1,1,15,15,0.0049572,"\int \frac{1}{\sqrt{1-a x}} \, dx","Integrate[1/Sqrt[1 - a*x],x]","-\frac{2 \sqrt{1-a x}}{a}","-\frac{2 \sqrt{1-a x}}{a}",1,"(-2*Sqrt[1 - a*x])/a","A",1
2,1,37,15,0.0335843,"\int \frac{-2 \log \left(-\sqrt{-1+a x}\right)+\log (-1+a x)}{2 \pi  \sqrt{-1+a x}} \, dx","Integrate[(-2*Log[-Sqrt[-1 + a*x]] + Log[-1 + a*x])/(2*Pi*Sqrt[-1 + a*x]),x]","\frac{\sqrt{a x-1} \left(\log (a x-1)-2 \log \left(-\sqrt{a x-1}\right)\right)}{\pi  a}","-\frac{2 \sqrt{1-a x}}{a}",1,"(Sqrt[-1 + a*x]*(-2*Log[-Sqrt[-1 + a*x]] + Log[-1 + a*x]))/(a*Pi)","C",1
3,1,99,82,0.190769,"\int \frac{1}{\left(2 x+\sqrt{1+x^2}\right)^2} \, dx","Integrate[(2*x + Sqrt[1 + x^2])^(-2),x]","\frac{1}{9} \left(\frac{12 x}{1-3 x^2}-\frac{\frac{6 x^2+6}{1-3 x^2}+\sqrt{3} \sqrt{-x^2-1} \tan ^{-1}\left(\frac{1}{2} \sqrt{3} \sqrt{-x^2-1}\right)}{\sqrt{x^2+1}}-\sqrt{3} \tanh ^{-1}\left(\sqrt{3} x\right)\right)","\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,"((12*x)/(1 - 3*x^2) - ((6 + 6*x^2)/(1 - 3*x^2) + Sqrt[3]*Sqrt[-1 - x^2]*ArcTan[(Sqrt[3]*Sqrt[-1 - x^2])/2])/Sqrt[1 + x^2] - Sqrt[3]*ArcTanh[Sqrt[3]*x])/9","A",1
4,1,167,43,3.7630081,"\int \frac{1}{\sqrt{-1+x^2} \left(-4+3 x^2\right)^2} \, dx","Integrate[1/(Sqrt[-1 + x^2]*(-4 + 3*x^2)^2),x]","-\frac{x \sqrt{x^2-1} \left(\frac{8 x^2 \left(x^2-1\right) \, _2F_1\left(2,3;\frac{7}{2};\frac{x^2}{4-3 x^2}\right)}{45 x^2-60}-\frac{x^2 \left(2 x^2-3\right) \sqrt{\frac{x^2-1}{3 x^2-4}} \left(2 \sqrt{\frac{x^2-x^4}{\left(4-3 x^2\right)^2}}-\sin ^{-1}\left(\sqrt{\frac{x^2}{4-3 x^2}}\right)\right)}{4 \left(\frac{x^2}{4-3 x^2}\right)^{5/2} \left(x^2-1\right)}\right)}{16 \left(1-\frac{3 x^2}{4}\right)^2}","\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,"-1/16*(x*Sqrt[-1 + x^2]*(-1/4*(x^2*(-3 + 2*x^2)*Sqrt[(-1 + x^2)/(-4 + 3*x^2)]*(2*Sqrt[(x^2 - x^4)/(4 - 3*x^2)^2] - ArcSin[Sqrt[x^2/(4 - 3*x^2)]]))/((x^2/(4 - 3*x^2))^(5/2)*(-1 + x^2)) + (8*x^2*(-1 + x^2)*Hypergeometric2F1[2, 3, 7/2, x^2/(4 - 3*x^2)])/(-60 + 45*x^2)))/(1 - (3*x^2)/4)^2","C",0
5,1,126,74,0.16553,"\int \frac{1}{\left(2 \sqrt{x}+\sqrt{1+x}\right)^2} \, dx","Integrate[(2*Sqrt[x] + Sqrt[1 + x])^(-2),x]","\frac{12 x^{3/2}+12 \sqrt{x}-8 \sqrt{x+1}+15 \sqrt{x+1} x \log (1-3 x)-5 \sqrt{x+1} \log (1-3 x)+10 \sqrt{-x-1} (3 x-1) \tan ^{-1}\left(\frac{2 \sqrt{x}}{\sqrt{-x-1}}\right)-8 \sqrt{x+1} (3 x-1) \sinh ^{-1}\left(\sqrt{x}\right)}{9 \sqrt{x+1} (3 x-1)}","-\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,"(12*Sqrt[x] + 12*x^(3/2) - 8*Sqrt[1 + x] - 8*Sqrt[1 + x]*(-1 + 3*x)*ArcSinh[Sqrt[x]] + 10*Sqrt[-1 - x]*(-1 + 3*x)*ArcTan[(2*Sqrt[x])/Sqrt[-1 - x]] - 5*Sqrt[1 + x]*Log[1 - 3*x] + 15*x*Sqrt[1 + x]*Log[1 - 3*x])/(9*Sqrt[1 + x]*(-1 + 3*x))","A",1
6,1,59,64,0.0864585,"\int \frac{\sqrt{-1+x^2}}{(-i+x)^2} \, dx","Integrate[Sqrt[-1 + x^2]/(-I + x)^2,x]","-\frac{\sqrt{x^2-1}}{x-i}+\tanh ^{-1}\left(\frac{x}{\sqrt{x^2-1}}\right)-\frac{\tanh ^{-1}\left(\frac{x+i}{\sqrt{2} \sqrt{x^2-1}}\right)}{\sqrt{2}}","\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)) + ArcTanh[x/Sqrt[-1 + x^2]] - ArcTanh[(I + x)/(Sqrt[2]*Sqrt[-1 + x^2])]/Sqrt[2]","A",1
7,1,75,48,0.1301653,"\int \frac{1}{\sqrt{-1+x^2} \left(1+x^2\right)^2} \, dx","Integrate[1/(Sqrt[-1 + x^2]*(1 + x^2)^2),x]","\frac{\sqrt{x^2-1} \left(3 \sqrt{2} \sqrt{\frac{x^2}{x^2-1}} \left(x^2+1\right) \tanh ^{-1}\left(\sqrt{2} \sqrt{\frac{x^2}{x^2-1}}\right)-2 x^2\right)}{8 \left(x^3+x\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,"(Sqrt[-1 + x^2]*(-2*x^2 + 3*Sqrt[2]*Sqrt[x^2/(-1 + x^2)]*(1 + x^2)*ArcTanh[Sqrt[2]*Sqrt[x^2/(-1 + x^2)]]))/(8*(x + x^3))","A",1
8,1,30,30,0.0582546,"\int \frac{1}{\left(\sqrt{-1+x}+\sqrt{x}\right)^2 \sqrt{-1+x}} \, dx","Integrate[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",1
9,1,340,220,0.8546599,"\int \frac{1}{\sqrt{-1+x^2} \left(\sqrt{x}+\sqrt{-1+x^2}\right)^2} \, dx","Integrate[1/(Sqrt[-1 + x^2]*(Sqrt[x] + Sqrt[-1 + x^2])^2),x]","\frac{2}{5} \left(\frac{\sqrt{x} (1-2 x)}{-x^2+x+1}+\frac{\sqrt{x^2-1} (1-2 x)}{x^2-x-1}-\frac{1}{2} \sqrt{\frac{5}{2} \left(1+\sqrt{5}\right)} \tan ^{-1}\left(\frac{-\sqrt{5} x+x-2}{\sqrt{2 \left(\sqrt{5}-1\right)} \sqrt{x^2-1}}\right)-\sqrt{\sqrt{5}-\frac{2}{5}} \tan ^{-1}\left(\frac{\left(\sqrt{5}-1\right) x+2}{\sqrt{2 \left(\sqrt{5}-1\right)} \sqrt{x^2-1}}\right)-\sqrt{\frac{5}{2 \left(1+\sqrt{5}\right)}} \tanh ^{-1}\left(\frac{\sqrt{5} x+x-2}{\sqrt{2 \left(1+\sqrt{5}\right)} \sqrt{x^2-1}}\right)-\sqrt{\frac{2}{5}+\sqrt{5}} \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{1}{10} \left(5 \sqrt{5}-11\right)} \tan ^{-1}\left(\sqrt{\frac{2}{\sqrt{5}-1}} \sqrt{x}\right)-\sqrt{\frac{1}{10} \left(11+5 \sqrt{5}\right)} \tanh ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} \sqrt{x}\right)\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])/(1 + x - x^2) + ((1 - 2*x)*Sqrt[-1 + x^2])/(-1 - x + x^2) + Sqrt[(-11 + 5*Sqrt[5])/10]*ArcTan[Sqrt[2/(-1 + Sqrt[5])]*Sqrt[x]] - (Sqrt[(5*(1 + Sqrt[5]))/2]*ArcTan[(-2 + x - Sqrt[5]*x)/(Sqrt[2*(-1 + Sqrt[5])]*Sqrt[-1 + x^2])])/2 - Sqrt[-2/5 + Sqrt[5]]*ArcTan[(2 + (-1 + Sqrt[5])*x)/(Sqrt[2*(-1 + Sqrt[5])]*Sqrt[-1 + x^2])] - Sqrt[(11 + 5*Sqrt[5])/10]*ArcTanh[Sqrt[2/(1 + Sqrt[5])]*Sqrt[x]] - Sqrt[5/(2*(1 + Sqrt[5]))]*ArcTanh[(-2 + x + Sqrt[5]*x)/(Sqrt[2*(1 + Sqrt[5])]*Sqrt[-1 + x^2])] - Sqrt[2/5 + Sqrt[5]]*ArcTanh[(2 - (1 + Sqrt[5])*x)/(Sqrt[2*(1 + Sqrt[5])]*Sqrt[-1 + x^2])]))/5","A",0
10,1,311,220,0.7126114,"\int \frac{\left(\sqrt{x}-\sqrt{-1+x^2}\right)^2}{\left(1+x-x^2\right)^2 \sqrt{-1+x^2}} \, dx","Integrate[(Sqrt[x] - Sqrt[-1 + x^2])^2/((1 + x - x^2)^2*Sqrt[-1 + x^2]),x]","\frac{1}{25} \left(\sqrt{\frac{2}{1+\sqrt{5}}} \left(5+2 \sqrt{5}\right) \tanh ^{-1}\left(\frac{\sqrt{5} x+x-2}{\sqrt{2 \left(1+\sqrt{5}\right)} \sqrt{x^2-1}}\right)+\frac{-20 x^{3/2}+20 \sqrt{x^2-1} x-10 \sqrt{x^2-1}+\sqrt{50 \sqrt{5}-110} \left(-x^2+x+1\right) \tan ^{-1}\left(\sqrt{\frac{2}{\sqrt{5}-1}} \sqrt{x}\right)+\sqrt{10 \left(1+\sqrt{5}\right)} \left(-x^2+x+1\right) \tan ^{-1}\left(\frac{-\sqrt{5} x+x-2}{\sqrt{2 \left(\sqrt{5}-1\right)} \sqrt{x^2-1}}\right)+5 \sqrt{\frac{2}{\sqrt{5}-1}} \left(x^2-x-1\right) \tan ^{-1}\left(\frac{-\sqrt{5} x+x-2}{\sqrt{2 \left(\sqrt{5}-1\right)} \sqrt{x^2-1}}\right)+10 \sqrt{x}}{-x^2+x+1}-\sqrt{110+50 \sqrt{5}} \tanh ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} \sqrt{x}\right)\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,"((10*Sqrt[x] - 20*x^(3/2) - 10*Sqrt[-1 + x^2] + 20*x*Sqrt[-1 + x^2] + Sqrt[-110 + 50*Sqrt[5]]*(1 + x - x^2)*ArcTan[Sqrt[2/(-1 + Sqrt[5])]*Sqrt[x]] + Sqrt[10*(1 + Sqrt[5])]*(1 + x - x^2)*ArcTan[(-2 + x - Sqrt[5]*x)/(Sqrt[2*(-1 + Sqrt[5])]*Sqrt[-1 + x^2])] + 5*Sqrt[2/(-1 + Sqrt[5])]*(-1 - x + x^2)*ArcTan[(-2 + x - Sqrt[5]*x)/(Sqrt[2*(-1 + Sqrt[5])]*Sqrt[-1 + x^2])])/(1 + x - x^2) - Sqrt[110 + 50*Sqrt[5]]*ArcTanh[Sqrt[2/(1 + Sqrt[5])]*Sqrt[x]] + Sqrt[2/(1 + Sqrt[5])]*(5 + 2*Sqrt[5])*ArcTanh[(-2 + x + Sqrt[5]*x)/(Sqrt[2*(1 + Sqrt[5])]*Sqrt[-1 + x^2])])/25","A",0
11,1,125,138,0.2026425,"\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","Integrate[1/(Sqrt[2]*(1 + x)^2*Sqrt[-I + x^2]) + 1/(Sqrt[2]*(1 + x)^2*Sqrt[I + x^2]),x]","\frac{i \left((1+i) \left(i \sqrt{x^2-i}+\sqrt{x^2+i}\right)+\sqrt{1-i} (x+1) \tanh ^{-1}\left(\frac{x+i}{\sqrt{1-i} \sqrt{x^2-i}}\right)+\sqrt{1+i} (x+1) \tanh ^{-1}\left(\frac{(1+i)^{3/2} (1+i x)}{2 \sqrt{x^2+i}}\right)\right)}{2 \sqrt{2} (x+1)}","-\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,"((I/2)*((1 + I)*(I*Sqrt[-I + x^2] + Sqrt[I + x^2]) + Sqrt[1 - I]*(1 + x)*ArcTanh[(I + x)/(Sqrt[1 - I]*Sqrt[-I + x^2])] + Sqrt[1 + I]*(1 + x)*ArcTanh[((1 + I)^(3/2)*(1 + I*x))/(2*Sqrt[I + x^2])]))/(Sqrt[2]*(1 + x))","A",1
12,0,0,125,0.2399212,"\int \frac{\sqrt{x^2+\sqrt{1+x^4}}}{(1+x)^2 \sqrt{1+x^4}} \, dx","Integrate[Sqrt[x^2 + Sqrt[1 + x^4]]/((1 + x)^2*Sqrt[1 + x^4]),x]","\int \frac{\sqrt{x^2+\sqrt{1+x^4}}}{(1+x)^2 \sqrt{1+x^4}} \, dx","-\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,"Integrate[Sqrt[x^2 + Sqrt[1 + x^4]]/((1 + x)^2*Sqrt[1 + x^4]), x]","F",-1
13,0,0,81,0.1734317,"\int \frac{\sqrt{x^2+\sqrt{1+x^4}}}{(1+x) \sqrt{1+x^4}} \, dx","Integrate[Sqrt[x^2 + Sqrt[1 + x^4]]/((1 + x)*Sqrt[1 + x^4]),x]","\int \frac{\sqrt{x^2+\sqrt{1+x^4}}}{(1+x) \sqrt{1+x^4}} \, dx","-\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,"Integrate[Sqrt[x^2 + Sqrt[1 + x^4]]/((1 + x)*Sqrt[1 + x^4]), x]","F",-1
14,1,31,31,0.0091819,"\int \frac{\sqrt{x^2+\sqrt{1+x^4}}}{\sqrt{1+x^4}} \, dx","Integrate[Sqrt[x^2 + Sqrt[1 + x^4]]/Sqrt[1 + x^4],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{\sqrt{x^4+1}+x^2}}\right)}{\sqrt{2}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{\sqrt{x^4+1}+x^2}}\right)}{\sqrt{2}}",1,"ArcTanh[(Sqrt[2]*x)/Sqrt[x^2 + Sqrt[1 + x^4]]]/Sqrt[2]","A",1
15,1,33,33,0.0108325,"\int \frac{\sqrt{-x^2+\sqrt{1+x^4}}}{\sqrt{1+x^4}} \, dx","Integrate[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",1
16,1,19,19,0.0175932,"\int \frac{(-1+x)^{3/2}+(1+x)^{3/2}}{(-1+x)^{3/2} (1+x)^{3/2}} \, dx","Integrate[((-1 + x)^(3/2) + (1 + x)^(3/2))/((-1 + x)^(3/2)*(1 + x)^(3/2)),x]","-\frac{2}{\sqrt{x+1}}-\frac{2}{\sqrt{x-1}}","-\frac{2}{\sqrt{x+1}}-\frac{2}{\sqrt{x-1}}",1,"-2/Sqrt[-1 + x] - 2/Sqrt[1 + x]","A",1
17,1,43,52,0.042058,"\int \left(x+\sqrt{a+x^2}\right)^b \, dx","Integrate[(x + Sqrt[a + x^2])^b,x]","\frac{\left(\sqrt{a+x^2}+x\right)^{b-1} \left((b-1) x \left(\sqrt{a+x^2}+x\right)+a b\right)}{b^2-1}","\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,"((x + Sqrt[a + x^2])^(-1 + b)*(a*b + (-1 + b)*x*(x + Sqrt[a + x^2])))/(-1 + b^2)","A",1
18,1,50,56,0.06831,"\int \left(x-\sqrt{a+x^2}\right)^b \, dx","Integrate[(x - Sqrt[a + x^2])^b,x]","\frac{1}{2} \left(x-\sqrt{a+x^2}\right)^{b-1} \left(\frac{\left(x-\sqrt{a+x^2}\right)^2}{b+1}+\frac{a}{b-1}\right)","\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,"((x - Sqrt[a + x^2])^(-1 + b)*(a/(-1 + b) + (x - Sqrt[a + x^2])^2/(1 + b)))/2","A",1
19,1,17,17,0.006773,"\int \frac{\left(x+\sqrt{a+x^2}\right)^b}{\sqrt{a+x^2}} \, dx","Integrate[(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",1
20,1,20,20,0.0070798,"\int \frac{\left(x-\sqrt{a+x^2}\right)^b}{\sqrt{a+x^2}} \, dx","Integrate[(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",1
21,1,36,42,0.0422629,"\int \frac{1}{\left(a+b e^{p x}\right)^2} \, dx","Integrate[(a + b*E^(p*x))^(-2),x]","\frac{\frac{a}{a+b e^{p x}}-\log \left(a+b e^{p x}\right)+p x}{a^2 p}","-\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,"(a/(a + b*E^(p*x)) + p*x - Log[a + b*E^(p*x)])/(a^2*p)","A",1
22,1,22,22,0.0206672,"\int \frac{1}{\left(b e^{-p x}+a e^{p x}\right)^2} \, dx","Integrate[(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*1/(a*(b + a*E^(2*p*x))*p)","A",1
23,1,49,62,0.0656316,"\int \frac{x}{\left(b e^{-p x}+a e^{p x}\right)^2} \, dx","Integrate[x/(b/E^(p*x) + a*E^(p*x))^2,x]","\frac{\frac{2 p x e^{2 p x}}{a e^{2 p x}+b}-\frac{\log \left(a e^{2 p x}+b\right)}{a}}{4 b p^2}","-\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,"((2*E^(2*p*x)*p*x)/(b + a*E^(2*p*x)) - Log[b + a*E^(2*p*x)]/a)/(4*b*p^2)","A",1
24,1,961,86,2.5201167,"\int \frac{1-x+3 x^2}{\sqrt{1-x+x^2} \left(1+x+x^2\right)^2} \, dx","Integrate[(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}+\frac{\left(7-i \sqrt{3}\right) \tan ^{-1}\left(\frac{3 \left(\left(-21-4 i \sqrt{3}\right) x^4+14 \left(7-2 i \sqrt{3}\right) x^3+\left(-103-36 i \sqrt{3}\right) x^2+\left(94+32 i \sqrt{3}\right) x-64 i \sqrt{3}-17\right)}{\left(84 i-113 \sqrt{3}\right) x^4+2 \left(52 \sqrt{3-3 i \sqrt{3}} \sqrt{x^2-x+1}+21 \sqrt{3}+138 i\right) x^3+\left(52 \sqrt{3-3 i \sqrt{3}} \sqrt{x^2-x+1}-59 \sqrt{3}-180 i\right) x^2+2 \left(26 \sqrt{3-3 i \sqrt{3}} \sqrt{x^2-x+1}-69 \sqrt{3}+132 i\right) x-52 \sqrt{3-3 i \sqrt{3}} \sqrt{x^2-x+1}+67 \sqrt{3}+96 i}\right)}{4 \sqrt{3-3 i \sqrt{3}}}-\frac{i \left(-7 i+\sqrt{3}\right) \tan ^{-1}\left(\frac{3 \left(\left(-21+4 i \sqrt{3}\right) x^4+14 \left(7+2 i \sqrt{3}\right) x^3+\left(-103+36 i \sqrt{3}\right) x^2+\left(94-32 i \sqrt{3}\right) x+64 i \sqrt{3}-17\right)}{\left(84 i+113 \sqrt{3}\right) x^4-2 \left(52 \sqrt{3+3 i \sqrt{3}} \sqrt{x^2-x+1}+21 \sqrt{3}-138 i\right) x^3+\left(-52 \sqrt{3+3 i \sqrt{3}} \sqrt{x^2-x+1}+59 \sqrt{3}-180 i\right) x^2+\left(-52 \sqrt{3+3 i \sqrt{3}} \sqrt{x^2-x+1}+138 \sqrt{3}+264 i\right) x+52 \sqrt{3+3 i \sqrt{3}} \sqrt{x^2-x+1}-67 \sqrt{3}+96 i}\right)}{4 \sqrt{3+3 i \sqrt{3}}}-\frac{\left(7 i+\sqrt{3}\right) \log \left(16 \left(x^2+x+1\right)^2\right)}{8 \sqrt{3-3 i \sqrt{3}}}-\frac{\left(-7 i+\sqrt{3}\right) \log \left(16 \left(x^2+x+1\right)^2\right)}{8 \sqrt{3+3 i \sqrt{3}}}+\frac{\left(7 i+\sqrt{3}\right) \log \left(\left(x^2+x+1\right) \left(\left(11 i+4 \sqrt{3}\right) x^2-\left(8 i \sqrt{1-i \sqrt{3}} \sqrt{x^2-x+1}+4 \sqrt{3}+17 i\right) x+10 i \sqrt{1-i \sqrt{3}} \sqrt{x^2-x+1}+4 \sqrt{3}+11 i\right)\right)}{8 \sqrt{3-3 i \sqrt{3}}}+\frac{\left(-7 i+\sqrt{3}\right) \log \left(\left(x^2+x+1\right) \left(\left(-11 i+4 \sqrt{3}\right) x^2+\left(8 i \sqrt{1+i \sqrt{3}} \sqrt{x^2-x+1}-4 \sqrt{3}+17 i\right) x-10 i \sqrt{1+i \sqrt{3}} \sqrt{x^2-x+1}+4 \sqrt{3}-11 i\right)\right)}{8 \sqrt{3+3 i \sqrt{3}}}","\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) + ((7 - I*Sqrt[3])*ArcTan[(3*(-17 - (64*I)*Sqrt[3] + (94 + (32*I)*Sqrt[3])*x + (-103 - (36*I)*Sqrt[3])*x^2 + 14*(7 - (2*I)*Sqrt[3])*x^3 + (-21 - (4*I)*Sqrt[3])*x^4))/(96*I + 67*Sqrt[3] + (84*I - 113*Sqrt[3])*x^4 - 52*Sqrt[3 - (3*I)*Sqrt[3]]*Sqrt[1 - x + x^2] + 2*x*(132*I - 69*Sqrt[3] + 26*Sqrt[3 - (3*I)*Sqrt[3]]*Sqrt[1 - x + x^2]) + x^2*(-180*I - 59*Sqrt[3] + 52*Sqrt[3 - (3*I)*Sqrt[3]]*Sqrt[1 - x + x^2]) + 2*x^3*(138*I + 21*Sqrt[3] + 52*Sqrt[3 - (3*I)*Sqrt[3]]*Sqrt[1 - x + x^2]))])/(4*Sqrt[3 - (3*I)*Sqrt[3]]) - ((I/4)*(-7*I + Sqrt[3])*ArcTan[(3*(-17 + (64*I)*Sqrt[3] + (94 - (32*I)*Sqrt[3])*x + (-103 + (36*I)*Sqrt[3])*x^2 + 14*(7 + (2*I)*Sqrt[3])*x^3 + (-21 + (4*I)*Sqrt[3])*x^4))/(96*I - 67*Sqrt[3] + (84*I + 113*Sqrt[3])*x^4 + 52*Sqrt[3 + (3*I)*Sqrt[3]]*Sqrt[1 - x + x^2] + x^2*(-180*I + 59*Sqrt[3] - 52*Sqrt[3 + (3*I)*Sqrt[3]]*Sqrt[1 - x + x^2]) + x*(264*I + 138*Sqrt[3] - 52*Sqrt[3 + (3*I)*Sqrt[3]]*Sqrt[1 - x + x^2]) - 2*x^3*(-138*I + 21*Sqrt[3] + 52*Sqrt[3 + (3*I)*Sqrt[3]]*Sqrt[1 - x + x^2]))])/Sqrt[3 + (3*I)*Sqrt[3]] - ((-7*I + Sqrt[3])*Log[16*(1 + x + x^2)^2])/(8*Sqrt[3 + (3*I)*Sqrt[3]]) - ((7*I + Sqrt[3])*Log[16*(1 + x + x^2)^2])/(8*Sqrt[3 - (3*I)*Sqrt[3]]) + ((7*I + Sqrt[3])*Log[(1 + x + x^2)*(11*I + 4*Sqrt[3] + (11*I + 4*Sqrt[3])*x^2 + (10*I)*Sqrt[1 - I*Sqrt[3]]*Sqrt[1 - x + x^2] - x*(17*I + 4*Sqrt[3] + (8*I)*Sqrt[1 - I*Sqrt[3]]*Sqrt[1 - x + x^2]))])/(8*Sqrt[3 - (3*I)*Sqrt[3]]) + ((-7*I + Sqrt[3])*Log[(1 + x + x^2)*(-11*I + 4*Sqrt[3] + (-11*I + 4*Sqrt[3])*x^2 - (10*I)*Sqrt[1 + I*Sqrt[3]]*Sqrt[1 - x + x^2] + x*(17*I - 4*Sqrt[3] + (8*I)*Sqrt[1 + I*Sqrt[3]]*Sqrt[1 - x + x^2]))])/(8*Sqrt[3 + (3*I)*Sqrt[3]])","C",1
