1,1,51,0,0.0291379,"\int \sin ^{-1}(x) \log (x) \, dx","Int[ArcSin[x]*Log[x],x]","-2 \sqrt{1-x^2}+\sqrt{1-x^2} \log (x)+\tanh ^{-1}\left(\sqrt{1-x^2}\right)-x \sin ^{-1}(x)+x \log (x) \sin ^{-1}(x)","-2 \sqrt{1-x^2}+\sqrt{1-x^2} \log (x)+\tanh ^{-1}\left(\sqrt{1-x^2}\right)-x (1-\log (x)) \sin ^{-1}(x)",1,"-2*Sqrt[1 - x^2] - x*ArcSin[x] + ArcTanh[Sqrt[1 - x^2]] + Sqrt[1 - x^2]*Log[x] + x*ArcSin[x]*Log[x]","A",8,7,5,1.400,1,"{4619, 261, 2387, 266, 50, 63, 206}"
2,1,17,0,0.0284056,"\int \frac{x \sin ^{-1}(x)}{\sqrt{1-x^2}} \, dx","Int[(x*ArcSin[x])/Sqrt[1 - x^2],x]","x-\sqrt{1-x^2} \sin ^{-1}(x)","x-\sqrt{1-x^2} \sin ^{-1}(x)",1,"x - Sqrt[1 - x^2]*ArcSin[x]","A",2,2,15,0.1333,1,"{4677, 8}"
3,0,0,0,0.1531404,"\int -\sin ^{-1}\left(\sqrt{x}-\sqrt{1+x}\right) \, dx","Int[-ArcSin[Sqrt[x] - Sqrt[1 + x]],x]","\int -\sin ^{-1}\left(\sqrt{x}-\sqrt{1+x}\right) \, dx","\frac{\left(\sqrt{x}+3 \sqrt{x+1}\right) \sqrt{\sqrt{x} \sqrt{x+1}-x}}{4 \sqrt{2}}-\left(x+\frac{3}{8}\right) \sin ^{-1}\left(\sqrt{x}-\sqrt{x+1}\right)",1,"-(x*ArcSin[Sqrt[x] - Sqrt[1 + x]]) + Defer[Subst][Defer[Int][Sqrt[1 - x^2 + x*Sqrt[-1 + x^2]], x], x, Sqrt[1 + x]]/Sqrt[2]","F",0,0,0,0,-1,"{}"
4,1,332,0,0.6685735,"\int \log \left(1+x \sqrt{1+x^2}\right) \, dx","Int[Log[1 + x*Sqrt[1 + x^2]],x]","x \log \left(\sqrt{x^2+1} x+1\right)+\sqrt{\frac{2}{5} \left(\sqrt{5}-1\right)} \tan ^{-1}\left(\sqrt{\frac{2}{\sqrt{5}-1}} \sqrt{x^2+1}\right)+\sqrt{\frac{2}{5 \left(\sqrt{5}-1\right)}} \tan ^{-1}\left(\sqrt{\frac{2}{\sqrt{5}-1}} \sqrt{x^2+1}\right)-\sqrt{\frac{2}{5} \left(1+\sqrt{5}\right)} \tanh ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} \sqrt{x^2+1}\right)+\sqrt{\frac{2}{5 \left(1+\sqrt{5}\right)}} \tanh ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} \sqrt{x^2+1}\right)-2 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(\sqrt{x^2+1} x+1\right)+\sqrt{2 \left(1+\sqrt{5}\right)} \tan ^{-1}\left(\sqrt{\sqrt{5}-2} \left(\sqrt{x^2+1}+x\right)\right)-\sqrt{2 \left(\sqrt{5}-1\right)} \tanh ^{-1}\left(\sqrt{2+\sqrt{5}} \left(\sqrt{x^2+1}+x\right)\right)-2 x",1,"-2*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[2/(5*(-1 + Sqrt[5]))]*ArcTan[Sqrt[2/(-1 + Sqrt[5])]*Sqrt[1 + x^2]] + Sqrt[(2*(-1 + Sqrt[5]))/5]*ArcTan[Sqrt[2/(-1 + Sqrt[5])]*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] + Sqrt[2/(5*(1 + Sqrt[5]))]*ArcTanh[Sqrt[2/(1 + Sqrt[5])]*Sqrt[1 + x^2]] - Sqrt[(2*(1 + Sqrt[5]))/5]*ArcTanh[Sqrt[2/(1 + Sqrt[5])]*Sqrt[1 + x^2]] + x*Log[1 + x*Sqrt[1 + x^2]]","B",32,13,14,0.9286,0,"{2548, 6742, 261, 1130, 203, 207, 1251, 824, 707, 1093, 1166, 1247, 699}"
5,1,289,0,0.4911709,"\int \frac{\cos ^2(x)}{\sqrt{1+\cos ^2(x)+\cos ^4(x)}} \, dx","Int[Cos[x]^2/Sqrt[1 + Cos[x]^2 + Cos[x]^4],x]","\frac{\cos ^2(x) \tan ^{-1}\left(\frac{\tan (x)}{\sqrt{\tan ^4(x)+3 \tan ^2(x)+3}}\right) \sqrt{\tan ^4(x)+3 \tan ^2(x)+3}}{2 \sqrt{\cos ^4(x) \left(\tan ^4(x)+3 \tan ^2(x)+3\right)}}-\frac{\left(1+\sqrt{3}\right) \cos ^2(x) \left(\tan ^2(x)+\sqrt{3}\right) \sqrt{\frac{\tan ^4(x)+3 \tan ^2(x)+3}{\left(\tan ^2(x)+\sqrt{3}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\tan (x)}{\sqrt[4]{3}}\right)|\frac{1}{4} \left(2-\sqrt{3}\right)\right)}{4 \sqrt[4]{3} \sqrt{\cos ^4(x) \left(\tan ^4(x)+3 \tan ^2(x)+3\right)}}+\frac{\left(2+\sqrt{3}\right) \cos ^2(x) \left(\tan ^2(x)+\sqrt{3}\right) \sqrt{\frac{\tan ^4(x)+3 \tan ^2(x)+3}{\left(\tan ^2(x)+\sqrt{3}\right)^2}} \Pi \left(\frac{1}{6} \left(3-2 \sqrt{3}\right);2 \tan ^{-1}\left(\frac{\tan (x)}{\sqrt[4]{3}}\right)|\frac{1}{4} \left(2-\sqrt{3}\right)\right)}{4 \sqrt[4]{3} \sqrt{\cos ^4(x) \left(\tan ^4(x)+3 \tan ^2(x)+3\right)}}","\frac{x}{3}+\frac{1}{3} \tan ^{-1}\left(\frac{\sin (x) \cos (x) \left(\cos ^2(x)+1\right)}{\sqrt{\cos ^4(x)+\cos ^2(x)+1} \cos ^2(x)+1}\right)",1,"(ArcTan[Tan[x]/Sqrt[3 + 3*Tan[x]^2 + Tan[x]^4]]*Cos[x]^2*Sqrt[3 + 3*Tan[x]^2 + Tan[x]^4])/(2*Sqrt[Cos[x]^4*(3 + 3*Tan[x]^2 + Tan[x]^4)]) - ((1 + Sqrt[3])*Cos[x]^2*EllipticF[2*ArcTan[Tan[x]/3^(1/4)], (2 - Sqrt[3])/4]*(Sqrt[3] + Tan[x]^2)*Sqrt[(3 + 3*Tan[x]^2 + Tan[x]^4)/(Sqrt[3] + Tan[x]^2)^2])/(4*3^(1/4)*Sqrt[Cos[x]^4*(3 + 3*Tan[x]^2 + Tan[x]^4)]) + ((2 + Sqrt[3])*Cos[x]^2*EllipticPi[(3 - 2*Sqrt[3])/6, 2*ArcTan[Tan[x]/3^(1/4)], (2 - Sqrt[3])/4]*(Sqrt[3] + Tan[x]^2)*Sqrt[(3 + 3*Tan[x]^2 + Tan[x]^4)/(Sqrt[3] + Tan[x]^2)^2])/(4*3^(1/4)*Sqrt[Cos[x]^4*(3 + 3*Tan[x]^2 + Tan[x]^4)])","C",5,4,19,0.2105,0,"{6719, 1216, 1103, 1706}"
6,1,56,0,0.068675,"\int \tan (x) \sqrt{1+\tan ^4(x)} \, dx","Int[Tan[x]*Sqrt[1 + Tan[x]^4],x]","\frac{1}{2} \sqrt{\tan ^4(x)+1}-\frac{\tanh ^{-1}\left(\frac{1-\tan ^2(x)}{\sqrt{2} \sqrt{\tan ^4(x)+1}}\right)}{\sqrt{2}}-\frac{1}{2} \sinh ^{-1}\left(\tan ^2(x)\right)","\frac{1}{2} \sqrt{\tan ^4(x)+1}-\frac{\tanh ^{-1}\left(\frac{1-\tan ^2(x)}{\sqrt{2} \sqrt{\tan ^4(x)+1}}\right)}{\sqrt{2}}-\frac{1}{2} \sinh ^{-1}\left(\tan ^2(x)\right)",1,"-ArcSinh[Tan[x]^2]/2 - ArcTanh[(1 - Tan[x]^2)/(Sqrt[2]*Sqrt[1 + Tan[x]^4])]/Sqrt[2] + Sqrt[1 + Tan[x]^4]/2","A",7,7,13,0.5385,1,"{3670, 1248, 735, 844, 215, 725, 206}"
7,1,15,0,0.0309224,"\int \frac{\tan (x)}{\sqrt{1+\sec ^3(x)}} \, dx","Int[Tan[x]/Sqrt[1 + Sec[x]^3],x]","-\frac{2}{3} \tanh ^{-1}\left(\sqrt{\sec ^3(x)+1}\right)","-\frac{2}{3} \tanh ^{-1}\left(\sqrt{\sec ^3(x)+1}\right)",1,"(-2*ArcTanh[Sqrt[1 + Sec[x]^3]])/3","A",4,4,13,0.3077,1,"{4139, 266, 63, 207}"
8,1,137,0,0.1803865,"\int \sqrt{2+2 \tan (x)+\tan ^2(x)} \, dx","Int[Sqrt[2 + 2*Tan[x] + Tan[x]^2],x]","-\sqrt{\frac{1}{2} \left(1+\sqrt{5}\right)} \tan ^{-1}\left(\frac{2 \sqrt{5}-\left(5+\sqrt{5}\right) \tan (x)}{\sqrt{10 \left(1+\sqrt{5}\right)} \sqrt{\tan ^2(x)+2 \tan (x)+2}}\right)-\sqrt{\frac{1}{2} \left(\sqrt{5}-1\right)} \tanh ^{-1}\left(\frac{\left(5-\sqrt{5}\right) \tan (x)+2 \sqrt{5}}{\sqrt{10 \left(\sqrt{5}-1\right)} \sqrt{\tan ^2(x)+2 \tan (x)+2}}\right)+\sinh ^{-1}(\tan (x)+1)","-\sqrt{\frac{1}{2} \left(1+\sqrt{5}\right)} \tan ^{-1}\left(\frac{2 \sqrt{5}-\left(5+\sqrt{5}\right) \tan (x)}{\sqrt{10 \left(1+\sqrt{5}\right)} \sqrt{\tan ^2(x)+2 \tan (x)+2}}\right)-\sqrt{\frac{1}{2} \left(\sqrt{5}-1\right)} \tanh ^{-1}\left(\frac{\left(5-\sqrt{5}\right) \tan (x)+2 \sqrt{5}}{\sqrt{10 \left(\sqrt{5}-1\right)} \sqrt{\tan ^2(x)+2 \tan (x)+2}}\right)+\sinh ^{-1}(\tan (x)+1)",1,"ArcSinh[1 + Tan[x]] - Sqrt[(1 + Sqrt[5])/2]*ArcTan[(2*Sqrt[5] - (5 + Sqrt[5])*Tan[x])/(Sqrt[10*(1 + Sqrt[5])]*Sqrt[2 + 2*Tan[x] + Tan[x]^2])] - Sqrt[(-1 + Sqrt[5])/2]*ArcTanh[(2*Sqrt[5] + (5 - Sqrt[5])*Tan[x])/(Sqrt[10*(-1 + Sqrt[5])]*Sqrt[2 + 2*Tan[x] + Tan[x]^2])]","A",9,7,14,0.5000,1,"{990, 619, 215, 1036, 1030, 207, 203}"
9,1,41,0,0.0224725,"\int \tan ^{-1}\left(\sqrt{-1+\sec (x)}\right) \sin (x) \, dx","Int[ArcTan[Sqrt[-1 + Sec[x]]]*Sin[x],x]","\frac{1}{2} \cos (x) \sqrt{\sec (x)-1}+\frac{1}{2} \tan ^{-1}\left(\sqrt{\sec (x)-1}\right)-\cos (x) \tan ^{-1}\left(\sqrt{\sec (x)-1}\right)","\frac{1}{2} \cos (x) \sqrt{\sec (x)-1}+\frac{1}{2} \tan ^{-1}\left(\sqrt{\sec (x)-1}\right)-\cos (x) \tan ^{-1}\left(\sqrt{\sec (x)-1}\right)",1,"ArcTan[Sqrt[-1 + Sec[x]]]/2 - ArcTan[Sqrt[-1 + Sec[x]]]*Cos[x] + (Cos[x]*Sqrt[-1 + Sec[x]])/2","A",7,7,12,0.5833,1,"{4335, 5203, 12, 242, 51, 63, 203}"
10,1,62,0,0.67604,"\int \frac{e^{\sin ^{-1}(x)} x^3}{\sqrt{1-x^2}} \, dx","Int[(E^ArcSin[x]*x^3)/Sqrt[1 - x^2],x]","\frac{1}{10} x^3 e^{\sin ^{-1}(x)}-\frac{3}{10} \sqrt{1-x^2} x^2 e^{\sin ^{-1}(x)}-\frac{3}{10} \sqrt{1-x^2} e^{\sin ^{-1}(x)}+\frac{3}{10} x e^{\sin ^{-1}(x)}","\frac{1}{10} \left(x^3-3 \sqrt{1-x^2} x^2-3 \sqrt{1-x^2}+3 x\right) e^{\sin ^{-1}(x)}",1,"(3*E^ArcSin[x]*x)/10 + (E^ArcSin[x]*x^3)/10 - (3*E^ArcSin[x]*Sqrt[1 - x^2])/10 - (3*E^ArcSin[x]*x^2*Sqrt[1 - x^2])/10","A",5,5,19,0.2632,1,"{4836, 6741, 6720, 4434, 4432}"
