1,1,52,51,0.0243981,"\int \sin ^{-1}(x) \log (x) \, dx","Integrate[ArcSin[x]*Log[x],x]","-2 \sqrt{1-x^2}+\left(\sqrt{1-x^2}-1\right) \log (x)+\log \left(\sqrt{1-x^2}+1\right)+x (\log (x)-1) \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]*(-1 + Log[x]) + (-1 + Sqrt[1 - x^2])*Log[x] + Log[1 + Sqrt[1 - x^2]]","A",1
2,1,17,17,0.0060325,"\int \frac{x \sin ^{-1}(x)}{\sqrt{1-x^2}} \, dx","Integrate[(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",1
3,1,205,69,0.665779,"\int -\sin ^{-1}\left(\sqrt{x}-\sqrt{1+x}\right) \, dx","Integrate[-ArcSin[Sqrt[x] - Sqrt[1 + x]],x]","-\frac{(x+1) \left(2 x-2 \sqrt{x+1} \sqrt{x}+1\right)^2 \left(2 \sqrt{\sqrt{x} \sqrt{x+1}-x} \left(-2 x+2 \sqrt{x+1} \sqrt{x}-3\right)+3 \sqrt{-4 x+4 \sqrt{x+1} \sqrt{x}-2} \log \left(2 \sqrt{\sqrt{x} \sqrt{x+1}-x}+\sqrt{-4 x+4 \sqrt{x+1} \sqrt{x}-2}\right)\right)}{8 \sqrt{2} \left(\sqrt{x+1}-\sqrt{x}\right)^3 \left(x-\sqrt{x+1} \sqrt{x}+1\right)^2}-x \sin ^{-1}\left(\sqrt{x}-\sqrt{x+1}\right)","\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]]) - ((1 + x)*(1 + 2*x - 2*Sqrt[x]*Sqrt[1 + x])^2*(2*Sqrt[-x + Sqrt[x]*Sqrt[1 + x]]*(-3 - 2*x + 2*Sqrt[x]*Sqrt[1 + x]) + 3*Sqrt[-2 - 4*x + 4*Sqrt[x]*Sqrt[1 + x]]*Log[2*Sqrt[-x + Sqrt[x]*Sqrt[1 + x]] + Sqrt[-2 - 4*x + 4*Sqrt[x]*Sqrt[1 + x]]]))/(8*Sqrt[2]*(-Sqrt[x] + Sqrt[1 + x])^3*(1 + x - Sqrt[x]*Sqrt[1 + x])^2)","B",1
4,1,194,97,0.4042102,"\int \log \left(1+x \sqrt{1+x^2}\right) \, dx","Integrate[Log[1 + x*Sqrt[1 + x^2]],x]","x \log \left(\sqrt{x^2+1} x+1\right)-\frac{\sqrt{2 \left(\sqrt{5}-1\right)} \tan ^{-1}\left(\sqrt{\frac{2}{\sqrt{5}-1}} \sqrt{x^2+1}\right)}{1-\sqrt{5}}-\sqrt{\frac{2}{1+\sqrt{5}}} \tanh ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} \sqrt{x^2+1}\right)-2 x+\frac{\left(5+\sqrt{5}\right) \tan ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} x\right)}{\sqrt{10 \left(1+\sqrt{5}\right)}}-\frac{\left(\sqrt{5}-5\right) \tanh ^{-1}\left(\sqrt{\frac{2}{\sqrt{5}-1}} x\right)}{\sqrt{10 \left(\sqrt{5}-1\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 + ((5 + Sqrt[5])*ArcTan[Sqrt[2/(1 + Sqrt[5])]*x])/Sqrt[10*(1 + Sqrt[5])] - (Sqrt[2*(-1 + Sqrt[5])]*ArcTan[Sqrt[2/(-1 + Sqrt[5])]*Sqrt[1 + x^2]])/(1 - Sqrt[5]) - ((-5 + Sqrt[5])*ArcTanh[Sqrt[2/(-1 + Sqrt[5])]*x])/Sqrt[10*(-1 + Sqrt[5])] - Sqrt[2/(1 + Sqrt[5])]*ArcTanh[Sqrt[2/(1 + Sqrt[5])]*Sqrt[1 + x^2]] + x*Log[1 + x*Sqrt[1 + x^2]]","A",1
5,1,159,45,2.2053034,"\int \frac{\cos ^2(x)}{\sqrt{1+\cos ^2(x)+\cos ^4(x)}} \, dx","Integrate[Cos[x]^2/Sqrt[1 + Cos[x]^2 + Cos[x]^4],x]","-\frac{2 i \cos ^2(x) \sqrt{1-\frac{2 i \tan ^2(x)}{\sqrt{3}-3 i}} \sqrt{1+\frac{2 i \tan ^2(x)}{\sqrt{3}+3 i}} \Pi \left(\frac{3}{2}+\frac{i \sqrt{3}}{2};i \sinh ^{-1}\left(\sqrt{-\frac{2 i}{-3 i+\sqrt{3}}} \tan (x)\right)|\frac{3 i-\sqrt{3}}{3 i+\sqrt{3}}\right)}{\sqrt{-\frac{i}{\sqrt{3}-3 i}} \sqrt{8 \cos (2 x)+\cos (4 x)+15}}","\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,"((-2*I)*Cos[x]^2*EllipticPi[3/2 + (I/2)*Sqrt[3], I*ArcSinh[Sqrt[(-2*I)/(-3*I + Sqrt[3])]*Tan[x]], (3*I - Sqrt[3])/(3*I + Sqrt[3])]*Sqrt[1 - ((2*I)*Tan[x]^2)/(-3*I + Sqrt[3])]*Sqrt[1 + ((2*I)*Tan[x]^2)/(3*I + Sqrt[3])])/(Sqrt[(-I)/(-3*I + Sqrt[3])]*Sqrt[15 + 8*Cos[2*x] + Cos[4*x]])","C",1
6,1,74,56,0.1186062,"\int \tan (x) \sqrt{1+\tan ^4(x)} \, dx","Integrate[Tan[x]*Sqrt[1 + Tan[x]^4],x]","\frac{\sqrt{\tan ^4(x)+1} \left(\sqrt{\cos (4 x)+3}-2 \sqrt{2} \cos ^2(x) \sinh ^{-1}(\cos (2 x))-2 \cos ^2(x) \tanh ^{-1}\left(\frac{2 \sin ^2(x)}{\sqrt{\cos (4 x)+3}}\right)\right)}{2 \sqrt{\cos (4 x)+3}}","\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,"((-2*Sqrt[2]*ArcSinh[Cos[2*x]]*Cos[x]^2 - 2*ArcTanh[(2*Sin[x]^2)/Sqrt[3 + Cos[4*x]]]*Cos[x]^2 + Sqrt[3 + Cos[4*x]])*Sqrt[1 + Tan[x]^4])/(2*Sqrt[3 + Cos[4*x]])","A",1
7,1,15,15,0.01524,"\int \frac{\tan (x)}{\sqrt{1+\sec ^3(x)}} \, dx","Integrate[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",1
8,1,99,137,10.2960377,"\int \sqrt{2+2 \tan (x)+\tan ^2(x)} \, dx","Integrate[Sqrt[2 + 2*Tan[x] + Tan[x]^2],x]","\sinh ^{-1}(\tan (x)+1)+\frac{1}{2} i \left(\sqrt{1+2 i} \tanh ^{-1}\left(\frac{(1+i) \tan (x)+(2+i)}{\sqrt{1+2 i} \sqrt{\tan ^2(x)+2 \tan (x)+2}}\right)-\sqrt{1-2 i} \tanh ^{-1}\left(\frac{(2-2 i) \tan (x)+(4-2 i)}{2 \sqrt{1-2 i} \sqrt{\tan ^2(x)+2 \tan (x)+2}}\right)\right)","-\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]] + (I/2)*(Sqrt[1 + 2*I]*ArcTanh[((2 + I) + (1 + I)*Tan[x])/(Sqrt[1 + 2*I]*Sqrt[2 + 2*Tan[x] + Tan[x]^2])] - Sqrt[1 - 2*I]*ArcTanh[((4 - 2*I) + (2 - 2*I)*Tan[x])/(2*Sqrt[1 - 2*I]*Sqrt[2 + 2*Tan[x] + Tan[x]^2])])","C",1
