1,1,22,0,0.1353233,"\int \frac{1}{\sqrt{2}+\cos (z)+\sin (z)} \, dz","Int[(Sqrt[2] + Cos[z] + Sin[z])^(-1),z]","-\frac{1-\sqrt{2} \sin (z)}{\cos (z)-\sin (z)}","-\frac{1-\sqrt{2} \sin (z)}{\cos (z)-\sin (z)}",1,"-((1 - Sqrt[2]*Sin[z])/(Cos[z] - Sin[z]))","A",1,1,12,0.08333,1,"{3114}"
2,1,32,0,0.1562348,"\int \frac{1}{\left(\sqrt{1-x}+\sqrt{1+x}\right)^2} \, dx","Int[(Sqrt[1 - x] + Sqrt[1 + x])^(-2),x]","\frac{\sqrt{1-x^2}}{2 x}-\frac{1}{2 x}+\frac{1}{2} \sin ^{-1}(x)","\frac{\sqrt{1-x^2}}{2 x}-\frac{1}{2 x}+\frac{1}{2} \sin ^{-1}(x)",1,"-1/(2*x) + Sqrt[1 - x^2]/(2*x) + ArcSin[x]/2","A",4,3,19,0.1579,1,"{6690, 277, 216}"
3,1,25,0,0.013607,"\int \frac{1}{(1+\cos (x))^2} \, dx","Int[(1 + Cos[x])^(-2),x]","\frac{\sin (x)}{3 (\cos (x)+1)}+\frac{\sin (x)}{3 (\cos (x)+1)^2}","\frac{\sin (x)}{3 (\cos (x)+1)}+\frac{\sin (x)}{3 (\cos (x)+1)^2}",1,"Sin[x]/(3*(1 + Cos[x])^2) + Sin[x]/(3*(1 + Cos[x]))","A",2,2,6,0.3333,1,"{2650, 2648}"
4,1,58,0,0.0815101,"\int \frac{\sin (x)}{\sqrt{1+x}} \, dx","Int[Sin[x]/Sqrt[1 + x],x]","\sqrt{2 \pi } \cos (1) S\left(\sqrt{\frac{2}{\pi }} \sqrt{x+1}\right)-\sqrt{2 \pi } \sin (1) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{x+1}\right)","\sqrt{2 \pi } \cos (1) S\left(\sqrt{\frac{2}{\pi }} \sqrt{x+1}\right)-\sqrt{2 \pi } \sin (1) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{x+1}\right)",1,"Sqrt[2*Pi]*Cos[1]*FresnelS[Sqrt[2/Pi]*Sqrt[1 + x]] - Sqrt[2*Pi]*FresnelC[Sqrt[2/Pi]*Sqrt[1 + x]]*Sin[1]","A",5,5,10,0.5000,1,"{3306, 3305, 3351, 3304, 3352}"
5,1,50,0,0.026043,"\int \frac{1}{(\cos (x)+\sin (x))^6} \, dx","Int[(Cos[x] + Sin[x])^(-6),x]","-\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))}","-\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,"-(Cos[x] - Sin[x])/(10*(Cos[x] + Sin[x])^5) - (Cos[x] - Sin[x])/(15*(Cos[x] + Sin[x])^3) + (2*Sin[x])/(15*(Cos[x] + Sin[x]))","A",3,2,7,0.2857,1,"{3076, 3075}"
6,1,334,0,0.3474678,"\int \log \left(\frac{1}{x^4}+x^4\right) \, dx","Int[Log[x^(-4) + x^4],x]","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)","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,"-4*x - Sqrt[2 + Sqrt[2]]*ArcTan[(Sqrt[2 - Sqrt[2]] - 2*x)/Sqrt[2 + Sqrt[2]]] - Sqrt[2 - Sqrt[2]]*ArcTan[(Sqrt[2 + Sqrt[2]] - 2*x)/Sqrt[2 - Sqrt[2]]] + Sqrt[2 + Sqrt[2]]*ArcTan[(Sqrt[2 - Sqrt[2]] + 2*x)/Sqrt[2 + Sqrt[2]]] + Sqrt[2 - Sqrt[2]]*ArcTan[(Sqrt[2 + Sqrt[2]] + 2*x)/Sqrt[2 - Sqrt[2]]] - (Sqrt[2 - Sqrt[2]]*Log[1 - Sqrt[2 - Sqrt[2]]*x + x^2])/2 + (Sqrt[2 - Sqrt[2]]*Log[1 + Sqrt[2 - Sqrt[2]]*x + x^2])/2 - (Sqrt[2 + Sqrt[2]]*Log[1 - Sqrt[2 + Sqrt[2]]*x + x^2])/2 + (Sqrt[2 + Sqrt[2]]*Log[1 + Sqrt[2 + Sqrt[2]]*x + x^2])/2 + x*Log[x^(-4) + x^4]","A",22,9,8,1.125,1,"{2523, 12, 388, 213, 1169, 634, 618, 204, 628}"
7,0,0,0,0.0486268,"\int \frac{\log (1+x)}{x \sqrt{1+\sqrt{1+x}}} \, dx","Int[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{PolyLog}\left(2,-\frac{\sqrt{2} \left(1-\sqrt{\sqrt{x+1}+1}\right)}{2-\sqrt{2}}\right)-\sqrt{2} \text{PolyLog}\left(2,\frac{\sqrt{2} \left(1-\sqrt{\sqrt{x+1}+1}\right)}{2+\sqrt{2}}\right)-\sqrt{2} \text{PolyLog}\left(2,-\frac{\sqrt{2} \left(\sqrt{\sqrt{x+1}+1}+1\right)}{2-\sqrt{2}}\right)+\sqrt{2} \text{PolyLog}\left(2,\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,"Defer[Int][Log[1 + x]/(x*Sqrt[1 + Sqrt[1 + x]]), x]","F",0,0,0,0,-1,"{}"
8,0,0,0,0.0432186,"\int \frac{\sqrt{1+\sqrt{1+x}} \log (1+x)}{x} \, dx","Int[(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{PolyLog}\left(2,-\frac{\sqrt{2} \left(1-\sqrt{\sqrt{x+1}+1}\right)}{2-\sqrt{2}}\right)-2 \sqrt{2} \text{PolyLog}\left(2,\frac{\sqrt{2} \left(1-\sqrt{\sqrt{x+1}+1}\right)}{2+\sqrt{2}}\right)-2 \sqrt{2} \text{PolyLog}\left(2,-\frac{\sqrt{2} \left(\sqrt{\sqrt{x+1}+1}+1\right)}{2-\sqrt{2}}\right)+2 \sqrt{2} \text{PolyLog}\left(2,\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,"Defer[Int][(Sqrt[1 + Sqrt[1 + x]]*Log[1 + x])/x, x]","F",0,0,0,0,-1,"{}"