11,1,68,0,0.1464237,"\int \frac{x \log \left(1+x^2\right) \log \left(x+\sqrt{1+x^2}\right)}{\sqrt{1+x^2}} \, dx","Int[(x*Log[1 + x^2]*Log[x + Sqrt[1 + x^2]])/Sqrt[1 + x^2],x]","x \left(-\log \left(x^2+1\right)\right)+\sqrt{x^2+1} \log \left(x^2+1\right) \log \left(\sqrt{x^2+1}+x\right)-2 \sqrt{x^2+1} \log \left(\sqrt{x^2+1}+x\right)+4 x-2 \tan ^{-1}(x)","x \left(-\log \left(x^2+1\right)\right)+\sqrt{x^2+1} \log \left(x^2+1\right) \log \left(\sqrt{x^2+1}+x\right)-2 \sqrt{x^2+1} \log \left(\sqrt{x^2+1}+x\right)+4 x-2 \tan ^{-1}(x)",1,"4*x - 2*ArcTan[x] - x*Log[1 + x^2] - 2*Sqrt[1 + x^2]*Log[x + Sqrt[1 + x^2]] + Sqrt[1 + x^2]*Log[1 + x^2]*Log[x + Sqrt[1 + x^2]]","A",7,8,29,0.2759,1,"{261, 2554, 8, 2557, 12, 2448, 321, 203}"
12,1,269,0,0.7459925,"\int \tan ^{-1}\left(x+\sqrt{1-x^2}\right) \, dx","Int[ArcTan[x + Sqrt[1 - x^2]],x]","-\frac{1}{8} \log \left(x^4-x^2+1\right)+\frac{1}{4} \sqrt{3} \tan ^{-1}\left(\frac{1-2 x^2}{\sqrt{3}}\right)+\frac{1}{12} \left(-\sqrt{3}+3 i\right) \tan ^{-1}\left(\frac{x}{\sqrt{-\frac{-\sqrt{3}+i}{\sqrt{3}+i}} \sqrt{1-x^2}}\right)+\frac{\tan ^{-1}\left(\frac{x}{\sqrt{-\frac{-\sqrt{3}+i}{\sqrt{3}+i}} \sqrt{1-x^2}}\right)}{\sqrt{3}}-\frac{1}{12} \left(\sqrt{3}+3 i\right) \tan ^{-1}\left(\frac{\sqrt{-\frac{-\sqrt{3}+i}{\sqrt{3}+i}} x}{\sqrt{1-x^2}}\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{-\frac{-\sqrt{3}+i}{\sqrt{3}+i}} x}{\sqrt{1-x^2}}\right)}{\sqrt{3}}+x \tan ^{-1}\left(\sqrt{1-x^2}+x\right)-\frac{1}{2} \sin ^{-1}(x)","-\frac{1}{8} \log \left(x^4-x^2+1\right)+\frac{1}{4} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x-1}{\sqrt{1-x^2}}\right)+\frac{1}{4} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x+1}{\sqrt{1-x^2}}\right)-\frac{1}{4} \sqrt{3} \tan ^{-1}\left(\frac{2 x^2-1}{\sqrt{3}}\right)+x \tan ^{-1}\left(\sqrt{1-x^2}+x\right)-\frac{1}{4} \tanh ^{-1}\left(x \sqrt{1-x^2}\right)-\frac{1}{2} \sin ^{-1}(x)",1,"-ArcSin[x]/2 + (Sqrt[3]*ArcTan[(1 - 2*x^2)/Sqrt[3]])/4 + ArcTan[x/(Sqrt[-((I - Sqrt[3])/(I + Sqrt[3]))]*Sqrt[1 - x^2])]/Sqrt[3] + ((3*I - Sqrt[3])*ArcTan[x/(Sqrt[-((I - Sqrt[3])/(I + Sqrt[3]))]*Sqrt[1 - x^2])])/12 + ArcTan[(Sqrt[-((I - Sqrt[3])/(I + Sqrt[3]))]*x)/Sqrt[1 - x^2]]/Sqrt[3] - ((3*I + Sqrt[3])*ArcTan[(Sqrt[-((I - Sqrt[3])/(I + Sqrt[3]))]*x)/Sqrt[1 - x^2]])/12 + x*ArcTan[x + Sqrt[1 - x^2]] - Log[1 - x^2 + x^4]/8","C",40,15,14,1.071,0,"{5203, 12, 6742, 216, 1114, 634, 618, 204, 628, 1174, 402, 377, 205, 1293, 1107}"
13,1,286,0,0.4565323,"\int \frac{x \tan ^{-1}\left(x+\sqrt{1-x^2}\right)}{\sqrt{1-x^2}} \, dx","Int[(x*ArcTan[x + Sqrt[1 - x^2]])/Sqrt[1 - x^2],x]","\frac{1}{8} \log \left(x^4-x^2+1\right)+\frac{1}{4} \sqrt{3} \tan ^{-1}\left(\frac{1-2 x^2}{\sqrt{3}}\right)-\frac{1}{12} \left(-\sqrt{3}+3 i\right) \tan ^{-1}\left(\frac{x}{\sqrt{-\frac{-\sqrt{3}+i}{\sqrt{3}+i}} \sqrt{1-x^2}}\right)+\frac{\tan ^{-1}\left(\frac{x}{\sqrt{-\frac{-\sqrt{3}+i}{\sqrt{3}+i}} \sqrt{1-x^2}}\right)}{2 \sqrt{3}}+\frac{1}{12} \left(\sqrt{3}+3 i\right) \tan ^{-1}\left(\frac{\sqrt{-\frac{-\sqrt{3}+i}{\sqrt{3}+i}} x}{\sqrt{1-x^2}}\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{-\frac{-\sqrt{3}+i}{\sqrt{3}+i}} x}{\sqrt{1-x^2}}\right)}{2 \sqrt{3}}-\sqrt{1-x^2} \tan ^{-1}\left(\sqrt{1-x^2}+x\right)-\frac{1}{2} \sin ^{-1}(x)","\frac{1}{8} \log \left(x^4-x^2+1\right)+\frac{1}{4} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x-1}{\sqrt{1-x^2}}\right)+\frac{1}{4} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x+1}{\sqrt{1-x^2}}\right)-\frac{1}{4} \sqrt{3} \tan ^{-1}\left(\frac{2 