1,0,0,51,0.0000383,"\int \sin ^{-1}(x) \log (x) \, dx","IntegrateAlgebraic[ArcSin[x]*Log[x],x]","\int \sin ^{-1}(x) \log (x) \, dx","-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,"Could not integrate","F",-1
2,0,0,17,0.0000376,"\int \frac{x \sin ^{-1}(x)}{\sqrt{1-x^2}} \, dx","IntegrateAlgebraic[(x*ArcSin[x])/Sqrt[1 - x^2],x]","\int \frac{x \sin ^{-1}(x)}{\sqrt{1-x^2}} \, dx","x-\sqrt{1-x^2} \sin ^{-1}(x)",1,"Could not integrate","F",-1
3,0,0,69,0.0000506,"\int -\sin ^{-1}\left(\sqrt{x}-\sqrt{1+x}\right) \, dx","IntegrateAlgebraic[-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,"Could not integrate","F",-1
4,0,0,97,0.0000344,"\int \log \left(1+x \sqrt{1+x^2}\right) \, dx","IntegrateAlgebraic[Log[1 + x*Sqrt[1 + x^2]],x]","\int \log \left(1+x \sqrt{1+x^2}\right) \, dx","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,"Could not integrate","F",-1
5,0,0,45,0.0000419,"\int \frac{\cos ^2(x)}{\sqrt{1+\cos ^2(x)+\cos ^4(x)}} \, dx","IntegrateAlgebraic[Cos[x]^2/Sqrt[1 + Cos[x]^2 + Cos[x]^4],x]","\int \frac{\cos ^2(x)}{\sqrt{1+\cos ^2(x)+\cos ^4(x)}} \, dx","\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,"Could not integrate","F",-1
6,0,0,56,0.0000329,"\int \tan (x) \sqrt{1+\tan ^4(x)} \, dx","IntegrateAlgebraic[Tan[x]*Sqrt[1 + Tan[x]^4],x]","\int \tan (x) \sqrt{1+\tan ^4(x)} \, dx","\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,"Could not integrate","F",-1
7,0,0,15,0.0000347,"\int \frac{\tan (x)}{\sqrt{1+\sec ^3(x)}} \, dx","IntegrateAlgebraic[Tan[x]/Sqrt[1 + Sec[x]^3],x]","\int \frac{\tan (x)}{\sqrt{1+\sec ^3(x)}} \, dx","-\frac{2}{3} \tanh ^{-1}\left(\sqrt{\sec ^3(x)+1}\right)",1,"Could not integrate","F",-1
8,0,0,137,0.000031,"\int \sqrt{2+2 \tan (x)+\tan ^2(x)} \, dx","IntegrateAlgebraic[Sqrt[2 + 2*Tan[x] + Tan[x]^2],x]","\int \sqrt{2+2 \tan (x)+\tan ^2(x)} \, dx","-\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,"Could not integrate","F",-1
9,0,0,41,0.0000356,"\int \tan ^{-1}\left(\sqrt{-1+\sec (x)}\right) \sin (x) \, dx","IntegrateAlgebraic[ArcTan[Sqrt[-1 + Sec[x]]]*Sin[x],x]","\int \tan ^{-1}\left(\sqrt{-1+\sec (x)}\right) \sin (x) \, dx","\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,"Could not integrate","F",-1
10,0,0,44,0.0000354,"\int \frac{e^{\sin ^{-1}(x)} x^3}{\sqrt{1-x^2}} \, dx","IntegrateAlgebraic[(E^ArcSin[x]*x^3)/Sqrt[1 - x^2],x]","\int \frac{e^{\sin ^{-1}(x)} x^3}{\sqrt{1-x^2}} \, dx","\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,"Could not integrate","F",-1
11,0,0,68,0.0000396,"\int \frac{x \log \left(1+x^2\right) \log \left(x+\sqrt{1+x^2}\right)}{\sqrt{1+x^2}} \, dx","IntegrateAlgebraic[(x*Log[1 + x^2]*Log[x + Sqrt[1 + x^2]])/Sqrt[1 + x^2],x]","\int \frac{x \log \left(1+x^2\right) \log \left(x+\sqrt{1+x^2}\right)}{\sqrt{1+x^2}} \, dx","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,"Could not integrate","F",-1