9,1,84,0,0.0586596,"\int \frac{1}{1+\sqrt{x+\sqrt{1+x^2}}} \, dx","Int[(1 + Sqrt[x + Sqrt[1 + x^2]])^(-1),x]","\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)","\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/(2*(x + Sqrt[1 + x^2])) + 1/Sqrt[x + Sqrt[1 + x^2]] + Sqrt[x + Sqrt[1 + x^2]] + Log[x + Sqrt[1 + x^2]]/2 - 2*Log[1 + Sqrt[x + Sqrt[1 + x^2]]]","A",4,3,19,0.1579,1,"{2117, 1821, 1620}"
10,1,41,0,0.1932433,"\int \frac{\sqrt{1+x}}{x+\sqrt{1+\sqrt{1+x}}} \, dx","Int[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}+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 + 2*Sqrt[1 + Sqrt[1 + x]])/Sqrt[5]])/Sqrt[5]","A",6,3,25,0.1200,1,"{800, 618, 206}"
11,1,73,0,0.108042,"\int \frac{1}{x-\sqrt{1+\sqrt{1+x}}} \, dx","Int[(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(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)+\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",5,2,19,0.1053,1,"{632, 31}"
12,1,73,0,0.2705405,"\int \frac{x}{x+\sqrt{1-\sqrt{1+x}}} \, dx","Int[x/(x + Sqrt[1 - Sqrt[1 + x]]),x]","\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}}","\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,"2*Sqrt[1 + x] - 4*Sqrt[1 - Sqrt[1 + x]] + (1 - Sqrt[1 + x])^2 + (8*ArcTanh[(1 + 2*Sqrt[1 - Sqrt[1 + x]])/Sqrt[5]])/Sqrt[5]","A",6,3,21,0.1429,1,"{1628, 618, 206}"
13,1,365,0,0.8589844,"\int \frac{\sqrt{x+\sqrt{1+x}}}{\sqrt{1+x} \left(1+x^2\right)} \, dx","Int[Sqrt[x + Sqrt[1 + x]]/(Sqrt[1 + x]*(1 + x^2)),x]","-\frac{i \tan ^{-1}\left(\frac{-\left(1-2 \sqrt{1-i}\right) \sqrt{x+1}+\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(1-2 \sqrt{1+i}\right) \sqrt{x+1}+\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(1+2 \sqrt{1-i}\right) \sqrt{x+1}-\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(1+2 \sqrt{1+i}\right) \sqrt{x+1}-\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(1-2 \sqrt{1-i}\right) \sqrt{x+1}+\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(1-2 \sqrt{1+i}\right) \sqrt{x+1}+\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(1+2 \sqrt{1-i}\right) \sqrt{x+1}-\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(1+2 \sqrt{1+i}\right) \sqrt{x+1}-\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,"((-I/2)*ArcTan[(2 + Sqrt[1 - I] - (1 - 2*Sqrt[1 - I])*Sqrt[1 + x])/(2*Sqrt[I + Sqrt[1 - I]]*Sqrt[x + Sqrt[1 + x]])])/Sqrt[(1 - I)/(I + Sqrt[1 - I])] + ((I/2)*ArcTan[(2 + Sqrt[1 + I] - (1 - 2*Sqrt[1 + I])*Sqrt[1 + x])/(2*Sqrt[-I + Sqrt[1 + I]]*Sqrt[x + Sqrt[1 + x]])])/Sqrt[(-1 - I)/(I - Sqrt[1 + I])] + ((I/2)*ArcTanh[(2 - Sqrt[1 - I] - (1 + 2*Sqrt[1 - I])*Sqrt[1 + x])/(2*Sqrt[-I + Sqrt[1 - I]]*Sqrt[x + Sqrt[1 + x]])])/Sqrt[(-1 + I)/(I - Sqrt[1 - I])] - ((I/2)*ArcTanh[(2 - Sqrt[1 + I] - (1 + 2*Sqrt[1 + I])*Sqrt[1 + x])/(2*Sqrt[I + Sqrt[1 + I]]*Sqrt[x + Sqrt[1 + x]])])/Sqrt[(1 + I)/(I + Sqrt[1 + I])]","A",20,8,28,0.2857,1,"{6741, 6728, 990, 621, 206, 1033, 724, 204}"
14,1,337,0,0.6211427,"\int \frac{\sqrt{x+\sqrt{1+x}}}{1+x^2} \, dx","Int[Sqrt[x + Sqrt[1 + x]]/(1 + x^2),x]","\frac{1}{2} i \sqrt{i+\sqrt{1-i}} \tan ^{-1}\left(\frac{-\left(1-2 \sqrt{1-i}\right) \sqrt{x+1}+\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(1-2 \sqrt{1+i}\right) \sqrt{x+1}+\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(1+2 \sqrt{1-i}\right) \sqrt{x+1}-\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(1+2 \sqrt{1+i}\right) \sqrt{x+1}-\sqrt{1+i}+2}{2 \sqrt{i+\sqrt{1+i}} \sqrt{x+\sqrt{x+1}}}\right)","\frac{1}{2} i \sqrt{i+\sqrt{1-i}} \tan ^{-1}\left(\frac{-\left(1-2 \sqrt{1-i}\right) \sqrt{x+1}+\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(1-2 \sqrt{1+i}\right) \sqrt{x+1}+\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(1+2 \sqrt{1-i}\right) \sqrt{x+1}-\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(1+2 \sqrt{1+i}\right) \sqrt{x+1}-\sqrt{1+i}+2}{2 \sqrt{i+\sqrt{1+i}} \sqrt{x+\sqrt{x+1}}}\right)",1,"(I/2)*Sqrt[I + Sqrt[1 - I]]*ArcTan[(2 + Sqrt[1 - I] - (1 - 2*Sqrt[1 - I])*Sqrt[1 + x])/(2*Sqrt[I + Sqrt[1 - I]]*Sqrt[x + Sqrt[1 + x]])] - (I/2)*Sqrt[-I + Sqrt[1 + I]]*ArcTan[(2 + Sqrt[1 + I] - (1 - 2*Sqrt[1 + I])*Sqrt[1 + x])/(2*Sqrt[-I + Sqrt[1 + I]]*Sqrt[x + Sqrt[1 + x]])] + (I/2)*Sqrt[-I + Sqrt[1 - I]]*ArcTanh[(2 - Sqrt[1 - I] - (1 + 2*Sqrt[1 - I])*Sqrt[1 + x])/(2*Sqrt[-I + Sqrt[1 - I]]*Sqrt[x + Sqrt[1 + x]])] - (I/2)*Sqrt[I + Sqrt[1 + I]]*ArcTanh[(2 - Sqrt[1 + I] - (1 + 2*Sqrt[1 + I])*Sqrt[1 + x])/(2*Sqrt[I + Sqrt[1 + I]]*Sqrt[x + Sqrt[1 + x]])]","A",22,9,21,0.4286,1,"{6741, 6728, 1021, 1078, 621, 206, 1033, 724, 204}"