x^2-1}{\sqrt{3}}\right)-\sqrt{1-x^2} \tan ^{-1}\left(\sqrt{1-x^2}+x\right)+\frac{1}{4} \tanh ^{-1}\left(x \sqrt{1-x^2}\right)-\frac{1}{2} \sin ^{-1}(x)",1,"-ArcSin[x]/2 + (Sqrt[3]*ArcTan[(1 - 2*x^2)/Sqrt[3]])/4 + ArcTan[x/(Sqrt[-((I - Sqrt[3])/(I + Sqrt[3]))]*Sqrt[1 - x^2])]/(2*Sqrt[3]) - ((3*I - Sqrt[3])*ArcTan[x/(Sqrt[-((I - Sqrt[3])/(I + Sqrt[3]))]*Sqrt[1 - x^2])])/12 + ArcTan[(Sqrt[-((I - Sqrt[3])/(I + Sqrt[3]))]*x)/Sqrt[1 - x^2]]/(2*Sqrt[3]) + ((3*I + Sqrt[3])*ArcTan[(Sqrt[-((I - Sqrt[3])/(I + Sqrt[3]))]*x)/Sqrt[1 - x^2]])/12 - Sqrt[1 - x^2]*ArcTan[x + Sqrt[1 - x^2]] + Log[1 - x^2 + x^4]/8","C",32,16,27,0.5926,0,"{261, 5207, 12, 6742, 1107, 618, 204, 1293, 216, 1174, 377, 205, 402, 1247, 634, 628}"
14,1,51,0,0.1213298,"\int \frac{\sin ^{-1}(x)}{1+\sqrt{1-x^2}} \, dx","Int[ArcSin[x]/(1 + Sqrt[1 - x^2]),x]","\frac{\sqrt{1-x^2} \sin ^{-1}(x)}{x}-\tanh ^{-1}\left(\sqrt{1-x^2}\right)-\log (x)+\frac{1}{2} \sin ^{-1}(x)^2-\frac{\sin ^{-1}(x)}{x}","-\log \left(\sqrt{1-x^2}+1\right)-\frac{x \sin ^{-1}(x)}{\sqrt{1-x^2}+1}+\frac{1}{2} \sin ^{-1}(x)^2",1,"-(ArcSin[x]/x) + (Sqrt[1 - x^2]*ArcSin[x])/x + ArcSin[x]^2/2 - ArcTanh[Sqrt[1 - x^2]] - Log[x]","A",9,11,18,0.6111,1,"{6742, 277, 216, 4791, 4627, 266, 63, 206, 4693, 29, 4641}"
15,1,34,0,0.0352362,"\int \frac{\log \left(x+\sqrt{1+x^2}\right)}{\left(1-x^2\right)^{3/2}} \, dx","Int[Log[x + Sqrt[1 + x^2]]/(1 - x^2)^(3/2),x]","\frac{x \log \left(\sqrt{x^2+1}+x\right)}{\sqrt{1-x^2}}-\frac{1}{2} \sin ^{-1}\left(x^2\right)","\frac{x \log \left(\sqrt{x^2+1}+x\right)}{\sqrt{1-x^2}}-\frac{1}{2} \sin ^{-1}\left(x^2\right)",1,"-ArcSin[x^2]/2 + (x*Log[x + Sqrt[1 + x^2]])/Sqrt[1 - x^2]","A",3,4,24,0.1667,1,"{191, 2554, 275, 216}"
16,1,22,0,0.0197991,"\int \frac{\sin ^{-1}(x)}{\left(1+x^2\right)^{3/2}} \, dx","Int[ArcSin[x]/(1 + x^2)^(3/2),x]","\frac{x \sin ^{-1}(x)}{\sqrt{x^2+1}}-\frac{1}{2} \sin ^{-1}\left(x^2\right)","\frac{x \sin ^{-1}(x)}{\sqrt{x^2+1}}-\frac{1}{2} \sin ^{-1}\left(x^2\right)",1,"(x*ArcSin[x])/Sqrt[1 + x^2] - ArcSin[x^2]/2","A",3,4,12,0.3333,1,"{191, 4665, 275, 216}"
17,1,32,0,0.0406656,"\int \frac{\log \left(x+\sqrt{-1+x^2}\right)}{\left(1+x^2\right)^{3/2}} \, dx","Int[Log[x + Sqrt[-1 + x^2]]/(1 + x^2)^(3/2),x]","\frac{x \log \left(\sqrt{x^2-1}+x\right)}{\sqrt{x^2+1}}-\frac{1}{2} \cosh ^{-1}\left(x^2\right)","\frac{x \log \left(\sqrt{x^2-1}+x\right)}{\sqrt{x^2+1}}-\frac{1}{2} \cosh ^{-1}\left(x^2\right)",1,"-ArcCosh[x^2]/2 + (x*Log[x + Sqrt[-1 + x^2]])/Sqrt[1 + x^2]","A",3,4,22,0.1818,1,"{191, 2554, 276, 52}"
18,1,43,0,0.044734,"\int \frac{\log (x)}{x^2 \sqrt{-1+x^2}} \, dx","Int[Log[x]/(x^2*Sqrt[-1 + x^2]),x]","\frac{\sqrt{x^2-1}}{x}+\frac{\sqrt{x^2-1} \log (x)}{x}-\tanh ^{-1}\left(\frac{x}{\sqrt{x^2-1}}\right)","\frac{\sqrt{x^2-1}}{x}+\frac{\sqrt{x^2-1} \log (x)}{x}-\tanh ^{-1}\left(\frac{x}{\sqrt{x^2-1}}\right)",1,"Sqrt[-1 + x^2]/x - ArcTanh[x/Sqrt[-1 + x^2]] + (Sqrt[-1 + x^2]*Log[x])/x","A",4,4,15,0.2667,1,"{2335, 277, 217, 206}"
19,1,28,0,0.0094395,"\int \frac{\sqrt{1+x^3}}{x} \, dx","Int[Sqrt[1 + x^3]/x,x]","\frac{2 \sqrt{x^3+1}}{3}-\frac{2}{3} \tanh ^{-1}\left(\sqrt{x^3+1}\right)","\frac{2 \sqrt{x^3+1}}{3}-\frac{2}{3} \tanh ^{-1}\left(\sqrt{x^3+1}\right)",1,"(2*Sqrt[1 + x^3])/3 - (2*ArcTanh[Sqrt[1 + x^3]])/3","A",4,4,13,0.3077,1,"{266, 50, 63, 207}"
20,1,26,0,0.0360943,"\int \frac{x \log \left(x+\sqrt{-1+x^2}\right)}{\sqrt{-1+x^2}} \, dx","Int[(x*Log[x + Sqrt[-1 + x^2]])/Sqrt[-1 + x^2],x]","\sqrt{x^2-1} \log \left(\sqrt{x^2-1}+x\right)-x","\sqrt{x^2-1} \log \left(\sqrt{x^2-1}+x\right)-x",1,"-x + Sqrt[-1 + x^2]*Log[x + Sqrt[-1 + x^2]]","A",2,3,23,0.1304,1,"{261, 2554, 8}"