12,0,0,141,0.0000361,"\int \tan ^{-1}\left(x+\sqrt{1-x^2}\right) \, dx","IntegrateAlgebraic[ArcTan[x + Sqrt[1 - x^2]],x]","\int \tan ^{-1}\left(x+\sqrt{1-x^2}\right) \, dx","\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,"Could not integrate","F",-1
13,0,0,152,0.0000424,"\int \frac{x \tan ^{-1}\left(x+\sqrt{1-x^2}\right)}{\sqrt{1-x^2}} \, dx","IntegrateAlgebraic[(x*ArcTan[x + Sqrt[1 - x^2]])/Sqrt[1 - x^2],x]","\int \frac{x \tan ^{-1}\left(x+\sqrt{1-x^2}\right)}{\sqrt{1-x^2}} \, dx","\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,"Could not integrate","F",-1
14,0,0,45,0.000036,"\int \frac{\sin ^{-1}(x)}{1+\sqrt{1-x^2}} \, dx","IntegrateAlgebraic[ArcSin[x]/(1 + Sqrt[1 - x^2]),x]","\int \frac{\sin ^{-1}(x)}{1+\sqrt{1-x^2}} \, dx","-\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,"Could not integrate","F",-1
15,0,0,34,0.0000387,"\int \frac{\log \left(x+\sqrt{1+x^2}\right)}{\left(1-x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[Log[x + Sqrt[1 + x^2]]/(1 - x^2)^(3/2),x]","\int \frac{\log \left(x+\sqrt{1+x^2}\right)}{\left(1-x^2\right)^{3/2}} \, dx","\frac{x \log \left(\sqrt{x^2+1}+x\right)}{\sqrt{1-x^2}}-\frac{1}{2} \sin ^{-1}\left(x^2\right)",1,"Could not integrate","F",-1
16,0,0,22,0.0000313,"\int \frac{\sin ^{-1}(x)}{\left(1+x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[ArcSin[x]/(1 + x^2)^(3/2),x]","\int \frac{\sin ^{-1}(x)}{\left(1+x^2\right)^{3/2}} \, dx","\frac{x \sin ^{-1}(x)}{\sqrt{x^2+1}}-\frac{1}{2} \sin ^{-1}\left(x^2\right)",1,"Could not integrate","F",-1
17,0,0,32,0.0000349,"\int \frac{\log \left(x+\sqrt{-1+x^2}\right)}{\left(1+x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[Log[x + Sqrt[-1 + x^2]]/(1 + x^2)^(3/2),x]","\int \frac{\log \left(x+\sqrt{-1+x^2}\right)}{\left(1+x^2\right)^{3/2}} \, dx","\frac{x \log \left(\sqrt{x^2-1}+x\right)}{\sqrt{x^2+1}}-\frac{1}{2} \cosh ^{-1}\left(x^2\right)",1,"Could not integrate","F",-1
18,0,0,43,0.0000318,"\int \frac{\log (x)}{x^2 \sqrt{-1+x^2}} \, dx","IntegrateAlgebraic[Log[x]/(x^2*Sqrt[-1 + x^2]),x]","\int \frac{\log (x)}{x^2 \sqrt{-1+x^2}} \, dx","\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,"Could not integrate","F",-1
19,1,28,28,0.0289471,"\int \frac{\sqrt{1+x^3}}{x} \, dx","IntegrateAlgebraic[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
20,0,0,26,0.0000552,"\int \frac{x \log \left(x+\sqrt{-1+x^2}\right)}{\sqrt{-1+x^2}} \, dx","IntegrateAlgebraic[(x*Log[x + Sqrt[-1 + x^2]])/Sqrt[-1 + x^2],x]","\int \frac{x \log \left(x+\sqrt{-1+x^2}\right)}{\sqrt{-1+x^2}} \, dx","\sqrt{x^2-1} \log \left(\sqrt{x^2-1}+x\right)-x",1,"Could not integrate","F",-1
