1,0,0,22,0.0000675,"\int \frac{1}{\sqrt{2}+\cos (z)+\sin (z)} \, dz","IntegrateAlgebraic[(Sqrt[2] + Cos[z] + Sin[z])^(-1),z]","\int \frac{1}{\sqrt{2}+\cos (z)+\sin (z)} \, dz","-\frac{1-\sqrt{2} \sin (z)}{\cos (z)-\sin (z)}",1,"Could not integrate","F",-1
2,1,84,32,0.0475008,"\int \frac{1}{\left(\sqrt{1-x}+\sqrt{1+x}\right)^2} \, dx","IntegrateAlgebraic[(Sqrt[1 - x] + Sqrt[1 + x])^(-2),x]","\frac{-x-\sqrt{1-x}+\sqrt{x+1}}{\sqrt{1-x} \left(2 \sqrt{x+1}-2\right)-2 \sqrt{x+1}+2}+2 \tan ^{-1}\left(\frac{\sqrt{x+1}-1}{\sqrt{1-x}-1}\right)","\frac{\sqrt{1-x^2}}{2 x}-\frac{1}{2 x}+\frac{1}{2} \sin ^{-1}(x)",1,"(-Sqrt[1 - x] - x + Sqrt[1 + x])/(2 - 2*Sqrt[1 + x] + Sqrt[1 - x]*(-2 + 2*Sqrt[1 + x])) + 2*ArcTan[(-1 + Sqrt[1 + x])/(-1 + Sqrt[1 - x])]","B",1
3,0,0,25,0.0000323,"\int \frac{1}{(1+\cos (x))^2} \, dx","IntegrateAlgebraic[(1 + Cos[x])^(-2),x]","\int \frac{1}{(1+\cos (x))^2} \, dx","\frac{\sin (x)}{3 (\cos (x)+1)}+\frac{\sin (x)}{3 (\cos (x)+1)^2}",1,"Could not integrate","F",-1
4,0,0,58,0.0000296,"\int \frac{\sin (x)}{\sqrt{1+x}} \, dx","IntegrateAlgebraic[Sin[x]/Sqrt[1 + x],x]","\int \frac{\sin (x)}{\sqrt{1+x}} \, dx","\sqrt{2 \pi } \cos (1) S\left(\sqrt{\frac{2}{\pi }} \sqrt{x+1}\right)-\sqrt{2 \pi } \sin (1) C\left(\sqrt{\frac{2}{\pi }} \sqrt{x+1}\right)",1,"Could not integrate","F",-1
5,0,0,50,0.0000359,"\int \frac{1}{(\cos (x)+\sin (x))^6} \, dx","IntegrateAlgebraic[(Cos[x] + Sin[x])^(-6),x]","\int \frac{1}{(\cos (x)+\sin (x))^6} \, dx","-\frac{\cos (x)-\sin (x)}{15 (\sin (x)+\cos (x))^3}-\frac{\cos (x)-\sin (x)}{10 (\sin (x)+\cos (x))^5}+\frac{2 \sin (x)}{15 (\sin (x)+\cos (x))}",1,"Could not integrate","F",-1
6,0,0,334,0.0000568,"\int \log \left(\frac{1}{x^4}+x^4\right) \, dx","IntegrateAlgebraic[Log[x^(-4) + x^4],x]","\int \log \left(\frac{1}{x^4}+x^4\right) \, dx","x \log \left(x^4+\frac{1}{x^4}\right)-\frac{1}{2} \sqrt{2-\sqrt{2}} \log \left(x^2-\sqrt{2-\sqrt{2}} x+1\right)+\frac{1}{2} \sqrt{2-\sqrt{2}} \log \left(x^2+\sqrt{2-\sqrt{2}} x+1\right)-\frac{1}{2} \sqrt{2+\sqrt{2}} \log \left(x^2-\sqrt{2+\sqrt{2}} x+1\right)+\frac{1}{2} \sqrt{2+\sqrt{2}} \log \left(x^2+\sqrt{2+\sqrt{2}} x+1\right)-4 x-\sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-2 x}{\sqrt{2+\sqrt{2}}}\right)-\sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-2 x}{\sqrt{2-\sqrt{2}}}\right)+\sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}}\right)+\sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{2}}}{\sqrt{2-\sqrt{2}}}\right)",1,"Could not integrate","F",-1
7,0,0,291,0.0000432,"\int \frac{\log (1+x)}{x \sqrt{1+\sqrt{1+x}}} \, dx","IntegrateAlgebraic[Log[1 + x]/(x*Sqrt[1 + Sqrt[1 + x]]),x]","\int \frac{\log (1+x)}{x \sqrt{1+\sqrt{1+x}}} \, dx","\sqrt{2} \text{Li}_2\left(-\frac{\sqrt{2} \left(1-\sqrt{\sqrt{x+1}+1}\right)}{2-\sqrt{2}}\right)-\sqrt{2} \text{Li}_2\left(\frac{\sqrt{2} \left(1-\sqrt{\sqrt{x+1}+1}\right)}{2+\sqrt{2}}\right)-\sqrt{2} \text{Li}_2\left(-\frac{\sqrt{2} \left(\sqrt{\sqrt{x+1}+1}+1\right)}{2-\sqrt{2}}\right)+\sqrt{2} \text{Li}_2\left(\frac{\sqrt{2} \left(\sqrt{\sqrt{x+1}+1}+1\right)}{2+\sqrt{2}}\right)-\frac{2 \log (x+1)}{\sqrt{\sqrt{x+1}+1}}-8 \tanh ^{-1}\left(\sqrt{\sqrt{x+1}+1}\right)-\sqrt{2} \log (x+1) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x+1}+1}}{\sqrt{2}}\right)+2 \sqrt{2} \tanh ^{-1}\left(\frac{1}{\sqrt{2}}\right) \log \left(1-\sqrt{\sqrt{x+1}+1}\right)-2 \sqrt{2} \tanh ^{-1}\left(\frac{1}{\sqrt{2}}\right) \log \left(\sqrt{\sqrt{x+1}+1}+1\right)",1,"Could not integrate","F",-1
