1,1,28,28,0.0162115,"\int \frac{\sqrt{1+x^8} \left(1+2 x^8\right)}{x+2 x^9+x^{17}} \, dx","Integrate[(Sqrt[1 + x^8]*(1 + 2*x^8))/(x + 2*x^9 + x^17),x]","-\frac{1}{4 \sqrt{x^8+1}}-\frac{1}{4} \tanh ^{-1}\left(\sqrt{x^8+1}\right)","-\frac{1}{4 \sqrt{x^8+1}}-\frac{1}{4} \tanh ^{-1}\left(\sqrt{x^8+1}\right)",1,"-1/4*1/Sqrt[1 + x^8] - ArcTanh[Sqrt[1 + x^8]]/4","A",1
2,1,2,2,0.0025595,"\int \frac{1}{1+x^2} \, dx","Integrate[(1 + x^2)^(-1),x]","\tan ^{-1}(x)","\tan ^{-1}(x)",1,"ArcTan[x]","A",1
3,1,14,14,0.0026139,"\int \frac{1}{x \sqrt{1+x^8}} \, dx","Integrate[1/(x*Sqrt[1 + x^8]),x]","-\frac{1}{4} \tanh ^{-1}\left(\sqrt{x^8+1}\right)","-\frac{1}{4} \tanh ^{-1}\left(\sqrt{x^8+1}\right)",1,"-1/4*ArcTanh[Sqrt[1 + x^8]]","A",1
4,1,20,252,0.0031848,"\int \frac{x}{\sqrt{1-x^3}} \, dx","Integrate[x/Sqrt[1 - x^3],x]","\frac{1}{2} x^2 \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};x^3\right)","\frac{2 \sqrt{2} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right),-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}+\frac{2 \sqrt{1-x^3}}{-x+\sqrt{3}+1}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}",1,"(x^2*Hypergeometric2F1[1/2, 2/3, 5/3, x^3])/2","C",1
5,1,16,16,0.002918,"\int \frac{1}{x \sqrt{1-x^3}} \, dx","Integrate[1/(x*Sqrt[1 - x^3]),x]","-\frac{2}{3} \tanh ^{-1}\left(\sqrt{1-x^3}\right)","-\frac{2}{3} \tanh ^{-1}\left(\sqrt{1-x^3}\right)",1,"(-2*ArcTanh[Sqrt[1 - x^3]])/3","A",1
6,1,1226,76,2.7592971,"\int \frac{x}{\sqrt{-71-96 x+10 x^2+x^4}} \, dx","Integrate[x/Sqrt[-71 - 96*x + 10*x^2 + x^4],x]","-\frac{2 \left(-x+2 \sqrt{2 \left(-1+\sqrt{3}\right)}+\sqrt{3}\right) \left(\left(\sqrt{3}+2 \sqrt{2 \left(-1+\sqrt{3}\right)}\right) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{\left(-x-2 \sqrt{2 \left(-1+\sqrt{3}\right)}+\sqrt{3}\right) \left(\sqrt{3}+2 \sqrt{2 \left(-1+\sqrt{3}\right)}-\text{Root}\left[\text{$\#$1}^4+10 \text{$\#$1}^2-96 \text{$\#$1}-71\&,4\right]\right)}{\left(-x+2 \sqrt{2 \left(-1+\sqrt{3}\right)}+\sqrt{3}\right) \left(\sqrt{3}-2 \sqrt{2 \left(-1+\sqrt{3}\right)}-\text{Root}\left[\text{$\#$1}^4+10 \text{$\#$1}^2-96 \text{$\#$1}-71\&,4\right]\right)}}\right),\frac{\left(\sqrt{3}+2 \sqrt{2 \left(-1+\sqrt{3}\right)}-\text{Root}\left[\text{$\#$1}^4+10 \text{$\#$1}^2-96 \text{$\#$1}-71\&,3\right]\right) \left(\sqrt{3}-2 \sqrt{2 \left(-1+\sqrt{3}\right)}-\text{Root}\left[\text{$\#$1}^4+10 \text{$\#$1}^2-96 \text{$\#$1}-71\&,4\right]\right)}{\left(\sqrt{3}-2 \sqrt{2 \left(-1+\sqrt{3}\right)}-\text{Root}\left[\text{$\#$1}^4+10 \text{$\#$1}^2-96 \text{$\#$1}-71\&,3\right]\right) \left(\sqrt{3}+2 \sqrt{2 \left(-1+\sqrt{3}\right)}-\text{Root}\left[\text{$\#$1}^4+10 \text{$\#$1}^2-96 \text{$\#$1}-71\&,4\right]\right)}\right)-4 \sqrt{2 \left(-1+\sqrt{3}\right)} \Pi \left(\frac{\sqrt{3}-2 \sqrt{2 \left(-1+\sqrt{3}\right)}-\text{Root}\left[\text{$\#$1}^4+10 \text{$\#$1}^2-96 \text{$\#$1}-71\&,4\right]}{\sqrt{3}+2 \sqrt{2 \left(-1+\sqrt{3}\right)}-\text{Root}\left[\text{$\#$1}^4+10 \text{$\#$1}^2-96 \text{$\#$1}-71\&,4\right]};\sin ^{-1}\left(\sqrt{\frac{\left(-x-2 \sqrt{2 \left(-1+\sqrt{3}\right)}+\sqrt{3}\right) \left(\sqrt{3}+2 \sqrt{2 \left(-1+\sqrt{3}\right)}-\text{Root}\left[\text{$\#$1}^4+10 \text{$\#$1}^2-96 \text{$\#$1}-71\&,4\right]\right)}{\left(-x+2 \sqrt{2 \left(-1+\sqrt{3}\right)}+\sqrt{3}\right) \left(\sqrt{3}-2 \sqrt{2 \left(-1+\sqrt{3}\right)}-\text{Root}\left[\text{$\#$1}^4+10 \text{$\#$1}^2-96 \text{$\#$1}-71\&,4\right]\right)}}\right)|\frac{\left(\sqrt{3}+2 \sqrt{2 \left(-1+\sqrt{3}\right)}-\text{Root}\left[\text{$\#$1}^4+10 \text{$\#$1}^2-96 \text{$\#$1}-71\&,3\right]\right) \left(\sqrt{3}-2 \sqrt{2 \left(-1+\sqrt{3}\right)}-\text{Root}\left[\text{$\#$1}^4+10 \text{$\#$1}^2-96 \text{$\#$1}-71\&,4\right]\right)}{\left(\sqrt{3}-2 \sqrt{2 \left(-1+\sqrt{3}\right)}-\text{Root}\left[\text{$\#$1}^4+10 \text{$\#$1}^2-96 \text{$\#$1}-71\&,3\right]\right) \left(\sqrt{3}+2 \sqrt{2 \left(-1+\sqrt{3}\right)}-\text{Root}\left[\text{$\#$1}^4+10 \text{$\#$1}^2-96 \text{$\#$1}-71\&,4\right]\right)}\right)\right) \sqrt{\frac{x-\text{Root}\left[\text{$\#$1}^4+10 \text{$\#$1}^2-96 \text{$\#$1}-71\&,3\right]}{\left(-x+2 \sqrt{2 \left(-1+\sqrt{3}\right)}+\sqrt{3}\right) \left(\sqrt{3}-2 \sqrt{2 \left(-1+\sqrt{3}\right)}-\text{Root}\left[\text{$\#$1}^4+10 \text{$\#$1}^2-96 \text{$\#$1}-71\&,3\right]\right)}} \sqrt{\frac{\left(-x-2 \sqrt{2 \left(-1+\sqrt{3}\right)}+\sqrt{3}\right) \left(\sqrt{3}+2 \sqrt{2 \left(-1+\sqrt{3}\right)}-\text{Root}\left[\text{$\#$1}^4+10 \text{$\#$1}^2-96 \text{$\#$1}-71\&,4\right]\right)}{\left(-x+2 \sqrt{2 \left(-1+\sqrt{3}\right)}+\sqrt{3}\right) \left(\sqrt{3}-2 \sqrt{2 \left(-1+\sqrt{3}\right)}-\text{Root}\left[\text{$\#$1}^4+10 \text{$\#$1}^2-96 \text{$\#$1}-71\&,4\right]\right)}} \left(x-\text{Root}\left[\text{$\#$1}^4+10 \text{$\#$1}^2-96 \text{$\#$1}-71\&,4\right]\right)}{\sqrt{x^4+10 x^2-96 x-71} \left(\sqrt{3}+2 \sqrt{2 \left(-1+\sqrt{3}\right)}-\text{Root}\left[\text{$\#$1}^4+10 \text{$\#$1}^2-96 \text{$\#$1}-71\&,4\right]\right) \sqrt{\frac{x-\text{Root}\left[\text{$\#$1}^4+10 \text{$\#$1}^2-96 \text{$\#$1}-71\&,4\right]}{\left(-x+2 \sqrt{2 \left(-1+\sqrt{3}\right)}+\sqrt{3}\right) \left(\sqrt{3}-2 \sqrt{2 \left(-1+\sqrt{3}\right)}-\text{Root}\left[\text{$\#$1}^4+10 \text{$\#$1}^2-96 \text{$\#$1}-71\&,4\right]\right)}}}","\frac{1}{8} \log \left(x^8+20 x^6-128 x^5+54 x^4-1408 x^3+3124 x^2+\sqrt{x^4+10 x^2-96 x-71} \left(x^6+15 x^4-80 x^3+27 x^2-528 x+781\right)+10001\right)",1,"(-2*(Sqrt[3] + 2*Sqrt[2*(-1 + Sqrt[3])] - x)*((Sqrt[3] + 2*Sqrt[2*(-1 + Sqrt[3])])*EllipticF[ArcSin[Sqrt[((Sqrt[3] - 2*Sqrt[2*(-1 + Sqrt[3])] - x)*(Sqrt[3] + 2*Sqrt[2*(-1 + Sqrt[3])] - Root[-71 - 96*#1 + 10*#1^2 + #1^4 & , 4, 0]))/((Sqrt[3] + 2*Sqrt[2*(-1 + Sqrt[3])] - x)*(Sqrt[3] - 2*Sqrt[2*(-1 + Sqrt[3])] - Root[-71 - 96*#1 + 10*#1^2 + #1^4 & , 4, 0]))]], ((Sqrt[3] + 2*Sqrt[2*(-1 + Sqrt[3])] - Root[-71 - 96*#1 + 10*#1^2 + #1^4 & , 3, 0])*(Sqrt[3] - 2*Sqrt[2*(-1 + Sqrt[3])] - Root[-71 - 96*#1 + 10*#1^2 + #1^4 & , 4, 0]))/((Sqrt[3] - 2*Sqrt[2*(-1 + Sqrt[3])] - Root[-71 - 96*#1 + 10*#1^2 + #1^4 & , 3, 0])*(Sqrt[3] + 2*Sqrt[2*(-1 + Sqrt[3])] - Root[-71 - 96*#1 + 10*#1^2 + #1^4 & , 4, 0]))] - 4*Sqrt[2*(-1 + Sqrt[3])]*EllipticPi[(Sqrt[3] - 