21,0,0,38,0.0000394,"\int \frac{x^3 \sin ^{-1}(x)}{\sqrt{1-x^4}} \, dx","IntegrateAlgebraic[(x^3*ArcSin[x])/Sqrt[1 - x^4],x]","\int \frac{x^3 \sin ^{-1}(x)}{\sqrt{1-x^4}} \, dx","-\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,"Could not integrate","F",-1
22,0,0,70,0.0000328,"\int \frac{x^3 \sec ^{-1}(x)}{\sqrt{-1+x^4}} \, dx","IntegrateAlgebraic[(x^3*ArcSec[x])/Sqrt[-1 + x^4],x]","\int \frac{x^3 \sec ^{-1}(x)}{\sqrt{-1+x^4}} \, dx","\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,"Could not integrate","F",-1
23,0,0,58,0.0000401,"\int \frac{x \tan ^{-1}(x) \log \left(x+\sqrt{1+x^2}\right)}{\sqrt{1+x^2}} \, dx","IntegrateAlgebraic[(x*ArcTan[x]*Log[x + Sqrt[1 + x^2]])/Sqrt[1 + x^2],x]","\int \frac{x \tan ^{-1}(x) \log \left(x+\sqrt{1+x^2}\right)}{\sqrt{1+x^2}} \, dx","-\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,"Could not integrate","F",-1
24,0,0,55,0.0000393,"\int \frac{x \log \left(1+\sqrt{1-x^2}\right)}{\sqrt{1-x^2}} \, dx","IntegrateAlgebraic[(x*Log[1 + Sqrt[1 - x^2]])/Sqrt[1 - x^2],x]","\int \frac{x \log \left(1+\sqrt{1-x^2}\right)}{\sqrt{1-x^2}} \, dx","\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,"Could not integrate","F",-1
25,0,0,26,0.0000366,"\int \frac{x \log \left(x+\sqrt{1+x^2}\right)}{\sqrt{1+x^2}} \, dx","IntegrateAlgebraic[(x*Log[x + Sqrt[1 + x^2]])/Sqrt[1 + x^2],x]","\int \frac{x \log \left(x+\sqrt{1+x^2}\right)}{\sqrt{1+x^2}} \, dx","\sqrt{x^2+1} \log \left(\sqrt{x^2+1}+x\right)-x",1,"Could not integrate","F",-1
26,0,0,78,0.0000398,"\int \frac{x \log \left(x+\sqrt{1-x^2}\right)}{\sqrt{1-x^2}} \, dx","IntegrateAlgebraic[(x*Log[x + Sqrt[1 - x^2]])/Sqrt[1 - x^2],x]","\int \frac{x \log \left(x+\sqrt{1-x^2}\right)}{\sqrt{1-x^2}} \, dx","\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,"Could not integrate","F",-1
27,0,0,39,0.0000343,"\int \frac{\log (x)}{x^2 \sqrt{1-x^2}} \, dx","IntegrateAlgebraic[Log[x]/(x^2*Sqrt[1 - x^2]),x]","\int \frac{\log (x)}{x^2 \sqrt{1-x^2}} \, dx","-\frac{\sqrt{1-x^2}}{x}-\frac{\sqrt{1-x^2} \log (x)}{x}-\sin ^{-1}(x)",1,"Could not integrate","F",-1
28,0,0,17,0.0000308,"\int \frac{x \tan ^{-1}(x)}{\sqrt{1+x^2}} \, dx","IntegrateAlgebraic[(x*ArcTan[x])/Sqrt[1 + x^2],x]","\int \frac{x \tan ^{-1}(x)}{\sqrt{1+x^2}} \, dx","\sqrt{x^2+1} \tan ^{-1}(x)-\sinh ^{-1}(x)",1,"Could not integrate","F",-1
29,0,0,57,0.0000748,"\int \frac{\tan ^{-1}(x)}{x^2 \sqrt{1-x^2}} \, dx","IntegrateAlgebraic[ArcTan[x]/(x^2*Sqrt[1 - x^2]),x]","\int \frac{\tan ^{-1}(x)}{x^2 \sqrt{1-x^2}} \, dx","-\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,"Could not integrate","F",-1
