1,1,15,0,0.0014936,"\int \frac{1}{\sqrt{1-a x}} \, dx","Int[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",1,1,10,0.1000,1,"{32}"
2,1,52,0,0.0558809,"\int \frac{-2 \log \left(-\sqrt{-1+a x}\right)+\log (-1+a x)}{2 \pi  \sqrt{-1+a x}} \, dx","Int[(-2*Log[-Sqrt[-1 + a*x]] + Log[-1 + a*x])/(2*Pi*Sqrt[-1 + a*x]),x]","\frac{\sqrt{a x-1} \log (a x-1)}{\pi  a}-\frac{2 \sqrt{a x-1} \log \left(-\sqrt{a x-1}\right)}{\pi  a}","-\frac{2 \sqrt{1-a x}}{a}",1,"(-2*Sqrt[-1 + a*x]*Log[-Sqrt[-1 + a*x]])/(a*Pi) + (Sqrt[-1 + a*x]*Log[-1 + a*x])/(a*Pi)","C",5,2,37,0.05405,1,"{12, 2295}"
3,1,82,0,0.0758864,"\int \frac{1}{\left(2 x+\sqrt{1+x^2}\right)^2} \, dx","Int[(2*x + Sqrt[1 + x^2])^(-2),x]","\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}}","\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)) - ArcTanh[Sqrt[3]*x]/(3*Sqrt[3]) + ArcTanh[(Sqrt[3]*Sqrt[1 + x^2])/2]/(3*Sqrt[3])","A",9,6,15,0.4000,1,"{6742, 199, 207, 444, 47, 63}"
4,1,43,0,0.0123968,"\int \frac{1}{\sqrt{-1+x^2} \left(-4+3 x^2\right)^2} \, dx","Int[1/(Sqrt[-1 + x^2]*(-4 + 3*x^2)^2),x]","\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)","\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*ArcTanh[x/(2*Sqrt[-1 + x^2])])/16","A",3,3,19,0.1579,1,"{382, 377, 207}"
5,1,74,0,0.0559415,"\int \frac{1}{\left(2 \sqrt{x}+\sqrt{1+x}\right)^2} \, dx","Int[(2*Sqrt[x] + Sqrt[1 + x])^(-2),x]","-\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)","-\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,"8/(9*(1 - 3*x)) - (4*Sqrt[x]*Sqrt[1 + x])/(3*(1 - 3*x)) - (8*ArcSinh[Sqrt[x]])/9 + (10*ArcTanh[(2*Sqrt[x])/Sqrt[1 + x]])/9 + (5*Log[1 - 3*x])/9","A",8,7,17,0.4118,1,"{6742, 97, 157, 54, 215, 93, 207}"
6,1,64,0,0.0260134,"\int \frac{\sqrt{-1+x^2}}{(-i+x)^2} \, dx","Int[Sqrt[-1 + x^2]/(-I + x)^2,x]","\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)","\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) - (I*ArcTan[(1 - I*x)/(Sqrt[2]*Sqrt[-1 + x^2])])/Sqrt[2] + ArcTanh[x/Sqrt[-1 + x^2]]","A",6,6,17,0.3529,1,"{733, 844, 217, 206, 725, 204}"
7,1,48,0,0.0134643,"\int \frac{1}{\sqrt{-1+x^2} \left(1+x^2\right)^2} \, dx","Int[1/(Sqrt[-1 + x^2]*(1 + x^2)^2),x]","\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)}","\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,"-(x*Sqrt[-1 + x^2])/(4*(1 + x^2)) + (3*ArcTanh[(Sqrt[2]*x)/Sqrt[-1 + x^2]])/(4*Sqrt[2])","A",3,3,17,0.1765,1,"{382, 377, 206}"
8,1,30,0,0.0824455,"\int \frac{1}{\left(\sqrt{-1+x}+\sqrt{x}\right)^2 \sqrt{-1+x}} \, dx","Int[1/((Sqrt[-1 + x] + Sqrt[x])^2*Sqrt[-1 + x]),x]","-\frac{4 x^{3/2}}{3}+\frac{4}{3} (x-1)^{3/2}+2 \sqrt{x-1}","-\frac{4 x^{3/2}}{3}+\frac{4}{3} (x-1)^{3/2}+2 \sqrt{x-1}",1,"2*Sqrt[-1 + x] + (4*(-1 + x)^(3/2))/3 - (4*x^(3/2))/3","A",4,2,23,0.08696,1,"{6689, 43}"
9,1,365,0,0.5057958,"\int \frac{1}{\sqrt{-1+x^2} \left(\sqrt{x}+\sqrt{-1+x^2}\right)^2} \, dx","Int[1/(Sqrt[-1 + x^2]*(Sqrt[x] + Sqrt[-1 + x^2])^2),x]","-\frac{2 \sqrt{x^2-1} (1-2 x)}{5 \left(-x^2+x+1\right)}+\frac{2 \sqrt{x} (1-2 x)}{5 \left(-x^2+x+1\right)}-\frac{2}{5} \sqrt{\frac{1}{5} \left(5 \sqrt{5}-2\right)} \tan ^{-1}\left(\frac{2-\left(1-\sqrt{5}\right) x}{\sqrt{2 \left(\sqrt{5}-1\right)} \sqrt{x^2-1}}\right)+\sqrt{\frac{2}{5 \left(\sqrt{5}-1\right)}} \tan ^{-1}\left(\frac{2-\left(1-\sqrt{5}\right) x}{\sqrt{2 \left(\sqrt{5}-1\right)} \sqrt{x^2-1}}\right)-\frac{2}{5} \sqrt{\frac{1}{5} \left(2+5 \sqrt{5}\right)} \tanh ^{-1}\left(\frac{2-\left(1+\sqrt{5}\right) x}{\sqrt{2 \left(1+\sqrt{5}\right)} \sqrt{x^2-1}}\right)+\sqrt{\frac{2}{5 \left(1+\sqrt{5}\right)}} \tanh ^{-1}\left(\frac{2-\left(1+\sqrt{5}\right) x}{\sqrt{2 \left(1+\sqrt{5}\right)} \sqrt{x^2-1}}\right)+\frac{1}{5} \sqrt{\frac{2}{5} \left(5 \sqrt{5}-11\right)} \tan ^{-1}\left(\sqrt{\frac{2}{\sqrt{5}-1}} \sqrt{x}\right)-\frac{1}{5} \sqrt{\frac{2}{5} \left(11+5 \sqrt{5}\right)} \tanh ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} \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*(1 - 2*x)*Sqrt[x])/(5*(1 + x - x^2)) - (2*(1 - 2*x)*Sqrt[-1 + x^2])/(5*(1 + x - x^2)) + (Sqrt[(2*(-11 + 5*Sqrt[5]))/5]*ArcTan[Sqrt[2/(-1 + Sqrt[5])]*Sqrt[x]])/5 + Sqrt[2/(5*(-1 + Sqrt[5]))]*ArcTan[(2 - (1 - Sqrt[5])*x)/(Sqrt[2*(-1 + Sqrt[5])]*Sqrt[-1 + x^2])] - (2*Sqrt[(-2 + 5*Sqrt[5])/5]*ArcTan[(2 - (1 - Sqrt[5])*x)/(Sqrt[2*(-1 + Sqrt[5])]*Sqrt[-1 + x^2])])/5 - (Sqrt[(2*(11 + 5*Sqrt[5]))/5]*ArcTanh[Sqrt[2/(1 + Sqrt[5])]*Sqrt[x]])/5 + Sqrt[2/(5*(1 + Sqrt[5]))]*ArcTanh[(2 - (1 + Sqrt[5])*x)/(Sqrt[2*(1 + Sqrt[5])]*Sqrt[-1 + x^2])] - (2*Sqrt[(2 + 5*Sqrt[5])/5]*ArcTanh[(2 - (1 + Sqrt[5])*x)/(Sqrt[2*(1 + Sqrt[5])]*Sqrt[-1 + x^2])])/5","A",18,12,27,0.4444,0,"{6742, 736, 826, 1166, 207, 203, 1018, 1034, 725, 206, 204, 985}"
10,1,541,0,0.7510868,"\int \frac{\left(\sqrt{x}-\sqrt{-1+x^2}\right)^2}{\left(1+x-x^2\right)^2 \sqrt{-1+x^2}} \, dx","Int[(Sqrt[x] - Sqrt[-1 + x^2])^2/((1 + x - x^2)^2*Sqrt[-1 + x^2]),x]","-\frac{\sqrt{x^2-1} (1-2 x)}{5 \left(-x^2+x+1\right)}+\frac{2 \sqrt{x} (1-2 x)}{5 \left(-x^2+x+1\right)}-\frac{(3-x) \sqrt{x^2-1}}{5 \left(-x^2+x+1\right)}+\frac{(x+2) \sqrt{x^2-1}}{5 \left(-x^2+x+1\right)}+\frac{1}{5} \sqrt{\frac{1}{5} \left(2+5 \sqrt{5}\right)} \tan ^{-1}\left(\frac{2-\left(1-\sqrt{5}\right) x}{\sqrt{2 \left(\sqrt{5}-1\right)} \sqrt{x^2-1}}\right)-\frac{1}{5} \sqrt{\frac{1}{5} \left(5 \sqrt{5}-2\right)} \tan ^{-1}\left(\frac{2-\left(1-\sqrt{5}\right) x}{\sqrt{2 \left(\sqrt{5}-1\right)} \sqrt{x^2-1}}\right)-\frac{1}{5} \sqrt{\frac{1}{10} \left(5 \sqrt{5}-11\right)} \tan ^{-1}\left(\frac{2-\left(1-\sqrt{5}\right) x}{\sqrt{2 \left(\sqrt{5}-1\right)} \sqrt{x^2-1}}\right)+\frac{1}{5} \sqrt{\frac{1}{10} \left(11+5 \sqrt{5}\right)} \tanh ^{-1}\left(\frac{2-\left(1+\sqrt{5}\right) x}{\sqrt{2 \left(1+\sqrt{5}\right)} \sqrt{x^2-1}}\right)-\frac{1}{5} \sqrt{\frac{1}{5} \left(2+5 \sqrt{5}\right)} \tanh ^{-1}\left(\frac{2-\left(1+\sqrt{5}\right) x}{\sqrt{2 \left(1+\sqrt{5}\right)} \sqrt{x^2-1}}\right)-\frac{1}{5} \sqrt{\frac{1}{5} \left(5 \sqrt{5}-2\right)} \tanh ^{-1}\left(\frac{2-\left(1+\sqrt{5}\right) x}{\sqrt{2 \left(1+\sqrt{5}\right)} \sqrt{x^2-1}}\right)+\frac{1}{5} \sqrt{\frac{2}{5} \left(5 \sqrt{5}-11\right)} \tan ^{-1}\left(\sqrt{\frac{2}{\sqrt{5}-1}} \sqrt{x}\right)-\frac{1}{5} \sqrt{\frac{2}{5} \left(11+5 \sqrt{5}\right)} \tanh ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} \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*(1 - 2*x)*Sqrt[x])/(5*(1 + x - x^2)) - ((1 - 2*x)*Sqrt[-1 + x^2])/(5*(1 + x - x^2)) - ((3 - x)*Sqrt[-1 + x^2])/(5*(1 + x - x^2)) + ((2 + x)*Sqrt[-1 + x^2])/(5*(1 + x - x^2)) + (Sqrt[(2*(-11 + 5*Sqrt[5]))/5]*ArcTan[Sqrt[2/(-1 + Sqrt[5])]*Sqrt[x]])/5 - (Sqrt[(-11 + 5*Sqrt[5])/10]*ArcTan[(2 - (1 - Sqrt[5])*x)/(Sqrt[2*(-1 + Sqrt[5])]*Sqrt[-1 + x^2])])/5 - (Sqrt[(-2 + 5*Sqrt[5])/5]*ArcTan[(2 - (1 - Sqrt[5])*x)/(Sqrt[2*(-1 + Sqrt[5])]*Sqrt[-1 + x^2])])/5 + (Sqrt[(2 + 5*Sqrt[5])/5]*ArcTan[(2 - (1 - Sqrt[5])*x)/(Sqrt[2*(-1 + Sqrt[5])]*Sqrt[-1 + x^2])])/5 - (Sqrt[(2*(11 + 5*Sqrt[5]))/5]*ArcTanh[Sqrt[2/(1 + Sqrt[5])]*Sqrt[x]])/5 - (Sqrt[(-2 + 5*Sqrt[5])/5]*ArcTanh[(2 - (1 + Sqrt[5])*x)/(Sqrt[2*(1 + Sqrt[5])]*Sqrt[-1 + x^2])])/5 - (Sqrt[(2 + 5*Sqrt[5])/5]*ArcTanh[(2 - (1 + Sqrt[5])*x)/(Sqrt[2*(1 + Sqrt[5])]*Sqrt[-1 + x^2])])/5 + (Sqrt[(11 + 5*Sqrt[5])/10]*ArcTanh[(2 - (1 + Sqrt[5])*x)/(Sqrt[2*(1 + Sqrt[5])]*Sqrt[-1 + x^2])])/5","B",25,13,39,0.3333,0,"{6742, 736, 826, 1166, 207, 203, 975, 1034, 725, 206, 204, 1018, 1065}"
11,1,138,0,0.0750856,"\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","Int[1/(Sqrt[2]*(1 + x)^2*Sqrt[-I + x^2]) + 1/(Sqrt[2]*(1 + x)^2*Sqrt[I + x^2]),x]","-\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}}","-\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 - I/2)*Sqrt[-I + x^2])/(Sqrt[2]*(1 + x)) - ((1/2 - I/2)*Sqrt[I + x^2])/(Sqrt[2]*(1 + x)) + ArcTanh[(I + x)/(Sqrt[1 - I]*Sqrt[-I + x^2])]/((1 - I)^(3/2)*Sqrt[2]) - ArcTanh[(I - x)/(Sqrt[1 + I]*Sqrt[I + x^2])]/((1 + I)^(3/2)*Sqrt[2])","A",7,3,45,0.06667,1,"{731, 725, 206}"
12,1,125,0,0.1852943,"\int \frac{\sqrt{x^2+\sqrt{1+x^4}}}{(1+x)^2 \sqrt{1+x^4}} \, dx","Int[Sqrt[x^2 + Sqrt[1 + x^4]]/((1 + x)^2*Sqrt[1 + x^4]),x]","-\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)","-\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,"-Sqrt[1 - I*x^2]/(2*(1 + x)) - Sqrt[1 + I*x^2]/(2*(1 + x)) - ((1 - I)^(3/2)*ArcTanh[(1 + I*x)/(Sqrt[1 - I]*Sqrt[1 - I*x^2])])/4 - ((1 + I)^(3/2)*ArcTanh[(1 - I*x)/(Sqrt[1 + I]*Sqrt[1 + I*x^2])])/4","A",7,4,32,0.1250,1,"{2133, 731, 725, 206}"
13,1,81,0,0.1624702,"\int \frac{\sqrt{x^2+\sqrt{1+x^4}}}{(1+x) \sqrt{1+x^4}} \, dx","Int[Sqrt[x^2 + Sqrt[1 + x^4]]/((1 + x)*Sqrt[1 + x^4]),x]","-\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)","-\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 - I]*ArcTanh[(1 + I*x)/(Sqrt[1 - I]*Sqrt[1 - I*x^2])])/2 - (Sqrt[1 + I]*ArcTanh[(1 - I*x)/(Sqrt[1 + I]*Sqrt[1 + I*x^2])])/2","A",5,3,32,0.09375,1,"{2133, 725, 206}"
14,1,31,0,0.0544915,"\int \frac{\sqrt{x^2+\sqrt{1+x^4}}}{\sqrt{1+x^4}} \, dx","Int[Sqrt[x^2 + Sqrt[1 + x^4]]/Sqrt[1 + x^4],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^2+\sqrt{x^4+1}}}\right)}{\sqrt{2}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^2+\sqrt{x^4+1}}}\right)}{\sqrt{2}}",1,"ArcTanh[(Sqrt[2]*x)/Sqrt[x^2 + Sqrt[1 + x^4]]]/Sqrt[2]","A",2,2,27,0.07407,1,"{2132, 206}"
15,1,33,0,0.0626,"\int \frac{\sqrt{-x^2+\sqrt{1+x^4}}}{\sqrt{1+x^4}} \, dx","Int[Sqrt[-x^2 + Sqrt[1 + x^4]]/Sqrt[1 + x^4],x]","\frac{\tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{\sqrt{x^4+1}-x^2}}\right)}{\sqrt{2}}","\frac{\tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{\sqrt{x^4+1}-x^2}}\right)}{\sqrt{2}}",1,"ArcTan[(Sqrt[2]*x)/Sqrt[-x^2 + Sqrt[1 + x^4]]]/Sqrt[2]","A",2,2,29,0.06897,1,"{2132, 203}"