8,0,0,308,0.0000423,"\int \frac{\sqrt{1+\sqrt{1+x}} \log (1+x)}{x} \, dx","IntegrateAlgebraic[(Sqrt[1 + Sqrt[1 + x]]*Log[1 + x])/x,x]","\int \frac{\sqrt{1+\sqrt{1+x}} \log (1+x)}{x} \, dx","2 \sqrt{2} \text{Li}_2\left(-\frac{\sqrt{2} \left(1-\sqrt{\sqrt{x+1}+1}\right)}{2-\sqrt{2}}\right)-2 \sqrt{2} \text{Li}_2\left(\frac{\sqrt{2} \left(1-\sqrt{\sqrt{x+1}+1}\right)}{2+\sqrt{2}}\right)-2 \sqrt{2} \text{Li}_2\left(-\frac{\sqrt{2} \left(\sqrt{\sqrt{x+1}+1}+1\right)}{2-\sqrt{2}}\right)+2 \sqrt{2} \text{Li}_2\left(\frac{\sqrt{2} \left(\sqrt{\sqrt{x+1}+1}+1\right)}{2+\sqrt{2}}\right)-16 \sqrt{\sqrt{x+1}+1}+4 \sqrt{\sqrt{x+1}+1} \log (x+1)+16 \tanh ^{-1}\left(\sqrt{\sqrt{x+1}+1}\right)-2 \sqrt{2} \log (x+1) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x+1}+1}}{\sqrt{2}}\right)+4 \sqrt{2} \tanh ^{-1}\left(\frac{1}{\sqrt{2}}\right) \log \left(1-\sqrt{\sqrt{x+1}+1}\right)-4 \sqrt{2} \tanh ^{-1}\left(\frac{1}{\sqrt{2}}\right) \log \left(\sqrt{\sqrt{x+1}+1}+1\right)",1,"Could not integrate","F",-1
9,1,110,84,0.0962149,"\int \frac{1}{1+\sqrt{x+\sqrt{1+x^2}}} \, dx","IntegrateAlgebraic[(1 + Sqrt[x + Sqrt[1 + x^2]])^(-1),x]","\frac{\sqrt{x^2+1} \left(2 \sqrt{\sqrt{x^2+1}+x}+5\right)+(2 x+2) \sqrt{\sqrt{x^2+1}+x}+5 x-1}{2 \sqrt{x^2+1}+2 x}+\frac{1}{2} \log \left(\sqrt{x^2+1}+x\right)-2 \log \left(\sqrt{\sqrt{x^2+1}+x}+1\right)","\sqrt{\sqrt{x^2+1}+x}+\frac{1}{\sqrt{\sqrt{x^2+1}+x}}-\frac{1}{2 \left(\sqrt{x^2+1}+x\right)}+\frac{1}{2} \log \left(\sqrt{x^2+1}+x\right)-2 \log \left(\sqrt{\sqrt{x^2+1}+x}+1\right)",1,"(-1 + 5*x + (2 + 2*x)*Sqrt[x + Sqrt[1 + x^2]] + Sqrt[1 + x^2]*(5 + 2*Sqrt[x + Sqrt[1 + x^2]]))/(2*x + 2*Sqrt[1 + x^2]) + Log[x + Sqrt[1 + x^2]]/2 - 2*Log[1 + Sqrt[x + Sqrt[1 + x^2]]]","A",1
10,1,44,41,0.5873703,"\int \frac{\sqrt{1+x}}{x+\sqrt{1+\sqrt{1+x}}} \, dx","IntegrateAlgebraic[Sqrt[1 + x]/(x + Sqrt[1 + Sqrt[1 + x]]),x]","2 \sqrt{x+1}+\frac{8 \tanh ^{-1}\left(\frac{2 \sqrt{\sqrt{x+1}+1}}{\sqrt{5}}+\frac{1}{\sqrt{5}}\right)}{\sqrt{5}}","2 \sqrt{x+1}+\frac{8 \tanh ^{-1}\left(\frac{2 \sqrt{\sqrt{x+1}+1}+1}{\sqrt{5}}\right)}{\sqrt{5}}",1,"2*Sqrt[1 + x] + (8*ArcTanh[1/Sqrt[5] + (2*Sqrt[1 + Sqrt[1 + x]])/Sqrt[5]])/Sqrt[5]","A",1
11,1,69,73,1.0939737,"\int \frac{1}{x-\sqrt{1+\sqrt{1+x}}} \, dx","IntegrateAlgebraic[(x - Sqrt[1 + Sqrt[1 + x]])^(-1),x]","\frac{2}{5} \left(5+\sqrt{5}\right) \log \left(2 \sqrt{\sqrt{x+1}+1}+\sqrt{5}-1\right)-\frac{2}{5} \left(\sqrt{5}-5\right) \log \left(-2 \sqrt{\sqrt{x+1}+1}+\sqrt{5}+1\right)","\frac{2}{5} \left(5+\sqrt{5}\right) \log \left(-2 \sqrt{\sqrt{x+1}+1}-\sqrt{5}+1\right)+\frac{2}{5} \left(5-\sqrt{5}\right) \log \left(-2 \sqrt{\sqrt{x+1}+1}+\sqrt{5}+1\right)",1,"(-2*(-5 + Sqrt[5])*Log[1 + Sqrt[5] - 2*Sqrt[1 + Sqrt[1 + x]]])/5 + (2*(5 + Sqrt[5])*Log[-1 + Sqrt[5] + 2*Sqrt[1 + Sqrt[1 + x]]])/5","A",1
