-x-1\right)}-\frac{4}{5} \sqrt{\frac{2}{5 \sqrt{5}-5}} \tan ^{-1}\left(\sqrt{\frac{1}{2}+\frac{\sqrt{5}}{2}} \sqrt{x}\right)+\frac{2}{5} \sqrt{\frac{2}{\sqrt{5}-1}} \tan ^{-1}\left(\sqrt{\frac{1}{2}+\frac{\sqrt{5}}{2}} \sqrt{x}\right)-\frac{4}{5} \sqrt{\frac{2}{5+5 \sqrt{5}}} \tanh ^{-1}\left(\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}} \sqrt{x}\right)-\frac{2}{5} \sqrt{\frac{2}{1+\sqrt{5}}} \tanh ^{-1}\left(\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}} \sqrt{x}\right)","\frac{2-4 x}{5 \left(\sqrt{x^2-1}+\sqrt{x}\right)}-\frac{1}{50} \sqrt{50 \sqrt{5}-110} \tan ^{-1}\left(\frac{\sqrt{2 \sqrt{5}-2} \sqrt{x^2-1}}{2-\left(1-\sqrt{5}\right) x}\right)-\frac{1}{50} \sqrt{110+50 \sqrt{5}} \tanh ^{-1}\left(\frac{\sqrt{2+2 \sqrt{5}} \sqrt{x^2-1}}{-\sqrt{5} x-x+2}\right)+\frac{1}{25} \sqrt{50 \sqrt{5}-110} \tan ^{-1}\left(\frac{1}{2} \sqrt{2+2 \sqrt{5}} \sqrt{x}\right)-\frac{1}{25} \sqrt{110+50 \sqrt{5}} \tanh ^{-1}\left(\frac{1}{2} \sqrt{2 \sqrt{5}-2} \sqrt{x}\right)",1,"(-2*Sqrt[x] + 4*x^(3/2) + 2*Sqrt[-1 + x^2] - 4*x*Sqrt[-1 + x^2])/(5*(-1 - x + x^2)) + (2*Sqrt[2/(-1 + Sqrt[5])]*ArcTan[Sqrt[1/2 + Sqrt[5]/2]*Sqrt[x]])/5 - (4*Sqrt[2/(-5 + 5*Sqrt[5])]*ArcTan[Sqrt[1/2 + Sqrt[5]/2]*Sqrt[x]])/5 - (Sqrt[-22/5 + 2*Sqrt[5]]*ArcTan[(Sqrt[-2 + Sqrt[5]]*Sqrt[-1 + x^2])/(1 + x)])/5 - (2*Sqrt[2/(1 + Sqrt[5])]*ArcTanh[Sqrt[-1/2 + Sqrt[5]/2]*Sqrt[x]])/5 - (4*Sqrt[2/(5 + 5*Sqrt[5])]*ArcTanh[Sqrt[-1/2 + Sqrt[5]/2]*Sqrt[x]])/5 + (Sqrt[22/5 + 2*Sqrt[5]]*ArcTanh[(Sqrt[2 + Sqrt[5]]*Sqrt[-1 + x^2])/(1 + x)])/5","A",0
11,1,177,138,4.2148428,"\int \left(\frac{1}{\sqrt{2} (1+x)^2 \sqrt{-i+x^2}}+\frac{1}{\sqrt{2} (1+x)^2 \sqrt{i+x^2}}\right) \, dx","IntegrateAlgebraic[1/(Sqrt[2]*(1 + x)^2*Sqrt[-I + x^2]) + 1/(Sqrt[2]*(1 + x)^2*Sqrt[I + x^2]),x]","-\frac{\sqrt[4]{-1} \sqrt{x^2-i}}{2 (x+1)}+\frac{(-1)^{3/4} \sqrt{x^2+i}}{2 (x+1)}-\sqrt{\frac{1}{2}-\frac{i}{2}} \tan ^{-1}\left(-\sqrt{-\frac{1}{2}-\frac{i}{2}} \sqrt{x^2-i}+\sqrt{-\frac{1}{2}-\frac{i}{2}} x+\sqrt{-\frac{1}{2}-\frac{i}{2}}\right)-\sqrt{\frac{1}{2}+\frac{i}{2}} \tan ^{-1}\left(-\sqrt{-\frac{1}{2}+\frac{i}{2}} \sqrt{x^2+i}+\sqrt{-\frac{1}{2}+\frac{i}{2}} x+\sqrt{-\frac{1}{2}+\frac{i}{2}}\right)","-\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{x^2-i}}{\sqrt{2} (x+1)}-\frac{\left(\frac{1}{2}-\frac{i}{2}\right) \sqrt{x^2+i}}{\sqrt{2} (x+1)}+\frac{\tanh ^{-1}\left(\frac{x+i}{\sqrt{1-i} \sqrt{x^2-i}}\right)}{(1-i)^{3/2} \sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{-x+i}{\sqrt{1+i} \sqrt{x^2+i}}\right)}{(1+i)^{3/2} \sqrt{2}}",1,"-1/2*((-1)^(1/4)*Sqrt[-I + x^2])/(1 + x) + ((-1)^(3/4)*Sqrt[I + x^2])/(2*(1 + x)) - Sqrt[1/2 - I/2]*ArcTan[Sqrt[-1/2 - I/2] + Sqrt[-1/2 - I/2]*x - Sqrt[-1/2 - I/2]*Sqrt[-I + x^2]] - Sqrt[1/2 + I/2]*ArcTan[Sqrt[-1/2 + I/2] + Sqrt[-1/2 + I/2]*x - Sqrt[-1/2 + I/2]*Sqrt[I + x^2]]","A",1
12,1,312,125,2.7786851,"\int \frac{\sqrt{x^2+\sqrt{1+x^4}}}{(1+x)^2 \sqrt{1+x^4}} \, dx","IntegrateAlgebraic[Sqrt[x^2 + Sqrt[1 + x^4]]/((1 + x)^2*Sqrt[1 + x^4]),x]","\frac{2 x^4+x^2+\left(-x^2-1\right) \left(\sqrt{x^4+1}+x^2\right) x+\sqrt{x^4+1} \left(2 x^2-\left(\sqrt{x^4+1}+x^2\right) x+1\right)+1}{2 \left(x^2-1\right) \left(\sqrt{x^4+1}+x^2\right)^{3/2}}+\frac{\tan ^{-1}\left(\sqrt{1+\sqrt{2}} \sqrt{\sqrt{x^4+1}+x^2}\right)}{2 \sqrt{\sqrt{2}-1}}-\frac{1}{2} \sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{2}-1\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)-\frac{\tanh ^{-1}\left(\sqrt{\sqrt{2}-1} \sqrt{\sqrt{x^4+1}+x^2}\right)}{2 \sqrt{1+\sqrt{2}}}+\frac{1}{2} \sqrt{\sqrt{2}-1} \tanh ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)","-\frac{\sqrt{1-i x^2}}{2 (x+1)}-\frac{\sqrt{1+i x^2}}{2 (x+1)}-\frac{1}{4} (1-i)^{3/2} \tanh ^{-1}\left(\frac{1+i x}{\sqrt{1-i} \sqrt{1-i x^2}}\right)-\frac{1}{4} (1+i)^{3/2} \tanh ^{-1}\left(\frac{1-i x}{\sqrt{1+i} \sqrt{1+i x^2}}\right)",1,"(1 + x^2 + 2*x^4 + x*(-1 - x^2)*(x^2 + Sqrt[1 + x^4]) + Sqrt[1 + x^4]*(1 + 2*x^2 - x*(x^2 + Sqrt[1 + x^4])))/(2*(-1 + x^2)*(x^2 + Sqrt[1 + x^4])^(3/2)) + ArcTan[Sqrt[1 + Sqrt[2]]*Sqrt[x^2 + Sqrt[1 + x^4]]]/(2*Sqrt[-1 + Sqrt[2]]) - (Sqrt[1 + Sqrt[2]]*ArcTan[(Sqrt[2*(-1 + Sqrt[2])]*x*Sqrt[x^2 + Sqrt[1 + x^4]])/(1 + x^2 + Sqrt[1 + x^4])])/2 - ArcTanh[Sqrt[-1 + Sqrt[2]]*Sqrt[x^2 + Sqrt[1 + x^4]]]/(2*Sqrt[1 + Sqrt[2]]) + (Sqrt[-1 + Sqrt[2]]*ArcTanh[(Sqrt[2*(1 + Sqrt[2])]*x*Sqrt[x^2 + Sqrt[1 + x^4]])/(1 + x^2 + Sqrt[1 + x^4])])/2","B",0
13,1,225,81,1.217875,"\int \frac{\sqrt{x^2+\sqrt{1+x^4}}}{(1+x) \sqrt{1+x^4}} \, dx","IntegrateAlgebraic[Sqrt[x^2 + Sqrt[1 + x^4]]/((1 + x)*Sqrt[1 + x^4]),x]","\sqrt{\frac{1}{2} \left(\sqrt{2}-1\right)} \tan ^{-1}\left(\sqrt{1+\sqrt{2}} \sqrt{\sqrt{x^4+1}+x^2}\right)-\sqrt{\frac{1}{2} \left(\sqrt{2}-1\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{2}-1\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)-\sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tanh ^{-1}\left(\sqrt{\sqrt{2}-1} \sqrt{\sqrt{x^4+1}+x^2}\right)+\sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tanh ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)","-\frac{1}{2} \sqrt{1-i} \tanh ^{-1}\left(\frac{1+i x}{\sqrt{1-i} \sqrt{1-i x^2}}\right)-\frac{1}{2} \sqrt{1+i} \tanh ^{-1}\left(\frac{1-i x}{\sqrt{1+i} \sqrt{1+i x^2}}\right)",1,"Sqrt[(-1 + Sqrt[2])/2]*ArcTan[Sqrt[1 + Sqrt[2]]*Sqrt[x^2 + Sqrt[1 + x^4]]] - Sqrt[(-1 + Sqrt[2])/2]*ArcTan[(Sqrt[2*(-1 + Sqrt[2])]*x*Sqrt[x^2 + Sqrt[1 + x^4]])/(1 + x^2 + Sqrt[1 + x^4])] - Sqrt[(1 + Sqrt[2])/2]*ArcTanh[Sqrt[-1 + Sqrt[2]]*Sqrt[x^2 + Sqrt[1 + x^4]]] + Sqrt[(1 + Sqrt[2])/2]*ArcTanh[(Sqrt[2*(1 + Sqrt[2])]*x*Sqrt[x^2 + Sqrt[1 + x^4]])/(1 + x^2 + Sqrt[1 + x^4])]","B",1
14,1,44,31,0.1583951,"\int \frac{\sqrt{x^2+\sqrt{1+x^4}}}{\sqrt{1+x^4}} \, dx","IntegrateAlgebraic[Sqrt[x^2 + Sqrt[1 + x^4]]/Sqrt[1 + x^4],x]","\frac{\log \left(\sqrt{x^4+1}+x^2+\sqrt{2} \sqrt{\sqrt{x^4+1}+x^2} x\right)}{\sqrt{2}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{\sqrt{x^4+1}+x^2}}\right)}{\sqrt{2}}",1,"Log[x^2 + Sqrt[1 + x^4] + Sqrt[2]*x*Sqrt[x^2 + Sqrt[1 + x^4]]]/Sqrt[2]","A",1
15,1,57,33,0.1746981,"\int \frac{\sqrt{-x^2+\sqrt{1+x^4}}}{\sqrt{1+x^4}} \, dx","IntegrateAlgebraic[Sqrt[-x^2 + Sqrt[1 + x^4]]/Sqrt[1 + x^4],x]","-\frac{i \log \left(-i \sqrt{x^4+1}+i x^2+\sqrt{2} \sqrt{\sqrt{x^4+1}-x^2} x\right)}{\sqrt{2}}","\frac{\tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{\sqrt{x^4+1}-x^2}}\right)}{\sqrt{2}}",1,"((-I)*Log[I*x^2 - I*Sqrt[1 + x^4] + Sqrt[2]*x*Sqrt[-x^2 + Sqrt[1 + x^4]]])/Sqrt[2]","C",1
16,1,19,19,0.2548583,"\int \frac{(-1+x)^{3/2}+(1+x)^{3/2}}{(-1+x)^{3/2} (1+x)^{3/2}} \, dx","IntegrateAlgebraic[((-1 + x)^(3/2) + (1 + x)^(3/2))/((-1 + x)^(3/2)*(1 + x)^(3/2)),x]","-\frac{2}{\sqrt{x+1}}-\frac{2}{\sqrt{x-1}}","-\frac{2}{\sqrt{x+1}}-\frac{2}{\sqrt{x-1}}",1,"-2/Sqrt[-1 + x] - 2/Sqrt[1 + x]","A",1
17,0,0,52,0.0000552,"\int \left(x+\sqrt{a+x^2}\right)^b \, dx","IntegrateAlgebraic[(x + Sqrt[a + x^2])^b,x]","\int \left(x+\sqrt{a+x^2}\right)^b \, dx","\frac{\left(\sqrt{a+x^2}+x\right)^{b+1}}{2 (b+1)}-\frac{a \left(\sqrt{a+x^2}+x\right)^{b-1}}{2 (1-b)}",1,"Could not integrate","F",-1
18,0,0,56,0.0000663,"\int \left(x-\sqrt{a+x^2}\right)^b \, dx","IntegrateAlgebraic[(x - Sqrt[a + x^2])^b,x]","\int \left(x-\sqrt{a+x^2}\right)^b \, dx","\frac{\left(x-\sqrt{a+x^2}\right)^{b+1}}{2 (b+1)}-\frac{a \left(x-\sqrt{a+x^2}\right)^{b-1}}{2 (1-b)}",1,"Could not integrate","F",-1
19,0,0,17,0.0000995,"\int \frac{\left(x+\sqrt{a+x^2}\right)^b}{\sqrt{a+x^2}} \, dx","IntegrateAlgebraic[(x + Sqrt[a + x^2])^b/Sqrt[a + x^2],x]","\int \frac{\left(x+\sqrt{a+x^2}\right)^b}{\sqrt{a+x^2}} \, dx","\frac{\left(\sqrt{a+x^2}+x\right)^b}{b}",1,"Could not integrate","F",-1
20,0,0,20,0.0000708,"\int \frac{\left(x-\sqrt{a+x^2}\right)^b}{\sqrt{a+x^2}} \, dx","IntegrateAlgebraic[(x - Sqrt[a + x^2])^b/Sqrt[a + x^2],x]","\int \frac{\left(x-\sqrt{a+x^2}\right)^b}{\sqrt{a+x^2}} \, dx","-\frac{\left(x-\sqrt{a+x^2}\right)^b}{b}",1,"Could not integrate","F",-1
21,0,0,42,0.0000667,"\int \frac{1}{\left(a+b e^{p x}\right)^2} \, dx","IntegrateAlgebraic[(a + b*E^(p*x))^(-2),x]","\int \frac{1}{\left(a+b e^{p x}\right)^2} \, dx","-\frac{\log \left(a+b e^{p x}\right)}{a^2 p}+\frac{x}{a^2}+\frac{1}{a p \left(a+b e^{p x}\right)}",1,"Could not integrate","F",-1
22,0,0,22,0.0000798,"\int \frac{1}{\left(b e^{-p x}+a e^{p x}\right)^2} \, dx","IntegrateAlgebraic[(b/E^(p*x) + a*E^(p*x))^(-2),x]","\int \frac{1}{\left(b e^{-p x}+a e^{p x}\right)^2} \, dx","-\frac{1}{2 a p \left(a e^{2 p x}+b\right)}",1,"Could not integrate","F",-1
23,0,0,62,0.0000825,"\int \frac{x}{\left(b e^{-p x}+a e^{p x}\right)^2} \, dx","IntegrateAlgebraic[x/(b/E^(p*x) + a*E^(p*x))^2,x]","\int \frac{x}{\left(b e^{-p x}+a e^{p x}\right)^2} \, dx","-\frac{\log \left(a e^{2 p x}+b\right)}{4 a b p^2}+\frac{x}{2 a b p}-\frac{x}{2 a p \left(a e^{2 p x}+b\right)}",1,"Could not integrate","F",-1
24,1,146,86,0.3347076,"\int \frac{1-x+3 x^2}{\sqrt{1-x+x^2} \left(1+x+x^2\right)^2} \, dx","IntegrateAlgebraic[(1 - x + 3*x^2)/(Sqrt[1 - x + x^2]*(1 + x + x^2)^2),x]","\frac{(x+1) \sqrt{x^2-x+1}}{x^2+x+1}-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^4-2 \text{$\#$1}^3+\text{$\#$1}^2+6 \text{$\#$1}+3\&,\frac{\text{$\#$1}^2 \log \left(-\text{$\#$1}+\sqrt{x^2-x+1}-x\right)+6 \text{$\#$1} \log \left(-\text{$\#$1}+\sqrt{x^2-x+1}-x\right)+2 \log \left(-\text{$\#$1}+\sqrt{x^2-x+1}-x\right)}{2 \text{$\#$1}^3-3 \text{$\#$1}^2+\text{$\#$1}+3}\&\right]","\frac{\sqrt{x^2-x+1} (x+1)}{x^2+x+1}+\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} (x+1)}{\sqrt{x^2-x+1}}\right)-\frac{\tanh ^{-1}\left(\frac{\sqrt{\frac{2}{3}} (1-x)}{\sqrt{x^2-x+1}}\right)}{\sqrt{6}}",1,"((1 + x)*Sqrt[1 - x + x^2])/(1 + x + x^2) - RootSum[3 + 6*#1 + #1^2 - 2*#1^3 + #1^4 & , (2*Log[-x + Sqrt[1 - x + x^2] - #1] + 6*Log[-x + Sqrt[1 - x + x^2] - #1]*#1 + Log[-x + Sqrt[1 - x + x^2] - #1]*#1^2)/(3 + #1 - 3*#1^2 + 2*#1^3) & ]/2","C",1
25,1,19,19,0.0162263,"\int \frac{\sqrt{x+\sqrt{a^2+x^2}}}{\sqrt{a^2+x^2}} \, dx","IntegrateAlgebraic[Sqrt[x + Sqrt[a^2 + x^2]]/Sqrt[a^2 + x^2],x]","2 \sqrt{\sqrt{a^2+x^2}+x}","2 \sqrt{\sqrt{a^2+x^2}+x}",1,"2*Sqrt[x + Sqrt[a^2 + x^2]]","A",1
26,1,26,26,0.0237354,"\int \frac{\sqrt{b x+\sqrt{a+b^2 x^2}}}{\sqrt{a+b^2 x^2}} \, dx","IntegrateAlgebraic[Sqrt[b*x + Sqrt[a + b^2*x^2]]/Sqrt[a + b^2*x^2],x]","\frac{2 \sqrt{\sqrt{a+b^2 x^2}+b x}}{b}","\frac{2 \sqrt{\sqrt{a+b^2 x^2}+b x}}{b}",1,"(2*Sqrt[b*x + Sqrt[a + b^2*x^2]])/b","A",1
27,1,63,63,0.0597766,"\int \frac{1}{x \sqrt{a^2+x^2} \sqrt{x+\sqrt{a^2+x^2}}} \, dx","IntegrateAlgebraic[1/(x*Sqrt[a^2 + x^2]*Sqrt[x + Sqrt[a^2 + x^2]]),x]","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{\sqrt{a^2+x^2}+x}}{\sqrt{a}}\right)}{a^{3/2}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a^2+x^2}+x}}{\sqrt{a}}\right)}{a^{3/2}}","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{\sqrt{a^2+x^2}+x}}{\sqrt{a}}\right)}{a^{3/2}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a^2+x^2}+x}}{\sqrt{a}}\right)}{a^{3/2}}",1,"(-2*ArcTan[Sqrt[x + Sqrt[a^2 + x^2]]/Sqrt[a]])/a^(3/2) - (2*ArcTanh[Sqrt[x + Sqrt[a^2 + x^2]]/Sqrt[a]])/a^(3/2)","A",1
28,1,82,82,0.000125,"\int \frac{\sqrt{x+\sqrt{a^2+x^2}}}{x} \, dx","IntegrateAlgebraic[Sqrt[x + Sqrt[a^2 + x^2]]/x,x]","2 \sqrt{\sqrt{a^2+x^2}+x}-2 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{\sqrt{a^2+x^2}+x}}{\sqrt{a}}\right)-2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a^2+x^2}+x}}{\sqrt{a}}\right)","2 \sqrt{\sqrt{a^2+x^2}+x}-2 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{\sqrt{a^2+x^2}+x}}{\sqrt{a}}\right)-2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a^2+x^2}+x}}{\sqrt{a}}\right)",1,"2*Sqrt[x + Sqrt[a^2 + x^2]] - 2*Sqrt[a]*ArcTan[Sqrt[x + Sqrt[a^2 + x^2]]/Sqrt[a]] - 2*Sqrt[a]*ArcTanh[Sqrt[x + Sqrt[a^2 + x^2]]/Sqrt[a]]","A",1
