1,1,14,14,0.0061581,"\int \frac{1}{a^2-b^2 x^2} \, dx","IntegrateAlgebraic[(a^2 - b^2*x^2)^(-1),x]","\frac{\tanh ^{-1}\left(\frac{b x}{a}\right)}{a b}","\frac{\tanh ^{-1}\left(\frac{b x}{a}\right)}{a b}",1,"ArcTanh[(b*x)/a]/(a*b)","A",1
2,1,14,14,0.0056534,"\int \frac{1}{a^2+b^2 x^2} \, dx","IntegrateAlgebraic[(a^2 + b^2*x^2)^(-1),x]","\frac{\tan ^{-1}\left(\frac{b x}{a}\right)}{a b}","\frac{\tan ^{-1}\left(\frac{b x}{a}\right)}{a b}",1,"ArcTan[(b*x)/a]/(a*b)","A",1
3,0,0,13,0.0000296,"\int \sec (2 a x) \, dx","IntegrateAlgebraic[Sec[2*a*x],x]","\int \sec (2 a x) \, dx","\frac{\tanh ^{-1}(\sin (2 a x))}{2 a}",1,"Could not integrate","F",-1
4,0,0,11,0.0000332,"\int \frac{1}{4} \csc \left(\frac{x}{3}\right) \, dx","IntegrateAlgebraic[Csc[x/3]/4,x]","\int \frac{1}{4} \csc \left(\frac{x}{3}\right) \, dx","-\frac{3}{4} \tanh ^{-1}\left(\cos \left(\frac{x}{3}\right)\right)",1,"Could not integrate","F",-1
5,0,0,15,0.0000332,"\int -\sec \left(\frac{\pi }{4}+2 x\right) \, dx","IntegrateAlgebraic[-Sec[Pi/4 + 2*x],x]","\int -\sec \left(\frac{\pi }{4}+2 x\right) \, dx","-\frac{1}{2} \tanh ^{-1}\left(\sin \left(2 x+\frac{\pi }{4}\right)\right)",1,"Could not integrate","F",-1
6,0,0,2,0.0000269,"\int \sec (x) \tan (x) \, dx","IntegrateAlgebraic[Sec[x]*Tan[x],x]","\int \sec (x) \tan (x) \, dx","\sec (x)",1,"Could not integrate","F",-1
7,0,0,4,0.0000263,"\int \cot (x) \csc (x) \, dx","IntegrateAlgebraic[Cot[x]*Csc[x],x]","\int \cot (x) \csc (x) \, dx","-\csc (x)",1,"Could not integrate","F",-1
8,0,0,6,0.0000379,"\int \csc (2 x) \tan (x) \, dx","IntegrateAlgebraic[Csc[2*x]*Tan[x],x]","\int \csc (2 x) \tan (x) \, dx","\frac{\tan (x)}{2}",1,"Could not integrate","F",-1
9,0,0,9,0.0000263,"\int \frac{1}{1+\cos (x)} \, dx","IntegrateAlgebraic[(1 + Cos[x])^(-1),x]","\int \frac{1}{1+\cos (x)} \, dx","\frac{\sin (x)}{\cos (x)+1}",1,"Could not integrate","F",-1
10,0,0,12,0.000027,"\int \frac{1}{1-\cos (x)} \, dx","IntegrateAlgebraic[(1 - Cos[x])^(-1),x]","\int \frac{1}{1-\cos (x)} \, dx","-\frac{\sin (x)}{1-\cos (x)}",1,"Could not integrate","F",-1
11,0,0,12,0.000033,"\int \frac{\sin (x)}{a-b \cos (x)} \, dx","IntegrateAlgebraic[Sin[x]/(a - b*Cos[x]),x]","\int \frac{\sin (x)}{a-b \cos (x)} \, dx","\frac{\log (a-b \cos (x))}{b}",1,"Could not integrate","F",-1
12,0,0,15,0.0000339,"\int \frac{\cos (x)}{a^2+b^2 \sin ^2(x)} \, dx","IntegrateAlgebraic[Cos[x]/(a^2 + b^2*Sin[x]^2),x]","\int \frac{\cos (x)}{a^2+b^2 \sin ^2(x)} \, dx","\frac{\tan ^{-1}\left(\frac{b \sin (x)}{a}\right)}{a b}",1,"Could not integrate","F",-1
13,0,0,15,0.0000375,"\int \frac{\cos (x)}{a^2-b^2 \sin ^2(x)} \, dx","IntegrateAlgebraic[Cos[x]/(a^2 - b^2*Sin[x]^2),x]","\int \frac{\cos (x)}{a^2-b^2 \sin ^2(x)} \, dx","\frac{\tanh ^{-1}\left(\frac{b \sin (x)}{a}\right)}{a b}",1,"Could not integrate","F",-1
14,0,0,17,0.0000371,"\int \frac{\sin (2 x)}{a^2+b^2 \sin ^2(x)} \, dx","IntegrateAlgebraic[Sin[2*x]/(a^2 + b^2*Sin[x]^2),x]","\int \frac{\sin (2 x)}{a^2+b^2 \sin ^2(x)} \, dx","\frac{\log \left(a^2+b^2 \sin ^2(x)\right)}{b^2}",1,"Could not integrate","F",-1
15,0,0,19,0.0000393,"\int \frac{\sin (2 x)}{a^2-b^2 \sin ^2(x)} \, dx","IntegrateAlgebraic[Sin[2*x]/(a^2 - b^2*Sin[x]^2),x]","\int \frac{\sin (2 x)}{a^2-b^2 \sin ^2(x)} \, dx","-\frac{\log \left(a^2-b^2 \sin ^2(x)\right)}{b^2}",1,"Could not integrate","F",-1
16,0,0,18,0.0000355,"\int \frac{\sin (2 x)}{a^2+b^2 \cos ^2(x)} \, dx","IntegrateAlgebraic[Sin[2*x]/(a^2 + b^2*Cos[x]^2),x]","\int \frac{\sin (2 x)}{a^2+b^2 \cos ^2(x)} \, dx","-\frac{\log \left(a^2+b^2 \cos ^2(x)\right)}{b^2}",1,"Could not integrate","F",-1
17,0,0,18,0.0000361,"\int \frac{\sin (2 x)}{a^2-b^2 \cos ^2(x)} \, dx","IntegrateAlgebraic[Sin[2*x]/(a^2 - b^2*Cos[x]^2),x]","\int \frac{\sin (2 x)}{a^2-b^2 \cos ^2(x)} \, dx","\frac{\log \left(a^2-b^2 \cos ^2(x)\right)}{b^2}",1,"Could not integrate","F",-1
18,0,0,41,0.0000306,"\int \frac{1}{4-\cos ^2(x)} \, dx","IntegrateAlgebraic[(4 - Cos[x]^2)^(-1),x]","\int \frac{1}{4-\cos ^2(x)} \, dx","\frac{x}{2 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{\sin (x) \cos (x)}{\sin ^2(x)+2 \sqrt{3}+3}\right)}{2 \sqrt{3}}",1,"Could not integrate","F",-1
19,0,0,6,0.0000808,"\int \frac{e^x}{-1+e^{2 x}} \, dx","IntegrateAlgebraic[E^x/(-1 + E^(2*x)),x]","\int \frac{e^x}{-1+e^{2 x}} \, dx","-\tanh ^{-1}\left(e^x\right)",1,"Could not integrate","F",-1
20,0,0,3,0.0000272,"\int \frac{1}{x \log (x)} \, dx","IntegrateAlgebraic[1/(x*Log[x]),x]","\int \frac{1}{x \log (x)} \, dx","\log (\log (x))",1,"Could not integrate","F",-1
21,0,0,3,0.0000286,"\int \frac{1}{x \left(1+\log ^2(x)\right)} \, dx","IntegrateAlgebraic[1/(x*(1 + Log[x]^2)),x]","\int \frac{1}{x \left(1+\log ^2(x)\right)} \, dx","\tan ^{-1}(\log (x))",1,"Could not integrate","F",-1
22,0,0,9,0.0000343,"\int \frac{1}{x (1-\log (x))} \, dx","IntegrateAlgebraic[1/(x*(1 - Log[x])),x]","\int \frac{1}{x (1-\log (x))} \, dx","-\log (1-\log (x))",1,"Could not integrate","F",-1
23,0,0,9,0.0000313,"\int \frac{1}{x \left(1+\log \left(\frac{x}{a}\right)\right)} \, dx","IntegrateAlgebraic[1/(x*(1 + Log[x/a])),x]","\int \frac{1}{x \left(1+\log \left(\frac{x}{a}\right)\right)} \, dx","\log \left(\log \left(\frac{x}{a}\right)+1\right)",1,"Could not integrate","F",-1
24,1,25,25,0.0096723,"\int \frac{\left(1-\sqrt{x}+x\right)^2}{x^2} \, dx","IntegrateAlgebraic[(1 - Sqrt[x] + x)^2/x^2,x]","x-4 \sqrt{x}+\frac{4}{\sqrt{x}}-\frac{1}{x}+3 \log (x)","x-4 \sqrt{x}+\frac{4}{\sqrt{x}}-\frac{1}{x}+3 \log (x)",1,"-x^(-1) + 4/Sqrt[x] - 4*Sqrt[x] + x + 3*Log[x]","A",1
25,1,30,30,0.0103945,"\int \frac{\left(2-x^{2/3}\right) \left(\sqrt{x}+x\right)}{x^{3/2}} \, dx","IntegrateAlgebraic[((2 - x^(2/3))*(Sqrt[x] + x))/x^(3/2),x]","-\frac{6 x^{7/6}}{7}-\frac{3 x^{2/3}}{2}+4 \sqrt{x}+2 \log (x)","-\frac{6 x^{7/6}}{7}-\frac{3 x^{2/3}}{2}+4 \sqrt{x}+2 \log (x)",1,"4*Sqrt[x] - (3*x^(2/3))/2 - (6*x^(7/6))/7 + 2*Log[x]","A",1
26,1,10,10,0.0044214,"\int \frac{-1+2 x}{3+2 x} \, dx","IntegrateAlgebraic[(-1 + 2*x)/(3 + 2*x),x]","x-2 \log (2 x+3)","x-2 \log (2 x+3)",1,"x - 2*Log[3 + 2*x]","A",1
27,1,47,47,0.043323,"\int \frac{-5+2 x}{-2+3 x^2} \, dx","IntegrateAlgebraic[(-5 + 2*x)/(-2 + 3*x^2),x]","\frac{1}{12} \left(4-5 \sqrt{6}\right) \log \left(\sqrt{6}-3 x\right)+\frac{1}{12} \left(4+5 \sqrt{6}\right) \log \left(3 x+\sqrt{6}\right)","\frac{1}{12} \left(4-5 \sqrt{6}\right) \log \left(\sqrt{6}-3 x\right)+\frac{1}{12} \left(4+5 \sqrt{6}\right) \log \left(3 x+\sqrt{6}\right)",1,"((4 - 5*Sqrt[6])*Log[Sqrt[6] - 3*x])/12 + ((4 + 5*Sqrt[6])*Log[Sqrt[6] + 3*x])/12","A",1
28,1,30,30,0.0217121,"\int \frac{-5+2 x}{2+3 x^2} \, dx","IntegrateAlgebraic[(-5 + 2*x)/(2 + 3*x^2),x]","\frac{1}{3} \log \left(3 x^2+2\right)-\frac{5 \tan ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{\sqrt{6}}","\frac{1}{3} \log \left(3 x^2+2\right)-\frac{5 \tan ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{\sqrt{6}}",1,"(-5*ArcTan[Sqrt[3/2]*x])/Sqrt[6] + Log[2 + 3*x^2]/3","A",1
29,0,0,21,0.0000335,"\int \sin \left(\frac{x}{4}\right) \sin (x) \, dx","IntegrateAlgebraic[Sin[x/4]*Sin[x],x]","\int \sin \left(\frac{x}{4}\right) \sin (x) \, dx","\frac{2}{3} \sin \left(\frac{3 x}{4}\right)-\frac{2}{5} \sin \left(\frac{5 x}{4}\right)",1,"Could not integrate","F",-1
30,0,0,15,0.0000333,"\int \cos (3 x) \cos (4 x) \, dx","IntegrateAlgebraic[Cos[3*x]*Cos[4*x],x]","\int \cos (3 x) \cos (4 x) \, dx","\frac{\sin (x)}{2}+\frac{1}{14} \sin (7 x)",1,"Could not integrate","F",-1
31,0,0,21,0.0000389,"\int -\tan (a-x) \tan (x) \, dx","IntegrateAlgebraic[-(Tan[a - x]*Tan[x]),x]","\int -\tan (a-x) \tan (x) \, dx","\cot (a) \log (\cos (a-x))-\cot (a) \log (\cos (x))-x",1,"Could not integrate","F",-1
32,0,0,14,0.0000327,"\int \sin ^2(x) \, dx","IntegrateAlgebraic[Sin[x]^2,x]","\int \sin ^2(x) \, dx","\frac{x}{2}-\frac{1}{2} \sin (x) \cos (x)",1,"Could not integrate","F",-1
33,0,0,14,0.0000287,"\int \cos ^2(x) \, dx","IntegrateAlgebraic[Cos[x]^2,x]","\int \cos ^2(x) \, dx","\frac{x}{2}+\frac{1}{2} \sin (x) \cos (x)",1,"Could not integrate","F",-1
34,0,0,8,0.0000288,"\int \cos ^3(x) \sin (x) \, dx","IntegrateAlgebraic[Cos[x]^3*Sin[x],x]","\int \cos ^3(x) \sin (x) \, dx","-\frac{1}{4} \cos ^4(x)",1,"Could not integrate","F",-1
35,0,0,11,0.0000283,"\int \cot ^3(x) \csc (x) \, dx","IntegrateAlgebraic[Cot[x]^3*Csc[x],x]","\int \cot ^3(x) \csc (x) \, dx","\csc (x)-\frac{\csc ^3(x)}{3}",1,"Could not integrate","F",-1
36,0,0,7,0.0000347,"\int \csc ^2(x) \sec ^2(x) \, dx","IntegrateAlgebraic[Csc[x]^2*Sec[x]^2,x]","\int \csc ^2(x) \sec ^2(x) \, dx","\tan (x)-\cot (x)",1,"Could not integrate","F",-1
37,0,0,14,0.0000268,"\int \cot ^2\left(\frac{3 x}{4}\right) \, dx","IntegrateAlgebraic[Cot[(3*x)/4]^2,x]","\int \cot ^2\left(\frac{3 x}{4}\right) \, dx","-x-\frac{4}{3} \cot \left(\frac{3 x}{4}\right)",1,"Could not integrate","F",-1
38,0,0,16,0.000031,"\int (1+\tan (2 x))^2 \, dx","IntegrateAlgebraic[(1 + Tan[2*x])^2,x]","\int (1+\tan (2 x))^2 \, dx","\frac{1}{2} \tan (2 x)-\log (\cos (2 x))",1,"Could not integrate","F",-1
39,0,0,10,0.0000299,"\int (-\cot (x)+\tan (x))^2 \, dx","IntegrateAlgebraic[(-Cot[x] + Tan[x])^2,x]","\int (-\cot (x)+\tan (x))^2 \, dx","-4 x+\tan (x)-\cot (x)",1,"Could not integrate","F",-1
40,0,0,14,0.0000319,"\int (-\sec (x)+\tan (x))^2 \, dx","IntegrateAlgebraic[(-Sec[x] + Tan[x])^2,x]","\int (-\sec (x)+\tan (x))^2 \, dx","-x-\frac{2 \cos (x)}{\sin (x)+1}",1,"Could not integrate","F",-1
41,0,0,11,0.0000562,"\int \frac{\sin (x)}{1+\sin (x)} \, dx","IntegrateAlgebraic[Sin[x]/(1 + Sin[x]),x]","\int \frac{\sin (x)}{1+\sin (x)} \, dx","x+\frac{\cos (x)}{\sin (x)+1}",1,"Could not integrate","F",-1
42,0,0,16,0.0000345,"\int \frac{\cos (x)}{1-\cos (x)} \, dx","IntegrateAlgebraic[Cos[x]/(1 - Cos[x]),x]","\int \frac{\cos (x)}{1-\cos (x)} \, dx","-x-\frac{\sin (x)}{1-\cos (x)}",1,"Could not integrate","F",-1
43,0,0,25,0.0000735,"\int e^{-x/2} \left(-1+e^{x/2}\right)^3 \, dx","IntegrateAlgebraic[(-1 + E^(x/2))^3/E^(x/2),x]","\int e^{-x/2} \left(-1+e^{x/2}\right)^3 \, dx","3 x+2 e^{-x/2}-6 e^{x/2}+e^x",1,"Could not integrate","F",-1
44,1,14,21,0.0059645,"\int \frac{1}{5-6 x+x^2} \, dx","IntegrateAlgebraic[(5 - 6*x + x^2)^(-1),x]","\frac{1}{2} \tanh ^{-1}\left(\frac{3}{2}-\frac{x}{2}\right)","\frac{1}{4} \log (5-x)-\frac{1}{4} \log (1-x)",1,"ArcTanh[3/2 - x/2]/2","A",1
45,1,16,14,0.0071684,"\int \frac{x^2}{13-6 x^3+x^6} \, dx","IntegrateAlgebraic[x^2/(13 - 6*x^3 + x^6),x]","-\frac{1}{6} \tan ^{-1}\left(\frac{3}{2}-\frac{x^3}{2}\right)","\frac{1}{6} \tan ^{-1}\left(\frac{1}{2} \left(x^3-3\right)\right)",1,"-1/6*ArcTan[3/2 - x^3/2]","A",1
46,1,47,51,0.0368264,"\int \frac{2+x}{-1-4 x+x^2} \, dx","IntegrateAlgebraic[(2 + x)/(-1 - 4*x + x^2),x]","\frac{1}{10} \left(5+4 \sqrt{5}\right) \log \left(-x+\sqrt{5}+2\right)+\frac{1}{10} \left(5-4 \sqrt{5}\right) \log \left(x+\sqrt{5}-2\right)","\frac{1}{10} \left(5-4 \sqrt{5}\right) \log \left(-x-\sqrt{5}+2\right)+\frac{1}{10} \left(5+4 \sqrt{5}\right) \log \left(-x+\sqrt{5}+2\right)",1,"((5 + 4*Sqrt[5])*Log[2 + Sqrt[5] - x])/10 + ((5 - 4*Sqrt[5])*Log[-2 + Sqrt[5] + x])/10","A",1
47,1,33,33,0.0154548,"\int \frac{1}{1+\sqrt[3]{1+x}} \, dx","IntegrateAlgebraic[(1 + (1 + x)^(1/3))^(-1),x]","\frac{3}{2} (x+1)^{2/3}-3 \sqrt[3]{x+1}+3 \log \left(\sqrt[3]{x+1}+1\right)","\frac{3}{2} (x+1)^{2/3}-3 \sqrt[3]{x+1}+3 \log \left(\sqrt[3]{x+1}+1\right)",1,"-3*(1 + x)^(1/3) + (3*(1 + x)^(2/3))/2 + 3*Log[1 + (1 + x)^(1/3)]","A",1
48,1,29,29,0.0122259,"\int \frac{1}{\sqrt{x} (b+a x)} \, dx","IntegrateAlgebraic[1/(Sqrt[x]*(b + a*x)),x]","\frac{2 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b}}",1,"(2*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]])/(Sqrt[a]*Sqrt[b])","A",1
49,1,23,27,0.0110591,"\int x^3 \sqrt{1+x^2} \, dx","IntegrateAlgebraic[x^3*Sqrt[1 + x^2],x]","\frac{1}{15} \sqrt{x^2+1} \left(3 x^4+x^2-2\right)","\frac{1}{5} \left(x^2+1\right)^{5/2}-\frac{1}{3} \left(x^2+1\right)^{3/2}",1,"(Sqrt[1 + x^2]*(-2 + x^2 + 3*x^4))/15","A",1
50,1,28,22,0.0924186,"\int \frac{x}{\sqrt{a^4-x^4}} \, dx","IntegrateAlgebraic[x/Sqrt[a^4 - x^4],x]","-\frac{1}{2} i \log \left(\sqrt{a^4-x^4}+i x^2\right)","\frac{1}{2} \tan ^{-1}\left(\frac{x^2}{\sqrt{a^4-x^4}}\right)",1,"(-1/2*I)*Log[I*x^2 + Sqrt[a^4 - x^4]]","C",1
51,1,22,22,0.0170878,"\int \frac{1}{x \sqrt{-a^2+x^2}} \, dx","IntegrateAlgebraic[1/(x*Sqrt[-a^2 + x^2]),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{x^2-a^2}}{a}\right)}{a}","\frac{\tan ^{-1}\left(\frac{\sqrt{x^2-a^2}}{a}\right)}{a}",1,"ArcTan[Sqrt[-a^2 + x^2]/a]/a","A",1
52,1,23,23,0.0173244,"\int \frac{1}{x \sqrt{a^2-x^2}} \, dx","IntegrateAlgebraic[1/(x*Sqrt[a^2 - x^2]),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a^2-x^2}}{a}\right)}{a}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a^2-x^2}}{a}\right)}{a}",1,"-(ArcTanh[Sqrt[a^2 - x^2]/a]/a)","A",1
53,1,21,21,0.0152874,"\int \frac{1}{x \sqrt{a^2+x^2}} \, dx","IntegrateAlgebraic[1/(x*Sqrt[a^2 + x^2]),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a^2+x^2}}{a}\right)}{a}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a^2+x^2}}{a}\right)}{a}",1,"-(ArcTanh[Sqrt[a^2 + x^2]/a]/a)","A",1
54,1,21,12,0.0903737,"\int \frac{1}{\sqrt{2+x-x^2}} \, dx","IntegrateAlgebraic[1/Sqrt[2 + x - x^2],x]","-2 \tan ^{-1}\left(\frac{\sqrt{-x^2+x+2}}{x+1}\right)","-\sin ^{-1}\left(\frac{1}{3} (1-2 x)\right)",1,"-2*ArcTan[Sqrt[2 + x - x^2]/(1 + x)]","A",1
55,1,33,19,0.0847208,"\int \frac{1}{\sqrt{5-4 x+3 x^2}} \, dx","IntegrateAlgebraic[1/Sqrt[5 - 4*x + 3*x^2],x]","-\frac{\log \left(\sqrt{3} \sqrt{3 x^2-4 x+5}-3 x+2\right)}{\sqrt{3}}","-\frac{\sinh ^{-1}\left(\frac{2-3 x}{\sqrt{11}}\right)}{\sqrt{3}}",1,"-(Log[2 - 3*x + Sqrt[3]*Sqrt[5 - 4*x + 3*x^2]]/Sqrt[3])","A",1
56,1,18,8,0.0771389,"\int \frac{1}{\sqrt{x-x^2}} \, dx","IntegrateAlgebraic[1/Sqrt[x - x^2],x]","-2 \tan ^{-1}\left(\frac{\sqrt{x-x^2}}{x}\right)","-\sin ^{-1}(1-2 x)",1,"-2*ArcTan[Sqrt[x - x^2]/x]","B",1
57,1,36,27,0.1689153,"\int \frac{1+2 x}{\sqrt{2+x-x^2}} \, dx","IntegrateAlgebraic[(1 + 2*x)/Sqrt[2 + x - x^2],x]","-2 \sqrt{-x^2+x+2}-4 \tan ^{-1}\left(\frac{\sqrt{-x^2+x+2}}{x+1}\right)","-2 \sqrt{-x^2+x+2}-2 \sin ^{-1}\left(\frac{1}{3} (1-2 x)\right)",1,"-2*Sqrt[2 + x - x^2] - 4*ArcTan[Sqrt[2 + x - x^2]/(1 + x)]","A",1
58,1,39,32,0.101857,"\int \frac{1}{x \sqrt{2+x-x^2}} \, dx","IntegrateAlgebraic[1/(x*Sqrt[2 + x - x^2]),x]","i \sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2}}+\frac{i \sqrt{-x^2+x+2}}{\sqrt{2}}\right)","-\frac{\tanh ^{-1}\left(\frac{x+4}{2 \sqrt{2} \sqrt{-x^2+x+2}}\right)}{\sqrt{2}}",1,"I*Sqrt[2]*ArcTan[x/Sqrt[2] + (I*Sqrt[2 + x - x^2])/Sqrt[2]]","C",1
59,1,21,21,0.1785999,"\int \frac{1}{(-2+x) \sqrt{2+x-x^2}} \, dx","IntegrateAlgebraic[1/((-2 + x)*Sqrt[2 + x - x^2]),x]","\frac{2 \sqrt{-x^2+x+2}}{3 (x-2)}","\frac{2 \sqrt{-x^2+x+2}}{3 (x-2)}",1,"(2*Sqrt[2 + x - x^2])/(3*(-2 + x))","A",1
60,0,0,28,0.000039,"\int \frac{\csc (x) (2+3 \sin (x))}{1-\cos (x)} \, dx","IntegrateAlgebraic[(Csc[x]*(2 + 3*Sin[x]))/(1 - Cos[x]),x]","\int \frac{\csc (x) (2+3 \sin (x))}{1-\cos (x)} \, dx","-\frac{1}{1-\cos (x)}-\frac{3 \sin (x)}{1-\cos (x)}-\tanh ^{-1}(\cos (x))",1,"Could not integrate","F",-1
61,0,0,37,0.0000337,"\int \frac{1}{2+3 \cos ^2(x)} \, dx","IntegrateAlgebraic[(2 + 3*Cos[x]^2)^(-1),x]","\int \frac{1}{2+3 \cos ^2(x)} \, dx","\frac{x}{\sqrt{10}}-\frac{\tan ^{-1}\left(\frac{3 \sin (x) \cos (x)}{3 \cos ^2(x)+\sqrt{10}+2}\right)}{\sqrt{10}}",1,"Could not integrate","F",-1
62,0,0,14,0.0000362,"\int \csc (2 x) (1-\tan (x)) \, dx","IntegrateAlgebraic[Csc[2*x]*(1 - Tan[x]),x]","\int \csc (2 x) (1-\tan (x)) \, dx","\frac{1}{2} \log (\tan (x))-\frac{\tan (x)}{2}",1,"Could not integrate","F",-1
63,0,0,11,0.0000338,"\int \frac{1+\tan ^2(x)}{1-\tan ^2(x)} \, dx","IntegrateAlgebraic[(1 + Tan[x]^2)/(1 - Tan[x]^2),x]","\int \frac{1+\tan ^2(x)}{1-\tan ^2(x)} \, dx","\frac{1}{2} \tanh ^{-1}(2 \sin (x) \cos (x))",1,"Could not integrate","F",-1
64,0,0,18,0.0000472,"\int \left(a^2-4 \cos ^2(x)\right)^{3/4} \sin (2 x) \, dx","IntegrateAlgebraic[(a^2 - 4*Cos[x]^2)^(3/4)*Sin[2*x],x]","\int \left(a^2-4 \cos ^2(x)\right)^{3/4} \sin (2 x) \, dx","\frac{1}{7} \left(a^2-4 \cos ^2(x)\right)^{7/4}",1,"Could not integrate","F",-1
65,0,0,18,0.0000391,"\int \frac{\sin (2 x)}{\sqrt[3]{a^2-4 \sin ^2(x)}} \, dx","IntegrateAlgebraic[Sin[2*x]/(a^2 - 4*Sin[x]^2)^(1/3),x]","\int \frac{\sin (2 x)}{\sqrt[3]{a^2-4 \sin ^2(x)}} \, dx","-\frac{3}{8} \left(a^2-4 \sin ^2(x)\right)^{2/3}",1,"Could not integrate","F",-1
66,0,0,17,0.0000569,"\int \frac{1}{\sqrt{-1+a^{2 x}}} \, dx","IntegrateAlgebraic[1/Sqrt[-1 + a^(2*x)],x]","\int \frac{1}{\sqrt{-1+a^{2 x}}} \, dx","\frac{\tan ^{-1}\left(\sqrt{a^{2 x}-1}\right)}{\log (a)}",1,"Could not integrate","F",-1
67,0,0,20,0.0000614,"\int \frac{e^{x/2}}{\sqrt{-1+e^x}} \, dx","IntegrateAlgebraic[E^(x/2)/Sqrt[-1 + E^x],x]","\int \frac{e^{x/2}}{\sqrt{-1+e^x}} \, dx","2 \tanh ^{-1}\left(\frac{e^{x/2}}{\sqrt{e^x-1}}\right)",1,"Could not integrate","F",-1
68,0,0,12,0.0000331,"\int \frac{\tan ^{-1}(x)^n}{1+x^2} \, dx","IntegrateAlgebraic[ArcTan[x]^n/(1 + x^2),x]","\int \frac{\tan ^{-1}(x)^n}{1+x^2} \, dx","\frac{\tan ^{-1}(x)^{n+1}}{n+1}",1,"Could not integrate","F",-1
69,0,0,42,0.0000386,"\int \frac{\sin ^{-1}\left(\frac{x}{a}\right)^{3/2}}{\sqrt{a^2-x^2}} \, dx","IntegrateAlgebraic[ArcSin[x/a]^(3/2)/Sqrt[a^2 - x^2],x]","\int \frac{\sin ^{-1}\left(\frac{x}{a}\right)^{3/2}}{\sqrt{a^2-x^2}} \, dx","\frac{2 a \sqrt{1-\frac{x^2}{a^2}} \sin ^{-1}\left(\frac{x}{a}\right)^{5/2}}{5 \sqrt{a^2-x^2}}",1,"Could not integrate","F",-1
70,0,0,8,0.000041,"\int \frac{1}{\sqrt{1-x^2} \cos ^{-1}(x)^3} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - x^2]*ArcCos[x]^3),x]","\int \frac{1}{\sqrt{1-x^2} \cos ^{-1}(x)^3} \, dx","\frac{1}{2 \cos ^{-1}(x)^2}",1,"Could not integrate","F",-1
71,0,0,28,0.0000282,"\int x \log ^2(x) \, dx","IntegrateAlgebraic[x*Log[x]^2,x]","\int x \log ^2(x) \, dx","\frac{x^2}{4}+\frac{1}{2} x^2 \log ^2(x)-\frac{1}{2} x^2 \log (x)",1,"Could not integrate","F",-1
72,0,0,17,0.0000321,"\int \frac{\log (x)}{x^5} \, dx","IntegrateAlgebraic[Log[x]/x^5,x]","\int \frac{\log (x)}{x^5} \, dx","-\frac{1}{16 x^4}-\frac{\log (x)}{4 x^4}",1,"Could not integrate","F",-1
73,0,0,36,0.0000384,"\int x^2 \log \left(\frac{-1+x}{x}\right) \, dx","IntegrateAlgebraic[x^2*Log[(-1 + x)/x],x]","\int x^2 \log \left(\frac{-1+x}{x}\right) \, dx","\frac{1}{3} x^3 \log \left(\frac{x-1}{x}\right)-\frac{x^2}{6}-\frac{x}{3}-\frac{1}{3} \log (x-1)",1,"Could not integrate","F",-1
74,0,0,19,0.0000326,"\int \cos ^5(x) \, dx","IntegrateAlgebraic[Cos[x]^5,x]","\int \cos ^5(x) \, dx","\frac{\sin ^5(x)}{5}-\frac{2 \sin ^3(x)}{3}+\sin (x)",1,"Could not integrate","F",-1
75,0,0,34,0.0000365,"\int \cos ^4(x) \sin ^2(x) \, dx","IntegrateAlgebraic[Cos[x]^4*Sin[x]^2,x]","\int \cos ^4(x) \sin ^2(x) \, dx","\frac{x}{16}-\frac{1}{6} \sin (x) \cos ^5(x)+\frac{1}{24} \sin (x) \cos ^3(x)+\frac{1}{16} \sin (x) \cos (x)",1,"Could not integrate","F",-1
76,0,0,26,0.0000285,"\int \csc ^5(x) \, dx","IntegrateAlgebraic[Csc[x]^5,x]","\int \csc ^5(x) \, dx","-\frac{3}{8} \tanh ^{-1}(\cos (x))-\frac{1}{4} \cot (x) \csc ^3(x)-\frac{3}{8} \cot (x) \csc (x)",1,"Could not integrate","F",-1
77,0,0,23,0.0000323,"\int e^{-x} \sin (x) \, dx","IntegrateAlgebraic[Sin[x]/E^x,x]","\int e^{-x} \sin (x) \, dx","-\frac{1}{2} e^{-x} \sin (x)-\frac{1}{2} e^{-x} \cos (x)",1,"Could not integrate","F",-1
78,0,0,27,0.0000336,"\int e^{2 x} \sin (3 x) \, dx","IntegrateAlgebraic[E^(2*x)*Sin[3*x],x]","\int e^{2 x} \sin (3 x) \, dx","\frac{2}{13} e^{2 x} \sin (3 x)-\frac{3}{13} e^{2 x} \cos (3 x)",1,"Could not integrate","F",-1
79,0,0,31,0.0000307,"\int a^x \cos (x) \, dx","IntegrateAlgebraic[a^x*Cos[x],x]","\int a^x \cos (x) \, dx","\frac{a^x \sin (x)}{\log ^2(a)+1}+\frac{a^x \log (a) \cos (x)}{\log ^2(a)+1}",1,"Could not integrate","F",-1
80,0,0,17,0.0000294,"\int \cos (\log (x)) \, dx","IntegrateAlgebraic[Cos[Log[x]],x]","\int \cos (\log (x)) \, dx","\frac{1}{2} x \sin (\log (x))+\frac{1}{2} x \cos (\log (x))",1,"Could not integrate","F",-1
81,0,0,12,0.0000307,"\int \log (\cos (x)) \sec ^2(x) \, dx","IntegrateAlgebraic[Log[Cos[x]]*Sec[x]^2,x]","\int \log (\cos (x)) \sec ^2(x) \, dx","-x+\tan (x)+\tan (x) \log (\cos (x))",1,"Could not integrate","F",-1
82,0,0,15,0.0000323,"\int x \tan ^2(x) \, dx","IntegrateAlgebraic[x*Tan[x]^2,x]","\int x \tan ^2(x) \, dx","-\frac{x^2}{2}+x \tan (x)+\log (\cos (x))",1,"Could not integrate","F",-1
83,0,0,22,0.0000264,"\int \frac{\sin ^{-1}(x)}{x^2} \, dx","IntegrateAlgebraic[ArcSin[x]/x^2,x]","\int \frac{\sin ^{-1}(x)}{x^2} \, dx","-\tanh ^{-1}\left(\sqrt{1-x^2}\right)-\frac{\sin ^{-1}(x)}{x}",1,"Could not integrate","F",-1
84,0,0,25,0.000029,"\int \sin ^{-1}(x)^2 \, dx","IntegrateAlgebraic[ArcSin[x]^2,x]","\int \sin ^{-1}(x)^2 \, dx","2 \sqrt{1-x^2} \sin ^{-1}(x)-2 x+x \sin ^{-1}(x)^2",1,"Could not integrate","F",-1
85,0,0,23,0.0000405,"\int \frac{x^2 \tan ^{-1}(x)}{1+x^2} \, dx","IntegrateAlgebraic[(x^2*ArcTan[x])/(1 + x^2),x]","\int \frac{x^2 \tan ^{-1}(x)}{1+x^2} \, dx","-\frac{1}{2} \log \left(x^2+1\right)-\frac{1}{2} \tan ^{-1}(x)^2+x \tan ^{-1}(x)",1,"Could not integrate","F",-1
86,0,0,38,0.0000366,"\int \cos ^{-1}\left(\sqrt{\frac{x}{1+x}}\right) \, dx","IntegrateAlgebraic[ArcCos[Sqrt[x/(1 + x)]],x]","\int \cos ^{-1}\left(\sqrt{\frac{x}{1+x}}\right) \, dx","(x+1) \left(\sqrt{\frac{1}{x+1}} \sqrt{\frac{x}{x+1}}+\cos ^{-1}\left(\sqrt{\frac{x}{x+1}}\right)\right)",1,"Could not integrate","F",-1
87,1,25,25,0.0052862,"\int \left(2 x+3 x^2\right)^3 \, dx","IntegrateAlgebraic[(2*x + 3*x^2)^3,x]","\frac{1}{35} \left(135 x^7+315 x^6+252 x^5+70 x^4\right)","\frac{27 x^7}{7}+9 x^6+\frac{36 x^5}{5}+2 x^4",1,"(70*x^4 + 252*x^5 + 315*x^6 + 135*x^7)/35","A",1
88,1,30,39,0.0051914,"\int (-1+x) \left(-1+2 x+3 x^2\right)^2 \, dx","IntegrateAlgebraic[(-1 + x)*(-1 + 2*x + 3*x^2)^2,x]","\frac{1}{30} x \left(45 x^5+18 x^4-105 x^3-20 x^2+75 x-30\right)","\frac{3 x^6}{2}+\frac{3 x^5}{5}-\frac{7 x^4}{2}-\frac{2 x^3}{3}+\frac{5 x^2}{2}-x",1,"(x*(-30 + 75*x - 20*x^2 - 105*x^3 + 18*x^4 + 45*x^5))/30","A",1
89,0,0,23,0.0000642,"\int x^{-1+k} \left(a+b x^k\right)^n \, dx","IntegrateAlgebraic[x^(-1 + k)*(a + b*x^k)^n,x]","\int x^{-1+k} \left(a+b x^k\right)^n \, dx","\frac{\left(a+b x^k\right)^{n+1}}{b k (n+1)}",1,"Could not integrate","F",-1
90,1,26,30,0.0104709,"\int \frac{x^3}{1+2 x} \, dx","IntegrateAlgebraic[x^3/(1 + 2*x),x]","\frac{1}{24} x \left(4 x^2-3 x+3\right)-\frac{1}{16} \log (2 x+1)","\frac{x^3}{6}-\frac{x^2}{8}+\frac{x}{8}-\frac{1}{16} \log (2 x+1)",1,"(x*(3 - 3*x + 4*x^2))/24 - Log[1 + 2*x]/16","A",1
91,1,39,41,0.0180259,"\int \frac{x^6}{2+3 x^2} \, dx","IntegrateAlgebraic[x^6/(2 + 3*x^2),x]","\frac{1}{135} x \left(9 x^4-10 x^2+20\right)-\frac{4}{27} \sqrt{\frac{2}{3}} \tan ^{-1}\left(\sqrt{\frac{3}{2}} x\right)","\frac{x^5}{15}-\frac{2 x^3}{27}+\frac{4 x}{27}-\frac{4}{27} \sqrt{\frac{2}{3}} \tan ^{-1}\left(\sqrt{\frac{3}{2}} x\right)",1,"(x*(20 - 10*x^2 + 9*x^4))/135 - (4*Sqrt[2/3]*ArcTan[Sqrt[3/2]*x])/27","A",1
92,1,19,21,0.0071497,"\int \frac{1}{2-7 x+3 x^2} \, dx","IntegrateAlgebraic[(2 - 7*x + 3*x^2)^(-1),x]","\frac{1}{5} \log (x-2)-\frac{1}{5} \log (3 x-1)","\frac{1}{5} \log (2-x)-\frac{1}{5} \log (1-3 x)",1,"Log[-2 + x]/5 - Log[-1 + 3*x]/5","A",1
93,1,36,33,0.0159166,"\int \frac{-1+3 x}{1-x+x^2} \, dx","IntegrateAlgebraic[(-1 + 3*x)/(1 - x + x^2),x]","\frac{3}{2} \log \left(x^2-x+1\right)-\frac{\tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 x}{\sqrt{3}}\right)}{\sqrt{3}}","\frac{3}{2} \log \left(x^2-x+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{\sqrt{3}}",1,"-(ArcTan[1/Sqrt[3] - (2*x)/Sqrt[3]]/Sqrt[3]) + (3*Log[1 - x + x^2])/2","A",1
94,1,27,25,0.0079627,"\int \frac{x^2}{5+2 x+x^2} \, dx","IntegrateAlgebraic[x^2/(5 + 2*x + x^2),x]","-\log \left(x^2+2 x+5\right)+x-\frac{3}{2} \tan ^{-1}\left(\frac{x}{2}+\frac{1}{2}\right)","-\log \left(x^2+2 x+5\right)+x-\frac{3}{2} \tan ^{-1}\left(\frac{x+1}{2}\right)",1,"x - (3*ArcTan[1/2 + x/2])/2 - Log[5 + 2*x + x^2]","A",1
95,1,55,47,0.0272489,"\int \frac{4 x^2-5 x^3+6 x^4}{1-x+2 x^2} \, dx","IntegrateAlgebraic[(4*x^2 - 5*x^3 + 6*x^4)/(1 - x + 2*x^2),x]","\frac{1}{4} \log \left(2 x^2-x+1\right)+\frac{1}{2} \left(2 x^3-x^2\right)-\frac{\tan ^{-1}\left(\frac{1}{\sqrt{7}}-\frac{4 x}{\sqrt{7}}\right)}{2 \sqrt{7}}","x^3-\frac{x^2}{2}+\frac{1}{4} \log \left(2 x^2-x+1\right)-\frac{\tan ^{-1}\left(\frac{1-4 x}{\sqrt{7}}\right)}{2 \sqrt{7}}",1,"(-x^2 + 2*x^3)/2 - ArcTan[1/Sqrt[7] - (4*x)/Sqrt[7]]/(2*Sqrt[7]) + Log[1 - x + 2*x^2]/4","A",1
96,1,23,25,0.0087757,"\int \frac{-1+x+x^2}{-6 x+x^2+x^3} \, dx","IntegrateAlgebraic[(-1 + x + x^2)/(-6*x + x^2 + x^3),x]","\frac{1}{2} \log (x-2)+\frac{\log (x)}{6}+\frac{1}{3} \log (x+3)","\frac{1}{2} \log (2-x)+\frac{\log (x)}{6}+\frac{1}{3} \log (x+3)",1,"Log[-2 + x]/2 + Log[x]/6 + Log[3 + x]/3","A",1
97,1,33,33,0.0189776,"\int \frac{11 a^2-7 a x+5 x^2}{-6 a^3+11 a^2 x-6 a x^2+x^3} \, dx","IntegrateAlgebraic[(11*a^2 - 7*a*x + 5*x^2)/(-6*a^3 + 11*a^2*x - 6*a*x^2 + x^3),x]","\frac{9}{2} \log (a-x)-17 \log (2 a-x)+\frac{35}{2} \log (3 a-x)","\frac{9}{2} \log (a-x)-17 \log (2 a-x)+\frac{35}{2} \log (3 a-x)",1,"(9*Log[a - x])/2 - 17*Log[2*a - x] + (35*Log[3*a - x])/2","A",1
98,1,21,37,0.0110048,"\int \frac{2-x+x^2}{4-5 x^2+x^4} \, dx","IntegrateAlgebraic[(2 - x + x^2)/(4 - 5*x^2 + x^4),x]","\frac{2}{3} \tanh ^{-1}(3-2 x)-\frac{4}{3} \tanh ^{-1}(2 x+3)","-\frac{1}{3} \log (1-x)+\frac{1}{3} \log (2-x)+\frac{2}{3} \log (x+1)-\frac{2}{3} \log (x+2)",1,"(2*ArcTanh[3 - 2*x])/3 - (4*ArcTanh[3 + 2*x])/3","A",1
99,1,31,31,0.035647,"\int \frac{-5+2 x^2}{6-5 x^2+x^4} \, dx","IntegrateAlgebraic[(-5 + 2*x^2)/(6 - 5*x^2 + x^4),x]","-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{\sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{3}}\right)}{\sqrt{3}}","-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{\sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{3}}\right)}{\sqrt{3}}",1,"-(ArcTanh[x/Sqrt[2]]/Sqrt[2]) - ArcTanh[x/Sqrt[3]]/Sqrt[3]","A",1
100,1,25,41,0.012906,"\int \frac{1}{(-4+x) (-3+x) (-2+x) (-1+x)} \, dx","IntegrateAlgebraic[1/((-4 + x)*(-3 + x)*(-2 + x)*(-1 + x)),x]","\frac{1}{6} \log (x-4)-\frac{1}{6} \log (x-1)-\tanh ^{-1}(5-2 x)","-\frac{1}{6} \log (1-x)+\frac{1}{2} \log (2-x)-\frac{1}{2} \log (3-x)+\frac{1}{6} \log (4-x)",1,"-ArcTanh[5 - 2*x] + Log[-4 + x]/6 - Log[-1 + x]/6","A",1
101,1,16,25,0.0129734,"\int \frac{1+x^2}{(-1+x)^3} \, dx","IntegrateAlgebraic[(1 + x^2)/(-1 + x)^3,x]","\frac{1-2 x}{(x-1)^2}+\log (x-1)","\frac{2}{1-x}-\frac{1}{(1-x)^2}+\log (1-x)",1,"(1 - 2*x)/(-1 + x)^2 + Log[-1 + x]","A",1
102,1,39,36,0.0202469,"\int \frac{x^5}{(3+x)^2} \, dx","IntegrateAlgebraic[x^5/(3 + x)^2,x]","\frac{x^5-5 x^4+30 x^3-270 x^2-1296 x+972}{4 (x+3)}+405 \log (x+3)","\frac{x^4}{4}-2 x^3+\frac{27 x^2}{2}-108 x+\frac{243}{x+3}+405 \log (x+3)",1,"(972 - 1296*x - 270*x^2 + 30*x^3 - 5*x^4 + x^5)/(4*(3 + x)) + 405*Log[3 + x]","A",1
103,1,31,41,0.0262415,"\int \frac{-2+5 x^3}{-27+18 x^2-8 x^3+x^4} \, dx","IntegrateAlgebraic[(-2 + 5*x^3)/(-27 + 18*x^2 - 8*x^3 + x^4),x]","\frac{955-407 x}{16 (x-3)^2}+\frac{313}{64} \log (x-3)+\frac{7}{64} \log (x+1)","\frac{407}{16 (3-x)}-\frac{133}{8 (3-x)^2}+\frac{313}{64} \log (3-x)+\frac{7}{64} \log (x+1)",1,"(955 - 407*x)/(16*(-3 + x)^2) + (313*Log[-3 + x])/64 + (7*Log[1 + x])/64","A",1
104,1,29,27,0.0256974,"\int \frac{-9+3 x-6 x^2+x^3}{(3+x)^2 (4+x)^2} \, dx","IntegrateAlgebraic[(-9 + 3*x - 6*x^2 + x^3)/((3 + x)^2*(4 + x)^2),x]","\frac{280 x+939}{(x+3) (x+4)}+264 \log (x+3)-263 \log (x+4)","\frac{99}{x+3}+\frac{181}{x+4}+264 \log (x+3)-263 \log (x+4)",1,"(939 + 280*x)/((3 + x)*(4 + x)) + 264*Log[3 + x] - 263*Log[4 + x]","A",1
105,1,35,39,0.0249907,"\int \frac{2+x^2+x^3}{x \left(-1+x^2\right)^2} \, dx","IntegrateAlgebraic[(2 + x^2 + x^3)/(x*(-1 + x^2)^2),x]","\frac{-x-3}{2 \left(x^2-1\right)}-\log \left(x^2-1\right)+2 \log (x)-\frac{1}{2} \tanh ^{-1}(x)","\frac{x+3}{2 \left(1-x^2\right)}-\frac{3}{4} \log (1-x)+2 \log (x)-\frac{5}{4} \log (x+1)",1,"(-3 - x)/(2*(-1 + x^2)) - ArcTanh[x]/2 + 2*Log[x] - Log[-1 + x^2]","A",1
106,1,41,46,0.0219679,"\int \frac{1}{x^3-x^4-x^5+x^6} \, dx","IntegrateAlgebraic[(x^3 - x^4 - x^5 + x^6)^(-1),x]","\frac{-3 x^2+x+1}{2 (x-1) x^2}-\frac{7}{4} \log (x-1)+2 \log (x)-\frac{1}{4} \log (x+1)","-\frac{1}{2 x^2}+\frac{1}{2 (1-x)}-\frac{1}{x}-\frac{7}{4} \log (1-x)+2 \log (x)-\frac{1}{4} \log (x+1)",1,"(1 + x - 3*x^2)/(2*(-1 + x)*x^2) - (7*Log[-1 + x])/4 + 2*Log[x] - Log[1 + x]/4","A",1
107,1,27,29,0.0124389,"\int \frac{1+x^4}{-1+x-x^2+x^3} \, dx","IntegrateAlgebraic[(1 + x^4)/(-1 + x - x^2 + x^3),x]","-\frac{1}{2} \log \left(x^2+1\right)+\frac{1}{2} x (x+2)+\log (x-1)-\tan ^{-1}(x)","\frac{x^2}{2}-\frac{1}{2} \log \left(x^2+1\right)+x+\log (1-x)-\tan ^{-1}(x)",1,"(x*(2 + x))/2 - ArcTan[x] + Log[-1 + x] - Log[1 + x^2]/2","A",1
108,1,27,27,0.0108618,"\int \frac{1}{x (1+x) \left(1+x^2\right)} \, dx","IntegrateAlgebraic[1/(x*(1 + x)*(1 + x^2)),x]","-\frac{1}{4} \log \left(x^2+1\right)+\log (x)-\frac{1}{2} \log (x+1)-\frac{1}{2} \tan ^{-1}(x)","-\frac{1}{4} \log \left(x^2+1\right)+\log (x)-\frac{1}{2} \log (x+1)-\frac{1}{2} \tan ^{-1}(x)",1,"-1/2*ArcTan[x] + Log[x] - Log[1 + x]/2 - Log[1 + x^2]/4","A",1
109,1,24,24,0.0171531,"\int \frac{x^2}{-2+x^2+x^4} \, dx","IntegrateAlgebraic[x^2/(-2 + x^2 + x^4),x]","\frac{1}{3} \sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)-\frac{1}{3} \tanh ^{-1}(x)","\frac{1}{3} \sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)-\frac{1}{3} \tanh ^{-1}(x)",1,"(Sqrt[2]*ArcTan[x/Sqrt[2]])/3 - ArcTanh[x]/3","A",1
110,1,41,41,0.0304301,"\int \frac{6 x+4 x^2+x^3}{2+4 x+3 x^2+2 x^3+x^4} \, dx","IntegrateAlgebraic[(6*x + 4*x^2 + x^3)/(2 + 4*x + 3*x^2 + 2*x^3 + x^4),x]","\frac{2}{3} \log \left(x^2+2\right)+\frac{1}{x+1}-\frac{1}{3} \log (x+1)+\frac{4}{3} \sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)","\frac{2}{3} \log \left(x^2+2\right)+\frac{1}{x+1}-\frac{1}{3} \log (x+1)+\frac{4}{3} \sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)",1,"(1 + x)^(-1) + (4*Sqrt[2]*ArcTan[x/Sqrt[2]])/3 - Log[1 + x]/3 + (2*Log[2 + x^2])/3","A",1
111,1,46,46,0.0266605,"\int \frac{x}{(1+x) (1+2 x)^2 \left(1+x^2\right)} \, dx","IntegrateAlgebraic[x/((1 + x)*(1 + 2*x)^2*(1 + x^2)),x]","-\frac{7}{100} \log \left(x^2+1\right)+\frac{2}{5 (2 x+1)}-\frac{1}{2} \log (x+1)+\frac{16}{25} \log (2 x+1)+\frac{1}{50} \tan ^{-1}(x)","-\frac{7}{100} \log \left(x^2+1\right)+\frac{2}{5 (2 x+1)}-\frac{1}{2} \log (x+1)+\frac{16}{25} \log (2 x+1)+\frac{1}{50} \tan ^{-1}(x)",1,"2/(5*(1 + 2*x)) + ArcTan[x]/50 - Log[1 + x]/2 + (16*Log[1 + 2*x])/25 - (7*Log[1 + x^2])/100","A",1
112,1,37,47,0.0318105,"\int \frac{-2+x+3 x^2}{(-1+x)^3 \left(1+x^2\right)} \, dx","IntegrateAlgebraic[(-2 + x + 3*x^2)/((-1 + x)^3*(1 + x^2)),x]","\frac{3}{4} \log \left(x^2+1\right)+\frac{4-5 x}{2 (x-1)^2}-\frac{3}{2} \log (x-1)-\tan ^{-1}(x)","\frac{3}{4} \log \left(x^2+1\right)+\frac{5}{2 (1-x)}-\frac{1}{2 (1-x)^2}-\frac{3}{2} \log (1-x)-\tan ^{-1}(x)",1,"(4 - 5*x)/(2*(-1 + x)^2) - ArcTan[x] - (3*Log[-1 + x])/2 + (3*Log[1 + x^2])/4","A",1
113,1,58,67,0.0001169,"\int \frac{1}{1+x^2+x^4} \, dx","IntegrateAlgebraic[(1 + x^2 + x^4)^(-1),x]","\sqrt{\frac{1}{6} \left(-1-i \sqrt{3}\right)} \tan ^{-1}\left(\sqrt[6]{-1} x\right)-\sqrt{\frac{1}{6} \left(-1+i \sqrt{3}\right)} \tan ^{-1}\left((-1)^{5/6} x\right)","-\frac{1}{4} \log \left(x^2-x+1\right)+\frac{1}{4} \log \left(x^2+x+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{2 \sqrt{3}}",1,"Sqrt[(-1 - I*Sqrt[3])/6]*ArcTan[(-1)^(1/6)*x] - Sqrt[(-1 + I*Sqrt[3])/6]*ArcTan[(-1)^(5/6)*x]","C",0
114,1,46,48,0.0363033,"\int \frac{3+2 x^3}{-9 x+x^5} \, dx","IntegrateAlgebraic[(3 + 2*x^3)/(-9*x + x^5),x]","\frac{1}{12} \log \left(x^4-9\right)-\frac{\log (x)}{3}+\frac{\tan ^{-1}\left(\frac{x}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{3}}\right)}{\sqrt{3}}","\frac{1}{12} \log \left(9-x^4\right)-\frac{\log (x)}{3}+\frac{\tan ^{-1}\left(\frac{x}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{3}}\right)}{\sqrt{3}}",1,"ArcTan[x/Sqrt[3]]/Sqrt[3] - ArcTanh[x/Sqrt[3]]/Sqrt[3] - Log[x]/3 + Log[-9 + x^4]/12","A",1
115,1,48,58,0.0334576,"\int \frac{-20+8 x+5 x^3}{(-4+x)^3 \left(8-4 x+x^2\right)} \, dx","IntegrateAlgebraic[(-20 + 8*x + 5*x^3)/((-4 + x)^3*(8 - 4*x + x^2)),x]","\frac{45}{32} \log \left(x^2-4 x+8\right)+\frac{81-41 x}{4 (x-4)^2}-\frac{45}{16} \log (x-4)-\frac{3}{16} \tan ^{-1}\left(1-\frac{x}{2}\right)","\frac{45}{32} \log \left(x^2-4 x+8\right)+\frac{41}{4 (4-x)}-\frac{83}{4 (4-x)^2}-\frac{45}{16} \log (4-x)-\frac{3}{16} \tan ^{-1}\left(1-\frac{x}{2}\right)",1,"(81 - 41*x)/(4*(-4 + x)^2) - (3*ArcTan[1 - x/2])/16 - (45*Log[-4 + x])/16 + (45*Log[8 - 4*x + x^2])/32","A",1
116,1,51,51,0.0348703,"\int \frac{1}{\left(1+x^2\right) \left(2+x^2\right) \left(3+x^2\right) \left(4+x^2\right)} \, dx","IntegrateAlgebraic[1/((1 + x^2)*(2 + x^2)*(3 + x^2)*(4 + x^2)),x]","-\frac{1}{12} \tan ^{-1}\left(\frac{x}{2}\right)+\frac{1}{6} \tan ^{-1}(x)-\frac{\tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{2 \sqrt{2}}+\frac{\tan ^{-1}\left(\frac{x}{\sqrt{3}}\right)}{2 \sqrt{3}}","-\frac{1}{12} \tan ^{-1}\left(\frac{x}{2}\right)+\frac{1}{6} \tan ^{-1}(x)-\frac{\tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{2 \sqrt{2}}+\frac{\tan ^{-1}\left(\frac{x}{\sqrt{3}}\right)}{2 \sqrt{3}}",1,"-1/12*ArcTan[x/2] + ArcTan[x]/6 - ArcTan[x/Sqrt[2]]/(2*Sqrt[2]) + ArcTan[x/Sqrt[3]]/(2*Sqrt[3])","A",1
117,1,29,41,0.0132425,"\int \frac{x}{\left(1+x^2\right) \left(2+x^2\right) \left(3+x^2\right) \left(4+x^2\right)} \, dx","IntegrateAlgebraic[x/((1 + x^2)*(2 + x^2)*(3 + x^2)*(4 + x^2)),x]","\frac{1}{2} \tanh ^{-1}\left(2 x^2+5\right)-\frac{1}{6} \tanh ^{-1}\left(\frac{2 x^2}{3}+\frac{5}{3}\right)","\frac{1}{12} \log \left(x^2+1\right)-\frac{1}{4} \log \left(x^2+2\right)+\frac{1}{4} \log \left(x^2+3\right)-\frac{1}{12} \log \left(x^2+4\right)",1,"-1/6*ArcTanh[5/3 + (2*x^2)/3] + ArcTanh[5 + 2*x^2]/2","A",1
118,1,59,56,0.0216675,"\int \frac{1}{a^3+x^3} \, dx","IntegrateAlgebraic[(a^3 + x^3)^(-1),x]","-\frac{\log \left(a^2-a x+x^2\right)}{6 a^2}+\frac{\log (a+x)}{3 a^2}-\frac{\tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 x}{\sqrt{3} a}\right)}{\sqrt{3} a^2}","-\frac{\log \left(a^2-a x+x^2\right)}{6 a^2}+\frac{\log (a+x)}{3 a^2}-\frac{\tan ^{-1}\left(\frac{a-2 x}{\sqrt{3} a}\right)}{\sqrt{3} a^2}",1,"-(ArcTan[1/Sqrt[3] - (2*x)/(Sqrt[3]*a)]/(Sqrt[3]*a^2)) + Log[a + x]/(3*a^2) - Log[a^2 - a*x + x^2]/(6*a^2)","A",1
119,1,59,56,0.015,"\int \frac{x}{a^3+x^3} \, dx","IntegrateAlgebraic[x/(a^3 + x^3),x]","\frac{\log \left(a^2-a x+x^2\right)}{6 a}-\frac{\log (a+x)}{3 a}-\frac{\tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 x}{\sqrt{3} a}\right)}{\sqrt{3} a}","\frac{\log \left(a^2-a x+x^2\right)}{6 a}-\frac{\log (a+x)}{3 a}-\frac{\tan ^{-1}\left(\frac{a-2 x}{\sqrt{3} a}\right)}{\sqrt{3} a}",1,"-(ArcTan[1/Sqrt[3] - (2*x)/(Sqrt[3]*a)]/(Sqrt[3]*a)) - Log[a + x]/(3*a) + Log[a^2 - a*x + x^2]/(6*a)","A",1
120,1,12,12,0.0049015,"\int \frac{x^2}{a^3+x^3} \, dx","IntegrateAlgebraic[x^2/(a^3 + x^3),x]","\frac{1}{3} \log \left(a^3+x^3\right)","\frac{1}{3} \log \left(a^3+x^3\right)",1,"Log[a^3 + x^3]/3","A",1
121,1,22,22,0.0078567,"\int \frac{1}{x \left(a^3+x^3\right)} \, dx","IntegrateAlgebraic[1/(x*(a^3 + x^3)),x]","\frac{\log (x)}{a^3}-\frac{\log \left(a^3+x^3\right)}{3 a^3}","\frac{\log (x)}{a^3}-\frac{\log \left(a^3+x^3\right)}{3 a^3}",1,"Log[x]/a^3 - Log[a^3 + x^3]/(3*a^3)","A",1
122,1,66,63,0.0260808,"\int \frac{1}{x^2 \left(a^3+x^3\right)} \, dx","IntegrateAlgebraic[1/(x^2*(a^3 + x^3)),x]","\frac{\log (a+x)}{3 a^4}+\frac{\tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 x}{\sqrt{3} a}\right)}{\sqrt{3} a^4}-\frac{1}{a^3 x}-\frac{\log \left(a^2-a x+x^2\right)}{6 a^4}","\frac{\log (a+x)}{3 a^4}+\frac{\tan ^{-1}\left(\frac{a-2 x}{\sqrt{3} a}\right)}{\sqrt{3} a^4}-\frac{1}{a^3 x}-\frac{\log \left(a^2-a x+x^2\right)}{6 a^4}",1,"-(1/(a^3*x)) + ArcTan[1/Sqrt[3] - (2*x)/(Sqrt[3]*a)]/(Sqrt[3]*a^4) + Log[a + x]/(3*a^4) - Log[a^2 - a*x + x^2]/(6*a^4)","A",1