30,0,0,45,0.0000335,"\int \frac{x \tan ^{-1}(x)}{\sqrt{1-x^2}} \, dx","IntegrateAlgebraic[(x*ArcTan[x])/Sqrt[1 - x^2],x]","\int \frac{x \tan ^{-1}(x)}{\sqrt{1-x^2}} \, dx","-\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,"Could not integrate","F",-1
31,0,0,29,0.000032,"\int \frac{\tan ^{-1}(x)}{x^2 \sqrt{1+x^2}} \, dx","IntegrateAlgebraic[ArcTan[x]/(x^2*Sqrt[1 + x^2]),x]","\int \frac{\tan ^{-1}(x)}{x^2 \sqrt{1+x^2}} \, dx","-\frac{\sqrt{x^2+1} \tan ^{-1}(x)}{x}-\tanh ^{-1}\left(\sqrt{x^2+1}\right)",1,"Could not integrate","F",-1
32,0,0,21,0.0000329,"\int \frac{\sin ^{-1}(x)}{x^2 \sqrt{1-x^2}} \, dx","IntegrateAlgebraic[ArcSin[x]/(x^2*Sqrt[1 - x^2]),x]","\int \frac{\sin ^{-1}(x)}{x^2 \sqrt{1-x^2}} \, dx","\log (x)-\frac{\sqrt{1-x^2} \sin ^{-1}(x)}{x}",1,"Could not integrate","F",-1
33,0,0,34,0.0000321,"\int \frac{x \log (x)}{\sqrt{-1+x^2}} \, dx","IntegrateAlgebraic[(x*Log[x])/Sqrt[-1 + x^2],x]","\int \frac{x \log (x)}{\sqrt{-1+x^2}} \, dx","-\sqrt{x^2-1}+\sqrt{x^2-1} \log (x)+\tan ^{-1}\left(\sqrt{x^2-1}\right)",1,"Could not integrate","F",-1
34,0,0,33,0.0000323,"\int \frac{\log (x)}{x^2 \sqrt{1+x^2}} \, dx","IntegrateAlgebraic[Log[x]/(x^2*Sqrt[1 + x^2]),x]","\int \frac{\log (x)}{x^2 \sqrt{1+x^2}} \, dx","-\frac{\sqrt{x^2+1}}{x}-\frac{\sqrt{x^2+1} \log (x)}{x}+\sinh ^{-1}(x)",1,"Could not integrate","F",-1
35,0,0,25,0.0000306,"\int \frac{x \sec ^{-1}(x)}{\sqrt{-1+x^2}} \, dx","IntegrateAlgebraic[(x*ArcSec[x])/Sqrt[-1 + x^2],x]","\int \frac{x \sec ^{-1}(x)}{\sqrt{-1+x^2}} \, dx","\sqrt{x^2-1} \sec ^{-1}(x)-\frac{x \log (x)}{\sqrt{x^2}}",1,"Could not integrate","F",-1
36,0,0,34,0.000089,"\int \frac{x \log (x)}{\sqrt{1+x^2}} \, dx","IntegrateAlgebraic[(x*Log[x])/Sqrt[1 + x^2],x]","\int \frac{x \log (x)}{\sqrt{1+x^2}} \, dx","-\sqrt{x^2+1}+\sqrt{x^2+1} \log (x)+\tanh ^{-1}\left(\sqrt{x^2+1}\right)",1,"Could not integrate","F",-1
37,0,0,16,0.0000322,"\int \frac{\sin (x)}{1+\sin ^2(x)} \, dx","IntegrateAlgebraic[Sin[x]/(1 + Sin[x]^2),x]","\int \frac{\sin (x)}{1+\sin ^2(x)} \, dx","-\frac{\tanh ^{-1}\left(\frac{\cos (x)}{\sqrt{2}}\right)}{\sqrt{2}}",1,"Could not integrate","F",-1
38,1,23,23,0.3156374,"\int \frac{1+x^2}{\left(1-x^2\right) \sqrt{1+x^4}} \, dx","IntegrateAlgebraic[(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",1
39,1,23,23,0.3116201,"\int \frac{1-x^2}{\left(1+x^2\right) \sqrt{1+x^4}} \, dx","IntegrateAlgebraic[(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",1
40,0,0,22,0.0000342,"\int \frac{\log (\sin (x))}{1+\sin (x)} \, dx","IntegrateAlgebraic[Log[Sin[x]]/(1 + Sin[x]),x]","\int \frac{\log (\sin (x))}{1+\sin (x)} \, dx","-x-\tanh ^{-1}(\cos (x))-\frac{\cos (x) \log (\sin (x))}{\sin (x)+1}",1,"Could not integrate","F",-1