29,0,0,606,0.0000408,"\int x^3 \log ^3(2+x) \log (3+x) \, dx","IntegrateAlgebraic[x^3*Log[2 + x]^3*Log[3 + x],x]","\int x^3 \log ^3(2+x) \log (3+x) \, dx","-\frac{5609 \text{Li}_2(-x-2)}{96}-\frac{563 \text{Li}_3(-x-2)}{8}-\frac{195 \text{Li}_4(-x-2)}{2}-\frac{195}{4} \text{Li}_2(-x-2) \log ^2(x+2)+\frac{563}{8} \text{Li}_2(-x-2) \log (x+2)+\frac{195}{2} \text{Li}_3(-x-2) \log (x+2)+\frac{3 x^4}{256}+\frac{1}{4} x^4 \log ^3(x+2) \log (x+3)+\frac{3}{64} x^4 \log ^2(x+2)-\frac{3}{16} x^4 \log ^2(x+2) \log (x+3)-\frac{3}{128} x^4 \log (x+2)+\frac{3}{32} x^4 \log (x+2) \log (x+3)-\frac{3}{128} x^4 \log (x+3)-\frac{763 x^3}{3456}-\frac{17}{48} x^3 \log ^2(x+2)+\frac{1}{2} x^3 \log ^2(x+2) \log (x+3)+\frac{83}{288} x^3 \log (x+2)-\frac{7}{12} x^3 \log (x+2) \log (x+3)+\frac{37}{144} x^3 \log (x+3)+\frac{8029 x^2}{2304}-\frac{3}{2} x^2 \log ^2(x+2) \log (x+3)-\frac{187}{64} x^2 \log (x+2)+\frac{13}{4} x^2 \log (x+2) \log (x+3)-\frac{115}{48} x^2 \log (x+3)-\frac{302177 x}{1152}+\frac{3}{256} (x+2)^4-\frac{71}{216} (x+2)^3+\frac{377}{64} (x+2)^2-\frac{1}{16} (x+2)^4 \log ^3(x+2)+\frac{3}{4} (x+2)^3 \log ^3(x+2)-\frac{33}{8} (x+2)^2 \log ^3(x+2)+\frac{65}{4} (x+2) \log ^3(x+2)-\frac{81}{4} \log ^3(x+2) \log (x+3)+6 x \log ^2(x+2) \log (x+3)+\frac{3}{64} (x+2)^4 \log ^2(x+2)-\frac{3}{4} (x+2)^3 \log ^2(x+2)+\frac{273}{32} (x+2)^2 \log ^2(x+2)-\frac{1251}{16} (x+2) \log ^2(x+2)-\frac{43}{12} \log ^2(x+2)+\frac{963}{16} \log ^2(x+2) \log (x+3)-25 x \log (x+2) \log (x+3)-\frac{3}{64} (x+2)^4 \log (x+2)+\frac{71}{72} (x+2)^3 \log (x+2)-\frac{377}{32} (x+2)^2 \log (x+2)+\frac{6733}{32} (x+2) \log (x+2)+\frac{2069}{144} \log (x+2)+\frac{415}{12} (x+3) \log (x+3)-\frac{4083}{32} \log (x+2) \log (x+3)+\frac{3891}{128} \log (x+3)",1,"Could not integrate","F",-1
30,0,0,17,0.000107,"\int \frac{\left(x+\sqrt{b+x^2}\right)^a}{\sqrt{b+x^2}} \, dx","IntegrateAlgebraic[(x + Sqrt[b + x^2])^a/Sqrt[b + x^2],x]","\int \frac{\left(x+\sqrt{b+x^2}\right)^a}{\sqrt{b+x^2}} \, dx","\frac{\left(\sqrt{b+x^2}+x\right)^a}{a}",1,"Could not integrate","F",-1
31,0,0,52,0.0000598,"\int \left(x+\sqrt{b+x^2}\right)^a \, dx","IntegrateAlgebraic[(x + Sqrt[b + x^2])^a,x]","\int \left(x+\sqrt{b+x^2}\right)^a \, dx","\frac{\left(\sqrt{b+x^2}+x\right)^{a+1}}{2 (a+1)}-\frac{b \left(\sqrt{b+x^2}+x\right)^{a-1}}{2 (1-a)}",1,"Could not integrate","F",-1
32,0,0,34,0.0000865,"\int \left(6+3 x^a+2 x^{2 a}\right)^{\frac{1}{a}} \left(x^a+x^{2 a}+x^{3 a}\right) \, dx","IntegrateAlgebraic[(6 + 3*x^a + 2*x^(2*a))^a^(-1)*(x^a + x^(2*a) + x^(3*a)),x]","\int \left(6+3 x^a+2 x^{2 a}\right)^{\frac{1}{a}} \left(x^a+x^{2 a}+x^{3 a}\right) \, dx","\frac{x^{a+1} \left(2 x^{2 a}+3 x^a+6\right)^{\frac{1}{a}+1}}{6 (a+1)}",1,"Could not integrate","F",-1
33,1,82,58,0.0687495,"\int \frac{1}{x \sqrt[3]{1-x^2}} \, dx","IntegrateAlgebraic[1/(x*(1 - x^2)^(1/3)),x]","\frac{1}{2} \log \left(\sqrt[3]{1-x^2}-1\right)-\frac{1}{4} \log \left(\left(1-x^2\right)^{2/3}+\sqrt[3]{1-x^2}+1\right)+\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{1-x^2}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)","\frac{3}{4} \log \left(1-\sqrt[3]{1-x^2}\right)+\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{1-x^2}+1}{\sqrt{3}}\right)-\frac{\log (x)}{2}",1,"(Sqrt[3]*ArcTan[1/Sqrt[3] + (2*(1 - x^2)^(1/3))/Sqrt[3]])/2 + Log[-1 + (1 - x^2)^(1/3)]/2 - Log[1 + (1 - x^2)^(1/3) + (1 - x^2)^(2/3)]/4","A",1
34,1,82,58,0.0619504,"\int \frac{1}{x \left(1-x^2\right)^{2/3}} \, dx","IntegrateAlgebraic[1/(x*(1 - x^2)^(2/3)),x]","\frac{1}{2} \log \left(\sqrt[3]{1-x^2}-1\right)-\frac{1}{4} \log \left(\left(1-x^2\right)^{2/3}+\sqrt[3]{1-x^2}+1\right)-\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{1-x^2}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)","\frac{3}{4} \log \left(1-\sqrt[3]{1-x^2}\right)-\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{1-x^2}+1}{\sqrt{3}}\right)-\frac{\log (x)}{2}",1,"-1/2*(Sqrt[3]*ArcTan[1/Sqrt[3] + (2*(1 - x^2)^(1/3))/Sqrt[3]]) + Log[-1 + (1 - x^2)^(1/3)]/2 - Log[1 + (1 - x^2)^(1/3) + (1 - x^2)^(2/3)]/4","A",1
35,1,86,49,0.1581422,"\int \frac{1}{\sqrt[3]{1-x^3}} \, dx","IntegrateAlgebraic[(1 - x^3)^(-1/3),x]","\frac{1}{3} \log \left(\sqrt[3]{1-x^3}+x\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{1-x^3}-x}\right)}{\sqrt{3}}-\frac{1}{6} \log \left(-\sqrt[3]{1-x^3} x+\left(1-x^3\right)^{2/3}+x^2\right)","\frac{1}{2} \log \left(\sqrt[3]{1-x^3}+x\right)-\frac{\tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt{3}}",1,"ArcTan[(Sqrt[3]*x)/(-x + 2*(1 - x^3)^(1/3))]/Sqrt[3] + Log[x + (1 - x^3)^(1/3)]/3 - Log[x^2 - x*(1 - x^3)^(1/3) + (1 - x^3)^(2/3)]/6","A",1
36,1,79,55,0.0663697,"\int \frac{1}{x \sqrt[3]{1-x^3}} \, dx","IntegrateAlgebraic[1/(x*(1 - x^3)^(1/3)),x]","\frac{1}{3} \log \left(\sqrt[3]{1-x^3}-1\right)-\frac{1}{6} \log \left(\left(1-x^3\right)^{2/3}+\sqrt[3]{1-x^3}+1\right)+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{1-x^3}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3}}","\frac{1}{2} \log \left(1-\sqrt[3]{1-x^3}\right)+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\log (x)}{2}",1,"ArcTan[1/Sqrt[3] + (2*(1 - x^3)^(1/3))/Sqrt[3]]/Sqrt[3] + Log[-1 + (1 - x^3)^(1/3)]/3 - Log[1 + (1 - x^3)^(1/3) + (1 - x^3)^(2/3)]/6","A",1
37,1,172,97,0.9943861,"\int \frac{1}{(1+x) \sqrt[3]{1-x^3}} \, dx","IntegrateAlgebraic[1/((1 + x)*(1 - x^3)^(1/3)),x]","\frac{\log \left(2 \sqrt[3]{1-x^3}+\sqrt[3]{2} x-\sqrt[3]{2}\right)}{2 \sqrt[3]{2}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{1-x^3}}{\sqrt[3]{1-x^3}-\sqrt[3]{2} x+\sqrt[3]{2}}\right)}{2 \sqrt[3]{2}}-\frac{\log \left(4 \left(1-x^3\right)^{2/3}+\left(2 \sqrt[3]{2}-2 \sqrt[3]{2} x\right) \sqrt[3]{1-x^3}+2^{2/3} x^2-2\ 2^{2/3} x+2^{2/3}\right)}{4 \sqrt[3]{2}}","\frac{3 \log \left(2^{2/3} \sqrt[3]{1-x^3}+x-1\right)}{4 \sqrt[3]{2}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1}{\sqrt{3}}\right)}{2 \sqrt[3]{2}}-\frac{\log \left((1-x) (x+1)^2\right)}{4 \sqrt[3]{2}}",1,"(Sqrt[3]*ArcTan[(Sqrt[3]*(1 - x^3)^(1/3))/(2^(1/3) - 2^(1/3)*x + (1 - x^3)^(1/3))])/(2*2^(1/3)) + Log[-2^(1/3) + 2^(1/3)*x + 2*(1 - x^3)^(1/3)]/(2*2^(1/3)) - Log[2^(2/3) - 2*2^(2/3)*x + 2^(2/3)*x^2 + (2*2^(1/3) - 2*2^(1/3)*x)*(1 - x^3)^(1/3) + 4*(1 - x^3)^(2/3)]/(4*2^(1/3))","A",1
38,0,0,145,5.1640459,"\int \frac{x}{(1+x) \sqrt[3]{1-x^3}} \, dx","IntegrateAlgebraic[x/((1 + x)*(1 - x^3)^(1/3)),x]","\int \frac{x}{(1+x) \sqrt[3]{1-x^3}} \, dx","\frac{1}{2} \log \left(\sqrt[3]{1-x^3}+x\right)-\frac{3 \log \left(2^{2/3} \sqrt[3]{1-x^3}+x-1\right)}{4 \sqrt[3]{2}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1}{\sqrt{3}}\right)}{2 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\log \left((1-x) (x+1)^2\right)}{4 \sqrt[3]{2}}",1,"Could not integrate","F",-1
39,1,181,110,0.2190397,"\int \frac{1}{x \sqrt[3]{2-3 x+x^2}} \, dx","IntegrateAlgebraic[1/(x*(2 - 3*x + x^2)^(1/3)),x]","\frac{\log \left(2 \sqrt[3]{x^2-3 x+2}+\sqrt[3]{2} x-2 \sqrt[3]{2}\right)}{2 \sqrt[3]{2}}-\frac{\log \left(2^{2/3} x^2+4 \left(x^2-3 x+2\right)^{2/3}+\left(4 \sqrt[3]{2}-2 \sqrt[3]{2} x\right) \sqrt[3]{x^2-3 x+2}-4\ 2^{2/3} x+4\ 2^{2/3}\right)}{4 \sqrt[3]{2}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x^2-3 x+2}}{\sqrt[3]{x^2-3 x+2}-\sqrt[3]{2} x+2 \sqrt[3]{2}}\right)}{2 \sqrt[3]{2}}","\frac{3 \log \left(-2^{2/3} \sqrt[3]{x^2-3 x+2}-x+2\right)}{4 \sqrt[3]{2}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt[3]{2} (2-x)}{\sqrt{3} \sqrt[3]{x^2-3 x+2}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt[3]{2}}-\frac{\log (2-x)}{4 \sqrt[3]{2}}-\frac{\log (x)}{2 \sqrt[3]{2}}",1,"(Sqrt[3]*ArcTan[(Sqrt[3]*(2 - 3*x + x^2)^(1/3))/(2*2^(1/3) - 2^(1/3)*x + (2 - 3*x + x^2)^(1/3))])/(2*2^(1/3)) + Log[-2*2^(1/3) + 2^(1/3)*x + 2*(2 - 3*x + x^2)^(1/3)]/(2*2^(1/3)) - Log[4*2^(2/3) - 4*2^(2/3)*x + 2^(2/3)*x^2 + (4*2^(1/3) - 2*2^(1/3)*x)*(2 - 3*x + x^2)^(1/3) + 4*(2 - 3*x + x^2)^(2/3)]/(4*2^(1/3))","A",1
40,1,136,81,0.2576116,"\int \frac{1}{\sqrt[3]{-5+7 x-3 x^2+x^3}} \, dx","IntegrateAlgebraic[(-5 + 7*x - 3*x^2 + x^3)^(-1/3),x]","-\frac{1}{2} \log \left(\sqrt[3]{x^3-3 x^2+7 x-5}-x+1\right)+\frac{1}{4} \log \left(x^2+\left(x^3-3 x^2+7 x-5\right)^{2/3}+(x-1) \sqrt[3]{x^3-3 x^2+7 x-5}-2 x+1\right)-\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x^3-3 x^2+7 x-5}}{\sqrt[3]{x^3-3 x^2+7 x-5}+2 x-2}\right)","-\frac{3}{4} \log \left(\sqrt[3]{x^3-3 x^2+7 x-5}-x+1\right)+\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{2 (x-1)}{\sqrt{3} \sqrt[3]{x^3-3 x^2+7 x-5}}+\frac{1}{\sqrt{3}}\right)+\frac{1}{4} \log (1-x)",1,"-1/2*(Sqrt[3]*ArcTan[(Sqrt[3]*(-5 + 7*x - 3*x^2 + x^3)^(1/3))/(-2 + 2*x + (-5 + 7*x - 3*x^2 + x^3)^(1/3))]) - Log[1 - x + (-5 + 7*x - 3*x^2 + x^3)^(1/3)]/2 + Log[1 - 2*x + x^2 + (-1 + x)*(-5 + 7*x - 3*x^2 + x^3)^(1/3) + (-5 + 7*x - 3*x^2 + x^3)^(2/3)]/4","A",1
41,1,92,66,0.180391,"\int \frac{1}{\sqrt[3]{x \left(-q+x^2\right)}} \, dx","IntegrateAlgebraic[(x*(-q + x^2))^(-1/3),x]","-\frac{1}{2} \log \left(\sqrt[3]{x^3-q x}-x\right)+\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-q x}+x}\right)+\frac{1}{4} \log \left(x \sqrt[3]{x^3-q x}+\left(x^3-q x\right)^{2/3}+x^2\right)","-\frac{3}{4} \log \left(\sqrt[3]{x \left(x^2-q\right)}-x\right)+\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{2 x}{\sqrt{3} \sqrt[3]{x \left(x^2-q\right)}}+\frac{1}{\sqrt{3}}\right)+\frac{\log (x)}{4}",1,"(Sqrt[3]*ArcTan[(Sqrt[3]*x)/(x + 2*(-(q*x) + x^3)^(1/3))])/2 - Log[-x + (-(q*x) + x^3)^(1/3)]/2 + Log[x^2 + x*(-(q*x) + x^3)^(1/3) + (-(q*x) + x^3)^(2/3)]/4","A",1
42,1,156,79,0.3659989,"\int \frac{1}{\sqrt[3]{(-1+x) \left(q-2 x+x^2\right)}} \, dx","IntegrateAlgebraic[((-1 + x)*(q - 2*x + x^2))^(-1/3),x]","-\frac{1}{2} \log \left(\sqrt[3]{(q+2) x-q+x^3-3 x^2}-x+1\right)+\frac{1}{4} \log \left(\left((q+2) x-q+x^3-3 x^2\right)^{2/3}+(x-1) \sqrt[3]{(q+2) x-q+x^3-3 x^2}+x^2-2 x+1\right)-\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{(q+2) x-q+x^3-3 x^2}}{\sqrt[3]{(q+2) x-q+x^3-3 x^2}+2 x-2}\right)","-\frac{3}{4} \log \left(\sqrt[3]{(x-1) \left(q+x^2-2 x\right)}-x+1\right)+\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{2 (x-1)}{\sqrt{3} \sqrt[3]{(x-1) \left(q+x^2-2 x\right)}}+\frac{1}{\sqrt{3}}\right)+\frac{1}{4} \log (1-x)",1,"-1/2*(Sqrt[3]*ArcTan[(Sqrt[3]*(-q + (2 + q)*x - 3*x^2 + x^3)^(1/3))/(-2 + 2*x + (-q + (2 + q)*x - 3*x^2 + x^3)^(1/3))]) - Log[1 - x + (-q + (2 + q)*x - 3*x^2 + x^3)^(1/3)]/2 + Log[1 - 2*x + x^2 + (-1 + x)*(-q + (2 + q)*x - 3*x^2 + x^3)^(1/3) + (-q + (2 + q)*x - 3*x^2 + x^3)^(2/3)]/4","A",1
43,1,233,118,0.5106208,"\int \frac{1}{x \sqrt[3]{(-1+x) \left(q-2 q x+x^2\right)}} \, dx","IntegrateAlgebraic[1/(x*((-1 + x)*(q - 2*q*x + x^2))^(1/3)),x]","\frac{\log \left(q^{2/3} x^2-2 q^{2/3} x+q^{2/3}+\left((-2 q-1) x^2+3 q x-q+x^3\right)^{2/3}+\left(\sqrt[3]{q} x-\sqrt[3]{q}\right) \sqrt[3]{(-2 q-1) x^2+3 q x-q+x^3}\right)}{4 \sqrt[3]{q}}-\frac{\log \left(\sqrt[3]{(-2 q-1) x^2+3 q x-q+x^3}-\sqrt[3]{q} x+\sqrt[3]{q}\right)}{2 \sqrt[3]{q}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{(-2 q-1) x^2+3 q x-q+x^3}}{\sqrt[3]{(-2 q-1) x^2+3 q x-q+x^3}+2 \sqrt[3]{q} x-2 \sqrt[3]{q}}\right)}{2 \sqrt[3]{q}}","-\frac{3 \log \left(\sqrt[3]{(x-1) \left(-2 q x+q+x^2\right)}-\sqrt[3]{q} (x-1)\right)}{4 \sqrt[3]{q}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{q} (x-1)}{\sqrt{3} \sqrt[3]{(x-1) \left(-2 q x+q+x^2\right)}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt[3]{q}}+\frac{\log (1-x)}{4 \sqrt[3]{q}}+\frac{\log (x)}{2 \sqrt[3]{q}}",1,"-1/2*(Sqrt[3]*ArcTan[(Sqrt[3]*(-q + 3*q*x + (-1 - 2*q)*x^2 + x^3)^(1/3))/(-2*q^(1/3) + 2*q^(1/3)*x + (-q + 3*q*x + (-1 - 2*q)*x^2 + x^3)^(1/3))])/q^(1/3) - Log[q^(1/3) - q^(1/3)*x + (-q + 3*q*x + (-1 - 2*q)*x^2 + x^3)^(1/3)]/(2*q^(1/3)) + Log[q^(2/3) - 2*q^(2/3)*x + q^(2/3)*x^2 + (-q^(1/3) + q^(1/3)*x)*(-q + 3*q*x + (-1 - 2*q)*x^2 + x^3)^(1/3) + (-q + 3*q*x + (-1 - 2*q)*x^2 + x^3)^(2/3)]/(4*q^(1/3))","A",1
44,1,161,111,0.2074575,"\int \frac{2-(1+k) x}{\sqrt[3]{(1-x) x (1-k x)} (1-(1+k) x)} \, dx","IntegrateAlgebraic[(2 - (1 + k)*x)/(((1 - x)*x*(1 - k*x))^(1/3)*(1 - (1 + k)*x)),x]","\frac{\log \left(k^{2/3} x^2+\sqrt[3]{k} x \sqrt[3]{k x^3+(-k-1) x^2+x}+\left(k x^3+(-k-1) x^2+x\right)^{2/3}\right)}{2 \sqrt[3]{k}}-\frac{\log \left(\sqrt[3]{k x^3+(-k-1) x^2+x}-\sqrt[3]{k} x\right)}{\sqrt[3]{k}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{k} x}{2 \sqrt[3]{k x^3+(-k-1) x^2+x}+\sqrt[3]{k} x}\right)}{\sqrt[3]{k}}","\frac{\log (x)}{2 \sqrt[3]{k}}+\frac{\log (1-(k+1) x)}{2 \sqrt[3]{k}}-\frac{3 \log \left(\sqrt[3]{(1-x) x (1-k x)}-\sqrt[3]{k} x\right)}{2 \sqrt[3]{k}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{k} x}{\sqrt[3]{(1-x) x (1-k x)}}+1}{\sqrt{3}}\right)}{\sqrt[3]{k}}",1,"(Sqrt[3]*ArcTan[(Sqrt[3]*k^(1/3)*x)/(k^(1/3)*x + 2*(x + (-1 - k)*x^2 + k*x^3)^(1/3))])/k^(1/3) - Log[-(k^(1/3)*x) + (x + (-1 - k)*x^2 + k*x^3)^(1/3)]/k^(1/3) + Log[k^(2/3)*x^2 + k^(1/3)*x*(x + (-1 - k)*x^2 + k*x^3)^(1/3) + (x + (-1 - k)*x^2 + k*x^3)^(2/3)]/(2*k^(1/3))","A",1