2*Sqrt[2*(-1 + Sqrt[3])] - Root[-71 - 96*#1 + 10*#1^2 + #1^4 & , 4, 0])/(Sqrt[3] + 2*Sqrt[2*(-1 + Sqrt[3])] - Root[-71 - 96*#1 + 10*#1^2 + #1^4 & , 4, 0]), ArcSin[Sqrt[((Sqrt[3] - 2*Sqrt[2*(-1 + Sqrt[3])] - x)*(Sqrt[3] + 2*Sqrt[2*(-1 + Sqrt[3])] - Root[-71 - 96*#1 + 10*#1^2 + #1^4 & , 4, 0]))/((Sqrt[3] + 2*Sqrt[2*(-1 + Sqrt[3])] - x)*(Sqrt[3] - 2*Sqrt[2*(-1 + Sqrt[3])] - Root[-71 - 96*#1 + 10*#1^2 + #1^4 & , 4, 0]))]], ((Sqrt[3] + 2*Sqrt[2*(-1 + Sqrt[3])] - Root[-71 - 96*#1 + 10*#1^2 + #1^4 & , 3, 0])*(Sqrt[3] - 2*Sqrt[2*(-1 + Sqrt[3])] - Root[-71 - 96*#1 + 10*#1^2 + #1^4 & , 4, 0]))/((Sqrt[3] - 2*Sqrt[2*(-1 + Sqrt[3])] - Root[-71 - 96*#1 + 10*#1^2 + #1^4 & , 3, 0])*(Sqrt[3] + 2*Sqrt[2*(-1 + Sqrt[3])] - Root[-71 - 96*#1 + 10*#1^2 + #1^4 & , 4, 0]))])*Sqrt[(x - Root[-71 - 96*#1 + 10*#1^2 + #1^4 & , 3, 0])/((Sqrt[3] + 2*Sqrt[2*(-1 + Sqrt[3])] - x)*(Sqrt[3] - 2*Sqrt[2*(-1 + Sqrt[3])] - Root[-71 - 96*#1 + 10*#1^2 + #1^4 & , 3, 0]))]*Sqrt[((Sqrt[3] - 2*Sqrt[2*(-1 + Sqrt[3])] - x)*(Sqrt[3] + 2*Sqrt[2*(-1 + Sqrt[3])] - Root[-71 - 96*#1 + 10*#1^2 + #1^4 & , 4, 0]))/((Sqrt[3] + 2*Sqrt[2*(-1 + Sqrt[3])] - x)*(Sqrt[3] - 2*Sqrt[2*(-1 + Sqrt[3])] - Root[-71 - 96*#1 + 10*#1^2 + #1^4 & , 4, 0]))]*(x - Root[-71 - 96*#1 + 10*#1^2 + #1^4 & , 4, 0]))/(Sqrt[-71 - 96*x + 10*x^2 + x^4]*(Sqrt[3] + 2*Sqrt[2*(-1 + Sqrt[3])] - Root[-71 - 96*#1 + 10*#1^2 + #1^4 & , 4, 0])*Sqrt[(x - Root[-71 - 96*#1 + 10*#1^2 + #1^4 & , 4, 0])/((Sqrt[3] + 2*Sqrt[2*(-1 + Sqrt[3])] - x)*(Sqrt[3] - 2*Sqrt[2*(-1 + Sqrt[3])] - Root[-71 - 96*#1 + 10*#1^2 + #1^4 & , 4, 0]))])","C",0
7,1,13,13,0.0306287,"\int \cot ^2(x) (x-\tan (x)) \, dx","Integrate[Cot[x]^2*(x - Tan[x]),x]","-\frac{x^2}{2}-x \cot (x)","-\frac{x^2}{2}-x \cot (x)",1,"-1/2*x^2 - x*Cot[x]","A",1
8,1,42,42,0.0155379,"\int \left(1+x \tan (x)+\tan ^2(x)\right) \, dx","Integrate[1 + x*Tan[x] + Tan[x]^2,x]","\frac{1}{2} i \operatorname{PolyLog}\left(2,-e^{2 i x}\right)+\frac{i x^2}{2}-x \log \left(1+e^{2 i x}\right)+\tan (x)","\frac{1}{2} i \operatorname{PolyLog}\left(2,-e^{2 i x}\right)+\frac{i x^2}{2}-x \log \left(1+e^{2 i x}\right)+\tan (x)",1,"(I/2)*x^2 - x*Log[1 + E^((2*I)*x)] + (I/2)*PolyLog[2, -E^((2*I)*x)] + Tan[x]","A",1