123,1,68,65,0.0277225,"\int \frac{1}{x^3 \left(a^3+x^3\right)} \, dx","IntegrateAlgebraic[1/(x^3*(a^3 + x^3)),x]","-\frac{\log (a+x)}{3 a^5}+\frac{\tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 x}{\sqrt{3} a}\right)}{\sqrt{3} a^5}-\frac{1}{2 a^3 x^2}+\frac{\log \left(a^2-a x+x^2\right)}{6 a^5}","-\frac{\log (a+x)}{3 a^5}+\frac{\tan ^{-1}\left(\frac{a-2 x}{\sqrt{3} a}\right)}{\sqrt{3} a^5}-\frac{1}{2 a^3 x^2}+\frac{\log \left(a^2-a x+x^2\right)}{6 a^5}",1,"-1/2*1/(a^3*x^2) + ArcTan[1/Sqrt[3] - (2*x)/(Sqrt[3]*a)]/(Sqrt[3]*a^5) - Log[a + x]/(3*a^5) + Log[a^2 - a*x + x^2]/(6*a^5)","A",1
124,1,33,33,0.0100706,"\int \frac{1}{x^4 \left(a^3+x^3\right)} \, dx","IntegrateAlgebraic[1/(x^4*(a^3 + x^3)),x]","-\frac{\log (x)}{a^6}-\frac{1}{3 a^3 x^3}+\frac{\log \left(a^3+x^3\right)}{3 a^6}","-\frac{\log (x)}{a^6}-\frac{1}{3 a^3 x^3}+\frac{\log \left(a^3+x^3\right)}{3 a^6}",1,"-1/3*1/(a^3*x^3) - Log[x]/a^6 + Log[a^3 + x^3]/(3*a^6)","A",1
125,1,80,73,0.0285545,"\int \frac{1}{x^5 \left(a^3+x^3\right)} \, dx","IntegrateAlgebraic[1/(x^5*(a^3 + x^3)),x]","-\frac{\log (a+x)}{3 a^7}-\frac{\tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 x}{\sqrt{3} a}\right)}{\sqrt{3} a^7}+\frac{\log \left(a^2-a x+x^2\right)}{6 a^7}+\frac{4 x^3-a^3}{4 a^6 x^4}","-\frac{\log (a+x)}{3 a^7}-\frac{\tan ^{-1}\left(\frac{a-2 x}{\sqrt{3} a}\right)}{\sqrt{3} a^7}+\frac{1}{a^6 x}-\frac{1}{4 a^3 x^4}+\frac{\log \left(a^2-a x+x^2\right)}{6 a^7}",1,"(-a^3 + 4*x^3)/(4*a^6*x^4) - ArcTan[1/Sqrt[3] - (2*x)/(Sqrt[3]*a)]/(Sqrt[3]*a^7) - Log[a + x]/(3*a^7) + Log[a^2 - a*x + x^2]/(6*a^7)","A",1
126,0,0,46,0.0000637,"\int \frac{x^{-m}}{a^3+x^3} \, dx","IntegrateAlgebraic[1/(x^m*(a^3 + x^3)),x]","\int \frac{x^{-m}}{a^3+x^3} \, dx","\frac{x^{1-m} \, _2F_1\left(1,\frac{1-m}{3};\frac{4-m}{3};-\frac{x^3}{a^3}\right)}{a^3 (1-m)}",1,"Could not integrate","F",-1
127,1,27,27,0.0094354,"\int \frac{1}{a^4-x^4} \, dx","IntegrateAlgebraic[(a^4 - x^4)^(-1),x]","\frac{\tan ^{-1}\left(\frac{x}{a}\right)}{2 a^3}+\frac{\tanh ^{-1}\left(\frac{x}{a}\right)}{2 a^3}","\frac{\tan ^{-1}\left(\frac{x}{a}\right)}{2 a^3}+\frac{\tanh ^{-1}\left(\frac{x}{a}\right)}{2 a^3}",1,"ArcTan[x/a]/(2*a^3) + ArcTanh[x/a]/(2*a^3)","A",1
128,1,15,15,0.0057433,"\int \frac{x}{a^4-x^4} \, dx","IntegrateAlgebraic[x/(a^4 - x^4),x]","\frac{\tanh ^{-1}\left(\frac{x^2}{a^2}\right)}{2 a^2}","\frac{\tanh ^{-1}\left(\frac{x^2}{a^2}\right)}{2 a^2}",1,"ArcTanh[x^2/a^2]/(2*a^2)","A",1
129,1,24,24,0.0090963,"\int \frac{1}{x \left(a^4-x^4\right)} \, dx","IntegrateAlgebraic[1/(x*(a^4 - x^4)),x]","\frac{\log (x)}{a^4}-\frac{\log \left(a^4-x^4\right)}{4 a^4}","\frac{\log (x)}{a^4}-\frac{\log \left(a^4-x^4\right)}{4 a^4}",1,"Log[x]/a^4 - Log[a^4 - x^4]/(4*a^4)","A",1
130,1,35,35,0.0139227,"\int \frac{1}{x^2 \left(a^4-x^4\right)} \, dx","IntegrateAlgebraic[1/(x^2*(a^4 - x^4)),x]","-\frac{\tan ^{-1}\left(\frac{x}{a}\right)}{2 a^5}+\frac{\tanh ^{-1}\left(\frac{x}{a}\right)}{2 a^5}-\frac{1}{a^4 x}","-\frac{\tan ^{-1}\left(\frac{x}{a}\right)}{2 a^5}+\frac{\tanh ^{-1}\left(\frac{x}{a}\right)}{2 a^5}-\frac{1}{a^4 x}",1,"-(1/(a^4*x)) - ArcTan[x/a]/(2*a^5) + ArcTanh[x/a]/(2*a^5)","A",1
131,1,50,26,0.0181823,"\int \frac{1}{x^3 \left(a^4-x^4\right)} \, dx","IntegrateAlgebraic[1/(x^3*(a^4 - x^4)),x]","-\frac{\log (a-x)}{4 a^6}-\frac{\log (a+x)}{4 a^6}-\frac{1}{2 a^4 x^2}+\frac{\log \left(a^2+x^2\right)}{4 a^6}","\frac{\tanh ^{-1}\left(\frac{x^2}{a^2}\right)}{2 a^6}-\frac{1}{2 a^4 x^2}",1,"-1/2*1/(a^4*x^2) - Log[a - x]/(4*a^6) - Log[a + x]/(4*a^6) + Log[a^2 + x^2]/(4*a^6)","A",1
132,1,37,37,0.0131279,"\int \frac{1}{x^4 \left(a^4-x^4\right)} \, dx","IntegrateAlgebraic[1/(x^4*(a^4 - x^4)),x]","\frac{\tan ^{-1}\left(\frac{x}{a}\right)}{2 a^7}+\frac{\tanh ^{-1}\left(\frac{x}{a}\right)}{2 a^7}-\frac{1}{3 a^4 x^3}","\frac{\tan ^{-1}\left(\frac{x}{a}\right)}{2 a^7}+\frac{\tanh ^{-1}\left(\frac{x}{a}\right)}{2 a^7}-\frac{1}{3 a^4 x^3}",1,"-1/3*1/(a^4*x^3) + ArcTan[x/a]/(2*a^7) + ArcTanh[x/a]/(2*a^7)","A",1
133,0,0,45,0.000071,"\int \frac{x^{-m}}{a^4-x^4} \, dx","IntegrateAlgebraic[1/(x^m*(a^4 - x^4)),x]","\int \frac{x^{-m}}{a^4-x^4} \, dx","\frac{x^{1-m} \, _2F_1\left(1,\frac{1-m}{4};\frac{5-m}{4};\frac{x^4}{a^4}\right)}{a^4 (1-m)}",1,"Could not integrate","F",-1
134,1,15,15,0.0056443,"\int \frac{x}{a^4+x^4} \, dx","IntegrateAlgebraic[x/(a^4 + x^4),x]","\frac{\tan ^{-1}\left(\frac{x^2}{a^2}\right)}{2 a^2}","\frac{\tan ^{-1}\left(\frac{x^2}{a^2}\right)}{2 a^2}",1,"ArcTan[x^2/a^2]/(2*a^2)","A",1
135,1,69,109,0.3136262,"\int \frac{x^2}{a^4+x^4} \, dx","IntegrateAlgebraic[x^2/(a^4 + x^4),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} a x}{a^2+x^2}\right)}{2 \sqrt{2} a}-\frac{\tan ^{-1}\left(\frac{\frac{a}{\sqrt{2}}-\frac{x^2}{\sqrt{2} a}}{x}\right)}{2 \sqrt{2} a}","\frac{\log \left(a^2-\sqrt{2} a x+x^2\right)}{4 \sqrt{2} a}-\frac{\log \left(a^2+\sqrt{2} a x+x^2\right)}{4 \sqrt{2} a}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} x}{a}\right)}{2 \sqrt{2} a}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} x}{a}+1\right)}{2 \sqrt{2} a}",1,"-1/2*ArcTan[(a/Sqrt[2] - x^2/(Sqrt[2]*a))/x]/(Sqrt[2]*a) - ArcTanh[(Sqrt[2]*a*x)/(a^2 + x^2)]/(2*Sqrt[2]*a)","A",1
136,1,260,201,0.2673586,"\int \frac{1}{a^5+x^5} \, dx","IntegrateAlgebraic[(a^5 + x^5)^(-1),x]","\frac{\log (a+x)}{5 a^4}+\frac{\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt{2-\frac{2}{\sqrt{5}}} x}{a}-\frac{1}{2} \sqrt{\frac{1}{10} \left(5-\sqrt{5}\right)}+\frac{1}{2} \sqrt{\frac{1}{10} \left(25-5 \sqrt{5}\right)}\right)}{5 a^4}-\frac{\sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(-\frac{\sqrt{2+\frac{2}{\sqrt{5}}} x}{a}+\frac{1}{2} \sqrt{\frac{1}{10} \left(25+5 \sqrt{5}\right)}+\frac{1}{2} \sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)}\right)}{5 a^4}+\frac{\left(-1-\sqrt{5}\right) \log \left(2 a^2-\sqrt{5} a x-a x+2 x^2\right)}{20 a^4}+\frac{\left(\sqrt{5}-1\right) \log \left(2 a^2+\sqrt{5} a x-a x+2 x^2\right)}{20 a^4}","\frac{\log (a+x)}{5 a^4}-\frac{\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\left(1-\sqrt{5}\right) a-4 x}{\sqrt{2 \left(5+\sqrt{5}\right)} a}\right)}{5 a^4}-\frac{\sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} \left(\left(1+\sqrt{5}\right) a-4 x\right)}{2 a}\right)}{5 a^4}-\frac{\left(1-\sqrt{5}\right) \log \left(a^2-\frac{1}{2} \left(1-\sqrt{5}\right) a x+x^2\right)}{20 a^4}-\frac{\left(1+\sqrt{5}\right) \log \left(a^2-\frac{1}{2} \left(1+\sqrt{5}\right) a x+x^2\right)}{20 a^4}",1,"(Sqrt[(5 + Sqrt[5])/2]*ArcTan[Sqrt[(25 - 5*Sqrt[5])/10]/2 - Sqrt[(5 - Sqrt[5])/10]/2 + (Sqrt[2 - 2/Sqrt[5]]*x)/a])/(5*a^4) - (Sqrt[(5 - Sqrt[5])/2]*ArcTan[Sqrt[(5 + Sqrt[5])/10]/2 + Sqrt[(25 + 5*Sqrt[5])/10]/2 - (Sqrt[2 + 2/Sqrt[5]]*x)/a])/(5*a^4) + Log[a + x]/(5*a^4) + ((-1 - Sqrt[5])*Log[2*a^2 - a*x - Sqrt[5]*a*x + 2*x^2])/(20*a^4) + ((-1 + Sqrt[5])*Log[2*a^2 - a*x + Sqrt[5]*a*x + 2*x^2])/(20*a^4)","A",1
137,1,260,201,0.1543558,"\int \frac{x}{a^5+x^5} \, dx","IntegrateAlgebraic[x/(a^5 + x^5),x]","-\frac{\log (a+x)}{5 a^3}-\frac{\sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt{2-\frac{2}{\sqrt{5}}} x}{a}-\frac{1}{2} \sqrt{\frac{1}{10} \left(5-\sqrt{5}\right)}+\frac{1}{2} \sqrt{\frac{1}{10} \left(25-5 \sqrt{5}\right)}\right)}{5 a^3}-\frac{\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(-\frac{\sqrt{2+\frac{2}{\sqrt{5}}} x}{a}+\frac{1}{2} \sqrt{\frac{1}{10} \left(25+5 \sqrt{5}\right)}+\frac{1}{2} \sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)}\right)}{5 a^3}+\frac{\left(1-\sqrt{5}\right) \log \left(2 a^2-\sqrt{5} a x-a x+2 x^2\right)}{20 a^3}+\frac{\left(1+\sqrt{5}\right) \log \left(2 a^2+\sqrt{5} a x-a x+2 x^2\right)}{20 a^3}","-\frac{\log (a+x)}{5 a^3}+\frac{\sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(\frac{\left(1-\sqrt{5}\right) a-4 x}{\sqrt{2 \left(5+\sqrt{5}\right)} a}\right)}{5 a^3}-\frac{\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} \left(\left(1+\sqrt{5}\right) a-4 x\right)}{2 a}\right)}{5 a^3}+\frac{\left(1+\sqrt{5}\right) \log \left(a^2-\frac{1}{2} \left(1-\sqrt{5}\right) a x+x^2\right)}{20 a^3}+\frac{\left(1-\sqrt{5}\right) \log \left(a^2-\frac{1}{2} \left(1+\sqrt{5}\right) a x+x^2\right)}{20 a^3}",1,"-1/5*(Sqrt[(5 - Sqrt[5])/2]*ArcTan[Sqrt[(25 - 5*Sqrt[5])/10]/2 - Sqrt[(5 - Sqrt[5])/10]/2 + (Sqrt[2 - 2/Sqrt[5]]*x)/a])/a^3 - (Sqrt[(5 + Sqrt[5])/2]*ArcTan[Sqrt[(5 + Sqrt[5])/10]/2 + Sqrt[(25 + 5*Sqrt[5])/10]/2 - (Sqrt[2 + 2/Sqrt[5]]*x)/a])/(5*a^3) - Log[a + x]/(5*a^3) + ((1 - Sqrt[5])*Log[2*a^2 - a*x - Sqrt[5]*a*x + 2*x^2])/(20*a^3) + ((1 + Sqrt[5])*Log[2*a^2 - a*x + Sqrt[5]*a*x + 2*x^2])/(20*a^3)","A",1
138,1,260,201,0.1615745,"\int \frac{x^2}{a^5+x^5} \, dx","IntegrateAlgebraic[x^2/(a^5 + x^5),x]","\frac{\left(\sqrt{5}-1\right) \log \left(2 a^2-\sqrt{5} a x-a x+2 x^2\right)}{20 a^2}+\frac{\left(-1-\sqrt{5}\right) \log \left(2 a^2+\sqrt{5} a x-a x+2 x^2\right)}{20 a^2}+\frac{\log (a+x)}{5 a^2}-\frac{\sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt{2-\frac{2}{\sqrt{5}}} x}{a}-\frac{1}{2} \sqrt{\frac{1}{10} \left(5-\sqrt{5}\right)}+\frac{1}{2} \sqrt{\frac{1}{10} \left(25-5 \sqrt{5}\right)}\right)}{5 a^2}-\frac{\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(-\frac{\sqrt{2+\frac{2}{\sqrt{5}}} x}{a}+\frac{1}{2} \sqrt{\frac{1}{10} \left(25+5 \sqrt{5}\right)}+\frac{1}{2} \sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)}\right)}{5 a^2}","-\frac{\left(1+\sqrt{5}\right) \log \left(a^2-\frac{1}{2} \left(1-\sqrt{5}\right) a x+x^2\right)}{20 a^2}-\frac{\left(1-\sqrt{5}\right) \log \left(a^2-\frac{1}{2} \left(1+\sqrt{5}\right) a x+x^2\right)}{20 a^2}+\frac{\log (a+x)}{5 a^2}+\frac{\sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(\frac{\left(1-\sqrt{5}\right) a-4 x}{\sqrt{2 \left(5+\sqrt{5}\right)} a}\right)}{5 a^2}-\frac{\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} \left(\left(1+\sqrt{5}\right) a-4 x\right)}{2 a}\right)}{5 a^2}",1,"-1/5*(Sqrt[(5 - Sqrt[5])/2]*ArcTan[Sqrt[(25 - 5*Sqrt[5])/10]/2 - Sqrt[(5 - Sqrt[5])/10]/2 + (Sqrt[2 - 2/Sqrt[5]]*x)/a])/a^2 - (Sqrt[(5 + Sqrt[5])/2]*ArcTan[Sqrt[(5 + Sqrt[5])/10]/2 + Sqrt[(25 + 5*Sqrt[5])/10]/2 - (Sqrt[2 + 2/Sqrt[5]]*x)/a])/(5*a^2) + Log[a + x]/(5*a^2) + ((-1 + Sqrt[5])*Log[2*a^2 - a*x - Sqrt[5]*a*x + 2*x^2])/(20*a^2) + ((-1 - Sqrt[5])*Log[2*a^2 - a*x + Sqrt[5]*a*x + 2*x^2])/(20*a^2)","A",1
139,1,260,201,0.140053,"\int \frac{x^3}{a^5+x^5} \, dx","IntegrateAlgebraic[x^3/(a^5 + x^5),x]","\frac{\left(1+\sqrt{5}\right) \log \left(2 a^2-\sqrt{5} a x-a x+2 x^2\right)}{20 a}+\frac{\left(1-\sqrt{5}\right) \log \left(2 a^2+\sqrt{5} a x-a x+2 x^2\right)}{20 a}-\frac{\log (a+x)}{5 a}+\frac{\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt{2-\frac{2}{\sqrt{5}}} x}{a}-\frac{1}{2} \sqrt{\frac{1}{10} \left(5-\sqrt{5}\right)}+\frac{1}{2} \sqrt{\frac{1}{10} \left(25-5 \sqrt{5}\right)}\right)}{5 a}-\frac{\sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(-\frac{\sqrt{2+\frac{2}{\sqrt{5}}} x}{a}+\frac{1}{2} \sqrt{\frac{1}{10} \left(25+5 \sqrt{5}\right)}+\frac{1}{2} \sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)}\right)}{5 a}","\frac{\left(1-\sqrt{5}\right) \log \left(a^2-\frac{1}{2} \left(1-\sqrt{5}\right) a x+x^2\right)}{20 a}+\frac{\left(1+\sqrt{5}\right) \log \left(a^2-\frac{1}{2} \left(1+\sqrt{5}\right) a x+x^2\right)}{20 a}-\frac{\log (a+x)}{5 a}-\frac{\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\left(1-\sqrt{5}\right) a-4 x}{\sqrt{2 \left(5+\sqrt{5}\right)} a}\right)}{5 a}-\frac{\sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} \left(\left(1+\sqrt{5}\right) a-4 x\right)}{2 a}\right)}{5 a}",1,"(Sqrt[(5 + Sqrt[5])/2]*ArcTan[Sqrt[(25 - 5*Sqrt[5])/10]/2 - Sqrt[(5 - Sqrt[5])/10]/2 + (Sqrt[2 - 2/Sqrt[5]]*x)/a])/(5*a) - (Sqrt[(5 - Sqrt[5])/2]*ArcTan[Sqrt[(5 + Sqrt[5])/10]/2 + Sqrt[(25 + 5*Sqrt[5])/10]/2 - (Sqrt[2 + 2/Sqrt[5]]*x)/a])/(5*a) - Log[a + x]/(5*a) + ((1 + Sqrt[5])*Log[2*a^2 - a*x - Sqrt[5]*a*x + 2*x^2])/(20*a) + ((1 - Sqrt[5])*Log[2*a^2 - a*x + Sqrt[5]*a*x + 2*x^2])/(20*a)","A",1
140,1,12,12,0.0042505,"\int \frac{x^4}{a^5+x^5} \, dx","IntegrateAlgebraic[x^4/(a^5 + x^5),x]","\frac{1}{5} \log \left(a^5+x^5\right)","\frac{1}{5} \log \left(a^5+x^5\right)",1,"Log[a^5 + x^5]/5","A",1
141,1,22,22,0.0078456,"\int \frac{1}{x \left(a^5+x^5\right)} \, dx","IntegrateAlgebraic[1/(x*(a^5 + x^5)),x]","\frac{\log (x)}{a^5}-\frac{\log \left(a^5+x^5\right)}{5 a^5}","\frac{\log (x)}{a^5}-\frac{\log \left(a^5+x^5\right)}{5 a^5}",1,"Log[x]/a^5 - Log[a^5 + x^5]/(5*a^5)","A",1
142,1,268,209,0.2500164,"\int \frac{1}{x^2 \left(a^5+x^5\right)} \, dx","IntegrateAlgebraic[1/(x^2*(a^5 + x^5)),x]","\frac{\log (a+x)}{5 a^6}-\frac{\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt{2-\frac{2}{\sqrt{5}}} x}{a}-\frac{1}{2} \sqrt{\frac{1}{10} \left(5-\sqrt{5}\right)}+\frac{1}{2} \sqrt{\frac{1}{10} \left(25-5 \sqrt{5}\right)}\right)}{5 a^6}+\frac{\sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(-\frac{\sqrt{2+\frac{2}{\sqrt{5}}} x}{a}+\frac{1}{2} \sqrt{\frac{1}{10} \left(25+5 \sqrt{5}\right)}+\frac{1}{2} \sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)}\right)}{5 a^6}-\frac{1}{a^5 x}+\frac{\left(-1-\sqrt{5}\right) \log \left(2 a^2-\sqrt{5} a x-a x+2 x^2\right)}{20 a^6}+\frac{\left(\sqrt{5}-1\right) \log \left(2 a^2+\sqrt{5} a x-a x+2 x^2\right)}{20 a^6}","\frac{\log (a+x)}{5 a^6}+\frac{\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\left(1-\sqrt{5}\right) a-4 x}{\sqrt{2 \left(5+\sqrt{5}\right)} a}\right)}{5 a^6}+\frac{\sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} \left(\left(1+\sqrt{5}\right) a-4 x\right)}{2 a}\right)}{5 a^6}-\frac{1}{a^5 x}-\frac{\left(1-\sqrt{5}\right) \log \left(a^2-\frac{1}{2} \left(1-\sqrt{5}\right) a x+x^2\right)}{20 a^6}-\frac{\left(1+\sqrt{5}\right) \log \left(a^2-\frac{1}{2} \left(1+\sqrt{5}\right) a x+x^2\right)}{20 a^6}",1,"-(1/(a^5*x)) - (Sqrt[(5 + Sqrt[5])/2]*ArcTan[Sqrt[(25 - 5*Sqrt[5])/10]/2 - Sqrt[(5 - Sqrt[5])/10]/2 + (Sqrt[2 - 2/Sqrt[5]]*x)/a])/(5*a^6) + (Sqrt[(5 - Sqrt[5])/2]*ArcTan[Sqrt[(5 + Sqrt[5])/10]/2 + Sqrt[(25 + 5*Sqrt[5])/10]/2 - (Sqrt[2 + 2/Sqrt[5]]*x)/a])/(5*a^6) + Log[a + x]/(5*a^6) + ((-1 - Sqrt[5])*Log[2*a^2 - a*x - Sqrt[5]*a*x + 2*x^2])/(20*a^6) + ((-1 + Sqrt[5])*Log[2*a^2 - a*x + Sqrt[5]*a*x + 2*x^2])/(20*a^6)","A",1
143,1,270,211,0.2317654,"\int \frac{1}{x^3 \left(a^5+x^5\right)} \, dx","IntegrateAlgebraic[1/(x^3*(a^5 + x^5)),x]","-\frac{\log (a+x)}{5 a^7}+\frac{\sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt{2-\frac{2}{\sqrt{5}}} x}{a}-\frac{1}{2} \sqrt{\frac{1}{10} \left(5-\sqrt{5}\right)}+\frac{1}{2} \sqrt{\frac{1}{10} \left(25-5 \sqrt{5}\right)}\right)}{5 a^7}+\frac{\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(-\frac{\sqrt{2+\frac{2}{\sqrt{5}}} x}{a}+\frac{1}{2} \sqrt{\frac{1}{10} \left(25+5 \sqrt{5}\right)}+\frac{1}{2} \sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)}\right)}{5 a^7}-\frac{1}{2 a^5 x^2}+\frac{\left(1-\sqrt{5}\right) \log \left(2 a^2-\sqrt{5} a x-a x+2 x^2\right)}{20 a^7}+\frac{\left(1+\sqrt{5}\right) \log \left(2 a^2+\sqrt{5} a x-a x+2 x^2\right)}{20 a^7}","-\frac{\log (a+x)}{5 a^7}-\frac{\sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(\frac{\left(1-\sqrt{5}\right) a-4 x}{\sqrt{2 \left(5+\sqrt{5}\right)} a}\right)}{5 a^7}+\frac{\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} \left(\left(1+\sqrt{5}\right) a-4 x\right)}{2 a}\right)}{5 a^7}-\frac{1}{2 a^5 x^2}+\frac{\left(1+\sqrt{5}\right) \log \left(a^2-\frac{1}{2} \left(1-\sqrt{5}\right) a x+x^2\right)}{20 a^7}+\frac{\left(1-\sqrt{5}\right) \log \left(a^2-\frac{1}{2} \left(1+\sqrt{5}\right) a x+x^2\right)}{20 a^7}",1,"-1/2*1/(a^5*x^2) + (Sqrt[(5 - Sqrt[5])/2]*ArcTan[Sqrt[(25 - 5*Sqrt[5])/10]/2 - Sqrt[(5 - Sqrt[5])/10]/2 + (Sqrt[2 - 2/Sqrt[5]]*x)/a])/(5*a^7) + (Sqrt[(5 + Sqrt[5])/2]*ArcTan[Sqrt[(5 + Sqrt[5])/10]/2 + Sqrt[(25 + 5*Sqrt[5])/10]/2 - (Sqrt[2 + 2/Sqrt[5]]*x)/a])/(5*a^7) - Log[a + x]/(5*a^7) + ((1 - Sqrt[5])*Log[2*a^2 - a*x - Sqrt[5]*a*x + 2*x^2])/(20*a^7) + ((1 + Sqrt[5])*Log[2*a^2 - a*x + Sqrt[5]*a*x + 2*x^2])/(20*a^7)","A",1
144,1,270,211,0.1987955,"\int \frac{1}{x^4 \left(a^5+x^5\right)} \, dx","IntegrateAlgebraic[1/(x^4*(a^5 + x^5)),x]","\frac{\log (a+x)}{5 a^8}+\frac{\sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt{2-\frac{2}{\sqrt{5}}} x}{a}-\frac{1}{2} \sqrt{\frac{1}{10} \left(5-\sqrt{5}\right)}+\frac{1}{2} \sqrt{\frac{1}{10} \left(25-5 \sqrt{5}\right)}\right)}{5 a^8}+\frac{\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(-\frac{\sqrt{2+\frac{2}{\sqrt{5}}} x}{a}+\frac{1}{2} \sqrt{\frac{1}{10} \left(25+5 \sqrt{5}\right)}+\frac{1}{2} \sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)}\right)}{5 a^8}-\frac{1}{3 a^5 x^3}+\frac{\left(\sqrt{5}-1\right) \log \left(2 a^2-\sqrt{5} a x-a x+2 x^2\right)}{20 a^8}+\frac{\left(-1-\sqrt{5}\right) \log \left(2 a^2+\sqrt{5} a x-a x+2 x^2\right)}{20 a^8}","\frac{\log (a+x)}{5 a^8}-\frac{\sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(\frac{\left(1-\sqrt{5}\right) a-4 x}{\sqrt{2 \left(5+\sqrt{5}\right)} a}\right)}{5 a^8}+\frac{\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} \left(\left(1+\sqrt{5}\right) a-4 x\right)}{2 a}\right)}{5 a^8}-\frac{1}{3 a^5 x^3}-\frac{\left(1+\sqrt{5}\right) \log \left(a^2-\frac{1}{2} \left(1-\sqrt{5}\right) a x+x^2\right)}{20 a^8}-\frac{\left(1-\sqrt{5}\right) \log \left(a^2-\frac{1}{2} \left(1+\sqrt{5}\right) a x+x^2\right)}{20 a^8}",1,"-1/3*1/(a^5*x^3) + (Sqrt[(5 - Sqrt[5])/2]*ArcTan[Sqrt[(25 - 5*Sqrt[5])/10]/2 - Sqrt[(5 - Sqrt[5])/10]/2 + (Sqrt[2 - 2/Sqrt[5]]*x)/a])/(5*a^8) + (Sqrt[(5 + Sqrt[5])/2]*ArcTan[Sqrt[(5 + Sqrt[5])/10]/2 + Sqrt[(25 + 5*Sqrt[5])/10]/2 - (Sqrt[2 + 2/Sqrt[5]]*x)/a])/(5*a^8) + Log[a + x]/(5*a^8) + ((-1 + Sqrt[5])*Log[2*a^2 - a*x - Sqrt[5]*a*x + 2*x^2])/(20*a^8) + ((-1 - Sqrt[5])*Log[2*a^2 - a*x + Sqrt[5]*a*x + 2*x^2])/(20*a^8)","A",1
145,0,0,46,0.0000611,"\int \frac{x^{-m}}{a^5+x^5} \, dx","IntegrateAlgebraic[1/(x^m*(a^5 + x^5)),x]","\int \frac{x^{-m}}{a^5+x^5} \, dx","\frac{x^{1-m} \, _2F_1\left(1,\frac{1-m}{5};\frac{6-m}{5};-\frac{x^5}{a^5}\right)}{a^5 (1-m)}",1,"Could not integrate","F",-1
146,1,21,35,0.0111993,"\int \frac{1+x^4}{1+x^6} \, dx","IntegrateAlgebraic[(1 + x^4)/(1 + x^6),x]","\frac{1}{3} \tan ^{-1}\left(\frac{x^2-1}{x}\right)+\frac{2}{3} \tan ^{-1}(x)","-\frac{1}{3} \tan ^{-1}\left(\sqrt{3}-2 x\right)+\frac{2}{3} \tan ^{-1}(x)+\frac{1}{3} \tan ^{-1}\left(2 x+\sqrt{3}\right)",1,"(2*ArcTan[x])/3 + ArcTan[(-1 + x^2)/x]/3","A",1
147,1,56,60,0.0393246,"\int \frac{1}{\left(5+3 x+x^2\right)^3} \, dx","IntegrateAlgebraic[(5 + 3*x + x^2)^(-3),x]","\frac{(2 x+3) \left(6 x^2+18 x+41\right)}{242 \left(x^2+3 x+5\right)^2}+\frac{12 \tan ^{-1}\left(\frac{2 x}{\sqrt{11}}+\frac{3}{\sqrt{11}}\right)}{121 \sqrt{11}}","\frac{3 (2 x+3)}{121 \left(x^2+3 x+5\right)}+\frac{2 x+3}{22 \left(x^2+3 x+5\right)^2}+\frac{12 \tan ^{-1}\left(\frac{2 x+3}{\sqrt{11}}\right)}{121 \sqrt{11}}",1,"((3 + 2*x)*(41 + 18*x + 6*x^2))/(242*(5 + 3*x + x^2)^2) + (12*ArcTan[3/Sqrt[11] + (2*x)/Sqrt[11]])/(121*Sqrt[11])","A",1
148,1,31,43,0.0189511,"\int \frac{1+x^2+x^4}{\left(1+x^2\right)^4} \, dx","IntegrateAlgebraic[(1 + x^2 + x^4)/(1 + x^2)^4,x]","\frac{x \left(21 x^4+40 x^2+27\right)}{48 \left(x^2+1\right)^3}+\frac{7}{16} \tan ^{-1}(x)","\frac{7 x}{16 \left(x^2+1\right)}-\frac{x}{24 \left(x^2+1\right)^2}+\frac{x}{6 \left(x^2+1\right)^3}+\frac{7}{16} \tan ^{-1}(x)",1,"(x*(27 + 40*x^2 + 21*x^4))/(48*(1 + x^2)^3) + (7*ArcTan[x])/16","A",1
149,1,113,90,0.1165007,"\int \frac{B+A x}{\left(c+2 b x+a x^2\right)^2} \, dx","IntegrateAlgebraic[(B + A*x)/(c + 2*b*x + a*x^2)^2,x]","\frac{-a B x+A b x+A c-b B}{2 \left(b^2-a c\right) \left(a x^2+2 b x+c\right)}+\frac{(A b-a B) \tan ^{-1}\left(\frac{a x}{\sqrt{a c-b^2}}+\frac{b}{\sqrt{a c-b^2}}\right)}{2 \left(b^2-a c\right) \sqrt{a c-b^2}}","-\frac{-x (A b-a B)-A c+b B}{2 \left(b^2-a c\right) \left(a x^2+2 b x+c\right)}-\frac{(A b-a B) \tanh ^{-1}\left(\frac{a x+b}{\sqrt{b^2-a c}}\right)}{2 \left(b^2-a c\right)^{3/2}}",1,"(-(b*B) + A*c + A*b*x - a*B*x)/(2*(b^2 - a*c)*(c + 2*b*x + a*x^2)) + ((A*b - a*B)*ArcTan[b/Sqrt[-b^2 + a*c] + (a*x)/Sqrt[-b^2 + a*c]])/(2*(b^2 - a*c)*Sqrt[-b^2 + a*c])","A",1
150,1,38,38,0.0210387,"\int \frac{-41+55 x-27 x^2+5 x^3}{\left(5-4 x+x^2\right)^2} \, dx","IntegrateAlgebraic[(-41 + 55*x - 27*x^2 + 5*x^3)/(5 - 4*x + x^2)^2,x]","\frac{1-x}{x^2-4 x+5}+\frac{5}{2} \log \left(x^2-4 x+5\right)-2 \tan ^{-1}(2-x)","\frac{1-x}{x^2-4 x+5}+\frac{5}{2} \log \left(x^2-4 x+5\right)-2 \tan ^{-1}(2-x)",1,"(1 - x)/(5 - 4*x + x^2) - 2*ArcTan[2 - x] + (5*Log[5 - 4*x + x^2])/2","A",1
151,1,56,57,0.0340847,"\int \frac{1}{\left(-1+x^3\right)^2} \, dx","IntegrateAlgebraic[(-1 + x^3)^(-2),x]","-\frac{x}{3 \left(x^3-1\right)}+\frac{1}{9} \log \left(x^2+x+1\right)-\frac{2}{9} \log (x-1)+\frac{2 \tan ^{-1}\left(\frac{2 x}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3}}","\frac{x}{3 \left(1-x^3\right)}+\frac{1}{9} \log \left(x^2+x+1\right)-\frac{2}{9} \log (1-x)+\frac{2 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"-1/3*x/(-1 + x^3) + (2*ArcTan[1/Sqrt[3] + (2*x)/Sqrt[3]])/(3*Sqrt[3]) - (2*Log[-1 + x])/9 + Log[1 + x + x^2]/9","A",1
152,1,33,36,0.0217877,"\int \frac{4+3 x^4}{x^2 \left(1+x^2\right)^3} \, dx","IntegrateAlgebraic[(4 + 3*x^4)/(x^2*(1 + x^2)^3),x]","\frac{-57 x^4-103 x^2-32}{8 x \left(x^2+1\right)^2}-\frac{57}{8} \tan ^{-1}(x)","-\frac{25 x}{8 \left(x^2+1\right)}-\frac{7 x}{4 \left(x^2+1\right)^2}-\frac{4}{x}-\frac{57}{8} \tan ^{-1}(x)",1,"(-32 - 103*x^2 - 57*x^4)/(8*x*(1 + x^2)^2) - (57*ArcTan[x])/8","A",1
153,1,73,49,0.0349304,"\int \frac{x}{1+x^6} \, dx","IntegrateAlgebraic[x/(1 + x^6),x]","-\frac{1}{12} \log \left(-x^2+\sqrt{3} x-1\right)+\frac{1}{6} \log \left(x^2+1\right)-\frac{1}{12} \log \left(x^2+\sqrt{3} x+1\right)-\frac{\tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 x^2}{\sqrt{3}}\right)}{2 \sqrt{3}}","\frac{1}{6} \log \left(x^2+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x^2}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{1}{12} \log \left(x^4-x^2+1\right)",1,"-1/2*ArcTan[1/Sqrt[3] - (2*x^2)/Sqrt[3]]/Sqrt[3] - Log[-1 + Sqrt[3]*x - x^2]/12 + Log[1 + x^2]/6 - Log[1 + Sqrt[3]*x + x^2]/12","A",1
154,0,0,13,0.0000713,"\int \frac{-1+x^{-1+n}}{-n x+x^n} \, dx","IntegrateAlgebraic[(-1 + x^(-1 + n))/(-(n*x) + x^n),x]","\int \frac{-1+x^{-1+n}}{-n x+x^n} \, dx","\frac{\log \left(x^n-n x\right)}{n}",1,"Could not integrate","F",-1
155,1,44,41,0.0193923,"\int \frac{x^3}{1-2 x^2+3 x^4} \, dx","IntegrateAlgebraic[x^3/(1 - 2*x^2 + 3*x^4),x]","\frac{1}{12} \log \left(3 x^4-2 x^2+1\right)-\frac{\tan ^{-1}\left(\frac{1}{\sqrt{2}}-\frac{3 x^2}{\sqrt{2}}\right)}{6 \sqrt{2}}","\frac{1}{12} \log \left(3 x^4-2 x^2+1\right)-\frac{\tan ^{-1}\left(\frac{1-3 x^2}{\sqrt{2}}\right)}{6 \sqrt{2}}",1,"-1/6*ArcTan[1/Sqrt[2] - (3*x^2)/Sqrt[2]]/Sqrt[2] + Log[1 - 2*x^2 + 3*x^4]/12","A",1
156,1,30,32,0.0088728,"\int \frac{x^5}{-4+x^2+3 x^4} \, dx","IntegrateAlgebraic[x^5/(-4 + x^2 + 3*x^4),x]","\frac{x^2}{6}+\frac{1}{14} \log \left(x^2-1\right)-\frac{8}{63} \log \left(3 x^2+4\right)","\frac{x^2}{6}+\frac{1}{14} \log \left(1-x^2\right)-\frac{8}{63} \log \left(3 x^2+4\right)",1,"x^2/6 + Log[-1 + x^2]/14 - (8*Log[4 + 3*x^2])/63","A",1
157,1,16,25,0.007947,"\int \frac{x^2}{9-10 x^3+x^6} \, dx","IntegrateAlgebraic[x^2/(9 - 10*x^3 + x^6),x]","\frac{1}{12} \tanh ^{-1}\left(\frac{5}{4}-\frac{x^3}{4}\right)","\frac{1}{24} \log \left(9-x^3\right)-\frac{1}{24} \log \left(1-x^3\right)",1,"ArcTanh[5/4 - x^3/4]/12","A",1
158,1,24,36,0.0187894,"\int \frac{1-4 x^2+x^3}{(-2+x)^4} \, dx","IntegrateAlgebraic[(1 - 4*x^2 + x^3)/(-2 + x)^4,x]","\frac{-6 x^2+30 x-29}{3 (x-2)^3}+\log (x-2)","\frac{2}{2-x}+\frac{2}{(2-x)^2}-\frac{7}{3 (2-x)^3}+\log (2-x)",1,"(-29 + 30*x - 6*x^2)/(3*(-2 + x)^3) + Log[-2 + x]","A",1
159,1,24,45,0.0093132,"\int \frac{x^3}{(-1+x)^{12}} \, dx","IntegrateAlgebraic[x^3/(-1 + x)^12,x]","\frac{-165 x^3+55 x^2-11 x+1}{1320 (x-1)^{11}}","-\frac{1}{8 (1-x)^8}+\frac{1}{3 (1-x)^9}-\frac{3}{10 (1-x)^{10}}+\frac{1}{11 (1-x)^{11}}",1,"(1 - 11*x + 55*x^2 - 165*x^3)/(1320*(-1 + x)^11)","A",1
160,1,37,55,0.0186003,"\int \frac{-3 x+x^4}{(1+2 x)^5} \, dx","IntegrateAlgebraic[(-3*x + x^4)/(1 + 2*x)^5,x]","\frac{384 x^3+432 x^2+368 x+49}{384 (2 x+1)^4}+\frac{1}{32} \log (2 x+1)","\frac{1}{8 (2 x+1)}-\frac{3}{32 (2 x+1)^2}+\frac{7}{24 (2 x+1)^3}-\frac{25}{128 (2 x+1)^4}+\frac{1}{32} \log (2 x+1)",1,"(49 + 368*x + 432*x^2 + 384*x^3)/(384*(1 + 2*x)^4) + Log[1 + 2*x]/32","A",1
161,1,31,36,0.0304089,"\int \frac{1}{(-1+x)^2 (1+x)^3} \, dx","IntegrateAlgebraic[1/((-1 + x)^2*(1 + x)^3),x]","\frac{-3 x^2-3 x+2}{8 (x-1) (x+1)^2}+\frac{3}{8} \tanh ^{-1}(x)","\frac{1}{8 (1-x)}-\frac{1}{4 (x+1)}-\frac{1}{8 (x+1)^2}+\frac{3}{8} \tanh ^{-1}(x)",1,"(2 - 3*x - 3*x^2)/(8*(-1 + x)*(1 + x)^2) + (3*ArcTanh[x])/8","A",1
162,1,36,35,0.0239952,"\int \frac{1}{(5-6 x)^2 x^2} \, dx","IntegrateAlgebraic[1/((5 - 6*x)^2*x^2),x]","\frac{5-12 x}{25 x (6 x-5)}+\frac{12 \log (x)}{125}-\frac{12}{125} \log (6 x-5)","\frac{6}{25 (5-6 x)}-\frac{1}{25 x}-\frac{12}{125} \log (5-6 x)+\frac{12 \log (x)}{125}",1,"(5 - 12*x)/(25*x*(-5 + 6*x)) + (12*Log[x])/125 - (12*Log[-5 + 6*x])/125","A",1
163,1,44,61,0.0313394,"\int \frac{1}{\left(-3-2 x+x^2\right)^3} \, dx","IntegrateAlgebraic[(-3 - 2*x + x^2)^(-3),x]","\frac{3 x^3-9 x^2-11 x+17}{128 \left(x^2-2 x-3\right)^2}+\frac{3}{256} \tanh ^{-1}\left(\frac{1}{2}-\frac{x}{2}\right)","\frac{3 (1-x)}{128 \left(-x^2+2 x+3\right)}+\frac{1-x}{16 \left(-x^2+2 x+3\right)^2}+\frac{3}{512} \log (3-x)-\frac{3}{512} \log (x+1)",1,"(17 - 11*x - 9*x^2 + 3*x^3)/(128*(-3 - 2*x + x^2)^2) + (3*ArcTanh[1/2 - x/2])/256","A",1
164,1,40,51,0.0233867,"\int \frac{1}{\left(13-4 x+x^2\right)^3} \, dx","IntegrateAlgebraic[(13 - 4*x + x^2)^(-3),x]","\frac{(x-2) \left(x^2-4 x+19\right)}{216 \left(x^2-4 x+13\right)^2}-\frac{1}{648} \tan ^{-1}\left(\frac{2}{3}-\frac{x}{3}\right)","-\frac{2-x}{216 \left(x^2-4 x+13\right)}-\frac{2-x}{36 \left(x^2-4 x+13\right)^2}+\frac{1}{648} \tan ^{-1}\left(\frac{x-2}{3}\right)",1,"((-2 + x)*(19 - 4*x + x^2))/(216*(13 - 4*x + x^2)^2) - ArcTan[2/3 - x/3]/648","A",1
165,1,43,54,0.0285909,"\int \frac{1}{(2+x)^3 (3+x)^4} \, dx","IntegrateAlgebraic[1/((2 + x)^3*(3 + x)^4),x]","\frac{60 x^4+630 x^3+2450 x^2+4175 x+2627}{6 (x+2)^2 (x+3)^3}-20 \tanh ^{-1}(2 x+5)","\frac{4}{x+2}+\frac{6}{x+3}-\frac{1}{2 (x+2)^2}+\frac{3}{2 (x+3)^2}+\frac{1}{3 (x+3)^3}+10 \log (x+2)-10 \log (x+3)",1,"(2627 + 4175*x + 2450*x^2 + 630*x^3 + 60*x^4)/(6*(2 + x)^2*(3 + x)^3) - 20*ArcTanh[5 + 2*x]","A",1
166,1,38,36,0.0461713,"\int \frac{x^6}{\left(-2+x^2\right)^2} \, dx","IntegrateAlgebraic[x^6/(-2 + x^2)^2,x]","\frac{x \left(x^4+10 x^2-30\right)}{3 \left(x^2-2\right)}-5 \sqrt{2} \tanh ^{-1}\left(\frac{x}{\sqrt{2}}\right)","\frac{x^3}{3}-\frac{2 x}{x^2-2}+4 x-5 \sqrt{2} \tanh ^{-1}\left(\frac{x}{\sqrt{2}}\right)",1,"(x*(-30 + 10*x^2 + x^4))/(3*(-2 + x^2)) - 5*Sqrt[2]*ArcTanh[x/Sqrt[2]]","A",1
167,1,40,58,0.025889,"\int \frac{x^8}{\left(4+x^2\right)^4} \, dx","IntegrateAlgebraic[x^8/(4 + x^2)^4,x]","\frac{x \left(12 x^6+231 x^4+1120 x^2+1680\right)}{12 \left(x^2+4\right)^3}-\frac{35}{8} \tan ^{-1}\left(\frac{x}{2}\right)","-\frac{x^7}{6 \left(x^2+4\right)^3}-\frac{7 x^5}{24 \left(x^2+4\right)^2}-\frac{35 x^3}{48 \left(x^2+4\right)}+\frac{35 x}{16}-\frac{35}{8} \tan ^{-1}\left(\frac{x}{2}\right)",1,"(x*(1680 + 1120*x^2 + 231*x^4 + 12*x^6))/(12*(4 + x^2)^3) - (35*ArcTan[x/2])/8","A",1
168,1,46,43,0.0478881,"\int \frac{-4+7 x}{\left(5+2 x+3 x^2\right)^2} \, dx","IntegrateAlgebraic[(-4 + 7*x)/(5 + 2*x + 3*x^2)^2,x]","\frac{-19 x-39}{28 \left(3 x^2+2 x+5\right)}-\frac{19 \tan ^{-1}\left(\frac{3 x}{\sqrt{14}}+\frac{1}{\sqrt{14}}\right)}{28 \sqrt{14}}","-\frac{19 x+39}{28 \left(3 x^2+2 x+5\right)}-\frac{19 \tan ^{-1}\left(\frac{3 x+1}{\sqrt{14}}\right)}{28 \sqrt{14}}",1,"(-39 - 19*x)/(28*(5 + 2*x + 3*x^2)) - (19*ArcTan[1/Sqrt[14] + (3*x)/Sqrt[14]])/(28*Sqrt[14])","A",1
169,1,48,43,0.058185,"\int \frac{5-4 x}{\left(-2-4 x+3 x^2\right)^2} \, dx","IntegrateAlgebraic[(5 - 4*x)/(-2 - 4*x + 3*x^2)^2,x]","\frac{18-7 x}{20 \left(3 x^2-4 x-2\right)}-\frac{7 \tanh ^{-1}\left(\sqrt{\frac{2}{5}}-\frac{3 x}{\sqrt{10}}\right)}{20 \sqrt{10}}","-\frac{18-7 x}{20 \left(-3 x^2+4 x+2\right)}-\frac{7 \tanh ^{-1}\left(\frac{2-3 x}{\sqrt{10}}\right)}{20 \sqrt{10}}",1,"(18 - 7*x)/(20*(-2 - 4*x + 3*x^2)) - (7*ArcTanh[Sqrt[2/5] - (3*x)/Sqrt[10]])/(20*Sqrt[10])","A",1
170,1,28,37,0.0157726,"\int \frac{x^5}{\left(1+x^4\right)^3} \, dx","IntegrateAlgebraic[x^5/(1 + x^4)^3,x]","\frac{1}{16} \tan ^{-1}\left(x^2\right)+\frac{\left(x^4-1\right) x^2}{16 \left(x^4+1\right)^2}","\frac{1}{16} \tan ^{-1}\left(x^2\right)+\frac{x^2}{16 \left(x^4+1\right)}-\frac{x^2}{8 \left(x^4+1\right)^2}",1,"(x^2*(-1 + x^4))/(16*(1 + x^4)^2) + ArcTan[x^2]/16","A",1
171,1,32,32,0.0186521,"\int \frac{x \left(1+x^2\right)^3}{\left(2+2 x^2+x^4\right)^2} \, dx","IntegrateAlgebraic[(x*(1 + x^2)^3)/(2 + 2*x^2 + x^4)^2,x]","\frac{1}{4 \left(x^4+2 x^2+2\right)}+\frac{1}{4} \log \left(x^4+2 x^2+2\right)","\frac{1}{4 \left(x^4+2 x^2+2\right)}+\frac{1}{4} \log \left(x^4+2 x^2+2\right)",1,"1/(4*(2 + 2*x^2 + x^4)) + Log[2 + 2*x^2 + x^4]/4","A",1
172,1,13,13,0.0061628,"\int \frac{x^3}{\left(a^4+x^4\right)^3} \, dx","IntegrateAlgebraic[x^3/(a^4 + x^4)^3,x]","-\frac{1}{8 \left(a^4+x^4\right)^2}","-\frac{1}{8 \left(a^4+x^4\right)^2}",1,"-1/8*1/(a^4 + x^4)^2","A",1
173,1,49,54,0.037359,"\int \frac{1}{x \left(a^4+x^4\right)^3} \, dx","IntegrateAlgebraic[1/(x*(a^4 + x^4)^3),x]","\frac{\log (x)}{a^{12}}-\frac{\log \left(a^4+x^4\right)}{4 a^{12}}+\frac{3 a^4+2 x^4}{8 a^8 \left(a^4+x^4\right)^2}","\frac{\log (x)}{a^{12}}+\frac{1}{8 a^4 \left(a^4+x^4\right)^2}-\frac{\log \left(a^4+x^4\right)}{4 a^{12}}+\frac{1}{4 a^8 \left(a^4+x^4\right)}",1,"(3*a^4 + 2*x^4)/(8*a^8*(a^4 + x^4)^2) + Log[x]/a^12 - Log[a^4 + x^4]/(4*a^12)","A",1
174,1,107,157,0.1403715,"\int \frac{1}{x^2 \left(a^4+x^4\right)^3} \, dx","IntegrateAlgebraic[1/(x^2*(a^4 + x^4)^3),x]","\frac{45 \tan ^{-1}\left(\frac{\frac{a}{\sqrt{2}}-\frac{x^2}{\sqrt{2} a}}{x}\right)}{64 \sqrt{2} a^{13}}+\frac{45 \tanh ^{-1}\left(\frac{\sqrt{2} a x}{a^2+x^2}\right)}{64 \sqrt{2} a^{13}}+\frac{-32 a^8-81 a^4 x^4-45 x^8}{32 a^{12} x \left(a^4+x^4\right)^2}","\frac{45 \tan ^{-1}\left(1-\frac{\sqrt{2} x}{a}\right)}{64 \sqrt{2} a^{13}}-\frac{45 \tan ^{-1}\left(\frac{\sqrt{2} x}{a}+1\right)}{64 \sqrt{2} a^{13}}-\frac{45}{32 a^{12} x}+\frac{1}{8 a^4 x \left(a^4+x^4\right)^2}-\frac{45 \log \left(a^2-\sqrt{2} a x+x^2\right)}{128 \sqrt{2} a^{13}}+\frac{45 \log \left(a^2+\sqrt{2} a x+x^2\right)}{128 \sqrt{2} a^{13}}+\frac{9}{32 a^8 x \left(a^4+x^4\right)}",1,"(-32*a^8 - 81*a^4*x^4 - 45*x^8)/(32*a^12*x*(a^4 + x^4)^2) + (45*ArcTan[(a/Sqrt[2] - x^2/(Sqrt[2]*a))/x])/(64*Sqrt[2]*a^13) + (45*ArcTanh[(Sqrt[2]*a*x)/(a^2 + x^2)])/(64*Sqrt[2]*a^13)","A",1
175,1,54,64,0.0632286,"\int \frac{1}{x^3 \left(a^4+x^4\right)^3} \, dx","IntegrateAlgebraic[1/(x^3*(a^4 + x^4)^3),x]","\frac{-8 a^8-25 a^4 x^4-15 x^8}{16 a^{12} x^2 \left(a^4+x^4\right)^2}-\frac{15 \tan ^{-1}\left(\frac{x^2}{a^2}\right)}{16 a^{14}}","-\frac{15}{16 a^{12} x^2}+\frac{1}{8 a^4 x^2 \left(a^4+x^4\right)^2}-\frac{15 \tan ^{-1}\left(\frac{x^2}{a^2}\right)}{16 a^{14}}+\frac{5}{16 a^8 x^2 \left(a^4+x^4\right)}",1,"(-8*a^8 - 25*a^4*x^4 - 15*x^8)/(16*a^12*x^2*(a^4 + x^4)^2) - (15*ArcTan[x^2/a^2])/(16*a^14)","A",1
176,1,33,39,0.0187189,"\int \frac{x^{14}}{\left(3+2 x^5\right)^3} \, dx","IntegrateAlgebraic[x^14/(3 + 2*x^5)^3,x]","\frac{3 \left(8 x^5+9\right)}{80 \left(2 x^5+3\right)^2}+\frac{1}{40} \log \left(2 x^5+3\right)","\frac{3}{20 \left(2 x^5+3\right)}-\frac{9}{80 \left(2 x^5+3\right)^2}+\frac{1}{40} \log \left(2 x^5+3\right)",1,"(3*(9 + 8*x^5))/(80*(3 + 2*x^5)^2) + Log[3 + 2*x^5]/40","A",1
177,1,340,319,0.6998132,"\int \frac{x^6}{\left(3+2 x^5\right)^3} \, dx","IntegrateAlgebraic[x^6/(3 + 2*x^5)^3,x]","-\frac{\sqrt[5]{5 \sqrt{5}-11} \log \left(2\ 2^{2/5} 3^{3/5} x^2-\sqrt[5]{2} 3^{4/5} \sqrt{5} x-\sqrt[5]{2} 3^{4/5} x+6\right)}{500\ 6^{3/5}}+\frac{\sqrt[5]{11+5 \sqrt{5}} \log \left(2\ 2^{2/5} 3^{3/5} x^2+\sqrt[5]{2} 3^{4/5} \sqrt{5} x-\sqrt[5]{2} 3^{4/5} x+6\right)}{500\ 6^{3/5}}+\frac{\left(4 x^5-9\right) x^2}{300 \left(2 x^5+3\right)^2}-\frac{\log \left(\sqrt[5]{2} 3^{4/5} x+3\right)}{250\ 2^{2/5} 3^{3/5}}-\frac{\sqrt[10]{25-11 \sqrt{5}} \tan ^{-1}\left(\frac{2 \sqrt[10]{50-22 \sqrt{5}} x}{\sqrt[5]{3} 5^{3/10}}+\sqrt{1-\frac{2}{\sqrt{5}}}\right)}{50 \sqrt{2} 3^{3/5} 5^{4/5}}-\frac{\sqrt[10]{25+11 \sqrt{5}} \tan ^{-1}\left(\sqrt{1+\frac{2}{\sqrt{5}}}-\frac{2 \sqrt[10]{50+22 \sqrt{5}} x}{\sqrt[5]{3} 5^{3/10}}\right)}{50 \sqrt{2} 3^{3/5} 5^{4/5}}","\frac{\left(1+\sqrt{5}\right) \log \left(2^{2/5} x^2-\frac{\sqrt[5]{3} \left(1-\sqrt{5}\right) x}{2^{4/5}}+3^{2/5}\right)}{1000\ 2^{2/5} 3^{3/5}}+\frac{\left(1-\sqrt{5}\right) \log \left(2^{2/5} x^2-\frac{\sqrt[5]{3} \left(1+\sqrt{5}\right) x}{2^{4/5}}+3^{2/5}\right)}{1000\ 2^{2/5} 3^{3/5}}+\frac{x^2}{150 \left(2 x^5+3\right)}-\frac{x^2}{20 \left(2 x^5+3\right)^2}-\frac{\log \left(\sqrt[5]{2} x+\sqrt[5]{3}\right)}{250\ 2^{2/5} 3^{3/5}}-\frac{\sqrt{5+\sqrt{5}} \tan ^{-1}\left(\sqrt{\frac{1}{5} \left(5+2 \sqrt{5}\right)}-\frac{2\ 2^{7/10} x}{\sqrt[5]{3} \sqrt{5-\sqrt{5}}}\right)}{250\ 2^{9/10} 3^{3/5}}-\frac{\sqrt{5-\sqrt{5}} \tan ^{-1}\left(\frac{2\ 2^{7/10} x}{\sqrt[5]{3} \sqrt{5+\sqrt{5}}}+\sqrt{\frac{1}{5} \left(5-2 \sqrt{5}\right)}\right)}{250\ 2^{9/10} 3^{3/5}}",1,"(x^2*(-9 + 4*x^5))/(300*(3 + 2*x^5)^2) - ((25 - 11*Sqrt[5])^(1/10)*ArcTan[Sqrt[1 - 2/Sqrt[5]] + (2*(50 - 22*Sqrt[5])^(1/10)*x)/(3^(1/5)*5^(3/10))])/(50*Sqrt[2]*3^(3/5)*5^(4/5)) - ((25 + 11*Sqrt[5])^(1/10)*ArcTan[Sqrt[1 + 2/Sqrt[5]] - (2*(50 + 22*Sqrt[5])^(1/10)*x)/(3^(1/5)*5^(3/10))])/(50*Sqrt[2]*3^(3/5)*5^(4/5)) - Log[3 + 2^(1/5)*3^(4/5)*x]/(250*2^(2/5)*3^(3/5)) - ((-11 + 5*Sqrt[5])^(1/5)*Log[6 - 2^(1/5)*3^(4/5)*x - 2^(1/5)*3^(4/5)*Sqrt[5]*x + 2*2^(2/5)*3^(3/5)*x^2])/(500*6^(3/5)) + ((11 + 5*Sqrt[5])^(1/5)*Log[6 - 2^(1/5)*3^(4/5)*x + 2^(1/5)*3^(4/5)*Sqrt[5]*x + 2*2^(2/5)*3^(3/5)*x^2])/(500*6^(3/5))","A",0
178,1,48,59,0.0872399,"\int \frac{9}{5 x^2 \left(3-2 x^2\right)^3} \, dx","IntegrateAlgebraic[9/(5*x^2*(3 - 2*x^2)^3),x]","\frac{-10 x^4+25 x^2-12}{20 x \left(2 x^2-3\right)^2}+\frac{\tanh ^{-1}\left(\sqrt{\frac{2}{3}} x\right)}{4 \sqrt{6}}","\frac{1}{8 x \left(3-2 x^2\right)}+\frac{3}{20 x \left(3-2 x^2\right)^2}-\frac{1}{8 x}+\frac{\tanh ^{-1}\left(\sqrt{\frac{2}{3}} x\right)}{4 \sqrt{6}}",1,"(-12 + 25*x^2 - 10*x^4)/(20*x*(-3 + 2*x^2)^2) + ArcTanh[Sqrt[2/3]*x]/(4*Sqrt[6])","A",1
179,1,33,36,0.0001137,"\int \frac{4+3 x^4}{x^2 \left(1+x^2\right)^3} \, dx","IntegrateAlgebraic[(4 + 3*x^4)/(x^2*(1 + x^2)^3),x]","\frac{-57 x^4-103 x^2-32}{8 x \left(x^2+1\right)^2}-\frac{57}{8} \tan ^{-1}(x)","-\frac{25 x}{8 \left(x^2+1\right)}-\frac{7 x}{4 \left(x^2+1\right)^2}-\frac{4}{x}-\frac{57}{8} \tan ^{-1}(x)",1,"(-32 - 103*x^2 - 57*x^4)/(8*x*(1 + x^2)^2) - (57*ArcTan[x])/8","A",1
180,1,35,38,0.0298496,"\int \frac{5-3 x+6 x^2+5 x^3-x^4}{-1+x+2 x^2-2 x^3-x^4+x^5} \, dx","IntegrateAlgebraic[(5 - 3*x + 6*x^2 + 5*x^3 - x^4)/(-1 + x + 2*x^2 - 2*x^3 - x^4 + x^5),x]","\frac{-2 x^2-7 x+3}{2 (x-1)^2 (x+1)}+\log (x-1)-2 \log (x+1)","\frac{2}{1-x}+\frac{1}{x+1}-\frac{3}{2 (1-x)^2}+\log (1-x)-2 \log (x+1)",1,"(3 - 7*x - 2*x^2)/(2*(-1 + x)^2*(1 + x)) + Log[-1 + x] - 2*Log[1 + x]","A",1