25,1,19,19,0.0115947,"\int \frac{\sqrt{x+\sqrt{a^2+x^2}}}{\sqrt{a^2+x^2}} \, dx","Integrate[Sqrt[x + Sqrt[a^2 + x^2]]/Sqrt[a^2 + x^2],x]","2 \sqrt{\sqrt{a^2+x^2}+x}","2 \sqrt{\sqrt{a^2+x^2}+x}",1,"2*Sqrt[x + Sqrt[a^2 + x^2]]","A",1
26,1,26,26,0.0178302,"\int \frac{\sqrt{b x+\sqrt{a+b^2 x^2}}}{\sqrt{a+b^2 x^2}} \, dx","Integrate[Sqrt[b*x + Sqrt[a + b^2*x^2]]/Sqrt[a + b^2*x^2],x]","\frac{2 \sqrt{\sqrt{a+b^2 x^2}+b x}}{b}","\frac{2 \sqrt{\sqrt{a+b^2 x^2}+b x}}{b}",1,"(2*Sqrt[b*x + Sqrt[a + b^2*x^2]])/b","A",1
27,1,56,63,0.2027669,"\int \frac{1}{x \sqrt{a^2+x^2} \sqrt{x+\sqrt{a^2+x^2}}} \, dx","Integrate[1/(x*Sqrt[a^2 + x^2]*Sqrt[x + Sqrt[a^2 + x^2]]),x]","-\frac{2 \left(\tan ^{-1}\left(\frac{\sqrt{\sqrt{a^2+x^2}+x}}{\sqrt{a}}\right)+\tanh ^{-1}\left(\frac{\sqrt{\sqrt{a^2+x^2}+x}}{\sqrt{a}}\right)\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]] + ArcTanh[Sqrt[x + Sqrt[a^2 + x^2]]/Sqrt[a]]))/a^(3/2)","A",1
28,1,127,82,0.0480722,"\int \frac{\sqrt{x+\sqrt{a^2+x^2}}}{x} \, dx","Integrate[Sqrt[x + Sqrt[a^2 + x^2]]/x,x]","-\frac{2 \sqrt{a^2+x^2} \left(\sqrt{a^2+x^2}+x\right) \left(-\sqrt{\sqrt{a^2+x^2}+x}+\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{\sqrt{a^2+x^2}+x}}{\sqrt{a}}\right)+\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a^2+x^2}+x}}{\sqrt{a}}\right)\right)}{x \left(\sqrt{a^2+x^2}+x\right)+a^2}","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[a^2 + x^2]*(x + Sqrt[a^2 + x^2])*(-Sqrt[x + Sqrt[a^2 + x^2]] + Sqrt[a]*ArcTan[Sqrt[x + Sqrt[a^2 + x^2]]/Sqrt[a]] + Sqrt[a]*ArcTanh[Sqrt[x + Sqrt[a^2 + x^2]]/Sqrt[a]]))/(a^2 + x*(x + Sqrt[a^2 + x^2]))","A",1
29,1,412,606,0.2618127,"\int x^3 \log ^3(2+x) \log (3+x) \, dx","Integrate[x^3*Log[2 + x]^3*Log[3 + x],x]","\frac{-224640 \operatorname{PolyLog}(4,-x-2)-24 \left(4680 \log ^2(x+2)-6756 \log (x+2)+5609\right) \operatorname{PolyLog}(2,-x-2)+288 (780 \log (x+2)-563) \operatorname{PolyLog}(3,-x-2)+54 x^4-144 x^4 \log ^3(x+2)+576 x^4 \log ^3(x+2) \log (x+3)+216 x^4 \log ^2(x+2)-432 x^4 \log ^2(x+2) \log (x+3)-162 x^4 \log (x+2)+216 x^4 \log (x+2) \log (x+3)-54 x^4 \log (x+3)-1050 x^3+576 x^3 \log ^3(x+2)-1680 x^3 \log ^2(x+2)+1152 x^3 \log ^2(x+2) \log (x+3)+2072 x^3 \log (x+2)-1344 x^3 \log (x+2) \log (x+3)+592 x^3 \log (x+3)+17705 x^2-2592 x^2 \log ^3(x+2)+11880 x^2 \log ^2(x+2)-3456 x^2 \log ^2(x+2) \log (x+3)-22836 x^2 \log (x+2)+7488 x^2 \log (x+2) \log (x+3)-5520 x^2 \log (x+3)-558290 x+15552 x \log ^3(x+2)+48384 \log ^3(x+2)-46656 \log ^3(x+2) \log (x+3)-118800 x \log ^2(x+2)+13824 x \log ^2(x+2) \log (x+3)-302016 \log ^2(x+2)+138672 \log ^2(x+2) \log (x+3)+400008 x \log (x+2)-57600 x \log (x+2) \log (x+3)+79680 x \log (x+3)+910528 \log (x+2)-293976 \log (x+2) \log (x+3)+309078 \log (x+3)-195984}{2304}","-\frac{5609}{96} \operatorname{PolyLog}(2,-x-2)-\frac{563}{8} \operatorname{PolyLog}(3,-x-2)-\frac{195}{2} \operatorname{PolyLog}(4,-x-2)-\frac{195}{4} \log ^2(x+2) \operatorname{PolyLog}(2,-x-2)+\frac{563}{8} \log (x+2) \operatorname{PolyLog}(2,-x-2)+\frac{195}{2} \log (x+2) \operatorname{PolyLog}(3,-x-2)+\frac{3 x^4}{256}+\frac{1}{4} x^4 \log ^3(x+2) \log (x+3)+\frac{3}{64} x^4 \log ^2(x+2)-\frac{3}{16} x^4 \log ^2(x+2) \log (x+3)-\frac{3}{128} x^4 \log (x+2)+\frac{3}{32} x^4 \log (x+2) \log (x+3)-\frac{3}{128} x^4 \log (x+3)-\frac{763 x^3}{3456}-\frac{17}{48} x^3 \log ^2(x+2)+\frac{1}{2} x^3 \log ^2(x+2) \log (x+3)+\frac{83}{288} x^3 \log (x+2)-\frac{7}{12} x^3 \log (x+2) \log (x+3)+\frac{37}{144} x^3 \log (x+3)+\frac{8029 x^2}{2304}-\frac{3}{2} x^2 \log ^2(x+2) \log (x+3)-\frac{187}{64} x^2 \log (x+2)+\frac{13}{4} x^2 \log (x+2) \log (x+3)-\frac{115}{48} x^2 \log (x+3)-\frac{302177 x}{1152}+\frac{3}{256} (x+2)^4-\frac{71}{216} (x+2)^3+\frac{377}{64} (x+2)^2-\frac{1}{16} (x+2)^4 \log ^3(x+2)+\frac{3}{4} (x+2)^3 \log ^3(x+2)-\frac{33}{8} (x+2)^2 \log ^3(x+2)+\frac{65}{4} (x+2) \log ^3(x+2)-\frac{81}{4} \log ^3(x+2) \log (x+3)+6 x \log ^2(x+2) \log (x+3)+\frac{3}{64} (x+2)^4 \log ^2(x+2)-\frac{3}{4} (x+2)^3 \log ^2(x+2)+\frac{273}{32} (x+2)^2 \log ^2(x+2)-\frac{1251}{16} (x+2) \log ^2(x+2)-\frac{43}{12} \log ^2(x+2)+\frac{963}{16} \log ^2(x+2) \log (x+3)-25 x \log (x+2) \log (x+3)-\frac{3}{64} (x+2)^4 \log (x+2)+\frac{71}{72} (x+2)^3 \log (x+2)-\frac{377}{32} (x+2)^2 \log (x+2)+\frac{6733}{32} (x+2) \log (x+2)+\frac{2069}{144} \log (x+2)+\frac{415}{12} (x+3) \log (x+3)-\frac{4083}{32} \log (x+2) \log (x+3)+\frac{3891}{128} \log (x+3)",1,"(-195984 - 558290*x + 17705*x^2 - 1050*x^3 + 54*x^4 + 910528*Log[2 + x] + 400008*x*Log[2 + x] - 22836*x^2*Log[2 + x] + 2072*x^3*Log[2 + x] - 162*x^4*Log[2 + x] - 302016*Log[2 + x]^2 - 118800*x*Log[2 + x]^2 + 11880*x^2*Log[2 + x]^2 - 1680*x^3*Log[2 + x]^2 + 216*x^4*Log[2 + x]^2 + 48384*Log[2 + x]^3 + 15552*x*Log[2 + x]^3 - 2592*x^2*Log[2 + x]^3 + 576*x^3*Log[2 + x]^3 - 144*x^4*Log[2 + x]^3 + 309078*Log[3 + x] + 79680*x*Log[3 + x] - 5520*x^2*Log[3 + x] + 592*x^3*Log[3 + x] - 54*x^4*Log[3 + x] - 293976*Log[2 + x]*Log[3 + x] - 57600*x*Log[2 + x]*Log[3 + x] + 7488*x^2*Log[2 + x]*Log[3 + x] - 1344*x^3*Log[2 + x]*Log[3 + x] + 216*x^4*Log[2 + x]*Log[3 + x] + 138672*Log[2 + x]^2*Log[3 + x] + 13824*x*Log[2 + x]^2*Log[3 + x] - 3456*x^2*Log[2 + x]^2*Log[3 + x] + 1152*x^3*Log[2 + x]^2*Log[3 + x] - 432*x^4*Log[2 + x]^2*Log[3 + x] - 46656*Log[2 + x]^3*Log[3 + x] + 576*x^4*Log[2 + x]^3*Log[3 + x] - 24*(5609 - 6756*Log[2 + x] + 4680*Log[2 + x]^2)*PolyLog[2, -2 - x] + 288*(-563 + 780*Log[2 + x])*PolyLog[3, -2 - x] - 224640*PolyLog[4, -2 - x])/2304","A",1
30,1,17,17,0.0107363,"\int \frac{\left(x+\sqrt{b+x^2}\right)^a}{\sqrt{b+x^2}} \, dx","Integrate[(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",1
31,1,46,52,0.061145,"\int \left(x+\sqrt{b+x^2}\right)^a \, dx","Integrate[(x + Sqrt[b + x^2])^a,x]","\frac{1}{2} \left(\sqrt{b+x^2}+x\right)^{a-1} \left(\frac{\left(\sqrt{b+x^2}+x\right)^2}{a+1}+\frac{b}{a-1}\right)","\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,"((x + Sqrt[b + x^2])^(-1 + a)*(b/(-1 + a) + (x + Sqrt[b + x^2])^2/(1 + a)))/2","A",1
32,1,33,34,0.1255271,"\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","Integrate[(6 + 3*x^a + 2*x^(2*a))^a^(-1)*(x^a + x^(2*a) + x^(3*a)),x]","\frac{x^{a+1} \left(2 x^{2 a}+3 x^a+6\right)^{\frac{1}{a}+1}}{6 a+6}","\frac{x^{a+1} \left(2 x^{2 a}+3 x^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 + 6*a)","A",1
33,1,57,58,0.0148211,"\int \frac{1}{x \sqrt[3]{1-x^2}} \, dx","Integrate[1/(x*(1 - x^2)^(1/3)),x]","\frac{1}{2} \left(\frac{3}{2} \log \left(1-\sqrt[3]{1-x^2}\right)+\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{1-x^2}+1}{\sqrt{3}}\right)-\log (x)\right)","\frac{3}{4} \log \left(1-\sqrt[3]{1-x^2}\right)+\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{1-x^2}+1}{\sqrt{3}}\right)-\frac{\log (x)}{2}",1,"(Sqrt[3]*ArcTan[(1 + 2*(1 - x^2)^(1/3))/Sqrt[3]] - Log[x] + (3*Log[1 - (1 - x^2)^(1/3)])/2)/2","A",1
34,1,81,58,0.0124882,"\int \frac{1}{x \left(1-x^2\right)^{2/3}} \, dx","Integrate[1/(x*(1 - x^2)^(2/3)),x]","\frac{1}{2} \log \left(1-\sqrt[3]{1-x^2}\right)-\frac{1}{4} \log \left(\left(1-x^2\right)^{2/3}+\sqrt[3]{1-x^2}+1\right)-\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{1-x^2}+1}{\sqrt{3}}\right)","\frac{3}{4} \log \left(1-\sqrt[3]{1-x^2}\right)-\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{1-x^2}+1}{\sqrt{3}}\right)-\frac{\log (x)}{2}",1,"-1/2*(Sqrt[3]*ArcTan[(1 + 2*(1 - x^2)^(1/3))/Sqrt[3]]) + Log[1 - (1 - x^2)^(1/3)]/2 - Log[1 + (1 - x^2)^(1/3) + (1 - x^2)^(2/3)]/4","A",1
35,1,86,49,0.0401205,"\int \frac{1}{\sqrt[3]{1-x^3}} \, dx","Integrate[(1 - x^3)^(-1/3),x]","\frac{1}{3} \log \left(\frac{x}{\sqrt[3]{1-x^3}}+1\right)+\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{1-x^3}}-1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{1}{6} \log \left(-\frac{x}{\sqrt[3]{1-x^3}}+\frac{x^2}{\left(1-x^3\right)^{2/3}}+1\right)","\frac{1}{2} \log \left(\sqrt[3]{1-x^3}+x\right)-\frac{\tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt{3}}",1,"ArcTan[(-1 + (2*x)/(1 - x^3)^(1/3))/Sqrt[3]]/Sqrt[3] - Log[1 + x^2/(1 - x^3)^(2/3) - x/(1 - x^3)^(1/3)]/6 + Log[1 + x/(1 - x^3)^(1/3)]/3","A",1
36,1,55,55,0.0126803,"\int \frac{1}{x \sqrt[3]{1-x^3}} \, dx","Integrate[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",1
37,0,0,97,0.0802845,"\int \frac{1}{(1+x) \sqrt[3]{1-x^3}} \, dx","Integrate[1/((1 + x)*(1 - x^3)^(1/3)),x]","\int \frac{1}{(1+x) \sqrt[3]{1-x^3}} \, dx","\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,"Integrate[1/((1 + x)*(1 - x^3)^(1/3)), x]","F",-1
38,0,0,145,0.0802952,"\int \frac{x}{(1+x) \sqrt[3]{1-x^3}} \, dx","Integrate[x/((1 + x)*(1 - x^3)^(1/3)),x]","\int \frac{x}{(1+x) \sqrt[3]{1-x^3}} \, dx","\frac{1}{2} \log \left(\sqrt[3]{1-x^3}+x\right)-\frac{3 \log \left(2^{2/3} \sqrt[3]{1-x^3}+x-1\right)}{4 \sqrt[3]{2}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1}{\sqrt{3}}\right)}{2 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\log \left((1-x) (x+1)^2\right)}{4 \sqrt[3]{2}}",1,"Integrate[x/((1 + x)*(1 - x^3)^(1/3)), x]","F",-1
39,1,59,110,0.0231916,"\int \frac{1}{x \sqrt[3]{2-3 x+x^2}} \, dx","Integrate[1/(x*(2 - 3*x + x^2)^(1/3)),x]","-\frac{3 \sqrt[3]{1-\frac{2}{x}} \sqrt[3]{1-\frac{1}{x}} F_1\left(\frac{2}{3};\frac{1}{3},\frac{1}{3};\frac{5}{3};\frac{1}{x},\frac{2}{x}\right)}{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,"(-3*(1 - 2/x)^(1/3)*(1 - x^(-1))^(1/3)*AppellF1[2/3, 1/3, 1/3, 5/3, x^(-1), 2/x])/(2*(2 - 3*x + x^2)^(1/3))","C",0
40,1,85,81,0.0147973,"\int \frac{1}{\sqrt[3]{-5+7 x-3 x^2+x^3}} \, dx","Integrate[(-5 + 7*x - 3*x^2 + x^3)^(-1/3),x]","\frac{3 \sqrt[3]{i x+(2-i)} \sqrt[3]{i (x-1)} (x-(1-2 i)) F_1\left(\frac{2}{3};\frac{1}{3},\frac{1}{3};\frac{5}{3};-\frac{1}{4} i (x-(1-2 i)),-\frac{1}{2} i (x-(1-2 i))\right)}{4 \sqrt[3]{x^3-3 x^2+7 x-5}}","-\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,"(3*((2 - I) + I*x)^(1/3)*(I*(-1 + x))^(1/3)*((-1 + 2*I) + x)*AppellF1[2/3, 1/3, 1/3, 5/3, (-1/4*I)*((-1 + 2*I) + x), (-1/2*I)*((-1 + 2*I) + x)])/(4*(-5 + 7*x - 3*x^2 + x^3)^(1/3))","C",0
41,1,127,66,0.0789495,"\int \frac{1}{\sqrt[3]{x \left(-q+x^2\right)}} \, dx","Integrate[(x*(-q + x^2))^(-1/3),x]","\frac{\sqrt[3]{x} \sqrt[3]{x^2-q} \left(-2 \log \left(1-\frac{x^{2/3}}{\sqrt[3]{x^2-q}}\right)+\log \left(\frac{x^{4/3}}{\left(x^2-q\right)^{2/3}}+\frac{x^{2/3}}{\sqrt[3]{x^2-q}}+1\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 x^{2/3}}{\sqrt[3]{x^2-q}}+1}{\sqrt{3}}\right)\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,"(x^(1/3)*(-q + x^2)^(1/3)*(2*Sqrt[3]*ArcTan[(1 + (2*x^(2/3))/(-q + x^2)^(1/3))/Sqrt[3]] - 2*Log[1 - x^(2/3)/(-q + x^2)^(1/3)] + Log[1 + x^(4/3)/(-q + x^2)^(2/3) + x^(2/3)/(-q + x^2)^(1/3)]))/(4*(-(q*x) + x^3)^(1/3))","A",1
42,1,140,79,0.1510492,"\int \frac{1}{\sqrt[3]{(-1+x) \left(q-2 x+x^2\right)}} \, dx","Integrate[((-1 + x)*(q - 2*x + x^2))^(-1/3),x]","\frac{\sqrt[3]{x-1} \sqrt[3]{q+(x-2) x} \left(-2 \log \left(1-\frac{(x-1)^{2/3}}{\sqrt[3]{q+(x-2) x}}\right)+\log \left(\frac{(x-1)^{4/3}}{(q+(x-2) x)^{2/3}}+\frac{(x-1)^{2/3}}{\sqrt[3]{q+(x-2) x}}+1\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 (x-1)^{2/3}}{\sqrt[3]{q+(x-2) x}}+1}{\sqrt{3}}\right)\right)}{4 \sqrt[3]{(x-1) (q+(x-2) x)}}","-\frac{3}{4} \log \left(\sqrt[3]{(x-1) \left(q+x^2-2 x\right)}-x+1\right)+\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{2 (x-1)}{\sqrt{3} \sqrt[3]{(x-1) \left(q+x^2-2 x\right)}}+\frac{1}{\sqrt{3}}\right)+\frac{1}{4} \log (1-x)",1,"((-1 + x)^(1/3)*(q + (-2 + x)*x)^(1/3)*(2*Sqrt[3]*ArcTan[(1 + (2*(-1 + x)^(2/3))/(q + (-2 + x)*x)^(1/3))/Sqrt[3]] - 2*Log[1 - (-1 + x)^(2/3)/(q + (-2 + x)*x)^(1/3)] + Log[1 + (-1 + x)^(4/3)/(q + (-2 + x)*x)^(2/3) + (-1 + x)^(2/3)/(q + (-2 + x)*x)^(1/3)]))/(4*((-1 + x)*(q + (-2 + x)*x))^(1/3))","A",1
43,1,55,118,0.1952283,"\int \frac{1}{x \sqrt[3]{(-1+x) \left(q-2 q x+x^2\right)}} \, dx","Integrate[1/(x*((-1 + x)*(q - 2*q*x + x^2))^(1/3)),x]","\frac{3 \left((x-1) \left(-2 q x+q+x^2\right)\right)^{2/3} \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{x^2-2 q x+q}{q (x-1)^2}\right)}{4 q (x-1)^2}","-\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,"(3*((-1 + x)*(q - 2*q*x + x^2))^(2/3)*Hypergeometric2F1[2/3, 1, 5/3, (q - 2*q*x + x^2)/(q*(-1 + x)^2)])/(4*q*(-1 + x)^2)","C",1