12,1,55,73,0.5806067,"\int \frac{x}{x+\sqrt{1-\sqrt{1+x}}} \, dx","IntegrateAlgebraic[x/(x + Sqrt[1 - Sqrt[1 + x]]),x]","x-4 \sqrt{1-\sqrt{x+1}}+\frac{8 \tanh ^{-1}\left(\frac{2 \sqrt{1-\sqrt{x+1}}}{\sqrt{5}}+\frac{1}{\sqrt{5}}\right)}{\sqrt{5}}","\left(1-\sqrt{x+1}\right)^2-4 \sqrt{1-\sqrt{x+1}}+2 \sqrt{x+1}+\frac{8 \tanh ^{-1}\left(\frac{2 \sqrt{1-\sqrt{x+1}}+1}{\sqrt{5}}\right)}{\sqrt{5}}",1,"x - 4*Sqrt[1 - Sqrt[1 + x]] + (8*ArcTanh[1/Sqrt[5] + (2*Sqrt[1 - Sqrt[1 + x]])/Sqrt[5]])/Sqrt[5]","A",1
13,1,209,365,0.6677329,"\int \frac{\sqrt{x+\sqrt{1+x}}}{\sqrt{1+x} \left(1+x^2\right)} \, dx","IntegrateAlgebraic[Sqrt[x + Sqrt[1 + x]]/(Sqrt[1 + x]*(1 + x^2)),x]","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^5+20 \text{$\#$1}^4-48 \text{$\#$1}^3+40 \text{$\#$1}^2-8 \text{$\#$1}+1\&,\frac{2 \text{$\#$1}^5 \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)-5 \text{$\#$1}^4 \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)+5 \text{$\#$1}^2 \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)-\log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+5 \text{$\#$1}^4+10 \text{$\#$1}^3-18 \text{$\#$1}^2+10 \text{$\#$1}-1}\&\right]","-\frac{i \tan ^{-1}\left(\frac{-\left(\left(1-2 \sqrt{1-i}\right) \sqrt{x+1}\right)+\sqrt{1-i}+2}{2 \sqrt{i+\sqrt{1-i}} \sqrt{x+\sqrt{x+1}}}\right)}{2 \sqrt{\frac{1-i}{i+\sqrt{1-i}}}}+\frac{i \tan ^{-1}\left(\frac{-\left(\left(1-2 \sqrt{1+i}\right) \sqrt{x+1}\right)+\sqrt{1+i}+2}{2 \sqrt{\sqrt{1+i}-i} \sqrt{x+\sqrt{x+1}}}\right)}{2 \sqrt{-\frac{1+i}{i-\sqrt{1+i}}}}+\frac{i \tanh ^{-1}\left(\frac{-\left(\left(1+2 \sqrt{1-i}\right) \sqrt{x+1}\right)-\sqrt{1-i}+2}{2 \sqrt{\sqrt{1-i}-i} \sqrt{x+\sqrt{x+1}}}\right)}{2 \sqrt{-\frac{1-i}{i-\sqrt{1-i}}}}-\frac{i \tanh ^{-1}\left(\frac{-\left(\left(1+2 \sqrt{1+i}\right) \sqrt{x+1}\right)-\sqrt{1+i}+2}{2 \sqrt{i+\sqrt{1+i}} \sqrt{x+\sqrt{x+1}}}\right)}{2 \sqrt{\frac{1+i}{i+\sqrt{1+i}}}}",1,"-1/2*RootSum[1 - 8*#1 + 40*#1^2 - 48*#1^3 + 20*#1^4 + 8*#1^5 - 4*#1^6 + #1^8 & , (-Log[Sqrt[1 + x] - Sqrt[x + Sqrt[1 + x]] + #1] + 5*Log[Sqrt[1 + x] - Sqrt[x + Sqrt[1 + x]] + #1]*#1^2 - 5*Log[Sqrt[1 + x] - Sqrt[x + Sqrt[1 + x]] + #1]*#1^4 + 2*Log[Sqrt[1 + x] - Sqrt[x + Sqrt[1 + x]] + #1]*#1^5)/(-1 + 10*#1 - 18*#1^2 + 10*#1^3 + 5*#1^4 - 3*#1^5 + #1^7) & ]","C",1
14,1,204,337,0.6529049,"\int \frac{\sqrt{x+\sqrt{1+x}}}{1+x^2} \, dx","IntegrateAlgebraic[Sqrt[x + Sqrt[1 + x]]/(1 + x^2),x]","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^5+20 \text{$\#$1}^4-48 \text{$\#$1}^3+40 \text{$\#$1}^2-8 \text{$\#$1}+1\&,\frac{\text{$\#$1}^6 \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)-2 \text{$\#$1}^5 \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)+2 \text{$\#$1} \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)+\log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+5 \text{$\#$1}^4+10 \text{$\#$1}^3-18 \text{$\#$1}^2+10 \text{$\#$1}-1}\&\right]","\frac{1}{2} i \sqrt{i+\sqrt{1-i}} \tan ^{-1}\left(\frac{-\left(\left(1-2 \sqrt{1-i}\right) \sqrt{x+1}\right)+\sqrt{1-i}+2}{2 \sqrt{i+\sqrt{1-i}} \sqrt{x+\sqrt{x+1}}}\right)-\frac{1}{2} i \sqrt{\sqrt{1+i}-i} \tan ^{-1}\left(\frac{-\left(\left(1-2 \sqrt{1+i}\right) \sqrt{x+1}\right)+\sqrt{1+i}+2}{2 \sqrt{\sqrt{1+i}-i} \sqrt{x+\sqrt{x+1}}}\right)+\frac{1}{2} i \sqrt{\sqrt{1-i}-i} \tanh ^{-1}\left(\frac{-\left(\left(1+2 \sqrt{1-i}\right) \sqrt{x+1}\right)-\sqrt{1-i}+2}{2 \sqrt{\sqrt{1-i}-i} \sqrt{x+\sqrt{x+1}}}\right)-\frac{1}{2} i \sqrt{i+\sqrt{1+i}} \tanh ^{-1}\left(\frac{-\left(\left(1+2 \sqrt{1+i}\right) \sqrt{x+1}\right)-\sqrt{1+i}+2}{2 \sqrt{i+\sqrt{1+i}} \sqrt{x+\sqrt{x+1}}}\right)",1,"RootSum[1 - 8*#1 + 40*#1^2 - 48*#1^3 + 20*#1^4 + 8*#1^5 - 4*#1^6 + #1^8 & , (Log[Sqrt[1 + x] - Sqrt[x + Sqrt[1 + x]] + #1] + 2*Log[Sqrt[1 + x] - Sqrt[x + Sqrt[1 + x]] + #1]*#1 - 2*Log[Sqrt[1 + x] - Sqrt[x + Sqrt[1 + x]] + #1]*#1^5 + Log[Sqrt[1 + x] - Sqrt[x + Sqrt[1 + x]] + #1]*#1^6)/(-1 + 10*#1 - 18*#1^2 + 10*#1^3 + 5*#1^4 - 3*#1^5 + #1^7) & ]/2","C",1
15,1,196,77,11.5477373,"\int \sqrt{1+\sqrt{x}+\sqrt{1+2 \sqrt{x}+2 x}} \, dx","IntegrateAlgebraic[Sqrt[1 + Sqrt[x] + Sqrt[1 + 2*Sqrt[x] + 2*x]],x]","\frac{4}{5} \sqrt{\sqrt{x}+\sqrt{2 x+2 \sqrt{x}+1}+1} x+\frac{2}{15} \sqrt{2 x+2 \sqrt{x}+1} \sqrt{\sqrt{x}+\sqrt{2 x+2 \sqrt{x}+1}+1}+\frac{2}{15} \sqrt{\sqrt{x}+\sqrt{2 x+2 \sqrt{x}+1}+1}+\frac{\frac{4}{15} \sqrt{\sqrt{x}+\sqrt{2 x+2 \sqrt{x}+1}+1}-\frac{4}{15} \sqrt{2 x+2 \sqrt{x}+1} \sqrt{\sqrt{x}+\sqrt{2 x+2 \sqrt{x}+1}+1}}{\sqrt{x}}","\frac{2 \sqrt{\sqrt{x}+\sqrt{2 x+2 \sqrt{x}+1}+1} \left(6 x^{3/2}+\sqrt{x}-\left(2-\sqrt{x}\right) \sqrt{2 x+2 \sqrt{x}+1}+2\right)}{15 \sqrt{x}}",1,"(2*Sqrt[1 + Sqrt[x] + Sqrt[1 + 2*Sqrt[x] + 2*x]])/15 + (4*x*Sqrt[1 + Sqrt[x] + Sqrt[1 + 2*Sqrt[x] + 2*x]])/5 + (2*Sqrt[1 + 2*Sqrt[x] + 2*x]*Sqrt[1 + Sqrt[x] + Sqrt[1 + 2*Sqrt[x] + 2*x]])/15 + ((4*Sqrt[1 + Sqrt[x] + Sqrt[1 + 2*Sqrt[x] + 2*x]])/15 - (4*Sqrt[1 + 2*Sqrt[x] + 2*x]*Sqrt[1 + Sqrt[x] + Sqrt[1 + 2*Sqrt[x] + 2*x]])/15)/Sqrt[x]","B",1
16,0,0,118,3.6092407,"\int \sqrt{\sqrt{2}+\sqrt{x}+\sqrt{2+2 \sqrt{2} \sqrt{x}+2 x}} \, dx","IntegrateAlgebraic[Sqrt[Sqrt[2] + Sqrt[x] + Sqrt[2 + 2*Sqrt[2]*Sqrt[x] + 2*x]],x]","\int \sqrt{\sqrt{2}+\sqrt{x}+\sqrt{2+2 \sqrt{2} \sqrt{x}+2 x}} \, dx","\frac{2 \sqrt{2} \sqrt{\sqrt{x}+\sqrt{2} \sqrt{x+\sqrt{2} \sqrt{x}+1}+\sqrt{2}} \left(3 \sqrt{2} x^{3/2}+\sqrt{2} \sqrt{x}-\sqrt{2} \left(2 \sqrt{2}-\sqrt{x}\right) \sqrt{x+\sqrt{2} \sqrt{x}+1}+4\right)}{15 \sqrt{x}}",1,"Could not integrate","F",-1
17,1,127,83,0.7387839,"\int \frac{\sqrt{x+\sqrt{1+x}}}{x^2} \, dx","IntegrateAlgebraic[Sqrt[x + Sqrt[1 + x]]/x^2,x]","-\frac{\sqrt{x+\sqrt{x+1}}}{x}-\frac{1}{4} \tan ^{-1}\left(\frac{2 x+\sqrt{x+1} \left(3-2 \sqrt{x+\sqrt{x+1}}\right)-2 \sqrt{x+\sqrt{x+1}}+1}{2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+2}\right)-\frac{3}{2} \tanh ^{-1}\left(-\sqrt{x+1}+\sqrt{x+\sqrt{x+1}}+1\right)","-\frac{\sqrt{x+\sqrt{x+1}}}{x}-\frac{1}{4} \tan ^{-1}\left(\frac{\sqrt{x+1}+3}{2 \sqrt{x+\sqrt{x+1}}}\right)+\frac{3}{4} \tanh ^{-1}\left(\frac{1-3 \sqrt{x+1}}{2 \sqrt{x+\sqrt{x+1}}}\right)",1,"-(Sqrt[x + Sqrt[1 + x]]/x) - ArcTan[(1 + 2*x - 2*Sqrt[x + Sqrt[1 + x]] + Sqrt[1 + x]*(3 - 2*Sqrt[x + Sqrt[1 + x]]))/(2 + 2*Sqrt[1 + x] - 2*Sqrt[x + Sqrt[1 + x]])]/4 - (3*ArcTanh[1 - Sqrt[1 + x] + Sqrt[x + Sqrt[1 + x]]])/2","A",1