181,1,74,64,0.044278,"\int \frac{1+x^2}{x \left(1+x^3\right)^2} \, dx","IntegrateAlgebraic[(1 + x^2)/(x*(1 + x^3)^2),x]","-\frac{1}{3} \log \left(x^3+1\right)+\frac{1}{18} \log \left(x^2-x+1\right)+\frac{x^2+1}{3 \left(x^3+1\right)}+\log (x)-\frac{1}{9} \log (x+1)-\frac{\tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 x}{\sqrt{3}}\right)}{3 \sqrt{3}}","-\frac{5}{18} \log \left(x^2-x+1\right)+\frac{x \left(x-x^2\right)}{3 \left(x^3+1\right)}+\log (x)-\frac{4}{9} \log (x+1)-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"(1 + x^2)/(3*(1 + x^3)) - ArcTan[1/Sqrt[3] - (2*x)/Sqrt[3]]/(3*Sqrt[3]) + Log[x] - Log[1 + x]/9 + Log[1 - x + x^2]/18 - Log[1 + x^3]/3","A",1
182,1,69,63,0.0539059,"\int \frac{-2-3 x+x^2}{(1+x)^2 \left(1+x+x^2\right)^2} \, dx","IntegrateAlgebraic[(-2 - 3*x + x^2)/((1 + x)^2*(1 + x + x^2)^2),x]","\frac{-11 x^2-18 x-13}{3 (x+1) \left(x^2+x+1\right)}+\frac{1}{2} \log \left(x^2+x+1\right)-\log (x+1)-\frac{25 \tan ^{-1}\left(\frac{2 x}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3}}","-\frac{5 x+7}{3 \left(x^2+x+1\right)}+\frac{1}{2} \log \left(x^2+x+1\right)-\frac{2}{x+1}-\log (x+1)-\frac{25 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"(-13 - 18*x - 11*x^2)/(3*(1 + x)*(1 + x + x^2)) - (25*ArcTan[1/Sqrt[3] + (2*x)/Sqrt[3]])/(3*Sqrt[3]) - Log[1 + x] + Log[1 + x + x^2]/2","A",1
183,1,33,43,0.0266462,"\int \frac{1}{(1-4 x)^3 (2-3 x)} \, dx","IntegrateAlgebraic[1/((1 - 4*x)^3*(2 - 3*x)),x]","\frac{24 x-1}{50 (4 x-1)^2}-\frac{18}{125} \tanh ^{-1}\left(\frac{x+1}{7 x-3}\right)","-\frac{3}{25 (1-4 x)}+\frac{1}{10 (1-4 x)^2}-\frac{9}{125} \log (1-4 x)+\frac{9}{125} \log (2-3 x)",1,"(-1 + 24*x)/(50*(-1 + 4*x)^2) - (18*ArcTanh[(1 + x)/(-3 + 7*x)])/125","A",1
184,1,20,27,0.0113031,"\int \frac{x^3}{\left(2-5 x^2\right)^7} \, dx","IntegrateAlgebraic[x^3/(2 - 5*x^2)^7,x]","\frac{15 x^2-1}{750 \left(5 x^2-2\right)^6}","\frac{1}{150 \left(2-5 x^2\right)^6}-\frac{1}{250 \left(2-5 x^2\right)^5}",1,"(-1 + 15*x^2)/(750*(-2 + 5*x^2)^6)","A",1
185,1,38,46,0.0215302,"\int \frac{x^7}{\left(2-5 x^2\right)^3} \, dx","IntegrateAlgebraic[x^7/(2 - 5*x^2)^3,x]","\frac{-125 x^6+150 x^4-12}{1250 \left(5 x^2-2\right)^2}-\frac{3}{625} \log \left(5 x^2-2\right)","-\frac{x^2}{250}-\frac{6}{625 \left(2-5 x^2\right)}+\frac{2}{625 \left(2-5 x^2\right)^2}-\frac{3}{625} \log \left(2-5 x^2\right)",1,"(-12 + 150*x^4 - 125*x^6)/(1250*(-2 + 5*x^2)^2) - (3*Log[-2 + 5*x^2])/625","A",1
186,1,41,44,0.0289782,"\int \frac{1}{(-2+x)^3 (1+x)^2} \, dx","IntegrateAlgebraic[1/((-2 + x)^3*(1 + x)^2),x]","\frac{2 x^2-5 x-1}{18 (x-2)^2 (x+1)}+\frac{1}{27} \log (x-2)-\frac{1}{27} \log (x+1)","\frac{2}{27 (x-2)}+\frac{1}{27 (x+1)}-\frac{1}{18 (x-2)^2}+\frac{1}{27} \log (x-2)-\frac{1}{27} \log (x+1)",1,"(-1 - 5*x + 2*x^2)/(18*(-2 + x)^2*(1 + x)) + Log[-2 + x]/27 - Log[1 + x]/27","A",1
187,1,43,54,0.0001362,"\int \frac{1}{(2+x)^3 (3+x)^4} \, dx","IntegrateAlgebraic[1/((2 + x)^3*(3 + x)^4),x]","\frac{60 x^4+630 x^3+2450 x^2+4175 x+2627}{6 (x+2)^2 (x+3)^3}-20 \tanh ^{-1}(2 x+5)","\frac{4}{x+2}+\frac{6}{x+3}-\frac{1}{2 (x+2)^2}+\frac{3}{2 (x+3)^2}+\frac{1}{3 (x+3)^3}+10 \log (x+2)-10 \log (x+3)",1,"(2627 + 4175*x + 2450*x^2 + 630*x^3 + 60*x^4)/(6*(2 + x)^2*(3 + x)^3) - 20*ArcTanh[5 + 2*x]","A",1
188,1,39,36,0.0001064,"\int \frac{x^5}{(3+x)^2} \, dx","IntegrateAlgebraic[x^5/(3 + x)^2,x]","\frac{x^5-5 x^4+30 x^3-270 x^2-1296 x+972}{4 (x+3)}+405 \log (x+3)","\frac{x^4}{4}-2 x^3+\frac{27 x^2}{2}-108 x+\frac{243}{x+3}+405 \log (x+3)",1,"(972 - 1296*x - 270*x^2 + 30*x^3 - 5*x^4 + x^5)/(4*(3 + x)) + 405*Log[3 + x]","A",1
189,1,41,44,0.0268663,"\int (\text{b1}+\text{c1} x) \left(a+2 b x+c x^2\right) \, dx","IntegrateAlgebraic[(b1 + c1*x)*(a + 2*b*x + c*x^2),x]","\frac{1}{12} x \left(12 a \text{b1}+6 a \text{c1} x+12 b \text{b1} x+8 b \text{c1} x^2+4 \text{b1} c x^2+3 c \text{c1} x^3\right)","\frac{1}{2} x^2 (a \text{c1}+2 b \text{b1})+a \text{b1} x+\frac{1}{3} x^3 (2 b \text{c1}+\text{b1} c)+\frac{1}{4} c \text{c1} x^4",1,"(x*(12*a*b1 + 12*b*b1*x + 6*a*c1*x + 4*b1*c*x^2 + 8*b*c1*x^2 + 3*c*c1*x^3))/12","A",1
190,1,105,96,0.0630271,"\int (\text{b1}+\text{c1} x) \left(a+2 b x+c x^2\right)^2 \, dx","IntegrateAlgebraic[(b1 + c1*x)*(a + 2*b*x + c*x^2)^2,x]","\frac{1}{30} \left(30 a^2 \text{b1} x+15 a^2 \text{c1} x^2+60 a b \text{b1} x^2+40 a b \text{c1} x^3+20 a \text{b1} c x^3+15 a c \text{c1} x^4+40 b^2 \text{b1} x^3+30 b^2 \text{c1} x^4+30 b \text{b1} c x^4+24 b c \text{c1} x^5+6 \text{b1} c^2 x^5+5 c^2 \text{c1} x^6\right)","a^2 \text{b1} x+\frac{1}{2} x^4 \left(a c \text{c1}+2 b^2 \text{c1}+2 b \text{b1} c\right)+\frac{2}{3} x^3 \left(2 a b \text{c1}+a \text{b1} c+2 b^2 \text{b1}\right)+\frac{1}{2} a x^2 (a \text{c1}+4 b \text{b1})+\frac{1}{5} c x^5 (4 b \text{c1}+\text{b1} c)+\frac{1}{6} c^2 \text{c1} x^6",1,"(30*a^2*b1*x + 60*a*b*b1*x^2 + 15*a^2*c1*x^2 + 40*b^2*b1*x^3 + 20*a*b1*c*x^3 + 40*a*b*c1*x^3 + 30*b*b1*c*x^4 + 30*b^2*c1*x^4 + 15*a*c*c1*x^4 + 6*b1*c^2*x^5 + 24*b*c*c1*x^5 + 5*c^2*c1*x^6)/30","A",1
191,1,195,167,0.0763156,"\int (\text{b1}+\text{c1} x) \left(a+2 b x+c x^2\right)^3 \, dx","IntegrateAlgebraic[(b1 + c1*x)*(a + 2*b*x + c*x^2)^3,x]","\frac{1}{280} \left(280 a^3 \text{b1} x+140 a^3 \text{c1} x^2+840 a^2 b \text{b1} x^2+560 a^2 b \text{c1} x^3+280 a^2 \text{b1} c x^3+210 a^2 c \text{c1} x^4+1120 a b^2 \text{b1} x^3+840 a b^2 \text{c1} x^4+840 a b \text{b1} c x^4+672 a b c \text{c1} x^5+168 a \text{b1} c^2 x^5+140 a c^2 \text{c1} x^6+560 b^3 \text{b1} x^4+448 b^3 \text{c1} x^5+672 b^2 \text{b1} c x^5+560 b^2 c \text{c1} x^6+280 b \text{b1} c^2 x^6+240 b c^2 \text{c1} x^7+40 \text{b1} c^3 x^7+35 c^3 \text{c1} x^8\right)","a^3 \text{b1} x+\frac{1}{4} x^4 \left(3 a^2 c \text{c1}+12 a b^2 \text{c1}+12 a b \text{b1} c+8 b^3 \text{b1}\right)+\frac{1}{2} a^2 x^2 (a \text{c1}+6 b \text{b1})+\frac{1}{2} c x^6 \left(a c \text{c1}+4 b^2 \text{c1}+2 b \text{b1} c\right)+a x^3 \left(2 a b \text{c1}+a \text{b1} c+4 b^2 \text{b1}\right)+\frac{1}{5} x^5 \left(12 a b c \text{c1}+3 a \text{b1} c^2+8 b^3 \text{c1}+12 b^2 \text{b1} c\right)+\frac{1}{7} c^2 x^7 (6 b \text{c1}+\text{b1} c)+\frac{1}{8} c^3 \text{c1} x^8",1,"(280*a^3*b1*x + 840*a^2*b*b1*x^2 + 140*a^3*c1*x^2 + 1120*a*b^2*b1*x^3 + 280*a^2*b1*c*x^3 + 560*a^2*b*c1*x^3 + 560*b^3*b1*x^4 + 840*a*b*b1*c*x^4 + 840*a*b^2*c1*x^4 + 210*a^2*c*c1*x^4 + 672*b^2*b1*c*x^5 + 168*a*b1*c^2*x^5 + 448*b^3*c1*x^5 + 672*a*b*c*c1*x^5 + 280*b*b1*c^2*x^6 + 560*b^2*c*c1*x^6 + 140*a*c^2*c1*x^6 + 40*b1*c^3*x^7 + 240*b*c^2*c1*x^7 + 35*c^3*c1*x^8)/280","A",1
192,1,315,263,0.1452587,"\int (\text{b1}+\text{c1} x) \left(a+2 b x+c x^2\right)^4 \, dx","IntegrateAlgebraic[(b1 + c1*x)*(a + 2*b*x + c*x^2)^4,x]","\frac{1}{630} \left(630 a^4 \text{b1} x+315 a^4 \text{c1} x^2+2520 a^3 b \text{b1} x^2+1680 a^3 b \text{c1} x^3+840 a^3 \text{b1} c x^3+630 a^3 c \text{c1} x^4+5040 a^2 b^2 \text{b1} x^3+3780 a^2 b^2 \text{c1} x^4+3780 a^2 b \text{b1} c x^4+3024 a^2 b c \text{c1} x^5+756 a^2 \text{b1} c^2 x^5+630 a^2 c^2 \text{c1} x^6+5040 a b^3 \text{b1} x^4+4032 a b^3 \text{c1} x^5+6048 a b^2 \text{b1} c x^5+5040 a b^2 c \text{c1} x^6+2520 a b \text{b1} c^2 x^6+2160 a b c^2 \text{c1} x^7+360 a \text{b1} c^3 x^7+315 a c^3 \text{c1} x^8+2016 b^4 \text{b1} x^5+1680 b^4 \text{c1} x^6+3360 b^3 \text{b1} c x^6+2880 b^3 c \text{c1} x^7+2160 b^2 \text{b1} c^2 x^7+1890 b^2 c^2 \text{c1} x^8+630 b \text{b1} c^3 x^8+560 b c^3 \text{c1} x^9+70 \text{b1} c^4 x^9+63 c^4 \text{c1} x^{10}\right)","a^4 \text{b1} x+\frac{1}{2} a^3 x^2 (a \text{c1}+8 b \text{b1})+\frac{4}{3} a^2 x^3 \left(2 a b \text{c1}+a \text{b1} c+6 b^2 \text{b1}\right)+a x^4 \left(a^2 c \text{c1}+6 a b^2 \text{c1}+6 a b \text{b1} c+8 b^3 \text{b1}\right)+\frac{1}{3} x^6 \left(3 a^2 c^2 \text{c1}+24 a b^2 c \text{c1}+12 a b \text{b1} c^2+8 b^4 \text{c1}+16 b^3 \text{b1} c\right)+\frac{2}{5} x^5 \left(12 a^2 b c \text{c1}+3 a^2 \text{b1} c^2+16 a b^3 \text{c1}+24 a b^2 \text{b1} c+8 b^4 \text{b1}\right)+\frac{1}{2} c^2 x^8 \left(a c \text{c1}+6 b^2 \text{c1}+2 b \text{b1} c\right)+\frac{4}{7} c x^7 \left(6 a b c \text{c1}+a \text{b1} c^2+8 b^3 \text{c1}+6 b^2 \text{b1} c\right)+\frac{1}{9} c^3 x^9 (8 b \text{c1}+\text{b1} c)+\frac{1}{10} c^4 \text{c1} x^{10}",1,"(630*a^4*b1*x + 2520*a^3*b*b1*x^2 + 315*a^4*c1*x^2 + 5040*a^2*b^2*b1*x^3 + 840*a^3*b1*c*x^3 + 1680*a^3*b*c1*x^3 + 5040*a*b^3*b1*x^4 + 3780*a^2*b*b1*c*x^4 + 3780*a^2*b^2*c1*x^4 + 630*a^3*c*c1*x^4 + 2016*b^4*b1*x^5 + 6048*a*b^2*b1*c*x^5 + 756*a^2*b1*c^2*x^5 + 4032*a*b^3*c1*x^5 + 3024*a^2*b*c*c1*x^5 + 3360*b^3*b1*c*x^6 + 2520*a*b*b1*c^2*x^6 + 1680*b^4*c1*x^6 + 5040*a*b^2*c*c1*x^6 + 630*a^2*c^2*c1*x^6 + 2160*b^2*b1*c^2*x^7 + 360*a*b1*c^3*x^7 + 2880*b^3*c*c1*x^7 + 2160*a*b*c^2*c1*x^7 + 630*b*b1*c^3*x^8 + 1890*b^2*c^2*c1*x^8 + 315*a*c^3*c1*x^8 + 70*b1*c^4*x^9 + 560*b*c^3*c1*x^9 + 63*c^4*c1*x^10)/630","A",1
193,0,0,159,0.0000677,"\int (\text{b1}+\text{c1} x) \left(a+2 b x+c x^2\right)^n \, dx","IntegrateAlgebraic[(b1 + c1*x)*(a + 2*b*x + c*x^2)^n,x]","\int (\text{b1}+\text{c1} x) \left(a+2 b x+c x^2\right)^n \, dx","\frac{\text{c1} \left(a+2 b x+c x^2\right)^{n+1}}{2 c (n+1)}-\frac{2^n (\text{b1} c-b \text{c1}) \left(-\frac{-\sqrt{b^2-a c}+b+c x}{\sqrt{b^2-a c}}\right)^{-n-1} \left(a+2 b x+c x^2\right)^{n+1} \, _2F_1\left(-n,n+1;n+2;\frac{b+c x+\sqrt{b^2-a c}}{2 \sqrt{b^2-a c}}\right)}{c (n+1) \sqrt{b^2-a c}}",1,"Could not integrate","F",-1
194,1,79,65,0.0585672,"\int \frac{\text{b1}+\text{c1} x}{a+2 b x+c x^2} \, dx","IntegrateAlgebraic[(b1 + c1*x)/(a + 2*b*x + c*x^2),x]","\frac{(\text{b1} c-b \text{c1}) \tan ^{-1}\left(\frac{c x}{\sqrt{a c-b^2}}+\frac{b}{\sqrt{a c-b^2}}\right)}{c \sqrt{a c-b^2}}+\frac{\text{c1} \log \left(a+2 b x+c x^2\right)}{2 c}","\frac{\text{c1} \log \left(a+2 b x+c x^2\right)}{2 c}-\frac{(\text{b1} c-b \text{c1}) \tanh ^{-1}\left(\frac{b+c x}{\sqrt{b^2-a c}}\right)}{c \sqrt{b^2-a c}}",1,"((b1*c - b*c1)*ArcTan[b/Sqrt[-b^2 + a*c] + (c*x)/Sqrt[-b^2 + a*c]])/(c*Sqrt[-b^2 + a*c]) + (c1*Log[a + 2*b*x + c*x^2])/(2*c)","A",1
195,1,113,89,0.1038612,"\int \frac{\text{b1}+\text{c1} x}{\left(a+2 b x+c x^2\right)^2} \, dx","IntegrateAlgebraic[(b1 + c1*x)/(a + 2*b*x + c*x^2)^2,x]","\frac{a \text{c1}-b \text{b1}+b \text{c1} x-\text{b1} c x}{2 \left(b^2-a c\right) \left(a+2 b x+c x^2\right)}+\frac{(b \text{c1}-\text{b1} c) \tan ^{-1}\left(\frac{c x}{\sqrt{a c-b^2}}+\frac{b}{\sqrt{a c-b^2}}\right)}{2 \left(b^2-a c\right) \sqrt{a c-b^2}}","\frac{(\text{b1} c-b \text{c1}) \tanh ^{-1}\left(\frac{b+c x}{\sqrt{b^2-a c}}\right)}{2 \left(b^2-a c\right)^{3/2}}-\frac{-a \text{c1}+x (\text{b1} c-b \text{c1})+b \text{b1}}{2 \left(b^2-a c\right) \left(a+2 b x+c x^2\right)}",1,"(-(b*b1) + a*c1 - b1*c*x + b*c1*x)/(2*(b^2 - a*c)*(a + 2*b*x + c*x^2)) + ((-(b1*c) + b*c1)*ArcTan[b/Sqrt[-b^2 + a*c] + (c*x)/Sqrt[-b^2 + a*c]])/(2*(b^2 - a*c)*Sqrt[-b^2 + a*c])","A",1
196,1,195,130,0.1794177,"\int \frac{\text{b1}+\text{c1} x}{\left(a+2 b x+c x^2\right)^3} \, dx","IntegrateAlgebraic[(b1 + c1*x)/(a + 2*b*x + c*x^2)^3,x]","\frac{-2 a^2 c \text{c1}-a b^2 \text{c1}+5 a b \text{b1} c-5 a b c \text{c1} x+5 a \text{b1} c^2 x-2 b^3 \text{b1}-4 b^3 \text{c1} x+4 b^2 \text{b1} c x-9 b^2 c \text{c1} x^2+9 b \text{b1} c^2 x^2-3 b c^2 \text{c1} x^3+3 \text{b1} c^3 x^3}{8 \left(b^2-a c\right)^2 \left(a+2 b x+c x^2\right)^2}-\frac{3 \left(b c \text{c1}-\text{b1} c^2\right) \tan ^{-1}\left(\frac{c x}{\sqrt{a c-b^2}}+\frac{b}{\sqrt{a c-b^2}}\right)}{8 \left(b^2-a c\right)^2 \sqrt{a c-b^2}}","\frac{3 (b+c x) (\text{b1} c-b \text{c1})}{8 \left(b^2-a c\right)^2 \left(a+2 b x+c x^2\right)}-\frac{-a \text{c1}+x (\text{b1} c-b \text{c1})+b \text{b1}}{4 \left(b^2-a c\right) \left(a+2 b x+c x^2\right)^2}-\frac{3 c (\text{b1} c-b \text{c1}) \tanh ^{-1}\left(\frac{b+c x}{\sqrt{b^2-a c}}\right)}{8 \left(b^2-a c\right)^{5/2}}",1,"(-2*b^3*b1 + 5*a*b*b1*c - a*b^2*c1 - 2*a^2*c*c1 + 4*b^2*b1*c*x + 5*a*b1*c^2*x - 4*b^3*c1*x - 5*a*b*c*c1*x + 9*b*b1*c^2*x^2 - 9*b^2*c*c1*x^2 + 3*b1*c^3*x^3 - 3*b*c^2*c1*x^3)/(8*(b^2 - a*c)^2*(a + 2*b*x + c*x^2)^2) - (3*(-(b1*c^2) + b*c*c1)*ArcTan[b/Sqrt[-b^2 + a*c] + (c*x)/Sqrt[-b^2 + a*c]])/(8*(b^2 - a*c)^2*Sqrt[-b^2 + a*c])","A",1
197,1,340,173,0.2858441,"\int \frac{\text{b1}+\text{c1} x}{\left(a+2 b x+c x^2\right)^4} \, dx","IntegrateAlgebraic[(b1 + c1*x)/(a + 2*b*x + c*x^2)^4,x]","\frac{8 a^3 c^2 \text{c1}+9 a^2 b^2 c \text{c1}-33 a^2 b \text{b1} c^2+33 a^2 b c^2 \text{c1} x-33 a^2 \text{b1} c^3 x-2 a b^4 \text{c1}+26 a b^3 \text{b1} c+54 a b^3 c \text{c1} x-54 a b^2 \text{b1} c^2 x+120 a b^2 c^2 \text{c1} x^2-120 a b \text{b1} c^3 x^2+40 a b c^3 \text{c1} x^3-40 a \text{b1} c^4 x^3-8 b^5 \text{b1}-12 b^5 \text{c1} x+12 b^4 \text{b1} c x+30 b^4 c \text{c1} x^2-30 b^3 \text{b1} c^2 x^2+110 b^3 c^2 \text{c1} x^3-110 b^2 \text{b1} c^3 x^3+75 b^2 c^3 \text{c1} x^4-75 b \text{b1} c^4 x^4+15 b c^4 \text{c1} x^5-15 \text{b1} c^5 x^5}{48 \left(b^2-a c\right)^3 \left(a+2 b x+c x^2\right)^3}+\frac{5 \left(b c^2 \text{c1}-\text{b1} c^3\right) \tan ^{-1}\left(\frac{c x}{\sqrt{a c-b^2}}+\frac{b}{\sqrt{a c-b^2}}\right)}{16 \left(b^2-a c\right)^3 \sqrt{a c-b^2}}","\frac{5 c^2 (\text{b1} c-b \text{c1}) \tanh ^{-1}\left(\frac{b+c x}{\sqrt{b^2-a c}}\right)}{16 \left(b^2-a c\right)^{7/2}}-\frac{5 c (b+c x) (\text{b1} c-b \text{c1})}{16 \left(b^2-a c\right)^3 \left(a+2 b x+c x^2\right)}+\frac{5 (b+c x) (\text{b1} c-b \text{c1})}{24 \left(b^2-a c\right)^2 \left(a+2 b x+c x^2\right)^2}-\frac{-a \text{c1}+x (\text{b1} c-b \text{c1})+b \text{b1}}{6 \left(b^2-a c\right) \left(a+2 b x+c x^2\right)^3}",1,"(-8*b^5*b1 + 26*a*b^3*b1*c - 33*a^2*b*b1*c^2 - 2*a*b^4*c1 + 9*a^2*b^2*c*c1 + 8*a^3*c^2*c1 + 12*b^4*b1*c*x - 54*a*b^2*b1*c^2*x - 33*a^2*b1*c^3*x - 12*b^5*c1*x + 54*a*b^3*c*c1*x + 33*a^2*b*c^2*c1*x - 30*b^3*b1*c^2*x^2 - 120*a*b*b1*c^3*x^2 + 30*b^4*c*c1*x^2 + 120*a*b^2*c^2*c1*x^2 - 110*b^2*b1*c^3*x^3 - 40*a*b1*c^4*x^3 + 110*b^3*c^2*c1*x^3 + 40*a*b*c^3*c1*x^3 - 75*b*b1*c^4*x^4 + 75*b^2*c^3*c1*x^4 - 15*b1*c^5*x^5 + 15*b*c^4*c1*x^5)/(48*(b^2 - a*c)^3*(a + 2*b*x + c*x^2)^3) + (5*(-(b1*c^3) + b*c^2*c1)*ArcTan[b/Sqrt[-b^2 + a*c] + (c*x)/Sqrt[-b^2 + a*c]])/(16*(b^2 - a*c)^3*Sqrt[-b^2 + a*c])","A",1
198,0,0,169,0.000064,"\int (\text{b1}+\text{c1} x) \left(a+2 b x+c x^2\right)^{-n} \, dx","IntegrateAlgebraic[(b1 + c1*x)/(a + 2*b*x + c*x^2)^n,x]","\int (\text{b1}+\text{c1} x) \left(a+2 b x+c x^2\right)^{-n} \, dx","\frac{\text{c1} \left(a+2 b x+c x^2\right)^{1-n}}{2 c (1-n)}-\frac{2^{-n} (\text{b1} c-b \text{c1}) \left(-\frac{-\sqrt{b^2-a c}+b+c x}{\sqrt{b^2-a c}}\right)^{n-1} \left(a+2 b x+c x^2\right)^{1-n} \, _2F_1\left(1-n,n;2-n;\frac{b+c x+\sqrt{b^2-a c}}{2 \sqrt{b^2-a c}}\right)}{c (1-n) \sqrt{b^2-a c}}",1,"Could not integrate","F",-1
199,1,47,49,0.0277827,"\int \frac{x}{3+6 x+2 x^2} \, dx","IntegrateAlgebraic[x/(3 + 6*x + 2*x^2),x]","\frac{1}{4} \left(1-\sqrt{3}\right) \log \left(-2 x+\sqrt{3}-3\right)+\frac{1}{4} \left(1+\sqrt{3}\right) \log \left(2 x+\sqrt{3}+3\right)","\frac{1}{4} \left(1-\sqrt{3}\right) \log \left(2 x-\sqrt{3}+3\right)+\frac{1}{4} \left(1+\sqrt{3}\right) \log \left(2 x+\sqrt{3}+3\right)",1,"((1 - Sqrt[3])*Log[-3 + Sqrt[3] - 2*x])/4 + ((1 + Sqrt[3])*Log[3 + Sqrt[3] + 2*x])/4","A",1
200,1,53,61,0.0621142,"\int \frac{-3+2 x}{\left(3+6 x+2 x^2\right)^3} \, dx","IntegrateAlgebraic[(-3 + 2*x)/(3 + 6*x + 2*x^2)^3,x]","\frac{-8 x^3-36 x^2-44 x-13}{4 \left(2 x^2+6 x+3\right)^2}+\frac{\tanh ^{-1}\left(\frac{2 x}{\sqrt{3}}+\sqrt{3}\right)}{\sqrt{3}}","-\frac{2 x+3}{2 \left(2 x^2+6 x+3\right)}+\frac{4 x+5}{4 \left(2 x^2+6 x+3\right)^2}+\frac{\tanh ^{-1}\left(\frac{2 x+3}{\sqrt{3}}\right)}{\sqrt{3}}",1,"(-13 - 44*x - 36*x^2 - 8*x^3)/(4*(3 + 6*x + 2*x^2)^2) + ArcTanh[Sqrt[3] + (2*x)/Sqrt[3]]/Sqrt[3]","A",1
201,1,36,36,0.0219452,"\int \frac{-1+x}{\left(4+5 x+x^2\right)^2} \, dx","IntegrateAlgebraic[(-1 + x)/(4 + 5*x + x^2)^2,x]","\frac{7 x+13}{9 \left(x^2+5 x+4\right)}+\frac{7}{27} \log (x+1)-\frac{7}{27} \log (x+4)","\frac{7 x+13}{9 \left(x^2+5 x+4\right)}+\frac{7}{27} \log (x+1)-\frac{7}{27} \log (x+4)",1,"(13 + 7*x)/(9*(4 + 5*x + x^2)) + (7*Log[1 + x])/27 - (7*Log[4 + x])/27","A",1
202,1,58,87,0.042371,"\int \frac{1}{\left(2+3 x+x^2\right)^5} \, dx","IntegrateAlgebraic[(2 + 3*x + x^2)^(-5),x]","\frac{(2 x+3) \left(420 x^6+3780 x^5+13790 x^4+26040 x^3+26824 x^2+14322 x+3105\right)}{12 \left(x^2+3 x+2\right)^4}-140 \tanh ^{-1}(2 x+3)","\frac{-2 x-3}{4 \left(x^2+3 x+2\right)^4}+\frac{35 (2 x+3)}{x^2+3 x+2}-\frac{35 (2 x+3)}{6 \left(x^2+3 x+2\right)^2}+\frac{7 (2 x+3)}{6 \left(x^2+3 x+2\right)^3}+70 \log (x+1)-70 \log (x+2)",1,"((3 + 2*x)*(3105 + 14322*x + 26824*x^2 + 26040*x^3 + 13790*x^4 + 3780*x^5 + 420*x^6))/(12*(2 + 3*x + x^2)^4) - 140*ArcTanh[3 + 2*x]","A",1
203,1,82,81,0.0486917,"\int \frac{1}{x^3 \left(7-6 x+2 x^2\right)^2} \, dx","IntegrateAlgebraic[1/(x^3*(7 - 6*x + 2*x^2)^2),x]","-\frac{40 \log \left(2 x^2-6 x+7\right)}{2401}+\frac{-276 x^3+814 x^2-630 x-245}{3430 x^2 \left(2 x^2-6 x+7\right)}+\frac{80 \log (x)}{2401}-\frac{234 \tan ^{-1}\left(\frac{3}{\sqrt{5}}-\frac{2 x}{\sqrt{5}}\right)}{12005 \sqrt{5}}","-\frac{2-3 x}{35 x^2 \left(2 x^2-6 x+7\right)}-\frac{1}{490 x^2}-\frac{40 \log \left(2 x^2-6 x+7\right)}{2401}-\frac{69}{1715 x}+\frac{80 \log (x)}{2401}-\frac{234 \tan ^{-1}\left(\frac{3-2 x}{\sqrt{5}}\right)}{12005 \sqrt{5}}",1,"(-245 - 630*x + 814*x^2 - 276*x^3)/(3430*x^2*(7 - 6*x + 2*x^2)) - (234*ArcTan[3/Sqrt[5] - (2*x)/Sqrt[5]])/(12005*Sqrt[5]) + (80*Log[x])/2401 - (40*Log[7 - 6*x + 2*x^2])/2401","A",1
204,1,62,104,0.042123,"\int \frac{x^9}{\left(2+3 x+x^2\right)^5} \, dx","IntegrateAlgebraic[x^9/(2 + 3*x + x^2)^5,x]","\frac{-17496 x^7-184200 x^6-813888 x^5-1955853 x^4-2759400 x^3-2286008 x^2-1030560 x-195280}{12 \left(x^2+3 x+2\right)^4}-1471 \log (x+1)+1472 \log (x+2)","-\frac{(1593 x+2206) x^2}{2 \left(x^2+3 x+2\right)}+\frac{(3 x+4) x^8}{4 \left(x^2+3 x+2\right)^4}-\frac{(81 x+110) x^6}{12 \left(x^2+3 x+2\right)^3}+\frac{(135 x+184) x^4}{2 \left(x^2+3 x+2\right)^2}+735 x-1471 \log (x+1)+1472 \log (x+2)",1,"(-195280 - 1030560*x - 2286008*x^2 - 2759400*x^3 - 1955853*x^4 - 813888*x^5 - 184200*x^6 - 17496*x^7)/(12*(2 + 3*x + x^2)^4) - 1471*Log[1 + x] + 1472*Log[2 + x]","A",1
205,1,66,102,0.0663634,"\int \frac{(1+2 x)^2}{\left(3+5 x+2 x^2\right)^5} \, dx","IntegrateAlgebraic[(1 + 2*x)^2/(3 + 5*x + 2*x^2)^5,x]","\frac{238080 x^7+2083200 x^6+7757440 x^5+15934000 x^4+19495776 x^3+14209160 x^2+5712464 x+977397}{12 \left(2 x^2+5 x+3\right)^4}+2480 \log (x+1)-2480 \log (2 x+3)","\frac{620 (4 x+5)}{2 x^2+5 x+3}-\frac{155 (4 x+5)}{3 \left(2 x^2+5 x+3\right)^2}+\frac{62 x+73}{3 \left(2 x^2+5 x+3\right)^3}+\frac{(2 x+1) (6 x+7)}{4 \left(2 x^2+5 x+3\right)^4}+2480 \log (x+1)-2480 \log (2 x+3)",1,"(977397 + 5712464*x + 14209160*x^2 + 19495776*x^3 + 15934000*x^4 + 7757440*x^5 + 2083200*x^6 + 238080*x^7)/(12*(3 + 5*x + 2*x^2)^4) + 2480*Log[1 + x] - 2480*Log[3 + 2*x]","A",1
206,1,37,40,0.0135257,"\int \frac{\left(a-b x^2\right)^3}{x^7} \, dx","IntegrateAlgebraic[(a - b*x^2)^3/x^7,x]","b^3 (-\log (x))-\frac{a \left(2 a^2-9 a b x^2+18 b^2 x^4\right)}{12 x^6}","-\frac{a^3}{6 x^6}+\frac{3 a^2 b}{4 x^4}-\frac{3 a b^2}{2 x^2}-b^3 \log (x)",1,"-1/12*(a*(2*a^2 - 9*a*b*x^2 + 18*b^2*x^4))/x^6 - b^3*Log[x]","A",1
207,1,62,83,0.033816,"\int \frac{x^{13}}{\left(a^4+x^4\right)^5} \, dx","IntegrateAlgebraic[x^13/(a^4 + x^4)^5,x]","\frac{5 \tan ^{-1}\left(\frac{x^2}{a^2}\right)}{256 a^6}-\frac{x^2 \left(15 a^{12}+55 a^8 x^4+73 a^4 x^8-15 x^{12}\right)}{768 a^4 \left(a^4+x^4\right)^4}","-\frac{x^{10}}{16 \left(a^4+x^4\right)^4}-\frac{5 x^6}{96 \left(a^4+x^4\right)^3}+\frac{5 x^2}{256 a^4 \left(a^4+x^4\right)}-\frac{5 x^2}{128 \left(a^4+x^4\right)^2}+\frac{5 \tan ^{-1}\left(\frac{x^2}{a^2}\right)}{256 a^6}",1,"-1/768*(x^2*(15*a^12 + 55*a^8*x^4 + 73*a^4*x^8 - 15*x^12))/(a^4*(a^4 + x^4)^4) + (5*ArcTan[x^2/a^2])/(256*a^6)","A",1
208,1,49,49,0.0116186,"\int \left(2 \sqrt{x}-x\right)^2 x^{3/2} \left(1+x^2\right) \, dx","IntegrateAlgebraic[(2*Sqrt[x] - x)^2*x^(3/2)*(1 + x^2),x]","\frac{2 x^{13/2}}{13}+\frac{8 x^{11/2}}{11}+\frac{2 x^{9/2}}{9}+\frac{8 x^{7/2}}{7}-\frac{2 x^6}{3}-x^4","\frac{2 x^{13/2}}{13}+\frac{8 x^{11/2}}{11}+\frac{2 x^{9/2}}{9}+\frac{8 x^{7/2}}{7}-\frac{2 x^6}{3}-x^4",1,"(8*x^(7/2))/7 - x^4 + (2*x^(9/2))/9 + (8*x^(11/2))/11 - (2*x^6)/3 + (2*x^(13/2))/13","A",1
209,1,55,55,0.0145316,"\int \left(-3 x^{3/5}+x^{3/2}\right)^2 \left(-\frac{x^{2/3}}{3}+4 x^{3/2}\right) \, dx","IntegrateAlgebraic[(-3*x^(3/5) + x^(3/2))^2*(-1/3*x^(2/3) + 4*x^(3/2)),x]","\frac{8 x^{11/2}}{11}-\frac{x^{14/3}}{14}-\frac{120 x^{23/5}}{23}+\frac{60 x^{113/30}}{113}+\frac{360 x^{37/10}}{37}-\frac{45 x^{43/15}}{43}","\frac{8 x^{11/2}}{11}-\frac{x^{14/3}}{14}-\frac{120 x^{23/5}}{23}+\frac{60 x^{113/30}}{113}+\frac{360 x^{37/10}}{37}-\frac{45 x^{43/15}}{43}",1,"(-45*x^(43/15))/43 + (360*x^(37/10))/37 + (60*x^(113/30))/113 - (120*x^(23/5))/23 - x^(14/3)/14 + (8*x^(11/2))/11","A",1
210,1,22,22,0.0078465,"\int \frac{1}{1+\sqrt{1+x}} \, dx","IntegrateAlgebraic[(1 + Sqrt[1 + x])^(-1),x]","2 \sqrt{x+1}-2 \log \left(\sqrt{x+1}+1\right)","2 \sqrt{x+1}-2 \log \left(\sqrt{x+1}+1\right)",1,"2*Sqrt[1 + x] - 2*Log[1 + Sqrt[1 + x]]","A",1
211,1,15,15,0.0097719,"\int \frac{x}{1+\sqrt{1+x}} \, dx","IntegrateAlgebraic[x/(1 + Sqrt[1 + x]),x]","\frac{2}{3} (x+1)^{3/2}-x","\frac{2}{3} (x+1)^{3/2}-x",1,"-x + (2*(1 + x)^(3/2))/3","A",1
212,1,23,25,0.0108938,"\int \frac{1+\sqrt{1+x}}{-1+\sqrt{1+x}} \, dx","IntegrateAlgebraic[(1 + Sqrt[1 + x])/(-1 + Sqrt[1 + x]),x]","x+4 \sqrt{x+1}+4 \log \left(\sqrt{x+1}-1\right)","x+4 \sqrt{x+1}+4 \log \left(1-\sqrt{x+1}\right)",1,"x + 4*Sqrt[1 + x] + 4*Log[-1 + Sqrt[1 + x]]","A",1
213,1,31,33,0.0125263,"\int \frac{1}{-\sqrt{1+x}+(1+x)^{2/3}} \, dx","IntegrateAlgebraic[(-Sqrt[1 + x] + (1 + x)^(2/3))^(-1),x]","3 \sqrt[3]{x+1}+6 \sqrt[6]{x+1}+6 \log \left(\sqrt[6]{x+1}-1\right)","3 \sqrt[3]{x+1}+6 \sqrt[6]{x+1}+6 \log \left(1-\sqrt[6]{x+1}\right)",1,"6*(1 + x)^(1/6) + 3*(1 + x)^(1/3) + 6*Log[-1 + (1 + x)^(1/6)]","A",1
214,1,56,29,0.02843,"\int \frac{\sqrt[3]{1+\sqrt[4]{x}}}{\sqrt{x}} \, dx","IntegrateAlgebraic[(1 + x^(1/4))^(1/3)/Sqrt[x],x]","\frac{12}{7} \sqrt[3]{\sqrt[4]{x}+1} \sqrt{x}+\frac{3}{7} \sqrt[3]{\sqrt[4]{x}+1} \sqrt[4]{x}-\frac{9}{7} \sqrt[3]{\sqrt[4]{x}+1}","\frac{12}{7} \left(\sqrt[4]{x}+1\right)^{7/3}-3 \left(\sqrt[4]{x}+1\right)^{4/3}",1,"(-9*(1 + x^(1/4))^(1/3))/7 + (3*(1 + x^(1/4))^(1/3)*x^(1/4))/7 + (12*(1 + x^(1/4))^(1/3)*Sqrt[x])/7","A",1
215,1,37,52,0.0407494,"\int \frac{1}{x^3 (1+x)^{3/2}} \, dx","IntegrateAlgebraic[1/(x^3*(1 + x)^(3/2)),x]","\frac{15 x^2+5 x-2}{4 x^2 \sqrt{x+1}}-\frac{15}{4} \tanh ^{-1}\left(\sqrt{x+1}\right)","-\frac{1}{2 x^2 \sqrt{x+1}}+\frac{5}{4 x \sqrt{x+1}}+\frac{15}{4 \sqrt{x+1}}-\frac{15}{4} \tanh ^{-1}\left(\sqrt{x+1}\right)",1,"(-2 + 5*x + 15*x^2)/(4*x^2*Sqrt[1 + x]) - (15*ArcTanh[Sqrt[1 + x]])/4","A",1
216,1,66,118,0.0682426,"\int \frac{1}{(1-x)^{7/2} x^5} \, dx","IntegrateAlgebraic[1/((1 - x)^(7/2)*x^5),x]","\frac{\sqrt{1-x} \left(-45045 x^6+105105 x^5-69069 x^4+6435 x^3+1430 x^2+520 x+240\right)}{960 (x-1)^3 x^4}-\frac{3003}{64} \tanh ^{-1}\left(\sqrt{1-x}\right)","-\frac{1}{4 (1-x)^{5/2} x^4}-\frac{13}{24 (1-x)^{5/2} x^3}-\frac{143}{96 (1-x)^{5/2} x^2}+\frac{3003}{64 \sqrt{1-x}}-\frac{429}{64 (1-x)^{5/2} x}+\frac{1001}{64 (1-x)^{3/2}}+\frac{3003}{320 (1-x)^{5/2}}-\frac{3003}{64} \tanh ^{-1}\left(\sqrt{1-x}\right)",1,"(Sqrt[1 - x]*(240 + 520*x + 1430*x^2 + 6435*x^3 - 69069*x^4 + 105105*x^5 - 45045*x^6))/(960*(-1 + x)^3*x^4) - (3003*ArcTanh[Sqrt[1 - x]])/64","A",1
217,1,97,104,0.0670873,"\int \frac{1}{(-1+x)^{2/3} x^5} \, dx","IntegrateAlgebraic[1/((-1 + x)^(2/3)*x^5),x]","\frac{\sqrt[3]{x-1} \left(220 x^3+132 x^2+99 x+81\right)}{324 x^4}+\frac{110}{243} \log \left(\sqrt[3]{x-1}+1\right)-\frac{55}{243} \log \left((x-1)^{2/3}-\sqrt[3]{x-1}+1\right)-\frac{110 \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{x-1}}{\sqrt{3}}\right)}{81 \sqrt{3}}","\frac{\sqrt[3]{x-1}}{4 x^4}+\frac{11 \sqrt[3]{x-1}}{36 x^3}+\frac{11 \sqrt[3]{x-1}}{27 x^2}+\frac{55 \sqrt[3]{x-1}}{81 x}+\frac{55}{81} \log \left(\sqrt[3]{x-1}+1\right)-\frac{55 \log (x)}{243}-\frac{110 \tan ^{-1}\left(\frac{1-2 \sqrt[3]{x-1}}{\sqrt{3}}\right)}{81 \sqrt{3}}",1,"((-1 + x)^(1/3)*(81 + 99*x + 132*x^2 + 220*x^3))/(324*x^4) - (110*ArcTan[1/Sqrt[3] - (2*(-1 + x)^(1/3))/Sqrt[3]])/(81*Sqrt[3]) + (110*Log[1 + (-1 + x)^(1/3)])/243 - (55*Log[1 - (-1 + x)^(1/3) + (-1 + x)^(2/3)])/243","A",1
218,1,38,38,0.0236232,"\int \sqrt{\frac{1-x}{1+x}} \, dx","IntegrateAlgebraic[Sqrt[(1 - x)/(1 + x)],x]","\sqrt{\frac{1-x}{x+1}} (x+1)-2 \tan ^{-1}\left(\sqrt{\frac{1-x}{x+1}}\right)","\sqrt{\frac{1-x}{x+1}} (x+1)-2 \tan ^{-1}\left(\sqrt{\frac{1-x}{x+1}}\right)",1,"Sqrt[(1 - x)/(1 + x)]*(1 + x) - 2*ArcTan[Sqrt[(1 - x)/(1 + x)]]","A",1
219,1,80,92,0.0762465,"\int x \sqrt{\frac{-a+x}{b-x}} \, dx","IntegrateAlgebraic[x*Sqrt[(-a + x)/(b - x)],x]","\frac{1}{4} \left(-a^2-2 a b+3 b^2\right) \tan ^{-1}\left(\sqrt{\frac{x-a}{b-x}}\right)+\frac{1}{4} \sqrt{\frac{x-a}{b-x}} \left(a b-a x-3 b^2+b x+2 x^2\right)","\frac{1}{2} (b-x)^2 \sqrt{\frac{x-a}{b-x}}+\frac{1}{4} (a-5 b) (b-x) \sqrt{\frac{x-a}{b-x}}-\frac{1}{4} (a-b) (a+3 b) \tan ^{-1}\left(\sqrt{\frac{x-a}{b-x}}\right)",1,"(Sqrt[(-a + x)/(b - x)]*(a*b - 3*b^2 - a*x + b*x + 2*x^2))/4 + ((-a^2 - 2*a*b + 3*b^2)*ArcTan[Sqrt[(-a + x)/(b - x)]])/4","A",1
220,1,121,54,0.5190142,"\int \frac{\sqrt{-5+x} \sqrt{3+x}}{(-1+x) \left(-25+x^2\right)} \, dx","IntegrateAlgebraic[(Sqrt[-5 + x]*Sqrt[3 + x])/((-1 + x)*(-25 + x^2)),x]","\frac{1}{6} \tan ^{-1}\left(\frac{1}{4} \sqrt{x-5} \sqrt{x+3}\right)-\frac{\tanh ^{-1}\left(\frac{-\frac{11 x}{\sqrt{5}}+\frac{\sqrt{x-5} \left(3 \sqrt{x+3}+2\right)}{\sqrt{5}}+6 \sqrt{5} \sqrt{x+3}-7 \sqrt{5}}{\sqrt{x-5} \left(2 \sqrt{x+3}-6\right)-2 \sqrt{x+3}+6}\right)}{3 \sqrt{5}}","\frac{1}{6} \tan ^{-1}\left(\frac{1}{4} \sqrt{x-5} \sqrt{x+3}\right)+\frac{\tanh ^{-1}\left(\frac{\sqrt{5} \sqrt{x+3}}{\sqrt{x-5}}\right)}{3 \sqrt{5}}",1,"ArcTan[(Sqrt[-5 + x]*Sqrt[3 + x])/4]/6 - ArcTanh[(-7*Sqrt[5] - (11*x)/Sqrt[5] + 6*Sqrt[5]*Sqrt[3 + x] + (Sqrt[-5 + x]*(2 + 3*Sqrt[3 + x]))/Sqrt[5])/(6 - 2*Sqrt[3 + x] + Sqrt[-5 + x]*(-6 + 2*Sqrt[3 + x]))]/(3*Sqrt[5])","B",1
221,1,294,304,42.7964475,"\int \frac{x^2 \sqrt{1+x} \sqrt[4]{1-x^2}}{\sqrt{1-x} \left(\sqrt{1-x}-\sqrt{1+x}\right)} \, dx","IntegrateAlgebraic[(x^2*Sqrt[1 + x]*(1 - x^2)^(1/4))/(Sqrt[1 - x]*(Sqrt[1 - x] - Sqrt[1 + x])),x]","\frac{1}{48} \sqrt{x+1} \sqrt[4]{1-x^2} \left(-8 x^2-2 x+7\right)+\frac{1}{48} \sqrt{1-x} \sqrt[4]{1-x^2} \left(8 x^2+22 x+29\right)-\frac{\tan ^{-1}\left(\frac{-\frac{\sqrt{1-x^2}}{\sqrt{2}}+\frac{x}{\sqrt{2}}+\frac{1}{\sqrt{2}}}{\sqrt{x+1} \sqrt[4]{1-x^2}}\right)}{16 \sqrt{2}}-\frac{5 \tan ^{-1}\left(\frac{\frac{\sqrt{1-x^2}}{\sqrt{2}}+\frac{x}{\sqrt{2}}-\frac{1}{\sqrt{2}}}{\sqrt{1-x} \sqrt[4]{1-x^2}}\right)}{16 \sqrt{2}}+\frac{5 \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{1-x} \sqrt[4]{1-x^2}}{-\sqrt{1-x^2}+x-1}\right)}{16 \sqrt{2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{x+1} \sqrt[4]{1-x^2}}{\sqrt{1-x^2}+x+1}\right)}{16 \sqrt{2}}","\frac{1}{6} \sqrt{x+1} \left(1-x^2\right)^{5/4}+\frac{x \left(1-x^2\right)^{5/4}}{6 \sqrt{1-x}}+\frac{7 \left(1-x^2\right)^{5/4}}{24 \sqrt{1-x}}+\frac{1}{24} (x+1)^{3/4} (1-x)^{5/4}+\frac{5}{16} \sqrt[4]{x+1} (1-x)^{3/4}-\frac{1}{16} (x+1)^{3/4} \sqrt[4]{1-x}+\frac{\log \left(\frac{\sqrt{1-x}}{\sqrt{x+1}}-\frac{\sqrt{2} \sqrt[4]{1-x}}{\sqrt[4]{x+1}}+1\right)}{8 \sqrt{2}}-\frac{\log \left(\frac{\sqrt{1-x}}{\sqrt{x+1}}+\frac{\sqrt{2} \sqrt[4]{1-x}}{\sqrt[4]{x+1}}+1\right)}{8 \sqrt{2}}-\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-x}}{\sqrt[4]{x+1}}\right)}{8 \sqrt{2}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-x}}{\sqrt[4]{x+1}}+1\right)}{8 \sqrt{2}}",1,"(Sqrt[1 + x]*(7 - 2*x - 8*x^2)*(1 - x^2)^(1/4))/48 + (Sqrt[1 - x]*(1 - x^2)^(1/4)*(29 + 22*x + 8*x^2))/48 - ArcTan[(1/Sqrt[2] + x/Sqrt[2] - Sqrt[1 - x^2]/Sqrt[2])/(Sqrt[1 + x]*(1 - x^2)^(1/4))]/(16*Sqrt[2]) - (5*ArcTan[(-(1/Sqrt[2]) + x/Sqrt[2] + Sqrt[1 - x^2]/Sqrt[2])/(Sqrt[1 - x]*(1 - x^2)^(1/4))])/(16*Sqrt[2]) + (5*ArcTanh[(Sqrt[2]*Sqrt[1 - x]*(1 - x^2)^(1/4))/(-1 + x - Sqrt[1 - x^2])])/(16*Sqrt[2]) + ArcTanh[(Sqrt[2]*Sqrt[1 + x]*(1 - x^2)^(1/4))/(1 + x + Sqrt[1 - x^2])]/(16*Sqrt[2])","A",1
222,0,0,292,117.7047782,"\int \frac{\sqrt{1-x} x (1+x)^{2/3}}{-(1-x)^{5/6} \sqrt[3]{1+x}+(1-x)^{2/3} \sqrt{1+x}} \, dx","IntegrateAlgebraic[(Sqrt[1 - x]*x*(1 + x)^(2/3))/(-((1 - x)^(5/6)*(1 + x)^(1/3)) + (1 - x)^(2/3)*Sqrt[1 + x]),x]","\int \frac{\sqrt{1-x} x (1+x)^{2/3}}{-(1-x)^{5/6} \sqrt[3]{1+x}+(1-x)^{2/3} \sqrt{1+x}} \, dx","-\frac{1}{12} (1-x)^{2/3} \sqrt[3]{x+1} (1-3 x)-\frac{1}{4} (1-x) (x+3)+\frac{1}{12} \sqrt[3]{1-x} (x+1)^{2/3} (3 x+1)+\frac{1}{12} \sqrt[6]{1-x} (x+1)^{5/6} (3 x+2)-\frac{1}{12} (1-x)^{5/6} \sqrt[6]{x+1} (3 x+10)+\frac{1}{4} \sqrt{1-x} x \sqrt{x+1}+\frac{1}{6} \tan ^{-1}\left(\frac{\sqrt[6]{x+1}}{\sqrt[6]{1-x}}\right)-\frac{4 \tan ^{-1}\left(\frac{\sqrt[3]{1-x}-2 \sqrt[3]{x+1}}{\sqrt{3} \sqrt[3]{1-x}}\right)}{3 \sqrt{3}}-\frac{5}{6} \tan ^{-1}\left(\frac{\sqrt[3]{1-x}-\sqrt[3]{x+1}}{\sqrt[6]{1-x} \sqrt[6]{x+1}}\right)+\frac{\tanh ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{1-x} \sqrt[6]{x+1}}{\sqrt[3]{1-x}+\sqrt[3]{x+1}}\right)}{6 \sqrt{3}}",1,"Could not integrate","F",-1
223,1,46,25,0.4196313,"\int \frac{1}{\sqrt[3]{(-1+x)^4 (1+x)^2}} \, dx","IntegrateAlgebraic[((-1 + x)^4*(1 + x)^2)^(-1/3),x]","-\frac{3 \left(x^6-2 x^5-x^4+4 x^3-x^2-2 x+1\right)^{2/3}}{2 (x-1)^3 (x+1)}","-\frac{3 (x-1) (x+1)}{2 \sqrt[3]{(x-1)^4 (x+1)^2}}",1,"(-3*(1 - 2*x - x^2 + 4*x^3 - x^4 - 2*x^5 + x^6)^(2/3))/(2*(-1 + x)^3*(1 + x))","A",1
224,1,25,25,26.0334832,"\int \frac{1}{\sqrt[4]{(-1+x)^3 (2+x)^5}} \, dx","IntegrateAlgebraic[((-1 + x)^3*(2 + x)^5)^(-1/4),x]","\frac{4 (x-1) (x+2)}{3 \sqrt[4]{(x-1)^3 (x+2)^5}}","\frac{4 (x-1) (x+2)}{3 \sqrt[4]{(x-1)^3 (x+2)^5}}",1,"(4*(-1 + x)*(2 + x))/(3*((-1 + x)^3*(2 + x)^5)^(1/4))","A",1
225,1,56,53,2.5206995,"\int \frac{1}{\sqrt[3]{(-1+x)^7 (1+x)^2}} \, dx","IntegrateAlgebraic[((-1 + x)^7*(1 + x)^2)^(-1/3),x]","\frac{3 (3 x-5) \left(x^9-5 x^8+8 x^7-14 x^5+14 x^4-8 x^2+5 x-1\right)^{2/3}}{16 (x-1)^6 (x+1)}","\frac{9 (x-1)^2 (x+1)}{16 \sqrt[3]{(x-1)^7 (x+1)^2}}-\frac{3 (x-1) (x+1)}{8 \sqrt[3]{(x-1)^7 (x+1)^2}}",1,"(3*(-5 + 3*x)*(-1 + 5*x - 8*x^2 + 14*x^4 - 14*x^5 + 8*x^7 - 5*x^8 + x^9)^(2/3))/(16*(-1 + x)^6*(1 + x))","A",1
226,1,132,67,0.2642429,"\int \frac{1}{\sqrt[3]{(-1+x)^2 (1+x)}} \, dx","IntegrateAlgebraic[((-1 + x)^2*(1 + x))^(-1/3),x]","-\log \left(\sqrt[3]{x^3-x^2-x+1}-x+1\right)+\frac{1}{2} \log \left(x^2+\left(x^3-x^2-x+1\right)^{2/3}+(x-1) \sqrt[3]{x^3-x^2-x+1}-2 x+1\right)-\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x^3-x^2-x+1}}{\sqrt[3]{x^3-x^2-x+1}+2 x-2}\right)","-\frac{1}{2} \log (x+1)-\frac{3}{2} \log \left(1-\frac{x-1}{\sqrt[3]{(x-1)^2 (x+1)}}\right)+\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 (x-1)}{\sqrt[3]{(x-1)^2 (x+1)}}+1}{\sqrt{3}}\right)",1,"-(Sqrt[3]*ArcTan[(Sqrt[3]*(1 - x - x^2 + x^3)^(1/3))/(-2 + 2*x + (1 - x - x^2 + x^3)^(1/3))]) - Log[1 - x + (1 - x - x^2 + x^3)^(1/3)] + Log[1 - 2*x + x^2 + (-1 + x)*(1 - x - x^2 + x^3)^(1/3) + (1 - x - x^2 + x^3)^(2/3)]/2","A",1
227,1,97,122,0.3695244,"\int \frac{\frac{1}{x}+x}{\sqrt{(-2+x) (1+x)^3}} \, dx","IntegrateAlgebraic[(x^(-1) + x)/Sqrt[(-2 + x)*(1 + x)^3],x]","-\frac{4 \sqrt{x^4+x^3-3 x^2-5 x-2}}{3 (x+1)^2}+\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{x^4+x^3-3 x^2-5 x-2}}{\sqrt{2} (x+1)^2}\right)+2 \tanh ^{-1}\left(\frac{\sqrt{x^4+x^3-3 x^2-5 x-2}}{(x+1)^2}\right)","-\frac{4 (x-2) (x+1)}{3 \sqrt{(x-2) (x+1)^3}}-\frac{\sqrt{2} \sqrt{x-2} (x+1)^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{x+1}}{\sqrt{x-2}}\right)}{\sqrt{(x-2) (x+1)^3}}+\frac{2 \sqrt{x-2} (x+1)^{3/2} \sinh ^{-1}\left(\frac{\sqrt{x-2}}{\sqrt{3}}\right)}{\sqrt{(x-2) (x+1)^3}}",1,"(-4*Sqrt[-2 - 5*x - 3*x^2 + x^3 + x^4])/(3*(1 + x)^2) + Sqrt[2]*ArcTan[Sqrt[-2 - 5*x - 3*x^2 + x^3 + x^4]/(Sqrt[2]*(1 + x)^2)] + 2*ArcTanh[Sqrt[-2 - 5*x - 3*x^2 + x^3 + x^4]/(1 + x)^2]","A",1
228,1,247,150,8.0436889,"\int \frac{\sqrt[3]{(-1+x)^2 (1+x)}}{x^2} \, dx","IntegrateAlgebraic[((-1 + x)^2*(1 + x))^(1/3)/x^2,x]","\frac{\sqrt[3]{x-1} (x+1)^{2/3} \sqrt[3]{(x-1)^2 (x+1)} \left(-\frac{(x-1)^{2/3} \sqrt[3]{x+1}}{x}-\log \left(\sqrt[3]{x-1}-\sqrt[3]{x+1}\right)-\frac{1}{3} \log \left(\sqrt[3]{x-1}+\sqrt[3]{x+1}\right)+\frac{1}{6} \log \left((x-1)^{2/3}-\sqrt[3]{x+1} \sqrt[3]{x-1}+(x+1)^{2/3}\right)+\frac{1}{2} \log \left((x-1)^{2/3}+\sqrt[3]{x+1} \sqrt[3]{x-1}+(x+1)^{2/3}\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x+1}}{2 \sqrt[3]{x-1}-\sqrt[3]{x+1}}\right)}{\sqrt{3}}+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x+1}}{2 \sqrt[3]{x-1}+\sqrt[3]{x+1}}\right)\right)}{x^2-1}","-\frac{\sqrt[3]{(x-1)^2 (x+1)}}{x}+\frac{\log (x)}{6}-\frac{2}{3} \log (x+1)-\frac{3}{2} \log \left(1-\frac{x-1}{\sqrt[3]{(x-1)^2 (x+1)}}\right)-\frac{1}{2} \log \left(\frac{x-1}{\sqrt[3]{(x-1)^2 (x+1)}}+1\right)-\frac{\tan ^{-1}\left(\frac{1-\frac{2 (x-1)}{\sqrt[3]{(x-1)^2 (x+1)}}}{\sqrt{3}}\right)}{\sqrt{3}}-\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 (x-1)}{\sqrt[3]{(x-1)^2 (x+1)}}+1}{\sqrt{3}}\right)",1,"((-1 + x)^(1/3)*(1 + x)^(2/3)*((-1 + x)^2*(1 + x))^(1/3)*(-(((-1 + x)^(2/3)*(1 + x)^(1/3))/x) - ArcTan[(Sqrt[3]*(1 + x)^(1/3))/(2*(-1 + x)^(1/3) - (1 + x)^(1/3))]/Sqrt[3] + Sqrt[3]*ArcTan[(Sqrt[3]*(1 + x)^(1/3))/(2*(-1 + x)^(1/3) + (1 + x)^(1/3))] - Log[(-1 + x)^(1/3) - (1 + x)^(1/3)] - Log[(-1 + x)^(1/3) + (1 + x)^(1/3)]/3 + Log[(-1 + x)^(2/3) - (-1 + x)^(1/3)*(1 + x)^(1/3) + (1 + x)^(2/3)]/6 + Log[(-1 + x)^(2/3) + (-1 + x)^(1/3)*(1 + x)^(1/3) + (1 + x)^(2/3)]/2))/(-1 + x^2)","A",1
229,1,39,43,0.266309,"\int \frac{1}{\left(-3-2 x+x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[(-3 - 2*x + x^2)^(-5/2),x]","\frac{\sqrt{x^2-2 x-3} \left(x^3-3 x^2-3 x+5\right)}{24 (x-3)^2 (x+1)^2}","\frac{1-x}{12 \left(x^2-2 x-3\right)^{3/2}}-\frac{1-x}{24 \sqrt{x^2-2 x-3}}",1,"(Sqrt[-3 - 2*x + x^2]*(5 - 3*x - 3*x^2 + x^3))/(24*(-3 + x)^2*(1 + x)^2)","A",1
230,1,26,42,0.0278684,"\int \frac{1}{\sqrt{9+3 x-5 x^2+x^3}} \, dx","IntegrateAlgebraic[1/Sqrt[9 + 3*x - 5*x^2 + x^3],x]","-\tanh ^{-1}\left(\frac{2 x-6}{\sqrt{x^3-5 x^2+3 x+9}}\right)","\frac{(3-x) \sqrt{x+1} \tanh ^{-1}\left(\frac{\sqrt{x+1}}{2}\right)}{\sqrt{x^3-5 x^2+3 x+9}}",1,"-ArcTanh[(-6 + 2*x)/Sqrt[9 + 3*x - 5*x^2 + x^3]]","A",1
231,1,67,139,3.6212692,"\int \frac{1}{\left(9+3 x-5 x^2+x^3\right)^{3/2}} \, dx","IntegrateAlgebraic[(9 + 3*x - 5*x^2 + x^3)^(-3/2),x]","\frac{(x-3) \sqrt{x+1} \left(\frac{15 x^2-70 x+43}{256 (x-3)^2 \sqrt{x+1}}-\frac{15}{512} \tanh ^{-1}\left(\frac{\sqrt{x+1}}{2}\right)\right)}{\sqrt{(x-3)^2 (x+1)}}","-\frac{15 (x+1) (3-x)^3}{256 \left(x^3-5 x^2+3 x+9\right)^{3/2}}+\frac{5 (x+1) (3-x)^2}{64 \left(x^3-5 x^2+3 x+9\right)^{3/2}}+\frac{(x+1) (3-x)}{8 \left(x^3-5 x^2+3 x+9\right)^{3/2}}+\frac{15 (x+1)^{3/2} (3-x)^3 \tanh ^{-1}\left(\frac{\sqrt{x+1}}{2}\right)}{512 \left(x^3-5 x^2+3 x+9\right)^{3/2}}",1,"((-3 + x)*Sqrt[1 + x]*((43 - 70*x + 15*x^2)/(256*(-3 + x)^2*Sqrt[1 + x]) - (15*ArcTanh[Sqrt[1 + x]/2])/512))/Sqrt[(-3 + x)^2*(1 + x)]","A",1
232,1,132,75,0.258267,"\int \frac{1}{\sqrt[3]{9+3 x-5 x^2+x^3}} \, dx","IntegrateAlgebraic[(9 + 3*x - 5*x^2 + x^3)^(-1/3),x]","-\log \left(\sqrt[3]{x^3-5 x^2+3 x+9}-x+3\right)+\frac{1}{2} \log \left(x^2+\left(x^3-5 x^2+3 x+9\right)^{2/3}+(x-3) \sqrt[3]{x^3-5 x^2+3 x+9}-6 x+9\right)-\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x^3-5 x^2+3 x+9}}{\sqrt[3]{x^3-5 x^2+3 x+9}+2 x-6}\right)","-\frac{3}{2} \log \left(1-\frac{x-3}{\sqrt[3]{x^3-5 x^2+3 x+9}}\right)+\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 (x-3)}{\sqrt[3]{x^3-5 x^2+3 x+9}}+1}{\sqrt{3}}\right)-\frac{1}{2} \log (x+1)",1,"-(Sqrt[3]*ArcTan[(Sqrt[3]*(9 + 3*x - 5*x^2 + x^3)^(1/3))/(-6 + 2*x + (9 + 3*x - 5*x^2 + x^3)^(1/3))]) - Log[3 - x + (9 + 3*x - 5*x^2 + x^3)^(1/3)] + Log[9 - 6*x + x^2 + (-3 + x)*(9 + 3*x - 5*x^2 + x^3)^(1/3) + (9 + 3*x - 5*x^2 + x^3)^(2/3)]/2","A",1