16,1,19,0,0.2700524,"\int \frac{(-1+x)^{3/2}+(1+x)^{3/2}}{(-1+x)^{3/2} (1+x)^{3/2}} \, dx","Int[((-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",2,1,30,0.03333,1,"{6688}"
17,1,52,0,0.0232867,"\int \left(x+\sqrt{a+x^2}\right)^b \, dx","Int[(x + Sqrt[a + x^2])^b,x]","\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)}","\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,"-(a*(x + Sqrt[a + x^2])^(-1 + b))/(2*(1 - b)) + (x + Sqrt[a + x^2])^(1 + b)/(2*(1 + b))","A",3,2,13,0.1538,1,"{2117, 14}"
18,1,56,0,0.0224871,"\int \left(x-\sqrt{a+x^2}\right)^b \, dx","Int[(x - Sqrt[a + x^2])^b,x]","\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)}","\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,"-(a*(x - Sqrt[a + x^2])^(-1 + b))/(2*(1 - b)) + (x - Sqrt[a + x^2])^(1 + b)/(2*(1 + b))","A",3,2,15,0.1333,1,"{2117, 14}"
19,1,17,0,0.0535661,"\int \frac{\left(x+\sqrt{a+x^2}\right)^b}{\sqrt{a+x^2}} \, dx","Int[(x + Sqrt[a + x^2])^b/Sqrt[a + x^2],x]","\frac{\left(\sqrt{a+x^2}+x\right)^b}{b}","\frac{\left(\sqrt{a+x^2}+x\right)^b}{b}",1,"(x + Sqrt[a + x^2])^b/b","A",2,2,23,0.08696,1,"{2122, 30}"
20,1,20,0,0.0598107,"\int \frac{\left(x-\sqrt{a+x^2}\right)^b}{\sqrt{a+x^2}} \, dx","Int[(x - Sqrt[a + x^2])^b/Sqrt[a + x^2],x]","-\frac{\left(x-\sqrt{a+x^2}\right)^b}{b}","-\frac{\left(x-\sqrt{a+x^2}\right)^b}{b}",1,"-((x - Sqrt[a + x^2])^b/b)","A",2,2,25,0.08000,1,"{2122, 30}"
21,1,42,0,0.0334166,"\int \frac{1}{\left(a+b e^{p x}\right)^2} \, dx","Int[(a + b*E^(p*x))^(-2),x]","-\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)}","-\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,"1/(a*(a + b*E^(p*x))*p) + x/a^2 - Log[a + b*E^(p*x)]/(a^2*p)","A",3,2,11,0.1818,1,"{2282, 44}"
22,1,22,0,0.0235268,"\int \frac{1}{\left(b e^{-p x}+a e^{p x}\right)^2} \, dx","Int[(b/E^(p*x) + a*E^(p*x))^(-2),x]","-\frac{1}{2 a p \left(a e^{2 p x}+b\right)}","-\frac{1}{2 a p \left(a e^{2 p x}+b\right)}",1,"-1/(2*a*(b + a*E^(2*p*x))*p)","A",2,2,18,0.1111,1,"{2282, 261}"
23,1,62,0,0.0907172,"\int \frac{x}{\left(b e^{-p x}+a e^{p x}\right)^2} \, dx","Int[x/(b/E^(p*x) + a*E^(p*x))^2,x]","-\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)}","-\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,"x/(2*a*b*p) - x/(2*a*(b + a*E^(2*p*x))*p) - Log[b + a*E^(2*p*x)]/(4*a*b*p^2)","A",6,6,20,0.3000,1,"{2283, 2191, 2282, 36, 29, 31}"
24,1,86,0,0.0839424,"\int \frac{1-x+3 x^2}{\sqrt{1-x+x^2} \left(1+x+x^2\right)^2} \, dx","Int[(1 - x + 3*x^2)/(Sqrt[1 - x + x^2]*(1 + x + x^2)^2),x]","\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}}","\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) + Sqrt[2]*ArcTan[(Sqrt[2]*(1 + x))/Sqrt[1 - x + x^2]] - ArcTanh[(Sqrt[2/3]*(1 - x))/Sqrt[1 - x + x^2]]/Sqrt[6]","A",6,5,31,0.1613,1,"{1060, 1035, 1029, 206, 204}"
25,1,19,0,0.0651093,"\int \frac{\sqrt{x+\sqrt{a^2+x^2}}}{\sqrt{a^2+x^2}} \, dx","Int[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",2,2,29,0.06897,1,"{2122, 30}"
26,1,26,0,0.0970069,"\int \frac{\sqrt{b x+\sqrt{a+b^2 x^2}}}{\sqrt{a+b^2 x^2}} \, dx","Int[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",2,2,35,0.05714,1,"{2122, 30}"
27,1,63,0,0.2190294,"\int \frac{1}{x \sqrt{a^2+x^2} \sqrt{x+\sqrt{a^2+x^2}}} \, dx","Int[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",5,5,32,0.1562,1,"{2120, 329, 212, 206, 203}"
28,1,82,0,0.0719809,"\int \frac{\sqrt{x+\sqrt{a^2+x^2}}}{x} \, dx","Int[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",6,6,21,0.2857,1,"{2119, 459, 329, 212, 206, 203}"
29,1,679,0,4.7989127,"\int x^3 \log ^3(2+x) \log (3+x) \, dx","Int[x^3*Log[2 + x]^3*Log[3 + x],x]","-\frac{5609}{96} \text{PolyLog}(2,-x-2)-\frac{563}{8} \text{PolyLog}(3,-x-2)-\frac{195}{2} \text{PolyLog}(4,-x-2)-\frac{195}{4} \log ^2(x+2) \text{PolyLog}(2,-x-2)+\frac{563}{8} \log (x+2) \text{PolyLog}(2,-x-2)+\frac{195}{2} \log (x+2) \text{PolyLog}(3,-x-2)+\frac{3 x^4}{256}-\frac{763 x^3}{3456}+\frac{8029 x^2}{2304}+\frac{3}{64} x^4 \log ^2(x+2)+\frac{1}{4} x^4 \log ^3(x+2) \log (x+3)-\frac{3}{16} x^4 \log ^2(x+2) \log (x+3)-\frac{17}{48} x^3 \log ^2(x+2)+\frac{1}{2} x^3 \log ^2(x+2) \log (x+3)-\frac{3}{2} x^2 \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{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{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+6 x \log ^2(x+2) \log (x+3)-\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{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{81}{4} \log ^3(x+2) \log (x+3)+\frac{963}{16} \log ^2(x+2) \log (x+3)-25 x \log (x+2) \log (x+3)-\frac{3}{128} (x+2)^4 \log (x+2)+\frac{1}{2} (x+2)^3 \log (x+2)-\frac{273}{32} (x+2)^2 \log (x+2)+\frac{6365}{32} (x+2) \log (x+2)+\frac{1}{128} \left(-3 (x+2)^4+32 (x+2)^3-144 (x+2)^2+384 (x+2)-192 \log (x+2)\right) \log (x+2)+\frac{17}{72} \left((x+2)^3-9 (x+2)^2+36 (x+2)-24 \log (x+2)\right) \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)","-\frac{5609}{96} \text{PolyLog}(2,-x-2)-\frac{563}{8} \text{PolyLog}(3,-x-2)-\frac{195}{2} \text{PolyLog}(4,-x-2)-\frac{195}{4} \log ^2(x+2) \text{PolyLog}(2,-x-2)+\frac{563}{8} \log (x+2) \text{PolyLog}(2,-x-2)+\frac{195}{2} \log (x+2) \text{PolyLog}(3,-x-2)+\frac{3 x^4}{256}-\frac{763 x^3}{3456}+\frac{8029 x^2}{2304}+\frac{3}{64} x^4 \log ^2(x+2)+\frac{1}{4} x^4 \log ^3(x+2) \log (x+3)-\frac{3}{16} x^4 \log ^2(x+2) \log (x+3)-\frac{17}{48} x^3 \log ^2(x+2)+\frac{1}{2} x^3 \log ^2(x+2) \log (x+3)-\frac{3}{2} x^2 \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{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{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+6 x \log ^2(x+2) \log (x+3)-\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{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{81}{4} \log ^3(x+2) \log (x+3)+\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,"(-302177*x)/1152 + (8029*x^2)/2304 - (763*x^3)/3456 + (3*x^4)/256 + (377*(2 + x)^2)/64 - (71*(2 + x)^3)/216 + (3*(2 + x)^4)/256 + (2069*Log[2 + x])/144 - (187*x^2*Log[2 + x])/64 + (83*x^3*Log[2 + x])/288 - (3*x^4*Log[2 + x])/128 + (6365*(2 + x)*Log[2 + x])/32 - (273*(2 + x)^2*Log[2 + x])/32 + ((2 + x)^3*Log[2 + x])/2 - (3*(2 + x)^4*Log[2 + x])/128 + ((384*(2 + x) - 144*(2 + x)^2 + 32*(2 + x)^3 - 3*(2 + x)^4 - 192*Log[2 + x])*Log[2 + x])/128 + (17*(36*(2 + x) - 9*(2 + x)^2 + (2 + x)^3 - 24*Log[2 + x])*Log[2 + x])/72 + (43*Log[2 + x]^2)/12 - (17*x^3*Log[2 + x]^2)/48 + (3*x^4*Log[2 + x]^2)/64 - (1251*(2 + x)*Log[2 + x]^2)/16 + (273*(2 + x)^2*Log[2 + x]^2)/32 - (3*(2 + x)^3*Log[2 + x]^2)/4 + (3*(2 + x)^4*Log[2 + x]^2)/64 + (65*(2 + x)*Log[2 + x]^3)/4 - (33*(2 + x)^2*Log[2 + x]^3)/8 + (3*(2 + x)^3*Log[2 + x]^3)/4 - ((2 + x)^4*Log[2 + x]^3)/16 + (3891*Log[3 + x])/128 - (115*x^2*Log[3 + x])/48 + (37*x^3*Log[3 + x])/144 - (3*x^4*Log[3 + x])/128 + (415*(3 + x)*Log[3 + x])/12 - (4083*Log[2 + x]*Log[3 + x])/32 - 25*x*Log[2 + x]*Log[3 + x] + (13*x^2*Log[2 + x]*Log[3 + x])/4 - (7*x^3*Log[2 + x]*Log[3 + x])/12 + (3*x^4*Log[2 + x]*Log[3 + x])/32 + (963*Log[2 + x]^2*Log[3 + x])/16 + 6*x*Log[2 + x]^2*Log[3 + x] - (3*x^2*Log[2 + x]^2*Log[3 + x])/2 + (x^3*Log[2 + x]^2*Log[3 + x])/2 - (3*x^4*Log[2 + x]^2*Log[3 + x])/16 - (81*Log[2 + x]^3*Log[3 + x])/4 + (x^4*Log[2 + x]^3*Log[3 + x])/4 - (5609*PolyLog[2, -2 - x])/96 + (563*Log[2 + x]*PolyLog[2, -2 - x])/8 - (195*Log[2 + x]^2*PolyLog[2, -2 - x])/4 - (563*PolyLog[3, -2 - x])/8 + (195*Log[2 + x]*PolyLog[3, -2 - x])/2 - (195*PolyLog[4, -2 - x])/2","A",359,30,14,2.143,1,"{2439, 2416, 2389, 2296, 2295, 2401, 2390, 2305, 2304, 2396, 2433, 2374, 2383, 6589, 2411, 2346, 2302, 30, 2330, 2319, 43, 2334, 2301, 6742, 2430, 2393, 2391, 2394, 2395, 2398}"
30,1,17,0,0.0545937,"\int \frac{\left(x+\sqrt{b+x^2}\right)^a}{\sqrt{b+x^2}} \, dx","Int[(x + Sqrt[b + x^2])^a/Sqrt[b + x^2],x]","\frac{\left(\sqrt{b+x^2}+x\right)^a}{a}","\frac{\left(\sqrt{b+x^2}+x\right)^a}{a}",1,"(x + Sqrt[b + x^2])^a/a","A",2,2,23,0.08696,1,"{2122, 30}"
31,1,52,0,0.0239267,"\int \left(x+\sqrt{b+x^2}\right)^a \, dx","Int[(x + Sqrt[b + x^2])^a,x]","\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)}","\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,"-(b*(x + Sqrt[b + x^2])^(-1 + a))/(2*(1 - a)) + (x + Sqrt[b + x^2])^(1 + a)/(2*(1 + a))","A",3,2,13,0.1538,1,"{2117, 14}"
32,1,34,0,0.0436392,"\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","Int[(6 + 3*x^a + 2*x^(2*a))^a^(-1)*(x^a + x^(2*a) + x^(3*a)),x]","\frac{x^{a+1} \left(3 x^a+2 x^{2 a}+6\right)^{\frac{1}{a}+1}}{6 (a+1)}","\frac{x^{a+1} \left(3 x^a+2 x^{2 a}+6\right)^{\frac{1}{a}+1}}{6 (a+1)}",1,"(x^(1 + a)*(6 + 3*x^a + 2*x^(2*a))^(1 + a^(-1)))/(6*(1 + a))","A",2,2,33,0.06061,1,"{1594, 1747}"
33,1,58,0,0.0357832,"\int \frac{1}{x \sqrt[3]{1-x^2}} \, dx","Int[1/(x*(1 - x^2)^(1/3)),x]","\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}","\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 + 2*(1 - x^2)^(1/3))/Sqrt[3]])/2 - Log[x]/2 + (3*Log[1 - (1 - x^2)^(1/3)])/4","A",5,5,15,0.3333,1,"{266, 55, 618, 204, 31}"
34,1,58,0,0.0346961,"\int \frac{1}{x \left(1-x^2\right)^{2/3}} \, dx","Int[1/(x*(1 - x^2)^(2/3)),x]","\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}","\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 + 2*(1 - x^2)^(1/3))/Sqrt[3]])/2 - Log[x]/2 + (3*Log[1 - (1 - x^2)^(1/3)])/4","A",5,5,15,0.3333,1,"{266, 57, 618, 204, 31}"
35,1,49,0,0.0050845,"\int \frac{1}{\sqrt[3]{1-x^3}} \, dx","Int[(1 - x^3)^(-1/3),x]","\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{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[(1 - (2*x)/(1 - x^3)^(1/3))/Sqrt[3]]/Sqrt[3]) + Log[x + (1 - x^3)^(1/3)]/2","A",1,1,11,0.09091,1,"{239}"