45,1,285,176,3.0276857,"\int \frac{1-k x}{(1+(-2+k) x) ((1-x) x (1-k x))^{2/3}} \, dx","IntegrateAlgebraic[(1 - k*x)/((1 + (-2 + k)*x)*((1 - x)*x*(1 - k*x))^(2/3)),x]","-\frac{(-1)^{2/3} \log \left(k^2 x^2+2 (-1)^{2/3} \sqrt[3]{2} (k-1)^{2/3} \left(k x^3+(-k-1) x^2+x\right)^{2/3}+\left(\sqrt[3]{-1} 2^{2/3} \sqrt[3]{k-1}-\sqrt[3]{-1} 2^{2/3} \sqrt[3]{k-1} k x\right) \sqrt[3]{k x^3+(-k-1) x^2+x}-2 k x+1\right)}{2\ 2^{2/3} \sqrt[3]{k-1}}+\frac{(-1)^{2/3} \log \left(\sqrt[3]{-1} 2^{2/3} \sqrt[3]{k-1} \sqrt[3]{k x^3+(-k-1) x^2+x}+k x-1\right)}{2^{2/3} \sqrt[3]{k-1}}+\frac{(-1)^{2/3} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} k x-\sqrt{3}}{-2 \sqrt[3]{-1} 2^{2/3} \sqrt[3]{k-1} \sqrt[3]{k x^3+(-k-1) x^2+x}+k x-1}\right)}{2^{2/3} \sqrt[3]{k-1}}","\frac{\log (1-(2-k) x)}{2^{2/3} \sqrt[3]{1-k}}+\frac{\log (1-k x)}{2\ 2^{2/3} \sqrt[3]{1-k}}-\frac{3 \log \left(k x+2^{2/3} \sqrt[3]{1-k} \sqrt[3]{(1-x) x (1-k x)}-1\right)}{2\ 2^{2/3} \sqrt[3]{1-k}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} (1-k x)}{\sqrt[3]{1-k} \sqrt[3]{(1-x) x (1-k x)}}+1}{\sqrt{3}}\right)}{2^{2/3} \sqrt[3]{1-k}}",1,"((-1)^(2/3)*Sqrt[3]*ArcTan[(-Sqrt[3] + Sqrt[3]*k*x)/(-1 + k*x - 2*(-1)^(1/3)*2^(2/3)*(-1 + k)^(1/3)*(x + (-1 - k)*x^2 + k*x^3)^(1/3))])/(2^(2/3)*(-1 + k)^(1/3)) + ((-1)^(2/3)*Log[-1 + k*x + (-1)^(1/3)*2^(2/3)*(-1 + k)^(1/3)*(x + (-1 - k)*x^2 + k*x^3)^(1/3)])/(2^(2/3)*(-1 + k)^(1/3)) - ((-1)^(2/3)*Log[1 - 2*k*x + k^2*x^2 + ((-1)^(1/3)*2^(2/3)*(-1 + k)^(1/3) - (-1)^(1/3)*2^(2/3)*(-1 + k)^(1/3)*k*x)*(x + (-1 - k)*x^2 + k*x^3)^(1/3) + 2*(-1)^(2/3)*2^(1/3)*(-1 + k)^(2/3)*(x + (-1 - k)*x^2 + k*x^3)^(2/3)])/(2*2^(2/3)*(-1 + k)^(1/3))","A",1
46,0,0,493,8.4048878,"\int \frac{a+b x+c x^2}{\left(1-x+x^2\right) \sqrt[3]{1-x^3}} \, dx","IntegrateAlgebraic[(a + b*x + c*x^2)/((1 - x + x^2)*(1 - x^3)^(1/3)),x]","\int \frac{a+b x+c x^2}{\left(1-x+x^2\right) \sqrt[3]{1-x^3}} \, dx","\frac{(a+b) \log \left(\frac{2^{2/3} (1-x)^2}{\left(1-x^3\right)^{2/3}}-\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{6 \sqrt[3]{2}}-\frac{(a+b) \log \left(\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{3 \sqrt[3]{2}}-\frac{(a+b) \log \left(2^{2/3} \sqrt[3]{1-x^3}+x-1\right)}{4 \sqrt[3]{2}}+\frac{(a+b) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}+\frac{(a+b) \tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1}{\sqrt{3}}\right)}{2 \sqrt[3]{2} \sqrt{3}}+\frac{(a+b) \log \left((1-x) (x+1)^2\right)}{12 \sqrt[3]{2}}-\frac{(a-c) \log \left(x^3+1\right)}{6 \sqrt[3]{2}}+\frac{(a-c) \log \left(-\sqrt[3]{1-x^3}-\sqrt[3]{2} x\right)}{2 \sqrt[3]{2}}-\frac{(a-c) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}-\frac{(b+c) \log \left(x^3+1\right)}{6 \sqrt[3]{2}}+\frac{(b+c) \log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{2 \sqrt[3]{2}}+\frac{(b+c) \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}+\frac{1}{2} c \log \left(\sqrt[3]{1-x^3}+x\right)-\frac{c \tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt{3}}",1,"Could not integrate","F",-1
47,1,189,407,0.9421575,"\int \frac{1}{(3-2 x)^{11/2} \left(1+x+2 x^2\right)^5} \, dx","IntegrateAlgebraic[1/((3 - 2*x)^(11/2)*(1 + x + 2*x^2)^5),x]","-\frac{5 \sqrt{149046503977+12577271771 i \sqrt{7}} \tan ^{-1}\left(\sqrt{-\frac{1}{4}-\frac{i}{4 \sqrt{7}}} \sqrt{3-2 x}\right)}{3373232128}-\frac{5 \sqrt{149046503977-12577271771 i \sqrt{7}} \tan ^{-1}\left(\sqrt{-\frac{1}{4}+\frac{i}{4 \sqrt{7}}} \sqrt{3-2 x}\right)}{3373232128}+\frac{\sqrt{3-2 x} \left(88070400 x^{12}-677249280 x^{11}+1873554048 x^{10}-2443779648 x^9+2343370048 x^8-3106712560 x^7+2888625656 x^6-1470758860 x^5+1627773523 x^4-1073855156 x^3+135202154 x^2-429812744 x+40289347\right)}{2168506368 (2 x-3)^5 \left(2 x^2+x+1\right)^4}","\frac{x}{28 (3-2 x)^{9/2} \left(2 x^2+x+1\right)^4}+\frac{5 (4377 x+3049)}{153664 (3-2 x)^{9/2} \left(2 x^2+x+1\right)}+\frac{3049 x+1387}{32928 (3-2 x)^{9/2} \left(2 x^2+x+1\right)^2}+\frac{73 x+23}{1176 (3-2 x)^{9/2} \left(2 x^2+x+1\right)^3}-\frac{38225}{240945152 \sqrt{3-2 x}}-\frac{141045}{120472576 (3-2 x)^{3/2}}-\frac{38491}{8605184 (3-2 x)^{5/2}}-\frac{462025}{30118144 (3-2 x)^{7/2}}-\frac{19255}{395136 (3-2 x)^{9/2}}+\frac{5 \sqrt{\frac{1}{2} \left(40815066112 \sqrt{14}-149046503977\right)} \log \left(-2 x-\sqrt{7+2 \sqrt{14}} \sqrt{3-2 x}+\sqrt{14}+3\right)}{6746464256}-\frac{5 \sqrt{\frac{1}{2} \left(40815066112 \sqrt{14}-149046503977\right)} \log \left(-2 x+\sqrt{7+2 \sqrt{14}} \sqrt{3-2 x}+\sqrt{14}+3\right)}{6746464256}+\frac{5 \sqrt{\frac{1}{2} \left(149046503977+40815066112 \sqrt{14}\right)} \tan ^{-1}\left(\frac{\sqrt{7+2 \sqrt{14}}-2 \sqrt{3-2 x}}{\sqrt{2 \sqrt{14}-7}}\right)}{3373232128}-\frac{5 \sqrt{\frac{1}{2} \left(149046503977+40815066112 \sqrt{14}\right)} \tan ^{-1}\left(\frac{2 \sqrt{3-2 x}+\sqrt{7+2 \sqrt{14}}}{\sqrt{2 \sqrt{14}-7}}\right)}{3373232128}",1,"(Sqrt[3 - 2*x]*(40289347 - 429812744*x + 135202154*x^2 - 1073855156*x^3 + 1627773523*x^4 - 1470758860*x^5 + 2888625656*x^6 - 3106712560*x^7 + 2343370048*x^8 - 2443779648*x^9 + 1873554048*x^10 - 677249280*x^11 + 88070400*x^12))/(2168506368*(-3 + 2*x)^5*(1 + x + 2*x^2)^4) - (5*Sqrt[149046503977 + (12577271771*I)*Sqrt[7]]*ArcTan[Sqrt[-1/4 - (I/4)/Sqrt[7]]*Sqrt[3 - 2*x]])/3373232128 - (5*Sqrt[149046503977 - (12577271771*I)*Sqrt[7]]*ArcTan[Sqrt[-1/4 + (I/4)/Sqrt[7]]*Sqrt[3 - 2*x]])/3373232128","C",0
48,1,264,648,1.6278476,"\int \frac{1}{(3-2 x)^{21/2} \left(1+x+2 x^2\right)^{10}} \, dx","IntegrateAlgebraic[1/((3 - 2*x)^(21/2)*(1 + x + 2*x^2)^10),x]","-\frac{11275 \sqrt{2293002953699236822393+30540258843957888971 i \sqrt{7}} \tan ^{-1}\left(\sqrt{-\frac{1}{4}-\frac{i}{4 \sqrt{7}}} \sqrt{3-2 x}\right)}{318603459702399434752}-\frac{11275 \sqrt{2293002953699236822393-30540258843957888971 i \sqrt{7}} \tan ^{-1}\left(\sqrt{-\frac{1}{4}+\frac{i}{4 \sqrt{7}}} \sqrt{3-2 x}\right)}{318603459702399434752}+\frac{\sqrt{3-2 x} \left(240031204937714427494400 x^{27}-2621948941596237063782400 x^{26}+12365045055896811105484800 x^{25}-33969890064381284111155200 x^{24}+65360120291258796757811200 x^{23}-106701725825102321939251200 x^{22}+162290307223249502039654400 x^{21}-216634228326470609547509760 x^{20}+253788172995391086570485760 x^{19}-287279159180291305208156160 x^{18}+304010591010966811155955200 x^{17}-282644664539994827031006720 x^{16}+258819256815163249845447936 x^{15}-229408132984166521977166336 x^{14}+172649692294614969274168896 x^{13}-133312541377246386115890240 x^{12}+102031573634317834547976132 x^{11}-59791102681494117572149176 x^{10}+41613884937255303086792337 x^9-27246604251076689552043953 x^8+10718131725916893151555068 x^7-8685973988079840377705700 x^6+3673303058277822225386926 x^5-809990362095044210054958 x^4+1362587089603925431664856 x^3+111926768697602999806116 x^2+205702452014540322797289 x-4884417100172357749737\right)}{860024524686669788479488 (2 x-3)^{10} \left(2 x^2+x+1\right)^9}","\frac{11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left(2 x^2+x+1\right)}+\frac{451 (14627273 x+28962039)}{283351498752 (3-2 x)^{19/2} \left(2 x^2+x+1\right)^2}+\frac{451 (998691 x+811091)}{10119696384 (3-2 x)^{19/2} \left(2 x^2+x+1\right)^3}+\frac{41 (5677637 x+3436375)}{5059848192 (3-2 x)^{19/2} \left(2 x^2+x+1\right)^4}+\frac{41 (92875 x+47471)}{90354432 (3-2 x)^{19/2} \left(2 x^2+x+1\right)^5}+\frac{5 (47471 x+21409)}{6453888 (3-2 x)^{19/2} \left(2 x^2+x+1\right)^6}+\frac{21409 x+8477}{691488 (3-2 x)^{19/2} \left(2 x^2+x+1\right)^7}+\frac{173 x+53}{7056 (3-2 x)^{19/2} \left(2 x^2+x+1\right)^8}+\frac{x}{63 (3-2 x)^{19/2} \left(2 x^2+x+1\right)^9}-\frac{24229218097975}{22757389978742816768 \sqrt{3-2 x}}-\frac{46601678385075}{11378694989371408384 (3-2 x)^{3/2}}-\frac{11557581705725}{812763927812243456 (3-2 x)^{5/2}}-\frac{132355162272575}{2844673747342852096 (3-2 x)^{7/2}}-\frac{37283626871975}{261245548225363968 (3-2 x)^{9/2}}-\frac{5846828446875}{14513641568075776 (3-2 x)^{11/2}}-\frac{13515743021825}{13476952884641792 (3-2 x)^{13/2}}-\frac{3029508823715}{1555033025150976 (3-2 x)^{15/2}}-\frac{815900548375}{629418129227776 (3-2 x)^{17/2}}+\frac{4718120139975}{351733660450816 (3-2 x)^{19/2}}+\frac{11275 \left(9756589235-2148932869 \sqrt{14}\right) \sqrt{\frac{1}{2} \left(2 \sqrt{14}-7\right)} \log \left(-2 x-\sqrt{7+2 \sqrt{14}} \sqrt{3-2 x}+\sqrt{14}+3\right)}{637206919404798869504}-\frac{11275 \left(9756589235-2148932869 \sqrt{14}\right) \sqrt{\frac{1}{2} \left(2 \sqrt{14}-7\right)} \log \left(-2 x+\sqrt{7+2 \sqrt{14}} \sqrt{3-2 x}+\sqrt{14}+3\right)}{637206919404798869504}+\frac{11275 \sqrt{\frac{1}{2} \left(7+2 \sqrt{14}\right)} \left(9756589235+2148932869 \sqrt{14}\right) \tan ^{-1}\left(\frac{\sqrt{7+2 \sqrt{14}}-2 \sqrt{3-2 x}}{\sqrt{2 \sqrt{14}-7}}\right)}{318603459702399434752}-\frac{11275 \sqrt{\frac{1}{2} \left(7+2 \sqrt{14}\right)} \left(9756589235+2148932869 \sqrt{14}\right) \tan ^{-1}\left(\frac{2 \sqrt{3-2 x}+\sqrt{7+2 \sqrt{14}}}{\sqrt{2 \sqrt{14}-7}}\right)}{318603459702399434752}",1,"(Sqrt[3 - 2*x]*(-4884417100172357749737 + 205702452014540322797289*x + 111926768697602999806116*x^2 + 1362587089603925431664856*x^3 - 809990362095044210054958*x^4 + 3673303058277822225386926*x^5 - 8685973988079840377705700*x^6 + 10718131725916893151555068*x^7 - 27246604251076689552043953*x^8 + 41613884937255303086792337*x^9 - 59791102681494117572149176*x^10 + 102031573634317834547976132*x^11 - 133312541377246386115890240*x^12 + 172649692294614969274168896*x^13 - 229408132984166521977166336*x^14 + 258819256815163249845447936*x^15 - 282644664539994827031006720*x^16 + 304010591010966811155955200*x^17 - 287279159180291305208156160*x^18 + 253788172995391086570485760*x^19 - 216634228326470609547509760*x^20 + 162290307223249502039654400*x^21 - 106701725825102321939251200*x^22 + 65360120291258796757811200*x^23 - 33969890064381284111155200*x^24 + 12365045055896811105484800*x^25 - 2621948941596237063782400*x^26 + 240031204937714427494400*x^27))/(860024524686669788479488*(-3 + 2*x)^10*(1 + x + 2*x^2)^9) - (11275*Sqrt[2293002953699236822393 + (30540258843957888971*I)*Sqrt[7]]*ArcTan[Sqrt[-1/4 - (I/4)/Sqrt[7]]*Sqrt[3 - 2*x]])/318603459702399434752 - (11275*Sqrt[2293002953699236822393 - (30540258843957888971*I)*Sqrt[7]]*ArcTan[Sqrt[-1/4 + (I/4)/Sqrt[7]]*Sqrt[3 - 2*x]])/318603459702399434752","C",0
49,1,414,1058,4.9052555,"\int \frac{1}{(3-2 x)^{41/2} \left(1+x+2 x^2\right)^{20}} \, dx","IntegrateAlgebraic[1/((3 - 2*x)^(41/2)*(1 + x + 2*x^2)^20),x]","-\frac{115 \sqrt{26470388201611752216024276905374076093636415173409188826601+8174286676615564254062463385463197516747256637092086555 i \sqrt{7}} \tan ^{-1}\left(\sqrt{-\frac{1}{4}-\frac{i}{4 \sqrt{7}}} \sqrt{3-2 x}\right)}{812065316274707684133031842207432842412032}-\frac{115 \sqrt{26470388201611752216024276905374076093636415173409188826601-8174286676615564254062463385463197516747256637092086555 i \sqrt{7}} \tan ^{-1}\left(\sqrt{-\frac{1}{4}+\frac{i}{4 \sqrt{7}}} \sqrt{3-2 x}\right)}{812065316274707684133031842207432842412032}+\frac{\sqrt{3-2 x} \left(52852595088141665875251392948545451373376947250790400 x^{57}-1098967795066273315162856093421299059440183747910041600 x^{56}+10607209489316853390896228799650834948444579920210821120 x^{55}-63571167550234753994014104400074223346580880315719352320 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\left(30297118912219360725028693061+8061110911143276053983022787 \sqrt{14}\right) \tan ^{-1}\left(\frac{\sqrt{7+2 \sqrt{14}}-2 \sqrt{3-2 x}}{\sqrt{-7+2 \sqrt{14}}}\right)}{812065316274707684133031842207432842412032}-\frac{115 \sqrt{\frac{1}{2} \left(7+2 \sqrt{14}\right)} \left(30297118912219360725028693061+8061110911143276053983022787 \sqrt{14}\right) \tan ^{-1}\left(\frac{2 \sqrt{3-2 x}+\sqrt{7+2 \sqrt{14}}}{\sqrt{-7+2 \sqrt{14}}}\right)}{812065316274707684133031842207432842412032}+\frac{115 \left(30297118912219360725028693061-8061110911143276053983022787 \sqrt{14}\right) \sqrt{\frac{1}{2} \left(-7+2 \sqrt{14}\right)} \log \left(-2 x-\sqrt{7+2 \sqrt{14}} \sqrt{3-2 x}+\sqrt{14}+3\right)}{1624130632549415368266063684414865684824064}-\frac{115 \left(30297118912219360725028693061-8061110911143276053983022787 \sqrt{14}\right) \sqrt{\frac{1}{2} \left(-7+2 \sqrt{14}\right)} \log \left(-2 x+\sqrt{7+2 \sqrt{14}} \sqrt{3-2 x}+\sqrt{14}+3\right)}{1624130632549415368266063684414865684824064}-\frac{927027754781476746208047620505}{58004665448193406009502274443388060172288 \sqrt{3-2 x}}+\frac{115 (965934812839019490346107 x+28561347681225760814815)}{195831528126838026966925312 (3-2 x)^{39/2} \left(2 x^2+x+1\right)}-\frac{4986681479187781853417316522775}{87006998172290109014253411665082090258432 (3-2 x)^{3/2}}-\frac{115 (88411609113007981044643-5712269536245152162963 x)}{125891696652967303050166272 (3-2 x)^{39/2} \left(2 x^2+x+1\right)^2}-\frac{405965372440630510720926890227}{2071595194578335928910795515835287863296 (3-2 x)^{5/2}}-\frac{115 (30673415406553789342019 x+26513224428169016478843)}{76434244396444433994743808 (3-2 x)^{39/2} \left(2 x^2+x+1\right)^3}-\frac{4611053278117143010907562317585}{7250583181024175751187784305423507521536 (3-2 x)^{7/2}}-\frac{23 (27513723463194262383705 x+10426142448623187379187)}{20018492580021161284337664 (3-2 x)^{39/2} \left(2 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x^2+x+1\right)^{14}}+\frac{34911619993974714062172751985}{124667917457770102671360389021696 (3-2 x)^{29/2}}+\frac{429411497 x+184959785}{25015269888 (3-2 x)^{39/2} \left(2 x^2+x+1\right)^{15}}+\frac{47657515074514118796095929535}{66632852434325399703658138959872 (3-2 x)^{31/2}}+\frac{5 (1831285 x+751303)}{595601664 (3-2 x)^{39/2} \left(2 x^2+x+1\right)^{16}}+\frac{2124315846756567455653862925}{1688851098565851144562763890688 (3-2 x)^{33/2}}+\frac{107329 x+40657}{7976808 (3-2 x)^{39/2} \left(2 x^2+x+1\right)^{17}}-\frac{304688229262620222736480811}{537361713180043545997243056128 (3-2 x)^{35/2}}+\frac{373 x+113}{33516 (3-2 x)^{39/2} \left(2 x^2+x+1\right)^{18}}-\frac{3948194343291401740321996415}{202881463139404195937734623232 (3-2 x)^{37/2}}+\frac{x}{133 (3-2 x)^{39/2} \left(2 x^2+x+1\right)^{19}}-\frac{13056959628363355534285785425}{106924014357253562723941220352 (3-2 x)^{39/2}}",1,"(Sqrt[3 - 2*x]*(142488114863139797187698618852924003909944526763627 + 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1674381797717888336240082619136481913141447194739865411447*x^17 - 2980031288821257171626437270731358463613690258748044875631*x^18 + 4826566229889649998651082918574281667310767186073269174097*x^19 - 8152620728427620176711248504306621849196751343566681977176*x^20 + 12908687419060491715559483506875260114803121732707547895900*x^21 - 19714530664252367893694794632442175393727220660187813722224*x^22 + 30015307199183492418426115232917702261364741866517547318384*x^23 - 43499929568624033785147670292431465440609985987022819309056*x^24 + 61490717519886743793977904289150681209548071542812762022208*x^25 - 85196415623233396170197188512975026308393874494506050046976*x^26 + 113537974641311616719165089124033846938888435216187251000320*x^27 - 147575029055999994839406287648843693901181887610273533861888*x^28 + 186886111688985929098566117844019918629526116042561389293568*x^29 - 228671395190671097020869564500875726797589816165421143277568*x^30 + 272316634459399870536836933035003973818695505518285221314560*x^31 - 315079971582181801347294250924732868231627903206246048727040*x^32 + 352587259766861713156680120052199648639816399610100338851840*x^33 - 382995579816527529641915302665409995875084862589265975050240*x^34 + 403232407441991792232348027512081003879684846626157308542976*x^35 - 410091833382540310980618746942733242840005307528588546801664*x^36 + 403492607520849908998883514652547403915763268860927101370368*x^37 - 383554582100586246362167645670892818138191443491318786949120*x^38 + 351087306412578660000108019219405351826065473130972707815424*x^39 - 309440537906112411118620445892815079684504011563969741324288*x^40 + 262207325852831458520928585736224018299226513096563188826112*x^41 - 212762579742469905820226823821664465308559175943457404354560*x^42 + 165018067996212231343716673011244333927488403644331103092736*x^43 - 122063250700174316553425220949165095613494323059071276548096*x^44 + 85640241664030935730039797515882941408552267458802253561856*x^45 - 56714708988068520613101313974891982297778777108353803878400*x^46 + 35302794239198802111604239039735944127462536376667298856960*x^47 - 20476557691160001147471559886237056465998405634456352194560*x^48 + 10935442488009047264366448391275604368754310437883074314240*x^49 - 5316604047160267290459856323292969345744886768161070776320*x^50 + 2313758021932448312425321649336084981029506072497608458240*x^51 - 870946973219521114804962921504691759517713269107195904000*x^52 + 268751102085050752152483783816672599931031121283482910720*x^53 - 63571167550234753994014104400074223346580880315719352320*x^54 + 10607209489316853390896228799650834948444579920210821120*x^55 - 1098967795066273315162856093421299059440183747910041600*x^56 + 52852595088141665875251392948545451373376947250790400*x^57))/(12030859925449512719117560803432677643538374233948160*(-3 + 2*x)^20*(1 + x + 2*x^2)^19) - (115*Sqrt[26470388201611752216024276905374076093636415173409188826601 + (8174286676615564254062463385463197516747256637092086555*I)*Sqrt[7]]*ArcTan[Sqrt[-1/4 - (I/4)/Sqrt[7]]*Sqrt[3 - 2*x]])/812065316274707684133031842207432842412032 - (115*Sqrt[26470388201611752216024276905374076093636415173409188826601 - (8174286676615564254062463385463197516747256637092086555*I)*Sqrt[7]]*ArcTan[Sqrt[-1/4 + (I/4)/Sqrt[7]]*Sqrt[3 - 2*x]])/812065316274707684133031842207432842412032","C",0
50,1,241,378,0.9258322,"\int \frac{1}{\left(3-2 x+x^2\right)^{11/2} \left(1+x+2 x^2\right)^5} \, dx","IntegrateAlgebraic[1/((3 - 2*x + x^2)^(11/2)*(1 + x + 2*x^2)^5),x]","\frac{4596238560 x^{17}-38639385552 x^{16}+188603773872 x^{15}-606785954952 x^{14}+1459208021718 x^{13}-2679143870481 x^{12}+3999656132532 x^{11}-4915797913008 x^{10}+5380603084494 x^9-5134334619701 x^8+4591320676952 x^7-3359813871472 x^6+2503427226914 x^5-1409335257371 x^4+1002897791524 x^3-266966654968 x^2+261702502714 x-53205422447}{1234800000000 \left(x^2-2 x+3\right)^{9/2} \left(2 x^2+x+1\right)^4}-\frac{\text{RootSum}\left[\text{$\#$1}^4-5 \text{$\#$1}^3+4 \text{$\#$1}^2+10 \text{$\#$1}+4\&,\frac{44900803 \text{$\#$1}^2 \log \left(-\text{$\#$1}+\sqrt{x^2-2 x+3}-x+1\right)+42834985 \text{$\#$1} \log \left(-\text{$\#$1}+\sqrt{x^2-2 x+3}-x+1\right)-89801606 \log \left(-\text{$\#$1}+\sqrt{x^2-2 x+3}-x+1\right)}{4 \text{$\#$1}^3-15 \text{$\#$1}^2+8 \text{$\#$1}+10}\&\right]}{68600000000}","-\frac{63043297-29625922 x}{41160000000 \left(x^2-2 x+3\right)^{3/2}}-\frac{31 (7434109-3088870 x)}{411600000000 \sqrt{x^2-2 x+3}}+\frac{3 (8233 x+8822)}{343000 \left(x^2-2 x+3\right)^{9/2} \left(2 x^2+x+1\right)}+\frac{8878 x+5485}{117600 \left(x^2-2 x+3\right)^{9/2} \left(2 x^2+x+1\right)^2}-\frac{30316369-15043110 x}{6860000000 \left(x^2-2 x+3\right)^{5/2}}+\frac{67 x+28}{1050 \left(x^2-2 x+3\right)^{9/2} \left(2 x^2+x+1\right)^3}-\frac{4878869-2578034 x}{411600000 \left(x^2-2 x+3\right)^{7/2}}-\frac{1-10 x}{280 \left(x^2-2 x+3\right)^{9/2} \left(2 x^2+x+1\right)^4}-\frac{3450497-2004270 x}{123480000 \left(x^2-2 x+3\right)^{9/2}}+\frac{\sqrt{\frac{1}{70} \left(151363871237318045+110320475741093888 \sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{5}{7 \left(151363871237318045+110320475741093888 \sqrt{2}\right)}} \left(\left(932587773+620347970 \sqrt{2}\right) x+312239803 \sqrt{2}+308108167\right)}{\sqrt{x^2-2 x+3}}\right)}{137200000000}-\frac{\sqrt{\frac{1}{70} \left(110320475741093888 \sqrt{2}-151363871237318045\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{5}{7 \left(110320475741093888 \sqrt{2}-151363871237318045\right)}} \left(\left(932587773-620347970 \sqrt{2}\right) x-312239803 \sqrt{2}+308108167\right)}{\sqrt{x^2-2 x+3}}\right)}{137200000000}",1,"(-53205422447 + 261702502714*x - 266966654968*x^2 + 1002897791524*x^3 - 1409335257371*x^4 + 2503427226914*x^5 - 3359813871472*x^6 + 4591320676952*x^7 - 5134334619701*x^8 + 5380603084494*x^9 - 4915797913008*x^10 + 3999656132532*x^11 - 2679143870481*x^12 + 1459208021718*x^13 - 606785954952*x^14 + 188603773872*x^15 - 38639385552*x^16 + 4596238560*x^17)/(1234800000000*(3 - 2*x + x^2)^(9/2)*(1 + x + 2*x^2)^4) - RootSum[4 + 10*#1 + 4*#1^2 - 5*#1^3 + #1^4 & , (-89801606*Log[1 - x + Sqrt[3 - 2*x + x^2] - #1] + 42834985*Log[1 - x + Sqrt[3 - 2*x + x^2] - #1]*#1 + 44900803*Log[1 - x + Sqrt[3 - 2*x + x^2] - #1]*#1^2)/(10 + 8*#1 - 15*#1^2 + 4*#1^3) & ]/68600000000","C",1
51,1,341,638,9.7825741,"\int \frac{1}{\left(3-2 x+x^2\right)^{21/2} \left(1+x+2 x^2\right)^{10}} \, dx","IntegrateAlgebraic[1/((3 - 2*x + x^2)^(21/2)*(1 + x + 2*x^2)^10),x]","\frac{3372249001933422237824271360 x^{37}-53502205399640031394796147712 x^{36}+469149394082989701729494575872 x^{35}-2847499220912667753383035299072 x^{34}+13254252261100740556512388253568 x^{33}-49770080058525077628064229832576 x^{32}+156010734937008739388220889457760 x^{31}-417516398850754397130111919794336 x^{30}+971538171913365251873706873353652 x^{29}-1993653213575521837888601204380228 x^{28}+3655553471852957606257345414140031 x^{27}-6054769996581738503753686155104785 x^{26}+9155494158513869230271529746307221 x^{25}-12740106677685048178693605103009787 x^{24}+16442770202470076313197215936814318 x^{23}-19772569734288744720189854470201506 x^{22}+22286437617621909921609206629636086 x^{21}-23584986647560742443188031208946882 x^{20}+23579397211179175240196614296051673 x^{19}-22218747553941794885903840542461607 x^{18}+19912295454080246583636391613811979 x^{17}-16801760806053390242995145349148613 x^{16}+13613407965006475288139078599341572 x^{15}-10279305650733178669223634020962076 x^{14}+7606288378303449524327938977040824 x^{13}-5069838234992751929471190426115248 x^{12}+3507425970596197680016078213030977 x^{11}-1974814483061344405275851094534735 x^{10}+1357002388430055881833293557852283 x^9-566969010759169461615951049236597 x^8+458426000073846882432457044306894 x^7-94704557665253489332536549937026 x^6+135183920426913231415208872303230 x^5-1023095318901774638403186272874 x^4+29398041153524973343917601742151 x^3+1933957195570062708781629134823 x^2+3397462350398947848063583843461 x-80038710871555316861345369643}{13420027826805600000000000000000 \left(x^2-2 x+3\right)^{19/2} \left(2 x^2+x+1\right)^9}-\frac{\text{RootSum}\left[\text{$\#$1}^4-5 \text{$\#$1}^3+4 \text{$\#$1}^2+10 \text{$\#$1}+4\&,\frac{21634177831191924841 \text{$\#$1}^2 \log \left(-\text{$\#$1}+\sqrt{x^2-2 x+3}-x+1\right)+62135959399493560795 \text{$\#$1} \log \left(-\text{$\#$1}+\sqrt{x^2-2 x+3}-x+1\right)-43268355662383849682 \log \left(-\text{$\#$1}+\sqrt{x^2-2 x+3}-x+1\right)}{4 \text{$\#$1}^3-15 \text{$\#$1}^2+8 \text{$\#$1}+10}\&\right]}{16141442800000000000000000}","-\frac{12105495874518671061833-5117656435043679338190 x}{10427372048800000000000000000 \sqrt{x^2-2 x+3}}-\frac{146548895467025 x+37857197792117}{2421216420000000 \left(x^2-2 x+3\right)^{19/2} \left(2 x^2+x+1\right)}-\frac{4179039782398459850819-1886993445589652402694 x}{1042737204880000000000000000 \left(x^2-2 x+3\right)^{3/2}}+\frac{1384103301166 x+5488221294349}{276710448000000 \left(x^2-2 x+3\right)^{19/2} \left(2 x^2+x+1\right)^2}-\frac{6551405511565449301689-3127298559983309301910 x}{521368602440000000000000000 \left(x^2-2 x+3\right)^{5/2}}+\frac{310705340015 x+277010166219}{12353145000000 \left(x^2-2 x+3\right)^{19/2} \left(2 x^2+x+1\right)^3}-\frac{1117646664729238460189-568839749685437871554 x}{31282116146400000000000000 \left(x^2-2 x+3\right)^{7/2}}+\frac{911061463974 x+592729157441}{29647548000000 \left(x^2-2 x+3\right)^{19/2} \left(2 x^2+x+1\right)^4}-\frac{838519439380295335657-466189390555853643870 x}{9384634843920000000000000 \left(x^2-2 x+3\right)^{9/2}}+\frac{813432205 x+447940041}{26471025000 \left(x^2-2 x+3\right)^{19/2} \left(2 x^2+x+1\right)^5}-\frac{3 (69053268515296359011-44840736195018286006 x)}{1147010925368000000000000 \left(x^2-2 x+3\right)^{11/2}}+\frac{17459234 x+8837931}{605052000 \left(x^2-2 x+3\right)^{19/2} \left(2 x^2+x+1\right)^6}-\frac{11 (7502325106308201089-7813986379726516886 x)}{406667509903200000000000 \left(x^2-2 x+3\right)^{13/2}}+\frac{29371 x+14453}{1080450 \left(x^2-2 x+3\right)^{19/2} \left(2 x^2+x+1\right)^7}+\frac{1942164996204584234 x+7851758375483333511}{15641058073200000000000 \left(x^2-2 x+3\right)^{15/2}}+\frac{2218 x+887}{88200 \left(x^2-2 x+3\right)^{19/2} \left(2 x^2+x+1\right)^8}+\frac{476849951294984711-125181871472148210 x}{104273720488000000000 \left(x^2-2 x+3\right)^{17/2}}-\frac{1-10 x}{630 \left(x^2-2 x+3\right)^{19/2} \left(2 x^2+x+1\right)^9}+\frac{37358055634422583-14024622879097678 x}{1840124479200000000 \left(x^2-2 x+3\right)^{19/2}}+\frac{\sqrt{\frac{1}{70} \left(81042225921274689605478944797800854846405+57305922523001707126026363878666500308992 \sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{5}{7 \left(81042225921274689605478944797800854846405+57305922523001707126026363878666500308992 \sqrt{2}\right)}} \left(\left(656826642296538601431+464885615909893491590 \sqrt{2}\right) x+191941026386645109841 \sqrt{2}+272944589523248381749\right)}{\sqrt{x^2-2 x+3}}\right)}{32282885600000000000000000}-\frac{\sqrt{\frac{1}{70} \left(57305922523001707126026363878666500308992 \sqrt{2}-81042225921274689605478944797800854846405\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{5}{7 \left(57305922523001707126026363878666500308992 \sqrt{2}-81042225921274689605478944797800854846405\right)}} \left(\left(656826642296538601431-464885615909893491590 \sqrt{2}\right) x-191941026386645109841 \sqrt{2}+272944589523248381749\right)}{\sqrt{x^2-2 x+3}}\right)}{32282885600000000000000000}",1,"(-80038710871555316861345369643 + 3397462350398947848063583843461*x + 1933957195570062708781629134823*x^2 + 29398041153524973343917601742151*x^3 - 1023095318901774638403186272874*x^4 + 135183920426913231415208872303230*x^5 - 94704557665253489332536549937026*x^6 + 458426000073846882432457044306894*x^7 - 566969010759169461615951049236597*x^8 + 1357002388430055881833293557852283*x^9 - 1974814483061344405275851094534735*x^10 + 3507425970596197680016078213030977*x^11 - 5069838234992751929471190426115248*x^12 + 7606288378303449524327938977040824*x^13 - 10279305650733178669223634020962076*x^14 + 13613407965006475288139078599341572*x^15 - 16801760806053390242995145349148613*x^16 + 19912295454080246583636391613811979*x^17 - 22218747553941794885903840542461607*x^18 + 23579397211179175240196614296051673*x^19 - 23584986647560742443188031208946882*x^20 + 22286437617621909921609206629636086*x^21 - 19772569734288744720189854470201506*x^22 + 16442770202470076313197215936814318*x^23 - 12740106677685048178693605103009787*x^24 + 9155494158513869230271529746307221*x^25 - 6054769996581738503753686155104785*x^26 + 3655553471852957606257345414140031*x^27 - 1993653213575521837888601204380228*x^28 + 971538171913365251873706873353652*x^29 - 417516398850754397130111919794336*x^30 + 156010734937008739388220889457760*x^31 - 49770080058525077628064229832576*x^32 + 13254252261100740556512388253568*x^33 - 2847499220912667753383035299072*x^34 + 469149394082989701729494575872*x^35 - 53502205399640031394796147712*x^36 + 3372249001933422237824271360*x^37)/(13420027826805600000000000000000*(3 - 2*x + x^2)^(19/2)*(1 + x + 2*x^2)^9) - RootSum[4 + 10*#1 + 4*#1^2 - 5*#1^3 + #1^4 & , (-43268355662383849682*Log[1 - x + Sqrt[3 - 2*x + x^2] - #1] + 62135959399493560795*Log[1 - x + Sqrt[3 - 2*x + x^2] - #1]*#1 + 21634177831191924841*Log[1 - x + Sqrt[3 - 2*x + x^2] - #1]*#1^2)/(10 + 8*#1 - 15*#1^2 + 4*#1^3) & ]/16141442800000000000000000","C",1
52,1,73,66,1.2168325,"\int \frac{-a-\sqrt{1+a^2}+x}{\left(-a+\sqrt{1+a^2}+x\right) \sqrt{(-a+x) \left(1+x^2\right)}} \, dx","IntegrateAlgebraic[(-a - Sqrt[1 + a^2] + x)/((-a + Sqrt[1 + a^2] + x)*Sqrt[(-a + x)*(1 + x^2)]),x]","-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{\sqrt{a^2+1}-a} \sqrt{-a x^2-a+x^3+x}}{x^2+1}\right)}{\sqrt{\sqrt{a^2+1}-a}}","-\sqrt{2} \sqrt{\sqrt{a^2+1}+a} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{\sqrt{a^2+1}-a} (x-a)}{\sqrt{\left(x^2+1\right) (x-a)}}\right)",1,"-((Sqrt[2]*ArcTan[(Sqrt[2]*Sqrt[-a + Sqrt[1 + a^2]]*Sqrt[-a + x - a*x^2 + x^3])/(1 + x^2)])/Sqrt[-a + Sqrt[1 + a^2]])","A",1
53,0,0,198,5.5591848,"\int \frac{a+b x}{\sqrt[3]{1-x^2} \left(3+x^2\right)} \, dx","IntegrateAlgebraic[(a + b*x)/((1 - x^2)^(1/3)*(3 + x^2)),x]","\int \frac{a+b x}{\sqrt[3]{1-x^2} \left(3+x^2\right)} \, dx","\frac{a \tan ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} \sqrt[3]{1-x^2}\right)}{x}\right)}{2\ 2^{2/3} \sqrt{3}}+\frac{a \tanh ^{-1}\left(\frac{x}{\sqrt[3]{2} \sqrt[3]{1-x^2}+1}\right)}{2\ 2^{2/3}}+\frac{a \tan ^{-1}\left(\frac{\sqrt{3}}{x}\right)}{2\ 2^{2/3} \sqrt{3}}-\frac{a \tanh ^{-1}(x)}{6\ 2^{2/3}}-\frac{b \log \left(x^2+3\right)}{4\ 2^{2/3}}+\frac{3 b \log \left(2^{2/3}-\sqrt[3]{1-x^2}\right)}{4\ 2^{2/3}}+\frac{\sqrt{3} b \tan ^{-1}\left(\frac{\sqrt[3]{2-2 x^2}+1}{\sqrt{3}}\right)}{2\ 2^{2/3}}",1,"Could not integrate","F",-1
54,0,0,198,11.4098369,"\int \frac{a+b x}{\left(3-x^2\right) \sqrt[3]{1+x^2}} \, dx","IntegrateAlgebraic[(a + b*x)/((3 - x^2)*(1 + x^2)^(1/3)),x]","\int \frac{a+b x}{\left(3-x^2\right) \sqrt[3]{1+x^2}} \, dx","\frac{a \tan ^{-1}\left(\frac{x}{\sqrt[3]{2} \sqrt[3]{x^2+1}+1}\right)}{2\ 2^{2/3}}-\frac{a \tanh ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} \sqrt[3]{x^2+1}\right)}{x}\right)}{2\ 2^{2/3} \sqrt{3}}-\frac{a \tan ^{-1}(x)}{6\ 2^{2/3}}-\frac{a \tanh ^{-1}\left(\frac{\sqrt{3}}{x}\right)}{2\ 2^{2/3} \sqrt{3}}+\frac{b \log \left(3-x^2\right)}{4\ 2^{2/3}}-\frac{3 b \log \left(2^{2/3}-\sqrt[3]{x^2+1}\right)}{4\ 2^{2/3}}-\frac{\sqrt{3} b \tan ^{-1}\left(\frac{\sqrt[3]{2} \sqrt[3]{x^2+1}+1}{\sqrt{3}}\right)}{2\ 2^{2/3}}",1,"Could not integrate","F",-1
55,1,198,97,0.2231651,"\int \frac{1}{x \sqrt[3]{4-6 x+3 x^2}} \, dx","IntegrateAlgebraic[1/(x*(4 - 6*x + 3*x^2)^(1/3)),x]","\frac{\log \left(2 \sqrt[3]{3 x^2-6 x+4}+2^{2/3} x-2\ 2^{2/3}\right)}{3\ 2^{2/3}}-\frac{\log \left(-\sqrt[3]{2} x^2-2 \left(3 x^2-6 x+4\right)^{2/3}+\left(2^{2/3} x-2\ 2^{2/3}\right) \sqrt[3]{3 x^2-6 x+4}+4 \sqrt[3]{2} x-4 \sqrt[3]{2}\right)}{6\ 2^{2/3}}-\frac{\tan ^{-1}\left(\frac{\frac{\sqrt[3]{3 x^2-6 x+4}}{\sqrt{3}}-\frac{2^{2/3} x}{\sqrt{3}}+\frac{2\ 2^{2/3}}{\sqrt{3}}}{\sqrt[3]{3 x^2-6 x+4}}\right)}{2^{2/3} \sqrt{3}}","\frac{\log \left(-3 \sqrt[3]{2} \sqrt[3]{3 x^2-6 x+4}-3 x+6\right)}{2\ 2^{2/3}}-\frac{\tan ^{-1}\left(\frac{2^{2/3} (2-x)}{\sqrt{3} \sqrt[3]{3 x^2-6 x+4}}+\frac{1}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3}}-\frac{\log (x)}{2\ 2^{2/3}}",1,"-(ArcTan[((2*2^(2/3))/Sqrt[3] - (2^(2/3)*x)/Sqrt[3] + (4 - 6*x + 3*x^2)^(1/3)/Sqrt[3])/(4 - 6*x + 3*x^2)^(1/3)]/(2^(2/3)*Sqrt[3])) + Log[-2*2^(2/3) + 2^(2/3)*x + 2*(4 - 6*x + 3*x^2)^(1/3)]/(3*2^(2/3)) - Log[-4*2^(1/3) + 4*2^(1/3)*x - 2^(1/3)*x^2 + (-2*2^(2/3) + 2^(2/3)*x)*(4 - 6*x + 3*x^2)^(1/3) - 2*(4 - 6*x + 3*x^2)^(2/3)]/(6*2^(2/3))","B",1
56,1,107,73,0.1288185,"\int x \sqrt[3]{1-x^3} \, dx","IntegrateAlgebraic[x*(1 - x^3)^(1/3),x]","-\frac{1}{9} \log \left(\sqrt[3]{1-x^3}+x\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{1-x^3}-x}\right)}{3 \sqrt{3}}+\frac{1}{3} \sqrt[3]{1-x^3} x^2+\frac{1}{18} \log \left(-\sqrt[3]{1-x^3} x+\left(1-x^3\right)^{2/3}+x^2\right)","-\frac{1}{6} \log \left(-\sqrt[3]{1-x^3}-x\right)-\frac{\tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{3 \sqrt{3}}+\frac{1}{3} \sqrt[3]{1-x^3} x^2",1,"(x^2*(1 - x^3)^(1/3))/3 + ArcTan[(Sqrt[3]*x)/(-x + 2*(1 - x^3)^(1/3))]/(3*Sqrt[3]) - Log[x + (1 - x^3)^(1/3)]/9 + Log[x^2 - x*(1 - x^3)^(1/3) + (1 - x^3)^(2/3)]/18","A",1
57,1,91,67,0.0703678,"\int \frac{\sqrt[3]{1-x^3}}{x} \, dx","IntegrateAlgebraic[(1 - x^3)^(1/3)/x,x]","\sqrt[3]{1-x^3}+\frac{1}{3} \log \left(\sqrt[3]{1-x^3}-1\right)-\frac{1}{6} \log \left(\left(1-x^3\right)^{2/3}+\sqrt[3]{1-x^3}+1\right)-\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{1-x^3}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3}}","\sqrt[3]{1-x^3}+\frac{1}{2} \log \left(1-\sqrt[3]{1-x^3}\right)-\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\log (x)}{2}",1,"(1 - x^3)^(1/3) - ArcTan[1/Sqrt[3] + (2*(1 - x^3)^(1/3))/Sqrt[3]]/Sqrt[3] + Log[-1 + (1 - x^3)^(1/3)]/3 - Log[1 + (1 - x^3)^(1/3) + (1 - x^3)^(2/3)]/6","A",1
58,0,0,482,4.9316954,"\int \frac{\sqrt[3]{1-x^3}}{1+x} \, dx","IntegrateAlgebraic[(1 - x^3)^(1/3)/(1 + x),x]","\int \frac{\sqrt[3]{1-x^3}}{1+x} \, dx","\sqrt[3]{1-x^3}-\frac{1}{3} \sqrt[3]{2} \log \left(x^3+1\right)+\frac{\log \left(2^{2/3}-\frac{1-x}{\sqrt[3]{1-x^3}}\right)}{3\ 2^{2/3}}-\frac{\log \left(\frac{2^{2/3} (1-x)^2}{\left(1-x^3\right)^{2/3}}-\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{3\ 2^{2/3}}+\frac{1}{3} \sqrt[3]{2} \log \left(\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)-\frac{\log \left(\frac{(1-x)^2}{\left(1-x^3\right)^{2/3}}+\frac{2^{2/3} (1-x)}{\sqrt[3]{1-x^3}}+2 \sqrt[3]{2}\right)}{6\ 2^{2/3}}+\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{2^{2/3}}-\frac{1}{2} \log \left(-\sqrt[3]{1-x^3}-x\right)+\frac{\log \left(-\sqrt[3]{1-x^3}-\sqrt[3]{2} x\right)}{2^{2/3}}+\frac{\sqrt[3]{2} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\sqrt[3]{2} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\sqrt[3]{2} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{\sqrt{3}}",1,"Could not integrate","F",-1
59,0,0,280,7.5749073,"\int \frac{\sqrt[3]{1-x^3}}{1-x+x^2} \, dx","IntegrateAlgebraic[(1 - x^3)^(1/3)/(1 - x + x^2),x]","\int \frac{\sqrt[3]{1-x^3}}{1-x+x^2} \, dx","\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{2\ 2^{2/3}}+\frac{3 \log \left(\sqrt[3]{1-x^3}-\sqrt[3]{2} (x-1)\right)}{2\ 2^{2/3}}+\frac{1}{2} \log \left(\sqrt[3]{1-x^3}+x\right)-\frac{\log \left(\sqrt[3]{1-x^3}+\sqrt[3]{2} x\right)}{2\ 2^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{2} (x-1)}{\sqrt[3]{1-x^3}}+1}{\sqrt{3}}\right)}{2^{2/3}}+\frac{\tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3}}-\frac{\log \left(-3 (x-1) \left(x^2-x+1\right)\right)}{2\ 2^{2/3}}",1,"Could not integrate","F",-1
60,0,0,232,4.8933493,"\int \frac{\sqrt[3]{1-x^3}}{2+x} \, dx","IntegrateAlgebraic[(1 - x^3)^(1/3)/(2 + x),x]","\int \frac{\sqrt[3]{1-x^3}}{2+x} \, dx","\frac{1}{2} x F_1\left(\frac{1}{3};-\frac{1}{3},1;\frac{4}{3};x^3,-\frac{x^3}{8}\right)+\sqrt[3]{1-x^3}-\frac{\log \left(x^3+8\right)}{\sqrt[3]{3}}+\frac{1}{2} 3^{2/3} \log \left(3^{2/3}-\sqrt[3]{1-x^3}\right)-\log \left(-\sqrt[3]{1-x^3}-x\right)+\frac{1}{2} 3^{2/3} \log \left(-\sqrt[3]{1-x^3}-\frac{1}{2} 3^{2/3} x\right)-\frac{2 \tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt{3}}+\sqrt[6]{3} \tan ^{-1}\left(\frac{1-\frac{3^{2/3} x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)-\sqrt[6]{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{1-x^3}}{3 \sqrt[6]{3}}+\frac{1}{\sqrt{3}}\right)",1,"Could not integrate","F",-1
61,0,0,168,5.8419532,"\int \frac{2+x}{\left(1+x+x^2\right) \sqrt[3]{2+x^3}} \, dx","IntegrateAlgebraic[(2 + x)/((1 + x + x^2)*(2 + x^3)^(1/3)),x]","\int \frac{2+x}{\left(1+x+x^2\right) \sqrt[3]{2+x^3}} \, dx","-\frac{x^2 F_1\left(\frac{2}{3};1,\frac{1}{3};\frac{5}{3};x^3,-\frac{x^3}{2}\right)}{2 \sqrt[3]{2}}+\frac{\log \left(1-x^3\right)}{6 \sqrt[3]{3}}+\frac{\log \left(\sqrt[3]{3}-\sqrt[3]{x^3+2}\right)}{2 \sqrt[3]{3}}-\frac{\log \left(\sqrt[3]{3} x-\sqrt[3]{x^3+2}\right)}{\sqrt[3]{3}}+\frac{2 \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{3} x}{\sqrt[3]{x^3+2}}+1}{\sqrt{3}}\right)}{3^{5/6}}+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{x^3+2}+\sqrt[3]{3}}{3^{5/6}}\right)}{3^{5/6}}",1,"Could not integrate","F",-1
62,1,25,25,0.0112172,"\int \frac{3-3 x+30 x^2+160 x^3}{9+24 x-12 x^2+80 x^3+320 x^4} \, dx","IntegrateAlgebraic[(3 - 3*x + 30*x^2 + 160*x^3)/(9 + 24*x - 12*x^2 + 80*x^3 + 320*x^4),x]","\frac{1}{8} \log \left(320 x^4+80 x^3-12 x^2+24 x+9\right)","\frac{1}{8} \log \left(320 x^4+80 x^3-12 x^2+24 x+9\right)",1,"Log[9 + 24*x - 12*x^2 + 80*x^3 + 320*x^4]/8","A",1
63,1,86,59,0.0277847,"\int \frac{3+12 x+20 x^2}{9+24 x-12 x^2+80 x^3+320 x^4} \, dx","IntegrateAlgebraic[(3 + 12*x + 20*x^2)/(9 + 24*x - 12*x^2 + 80*x^3 + 320*x^4),x]","\frac{1}{8} \text{RootSum}\left[320 \text{$\#$1}^4+80 \text{$\#$1}^3-12 \text{$\#$1}^2+24 \text{$\#$1}+9\&,\frac{20 \text{$\#$1}^2 \log (x-\text{$\#$1})+12 \text{$\#$1} \log (x-\text{$\#$1})+3 \log (x-\text{$\#$1})}{160 \text{$\#$1}^3+30 \text{$\#$1}^2-3 \text{$\#$1}+3}\&\right]","\frac{\tan ^{-1}\left(\frac{800 x^3-40 x^2+30 x+57}{6 \sqrt{11}}\right)}{2 \sqrt{11}}-\frac{\tan ^{-1}\left(\frac{7-40 x}{5 \sqrt{11}}\right)}{2 \sqrt{11}}",1,"RootSum[9 + 24*#1 - 12*#1^2 + 80*#1^3 + 320*#1^4 & , (3*Log[x - #1] + 12*Log[x - #1]*#1 + 20*Log[x - #1]*#1^2)/(3 - 3*#1 + 30*#1^2 + 160*#1^3) & ]/8","C",1
64,1,99,78,0.0302081,"\int \frac{-84-576 x-400 x^2+2560 x^3}{9+24 x-12 x^2+80 x^3+320 x^4} \, dx","IntegrateAlgebraic[(-84 - 576*x - 400*x^2 + 2560*x^3)/(9 + 24*x - 12*x^2 + 80*x^3 + 320*x^4),x]","\frac{1}{2} \text{RootSum}\left[320 \text{$\#$1}^4+80 \text{$\#$1}^3-12 \text{$\#$1}^2+24 \text{$\#$1}+9\&,\frac{640 \text{$\#$1}^3 \log (x-\text{$\#$1})-100 \text{$\#$1}^2 \log (x-\text{$\#$1})-144 \text{$\#$1} \log (x-\text{$\#$1})-21 \log (x-\text{$\#$1})}{160 \text{$\#$1}^3+30 \text{$\#$1}^2-3 \text{$\#$1}+3}\&\right]","-2 \sqrt{11} \tan ^{-1}\left(\frac{800 x^3-40 x^2+30 x+57}{6 \sqrt{11}}\right)+2 \log \left(320 x^4+80 x^3-12 x^2+24 x+9\right)+2 \sqrt{11} \tan ^{-1}\left(\frac{7-40 x}{5 \sqrt{11}}\right)",1,"RootSum[9 + 24*#1 - 12*#1^2 + 80*#1^3 + 320*#1^4 & , (-21*Log[x - #1] - 144*Log[x - #1]*#1 - 100*Log[x - #1]*#1^2 + 640*Log[x - #1]*#1^3)/(3 - 3*#1 + 30*#1^2 + 160*#1^3) & ]/2","C",1
65,1,71,49,0.1903832,"\int \frac{\sqrt{1-x^4}}{1+x^4} \, dx","IntegrateAlgebraic[Sqrt[1 - x^4]/(1 + x^4),x]","\frac{1}{4} \tan ^{-1}\left(\frac{\frac{x^4}{2}+x^2-\frac{1}{2}}{x \sqrt{1-x^4}}\right)-\frac{1}{4} \tanh ^{-1}\left(\frac{\frac{x^4}{2}-x^2-\frac{1}{2}}{x \sqrt{1-x^4}}\right)","\frac{1}{2} \tan ^{-1}\left(\frac{x \left(x^2+1\right)}{\sqrt{1-x^4}}\right)+\frac{1}{2} \tanh ^{-1}\left(\frac{x \left(1-x^2\right)}{\sqrt{1-x^4}}\right)",1,"ArcTan[(-1/2 + x^2 + x^4/2)/(x*Sqrt[1 - x^4])]/4 - ArcTanh[(-1/2 - x^2 + x^4/2)/(x*Sqrt[1 - x^4])]/4","A",1