21,1,38,0,0.0524984,"\int \frac{x^3 \sin ^{-1}(x)}{\sqrt{1-x^4}} \, dx","Int[(x^3*ArcSin[x])/Sqrt[1 - x^4],x]","\frac{1}{4} \sqrt{x^2+1} x-\frac{1}{2} \sqrt{1-x^4} \sin ^{-1}(x)+\frac{1}{4} \sinh ^{-1}(x)","\frac{1}{4} \sqrt{x^2+1} x-\frac{1}{2} \sqrt{1-x^4} \sin ^{-1}(x)+\frac{1}{4} \sinh ^{-1}(x)",1,"(x*Sqrt[1 + x^2])/4 - (Sqrt[1 - x^4]*ArcSin[x])/2 + ArcSinh[x]/4","A",5,6,17,0.3529,1,"{261, 4787, 12, 26, 195, 215}"
22,1,94,0,0.1320219,"\int \frac{x^3 \sec ^{-1}(x)}{\sqrt{-1+x^4}} \, dx","Int[(x^3*ArcSec[x])/Sqrt[-1 + x^4],x]","-\frac{\sqrt{x^4-1}}{2 \sqrt{1-\frac{1}{x^2}} x}+\frac{\sqrt{1-x^2} \tan ^{-1}\left(\frac{\sqrt{x^4-1}}{\sqrt{1-x^2}}\right)}{2 \sqrt{1-\frac{1}{x^2}} x}+\frac{1}{2} \sqrt{x^4-1} \sec ^{-1}(x)","-\frac{\sqrt{x^4-1}}{2 \sqrt{1-\frac{1}{x^2}} x}+\frac{1}{2} \sqrt{x^4-1} \sec ^{-1}(x)+\frac{1}{2} \tanh ^{-1}\left(\frac{\sqrt{1-\frac{1}{x^2}} x}{\sqrt{x^4-1}}\right)",1,"-Sqrt[-1 + x^4]/(2*Sqrt[1 - x^(-2)]*x) + (Sqrt[-1 + x^4]*ArcSec[x])/2 + (Sqrt[1 - x^2]*ArcTan[Sqrt[-1 + x^4]/Sqrt[1 - x^2]])/(2*Sqrt[1 - x^(-2)]*x)","A",7,8,15,0.5333,1,"{261, 5246, 12, 1572, 1252, 865, 875, 203}"
23,1,58,0,0.1417653,"\int \frac{x \tan ^{-1}(x) \log \left(x+\sqrt{1+x^2}\right)}{\sqrt{1+x^2}} \, dx","Int[(x*ArcTan[x]*Log[x + Sqrt[1 + x^2]])/Sqrt[1 + x^2],x]","-\frac{1}{2} \log ^2\left(\sqrt{x^2+1}+x\right)+\frac{1}{2} \log \left(x^2+1\right)+\sqrt{x^2+1} \log \left(\sqrt{x^2+1}+x\right) \tan ^{-1}(x)-x \tan ^{-1}(x)","-\frac{1}{2} \log ^2\left(\sqrt{x^2+1}+x\right)+\frac{1}{2} \log \left(x^2+1\right)+\sqrt{x^2+1} \log \left(\sqrt{x^2+1}+x\right) \tan ^{-1}(x)-x \tan ^{-1}(x)",1,"-(x*ArcTan[x]) + Log[1 + x^2]/2 + Sqrt[1 + x^2]*ArcTan[x]*Log[x + Sqrt[1 + x^2]] - Log[x + Sqrt[1 + x^2]]^2/2","A",4,9,25,0.3600,1,"{4930, 215, 261, 2554, 8, 5212, 6686, 4846, 260}"
24,1,55,0,0.0533209,"\int \frac{x \log \left(1+\sqrt{1-x^2}\right)}{\sqrt{1-x^2}} \, dx","Int[(x*Log[1 + Sqrt[1 - x^2]])/Sqrt[1 - x^2],x]","\sqrt{1-x^2}-\sqrt{1-x^2} \log \left(\sqrt{1-x^2}+1\right)-\log \left(\sqrt{1-x^2}+1\right)","\sqrt{1-x^2}-\sqrt{1-x^2} \log \left(\sqrt{1-x^2}+1\right)-\log \left(\sqrt{1-x^2}+1\right)",1,"Sqrt[1 - x^2] - Log[1 + Sqrt[1 - x^2]] - Sqrt[1 - x^2]*Log[1 + Sqrt[1 - x^2]]","A",5,5,27,0.1852,1,"{261, 2554, 1591, 190, 43}"
25,1,26,0,0.0332712,"\int \frac{x \log \left(x+\sqrt{1+x^2}\right)}{\sqrt{1+x^2}} \, dx","Int[(x*Log[x + Sqrt[1 + x^2]])/Sqrt[1 + x^2],x]","\sqrt{x^2+1} \log \left(\sqrt{x^2+1}+x\right)-x","\sqrt{x^2+1} \log \left(\sqrt{x^2+1}+x\right)-x",1,"-x + Sqrt[1 + x^2]*Log[x + Sqrt[1 + x^2]]","A",2,3,23,0.1304,1,"{261, 2554, 8}"
26,1,78,0,0.2710995,"\int \frac{x \log \left(x+\sqrt{1-x^2}\right)}{\sqrt{1-x^2}} \, dx","Int[(x*Log[x + Sqrt[1 - x^2]])/Sqrt[1 - x^2],x]","\sqrt{1-x^2}-\sqrt{1-x^2} \log \left(\sqrt{1-x^2}+x\right)-\frac{\tanh ^{-1}\left(\sqrt{2} \sqrt{1-x^2}\right)}{\sqrt{2}}+\frac{\tanh ^{-1}\left(\sqrt{2} x\right)}{\sqrt{2}}","\sqrt{1-x^2}-\sqrt{1-x^2} \log \left(\sqrt{1-x^2}+x\right)-\frac{\tanh ^{-1}\left(\sqrt{2} \sqrt{1-x^2}\right)}{\sqrt{2}}+\frac{\tanh ^{-1}\left(\sqrt{2} x\right)}{\sqrt{2}}",1,"Sqrt[1 - x^2] + ArcTanh[Sqrt[2]*x]/Sqrt[2] - ArcTanh[Sqrt[2]*Sqrt[1 - x^2]]/Sqrt[2] - Sqrt[1 - x^2]*Log[x + Sqrt[1 - x^2]]","A",18,11,27,0.4074,1,"{261, 2554, 6742, 2107, 321, 206, 444, 50, 63, 207, 388}"
27,1,39,0,0.0483891,"\int \frac{\log (x)}{x^2 \sqrt{1-x^2}} \, dx","Int[Log[x]/(x^2*Sqrt[1 - x^2]),x]","-\frac{\sqrt{1-x^2}}{x}-\frac{\sqrt{1-x^2} \log (x)}{x}-\sin ^{-1}(x)","-\frac{\sqrt{1-x^2}}{x}-\frac{\sqrt{1-x^2} \log (x)}{x}-\sin ^{-1}(x)",1,"-(Sqrt[1 - x^2]/x) - ArcSin[x] - (Sqrt[1 - x^2]*Log[x])/x","A",3,3,17,0.1765,1,"{2335, 277, 216}"
28,1,17,0,0.0280095,"\int \frac{x \tan ^{-1}(x)}{\sqrt{1+x^2}} \, dx","Int[(x*ArcTan[x])/Sqrt[1 + x^2],x]","\sqrt{x^2+1} \tan ^{-1}(x)-\sinh ^{-1}(x)","\sqrt{x^2+1} \tan ^{-1}(x)-\sinh ^{-1}(x)",1,"-ArcSinh[x] + Sqrt[1 + x^2]*ArcTan[x]","A",2,2,13,0.1538,1,"{4930, 215}"