36,1,55,0,0.0332979,"\int \frac{1}{x \sqrt[3]{1-x^3}} \, dx","Int[1/(x*(1 - x^3)^(1/3)),x]","\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}","\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 + 2*(1 - x^3)^(1/3))/Sqrt[3]]/Sqrt[3] - Log[x]/2 + Log[1 - (1 - x^3)^(1/3)]/2","A",5,5,15,0.3333,1,"{266, 55, 618, 204, 31}"
37,1,97,0,0.0438348,"\int \frac{1}{(1+x) \sqrt[3]{1-x^3}} \, dx","Int[1/((1 + x)*(1 - x^3)^(1/3)),x]","\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}}","\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[(1 + (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/Sqrt[3]])/(2*2^(1/3)) - Log[(1 - x)*(1 + x)^2]/(4*2^(1/3)) + (3*Log[-1 + x + 2^(2/3)*(1 - x^3)^(1/3)])/(4*2^(1/3))","A",1,1,17,0.05882,1,"{2148}"
38,1,145,0,0.1073685,"\int \frac{x}{(1+x) \sqrt[3]{1-x^3}} \, dx","Int[x/((1 + x)*(1 - x^3)^(1/3)),x]","\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}}","\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,"(Sqrt[3]*ArcTan[(1 + (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/Sqrt[3]])/(2*2^(1/3)) - ArcTan[(1 - (2*x)/(1 - x^3)^(1/3))/Sqrt[3]]/Sqrt[3] + Log[(1 - x)*(1 + x)^2]/(4*2^(1/3)) + Log[x + (1 - x^3)^(1/3)]/2 - (3*Log[-1 + x + 2^(2/3)*(1 - x^3)^(1/3)])/(4*2^(1/3))","A",3,3,18,0.1667,1,"{2152, 239, 2148}"
39,1,176,0,0.0249725,"\int \frac{1}{x \sqrt[3]{2-3 x+x^2}} \, dx","Int[1/(x*(2 - 3*x + x^2)^(1/3)),x]","\frac{3 \sqrt[3]{x-2} \sqrt[3]{x-1} \log \left(-\frac{(x-2)^{2/3}}{\sqrt[3]{2}}-\sqrt[3]{2} \sqrt[3]{x-1}\right)}{4 \sqrt[3]{2} \sqrt[3]{x^2-3 x+2}}-\frac{\sqrt[3]{x-2} \sqrt[3]{x-1} \log (x)}{2 \sqrt[3]{2} \sqrt[3]{x^2-3 x+2}}-\frac{\sqrt{3} \sqrt[3]{x-2} \sqrt[3]{x-1} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{\sqrt[3]{2} (x-2)^{2/3}}{\sqrt{3} \sqrt[3]{x-1}}\right)}{2 \sqrt[3]{2} \sqrt[3]{x^2-3 x+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]*(-2 + x)^(1/3)*(-1 + x)^(1/3)*ArcTan[1/Sqrt[3] - (2^(1/3)*(-2 + x)^(2/3))/(Sqrt[3]*(-1 + x)^(1/3))])/(2*2^(1/3)*(2 - 3*x + x^2)^(1/3)) + (3*(-2 + x)^(1/3)*(-1 + x)^(1/3)*Log[-((-2 + x)^(2/3)/2^(1/3)) - 2^(1/3)*(-1 + x)^(1/3)])/(4*2^(1/3)*(2 - 3*x + x^2)^(1/3)) - ((-2 + x)^(1/3)*(-1 + x)^(1/3)*Log[x])/(2*2^(1/3)*(2 - 3*x + x^2)^(1/3))","A",2,2,16,0.1250,1,"{755, 123}"
40,1,131,0,0.0728112,"\int \frac{1}{\sqrt[3]{-5+7 x-3 x^2+x^3}} \, dx","Int[(-5 + 7*x - 3*x^2 + x^3)^(-1/3),x]","\frac{\sqrt{3} \sqrt[3]{(x-1)^2+4} \sqrt[3]{x-1} \tan ^{-1}\left(\frac{\frac{2 (x-1)^{2/3}}{\sqrt[3]{(x-1)^2+4}}+1}{\sqrt{3}}\right)}{2 \sqrt[3]{(x-1)^3+4 (x-1)}}-\frac{3 \sqrt[3]{(x-1)^2+4} \sqrt[3]{x-1} \log \left((x-1)^{2/3}-\sqrt[3]{(x-1)^2+4}\right)}{4 \sqrt[3]{(x-1)^3+4 (x-1)}}","-\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,"(Sqrt[3]*(4 + (-1 + x)^2)^(1/3)*(-1 + x)^(1/3)*ArcTan[(1 + (2*(-1 + x)^(2/3))/(4 + (-1 + x)^2)^(1/3))/Sqrt[3]])/(2*(4*(-1 + x) + (-1 + x)^3)^(1/3)) - (3*(4 + (-1 + x)^2)^(1/3)*(-1 + x)^(1/3)*Log[-(4 + (-1 + x)^2)^(1/3) + (-1 + x)^(2/3)])/(4*(4*(-1 + x) + (-1 + x)^3)^(1/3))","A",5,5,17,0.2941,1,"{2067, 2011, 329, 275, 239}"
41,1,117,0,0.0564275,"\int \frac{1}{\sqrt[3]{x \left(-q+x^2\right)}} \, dx","Int[(x*(-q + x^2))^(-1/3),x]","\frac{\sqrt{3} \sqrt[3]{x} \sqrt[3]{x^2-q} \tan ^{-1}\left(\frac{\frac{2 x^{2/3}}{\sqrt[3]{x^2-q}}+1}{\sqrt{3}}\right)}{2 \sqrt[3]{x^3-q x}}-\frac{3 \sqrt[3]{x} \sqrt[3]{x^2-q} \log \left(x^{2/3}-\sqrt[3]{x^2-q}\right)}{4 \sqrt[3]{x^3-q x}}","-\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]*x^(1/3)*(-q + x^2)^(1/3)*ArcTan[(1 + (2*x^(2/3))/(-q + x^2)^(1/3))/Sqrt[3]])/(2*(-(q*x) + x^3)^(1/3)) - (3*x^(1/3)*(-q + x^2)^(1/3)*Log[x^(2/3) - (-q + x^2)^(1/3)])/(4*(-(q*x) + x^3)^(1/3))","A",5,5,13,0.3846,1,"{1979, 2011, 329, 275, 239}"
42,1,145,0,0.0978022,"\int \frac{1}{\sqrt[3]{(-1+x) \left(q-2 x+x^2\right)}} \, dx","Int[((-1 + x)*(q - 2*x + x^2))^(-1/3),x]","\frac{\sqrt{3} \sqrt[3]{x-1} \sqrt[3]{q+(x-1)^2-1} \tan ^{-1}\left(\frac{\frac{2 (x-1)^{2/3}}{\sqrt[3]{q+(x-1)^2-1}}+1}{\sqrt{3}}\right)}{2 \sqrt[3]{(x-1)^3-(1-q) (x-1)}}-\frac{3 \sqrt[3]{x-1} \sqrt[3]{q+(x-1)^2-1} \log \left((x-1)^{2/3}-\sqrt[3]{q+(x-1)^2-1}\right)}{4 \sqrt[3]{(x-1)^3-(1-q) (x-1)}}","-\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,"(Sqrt[3]*(-1 + q + (-1 + x)^2)^(1/3)*(-1 + x)^(1/3)*ArcTan[(1 + (2*(-1 + x)^(2/3))/(-1 + q + (-1 + x)^2)^(1/3))/Sqrt[3]])/(2*(-((1 - q)*(-1 + x)) + (-1 + x)^3)^(1/3)) - (3*(-1 + q + (-1 + x)^2)^(1/3)*(-1 + x)^(1/3)*Log[-(-1 + q + (-1 + x)^2)^(1/3) + (-1 + x)^(2/3)])/(4*(-((1 - q)*(-1 + x)) + (-1 + x)^3)^(1/3))","A",5,5,16,0.3125,1,"{2067, 2011, 329, 275, 239}"
43,0,0,0,21.9368582,"\int \frac{1}{x \sqrt[3]{(-1+x) \left(q-2 q x+x^2\right)}} \, dx","Int[1/(x*((-1 + x)*(q - 2*q*x + x^2))^(1/3)),x]","\int \frac{1}{x \sqrt[3]{(-1+x) \left(q-2 q x+x^2\right)}} \, dx","-\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*q - (1 - 5*q + 4*q^2 + (1 + 6*q - 15*q^2 + 8*q^3 + 3*Sqrt[3]*Sqrt[-((-1 + q)^3*q)])^(2/3))/(1 + 6*q - 15*q^2 + 8*q^3 + 3*Sqrt[3]*Sqrt[-((-1 + q)^3*q)])^(1/3) + 3*x)^(1/3)*(-1 + 5*q - 4*q^2 + ((1 - 4*q)^2*(1 - q)^2)/(1 + 6*q - 15*q^2 + 8*q^3 + 3*Sqrt[3]*Sqrt[(1 - q)^3*q])^(2/3) + (1 + 6*q - 15*q^2 + 8*q^3 + 3*Sqrt[3]*Sqrt[(1 - q)^3*q])^(2/3) + (3*(1 - 5*q + 4*q^2 + (1 + 6*q - 15*q^2 + 8*q^3 + 3*Sqrt[3]*Sqrt[(1 - q)^3*q])^(2/3))*((-1 - 2*q)/3 + x))/(1 + 6*q - 15*q^2 + 8*q^3 + 3*Sqrt[3]*Sqrt[(1 - q)^3*q])^(1/3) + 9*((-1 - 2*q)/3 + x)^2)^(1/3)*Defer[Subst][Defer[Int][1/(((1 + 2*q)/3 + x)*(-(1 - 5*q + 4*q^2 + (1 + 6*q - 15*q^2 + 8*q^3 + 3*Sqrt[3]*Sqrt[(1 - q)^3*q])^(2/3))/(3*(1 + 6*q - 15*q^2 + 8*q^3 + 3*Sqrt[3]*Sqrt[(1 - q)^3*q])^(1/3)) + x)^(1/3)*((-1 + 5*q - 4*q^2 + ((1 - 4*q)^2*(1 - q)^2)/(1 + 6*q - 15*q^2 + 8*q^3 + 3*Sqrt[3]*Sqrt[(1 - q)^3*q])^(2/3) + (1 + 6*q - 15*q^2 + 8*q^3 + 3*Sqrt[3]*Sqrt[(1 - q)^3*q])^(2/3))/9 + ((1 - 5*q + 4*q^2 + (1 + 6*q - 15*q^2 + 8*q^3 + 3*Sqrt[3]*Sqrt[(1 - q)^3*q])^(2/3))*x)/(3*(1 + 6*q - 15*q^2 + 8*q^3 + 3*Sqrt[3]*Sqrt[(1 - q)^3*q])^(1/3)) + x^2)^(1/3)), x], x, (-1 - 2*q)/3 + x])/(3*(-q + 3*q*x + (-1 - 2*q)*x^2 + x^3)^(1/3))","F",0,0,0,0,-1,"{}"
44,0,0,0,0.6107473,"\int \frac{2-(1+k) x}{\sqrt[3]{(1-x) x (1-k x)} (1-(1+k) x)} \, dx","Int[(2 - (1 + k)*x)/(((1 - x)*x*(1 - k*x))^(1/3)*(1 - (1 + k)*x)),x]","\int \frac{2-(1+k) x}{\sqrt[3]{(1-x) x (1-k x)} (1-(1+k) x)} \, dx","\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,"(3*(1 - x)^(1/3)*x*(1 - k*x)^(1/3)*AppellF1[2/3, 1/3, 1/3, 5/3, x, k*x])/(2*((1 - x)*x*(1 - k*x))^(1/3)) + ((1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Int][1/((1 - x)^(1/3)*x^(1/3)*(1 + (-1 - k)*x)*(1 - k*x)^(1/3)), x])/((1 - x)*x*(1 - k*x))^(1/3)","F",0,0,0,0,-1,"{}"
45,0,0,0,0.4616827,"\int \frac{1-k x}{(1+(-2+k) x) ((1-x) x (1-k x))^{2/3}} \, dx","Int[(1 - k*x)/((1 + (-2 + k)*x)*((1 - x)*x*(1 - k*x))^(2/3)),x]","\int \frac{1-k x}{(1+(-2+k) x) ((1-x) x (1-k x))^{2/3}} \, dx","\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 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Int][(1 - k*x)^(1/3)/((1 - x)^(2/3)*x^(2/3)*(1 + (-2 + k)*x)), x])/((1 - x)*x*(1 - k*x))^(2/3)","F",0,0,0,0,-1,"{}"
46,1,576,0,0.8461662,"\int \frac{a+b x+c x^2}{\left(1-x+x^2\right) \sqrt[3]{1-x^3}} \, dx","Int[(a + b*x + c*x^2)/((1 - x + x^2)*(1 - x^3)^(1/3)),x]","-\frac{\log \left(2\ 2^{2/3} \sqrt[3]{1-x^3}+2 x-i \sqrt{3}+1\right) \left(3 i b-\sqrt{3} \left(2 a+b-i \sqrt{3} c-c\right)\right)}{4 \sqrt[3]{2} \left(\sqrt{3}+i\right)}-\frac{\log \left(2\ 2^{2/3} \sqrt[3]{1-x^3}+2 x+i \sqrt{3}+1\right) \left(\sqrt{3} \left(2 a+b+i \sqrt{3} c-c\right)+3 i b\right)}{4 \sqrt[3]{2} \left(-\sqrt{3}+i\right)}-\frac{\tan ^{-1}\left(\frac{2-\frac{\sqrt[3]{2} \left(2 x-i \sqrt{3}+1\right)}{\sqrt[3]{1-x^3}}}{2 \sqrt{3}}\right) \left(2 a-i \sqrt{3} b+b-\left(1+i \sqrt{3}\right) c\right)}{2 \sqrt[3]{2} \left(\sqrt{3}+i\right)}+\frac{\tan ^{-1}\left(\frac{2-\frac{\sqrt[3]{2} \left(2 x+i \sqrt{3}+1\right)}{\sqrt[3]{1-x^3}}}{2 \sqrt{3}}\right) \left(2 a+i \sqrt{3} b+b+i \sqrt{3} c-c\right)}{2 \sqrt[3]{2} \left(-\sqrt{3}+i\right)}+\frac{\log \left(-\left(-2 x-i \sqrt{3}+1\right)^2 \left(2 x-i \sqrt{3}+1\right)\right) \left(3 i b-\sqrt{3} \left(2 a+b-i \sqrt{3} c-c\right)\right)}{12 \sqrt[3]{2} \left(\sqrt{3}+i\right)}+\frac{\log \left(-\left(-2 x+i \sqrt{3}+1\right)^2 \left(2 x+i \sqrt{3}+1\right)\right) \left(\sqrt{3} \left(2 a+b+i \sqrt{3} c-c\right)+3 i b\right)}{12 \sqrt[3]{2} \left(-\sqrt{3}+i\right)}+\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}}","\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,"-((c*ArcTan[(1 - (2*x)/(1 - x^3)^(1/3))/Sqrt[3]])/Sqrt[3]) - ((2*a + b - I*Sqrt[3]*b - (1 + I*Sqrt[3])*c)*ArcTan[(2 - (2^(1/3)*(1 - I*Sqrt[3] + 2*x))/(1 - x^3)^(1/3))/(2*Sqrt[3])])/(2*2^(1/3)*(I + Sqrt[3])) + ((2*a + b + I*Sqrt[3]*b - c + I*Sqrt[3]*c)*ArcTan[(2 - (2^(1/3)*(1 + I*Sqrt[3] + 2*x))/(1 - x^3)^(1/3))/(2*Sqrt[3])])/(2*2^(1/3)*(I - Sqrt[3])) + (((3*I)*b - Sqrt[3]*(2*a + b - c - I*Sqrt[3]*c))*Log[-((1 - I*Sqrt[3] - 2*x)^2*(1 - I*Sqrt[3] + 2*x))])/(12*2^(1/3)*(I + Sqrt[3])) + (((3*I)*b + Sqrt[3]*(2*a + b - c + I*Sqrt[3]*c))*Log[-((1 + I*Sqrt[3] - 2*x)^2*(1 + I*Sqrt[3] + 2*x))])/(12*2^(1/3)*(I - Sqrt[3])) + (c*Log[x + (1 - x^3)^(1/3)])/2 - (((3*I)*b - Sqrt[3]*(2*a + b - c - I*Sqrt[3]*c))*Log[1 - I*Sqrt[3] + 2*x + 2*2^(2/3)*(1 - x^3)^(1/3)])/(4*2^(1/3)*(I + Sqrt[3])) - (((3*I)*b + Sqrt[3]*(2*a + b - c + I*Sqrt[3]*c))*Log[1 + I*Sqrt[3] + 2*x + 2*2^(2/3)*(1 - x^3)^(1/3)])/(4*2^(1/3)*(I - Sqrt[3]))","C",7,3,32,0.09375,1,"{6728, 239, 2148}"