66,1,53,53,0.1964192,"\int \frac{\sqrt{1+x^4}}{1-x^4} \, dx","IntegrateAlgebraic[Sqrt[1 + x^4]/(1 - x^4),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{2 \sqrt{2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{2 \sqrt{2}}","\frac{\tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{2 \sqrt{2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{2 \sqrt{2}}",1,"ArcTan[(Sqrt[2]*x)/Sqrt[1 + x^4]]/(2*Sqrt[2]) + ArcTanh[(Sqrt[2]*x)/Sqrt[1 + x^4]]/(2*Sqrt[2])","A",1
67,1,79,75,0.3349415,"\int \frac{\sqrt{1+p x^2+x^4}}{1-x^4} \, dx","IntegrateAlgebraic[Sqrt[1 + p*x^2 + x^4]/(1 - x^4),x]","\frac{1}{4} \sqrt{2-p} \tan ^{-1}\left(\frac{\sqrt{2-p} x}{\sqrt{p x^2+x^4+1}}\right)-\frac{1}{4} \sqrt{-p-2} \tan ^{-1}\left(\frac{\sqrt{-p-2} x}{\sqrt{p x^2+x^4+1}}\right)","\frac{1}{4} \sqrt{2-p} \tan ^{-1}\left(\frac{\sqrt{2-p} x}{\sqrt{p x^2+x^4+1}}\right)+\frac{1}{4} \sqrt{p+2} \tanh ^{-1}\left(\frac{\sqrt{p+2} x}{\sqrt{p x^2+x^4+1}}\right)",1,"-1/4*(Sqrt[-2 - p]*ArcTan[(Sqrt[-2 - p]*x)/Sqrt[1 + p*x^2 + x^4]]) + (Sqrt[2 - p]*ArcTan[(Sqrt[2 - p]*x)/Sqrt[1 + p*x^2 + x^4]])/4","A",1
68,1,105,171,0.3613785,"\int \frac{\sqrt{1+p x^2-x^4}}{1+x^4} \, dx","IntegrateAlgebraic[Sqrt[1 + p*x^2 - x^4]/(1 + x^4),x]","\frac{(2-i p) \tan ^{-1}\left(\frac{\sqrt{-p-2 i} x}{\sqrt{p x^2-x^4+1}}\right)}{4 \sqrt{-p-2 i}}+\frac{(2+i p) \tan ^{-1}\left(\frac{\sqrt{-p+2 i} x}{\sqrt{p x^2-x^4+1}}\right)}{4 \sqrt{-p+2 i}}","\frac{\sqrt{\sqrt{p^2+4}-p} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{p^2+4}-p} x \left(\sqrt{p^2+4}+p-2 x^2\right)}{2 \sqrt{2} \sqrt{p x^2-x^4+1}}\right)}{2 \sqrt{2}}-\frac{\sqrt{\sqrt{p^2+4}+p} \tan ^{-1}\left(\frac{\sqrt{\sqrt{p^2+4}+p} x \left(-\sqrt{p^2+4}+p-2 x^2\right)}{2 \sqrt{2} \sqrt{p x^2-x^4+1}}\right)}{2 \sqrt{2}}",1,"((2 - I*p)*ArcTan[(Sqrt[-2*I - p]*x)/Sqrt[1 + p*x^2 - x^4]])/(4*Sqrt[-2*I - p]) + ((2 + I*p)*ArcTan[(Sqrt[2*I - p]*x)/Sqrt[1 + p*x^2 - x^4]])/(4*Sqrt[2*I - p])","C",1
69,0,0,80,11.249188,"\int \frac{a+b x}{\left(2-x^2\right) \sqrt[4]{-1+x^2}} \, dx","IntegrateAlgebraic[(a + b*x)/((2 - x^2)*(-1 + x^2)^(1/4)),x]","\int \frac{a+b x}{\left(2-x^2\right) \sqrt[4]{-1+x^2}} \, dx","\frac{a \tan ^{-1}\left(\frac{x}{\sqrt{2} \sqrt[4]{x^2-1}}\right)}{2 \sqrt{2}}+\frac{a \tanh ^{-1}\left(\frac{x}{\sqrt{2} \sqrt[4]{x^2-1}}\right)}{2 \sqrt{2}}-b \tan ^{-1}\left(\sqrt[4]{x^2-1}\right)+b \tanh ^{-1}\left(\sqrt[4]{x^2-1}\right)",1,"Could not integrate","F",-1
70,0,0,88,5.5321871,"\int \frac{a+b x}{\sqrt[4]{-1-x^2} \left(2+x^2\right)} \, dx","IntegrateAlgebraic[(a + b*x)/((-1 - x^2)^(1/4)*(2 + x^2)),x]","\int \frac{a+b x}{\sqrt[4]{-1-x^2} \left(2+x^2\right)} \, dx","\frac{a \tan ^{-1}\left(\frac{x}{\sqrt{2} \sqrt[4]{-x^2-1}}\right)}{2 \sqrt{2}}+\frac{a \tanh ^{-1}\left(\frac{x}{\sqrt{2} \sqrt[4]{-x^2-1}}\right)}{2 \sqrt{2}}+b \tan ^{-1}\left(\sqrt[4]{-x^2-1}\right)-b \tanh ^{-1}\left(\sqrt[4]{-x^2-1}\right)",1,"Could not integrate","F",-1
71,0,0,149,11.5069554,"\int \frac{a+b x}{\sqrt[4]{1-x^2} \left(2-x^2\right)} \, dx","IntegrateAlgebraic[(a + b*x)/((1 - x^2)^(1/4)*(2 - x^2)),x]","\int \frac{a+b x}{\sqrt[4]{1-x^2} \left(2-x^2\right)} \, dx","\frac{1}{2} a \tan ^{-1}\left(\frac{1-\sqrt{1-x^2}}{x \sqrt[4]{1-x^2}}\right)+\frac{1}{2} a \tanh ^{-1}\left(\frac{\sqrt{1-x^2}+1}{x \sqrt[4]{1-x^2}}\right)+\frac{b \tan ^{-1}\left(\frac{1-\sqrt{1-x^2}}{\sqrt{2} \sqrt[4]{1-x^2}}\right)}{\sqrt{2}}+\frac{b \tanh ^{-1}\left(\frac{\sqrt{1-x^2}+1}{\sqrt{2} \sqrt[4]{1-x^2}}\right)}{\sqrt{2}}",1,"Could not integrate","F",-1
72,0,0,135,5.4802041,"\int \frac{a+b x}{\sqrt[4]{1+x^2} \left(2+x^2\right)} \, dx","IntegrateAlgebraic[(a + b*x)/((1 + x^2)^(1/4)*(2 + x^2)),x]","\int \frac{a+b x}{\sqrt[4]{1+x^2} \left(2+x^2\right)} \, dx","-\frac{1}{2} a \tan ^{-1}\left(\frac{\sqrt{x^2+1}+1}{x \sqrt[4]{x^2+1}}\right)-\frac{1}{2} a \tanh ^{-1}\left(\frac{1-\sqrt{x^2+1}}{x \sqrt[4]{x^2+1}}\right)-\frac{b \tan ^{-1}\left(\frac{1-\sqrt{x^2+1}}{\sqrt{2} \sqrt[4]{x^2+1}}\right)}{\sqrt{2}}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{x^2+1}+1}{\sqrt{2} \sqrt[4]{x^2+1}}\right)}{\sqrt{2}}",1,"Could not integrate","F",-1
73,0,0,127,41.1163196,"\int \frac{x}{\sqrt{1-x^3} \left(4-x^3\right)} \, dx","IntegrateAlgebraic[x/(Sqrt[1 - x^3]*(4 - x^3)),x]","\int \frac{x}{\sqrt{1-x^3} \left(4-x^3\right)} \, dx","-\frac{\tan ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} x\right)}{\sqrt{1-x^3}}\right)}{3\ 2^{2/3} \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{\sqrt{1-x^3}}{\sqrt{3}}\right)}{3\ 2^{2/3} \sqrt{3}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[3]{2} x+1}{\sqrt{1-x^3}}\right)}{3\ 2^{2/3}}+\frac{\tanh ^{-1}\left(\sqrt{1-x^3}\right)}{9\ 2^{2/3}}",1,"Could not integrate","F",-1
74,0,0,157,29.1187127,"\int \frac{x}{\left(4-d x^3\right) \sqrt{-1+d x^3}} \, dx","IntegrateAlgebraic[x/((4 - d*x^3)*Sqrt[-1 + d*x^3]),x]","\int \frac{x}{\left(4-d x^3\right) \sqrt{-1+d x^3}} \, dx","-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{2} \sqrt[3]{d} x+1}{\sqrt{d x^3-1}}\right)}{3\ 2^{2/3} d^{2/3}}-\frac{\tan ^{-1}\left(\sqrt{d x^3-1}\right)}{9\ 2^{2/3} d^{2/3}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} \sqrt[3]{d} x\right)}{\sqrt{d x^3-1}}\right)}{3\ 2^{2/3} \sqrt{3} d^{2/3}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d x^3-1}}{\sqrt{3}}\right)}{3\ 2^{2/3} \sqrt{3} d^{2/3}}",1,"Could not integrate","F",-1
75,0,0,74,42.2352387,"\int \frac{x}{\sqrt{-1+x^3} \left(8+x^3\right)} \, dx","IntegrateAlgebraic[x/(Sqrt[-1 + x^3]*(8 + x^3)),x]","\int \frac{x}{\sqrt{-1+x^3} \left(8+x^3\right)} \, dx","\frac{1}{18} \tan ^{-1}\left(\frac{(1-x)^2}{3 \sqrt{x^3-1}}\right)+\frac{1}{18} \tan ^{-1}\left(\frac{\sqrt{x^3-1}}{3}\right)-\frac{\tanh ^{-1}\left(\frac{\sqrt{3} (1-x)}{\sqrt{x^3-1}}\right)}{6 \sqrt{3}}",1,"Could not integrate","F",-1
76,0,0,103,28.8617432,"\int \frac{x}{\left(8-d x^3\right) \sqrt{1+d x^3}} \, dx","IntegrateAlgebraic[x/((8 - d*x^3)*Sqrt[1 + d*x^3]),x]","\int \frac{x}{\left(8-d x^3\right) \sqrt{1+d x^3}} \, dx","-\frac{\tan ^{-1}\left(\frac{\sqrt{3} \left(\sqrt[3]{d} x+1\right)}{\sqrt{d x^3+1}}\right)}{6 \sqrt{3} d^{2/3}}+\frac{\tanh ^{-1}\left(\frac{\left(\sqrt[3]{d} x+1\right)^2}{3 \sqrt{d x^3+1}}\right)}{18 d^{2/3}}-\frac{\tanh ^{-1}\left(\frac{1}{3} \sqrt{d x^3+1}\right)}{18 d^{2/3}}",1,"Could not integrate","F",-1
77,0,0,81,7.9543041,"\int \frac{1}{\sqrt[3]{1-3 x^2} \left(3-x^2\right)} \, dx","IntegrateAlgebraic[1/((1 - 3*x^2)^(1/3)*(3 - x^2)),x]","\int \frac{1}{\sqrt[3]{1-3 x^2} \left(3-x^2\right)} \, dx","\frac{1}{4} \tan ^{-1}\left(\frac{1-\sqrt[3]{1-3 x^2}}{x}\right)-\frac{\tanh ^{-1}\left(\frac{\left(1-\sqrt[3]{1-3 x^2}\right)^2}{3 \sqrt{3} x}\right)}{4 \sqrt{3}}+\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{3}}\right)}{4 \sqrt{3}}",1,"Could not integrate","F",-1
78,0,0,81,3.8585742,"\int \frac{1}{\left(3+x^2\right) \sqrt[3]{1+3 x^2}} \, dx","IntegrateAlgebraic[1/((3 + x^2)*(1 + 3*x^2)^(1/3)),x]","\int \frac{1}{\left(3+x^2\right) \sqrt[3]{1+3 x^2}} \, dx","\frac{\tan ^{-1}\left(\frac{\left(1-\sqrt[3]{3 x^2+1}\right)^2}{3 \sqrt{3} x}\right)}{4 \sqrt{3}}-\frac{1}{4} \tanh ^{-1}\left(\frac{1-\sqrt[3]{3 x^2+1}}{x}\right)+\frac{\tan ^{-1}\left(\frac{x}{\sqrt{3}}\right)}{4 \sqrt{3}}",1,"Could not integrate","F",-1
79,0,0,113,3.8318628,"\int \frac{1}{\sqrt[3]{1-x^2} \left(3+x^2\right)} \, dx","IntegrateAlgebraic[1/((1 - x^2)^(1/3)*(3 + x^2)),x]","\int \frac{1}{\sqrt[3]{1-x^2} \left(3+x^2\right)} \, dx","\frac{\tan ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} \sqrt[3]{1-x^2}\right)}{x}\right)}{2\ 2^{2/3} \sqrt{3}}+\frac{\tanh ^{-1}\left(\frac{x}{\sqrt[3]{2} \sqrt[3]{1-x^2}+1}\right)}{2\ 2^{2/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt{3}}{x}\right)}{2\ 2^{2/3} \sqrt{3}}-\frac{\tanh ^{-1}(x)}{6\ 2^{2/3}}",1,"Could not integrate","F",-1
80,0,0,109,7.5346664,"\int \frac{1}{\left(3-x^2\right) \sqrt[3]{1+x^2}} \, dx","IntegrateAlgebraic[1/((3 - x^2)*(1 + x^2)^(1/3)),x]","\int \frac{1}{\left(3-x^2\right) \sqrt[3]{1+x^2}} \, dx","\frac{\tan ^{-1}\left(\frac{x}{\sqrt[3]{2} \sqrt[3]{x^2+1}+1}\right)}{2\ 2^{2/3}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} \sqrt[3]{x^2+1}\right)}{x}\right)}{2\ 2^{2/3} \sqrt{3}}-\frac{\tan ^{-1}(x)}{6\ 2^{2/3}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{3}}{x}\right)}{2\ 2^{2/3} \sqrt{3}}",1,"Could not integrate","F",-1
81,1,37,87,0.0939601,"\int \frac{a+x}{(-a+x) \sqrt{a^2 x-\left(1+a^2\right) x^2+x^3}} \, dx","IntegrateAlgebraic[(a + x)/((-a + x)*Sqrt[a^2*x - (1 + a^2)*x^2 + x^3]),x]","-\frac{2 \tan ^{-1}\left(\frac{(a-1) x}{\sqrt{\left(-a^2-1\right) x^2+a^2 x+x^3}}\right)}{a-1}","-\frac{2 \sqrt{x} \sqrt{-\left(a^2+1\right) x+a^2+x^2} \tan ^{-1}\left(\frac{(1-a) \sqrt{x}}{\sqrt{-\left(a^2+1\right) x+a^2+x^2}}\right)}{(1-a) \sqrt{-\left(a^2+1\right) x^2+a^2 x+x^3}}",1,"(-2*ArcTan[((-1 + a)*x)/Sqrt[a^2*x + (-1 - a^2)*x^2 + x^3]])/(-1 + a)","A",1
82,1,46,1,0.2184425,"\int \frac{-2+a+x}{(-a+x) \sqrt{(2-a) a x+\left(-1-2 a+a^2\right) x^2+x^3}} \, dx","IntegrateAlgebraic[(-2 + a + x)/((-a + x)*Sqrt[(2 - a)*a*x + (-1 - 2*a + a^2)*x^2 + x^3]),x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\left(a^2-2 a-1\right) x^2+\left(2 a-a^2\right) x+x^3}}{a (x-1)}\right)}{a}","0",1,"(-2*ArcTanh[Sqrt[(2*a - a^2)*x + (-1 - 2*a + a^2)*x^2 + x^3]/(a*(-1 + x))])/a","C",1
83,1,50,46,0.2158171,"\int \frac{-a+(-1+2 a) x}{(-a+x) \sqrt{a^2 x-\left(-1+2 a+a^2\right) x^2+(-1+2 a) x^3}} \, dx","IntegrateAlgebraic[(-a + (-1 + 2*a)*x)/((-a + x)*Sqrt[a^2*x - (-1 + 2*a + a^2)*x^2 + (-1 + 2*a)*x^3]),x]","2 \tanh ^{-1}\left(\frac{\sqrt{\left(-a^2-2 a+1\right) x^2+a^2 x+(2 a-1) x^3}}{a^2+(1-2 a) x}\right)","\log \left(\frac{-2 \left(\sqrt{(1-x) x \left(a^2-2 a x+x\right)}+x\right)-a^2+2 a x+x^2}{(a-x)^2}\right)",1,"2*ArcTanh[Sqrt[a^2*x + (1 - 2*a - a^2)*x^2 + (-1 + 2*a)*x^3]/(a^2 + (1 - 2*a)*x)]","A",1
84,1,34,32,1.294911,"\int \frac{1-\sqrt[3]{2} x}{\left(2^{2/3}+x\right) \sqrt{1+x^3}} \, dx","IntegrateAlgebraic[(1 - 2^(1/3)*x)/((2^(2/3) + x)*Sqrt[1 + x^3]),x]","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{x^3+1}}{\sqrt{3} \left(\sqrt[3]{2} x+1\right)}\right)}{\sqrt{3}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{3} \left(\sqrt[3]{2} x+1\right)}{\sqrt{x^3+1}}\right)}{\sqrt{3}}",1,"(-2*ArcTan[Sqrt[1 + x^3]/(Sqrt[3]*(1 + 2^(1/3)*x))])/Sqrt[3]","A",1
85,1,31,23,0.8295683,"\int \frac{1+x}{(-2+x) \sqrt{1+x^3}} \, dx","IntegrateAlgebraic[(1 + x)/((-2 + x)*Sqrt[1 + x^3]),x]","-\frac{2}{3} \tanh ^{-1}\left(\frac{\frac{x^2}{3}+\frac{2 x}{3}+\frac{1}{3}}{\sqrt{x^3+1}}\right)","-\frac{2}{3} \tanh ^{-1}\left(\frac{(x+1)^2}{3 \sqrt{x^3+1}}\right)",1,"(-2*ArcTanh[(1/3 + (2*x)/3 + x^2/3)/Sqrt[1 + x^3]])/3","A",1
86,0,0,218,24.7626118,"\int \frac{x}{\sqrt{1+x^3} \left(10+6 \sqrt{3}+x^3\right)} \, dx","IntegrateAlgebraic[x/(Sqrt[1 + x^3]*(10 + 6*Sqrt[3] + x^3)),x]","\int \frac{x}{\sqrt{1+x^3} \left(10+6 \sqrt{3}+x^3\right)} \, dx","-\frac{\left(2-\sqrt{3}\right) \tan ^{-1}\left(\frac{\sqrt[4]{3} \left(1+\sqrt{3}\right) (x+1)}{\sqrt{2} \sqrt{x^3+1}}\right)}{2 \sqrt{2} 3^{3/4}}-\frac{\left(2-\sqrt{3}\right) \tan ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt{x^3+1}}{\sqrt{2} 3^{3/4}}\right)}{3 \sqrt{2} 3^{3/4}}-\frac{\left(2-\sqrt{3}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{3} \left(-2 x+\sqrt{3}+1\right)}{\sqrt{2} \sqrt{x^3+1}}\right)}{3 \sqrt{2} \sqrt[4]{3}}-\frac{\left(2-\sqrt{3}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{3} \left(1-\sqrt{3}\right) (x+1)}{\sqrt{2} \sqrt{x^3+1}}\right)}{6 \sqrt{2} \sqrt[4]{3}}",1,"Could not integrate","F",-1
87,0,0,210,49.8962902,"\int \frac{x}{\sqrt{1+x^3} \left(10-6 \sqrt{3}+x^3\right)} \, dx","IntegrateAlgebraic[x/(Sqrt[1 + x^3]*(10 - 6*Sqrt[3] + x^3)),x]","\int \frac{x}{\sqrt{1+x^3} \left(10-6 \sqrt{3}+x^3\right)} \, dx","-\frac{\left(2+\sqrt{3}\right) \tan ^{-1}\left(\frac{\sqrt[4]{3} \left(-2 x-\sqrt{3}+1\right)}{\sqrt{2} \sqrt{x^3+1}}\right)}{3 \sqrt{2} \sqrt[4]{3}}-\frac{\left(2+\sqrt{3}\right) \tan ^{-1}\left(\frac{\sqrt[4]{3} \left(1+\sqrt{3}\right) (x+1)}{\sqrt{2} \sqrt{x^3+1}}\right)}{6 \sqrt{2} \sqrt[4]{3}}+\frac{\left(2+\sqrt{3}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{3} \left(1-\sqrt{3}\right) (x+1)}{\sqrt{2} \sqrt{x^3+1}}\right)}{2 \sqrt{2} 3^{3/4}}+\frac{\left(2+\sqrt{3}\right) \tanh ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt{x^3+1}}{\sqrt{2} 3^{3/4}}\right)}{3 \sqrt{2} 3^{3/4}}",1,"Could not integrate","F",-1