29,1,57,0,0.0795967,"\int \frac{\tan ^{-1}(x)}{x^2 \sqrt{1-x^2}} \, dx","Int[ArcTan[x]/(x^2*Sqrt[1 - x^2]),x]","-\frac{\sqrt{1-x^2} \tan ^{-1}(x)}{x}-\tanh ^{-1}\left(\sqrt{1-x^2}\right)+\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{1-x^2}}{\sqrt{2}}\right)","-\frac{\sqrt{1-x^2} \tan ^{-1}(x)}{x}-\tanh ^{-1}\left(\sqrt{1-x^2}\right)+\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{1-x^2}}{\sqrt{2}}\right)",1,"-((Sqrt[1 - x^2]*ArcTan[x])/x) - ArcTanh[Sqrt[1 - x^2]] + Sqrt[2]*ArcTanh[Sqrt[1 - x^2]/Sqrt[2]]","A",7,6,17,0.3529,1,"{264, 4976, 446, 83, 63, 206}"
30,1,45,0,0.0422879,"\int \frac{x \tan ^{-1}(x)}{\sqrt{1-x^2}} \, dx","Int[(x*ArcTan[x])/Sqrt[1 - x^2],x]","-\sqrt{1-x^2} \tan ^{-1}(x)+\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{1-x^2}}\right)-\sin ^{-1}(x)","-\sqrt{1-x^2} \tan ^{-1}(x)+\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{1-x^2}}\right)-\sin ^{-1}(x)",1,"-ArcSin[x] - Sqrt[1 - x^2]*ArcTan[x] + Sqrt[2]*ArcTan[(Sqrt[2]*x)/Sqrt[1 - x^2]]","A",5,5,15,0.3333,1,"{4974, 402, 216, 377, 203}"
31,1,29,0,0.0478196,"\int \frac{\tan ^{-1}(x)}{x^2 \sqrt{1+x^2}} \, dx","Int[ArcTan[x]/(x^2*Sqrt[1 + x^2]),x]","-\frac{\sqrt{x^2+1} \tan ^{-1}(x)}{x}-\tanh ^{-1}\left(\sqrt{x^2+1}\right)","-\frac{\sqrt{x^2+1} \tan ^{-1}(x)}{x}-\tanh ^{-1}\left(\sqrt{x^2+1}\right)",1,"-((Sqrt[1 + x^2]*ArcTan[x])/x) - ArcTanh[Sqrt[1 + x^2]]","A",4,4,15,0.2667,1,"{4944, 266, 63, 207}"
32,1,21,0,0.0436064,"\int \frac{\sin ^{-1}(x)}{x^2 \sqrt{1-x^2}} \, dx","Int[ArcSin[x]/(x^2*Sqrt[1 - x^2]),x]","\log (x)-\frac{\sqrt{1-x^2} \sin ^{-1}(x)}{x}","\log (x)-\frac{\sqrt{1-x^2} \sin ^{-1}(x)}{x}",1,"-((Sqrt[1 - x^2]*ArcSin[x])/x) + Log[x]","A",2,2,17,0.1176,1,"{4681, 29}"
33,1,34,0,0.0337325,"\int \frac{x \log (x)}{\sqrt{-1+x^2}} \, dx","Int[(x*Log[x])/Sqrt[-1 + x^2],x]","-\sqrt{x^2-1}+\sqrt{x^2-1} \log (x)+\tan ^{-1}\left(\sqrt{x^2-1}\right)","-\sqrt{x^2-1}+\sqrt{x^2-1} \log (x)+\tan ^{-1}\left(\sqrt{x^2-1}\right)",1,"-Sqrt[-1 + x^2] + ArcTan[Sqrt[-1 + x^2]] + Sqrt[-1 + x^2]*Log[x]","A",5,5,13,0.3846,1,"{2338, 266, 50, 63, 203}"
34,1,33,0,0.042239,"\int \frac{\log (x)}{x^2 \sqrt{1+x^2}} \, dx","Int[Log[x]/(x^2*Sqrt[1 + x^2]),x]","-\frac{\sqrt{x^2+1}}{x}-\frac{\sqrt{x^2+1} \log (x)}{x}+\sinh ^{-1}(x)","-\frac{\sqrt{x^2+1}}{x}-\frac{\sqrt{x^2+1} \log (x)}{x}+\sinh ^{-1}(x)",1,"-(Sqrt[1 + x^2]/x) + ArcSinh[x] - (Sqrt[1 + x^2]*Log[x])/x","A",3,3,15,0.2000,1,"{2335, 277, 215}"
35,1,25,0,0.0293864,"\int \frac{x \sec ^{-1}(x)}{\sqrt{-1+x^2}} \, dx","Int[(x*ArcSec[x])/Sqrt[-1 + x^2],x]","\sqrt{x^2-1} \sec ^{-1}(x)-\frac{x \log (x)}{\sqrt{x^2}}","\sqrt{x^2-1} \sec ^{-1}(x)-\frac{x \log (x)}{\sqrt{x^2}}",1,"Sqrt[-1 + x^2]*ArcSec[x] - (x*Log[x])/Sqrt[x^2]","A",2,2,13,0.1538,1,"{5236, 29}"
36,1,34,0,0.0346594,"\int \frac{x \log (x)}{\sqrt{1+x^2}} \, dx","Int[(x*Log[x])/Sqrt[1 + x^2],x]","-\sqrt{x^2+1}+\sqrt{x^2+1} \log (x)+\tanh ^{-1}\left(\sqrt{x^2+1}\right)","-\sqrt{x^2+1}+\sqrt{x^2+1} \log (x)+\tanh ^{-1}\left(\sqrt{x^2+1}\right)",1,"-Sqrt[1 + x^2] + ArcTanh[Sqrt[1 + x^2]] + Sqrt[1 + x^2]*Log[x]","A",5,5,13,0.3846,1,"{2338, 266, 50, 63, 207}"
37,1,16,0,0.0184993,"\int \frac{\sin (x)}{1+\sin ^2(x)} \, dx","Int[Sin[x]/(1 + Sin[x]^2),x]","-\frac{\tanh ^{-1}\left(\frac{\cos (x)}{\sqrt{2}}\right)}{\sqrt{2}}","-\frac{\tanh ^{-1}\left(\frac{\cos (x)}{\sqrt{2}}\right)}{\sqrt{2}}",1,"-(ArcTanh[Cos[x]/Sqrt[2]]/Sqrt[2])","A",2,2,11,0.1818,1,"{3186, 206}"
38,1,23,0,0.0321883,"\int \frac{1+x^2}{\left(1-x^2\right) \sqrt{1+x^4}} \, dx","Int[(1 + x^2)/((1 - x^2)*Sqrt[1 + x^4]),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{\sqrt{2}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{\sqrt{2}}",1,"ArcTanh[(Sqrt[2]*x)/Sqrt[1 + x^4]]/Sqrt[2]","A",2,2,24,0.08333,1,"{1699, 206}"