47,1,407,0,0.6762735,"\int \frac{1}{(3-2 x)^{11/2} \left(1+x+2 x^2\right)^5} \, dx","Int[1/((3 - 2*x)^(11/2)*(1 + x + 2*x^2)^5),x]","\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}","\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,"-19255/(395136*(3 - 2*x)^(9/2)) - 462025/(30118144*(3 - 2*x)^(7/2)) - 38491/(8605184*(3 - 2*x)^(5/2)) - 141045/(120472576*(3 - 2*x)^(3/2)) - 38225/(240945152*Sqrt[3 - 2*x]) + x/(28*(3 - 2*x)^(9/2)*(1 + x + 2*x^2)^4) + (23 + 73*x)/(1176*(3 - 2*x)^(9/2)*(1 + x + 2*x^2)^3) + (1387 + 3049*x)/(32928*(3 - 2*x)^(9/2)*(1 + x + 2*x^2)^2) + (5*(3049 + 4377*x))/(153664*(3 - 2*x)^(9/2)*(1 + x + 2*x^2)) + (5*Sqrt[(149046503977 + 40815066112*Sqrt[14])/2]*ArcTan[(Sqrt[7 + 2*Sqrt[14]] - 2*Sqrt[3 - 2*x])/Sqrt[-7 + 2*Sqrt[14]]])/3373232128 - (5*Sqrt[(149046503977 + 40815066112*Sqrt[14])/2]*ArcTan[(Sqrt[7 + 2*Sqrt[14]] + 2*Sqrt[3 - 2*x])/Sqrt[-7 + 2*Sqrt[14]]])/3373232128 + (5*Sqrt[(-149046503977 + 40815066112*Sqrt[14])/2]*Log[3 + Sqrt[14] - Sqrt[7 + 2*Sqrt[14]]*Sqrt[3 - 2*x] - 2*x])/6746464256 - (5*Sqrt[(-149046503977 + 40815066112*Sqrt[14])/2]*Log[3 + Sqrt[14] + Sqrt[7 + 2*Sqrt[14]]*Sqrt[3 - 2*x] - 2*x])/6746464256","A",19,9,20,0.4500,1,"{740, 822, 828, 826, 1169, 634, 618, 204, 628}"
48,1,648,0,1.1580983,"\int \frac{1}{(3-2 x)^{21/2} \left(1+x+2 x^2\right)^{10}} \, dx","Int[1/((3 - 2*x)^(21/2)*(1 + x + 2*x^2)^10),x]","\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}","\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,"4718120139975/(351733660450816*(3 - 2*x)^(19/2)) - 815900548375/(629418129227776*(3 - 2*x)^(17/2)) - 3029508823715/(1555033025150976*(3 - 2*x)^(15/2)) - 13515743021825/(13476952884641792*(3 - 2*x)^(13/2)) - 5846828446875/(14513641568075776*(3 - 2*x)^(11/2)) - 37283626871975/(261245548225363968*(3 - 2*x)^(9/2)) - 132355162272575/(2844673747342852096*(3 - 2*x)^(7/2)) - 11557581705725/(812763927812243456*(3 - 2*x)^(5/2)) - 46601678385075/(11378694989371408384*(3 - 2*x)^(3/2)) - 24229218097975/(22757389978742816768*Sqrt[3 - 2*x]) + x/(63*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^9) + (53 + 173*x)/(7056*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^8) + (8477 + 21409*x)/(691488*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^7) + (5*(21409 + 47471*x))/(6453888*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^6) + (41*(47471 + 92875*x))/(90354432*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^5) + (41*(3436375 + 5677637*x))/(5059848192*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^4) + (451*(811091 + 998691*x))/(10119696384*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^3) + (451*(28962039 + 14627273*x))/(283351498752*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^2) + (11275*(14627273 - 35058731*x))/(3966920982528*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)) + (11275*Sqrt[(7 + 2*Sqrt[14])/2]*(9756589235 + 2148932869*Sqrt[14])*ArcTan[(Sqrt[7 + 2*Sqrt[14]] - 2*Sqrt[3 - 2*x])/Sqrt[-7 + 2*Sqrt[14]]])/318603459702399434752 - (11275*Sqrt[(7 + 2*Sqrt[14])/2]*(9756589235 + 2148932869*Sqrt[14])*ArcTan[(Sqrt[7 + 2*Sqrt[14]] + 2*Sqrt[3 - 2*x])/Sqrt[-7 + 2*Sqrt[14]]])/318603459702399434752 + (11275*(9756589235 - 2148932869*Sqrt[14])*Sqrt[(-7 + 2*Sqrt[14])/2]*Log[3 + Sqrt[14] - Sqrt[7 + 2*Sqrt[14]]*Sqrt[3 - 2*x] - 2*x])/637206919404798869504 - (11275*(9756589235 - 2148932869*Sqrt[14])*Sqrt[(-7 + 2*Sqrt[14])/2]*Log[3 + Sqrt[14] + Sqrt[7 + 2*Sqrt[14]]*Sqrt[3 - 2*x] - 2*x])/637206919404798869504","A",29,9,20,0.4500,1,"{740, 822, 828, 826, 1169, 634, 618, 204, 628}"
49,1,1058,0,2.4897208,"\int \frac{1}{(3-2 x)^{41/2} \left(1+x+2 x^2\right)^{20}} \, dx","Int[1/((3 - 2*x)^(41/2)*(1 + x + 2*x^2)^20),x]","\frac{23 (2599313568802265110081-10426142448623187379187 x)}{20375965661807253450129408 (3-2 x)^{39/2} \left(2 x^2+x+1\right)^5}+\frac{115 \sqrt{\frac{1}{2} \left(7+2 \sqrt{14}\right)} \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 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173441368149804378661935869705/(896508488907352010051592447177261056*(3 - 2*x)^(19/2)) - 22724090823469905152713519545/(1604278348571050965355481221264572416*(3 - 2*x)^(17/2)) - 101190274412779618678573275245/(3963511214116714149701777134888943616*(3 - 2*x)^(15/2)) - 460503190416958283087439337135/(34350430522344855964082068502370844672*(3 - 2*x)^(13/2)) - 2211619588790911794826342607495/(406920484649315986036049119181931544576*(3 - 2*x)^(11/2)) - 143401467550777247627940437025/(73985542663511997461099839851260280832*(3 - 2*x)^(9/2)) - 4611053278117143010907562317585/(7250583181024175751187784305423507521536*(3 - 2*x)^(7/2)) - 405965372440630510720926890227/(2071595194578335928910795515835287863296*(3 - 2*x)^(5/2)) - 4986681479187781853417316522775/(87006998172290109014253411665082090258432*(3 - 2*x)^(3/2)) - 927027754781476746208047620505/(58004665448193406009502274443388060172288*Sqrt[3 - 2*x]) + x/(133*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^19) + (113 + 373*x)/(33516*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^18) + (40657 + 107329*x)/(7976808*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^17) + (5*(751303 + 1831285*x))/(595601664*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^16) + (184959785 + 429411497*x)/(25015269888*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^15) + (41652915209 + 92630823167*x)/(4902992898048*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^14) + (2871555518177 + 6100156355517*x)/(297448235814912*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^13) + (77559130805859 + 156274047129113*x)/(7138757659557888*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^12) + (5*(2656658801194921 + 5020880176134289*x))/(1099368679571914752*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^11) + (45187921585208601 + 78752911037377255*x)/(3420258114223734784*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^10) + (6063974149878048635 + 9477172618423641847*x)/(430952522392190582784*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^9) + (691833601144925854831 + 919498192874055581221*x)/(48266682507925345271808*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^8) + (23*(919498192874055581221 + 908287136092467468517*x))/(1576711628592227945545728*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^7) + (115*(908287136092467468517 + 298281884944522225747*x))/(10187982830903626725064704*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^6) + (23*(2599313568802265110081 - 10426142448623187379187*x))/(20375965661807253450129408*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^5) - (23*(10426142448623187379187 + 27513723463194262383705*x))/(20018492580021161284337664*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^4) - (115*(26513224428169016478843 + 30673415406553789342019*x))/(76434244396444433994743808*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^3) - (115*(88411609113007981044643 - 5712269536245152162963*x))/(125891696652967303050166272*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^2) + (115*(28561347681225760814815 + 965934812839019490346107*x))/(195831528126838026966925312*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)) + (115*Sqrt[(7 + 2*Sqrt[14])/2]*(30297118912219360725028693061 + 8061110911143276053983022787*Sqrt[14])*ArcTan[(Sqrt[7 + 2*Sqrt[14]] - 2*Sqrt[3 - 2*x])/Sqrt[-7 + 2*Sqrt[14]]])/812065316274707684133031842207432842412032 - (115*Sqrt[(7 + 2*Sqrt[14])/2]*(30297118912219360725028693061 + 8061110911143276053983022787*Sqrt[14])*ArcTan[(Sqrt[7 + 2*Sqrt[14]] + 2*Sqrt[3 - 2*x])/Sqrt[-7 + 2*Sqrt[14]]])/812065316274707684133031842207432842412032 + (115*(30297118912219360725028693061 - 8061110911143276053983022787*Sqrt[14])*Sqrt[(-7 + 2*Sqrt[14])/2]*Log[3 + Sqrt[14] - Sqrt[7 + 2*Sqrt[14]]*Sqrt[3 - 2*x] - 2*x])/1624130632549415368266063684414865684824064 - (115*(30297118912219360725028693061 - 8061110911143276053983022787*Sqrt[14])*Sqrt[(-7 + 2*Sqrt[14])/2]*Log[3 + Sqrt[14] + Sqrt[7 + 2*Sqrt[14]]*Sqrt[3 - 2*x] - 2*x])/1624130632549415368266063684414865684824064","A",49,9,20,0.4500,1,"{740, 822, 828, 826, 1169, 634, 618, 204, 628}"
50,1,378,0,0.7738186,"\int \frac{1}{\left(3-2 x+x^2\right)^{11/2} \left(1+x+2 x^2\right)^5} \, dx","Int[1/((3 - 2*x + x^2)^(11/2)*(1 + x + 2*x^2)^5),x]","-\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}","-\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,"-(3450497 - 2004270*x)/(123480000*(3 - 2*x + x^2)^(9/2)) - (4878869 - 2578034*x)/(411600000*(3 - 2*x + x^2)^(7/2)) - (30316369 - 15043110*x)/(6860000000*(3 - 2*x + x^2)^(5/2)) - (63043297 - 29625922*x)/(41160000000*(3 - 2*x + x^2)^(3/2)) - (31*(7434109 - 3088870*x))/(411600000000*Sqrt[3 - 2*x + x^2]) - (1 - 10*x)/(280*(3 - 2*x + x^2)^(9/2)*(1 + x + 2*x^2)^4) + (28 + 67*x)/(1050*(3 - 2*x + x^2)^(9/2)*(1 + x + 2*x^2)^3) + (5485 + 8878*x)/(117600*(3 - 2*x + x^2)^(9/2)*(1 + x + 2*x^2)^2) + (3*(8822 + 8233*x))/(343000*(3 - 2*x + x^2)^(9/2)*(1 + x + 2*x^2)) + (Sqrt[(151363871237318045 + 110320475741093888*Sqrt[2])/70]*ArcTan[(Sqrt[5/(7*(151363871237318045 + 110320475741093888*Sqrt[2]))]*(308108167 + 312239803*Sqrt[2] + (932587773 + 620347970*Sqrt[2])*x))/Sqrt[3 - 2*x + x^2]])/137200000000 - (Sqrt[(-151363871237318045 + 110320475741093888*Sqrt[2])/70]*ArcTanh[(Sqrt[5/(7*(-151363871237318045 + 110320475741093888*Sqrt[2]))]*(308108167 - 312239803*Sqrt[2] + (932587773 - 620347970*Sqrt[2])*x))/Sqrt[3 - 2*x + x^2]])/137200000000","A",14,6,23,0.2609,1,"{974, 1060, 1035, 1029, 206, 204}"