18,1,194,96,1.4484634,"\int \sqrt{\sqrt{1+\frac{1}{x}}+\frac{1}{x}} \, dx","IntegrateAlgebraic[Sqrt[Sqrt[1 + x^(-1)] + x^(-1)],x]","\sqrt{\frac{\sqrt{\frac{x+1}{x}} x+1}{x}} x-\frac{1}{4} \tan ^{-1}\left(\frac{-2 \sqrt{\frac{x+1}{x}} x+2 \sqrt{\frac{\sqrt{\frac{x+1}{x}} x+1}{x}} x-2 x}{2 \sqrt{\frac{\sqrt{\frac{x+1}{x}} x+1}{x}} x-x+\sqrt{\frac{x+1}{x}} \left(2 x \sqrt{\frac{\sqrt{\frac{x+1}{x}} x+1}{x}}-3 x\right)-2}\right)+\frac{3}{2} \tanh ^{-1}\left(-\sqrt{\frac{x+1}{x}}+\sqrt{\frac{\sqrt{\frac{x+1}{x}} x+1}{x}}+1\right)","\sqrt{\sqrt{\frac{1}{x}+1}+\frac{1}{x}} x+\frac{1}{4} \tan ^{-1}\left(\frac{\sqrt{\frac{1}{x}+1}+3}{2 \sqrt{\sqrt{\frac{1}{x}+1}+\frac{1}{x}}}\right)-\frac{3}{4} \tanh ^{-1}\left(\frac{1-3 \sqrt{\frac{1}{x}+1}}{2 \sqrt{\sqrt{\frac{1}{x}+1}+\frac{1}{x}}}\right)",1,"x*Sqrt[(1 + x*Sqrt[(1 + x)/x])/x] - ArcTan[(-2*x - 2*x*Sqrt[(1 + x)/x] + 2*x*Sqrt[(1 + x*Sqrt[(1 + x)/x])/x])/(-2 - x + 2*x*Sqrt[(1 + x*Sqrt[(1 + x)/x])/x] + Sqrt[(1 + x)/x]*(-3*x + 2*x*Sqrt[(1 + x*Sqrt[(1 + x)/x])/x]))]/4 + (3*ArcTanh[1 - Sqrt[(1 + x)/x] + Sqrt[(1 + x*Sqrt[(1 + x)/x])/x]])/2","B",1
19,0,0,25,0.0000763,"\int \frac{\sqrt{1+e^{-x}}}{-e^{-x}+e^x} \, dx","IntegrateAlgebraic[Sqrt[1 + E^(-x)]/(-E^(-x) + E^x),x]","\int \frac{\sqrt{1+e^{-x}}}{-e^{-x}+e^x} \, dx","-\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{e^{-x}+1}}{\sqrt{2}}\right)",1,"Could not integrate","F",-1
20,0,0,25,0.0000336,"\int \sqrt{1+e^{-x}} \text{csch}(x) \, dx","IntegrateAlgebraic[Sqrt[1 + E^(-x)]*Csch[x],x]","\int \sqrt{1+e^{-x}} \text{csch}(x) \, dx","-2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{e^{-x}+1}}{\sqrt{2}}\right)",1,"Could not integrate","F",-1
21,0,0,108,0.0000299,"\int \frac{1}{(\cos (x)+\cos (3 x))^5} \, dx","IntegrateAlgebraic[(Cos[x] + Cos[3*x])^(-5),x]","\int \frac{1}{(\cos (x)+\cos (3 x))^5} \, dx","-\frac{437 \sin (x)}{512 \left(1-2 \sin ^2(x)\right)}+\frac{203 \sin (x)}{768 \left(1-2 \sin ^2(x)\right)^2}-\frac{17 \sin (x)}{192 \left(1-2 \sin ^2(x)\right)^3}+\frac{\sin (x)}{32 \left(1-2 \sin ^2(x)\right)^4}-\frac{523}{256} \tanh ^{-1}(\sin (x))+\frac{1483 \tanh ^{-1}\left(\sqrt{2} \sin (x)\right)}{512 \sqrt{2}}-\frac{1}{128} \tan (x) \sec ^3(x)-\frac{43}{256} \tan (x) \sec (x)",1,"Could not integrate","F",-1
22,0,0,29,0.0000323,"\int \frac{1}{(1+\cos (x)+\sin (x))^2} \, dx","IntegrateAlgebraic[(1 + Cos[x] + Sin[x])^(-2),x]","\int \frac{1}{(1+\cos (x)+\sin (x))^2} \, dx","-\log \left(\tan \left(\frac{x}{2}\right)+1\right)-\frac{\cos (x)-\sin (x)}{\sin (x)+\cos (x)+1}",1,"Could not integrate","F",-1
23,0,0,26,0.000031,"\int \sqrt{1+\tanh (4 x)} \, dx","IntegrateAlgebraic[Sqrt[1 + Tanh[4*x]],x]","\int \sqrt{1+\tanh (4 x)} \, dx","\frac{\tanh ^{-1}\left(\frac{\sqrt{\tanh (4 x)+1}}{\sqrt{2}}\right)}{2 \sqrt{2}}",1,"Could not integrate","F",-1
24,0,0,110,0.0000646,"\int \frac{\tanh (x)}{\sqrt{e^x+e^{2 x}}} \, dx","IntegrateAlgebraic[Tanh[x]/Sqrt[E^x + E^(2*x)],x]","\int \frac{\tanh (x)}{\sqrt{e^x+e^{2 x}}} \, dx","2 e^{-x} \sqrt{e^x+e^{2 x}}-\frac{\tan ^{-1}\left(\frac{i-(1-2 i) e^x}{2 \sqrt{1+i} \sqrt{e^x+e^{2 x}}}\right)}{\sqrt{1+i}}+\frac{\tan ^{-1}\left(\frac{(1+2 i) e^x+i}{2 \sqrt{1-i} \sqrt{e^x+e^{2 x}}}\right)}{\sqrt{1-i}}",1,"Could not integrate","F",-1
25,0,0,40,0.0000346,"\int \sqrt{\text{sech}(x) \sinh (2 x)} \, dx","IntegrateAlgebraic[Sqrt[Sech[x]*Sinh[2*x]],x]","\int \sqrt{\text{sech}(x) \sinh (2 x)} \, dx","\frac{2 i \sqrt{2} \sqrt{\sinh (x)} E\left(\left.\frac{\pi }{4}-\frac{i x}{2}\right|2\right)}{\sqrt{i \sinh (x)}}",1,"Could not integrate","F",-1
