1,1,28,28,0.0442336,"\int \frac{\sqrt{1+x^8} \left(1+2 x^8\right)}{x+2 x^9+x^{17}} \, dx","IntegrateAlgebraic[(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
2,1,2,2,0.003917,"\int \frac{1}{1+x^2} \, dx","IntegrateAlgebraic[(1 + x^2)^(-1),x]","\tan ^{-1}(x)","\tan ^{-1}(x)",1,"ArcTan[x]","A",1
3,1,14,14,0.0268715,"\int \frac{1}{x \sqrt{1+x^8}} \, dx","IntegrateAlgebraic[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
4,0,0,252,10.5708351,"\int \frac{x}{\sqrt{1-x^3}} \, dx","IntegrateAlgebraic[x/Sqrt[1 - x^3],x]","\int \frac{x}{\sqrt{1-x^3}} \, dx","\frac{2 \sqrt{1-x^3}}{-x+\sqrt{3}+1}+\frac{2 \sqrt{2} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} F\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{\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,"Could not integrate","F",-1
5,1,16,16,0.0256294,"\int \frac{1}{x \sqrt{1-x^3}} \, dx","IntegrateAlgebraic[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
6,1,78,76,4.3794926,"\int \frac{x}{\sqrt{-71-96 x+10 x^2+x^4}} \, dx","IntegrateAlgebraic[x/Sqrt[-71 - 96*x + 10*x^2 + x^4],x]","-\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)","\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,"-1/8*Log[-10001 - 3124*x^2 + 1408*x^3 - 54*x^4 + 128*x^5 - 20*x^6 - x^8 + Sqrt[-71 - 96*x + 10*x^2 + x^4]*(781 - 528*x + 27*x^2 - 80*x^3 + 15*x^4 + x^6)]","A",1
7,0,0,13,0.0000643,"\int \cot ^2(x) (x-\tan (x)) \, dx","IntegrateAlgebraic[Cot[x]^2*(x - Tan[x]),x]","\int \cot ^2(x) (x-\tan (x)) \, dx","-\frac{x^2}{2}-x \cot (x)",1,"Could not integrate","F",-1
8,0,0,42,0.0000318,"\int \left(1+x \tan (x)+\tan ^2(x)\right) \, dx","IntegrateAlgebraic[1 + x*Tan[x] + Tan[x]^2,x]","\int \left(1+x \tan (x)+\tan ^2(x)\right) \, dx","\frac{1}{2} i \text{Li}_2\left(-e^{2 i x}\right)+\frac{i x^2}{2}-x \log \left(1+e^{2 i x}\right)+\tan (x)",1,"Could not integrate","F",-1
9,0,0,2,0.0000366,"\int \frac{\sin (x)}{x} \, dx","IntegrateAlgebraic[Sin[x]/x,x]","\int \frac{\sin (x)}{x} \, dx","\text{Si}(x)",1,"Could not integrate","F",-1
10,0,0,17,0.0001006,"\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","IntegrateAlgebraic[(5*x^2 + 3*(E^x + x)^(1/3) + E^x*(3*x + 2*x^2))/(x*(E^x + x)^(1/3)),x]","\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","3 \left(x+e^x\right)^{2/3} x+3 \log (x)",1,"Could not integrate","F",-1
11,0,0,13,0.0000352,"\int \left(\frac{1}{x}+\frac{1+\frac{1}{x}}{(x+\log (x))^{3/2}}\right) \, dx","IntegrateAlgebraic[x^(-1) + (1 + x^(-1))/(x + Log[x])^(3/2),x]","\int \left(\frac{1}{x}+\frac{1+\frac{1}{x}}{(x+\log (x))^{3/2}}\right) \, dx","\log (x)-\frac{2}{\sqrt{x+\log (x)}}",1,"Could not integrate","F",-1
12,0,0,13,0.0000548,"\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","IntegrateAlgebraic[(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]","\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","\log (x)-\frac{2}{\sqrt{x+\log (x)}}",1,"Could not integrate","F",-1
13,0,0,23,0.0000465,"\int \frac{-x^2-\log (x)+2 \log ^2(x)}{-x^2 \log (x)+\log ^3(x)} \, dx","IntegrateAlgebraic[(-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,"Could not integrate","F",-1
14,1,19,39,0.0141833,"\int \frac{6-3 x^2+x^4}{4+5 x^2-5 x^4+x^6} \, dx","IntegrateAlgebraic[(6 - 3*x^2 + x^4)/(4 + 5*x^2 - 5*x^4 + x^6),x]","-\tan ^{-1}\left(\frac{x^2-2}{x \left(x^2-3\right)}\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,"-ArcTan[(-2 + x^2)/(x*(-3 + x^2))]","A",1