51,1,638,0,1.3971349,"\int \frac{1}{\left(3-2 x+x^2\right)^{21/2} \left(1+x+2 x^2\right)^{10}} \, dx","Int[1/((3 - 2*x + x^2)^(21/2)*(1 + x + 2*x^2)^10),x]","-\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}","-\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,"(37358055634422583 - 14024622879097678*x)/(1840124479200000000*(3 - 2*x + x^2)^(19/2)) + (476849951294984711 - 125181871472148210*x)/(104273720488000000000*(3 - 2*x + x^2)^(17/2)) + (7851758375483333511 + 1942164996204584234*x)/(15641058073200000000000*(3 - 2*x + x^2)^(15/2)) - (11*(7502325106308201089 - 7813986379726516886*x))/(406667509903200000000000*(3 - 2*x + x^2)^(13/2)) - (3*(69053268515296359011 - 44840736195018286006*x))/(1147010925368000000000000*(3 - 2*x + x^2)^(11/2)) - (838519439380295335657 - 466189390555853643870*x)/(9384634843920000000000000*(3 - 2*x + x^2)^(9/2)) - (1117646664729238460189 - 568839749685437871554*x)/(31282116146400000000000000*(3 - 2*x + x^2)^(7/2)) - (6551405511565449301689 - 3127298559983309301910*x)/(521368602440000000000000000*(3 - 2*x + x^2)^(5/2)) - (4179039782398459850819 - 1886993445589652402694*x)/(1042737204880000000000000000*(3 - 2*x + x^2)^(3/2)) - (12105495874518671061833 - 5117656435043679338190*x)/(10427372048800000000000000000*Sqrt[3 - 2*x + x^2]) - (1 - 10*x)/(630*(3 - 2*x + x^2)^(19/2)*(1 + x + 2*x^2)^9) + (887 + 2218*x)/(88200*(3 - 2*x + x^2)^(19/2)*(1 + x + 2*x^2)^8) + (14453 + 29371*x)/(1080450*(3 - 2*x + x^2)^(19/2)*(1 + x + 2*x^2)^7) + (8837931 + 17459234*x)/(605052000*(3 - 2*x + x^2)^(19/2)*(1 + x + 2*x^2)^6) + (447940041 + 813432205*x)/(26471025000*(3 - 2*x + x^2)^(19/2)*(1 + x + 2*x^2)^5) + (592729157441 + 911061463974*x)/(29647548000000*(3 - 2*x + x^2)^(19/2)*(1 + x + 2*x^2)^4) + (277010166219 + 310705340015*x)/(12353145000000*(3 - 2*x + x^2)^(19/2)*(1 + x + 2*x^2)^3) + (5488221294349 + 1384103301166*x)/(276710448000000*(3 - 2*x + x^2)^(19/2)*(1 + x + 2*x^2)^2) - (37857197792117 + 146548895467025*x)/(2421216420000000*(3 - 2*x + x^2)^(19/2)*(1 + x + 2*x^2)) + (Sqrt[(81042225921274689605478944797800854846405 + 57305922523001707126026363878666500308992*Sqrt[2])/70]*ArcTan[(Sqrt[5/(7*(81042225921274689605478944797800854846405 + 57305922523001707126026363878666500308992*Sqrt[2]))]*(272944589523248381749 + 191941026386645109841*Sqrt[2] + (656826642296538601431 + 464885615909893491590*Sqrt[2])*x))/Sqrt[3 - 2*x + x^2]])/32282885600000000000000000 - (Sqrt[(-81042225921274689605478944797800854846405 + 57305922523001707126026363878666500308992*Sqrt[2])/70]*ArcTanh[(Sqrt[5/(7*(-81042225921274689605478944797800854846405 + 57305922523001707126026363878666500308992*Sqrt[2]))]*(272944589523248381749 - 191941026386645109841*Sqrt[2] + (656826642296538601431 - 464885615909893491590*Sqrt[2])*x))/Sqrt[3 - 2*x + x^2]])/32282885600000000000000000","A",24,6,23,0.2609,1,"{974, 1060, 1035, 1029, 206, 204}"
52,1,204,0,1.23427,"\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","Int[(-a - Sqrt[1 + a^2] + x)/((-a + Sqrt[1 + a^2] + x)*Sqrt[(-a + x)*(1 + x^2)]),x]","\frac{4 \sqrt{a^2+1} \sqrt{x^2+1} \sqrt{\frac{a-x}{a+i}} \Pi \left(\frac{2}{1-i \left(a-\sqrt{a^2+1}\right)};\sin ^{-1}\left(\frac{\sqrt{1-i x}}{\sqrt{2}}\right)|\frac{2}{1-i a}\right)}{\left(1-i \left(a-\sqrt{a^2+1}\right)\right) \sqrt{\left(x^2+1\right) (-(a-x))}}+\frac{2 i \sqrt{x^2+1} \sqrt{\frac{a-x}{a+i}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-i x}}{\sqrt{2}}\right)|\frac{2}{1-i a}\right)}{\sqrt{\left(x^2+1\right) (-(a-x))}}","-\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,"((2*I)*Sqrt[(a - x)/(I + a)]*Sqrt[1 + x^2]*EllipticF[ArcSin[Sqrt[1 - I*x]/Sqrt[2]], 2/(1 - I*a)])/Sqrt[-((a - x)*(1 + x^2))] + (4*Sqrt[1 + a^2]*Sqrt[(a - x)/(I + a)]*Sqrt[1 + x^2]*EllipticPi[2/(1 - I*(a - Sqrt[1 + a^2])), ArcSin[Sqrt[1 - I*x]/Sqrt[2]], 2/(1 - I*a)])/((1 - I*(a - Sqrt[1 + a^2]))*Sqrt[-((a - x)*(1 + x^2))])","C",9,8,48,0.1667,1,"{6719, 6742, 719, 419, 932, 168, 538, 537}"
53,1,198,0,0.0971639,"\int \frac{a+b x}{\sqrt[3]{1-x^2} \left(3+x^2\right)} \, dx","Int[(a + b*x)/((1 - x^2)^(1/3)*(3 + x^2)),x]","\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}}","\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,"(a*ArcTan[Sqrt[3]/x])/(2*2^(2/3)*Sqrt[3]) + (Sqrt[3]*b*ArcTan[(1 + (2 - 2*x^2)^(1/3))/Sqrt[3]])/(2*2^(2/3)) + (a*ArcTan[(Sqrt[3]*(1 - 2^(1/3)*(1 - x^2)^(1/3)))/x])/(2*2^(2/3)*Sqrt[3]) - (a*ArcTanh[x])/(6*2^(2/3)) + (a*ArcTanh[x/(1 + 2^(1/3)*(1 - x^2)^(1/3))])/(2*2^(2/3)) - (b*Log[3 + x^2])/(4*2^(2/3)) + (3*b*Log[2^(2/3) - (1 - x^2)^(1/3)])/(4*2^(2/3))","A",7,7,24,0.2917,1,"{1010, 393, 444, 55, 617, 204, 31}"
54,1,198,0,0.0905163,"\int \frac{a+b x}{\left(3-x^2\right) \sqrt[3]{1+x^2}} \, dx","Int[(a + b*x)/((3 - x^2)*(1 + x^2)^(1/3)),x]","\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}}","\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,"-(a*ArcTan[x])/(6*2^(2/3)) + (a*ArcTan[x/(1 + 2^(1/3)*(1 + x^2)^(1/3))])/(2*2^(2/3)) - (Sqrt[3]*b*ArcTan[(1 + 2^(1/3)*(1 + x^2)^(1/3))/Sqrt[3]])/(2*2^(2/3)) - (a*ArcTanh[Sqrt[3]/x])/(2*2^(2/3)*Sqrt[3]) - (a*ArcTanh[(Sqrt[3]*(1 - 2^(1/3)*(1 + x^2)^(1/3)))/x])/(2*2^(2/3)*Sqrt[3]) + (b*Log[3 - x^2])/(4*2^(2/3)) - (3*b*Log[2^(2/3) - (1 + x^2)^(1/3)])/(4*2^(2/3))","A",7,7,24,0.2917,1,"{1010, 392, 444, 55, 617, 204, 31}"
55,1,97,0,0.0133008,"\int \frac{1}{x \sqrt[3]{4-6 x+3 x^2}} \, dx","Int[1/(x*(4 - 6*x + 3*x^2)^(1/3)),x]","\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}}","\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[1/Sqrt[3] + (2^(2/3)*(2 - x))/(Sqrt[3]*(4 - 6*x + 3*x^2)^(1/3))]/(2^(2/3)*Sqrt[3])) - Log[x]/(2*2^(2/3)) + Log[6 - 3*x - 3*2^(1/3)*(4 - 6*x + 3*x^2)^(1/3)]/(2*2^(2/3))","A",1,1,18,0.05556,1,"{750}"
56,1,107,0,0.0435833,"\int x \sqrt[3]{1-x^3} \, dx","Int[x*(1 - x^3)^(1/3),x]","\frac{1}{3} \sqrt[3]{1-x^3} x^2+\frac{1}{18} \log \left(\frac{x^2}{\left(1-x^3\right)^{2/3}}-\frac{x}{\sqrt[3]{1-x^3}}+1\right)-\frac{1}{9} \log \left(\frac{x}{\sqrt[3]{1-x^3}}+1\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-\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}}",1,"(x^2*(1 - x^3)^(1/3))/3 - ArcTan[(1 - (2*x)/(1 - x^3)^(1/3))/Sqrt[3]]/(3*Sqrt[3]) + Log[1 + x^2/(1 - x^3)^(2/3) - x/(1 - x^3)^(1/3)]/18 - Log[1 + x/(1 - x^3)^(1/3)]/9","A",8,8,13,0.6154,1,"{279, 331, 292, 31, 634, 618, 204, 628}"
57,1,67,0,0.0372041,"\int \frac{\sqrt[3]{1-x^3}}{x} \, dx","Int[(1 - x^3)^(1/3)/x,x]","\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}","\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 + 2*(1 - x^3)^(1/3))/Sqrt[3]]/Sqrt[3] - Log[x]/2 + Log[1 - (1 - x^3)^(1/3)]/2","A",6,6,15,0.4000,1,"{266, 50, 57, 618, 204, 31}"
58,0,0,0,0.0520396,"\int \frac{\sqrt[3]{1-x^3}}{1+x} \, dx","Int[(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,"Defer[Int][(1 - x^3)^(1/3)/(1 + x), x]","F",0,0,0,0,-1,"{}"
59,0,0,0,0.2354823,"\int \frac{\sqrt[3]{1-x^3}}{1-x+x^2} \, dx","Int[(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(-3 (x-1) \left(x^2-x+1\right)\right)}{2\ 2^{2/3}}+\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}}",1,"((2*I)*Defer[Int][(1 - x^3)^(1/3)/(1 + I*Sqrt[3] - 2*x), x])/Sqrt[3] + ((2*I)*Defer[Int][(1 - x^3)^(1/3)/(-1 + I*Sqrt[3] + 2*x), x])/Sqrt[3]","F",0,0,0,0,-1,"{}"
60,0,0,0,0.0499624,"\int \frac{\sqrt[3]{1-x^3}}{2+x} \, dx","Int[(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,"Defer[Int][(1 - x^3)^(1/3)/(2 + x), x]","F",0,0,0,0,-1,"{}"
61,0,0,0,0.2042616,"\int \frac{2+x}{\left(1+x+x^2\right) \sqrt[3]{2+x^3}} \, dx","Int[(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,"(1 - I*Sqrt[3])*Defer[Int][1/((1 - I*Sqrt[3] + 2*x)*(2 + x^3)^(1/3)), x] + (1 + I*Sqrt[3])*Defer[Int][1/((1 + I*Sqrt[3] + 2*x)*(2 + x^3)^(1/3)), x]","F",0,0,0,0,-1,"{}"
62,1,25,0,0.0226836,"\int \frac{3-3 x+30 x^2+160 x^3}{9+24 x-12 x^2+80 x^3+320 x^4} \, dx","Int[(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",1,1,38,0.02632,1,"{1587}"
63,1,59,0,0.031717,"\int \frac{3+12 x+20 x^2}{9+24 x-12 x^2+80 x^3+320 x^4} \, dx","Int[(3 + 12*x + 20*x^2)/(9 + 24*x - 12*x^2 + 80*x^3 + 320*x^4),x]","\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}}","\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,"-ArcTan[(7 - 40*x)/(5*Sqrt[11])]/(2*Sqrt[11]) + ArcTan[(57 + 30*x - 40*x^2 + 800*x^3)/(6*Sqrt[11])]/(2*Sqrt[11])","A",1,1,33,0.03030,1,"{2090}"
64,1,78,0,0.07667,"\int -\frac{84+576 x+400 x^2-2560 x^3}{9+24 x-12 x^2+80 x^3+320 x^4} \, dx","Int[-((84 + 576*x + 400*x^2 - 2560*x^3)/(9 + 24*x - 12*x^2 + 80*x^3 + 320*x^4)),x]","2 \log \left(320 x^4+80 x^3-12 x^2+24 x+9\right)-2 \sqrt{11} \tan ^{-1}\left(\frac{800 x^3-40 x^2+30 x+57}{6 \sqrt{11}}\right)+2 \sqrt{11} \tan ^{-1}\left(\frac{7-40 x}{5 \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{800 x^3-40 x^2+30 x+57}{6 \sqrt{11}}\right)+2 \sqrt{11} \tan ^{-1}\left(\frac{7-40 x}{5 \sqrt{11}}\right)",1,"2*Sqrt[11]*ArcTan[(7 - 40*x)/(5*Sqrt[11])] - 2*Sqrt[11]*ArcTan[(57 + 30*x - 40*x^2 + 800*x^3)/(6*Sqrt[11])] + 2*Log[9 + 24*x - 12*x^2 + 80*x^3 + 320*x^4]","A",2,2,39,0.05128,1,"{2100, 2090}"
65,1,49,0,0.0072942,"\int \frac{\sqrt{1-x^4}}{1+x^4} \, dx","Int[Sqrt[1 - x^4]/(1 + x^4),x]","\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)","\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[(x*(1 + x^2))/Sqrt[1 - x^4]]/2 + ArcTanh[(x*(1 - x^2))/Sqrt[1 - x^4]]/2","A",1,1,19,0.05263,1,"{405}"
66,1,53,0,0.0145405,"\int \frac{\sqrt{1+x^4}}{1-x^4} \, dx","Int[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",4,4,19,0.2105,1,"{404, 212, 206, 203}"
67,1,75,0,0.0944013,"\int \frac{\sqrt{1+p x^2+x^4}}{1-x^4} \, dx","Int[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} \tanh ^{-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,"(Sqrt[2 - p]*ArcTan[(Sqrt[2 - p]*x)/Sqrt[1 + p*x^2 + x^4]])/4 + (Sqrt[2 + p]*ArcTanh[(Sqrt[2 + p]*x)/Sqrt[1 + p*x^2 + x^4]])/4","A",4,4,24,0.1667,1,"{2071, 1093, 205, 208}"