26,0,0,185,0.0000392,"\int \log \left(x^2+\sqrt{1-x^2}\right) \, dx","IntegrateAlgebraic[Log[x^2 + Sqrt[1 - x^2]],x]","\int \log \left(x^2+\sqrt{1-x^2}\right) \, dx","x \log \left(x^2+\sqrt{1-x^2}\right)+\sqrt{\frac{1}{2} \left(1+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{1}{2} \left(1+\sqrt{5}\right)} x}{\sqrt{1-x^2}}\right)-\sqrt{\frac{1}{2} \left(\sqrt{5}-1\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{2} \left(\sqrt{5}-1\right)} x}{\sqrt{1-x^2}}\right)-2 x-\sin ^{-1}(x)+\sqrt{\frac{1}{2} \left(1+\sqrt{5}\right)} \tan ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} x\right)+\sqrt{\frac{1}{2} \left(\sqrt{5}-1\right)} \tanh ^{-1}\left(\sqrt{\frac{2}{\sqrt{5}-1}} x\right)",1,"Could not integrate","F",-1
27,0,0,102,0.0000742,"\int \frac{\log \left(1+e^x\right)}{1+e^{2 x}} \, dx","IntegrateAlgebraic[Log[1 + E^x]/(1 + E^(2*x)),x]","\int \frac{\log \left(1+e^x\right)}{1+e^{2 x}} \, dx","-\text{Li}_2\left(-e^x\right)-\frac{1}{2} \text{Li}_2\left(\left(\frac{1}{2}-\frac{i}{2}\right) \left(1+e^x\right)\right)-\frac{1}{2} \text{Li}_2\left(\left(\frac{1}{2}+\frac{i}{2}\right) \left(1+e^x\right)\right)-\frac{1}{2} \log \left(\left(\frac{1}{2}-\frac{i}{2}\right) \left(-e^x+i\right)\right) \log \left(e^x+1\right)-\frac{1}{2} \log \left(\left(-\frac{1}{2}-\frac{i}{2}\right) \left(e^x+i\right)\right) \log \left(e^x+1\right)",1,"Could not integrate","F",-1
28,0,0,159,0.0000382,"\int \cosh (x) \log ^2\left(1+\cosh ^2(x)\right) \, dx","IntegrateAlgebraic[Cosh[x]*Log[1 + Cosh[x]^2]^2,x]","\int \cosh (x) \log ^2\left(1+\cosh ^2(x)\right) \, dx","4 i \sqrt{2} \text{Li}_2\left(1-\frac{2 \sqrt{2}}{i \sinh (x)+\sqrt{2}}\right)+8 \sinh (x)+\sinh (x) \log ^2\left(\sinh ^2(x)+2\right)-4 \sinh (x) \log \left(\sinh ^2(x)+2\right)+4 i \sqrt{2} \tan ^{-1}\left(\frac{\sinh (x)}{\sqrt{2}}\right)^2-8 \sqrt{2} \tan ^{-1}\left(\frac{\sinh (x)}{\sqrt{2}}\right)+4 \sqrt{2} \log \left(\sinh ^2(x)+2\right) \tan ^{-1}\left(\frac{\sinh (x)}{\sqrt{2}}\right)+8 \sqrt{2} \log \left(\frac{2 \sqrt{2}}{\sqrt{2}+i \sinh (x)}\right) \tan ^{-1}\left(\frac{\sinh (x)}{\sqrt{2}}\right)",1,"Could not integrate","F",-1
29,0,0,395,0.0000417,"\int \cosh (x) \log ^2\left(\cosh ^2(x)+\sinh (x)\right) \, dx","IntegrateAlgebraic[Cosh[x]*Log[Cosh[x]^2 + Sinh[x]]^2,x]","\int \cosh (x) \log ^2\left(\cosh ^2(x)+\sinh (x)\right) \, dx","-\left(1+i \sqrt{3}\right) \text{Li}_2\left(-\frac{2 i \sinh (x)-\sqrt{3}+i}{2 \sqrt{3}}\right)-\left(1-i \sqrt{3}\right) \text{Li}_2\left(\frac{2 i \sinh (x)+\sqrt{3}+i}{2 \sqrt{3}}\right)+8 \sinh (x)+\sinh (x) \log ^2\left(\sinh ^2(x)+\sinh (x)+1\right)-\frac{1}{2} \left(1-i \sqrt{3}\right) \log ^2\left(2 \sinh (x)-i \sqrt{3}+1\right)-\frac{1}{2} \left(1+i \sqrt{3}\right) \log ^2\left(2 \sinh (x)+i \sqrt{3}+1\right)+\left(1-i \sqrt{3}\right) \log \left(\sinh ^2(x)+\sinh (x)+1\right) \log \left(2 \sinh (x)-i \sqrt{3}+1\right)+\left(1+i \sqrt{3}\right) \log \left(2 \sinh (x)+i \sqrt{3}+1\right) \log \left(\sinh ^2(x)+\sinh (x)+1\right)-2 \log \left(\sinh ^2(x)+\sinh (x)+1\right)-4 \sinh (x) \log \left(\sinh ^2(x)+\sinh (x)+1\right)-\left(1-i \sqrt{3}\right) \log \left(-\frac{i \left(2 \sinh (x)+i \sqrt{3}+1\right)}{2 \sqrt{3}}\right) \log \left(2 \sinh (x)-i \sqrt{3}+1\right)-\left(1+i \sqrt{3}\right) \log \left(\frac{i \left(2 \sinh (x)-i \sqrt{3}+1\right)}{2 \sqrt{3}}\right) \log \left(2 \sinh (x)+i \sqrt{3}+1\right)-4 \sqrt{3} \tan ^{-1}\left(\frac{2 \sinh (x)+1}{\sqrt{3}}\right)",1,"Could not integrate","F",-1