44,0,0,111,1.6378414,"\int \frac{2-(1+k) x}{\sqrt[3]{(1-x) x (1-k x)} (1-(1+k) x)} \, dx","Integrate[(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,"Integrate[(2 - (1 + k)*x)/(((1 - x)*x*(1 - k*x))^(1/3)*(1 - (1 + k)*x)), x]","F",-1
45,0,0,176,0.6664408,"\int \frac{1-k x}{(1+(-2+k) x) ((1-x) x (1-k x))^{2/3}} \, dx","Integrate[(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,"Integrate[(1 - k*x)/((1 + (-2 + k)*x)*((1 - x)*x*(1 - k*x))^(2/3)), x]","F",-1
46,0,0,493,0.3958597,"\int \frac{a+b x+c x^2}{\left(1-x+x^2\right) \sqrt[3]{1-x^3}} \, dx","Integrate[(a + b*x + c*x^2)/((1 - x + x^2)*(1 - x^3)^(1/3)),x]","\int \frac{a+b x+c x^2}{\left(1-x+x^2\right) \sqrt[3]{1-x^3}} \, dx","\frac{(a+b) \log \left(\frac{2^{2/3} (1-x)^2}{\left(1-x^3\right)^{2/3}}-\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{6 \sqrt[3]{2}}-\frac{(a+b) \log \left(\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{3 \sqrt[3]{2}}-\frac{(a+b) \log \left(2^{2/3} \sqrt[3]{1-x^3}+x-1\right)}{4 \sqrt[3]{2}}+\frac{(a+b) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}+\frac{(a+b) \tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1}{\sqrt{3}}\right)}{2 \sqrt[3]{2} \sqrt{3}}+\frac{(a+b) \log \left((1-x) (x+1)^2\right)}{12 \sqrt[3]{2}}-\frac{(a-c) \log \left(x^3+1\right)}{6 \sqrt[3]{2}}+\frac{(a-c) \log \left(-\sqrt[3]{1-x^3}-\sqrt[3]{2} x\right)}{2 \sqrt[3]{2}}-\frac{(a-c) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}-\frac{(b+c) \log \left(x^3+1\right)}{6 \sqrt[3]{2}}+\frac{(b+c) \log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{2 \sqrt[3]{2}}+\frac{(b+c) \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}+\frac{1}{2} c \log \left(\sqrt[3]{1-x^3}+x\right)-\frac{c \tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt{3}}",1,"Integrate[(a + b*x + c*x^2)/((1 - x + x^2)*(1 - x^3)^(1/3)), x]","F",-1
47,1,198,407,2.1292177,"\int \frac{1}{(3-2 x)^{11/2} \left(1+x+2 x^2\right)^5} \, dx","Integrate[1/((3 - 2*x)^(11/2)*(1 + x + 2*x^2)^5),x]","\frac{45 i \sqrt{14-2 i \sqrt{7}} \left(146319 \sqrt{7}+115739 i\right) \tanh ^{-1}\left(\frac{\sqrt{6-4 x}}{\sqrt{7-i \sqrt{7}}}\right)-45 i \sqrt{14+2 i \sqrt{7}} \left(146319 \sqrt{7}-115739 i\right) \tanh ^{-1}\left(\frac{\sqrt{6-4 x}}{\sqrt{7+i \sqrt{7}}}\right)+\frac{56 \left(-88070400 x^{12}+677249280 x^{11}-1873554048 x^{10}+2443779648 x^9-2343370048 x^8+3106712560 x^7-2888625656 x^6+1470758860 x^5-1627773523 x^4+1073855156 x^3-135202154 x^2+429812744 x-40289347\right)}{(3-2 x)^{9/2} \left(2 x^2+x+1\right)^4}}{121436356608}","\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,"((56*(-40289347 + 429812744*x - 135202154*x^2 + 1073855156*x^3 - 1627773523*x^4 + 1470758860*x^5 - 2888625656*x^6 + 3106712560*x^7 - 2343370048*x^8 + 2443779648*x^9 - 1873554048*x^10 + 677249280*x^11 - 88070400*x^12))/((3 - 2*x)^(9/2)*(1 + x + 2*x^2)^4) + (45*I)*Sqrt[14 - (2*I)*Sqrt[7]]*(115739*I + 146319*Sqrt[7])*ArcTanh[Sqrt[6 - 4*x]/Sqrt[7 - I*Sqrt[7]]] - (45*I)*Sqrt[14 + (2*I)*Sqrt[7]]*(-115739*I + 146319*Sqrt[7])*ArcTanh[Sqrt[6 - 4*x]/Sqrt[7 + I*Sqrt[7]]])/121436356608","C",1
48,1,610,648,6.0924655,"\int \frac{1}{(3-2 x)^{21/2} \left(1+x+2 x^2\right)^{10}} \, dx","Integrate[1/((3 - 2*x)^(21/2)*(1 + x + 2*x^2)^10),x]","\frac{x}{63 (3-2 x)^{19/2} \left(2 x^2+x+1\right)^9}+\frac{\frac{67816 x+20776}{1568 (3-2 x)^{19/2} \left(2 x^2+x+1\right)^8}+\frac{\frac{117492592 x+46521776}{1372 (3-2 x)^{19/2} \left(2 x^2+x+1\right)^7}+\frac{\frac{164128134240 x+74020332960}{1176 (3-2 x)^{19/2} \left(2 x^2+x+1\right)^6}+\frac{\frac{184316990760000 x+94209549053760}{980 (3-2 x)^{19/2} \left(2 x^2+x+1\right)^5}+\frac{1}{980} \left(\frac{157747397367934080 x+95476201213680000}{784 (3-2 x)^{19/2} \left(2 x^2+x+1\right)^4}+\frac{1}{784} \left(\frac{89735798552133000960 x+72879297583985544960}{588 (3-2 x)^{19/2} \left(2 x^2+x+1\right)^3}+\frac{1}{588} \left(\frac{18400346379541577848320 x+36432734212165998389760}{392 (3-2 x)^{19/2} \left(2 x^2+x+1\right)^2}+\frac{1}{392} \left(\frac{6440121232839552246912000-15435719146659136558464000 x}{196 (3-2 x)^{19/2} \left(2 x^2+x+1\right)}+\frac{1}{196} \left(\frac{39479926882545221954112000}{19 (3-2 x)^{19/2}}+\frac{1}{266} \left(-\frac{908021664138480966930240000}{17 (3-2 x)^{17/2}}+\frac{1}{238} \left(-\frac{19105520493023248582746201600}{(3-2 x)^{15/2}}+\frac{1}{210} \left(-\frac{26849557435537239465884310720000}{13 (3-2 x)^{13/2}}+\frac{1}{182} \left(-\frac{150994423858598796539274120000000}{(3-2 x)^{11/2}}+\frac{1}{154} \left(-\frac{8237718113587514139784976619840000}{(3-2 x)^{9/2}}+\frac{1}{126} \left(-\frac{338389312036560466460044072847040000}{(3-2 x)^{7/2}}+\frac{1}{98} \left(-\frac{10135305528576510550836394515648960000}{(3-2 x)^{5/2}}+\frac{1}{70} \left(-\frac{204334375738495648812805956791073600000}{(3-2 x)^{3/2}}+\frac{1}{42} \left(-\frac{2230994866519889796828561036406228800000}{\sqrt{3-2 x}}+\frac{1}{7} \left(\frac{\sqrt{\frac{1}{2} \left(7-i \sqrt{7}\right)} \left(-31233928131278457155599854509687203200000-71750597240923349846054347713013891200000 i \sqrt{7}\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{3-2 x}}{\sqrt{7-i \sqrt{7}}}\right)}{-14+2 i \sqrt{7}}+\frac{\sqrt{\frac{1}{2} \left(7+i \sqrt{7}\right)} \left(-31233928131278457155599854509687203200000+71750597240923349846054347713013891200000 i \sqrt{7}\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{3-2 x}}{\sqrt{7+i \sqrt{7}}}\right)}{-14-2 i \sqrt{7}}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)}{1176}}{1372}}{1568}}{1764}","\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,"x/(63*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^9) + ((20776 + 67816*x)/(1568*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^8) + ((46521776 + 117492592*x)/(1372*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^7) + ((74020332960 + 164128134240*x)/(1176*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^6) + ((94209549053760 + 184316990760000*x)/(980*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^5) + ((95476201213680000 + 157747397367934080*x)/(784*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^4) + ((72879297583985544960 + 89735798552133000960*x)/(588*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^3) + ((36432734212165998389760 + 18400346379541577848320*x)/(392*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^2) + ((6440121232839552246912000 - 15435719146659136558464000*x)/(196*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)) + (39479926882545221954112000/(19*(3 - 2*x)^(19/2)) + (-908021664138480966930240000/(17*(3 - 2*x)^(17/2)) + (-19105520493023248582746201600/(3 - 2*x)^(15/2) + (-26849557435537239465884310720000/(13*(3 - 2*x)^(13/2)) + (-150994423858598796539274120000000/(3 - 2*x)^(11/2) + (-8237718113587514139784976619840000/(3 - 2*x)^(9/2) + (-338389312036560466460044072847040000/(3 - 2*x)^(7/2) + (-10135305528576510550836394515648960000/(3 - 2*x)^(5/2) + (-204334375738495648812805956791073600000/(3 - 2*x)^(3/2) + (-2230994866519889796828561036406228800000/Sqrt[3 - 2*x] + ((Sqrt[(7 - I*Sqrt[7])/2]*(-31233928131278457155599854509687203200000 - (71750597240923349846054347713013891200000*I)*Sqrt[7])*ArcTanh[(Sqrt[2]*Sqrt[3 - 2*x])/Sqrt[7 - I*Sqrt[7]]])/(-14 + (2*I)*Sqrt[7]) + (Sqrt[(7 + I*Sqrt[7])/2]*(-31233928131278457155599854509687203200000 + (71750597240923349846054347713013891200000*I)*Sqrt[7])*ArcTanh[(Sqrt[2]*Sqrt[3 - 2*x])/Sqrt[7 + I*Sqrt[7]]])/(-14 - (2*I)*Sqrt[7]))/7)/42)/70)/98)/126)/154)/182)/210)/238)/266)/196)/392)/588)/784)/980)/1176)/1372)/1568)/1764","C",1
49,1,1100,1058,6.1754992,"\int \frac{1}{(3-2 x)^{41/2} \left(1+x+2 x^2\right)^{20}} \, dx","Integrate[1/((3 - 2*x)^(41/2)*(1 + x + 2*x^2)^20),x]","\frac{x}{133 (3-2 x)^{39/2} \left(2 x^2+x+1\right)^{19}}+\frac{\frac{146216 x+44296}{3528 (3-2 x)^{39/2} \left(2 x^2+x+1\right)^{18}}+\frac{\frac{589021552 x+223125616}{3332 (3-2 x)^{39/2} \left(2 x^2+x+1\right)^{17}}+\frac{\frac{2110519336800 x+865861681440}{3136 (3-2 x)^{39/2} \left(2 x^2+x+1\right)^{16}}+\frac{\frac{6928434268875840 x+2984274342235200}{2940 (3-2 x)^{39/2} \left(2 x^2+x+1\right)^{15}}+\frac{\frac{20924013532366815360 x+9408813737133390720}{2744 (3-2 x)^{39/2} \left(2 x^2+x+1\right)^{14}}+\frac{\frac{57873497074462503141120 x+27243065619141593598720}{2548 (3-2 x)^{39/2} \left(2 x^2+x+1\right)^{13}}+\frac{\frac{145295342948683106164016640 x+72110377354780278913835520}{2352 (3-2 x)^{39/2} \left(2 x^2+x+1\right)^{12}}+\frac{\frac{326770416680301421681066214400 x+172901458108932896335179801600}{2156 (3-2 x)^{39/2} \left(2 x^2+x+1\right)^{11}}+\frac{\frac{645802967231886306826540424448000 x+370557652515461812186329087129600}{1960 (3-2 x)^{39/2} \left(2 x^2+x+1\right)^{10}}+\frac{\frac{1088028437838790621809440473088716800 x+696175598675973438759010577554944000}{1764 (3-2 x)^{39/2} \left(2 x^2+x+1\right)^9}+\frac{\frac{1477884081820868038735185945420330393600 x+1111965063471244015489248163496668569600}{1568 (3-2 x)^{39/2} \left(2 x^2+x+1\right)^8}+\frac{\frac{1410229454280293592108580217248432347955200 x+1427636023038958525418189623276039160217600}{1372 (3-2 x)^{39/2} \left(2 x^2+x+1\right)^7}+\frac{\frac{421439161286999121770135584246204836237312000 x+1283308803395067168818807997696073436639232000}{1176 (3-2 x)^{39/2} \left(2 x^2+x+1\right)^6}+\frac{\frac{359909043739097249991695788946258930146664448000-1443636121324398194831693460992758930913796096000 x}{980 (3-2 x)^{39/2} \left(2 x^2+x+1\right)^5}+\frac{1}{980} \left(\frac{-3040089329780519199031170166260953381570260254720000 x-1152021624816869759475691381872221626869209284608000}{784 (3-2 x)^{39/2} \left(2 x^2+x+1\right)^4}+\frac{1}{784} \left(\frac{-2609695511325529255410382651665073470845732989009920000 x-2255746282697145245681128263365627409125133109002240000}{588 (3-2 x)^{39/2} \left(2 x^2+x+1\right)^3}+\frac{1}{588} \left(\frac{115668033214143596894295804604678509924267822733393920000 x-1790251120769313069211522499042240401000172830460805120000}{392 (3-2 x)^{39/2} \left(2 x^2+x+1\right)^2}+\frac{1}{392} \left(\frac{2464467090087282692969213073458776810025190662610343034880000 x+72870860924910466043406356900947461252288728322038169600000}{196 (3-2 x)^{39/2} \left(2 x^2+x+1\right)}+\frac{1}{196} \left(\frac{1}{546} \left(\frac{1}{518} \left(\frac{1}{490} \left(\frac{1}{462} \left(\frac{1}{434} \left(\frac{1}{406} \left(\frac{1}{378} \left(\frac{1}{350} \left(\frac{1}{322} \left(\frac{1}{294} \left(\frac{1}{266} \left(\frac{1}{238} \left(\frac{1}{210} \left(\frac{1}{182} \left(\frac{1}{154} \left(\frac{1}{126} \left(\frac{1}{98} \left(\frac{1}{70} \left(\frac{1}{42} \left(\frac{1}{7} \left(\frac{\sqrt{\frac{1}{2} \left(7-i \sqrt{7}\right)} \left(-1858108368071384082365375489497327979997317265656094102900994881309741240965074545186816000000000-3853414006278103146767987622401496699336335555921865837542016885265897482833115690092544000000000 i \sqrt{7}\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{3-2 x}}{\sqrt{7-i \sqrt{7}}}\right)}{-14+2 i \sqrt{7}}+\frac{\sqrt{\frac{1}{2} \left(7+i \sqrt{7}\right)} \left(-1858108368071384082365375489497327979997317265656094102900994881309741240965074545186816000000000+3853414006278103146767987622401496699336335555921865837542016885265897482833115690092544000000000 i \sqrt{7}\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{3-2 x}}{\sqrt{7+i \sqrt{7}}}\right)}{-14-2 i \sqrt{7}}\right)-\frac{132722026290813148740383963535523427142665518975435293064356777236410088640362467513344000000000}{\sqrt{3-2 x}}\right)-\frac{11332385663391839740343974428370683887566771471384841151672642393999283182139266339840000000000}{(3-2 x)^{3/2}}\right)-\frac{553541210002735957048844214716028245499086746401723523324780660557661668413725058949120000000}{(3-2 x)^{5/2}}\right)-\frac{18330190892216697744173706790143700087358561576136178754174544727578117325359791923200000000}{(3-2 x)^{7/2}}\right)-\frac{443379872262112313052073614945722839817152039380963932483996666511839997547213824000000000}{(3-2 x)^{9/2}}\right)-\frac{8073268485314233063840337934095431560069216535225849300748018943930634745621913600000000}{(3-2 x)^{11/2}}\right)-\frac{109415183151546322431572415879018096250836012099731766901467841654602614755123200000000}{(3-2 x)^{13/2}}\right)-\frac{992239519653790860422623948957964852355985846800936213338418761762097950023680000000}{(3-2 x)^{15/2}}\right)-\frac{2313064137166228597053737241416368284722516912423159767489332810437803253760000000}{(3-2 x)^{17/2}}\right)+\frac{118767476492930264374166633243140666046068763101817907661320807641190359040000000}{(3-2 x)^{19/2}}\right)+\frac{2893692593980364723231826294558630623656919099359688069727689450554368000000000}{(3-2 x)^{21/2}}\right)+\frac{42926886721523802306414887155091882259902542088067698170622802545418240000000}{(3-2 x)^{23/2}}\right)+\frac{487904184130260773926886832047572655461484781443782543411352841560457216000}{(3-2 x)^{25/2}}\right)+\frac{4496423323436580179825935667807239175646629240803415910250222313472000000}{(3-2 x)^{27/2}}\right)+\frac{980445504127015992472138196645778610361943940861637274650890661068800000}{29 (3-2 x)^{29/2}}\right)+\frac{6167726649054233403507372547934021941920835094010816556282758758400000}{31 (3-2 x)^{31/2}}\right)+\frac{757366667762147355602446006474261151597409525795681824661504000000}{(3-2 x)^{33/2}}\right)-\frac{696740950089909200017539783692427216704271188038402697920512000}{(3-2 x)^{35/2}}\right)-\frac{1708089006242241264480481073293611769771298388785813753364480000}{37 (3-2 x)^{37/2}}\right)-\frac{530550566665897087493026465460148012491929957574880460800000}{(3-2 