68,1,171,0,0.0800218,"\int \frac{\sqrt{1+p x^2-x^4}}{1+x^4} \, dx","Int[Sqrt[1 + p*x^2 - x^4]/(1 + x^4),x]","\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}}","\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,"-(Sqrt[p + Sqrt[4 + p^2]]*ArcTan[(Sqrt[p + Sqrt[4 + p^2]]*x*(p - Sqrt[4 + p^2] - 2*x^2))/(2*Sqrt[2]*Sqrt[1 + p*x^2 - x^4])])/(2*Sqrt[2]) + (Sqrt[-p + Sqrt[4 + p^2]]*ArcTanh[(Sqrt[-p + Sqrt[4 + p^2]]*x*(p + Sqrt[4 + p^2] - 2*x^2))/(2*Sqrt[2]*Sqrt[1 + p*x^2 - x^4])])/(2*Sqrt[2])","A",1,1,24,0.04167,1,"{2072}"
69,1,80,0,0.0398388,"\int \frac{a+b x}{\left(2-x^2\right) \sqrt[4]{-1+x^2}} \, dx","Int[(a + b*x)/((2 - x^2)*(-1 + x^2)^(1/4)),x]","\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)","\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,"(a*ArcTan[x/(Sqrt[2]*(-1 + x^2)^(1/4))])/(2*Sqrt[2]) - b*ArcTan[(-1 + x^2)^(1/4)] + (a*ArcTanh[x/(Sqrt[2]*(-1 + x^2)^(1/4))])/(2*Sqrt[2]) + b*ArcTanh[(-1 + x^2)^(1/4)]","A",7,7,24,0.2917,1,"{1010, 398, 444, 63, 298, 203, 206}"
70,1,88,0,0.0475753,"\int \frac{a+b x}{\sqrt[4]{-1-x^2} \left(2+x^2\right)} \, dx","Int[(a + b*x)/((-1 - x^2)^(1/4)*(2 + x^2)),x]","\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)","\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,"(a*ArcTan[x/(Sqrt[2]*(-1 - x^2)^(1/4))])/(2*Sqrt[2]) + b*ArcTan[(-1 - x^2)^(1/4)] + (a*ArcTanh[x/(Sqrt[2]*(-1 - x^2)^(1/4))])/(2*Sqrt[2]) - b*ArcTanh[(-1 - x^2)^(1/4)]","A",7,7,24,0.2917,1,"{1010, 398, 444, 63, 298, 203, 206}"
71,1,149,0,0.0450532,"\int \frac{a+b x}{\sqrt[4]{1-x^2} \left(2-x^2\right)} \, dx","Int[(a + b*x)/((1 - x^2)^(1/4)*(2 - x^2)),x]","\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}}","\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,"(b*ArcTan[(1 - Sqrt[1 - x^2])/(Sqrt[2]*(1 - x^2)^(1/4))])/Sqrt[2] + (a*ArcTan[(1 - Sqrt[1 - x^2])/(x*(1 - x^2)^(1/4))])/2 + (b*ArcTanh[(1 + Sqrt[1 - x^2])/(Sqrt[2]*(1 - x^2)^(1/4))])/Sqrt[2] + (a*ArcTanh[(1 + Sqrt[1 - x^2])/(x*(1 - x^2)^(1/4))])/2","A",3,3,26,0.1154,1,"{1010, 397, 439}"
72,1,135,0,0.035622,"\int \frac{a+b x}{\sqrt[4]{1+x^2} \left(2+x^2\right)} \, dx","Int[(a + b*x)/((1 + x^2)^(1/4)*(2 + x^2)),x]","-\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}}","-\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,"-((b*ArcTan[(1 - Sqrt[1 + x^2])/(Sqrt[2]*(1 + x^2)^(1/4))])/Sqrt[2]) - (a*ArcTan[(1 + Sqrt[1 + x^2])/(x*(1 + x^2)^(1/4))])/2 - (a*ArcTanh[(1 - Sqrt[1 + x^2])/(x*(1 + x^2)^(1/4))])/2 - (b*ArcTanh[(1 + Sqrt[1 + x^2])/(Sqrt[2]*(1 + x^2)^(1/4))])/Sqrt[2]","A",3,3,22,0.1364,1,"{1010, 397, 439}"
73,1,127,0,0.0192024,"\int \frac{x}{\sqrt{1-x^3} \left(4-x^3\right)} \, dx","Int[x/(Sqrt[1 - x^3]*(4 - x^3)),x]","-\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}}","-\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,"-ArcTan[(Sqrt[3]*(1 - 2^(1/3)*x))/Sqrt[1 - x^3]]/(3*2^(2/3)*Sqrt[3]) + ArcTan[Sqrt[1 - x^3]/Sqrt[3]]/(3*2^(2/3)*Sqrt[3]) - ArcTanh[(1 + 2^(1/3)*x)/Sqrt[1 - x^3]]/(3*2^(2/3)) + ArcTanh[Sqrt[1 - x^3]]/(9*2^(2/3))","A",1,1,22,0.04545,1,"{484}"
74,1,157,0,0.0329981,"\int \frac{x}{\left(4-d x^3\right) \sqrt{-1+d x^3}} \, dx","Int[x/((4 - d*x^3)*Sqrt[-1 + d*x^3]),x]","-\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}}","-\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,"-ArcTan[(1 + 2^(1/3)*d^(1/3)*x)/Sqrt[-1 + d*x^3]]/(3*2^(2/3)*d^(2/3)) - ArcTan[Sqrt[-1 + d*x^3]]/(9*2^(2/3)*d^(2/3)) - ArcTanh[(Sqrt[3]*(1 - 2^(1/3)*d^(1/3)*x))/Sqrt[-1 + d*x^3]]/(3*2^(2/3)*Sqrt[3]*d^(2/3)) - ArcTanh[Sqrt[-1 + d*x^3]/Sqrt[3]]/(3*2^(2/3)*Sqrt[3]*d^(2/3))","A",1,1,23,0.04348,1,"{485}"
75,1,74,0,0.1555234,"\int \frac{x}{\sqrt{-1+x^3} \left(8+x^3\right)} \, dx","Int[x/(Sqrt[-1 + x^3]*(8 + x^3)),x]","\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}}","\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,"ArcTan[(1 - x)^2/(3*Sqrt[-1 + x^3])]/18 + ArcTan[Sqrt[-1 + x^3]/3]/18 - ArcTanh[(Sqrt[3]*(1 - x))/Sqrt[-1 + x^3]]/(6*Sqrt[3])","A",8,8,18,0.4444,1,"{486, 444, 63, 204, 2138, 203, 2145, 206}"
76,1,103,0,0.3049984,"\int \frac{x}{\left(8-d x^3\right) \sqrt{1+d x^3}} \, dx","Int[x/((8 - d*x^3)*Sqrt[1 + d*x^3]),x]","-\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}}","-\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,"-ArcTan[(Sqrt[3]*(1 + d^(1/3)*x))/Sqrt[1 + d*x^3]]/(6*Sqrt[3]*d^(2/3)) + ArcTanh[(1 + d^(1/3)*x)^2/(3*Sqrt[1 + d*x^3])]/(18*d^(2/3)) - ArcTanh[Sqrt[1 + d*x^3]/3]/(18*d^(2/3))","A",8,7,23,0.3043,1,"{486, 444, 63, 206, 2138, 2145, 205}"
77,1,81,0,0.0114325,"\int \frac{1}{\sqrt[3]{1-3 x^2} \left(3-x^2\right)} \, dx","Int[1/((1 - 3*x^2)^(1/3)*(3 - x^2)),x]","\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}}","\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,"ArcTan[(1 - (1 - 3*x^2)^(1/3))/x]/4 + ArcTanh[x/Sqrt[3]]/(4*Sqrt[3]) - ArcTanh[(1 - (1 - 3*x^2)^(1/3))^2/(3*Sqrt[3]*x)]/(4*Sqrt[3])","A",1,1,21,0.04762,1,"{395}"
78,1,81,0,0.0107141,"\int \frac{1}{\left(3+x^2\right) \sqrt[3]{1+3 x^2}} \, dx","Int[1/((3 + x^2)*(1 + 3*x^2)^(1/3)),x]","\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}}","\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,"ArcTan[x/Sqrt[3]]/(4*Sqrt[3]) + ArcTan[(1 - (1 + 3*x^2)^(1/3))^2/(3*Sqrt[3]*x)]/(4*Sqrt[3]) - ArcTanh[(1 - (1 + 3*x^2)^(1/3))/x]/4","A",1,1,19,0.05263,1,"{394}"
79,1,113,0,0.0136163,"\int \frac{1}{\sqrt[3]{1-x^2} \left(3+x^2\right)} \, dx","Int[1/((1 - x^2)^(1/3)*(3 + x^2)),x]","\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}}","\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,"ArcTan[Sqrt[3]/x]/(2*2^(2/3)*Sqrt[3]) + ArcTan[(Sqrt[3]*(1 - 2^(1/3)*(1 - x^2)^(1/3)))/x]/(2*2^(2/3)*Sqrt[3]) - ArcTanh[x]/(6*2^(2/3)) + ArcTanh[x/(1 + 2^(1/3)*(1 - x^2)^(1/3))]/(2*2^(2/3))","A",1,1,19,0.05263,1,"{393}"
80,1,109,0,0.0121913,"\int \frac{1}{\left(3-x^2\right) \sqrt[3]{1+x^2}} \, dx","Int[1/((3 - x^2)*(1 + x^2)^(1/3)),x]","\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}}","\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,"-ArcTan[x]/(6*2^(2/3)) + ArcTan[x/(1 + 2^(1/3)*(1 + x^2)^(1/3))]/(2*2^(2/3)) - ArcTanh[Sqrt[3]/x]/(2*2^(2/3)*Sqrt[3]) - ArcTanh[(Sqrt[3]*(1 - 2^(1/3)*(1 + x^2)^(1/3)))/x]/(2*2^(2/3)*Sqrt[3])","A",1,1,19,0.05263,1,"{392}"
81,1,87,0,0.8738629,"\int \frac{a+x}{(-a+x) \sqrt{a^2 x-\left(1+a^2\right) x^2+x^3}} \, dx","Int[(a + x)/((-a + x)*Sqrt[a^2*x - (1 + a^2)*x^2 + x^3]),x]","-\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}}","-\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*Sqrt[x]*Sqrt[a^2 - (1 + a^2)*x + x^2]*ArcTan[((1 - a)*Sqrt[x])/Sqrt[a^2 - (1 + a^2)*x + x^2]])/((1 - a)*Sqrt[a^2*x - (1 + a^2)*x^2 + x^3])","A",4,4,34,0.1176,1,"{2056, 6733, 1698, 205}"
82,1,529,0,1.6685767,"\int \frac{-2+a+x}{(-a+x) \sqrt{(2-a) a x+\left(-1-2 a+a^2\right) x^2+x^3}} \, dx","Int[(-2 + a + x)/((-a + x)*Sqrt[(2 - a)*a*x + (-1 - 2*a + a^2)*x^2 + x^3]),x]","\frac{2 (1-a) \sqrt{x} \sqrt{-\left(-a^2+2 a+1\right) x+(2-a) a+x^2} \tan ^{-1}\left(\frac{\sqrt{-a^2+2 a-1} \sqrt{x}}{\sqrt{-\left(-a^2+2 a+1\right) x+(2-a) a+x^2}}\right)}{a \sqrt{-a^2+2 a-1} \sqrt{-\left(-a^2+2 a+1\right) x^2+(2-a) a x+x^3}}+\frac{((2-a) a)^{3/4} \sqrt{x} \left(\frac{x}{\sqrt{(2-a) a}}+1\right) \sqrt{\frac{-\left(-a^2+2 a+1\right) x+(2-a) a+x^2}{(2-a) a \left(\frac{x}{\sqrt{(2-a) a}}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{(2-a) a}}\right)|\frac{1}{4} \left(\frac{-a^2+2 a+1}{\sqrt{(2-a) a}}+2\right)\right)}{a \sqrt{-\left(-a^2+2 a+1\right) x^2+(2-a) a x+x^3}}+\frac{(2-a) \left(1-\sqrt{(2-a) a}\right) \sqrt{x} \left(\frac{x}{\sqrt{(2-a) a}}+1\right) \sqrt{\frac{-\left(-a^2+2 a+1\right) x+(2-a) a+x^2}{(2-a) a \left(\frac{x}{\sqrt{(2-a) a}}+1\right)^2}} \Pi \left(\frac{\left(\sqrt{2-a}+\sqrt{a}\right)^2}{4 \sqrt{(2-a) a}};2 \tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{(2-a) a}}\right)|\frac{1}{4} \left(\frac{-a^2+2 a+1}{\sqrt{(2-a) a}}+2\right)\right)}{((2-a) a)^{3/4} \sqrt{-\left(-a^2+2 a+1\right) x^2+(2-a) a x+x^3}}","0",1,"(2*(1 - a)*Sqrt[x]*Sqrt[(2 - a)*a - (1 + 2*a - a^2)*x + x^2]*ArcTan[(Sqrt[-1 + 2*a - a^2]*Sqrt[x])/Sqrt[(2 - a)*a - (1 + 2*a - a^2)*x + x^2]])/(a*Sqrt[-1 + 2*a - a^2]*Sqrt[(2 - a)*a*x - (1 + 2*a - a^2)*x^2 + x^3]) + (((2 - a)*a)^(3/4)*Sqrt[x]*(1 + x/Sqrt[(2 - a)*a])*Sqrt[((2 - a)*a - (1 + 2*a - a^2)*x + x^2)/((2 - a)*a*(1 + x/Sqrt[(2 - a)*a])^2)]*EllipticF[2*ArcTan[Sqrt[x]/((2 - a)*a)^(1/4)], (2 + (1 + 2*a - a^2)/Sqrt[(2 - a)*a])/4])/(a*Sqrt[(2 - a)*a*x - (1 + 2*a - a^2)*x^2 + x^3]) + ((2 - a)*(1 - Sqrt[(2 - a)*a])*Sqrt[x]*(1 + x/Sqrt[(2 - a)*a])*Sqrt[((2 - a)*a - (1 + 2*a - a^2)*x + x^2)/((2 - a)*a*(1 + x/Sqrt[(2 - a)*a])^2)]*EllipticPi[(Sqrt[2 - a] + Sqrt[a])^2/(4*Sqrt[(2 - a)*a]), 2*ArcTan[Sqrt[x]/((2 - a)*a)^(1/4)], (2 + (1 + 2*a - a^2)/Sqrt[(2 - a)*a])/4])/(((2 - a)*a)^(3/4)*Sqrt[(2 - a)*a*x - (1 + 2*a - a^2)*x^2 + x^3])","C",5,5,40,0.1250,0,"{2056, 6733, 1708, 1103, 1706}"
83,1,180,0,1.4923597,"\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","Int[(-a + (-1 + 2*a)*x)/((-a + x)*Sqrt[a^2*x - (-1 + 2*a + a^2)*x^2 + (-1 + 2*a)*x^3]),x]","\frac{4 (1-a) \sqrt{1-x} \sqrt{x} \sqrt{\frac{(1-2 a) x}{a^2}+1} \Pi \left(\frac{1}{a};\sin ^{-1}\left(\sqrt{x}\right)|-\frac{1-2 a}{a^2}\right)}{\sqrt{\left(-a^2-2 a+1\right) x^2+a^2 x-(1-2 a) x^3}}-\frac{2 (1-2 a) \sqrt{1-x} \sqrt{x} \sqrt{\frac{(1-2 a) x}{a^2}+1} F\left(\sin ^{-1}\left(\sqrt{x}\right)|-\frac{1-2 a}{a^2}\right)}{\sqrt{\left(-a^2-2 a+1\right) x^2+a^2 x-(1-2 a) x^3}}","\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*(1 - 2*a)*Sqrt[1 - x]*Sqrt[x]*Sqrt[1 + ((1 - 2*a)*x)/a^2]*EllipticF[ArcSin[Sqrt[x]], -((1 - 2*a)/a^2)])/Sqrt[a^2*x + (1 - 2*a - a^2)*x^2 - (1 - 2*a)*x^3] + (4*(1 - a)*Sqrt[1 - x]*Sqrt[x]*Sqrt[1 + ((1 - 2*a)*x)/a^2]*EllipticPi[a^(-1), ArcSin[Sqrt[x]], -((1 - 2*a)/a^2)])/Sqrt[a^2*x + (1 - 2*a - a^2)*x^2 - (1 - 2*a)*x^3]","C",7,7,51,0.1373,1,"{2056, 6733, 1710, 1104, 419, 1220, 537}"