39,1,23,0,0.0315036,"\int \frac{1-x^2}{\left(1+x^2\right) \sqrt{1+x^4}} \, dx","Int[(1 - x^2)/((1 + x^2)*Sqrt[1 + x^4]),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{\sqrt{2}}","\frac{\tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{\sqrt{2}}",1,"ArcTan[(Sqrt[2]*x)/Sqrt[1 + x^4]]/Sqrt[2]","A",2,2,24,0.08333,1,"{1699, 203}"
40,1,22,0,0.0713951,"\int \frac{\log (\sin (x))}{1+\sin (x)} \, dx","Int[Log[Sin[x]]/(1 + Sin[x]),x]","-x-\tanh ^{-1}(\cos (x))-\frac{\cos (x) \log (\sin (x))}{\sin (x)+1}","-x-\tanh ^{-1}(\cos (x))-\frac{\cos (x) \log (\sin (x))}{\sin (x)+1}",1,"-x - ArcTanh[Cos[x]] - (Cos[x]*Log[Sin[x]])/(1 + Sin[x])","A",4,5,10,0.5000,1,"{2648, 2554, 2839, 3770, 8}"
41,1,42,0,0.1531842,"\int \log (\sin (x)) \sqrt{1+\sin (x)} \, dx","Int[Log[Sin[x]]*Sqrt[1 + Sin[x]],x]","\frac{4 \cos (x)}{\sqrt{\sin (x)+1}}-\frac{2 \cos (x) \log (\sin (x))}{\sqrt{\sin (x)+1}}-4 \tanh ^{-1}\left(\frac{\cos (x)}{\sqrt{\sin (x)+1}}\right)","\frac{4 \cos (x)}{\sqrt{\sin (x)+1}}-\frac{2 \cos (x) \log (\sin (x))}{\sqrt{\sin (x)+1}}-4 \tanh ^{-1}\left(\frac{\cos (x)}{\sqrt{\sin (x)+1}}\right)",1,"-4*ArcTanh[Cos[x]/Sqrt[1 + Sin[x]]] + (4*Cos[x])/Sqrt[1 + Sin[x]] - (2*Cos[x]*Log[Sin[x]])/Sqrt[1 + Sin[x]]","A",6,7,12,0.5833,1,"{2646, 2554, 12, 2874, 2981, 2773, 206}"
42,1,59,0,0.1835599,"\int \frac{\sec (x)}{\sqrt{-1+\sec ^4(x)}} \, dx","Int[Sec[x]/Sqrt[-1 + Sec[x]^4],x]","-\frac{\sqrt{1-\cos ^4(x)} \sec ^2(x) \tanh ^{-1}\left(\frac{\sqrt{2} \sin (x)}{\sqrt{2 \sin ^2(x)-\sin ^4(x)}}\right)}{\sqrt{2} \sqrt{\sec ^4(x)-1}}","-\frac{\tanh ^{-1}\left(\frac{\cos (x) \cot (x) \sqrt{\sec ^4(x)-1}}{\sqrt{2}}\right)}{\sqrt{2}}",1,"-((ArcTanh[(Sqrt[2]*Sin[x])/Sqrt[2*Sin[x]^2 - Sin[x]^4]]*Sqrt[1 - Cos[x]^4]*Sec[x]^2)/(Sqrt[2]*Sqrt[-1 + Sec[x]^4]))","B",5,5,13,0.3846,1,"{4148, 6722, 1988, 2008, 206}"
43,1,34,0,0.0454887,"\int \frac{\tan (x)}{\sqrt{1+\tan ^4(x)}} \, dx","Int[Tan[x]/Sqrt[1 + Tan[x]^4],x]","-\frac{\tanh ^{-1}\left(\frac{1-\tan ^2(x)}{\sqrt{2} \sqrt{\tan ^4(x)+1}}\right)}{2 \sqrt{2}}","-\frac{\tanh ^{-1}\left(\frac{1-\tan ^2(x)}{\sqrt{2} \sqrt{\tan ^4(x)+1}}\right)}{2 \sqrt{2}}",1,"-ArcTanh[(1 - Tan[x]^2)/(Sqrt[2]*Sqrt[1 + Tan[x]^4])]/(2*Sqrt[2])","A",4,4,13,0.3077,1,"{3670, 1248, 725, 206}"
44,1,50,0,0.0457867,"\int \frac{\sin (x)}{\sqrt{1-\sin ^6(x)}} \, dx","Int[Sin[x]/Sqrt[1 - Sin[x]^6],x]","\frac{\tanh ^{-1}\left(\frac{\cos (x) \left(6-3 \cos ^2(x)\right)}{2 \sqrt{3} \sqrt{\cos ^6(x)-3 \cos ^4(x)+3 \cos ^2(x)}}\right)}{2 \sqrt{3}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{3} \left(\sin ^2(x)+1\right) \cos (x)}{2 \sqrt{1-\sin ^6(x)}}\right)}{2 \sqrt{3}}",1,"ArcTanh[(Cos[x]*(6 - 3*Cos[x]^2))/(2*Sqrt[3]*Sqrt[3*Cos[x]^2 - 3*Cos[x]^4 + Cos[x]^6])]/(2*Sqrt[3])","A",4,4,15,0.2667,1,"{3216, 1996, 1904, 206}"
45,0,0,0,0.794238,"\int \sqrt{-\sqrt{-1+\sec (x)}+\sqrt{1+\sec (x)}} \, dx","Int[Sqrt[-Sqrt[-1 + Sec[x]] + Sqrt[1 + Sec[x]]],x]","\int \sqrt{-\sqrt{-1+\sec (x)}+\sqrt{1+\sec (x)}} \, dx","\sqrt{2} \cot (x) \sqrt{\sec (x)-1} \sqrt{\sec (x)+1} \left(\sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{\sqrt{2 \sqrt{2}-2} \left(-\sqrt{\sec (x)-1}+\sqrt{\sec (x)+1}-\sqrt{2}\right)}{2 \sqrt{\sqrt{\sec (x)+1}-\sqrt{\sec (x)-1}}}\right)-\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2+2 \sqrt{2}} \left(-\sqrt{\sec (x)-1}+\sqrt{\sec (x)+1}-\sqrt{2}\right)}{2 \sqrt{\sqrt{\sec (x)+1}-\sqrt{\sec (x)-1}}}\right)-\sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt{2 \sqrt{2}-2} \sqrt{\sqrt{\sec (x)+1}-\sqrt{\sec (x)-1}}}{-\sqrt{\sec (x)-1}+\sqrt{\sec (x)+1}+\sqrt{2}}\right)+\sqrt{\sqrt{2}-1} \tanh ^{-1}\left(\frac{\sqrt{2+2 \sqrt{2}} \sqrt{\sqrt{\sec (x)+1}-\sqrt{\sec (x)-1}}}{-\sqrt{\sec (x)-1}+\sqrt{\sec (x)+1}+\sqrt{2}}\right)\right)",1,"Defer[Int][Sqrt[-Sqrt[-1 + Sec[x]] + Sqrt[1 + Sec[x]]], x]","F",0,0,0,0,-1,"{}"