x)^{39/2}}\right)\right)\right)\right)\right)}{1176}}{1372}}{1568}}{1764}}{1960}}{2156}}{2352}}{2548}}{2744}}{2940}}{3136}}{3332}}{3528}}{3724}","\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 x^2+x+1\right)^3}-\frac{4611053278117143010907562317585}{7250583181024175751187784305423507521536 (3-2 x)^{7/2}}-\frac{23 (27513723463194262383705 x+10426142448623187379187)}{20018492580021161284337664 (3-2 x)^{39/2} \left(2 x^2+x+1\right)^4}-\frac{143401467550777247627940437025}{73985542663511997461099839851260280832 (3-2 x)^{9/2}}-\frac{2211619588790911794826342607495}{406920484649315986036049119181931544576 (3-2 x)^{11/2}}+\frac{115 (298281884944522225747 x+908287136092467468517)}{10187982830903626725064704 (3-2 x)^{39/2} \left(2 x^2+x+1\right)^6}-\frac{460503190416958283087439337135}{34350430522344855964082068502370844672 (3-2 x)^{13/2}}+\frac{23 (908287136092467468517 x+919498192874055581221)}{1576711628592227945545728 (3-2 x)^{39/2} \left(2 x^2+x+1\right)^7}-\frac{101190274412779618678573275245}{3963511214116714149701777134888943616 (3-2 x)^{15/2}}+\frac{919498192874055581221 x+691833601144925854831}{48266682507925345271808 (3-2 x)^{39/2} \left(2 x^2+x+1\right)^8}-\frac{22724090823469905152713519545}{1604278348571050965355481221264572416 (3-2 x)^{17/2}}+\frac{9477172618423641847 x+6063974149878048635}{430952522392190582784 (3-2 x)^{39/2} \left(2 x^2+x+1\right)^9}+\frac{173441368149804378661935869705}{896508488907352010051592447177261056 (3-2 x)^{19/2}}+\frac{78752911037377255 x+45187921585208601}{3420258114223734784 (3-2 x)^{39/2} \left(2 x^2+x+1\right)^{10}}+\frac{14011818498091020272474956375}{10110997995195699361484125344104448 (3-2 x)^{21/2}}+\frac{5 (5020880176134289 x+2656658801194921)}{1099368679571914752 (3-2 x)^{39/2} \left(2 x^2+x+1\right)^{11}}+\frac{11155168222970774232376891145}{1685166332532616560247354224017408 (3-2 x)^{23/2}}+\frac{156274047129113 x+77559130805859}{7138757659557888 (3-2 x)^{39/2} \left(2 x^2+x+1\right)^{12}}+\frac{15848613964169066543734380171}{601845118761648771516912222863360 (3-2 x)^{25/2}}+\frac{6100156355517 x+2871555518177}{297448235814912 (3-2 x)^{39/2} \left(2 x^2+x+1\right)^{13}}+\frac{149066309808794760843017404825}{1624981820656451683095663001731072 (3-2 x)^{27/2}}+\frac{92630823167 x+41652915209}{4902992898048 (3-2 x)^{39/2} \left(2 x^2+x+1\right)^{14}}+\frac{34911619993974714062172751985}{124667917457770102671360389021696 (3-2 x)^{29/2}}+\frac{429411497 x+184959785}{25015269888 (3-2 x)^{39/2} \left(2 x^2+x+1\right)^{15}}+\frac{47657515074514118796095929535}{66632852434325399703658138959872 (3-2 x)^{31/2}}+\frac{5 (1831285 x+751303)}{595601664 (3-2 x)^{39/2} \left(2 x^2+x+1\right)^{16}}+\frac{2124315846756567455653862925}{1688851098565851144562763890688 (3-2 x)^{33/2}}+\frac{107329 x+40657}{7976808 (3-2 x)^{39/2} \left(2 x^2+x+1\right)^{17}}-\frac{304688229262620222736480811}{537361713180043545997243056128 (3-2 x)^{35/2}}+\frac{373 x+113}{33516 (3-2 x)^{39/2} \left(2 x^2+x+1\right)^{18}}-\frac{3948194343291401740321996415}{202881463139404195937734623232 (3-2 x)^{37/2}}+\frac{x}{133 (3-2 x)^{39/2} \left(2 x^2+x+1\right)^{19}}-\frac{13056959628363355534285785425}{106924014357253562723941220352 (3-2 x)^{39/2}}",1,"x/(133*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^19) + ((44296 + 146216*x)/(3528*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^18) + ((223125616 + 589021552*x)/(3332*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^17) + ((865861681440 + 2110519336800*x)/(3136*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^16) + ((2984274342235200 + 6928434268875840*x)/(2940*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^15) + ((9408813737133390720 + 20924013532366815360*x)/(2744*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^14) + ((27243065619141593598720 + 57873497074462503141120*x)/(2548*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^13) + ((72110377354780278913835520 + 145295342948683106164016640*x)/(2352*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^12) + ((172901458108932896335179801600 + 326770416680301421681066214400*x)/(2156*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^11) + ((370557652515461812186329087129600 + 645802967231886306826540424448000*x)/(1960*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^10) + ((696175598675973438759010577554944000 + 1088028437838790621809440473088716800*x)/(1764*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^9) + ((1111965063471244015489248163496668569600 + 1477884081820868038735185945420330393600*x)/(1568*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^8) + ((1427636023038958525418189623276039160217600 + 1410229454280293592108580217248432347955200*x)/(1372*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^7) + ((1283308803395067168818807997696073436639232000 + 421439161286999121770135584246204836237312000*x)/(1176*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^6) + ((359909043739097249991695788946258930146664448000 - 1443636121324398194831693460992758930913796096000*x)/(980*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^5) + ((-1152021624816869759475691381872221626869209284608000 - 3040089329780519199031170166260953381570260254720000*x)/(784*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^4) + ((-2255746282697145245681128263365627409125133109002240000 - 2609695511325529255410382651665073470845732989009920000*x)/(588*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^3) + ((-1790251120769313069211522499042240401000172830460805120000 + 115668033214143596894295804604678509924267822733393920000*x)/(392*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^2) + ((72870860924910466043406356900947461252288728322038169600000 + 2464467090087282692969213073458776810025190662610343034880000*x)/(196*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)) + (-530550566665897087493026465460148012491929957574880460800000/(3 - 2*x)^(39/2) + (-1708089006242241264480481073293611769771298388785813753364480000/(37*(3 - 2*x)^(37/2)) + (-696740950089909200017539783692427216704271188038402697920512000/(3 - 2*x)^(35/2) + (757366667762147355602446006474261151597409525795681824661504000000/(3 - 2*x)^(33/2) + (6167726649054233403507372547934021941920835094010816556282758758400000/(31*(3 - 2*x)^(31/2)) + (980445504127015992472138196645778610361943940861637274650890661068800000/(29*(3 - 2*x)^(29/2)) + (4496423323436580179825935667807239175646629240803415910250222313472000000/(3 - 2*x)^(27/2) + (487904184130260773926886832047572655461484781443782543411352841560457216000/(3 - 2*x)^(25/2) + (42926886721523802306414887155091882259902542088067698170622802545418240000000/(3 - 2*x)^(23/2) + (2893692593980364723231826294558630623656919099359688069727689450554368000000000/(3 - 2*x)^(21/2) + (118767476492930264374166633243140666046068763101817907661320807641190359040000000/(3 - 2*x)^(19/2) + (-2313064137166228597053737241416368284722516912423159767489332810437803253760000000/(3 - 2*x)^(17/2) + (-992239519653790860422623948957964852355985846800936213338418761762097950023680000000/(3 - 2*x)^(15/2) + (-109415183151546322431572415879018096250836012099731766901467841654602614755123200000000/(3 - 2*x)^(13/2) + (-8073268485314233063840337934095431560069216535225849300748018943930634745621913600000000/(3 - 2*x)^(11/2) + (-443379872262112313052073614945722839817152039380963932483996666511839997547213824000000000/(3 - 2*x)^(9/2) + (-18330190892216697744173706790143700087358561576136178754174544727578117325359791923200000000/(3 - 2*x)^(7/2) + (-553541210002735957048844214716028245499086746401723523324780660557661668413725058949120000000/(3 - 2*x)^(5/2) + (-11332385663391839740343974428370683887566771471384841151672642393999283182139266339840000000000/(3 - 2*x)^(3/2) + (-132722026290813148740383963535523427142665518975435293064356777236410088640362467513344000000000/Sqrt[3 - 2*x] + ((Sqrt[(7 - I*Sqrt[7])/2]*(-1858108368071384082365375489497327979997317265656094102900994881309741240965074545186816000000000 - (3853414006278103146767987622401496699336335555921865837542016885265897482833115690092544000000000*I)*Sqrt[7])*ArcTanh[(Sqrt[2]*Sqrt[3 - 2*x])/Sqrt[7 - I*Sqrt[7]]])/(-14 + (2*I)*Sqrt[7]) + (Sqrt[(7 + I*Sqrt[7])/2]*(-1858108368071384082365375489497327979997317265656094102900994881309741240965074545186816000000000 + (3853414006278103146767987622401496699336335555921865837542016885265897482833115690092544000000000*I)*Sqrt[7])*ArcTanh[(Sqrt[2]*Sqrt[3 - 2*x])/Sqrt[7 + I*Sqrt[7]]])/(-14 - (2*I)*Sqrt[7]))/7)/42)/70)/98)/126)/154)/182)/210)/238)/266)/294)/322)/350)/378)/406)/434)/462)/490)/518)/546)/196)/392)/588)/784)/980)/1176)/1372)/1568)/1764)/1960)/2156)/2352)/2548)/2744)/2940)/3136)/3332)/3528)/3724","C",1
50,1,342,378,6.1349522,"\int \frac{1}{\left(3-2 x+x^2\right)^{11/2} \left(1+x+2 x^2\right)^5} \, dx","Integrate[1/((3 - 2*x + x^2)^(11/2)*(1 + x + 2*x^2)^5),x]","\frac{-9 i \sqrt{50+10 i \sqrt{7}} \left(932587773 \sqrt{7}-299844895 i\right) \sqrt{x^2-2 x+3} \left(2 x^4-3 x^3+5 x^2+x+3\right)^4 \tanh ^{-1}\left(\frac{\left(-5-i \sqrt{7}\right) x+i \sqrt{7}+13}{\sqrt{50+10 i \sqrt{7}} \sqrt{x^2-2 x+3}}\right)+9 \sqrt{50-10 i \sqrt{7}} \left(299844895-932587773 i \sqrt{7}\right) \sqrt{x^2-2 x+3} \left(2 x^4-3 x^3+5 x^2+x+3\right)^4 \tanh ^{-1}\left(\frac{\left(5-i \sqrt{7}\right) x+i \sqrt{7}-13}{\sqrt{50-10 i \sqrt{7}} \sqrt{x^2-2 x+3}}\right)+560 \left(4596238560 x^{17}-38639385552 x^{16}+188603773872 x^{15}-606785954952 x^{14}+1459208021718 x^{13}-2679143870481 x^{12}+3999656132532 x^{11}-4915797913008 x^{10}+5380603084494 x^9-5134334619701 x^8+4591320676952 x^7-3359813871472 x^6+2503427226914 x^5-1409335257371 x^4+1002897791524 x^3-266966654968 x^2+261702502714 x-53205422447\right)}{691488000000000 \left(x^2-2 x+3\right)^{9/2} \left(2 x^2+x+1\right)^4}","-\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,"(560*(-53205422447 + 261702502714*x - 266966654968*x^2 + 1002897791524*x^3 - 1409335257371*x^4 + 2503427226914*x^5 - 3359813871472*x^6 + 4591320676952*x^7 - 5134334619701*x^8 + 5380603084494*x^9 - 4915797913008*x^10 + 3999656132532*x^11 - 2679143870481*x^12 + 1459208021718*x^13 - 606785954952*x^14 + 188603773872*x^15 - 38639385552*x^16 + 4596238560*x^17) - (9*I)*Sqrt[50 + (10*I)*Sqrt[7]]*(-299844895*I + 932587773*Sqrt[7])*Sqrt[3 - 2*x + x^2]*(3 + x + 5*x^2 - 3*x^3 + 2*x^4)^4*ArcTanh[(13 + I*Sqrt[7] + (-5 - I*Sqrt[7])*x)/(Sqrt[50 + (10*I)*Sqrt[7]]*Sqrt[3 - 2*x + x^2])] + 9*Sqrt[50 - (10*I)*Sqrt[7]]*(299844895 - (932587773*I)*Sqrt[7])*Sqrt[3 - 2*x + x^2]*(3 + x + 5*x^2 - 3*x^3 + 2*x^4)^4*ArcTanh[(-13 + I*Sqrt[7] + (5 - I*Sqrt[7])*x)/(Sqrt[50 - (10*I)*Sqrt[7]]*Sqrt[3 - 2*x + x^2])])/(691488000000000*(3 - 2*x + x^2)^(9/2)*(1 + x + 2*x^2)^4)","C",1
51,1,1431,638,11.6011254,"\int \frac{1}{\left(3-2 x+x^2\right)^{21/2} \left(1+x+2 x^2\right)^{10}} \, dx","Integrate[1/((3 - 2*x + x^2)^(21/2)*(1 + x + 2*x^2)^10),x]","\sqrt{x^2-2 x+3} \left(\frac{-334647150510 x-539608494637}{1210104000000000000 \left(2 x^2+x+1\right)^6}-\frac{11 (484788625685 x-411521923277)}{363375000000000000000 \left(x^2-2 x+3\right)}+\frac{367152793968978953465 x+65571203144429922747}{363182463000000000000000000 \left(2 x^2+x+1\right)}-\frac{11 (15286717673 x+3311570647)}{36337500000000000000 \left(x^2-2 x+3\right)^2}+\frac{4797048907791526114 x+1082422109196374795}{8301313440000000000000000 \left(2 x^2+x+1\right)^2}-\frac{11 (112950205 x+1626125723)}{3028125000000000000 \left(x^2-2 x+3\right)^3}+\frac{169630389653846945 x+62819559864314747}{370594350000000000000000 \left(2 x^2+x+1\right)^3}+\frac{430593031 x-1340879383}{181687500000000000 \left(x^2-2 x+3\right)^4}+\frac{129196597088670934 x+42018358198215561}{296475480000000000000000 \left(2 x^2+x+1\right)^4}+\frac{7 (43964675 x-73161291)}{90843750000000000 \left(x^2-2 x+3\right)^5}+\frac{56711874696335 x-40800462989458}{264710250000000000000 \left(2 x^2+x+1\right)^5}+\frac{7 (833371 x-678331)}{2220625000000000 \left(x^2-2 x+3\right)^6}+\frac{1642511 x+1062937}{1574625000000000 \left(x^2-2 x+3\right)^7}+\frac{-4965311863 x-2596903794}{10804500000000000 \left(2 x^2+x+1\right)^7}+\frac{82361-4841 x}{60562500000000 \left(x^2-2 x+3\right)^8}-\frac{73 (1604678 x-888423)}{882000000000000 \left(2 x^2+x+1\right)^8}+\frac{265-113 x}{403750000000 \left(x^2-2 x+3\right)^9}+\frac{221770 x+251943}{6300000000000 \left(2 x^2+x+1\right)^9}+\frac{1-x}{11875000000 \left(x^2-2 x+3\right)^{10}}\right)+\frac{\left(232442807954946745795 i+21634177831191924841 \sqrt{7}\right) \tan ^{-1}\left(\frac{-207342833228459577163557043035558264835165 i \sqrt{7} x^4-176004816500761880926774485599831047775825 x^4-143264806307504267815065909696666250772480 i \sqrt{10 \left(-5+i \sqrt{7}\right)} \sqrt{x^2-2 x+3} x^3+197868296377913870863837680953446009396860 i \sqrt{7} x^3-180084985147246689199448745264977678818020 x^3+300856093245758962411638410362999126622208 i \sqrt{10 \left(-5+i \sqrt{7}\right)} \sqrt{x^2-2 x+3} x^2-460764064177139993399975100872663310399420 i \sqrt{7} x^2+491153540508443587025809789813541985707360 x^2+114611845046003414252052727757333000617984 i \sqrt{10 \left(-5+i \sqrt{7}\right)} \sqrt{x^2-2 x+3} x-105711500937472192718115651350352447938680 i \sqrt{7} x-1506241361872688008559268776761430483700000 x+186244248199755548159585682605666126004224 i \sqrt{10 \left(-5+i \sqrt{7}\right)} \sqrt{x^2-2 x+3}+188630894626466690216855285995045889396405 i \sqrt{7}-135063738860435016899586558948733259113515}{16381317765107264789462917221030750634835 \sqrt{7} x^4+944749064886626467328385369190460703669697 i x^4+63430431602720043279192866968369397935660 \sqrt{7} x^3-3134217746230760357128318797499380812303788 i x^3-2027867550801106189867763431094227596320 \sqrt{7} x^2+2511300259855822962340893027852239157667820 i x^2+6150574559311228258394328777942059796320 \sqrt{7} x+1890613486065620301760074218556745311646936 i x+423642940259238735473942663180025956729505 \sqrt{7}+2368773290838836979864678493023884746594823 i}\right)}{16141442800000000000000000 \sqrt{70 \left(-5+i \sqrt{7}\right)}}-\frac{i \left(-232442807954946745795 i+21634177831191924841 \sqrt{7}\right) \tan ^{-1}\left(\frac{35 \left(468037650431636136841797634886592875281 \sqrt{7} x^4-795837271959975808913244203765619963595 i x^4+1812298045792001236548367627667697083876 \sqrt{7} x^3-15238894149752825683924814021007863070620 i x^3-57939072880031605424793240888406502752 \sqrt{7} x^2+26487288329265127577733965853364310310620 i x^2+175730701694606521668409393655487422752 \sqrt{7} x-40919031596617332707196094500783237405000 i x+12104084007406821013541218948000741620843 \sqrt{7}+4362494290663946676585186218212607628595 i\right)}{-207342833228459577163557043035558264835165 i \sqrt{7} x^4+176004816500761880926774485599831047775825 x^4+28652961261500853563013181939333250154496 i \sqrt{70 \left(5+i \sqrt{7}\right)} \sqrt{x^2-2 x+3} x^3+197868296377913870863837680953446009396860 i \sqrt{7} x^3+180084985147246689199448745264977678818020 x^3-14326480630750426781506590969666625077248 i \sqrt{70 \left(5+i \sqrt{7}\right)} \sqrt{x^2-2 x+3} x^2-460764064177139993399975100872663310399420 i \sqrt{7} x^2-491153540508443587025809789813541985707360 x^2-105711500937472192718115651350352447938680 i \sqrt{7} x+1506241361872688008559268776761430483700000 x-14326480630750426781506590969666625077248 i \sqrt{70 \left(5+i \sqrt{7}\right)} \sqrt{x^2-2 x+3}+188630894626466690216855285995045889396405 i \sqrt{7}+135063738860435016899586558948733259113515}\right)}{16141442800000000000000000 \sqrt{70 \left(5+i \sqrt{7}\right)}}+\frac{i \left(232442807954946745795 i+21634177831191924841 \sqrt{7}\right) \log \left(\left(-4 i x+\sqrt{7}-i\right)^2 \left(4 i x+\sqrt{7}+i\right)^2\right)}{32282885600000000000000000 \sqrt{70 \left(-5+i \sqrt{7}\right)}}-\frac{\left(-232442807954946745795 i+21634177831191924841 \sqrt{7}\right) \log \left(\left(-4 i x+\sqrt{7}-i\right)^2 \left(4 i x+\sqrt{7}+i\right)^2\right)}{32282885600000000000000000 \sqrt{70 \left(5+i \sqrt{7}\right)}}-\frac{i \left(232442807954946745795 i+21634177831191924841 \sqrt{7}\right) \log \left(\left(2 x^2+x+1\right) \left(5 \sqrt{7} x^2+9 i x^2-i \sqrt{70 \left(-5+i \sqrt{7}\right)} \sqrt{x^2-2 x+3} x-10 \sqrt{7} x+22 i x+i \sqrt{70 \left(-5+i \sqrt{7}\right)} \sqrt{x^2-2 x+3}+15 \sqrt{7}-13 i\right)\right)}{32282885600000000000000000 \sqrt{70 \left(-5+i \sqrt{7}\right)}}+\frac{\left(-232442807954946745795 i+21634177831191924841 \sqrt{7}\right) \log \left(\left(2 x^2+x+1\right) \left(5 \sqrt{7} x^2-41 i x^2+5 i \sqrt{10 \left(5+i \sqrt{7}\right)} \sqrt{x^2-2 x+3} x-10 \sqrt{7} x+122 i x-13 i \sqrt{10 \left(5+i \sqrt{7}\right)} \sqrt{x^2-2 x+3}+15 \sqrt{7}-163 i\right)\right)}{32282885600000000000000000 \sqrt{70 \left(5+i \sqrt{7}\right)}}","-\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,"Sqrt[3 - 2*x + x^2]*((1 - x)/(11875000000*(3 - 2*x + x^2)^10) + (265 - 113*x)/(403750000000*(3 - 2*x + x^2)^9) + (82361 - 4841*x)/(60562500000000*(3 - 2*x + x^2)^8) + (1062937 + 1642511*x)/(1574625000000000*(3 - 2*x + x^2)^7) + (7*(-678331 + 833371*x))/(2220625000000000*(3 - 2*x + x^2)^6) + (7*(-73161291 + 43964675*x))/(90843750000000000*(3 - 2*x + x^2)^5) + (-1340879383 + 430593031*x)/(181687500000000000*(3 - 2*x + x^2)^4) - (11*(1626125723 + 112950205*x))/(3028125000000000000*(3 - 2*x + x^2)^3) - (11*(3311570647 + 15286717673*x))/(36337500000000000000*(3 - 2*x + x^2)^2) - (11*(-411521923277 + 484788625685*x))/(363375000000000000000*(3 - 2*x + x^2)) + (251943 + 221770*x)/(6300000000000*(1 + x + 2*x^2)^9) - (73*(-888423 + 1604678*x))/(882000000000000*(1 + x + 2*x^2)^8) + (-2596903794 - 4965311863*x)/(10804500000000000*(1 + x + 2*x^2)^7) + (-539608494637 - 334647150510*x)/(1210104000000000000*(1 + x + 2*x^2)^6) + (-40800462989458 + 56711874696335*x)/(264710250000000000000*(1 + x + 2*x^2)^5) + (42018358198215561 + 129196597088670934*x)/(296475480000000000000000*(1 + x + 2*x^2)^4) + (62819559864314747 + 169630389653846945*x)/(370594350000000000000000*(1 + x + 2*x^2)^3) + (1082422109196374795 + 4797048907791526114*x)/(8301313440000000000000000*(1 + x + 2*x^2)^2) + (65571203144429922747 + 367152793968978953465*x)/(363182463000000000000000000*(1 + x + 2*x^2))) + ((232442807954946745795*I + 21634177831191924841*Sqrt[7])*ArcTan[(-135063738860435016899586558948733259113515 + (188630894626466690216855285995045889396405*I)*Sqrt[7] - 1506241361872688008559268776761430483700000*x - (105711500937472192718115651350352447938680*I)*Sqrt[7]*x + 491153540508443587025809789813541985707360*x^2 - (460764064177139993399975100872663310399420*I)*Sqrt[7]*x^2 - 180084985147246689199448745264977678818020*x^3 + (197868296377913870863837680953446009396860*I)*Sqrt[7]*x^3 - 176004816500761880926774485599831047775825*x^4 - (207342833228459577163557043035558264835165*I)*Sqrt[7]*x^4 + (186244248199755548159585682605666126004224*I)*Sqrt[10*(-5 + I*Sqrt[7])]*Sqrt[3 - 2*x + x^2] + (114611845046003414252052727757333000617984*I)*Sqrt[10*(-5 + I*Sqrt[7])]*x*Sqrt[3 - 2*x + x^2] + (300856093245758962411638410362999126622208*I)*Sqrt[10*(-5 + I*Sqrt[7])]*x^2*Sqrt[3 - 2*x + x^2] - (143264806307504267815065909696666250772480*I)*Sqrt[10*(-5 + I*Sqrt[7])]*x^3*Sqrt[3 - 2*x + x^2])/(2368773290838836979864678493023884746594823*I + 423642940259238735473942663180025956729505*Sqrt[7] + (1890613486065620301760074218556745311646936*I)*x + 6150574559311228258394328777942059796320*Sqrt[7]*x + (2511300259855822962340893027852239157667820*I)*x^2 - 2027867550801106189867763431094227596320*Sqrt[7]*x^2 - (3134217746230760357128318797499380812303788*I)*x^3 + 63430431602720043279192866968369397935660*Sqrt[7]*x^3 + (944749064886626467328385369190460703669697*I)*x^4 + 16381317765107264789462917221030750634835*Sqrt[7]*x^4)])/(16141442800000000000000000*Sqrt[70*(-5 + I*Sqrt[7])]) - ((I/16141442800000000000000000)*(-232442807954946745795*I + 21634177831191924841*Sqrt[7])*ArcTan[(35*(4362494290663946676585186218212607628595*I + 12104084007406821013541218948000741620843*Sqrt[7] - (40919031596617332707196094500783237405000*I)*x + 175730701694606521668409393655487422752*Sqrt[7]*x + (26487288329265127577733965853364310310620*I)*x^2 - 57939072880031605424793240888406502752*Sqrt[7]*x^2 - (15238894149752825683924814021007863070620*I)*x^3 + 1812298045792001236548367627667697083876*Sqrt[7]*x^3 - (795837271959975808913244203765619963595*I)*x^4 + 468037650431636136841797634886592875281*Sqrt[7]*x^4))/(135063738860435016899586558948733259113515 + (188630894626466690216855285995045889396405*I)*Sqrt[7] + 1506241361872688008559268776761430483700000*x - (105711500937472192718115651350352447938680*I)*Sqrt[7]*x - 491153540508443587025809789813541985707360*x^2 - (460764064177139993399975100872663310399420*I)*Sqrt[7]*x^2 + 180084985147246689199448745264977678818020*x^3 + (197868296377913870863837680953446009396860*I)*Sqrt[7]*x^3 + 176004816500761880926774485599831047775825*x^4 - (207342833228459577163557043035558264835165*I)*Sqrt[7]*x^4 - (14326480630750426781506590969666625077248*I)*Sqrt[70*(5 + I*Sqrt[7])]*Sqrt[3 - 2*x + x^2] - (14326480630750426781506590969666625077248*I)*Sqrt[70*(5 + I*Sqrt[7])]*x^2*Sqrt[3 - 2*x + x^2] + (28652961261500853563013181939333250154496*I)*Sqrt[70*(5 + I*Sqrt[7])]*x^3*Sqrt[3 - 2*x + x^2])])/Sqrt[70*(5 + I*Sqrt[7])] - ((-232442807954946745795*I + 21634177831191924841*Sqrt[7])*Log[(-I + Sqrt[7] - (4*I)*x)^2*(I + Sqrt[7] + (4*I)*x)^2])/(32282885600000000000000000*Sqrt[70*(5 + I*Sqrt[7])]) + ((I/32282885600000000000000000)*(232442807954946745795*I + 21634177831191924841*Sqrt[7])*Log[(-I + Sqrt[7] - (4*I)*x)^2*(I + Sqrt[7] + (4*I)*x)^2])/Sqrt[70*(-5 + I*Sqrt[7])] - ((I/32282885600000000000000000)*(232442807954946745795*I + 21634177831191924841*Sqrt[7])*Log[(1 + x + 2*x^2)*(-13*I + 15*Sqrt[7] + (22*I)*x - 10*Sqrt[7]*x + (9*I)*x^2 + 5*Sqrt[7]*x^2 + I*Sqrt[70*(-5 + I*Sqrt[7])]*Sqrt[3 - 2*x + x^2] - I*Sqrt[70*(-5 + I*Sqrt[7])]*x*Sqrt[3 - 2*x + x^2])])/Sqrt[70*(-5 + I*Sqrt[7])] + ((-232442807954946745795*I + 21634177831191924841*Sqrt[7])*Log[(1 + x + 2*x^2)*(-163*I + 15*Sqrt[7] + (122*I)*x - 10*Sqrt[7]*x - (41*I)*x^2 + 5*Sqrt[7]*x^2 - (13*I)*Sqrt[10*(5 + I*Sqrt[7])]*Sqrt[3 - 2*x + x^2] + (5*I)*Sqrt[10*(5 + I*Sqrt[7])]*x*Sqrt[3 - 2*x + x^2])])/(32282885600000000000000000*Sqrt[70*(5 + I*Sqrt[7])])","C",0
52,1,213,66,1.1504456,"\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","Integrate[(-a - Sqrt[1 + a^2] + x)/((-a + Sqrt[1 + a^2] + x)*Sqrt[(-a + x)*(1 + x^2)]),x]","\frac{2 \sqrt{\frac{a-x}{a+i}} \left(2 i \sqrt{a^2+1} \sqrt{1-i x} \sqrt{x^2+1} \Pi \left(\frac{2 i}{a-\sqrt{a^2+1}+i};\sin ^{-1}\left(\frac{\sqrt{1-i x}}{\sqrt{2}}\right)|\frac{2 i}{a+i}\right)-\left(\sqrt{a^2+1}-a-i\right) \sqrt{1+i x} (x+i) \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{1-i x}}{\sqrt{2}}\right),\frac{2 i}{a+i}\right)\right)}{\left(-\sqrt{a^2+1}+a+i\right) \sqrt{1-i x} \sqrt{\left(x^2+1\right) (x-a)}}","-\sqrt{2} \sqrt{\sqrt{a^2+1}+a} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{\sqrt{a^2+1}-a} (x-a)}{\sqrt{\left(x^2+1\right) (x-a)}}\right)",1,"(2*Sqrt[(a - x)/(I + a)]*(-((-I - a + Sqrt[1 + a^2])*Sqrt[1 + I*x]*(I + x)*EllipticF[ArcSin[Sqrt[1 - I*x]/Sqrt[2]], (2*I)/(I + a)]) + (2*I)*Sqrt[1 + a^2]*Sqrt[1 - I*x]*Sqrt[1 + x^2]*EllipticPi[(2*I)/(I + a - Sqrt[1 + a^2]), ArcSin[Sqrt[1 - I*x]/Sqrt[2]], (2*I)/(I + a)]))/((I + a - Sqrt[1 + a^2])*Sqrt[1 - I*x]*Sqrt[(-a + x)*(1 + x^2)])","C",1
53,1,145,198,0.233936,"\int \frac{a+b x}{\sqrt[3]{1-x^2} \left(3+x^2\right)} \, dx","Integrate[(a + b*x)/((1 - x^2)^(1/3)*(3 + x^2)),x]","\frac{1}{6} b x^2 F_1\left(1;\frac{1}{3},1;2;x^2,-\frac{x^2}{3}\right)-\frac{9 a x F_1\left(\frac{1}{2};\frac{1}{3},1;\frac{3}{2};x^2,-\frac{x^2}{3}\right)}{\sqrt[3]{1-x^2} \left(x^2+3\right) \left(2 x^2 \left(F_1\left(\frac{3}{2};\frac{1}{3},2;\frac{5}{2};x^2,-\frac{x^2}{3}\right)-F_1\left(\frac{3}{2};\frac{4}{3},1;\frac{5}{2};x^2,-\frac{x^2}{3}\right)\right)-9 F_1\left(\frac{1}{2};\frac{1}{3},1;\frac{3}{2};x^2,-\frac{x^2}{3}\right)\right)}","\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,"(b*x^2*AppellF1[1, 1/3, 1, 2, x^2, -1/3*x^2])/6 - (9*a*x*AppellF1[1/2, 1/3, 1, 3/2, x^2, -1/3*x^2])/((1 - x^2)^(1/3)*(3 + x^2)*(-9*AppellF1[1/2, 1/3, 1, 3/2, x^2, -1/3*x^2] + 2*x^2*(AppellF1[3/2, 1/3, 2, 5/2, x^2, -1/3*x^2] - AppellF1[3/2, 4/3, 1, 5/2, x^2, -1/3*x^2])))","C",0
54,1,153,198,0.2381647,"\int \frac{a+b x}{\left(3-x^2\right) \sqrt[3]{1+x^2}} \, dx","Integrate[(a + b*x)/((3 - x^2)*(1 + x^2)^(1/3)),x]","\frac{1}{6} b x^2 F_1\left(1;\frac{1}{3},1;2;-x^2,\frac{x^2}{3}\right)-\frac{9 a x F_1\left(\frac{1}{2};\frac{1}{3},1;\frac{3}{2};-x^2,\frac{x^2}{3}\right)}{\left(x^2-3\right) \sqrt[3]{x^2+1} \left(2 x^2 \left(F_1\left(\frac{3}{2};\frac{1}{3},2;\frac{5}{2};-x^2,\frac{x^2}{3}\right)-F_1\left(\frac{3}{2};\frac{4}{3},1;\frac{5}{2};-x^2,\frac{x^2}{3}\right)\right)+9 F_1\left(\frac{1}{2};\frac{1}{3},1;\frac{3}{2};-x^2,\frac{x^2}{3}\right)\right)}","\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,"(b*x^2*AppellF1[1, 1/3, 1, 2, -x^2, x^2/3])/6 - (9*a*x*AppellF1[1/2, 1/3, 1, 3/2, -x^2, x^2/3])/((-3 + x^2)*(1 + x^2)^(1/3)*(9*AppellF1[1/2, 1/3, 1, 3/2, -x^2, x^2/3] + 2*x^2*(AppellF1[3/2, 1/3, 2, 5/2, -x^2, x^2/3] - AppellF1[3/2, 4/3, 1, 5/2, -x^2, x^2/3])))","C",0
55,1,111,97,0.0548926,"\int \frac{1}{x \sqrt[3]{4-6 x+3 x^2}} \, dx","Integrate[1/(x*(4 - 6*x + 3*x^2)^(1/3)),x]","-\frac{\sqrt[3]{\frac{3 x+i \sqrt{3}-3}{x}} \sqrt[3]{\frac{9 x-3 i \sqrt{3}-9}{x}} F_1\left(\frac{2}{3};\frac{1}{3},\frac{1}{3};\frac{5}{3};\frac{3-i \sqrt{3}}{3 x},\frac{3+i \sqrt{3}}{3 x}\right)}{2 \sqrt[3]{3 x^2-6 x+4}}","\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,"-1/2*(((-3 + I*Sqrt[3] + 3*x)/x)^(1/3)*((-9 - (3*I)*Sqrt[3] + 9*x)/x)^(1/3)*AppellF1[2/3, 1/3, 1/3, 5/3, (3 - I*Sqrt[3])/(3*x), (3 + I*Sqrt[3])/(3*x)])/(4 - 6*x + 3*x^2)^(1/3)","C",0
56,1,20,73,0.002758,"\int x \sqrt[3]{1-x^3} \, dx","Integrate[x*(1 - x^3)^(1/3),x]","\frac{1}{2} x^2 \, _2F_1\left(-\frac{1}{3},\frac{2}{3};\frac{5}{3};x^3\right)","-\frac{1}{6} \log \left(-\sqrt[3]{1-x^3}-x\right)-\frac{\tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{3 \sqrt{3}}+\frac{1}{3} \sqrt[3]{1-x^3} x^2",1,"(x^2*Hypergeometric2F1[-1/3, 2/3, 5/3, x^3])/2","C",1
57,1,90,67,0.0213427,"\int \frac{\sqrt[3]{1-x^3}}{x} \, dx","Integrate[(1 - x^3)^(1/3)/x,x]","\sqrt[3]{1-x^3}+\frac{1}{3} \log \left(1-\sqrt[3]{1-x^3}\right)-\frac{1}{6} \log \left(\left(1-x^3\right)^{2/3}+\sqrt[3]{1-x^3}+1\right)-\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{\sqrt{3}}","\sqrt[3]{1-x^3}+\frac{1}{2} \log \left(1-\sqrt[3]{1-x^3}\right)-\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\log (x)}{2}",1,"(1 - x^3)^(1/3) - ArcTan[(1 + 2*(1 - x^3)^(1/3))/Sqrt[3]]/Sqrt[3] + Log[1 - (1 - x^3)^(1/3)]/3 - Log[1 + (1 - x^3)^(1/3) + (1 - x^3)^(2/3)]/6","A",1
58,0,0,482,0.3526096,"\int \frac{\sqrt[3]{1-x^3}}{1+x} \, dx","Integrate[(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,"Integrate[(1 - x^3)^(1/3)/(1 + x), x]","F",-1