15,1,77,0,0.0710915,"\int \sqrt{1+\sqrt{x}+\sqrt{1+2 \sqrt{x}+2 x}} \, dx","Int[Sqrt[1 + Sqrt[x] + Sqrt[1 + 2*Sqrt[x] + 2*x]],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}}","\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]]*(2 + Sqrt[x] + 6*x^(3/2) - (2 - Sqrt[x])*Sqrt[1 + 2*Sqrt[x] + 2*x]))/(15*Sqrt[x])","A",2,1,27,0.03704,1,"{2114}"
16,1,118,0,0.1909368,"\int \sqrt{\sqrt{2}+\sqrt{x}+\sqrt{2+2 \sqrt{2} \sqrt{x}+2 x}} \, dx","Int[Sqrt[Sqrt[2] + Sqrt[x] + Sqrt[2 + 2*Sqrt[2]*Sqrt[x] + 2*x]],x]","\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}}","\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,"(2*Sqrt[2]*Sqrt[Sqrt[2] + Sqrt[x] + Sqrt[2]*Sqrt[1 + Sqrt[2]*Sqrt[x] + x]]*(4 + Sqrt[2]*Sqrt[x] + 3*Sqrt[2]*x^(3/2) - Sqrt[2]*(2*Sqrt[2] - Sqrt[x])*Sqrt[1 + Sqrt[2]*Sqrt[x] + x]))/(15*Sqrt[x])","A",3,2,36,0.05556,1,"{2115, 2114}"
17,1,83,0,0.1000126,"\int \frac{\sqrt{x+\sqrt{1+x}}}{x^2} \, dx","Int[Sqrt[x + Sqrt[1 + x]]/x^2,x]","-\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)","-\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[(3 + Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])]/4 + (3*ArcTanh[(1 - 3*Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])])/4","A",7,5,17,0.2941,1,"{1014, 1033, 724, 206, 204}"
18,1,96,0,0.0838966,"\int \sqrt{\sqrt{1+\frac{1}{x}}+\frac{1}{x}} \, dx","Int[Sqrt[Sqrt[1 + x^(-1)] + x^(-1)],x]","\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)","\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,"Sqrt[Sqrt[1 + x^(-1)] + x^(-1)]*x + ArcTan[(3 + Sqrt[1 + x^(-1)])/(2*Sqrt[Sqrt[1 + x^(-1)] + x^(-1)])]/4 - (3*ArcTanh[(1 - 3*Sqrt[1 + x^(-1)])/(2*Sqrt[Sqrt[1 + x^(-1)] + x^(-1)])])/4","A",7,5,17,0.2941,1,"{1014, 1033, 724, 206, 204}"
19,1,25,0,0.0749026,"\int \frac{\sqrt{1+e^{-x}}}{-e^{-x}+e^x} \, dx","Int[Sqrt[1 + E^(-x)]/(-E^(-x) + E^x),x]","-\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{e^{-x}+1}}{\sqrt{2}}\right)","-\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{e^{-x}+1}}{\sqrt{2}}\right)",1,"-(Sqrt[2]*ArcTanh[Sqrt[1 + E^(-x)]/Sqrt[2]])","A",6,6,25,0.2400,1,"{2282, 1446, 1469, 627, 63, 206}"
20,1,25,0,0.0510541,"\int \sqrt{1+e^{-x}} \text{csch}(x) \, dx","Int[Sqrt[1 + E^(-x)]*Csch[x],x]","-2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{e^{-x}+1}}{\sqrt{2}}\right)","-2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{e^{-x}+1}}{\sqrt{2}}\right)",1,"-2*Sqrt[2]*ArcTanh[Sqrt[1 + E^(-x)]/Sqrt[2]]","A",7,7,14,0.5000,1,"{2282, 12, 1446, 1469, 627, 63, 206}"
21,1,786,0,1.1165923,"\int \frac{1}{(\cos (x)+\cos (3 x))^5} \, dx","Int[(Cos[x] + Cos[3*x])^(-5),x]","\frac{451 \left(\tan \left(\frac{x}{2}\right)+1\right)}{512 \left(-\tan ^2\left(\frac{x}{2}\right)-2 \tan \left(\frac{x}{2}\right)+1\right)}-\frac{15 \tan \left(\frac{x}{2}\right)+89}{64 \left(-\tan ^2\left(\frac{x}{2}\right)-2 \tan \left(\frac{x}{2}\right)+1\right)}+\frac{89-15 \tan \left(\frac{x}{2}\right)}{64 \left(-\tan ^2\left(\frac{x}{2}\right)+2 \tan \left(\frac{x}{2}\right)+1\right)}-\frac{451 \left(1-\tan \left(\frac{x}{2}\right)\right)}{512 \left(-\tan ^2\left(\frac{x}{2}\right)+2 \tan \left(\frac{x}{2}\right)+1\right)}-\frac{1-43 \tan \left(\frac{x}{2}\right)}{32 \left(-\tan ^2\left(\frac{x}{2}\right)-2 \tan \left(\frac{x}{2}\right)+1\right)^2}-\frac{65 \left(\tan \left(\frac{x}{2}\right)+1\right)}{384 \left(-\tan ^2\left(\frac{x}{2}\right)-2 \tan \left(\frac{x}{2}\right)+1\right)^2}+\frac{65 \left(1-\tan \left(\frac{x}{2}\right)\right)}{384 \left(-\tan ^2\left(\frac{x}{2}\right)+2 \tan \left(\frac{x}{2}\right)+1\right)^2}+\frac{43 \tan \left(\frac{x}{2}\right)+1}{32 \left(-\tan ^2\left(\frac{x}{2}\right)+2 \tan \left(\frac{x}{2}\right)+1\right)^2}+\frac{119 \left(\tan \left(\frac{x}{2}\right)+1\right)}{48 \left(-\tan ^2\left(\frac{x}{2}\right)-2 \tan \left(\frac{x}{2}\right)+1\right)^3}-\frac{11 \left(3 \tan \left(\frac{x}{2}\right)+1\right)}{12 \left(-\tan ^2\left(\frac{x}{2}\right)-2 \tan \left(\frac{x}{2}\right)+1\right)^3}+\frac{11 \left(1-3 \tan \left(\frac{x}{2}\right)\right)}{12 \left(-\tan ^2\left(\frac{x}{2}\right)+2 \tan \left(\frac{x}{2}\right)+1\right)^3}-\frac{119 \left(1-\tan \left(\frac{x}{2}\right)\right)}{48 \left(-\tan ^2\left(\frac{x}{2}\right)+2 \tan \left(\frac{x}{2}\right)+1\right)^3}-\frac{7-17 \tan \left(\frac{x}{2}\right)}{4 \left(-\tan ^2\left(\frac{x}{2}\right)-2 \tan \left(\frac{x}{2}\right)+1\right)^4}+\frac{17 \tan \left(\frac{x}{2}\right)+7}{4 \left(-\tan ^2\left(\frac{x}{2}\right)+2 \tan \left(\frac{x}{2}\right)+1\right)^4}+\frac{45}{256 \left(1-\tan \left(\frac{x}{2}\right)\right)}-\frac{45}{256 \left(\tan \left(\frac{x}{2}\right)+1\right)}-\frac{47}{256 \left(1-\tan \left(\frac{x}{2}\right)\right)^2}+\frac{47}{256 \left(\tan \left(\frac{x}{2}\right)+1\right)^2}+\frac{1}{64 \left(1-\tan \left(\frac{x}{2}\right)\right)^3}-\frac{1}{64 \left(\tan \left(\frac{x}{2}\right)+1\right)^3}-\frac{1}{128 \left(1-\tan \left(\frac{x}{2}\right)\right)^4}+\frac{1}{128 \left(\tan \left(\frac{x}{2}\right)+1\right)^4}-\frac{523}{256} \tanh ^{-1}(\sin (x))-\frac{1483 \log \left(-\sqrt{2} \sin (x)-\sin (x)+\sqrt{2} \cos (x)+\cos (x)+\sqrt{2}+2\right)}{2048 \sqrt{2}}-\frac{1483 \log \left(-\sqrt{2} \sin (x)+\sin (x)-\sqrt{2} \cos (x)+\cos (x)-\sqrt{2}+2\right)}{2048 \sqrt{2}}+\frac{1483 \log \left(\sqrt{2} \sin (x)-\sin (x)-\sqrt{2} \cos (x)+\cos (x)-\sqrt{2}+2\right)}{2048 \sqrt{2}}+\frac{1483 \log \left(\sqrt{2} \sin (x)+\sin (x)+\sqrt{2} \cos (x)+\cos (x)+\sqrt{2}+2\right)}{2048 \sqrt{2}}","-\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,"(-523*ArcTanh[Sin[x]])/256 - (1483*Log[2 + Sqrt[2] + Cos[x] + Sqrt[2]*Cos[x] - Sin[x] - Sqrt[2]*Sin[x]])/(2048*Sqrt[2]) - (1483*Log[2 - Sqrt[2] + Cos[x] - Sqrt[2]*Cos[x] + Sin[x] - Sqrt[2]*Sin[x]])/(2048*Sqrt[2]) + (1483*Log[2 - Sqrt[2] + Cos[x] - Sqrt[2]*Cos[x] - Sin[x] + Sqrt[2]*Sin[x]])/(2048*Sqrt[2]) + (1483*Log[2 + Sqrt[2] + Cos[x] + Sqrt[2]*Cos[x] + Sin[x] + Sqrt[2]*Sin[x]])/(2048*Sqrt[2]) - 1/(128*(1 - Tan[x/2])^4) + 1/(64*(1 - Tan[x/2])^3) - 47/(256*(1 - Tan[x/2])^2) + 45/(256*(1 - Tan[x/2])) + 1/(128*(1 + Tan[x/2])^4) - 1/(64*(1 + Tan[x/2])^3) + 47/(256*(1 + Tan[x/2])^2) - 45/(256*(1 + Tan[x/2])) - (7 - 17*Tan[x/2])/(4*(1 - 2*Tan[x/2] - Tan[x/2]^2)^4) + (119*(1 + Tan[x/2]))/(48*(1 - 2*Tan[x/2] - Tan[x/2]^2)^3) - (11*(1 + 3*Tan[x/2]))/(12*(1 - 2*Tan[x/2] - Tan[x/2]^2)^3) - (1 - 43*Tan[x/2])/(32*(1 - 2*Tan[x/2] - Tan[x/2]^2)^2) - (65*(1 + Tan[x/2]))/(384*(1 - 2*Tan[x/2] - Tan[x/2]^2)^2) + (451*(1 + Tan[x/2]))/(512*(1 - 2*Tan[x/2] - Tan[x/2]^2)) - (89 + 15*Tan[x/2])/(64*(1 - 2*Tan[x/2] - Tan[x/2]^2)) + (7 + 17*Tan[x/2])/(4*(1 + 2*Tan[x/2] - Tan[x/2]^2)^4) + (11*(1 - 3*Tan[x/2]))/(12*(1 + 2*Tan[x/2] - Tan[x/2]^2)^3) - (119*(1 - Tan[x/2]))/(48*(1 + 2*Tan[x/2] - Tan[x/2]^2)^3) + (65*(1 - Tan[x/2]))/(384*(1 + 2*Tan[x/2] - Tan[x/2]^2)^2) + (1 + 43*Tan[x/2])/(32*(1 + 2*Tan[x/2] - Tan[x/2]^2)^2) + (89 - 15*Tan[x/2])/(64*(1 + 2*Tan[x/2] - Tan[x/2]^2)) - (451*(1 - Tan[x/2]))/(512*(1 + 2*Tan[x/2] - Tan[x/2]^2))","B",45,7,9,0.7778,0,"{12, 2073, 207, 638, 614, 618, 206}"
22,1,29,0,0.0201917,"\int \frac{1}{(1+\cos (x)+\sin (x))^2} \, dx","Int[(1 + Cos[x] + Sin[x])^(-2),x]","-\log \left(\tan \left(\frac{x}{2}\right)+1\right)-\frac{\cos (x)-\sin (x)}{\sin (x)+\cos (x)+1}","-\log \left(\tan \left(\frac{x}{2}\right)+1\right)-\frac{\cos (x)-\sin (x)}{\sin (x)+\cos (x)+1}",1,"-Log[1 + Tan[x/2]] - (Cos[x] - Sin[x])/(1 + Cos[x] + Sin[x])","A",3,3,8,0.3750,1,"{3129, 3124, 31}"
