1,1,11,11,0.0106186,"\int \frac{x}{\left(-1+x^2\right)^{3/4}} \, dx","Integrate[x/(-1 + x^2)^(3/4),x]","2 \sqrt[4]{x^2-1}","2 \sqrt[4]{x^2-1}",1,"2*(-1 + x^2)^(1/4)","A",1
2,1,12,12,0.047548,"\int \frac{1+3 x^2}{\sqrt{-1+x+x^3}} \, dx","Integrate[(1 + 3*x^2)/Sqrt[-1 + x + x^3],x]","2 \sqrt{x^3+x-1}","2 \sqrt{x^3+x-1}",1,"2*Sqrt[-1 + x + x^3]","A",1
3,1,12,12,0.0061134,"\int \frac{-1+x^8}{\sqrt{-1+x^4} \left(1-2 x^4+x^8\right)} \, dx","Integrate[(-1 + x^8)/(Sqrt[-1 + x^4]*(1 - 2*x^4 + x^8)),x]","-\frac{x}{\sqrt{x^4-1}}","-\frac{x}{\sqrt{x^4-1}}",1,"-(x/Sqrt[-1 + x^4])","A",1
4,1,13,13,0.0017054,"\int \frac{x}{\sqrt[3]{-1+x^2}} \, dx","Integrate[x/(-1 + x^2)^(1/3),x]","\frac{3}{4} \left(x^2-1\right)^{2/3}","\frac{3}{4} \left(x^2-1\right)^{2/3}",1,"(3*(-1 + x^2)^(2/3))/4","A",1
5,1,13,13,0.0017022,"\int \frac{x}{\sqrt[4]{-1+x^2}} \, dx","Integrate[x/(-1 + x^2)^(1/4),x]","\frac{2}{3} \left(x^2-1\right)^{3/4}","\frac{2}{3} \left(x^2-1\right)^{3/4}",1,"(2*(-1 + x^2)^(3/4))/3","A",1
6,1,13,13,0.0020574,"\int x \sqrt[4]{-1+x^2} \, dx","Integrate[x*(-1 + x^2)^(1/4),x]","\frac{2}{5} \left(x^2-1\right)^{5/4}","\frac{2}{5} \left(x^2-1\right)^{5/4}",1,"(2*(-1 + x^2)^(5/4))/5","A",1
7,1,13,13,0.0020266,"\int x \sqrt[3]{-1+x^2} \, dx","Integrate[x*(-1 + x^2)^(1/3),x]","\frac{3}{8} \left(x^2-1\right)^{4/3}","\frac{3}{8} \left(x^2-1\right)^{4/3}",1,"(3*(-1 + x^2)^(4/3))/8","A",1
8,1,13,13,0.0021572,"\int x \left(-1+x^2\right)^{2/3} \, dx","Integrate[x*(-1 + x^2)^(2/3),x]","\frac{3}{10} \left(x^2-1\right)^{5/3}","\frac{3}{10} \left(x^2-1\right)^{5/3}",1,"(3*(-1 + x^2)^(5/3))/10","A",1
9,1,13,13,0.0021769,"\int x \left(-1+x^2\right)^{3/4} \, dx","Integrate[x*(-1 + x^2)^(3/4),x]","\frac{2}{7} \left(x^2-1\right)^{7/4}","\frac{2}{7} \left(x^2-1\right)^{7/4}",1,"(2*(-1 + x^2)^(7/4))/7","A",1
10,1,13,13,0.0019323,"\int \frac{x}{\sqrt[3]{1+x^2}} \, dx","Integrate[x/(1 + x^2)^(1/3),x]","\frac{3}{4} \left(x^2+1\right)^{2/3}","\frac{3}{4} \left(x^2+1\right)^{2/3}",1,"(3*(1 + x^2)^(2/3))/4","A",1
11,1,13,13,0.0016318,"\int \frac{x}{\sqrt[4]{1+x^2}} \, dx","Integrate[x/(1 + x^2)^(1/4),x]","\frac{2}{3} \left(x^2+1\right)^{3/4}","\frac{2}{3} \left(x^2+1\right)^{3/4}",1,"(2*(1 + x^2)^(3/4))/3","A",1
12,1,13,13,0.0019556,"\int x \sqrt[4]{1+x^2} \, dx","Integrate[x*(1 + x^2)^(1/4),x]","\frac{2}{5} \left(x^2+1\right)^{5/4}","\frac{2}{5} \left(x^2+1\right)^{5/4}",1,"(2*(1 + x^2)^(5/4))/5","A",1
13,1,13,13,0.0019554,"\int x \sqrt[3]{1+x^2} \, dx","Integrate[x*(1 + x^2)^(1/3),x]","\frac{3}{8} \left(x^2+1\right)^{4/3}","\frac{3}{8} \left(x^2+1\right)^{4/3}",1,"(3*(1 + x^2)^(4/3))/8","A",1
14,1,13,13,0.0021166,"\int x \left(1+x^2\right)^{3/4} \, dx","Integrate[x*(1 + x^2)^(3/4),x]","\frac{2}{7} \left(x^2+1\right)^{7/4}","\frac{2}{7} \left(x^2+1\right)^{7/4}",1,"(2*(1 + x^2)^(7/4))/7","A",1
15,1,13,13,0.0024549,"\int \frac{x^2}{\sqrt[4]{-1+x^3}} \, dx","Integrate[x^2/(-1 + x^3)^(1/4),x]","\frac{4}{9} \left(x^3-1\right)^{3/4}","\frac{4}{9} \left(x^3-1\right)^{3/4}",1,"(4*(-1 + x^3)^(3/4))/9","A",1
16,1,13,13,0.0026485,"\int x^2 \sqrt[4]{-1+x^3} \, dx","Integrate[x^2*(-1 + x^3)^(1/4),x]","\frac{4}{15} \left(x^3-1\right)^{5/4}","\frac{4}{15} \left(x^3-1\right)^{5/4}",1,"(4*(-1 + x^3)^(5/4))/15","A",1
17,1,13,13,0.0028723,"\int x^2 \left(-1+x^3\right)^{3/4} \, dx","Integrate[x^2*(-1 + x^3)^(3/4),x]","\frac{4}{21} \left(x^3-1\right)^{7/4}","\frac{4}{21} \left(x^3-1\right)^{7/4}",1,"(4*(-1 + x^3)^(7/4))/21","A",1
18,1,13,13,0.002321,"\int \frac{x^2}{\sqrt{1+x^3}} \, dx","Integrate[x^2/Sqrt[1 + x^3],x]","\frac{2 \sqrt{x^3+1}}{3}","\frac{2 \sqrt{x^3+1}}{3}",1,"(2*Sqrt[1 + x^3])/3","A",1
19,1,13,13,0.0022728,"\int \frac{x^2}{\sqrt[4]{1+x^3}} \, dx","Integrate[x^2/(1 + x^3)^(1/4),x]","\frac{4}{9} \left(x^3+1\right)^{3/4}","\frac{4}{9} \left(x^3+1\right)^{3/4}",1,"(4*(1 + x^3)^(3/4))/9","A",1
20,1,13,13,0.0025777,"\int x^2 \sqrt[4]{1+x^3} \, dx","Integrate[x^2*(1 + x^3)^(1/4),x]","\frac{4}{15} \left(x^3+1\right)^{5/4}","\frac{4}{15} \left(x^3+1\right)^{5/4}",1,"(4*(1 + x^3)^(5/4))/15","A",1
21,1,13,13,0.0026063,"\int x^2 \sqrt[3]{1+x^3} \, dx","Integrate[x^2*(1 + x^3)^(1/3),x]","\frac{1}{4} \left(x^3+1\right)^{4/3}","\frac{1}{4} \left(x^3+1\right)^{4/3}",1,"(1 + x^3)^(4/3)/4","A",1
22,1,13,13,0.0026837,"\int x^2 \sqrt{1+x^3} \, dx","Integrate[x^2*Sqrt[1 + x^3],x]","\frac{2}{9} \left(x^3+1\right)^{3/2}","\frac{2}{9} \left(x^3+1\right)^{3/2}",1,"(2*(1 + x^3)^(3/2))/9","A",1
23,1,13,13,0.0028879,"\int x^2 \left(1+x^3\right)^{2/3} \, dx","Integrate[x^2*(1 + x^3)^(2/3),x]","\frac{1}{5} \left(x^3+1\right)^{5/3}","\frac{1}{5} \left(x^3+1\right)^{5/3}",1,"(1 + x^3)^(5/3)/5","A",1
24,1,13,13,0.0027226,"\int x^2 \left(1+x^3\right)^{3/4} \, dx","Integrate[x^2*(1 + x^3)^(3/4),x]","\frac{4}{21} \left(x^3+1\right)^{7/4}","\frac{4}{21} \left(x^3+1\right)^{7/4}",1,"(4*(1 + x^3)^(7/4))/21","A",1
25,1,19,13,0.0328899,"\int \left(1+3 x^2\right) \sqrt[3]{x+x^3} \, dx","Integrate[(1 + 3*x^2)*(x + x^3)^(1/3),x]","\frac{3}{4} x \left(x^2+1\right) \sqrt[3]{x^3+x}","\frac{3}{4} \left(x^3+x\right)^{4/3}",1,"(3*x*(1 + x^2)*(x + x^3)^(1/3))/4","A",1
26,1,13,13,0.0024943,"\int \frac{1}{x^2 \left(-1+x^4\right)^{3/4}} \, dx","Integrate[1/(x^2*(-1 + x^4)^(3/4)),x]","\frac{\sqrt[4]{x^4-1}}{x}","\frac{\sqrt[4]{x^4-1}}{x}",1,"(-1 + x^4)^(1/4)/x","A",1
27,1,13,13,0.002299,"\int \frac{x^3}{\sqrt[3]{-1+x^4}} \, dx","Integrate[x^3/(-1 + x^4)^(1/3),x]","\frac{3}{8} \left(x^4-1\right)^{2/3}","\frac{3}{8} \left(x^4-1\right)^{2/3}",1,"(3*(-1 + x^4)^(2/3))/8","A",1
28,1,13,13,0.0026851,"\int x^3 \sqrt[3]{-1+x^4} \, dx","Integrate[x^3*(-1 + x^4)^(1/3),x]","\frac{3}{16} \left(x^4-1\right)^{4/3}","\frac{3}{16} \left(x^4-1\right)^{4/3}",1,"(3*(-1 + x^4)^(4/3))/16","A",1
29,1,13,13,0.0028314,"\int x^3 \left(-1+x^4\right)^{2/3} \, dx","Integrate[x^3*(-1 + x^4)^(2/3),x]","\frac{3}{20} \left(x^4-1\right)^{5/3}","\frac{3}{20} \left(x^4-1\right)^{5/3}",1,"(3*(-1 + x^4)^(5/3))/20","A",1
30,1,13,13,0.0029529,"\int x^3 \left(-1+x^4\right)^{3/4} \, dx","Integrate[x^3*(-1 + x^4)^(3/4),x]","\frac{1}{7} \left(x^4-1\right)^{7/4}","\frac{1}{7} \left(x^4-1\right)^{7/4}",1,"(-1 + x^4)^(7/4)/7","A",1
31,1,13,13,0.0049577,"\int \frac{-1+x^4}{x^2 \sqrt{1+x^4}} \, dx","Integrate[(-1 + x^4)/(x^2*Sqrt[1 + x^4]),x]","\frac{\sqrt{x^4+1}}{x}","\frac{\sqrt{x^4+1}}{x}",1,"Sqrt[1 + x^4]/x","A",1
32,1,13,13,0.0022646,"\int \frac{x^3}{\sqrt[3]{1+x^4}} \, dx","Integrate[x^3/(1 + x^4)^(1/3),x]","\frac{3}{8} \left(x^4+1\right)^{2/3}","\frac{3}{8} \left(x^4+1\right)^{2/3}",1,"(3*(1 + x^4)^(2/3))/8","A",1
33,1,13,13,0.002458,"\int x^3 \sqrt[4]{1+x^4} \, dx","Integrate[x^3*(1 + x^4)^(1/4),x]","\frac{1}{5} \left(x^4+1\right)^{5/4}","\frac{1}{5} \left(x^4+1\right)^{5/4}",1,"(1 + x^4)^(5/4)/5","A",1
34,1,13,13,0.0026526,"\int x^3 \sqrt[3]{1+x^4} \, dx","Integrate[x^3*(1 + x^4)^(1/3),x]","\frac{3}{16} \left(x^4+1\right)^{4/3}","\frac{3}{16} \left(x^4+1\right)^{4/3}",1,"(3*(1 + x^4)^(4/3))/16","A",1
35,1,13,13,0.002803,"\int x^3 \left(1+x^4\right)^{2/3} \, dx","Integrate[x^3*(1 + x^4)^(2/3),x]","\frac{3}{20} \left(x^4+1\right)^{5/3}","\frac{3}{20} \left(x^4+1\right)^{5/3}",1,"(3*(1 + x^4)^(5/3))/20","A",1
36,1,13,13,0.003088,"\int x^4 \left(-1+x^5\right)^{2/3} \, dx","Integrate[x^4*(-1 + x^5)^(2/3),x]","\frac{3}{25} \left(x^5-1\right)^{5/3}","\frac{3}{25} \left(x^5-1\right)^{5/3}",1,"(3*(-1 + x^5)^(5/3))/25","A",1
37,1,13,13,0.0029079,"\int x^4 \left(1+x^5\right)^{2/3} \, dx","Integrate[x^4*(1 + x^5)^(2/3),x]","\frac{3}{25} \left(x^5+1\right)^{5/3}","\frac{3}{25} \left(x^5+1\right)^{5/3}",1,"(3*(1 + x^5)^(5/3))/25","A",1
38,1,13,13,0.0024449,"\int \frac{x^5}{\sqrt[3]{-1+x^6}} \, dx","Integrate[x^5/(-1 + x^6)^(1/3),x]","\frac{1}{4} \left(x^6-1\right)^{2/3}","\frac{1}{4} \left(x^6-1\right)^{2/3}",1,"(-1 + x^6)^(2/3)/4","A",1
39,1,13,13,0.0026084,"\int x^5 \sqrt[4]{-1+x^6} \, dx","Integrate[x^5*(-1 + x^6)^(1/4),x]","\frac{2}{15} \left(x^6-1\right)^{5/4}","\frac{2}{15} \left(x^6-1\right)^{5/4}",1,"(2*(-1 + x^6)^(5/4))/15","A",1
40,1,13,13,0.0026569,"\int x^5 \sqrt[3]{-1+x^6} \, dx","Integrate[x^5*(-1 + x^6)^(1/3),x]","\frac{1}{8} \left(x^6-1\right)^{4/3}","\frac{1}{8} \left(x^6-1\right)^{4/3}",1,"(-1 + x^6)^(4/3)/8","A",1
41,1,13,13,0.0027947,"\int x^5 \sqrt{-1+x^6} \, dx","Integrate[x^5*Sqrt[-1 + x^6],x]","\frac{1}{9} \left(x^6-1\right)^{3/2}","\frac{1}{9} \left(x^6-1\right)^{3/2}",1,"(-1 + x^6)^(3/2)/9","A",1
42,1,13,13,0.0029248,"\int x^5 \left(-1+x^6\right)^{3/4} \, dx","Integrate[x^5*(-1 + x^6)^(3/4),x]","\frac{2}{21} \left(x^6-1\right)^{7/4}","\frac{2}{21} \left(x^6-1\right)^{7/4}",1,"(2*(-1 + x^6)^(7/4))/21","A",1
43,1,13,13,0.005836,"\int \frac{-2+x^6}{x^3 \sqrt{1+x^6}} \, dx","Integrate[(-2 + x^6)/(x^3*Sqrt[1 + x^6]),x]","\frac{\sqrt{x^6+1}}{x^2}","\frac{\sqrt{x^6+1}}{x^2}",1,"Sqrt[1 + x^6]/x^2","A",1
44,1,13,13,0.0022463,"\int \frac{x^5}{\sqrt[3]{1+x^6}} \, dx","Integrate[x^5/(1 + x^6)^(1/3),x]","\frac{1}{4} \left(x^6+1\right)^{2/3}","\frac{1}{4} \left(x^6+1\right)^{2/3}",1,"(1 + x^6)^(2/3)/4","A",1
45,1,13,13,0.0027378,"\int x^5 \sqrt[4]{1+x^6} \, dx","Integrate[x^5*(1 + x^6)^(1/4),x]","\frac{2}{15} \left(x^6+1\right)^{5/4}","\frac{2}{15} \left(x^6+1\right)^{5/4}",1,"(2*(1 + x^6)^(5/4))/15","A",1
46,1,13,13,0.0024393,"\int x^5 \sqrt[3]{1+x^6} \, dx","Integrate[x^5*(1 + x^6)^(1/3),x]","\frac{1}{8} \left(x^6+1\right)^{4/3}","\frac{1}{8} \left(x^6+1\right)^{4/3}",1,"(1 + x^6)^(4/3)/8","A",1
47,1,14,14,0.0053242,"\int \frac{-4+x^3}{x^2 \left(-1+x^3\right)^{3/4}} \, dx","Integrate[(-4 + x^3)/(x^2*(-1 + x^3)^(3/4)),x]","-\frac{4 \sqrt[4]{x^3-1}}{x}","-\frac{4 \sqrt[4]{x^3-1}}{x}",1,"(-4*(-1 + x^3)^(1/4))/x","A",1
48,1,14,14,0.0019709,"\int \frac{1}{x \sqrt{1+x^3}} \, dx","Integrate[1/(x*Sqrt[1 + x^3]),x]","-\frac{2}{3} \tanh ^{-1}\left(\sqrt{x^3+1}\right)","-\frac{2}{3} \tanh ^{-1}\left(\sqrt{x^3+1}\right)",1,"(-2*ArcTanh[Sqrt[1 + x^3]])/3","A",1
49,1,14,14,0.0053805,"\int \frac{4+x^3}{x^2 \left(1+x^3\right)^{3/4}} \, dx","Integrate[(4 + x^3)/(x^2*(1 + x^3)^(3/4)),x]","-\frac{4 \sqrt[4]{x^3+1}}{x}","-\frac{4 \sqrt[4]{x^3+1}}{x}",1,"(-4*(1 + x^3)^(1/4))/x","A",1
50,1,14,14,0.0384144,"\int \frac{\left(2+3 x^2\right) \sqrt[3]{x+x^3}}{1+x^2} \, dx","Integrate[((2 + 3*x^2)*(x + x^3)^(1/3))/(1 + x^2),x]","\frac{3}{2} x \sqrt[3]{x^3+x}","\frac{3}{2} x \sqrt[3]{x^3+x}",1,"(3*x*(x + x^3)^(1/3))/2","A",1
51,1,14,14,0.0091569,"\int \frac{-2+x}{(-1+x) \sqrt[4]{-x^2+x^3}} \, dx","Integrate[(-2 + x)/((-1 + x)*(-x^2 + x^3)^(1/4)),x]","\frac{4 x}{\sqrt[4]{(x-1) x^2}}","\frac{4 x}{\sqrt[4]{(x-1) x^2}}",1,"(4*x)/((-1 + x)*x^2)^(1/4)","A",1
52,1,14,14,0.0082302,"\int \frac{2+x}{(1+x) \sqrt[4]{x^2+x^3}} \, dx","Integrate[(2 + x)/((1 + x)*(x^2 + x^3)^(1/4)),x]","\frac{4 x}{\sqrt[4]{x^2 (x+1)}}","\frac{4 x}{\sqrt[4]{x^2 (x+1)}}",1,"(4*x)/(x^2*(1 + x))^(1/4)","A",1
53,1,14,14,0.002915,"\int \frac{1}{x^2 \left(1+x^4\right)^{3/4}} \, dx","Integrate[1/(x^2*(1 + x^4)^(3/4)),x]","-\frac{\sqrt[4]{x^4+1}}{x}","-\frac{\sqrt[4]{x^4+1}}{x}",1,"-((1 + x^4)^(1/4)/x)","A",1
54,1,14,14,0.0049433,"\int \frac{3+x^4}{x^4 \sqrt{1+x^4}} \, dx","Integrate[(3 + x^4)/(x^4*Sqrt[1 + x^4]),x]","-\frac{\sqrt{x^4+1}}{x^3}","-\frac{\sqrt{x^4+1}}{x^3}",1,"-(Sqrt[1 + x^4]/x^3)","A",1
55,1,14,14,0.0065171,"\int \frac{-1+4 x^3}{\sqrt{-1-2 x+2 x^4}} \, dx","Integrate[(-1 + 4*x^3)/Sqrt[-1 - 2*x + 2*x^4],x]","\sqrt{2 x^4-2 x-1}","\sqrt{2 x^4-2 x-1}",1,"Sqrt[-1 - 2*x + 2*x^4]","A",1
56,1,14,14,0.0057295,"\int \frac{-4+x^5}{x^2 \left(1+x^5\right)^{3/4}} \, dx","Integrate[(-4 + x^5)/(x^2*(1 + x^5)^(3/4)),x]","\frac{4 \sqrt[4]{x^5+1}}{x}","\frac{4 \sqrt[4]{x^5+1}}{x}",1,"(4*(1 + x^5)^(1/4))/x","A",1
57,1,14,14,0.0063958,"\int \frac{4+x^5}{x^2 \left(-1+x^5\right)^{3/4}} \, dx","Integrate[(4 + x^5)/(x^2*(-1 + x^5)^(3/4)),x]","\frac{4 \sqrt[4]{x^5-1}}{x}","\frac{4 \sqrt[4]{x^5-1}}{x}",1,"(4*(-1 + x^5)^(1/4))/x","A",1
58,1,2691,14,4.9204984,"\int \frac{2+5 x^3}{\sqrt{1+x^3} \left(1+x^2+x^5\right)} \, dx","Integrate[(2 + 5*x^3)/(Sqrt[1 + x^3]*(1 + x^2 + x^5)),x]","\text{Result too large to show}","2 \tan ^{-1}\left(x \sqrt{x^3+1}\right)",1,"((-4*I)*Sqrt[(1 + x)/(1 + (-1)^(1/3))]*Sqrt[1 - x + x^2]*EllipticPi[(I*Sqrt[3])/((-1)^(1/3) - Root[1 + #1^2 + #1^5 & , 1, 0]), ArcSin[Sqrt[(1 + (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)])/(Sqrt[1 + x^3]*((-1)^(1/3) - Root[1 + #1^2 + #1^5 & , 1, 0])*(Root[1 + #1^2 + #1^5 & , 1, 0] - Root[1 + #1^2 + #1^5 & , 2, 0])*(Root[1 + #1^2 + #1^5 & , 1, 0] - Root[1 + #1^2 + #1^5 & , 3, 0])*(Root[1 + #1^2 + #1^5 & , 1, 0] - Root[1 + #1^2 + #1^5 & , 4, 0])*(Root[1 + #1^2 + #1^5 & , 1, 0] - Root[1 + #1^2 + #1^5 & , 5, 0])) - ((10*I)*Sqrt[(1 + x)/(1 + (-1)^(1/3))]*Sqrt[1 - x + x^2]*EllipticPi[(I*Sqrt[3])/((-1)^(1/3) - Root[1 + #1^2 + #1^5 & , 1, 0]), ArcSin[Sqrt[(1 + (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)]*Root[1 + #1^2 + #1^5 & , 1, 0]^3)/(Sqrt[1 + x^3]*((-1)^(1/3) - Root[1 + #1^2 + #1^5 & , 1, 0])*(Root[1 + #1^2 + #1^5 & , 1, 0] - Root[1 + #1^2 + #1^5 & , 2, 0])*(Root[1 + #1^2 + #1^5 & , 1, 0] - Root[1 + #1^2 + #1^5 & , 3, 0])*(Root[1 + #1^2 + #1^5 & , 1, 0] - Root[1 + #1^2 + #1^5 & , 4, 0])*(Root[1 + #1^2 + #1^5 & , 1, 0] - Root[1 + #1^2 + #1^5 & , 5, 0])) - ((4*I)*Sqrt[(1 + x)/(1 + (-1)^(1/3))]*Sqrt[1 - x + x^2]*EllipticPi[(I*Sqrt[3])/((-1)^(1/3) - Root[1 + #1^2 + #1^5 & , 2, 0]), ArcSin[Sqrt[(1 + (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)])/(Sqrt[1 + x^3]*((-1)^(1/3) - Root[1 + #1^2 + #1^5 & , 2, 0])*(-Root[1 + #1^2 + #1^5 & , 1, 0] + Root[1 + #1^2 + #1^5 & , 2, 0])*(Root[1 + #1^2 + #1^5 & , 2, 0] - Root[1 + #1^2 + #1^5 & , 3, 0])*(Root[1 + #1^2 + #1^5 & , 2, 0] - Root[1 + #1^2 + #1^5 & , 4, 0])*(Root[1 + #1^2 + #1^5 & , 2, 0] - Root[1 + #1^2 + #1^5 & , 5, 0])) - ((10*I)*Sqrt[(1 + x)/(1 + (-1)^(1/3))]*Sqrt[1 - x + x^2]*EllipticPi[(I*Sqrt[3])/((-1)^(1/3) - Root[1 + #1^2 + #1^5 & , 2, 0]), ArcSin[Sqrt[(1 + (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)]*Root[1 + #1^2 + #1^5 & , 2, 0]^3)/(Sqrt[1 + x^3]*((-1)^(1/3) - Root[1 + #1^2 + #1^5 & , 2, 0])*(-Root[1 + #1^2 + #1^5 & , 1, 0] + Root[1 + #1^2 + #1^5 & , 2, 0])*(Root[1 + #1^2 + #1^5 & , 2, 0] - Root[1 + #1^2 + #1^5 & , 3, 0])*(Root[1 + #1^2 + #1^5 & , 2, 0] - Root[1 + #1^2 + #1^5 & , 4, 0])*(Root[1 + #1^2 + #1^5 & , 2, 0] - Root[1 + #1^2 + #1^5 & , 5, 0])) - ((4*I)*Sqrt[(1 + x)/(1 + (-1)^(1/3))]*Sqrt[1 - x + x^2]*EllipticPi[(I*Sqrt[3])/((-1)^(1/3) - Root[1 + #1^2 + #1^5 & , 3, 0]), ArcSin[Sqrt[(1 + (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)])/(Sqrt[1 + x^3]*((-1)^(1/3) - Root[1 + #1^2 + #1^5 & , 3, 0])*(-Root[1 + #1^2 + #1^5 & , 1, 0] + Root[1 + #1^2 + #1^5 & , 3, 0])*(-Root[1 + #1^2 + #1^5 & , 2, 0] + Root[1 + #1^2 + #1^5 & , 3, 0])*(Root[1 + #1^2 + #1^5 & , 3, 0] - Root[1 + #1^2 + #1^5 & , 4, 0])*(Root[1 + #1^2 + #1^5 & , 3, 0] - Root[1 + #1^2 + #1^5 & , 5, 0])) - ((10*I)*Sqrt[(1 + x)/(1 + (-1)^(1/3))]*Sqrt[1 - x + x^2]*EllipticPi[(I*Sqrt[3])/((-1)^(1/3) - Root[1 + #1^2 + #1^5 & , 3, 0]), ArcSin[Sqrt[(1 + (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)]*Root[1 + #1^2 + #1^5 & , 3, 0]^3)/(Sqrt[1 + x^3]*((-1)^(1/3) - Root[1 + #1^2 + #1^5 & , 3, 0])*(-Root[1 + #1^2 + #1^5 & , 1, 0] + Root[1 + #1^2 + #1^5 & , 3, 0])*(-Root[1 + #1^2 + #1^5 & , 2, 0] + Root[1 + #1^2 + #1^5 & , 3, 0])*(Root[1 + #1^2 + #1^5 & , 3, 0] - Root[1 + #1^2 + #1^5 & , 4, 0])*(Root[1 + #1^2 + #1^5 & , 3, 0] - Root[1 + #1^2 + #1^5 & , 5, 0])) - ((4*I)*Sqrt[(1 + x)/(1 + (-1)^(1/3))]*Sqrt[1 - x + x^2]*EllipticPi[(I*Sqrt[3])/((-1)^(1/3) - Root[1 + #1^2 + #1^5 & , 4, 0]), ArcSin[Sqrt[(1 + (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)])/(Sqrt[1 + x^3]*((-1)^(1/3) - Root[1 + #1^2 + #1^5 & , 4, 0])*(-Root[1 + #1^2 + #1^5 & , 1, 0] + Root[1 + #1^2 + #1^5 & , 4, 0])*(-Root[1 + #1^2 + #1^5 & , 2, 0] + Root[1 + #1^2 + #1^5 & , 4, 0])*(-Root[1 + #1^2 + #1^5 & , 3, 0] + Root[1 + #1^2 + #1^5 & , 4, 0])*(Root[1 + #1^2 + #1^5 & , 4, 0] - Root[1 + #1^2 + #1^5 & , 5, 0])) - ((10*I)*Sqrt[(1 + x)/(1 + (-1)^(1/3))]*Sqrt[1 - x + x^2]*EllipticPi[(I*Sqrt[3])/((-1)^(1/3) - Root[1 + #1^2 + #1^5 & , 4, 0]), ArcSin[Sqrt[(1 + (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)]*Root[1 + #1^2 + #1^5 & , 4, 0]^3)/(Sqrt[1 + x^3]*((-1)^(1/3) - Root[1 + #1^2 + #1^5 & , 4, 0])*(-Root[1 + #1^2 + #1^5 & , 1, 0] + Root[1 + #1^2 + #1^5 & , 4, 0])*(-Root[1 + #1^2 + #1^5 & , 2, 0] + Root[1 + #1^2 + #1^5 & , 4, 0])*(-Root[1 + #1^2 + #1^5 & , 3, 0] + Root[1 + #1^2 + #1^5 & , 4, 0])*(Root[1 + #1^2 + #1^5 & , 4, 0] - Root[1 + #1^2 + #1^5 & , 5, 0])) - ((4*I)*Sqrt[(1 + x)/(1 + (-1)^(1/3))]*Sqrt[1 - x + x^2]*EllipticPi[(I*Sqrt[3])/((-1)^(1/3) - Root[1 + #1^2 + #1^5 & , 5, 0]), ArcSin[Sqrt[(1 + (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)])/(Sqrt[1 + x^3]*((-1)^(1/3) - Root[1 + #1^2 + #1^5 & , 5, 0])*(-Root[1 + #1^2 + #1^5 & , 1, 0] + Root[1 + #1^2 + #1^5 & , 5, 0])*(-Root[1 + #1^2 + #1^5 & , 2, 0] + Root[1 + #1^2 + #1^5 & , 5, 0])*(-Root[1 + #1^2 + #1^5 & , 3, 0] + Root[1 + #1^2 + #1^5 & , 5, 0])*(-Root[1 + #1^2 + #1^5 & , 4, 0] + Root[1 + #1^2 + #1^5 & , 5, 0])) - ((10*I)*Sqrt[(1 + x)/(1 + (-1)^(1/3))]*Sqrt[1 - x + x^2]*EllipticPi[(I*Sqrt[3])/((-1)^(1/3) - Root[1 + #1^2 + #1^5 & , 5, 0]), ArcSin[Sqrt[(1 + (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)]*Root[1 + #1^2 + #1^5 & , 5, 0]^3)/(Sqrt[1 + x^3]*((-1)^(1/3) - Root[1 + #1^2 + #1^5 & , 5, 0])*(-Root[1 + #1^2 + #1^5 & , 1, 0] + Root[1 + #1^2 + #1^5 & , 5, 0])*(-Root[1 + #1^2 + #1^5 & , 2, 0] + Root[1 + #1^2 + #1^5 & , 5, 0])*(-Root[1 + #1^2 + #1^5 & , 3, 0] + Root[1 + #1^2 + #1^5 & , 5, 0])*(-Root[1 + #1^2 + #1^5 & , 4, 0] + Root[1 + #1^2 + #1^5 & , 5, 0]))","C",0
59,1,14,14,0.0023347,"\int \frac{1}{x \sqrt{-1+x^6}} \, dx","Integrate[1/(x*Sqrt[-1 + x^6]),x]","\frac{1}{3} \tan ^{-1}\left(\sqrt{x^6-1}\right)","\frac{1}{3} \tan ^{-1}\left(\sqrt{x^6-1}\right)",1,"ArcTan[Sqrt[-1 + x^6]]/3","A",1
60,1,14,14,0.0056578,"\int \frac{-2+x^6}{x^2 \left(1+x^6\right)^{3/4}} \, dx","Integrate[(-2 + x^6)/(x^2*(1 + x^6)^(3/4)),x]","\frac{2 \sqrt[4]{x^6+1}}{x}","\frac{2 \sqrt[4]{x^6+1}}{x}",1,"(2*(1 + x^6)^(1/4))/x","A",1
61,1,14,14,0.0019853,"\int \frac{1}{x \sqrt{1+x^6}} \, dx","Integrate[1/(x*Sqrt[1 + x^6]),x]","-\frac{1}{3} \tanh ^{-1}\left(\sqrt{x^6+1}\right)","-\frac{1}{3} \tanh ^{-1}\left(\sqrt{x^6+1}\right)",1,"-1/3*ArcTanh[Sqrt[1 + x^6]]","A",1
62,1,14,14,0.0056511,"\int \frac{2+x^6}{x^2 \left(-1+x^6\right)^{3/4}} \, dx","Integrate[(2 + x^6)/(x^2*(-1 + x^6)^(3/4)),x]","\frac{2 \sqrt[4]{x^6-1}}{x}","\frac{2 \sqrt[4]{x^6-1}}{x}",1,"(2*(-1 + x^6)^(1/4))/x","A",1
63,0,0,14,0.1413653,"\int \frac{-1+2 x^6}{\sqrt{1+x^6} \left(1-x^2+x^6\right)} \, dx","Integrate[(-1 + 2*x^6)/(Sqrt[1 + x^6]*(1 - x^2 + x^6)),x]","\int \frac{-1+2 x^6}{\sqrt{1+x^6} \left(1-x^2+x^6\right)} \, dx","-\tanh ^{-1}\left(\frac{x}{\sqrt{x^6+1}}\right)",1,"Integrate[(-1 + 2*x^6)/(Sqrt[1 + x^6]*(1 - x^2 + x^6)), x]","F",-1
64,0,0,14,0.134871,"\int \frac{1+2 x^6}{\sqrt{-1+x^6} \left(-1+x^2+x^6\right)} \, dx","Integrate[(1 + 2*x^6)/(Sqrt[-1 + x^6]*(-1 + x^2 + x^6)),x]","\int \frac{1+2 x^6}{\sqrt{-1+x^6} \left(-1+x^2+x^6\right)} \, dx","-\tan ^{-1}\left(\frac{x}{\sqrt{x^6-1}}\right)",1,"Integrate[(1 + 2*x^6)/(Sqrt[-1 + x^6]*(-1 + x^2 + x^6)), x]","F",-1
65,1,15,15,0.023599,"\int \frac{-1+3 x^2}{\sqrt[3]{-x+x^3}} \, dx","Integrate[(-1 + 3*x^2)/(-x + x^3)^(1/3),x]","\frac{3}{2} \left(x \left(x^2-1\right)\right)^{2/3}","\frac{3}{2} \left(x^3-x\right)^{2/3}",1,"(3*(x*(-1 + x^2))^(2/3))/2","A",1
66,1,15,15,0.0310996,"\int \left(-1+3 x^2\right) \sqrt[3]{-x+x^3} \, dx","Integrate[(-1 + 3*x^2)*(-x + x^3)^(1/3),x]","\frac{3}{4} \left(x \left(x^2-1\right)\right)^{4/3}","\frac{3}{4} \left(x^3-x\right)^{4/3}",1,"(3*(x*(-1 + x^2))^(4/3))/4","A",1
67,1,3866,15,3.5231569,"\int \frac{2+x-x^3}{\sqrt{1+x+x^3} \left(1+x-x^2+x^3\right)} \, dx","Integrate[(2 + x - x^3)/(Sqrt[1 + x + x^3]*(1 + x - x^2 + x^3)),x]","\text{Result too large to show}","2 \tanh ^{-1}\left(\frac{x}{\sqrt{x^3+x+1}}\right)",1,"(2*Sqrt[(-x + Root[1 + #1 + #1^3 & , 1, 0])/(Root[1 + #1 + #1^3 & , 1, 0] - Root[1 + #1 + #1^3 & , 3, 0])]*(-((EllipticF[ArcSin[Sqrt[(-x + Root[1 + #1 + #1^3 & , 3, 0])/(-Root[1 + #1 + #1^3 & , 2, 0] + Root[1 + #1 + #1^3 & , 3, 0])]], (Root[1 + #1 + #1^3 & , 2, 0] - Root[1 + #1 + #1^3 & , 3, 0])/(Root[1 + #1 + #1^3 & , 1, 0] - Root[1 + #1 + #1^3 & , 3, 0])]*(x - Root[1 + #1 + #1^3 & , 3, 0])*Sqrt[(-x + Root[1 + #1 + #1^3 & , 2, 0])/(Root[1 + #1 + #1^3 & , 2, 0] - Root[1 + #1 + #1^3 & , 3, 0])])/Sqrt[(x - Root[1 + #1 + #1^3 & , 3, 0])/(Root[1 + #1 + #1^3 & , 2, 0] - Root[1 + #1 + #1^3 & , 3, 0])]) + (2*EllipticPi[(-Root[1 + #1 + #1^3 & , 2, 0] + Root[1 + #1 + #1^3 & , 3, 0])/(Root[1 + #1 + #1^3 & , 3, 0] - Root[1 + #1 - #1^2 + #1^3 & , 1, 0]), ArcSin[Sqrt[(-x + Root[1 + #1 + #1^3 & , 3, 0])/(-Root[1 + #1 + #1^3 & , 2, 0] + Root[1 + #1 + #1^3 & , 3, 0])]], (Root[1 + #1 + #1^3 & , 2, 0] - Root[1 + #1 + #1^3 & , 3, 0])/(Root[1 + #1 + #1^3 & , 1, 0] - Root[1 + #1 + #1^3 & , 3, 0])]*Sqrt[-(((x - Root[1 + #1 + #1^3 & , 2, 0])*(x - Root[1 + #1 + #1^3 & , 3, 0]))/(Root[1 + #1 + #1^3 & , 2, 0] - Root[1 + #1 + #1^3 & , 3, 0])^2)]*(Root[1 + #1 + #1^3 & , 2, 0] - Root[1 + #1 + #1^3 & , 3, 0]))/((Root[1 + #1 + #1^3 & , 3, 0] - Root[1 + #1 - #1^2 + #1^3 & , 1, 0])*(Root[1 + #1 - #1^2 + #1^3 & , 1, 0] - Root[1 + #1 - #1^2 + #1^3 & , 2, 0])*(Root[1 + #1 - #1^2 + #1^3 & , 1, 0] - Root[1 + #1 - #1^2 + #1^3 & , 3, 0])) + (EllipticPi[(-Root[1 + #1 + #1^3 & , 2, 0] + Root[1 + #1 + #1^3 & , 3, 0])/(Root[1 + #1 + #1^3 & , 3, 0] - Root[1 + #1 - #1^2 + #1^3 & , 1, 0]), ArcSin[Sqrt[(-x + Root[1 + #1 + #1^3 & , 3, 0])/(-Root[1 + #1 + #1^3 & , 2, 0] + Root[1 + #1 + #1^3 & , 3, 0])]], (Root[1 + #1 + #1^3 & , 2, 0] - Root[1 + #1 + #1^3 & , 3, 0])/(Root[1 + #1 + #1^3 & , 1, 0] - Root[1 + #1 + #1^3 & , 3, 0])]*Sqrt[-(((x - Root[1 + #1 + #1^3 & , 2, 0])*(x - Root[1 + #1 + #1^3 & , 3, 0]))/(Root[1 + #1 + #1^3 & , 2, 0] - Root[1 + #1 + #1^3 & , 3, 0])^2)]*(Root[1 + #1 + #1^3 & , 2, 0] - Root[1 + #1 + #1^3 & , 3, 0])*Root[1 + #1 - #1^2 + #1^3 & , 1, 0])/((Root[1 + #1 + #1^3 & , 3, 0] - Root[1 + #1 - #1^2 + #1^3 & , 1, 0])*(Root[1 + #1 - #1^2 + #1^3 & , 1, 0] - Root[1 + #1 - #1^2 + #1^3 & , 2, 0])*(Root[1 + #1 - #1^2 + #1^3 & , 1, 0] - Root[1 + #1 - #1^2 + #1^3 & , 3, 0])) - (EllipticPi[(-Root[1 + #1 + #1^3 & , 2, 0] + Root[1 + #1 + #1^3 & , 3, 0])/(Root[1 + #1 + #1^3 & , 3, 0] - Root[1 + #1 - #1^2 + #1^3 & , 1, 0]), ArcSin[Sqrt[(-x + Root[1 + #1 + #1^3 & , 3, 0])/(-Root[1 + #1 + #1^3 & , 2, 0] + Root[1 + #1 + #1^3 & , 3, 0])]], (Root[1 + #1 + #1^3 & , 2, 0] - Root[1 + #1 + #1^3 & , 3, 0])/(Root[1 + #1 + #1^3 & , 1, 0] - Root[1 + #1 + #1^3 & , 3, 0])]*Sqrt[-(((x - Root[1 + #1 + #1^3 & , 2, 0])*(x - Root[1 + #1 + #1^3 & , 3, 0]))/(Root[1 + #1 + #1^3 & , 2, 0] - Root[1 + #1 + #1^3 & , 3, 0])^2)]*(Root[1 + #1 + #1^3 & , 2, 0] - Root[1 + #1 + #1^3 & , 3, 0])*Root[1 + #1 - #1^2 + #1^3 & , 1, 0]^3)/((Root[1 + #1 + #1^3 & , 3, 0] - Root[1 + #1 - #1^2 + #1^3 & , 1, 0])*(Root[1 + #1 - #1^2 + #1^3 & , 1, 0] - Root[1 + #1 - #1^2 + #1^3 & , 2, 0])*(Root[1 + #1 - #1^2 + #1^3 & , 1, 0] - Root[1 + #1 - #1^2 + #1^3 & , 3, 0])) + (2*EllipticPi[(-Root[1 + #1 + #1^3 & , 2, 0] + Root[1 + #1 + #1^3 & , 3, 0])/(Root[1 + #1 + #1^3 & , 3, 0] - Root[1 + #1 - #1^2 + #1^3 & , 2, 0]), ArcSin[Sqrt[(-x + Root[1 + #1 + #1^3 & , 3, 0])/(-Root[1 + #1 + #1^3 & , 2, 0] + Root[1 + #1 + #1^3 & , 3, 0])]], (Root[1 + #1 + #1^3 & , 2, 0] - Root[1 + #1 + #1^3 & , 3, 0])/(Root[1 + #1 + #1^3 & , 1, 0] - Root[1 + #1 + #1^3 & , 3, 0])]*Sqrt[-(((x - Root[1 + #1 + #1^3 & , 2, 0])*(x - Root[1 + #1 + #1^3 & , 3, 0]))/(Root[1 + #1 + #1^3 & , 2, 0] - Root[1 + #1 + #1^3 & , 3, 0])^2)]*(Root[1 + #1 + #1^3 & , 2, 0] - Root[1 + #1 + #1^3 & , 3, 0]))/((Root[1 + #1 + #1^3 & , 3, 0] - Root[1 + #1 - #1^2 + #1^3 & , 2, 0])*(-Root[1 + #1 - #1^2 + #1^3 & , 1, 0] + Root[1 + #1 - #1^2 + #1^3 & , 2, 0])*(Root[1 + #1 - #1^2 + #1^3 & , 2, 0] - Root[1 + #1 - #1^2 + #1^3 & , 3, 0])) + (EllipticPi[(-Root[1 + #1 + #1^3 & , 2, 0] + Root[1 + #1 + #1^3 & , 3, 0])/(Root[1 + #1 + #1^3 & , 3, 0] - Root[1 + #1 - #1^2 + #1^3 & , 2, 0]), ArcSin[Sqrt[(-x + Root[1 + #1 + #1^3 & , 3, 0])/(-Root[1 + #1 + #1^3 & , 2, 0] + Root[1 + #1 + #1^3 & , 3, 0])]], (Root[1 + #1 + #1^3 & , 2, 0] - Root[1 + #1 + #1^3 & , 3, 0])/(Root[1 + #1 + #1^3 & , 1, 0] - Root[1 + #1 + #1^3 & , 3, 0])]*Sqrt[-(((x - Root[1 + #1 + #1^3 & , 2, 0])*(x - Root[1 + #1 + #1^3 & , 3, 0]))/(Root[1 + #1 + #1^3 & , 2, 0] - Root[1 + #1 + #1^3 & , 3, 0])^2)]*(Root[1 + #1 + #1^3 & , 2, 0] - Root[1 + #1 + #1^3 & , 3, 0])*Root[1 + #1 - #1^2 + #1^3 & , 2, 0])/((Root[1 + #1 + #1^3 & , 3, 0] - Root[1 + #1 - #1^2 + #1^3 & , 2, 0])*(-Root[1 + #1 - #1^2 + #1^3 & , 1, 0] + Root[1 + #1 - #1^2 + #1^3 & , 2, 0])*(Root[1 + #1 - #1^2 + #1^3 & , 2, 0] - Root[1 + #1 - #1^2 + #1^3 & , 3, 0])) - (EllipticPi[(-Root[1 + #1 + #1^3 & , 2, 0] + Root[1 + #1 + #1^3 & , 3, 0])/(Root[1 + #1 + #1^3 & , 3, 0] - Root[1 + #1 - #1^2 + #1^3 & , 2, 0]), ArcSin[Sqrt[(-x + Root[1 + #1 + #1^3 & , 3, 0])/(-Root[1 + #1 + #1^3 & , 2, 0] + Root[1 + #1 + #1^3 & , 3, 0])]], (Root[1 + #1 + #1^3 & , 2, 0] - Root[1 + #1 + #1^3 & , 3, 0])/(Root[1 + #1 + #1^3 & , 1, 0] - Root[1 + #1 + #1^3 & , 3, 0])]*Sqrt[-(((x - Root[1 + #1 + #1^3 & , 2, 0])*(x - Root[1 + #1 + #1^3 & , 3, 0]))/(Root[1 + #1 + #1^3 & , 2, 0] - Root[1 + #1 + #1^3 & , 3, 0])^2)]*(Root[1 + #1 + #1^3 & , 2, 0] - Root[1 + #1 + #1^3 & , 3, 0])*Root[1 + #1 - #1^2 + #1^3 & , 2, 0]^3)/((Root[1 + #1 + #1^3 & , 3, 0] - Root[1 + #1 - #1^2 + #1^3 & , 2, 0])*(-Root[1 + #1 - #1^2 + #1^3 & , 1, 0] + Root[1 + #1 - #1^2 + #1^3 & , 2, 0])*(Root[1 + #1 - #1^2 + #1^3 & , 2, 0] - Root[1 + #1 - #1^2 + #1^3 & , 3, 0])) + (2*EllipticPi[(-Root[1 + #1 + #1^3 & , 2, 0] + Root[1 + #1 + #1^3 & , 3, 0])/(Root[1 + #1 + #1^3 & , 3, 0] - Root[1 + #1 - #1^2 + #1^3 & , 3, 0]), ArcSin[Sqrt[(-x + Root[1 + #1 + #1^3 & , 3, 0])/(-Root[1 + #1 + #1^3 & , 2, 0] + Root[1 + #1 + #1^3 & , 3, 0])]], (Root[1 + #1 + #1^3 & , 2, 0] - Root[1 + #1 + #1^3 & , 3, 0])/(Root[1 + #1 + #1^3 & , 1, 0] - Root[1 + #1 + #1^3 & , 3, 0])]*Sqrt[-(((x - Root[1 + #1 + #1^3 & , 2, 0])*(x - Root[1 + #1 + #1^3 & , 3, 0]))/(Root[1 + #1 + #1^3 & , 2, 0] - Root[1 + #1 + #1^3 & , 3, 0])^2)]*(Root[1 + #1 + #1^3 & , 2, 0] - Root[1 + #1 + #1^3 & , 3, 0]))/((Root[1 + #1 + #1^3 & , 3, 0] - Root[1 + #1 - #1^2 + #1^3 & , 3, 0])*(-Root[1 + #1 - #1^2 + #1^3 & , 1, 0] + Root[1 + #1 - #1^2 + #1^3 & , 3, 0])*(-Root[1 + #1 - #1^2 + #1^3 & , 2, 0] + Root[1 + #1 - #1^2 + #1^3 & , 3, 0])) + (EllipticPi[(-Root[1 + #1 + #1^3 & , 2, 0] + Root[1 + #1 + #1^3 & , 3, 0])/(Root[1 + #1 + #1^3 & , 3, 0] - Root[1 + #1 - #1^2 + #1^3 & , 3, 0]), ArcSin[Sqrt[(-x + Root[1 + #1 + #1^3 & , 3, 0])/(-Root[1 + #1 + #1^3 & , 2, 0] + Root[1 + #1 + #1^3 & , 3, 0])]], (Root[1 + #1 + #1^3 & , 2, 0] - Root[1 + #1 + #1^3 & , 3, 0])/(Root[1 + #1 + #1^3 & , 1, 0] - Root[1 + #1 + #1^3 & , 3, 0])]*Sqrt[-(((x - Root[1 + #1 + #1^3 & , 2, 0])*(x - Root[1 + #1 + #1^3 & , 3, 0]))/(Root[1 + #1 + #1^3 & , 2, 0] - Root[1 + #1 + #1^3 & , 3, 0])^2)]*(Root[1 + #1 + #1^3 & , 2, 0] - Root[1 + #1 + #1^3 & , 3, 0])*Root[1 + #1 - #1^2 + #1^3 & , 3, 0])/((Root[1 + #1 + #1^3 & , 3, 0] - Root[1 + #1 - #1^2 + #1^3 & , 3, 0])*(-Root[1 + #1 - #1^2 + #1^3 & , 1, 0] + Root[1 + #1 - #1^2 + #1^3 & , 3, 0])*(-Root[1 + #1 - #1^2 + #1^3 & , 2, 0] + Root[1 + #1 - #1^2 + #1^3 & , 3, 0])) - (EllipticPi[(-Root[1 + #1 + #1^3 & , 2, 0] + Root[1 + #1 + #1^3 & , 3, 0])/(Root[1 + #1 + #1^3 & , 3, 0] - Root[1 + #1 - #1^2 + #1^3 & , 3, 0]), ArcSin[Sqrt[(-x + Root[1 + #1 + #1^3 & , 3, 0])/(-Root[1 + #1 + #1^3 & , 2, 0] + Root[1 + #1 + #1^3 & , 3, 0])]], (Root[1 + #1 + #1^3 & , 2, 0] - Root[1 + #1 + #1^3 & , 3, 0])/(Root[1 + #1 + #1^3 & , 1, 0] - Root[1 + #1 + #1^3 & , 3, 0])]*Sqrt[-(((x - Root[1 + #1 + #1^3 & , 2, 0])*(x - Root[1 + #1 + #1^3 & , 3, 0]))/(Root[1 + #1 + #1^3 & , 2, 0] - Root[1 + #1 + #1^3 & , 3, 0])^2)]*(Root[1 + #1 + #1^3 & , 2, 0] - Root[1 + #1 + #1^3 & , 3, 0])*Root[1 + #1 - #1^2 + #1^3 & , 3, 0]^3)/((Root[1 + #1 + #1^3 & , 3, 0] - Root[1 + #1 - #1^2 + #1^3 & , 3, 0])*(-Root[1 + #1 - #1^2 + #1^3 & , 1, 0] + Root[1 + #1 - #1^2 + #1^3 & , 3, 0])*(-Root[1 + #1 - #1^2 + #1^3 & , 2, 0] + Root[1 + #1 - #1^2 + #1^3 & , 3, 0]))))/Sqrt[1 + x + x^3]","C",0