233,1,26,29,3.2232258,"\int \frac{1}{\left(9+3 x-5 x^2+x^3\right)^{2/3}} \, dx","IntegrateAlgebraic[(9 + 3*x - 5*x^2 + x^3)^(-2/3),x]","-\frac{3 \sqrt[3]{x^3-5 x^2+3 x+9}}{4 (x-3)}","\frac{3 (3-x) (x+1)}{4 \left(x^3-5 x^2+3 x+9\right)^{2/3}}",1,"(-3*(9 + 3*x - 5*x^2 + x^3)^(1/3))/(4*(-3 + x))","A",1
234,1,37,92,4.8768535,"\int \frac{1}{\left(9+3 x-5 x^2+x^3\right)^{4/3}} \, dx","IntegrateAlgebraic[(9 + 3*x - 5*x^2 + x^3)^(-4/3),x]","\frac{3 (x-3) (x+1) \left(9 (x+1)^2-60 (x+1)+80\right)}{320 \left((x-3)^2 (x+1)\right)^{4/3}}","-\frac{27 (x+1) (3-x)^3}{320 \left(x^3-5 x^2+3 x+9\right)^{4/3}}+\frac{9 (x+1) (3-x)^2}{80 \left(x^3-5 x^2+3 x+9\right)^{4/3}}+\frac{3 (x+1) (3-x)}{20 \left(x^3-5 x^2+3 x+9\right)^{4/3}}",1,"(3*(-3 + x)*(1 + x)*(80 - 60*(1 + x) + 9*(1 + x)^2))/(320*((-3 + x)^2*(1 + x))^(4/3))","A",1
235,1,32,19,0.1042727,"\int \frac{1}{\sqrt{4+3 x-2 x^2}} \, dx","IntegrateAlgebraic[1/Sqrt[4 + 3*x - 2*x^2],x]","\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{-2 x^2+3 x+4}-2}\right)","-\frac{\sin ^{-1}\left(\frac{3-4 x}{\sqrt{41}}\right)}{\sqrt{2}}",1,"Sqrt[2]*ArcTan[(Sqrt[2]*x)/(-2 + Sqrt[4 + 3*x - 2*x^2])]","A",1
236,1,23,8,0.0907301,"\int \frac{1}{\sqrt{-3+4 x-x^2}} \, dx","IntegrateAlgebraic[1/Sqrt[-3 + 4*x - x^2],x]","-2 \tan ^{-1}\left(\frac{\sqrt{-x^2+4 x-3}}{x-1}\right)","-\sin ^{-1}(2-x)",1,"-2*ArcTan[Sqrt[-3 + 4*x - x^2]/(-1 + x)]","B",1
237,1,33,12,0.0977894,"\int \frac{1}{\sqrt{-2-5 x-3 x^2}} \, dx","IntegrateAlgebraic[1/Sqrt[-2 - 5*x - 3*x^2],x]","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{-3 x^2-5 x-2}}{\sqrt{3} (x+1)}\right)}{\sqrt{3}}","\frac{\sin ^{-1}(6 x+5)}{\sqrt{3}}",1,"(-2*ArcTan[Sqrt[-2 - 5*x - 3*x^2]/(Sqrt[3]*(1 + x))])/Sqrt[3]","B",1
238,1,55,31,0.088305,"\int \frac{1}{\sqrt{1-x^2} \left(4+x^2\right)} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - x^2]*(4 + x^2)),x]","-\frac{i \tanh ^{-1}\left(\frac{x^2}{2 \sqrt{5}}+\frac{i \sqrt{1-x^2} x}{2 \sqrt{5}}+\frac{2}{\sqrt{5}}\right)}{2 \sqrt{5}}","\frac{\tan ^{-1}\left(\frac{\sqrt{5} x}{2 \sqrt{1-x^2}}\right)}{2 \sqrt{5}}",1,"((-1/2*I)*ArcTanh[2/Sqrt[5] + x^2/(2*Sqrt[5]) + ((I/2)*x*Sqrt[1 - x^2])/Sqrt[5]])/Sqrt[5]","C",1
239,1,48,31,0.0805141,"\int \frac{1}{\left(4+x^2\right) \sqrt{1+4 x^2}} \, dx","IntegrateAlgebraic[1/((4 + x^2)*Sqrt[1 + 4*x^2]),x]","\frac{\tanh ^{-1}\left(\frac{x^2}{\sqrt{15}}-\frac{\sqrt{4 x^2+1} x}{2 \sqrt{15}}+\frac{4}{\sqrt{15}}\right)}{2 \sqrt{15}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{15} x}{2 \sqrt{4 x^2+1}}\right)}{2 \sqrt{15}}",1,"ArcTanh[4/Sqrt[15] + x^2/Sqrt[15] - (x*Sqrt[1 + 4*x^2])/(2*Sqrt[15])]/(2*Sqrt[15])","A",1
240,1,24,24,0.0410619,"\int \frac{x}{\left(3-x^2\right) \sqrt{5-x^2}} \, dx","IntegrateAlgebraic[x/((3 - x^2)*Sqrt[5 - x^2]),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{5-x^2}}{\sqrt{2}}\right)}{\sqrt{2}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{5-x^2}}{\sqrt{2}}\right)}{\sqrt{2}}",1,"ArcTanh[Sqrt[5 - x^2]/Sqrt[2]]/Sqrt[2]","A",1
241,1,25,25,0.0251032,"\int \frac{x}{\sqrt{3-x^2} \left(5-x^2\right)} \, dx","IntegrateAlgebraic[x/(Sqrt[3 - x^2]*(5 - x^2)),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{3-x^2}}{\sqrt{2}}\right)}{\sqrt{2}}","-\frac{\tan ^{-1}\left(\frac{\sqrt{3-x^2}}{\sqrt{2}}\right)}{\sqrt{2}}",1,"-(ArcTan[Sqrt[3 - x^2]/Sqrt[2]]/Sqrt[2])","A",1
242,1,65,43,0.0939318,"\int \frac{1}{\sqrt{2+x^2} \left(-1+x^4\right)} \, dx","IntegrateAlgebraic[1/(Sqrt[2 + x^2]*(-1 + x^4)),x]","\frac{1}{2} \tan ^{-1}\left(x^2-\sqrt{x^2+2} x+1\right)-\frac{\tanh ^{-1}\left(-\frac{x^2}{\sqrt{3}}+\frac{\sqrt{x^2+2} x}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3}}","-\frac{1}{2} \tan ^{-1}\left(\frac{x}{\sqrt{x^2+2}}\right)-\frac{\tanh ^{-1}\left(\frac{\sqrt{3} x}{\sqrt{x^2+2}}\right)}{2 \sqrt{3}}",1,"ArcTan[1 + x^2 - x*Sqrt[2 + x^2]]/2 - ArcTanh[1/Sqrt[3] - x^2/Sqrt[3] + (x*Sqrt[2 + x^2])/Sqrt[3]]/(2*Sqrt[3])","A",1
243,1,80,62,0.2013494,"\int \frac{x}{\left(-1+x^2\right) \sqrt{4+2 x+x^2}} \, dx","IntegrateAlgebraic[x/((-1 + x^2)*Sqrt[4 + 2*x + x^2]),x]","\frac{\tanh ^{-1}\left(-\frac{\sqrt{x^2+2 x+4}}{\sqrt{3}}+\frac{x}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{x^2+2 x+4}}{\sqrt{7}}-\frac{x}{\sqrt{7}}+\frac{1}{\sqrt{7}}\right)}{\sqrt{7}}","-\frac{\tanh ^{-1}\left(\frac{2 x+5}{\sqrt{7} \sqrt{x^2+2 x+4}}\right)}{2 \sqrt{7}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{x^2+2 x+4}}{\sqrt{3}}\right)}{2 \sqrt{3}}",1,"ArcTanh[1/Sqrt[3] + x/Sqrt[3] - Sqrt[4 + 2*x + x^2]/Sqrt[3]]/Sqrt[3] - ArcTanh[1/Sqrt[7] - x/Sqrt[7] + Sqrt[4 + 2*x + x^2]/Sqrt[7]]/Sqrt[7]","A",1
244,1,119,82,0.3625207,"\int \frac{1}{\sqrt{5+2 x+x^2} \left(-8+x^3\right)} \, dx","IntegrateAlgebraic[1/(Sqrt[5 + 2*x + x^2]*(-8 + x^3)),x]","\frac{\tan ^{-1}\left(\frac{x^2}{\sqrt{3}}-\frac{(x+1) \sqrt{x^2+2 x+5}}{\sqrt{3}}+\frac{2 x}{\sqrt{3}}+\frac{4}{\sqrt{3}}\right)}{4 \sqrt{3}}+\frac{1}{12} \tanh ^{-1}\left(\sqrt{x^2+2 x+5}\right)-\frac{\tanh ^{-1}\left(\frac{\sqrt{x^2+2 x+5}}{\sqrt{13}}-\frac{x}{\sqrt{13}}+\frac{2}{\sqrt{13}}\right)}{6 \sqrt{13}}","-\frac{\tan ^{-1}\left(\frac{x+1}{\sqrt{3} \sqrt{x^2+2 x+5}}\right)}{4 \sqrt{3}}-\frac{\tanh ^{-1}\left(\frac{3 x+7}{\sqrt{13} \sqrt{x^2+2 x+5}}\right)}{12 \sqrt{13}}+\frac{1}{12} \tanh ^{-1}\left(\sqrt{x^2+2 x+5}\right)",1,"ArcTan[4/Sqrt[3] + (2*x)/Sqrt[3] + x^2/Sqrt[3] - ((1 + x)*Sqrt[5 + 2*x + x^2])/Sqrt[3]]/(4*Sqrt[3]) + ArcTanh[Sqrt[5 + 2*x + x^2]]/12 - ArcTanh[2/Sqrt[13] - x/Sqrt[13] + Sqrt[5 + 2*x + x^2]/Sqrt[13]]/(6*Sqrt[13])","A",1
245,1,102,63,0.2378599,"\int \frac{x}{\left(4+x+x^2\right) \sqrt{5+4 x+4 x^2}} \, dx","IntegrateAlgebraic[x/((4 + x + x^2)*Sqrt[5 + 4*x + 4*x^2]),x]","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^4-4 \text{$\#$1}^3+58 \text{$\#$1}^2-108 \text{$\#$1}+69\&,\frac{\text{$\#$1}^2 \log \left(-\text{$\#$1}+\sqrt{4 x^2+4 x+5}-2 x\right)-5 \log \left(-\text{$\#$1}+\sqrt{4 x^2+4 x+5}-2 x\right)}{\text{$\#$1}^3-3 \text{$\#$1}^2+29 \text{$\#$1}-27}\&\right]","\frac{\tan ^{-1}\left(\frac{\sqrt{4 x^2+4 x+5}}{\sqrt{11}}\right)}{\sqrt{11}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{\frac{11}{15}} (2 x+1)}{\sqrt{4 x^2+4 x+5}}\right)}{\sqrt{165}}",1,"RootSum[69 - 108*#1 + 58*#1^2 - 4*#1^3 + #1^4 & , (-5*Log[-2*x + Sqrt[5 + 4*x + 4*x^2] - #1] + Log[-2*x + Sqrt[5 + 4*x + 4*x^2] - #1]*#1^2)/(-27 + 29*#1 - 3*#1^2 + #1^3) & ]/2","C",1
246,1,103,56,0.2192477,"\int \frac{3+x}{\left(1+x^2\right) \sqrt{1+x+x^2}} \, dx","IntegrateAlgebraic[(3 + x)/((1 + x^2)*Sqrt[1 + x + x^2]),x]","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^4+2 \text{$\#$1}^2-4 \text{$\#$1}+2\&,\frac{\text{$\#$1}^2 \log \left(-\text{$\#$1}+\sqrt{x^2+x+1}-x\right)-6 \text{$\#$1} \log \left(-\text{$\#$1}+\sqrt{x^2+x+1}-x\right)+2 \log \left(-\text{$\#$1}+\sqrt{x^2+x+1}-x\right)}{\text{$\#$1}^3+\text{$\#$1}-1}\&\right]","\sqrt{2} \tanh ^{-1}\left(\frac{x+1}{\sqrt{2} \sqrt{x^2+x+1}}\right)-2 \sqrt{2} \tan ^{-1}\left(\frac{1-x}{\sqrt{2} \sqrt{x^2+x+1}}\right)",1,"RootSum[2 - 4*#1 + 2*#1^2 + #1^4 & , (2*Log[-x + Sqrt[1 + x + x^2] - #1] - 6*Log[-x + Sqrt[1 + x + x^2] - #1]*#1 + Log[-x + Sqrt[1 + x + x^2] - #1]*#1^2)/(-1 + #1 + #1^3) & ]/2","C",1
247,1,123,70,0.3046384,"\int \frac{1+2 x}{\sqrt{-1+6 x+x^2} \left(4+4 x+3 x^2\right)} \, dx","IntegrateAlgebraic[(1 + 2*x)/(Sqrt[-1 + 6*x + x^2]*(4 + 4*x + 3*x^2)),x]","\text{RootSum}\left[3 \text{$\#$1}^4-8 \text{$\#$1}^3+46 \text{$\#$1}^2-104 \text{$\#$1}+171\&,\frac{\text{$\#$1}^2 \log \left(-\text{$\#$1}+\sqrt{x^2+6 x-1}-x\right)-\text{$\#$1} \log \left(-\text{$\#$1}+\sqrt{x^2+6 x-1}-x\right)+4 \log \left(-\text{$\#$1}+\sqrt{x^2+6 x-1}-x\right)}{3 \text{$\#$1}^3-6 \text{$\#$1}^2+23 \text{$\#$1}-26}\&\right]","-\frac{5 \tan ^{-1}\left(\frac{\sqrt{\frac{7}{2}} (2-x)}{2 \sqrt{x^2+6 x-1}}\right)}{6 \sqrt{14}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{7} (x+1)}{\sqrt{x^2+6 x-1}}\right)}{3 \sqrt{7}}",1,"RootSum[171 - 104*#1 + 46*#1^2 - 8*#1^3 + 3*#1^4 & , (4*Log[-x + Sqrt[-1 + 6*x + x^2] - #1] - Log[-x + Sqrt[-1 + 6*x + x^2] - #1]*#1 + Log[-x + Sqrt[-1 + 6*x + x^2] - #1]*#1^2)/(-26 + 23*#1 - 6*#1^2 + 3*#1^3) & ]","C",1
248,1,143,80,1.1340767,"\int \frac{B+A x}{\left(17-18 x+5 x^2\right) \sqrt{13-22 x+10 x^2}} \, dx","IntegrateAlgebraic[(B + A*x)/((17 - 18*x + 5*x^2)*Sqrt[13 - 22*x + 10*x^2]),x]","\frac{1}{70} \left((1+4 i) \sqrt{35} A+(1+2 i) \sqrt{35} B\right) \tanh ^{-1}\left(\frac{(2-i) \sqrt{10 x^2-22 x+13}+(-2+i) \sqrt{10} x+(4-i) \sqrt{10}}{\sqrt{35}}\right)-\frac{1}{70} i \left((4+i) \sqrt{35} A+(2+i) \sqrt{35} B\right) \tanh ^{-1}\left(\frac{(2+i) \sqrt{10 x^2-22 x+13}+(-2-i) \sqrt{10} x+(4+i) \sqrt{10}}{\sqrt{35}}\right)","-\frac{(2 A+B) \tan ^{-1}\left(\frac{\sqrt{35} (2-x)}{\sqrt{10 x^2-22 x+13}}\right)}{\sqrt{35}}-\frac{(A+B) \tanh ^{-1}\left(\frac{\sqrt{35} (1-x)}{2 \sqrt{10 x^2-22 x+13}}\right)}{2 \sqrt{35}}",1,"(((1 + 4*I)*Sqrt[35]*A + (1 + 2*I)*Sqrt[35]*B)*ArcTanh[((4 - I)*Sqrt[10] - (2 - I)*Sqrt[10]*x + (2 - I)*Sqrt[13 - 22*x + 10*x^2])/Sqrt[35]])/70 - (I/70)*((4 + I)*Sqrt[35]*A + (2 + I)*Sqrt[35]*B)*ArcTanh[((4 + I)*Sqrt[10] - (2 + I)*Sqrt[10]*x + (2 + I)*Sqrt[13 - 22*x + 10*x^2])/Sqrt[35]]","C",1
249,1,91,38,0.5019438,"\int \frac{-2+x}{\left(17-18 x+5 x^2\right) \sqrt{13-22 x+10 x^2}} \, dx","IntegrateAlgebraic[(-2 + x)/((17 - 18*x + 5*x^2)*Sqrt[13 - 22*x + 10*x^2]),x]","-\frac{\tanh ^{-1}\left(\frac{-50 x^2+\left(5 \sqrt{10} x-9 \sqrt{10}\right) \sqrt{10 x^2-22 x+13}+145 x-135}{-2 \sqrt{35} \sqrt{10 x^2-22 x+13}+10 \sqrt{14} x-20 \sqrt{14}}\right)}{2 \sqrt{35}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{35} (1-x)}{2 \sqrt{10 x^2-22 x+13}}\right)}{2 \sqrt{35}}",1,"-1/2*ArcTanh[(-135 + 145*x - 50*x^2 + (-9*Sqrt[10] + 5*Sqrt[10]*x)*Sqrt[13 - 22*x + 10*x^2])/(-20*Sqrt[14] + 10*Sqrt[14]*x - 2*Sqrt[35]*Sqrt[13 - 22*x + 10*x^2])]/Sqrt[35]","B",1
250,1,54,65,0.0492748,"\int x^4 \sqrt{5-x^2} \, dx","IntegrateAlgebraic[x^4*Sqrt[5 - x^2],x]","\frac{1}{48} \sqrt{5-x^2} \left(8 x^5-10 x^3-75 x\right)+\frac{125}{16} i \log \left(\sqrt{5-x^2}-i x\right)","-\frac{25}{16} \sqrt{5-x^2} x+\frac{1}{6} \sqrt{5-x^2} x^5-\frac{5}{24} \sqrt{5-x^2} x^3+\frac{125}{16} \sin ^{-1}\left(\frac{x}{\sqrt{5}}\right)",1,"(Sqrt[5 - x^2]*(-75*x - 10*x^3 + 8*x^5))/48 + ((125*I)/16)*Log[(-I)*x + Sqrt[5 - x^2]]","C",1
251,1,28,49,0.0334841,"\int \frac{1}{x^6 \sqrt{2+x^2}} \, dx","IntegrateAlgebraic[1/(x^6*Sqrt[2 + x^2]),x]","\frac{\sqrt{x^2+2} \left(-2 x^4+2 x^2-3\right)}{30 x^5}","-\frac{\sqrt{x^2+2}}{15 x}-\frac{\sqrt{x^2+2}}{10 x^5}+\frac{\sqrt{x^2+2}}{15 x^3}",1,"(Sqrt[2 + x^2]*(-3 + 2*x^2 - 2*x^4))/(30*x^5)","A",1
252,1,28,49,0.0422978,"\int \frac{1}{\left(3+2 x^2\right)^{7/2}} \, dx","IntegrateAlgebraic[(3 + 2*x^2)^(-7/2),x]","\frac{x \left(32 x^4+120 x^2+135\right)}{405 \left(2 x^2+3\right)^{5/2}}","\frac{8 x}{405 \sqrt{2 x^2+3}}+\frac{4 x}{135 \left(2 x^2+3\right)^{3/2}}+\frac{x}{15 \left(2 x^2+3\right)^{5/2}}",1,"(x*(135 + 120*x^2 + 32*x^4))/(405*(3 + 2*x^2)^(5/2))","A",1
253,1,12,12,0.0115623,"\int \frac{x}{1+x^2+a \sqrt{1+x^2}} \, dx","IntegrateAlgebraic[x/(1 + x^2 + a*Sqrt[1 + x^2]),x]","\log \left(a+\sqrt{x^2+1}\right)","\log \left(a+\sqrt{x^2+1}\right)",1,"Log[a + Sqrt[1 + x^2]]","A",1
254,1,26,12,0.1735383,"\int \frac{1-x+x^2}{\left(1+x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[(1 - x + x^2)/(1 + x^2)^(3/2),x]","\frac{1}{\sqrt{x^2+1}}-\log \left(\sqrt{x^2+1}-x\right)","\frac{1}{\sqrt{x^2+1}}+\sinh ^{-1}(x)",1,"1/Sqrt[1 + x^2] - Log[-x + Sqrt[1 + x^2]]","B",1
255,1,57,27,0.0905606,"\int \frac{\sqrt{1+x^2}}{2+x^2} \, dx","IntegrateAlgebraic[Sqrt[1 + x^2]/(2 + x^2),x]","-\log \left(\sqrt{x^2+1}-x\right)-\frac{\tanh ^{-1}\left(\frac{x^2}{\sqrt{2}}-\frac{\sqrt{x^2+1} x}{\sqrt{2}}+\sqrt{2}\right)}{\sqrt{2}}","\sinh ^{-1}(x)-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{2} \sqrt{x^2+1}}\right)}{\sqrt{2}}",1,"-(ArcTanh[Sqrt[2] + x^2/Sqrt[2] - (x*Sqrt[1 + x^2])/Sqrt[2]]/Sqrt[2]) - Log[-x + Sqrt[1 + x^2]]","B",1
256,1,64,48,0.0815477,"\int \frac{1}{\sqrt{1+x^2} \left(2+x^2\right)^2} \, dx","IntegrateAlgebraic[1/(Sqrt[1 + x^2]*(2 + x^2)^2),x]","\frac{3 \tanh ^{-1}\left(\frac{x^2}{\sqrt{2}}-\frac{\sqrt{x^2+1} x}{\sqrt{2}}+\sqrt{2}\right)}{4 \sqrt{2}}-\frac{x \sqrt{x^2+1}}{4 \left(x^2+2\right)}","\frac{3 \tanh ^{-1}\left(\frac{x}{\sqrt{2} \sqrt{x^2+1}}\right)}{4 \sqrt{2}}-\frac{x \sqrt{x^2+1}}{4 \left(x^2+2\right)}",1,"-1/4*(x*Sqrt[1 + x^2])/(2 + x^2) + (3*ArcTanh[Sqrt[2] + x^2/Sqrt[2] - (x*Sqrt[1 + x^2])/Sqrt[2]])/(4*Sqrt[2])","A",1
257,1,66,41,0.1184516,"\int \frac{x^2}{\left(-6+x^2\right) \sqrt{-2+x^2}} \, dx","IntegrateAlgebraic[x^2/((-6 + x^2)*Sqrt[-2 + x^2]),x]","-\log \left(\sqrt{x^2-2}-x\right)-\sqrt{\frac{3}{2}} \tanh ^{-1}\left(-\frac{x^2}{2 \sqrt{6}}+\frac{\sqrt{x^2-2} x}{2 \sqrt{6}}+\sqrt{\frac{3}{2}}\right)","\tanh ^{-1}\left(\frac{x}{\sqrt{x^2-2}}\right)-\sqrt{\frac{3}{2}} \tanh ^{-1}\left(\frac{\sqrt{\frac{2}{3}} x}{\sqrt{x^2-2}}\right)",1,"-(Sqrt[3/2]*ArcTanh[Sqrt[3/2] - x^2/(2*Sqrt[6]) + (x*Sqrt[-2 + x^2])/(2*Sqrt[6])]) - Log[-x + Sqrt[-2 + x^2]]","A",1
258,1,54,47,0.12341,"\int \frac{5+x^2}{\sqrt{1-x^2} \left(1+x^2\right)^2} \, dx","IntegrateAlgebraic[(5 + x^2)/(Sqrt[1 - x^2]*(1 + x^2)^2),x]","\frac{x \sqrt{1-x^2}}{x^2+1}-2 \sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} x \sqrt{1-x^2}}{x^2-1}\right)","\frac{\sqrt{1-x^2} x}{x^2+1}+2 \sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{1-x^2}}\right)",1,"(x*Sqrt[1 - x^2])/(1 + x^2) - 2*Sqrt[2]*ArcTan[(Sqrt[2]*x*Sqrt[1 - x^2])/(-1 + x^2)]","A",1
259,1,108,88,0.3165911,"\int \frac{4 x-\sqrt{1-x^2}}{5+\sqrt{1-x^2}} \, dx","IntegrateAlgebraic[(4*x - Sqrt[1 - x^2])/(5 + Sqrt[1 - x^2]),x]","-4 \sqrt{1-x^2}-20 \log \left(\sqrt{1-x^2}-1\right)+20 \log \left(-x^2+4 \sqrt{1-x^2}-4\right)+10 \tan ^{-1}\left(\frac{x}{\sqrt{1-x^2}-1}\right)-\frac{25 \tan ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt{1-x^2}-1}\right)}{\sqrt{6}}-x","-4 \sqrt{1-x^2}+20 \log \left(\sqrt{1-x^2}+5\right)-\frac{25 \tan ^{-1}\left(\frac{5 x}{2 \sqrt{6} \sqrt{1-x^2}}\right)}{2 \sqrt{6}}-x+5 \sin ^{-1}(x)+\frac{25 \tan ^{-1}\left(\frac{x}{2 \sqrt{6}}\right)}{2 \sqrt{6}}",1,"-x - 4*Sqrt[1 - x^2] + 10*ArcTan[x/(-1 + Sqrt[1 - x^2])] - (25*ArcTan[(Sqrt[3/2]*x)/(-1 + Sqrt[1 - x^2])])/Sqrt[6] - 20*Log[-1 + Sqrt[1 - x^2]] + 20*Log[-4 - x^2 + 4*Sqrt[1 - x^2]]","A",1
260,1,117,136,0.3192267,"\int \frac{x^2 \left(2-\sqrt{1+x^2}\right)}{\sqrt{1+x^2} \left(1-x^3+\left(1+x^2\right)^{3/2}\right)} \, dx","IntegrateAlgebraic[(x^2*(2 - Sqrt[1 + x^2]))/(Sqrt[1 + x^2]*(1 - x^3 + (1 + x^2)^(3/2))),x]","\frac{1}{18} \sqrt{x^2+1} (16-3 x)+\frac{1}{18} \left(16 x-3 x^2\right)+\frac{55}{54} \log \left(\sqrt{x^2+1}-x\right)-\frac{7}{27} \log \left(-x^2+(x+1) \sqrt{x^2+1}-x-2\right)+\frac{8}{27} \sqrt{2} \tan ^{-1}\left(-\frac{\sqrt{x^2+1}}{\sqrt{2}}+\frac{x}{\sqrt{2}}+\frac{1}{\sqrt{2}}\right)","-\frac{x^2}{6}-\frac{1}{6} \sqrt{x^2+1} x+\frac{8 \sqrt{x^2+1}}{9}-\frac{7}{54} \log \left(3 x^2+2 x+3\right)+\frac{4}{27} \sqrt{2} \tan ^{-1}\left(\frac{x+1}{\sqrt{2} \sqrt{x^2+1}}\right)+\frac{7}{27} \tanh ^{-1}\left(\frac{1-x}{2 \sqrt{x^2+1}}\right)+\frac{8 x}{9}+\frac{4}{27} \sqrt{2} \tan ^{-1}\left(\frac{3 x+1}{2 \sqrt{2}}\right)-\frac{41}{54} \sinh ^{-1}(x)",1,"(16*x - 3*x^2)/18 + ((16 - 3*x)*Sqrt[1 + x^2])/18 + (8*Sqrt[2]*ArcTan[1/Sqrt[2] + x/Sqrt[2] - Sqrt[1 + x^2]/Sqrt[2]])/27 + (55*Log[-x + Sqrt[1 + x^2]])/54 - (7*Log[-2 - x - x^2 + (1 + x)*Sqrt[1 + x^2]])/27","A",1
261,1,113,64,0.1830863,"\int x \sqrt{2 r x-x^2} \, dx","IntegrateAlgebraic[x*Sqrt[2*r*x - x^2],x]","-\frac{1}{2} i r^3 \tanh ^{-1}\left(\frac{x}{r}+\frac{i \sqrt{2 r x-x^2}}{r}\right)+\frac{1}{6} \sqrt{2 r x-x^2} \left(-3 r^2-r x+2 x^2\right)+\frac{1}{4} i r^3 \log \left(r^2-2 i x \sqrt{2 r x-x^2}+2 r x-2 x^2\right)","r^3 \tan ^{-1}\left(\frac{x}{\sqrt{2 r x-x^2}}\right)-\frac{1}{2} r (r-x) \sqrt{2 r x-x^2}-\frac{1}{3} \left(2 r x-x^2\right)^{3/2}",1,"(Sqrt[2*r*x - x^2]*(-3*r^2 - r*x + 2*x^2))/6 - (I/2)*r^3*ArcTanh[x/r + (I*Sqrt[2*r*x - x^2])/r] + (I/4)*r^3*Log[r^2 + 2*r*x - 2*x^2 - (2*I)*x*Sqrt[2*r*x - x^2]]","C",1
262,1,121,89,0.199671,"\int x^2 \sqrt{2 r x-x^2} \, dx","IntegrateAlgebraic[x^2*Sqrt[2*r*x - x^2],x]","-\frac{5}{8} i r^4 \tanh ^{-1}\left(\frac{x}{r}+\frac{i \sqrt{2 r x-x^2}}{r}\right)+\frac{5}{16} i r^4 \log \left(r^2-2 i x \sqrt{2 r x-x^2}+2 r x-2 x^2\right)+\frac{1}{24} \sqrt{2 r x-x^2} \left(-15 r^3-5 r^2 x-2 r x^2+6 x^3\right)","\frac{5}{4} r^4 \tan ^{-1}\left(\frac{x}{\sqrt{2 r x-x^2}}\right)-\frac{5}{8} r^2 (r-x) \sqrt{2 r x-x^2}-\frac{5}{12} r \left(2 r x-x^2\right)^{3/2}-\frac{1}{4} x \left(2 r x-x^2\right)^{3/2}",1,"(Sqrt[2*r*x - x^2]*(-15*r^3 - 5*r^2*x - 2*r*x^2 + 6*x^3))/24 - ((5*I)/8)*r^4*ArcTanh[x/r + (I*Sqrt[2*r*x - x^2])/r] + ((5*I)/16)*r^4*Log[r^2 + 2*r*x - 2*x^2 - (2*I)*x*Sqrt[2*r*x - x^2]]","C",1
263,1,129,113,0.2344611,"\int x^3 \sqrt{2 r x-x^2} \, dx","IntegrateAlgebraic[x^3*Sqrt[2*r*x - x^2],x]","-\frac{7}{8} i r^5 \tanh ^{-1}\left(\frac{x}{r}+\frac{i \sqrt{2 r x-x^2}}{r}\right)+\frac{7}{16} i r^5 \log \left(r^2-2 i x \sqrt{2 r x-x^2}+2 r x-2 x^2\right)+\frac{1}{120} \sqrt{2 r x-x^2} \left(-105 r^4-35 r^3 x-14 r^2 x^2-6 r x^3+24 x^4\right)","\frac{7}{4} r^5 \tan ^{-1}\left(\frac{x}{\sqrt{2 r x-x^2}}\right)-\frac{7}{8} r^3 (r-x) \sqrt{2 r x-x^2}-\frac{7}{12} r^2 \left(2 r x-x^2\right)^{3/2}-\frac{7}{20} r x \left(2 r x-x^2\right)^{3/2}-\frac{1}{5} x^2 \left(2 r x-x^2\right)^{3/2}",1,"(Sqrt[2*r*x - x^2]*(-105*r^4 - 35*r^3*x - 14*r^2*x^2 - 6*r*x^3 + 24*x^4))/120 - ((7*I)/8)*r^5*ArcTanh[x/r + (I*Sqrt[2*r*x - x^2])/r] + ((7*I)/16)*r^5*Log[r^2 + 2*r*x - 2*x^2 - (2*I)*x*Sqrt[2*r*x - x^2]]","C",1
264,1,57,49,0.1878939,"\int \frac{1}{\left(-1+x^2\right) \sqrt{2 x+x^2}} \, dx","IntegrateAlgebraic[1/((-1 + x^2)*Sqrt[2*x + x^2]),x]","\tan ^{-1}\left(-\sqrt{x^2+2 x}+x+1\right)-\frac{\tanh ^{-1}\left(\frac{\sqrt{x^2+2 x}}{\sqrt{3}}-\frac{x}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3}}","-\frac{1}{2} \tan ^{-1}\left(\sqrt{x^2+2 x}\right)-\frac{\tanh ^{-1}\left(\frac{2 x+1}{\sqrt{3} \sqrt{x^2+2 x}}\right)}{2 \sqrt{3}}",1,"ArcTan[1 + x - Sqrt[2*x + x^2]] - ArcTanh[1/Sqrt[3] - x/Sqrt[3] + Sqrt[2*x + x^2]/Sqrt[3]]/Sqrt[3]","A",1
265,1,57,79,0.3121034,"\int \frac{-2+3 x}{(1+x)^3 \sqrt{2 x-x^2}} \, dx","IntegrateAlgebraic[(-2 + 3*x)/((1 + x)^3*Sqrt[2*x - x^2]),x]","\frac{\sqrt{2 x-x^2} (-4 x-9)}{6 (x+1)^2}+\frac{\tan ^{-1}\left(\frac{\sqrt{2 x-x^2}}{\sqrt{3} x}\right)}{\sqrt{3}}","-\frac{2 \sqrt{2 x-x^2}}{3 (x+1)}-\frac{5 \sqrt{2 x-x^2}}{6 (x+1)^2}+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3} \sqrt{2 x-x^2}}\right)}{2 \sqrt{3}}",1,"((-9 - 4*x)*Sqrt[2*x - x^2])/(6*(1 + x)^2) + ArcTan[Sqrt[2*x - x^2]/(Sqrt[3]*x)]/Sqrt[3]","A",1
266,1,20,12,0.0617189,"\int \frac{1}{\sqrt{1+x+x^2}} \, dx","IntegrateAlgebraic[1/Sqrt[1 + x + x^2],x]","-\log \left(2 \sqrt{x^2+x+1}-2 x-1\right)","\sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)",1,"-Log[-1 - 2*x + 2*Sqrt[1 + x + x^2]]","A",1
267,1,47,53,0.0786694,"\int \frac{x^3}{\sqrt{1+x+x^2}} \, dx","IntegrateAlgebraic[x^3/Sqrt[1 + x + x^2],x]","\frac{1}{24} \sqrt{x^2+x+1} \left(8 x^2-10 x-1\right)-\frac{7}{16} \log \left(2 \sqrt{x^2+x+1}-2 x-1\right)","\frac{1}{3} \sqrt{x^2+x+1} x^2-\frac{1}{24} (10 x+1) \sqrt{x^2+x+1}+\frac{7}{16} \sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)",1,"(Sqrt[1 + x + x^2]*(-1 - 10*x + 8*x^2))/24 - (7*Log[-1 - 2*x + 2*Sqrt[1 + x + x^2]])/16","A",1
268,1,19,19,0.146726,"\int \frac{1}{\left(1+x+x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[(1 + x + x^2)^(-3/2),x]","\frac{2 (2 x+1)}{3 \sqrt{x^2+x+1}}","\frac{2 (2 x+1)}{3 \sqrt{x^2+x+1}}",1,"(2*(1 + 2*x))/(3*Sqrt[1 + x + x^2])","A",1
269,1,17,17,0.1311669,"\int \frac{x}{\left(1+x+x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[x/(1 + x + x^2)^(3/2),x]","-\frac{2 (x+2)}{3 \sqrt{x^2+x+1}}","-\frac{2 (x+2)}{3 \sqrt{x^2+x+1}}",1,"(-2*(2 + x))/(3*Sqrt[1 + x + x^2])","A",1
270,1,47,56,0.1830862,"\int \frac{x^3}{\left(1+x+x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[x^3/(1 + x + x^2)^(3/2),x]","\frac{3 x^2+7 x+5}{3 \sqrt{x^2+x+1}}+\frac{3}{2} \log \left(2 \sqrt{x^2+x+1}-2 x-1\right)","-\frac{2 (x+2) x^2}{3 \sqrt{x^2+x+1}}+\frac{1}{3} (2 x+5) \sqrt{x^2+x+1}-\frac{3}{2} \sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)",1,"(5 + 7*x + 3*x^2)/(3*Sqrt[1 + x + x^2]) + (3*Log[-1 - 2*x + 2*Sqrt[1 + x + x^2]])/2","A",1
271,1,52,65,0.0868376,"\int x^2 \sqrt{1+x+x^2} \, dx","IntegrateAlgebraic[x^2*Sqrt[1 + x + x^2],x]","\frac{1}{192} \sqrt{x^2+x+1} \left(48 x^3+8 x^2+14 x-37\right)-\frac{3}{128} \log \left(2 \sqrt{x^2+x+1}-2 x-1\right)","\frac{1}{4} x \left(x^2+x+1\right)^{3/2}-\frac{5}{24} \left(x^2+x+1\right)^{3/2}+\frac{1}{64} (2 x+1) \sqrt{x^2+x+1}+\frac{3}{128} \sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)",1,"(Sqrt[1 + x + x^2]*(-37 + 14*x + 8*x^2 + 48*x^3))/192 - (3*Log[-1 - 2*x + 2*Sqrt[1 + x + x^2]])/128","A",1
272,1,52,55,0.1470464,"\int \left(1+x+x^2\right)^{3/2} \, dx","IntegrateAlgebraic[(1 + x + x^2)^(3/2),x]","\frac{1}{64} \sqrt{x^2+x+1} \left(16 x^3+24 x^2+42 x+17\right)-\frac{27}{128} \log \left(2 \sqrt{x^2+x+1}-2 x-1\right)","\frac{1}{8} (2 x+1) \left(x^2+x+1\right)^{3/2}+\frac{9}{64} (2 x+1) \sqrt{x^2+x+1}+\frac{27}{128} \sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)",1,"(Sqrt[1 + x + x^2]*(17 + 42*x + 24*x^2 + 16*x^3))/64 - (27*Log[-1 - 2*x + 2*Sqrt[1 + x + x^2]])/128","A",1
273,1,62,74,0.2809365,"\int \left(1+x+x^2\right)^{5/2} \, dx","IntegrateAlgebraic[(1 + x + x^2)^(5/2),x]","\frac{\sqrt{x^2+x+1} \left(256 x^5+640 x^4+1264 x^3+1256 x^2+1142 x+383\right)}{1536}-\frac{135 \log \left(2 \sqrt{x^2+x+1}-2 x-1\right)}{1024}","\frac{1}{12} (2 x+1) \left(x^2+x+1\right)^{5/2}+\frac{5}{64} (2 x+1) \left(x^2+x+1\right)^{3/2}+\frac{45}{512} (2 x+1) \sqrt{x^2+x+1}+\frac{135 \sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{1024}",1,"(Sqrt[1 + x + x^2]*(383 + 1142*x + 1256*x^2 + 1264*x^3 + 640*x^4 + 256*x^5))/1536 - (135*Log[-1 - 2*x + 2*Sqrt[1 + x + x^2]])/1024","A",1
274,1,33,38,0.0820179,"\int \frac{1}{x^2 \sqrt{1+x+x^2}} \, dx","IntegrateAlgebraic[1/(x^2*Sqrt[1 + x + x^2]),x]","-\frac{\sqrt{x^2+x+1}}{x}-\tanh ^{-1}\left(x-\sqrt{x^2+x+1}\right)","\frac{1}{2} \tanh ^{-1}\left(\frac{x+2}{2 \sqrt{x^2+x+1}}\right)-\frac{\sqrt{x^2+x+1}}{x}",1,"-(Sqrt[1 + x + x^2]/x) - ArcTanh[x - Sqrt[1 + x + x^2]]","A",1
275,1,42,57,0.141062,"\int \frac{1}{x^3 \sqrt{1+x+x^2}} \, dx","IntegrateAlgebraic[1/(x^3*Sqrt[1 + x + x^2]),x]","\frac{(3 x-2) \sqrt{x^2+x+1}}{4 x^2}-\frac{1}{4} \tanh ^{-1}\left(x-\sqrt{x^2+x+1}\right)","\frac{3 \sqrt{x^2+x+1}}{4 x}-\frac{\sqrt{x^2+x+1}}{2 x^2}+\frac{1}{8} \tanh ^{-1}\left(\frac{x+2}{2 \sqrt{x^2+x+1}}\right)",1,"((-2 + 3*x)*Sqrt[1 + x + x^2])/(4*x^2) - ArcTanh[x - Sqrt[1 + x + x^2]]/4","A",1
276,1,45,62,0.2043401,"\int \frac{1}{x^2 \left(1+x+x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[1/(x^2*(1 + x + x^2)^(3/2)),x]","\frac{-5 x^2-7 x-3}{3 x \sqrt{x^2+x+1}}-3 \tanh ^{-1}\left(x-\sqrt{x^2+x+1}\right)","\frac{2 (1-x)}{3 x \sqrt{x^2+x+1}}-\frac{5 \sqrt{x^2+x+1}}{3 x}+\frac{3}{2} \tanh ^{-1}\left(\frac{x+2}{2 \sqrt{x^2+x+1}}\right)",1,"(-3 - 7*x - 5*x^2)/(3*x*Sqrt[1 + x + x^2]) - 3*ArcTanh[x - Sqrt[1 + x + x^2]]","A",1
277,1,52,79,0.2168096,"\int \frac{1}{x^3 \left(1+x+x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[1/(x^3*(1 + x + x^2)^(3/2)),x]","\frac{3}{4} \tanh ^{-1}\left(x-\sqrt{x^2+x+1}\right)+\frac{37 x^3+23 x^2+15 x-6}{12 x^2 \sqrt{x^2+x+1}}","\frac{2 (1-x)}{3 x^2 \sqrt{x^2+x+1}}+\frac{37 \sqrt{x^2+x+1}}{12 x}-\frac{7 \sqrt{x^2+x+1}}{6 x^2}-\frac{3}{8} \tanh ^{-1}\left(\frac{x+2}{2 \sqrt{x^2+x+1}}\right)",1,"(-6 + 15*x + 23*x^2 + 37*x^3)/(12*x^2*Sqrt[1 + x + x^2]) + (3*ArcTanh[x - Sqrt[1 + x + x^2]])/4","A",1
278,1,18,22,0.1436053,"\int \frac{1}{(1+x) \sqrt{1+x+x^2}} \, dx","IntegrateAlgebraic[1/((1 + x)*Sqrt[1 + x + x^2]),x]","2 \tanh ^{-1}\left(-\sqrt{x^2+x+1}+x+1\right)","-\tanh ^{-1}\left(\frac{1-x}{2 \sqrt{x^2+x+1}}\right)",1,"2*ArcTanh[1 + x - Sqrt[1 + x + x^2]]","A",1
279,1,105,86,0.2278902,"\int \frac{1}{\sqrt{4+2 x+x^2} \left(-x+x^3\right)} \, dx","IntegrateAlgebraic[1/(Sqrt[4 + 2*x + x^2]*(-x + x^3)),x]","-\tanh ^{-1}\left(\frac{x}{2}-\frac{1}{2} \sqrt{x^2+2 x+4}\right)+\frac{\tanh ^{-1}\left(-\frac{\sqrt{x^2+2 x+4}}{\sqrt{3}}+\frac{x}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{x^2+2 x+4}}{\sqrt{7}}-\frac{x}{\sqrt{7}}+\frac{1}{\sqrt{7}}\right)}{\sqrt{7}}","\frac{1}{2} \tanh ^{-1}\left(\frac{x+4}{2 \sqrt{x^2+2 x+4}}\right)-\frac{\tanh ^{-1}\left(\frac{2 x+5}{\sqrt{7} \sqrt{x^2+2 x+4}}\right)}{2 \sqrt{7}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{x^2+2 x+4}}{\sqrt{3}}\right)}{2 \sqrt{3}}",1,"-ArcTanh[x/2 - Sqrt[4 + 2*x + x^2]/2] + ArcTanh[1/Sqrt[3] + x/Sqrt[3] - Sqrt[4 + 2*x + x^2]/Sqrt[3]]/Sqrt[3] - ArcTanh[1/Sqrt[7] - x/Sqrt[7] + Sqrt[4 + 2*x + x^2]/Sqrt[7]]/Sqrt[7]","A",1
280,1,81,62,0.2317874,"\int \frac{\sqrt{4+2 x+x^2}}{(-1+x)^2} \, dx","IntegrateAlgebraic[Sqrt[4 + 2*x + x^2]/(-1 + x)^2,x]","\frac{\sqrt{x^2+2 x+4}}{1-x}-\log \left(\sqrt{x^2+2 x+4}-x-1\right)-\frac{4 \tanh ^{-1}\left(\frac{\sqrt{x^2+2 x+4}}{\sqrt{7}}-\frac{x}{\sqrt{7}}+\frac{1}{\sqrt{7}}\right)}{\sqrt{7}}","\frac{\sqrt{x^2+2 x+4}}{1-x}-\frac{2 \tanh ^{-1}\left(\frac{2 x+5}{\sqrt{7} \sqrt{x^2+2 x+4}}\right)}{\sqrt{7}}+\sinh ^{-1}\left(\frac{x+1}{\sqrt{3}}\right)",1,"Sqrt[4 + 2*x + x^2]/(1 - x) - (4*ArcTanh[1/Sqrt[7] - x/Sqrt[7] + Sqrt[4 + 2*x + x^2]/Sqrt[7]])/Sqrt[7] - Log[-1 - x + Sqrt[4 + 2*x + x^2]]","A",1
281,1,244,76,1.6799879,"\int \frac{3+2 x}{\left(3+2 x+x^2\right)^2 \sqrt{4+2 x+x^2}} \, dx","IntegrateAlgebraic[(3 + 2*x)/((3 + 2*x + x^2)^2*Sqrt[4 + 2*x + x^2]),x]","\frac{\sqrt{x^2+2 x+4} (x-3)}{4 \left(x^2+2 x+3\right)}-i \tan ^{-1}\left(-\sqrt{\frac{1}{9}-\frac{2 i \sqrt{2}}{9}} \sqrt{x^2+2 x+4}+\sqrt{\frac{1}{9}-\frac{2 i \sqrt{2}}{9}} x+\sqrt{\frac{1}{9}-\frac{2 i \sqrt{2}}{9}}\right)+i \tan ^{-1}\left(-\sqrt{\frac{1}{9}+\frac{2 i \sqrt{2}}{9}} \sqrt{x^2+2 x+4}+\sqrt{\frac{1}{9}+\frac{2 i \sqrt{2}}{9}} x+\sqrt{\frac{1}{9}+\frac{2 i \sqrt{2}}{9}}\right)+\frac{\tan ^{-1}\left(\frac{x^2}{\sqrt{2}}-\frac{(x+1) \sqrt{x^2+2 x+4}}{\sqrt{2}}+\sqrt{2} x+\frac{3}{\sqrt{2}}\right)}{4 \sqrt{2}}","-\frac{\sqrt{x^2+2 x+4} (3-x)}{4 \left(x^2+2 x+3\right)}-\frac{\tan ^{-1}\left(\frac{x+1}{\sqrt{2} \sqrt{x^2+2 x+4}}\right)}{4 \sqrt{2}}+\tanh ^{-1}\left(\sqrt{x^2+2 x+4}\right)",1,"((-3 + x)*Sqrt[4 + 2*x + x^2])/(4*(3 + 2*x + x^2)) - I*ArcTan[Sqrt[1/9 - ((2*I)/9)*Sqrt[2]] + Sqrt[1/9 - ((2*I)/9)*Sqrt[2]]*x - Sqrt[1/9 - ((2*I)/9)*Sqrt[2]]*Sqrt[4 + 2*x + x^2]] + I*ArcTan[Sqrt[1/9 + ((2*I)/9)*Sqrt[2]] + Sqrt[1/9 + ((2*I)/9)*Sqrt[2]]*x - Sqrt[1/9 + ((2*I)/9)*Sqrt[2]]*Sqrt[4 + 2*x + x^2]] + ArcTan[3/Sqrt[2] + Sqrt[2]*x + x^2/Sqrt[2] - ((1 + x)*Sqrt[4 + 2*x + x^2])/Sqrt[2]]/(4*Sqrt[2])","C",0
282,1,26,36,0.131364,"\int \frac{3 x^2+2 x^3}{\sqrt{-3+2 x+x^2} \left(-3+x+2 x^2\right)} \, dx","IntegrateAlgebraic[(3*x^2 + 2*x^3)/(Sqrt[-3 + 2*x + x^2]*(-3 + x + 2*x^2)),x]","\frac{(2 x-3) \sqrt{x^2+2 x-3}}{2 (x-1)}","\frac{\sqrt{x^2+2 x-3}}{2 (1-x)}+\sqrt{x^2+2 x-3}",1,"((-3 + 2*x)*Sqrt[-3 + 2*x + x^2])/(2*(-1 + x))","A",1
283,1,254,87,1.5892963,"\int \frac{1+x^4}{\left(1+x+x^2\right) \sqrt{2+x+x^2}} \, dx","IntegrateAlgebraic[(1 + x^4)/((1 + x + x^2)*Sqrt[2 + x + x^2]),x]","\frac{1}{4} \sqrt{x^2+x+2} (2 x-7)+\frac{1}{8} \log \left(2 \sqrt{x^2+x+2}-2 x-1\right)+i \tan ^{-1}\left(-2 \sqrt{-\frac{1}{49}-\frac{4 i \sqrt{3}}{49}} \sqrt{x^2+x+2}+2 \sqrt{-\frac{1}{49}-\frac{4 i \sqrt{3}}{49}} x+\sqrt{-\frac{1}{49}-\frac{4 i \sqrt{3}}{49}}\right)-i \tan ^{-1}\left(-2 \sqrt{-\frac{1}{49}+\frac{4 i \sqrt{3}}{49}} \sqrt{x^2+x+2}+2 \sqrt{-\frac{1}{49}+\frac{4 i \sqrt{3}}{49}} x+\sqrt{-\frac{1}{49}+\frac{4 i \sqrt{3}}{49}}\right)-\frac{\tan ^{-1}\left(\frac{2 x^2}{\sqrt{3}}-\frac{(2 x+1) \sqrt{x^2+x+2}}{\sqrt{3}}+\frac{2 x}{\sqrt{3}}+\frac{2}{\sqrt{3}}\right)}{\sqrt{3}}","\frac{1}{2} \sqrt{x^2+x+2} x-\frac{7}{4} \sqrt{x^2+x+2}+\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3} \sqrt{x^2+x+2}}\right)}{\sqrt{3}}-\tanh ^{-1}\left(\sqrt{x^2+x+2}\right)-\frac{1}{8} \sinh ^{-1}\left(\frac{2 x+1}{\sqrt{7}}\right)",1,"((-7 + 2*x)*Sqrt[2 + x + x^2])/4 + I*ArcTan[Sqrt[-1/49 - ((4*I)/49)*Sqrt[3]] + 2*Sqrt[-1/49 - ((4*I)/49)*Sqrt[3]]*x - 2*Sqrt[-1/49 - ((4*I)/49)*Sqrt[3]]*Sqrt[2 + x + x^2]] - I*ArcTan[Sqrt[-1/49 + ((4*I)/49)*Sqrt[3]] + 2*Sqrt[-1/49 + ((4*I)/49)*Sqrt[3]]*x - 2*Sqrt[-1/49 + ((4*I)/49)*Sqrt[3]]*Sqrt[2 + x + x^2]] - ArcTan[2/Sqrt[3] + (2*x)/Sqrt[3] + (2*x^2)/Sqrt[3] - ((1 + 2*x)*Sqrt[2 + x + x^2])/Sqrt[3]]/Sqrt[3] + Log[-1 - 2*x + 2*Sqrt[2 + x + x^2]]/8","C",0
284,1,39,58,0.2893583,"\int \frac{1}{\left(4+2 x+x^2\right)^{7/2}} \, dx","IntegrateAlgebraic[(4 + 2*x + x^2)^(-7/2),x]","\frac{(x+1) \left(8 x^4+32 x^3+108 x^2+152 x+203\right)}{405 \left(x^2+2 x+4\right)^{5/2}}","\frac{8 (x+1)}{405 \sqrt{x^2+2 x+4}}+\frac{4 (x+1)}{135 \left(x^2+2 x+4\right)^{3/2}}+\frac{x+1}{15 \left(x^2+2 x+4\right)^{5/2}}",1,"((1 + x)*(203 + 152*x + 108*x^2 + 32*x^3 + 8*x^4))/(405*(4 + 2*x + x^2)^(5/2))","A",1
285,1,57,47,0.3022718,"\int \frac{1}{\left(1+8 x+3 x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[(1 + 8*x + 3*x^2)^(-5/2),x]","\frac{3 \sqrt{3 x^2+8 x+1} \left(54 x^3+216 x^2+171 x-28\right)}{169 \left(-3 x+\sqrt{13}-4\right)^2 \left(3 x+\sqrt{13}+4\right)^2}","\frac{2 (3 x+4)}{169 \sqrt{3 x^2+8 x+1}}-\frac{3 x+4}{39 \left(3 x^2+8 x+1\right)^{3/2}}",1,"(3*Sqrt[1 + 8*x + 3*x^2]*(-28 + 171*x + 216*x^2 + 54*x^3))/(169*(-4 + Sqrt[13] - 3*x)^2*(4 + Sqrt[13] + 3*x)^2)","A",1
286,1,57,47,0.3133761,"\int \frac{1}{\left(5+4 x-3 x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[(5 + 4*x - 3*x^2)^(-5/2),x]","-\frac{3 \sqrt{-3 x^2+4 x+5} \left(54 x^3-108 x^2-99 x+98\right)}{361 \left(-3 x+\sqrt{19}+2\right)^2 \left(3 x+\sqrt{19}-2\right)^2}","-\frac{2 (2-3 x)}{361 \sqrt{-3 x^2+4 x+5}}-\frac{2-3 x}{57 \left(-3 x^2+4 x+5\right)^{3/2}}",1,"(-3*Sqrt[5 + 4*x - 3*x^2]*(98 - 99*x - 108*x^2 + 54*x^3))/(361*(2 + Sqrt[19] - 3*x)^2*(-2 + Sqrt[19] + 3*x)^2)","A",1
287,1,46,29,0.2855416,"\int \frac{1}{1+\sqrt{2+2 x+x^2}} \, dx","IntegrateAlgebraic[(1 + Sqrt[2 + 2*x + x^2])^(-1),x]","\frac{\sqrt{x^2+2 x+2}}{-x-1}-\log \left(\sqrt{x^2+2 x+2}-x-1\right)+\frac{1}{x+1}","-\frac{\sqrt{x^2+2 x+2}}{x+1}+\frac{1}{x+1}+\sinh ^{-1}(x+1)",1,"(1 + x)^(-1) + Sqrt[2 + 2*x + x^2]/(-1 - x) - Log[-1 - x + Sqrt[2 + 2*x + x^2]]","A",1
288,1,54,45,0.1172934,"\int \frac{1}{x+\sqrt{1+x+x^2}} \, dx","IntegrateAlgebraic[(x + Sqrt[1 + x + x^2])^(-1),x]","\sqrt{x^2+x+1}+2 \log \left(\sqrt{x^2+x+1}-x-2\right)-\frac{1}{2} \log \left(2 \sqrt{x^2+x+1}-2 x-1\right)-x","\sqrt{x^2+x+1}+2 \log \left(\sqrt{x^2+x+1}+x\right)-x-\frac{3}{2} \sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)",1,"-x + Sqrt[1 + x + x^2] + 2*Log[-2 - x + Sqrt[1 + x + x^2]] - Log[-1 - 2*x + 2*Sqrt[1 + x + x^2]]/2","A",1
289,1,67,79,0.1896689,"\int \frac{x^2}{1+2 x+2 \sqrt{1+x+x^2}} \, dx","IntegrateAlgebraic[x^2/(1 + 2*x + 2*Sqrt[1 + x + x^2]),x]","-\frac{1}{64} \log \left(2 \sqrt{x^2+x+1}-2 x-1\right)+\frac{1}{18} \left(-3 x^4-2 x^3\right)+\frac{1}{288} \sqrt{x^2+x+1} \left(48 x^3+8 x^2+14 x-37\right)","-\frac{x^4}{6}-\frac{x^3}{9}+\frac{1}{6} \left(x^2+x+1\right)^{3/2} x-\frac{5}{36} \left(x^2+x+1\right)^{3/2}+\frac{1}{96} (2 x+1) \sqrt{x^2+x+1}+\frac{1}{64} \sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)",1,"(Sqrt[1 + x + x^2]*(-37 + 14*x + 8*x^2 + 48*x^3))/288 + (-2*x^3 - 3*x^4)/18 - Log[-1 - 2*x + 2*Sqrt[1 + x + x^2]]/64","A",1
290,1,72,80,0.2556767,"\int \frac{-3 x+\sqrt{1+x+x^2}}{-1+\sqrt{1+x+x^2}} \, dx","IntegrateAlgebraic[(-3*x + Sqrt[1 + x + x^2])/(-1 + Sqrt[1 + x + x^2]),x]","-3 \sqrt{x^2+x+1}-8 \log \left(\sqrt{x^2+x+1}-x-2\right)+2 \log \left(\sqrt{x^2+x+1}-x-1\right)+\frac{1}{2} \log \left(2 \sqrt{x^2+x+1}-2 x-1\right)+x","-3 \sqrt{x^2+x+1}+4 \tanh ^{-1}\left(\frac{1-x}{2 \sqrt{x^2+x+1}}\right)-\tanh ^{-1}\left(\frac{x+2}{2 \sqrt{x^2+x+1}}\right)+x+\log (x)-4 \log (x+1)+\frac{5}{2} \sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)",1,"x - 3*Sqrt[1 + x + x^2] - 8*Log[-2 - x + Sqrt[1 + x + x^2]] + 2*Log[-1 - x + Sqrt[1 + x + x^2]] + Log[-1 - 2*x + 2*Sqrt[1 + x + x^2]]/2","A",1
291,1,165,158,2.9854193,"\int \frac{1+x}{-\sqrt{1+x+x^2}+\sqrt{4+2 x+x^2}} \, dx","IntegrateAlgebraic[(1 + x)/(-Sqrt[1 + x + x^2] + Sqrt[4 + 2*x + x^2]),x]","\frac{1}{2} \sqrt{x^2+2 x+4} (x-3)+\frac{1}{4} (2 x-7) \sqrt{x^2+x+1}-\frac{43}{8} \log \left(2 \sqrt{x^2+x+1}-2 x-1\right)-\frac{11}{2} \log \left(\sqrt{x^2+2 x+4}-x-1\right)-4 \sqrt{7} \tanh ^{-1}\left(-\frac{\sqrt{x^2+x+1}}{\sqrt{7}}+\frac{x}{\sqrt{7}}+\frac{3}{\sqrt{7}}\right)-4 \sqrt{7} \tanh ^{-1}\left(-\frac{\sqrt{x^2+2 x+4}}{\sqrt{7}}+\frac{x}{\sqrt{7}}+\frac{3}{\sqrt{7}}\right)","\frac{1}{2} \sqrt{x^2+2 x+4} (x+1)+\frac{1}{4} (2 x+1) \sqrt{x^2+x+1}-2 \sqrt{x^2+x+1}-2 \sqrt{x^2+2 x+4}-2 \sqrt{7} \tanh ^{-1}\left(\frac{5 x+1}{2 \sqrt{7} \sqrt{x^2+x+1}}\right)+2 \sqrt{7} \tanh ^{-1}\left(\frac{1-2 x}{\sqrt{7} \sqrt{x^2+2 x+4}}\right)+\frac{11}{2} \sinh ^{-1}\left(\frac{x+1}{\sqrt{3}}\right)+\frac{43}{8} \sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)",1,"((-7 + 2*x)*Sqrt[1 + x + x^2])/4 + ((-3 + x)*Sqrt[4 + 2*x + x^2])/2 - 4*Sqrt[7]*ArcTanh[3/Sqrt[7] + x/Sqrt[7] - Sqrt[1 + x + x^2]/Sqrt[7]] - 4*Sqrt[7]*ArcTanh[3/Sqrt[7] + x/Sqrt[7] - Sqrt[4 + 2*x + x^2]/Sqrt[7]] - (43*Log[-1 - 2*x + 2*Sqrt[1 + x + x^2]])/8 - (11*Log[-1 - x + Sqrt[4 + 2*x + x^2]])/2","A",1
292,1,32,41,0.0219985,"\int \frac{1}{\sqrt{-1+x} x^3} \, dx","IntegrateAlgebraic[1/(Sqrt[-1 + x]*x^3),x]","\frac{\sqrt{x-1} (3 x+2)}{4 x^2}+\frac{3}{4} \tan ^{-1}\left(\sqrt{x-1}\right)","\frac{\sqrt{x-1}}{2 x^2}+\frac{3 \sqrt{x-1}}{4 x}+\frac{3}{4} \tan ^{-1}\left(\sqrt{x-1}\right)",1,"(Sqrt[-1 + x]*(2 + 3*x))/(4*x^2) + (3*ArcTan[Sqrt[-1 + x]])/4","A",1
293,1,19,13,0.0086344,"\int \frac{1}{\left(1-\frac{3}{x}\right)^{4/3} x^2} \, dx","IntegrateAlgebraic[1/((1 - 3/x)^(4/3)*x^2),x]","-\frac{\left(\frac{x-3}{x}\right)^{2/3} x}{x-3}","-\frac{1}{\sqrt[3]{1-\frac{3}{x}}}",1,"-((((-3 + x)/x)^(2/3)*x)/(-3 + x))","A",1
294,1,88,71,0.0550117,"\int \frac{(-1+3 x)^{4/3}}{x^2} \, dx","IntegrateAlgebraic[(-1 + 3*x)^(4/3)/x^2,x]","\frac{\sqrt[3]{3 x-1} (9 x+1)}{x}-4 \log \left(\sqrt[3]{3 x-1}+1\right)+2 \log \left((3 x-1)^{2/3}-\sqrt[3]{3 x-1}+1\right)+4 \sqrt{3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{3 x-1}}{\sqrt{3}}\right)","-\frac{(3 x-1)^{4/3}}{x}+12 \sqrt[3]{3 x-1}+2 \log (x)-6 \log \left(\sqrt[3]{3 x-1}+1\right)+4 \sqrt{3} \tan ^{-1}\left(\frac{1-2 \sqrt[3]{3 x-1}}{\sqrt{3}}\right)",1,"((-1 + 3*x)^(1/3)*(1 + 9*x))/x + 4*Sqrt[3]*ArcTan[1/Sqrt[3] - (2*(-1 + 3*x)^(1/3))/Sqrt[3]] - 4*Log[1 + (-1 + 3*x)^(1/3)] + 2*Log[1 - (-1 + 3*x)^(1/3) + (-1 + 3*x)^(2/3)]","A",1
295,1,33,40,0.0080207,"\int (4-3 x)^{4/3} x^2 \, dx","IntegrateAlgebraic[(4 - 3*x)^(4/3)*x^2,x]","\frac{1}{455} \sqrt[3]{4-3 x} \left(-315 x^4+588 x^3-32 x^2-64 x-256\right)","-\frac{1}{117} (4-3 x)^{13/3}+\frac{4}{45} (4-3 x)^{10/3}-\frac{16}{63} (4-3 x)^{7/3}",1,"((4 - 3*x)^(1/3)*(-256 - 64*x - 32*x^2 + 588*x^3 - 315*x^4))/455","A",1
296,1,48,48,7.8161972,"\int \frac{\left(1-2 \sqrt[3]{x}\right)^{3/4}}{x} \, dx","IntegrateAlgebraic[(1 - 2*x^(1/3))^(3/4)/x,x]","4 \left(1-2 \sqrt[3]{x}\right)^{3/4}+6 \tan ^{-1}\left(\sqrt[4]{1-2 \sqrt[3]{x}}\right)-6 \tanh ^{-1}\left(\sqrt[4]{1-2 \sqrt[3]{x}}\right)","4 \left(1-2 \sqrt[3]{x}\right)^{3/4}+6 \tan ^{-1}\left(\sqrt[4]{1-2 \sqrt[3]{x}}\right)-6 \tanh ^{-1}\left(\sqrt[4]{1-2 \sqrt[3]{x}}\right)",1,"4*(1 - 2*x^(1/3))^(3/4) + 6*ArcTan[(1 - 2*x^(1/3))^(1/4)] - 6*ArcTanh[(1 - 2*x^(1/3))^(1/4)]","A",1
297,1,80,69,0.2955936,"\int \frac{x}{\left(3-2 \sqrt{x}\right)^{3/4}} \, dx","IntegrateAlgebraic[x/(3 - 2*Sqrt[x])^(3/4),x]","-\frac{4}{13} \sqrt[4]{3-2 \sqrt{x}} x^{3/2}-\frac{8}{13} \sqrt[4]{3-2 \sqrt{x}} x-\frac{96}{65} \sqrt[4]{3-2 \sqrt{x}} \sqrt{x}-\frac{576}{65} \sqrt[4]{3-2 \sqrt{x}}","\frac{1}{26} \left(3-2 \sqrt{x}\right)^{13/4}-\frac{1}{2} \left(3-2 \sqrt{x}\right)^{9/4}+\frac{27}{10} \left(3-2 \sqrt{x}\right)^{5/4}-\frac{27}{2} \sqrt[4]{3-2 \sqrt{x}}",1,"(-576*(3 - 2*Sqrt[x])^(1/4))/65 - (96*(3 - 2*Sqrt[x])^(1/4)*Sqrt[x])/65 - (8*(3 - 2*Sqrt[x])^(1/4)*x)/13 - (4*(3 - 2*Sqrt[x])^(1/4)*x^(3/2))/13","A",1