9,1,283,41,4.3772869,"\int \tan ^{-1}\left(\sqrt{-1+\sec (x)}\right) \sin (x) \, dx","Integrate[ArcTan[Sqrt[-1 + Sec[x]]]*Sin[x],x]","-\frac{1}{2} \left(-3-2 \sqrt{2}\right) \left(\left(\sqrt{2}-2\right) \cos \left(\frac{x}{2}\right)-\sqrt{2}+1\right) \cos ^2\left(\frac{x}{4}\right) \sqrt{-\tan ^2\left(\frac{x}{4}\right)-2 \sqrt{2}+3} \sqrt{\left(2 \sqrt{2}-3\right) \tan ^2\left(\frac{x}{4}\right)+1} \cot \left(\frac{x}{4}\right) \sqrt{\sec (x)-1} \sec (x) \sqrt{\left(\left(10-7 \sqrt{2}\right) \cos \left(\frac{x}{2}\right)-5 \sqrt{2}+7\right) \sec ^2\left(\frac{x}{4}\right)} \sqrt{\left(\left(2+\sqrt{2}\right) \cos \left(\frac{x}{2}\right)-\sqrt{2}-1\right) \sec ^2\left(\frac{x}{4}\right)} \left(\operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\tan \left(\frac{x}{4}\right)}{\sqrt{3-2 \sqrt{2}}}\right),17-12 \sqrt{2}\right)-2 \Pi \left(-3+2 \sqrt{2};\sin ^{-1}\left(\frac{\tan \left(\frac{x}{4}\right)}{\sqrt{3-2 \sqrt{2}}}\right)|17-12 \sqrt{2}\right)\right)+\frac{1}{2} \cos (x) \sqrt{\sec (x)-1}-\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]]]*Cos[x]) + (Cos[x]*Sqrt[-1 + Sec[x]])/2 - ((-3 - 2*Sqrt[2])*Cos[x/4]^2*(1 - Sqrt[2] + (-2 + Sqrt[2])*Cos[x/2])*Cot[x/4]*(EllipticF[ArcSin[Tan[x/4]/Sqrt[3 - 2*Sqrt[2]]], 17 - 12*Sqrt[2]] - 2*EllipticPi[-3 + 2*Sqrt[2], ArcSin[Tan[x/4]/Sqrt[3 - 2*Sqrt[2]]], 17 - 12*Sqrt[2]])*Sqrt[(7 - 5*Sqrt[2] + (10 - 7*Sqrt[2])*Cos[x/2])*Sec[x/4]^2]*Sqrt[(-1 - Sqrt[2] + (2 + Sqrt[2])*Cos[x/2])*Sec[x/4]^2]*Sqrt[-1 + Sec[x]]*Sec[x]*Sqrt[3 - 2*Sqrt[2] - Tan[x/4]^2]*Sqrt[1 + (-3 + 2*Sqrt[2])*Tan[x/4]^2])/2","C",0
10,1,38,44,0.1718855,"\int \frac{e^{\sin ^{-1}(x)} x^3}{\sqrt{1-x^2}} \, dx","Integrate[(E^ArcSin[x]*x^3)/Sqrt[1 - x^2],x]","-\frac{1}{40} e^{\sin ^{-1}(x)} \left(15 \left(\sqrt{1-x^2}-x\right)+\sin \left(3 \sin ^{-1}(x)\right)-3 \cos \left(3 \sin ^{-1}(x)\right)\right)","\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,"-1/40*(E^ArcSin[x]*(15*(-x + Sqrt[1 - x^2]) - 3*Cos[3*ArcSin[x]] + Sin[3*ArcSin[x]]))","A",1
11,1,64,68,0.0543849,"\int \frac{x \log \left(1+x^2\right) \log \left(x+\sqrt{1+x^2}\right)}{\sqrt{1+x^2}} \, dx","Integrate[(x*Log[1 + x^2]*Log[x + Sqrt[1 + x^2]])/Sqrt[1 + x^2],x]","-2 \sqrt{x^2+1} \log \left(\sqrt{x^2+1}+x\right)+\log \left(x^2+1\right) \left(\sqrt{x^2+1} \log \left(\sqrt{x^2+1}+x\right)-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] - 2*Sqrt[1 + x^2]*Log[x + Sqrt[1 + x^2]] + Log[1 + x^2]*(-x + Sqrt[1 + x^2]*Log[x + Sqrt[1 + x^2]])","A",1
12,1,1822,141,3.7956396,"\int \tan ^{-1}\left(x+\sqrt{1-x^2}\right) \, dx","Integrate[ArcTan[x + Sqrt[1 - x^2]],x]","x \tan ^{-1}\left(x+\sqrt{1-x^2}\right)+\frac{1}{16} \left(-8 \sin ^{-1}(x)+2 \sqrt{2+2 i \sqrt{3}} \tan ^{-1}\left(\frac{\left(-2 x^2+i \sqrt{3}+1\right) \left(x^2-1\right)}{2 \sqrt{3} x^4+\left(-2 \sqrt{2-2 i \sqrt{3}} \sqrt{1-x^2}-2 i \sqrt{3}-6\right) x^3+\left(2 \sqrt{6-6 i \sqrt{3}} \sqrt{1-x^2}-\sqrt{3}+3 i\right) x^2+\left(-2 \sqrt{2-2 i \sqrt{3}} \sqrt{1-x^2}+2 i \sqrt{3}+6\right) x-\sqrt{3}-3 i}\right)-2 \sqrt{2+2 i \sqrt{3}} \tan ^{-1}\left(\frac{\left(-2 x^2+i \sqrt{3}+1\right) \left(x^2-1\right)}{2 \sqrt{3} x^4+2 \left(\sqrt{2-2 i \sqrt{3}} \sqrt{1-x^2}+i \sqrt{3}+3\right) x^3+\left(2 \sqrt{6-6 i \sqrt{3}} \sqrt{1-x^2}-\sqrt{3}+3 i\right) x^2+2 \left(\sqrt{2-2 i \sqrt{3}} \sqrt{1-x^2}-i \sqrt{3}-3\right) x-\sqrt{3}-3 i}\right)-2 \sqrt{2-2 i \sqrt{3}} \tan ^{-1}\left(\frac{\left(x^2-1\right) \left(2 x^2+i \sqrt{3}-1\right)}{2 \sqrt{3} x^4+\left(-2 \sqrt{2+2 i \sqrt{3}} \sqrt{1-x^2}+2 i \sqrt{3}-6\right) x^3+\left(2 \sqrt{6+6 i \sqrt{3}} \sqrt{1-x^2}-\sqrt{3}-3 i\right) x^2+\left(-2 \sqrt{2+2 i \sqrt{3}} \sqrt{1-x^2}-2 i \sqrt{3}+6\right) x-\sqrt{3}+3 i}\right)+2 \sqrt{2-2 i \sqrt{3}} \tan ^{-1}\left(\frac{\left(x^2-1\right) \left(2 x^2+i \sqrt{3}-1\right)}{2 \sqrt{3} x^4+2 \left(\sqrt{2+2 i \sqrt{3}} \sqrt{1-x^2}-i \sqrt{3}+3\right) x^3+\left(2 \sqrt{6+6 i \sqrt{3}} \sqrt{1-x^2}-\sqrt{3}-3 i\right) x^2+2 \left(\sqrt{2+2 