88,0,0,222,49.8186275,"\int \frac{x}{\sqrt{-1+x^3} \left(-10-6 \sqrt{3}+x^3\right)} \, dx","IntegrateAlgebraic[x/(Sqrt[-1 + x^3]*(-10 - 6*Sqrt[3] + x^3)),x]","\int \frac{x}{\sqrt{-1+x^3} \left(-10-6 \sqrt{3}+x^3\right)} \, dx","\frac{\left(2-\sqrt{3}\right) \tan ^{-1}\left(\frac{\sqrt[4]{3} \left(1-\sqrt{3}\right) (1-x)}{\sqrt{2} \sqrt{x^3-1}}\right)}{6 \sqrt{2} \sqrt[4]{3}}+\frac{\left(2-\sqrt{3}\right) \tan ^{-1}\left(\frac{\sqrt[4]{3} \left(2 x+\sqrt{3}+1\right)}{\sqrt{2} \sqrt{x^3-1}}\right)}{3 \sqrt{2} \sqrt[4]{3}}+\frac{\left(2-\sqrt{3}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{3} \left(1+\sqrt{3}\right) (1-x)}{\sqrt{2} \sqrt{x^3-1}}\right)}{2 \sqrt{2} 3^{3/4}}-\frac{\left(2-\sqrt{3}\right) \tanh ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt{x^3-1}}{\sqrt{2} 3^{3/4}}\right)}{3 \sqrt{2} 3^{3/4}}",1,"Could not integrate","F",-1
89,0,0,214,24.6696691,"\int \frac{x}{\sqrt{-1+x^3} \left(-10+6 \sqrt{3}+x^3\right)} \, dx","IntegrateAlgebraic[x/(Sqrt[-1 + x^3]*(-10 + 6*Sqrt[3] + x^3)),x]","\int \frac{x}{\sqrt{-1+x^3} \left(-10+6 \sqrt{3}+x^3\right)} \, dx","-\frac{\left(2+\sqrt{3}\right) \tan ^{-1}\left(\frac{\sqrt[4]{3} \left(1-\sqrt{3}\right) (1-x)}{\sqrt{2} \sqrt{x^3-1}}\right)}{2 \sqrt{2} 3^{3/4}}+\frac{\left(2+\sqrt{3}\right) \tan ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt{x^3-1}}{\sqrt{2} 3^{3/4}}\right)}{3 \sqrt{2} 3^{3/4}}+\frac{\left(2+\sqrt{3}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{3} \left(1+\sqrt{3}\right) (1-x)}{\sqrt{2} \sqrt{x^3-1}}\right)}{6 \sqrt{2} \sqrt[4]{3}}+\frac{\left(2+\sqrt{3}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{3} \left(2 x-\sqrt{3}+1\right)}{\sqrt{2} \sqrt{x^3-1}}\right)}{3 \sqrt{2} \sqrt[4]{3}}",1,"Could not integrate","F",-1
90,0,0,65,2.3212058,"\int \frac{1-\sqrt{3}+x}{\left(1+\sqrt{3}+x\right) \sqrt{-4+4 \sqrt{3} x^2+x^4}} \, dx","IntegrateAlgebraic[(1 - Sqrt[3] + x)/((1 + Sqrt[3] + x)*Sqrt[-4 + 4*Sqrt[3]*x^2 + x^4]),x]","\int \frac{1-\sqrt{3}+x}{\left(1+\sqrt{3}+x\right) \sqrt{-4+4 \sqrt{3} x^2+x^4}} \, dx","\frac{1}{3} \sqrt{2 \sqrt{3}-3} \tanh ^{-1}\left(\frac{\left(x-\sqrt{3}+1\right)^2}{\sqrt{3 \left(2 \sqrt{3}-3\right)} \sqrt{x^4+4 \sqrt{3} x^2-4}}\right)",1,"Could not integrate","F",-1
91,0,0,63,2.6396171,"\int \frac{1+\sqrt{3}+x}{\left(1-\sqrt{3}+x\right) \sqrt{-4-4 \sqrt{3} x^2+x^4}} \, dx","IntegrateAlgebraic[(1 + Sqrt[3] + x)/((1 - Sqrt[3] + x)*Sqrt[-4 - 4*Sqrt[3]*x^2 + x^4]),x]","\int \frac{1+\sqrt{3}+x}{\left(1-\sqrt{3}+x\right) \sqrt{-4-4 \sqrt{3} x^2+x^4}} \, dx","-\frac{1}{3} \sqrt{3+2 \sqrt{3}} \tan ^{-1}\left(\frac{\left(x+\sqrt{3}+1\right)^2}{\sqrt{3 \left(3+2 \sqrt{3}\right)} \sqrt{x^4-4 \sqrt{3} x^2-4}}\right)",1,"Could not integrate","F",-1
92,1,92,53,0.8136763,"\int \frac{-1+x}{(1+x) \sqrt[3]{2+x^3}} \, dx","IntegrateAlgebraic[(-1 + x)/((1 + x)*(2 + x^3)^(1/3)),x]","-\log \left(\sqrt[3]{x^3+2}-x-2\right)-\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x^3+2}}{\sqrt[3]{x^3+2}+2 x+4}\right)+\frac{1}{2} \log \left(\left(x^3+2\right)^{2/3}+(x+2) \sqrt[3]{x^3+2}+x^2+4 x+4\right)","-\frac{3}{2} \log \left(-\sqrt[3]{x^3+2}+x+2\right)+\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 (x+2)}{\sqrt[3]{x^3+2}}+1}{\sqrt{3}}\right)+\log (x+1)",1,"-(Sqrt[3]*ArcTan[(Sqrt[3]*(2 + x^3)^(1/3))/(4 + 2*x + (2 + x^3)^(1/3))]) - Log[-2 - x + (2 + x^3)^(1/3)] + Log[4 + 4*x + x^2 + (2 + x)*(2 + x^3)^(1/3) + (2 + x^3)^(2/3)]/2","A",1
93,0,0,108,4.4419987,"\int \frac{1}{(1+x) \sqrt[3]{2+x^3}} \, dx","IntegrateAlgebraic[1/((1 + x)*(2 + x^3)^(1/3)),x]","\int \frac{1}{(1+x) \sqrt[3]{2+x^3}} \, dx","\frac{3}{4} \log \left(-\sqrt[3]{x^3+2}+x+2\right)-\frac{1}{4} \log \left(\sqrt[3]{x^3+2}-x\right)+\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3+2}}+1}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 (x+2)}{\sqrt[3]{x^3+2}}+1}{\sqrt{3}}\right)-\frac{1}{2} \log (x+1)",1,"Could not integrate","F",-1
94,1,240,98,1.0707023,"\int \frac{1}{\left(1-x^3\right) \sqrt[3]{a+b x^3}} \, dx","IntegrateAlgebraic[1/((1 - x^3)*(a + b*x^3)^(1/3)),x]","\frac{\left(1+i \sqrt{3}\right) \log \left(2 x \sqrt[3]{a+b}+\left(1+i \sqrt{3}\right) \sqrt[3]{a+b x^3}\right)}{6 \sqrt[3]{a+b}}-\frac{\sqrt{-1+i \sqrt{3}} \tan ^{-1}\left(\frac{3 x \sqrt[3]{a+b}}{-\sqrt{3} \sqrt[3]{a+b x^3}-3 i \sqrt[3]{a+b x^3}+\sqrt{3} x \sqrt[3]{a+b}}\right)}{\sqrt{6} \sqrt[3]{a+b}}-\frac{i \left(\sqrt{3}-i\right) \log \left(\left(\sqrt{3}+i\right) \left(a+b x^3\right)^{2/3}+\left(-\sqrt{3} x+i x\right) \sqrt[3]{a+b} \sqrt[3]{a+b x^3}-2 i x^2 (a+b)^{2/3}\right)}{12 \sqrt[3]{a+b}}","\frac{\log \left(1-x^3\right)}{6 \sqrt[3]{a+b}}-\frac{\log \left(x \sqrt[3]{a+b}-\sqrt[3]{a+b x^3}\right)}{2 \sqrt[3]{a+b}}+\frac{\tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{a+b}}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{a+b}}",1,"-((Sqrt[-1 + I*Sqrt[3]]*ArcTan[(3*(a + b)^(1/3)*x)/(Sqrt[3]*(a + b)^(1/3)*x - (3*I)*(a + b*x^3)^(1/3) - Sqrt[3]*(a + b*x^3)^(1/3))])/(Sqrt[6]*(a + b)^(1/3))) + ((1 + I*Sqrt[3])*Log[2*(a + b)^(1/3)*x + (1 + I*Sqrt[3])*(a + b*x^3)^(1/3)])/(6*(a + b)^(1/3)) - ((I/12)*(-I + Sqrt[3])*Log[(-2*I)*(a + b)^(2/3)*x^2 + (a + b)^(1/3)*(I*x - Sqrt[3]*x)*(a + b*x^3)^(1/3) + (I + Sqrt[3])*(a + b*x^3)^(2/3)])/(a + b)^(1/3)","C",0
95,0,0,154,7.2955958,"\int \frac{1+x}{\left(1+x+x^2\right) \sqrt[3]{a+b x^3}} \, dx","IntegrateAlgebraic[(1 + x)/((1 + x + x^2)*(a + b*x^3)^(1/3)),x]","\int \frac{1+x}{\left(1+x+x^2\right) \sqrt[3]{a+b x^3}} \, dx","\frac{\log \left(\sqrt[3]{a+b}-\sqrt[3]{a+b x^3}\right)}{2 \sqrt[3]{a+b}}-\frac{\log \left(x \sqrt[3]{a+b}-\sqrt[3]{a+b x^3}\right)}{2 \sqrt[3]{a+b}}+\frac{\tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{a+b}}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{a+b}}+\frac{\tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a+b x^3}}{\sqrt[3]{a+b}}+1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{a+b}}",1,"Could not integrate","F",-1
96,1,223,96,0.4299464,"\int \frac{x^2}{\left(1-x^3\right) \sqrt[3]{a+b x^3}} \, dx","IntegrateAlgebraic[x^2/((1 - x^3)*(a + b*x^3)^(1/3)),x]","\frac{\left(1+i \sqrt{3}\right) \log \left(2 \sqrt[3]{a+b}+\left(1+i \sqrt{3}\right) \sqrt[3]{a+b x^3}\right)}{6 \sqrt[3]{a+b}}-\frac{i \left(\sqrt{3}-i\right) \log \left(\left(-1-i \sqrt{3}\right) \sqrt[3]{a+b} \sqrt[3]{a+b x^3}+\left(-1+i \sqrt{3}\right) \left(a+b x^3\right)^{2/3}+2 (a+b)^{2/3}\right)}{12 \sqrt[3]{a+b}}+\frac{\left(3-i \sqrt{3}\right) \tanh ^{-1}\left(\frac{\sqrt[3]{a+b x^3}}{\sqrt[3]{a+b}}+\frac{i \left(\sqrt[3]{a+b}-\sqrt[3]{a+b x^3}\right)}{\sqrt{3} \sqrt[3]{a+b}}\right)}{6 \sqrt[3]{a+b}}","\frac{\log \left(1-x^3\right)}{6 \sqrt[3]{a+b}}-\frac{\log \left(\sqrt[3]{a+b}-\sqrt[3]{a+b x^3}\right)}{2 \sqrt[3]{a+b}}-\frac{\tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a+b x^3}}{\sqrt[3]{a+b}}+1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{a+b}}",1,"((3 - I*Sqrt[3])*ArcTanh[(a + b*x^3)^(1/3)/(a + b)^(1/3) + (I*((a + b)^(1/3) - (a + b*x^3)^(1/3)))/(Sqrt[3]*(a + b)^(1/3))])/(6*(a + b)^(1/3)) + ((1 + I*Sqrt[3])*Log[2*(a + b)^(1/3) + (1 + I*Sqrt[3])*(a + b*x^3)^(1/3)])/(6*(a + b)^(1/3)) - ((I/12)*(-I + Sqrt[3])*Log[2*(a + b)^(2/3) + (-1 - I*Sqrt[3])*(a + b)^(1/3)*(a + b*x^3)^(1/3) + (-1 + I*Sqrt[3])*(a + b*x^3)^(2/3)])/(a + b)^(1/3)","C",1
97,1,126,88,0.2898629,"\int \frac{1}{\sqrt[3]{1-x^3} \left(1+x^3\right)} \, dx","IntegrateAlgebraic[1/((1 - x^3)^(1/3)*(1 + x^3)),x]","\frac{\log \left(2^{2/3} \sqrt[3]{1-x^3}+2 x\right)}{3 \sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{1-x^3}-x}\right)}{\sqrt[3]{2} \sqrt{3}}-\frac{\log \left(2^{2/3} \sqrt[3]{1-x^3} x-\sqrt[3]{2} \left(1-x^3\right)^{2/3}-2 x^2\right)}{6 \sqrt[3]{2}}","-\frac{\log \left(x^3+1\right)}{6 \sqrt[3]{2}}+\frac{\log \left(-\sqrt[3]{1-x^3}-\sqrt[3]{2} x\right)}{2 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}",1,"ArcTan[(Sqrt[3]*x)/(-x + 2^(2/3)*(1 - x^3)^(1/3))]/(2^(1/3)*Sqrt[3]) + Log[2*x + 2^(2/3)*(1 - x^3)^(1/3)]/(3*2^(1/3)) - Log[-2*x^2 + 2^(2/3)*x*(1 - x^3)^(1/3) - 2^(1/3)*(1 - x^3)^(2/3)]/(6*2^(1/3))","A",1
98,1,340,233,1.0440919,"\int \frac{x}{\sqrt[3]{1-x^3} \left(1+x^3\right)} \, dx","IntegrateAlgebraic[x/((1 - x^3)^(1/3)*(1 + x^3)),x]","-\frac{\log \left(-\sqrt[3]{1-x^3}+\sqrt[3]{2} x-\sqrt[3]{2}\right)}{3 \sqrt[3]{2}}-\frac{\log \left(2 \sqrt[3]{1-x^3}+\sqrt[3]{2} x-\sqrt[3]{2}\right)}{6 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{1-x^3}}{\sqrt[3]{1-x^3}-\sqrt[3]{2} x+\sqrt[3]{2}}\right)}{2 \sqrt[3]{2} \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{1-x^3}}{\sqrt[3]{1-x^3}+2 \sqrt[3]{2} x-2 \sqrt[3]{2}}\right)}{\sqrt[3]{2} \sqrt{3}}+\frac{\log \left(\left(1-x^3\right)^{2/3}+\left(\sqrt[3]{2} x-\sqrt[3]{2}\right) \sqrt[3]{1-x^3}+2^{2/3} x^2-2\ 2^{2/3} x+2^{2/3}\right)}{6 \sqrt[3]{2}}+\frac{\log \left(4 \left(1-x^3\right)^{2/3}+\left(2 \sqrt[3]{2}-2 \sqrt[3]{2} x\right) \sqrt[3]{1-x^3}+2^{2/3} x^2-2\ 2^{2/3} x+2^{2/3}\right)}{12 \sqrt[3]{2}}","\frac{\log \left(\frac{2^{2/3} (1-x)^2}{\left(1-x^3\right)^{2/3}}-\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{6 \sqrt[3]{2}}-\frac{\log \left(\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{3 \sqrt[3]{2}}-\frac{\log \left(2^{2/3} \sqrt[3]{1-x^3}+x-1\right)}{4 \sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1}{\sqrt{3}}\right)}{2 \sqrt[3]{2} \sqrt{3}}+\frac{\log \left((1-x) (x+1)^2\right)}{12 \sqrt[3]{2}}",1,"-1/2*ArcTan[(Sqrt[3]*(1 - x^3)^(1/3))/(2^(1/3) - 2^(1/3)*x + (1 - x^3)^(1/3))]/(2^(1/3)*Sqrt[3]) - ArcTan[(Sqrt[3]*(1 - x^3)^(1/3))/(-2*2^(1/3) + 2*2^(1/3)*x + (1 - x^3)^(1/3))]/(2^(1/3)*Sqrt[3]) - Log[-2^(1/3) + 2^(1/3)*x - (1 - x^3)^(1/3)]/(3*2^(1/3)) - Log[-2^(1/3) + 2^(1/3)*x + 2*(1 - x^3)^(1/3)]/(6*2^(1/3)) + Log[2^(2/3) - 2*2^(2/3)*x + 2^(2/3)*x^2 + (-2^(1/3) + 2^(1/3)*x)*(1 - x^3)^(1/3) + (1 - x^3)^(2/3)]/(6*2^(1/3)) + Log[2^(2/3) - 2*2^(2/3)*x + 2^(2/3)*x^2 + (2*2^(1/3) - 2*2^(1/3)*x)*(1 - x^3)^(1/3) + 4*(1 - x^3)^(2/3)]/(12*2^(1/3))","A",1
99,1,116,82,0.1681347,"\int \frac{x^2}{\sqrt[3]{1-x^3} \left(1+x^3\right)} \, dx","IntegrateAlgebraic[x^2/((1 - x^3)^(1/3)*(1 + x^3)),x]","\frac{\log \left(2^{2/3} \sqrt[3]{1-x^3}-2\right)}{3 \sqrt[3]{2}}-\frac{\log \left(\sqrt[3]{2} \left(1-x^3\right)^{2/3}+2^{2/3} \sqrt[3]{1-x^3}+2\right)}{6 \sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}","-\frac{\log \left(x^3+1\right)}{6 \sqrt[3]{2}}+\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{2 \sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}",1,"ArcTan[1/Sqrt[3] + (2^(2/3)*(1 - x^3)^(1/3))/Sqrt[3]]/(2^(1/3)*Sqrt[3]) + Log[-2 + 2^(2/3)*(1 - x^3)^(1/3)]/(3*2^(1/3)) - Log[2 + 2^(2/3)*(1 - x^3)^(1/3) + 2^(1/3)*(1 - x^3)^(2/3)]/(6*2^(1/3))","A",1
100,1,167,135,1.0128869,"\int \frac{1+x}{\left(1-x+x^2\right) \sqrt[3]{1-x^3}} \, dx","IntegrateAlgebraic[(1 + x)/((1 - x + x^2)*(1 - x^3)^(1/3)),x]","-\frac{\log \left(-\sqrt[3]{1-x^3}+\sqrt[3]{2} x-\sqrt[3]{2}\right)}{\sqrt[3]{2}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{1-x^3}}{\sqrt[3]{1-x^3}+2 \sqrt[3]{2} x-2 \sqrt[3]{2}}\right)}{\sqrt[3]{2}}+\frac{\log \left(\left(1-x^3\right)^{2/3}+\left(\sqrt[3]{2} x-\sqrt[3]{2}\right) \sqrt[3]{1-x^3}+2^{2/3} x^2-2\ 2^{2/3} x+2^{2/3}\right)}{2 \sqrt[3]{2}}","\frac{\log \left(\frac{2^{2/3} (1-x)^2}{\left(1-x^3\right)^{2/3}}-\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{2 \sqrt[3]{2}}-\frac{\log \left(\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{\sqrt[3]{2}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt[3]{2}}",1,"-((Sqrt[3]*ArcTan[(Sqrt[3]*(1 - x^3)^(1/3))/(-2*2^(1/3) + 2*2^(1/3)*x + (1 - x^3)^(1/3))])/2^(1/3)) - Log[-2^(1/3) + 2^(1/3)*x - (1 - x^3)^(1/3)]/2^(1/3) + Log[2^(2/3) - 2*2^(2/3)*x + 2^(2/3)*x^2 + (-2^(1/3) + 2^(1/3)*x)*(1 - x^3)^(1/3) + (1 - x^3)^(2/3)]/(2*2^(1/3))","A",1
101,1,167,135,1.0069407,"\int \frac{(1+x)^2}{\sqrt[3]{1-x^3} \left(1+x^3\right)} \, dx","IntegrateAlgebraic[(1 + x)^2/((1 - x^3)^(1/3)*(1 + x^3)),x]","-\frac{\log \left(-\sqrt[3]{1-x^3}+\sqrt[3]{2} x-\sqrt[3]{2}\right)}{\sqrt[3]{2}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{1-x^3}}{\sqrt[3]{1-x^3}+2 \sqrt[3]{2} x-2 \sqrt[3]{2}}\right)}{\sqrt[3]{2}}+\frac{\log \left(\left(1-x^3\right)^{2/3}+\left(\sqrt[3]{2} x-\sqrt[3]{2}\right) \sqrt[3]{1-x^3}+2^{2/3} x^2-2\ 2^{2/3} x+2^{2/3}\right)}{2 \sqrt[3]{2}}","\frac{\log \left(\frac{2^{2/3} (1-x)^2}{\left(1-x^3\right)^{2/3}}-\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{2 \sqrt[3]{2}}-\frac{\log \left(\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{\sqrt[3]{2}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt[3]{2}}",1,"-((Sqrt[3]*ArcTan[(Sqrt[3]*(1 - x^3)^(1/3))/(-2*2^(1/3) + 2*2^(1/3)*x + (1 - x^3)^(1/3))])/2^(1/3)) - Log[-2^(1/3) + 2^(1/3)*x - (1 - x^3)^(1/3)]/2^(1/3) + Log[2^(2/3) - 2*2^(2/3)*x + 2^(2/3)*x^2 + (-2^(1/3) + 2^(1/3)*x)*(1 - x^3)^(1/3) + (1 - x^3)^(2/3)]/(2*2^(1/3))","A",1