59,0,0,280,0.1053754,"\int \frac{\sqrt[3]{1-x^3}}{1-x+x^2} \, dx","Integrate[(1 - x^3)^(1/3)/(1 - x + x^2),x]","\int \frac{\sqrt[3]{1-x^3}}{1-x+x^2} \, dx","\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{2\ 2^{2/3}}+\frac{3 \log \left(\sqrt[3]{1-x^3}-\sqrt[3]{2} (x-1)\right)}{2\ 2^{2/3}}+\frac{1}{2} \log \left(\sqrt[3]{1-x^3}+x\right)-\frac{\log \left(\sqrt[3]{1-x^3}+\sqrt[3]{2} x\right)}{2\ 2^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{2} (x-1)}{\sqrt[3]{1-x^3}}+1}{\sqrt{3}}\right)}{2^{2/3}}+\frac{\tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3}}-\frac{\log \left(-3 (x-1) \left(x^2-x+1\right)\right)}{2\ 2^{2/3}}",1,"Integrate[(1 - x^3)^(1/3)/(1 - x + x^2), x]","F",-1
60,0,0,232,0.3440485,"\int \frac{\sqrt[3]{1-x^3}}{2+x} \, dx","Integrate[(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,"Integrate[(1 - x^3)^(1/3)/(2 + x), x]","F",-1
61,0,0,168,0.1384373,"\int \frac{2+x}{\left(1+x+x^2\right) \sqrt[3]{2+x^3}} \, dx","Integrate[(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,"Integrate[(2 + x)/((1 + x + x^2)*(2 + x^3)^(1/3)), x]","F",-1
62,1,25,25,0.0071824,"\int \frac{3-3 x+30 x^2+160 x^3}{9+24 x-12 x^2+80 x^3+320 x^4} \, dx","Integrate[(3 - 3*x + 30*x^2 + 160*x^3)/(9 + 24*x - 12*x^2 + 80*x^3 + 320*x^4),x]","\frac{1}{8} \log \left(320 x^4+80 x^3-12 x^2+24 x+9\right)","\frac{1}{8} \log \left(320 x^4+80 x^3-12 x^2+24 x+9\right)",1,"Log[9 + 24*x - 12*x^2 + 80*x^3 + 320*x^4]/8","A",1
63,1,86,59,0.0180182,"\int \frac{3+12 x+20 x^2}{9+24 x-12 x^2+80 x^3+320 x^4} \, dx","Integrate[(3 + 12*x + 20*x^2)/(9 + 24*x - 12*x^2 + 80*x^3 + 320*x^4),x]","\frac{1}{8} \text{RootSum}\left[320 \text{$\#$1}^4+80 \text{$\#$1}^3-12 \text{$\#$1}^2+24 \text{$\#$1}+9\&,\frac{20 \text{$\#$1}^2 \log (x-\text{$\#$1})+12 \text{$\#$1} \log (x-\text{$\#$1})+3 \log (x-\text{$\#$1})}{160 \text{$\#$1}^3+30 \text{$\#$1}^2-3 \text{$\#$1}+3}\&\right]","\frac{\tan ^{-1}\left(\frac{800 x^3-40 x^2+30 x+57}{6 \sqrt{11}}\right)}{2 \sqrt{11}}-\frac{\tan ^{-1}\left(\frac{7-40 x}{5 \sqrt{11}}\right)}{2 \sqrt{11}}",1,"RootSum[9 + 24*#1 - 12*#1^2 + 80*#1^3 + 320*#1^4 & , (3*Log[x - #1] + 12*Log[x - #1]*#1 + 20*Log[x - #1]*#1^2)/(3 - 3*#1 + 30*#1^2 + 160*#1^3) & ]/8","C",1
64,1,99,78,0.0205837,"\int \frac{-84-576 x-400 x^2+2560 x^3}{9+24 x-12 x^2+80 x^3+320 x^4} \, dx","Integrate[(-84 - 576*x - 400*x^2 + 2560*x^3)/(9 + 24*x - 12*x^2 + 80*x^3 + 320*x^4),x]","\frac{1}{2} \text{RootSum}\left[320 \text{$\#$1}^4+80 \text{$\#$1}^3-12 \text{$\#$1}^2+24 \text{$\#$1}+9\&,\frac{640 \text{$\#$1}^3 \log (x-\text{$\#$1})-100 \text{$\#$1}^2 \log (x-\text{$\#$1})-144 \text{$\#$1} \log (x-\text{$\#$1})-21 \log (x-\text{$\#$1})}{160 \text{$\#$1}^3+30 \text{$\#$1}^2-3 \text{$\#$1}+3}\&\right]","-2 \sqrt{11} \tan ^{-1}\left(\frac{800 x^3-40 x^2+30 x+57}{6 \sqrt{11}}\right)+2 \log \left(320 x^4+80 x^3-12 x^2+24 x+9\right)+2 \sqrt{11} \tan ^{-1}\left(\frac{7-40 x}{5 \sqrt{11}}\right)",1,"RootSum[9 + 24*#1 - 12*#1^2 + 80*#1^3 + 320*#1^4 & , (-21*Log[x - #1] - 144*Log[x - #1]*#1 - 100*Log[x - #1]*#1^2 + 640*Log[x - #1]*#1^3)/(3 - 3*#1 + 30*#1^2 + 160*#1^3) & ]/2","C",1
65,1,110,49,0.0954181,"\int \frac{\sqrt{1-x^4}}{1+x^4} \, dx","Integrate[Sqrt[1 - x^4]/(1 + x^4),x]","-\frac{5 x \sqrt{1-x^4} F_1\left(\frac{1}{4};-\frac{1}{2},1;\frac{5}{4};x^4,-x^4\right)}{\left(x^4+1\right) \left(2 x^4 \left(2 F_1\left(\frac{5}{4};-\frac{1}{2},2;\frac{9}{4};x^4,-x^4\right)+F_1\left(\frac{5}{4};\frac{1}{2},1;\frac{9}{4};x^4,-x^4\right)\right)-5 F_1\left(\frac{1}{4};-\frac{1}{2},1;\frac{5}{4};x^4,-x^4\right)\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,"(-5*x*Sqrt[1 - x^4]*AppellF1[1/4, -1/2, 1, 5/4, x^4, -x^4])/((1 + x^4)*(-5*AppellF1[1/4, -1/2, 1, 5/4, x^4, -x^4] + 2*x^4*(2*AppellF1[5/4, -1/2, 2, 9/4, x^4, -x^4] + AppellF1[5/4, 1/2, 1, 9/4, x^4, -x^4])))","C",0
66,1,108,53,0.0911849,"\int \frac{\sqrt{1+x^4}}{1-x^4} \, dx","Integrate[Sqrt[1 + x^4]/(1 - x^4),x]","-\frac{5 x \sqrt{x^4+1} F_1\left(\frac{1}{4};-\frac{1}{2},1;\frac{5}{4};-x^4,x^4\right)}{\left(x^4-1\right) \left(2 x^4 \left(2 F_1\left(\frac{5}{4};-\frac{1}{2},2;\frac{9}{4};-x^4,x^4\right)+F_1\left(\frac{5}{4};\frac{1}{2},1;\frac{9}{4};-x^4,x^4\right)\right)+5 F_1\left(\frac{1}{4};-\frac{1}{2},1;\frac{5}{4};-x^4,x^4\right)\right)}","\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,"(-5*x*Sqrt[1 + x^4]*AppellF1[1/4, -1/2, 1, 5/4, -x^4, x^4])/((-1 + x^4)*(5*AppellF1[1/4, -1/2, 1, 5/4, -x^4, x^4] + 2*x^4*(2*AppellF1[5/4, -1/2, 2, 9/4, -x^4, x^4] + AppellF1[5/4, 1/2, 1, 9/4, -x^4, x^4])))","C",0
67,1,5727,75,7.0760569,"\int \frac{\sqrt{1+p x^2+x^4}}{1-x^4} \, dx","Integrate[Sqrt[1 + p*x^2 + x^4]/(1 - x^4),x]","\text{Result too large to show}","\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,"Result too large to show","C",1
68,1,322,171,0.4209845,"\int \frac{\sqrt{1+p x^2-x^4}}{1+x^4} \, dx","Integrate[Sqrt[1 + p*x^2 - x^4]/(1 + x^4),x]","\frac{\sqrt{\frac{4 x^2}{\sqrt{p^2+4}-p}+2} \sqrt{1-\frac{2 x^2}{\sqrt{p^2+4}+p}} \left(2 i \operatorname{EllipticF}\left(i \sinh ^{-1}\left(\sqrt{2} \sqrt{\frac{1}{\sqrt{p^2+4}-p}} x\right),\frac{p-\sqrt{p^2+4}}{\sqrt{p^2+4}+p}\right)-(p+2 i) \Pi \left(\frac{1}{2} i \left(p-\sqrt{p^2+4}\right);i \sinh ^{-1}\left(\sqrt{2} \sqrt{\frac{1}{\sqrt{p^2+4}-p}} x\right)|\frac{p-\sqrt{p^2+4}}{p+\sqrt{p^2+4}}\right)+(p-2 i) \Pi \left(\frac{1}{2} i \left(\sqrt{p^2+4}-p\right);i \sinh ^{-1}\left(\sqrt{2} \sqrt{\frac{1}{\sqrt{p^2+4}-p}} x\right)|\frac{p-\sqrt{p^2+4}}{p+\sqrt{p^2+4}}\right)\right)}{4 \sqrt{\frac{1}{\sqrt{p^2+4}-p}} \sqrt{p x^2-x^4+1}}","\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[2 + (4*x^2)/(-p + Sqrt[4 + p^2])]*Sqrt[1 - (2*x^2)/(p + Sqrt[4 + p^2])]*((2*I)*EllipticF[I*ArcSinh[Sqrt[2]*Sqrt[(-p + Sqrt[4 + p^2])^(-1)]*x], (p - Sqrt[4 + p^2])/(p + Sqrt[4 + p^2])] - (2*I + p)*EllipticPi[(I/2)*(p - Sqrt[4 + p^2]), I*ArcSinh[Sqrt[2]*Sqrt[(-p + Sqrt[4 + p^2])^(-1)]*x], (p - Sqrt[4 + p^2])/(p + Sqrt[4 + p^2])] + (-2*I + p)*EllipticPi[(I/2)*(-p + Sqrt[4 + p^2]), I*ArcSinh[Sqrt[2]*Sqrt[(-p + Sqrt[4 + p^2])^(-1)]*x], (p - Sqrt[4 + p^2])/(p + Sqrt[4 + p^2])]))/(4*Sqrt[(-p + Sqrt[4 + p^2])^(-1)]*Sqrt[1 + p*x^2 - x^4])","C",1
69,1,157,80,0.256121,"\int \frac{a+b x}{\left(2-x^2\right) \sqrt[4]{-1+x^2}} \, dx","Integrate[(a + b*x)/((2 - x^2)*(-1 + x^2)^(1/4)),x]","\frac{x \left(b x \sqrt[4]{1-x^2} \left(x^2-2\right) F_1\left(1;\frac{1}{4},1;2;x^2,\frac{x^2}{2}\right)-\frac{24 a F_1\left(\frac{1}{2};\frac{1}{4},1;\frac{3}{2};x^2,\frac{x^2}{2}\right)}{x^2 \left(2 F_1\left(\frac{3}{2};\frac{1}{4},2;\frac{5}{2};x^2,\frac{x^2}{2}\right)+F_1\left(\frac{3}{2};\frac{5}{4},1;\frac{5}{2};x^2,\frac{x^2}{2}\right)\right)+6 F_1\left(\frac{1}{2};\frac{1}{4},1;\frac{3}{2};x^2,\frac{x^2}{2}\right)}\right)}{4 \left(x^2-2\right) \sqrt[4]{x^2-1}}","\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,"(x*(b*x*(1 - x^2)^(1/4)*(-2 + x^2)*AppellF1[1, 1/4, 1, 2, x^2, x^2/2] - (24*a*AppellF1[1/2, 1/4, 1, 3/2, x^2, x^2/2])/(6*AppellF1[1/2, 1/4, 1, 3/2, x^2, x^2/2] + x^2*(2*AppellF1[3/2, 1/4, 2, 5/2, x^2, x^2/2] + AppellF1[3/2, 5/4, 1, 5/2, x^2, x^2/2]))))/(4*(-2 + x^2)*(-1 + x^2)^(1/4))","C",0
70,1,162,88,0.2639802,"\int \frac{a+b x}{\sqrt[4]{-1-x^2} \left(2+x^2\right)} \, dx","Integrate[(a + b*x)/((-1 - x^2)^(1/4)*(2 + x^2)),x]","\frac{x \left(b x \sqrt[4]{x^2+1} F_1\left(1;\frac{1}{4},1;2;-x^2,-\frac{x^2}{2}\right)-\frac{24 a F_1\left(\frac{1}{2};\frac{1}{4},1;\frac{3}{2};-x^2,-\frac{x^2}{2}\right)}{\left(x^2+2\right) \left(x^2 \left(2 F_1\left(\frac{3}{2};\frac{1}{4},2;\frac{5}{2};-x^2,-\frac{x^2}{2}\right)+F_1\left(\frac{3}{2};\frac{5}{4},1;\frac{5}{2};-x^2,-\frac{x^2}{2}\right)\right)-6 F_1\left(\frac{1}{2};\frac{1}{4},1;\frac{3}{2};-x^2,-\frac{x^2}{2}\right)\right)}\right)}{4 \sqrt[4]{-x^2-1}}","\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,"(x*(b*x*(1 + x^2)^(1/4)*AppellF1[1, 1/4, 1, 2, -x^2, -1/2*x^2] - (24*a*AppellF1[1/2, 1/4, 1, 3/2, -x^2, -1/2*x^2])/((2 + x^2)*(-6*AppellF1[1/2, 1/4, 1, 3/2, -x^2, -1/2*x^2] + x^2*(2*AppellF1[3/2, 1/4, 2, 5/2, -x^2, -1/2*x^2] + AppellF1[3/2, 5/4, 1, 5/2, -x^2, -1/2*x^2])))))/(4*(-1 - x^2)^(1/4))","C",0
71,1,144,149,0.2148254,"\int \frac{a+b x}{\sqrt[4]{1-x^2} \left(2-x^2\right)} \, dx","Integrate[(a + b*x)/((1 - x^2)^(1/4)*(2 - x^2)),x]","\frac{1}{4} b x^2 F_1\left(1;\frac{1}{4},1;2;x^2,\frac{x^2}{2}\right)-\frac{6 a x F_1\left(\frac{1}{2};\frac{1}{4},1;\frac{3}{2};x^2,\frac{x^2}{2}\right)}{\sqrt[4]{1-x^2} \left(x^2-2\right) \left(x^2 \left(2 F_1\left(\frac{3}{2};\frac{1}{4},2;\frac{5}{2};x^2,\frac{x^2}{2}\right)+F_1\left(\frac{3}{2};\frac{5}{4},1;\frac{5}{2};x^2,\frac{x^2}{2}\right)\right)+6 F_1\left(\frac{1}{2};\frac{1}{4},1;\frac{3}{2};x^2,\frac{x^2}{2}\right)\right)}","\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*x^2*AppellF1[1, 1/4, 1, 2, x^2, x^2/2])/4 - (6*a*x*AppellF1[1/2, 1/4, 1, 3/2, x^2, x^2/2])/((1 - x^2)^(1/4)*(-2 + x^2)*(6*AppellF1[1/2, 1/4, 1, 3/2, x^2, x^2/2] + x^2*(2*AppellF1[3/2, 1/4, 2, 5/2, x^2, x^2/2] + AppellF1[3/2, 5/4, 1, 5/2, x^2, x^2/2])))","C",0
72,1,152,135,0.1864078,"\int \frac{a+b x}{\sqrt[4]{1+x^2} \left(2+x^2\right)} \, dx","Integrate[(a + b*x)/((1 + x^2)^(1/4)*(2 + x^2)),x]","\frac{1}{4} b x^2 F_1\left(1;\frac{1}{4},1;2;-x^2,-\frac{x^2}{2}\right)-\frac{6 a x F_1\left(\frac{1}{2};\frac{1}{4},1;\frac{3}{2};-x^2,-\frac{x^2}{2}\right)}{\sqrt[4]{x^2+1} \left(x^2+2\right) \left(x^2 \left(2 F_1\left(\frac{3}{2};\frac{1}{4},2;\frac{5}{2};-x^2,-\frac{x^2}{2}\right)+F_1\left(\frac{3}{2};\frac{5}{4},1;\frac{5}{2};-x^2,-\frac{x^2}{2}\right)\right)-6 F_1\left(\frac{1}{2};\frac{1}{4},1;\frac{3}{2};-x^2,-\frac{x^2}{2}\right)\right)}","-\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*x^2*AppellF1[1, 1/4, 1, 2, -x^2, -1/2*x^2])/4 - (6*a*x*AppellF1[1/2, 1/4, 1, 3/2, -x^2, -1/2*x^2])/((1 + x^2)^(1/4)*(2 + x^2)*(-6*AppellF1[1/2, 1/4, 1, 3/2, -x^2, -1/2*x^2] + x^2*(2*AppellF1[3/2, 1/4, 2, 5/2, -x^2, -1/2*x^2] + AppellF1[3/2, 5/4, 1, 5/2, -x^2, -1/2*x^2])))","C",0
73,1,28,127,0.0205817,"\int \frac{x}{\sqrt{1-x^3} \left(4-x^3\right)} \, dx","Integrate[x/(Sqrt[1 - x^3]*(4 - x^3)),x]","\frac{1}{8} x^2 F_1\left(\frac{2}{3};\frac{1}{2},1;\frac{5}{3};x^3,\frac{x^3}{4}\right)","-\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,"(x^2*AppellF1[2/3, 1/2, 1, 5/3, x^3, x^3/4])/8","C",0
74,1,54,157,0.0300574,"\int \frac{x}{\left(4-d x^3\right) \sqrt{-1+d x^3}} \, dx","Integrate[x/((4 - d*x^3)*Sqrt[-1 + d*x^3]),x]","\frac{x^2 \sqrt{1-d x^3} F_1\left(\frac{2}{3};\frac{1}{2},1;\frac{5}{3};d x^3,\frac{d x^3}{4}\right)}{8 \sqrt{d x^3-1}}","-\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,"(x^2*Sqrt[1 - d*x^3]*AppellF1[2/3, 1/2, 1, 5/3, d*x^3, (d*x^3)/4])/(8*Sqrt[-1 + d*x^3])","C",0
75,1,48,74,0.0209434,"\int \frac{x}{\sqrt{-1+x^3} \left(8+x^3\right)} \, dx","Integrate[x/(Sqrt[-1 + x^3]*(8 + x^3)),x]","\frac{x^2 \sqrt{1-x^3} F_1\left(\frac{2}{3};\frac{1}{2},1;\frac{5}{3};x^3,-\frac{x^3}{8}\right)}{16 \sqrt{x^3-1}}","\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,"(x^2*Sqrt[1 - x^3]*AppellF1[2/3, 1/2, 1, 5/3, x^3, -1/8*x^3])/(16*Sqrt[-1 + x^3])","C",0
76,1,32,103,0.028071,"\int \frac{x}{\left(8-d x^3\right) \sqrt{1+d x^3}} \, dx","Integrate[x/((8 - d*x^3)*Sqrt[1 + d*x^3]),x]","\frac{1}{16} x^2 F_1\left(\frac{2}{3};\frac{1}{2},1;\frac{5}{3};-d x^3,\frac{d x^3}{8}\right)","-\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,"(x^2*AppellF1[2/3, 1/2, 1, 5/3, -(d*x^3), (d*x^3)/8])/16","C",0
77,1,126,81,0.0984806,"\int \frac{1}{\sqrt[3]{1-3 x^2} \left(3-x^2\right)} \, dx","Integrate[1/((1 - 3*x^2)^(1/3)*(3 - x^2)),x]","-\frac{9 x F_1\left(\frac{1}{2};\frac{1}{3},1;\frac{3}{2};3 x^2,\frac{x^2}{3}\right)}{\sqrt[3]{1-3 x^2} \left(x^2-3\right) \left(2 x^2 \left(F_1\left(\frac{3}{2};\frac{1}{3},2;\frac{5}{2};3 x^2,\frac{x^2}{3}\right)+3 F_1\left(\frac{3}{2};\frac{4}{3},1;\frac{5}{2};3 x^2,\frac{x^2}{3}\right)\right)+9 F_1\left(\frac{1}{2};\frac{1}{3},1;\frac{3}{2};3 x^2,\frac{x^2}{3}\right)\right)}","\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,"(-9*x*AppellF1[1/2, 1/3, 1, 3/2, 3*x^2, x^2/3])/((1 - 3*x^2)^(1/3)*(-3 + x^2)*(9*AppellF1[1/2, 1/3, 1, 3/2, 3*x^2, x^2/3] + 2*x^2*(AppellF1[3/2, 1/3, 2, 5/2, 3*x^2, x^2/3] + 3*AppellF1[3/2, 4/3, 1, 5/2, 3*x^2, x^2/3])))","C",0
78,1,126,81,0.0954865,"\int \frac{1}{\left(3+x^2\right) \sqrt[3]{1+3 x^2}} \, dx","Integrate[1/((3 + x^2)*(1 + 3*x^2)^(1/3)),x]","-\frac{9 x F_1\left(\frac{1}{2};\frac{1}{3},1;\frac{3}{2};-3 x^2,-\frac{x^2}{3}\right)}{\left(x^2+3\right) \sqrt[3]{3 x^2+1} \left(2 x^2 \left(F_1\left(\frac{3}{2};\frac{1}{3},2;\frac{5}{2};-3 x^2,-\frac{x^2}{3}\right)+3 F_1\left(\frac{3}{2};\frac{4}{3},1;\frac{5}{2};-3 x^2,-\frac{x^2}{3}\right)\right)-9 F_1\left(\frac{1}{2};\frac{1}{3},1;\frac{3}{2};-3 x^2,-\frac{x^2}{3}\right)\right)}","\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,"(-9*x*AppellF1[1/2, 1/3, 1, 3/2, -3*x^2, -1/3*x^2])/((3 + x^2)*(1 + 3*x^2)^(1/3)*(-9*AppellF1[1/2, 1/3, 1, 3/2, -3*x^2, -1/3*x^2] + 2*x^2*(AppellF1[3/2, 1/3, 2, 5/2, -3*x^2, -1/3*x^2] + 3*AppellF1[3/2, 4/3, 1, 5/2, -3*x^2, -1/3*x^2])))","C",0
79,1,118,113,0.0694107,"\int \frac{1}{\sqrt[3]{1-x^2} \left(3+x^2\right)} \, dx","Integrate[1/((1 - x^2)^(1/3)*(3 + x^2)),x]","-\frac{9 x F_1\left(\frac{1}{2};\frac{1}{3},1;\frac{3}{2};x^2,-\frac{x^2}{3}\right)}{\sqrt[3]{1-x^2} \left(x^2+3\right) \left(2 x^2 \left(F_1\left(\frac{3}{2};\frac{1}{3},2;\frac{5}{2};x^2,-\frac{x^2}{3}\right)-F_1\left(\frac{3}{2};\frac{4}{3},1;\frac{5}{2};x^2,-\frac{x^2}{3}\right)\right)-9 F_1\left(\frac{1}{2};\frac{1}{3},1;\frac{3}{2};x^2,-\frac{x^2}{3}\right)\right)}","\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,"(-9*x*AppellF1[1/2, 1/3, 1, 3/2, x^2, -1/3*x^2])/((1 - x^2)^(1/3)*(3 + x^2)*(-9*AppellF1[1/2, 1/3, 1, 3/2, x^2, -1/3*x^2] + 2*x^2*(AppellF1[3/2, 1/3, 2, 5/2, x^2, -1/3*x^2] - AppellF1[3/2, 4/3, 1, 5/2, x^2, -1/3*x^2])))","C",0