i \sqrt{3}} \sqrt{1-x^2}+i \sqrt{3}-3\right) x-\sqrt{3}+3 i}\right)+2 i \sqrt{3} \log \left(x^2-\frac{i \sqrt{3}}{2}-\frac{1}{2}\right)-2 \log \left(x^2-\frac{i \sqrt{3}}{2}-\frac{1}{2}\right)-2 i \sqrt{3} \log \left(x^2+\frac{1}{2} i \left(i+\sqrt{3}\right)\right)-2 \log \left(x^2+\frac{1}{2} i \left(i+\sqrt{3}\right)\right)+i \sqrt{2+2 i \sqrt{3}} \log \left(16 \left(x^2+\sqrt{3} x+1\right)^2\right)-i \sqrt{2-2 i \sqrt{3}} \log \left(16 \left(x^2+\sqrt{3} x+1\right)^2\right)-i \sqrt{2+2 i \sqrt{3}} \log \left(\left(4 x^2-4 \sqrt{3} x+4\right)^2\right)+i \sqrt{2-2 i \sqrt{3}} \log \left(\left(4 x^2-4 \sqrt{3} x+4\right)^2\right)-i \sqrt{2+2 i \sqrt{3}} \log \left(-\left(\left(-i+\sqrt{3}\right) x^4\right)+i \left(\sqrt{6-6 i \sqrt{3}} \sqrt{1-x^2}+3 \sqrt{3}+3 i\right) x^3+5 i \left(\sqrt{2-2 i \sqrt{3}} \sqrt{1-x^2}+2\right) x^2+\left(3 i \sqrt{6-6 i \sqrt{3}} \sqrt{1-x^2}+5 i \sqrt{3}+3\right) x+2 i \sqrt{2-2 i \sqrt{3}} \sqrt{1-x^2}+\sqrt{3}+3 i\right)+i \sqrt{2+2 i \sqrt{3}} \log \left(-\left(\left(-i+\sqrt{3}\right) x^4\right)+\left(-i \sqrt{6-6 i \sqrt{3}} \sqrt{1-x^2}-3 i \sqrt{3}+3\right) x^3+5 i \left(\sqrt{2-2 i \sqrt{3}} \sqrt{1-x^2}+2\right) x^2-i \left(3 \sqrt{6-6 i \sqrt{3}} \sqrt{1-x^2}+5 \sqrt{3}-3 i\right) x+2 i \sqrt{2-2 i \sqrt{3}} \sqrt{1-x^2}+\sqrt{3}+3 i\right)+i \sqrt{2-2 i \sqrt{3}} \log \left(-\left(\left(i+\sqrt{3}\right) x^4\right)-i \left(\sqrt{6+6 i \sqrt{3}} \sqrt{1-x^2}+3 \sqrt{3}-3 i\right) x^3-5 i \left(\sqrt{2+2 i \sqrt{3}} \sqrt{1-x^2}+2\right) x^2+\left(-3 i \sqrt{6+6 i \sqrt{3}} \sqrt{1-x^2}-5 i \sqrt{3}+3\right) x-2 i \sqrt{2+2 i \sqrt{3}} \sqrt{1-x^2}+\sqrt{3}-3 i\right)-i \sqrt{2-2 i \sqrt{3}} \log \left(-\left(\left(i+\sqrt{3}\right) x^4\right)+\left(i \sqrt{6+6 i \sqrt{3}} \sqrt{1-x^2}+3 i \sqrt{3}+3\right) x^3-5 i \left(\sqrt{2+2 i \sqrt{3}} \sqrt{1-x^2}+2\right) x^2+i \left(3 \sqrt{6+6 i \sqrt{3}} \sqrt{1-x^2}+5 \sqrt{3}+3 i\right) x-2 i \sqrt{2+2 i \sqrt{3}} \sqrt{1-x^2}+\sqrt{3}-3 i\right)\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}{8} \log \left(x^4-x^2+1\right)-\frac{1}{2} \sin ^{-1}(x)",1,"x*ArcTan[x + Sqrt[1 - x^2]] + (-8*ArcSin[x] + 2*Sqrt[2 + (2*I)*Sqrt[3]]*ArcTan[((1 + I*Sqrt[3] - 2*x^2)*(-1 + x^2))/(-3*I - Sqrt[3] + 2*Sqrt[3]*x^4 + x^3*(-6 - (2*I)*Sqrt[3] - 2*Sqrt[2 - (2*I)*Sqrt[3]]*Sqrt[1 - x^2]) + x*(6 + (2*I)*Sqrt[3] - 2*Sqrt[2 - (2*I)*Sqrt[3]]*Sqrt[1 - x^2]) + x^2*(3*I - Sqrt[3] + 2*Sqrt[6 - (6*I)*Sqrt[3]]*Sqrt[1 - x^2]))] - 2*Sqrt[2 + (2*I)*Sqrt[3]]*ArcTan[((1 + I*Sqrt[3] - 2*x^2)*(-1 + x^2))/(-3*I - Sqrt[3] + 2*Sqrt[3]*x^4 + 2*x*(-3 - I*Sqrt[3] + Sqrt[2 - (2*I)*Sqrt[3]]*Sqrt[1 - x^2]) + 2*x^3*(3 + I*Sqrt[3] + Sqrt[2 - (2*I)*Sqrt[3]]*Sqrt[1 - x^2]) + x^2*(3*I - Sqrt[3] + 2*Sqrt[6 - (6*I)*Sqrt[3]]*Sqrt[1 - x^2]))] - 2*Sqrt[2 - (2*I)*Sqrt[3]]*ArcTan[((-1 + x^2)*(-1 + I*Sqrt[3] + 2*x^2))/(3*I - Sqrt[3] + 2*Sqrt[3]*x^4 + x*(6 - (2*I)*Sqrt[3] - 2*Sqrt[2 + (2*I)*Sqrt[3]]*Sqrt[1 - x^2]) + x^3*(-6 + (2*I)*Sqrt[3] - 2*Sqrt[2 + (2*I)*Sqrt[3]]*Sqrt[1 - x^2]) + x^2*(-3*I - Sqrt[3] + 2*Sqrt[6 + (6*I)*Sqrt[3]]*Sqrt[1 - x^2]))] + 2*Sqrt[2 - (2*I)*Sqrt[3]]*ArcTan[((-1 + x^2)*(-1 + I*Sqrt[3] + 2*x^2))/(3*I - Sqrt[3] + 2*Sqrt[3]*x^4 + 2*x^3*(3 - I*Sqrt[3] + Sqrt[2 + (2*I)*Sqrt[3]]*Sqrt[1 - x^2]) + 2*x*(-3 + I*Sqrt[3] + Sqrt[2 + (2*I)*Sqrt[3]]*Sqrt[1 - x^2]) + x^2*(-3*I - Sqrt[3] + 2*Sqrt[6 + (6*I)*Sqrt[3]]*Sqrt[1 - x^2]))] - 2*Log[-1/2 - (I/2)*Sqrt[3] + x^2] + (2*I)*Sqrt[3]*Log[-1/2 - (I/2)*Sqrt[3] + x^2] - 2*Log[(I/2)*(I + Sqrt[3]) + x^2] - (2*I)*Sqrt[3]*Log[(I/2)*(I + Sqrt[3]) + x^2] - I*Sqrt[2 - (2*I)*Sqrt[3]]*Log[16*(1 + Sqrt[3]*x + x^2)^2] + I*Sqrt[2 + (2*I)*Sqrt[3]]*Log[16*(1 + Sqrt[3]*x + x^2)^2] + I*Sqrt[2 - (2*I)*Sqrt[3]]*Log[(4 - 4*Sqrt[3]*x + 4*x^2)^2] - I*Sqrt[2 + (2*I)*Sqrt[3]]*Log[(4 - 4*Sqrt[3]*x + 4*x^2)^2] - I*Sqrt[2 + (2*I)*Sqrt[3]]*Log[3*I + Sqrt[3] - (-I + Sqrt[3])*x^4 + (2*I)*Sqrt[2 - (2*I)*Sqrt[3]]*Sqrt[1 - x^2] + (5*I)*x^2*(2 + Sqrt[2 - (2*I)*Sqrt[3]]*Sqrt[1 - x^2]) + x*(3 + (5*I)*Sqrt[3] + (3*I)*Sqrt[6 - (6*I)*Sqrt[3]]*Sqrt[1 - x^2]) + I*x^3*(3*I + 3*Sqrt[3] + Sqrt[6 - (6*I)*Sqrt[3]]*Sqrt[1 - x^2])] + I*Sqrt[2 + (2*I)*Sqrt[3]]*Log[3*I + Sqrt[3] - (-I + Sqrt[3])*x^4 + (2*I)*Sqrt[2 - (2*I)*Sqrt[3]]*Sqrt[1 - x^2] + (5*I)*x^2*(2 + Sqrt[2 - (2*I)*Sqrt[3]]*Sqrt[1 - x^2]) + x^3*(3 - (3*I)*Sqrt[3] - I*Sqrt[6 - (6*I)*Sqrt[3]]*Sqrt[1 - x^2]) - I*x*(-3*I + 5*Sqrt[3] + 3*Sqrt[6 - (6*I)*Sqrt[3]]*Sqrt[1 - x^2])] + I*Sqrt[2 - (2*I)*Sqrt[3]]*Log[-3*I + Sqrt[3] - (I + Sqrt[3])*x^4 - (2*I)*Sqrt[2 + (2*I)*Sqrt[3]]*Sqrt[1 - x^2] - (5*I)*x^2*(2 + Sqrt[2 + (2*I)*Sqrt[3]]*Sqrt[1 - x^2]) + x*(3 - (5*I)*Sqrt[3] - (3*I)*Sqrt[6 + (6*I)*Sqrt[3]]*Sqrt[1 - x^2]) - I*x^3*(-3*I + 3*Sqrt[3] + Sqrt[6 + (6*I)*Sqrt[3]]*Sqrt[1 - x^2])] - I*Sqrt[2 - (2*I)*Sqrt[3]]*Log[-3*I + Sqrt[3] - (I + Sqrt[3])*x^4 - (2*I)*Sqrt[2 + (2*I)*Sqrt[3]]*Sqrt[1 - x^2] - (5*I)*x^2*(2 + Sqrt[2 + (2*I)*Sqrt[3]]*Sqrt[1 - x^2]) + x^3*(3 + (3*I)*Sqrt[3] + I*Sqrt[6 + (6*I)*Sqrt[3]]*Sqrt[1 - x^2]) + I*x*(3*I + 5*Sqrt[3] + 3*Sqrt[6 + (6*I)*Sqrt[3]]*Sqrt[1 - x^2])])/16","C",0
13,1,2180,152,4.9526756,"\int \frac{x \tan ^{-1}\left(x+\sqrt{1-x^2}\right)}{\sqrt{1-x^2}} \, dx","Integrate[(x*ArcTan[x + Sqrt[1 - x^2]])/Sqrt[1 - x^2],x]","\text{Result too large to show}","\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}{8} \log \left(x^4-x^2+1\right)-\frac{1}{2} \sin ^{-1}(x)",1,"(-24*ArcSin[x] - 48*Sqrt[1 - x^2]*ArcTan[x + Sqrt[1 - x^2]] + (2*(-3*I + Sqrt[3])*ArcTan[(3 - I*Sqrt[3] + (-3 - I*Sqrt[3])*x^4 + 2*x*(-6*I + 2*Sqrt[3] - I*Sqrt[2 - (2*I)*Sqrt[3]]*Sqrt[1 - x^2]) - 2*x^3*(6*I + 2*Sqrt[3] + I*Sqrt[2 - (2*I)*Sqrt[3]]*Sqrt[1 - x^2]) - (2*I)*Sqrt[3]*x^2*(6 + Sqrt[2 - (2*I)*Sqrt[3]]*Sqrt[1 - x^2]))/(I - Sqrt[3] + (6*I)*(I + Sqrt[3])*x - 2*(-15*I + Sqrt[3])*x^2 + 6*(1 + (3*I)*Sqrt[3])*x^3 + (11*I + 3*Sqrt[3])*x^4)])/Sqrt[(1 - I*Sqrt[3])/6] - (2*(-3*I + Sqrt[3])*ArcTan[(3 - I*Sqrt[3] + (-3 - I*Sqrt[3])*x^4 + 2*x^3*(6*I + 2*Sqrt[3] + I*Sqrt[2 - (2*I)*Sqrt[3]]*Sqrt[1 - x^2]) + x*(12*I - 4*Sqrt[3] + (2*I)*Sqrt[2 - (2*I)*Sqrt[3]]*Sqrt[1 - x^2]) - (2*I)*Sqrt[3]*x^2*(6 + Sqrt[2 - (2*I)*Sqrt[3]]*Sqrt[1 - x^2]))/(I - Sqrt[3] + (6 - (6*I)*Sqrt[3])*x - 2*(-15*I + Sqrt[3])*x^2 + (-6 - (18*I)*Sqrt[3])*x^3 + (11*I + 3*Sqrt[3])*x^4)])/Sqrt[(1 - I*Sqrt[3])/6] - (2*(3*I + Sqrt[3])*ArcTan[(-3 - I*Sqrt[3] + (3 - I*Sqrt[3])*x^4 + 2*x^3*(-6*I + 2*Sqrt[3] - I*Sqrt[2 + (2*I)*Sqrt[3]]*Sqrt[1 - x^2]) - 2*x*(6*I + 2*Sqrt[3] + I*Sqrt[2 + (2*I)*Sqrt[3]]*Sqrt[1 - x^2]) - (2*I)*Sqrt[3]*x^2*(6 + Sqrt[2 + (2*I)*Sqrt[3]]*Sqrt[1 - x^2]))/(-I - Sqrt[3] + (-6 - (6*I)*Sqrt[3])*x - 2*(15*I + Sqrt[3])*x^2 + 6*(1 - (3*I)*Sqrt[3])*x^3 + (-11*I + 3*Sqrt[3])*x^4)])/Sqrt[(1 + I*Sqrt[3])/6] + (2*(3*I + Sqrt[3])*ArcTan[(-3 - I*Sqrt[3] + (3 - I*Sqrt[3])*x^4 + 2*x*(6*I + 2*Sqrt[3] + I*Sqrt[2 + (2*I)*Sqrt[3]]*Sqrt[1 - x^2]) + x^3*(12*I - 4*Sqrt[3] + (2*I)*Sqrt[2 + (2*I)*Sqrt[3]]*Sqrt[1 - x^2]) - (2*I)*Sqrt[3]*x^2*(6 + Sqrt[2 + (2*I)*Sqrt[3]]*Sqrt[1 - x^2]))/(-I - Sqrt[3] + (6 + (6*I)*Sqrt[3])*x - 2*(15*I + Sqrt[3])*x^2 + (-6 + (18*I)*Sqrt[3])*x^3 + (-11*I + 3*Sqrt[3])*x^4)])/Sqrt[(1 + I*Sqrt[3])/6] + 2*Sqrt[3]*(3*I + Sqrt[3])*Log[-1/2 - (I/2)*Sqrt[3] + x^2] + 2*Sqrt[3]*(-3*I + Sqrt[3])*Log[(I/2)*(I + Sqrt[3]) + x^2] + ((3 - I*Sqrt[3])*Log[16*(1 + Sqrt[3]*x + x^2)^2])/Sqrt[(1 + I*Sqrt[3])/6] + ((3 + I*Sqrt[3])*Log[16*(1 + Sqrt[3]*x + x^2)^2])/Sqrt[(1 - I*Sqrt[3])/6] - (I*(-3*I + Sqrt[3])*Log[(4 - 4*Sqrt[3]*x + 4*x^2)^2])/Sqrt[(1 - I*Sqrt[3])/6] + (I*(3*I + Sqrt[3])*Log[(4 - 4*Sqrt[3]*x + 4*x^2)^2])/Sqrt[(1 + I*Sqrt[3])/6] - (I*(-3*I + Sqrt[3])*Log[3*I + Sqrt[3] - (-I + Sqrt[3])*x^4 + (2*I)*Sqrt[2 - (2*I)*Sqrt[3]]*Sqrt[1 - x^2] + (5*I)*x^2*(2 + Sqrt[2 - (2*I)*Sqrt[3]]*Sqrt[1 - x^2]) + x*(3 + (5*I)*Sqrt[3] + (3*I)*Sqrt[6 - (6*I)*Sqrt[3]]*Sqrt[1 - x^2]) + I*x^3*(3*I + 3*Sqrt[3] + Sqrt[6 - (6*I)*Sqrt[3]]*Sqrt[1 - x^2])])/Sqrt[(1 - I*Sqrt[3])/6] + ((3 + I*Sqrt[3])*Log[3*I + Sqrt[3] - (-I + Sqrt[3])*x^4 + (2*I)*Sqrt[2 - (2*I)*Sqrt[3]]*Sqrt[1 - x^2] + (5*I)*x^2*(2 + Sqrt[2 - (2*I)*Sqrt[3]]*Sqrt[1 - x^2]) + x^3*(3 - (3*I)*Sqrt[3] - I*Sqrt[6 - (6*I)*Sqrt[3]]*Sqrt[1 - x^2]) - I*x*(-3*I + 5*Sqrt[3] + 3*Sqrt[6 - (6*I)*Sqrt[3]]*Sqrt[1 - x^2])])/Sqrt[(1 - I*Sqrt[3])/6] + (I*(3*I + Sqrt[3])*Log[-3*I + Sqrt[3] - (I + Sqrt[3])*x^4 - (2*I)*Sqrt[2 + (2*I)*Sqrt[3]]*Sqrt[1 - x^2] - (5*I)*x^2*(2 + Sqrt[2 + (2*I)*Sqrt[3]]*Sqrt[1 - x^2]) + x*(3 - (5*I)*Sqrt[3] - (3*I)*Sqrt[6 + (6*I)*Sqrt[3]]*Sqrt[1 - x^2]) - I*x^3*(-3*I + 3*Sqrt[3] + Sqrt[6 + (6*I)*Sqrt[3]]*Sqrt[1 - x^2])])/Sqrt[(1 + I*Sqrt[3])/6] + ((3 - I*Sqrt[3])*Log[-3*I + Sqrt[3] - (I + Sqrt[3])*x^4 - (2*I)*Sqrt[2 + (2*I)*Sqrt[3]]*Sqrt[1 - x^2] - (5*I)*x^2*(2 + Sqrt[2 + (2*I)*Sqrt[3]]*Sqrt[1 - x^2]) + x^3*(3 + (3*I)*Sqrt[3] + I*Sqrt[6 + (6*I)*Sqrt[3]]*Sqrt[1 - x^2]) + I*x*(3*I + 5*Sqrt[3] + 3*Sqrt[6 + (6*I)*Sqrt[3]]*Sqrt[1 - x^2])])/Sqrt[(1 + I*Sqrt[3])/6])/48","C",1