68,1,1547,15,3.5050567,"\int \frac{1+x^4}{\left(1-x^4\right) \sqrt{-1+x^2+x^4}} \, dx","Integrate[(1 + x^4)/((1 - x^4)*Sqrt[-1 + x^2 + x^4]),x]","\frac{-\frac{\left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right) \sqrt{\frac{2 x+i \sqrt{2 \left(1+\sqrt{5}\right)}}{-2 i \sqrt{1+\sqrt{5}} x+2 \sqrt{-1+\sqrt{5}} x-\sqrt{10}+(1+2 i) \sqrt{2}}} \sqrt{\frac{i \sqrt{2 \left(1+\sqrt{5}\right)}-2 x}{\sqrt{2} \left((-1+2 i)+\sqrt{5}\right)-2 \left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right) x}} \sqrt{\frac{2 \left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right) x+\sqrt{2} \left((-1-2 i)+\sqrt{5}\right)}{\sqrt{2} \left((-1+2 i)+\sqrt{5}\right)-2 \left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right) x}} \left(\left(2+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) F\left(\sin ^{-1}\left(\sqrt{\frac{\left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right) \left(2 x+\sqrt{2 \left(-1+\sqrt{5}\right)}\right)}{\left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right) \left(\sqrt{2 \left(-1+\sqrt{5}\right)}-2 x\right)}}\right)|-\frac{3}{5}-\frac{4 i}{5}\right)-2 \sqrt{2 \left(-1+\sqrt{5}\right)} \Pi \left(\frac{\left(-2+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) \left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right)}{\left(2+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) \left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right)};\sin ^{-1}\left(\sqrt{\frac{\left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right) \left(2 x+\sqrt{2 \left(-1+\sqrt{5}\right)}\right)}{\left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right) \left(\sqrt{2 \left(-1+\sqrt{5}\right)}-2 x\right)}}\right)|-\frac{3}{5}-\frac{4 i}{5}\right)\right) \left(\sqrt{2 \left(-1+\sqrt{5}\right)}-2 x\right)^2}{\left(-2+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) \left(2+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) \left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right)}+\frac{\left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right) \sqrt{\frac{2 x+i \sqrt{2 \left(1+\sqrt{5}\right)}}{-2 i \sqrt{1+\sqrt{5}} x+2 \sqrt{-1+\sqrt{5}} x-\sqrt{10}+(1+2 i) \sqrt{2}}} \sqrt{\frac{i \sqrt{2 \left(1+\sqrt{5}\right)}-2 x}{\sqrt{2} \left((-1+2 i)+\sqrt{5}\right)-2 \left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right) x}} \sqrt{\frac{2 \left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right) x+\sqrt{2} \left((-1-2 i)+\sqrt{5}\right)}{\sqrt{2} \left((-1+2 i)+\sqrt{5}\right)-2 \left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right) x}} \left(\left(-2+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) F\left(\sin ^{-1}\left(\sqrt{\frac{\left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right) \left(2 x+\sqrt{2 \left(-1+\sqrt{5}\right)}\right)}{\left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right) \left(\sqrt{2 \left(-1+\sqrt{5}\right)}-2 x\right)}}\right)|-\frac{3}{5}-\frac{4 i}{5}\right)-2 \sqrt{2 \left(-1+\sqrt{5}\right)} \Pi \left(\frac{\left(2+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) \left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right)}{\left(-2+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) \left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right)};\sin ^{-1}\left(\sqrt{\frac{\left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right) \left(2 x+\sqrt{2 \left(-1+\sqrt{5}\right)}\right)}{\left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right) \left(\sqrt{2 \left(-1+\sqrt{5}\right)}-2 x\right)}}\right)|-\frac{3}{5}-\frac{4 i}{5}\right)\right) \left(\sqrt{2 \left(-1+\sqrt{5}\right)}-2 x\right)^2}{\left(-2+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) \left(2+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) \left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right)}+\frac{2 i \sqrt{-x^4-x^2+1} F\left(i \sinh ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} x\right)|-\frac{3}{2}-\frac{\sqrt{5}}{2}\right)}{\sqrt{-1+\sqrt{5}}}-\frac{2 i \sqrt{-x^4-x^2+1} \Pi \left(\frac{1}{2} \left(1+\sqrt{5}\right);i \sinh ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} x\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{\sqrt{-1+\sqrt{5}}}}{\sqrt{2} \sqrt{x^4+x^2-1}}","\tanh ^{-1}\left(\frac{x}{\sqrt{x^4+x^2-1}}\right)",1,"(((2*I)*Sqrt[1 - x^2 - x^4]*EllipticF[I*ArcSinh[Sqrt[2/(1 + Sqrt[5])]*x], -3/2 - Sqrt[5]/2])/Sqrt[-1 + Sqrt[5]] - ((2*I)*Sqrt[1 - x^2 - x^4]*EllipticPi[(1 + Sqrt[5])/2, I*ArcSinh[Sqrt[2/(1 + Sqrt[5])]*x], (-3 - Sqrt[5])/2])/Sqrt[-1 + Sqrt[5]] - ((Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] - 2*x)^2*Sqrt[(I*Sqrt[2*(1 + Sqrt[5])] + 2*x)/((1 + 2*I)*Sqrt[2] - Sqrt[10] + 2*Sqrt[-1 + Sqrt[5]]*x - (2*I)*Sqrt[1 + Sqrt[5]]*x)]*Sqrt[(I*Sqrt[2*(1 + Sqrt[5])] - 2*x)/(Sqrt[2]*((-1 + 2*I) + Sqrt[5]) - 2*(Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])*x)]*Sqrt[(Sqrt[2]*((-1 - 2*I) + Sqrt[5]) + 2*(Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]])*x)/(Sqrt[2]*((-1 + 2*I) + Sqrt[5]) - 2*(Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])*x)]*((2 + Sqrt[2*(-1 + Sqrt[5])])*EllipticF[ArcSin[Sqrt[((Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] + 2*x))/((Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] - 2*x))]], -3/5 - (4*I)/5] - 2*Sqrt[2*(-1 + Sqrt[5])]*EllipticPi[((-2 + Sqrt[2*(-1 + Sqrt[5])])*(Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]]))/((2 + Sqrt[2*(-1 + Sqrt[5])])*(Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]])), ArcSin[Sqrt[((Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] + 2*x))/((Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] - 2*x))]], -3/5 - (4*I)/5]))/((-2 + Sqrt[2*(-1 + Sqrt[5])])*(2 + Sqrt[2*(-1 + Sqrt[5])])*(Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]])) + ((Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] - 2*x)^2*Sqrt[(I*Sqrt[2*(1 + Sqrt[5])] + 2*x)/((1 + 2*I)*Sqrt[2] - Sqrt[10] + 2*Sqrt[-1 + Sqrt[5]]*x - (2*I)*Sqrt[1 + Sqrt[5]]*x)]*Sqrt[(I*Sqrt[2*(1 + Sqrt[5])] - 2*x)/(Sqrt[2]*((-1 + 2*I) + Sqrt[5]) - 2*(Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])*x)]*Sqrt[(Sqrt[2]*((-1 - 2*I) + Sqrt[5]) + 2*(Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]])*x)/(Sqrt[2]*((-1 + 2*I) + Sqrt[5]) - 2*(Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])*x)]*((-2 + Sqrt[2*(-1 + Sqrt[5])])*EllipticF[ArcSin[Sqrt[((Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] + 2*x))/((Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] - 2*x))]], -3/5 - (4*I)/5] - 2*Sqrt[2*(-1 + Sqrt[5])]*EllipticPi[((2 + Sqrt[2*(-1 + Sqrt[5])])*(Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]]))/((-2 + Sqrt[2*(-1 + Sqrt[5])])*(Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]])), ArcSin[Sqrt[((Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] + 2*x))/((Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] - 2*x))]], -3/5 - (4*I)/5]))/((-2 + Sqrt[2*(-1 + Sqrt[5])])*(2 + Sqrt[2*(-1 + Sqrt[5])])*(Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]])))/(Sqrt[2]*Sqrt[-1 + x^2 + x^4])","C",0
69,1,16,16,0.0096907,"\int \frac{-4+x^3}{x^4 \sqrt[4]{-1+x^3}} \, dx","Integrate[(-4 + x^3)/(x^4*(-1 + x^3)^(1/4)),x]","-\frac{4 \left(x^3-1\right)^{3/4}}{3 x^3}","-\frac{4 \left(x^3-1\right)^{3/4}}{3 x^3}",1,"(-4*(-1 + x^3)^(3/4))/(3*x^3)","A",1
70,1,16,16,0.0029555,"\int \frac{\sqrt[3]{-1+x^3}}{x^5} \, dx","Integrate[(-1 + x^3)^(1/3)/x^5,x]","\frac{\left(x^3-1\right)^{4/3}}{4 x^4}","\frac{\left(x^3-1\right)^{4/3}}{4 x^4}",1,"(-1 + x^3)^(4/3)/(4*x^4)","A",1
71,1,16,16,0.0031429,"\int \frac{\left(-1+x^3\right)^{2/3}}{x^6} \, dx","Integrate[(-1 + x^3)^(2/3)/x^6,x]","\frac{\left(x^3-1\right)^{5/3}}{5 x^5}","\frac{\left(x^3-1\right)^{5/3}}{5 x^5}",1,"(-1 + x^3)^(5/3)/(5*x^5)","A",1
72,1,16,16,0.0024007,"\int \frac{\sqrt[3]{1+x^3}}{x^5} \, dx","Integrate[(1 + x^3)^(1/3)/x^5,x]","-\frac{\left(x^3+1\right)^{4/3}}{4 x^4}","-\frac{\left(x^3+1\right)^{4/3}}{4 x^4}",1,"-1/4*(1 + x^3)^(4/3)/x^4","A",1
73,1,16,16,0.0026511,"\int \frac{\left(1+x^3\right)^{2/3}}{x^6} \, dx","Integrate[(1 + x^3)^(2/3)/x^6,x]","-\frac{\left(x^3+1\right)^{5/3}}{5 x^5}","-\frac{\left(x^3+1\right)^{5/3}}{5 x^5}",1,"-1/5*(1 + x^3)^(5/3)/x^5","A",1
74,1,16,16,0.0076429,"\int \frac{\left(-2+x^3\right) \left(1+x^3\right)^{3/2}}{x^6} \, dx","Integrate[((-2 + x^3)*(1 + x^3)^(3/2))/x^6,x]","\frac{2 \left(x^3+1\right)^{5/2}}{5 x^5}","\frac{2 \left(x^3+1\right)^{5/2}}{5 x^5}",1,"(2*(1 + x^3)^(5/2))/(5*x^5)","A",1
75,1,16,16,0.0088565,"\int \frac{4+x^3}{x^4 \sqrt[4]{1+x^3}} \, dx","Integrate[(4 + x^3)/(x^4*(1 + x^3)^(1/4)),x]","-\frac{4 \left(x^3+1\right)^{3/4}}{3 x^3}","-\frac{4 \left(x^3+1\right)^{3/4}}{3 x^3}",1,"(-4*(1 + x^3)^(3/4))/(3*x^3)","A",1
76,1,16,16,0.0078774,"\int \frac{1}{x^2 \sqrt[3]{x+x^3}} \, dx","Integrate[1/(x^2*(x + x^3)^(1/3)),x]","-\frac{3 \left(x^3+x\right)^{2/3}}{4 x^2}","-\frac{3 \left(x^3+x\right)^{2/3}}{4 x^2}",1,"(-3*(x + x^3)^(2/3))/(4*x^2)","A",1
77,1,21,16,0.0150068,"\int \frac{\left(1+x^2\right) \left(3+x^2\right)}{x^6 \sqrt[4]{x+x^3}} \, dx","Integrate[((1 + x^2)*(3 + x^2))/(x^6*(x + x^3)^(1/4)),x]","-\frac{4 \left(x^2+1\right) \left(x^3+x\right)^{3/4}}{7 x^6}","-\frac{4 \left(x^3+x\right)^{7/4}}{7 x^7}",1,"(-4*(1 + x^2)*(x + x^3)^(3/4))/(7*x^6)","A",1
78,1,21,16,0.0036829,"\int \frac{\sqrt[3]{x+x^3}}{x^4} \, dx","Integrate[(x + x^3)^(1/3)/x^4,x]","-\frac{3 \left(x^2+1\right) \sqrt[3]{x^3+x}}{8 x^3}","-\frac{3 \left(x^3+x\right)^{4/3}}{8 x^4}",1,"(-3*(1 + x^2)*(x + x^3)^(1/3))/(8*x^3)","A",1
79,1,16,16,0.0024358,"\int \frac{1}{x^4 \sqrt[4]{-1+x^4}} \, dx","Integrate[1/(x^4*(-1 + x^4)^(1/4)),x]","\frac{\left(x^4-1\right)^{3/4}}{3 x^3}","\frac{\left(x^4-1\right)^{3/4}}{3 x^3}",1,"(-1 + x^4)^(3/4)/(3*x^3)","A",1
80,1,16,16,0.0027228,"\int \frac{\left(-1+x^4\right)^{3/4}}{x^8} \, dx","Integrate[(-1 + x^4)^(3/4)/x^8,x]","\frac{\left(x^4-1\right)^{7/4}}{7 x^7}","\frac{\left(x^4-1\right)^{7/4}}{7 x^7}",1,"(-1 + x^4)^(7/4)/(7*x^7)","A",1
81,1,77,16,0.0598093,"\int \frac{-1+x^4}{x^2 \sqrt{x+x^3}} \, dx","Integrate[(-1 + x^4)/(x^2*Sqrt[x + x^3]),x]","\frac{2 \left(x^2 \left(-\sqrt{x^2+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-x^2\right)+x^2+1\right)+\sqrt{x^2+1} \, _2F_1\left(-\frac{3}{4},\frac{1}{2};\frac{1}{4};-x^2\right)\right)}{3 x \sqrt{x^3+x}}","\frac{2 \left(x^3+x\right)^{3/2}}{3 x^3}",1,"(2*(Sqrt[1 + x^2]*Hypergeometric2F1[-3/4, 1/2, 1/4, -x^2] + x^2*(1 + x^2 - Sqrt[1 + x^2]*Hypergeometric2F1[1/4, 1/2, 5/4, -x^2])))/(3*x*Sqrt[x + x^3])","C",1
82,1,16,16,0.0033467,"\int \frac{1}{x^4 \sqrt[4]{1+x^4}} \, dx","Integrate[1/(x^4*(1 + x^4)^(1/4)),x]","-\frac{\left(x^4+1\right)^{3/4}}{3 x^3}","-\frac{\left(x^4+1\right)^{3/4}}{3 x^3}",1,"-1/3*(1 + x^4)^(3/4)/x^3","A",1
83,1,16,16,0.0089371,"\int \frac{\left(-3+x^4\right) \sqrt[3]{1+x^4}}{x^5} \, dx","Integrate[((-3 + x^4)*(1 + x^4)^(1/3))/x^5,x]","\frac{3 \left(x^4+1\right)^{4/3}}{4 x^4}","\frac{3 \left(x^4+1\right)^{4/3}}{4 x^4}",1,"(3*(1 + x^4)^(4/3))/(4*x^4)","A",1
84,1,40,16,0.0173329,"\int \frac{\left(-1+x^2\right) \left(1+x^2\right) \sqrt{1+x^4}}{x^4} \, dx","Integrate[((-1 + x^2)*(1 + x^2)*Sqrt[1 + x^4])/x^4,x]","x \, _2F_1\left(-\frac{1}{2},\frac{1}{4};\frac{5}{4};-x^4\right)+\frac{\, _2F_1\left(-\frac{3}{4},-\frac{1}{2};\frac{1}{4};-x^4\right)}{3 x^3}","\frac{\left(x^4+1\right)^{3/2}}{3 x^3}",1,"Hypergeometric2F1[-3/4, -1/2, 1/4, -x^4]/(3*x^3) + x*Hypergeometric2F1[-1/2, 1/4, 5/4, -x^4]","C",1
85,1,16,16,0.005593,"\int \frac{\left(-3+x^4\right) \left(1+x^4\right)^{2/3}}{x^6} \, dx","Integrate[((-3 + x^4)*(1 + x^4)^(2/3))/x^6,x]","\frac{3 \left(x^4+1\right)^{5/3}}{5 x^5}","\frac{3 \left(x^4+1\right)^{5/3}}{5 x^5}",1,"(3*(1 + x^4)^(5/3))/(5*x^5)","A",1
86,1,16,16,0.0031939,"\int \frac{\left(1+x^4\right)^{3/4}}{x^8} \, dx","Integrate[(1 + x^4)^(3/4)/x^8,x]","-\frac{\left(x^4+1\right)^{7/4}}{7 x^7}","-\frac{\left(x^4+1\right)^{7/4}}{7 x^7}",1,"-1/7*(1 + x^4)^(7/4)/x^7","A",1
87,1,16,16,0.006516,"\int \frac{\left(-1+x^4\right)^{2/3} \left(3+x^4\right)}{x^6} \, dx","Integrate[((-1 + x^4)^(2/3)*(3 + x^4))/x^6,x]","\frac{3 \left(x^4-1\right)^{5/3}}{5 x^5}","\frac{3 \left(x^4-1\right)^{5/3}}{5 x^5}",1,"(3*(-1 + x^4)^(5/3))/(5*x^5)","A",1
88,1,16,16,0.0081593,"\int \frac{\sqrt[3]{1+x^4} \left(3+x^4\right)}{x^9} \, dx","Integrate[((1 + x^4)^(1/3)*(3 + x^4))/x^9,x]","-\frac{3 \left(x^4+1\right)^{4/3}}{8 x^8}","-\frac{3 \left(x^4+1\right)^{4/3}}{8 x^8}",1,"(-3*(1 + x^4)^(4/3))/(8*x^8)","A",1
89,1,16,16,0.0073262,"\int \frac{1}{x^2 \sqrt{x+x^4}} \, dx","Integrate[1/(x^2*Sqrt[x + x^4]),x]","-\frac{2 \sqrt{x^4+x}}{3 x^2}","-\frac{2 \sqrt{x^4+x}}{3 x^2}",1,"(-2*Sqrt[x + x^4])/(3*x^2)","A",1
90,1,21,16,0.0071665,"\int \frac{1+x^3}{x^6 \sqrt[4]{x+x^4}} \, dx","Integrate[(1 + x^3)/(x^6*(x + x^4)^(1/4)),x]","-\frac{4 \left(x^3+1\right) \left(x^4+x\right)^{3/4}}{21 x^6}","-\frac{4 \left(x^4+x\right)^{7/4}}{21 x^7}",1,"(-4*(1 + x^3)*(x + x^4)^(3/4))/(21*x^6)","A",1
91,1,61,16,0.0425176,"\int \frac{\left(-2+x^3\right) \sqrt[3]{x+x^4}}{\left(1+x^3\right)^2} \, dx","Integrate[((-2 + x^3)*(x + x^4)^(1/3))/(1 + x^3)^2,x]","\frac{3 \sqrt[3]{x^4+x} \left(2 x^4 \, _2F_1\left(\frac{13}{9},\frac{5}{3};\frac{22}{9};-x^3\right)-13 x \, _2F_1\left(\frac{4}{9},\frac{5}{3};\frac{13}{9};-x^3\right)\right)}{26 \sqrt[3]{x^3+1}}","-\frac{3 x^2}{2 \left(x^4+x\right)^{2/3}}",1,"(3*(x + x^4)^(1/3)*(-13*x*Hypergeometric2F1[4/9, 5/3, 13/9, -x^3] + 2*x^4*Hypergeometric2F1[13/9, 5/3, 22/9, -x^3]))/(26*(1 + x^3)^(1/3))","C",1
92,1,16,16,0.0060448,"\int \frac{\sqrt[4]{x^2+x^4}}{x^2 \left(1+x^2\right)} \, dx","Integrate[(x^2 + x^4)^(1/4)/(x^2*(1 + x^2)),x]","-\frac{2 \sqrt[4]{x^4+x^2}}{x}","-\frac{2 \sqrt[4]{x^4+x^2}}{x}",1,"(-2*(x^2 + x^4)^(1/4))/x","A",1
93,1,16,16,0.0091118,"\int \frac{\left(-6+x^5\right) \left(-1+x^5\right)^{2/3}}{x^{11}} \, dx","Integrate[((-6 + x^5)*(-1 + x^5)^(2/3))/x^11,x]","-\frac{3 \left(x^5-1\right)^{5/3}}{5 x^{10}}","-\frac{3 \left(x^5-1\right)^{5/3}}{5 x^{10}}",1,"(-3*(-1 + x^5)^(5/3))/(5*x^10)","A",1
94,1,16,16,0.006477,"\int \frac{\left(-4+x^5\right) \left(1+x^5\right)^{3/4}}{x^8} \, dx","Integrate[((-4 + x^5)*(1 + x^5)^(3/4))/x^8,x]","\frac{4 \left(x^5+1\right)^{7/4}}{7 x^7}","\frac{4 \left(x^5+1\right)^{7/4}}{7 x^7}",1,"(4*(1 + x^5)^(7/4))/(7*x^7)","A",1
95,1,16,16,0.0088915,"\int \frac{\left(-1+x^5\right)^{3/4} \left(4+x^5\right)}{x^8} \, dx","Integrate[((-1 + x^5)^(3/4)*(4 + x^5))/x^8,x]","\frac{4 \left(x^5-1\right)^{7/4}}{7 x^7}","\frac{4 \left(x^5-1\right)^{7/4}}{7 x^7}",1,"(4*(-1 + x^5)^(7/4))/(7*x^7)","A",1
96,1,16,16,0.0067552,"\int \frac{\left(1+x^5\right)^{2/3} \left(6+x^5\right)}{x^{11}} \, dx","Integrate[((1 + x^5)^(2/3)*(6 + x^5))/x^11,x]","-\frac{3 \left(x^5+1\right)^{5/3}}{5 x^{10}}","-\frac{3 \left(x^5+1\right)^{5/3}}{5 x^{10}}",1,"(-3*(1 + x^5)^(5/3))/(5*x^10)","A",1
97,1,21,16,0.011328,"\int \frac{\left(-3+x^4\right) \left(1+x^4\right)}{x^6 \sqrt[4]{x+x^5}} \, dx","Integrate[((-3 + x^4)*(1 + x^4))/(x^6*(x + x^5)^(1/4)),x]","\frac{4 \left(x^4+1\right) \left(x^5+x\right)^{3/4}}{7 x^6}","\frac{4 \left(x^5+x\right)^{7/4}}{7 x^7}",1,"(4*(1 + x^4)*(x + x^5)^(3/4))/(7*x^6)","A",1
98,1,16,16,0.0089674,"\int \frac{\left(-1+x^2\right) \sqrt[4]{x^3+x^5}}{x^2 \left(1+x^2\right)} \, dx","Integrate[((-1 + x^2)*(x^3 + x^5)^(1/4))/(x^2*(1 + x^2)),x]","\frac{4 \sqrt[4]{x^5+x^3}}{x}","\frac{4 \sqrt[4]{x^5+x^3}}{x}",1,"(4*(x^3 + x^5)^(1/4))/x","A",1
99,0,0,16,0.2618722,"\int \frac{-2 b+3 a x^5}{\sqrt{b+a x^5} \left(b+x^2+a x^5\right)} \, dx","Integrate[(-2*b + 3*a*x^5)/(Sqrt[b + a*x^5]*(b + x^2 + a*x^5)),x]","\int \frac{-2 b+3 a x^5}{\sqrt{b+a x^5} \left(b+x^2+a x^5\right)} \, dx","-2 \tan ^{-1}\left(\frac{x}{\sqrt{a x^5+b}}\right)",1,"Integrate[(-2*b + 3*a*x^5)/(Sqrt[b + a*x^5]*(b + x^2 + a*x^5)), x]","F",-1
100,1,16,16,0.0023191,"\int \frac{1}{x^4 \sqrt{-1+x^6}} \, dx","Integrate[1/(x^4*Sqrt[-1 + x^6]),x]","\frac{\sqrt{x^6-1}}{3 x^3}","\frac{\sqrt{x^6-1}}{3 x^3}",1,"Sqrt[-1 + x^6]/(3*x^3)","A",1
101,1,16,16,0.002273,"\int \frac{\sqrt[3]{-1+x^6}}{x^9} \, dx","Integrate[(-1 + x^6)^(1/3)/x^9,x]","\frac{\left(x^6-1\right)^{4/3}}{8 x^8}","\frac{\left(x^6-1\right)^{4/3}}{8 x^8}",1,"(-1 + x^6)^(4/3)/(8*x^8)","A",1
102,1,16,16,0.0024397,"\int \frac{\sqrt{-1+x^6}}{x^{10}} \, dx","Integrate[Sqrt[-1 + x^6]/x^10,x]","\frac{\left(x^6-1\right)^{3/2}}{9 x^9}","\frac{\left(x^6-1\right)^{3/2}}{9 x^9}",1,"(-1 + x^6)^(3/2)/(9*x^9)","A",1
103,1,16,16,0.0024307,"\int \frac{1}{x^4 \sqrt{1+x^6}} \, dx","Integrate[1/(x^4*Sqrt[1 + x^6]),x]","-\frac{\sqrt{x^6+1}}{3 x^3}","-\frac{\sqrt{x^6+1}}{3 x^3}",1,"-1/3*Sqrt[1 + x^6]/x^3","A",1
104,1,16,16,0.0025498,"\int \frac{1}{x^5 \sqrt[3]{1+x^6}} \, dx","Integrate[1/(x^5*(1 + x^6)^(1/3)),x]","-\frac{\left(x^6+1\right)^{2/3}}{4 x^4}","-\frac{\left(x^6+1\right)^{2/3}}{4 x^4}",1,"-1/4*(1 + x^6)^(2/3)/x^4","A",1
105,1,16,16,0.009428,"\int \frac{-2+x^6}{x^4 \sqrt[4]{1+x^6}} \, dx","Integrate[(-2 + x^6)/(x^4*(1 + x^6)^(1/4)),x]","\frac{2 \left(x^6+1\right)^{3/4}}{3 x^3}","\frac{2 \left(x^6+1\right)^{3/4}}{3 x^3}",1,"(2*(1 + x^6)^(3/4))/(3*x^3)","A",1
106,1,16,16,0.0026968,"\int \frac{\sqrt{1+x^6}}{x^{10}} \, dx","Integrate[Sqrt[1 + x^6]/x^10,x]","-\frac{\left(x^6+1\right)^{3/2}}{9 x^9}","-\frac{\left(x^6+1\right)^{3/2}}{9 x^9}",1,"-1/9*(1 + x^6)^(3/2)/x^9","A",1
107,1,16,16,0.006129,"\int \frac{\left(-2+x^6\right) \left(1+x^6\right)^{3/4}}{x^8} \, dx","Integrate[((-2 + x^6)*(1 + x^6)^(3/4))/x^8,x]","\frac{2 \left(x^6+1\right)^{7/4}}{7 x^7}","\frac{2 \left(x^6+1\right)^{7/4}}{7 x^7}",1,"(2*(1 + x^6)^(7/4))/(7*x^7)","A",1
108,1,16,16,0.0052486,"\int \frac{\sqrt[3]{-1+x^6} \left(1+x^6\right)}{x^5} \, dx","Integrate[((-1 + x^6)^(1/3)*(1 + x^6))/x^5,x]","\frac{\left(x^6-1\right)^{4/3}}{4 x^4}","\frac{\left(x^6-1\right)^{4/3}}{4 x^4}",1,"(-1 + x^6)^(4/3)/(4*x^4)","A",1
109,1,16,16,0.0072594,"\int \frac{2+x^6}{x^4 \sqrt[4]{-1+x^6}} \, dx","Integrate[(2 + x^6)/(x^4*(-1 + x^6)^(1/4)),x]","\frac{2 \left(x^6-1\right)^{3/4}}{3 x^3}","\frac{2 \left(x^6-1\right)^{3/4}}{3 x^3}",1,"(2*(-1 + x^6)^(3/4))/(3*x^3)","A",1
110,1,16,16,0.0054458,"\int \frac{\left(-1+x^6\right)^{3/4} \left(2+x^6\right)}{x^8} \, dx","Integrate[((-1 + x^6)^(3/4)*(2 + x^6))/x^8,x]","\frac{2 \left(x^6-1\right)^{7/4}}{7 x^7}","\frac{2 \left(x^6-1\right)^{7/4}}{7 x^7}",1,"(2*(-1 + x^6)^(7/4))/(7*x^7)","A",1
111,1,16,16,0.0112578,"\int \frac{-3+2 x^5}{x^3 \sqrt[4]{x+x^6}} \, dx","Integrate[(-3 + 2*x^5)/(x^3*(x + x^6)^(1/4)),x]","\frac{4 \left(x^6+x\right)^{3/4}}{3 x^3}","\frac{4 \left(x^6+x\right)^{3/4}}{3 x^3}",1,"(4*(x + x^6)^(3/4))/(3*x^3)","A",1
112,1,83,16,0.0241783,"\int \frac{\sqrt[3]{x+x^4} \left(-2-x^3+x^6\right)}{x^6} \, dx","Integrate[((x + x^4)^(1/3)*(-2 - x^3 + x^6))/x^6,x]","\frac{3 \sqrt[3]{x^4+x} \left(28 x^3 \, _2F_1\left(-\frac{5}{9},-\frac{1}{3};\frac{4}{9};-x^3\right)+20 \, _2F_1\left(-\frac{14}{9},-\frac{1}{3};-\frac{5}{9};-x^3\right)+35 x^6 \, _2F_1\left(-\frac{1}{3},\frac{4}{9};\frac{13}{9};-x^3\right)\right)}{140 x^5 \sqrt[3]{x^3+1}}","\frac{3 \left(x^4+x\right)^{7/3}}{7 x^7}",1,"(3*(x + x^4)^(1/3)*(20*Hypergeometric2F1[-14/9, -1/3, -5/9, -x^3] + 28*x^3*Hypergeometric2F1[-5/9, -1/3, 4/9, -x^3] + 35*x^6*Hypergeometric2F1[-1/3, 4/9, 13/9, -x^3]))/(140*x^5*(1 + x^3)^(1/3))","C",1
113,1,933,16,5.6209586,"\int \frac{x \left(2+x^6\right)}{\sqrt{-1+x^6} \left(-1-x^4+x^6\right)} \, dx","Integrate[(x*(2 + x^6))/(Sqrt[-1 + x^6]*(-1 - x^4 + x^6)),x]","\frac{\sqrt{\frac{1-x^2}{1+\sqrt[3]{-1}}} \sqrt{x^4+x^2+1} \left(-\frac{\sqrt{3} \left(\left(1+\sqrt[3]{-1}\right) x^2+i \sqrt{3}\right) F\left(\sin ^{-1}\left(\sqrt{\frac{1-(-1)^{2/3} x^2}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{(-1)^{2/3} x^2-1}-\frac{3 i \left(\frac{\left(3+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,1\right]^2\right) \Pi \left(\frac{i \sqrt{3}}{\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,1\right]};\sin ^{-1}\left(\sqrt{\frac{1-(-1)^{2/3} x^2}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,1\right]}+\frac{-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,2\right]^3 \left(\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,1\right]-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,3\right]\right) \left(\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,3\right]\right) \Pi \left(\frac{i \sqrt{3}}{\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,2\right]};\sin ^{-1}\left(\sqrt{\frac{1-(-1)^{2/3} x^2}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)-2 \left(\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,1\right]-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,3\right]\right) \left(\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,3\right]\right) \Pi \left(\frac{i \sqrt{3}}{\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,2\right]};\sin ^{-1}\left(\sqrt{\frac{1-(-1)^{2/3} x^2}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)+\Pi \left(\frac{i \sqrt{3}}{\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,3\right]};\sin ^{-1}\left(\sqrt{\frac{1-(-1)^{2/3} x^2}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right) \left(\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,1\right]-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,2\right]\right) \left(\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,2\right]\right) \text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,3\right]^3+2 \Pi \left(\frac{i \sqrt{3}}{\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,3\right]};\sin ^{-1}\left(\sqrt{\frac{1-(-1)^{2/3} x^2}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right) \left(\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,1\right]-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,2\right]\right) \left(\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,2\right]\right)}{\left(\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,2\right]\right) \left(\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,2\right]-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,3\right]\right) \left(\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,3\right]\right)}\right)}{\left(\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,1\right]-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,2\right]\right) \left(\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,1\right]-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,3\right]\right)}\right)}{3 \sqrt{x^6-1}}","-\tanh ^{-1}\left(\frac{x^2}{\sqrt{x^6-1}}\right)",1,"(Sqrt[(1 - x^2)/(1 + (-1)^(1/3))]*Sqrt[1 + x^2 + x^4]*(-((Sqrt[3]*(I*Sqrt[3] + (1 + (-1)^(1/3))*x^2)*EllipticF[ArcSin[Sqrt[(1 - (-1)^(2/3)*x^2)/(1 + (-1)^(1/3))]], (-1)^(1/3)])/(-1 + (-1)^(2/3)*x^2)) - ((3*I)*((EllipticPi[(I*Sqrt[3])/((-1)^(1/3) + Root[-1 - #1^2 + #1^3 & , 1, 0]), ArcSin[Sqrt[(1 - (-1)^(2/3)*x^2)/(1 + (-1)^(1/3))]], (-1)^(1/3)]*(3 + Root[-1 - #1^2 + #1^3 & , 1, 0]^2))/((-1)^(1/3) + Root[-1 - #1^2 + #1^3 & , 1, 0]) + (2*EllipticPi[(I*Sqrt[3])/((-1)^(1/3) + Root[-1 - #1^2 + #1^3 & , 3, 0]), ArcSin[Sqrt[(1 - (-1)^(2/3)*x^2)/(1 + (-1)^(1/3))]], (-1)^(1/3)]*(Root[-1 - #1^2 + #1^3 & , 1, 0] - Root[-1 - #1^2 + #1^3 & , 2, 0])*((-1)^(1/3) + Root[-1 - #1^2 + #1^3 & , 2, 0]) + EllipticPi[(I*Sqrt[3])/((-1)^(1/3) + Root[-1 - #1^2 + #1^3 & , 3, 0]), ArcSin[Sqrt[(1 - (-1)^(2/3)*x^2)/(1 + (-1)^(1/3))]], (-1)^(1/3)]*(Root[-1 - #1^2 + #1^3 & , 1, 0] - Root[-1 - #1^2 + #1^3 & , 2, 0])*((-1)^(1/3) + Root[-1 - #1^2 + #1^3 & , 2, 0])*Root[-1 - #1^2 + #1^3 & , 3, 0]^3 - 2*EllipticPi[(I*Sqrt[3])/((-1)^(1/3) + Root[-1 - #1^2 + #1^3 & , 2, 0]), ArcSin[Sqrt[(1 - (-1)^(2/3)*x^2)/(1 + (-1)^(1/3))]], (-1)^(1/3)]*(Root[-1 - #1^2 + #1^3 & , 1, 0] - Root[-1 - #1^2 + #1^3 & , 3, 0])*((-1)^(1/3) + Root[-1 - #1^2 + #1^3 & , 3, 0]) - EllipticPi[(I*Sqrt[3])/((-1)^(1/3) + Root[-1 - #1^2 + #1^3 & , 2, 0]), ArcSin[Sqrt[(1 - (-1)^(2/3)*x^2)/(1 + (-1)^(1/3))]], (-1)^(1/3)]*Root[-1 - #1^2 + #1^3 & , 2, 0]^3*(Root[-1 - #1^2 + #1^3 & , 1, 0] - Root[-1 - #1^2 + #1^3 & , 3, 0])*((-1)^(1/3) + Root[-1 - #1^2 + #1^3 & , 3, 0]))/(((-1)^(1/3) + Root[-1 - #1^2 + #1^3 & , 2, 0])*(Root[-1 - #1^2 + #1^3 & , 2, 0] - Root[-1 - #1^2 + #1^3 & , 3, 0])*((-1)^(1/3) + Root[-1 - #1^2 + #1^3 & , 3, 0]))))/((Root[-1 - #1^2 + #1^3 & , 1, 0] - Root[-1 - #1^2 + #1^3 & , 2, 0])*(Root[-1 - #1^2 + #1^3 & , 1, 0] - Root[-1 - #1^2 + #1^3 & , 3, 0]))))/(3*Sqrt[-1 + x^6])","C",0
114,1,76,16,0.0362534,"\int \frac{-1+x^8}{x^4 \sqrt{-1+x^4}} \, dx","Integrate[(-1 + x^8)/(x^4*Sqrt[-1 + x^4]),x]","\frac{x^4 \left(\sqrt{1-x^4} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};x^4\right)+x^4-1\right)+\sqrt{1-x^4} \, _2F_1\left(-\frac{3}{4},\frac{1}{2};\frac{1}{4};x^4\right)}{3 x^3 \sqrt{x^4-1}}","\frac{\left(x^4-1\right)^{3/2}}{3 x^3}",1,"(Sqrt[1 - x^4]*Hypergeometric2F1[-3/4, 1/2, 1/4, x^4] + x^4*(-1 + x^4 + Sqrt[1 - x^4]*Hypergeometric2F1[1/4, 1/2, 5/4, x^4]))/(3*x^3*Sqrt[-1 + x^4])","C",1
115,1,16,16,0.0060485,"\int \frac{\left(-1+x^8\right) \sqrt{1+x^8}}{x^7} \, dx","Integrate[((-1 + x^8)*Sqrt[1 + x^8])/x^7,x]","\frac{\left(x^8+1\right)^{3/2}}{6 x^6}","\frac{\left(x^8+1\right)^{3/2}}{6 x^6}",1,"(1 + x^8)^(3/2)/(6*x^6)","A",1
116,1,249,17,1.2309132,"\int \frac{2+x+2 x^2}{(-1+2 x) \sqrt{x+x^4}} \, dx","Integrate[(2 + x + 2*x^2)/((-1 + 2*x)*Sqrt[x + x^4]),x]","\frac{2 \left(\sqrt{6} \left(1+\sqrt[3]{-1}\right) \sqrt{\frac{x-\sqrt[3]{-1}}{\left(1+\sqrt[3]{-1}\right) x}} \sqrt{\frac{(x+1) \left(2 x+i \sqrt{3}-1\right)}{x^2}} x^2 F\left(\sin ^{-1}\left(\sqrt{\frac{(-1)^{2/3} (x+1)}{\left(-1+(-1)^{2/3}\right) x}}\right)|1+(-1)^{2/3}\right)-\sqrt{6} \left(1+\sqrt[3]{-1}\right) \sqrt{\frac{x-\sqrt[3]{-1}}{\left(1+\sqrt[3]{-1}\right) x}} \sqrt{\frac{(x+1) \left(2 x+i \sqrt{3}-1\right)}{x^2}} x^2 \Pi \left(\frac{1}{3} \left(1+\sqrt[3]{-1}\right);\sin ^{-1}\left(\sqrt{\frac{(-1)^{2/3} (x+1)}{\left(-1+(-1)^{2/3}\right) x}}\right)|1+(-1)^{2/3}\right)+\sqrt{x^3+1} \sqrt{x} \sinh ^{-1}\left(x^{3/2}\right)\right)}{3 \sqrt{x^4+x}}","2 \tanh ^{-1}\left(\frac{(x-2) x}{\sqrt{x^4+x}}\right)",1,"(2*(Sqrt[x]*Sqrt[1 + x^3]*ArcSinh[x^(3/2)] + Sqrt[6]*(1 + (-1)^(1/3))*x^2*Sqrt[(-(-1)^(1/3) + x)/((1 + (-1)^(1/3))*x)]*Sqrt[((1 + x)*(-1 + I*Sqrt[3] + 2*x))/x^2]*EllipticF[ArcSin[Sqrt[((-1)^(2/3)*(1 + x))/((-1 + (-1)^(2/3))*x)]], 1 + (-1)^(2/3)] - Sqrt[6]*(1 + (-1)^(1/3))*x^2*Sqrt[(-(-1)^(1/3) + x)/((1 + (-1)^(1/3))*x)]*Sqrt[((1 + x)*(-1 + I*Sqrt[3] + 2*x))/x^2]*EllipticPi[(1 + (-1)^(1/3))/3, ArcSin[Sqrt[((-1)^(2/3)*(1 + x))/((-1 + (-1)^(2/3))*x)]], 1 + (-1)^(2/3)]))/(3*Sqrt[x + x^4])","C",1
117,1,93,17,0.1250882,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{1+x^2+x^4}} \, dx","Integrate[(-1 + x^2)/((1 + x^2)*Sqrt[1 + x^2 + x^4]),x]","\frac{(-1)^{2/3} \sqrt{\sqrt[3]{-1} x^2+1} \sqrt{1-(-1)^{2/3} x^2} \left(F\left(i \sinh ^{-1}\left((-1)^{5/6} x\right)|(-1)^{2/3}\right)-2 \Pi \left(\sqrt[3]{-1};i \sinh ^{-1}\left((-1)^{5/6} x\right)|(-1)^{2/3}\right)\right)}{\sqrt{x^4+x^2+1}}","-\tan ^{-1}\left(\frac{x}{\sqrt{x^4+x^2+1}}\right)",1,"((-1)^(2/3)*Sqrt[1 + (-1)^(1/3)*x^2]*Sqrt[1 - (-1)^(2/3)*x^2]*(EllipticF[I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)] - 2*EllipticPi[(-1)^(1/3), I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)]))/Sqrt[1 + x^2 + x^4]","C",1
118,1,120,17,0.2335846,"\int \frac{-1+x^4}{\left(1+x^4\right) \sqrt{1+x^2+x^4}} \, dx","Integrate[(-1 + x^4)/((1 + x^4)*Sqrt[1 + x^2 + x^4]),x]","\frac{(-1)^{2/3} \sqrt{\sqrt[3]{-1} x^2+1} \sqrt{1-(-1)^{2/3} x^2} \left(F\left(i \sinh ^{-1}\left((-1)^{5/6} x\right)|(-1)^{2/3}\right)-\Pi \left(-(-1)^{5/6};i \sinh ^{-1}\left((-1)^{5/6} x\right)|(-1)^{2/3}\right)-\Pi \left((-1)^{5/6};i \sinh ^{-1}\left((-1)^{5/6} x\right)|(-1)^{2/3}\right)\right)}{\sqrt{x^4+x^2+1}}","-\tanh ^{-1}\left(\frac{x}{\sqrt{x^4+x^2+1}}\right)",1,"((-1)^(2/3)*Sqrt[1 + (-1)^(1/3)*x^2]*Sqrt[1 - (-1)^(2/3)*x^2]*(EllipticF[I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)] - EllipticPi[-(-1)^(5/6), I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)] - EllipticPi[(-1)^(5/6), I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)]))/Sqrt[1 + x^2 + x^4]","C",1
119,0,0,17,0.1439557,"\int \frac{-1+2 x^2+2 x^4}{\left(1+2 x^2\right) \sqrt{-1+x^6}} \, dx","Integrate[(-1 + 2*x^2 + 2*x^4)/((1 + 2*x^2)*Sqrt[-1 + x^6]),x]","\int \frac{-1+2 x^2+2 x^4}{\left(1+2 x^2\right) \sqrt{-1+x^6}} \, dx","\tanh ^{-1}\left(\frac{x \left(x^2-1\right)}{\sqrt{x^6-1}}\right)",1,"Integrate[(-1 + 2*x^2 + 2*x^4)/((1 + 2*x^2)*Sqrt[-1 + x^6]), x]","F",-1
120,1,18,18,0.0056704,"\int \frac{x^3}{\left(-1+x^2\right)^{3/4}} \, dx","Integrate[x^3/(-1 + x^2)^(3/4),x]","\frac{2}{5} \sqrt[4]{x^2-1} \left(x^2+4\right)","\frac{2}{5} \sqrt[4]{x^2-1} \left(x^2+4\right)",1,"(2*(-1 + x^2)^(1/4)*(4 + x^2))/5","A",1
121,1,21,18,0.0357012,"\int \frac{3+x}{(-1+x)^2 \sqrt[3]{-1+x^2}} \, dx","Integrate[(3 + x)/((-1 + x)^2*(-1 + x^2)^(1/3)),x]","-\frac{3 (x+1)}{2 (x-1) \sqrt[3]{x^2-1}}","-\frac{3 \left(x^2-1\right)^{2/3}}{2 (x-1)^2}",1,"(-3*(1 + x))/(2*(-1 + x)*(-1 + x^2)^(1/3))","A",1
122,1,18,18,0.0054947,"\int \frac{x^3}{\left(1+x^2\right)^{2/3}} \, dx","Integrate[x^3/(1 + x^2)^(2/3),x]","\frac{3}{8} \left(x^2-3\right) \sqrt[3]{x^2+1}","\frac{3}{8} \left(x^2-3\right) \sqrt[3]{x^2+1}",1,"(3*(-3 + x^2)*(1 + x^2)^(1/3))/8","A",1
123,1,18,18,0.0087427,"\int \frac{1}{x^2 \sqrt[3]{-x+x^3}} \, dx","Integrate[1/(x^2*(-x + x^3)^(1/3)),x]","\frac{3 \left(x \left(x^2-1\right)\right)^{2/3}}{4 x^2}","\frac{3 \left(x^3-x\right)^{2/3}}{4 x^2}",1,"(3*(x*(-1 + x^2))^(2/3))/(4*x^2)","A",1
124,1,18,18,0.0065849,"\int \frac{\sqrt[3]{-x+x^3}}{x^4} \, dx","Integrate[(-x + x^3)^(1/3)/x^4,x]","\frac{3 \left(x \left(x^2-1\right)\right)^{4/3}}{8 x^4}","\frac{3 \left(x^3-x\right)^{4/3}}{8 x^4}",1,"(3*(x*(-1 + x^2))^(4/3))/(8*x^4)","A",1
125,1,12,18,0.0224181,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{x+x^3}} \, dx","Integrate[(-1 + x^2)/((1 + x^2)*Sqrt[x + x^3]),x]","-\frac{2 x}{\sqrt{x^3+x}}","-\frac{2 \sqrt{x^3+x}}{x^2+1}",1,"(-2*x)/Sqrt[x + x^3]","A",1
126,1,18,18,0.0067603,"\int \frac{1}{x \sqrt[3]{x^2+x^3}} \, dx","Integrate[1/(x*(x^2 + x^3)^(1/3)),x]","-\frac{3 (x+1)}{2 \sqrt[3]{x^2 (x+1)}}","-\frac{3 \left(x^3+x^2\right)^{2/3}}{2 x^2}",1,"(-3*(1 + x))/(2*(x^2*(1 + x))^(1/3))","A",1
127,1,18,18,0.0106575,"\int \frac{2+x}{x^2 \sqrt[4]{x^2+x^3}} \, dx","Integrate[(2 + x)/(x^2*(x^2 + x^3)^(1/4)),x]","-\frac{4 \left(x^2 (x+1)\right)^{3/4}}{3 x^3}","-\frac{4 \left(x^3+x^2\right)^{3/4}}{3 x^3}",1,"(-4*(x^2*(1 + x))^(3/4))/(3*x^3)","A",1
128,1,18,18,0.0114195,"\int \frac{\left(-2 b+a x^3\right) \sqrt{b+a x^3}}{x^4} \, dx","Integrate[((-2*b + a*x^3)*Sqrt[b + a*x^3])/x^4,x]","\frac{2 \left(a x^3+b\right)^{3/2}}{3 x^3}","\frac{2 \left(a x^3+b\right)^{3/2}}{3 x^3}",1,"(2*(b + a*x^3)^(3/2))/(3*x^3)","A",1
129,1,33,18,0.1419739,"\int \frac{1+x+x^2}{(-1+x)^2 \sqrt{-1+x^4}} \, dx","Integrate[(1 + x + x^2)/((-1 + x)^2*Sqrt[-1 + x^4]),x]","\frac{-x^3-x^2-x-1}{2 (x-1) \sqrt{x^4-1}}","-\frac{\sqrt{x^4-1}}{2 (x-1)^2}",1,"(-1 - x - x^2 - x^3)/(2*(-1 + x)*Sqrt[-1 + x^4])","A",1