41,0,0,42,0.0000375,"\int \log (\sin (x)) \sqrt{1+\sin (x)} \, dx","IntegrateAlgebraic[Log[Sin[x]]*Sqrt[1 + Sin[x]],x]","\int \log (\sin (x)) \sqrt{1+\sin (x)} \, dx","\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,"Could not integrate","F",-1
42,0,0,28,0.0000343,"\int \frac{\sec (x)}{\sqrt{-1+\sec ^4(x)}} \, dx","IntegrateAlgebraic[Sec[x]/Sqrt[-1 + Sec[x]^4],x]","\int \frac{\sec (x)}{\sqrt{-1+\sec ^4(x)}} \, dx","-\frac{\tanh ^{-1}\left(\frac{\cos (x) \cot (x) \sqrt{\sec ^4(x)-1}}{\sqrt{2}}\right)}{\sqrt{2}}",1,"Could not integrate","F",-1
43,0,0,34,0.0000328,"\int \frac{\tan (x)}{\sqrt{1+\tan ^4(x)}} \, dx","IntegrateAlgebraic[Tan[x]/Sqrt[1 + Tan[x]^4],x]","\int \frac{\tan (x)}{\sqrt{1+\tan ^4(x)}} \, dx","-\frac{\tanh ^{-1}\left(\frac{1-\tan ^2(x)}{\sqrt{2} \sqrt{\tan ^4(x)+1}}\right)}{2 \sqrt{2}}",1,"Could not integrate","F",-1
44,0,0,39,0.0000342,"\int \frac{\sin (x)}{\sqrt{1-\sin ^6(x)}} \, dx","IntegrateAlgebraic[Sin[x]/Sqrt[1 - Sin[x]^6],x]","\int \frac{\sin (x)}{\sqrt{1-\sin ^6(x)}} \, dx","\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,"Could not integrate","F",-1
45,0,0,337,0.000038,"\int \sqrt{-\sqrt{-1+\sec (x)}+\sqrt{1+\sec (x)}} \, dx","IntegrateAlgebraic[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,"Could not integrate","F",-1
46,0,0,77,0.0000574,"\int x \tan ^{-1}(x)^2 \log \left(1+x^2\right) \, dx","IntegrateAlgebraic[x*ArcTan[x]^2*Log[1 + x^2],x]","\int x \tan ^{-1}(x)^2 \log \left(1+x^2\right) \, dx","\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,"Could not integrate","F",-1
47,0,0,120,0.0000673,"\int \tan ^{-1}\left(x \sqrt{1+x^2}\right) \, dx","IntegrateAlgebraic[ArcTan[x*Sqrt[1 + x^2]],x]","\int \tan ^{-1}\left(x \sqrt{1+x^2}\right) \, dx","-\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,"Could not integrate","F",-1
48,0,0,31,0.0000523,"\int -\tan ^{-1}\left(\sqrt{x}-\sqrt{1+x}\right) \, dx","IntegrateAlgebraic[-ArcTan[Sqrt[x] - Sqrt[1 + x]],x]","\int -\tan ^{-1}\left(\sqrt{x}-\sqrt{1+x}\right) \, dx","\frac{\sqrt{x}}{2}-(x+1) \tan ^{-1}\left(\sqrt{x}-\sqrt{x+1}\right)",1,"Could not integrate","F",-1
49,0,0,29,0.0000346,"\int \sin ^{-1}\left(\frac{x}{\sqrt{1-x^2}}\right) \, dx","IntegrateAlgebraic[ArcSin[x/Sqrt[1 - x^2]],x]","\int \sin ^{-1}\left(\frac{x}{\sqrt{1-x^2}}\right) \, dx","x \sin ^{-1}\left(\frac{x}{\sqrt{1-x^2}}\right)+\tan ^{-1}\left(\sqrt{1-2 x^2}\right)",1,"Could not integrate","F",-1
50,0,0,106,0.0000316,"\int \tan ^{-1}\left(x \sqrt{1-x^2}\right) \, dx","IntegrateAlgebraic[ArcTan[x*Sqrt[1 - x^2]],x]","\int \tan ^{-1}\left(x \sqrt{1-x^2}\right) \, dx","-\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,"Could not integrate","F",-1