14,1,44,45,0.0449752,"\int \frac{\sin ^{-1}(x)}{1+\sqrt{1-x^2}} \, dx","Integrate[ArcSin[x]/(1 + Sqrt[1 - x^2]),x]","-\log \left(\sqrt{1-x^2}+1\right)+\frac{\left(\sqrt{1-x^2}-1\right) \sin ^{-1}(x)}{x}+\frac{1}{2} \sin ^{-1}(x)^2","-\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,"((-1 + Sqrt[1 - x^2])*ArcSin[x])/x + ArcSin[x]^2/2 - Log[1 + Sqrt[1 - x^2]]","A",1
15,1,64,34,0.1008964,"\int \frac{\log \left(x+\sqrt{1+x^2}\right)}{\left(1-x^2\right)^{3/2}} \, dx","Integrate[Log[x + Sqrt[1 + x^2]]/(1 - x^2)^(3/2),x]","\frac{1}{2} \sqrt{1-x^2} \left(-\frac{2 x \log \left(\sqrt{x^2+1}+x\right)}{x^2-1}-\frac{\sqrt{x^2+1} \sin ^{-1}\left(x^2\right)}{\sqrt{1-x^4}}\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,"(Sqrt[1 - x^2]*(-((Sqrt[1 + x^2]*ArcSin[x^2])/Sqrt[1 - x^4]) - (2*x*Log[x + Sqrt[1 + x^2]])/(-1 + x^2)))/2","A",1
16,1,22,22,0.0284532,"\int \frac{\sin ^{-1}(x)}{\left(1+x^2\right)^{3/2}} \, dx","Integrate[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",1
17,1,89,32,0.0880458,"\int \frac{\log \left(x+\sqrt{-1+x^2}\right)}{\left(1+x^2\right)^{3/2}} \, dx","Integrate[Log[x + Sqrt[-1 + x^2]]/(1 + x^2)^(3/2),x]","\frac{4 x \log \left(\sqrt{x^2-1}+x\right)+\frac{\sqrt{x^2-1} \left(x^2+1\right) \left(\log \left(1-\frac{x^2}{\sqrt{x^4-1}}\right)-\log \left(\frac{x^2}{\sqrt{x^4-1}}+1\right)\right)}{\sqrt{x^4-1}}}{4 \sqrt{x^2+1}}","\frac{x \log \left(\sqrt{x^2-1}+x\right)}{\sqrt{x^2+1}}-\frac{1}{2} \cosh ^{-1}\left(x^2\right)",1,"(4*x*Log[x + Sqrt[-1 + x^2]] + (Sqrt[-1 + x^2]*(1 + x^2)*(Log[1 - x^2/Sqrt[-1 + x^4]] - Log[1 + x^2/Sqrt[-1 + x^4]]))/Sqrt[-1 + x^4])/(4*Sqrt[1 + x^2])","B",1
18,1,43,43,0.0248984,"\int \frac{\log (x)}{x^2 \sqrt{-1+x^2}} \, dx","Integrate[Log[x]/(x^2*Sqrt[-1 + x^2]),x]","\frac{\sqrt{x^2-1}}{x}+\frac{\sqrt{x^2-1} \log (x)}{x}-\log \left(\sqrt{x^2-1}+x\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 + (Sqrt[-1 + x^2]*Log[x])/x - Log[x + Sqrt[-1 + x^2]]","A",1
19,1,28,28,0.0052122,"\int \frac{\sqrt{1+x^3}}{x} \, dx","Integrate[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",1
20,1,26,26,0.0224293,"\int \frac{x \log \left(x+\sqrt{-1+x^2}\right)}{\sqrt{-1+x^2}} \, dx","Integrate[(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",1
21,1,85,38,0.0886433,"\int \frac{x^3 \sin ^{-1}(x)}{\sqrt{1-x^4}} \, dx","Integrate[(x^3*ArcSin[x])/Sqrt[1 - x^4],x]","\frac{1}{4} \left(-2 \sqrt{1-x^4} \sin ^{-1}(x)+\log \left(1-x^2\right)+\frac{\sqrt{1-x^4} x}{\sqrt{1-x^2}}-\log \left(x^3+\sqrt{1-x^2} \sqrt{1-x^4}-x\right)\right)","-\frac{1}{2} \sqrt{1-x^4} \sin ^{-1}(x)+\frac{1}{4} \sqrt{x^2+1} x+\frac{1}{4} \sinh ^{-1}(x)",1,"((x*Sqrt[1 - x^4])/Sqrt[1 - x^2] - 2*Sqrt[1 - x^4]*ArcSin[x] + Log[1 - x^2] - Log[-x + x^3 + Sqrt[1 - x^2]*Sqrt[1 - x^4]])/4","B",1
22,1,88,70,0.1009896,"\int \frac{x^3 \sec ^{-1}(x)}{\sqrt{-1+x^4}} \, dx","Integrate[(x^3*ArcSec[x])/Sqrt[-1 + x^4],x]","\frac{1}{2} \left(\sqrt{x^4-1} \sec ^{-1}(x)-\log \left(x-x^3\right)-\frac{\sqrt{1-\frac{1}{x^2}} \sqrt{x^4-1} x}{x^2-1}+\log \left(-x^2-\sqrt{1-\frac{1}{x^2}} \sqrt{x^4-1} x+1\right)\right)","\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} \tanh ^{-1}\left(\frac{\sqrt{1-\frac{1}{x^2}} x}{\sqrt{x^4-1}}\right)",1,"(-((Sqrt[1 - x^(-2)]*x*Sqrt[-1 + x^4])/(-1 + x^2)) + Sqrt[-1 + x^4]*ArcSec[x] - Log[x - x^3] + Log[1 - x^2 - Sqrt[1 - x^(-2)]*x*Sqrt[-1 + x^4]])/2","A",1
23,1,58,58,0.0406101,"\int \frac{x \tan ^{-1}(x) \log \left(x+\sqrt{1+x^2}\right)}{\sqrt{1+x^2}} \, dx","Integrate[(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",1
24,1,41,55,0.0225706,"\int \frac{x \log \left(1+\sqrt{1-x^2}\right)}{\sqrt{1-x^2}} \, dx","Integrate[(x*Log[1 + Sqrt[1 - x^2]])/Sqrt[1 - x^2],x]","\sqrt{1-x^2}-\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] - (1 + Sqrt[1 - x^2])*Log[1 + Sqrt[1 - x^2]]","A",1
25,1,26,26,0.0202931,"\int \frac{x \log \left(x+\sqrt{1+x^2}\right)}{\sqrt{1+x^2}} \, dx","Integrate[(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",1