130,1,18,18,0.0122167,"\int \frac{-1+x^4}{x^2 \sqrt{-x+x^3}} \, dx","Integrate[(-1 + x^4)/(x^2*Sqrt[-x + x^3]),x]","\frac{2 \left(x \left(x^2-1\right)\right)^{3/2}}{3 x^3}","\frac{2 \left(x^3-x\right)^{3/2}}{3 x^3}",1,"(2*(x*(-1 + x^2))^(3/2))/(3*x^3)","A",1
131,1,18,18,0.0089035,"\int \frac{1}{x^2 \sqrt{-x+x^4}} \, dx","Integrate[1/(x^2*Sqrt[-x + x^4]),x]","\frac{2 \sqrt{x \left(x^3-1\right)}}{3 x^2}","\frac{2 \sqrt{x^4-x}}{3 x^2}",1,"(2*Sqrt[x*(-1 + x^3)])/(3*x^2)","A",1
132,1,18,18,0.0080988,"\int \frac{1}{x^3 \sqrt[4]{-x+x^4}} \, dx","Integrate[1/(x^3*(-x + x^4)^(1/4)),x]","\frac{4 \left(x \left(x^3-1\right)\right)^{3/4}}{9 x^3}","\frac{4 \left(x^4-x\right)^{3/4}}{9 x^3}",1,"(4*(x*(-1 + x^3))^(3/4))/(9*x^3)","A",1
133,1,18,18,0.0092767,"\int \frac{-1+x^3}{x^6 \sqrt[4]{-x+x^4}} \, dx","Integrate[(-1 + x^3)/(x^6*(-x + x^4)^(1/4)),x]","\frac{4 \left(x \left(x^3-1\right)\right)^{7/4}}{21 x^7}","\frac{4 \left(x^4-x\right)^{7/4}}{21 x^7}",1,"(4*(x*(-1 + x^3))^(7/4))/(21*x^7)","A",1
134,1,18,18,0.0068899,"\int \frac{\sqrt[4]{-x+x^4}}{x^5} \, dx","Integrate[(-x + x^4)^(1/4)/x^5,x]","\frac{4 \left(x \left(x^3-1\right)\right)^{5/4}}{15 x^5}","\frac{4 \left(x^4-x\right)^{5/4}}{15 x^5}",1,"(4*(x*(-1 + x^3))^(5/4))/(15*x^5)","A",1
135,1,61,18,0.0474197,"\int \frac{\left(2+x^3\right) \sqrt[3]{-x+x^4}}{\left(-1+x^3\right)^2} \, dx","Integrate[((2 + x^3)*(-x + x^4)^(1/3))/(-1 + x^3)^2,x]","\frac{3 \sqrt[3]{x \left(x^3-1\right)} \left(13 x \, _2F_1\left(\frac{4}{9},\frac{5}{3};\frac{13}{9};x^3\right)+2 x^4 \, _2F_1\left(\frac{13}{9},\frac{5}{3};\frac{22}{9};x^3\right)\right)}{26 \sqrt[3]{1-x^3}}","-\frac{3 x^2}{2 \left(x^4-x\right)^{2/3}}",1,"(3*(x*(-1 + x^3))^(1/3)*(13*x*Hypergeometric2F1[4/9, 5/3, 13/9, x^3] + 2*x^4*Hypergeometric2F1[13/9, 5/3, 22/9, x^3]))/(26*(1 - x^3)^(1/3))","C",1
136,1,18,18,0.0072532,"\int \frac{\sqrt{-x+x^4}}{x^6} \, dx","Integrate[Sqrt[-x + x^4]/x^6,x]","\frac{2 \left(x \left(x^3-1\right)\right)^{3/2}}{9 x^6}","\frac{2 \left(x^4-x\right)^{3/2}}{9 x^6}",1,"(2*(x*(-1 + x^3))^(3/2))/(9*x^6)","A",1
137,1,33,18,0.0059493,"\int \frac{x}{\sqrt{x+x^4}} \, dx","Integrate[x/Sqrt[x + x^4],x]","\frac{2 \sqrt{x} \sqrt{x^3+1} \sinh ^{-1}\left(x^{3/2}\right)}{3 \sqrt{x^4+x}}","\frac{2}{3} \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4+x}}\right)",1,"(2*Sqrt[x]*Sqrt[1 + x^3]*ArcSinh[x^(3/2)])/(3*Sqrt[x + x^4])","A",1
138,1,60,18,0.0441084,"\int \frac{-2+x^3}{\left(1+x^3\right) \sqrt[3]{x+x^4}} \, dx","Integrate[(-2 + x^3)/((1 + x^3)*(x + x^4)^(1/3)),x]","\frac{3 \sqrt[3]{x^3+1} \left(x^4 \, _2F_1\left(\frac{11}{9},\frac{4}{3};\frac{20}{9};-x^3\right)-11 x \, _2F_1\left(\frac{2}{9},\frac{4}{3};\frac{11}{9};-x^3\right)\right)}{11 \sqrt[3]{x^4+x}}","-\frac{3 \left(x^4+x\right)^{2/3}}{x^3+1}",1,"(3*(1 + x^3)^(1/3)*(-11*x*Hypergeometric2F1[2/9, 4/3, 11/9, -x^3] + x^4*Hypergeometric2F1[11/9, 4/3, 20/9, -x^3]))/(11*(x + x^4)^(1/3))","C",1
139,1,20,18,0.0106445,"\int \frac{-1+x^2}{x \sqrt[3]{x^2+x^4}} \, dx","Integrate[(-1 + x^2)/(x*(x^2 + x^4)^(1/3)),x]","\frac{3 \left(x^2+1\right)}{2 \sqrt[3]{x^4+x^2}}","\frac{3 \left(x^4+x^2\right)^{2/3}}{2 x^2}",1,"(3*(1 + x^2))/(2*(x^2 + x^4)^(1/3))","A",1
140,1,18,18,0.0077413,"\int \frac{1}{x^2 \sqrt[4]{x^2+x^4}} \, dx","Integrate[1/(x^2*(x^2 + x^4)^(1/4)),x]","-\frac{2 \left(x^4+x^2\right)^{3/4}}{3 x^3}","-\frac{2 \left(x^4+x^2\right)^{3/4}}{3 x^3}",1,"(-2*(x^2 + x^4)^(3/4))/(3*x^3)","A",1
141,1,23,18,0.0042997,"\int \frac{\sqrt[4]{x^2+x^4}}{x^4} \, dx","Integrate[(x^2 + x^4)^(1/4)/x^4,x]","-\frac{2 \left(x^2+1\right) \sqrt[4]{x^4+x^2}}{5 x^3}","-\frac{2 \left(x^4+x^2\right)^{5/4}}{5 x^5}",1,"(-2*(1 + x^2)*(x^2 + x^4)^(1/4))/(5*x^3)","A",1
142,1,23,18,0.0066373,"\int \frac{\left(-1+x^2\right) \sqrt[3]{x^2+x^4}}{x^3} \, dx","Integrate[((-1 + x^2)*(x^2 + x^4)^(1/3))/x^3,x]","\frac{3 \left(x^2+1\right) \sqrt[3]{x^4+x^2}}{4 x^2}","\frac{3 \left(x^4+x^2\right)^{4/3}}{4 x^4}",1,"(3*(1 + x^2)*(x^2 + x^4)^(1/3))/(4*x^2)","A",1
143,1,18,18,0.0073746,"\int \frac{1}{x \sqrt[4]{x^3+x^4}} \, dx","Integrate[1/(x*(x^3 + x^4)^(1/4)),x]","-\frac{4 (x+1)}{3 \sqrt[4]{x^3 (x+1)}}","-\frac{4 \left(x^4+x^3\right)^{3/4}}{3 x^3}",1,"(-4*(1 + x))/(3*(x^3*(1 + x))^(1/4))","A",1
144,1,18,18,0.010283,"\int \frac{(1+x) \sqrt[4]{x^3+x^4}}{x^4} \, dx","Integrate[((1 + x)*(x^3 + x^4)^(1/4))/x^4,x]","-\frac{4 \left(x^3 (x+1)\right)^{9/4}}{9 x^9}","-\frac{4 \left(x^4+x^3\right)^{9/4}}{9 x^9}",1,"(-4*(x^3*(1 + x))^(9/4))/(9*x^9)","A",1
145,1,17638,18,6.2050336,"\int \frac{-2-x+2 x^4}{\left(1+x+x^4\right) \sqrt{1+x+x^2+x^4}} \, dx","Integrate[(-2 - x + 2*x^4)/((1 + x + x^4)*Sqrt[1 + x + x^2 + x^4]),x]","\text{Result too large to show}","-2 \tanh ^{-1}\left(\frac{x}{\sqrt{x^4+x^2+x+1}}\right)",1,"Result too large to show","C",0
146,1,18,18,0.0107758,"\int \frac{3+x^4}{x^3 \sqrt[4]{-x+x^5}} \, dx","Integrate[(3 + x^4)/(x^3*(-x + x^5)^(1/4)),x]","\frac{4 \left(x \left(x^4-1\right)\right)^{3/4}}{3 x^3}","\frac{4 \left(x^5-x\right)^{3/4}}{3 x^3}",1,"(4*(x*(-1 + x^4))^(3/4))/(3*x^3)","A",1
147,1,18,18,0.0109775,"\int \frac{\left(-1+x^4\right) \left(3+x^4\right)}{x^6 \sqrt[4]{-x+x^5}} \, dx","Integrate[((-1 + x^4)*(3 + x^4))/(x^6*(-x + x^5)^(1/4)),x]","\frac{4 \left(x \left(x^4-1\right)\right)^{7/4}}{7 x^7}","\frac{4 \left(x^5-x\right)^{7/4}}{7 x^7}",1,"(4*(x*(-1 + x^4))^(7/4))/(7*x^7)","A",1
148,1,60,18,0.0418407,"\int \frac{-3+x^4}{\left(1+x^4\right) \sqrt[4]{x+x^5}} \, dx","Integrate[(-3 + x^4)/((1 + x^4)*(x + x^5)^(1/4)),x]","\frac{4 \sqrt[4]{x^4+1} \left(x^5 \, _2F_1\left(\frac{19}{16},\frac{5}{4};\frac{35}{16};-x^4\right)-19 x \, _2F_1\left(\frac{3}{16},\frac{5}{4};\frac{19}{16};-x^4\right)\right)}{19 \sqrt[4]{x^5+x}}","-\frac{4 \left(x^5+x\right)^{3/4}}{x^4+1}",1,"(4*(1 + x^4)^(1/4)*(-19*x*Hypergeometric2F1[3/16, 5/4, 19/16, -x^4] + x^5*Hypergeometric2F1[19/16, 5/4, 35/16, -x^4]))/(19*(x + x^5)^(1/4))","C",1
149,1,23,18,0.0084348,"\int \frac{\left(-1+2 x^3\right) \sqrt[3]{x^2+x^5}}{x^3} \, dx","Integrate[((-1 + 2*x^3)*(x^2 + x^5)^(1/3))/x^3,x]","\frac{3 \left(x^3+1\right) \sqrt[3]{x^5+x^2}}{4 x^2}","\frac{3 \left(x^5+x^2\right)^{4/3}}{4 x^4}",1,"(3*(1 + x^3)*(x^2 + x^5)^(1/3))/(4*x^2)","A",1
150,1,20,18,0.0104917,"\int \frac{-1+x^2}{x \sqrt[4]{x^3+x^5}} \, dx","Integrate[(-1 + x^2)/(x*(x^3 + x^5)^(1/4)),x]","\frac{4 \left(x^2+1\right)}{3 \sqrt[4]{x^5+x^3}}","\frac{4 \left(x^5+x^3\right)^{3/4}}{3 x^3}",1,"(4*(1 + x^2))/(3*(x^3 + x^5)^(1/4))","A",1
151,1,65,18,0.041535,"\int \frac{\left(-1+x^4\right) \sqrt[4]{x^3+x^5}}{x^4} \, dx","Integrate[((-1 + x^4)*(x^3 + x^5)^(1/4))/x^4,x]","\frac{4 \sqrt[4]{x^5+x^3} \left(7 \, _2F_1\left(-\frac{9}{8},-\frac{1}{4};-\frac{1}{8};-x^2\right)+9 x^4 \, _2F_1\left(-\frac{1}{4},\frac{7}{8};\frac{15}{8};-x^2\right)\right)}{63 x^3 \sqrt[4]{x^2+1}}","\frac{4 \left(x^5+x^3\right)^{9/4}}{9 x^9}",1,"(4*(x^3 + x^5)^(1/4)*(7*Hypergeometric2F1[-9/8, -1/4, -1/8, -x^2] + 9*x^4*Hypergeometric2F1[-1/4, 7/8, 15/8, -x^2]))/(63*x^3*(1 + x^2)^(1/4))","C",1
152,1,18,18,0.0023758,"\int \frac{x^2}{\sqrt{-1+x^6}} \, dx","Integrate[x^2/Sqrt[-1 + x^6],x]","\frac{1}{3} \tanh ^{-1}\left(\frac{x^3}{\sqrt{x^6-1}}\right)","\frac{1}{3} \log \left(\sqrt{x^6-1}+x^3\right)",1,"ArcTanh[x^3/Sqrt[-1 + x^6]]/3","A",1
153,1,8,18,0.0019459,"\int \frac{x^2}{\sqrt{1+x^6}} \, dx","Integrate[x^2/Sqrt[1 + x^6],x]","\frac{1}{3} \sinh ^{-1}\left(x^3\right)","\frac{1}{3} \log \left(\sqrt{x^6+1}+x^3\right)",1,"ArcSinh[x^3]/3","A",1
154,1,18,18,0.0139785,"\int \frac{\left(-1+x^5\right) \left(3+2 x^5\right)}{x^6 \sqrt[4]{-x+x^6}} \, dx","Integrate[((-1 + x^5)*(3 + 2*x^5))/(x^6*(-x + x^6)^(1/4)),x]","\frac{4 \left(x \left(x^5-1\right)\right)^{7/4}}{7 x^7}","\frac{4 \left(x^6-x\right)^{7/4}}{7 x^7}",1,"(4*(x*(-1 + x^5))^(7/4))/(7*x^7)","A",1
155,1,18,18,0.0083423,"\int \frac{1}{x^3 \sqrt[3]{x^2+x^6}} \, dx","Integrate[1/(x^3*(x^2 + x^6)^(1/3)),x]","-\frac{3 \left(x^6+x^2\right)^{2/3}}{8 x^4}","-\frac{3 \left(x^6+x^2\right)^{2/3}}{8 x^4}",1,"(-3*(x^2 + x^6)^(2/3))/(8*x^4)","A",1
156,1,18,18,0.0112336,"\int \frac{-1+x^4}{x^2 \sqrt[4]{x^2+x^6}} \, dx","Integrate[(-1 + x^4)/(x^2*(x^2 + x^6)^(1/4)),x]","\frac{2 \left(x^6+x^2\right)^{3/4}}{3 x^3}","\frac{2 \left(x^6+x^2\right)^{3/4}}{3 x^3}",1,"(2*(x^2 + x^6)^(3/4))/(3*x^3)","A",1
157,1,23,18,0.0072996,"\int \frac{\left(-1+x^4\right) \sqrt[4]{x^2+x^6}}{x^4} \, dx","Integrate[((-1 + x^4)*(x^2 + x^6)^(1/4))/x^4,x]","\frac{2 \left(x^4+1\right) \sqrt[4]{x^6+x^2}}{5 x^3}","\frac{2 \left(x^6+x^2\right)^{5/4}}{5 x^5}",1,"(2*(1 + x^4)*(x^2 + x^6)^(1/4))/(5*x^3)","A",1
158,1,31,18,0.1129905,"\int \frac{\sqrt{1+\sqrt{1+x^2}}}{\sqrt{1+x^2}} \, dx","Integrate[Sqrt[1 + Sqrt[1 + x^2]]/Sqrt[1 + x^2],x]","\frac{2 \left(\sqrt{x^2+1}-1\right) \sqrt{\sqrt{x^2+1}+1}}{x}","\frac{2 x}{\sqrt{\sqrt{x^2+1}+1}}",1,"(2*(-1 + Sqrt[1 + x^2])*Sqrt[1 + Sqrt[1 + x^2]])/x","A",1
159,1,19,19,0.1241318,"\int \frac{-2-2 x+x^2}{\left(1+x+x^2\right) \sqrt{-1+x^3}} \, dx","Integrate[(-2 - 2*x + x^2)/((1 + x + x^2)*Sqrt[-1 + x^3]),x]","-\frac{2 \sqrt{x^3-1}}{x^2+x+1}","-\frac{2 \sqrt{x^3-1}}{x^2+x+1}",1,"(-2*Sqrt[-1 + x^3])/(1 + x + x^2)","A",1
160,1,19,19,0.0202624,"\int \frac{b+a x^2}{x \sqrt{-b x+a x^3}} \, dx","Integrate[(b + a*x^2)/(x*Sqrt[-(b*x) + a*x^3]),x]","\frac{2 \sqrt{a x^3-b x}}{x}","\frac{2 \sqrt{a x^3-b x}}{x}",1,"(2*Sqrt[-(b*x) + a*x^3])/x","A",1
161,1,307,19,1.4879994,"\int \frac{-1-2 x+2 x^2}{\left(1+2 x^2\right) \sqrt{x+x^4}} \, dx","Integrate[(-1 - 2*x + 2*x^2)/((1 + 2*x^2)*Sqrt[x + x^4]),x]","-\frac{2 \sqrt{\frac{1}{x^2}-\frac{1}{x}+1} \sqrt{\frac{\frac{1}{x}+1}{1+\sqrt[3]{-1}}} x^2 \left(\frac{i \sqrt{3} \left(\sqrt{3} x+(-1)^{5/6}+i\right) F\left(\sin ^{-1}\left(\sqrt{\frac{x+(-1)^{2/3}}{\left(1+\sqrt[3]{-1}\right) x}}\right)|\sqrt[3]{-1}\right)}{x+(-1)^{2/3}}-\frac{3 i \left(\sqrt{2}-i\right) \Pi \left(\frac{2 \sqrt{3}}{-i-2 \sqrt{2}+\sqrt{3}};\sin ^{-1}\left(\sqrt{\frac{x+(-1)^{2/3}}{\left(1+\sqrt[3]{-1}\right) x}}\right)|\sqrt[3]{-1}\right)}{(-1)^{5/6}+\sqrt{2}}+\frac{3 \left(5+i \sqrt{2}+i \sqrt{3}+\sqrt{6}\right) \Pi \left(\frac{2 \sqrt{3}}{-i+2 \sqrt{2}+\sqrt{3}};\sin ^{-1}\left(\sqrt{\frac{x+(-1)^{2/3}}{\left(1+\sqrt[3]{-1}\right) x}}\right)|\sqrt[3]{-1}\right)}{5 i+2 \sqrt{2}+\sqrt{3}+2 i \sqrt{6}}\right)}{3 \sqrt{x^4+x}}","\tan ^{-1}\left(\frac{2 \sqrt{x^4+x}}{2 x-1}\right)",1,"(-2*Sqrt[1 + x^(-2) - x^(-1)]*Sqrt[(1 + x^(-1))/(1 + (-1)^(1/3))]*x^2*((I*Sqrt[3]*(I + (-1)^(5/6) + Sqrt[3]*x)*EllipticF[ArcSin[Sqrt[((-1)^(2/3) + x)/((1 + (-1)^(1/3))*x)]], (-1)^(1/3)])/((-1)^(2/3) + x) - ((3*I)*(-I + Sqrt[2])*EllipticPi[(2*Sqrt[3])/(-I - 2*Sqrt[2] + Sqrt[3]), ArcSin[Sqrt[((-1)^(2/3) + x)/((1 + (-1)^(1/3))*x)]], (-1)^(1/3)])/((-1)^(5/6) + Sqrt[2]) + (3*(5 + I*Sqrt[2] + I*Sqrt[3] + Sqrt[6])*EllipticPi[(2*Sqrt[3])/(-I + 2*Sqrt[2] + Sqrt[3]), ArcSin[Sqrt[((-1)^(2/3) + x)/((1 + (-1)^(1/3))*x)]], (-1)^(1/3)])/(5*I + 2*Sqrt[2] + Sqrt[3] + (2*I)*Sqrt[6])))/(3*Sqrt[x + x^4])","C",1
162,1,1511,19,4.9920393,"\int \frac{1+x^4}{\left(-1+x^4\right) \sqrt{-1-x^2+x^4}} \, dx","Integrate[(1 + x^4)/((-1 + x^4)*Sqrt[-1 - x^2 + x^4]),x]","-\frac{i \left(\frac{\left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right) \sqrt{\frac{i \left(2 x+\sqrt{2 \left(1+\sqrt{5}\right)}\right)}{-2 \sqrt{1+\sqrt{5}} x+2 i \sqrt{-1+\sqrt{5}} x+\sqrt{10}-(1-2 i) \sqrt{2}}} \sqrt{-\frac{i \left(\sqrt{2 \left(1+\sqrt{5}\right)}-2 x\right)}{2 \left(i \sqrt{-1+\sqrt{5}}+\sqrt{1+\sqrt{5}}\right) x+\sqrt{2} \left((-1-2 i)+\sqrt{5}\right)}} \sqrt{\frac{2 \left(-i \sqrt{-1+\sqrt{5}}+\sqrt{1+\sqrt{5}}\right) x+\sqrt{2} \left((-1+2 i)+\sqrt{5}\right)}{2 \left(i \sqrt{-1+\sqrt{5}}+\sqrt{1+\sqrt{5}}\right) x+\sqrt{2} \left((-1-2 i)+\sqrt{5}\right)}} \left(\left(2-i \sqrt{2 \left(-1+\sqrt{5}\right)}\right) F\left(\sin ^{-1}\left(\sqrt{\frac{2 \left(-i \sqrt{-1+\sqrt{5}}+\sqrt{1+\sqrt{5}}\right) x+\sqrt{2} \left((-1+2 i)+\sqrt{5}\right)}{2 \left(i \sqrt{-1+\sqrt{5}}+\sqrt{1+\sqrt{5}}\right) x+\sqrt{2} \left((-1-2 i)+\sqrt{5}\right)}}\right)|-\frac{3}{5}+\frac{4 i}{5}\right)+2 i \sqrt{2 \left(-1+\sqrt{5}\right)} \Pi \left(\frac{\left(-2 i+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) \left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right)}{\left(2 i+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) \left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right)};\sin ^{-1}\left(\sqrt{\frac{2 \left(-i \sqrt{-1+\sqrt{5}}+\sqrt{1+\sqrt{5}}\right) x+\sqrt{2} \left((-1+2 i)+\sqrt{5}\right)}{2 \left(i \sqrt{-1+\sqrt{5}}+\sqrt{1+\sqrt{5}}\right) x+\sqrt{2} \left((-1-2 i)+\sqrt{5}\right)}}\right)|-\frac{3}{5}+\frac{4 i}{5}\right)\right) \left(2 i x+\sqrt{2 \left(-1+\sqrt{5}\right)}\right)^2}{\left(1+\sqrt{5}\right) \left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right)}+\frac{\left(i \sqrt{-1+\sqrt{5}}+\sqrt{1+\sqrt{5}}\right) \sqrt{\frac{i \left(2 x+\sqrt{2 \left(1+\sqrt{5}\right)}\right)}{-2 \sqrt{1+\sqrt{5}} x+2 i \sqrt{-1+\sqrt{5}} x+\sqrt{10}-(1-2 i) \sqrt{2}}} \sqrt{-\frac{i \left(\sqrt{2 \left(1+\sqrt{5}\right)}-2 x\right)}{2 \left(i \sqrt{-1+\sqrt{5}}+\sqrt{1+\sqrt{5}}\right) x+\sqrt{2} \left((-1-2 i)+\sqrt{5}\right)}} \sqrt{\frac{2 \left(-i \sqrt{-1+\sqrt{5}}+\sqrt{1+\sqrt{5}}\right) x+\sqrt{2} \left((-1+2 i)+\sqrt{5}\right)}{2 \left(i \sqrt{-1+\sqrt{5}}+\sqrt{1+\sqrt{5}}\right) x+\sqrt{2} \left((-1-2 i)+\sqrt{5}\right)}} \left(\left(-2 i+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) F\left(\sin ^{-1}\left(\sqrt{\frac{2 \left(-i \sqrt{-1+\sqrt{5}}+\sqrt{1+\sqrt{5}}\right) x+\sqrt{2} \left((-1+2 i)+\sqrt{5}\right)}{2 \left(i \sqrt{-1+\sqrt{5}}+\sqrt{1+\sqrt{5}}\right) x+\sqrt{2} \left((-1-2 i)+\sqrt{5}\right)}}\right)|-\frac{3}{5}+\frac{4 i}{5}\right)-2 \sqrt{2 \left(-1+\sqrt{5}\right)} \Pi \left(\frac{\left(2 i+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) \left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right)}{\left(-2 i+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) \left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right)};\sin ^{-1}\left(\sqrt{\frac{2 \left(-i \sqrt{-1+\sqrt{5}}+\sqrt{1+\sqrt{5}}\right) x+\sqrt{2} \left((-1+2 i)+\sqrt{5}\right)}{2 \left(i \sqrt{-1+\sqrt{5}}+\sqrt{1+\sqrt{5}}\right) x+\sqrt{2} \left((-1-2 i)+\sqrt{5}\right)}}\right)|-\frac{3}{5}+\frac{4 i}{5}\right)\right) \left(2 i x+\sqrt{2 \left(-1+\sqrt{5}\right)}\right)^2}{\left(1+\sqrt{5}\right) \left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right)}+\frac{4 \sqrt{-x^4+x^2+1} F\left(i \sinh ^{-1}\left(\sqrt{\frac{2}{-1+\sqrt{5}}} x\right)|\frac{1}{2} \left(-3+\sqrt{5}\right)\right)}{\sqrt{1+\sqrt{5}}}-\frac{4 \sqrt{-x^4+x^2+1} \Pi \left(\frac{1}{2} \left(-1+\sqrt{5}\right);i \sinh ^{-1}\left(\sqrt{\frac{2}{-1+\sqrt{5}}} x\right)|\frac{1}{2} \left(-3+\sqrt{5}\right)\right)}{\sqrt{1+\sqrt{5}}}\right)}{2 \sqrt{2} \sqrt{x^4-x^2-1}}","-\tan ^{-1}\left(\frac{x}{\sqrt{x^4-x^2-1}}\right)",1,"((-1/2*I)*((4*Sqrt[1 + x^2 - x^4]*EllipticF[I*ArcSinh[Sqrt[2/(-1 + Sqrt[5])]*x], (-3 + Sqrt[5])/2])/Sqrt[1 + Sqrt[5]] - (4*Sqrt[1 + x^2 - x^4]*EllipticPi[(-1 + Sqrt[5])/2, I*ArcSinh[Sqrt[2/(-1 + Sqrt[5])]*x], (-3 + Sqrt[5])/2])/Sqrt[1 + Sqrt[5]] + ((Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] + (2*I)*x)^2*Sqrt[(I*(Sqrt[2*(1 + Sqrt[5])] + 2*x))/((-1 + 2*I)*Sqrt[2] + Sqrt[10] + (2*I)*Sqrt[-1 + Sqrt[5]]*x - 2*Sqrt[1 + Sqrt[5]]*x)]*Sqrt[((-I)*(Sqrt[2*(1 + Sqrt[5])] - 2*x))/(Sqrt[2]*((-1 - 2*I) + Sqrt[5]) + 2*(I*Sqrt[-1 + Sqrt[5]] + Sqrt[1 + Sqrt[5]])*x)]*Sqrt[(Sqrt[2]*((-1 + 2*I) + Sqrt[5]) + 2*((-I)*Sqrt[-1 + Sqrt[5]] + Sqrt[1 + Sqrt[5]])*x)/(Sqrt[2]*((-1 - 2*I) + Sqrt[5]) + 2*(I*Sqrt[-1 + Sqrt[5]] + Sqrt[1 + Sqrt[5]])*x)]*((2 - I*Sqrt[2*(-1 + Sqrt[5])])*EllipticF[ArcSin[Sqrt[(Sqrt[2]*((-1 + 2*I) + Sqrt[5]) + 2*((-I)*Sqrt[-1 + Sqrt[5]] + Sqrt[1 + Sqrt[5]])*x)/(Sqrt[2]*((-1 - 2*I) + Sqrt[5]) + 2*(I*Sqrt[-1 + Sqrt[5]] + Sqrt[1 + Sqrt[5]])*x)]], -3/5 + (4*I)/5] + (2*I)*Sqrt[2*(-1 + Sqrt[5])]*EllipticPi[((-2*I + Sqrt[2*(-1 + Sqrt[5])])*(Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]]))/((2*I + Sqrt[2*(-1 + Sqrt[5])])*(Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])), ArcSin[Sqrt[(Sqrt[2]*((-1 + 2*I) + Sqrt[5]) + 2*((-I)*Sqrt[-1 + Sqrt[5]] + Sqrt[1 + Sqrt[5]])*x)/(Sqrt[2]*((-1 - 2*I) + Sqrt[5]) + 2*(I*Sqrt[-1 + Sqrt[5]] + Sqrt[1 + Sqrt[5]])*x)]], -3/5 + (4*I)/5]))/((1 + Sqrt[5])*(Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])) + ((I*Sqrt[-1 + Sqrt[5]] + Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] + (2*I)*x)^2*Sqrt[(I*(Sqrt[2*(1 + Sqrt[5])] + 2*x))/((-1 + 2*I)*Sqrt[2] + Sqrt[10] + (2*I)*Sqrt[-1 + Sqrt[5]]*x - 2*Sqrt[1 + Sqrt[5]]*x)]*Sqrt[((-I)*(Sqrt[2*(1 + Sqrt[5])] - 2*x))/(Sqrt[2]*((-1 - 2*I) + Sqrt[5]) + 2*(I*Sqrt[-1 + Sqrt[5]] + Sqrt[1 + Sqrt[5]])*x)]*Sqrt[(Sqrt[2]*((-1 + 2*I) + Sqrt[5]) + 2*((-I)*Sqrt[-1 + Sqrt[5]] + Sqrt[1 + Sqrt[5]])*x)/(Sqrt[2]*((-1 - 2*I) + Sqrt[5]) + 2*(I*Sqrt[-1 + Sqrt[5]] + Sqrt[1 + Sqrt[5]])*x)]*((-2*I + Sqrt[2*(-1 + Sqrt[5])])*EllipticF[ArcSin[Sqrt[(Sqrt[2]*((-1 + 2*I) + Sqrt[5]) + 2*((-I)*Sqrt[-1 + Sqrt[5]] + Sqrt[1 + Sqrt[5]])*x)/(Sqrt[2]*((-1 - 2*I) + Sqrt[5]) + 2*(I*Sqrt[-1 + Sqrt[5]] + Sqrt[1 + Sqrt[5]])*x)]], -3/5 + (4*I)/5] - 2*Sqrt[2*(-1 + Sqrt[5])]*EllipticPi[((2*I + Sqrt[2*(-1 + Sqrt[5])])*(Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]]))/((-2*I + Sqrt[2*(-1 + Sqrt[5])])*(Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])), ArcSin[Sqrt[(Sqrt[2]*((-1 + 2*I) + Sqrt[5]) + 2*((-I)*Sqrt[-1 + Sqrt[5]] + Sqrt[1 + Sqrt[5]])*x)/(Sqrt[2]*((-1 - 2*I) + Sqrt[5]) + 2*(I*Sqrt[-1 + Sqrt[5]] + Sqrt[1 + Sqrt[5]])*x)]], -3/5 + (4*I)/5]))/((1 + Sqrt[5])*(Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]]))))/(Sqrt[2]*Sqrt[-1 - x^2 + x^4])","C",0
163,1,19,19,0.0120651,"\int \frac{x}{\sqrt[5]{1-4 x+6 x^2-4 x^3+x^4}} \, dx","Integrate[x/(1 - 4*x + 6*x^2 - 4*x^3 + x^4)^(1/5),x]","\frac{5 (x-1) (x+5)}{6 \sqrt[5]{(x-1)^4}}","\frac{5 (x-1) (x+5)}{6 \sqrt[5]{(x-1)^4}}",1,"(5*(-1 + x)*(5 + x))/(6*((-1 + x)^4)^(1/5))","A",1
164,1,19,19,0.0591041,"\int \frac{-2+x^6}{x^4 \sqrt[4]{1+x^4+x^6}} \, dx","Integrate[(-2 + x^6)/(x^4*(1 + x^4 + x^6)^(1/4)),x]","\frac{2 \left(x^6+x^4+1\right)^{3/4}}{3 x^3}","\frac{2 \left(x^6+x^4+1\right)^{3/4}}{3 x^3}",1,"(2*(1 + x^4 + x^6)^(3/4))/(3*x^3)","A",1
165,1,19,19,0.0437685,"\int \frac{1+x^8}{x^4 \sqrt[4]{-1+x^4+x^8}} \, dx","Integrate[(1 + x^8)/(x^4*(-1 + x^4 + x^8)^(1/4)),x]","\frac{\left(x^8+x^4-1\right)^{3/4}}{3 x^3}","\frac{\left(x^8+x^4-1\right)^{3/4}}{3 x^3}",1,"(-1 + x^4 + x^8)^(3/4)/(3*x^3)","A",1
166,1,19,19,0.0491884,"\int \frac{-1+x^8}{x^4 \sqrt[4]{1+x^4+x^8}} \, dx","Integrate[(-1 + x^8)/(x^4*(1 + x^4 + x^8)^(1/4)),x]","\frac{\left(x^8+x^4+1\right)^{3/4}}{3 x^3}","\frac{\left(x^8+x^4+1\right)^{3/4}}{3 x^3}",1,"(1 + x^4 + x^8)^(3/4)/(3*x^3)","A",1
167,1,14,20,0.0262782,"\int \frac{1+x^2}{\left(-1+x^2\right) \sqrt{-x+x^3}} \, dx","Integrate[(1 + x^2)/((-1 + x^2)*Sqrt[-x + x^3]),x]","-\frac{2 x}{\sqrt{x \left(x^2-1\right)}}","-\frac{2 \sqrt{x^3-x}}{x^2-1}",1,"(-2*x)/Sqrt[x*(-1 + x^2)]","A",1
168,1,14,20,0.006469,"\int \frac{1}{\left(1+x^2\right) \sqrt[3]{x+x^3}} \, dx","Integrate[1/((1 + x^2)*(x + x^3)^(1/3)),x]","\frac{3 x}{2 \sqrt[3]{x^3+x}}","\frac{3 \left(x^3+x\right)^{2/3}}{2 \left(x^2+1\right)}",1,"(3*x)/(2*(x + x^3)^(1/3))","A",1
169,1,18,20,0.0063236,"\int \frac{1}{x \sqrt[3]{-x^2+x^3}} \, dx","Integrate[1/(x*(-x^2 + x^3)^(1/3)),x]","\frac{3 (x-1)}{2 \sqrt[3]{(x-1) x^2}}","\frac{3 \left(x^3-x^2\right)^{2/3}}{2 x^2}",1,"(3*(-1 + x))/(2*((-1 + x)*x^2)^(1/3))","A",1
170,1,20,20,0.0059212,"\int \frac{x^2}{\sqrt{-b+a x^3}} \, dx","Integrate[x^2/Sqrt[-b + a*x^3],x]","\frac{2 \sqrt{a x^3-b}}{3 a}","\frac{2 \sqrt{a x^3-b}}{3 a}",1,"(2*Sqrt[-b + a*x^3])/(3*a)","A",1
171,1,20,20,0.006621,"\int x^2 \sqrt{-b+a x^3} \, dx","Integrate[x^2*Sqrt[-b + a*x^3],x]","\frac{2 \left(a x^3-b\right)^{3/2}}{9 a}","\frac{2 \left(a x^3-b\right)^{3/2}}{9 a}",1,"(2*(-b + a*x^3)^(3/2))/(9*a)","A",1
172,1,20,20,0.0082194,"\int \frac{\sqrt{-b+a x^3} \left(2 b+a x^3\right)}{x^4} \, dx","Integrate[(Sqrt[-b + a*x^3]*(2*b + a*x^3))/x^4,x]","\frac{2 \left(a x^3-b\right)^{3/2}}{3 x^3}","\frac{2 \left(a x^3-b\right)^{3/2}}{3 x^3}",1,"(2*(-b + a*x^3)^(3/2))/(3*x^3)","A",1
173,1,20,20,0.0089355,"\int \frac{1}{x^2 \sqrt[4]{-x^2+x^4}} \, dx","Integrate[1/(x^2*(-x^2 + x^4)^(1/4)),x]","\frac{2 \left(x^2 \left(x^2-1\right)\right)^{3/4}}{3 x^3}","\frac{2 \left(x^4-x^2\right)^{3/4}}{3 x^3}",1,"(2*(x^2*(-1 + x^2))^(3/4))/(3*x^3)","A",1
174,1,20,20,0.0072641,"\int \frac{\sqrt[4]{-x^2+x^4}}{x^4} \, dx","Integrate[(-x^2 + x^4)^(1/4)/x^4,x]","\frac{2 \left(x^2 \left(x^2-1\right)\right)^{5/4}}{5 x^5}","\frac{2 \left(x^4-x^2\right)^{5/4}}{5 x^5}",1,"(2*(x^2*(-1 + x^2))^(5/4))/(5*x^5)","A",1
175,1,20,20,0.0102739,"\int \frac{\left(1+x^2\right) \sqrt[3]{-x^2+x^4}}{x^3} \, dx","Integrate[((1 + x^2)*(-x^2 + x^4)^(1/3))/x^3,x]","\frac{3 \left(x^2 \left(x^2-1\right)\right)^{4/3}}{4 x^4}","\frac{3 \left(x^4-x^2\right)^{4/3}}{4 x^4}",1,"(3*(x^2*(-1 + x^2))^(4/3))/(4*x^4)","A",1
176,1,18,20,0.0061076,"\int \frac{1}{x \sqrt[4]{-x^3+x^4}} \, dx","Integrate[1/(x*(-x^3 + x^4)^(1/4)),x]","\frac{4 (x-1)}{3 \sqrt[4]{(x-1) x^3}}","\frac{4 \left(x^4-x^3\right)^{3/4}}{3 x^3}",1,"(4*(-1 + x))/(3*((-1 + x)*x^3)^(1/4))","A",1
177,1,18,20,0.0105993,"\int \frac{(-1+x) \sqrt[4]{-x^3+x^4}}{x^4} \, dx","Integrate[((-1 + x)*(-x^3 + x^4)^(1/4))/x^4,x]","\frac{4 \left((x-1) x^3\right)^{9/4}}{9 x^9}","\frac{4 \left(x^4-x^3\right)^{9/4}}{9 x^9}",1,"(4*((-1 + x)*x^3)^(9/4))/(9*x^9)","A",1
178,1,18,20,0.0051114,"\int \frac{\sqrt[4]{-x^3+x^4}}{x^3} \, dx","Integrate[(-x^3 + x^4)^(1/4)/x^3,x]","\frac{4 \left((x-1) x^3\right)^{5/4}}{5 x^5}","\frac{4 \left(x^4-x^3\right)^{5/4}}{5 x^5}",1,"(4*((-1 + x)*x^3)^(5/4))/(5*x^5)","A",1
179,1,20,20,0.0082246,"\int x \left(1+2 x^2\right) \sqrt{-1+2 x^2+2 x^4} \, dx","Integrate[x*(1 + 2*x^2)*Sqrt[-1 + 2*x^2 + 2*x^4],x]","\frac{1}{6} \left(2 x^4+2 x^2-1\right)^{3/2}","\frac{1}{6} \left(2 x^4+2 x^2-1\right)^{3/2}",1,"(-1 + 2*x^2 + 2*x^4)^(3/2)/6","A",1
180,1,20,20,0.0113191,"\int \frac{\left(1+2 x^3\right) \sqrt[3]{-x^2+x^5}}{x^3} \, dx","Integrate[((1 + 2*x^3)*(-x^2 + x^5)^(1/3))/x^3,x]","\frac{3 \left(x^2 \left(x^3-1\right)\right)^{4/3}}{4 x^4}","\frac{3 \left(x^5-x^2\right)^{4/3}}{4 x^4}",1,"(3*(x^2*(-1 + x^3))^(4/3))/(4*x^4)","A",1
181,1,20,20,0.0151831,"\int \frac{-1+x^4}{x^2 \sqrt[4]{-x^3+x^5}} \, dx","Integrate[(-1 + x^4)/(x^2*(-x^3 + x^5)^(1/4)),x]","\frac{4 \left(x^3 \left(x^2-1\right)\right)^{7/4}}{7 x^7}","\frac{4 \left(x^5-x^3\right)^{7/4}}{7 x^7}",1,"(4*(x^3*(-1 + x^2))^(7/4))/(7*x^7)","A",1
182,1,65,20,0.0443315,"\int \frac{\left(-1+x^4\right) \sqrt[4]{-x^3+x^5}}{x^4} \, dx","Integrate[((-1 + x^4)*(-x^3 + x^5)^(1/4))/x^4,x]","\frac{4 \sqrt[4]{x^3 \left(x^2-1\right)} \left(7 \, _2F_1\left(-\frac{9}{8},-\frac{1}{4};-\frac{1}{8};x^2\right)+9 x^4 \, _2F_1\left(-\frac{1}{4},\frac{7}{8};\frac{15}{8};x^2\right)\right)}{63 x^3 \sqrt[4]{1-x^2}}","\frac{4 \left(x^5-x^3\right)^{9/4}}{9 x^9}",1,"(4*(x^3*(-1 + x^2))^(1/4)*(7*Hypergeometric2F1[-9/8, -1/4, -1/8, x^2] + 9*x^4*Hypergeometric2F1[-1/4, 7/8, 15/8, x^2]))/(63*x^3*(1 - x^2)^(1/4))","C",1
183,1,17,20,0.1082763,"\int \frac{-1-2 x^2+2 x^4}{x^2 \left(1+x^2\right) \sqrt{1+x^6}} \, dx","Integrate[(-1 - 2*x^2 + 2*x^4)/(x^2*(1 + x^2)*Sqrt[1 + x^6]),x]","\frac{\sqrt{x^6+1}}{x^3+x}","\frac{\sqrt{x^6+1}}{x \left(x^2+1\right)}",1,"Sqrt[1 + x^6]/(x + x^3)","A",1
184,1,20,20,0.0094994,"\int \frac{1}{x^3 \sqrt[3]{-x^2+x^6}} \, dx","Integrate[1/(x^3*(-x^2 + x^6)^(1/3)),x]","\frac{3 \left(x^2 \left(x^4-1\right)\right)^{2/3}}{8 x^4}","\frac{3 \left(x^6-x^2\right)^{2/3}}{8 x^4}",1,"(3*(x^2*(-1 + x^4))^(2/3))/(8*x^4)","A",1
185,1,20,20,0.0130408,"\int \frac{1+x^4}{x^2 \sqrt[4]{-x^2+x^6}} \, dx","Integrate[(1 + x^4)/(x^2*(-x^2 + x^6)^(1/4)),x]","\frac{2 \left(x^2 \left(x^4-1\right)\right)^{3/4}}{3 x^3}","\frac{2 \left(x^6-x^2\right)^{3/4}}{3 x^3}",1,"(2*(x^2*(-1 + x^4))^(3/4))/(3*x^3)","A",1
186,1,20,20,0.0107982,"\int \frac{\left(1+x^4\right) \sqrt[4]{-x^2+x^6}}{x^4} \, dx","Integrate[((1 + x^4)*(-x^2 + x^6)^(1/4))/x^4,x]","\frac{2 \left(x^2 \left(x^4-1\right)\right)^{5/4}}{5 x^5}","\frac{2 \left(x^6-x^2\right)^{5/4}}{5 x^5}",1,"(2*(x^2*(-1 + x^4))^(5/4))/(5*x^5)","A",1
187,1,20,20,0.011807,"\int \frac{-1+x^8}{x^4 \sqrt[4]{-x^2+x^6}} \, dx","Integrate[(-1 + x^8)/(x^4*(-x^2 + x^6)^(1/4)),x]","\frac{2 \left(x^2 \left(x^4-1\right)\right)^{7/4}}{7 x^7}","\frac{2 \left(x^6-x^2\right)^{7/4}}{7 x^7}",1,"(2*(x^2*(-1 + x^4))^(7/4))/(7*x^7)","A",1
188,1,14,20,0.0070533,"\int \frac{1+x^8}{\sqrt[4]{1-x^8} \left(-1+x^8\right)} \, dx","Integrate[(1 + x^8)/((1 - x^8)^(1/4)*(-1 + x^8)),x]","-\frac{x}{\sqrt[4]{1-x^8}}","\frac{x \left(1-x^8\right)^{3/4}}{x^8-1}",1,"-(x/(1 - x^8)^(1/4))","A",1
189,1,37,20,0.0065334,"\int \frac{1}{\sqrt{-x^2+x^8}} \, dx","Integrate[1/Sqrt[-x^2 + x^8],x]","\frac{x \sqrt{x^6-1} \tan ^{-1}\left(\sqrt{x^6-1}\right)}{3 \sqrt{x^2 \left(x^6-1\right)}}","-\frac{1}{3} \tan ^{-1}\left(\frac{x}{\sqrt{x^8-x^2}}\right)",1,"(x*Sqrt[-1 + x^6]*ArcTan[Sqrt[-1 + x^6]])/(3*Sqrt[x^2*(-1 + x^6)])","A",1
190,0,0,20,0.0764974,"\int \frac{\sqrt{1+\sqrt{1+x^2}}}{1+x^2} \, dx","Integrate[Sqrt[1 + Sqrt[1 + x^2]]/(1 + x^2),x]","\int \frac{\sqrt{1+\sqrt{1+x^2}}}{1+x^2} \, dx","2 \tan ^{-1}\left(\frac{x}{\sqrt{\sqrt{x^2+1}+1}}\right)",1,"Integrate[Sqrt[1 + Sqrt[1 + x^2]]/(1 + x^2), x]","F",-1
191,1,25,21,0.0162832,"\int \frac{-1+x}{(2+x) \sqrt{-1+x^3}} \, dx","Integrate[(-1 + x)/((2 + x)*Sqrt[-1 + x^3]),x]","\frac{2}{3} \tan ^{-1}\left(\frac{(1-x)^2}{3 \sqrt{x^3-1}}\right)","-\frac{2}{3} \tan ^{-1}\left(\frac{3 \sqrt{x^3-1}}{(x-1)^2}\right)",1,"(2*ArcTan[(1 - x)^2/(3*Sqrt[-1 + x^3])])/3","A",1
192,1,298,21,0.9875642,"\int \frac{-2-2 x+x^2}{\left(2+x^2\right) \sqrt{-1+x^3}} \, dx","Integrate[(-2 - 2*x + x^2)/((2 + x^2)*Sqrt[-1 + x^3]),x]","\frac{2 \sqrt{\frac{1-x}{1+\sqrt[3]{-1}}} \sqrt{x^2+x+1} \left(-\frac{\sqrt{3} \left(1+\sqrt[3]{-1}\right) \left(x+\sqrt[3]{-1}\right) F\left(\sin ^{-1}\left(\sqrt{\frac{1-(-1)^{2/3} x}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{(-1)^{2/3} x-1}-\frac{3 i \left(\sqrt{2}-i\right) \Pi \left(\frac{2 \sqrt{3}}{-i-2 \sqrt{2}+\sqrt{3}};\sin ^{-1}\left(\sqrt{\frac{1-(-1)^{2/3} x}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{(-1)^{5/6}+\sqrt{2}}+\frac{3 \left(5+i \sqrt{2}+i \sqrt{3}+\sqrt{6}\right) \Pi \left(\frac{2 \sqrt{3}}{-i+2 \sqrt{2}+\sqrt{3}};\sin ^{-1}\left(\sqrt{\frac{1-(-1)^{2/3} x}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{5 i+2 \sqrt{2}+\sqrt{3}+2 i \sqrt{6}}\right)}{3 \sqrt{x^3-1}}","-2 \tanh ^{-1}\left(\frac{\sqrt{x^3-1}}{x^2+x+1}\right)",1,"(2*Sqrt[(1 - x)/(1 + (-1)^(1/3))]*Sqrt[1 + x + x^2]*(-((Sqrt[3]*(1 + (-1)^(1/3))*((-1)^(1/3) + x)*EllipticF[ArcSin[Sqrt[(1 - (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)])/(-1 + (-1)^(2/3)*x)) - ((3*I)*(-I + Sqrt[2])*EllipticPi[(2*Sqrt[3])/(-I - 2*Sqrt[2] + Sqrt[3]), ArcSin[Sqrt[(1 - (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)])/((-1)^(5/6) + Sqrt[2]) + (3*(5 + I*Sqrt[2] + I*Sqrt[3] + Sqrt[6])*EllipticPi[(2*Sqrt[3])/(-I + 2*Sqrt[2] + Sqrt[3]), ArcSin[Sqrt[(1 - (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)])/(5*I + 2*Sqrt[2] + Sqrt[3] + (2*I)*Sqrt[6])))/(3*Sqrt[-1 + x^3])","C",1
193,1,234,21,0.2545639,"\int \frac{-2-2 x+x^2}{\left(2 x+x^2\right) \sqrt{-1+x^3}} \, dx","Integrate[(-2 - 2*x + x^2)/((2*x + x^2)*Sqrt[-1 + x^3]),x]","-\frac{2}{3} \tan ^{-1}\left(\sqrt{x^3-1}\right)+\frac{2 \sqrt{\frac{1-x}{1+\sqrt[3]{-1}}} \left(x+\sqrt[3]{-1}\right) \sqrt{\frac{(-1)^{2/3} x+\sqrt[3]{-1}}{1+\sqrt[3]{-1}}} F\left(\sin ^{-1}\left(\sqrt{\frac{1-(-1)^{2/3} x}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{\sqrt{\frac{1-(-1)^{2/3} x}{1+\sqrt[3]{-1}}} \sqrt{x^3-1}}+\frac{6 i \sqrt{\frac{1-x}{1+\sqrt[3]{-1}}} \sqrt{x^2+x+1} \Pi \left(\frac{2 \sqrt{3}}{3 i+\sqrt{3}};\sin ^{-1}\left(\sqrt{\frac{1-(-1)^{2/3} x}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{\left(\sqrt[3]{-1}-2\right) \sqrt{x^3-1}}","-2 \tan ^{-1}\left(\frac{\sqrt{x^3-1}}{x^2+x+1}\right)",1,"(-2*ArcTan[Sqrt[-1 + x^3]])/3 + (2*Sqrt[(1 - x)/(1 + (-1)^(1/3))]*((-1)^(1/3) + x)*Sqrt[((-1)^(1/3) + (-1)^(2/3)*x)/(1 + (-1)^(1/3))]*EllipticF[ArcSin[Sqrt[(1 - (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)])/(Sqrt[(1 - (-1)^(2/3)*x)/(1 + (-1)^(1/3))]*Sqrt[-1 + x^3]) + ((6*I)*Sqrt[(1 - x)/(1 + (-1)^(1/3))]*Sqrt[1 + x + x^2]*EllipticPi[(2*Sqrt[3])/(3*I + Sqrt[3]), ArcSin[Sqrt[(1 - (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)])/((-2 + (-1)^(1/3))*Sqrt[-1 + x^3])","C",0
194,1,19,21,0.1151547,"\int \frac{-1+2 x+2 x^2}{(-1+x) x \sqrt{-x+x^4}} \, dx","Integrate[(-1 + 2*x + 2*x^2)/((-1 + x)*x*Sqrt[-x + x^4]),x]","-\frac{2 \left(x^2+x+1\right)}{\sqrt{x \left(x^3-1\right)}}","-\frac{2 \sqrt{x^4-x}}{(x-1) x}",1,"(-2*(1 + x + x^2))/Sqrt[x*(-1 + x^3)]","A",1
195,1,320,21,1.2807798,"\int \frac{-1+2 x+2 x^2}{\left(1+2 x^2\right) \sqrt{-x+x^4}} \, dx","Integrate[(-1 + 2*x + 2*x^2)/((1 + 2*x^2)*Sqrt[-x + x^4]),x]","-\frac{2 \sqrt{\frac{1}{x^2}+\frac{1}{x}+1} \sqrt{\frac{x-1}{\left(1+\sqrt[3]{-1}\right) x}} x^2 \left(\frac{\sqrt{3} \left(i \sqrt{3} x+\sqrt[3]{-1}+1\right) F\left(\sin ^{-1}\left(\sqrt{\frac{x-(-1)^{2/3}}{\left(1+\sqrt[3]{-1}\right) x}}\right)|\sqrt[3]{-1}\right)}{(-1)^{2/3}-x}+\frac{6 \left(\left(-2 i+\sqrt[6]{-1}+2 \sqrt{2}+(-1)^{2/3} \sqrt{2}\right) \Pi \left(\frac{2 \sqrt{3}}{-i-2 \sqrt{2}+\sqrt{3}};\sin ^{-1}\left(\sqrt{\frac{x-(-1)^{2/3}}{\left(1+\sqrt[3]{-1}\right) x}}\right)|\sqrt[3]{-1}\right)+\frac{3}{2} \left(3 i+\sqrt{2}-\sqrt{3}-i \sqrt{6}\right) \Pi \left(\frac{2 \sqrt{3}}{-i+2 \sqrt{2}+\sqrt{3}};\sin ^{-1}\left(\sqrt{\frac{x-(-1)^{2/3}}{\left(1+\sqrt[3]{-1}\right) x}}\right)|\sqrt[3]{-1}\right)\right)}{-3 i \sqrt{2}+2 i \sqrt{3}+\sqrt{6}}\right)}{3 \sqrt{x \left(x^3-1\right)}}","\tan ^{-1}\left(\frac{2 \sqrt{x^4-x}}{2 x+1}\right)",1,"(-2*Sqrt[1 + x^(-2) + x^(-1)]*Sqrt[(-1 + x)/((1 + (-1)^(1/3))*x)]*x^2*((Sqrt[3]*(1 + (-1)^(1/3) + I*Sqrt[3]*x)*EllipticF[ArcSin[Sqrt[(-(-1)^(2/3) + x)/((1 + (-1)^(1/3))*x)]], (-1)^(1/3)])/((-1)^(2/3) - x) + (6*((-2*I + (-1)^(1/6) + 2*Sqrt[2] + (-1)^(2/3)*Sqrt[2])*EllipticPi[(2*Sqrt[3])/(-I - 2*Sqrt[2] + Sqrt[3]), ArcSin[Sqrt[(-(-1)^(2/3) + x)/((1 + (-1)^(1/3))*x)]], (-1)^(1/3)] + (3*(3*I + Sqrt[2] - Sqrt[3] - I*Sqrt[6])*EllipticPi[(2*Sqrt[3])/(-I + 2*Sqrt[2] + Sqrt[3]), ArcSin[Sqrt[(-(-1)^(2/3) + x)/((1 + (-1)^(1/3))*x)]], (-1)^(1/3)])/2))/((-3*I)*Sqrt[2] + (2*I)*Sqrt[3] + Sqrt[6])))/(3*Sqrt[x*(-1 + x^3)])","C",1