84,1,32,0,0.0963157,"\int \frac{1-\sqrt[3]{2} x}{\left(2^{2/3}+x\right) \sqrt{1+x^3}} \, dx","Int[(1 - 2^(1/3)*x)/((2^(2/3) + x)*Sqrt[1 + x^3]),x]","\frac{2 \tan ^{-1}\left(\frac{\sqrt{3} \left(\sqrt[3]{2} x+1\right)}{\sqrt{x^3+1}}\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[3]*(1 + 2^(1/3)*x))/Sqrt[1 + x^3]])/Sqrt[3]","A",2,2,29,0.06897,1,"{2137, 203}"
85,1,23,0,0.0539309,"\int \frac{1+x}{(-2+x) \sqrt{1+x^3}} \, dx","Int[(1 + x)/((-2 + x)*Sqrt[1 + x^3]),x]","-\frac{2}{3} \tanh ^{-1}\left(\frac{(x+1)^2}{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 + x)^2/(3*Sqrt[1 + x^3])])/3","A",2,2,18,0.1111,1,"{2138, 206}"
86,1,218,0,0.0409792,"\int \frac{x}{\sqrt{1+x^3} \left(10+6 \sqrt{3}+x^3\right)} \, dx","Int[x/(Sqrt[1 + x^3]*(10 + 6*Sqrt[3] + x^3)),x]","-\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}}","-\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,"-((2 - Sqrt[3])*ArcTan[(3^(1/4)*(1 + Sqrt[3])*(1 + x))/(Sqrt[2]*Sqrt[1 + x^3])])/(2*Sqrt[2]*3^(3/4)) - ((2 - Sqrt[3])*ArcTan[((1 - Sqrt[3])*Sqrt[1 + x^3])/(Sqrt[2]*3^(3/4))])/(3*Sqrt[2]*3^(3/4)) - ((2 - Sqrt[3])*ArcTanh[(3^(1/4)*(1 + Sqrt[3] - 2*x))/(Sqrt[2]*Sqrt[1 + x^3])])/(3*Sqrt[2]*3^(1/4)) - ((2 - Sqrt[3])*ArcTanh[(3^(1/4)*(1 - Sqrt[3])*(1 + x))/(Sqrt[2]*Sqrt[1 + x^3])])/(6*Sqrt[2]*3^(1/4))","A",1,1,25,0.04000,1,"{487}"
87,1,210,0,0.0317457,"\int \frac{x}{\sqrt{1+x^3} \left(10-6 \sqrt{3}+x^3\right)} \, dx","Int[x/(Sqrt[1 + x^3]*(10 - 6*Sqrt[3] + x^3)),x]","-\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}}","-\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,"-((2 + Sqrt[3])*ArcTan[(3^(1/4)*(1 - Sqrt[3] - 2*x))/(Sqrt[2]*Sqrt[1 + x^3])])/(3*Sqrt[2]*3^(1/4)) - ((2 + Sqrt[3])*ArcTan[(3^(1/4)*(1 + Sqrt[3])*(1 + x))/(Sqrt[2]*Sqrt[1 + x^3])])/(6*Sqrt[2]*3^(1/4)) + ((2 + Sqrt[3])*ArcTanh[(3^(1/4)*(1 - Sqrt[3])*(1 + x))/(Sqrt[2]*Sqrt[1 + x^3])])/(2*Sqrt[2]*3^(3/4)) + ((2 + Sqrt[3])*ArcTanh[((1 + Sqrt[3])*Sqrt[1 + x^3])/(Sqrt[2]*3^(3/4))])/(3*Sqrt[2]*3^(3/4))","A",1,1,25,0.04000,1,"{487}"
88,1,222,0,0.0295865,"\int \frac{x}{\sqrt{-1+x^3} \left(-10-6 \sqrt{3}+x^3\right)} \, dx","Int[x/(Sqrt[-1 + x^3]*(-10 - 6*Sqrt[3] + x^3)),x]","\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}}","\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,"((2 - Sqrt[3])*ArcTan[(3^(1/4)*(1 - Sqrt[3])*(1 - x))/(Sqrt[2]*Sqrt[-1 + x^3])])/(6*Sqrt[2]*3^(1/4)) + ((2 - Sqrt[3])*ArcTan[(3^(1/4)*(1 + Sqrt[3] + 2*x))/(Sqrt[2]*Sqrt[-1 + x^3])])/(3*Sqrt[2]*3^(1/4)) + ((2 - Sqrt[3])*ArcTanh[(3^(1/4)*(1 + Sqrt[3])*(1 - x))/(Sqrt[2]*Sqrt[-1 + x^3])])/(2*Sqrt[2]*3^(3/4)) - ((2 - Sqrt[3])*ArcTanh[((1 - Sqrt[3])*Sqrt[-1 + x^3])/(Sqrt[2]*3^(3/4))])/(3*Sqrt[2]*3^(3/4))","A",1,1,25,0.04000,1,"{488}"
89,1,214,0,0.0290123,"\int \frac{x}{\sqrt{-1+x^3} \left(-10+6 \sqrt{3}+x^3\right)} \, dx","Int[x/(Sqrt[-1 + x^3]*(-10 + 6*Sqrt[3] + x^3)),x]","-\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}}","-\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,"-((2 + Sqrt[3])*ArcTan[(3^(1/4)*(1 - Sqrt[3])*(1 - x))/(Sqrt[2]*Sqrt[-1 + x^3])])/(2*Sqrt[2]*3^(3/4)) + ((2 + Sqrt[3])*ArcTan[((1 + Sqrt[3])*Sqrt[-1 + x^3])/(Sqrt[2]*3^(3/4))])/(3*Sqrt[2]*3^(3/4)) + ((2 + Sqrt[3])*ArcTanh[(3^(1/4)*(1 + Sqrt[3])*(1 - x))/(Sqrt[2]*Sqrt[-1 + x^3])])/(6*Sqrt[2]*3^(1/4)) + ((2 + Sqrt[3])*ArcTanh[(3^(1/4)*(1 - Sqrt[3] + 2*x))/(Sqrt[2]*Sqrt[-1 + x^3])])/(3*Sqrt[2]*3^(1/4))","A",1,1,25,0.04000,1,"{488}"
90,1,65,0,0.1289679,"\int \frac{1-\sqrt{3}+x}{\left(1+\sqrt{3}+x\right) \sqrt{-4+4 \sqrt{3} x^2+x^4}} \, dx","Int[(1 - Sqrt[3] + x)/((1 + Sqrt[3] + x)*Sqrt[-4 + 4*Sqrt[3]*x^2 + x^4]),x]","\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)","\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,"(Sqrt[-3 + 2*Sqrt[3]]*ArcTanh[(1 - Sqrt[3] + x)^2/(Sqrt[3*(-3 + 2*Sqrt[3])]*Sqrt[-4 + 4*Sqrt[3]*x^2 + x^4])])/3","A",2,2,40,0.05000,1,"{1740, 207}"
91,1,63,0,0.1277598,"\int \frac{1+\sqrt{3}+x}{\left(1-\sqrt{3}+x\right) \sqrt{-4-4 \sqrt{3} x^2+x^4}} \, dx","Int[(1 + Sqrt[3] + x)/((1 - Sqrt[3] + x)*Sqrt[-4 - 4*Sqrt[3]*x^2 + x^4]),x]","-\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)","-\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,"-(Sqrt[3 + 2*Sqrt[3]]*ArcTan[(1 + Sqrt[3] + x)^2/(Sqrt[3*(3 + 2*Sqrt[3])]*Sqrt[-4 - 4*Sqrt[3]*x^2 + x^4])])/3","A",2,2,40,0.05000,1,"{1740, 203}"
92,1,53,0,0.0552897,"\int \frac{-1+x}{(1+x) \sqrt[3]{2+x^3}} \, dx","Int[(-1 + x)/((1 + x)*(2 + x^3)^(1/3)),x]","-\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)","-\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[(1 + (2*(2 + x))/(2 + x^3)^(1/3))/Sqrt[3]] + Log[1 + x] - (3*Log[2 + x - (2 + x^3)^(1/3)])/2","A",1,1,18,0.05556,1,"{2151}"
93,1,108,0,0.0925279,"\int \frac{1}{(1+x) \sqrt[3]{2+x^3}} \, dx","Int[1/((1 + x)*(2 + x^3)^(1/3)),x]","\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)","\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,"ArcTan[(1 + (2*x)/(2 + x^3)^(1/3))/Sqrt[3]]/(2*Sqrt[3]) - (Sqrt[3]*ArcTan[(1 + (2*(2 + x))/(2 + x^3)^(1/3))/Sqrt[3]])/2 - Log[1 + x]/2 + (3*Log[2 + x - (2 + x^3)^(1/3)])/4 - Log[-x + (2 + x^3)^(1/3)]/4","A",3,3,15,0.2000,1,"{2149, 239, 2151}"
94,1,135,0,0.093337,"\int \frac{1}{\left(1-x^3\right) \sqrt[3]{a+b x^3}} \, dx","Int[1/((1 - x^3)*(a + b*x^3)^(1/3)),x]","-\frac{\log \left(1-\frac{x \sqrt[3]{a+b}}{\sqrt[3]{a+b x^3}}\right)}{3 \sqrt[3]{a+b}}+\frac{\log \left(\frac{x^2 (a+b)^{2/3}}{\left(a+b x^3\right)^{2/3}}+\frac{x \sqrt[3]{a+b}}{\sqrt[3]{a+b x^3}}+1\right)}{6 \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{\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,"ArcTan[(1 + (2*(a + b)^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]]/(Sqrt[3]*(a + b)^(1/3)) - Log[1 - ((a + b)^(1/3)*x)/(a + b*x^3)^(1/3)]/(3*(a + b)^(1/3)) + Log[1 + ((a + b)^(2/3)*x^2)/(a + b*x^3)^(2/3) + ((a + b)^(1/3)*x)/(a + b*x^3)^(1/3)]/(6*(a + b)^(1/3))","A",7,7,21,0.3333,1,"{377, 200, 31, 634, 617, 204, 628}"
95,0,0,0,0.2995816,"\int \frac{1+x}{\left(1+x+x^2\right) \sqrt[3]{a+b x^3}} \, dx","Int[(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,"((3 - I*Sqrt[3])*Defer[Int][1/((1 - I*Sqrt[3] + 2*x)*(a + b*x^3)^(1/3)), x])/3 + ((3 + I*Sqrt[3])*Defer[Int][1/((1 + I*Sqrt[3] + 2*x)*(a + b*x^3)^(1/3)), x])/3","F",0,0,0,0,-1,"{}"
96,1,96,0,0.0781431,"\int \frac{x^2}{\left(1-x^3\right) \sqrt[3]{a+b x^3}} \, dx","Int[x^2/((1 - x^3)*(a + b*x^3)^(1/3)),x]","\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}}","\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,"-(ArcTan[(1 + (2*(a + b*x^3)^(1/3))/(a + b)^(1/3))/Sqrt[3]]/(Sqrt[3]*(a + b)^(1/3))) + Log[1 - x^3]/(6*(a + b)^(1/3)) - Log[(a + b)^(1/3) - (a + b*x^3)^(1/3)]/(2*(a + b)^(1/3))","A",5,5,24,0.2083,1,"{444, 55, 617, 204, 31}"
97,1,122,0,0.0618137,"\int \frac{1}{\sqrt[3]{1-x^3} \left(1+x^3\right)} \, dx","Int[1/((1 - x^3)^(1/3)*(1 + x^3)),x]","-\frac{\log \left(\frac{2^{2/3} x^2}{\left(1-x^3\right)^{2/3}}-\frac{\sqrt[3]{2} x}{\sqrt[3]{1-x^3}}+1\right)}{6 \sqrt[3]{2}}+\frac{\log \left(\frac{\sqrt[3]{2} x}{\sqrt[3]{1-x^3}}+1\right)}{3 \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}}","-\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[(1 - (2*2^(1/3)*x)/(1 - x^3)^(1/3))/Sqrt[3]]/(2^(1/3)*Sqrt[3])) - Log[1 + (2^(2/3)*x^2)/(1 - x^3)^(2/3) - (2^(1/3)*x)/(1 - x^3)^(1/3)]/(6*2^(1/3)) + Log[1 + (2^(1/3)*x)/(1 - x^3)^(1/3)]/(3*2^(1/3))","A",7,7,19,0.3684,1,"{377, 200, 31, 634, 617, 204, 628}"
98,1,26,0,0.0108413,"\int \frac{x}{\sqrt[3]{1-x^3} \left(1+x^3\right)} \, dx","Int[x/((1 - x^3)^(1/3)*(1 + x^3)),x]","\frac{1}{2} x^2 F_1\left(\frac{2}{3};\frac{1}{3},1;\frac{5}{3};x^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)}{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,"(x^2*AppellF1[2/3, 1/3, 1, 5/3, x^3, -x^3])/2","C",1,1,20,0.05000,0,"{510}"
99,1,82,0,0.0578244,"\int \frac{x^2}{\sqrt[3]{1-x^3} \left(1+x^3\right)} \, dx","Int[x^2/((1 - x^3)^(1/3)*(1 + x^3)),x]","-\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}}","-\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 + 2^(2/3)*(1 - x^3)^(1/3))/Sqrt[3]]/(2^(1/3)*Sqrt[3]) - Log[1 + x^3]/(6*2^(1/3)) + Log[2^(1/3) - (1 - x^3)^(1/3)]/(2*2^(1/3))","A",5,5,22,0.2273,1,"{444, 55, 617, 204, 31}"
100,1,409,0,0.3367262,"\int \frac{1+x}{\left(1-x+x^2\right) \sqrt[3]{1-x^3}} \, dx","Int[(1 + x)/((1 - x + x^2)*(1 - x^3)^(1/3)),x]","-\frac{3 \left(-\sqrt{3}+i\right) \log \left(2\ 2^{2/3} \sqrt[3]{1-x^3}+2 x-i \sqrt{3}+1\right)}{4 \sqrt[3]{2} \left(\sqrt{3}+i\right)}-\frac{3 \left(\sqrt{3}+i\right) \log \left(2\ 2^{2/3} \sqrt[3]{1-x^3}+2 x+i \sqrt{3}+1\right)}{4 \sqrt[3]{2} \left(-\sqrt{3}+i\right)}-\frac{\left(3-i \sqrt{3}\right) \tan ^{-1}\left(\frac{2-\frac{\sqrt[3]{2} \left(2 x-i \sqrt{3}+1\right)}{\sqrt[3]{1-x^3}}}{2 \sqrt{3}}\right)}{2 \sqrt[3]{2} \left(\sqrt{3}+i\right)}+\frac{\left(3+i \sqrt{3}\right) \tan ^{-1}\left(\frac{2-\frac{\sqrt[3]{2} \left(2 x+i \sqrt{3}+1\right)}{\sqrt[3]{1-x^3}}}{2 \sqrt{3}}\right)}{2 \sqrt[3]{2} \left(-\sqrt{3}+i\right)}+\frac{\left(-\sqrt{3}+i\right) \log \left(-\left(-2 x-i \sqrt{3}+1\right)^2 \left(2 x-i \sqrt{3}+1\right)\right)}{4 \sqrt[3]{2} \left(\sqrt{3}+i\right)}+\frac{\left(\sqrt{3}+i\right) \log \left(-\left(-2 x+i \sqrt{3}+1\right)^2 \left(2 x+i \sqrt{3}+1\right)\right)}{4 \sqrt[3]{2} \left(-\sqrt{3}+i\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)}{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,"-((3 - I*Sqrt[3])*ArcTan[(2 - (2^(1/3)*(1 - I*Sqrt[3] + 2*x))/(1 - x^3)^(1/3))/(2*Sqrt[3])])/(2*2^(1/3)*(I + Sqrt[3])) + ((3 + I*Sqrt[3])*ArcTan[(2 - (2^(1/3)*(1 + I*Sqrt[3] + 2*x))/(1 - x^3)^(1/3))/(2*Sqrt[3])])/(2*2^(1/3)*(I - Sqrt[3])) + ((I - Sqrt[3])*Log[-((1 - I*Sqrt[3] - 2*x)^2*(1 - I*Sqrt[3] + 2*x))])/(4*2^(1/3)*(I + Sqrt[3])) + ((I + Sqrt[3])*Log[-((1 + I*Sqrt[3] - 2*x)^2*(1 + I*Sqrt[3] + 2*x))])/(4*2^(1/3)*(I - Sqrt[3])) - (3*(I - Sqrt[3])*Log[1 - I*Sqrt[3] + 2*x + 2*2^(2/3)*(1 - x^3)^(1/3)])/(4*2^(1/3)*(I + Sqrt[3])) - (3*(I + Sqrt[3])*Log[1 + I*Sqrt[3] + 2*x + 2*2^(2/3)*(1 - x^3)^(1/3)])/(4*2^(1/3)*(I - Sqrt[3]))","C",4,2,25,0.08000,1,"{6728, 2148}"