26,1,119,78,0.0635663,"\int \frac{x \log \left(x+\sqrt{1-x^2}\right)}{\sqrt{1-x^2}} \, dx","Integrate[(x*Log[x + Sqrt[1 - x^2]])/Sqrt[1 - x^2],x]","\frac{1}{4} \left(4 \sqrt{1-x^2}-\sqrt{2} \log \left(\sqrt{2-2 x^2}-\sqrt{2} x+2\right)-\sqrt{2} \log \left(\sqrt{2-2 x^2}+\sqrt{2} x+2\right)-4 \sqrt{1-x^2} \log \left(\sqrt{1-x^2}+x\right)+2 \sqrt{2} \log \left(2 x+\sqrt{2}\right)\right)","\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,"(4*Sqrt[1 - x^2] + 2*Sqrt[2]*Log[Sqrt[2] + 2*x] - Sqrt[2]*Log[2 - Sqrt[2]*x + Sqrt[2 - 2*x^2]] - Sqrt[2]*Log[2 + Sqrt[2]*x + Sqrt[2 - 2*x^2]] - 4*Sqrt[1 - x^2]*Log[x + Sqrt[1 - x^2]])/4","A",1
27,1,25,39,0.0328186,"\int \frac{\log (x)}{x^2 \sqrt{1-x^2}} \, dx","Integrate[Log[x]/(x^2*Sqrt[1 - x^2]),x]","-\frac{\sqrt{1-x^2} (\log (x)+1)}{x}-\sin ^{-1}(x)","-\frac{\sqrt{1-x^2}}{x}-\frac{\sqrt{1-x^2} \log (x)}{x}-\sin ^{-1}(x)",1,"-ArcSin[x] - (Sqrt[1 - x^2]*(1 + Log[x]))/x","A",1
28,1,17,17,0.0158263,"\int \frac{x \tan ^{-1}(x)}{\sqrt{1+x^2}} \, dx","Integrate[(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",1
29,1,77,57,0.0692169,"\int \frac{\tan ^{-1}(x)}{x^2 \sqrt{1-x^2}} \, dx","Integrate[ArcTan[x]/(x^2*Sqrt[1 - x^2]),x]","-\frac{\log \left(x^2+1\right)}{\sqrt{2}}+\frac{\log \left(-x^2+2 \sqrt{2-2 x^2}+3\right)}{\sqrt{2}}-\log \left(\sqrt{1-x^2}+1\right)-\frac{\sqrt{1-x^2} \tan ^{-1}(x)}{x}+\log (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)",1,"-((Sqrt[1 - x^2]*ArcTan[x])/x) + Log[x] - Log[1 + x^2]/Sqrt[2] + Log[3 - x^2 + 2*Sqrt[2 - 2*x^2]]/Sqrt[2] - Log[1 + Sqrt[1 - x^2]]","A",1
30,1,45,45,0.0356311,"\int \frac{x \tan ^{-1}(x)}{\sqrt{1-x^2}} \, dx","Integrate[(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",1
31,1,33,29,0.026305,"\int \frac{\tan ^{-1}(x)}{x^2 \sqrt{1+x^2}} \, dx","Integrate[ArcTan[x]/(x^2*Sqrt[1 + x^2]),x]","-\log \left(\sqrt{x^2+1}+1\right)-\frac{\sqrt{x^2+1} \tan ^{-1}(x)}{x}+\log (x)","-\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) + Log[x] - Log[1 + Sqrt[1 + x^2]]","A",1
32,1,21,21,0.0153351,"\int \frac{\sin ^{-1}(x)}{x^2 \sqrt{1-x^2}} \, dx","Integrate[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",1
33,1,27,34,0.0200681,"\int \frac{x \log (x)}{\sqrt{-1+x^2}} \, dx","Integrate[(x*Log[x])/Sqrt[-1 + x^2],x]","\sqrt{x^2-1} (\log (x)-1)-\tan ^{-1}\left(\frac{1}{\sqrt{x^2-1}}\right)","-\sqrt{x^2-1}+\sqrt{x^2-1} \log (x)+\tan ^{-1}\left(\sqrt{x^2-1}\right)",1,"-ArcTan[1/Sqrt[-1 + x^2]] + Sqrt[-1 + x^2]*(-1 + Log[x])","A",1
34,1,21,33,0.0252259,"\int \frac{\log (x)}{x^2 \sqrt{1+x^2}} \, dx","Integrate[Log[x]/(x^2*Sqrt[1 + x^2]),x]","\sinh ^{-1}(x)-\frac{\sqrt{x^2+1} (\log (x)+1)}{x}","-\frac{\sqrt{x^2+1}}{x}-\frac{\sqrt{x^2+1} \log (x)}{x}+\sinh ^{-1}(x)",1,"ArcSinh[x] - (Sqrt[1 + x^2]*(1 + Log[x]))/x","A",1
35,1,35,25,0.0434859,"\int \frac{x \sec ^{-1}(x)}{\sqrt{-1+x^2}} \, dx","Integrate[(x*ArcSec[x])/Sqrt[-1 + x^2],x]","\frac{\left(x^2-1\right) \sec ^{-1}(x)-\sqrt{1-\frac{1}{x^2}} x \log (x)}{\sqrt{x^2-1}}","\sqrt{x^2-1} \sec ^{-1}(x)-\frac{x \log (x)}{\sqrt{x^2}}",1,"((-1 + x^2)*ArcSec[x] - Sqrt[1 - x^(-2)]*x*Log[x])/Sqrt[-1 + x^2]","A",1
36,1,40,34,0.0179149,"\int \frac{x \log (x)}{\sqrt{1+x^2}} \, dx","Integrate[(x*Log[x])/Sqrt[1 + x^2],x]","-\sqrt{x^2+1}+\sqrt{x^2+1} \log (x)+\log \left(\sqrt{x^2+1}+1\right)-\log (x)","-\sqrt{x^2+1}+\sqrt{x^2+1} \log (x)+\tanh ^{-1}\left(\sqrt{x^2+1}\right)",1,"-Sqrt[1 + x^2] - Log[x] + Sqrt[1 + x^2]*Log[x] + Log[1 + Sqrt[1 + x^2]]","A",1
37,1,46,16,0.0528175,"\int \frac{\sin (x)}{1+\sin ^2(x)} \, dx","Integrate[Sin[x]/(1 + Sin[x]^2),x]","-\frac{i \left(\tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right)-i}{\sqrt{2}}\right)-\tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right)+i}{\sqrt{2}}\right)\right)}{\sqrt{2}}","-\frac{\tanh ^{-1}\left(\frac{\cos (x)}{\sqrt{2}}\right)}{\sqrt{2}}",1,"((-I)*(ArcTan[(-I + Tan[x/2])/Sqrt[2]] - ArcTan[(I + Tan[x/2])/Sqrt[2]]))/Sqrt[2]","C",1
38,1,36,23,0.1013148,"\int \frac{1+x^2}{\left(1-x^2\right) \sqrt{1+x^4}} \, dx","Integrate[(1 + x^2)/((1 - x^2)*Sqrt[1 + x^4]),x]","\sqrt[4]{-1} \left(\operatorname{EllipticF}\left(i \sinh ^{-1}\left(\sqrt[4]{-1} x\right),-1\right)-2 \Pi \left(i;\left.\sin ^{-1}\left((-1)^{3/4} x\right)\right|-1\right)\right)","\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{\sqrt{2}}",1,"(-1)^(1/4)*(EllipticF[I*ArcSinh[(-1)^(1/4)*x], -1] - 2*EllipticPi[I, ArcSin[(-1)^(3/4)*x], -1])","C",1