46,1,77,0,0.2195273,"\int x \tan ^{-1}(x)^2 \log \left(1+x^2\right) \, dx","Int[x*ArcTan[x]^2*Log[1 + x^2],x]","\frac{1}{4} \log ^2\left(x^2+1\right)-\frac{3}{2} \log \left(x^2+1\right)-\frac{1}{2} x^2 \tan ^{-1}(x)^2+\frac{1}{2} \left(x^2+1\right) \log \left(x^2+1\right) \tan ^{-1}(x)^2-x \log \left(x^2+1\right) \tan ^{-1}(x)-\frac{3}{2} \tan ^{-1}(x)^2+3 x \tan ^{-1}(x)","\frac{1}{4} \log ^2\left(x^2+1\right)-\frac{3}{2} \log \left(x^2+1\right)-\frac{1}{2} x^2 \tan ^{-1}(x)^2+\frac{1}{2} \left(x^2+1\right) \log \left(x^2+1\right) \tan ^{-1}(x)^2-x \log \left(x^2+1\right) \tan ^{-1}(x)-\frac{3}{2} \tan ^{-1}(x)^2+3 x \tan ^{-1}(x)",1,"3*x*ArcTan[x] - (3*ArcTan[x]^2)/2 - (x^2*ArcTan[x]^2)/2 - (3*Log[1 + x^2])/2 - x*ArcTan[x]*Log[1 + x^2] + ((1 + x^2)*ArcTan[x]^2*Log[1 + x^2])/2 + Log[1 + x^2]^2/4","A",13,10,12,0.8333,1,"{4852, 4916, 4846, 260, 4884, 5023, 5009, 2475, 2390, 2301}"
47,1,120,0,0.1306764,"\int \tan ^{-1}\left(x \sqrt{1+x^2}\right) \, dx","Int[ArcTan[x*Sqrt[1 + x^2]],x]","-\frac{1}{4} \sqrt{3} \log \left(x^2-\sqrt{3} \sqrt{x^2+1}+2\right)+\frac{1}{4} \sqrt{3} \log \left(x^2+\sqrt{3} \sqrt{x^2+1}+2\right)+x \tan ^{-1}\left(x \sqrt{x^2+1}\right)+\frac{1}{2} \tan ^{-1}\left(\sqrt{3}-2 \sqrt{x^2+1}\right)-\frac{1}{2} \tan ^{-1}\left(2 \sqrt{x^2+1}+\sqrt{3}\right)","-\frac{1}{4} \sqrt{3} \log \left(x^2-\sqrt{3} \sqrt{x^2+1}+2\right)+\frac{1}{4} \sqrt{3} \log \left(x^2+\sqrt{3} \sqrt{x^2+1}+2\right)+x \tan ^{-1}\left(x \sqrt{x^2+1}\right)+\frac{1}{2} \tan ^{-1}\left(\sqrt{3}-2 \sqrt{x^2+1}\right)-\frac{1}{2} \tan ^{-1}\left(2 \sqrt{x^2+1}+\sqrt{3}\right)",1,"x*ArcTan[x*Sqrt[1 + x^2]] + ArcTan[Sqrt[3] - 2*Sqrt[1 + x^2]]/2 - ArcTan[Sqrt[3] + 2*Sqrt[1 + x^2]]/2 - (Sqrt[3]*Log[2 + x^2 - Sqrt[3]*Sqrt[1 + x^2]])/4 + (Sqrt[3]*Log[2 + x^2 + Sqrt[3]*Sqrt[1 + x^2]])/4","A",12,8,12,0.6667,1,"{5203, 1685, 826, 1169, 634, 618, 204, 628}"
48,1,37,0,0.0093372,"\int -\tan ^{-1}\left(\sqrt{x}-\sqrt{1+x}\right) \, dx","Int[-ArcTan[Sqrt[x] - Sqrt[1 + x]],x]","\frac{\pi  x}{4}+\frac{\sqrt{x}}{2}-\frac{1}{2} x \tan ^{-1}\left(\sqrt{x}\right)-\frac{1}{2} \tan ^{-1}\left(\sqrt{x}\right)","\frac{\sqrt{x}}{2}-(x+1) \tan ^{-1}\left(\sqrt{x}-\sqrt{x+1}\right)",1,"Sqrt[x]/2 + (Pi*x)/4 - ArcTan[Sqrt[x]]/2 - (x*ArcTan[Sqrt[x]])/2","A",6,6,18,0.3333,0,"{5159, 8, 5027, 50, 63, 203}"
49,1,29,0,0.0241646,"\int \sin ^{-1}\left(\frac{x}{\sqrt{1-x^2}}\right) \, dx","Int[ArcSin[x/Sqrt[1 - x^2]],x]","x \sin ^{-1}\left(\frac{x}{\sqrt{1-x^2}}\right)+\tan ^{-1}\left(\sqrt{1-2 x^2}\right)","x \sin ^{-1}\left(\frac{x}{\sqrt{1-x^2}}\right)+\tan ^{-1}\left(\sqrt{1-2 x^2}\right)",1,"x*ArcSin[x/Sqrt[1 - x^2]] + ArcTan[Sqrt[1 - 2*x^2]]","A",4,4,14,0.2857,1,"{4840, 444, 63, 203}"
50,1,106,0,0.1095565,"\int \tan ^{-1}\left(x \sqrt{1-x^2}\right) \, dx","Int[ArcTan[x*Sqrt[1 - x^2]],x]","-\sqrt{\frac{2}{\sqrt{5}-1}} \tan ^{-1}\left(\sqrt{\frac{2}{\sqrt{5}-1}} \sqrt{1-x^2}\right)+x \tan ^{-1}\left(x \sqrt{1-x^2}\right)+\sqrt{\frac{2}{1+\sqrt{5}}} \tanh ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} \sqrt{1-x^2}\right)","-\sqrt{\frac{1}{2} \left(1+\sqrt{5}\right)} \tan ^{-1}\left(\sqrt{\frac{1}{2} \left(1+\sqrt{5}\right)} \sqrt{1-x^2}\right)+x \tan ^{-1}\left(x \sqrt{1-x^2}\right)+\sqrt{\frac{1}{2} \left(\sqrt{5}-1\right)} \tanh ^{-1}\left(\sqrt{\frac{1}{2} \left(\sqrt{5}-1\right)} \sqrt{1-x^2}\right)",1,"-(Sqrt[2/(-1 + Sqrt[5])]*ArcTan[Sqrt[2/(-1 + Sqrt[5])]*Sqrt[1 - x^2]]) + x*ArcTan[x*Sqrt[1 - x^2]] + Sqrt[2/(1 + Sqrt[5])]*ArcTanh[Sqrt[2/(1 + Sqrt[5])]*Sqrt[1 - x^2]]","A",6,6,14,0.4286,1,"{5203, 1685, 826, 1166, 204, 206}"