196,1,250,21,1.1345511,"\int \frac{-1-2 x+2 x^2}{(-1+2 x) \sqrt{x+x^4}} \, dx","Integrate[(-1 - 2*x + 2*x^2)/((-1 + 2*x)*Sqrt[x + x^4]),x]","\frac{-\sqrt{6} \left(1+\sqrt[3]{-1}\right) \sqrt{\frac{x-\sqrt[3]{-1}}{\left(1+\sqrt[3]{-1}\right) x}} \sqrt{\frac{(x+1) \left(2 x+i \sqrt{3}-1\right)}{x^2}} x^2 F\left(\sin ^{-1}\left(\sqrt{\frac{(-1)^{2/3} (x+1)}{\left(-1+(-1)^{2/3}\right) x}}\right)|1+(-1)^{2/3}\right)+\sqrt{6} \left(1+\sqrt[3]{-1}\right) \sqrt{\frac{x-\sqrt[3]{-1}}{\left(1+\sqrt[3]{-1}\right) x}} \sqrt{\frac{(x+1) \left(2 x+i \sqrt{3}-1\right)}{x^2}} x^2 \Pi \left(\frac{1}{3} \left(1+\sqrt[3]{-1}\right);\sin ^{-1}\left(\sqrt{\frac{(-1)^{2/3} (x+1)}{\left(-1+(-1)^{2/3}\right) x}}\right)|1+(-1)^{2/3}\right)+2 \sqrt{x^3+1} \sqrt{x} \sinh ^{-1}\left(x^{3/2}\right)}{3 \sqrt{x^4+x}}","\tanh ^{-1}\left(\frac{2 \sqrt{x^4+x}}{2 x^2+1}\right)",1,"(2*Sqrt[x]*Sqrt[1 + x^3]*ArcSinh[x^(3/2)] - Sqrt[6]*(1 + (-1)^(1/3))*x^2*Sqrt[(-(-1)^(1/3) + x)/((1 + (-1)^(1/3))*x)]*Sqrt[((1 + x)*(-1 + I*Sqrt[3] + 2*x))/x^2]*EllipticF[ArcSin[Sqrt[((-1)^(2/3)*(1 + x))/((-1 + (-1)^(2/3))*x)]], 1 + (-1)^(2/3)] + Sqrt[6]*(1 + (-1)^(1/3))*x^2*Sqrt[(-(-1)^(1/3) + x)/((1 + (-1)^(1/3))*x)]*Sqrt[((1 + x)*(-1 + I*Sqrt[3] + 2*x))/x^2]*EllipticPi[(1 + (-1)^(1/3))/3, ArcSin[Sqrt[((-1)^(2/3)*(1 + x))/((-1 + (-1)^(2/3))*x)]], 1 + (-1)^(2/3)])/(3*Sqrt[x + x^4])","C",1
197,1,15,21,0.4216613,"\int \frac{-1-2 x+2 x^2}{\left(1-x+x^2\right) \sqrt{x+x^4}} \, dx","Integrate[(-1 - 2*x + 2*x^2)/((1 - x + x^2)*Sqrt[x + x^4]),x]","-\frac{2 x (x+1)}{\sqrt{x^4+x}}","-\frac{2 \sqrt{x^4+x}}{x^2-x+1}",1,"(-2*x*(1 + x))/Sqrt[x + x^4]","A",1
198,1,14,21,0.0061422,"\int \frac{1}{(1+x) \sqrt[4]{x^3+x^4}} \, dx","Integrate[1/((1 + x)*(x^3 + x^4)^(1/4)),x]","\frac{4 x}{\sqrt[4]{x^3 (x+1)}}","\frac{4 \left(x^4+x^3\right)^{3/4}}{x^2 (x+1)}",1,"(4*x)/(x^3*(1 + x))^(1/4)","A",1
199,1,99,21,0.2655607,"\int \frac{1+2 x^4}{\left(-1+2 x^4\right) \sqrt{-1-x^2+2 x^4}} \, dx","Integrate[(1 + 2*x^4)/((-1 + 2*x^4)*Sqrt[-1 - x^2 + 2*x^4]),x]","-\frac{i \sqrt{-2 x^4+x^2+1} \left(F\left(i \sinh ^{-1}\left(\sqrt{2} x\right)|-\frac{1}{2}\right)-\Pi \left(-\frac{1}{\sqrt{2}};i \sinh ^{-1}\left(\sqrt{2} x\right)|-\frac{1}{2}\right)-\Pi \left(\frac{1}{\sqrt{2}};i \sinh ^{-1}\left(\sqrt{2} x\right)|-\frac{1}{2}\right)\right)}{\sqrt{4 x^4-2 x^2-2}}","-\tan ^{-1}\left(\frac{x}{\sqrt{2 x^4-x^2-1}}\right)",1,"((-I)*Sqrt[1 + x^2 - 2*x^4]*(EllipticF[I*ArcSinh[Sqrt[2]*x], -1/2] - EllipticPi[-(1/Sqrt[2]), I*ArcSinh[Sqrt[2]*x], -1/2] - EllipticPi[1/Sqrt[2], I*ArcSinh[Sqrt[2]*x], -1/2]))/Sqrt[-2 - 2*x^2 + 4*x^4]","C",0
200,1,107,21,0.3347827,"\int \frac{-1+2 x^4}{\left(1+2 x^2+2 x^4\right) \sqrt{1+3 x^2+2 x^4}} \, dx","Integrate[(-1 + 2*x^4)/((1 + 2*x^2 + 2*x^4)*Sqrt[1 + 3*x^2 + 2*x^4]),x]","-\frac{i \sqrt{x^2+1} \sqrt{2 x^2+1} \left(F\left(i \sinh ^{-1}\left(\sqrt{2} x\right)|\frac{1}{2}\right)-\Pi \left(\frac{1}{2}-\frac{i}{2};i \sinh ^{-1}\left(\sqrt{2} x\right)|\frac{1}{2}\right)-\Pi \left(\frac{1}{2}+\frac{i}{2};i \sinh ^{-1}\left(\sqrt{2} x\right)|\frac{1}{2}\right)\right)}{\sqrt{4 x^4+6 x^2+2}}","-\tanh ^{-1}\left(\frac{x}{\sqrt{2 x^4+3 x^2+1}}\right)",1,"((-I)*Sqrt[1 + x^2]*Sqrt[1 + 2*x^2]*(EllipticF[I*ArcSinh[Sqrt[2]*x], 1/2] - EllipticPi[1/2 - I/2, I*ArcSinh[Sqrt[2]*x], 1/2] - EllipticPi[1/2 + I/2, I*ArcSinh[Sqrt[2]*x], 1/2]))/Sqrt[2 + 6*x^2 + 4*x^4]","C",1
201,1,21,21,0.0534071,"\int \frac{\sqrt[4]{-1+x^4-x^5} \left(-4+x^5\right)}{x^6} \, dx","Integrate[((-1 + x^4 - x^5)^(1/4)*(-4 + x^5))/x^6,x]","-\frac{4 \left(-x^5+x^4-1\right)^{5/4}}{5 x^5}","-\frac{4 \left(-x^5+x^4-1\right)^{5/4}}{5 x^5}",1,"(-4*(-1 + x^4 - x^5)^(5/4))/(5*x^5)","A",1
202,1,21,21,0.0414472,"\int \frac{\left(1+x^8\right) \sqrt{-1-2 x^4+x^8}}{x^7} \, dx","Integrate[((1 + x^8)*Sqrt[-1 - 2*x^4 + x^8])/x^7,x]","\frac{\left(x^8-2 x^4-1\right)^{3/2}}{6 x^6}","\frac{\left(x^8-2 x^4-1\right)^{3/2}}{6 x^6}",1,"(-1 - 2*x^4 + x^8)^(3/2)/(6*x^6)","A",1
203,1,27,21,0.0532794,"\int \frac{x^2 \left(-2+x^3\right) \sqrt{1+x^3}}{4+12 x^3+13 x^6+4 x^9} \, dx","Integrate[(x^2*(-2 + x^3)*Sqrt[1 + x^3])/(4 + 12*x^3 + 13*x^6 + 4*x^9),x]","\frac{1}{3} \tan ^{-1}\left(\frac{6 \left(x^3+1\right)^{3/2}}{3 \left(x^3+1\right)-3}\right)","-\frac{1}{3} \tan ^{-1}\left(\frac{x^3}{2 \left(x^3+1\right)^{3/2}}\right)",1,"ArcTan[(6*(1 + x^3)^(3/2))/(-3 + 3*(1 + x^3))]/3","A",1
204,1,16,22,0.0060291,"\int \frac{1}{\left(-1+x^2\right) \sqrt[3]{-x+x^3}} \, dx","Integrate[1/((-1 + x^2)*(-x + x^3)^(1/3)),x]","-\frac{3 x}{2 \sqrt[3]{x \left(x^2-1\right)}}","-\frac{3 \left(x^3-x\right)^{2/3}}{2 \left(x^2-1\right)}",1,"(-3*x)/(2*(x*(-1 + x^2))^(1/3))","A",1
205,1,16,22,0.0065203,"\int \frac{1}{\left(-1+x^3\right) \sqrt[4]{-x+x^4}} \, dx","Integrate[1/((-1 + x^3)*(-x + x^4)^(1/4)),x]","-\frac{4 x}{3 \sqrt[4]{x \left(x^3-1\right)}}","-\frac{4 \left(x^4-x\right)^{3/4}}{3 \left(x^3-1\right)}",1,"(-4*x)/(3*(x*(-1 + x^3))^(1/4))","A",1
206,1,22,22,0.1286871,"\int \frac{\sqrt{b+\sqrt{b^2+a x^2}}}{\sqrt{b^2+a x^2}} \, dx","Integrate[Sqrt[b + Sqrt[b^2 + a*x^2]]/Sqrt[b^2 + a*x^2],x]","\frac{2 x}{\sqrt{\sqrt{a x^2+b^2}+b}}","\frac{2 x}{\sqrt{\sqrt{a x^2+b^2}+b}}",1,"(2*x)/Sqrt[b + Sqrt[b^2 + a*x^2]]","A",1
207,1,23,23,0.0034234,"\int \frac{1}{x \sqrt[4]{1+x^2}} \, dx","Integrate[1/(x*(1 + x^2)^(1/4)),x]","\tan ^{-1}\left(\sqrt[4]{x^2+1}\right)-\tanh ^{-1}\left(\sqrt[4]{x^2+1}\right)","\tan ^{-1}\left(\sqrt[4]{x^2+1}\right)-\tanh ^{-1}\left(\sqrt[4]{x^2+1}\right)",1,"ArcTan[(1 + x^2)^(1/4)] - ArcTanh[(1 + x^2)^(1/4)]","A",1
208,1,21,23,0.0105629,"\int \frac{-5+2 x}{\sqrt[4]{4-4 x+x^2}} \, dx","Integrate[(-5 + 2*x)/(4 - 4*x + x^2)^(1/4),x]","\frac{2 (x-2) (2 x-7)}{3 \sqrt[4]{(x-2)^2}}","\frac{2 \left((x-2)^2\right)^{3/4} (2 x-7)}{3 (x-2)}",1,"(2*(-2 + x)*(-7 + 2*x))/(3*((-2 + x)^2)^(1/4))","A",1
209,1,20,23,0.005379,"\int x^5 \sqrt[3]{1+x^3} \, dx","Integrate[x^5*(1 + x^3)^(1/3),x]","\frac{1}{28} \left(x^3+1\right)^{4/3} \left(4 x^3-3\right)","\frac{1}{28} \sqrt[3]{x^3+1} \left(4 x^6+x^3-3\right)",1,"((1 + x^3)^(4/3)*(-3 + 4*x^3))/28","A",1
210,1,18,23,0.0122478,"\int \frac{\left(1+3 x^2\right) \sqrt[3]{-x+x^3}}{x^2} \, dx","Integrate[((1 + 3*x^2)*(-x + x^3)^(1/3))/x^2,x]","\frac{3 \left(x \left(x^2-1\right)\right)^{4/3}}{2 x^2}","\frac{3 \left(x^2-1\right) \sqrt[3]{x^3-x}}{2 x}",1,"(3*(x*(-1 + x^2))^(4/3))/(2*x^2)","A",1
211,1,14,23,0.0062508,"\int \frac{1}{(-1+x) \sqrt[3]{-x^2+x^3}} \, dx","Integrate[1/((-1 + x)*(-x^2 + x^3)^(1/3)),x]","-\frac{3 x}{\sqrt[3]{(x-1) x^2}}","-\frac{3 \left(x^3-x^2\right)^{2/3}}{(x-1) x}",1,"(-3*x)/((-1 + x)*x^2)^(1/3)","A",1
212,1,23,23,0.0114174,"\int \frac{1}{x^2 \sqrt[3]{x^2+x^3}} \, dx","Integrate[1/(x^2*(x^2 + x^3)^(1/3)),x]","\frac{3 \left(x^2 (x+1)\right)^{2/3} (3 x-2)}{10 x^3}","\frac{3 (3 x-2) \left(x^3+x^2\right)^{2/3}}{10 x^3}",1,"(3*(x^2*(1 + x))^(2/3)*(-2 + 3*x))/(10*x^3)","A",1
213,1,23,23,0.0403468,"\int \frac{\left(3+2 x^2\right) \sqrt{x+2 x^3}}{\left(1+2 x^2\right)^2} \, dx","Integrate[((3 + 2*x^2)*Sqrt[x + 2*x^3])/(1 + 2*x^2)^2,x]","\frac{2 x \sqrt{2 x^3+x}}{2 x^2+1}","\frac{2 x \sqrt{2 x^3+x}}{2 x^2+1}",1,"(2*x*Sqrt[x + 2*x^3])/(1 + 2*x^2)","A",1
214,1,23,23,0.0065257,"\int \frac{1}{x^6 \left(-1+x^4\right)^{3/4}} \, dx","Integrate[1/(x^6*(-1 + x^4)^(3/4)),x]","\frac{\sqrt[4]{x^4-1} \left(4 x^4+1\right)}{5 x^5}","\frac{\sqrt[4]{x^4-1} \left(4 x^4+1\right)}{5 x^5}",1,"((-1 + x^4)^(1/4)*(1 + 4*x^4))/(5*x^5)","A",1
215,1,23,23,0.0048427,"\int \frac{1}{x^4 \left(1+x^4\right)^{5/4}} \, dx","Integrate[1/(x^4*(1 + x^4)^(5/4)),x]","-\frac{4 x^4+1}{3 x^3 \sqrt[4]{x^4+1}}","\frac{-4 x^4-1}{3 x^3 \sqrt[4]{x^4+1}}",1,"-1/3*(1 + 4*x^4)/(x^3*(1 + x^4)^(1/4))","A",1
216,1,23,23,0.0060825,"\int \frac{1}{x^6 \left(1+x^4\right)^{3/4}} \, dx","Integrate[1/(x^6*(1 + x^4)^(3/4)),x]","\frac{\sqrt[4]{x^4+1} \left(4 x^4-1\right)}{5 x^5}","\frac{\sqrt[4]{x^4+1} \left(4 x^4-1\right)}{5 x^5}",1,"((1 + x^4)^(1/4)*(-1 + 4*x^4))/(5*x^5)","A",1
217,1,23,23,0.0071607,"\int \frac{-1+x^4}{x^6 \left(1+x^4\right)^{3/4}} \, dx","Integrate[(-1 + x^4)/(x^6*(1 + x^4)^(3/4)),x]","\frac{\left(1-9 x^4\right) \sqrt[4]{x^4+1}}{5 x^5}","\frac{\left(1-9 x^4\right) \sqrt[4]{x^4+1}}{5 x^5}",1,"((1 - 9*x^4)*(1 + x^4)^(1/4))/(5*x^5)","A",1
218,1,36,23,0.1013425,"\int \frac{1+x^2}{\left(1-x^2\right) \sqrt{1+x^4}} \, dx","Integrate[(1 + x^2)/((1 - x^2)*Sqrt[1 + x^4]),x]","\sqrt[4]{-1} \left(F\left(\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)-2 \Pi \left(i;\left.\sin ^{-1}\left((-1)^{3/4} x\right)\right|-1\right)\right)","\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{\sqrt{2}}",1,"(-1)^(1/4)*(EllipticF[I*ArcSinh[(-1)^(1/4)*x], -1] - 2*EllipticPi[I, ArcSin[(-1)^(3/4)*x], -1])","C",1
219,1,167,23,0.644076,"\int \frac{-1+2 x+2 x^2}{(1+2 x) \sqrt{-x+x^4}} \, dx","Integrate[(-1 + 2*x + 2*x^2)/((1 + 2*x)*Sqrt[-x + x^4]),x]","\frac{-2 \left((-1)^{2/3}-1\right) \sqrt{x} \sqrt{1-x^3} \sin ^{-1}\left(x^{3/2}\right)-6 (-1)^{2/3} \sqrt{-\frac{\left(1+\sqrt[3]{-1}\right) x \left(\sqrt[3]{-1} x+1\right)}{(x-1)^2}} \sqrt{\frac{(-1)^{2/3} x-1}{x-1}} (x-1)^2 \Pi \left(\frac{1}{2} \left(3-i \sqrt{3}\right);\sin ^{-1}\left(\sqrt{\frac{\left(1+\sqrt[3]{-1}\right) x}{x-1}}\right)|\frac{\sqrt[3]{-1}}{-1+\sqrt[3]{-1}}\right)}{3 \left(1-(-1)^{2/3}\right) \sqrt{x \left(x^3-1\right)}}","\tanh ^{-1}\left(\frac{2 \sqrt{x^4-x}}{2 x^2+1}\right)",1,"(-2*(-1 + (-1)^(2/3))*Sqrt[x]*Sqrt[1 - x^3]*ArcSin[x^(3/2)] - 6*(-1)^(2/3)*(-1 + x)^2*Sqrt[-(((1 + (-1)^(1/3))*x*(1 + (-1)^(1/3)*x))/(-1 + x)^2)]*Sqrt[(-1 + (-1)^(2/3)*x)/(-1 + x)]*EllipticPi[(3 - I*Sqrt[3])/2, ArcSin[Sqrt[((1 + (-1)^(1/3))*x)/(-1 + x)]], (-1)^(1/3)/(-1 + (-1)^(1/3))])/(3*(1 - (-1)^(2/3))*Sqrt[x*(-1 + x^3)])","C",1
220,1,23,23,0.010596,"\int \frac{1}{x^5 \sqrt{x+x^4}} \, dx","Integrate[1/(x^5*Sqrt[x + x^4]),x]","\frac{2 \left(2 x^3-1\right) \sqrt{x^4+x}}{9 x^5}","\frac{2 \left(2 x^3-1\right) \sqrt{x^4+x}}{9 x^5}",1,"(2*(-1 + 2*x^3)*Sqrt[x + x^4])/(9*x^5)","A",1
221,1,23,23,0.0135235,"\int \frac{-1+x^3}{x^6 \sqrt[4]{x+x^4}} \, dx","Integrate[(-1 + x^3)/(x^6*(x + x^4)^(1/4)),x]","-\frac{4 \left(11 x^3-3\right) \left(x^4+x\right)^{3/4}}{63 x^6}","-\frac{4 \left(11 x^3-3\right) \left(x^4+x\right)^{3/4}}{63 x^6}",1,"(-4*(-3 + 11*x^3)*(x + x^4)^(3/4))/(63*x^6)","A",1
222,1,23,23,0.0090597,"\int \frac{1+2 x^3}{x^6 \sqrt[4]{x+x^4}} \, dx","Integrate[(1 + 2*x^3)/(x^6*(x + x^4)^(1/4)),x]","-\frac{4 \left(10 x^3+3\right) \left(x^4+x\right)^{3/4}}{63 x^6}","-\frac{4 \left(10 x^3+3\right) \left(x^4+x\right)^{3/4}}{63 x^6}",1,"(-4*(3 + 10*x^3)*(x + x^4)^(3/4))/(63*x^6)","A",1
223,1,14,23,0.0245659,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt[3]{x^2+x^4}} \, dx","Integrate[(-1 + x^2)/((1 + x^2)*(x^2 + x^4)^(1/3)),x]","-\frac{3 x}{\sqrt[3]{x^4+x^2}}","-\frac{3 \left(x^4+x^2\right)^{2/3}}{x \left(x^2+1\right)}",1,"(-3*x)/(x^2 + x^4)^(1/3)","A",1
224,1,14,23,0.0061739,"\int \frac{1}{\left(1+x^2\right) \sqrt[4]{x^2+x^4}} \, dx","Integrate[1/((1 + x^2)*(x^2 + x^4)^(1/4)),x]","\frac{2 x}{\sqrt[4]{x^4+x^2}}","\frac{2 \left(x^4+x^2\right)^{3/4}}{x \left(x^2+1\right)}",1,"(2*x)/(x^2 + x^4)^(1/4)","A",1
225,1,14,23,0.0060367,"\int \frac{1}{(-1+x) \sqrt[4]{-x^3+x^4}} \, dx","Integrate[1/((-1 + x)*(-x^3 + x^4)^(1/4)),x]","-\frac{4 x}{\sqrt[4]{(x-1) x^3}}","-\frac{4 \left(x^4-x^3\right)^{3/4}}{(x-1) x^2}",1,"(-4*x)/((-1 + x)*x^3)^(1/4)","A",1
226,1,23,23,0.0069234,"\int \frac{1}{x \sqrt{x^3+x^4}} \, dx","Integrate[1/(x*Sqrt[x^3 + x^4]),x]","\frac{2 \left(2 x^2+x-1\right)}{3 \sqrt{x^3 (x+1)}}","\frac{2 (2 x-1) \sqrt{x^4+x^3}}{3 x^3}",1,"(2*(-1 + x + 2*x^2))/(3*Sqrt[x^3*(1 + x)])","A",1
227,1,23,23,0.0081351,"\int \frac{1}{x^2 \sqrt[4]{x^3+x^4}} \, dx","Integrate[1/(x^2*(x^3 + x^4)^(1/4)),x]","\frac{4 \left(x^3 (x+1)\right)^{3/4} (4 x-3)}{21 x^4}","\frac{4 (4 x-3) \left(x^4+x^3\right)^{3/4}}{21 x^4}",1,"(4*(x^3*(1 + x))^(3/4)*(-3 + 4*x))/(21*x^4)","A",1
228,1,305,23,0.5888039,"\int \frac{1+2 x}{\sqrt{3+x^2+2 x^3+x^4}} \, dx","Integrate[(1 + 2*x)/Sqrt[3 + x^2 + 2*x^3 + x^4],x]","-\frac{(-1)^{2/3} \sqrt{2} \sqrt[4]{3} \sqrt{\frac{2 i x+\sqrt{3}+3 i}{x+(-1)^{2/3}}} \left(x+(-1)^{2/3}\right)^2 \sqrt{\frac{2 \sqrt{3} x+3 \sqrt{3}+3 i}{\left(\sqrt{3}-2 i\right) \left(x+(-1)^{2/3}\right)}} \sqrt{\frac{\left(4-2 i \sqrt{3}\right) x-i \sqrt{3}-5}{x+(-1)^{2/3}}} \left(\left(\sqrt{3}+2 i\right) F\left(\sin ^{-1}\left(\frac{\sqrt{-\frac{2 \left(2 i+\sqrt{3}\right) x+\sqrt{3}-5 i}{-2 i x+\sqrt{3}+i}}}{\sqrt{2}}\right)|\frac{4}{7}\right)-2 \sqrt{3} \Pi \left(\frac{2 i}{2 i+\sqrt{3}};\sin ^{-1}\left(\frac{\sqrt{-\frac{2 \left(2 i+\sqrt{3}\right) x+\sqrt{3}-5 i}{-2 i x+\sqrt{3}+i}}}{\sqrt{2}}\right)|\frac{4}{7}\right)\right)}{\left(\sqrt{3}+9 i\right) \sqrt{x^4+2 x^3+x^2+3}}","\log \left(x^2+\sqrt{x^4+2 x^3+x^2+3}+x\right)",1,"-(((-1)^(2/3)*Sqrt[2]*3^(1/4)*Sqrt[(3*I + Sqrt[3] + (2*I)*x)/((-1)^(2/3) + x)]*((-1)^(2/3) + x)^2*Sqrt[(3*I + 3*Sqrt[3] + 2*Sqrt[3]*x)/((-2*I + Sqrt[3])*((-1)^(2/3) + x))]*Sqrt[(-5 - I*Sqrt[3] + (4 - (2*I)*Sqrt[3])*x)/((-1)^(2/3) + x)]*((2*I + Sqrt[3])*EllipticF[ArcSin[Sqrt[-((-5*I + Sqrt[3] + 2*(2*I + Sqrt[3])*x)/(I + Sqrt[3] - (2*I)*x))]/Sqrt[2]], 4/7] - 2*Sqrt[3]*EllipticPi[(2*I)/(2*I + Sqrt[3]), ArcSin[Sqrt[-((-5*I + Sqrt[3] + 2*(2*I + Sqrt[3])*x)/(I + Sqrt[3] - (2*I)*x))]/Sqrt[2]], 4/7]))/((9*I + Sqrt[3])*Sqrt[3 + x^2 + 2*x^3 + x^4]))","C",0
229,1,23,23,0.0071296,"\int \frac{-1+2 x^4}{x^8 \sqrt[4]{-1+x^4}} \, dx","Integrate[(-1 + 2*x^4)/(x^8*(-1 + x^4)^(1/4)),x]","\frac{\left(x^4-1\right)^{3/4} \left(10 x^4-3\right)}{21 x^7}","\frac{\left(x^4-1\right)^{3/4} \left(10 x^4-3\right)}{21 x^7}",1,"((-1 + x^4)^(3/4)*(-3 + 10*x^4))/(21*x^7)","A",1
230,1,23,23,0.0085562,"\int \frac{1+2 x^4}{x^4 \left(1+x^4\right)^{5/4}} \, dx","Integrate[(1 + 2*x^4)/(x^4*(1 + x^4)^(5/4)),x]","\frac{2 x^4-1}{3 x^3 \sqrt[4]{x^4+1}}","\frac{2 x^4-1}{3 x^3 \sqrt[4]{x^4+1}}",1,"(-1 + 2*x^4)/(3*x^3*(1 + x^4)^(1/4))","A",1
231,1,23,23,0.052748,"\int \frac{\left(1+4 x^3\right) \left(1+2 x+2 x^4\right)}{\sqrt{x+x^4}} \, dx","Integrate[((1 + 4*x^3)*(1 + 2*x + 2*x^4))/Sqrt[x + x^4],x]","\frac{2}{3} \sqrt{x^4+x} \left(2 x^4+2 x+3\right)","\frac{2}{3} \sqrt{x^4+x} \left(2 x^4+2 x+3\right)",1,"(2*Sqrt[x + x^4]*(3 + 2*x + 2*x^4))/3","A",1
232,1,14,23,0.0263094,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt[4]{x^3+x^5}} \, dx","Integrate[(-1 + x^2)/((1 + x^2)*(x^3 + x^5)^(1/4)),x]","-\frac{4 x}{\sqrt[4]{x^5+x^3}}","-\frac{4 \left(x^5+x^3\right)^{3/4}}{x^2 \left(x^2+1\right)}",1,"(-4*x)/(x^3 + x^5)^(1/4)","A",1
233,1,23,23,0.0049336,"\int \frac{1}{x^{10} \sqrt{-1+x^6}} \, dx","Integrate[1/(x^10*Sqrt[-1 + x^6]),x]","\frac{\sqrt{x^6-1} \left(2 x^6+1\right)}{9 x^9}","\frac{\sqrt{x^6-1} \left(2 x^6+1\right)}{9 x^9}",1,"(Sqrt[-1 + x^6]*(1 + 2*x^6))/(9*x^9)","A",1
234,1,23,23,0.0055487,"\int \frac{1+x^6}{x^{10} \sqrt{-1+x^6}} \, dx","Integrate[(1 + x^6)/(x^10*Sqrt[-1 + x^6]),x]","\frac{\sqrt{x^6-1} \left(5 x^6+1\right)}{9 x^9}","\frac{\sqrt{x^6-1} \left(5 x^6+1\right)}{9 x^9}",1,"(Sqrt[-1 + x^6]*(1 + 5*x^6))/(9*x^9)","A",1
235,1,14,23,0.0266185,"\int \frac{-1+3 x^4}{\left(1+x^4\right) \sqrt[3]{x^2+x^6}} \, dx","Integrate[(-1 + 3*x^4)/((1 + x^4)*(x^2 + x^6)^(1/3)),x]","-\frac{3 x}{\sqrt[3]{x^6+x^2}}","-\frac{3 \left(x^6+x^2\right)^{2/3}}{x \left(x^4+1\right)}",1,"(-3*x)/(x^2 + x^6)^(1/3)","A",1
236,1,14,23,0.0224685,"\int \frac{-1+x^4}{\left(1+x^4\right) \sqrt[4]{x^2+x^6}} \, dx","Integrate[(-1 + x^4)/((1 + x^4)*(x^2 + x^6)^(1/4)),x]","-\frac{2 x}{\sqrt[4]{x^6+x^2}}","-\frac{2 \left(x^6+x^2\right)^{3/4}}{x \left(x^4+1\right)}",1,"(-2*x)/(x^2 + x^6)^(1/4)","A",1
237,1,25,23,0.2130027,"\int \frac{x^2 \left(3+2 x^2\right) \left(1+x^2+2 x^6\right)}{\left(1+x^2\right)^2 \sqrt{1+x^2+x^6}} \, dx","Integrate[(x^2*(3 + 2*x^2)*(1 + x^2 + 2*x^6))/((1 + x^2)^2*Sqrt[1 + x^2 + x^6]),x]","\sqrt{x^6+x^2+1} \left(x-\frac{x}{x^2+1}\right)","\frac{x^3 \sqrt{x^6+x^2+1}}{x^2+1}",1,"Sqrt[1 + x^2 + x^6]*(x - x/(1 + x^2))","A",1
238,1,37,24,0.0083886,"\int \frac{1}{\sqrt{3-5 x+x^2+x^3}} \, dx","Integrate[1/Sqrt[3 - 5*x + x^2 + x^3],x]","-\frac{(x-1) \sqrt{x+3} \tanh ^{-1}\left(\frac{\sqrt{x+3}}{2}\right)}{\sqrt{(x-1)^2 (x+3)}}","-\tanh ^{-1}\left(\frac{2 x-2}{\sqrt{x^3+x^2-5 x+3}}\right)",1,"-(((-1 + x)*Sqrt[3 + x]*ArcTanh[Sqrt[3 + x]/2])/Sqrt[(-1 + x)^2*(3 + x)])","A",1
239,1,107,24,0.3000334,"\int \frac{-1+x}{(1+x) \sqrt{x+x^2+x^3}} \, dx","Integrate[(-1 + x)/((1 + x)*Sqrt[x + x^2 + x^3]),x]","\frac{2 (-1)^{2/3} \sqrt{\frac{\sqrt[3]{-1}}{x}+1} \sqrt{1-\frac{(-1)^{2/3}}{x}} x^{3/2} \left(F\left(i \sinh ^{-1}\left(\frac{(-1)^{5/6}}{\sqrt{x}}\right)|(-1)^{2/3}\right)-2 \Pi \left(\sqrt[3]{-1};i \sinh ^{-1}\left(\frac{(-1)^{5/6}}{\sqrt{x}}\right)|(-1)^{2/3}\right)\right)}{\sqrt{x \left(x^2+x+1\right)}}","-2 \tan ^{-1}\left(\frac{\sqrt{x^3+x^2+x}}{x^2+x+1}\right)",1,"(2*(-1)^(2/3)*Sqrt[1 + (-1)^(1/3)/x]*Sqrt[1 - (-1)^(2/3)/x]*x^(3/2)*(EllipticF[I*ArcSinh[(-1)^(5/6)/Sqrt[x]], (-1)^(2/3)] - 2*EllipticPi[(-1)^(1/3), I*ArcSinh[(-1)^(5/6)/Sqrt[x]], (-1)^(2/3)]))/Sqrt[x*(1 + x + x^2)]","C",1
240,1,136,24,0.5259715,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{x+x^2+x^3}} \, dx","Integrate[(-1 + x^2)/((1 + x^2)*Sqrt[x + x^2 + x^3]),x]","-\frac{2 (-1)^{2/3} \sqrt{\frac{\sqrt[3]{-1}}{x}+1} \sqrt{1-\frac{(-1)^{2/3}}{x}} x^{3/2} \left(-F\left(i \sinh ^{-1}\left(\frac{(-1)^{5/6}}{\sqrt{x}}\right)|(-1)^{2/3}\right)+\Pi \left(-(-1)^{5/6};i \sinh ^{-1}\left(\frac{(-1)^{5/6}}{\sqrt{x}}\right)|(-1)^{2/3}\right)+\Pi \left((-1)^{5/6};i \sinh ^{-1}\left(\frac{(-1)^{5/6}}{\sqrt{x}}\right)|(-1)^{2/3}\right)\right)}{\sqrt{x \left(x^2+x+1\right)}}","-2 \tanh ^{-1}\left(\frac{\sqrt{x^3+x^2+x}}{x^2+x+1}\right)",1,"(-2*(-1)^(2/3)*Sqrt[1 + (-1)^(1/3)/x]*Sqrt[1 - (-1)^(2/3)/x]*x^(3/2)*(-EllipticF[I*ArcSinh[(-1)^(5/6)/Sqrt[x]], (-1)^(2/3)] + EllipticPi[-(-1)^(5/6), I*ArcSinh[(-1)^(5/6)/Sqrt[x]], (-1)^(2/3)] + EllipticPi[(-1)^(5/6), I*ArcSinh[(-1)^(5/6)/Sqrt[x]], (-1)^(2/3)]))/Sqrt[x*(1 + x + x^2)]","C",1
241,1,41,24,0.0932969,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{1+x^4}} \, dx","Integrate[(-1 + x^2)/((1 + x^2)*Sqrt[1 + x^4]),x]","-\sqrt[4]{-1} \left(F\left(\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)-2 \Pi \left(-i;\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)\right)","-\frac{\tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{\sqrt{2}}",1,"-((-1)^(1/4)*(EllipticF[I*ArcSinh[(-1)^(1/4)*x], -1] - 2*EllipticPi[-I, I*ArcSinh[(-1)^(1/4)*x], -1]))","C",1
242,1,37,24,0.101298,"\int \frac{1+x^2}{\left(-1+x^2\right) \sqrt{1+x^4}} \, dx","Integrate[(1 + x^2)/((-1 + x^2)*Sqrt[1 + x^4]),x]","-\sqrt[4]{-1} \left(F\left(\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)-2 \Pi \left(i;\left.\sin ^{-1}\left((-1)^{3/4} x\right)\right|-1\right)\right)","-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{\sqrt{2}}",1,"-((-1)^(1/4)*(EllipticF[I*ArcSinh[(-1)^(1/4)*x], -1] - 2*EllipticPi[I, ArcSin[(-1)^(3/4)*x], -1]))","C",1
243,0,0,24,0.1748011,"\int \frac{2-3 x^5}{\sqrt{1+x^5} \left(1-a x^2+x^5\right)} \, dx","Integrate[(2 - 3*x^5)/(Sqrt[1 + x^5]*(1 - a*x^2 + x^5)),x]","\int \frac{2-3 x^5}{\sqrt{1+x^5} \left(1-a x^2+x^5\right)} \, dx","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{x^5+1}}\right)}{\sqrt{a}}",1,"Integrate[(2 - 3*x^5)/(Sqrt[1 + x^5]*(1 - a*x^2 + x^5)), x]","F",-1
244,0,0,24,0.1815461,"\int \frac{2+3 x^5}{\sqrt{-1+x^5} \left(-1-a x^2+x^5\right)} \, dx","Integrate[(2 + 3*x^5)/(Sqrt[-1 + x^5]*(-1 - a*x^2 + x^5)),x]","\int \frac{2+3 x^5}{\sqrt{-1+x^5} \left(-1-a x^2+x^5\right)} \, dx","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{x^5-1}}\right)}{\sqrt{a}}",1,"Integrate[(2 + 3*x^5)/(Sqrt[-1 + x^5]*(-1 - a*x^2 + x^5)), x]","F",-1
245,0,0,24,0.2393961,"\int \frac{2+3 x^5}{\sqrt{-1+x^5} \left(-a-x^2+a x^5\right)} \, dx","Integrate[(2 + 3*x^5)/(Sqrt[-1 + x^5]*(-a - x^2 + a*x^5)),x]","\int \frac{2+3 x^5}{\sqrt{-1+x^5} \left(-a-x^2+a x^5\right)} \, dx","-\frac{2 \tanh ^{-1}\left(\frac{x}{\sqrt{a} \sqrt{x^5-1}}\right)}{\sqrt{a}}",1,"Integrate[(2 + 3*x^5)/(Sqrt[-1 + x^5]*(-a - x^2 + a*x^5)), x]","F",-1
246,0,0,24,0.2232825,"\int \frac{-2+3 x^5}{\sqrt{1+x^5} \left(a-x^2+a x^5\right)} \, dx","Integrate[(-2 + 3*x^5)/(Sqrt[1 + x^5]*(a - x^2 + a*x^5)),x]","\int \frac{-2+3 x^5}{\sqrt{1+x^5} \left(a-x^2+a x^5\right)} \, dx","-\frac{2 \tanh ^{-1}\left(\frac{x}{\sqrt{a} \sqrt{x^5+1}}\right)}{\sqrt{a}}",1,"Integrate[(-2 + 3*x^5)/(Sqrt[1 + x^5]*(a - x^2 + a*x^5)), x]","F",-1
247,1,24,24,0.3521384,"\int \frac{-1-2 x^2+2 x^4}{\left(1-x^2+x^4\right) \sqrt{1+x^6}} \, dx","Integrate[(-1 - 2*x^2 + 2*x^4)/((1 - x^2 + x^4)*Sqrt[1 + x^6]),x]","-\frac{x \sqrt{x^6+1}}{x^4-x^2+1}","-\frac{x \sqrt{x^6+1}}{x^4-x^2+1}",1,"-((x*Sqrt[1 + x^6])/(1 - x^2 + x^4))","A",1
248,0,0,24,0.4696796,"\int \frac{-1+4 x^5}{\left(1-a x+x^5\right) \sqrt{x+x^6}} \, dx","Integrate[(-1 + 4*x^5)/((1 - a*x + x^5)*Sqrt[x + x^6]),x]","\int \frac{-1+4 x^5}{\left(1-a x+x^5\right) \sqrt{x+x^6}} \, dx","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{x^6+x}}\right)}{\sqrt{a}}",1,"Integrate[(-1 + 4*x^5)/((1 - a*x + x^5)*Sqrt[x + x^6]), x]","F",-1
249,0,0,24,0.4552111,"\int \frac{-1+4 x^5}{\left(a-x+a x^5\right) \sqrt{x+x^6}} \, dx","Integrate[(-1 + 4*x^5)/((a - x + a*x^5)*Sqrt[x + x^6]),x]","\int \frac{-1+4 x^5}{\left(a-x+a x^5\right) \sqrt{x+x^6}} \, dx","-\frac{2 \tanh ^{-1}\left(\frac{x}{\sqrt{a} \sqrt{x^6+x}}\right)}{\sqrt{a}}",1,"Integrate[(-1 + 4*x^5)/((a - x + a*x^5)*Sqrt[x + x^6]), x]","F",-1
250,1,20,25,0.0068764,"\int x^3 \left(-1+x^2\right)^{2/3} \, dx","Integrate[x^3*(-1 + x^2)^(2/3),x]","\frac{3}{80} \left(x^2-1\right)^{5/3} \left(5 x^2+3\right)","\frac{3}{80} \left(x^2-1\right)^{2/3} \left(5 x^4-2 x^2-3\right)",1,"(3*(-1 + x^2)^(5/3)*(3 + 5*x^2))/80","A",1
251,1,20,25,0.006695,"\int x^3 \left(-1+x^2\right)^{3/4} \, dx","Integrate[x^3*(-1 + x^2)^(3/4),x]","\frac{2}{77} \left(x^2-1\right)^{7/4} \left(7 x^2+4\right)","\frac{2}{77} \left(x^2-1\right)^{3/4} \left(7 x^4-3 x^2-4\right)",1,"(2*(-1 + x^2)^(7/4)*(4 + 7*x^2))/77","A",1
252,1,25,25,0.003407,"\int \frac{1}{x \left(1+x^2\right)^{3/4}} \, dx","Integrate[1/(x*(1 + x^2)^(3/4)),x]","-\tan ^{-1}\left(\sqrt[4]{x^2+1}\right)-\tanh ^{-1}\left(\sqrt[4]{x^2+1}\right)","-\tan ^{-1}\left(\sqrt[4]{x^2+1}\right)-\tanh ^{-1}\left(\sqrt[4]{x^2+1}\right)",1,"-ArcTan[(1 + x^2)^(1/4)] - ArcTanh[(1 + x^2)^(1/4)]","A",1
253,1,20,25,0.0063023,"\int x^3 \left(1+x^2\right)^{3/4} \, dx","Integrate[x^3*(1 + x^2)^(3/4),x]","\frac{2}{77} \left(x^2+1\right)^{7/4} \left(7 x^2-4\right)","\frac{2}{77} \left(x^2+1\right)^{3/4} \left(7 x^4+3 x^2-4\right)",1,"(2*(1 + x^2)^(7/4)*(-4 + 7*x^2))/77","A",1
254,1,20,25,0.0061394,"\int x^5 \sqrt[3]{-1+x^3} \, dx","Integrate[x^5*(-1 + x^3)^(1/3),x]","\frac{1}{28} \left(x^3-1\right)^{4/3} \left(4 x^3+3\right)","\frac{1}{28} \sqrt[3]{x^3-1} \left(4 x^6-x^3-3\right)",1,"((-1 + x^3)^(4/3)*(3 + 4*x^3))/28","A",1
255,1,20,25,0.0070515,"\int x^5 \left(-1+x^3\right)^{3/4} \, dx","Integrate[x^5*(-1 + x^3)^(3/4),x]","\frac{4}{231} \left(x^3-1\right)^{7/4} \left(7 x^3+4\right)","\frac{4}{231} \left(x^3-1\right)^{3/4} \left(7 x^6-3 x^3-4\right)",1,"(4*(-1 + x^3)^(7/4)*(4 + 7*x^3))/231","A",1
256,1,25,25,0.0068974,"\int \frac{x^8}{\sqrt[4]{1+x^3}} \, dx","Integrate[x^8/(1 + x^3)^(1/4),x]","\frac{4}{693} \left(x^3+1\right)^{3/4} \left(21 x^6-24 x^3+32\right)","\frac{4}{693} \left(x^3+1\right)^{3/4} \left(21 x^6-24 x^3+32\right)",1,"(4*(1 + x^3)^(3/4)*(32 - 24*x^3 + 21*x^6))/693","A",1
257,1,20,25,0.0058652,"\int x^5 \left(1+x^3\right)^{2/3} \, dx","Integrate[x^5*(1 + x^3)^(2/3),x]","\frac{1}{40} \left(x^3+1\right)^{5/3} \left(5 x^3-3\right)","\frac{1}{40} \left(x^3+1\right)^{2/3} \left(5 x^6+2 x^3-3\right)",1,"((1 + x^3)^(5/3)*(-3 + 5*x^3))/40","A",1
258,1,23,25,0.0100419,"\int \frac{1}{x^2 \sqrt[3]{-x^2+x^3}} \, dx","Integrate[1/(x^2*(-x^2 + x^3)^(1/3)),x]","\frac{3 \left((x-1) x^2\right)^{2/3} (3 x+2)}{10 x^3}","\frac{3 (3 x+2) \left(x^3-x^2\right)^{2/3}}{10 x^3}",1,"(3*((-1 + x)*x^2)^(2/3)*(2 + 3*x))/(10*x^3)","A",1
259,1,20,25,0.0063521,"\int x^7 \left(1+x^4\right)^{2/3} \, dx","Integrate[x^7*(1 + x^4)^(2/3),x]","\frac{3}{160} \left(x^4+1\right)^{5/3} \left(5 x^4-3\right)","\frac{3}{160} \left(x^4+1\right)^{2/3} \left(5 x^8+2 x^4-3\right)",1,"(3*(1 + x^4)^(5/3)*(-3 + 5*x^4))/160","A",1
260,1,25,25,0.0099895,"\int \frac{1}{x^5 \sqrt{-x+x^4}} \, dx","Integrate[1/(x^5*Sqrt[-x + x^4]),x]","\frac{2 \sqrt{x \left(x^3-1\right)} \left(2 x^3+1\right)}{9 x^5}","\frac{2 \left(2 x^3+1\right) \sqrt{x^4-x}}{9 x^5}",1,"(2*Sqrt[x*(-1 + x^3)]*(1 + 2*x^3))/(9*x^5)","A",1
261,1,25,25,0.0116257,"\int \frac{1+x^3}{x^6 \sqrt[4]{-x+x^4}} \, dx","Integrate[(1 + x^3)/(x^6*(-x + x^4)^(1/4)),x]","\frac{4 \left(x \left(x^3-1\right)\right)^{3/4} \left(11 x^3+3\right)}{63 x^6}","\frac{4 \left(11 x^3+3\right) \left(x^4-x\right)^{3/4}}{63 x^6}",1,"(4*(x*(-1 + x^3))^(3/4)*(3 + 11*x^3))/(63*x^6)","A",1
262,1,16,25,0.0269546,"\int \frac{1+x^2}{\left(-1+x^2\right) \sqrt[3]{-x^2+x^4}} \, dx","Integrate[(1 + x^2)/((-1 + x^2)*(-x^2 + x^4)^(1/3)),x]","-\frac{3 x}{\sqrt[3]{x^2 \left(x^2-1\right)}}","-\frac{3 \left(x^4-x^2\right)^{2/3}}{x \left(x^2-1\right)}",1,"(-3*x)/(x^2*(-1 + x^2))^(1/3)","A",1
263,1,16,25,0.0059402,"\int \frac{1}{\left(-1+x^2\right) \sqrt[4]{-x^2+x^4}} \, dx","Integrate[1/((-1 + x^2)*(-x^2 + x^4)^(1/4)),x]","-\frac{2 x}{\sqrt[4]{x^2 \left(x^2-1\right)}}","-\frac{2 \left(x^4-x^2\right)^{3/4}}{x \left(x^2-1\right)}",1,"(-2*x)/(x^2*(-1 + x^2))^(1/4)","A",1
264,1,25,25,0.0142031,"\int \frac{1}{x^4 \sqrt[4]{x^2+x^4}} \, dx","Integrate[1/(x^4*(x^2 + x^4)^(1/4)),x]","\frac{2 \left(4 x^2-3\right) \left(x^4+x^2\right)^{3/4}}{21 x^5}","\frac{2 \left(4 x^2-3\right) \left(x^4+x^2\right)^{3/4}}{21 x^5}",1,"(2*(-3 + 4*x^2)*(x^2 + x^4)^(3/4))/(21*x^5)","A",1
265,1,728,25,2.3733215,"\int \frac{-1+2 x}{\sqrt{-3+x^2-2 x^3+x^4}} \, dx","Integrate[(-1 + 2*x)/Sqrt[-3 + x^2 - 2*x^3 + x^4],x]","\frac{\sqrt{4 \sqrt{3}-1} \left(-2 x+i \sqrt{4 \sqrt{3}-1}+1\right) \left(-2 x+\sqrt{1+4 \sqrt{3}}+1\right) \sqrt{\frac{\left(\sqrt{4 \sqrt{3}-1}+i \sqrt{1+4 \sqrt{3}}\right) \left(-2 i x+\sqrt{4 \sqrt{3}-1}+i\right)}{\left(\sqrt{4 \sqrt{3}-1}-i \sqrt{1+4 \sqrt{3}}\right) \left(2 i x+\sqrt{4 \sqrt{3}-1}-i\right)}} \sqrt{\frac{2 x+\sqrt{1+4 \sqrt{3}}-1}{\left(\sqrt{1+4 \sqrt{3}}-i \sqrt{4 \sqrt{3}-1}\right) \left(2 i x+\sqrt{4 \sqrt{3}-1}-i\right)}} \left(F\left(\sin ^{-1}\left(\sqrt{\frac{\left(\sqrt{-1+4 \sqrt{3}}+i \sqrt{1+4 \sqrt{3}}\right) \left(-2 i x+\sqrt{-1+4 \sqrt{3}}+i\right)}{\left(\sqrt{-1+4 \sqrt{3}}-i \sqrt{1+4 \sqrt{3}}\right) \left(2 i x+\sqrt{-1+4 \sqrt{3}}-i\right)}}\right)|\frac{i-\sqrt{47}}{i+\sqrt{47}}\right)-2 \Pi \left(-\frac{\sqrt{-1+4 \sqrt{3}}-i \sqrt{1+4 \sqrt{3}}}{\sqrt{-1+4 \sqrt{3}}+i \sqrt{1+4 \sqrt{3}}};\sin ^{-1}\left(\sqrt{\frac{\left(\sqrt{-1+4 \sqrt{3}}+i \sqrt{1+4 \sqrt{3}}\right) \left(-2 i x+\sqrt{-1+4 \sqrt{3}}+i\right)}{\left(\sqrt{-1+4 \sqrt{3}}-i \sqrt{1+4 \sqrt{3}}\right) \left(2 i x+\sqrt{-1+4 \sqrt{3}}-i\right)}}\right)|\frac{i-\sqrt{47}}{i+\sqrt{47}}\right)\right)}{\left(\sqrt{4 \sqrt{3}-1}+i \sqrt{1+4 \sqrt{3}}\right) \sqrt{\frac{-2 x+\sqrt{1+4 \sqrt{3}}+1}{\left(\sqrt{1+4 \sqrt{3}}+i \sqrt{4 \sqrt{3}-1}\right) \left(2 i x+\sqrt{4 \sqrt{3}-1}-i\right)}} \sqrt{x^4-2 x^3+x^2-3}}","\log \left(x^2+\sqrt{x^4-2 x^3+x^2-3}-x\right)",1,"(Sqrt[-1 + 4*Sqrt[3]]*(1 + I*Sqrt[-1 + 4*Sqrt[3]] - 2*x)*(1 + Sqrt[1 + 4*Sqrt[3]] - 2*x)*Sqrt[((Sqrt[-1 + 4*Sqrt[3]] + I*Sqrt[1 + 4*Sqrt[3]])*(I + Sqrt[-1 + 4*Sqrt[3]] - (2*I)*x))/((Sqrt[-1 + 4*Sqrt[3]] - I*Sqrt[1 + 4*Sqrt[3]])*(-I + Sqrt[-1 + 4*Sqrt[3]] + (2*I)*x))]*Sqrt[(-1 + Sqrt[1 + 4*Sqrt[3]] + 2*x)/(((-I)*Sqrt[-1 + 4*Sqrt[3]] + Sqrt[1 + 4*Sqrt[3]])*(-I + Sqrt[-1 + 4*Sqrt[3]] + (2*I)*x))]*(EllipticF[ArcSin[Sqrt[((Sqrt[-1 + 4*Sqrt[3]] + I*Sqrt[1 + 4*Sqrt[3]])*(I + Sqrt[-1 + 4*Sqrt[3]] - (2*I)*x))/((Sqrt[-1 + 4*Sqrt[3]] - I*Sqrt[1 + 4*Sqrt[3]])*(-I + Sqrt[-1 + 4*Sqrt[3]] + (2*I)*x))]], (I - Sqrt[47])/(I + Sqrt[47])] - 2*EllipticPi[-((Sqrt[-1 + 4*Sqrt[3]] - I*Sqrt[1 + 4*Sqrt[3]])/(Sqrt[-1 + 4*Sqrt[3]] + I*Sqrt[1 + 4*Sqrt[3]])), ArcSin[Sqrt[((Sqrt[-1 + 4*Sqrt[3]] + I*Sqrt[1 + 4*Sqrt[3]])*(I + Sqrt[-1 + 4*Sqrt[3]] - (2*I)*x))/((Sqrt[-1 + 4*Sqrt[3]] - I*Sqrt[1 + 4*Sqrt[3]])*(-I + Sqrt[-1 + 4*Sqrt[3]] + (2*I)*x))]], (I - Sqrt[47])/(I + Sqrt[47])]))/((Sqrt[-1 + 4*Sqrt[3]] + I*Sqrt[1 + 4*Sqrt[3]])*Sqrt[(1 + Sqrt[1 + 4*Sqrt[3]] - 2*x)/((I*Sqrt[-1 + 4*Sqrt[3]] + Sqrt[1 + 4*Sqrt[3]])*(-I + Sqrt[-1 + 4*Sqrt[3]] + (2*I)*x))]*Sqrt[-3 + x^2 - 2*x^3 + x^4])","C",0