298,1,132,193,0.3374021,"\int \frac{\left(-1+2 \sqrt{x}\right)^{5/4}}{x^2} \, dx","IntegrateAlgebraic[(-1 + 2*Sqrt[x])^(5/4)/x^2,x]","-\frac{9 \sqrt[4]{2 \sqrt{x}-1}}{2 \sqrt{x}}+\frac{\sqrt[4]{2 \sqrt{x}-1}}{x}-\frac{5 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{2 \sqrt{x}-1}}{\sqrt{2 \sqrt{x}-1}-1}\right)}{2 \sqrt{2}}+\frac{5 \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{2 \sqrt{x}-1}}{\sqrt{2 \sqrt{x}-1}+1}\right)}{2 \sqrt{2}}","-\frac{\left(2 \sqrt{x}-1\right)^{5/4}}{x}-\frac{5 \sqrt[4]{2 \sqrt{x}-1}}{2 \sqrt{x}}-\frac{5 \log \left(\sqrt{2 \sqrt{x}-1}-\sqrt{2} \sqrt[4]{2 \sqrt{x}-1}+1\right)}{4 \sqrt{2}}+\frac{5 \log \left(\sqrt{2 \sqrt{x}-1}+\sqrt{2} \sqrt[4]{2 \sqrt{x}-1}+1\right)}{4 \sqrt{2}}-\frac{5 \tan ^{-1}\left(1-\sqrt{2} \sqrt[4]{2 \sqrt{x}-1}\right)}{2 \sqrt{2}}+\frac{5 \tan ^{-1}\left(\sqrt{2} \sqrt[4]{2 \sqrt{x}-1}+1\right)}{2 \sqrt{2}}",1,"(-1 + 2*Sqrt[x])^(1/4)/x - (9*(-1 + 2*Sqrt[x])^(1/4))/(2*Sqrt[x]) - (5*ArcTan[(Sqrt[2]*(-1 + 2*Sqrt[x])^(1/4))/(-1 + Sqrt[-1 + 2*Sqrt[x]])])/(2*Sqrt[2]) + (5*ArcTanh[(Sqrt[2]*(-1 + 2*Sqrt[x])^(1/4))/(1 + Sqrt[-1 + 2*Sqrt[x]])])/(2*Sqrt[2])","A",1
299,1,13,13,0.0186811,"\int x^6 \sqrt[3]{1+x^7} \, dx","IntegrateAlgebraic[x^6*(1 + x^7)^(1/3),x]","\frac{3}{28} \left(x^7+1\right)^{4/3}","\frac{3}{28} \left(x^7+1\right)^{4/3}",1,"(3*(1 + x^7)^(4/3))/28","A",1
300,1,13,13,0.033613,"\int \frac{x^6}{\left(1+x^7\right)^{5/3}} \, dx","IntegrateAlgebraic[x^6/(1 + x^7)^(5/3),x]","-\frac{3}{14 \left(x^7+1\right)^{2/3}}","-\frac{3}{14 \left(x^7+1\right)^{2/3}}",1,"-3/(14*(1 + x^7)^(2/3))","A",1
301,1,86,59,0.0751188,"\int \frac{1}{x \left(-27+2 x^7\right)^{2/3}} \, dx","IntegrateAlgebraic[1/(x*(-27 + 2*x^7)^(2/3)),x]","\frac{1}{63} \log \left(\sqrt[3]{2 x^7-27}+3\right)-\frac{1}{126} \log \left(\left(2 x^7-27\right)^{2/3}-3 \sqrt[3]{2 x^7-27}+9\right)-\frac{\tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{2 x^7-27}}{3 \sqrt{3}}\right)}{21 \sqrt{3}}","\frac{1}{42} \log \left(\sqrt[3]{2 x^7-27}+3\right)-\frac{\tan ^{-1}\left(\frac{3-2 \sqrt[3]{2 x^7-27}}{3 \sqrt{3}}\right)}{21 \sqrt{3}}-\frac{\log (x)}{18}",1,"-1/21*ArcTan[1/Sqrt[3] - (2*(-27 + 2*x^7)^(1/3))/(3*Sqrt[3])]/Sqrt[3] + Log[3 + (-27 + 2*x^7)^(1/3)]/63 - Log[9 - 3*(-27 + 2*x^7)^(1/3) + (-27 + 2*x^7)^(2/3)]/126","A",1
302,1,90,70,0.0897134,"\int \frac{\left(1+x^7\right)^{2/3}}{x^8} \, dx","IntegrateAlgebraic[(1 + x^7)^(2/3)/x^8,x]","-\frac{\left(x^7+1\right)^{2/3}}{7 x^7}+\frac{2}{21} \log \left(\sqrt[3]{x^7+1}-1\right)-\frac{1}{21} \log \left(\left(x^7+1\right)^{2/3}+\sqrt[3]{x^7+1}+1\right)+\frac{2 \tan ^{-1}\left(\frac{2 \sqrt[3]{x^7+1}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{7 \sqrt{3}}","-\frac{\left(x^7+1\right)^{2/3}}{7 x^7}+\frac{1}{7} \log \left(1-\sqrt[3]{x^7+1}\right)+\frac{2 \tan ^{-1}\left(\frac{2 \sqrt[3]{x^7+1}+1}{\sqrt{3}}\right)}{7 \sqrt{3}}-\frac{\log (x)}{3}",1,"-1/7*(1 + x^7)^(2/3)/x^7 + (2*ArcTan[1/Sqrt[3] + (2*(1 + x^7)^(1/3))/Sqrt[3]])/(7*Sqrt[3]) + (2*Log[-1 + (1 + x^7)^(1/3)])/21 - Log[1 + (1 + x^7)^(1/3) + (1 + x^7)^(2/3)]/21","A",1
303,1,68,68,0.1556049,"\int \frac{\sqrt[4]{3+4 x^4}}{x^2} \, dx","IntegrateAlgebraic[(3 + 4*x^4)^(1/4)/x^2,x]","-\frac{\sqrt[4]{4 x^4+3}}{x}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt[4]{4 x^4+3}}\right)}{\sqrt{2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt[4]{4 x^4+3}}\right)}{\sqrt{2}}","-\frac{\sqrt[4]{4 x^4+3}}{x}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt[4]{4 x^4+3}}\right)}{\sqrt{2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt[4]{4 x^4+3}}\right)}{\sqrt{2}}",1,"-((3 + 4*x^4)^(1/4)/x) - ArcTan[(Sqrt[2]*x)/(3 + 4*x^4)^(1/4)]/Sqrt[2] + ArcTanh[(Sqrt[2]*x)/(3 + 4*x^4)^(1/4)]/Sqrt[2]","A",1
304,1,83,93,0.1762769,"\int x^2 \left(3+4 x^4\right)^{5/4} \, dx","IntegrateAlgebraic[x^2*(3 + 4*x^4)^(5/4),x]","-\frac{45 \tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt[4]{4 x^4+3}}\right)}{128 \sqrt{2}}+\frac{45 \tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt[4]{4 x^4+3}}\right)}{128 \sqrt{2}}+\frac{1}{32} \sqrt[4]{4 x^4+3} \left(16 x^7+27 x^3\right)","-\frac{45 \tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt[4]{4 x^4+3}}\right)}{128 \sqrt{2}}+\frac{45 \tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt[4]{4 x^4+3}}\right)}{128 \sqrt{2}}+\frac{1}{8} \left(4 x^4+3\right)^{5/4} x^3+\frac{15}{32} \sqrt[4]{4 x^4+3} x^3",1,"((3 + 4*x^4)^(1/4)*(27*x^3 + 16*x^7))/32 - (45*ArcTan[(Sqrt[2]*x)/(3 + 4*x^4)^(1/4)])/(128*Sqrt[2]) + (45*ArcTanh[(Sqrt[2]*x)/(3 + 4*x^4)^(1/4)])/(128*Sqrt[2])","A",1
305,1,83,93,0.1756508,"\int x^6 \sqrt[4]{3+4 x^4} \, dx","IntegrateAlgebraic[x^6*(3 + 4*x^4)^(1/4),x]","\frac{27 \tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt[4]{4 x^4+3}}\right)}{512 \sqrt{2}}-\frac{27 \tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt[4]{4 x^4+3}}\right)}{512 \sqrt{2}}+\frac{1}{128} \sqrt[4]{4 x^4+3} \left(16 x^7+3 x^3\right)","\frac{27 \tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt[4]{4 x^4+3}}\right)}{512 \sqrt{2}}-\frac{27 \tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt[4]{4 x^4+3}}\right)}{512 \sqrt{2}}+\frac{1}{8} \sqrt[4]{4 x^4+3} x^7+\frac{3}{128} \sqrt[4]{4 x^4+3} x^3",1,"((3 + 4*x^4)^(1/4)*(3*x^3 + 16*x^7))/128 + (27*ArcTan[(Sqrt[2]*x)/(3 + 4*x^4)^(1/4)])/(512*Sqrt[2]) - (27*ArcTanh[(Sqrt[2]*x)/(3 + 4*x^4)^(1/4)])/(512*Sqrt[2])","A",1
306,1,105,93,0.1462622,"\int \sqrt[3]{x \left(1-x^2\right)} \, dx","IntegrateAlgebraic[(x*(1 - x^2))^(1/3),x]","\frac{1}{2} \sqrt[3]{x-x^3} x-\frac{1}{6} \log \left(\sqrt[3]{x-x^3}+x\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x-x^3}-x}\right)}{2 \sqrt{3}}+\frac{1}{12} \log \left(-\sqrt[3]{x-x^3} x+\left(x-x^3\right)^{2/3}+x^2\right)","\frac{1}{2} \sqrt[3]{x \left(1-x^2\right)} x-\frac{1}{4} \log \left(\sqrt[3]{x \left(1-x^2\right)}+x\right)+\frac{\tan ^{-1}\left(\frac{2 x-\sqrt[3]{x \left(1-x^2\right)}}{\sqrt{3} \sqrt[3]{x \left(1-x^2\right)}}\right)}{2 \sqrt{3}}+\frac{\log (x)}{12}",1,"(x*(x - x^3)^(1/3))/2 + ArcTan[(Sqrt[3]*x)/(-x + 2*(x - x^3)^(1/3))]/(2*Sqrt[3]) - Log[x + (x - x^3)^(1/3)]/6 + Log[x^2 - x*(x - x^3)^(1/3) + (x - x^3)^(2/3)]/12","A",1
307,1,69,126,0.5004277,"\int \sqrt{\left(1+\sqrt[3]{x}\right) x} \, dx","IntegrateAlgebraic[Sqrt[(1 + x^(1/3))*x],x]","\frac{\sqrt{x^{4/3}+x} \left(384 x^{4/3}-56 x^{2/3}+48 x+70 \sqrt[3]{x}-105\right)}{640 \sqrt[3]{x}}+\frac{21}{128} \tanh ^{-1}\left(\frac{x^{2/3}}{\sqrt{x^{4/3}+x}}\right)","\frac{3}{40} \sqrt{\left(\sqrt[3]{x}+1\right) x} x^{2/3}+\frac{21}{128} \tanh ^{-1}\left(\frac{x^{2/3}}{\sqrt{\left(\sqrt[3]{x}+1\right) x}}\right)+\frac{3}{5} \sqrt{\left(\sqrt[3]{x}+1\right) x} x-\frac{7}{80} \sqrt{\left(\sqrt[3]{x}+1\right) x} \sqrt[3]{x}+\frac{7}{64} \sqrt{\left(\sqrt[3]{x}+1\right) x}-\frac{21 \sqrt{\left(\sqrt[3]{x}+1\right) x}}{128 \sqrt[3]{x}}",1,"(Sqrt[x + x^(4/3)]*(-105 + 70*x^(1/3) - 56*x^(2/3) + 48*x + 384*x^(4/3)))/(640*x^(1/3)) + (21*ArcTanh[x^(2/3)/Sqrt[x + x^(4/3)]])/128","A",1
308,1,48,34,0.4152869,"\int \frac{x^3}{\left(-1+x^4\right) \sqrt{1+2 x^8}} \, dx","IntegrateAlgebraic[x^3/((-1 + x^4)*Sqrt[1 + 2*x^8]),x]","\frac{\tanh ^{-1}\left(-\frac{\sqrt{2 x^8+1}}{\sqrt{3}}-\sqrt{\frac{2}{3}} x^4+\sqrt{\frac{2}{3}}\right)}{2 \sqrt{3}}","-\frac{\tanh ^{-1}\left(\frac{2 x^4+1}{\sqrt{3} \sqrt{2 x^8+1}}\right)}{4 \sqrt{3}}",1,"ArcTanh[Sqrt[2/3] - Sqrt[2/3]*x^4 - Sqrt[1 + 2*x^8]/Sqrt[3]]/(2*Sqrt[3])","A",1
309,1,55,58,0.1272773,"\int x^9 \sqrt{1+x^5+x^{10}} \, dx","IntegrateAlgebraic[x^9*Sqrt[1 + x^5 + x^10],x]","\frac{1}{120} \sqrt{x^{10}+x^5+1} \left(8 x^{10}+2 x^5+5\right)+\frac{3}{80} \log \left(-2 x^5+2 \sqrt{x^{10}+x^5+1}-1\right)","-\frac{3}{80} \sinh ^{-1}\left(\frac{2 x^5+1}{\sqrt{3}}\right)+\frac{1}{15} \left(x^{10}+x^5+1\right)^{3/2}-\frac{1}{40} \left(2 x^5+1\right) \sqrt{x^{10}+x^5+1}",1,"(Sqrt[1 + x^5 + x^10]*(5 + 2*x^5 + 8*x^10))/120 + (3*Log[-1 - 2*x^5 + 2*Sqrt[1 + x^5 + x^10]])/80","A",1
310,1,60,71,0.2087431,"\int \frac{1}{x^5 \sqrt{4+2 x^2+x^4}} \, dx","IntegrateAlgebraic[1/(x^5*Sqrt[4 + 2*x^2 + x^4]),x]","\frac{\left(3 x^2-4\right) \sqrt{x^4+2 x^2+4}}{64 x^4}-\frac{1}{64} \tanh ^{-1}\left(\frac{x^2}{2}-\frac{1}{2} \sqrt{x^4+2 x^2+4}\right)","\frac{3 \sqrt{x^4+2 x^2+4}}{64 x^2}-\frac{\sqrt{x^4+2 x^2+4}}{16 x^4}+\frac{1}{128} \tanh ^{-1}\left(\frac{x^2+4}{2 \sqrt{x^4+2 x^2+4}}\right)",1,"((-4 + 3*x^2)*Sqrt[4 + 2*x^2 + x^4])/(64*x^4) - ArcTanh[x^2/2 - Sqrt[4 + 2*x^2 + x^4]/2]/64","A",1
311,1,52,21,0.227718,"\int \frac{-1+x^2}{x \sqrt{1+3 x^2+x^4}} \, dx","IntegrateAlgebraic[(-1 + x^2)/(x*Sqrt[1 + 3*x^2 + x^4]),x]","-\frac{1}{2} \log \left(-2 x^2+2 \sqrt{x^4+3 x^2+1}-3\right)-\tanh ^{-1}\left(x^2-\sqrt{x^4+3 x^2+1}\right)","\tanh ^{-1}\left(\frac{x^2+1}{\sqrt{x^4+3 x^2+1}}\right)",1,"-ArcTanh[x^2 - Sqrt[1 + 3*x^2 + x^4]] - Log[-3 - 2*x^2 + 2*Sqrt[1 + 3*x^2 + x^4]]/2","B",1
312,1,17,17,0.0208757,"\int \left(-3 x+2 x^3\right) \left(-3 x^2+x^4\right)^{3/5} \, dx","IntegrateAlgebraic[(-3*x + 2*x^3)*(-3*x^2 + x^4)^(3/5),x]","\frac{5}{16} \left(x^4-3 x^2\right)^{8/5}","\frac{5}{16} \left(x^4-3 x^2\right)^{8/5}",1,"(5*(-3*x^2 + x^4)^(8/5))/16","A",1
313,1,43,46,0.0374933,"\int \frac{-2 x^5+3 x^8-x^2 \left(-1+3 x^3\right)^{2/3}}{\left(-1+3 x^3\right)^{3/4}} \, dx","IntegrateAlgebraic[(-2*x^5 + 3*x^8 - x^2*(-1 + 3*x^3)^(2/3))/(-1 + 3*x^3)^(3/4),x]","\frac{4}{243} \sqrt[4]{3 x^3-1} \left(9 x^6-6 x^3-8\right)-\frac{4}{33} \left(3 x^3-1\right)^{11/12}","\frac{4}{243} \left(3 x^3-1\right)^{9/4}-\frac{4}{33} \left(3 x^3-1\right)^{11/12}-\frac{4}{27} \sqrt[4]{3 x^3-1}",1,"(-4*(-1 + 3*x^3)^(11/12))/33 + (4*(-1 + 3*x^3)^(1/4)*(-8 - 6*x^3 + 9*x^6))/243","A",1
314,1,113,78,0.2395951,"\int \frac{1}{\left(-1+x^3\right) \sqrt[3]{2+x^3}} \, dx","IntegrateAlgebraic[1/((-1 + x^3)*(2 + x^3)^(1/3)),x]","\frac{\log \left(3^{2/3} \sqrt[3]{x^3+2}-3 x\right)}{3 \sqrt[3]{3}}-\frac{\tan ^{-1}\left(\frac{3^{5/6} x}{2 \sqrt[3]{x^3+2}+\sqrt[3]{3} x}\right)}{3^{5/6}}-\frac{\log \left(3^{2/3} \sqrt[3]{x^3+2} x+\sqrt[3]{3} \left(x^3+2\right)^{2/3}+3 x^2\right)}{6 \sqrt[3]{3}}","-\frac{\log \left(x^3-1\right)}{6 \sqrt[3]{3}}+\frac{\log \left(\sqrt[3]{3} x-\sqrt[3]{x^3+2}\right)}{2 \sqrt[3]{3}}-\frac{\tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{3} x}{\sqrt[3]{x^3+2}}+1}{\sqrt{3}}\right)}{3^{5/6}}",1,"-(ArcTan[(3^(5/6)*x)/(3^(1/3)*x + 2*(2 + x^3)^(1/3))]/3^(5/6)) + Log[-3*x + 3^(2/3)*(2 + x^3)^(1/3)]/(3*3^(1/3)) - Log[3*x^2 + 3^(2/3)*x*(2 + x^3)^(1/3) + 3^(1/3)*(2 + x^3)^(2/3)]/(6*3^(1/3))","A",1
315,1,85,141,0.2140998,"\int \frac{1}{\left(1+x^4\right) \sqrt[4]{2+x^4}} \, dx","IntegrateAlgebraic[1/((1 + x^4)*(2 + x^4)^(1/4)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{x^4+2}}{\sqrt{x^4+2}-x^2}\right)}{2 \sqrt{2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{x^4+2}}{\sqrt{x^4+2}+x^2}\right)}{2 \sqrt{2}}","-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} x}{\sqrt[4]{x^4+2}}\right)}{2 \sqrt{2}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt[4]{x^4+2}}+1\right)}{2 \sqrt{2}}-\frac{\log \left(-\frac{\sqrt{2} x}{\sqrt[4]{x^4+2}}+\frac{x^2}{\sqrt{x^4+2}}+1\right)}{4 \sqrt{2}}+\frac{\log \left(\frac{\sqrt{2} x}{\sqrt[4]{x^4+2}}+\frac{x^2}{\sqrt{x^4+2}}+1\right)}{4 \sqrt{2}}",1,"ArcTan[(Sqrt[2]*x*(2 + x^4)^(1/4))/(-x^2 + Sqrt[2 + x^4])]/(2*Sqrt[2]) + ArcTanh[(Sqrt[2]*x*(2 + x^4)^(1/4))/(x^2 + Sqrt[2 + x^4])]/(2*Sqrt[2])","A",1
316,1,94,63,0.1518959,"\int \frac{-1+x^3}{\sqrt[3]{2+x^3}} \, dx","IntegrateAlgebraic[(-1 + x^3)/(2 + x^3)^(1/3),x]","\frac{1}{3} \left(x^3+2\right)^{2/3} x+\frac{5}{9} \log \left(\sqrt[3]{x^3+2}-x\right)-\frac{5 \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+2}+x}\right)}{3 \sqrt{3}}-\frac{5}{18} \log \left(\sqrt[3]{x^3+2} x+\left(x^3+2\right)^{2/3}+x^2\right)","\frac{1}{3} \left(x^3+2\right)^{2/3} x+\frac{5}{6} \log \left(\sqrt[3]{x^3+2}-x\right)-\frac{5 \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3+2}}+1}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"(x*(2 + x^3)^(2/3))/3 - (5*ArcTan[(Sqrt[3]*x)/(x + 2*(2 + x^3)^(1/3))])/(3*Sqrt[3]) + (5*Log[-x + (2 + x^3)^(1/3)])/9 - (5*Log[x^2 + x*(2 + x^3)^(1/3) + (2 + x^3)^(2/3)])/18","A",1
317,1,74,74,0.2186659,"\int \frac{\left(1+x^4\right)^{3/4}}{\left(2+x^4\right)^2} \, dx","IntegrateAlgebraic[(1 + x^4)^(3/4)/(2 + x^4)^2,x]","\frac{\left(x^4+1\right)^{3/4} x}{8 \left(x^4+2\right)}+\frac{3 \tan ^{-1}\left(\frac{x}{\sqrt[4]{2} \sqrt[4]{x^4+1}}\right)}{16\ 2^{3/4}}+\frac{3 \tanh ^{-1}\left(\frac{x}{\sqrt[4]{2} \sqrt[4]{x^4+1}}\right)}{16\ 2^{3/4}}","\frac{\left(x^4+1\right)^{3/4} x}{8 \left(x^4+2\right)}+\frac{3 \tan ^{-1}\left(\frac{x}{\sqrt[4]{2} \sqrt[4]{x^4+1}}\right)}{16\ 2^{3/4}}+\frac{3 \tanh ^{-1}\left(\frac{x}{\sqrt[4]{2} \sqrt[4]{x^4+1}}\right)}{16\ 2^{3/4}}",1,"(x*(1 + x^4)^(3/4))/(8*(2 + x^4)) + (3*ArcTan[x/(2^(1/4)*(1 + x^4)^(1/4))])/(16*2^(3/4)) + (3*ArcTanh[x/(2^(1/4)*(1 + x^4)^(1/4))])/(16*2^(3/4))","A",1
318,1,27,48,1.1249567,"\int \frac{\left(-2+x^5\right)^2}{\left(3+x^5\right)^{16/5}} \, dx","IntegrateAlgebraic[(-2 + x^5)^2/(3 + x^5)^(16/5),x]","\frac{97 x^{11}+462 x^6+1188 x}{891 \left(x^5+3\right)^{11/5}}","\frac{97 x}{891 \sqrt[5]{x^5+3}}+\frac{5 x}{297 \left(x^5+3\right)^{6/5}}-\frac{5 \left(x^5-2\right) x}{33 \left(x^5+3\right)^{11/5}}",1,"(1188*x + 462*x^6 + 97*x^11)/(891*(3 + x^5)^(11/5))","A",1
319,1,189,90,0.3827151,"\int \frac{1}{\left(3 x+3 x^2+x^3\right) \sqrt[3]{3+3 x+3 x^2+x^3}} \, dx","IntegrateAlgebraic[1/((3*x + 3*x^2 + x^3)*(3 + 3*x + 3*x^2 + x^3)^(1/3)),x]","\frac{\log \left(-\sqrt[3]{x^3+3 x^2+3 x+3}+\sqrt[3]{3} x+\sqrt[3]{3}\right)}{3 \sqrt[3]{3}}-\frac{\log \left(3^{2/3} x^2+\left(x^3+3 x^2+3 x+3\right)^{2/3}+\left(\sqrt[3]{3} x+\sqrt[3]{3}\right) \sqrt[3]{x^3+3 x^2+3 x+3}+2\ 3^{2/3} x+3^{2/3}\right)}{6 \sqrt[3]{3}}+\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x^3+3 x^2+3 x+3}}{\sqrt[3]{x^3+3 x^2+3 x+3}+2 \sqrt[3]{3} x+2 \sqrt[3]{3}}\right)}{3^{5/6}}","-\frac{\log \left(1-(x+1)^3\right)}{6 \sqrt[3]{3}}+\frac{\log \left(\sqrt[3]{3} (x+1)-\sqrt[3]{(x+1)^3+2}\right)}{2 \sqrt[3]{3}}-\frac{\tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{3} (x+1)}{\sqrt[3]{(x+1)^3+2}}+1}{\sqrt{3}}\right)}{3^{5/6}}",1,"ArcTan[(Sqrt[3]*(3 + 3*x + 3*x^2 + x^3)^(1/3))/(2*3^(1/3) + 2*3^(1/3)*x + (3 + 3*x + 3*x^2 + x^3)^(1/3))]/3^(5/6) + Log[3^(1/3) + 3^(1/3)*x - (3 + 3*x + 3*x^2 + x^3)^(1/3)]/(3*3^(1/3)) - Log[3^(2/3) + 2*3^(2/3)*x + 3^(2/3)*x^2 + (3^(1/3) + 3^(1/3)*x)*(3 + 3*x + 3*x^2 + x^3)^(1/3) + (3 + 3*x + 3*x^2 + x^3)^(2/3)]/(6*3^(1/3))","B",1
320,1,23,23,0.0001177,"\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
321,1,23,23,0.0001145,"\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
322,1,35,16,0.1883457,"\int \frac{1+x^2}{x \sqrt{1+x^4}} \, dx","IntegrateAlgebraic[(1 + x^2)/(x*Sqrt[1 + x^4]),x]","\frac{1}{2} \log \left(\sqrt{x^4+1}+x^2\right)-\tanh ^{-1}\left(\sqrt{x^4+1}+x^2\right)","\tanh ^{-1}\left(\frac{x^2-1}{\sqrt{x^4+1}}\right)",1,"-ArcTanh[x^2 + Sqrt[1 + x^4]] + Log[x^2 + Sqrt[1 + x^4]]/2","B",1
323,1,41,16,0.1882923,"\int \frac{-1+x^2}{x \sqrt{1+x^4}} \, dx","IntegrateAlgebraic[(-1 + x^2)/(x*Sqrt[1 + x^4]),x]","\frac{1}{2} \log \left(\sqrt{x^4+1}+x^2+1\right)-\tanh ^{-1}\left(-2 \sqrt{x^4+1}-2 x^2+1\right)","\tanh ^{-1}\left(\frac{x^2+1}{\sqrt{x^4+1}}\right)",1,"-ArcTanh[1 - 2*x^2 - 2*Sqrt[1 + x^4]] + Log[1 + x^2 + Sqrt[1 + x^4]]/2","B",1
324,1,26,26,0.2093295,"\int \frac{1+x^2}{\left(1-x^2\right) \sqrt{1+x^2+x^4}} \, dx","IntegrateAlgebraic[(1 + x^2)/((1 - x^2)*Sqrt[1 + x^2 + x^4]),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{3} x}{\sqrt{x^4+x^2+1}}\right)}{\sqrt{3}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{3} x}{\sqrt{x^4+x^2+1}}\right)}{\sqrt{3}}",1,"ArcTanh[(Sqrt[3]*x)/Sqrt[1 + x^2 + x^4]]/Sqrt[3]","A",1
325,1,15,15,0.1703271,"\int \frac{1-x^2}{\left(1+x^2\right) \sqrt{1+x^2+x^4}} \, dx","IntegrateAlgebraic[(1 - x^2)/((1 + x^2)*Sqrt[1 + x^2 + x^4]),x]","\tan ^{-1}\left(\frac{x}{\sqrt{x^4+x^2+1}}\right)","\tan ^{-1}\left(\frac{x}{\sqrt{x^4+x^2+1}}\right)",1,"ArcTan[x/Sqrt[1 + x^2 + x^4]]","A",1
326,1,16,16,0.7961703,"\int \frac{-1+x^4}{x^2 \sqrt{1+x^2+x^4}} \, dx","IntegrateAlgebraic[(-1 + x^4)/(x^2*Sqrt[1 + x^2 + x^4]),x]","\frac{\sqrt{x^4+x^2+1}}{x}","\frac{\sqrt{x^4+x^2+1}}{x}",1,"Sqrt[1 + x^2 + x^4]/x","A",1
327,1,67,74,0.67248,"\int \frac{1-x^2}{\left(1+2 a x+x^2\right) \sqrt{1+2 a x+2 b x^2+2 a x^3+x^4}} \, dx","IntegrateAlgebraic[(1 - x^2)/((1 + 2*a*x + x^2)*Sqrt[1 + 2*a*x + 2*b*x^2 + 2*a*x^3 + x^4]),x]","-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{b-1} x}{-\sqrt{2 a x^3+2 a x+2 b x^2+x^4+1}+2 a x+x^2+1}\right)}{\sqrt{b-1}}","\frac{\tan ^{-1}\left(\frac{2 x \left(a^2-b+1\right)+a x^2+a}{\sqrt{2} \sqrt{1-b} \sqrt{2 a x^3+2 a x+2 b x^2+x^4+1}}\right)}{\sqrt{2} \sqrt{1-b}}",1,"-((Sqrt[2]*ArcTanh[(Sqrt[2]*Sqrt[-1 + b]*x)/(1 + 2*a*x + x^2 - Sqrt[1 + 2*a*x + 2*b*x^2 + 2*a*x^3 + x^4])])/Sqrt[-1 + b])","A",1
328,1,96,22,0.2598894,"\int \frac{1}{\left(1+x^4\right) \sqrt{-x^2+\sqrt{1+x^4}}} \, dx","IntegrateAlgebraic[1/((1 + x^4)*Sqrt[-x^2 + Sqrt[1 + x^4]]),x]","i \tanh ^{-1}\left(\sqrt{2} x^4+\frac{\sqrt{x^4+1} \left(-2 x^2+i \sqrt{2} x \sqrt{\sqrt{x^4+1}-x^2}\right)}{\sqrt{2}}-i \sqrt{\sqrt{x^4+1}-x^2} x^3+\sqrt{2}\right)","\tan ^{-1}\left(\frac{x}{\sqrt{\sqrt{x^4+1}-x^2}}\right)",1,"I*ArcTanh[Sqrt[2] + Sqrt[2]*x^4 - I*x^3*Sqrt[-x^2 + Sqrt[1 + x^4]] + (Sqrt[1 + x^4]*(-2*x^2 + I*Sqrt[2]*x*Sqrt[-x^2 + Sqrt[1 + x^4]]))/Sqrt[2]]","C",1
329,0,0,24,0.0000762,"\int \frac{1}{\left(1+x^{2 n}\right) \sqrt{-x^2+\left(1+x^{2 n}\right)^{\frac{1}{n}}}} \, dx","IntegrateAlgebraic[1/((1 + x^(2*n))*Sqrt[-x^2 + (1 + x^(2*n))^n^(-1)]),x]","\int \frac{1}{\left(1+x^{2 n}\right) \sqrt{-x^2+\left(1+x^{2 n}\right)^{\frac{1}{n}}}} \, dx","\tan ^{-1}\left(\frac{x}{\sqrt{\left(x^{2 n}+1\right)^{\frac{1}{n}}-x^2}}\right)",1,"Could not integrate","F",-1
330,0,0,14,0.0000308,"\int \cos ^2(x) \, dx","IntegrateAlgebraic[Cos[x]^2,x]","\int \cos ^2(x) \, dx","\frac{x}{2}+\frac{1}{2} \sin (x) \cos (x)",1,"Could not integrate","F",-1
331,0,0,11,0.0000252,"\int \cos ^3(x) \, dx","IntegrateAlgebraic[Cos[x]^3,x]","\int \cos ^3(x) \, dx","\sin (x)-\frac{\sin ^3(x)}{3}",1,"Could not integrate","F",-1
332,0,0,24,0.0000325,"\int \sin ^4(x) \, dx","IntegrateAlgebraic[Sin[x]^4,x]","\int \sin ^4(x) \, dx","\frac{3 x}{8}-\frac{1}{4} \sin ^3(x) \cos (x)-\frac{3}{8} \sin (x) \cos (x)",1,"Could not integrate","F",-1
333,0,0,34,0.00003,"\int \cos ^6(x) \, dx","IntegrateAlgebraic[Cos[x]^6,x]","\int \cos ^6(x) \, dx","\frac{5 x}{16}+\frac{1}{6} \sin (x) \cos ^5(x)+\frac{5}{24} \sin (x) \cos ^3(x)+\frac{5}{16} \sin (x) \cos (x)",1,"Could not integrate","F",-1
334,0,0,44,0.0000302,"\int \sin ^8(x) \, dx","IntegrateAlgebraic[Sin[x]^8,x]","\int \sin ^8(x) \, dx","\frac{35 x}{128}-\frac{1}{8} \sin ^7(x) \cos (x)-\frac{7}{48} \sin ^5(x) \cos (x)-\frac{35}{192} \sin ^3(x) \cos (x)-\frac{35}{128} \sin (x) \cos (x)",1,"Could not integrate","F",-1
335,0,0,20,0.0000458,"\int \cos ^4\left(\frac{\pi }{4}+\frac{x}{2}\right) \, dx","IntegrateAlgebraic[Cos[Pi/4 + x/2]^4,x]","\int \cos ^4\left(\frac{\pi }{4}+\frac{x}{2}\right) \, dx","\frac{3 x}{8}+\frac{\cos (x)}{2}-\frac{1}{8} \sin (x) \cos (x)",1,"Could not integrate","F",-1
336,0,0,31,0.0000327,"\int -\sin ^3\left(\frac{\pi }{12}-3 x\right) \, dx","IntegrateAlgebraic[-Sin[Pi/12 - 3*x]^3,x]","\int -\sin ^3\left(\frac{\pi }{12}-3 x\right) \, dx","\frac{1}{9} \cos ^3\left(\frac{\pi }{12}-3 x\right)-\frac{1}{3} \cos \left(\frac{\pi }{12}-3 x\right)",1,"Could not integrate","F",-1
337,0,0,21,0.000031,"\int \csc ^6(x) \, dx","IntegrateAlgebraic[Csc[x]^6,x]","\int \csc ^6(x) \, dx","-\frac{1}{5} \cot ^5(x)-\frac{2 \cot ^3(x)}{3}-\cot (x)",1,"Could not integrate","F",-1
338,0,0,36,0.0000269,"\int \csc ^7(x) \, dx","IntegrateAlgebraic[Csc[x]^7,x]","\int \csc ^7(x) \, dx","-\frac{5}{16} \tanh ^{-1}(\cos (x))-\frac{1}{6} \cot (x) \csc ^5(x)-\frac{5}{24} \cot (x) \csc ^3(x)-\frac{5}{16} \cot (x) \csc (x)",1,"Could not integrate","F",-1
339,0,0,41,0.0000364,"\int \sec ^{12}(x) \, dx","IntegrateAlgebraic[Sec[x]^12,x]","\int \sec ^{12}(x) \, dx","\frac{\tan ^{11}(x)}{11}+\frac{5 \tan ^9(x)}{9}+\frac{10 \tan ^7(x)}{7}+2 \tan ^5(x)+\frac{5 \tan ^3(x)}{3}+\tan (x)",1,"Could not integrate","F",-1
340,0,0,40,0.000033,"\int \sec ^3\left(\frac{\pi }{4}+3 x\right) \, dx","IntegrateAlgebraic[Sec[Pi/4 + 3*x]^3,x]","\int \sec ^3\left(\frac{\pi }{4}+3 x\right) \, dx","\frac{1}{6} \tanh ^{-1}\left(\sin \left(3 x+\frac{\pi }{4}\right)\right)+\frac{1}{6} \tan \left(3 x+\frac{\pi }{4}\right) \sec \left(3 x+\frac{\pi }{4}\right)",1,"Could not integrate","F",-1
341,0,0,22,0.0000311,"\int \tan ^6(x) \, dx","IntegrateAlgebraic[Tan[x]^6,x]","\int \tan ^6(x) \, dx","-x+\frac{\tan ^5(x)}{5}-\frac{\tan ^3(x)}{3}+\tan (x)",1,"Could not integrate","F",-1
342,0,0,20,0.000028,"\int \cot ^5(x) \, dx","IntegrateAlgebraic[Cot[x]^5,x]","\int \cot ^5(x) \, dx","-\frac{1}{4} \cot ^4(x)+\frac{\cot ^2(x)}{2}+\log (\sin (x))",1,"Could not integrate","F",-1
343,0,0,32,0.0000353,"\int \cot ^4\left(\frac{\pi }{4}+\frac{x}{3}\right) \, dx","IntegrateAlgebraic[Cot[Pi/4 + x/3]^4,x]","\int \cot ^4\left(\frac{\pi }{4}+\frac{x}{3}\right) \, dx","x-\cot ^3\left(\frac{x}{3}+\frac{\pi }{4}\right)+3 \cot \left(\frac{x}{3}+\frac{\pi }{4}\right)",1,"Could not integrate","F",-1
344,0,0,56,0.0000344,"\int \cos ^6(x) \sin ^4(x) \, dx","IntegrateAlgebraic[Cos[x]^6*Sin[x]^4,x]","\int \cos ^6(x) \sin ^4(x) \, dx","\frac{3 x}{256}-\frac{1}{10} \sin ^3(x) \cos ^7(x)-\frac{3}{80} \sin (x) \cos ^7(x)+\frac{1}{160} \sin (x) \cos ^5(x)+\frac{1}{128} \sin (x) \cos ^3(x)+\frac{3}{256} \sin (x) \cos (x)",1,"Could not integrate","F",-1
345,0,0,33,0.0000859,"\int \cos ^6(x) \sin ^7(x) \, dx","IntegrateAlgebraic[Cos[x]^6*Sin[x]^7,x]","\int \cos ^6(x) \sin ^7(x) \, dx","\frac{\cos ^{13}(x)}{13}-\frac{3 \cos ^{11}(x)}{11}+\frac{\cos ^9(x)}{3}-\frac{\cos ^7(x)}{7}",1,"Could not integrate","F",-1
346,0,0,46,0.0000353,"\int \sin ^{10}(x) \tan (x) \, dx","IntegrateAlgebraic[Sin[x]^10*Tan[x],x]","\int \sin ^{10}(x) \tan (x) \, dx","\frac{\cos ^{10}(x)}{10}-\frac{5 \cos ^8(x)}{8}+\frac{5 \cos ^6(x)}{3}-\frac{5 \cos ^4(x)}{2}+\frac{5 \cos ^2(x)}{2}-\log (\cos (x))",1,"Could not integrate","F",-1
347,0,0,41,0.000052,"\int \csc ^6(x) \sec ^6(x) \, dx","IntegrateAlgebraic[Csc[x]^6*Sec[x]^6,x]","\int \csc ^6(x) \sec ^6(x) \, dx","\frac{\tan ^5(x)}{5}+\frac{5 \tan ^3(x)}{3}+10 \tan (x)-\frac{1}{5} \cot ^5(x)-\frac{5 \cot ^3(x)}{3}-10 \cot (x)",1,"Could not integrate","F",-1
348,0,0,24,0.0000385,"\int \cos ^2(x) \sin ^2(x) \, dx","IntegrateAlgebraic[Cos[x]^2*Sin[x]^2,x]","\int \cos ^2(x) \sin ^2(x) \, dx","\frac{x}{8}-\frac{1}{4} \sin (x) \cos ^3(x)+\frac{1}{8} \sin (x) \cos (x)",1,"Could not integrate","F",-1
349,0,0,46,0.0000316,"\int \cos ^4(x) \sin ^4(x) \, dx","IntegrateAlgebraic[Cos[x]^4*Sin[x]^4,x]","\int \cos ^4(x) \sin ^4(x) \, dx","\frac{3 x}{128}-\frac{1}{8} \sin ^3(x) \cos ^5(x)-\frac{1}{16} \sin (x) \cos ^5(x)+\frac{1}{64} \sin (x) \cos ^3(x)+\frac{3}{128} \sin (x) \cos (x)",1,"Could not integrate","F",-1
350,0,0,68,0.0000358,"\int \cos ^6(x) \sin ^6(x) \, dx","IntegrateAlgebraic[Cos[x]^6*Sin[x]^6,x]","\int \cos ^6(x) \sin ^6(x) \, dx","\frac{5 x}{1024}-\frac{1}{12} \sin ^5(x) \cos ^7(x)-\frac{1}{24} \sin ^3(x) \cos ^7(x)-\frac{1}{64} \sin (x) \cos ^7(x)+\frac{1}{384} \sin (x) \cos ^5(x)+\frac{5 \sin (x) \cos ^3(x)}{1536}+\frac{5 \sin (x) \cos (x)}{1024}",1,"Could not integrate","F",-1
351,0,0,90,0.0000402,"\int \cos ^8(x) \sin ^8(x) \, dx","IntegrateAlgebraic[Cos[x]^8*Sin[x]^8,x]","\int \cos ^8(x) \sin ^8(x) \, dx","\frac{35 x}{32768}-\frac{1}{16} \sin ^7(x) \cos ^9(x)-\frac{1}{32} \sin ^5(x) \cos ^9(x)-\frac{5}{384} \sin ^3(x) \cos ^9(x)-\frac{1}{256} \sin (x) \cos ^9(x)+\frac{\sin (x) \cos ^7(x)}{2048}+\frac{7 \sin (x) \cos ^5(x)}{12288}+\frac{35 \sin (x) \cos ^3(x)}{49152}+\frac{35 \sin (x) \cos (x)}{32768}",1,"Could not integrate","F",-1
352,0,0,68,0.0000483,"\int \cos ^{2 m}(x) \sin ^{2 m}(x) \, dx","IntegrateAlgebraic[Cos[x]^(2*m)*Sin[x]^(2*m),x]","\int \cos ^{2 m}(x) \sin ^{2 m}(x) \, dx","\frac{\sin ^{2 m+1}(x) \cos ^{2 m-1}(x) \cos ^2(x)^{\frac{1}{2}-m} \, _2F_1\left(\frac{1}{2} (1-2 m),\frac{1}{2} (2 m+1);\frac{1}{2} (2 m+3);\sin ^2(x)\right)}{2 m+1}",1,"Could not integrate","F",-1
353,0,0,32,0.0000457,"\int \csc ^3\left(\frac{\pi }{4}+2 x\right) \sec \left(\frac{\pi }{4}+2 x\right) \, dx","IntegrateAlgebraic[Csc[Pi/4 + 2*x]^3*Sec[Pi/4 + 2*x],x]","\int \csc ^3\left(\frac{\pi }{4}+2 x\right) \sec \left(\frac{\pi }{4}+2 x\right) \, dx","\frac{1}{2} \log \left(\tan \left(2 x+\frac{\pi }{4}\right)\right)-\frac{1}{4} \cot ^2\left(2 x+\frac{\pi }{4}\right)",1,"Could not integrate","F",-1
354,0,0,8,0.0000309,"\int \sec ^2(x) \tan ^2(x) \, dx","IntegrateAlgebraic[Sec[x]^2*Tan[x]^2,x]","\int \sec ^2(x) \tan ^2(x) \, dx","\frac{\tan ^3(x)}{3}",1,"Could not integrate","F",-1
355,0,0,11,0.0000301,"\int \cot ^3(x) \csc (x) \, dx","IntegrateAlgebraic[Cot[x]^3*Csc[x],x]","\int \cot ^3(x) \csc (x) \, dx","\csc (x)-\frac{\csc ^3(x)}{3}",1,"Could not integrate","F",-1
356,0,0,8,0.0000354,"\int \sec ^3(x) \tan (x) \, dx","IntegrateAlgebraic[Sec[x]^3*Tan[x],x]","\int \sec ^3(x) \tan (x) \, dx","\frac{\sec ^3(x)}{3}",1,"Could not integrate","F",-1
357,0,0,26,0.0000298,"\int \cot ^2(x) \csc ^3(x) \, dx","IntegrateAlgebraic[Cot[x]^2*Csc[x]^3,x]","\int \cot ^2(x) \csc ^3(x) \, dx","\frac{1}{8} \tanh ^{-1}(\cos (x))-\frac{1}{4} \cot (x) \csc ^3(x)+\frac{1}{8} \cot (x) \csc (x)",1,"Could not integrate","F",-1
358,0,0,17,0.0000353,"\int \cot ^3(x) \csc ^4(x) \, dx","IntegrateAlgebraic[Cot[x]^3*Csc[x]^4,x]","\int \cot ^3(x) \csc ^4(x) \, dx","\frac{\csc ^4(x)}{4}-\frac{\csc ^6(x)}{6}",1,"Could not integrate","F",-1
359,0,0,31,0.0000298,"\int \sec ^{\frac{13}{2}}(x) \sin ^5(x) \, dx","IntegrateAlgebraic[Sec[x]^(13/2)*Sin[x]^5,x]","\int \sec ^{\frac{13}{2}}(x) \sin ^5(x) \, dx","\frac{2}{11} \sec ^{\frac{11}{2}}(x)-\frac{4}{7} \sec ^{\frac{7}{2}}(x)+\frac{2}{3} \sec ^{\frac{3}{2}}(x)",1,"Could not integrate","F",-1
360,0,0,21,0.0000356,"\int \sec ^4(x) \tan ^{\frac{3}{2}}(x) \, dx","IntegrateAlgebraic[Sec[x]^4*Tan[x]^(3/2),x]","\int \sec ^4(x) \tan ^{\frac{3}{2}}(x) \, dx","\frac{2}{9} \tan ^{\frac{9}{2}}(x)+\frac{2}{5} \tan ^{\frac{5}{2}}(x)",1,"Could not integrate","F",-1
361,0,0,38,0.0000337,"\int \cot ^4(x) \csc ^3(x) \, dx","IntegrateAlgebraic[Cot[x]^4*Csc[x]^3,x]","\int \cot ^4(x) \csc ^3(x) \, dx","-\frac{1}{16} \tanh ^{-1}(\cos (x))-\frac{1}{6} \cot ^3(x) \csc ^3(x)+\frac{1}{8} \cot (x) \csc ^3(x)-\frac{1}{16} \cot (x) \csc (x)",1,"Could not integrate","F",-1
362,0,0,76,0.0000454,"\int \sec ^3\left(\frac{\pi }{4}+\frac{x}{2}\right) \tan ^2\left(\frac{\pi }{4}+\frac{x}{2}\right) \, dx","IntegrateAlgebraic[Sec[Pi/4 + x/2]^3*Tan[Pi/4 + x/2]^2,x]","\int \sec ^3\left(\frac{\pi }{4}+\frac{x}{2}\right) \tan ^2\left(\frac{\pi }{4}+\frac{x}{2}\right) \, dx","-\frac{1}{4} \tanh ^{-1}\left(\sin \left(\frac{x}{2}+\frac{\pi }{4}\right)\right)+\frac{1}{2} \tan \left(\frac{x}{2}+\frac{\pi }{4}\right) \sec ^3\left(\frac{x}{2}+\frac{\pi }{4}\right)-\frac{1}{4} \tan \left(\frac{x}{2}+\frac{\pi }{4}\right) \sec \left(\frac{x}{2}+\frac{\pi }{4}\right)",1,"Could not integrate","F",-1
363,0,0,88,0.000049,"\int \left(1+\cot ^3(x)\right) \left(a \sec ^2(x)-\sin (2 x)\right)^2 \, dx","IntegrateAlgebraic[(1 + Cot[x]^3)*(a*Sec[x]^2 - Sin[2*x])^2,x]","\int \left(1+\cot ^3(x)\right) \left(a \sec ^2(x)-\sin (2 x)\right)^2 \, dx","\frac{1}{3} a^2 \tan ^3(x)+a^2 \tan (x)-\frac{1}{2} a^2 \cot ^2(x)+\left(a^2+4\right) \log (\sin (x))+4 a x+4 a \cot (x)+(4-a) a \log (\cos (x))+\frac{x}{2}+\cos ^4(x)+2 \cos ^2(x)-\sin (x) \cos ^3(x)+\frac{1}{2} \sin (x) \cos (x)",1,"Could not integrate","F",-1
364,0,0,70,0.0000412,"\int (4-3 \cos (x)) \left(1-\frac{\sin (x)}{2}\right)^4 \, dx","IntegrateAlgebraic[(4 - 3*Cos[x])*(1 - Sin[x]/2)^4,x]","\int (4-3 \cos (x)) \left(1-\frac{\sin (x)}{2}\right)^4 \, dx","\frac{227 x}{32}-\frac{3}{80} \sin ^5(x)+\frac{3 \sin ^4(x)}{8}-\frac{3 \sin ^3(x)}{2}-3 \sin (x)-\frac{2 \cos ^3(x)}{3}-3 \cos ^2(x)+10 \cos (x)-\frac{1}{16} \sin ^3(x) \cos (x)-\frac{99}{32} \sin (x) \cos (x)",1,"Could not integrate","F",-1
365,0,0,33,0.0000404,"\int \left(\frac{1}{2}-3 \cot (x)\right) (3-2 \cot (x))^3 \, dx","IntegrateAlgebraic[(1/2 - 3*Cot[x])*(3 - 2*Cot[x])^3,x]","\int \left(\frac{1}{2}-3 \cot (x)\right) (3-2 \cot (x))^3 \, dx","-\frac{285 x}{2}+(3-2 \cot (x))^3+5 (3-2 \cot (x))^2-42 \cot (x)+4 \log (\sin (x))",1,"Could not integrate","F",-1
366,0,0,16,0.0000348,"\int \cos (5 x) \sec ^5(x) \, dx","IntegrateAlgebraic[Cos[5*x]*Sec[x]^5,x]","\int \cos (5 x) \sec ^5(x) \, dx","16 x+\frac{5 \tan ^3(x)}{3}-15 \tan (x)",1,"Could not integrate","F",-1
367,0,0,12,0.0000278,"\int \cos (4 x) \sec (x) \, dx","IntegrateAlgebraic[Cos[4*x]*Sec[x],x]","\int \cos (4 x) \sec (x) \, dx","\tanh ^{-1}(\sin (x))-\frac{8 \sin ^3(x)}{3}",1,"Could not integrate","F",-1
368,0,0,17,0.0000363,"\int \cos (x) \cos (4 x) \, dx","IntegrateAlgebraic[Cos[x]*Cos[4*x],x]","\int \cos (x) \cos (4 x) \, dx","\frac{1}{6} \sin (3 x)+\frac{1}{10} \sin (5 x)",1,"Could not integrate","F",-1
369,0,0,26,0.0000298,"\int \cos (4 x) \sec ^5(x) \, dx","IntegrateAlgebraic[Cos[4*x]*Sec[x]^5,x]","\int \cos (4 x) \sec ^5(x) \, dx","\frac{35}{8} \tanh ^{-1}(\sin (x))+\frac{1}{4} \tan (x) \sec ^3(x)-\frac{29}{8} \tan (x) \sec (x)",1,"Could not integrate","F",-1
370,0,0,38,0.0000529,"\int \cos ^4(x) \cos (4 x) \, dx","IntegrateAlgebraic[Cos[x]^4*Cos[4*x],x]","\int \cos ^4(x) \cos (4 x) \, dx","\frac{x}{16}+\frac{1}{8} \sin (2 x)+\frac{3}{32} \sin (4 x)+\frac{1}{24} \sin (6 x)+\frac{1}{128} \sin (8 x)",1,"Could not integrate","F",-1
371,0,0,20,0.0000345,"\int \cos (5 x) \csc ^5(x) \, dx","IntegrateAlgebraic[Cos[5*x]*Csc[x]^5,x]","\int \cos (5 x) \csc ^5(x) \, dx","-\frac{1}{4} \csc ^4(x)+6 \csc ^2(x)+16 \log (\sin (x))",1,"Could not integrate","F",-1
372,0,0,12,0.0000354,"\int \csc ^4(x) \sin (4 x) \, dx","IntegrateAlgebraic[Csc[x]^4*Sin[4*x],x]","\int \csc ^4(x) \sin (4 x) \, dx","-2 \csc ^2(x)-8 \log (\sin (x))",1,"Could not integrate","F",-1
373,0,0,64,0.0000339,"\int \frac{\cot (x)}{2+\sin (2 x)} \, dx","IntegrateAlgebraic[Cot[x]/(2 + Sin[2*x]),x]","\int \frac{\cot (x)}{2+\sin (2 x)} \, dx","-\frac{x}{2 \sqrt{3}}+\frac{1}{2} \log (\sin (x))+\frac{\tan ^{-1}\left(\frac{1-2 \cos ^2(x)}{2 \sin (x) \cos (x)+\sqrt{3}+2}\right)}{2 \sqrt{3}}-\frac{1}{4} \log (\sin (x) \cos (x)+1)",1,"Could not integrate","F",-1
374,0,0,11,0.0000377,"\int \cos (x) \cot (x) \sec (3 x) \, dx","IntegrateAlgebraic[Cos[x]*Cot[x]*Sec[3*x],x]","\int \cos (x) \cot (x) \sec (3 x) \, dx","-\frac{1}{2} \log \left(\csc ^2(x)-4\right)",1,"Could not integrate","F",-1
375,0,0,7,0.0000399,"\int \frac{\sin (2 x)}{\cos ^4(x)+\sin ^4(x)} \, dx","IntegrateAlgebraic[Sin[2*x]/(Cos[x]^4 + Sin[x]^4),x]","\int \frac{\sin (2 x)}{\cos ^4(x)+\sin ^4(x)} \, dx","-\tan ^{-1}(\cos (2 x))",1,"Could not integrate","F",-1
376,0,0,53,0.0000452,"\int \frac{1}{4+\sqrt{3} \cos (x)+\sin (x)} \, dx","IntegrateAlgebraic[(4 + Sqrt[3]*Cos[x] + Sin[x])^(-1),x]","\int \frac{1}{4+\sqrt{3} \cos (x)+\sin (x)} \, dx","\frac{x}{2 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{\cos (x)-\sqrt{3} \sin (x)}{\sin (x)+\sqrt{3} \cos (x)+2 \left(2+\sqrt{3}\right)}\right)}{\sqrt{3}}",1,"Could not integrate","F",-1
377,0,0,33,0.0000381,"\int \frac{1}{3+4 \cos (x)+4 \sin (x)} \, dx","IntegrateAlgebraic[(3 + 4*Cos[x] + 4*Sin[x])^(-1),x]","\int \frac{1}{3+4 \cos (x)+4 \sin (x)} \, dx","-\frac{\tanh ^{-1}\left(\frac{\sqrt{23} (\cos (x)-\sin (x))}{3 \sin (x)+3 \cos (x)+8}\right)}{\sqrt{23}}",1,"Could not integrate","F",-1
378,0,0,27,0.0000367,"\int \frac{1}{4-3 \cos ^2(x)+5 \sin ^2(x)} \, dx","IntegrateAlgebraic[(4 - 3*Cos[x]^2 + 5*Sin[x]^2)^(-1),x]","\int \frac{1}{4-3 \cos ^2(x)+5 \sin ^2(x)} \, dx","\frac{x}{3}+\frac{1}{3} \tan ^{-1}\left(\frac{2 \sin (x) \cos (x)}{2 \sin ^2(x)+1}\right)",1,"Could not integrate","F",-1
379,0,0,28,0.0000379,"\int \frac{1}{4+4 \cot (x)+\tan (x)} \, dx","IntegrateAlgebraic[(4 + 4*Cot[x] + Tan[x])^(-1),x]","\int \frac{1}{4+4 \cot (x)+\tan (x)} \, dx","\frac{4 x}{25}+\frac{2}{5 (\tan (x)+2)}-\frac{3}{25} \log (\sin (x)+2 \cos (x))",1,"Could not integrate","F",-1
380,0,0,67,0.0000352,"\int \frac{1}{(2 \sec (x)+\sin (x))^2} \, dx","IntegrateAlgebraic[(2*Sec[x] + Sin[x])^(-2),x]","\int \frac{1}{(2 \sec (x)+\sin (x))^2} \, dx","\frac{8 x}{15 \sqrt{15}}+\frac{4 \tan (x)+1}{15 \left(2 \tan ^2(x)+\tan (x)+2\right)}-\frac{8 \tan ^{-1}\left(\frac{1-2 \cos ^2(x)}{2 \sin (x) \cos (x)+\sqrt{15}+4}\right)}{15 \sqrt{15}}",1,"Could not integrate","F",-1
381,0,0,55,0.0000358,"\int \frac{1}{(\cos (x)+2 \sec (x))^2} \, dx","IntegrateAlgebraic[(Cos[x] + 2*Sec[x])^(-2),x]","\int \frac{1}{(\cos (x)+2 \sec (x))^2} \, dx","\frac{x}{6 \sqrt{6}}+\frac{\tan (x)}{6 \left(2 \tan ^2(x)+3\right)}-\frac{\tan ^{-1}\left(\frac{\sin (x) \cos (x)}{\cos ^2(x)+\sqrt{6}+2}\right)}{6 \sqrt{6}}",1,"Could not integrate","F",-1
382,0,0,42,0.0000414,"\int \frac{5-\tan (x)-6 \tan ^2(x)}{(1+3 \tan (x))^3} \, dx","IntegrateAlgebraic[(5 - Tan[x] - 6*Tan[x]^2)/(1 + 3*Tan[x])^3,x]","\int \frac{5-\tan (x)-6 \tan ^2(x)}{(1+3 \tan (x))^3} \, dx","-\frac{67 x}{250}-\frac{29}{50 (3 \tan (x)+1)}-\frac{7}{10 (3 \tan (x)+1)^2}-\frac{28}{125} \log (3 \sin (x)+\cos (x))",1,"Could not integrate","F",-1
383,0,0,9,0.000036,"\int \cos ^2(x) \sec (3 x) \, dx","IntegrateAlgebraic[Cos[x]^2*Sec[3*x],x]","\int \cos ^2(x) \sec (3 x) \, dx","\frac{1}{2} \tanh ^{-1}(2 \sin (x))",1,"Could not integrate","F",-1
384,0,0,15,0.0000278,"\int \sec (2 x) \sin (x) \, dx","IntegrateAlgebraic[Sec[2*x]*Sin[x],x]","\int \sec (2 x) \sin (x) \, dx","\frac{\tanh ^{-1}\left(\sqrt{2} \cos (x)\right)}{\sqrt{2}}",1,"Could not integrate","F",-1
385,0,0,17,0.0000322,"\int \sec (2 x) \sin ^2(x) \, dx","IntegrateAlgebraic[Sec[2*x]*Sin[x]^2,x]","\int \sec (2 x) \sin ^2(x) \, dx","\frac{1}{4} \tanh ^{-1}(2 \sin (x) \cos (x))-\frac{x}{2}",1,"Could not integrate","F",-1
386,0,0,21,0.0000295,"\int \sec (3 x) \sin ^3(x) \, dx","IntegrateAlgebraic[Sec[3*x]*Sin[x]^3,x]","\int \sec (3 x) \sin ^3(x) \, dx","\frac{1}{3} \log (\cos (x))-\frac{1}{24} \log \left(3-4 \cos ^2(x)\right)",1,"Could not integrate","F",-1
387,0,0,21,0.0000611,"\int \cos (x) \csc (3 x) \, dx","IntegrateAlgebraic[Cos[x]*Csc[3*x],x]","\int \cos (x) \csc (3 x) \, dx","\frac{1}{3} \log (\sin (x))-\frac{1}{6} \log \left(3-4 \sin ^2(x)\right)",1,"Could not integrate","F",-1
388,0,0,26,0.0000303,"\int \csc (4 x) \sin (x) \, dx","IntegrateAlgebraic[Csc[4*x]*Sin[x],x]","\int \csc (4 x) \sin (x) \, dx","\frac{\tanh ^{-1}\left(\sqrt{2} \sin (x)\right)}{2 \sqrt{2}}-\frac{1}{4} \tanh ^{-1}(\sin (x))",1,"Could not integrate","F",-1
389,0,0,26,0.0000306,"\int \csc (4 x) \sin ^3(x) \, dx","IntegrateAlgebraic[Csc[4*x]*Sin[x]^3,x]","\int \csc (4 x) \sin ^3(x) \, dx","\frac{\tanh ^{-1}\left(\sqrt{2} \sin (x)\right)}{4 \sqrt{2}}-\frac{1}{4} \tanh ^{-1}(\sin (x))",1,"Could not integrate","F",-1
390,0,0,16,0.0000325,"\int \sqrt{1+\sin (2 x)} \, dx","IntegrateAlgebraic[Sqrt[1 + Sin[2*x]],x]","\int \sqrt{1+\sin (2 x)} \, dx","-\frac{\cos (2 x)}{\sqrt{\sin (2 x)+1}}",1,"Could not integrate","F",-1
391,0,0,17,0.0000334,"\int \sqrt{1-\sin (2 x)} \, dx","IntegrateAlgebraic[Sqrt[1 - Sin[2*x]],x]","\int \sqrt{1-\sin (2 x)} \, dx","\frac{\cos (2 x)}{\sqrt{1-\sin (2 x)}}",1,"Could not integrate","F",-1
392,0,0,27,0.000034,"\int \frac{1}{\sqrt{1+\cos (2 x)}} \, dx","IntegrateAlgebraic[1/Sqrt[1 + Cos[2*x]],x]","\int \frac{1}{\sqrt{1+\cos (2 x)}} \, dx","\frac{\tanh ^{-1}\left(\frac{\sin (2 x)}{\sqrt{2} \sqrt{\cos (2 x)+1}}\right)}{\sqrt{2}}",1,"Could not integrate","F",-1