30,0,0,981,0.0000418,"\int \frac{\log \left(x+\sqrt{1+x}\right)}{1+x^2} \, dx","IntegrateAlgebraic[Log[x + Sqrt[1 + x]]/(1 + x^2),x]","\int \frac{\log \left(x+\sqrt{1+x}\right)}{1+x^2} \, dx","\frac{1}{2} i \log \left(\sqrt{1-i}-\sqrt{x+1}\right) \log \left(x+\sqrt{x+1}\right)-\frac{1}{2} i \log \left(\sqrt{1+i}-\sqrt{x+1}\right) \log \left(x+\sqrt{x+1}\right)+\frac{1}{2} i \log \left(\sqrt{x+1}+\sqrt{1-i}\right) \log \left(x+\sqrt{x+1}\right)-\frac{1}{2} i \log \left(\sqrt{x+1}+\sqrt{1+i}\right) \log \left(x+\sqrt{x+1}\right)-\frac{1}{2} i \log \left(\sqrt{x+1}+\sqrt{1-i}\right) \log \left(\frac{2 \sqrt{x+1}-\sqrt{5}+1}{1-2 \sqrt{1-i}-\sqrt{5}}\right)-\frac{1}{2} i \log \left(\sqrt{1-i}-\sqrt{x+1}\right) \log \left(\frac{2 \sqrt{x+1}-\sqrt{5}+1}{1+2 \sqrt{1-i}-\sqrt{5}}\right)+\frac{1}{2} i \log \left(\sqrt{x+1}+\sqrt{1+i}\right) \log \left(\frac{2 \sqrt{x+1}-\sqrt{5}+1}{1-2 \sqrt{1+i}-\sqrt{5}}\right)+\frac{1}{2} i \log \left(\sqrt{1+i}-\sqrt{x+1}\right) \log \left(\frac{2 \sqrt{x+1}-\sqrt{5}+1}{1+2 \sqrt{1+i}-\sqrt{5}}\right)-\frac{1}{2} i \log \left(\sqrt{x+1}+\sqrt{1-i}\right) \log \left(\frac{2 \sqrt{x+1}+\sqrt{5}+1}{1-2 \sqrt{1-i}+\sqrt{5}}\right)-\frac{1}{2} i \log \left(\sqrt{1-i}-\sqrt{x+1}\right) \log \left(\frac{2 \sqrt{x+1}+\sqrt{5}+1}{1+2 \sqrt{1-i}+\sqrt{5}}\right)+\frac{1}{2} i \log \left(\sqrt{x+1}+\sqrt{1+i}\right) \log \left(\frac{2 \sqrt{x+1}+\sqrt{5}+1}{1-2 \sqrt{1+i}+\sqrt{5}}\right)+\frac{1}{2} i \log \left(\sqrt{1+i}-\sqrt{x+1}\right) \log \left(\frac{2 \sqrt{x+1}+\sqrt{5}+1}{1+2 \sqrt{1+i}+\sqrt{5}}\right)-\frac{1}{2} i \text{Li}_2\left(\frac{2 \left(\sqrt{1-i}-\sqrt{x+1}\right)}{1+2 \sqrt{1-i}-\sqrt{5}}\right)-\frac{1}{2} i \text{Li}_2\left(\frac{2 \left(\sqrt{1-i}-\sqrt{x+1}\right)}{1+2 \sqrt{1-i}+\sqrt{5}}\right)+\frac{1}{2} i \text{Li}_2\left(\frac{2 \left(\sqrt{1+i}-\sqrt{x+1}\right)}{1+2 \sqrt{1+i}-\sqrt{5}}\right)+\frac{1}{2} i \text{Li}_2\left(\frac{2 \left(\sqrt{1+i}-\sqrt{x+1}\right)}{1+2 \sqrt{1+i}+\sqrt{5}}\right)-\frac{1}{2} i \text{Li}_2\left(-\frac{2 \left(\sqrt{x+1}+\sqrt{1-i}\right)}{1-2 \sqrt{1-i}-\sqrt{5}}\right)-\frac{1}{2} i \text{Li}_2\left(-\frac{2 \left(\sqrt{x+1}+\sqrt{1-i}\right)}{1-2 \sqrt{1-i}+\sqrt{5}}\right)+\frac{1}{2} i \text{Li}_2\left(-\frac{2 \left(\sqrt{x+1}+\sqrt{1+i}\right)}{1-2 \sqrt{1+i}-\sqrt{5}}\right)+\frac{1}{2} i \text{Li}_2\left(-\frac{2 \left(\sqrt{x+1}+\sqrt{1+i}\right)}{1-2 \sqrt{1+i}+\sqrt{5}}\right)",1,"Could not integrate","F",-1
31,0,0,555,0.0000417,"\int \frac{\log ^2\left(x+\sqrt{1+x}\right)}{(1+x)^2} \, dx","IntegrateAlgebraic[Log[x + Sqrt[1 + x]]^2/(1 + x)^2,x]","\int \frac{\log ^2\left(x+\sqrt{1+x}\right)}{(1+x)^2} \, dx","6 \text{Li}_2\left(-\frac{2 \sqrt{x+1}}{1+\sqrt{5}}\right)-\left(3+\sqrt{5}\right) \text{Li}_2\left(-\frac{2 \sqrt{x+1}-\sqrt{5}+1}{2 \sqrt{5}}\right)-\left(3-\sqrt{5}\right) \text{Li}_2\left(\frac{2 \sqrt{x+1}+\sqrt{5}+1}{2 \sqrt{5}}\right)-6 \text{Li}_2\left(\frac{2 \sqrt{x+1}}{1-\sqrt{5}}+1\right)-\frac{\log ^2\left(x+\sqrt{x+1}\right)}{x+1}-\frac{1}{2} \left(3+\sqrt{5}\right) \log ^2\left(2 \sqrt{x+1}-\sqrt{5}+1\right)-\frac{1}{2} \left(3-\sqrt{5}\right) \log ^2\left(2 \sqrt{x+1}+\sqrt{5}+1\right)-6 \log \left(\sqrt{x+1}\right) \log \left(x+\sqrt{x+1}\right)+\left(3+\sqrt{5}\right) \log \left(2 \sqrt{x+1}-\sqrt{5}+1\right) \log \left(x+\sqrt{x+1}\right)+\left(3-\sqrt{5}\right) \log \left(2 \sqrt{x+1}+\sqrt{5}+1\right) \log \left(x+\sqrt{x+1}\right)+\frac{2 \log \left(x+\sqrt{x+1}\right)}{\sqrt{x+1}}+\log (x+1)+6 \log \left(\frac{1}{2} \left(\sqrt{5}-1\right)\right) \log \left(2 \sqrt{x+1}-\sqrt{5}+1\right)-\left(1+\sqrt{5}\right) \log \left(2 \sqrt{x+1}-\sqrt{5}+1\right)-\left(3-\sqrt{5}\right) \log \left(-\frac{2 \sqrt{x+1}-\sqrt{5}+1}{2 \sqrt{5}}\right) \log \left(2 \sqrt{x+1}+\sqrt{5}+1\right)-\left(1-\sqrt{5}\right) \log \left(2 \sqrt{x+1}+\sqrt{5}+1\right)-\left(3+\sqrt{5}\right) \log \left(2 \sqrt{x+1}-\sqrt{5}+1\right) \log \left(\frac{2 \sqrt{x+1}+\sqrt{5}+1}{2 \sqrt{5}}\right)+6 \log \left(\sqrt{x+1}\right) \log \left(\frac{2 \sqrt{x+1}}{1+\sqrt{5}}+1\right)",1,"Could not integrate","F",-1
32,0,0,313,0.0000388,"\int \frac{\log \left(x+\sqrt{1+x}\right)}{x} \, dx","IntegrateAlgebraic[Log[x + Sqrt[1 + x]]/x,x]","\int \frac{\log \left(x+\sqrt{1+x}\right)}{x} \, dx","-\text{Li}_2\left(\frac{2 \left(1-\sqrt{x+1}\right)}{3-\sqrt{5}}\right)-\text{Li}_2\left(\frac{2 \left(1-\sqrt{x+1}\right)}{3+\sqrt{5}}\right)-\text{Li}_2\left(\frac{2 \left(\sqrt{x+1}+1\right)}{1-\sqrt{5}}\right)-\text{Li}_2\left(\frac{2 \left(\sqrt{x+1}+1\right)}{1+\sqrt{5}}\right)+\log \left(\sqrt{x+1}-1\right) \log \left(x+\sqrt{x+1}\right)+\log \left(\sqrt{x+1}+1\right) \log \left(x+\sqrt{x+1}\right)-\log \left(\sqrt{x+1}-1\right) \log \left(\frac{2 \sqrt{x+1}-\sqrt{5}+1}{3-\sqrt{5}}\right)-\log \left(\sqrt{x+1}+1\right) \log \left(-\frac{2 \sqrt{x+1}-\sqrt{5}+1}{1+\sqrt{5}}\right)-\log \left(\sqrt{x+1}+1\right) \log \left(-\frac{2 \sqrt{x+1}+\sqrt{5}+1}{1-\sqrt{5}}\right)-\log \left(\sqrt{x+1}-1\right) \log \left(\frac{2 \sqrt{x+1}+\sqrt{5}+1}{3+\sqrt{5}}\right)",1,"Could not integrate","F",-1
33,0,0,80,0.0000347,"\int \tan ^{-1}(2 \tan (x)) \, dx","IntegrateAlgebraic[ArcTan[2*Tan[x]],x]","\int \tan ^{-1}(2 \tan (x)) \, dx","-\frac{1}{4} \text{Li}_2\left(\frac{1}{3} e^{2 i x}\right)+\frac{1}{4} \text{Li}_2\left(3 e^{2 i x}\right)+\frac{1}{2} i x \log \left(1-3 e^{2 i x}\right)-\frac{1}{2} i x \log \left(1-\frac{1}{3} e^{2 i x}\right)+x \tan ^{-1}(2 \tan (x))",1,"Could not integrate","F",-1
34,0,0,57,0.000057,"\int \frac{\tan ^{-1}(x) \log (x)}{x} \, dx","IntegrateAlgebraic[(ArcTan[x]*Log[x])/x,x]","\int \frac{\tan ^{-1}(x) \log (x)}{x} \, dx","-\frac{1}{2} i \text{Li}_3(-i x)+\frac{1}{2} i \text{Li}_3(i x)+\frac{1}{2} i \text{Li}_2(-i x) \log (x)-\frac{1}{2} i \text{Li}_2(i x) \log (x)",1,"Could not integrate","F",-1
35,0,0,121,0.0000388,"\int \sqrt{1+x^2} \tan ^{-1}(x)^2 \, dx","IntegrateAlgebraic[Sqrt[1 + x^2]*ArcTan[x]^2,x]","\int \sqrt{1+x^2} \tan ^{-1}(x)^2 \, dx","i \tan ^{-1}(x) \text{Li}_2\left(-i e^{i \tan ^{-1}(x)}\right)-i \tan ^{-1}(x) \text{Li}_2\left(i e^{i \tan ^{-1}(x)}\right)-\text{Li}_3\left(-i e^{i \tan ^{-1}(x)}\right)+\text{Li}_3\left(i e^{i \tan ^{-1}(x)}\right)+\frac{1}{2} x \sqrt{x^2+1} \tan ^{-1}(x)^2-\sqrt{x^2+1} \tan ^{-1}(x)-i \tan ^{-1}\left(e^{i \tan ^{-1}(x)}\right) \tan ^{-1}(x)^2+\sinh ^{-1}(x)",1,"Could not integrate","F",-1