266,1,613,25,2.3577178,"\int \frac{-1+2 x}{\sqrt{4+x^2-2 x^3+x^4}} \, dx","Integrate[(-1 + 2*x)/Sqrt[4 + x^2 - 2*x^3 + x^4],x]","\frac{\left(-2 x+\sqrt{1-8 i}+1\right) \sqrt{\frac{\sqrt{1-8 i} \left(-2 x+\sqrt{1+8 i}+1\right)}{\left(\sqrt{1-8 i}+\sqrt{1+8 i}\right) \left(-2 x+\sqrt{1-8 i}+1\right)}} \left(2 x+\sqrt{1-8 i}-1\right) \sqrt{\frac{\sqrt{1-8 i} \left(2 x+\sqrt{1+8 i}-1\right)}{\left(\sqrt{1+8 i}-\sqrt{1-8 i}\right) \left(-2 x+\sqrt{1-8 i}+1\right)}} \left(\left(1+\sqrt{1-8 i}\right) F\left(\sin ^{-1}\left(\sqrt{\frac{\left(\sqrt{1-8 i}-\sqrt{1+8 i}\right) \left(2 x+\sqrt{1-8 i}-1\right)}{\left(\sqrt{1-8 i}+\sqrt{1+8 i}\right) \left(-2 x+\sqrt{1-8 i}+1\right)}}\right)|\frac{\left(\sqrt{1-8 i}+\sqrt{1+8 i}\right)^2}{\left(\sqrt{1-8 i}-\sqrt{1+8 i}\right)^2}\right)-F\left(\sin ^{-1}\left(\sqrt{-\frac{2 \sqrt{1+8 i} x-2 \sqrt{1-8 i} x+\sqrt{65}-\sqrt{1+8 i}+\sqrt{1-8 i}-(1-8 i)}{\left(\sqrt{1-8 i}+\sqrt{1+8 i}\right) \left(-2 x+\sqrt{1-8 i}+1\right)}}\right)|\frac{\left(\sqrt{1-8 i}+\sqrt{1+8 i}\right)^2}{\left(\sqrt{1-8 i}-\sqrt{1+8 i}\right)^2}\right)-2 \sqrt{1-8 i} \Pi \left(-\frac{\sqrt{1-8 i}+\sqrt{1+8 i}}{\sqrt{1-8 i}-\sqrt{1+8 i}};\sin ^{-1}\left(\sqrt{\frac{\left(\sqrt{1-8 i}-\sqrt{1+8 i}\right) \left(2 x+\sqrt{1-8 i}-1\right)}{\left(\sqrt{1-8 i}+\sqrt{1+8 i}\right) \left(-2 x+\sqrt{1-8 i}+1\right)}}\right)|\frac{\left(\sqrt{1-8 i}+\sqrt{1+8 i}\right)^2}{\left(\sqrt{1-8 i}-\sqrt{1+8 i}\right)^2}\right)\right)}{\sqrt{1-8 i} \sqrt{\frac{\left(\sqrt{1-8 i}-\sqrt{1+8 i}\right) \left(2 x+\sqrt{1-8 i}-1\right)}{\left(\sqrt{1-8 i}+\sqrt{1+8 i}\right) \left(-2 x+\sqrt{1-8 i}+1\right)}} \sqrt{x^4-2 x^3+x^2+4}}","\log \left(x^2+\sqrt{x^4-2 x^3+x^2+4}-x\right)",1,"((1 + Sqrt[1 - 8*I] - 2*x)*Sqrt[(Sqrt[1 - 8*I]*(1 + Sqrt[1 + 8*I] - 2*x))/((Sqrt[1 - 8*I] + Sqrt[1 + 8*I])*(1 + Sqrt[1 - 8*I] - 2*x))]*(-1 + Sqrt[1 - 8*I] + 2*x)*Sqrt[(Sqrt[1 - 8*I]*(-1 + Sqrt[1 + 8*I] + 2*x))/((-Sqrt[1 - 8*I] + Sqrt[1 + 8*I])*(1 + Sqrt[1 - 8*I] - 2*x))]*((1 + Sqrt[1 - 8*I])*EllipticF[ArcSin[Sqrt[((Sqrt[1 - 8*I] - Sqrt[1 + 8*I])*(-1 + Sqrt[1 - 8*I] + 2*x))/((Sqrt[1 - 8*I] + Sqrt[1 + 8*I])*(1 + Sqrt[1 - 8*I] - 2*x))]], (Sqrt[1 - 8*I] + Sqrt[1 + 8*I])^2/(Sqrt[1 - 8*I] - Sqrt[1 + 8*I])^2] - EllipticF[ArcSin[Sqrt[-(((-1 + 8*I) + Sqrt[1 - 8*I] - Sqrt[1 + 8*I] + Sqrt[65] - 2*Sqrt[1 - 8*I]*x + 2*Sqrt[1 + 8*I]*x)/((Sqrt[1 - 8*I] + Sqrt[1 + 8*I])*(1 + Sqrt[1 - 8*I] - 2*x)))]], (Sqrt[1 - 8*I] + Sqrt[1 + 8*I])^2/(Sqrt[1 - 8*I] - Sqrt[1 + 8*I])^2] - 2*Sqrt[1 - 8*I]*EllipticPi[-((Sqrt[1 - 8*I] + Sqrt[1 + 8*I])/(Sqrt[1 - 8*I] - Sqrt[1 + 8*I])), ArcSin[Sqrt[((Sqrt[1 - 8*I] - Sqrt[1 + 8*I])*(-1 + Sqrt[1 - 8*I] + 2*x))/((Sqrt[1 - 8*I] + Sqrt[1 + 8*I])*(1 + Sqrt[1 - 8*I] - 2*x))]], (Sqrt[1 - 8*I] + Sqrt[1 + 8*I])^2/(Sqrt[1 - 8*I] - Sqrt[1 + 8*I])^2]))/(Sqrt[1 - 8*I]*Sqrt[((Sqrt[1 - 8*I] - Sqrt[1 + 8*I])*(-1 + Sqrt[1 - 8*I] + 2*x))/((Sqrt[1 - 8*I] + Sqrt[1 + 8*I])*(1 + Sqrt[1 - 8*I] - 2*x))]*Sqrt[4 + x^2 - 2*x^3 + x^4])","C",0
267,1,803,25,3.0443864,"\int \frac{-1+2 x}{\sqrt{13+x^2-2 x^3+x^4}} \, dx","Integrate[(-1 + 2*x)/Sqrt[13 + x^2 - 2*x^3 + x^4],x]","\frac{\left(-2 x+\sqrt{1-4 i \sqrt{13}}+1\right) \sqrt{\frac{\sqrt{1-4 i \sqrt{13}} \left(-2 x+\sqrt{1+4 i \sqrt{13}}+1\right)}{\left(\sqrt{1-4 i \sqrt{13}}+\sqrt{1+4 i \sqrt{13}}\right) \left(-2 x+\sqrt{1-4 i \sqrt{13}}+1\right)}} \left(2 x+\sqrt{1-4 i \sqrt{13}}-1\right) \sqrt{-\frac{\sqrt{1-4 i \sqrt{13}} \left(2 x+\sqrt{1+4 i \sqrt{13}}-1\right)}{\left(\sqrt{1-4 i \sqrt{13}}-\sqrt{1+4 i \sqrt{13}}\right) \left(-2 x+\sqrt{1-4 i \sqrt{13}}+1\right)}} \left(F\left(\sin ^{-1}\left(\sqrt{\frac{\left(\sqrt{1-4 i \sqrt{13}}-\sqrt{1+4 i \sqrt{13}}\right) \left(2 x+\sqrt{1-4 i \sqrt{13}}-1\right)}{\left(\sqrt{1-4 i \sqrt{13}}+\sqrt{1+4 i \sqrt{13}}\right) \left(-2 x+\sqrt{1-4 i \sqrt{13}}+1\right)}}\right)|\frac{\left(\sqrt{1-4 i \sqrt{13}}+\sqrt{1+4 i \sqrt{13}}\right)^2}{\left(\sqrt{1-4 i \sqrt{13}}-\sqrt{1+4 i \sqrt{13}}\right)^2}\right)-2 \Pi \left(-\frac{\sqrt{1-4 i \sqrt{13}}+\sqrt{1+4 i \sqrt{13}}}{\sqrt{1-4 i \sqrt{13}}-\sqrt{1+4 i \sqrt{13}}};\sin ^{-1}\left(\sqrt{\frac{\left(\sqrt{1-4 i \sqrt{13}}-\sqrt{1+4 i \sqrt{13}}\right) \left(2 x+\sqrt{1-4 i \sqrt{13}}-1\right)}{\left(\sqrt{1-4 i \sqrt{13}}+\sqrt{1+4 i \sqrt{13}}\right) \left(-2 x+\sqrt{1-4 i \sqrt{13}}+1\right)}}\right)|\frac{\left(\sqrt{1-4 i \sqrt{13}}+\sqrt{1+4 i \sqrt{13}}\right)^2}{\left(\sqrt{1-4 i \sqrt{13}}-\sqrt{1+4 i \sqrt{13}}\right)^2}\right)\right)}{\sqrt{\frac{\left(\sqrt{1-4 i \sqrt{13}}-\sqrt{1+4 i \sqrt{13}}\right) \left(2 x+\sqrt{1-4 i \sqrt{13}}-1\right)}{\left(\sqrt{1-4 i \sqrt{13}}+\sqrt{1+4 i \sqrt{13}}\right) \left(-2 x+\sqrt{1-4 i \sqrt{13}}+1\right)}} \sqrt{x^4-2 x^3+x^2+13}}","\log \left(x^2+\sqrt{x^4-2 x^3+x^2+13}-x\right)",1,"((1 + Sqrt[1 - (4*I)*Sqrt[13]] - 2*x)*Sqrt[(Sqrt[1 - (4*I)*Sqrt[13]]*(1 + Sqrt[1 + (4*I)*Sqrt[13]] - 2*x))/((Sqrt[1 - (4*I)*Sqrt[13]] + Sqrt[1 + (4*I)*Sqrt[13]])*(1 + Sqrt[1 - (4*I)*Sqrt[13]] - 2*x))]*(-1 + Sqrt[1 - (4*I)*Sqrt[13]] + 2*x)*Sqrt[-((Sqrt[1 - (4*I)*Sqrt[13]]*(-1 + Sqrt[1 + (4*I)*Sqrt[13]] + 2*x))/((Sqrt[1 - (4*I)*Sqrt[13]] - Sqrt[1 + (4*I)*Sqrt[13]])*(1 + Sqrt[1 - (4*I)*Sqrt[13]] - 2*x)))]*(EllipticF[ArcSin[Sqrt[((Sqrt[1 - (4*I)*Sqrt[13]] - Sqrt[1 + (4*I)*Sqrt[13]])*(-1 + Sqrt[1 - (4*I)*Sqrt[13]] + 2*x))/((Sqrt[1 - (4*I)*Sqrt[13]] + Sqrt[1 + (4*I)*Sqrt[13]])*(1 + Sqrt[1 - (4*I)*Sqrt[13]] - 2*x))]], (Sqrt[1 - (4*I)*Sqrt[13]] + Sqrt[1 + (4*I)*Sqrt[13]])^2/(Sqrt[1 - (4*I)*Sqrt[13]] - Sqrt[1 + (4*I)*Sqrt[13]])^2] - 2*EllipticPi[-((Sqrt[1 - (4*I)*Sqrt[13]] + Sqrt[1 + (4*I)*Sqrt[13]])/(Sqrt[1 - (4*I)*Sqrt[13]] - Sqrt[1 + (4*I)*Sqrt[13]])), ArcSin[Sqrt[((Sqrt[1 - (4*I)*Sqrt[13]] - Sqrt[1 + (4*I)*Sqrt[13]])*(-1 + Sqrt[1 - (4*I)*Sqrt[13]] + 2*x))/((Sqrt[1 - (4*I)*Sqrt[13]] + Sqrt[1 + (4*I)*Sqrt[13]])*(1 + Sqrt[1 - (4*I)*Sqrt[13]] - 2*x))]], (Sqrt[1 - (4*I)*Sqrt[13]] + Sqrt[1 + (4*I)*Sqrt[13]])^2/(Sqrt[1 - (4*I)*Sqrt[13]] - Sqrt[1 + (4*I)*Sqrt[13]])^2]))/(Sqrt[((Sqrt[1 - (4*I)*Sqrt[13]] - Sqrt[1 + (4*I)*Sqrt[13]])*(-1 + Sqrt[1 - (4*I)*Sqrt[13]] + 2*x))/((Sqrt[1 - (4*I)*Sqrt[13]] + Sqrt[1 + (4*I)*Sqrt[13]])*(1 + Sqrt[1 - (4*I)*Sqrt[13]] - 2*x))]*Sqrt[13 + x^2 - 2*x^3 + x^4])","C",1
268,1,23,25,0.0084608,"\int \frac{1}{x^2 \sqrt[4]{-x^3+x^4}} \, dx","Integrate[1/(x^2*(-x^3 + x^4)^(1/4)),x]","\frac{4 \left((x-1) x^3\right)^{3/4} (4 x+3)}{21 x^4}","\frac{4 (4 x+3) \left(x^4-x^3\right)^{3/4}}{21 x^4}",1,"(4*((-1 + x)*x^3)^(3/4)*(3 + 4*x))/(21*x^4)","A",1
269,1,23,25,0.0081728,"\int \frac{-1+x^4}{x^8 \sqrt[4]{-1+2 x^4}} \, dx","Integrate[(-1 + x^4)/(x^8*(-1 + 2*x^4)^(1/4)),x]","-\frac{\left(x^4+3\right) \left(2 x^4-1\right)^{3/4}}{21 x^7}","\frac{\left(-x^4-3\right) \left(2 x^4-1\right)^{3/4}}{21 x^7}",1,"-1/21*((3 + x^4)*(-1 + 2*x^4)^(3/4))/x^7","A",1
270,1,16,25,0.0283759,"\int \frac{1+x^2}{\left(-1+x^2\right) \sqrt[4]{-x^3+x^5}} \, dx","Integrate[(1 + x^2)/((-1 + x^2)*(-x^3 + x^5)^(1/4)),x]","-\frac{4 x}{\sqrt[4]{x^3 \left(x^2-1\right)}}","-\frac{4 \left(x^5-x^3\right)^{3/4}}{x^2 \left(x^2-1\right)}",1,"(-4*x)/(x^3*(-1 + x^2))^(1/4)","A",1
271,1,16,25,0.0289813,"\int \frac{1+3 x^4}{\left(-1+x^4\right) \sqrt[3]{-x^2+x^6}} \, dx","Integrate[(1 + 3*x^4)/((-1 + x^4)*(-x^2 + x^6)^(1/3)),x]","-\frac{3 x}{\sqrt[3]{x^2 \left(x^4-1\right)}}","-\frac{3 \left(x^6-x^2\right)^{2/3}}{x \left(x^4-1\right)}",1,"(-3*x)/(x^2*(-1 + x^4))^(1/3)","A",1
272,1,16,25,0.0263195,"\int \frac{1+x^4}{\left(-1+x^4\right) \sqrt[4]{-x^2+x^6}} \, dx","Integrate[(1 + x^4)/((-1 + x^4)*(-x^2 + x^6)^(1/4)),x]","-\frac{2 x}{\sqrt[4]{x^2 \left(x^4-1\right)}}","-\frac{2 \left(x^6-x^2\right)^{3/4}}{x \left(x^4-1\right)}",1,"(-2*x)/(x^2*(-1 + x^4))^(1/4)","A",1
273,1,25,25,0.0118867,"\int \frac{1}{x^7 \sqrt[3]{x^2+x^6}} \, dx","Integrate[1/(x^7*(x^2 + x^6)^(1/3)),x]","\frac{3 \left(3 x^4-2\right) \left(x^6+x^2\right)^{2/3}}{40 x^8}","\frac{3 \left(3 x^4-2\right) \left(x^6+x^2\right)^{2/3}}{40 x^8}",1,"(3*(-2 + 3*x^4)*(x^2 + x^6)^(2/3))/(40*x^8)","A",1
274,1,23,26,0.0052142,"\int \frac{\sqrt[3]{-1+x^3}}{x^8} \, dx","Integrate[(-1 + x^3)^(1/3)/x^8,x]","\frac{\left(x^3-1\right)^{4/3} \left(3 x^3+4\right)}{28 x^7}","\frac{\sqrt[3]{x^3-1} \left(3 x^6+x^3-4\right)}{28 x^7}",1,"((-1 + x^3)^(4/3)*(4 + 3*x^3))/(28*x^7)","A",1
275,1,17,26,0.0471034,"\int \frac{b+a x^2}{\left(-b+a x^2\right) \sqrt{-b x+a x^3}} \, dx","Integrate[(b + a*x^2)/((-b + a*x^2)*Sqrt[-(b*x) + a*x^3]),x]","-\frac{2 x}{\sqrt{a x^3-b x}}","\frac{2 \sqrt{a x^3-b x}}{b-a x^2}",1,"(-2*x)/Sqrt[-(b*x) + a*x^3]","A",1
276,1,2764,26,6.2820982,"\int \frac{-2 b+a x^3}{\sqrt{b+a x^3} \left(b-c x^2+a x^3\right)} \, dx","Integrate[(-2*b + a*x^3)/(Sqrt[b + a*x^3]*(b - c*x^2 + a*x^3)),x]","\text{Result too large to show}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a x^3+b}}\right)}{\sqrt{c}}",1,"(2*Sqrt[(b^(1/3)/a^(1/3) + x)/(b^(1/3)/a^(1/3) + ((-1)^(1/3)*b^(1/3))/a^(1/3))]*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) + x)*Sqrt[(((-1)^(2/3)*b^(1/3))/a^(1/3) + x)/(((-1)^(1/3)*b^(1/3))/a^(1/3) + ((-1)^(2/3)*b^(1/3))/a^(1/3))]*EllipticF[ArcSin[Sqrt[((-1)^(1/3)*b^(1/3) - a^(1/3)*x)/(((-1)^(1/3) + (-1)^(2/3))*b^(1/3))]], (-1)^(1/3)])/(Sqrt[(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) + x)/(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) - ((-1)^(2/3)*b^(1/3))/a^(1/3))]*Sqrt[b + a*x^3]) - (4*(((-1)^(1/3)*b^(1/3))/a^(1/3) + ((-1)^(2/3)*b^(1/3))/a^(1/3))*b*Sqrt[(b^(1/3)/a^(1/3) + x)/(b^(1/3)/a^(1/3) + ((-1)^(1/3)*b^(1/3))/a^(1/3))]*Sqrt[((-(((-1)^(2/3)*b^(1/3))/a^(1/3)) - x)*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) + x))/(((-1)^(1/3)*b^(1/3))/a^(1/3) + ((-1)^(2/3)*b^(1/3))/a^(1/3))^2]*EllipticPi[((-1)^(1/3)*b^(1/3) + (-1)^(2/3)*b^(1/3))/((-1)^(1/3)*b^(1/3) - a^(1/3)*Root[b - c*#1^2 + a*#1^3 & , 1]), ArcSin[Sqrt[((-1)^(1/3)*b^(1/3) - a^(1/3)*x)/(((-1)^(1/3) + (-1)^(2/3))*b^(1/3))]], (-1)^(1/3)])/(a*Sqrt[b + a*x^3]*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) + Root[b - c*#1^2 + a*#1^3 & , 1])*(Root[b - c*#1^2 + a*#1^3 & , 1] - Root[b - c*#1^2 + a*#1^3 & , 2])*(Root[b - c*#1^2 + a*#1^3 & , 1] - Root[b - c*#1^2 + a*#1^3 & , 3])) + (2*(((-1)^(1/3)*b^(1/3))/a^(1/3) + ((-1)^(2/3)*b^(1/3))/a^(1/3))*Sqrt[(b^(1/3)/a^(1/3) + x)/(b^(1/3)/a^(1/3) + ((-1)^(1/3)*b^(1/3))/a^(1/3))]*Sqrt[((-(((-1)^(2/3)*b^(1/3))/a^(1/3)) - x)*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) + x))/(((-1)^(1/3)*b^(1/3))/a^(1/3) + ((-1)^(2/3)*b^(1/3))/a^(1/3))^2]*EllipticPi[((-1)^(1/3)*b^(1/3) + (-1)^(2/3)*b^(1/3))/((-1)^(1/3)*b^(1/3) - a^(1/3)*Root[b - c*#1^2 + a*#1^3 & , 1]), ArcSin[Sqrt[((-1)^(1/3)*b^(1/3) - a^(1/3)*x)/(((-1)^(1/3) + (-1)^(2/3))*b^(1/3))]], (-1)^(1/3)]*Root[b - c*#1^2 + a*#1^3 & , 1]^3)/(Sqrt[b + a*x^3]*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) + Root[b - c*#1^2 + a*#1^3 & , 1])*(Root[b - c*#1^2 + a*#1^3 & , 1] - Root[b - c*#1^2 + a*#1^3 & , 2])*(Root[b - c*#1^2 + a*#1^3 & , 1] - Root[b - c*#1^2 + a*#1^3 & , 3])) - (4*(((-1)^(1/3)*b^(1/3))/a^(1/3) + ((-1)^(2/3)*b^(1/3))/a^(1/3))*b*Sqrt[(b^(1/3)/a^(1/3) + x)/(b^(1/3)/a^(1/3) + ((-1)^(1/3)*b^(1/3))/a^(1/3))]*Sqrt[((-(((-1)^(2/3)*b^(1/3))/a^(1/3)) - x)*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) + x))/(((-1)^(1/3)*b^(1/3))/a^(1/3) + ((-1)^(2/3)*b^(1/3))/a^(1/3))^2]*EllipticPi[((-1)^(1/3)*b^(1/3) + (-1)^(2/3)*b^(1/3))/((-1)^(1/3)*b^(1/3) - a^(1/3)*Root[b - c*#1^2 + a*#1^3 & , 2]), ArcSin[Sqrt[((-1)^(1/3)*b^(1/3) - a^(1/3)*x)/(((-1)^(1/3) + (-1)^(2/3))*b^(1/3))]], (-1)^(1/3)])/(a*Sqrt[b + a*x^3]*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) + Root[b - c*#1^2 + a*#1^3 & , 2])*(-Root[b - c*#1^2 + a*#1^3 & , 1] + Root[b - c*#1^2 + a*#1^3 & , 2])*(Root[b - c*#1^2 + a*#1^3 & , 2] - Root[b - c*#1^2 + a*#1^3 & , 3])) + (2*(((-1)^(1/3)*b^(1/3))/a^(1/3) + ((-1)^(2/3)*b^(1/3))/a^(1/3))*Sqrt[(b^(1/3)/a^(1/3) + x)/(b^(1/3)/a^(1/3) + ((-1)^(1/3)*b^(1/3))/a^(1/3))]*Sqrt[((-(((-1)^(2/3)*b^(1/3))/a^(1/3)) - x)*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) + x))/(((-1)^(1/3)*b^(1/3))/a^(1/3) + ((-1)^(2/3)*b^(1/3))/a^(1/3))^2]*EllipticPi[((-1)^(1/3)*b^(1/3) + (-1)^(2/3)*b^(1/3))/((-1)^(1/3)*b^(1/3) - a^(1/3)*Root[b - c*#1^2 + a*#1^3 & , 2]), ArcSin[Sqrt[((-1)^(1/3)*b^(1/3) - a^(1/3)*x)/(((-1)^(1/3) + (-1)^(2/3))*b^(1/3))]], (-1)^(1/3)]*Root[b - c*#1^2 + a*#1^3 & , 2]^3)/(Sqrt[b + a*x^3]*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) + Root[b - c*#1^2 + a*#1^3 & , 2])*(-Root[b - c*#1^2 + a*#1^3 & , 1] + Root[b - c*#1^2 + a*#1^3 & , 2])*(Root[b - c*#1^2 + a*#1^3 & , 2] - Root[b - c*#1^2 + a*#1^3 & , 3])) - (4*(((-1)^(1/3)*b^(1/3))/a^(1/3) + ((-1)^(2/3)*b^(1/3))/a^(1/3))*b*Sqrt[(b^(1/3)/a^(1/3) + x)/(b^(1/3)/a^(1/3) + ((-1)^(1/3)*b^(1/3))/a^(1/3))]*Sqrt[((-(((-1)^(2/3)*b^(1/3))/a^(1/3)) - x)*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) + x))/(((-1)^(1/3)*b^(1/3))/a^(1/3) + ((-1)^(2/3)*b^(1/3))/a^(1/3))^2]*EllipticPi[((-1)^(1/3)*b^(1/3) + (-1)^(2/3)*b^(1/3))/((-1)^(1/3)*b^(1/3) - a^(1/3)*Root[b - c*#1^2 + a*#1^3 & , 3]), ArcSin[Sqrt[((-1)^(1/3)*b^(1/3) - a^(1/3)*x)/(((-1)^(1/3) + (-1)^(2/3))*b^(1/3))]], (-1)^(1/3)])/(a*Sqrt[b + a*x^3]*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) + Root[b - c*#1^2 + a*#1^3 & , 3])*(-Root[b - c*#1^2 + a*#1^3 & , 1] + Root[b - c*#1^2 + a*#1^3 & , 3])*(-Root[b - c*#1^2 + a*#1^3 & , 2] + Root[b - c*#1^2 + a*#1^3 & , 3])) + (2*(((-1)^(1/3)*b^(1/3))/a^(1/3) + ((-1)^(2/3)*b^(1/3))/a^(1/3))*Sqrt[(b^(1/3)/a^(1/3) + x)/(b^(1/3)/a^(1/3) + ((-1)^(1/3)*b^(1/3))/a^(1/3))]*Sqrt[((-(((-1)^(2/3)*b^(1/3))/a^(1/3)) - x)*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) + x))/(((-1)^(1/3)*b^(1/3))/a^(1/3) + ((-1)^(2/3)*b^(1/3))/a^(1/3))^2]*EllipticPi[((-1)^(1/3)*b^(1/3) + (-1)^(2/3)*b^(1/3))/((-1)^(1/3)*b^(1/3) - a^(1/3)*Root[b - c*#1^2 + a*#1^3 & , 3]), ArcSin[Sqrt[((-1)^(1/3)*b^(1/3) - a^(1/3)*x)/(((-1)^(1/3) + (-1)^(2/3))*b^(1/3))]], (-1)^(1/3)]*Root[b - c*#1^2 + a*#1^3 & , 3]^3)/(Sqrt[b + a*x^3]*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) + Root[b - c*#1^2 + a*#1^3 & , 3])*(-Root[b - c*#1^2 + a*#1^3 & , 1] + Root[b - c*#1^2 + a*#1^3 & , 3])*(-Root[b - c*#1^2 + a*#1^3 & , 2] + Root[b - c*#1^2 + a*#1^3 & , 3]))","C",0
277,1,2725,26,6.3172485,"\int \frac{-2 b+a x^3}{\sqrt{b+a x^3} \left(b+c x^2+a x^3\right)} \, dx","Integrate[(-2*b + a*x^3)/(Sqrt[b + a*x^3]*(b + c*x^2 + a*x^3)),x]","\text{Result too large to show}","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a x^3+b}}\right)}{\sqrt{c}}",1,"(2*Sqrt[(b^(1/3)/a^(1/3) + x)/(b^(1/3)/a^(1/3) + ((-1)^(1/3)*b^(1/3))/a^(1/3))]*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) + x)*Sqrt[(((-1)^(2/3)*b^(1/3))/a^(1/3) + x)/(((-1)^(1/3)*b^(1/3))/a^(1/3) + ((-1)^(2/3)*b^(1/3))/a^(1/3))]*EllipticF[ArcSin[Sqrt[((-1)^(1/3)*b^(1/3) - a^(1/3)*x)/(((-1)^(1/3) + (-1)^(2/3))*b^(1/3))]], (-1)^(1/3)])/(Sqrt[(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) + x)/(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) - ((-1)^(2/3)*b^(1/3))/a^(1/3))]*Sqrt[b + a*x^3]) - (4*(((-1)^(1/3)*b^(1/3))/a^(1/3) + ((-1)^(2/3)*b^(1/3))/a^(1/3))*b*Sqrt[(b^(1/3)/a^(1/3) + x)/(b^(1/3)/a^(1/3) + ((-1)^(1/3)*b^(1/3))/a^(1/3))]*Sqrt[((-(((-1)^(2/3)*b^(1/3))/a^(1/3)) - x)*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) + x))/(((-1)^(1/3)*b^(1/3))/a^(1/3) + ((-1)^(2/3)*b^(1/3))/a^(1/3))^2]*EllipticPi[((-1)^(1/3)*b^(1/3) + (-1)^(2/3)*b^(1/3))/((-1)^(1/3)*b^(1/3) - a^(1/3)*Root[b + c*#1^2 + a*#1^3 & , 1]), ArcSin[Sqrt[((-1)^(1/3)*b^(1/3) - a^(1/3)*x)/(((-1)^(1/3) + (-1)^(2/3))*b^(1/3))]], (-1)^(1/3)])/(a*Sqrt[b + a*x^3]*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) + Root[b + c*#1^2 + a*#1^3 & , 1])*(Root[b + c*#1^2 + a*#1^3 & , 1] - Root[b + c*#1^2 + a*#1^3 & , 2])*(Root[b + c*#1^2 + a*#1^3 & , 1] - Root[b + c*#1^2 + a*#1^3 & , 3])) + (2*(((-1)^(1/3)*b^(1/3))/a^(1/3) + ((-1)^(2/3)*b^(1/3))/a^(1/3))*Sqrt[(b^(1/3)/a^(1/3) + x)/(b^(1/3)/a^(1/3) + ((-1)^(1/3)*b^(1/3))/a^(1/3))]*Sqrt[((-(((-1)^(2/3)*b^(1/3))/a^(1/3)) - x)*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) + x))/(((-1)^(1/3)*b^(1/3))/a^(1/3) + ((-1)^(2/3)*b^(1/3))/a^(1/3))^2]*EllipticPi[((-1)^(1/3)*b^(1/3) + (-1)^(2/3)*b^(1/3))/((-1)^(1/3)*b^(1/3) - a^(1/3)*Root[b + c*#1^2 + a*#1^3 & , 1]), ArcSin[Sqrt[((-1)^(1/3)*b^(1/3) - a^(1/3)*x)/(((-1)^(1/3) + (-1)^(2/3))*b^(1/3))]], (-1)^(1/3)]*Root[b + c*#1^2 + a*#1^3 & , 1]^3)/(Sqrt[b + a*x^3]*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) + Root[b + c*#1^2 + a*#1^3 & , 1])*(Root[b + c*#1^2 + a*#1^3 & , 1] - Root[b + c*#1^2 + a*#1^3 & , 2])*(Root[b + c*#1^2 + a*#1^3 & , 1] - Root[b + c*#1^2 + a*#1^3 & , 3])) - (4*(((-1)^(1/3)*b^(1/3))/a^(1/3) + ((-1)^(2/3)*b^(1/3))/a^(1/3))*b*Sqrt[(b^(1/3)/a^(1/3) + x)/(b^(1/3)/a^(1/3) + ((-1)^(1/3)*b^(1/3))/a^(1/3))]*Sqrt[((-(((-1)^(2/3)*b^(1/3))/a^(1/3)) - x)*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) + x))/(((-1)^(1/3)*b^(1/3))/a^(1/3) + ((-1)^(2/3)*b^(1/3))/a^(1/3))^2]*EllipticPi[((-1)^(1/3)*b^(1/3) + (-1)^(2/3)*b^(1/3))/((-1)^(1/3)*b^(1/3) - a^(1/3)*Root[b + c*#1^2 + a*#1^3 & , 2]), ArcSin[Sqrt[((-1)^(1/3)*b^(1/3) - a^(1/3)*x)/(((-1)^(1/3) + (-1)^(2/3))*b^(1/3))]], (-1)^(1/3)])/(a*Sqrt[b + a*x^3]*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) + Root[b + c*#1^2 + a*#1^3 & , 2])*(-Root[b + c*#1^2 + a*#1^3 & , 1] + Root[b + c*#1^2 + a*#1^3 & , 2])*(Root[b + c*#1^2 + a*#1^3 & , 2] - Root[b + c*#1^2 + a*#1^3 & , 3])) + (2*(((-1)^(1/3)*b^(1/3))/a^(1/3) + ((-1)^(2/3)*b^(1/3))/a^(1/3))*Sqrt[(b^(1/3)/a^(1/3) + x)/(b^(1/3)/a^(1/3) + ((-1)^(1/3)*b^(1/3))/a^(1/3))]*Sqrt[((-(((-1)^(2/3)*b^(1/3))/a^(1/3)) - x)*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) + x))/(((-1)^(1/3)*b^(1/3))/a^(1/3) + ((-1)^(2/3)*b^(1/3))/a^(1/3))^2]*EllipticPi[((-1)^(1/3)*b^(1/3) + (-1)^(2/3)*b^(1/3))/((-1)^(1/3)*b^(1/3) - a^(1/3)*Root[b + c*#1^2 + a*#1^3 & , 2]), ArcSin[Sqrt[((-1)^(1/3)*b^(1/3) - a^(1/3)*x)/(((-1)^(1/3) + (-1)^(2/3))*b^(1/3))]], (-1)^(1/3)]*Root[b + c*#1^2 + a*#1^3 & , 2]^3)/(Sqrt[b + a*x^3]*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) + Root[b + c*#1^2 + a*#1^3 & , 2])*(-Root[b + c*#1^2 + a*#1^3 & , 1] + Root[b + c*#1^2 + a*#1^3 & , 2])*(Root[b + c*#1^2 + a*#1^3 & , 2] - Root[b + c*#1^2 + a*#1^3 & , 3])) - (4*(((-1)^(1/3)*b^(1/3))/a^(1/3) + ((-1)^(2/3)*b^(1/3))/a^(1/3))*b*Sqrt[(b^(1/3)/a^(1/3) + x)/(b^(1/3)/a^(1/3) + ((-1)^(1/3)*b^(1/3))/a^(1/3))]*Sqrt[((-(((-1)^(2/3)*b^(1/3))/a^(1/3)) - x)*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) + x))/(((-1)^(1/3)*b^(1/3))/a^(1/3) + ((-1)^(2/3)*b^(1/3))/a^(1/3))^2]*EllipticPi[((-1)^(1/3)*b^(1/3) + (-1)^(2/3)*b^(1/3))/((-1)^(1/3)*b^(1/3) - a^(1/3)*Root[b + c*#1^2 + a*#1^3 & , 3]), ArcSin[Sqrt[((-1)^(1/3)*b^(1/3) - a^(1/3)*x)/(((-1)^(1/3) + (-1)^(2/3))*b^(1/3))]], (-1)^(1/3)])/(a*Sqrt[b + a*x^3]*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) + Root[b + c*#1^2 + a*#1^3 & , 3])*(-Root[b + c*#1^2 + a*#1^3 & , 1] + Root[b + c*#1^2 + a*#1^3 & , 3])*(-Root[b + c*#1^2 + a*#1^3 & , 2] + Root[b + c*#1^2 + a*#1^3 & , 3])) + (2*(((-1)^(1/3)*b^(1/3))/a^(1/3) + ((-1)^(2/3)*b^(1/3))/a^(1/3))*Sqrt[(b^(1/3)/a^(1/3) + x)/(b^(1/3)/a^(1/3) + ((-1)^(1/3)*b^(1/3))/a^(1/3))]*Sqrt[((-(((-1)^(2/3)*b^(1/3))/a^(1/3)) - x)*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) + x))/(((-1)^(1/3)*b^(1/3))/a^(1/3) + ((-1)^(2/3)*b^(1/3))/a^(1/3))^2]*EllipticPi[((-1)^(1/3)*b^(1/3) + (-1)^(2/3)*b^(1/3))/((-1)^(1/3)*b^(1/3) - a^(1/3)*Root[b + c*#1^2 + a*#1^3 & , 3]), ArcSin[Sqrt[((-1)^(1/3)*b^(1/3) - a^(1/3)*x)/(((-1)^(1/3) + (-1)^(2/3))*b^(1/3))]], (-1)^(1/3)]*Root[b + c*#1^2 + a*#1^3 & , 3]^3)/(Sqrt[b + a*x^3]*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) + Root[b + c*#1^2 + a*#1^3 & , 3])*(-Root[b + c*#1^2 + a*#1^3 & , 1] + Root[b + c*#1^2 + a*#1^3 & , 3])*(-Root[b + c*#1^2 + a*#1^3 & , 2] + Root[b + c*#1^2 + a*#1^3 & , 3]))","C",0
278,1,74,26,0.2268662,"\int \frac{1+x^2}{\left(-1+x^2\right) \left(2+x^2\right) \sqrt{-3+x^4}} \, dx","Integrate[(1 + x^2)/((-1 + x^2)*(2 + x^2)*Sqrt[-3 + x^4]),x]","\frac{\sqrt{3-x^4} \left(\Pi \left(-\frac{\sqrt{3}}{2};\left.\sin ^{-1}\left(\frac{x}{\sqrt[4]{3}}\right)\right|-1\right)+4 i \Pi \left(-\sqrt{3};\left.i \sinh ^{-1}\left(\frac{x}{\sqrt[4]{3}}\right)\right|-1\right)\right)}{6 \sqrt[4]{3} \sqrt{x^4-3}}","\frac{\tan ^{-1}\left(\frac{x \sqrt{x^4-3}}{\sqrt{2}}\right)}{3 \sqrt{2}}",1,"(Sqrt[3 - x^4]*((4*I)*EllipticPi[-Sqrt[3], I*ArcSinh[x/3^(1/4)], -1] + EllipticPi[-1/2*Sqrt[3], ArcSin[x/3^(1/4)], -1]))/(6*3^(1/4)*Sqrt[-3 + x^4])","C",1
279,1,23,26,0.0087275,"\int \frac{\left(-4+x^4\right) \left(1+x^4\right)^{3/4}}{x^{12}} \, dx","Integrate[((-4 + x^4)*(1 + x^4)^(3/4))/x^12,x]","\frac{\left(28-27 x^4\right) \left(x^4+1\right)^{7/4}}{77 x^{11}}","\frac{\left(x^4+1\right)^{3/4} \left(-27 x^8+x^4+28\right)}{77 x^{11}}",1,"((28 - 27*x^4)*(1 + x^4)^(7/4))/(77*x^11)","A",1
280,1,92,26,0.4165106,"\int \frac{\sqrt{-1+x^4} \left(1+x^4\right)}{x^2 \left(-1+x^2+x^4\right)} \, dx","Integrate[(Sqrt[-1 + x^4]*(1 + x^4))/(x^2*(-1 + x^2 + x^4)),x]","\frac{x^4-\sqrt{1-x^4} x F\left(\left.\sin ^{-1}(x)\right|-1\right)+\sqrt{1-x^4} x \Pi \left(-\frac{2}{1+\sqrt{5}};\left.\sin ^{-1}(x)\right|-1\right)+\sqrt{1-x^4} x \Pi \left(\frac{1}{2} \left(1+\sqrt{5}\right);\left.\sin ^{-1}(x)\right|-1\right)-1}{x \sqrt{x^4-1}}","\frac{\sqrt{x^4-1}}{x}+\tan ^{-1}\left(\frac{x}{\sqrt{x^4-1}}\right)",1,"(-1 + x^4 - x*Sqrt[1 - x^4]*EllipticF[ArcSin[x], -1] + x*Sqrt[1 - x^4]*EllipticPi[-2/(1 + Sqrt[5]), ArcSin[x], -1] + x*Sqrt[1 - x^4]*EllipticPi[(1 + Sqrt[5])/2, ArcSin[x], -1])/(x*Sqrt[-1 + x^4])","C",1
281,1,93,26,0.0579955,"\int \frac{\left(-1+x^4\right) \left(1+x^2+x^4\right)}{x^4 \sqrt{1+x^4}} \, dx","Integrate[((-1 + x^4)*(1 + x^2 + x^4))/(x^4*Sqrt[1 + x^4]),x]","\frac{\, _2F_1\left(-\frac{3}{4},\frac{1}{2};\frac{1}{4};-x^4\right)+x^4 \left(-\, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-x^4\right)+x^2 \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};-x^4\right)+\sqrt{x^4+1}\right)+3 x^2 \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{4};-x^4\right)}{3 x^3}","\frac{\sqrt{x^4+1} \left(x^4+3 x^2+1\right)}{3 x^3}",1,"(Hypergeometric2F1[-3/4, 1/2, 1/4, -x^4] + 3*x^2*Hypergeometric2F1[-1/4, 1/2, 3/4, -x^4] + x^4*(Sqrt[1 + x^4] - Hypergeometric2F1[1/4, 1/2, 5/4, -x^4] + x^2*Hypergeometric2F1[1/2, 3/4, 7/4, -x^4]))/(3*x^3)","C",1
282,1,115,26,0.0749616,"\int \frac{\left(-4+x^3\right) \left(-1+x^3+x^4\right)}{x^6 \left(-1+x^3\right)^{3/4}} \, dx","Integrate[((-4 + x^3)*(-1 + x^3 + x^4))/(x^6*(-1 + x^3)^(3/4)),x]","\frac{\left(1-x^3\right)^{3/4} \left(5 x^3 \left(2 x^3 \, _2F_1\left(\frac{1}{3},\frac{3}{4};\frac{4}{3};x^3\right)+8 x \, _2F_1\left(-\frac{1}{3},\frac{3}{4};\frac{2}{3};x^3\right)+5 \, _2F_1\left(-\frac{2}{3},\frac{3}{4};\frac{1}{3};x^3\right)+x^4 \, _2F_1\left(\frac{2}{3},\frac{3}{4};\frac{5}{3};x^3\right)\right)-8 \, _2F_1\left(-\frac{5}{3},\frac{3}{4};-\frac{2}{3};x^3\right)\right)}{10 x^5 \left(x^3-1\right)^{3/4}}","-\frac{4 \sqrt[4]{x^3-1} \left(5 x^4+x^3-1\right)}{5 x^5}",1,"((1 - x^3)^(3/4)*(-8*Hypergeometric2F1[-5/3, 3/4, -2/3, x^3] + 5*x^3*(5*Hypergeometric2F1[-2/3, 3/4, 1/3, x^3] + 8*x*Hypergeometric2F1[-1/3, 3/4, 2/3, x^3] + 2*x^3*Hypergeometric2F1[1/3, 3/4, 4/3, x^3] + x^4*Hypergeometric2F1[2/3, 3/4, 5/3, x^3])))/(10*x^5*(-1 + x^3)^(3/4))","C",1
283,0,0,26,0.5750394,"\int \frac{1+3 x^4}{\left(-1-a x+x^4\right) \sqrt{-x+x^5}} \, dx","Integrate[(1 + 3*x^4)/((-1 - a*x + x^4)*Sqrt[-x + x^5]),x]","\int \frac{1+3 x^4}{\left(-1-a x+x^4\right) \sqrt{-x+x^5}} \, dx","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{x^5-x}}\right)}{\sqrt{a}}",1,"Integrate[(1 + 3*x^4)/((-1 - a*x + x^4)*Sqrt[-x + x^5]), x]","F",-1
284,0,0,26,0.7513409,"\int \frac{1+3 x^4}{\left(-a-x+a x^4\right) \sqrt{-x+x^5}} \, dx","Integrate[(1 + 3*x^4)/((-a - x + a*x^4)*Sqrt[-x + x^5]),x]","\int \frac{1+3 x^4}{\left(-a-x+a x^4\right) \sqrt{-x+x^5}} \, dx","-\frac{2 \tanh ^{-1}\left(\frac{x}{\sqrt{a} \sqrt{x^5-x}}\right)}{\sqrt{a}}",1,"Integrate[(1 + 3*x^4)/((-a - x + a*x^4)*Sqrt[-x + x^5]), x]","F",-1
285,1,238,26,0.2983952,"\int \frac{\left(4+x^5\right) \left(-1+x^4+x^5\right)}{x^6 \left(-1+x^5\right)^{3/4}} \, dx","Integrate[((4 + x^5)*(-1 + x^4 + x^5))/(x^6*(-1 + x^5)^(3/4)),x]","\frac{1}{20} \left(-64 \sqrt[4]{x^5-1} \, _2F_1\left(\frac{1}{4},2;\frac{5}{4};1-x^5\right)-\frac{80 \left(1-x^5\right)^{3/4} \, _2F_1\left(-\frac{1}{5},\frac{3}{4};\frac{4}{5};x^5\right)}{\left(x^5-1\right)^{3/4} x}+\frac{5 \left(1-x^5\right)^{3/4} x^4 \, _2F_1\left(\frac{3}{4},\frac{4}{5};\frac{9}{5};x^5\right)}{\left(x^5-1\right)^{3/4}}+16 \sqrt[4]{x^5-1}-6 \sqrt{2} \log \left(\sqrt{x^5-1}-\sqrt{2} \sqrt[4]{x^5-1}+1\right)+6 \sqrt{2} \log \left(\sqrt{x^5-1}+\sqrt{2} \sqrt[4]{x^5-1}+1\right)-12 \sqrt{2} \tan ^{-1}\left(1-\sqrt{2} \sqrt[4]{x^5-1}\right)+12 \sqrt{2} \tan ^{-1}\left(\sqrt{2} \sqrt[4]{x^5-1}+1\right)\right)","\frac{4 \sqrt[4]{x^5-1} \left(x^5+5 x^4-1\right)}{5 x^5}",1,"(16*(-1 + x^5)^(1/4) - 12*Sqrt[2]*ArcTan[1 - Sqrt[2]*(-1 + x^5)^(1/4)] + 12*Sqrt[2]*ArcTan[1 + Sqrt[2]*(-1 + x^5)^(1/4)] - (80*(1 - x^5)^(3/4)*Hypergeometric2F1[-1/5, 3/4, 4/5, x^5])/(x*(-1 + x^5)^(3/4)) - 64*(-1 + x^5)^(1/4)*Hypergeometric2F1[1/4, 2, 5/4, 1 - x^5] + (5*x^4*(1 - x^5)^(3/4)*Hypergeometric2F1[3/4, 4/5, 9/5, x^5])/(-1 + x^5)^(3/4) - 6*Sqrt[2]*Log[1 - Sqrt[2]*(-1 + x^5)^(1/4) + Sqrt[-1 + x^5]] + 6*Sqrt[2]*Log[1 + Sqrt[2]*(-1 + x^5)^(1/4) + Sqrt[-1 + x^5]])/20","C",1
286,1,107,26,0.0805536,"\int \frac{\left(-4+x^5\right) \left(1+x^4+x^5\right)}{x^6 \left(1+x^5\right)^{3/4}} \, dx","Integrate[((-4 + x^5)*(1 + x^4 + x^5))/(x^6*(1 + x^5)^(3/4)),x]","-\frac{16}{5} \sqrt[4]{x^5+1} \, _2F_1\left(\frac{1}{4},2;\frac{5}{4};x^5+1\right)+\frac{4 \, _2F_1\left(-\frac{1}{5},\frac{3}{4};\frac{4}{5};-x^5\right)}{x}+\frac{1}{4} x^4 \, _2F_1\left(\frac{3}{4},\frac{4}{5};\frac{9}{5};-x^5\right)+\frac{4}{5} \sqrt[4]{x^5+1}+\frac{6}{5} \left(\tan ^{-1}\left(\sqrt[4]{x^5+1}\right)+\tanh ^{-1}\left(\sqrt[4]{x^5+1}\right)\right)","\frac{4 \sqrt[4]{x^5+1} \left(x^5+5 x^4+1\right)}{5 x^5}",1,"(4*(1 + x^5)^(1/4))/5 + (6*(ArcTan[(1 + x^5)^(1/4)] + ArcTanh[(1 + x^5)^(1/4)]))/5 + (4*Hypergeometric2F1[-1/5, 3/4, 4/5, -x^5])/x - (16*(1 + x^5)^(1/4)*Hypergeometric2F1[1/4, 2, 5/4, 1 + x^5])/5 + (x^4*Hypergeometric2F1[3/4, 4/5, 9/5, -x^5])/4","C",1
287,1,23,26,0.0082925,"\int \frac{\sqrt{-1+x^6}}{x^{16}} \, dx","Integrate[Sqrt[-1 + x^6]/x^16,x]","\frac{\left(x^6-1\right)^{3/2} \left(2 x^6+3\right)}{45 x^{15}}","\frac{\sqrt{x^6-1} \left(2 x^{12}+x^6-3\right)}{45 x^{15}}",1,"((-1 + x^6)^(3/2)*(3 + 2*x^6))/(45*x^15)","A",1
288,0,0,26,0.2674352,"\int \frac{-1-2 x^2+2 x^4}{\left(1+2 x^4\right) \sqrt{1+x^6}} \, dx","Integrate[(-1 - 2*x^2 + 2*x^4)/((1 + 2*x^4)*Sqrt[1 + x^6]),x]","\int \frac{-1-2 x^2+2 x^4}{\left(1+2 x^4\right) \sqrt{1+x^6}} \, dx","-\tan ^{-1}\left(\frac{x \sqrt{x^6+1}}{x^4-x^2+1}\right)",1,"Integrate[(-1 - 2*x^2 + 2*x^4)/((1 + 2*x^4)*Sqrt[1 + x^6]), x]","F",-1
289,0,0,26,0.5023918,"\int \frac{1+4 x^5}{\left(-1-a x+x^5\right) \sqrt{-x+x^6}} \, dx","Integrate[(1 + 4*x^5)/((-1 - a*x + x^5)*Sqrt[-x + x^6]),x]","\int \frac{1+4 x^5}{\left(-1-a x+x^5\right) \sqrt{-x+x^6}} \, dx","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{x^6-x}}\right)}{\sqrt{a}}",1,"Integrate[(1 + 4*x^5)/((-1 - a*x + x^5)*Sqrt[-x + x^6]), x]","F",-1
290,0,0,26,0.5274267,"\int \frac{1+4 x^5}{\left(-a-x+a x^5\right) \sqrt{-x+x^6}} \, dx","Integrate[(1 + 4*x^5)/((-a - x + a*x^5)*Sqrt[-x + x^6]),x]","\int \frac{1+4 x^5}{\left(-a-x+a x^5\right) \sqrt{-x+x^6}} \, dx","-\frac{2 \tanh ^{-1}\left(\frac{x}{\sqrt{a} \sqrt{x^6-x}}\right)}{\sqrt{a}}",1,"Integrate[(1 + 4*x^5)/((-a - x + a*x^5)*Sqrt[-x + x^6]), x]","F",-1
291,1,117,26,0.0654757,"\int \frac{\left(2+x^6\right) \left(-1-x^4+x^6\right)}{x^6 \left(-1+x^6\right)^{3/4}} \, dx","Integrate[((2 + x^6)*(-1 - x^4 + x^6))/(x^6*(-1 + x^6)^(3/4)),x]","\frac{\left(1-x^6\right)^{3/4} \left(14 \, _2F_1\left(-\frac{5}{6},\frac{3}{4};\frac{1}{6};x^6\right)+x^4 \left(-7 x^6 \, _2F_1\left(\frac{3}{4},\frac{5}{6};\frac{11}{6};x^6\right)+70 \, _2F_1\left(-\frac{1}{6},\frac{3}{4};\frac{5}{6};x^6\right)+5 x^8 \, _2F_1\left(\frac{3}{4},\frac{7}{6};\frac{13}{6};x^6\right)+35 x^2 \, _2F_1\left(\frac{1}{6},\frac{3}{4};\frac{7}{6};x^6\right)\right)\right)}{35 x^5 \left(x^6-1\right)^{3/4}}","\frac{2 \sqrt[4]{x^6-1} \left(x^6-5 x^4-1\right)}{5 x^5}",1,"((1 - x^6)^(3/4)*(14*Hypergeometric2F1[-5/6, 3/4, 1/6, x^6] + x^4*(70*Hypergeometric2F1[-1/6, 3/4, 5/6, x^6] + 35*x^2*Hypergeometric2F1[1/6, 3/4, 7/6, x^6] - 7*x^6*Hypergeometric2F1[3/4, 5/6, 11/6, x^6] + 5*x^8*Hypergeometric2F1[3/4, 7/6, 13/6, x^6])))/(35*x^5*(-1 + x^6)^(3/4))","C",1
292,1,105,26,0.0371674,"\int \frac{\left(-2+x^6\right) \left(1-x^4+x^6\right)}{x^6 \left(1+x^6\right)^{3/4}} \, dx","Integrate[((-2 + x^6)*(1 - x^4 + x^6))/(x^6*(1 + x^6)^(3/4)),x]","-x \, _2F_1\left(\frac{1}{6},\frac{3}{4};\frac{7}{6};-x^6\right)-\frac{2 \, _2F_1\left(-\frac{1}{6},\frac{3}{4};\frac{5}{6};-x^6\right)}{x}+\frac{1}{7} x^7 \, _2F_1\left(\frac{3}{4},\frac{7}{6};\frac{13}{6};-x^6\right)-\frac{1}{5} x^5 \, _2F_1\left(\frac{3}{4},\frac{5}{6};\frac{11}{6};-x^6\right)+\frac{2 \, _2F_1\left(-\frac{5}{6},\frac{3}{4};\frac{1}{6};-x^6\right)}{5 x^5}","\frac{2 \sqrt[4]{x^6+1} \left(x^6-5 x^4+1\right)}{5 x^5}",1,"(2*Hypergeometric2F1[-5/6, 3/4, 1/6, -x^6])/(5*x^5) - (2*Hypergeometric2F1[-1/6, 3/4, 5/6, -x^6])/x - x*Hypergeometric2F1[1/6, 3/4, 7/6, -x^6] - (x^5*Hypergeometric2F1[3/4, 5/6, 11/6, -x^6])/5 + (x^7*Hypergeometric2F1[3/4, 7/6, 13/6, -x^6])/7","C",1
293,0,0,26,0.241233,"\int \frac{\sqrt{-1+x^6} \left(1+2 x^6\right)}{x^2 \left(-1+x^2+x^6\right)} \, dx","Integrate[(Sqrt[-1 + x^6]*(1 + 2*x^6))/(x^2*(-1 + x^2 + x^6)),x]","\int \frac{\sqrt{-1+x^6} \left(1+2 x^6\right)}{x^2 \left(-1+x^2+x^6\right)} \, dx","\frac{\sqrt{x^6-1}}{x}+\tan ^{-1}\left(\frac{x}{\sqrt{x^6-1}}\right)",1,"Integrate[(Sqrt[-1 + x^6]*(1 + 2*x^6))/(x^2*(-1 + x^2 + x^6)), x]","F",-1
294,1,26,26,0.1248118,"\int \frac{\left(-1+x^3-x^5-2 x^7\right)^{2/3} \left(1-x^3+x^5+2 x^7\right) \left(-3+2 x^5+8 x^7\right)}{x^9} \, dx","Integrate[((-1 + x^3 - x^5 - 2*x^7)^(2/3)*(1 - x^3 + x^5 + 2*x^7)*(-3 + 2*x^5 + 8*x^7))/x^9,x]","\frac{3 \left(-2 x^7-x^5+x^3-1\right)^{8/3}}{8 x^8}","\frac{3 \left(-2 x^7-x^5+x^3-1\right)^{8/3}}{8 x^8}",1,"(3*(-1 + x^3 - x^5 - 2*x^7)^(8/3))/(8*x^8)","A",1