102,1,152,119,1.0133627,"\int \frac{1-x}{\left(1+x+x^2\right) \sqrt[3]{1+x^3}} \, dx","IntegrateAlgebraic[(1 - x)/((1 + x + x^2)*(1 + x^3)^(1/3)),x]","\frac{\log \left(\sqrt[3]{x^3+1}+\sqrt[3]{2} x+\sqrt[3]{2}\right)}{\sqrt[3]{2}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x^3+1}}{\sqrt[3]{x^3+1}-2 \sqrt[3]{2} x-2 \sqrt[3]{2}}\right)}{\sqrt[3]{2}}-\frac{\log \left(\left(x^3+1\right)^{2/3}+\left(-\sqrt[3]{2} x-\sqrt[3]{2}\right) \sqrt[3]{x^3+1}+2^{2/3} x^2+2\ 2^{2/3} x+2^{2/3}\right)}{2 \sqrt[3]{2}}","-\frac{\log \left(\frac{2^{2/3} (x+1)^2}{\left(x^3+1\right)^{2/3}}-\frac{\sqrt[3]{2} (x+1)}{\sqrt[3]{x^3+1}}+1\right)}{2 \sqrt[3]{2}}+\frac{\log \left(\frac{\sqrt[3]{2} (x+1)}{\sqrt[3]{x^3+1}}+1\right)}{\sqrt[3]{2}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} (x+1)}{\sqrt[3]{x^3+1}}}{\sqrt{3}}\right)}{\sqrt[3]{2}}",1,"(Sqrt[3]*ArcTan[(Sqrt[3]*(1 + x^3)^(1/3))/(-2*2^(1/3) - 2*2^(1/3)*x + (1 + x^3)^(1/3))])/2^(1/3) + Log[2^(1/3) + 2^(1/3)*x + (1 + x^3)^(1/3)]/2^(1/3) - Log[2^(2/3) + 2*2^(2/3)*x + 2^(2/3)*x^2 + (-2^(1/3) - 2^(1/3)*x)*(1 + x^3)^(1/3) + (1 + x^3)^(2/3)]/(2*2^(1/3))","A",1
103,0,0,43,13.1693248,"\int \frac{\left(1-x^3\right)^{2/3}}{\left(1+x+x^2\right)^2} \, dx","IntegrateAlgebraic[(1 - x^3)^(2/3)/(1 + x + x^2)^2,x]","\int \frac{\left(1-x^3\right)^{2/3}}{\left(1+x+x^2\right)^2} \, dx","x^2 \left(-\, _2F_1\left(\frac{2}{3},\frac{4}{3};\frac{5}{3};x^3\right)\right)+\frac{x}{\sqrt[3]{1-x^3}}+\frac{1}{\sqrt[3]{1-x^3}}",1,"Could not integrate","F",-1
104,0,0,43,11.7195715,"\int \frac{1-x}{\left(1+x+x^2\right) \sqrt[3]{1-x^3}} \, dx","IntegrateAlgebraic[(1 - x)/((1 + x + x^2)*(1 - x^3)^(1/3)),x]","\int \frac{1-x}{\left(1+x+x^2\right) \sqrt[3]{1-x^3}} \, dx","x^2 \left(-\, _2F_1\left(\frac{2}{3},\frac{4}{3};\frac{5}{3};x^3\right)\right)+\frac{x}{\sqrt[3]{1-x^3}}+\frac{1}{\sqrt[3]{1-x^3}}",1,"Could not integrate","F",-1
105,0,0,39,11.1076364,"\int \frac{(1-x)^2}{\left(1-x^3\right)^{4/3}} \, dx","IntegrateAlgebraic[(1 - x)^2/(1 - x^3)^(4/3),x]","\int \frac{(1-x)^2}{\left(1-x^3\right)^{4/3}} \, dx","x^2 \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};x^3\right)+\frac{(1-2 x) x+1}{\sqrt[3]{1-x^3}}",1,"Could not integrate","F",-1
106,1,105,67,0.155621,"\int \left(1-x^3\right)^{2/3} \, dx","IntegrateAlgebraic[(1 - x^3)^(2/3),x]","\frac{1}{3} \left(1-x^3\right)^{2/3} x+\frac{2}{9} \log \left(\sqrt[3]{1-x^3}+x\right)+\frac{2 \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{1-x^3}-x}\right)}{3 \sqrt{3}}-\frac{1}{9} \log \left(-\sqrt[3]{1-x^3} x+\left(1-x^3\right)^{2/3}+x^2\right)","\frac{1}{3} \left(1-x^3\right)^{2/3} x+\frac{1}{3} \log \left(\sqrt[3]{1-x^3}+x\right)-\frac{2 \tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"(x*(1 - x^3)^(2/3))/3 + (2*ArcTan[(Sqrt[3]*x)/(-x + 2*(1 - x^3)^(1/3))])/(3*Sqrt[3]) + (2*Log[x + (1 - x^3)^(1/3)])/9 - Log[x^2 - x*(1 - x^3)^(1/3) + (1 - x^3)^(2/3)]/9","A",1
107,1,94,70,0.0733106,"\int \frac{\left(1-x^3\right)^{2/3}}{x} \, dx","IntegrateAlgebraic[(1 - x^3)^(2/3)/x,x]","\frac{1}{2} \left(1-x^3\right)^{2/3}+\frac{1}{3} \log \left(\sqrt[3]{1-x^3}-1\right)-\frac{1}{6} \log \left(\left(1-x^3\right)^{2/3}+\sqrt[3]{1-x^3}+1\right)+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{1-x^3}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3}}","\frac{1}{2} \left(1-x^3\right)^{2/3}+\frac{1}{2} \log \left(1-\sqrt[3]{1-x^3}\right)+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\log (x)}{2}",1,"(1 - x^3)^(2/3)/2 + ArcTan[1/Sqrt[3] + (2*(1 - x^3)^(1/3))/Sqrt[3]]/Sqrt[3] + Log[-1 + (1 - x^3)^(1/3)]/3 - Log[1 + (1 - x^3)^(1/3) + (1 - x^3)^(2/3)]/6","A",1
108,0,0,384,5.4002674,"\int \frac{\left(1-x^3\right)^{2/3}}{a+b x} \, dx","IntegrateAlgebraic[(1 - x^3)^(2/3)/(a + b*x),x]","\int \frac{\left(1-x^3\right)^{2/3}}{a+b x} \, dx","-\frac{\left(a^3+b^3\right)^{2/3} \log \left(a^3+b^3 x^3\right)}{3 b^3}+\frac{\left(a^3+b^3\right)^{2/3} \log \left(-\frac{x \sqrt[3]{a^3+b^3}}{a}-\sqrt[3]{1-x^3}\right)}{2 b^3}+\frac{\left(a^3+b^3\right)^{2/3} \log \left(\sqrt[3]{a^3+b^3}-b \sqrt[3]{1-x^3}\right)}{2 b^3}-\frac{\left(a^3+b^3\right)^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 x \sqrt[3]{a^3+b^3}}{a \sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt{3} b^3}+\frac{\left(a^3+b^3\right)^{2/3} \tan ^{-1}\left(\frac{\frac{2 b \sqrt[3]{1-x^3}}{\sqrt[3]{a^3+b^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} b^3}-\frac{a^2 \log \left(\sqrt[3]{1-x^3}+x\right)}{2 b^3}+\frac{a^2 \tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt{3} b^3}-\frac{x^2 \left(a^3+b^3\right) F_1\left(\frac{2}{3};\frac{1}{3},1;\frac{5}{3};x^3,-\frac{b^3 x^3}{a^3}\right)}{2 a^2 b^2}+\frac{a x^2 \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};x^3\right)}{2 b^2}+\frac{\left(1-x^3\right)^{2/3}}{2 b}",1,"Could not integrate","F",-1
109,0,0,234,13.238118,"\int \frac{\left(1-x^3\right)^{2/3}}{\left(1-x+x^2\right)^2} \, dx","IntegrateAlgebraic[(1 - x^3)^(2/3)/(1 - x + x^2)^2,x]","\int \frac{\left(1-x^3\right)^{2/3}}{\left(1-x+x^2\right)^2} \, dx","\frac{1}{3} x^2 \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};x^3\right)+\frac{\left(1-x^3\right)^{2/3} x}{3 \left(x^3+1\right)}-\frac{\left(1-x^3\right)^{2/3}}{3 \left(x^3+1\right)}-\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{3 \sqrt[3]{2}}+\frac{\log \left(-\sqrt[3]{1-x^3}-\sqrt[3]{2} x\right)}{3 \sqrt[3]{2}}-\frac{2^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{3 \sqrt{3}}-\frac{2^{2/3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{3 \sqrt{3}}+\frac{2 \left(1-x^3\right)^{2/3} x^2}{3 \left(x^3+1\right)}",1,"Could not integrate","F",-1
110,0,0,199,20.1234224,"\int \frac{(1-2 x) \left(1-x^3\right)^{2/3}}{\left(1-x+x^2\right)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)*(1 - x^3)^(2/3))/(1 - x + x^2)^2,x]","\int \frac{(1-2 x) \left(1-x^3\right)^{2/3}}{\left(1-x+x^2\right)^2} \, dx","\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{\sqrt[3]{2}}-\frac{\log \left(-\sqrt[3]{1-x^3}-\sqrt[3]{2} x\right)}{\sqrt[3]{2}}+\log \left(\sqrt[3]{1-x^3}+x\right)-\frac{2 \tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{2^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{2^{2/3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\left(1-x^3\right)^{2/3}}{x^2-x+1}",1,"Could not integrate","F",-1
111,0,0,177,4.970008,"\int \frac{\left(1-x^3\right)^{2/3}}{1+x} \, dx","IntegrateAlgebraic[(1 - x^3)^(2/3)/(1 + x),x]","\int \frac{\left(1-x^3\right)^{2/3}}{1+x} \, dx","\frac{1}{2} x^2 \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};x^3\right)+\frac{1}{2} \left(1-x^3\right)^{2/3}-\frac{1}{2} \log \left(\sqrt[3]{1-x^3}+x\right)+\frac{3 \log \left(2^{2/3} \sqrt[3]{1-x^3}+x-1\right)}{2 \sqrt[3]{2}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1}{\sqrt{3}}\right)}{\sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\log \left((1-x) (x+1)^2\right)}{2 \sqrt[3]{2}}",1,"Could not integrate","F",-1
112,0,0,177,36.9977354,"\int \frac{\left(1-x+x^2\right) \left(1-x^3\right)^{2/3}}{1+x^3} \, dx","IntegrateAlgebraic[((1 - x + x^2)*(1 - x^3)^(2/3))/(1 + x^3),x]","\int \frac{\left(1-x+x^2\right) \left(1-x^3\right)^{2/3}}{1+x^3} \, dx","\frac{1}{2} x^2 \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};x^3\right)+\frac{1}{2} \left(1-x^3\right)^{2/3}-\frac{1}{2} \log \left(\sqrt[3]{1-x^3}+x\right)+\frac{3 \log \left(2^{2/3} \sqrt[3]{1-x^3}+x-1\right)}{2 \sqrt[3]{2}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1}{\sqrt{3}}\right)}{\sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\log \left((1-x) (x+1)^2\right)}{2 \sqrt[3]{2}}",1,"Could not integrate","F",-1
113,1,212,132,0.3804568,"\int \frac{\left(1-x^3\right)^{2/3}}{1+x^3} \, dx","IntegrateAlgebraic[(1 - x^3)^(2/3)/(1 + x^3),x]","-\frac{1}{3} \log \left(\sqrt[3]{1-x^3}+x\right)+\frac{1}{3} 2^{2/3} \log \left(2^{2/3} \sqrt[3]{1-x^3}+2 x\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{1-x^3}-x}\right)}{\sqrt{3}}+\frac{2^{2/3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{1-x^3}-x}\right)}{\sqrt{3}}+\frac{1}{6} \log \left(-\sqrt[3]{1-x^3} x+\left(1-x^3\right)^{2/3}+x^2\right)-\frac{\log \left(2^{2/3} \sqrt[3]{1-x^3} x-\sqrt[3]{2} \left(1-x^3\right)^{2/3}-2 x^2\right)}{3 \sqrt[3]{2}}","-\frac{\log \left(x^3+1\right)}{3 \sqrt[3]{2}}+\frac{\log \left(-\sqrt[3]{1-x^3}-\sqrt[3]{2} x\right)}{\sqrt[3]{2}}-\frac{1}{2} \log \left(\sqrt[3]{1-x^3}+x\right)+\frac{\tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{2^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt{3}}",1,"-(ArcTan[(Sqrt[3]*x)/(-x + 2*(1 - x^3)^(1/3))]/Sqrt[3]) + (2^(2/3)*ArcTan[(Sqrt[3]*x)/(-x + 2^(2/3)*(1 - x^3)^(1/3))])/Sqrt[3] - Log[x + (1 - x^3)^(1/3)]/3 + (2^(2/3)*Log[2*x + 2^(2/3)*(1 - x^3)^(1/3)])/3 + Log[x^2 - x*(1 - x^3)^(1/3) + (1 - x^3)^(2/3)]/6 - Log[-2*x^2 + 2^(2/3)*x*(1 - x^3)^(1/3) - 2^(1/3)*(1 - x^3)^(2/3)]/(3*2^(1/3))","A",1
114,0,0,250,14.2249923,"\int \frac{x \left(1-x^3\right)^{2/3}}{1+x^3} \, dx","IntegrateAlgebraic[(x*(1 - x^3)^(2/3))/(1 + x^3),x]","\int \frac{x \left(1-x^3\right)^{2/3}}{1+x^3} \, dx","-\frac{1}{2} x^2 \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};x^3\right)+\frac{\log \left(\frac{2^{2/3} (1-x)^2}{\left(1-x^3\right)^{2/3}}-\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{3 \sqrt[3]{2}}-\frac{1}{3} 2^{2/3} \log \left(\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)-\frac{\log \left(2^{2/3} \sqrt[3]{1-x^3}+x-1\right)}{2 \sqrt[3]{2}}+\frac{2^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}+\frac{\log \left((1-x) (x+1)^2\right)}{6 \sqrt[3]{2}}",1,"Could not integrate","F",-1
115,0,0,383,16.5816076,"\int \frac{(1-x) \left(1-x^3\right)^{2/3}}{1+x^3} \, dx","IntegrateAlgebraic[((1 - x)*(1 - x^3)^(2/3))/(1 + x^3),x]","\int \frac{(1-x) \left(1-x^3\right)^{2/3}}{1+x^3} \, dx","\frac{1}{2} x^2 \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};x^3\right)-\frac{\log \left(x^3+1\right)}{3 \sqrt[3]{2}}-\frac{\log \left(\frac{2^{2/3} (1-x)^2}{\left(1-x^3\right)^{2/3}}-\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{3 \sqrt[3]{2}}+\frac{1}{3} 2^{2/3} \log \left(\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)+\frac{\log \left(-\sqrt[3]{1-x^3}-\sqrt[3]{2} x\right)}{\sqrt[3]{2}}-\frac{1}{2} \log \left(\sqrt[3]{1-x^3}+x\right)+\frac{\log \left(2^{2/3} \sqrt[3]{1-x^3}+x-1\right)}{2 \sqrt[3]{2}}-\frac{2^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{2^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\log \left((1-x) (x+1)^2\right)}{6 \sqrt[3]{2}}",1,"Could not integrate","F",-1
116,1,338,272,2.5002895,"\int \frac{\sqrt[3]{1-x^3}}{1+x^3} \, dx","IntegrateAlgebraic[(1 - x^3)^(1/3)/(1 + x^3),x]","\frac{1}{3} \sqrt[3]{2} \log \left(-\sqrt[3]{1-x^3}+\sqrt[3]{2} x-\sqrt[3]{2}\right)+\frac{\log \left(2 \sqrt[3]{1-x^3}+\sqrt[3]{2} x-\sqrt[3]{2}\right)}{3\ 2^{2/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{1-x^3}}{\sqrt[3]{1-x^3}-\sqrt[3]{2} x+\sqrt[3]{2}}\right)}{2^{2/3} \sqrt{3}}-\frac{\sqrt[3]{2} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{1-x^3}}{\sqrt[3]{1-x^3}+2 \sqrt[3]{2} x-2 \sqrt[3]{2}}\right)}{\sqrt{3}}-\frac{\log \left(\left(1-x^3\right)^{2/3}+\left(\sqrt[3]{2} x-\sqrt[3]{2}\right) \sqrt[3]{1-x^3}+2^{2/3} x^2-2\ 2^{2/3} x+2^{2/3}\right)}{3\ 2^{2/3}}-\frac{\log \left(4 \left(1-x^3\right)^{2/3}+\left(2 \sqrt[3]{2}-2 \sqrt[3]{2} x\right) \sqrt[3]{1-x^3}+2^{2/3} x^2-2\ 2^{2/3} x+2^{2/3}\right)}{6\ 2^{2/3}}","\frac{\log \left(2^{2/3}-\frac{1-x}{\sqrt[3]{1-x^3}}\right)}{3\ 2^{2/3}}-\frac{\log \left(\frac{2^{2/3} (1-x)^2}{\left(1-x^3\right)^{2/3}}-\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{3\ 2^{2/3}}+\frac{1}{3} \sqrt[3]{2} \log \left(\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)-\frac{\log \left(\frac{(1-x)^2}{\left(1-x^3\right)^{2/3}}+\frac{2^{2/3} (1-x)}{\sqrt[3]{1-x^3}}+2 \sqrt[3]{2}\right)}{6\ 2^{2/3}}+\frac{\sqrt[3]{2} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3}}",1,"-(ArcTan[(Sqrt[3]*(1 - x^3)^(1/3))/(2^(1/3) - 2^(1/3)*x + (1 - x^3)^(1/3))]/(2^(2/3)*Sqrt[3])) - (2^(1/3)*ArcTan[(Sqrt[3]*(1 - x^3)^(1/3))/(-2*2^(1/3) + 2*2^(1/3)*x + (1 - x^3)^(1/3))])/Sqrt[3] + (2^(1/3)*Log[-2^(1/3) + 2^(1/3)*x - (1 - x^3)^(1/3)])/3 + Log[-2^(1/3) + 2^(1/3)*x + 2*(1 - x^3)^(1/3)]/(3*2^(2/3)) - Log[2^(2/3) - 2*2^(2/3)*x + 2^(2/3)*x^2 + (-2^(1/3) + 2^(1/3)*x)*(1 - x^3)^(1/3) + (1 - x^3)^(2/3)]/(3*2^(2/3)) - Log[2^(2/3) - 2*2^(2/3)*x + 2^(2/3)*x^2 + (2*2^(1/3) - 2*2^(1/3)*x)*(1 - x^3)^(1/3) + 4*(1 - x^3)^(2/3)]/(6*2^(2/3))","A",1