80,1,124,109,0.1006134,"\int \frac{1}{\left(3-x^2\right) \sqrt[3]{1+x^2}} \, dx","Integrate[1/((3 - x^2)*(1 + x^2)^(1/3)),x]","-\frac{9 x F_1\left(\frac{1}{2};\frac{1}{3},1;\frac{3}{2};-x^2,\frac{x^2}{3}\right)}{\left(x^2-3\right) \sqrt[3]{x^2+1} \left(2 x^2 \left(F_1\left(\frac{3}{2};\frac{1}{3},2;\frac{5}{2};-x^2,\frac{x^2}{3}\right)-F_1\left(\frac{3}{2};\frac{4}{3},1;\frac{5}{2};-x^2,\frac{x^2}{3}\right)\right)+9 F_1\left(\frac{1}{2};\frac{1}{3},1;\frac{3}{2};-x^2,\frac{x^2}{3}\right)\right)}","\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,"(-9*x*AppellF1[1/2, 1/3, 1, 3/2, -x^2, x^2/3])/((-3 + x^2)*(1 + x^2)^(1/3)*(9*AppellF1[1/2, 1/3, 1, 3/2, -x^2, x^2/3] + 2*x^2*(AppellF1[3/2, 1/3, 2, 5/2, -x^2, x^2/3] - AppellF1[3/2, 4/3, 1, 5/2, -x^2, x^2/3])))","C",0
81,1,159,87,0.9340146,"\int \frac{a+x}{(-a+x) \sqrt{a^2 x-\left(1+a^2\right) x^2+x^3}} \, dx","Integrate[(a + x)/((-a + x)*Sqrt[a^2*x - (1 + a^2)*x^2 + x^3]),x]","-\frac{2 i \left(a^2-x\right)^{3/2} \sqrt{\frac{x-1}{x-a^2}} \sqrt{\frac{x}{x-a^2}} \left((a+1) \operatorname{EllipticF}\left(i \sinh ^{-1}\left(\frac{\sqrt{-a^2}}{\sqrt{a^2-x}}\right),1-\frac{1}{a^2}\right)-2 \Pi \left(\frac{a-1}{a};i \sinh ^{-1}\left(\frac{\sqrt{-a^2}}{\sqrt{a^2-x}}\right)|1-\frac{1}{a^2}\right)\right)}{(a-1) \sqrt{-a^2} \sqrt{(x-1) x \left(x-a^2\right)}}","-\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*I)*(a^2 - x)^(3/2)*Sqrt[(-1 + x)/(-a^2 + x)]*Sqrt[x/(-a^2 + x)]*((1 + a)*EllipticF[I*ArcSinh[Sqrt[-a^2]/Sqrt[a^2 - x]], 1 - a^(-2)] - 2*EllipticPi[(-1 + a)/a, I*ArcSinh[Sqrt[-a^2]/Sqrt[a^2 - x]], 1 - a^(-2)]))/((-1 + a)*Sqrt[-a^2]*Sqrt[(-1 + x)*x*(-a^2 + x)])","C",1
82,1,127,1,0.602017,"\int \frac{-2+a+x}{(-a+x) \sqrt{(2-a) a x+\left(-1-2 a+a^2\right) x^2+x^3}} \, dx","Integrate[(-2 + a + x)/((-a + x)*Sqrt[(2 - a)*a*x + (-1 - 2*a + a^2)*x^2 + x^3]),x]","\frac{2 \sqrt{\frac{1}{x-1}+1} (x-1)^{3/2} \sqrt{\frac{(a-1)^2}{x-1}+1} \left(\operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{-(a-1)^2}}{\sqrt{x-1}}\right),\frac{1}{(a-1)^2}\right)-2 \Pi \left(\frac{1}{1-a};\sin ^{-1}\left(\frac{\sqrt{-(a-1)^2}}{\sqrt{x-1}}\right)|\frac{1}{(a-1)^2}\right)\right)}{\sqrt{-(a-1)^2} \sqrt{(x-1) x \left(a^2-2 a+x\right)}}","0",1,"(2*Sqrt[1 + (-1 + x)^(-1)]*Sqrt[1 + (-1 + a)^2/(-1 + x)]*(-1 + x)^(3/2)*(EllipticF[ArcSin[Sqrt[-(-1 + a)^2]/Sqrt[-1 + x]], (-1 + a)^(-2)] - 2*EllipticPi[(1 - a)^(-1), ArcSin[Sqrt[-(-1 + a)^2]/Sqrt[-1 + x]], (-1 + a)^(-2)]))/(Sqrt[-(-1 + a)^2]*Sqrt[(-1 + x)*x*(-2*a + a^2 + x)])","C",1
83,1,133,46,1.0909069,"\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","Integrate[(-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{2 i (x-1)^{3/2} \sqrt{\frac{x}{x-1}} \sqrt{-\frac{a^2-2 a x+x}{(2 a-1) (x-1)}} \left(2 a \Pi \left(1-a;i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|-\frac{(a-1)^2}{2 a-1}\right)-\operatorname{EllipticF}\left(i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right),-\frac{(a-1)^2}{2 a-1}\right)\right)}{\sqrt{-\left((x-1) x \left(a^2-2 a x+x\right)\right)}}","\log \left(\frac{-2 \left(\sqrt{(1-x) x \left(a^2-2 a x+x\right)}+x\right)-a^2+2 a x+x^2}{(a-x)^2}\right)",1,"((2*I)*(-1 + x)^(3/2)*Sqrt[x/(-1 + x)]*Sqrt[-((a^2 + x - 2*a*x)/((-1 + 2*a)*(-1 + x)))]*(-EllipticF[I*ArcSinh[1/Sqrt[-1 + x]], -((-1 + a)^2/(-1 + 2*a))] + 2*a*EllipticPi[1 - a, I*ArcSinh[1/Sqrt[-1 + x]], -((-1 + a)^2/(-1 + 2*a))]))/Sqrt[-((-1 + x)*x*(a^2 + x - 2*a*x))]","C",1
84,1,323,32,0.4625053,"\int \frac{1-\sqrt[3]{2} x}{\left(2^{2/3}+x\right) \sqrt{1+x^3}} \, dx","Integrate[(1 - 2^(1/3)*x)/((2^(2/3) + x)*Sqrt[1 + x^3]),x]","-\frac{2 \sqrt{\frac{2}{3}} \sqrt{\frac{i (x+1)}{\sqrt{3}+3 i}} \left(\sqrt{2 i x+\sqrt{3}-i} \left(\left(-3 i \sqrt[3]{2}+4 \sqrt{3}+\sqrt[3]{2} \sqrt{3}\right) x+\sqrt[3]{2} \sqrt{3}-2 \sqrt{3}+3 i \sqrt[3]{2}+6 i\right) \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{-2 i x+\sqrt{3}+i}}{\sqrt{2} \sqrt[4]{3}}\right),\frac{2 \sqrt{3}}{\sqrt{3}+3 i}\right)-6 i \sqrt{3} \sqrt{-2 i x+\sqrt{3}+i} \sqrt{x^2-x+1} \Pi \left(\frac{2 \sqrt{3}}{i+2 i 2^{2/3}+\sqrt{3}};\sin ^{-1}\left(\frac{\sqrt{-2 i x+\sqrt{3}+i}}{\sqrt{2} \sqrt[4]{3}}\right)|\frac{2 \sqrt{3}}{3 i+\sqrt{3}}\right)\right)}{\left(1+2\ 2^{2/3}-i \sqrt{3}\right) \sqrt{-2 i x+\sqrt{3}+i} \sqrt{x^3+1}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{3} \left(\sqrt[3]{2} x+1\right)}{\sqrt{x^3+1}}\right)}{\sqrt{3}}",1,"(-2*Sqrt[2/3]*Sqrt[(I*(1 + x))/(3*I + Sqrt[3])]*(Sqrt[-I + Sqrt[3] + (2*I)*x]*(6*I + (3*I)*2^(1/3) - 2*Sqrt[3] + 2^(1/3)*Sqrt[3] + ((-3*I)*2^(1/3) + 4*Sqrt[3] + 2^(1/3)*Sqrt[3])*x)*EllipticF[ArcSin[Sqrt[I + Sqrt[3] - (2*I)*x]/(Sqrt[2]*3^(1/4))], (2*Sqrt[3])/(3*I + Sqrt[3])] - (6*I)*Sqrt[3]*Sqrt[I + Sqrt[3] - (2*I)*x]*Sqrt[1 - x + x^2]*EllipticPi[(2*Sqrt[3])/(I + (2*I)*2^(2/3) + Sqrt[3]), ArcSin[Sqrt[I + Sqrt[3] - (2*I)*x]/(Sqrt[2]*3^(1/4))], (2*Sqrt[3])/(3*I + Sqrt[3])]))/((1 + 2*2^(2/3) - I*Sqrt[3])*Sqrt[I + Sqrt[3] - (2*I)*x]*Sqrt[1 + x^3])","C",0
85,1,46,23,0.007773,"\int \frac{1+x}{(-2+x) \sqrt{1+x^3}} \, dx","Integrate[(1 + x)/((-2 + x)*Sqrt[1 + x^3]),x]","\frac{1}{3} \log \left(3-\frac{(x+1)^2}{\sqrt{x^3+1}}\right)-\frac{1}{3} \log \left(\frac{(x+1)^2}{\sqrt{x^3+1}}+3\right)","-\frac{2}{3} \tanh ^{-1}\left(\frac{(x+1)^2}{3 \sqrt{x^3+1}}\right)",1,"Log[3 - (1 + x)^2/Sqrt[1 + x^3]]/3 - Log[3 + (1 + x)^2/Sqrt[1 + x^3]]/3","A",1
86,1,47,218,0.0597932,"\int \frac{x}{\sqrt{1+x^3} \left(10+6 \sqrt{3}+x^3\right)} \, dx","Integrate[x/(Sqrt[1 + x^3]*(10 + 6*Sqrt[3] + x^3)),x]","\frac{x^2 F_1\left(\frac{2}{3};\frac{1}{2},1;\frac{5}{3};-x^3,-\frac{x^3}{10+6 \sqrt{3}}\right)}{20+12 \sqrt{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,"(x^2*AppellF1[2/3, 1/2, 1, 5/3, -x^3, -(x^3/(10 + 6*Sqrt[3]))])/(20 + 12*Sqrt[3])","C",0
87,1,50,210,0.0770743,"\int \frac{x}{\sqrt{1+x^3} \left(10-6 \sqrt{3}+x^3\right)} \, dx","Integrate[x/(Sqrt[1 + x^3]*(10 - 6*Sqrt[3] + x^3)),x]","-\frac{x^2 F_1\left(\frac{2}{3};\frac{1}{2},1;\frac{5}{3};-x^3,\frac{1}{4} \left(5+3 \sqrt{3}\right) x^3\right)}{4 \left(3 \sqrt{3}-5\right)}","-\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,"-1/4*(x^2*AppellF1[2/3, 1/2, 1, 5/3, -x^3, ((5 + 3*Sqrt[3])*x^3)/4])/(-5 + 3*Sqrt[3])","C",0
88,1,65,222,0.073371,"\int \frac{x}{\sqrt{-1+x^3} \left(-10-6 \sqrt{3}+x^3\right)} \, dx","Integrate[x/(Sqrt[-1 + x^3]*(-10 - 6*Sqrt[3] + x^3)),x]","-\frac{x^2 \sqrt{1-x^3} F_1\left(\frac{2}{3};\frac{1}{2},1;\frac{5}{3};x^3,\frac{x^3}{10+6 \sqrt{3}}\right)}{\left(20+12 \sqrt{3}\right) \sqrt{x^3-1}}","\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,"-((x^2*Sqrt[1 - x^3]*AppellF1[2/3, 1/2, 1, 5/3, x^3, x^3/(10 + 6*Sqrt[3])])/((20 + 12*Sqrt[3])*Sqrt[-1 + x^3]))","C",0
89,1,68,214,0.0570991,"\int \frac{x}{\sqrt{-1+x^3} \left(-10+6 \sqrt{3}+x^3\right)} \, dx","Integrate[x/(Sqrt[-1 + x^3]*(-10 + 6*Sqrt[3] + x^3)),x]","\frac{x^2 \sqrt{1-x^3} F_1\left(\frac{2}{3};\frac{1}{2},1;\frac{5}{3};x^3,-\frac{x^3}{-10+6 \sqrt{3}}\right)}{4 \left(3 \sqrt{3}-5\right) \sqrt{x^3-1}}","-\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,"(x^2*Sqrt[1 - x^3]*AppellF1[2/3, 1/2, 1, 5/3, x^3, -(x^3/(-10 + 6*Sqrt[3]))])/(4*(-5 + 3*Sqrt[3])*Sqrt[-1 + x^3])","C",0
90,1,685,65,3.210943,"\int \frac{1-\sqrt{3}+x}{\left(1+\sqrt{3}+x\right) \sqrt{-4+4 \sqrt{3} x^2+x^4}} \, dx","Integrate[(1 - Sqrt[3] + x)/((1 + Sqrt[3] + x)*Sqrt[-4 + 4*Sqrt[3]*x^2 + x^4]),x]","\frac{\left(x+\sqrt{3}-1\right)^2 \sqrt{-x^3+\left(\sqrt{3}-1\right) x^2-2 \left(2+\sqrt{3}\right) x+2 \left(1+\sqrt{3}\right)} \sqrt{\frac{-\frac{4}{x+\sqrt{3}-1}+\sqrt{3}+1}{3+\sqrt{3}+i \sqrt{2 \left(2+\sqrt{3}\right)}}} \left(\left(\frac{2 \left(2 i \sqrt{3}-\sqrt{2 \left(2+\sqrt{3}\right)}+\sqrt{6 \left(2+\sqrt{3}\right)}\right)}{x+\sqrt{3}-1}+i \left(-1+\sqrt{3}+i \sqrt{2 \left(2+\sqrt{3}\right)}\right)\right) \sqrt{\sqrt{2 \left(2+\sqrt{3}\right)}+i \left(\frac{8}{x+\sqrt{3}-1}-\sqrt{3}+1\right)} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{\sqrt{2 \left(2+\sqrt{3}\right)}-i \left(\frac{8}{x+\sqrt{3}-1}-\sqrt{3}+1\right)}}{2^{3/4} \sqrt[4]{2+\sqrt{3}}}\right),\frac{2 i \sqrt{2 \left(2+\sqrt{3}\right)}}{3+\sqrt{3}+i \sqrt{2 \left(2+\sqrt{3}\right)}}\right)+2 \sqrt{6} \sqrt{\frac{x^2+2 \sqrt{3}+4}{\left(x+\sqrt{3}-1\right)^2}} \sqrt{\sqrt{2 \left(2+\sqrt{3}\right)}-i \left(\frac{8}{x+\sqrt{3}-1}-\sqrt{3}+1\right)} \Pi \left(\frac{2 \sqrt{2 \left(2+\sqrt{3}\right)}}{\sqrt{2 \left(2+\sqrt{3}\right)}+i \left(3+\sqrt{3}\right)};\sin ^{-1}\left(\frac{\sqrt{\sqrt{2 \left(2+\sqrt{3}\right)}-i \left(-\sqrt{3}+1+\frac{8}{x+\sqrt{3}-1}\right)}}{2^{3/4} \sqrt[4]{2+\sqrt{3}}}\right)|\frac{2 i \sqrt{2 \left(2+\sqrt{3}\right)}}{3+\sqrt{3}+i \sqrt{2 \left(2+\sqrt{3}\right)}}\right)\right)}{\left(\sqrt{2 \left(2+\sqrt{3}\right)}+i \left(3+\sqrt{3}\right)\right) \sqrt{-\frac{x^3}{2}+\frac{1}{2} \left(\sqrt{3}-1\right) x^2-\left(2+\sqrt{3}\right) x+\sqrt{3}+1} \sqrt{x^4+4 \sqrt{3} x^2-4} \sqrt{\sqrt{2 \left(2+\sqrt{3}\right)}-i \left(\frac{8}{x+\sqrt{3}-1}-\sqrt{3}+1\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,"((-1 + Sqrt[3] + x)^2*Sqrt[2*(1 + Sqrt[3]) - 2*(2 + Sqrt[3])*x + (-1 + Sqrt[3])*x^2 - x^3]*Sqrt[(1 + Sqrt[3] - 4/(-1 + Sqrt[3] + x))/(3 + Sqrt[3] + I*Sqrt[2*(2 + Sqrt[3])])]*((I*(-1 + Sqrt[3] + I*Sqrt[2*(2 + Sqrt[3])]) + (2*((2*I)*Sqrt[3] - Sqrt[2*(2 + Sqrt[3])] + Sqrt[6*(2 + Sqrt[3])]))/(-1 + Sqrt[3] + x))*Sqrt[Sqrt[2*(2 + Sqrt[3])] + I*(1 - Sqrt[3] + 8/(-1 + Sqrt[3] + x))]*EllipticF[ArcSin[Sqrt[Sqrt[2*(2 + Sqrt[3])] - I*(1 - Sqrt[3] + 8/(-1 + Sqrt[3] + x))]/(2^(3/4)*(2 + Sqrt[3])^(1/4))], ((2*I)*Sqrt[2*(2 + Sqrt[3])])/(3 + Sqrt[3] + I*Sqrt[2*(2 + Sqrt[3])])] + 2*Sqrt[6]*Sqrt[(4 + 2*Sqrt[3] + x^2)/(-1 + Sqrt[3] + x)^2]*Sqrt[Sqrt[2*(2 + Sqrt[3])] - I*(1 - Sqrt[3] + 8/(-1 + Sqrt[3] + x))]*EllipticPi[(2*Sqrt[2*(2 + Sqrt[3])])/(Sqrt[2*(2 + Sqrt[3])] + I*(3 + Sqrt[3])), ArcSin[Sqrt[Sqrt[2*(2 + Sqrt[3])] - I*(1 - Sqrt[3] + 8/(-1 + Sqrt[3] + x))]/(2^(3/4)*(2 + Sqrt[3])^(1/4))], ((2*I)*Sqrt[2*(2 + Sqrt[3])])/(3 + Sqrt[3] + I*Sqrt[2*(2 + Sqrt[3])])]))/((Sqrt[2*(2 + Sqrt[3])] + I*(3 + Sqrt[3]))*Sqrt[1 + Sqrt[3] - (2 + Sqrt[3])*x + ((-1 + Sqrt[3])*x^2)/2 - x^3/2]*Sqrt[-4 + 4*Sqrt[3]*x^2 + x^4]*Sqrt[Sqrt[2*(2 + Sqrt[3])] - I*(1 - Sqrt[3] + 8/(-1 + Sqrt[3] + x))])","C",0
91,1,876,63,7.9910813,"\int \frac{1+\sqrt{3}+x}{\left(1-\sqrt{3}+x\right) \sqrt{-4-4 \sqrt{3} x^2+x^4}} \, dx","Integrate[(1 + Sqrt[3] + x)/((1 - Sqrt[3] + x)*Sqrt[-4 - 4*Sqrt[3]*x^2 + x^4]),x]","-\frac{\sqrt{2} \sqrt{\frac{\sqrt{3}-1-\frac{4}{-x+\sqrt{3}+1}}{-3+\sqrt{3}-i \sqrt{4-2 \sqrt{3}}}} \left(-x+\sqrt{3}+1\right)^2 \left(\left(\frac{2 \left(2 i \sqrt{3} \sqrt{i \left(\sqrt{3}+1-\frac{8}{-x+\sqrt{3}+1}\right)+\sqrt{4-2 \sqrt{3}}}+\sqrt{6} \sqrt{2 \sqrt{4-2 \sqrt{3}}-\sqrt{12-6 \sqrt{3}}+i \sqrt{3}-i+\frac{8 i \left(-2+\sqrt{3}\right)}{-x+\sqrt{3}+1}}+\sqrt{-\frac{2 i \left(\left(-1+\sqrt{3}\right) x-8 \sqrt{3}+14\right)}{-x+\sqrt{3}+1}+4 \sqrt{4-2 \sqrt{3}}-2 \sqrt{12-6 \sqrt{3}}}\right)}{x-\sqrt{3}-1}+i \sqrt{3} \sqrt{i \left(\sqrt{3}+1-\frac{8}{-x+\sqrt{3}+1}\right)+\sqrt{4-2 \sqrt{3}}}+i \sqrt{i \left(\sqrt{3}+1-\frac{8}{-x+\sqrt{3}+1}\right)+\sqrt{4-2 \sqrt{3}}}+\sqrt{-\frac{2 i \left(\left(-1+\sqrt{3}\right) x-8 \sqrt{3}+14\right)}{-x+\sqrt{3}+1}+4 \sqrt{4-2 \sqrt{3}}-2 \sqrt{12-6 \sqrt{3}}}\right) \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{\sqrt{4-2 \sqrt{3}}-i \left(\sqrt{3}+1-\frac{8}{-x+\sqrt{3}+1}\right)}}{2^{3/4} \sqrt[4]{2-\sqrt{3}}}\right),\frac{2 \sqrt{4-2 \sqrt{3}}}{\sqrt{4-2 \sqrt{3}}+i \left(-3+\sqrt{3}\right)}\right)+2 \sqrt{6} \sqrt{\sqrt{4-2 \sqrt{3}}-i \left(\sqrt{3}+1-\frac{8}{-x+\sqrt{3}+1}\right)} \sqrt{\frac{x^2-2 \sqrt{3}+4}{\left(-x+\sqrt{3}+1\right)^2}} \Pi \left(\frac{2 \sqrt{4-2 \sqrt{3}}}{\sqrt{4-2 \sqrt{3}}-i \left(-3+\sqrt{3}\right)};\sin ^{-1}\left(\frac{\sqrt{\sqrt{4-2 \sqrt{3}}-i \left(\sqrt{3}+1-\frac{8}{-x+\sqrt{3}+1}\right)}}{2^{3/4} \sqrt[4]{2-\sqrt{3}}}\right)|\frac{2 \sqrt{4-2 \sqrt{3}}}{\sqrt{4-2 \sqrt{3}}+i \left(-3+\sqrt{3}\right)}\right)\right)}{\left(\sqrt{4-2 \sqrt{3}}-i \left(-3+\sqrt{3}\right)\right) \sqrt{\sqrt{4-2 \sqrt{3}}-i \left(\sqrt{3}+1-\frac{8}{-x+\sqrt{3}+1}\right)} \sqrt{x^4-4 \sqrt{3} x^2-4}}","-\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[2]*Sqrt[(-1 + Sqrt[3] - 4/(1 + Sqrt[3] - x))/(-3 + Sqrt[3] - I*Sqrt[4 - 2*Sqrt[3]])]*(1 + Sqrt[3] - x)^2*((I*Sqrt[Sqrt[4 - 2*Sqrt[3]] + I*(1 + Sqrt[3] - 8/(1 + Sqrt[3] - x))] + I*Sqrt[3]*Sqrt[Sqrt[4 - 2*Sqrt[3]] + I*(1 + Sqrt[3] - 8/(1 + Sqrt[3] - x))] + Sqrt[-2*Sqrt[12 - 6*Sqrt[3]] + 4*Sqrt[4 - 2*Sqrt[3]] - ((2*I)*(14 - 8*Sqrt[3] + (-1 + Sqrt[3])*x))/(1 + Sqrt[3] - x)] + (2*((2*I)*Sqrt[3]*Sqrt[Sqrt[4 - 2*Sqrt[3]] + I*(1 + Sqrt[3] - 8/(1 + Sqrt[3] - x))] + Sqrt[6]*Sqrt[-I + I*Sqrt[3] - Sqrt[12 - 6*Sqrt[3]] + 2*Sqrt[4 - 2*Sqrt[3]] + ((8*I)*(-2 + Sqrt[3]))/(1 + Sqrt[3] - x)] + Sqrt[-2*Sqrt[12 - 6*Sqrt[3]] + 4*Sqrt[4 - 2*Sqrt[3]] - ((2*I)*(14 - 8*Sqrt[3] + (-1 + Sqrt[3])*x))/(1 + Sqrt[3] - x)]))/(-1 - Sqrt[3] + x))*EllipticF[ArcSin[Sqrt[Sqrt[4 - 2*Sqrt[3]] - I*(1 + Sqrt[3] - 8/(1 + Sqrt[3] - x))]/(2^(3/4)*(2 - Sqrt[3])^(1/4))], (2*Sqrt[4 - 2*Sqrt[3]])/(Sqrt[4 - 2*Sqrt[3]] + I*(-3 + Sqrt[3]))] + 2*Sqrt[6]*Sqrt[Sqrt[4 - 2*Sqrt[3]] - I*(1 + Sqrt[3] - 8/(1 + Sqrt[3] - x))]*Sqrt[(4 - 2*Sqrt[3] + x^2)/(1 + Sqrt[3] - x)^2]*EllipticPi[(2*Sqrt[4 - 2*Sqrt[3]])/(Sqrt[4 - 2*Sqrt[3]] - I*(-3 + Sqrt[3])), ArcSin[Sqrt[Sqrt[4 - 2*Sqrt[3]] - I*(1 + Sqrt[3] - 8/(1 + Sqrt[3] - x))]/(2^(3/4)*(2 - Sqrt[3])^(1/4))], (2*Sqrt[4 - 2*Sqrt[3]])/(Sqrt[4 - 2*Sqrt[3]] + I*(-3 + Sqrt[3]))]))/((Sqrt[4 - 2*Sqrt[3]] - I*(-3 + Sqrt[3]))*Sqrt[Sqrt[4 - 2*Sqrt[3]] - I*(1 + Sqrt[3] - 8/(1 + Sqrt[3] - x))]*Sqrt[-4 - 4*Sqrt[3]*x^2 + x^4]))","C",0