23,1,26,0,0.0134693,"\int \sqrt{1+\tanh (4 x)} \, dx","Int[Sqrt[1 + Tanh[4*x]],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{\tanh (4 x)+1}}{\sqrt{2}}\right)}{2 \sqrt{2}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{\tanh (4 x)+1}}{\sqrt{2}}\right)}{2 \sqrt{2}}",1,"ArcTanh[Sqrt[1 + Tanh[4*x]]/Sqrt[2]]/(2*Sqrt[2])","A",2,2,10,0.2000,1,"{3480, 206}"
24,1,147,0,0.6069288,"\int \frac{\tanh (x)}{\sqrt{e^x+e^{2 x}}} \, dx","Int[Tanh[x]/Sqrt[E^x + E^(2*x)],x]","\frac{2 \left(e^x+1\right)}{\sqrt{e^x+e^{2 x}}}-\frac{(1-i)^{3/2} \sqrt{e^x} \sqrt{e^x+1} \tanh ^{-1}\left(\frac{\sqrt{1-i} \sqrt{e^x}}{\sqrt{e^x+1}}\right)}{\sqrt{e^x+e^{2 x}}}-\frac{(1+i)^{3/2} \sqrt{e^x} \sqrt{e^x+1} \tanh ^{-1}\left(\frac{\sqrt{1+i} \sqrt{e^x}}{\sqrt{e^x+1}}\right)}{\sqrt{e^x+e^{2 x}}}","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,"(2*(1 + E^x))/Sqrt[E^x + E^(2*x)] - ((1 - I)^(3/2)*Sqrt[E^x]*Sqrt[1 + E^x]*ArcTanh[(Sqrt[1 - I]*Sqrt[E^x])/Sqrt[1 + E^x]])/Sqrt[E^x + E^(2*x)] - ((1 + I)^(3/2)*Sqrt[E^x]*Sqrt[1 + E^x]*ArcTanh[(Sqrt[1 + I]*Sqrt[E^x])/Sqrt[1 + E^x]])/Sqrt[E^x + E^(2*x)]","A",11,7,16,0.4375,1,"{2282, 6724, 1586, 6725, 94, 93, 208}"
25,1,40,0,0.0812508,"\int \sqrt{\text{sech}(x) \sinh (2 x)} \, dx","Int[Sqrt[Sech[x]*Sinh[2*x]],x]","\frac{2 i E\left(\left.\frac{\pi }{4}-\frac{i x}{2}\right|2\right) \sqrt{\sinh (2 x) \text{sech}(x)}}{\sqrt{i \sinh (x)}}","\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,"((2*I)*EllipticE[Pi/4 - (I/2)*x, 2]*Sqrt[Sech[x]*Sinh[2*x]])/Sqrt[I*Sinh[x]]","A",5,5,11,0.4545,1,"{4398, 4400, 4221, 4309, 2639}"
26,1,349,0,0.9760957,"\int \log \left(x^2+\sqrt{1-x^2}\right) \, dx","Int[Log[x^2 + Sqrt[1 - x^2]],x]","x \log \left(x^2+\sqrt{1-x^2}\right)+2 \sqrt{\frac{1}{5} \left(2+\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}{10} \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}{10} \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 \sqrt{\frac{1}{5} \left(\sqrt{5}-2\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)+2 \sqrt{\frac{1}{5} \left(2+\sqrt{5}\right)} \tan ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} x\right)-\sqrt{\frac{1}{10} \left(1+\sqrt{5}\right)} \tan ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} x\right)+\sqrt{\frac{1}{10} \left(\sqrt{5}-1\right)} \tanh ^{-1}\left(\sqrt{\frac{2}{\sqrt{5}-1}} x\right)+2 \sqrt{\frac{1}{5} \left(\sqrt{5}-2\right)} \tanh ^{-1}\left(\sqrt{\frac{2}{\sqrt{5}-1}} x\right)","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,"-2*x - ArcSin[x] - Sqrt[(1 + Sqrt[5])/10]*ArcTan[Sqrt[2/(1 + Sqrt[5])]*x] + 2*Sqrt[(2 + Sqrt[5])/5]*ArcTan[Sqrt[2/(1 + Sqrt[5])]*x] - Sqrt[(1 + Sqrt[5])/10]*ArcTan[(Sqrt[(1 + Sqrt[5])/2]*x)/Sqrt[1 - x^2]] + 2*Sqrt[(2 + Sqrt[5])/5]*ArcTan[(Sqrt[(1 + Sqrt[5])/2]*x)/Sqrt[1 - x^2]] + 2*Sqrt[(-2 + Sqrt[5])/5]*ArcTanh[Sqrt[2/(-1 + Sqrt[5])]*x] + Sqrt[(-1 + Sqrt[5])/10]*ArcTanh[Sqrt[2/(-1 + Sqrt[5])]*x] - 2*Sqrt[(-2 + Sqrt[5])/5]*ArcTanh[(Sqrt[(-1 + Sqrt[5])/2]*x)/Sqrt[1 - x^2]] - Sqrt[(-1 + Sqrt[5])/10]*ArcTanh[(Sqrt[(-1 + Sqrt[5])/2]*x)/Sqrt[1 - x^2]] + x*Log[x^2 + Sqrt[1 - x^2]]","A",31,12,16,0.7500,0,"{2548, 6742, 1293, 216, 1692, 377, 207, 203, 1166, 1130, 1174, 402}"
27,1,102,0,0.1462474,"\int \frac{\log \left(1+e^x\right)}{1+e^{2 x}} \, dx","Int[Log[1 + E^x]/(1 + E^(2*x)),x]","-\text{PolyLog}\left(2,-e^x\right)-\frac{1}{2} \text{PolyLog}\left(2,\left(\frac{1}{2}-\frac{i}{2}\right) \left(e^x+1\right)\right)-\frac{1}{2} \text{PolyLog}\left(2,\left(\frac{1}{2}+\frac{i}{2}\right) \left(e^x+1\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)","-\text{PolyLog}\left(2,-e^x\right)-\frac{1}{2} \text{PolyLog}\left(2,\left(\frac{1}{2}-\frac{i}{2}\right) \left(e^x+1\right)\right)-\frac{1}{2} \text{PolyLog}\left(2,\left(\frac{1}{2}+\frac{i}{2}\right) \left(e^x+1\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,"-(Log[(1/2 - I/2)*(I - E^x)]*Log[1 + E^x])/2 - (Log[(-1/2 - I/2)*(I + E^x)]*Log[1 + E^x])/2 - PolyLog[2, -E^x] - PolyLog[2, (1/2 - I/2)*(1 + E^x)]/2 - PolyLog[2, (1/2 + I/2)*(1 + E^x)]/2","A",12,10,16,0.6250,1,"{2282, 266, 36, 29, 31, 2416, 2391, 260, 2394, 2393}"