101,1,409,0,0.3005032,"\int \frac{(1+x)^2}{\sqrt[3]{1-x^3} \left(1+x^3\right)} \, dx","Int[(1 + x)^2/((1 - x^3)^(1/3)*(1 + x^3)),x]","-\frac{3 \left(-\sqrt{3}+i\right) \log \left(2\ 2^{2/3} \sqrt[3]{1-x^3}+2 x-i \sqrt{3}+1\right)}{4 \sqrt[3]{2} \left(\sqrt{3}+i\right)}-\frac{3 \left(\sqrt{3}+i\right) \log \left(2\ 2^{2/3} \sqrt[3]{1-x^3}+2 x+i \sqrt{3}+1\right)}{4 \sqrt[3]{2} \left(-\sqrt{3}+i\right)}-\frac{\left(3-i \sqrt{3}\right) \tan ^{-1}\left(\frac{2-\frac{\sqrt[3]{2} \left(2 x-i \sqrt{3}+1\right)}{\sqrt[3]{1-x^3}}}{2 \sqrt{3}}\right)}{2 \sqrt[3]{2} \left(\sqrt{3}+i\right)}+\frac{\left(3+i \sqrt{3}\right) \tan ^{-1}\left(\frac{2-\frac{\sqrt[3]{2} \left(2 x+i \sqrt{3}+1\right)}{\sqrt[3]{1-x^3}}}{2 \sqrt{3}}\right)}{2 \sqrt[3]{2} \left(-\sqrt{3}+i\right)}+\frac{\left(-\sqrt{3}+i\right) \log \left(-\left(-2 x-i \sqrt{3}+1\right)^2 \left(2 x-i \sqrt{3}+1\right)\right)}{4 \sqrt[3]{2} \left(\sqrt{3}+i\right)}+\frac{\left(\sqrt{3}+i\right) \log \left(-\left(-2 x+i \sqrt{3}+1\right)^2 \left(2 x+i \sqrt{3}+1\right)\right)}{4 \sqrt[3]{2} \left(-\sqrt{3}+i\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)}{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,"-((3 - I*Sqrt[3])*ArcTan[(2 - (2^(1/3)*(1 - I*Sqrt[3] + 2*x))/(1 - x^3)^(1/3))/(2*Sqrt[3])])/(2*2^(1/3)*(I + Sqrt[3])) + ((3 + I*Sqrt[3])*ArcTan[(2 - (2^(1/3)*(1 + I*Sqrt[3] + 2*x))/(1 - x^3)^(1/3))/(2*Sqrt[3])])/(2*2^(1/3)*(I - Sqrt[3])) + ((I - Sqrt[3])*Log[-((1 - I*Sqrt[3] - 2*x)^2*(1 - I*Sqrt[3] + 2*x))])/(4*2^(1/3)*(I + Sqrt[3])) + ((I + Sqrt[3])*Log[-((1 + I*Sqrt[3] - 2*x)^2*(1 + I*Sqrt[3] + 2*x))])/(4*2^(1/3)*(I - Sqrt[3])) - (3*(I - Sqrt[3])*Log[1 - I*Sqrt[3] + 2*x + 2*2^(2/3)*(1 - x^3)^(1/3)])/(4*2^(1/3)*(I + Sqrt[3])) - (3*(I + Sqrt[3])*Log[1 + I*Sqrt[3] + 2*x + 2*2^(2/3)*(1 - x^3)^(1/3)])/(4*2^(1/3)*(I - Sqrt[3]))","C",5,3,24,0.1250,1,"{1586, 6728, 2148}"
102,1,399,0,0.2990488,"\int \frac{1-x}{\left(1+x+x^2\right) \sqrt[3]{1+x^3}} \, dx","Int[(1 - x)/((1 + x + x^2)*(1 + x^3)^(1/3)),x]","\frac{3 \left(-\sqrt{3}+i\right) \log \left(2\ 2^{2/3} \sqrt[3]{x^3+1}-2 x-i \sqrt{3}+1\right)}{4 \sqrt[3]{2} \left(\sqrt{3}+i\right)}+\frac{3 \left(\sqrt{3}+i\right) \log \left(2\ 2^{2/3} \sqrt[3]{x^3+1}-2 x+i \sqrt{3}+1\right)}{4 \sqrt[3]{2} \left(-\sqrt{3}+i\right)}+\frac{\left(3-i \sqrt{3}\right) \tan ^{-1}\left(\frac{2-\frac{\sqrt[3]{2} \left(-2 x-i \sqrt{3}+1\right)}{\sqrt[3]{x^3+1}}}{2 \sqrt{3}}\right)}{2 \sqrt[3]{2} \left(\sqrt{3}+i\right)}-\frac{\left(3+i \sqrt{3}\right) \tan ^{-1}\left(\frac{2-\frac{\sqrt[3]{2} \left(-2 x+i \sqrt{3}+1\right)}{\sqrt[3]{x^3+1}}}{2 \sqrt{3}}\right)}{2 \sqrt[3]{2} \left(-\sqrt{3}+i\right)}-\frac{\left(-\sqrt{3}+i\right) \log \left(\left(-2 x-i \sqrt{3}+1\right) \left(2 x-i \sqrt{3}+1\right)^2\right)}{4 \sqrt[3]{2} \left(\sqrt{3}+i\right)}-\frac{\left(\sqrt{3}+i\right) \log \left(\left(-2 x+i \sqrt{3}+1\right) \left(2 x+i \sqrt{3}+1\right)^2\right)}{4 \sqrt[3]{2} \left(-\sqrt{3}+i\right)}","-\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,"((3 - I*Sqrt[3])*ArcTan[(2 - (2^(1/3)*(1 - I*Sqrt[3] - 2*x))/(1 + x^3)^(1/3))/(2*Sqrt[3])])/(2*2^(1/3)*(I + Sqrt[3])) - ((3 + I*Sqrt[3])*ArcTan[(2 - (2^(1/3)*(1 + I*Sqrt[3] - 2*x))/(1 + x^3)^(1/3))/(2*Sqrt[3])])/(2*2^(1/3)*(I - Sqrt[3])) - ((I - Sqrt[3])*Log[(1 - I*Sqrt[3] - 2*x)*(1 - I*Sqrt[3] + 2*x)^2])/(4*2^(1/3)*(I + Sqrt[3])) - ((I + Sqrt[3])*Log[(1 + I*Sqrt[3] - 2*x)*(1 + I*Sqrt[3] + 2*x)^2])/(4*2^(1/3)*(I - Sqrt[3])) + (3*(I - Sqrt[3])*Log[1 - I*Sqrt[3] - 2*x + 2*2^(2/3)*(1 + x^3)^(1/3)])/(4*2^(1/3)*(I + Sqrt[3])) + (3*(I + Sqrt[3])*Log[1 + I*Sqrt[3] - 2*x + 2*2^(2/3)*(1 + x^3)^(1/3)])/(4*2^(1/3)*(I - Sqrt[3]))","C",4,2,23,0.08696,1,"{6728, 2148}"
103,0,0,0,0.4250687,"\int \frac{\left(1-x^3\right)^{2/3}}{\left(1+x+x^2\right)^2} \, dx","Int[(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,"(-4*Defer[Int][(1 - x^3)^(2/3)/(-1 + I*Sqrt[3] - 2*x)^2, x])/3 + (((4*I)/3)*Defer[Int][(1 - x^3)^(2/3)/(-1 + I*Sqrt[3] - 2*x), x])/Sqrt[3] - (4*Defer[Int][(1 - x^3)^(2/3)/(1 + I*Sqrt[3] + 2*x)^2, x])/3 + (((4*I)/3)*Defer[Int][(1 - x^3)^(2/3)/(1 + I*Sqrt[3] + 2*x), x])/Sqrt[3]","F",0,0,0,0,-1,"{}"
104,0,0,0,0.2200717,"\int \frac{1-x}{\left(1+x+x^2\right) \sqrt[3]{1-x^3}} \, dx","Int[(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,"-((1 + I*Sqrt[3])*Defer[Int][1/((1 - I*Sqrt[3] + 2*x)*(1 - x^3)^(1/3)), x]) - (1 - I*Sqrt[3])*Defer[Int][1/((1 + I*Sqrt[3] + 2*x)*(1 - x^3)^(1/3)), x]","F",0,0,0,0,-1,"{}"
105,1,39,0,0.0289564,"\int \frac{(1-x)^2}{\left(1-x^3\right)^{4/3}} \, dx","Int[(1 - x)^2/(1 - x^3)^(4/3),x]","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}}","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,"(1 + (1 - 2*x)*x)/(1 - x^3)^(1/3) + x^2*Hypergeometric2F1[1/3, 2/3, 5/3, x^3]","A",3,3,19,0.1579,1,"{1854, 12, 364}"
106,1,67,0,0.0098674,"\int \left(1-x^3\right)^{2/3} \, dx","Int[(1 - x^3)^(2/3),x]","\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}}","\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[(1 - (2*x)/(1 - x^3)^(1/3))/Sqrt[3]])/(3*Sqrt[3]) + Log[x + (1 - x^3)^(1/3)]/3","A",2,2,11,0.1818,1,"{195, 239}"
107,1,70,0,0.038365,"\int \frac{\left(1-x^3\right)^{2/3}}{x} \, dx","Int[(1 - x^3)^(2/3)/x,x]","\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}","\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 + 2*(1 - x^3)^(1/3))/Sqrt[3]]/Sqrt[3] - Log[x]/2 + Log[1 - (1 - x^3)^(1/3)]/2","A",6,6,15,0.4000,1,"{266, 50, 55, 618, 204, 31}"
108,0,0,0,0.0682516,"\int \frac{\left(1-x^3\right)^{2/3}}{a+b x} \, dx","Int[(1 - x^3)^(2/3)/(a + b*x),x]","\int \frac{\left(1-x^3\right)^{2/3}}{a+b x} \, dx","-\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^2 \log \left(\sqrt[3]{1-x^3}+x\right)}{2 b^3}-\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{a^2 \tan ^{-1}\left(\frac{1-\frac{2 x}{\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{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 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,"Defer[Int][(1 - x^3)^(2/3)/(a + b*x), x]","F",0,0,0,0,-1,"{}"
109,0,0,0,0.4148513,"\int \frac{\left(1-x^3\right)^{2/3}}{\left(1-x+x^2\right)^2} \, dx","Int[(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{2 \left(1-x^3\right)^{2/3} x^2}{3 \left(x^3+1\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}}",1,"(-4*Defer[Int][(1 - x^3)^(2/3)/(1 + I*Sqrt[3] - 2*x)^2, x])/3 + (((4*I)/3)*Defer[Int][(1 - x^3)^(2/3)/(1 + I*Sqrt[3] - 2*x), x])/Sqrt[3] - (4*Defer[Int][(1 - x^3)^(2/3)/(-1 + I*Sqrt[3] + 2*x)^2, x])/3 + (((4*I)/3)*Defer[Int][(1 - x^3)^(2/3)/(-1 + I*Sqrt[3] + 2*x), x])/Sqrt[3]","F",0,0,0,0,-1,"{}"
110,0,0,0,0.9452572,"\int \frac{(1-2 x) \left(1-x^3\right)^{2/3}}{\left(1-x+x^2\right)^2} \, dx","Int[((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{\left(1-x^3\right)^{2/3}}{x^2-x+1}+\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}}",1,"(-4*Defer[Int][(1 - x^3)^(2/3)/(1 + I*Sqrt[3] - 2*x)^2, x])/3 + (4*(1 + I*Sqrt[3])*Defer[Int][(1 - x^3)^(2/3)/(1 + I*Sqrt[3] - 2*x)^2, x])/3 - (4*Defer[Int][(1 - x^3)^(2/3)/(-1 + I*Sqrt[3] + 2*x)^2, x])/3 + (4*(1 - I*Sqrt[3])*Defer[Int][(1 - x^3)^(2/3)/(-1 + I*Sqrt[3] + 2*x)^2, x])/3","F",0,0,0,0,-1,"{}"
111,0,0,0,0.0599141,"\int \frac{\left(1-x^3\right)^{2/3}}{1+x} \, dx","Int[(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,"Defer[Int][(1 - x^3)^(2/3)/(1 + x), x]","F",0,0,0,0,-1,"{}"
112,0,0,0,0.0706373,"\int \frac{\left(1-x+x^2\right) \left(1-x^3\right)^{2/3}}{1+x^3} \, dx","Int[((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,"Defer[Int][(1 - x^3)^(2/3)/(1 + x), x]","F",0,0,0,0,-1,"{}"
113,1,21,0,0.0082518,"\int \frac{\left(1-x^3\right)^{2/3}}{1+x^3} \, dx","Int[(1 - x^3)^(2/3)/(1 + x^3),x]","x F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,-x^3\right)","-\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,"x*AppellF1[1/3, -2/3, 1, 4/3, x^3, -x^3]","C",1,1,19,0.05263,0,"{429}"
114,1,26,0,0.0119922,"\int \frac{x \left(1-x^3\right)^{2/3}}{1+x^3} \, dx","Int[(x*(1 - x^3)^(2/3))/(1 + x^3),x]","\frac{1}{2} x^2 F_1\left(\frac{2}{3};-\frac{2}{3},1;\frac{5}{3};x^3,-x^3\right)","-\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,"(x^2*AppellF1[2/3, -2/3, 1, 5/3, x^3, -x^3])/2","C",1,1,20,0.05000,0,"{510}"
115,0,0,0,0.3989478,"\int \frac{(1-x) \left(1-x^3\right)^{2/3}}{1+x^3} \, dx","Int[((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,"(-2*Defer[Int][(1 - x^3)^(2/3)/(-1 - x), x])/3 - ((1 + (-1)^(2/3))*Defer[Int][(1 - x^3)^(2/3)/(-1 + (-1)^(1/3)*x), x])/3 - ((1 - (-1)^(1/3))*Defer[Int][(1 - x^3)^(2/3)/(-1 - (-1)^(2/3)*x), x])/3","F",0,0,0,0,-1,"{}"
116,1,21,0,0.0078488,"\int \frac{\sqrt[3]{1-x^3}}{1+x^3} \, dx","Int[(1 - x^3)^(1/3)/(1 + x^3),x]","x F_1\left(\frac{1}{3};-\frac{1}{3},1;\frac{4}{3};x^3,-x^3\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{\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,"x*AppellF1[1/3, -1/3, 1, 4/3, x^3, -x^3]","C",1,1,19,0.05263,0,"{429}"