9,1,2,2,0.0132391,"\int \frac{\sin (x)}{x} \, dx","Integrate[Sin[x]/x,x]","\text{Si}(x)","\text{Si}(x)",1,"SinIntegral[x]","A",1
10,1,17,17,0.2692468,"\int \frac{5 x^2+3 \sqrt[3]{e^x+x}+e^x \left(3 x+2 x^2\right)}{x \sqrt[3]{e^x+x}} \, dx","Integrate[(5*x^2 + 3*(E^x + x)^(1/3) + E^x*(3*x + 2*x^2))/(x*(E^x + x)^(1/3)),x]","3 \left(x+e^x\right)^{2/3} x+3 \log (x)","3 \left(x+e^x\right)^{2/3} x+3 \log (x)",1,"3*x*(E^x + x)^(2/3) + 3*Log[x]","A",1
11,1,13,13,0.0237084,"\int \left(\frac{1}{x}+\frac{1+\frac{1}{x}}{(x+\log (x))^{3/2}}\right) \, dx","Integrate[x^(-1) + (1 + x^(-1))/(x + Log[x])^(3/2),x]","\log (x)-\frac{2}{\sqrt{x+\log (x)}}","\log (x)-\frac{2}{\sqrt{x+\log (x)}}",1,"Log[x] - 2/Sqrt[x + Log[x]]","A",1
12,1,13,13,0.1660905,"\int \frac{x^2+2 x \log (x)+\log ^2(x)+(1+x) \sqrt{x+\log (x)}}{x^3+2 x^2 \log (x)+x \log ^2(x)} \, dx","Integrate[(x^2 + 2*x*Log[x] + Log[x]^2 + (1 + x)*Sqrt[x + Log[x]])/(x^3 + 2*x^2*Log[x] + x*Log[x]^2),x]","\log (x)-\frac{2}{\sqrt{x+\log (x)}}","\log (x)-\frac{2}{\sqrt{x+\log (x)}}",1,"Log[x] - 2/Sqrt[x + Log[x]]","A",1
13,0,0,23,0.2886562,"\int \frac{-x^2-\log (x)+2 \log ^2(x)}{-x^2 \log (x)+\log ^3(x)} \, dx","Integrate[(-x^2 - Log[x] + 2*Log[x]^2)/(-(x^2*Log[x]) + Log[x]^3),x]","\int \frac{-x^2-\log (x)+2 \log ^2(x)}{-x^2 \log (x)+\log ^3(x)} \, dx","\text{li}(x)-\frac{1}{2} \log (x-\log (x))+\frac{1}{2} \log (x+\log (x))",1,"Integrate[(-x^2 - Log[x] + 2*Log[x]^2)/(-(x^2*Log[x]) + Log[x]^3), x]","F",-1
14,1,41,39,0.0120069,"\int \frac{6-3 x^2+x^4}{4+5 x^2-5 x^4+x^6} \, dx","Integrate[(6 - 3*x^2 + x^4)/(4 + 5*x^2 - 5*x^4 + x^6),x]","\frac{1}{2} \tan ^{-1}\left(\frac{x \left(x^2-3\right)}{x^2-2}\right)-\frac{1}{2} \tan ^{-1}\left(\frac{x \left(x^2-3\right)}{2-x^2}\right)","\tan ^{-1}\left(\frac{1}{2} x \left(x^4-3 x^2+1\right)\right)-\tan ^{-1}\left(\sqrt{3}-2 x\right)+\tan ^{-1}\left(2 x+\sqrt{3}\right)",1,"-1/2*ArcTan[(x*(-3 + x^2))/(2 - x^2)] + ArcTan[(x*(-3 + x^2))/(-2 + x^2)]/2","A",1