92,0,0,53,0.1561919,"\int \frac{-1+x}{(1+x) \sqrt[3]{2+x^3}} \, dx","Integrate[(-1 + x)/((1 + x)*(2 + x^3)^(1/3)),x]","\int \frac{-1+x}{(1+x) \sqrt[3]{2+x^3}} \, dx","-\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,"Integrate[(-1 + x)/((1 + x)*(2 + x^3)^(1/3)), x]","F",-1
93,0,0,108,0.0364828,"\int \frac{1}{(1+x) \sqrt[3]{2+x^3}} \, dx","Integrate[1/((1 + x)*(2 + x^3)^(1/3)),x]","\int \frac{1}{(1+x) \sqrt[3]{2+x^3}} \, dx","\frac{3}{4} \log \left(-\sqrt[3]{x^3+2}+x+2\right)-\frac{1}{4} \log \left(\sqrt[3]{x^3+2}-x\right)+\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3+2}}+1}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 (x+2)}{\sqrt[3]{x^3+2}}+1}{\sqrt{3}}\right)-\frac{1}{2} \log (x+1)",1,"Integrate[1/((1 + x)*(2 + x^3)^(1/3)), x]","F",-1
94,1,120,98,0.0865342,"\int \frac{1}{\left(1-x^3\right) \sqrt[3]{a+b x^3}} \, dx","Integrate[1/((1 - x^3)*(a + b*x^3)^(1/3)),x]","\frac{-2 \log \left(1-\frac{x \sqrt[3]{a+b}}{\sqrt[3]{a+b x^3}}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{a+b}}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)+\log \left(\frac{x \sqrt[3]{a+b}}{\sqrt[3]{a+b x^3}}+\frac{x^2 (a+b)^{2/3}}{\left(a+b x^3\right)^{2/3}}+1\right)}{6 \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,"(2*Sqrt[3]*ArcTan[(1 + (2*(a + b)^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]] - 2*Log[1 - ((a + b)^(1/3)*x)/(a + b*x^3)^(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",1
95,0,0,154,0.1989841,"\int \frac{1+x}{\left(1+x+x^2\right) \sqrt[3]{a+b x^3}} \, dx","Integrate[(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,"Integrate[(1 + x)/((1 + x + x^2)*(a + b*x^3)^(1/3)), x]","F",-1
96,1,80,96,0.0402776,"\int \frac{x^2}{\left(1-x^3\right) \sqrt[3]{a+b x^3}} \, dx","Integrate[x^2/((1 - x^3)*(a + b*x^3)^(1/3)),x]","\frac{-3 \log \left(\sqrt[3]{a+b}-\sqrt[3]{a+b x^3}\right)-2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a+b x^3}}{\sqrt[3]{a+b}}+1}{\sqrt{3}}\right)+\log \left(1-x^3\right)}{6 \sqrt[3]{a+b}}","\frac{\log \left(1-x^3\right)}{6 \sqrt[3]{a+b}}-\frac{\log \left(\sqrt[3]{a+b}-\sqrt[3]{a+b x^3}\right)}{2 \sqrt[3]{a+b}}-\frac{\tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a+b x^3}}{\sqrt[3]{a+b}}+1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{a+b}}",1,"(-2*Sqrt[3]*ArcTan[(1 + (2*(a + b*x^3)^(1/3))/(a + b)^(1/3))/Sqrt[3]] + Log[1 - x^3] - 3*Log[(a + b)^(1/3) - (a + b*x^3)^(1/3)])/(6*(a + b)^(1/3))","A",1
97,1,112,88,0.0726022,"\int \frac{1}{\sqrt[3]{1-x^3} \left(1+x^3\right)} \, dx","Integrate[1/((1 - x^3)^(1/3)*(1 + x^3)),x]","\frac{2 \log \left(\frac{\sqrt[3]{2} x}{\sqrt[3]{1-x^3}}+1\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}-1}{\sqrt{3}}\right)-\log \left(-\frac{\sqrt[3]{2} x}{\sqrt[3]{1-x^3}}+\frac{2^{2/3} x^2}{\left(1-x^3\right)^{2/3}}+1\right)}{6 \sqrt[3]{2}}","-\frac{\log \left(x^3+1\right)}{6 \sqrt[3]{2}}+\frac{\log \left(-\sqrt[3]{1-x^3}-\sqrt[3]{2} x\right)}{2 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}",1,"(2*Sqrt[3]*ArcTan[(-1 + (2*2^(1/3)*x)/(1 - x^3)^(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)] + 2*Log[1 + (2^(1/3)*x)/(1 - x^3)^(1/3)])/(6*2^(1/3))","A",1
98,1,26,233,0.0167643,"\int \frac{x}{\sqrt[3]{1-x^3} \left(1+x^3\right)} \, dx","Integrate[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",0
99,1,73,82,0.0284095,"\int \frac{x^2}{\sqrt[3]{1-x^3} \left(1+x^3\right)} \, dx","Integrate[x^2/((1 - x^3)^(1/3)*(1 + x^3)),x]","\frac{-\log \left(x^3+1\right)+3 \log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{6 \sqrt[3]{2}}","-\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,"(2*Sqrt[3]*ArcTan[(1 + 2^(2/3)*(1 - x^3)^(1/3))/Sqrt[3]] - Log[1 + x^3] + 3*Log[2^(1/3) - (1 - x^3)^(1/3)])/(6*2^(1/3))","A",1
100,0,0,135,0.1375298,"\int \frac{1+x}{\left(1-x+x^2\right) \sqrt[3]{1-x^3}} \, dx","Integrate[(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","\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,"Integrate[(1 + x)/((1 - x + x^2)*(1 - x^3)^(1/3)), x]","F",-1
101,1,150,135,0.3082352,"\int \frac{(1+x)^2}{\sqrt[3]{1-x^3} \left(1+x^3\right)} \, dx","Integrate[(1 + x)^2/((1 - x^3)^(1/3)*(1 + x^3)),x]","\frac{1}{3} x^3 F_1\left(1;\frac{1}{3},1;2;x^3,-x^3\right)+x^2 F_1\left(\frac{2}{3};\frac{1}{3},1;\frac{5}{3};x^3,-x^3\right)+\frac{2 \log \left(\frac{\sqrt[3]{2} x}{\sqrt[3]{x^3-1}}+1\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{2} x}{\sqrt[3]{x^3-1}}-1}{\sqrt{3}}\right)-\log \left(-\frac{\sqrt[3]{2} x}{\sqrt[3]{x^3-1}}+\frac{2^{2/3} x^2}{\left(x^3-1\right)^{2/3}}+1\right)}{6 \sqrt[3]{2}}","\frac{\log \left(\frac{2^{2/3} (1-x)^2}{\left(1-x^3\right)^{2/3}}-\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{2 \sqrt[3]{2}}-\frac{\log \left(\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{\sqrt[3]{2}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt[3]{2}}",1,"x^2*AppellF1[2/3, 1/3, 1, 5/3, x^3, -x^3] + (x^3*AppellF1[1, 1/3, 1, 2, x^3, -x^3])/3 + (2*Sqrt[3]*ArcTan[(-1 + (2*2^(1/3)*x)/(-1 + x^3)^(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)] + 2*Log[1 + (2^(1/3)*x)/(-1 + x^3)^(1/3)])/(6*2^(1/3))","C",0
102,0,0,119,0.1278072,"\int \frac{1-x}{\left(1+x+x^2\right) \sqrt[3]{1+x^3}} \, dx","Integrate[(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","-\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,"Integrate[(1 - x)/((1 + x + x^2)*(1 + x^3)^(1/3)), x]","F",-1
103,1,43,43,0.1538869,"\int \frac{\left(1-x^3\right)^{2/3}}{\left(1+x+x^2\right)^2} \, dx","Integrate[(1 - x^3)^(2/3)/(1 + x + x^2)^2,x]","x^2 \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};x^3\right)+\frac{(2 x+1) \left(1-x^3\right)^{2/3}}{x^2+x+1}","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 + 2*x)*(1 - x^3)^(2/3))/(1 + x + x^2) + x^2*Hypergeometric2F1[1/3, 2/3, 5/3, x^3]","A",1
104,1,43,43,0.084888,"\int \frac{1-x}{\left(1+x+x^2\right) \sqrt[3]{1-x^3}} \, dx","Integrate[(1 - x)/((1 + x + x^2)*(1 - x^3)^(1/3)),x]","x^2 \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};x^3\right)+\frac{(2 x+1) \left(1-x^3\right)^{2/3}}{x^2+x+1}","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 + 2*x)*(1 - x^3)^(2/3))/(1 + x + x^2) + x^2*Hypergeometric2F1[1/3, 2/3, 5/3, x^3]","A",1
105,1,43,39,0.0186069,"\int \frac{(1-x)^2}{\left(1-x^3\right)^{4/3}} \, dx","Integrate[(1 - x)^2/(1 - x^3)^(4/3),x]","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}}","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 - x^3)^(-1/3) + x/(1 - x^3)^(1/3) - x^2*Hypergeometric2F1[2/3, 4/3, 5/3, x^3]","A",1
106,1,101,67,0.1197271,"\int \left(1-x^3\right)^{2/3} \, dx","Integrate[(1 - x^3)^(2/3),x]","\frac{3 (x-1) \left(1-x^3\right)^{2/3} F_1\left(\frac{5}{3};-\frac{2}{3},-\frac{2}{3};\frac{8}{3};-\frac{x-1}{1-(-1)^{2/3}},-\frac{x-1}{1+\sqrt[3]{-1}}\right)}{5 \left(\frac{x-1}{1+\sqrt[3]{-1}}+1\right)^{2/3} \left(\frac{x-1}{1-(-1)^{2/3}}+1\right)^{2/3}}","\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,"(3*(-1 + x)*(1 - x^3)^(2/3)*AppellF1[5/3, -2/3, -2/3, 8/3, -((-1 + x)/(1 - (-1)^(2/3))), -((-1 + x)/(1 + (-1)^(1/3)))])/(5*(1 + (-1 + x)/(1 + (-1)^(1/3)))^(2/3)*(1 + (-1 + x)/(1 - (-1)^(2/3)))^(2/3))","C",0
107,1,65,70,0.0267047,"\int \frac{\left(1-x^3\right)^{2/3}}{x} \, dx","Integrate[(1 - x^3)^(2/3)/x,x]","\frac{1}{2} \left(\left(1-x^3\right)^{2/3}+\log \left(1-\sqrt[3]{1-x^3}\right)-\log (x)\right)+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{\sqrt{3}}","\frac{1}{2} \left(1-x^3\right)^{2/3}+\frac{1}{2} \log \left(1-\sqrt[3]{1-x^3}\right)+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\log (x)}{2}",1,"ArcTan[(1 + 2*(1 - x^3)^(1/3))/Sqrt[3]]/Sqrt[3] + ((1 - x^3)^(2/3) - Log[x] + Log[1 - (1 - x^3)^(1/3)])/2","A",1
108,0,0,384,0.2821809,"\int \frac{\left(1-x^3\right)^{2/3}}{a+b x} \, dx","Integrate[(1 - x^3)^(2/3)/(a + b*x),x]","\int \frac{\left(1-x^3\right)^{2/3}}{a+b x} \, dx","-\frac{\left(a^3+b^3\right)^{2/3} \log \left(a^3+b^3 x^3\right)}{3 b^3}+\frac{\left(a^3+b^3\right)^{2/3} \log \left(-\frac{x \sqrt[3]{a^3+b^3}}{a}-\sqrt[3]{1-x^3}\right)}{2 b^3}+\frac{\left(a^3+b^3\right)^{2/3} \log \left(\sqrt[3]{a^3+b^3}-b \sqrt[3]{1-x^3}\right)}{2 b^3}-\frac{\left(a^3+b^3\right)^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 x \sqrt[3]{a^3+b^3}}{a \sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt{3} b^3}+\frac{\left(a^3+b^3\right)^{2/3} \tan ^{-1}\left(\frac{\frac{2 b \sqrt[3]{1-x^3}}{\sqrt[3]{a^3+b^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} b^3}-\frac{a^2 \log \left(\sqrt[3]{1-x^3}+x\right)}{2 b^3}+\frac{a^2 \tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt{3} b^3}-\frac{x^2 \left(a^3+b^3\right) F_1\left(\frac{2}{3};\frac{1}{3},1;\frac{5}{3};x^3,-\frac{b^3 x^3}{a^3}\right)}{2 a^2 b^2}+\frac{a x^2 \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};x^3\right)}{2 b^2}+\frac{\left(1-x^3\right)^{2/3}}{2 b}",1,"Integrate[(1 - x^3)^(2/3)/(a + b*x), x]","F",-1
109,0,0,234,0.3524392,"\int \frac{\left(1-x^3\right)^{2/3}}{\left(1-x+x^2\right)^2} \, dx","Integrate[(1 - x^3)^(2/3)/(1 - x + x^2)^2,x]","\int \frac{\left(1-x^3\right)^{2/3}}{\left(1-x+x^2\right)^2} \, dx","\frac{1}{3} x^2 \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};x^3\right)+\frac{\left(1-x^3\right)^{2/3} x}{3 \left(x^3+1\right)}-\frac{\left(1-x^3\right)^{2/3}}{3 \left(x^3+1\right)}-\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{3 \sqrt[3]{2}}+\frac{\log \left(-\sqrt[3]{1-x^3}-\sqrt[3]{2} x\right)}{3 \sqrt[3]{2}}-\frac{2^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{3 \sqrt{3}}-\frac{2^{2/3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{3 \sqrt{3}}+\frac{2 \left(1-x^3\right)^{2/3} x^2}{3 \left(x^3+1\right)}",1,"Integrate[(1 - x^3)^(2/3)/(1 - x + x^2)^2, x]","F",-1
110,0,0,199,0.2844141,"\int \frac{(1-2 x) \left(1-x^3\right)^{2/3}}{\left(1-x+x^2\right)^2} \, dx","Integrate[((1 - 2*x)*(1 - x^3)^(2/3))/(1 - x + x^2)^2,x]","\int \frac{(1-2 x) \left(1-x^3\right)^{2/3}}{\left(1-x+x^2\right)^2} \, dx","\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{\sqrt[3]{2}}-\frac{\log \left(-\sqrt[3]{1-x^3}-\sqrt[3]{2} x\right)}{\sqrt[3]{2}}+\log \left(\sqrt[3]{1-x^3}+x\right)-\frac{2 \tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{2^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{2^{2/3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\left(1-x^3\right)^{2/3}}{x^2-x+1}",1,"Integrate[((1 - 2*x)*(1 - x^3)^(2/3))/(1 - x + x^2)^2, x]","F",-1
111,0,0,177,0.3260967,"\int \frac{\left(1-x^3\right)^{2/3}}{1+x} \, dx","Integrate[(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,"Integrate[(1 - x^3)^(2/3)/(1 + x), x]","F",-1
112,0,0,177,0.1532514,"\int \frac{\left(1-x+x^2\right) \left(1-x^3\right)^{2/3}}{1+x^3} \, dx","Integrate[((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,"Integrate[((1 - x + x^2)*(1 - x^3)^(2/3))/(1 + x^3), x]","F",-1
113,1,111,132,0.0958726,"\int \frac{\left(1-x^3\right)^{2/3}}{1+x^3} \, dx","Integrate[(1 - x^3)^(2/3)/(1 + x^3),x]","-\frac{4 x \left(1-x^3\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,-x^3\right)}{\left(x^3+1\right) \left(x^3 \left(3 F_1\left(\frac{4}{3};-\frac{2}{3},2;\frac{7}{3};x^3,-x^3\right)+2 F_1\left(\frac{4}{3};\frac{1}{3},1;\frac{7}{3};x^3,-x^3\right)\right)-4 F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,-x^3\right)\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,"(-4*x*(1 - x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, -x^3])/((1 + x^3)*(-4*AppellF1[1/3, -2/3, 1, 4/3, x^3, -x^3] + x^3*(3*AppellF1[4/3, -2/3, 2, 7/3, x^3, -x^3] + 2*AppellF1[4/3, 1/3, 1, 7/3, x^3, -x^3])))","C",0
114,1,26,250,0.0139889,"\int \frac{x \left(1-x^3\right)^{2/3}}{1+x^3} \, dx","Integrate[(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",0
115,1,138,383,0.156651,"\int \frac{(1-x) \left(1-x^3\right)^{2/3}}{1+x^3} \, dx","Integrate[((1 - x)*(1 - x^3)^(2/3))/(1 + x^3),x]","-\frac{4 \left(1-x^3\right)^{2/3} x F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,-x^3\right)}{\left(x^3+1\right) \left(x^3 \left(3 F_1\left(\frac{4}{3};-\frac{2}{3},2;\frac{7}{3};x^3,-x^3\right)+2 F_1\left(\frac{4}{3};\frac{1}{3},1;\frac{7}{3};x^3,-x^3\right)\right)-4 F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,-x^3\right)\right)}-\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(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,"-1/2*(x^2*AppellF1[2/3, -2/3, 1, 5/3, x^3, -x^3]) - (4*x*(1 - x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, -x^3])/((1 + x^3)*(-4*AppellF1[1/3, -2/3, 1, 4/3, x^3, -x^3] + x^3*(3*AppellF1[4/3, -2/3, 2, 7/3, x^3, -x^3] + 2*AppellF1[4/3, 1/3, 1, 7/3, x^3, -x^3])))","C",0
116,1,109,272,0.0928435,"\int \frac{\sqrt[3]{1-x^3}}{1+x^3} \, dx","Integrate[(1 - x^3)^(1/3)/(1 + x^3),x]","-\frac{4 x \sqrt[3]{1-x^3} F_1\left(\frac{1}{3};-\frac{1}{3},1;\frac{4}{3};x^3,-x^3\right)}{\left(x^3+1\right) \left(x^3 \left(3 F_1\left(\frac{4}{3};-\frac{1}{3},2;\frac{7}{3};x^3,-x^3\right)+F_1\left(\frac{4}{3};\frac{2}{3},1;\frac{7}{3};x^3,-x^3\right)\right)-4 F_1\left(\frac{1}{3};-\frac{1}{3},1;\frac{4}{3};x^3,-x^3\right)\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,"(-4*x*(1 - x^3)^(1/3)*AppellF1[1/3, -1/3, 1, 4/3, x^3, -x^3])/((1 + x^3)*(-4*AppellF1[1/3, -1/3, 1, 4/3, x^3, -x^3] + x^3*(3*AppellF1[4/3, -1/3, 2, 7/3, x^3, -x^3] + AppellF1[4/3, 2/3, 1, 7/3, x^3, -x^3])))","C",0