39,1,40,23,0.095507,"\int \frac{1-x^2}{\left(1+x^2\right) \sqrt{1+x^4}} \, dx","Integrate[(1 - x^2)/((1 + x^2)*Sqrt[1 + x^4]),x]","\sqrt[4]{-1} \left(\operatorname{EllipticF}\left(i \sinh ^{-1}\left(\sqrt[4]{-1} x\right),-1\right)-2 \Pi \left(-i;\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)\right)","\frac{\tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{\sqrt{2}}",1,"(-1)^(1/4)*(EllipticF[I*ArcSinh[(-1)^(1/4)*x], -1] - 2*EllipticPi[-I, I*ArcSinh[(-1)^(1/4)*x], -1])","C",1
40,1,39,22,0.0507049,"\int \frac{\log (\sin (x))}{1+\sin (x)} \, dx","Integrate[Log[Sin[x]]/(1 + Sin[x]),x]","-x-2 \log \left(\cos \left(\frac{x}{2}\right)\right)+\frac{2 \sin \left(\frac{x}{2}\right) \log (\sin (x))}{\sin \left(\frac{x}{2}\right)+\cos \left(\frac{x}{2}\right)}","-x-\tanh ^{-1}(\cos (x))-\frac{\cos (x) \log (\sin (x))}{\sin (x)+1}",1,"-x - 2*Log[Cos[x/2]] + (2*Log[Sin[x]]*Sin[x/2])/(Cos[x/2] + Sin[x/2])","A",1
41,1,87,42,0.0942936,"\int \log (\sin (x)) \sqrt{1+\sin (x)} \, dx","Integrate[Log[Sin[x]]*Sqrt[1 + Sin[x]],x]","\frac{2 \sqrt{\sin (x)+1} \left(\sin \left(\frac{x}{2}\right) (\log (\sin (x))-2)-\log \left(-\sin \left(\frac{x}{2}\right)+\cos \left(\frac{x}{2}\right)+1\right)+\log \left(\sin \left(\frac{x}{2}\right)-\cos \left(\frac{x}{2}\right)+1\right)-\cos \left(\frac{x}{2}\right) (\log (\sin (x))-2)\right)}{\sin \left(\frac{x}{2}\right)+\cos \left(\frac{x}{2}\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,"(2*(-Log[1 + Cos[x/2] - Sin[x/2]] + Log[1 - Cos[x/2] + Sin[x/2]] - Cos[x/2]*(-2 + Log[Sin[x]]) + (-2 + Log[Sin[x]])*Sin[x/2])*Sqrt[1 + Sin[x]])/(Cos[x/2] + Sin[x/2])","B",1
42,1,45,28,0.0374103,"\int \frac{\sec (x)}{\sqrt{-1+\sec ^4(x)}} \, dx","Integrate[Sec[x]/Sqrt[-1 + Sec[x]^4],x]","-\frac{\sqrt{\cos (2 x)+3} \tan (x) \sec (x) \tanh ^{-1}\left(\frac{1}{2} \sqrt{4-2 \sin ^2(x)}\right)}{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,"-1/2*(ArcTanh[Sqrt[4 - 2*Sin[x]^2]/2]*Sqrt[3 + Cos[2*x]]*Sec[x]*Tan[x])/Sqrt[-1 + Sec[x]^4]","A",1
43,1,55,34,0.0727124,"\int \frac{\tan (x)}{\sqrt{1+\tan ^4(x)}} \, dx","Integrate[Tan[x]/Sqrt[1 + Tan[x]^4],x]","-\frac{\sqrt{\cos (4 x)+3} \sec ^2(x) \log \left(\sqrt{2} \cos (2 x)+\sqrt{\cos (4 x)+3}\right)}{4 \sqrt{2} \sqrt{\tan ^4(x)+1}}","-\frac{\tanh ^{-1}\left(\frac{1-\tan ^2(x)}{\sqrt{2} \sqrt{\tan ^4(x)+1}}\right)}{2 \sqrt{2}}",1,"-1/4*(Sqrt[3 + Cos[4*x]]*Log[Sqrt[2]*Cos[2*x] + Sqrt[3 + Cos[4*x]]]*Sec[x]^2)/(Sqrt[2]*Sqrt[1 + Tan[x]^4])","A",1
44,1,65,39,0.0884539,"\int \frac{\sin (x)}{\sqrt{1-\sin ^6(x)}} \, dx","Integrate[Sin[x]/Sqrt[1 - Sin[x]^6],x]","-\frac{\cos (x) \sqrt{-8 \cos (2 x)+\cos (4 x)+15} \tanh ^{-1}\left(\frac{\sqrt{\frac{3}{2}} (\cos (2 x)-3)}{\sqrt{-8 \cos (2 x)+\cos (4 x)+15}}\right)}{4 \sqrt{6-6 \sin ^6(x)}}","\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,"-1/4*(ArcTanh[(Sqrt[3/2]*(-3 + Cos[2*x]))/Sqrt[15 - 8*Cos[2*x] + Cos[4*x]]]*Cos[x]*Sqrt[15 - 8*Cos[2*x] + Cos[4*x]])/Sqrt[6 - 6*Sin[x]^6]","A",1
45,1,552,337,2.1817323,"\int \sqrt{-\sqrt{-1+\sec (x)}+\sqrt{1+\sec (x)}} \, dx","Integrate[Sqrt[-Sqrt[-1 + Sec[x]] + Sqrt[1 + Sec[x]]],x]","\frac{\sqrt[4]{2} \sin (x) \cos (x) \left(\sqrt{\sec (x)-1}-\sqrt{\sec (x)+1}\right)^2 \left(2 \sin \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\frac{\sec \left(\frac{\pi }{8}\right) \sqrt{\sqrt{\sec (x)+1}-\sqrt{\sec (x)-1}}}{\sqrt[4]{2}}-\tan \left(\frac{\pi }{8}\right)\right)+2 \sin \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\frac{\sec \left(\frac{\pi }{8}\right) \sqrt{\sqrt{\sec (x)+1}-\sqrt{\sec (x)-1}}}{\sqrt[4]{2}}+\tan \left(\frac{\pi }{8}\right)\right)+\cos \left(\frac{\pi }{8}\right) \log \left(\sqrt{2} \left(\sqrt{\sec (x)+1}-\sqrt{\sec (x)-1}\right)-2\ 2^{3/4} \sin \left(\frac{\pi }{8}\right) \sqrt{\sqrt{\sec (x)+1}-\sqrt{\sec (x)-1}}+2\right)-\cos \left(\frac{\pi }{8}\right) \log \left(\sqrt{2} \left(\sqrt{\sec (x)+1}-\sqrt{\sec (x)-1}\right)+2\ 2^{3/4} \sin \left(\frac{\pi }{8}\right) \sqrt{\sqrt{\sec (x)+1}-\sqrt{\sec (x)-1}}+2\right)-\sin \left(\frac{\pi }{8}\right) \log \left(\sqrt{2} \left(\sqrt{\sec (x)+1}-\sqrt{\sec (x)-1}\right)-2\ 2^{3/4} \cos \left(\frac{\pi }{8}\right) \sqrt{\sqrt{\sec (x)+1}-\sqrt{\sec (x)-1}}+2\right)+\sin \left(\frac{\pi }{8}\right) \log \left(\sqrt{2} \left(\sqrt{\sec (x)+1}-\sqrt{\sec (x)-1}\right)+\sqrt[4]{2} \csc \left(\frac{\pi }{8}\right) \sqrt{\sqrt{\sec (x)+1}-\sqrt{\sec (x)-1}}+2\right)+2 \cos \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\cot \left(\frac{\pi }{8}\right)-\frac{\csc \left(\frac{\pi }{8}\right) \sqrt{\sqrt{\sec (x)+1}-\sqrt{\sec (x)-1}}}{\sqrt[4]{2}}\right)-2 \cos \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\frac{\csc \left(\frac{\pi }{8}\right) \sqrt{\sqrt{\sec (x)+1}-\sqrt{\sec (x)-1}}}{\sqrt[4]{2}}+\cot \left(\frac{\pi }{8}\right)\right)\right)}{\cos (2 x)+2 \cos (x) \sqrt{\sec (x)-1} \sqrt{\sec (x)+1}-1}","\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,"(2^(1/4)*Cos[x]*(Sqrt[-1 + Sec[x]] - Sqrt[1 + Sec[x]])^2*(2*ArcTan[Cot[Pi/8] - (Csc[Pi/8]*Sqrt[-Sqrt[-1 + Sec[x]] + Sqrt[1 + Sec[x]]])/2^(1/4)]*Cos[Pi/8] - 2*ArcTan[Cot[Pi/8] + (Csc[Pi/8]*Sqrt[-Sqrt[-1 + Sec[x]] + Sqrt[1 + Sec[x]]])/2^(1/4)]*Cos[Pi/8] + Cos[Pi/8]*Log[2 + Sqrt[2]*(-Sqrt[-1 + Sec[x]] + Sqrt[1 + Sec[x]]) - 2*2^(3/4)*Sqrt[-Sqrt[-1 + Sec[x]] + Sqrt[1 + Sec[x]]]*Sin[Pi/8]] - Cos[Pi/8]*Log[2 + Sqrt[2]*(-Sqrt[-1 + Sec[x]] + Sqrt[1 + Sec[x]]) + 2*2^(3/4)*Sqrt[-Sqrt[-1 + Sec[x]] + Sqrt[1 + Sec[x]]]*Sin[Pi/8]] + 2*ArcTan[(Sec[Pi/8]*Sqrt[-Sqrt[-1 + Sec[x]] + Sqrt[1 + Sec[x]]])/2^(1/4) - Tan[Pi/8]]*Sin[Pi/8] + 2*ArcTan[(Sec[Pi/8]*Sqrt[-Sqrt[-1 + Sec[x]] + Sqrt[1 + Sec[x]]])/2^(1/4) + Tan[Pi/8]]*Sin[Pi/8] - Log[2 - 2*2^(3/4)*Cos[Pi/8]*Sqrt[-Sqrt[-1 + Sec[x]] + Sqrt[1 + Sec[x]]] + Sqrt[2]*(-Sqrt[-1 + Sec[x]] + Sqrt[1 + Sec[x]])]*Sin[Pi/8] + Log[2 + 2^(1/4)*Csc[Pi/8]*Sqrt[-Sqrt[-1 + Sec[x]] + Sqrt[1 + Sec[x]]] + Sqrt[2]*(-Sqrt[-1 + Sec[x]] + Sqrt[1 + Sec[x]])]*Sin[Pi/8])*Sin[x])/(-1 + Cos[2*x] + 2*Cos[x]*Sqrt[-1 + Sec[x]]*Sqrt[1 + Sec[x]])","A",0
46,1,58,77,0.0224165,"\int x \tan ^{-1}(x)^2 \log \left(1+x^2\right) \, dx","Integrate[x*ArcTan[x]^2*Log[1 + x^2],x]","\frac{1}{4} \left(\left(\log \left(x^2+1\right)-6\right) \log \left(x^2+1\right)+2 \left(-x^2+\left(x^2+1\right) \log \left(x^2+1\right)-3\right) \tan ^{-1}(x)^2-4 x \left(\log \left(x^2+1\right)-3\right) \tan ^{-1}(x)\right)","\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,"(-4*x*ArcTan[x]*(-3 + Log[1 + x^2]) + (-6 + Log[1 + x^2])*Log[1 + x^2] + 2*ArcTan[x]^2*(-3 - x^2 + (1 + x^2)*Log[1 + x^2]))/4","A",1
47,1,136,120,0.3127511,"\int \tan ^{-1}\left(x \sqrt{1+x^2}\right) \, dx","Integrate[ArcTan[x*Sqrt[1 + x^2]],x]","\frac{1}{4} \left(4 x \tan ^{-1}\left(x \sqrt{x^2+1}\right)+\left(1+i \sqrt{3}\right) \sqrt{2-2 i \sqrt{3}} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{x^2+1}}{\sqrt{1-i \sqrt{3}}}\right)+\left(1-i \sqrt{3}\right) \sqrt{2+2 i \sqrt{3}} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{x^2+1}}{\sqrt{1+i \sqrt{3}}}\right)\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,"(4*x*ArcTan[x*Sqrt[1 + x^2]] + (1 + I*Sqrt[3])*Sqrt[2 - (2*I)*Sqrt[3]]*ArcTanh[(Sqrt[2]*Sqrt[1 + x^2])/Sqrt[1 - I*Sqrt[3]]] + (1 - I*Sqrt[3])*Sqrt[2 + (2*I)*Sqrt[3]]*ArcTanh[(Sqrt[2]*Sqrt[1 + x^2])/Sqrt[1 + I*Sqrt[3]]])/4","C",1
48,1,39,31,0.3913885,"\int -\tan ^{-1}\left(\sqrt{x}-\sqrt{1+x}\right) \, dx","Integrate[-ArcTan[Sqrt[x] - Sqrt[1 + x]],x]","\frac{\sqrt{x}}{2}-\frac{1}{2} \tan ^{-1}\left(\sqrt{x}\right)-x \tan ^{-1}\left(\sqrt{x}-\sqrt{x+1}\right)","\frac{\sqrt{x}}{2}-(x+1) \tan ^{-1}\left(\sqrt{x}-\sqrt{x+1}\right)",1,"Sqrt[x]/2 - ArcTan[Sqrt[x]]/2 - x*ArcTan[Sqrt[x] - Sqrt[1 + x]]","A",1
49,1,29,29,0.0120795,"\int \sin ^{-1}\left(\frac{x}{\sqrt{1-x^2}}\right) \, dx","Integrate[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",1
50,1,106,106,0.1834205,"\int \tan ^{-1}\left(x \sqrt{1-x^2}\right) \, dx","Integrate[ArcTan[x*Sqrt[1 - x^2]],x]","x \tan ^{-1}\left(x \sqrt{1-x^2}\right)-\frac{\sqrt{\frac{2}{\sqrt{5}-1}} \left(\left(1+\sqrt{5}\right) \tan ^{-1}\left(\sqrt{\frac{2}{\sqrt{5}-1}} \sqrt{1-x^2}\right)-2 \tanh ^{-1}\left(\frac{\sqrt{2-2 x^2}}{\sqrt{1+\sqrt{5}}}\right)\right)}{1+\sqrt{5}}","-\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,"x*ArcTan[x*Sqrt[1 - x^2]] - (Sqrt[2/(-1 + Sqrt[5])]*((1 + Sqrt[5])*ArcTan[Sqrt[2/(-1 + Sqrt[5])]*Sqrt[1 - x^2]] - 2*ArcTanh[Sqrt[2 - 2*x^2]/Sqrt[1 + Sqrt[5]]]))/(1 + Sqrt[5])","A",1