393,0,0,30,0.0000332,"\int \frac{1}{\sqrt{1-\cos (2 x)}} \, dx","IntegrateAlgebraic[1/Sqrt[1 - Cos[2*x]],x]","\int \frac{1}{\sqrt{1-\cos (2 x)}} \, dx","-\frac{\tanh ^{-1}\left(\frac{\sin (2 x)}{\sqrt{2} \sqrt{1-\cos (2 x)}}\right)}{\sqrt{2}}",1,"Could not integrate","F",-1
394,0,0,53,0.0000291,"\int \frac{1}{(1-\cos (3 x))^{3/2}} \, dx","IntegrateAlgebraic[(1 - Cos[3*x])^(-3/2),x]","\int \frac{1}{(1-\cos (3 x))^{3/2}} \, dx","-\frac{\sin (3 x)}{6 (1-\cos (3 x))^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sin (3 x)}{\sqrt{2} \sqrt{1-\cos (3 x)}}\right)}{6 \sqrt{2}}",1,"Could not integrate","F",-1
395,0,0,73,0.0000587,"\int \left(1-\sin \left(\frac{2 x}{3}\right)\right)^{5/2} \, dx","IntegrateAlgebraic[(1 - Sin[(2*x)/3])^(5/2),x]","\int \left(1-\sin \left(\frac{2 x}{3}\right)\right)^{5/2} \, dx","\frac{3}{5} \left(1-\sin \left(\frac{2 x}{3}\right)\right)^{3/2} \cos \left(\frac{2 x}{3}\right)+\frac{8}{5} \sqrt{1-\sin \left(\frac{2 x}{3}\right)} \cos \left(\frac{2 x}{3}\right)+\frac{32 \cos \left(\frac{2 x}{3}\right)}{5 \sqrt{1-\sin \left(\frac{2 x}{3}\right)}}",1,"Could not integrate","F",-1
396,0,0,55,0.0000507,"\int \frac{\cos (x) \left(-\cos ^2(x)+2 \sqrt[4]{1+2 \sin (x)}\right)}{(1+2 \sin (x))^{3/2}} \, dx","IntegrateAlgebraic[(Cos[x]*(-Cos[x]^2 + 2*(1 + 2*Sin[x])^(1/4)))/(1 + 2*Sin[x])^(3/2),x]","\int \frac{\cos (x) \left(-\cos ^2(x)+2 \sqrt[4]{1+2 \sin (x)}\right)}{(1+2 \sin (x))^{3/2}} \, dx","\frac{1}{12} (2 \sin (x)+1)^{3/2}-\frac{1}{2} \sqrt{2 \sin (x)+1}-\frac{4}{\sqrt[4]{2 \sin (x)+1}}+\frac{3}{4 \sqrt{2 \sin (x)+1}}",1,"Could not integrate","F",-1
397,0,0,98,0.0000345,"\int \sqrt{\tan (x)} \, dx","IntegrateAlgebraic[Sqrt[Tan[x]],x]","\int \sqrt{\tan (x)} \, dx","-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (x)}\right)}{\sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\tan (x)}+1\right)}{\sqrt{2}}+\frac{\log \left(\tan (x)-\sqrt{2} \sqrt{\tan (x)}+1\right)}{2 \sqrt{2}}-\frac{\log \left(\tan (x)+\sqrt{2} \sqrt{\tan (x)}+1\right)}{2 \sqrt{2}}",1,"Could not integrate","F",-1
398,0,0,57,0.0000337,"\int \frac{1}{\sqrt[3]{\tan (5 x)}} \, dx","IntegrateAlgebraic[Tan[5*x]^(-1/3),x]","\int \frac{1}{\sqrt[3]{\tan (5 x)}} \, dx","-\frac{1}{10} \sqrt{3} \tan ^{-1}\left(\frac{1-2 \tan ^{\frac{2}{3}}(5 x)}{\sqrt{3}}\right)+\frac{3}{20} \log \left(\tan ^{\frac{2}{3}}(5 x)+1\right)-\frac{1}{20} \log \left(\tan ^2(5 x)+1\right)",1,"Could not integrate","F",-1
399,0,0,87,0.0000369,"\int \frac{1}{(4+3 \tan (2 x))^{3/2}} \, dx","IntegrateAlgebraic[(4 + 3*Tan[2*x])^(-3/2),x]","\int \frac{1}{(4+3 \tan (2 x))^{3/2}} \, dx","-\frac{9 \tan ^{-1}\left(\frac{1-3 \tan (2 x)}{\sqrt{2} \sqrt{3 \tan (2 x)+4}}\right)}{250 \sqrt{2}}-\frac{3}{25 \sqrt{3 \tan (2 x)+4}}+\frac{13 \tanh ^{-1}\left(\frac{\tan (2 x)+3}{\sqrt{2} \sqrt{3 \tan (2 x)+4}}\right)}{250 \sqrt{2}}",1,"Could not integrate","F",-1
400,0,0,40,0.0000491,"\int \frac{\sec ^2(x) \left(-\sqrt{4-3 \tan (x)}+3 \tan (x)\right)}{(4-3 \tan (x))^{3/2}} \, dx","IntegrateAlgebraic[(Sec[x]^2*(-Sqrt[4 - 3*Tan[x]] + 3*Tan[x]))/(4 - 3*Tan[x])^(3/2),x]","\int \frac{\sec ^2(x) \left(-\sqrt{4-3 \tan (x)}+3 \tan (x)\right)}{(4-3 \tan (x))^{3/2}} \, dx","\frac{2}{3} \sqrt{4-3 \tan (x)}+\frac{8}{3 \sqrt{4-3 \tan (x)}}+\frac{1}{3} \log (4-3 \tan (x))",1,"Could not integrate","F",-1
401,0,0,84,0.0000379,"\int \frac{\tan (x)}{\left(-1+\sqrt{\tan (x)}\right)^2} \, dx","IntegrateAlgebraic[Tan[x]/(-1 + Sqrt[Tan[x]])^2,x]","\int \frac{\tan (x)}{\left(-1+\sqrt{\tan (x)}\right)^2} \, dx","-\frac{x}{2}+\frac{\tan ^{-1}\left(\frac{1-\tan (x)}{\sqrt{2} \sqrt{\tan (x)}}\right)}{\sqrt{2}}+\frac{1}{1-\sqrt{\tan (x)}}+\log \left(1-\sqrt{\tan (x)}\right)+\frac{1}{2} \log (\cos (x))+\frac{\tanh ^{-1}\left(\frac{\tan (x)+1}{\sqrt{2} \sqrt{\tan (x)}}\right)}{\sqrt{2}}",1,"Could not integrate","F",-1
402,0,0,31,0.0000337,"\int \frac{\sin (x)}{\sqrt{\sin (2 x)}} \, dx","IntegrateAlgebraic[Sin[x]/Sqrt[Sin[2*x]],x]","\int \frac{\sin (x)}{\sqrt{\sin (2 x)}} \, dx","-\frac{1}{2} \sin ^{-1}(\cos (x)-\sin (x))-\frac{1}{2} \log \left(\sin (x)+\sqrt{\sin (2 x)}+\cos (x)\right)",1,"Could not integrate","F",-1
403,0,0,31,0.0000367,"\int \frac{\cos (x)}{\sqrt{\sin (2 x)}} \, dx","IntegrateAlgebraic[Cos[x]/Sqrt[Sin[2*x]],x]","\int \frac{\cos (x)}{\sqrt{\sin (2 x)}} \, dx","\frac{1}{2} \log \left(\sin (x)+\sqrt{\sin (2 x)}+\cos (x)\right)-\frac{1}{2} \sin ^{-1}(\cos (x)-\sin (x))",1,"Could not integrate","F",-1
404,0,0,45,0.0000349,"\int \sin (x) \sqrt{\sin (2 x)} \, dx","IntegrateAlgebraic[Sin[x]*Sqrt[Sin[2*x]],x]","\int \sin (x) \sqrt{\sin (2 x)} \, dx","-\frac{1}{4} \sin ^{-1}(\cos (x)-\sin (x))-\frac{1}{2} \sqrt{\sin (2 x)} \cos (x)+\frac{1}{4} \log \left(\sin (x)+\sqrt{\sin (2 x)}+\cos (x)\right)",1,"Could not integrate","F",-1
405,0,0,47,0.00004,"\int (\cos (x)-\sin (x)) \sqrt{\sin (2 x)} \, dx","IntegrateAlgebraic[(Cos[x] - Sin[x])*Sqrt[Sin[2*x]],x]","\int (\cos (x)-\sin (x)) \sqrt{\sin (2 x)} \, dx","\frac{1}{2} \sin (x) \sqrt{\sin (2 x)}+\frac{1}{2} \sqrt{\sin (2 x)} \cos (x)-\frac{1}{2} \log \left(\sin (x)+\sqrt{\sin (2 x)}+\cos (x)\right)",1,"Could not integrate","F",-1
406,0,0,61,0.0000369,"\int \frac{\sin ^7(x)}{\sin ^{\frac{7}{2}}(2 x)} \, dx","IntegrateAlgebraic[Sin[x]^7/Sin[2*x]^(7/2),x]","\int \frac{\sin ^7(x)}{\sin ^{\frac{7}{2}}(2 x)} \, dx","\frac{\sin ^5(x)}{5 \sin ^{\frac{5}{2}}(2 x)}-\frac{\sin (x)}{4 \sqrt{\sin (2 x)}}-\frac{1}{16} \sin ^{-1}(\cos (x)-\sin (x))+\frac{1}{16} \log \left(\sin (x)+\sqrt{\sin (2 x)}+\cos (x)\right)",1,"Could not integrate","F",-1
407,0,0,61,0.0000395,"\int \frac{\cos ^7(x)}{\sin ^{\frac{7}{2}}(2 x)} \, dx","IntegrateAlgebraic[Cos[x]^7/Sin[2*x]^(7/2),x]","\int \frac{\cos ^7(x)}{\sin ^{\frac{7}{2}}(2 x)} \, dx","-\frac{\cos ^5(x)}{5 \sin ^{\frac{5}{2}}(2 x)}-\frac{1}{16} \sin ^{-1}(\cos (x)-\sin (x))+\frac{\cos (x)}{4 \sqrt{\sin (2 x)}}-\frac{1}{16} \log \left(\sin (x)+\sqrt{\sin (2 x)}+\cos (x)\right)",1,"Could not integrate","F",-1
408,0,0,16,0.000038,"\int \csc ^5(x) \sin ^{\frac{3}{2}}(2 x) \, dx","IntegrateAlgebraic[Csc[x]^5*Sin[2*x]^(3/2),x]","\int \csc ^5(x) \sin ^{\frac{3}{2}}(2 x) \, dx","-\frac{1}{5} \sin ^{\frac{5}{2}}(2 x) \csc ^5(x)",1,"Could not integrate","F",-1
409,0,0,31,0.0000317,"\int \frac{\sec ^3(x)}{\sqrt{\sin (2 x)}} \, dx","IntegrateAlgebraic[Sec[x]^3/Sqrt[Sin[2*x]],x]","\int \frac{\sec ^3(x)}{\sqrt{\sin (2 x)}} \, dx","\frac{1}{5} \sqrt{\sin (2 x)} \sec ^3(x)+\frac{4}{5} \sqrt{\sin (2 x)} \sec (x)",1,"Could not integrate","F",-1
410,0,0,29,0.0000474,"\int \frac{\csc (x)}{\sin ^{\frac{3}{2}}(2 x)} \, dx","IntegrateAlgebraic[Csc[x]/Sin[2*x]^(3/2),x]","\int \frac{\csc (x)}{\sin ^{\frac{3}{2}}(2 x)} \, dx","\frac{4 \sin (x)}{3 \sqrt{\sin (2 x)}}-\frac{2 \cos (x)}{3 \sin ^{\frac{3}{2}}(2 x)}",1,"Could not integrate","F",-1
411,0,0,68,0.0000542,"\int \frac{\cos ^3(x) (\cos (2 x)-3 \tan (x))}{\left(\sin ^2(x)-\sin (2 x)\right) \sin ^{\frac{5}{2}}(2 x)} \, dx","IntegrateAlgebraic[(Cos[x]^3*(Cos[2*x] - 3*Tan[x]))/((Sin[x]^2 - Sin[2*x])*Sin[2*x]^(5/2)),x]","\int \frac{\cos ^3(x) (\cos (2 x)-3 \tan (x))}{\left(\sin ^2(x)-\sin (2 x)\right) \sin ^{\frac{5}{2}}(2 x)} \, dx","-\frac{9 \cos (x)}{16 \sqrt{\sin (2 x)}}+\frac{\cos (x) \cot ^2(x)}{20 \sqrt{\sin (2 x)}}-\frac{5 \cos (x) \cot (x)}{24 \sqrt{\sin (2 x)}}+\frac{33}{32} \tanh ^{-1}\left(\frac{1}{2} \sqrt{\sin (2 x)} \sec (x)\right)",1,"Could not integrate","F",-1
412,0,0,19,0.0000362,"\int \sqrt{\sec ^4(x) \tan (x)} \, dx","IntegrateAlgebraic[Sqrt[Sec[x]^4*Tan[x]],x]","\int \sqrt{\sec ^4(x) \tan (x)} \, dx","\frac{2}{3} \sin (x) \cos (x) \sqrt{\tan (x) \sec ^4(x)}",1,"Could not integrate","F",-1
413,0,0,92,0.0000344,"\int \sqrt{\sin ^4(x) \tan (x)} \, dx","IntegrateAlgebraic[Sqrt[Sin[x]^4*Tan[x]],x]","\int \sqrt{\sin ^4(x) \tan (x)} \, dx","-\frac{1}{2} \cot (x) \sqrt{\sin ^4(x) \tan (x)}+\frac{3 \tan ^{-1}\left(\frac{(1-\cot (x)) \csc ^2(x) \sqrt{\sin ^4(x) \tan (x)}}{\sqrt{2}}\right)}{4 \sqrt{2}}+\frac{3 \log \left(\sin (x)+\cos (x)-\sqrt{2} \cot (x) \csc (x) \sqrt{\sin ^4(x) \tan (x)}\right)}{4 \sqrt{2}}",1,"Could not integrate","F",-1
414,0,0,47,0.0000383,"\int \sqrt[3]{\sec ^{12}(x) \tan ^2(x)} \, dx","IntegrateAlgebraic[(Sec[x]^12*Tan[x]^2)^(1/3),x]","\int \sqrt[3]{\sec ^{12}(x) \tan ^2(x)} \, dx","\frac{3}{5} \sin (x) \cos ^3(x) \sqrt[3]{\tan ^2(x) \sec ^{12}(x)}+\frac{3}{11} \sin ^3(x) \cos (x) \sqrt[3]{\tan ^2(x) \sec ^{12}(x)}",1,"Could not integrate","F",-1
415,0,0,70,0.000037,"\int \frac{1}{\sqrt[4]{\cos ^{11}(x) \sin ^{13}(x)}} \, dx","IntegrateAlgebraic[(Cos[x]^11*Sin[x]^13)^(-1/4),x]","\int \frac{1}{\sqrt[4]{\cos ^{11}(x) \sin ^{13}(x)}} \, dx","\frac{4 \sin ^5(x) \cos (x)}{7 \sqrt[4]{\sin ^{13}(x) \cos ^{11}(x)}}-\frac{4 \sin (x) \cos ^5(x)}{9 \sqrt[4]{\sin ^{13}(x) \cos ^{11}(x)}}-\frac{8 \sin ^3(x) \cos ^3(x)}{\sqrt[4]{\sin ^{13}(x) \cos ^{11}(x)}}",1,"Could not integrate","F",-1
416,0,0,108,0.0000469,"\int \frac{\cos (2 x)-\sqrt{\sin (2 x)}}{\sqrt{\cos ^3(x) \sin (x)}} \, dx","IntegrateAlgebraic[(Cos[2*x] - Sqrt[Sin[2*x]])/Sqrt[Cos[x]^3*Sin[x]],x]","\int \frac{\cos (2 x)-\sqrt{\sin (2 x)}}{\sqrt{\cos ^3(x) \sin (x)}} \, dx","-\frac{\sqrt{\sin (2 x)} \cos (x) \sin ^{-1}(\cos (x)-\sin (x))}{\sqrt{\sin (x) \cos ^3(x)}}-\frac{\sin (2 x)}{\sqrt{\sin (x) \cos ^3(x)}}-\frac{\sqrt{\sin (2 x)} \cos (x) \tanh ^{-1}(\sin (x))}{\sqrt{\sin (x) \cos ^3(x)}}-\sqrt{2} \log \left(\sin (x)+\cos (x)-\sqrt{2} \sec (x) \sqrt{\sin (x) \cos ^3(x)}\right)",1,"Could not integrate","F",-1
417,0,0,364,0.0000555,"\int \frac{\sqrt{\cos (x) \sin ^3(x)}-2 \sin (2 x)}{-\sqrt{\cos ^3(x) \sin (x)}+\sqrt{\tan (x)}} \, dx","IntegrateAlgebraic[(Sqrt[Cos[x]*Sin[x]^3] - 2*Sin[2*x])/(-Sqrt[Cos[x]^3*Sin[x]] + Sqrt[Tan[x]]),x]","\int \frac{\sqrt{\cos (x) \sin ^3(x)}-2 \sin (2 x)}{-\sqrt{\cos ^3(x) \sin (x)}+\sqrt{\tan (x)}} \, dx","-\sqrt[4]{2} \tan ^{-1}\left(\frac{\sqrt{2}-\tan (x)}{2^{3/4} \sqrt{\tan (x)}}\right)+\frac{4}{\sqrt{\tan (x)}}-\sqrt[4]{2} \coth ^{-1}\left(\frac{\tan (x)+\sqrt{2}}{2^{3/4} \sqrt{\tan (x)}}\right)-2 \sqrt{2} \tan ^{-1}\left(\frac{\cos (x) (\cos (x)-\sin (x))}{\sqrt{2} \sqrt{\sin (x) \cos ^3(x)}}\right)+\sqrt[4]{2} \tan ^{-1}\left(\frac{\cos (x) \left(\sqrt{2} \cos (x)-\sin (x)\right)}{2^{3/4} \sqrt{\sin (x) \cos ^3(x)}}\right)-2 \sqrt{2} \coth ^{-1}\left(\frac{\cos (x) (\sin (x)+\cos (x))}{\sqrt{2} \sqrt{\sin (x) \cos ^3(x)}}\right)+\sqrt[4]{2} \coth ^{-1}\left(\frac{\cos (x) \left(\sin (x)+\sqrt{2} \cos (x)\right)}{2^{3/4} \sqrt{\sin (x) \cos ^3(x)}}\right)+4 \csc (x) \sec (x) \sqrt{\sin (x) \cos ^3(x)}+\frac{1}{2} \csc ^2(x) \sec ^2(x) \log (\sin (x)) \sqrt{\sin (x) \cos ^3(x)} \sqrt{\sin ^3(x) \cos (x)}-\frac{1}{4} \sqrt{\tan (x)} \csc ^2(x) \log \left(\cos ^2(x)+1\right) \sqrt{\sin ^3(x) \cos (x)}+\frac{1}{4} \csc ^2(x) \sec ^2(x) \log \left(\cos ^2(x)+1\right) \sqrt{\sin (x) \cos ^3(x)} \sqrt{\sin ^3(x) \cos (x)}+\frac{1}{2} \sqrt{\tan (x)} \csc ^2(x) \log (\sin (x)) \sqrt{\sin ^3(x) \cos (x)}",1,"Could not integrate","F",-1
418,0,0,125,0.0000831,"\int \frac{-3 \tan (x)+\sqrt[3]{\sec ^6(x) \tan (x)}}{\left(\cos ^5(x) \sin (x)\right)^{2/3}} \, dx","IntegrateAlgebraic[(-3*Tan[x] + (Sec[x]^6*Tan[x])^(1/3))/(Cos[x]^5*Sin[x])^(2/3),x]","\int \frac{-3 \tan (x)+\sqrt[3]{\sec ^6(x) \tan (x)}}{\left(\cos ^5(x) \sin (x)\right)^{2/3}} \, dx","-\frac{9 \sin ^4(x)}{10 \left(\sin (x) \cos ^5(x)\right)^{2/3}}-\frac{9}{4} \sec ^8(x) \left(\sin (x) \cos ^5(x)\right)^{4/3}+\frac{3}{14} \tan ^4(x) \sqrt[3]{\sin (x) \cos ^5(x)} \sqrt[3]{\tan (x) \sec ^6(x)}+\frac{3}{4} \tan ^2(x) \sqrt[3]{\sin (x) \cos ^5(x)} \sqrt[3]{\tan (x) \sec ^6(x)}+\frac{3}{2} \sqrt[3]{\sin (x) \cos ^5(x)} \sqrt[3]{\tan (x) \sec ^6(x)}",1,"Could not integrate","F",-1
419,0,0,73,0.0000395,"\int \left(1+2 \cos ^2(x)\right)^{5/2} \sin (x) \, dx","IntegrateAlgebraic[(1 + 2*Cos[x]^2)^(5/2)*Sin[x],x]","\int \left(1+2 \cos ^2(x)\right)^{5/2} \sin (x) \, dx","-\frac{1}{6} \cos (x) \left(2 \cos ^2(x)+1\right)^{5/2}-\frac{5}{24} \cos (x) \left(2 \cos ^2(x)+1\right)^{3/2}-\frac{5}{16} \cos (x) \sqrt{2 \cos ^2(x)+1}-\frac{5 \sinh ^{-1}\left(\sqrt{2} \cos (x)\right)}{16 \sqrt{2}}",1,"Could not integrate","F",-1
420,0,0,69,0.0000414,"\int \cos (x) \left(5 \cos ^2(x)+\sin ^2(x)\right)^{5/2} \, dx","IntegrateAlgebraic[Cos[x]*(5*Cos[x]^2 + Sin[x]^2)^(5/2),x]","\int \cos (x) \left(5 \cos ^2(x)+\sin ^2(x)\right)^{5/2} \, dx","\frac{625}{32} \sin ^{-1}\left(\frac{2 \sin (x)}{\sqrt{5}}\right)+\frac{1}{6} \sin (x) \left(5-4 \sin ^2(x)\right)^{5/2}+\frac{25}{24} \sin (x) \left(5-4 \sin ^2(x)\right)^{3/2}+\frac{125}{16} \sin (x) \sqrt{5-4 \sin ^2(x)}",1,"Could not integrate","F",-1
421,0,0,58,0.00004,"\int \cos (x) \left(-\cos ^2(x)-5 \sin ^2(x)\right)^{3/2} \, dx","IntegrateAlgebraic[Cos[x]*(-Cos[x]^2 - 5*Sin[x]^2)^(3/2),x]","\int \cos (x) \left(-\cos ^2(x)-5 \sin ^2(x)\right)^{3/2} \, dx","\frac{1}{4} \sin (x) \left(-4 \sin ^2(x)-1\right)^{3/2}-\frac{3}{8} \sin (x) \sqrt{-4 \sin ^2(x)-1}+\frac{3}{16} \tan ^{-1}\left(\frac{2 \sin (x)}{\sqrt{-4 \sin ^2(x)-1}}\right)",1,"Could not integrate","F",-1
422,0,0,55,0.0000414,"\int \frac{\sin (x)}{\left(5 \cos ^2(x)-2 \sin ^2(x)\right)^{7/2}} \, dx","IntegrateAlgebraic[Sin[x]/(5*Cos[x]^2 - 2*Sin[x]^2)^(7/2),x]","\int \frac{\sin (x)}{\left(5 \cos ^2(x)-2 \sin ^2(x)\right)^{7/2}} \, dx","\frac{\cos (x)}{15 \sqrt{7 \cos ^2(x)-2}}-\frac{\cos (x)}{15 \left(7 \cos ^2(x)-2\right)^{3/2}}+\frac{\cos (x)}{10 \left(7 \cos ^2(x)-2\right)^{5/2}}",1,"Could not integrate","F",-1
423,0,0,39,0.0000416,"\int \frac{\cos (x) \cos (2 x)}{\left(2-5 \sin ^2(x)\right)^{3/2}} \, dx","IntegrateAlgebraic[(Cos[x]*Cos[2*x])/(2 - 5*Sin[x]^2)^(3/2),x]","\int \frac{\cos (x) \cos (2 x)}{\left(2-5 \sin ^2(x)\right)^{3/2}} \, dx","\frac{2 \sin ^{-1}\left(\sqrt{\frac{5}{2}} \sin (x)\right)}{5 \sqrt{5}}+\frac{\sin (x)}{10 \sqrt{2-5 \sin ^2(x)}}",1,"Could not integrate","F",-1
424,0,0,48,0.0000978,"\int \frac{\sin (5 x)}{\left(5 \cos ^2(x)+9 \sin ^2(x)\right)^{5/2}} \, dx","IntegrateAlgebraic[Sin[5*x]/(5*Cos[x]^2 + 9*Sin[x]^2)^(5/2),x]","\int \frac{\sin (5 x)}{\left(5 \cos ^2(x)+9 \sin ^2(x)\right)^{5/2}} \, dx","\frac{295 \cos (x)}{243 \sqrt{9-4 \cos ^2(x)}}-\frac{55 \cos (x)}{27 \left(9-4 \cos ^2(x)\right)^{3/2}}-\frac{1}{2} \sin ^{-1}\left(\frac{2 \cos (x)}{3}\right)",1,"Could not integrate","F",-1
425,0,0,49,0.0000455,"\int \frac{\cos (x) \cos (2 x) \sin (3 x)}{\left(-5+4 \sin ^2(x)\right)^{5/2}} \, dx","IntegrateAlgebraic[(Cos[x]*Cos[2*x]*Sin[3*x])/(-5 + 4*Sin[x]^2)^(5/2),x]","\int \frac{\cos (x) \cos (2 x) \sin (3 x)}{\left(-5+4 \sin ^2(x)\right)^{5/2}} \, dx","\frac{1}{8} \sqrt{4 \sin ^2(x)-5}-\frac{5}{8 \sqrt{4 \sin ^2(x)-5}}-\frac{1}{4 \left(4 \sin ^2(x)-5\right)^{3/2}}",1,"Could not integrate","F",-1
426,0,0,111,0.0000839,"\int \frac{\csc ^2(x) \left(-2 \cos ^3(x) (-1+\sin (x))+\cos (2 x) \sin (x)\right)}{\sqrt{-5+\sin ^2(x)}} \, dx","IntegrateAlgebraic[(Csc[x]^2*(-2*Cos[x]^3*(-1 + Sin[x]) + Cos[2*x]*Sin[x]))/Sqrt[-5 + Sin[x]^2],x]","\int \frac{\csc ^2(x) \left(-2 \cos ^3(x) (-1+\sin (x))+\cos (2 x) \sin (x)\right)}{\sqrt{-5+\sin ^2(x)}} \, dx","2 \sqrt{\sin ^2(x)-5}-\frac{2 \tan ^{-1}\left(\frac{\sqrt{\sin ^2(x)-5}}{\sqrt{5}}\right)}{\sqrt{5}}-2 \tanh ^{-1}\left(\frac{\sin (x)}{\sqrt{\sin ^2(x)-5}}\right)+\frac{2}{5} \sqrt{\sin ^2(x)-5} \csc (x)+2 \tan ^{-1}\left(\frac{\cos (x)}{\sqrt{\sin ^2(x)-5}}\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{5} \cos (x)}{\sqrt{\sin ^2(x)-5}}\right)}{\sqrt{5}}",1,"Could not integrate","F",-1
427,0,0,112,0.0001707,"\int \frac{\cos (3 x)}{-\sqrt{-1+8 \cos ^2(x)}+\sqrt{3 \cos ^2(x)-\sin ^2(x)}} \, dx","IntegrateAlgebraic[Cos[3*x]/(-Sqrt[-1 + 8*Cos[x]^2] + Sqrt[3*Cos[x]^2 - Sin[x]^2]),x]","\int \frac{\cos (3 x)}{-\sqrt{-1+8 \cos ^2(x)}+\sqrt{3 \cos ^2(x)-\sin ^2(x)}} \, dx","\frac{5 \sin ^{-1}\left(2 \sqrt{\frac{2}{7}} \sin (x)\right)}{4 \sqrt{2}}+\frac{3}{4} \sin ^{-1}\left(\frac{2 \sin (x)}{\sqrt{3}}\right)-\frac{1}{2} \sin (x) \sqrt{4 \cos ^2(x)-1}-\frac{1}{2} \sin (x) \sqrt{8 \cos ^2(x)-1}-\frac{3}{4} \tan ^{-1}\left(\frac{\sin (x)}{\sqrt{4 \cos ^2(x)-1}}\right)-\frac{3}{4} \tan ^{-1}\left(\frac{\sin (x)}{\sqrt{8 \cos ^2(x)-1}}\right)",1,"Could not integrate","F",-1
428,0,0,33,0.0000405,"\int \left(2-3 \sin ^2(x)\right)^{3/5} \sin (4 x) \, dx","IntegrateAlgebraic[(2 - 3*Sin[x]^2)^(3/5)*Sin[4*x],x]","\int \left(2-3 \sin ^2(x)\right)^{3/5} \sin (4 x) \, dx","\frac{5}{36} \left(2-3 \sin ^2(x)\right)^{8/5}-\frac{20}{117} \left(2-3 \sin ^2(x)\right)^{13/5}",1,"Could not integrate","F",-1
429,0,0,33,0.000053,"\int \cos (x) \sqrt{\cos (2 x)} \, dx","IntegrateAlgebraic[Cos[x]*Sqrt[Cos[2*x]],x]","\int \cos (x) \sqrt{\cos (2 x)} \, dx","\frac{\sin ^{-1}\left(\sqrt{2} \sin (x)\right)}{2 \sqrt{2}}+\frac{1}{2} \sin (x) \sqrt{\cos (2 x)}",1,"Could not integrate","F",-1
430,0,0,55,0.0000398,"\int \cos ^{\frac{3}{2}}(2 x) \sin (x) \, dx","IntegrateAlgebraic[Cos[2*x]^(3/2)*Sin[x],x]","\int \cos ^{\frac{3}{2}}(2 x) \sin (x) \, dx","-\frac{1}{4} \cos (x) \cos ^{\frac{3}{2}}(2 x)+\frac{3}{8} \cos (x) \sqrt{\cos (2 x)}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{2} \cos (x)}{\sqrt{\cos (2 x)}}\right)}{8 \sqrt{2}}",1,"Could not integrate","F",-1
431,0,0,16,0.0000392,"\int \frac{\sin (x)}{\cos ^{\frac{5}{2}}(2 x)} \, dx","IntegrateAlgebraic[Sin[x]/Cos[2*x]^(5/2),x]","\int \frac{\sin (x)}{\cos ^{\frac{5}{2}}(2 x)} \, dx","-\frac{\cos (3 x)}{3 \cos ^{\frac{3}{2}}(2 x)}",1,"Could not integrate","F",-1
432,0,0,49,0.0000387,"\int \cos ^{\frac{3}{2}}(2 x) \sec ^3(x) \, dx","IntegrateAlgebraic[Cos[2*x]^(3/2)*Sec[x]^3,x]","\int \cos ^{\frac{3}{2}}(2 x) \sec ^3(x) \, dx","2 \sqrt{2} \sin ^{-1}\left(\sqrt{2} \sin (x)\right)-\frac{5}{2} \tan ^{-1}\left(\frac{\sin (x)}{\sqrt{\cos (2 x)}}\right)-\frac{1}{2} \sqrt{\cos (2 x)} \tan (x) \sec (x)",1,"Could not integrate","F",-1
433,0,0,87,0.0000489,"\int \frac{\sin ^2(x) \left(3 \sin ^3(x)-\cos (x) \sin (4 x)\right)}{\cos ^{\frac{7}{2}}(2 x)} \, dx","IntegrateAlgebraic[(Sin[x]^2*(3*Sin[x]^3 - Cos[x]*Sin[4*x]))/Cos[2*x]^(7/2),x]","\int \frac{\sin ^2(x) \left(3 \sin ^3(x)-\cos (x) \sin (4 x)\right)}{\cos ^{\frac{7}{2}}(2 x)} \, dx","-\frac{11 \cos (x)}{20 \cos ^{\frac{3}{2}}(2 x)}-\frac{2 \cos ^3(x)}{3 \cos ^{\frac{3}{2}}(2 x)}+\frac{63 \cos (x)}{20 \sqrt{\cos (2 x)}}+\frac{3 \sin ^2(x) \cos (x)}{10 \cos ^{\frac{5}{2}}(2 x)}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \cos (x)}{\sqrt{\cos (2 x)}}\right)}{\sqrt{2}}",1,"Could not integrate","F",-1
434,0,0,68,0.0000363,"\int \left(4-5 \sec ^2(x)\right)^{3/2} \, dx","IntegrateAlgebraic[(4 - 5*Sec[x]^2)^(3/2),x]","\int \left(4-5 \sec ^2(x)\right)^{3/2} \, dx","-\frac{5}{2} \tan (x) \sqrt{-5 \tan ^2(x)-1}+8 \tan ^{-1}\left(\frac{2 \tan (x)}{\sqrt{-5 \tan ^2(x)-1}}\right)-\frac{7}{2} \sqrt{5} \tan ^{-1}\left(\frac{\sqrt{5} \tan (x)}{\sqrt{-5 \tan ^2(x)-1}}\right)",1,"Could not integrate","F",-1
435,0,0,40,0.0000373,"\int \frac{1}{\left(4-5 \sec ^2(x)\right)^{3/2}} \, dx","IntegrateAlgebraic[(4 - 5*Sec[x]^2)^(-3/2),x]","\int \frac{1}{\left(4-5 \sec ^2(x)\right)^{3/2}} \, dx","\frac{1}{8} \tan ^{-1}\left(\frac{2 \tan (x)}{\sqrt{-5 \tan ^2(x)-1}}\right)-\frac{5 \tan (x)}{4 \sqrt{-5 \tan ^2(x)-1}}",1,"Could not integrate","F",-1
436,0,0,94,0.0000421,"\int \frac{-2 \cot ^2(x)+\sin (x)}{\left(1+5 \tan ^2(x)\right)^{3/2}} \, dx","IntegrateAlgebraic[(-2*Cot[x]^2 + Sin[x])/(1 + 5*Tan[x]^2)^(3/2),x]","\int \frac{-2 \cot ^2(x)+\sin (x)}{\left(1+5 \tan ^2(x)\right)^{3/2}} \, dx","-\frac{1}{8} \cos (x) \sqrt{5 \tan ^2(x)+1}-\frac{\cos (x)}{4 \sqrt{5 \tan ^2(x)+1}}-\frac{1}{4} \tanh ^{-1}\left(\frac{2 \tan (x)}{\sqrt{5 \tan ^2(x)+1}}\right)+\frac{9}{2} \sqrt{5 \tan ^2(x)+1} \cot (x)-\frac{5 \cot (x)}{2 \sqrt{5 \tan ^2(x)+1}}",1,"Could not integrate","F",-1
437,0,0,39,0.0000807,"\int \frac{(-3+\cos (2 x)) \sec ^4(x)}{\sqrt{4-\cot ^2(x)}} \, dx","IntegrateAlgebraic[((-3 + Cos[2*x])*Sec[x]^4)/Sqrt[4 - Cot[x]^2],x]","\int \frac{(-3+\cos (2 x)) \sec ^4(x)}{\sqrt{4-\cot ^2(x)}} \, dx","-\frac{1}{3} \tan ^3(x) \sqrt{4-\cot ^2(x)}-\frac{2}{3} \tan (x) \sqrt{4-\cot ^2(x)}",1,"Could not integrate","F",-1
438,0,0,73,0.0000648,"\int \frac{\left(3+\sin ^2(x)\right) \tan ^3(x)}{\left(-2+\cos ^2(x)\right) \left(5-4 \sec ^2(x)\right)^{3/2}} \, dx","IntegrateAlgebraic[((3 + Sin[x]^2)*Tan[x]^3)/((-2 + Cos[x]^2)*(5 - 4*Sec[x]^2)^(3/2)),x]","\int \frac{\left(3+\sin ^2(x)\right) \tan ^3(x)}{\left(-2+\cos ^2(x)\right) \left(5-4 \sec ^2(x)\right)^{3/2}} \, dx","-\frac{2}{15 \sqrt{5-4 \sec ^2(x)}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{5-4 \sec ^2(x)}}{\sqrt{3}}\right)}{6 \sqrt{3}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{5-4 \sec ^2(x)}}{\sqrt{5}}\right)}{5 \sqrt{5}}",1,"Could not integrate","F",-1
439,0,0,57,0.0000632,"\int \frac{\csc ^2(x) \left(\sec ^2(x)-3 \tan (x) \sqrt{4 \sec ^2(x)+5 \tan ^2(x)}\right)}{\left(4 \sec ^2(x)+5 \tan ^2(x)\right)^{3/2}} \, dx","IntegrateAlgebraic[(Csc[x]^2*(Sec[x]^2 - 3*Tan[x]*Sqrt[4*Sec[x]^2 + 5*Tan[x]^2]))/(4*Sec[x]^2 + 5*Tan[x]^2)^(3/2),x]","\int \frac{\csc ^2(x) \left(\sec ^2(x)-3 \tan (x) \sqrt{4 \sec ^2(x)+5 \tan ^2(x)}\right)}{\left(4 \sec ^2(x)+5 \tan ^2(x)\right)^{3/2}} \, dx","-\frac{7 \tan (x)}{8 \sqrt{9 \tan ^2(x)+4}}+\frac{3}{8} \log \left(9 \tan ^2(x)+4\right)-\frac{3}{4} \log (\tan (x))-\frac{\cot (x)}{4 \sqrt{9 \tan ^2(x)+4}}",1,"Could not integrate","F",-1
440,0,0,66,0.0000398,"\int \tan (x) \left(1+5 \tan ^2(x)\right)^{5/2} \, dx","IntegrateAlgebraic[Tan[x]*(1 + 5*Tan[x]^2)^(5/2),x]","\int \tan (x) \left(1+5 \tan ^2(x)\right)^{5/2} \, dx","\frac{1}{5} \left(5 \tan ^2(x)+1\right)^{5/2}-\frac{4}{3} \left(5 \tan ^2(x)+1\right)^{3/2}+16 \sqrt{5 \tan ^2(x)+1}-32 \tan ^{-1}\left(\frac{1}{2} \sqrt{5 \tan ^2(x)+1}\right)",1,"Could not integrate","F",-1
441,0,0,54,0.00004,"\int \frac{\tan (x)}{\left(1+5 \tan ^2(x)\right)^{5/2}} \, dx","IntegrateAlgebraic[Tan[x]/(1 + 5*Tan[x]^2)^(5/2),x]","\int \frac{\tan (x)}{\left(1+5 \tan ^2(x)\right)^{5/2}} \, dx","\frac{1}{16 \sqrt{5 \tan ^2(x)+1}}-\frac{1}{12 \left(5 \tan ^2(x)+1\right)^{3/2}}+\frac{1}{32} \tan ^{-1}\left(\frac{1}{2} \sqrt{5 \tan ^2(x)+1}\right)",1,"Could not integrate","F",-1
442,0,0,133,0.0000417,"\int \frac{\tan (x)}{\sqrt[3]{a^3+b^3 \tan ^2(x)}} \, dx","IntegrateAlgebraic[Tan[x]/(a^3 + b^3*Tan[x]^2)^(1/3),x]","\int \frac{\tan (x)}{\sqrt[3]{a^3+b^3 \tan ^2(x)}} \, dx","\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a^3+b^3 \tan ^2(x)}}{\sqrt[3]{a^3-b^3}}+1}{\sqrt{3}}\right)}{2 \sqrt[3]{a^3-b^3}}+\frac{3 \log \left(\sqrt[3]{a^3-b^3}-\sqrt[3]{a^3+b^3 \tan ^2(x)}\right)}{4 \sqrt[3]{a^3-b^3}}+\frac{\log (\cos (x))}{2 \sqrt[3]{a^3-b^3}}",1,"Could not integrate","F",-1
443,0,0,69,0.0000403,"\int \tan (x) \left(1-7 \tan ^2(x)\right)^{2/3} \, dx","IntegrateAlgebraic[Tan[x]*(1 - 7*Tan[x]^2)^(2/3),x]","\int \tan (x) \left(1-7 \tan ^2(x)\right)^{2/3} \, dx","\frac{3}{4} \left(1-7 \tan ^2(x)\right)^{2/3}+2 \sqrt{3} \tan ^{-1}\left(\frac{\sqrt[3]{1-7 \tan ^2(x)}+1}{\sqrt{3}}\right)+3 \log \left(2-\sqrt[3]{1-7 \tan ^2(x)}\right)+2 \log (\cos (x))",1,"Could not integrate","F",-1
444,0,0,52,0.0000412,"\int \frac{\cot (x)}{\sqrt[4]{a^4+b^4 \csc ^2(x)}} \, dx","IntegrateAlgebraic[Cot[x]/(a^4 + b^4*Csc[x]^2)^(1/4),x]","\int \frac{\cot (x)}{\sqrt[4]{a^4+b^4 \csc ^2(x)}} \, dx","\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a^4+b^4 \csc ^2(x)}}{a}\right)}{a}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a^4+b^4 \csc ^2(x)}}{a}\right)}{a}",1,"Could not integrate","F",-1
445,0,0,54,0.000042,"\int \frac{\cot (x)}{\sqrt[4]{a^4-b^4 \csc ^2(x)}} \, dx","IntegrateAlgebraic[Cot[x]/(a^4 - b^4*Csc[x]^2)^(1/4),x]","\int \frac{\cot (x)}{\sqrt[4]{a^4-b^4 \csc ^2(x)}} \, dx","\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a^4-b^4 \csc ^2(x)}}{a}\right)}{a}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a^4-b^4 \csc ^2(x)}}{a}\right)}{a}",1,"Could not integrate","F",-1
446,0,0,133,0.0000651,"\int \frac{\sec ^2(x) \tan (x) \left(\sqrt[3]{1-3 \sec ^2(x)} \sin ^2(x)+3 \tan ^2(x)\right)}{\left(1-3 \sec ^2(x)\right)^{5/6} \left(1-\sqrt{1-3 \sec ^2(x)}\right)} \, dx","IntegrateAlgebraic[(Sec[x]^2*Tan[x]*((1 - 3*Sec[x]^2)^(1/3)*Sin[x]^2 + 3*Tan[x]^2))/((1 - 3*Sec[x]^2)^(5/6)*(1 - Sqrt[1 - 3*Sec[x]^2])),x]","\int \frac{\sec ^2(x) \tan (x) \left(\sqrt[3]{1-3 \sec ^2(x)} \sin ^2(x)+3 \tan ^2(x)\right)}{\left(1-3 \sec ^2(x)\right)^{5/6} \left(1-\sqrt{1-3 \sec ^2(x)}\right)} \, dx","-\frac{1}{4} \left(1-3 \sec ^2(x)\right)^{2/3}-\sqrt[6]{1-3 \sec ^2(x)}+\frac{1}{2 \left(1-\sqrt{1-3 \sec ^2(x)}\right)}+\frac{1}{4} \log \left(\sec ^2(x)\right)-\frac{3}{2} \log \left(1-\sqrt[6]{1-3 \sec ^2(x)}\right)+\frac{1}{3} \log \left(1-\sqrt{1-3 \sec ^2(x)}\right)+\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[6]{1-3 \sec ^2(x)}+1}{\sqrt{3}}\right)",1,"Could not integrate","F",-1
447,0,0,100,0.000128,"\int \frac{\sec ^2(x) \left(-\cos (2 x)+2 \tan ^2(x)\right)}{(\tan (x) \tan (2 x))^{3/2}} \, dx","IntegrateAlgebraic[(Sec[x]^2*(-Cos[2*x] + 2*Tan[x]^2))/(Tan[x]*Tan[2*x])^(3/2),x]","\int \frac{\sec ^2(x) \left(-\cos (2 x)+2 \tan ^2(x)\right)}{(\tan (x) \tan (2 x))^{3/2}} \, dx","\frac{2 \tan ^3(x)}{3 (\tan (x) \tan (2 x))^{3/2}}+\frac{3 \tan (x)}{4 \sqrt{\tan (x) \tan (2 x)}}+\frac{\tan (x)}{2 (\tan (x) \tan (2 x))^{3/2}}+2 \tanh ^{-1}\left(\frac{\tan (x)}{\sqrt{\tan (x) \tan (2 x)}}\right)-\frac{11 \tanh ^{-1}\left(\frac{\sqrt{2} \tan (x)}{\sqrt{\tan (x) \tan (2 x)}}\right)}{4 \sqrt{2}}",1,"Could not integrate","F",-1
448,0,0,112,0.0000443,"\int \frac{\tan (x)}{\left(a^3-b^3 \cos ^n(x)\right)^{4/3}} \, dx","IntegrateAlgebraic[Tan[x]/(a^3 - b^3*Cos[x]^n)^(4/3),x]","\int \frac{\tan (x)}{\left(a^3-b^3 \cos ^n(x)\right)^{4/3}} \, dx","\frac{\log (\cos (x))}{2 a^4}-\frac{3}{a^3 n \sqrt[3]{a^3-b^3 \cos ^n(x)}}-\frac{3 \log \left(a-\sqrt[3]{a^3-b^3 \cos ^n(x)}\right)}{2 a^4 n}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3-b^3 \cos ^n(x)}+a}{\sqrt{3} a}\right)}{a^4 n}",1,"Could not integrate","F",-1
449,0,0,95,0.0000403,"\int \left(1+2 \cos ^9(x)\right)^{5/6} \tan (x) \, dx","IntegrateAlgebraic[(1 + 2*Cos[x]^9)^(5/6)*Tan[x],x]","\int \left(1+2 \cos ^9(x)\right)^{5/6} \tan (x) \, dx","-\frac{2}{15} \left(2 \cos ^9(x)+1\right)^{5/6}+\frac{\tan ^{-1}\left(\frac{1-\sqrt[3]{2 \cos ^9(x)+1}}{\sqrt{3} \sqrt[6]{2 \cos ^9(x)+1}}\right)}{3 \sqrt{3}}+\frac{1}{3} \tanh ^{-1}\left(\sqrt[6]{2 \cos ^9(x)+1}\right)-\frac{1}{9} \tanh ^{-1}\left(\sqrt{2 \cos ^9(x)+1}\right)",1,"Could not integrate","F",-1
450,0,0,49,0.0000407,"\int \frac{\cos (x) \sin ^8(x)}{\left(2-5 \sin ^3(x)\right)^{4/3}} \, dx","IntegrateAlgebraic[(Cos[x]*Sin[x]^8)/(2 - 5*Sin[x]^3)^(4/3),x]","\int \frac{\cos (x) \sin ^8(x)}{\left(2-5 \sin ^3(x)\right)^{4/3}} \, dx","-\frac{1}{625} \left(2-5 \sin ^3(x)\right)^{5/3}+\frac{2}{125} \left(2-5 \sin ^3(x)\right)^{2/3}+\frac{4}{125 \sqrt[3]{2-5 \sin ^3(x)}}",1,"Could not integrate","F",-1
451,0,0,20,0.0000524,"\int \frac{\sec ^2(x) \tan (x) \left(1+\sqrt[3]{1-8 \tan ^2(x)}\right)}{\left(1-8 \tan ^2(x)\right)^{2/3}} \, dx","IntegrateAlgebraic[(Sec[x]^2*Tan[x]*(1 + (1 - 8*Tan[x]^2)^(1/3)))/(1 - 8*Tan[x]^2)^(2/3),x]","\int \frac{\sec ^2(x) \tan (x) \left(1+\sqrt[3]{1-8 \tan ^2(x)}\right)}{\left(1-8 \tan ^2(x)\right)^{2/3}} \, dx","-\frac{3}{32} \left(\sqrt[3]{1-8 \tan ^2(x)}+1\right)^2",1,"Could not integrate","F",-1
452,0,0,27,0.0000421,"\int \frac{\csc (x) \sec (x) \left(1+\sqrt[3]{1-8 \tan ^2(x)}\right)}{\left(1-8 \tan ^2(x)\right)^{2/3}} \, dx","IntegrateAlgebraic[(Csc[x]*Sec[x]*(1 + (1 - 8*Tan[x]^2)^(1/3)))/(1 - 8*Tan[x]^2)^(2/3),x]","\int \frac{\csc (x) \sec (x) \left(1+\sqrt[3]{1-8 \tan ^2(x)}\right)}{\left(1-8 \tan ^2(x)\right)^{2/3}} \, dx","\frac{3}{2} \log \left(1-\sqrt[3]{1-8 \tan ^2(x)}\right)-\log (\tan (x))",1,"Could not integrate","F",-1
453,0,0,101,0.0000906,"\int \frac{\left(5 \cos ^2(x)-\sqrt{-1+5 \sin ^2(x)}\right) \tan (x)}{\sqrt[4]{-1+5 \sin ^2(x)} \left(2+\sqrt{-1+5 \sin ^2(x)}\right)} \, dx","IntegrateAlgebraic[((5*Cos[x]^2 - Sqrt[-1 + 5*Sin[x]^2])*Tan[x])/((-1 + 5*Sin[x]^2)^(1/4)*(2 + Sqrt[-1 + 5*Sin[x]^2])),x]","\int \frac{\left(5 \cos ^2(x)-\sqrt{-1+5 \sin ^2(x)}\right) \tan (x)}{\sqrt[4]{-1+5 \sin ^2(x)} \left(2+\sqrt{-1+5 \sin ^2(x)}\right)} \, dx","2 \sqrt[4]{5 \sin ^2(x)-1}-\frac{\sqrt[4]{5 \sin ^2(x)-1}}{2 \left(\sqrt{5 \sin ^2(x)-1}+2\right)}-\frac{3 \tan ^{-1}\left(\frac{\sqrt[4]{5 \sin ^2(x)-1}}{\sqrt{2}}\right)}{\sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{5 \sin ^2(x)-1}}{\sqrt{2}}\right)}{2 \sqrt{2}}",1,"Could not integrate","F",-1
454,0,0,25,0.0000399,"\int \cos ^3(x) \cos ^{\frac{2}{3}}(2 x) \sin (x) \, dx","IntegrateAlgebraic[Cos[x]^3*Cos[2*x]^(2/3)*Sin[x],x]","\int \cos ^3(x) \cos ^{\frac{2}{3}}(2 x) \sin (x) \, dx","-\frac{3}{64} \cos ^{\frac{8}{3}}(2 x)-\frac{3}{40} \cos ^{\frac{5}{3}}(2 x)",1,"Could not integrate","F",-1
455,0,0,102,0.0000351,"\int \frac{\sin ^6(x) \tan (x)}{\cos ^{\frac{3}{4}}(2 x)} \, dx","IntegrateAlgebraic[(Sin[x]^6*Tan[x])/Cos[2*x]^(3/4),x]","\int \frac{\sin ^6(x) \tan (x)}{\cos ^{\frac{3}{4}}(2 x)} \, dx","\frac{1}{36} \cos ^{\frac{9}{4}}(2 x)-\frac{1}{5} \cos ^{\frac{5}{4}}(2 x)+\frac{7}{4} \sqrt[4]{\cos (2 x)}+\frac{\tan ^{-1}\left(\frac{1-\sqrt{\cos (2 x)}}{\sqrt{2} \sqrt[4]{\cos (2 x)}}\right)}{\sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{\cos (2 x)}+1}{\sqrt{2} \sqrt[4]{\cos (2 x)}}\right)}{\sqrt{2}}",1,"Could not integrate","F",-1
456,0,0,17,0.0000552,"\int \sqrt{\tan (x) \tan (2 x)} \, dx","IntegrateAlgebraic[Sqrt[Tan[x]*Tan[2*x]],x]","\int \sqrt{\tan (x) \tan (2 x)} \, dx","-\tanh ^{-1}\left(\frac{\tan (x)}{\sqrt{\tan (x) \tan (2 x)}}\right)",1,"Could not integrate","F",-1
457,0,0,32,0.000028,"\int \sqrt{\cot (2 x) \tan (x)} \, dx","IntegrateAlgebraic[Sqrt[Cot[2*x]*Tan[x]],x]","\int \sqrt{\cot (2 x) \tan (x)} \, dx","\tan ^{-1}\left(\frac{\sqrt{2} \tan (x)}{\sqrt{1-\tan ^2(x)}}\right)-\frac{\sin ^{-1}(\tan (x))}{\sqrt{2}}",1,"Could not integrate","F",-1
458,1,31,31,0.0089998,"\int \frac{1}{x^5 \left(5+x^2\right)} \, dx","IntegrateAlgebraic[1/(x^5*(5 + x^2)),x]","-\frac{1}{250} \log \left(x^2+5\right)+\frac{2 x^2-5}{100 x^4}+\frac{\log (x)}{125}","-\frac{1}{20 x^4}+\frac{1}{50 x^2}-\frac{1}{250} \log \left(x^2+5\right)+\frac{\log (x)}{125}",1,"(-5 + 2*x^2)/(100*x^4) + Log[x]/125 - Log[5 + x^2]/250","A",1
459,1,37,39,0.0216369,"\int \frac{1}{x^6 \left(5+x^2\right)} \, dx","IntegrateAlgebraic[1/(x^6*(5 + x^2)),x]","\frac{-3 x^4+5 x^2-15}{375 x^5}-\frac{\tan ^{-1}\left(\frac{x}{\sqrt{5}}\right)}{125 \sqrt{5}}","-\frac{1}{25 x^5}+\frac{1}{75 x^3}-\frac{1}{125 x}-\frac{\tan ^{-1}\left(\frac{x}{\sqrt{5}}\right)}{125 \sqrt{5}}",1,"(-15 + 5*x^2 - 3*x^4)/(375*x^5) - ArcTan[x/Sqrt[5]]/(125*Sqrt[5])","A",1
460,1,40,58,0.025648,"\int \frac{1}{x \left(-4+x^2\right)^4} \, dx","IntegrateAlgebraic[1/(x*(-4 + x^2)^4),x]","-\frac{1}{512} \log \left(x^2-4\right)+\frac{-3 x^4+30 x^2-88}{384 \left(x^2-4\right)^3}+\frac{\log (x)}{256}","\frac{1}{128 \left(4-x^2\right)}+\frac{1}{64 \left(4-x^2\right)^2}+\frac{1}{24 \left(4-x^2\right)^3}-\frac{1}{512} \log \left(4-x^2\right)+\frac{\log (x)}{256}",1,"(-88 + 30*x^2 - 3*x^4)/(384*(-4 + x^2)^3) + Log[x]/256 - Log[-4 + x^2]/512","A",1
461,1,46,52,0.0429687,"\int \frac{1}{x \left(-2+x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[1/(x*(-2 + x^2)^(5/2)),x]","\frac{3 x^2-8}{12 \left(x^2-2\right)^{3/2}}+\frac{\tan ^{-1}\left(\frac{\sqrt{x^2-2}}{\sqrt{2}}\right)}{4 \sqrt{2}}","\frac{1}{4 \sqrt{x^2-2}}-\frac{1}{6 \left(x^2-2\right)^{3/2}}+\frac{\tan ^{-1}\left(\frac{\sqrt{x^2-2}}{\sqrt{2}}\right)}{4 \sqrt{2}}",1,"(-8 + 3*x^2)/(12*(-2 + x^2)^(3/2)) + ArcTan[Sqrt[-2 + x^2]/Sqrt[2]]/(4*Sqrt[2])","A",1
462,1,49,61,0.0477075,"\int \frac{\left(-10+x^2\right)^{5/2}}{x} \, dx","IntegrateAlgebraic[(-10 + x^2)^(5/2)/x,x]","\frac{1}{15} \sqrt{x^2-10} \left(3 x^4-110 x^2+2300\right)-100 \sqrt{10} \tan ^{-1}\left(\frac{\sqrt{x^2-10}}{\sqrt{10}}\right)","\frac{1}{5} \left(x^2-10\right)^{5/2}-\frac{10}{3} \left(x^2-10\right)^{3/2}+100 \sqrt{x^2-10}-100 \sqrt{10} \tan ^{-1}\left(\frac{\sqrt{x^2-10}}{\sqrt{10}}\right)",1,"(Sqrt[-10 + x^2]*(2300 - 110*x^2 + 3*x^4))/15 - 100*Sqrt[10]*ArcTan[Sqrt[-10 + x^2]/Sqrt[10]]","A",1
463,0,0,16,0.00005,"\int x^{1+2 n} \, dx","IntegrateAlgebraic[x^(1 + 2*n),x]","\int x^{1+2 n} \, dx","\frac{x^{2 (n+1)}}{2 (n+1)}",1,"Could not integrate","F",-1
464,1,39,46,0.0200896,"\int \frac{x^7}{\left(-5+x^2\right)^3} \, dx","IntegrateAlgebraic[x^7/(-5 + x^2)^3,x]","\frac{15}{2} \log \left(x^2-5\right)+\frac{2 x^6-20 x^4-100 x^2+625}{4 \left(x^2-5\right)^2}","\frac{x^2}{2}+\frac{75}{2 \left(5-x^2\right)}-\frac{125}{4 \left(5-x^2\right)^2}+\frac{15}{2} \log \left(5-x^2\right)",1,"(625 - 100*x^2 - 20*x^4 + 2*x^6)/(4*(-5 + x^2)^2) + (15*Log[-5 + x^2])/2","A",1
465,1,23,40,0.0112136,"\int \frac{-4 x^3+3 x^5}{\left(-1+x^2\right)^5} \, dx","IntegrateAlgebraic[(-4*x^3 + 3*x^5)/(-1 + x^2)^5,x]","\frac{-18 x^4+28 x^2-7}{24 \left(x^2-1\right)^4}","-\frac{3}{4 \left(1-x^2\right)^2}+\frac{1}{3 \left(1-x^2\right)^3}+\frac{1}{8 \left(1-x^2\right)^4}",1,"(-7 + 28*x^2 - 18*x^4)/(24*(-1 + x^2)^4)","A",1
466,1,25,27,0.0228524,"\int x^3 \left(1+x^2\right)^{9/14} \, dx","IntegrateAlgebraic[x^3*(1 + x^2)^(9/14),x]","\frac{7}{851} \left(x^2+1\right)^{9/14} \left(23 x^4+9 x^2-14\right)","\frac{7}{37} \left(x^2+1\right)^{37/14}-\frac{7}{23} \left(x^2+1\right)^{23/14}",1,"(7*(1 + x^2)^(9/14)*(-14 + 9*x^2 + 23*x^4))/851","A",1
467,1,25,38,0.0274376,"\int \frac{x^5}{\left(-4+x^2\right)^{13/6}} \, dx","IntegrateAlgebraic[x^5/(-4 + x^2)^(13/6),x]","\frac{3 \left(7 x^4-336 x^2+1152\right)}{35 \left(x^2-4\right)^{7/6}}","\frac{3}{5} \left(x^2-4\right)^{5/6}-\frac{24}{\sqrt[6]{x^2-4}}-\frac{48}{7 \left(x^2-4\right)^{7/6}}",1,"(3*(1152 - 336*x^2 + 7*x^4))/(35*(-4 + x^2)^(7/6))","A",1
468,1,23,33,0.0339904,"\int \frac{1}{\left(1+2 x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[(1 + 2*x^2)^(-5/2),x]","\frac{x \left(4 x^2+3\right)}{3 \left(2 x^2+1\right)^{3/2}}","\frac{2 x}{3 \sqrt{2 x^2+1}}+\frac{x}{3 \left(2 x^2+1\right)^{3/2}}",1,"(x*(3 + 4*x^2))/(3*(1 + 2*x^2)^(3/2))","A",1
469,1,27,43,0.2776601,"\int \frac{1}{\left(-1-2 x+x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[(-1 - 2*x + x^2)^(-5/2),x]","\frac{(x-1) \left(x^2-2 x-2\right)}{6 \left(x^2-2 x-1\right)^{3/2}}","\frac{1-x}{6 \left(x^2-2 x-1\right)^{3/2}}-\frac{1-x}{6 \sqrt{x^2-2 x-1}}",1,"((-1 + x)*(-2 - 2*x + x^2))/(6*(-1 - 2*x + x^2)^(3/2))","A",1
470,1,28,47,0.0498002,"\int \frac{1}{x^4 \left(-8+x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[1/(x^4*(-8 + x^2)^(3/2)),x]","\frac{-x^4+4 x^2+8}{192 x^3 \sqrt{x^2-8}}","-\frac{x}{192 \sqrt{x^2-8}}+\frac{1}{48 \sqrt{x^2-8} x}+\frac{1}{24 \sqrt{x^2-8} x^3}",1,"(8 + 4*x^2 - x^4)/(192*x^3*Sqrt[-8 + x^2])","A",1
471,1,28,28,0.0088269,"\int \frac{\left(5+x^2\right)^2}{x^{13/3}} \, dx","IntegrateAlgebraic[(5 + x^2)^2/x^(13/3),x]","\frac{3 x^{2/3}}{2}-\frac{15}{2 x^{4/3}}-\frac{15}{2 x^{10/3}}","\frac{3 x^{2/3}}{2}-\frac{15}{2 x^{4/3}}-\frac{15}{2 x^{10/3}}",1,"-15/(2*x^(10/3)) - 15/(2*x^(4/3)) + (3*x^(2/3))/2","A",1
472,1,49,52,0.0335932,"\int \frac{1}{x^7 \left(1+x^2\right)^3} \, dx","IntegrateAlgebraic[1/(x^7*(1 + x^2)^3),x]","5 \log \left(x^2+1\right)+\frac{-60 x^8-90 x^6-20 x^4+5 x^2-2}{12 x^6 \left(x^2+1\right)^2}-10 \log (x)","-\frac{1}{6 x^6}+\frac{3}{4 x^4}-\frac{2}{x^2+1}-\frac{3}{x^2}-\frac{1}{4 \left(x^2+1\right)^2}+5 \log \left(x^2+1\right)-10 \log (x)",1,"(-2 + 5*x^2 - 20*x^4 - 90*x^6 - 60*x^8)/(12*x^6*(1 + x^2)^2) - 10*Log[x] + 5*Log[1 + x^2]","A",1
473,1,25,25,8.5442857,"\int \frac{\left(\frac{2+x^2}{x^2}\right)^{7/9}}{\left(2+x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[((2 + x^2)/x^2)^(7/9)/(2 + x^2)^(3/2),x]","-\frac{9 \left(\frac{2}{x^2}+1\right)^{7/9} x}{10 \sqrt{x^2+2}}","-\frac{9 \left(\frac{2}{x^2}+1\right)^{7/9} x}{10 \sqrt{x^2+2}}",1,"(-9*(1 + 2/x^2)^(7/9)*x)/(10*Sqrt[2 + x^2])","A",1