28,1,159,0,0.2028655,"\int \cosh (x) \log ^2\left(1+\cosh ^2(x)\right) \, dx","Int[Cosh[x]*Log[1 + Cosh[x]^2]^2,x]","4 i \sqrt{2} \text{PolyLog}\left(2,1-\frac{2 \sqrt{2}}{\sqrt{2}+i \sinh (x)}\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)","4 i \sqrt{2} \text{PolyLog}\left(2,1-\frac{2 \sqrt{2}}{\sqrt{2}+i \sinh (x)}\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,"-8*Sqrt[2]*ArcTan[Sinh[x]/Sqrt[2]] + (4*I)*Sqrt[2]*ArcTan[Sinh[x]/Sqrt[2]]^2 + 8*Sqrt[2]*ArcTan[Sinh[x]/Sqrt[2]]*Log[(2*Sqrt[2])/(Sqrt[2] + I*Sinh[x])] + 4*Sqrt[2]*ArcTan[Sinh[x]/Sqrt[2]]*Log[2 + Sinh[x]^2] + (4*I)*Sqrt[2]*PolyLog[2, 1 - (2*Sqrt[2])/(Sqrt[2] + I*Sinh[x])] + 8*Sinh[x] - 4*Log[2 + Sinh[x]^2]*Sinh[x] + Log[2 + Sinh[x]^2]^2*Sinh[x]","A",13,12,12,1.000,1,"{4358, 2450, 2476, 2448, 321, 203, 2470, 12, 4920, 4854, 2402, 2315}"
29,1,395,0,0.5369774,"\int \cosh (x) \log ^2\left(\cosh ^2(x)+\sinh (x)\right) \, dx","Int[Cosh[x]*Log[Cosh[x]^2 + Sinh[x]]^2,x]","-\left(1+i \sqrt{3}\right) \text{PolyLog}\left(2,-\frac{2 i \sinh (x)-\sqrt{3}+i}{2 \sqrt{3}}\right)-\left(1-i \sqrt{3}\right) \text{PolyLog}\left(2,\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)","-\left(1+i \sqrt{3}\right) \text{PolyLog}\left(2,-\frac{2 i \sinh (x)-\sqrt{3}+i}{2 \sqrt{3}}\right)-\left(1-i \sqrt{3}\right) \text{PolyLog}\left(2,\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,"-4*Sqrt[3]*ArcTan[(1 + 2*Sinh[x])/Sqrt[3]] - ((1 - I*Sqrt[3])*Log[1 - I*Sqrt[3] + 2*Sinh[x]]^2)/2 - (1 + I*Sqrt[3])*Log[((I/2)*(1 - I*Sqrt[3] + 2*Sinh[x]))/Sqrt[3]]*Log[1 + I*Sqrt[3] + 2*Sinh[x]] - ((1 + I*Sqrt[3])*Log[1 + I*Sqrt[3] + 2*Sinh[x]]^2)/2 - (1 - I*Sqrt[3])*Log[1 - I*Sqrt[3] + 2*Sinh[x]]*Log[((-I/2)*(1 + I*Sqrt[3] + 2*Sinh[x]))/Sqrt[3]] - 2*Log[1 + Sinh[x] + Sinh[x]^2] + (1 - I*Sqrt[3])*Log[1 - I*Sqrt[3] + 2*Sinh[x]]*Log[1 + Sinh[x] + Sinh[x]^2] + (1 + I*Sqrt[3])*Log[1 + I*Sqrt[3] + 2*Sinh[x]]*Log[1 + Sinh[x] + Sinh[x]^2] - (1 + I*Sqrt[3])*PolyLog[2, -(I - Sqrt[3] + (2*I)*Sinh[x])/(2*Sqrt[3])] - (1 - I*Sqrt[3])*PolyLog[2, (I + Sqrt[3] + (2*I)*Sinh[x])/(2*Sqrt[3])] + 8*Sinh[x] - 4*Log[1 + Sinh[x] + Sinh[x]^2]*Sinh[x] + Log[1 + Sinh[x] + Sinh[x]^2]^2*Sinh[x]","A",28,15,13,1.154,1,"{4358, 2523, 2528, 773, 634, 618, 204, 628, 2524, 2418, 2390, 2301, 2394, 2393, 2391}"
30,1,981,0,1.251688,"\int \frac{\log \left(x+\sqrt{1+x}\right)}{1+x^2} \, dx","Int[Log[x + Sqrt[1 + x]]/(1 + x^2),x]","\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{PolyLog}\left(2,\frac{2 \left(\sqrt{1-i}-\sqrt{x+1}\right)}{1+2 \sqrt{1-i}-\sqrt{5}}\right)-\frac{1}{2} i \text{PolyLog}\left(2,\frac{2 \left(\sqrt{1-i}-\sqrt{x+1}\right)}{1+2 \sqrt{1-i}+\sqrt{5}}\right)+\frac{1}{2} i \text{PolyLog}\left(2,\frac{2 \left(\sqrt{1+i}-\sqrt{x+1}\right)}{1+2 \sqrt{1+i}-\sqrt{5}}\right)+\frac{1}{2} i \text{PolyLog}\left(2,\frac{2 \left(\sqrt{1+i}-\sqrt{x+1}\right)}{1+2 \sqrt{1+i}+\sqrt{5}}\right)-\frac{1}{2} i \text{PolyLog}\left(2,-\frac{2 \left(\sqrt{x+1}+\sqrt{1-i}\right)}{1-2 \sqrt{1-i}-\sqrt{5}}\right)-\frac{1}{2} i \text{PolyLog}\left(2,-\frac{2 \left(\sqrt{x+1}+\sqrt{1-i}\right)}{1-2 \sqrt{1-i}+\sqrt{5}}\right)+\frac{1}{2} i \text{PolyLog}\left(2,-\frac{2 \left(\sqrt{x+1}+\sqrt{1+i}\right)}{1-2 \sqrt{1+i}-\sqrt{5}}\right)+\frac{1}{2} i \text{PolyLog}\left(2,-\frac{2 \left(\sqrt{x+1}+\sqrt{1+i}\right)}{1-2 \sqrt{1+i}+\sqrt{5}}\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{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{PolyLog}\left(2,\frac{2 \left(\sqrt{1-i}-\sqrt{x+1}\right)}{1+2 \sqrt{1-i}-\sqrt{5}}\right)-\frac{1}{2} i \text{PolyLog}\left(2,\frac{2 \left(\sqrt{1-i}-\sqrt{x+1}\right)}{1+2 \sqrt{1-i}+\sqrt{5}}\right)+\frac{1}{2} i \text{PolyLog}\left(2,\frac{2 \left(\sqrt{1+i}-\sqrt{x+1}\right)}{1+2 \sqrt{1+i}-\sqrt{5}}\right)+\frac{1}{2} i \text{PolyLog}\left(2,\frac{2 \left(\sqrt{1+i}-\sqrt{x+1}\right)}{1+2 \sqrt{1+i}+\sqrt{5}}\right)-\frac{1}{2} i \text{PolyLog}\left(2,-\frac{2 \left(\sqrt{x+1}+\sqrt{1-i}\right)}{1-2 \sqrt{1-i}-\sqrt{5}}\right)-\frac{1}{2} i \text{PolyLog}\left(2,-\frac{2 \left(\sqrt{x+1}+\sqrt{1-i}\right)}{1-2 \sqrt{1-i}+\sqrt{5}}\right)+\frac{1}{2} i \text{PolyLog}\left(2,-\frac{2 \left(\sqrt{x+1}+\sqrt{1+i}\right)}{1-2 \sqrt{1+i}-\sqrt{5}}\right)+\frac{1}{2} i \text{PolyLog}\left(2,-\frac{2 \left(\sqrt{x+1}+\sqrt{1+i}\right)}{1-2 \sqrt{1+i}+\sqrt{5}}\right)",1,"(I/2)*Log[Sqrt[1 - I] - Sqrt[1 + x]]*Log[x + Sqrt[1 + x]] - (I/2)*Log[Sqrt[1 + I] - Sqrt[1 + x]]*Log[x + Sqrt[1 + x]] + (I/2)*Log[Sqrt[1 - I] + Sqrt[1 + x]]*Log[x + Sqrt[1 + x]] - (I/2)*Log[Sqrt[1 + I] + Sqrt[1 + x]]*Log[x + Sqrt[1 + x]] - (I/2)*Log[Sqrt[1 - I] + Sqrt[1 + x]]*Log[(1 - Sqrt[5] + 2*Sqrt[1 + x])/(1 - 2*Sqrt[1 - I] - Sqrt[5])] - (I/2)*Log[Sqrt[1 - I] - Sqrt[1 + x]]*Log[(1 - Sqrt[5] + 2*Sqrt[1 + x])/(1 + 2*Sqrt[1 - I] - Sqrt[5])] + (I/2)*Log[Sqrt[1 + I] + Sqrt[1 + x]]*Log[(1 - Sqrt[5] + 2*Sqrt[1 + x])/(1 - 2*Sqrt[1 + I] - Sqrt[5])] + (I/2)*Log[Sqrt[1 + I] - Sqrt[1 + x]]*Log[(1 - Sqrt[5] + 2*Sqrt[1 + x])/(1 + 2*Sqrt[1 + I] - Sqrt[5])] - (I/2)*Log[Sqrt[1 - I] + Sqrt[1 + x]]*Log[(1 + Sqrt[5] + 2*Sqrt[1 + x])/(1 - 2*Sqrt[1 - I] + Sqrt[5])] - (I/2)*Log[Sqrt[1 - I] - Sqrt[1 + x]]*Log[(1 + Sqrt[5] + 2*Sqrt[1 + x])/(1 + 2*Sqrt[1 - I] + Sqrt[5])] + (I/2)*Log[Sqrt[1 + I] + Sqrt[1 + x]]*Log[(1 + Sqrt[5] + 2*Sqrt[1 + x])/(1 - 2*Sqrt[1 + I] + Sqrt[5])] + (I/2)*Log[Sqrt[1 + I] - Sqrt[1 + x]]*Log[(1 + Sqrt[5] + 2*Sqrt[1 + x])/(1 + 2*Sqrt[1 + I] + Sqrt[5])] - (I/2)*PolyLog[2, (2*(Sqrt[1 - I] - Sqrt[1 + x]))/(1 + 2*Sqrt[1 - I] - Sqrt[5])] - (I/2)*PolyLog[2, (2*(Sqrt[1 - I] - Sqrt[1 + x]))/(1 + 2*Sqrt[1 - I] + Sqrt[5])] + (I/2)*PolyLog[2, (2*(Sqrt[1 + I] - Sqrt[1 + x]))/(1 + 2*Sqrt[1 + I] - Sqrt[5])] + (I/2)*PolyLog[2, (2*(Sqrt[1 + I] - Sqrt[1 + x]))/(1 + 2*Sqrt[1 + I] + Sqrt[5])] - (I/2)*PolyLog[2, (-2*(Sqrt[1 - I] + Sqrt[1 + x]))/(1 - 2*Sqrt[1 - I] - Sqrt[5])] - (I/2)*PolyLog[2, (-2*(Sqrt[1 - I] + Sqrt[1 + x]))/(1 - 2*Sqrt[1 - I] + Sqrt[5])] + (I/2)*PolyLog[2, (-2*(Sqrt[1 + I] + Sqrt[1 + x]))/(1 - 2*Sqrt[1 + I] - Sqrt[5])] + (I/2)*PolyLog[2, (-2*(Sqrt[1 + I] + Sqrt[1 + x]))/(1 - 2*Sqrt[1 + I] + Sqrt[5])]","A",44,10,18,0.5556,1,"{2530, 1591, 203, 6741, 2528, 2524, 2418, 2394, 2393, 2391}"
31,1,555,0,0.7115063,"\int \frac{\log ^2\left(x+\sqrt{1+x}\right)}{(1+x)^2} \, dx","Int[Log[x + Sqrt[1 + x]]^2/(1 + x)^2,x]","6 \text{PolyLog}\left(2,-\frac{2 \sqrt{x+1}}{1+\sqrt{5}}\right)-\left(3+\sqrt{5}\right) \text{PolyLog}\left(2,-\frac{2 \sqrt{x+1}-\sqrt{5}+1}{2 \sqrt{5}}\right)-\left(3-\sqrt{5}\right) \text{PolyLog}\left(2,\frac{2 \sqrt{x+1}+\sqrt{5}+1}{2 \sqrt{5}}\right)-6 \text{PolyLog}\left(2,\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)","6 \text{PolyLog}\left(2,-\frac{2 \sqrt{x+1}}{1+\sqrt{5}}\right)-\left(3+\sqrt{5}\right) \text{PolyLog}\left(2,-\frac{2 \sqrt{x+1}-\sqrt{5}+1}{2 \sqrt{5}}\right)-\left(3-\sqrt{5}\right) \text{PolyLog}\left(2,\frac{2 \sqrt{x+1}+\sqrt{5}+1}{2 \sqrt{5}}\right)-6 \text{PolyLog}\left(2,\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,"Log[1 + x] + (2*Log[x + Sqrt[1 + x]])/Sqrt[1 + x] - 6*Log[Sqrt[1 + x]]*Log[x + Sqrt[1 + x]] - Log[x + Sqrt[1 + x]]^2/(1 + x) - (1 + Sqrt[5])*Log[1 - Sqrt[5] + 2*Sqrt[1 + x]] + 6*Log[(-1 + Sqrt[5])/2]*Log[1 - Sqrt[5] + 2*Sqrt[1 + x]] + (3 + Sqrt[5])*Log[x + Sqrt[1 + x]]*Log[1 - Sqrt[5] + 2*Sqrt[1 + x]] - ((3 + Sqrt[5])*Log[1 - Sqrt[5] + 2*Sqrt[1 + x]]^2)/2 - (1 - Sqrt[5])*Log[1 + Sqrt[5] + 2*Sqrt[1 + x]] + (3 - Sqrt[5])*Log[x + Sqrt[1 + x]]*Log[1 + Sqrt[5] + 2*Sqrt[1 + x]] - (3 - Sqrt[5])*Log[-(1 - Sqrt[5] + 2*Sqrt[1 + x])/(2*Sqrt[5])]*Log[1 + Sqrt[5] + 2*Sqrt[1 + x]] - ((3 - Sqrt[5])*Log[1 + Sqrt[5] + 2*Sqrt[1 + x]]^2)/2 - (3 + Sqrt[5])*Log[1 - Sqrt[5] + 2*Sqrt[1 + x]]*Log[(1 + Sqrt[5] + 2*Sqrt[1 + x])/(2*Sqrt[5])] + 6*Log[Sqrt[1 + x]]*Log[1 + (2*Sqrt[1 + x])/(1 + Sqrt[5])] + 6*PolyLog[2, (-2*Sqrt[1 + x])/(1 + Sqrt[5])] - (3 + Sqrt[5])*PolyLog[2, -(1 - Sqrt[5] + 2*Sqrt[1 + x])/(2*Sqrt[5])] - (3 - Sqrt[5])*PolyLog[2, (1 + Sqrt[5] + 2*Sqrt[1 + x])/(2*Sqrt[5])] - 6*PolyLog[2, 1 + (2*Sqrt[1 + x])/(1 - Sqrt[5])]","A",35,16,18,0.8889,1,"{2525, 2528, 800, 632, 31, 2524, 2357, 2316, 2315, 2317, 2391, 2418, 2390, 2301, 2394, 2393}"