295,0,0,26,0.3128354,"\int \frac{x^4 \left(9+4 x^5\right)}{\sqrt{x+x^6} \left(-a-a x^5+x^9\right)} \, dx","Integrate[(x^4*(9 + 4*x^5))/(Sqrt[x + x^6]*(-a - a*x^5 + x^9)),x]","\int \frac{x^4 \left(9+4 x^5\right)}{\sqrt{x+x^6} \left(-a-a x^5+x^9\right)} \, dx","-\frac{2 \tanh ^{-1}\left(\frac{x^5}{\sqrt{a} \sqrt{x^6+x}}\right)}{\sqrt{a}}",1,"Integrate[(x^4*(9 + 4*x^5))/(Sqrt[x + x^6]*(-a - a*x^5 + x^9)), x]","F",-1
296,0,0,26,0.2685028,"\int \frac{x^4 \left(9+5 x^4\right)}{\sqrt{x+x^5} \left(-1-x^4+a x^9\right)} \, dx","Integrate[(x^4*(9 + 5*x^4))/(Sqrt[x + x^5]*(-1 - x^4 + a*x^9)),x]","\int \frac{x^4 \left(9+5 x^4\right)}{\sqrt{x+x^5} \left(-1-x^4+a x^9\right)} \, dx","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{x^5+x}}{\sqrt{a} x^5}\right)}{\sqrt{a}}",1,"Integrate[(x^4*(9 + 5*x^4))/(Sqrt[x + x^5]*(-1 - x^4 + a*x^9)), x]","F",-1
297,0,0,26,0.3401441,"\int \frac{x^4 \left(9+4 x^5\right)}{\sqrt{x+x^6} \left(-1-x^5+a x^9\right)} \, dx","Integrate[(x^4*(9 + 4*x^5))/(Sqrt[x + x^6]*(-1 - x^5 + a*x^9)),x]","\int \frac{x^4 \left(9+4 x^5\right)}{\sqrt{x+x^6} \left(-1-x^5+a x^9\right)} \, dx","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{x^6+x}}{\sqrt{a} x^5}\right)}{\sqrt{a}}",1,"Integrate[(x^4*(9 + 4*x^5))/(Sqrt[x + x^6]*(-1 - x^5 + a*x^9)), x]","F",-1
298,1,22,27,0.0112639,"\int x^5 \sqrt{1-2 x^3} \, dx","Integrate[x^5*Sqrt[1 - 2*x^3],x]","-\frac{1}{45} \left(1-2 x^3\right)^{3/2} \left(3 x^3+1\right)","\frac{1}{45} \sqrt{1-2 x^3} \left(6 x^6-x^3-1\right)",1,"-1/45*((1 - 2*x^3)^(3/2)*(1 + 3*x^3))","A",1
299,1,812,27,1.0596815,"\int \frac{2+x}{(-1+x) \sqrt{-1+3 x+x^3}} \, dx","Integrate[(2 + x)/((-1 + x)*Sqrt[-1 + 3*x + x^3]),x]","\frac{2 \sqrt{\frac{-x+\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+6 \text{$\#$1}+3\&,1\right]+1}{\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+6 \text{$\#$1}+3\&,1\right]-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+6 \text{$\#$1}+3\&,3\right]}} \left(\frac{3 \sqrt{-\frac{\left(x-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+6 \text{$\#$1}+3\&,2\right]-1\right) \left(x-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+6 \text{$\#$1}+3\&,3\right]-1\right)}{\left(\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+6 \text{$\#$1}+3\&,2\right]-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+6 \text{$\#$1}+3\&,3\right]\right)^2}} \left(\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+6 \text{$\#$1}+3\&,2\right]-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+6 \text{$\#$1}+3\&,3\right]\right) \Pi \left(1-\frac{\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+6 \text{$\#$1}+3\&,2\right]}{\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+6 \text{$\#$1}+3\&,3\right]};\sin ^{-1}\left(\sqrt{\frac{-x+\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+6 \text{$\#$1}+3\&,3\right]+1}{-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+6 \text{$\#$1}+3\&,2\right]+\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+6 \text{$\#$1}+3\&,3\right]}}\right)|\frac{\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+6 \text{$\#$1}+3\&,2\right]-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+6 \text{$\#$1}+3\&,3\right]}{\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+6 \text{$\#$1}+3\&,1\right]-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+6 \text{$\#$1}+3\&,3\right]}\right)}{\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+6 \text{$\#$1}+3\&,3\right]}+\frac{F\left(\sin ^{-1}\left(\sqrt{\frac{-x+\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+6 \text{$\#$1}+3\&,3\right]+1}{-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+6 \text{$\#$1}+3\&,2\right]+\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+6 \text{$\#$1}+3\&,3\right]}}\right)|\frac{\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+6 \text{$\#$1}+3\&,2\right]-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+6 \text{$\#$1}+3\&,3\right]}{\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+6 \text{$\#$1}+3\&,1\right]-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+6 \text{$\#$1}+3\&,3\right]}\right) \left(x-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+6 \text{$\#$1}+3\&,3\right]-1\right) \sqrt{\frac{-x+\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+6 \text{$\#$1}+3\&,2\right]+1}{\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+6 \text{$\#$1}+3\&,2\right]-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+6 \text{$\#$1}+3\&,3\right]}}}{\sqrt{\frac{-x+\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+6 \text{$\#$1}+3\&,3\right]+1}{-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+6 \text{$\#$1}+3\&,2\right]+\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+6 \text{$\#$1}+3\&,3\right]}}}\right)}{\sqrt{x^3+3 x-1}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{3} x}{\sqrt{x^3+3 x-1}}\right)}{\sqrt{3}}",1,"(2*Sqrt[(1 - x + Root[3 + 6*#1 + 3*#1^2 + #1^3 & , 1, 0])/(Root[3 + 6*#1 + 3*#1^2 + #1^3 & , 1, 0] - Root[3 + 6*#1 + 3*#1^2 + #1^3 & , 3, 0])]*((3*EllipticPi[1 - Root[3 + 6*#1 + 3*#1^2 + #1^3 & , 2, 0]/Root[3 + 6*#1 + 3*#1^2 + #1^3 & , 3, 0], ArcSin[Sqrt[(1 - x + Root[3 + 6*#1 + 3*#1^2 + #1^3 & , 3, 0])/(-Root[3 + 6*#1 + 3*#1^2 + #1^3 & , 2, 0] + Root[3 + 6*#1 + 3*#1^2 + #1^3 & , 3, 0])]], (Root[3 + 6*#1 + 3*#1^2 + #1^3 & , 2, 0] - Root[3 + 6*#1 + 3*#1^2 + #1^3 & , 3, 0])/(Root[3 + 6*#1 + 3*#1^2 + #1^3 & , 1, 0] - Root[3 + 6*#1 + 3*#1^2 + #1^3 & , 3, 0])]*Sqrt[-(((-1 + x - Root[3 + 6*#1 + 3*#1^2 + #1^3 & , 2, 0])*(-1 + x - Root[3 + 6*#1 + 3*#1^2 + #1^3 & , 3, 0]))/(Root[3 + 6*#1 + 3*#1^2 + #1^3 & , 2, 0] - Root[3 + 6*#1 + 3*#1^2 + #1^3 & , 3, 0])^2)]*(Root[3 + 6*#1 + 3*#1^2 + #1^3 & , 2, 0] - Root[3 + 6*#1 + 3*#1^2 + #1^3 & , 3, 0]))/Root[3 + 6*#1 + 3*#1^2 + #1^3 & , 3, 0] + (EllipticF[ArcSin[Sqrt[(1 - x + Root[3 + 6*#1 + 3*#1^2 + #1^3 & , 3, 0])/(-Root[3 + 6*#1 + 3*#1^2 + #1^3 & , 2, 0] + Root[3 + 6*#1 + 3*#1^2 + #1^3 & , 3, 0])]], (Root[3 + 6*#1 + 3*#1^2 + #1^3 & , 2, 0] - Root[3 + 6*#1 + 3*#1^2 + #1^3 & , 3, 0])/(Root[3 + 6*#1 + 3*#1^2 + #1^3 & , 1, 0] - Root[3 + 6*#1 + 3*#1^2 + #1^3 & , 3, 0])]*(-1 + x - Root[3 + 6*#1 + 3*#1^2 + #1^3 & , 3, 0])*Sqrt[(1 - x + Root[3 + 6*#1 + 3*#1^2 + #1^3 & , 2, 0])/(Root[3 + 6*#1 + 3*#1^2 + #1^3 & , 2, 0] - Root[3 + 6*#1 + 3*#1^2 + #1^3 & , 3, 0])])/Sqrt[(1 - x + Root[3 + 6*#1 + 3*#1^2 + #1^3 & , 3, 0])/(-Root[3 + 6*#1 + 3*#1^2 + #1^3 & , 2, 0] + Root[3 + 6*#1 + 3*#1^2 + #1^3 & , 3, 0])]))/Sqrt[-1 + 3*x + x^3]","C",0
300,1,148,27,0.362181,"\int \frac{-1+2 x}{(1+x) \sqrt{-x-x^2+x^3}} \, dx","Integrate[(-1 + 2*x)/((1 + x)*Sqrt[-x - x^2 + x^3]),x]","-\frac{2 i \sqrt{\frac{2}{\sqrt{5}-1}} \sqrt{-\frac{1}{x^2}-\frac{1}{x}+1} x^{3/2} \left(F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{1+\sqrt{5}}}}{\sqrt{x}}\right)|-\frac{3}{2}-\frac{\sqrt{5}}{2}\right)-3 \Pi \left(\frac{1}{2} \left(1+\sqrt{5}\right);i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{1+\sqrt{5}}}}{\sqrt{x}}\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)\right)}{\sqrt{x \left(x^2-x-1\right)}}","2 \tan ^{-1}\left(\frac{\sqrt{x^3-x^2-x}}{2 x+1}\right)",1,"((-2*I)*Sqrt[2/(-1 + Sqrt[5])]*Sqrt[1 - x^(-2) - x^(-1)]*x^(3/2)*(EllipticF[I*ArcSinh[Sqrt[2/(1 + Sqrt[5])]/Sqrt[x]], -3/2 - Sqrt[5]/2] - 3*EllipticPi[(1 + Sqrt[5])/2, I*ArcSinh[Sqrt[2/(1 + Sqrt[5])]/Sqrt[x]], (-3 - Sqrt[5])/2]))/Sqrt[x*(-1 - x + x^2)]","C",0
301,1,27,27,0.014819,"\int \frac{x^5}{\sqrt{b+a x^3}} \, dx","Integrate[x^5/Sqrt[b + a*x^3],x]","\frac{2 \left(a x^3-2 b\right) \sqrt{a x^3+b}}{9 a^2}","\frac{2 \left(a x^3-2 b\right) \sqrt{a x^3+b}}{9 a^2}",1,"(2*(-2*b + a*x^3)*Sqrt[b + a*x^3])/(9*a^2)","A",1
302,1,27,27,0.0126329,"\int \frac{1}{x^4 \sqrt[4]{-x^2+x^4}} \, dx","Integrate[1/(x^4*(-x^2 + x^4)^(1/4)),x]","\frac{2 \left(x^2 \left(x^2-1\right)\right)^{3/4} \left(4 x^2+3\right)}{21 x^5}","\frac{2 \left(4 x^2+3\right) \left(x^4-x^2\right)^{3/4}}{21 x^5}",1,"(2*(x^2*(-1 + x^2))^(3/4)*(3 + 4*x^2))/(21*x^5)","A",1
303,1,27,27,0.0069243,"\int \frac{1}{x \sqrt{b+a x^4}} \, dx","Integrate[1/(x*Sqrt[b + a*x^4]),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a x^4+b}}{\sqrt{b}}\right)}{2 \sqrt{b}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a x^4+b}}{\sqrt{b}}\right)}{2 \sqrt{b}}",1,"-1/2*ArcTanh[Sqrt[b + a*x^4]/Sqrt[b]]/Sqrt[b]","A",1
304,1,27,27,0.0103889,"\int \frac{1}{x^7 \sqrt[3]{-x^2+x^6}} \, dx","Integrate[1/(x^7*(-x^2 + x^6)^(1/3)),x]","\frac{3 \left(x^2 \left(x^4-1\right)\right)^{2/3} \left(3 x^4+2\right)}{40 x^8}","\frac{3 \left(3 x^4+2\right) \left(x^6-x^2\right)^{2/3}}{40 x^8}",1,"(3*(x^2*(-1 + x^4))^(2/3)*(2 + 3*x^4))/(40*x^8)","A",1
305,1,28,28,0.0048078,"\int \frac{\sqrt{-1+x^3}}{x} \, dx","Integrate[Sqrt[-1 + x^3]/x,x]","\frac{2 \sqrt{x^3-1}}{3}-\frac{2}{3} \tan ^{-1}\left(\sqrt{x^3-1}\right)","\frac{2 \sqrt{x^3-1}}{3}-\frac{2}{3} \tan ^{-1}\left(\sqrt{x^3-1}\right)",1,"(2*Sqrt[-1 + x^3])/3 - (2*ArcTan[Sqrt[-1 + x^3]])/3","A",1
306,1,23,28,0.0080377,"\int \frac{\left(-1+x^3\right) \sqrt[3]{1+x^3}}{x^8} \, dx","Integrate[((-1 + x^3)*(1 + x^3)^(1/3))/x^8,x]","\frac{\left(2-5 x^3\right) \left(x^3+1\right)^{4/3}}{14 x^7}","\frac{\sqrt[3]{x^3+1} \left(-5 x^6-3 x^3+2\right)}{14 x^7}",1,"((2 - 5*x^3)*(1 + x^3)^(4/3))/(14*x^7)","A",1
307,1,28,28,0.0045454,"\int \frac{\sqrt{1+x^3}}{x} \, dx","Integrate[Sqrt[1 + x^3]/x,x]","\frac{2 \sqrt{x^3+1}}{3}-\frac{2}{3} \tanh ^{-1}\left(\sqrt{x^3+1}\right)","\frac{2 \sqrt{x^3+1}}{3}-\frac{2}{3} \tanh ^{-1}\left(\sqrt{x^3+1}\right)",1,"(2*Sqrt[1 + x^3])/3 - (2*ArcTanh[Sqrt[1 + x^3]])/3","A",1
308,1,23,28,0.006547,"\int \frac{\sqrt[3]{-1+x^3} \left(1+x^3\right)}{x^8} \, dx","Integrate[((-1 + x^3)^(1/3)*(1 + x^3))/x^8,x]","\frac{\left(x^3-1\right)^{4/3} \left(5 x^3+2\right)}{14 x^7}","\frac{\sqrt[3]{x^3-1} \left(5 x^6-3 x^3-2\right)}{14 x^7}",1,"((-1 + x^3)^(4/3)*(2 + 5*x^3))/(14*x^7)","A",1
309,1,23,28,0.0076808,"\int \frac{\left(-1+x^3\right)^{2/3} \left(2+x^3\right)}{x^9} \, dx","Integrate[((-1 + x^3)^(2/3)*(2 + x^3))/x^9,x]","\frac{\left(x^3-1\right)^{5/3} \left(7 x^3+5\right)}{20 x^8}","\frac{\left(x^3-1\right)^{2/3} \left(7 x^6-2 x^3-5\right)}{20 x^8}",1,"((-1 + x^3)^(5/3)*(5 + 7*x^3))/(20*x^8)","A",1
310,1,21,28,0.0074309,"\int \frac{\left(1+x^3\right)^{2/3} \left(2+x^3\right)}{x^9} \, dx","Integrate[((1 + x^3)^(2/3)*(2 + x^3))/x^9,x]","-\frac{\left(x^3+1\right)^{5/3} \left(x^3+5\right)}{20 x^8}","\frac{\left(x^3+1\right)^{2/3} \left(-x^6-6 x^3-5\right)}{20 x^8}",1,"-1/20*((1 + x^3)^(5/3)*(5 + x^3))/x^8","A",1
311,1,28,28,0.0162427,"\int \frac{1}{x^6 \sqrt[3]{x+x^3}} \, dx","Integrate[1/(x^6*(x + x^3)^(1/3)),x]","-\frac{3 \left(x^3+x\right)^{2/3} \left(9 x^4-6 x^2+5\right)}{80 x^6}","-\frac{3 \left(x^3+x\right)^{2/3} \left(9 x^4-6 x^2+5\right)}{80 x^6}",1,"(-3*(x + x^3)^(2/3)*(5 - 6*x^2 + 9*x^4))/(80*x^6)","A",1
312,1,70,28,0.0269781,"\int \frac{-2-x+2 x^2}{(-1+x) x \sqrt[4]{-x^2+x^3}} \, dx","Integrate[(-2 - x + 2*x^2)/((-1 + x)*x*(-x^2 + x^3)^(1/4)),x]","-\frac{4 \sqrt{x} \left(2 \, _2F_1\left(-\frac{1}{2},-\frac{1}{4};\frac{3}{4};1-x\right)-\, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{4};1-x\right)-2 \, _2F_1\left(-\frac{1}{4},\frac{3}{2};\frac{3}{4};1-x\right)\right)}{\sqrt[4]{(x-1) x^2}}","\frac{4 (2 x-1) \left(x^3-x^2\right)^{3/4}}{(x-1) x^2}",1,"(-4*Sqrt[x]*(2*Hypergeometric2F1[-1/2, -1/4, 3/4, 1 - x] - Hypergeometric2F1[-1/4, 1/2, 3/4, 1 - x] - 2*Hypergeometric2F1[-1/4, 3/2, 3/4, 1 - x]))/((-1 + x)*x^2)^(1/4)","C",1
313,1,1600,28,7.3061494,"\int \frac{2+x}{(-1+x) \sqrt{-x-x^2+x^3}} \, dx","Integrate[(2 + x)/((-1 + x)*Sqrt[-x - x^2 + x^3]),x]","-\frac{2 \sqrt{2} \left(\frac{1}{x}-1\right) x^{3/2} (x+2) \left(\frac{3 \left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right) \sqrt{\frac{i \sqrt{2 \left(1+\sqrt{5}\right)}+\frac{2}{\sqrt{x}}}{-\sqrt{10}+(1+2 i) \sqrt{2}-\frac{2 i \sqrt{1+\sqrt{5}}}{\sqrt{x}}+\frac{2 \sqrt{-1+\sqrt{5}}}{\sqrt{x}}}} \sqrt{\frac{i \sqrt{2 \left(1+\sqrt{5}\right)}-\frac{2}{\sqrt{x}}}{\sqrt{2} \left((-1+2 i)+\sqrt{5}\right)-\frac{2 \left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right)}{\sqrt{x}}}} \sqrt{\frac{\sqrt{2} \left((-1-2 i)+\sqrt{5}\right)+\frac{2 \left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right)}{\sqrt{x}}}{\sqrt{2} \left((-1+2 i)+\sqrt{5}\right)-\frac{2 \left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right)}{\sqrt{x}}}} \left(\left(2+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) F\left(\sin ^{-1}\left(\sqrt{\frac{\left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right) \left(\sqrt{2 \left(-1+\sqrt{5}\right)}+\frac{2}{\sqrt{x}}\right)}{\left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right) \left(\sqrt{2 \left(-1+\sqrt{5}\right)}-\frac{2}{\sqrt{x}}\right)}}\right)|-\frac{3}{5}-\frac{4 i}{5}\right)-2 \sqrt{2 \left(-1+\sqrt{5}\right)} \Pi \left(\frac{\left(-2+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) \left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right)}{\left(2+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) \left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right)};\sin ^{-1}\left(\sqrt{\frac{\left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right) \left(\sqrt{2 \left(-1+\sqrt{5}\right)}+\frac{2}{\sqrt{x}}\right)}{\left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right) \left(\sqrt{2 \left(-1+\sqrt{5}\right)}-\frac{2}{\sqrt{x}}\right)}}\right)|-\frac{3}{5}-\frac{4 i}{5}\right)\right) \left(\sqrt{2 \left(-1+\sqrt{5}\right)}-\frac{2}{\sqrt{x}}\right)^2}{2 \left(-2+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) \left(2+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) \left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right)}-\frac{3 \left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right) \sqrt{\frac{i \sqrt{2 \left(1+\sqrt{5}\right)}+\frac{2}{\sqrt{x}}}{-\sqrt{10}+(1+2 i) \sqrt{2}-\frac{2 i \sqrt{1+\sqrt{5}}}{\sqrt{x}}+\frac{2 \sqrt{-1+\sqrt{5}}}{\sqrt{x}}}} \sqrt{\frac{i \sqrt{2 \left(1+\sqrt{5}\right)}-\frac{2}{\sqrt{x}}}{\sqrt{2} \left((-1+2 i)+\sqrt{5}\right)-\frac{2 \left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right)}{\sqrt{x}}}} \sqrt{\frac{\sqrt{2} \left((-1-2 i)+\sqrt{5}\right)+\frac{2 \left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right)}{\sqrt{x}}}{\sqrt{2} \left((-1+2 i)+\sqrt{5}\right)-\frac{2 \left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right)}{\sqrt{x}}}} \left(\left(-2+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) F\left(\sin ^{-1}\left(\sqrt{\frac{\left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right) \left(\sqrt{2 \left(-1+\sqrt{5}\right)}+\frac{2}{\sqrt{x}}\right)}{\left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right) \left(\sqrt{2 \left(-1+\sqrt{5}\right)}-\frac{2}{\sqrt{x}}\right)}}\right)|-\frac{3}{5}-\frac{4 i}{5}\right)-2 \sqrt{2 \left(-1+\sqrt{5}\right)} \Pi \left(\frac{\left(2+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) \left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right)}{\left(-2+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) \left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right)};\sin ^{-1}\left(\sqrt{\frac{\left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right) \left(\sqrt{2 \left(-1+\sqrt{5}\right)}+\frac{2}{\sqrt{x}}\right)}{\left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right) \left(\sqrt{2 \left(-1+\sqrt{5}\right)}-\frac{2}{\sqrt{x}}\right)}}\right)|-\frac{3}{5}-\frac{4 i}{5}\right)\right) \left(\sqrt{2 \left(-1+\sqrt{5}\right)}-\frac{2}{\sqrt{x}}\right)^2}{2 \left(-2+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) \left(2+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) \left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right)}-\frac{2 i \sqrt{1-\frac{1}{x}-\frac{1}{x^2}} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{1+\sqrt{5}}}}{\sqrt{x}}\right)|-\frac{3}{2}-\frac{\sqrt{5}}{2}\right)}{\sqrt{-1+\sqrt{5}}}\right)}{\left(x+1-\frac{2}{x}\right) \sqrt{x \left(x^2-x-1\right)}}","-2 \tan ^{-1}\left(\frac{\sqrt{x^3-x^2-x}}{(x-2) x}\right)",1,"(-2*Sqrt[2]*(-1 + x^(-1))*x^(3/2)*(2 + x)*(((-2*I)*Sqrt[1 - x^(-2) - x^(-1)]*EllipticF[I*ArcSinh[Sqrt[2/(1 + Sqrt[5])]/Sqrt[x]], -3/2 - Sqrt[5]/2])/Sqrt[-1 + Sqrt[5]] + (3*(Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] - 2/Sqrt[x])^2*Sqrt[(I*Sqrt[2*(1 + Sqrt[5])] + 2/Sqrt[x])/((1 + 2*I)*Sqrt[2] - Sqrt[10] + (2*Sqrt[-1 + Sqrt[5]])/Sqrt[x] - ((2*I)*Sqrt[1 + Sqrt[5]])/Sqrt[x])]*Sqrt[(I*Sqrt[2*(1 + Sqrt[5])] - 2/Sqrt[x])/(Sqrt[2]*((-1 + 2*I) + Sqrt[5]) - (2*(Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]]))/Sqrt[x])]*Sqrt[(Sqrt[2]*((-1 - 2*I) + Sqrt[5]) + (2*(Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]]))/Sqrt[x])/(Sqrt[2]*((-1 + 2*I) + Sqrt[5]) - (2*(Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]]))/Sqrt[x])]*((2 + Sqrt[2*(-1 + Sqrt[5])])*EllipticF[ArcSin[Sqrt[((Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] + 2/Sqrt[x]))/((Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] - 2/Sqrt[x]))]], -3/5 - (4*I)/5] - 2*Sqrt[2*(-1 + Sqrt[5])]*EllipticPi[((-2 + Sqrt[2*(-1 + Sqrt[5])])*(Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]]))/((2 + Sqrt[2*(-1 + Sqrt[5])])*(Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]])), ArcSin[Sqrt[((Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] + 2/Sqrt[x]))/((Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] - 2/Sqrt[x]))]], -3/5 - (4*I)/5]))/(2*(-2 + Sqrt[2*(-1 + Sqrt[5])])*(2 + Sqrt[2*(-1 + Sqrt[5])])*(Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]])) - (3*(Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] - 2/Sqrt[x])^2*Sqrt[(I*Sqrt[2*(1 + Sqrt[5])] + 2/Sqrt[x])/((1 + 2*I)*Sqrt[2] - Sqrt[10] + (2*Sqrt[-1 + Sqrt[5]])/Sqrt[x] - ((2*I)*Sqrt[1 + Sqrt[5]])/Sqrt[x])]*Sqrt[(I*Sqrt[2*(1 + Sqrt[5])] - 2/Sqrt[x])/(Sqrt[2]*((-1 + 2*I) + Sqrt[5]) - (2*(Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]]))/Sqrt[x])]*Sqrt[(Sqrt[2]*((-1 - 2*I) + Sqrt[5]) + (2*(Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]]))/Sqrt[x])/(Sqrt[2]*((-1 + 2*I) + Sqrt[5]) - (2*(Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]]))/Sqrt[x])]*((-2 + Sqrt[2*(-1 + Sqrt[5])])*EllipticF[ArcSin[Sqrt[((Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] + 2/Sqrt[x]))/((Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] - 2/Sqrt[x]))]], -3/5 - (4*I)/5] - 2*Sqrt[2*(-1 + Sqrt[5])]*EllipticPi[((2 + Sqrt[2*(-1 + Sqrt[5])])*(Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]]))/((-2 + Sqrt[2*(-1 + Sqrt[5])])*(Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]])), ArcSin[Sqrt[((Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] + 2/Sqrt[x]))/((Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] - 2/Sqrt[x]))]], -3/5 - (4*I)/5]))/(2*(-2 + Sqrt[2*(-1 + Sqrt[5])])*(2 + Sqrt[2*(-1 + Sqrt[5])])*(Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]]))))/((1 - 2/x + x)*Sqrt[x*(-1 - x + x^2)])","C",0
314,1,124,28,0.0915007,"\int \frac{\left(3+x^2\right) \left(1+x^2+x^3\right)}{x^6 \sqrt[4]{x+x^3}} \, dx","Integrate[((3 + x^2)*(1 + x^2 + x^3))/(x^6*(x + x^3)^(1/4)),x]","-\frac{4 \sqrt[4]{x^2+1} \left(7 x^2 \left(60 \, _2F_1\left(-\frac{13}{8},\frac{1}{4};-\frac{5}{8};-x^2\right)+13 x \left(5 \, _2F_1\left(-\frac{9}{8},\frac{1}{4};-\frac{1}{8};-x^2\right)+3 x \left(\, _2F_1\left(-\frac{5}{8},\frac{1}{4};\frac{3}{8};-x^2\right)+5 x \, _2F_1\left(-\frac{1}{8},\frac{1}{4};\frac{7}{8};-x^2\right)\right)\right)\right)+195 \, _2F_1\left(-\frac{21}{8},\frac{1}{4};-\frac{13}{8};-x^2\right)\right)}{1365 x^5 \sqrt[4]{x^3+x}}","-\frac{4 \left(x^3+x\right)^{3/4} \left(7 x^3+3 x^2+3\right)}{21 x^6}",1,"(-4*(1 + x^2)^(1/4)*(195*Hypergeometric2F1[-21/8, 1/4, -13/8, -x^2] + 7*x^2*(60*Hypergeometric2F1[-13/8, 1/4, -5/8, -x^2] + 13*x*(5*Hypergeometric2F1[-9/8, 1/4, -1/8, -x^2] + 3*x*(Hypergeometric2F1[-5/8, 1/4, 3/8, -x^2] + 5*x*Hypergeometric2F1[-1/8, 1/4, 7/8, -x^2])))))/(1365*x^5*(x + x^3)^(1/4))","C",1
315,1,31,28,0.0082414,"\int \frac{\sqrt[3]{-1+x^3} \left(-1+2 x^3\right)}{x^{11}} \, dx","Integrate[((-1 + x^3)^(1/3)*(-1 + 2*x^3))/x^11,x]","\frac{\sqrt[3]{x^3-1} \left(3 x^9+x^6-6 x^3+2\right)}{20 x^{10}}","\frac{\left(x^3-1\right)^{4/3} \left(3 x^6+4 x^3-2\right)}{20 x^{10}}",1,"((-1 + x^3)^(1/3)*(2 - 6*x^3 + x^6 + 3*x^9))/(20*x^10)","A",1
316,1,23,28,0.0056442,"\int \frac{\sqrt[3]{-1+x^3} \left(-1+2 x^3\right)}{x^8} \, dx","Integrate[((-1 + x^3)^(1/3)*(-1 + 2*x^3))/x^8,x]","\frac{\left(x^3-1\right)^{4/3} \left(11 x^3-4\right)}{28 x^7}","\frac{\sqrt[3]{x^3-1} \left(11 x^6-15 x^3+4\right)}{28 x^7}",1,"((-1 + x^3)^(4/3)*(-4 + 11*x^3))/(28*x^7)","A",1
317,1,125,28,0.0758371,"\int \frac{\left(3+x^2\right) \left(-1-x^2+2 x^3\right)}{x^6 \sqrt[4]{x+x^3}} \, dx","Integrate[((3 + x^2)*(-1 - x^2 + 2*x^3))/(x^6*(x + x^3)^(1/4)),x]","-\frac{4 \sqrt[4]{x^2+1} \left(7 x^2 \left(13 x \left(30 x^2 \, _2F_1\left(-\frac{1}{8},\frac{1}{4};\frac{7}{8};-x^2\right)-3 x \, _2F_1\left(-\frac{5}{8},\frac{1}{4};\frac{3}{8};-x^2\right)+10 \, _2F_1\left(-\frac{9}{8},\frac{1}{4};-\frac{1}{8};-x^2\right)\right)-60 \, _2F_1\left(-\frac{13}{8},\frac{1}{4};-\frac{5}{8};-x^2\right)\right)-195 \, _2F_1\left(-\frac{21}{8},\frac{1}{4};-\frac{13}{8};-x^2\right)\right)}{1365 x^5 \sqrt[4]{x^3+x}}","-\frac{4 \left(x^3+x\right)^{3/4} \left(14 x^3-3 x^2-3\right)}{21 x^6}",1,"(-4*(1 + x^2)^(1/4)*(-195*Hypergeometric2F1[-21/8, 1/4, -13/8, -x^2] + 7*x^2*(-60*Hypergeometric2F1[-13/8, 1/4, -5/8, -x^2] + 13*x*(10*Hypergeometric2F1[-9/8, 1/4, -1/8, -x^2] - 3*x*Hypergeometric2F1[-5/8, 1/4, 3/8, -x^2] + 30*x^2*Hypergeometric2F1[-1/8, 1/4, 7/8, -x^2]))))/(1365*x^5*(x + x^3)^(1/4))","C",1
318,1,2752,28,6.2493168,"\int \frac{2 b+a x^3}{\sqrt{-b+a x^3} \left(-b+x^2+a x^3\right)} \, dx","Integrate[(2*b + a*x^3)/(Sqrt[-b + a*x^3]*(-b + x^2 + a*x^3)),x]","\text{Result too large to show}","2 \tan ^{-1}\left(\frac{x \sqrt{a x^3-b}}{b-a x^3}\right)",1,"(2*Sqrt[(-(b^(1/3)/a^(1/3)) + x)/(-(b^(1/3)/a^(1/3)) - ((-1)^(1/3)*b^(1/3))/a^(1/3))]*(((-1)^(1/3)*b^(1/3))/a^(1/3) + x)*Sqrt[(-(((-1)^(2/3)*b^(1/3))/a^(1/3)) + x)/(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) - ((-1)^(2/3)*b^(1/3))/a^(1/3))]*EllipticF[ArcSin[Sqrt[((-1)^(1/3)*b^(1/3) + a^(1/3)*x)/(((-1)^(1/3) + (-1)^(2/3))*b^(1/3))]], (-1)^(1/3)])/(Sqrt[(((-1)^(1/3)*b^(1/3))/a^(1/3) + x)/(((-1)^(1/3)*b^(1/3))/a^(1/3) + ((-1)^(2/3)*b^(1/3))/a^(1/3))]*Sqrt[-b + a*x^3]) + (4*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) - ((-1)^(2/3)*b^(1/3))/a^(1/3))*b*Sqrt[(-(b^(1/3)/a^(1/3)) + x)/(-(b^(1/3)/a^(1/3)) - ((-1)^(1/3)*b^(1/3))/a^(1/3))]*Sqrt[((((-1)^(2/3)*b^(1/3))/a^(1/3) - x)*(((-1)^(1/3)*b^(1/3))/a^(1/3) + x))/(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) - ((-1)^(2/3)*b^(1/3))/a^(1/3))^2]*EllipticPi[((-1)^(1/3)*b^(1/3) + (-1)^(2/3)*b^(1/3))/((-1)^(1/3)*b^(1/3) + a^(1/3)*Root[-b + #1^2 + a*#1^3 & , 1]), ArcSin[Sqrt[((-1)^(1/3)*b^(1/3) + a^(1/3)*x)/(((-1)^(1/3) + (-1)^(2/3))*b^(1/3))]], (-1)^(1/3)])/(a*Sqrt[-b + a*x^3]*(((-1)^(1/3)*b^(1/3))/a^(1/3) + Root[-b + #1^2 + a*#1^3 & , 1])*(Root[-b + #1^2 + a*#1^3 & , 1] - Root[-b + #1^2 + a*#1^3 & , 2])*(Root[-b + #1^2 + a*#1^3 & , 1] - Root[-b + #1^2 + a*#1^3 & , 3])) + (2*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) - ((-1)^(2/3)*b^(1/3))/a^(1/3))*Sqrt[(-(b^(1/3)/a^(1/3)) + x)/(-(b^(1/3)/a^(1/3)) - ((-1)^(1/3)*b^(1/3))/a^(1/3))]*Sqrt[((((-1)^(2/3)*b^(1/3))/a^(1/3) - x)*(((-1)^(1/3)*b^(1/3))/a^(1/3) + x))/(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) - ((-1)^(2/3)*b^(1/3))/a^(1/3))^2]*EllipticPi[((-1)^(1/3)*b^(1/3) + (-1)^(2/3)*b^(1/3))/((-1)^(1/3)*b^(1/3) + a^(1/3)*Root[-b + #1^2 + a*#1^3 & , 1]), ArcSin[Sqrt[((-1)^(1/3)*b^(1/3) + a^(1/3)*x)/(((-1)^(1/3) + (-1)^(2/3))*b^(1/3))]], (-1)^(1/3)]*Root[-b + #1^2 + a*#1^3 & , 1]^3)/(Sqrt[-b + a*x^3]*(((-1)^(1/3)*b^(1/3))/a^(1/3) + Root[-b + #1^2 + a*#1^3 & , 1])*(Root[-b + #1^2 + a*#1^3 & , 1] - Root[-b + #1^2 + a*#1^3 & , 2])*(Root[-b + #1^2 + a*#1^3 & , 1] - Root[-b + #1^2 + a*#1^3 & , 3])) + (4*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) - ((-1)^(2/3)*b^(1/3))/a^(1/3))*b*Sqrt[(-(b^(1/3)/a^(1/3)) + x)/(-(b^(1/3)/a^(1/3)) - ((-1)^(1/3)*b^(1/3))/a^(1/3))]*Sqrt[((((-1)^(2/3)*b^(1/3))/a^(1/3) - x)*(((-1)^(1/3)*b^(1/3))/a^(1/3) + x))/(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) - ((-1)^(2/3)*b^(1/3))/a^(1/3))^2]*EllipticPi[((-1)^(1/3)*b^(1/3) + (-1)^(2/3)*b^(1/3))/((-1)^(1/3)*b^(1/3) + a^(1/3)*Root[-b + #1^2 + a*#1^3 & , 2]), ArcSin[Sqrt[((-1)^(1/3)*b^(1/3) + a^(1/3)*x)/(((-1)^(1/3) + (-1)^(2/3))*b^(1/3))]], (-1)^(1/3)])/(a*Sqrt[-b + a*x^3]*(((-1)^(1/3)*b^(1/3))/a^(1/3) + Root[-b + #1^2 + a*#1^3 & , 2])*(-Root[-b + #1^2 + a*#1^3 & , 1] + Root[-b + #1^2 + a*#1^3 & , 2])*(Root[-b + #1^2 + a*#1^3 & , 2] - Root[-b + #1^2 + a*#1^3 & , 3])) + (2*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) - ((-1)^(2/3)*b^(1/3))/a^(1/3))*Sqrt[(-(b^(1/3)/a^(1/3)) + x)/(-(b^(1/3)/a^(1/3)) - ((-1)^(1/3)*b^(1/3))/a^(1/3))]*Sqrt[((((-1)^(2/3)*b^(1/3))/a^(1/3) - x)*(((-1)^(1/3)*b^(1/3))/a^(1/3) + x))/(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) - ((-1)^(2/3)*b^(1/3))/a^(1/3))^2]*EllipticPi[((-1)^(1/3)*b^(1/3) + (-1)^(2/3)*b^(1/3))/((-1)^(1/3)*b^(1/3) + a^(1/3)*Root[-b + #1^2 + a*#1^3 & , 2]), ArcSin[Sqrt[((-1)^(1/3)*b^(1/3) + a^(1/3)*x)/(((-1)^(1/3) + (-1)^(2/3))*b^(1/3))]], (-1)^(1/3)]*Root[-b + #1^2 + a*#1^3 & , 2]^3)/(Sqrt[-b + a*x^3]*(((-1)^(1/3)*b^(1/3))/a^(1/3) + Root[-b + #1^2 + a*#1^3 & , 2])*(-Root[-b + #1^2 + a*#1^3 & , 1] + Root[-b + #1^2 + a*#1^3 & , 2])*(Root[-b + #1^2 + a*#1^3 & , 2] - Root[-b + #1^2 + a*#1^3 & , 3])) + (4*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) - ((-1)^(2/3)*b^(1/3))/a^(1/3))*b*Sqrt[(-(b^(1/3)/a^(1/3)) + x)/(-(b^(1/3)/a^(1/3)) - ((-1)^(1/3)*b^(1/3))/a^(1/3))]*Sqrt[((((-1)^(2/3)*b^(1/3))/a^(1/3) - x)*(((-1)^(1/3)*b^(1/3))/a^(1/3) + x))/(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) - ((-1)^(2/3)*b^(1/3))/a^(1/3))^2]*EllipticPi[((-1)^(1/3)*b^(1/3) + (-1)^(2/3)*b^(1/3))/((-1)^(1/3)*b^(1/3) + a^(1/3)*Root[-b + #1^2 + a*#1^3 & , 3]), ArcSin[Sqrt[((-1)^(1/3)*b^(1/3) + a^(1/3)*x)/(((-1)^(1/3) + (-1)^(2/3))*b^(1/3))]], (-1)^(1/3)])/(a*Sqrt[-b + a*x^3]*(((-1)^(1/3)*b^(1/3))/a^(1/3) + Root[-b + #1^2 + a*#1^3 & , 3])*(-Root[-b + #1^2 + a*#1^3 & , 1] + Root[-b + #1^2 + a*#1^3 & , 3])*(-Root[-b + #1^2 + a*#1^3 & , 2] + Root[-b + #1^2 + a*#1^3 & , 3])) + (2*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) - ((-1)^(2/3)*b^(1/3))/a^(1/3))*Sqrt[(-(b^(1/3)/a^(1/3)) + x)/(-(b^(1/3)/a^(1/3)) - ((-1)^(1/3)*b^(1/3))/a^(1/3))]*Sqrt[((((-1)^(2/3)*b^(1/3))/a^(1/3) - x)*(((-1)^(1/3)*b^(1/3))/a^(1/3) + x))/(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) - ((-1)^(2/3)*b^(1/3))/a^(1/3))^2]*EllipticPi[((-1)^(1/3)*b^(1/3) + (-1)^(2/3)*b^(1/3))/((-1)^(1/3)*b^(1/3) + a^(1/3)*Root[-b + #1^2 + a*#1^3 & , 3]), ArcSin[Sqrt[((-1)^(1/3)*b^(1/3) + a^(1/3)*x)/(((-1)^(1/3) + (-1)^(2/3))*b^(1/3))]], (-1)^(1/3)]*Root[-b + #1^2 + a*#1^3 & , 3]^3)/(Sqrt[-b + a*x^3]*(((-1)^(1/3)*b^(1/3))/a^(1/3) + Root[-b + #1^2 + a*#1^3 & , 3])*(-Root[-b + #1^2 + a*#1^3 & , 1] + Root[-b + #1^2 + a*#1^3 & , 3])*(-Root[-b + #1^2 + a*#1^3 & , 2] + Root[-b + #1^2 + a*#1^3 & , 3]))","C",0
319,1,23,28,0.00786,"\int \frac{\left(-4+x^4\right) \left(-1+x^4\right)^{3/4}}{x^{12}} \, dx","Integrate[((-4 + x^4)*(-1 + x^4)^(3/4))/x^12,x]","-\frac{\left(x^4-1\right)^{7/4} \left(5 x^4+28\right)}{77 x^{11}}","\frac{\left(x^4-1\right)^{3/4} \left(-5 x^8-23 x^4+28\right)}{77 x^{11}}",1,"-1/77*((-1 + x^4)^(7/4)*(28 + 5*x^4))/x^11","A",1
320,1,28,28,0.0043919,"\int \frac{\sqrt{1+x^4}}{x} \, dx","Integrate[Sqrt[1 + x^4]/x,x]","\frac{\sqrt{x^4+1}}{2}-\frac{1}{2} \tanh ^{-1}\left(\sqrt{x^4+1}\right)","\frac{\sqrt{x^4+1}}{2}-\frac{1}{2} \tanh ^{-1}\left(\sqrt{x^4+1}\right)",1,"Sqrt[1 + x^4]/2 - ArcTanh[Sqrt[1 + x^4]]/2","A",1
321,1,25,28,0.0082072,"\int \frac{\sqrt[4]{-x+x^4}}{x^8} \, dx","Integrate[(-x + x^4)^(1/4)/x^8,x]","\frac{4 \left(x \left(x^3-1\right)\right)^{5/4} \left(4 x^3+5\right)}{135 x^8}","\frac{4 \sqrt[4]{x^4-x} \left(4 x^6+x^3-5\right)}{135 x^7}",1,"(4*(x*(-1 + x^3))^(5/4)*(5 + 4*x^3))/(135*x^8)","A",1
322,1,28,28,0.0059641,"\int \frac{\sqrt[4]{x+x^4}}{x^8} \, dx","Integrate[(x + x^4)^(1/4)/x^8,x]","-\frac{4 \left(5-4 x^3\right) \left(x^3+1\right) \sqrt[4]{x^4+x}}{135 x^7}","\frac{4 \sqrt[4]{x^4+x} \left(4 x^6-x^3-5\right)}{135 x^7}",1,"(-4*(5 - 4*x^3)*(1 + x^3)*(x + x^4)^(1/4))/(135*x^7)","A",1