474,1,35,50,0.2873913,"\int \frac{x^4}{\left(\sqrt{10}-x^2\right)^{9/2}} \, dx","IntegrateAlgebraic[x^4/(Sqrt[10] - x^2)^(9/2),x]","-\frac{x^5 \left(2 x^2-7 \sqrt{10}\right)}{350 \left(\sqrt{10}-x^2\right)^{7/2}}","\frac{x^5}{175 \left(\sqrt{10}-x^2\right)^{5/2}}+\frac{x^5}{7 \sqrt{10} \left(\sqrt{10}-x^2\right)^{7/2}}",1,"-1/350*(x^5*(-7*Sqrt[10] + 2*x^2))/(Sqrt[10] - x^2)^(7/2)","A",1
475,1,44,24,0.0572706,"\int \frac{x^2}{\left(3-x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[x^2/(3 - x^2)^(3/2),x]","-\frac{\sqrt{3-x^2} x}{x^2-3}-i \log \left(\sqrt{3-x^2}-i x\right)","\frac{x}{\sqrt{3-x^2}}-\sin ^{-1}\left(\frac{x}{\sqrt{3}}\right)",1,"-((x*Sqrt[3 - x^2])/(-3 + x^2)) - I*Log[(-I)*x + Sqrt[3 - x^2]]","C",1
476,1,46,40,0.0718931,"\int \frac{\left(25-x^2\right)^{3/2}}{x^4} \, dx","IntegrateAlgebraic[(25 - x^2)^(3/2)/x^4,x]","\frac{\sqrt{25-x^2} \left(4 x^2-25\right)}{3 x^3}-2 \tan ^{-1}\left(\frac{\sqrt{25-x^2}}{x+5}\right)","\frac{\sqrt{25-x^2}}{x}-\frac{\left(25-x^2\right)^{3/2}}{3 x^3}+\sin ^{-1}\left(\frac{x}{5}\right)",1,"(Sqrt[25 - x^2]*(-25 + 4*x^2))/(3*x^3) - 2*ArcTan[Sqrt[25 - x^2]/(5 + x)]","A",1
477,1,37,49,0.0625498,"\int \frac{1}{\left(1-2 x^2\right)^{7/2}} \, dx","IntegrateAlgebraic[(1 - 2*x^2)^(-7/2),x]","-\frac{x \sqrt{1-2 x^2} \left(32 x^4-40 x^2+15\right)}{15 \left(2 x^2-1\right)^3}","\frac{8 x}{15 \sqrt{1-2 x^2}}+\frac{4 x}{15 \left(1-2 x^2\right)^{3/2}}+\frac{x}{5 \left(1-2 x^2\right)^{5/2}}",1,"-1/15*(x*Sqrt[1 - 2*x^2]*(15 - 40*x^2 + 32*x^4))/(-1 + 2*x^2)^3","A",1
478,1,55,47,0.3239863,"\int \frac{1}{\left(-7+6 x-x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[(-7 + 6*x - x^2)^(-5/2),x]","\frac{\sqrt{-x^2+6 x-7} \left(-x^3+9 x^2-24 x+18\right)}{6 \left(-x+\sqrt{2}+3\right)^2 \left(x+\sqrt{2}-3\right)^2}","-\frac{3-x}{6 \sqrt{-x^2+6 x-7}}-\frac{3-x}{6 \left(-x^2+6 x-7\right)^{3/2}}",1,"(Sqrt[-7 + 6*x - x^2]*(18 - 24*x + 9*x^2 - x^3))/(6*(3 + Sqrt[2] - x)^2*(-3 + Sqrt[2] + x)^2)","A",1
479,1,38,36,0.0065718,"\int \left(1-2 x-2 x^2\right)^3 \, dx","IntegrateAlgebraic[(1 - 2*x - 2*x^2)^3,x]","\frac{1}{35} \left(-40 x^7-140 x^6-84 x^5+140 x^4+70 x^3-105 x^2+35 x\right)","-\frac{8 x^7}{7}-4 x^6-\frac{12 x^5}{5}+4 x^4+2 x^3-3 x^2+x",1,"(35*x - 105*x^2 + 70*x^3 + 140*x^4 - 84*x^5 - 140*x^6 - 40*x^7)/35","A",1
480,1,30,39,0.006057,"\int (-1+5 x) \left(-1-x+x^2\right)^2 \, dx","IntegrateAlgebraic[(-1 + 5*x)*(-1 - x + x^2)^2,x]","\frac{1}{60} x \left(50 x^5-132 x^4-45 x^3+220 x^2+90 x-60\right)","\frac{5 x^6}{6}-\frac{11 x^5}{5}-\frac{3 x^4}{4}+\frac{11 x^3}{3}+\frac{3 x^2}{2}-x",1,"(x*(-60 + 90*x + 220*x^2 - 45*x^3 - 132*x^4 + 50*x^5))/60","A",1
481,1,33,47,0.3654678,"\int \frac{1+3 x}{\left(1-8 x+2 x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[(1 + 3*x)/(1 - 8*x + 2*x^2)^(5/2),x]","\frac{8 x^3-48 x^2+54 x-1}{42 \left(2 x^2-8 x+1\right)^{3/2}}","\frac{1-2 x}{6 \left(2 x^2-8 x+1\right)^{3/2}}-\frac{2 (2-x)}{21 \sqrt{2 x^2-8 x+1}}",1,"(-1 + 54*x - 48*x^2 + 8*x^3)/(42*(1 - 8*x + 2*x^2)^(3/2))","A",1
482,1,45,45,0.2905641,"\int \frac{-1-8 x+8 x^3}{\left(1+2 x-4 x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[(-1 - 8*x + 8*x^3)/(1 + 2*x - 4*x^2)^(5/2),x]","\frac{\sqrt{-4 x^2+2 x+1} \left(488 x^3-216 x^2-156 x-27\right)}{75 \left(4 x^2-2 x-1\right)^2}","-\frac{4 (x+1)}{15 \left(-4 x^2+2 x+1\right)^{3/2}}-\frac{122 x+7}{75 \sqrt{-4 x^2+2 x+1}}",1,"(Sqrt[1 + 2*x - 4*x^2]*(-27 - 156*x - 216*x^2 + 488*x^3))/(75*(-1 - 2*x + 4*x^2)^2)","A",1
483,0,0,83,0.0000355,"\int x^2 \cos ^5(x) \, dx","IntegrateAlgebraic[x^2*Cos[x]^5,x]","\int x^2 \cos ^5(x) \, dx","\frac{8}{15} x^2 \sin (x)+\frac{1}{5} x^2 \sin (x) \cos ^4(x)+\frac{4}{15} x^2 \sin (x) \cos ^2(x)-\frac{2 \sin ^5(x)}{125}+\frac{76 \sin ^3(x)}{675}-\frac{298 \sin (x)}{225}+\frac{2}{25} x \cos ^5(x)+\frac{8}{45} x \cos ^3(x)+\frac{16}{15} x \cos (x)",1,"Could not integrate","F",-1
484,0,0,73,0.0000366,"\int x^3 \sin ^3(x) \, dx","IntegrateAlgebraic[x^3*Sin[x]^3,x]","\int x^3 \sin ^3(x) \, dx","-\frac{2}{3} x^3 \cos (x)-\frac{1}{3} x^3 \sin ^2(x) \cos (x)+\frac{1}{3} x^2 \sin ^3(x)+2 x^2 \sin (x)-\frac{2 \sin ^3(x)}{27}-\frac{40 \sin (x)}{9}+\frac{40}{9} x \cos (x)+\frac{2}{9} x \sin ^2(x) \cos (x)",1,"Could not integrate","F",-1
485,0,0,105,0.0000343,"\int x^2 \sin ^6(x) \, dx","IntegrateAlgebraic[x^2*Sin[x]^6,x]","\int x^2 \sin ^6(x) \, dx","\frac{5 x^3}{48}-\frac{1}{6} x^2 \sin ^5(x) \cos (x)-\frac{5}{24} x^2 \sin ^3(x) \cos (x)-\frac{5}{16} x^2 \sin (x) \cos (x)-\frac{245 x}{1152}+\frac{1}{18} x \sin ^6(x)+\frac{5}{48} x \sin ^4(x)+\frac{5}{16} x \sin ^2(x)+\frac{1}{108} \sin ^5(x) \cos (x)+\frac{65 \sin ^3(x) \cos (x)}{1728}+\frac{245 \sin (x) \cos (x)}{1152}",1,"Could not integrate","F",-1
486,0,0,44,0.0000382,"\int x^2 \cos (x) \sin ^2(x) \, dx","IntegrateAlgebraic[x^2*Cos[x]*Sin[x]^2,x]","\int x^2 \cos (x) \sin ^2(x) \, dx","\frac{1}{3} x^2 \sin ^3(x)-\frac{2 \sin ^3(x)}{27}-\frac{4 \sin (x)}{9}+\frac{4}{9} x \cos (x)+\frac{2}{9} x \sin ^2(x) \cos (x)",1,"Could not integrate","F",-1
487,0,0,33,0.000037,"\int x \cos ^2(x) \cot ^2(x) \, dx","IntegrateAlgebraic[x*Cos[x]^2*Cot[x]^2,x]","\int x \cos ^2(x) \cot ^2(x) \, dx","-\frac{3 x^2}{4}-\frac{\cos ^2(x)}{4}-x \cot (x)+\log (\sin (x))-\frac{1}{2} x \sin (x) \cos (x)",1,"Could not integrate","F",-1
488,0,0,30,0.0000359,"\int x \sec (x) \tan ^3(x) \, dx","IntegrateAlgebraic[x*Sec[x]*Tan[x]^3,x]","\int x \sec (x) \tan ^3(x) \, dx","\frac{1}{3} x \sec ^3(x)-x \sec (x)+\frac{5}{6} \tanh ^{-1}(\sin (x))-\frac{1}{6} \tan (x) \sec (x)",1,"Could not integrate","F",-1
489,0,0,16,0.0000338,"\int x \sec ^2(x) \tan (x) \, dx","IntegrateAlgebraic[x*Sec[x]^2*Tan[x],x]","\int x \sec ^2(x) \tan (x) \, dx","\frac{1}{2} x \sec ^2(x)-\frac{\tan (x)}{2}",1,"Could not integrate","F",-1
490,0,0,62,0.000031,"\int x \sin ^2(x) \tan (x) \, dx","IntegrateAlgebraic[x*Sin[x]^2*Tan[x],x]","\int x \sin ^2(x) \tan (x) \, dx","\frac{1}{2} i \text{Li}_2\left(-e^{2 i x}\right)+\frac{i x^2}{2}+\frac{x}{4}-x \log \left(1+e^{2 i x}\right)-\frac{1}{2} x \sin ^2(x)-\frac{1}{4} \sin (x) \cos (x)",1,"Could not integrate","F",-1
491,0,0,59,0.0000349,"\int x \tan ^3(x) \, dx","IntegrateAlgebraic[x*Tan[x]^3,x]","\int x \tan ^3(x) \, dx","-\frac{1}{2} i \text{Li}_2\left(-e^{2 i x}\right)-\frac{i x^2}{2}+\frac{x}{2}+x \log \left(1+e^{2 i x}\right)+\frac{1}{2} x \tan ^2(x)-\frac{\tan (x)}{2}",1,"Could not integrate","F",-1
492,0,0,12,0.000046,"\int \frac{2 x+\sin (2 x)}{(\cos (x)+x \sin (x))^2} \, dx","IntegrateAlgebraic[(2*x + Sin[2*x])/(Cos[x] + x*Sin[x])^2,x]","\int \frac{2 x+\sin (2 x)}{(\cos (x)+x \sin (x))^2} \, dx","\frac{2}{\frac{\cot (x)}{x}+1}",1,"Could not integrate","F",-1
493,0,0,20,0.0000339,"\int \frac{x^2}{(x \cos (x)-\sin (x))^2} \, dx","IntegrateAlgebraic[x^2/(x*Cos[x] - Sin[x])^2,x]","\int \frac{x^2}{(x \cos (x)-\sin (x))^2} \, dx","\frac{x \csc (x)}{x \cos (x)-\sin (x)}-\cot (x)",1,"Could not integrate","F",-1
494,0,0,22,0.0000706,"\int a^{m x} b^{n x} \, dx","IntegrateAlgebraic[a^(m*x)*b^(n*x),x]","\int a^{m x} b^{n x} \, dx","\frac{a^{m x} b^{n x}}{m \log (a)+n \log (b)}",1,"Could not integrate","F",-1
495,0,0,34,0.0000745,"\int a^{-x} b^{-x} \left(a^x-b^x\right)^2 \, dx","IntegrateAlgebraic[(a^x - b^x)^2/(a^x*b^x),x]","\int a^{-x} b^{-x} \left(a^x-b^x\right)^2 \, dx","\frac{a^x b^{-x}-a^{-x} b^x}{\log (a)-\log (b)}-2 x",1,"Could not integrate","F",-1
496,0,0,9,0.0000608,"\int \left(-e^{-x}+e^x\right) \, dx","IntegrateAlgebraic[-E^(-x) + E^x,x]","\int \left(-e^{-x}+e^x\right) \, dx","e^{-x}+e^x",1,"Could not integrate","F",-1
497,0,0,22,0.0000623,"\int \left(-e^{-x}+e^x\right)^2 \, dx","IntegrateAlgebraic[(-E^(-x) + E^x)^2,x]","\int \left(-e^{-x}+e^x\right)^2 \, dx","-2 x-\frac{e^{-2 x}}{2}+\frac{e^{2 x}}{2}",1,"Could not integrate","F",-1
498,0,0,31,0.0000691,"\int \left(-e^{-x}+e^x\right)^3 \, dx","IntegrateAlgebraic[(-E^(-x) + E^x)^3,x]","\int \left(-e^{-x}+e^x\right)^3 \, dx","\frac{e^{-3 x}}{3}-3 e^{-x}-3 e^x+\frac{e^{3 x}}{3}",1,"Could not integrate","F",-1
499,0,0,36,0.0000668,"\int \left(-e^{-x}+e^x\right)^4 \, dx","IntegrateAlgebraic[(-E^(-x) + E^x)^4,x]","\int \left(-e^{-x}+e^x\right)^4 \, dx","6 x-\frac{e^{-4 x}}{4}+2 e^{-2 x}-2 e^{2 x}+\frac{e^{4 x}}{4}",1,"Could not integrate","F",-1
500,0,0,48,0.0000565,"\int \left(-e^{-x}+e^x\right)^n \, dx","IntegrateAlgebraic[(-E^(-x) + E^x)^n,x]","\int \left(-e^{-x}+e^x\right)^n \, dx","-\frac{\left(1-e^{2 x}\right) \left(e^x-e^{-x}\right)^n \, _2F_1\left(1,\frac{n+2}{2};1-\frac{n}{2};e^{2 x}\right)}{n}",1,"Could not integrate","F",-1
501,0,0,43,0.0001032,"\int \left(a^{-4 x}-a^{2 x}\right)^3 \, dx","IntegrateAlgebraic[(a^(-4*x) - a^(2*x))^3,x]","\int \left(a^{-4 x}-a^{2 x}\right)^3 \, dx","-\frac{a^{-12 x}}{12 \log (a)}+\frac{a^{-6 x}}{2 \log (a)}-\frac{a^{6 x}}{6 \log (a)}+3 x",1,"Could not integrate","F",-1
502,0,0,27,0.0000593,"\int \left(a^{k x}+a^{l x}\right) \, dx","IntegrateAlgebraic[a^(k*x) + a^(l*x),x]","\int \left(a^{k x}+a^{l x}\right) \, dx","\frac{a^{k x}}{k \log (a)}+\frac{a^{l x}}{l \log (a)}",1,"Could not integrate","F",-1
503,0,0,53,0.0000675,"\int \left(a^{k x}+a^{l x}\right)^2 \, dx","IntegrateAlgebraic[(a^(k*x) + a^(l*x))^2,x]","\int \left(a^{k x}+a^{l x}\right)^2 \, dx","\frac{2 a^{x (k+l)}}{\log (a) (k+l)}+\frac{a^{2 k x}}{2 k \log (a)}+\frac{a^{2 l x}}{2 l \log (a)}",1,"Could not integrate","F",-1
504,0,0,79,0.0000716,"\int \left(a^{k x}+a^{l x}\right)^3 \, dx","IntegrateAlgebraic[(a^(k*x) + a^(l*x))^3,x]","\int \left(a^{k x}+a^{l x}\right)^3 \, dx","\frac{3 a^{x (2 k+l)}}{\log (a) (2 k+l)}+\frac{3 a^{x (k+2 l)}}{\log (a) (k+2 l)}+\frac{a^{3 k x}}{3 k \log (a)}+\frac{a^{3 l x}}{3 l \log (a)}",1,"Could not integrate","F",-1
505,0,0,98,0.0000691,"\int \left(a^{k x}+a^{l x}\right)^4 \, dx","IntegrateAlgebraic[(a^(k*x) + a^(l*x))^4,x]","\int \left(a^{k x}+a^{l x}\right)^4 \, dx","\frac{3 a^{2 x (k+l)}}{\log (a) (k+l)}+\frac{4 a^{x (3 k+l)}}{\log (a) (3 k+l)}+\frac{4 a^{x (k+3 l)}}{\log (a) (k+3 l)}+\frac{a^{4 k x}}{4 k \log (a)}+\frac{a^{4 l x}}{4 l \log (a)}",1,"Could not integrate","F",-1
506,0,0,72,0.0000585,"\int \left(a^{k x}+a^{l x}\right)^n \, dx","IntegrateAlgebraic[(a^(k*x) + a^(l*x))^n,x]","\int \left(a^{k x}+a^{l x}\right)^n \, dx","\frac{\left(a^{x (k-l)}+1\right) \left(a^{k x}+a^{l x}\right)^n \, _2F_1\left(1,\frac{k n}{k-l}+1;\frac{l n}{k-l}+1;-a^{(k-l) x}\right)}{l n \log (a)}",1,"Could not integrate","F",-1
507,0,0,28,0.0000702,"\int \left(a^{k x}-a^{l x}\right) \, dx","IntegrateAlgebraic[a^(k*x) - a^(l*x),x]","\int \left(a^{k x}-a^{l x}\right) \, dx","\frac{a^{k x}}{k \log (a)}-\frac{a^{l x}}{l \log (a)}",1,"Could not integrate","F",-1
508,0,0,53,0.0000874,"\int \left(a^{k x}-a^{l x}\right)^2 \, dx","IntegrateAlgebraic[(a^(k*x) - a^(l*x))^2,x]","\int \left(a^{k x}-a^{l x}\right)^2 \, dx","-\frac{2 a^{x (k+l)}}{\log (a) (k+l)}+\frac{a^{2 k x}}{2 k \log (a)}+\frac{a^{2 l x}}{2 l \log (a)}",1,"Could not integrate","F",-1
509,0,0,79,0.0001087,"\int \left(a^{k x}-a^{l x}\right)^3 \, dx","IntegrateAlgebraic[(a^(k*x) - a^(l*x))^3,x]","\int \left(a^{k x}-a^{l x}\right)^3 \, dx","-\frac{3 a^{x (2 k+l)}}{\log (a) (2 k+l)}+\frac{3 a^{x (k+2 l)}}{\log (a) (k+2 l)}+\frac{a^{3 k x}}{3 k \log (a)}-\frac{a^{3 l x}}{3 l \log (a)}",1,"Could not integrate","F",-1
510,0,0,98,0.0001038,"\int \left(a^{k x}-a^{l x}\right)^4 \, dx","IntegrateAlgebraic[(a^(k*x) - a^(l*x))^4,x]","\int \left(a^{k x}-a^{l x}\right)^4 \, dx","\frac{3 a^{2 x (k+l)}}{\log (a) (k+l)}-\frac{4 a^{x (3 k+l)}}{\log (a) (3 k+l)}-\frac{4 a^{x (k+3 l)}}{\log (a) (k+3 l)}+\frac{a^{4 k x}}{4 k \log (a)}+\frac{a^{4 l x}}{4 l \log (a)}",1,"Could not integrate","F",-1
511,0,0,74,0.0000627,"\int \left(a^{k x}-a^{l x}\right)^n \, dx","IntegrateAlgebraic[(a^(k*x) - a^(l*x))^n,x]","\int \left(a^{k x}-a^{l x}\right)^n \, dx","\frac{\left(1-a^{x (k-l)}\right) \left(a^{k x}-a^{l x}\right)^n \, _2F_1\left(1,\frac{k n}{k-l}+1;\frac{l n}{k-l}+1;a^{(k-l) x}\right)}{l n \log (a)}",1,"Could not integrate","F",-1
512,0,0,15,0.0000905,"\int \left(1+a^{m x}\right) \, dx","IntegrateAlgebraic[1 + a^(m*x),x]","\int \left(1+a^{m x}\right) \, dx","\frac{a^{m x}}{m \log (a)}+x",1,"Could not integrate","F",-1
513,0,0,33,0.0001044,"\int \left(1+a^{m x}\right)^2 \, dx","IntegrateAlgebraic[(1 + a^(m*x))^2,x]","\int \left(1+a^{m x}\right)^2 \, dx","\frac{2 a^{m x}}{m \log (a)}+\frac{a^{2 m x}}{2 m \log (a)}+x",1,"Could not integrate","F",-1
514,0,0,50,0.0000628,"\int \left(1+a^{m x}\right)^3 \, dx","IntegrateAlgebraic[(1 + a^(m*x))^3,x]","\int \left(1+a^{m x}\right)^3 \, dx","\frac{3 a^{m x}}{m \log (a)}+\frac{3 a^{2 m x}}{2 m \log (a)}+\frac{a^{3 m x}}{3 m \log (a)}+x",1,"Could not integrate","F",-1
515,0,0,65,0.000061,"\int \left(1+a^{m x}\right)^4 \, dx","IntegrateAlgebraic[(1 + a^(m*x))^4,x]","\int \left(1+a^{m x}\right)^4 \, dx","\frac{4 a^{m x}}{m \log (a)}+\frac{3 a^{2 m x}}{m \log (a)}+\frac{4 a^{3 m x}}{3 m \log (a)}+\frac{a^{4 m x}}{4 m \log (a)}+x",1,"Could not integrate","F",-1
516,0,0,40,0.0000528,"\int \left(1+a^{m x}\right)^n \, dx","IntegrateAlgebraic[(1 + a^(m*x))^n,x]","\int \left(1+a^{m x}\right)^n \, dx","-\frac{\left(a^{m x}+1\right)^{n+1} \, _2F_1\left(1,n+1;n+2;a^{m x}+1\right)}{m (n+1) \log (a)}",1,"Could not integrate","F",-1
517,0,0,16,0.0000935,"\int \left(1-a^{m x}\right) \, dx","IntegrateAlgebraic[1 - a^(m*x),x]","\int \left(1-a^{m x}\right) \, dx","x-\frac{a^{m x}}{m \log (a)}",1,"Could not integrate","F",-1
518,0,0,33,0.0000561,"\int \left(1-a^{m x}\right)^2 \, dx","IntegrateAlgebraic[(1 - a^(m*x))^2,x]","\int \left(1-a^{m x}\right)^2 \, dx","-\frac{2 a^{m x}}{m \log (a)}+\frac{a^{2 m x}}{2 m \log (a)}+x",1,"Could not integrate","F",-1
519,0,0,50,0.0000629,"\int \left(1-a^{m x}\right)^3 \, dx","IntegrateAlgebraic[(1 - a^(m*x))^3,x]","\int \left(1-a^{m x}\right)^3 \, dx","-\frac{3 a^{m x}}{m \log (a)}+\frac{3 a^{2 m x}}{2 m \log (a)}-\frac{a^{3 m x}}{3 m \log (a)}+x",1,"Could not integrate","F",-1
520,0,0,65,0.0000643,"\int \left(1-a^{m x}\right)^4 \, dx","IntegrateAlgebraic[(1 - a^(m*x))^4,x]","\int \left(1-a^{m x}\right)^4 \, dx","-\frac{4 a^{m x}}{m \log (a)}+\frac{3 a^{2 m x}}{m \log (a)}-\frac{4 a^{3 m x}}{3 m \log (a)}+\frac{a^{4 m x}}{4 m \log (a)}+x",1,"Could not integrate","F",-1
521,0,0,44,0.0000519,"\int \left(1-a^{m x}\right)^n \, dx","IntegrateAlgebraic[(1 - a^(m*x))^n,x]","\int \left(1-a^{m x}\right)^n \, dx","-\frac{\left(1-a^{m x}\right)^{n+1} \, _2F_1\left(1,n+1;n+2;1-a^{m x}\right)}{m (n+1) \log (a)}",1,"Could not integrate","F",-1
522,0,0,24,0.0000904,"\int \frac{1}{b+a e^{n x}} \, dx","IntegrateAlgebraic[(b + a*E^(n*x))^(-1),x]","\int \frac{1}{b+a e^{n x}} \, dx","\frac{x}{b}-\frac{\log \left(a e^{n x}+b\right)}{b n}",1,"Could not integrate","F",-1
523,0,0,100,0.0000699,"\int \frac{e^x}{b+a e^{3 x}} \, dx","IntegrateAlgebraic[E^x/(b + a*E^(3*x)),x]","\int \frac{e^x}{b+a e^{3 x}} \, dx","\frac{\log \left(\sqrt[3]{a} e^x+\sqrt[3]{b}\right)}{2 \sqrt[3]{a} b^{2/3}}-\frac{\log \left(a e^{3 x}+b\right)}{6 \sqrt[3]{a} b^{2/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} e^x}{\sqrt{3} \sqrt[3]{b}}\right)}{\sqrt{3} \sqrt[3]{a} b^{2/3}}",1,"Could not integrate","F",-1
524,0,0,12,0.0000696,"\int \frac{-1+e^x}{1+e^x} \, dx","IntegrateAlgebraic[(-1 + E^x)/(1 + E^x),x]","\int \frac{-1+e^x}{1+e^x} \, dx","2 \log \left(e^x+1\right)-x",1,"Could not integrate","F",-1
525,0,0,47,0.000135,"\int \frac{e^{4 x}}{1-2 e^{2 x}+3 e^{4 x}} \, dx","IntegrateAlgebraic[E^(4*x)/(1 - 2*E^(2*x) + 3*E^(4*x)),x]","\int \frac{e^{4 x}}{1-2 e^{2 x}+3 e^{4 x}} \, dx","\frac{1}{12} \log \left(-2 e^{2 x}+3 e^{4 x}+1\right)-\frac{\tan ^{-1}\left(\frac{1-3 e^{2 x}}{\sqrt{2}}\right)}{6 \sqrt{2}}",1,"Could not integrate","F",-1
526,0,0,39,0.0001045,"\int \frac{e^x+e^{5 x}}{-1+e^x-e^{2 x}+e^{3 x}} \, dx","IntegrateAlgebraic[(E^x + E^(5*x))/(-1 + E^x - E^(2*x) + E^(3*x)),x]","\int \frac{e^x+e^{5 x}}{-1+e^x-e^{2 x}+e^{3 x}} \, dx","e^x+\frac{e^{2 x}}{2}+\log \left(1-e^x\right)-\frac{1}{2} \log \left(e^{2 x}+1\right)-\tan ^{-1}\left(e^x\right)",1,"Could not integrate","F",-1
527,0,0,30,0.0000672,"\int e^{n x} \left(a+b e^{n x}\right)^{r/s} \, dx","IntegrateAlgebraic[E^(n*x)*(a + b*E^(n*x))^(r/s),x]","\int e^{n x} \left(a+b e^{n x}\right)^{r/s} \, dx","\frac{s \left(a+b e^{n x}\right)^{\frac{r+s}{s}}}{b n (r+s)}",1,"Could not integrate","F",-1
528,0,0,54,0.0000679,"\int \sqrt[4]{1-2 e^{x/3}} \, dx","IntegrateAlgebraic[(1 - 2*E^(x/3))^(1/4),x]","\int \sqrt[4]{1-2 e^{x/3}} \, dx","12 \sqrt[4]{1-2 e^{x/3}}-6 \tan ^{-1}\left(\sqrt[4]{1-2 e^{x/3}}\right)-6 \tanh ^{-1}\left(\sqrt[4]{1-2 e^{x/3}}\right)",1,"Could not integrate","F",-1
529,0,0,59,0.0000542,"\int \left(a+b e^{n x}\right)^{r/s} \, dx","IntegrateAlgebraic[(a + b*E^(n*x))^(r/s),x]","\int \left(a+b e^{n x}\right)^{r/s} \, dx","-\frac{s \left(a+b e^{n x}\right)^{\frac{r+s}{s}} \, _2F_1\left(1,\frac{r+s}{s};\frac{r}{s}+2;\frac{e^{n x} b}{a}+1\right)}{a n (r+s)}",1,"Could not integrate","F",-1
530,0,0,18,0.0000749,"\int \frac{e^x}{\sqrt{a^2+e^{2 x}}} \, dx","IntegrateAlgebraic[E^x/Sqrt[a^2 + E^(2*x)],x]","\int \frac{e^x}{\sqrt{a^2+e^{2 x}}} \, dx","\tanh ^{-1}\left(\frac{e^x}{\sqrt{a^2+e^{2 x}}}\right)",1,"Could not integrate","F",-1
531,0,0,20,0.0000677,"\int \frac{e^x}{\sqrt{-a^2+e^{2 x}}} \, dx","IntegrateAlgebraic[E^x/Sqrt[-a^2 + E^(2*x)],x]","\int \frac{e^x}{\sqrt{-a^2+e^{2 x}}} \, dx","\tanh ^{-1}\left(\frac{e^x}{\sqrt{e^{2 x}-a^2}}\right)",1,"Could not integrate","F",-1
532,0,0,40,0.0000845,"\int \frac{e^{3 x/4}}{\left(-2+e^{3 x/4}\right) \sqrt{-2+e^{3 x/4}+e^{3 x/2}}} \, dx","IntegrateAlgebraic[E^((3*x)/4)/((-2 + E^((3*x)/4))*Sqrt[-2 + E^((3*x)/4) + E^((3*x)/2)]),x]","\int \frac{e^{3 x/4}}{\left(-2+e^{3 x/4}\right) \sqrt{-2+e^{3 x/4}+e^{3 x/2}}} \, dx","\frac{2}{3} \tanh ^{-1}\left(\frac{2-5 e^{3 x/4}}{4 \sqrt{e^{3 x/4}+e^{3 x/2}-2}}\right)",1,"Could not integrate","F",-1
533,0,0,37,0.0000709,"\int e^{-2 x} \left(-3+e^{7 x}\right)^{2/3} \, dx","IntegrateAlgebraic[(-3 + E^(7*x))^(2/3)/E^(2*x),x]","\int e^{-2 x} \left(-3+e^{7 x}\right)^{2/3} \, dx","\frac{1}{6} e^{-2 x} \left(e^{7 x}-3\right)^{5/3} \, _2F_1\left(1,\frac{29}{21};\frac{5}{7};\frac{e^{7 x}}{3}\right)",1,"Could not integrate","F",-1
534,0,0,73,0.000079,"\int \frac{e^{2 x}}{\left(3-e^{x/2}\right)^{3/4}} \, dx","IntegrateAlgebraic[E^(2*x)/(3 - E^(x/2))^(3/4),x]","\int \frac{e^{2 x}}{\left(3-e^{x/2}\right)^{3/4}} \, dx","\frac{8}{13} \left(3-e^{x/2}\right)^{13/4}-8 \left(3-e^{x/2}\right)^{9/4}+\frac{216}{5} \left(3-e^{x/2}\right)^{5/4}-216 \sqrt[4]{3-e^{x/2}}",1,"Could not integrate","F",-1
535,0,0,44,0.0000582,"\int e^{-x/2} x^3 \, dx","IntegrateAlgebraic[x^3/E^(x/2),x]","\int e^{-x/2} x^3 \, dx","-2 e^{-x/2} x^3-12 e^{-x/2} x^2-48 e^{-x/2} x-96 e^{-x/2}",1,"Could not integrate","F",-1
536,0,0,39,0.0000568,"\int \frac{e^{-x/2}}{x^3} \, dx","IntegrateAlgebraic[1/(E^(x/2)*x^3),x]","\int \frac{e^{-x/2}}{x^3} \, dx","\frac{\text{Ei}\left(-\frac{x}{2}\right)}{8}-\frac{e^{-x/2}}{2 x^2}+\frac{e^{-x/2}}{4 x}",1,"Could not integrate","F",-1
537,0,0,44,0.0000634,"\int a^{3 x} x^2 \, dx","IntegrateAlgebraic[a^(3*x)*x^2,x]","\int a^{3 x} x^2 \, dx","\frac{x^2 a^{3 x}}{3 \log (a)}+\frac{2 a^{3 x}}{27 \log ^3(a)}-\frac{2 x a^{3 x}}{9 \log ^2(a)}",1,"Could not integrate","F",-1
538,0,0,12,0.0000674,"\int e^{x^2} x \left(1+x^2\right) \, dx","IntegrateAlgebraic[E^x^2*x*(1 + x^2),x]","\int e^{x^2} x \left(1+x^2\right) \, dx","\frac{1}{2} e^{x^2} x^2",1,"Could not integrate","F",-1
539,0,0,32,0.0000638,"\int \frac{x}{\left(e^{-x}+e^x\right)^2} \, dx","IntegrateAlgebraic[x/(E^(-x) + E^x)^2,x]","\int \frac{x}{\left(e^{-x}+e^x\right)^2} \, dx","-\frac{x}{2 \left(e^{2 x}+1\right)}+\frac{x}{2}-\frac{1}{4} \log \left(e^{2 x}+1\right)",1,"Could not integrate","F",-1
540,0,0,15,0.0000695,"\int \frac{e^x \left(1-x-x^2\right)}{\sqrt{1-x^2}} \, dx","IntegrateAlgebraic[(E^x*(1 - x - x^2))/Sqrt[1 - x^2],x]","\int \frac{e^x \left(1-x-x^2\right)}{\sqrt{1-x^2}} \, dx","e^x \sqrt{1-x^2}",1,"Could not integrate","F",-1
541,0,0,27,0.0000345,"\int e^{-3 x} \cos (2 x) \, dx","IntegrateAlgebraic[Cos[2*x]/E^(3*x),x]","\int e^{-3 x} \cos (2 x) \, dx","\frac{2}{13} e^{-3 x} \sin (2 x)-\frac{3}{13} e^{-3 x} \cos (2 x)",1,"Could not integrate","F",-1
542,0,0,35,0.0000428,"\int \frac{\cos \left(\frac{x}{2}\right)+\sin \left(\frac{x}{2}\right)}{\sqrt[3]{e^x}} \, dx","IntegrateAlgebraic[(Cos[x/2] + Sin[x/2])/(E^x)^(1/3),x]","\int \frac{\cos \left(\frac{x}{2}\right)+\sin \left(\frac{x}{2}\right)}{\sqrt[3]{e^x}} \, dx","\frac{6 \sin \left(\frac{x}{2}\right)}{13 \sqrt[3]{e^x}}-\frac{30 \cos \left(\frac{x}{2}\right)}{13 \sqrt[3]{e^x}}",1,"Could not integrate","F",-1
543,0,0,57,0.0000594,"\int \frac{\cos \left(\frac{3 x}{2}\right)}{\sqrt[4]{3^{3 x}}} \, dx","IntegrateAlgebraic[Cos[(3*x)/2]/(3^(3*x))^(1/4),x]","\int \frac{\cos \left(\frac{3 x}{2}\right)}{\sqrt[4]{3^{3 x}}} \, dx","\frac{8 \sin \left(\frac{3 x}{2}\right)}{3 \sqrt[4]{3^{3 x}} \left(4+\log ^2(3)\right)}-\frac{4 \log (3) \cos \left(\frac{3 x}{2}\right)}{3 \sqrt[4]{3^{3 x}} \left(4+\log ^2(3)\right)}",1,"Could not integrate","F",-1
544,0,0,54,0.0000363,"\int e^{m x} \cos ^2(x) \, dx","IntegrateAlgebraic[E^(m*x)*Cos[x]^2,x]","\int e^{m x} \cos ^2(x) \, dx","\frac{2 e^{m x}}{m \left(m^2+4\right)}+\frac{m e^{m x} \cos ^2(x)}{m^2+4}+\frac{2 e^{m x} \sin (x) \cos (x)}{m^2+4}",1,"Could not integrate","F",-1
545,0,0,82,0.0000397,"\int e^{m x} \sin ^3(x) \, dx","IntegrateAlgebraic[E^(m*x)*Sin[x]^3,x]","\int e^{m x} \sin ^3(x) \, dx","\frac{m e^{m x} \sin ^3(x)}{m^2+9}-\frac{3 e^{m x} \sin ^2(x) \cos (x)}{m^2+9}+\frac{6 m e^{m x} \sin (x)}{m^4+10 m^2+9}-\frac{6 e^{m x} \cos (x)}{m^4+10 m^2+9}",1,"Could not integrate","F",-1
546,0,0,79,0.0000365,"\int \frac{\cos ^3\left(\frac{x}{3}\right)}{\sqrt{e^x}} \, dx","IntegrateAlgebraic[Cos[x/3]^3/Sqrt[E^x],x]","\int \frac{\cos ^3\left(\frac{x}{3}\right)}{\sqrt{e^x}} \, dx","\frac{32 \sin \left(\frac{x}{3}\right)}{65 \sqrt{e^x}}-\frac{2 \cos ^3\left(\frac{x}{3}\right)}{5 \sqrt{e^x}}-\frac{48 \cos \left(\frac{x}{3}\right)}{65 \sqrt{e^x}}+\frac{4 \sin \left(\frac{x}{3}\right) \cos ^2\left(\frac{x}{3}\right)}{5 \sqrt{e^x}}",1,"Could not integrate","F",-1
547,0,0,36,0.000071,"\int e^{2 x} \cos ^2(x) \sin ^2(x) \, dx","IntegrateAlgebraic[E^(2*x)*Cos[x]^2*Sin[x]^2,x]","\int e^{2 x} \cos ^2(x) \sin ^2(x) \, dx","\frac{e^{2 x}}{16}-\frac{1}{40} e^{2 x} \sin (4 x)-\frac{1}{80} e^{2 x} \cos (4 x)",1,"Could not integrate","F",-1
548,0,0,36,0.0000373,"\int e^{3 x} \cos ^2\left(\frac{3 x}{2}\right) \sin ^2\left(\frac{3 x}{2}\right) \, dx","IntegrateAlgebraic[E^(3*x)*Cos[(3*x)/2]^2*Sin[(3*x)/2]^2,x]","\int e^{3 x} \cos ^2\left(\frac{3 x}{2}\right) \sin ^2\left(\frac{3 x}{2}\right) \, dx","\frac{e^{3 x}}{24}-\frac{1}{60} e^{3 x} \sin (6 x)-\frac{1}{120} e^{3 x} \cos (6 x)",1,"Could not integrate","F",-1
549,0,0,58,0.0000344,"\int e^{m x} \tan ^2(x) \, dx","IntegrateAlgebraic[E^(m*x)*Tan[x]^2,x]","\int e^{m x} \tan ^2(x) \, dx","-\frac{e^{m x}}{m}+\frac{4 e^{(m+2 i) x} \, _2F_1\left(2,1-\frac{i m}{2};2-\frac{i m}{2};-e^{2 i x}\right)}{m+2 i}",1,"Could not integrate","F",-1
550,0,0,45,0.0000391,"\int e^{m x} \csc ^2(x) \, dx","IntegrateAlgebraic[E^(m*x)*Csc[x]^2,x]","\int e^{m x} \csc ^2(x) \, dx","-\frac{4 e^{(m+2 i) x} \, _2F_1\left(2,1-\frac{i m}{2};2-\frac{i m}{2};e^{2 i x}\right)}{m+2 i}",1,"Could not integrate","F",-1
551,0,0,51,0.0000393,"\int e^{m x} \sec ^3(x) \, dx","IntegrateAlgebraic[E^(m*x)*Sec[x]^3,x]","\int e^{m x} \sec ^3(x) \, dx","\frac{8 e^{(m+3 i) x} \, _2F_1\left(3,\frac{1}{2} (3-i m);\frac{1}{2} (5-i m);-e^{2 i x}\right)}{m+3 i}",1,"Could not integrate","F",-1
552,0,0,28,0.0000377,"\int \frac{e^x}{1+\cos (x)} \, dx","IntegrateAlgebraic[E^x/(1 + Cos[x]),x]","\int \frac{e^x}{1+\cos (x)} \, dx","(1-i) e^{(1+i) x} \, _2F_1\left(1-i,2;2-i;-e^{i x}\right)",1,"Could not integrate","F",-1
553,0,0,26,0.00004,"\int \frac{e^x}{1-\cos (x)} \, dx","IntegrateAlgebraic[E^x/(1 - Cos[x]),x]","\int \frac{e^x}{1-\cos (x)} \, dx","(-1+i) e^{(1+i) x} \, _2F_1\left(1-i,2;2-i;e^{i x}\right)",1,"Could not integrate","F",-1
554,0,0,30,0.0000396,"\int \frac{e^x}{1+\sin (x)} \, dx","IntegrateAlgebraic[E^x/(1 + Sin[x]),x]","\int \frac{e^x}{1+\sin (x)} \, dx","(-1+i) e^{(1-i) x} \, _2F_1\left(1+i,2;2+i;-i e^{-i x}\right)",1,"Could not integrate","F",-1
555,0,0,30,0.0000396,"\int \frac{e^x}{1-\sin (x)} \, dx","IntegrateAlgebraic[E^x/(1 - Sin[x]),x]","\int \frac{e^x}{1-\sin (x)} \, dx","(1+i) e^{(1+i) x} \, _2F_1\left(1-i,2;2-i;-i e^{i x}\right)",1,"Could not integrate","F",-1
556,0,0,15,0.000044,"\int \frac{e^x (1-\sin (x))}{1-\cos (x)} \, dx","IntegrateAlgebraic[(E^x*(1 - Sin[x]))/(1 - Cos[x]),x]","\int \frac{e^x (1-\sin (x))}{1-\cos (x)} \, dx","-\frac{e^x \sin (x)}{1-\cos (x)}",1,"Could not integrate","F",-1
557,0,0,41,0.0000342,"\int \frac{e^x (1+\sin (x))}{1-\cos (x)} \, dx","IntegrateAlgebraic[(E^x*(1 + Sin[x]))/(1 - Cos[x]),x]","\int \frac{e^x (1+\sin (x))}{1-\cos (x)} \, dx","\frac{e^x \sin (x)}{1-\cos (x)}-(2-2 i) e^{(1+i) x} \, _2F_1\left(1-i,2;2-i;e^{i x}\right)",1,"Could not integrate","F",-1
558,0,0,12,0.0000407,"\int \frac{e^x (1+\sin (x))}{1+\cos (x)} \, dx","IntegrateAlgebraic[(E^x*(1 + Sin[x]))/(1 + Cos[x]),x]","\int \frac{e^x (1+\sin (x))}{1+\cos (x)} \, dx","\frac{e^x \sin (x)}{\cos (x)+1}",1,"Could not integrate","F",-1
559,0,0,42,0.0000343,"\int \frac{e^x (1-\sin (x))}{1+\cos (x)} \, dx","IntegrateAlgebraic[(E^x*(1 - Sin[x]))/(1 + Cos[x]),x]","\int \frac{e^x (1-\sin (x))}{1+\cos (x)} \, dx","-\frac{e^x \sin (x)}{\cos (x)+1}+(2-2 i) e^{(1+i) x} \, _2F_1\left(1-i,2;2-i;-e^{i x}\right)",1,"Could not integrate","F",-1
560,0,0,46,0.0000424,"\int \frac{e^x (1-\cos (x))}{1-\sin (x)} \, dx","IntegrateAlgebraic[(E^x*(1 - Cos[x]))/(1 - Sin[x]),x]","\int \frac{e^x (1-\cos (x))}{1-\sin (x)} \, dx","-\frac{e^x \cos (x)}{1-\sin (x)}+(2+2 i) e^{(1+i) x} \, _2F_1\left(1-i,2;2-i;-i e^{i x}\right)",1,"Could not integrate","F",-1
561,0,0,14,0.0000422,"\int \frac{e^x (1+\cos (x))}{1-\sin (x)} \, dx","IntegrateAlgebraic[(E^x*(1 + Cos[x]))/(1 - Sin[x]),x]","\int \frac{e^x (1+\cos (x))}{1-\sin (x)} \, dx","\frac{e^x \cos (x)}{1-\sin (x)}",1,"Could not integrate","F",-1
562,0,0,43,0.0000653,"\int \frac{e^x (1+\cos (x))}{1+\sin (x)} \, dx","IntegrateAlgebraic[(E^x*(1 + Cos[x]))/(1 + Sin[x]),x]","\int \frac{e^x (1+\cos (x))}{1+\sin (x)} \, dx","\frac{e^x \cos (x)}{\sin (x)+1}-(2+2 i) e^{(1+i) x} \, _2F_1\left(1-i,2;2-i;i e^{i x}\right)",1,"Could not integrate","F",-1
563,0,0,13,0.0000434,"\int \frac{e^x (1-\cos (x))}{1+\sin (x)} \, dx","IntegrateAlgebraic[(E^x*(1 - Cos[x]))/(1 + Sin[x]),x]","\int \frac{e^x (1-\cos (x))}{1+\sin (x)} \, dx","-\frac{e^x \cos (x)}{\sin (x)+1}",1,"Could not integrate","F",-1
564,0,0,30,0.0000302,"\int e^x x \cos (x) \, dx","IntegrateAlgebraic[E^x*x*Cos[x],x]","\int e^x x \cos (x) \, dx","-\frac{1}{2} e^x \sin (x)+\frac{1}{2} e^x x \sin (x)+\frac{1}{2} e^x x \cos (x)",1,"Could not integrate","F",-1
565,0,0,50,0.000033,"\int e^x x^2 \sin (x) \, dx","IntegrateAlgebraic[E^x*x^2*Sin[x],x]","\int e^x x^2 \sin (x) \, dx","\frac{1}{2} e^x x^2 \sin (x)-\frac{1}{2} e^x x^2 \cos (x)-\frac{1}{2} e^x \sin (x)+e^x x \cos (x)-\frac{1}{2} e^x \cos (x)",1,"Could not integrate","F",-1
566,0,0,75,0.0000398,"\int e^{-3 x} x^2 \sin (x) \, dx","IntegrateAlgebraic[(x^2*Sin[x])/E^(3*x),x]","\int e^{-3 x} x^2 \sin (x) \, dx","-\frac{3}{10} e^{-3 x} x^2 \sin (x)-\frac{1}{10} e^{-3 x} x^2 \cos (x)-\frac{4}{25} e^{-3 x} x \sin (x)-\frac{9}{250} e^{-3 x} \sin (x)-\frac{3}{25} e^{-3 x} x \cos (x)-\frac{13}{250} e^{-3 x} \cos (x)",1,"Could not integrate","F",-1
567,0,0,187,0.0000406,"\int e^{x/2} x^2 \cos ^3(x) \, dx","IntegrateAlgebraic[E^(x/2)*x^2*Cos[x]^3,x]","\int e^{x/2} x^2 \cos ^3(x) \, dx","\frac{96}{185} e^{x/2} x^2 \sin (x)+\frac{2}{37} e^{x/2} x^2 \cos ^3(x)+\frac{48}{185} e^{x/2} x^2 \cos (x)+\frac{12}{37} e^{x/2} x^2 \sin (x) \cos ^2(x)-\frac{24}{125} e^{x/2} \sin (x)-\frac{24}{25} e^{x/2} x \sin (x)-\frac{792 e^{x/2} \sin (3 x)}{50653}-\frac{24 e^{x/2} x \sin (3 x)}{1369}-\frac{132}{125} e^{x/2} \cos (x)+\frac{18}{25} e^{x/2} x \cos (x)-\frac{428 e^{x/2} \cos (3 x)}{50653}+\frac{70 e^{x/2} x \cos (3 x)}{1369}",1,"Could not integrate","F",-1
568,0,0,87,0.00004,"\int e^{2 x} x^2 \sin (4 x) \, dx","IntegrateAlgebraic[E^(2*x)*x^2*Sin[4*x],x]","\int e^{2 x} x^2 \sin (4 x) \, dx","\frac{1}{10} e^{2 x} x^2 \sin (4 x)-\frac{1}{5} e^{2 x} x^2 \cos (4 x)+\frac{3}{50} e^{2 x} x \sin (4 x)-\frac{11}{500} e^{2 x} \sin (4 x)+\frac{2}{25} e^{2 x} x \cos (4 x)+\frac{1}{250} e^{2 x} \cos (4 x)",1,"Could not integrate","F",-1
569,0,0,185,0.0000419,"\int e^{x/2} x^2 \cos (x) \sin ^2(x) \, dx","IntegrateAlgebraic[E^(x/2)*x^2*Cos[x]*Sin[x]^2,x]","\int e^{x/2} x^2 \cos (x) \sin ^2(x) \, dx","\frac{1}{5} e^{x/2} x^2 \sin (x)-\frac{3}{37} e^{x/2} x^2 \sin (3 x)+\frac{1}{10} e^{x/2} x^2 \cos (x)-\frac{1}{74} e^{x/2} x^2 \cos (3 x)-\frac{8}{25} e^{x/2} x \sin (x)+\frac{24 e^{x/2} x \sin (3 x)}{1369}-\frac{8}{125} e^{x/2} \sin (x)+\frac{792 e^{x/2} \sin (3 x)}{50653}+\frac{6}{25} e^{x/2} x \cos (x)-\frac{70 e^{x/2} x \cos (3 x)}{1369}-\frac{44}{125} e^{x/2} \cos (x)+\frac{428 e^{x/2} \cos (3 x)}{50653}",1,"Could not integrate","F",-1
570,0,0,2,0.0000349,"\int \cosh (x) \, dx","IntegrateAlgebraic[Cosh[x],x]","\int \cosh (x) \, dx","\sinh (x)",1,"Could not integrate","F",-1
571,0,0,2,0.0000252,"\int \sinh (x) \, dx","IntegrateAlgebraic[Sinh[x],x]","\int \sinh (x) \, dx","\cosh (x)",1,"Could not integrate","F",-1
572,0,0,3,0.0000243,"\int \tanh (x) \, dx","IntegrateAlgebraic[Tanh[x],x]","\int \tanh (x) \, dx","\log (\cosh (x))",1,"Could not integrate","F",-1
573,0,0,3,0.0000244,"\int \coth (x) \, dx","IntegrateAlgebraic[Coth[x],x]","\int \coth (x) \, dx","\log (\sinh (x))",1,"Could not integrate","F",-1
574,0,0,3,0.0000267,"\int \text{sech}(x) \, dx","IntegrateAlgebraic[Sech[x],x]","\int \text{sech}(x) \, dx","\tan ^{-1}(\sinh (x))",1,"Could not integrate","F",-1
575,0,0,5,0.0000248,"\int \text{csch}(x) \, dx","IntegrateAlgebraic[Csch[x],x]","\int \text{csch}(x) \, dx","-\tanh ^{-1}(\cosh (x))",1,"Could not integrate","F",-1
576,0,0,14,0.0000268,"\int \cosh ^2(x) \, dx","IntegrateAlgebraic[Cosh[x]^2,x]","\int \cosh ^2(x) \, dx","\frac{x}{2}+\frac{1}{2} \sinh (x) \cosh (x)",1,"Could not integrate","F",-1
577,0,0,19,0.000028,"\int \sinh ^5(x) \, dx","IntegrateAlgebraic[Sinh[x]^5,x]","\int \sinh ^5(x) \, dx","\frac{\cosh ^5(x)}{5}-\frac{2 \cosh ^3(x)}{3}+\cosh (x)",1,"Could not integrate","F",-1
578,0,0,14,0.0000277,"\int \tanh ^4(x) \, dx","IntegrateAlgebraic[Tanh[x]^4,x]","\int \tanh ^4(x) \, dx","x-\frac{1}{3} \tanh ^3(x)-\tanh (x)",1,"Could not integrate","F",-1
579,0,0,16,0.0000261,"\int \text{csch}^3(x) \, dx","IntegrateAlgebraic[Csch[x]^3,x]","\int \text{csch}^3(x) \, dx","\frac{1}{2} \tanh ^{-1}(\cosh (x))-\frac{1}{2} \coth (x) \text{csch}(x)",1,"Could not integrate","F",-1
580,0,0,26,0.00003,"\int \text{sech}^5(x) \, dx","IntegrateAlgebraic[Sech[x]^5,x]","\int \text{sech}^5(x) \, dx","\frac{3}{8} \tan ^{-1}(\sinh (x))+\frac{1}{4} \tanh (x) \text{sech}^3(x)+\frac{3}{8} \tanh (x) \text{sech}(x)",1,"Could not integrate","F",-1
581,0,0,18,0.000034,"\int \sinh ^4(x) \tanh (x) \, dx","IntegrateAlgebraic[Sinh[x]^4*Tanh[x],x]","\int \sinh ^4(x) \tanh (x) \, dx","\frac{\cosh ^4(x)}{4}-\cosh ^2(x)+\log (\cosh (x))",1,"Could not integrate","F",-1
582,0,0,31,0.0000327,"\int \text{sech}^{\frac{23}{4}}(x) \sinh ^5(x) \, dx","IntegrateAlgebraic[Sech[x]^(23/4)*Sinh[x]^5,x]","\int \text{sech}^{\frac{23}{4}}(x) \sinh ^5(x) \, dx","-\frac{4}{19} \text{sech}^{\frac{19}{4}}(x)+\frac{8}{11} \text{sech}^{\frac{11}{4}}(x)-\frac{4}{3} \text{sech}^{\frac{3}{4}}(x)",1,"Could not integrate","F",-1
583,0,0,41,0.000074,"\int \frac{1}{a+b \cosh (x)} \, dx","IntegrateAlgebraic[(a + b*Cosh[x])^(-1),x]","\int \frac{1}{a+b \cosh (x)} \, dx","\frac{2 \tanh ^{-1}\left(\frac{(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}",1,"Could not integrate","F",-1
584,0,0,25,0.000037,"\int \frac{1}{(1+\cosh (x))^2} \, dx","IntegrateAlgebraic[(1 + Cosh[x])^(-2),x]","\int \frac{1}{(1+\cosh (x))^2} \, dx","\frac{\sinh (x)}{3 (\cosh (x)+1)}+\frac{\sinh (x)}{3 (\cosh (x)+1)^2}",1,"Could not integrate","F",-1
585,0,0,39,0.0000363,"\int \frac{1}{a+b \tanh (x)} \, dx","IntegrateAlgebraic[(a + b*Tanh[x])^(-1),x]","\int \frac{1}{a+b \tanh (x)} \, dx","\frac{a x}{a^2-b^2}-\frac{b \log (a \cosh (x)+b \sinh (x))}{a^2-b^2}",1,"Could not integrate","F",-1
586,0,0,31,0.0000576,"\int \frac{1}{a^2+b^2 \cosh ^2(x)} \, dx","IntegrateAlgebraic[(a^2 + b^2*Cosh[x]^2)^(-1),x]","\int \frac{1}{a^2+b^2 \cosh ^2(x)} \, dx","\frac{\tanh ^{-1}\left(\frac{a \tanh (x)}{\sqrt{a^2+b^2}}\right)}{a \sqrt{a^2+b^2}}",1,"Could not integrate","F",-1
587,0,0,35,0.0000374,"\int \frac{1}{a^2-b^2 \cosh ^2(x)} \, dx","IntegrateAlgebraic[(a^2 - b^2*Cosh[x]^2)^(-1),x]","\int \frac{1}{a^2-b^2 \cosh ^2(x)} \, dx","\frac{\tanh ^{-1}\left(\frac{a \tanh (x)}{\sqrt{a^2-b^2}}\right)}{a \sqrt{a^2-b^2}}",1,"Could not integrate","F",-1
588,0,0,25,0.0000322,"\int \frac{1}{1-\sinh ^4(x)} \, dx","IntegrateAlgebraic[(1 - Sinh[x]^4)^(-1),x]","\int \frac{1}{1-\sinh ^4(x)} \, dx","\frac{\tanh ^{-1}\left(\sqrt{2} \tanh (x)\right)}{2 \sqrt{2}}+\frac{\tanh (x)}{2}",1,"Could not integrate","F",-1
589,0,0,33,0.0000429,"\int \frac{\cosh ^3(x)-\sinh ^3(x)}{\cosh ^3(x)+\sinh ^3(x)} \, dx","IntegrateAlgebraic[(Cosh[x]^3 - Sinh[x]^3)/(Cosh[x]^3 + Sinh[x]^3),x]","\int \frac{\cosh ^3(x)-\sinh ^3(x)}{\cosh ^3(x)+\sinh ^3(x)} \, dx","-\frac{1}{3 (\tanh (x)+1)}-\frac{4 \tan ^{-1}\left(\frac{1-2 \tanh (x)}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"Could not integrate","F",-1
590,0,0,30,0.000034,"\int \cosh (x) \cosh (2 x) \cosh (3 x) \, dx","IntegrateAlgebraic[Cosh[x]*Cosh[2*x]*Cosh[3*x],x]","\int \cosh (x) \cosh (2 x) \cosh (3 x) \, dx","\frac{x}{4}+\frac{1}{8} \sinh (2 x)+\frac{1}{16} \sinh (4 x)+\frac{1}{24} \sinh (6 x)",1,"Could not integrate","F",-1
591,0,0,30,0.0000375,"\int \cosh \left(\frac{3 x}{2}\right) \sinh (x) \sinh \left(\frac{5 x}{2}\right) \, dx","IntegrateAlgebraic[Cosh[(3*x)/2]*Sinh[x]*Sinh[(5*x)/2],x]","\int \cosh \left(\frac{3 x}{2}\right) \sinh (x) \sinh \left(\frac{5 x}{2}\right) \, dx","-\frac{x}{4}+\frac{1}{8} \sinh (2 x)-\frac{1}{12} \sinh (3 x)+\frac{1}{20} \sinh (5 x)",1,"Could not integrate","F",-1
592,0,0,69,0.0000729,"\int \frac{\cosh (x) (-\cosh (2 x)+\tanh (x))}{\sqrt{\sinh (2 x)} \left(\sinh ^2(x)+\sinh (2 x)\right)} \, dx","IntegrateAlgebraic[(Cosh[x]*(-Cosh[2*x] + Tanh[x]))/(Sqrt[Sinh[2*x]]*(Sinh[x]^2 + Sinh[2*x])),x]","\int \frac{\cosh (x) (-\cosh (2 x)+\tanh (x))}{\sqrt{\sinh (2 x)} \left(\sinh ^2(x)+\sinh (2 x)\right)} \, dx","\frac{1}{6} \tan ^{-1}\left(\frac{\sinh (x)}{\sqrt{\sinh (2 x)}}\right)+\frac{\cosh (x)}{\sqrt{\sinh (2 x)}}+\sqrt{2} \tan ^{-1}\left(\text{sech}(x) \sqrt{\sinh (x) \cosh (x)}\right)-\frac{1}{3} \sqrt{2} \tanh ^{-1}\left(\text{sech}(x) \sqrt{\sinh (x) \cosh (x)}\right)",1,"Could not integrate","F",-1
593,0,0,37,0.0000405,"\int \frac{\sinh (x)}{\left(-9+4 \cosh ^2(x)\right)^{5/2}} \, dx","IntegrateAlgebraic[Sinh[x]/(-9 + 4*Cosh[x]^2)^(5/2),x]","\int \frac{\sinh (x)}{\left(-9+4 \cosh ^2(x)\right)^{5/2}} \, dx","\frac{2 \cosh (x)}{243 \sqrt{4 \cosh ^2(x)-9}}-\frac{\cosh (x)}{27 \left(4 \cosh ^2(x)-9\right)^{3/2}}",1,"Could not integrate","F",-1
594,0,0,29,0.0000411,"\int \frac{\sinh ^2(x) \sinh (2 x)}{\left(1-\sinh ^2(x)\right)^{3/2}} \, dx","IntegrateAlgebraic[(Sinh[x]^2*Sinh[2*x])/(1 - Sinh[x]^2)^(3/2),x]","\int \frac{\sinh ^2(x) \sinh (2 x)}{\left(1-\sinh ^2(x)\right)^{3/2}} \, dx","2 \sqrt{1-\sinh ^2(x)}+\frac{2}{\sqrt{1-\sinh ^2(x)}}",1,"Could not integrate","F",-1
595,0,0,15,0.0000351,"\int \frac{\cosh (x)}{\sqrt{\cosh (2 x)}} \, dx","IntegrateAlgebraic[Cosh[x]/Sqrt[Cosh[2*x]],x]","\int \frac{\cosh (x)}{\sqrt{\cosh (2 x)}} \, dx","\frac{\sinh ^{-1}\left(\sqrt{2} \sinh (x)\right)}{\sqrt{2}}",1,"Could not integrate","F",-1