32,1,313,0,0.3773842,"\int \frac{\log \left(x+\sqrt{1+x}\right)}{x} \, dx","Int[Log[x + Sqrt[1 + x]]/x,x]","-\text{PolyLog}\left(2,\frac{2 \left(1-\sqrt{x+1}\right)}{3-\sqrt{5}}\right)-\text{PolyLog}\left(2,\frac{2 \left(1-\sqrt{x+1}\right)}{3+\sqrt{5}}\right)-\text{PolyLog}\left(2,\frac{2 \left(\sqrt{x+1}+1\right)}{1-\sqrt{5}}\right)-\text{PolyLog}\left(2,\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)","-\text{PolyLog}\left(2,\frac{2 \left(1-\sqrt{x+1}\right)}{3-\sqrt{5}}\right)-\text{PolyLog}\left(2,\frac{2 \left(1-\sqrt{x+1}\right)}{3+\sqrt{5}}\right)-\text{PolyLog}\left(2,\frac{2 \left(\sqrt{x+1}+1\right)}{1-\sqrt{5}}\right)-\text{PolyLog}\left(2,\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,"Log[-1 + Sqrt[1 + x]]*Log[x + Sqrt[1 + x]] + Log[1 + Sqrt[1 + x]]*Log[x + Sqrt[1 + x]] - Log[-1 + Sqrt[1 + x]]*Log[(1 - Sqrt[5] + 2*Sqrt[1 + x])/(3 - Sqrt[5])] - Log[1 + Sqrt[1 + x]]*Log[-((1 - Sqrt[5] + 2*Sqrt[1 + x])/(1 + Sqrt[5]))] - Log[1 + Sqrt[1 + x]]*Log[-((1 + Sqrt[5] + 2*Sqrt[1 + x])/(1 - Sqrt[5]))] - Log[-1 + Sqrt[1 + x]]*Log[(1 + Sqrt[5] + 2*Sqrt[1 + x])/(3 + Sqrt[5])] - PolyLog[2, (2*(1 - Sqrt[1 + x]))/(3 - Sqrt[5])] - PolyLog[2, (2*(1 - Sqrt[1 + x]))/(3 + Sqrt[5])] - PolyLog[2, (2*(1 + Sqrt[1 + x]))/(1 - Sqrt[5])] - PolyLog[2, (2*(1 + Sqrt[1 + x]))/(1 + Sqrt[5])]","A",21,7,14,0.5000,1,"{2530, 2528, 2524, 2418, 2394, 2393, 2391}"
33,1,80,0,0.0832127,"\int \tan ^{-1}(2 \tan (x)) \, dx","Int[ArcTan[2*Tan[x]],x]","-\frac{1}{4} \text{PolyLog}\left(2,\frac{1}{3} e^{2 i x}\right)+\frac{1}{4} \text{PolyLog}\left(2,3 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))","-\frac{1}{4} \text{PolyLog}\left(2,\frac{1}{3} e^{2 i x}\right)+\frac{1}{4} \text{PolyLog}\left(2,3 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,"x*ArcTan[2*Tan[x]] + (I/2)*x*Log[1 - 3*E^((2*I)*x)] - (I/2)*x*Log[1 - E^((2*I)*x)/3] - PolyLog[2, E^((2*I)*x)/3]/4 + PolyLog[2, 3*E^((2*I)*x)]/4","A",7,4,5,0.8000,1,"{5167, 2190, 2279, 2391}"
34,1,57,0,0.075564,"\int \frac{\tan ^{-1}(x) \log (x)}{x} \, dx","Int[(ArcTan[x]*Log[x])/x,x]","-\frac{1}{2} i \text{PolyLog}(3,-i x)+\frac{1}{2} i \text{PolyLog}(3,i x)+\frac{1}{2} i \log (x) \text{PolyLog}(2,-i x)-\frac{1}{2} i \log (x) \text{PolyLog}(2,i x)","-\frac{1}{2} i \text{PolyLog}(3,-i x)+\frac{1}{2} i \text{PolyLog}(3,i x)+\frac{1}{2} i \log (x) \text{PolyLog}(2,-i x)-\frac{1}{2} i \log (x) \text{PolyLog}(2,i x)",1,"(I/2)*Log[x]*PolyLog[2, (-I)*x] - (I/2)*Log[x]*PolyLog[2, I*x] - (I/2)*PolyLog[3, (-I)*x] + (I/2)*PolyLog[3, I*x]","A",5,5,8,0.6250,1,"{4848, 2391, 5005, 2374, 6589}"
35,1,121,0,0.1094594,"\int \sqrt{1+x^2} \tan ^{-1}(x)^2 \, dx","Int[Sqrt[1 + x^2]*ArcTan[x]^2,x]","i \tan ^{-1}(x) \text{PolyLog}\left(2,-i e^{i \tan ^{-1}(x)}\right)-i \tan ^{-1}(x) \text{PolyLog}\left(2,i e^{i \tan ^{-1}(x)}\right)-\text{PolyLog}\left(3,-i e^{i \tan ^{-1}(x)}\right)+\text{PolyLog}\left(3,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)","i \tan ^{-1}(x) \text{PolyLog}\left(2,-i e^{i \tan ^{-1}(x)}\right)-i \tan ^{-1}(x) \text{PolyLog}\left(2,i e^{i \tan ^{-1}(x)}\right)-\text{PolyLog}\left(3,-i e^{i \tan ^{-1}(x)}\right)+\text{PolyLog}\left(3,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,"ArcSinh[x] - Sqrt[1 + x^2]*ArcTan[x] + (x*Sqrt[1 + x^2]*ArcTan[x]^2)/2 - I*ArcTan[E^(I*ArcTan[x])]*ArcTan[x]^2 + I*ArcTan[x]*PolyLog[2, (-I)*E^(I*ArcTan[x])] - I*ArcTan[x]*PolyLog[2, I*E^(I*ArcTan[x])] - PolyLog[3, (-I)*E^(I*ArcTan[x])] + PolyLog[3, I*E^(I*ArcTan[x])]","A",10,7,14,0.5000,1,"{4880, 4888, 4181, 2531, 2282, 6589, 215}"