323,1,1430,28,4.2400762,"\int \frac{2+x^2}{\left(-1+x^2\right) \sqrt{-1-x^2+x^4}} \, dx","Integrate[(2 + x^2)/((-1 + x^2)*Sqrt[-1 - x^2 + x^4]),x]","-\frac{i \left(3 \left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right) \sqrt{\frac{i \left(2 x+\sqrt{2 \left(1+\sqrt{5}\right)}\right)}{-2 \sqrt{1+\sqrt{5}} x+2 i \sqrt{-1+\sqrt{5}} x+\sqrt{10}-(1-2 i) \sqrt{2}}} \sqrt{-\frac{i \left(\sqrt{2 \left(1+\sqrt{5}\right)}-2 x\right)}{2 \left(i \sqrt{-1+\sqrt{5}}+\sqrt{1+\sqrt{5}}\right) x+\sqrt{2} \left((-1-2 i)+\sqrt{5}\right)}} \sqrt{\frac{2 \left(-i \sqrt{-1+\sqrt{5}}+\sqrt{1+\sqrt{5}}\right) x+\sqrt{2} \left((-1+2 i)+\sqrt{5}\right)}{2 \left(i \sqrt{-1+\sqrt{5}}+\sqrt{1+\sqrt{5}}\right) x+\sqrt{2} \left((-1-2 i)+\sqrt{5}\right)}} \left(\left(2-i \sqrt{2 \left(-1+\sqrt{5}\right)}\right) F\left(\sin ^{-1}\left(\sqrt{\frac{2 \left(-i \sqrt{-1+\sqrt{5}}+\sqrt{1+\sqrt{5}}\right) x+\sqrt{2} \left((-1+2 i)+\sqrt{5}\right)}{2 \left(i \sqrt{-1+\sqrt{5}}+\sqrt{1+\sqrt{5}}\right) x+\sqrt{2} \left((-1-2 i)+\sqrt{5}\right)}}\right)|-\frac{3}{5}+\frac{4 i}{5}\right)+2 i \sqrt{2 \left(-1+\sqrt{5}\right)} \Pi \left(\frac{\left(-2 i+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) \left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right)}{\left(2 i+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) \left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right)};\sin ^{-1}\left(\sqrt{\frac{2 \left(-i \sqrt{-1+\sqrt{5}}+\sqrt{1+\sqrt{5}}\right) x+\sqrt{2} \left((-1+2 i)+\sqrt{5}\right)}{2 \left(i \sqrt{-1+\sqrt{5}}+\sqrt{1+\sqrt{5}}\right) x+\sqrt{2} \left((-1-2 i)+\sqrt{5}\right)}}\right)|-\frac{3}{5}+\frac{4 i}{5}\right)\right) \left(2 i x+\sqrt{2 \left(-1+\sqrt{5}\right)}\right)^2+3 \left(i \sqrt{-1+\sqrt{5}}+\sqrt{1+\sqrt{5}}\right) \sqrt{\frac{i \left(2 x+\sqrt{2 \left(1+\sqrt{5}\right)}\right)}{-2 \sqrt{1+\sqrt{5}} x+2 i \sqrt{-1+\sqrt{5}} x+\sqrt{10}-(1-2 i) \sqrt{2}}} \sqrt{-\frac{i \left(\sqrt{2 \left(1+\sqrt{5}\right)}-2 x\right)}{2 \left(i \sqrt{-1+\sqrt{5}}+\sqrt{1+\sqrt{5}}\right) x+\sqrt{2} \left((-1-2 i)+\sqrt{5}\right)}} \sqrt{\frac{2 \left(-i \sqrt{-1+\sqrt{5}}+\sqrt{1+\sqrt{5}}\right) x+\sqrt{2} \left((-1+2 i)+\sqrt{5}\right)}{2 \left(i \sqrt{-1+\sqrt{5}}+\sqrt{1+\sqrt{5}}\right) x+\sqrt{2} \left((-1-2 i)+\sqrt{5}\right)}} \left(\left(-2 i+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) F\left(\sin ^{-1}\left(\sqrt{\frac{2 \left(-i \sqrt{-1+\sqrt{5}}+\sqrt{1+\sqrt{5}}\right) x+\sqrt{2} \left((-1+2 i)+\sqrt{5}\right)}{2 \left(i \sqrt{-1+\sqrt{5}}+\sqrt{1+\sqrt{5}}\right) x+\sqrt{2} \left((-1-2 i)+\sqrt{5}\right)}}\right)|-\frac{3}{5}+\frac{4 i}{5}\right)-2 \sqrt{2 \left(-1+\sqrt{5}\right)} \Pi \left(\frac{\left(2 i+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) \left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right)}{\left(-2 i+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) \left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right)};\sin ^{-1}\left(\sqrt{\frac{2 \left(-i \sqrt{-1+\sqrt{5}}+\sqrt{1+\sqrt{5}}\right) x+\sqrt{2} \left((-1+2 i)+\sqrt{5}\right)}{2 \left(i \sqrt{-1+\sqrt{5}}+\sqrt{1+\sqrt{5}}\right) x+\sqrt{2} \left((-1-2 i)+\sqrt{5}\right)}}\right)|-\frac{3}{5}+\frac{4 i}{5}\right)\right) \left(2 i x+\sqrt{2 \left(-1+\sqrt{5}\right)}\right)^2+4 \sqrt{1+\sqrt{5}} \left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right) \sqrt{-x^4+x^2+1} F\left(i \sinh ^{-1}\left(\sqrt{\frac{2}{-1+\sqrt{5}}} x\right)|\frac{1}{2} \left(-3+\sqrt{5}\right)\right)\right)}{2 \sqrt{2} \left(1+\sqrt{5}\right) \left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right) \sqrt{x^4-x^2-1}}","-\tan ^{-1}\left(\frac{\sqrt{x^4-x^2-1}}{x \left(x^2-2\right)}\right)",1,"((-1/2*I)*(4*Sqrt[1 + Sqrt[5]]*(Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])*Sqrt[1 + x^2 - x^4]*EllipticF[I*ArcSinh[Sqrt[2/(-1 + Sqrt[5])]*x], (-3 + Sqrt[5])/2] + 3*(Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] + (2*I)*x)^2*Sqrt[(I*(Sqrt[2*(1 + Sqrt[5])] + 2*x))/((-1 + 2*I)*Sqrt[2] + Sqrt[10] + (2*I)*Sqrt[-1 + Sqrt[5]]*x - 2*Sqrt[1 + Sqrt[5]]*x)]*Sqrt[((-I)*(Sqrt[2*(1 + Sqrt[5])] - 2*x))/(Sqrt[2]*((-1 - 2*I) + Sqrt[5]) + 2*(I*Sqrt[-1 + Sqrt[5]] + Sqrt[1 + Sqrt[5]])*x)]*Sqrt[(Sqrt[2]*((-1 + 2*I) + Sqrt[5]) + 2*((-I)*Sqrt[-1 + Sqrt[5]] + Sqrt[1 + Sqrt[5]])*x)/(Sqrt[2]*((-1 - 2*I) + Sqrt[5]) + 2*(I*Sqrt[-1 + Sqrt[5]] + Sqrt[1 + Sqrt[5]])*x)]*((2 - I*Sqrt[2*(-1 + Sqrt[5])])*EllipticF[ArcSin[Sqrt[(Sqrt[2]*((-1 + 2*I) + Sqrt[5]) + 2*((-I)*Sqrt[-1 + Sqrt[5]] + Sqrt[1 + Sqrt[5]])*x)/(Sqrt[2]*((-1 - 2*I) + Sqrt[5]) + 2*(I*Sqrt[-1 + Sqrt[5]] + Sqrt[1 + Sqrt[5]])*x)]], -3/5 + (4*I)/5] + (2*I)*Sqrt[2*(-1 + Sqrt[5])]*EllipticPi[((-2*I + Sqrt[2*(-1 + Sqrt[5])])*(Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]]))/((2*I + Sqrt[2*(-1 + Sqrt[5])])*(Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])), ArcSin[Sqrt[(Sqrt[2]*((-1 + 2*I) + Sqrt[5]) + 2*((-I)*Sqrt[-1 + Sqrt[5]] + Sqrt[1 + Sqrt[5]])*x)/(Sqrt[2]*((-1 - 2*I) + Sqrt[5]) + 2*(I*Sqrt[-1 + Sqrt[5]] + Sqrt[1 + Sqrt[5]])*x)]], -3/5 + (4*I)/5]) + 3*(I*Sqrt[-1 + Sqrt[5]] + Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] + (2*I)*x)^2*Sqrt[(I*(Sqrt[2*(1 + Sqrt[5])] + 2*x))/((-1 + 2*I)*Sqrt[2] + Sqrt[10] + (2*I)*Sqrt[-1 + Sqrt[5]]*x - 2*Sqrt[1 + Sqrt[5]]*x)]*Sqrt[((-I)*(Sqrt[2*(1 + Sqrt[5])] - 2*x))/(Sqrt[2]*((-1 - 2*I) + Sqrt[5]) + 2*(I*Sqrt[-1 + Sqrt[5]] + Sqrt[1 + Sqrt[5]])*x)]*Sqrt[(Sqrt[2]*((-1 + 2*I) + Sqrt[5]) + 2*((-I)*Sqrt[-1 + Sqrt[5]] + Sqrt[1 + Sqrt[5]])*x)/(Sqrt[2]*((-1 - 2*I) + Sqrt[5]) + 2*(I*Sqrt[-1 + Sqrt[5]] + Sqrt[1 + Sqrt[5]])*x)]*((-2*I + Sqrt[2*(-1 + Sqrt[5])])*EllipticF[ArcSin[Sqrt[(Sqrt[2]*((-1 + 2*I) + Sqrt[5]) + 2*((-I)*Sqrt[-1 + Sqrt[5]] + Sqrt[1 + Sqrt[5]])*x)/(Sqrt[2]*((-1 - 2*I) + Sqrt[5]) + 2*(I*Sqrt[-1 + Sqrt[5]] + Sqrt[1 + Sqrt[5]])*x)]], -3/5 + (4*I)/5] - 2*Sqrt[2*(-1 + Sqrt[5])]*EllipticPi[((2*I + Sqrt[2*(-1 + Sqrt[5])])*(Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]]))/((-2*I + Sqrt[2*(-1 + Sqrt[5])])*(Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])), ArcSin[Sqrt[(Sqrt[2]*((-1 + 2*I) + Sqrt[5]) + 2*((-I)*Sqrt[-1 + Sqrt[5]] + Sqrt[1 + Sqrt[5]])*x)/(Sqrt[2]*((-1 - 2*I) + Sqrt[5]) + 2*(I*Sqrt[-1 + Sqrt[5]] + Sqrt[1 + Sqrt[5]])*x)]], -3/5 + (4*I)/5])))/(Sqrt[2]*(1 + Sqrt[5])*(Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])*Sqrt[-1 - x^2 + x^4])","C",0
324,1,105,28,0.049585,"\int \frac{\left(4+x^3\right) \left(-1-x^3+x^4\right)}{x^6 \left(1+x^3\right)^{3/4}} \, dx","Integrate[((4 + x^3)*(-1 - x^3 + x^4))/(x^6*(1 + x^3)^(3/4)),x]","-x \, _2F_1\left(\frac{1}{3},\frac{3}{4};\frac{4}{3};-x^3\right)-\frac{4 \, _2F_1\left(-\frac{1}{3},\frac{3}{4};\frac{2}{3};-x^3\right)}{x}+\frac{4 \, _2F_1\left(-\frac{5}{3},\frac{3}{4};-\frac{2}{3};-x^3\right)}{5 x^5}+\frac{1}{2} x^2 \, _2F_1\left(\frac{2}{3},\frac{3}{4};\frac{5}{3};-x^3\right)+\frac{5 \, _2F_1\left(-\frac{2}{3},\frac{3}{4};\frac{1}{3};-x^3\right)}{2 x^2}","-\frac{4 \sqrt[4]{x^3+1} \left(5 x^4-x^3-1\right)}{5 x^5}",1,"(4*Hypergeometric2F1[-5/3, 3/4, -2/3, -x^3])/(5*x^5) + (5*Hypergeometric2F1[-2/3, 3/4, 1/3, -x^3])/(2*x^2) - (4*Hypergeometric2F1[-1/3, 3/4, 2/3, -x^3])/x - x*Hypergeometric2F1[1/3, 3/4, 4/3, -x^3] + (x^2*Hypergeometric2F1[2/3, 3/4, 5/3, -x^3])/2","C",1
325,1,118,28,0.1213942,"\int \frac{\left(4+x^3\right) \left(-1-x^3+x^4\right)}{x^8 \sqrt[4]{1+x^3}} \, dx","Integrate[((4 + x^3)*(-1 - x^3 + x^4))/(x^8*(1 + x^3)^(1/4)),x]","\frac{\, _2F_1\left(-\frac{1}{3},\frac{1}{4};\frac{2}{3};-x^3\right)}{x}+\frac{16}{9} \left(x^3+1\right)^{3/4} \, _2F_1\left(\frac{3}{4},2;\frac{7}{4};x^3+1\right)+\frac{4 \, _2F_1\left(-\frac{7}{3},\frac{1}{4};-\frac{4}{3};-x^3\right)}{7 x^7}+\frac{5 \, _2F_1\left(-\frac{4}{3},\frac{1}{4};-\frac{1}{3};-x^3\right)}{4 x^4}+\frac{2}{3} \tan ^{-1}\left(\sqrt[4]{x^3+1}\right)-\frac{2}{3} \tanh ^{-1}\left(\sqrt[4]{x^3+1}\right)","-\frac{4 \left(x^3+1\right)^{3/4} \left(7 x^4-3 x^3-3\right)}{21 x^7}",1,"(2*ArcTan[(1 + x^3)^(1/4)])/3 - (2*ArcTanh[(1 + x^3)^(1/4)])/3 + (4*Hypergeometric2F1[-7/3, 1/4, -4/3, -x^3])/(7*x^7) + (5*Hypergeometric2F1[-4/3, 1/4, -1/3, -x^3])/(4*x^4) + Hypergeometric2F1[-1/3, 1/4, 2/3, -x^3]/x + (16*(1 + x^3)^(3/4)*Hypergeometric2F1[3/4, 2, 7/4, 1 + x^3])/9","C",1
326,1,145,28,0.1050427,"\int \frac{\left(-4+x^3\right) \left(1-x^3+x^4\right)}{x^8 \sqrt[4]{-1+x^3}} \, dx","Integrate[((-4 + x^3)*(1 - x^3 + x^4))/(x^8*(-1 + x^3)^(1/4)),x]","\frac{-315 \sqrt[4]{1-x^3} x^3 \, _2F_1\left(-\frac{4}{3},\frac{1}{4};-\frac{1}{3};x^3\right)+144 \sqrt[4]{1-x^3} \, _2F_1\left(-\frac{7}{3},\frac{1}{4};-\frac{4}{3};x^3\right)+28 x^6 \left(9 \sqrt[4]{1-x^3} \, _2F_1\left(-\frac{1}{3},\frac{1}{4};\frac{2}{3};x^3\right)+4 x \left(x^3-1\right) \left(\, _2F_1\left(\frac{3}{4},1;\frac{7}{4};1-x^3\right)-4 \, _2F_1\left(\frac{3}{4},2;\frac{7}{4};1-x^3\right)\right)\right)}{252 x^7 \sqrt[4]{x^3-1}}","-\frac{4 \left(x^3-1\right)^{3/4} \left(7 x^4-3 x^3+3\right)}{21 x^7}",1,"(144*(1 - x^3)^(1/4)*Hypergeometric2F1[-7/3, 1/4, -4/3, x^3] - 315*x^3*(1 - x^3)^(1/4)*Hypergeometric2F1[-4/3, 1/4, -1/3, x^3] + 28*x^6*(9*(1 - x^3)^(1/4)*Hypergeometric2F1[-1/3, 1/4, 2/3, x^3] + 4*x*(-1 + x^3)*(Hypergeometric2F1[3/4, 1, 7/4, 1 - x^3] - 4*Hypergeometric2F1[3/4, 2, 7/4, 1 - x^3])))/(252*x^7*(-1 + x^3)^(1/4))","C",1
327,1,31,28,0.0075909,"\int \frac{x}{\sqrt{x^3+x^4}} \, dx","Integrate[x/Sqrt[x^3 + x^4],x]","\frac{2 x^{3/2} \sqrt{x+1} \sinh ^{-1}\left(\sqrt{x}\right)}{\sqrt{x^3 (x+1)}}","\log (x)-\log \left(-2 x^2+2 \sqrt{x^4+x^3}-x\right)",1,"(2*x^(3/2)*Sqrt[1 + x]*ArcSinh[Sqrt[x]])/Sqrt[x^3*(1 + x)]","A",1
328,1,20,28,0.0121633,"\int \frac{1}{x (1+x) \sqrt[4]{x^3+x^4}} \, dx","Integrate[1/(x*(1 + x)*(x^3 + x^4)^(1/4)),x]","-\frac{4 (4 x+1)}{3 \sqrt[4]{x^3 (x+1)}}","-\frac{4 (4 x+1) \left(x^4+x^3\right)^{3/4}}{3 x^3 (x+1)}",1,"(-4*(1 + 4*x))/(3*(x^3*(1 + x))^(1/4))","A",1
329,1,102,28,0.0393138,"\int \frac{\left(4+x^3\right) \left(-1-x^3+2 x^4\right)}{x^6 \left(1+x^3\right)^{3/4}} \, dx","Integrate[((4 + x^3)*(-1 - x^3 + 2*x^4))/(x^6*(1 + x^3)^(3/4)),x]","-x \, _2F_1\left(\frac{1}{3},\frac{3}{4};\frac{4}{3};-x^3\right)-\frac{8 \, _2F_1\left(-\frac{1}{3},\frac{3}{4};\frac{2}{3};-x^3\right)}{x}+\frac{4 \, _2F_1\left(-\frac{5}{3},\frac{3}{4};-\frac{2}{3};-x^3\right)}{5 x^5}+x^2 \, _2F_1\left(\frac{2}{3},\frac{3}{4};\frac{5}{3};-x^3\right)+\frac{5 \, _2F_1\left(-\frac{2}{3},\frac{3}{4};\frac{1}{3};-x^3\right)}{2 x^2}","-\frac{4 \sqrt[4]{x^3+1} \left(10 x^4-x^3-1\right)}{5 x^5}",1,"(4*Hypergeometric2F1[-5/3, 3/4, -2/3, -x^3])/(5*x^5) + (5*Hypergeometric2F1[-2/3, 3/4, 1/3, -x^3])/(2*x^2) - (8*Hypergeometric2F1[-1/3, 3/4, 2/3, -x^3])/x - x*Hypergeometric2F1[1/3, 3/4, 4/3, -x^3] + x^2*Hypergeometric2F1[2/3, 3/4, 5/3, -x^3]","C",1
330,1,123,28,0.0964396,"\int \frac{\left(-3+x^4\right) \left(1-x^3+x^4\right)}{x^6 \sqrt[4]{x+x^5}} \, dx","Integrate[((-3 + x^4)*(1 - x^3 + x^4))/(x^6*(x + x^5)^(1/4)),x]","\frac{4 \sqrt[4]{x^4+1} \left(165 \, _2F_1\left(-\frac{21}{16},\frac{1}{4};-\frac{5}{16};-x^4\right)+x^3 \left(-165 x^4 \, _2F_1\left(\frac{1}{4},\frac{7}{16};\frac{23}{16};-x^4\right)+462 x \, _2F_1\left(-\frac{5}{16},\frac{1}{4};\frac{11}{16};-x^4\right)-385 \, _2F_1\left(-\frac{9}{16},\frac{1}{4};\frac{7}{16};-x^4\right)+105 x^5 \, _2F_1\left(\frac{1}{4},\frac{11}{16};\frac{27}{16};-x^4\right)\right)\right)}{1155 x^5 \sqrt[4]{x^5+x}}","\frac{4 \left(3 x^4-7 x^3+3\right) \left(x^5+x\right)^{3/4}}{21 x^6}",1,"(4*(1 + x^4)^(1/4)*(165*Hypergeometric2F1[-21/16, 1/4, -5/16, -x^4] + x^3*(-385*Hypergeometric2F1[-9/16, 1/4, 7/16, -x^4] + 462*x*Hypergeometric2F1[-5/16, 1/4, 11/16, -x^4] - 165*x^4*Hypergeometric2F1[1/4, 7/16, 23/16, -x^4] + 105*x^5*Hypergeometric2F1[1/4, 11/16, 27/16, -x^4])))/(1155*x^5*(x + x^5)^(1/4))","C",1
331,1,28,28,0.0044942,"\int \frac{\sqrt{-1+x^6}}{x} \, dx","Integrate[Sqrt[-1 + x^6]/x,x]","\frac{\sqrt{x^6-1}}{3}-\frac{1}{3} \tan ^{-1}\left(\sqrt{x^6-1}\right)","\frac{\sqrt{x^6-1}}{3}-\frac{1}{3} \tan ^{-1}\left(\sqrt{x^6-1}\right)",1,"Sqrt[-1 + x^6]/3 - ArcTan[Sqrt[-1 + x^6]]/3","A",1
332,1,24,28,0.0056506,"\int \frac{-1+x^6}{x \sqrt{1+x^6}} \, dx","Integrate[(-1 + x^6)/(x*Sqrt[1 + x^6]),x]","\frac{1}{3} \left(\sqrt{x^6+1}+\tanh ^{-1}\left(\sqrt{x^6+1}\right)\right)","\frac{\sqrt{x^6+1}}{3}+\frac{1}{3} \tanh ^{-1}\left(\sqrt{x^6+1}\right)",1,"(Sqrt[1 + x^6] + ArcTanh[Sqrt[1 + x^6]])/3","A",1
333,1,28,28,0.0038044,"\int \frac{\sqrt{1+x^6}}{x} \, dx","Integrate[Sqrt[1 + x^6]/x,x]","\frac{\sqrt{x^6+1}}{3}-\frac{1}{3} \tanh ^{-1}\left(\sqrt{x^6+1}\right)","\frac{\sqrt{x^6+1}}{3}-\frac{1}{3} \tanh ^{-1}\left(\sqrt{x^6+1}\right)",1,"Sqrt[1 + x^6]/3 - ArcTanh[Sqrt[1 + x^6]]/3","A",1
334,1,23,28,0.0090043,"\int \frac{\sqrt[3]{-1+x^6} \left(1+x^6\right)}{x^{15}} \, dx","Integrate[((-1 + x^6)^(1/3)*(1 + x^6))/x^15,x]","\frac{\left(x^6-1\right)^{4/3} \left(5 x^6+2\right)}{28 x^{14}}","\frac{\sqrt[3]{x^6-1} \left(5 x^{12}-3 x^6-2\right)}{28 x^{14}}",1,"((-1 + x^6)^(4/3)*(2 + 5*x^6))/(28*x^14)","A",1
335,1,126,28,0.1034097,"\int \frac{\left(1-x^3+x^5\right) \left(-3+2 x^5\right)}{x^6 \sqrt[4]{x+x^6}} \, dx","Integrate[((1 - x^3 + x^5)*(-3 + 2*x^5))/(x^6*(x + x^6)^(1/4)),x]","\frac{4 \sqrt[4]{x^5+1} \left(627 \, _2F_1\left(-\frac{21}{20},\frac{1}{4};-\frac{1}{20};-x^5\right)+7 x^3 \left(-114 x^5 \, _2F_1\left(\frac{1}{4},\frac{11}{20};\frac{31}{20};-x^5\right)-209 \, _2F_1\left(-\frac{9}{20},\frac{1}{4};\frac{11}{20};-x^5\right)+66 x^7 \, _2F_1\left(\frac{1}{4},\frac{19}{20};\frac{39}{20};-x^5\right)+627 x^2 \, _2F_1\left(-\frac{1}{20},\frac{1}{4};\frac{19}{20};-x^5\right)\right)\right)}{4389 x^5 \sqrt[4]{x^6+x}}","\frac{4 \left(3 x^5-7 x^3+3\right) \left(x^6+x\right)^{3/4}}{21 x^6}",1,"(4*(1 + x^5)^(1/4)*(627*Hypergeometric2F1[-21/20, 1/4, -1/20, -x^5] + 7*x^3*(-209*Hypergeometric2F1[-9/20, 1/4, 11/20, -x^5] + 627*x^2*Hypergeometric2F1[-1/20, 1/4, 19/20, -x^5] - 114*x^5*Hypergeometric2F1[1/4, 11/20, 31/20, -x^5] + 66*x^7*Hypergeometric2F1[1/4, 19/20, 39/20, -x^5])))/(4389*x^5*(x + x^6)^(1/4))","C",1
336,1,108,28,0.0450488,"\int \frac{\left(-2+x^6\right) \left(1-x^4+x^6\right)}{x^8 \sqrt[4]{1+x^6}} \, dx","Integrate[((-2 + x^6)*(1 - x^4 + x^6))/(x^8*(1 + x^6)^(1/4)),x]","\frac{\, _2F_1\left(-\frac{1}{6},\frac{1}{4};\frac{5}{6};-x^6\right)}{x}+\frac{2 \, _2F_1\left(-\frac{7}{6},\frac{1}{4};-\frac{1}{6};-x^6\right)}{7 x^7}+\frac{1}{5} x^5 \, _2F_1\left(\frac{1}{4},\frac{5}{6};\frac{11}{6};-x^6\right)-\frac{1}{3} x^3 \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{3}{2};-x^6\right)-\frac{2 \, _2F_1\left(-\frac{1}{2},\frac{1}{4};\frac{1}{2};-x^6\right)}{3 x^3}","\frac{2 \left(x^6+1\right)^{3/4} \left(3 x^6-7 x^4+3\right)}{21 x^7}",1,"(2*Hypergeometric2F1[-7/6, 1/4, -1/6, -x^6])/(7*x^7) - (2*Hypergeometric2F1[-1/2, 1/4, 1/2, -x^6])/(3*x^3) + Hypergeometric2F1[-1/6, 1/4, 5/6, -x^6]/x - (x^3*Hypergeometric2F1[1/4, 1/2, 3/2, -x^6])/3 + (x^5*Hypergeometric2F1[1/4, 5/6, 11/6, -x^6])/5","C",1
337,1,23,28,0.0091604,"\int \frac{\sqrt[3]{-1+x^6} \left(-1+2 x^6\right)}{x^{15}} \, dx","Integrate[((-1 + x^6)^(1/3)*(-1 + 2*x^6))/x^15,x]","\frac{\left(x^6-1\right)^{4/3} \left(11 x^6-4\right)}{56 x^{14}}","\frac{\sqrt[3]{x^6-1} \left(11 x^{12}-15 x^6+4\right)}{56 x^{14}}",1,"((-1 + x^6)^(4/3)*(-4 + 11*x^6))/(56*x^14)","A",1
338,1,28,28,0.0610007,"\int \frac{x^2 \left(-2+x^3\right) \sqrt{1+x^3}}{1+3 x^3+x^9} \, dx","Integrate[(x^2*(-2 + x^3)*Sqrt[1 + x^3])/(1 + 3*x^3 + x^9),x]","-\frac{2 \tanh ^{-1}\left(\frac{\left(x^3+1\right)^{3/2}}{\sqrt{3} x^3}\right)}{3 \sqrt{3}}","-\frac{2 \tanh ^{-1}\left(\frac{\left(x^3+1\right)^{3/2}}{\sqrt{3} x^3}\right)}{3 \sqrt{3}}",1,"(-2*ArcTanh[(1 + x^3)^(3/2)/(Sqrt[3]*x^3)])/(3*Sqrt[3])","A",1
339,0,0,28,0.315294,"\int \frac{x^4 \left(-9+4 x^5\right)}{\sqrt{-x+x^6} \left(a-a x^5+x^9\right)} \, dx","Integrate[(x^4*(-9 + 4*x^5))/(Sqrt[-x + x^6]*(a - a*x^5 + x^9)),x]","\int \frac{x^4 \left(-9+4 x^5\right)}{\sqrt{-x+x^6} \left(a-a x^5+x^9\right)} \, dx","-\frac{2 \tanh ^{-1}\left(\frac{x^5}{\sqrt{a} \sqrt{x^6-x}}\right)}{\sqrt{a}}",1,"Integrate[(x^4*(-9 + 4*x^5))/(Sqrt[-x + x^6]*(a - a*x^5 + x^9)), x]","F",-1
340,0,0,28,0.2467233,"\int \frac{x^4 \left(-9+5 x^4\right)}{\sqrt{-x+x^5} \left(1-x^4+a x^9\right)} \, dx","Integrate[(x^4*(-9 + 5*x^4))/(Sqrt[-x + x^5]*(1 - x^4 + a*x^9)),x]","\int \frac{x^4 \left(-9+5 x^4\right)}{\sqrt{-x+x^5} \left(1-x^4+a x^9\right)} \, dx","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{x^5-x}}{\sqrt{a} x^5}\right)}{\sqrt{a}}",1,"Integrate[(x^4*(-9 + 5*x^4))/(Sqrt[-x + x^5]*(1 - x^4 + a*x^9)), x]","F",-1
341,0,0,28,0.2649129,"\int \frac{x^4 \left(-9+4 x^5\right)}{\sqrt{-x+x^6} \left(1-x^5+a x^9\right)} \, dx","Integrate[(x^4*(-9 + 4*x^5))/(Sqrt[-x + x^6]*(1 - x^5 + a*x^9)),x]","\int \frac{x^4 \left(-9+4 x^5\right)}{\sqrt{-x+x^6} \left(1-x^5+a x^9\right)} \, dx","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{x^6-x}}{\sqrt{a} x^5}\right)}{\sqrt{a}}",1,"Integrate[(x^4*(-9 + 4*x^5))/(Sqrt[-x + x^6]*(1 - x^5 + a*x^9)), x]","F",-1
342,1,33,28,0.0259556,"\int \frac{1+x^{12}}{x^{16} \sqrt{-1+x^6}} \, dx","Integrate[(1 + x^12)/(x^16*Sqrt[-1 + x^6]),x]","\frac{23 x^{18}-19 x^{12}-x^6-3}{45 x^{15} \sqrt{x^6-1}}","\frac{\sqrt{x^6-1} \left(23 x^{12}+4 x^6+3\right)}{45 x^{15}}",1,"(-3 - x^6 - 19*x^12 + 23*x^18)/(45*x^15*Sqrt[-1 + x^6])","A",1
343,0,0,29,0.2449478,"\int \frac{-1+x}{(-3+x) (1+x) \sqrt[4]{-2-2 x+x^2}} \, dx","Integrate[(-1 + x)/((-3 + x)*(1 + x)*(-2 - 2*x + x^2)^(1/4)),x]","\int \frac{-1+x}{(-3+x) (1+x) \sqrt[4]{-2-2 x+x^2}} \, dx","\tan ^{-1}\left(\sqrt[4]{x^2-2 x-2}\right)-\tanh ^{-1}\left(\sqrt[4]{x^2-2 x-2}\right)",1,"Integrate[(-1 + x)/((-3 + x)*(1 + x)*(-2 - 2*x + x^2)^(1/4)), x]","F",-1
344,1,27,29,0.0061646,"\int \frac{1}{(-1+x) \sqrt[4]{2-2 x+x^2}} \, dx","Integrate[1/((-1 + x)*(2 - 2*x + x^2)^(1/4)),x]","\tan ^{-1}\left(\sqrt[4]{(x-1)^2+1}\right)-\tanh ^{-1}\left(\sqrt[4]{(x-1)^2+1}\right)","\tan ^{-1}\left(\sqrt[4]{x^2-2 x+2}\right)-\tanh ^{-1}\left(\sqrt[4]{x^2-2 x+2}\right)",1,"ArcTan[(1 + (-1 + x)^2)^(1/4)] - ArcTanh[(1 + (-1 + x)^2)^(1/4)]","A",1
345,1,27,29,0.0058111,"\int \frac{1}{(1+x) \sqrt[4]{2+2 x+x^2}} \, dx","Integrate[1/((1 + x)*(2 + 2*x + x^2)^(1/4)),x]","\tan ^{-1}\left(\sqrt[4]{(x+1)^2+1}\right)-\tanh ^{-1}\left(\sqrt[4]{(x+1)^2+1}\right)","\tan ^{-1}\left(\sqrt[4]{x^2+2 x+2}\right)-\tanh ^{-1}\left(\sqrt[4]{x^2+2 x+2}\right)",1,"ArcTan[(1 + (1 + x)^2)^(1/4)] - ArcTanh[(1 + (1 + x)^2)^(1/4)]","A",1
346,1,29,29,0.0031911,"\int \frac{1}{x \sqrt[4]{1+x^3}} \, dx","Integrate[1/(x*(1 + x^3)^(1/4)),x]","\frac{2}{3} \tan ^{-1}\left(\sqrt[4]{x^3+1}\right)-\frac{2}{3} \tanh ^{-1}\left(\sqrt[4]{x^3+1}\right)","\frac{2}{3} \tan ^{-1}\left(\sqrt[4]{x^3+1}\right)-\frac{2}{3} \tanh ^{-1}\left(\sqrt[4]{x^3+1}\right)",1,"(2*ArcTan[(1 + x^3)^(1/4)])/3 - (2*ArcTanh[(1 + x^3)^(1/4)])/3","A",1
347,1,29,29,0.0066597,"\int \frac{1}{x \sqrt{-b+a x^3}} \, dx","Integrate[1/(x*Sqrt[-b + a*x^3]),x]","\frac{2 \tan ^{-1}\left(\frac{\sqrt{a x^3-b}}{\sqrt{b}}\right)}{3 \sqrt{b}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{a x^3-b}}{\sqrt{b}}\right)}{3 \sqrt{b}}",1,"(2*ArcTan[Sqrt[-b + a*x^3]/Sqrt[b]])/(3*Sqrt[b])","A",1
348,1,29,29,0.0131182,"\int \frac{x^5}{\sqrt{-b+a x^3}} \, dx","Integrate[x^5/Sqrt[-b + a*x^3],x]","\frac{2 \sqrt{a x^3-b} \left(a x^3+2 b\right)}{9 a^2}","\frac{2 \sqrt{a x^3-b} \left(a x^3+2 b\right)}{9 a^2}",1,"(2*Sqrt[-b + a*x^3]*(2*b + a*x^3))/(9*a^2)","A",1
349,1,742,29,1.7172055,"\int \frac{1+x}{(-1+x) \sqrt{1-x^2+x^4}} \, dx","Integrate[(1 + x)/((-1 + x)*Sqrt[1 - x^2 + x^4]),x]","\frac{2 \sqrt[3]{-1} \left(\sqrt{1-\sqrt[3]{-1}}+\sqrt{1+(-1)^{2/3}}\right) \left(\sqrt{1-\sqrt[3]{-1}}-x\right)^2 \sqrt{\frac{\sqrt{1-\sqrt[3]{-1}} \left(\sqrt{1+(-1)^{2/3}}-x\right)}{\left(\sqrt{1-\sqrt[3]{-1}}+\sqrt{1+(-1)^{2/3}}\right) \left(\sqrt{1-\sqrt[3]{-1}}-x\right)}} \sqrt{-\frac{\sqrt{1-\sqrt[3]{-1}} \left(x+\sqrt{1+(-1)^{2/3}}\right)}{\left(\sqrt{1-\sqrt[3]{-1}}-\sqrt{1+(-1)^{2/3}}\right) \left(\sqrt{1-\sqrt[3]{-1}}-x\right)}} \sqrt{\frac{\left(\sqrt{1-\sqrt[3]{-1}}-\sqrt{1+(-1)^{2/3}}\right) x-\sqrt[3]{-1}}{\left(\sqrt{1-\sqrt[3]{-1}}+\sqrt{1+(-1)^{2/3}}\right) \left(\sqrt{1-\sqrt[3]{-1}}-x\right)}} \left(\left(-2+\sqrt[3]{-1}-2 \sqrt{1-\sqrt[3]{-1}}\right) F\left(\sin ^{-1}\left(\sqrt{\frac{\left(\sqrt{1-\sqrt[3]{-1}}-\sqrt{1+(-1)^{2/3}}\right) \left(x+\sqrt{1-\sqrt[3]{-1}}\right)}{\left(\sqrt{1-\sqrt[3]{-1}}+\sqrt{1+(-1)^{2/3}}\right) \left(\sqrt{1-\sqrt[3]{-1}}-x\right)}}\right)|\frac{\left(\sqrt{1-\sqrt[3]{-1}}+\sqrt{1+(-1)^{2/3}}\right)^2}{\left(\sqrt{1-\sqrt[3]{-1}}-\sqrt{1+(-1)^{2/3}}\right)^2}\right)+4 \sqrt{1-\sqrt[3]{-1}} \Pi \left(\frac{\left(-1+\sqrt{1-\sqrt[3]{-1}}\right) \left(\sqrt{1-\sqrt[3]{-1}}+\sqrt{1+(-1)^{2/3}}\right)}{\left(1+\sqrt{1-\sqrt[3]{-1}}\right) \left(\sqrt{1-\sqrt[3]{-1}}-\sqrt{1+(-1)^{2/3}}\right)};\sin ^{-1}\left(\sqrt{\frac{\left(\sqrt{1-\sqrt[3]{-1}}-\sqrt{1+(-1)^{2/3}}\right) \left(x+\sqrt{1-\sqrt[3]{-1}}\right)}{\left(\sqrt{1-\sqrt[3]{-1}}+\sqrt{1+(-1)^{2/3}}\right) \left(\sqrt{1-\sqrt[3]{-1}}-x\right)}}\right)|\frac{\left(\sqrt{1-\sqrt[3]{-1}}+\sqrt{1+(-1)^{2/3}}\right)^2}{\left(\sqrt{1-\sqrt[3]{-1}}-\sqrt{1+(-1)^{2/3}}\right)^2}\right)\right)}{\sqrt{x^4-x^2+1}}","-2 \tanh ^{-1}\left(\frac{x}{x^2+\sqrt{x^4-x^2+1}-2 x+1}\right)",1,"(2*(-1)^(1/3)*(Sqrt[1 - (-1)^(1/3)] + Sqrt[1 + (-1)^(2/3)])*(Sqrt[1 - (-1)^(1/3)] - x)^2*Sqrt[(Sqrt[1 - (-1)^(1/3)]*(Sqrt[1 + (-1)^(2/3)] - x))/((Sqrt[1 - (-1)^(1/3)] + Sqrt[1 + (-1)^(2/3)])*(Sqrt[1 - (-1)^(1/3)] - x))]*Sqrt[-((Sqrt[1 - (-1)^(1/3)]*(Sqrt[1 + (-1)^(2/3)] + x))/((Sqrt[1 - (-1)^(1/3)] - Sqrt[1 + (-1)^(2/3)])*(Sqrt[1 - (-1)^(1/3)] - x)))]*Sqrt[(-(-1)^(1/3) + (Sqrt[1 - (-1)^(1/3)] - Sqrt[1 + (-1)^(2/3)])*x)/((Sqrt[1 - (-1)^(1/3)] + Sqrt[1 + (-1)^(2/3)])*(Sqrt[1 - (-1)^(1/3)] - x))]*((-2 + (-1)^(1/3) - 2*Sqrt[1 - (-1)^(1/3)])*EllipticF[ArcSin[Sqrt[((Sqrt[1 - (-1)^(1/3)] - Sqrt[1 + (-1)^(2/3)])*(Sqrt[1 - (-1)^(1/3)] + x))/((Sqrt[1 - (-1)^(1/3)] + Sqrt[1 + (-1)^(2/3)])*(Sqrt[1 - (-1)^(1/3)] - x))]], (Sqrt[1 - (-1)^(1/3)] + Sqrt[1 + (-1)^(2/3)])^2/(Sqrt[1 - (-1)^(1/3)] - Sqrt[1 + (-1)^(2/3)])^2] + 4*Sqrt[1 - (-1)^(1/3)]*EllipticPi[((-1 + Sqrt[1 - (-1)^(1/3)])*(Sqrt[1 - (-1)^(1/3)] + Sqrt[1 + (-1)^(2/3)]))/((1 + Sqrt[1 - (-1)^(1/3)])*(Sqrt[1 - (-1)^(1/3)] - Sqrt[1 + (-1)^(2/3)])), ArcSin[Sqrt[((Sqrt[1 - (-1)^(1/3)] - Sqrt[1 + (-1)^(2/3)])*(Sqrt[1 - (-1)^(1/3)] + x))/((Sqrt[1 - (-1)^(1/3)] + Sqrt[1 + (-1)^(2/3)])*(Sqrt[1 - (-1)^(1/3)] - x))]], (Sqrt[1 - (-1)^(1/3)] + Sqrt[1 + (-1)^(2/3)])^2/(Sqrt[1 - (-1)^(1/3)] - Sqrt[1 + (-1)^(2/3)])^2]))/Sqrt[1 - x^2 + x^4]","C",0
350,1,29,29,0.0454782,"\int \frac{\left(-1+x^4\right) \left(1+x^4\right)}{\left(1+x^2+x^4\right)^{5/2}} \, dx","Integrate[((-1 + x^4)*(1 + x^4))/(1 + x^2 + x^4)^(5/2),x]","-\frac{x \left(3 x^4+2 x^2+3\right)}{3 \left(x^4+x^2+1\right)^{3/2}}","-\frac{x \left(3 x^4+2 x^2+3\right)}{3 \left(x^4+x^2+1\right)^{3/2}}",1,"-1/3*(x*(3 + 2*x^2 + 3*x^4))/(1 + x^2 + x^4)^(3/2)","A",1
351,0,0,29,0.1959269,"\int \frac{x^2 \left(-4+x^3\right)}{\left(-1+x^3\right)^{3/4} \left(1-x^3+x^4\right)} \, dx","Integrate[(x^2*(-4 + x^3))/((-1 + x^3)^(3/4)*(1 - x^3 + x^4)),x]","\int \frac{x^2 \left(-4+x^3\right)}{\left(-1+x^3\right)^{3/4} \left(1-x^3+x^4\right)} \, dx","2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^3-1}}\right)-2 \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^3-1}}\right)",1,"Integrate[(x^2*(-4 + x^3))/((-1 + x^3)^(3/4)*(1 - x^3 + x^4)), x]","F",-1
352,1,736,29,2.4831455,"\int \frac{1+2 x}{\sqrt{-4-4 x-3 x^2+2 x^3+x^4}} \, dx","Integrate[(1 + 2*x)/Sqrt[-4 - 4*x - 3*x^2 + 2*x^3 + x^4],x]","\frac{i \sqrt{8 \sqrt{2}-9} \left(-2 x+\sqrt{9+8 \sqrt{2}}-1\right) \sqrt{\frac{\left(\sqrt{8 \sqrt{2}-9}+i \sqrt{9+8 \sqrt{2}}\right) \left(-2 i x+\sqrt{8 \sqrt{2}-9}-i\right)}{\left(\sqrt{8 \sqrt{2}-9}-i \sqrt{9+8 \sqrt{2}}\right) \left(2 i x+\sqrt{8 \sqrt{2}-9}+i\right)}} \left(2 i x+\sqrt{8 \sqrt{2}-9}+i\right) \sqrt{\frac{2 x+\sqrt{9+8 \sqrt{2}}+1}{\left(\sqrt{9+8 \sqrt{2}}-i \sqrt{8 \sqrt{2}-9}\right) \left(2 i x+\sqrt{8 \sqrt{2}-9}+i\right)}} \left(F\left(\sin ^{-1}\left(\sqrt{\frac{\left(\sqrt{-9+8 \sqrt{2}}+i \sqrt{9+8 \sqrt{2}}\right) \left(-2 i x+\sqrt{-9+8 \sqrt{2}}-i\right)}{\left(\sqrt{-9+8 \sqrt{2}}-i \sqrt{9+8 \sqrt{2}}\right) \left(2 i x+\sqrt{-9+8 \sqrt{2}}+i\right)}}\right)|\frac{9 i-\sqrt{47}}{9 i+\sqrt{47}}\right)-2 \Pi \left(-\frac{\sqrt{-9+8 \sqrt{2}}-i \sqrt{9+8 \sqrt{2}}}{\sqrt{-9+8 \sqrt{2}}+i \sqrt{9+8 \sqrt{2}}};\sin ^{-1}\left(\sqrt{\frac{\left(\sqrt{-9+8 \sqrt{2}}+i \sqrt{9+8 \sqrt{2}}\right) \left(-2 i x+\sqrt{-9+8 \sqrt{2}}-i\right)}{\left(\sqrt{-9+8 \sqrt{2}}-i \sqrt{9+8 \sqrt{2}}\right) \left(2 i x+\sqrt{-9+8 \sqrt{2}}+i\right)}}\right)|\frac{9 i-\sqrt{47}}{9 i+\sqrt{47}}\right)\right)}{\left(\sqrt{8 \sqrt{2}-9}+i \sqrt{9+8 \sqrt{2}}\right) \sqrt{\frac{-2 x+\sqrt{9+8 \sqrt{2}}-1}{\left(\sqrt{9+8 \sqrt{2}}+i \sqrt{8 \sqrt{2}-9}\right) \left(2 i x+\sqrt{8 \sqrt{2}-9}+i\right)}} \sqrt{x^4+2 x^3-3 x^2-4 x-4}}","\log \left(x^2+\sqrt{x^4+2 x^3-3 x^2-4 x-4}+x-2\right)",1,"(I*Sqrt[-9 + 8*Sqrt[2]]*(-1 + Sqrt[9 + 8*Sqrt[2]] - 2*x)*Sqrt[((Sqrt[-9 + 8*Sqrt[2]] + I*Sqrt[9 + 8*Sqrt[2]])*(-I + Sqrt[-9 + 8*Sqrt[2]] - (2*I)*x))/((Sqrt[-9 + 8*Sqrt[2]] - I*Sqrt[9 + 8*Sqrt[2]])*(I + Sqrt[-9 + 8*Sqrt[2]] + (2*I)*x))]*(I + Sqrt[-9 + 8*Sqrt[2]] + (2*I)*x)*Sqrt[(1 + Sqrt[9 + 8*Sqrt[2]] + 2*x)/(((-I)*Sqrt[-9 + 8*Sqrt[2]] + Sqrt[9 + 8*Sqrt[2]])*(I + Sqrt[-9 + 8*Sqrt[2]] + (2*I)*x))]*(EllipticF[ArcSin[Sqrt[((Sqrt[-9 + 8*Sqrt[2]] + I*Sqrt[9 + 8*Sqrt[2]])*(-I + Sqrt[-9 + 8*Sqrt[2]] - (2*I)*x))/((Sqrt[-9 + 8*Sqrt[2]] - I*Sqrt[9 + 8*Sqrt[2]])*(I + Sqrt[-9 + 8*Sqrt[2]] + (2*I)*x))]], (9*I - Sqrt[47])/(9*I + Sqrt[47])] - 2*EllipticPi[-((Sqrt[-9 + 8*Sqrt[2]] - I*Sqrt[9 + 8*Sqrt[2]])/(Sqrt[-9 + 8*Sqrt[2]] + I*Sqrt[9 + 8*Sqrt[2]])), ArcSin[Sqrt[((Sqrt[-9 + 8*Sqrt[2]] + I*Sqrt[9 + 8*Sqrt[2]])*(-I + Sqrt[-9 + 8*Sqrt[2]] - (2*I)*x))/((Sqrt[-9 + 8*Sqrt[2]] - I*Sqrt[9 + 8*Sqrt[2]])*(I + Sqrt[-9 + 8*Sqrt[2]] + (2*I)*x))]], (9*I - Sqrt[47])/(9*I + Sqrt[47])]))/((Sqrt[-9 + 8*Sqrt[2]] + I*Sqrt[9 + 8*Sqrt[2]])*Sqrt[(-1 + Sqrt[9 + 8*Sqrt[2]] - 2*x)/((I*Sqrt[-9 + 8*Sqrt[2]] + Sqrt[9 + 8*Sqrt[2]])*(I + Sqrt[-9 + 8*Sqrt[2]] + (2*I)*x))]*Sqrt[-4 - 4*x - 3*x^2 + 2*x^3 + x^4])","C",0
353,1,29,29,0.0084069,"\int \frac{1}{x \sqrt{-b+a x^4}} \, dx","Integrate[1/(x*Sqrt[-b + a*x^4]),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{a x^4-b}}{\sqrt{b}}\right)}{2 \sqrt{b}}","\frac{\tan ^{-1}\left(\frac{\sqrt{a x^4-b}}{\sqrt{b}}\right)}{2 \sqrt{b}}",1,"ArcTan[Sqrt[-b + a*x^4]/Sqrt[b]]/(2*Sqrt[b])","A",1
354,0,0,29,0.3381739,"\int \frac{-1+2 x^6}{\left(1+x^6\right) \sqrt{1-2 x^2+x^6}} \, dx","Integrate[(-1 + 2*x^6)/((1 + x^6)*Sqrt[1 - 2*x^2 + x^6]),x]","\int \frac{-1+2 x^6}{\left(1+x^6\right) \sqrt{1-2 x^2+x^6}} \, dx","-\frac{\tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^6-2 x^2+1}}\right)}{\sqrt{2}}",1,"Integrate[(-1 + 2*x^6)/((1 + x^6)*Sqrt[1 - 2*x^2 + x^6]), x]","F",-1
355,0,0,29,0.2609362,"\int \frac{1+2 x^6}{\left(-1+x^6\right) \sqrt{-1-2 x^2+x^6}} \, dx","Integrate[(1 + 2*x^6)/((-1 + x^6)*Sqrt[-1 - 2*x^2 + x^6]),x]","\int \frac{1+2 x^6}{\left(-1+x^6\right) \sqrt{-1-2 x^2+x^6}} \, dx","-\frac{\tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^6-2 x^2-1}}\right)}{\sqrt{2}}",1,"Integrate[(1 + 2*x^6)/((-1 + x^6)*Sqrt[-1 - 2*x^2 + x^6]), x]","F",-1
356,1,25,30,0.0072308,"\int x^8 \sqrt[3]{-1+x^3} \, dx","Integrate[x^8*(-1 + x^3)^(1/3),x]","\frac{1}{140} \left(x^3-1\right)^{4/3} \left(14 x^6+12 x^3+9\right)","\frac{1}{140} \sqrt[3]{x^3-1} \left(14 x^9-2 x^6-3 x^3-9\right)",1,"((-1 + x^3)^(4/3)*(9 + 12*x^3 + 14*x^6))/140","A",1
357,1,25,30,0.0078647,"\int x^8 \sqrt[4]{1+x^3} \, dx","Integrate[x^8*(1 + x^3)^(1/4),x]","\frac{4 \left(x^3+1\right)^{5/4} \left(45 x^6-40 x^3+32\right)}{1755}","\frac{4 \sqrt[4]{x^3+1} \left(45 x^9+5 x^6-8 x^3+32\right)}{1755}",1,"(4*(1 + x^3)^(5/4)*(32 - 40*x^3 + 45*x^6))/1755","A",1
358,1,30,30,0.015151,"\int \frac{1}{x^6 \sqrt[3]{-x+x^3}} \, dx","Integrate[1/(x^6*(-x + x^3)^(1/3)),x]","\frac{3 \left(x \left(x^2-1\right)\right)^{2/3} \left(9 x^4+6 x^2+5\right)}{80 x^6}","\frac{3 \left(x^3-x\right)^{2/3} \left(9 x^4+6 x^2+5\right)}{80 x^6}",1,"(3*(x*(-1 + x^2))^(2/3)*(5 + 6*x^2 + 9*x^4))/(80*x^6)","A",1
359,1,28,30,0.0114378,"\int \frac{1}{x^3 \sqrt[3]{-x^2+x^3}} \, dx","Integrate[1/(x^3*(-x^2 + x^3)^(1/3)),x]","\frac{3 \left((x-1) x^2\right)^{2/3} \left(9 x^2+6 x+5\right)}{40 x^4}","\frac{3 \left(9 x^2+6 x+5\right) \left(x^3-x^2\right)^{2/3}}{40 x^4}",1,"(3*((-1 + x)*x^2)^(2/3)*(5 + 6*x + 9*x^2))/(40*x^4)","A",1
360,1,119,30,0.108587,"\int \frac{\left(-3+x^2\right) \left(1-x^2+x^3\right)}{x^6 \sqrt[4]{-x+x^3}} \, dx","Integrate[((-3 + x^2)*(1 - x^2 + x^3))/(x^6*(-x + x^3)^(1/4)),x]","-\frac{4 \sqrt[4]{1-x^2} \left(7 x^2 \left(60 \, _2F_1\left(-\frac{13}{8},\frac{1}{4};-\frac{5}{8};x^2\right)+13 x \left(15 x^2 \, _2F_1\left(-\frac{1}{8},\frac{1}{4};\frac{7}{8};x^2\right)-3 x \, _2F_1\left(-\frac{5}{8},\frac{1}{4};\frac{3}{8};x^2\right)-5 \, _2F_1\left(-\frac{9}{8},\frac{1}{4};-\frac{1}{8};x^2\right)\right)\right)-195 \, _2F_1\left(-\frac{21}{8},\frac{1}{4};-\frac{13}{8};x^2\right)\right)}{1365 x^5 \sqrt[4]{x \left(x^2-1\right)}}","-\frac{4 \left(x^3-x\right)^{3/4} \left(7 x^3-3 x^2+3\right)}{21 x^6}",1,"(-4*(1 - x^2)^(1/4)*(-195*Hypergeometric2F1[-21/8, 1/4, -13/8, x^2] + 7*x^2*(60*Hypergeometric2F1[-13/8, 1/4, -5/8, x^2] + 13*x*(-5*Hypergeometric2F1[-9/8, 1/4, -1/8, x^2] - 3*x*Hypergeometric2F1[-5/8, 1/4, 3/8, x^2] + 15*x^2*Hypergeometric2F1[-1/8, 1/4, 7/8, x^2]))))/(1365*x^5*(x*(-1 + x^2))^(1/4))","C",1