596,0,0,16,0.0000274,"\int x \tanh ^2(x) \, dx","IntegrateAlgebraic[x*Tanh[x]^2,x]","\int x \tanh ^2(x) \, dx","\frac{x^2}{2}-x \tanh (x)+\log (\cosh (x))",1,"Could not integrate","F",-1
597,0,0,16,0.0000306,"\int x \coth ^2(x) \, dx","IntegrateAlgebraic[x*Coth[x]^2,x]","\int x \coth ^2(x) \, dx","\frac{x^2}{2}-x \coth (x)+\log (\sinh (x))",1,"Could not integrate","F",-1
598,0,0,20,0.0000562,"\int \frac{x+\cosh (x)+\sinh (x)}{\cosh (x)-\sinh (x)} \, dx","IntegrateAlgebraic[(x + Cosh[x] + Sinh[x])/(Cosh[x] - Sinh[x]),x]","\int \frac{x+\cosh (x)+\sinh (x)}{\cosh (x)-\sinh (x)} \, dx","e^x x-e^x+\frac{e^{2 x}}{2}",1,"Could not integrate","F",-1
599,0,0,15,0.0000514,"\int \frac{x+\cosh (x)+\sinh (x)}{1+\cosh (x)} \, dx","IntegrateAlgebraic[(x + Cosh[x] + Sinh[x])/(1 + Cosh[x]),x]","\int \frac{x+\cosh (x)+\sinh (x)}{1+\cosh (x)} \, dx","x-(1-x) \tanh \left(\frac{x}{2}\right)",1,"Could not integrate","F",-1
600,0,0,20,0.0000358,"\int e^{2 x} \text{csch}^4(x) \, dx","IntegrateAlgebraic[E^(2*x)*Csch[x]^4,x]","\int e^{2 x} \text{csch}^4(x) \, dx","\frac{8 e^{6 x}}{3 \left(1-e^{2 x}\right)^3}",1,"Could not integrate","F",-1
601,0,0,13,0.0000311,"\int e^{-2 x} \text{sech}^4(x) \, dx","IntegrateAlgebraic[Sech[x]^4/E^(2*x),x]","\int e^{-2 x} \text{sech}^4(x) \, dx","-\frac{8}{3 \left(e^{2 x}+1\right)^3}",1,"Could not integrate","F",-1
602,0,0,9,0.000035,"\int \frac{e^x}{\cosh (x)-\sinh (x)} \, dx","IntegrateAlgebraic[E^x/(Cosh[x] - Sinh[x]),x]","\int \frac{e^x}{\cosh (x)-\sinh (x)} \, dx","\frac{e^{2 x}}{2}",1,"Could not integrate","F",-1
603,0,0,13,0.0000335,"\int \frac{e^{m x}}{\cosh (x)+\sinh (x)} \, dx","IntegrateAlgebraic[E^(m*x)/(Cosh[x] + Sinh[x]),x]","\int \frac{e^{m x}}{\cosh (x)+\sinh (x)} \, dx","\frac{e^{(m-1) x}}{m-1}",1,"Could not integrate","F",-1
604,0,0,1,0.0000326,"\int \frac{e^x}{\cosh (x)+\sinh (x)} \, dx","IntegrateAlgebraic[E^x/(Cosh[x] + Sinh[x]),x]","\int \frac{e^x}{\cosh (x)+\sinh (x)} \, dx","x",1,"Could not integrate","F",-1
605,0,0,22,0.000032,"\int \frac{e^x}{1-\cosh (x)} \, dx","IntegrateAlgebraic[E^x/(1 - Cosh[x]),x]","\int \frac{e^x}{1-\cosh (x)} \, dx","-\frac{2}{1-e^x}-2 \log \left(1-e^x\right)",1,"Could not integrate","F",-1
606,0,0,13,0.000037,"\int \frac{e^x (1+\sinh (x))}{1+\cosh (x)} \, dx","IntegrateAlgebraic[(E^x*(1 + Sinh[x]))/(1 + Cosh[x]),x]","\int \frac{e^x (1+\sinh (x))}{1+\cosh (x)} \, dx","e^x+\frac{2}{e^x+1}",1,"Could not integrate","F",-1
607,0,0,15,0.0000336,"\int \frac{e^x (1-\sinh (x))}{1-\cosh (x)} \, dx","IntegrateAlgebraic[(E^x*(1 - Sinh[x]))/(1 - Cosh[x]),x]","\int \frac{e^x (1-\sinh (x))}{1-\cosh (x)} \, dx","e^x-\frac{2}{1-e^x}",1,"Could not integrate","F",-1
608,0,0,26,0.0000559,"\int x^m \log (x) \, dx","IntegrateAlgebraic[x^m*Log[x],x]","\int x^m \log (x) \, dx","\frac{x^{m+1} \log (x)}{m+1}-\frac{x^{m+1}}{(m+1)^2}",1,"Could not integrate","F",-1
609,0,0,42,0.0000332,"\int x^m \log ^2(x) \, dx","IntegrateAlgebraic[x^m*Log[x]^2,x]","\int x^m \log ^2(x) \, dx","\frac{2 x^{m+1}}{(m+1)^3}+\frac{x^{m+1} \log ^2(x)}{m+1}-\frac{2 x^{m+1} \log (x)}{(m+1)^2}",1,"Could not integrate","F",-1
610,0,0,34,0.0000385,"\int \frac{\log ^2(x)}{x^{5/2}} \, dx","IntegrateAlgebraic[Log[x]^2/x^(5/2),x]","\int \frac{\log ^2(x)}{x^{5/2}} \, dx","-\frac{16}{27 x^{3/2}}-\frac{2 \log ^2(x)}{3 x^{3/2}}-\frac{8 \log (x)}{9 x^{3/2}}",1,"Could not integrate","F",-1
611,0,0,28,0.000031,"\int (a+b x) \log (x) \, dx","IntegrateAlgebraic[(a + b*x)*Log[x],x]","\int (a+b x) \log (x) \, dx","-a x+a x \log (x)-\frac{b x^2}{4}+\frac{1}{2} b x^2 \log (x)",1,"Could not integrate","F",-1
612,0,0,67,0.000036,"\int (a+b x)^3 \log (x) \, dx","IntegrateAlgebraic[(a + b*x)^3*Log[x],x]","\int (a+b x)^3 \log (x) \, dx","-\frac{a^4 \log (x)}{4 b}-a^3 x-\frac{3}{4} a^2 b x^2-\frac{1}{3} a b^2 x^3+\frac{\log (x) (a+b x)^4}{4 b}-\frac{b^3 x^4}{16}",1,"Could not integrate","F",-1
613,0,0,23,0.0000425,"\int \left(-1-8 \log ^2(x)+3 \log ^3(x)\right) \, dx","IntegrateAlgebraic[-1 - 8*Log[x]^2 + 3*Log[x]^3,x]","\int \left(-1-8 \log ^2(x)+3 \log ^3(x)\right) \, dx","-35 x+3 x \log ^3(x)-17 x \log ^2(x)+34 x \log (x)",1,"Could not integrate","F",-1
614,0,0,60,0.0000344,"\int \left(1+x^4\right) \left(1-2 \log (x)+\log ^3(x)\right) \, dx","IntegrateAlgebraic[(1 + x^4)*(1 - 2*Log[x] + Log[x]^3),x]","\int \left(1+x^4\right) \left(1-2 \log (x)+\log ^3(x)\right) \, dx","\frac{169 x^5}{625}+\frac{1}{5} x^5 \log ^3(x)-\frac{3}{25} x^5 \log ^2(x)-\frac{44}{125} x^5 \log (x)-3 x+x \log ^3(x)-3 x \log ^2(x)+4 x \log (x)",1,"Could not integrate","F",-1
615,0,0,43,0.0000347,"\int \frac{1}{x^3 \log ^4(x)} \, dx","IntegrateAlgebraic[1/(x^3*Log[x]^4),x]","\int \frac{1}{x^3 \log ^4(x)} \, dx","-\frac{4}{3} \text{Ei}(-2 \log (x))-\frac{1}{3 x^2 \log ^3(x)}+\frac{1}{3 x^2 \log ^2(x)}-\frac{2}{3 x^2 \log (x)}",1,"Could not integrate","F",-1
616,0,0,29,0.0000403,"\int \frac{\log (x)}{a+b x} \, dx","IntegrateAlgebraic[Log[x]/(a + b*x),x]","\int \frac{\log (x)}{a+b x} \, dx","\frac{\text{Li}_2\left(-\frac{b x}{a}\right)}{b}+\frac{\log (x) \log \left(\frac{b x}{a}+1\right)}{b}",1,"Could not integrate","F",-1
617,0,0,29,0.0000511,"\int \frac{\log (x)}{(a+b x)^2} \, dx","IntegrateAlgebraic[Log[x]/(a + b*x)^2,x]","\int \frac{\log (x)}{(a+b x)^2} \, dx","\frac{x \log (x)}{a (a+b x)}-\frac{\log (a+b x)}{a b}",1,"Could not integrate","F",-1
618,0,0,12,0.0000299,"\int \frac{\log ^n(x)}{x} \, dx","IntegrateAlgebraic[Log[x]^n/x,x]","\int \frac{\log ^n(x)}{x} \, dx","\frac{\log ^{n+1}(x)}{n+1}",1,"Could not integrate","F",-1
619,0,0,19,0.000035,"\int \frac{(a+b \log (x))^n}{x} \, dx","IntegrateAlgebraic[(a + b*Log[x])^n/x,x]","\int \frac{(a+b \log (x))^n}{x} \, dx","\frac{(a+b \log (x))^{n+1}}{b (n+1)}",1,"Could not integrate","F",-1
620,0,0,11,0.000032,"\int \frac{1}{x (a+b \log (x))} \, dx","IntegrateAlgebraic[1/(x*(a + b*Log[x])),x]","\int \frac{1}{x (a+b \log (x))} \, dx","\frac{\log (a+b \log (x))}{b}",1,"Could not integrate","F",-1
621,0,0,23,0.0000363,"\int \frac{(a+b \log (x))^{-n}}{x} \, dx","IntegrateAlgebraic[1/(x*(a + b*Log[x])^n),x]","\int \frac{(a+b \log (x))^{-n}}{x} \, dx","\frac{(a+b \log (x))^{1-n}}{b (1-n)}",1,"Could not integrate","F",-1
622,0,0,16,0.0000362,"\int \frac{1}{x \sqrt{a^2+\log ^2(x)}} \, dx","IntegrateAlgebraic[1/(x*Sqrt[a^2 + Log[x]^2]),x]","\int \frac{1}{x \sqrt{a^2+\log ^2(x)}} \, dx","\tanh ^{-1}\left(\frac{\log (x)}{\sqrt{a^2+\log ^2(x)}}\right)",1,"Could not integrate","F",-1
623,0,0,18,0.0000338,"\int \frac{1}{x \sqrt{-a^2+\log ^2(x)}} \, dx","IntegrateAlgebraic[1/(x*Sqrt[-a^2 + Log[x]^2]),x]","\int \frac{1}{x \sqrt{-a^2+\log ^2(x)}} \, dx","\tanh ^{-1}\left(\frac{\log (x)}{\sqrt{\log ^2(x)-a^2}}\right)",1,"Could not integrate","F",-1
624,0,0,18,0.0000331,"\int \frac{1}{x \sqrt{a^2-\log ^2(x)}} \, dx","IntegrateAlgebraic[1/(x*Sqrt[a^2 - Log[x]^2]),x]","\int \frac{1}{x \sqrt{a^2-\log ^2(x)}} \, dx","\tan ^{-1}\left(\frac{\log (x)}{\sqrt{a^2-\log ^2(x)}}\right)",1,"Could not integrate","F",-1
625,0,0,22,0.0000404,"\int \frac{1}{x \log (x) \sqrt{a^2+\log ^2(x)}} \, dx","IntegrateAlgebraic[1/(x*Log[x]*Sqrt[a^2 + Log[x]^2]),x]","\int \frac{1}{x \log (x) \sqrt{a^2+\log ^2(x)}} \, dx","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a^2+\log ^2(x)}}{a}\right)}{a}",1,"Could not integrate","F",-1
626,0,0,24,0.0000373,"\int \frac{1}{x \log (x) \sqrt{a^2-\log ^2(x)}} \, dx","IntegrateAlgebraic[1/(x*Log[x]*Sqrt[a^2 - Log[x]^2]),x]","\int \frac{1}{x \log (x) \sqrt{a^2-\log ^2(x)}} \, dx","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a^2-\log ^2(x)}}{a}\right)}{a}",1,"Could not integrate","F",-1
627,0,0,23,0.0000699,"\int \frac{1}{x \log (x) \sqrt{-a^2+\log ^2(x)}} \, dx","IntegrateAlgebraic[1/(x*Log[x]*Sqrt[-a^2 + Log[x]^2]),x]","\int \frac{1}{x \log (x) \sqrt{-a^2+\log ^2(x)}} \, dx","\frac{\tan ^{-1}\left(\frac{\sqrt{\log ^2(x)-a^2}}{a}\right)}{a}",1,"Could not integrate","F",-1
628,0,0,11,0.0000292,"\int \frac{\log (\log (x))}{x} \, dx","IntegrateAlgebraic[Log[Log[x]]/x,x]","\int \frac{\log (\log (x))}{x} \, dx","\log (x) \log (\log (x))-\log (x)",1,"Could not integrate","F",-1
629,0,0,20,0.0000288,"\int \frac{\log ^2(\log (x))}{x} \, dx","IntegrateAlgebraic[Log[Log[x]]^2/x,x]","\int \frac{\log ^2(\log (x))}{x} \, dx","\log (x) \log ^2(\log (x))-2 \log (x) \log (\log (x))+2 \log (x)",1,"Could not integrate","F",-1
630,0,0,29,0.0000345,"\int \frac{\log ^3(\log (x))}{x} \, dx","IntegrateAlgebraic[Log[Log[x]]^3/x,x]","\int \frac{\log ^3(\log (x))}{x} \, dx","\log (x) \log ^3(\log (x))-3 \log (x) \log ^2(\log (x))+6 \log (x) \log (\log (x))-6 \log (x)",1,"Could not integrate","F",-1
631,0,0,38,0.0000305,"\int \frac{\log ^4(\log (x))}{x} \, dx","IntegrateAlgebraic[Log[Log[x]]^4/x,x]","\int \frac{\log ^4(\log (x))}{x} \, dx","\log (x) \log ^4(\log (x))-4 \log (x) \log ^3(\log (x))+12 \log (x) \log ^2(\log (x))-24 \log (x) \log (\log (x))+24 \log (x)",1,"Could not integrate","F",-1
632,0,0,24,0.0000366,"\int \frac{\log ^n(\log (x))}{x} \, dx","IntegrateAlgebraic[Log[Log[x]]^n/x,x]","\int \frac{\log ^n(\log (x))}{x} \, dx","(-\log (\log (x)))^{-n} \log ^n(\log (x)) \Gamma (n+1,-\log (\log (x)))",1,"Could not integrate","F",-1
633,0,0,4,0.0000381,"\int \frac{\cot (x)}{\log (\sin (x))} \, dx","IntegrateAlgebraic[Cot[x]/Log[Sin[x]],x]","\int \frac{\cot (x)}{\log (\sin (x))} \, dx","\log (\log (\sin (x)))",1,"Could not integrate","F",-1
634,0,0,7,0.000029,"\int (\cos (x)+\sec (x)) \tan (x) \, dx","IntegrateAlgebraic[(Cos[x] + Sec[x])*Tan[x],x]","\int (\cos (x)+\sec (x)) \tan (x) \, dx","\sec (x)-\cos (x)",1,"Could not integrate","F",-1
635,0,0,11,0.0000269,"\int \log (\cosh (x)) \sinh (x) \, dx","IntegrateAlgebraic[Log[Cosh[x]]*Sinh[x],x]","\int \log (\cosh (x)) \sinh (x) \, dx","\cosh (x) \log (\cosh (x))-\cosh (x)",1,"Could not integrate","F",-1
636,0,0,9,0.0000284,"\int \log (\cosh (x)) \tanh (x) \, dx","IntegrateAlgebraic[Log[Cosh[x]]*Tanh[x],x]","\int \log (\cosh (x)) \tanh (x) \, dx","\frac{1}{2} \log ^2(\cosh (x))",1,"Could not integrate","F",-1
637,0,0,26,0.0000307,"\int \log \left(x-\sqrt{1+x^2}\right) \, dx","IntegrateAlgebraic[Log[x - Sqrt[1 + x^2]],x]","\int \log \left(x-\sqrt{1+x^2}\right) \, dx","\sqrt{x^2+1}+x \log \left(x-\sqrt{x^2+1}\right)",1,"Could not integrate","F",-1
638,0,0,35,0.0000274,"\int \frac{\log (-1+x)}{x^3} \, dx","IntegrateAlgebraic[Log[-1 + x]/x^3,x]","\int \frac{\log (-1+x)}{x^3} \, dx","-\frac{\log (x-1)}{2 x^2}+\frac{1}{2 x}+\frac{1}{2} \log (1-x)-\frac{\log (x)}{2}",1,"Could not integrate","F",-1
639,0,0,32,0.0000437,"\int \left(-e^{-x}+e^x\right) \log \left(1+e^{2 x}\right) \, dx","IntegrateAlgebraic[(-E^(-x) + E^x)*Log[1 + E^(2*x)],x]","\int \left(-e^{-x}+e^x\right) \log \left(1+e^{2 x}\right) \, dx","-2 e^x+e^{-x} \log \left(e^{2 x}+1\right)+e^x \log \left(e^{2 x}+1\right)",1,"Could not integrate","F",-1
640,0,0,52,0.000033,"\int e^{3 x/2} \log \left(-1+e^x\right) \, dx","IntegrateAlgebraic[E^((3*x)/2)*Log[-1 + E^x],x]","\int e^{3 x/2} \log \left(-1+e^x\right) \, dx","-\frac{4 e^{x/2}}{3}-\frac{4}{9} e^{3 x/2}+\frac{2}{3} e^{3 x/2} \log \left(e^x-1\right)+\frac{4}{3} \tanh ^{-1}\left(e^{x/2}\right)",1,"Could not integrate","F",-1
641,0,0,30,0.0000336,"\int \cos ^3(x) \log (\sin (x)) \, dx","IntegrateAlgebraic[Cos[x]^3*Log[Sin[x]],x]","\int \cos ^3(x) \log (\sin (x)) \, dx","\frac{\sin ^3(x)}{9}-\sin (x)-\frac{1}{3} \sin ^3(x) \log (\sin (x))+\sin (x) \log (\sin (x))",1,"Could not integrate","F",-1
642,0,0,30,0.0000382,"\int \log (\tan (x)) \sec ^4(x) \, dx","IntegrateAlgebraic[Log[Tan[x]]*Sec[x]^4,x]","\int \log (\tan (x)) \sec ^4(x) \, dx","-\frac{\tan ^3(x)}{9}-\tan (x)+\frac{1}{3} \tan ^3(x) \log (\tan (x))+\tan (x) \log (\tan (x))",1,"Could not integrate","F",-1
643,0,0,28,0.0000331,"\int \frac{\log \left(\cos \left(\frac{x}{2}\right)\right)}{1+\cos (x)} \, dx","IntegrateAlgebraic[Log[Cos[x/2]]/(1 + Cos[x]),x]","\int \frac{\log \left(\cos \left(\frac{x}{2}\right)\right)}{1+\cos (x)} \, dx","-\frac{x}{2}+\tan \left(\frac{x}{2}\right)+\frac{\sin (x) \log \left(\cos \left(\frac{x}{2}\right)\right)}{\cos (x)+1}",1,"Could not integrate","F",-1
644,0,0,60,0.0000333,"\int \frac{\cos (x) \log (\sin (x))}{(1+\cos (x))^2} \, dx","IntegrateAlgebraic[(Cos[x]*Log[Sin[x]])/(1 + Cos[x])^2,x]","\int \frac{\cos (x) \log (\sin (x))}{(1+\cos (x))^2} \, dx","-\frac{2 x}{3}+\frac{8 \sin (x)}{9 (\cos (x)+1)}-\frac{\sin (x)}{9 (\cos (x)+1)^2}+\frac{2 \sin (x) \log (\sin (x))}{3 (\cos (x)+1)}-\frac{\sin (x) \log (\sin (x))}{3 (\cos (x)+1)^2}",1,"Could not integrate","F",-1
645,0,0,65,0.0000374,"\int \frac{\cos ^{-1}(x)^2}{x^5} \, dx","IntegrateAlgebraic[ArcCos[x]^2/x^5,x]","\int \frac{\cos ^{-1}(x)^2}{x^5} \, dx","-\frac{\cos ^{-1}(x)^2}{4 x^4}-\frac{1}{12 x^2}+\frac{\sqrt{1-x^2} \cos ^{-1}(x)}{3 x}+\frac{\sqrt{1-x^2} \cos ^{-1}(x)}{6 x^3}+\frac{\log (x)}{3}",1,"Could not integrate","F",-1
646,0,0,61,0.0000326,"\int x^2 \sin ^{-1}(x)^2 \, dx","IntegrateAlgebraic[x^2*ArcSin[x]^2,x]","\int x^2 \sin ^{-1}(x)^2 \, dx","-\frac{2 x^3}{27}+\frac{1}{3} x^3 \sin ^{-1}(x)^2+\frac{2}{9} \sqrt{1-x^2} x^2 \sin ^{-1}(x)+\frac{4}{9} \sqrt{1-x^2} \sin ^{-1}(x)-\frac{4 x}{9}",1,"Could not integrate","F",-1
647,0,0,53,0.0000376,"\int x^3 \tan ^{-1}(x)^2 \, dx","IntegrateAlgebraic[x^3*ArcTan[x]^2,x]","\int x^3 \tan ^{-1}(x)^2 \, dx","\frac{1}{4} x^4 \tan ^{-1}(x)^2-\frac{1}{6} x^3 \tan ^{-1}(x)+\frac{x^2}{12}-\frac{1}{3} \log \left(x^2+1\right)+\frac{1}{2} x \tan ^{-1}(x)-\frac{1}{4} \tan ^{-1}(x)^2",1,"Could not integrate","F",-1
648,0,0,61,0.0000367,"\int \frac{\tan ^{-1}(x)^2}{x^5} \, dx","IntegrateAlgebraic[ArcTan[x]^2/x^5,x]","\int \frac{\tan ^{-1}(x)^2}{x^5} \, dx","-\frac{\tan ^{-1}(x)^2}{4 x^4}-\frac{\tan ^{-1}(x)}{6 x^3}-\frac{1}{12 x^2}+\frac{1}{3} \log \left(x^2+1\right)-\frac{2 \log (x)}{3}+\frac{1}{4} \tan ^{-1}(x)^2+\frac{\tan ^{-1}(x)}{2 x}",1,"Could not integrate","F",-1
649,0,0,63,0.0000337,"\int x^3 \csc ^{-1}(x)^2 \, dx","IntegrateAlgebraic[x^3*ArcCsc[x]^2,x]","\int x^3 \csc ^{-1}(x)^2 \, dx","\frac{1}{4} x^4 \csc ^{-1}(x)^2+\frac{x^2}{12}+\frac{1}{3} \sqrt{1-\frac{1}{x^2}} x \csc ^{-1}(x)+\frac{1}{6} \sqrt{1-\frac{1}{x^2}} x^3 \csc ^{-1}(x)+\frac{\log (x)}{3}",1,"Could not integrate","F",-1
650,0,0,148,0.0000346,"\int \frac{\sec ^{-1}(x)^4}{x^5} \, dx","IntegrateAlgebraic[ArcSec[x]^4/x^5,x]","\int \frac{\sec ^{-1}(x)^4}{x^5} \, dx","-\frac{3}{128 x^4}-\frac{\sec ^{-1}(x)^4}{4 x^4}+\frac{3 \sec ^{-1}(x)^2}{16 x^4}-\frac{45}{128 x^2}+\frac{3 \sqrt{1-\frac{1}{x^2}} \sec ^{-1}(x)^3}{8 x}+\frac{9 \sec ^{-1}(x)^2}{16 x^2}-\frac{45 \sqrt{1-\frac{1}{x^2}} \sec ^{-1}(x)}{64 x}+\frac{\sqrt{1-\frac{1}{x^2}} \sec ^{-1}(x)^3}{4 x^3}-\frac{3 \sqrt{1-\frac{1}{x^2}} \sec ^{-1}(x)}{32 x^3}+\frac{3}{32} \sec ^{-1}(x)^4-\frac{45}{128} \sec ^{-1}(x)^2",1,"Could not integrate","F",-1
651,0,0,34,0.0000403,"\int \sqrt{1-x^2} \sin ^{-1}(x) \, dx","IntegrateAlgebraic[Sqrt[1 - x^2]*ArcSin[x],x]","\int \sqrt{1-x^2} \sin ^{-1}(x) \, dx","-\frac{x^2}{4}+\frac{1}{2} \sqrt{1-x^2} x \sin ^{-1}(x)+\frac{1}{4} \sin ^{-1}(x)^2",1,"Could not integrate","F",-1
652,0,0,34,0.0000377,"\int \sqrt{1-x^2} \cos ^{-1}(x) \, dx","IntegrateAlgebraic[Sqrt[1 - x^2]*ArcCos[x],x]","\int \sqrt{1-x^2} \cos ^{-1}(x) \, dx","\frac{x^2}{4}+\frac{1}{2} \sqrt{1-x^2} x \cos ^{-1}(x)-\frac{1}{4} \cos ^{-1}(x)^2",1,"Could not integrate","F",-1
653,0,0,30,0.000039,"\int x \sqrt{1-x^2} \cos ^{-1}(x) \, dx","IntegrateAlgebraic[x*Sqrt[1 - x^2]*ArcCos[x],x]","\int x \sqrt{1-x^2} \cos ^{-1}(x) \, dx","\frac{x^3}{9}-\frac{1}{3} \left(1-x^2\right)^{3/2} \cos ^{-1}(x)-\frac{x}{3}",1,"Could not integrate","F",-1
654,0,0,59,0.000036,"\int \left(1-x^2\right)^{3/2} \sin ^{-1}(x) \, dx","IntegrateAlgebraic[(1 - x^2)^(3/2)*ArcSin[x],x]","\int \left(1-x^2\right)^{3/2} \sin ^{-1}(x) \, dx","\frac{x^4}{16}-\frac{5 x^2}{16}+\frac{1}{4} \left(1-x^2\right)^{3/2} x \sin ^{-1}(x)+\frac{3}{8} \sqrt{1-x^2} x \sin ^{-1}(x)+\frac{3}{16} \sin ^{-1}(x)^2",1,"Could not integrate","F",-1
655,0,0,37,0.0000357,"\int x \left(1-x^2\right)^{3/2} \sin ^{-1}(x) \, dx","IntegrateAlgebraic[x*(1 - x^2)^(3/2)*ArcSin[x],x]","\int x \left(1-x^2\right)^{3/2} \sin ^{-1}(x) \, dx","\frac{x^5}{25}-\frac{2 x^3}{15}-\frac{1}{5} \left(1-x^2\right)^{5/2} \sin ^{-1}(x)+\frac{x}{5}",1,"Could not integrate","F",-1
656,0,0,61,0.0000393,"\int x^3 \left(1-x^2\right)^{3/2} \cos ^{-1}(x) \, dx","IntegrateAlgebraic[x^3*(1 - x^2)^(3/2)*ArcCos[x],x]","\int x^3 \left(1-x^2\right)^{3/2} \cos ^{-1}(x) \, dx","-\frac{x^7}{49}+\frac{8 x^5}{175}-\frac{x^3}{105}+\frac{1}{7} \left(1-x^2\right)^{7/2} \cos ^{-1}(x)-\frac{1}{5} \left(1-x^2\right)^{5/2} \cos ^{-1}(x)-\frac{2 x}{35}",1,"Could not integrate","F",-1
657,0,0,95,0.0000384,"\int \frac{\left(1-x^2\right)^{3/2} \cos ^{-1}(x)}{x} \, dx","IntegrateAlgebraic[((1 - x^2)^(3/2)*ArcCos[x])/x,x]","\int \frac{\left(1-x^2\right)^{3/2} \cos ^{-1}(x)}{x} \, dx","-i \text{Li}_2\left(-i e^{i \cos ^{-1}(x)}\right)+i \text{Li}_2\left(i e^{i \cos ^{-1}(x)}\right)-\frac{x^3}{9}+\frac{1}{3} \left(1-x^2\right)^{3/2} \cos ^{-1}(x)+\sqrt{1-x^2} \cos ^{-1}(x)+\frac{4 x}{3}+2 i \cos ^{-1}(x) \tan ^{-1}\left(e^{i \cos ^{-1}(x)}\right)",1,"Could not integrate","F",-1
658,0,0,41,0.0000445,"\int \frac{\left(1-x^2\right)^{3/2} \sin ^{-1}(x)}{x^6} \, dx","IntegrateAlgebraic[((1 - x^2)^(3/2)*ArcSin[x])/x^6,x]","\int \frac{\left(1-x^2\right)^{3/2} \sin ^{-1}(x)}{x^6} \, dx","-\frac{1}{20 x^4}+\frac{1}{5 x^2}-\frac{\left(1-x^2\right)^{5/2} \sin ^{-1}(x)}{5 x^5}+\frac{\log (x)}{5}",1,"Could not integrate","F",-1
659,0,0,34,0.0000413,"\int \frac{x^2 \sin ^{-1}(x)}{\sqrt{1-x^2}} \, dx","IntegrateAlgebraic[(x^2*ArcSin[x])/Sqrt[1 - x^2],x]","\int \frac{x^2 \sin ^{-1}(x)}{\sqrt{1-x^2}} \, dx","\frac{x^2}{4}-\frac{1}{2} \sqrt{1-x^2} x \sin ^{-1}(x)+\frac{1}{4} \sin ^{-1}(x)^2",1,"Could not integrate","F",-1
660,0,0,61,0.0000362,"\int \frac{x^4 \sin ^{-1}(x)}{\sqrt{1-x^2}} \, dx","IntegrateAlgebraic[(x^4*ArcSin[x])/Sqrt[1 - x^2],x]","\int \frac{x^4 \sin ^{-1}(x)}{\sqrt{1-x^2}} \, dx","\frac{x^4}{16}+\frac{3 x^2}{16}-\frac{3}{8} \sqrt{1-x^2} x \sin ^{-1}(x)-\frac{1}{4} \sqrt{1-x^2} x^3 \sin ^{-1}(x)+\frac{3}{16} \sin ^{-1}(x)^2",1,"Could not integrate","F",-1
661,0,0,19,0.0000369,"\int \frac{x \sin ^{-1}(x)}{\left(1-x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[(x*ArcSin[x])/(1 - x^2)^(3/2),x]","\int \frac{x \sin ^{-1}(x)}{\left(1-x^2\right)^{3/2}} \, dx","\frac{\sin ^{-1}(x)}{\sqrt{1-x^2}}-\tanh ^{-1}(x)",1,"Could not integrate","F",-1
662,0,0,17,0.0000305,"\int \frac{x \cos ^{-1}(x)}{\left(1-x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[(x*ArcCos[x])/(1 - x^2)^(3/2),x]","\int \frac{x \cos ^{-1}(x)}{\left(1-x^2\right)^{3/2}} \, dx","\frac{\cos ^{-1}(x)}{\sqrt{1-x^2}}+\tanh ^{-1}(x)",1,"Could not integrate","F",-1
663,0,0,62,0.0000333,"\int \frac{\sin ^{-1}(x)}{\left(1-x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[ArcSin[x]/(1 - x^2)^(5/2),x]","\int \frac{\sin ^{-1}(x)}{\left(1-x^2\right)^{5/2}} \, dx","-\frac{1}{6 \left(1-x^2\right)}+\frac{1}{3} \log \left(1-x^2\right)+\frac{2 x \sin ^{-1}(x)}{3 \sqrt{1-x^2}}+\frac{x \sin ^{-1}(x)}{3 \left(1-x^2\right)^{3/2}}",1,"Could not integrate","F",-1
664,0,0,36,0.0000396,"\int \frac{x^3 \sin ^{-1}(x)}{\left(1-x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[(x^3*ArcSin[x])/(1 - x^2)^(3/2),x]","\int \frac{x^3 \sin ^{-1}(x)}{\left(1-x^2\right)^{3/2}} \, dx","\sqrt{1-x^2} \sin ^{-1}(x)+\frac{\sin ^{-1}(x)}{\sqrt{1-x^2}}-x-\tanh ^{-1}(x)",1,"Could not integrate","F",-1
665,0,0,62,0.0000324,"\int \frac{\sin ^{-1}(x)}{x \left(1-x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[ArcSin[x]/(x*(1 - x^2)^(3/2)),x]","\int \frac{\sin ^{-1}(x)}{x \left(1-x^2\right)^{3/2}} \, dx","i \text{Li}_2\left(-e^{i \sin ^{-1}(x)}\right)-i \text{Li}_2\left(e^{i \sin ^{-1}(x)}\right)+\frac{\sin ^{-1}(x)}{\sqrt{1-x^2}}-\tanh ^{-1}(x)-2 \sin ^{-1}(x) \tanh ^{-1}\left(e^{i \sin ^{-1}(x)}\right)",1,"Could not integrate","F",-1
666,0,0,54,0.0000747,"\int \frac{\cos ^{-1}(x)}{x^4 \sqrt{1-x^2}} \, dx","IntegrateAlgebraic[ArcCos[x]/(x^4*Sqrt[1 - x^2]),x]","\int \frac{\cos ^{-1}(x)}{x^4 \sqrt{1-x^2}} \, dx","\frac{1}{6 x^2}-\frac{2 \sqrt{1-x^2} \cos ^{-1}(x)}{3 x}-\frac{\sqrt{1-x^2} \cos ^{-1}(x)}{3 x^3}-\frac{2 \log (x)}{3}",1,"Could not integrate","F",-1
667,0,0,66,0.0000363,"\int x \sqrt{1-x^2} \cos ^{-1}(x)^2 \, dx","IntegrateAlgebraic[x*Sqrt[1 - x^2]*ArcCos[x]^2,x]","\int x \sqrt{1-x^2} \cos ^{-1}(x)^2 \, dx","\frac{2}{9} x^3 \cos ^{-1}(x)+\frac{2}{27} \left(1-x^2\right)^{3/2}+\frac{4 \sqrt{1-x^2}}{9}-\frac{1}{3} \left(1-x^2\right)^{3/2} \cos ^{-1}(x)^2-\frac{2}{3} x \cos ^{-1}(x)",1,"Could not integrate","F",-1
668,0,0,73,0.0000508,"\int \frac{x^2 \sin ^{-1}(x)^3}{\sqrt{1-x^2}} \, dx","IntegrateAlgebraic[(x^2*ArcSin[x]^3)/Sqrt[1 - x^2],x]","\int \frac{x^2 \sin ^{-1}(x)^3}{\sqrt{1-x^2}} \, dx","-\frac{3 x^2}{8}-\frac{1}{2} x \sqrt{1-x^2} \sin ^{-1}(x)^3+\frac{3}{4} x^2 \sin ^{-1}(x)^2+\frac{3}{4} x \sqrt{1-x^2} \sin ^{-1}(x)+\frac{1}{8} \sin ^{-1}(x)^4-\frac{3}{8} \sin ^{-1}(x)^2",1,"Could not integrate","F",-1
669,0,0,32,0.0000376,"\int \frac{x \tan ^{-1}(x)}{\left(1+x^2\right)^2} \, dx","IntegrateAlgebraic[(x*ArcTan[x])/(1 + x^2)^2,x]","\int \frac{x \tan ^{-1}(x)}{\left(1+x^2\right)^2} \, dx","\frac{x}{4 \left(x^2+1\right)}-\frac{\tan ^{-1}(x)}{2 \left(x^2+1\right)}+\frac{1}{4} \tan ^{-1}(x)",1,"Could not integrate","F",-1
670,0,0,44,0.0000346,"\int \frac{x \tan ^{-1}(x)}{\left(1+x^2\right)^3} \, dx","IntegrateAlgebraic[(x*ArcTan[x])/(1 + x^2)^3,x]","\int \frac{x \tan ^{-1}(x)}{\left(1+x^2\right)^3} \, dx","\frac{3 x}{32 \left(x^2+1\right)}+\frac{x}{16 \left(x^2+1\right)^2}-\frac{\tan ^{-1}(x)}{4 \left(x^2+1\right)^2}+\frac{3}{32} \tan ^{-1}(x)",1,"Could not integrate","F",-1
671,0,0,23,0.0000389,"\int \frac{x^2 \tan ^{-1}(x)}{1+x^2} \, dx","IntegrateAlgebraic[(x^2*ArcTan[x])/(1 + x^2),x]","\int \frac{x^2 \tan ^{-1}(x)}{1+x^2} \, dx","-\frac{1}{2} \log \left(x^2+1\right)-\frac{1}{2} \tan ^{-1}(x)^2+x \tan ^{-1}(x)",1,"Could not integrate","F",-1
672,0,0,67,0.0000358,"\int \frac{x^3 \tan ^{-1}(x)}{1+x^2} \, dx","IntegrateAlgebraic[(x^3*ArcTan[x])/(1 + x^2),x]","\int \frac{x^3 \tan ^{-1}(x)}{1+x^2} \, dx","\frac{1}{2} i \text{Li}_2\left(1-\frac{2}{i x+1}\right)+\frac{1}{2} x^2 \tan ^{-1}(x)-\frac{x}{2}+\frac{1}{2} i \tan ^{-1}(x)^2+\frac{1}{2} \tan ^{-1}(x)+\log \left(\frac{2}{1+i x}\right) \tan ^{-1}(x)",1,"Could not integrate","F",-1
673,0,0,34,0.0000382,"\int \frac{x^2 \tan ^{-1}(x)}{\left(1+x^2\right)^2} \, dx","IntegrateAlgebraic[(x^2*ArcTan[x])/(1 + x^2)^2,x]","\int \frac{x^2 \tan ^{-1}(x)}{\left(1+x^2\right)^2} \, dx","-\frac{1}{4 \left(x^2+1\right)}-\frac{x \tan ^{-1}(x)}{2 \left(x^2+1\right)}+\frac{1}{4} \tan ^{-1}(x)^2",1,"Could not integrate","F",-1
674,0,0,79,0.0000325,"\int \frac{x^3 \tan ^{-1}(x)}{\left(1+x^2\right)^2} \, dx","IntegrateAlgebraic[(x^3*ArcTan[x])/(1 + x^2)^2,x]","\int \frac{x^3 \tan ^{-1}(x)}{\left(1+x^2\right)^2} \, dx","-\frac{1}{2} i \text{Li}_2\left(1-\frac{2}{i x+1}\right)-\frac{x}{4 \left(x^2+1\right)}+\frac{\tan ^{-1}(x)}{2 \left(x^2+1\right)}-\frac{1}{2} i \tan ^{-1}(x)^2-\frac{1}{4} \tan ^{-1}(x)-\log \left(\frac{2}{1+i x}\right) \tan ^{-1}(x)",1,"Could not integrate","F",-1
675,0,0,89,0.0000388,"\int \frac{x^5 \tan ^{-1}(x)}{\left(1+x^2\right)^2} \, dx","IntegrateAlgebraic[(x^5*ArcTan[x])/(1 + x^2)^2,x]","\int \frac{x^5 \tan ^{-1}(x)}{\left(1+x^2\right)^2} \, dx","i \text{Li}_2\left(1-\frac{2}{i x+1}\right)+\frac{x}{4 \left(x^2+1\right)}+\frac{1}{2} x^2 \tan ^{-1}(x)-\frac{\tan ^{-1}(x)}{2 \left(x^2+1\right)}-\frac{x}{2}+i \tan ^{-1}(x)^2+\frac{3}{4} \tan ^{-1}(x)+2 \log \left(\frac{2}{1+i x}\right) \tan ^{-1}(x)",1,"Could not integrate","F",-1
676,0,0,22,0.0000371,"\int \frac{\left(1+x^2\right) \tan ^{-1}(x)}{x^2} \, dx","IntegrateAlgebraic[((1 + x^2)*ArcTan[x])/x^2,x]","\int \frac{\left(1+x^2\right) \tan ^{-1}(x)}{x^2} \, dx","-\log \left(x^2+1\right)+\log (x)+x \tan ^{-1}(x)-\frac{\tan ^{-1}(x)}{x}",1,"Could not integrate","F",-1
677,0,0,31,0.0000322,"\int \frac{\left(1+x^2\right) \tan ^{-1}(x)}{x^5} \, dx","IntegrateAlgebraic[((1 + x^2)*ArcTan[x])/x^5,x]","\int \frac{\left(1+x^2\right) \tan ^{-1}(x)}{x^5} \, dx","-\frac{1}{12 x^3}-\frac{\left(x^2+1\right)^2 \tan ^{-1}(x)}{4 x^4}-\frac{1}{4 x}",1,"Could not integrate","F",-1
678,0,0,63,0.000037,"\int \frac{\left(1+x^2\right)^2 \tan ^{-1}(x)}{x^5} \, dx","IntegrateAlgebraic[((1 + x^2)^2*ArcTan[x])/x^5,x]","\int \frac{\left(1+x^2\right)^2 \tan ^{-1}(x)}{x^5} \, dx","\frac{1}{2} i \text{Li}_2(-i x)-\frac{1}{2} i \text{Li}_2(i x)-\frac{\tan ^{-1}(x)}{4 x^4}-\frac{1}{12 x^3}-\frac{\tan ^{-1}(x)}{x^2}-\frac{3}{4 x}-\frac{3}{4} \tan ^{-1}(x)",1,"Could not integrate","F",-1
679,0,0,28,0.0000382,"\int \frac{\tan ^{-1}(x)}{x^2 \left(1+x^2\right)} \, dx","IntegrateAlgebraic[ArcTan[x]/(x^2*(1 + x^2)),x]","\int \frac{\tan ^{-1}(x)}{x^2 \left(1+x^2\right)} \, dx","-\frac{1}{2} \log \left(x^2+1\right)+\log (x)-\frac{1}{2} \tan ^{-1}(x)^2-\frac{\tan ^{-1}(x)}{x}",1,"Could not integrate","F",-1
680,0,0,39,0.0000296,"\int \frac{\tan ^{-1}(x)^2}{x^3} \, dx","IntegrateAlgebraic[ArcTan[x]^2/x^3,x]","\int \frac{\tan ^{-1}(x)^2}{x^3} \, dx","-\frac{1}{2} \log \left(x^2+1\right)-\frac{\tan ^{-1}(x)^2}{2 x^2}+\log (x)-\frac{1}{2} \tan ^{-1}(x)^2-\frac{\tan ^{-1}(x)}{x}",1,"Could not integrate","F",-1
681,0,0,60,0.0000617,"\int \frac{\left(1+x^2\right) \tan ^{-1}(x)^2}{x^5} \, dx","IntegrateAlgebraic[((1 + x^2)*ArcTan[x]^2)/x^5,x]","\int \frac{\left(1+x^2\right) \tan ^{-1}(x)^2}{x^5} \, dx","-\frac{\tan ^{-1}(x)}{6 x^3}-\frac{1}{12 x^2}-\frac{1}{6} \log \left(x^2+1\right)-\frac{\left(x^2+1\right)^2 \tan ^{-1}(x)^2}{4 x^4}+\frac{\log (x)}{3}-\frac{\tan ^{-1}(x)}{2 x}",1,"Could not integrate","F",-1
682,0,0,79,0.0000388,"\int \frac{x^3 \tan ^{-1}(x)^2}{\left(1+x^2\right)^3} \, dx","IntegrateAlgebraic[(x^3*ArcTan[x]^2)/(1 + x^2)^3,x]","\int \frac{x^3 \tan ^{-1}(x)^2}{\left(1+x^2\right)^3} \, dx","\frac{5}{32 \left(x^2+1\right)}-\frac{1}{32 \left(x^2+1\right)^2}+\frac{3 x \tan ^{-1}(x)}{16 \left(x^2+1\right)}+\frac{x^4 \tan ^{-1}(x)^2}{4 \left(x^2+1\right)^2}+\frac{x^3 \tan ^{-1}(x)}{8 \left(x^2+1\right)^2}-\frac{3}{32} \tan ^{-1}(x)^2",1,"Could not integrate","F",-1
683,0,0,107,0.0000401,"\int \frac{\sqrt{-1+x^2} \sec ^{-1}(x)}{x^2} \, dx","IntegrateAlgebraic[(Sqrt[-1 + x^2]*ArcSec[x])/x^2,x]","\int \frac{\sqrt{-1+x^2} \sec ^{-1}(x)}{x^2} \, dx","\frac{i \sqrt{x^2} \text{Li}_2\left(-i e^{i \sec ^{-1}(x)}\right)}{x}-\frac{i \sqrt{x^2} \text{Li}_2\left(i e^{i \sec ^{-1}(x)}\right)}{x}-\frac{1}{\sqrt{x^2}}-\frac{\sqrt{x^2-1} \sec ^{-1}(x)}{x}-\frac{2 i \sqrt{x^2} \sec ^{-1}(x) \tan ^{-1}\left(e^{i \sec ^{-1}(x)}\right)}{x}",1,"Could not integrate","F",-1
684,0,0,106,0.0000399,"\int \frac{\left(-1+x^2\right)^{5/2} \csc ^{-1}(x)}{x^3} \, dx","IntegrateAlgebraic[((-1 + x^2)^(5/2)*ArcCsc[x])/x^3,x]","\int \frac{\left(-1+x^2\right)^{5/2} \csc ^{-1}(x)}{x^3} \, dx","-\frac{7 x \log (x)}{3 \sqrt{x^2}}+\frac{\left(x^2-1\right)^{5/2} \csc ^{-1}(x)}{3 x^2}-\frac{5 \left(x^2-1\right)^{3/2} \csc ^{-1}(x)}{3 x^2}-\frac{5 \sqrt{x^2-1} \csc ^{-1}(x)}{2 x^2}-\frac{5 x \csc ^{-1}(x)^2}{4 \sqrt{x^2}}+\frac{2 x^4+3}{12 x \sqrt{x^2}}",1,"Could not integrate","F",-1
685,0,0,41,0.0000404,"\int \frac{\sqrt{-1+x^2} \sec ^{-1}(x)}{x^4} \, dx","IntegrateAlgebraic[(Sqrt[-1 + x^2]*ArcSec[x])/x^4,x]","\int \frac{\sqrt{-1+x^2} \sec ^{-1}(x)}{x^4} \, dx","\frac{1}{3 \sqrt{x^2}}-\frac{1}{9 \left(x^2\right)^{3/2}}+\frac{\left(x^2-1\right)^{3/2} \sec ^{-1}(x)}{3 x^3}",1,"Could not integrate","F",-1
686,0,0,65,0.0000377,"\int \frac{\sec ^{-1}(x)}{\left(-1+x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[ArcSec[x]/(-1 + x^2)^(5/2),x]","\int \frac{\sec ^{-1}(x)}{\left(-1+x^2\right)^{5/2}} \, dx","\frac{\sqrt{x^2}}{6 \left(1-x^2\right)}+\frac{2 x \sec ^{-1}(x)}{3 \sqrt{x^2-1}}-\frac{x \sec ^{-1}(x)}{3 \left(x^2-1\right)^{3/2}}+\frac{5}{6} \coth ^{-1}\left(\sqrt{x^2}\right)",1,"Could not integrate","F",-1
687,0,0,51,0.0000383,"\int \frac{x^2 \sec ^{-1}(x)}{\left(-1+x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[(x^2*ArcSec[x])/(-1 + x^2)^(5/2),x]","\int \frac{x^2 \sec ^{-1}(x)}{\left(-1+x^2\right)^{5/2}} \, dx","\frac{\sqrt{x^2}}{6 \left(1-x^2\right)}-\frac{1}{6} \coth ^{-1}\left(\sqrt{x^2}\right)-\frac{x^3 \sec ^{-1}(x)}{3 \left(x^2-1\right)^{3/2}}",1,"Could not integrate","F",-1
688,0,0,82,0.0000408,"\int \frac{x^3 \sec ^{-1}(x)}{\left(-1+x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[(x^3*ArcSec[x])/(-1 + x^2)^(5/2),x]","\int \frac{x^3 \sec ^{-1}(x)}{\left(-1+x^2\right)^{5/2}} \, dx","\frac{x}{6 \sqrt{x^2} \left(1-x^2\right)}-\frac{2 x \log (x)}{3 \sqrt{x^2}}+\frac{x \log \left(x^2-1\right)}{3 \sqrt{x^2}}-\frac{\sec ^{-1}(x)}{\sqrt{x^2-1}}-\frac{\sec ^{-1}(x)}{3 \left(x^2-1\right)^{3/2}}",1,"Could not integrate","F",-1
689,0,0,175,0.0000407,"\int \frac{x^6 \sec ^{-1}(x)}{\left(-1+x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[(x^6*ArcSec[x])/(-1 + x^2)^(5/2),x]","\int \frac{x^6 \sec ^{-1}(x)}{\left(-1+x^2\right)^{5/2}} \, dx","\frac{5 i \sqrt{x^2} \text{Li}_2\left(-i e^{i \sec ^{-1}(x)}\right)}{2 x}-\frac{5 i \sqrt{x^2} \text{Li}_2\left(i e^{i \sec ^{-1}(x)}\right)}{2 x}+\frac{\sqrt{x^2} \left(2-3 x^2\right)}{6 \left(x^2-1\right)}-\frac{5 x \sec ^{-1}(x)}{2 \sqrt{x^2-1}}-\frac{13}{6} \coth ^{-1}\left(\sqrt{x^2}\right)-\frac{5 i \sqrt{x^2} \sec ^{-1}(x) \tan ^{-1}\left(e^{i \sec ^{-1}(x)}\right)}{x}+\frac{x^5 \sec ^{-1}(x)}{2 \left(x^2-1\right)^{3/2}}-\frac{5 x^3 \sec ^{-1}(x)}{6 \left(x^2-1\right)^{3/2}}",1,"Could not integrate","F",-1
690,0,0,23,0.0000419,"\int \frac{\sec ^{-1}(x)}{x^2 \sqrt{-1+x^2}} \, dx","IntegrateAlgebraic[ArcSec[x]/(x^2*Sqrt[-1 + x^2]),x]","\int \frac{\sec ^{-1}(x)}{x^2 \sqrt{-1+x^2}} \, dx","\frac{1}{\sqrt{x^2}}+\frac{\sqrt{x^2-1} \sec ^{-1}(x)}{x}",1,"Could not integrate","F",-1
691,0,0,70,0.000034,"\int \frac{\csc ^{-1}(x)}{x^2 \left(-1+x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[ArcCsc[x]/(x^2*(-1 + x^2)^(5/2)),x]","\int \frac{\csc ^{-1}(x)}{x^2 \left(-1+x^2\right)^{5/2}} \, dx","-\frac{1}{\sqrt{x^2}}+\frac{\sqrt{x^2}}{6 \left(x^2-1\right)}-\frac{11}{6} \coth ^{-1}\left(\sqrt{x^2}\right)+\frac{\left(8 x^4-12 x^2+3\right) \csc ^{-1}(x)}{3 x \left(x^2-1\right)^{3/2}}",1,"Could not integrate","F",-1
692,0,0,74,0.0000379,"\int \frac{\csc ^{-1}(x)^4}{x^2 \sqrt{-1+x^2}} \, dx","IntegrateAlgebraic[ArcCsc[x]^4/(x^2*Sqrt[-1 + x^2]),x]","\int \frac{\csc ^{-1}(x)^4}{x^2 \sqrt{-1+x^2}} \, dx","\frac{24 \sqrt{x^2-1}}{x}+\frac{\sqrt{x^2-1} \csc ^{-1}(x)^4}{x}-\frac{4 \csc ^{-1}(x)^3}{\sqrt{x^2}}-\frac{12 \sqrt{x^2-1} \csc ^{-1}(x)^2}{x}+\frac{24 \csc ^{-1}(x)}{\sqrt{x^2}}",1,"Could not integrate","F",-1
693,0,0,133,0.0000425,"\int \frac{\left(-1+x^2\right)^{3/2} \sec ^{-1}(x)^2}{x^5} \, dx","IntegrateAlgebraic[((-1 + x^2)^(3/2)*ArcSec[x]^2)/x^5,x]","\int \frac{\left(-1+x^2\right)^{3/2} \sec ^{-1}(x)^2}{x^5} \, dx","\frac{x \sec ^{-1}(x)^3}{8 \sqrt{x^2}}-\frac{3 \sqrt{x^2-1} \sec ^{-1}(x)^2}{8 x^2}+\frac{9 x \sec ^{-1}(x)}{64 \sqrt{x^2}}-\frac{3 \sec ^{-1}(x)}{8 x \sqrt{x^2}}+\frac{\sqrt{x^2-1} \left(17 x^2-2\right)}{64 x^4}-\frac{\left(x^2-1\right)^{3/2} \sec ^{-1}(x)^2}{4 x^4}+\frac{\left(x^2-1\right)^2 \sec ^{-1}(x)}{8 x^3 \sqrt{x^2}}",1,"Could not integrate","F",-1
694,0,0,110,0.000076,"\int \frac{\sqrt{-1+x^2} \sec ^{-1}(x)^3}{x^4} \, dx","IntegrateAlgebraic[(Sqrt[-1 + x^2]*ArcSec[x]^3)/x^4,x]","\int \frac{\sqrt{-1+x^2} \sec ^{-1}(x)^3}{x^4} \, dx","\frac{2 \left(1-21 x^2\right)}{27 \left(x^2\right)^{3/2}}+\frac{\left(x^2-1\right) \sec ^{-1}(x)^2}{3 \left(x^2\right)^{3/2}}+\frac{2 \sec ^{-1}(x)^2}{3 \sqrt{x^2}}-\frac{4 \sqrt{x^2-1} \sec ^{-1}(x)}{3 x}+\frac{\left(x^2-1\right)^{3/2} \sec ^{-1}(x)^3}{3 x^3}-\frac{2 \left(x^2-1\right)^{3/2} \sec ^{-1}(x)}{9 x^3}",1,"Could not integrate","F",-1
695,0,0,55,0.0000408,"\int \sin ^{-1}\left(\sqrt{\frac{-a+x}{a+x}}\right) \, dx","IntegrateAlgebraic[ArcSin[Sqrt[(-a + x)/(a + x)]],x]","\int \sin ^{-1}\left(\sqrt{\frac{-a+x}{a+x}}\right) \, dx","(a+x) \sin ^{-1}\left(\sqrt{\frac{x-a}{a+x}}\right)-\frac{\sqrt{2} a \sqrt{\frac{x-a}{a+x}}}{\sqrt{\frac{a}{a+x}}}",1,"Could not integrate","F",-1
696,0,0,40,0.0000575,"\int \tan ^{-1}\left(\sqrt{\frac{-a+x}{a+x}}\right) \, dx","IntegrateAlgebraic[ArcTan[Sqrt[(-a + x)/(a + x)]],x]","\int \tan ^{-1}\left(\sqrt{\frac{-a+x}{a+x}}\right) \, dx","x \tan ^{-1}\left(\sqrt{-\frac{a-x}{a+x}}\right)-a \tanh ^{-1}\left(\sqrt{-\frac{a-x}{a+x}}\right)",1,"Could not integrate","F",-1
697,0,0,39,0.0000351,"\int \frac{\tan ^{-1}(x)}{(1+x)^3} \, dx","IntegrateAlgebraic[ArcTan[x]/(1 + x)^3,x]","\int \frac{\tan ^{-1}(x)}{(1+x)^3} \, dx","-\frac{1}{8} \log \left(x^2+1\right)-\frac{1}{4 (x+1)}+\frac{1}{4} \log (x+1)-\frac{\tan ^{-1}(x)}{2 (x+1)^2}",1,"Could not integrate","F",-1
698,0,0,122,0.0000375,"\int -\frac{\tan ^{-1}(a-x)}{a+x} \, dx","IntegrateAlgebraic[-(ArcTan[a - x]/(a + x)),x]","\int -\frac{\tan ^{-1}(a-x)}{a+x} \, dx","-\frac{1}{2} i \text{Li}_2\left(1-\frac{2}{1-i (a-x)}\right)+\frac{1}{2} i \text{Li}_2\left(\frac{2 (a+x)}{(i-2 a) (1-i (a-x))}+1\right)+\log \left(\frac{2}{1-i (a-x)}\right) \tan ^{-1}(a-x)-\log \left(-\frac{2 (a+x)}{(-2 a+i) (1-i (a-x))}\right) \tan ^{-1}(a-x)",1,"Could not integrate","F",-1
699,0,0,28,0.0000434,"\int \frac{\sin ^{-1}\left(\sqrt{1-x^2}\right)}{\sqrt{1-x^2}} \, dx","IntegrateAlgebraic[ArcSin[Sqrt[1 - x^2]]/Sqrt[1 - x^2],x]","\int \frac{\sin ^{-1}\left(\sqrt{1-x^2}\right)}{\sqrt{1-x^2}} \, dx","-\frac{\sqrt{x^2} \sin ^{-1}\left(\sqrt{1-x^2}\right)^2}{2 x}",1,"Could not integrate","F",-1
700,0,0,31,0.0000347,"\int \frac{x \tan ^{-1}\left(\sqrt{1+x^2}\right)}{\sqrt{1+x^2}} \, dx","IntegrateAlgebraic[(x*ArcTan[Sqrt[1 + x^2]])/Sqrt[1 + x^2],x]","\int \frac{x \tan ^{-1}\left(\sqrt{1+x^2}\right)}{\sqrt{1+x^2}} \, dx","\sqrt{x^2+1} \tan ^{-1}\left(\sqrt{x^2+1}\right)-\frac{1}{2} \log \left(x^2+2\right)",1,"Could not integrate","F",-1
701,0,0,57,0.0000633,"\int \frac{\sin ^{-1}(x)}{(1-x)^{5/2}} \, dx","IntegrateAlgebraic[ArcSin[x]/(1 - x)^(5/2),x]","\int \frac{\sin ^{-1}(x)}{(1-x)^{5/2}} \, dx","-\frac{\sqrt{x+1}}{3 (1-x)}+\frac{2 \sin ^{-1}(x)}{3 (1-x)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{x+1}}{\sqrt{2}}\right)}{3 \sqrt{2}}",1,"Could not integrate","F",-1
702,0,0,82,0.000035,"\int (-1+x)^{5/2} \csc ^{-1}(x) \, dx","IntegrateAlgebraic[(-1 + x)^(5/2)*ArcCsc[x],x]","\int (-1+x)^{5/2} \csc ^{-1}(x) \, dx","\frac{4 x \sqrt{x^2-1} \left(3 x^2-19 x+83\right)}{105 \sqrt{x^2} \sqrt{x-1}}+\frac{4 x \tanh ^{-1}\left(\frac{\sqrt{x^2-1}}{\sqrt{x-1}}\right)}{7 \sqrt{x^2}}+\frac{2}{7} (x-1)^{7/2} \csc ^{-1}(x)",1,"Could not integrate","F",-1
703,0,0,49,0.0000362,"\int \sin ^{-1}(\sinh (x)) \text{sech}^4(x) \, dx","IntegrateAlgebraic[ArcSin[Sinh[x]]*Sech[x]^4,x]","\int \sin ^{-1}(\sinh (x)) \text{sech}^4(x) \, dx","-\frac{2}{3} \sin ^{-1}\left(\frac{\cosh (x)}{\sqrt{2}}\right)+\frac{1}{6} \sqrt{1-\sinh ^2(x)} \text{sech}(x)-\frac{1}{3} \tanh ^3(x) \sin ^{-1}(\sinh (x))+\tanh (x) \sin ^{-1}(\sinh (x))",1,"Could not integrate","F",-1
704,0,0,36,0.0000395,"\int \cot ^{-1}(\cosh (x)) \coth (x) \text{csch}^3(x) \, dx","IntegrateAlgebraic[ArcCot[Cosh[x]]*Coth[x]*Csch[x]^3,x]","\int \cot ^{-1}(\cosh (x)) \coth (x) \text{csch}^3(x) \, dx","\frac{\tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{2}}\right)}{6 \sqrt{2}}+\frac{\coth (x)}{6}-\frac{1}{3} \text{csch}^3(x) \cot ^{-1}(\cosh (x))",1,"Could not integrate","F",-1
705,0,0,28,0.0000346,"\int e^x \sin ^{-1}(\tanh (x)) \, dx","IntegrateAlgebraic[E^x*ArcSin[Tanh[x]],x]","\int e^x \sin ^{-1}(\tanh (x)) \, dx","e^x \sin ^{-1}(\tanh (x))-\log \left(e^{2 x}+1\right) \cosh (x) \sqrt{\text{sech}^2(x)}",1,"Could not integrate","F",-1