361,1,1680,30,6.7080089,"\int \frac{1+x^2}{\left(-1+x^2\right) \sqrt{-x-x^2+x^3}} \, dx","Integrate[(1 + x^2)/((-1 + x^2)*Sqrt[-x - x^2 + x^3]),x]","-\frac{\sqrt{2} \left(\frac{1}{x^2}-1\right) x^{3/2} \left(x^2+1\right) \left(\frac{\left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right) \sqrt{\frac{i \sqrt{2 \left(1+\sqrt{5}\right)}+\frac{2}{\sqrt{x}}}{-\sqrt{10}+(1+2 i) \sqrt{2}-\frac{2 i \sqrt{1+\sqrt{5}}}{\sqrt{x}}+\frac{2 \sqrt{-1+\sqrt{5}}}{\sqrt{x}}}} \sqrt{\frac{i \sqrt{2 \left(1+\sqrt{5}\right)}-\frac{2}{\sqrt{x}}}{\sqrt{2} \left((-1+2 i)+\sqrt{5}\right)-\frac{2 \left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right)}{\sqrt{x}}}} \sqrt{\frac{\sqrt{2} \left((-1-2 i)+\sqrt{5}\right)+\frac{2 \left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right)}{\sqrt{x}}}{\sqrt{2} \left((-1+2 i)+\sqrt{5}\right)-\frac{2 \left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right)}{\sqrt{x}}}} \left(\left(2+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) F\left(\sin ^{-1}\left(\sqrt{\frac{\left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right) \left(\sqrt{2 \left(-1+\sqrt{5}\right)}+\frac{2}{\sqrt{x}}\right)}{\left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right) \left(\sqrt{2 \left(-1+\sqrt{5}\right)}-\frac{2}{\sqrt{x}}\right)}}\right)|-\frac{3}{5}-\frac{4 i}{5}\right)-2 \sqrt{2 \left(-1+\sqrt{5}\right)} \Pi \left(\frac{\left(-2+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) \left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right)}{\left(2+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) \left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right)};\sin ^{-1}\left(\sqrt{\frac{\left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right) \left(\sqrt{2 \left(-1+\sqrt{5}\right)}+\frac{2}{\sqrt{x}}\right)}{\left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right) \left(\sqrt{2 \left(-1+\sqrt{5}\right)}-\frac{2}{\sqrt{x}}\right)}}\right)|-\frac{3}{5}-\frac{4 i}{5}\right)\right) \left(\sqrt{2 \left(-1+\sqrt{5}\right)}-\frac{2}{\sqrt{x}}\right)^2}{\left(-2+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) \left(2+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) \left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right)}-\frac{\left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right) \sqrt{\frac{i \sqrt{2 \left(1+\sqrt{5}\right)}+\frac{2}{\sqrt{x}}}{-\sqrt{10}+(1+2 i) \sqrt{2}-\frac{2 i \sqrt{1+\sqrt{5}}}{\sqrt{x}}+\frac{2 \sqrt{-1+\sqrt{5}}}{\sqrt{x}}}} \sqrt{\frac{i \sqrt{2 \left(1+\sqrt{5}\right)}-\frac{2}{\sqrt{x}}}{\sqrt{2} \left((-1+2 i)+\sqrt{5}\right)-\frac{2 \left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right)}{\sqrt{x}}}} \sqrt{\frac{\sqrt{2} \left((-1-2 i)+\sqrt{5}\right)+\frac{2 \left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right)}{\sqrt{x}}}{\sqrt{2} \left((-1+2 i)+\sqrt{5}\right)-\frac{2 \left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right)}{\sqrt{x}}}} \left(\left(-2+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) F\left(\sin ^{-1}\left(\sqrt{\frac{\left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right) \left(\sqrt{2 \left(-1+\sqrt{5}\right)}+\frac{2}{\sqrt{x}}\right)}{\left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right) \left(\sqrt{2 \left(-1+\sqrt{5}\right)}-\frac{2}{\sqrt{x}}\right)}}\right)|-\frac{3}{5}-\frac{4 i}{5}\right)-2 \sqrt{2 \left(-1+\sqrt{5}\right)} \Pi \left(\frac{\left(2+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) \left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right)}{\left(-2+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) \left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right)};\sin ^{-1}\left(\sqrt{\frac{\left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right) \left(\sqrt{2 \left(-1+\sqrt{5}\right)}+\frac{2}{\sqrt{x}}\right)}{\left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right) \left(\sqrt{2 \left(-1+\sqrt{5}\right)}-\frac{2}{\sqrt{x}}\right)}}\right)|-\frac{3}{5}-\frac{4 i}{5}\right)\right) \left(\sqrt{2 \left(-1+\sqrt{5}\right)}-\frac{2}{\sqrt{x}}\right)^2}{\left(-2+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) \left(2+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) \left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right)}-\frac{2 i \sqrt{1-\frac{1}{x}-\frac{1}{x^2}} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{1+\sqrt{5}}}}{\sqrt{x}}\right)|-\frac{3}{2}-\frac{\sqrt{5}}{2}\right)}{\sqrt{-1+\sqrt{5}}}+\frac{2 i \sqrt{1-\frac{1}{x}-\frac{1}{x^2}} \Pi \left(\frac{1}{2} \left(1+\sqrt{5}\right);i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{1+\sqrt{5}}}}{\sqrt{x}}\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{\sqrt{-1+\sqrt{5}}}\right)}{\left(x^2-\frac{1}{x^2}\right) \sqrt{x \left(x^2-x-1\right)}}","-2 \tan ^{-1}\left(\frac{\sqrt{x^3-x^2-x}}{x^2-x-1}\right)",1,"-((Sqrt[2]*(-1 + x^(-2))*x^(3/2)*(1 + x^2)*(((-2*I)*Sqrt[1 - x^(-2) - x^(-1)]*EllipticF[I*ArcSinh[Sqrt[2/(1 + Sqrt[5])]/Sqrt[x]], -3/2 - Sqrt[5]/2])/Sqrt[-1 + Sqrt[5]] + ((2*I)*Sqrt[1 - x^(-2) - x^(-1)]*EllipticPi[(1 + Sqrt[5])/2, I*ArcSinh[Sqrt[2/(1 + Sqrt[5])]/Sqrt[x]], (-3 - Sqrt[5])/2])/Sqrt[-1 + Sqrt[5]] + ((Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] - 2/Sqrt[x])^2*Sqrt[(I*Sqrt[2*(1 + Sqrt[5])] + 2/Sqrt[x])/((1 + 2*I)*Sqrt[2] - Sqrt[10] + (2*Sqrt[-1 + Sqrt[5]])/Sqrt[x] - ((2*I)*Sqrt[1 + Sqrt[5]])/Sqrt[x])]*Sqrt[(I*Sqrt[2*(1 + Sqrt[5])] - 2/Sqrt[x])/(Sqrt[2]*((-1 + 2*I) + Sqrt[5]) - (2*(Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]]))/Sqrt[x])]*Sqrt[(Sqrt[2]*((-1 - 2*I) + Sqrt[5]) + (2*(Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]]))/Sqrt[x])/(Sqrt[2]*((-1 + 2*I) + Sqrt[5]) - (2*(Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]]))/Sqrt[x])]*((2 + Sqrt[2*(-1 + Sqrt[5])])*EllipticF[ArcSin[Sqrt[((Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] + 2/Sqrt[x]))/((Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] - 2/Sqrt[x]))]], -3/5 - (4*I)/5] - 2*Sqrt[2*(-1 + Sqrt[5])]*EllipticPi[((-2 + Sqrt[2*(-1 + Sqrt[5])])*(Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]]))/((2 + Sqrt[2*(-1 + Sqrt[5])])*(Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]])), ArcSin[Sqrt[((Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] + 2/Sqrt[x]))/((Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] - 2/Sqrt[x]))]], -3/5 - (4*I)/5]))/((-2 + Sqrt[2*(-1 + Sqrt[5])])*(2 + Sqrt[2*(-1 + Sqrt[5])])*(Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]])) - ((Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] - 2/Sqrt[x])^2*Sqrt[(I*Sqrt[2*(1 + Sqrt[5])] + 2/Sqrt[x])/((1 + 2*I)*Sqrt[2] - Sqrt[10] + (2*Sqrt[-1 + Sqrt[5]])/Sqrt[x] - ((2*I)*Sqrt[1 + Sqrt[5]])/Sqrt[x])]*Sqrt[(I*Sqrt[2*(1 + Sqrt[5])] - 2/Sqrt[x])/(Sqrt[2]*((-1 + 2*I) + Sqrt[5]) - (2*(Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]]))/Sqrt[x])]*Sqrt[(Sqrt[2]*((-1 - 2*I) + Sqrt[5]) + (2*(Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]]))/Sqrt[x])/(Sqrt[2]*((-1 + 2*I) + Sqrt[5]) - (2*(Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]]))/Sqrt[x])]*((-2 + Sqrt[2*(-1 + Sqrt[5])])*EllipticF[ArcSin[Sqrt[((Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] + 2/Sqrt[x]))/((Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] - 2/Sqrt[x]))]], -3/5 - (4*I)/5] - 2*Sqrt[2*(-1 + Sqrt[5])]*EllipticPi[((2 + Sqrt[2*(-1 + Sqrt[5])])*(Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]]))/((-2 + Sqrt[2*(-1 + Sqrt[5])])*(Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]])), ArcSin[Sqrt[((Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] + 2/Sqrt[x]))/((Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] - 2/Sqrt[x]))]], -3/5 - (4*I)/5]))/((-2 + Sqrt[2*(-1 + Sqrt[5])])*(2 + Sqrt[2*(-1 + Sqrt[5])])*(Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]]))))/((-x^(-2) + x^2)*Sqrt[x*(-1 - x + x^2)]))","C",0
362,1,23,30,0.0126973,"\int \frac{-1+x^3}{x^3 \left(1+x^3\right) \sqrt[4]{x+x^4}} \, dx","Integrate[(-1 + x^3)/(x^3*(1 + x^3)*(x + x^4)^(1/4)),x]","\frac{28 x^3+4}{9 x^2 \sqrt[4]{x^4+x}}","\frac{4 \left(7 x^3+1\right) \left(x^4+x\right)^{3/4}}{9 x^3 \left(x^3+1\right)}",1,"(4 + 28*x^3)/(9*x^2*(x + x^4)^(1/4))","A",1
363,1,27,30,0.0147387,"\int \frac{\sqrt[4]{-x^2+x^4}}{x^6} \, dx","Integrate[(-x^2 + x^4)^(1/4)/x^6,x]","\frac{2 \left(x^2 \left(x^2-1\right)\right)^{5/4} \left(4 x^2+5\right)}{45 x^7}","\frac{2 \sqrt[4]{x^4-x^2} \left(4 x^4+x^2-5\right)}{45 x^5}",1,"(2*(x^2*(-1 + x^2))^(5/4)*(5 + 4*x^2))/(45*x^7)","A",1
364,1,717,30,3.3669218,"\int \frac{-1+2 x}{\sqrt{1+x-2 x^3+x^4}} \, dx","Integrate[(-1 + 2*x)/Sqrt[1 + x - 2*x^3 + x^4],x]","\frac{\left(-2 x+\sqrt{1+4 \sqrt[3]{-1}}+1\right) \sqrt{\frac{\sqrt{1+4 \sqrt[3]{-1}} \left(-2 x+\sqrt{1-4 (-1)^{2/3}}+1\right)}{\left(\sqrt{1+4 \sqrt[3]{-1}}+\sqrt{1-4 (-1)^{2/3}}\right) \left(-2 x+\sqrt{1+4 \sqrt[3]{-1}}+1\right)}} \left(2 x+\sqrt{1+4 \sqrt[3]{-1}}-1\right) \sqrt{-\frac{\sqrt{1+4 \sqrt[3]{-1}} \left(2 x+\sqrt{1-4 (-1)^{2/3}}-1\right)}{\left(\sqrt{1+4 \sqrt[3]{-1}}-\sqrt{1-4 (-1)^{2/3}}\right) \left(-2 x+\sqrt{1+4 \sqrt[3]{-1}}+1\right)}} \left(F\left(\sin ^{-1}\left(\sqrt{\frac{\left(\sqrt{1+4 \sqrt[3]{-1}}-\sqrt{1-4 (-1)^{2/3}}\right) \left(2 x+\sqrt{1+4 \sqrt[3]{-1}}-1\right)}{\left(\sqrt{1+4 \sqrt[3]{-1}}+\sqrt{1-4 (-1)^{2/3}}\right) \left(-2 x+\sqrt{1+4 \sqrt[3]{-1}}+1\right)}}\right)|\frac{\left(\sqrt{1+4 \sqrt[3]{-1}}+\sqrt{1-4 (-1)^{2/3}}\right)^2}{\left(\sqrt{1+4 \sqrt[3]{-1}}-\sqrt{1-4 (-1)^{2/3}}\right)^2}\right)-2 \Pi \left(-\frac{\sqrt{1+4 \sqrt[3]{-1}}+\sqrt{1-4 (-1)^{2/3}}}{\sqrt{1+4 \sqrt[3]{-1}}-\sqrt{1-4 (-1)^{2/3}}};\sin ^{-1}\left(\sqrt{\frac{\left(\sqrt{1+4 \sqrt[3]{-1}}-\sqrt{1-4 (-1)^{2/3}}\right) \left(2 x+\sqrt{1+4 \sqrt[3]{-1}}-1\right)}{\left(\sqrt{1+4 \sqrt[3]{-1}}+\sqrt{1-4 (-1)^{2/3}}\right) \left(-2 x+\sqrt{1+4 \sqrt[3]{-1}}+1\right)}}\right)|\frac{\left(\sqrt{1+4 \sqrt[3]{-1}}+\sqrt{1-4 (-1)^{2/3}}\right)^2}{\left(\sqrt{1+4 \sqrt[3]{-1}}-\sqrt{1-4 (-1)^{2/3}}\right)^2}\right)\right)}{\sqrt{\frac{\left(\sqrt{1+4 \sqrt[3]{-1}}-\sqrt{1-4 (-1)^{2/3}}\right) \left(2 x+\sqrt{1+4 \sqrt[3]{-1}}-1\right)}{\left(\sqrt{1+4 \sqrt[3]{-1}}+\sqrt{1-4 (-1)^{2/3}}\right) \left(-2 x+\sqrt{1+4 \sqrt[3]{-1}}+1\right)}} \sqrt{x^4-2 x^3+x+1}}","-\log \left(-2 x^2+2 \sqrt{x^4-2 x^3+x+1}+2 x+1\right)",1,"((1 + Sqrt[1 + 4*(-1)^(1/3)] - 2*x)*Sqrt[(Sqrt[1 + 4*(-1)^(1/3)]*(1 + Sqrt[1 - 4*(-1)^(2/3)] - 2*x))/((Sqrt[1 + 4*(-1)^(1/3)] + Sqrt[1 - 4*(-1)^(2/3)])*(1 + Sqrt[1 + 4*(-1)^(1/3)] - 2*x))]*(-1 + Sqrt[1 + 4*(-1)^(1/3)] + 2*x)*Sqrt[-((Sqrt[1 + 4*(-1)^(1/3)]*(-1 + Sqrt[1 - 4*(-1)^(2/3)] + 2*x))/((Sqrt[1 + 4*(-1)^(1/3)] - Sqrt[1 - 4*(-1)^(2/3)])*(1 + Sqrt[1 + 4*(-1)^(1/3)] - 2*x)))]*(EllipticF[ArcSin[Sqrt[((Sqrt[1 + 4*(-1)^(1/3)] - Sqrt[1 - 4*(-1)^(2/3)])*(-1 + Sqrt[1 + 4*(-1)^(1/3)] + 2*x))/((Sqrt[1 + 4*(-1)^(1/3)] + Sqrt[1 - 4*(-1)^(2/3)])*(1 + Sqrt[1 + 4*(-1)^(1/3)] - 2*x))]], (Sqrt[1 + 4*(-1)^(1/3)] + Sqrt[1 - 4*(-1)^(2/3)])^2/(Sqrt[1 + 4*(-1)^(1/3)] - Sqrt[1 - 4*(-1)^(2/3)])^2] - 2*EllipticPi[-((Sqrt[1 + 4*(-1)^(1/3)] + Sqrt[1 - 4*(-1)^(2/3)])/(Sqrt[1 + 4*(-1)^(1/3)] - Sqrt[1 - 4*(-1)^(2/3)])), ArcSin[Sqrt[((Sqrt[1 + 4*(-1)^(1/3)] - Sqrt[1 - 4*(-1)^(2/3)])*(-1 + Sqrt[1 + 4*(-1)^(1/3)] + 2*x))/((Sqrt[1 + 4*(-1)^(1/3)] + Sqrt[1 - 4*(-1)^(2/3)])*(1 + Sqrt[1 + 4*(-1)^(1/3)] - 2*x))]], (Sqrt[1 + 4*(-1)^(1/3)] + Sqrt[1 - 4*(-1)^(2/3)])^2/(Sqrt[1 + 4*(-1)^(1/3)] - Sqrt[1 - 4*(-1)^(2/3)])^2]))/(Sqrt[((Sqrt[1 + 4*(-1)^(1/3)] - Sqrt[1 - 4*(-1)^(2/3)])*(-1 + Sqrt[1 + 4*(-1)^(1/3)] + 2*x))/((Sqrt[1 + 4*(-1)^(1/3)] + Sqrt[1 - 4*(-1)^(2/3)])*(1 + Sqrt[1 + 4*(-1)^(1/3)] - 2*x))]*Sqrt[1 + x - 2*x^3 + x^4])","C",0
365,1,20,30,0.0118644,"\int \frac{1+x}{(-1+x) x \sqrt[4]{-x^3+x^4}} \, dx","Integrate[(1 + x)/((-1 + x)*x*(-x^3 + x^4)^(1/4)),x]","-\frac{4 (7 x-1)}{3 \sqrt[4]{(x-1) x^3}}","-\frac{4 (7 x-1) \left(x^4-x^3\right)^{3/4}}{3 (x-1) x^3}",1,"(-4*(-1 + 7*x))/(3*((-1 + x)*x^3)^(1/4))","A",1
366,1,117,30,0.1039607,"\int \frac{\left(3+x^4\right) \left(-1-x^3+x^4\right)}{x^6 \sqrt[4]{-x+x^5}} \, dx","Integrate[((3 + x^4)*(-1 - x^3 + x^4))/(x^6*(-x + x^5)^(1/4)),x]","\frac{4 \sqrt[4]{1-x^4} \left(165 \, _2F_1\left(-\frac{21}{16},\frac{1}{4};-\frac{5}{16};x^4\right)+x^3 \left(-165 x^4 \, _2F_1\left(\frac{1}{4},\frac{7}{16};\frac{23}{16};x^4\right)-462 x \, _2F_1\left(-\frac{5}{16},\frac{1}{4};\frac{11}{16};x^4\right)+385 \, _2F_1\left(-\frac{9}{16},\frac{1}{4};\frac{7}{16};x^4\right)+105 x^5 \, _2F_1\left(\frac{1}{4},\frac{11}{16};\frac{27}{16};x^4\right)\right)\right)}{1155 x^5 \sqrt[4]{x \left(x^4-1\right)}}","\frac{4 \left(3 x^4-7 x^3-3\right) \left(x^5-x\right)^{3/4}}{21 x^6}",1,"(4*(1 - x^4)^(1/4)*(165*Hypergeometric2F1[-21/16, 1/4, -5/16, x^4] + x^3*(385*Hypergeometric2F1[-9/16, 1/4, 7/16, x^4] - 462*x*Hypergeometric2F1[-5/16, 1/4, 11/16, x^4] - 165*x^4*Hypergeometric2F1[1/4, 7/16, 23/16, x^4] + 105*x^5*Hypergeometric2F1[1/4, 11/16, 27/16, x^4])))/(1155*x^5*(x*(-1 + x^4))^(1/4))","C",1
367,1,117,30,0.0726657,"\int \frac{\left(3+x^4\right) \left(-1+x^3+x^4\right)}{x^6 \sqrt[4]{-x+x^5}} \, dx","Integrate[((3 + x^4)*(-1 + x^3 + x^4))/(x^6*(-x + x^5)^(1/4)),x]","\frac{4 \sqrt[4]{1-x^4} \left(165 \, _2F_1\left(-\frac{21}{16},\frac{1}{4};-\frac{5}{16};x^4\right)+x^3 \left(165 x^4 \, _2F_1\left(\frac{1}{4},\frac{7}{16};\frac{23}{16};x^4\right)-462 x \, _2F_1\left(-\frac{5}{16},\frac{1}{4};\frac{11}{16};x^4\right)-385 \, _2F_1\left(-\frac{9}{16},\frac{1}{4};\frac{7}{16};x^4\right)+105 x^5 \, _2F_1\left(\frac{1}{4},\frac{11}{16};\frac{27}{16};x^4\right)\right)\right)}{1155 x^5 \sqrt[4]{x \left(x^4-1\right)}}","\frac{4 \left(3 x^4+7 x^3-3\right) \left(x^5-x\right)^{3/4}}{21 x^6}",1,"(4*(1 - x^4)^(1/4)*(165*Hypergeometric2F1[-21/16, 1/4, -5/16, x^4] + x^3*(-385*Hypergeometric2F1[-9/16, 1/4, 7/16, x^4] - 462*x*Hypergeometric2F1[-5/16, 1/4, 11/16, x^4] + 165*x^4*Hypergeometric2F1[1/4, 7/16, 23/16, x^4] + 105*x^5*Hypergeometric2F1[1/4, 11/16, 27/16, x^4])))/(1155*x^5*(x*(-1 + x^4))^(1/4))","C",1
368,0,0,30,0.468674,"\int \frac{-1+3 x^4}{\left(1-a x+x^4\right) \sqrt{x+x^5}} \, dx","Integrate[(-1 + 3*x^4)/((1 - a*x + x^4)*Sqrt[x + x^5]),x]","\int \frac{-1+3 x^4}{\left(1-a x+x^4\right) \sqrt{x+x^5}} \, dx","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x^5+x}}{x^4+1}\right)}{\sqrt{a}}",1,"Integrate[(-1 + 3*x^4)/((1 - a*x + x^4)*Sqrt[x + x^5]), x]","F",-1
369,0,0,30,0.4435467,"\int \frac{-1+3 x^4}{\left(a-x+a x^4\right) \sqrt{x+x^5}} \, dx","Integrate[(-1 + 3*x^4)/((a - x + a*x^4)*Sqrt[x + x^5]),x]","\int \frac{-1+3 x^4}{\left(a-x+a x^4\right) \sqrt{x+x^5}} \, dx","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{x^5+x}}{\sqrt{a} \left(x^4+1\right)}\right)}{\sqrt{a}}",1,"Integrate[(-1 + 3*x^4)/((a - x + a*x^4)*Sqrt[x + x^5]), x]","F",-1
370,1,947,30,5.565993,"\int \frac{\sqrt{-1+x^6} \left(2+x^6\right)}{x^3 \left(-1-x^4+x^6\right)} \, dx","Integrate[(Sqrt[-1 + x^6]*(2 + x^6))/(x^3*(-1 - x^4 + x^6)),x]","\frac{\sqrt{\frac{1-x^2}{1+\sqrt[3]{-1}}} \sqrt{x^4+x^2+1} \left(-\frac{\sqrt{3} \left(\left(1+\sqrt[3]{-1}\right) x^2+i \sqrt{3}\right) F\left(\sin ^{-1}\left(\sqrt{\frac{1-(-1)^{2/3} x^2}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{(-1)^{2/3} x^2-1}-\frac{3 i \left(\frac{\left(3+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,1\right]^2\right) \Pi \left(\frac{i \sqrt{3}}{\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,1\right]};\sin ^{-1}\left(\sqrt{\frac{1-(-1)^{2/3} x^2}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,1\right]}+\frac{-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,2\right]^3 \left(\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,1\right]-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,3\right]\right) \left(\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,3\right]\right) \Pi \left(\frac{i \sqrt{3}}{\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,2\right]};\sin ^{-1}\left(\sqrt{\frac{1-(-1)^{2/3} x^2}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)-2 \left(\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,1\right]-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,3\right]\right) \left(\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,3\right]\right) \Pi \left(\frac{i \sqrt{3}}{\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,2\right]};\sin ^{-1}\left(\sqrt{\frac{1-(-1)^{2/3} x^2}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)+\Pi \left(\frac{i \sqrt{3}}{\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,3\right]};\sin ^{-1}\left(\sqrt{\frac{1-(-1)^{2/3} x^2}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right) \left(\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,1\right]-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,2\right]\right) \left(\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,2\right]\right) \text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,3\right]^3+2 \Pi \left(\frac{i \sqrt{3}}{\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,3\right]};\sin ^{-1}\left(\sqrt{\frac{1-(-1)^{2/3} x^2}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right) \left(\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,1\right]-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,2\right]\right) \left(\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,2\right]\right)}{\left(\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,2\right]\right) \left(\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,2\right]-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,3\right]\right) \left(\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,3\right]\right)}\right)}{\left(\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,1\right]-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,2\right]\right) \left(\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,1\right]-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2-1\&,3\right]\right)}\right)}{3 \sqrt{x^6-1}}+\frac{\sqrt{x^6-1}}{x^2}","\frac{\sqrt{x^6-1}}{x^2}-\tanh ^{-1}\left(\frac{x^2}{\sqrt{x^6-1}}\right)",1,"Sqrt[-1 + x^6]/x^2 + (Sqrt[(1 - x^2)/(1 + (-1)^(1/3))]*Sqrt[1 + x^2 + x^4]*(-((Sqrt[3]*(I*Sqrt[3] + (1 + (-1)^(1/3))*x^2)*EllipticF[ArcSin[Sqrt[(1 - (-1)^(2/3)*x^2)/(1 + (-1)^(1/3))]], (-1)^(1/3)])/(-1 + (-1)^(2/3)*x^2)) - ((3*I)*((EllipticPi[(I*Sqrt[3])/((-1)^(1/3) + Root[-1 - #1^2 + #1^3 & , 1, 0]), ArcSin[Sqrt[(1 - (-1)^(2/3)*x^2)/(1 + (-1)^(1/3))]], (-1)^(1/3)]*(3 + Root[-1 - #1^2 + #1^3 & , 1, 0]^2))/((-1)^(1/3) + Root[-1 - #1^2 + #1^3 & , 1, 0]) + (2*EllipticPi[(I*Sqrt[3])/((-1)^(1/3) + Root[-1 - #1^2 + #1^3 & , 3, 0]), ArcSin[Sqrt[(1 - (-1)^(2/3)*x^2)/(1 + (-1)^(1/3))]], (-1)^(1/3)]*(Root[-1 - #1^2 + #1^3 & , 1, 0] - Root[-1 - #1^2 + #1^3 & , 2, 0])*((-1)^(1/3) + Root[-1 - #1^2 + #1^3 & , 2, 0]) + EllipticPi[(I*Sqrt[3])/((-1)^(1/3) + Root[-1 - #1^2 + #1^3 & , 3, 0]), ArcSin[Sqrt[(1 - (-1)^(2/3)*x^2)/(1 + (-1)^(1/3))]], (-1)^(1/3)]*(Root[-1 - #1^2 + #1^3 & , 1, 0] - Root[-1 - #1^2 + #1^3 & , 2, 0])*((-1)^(1/3) + Root[-1 - #1^2 + #1^3 & , 2, 0])*Root[-1 - #1^2 + #1^3 & , 3, 0]^3 - 2*EllipticPi[(I*Sqrt[3])/((-1)^(1/3) + Root[-1 - #1^2 + #1^3 & , 2, 0]), ArcSin[Sqrt[(1 - (-1)^(2/3)*x^2)/(1 + (-1)^(1/3))]], (-1)^(1/3)]*(Root[-1 - #1^2 + #1^3 & , 1, 0] - Root[-1 - #1^2 + #1^3 & , 3, 0])*((-1)^(1/3) + Root[-1 - #1^2 + #1^3 & , 3, 0]) - EllipticPi[(I*Sqrt[3])/((-1)^(1/3) + Root[-1 - #1^2 + #1^3 & , 2, 0]), ArcSin[Sqrt[(1 - (-1)^(2/3)*x^2)/(1 + (-1)^(1/3))]], (-1)^(1/3)]*Root[-1 - #1^2 + #1^3 & , 2, 0]^3*(Root[-1 - #1^2 + #1^3 & , 1, 0] - Root[-1 - #1^2 + #1^3 & , 3, 0])*((-1)^(1/3) + Root[-1 - #1^2 + #1^3 & , 3, 0]))/(((-1)^(1/3) + Root[-1 - #1^2 + #1^3 & , 2, 0])*(Root[-1 - #1^2 + #1^3 & , 2, 0] - Root[-1 - #1^2 + #1^3 & , 3, 0])*((-1)^(1/3) + Root[-1 - #1^2 + #1^3 & , 3, 0]))))/((Root[-1 - #1^2 + #1^3 & , 1, 0] - Root[-1 - #1^2 + #1^3 & , 2, 0])*(Root[-1 - #1^2 + #1^3 & , 1, 0] - Root[-1 - #1^2 + #1^3 & , 3, 0]))))/(3*Sqrt[-1 + x^6])","C",0
371,0,0,30,0.3131424,"\int \frac{\sqrt{1-x^6} \left(1+2 x^6\right)}{x^2 \left(-1-x^2+x^6\right)} \, dx","Integrate[(Sqrt[1 - x^6]*(1 + 2*x^6))/(x^2*(-1 - x^2 + x^6)),x]","\int \frac{\sqrt{1-x^6} \left(1+2 x^6\right)}{x^2 \left(-1-x^2+x^6\right)} \, dx","\frac{\sqrt{1-x^6}}{x}+\tan ^{-1}\left(\frac{x}{\sqrt{1-x^6}}\right)",1,"Integrate[(Sqrt[1 - x^6]*(1 + 2*x^6))/(x^2*(-1 - x^2 + x^6)), x]","F",-1
372,1,41,31,0.0163547,"\int \frac{1}{x^4 \sqrt{-1+x^3}} \, dx","Integrate[1/(x^4*Sqrt[-1 + x^3]),x]","\frac{1}{3} \sqrt{x^3-1} \left(\frac{1}{x^3}+\frac{\tanh ^{-1}\left(\sqrt{1-x^3}\right)}{\sqrt{1-x^3}}\right)","\frac{\sqrt{x^3-1}}{3 x^3}+\frac{1}{3} \tan ^{-1}\left(\sqrt{x^3-1}\right)",1,"(Sqrt[-1 + x^3]*(x^(-3) + ArcTanh[Sqrt[1 - x^3]]/Sqrt[1 - x^3]))/3","A",1
373,1,496,31,0.7214293,"\int \frac{-2-2 x+x^2}{\left(3-x+x^2\right) \sqrt{-1+x^3}} \, dx","Integrate[(-2 - 2*x + x^2)/((3 - x + x^2)*Sqrt[-1 + x^3]),x]","\frac{2 \sqrt{\frac{1-x}{1+\sqrt[3]{-1}}} \left(\frac{(-1)^{5/6} \left(1+\sqrt[3]{-1}\right) \sqrt{x^2+x+1} \Pi \left(\frac{2 \sqrt{3}}{-2 i+\sqrt{3}-\sqrt{11}};\sin ^{-1}\left(\sqrt{\frac{1-(-1)^{2/3} x}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{-3+2 i \sqrt{3}+\sqrt{33}}-\frac{i \sqrt{11} \sqrt{x^2+x+1} \Pi \left(\frac{2 \sqrt{3}}{-2 i+\sqrt{3}-\sqrt{11}};\sin ^{-1}\left(\sqrt{\frac{1-(-1)^{2/3} x}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{2 i-\sqrt{3}+\sqrt{11}}-\frac{(-1)^{5/6} \left(1+\sqrt[3]{-1}\right) \sqrt{x^2+x+1} \Pi \left(\frac{2 \sqrt{3}}{-2 i+\sqrt{3}+\sqrt{11}};\sin ^{-1}\left(\sqrt{\frac{1-(-1)^{2/3} x}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{3-2 i \sqrt{3}+\sqrt{33}}-\frac{i \sqrt{11} \sqrt{x^2+x+1} \Pi \left(\frac{2 \sqrt{3}}{-2 i+\sqrt{3}+\sqrt{11}};\sin ^{-1}\left(\sqrt{\frac{1-(-1)^{2/3} x}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{-2 i+\sqrt{3}+\sqrt{11}}+\frac{\left(x+\sqrt[3]{-1}\right) \sqrt{\frac{(-1)^{2/3} x+\sqrt[3]{-1}}{1+\sqrt[3]{-1}}} F\left(\sin ^{-1}\left(\sqrt{\frac{1-(-1)^{2/3} x}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{\sqrt{\frac{1-(-1)^{2/3} x}{1+\sqrt[3]{-1}}}}\right)}{\sqrt{x^3-1}}","-\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{x^3-1}}{x^2+x+1}\right)",1,"(2*Sqrt[(1 - x)/(1 + (-1)^(1/3))]*((((-1)^(1/3) + x)*Sqrt[((-1)^(1/3) + (-1)^(2/3)*x)/(1 + (-1)^(1/3))]*EllipticF[ArcSin[Sqrt[(1 - (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)])/Sqrt[(1 - (-1)^(2/3)*x)/(1 + (-1)^(1/3))] - (I*Sqrt[11]*Sqrt[1 + x + x^2]*EllipticPi[(2*Sqrt[3])/(-2*I + Sqrt[3] - Sqrt[11]), ArcSin[Sqrt[(1 - (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)])/(2*I - Sqrt[3] + Sqrt[11]) + ((-1)^(5/6)*(1 + (-1)^(1/3))*Sqrt[1 + x + x^2]*EllipticPi[(2*Sqrt[3])/(-2*I + Sqrt[3] - Sqrt[11]), ArcSin[Sqrt[(1 - (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)])/(-3 + (2*I)*Sqrt[3] + Sqrt[33]) - (I*Sqrt[11]*Sqrt[1 + x + x^2]*EllipticPi[(2*Sqrt[3])/(-2*I + Sqrt[3] + Sqrt[11]), ArcSin[Sqrt[(1 - (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)])/(-2*I + Sqrt[3] + Sqrt[11]) - ((-1)^(5/6)*(1 + (-1)^(1/3))*Sqrt[1 + x + x^2]*EllipticPi[(2*Sqrt[3])/(-2*I + Sqrt[3] + Sqrt[11]), ArcSin[Sqrt[(1 - (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)])/(3 - (2*I)*Sqrt[3] + Sqrt[33])))/Sqrt[-1 + x^3]","C",0
374,1,291,31,0.5880094,"\int \frac{-2-2 x+x^2}{\left(-1+3 x+x^2\right) \sqrt{-1+x^3}} \, dx","Integrate[(-2 - 2*x + x^2)/((-1 + 3*x + x^2)*Sqrt[-1 + x^3]),x]","\frac{2 \sqrt{\frac{1-x}{1+\sqrt[3]{-1}}} \sqrt{x^2+x+1} \left(-\frac{\sqrt{3} \left(1+\sqrt[3]{-1}\right) \left(x+\sqrt[3]{-1}\right) F\left(\sin ^{-1}\left(\sqrt{\frac{1-(-1)^{2/3} x}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{(-1)^{2/3} x-1}+\frac{6 i \left(\left(-1+5 \sqrt[3]{-1}+\sqrt{13}+\sqrt[3]{-1} \sqrt{13}\right) \Pi \left(\frac{2 \sqrt{3}}{2 i+\sqrt{3}+i \sqrt{13}};\sin ^{-1}\left(\sqrt{\frac{1-(-1)^{2/3} x}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)-\left(1-5 \sqrt[3]{-1}+\sqrt{13}+\sqrt[3]{-1} \sqrt{13}\right) \Pi \left(\frac{2 i \sqrt{3}}{-3+2 \sqrt[3]{-1}+\sqrt{13}};\sin ^{-1}\left(\sqrt{\frac{1-(-1)^{2/3} x}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)\right)}{-12-4 i \sqrt{3}}\right)}{3 \sqrt{x^3-1}}","-\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{x^3-1}}{x^2+x+1}\right)",1,"(2*Sqrt[(1 - x)/(1 + (-1)^(1/3))]*Sqrt[1 + x + x^2]*(-((Sqrt[3]*(1 + (-1)^(1/3))*((-1)^(1/3) + x)*EllipticF[ArcSin[Sqrt[(1 - (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)])/(-1 + (-1)^(2/3)*x)) + ((6*I)*((-1 + 5*(-1)^(1/3) + Sqrt[13] + (-1)^(1/3)*Sqrt[13])*EllipticPi[(2*Sqrt[3])/(2*I + Sqrt[3] + I*Sqrt[13]), ArcSin[Sqrt[(1 - (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)] - (1 - 5*(-1)^(1/3) + Sqrt[13] + (-1)^(1/3)*Sqrt[13])*EllipticPi[((2*I)*Sqrt[3])/(-3 + 2*(-1)^(1/3) + Sqrt[13]), ArcSin[Sqrt[(1 - (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)]))/(-12 - (4*I)*Sqrt[3])))/(3*Sqrt[-1 + x^3])","C",1
375,1,48,31,0.0118498,"\int \frac{\sqrt{-1+x^3}}{x^4} \, dx","Integrate[Sqrt[-1 + x^3]/x^4,x]","-\frac{x^3+\sqrt{1-x^3} x^3 \tanh ^{-1}\left(\sqrt{1-x^3}\right)-1}{3 x^3 \sqrt{x^3-1}}","\frac{1}{3} \tan ^{-1}\left(\sqrt{x^3-1}\right)-\frac{\sqrt{x^3-1}}{3 x^3}",1,"-1/3*(-1 + x^3 + x^3*Sqrt[1 - x^3]*ArcTanh[Sqrt[1 - x^3]])/(x^3*Sqrt[-1 + x^3])","A",1
376,1,31,31,0.0078693,"\int \frac{1}{x^4 \sqrt{1+x^3}} \, dx","Integrate[1/(x^4*Sqrt[1 + x^3]),x]","\frac{1}{3} \tanh ^{-1}\left(\sqrt{x^3+1}\right)-\frac{\sqrt{x^3+1}}{3 x^3}","\frac{1}{3} \tanh ^{-1}\left(\sqrt{x^3+1}\right)-\frac{\sqrt{x^3+1}}{3 x^3}",1,"-1/3*Sqrt[1 + x^3]/x^3 + ArcTanh[Sqrt[1 + x^3]]/3","A",1
377,1,46,31,0.0073666,"\int \frac{1+x}{(-2+x) \sqrt{1+x^3}} \, dx","Integrate[(1 + x)/((-2 + x)*Sqrt[1 + x^3]),x]","\frac{1}{3} \log \left(3-\frac{(x+1)^2}{\sqrt{x^3+1}}\right)-\frac{1}{3} \log \left(\frac{(x+1)^2}{\sqrt{x^3+1}}+3\right)","-\frac{2}{3} \tanh ^{-1}\left(\frac{\frac{x^2}{3}+\frac{2 x}{3}+\frac{1}{3}}{\sqrt{x^3+1}}\right)",1,"Log[3 - (1 + x)^2/Sqrt[1 + x^3]]/3 - Log[3 + (1 + x)^2/Sqrt[1 + x^3]]/3","A",1
378,1,44,31,0.0103119,"\int \frac{\sqrt{1+x^3}}{x^4} \, dx","Integrate[Sqrt[1 + x^3]/x^4,x]","-\frac{1}{3 x^3 \sqrt{x^3+1}}-\frac{1}{3 \sqrt{x^3+1}}-\frac{1}{3} \tanh ^{-1}\left(\sqrt{x^3+1}\right)","-\frac{\sqrt{x^3+1}}{3 x^3}-\frac{1}{3} \tanh ^{-1}\left(\sqrt{x^3+1}\right)",1,"-1/3*1/Sqrt[1 + x^3] - 1/(3*x^3*Sqrt[1 + x^3]) - ArcTanh[Sqrt[1 + x^3]]/3","A",1
379,1,69,31,0.1963984,"\int \frac{1+x}{(-1+2 x) \sqrt{x+x^4}} \, dx","Integrate[(1 + x)/((-1 + 2*x)*Sqrt[x + x^4]),x]","-\frac{\sqrt{\frac{1}{x^3}+1} x^2 \left(\log \left(\frac{\left(\frac{1}{x}+1\right)^2}{\sqrt{\frac{1}{x^3}+1}}+3\right)-\log \left(3-\frac{\left(\frac{1}{x}+1\right)^2}{\sqrt{\frac{1}{x^3}+1}}\right)\right)}{3 \sqrt{x^4+x}}","-\frac{2}{3} \tanh ^{-1}\left(\frac{\frac{x^2}{3}+\frac{2 x}{3}+\frac{1}{3}}{\sqrt{x^4+x}}\right)",1,"-1/3*(Sqrt[1 + x^(-3)]*x^2*(-Log[3 - (1 + x^(-1))^2/Sqrt[1 + x^(-3)]] + Log[3 + (1 + x^(-1))^2/Sqrt[1 + x^(-3)]]))/Sqrt[x + x^4]","B",1
380,1,701,31,1.5620679,"\int \frac{-1+x}{\sqrt{-5+4 x^2-4 x^3+x^4}} \, dx","Integrate[(-1 + x)/Sqrt[-5 + 4*x^2 - 4*x^3 + x^4],x]","\frac{2 \sqrt{\sqrt{5}-1} \left(-x+i \sqrt{\sqrt{5}-1}+1\right) \left(-x+\sqrt{1+\sqrt{5}}+1\right) \sqrt{\frac{\left(\sqrt{1+\sqrt{5}}-i \sqrt{\sqrt{5}-1}\right) \left(x+i \sqrt{\sqrt{5}-1}-1\right)}{\left(\sqrt{1+\sqrt{5}}+i \sqrt{\sqrt{5}-1}\right) \left(x-i \sqrt{\sqrt{5}-1}-1\right)}} \sqrt{\frac{i \left(x+\sqrt{1+\sqrt{5}}-1\right)}{\left(\sqrt{\sqrt{5}-1}+i \sqrt{1+\sqrt{5}}\right) \left(i x+\sqrt{\sqrt{5}-1}-i\right)}} \left(F\left(\sin ^{-1}\left(\sqrt{\frac{\sqrt{1+\sqrt{5}} x-i \sqrt{-1+\sqrt{5}} x-\sqrt{1+\sqrt{5}}+i \sqrt{-1+\sqrt{5}}+\sqrt{5}-(1-2 i)}{\sqrt{1+\sqrt{5}} x+i \sqrt{-1+\sqrt{5}} x-\sqrt{1+\sqrt{5}}-i \sqrt{-1+\sqrt{5}}+\sqrt{5}-(1+2 i)}}\right)|-\frac{3}{5}+\frac{4 i}{5}\right)-2 \Pi \left(-\frac{\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}}{\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}};\sin ^{-1}\left(\sqrt{\frac{\sqrt{1+\sqrt{5}} x-i \sqrt{-1+\sqrt{5}} x-\sqrt{1+\sqrt{5}}+i \sqrt{-1+\sqrt{5}}+\sqrt{5}-(1-2 i)}{\sqrt{1+\sqrt{5}} x+i \sqrt{-1+\sqrt{5}} x-\sqrt{1+\sqrt{5}}-i \sqrt{-1+\sqrt{5}}+\sqrt{5}-(1+2 i)}}\right)|-\frac{3}{5}+\frac{4 i}{5}\right)\right)}{\left(\sqrt{\sqrt{5}-1}+i \sqrt{1+\sqrt{5}}\right) \sqrt{-\frac{i \left(-x+\sqrt{1+\sqrt{5}}+1\right)}{\left(\sqrt{\sqrt{5}-1}-i \sqrt{1+\sqrt{5}}\right) \left(i x+\sqrt{\sqrt{5}-1}-i\right)}} \sqrt{x^4-4 x^3+4 x^2-5}}","\frac{1}{2} \log \left(x^2+\sqrt{x^4-4 x^3+4 x^2-5}-2 x\right)",1,"(2*Sqrt[-1 + Sqrt[5]]*(1 + I*Sqrt[-1 + Sqrt[5]] - x)*(1 + Sqrt[1 + Sqrt[5]] - x)*Sqrt[(((-I)*Sqrt[-1 + Sqrt[5]] + Sqrt[1 + Sqrt[5]])*(-1 + I*Sqrt[-1 + Sqrt[5]] + x))/((I*Sqrt[-1 + Sqrt[5]] + Sqrt[1 + Sqrt[5]])*(-1 - I*Sqrt[-1 + Sqrt[5]] + x))]*Sqrt[(I*(-1 + Sqrt[1 + Sqrt[5]] + x))/((Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])*(-I + Sqrt[-1 + Sqrt[5]] + I*x))]*(EllipticF[ArcSin[Sqrt[((-1 + 2*I) + Sqrt[5] + I*Sqrt[-1 + Sqrt[5]] - Sqrt[1 + Sqrt[5]] - I*Sqrt[-1 + Sqrt[5]]*x + Sqrt[1 + Sqrt[5]]*x)/((-1 - 2*I) + Sqrt[5] - I*Sqrt[-1 + Sqrt[5]] - Sqrt[1 + Sqrt[5]] + I*Sqrt[-1 + Sqrt[5]]*x + Sqrt[1 + Sqrt[5]]*x)]], -3/5 + (4*I)/5] - 2*EllipticPi[-((Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]])/(Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])), ArcSin[Sqrt[((-1 + 2*I) + Sqrt[5] + I*Sqrt[-1 + Sqrt[5]] - Sqrt[1 + Sqrt[5]] - I*Sqrt[-1 + Sqrt[5]]*x + Sqrt[1 + Sqrt[5]]*x)/((-1 - 2*I) + Sqrt[5] - I*Sqrt[-1 + Sqrt[5]] - Sqrt[1 + Sqrt[5]] + I*Sqrt[-1 + Sqrt[5]]*x + Sqrt[1 + Sqrt[5]]*x)]], -3/5 + (4*I)/5]))/((Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])*Sqrt[((-I)*(1 + Sqrt[1 + Sqrt[5]] - x))/((Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]])*(-I + Sqrt[-1 + Sqrt[5]] + I*x))]*Sqrt[-5 + 4*x^2 - 4*x^3 + x^4])","C",0
381,1,898,31,2.2764966,"\int \frac{2+x}{\sqrt{13+16 x^2+8 x^3+x^4}} \, dx","Integrate[(2 + x)/Sqrt[13 + 16*x^2 + 8*x^3 + x^4],x]","\frac{2 \left(\sqrt{4-i \sqrt{13}}+\sqrt{4+i \sqrt{13}}\right) \sqrt{\frac{\sqrt{4-i \sqrt{13}} \left(-x+\sqrt{4+i \sqrt{13}}-2\right)}{\left(\sqrt{4-i \sqrt{13}}+\sqrt{4+i \sqrt{13}}\right) \left(-x+\sqrt{4-i \sqrt{13}}-2\right)}} \left(x-\sqrt{4-i \sqrt{13}}+2\right)^2 \sqrt{\frac{\left(-\sqrt{4-i \sqrt{13}}+\sqrt{4+i \sqrt{13}}\right) \left(x+\sqrt{4-i \sqrt{13}}+2\right)}{\left(\sqrt{4-i \sqrt{13}}+\sqrt{4+i \sqrt{13}}\right) \left(x-\sqrt{4-i \sqrt{13}}+2\right)}} \sqrt{-\frac{\sqrt{4-i \sqrt{13}} \left(x+\sqrt{4+i \sqrt{13}}+2\right)}{\left(\sqrt{4-i \sqrt{13}}-\sqrt{4+i \sqrt{13}}\right) \left(-x+\sqrt{4-i \sqrt{13}}-2\right)}} \left(F\left(\sin ^{-1}\left(\sqrt{\frac{i \left(\sqrt{4-i \sqrt{13}}-\sqrt{4+i \sqrt{13}}\right) x-2 i \sqrt{4+i \sqrt{13}}+2 i \sqrt{4-i \sqrt{13}}-i \sqrt{29}+\sqrt{13}+4 i}{-i \left(\sqrt{4-i \sqrt{13}}+\sqrt{4+i \sqrt{13}}\right) x-2 i \sqrt{4+i \sqrt{13}}-2 i \sqrt{4-i \sqrt{13}}+i \sqrt{29}+\sqrt{13}+4 i}}\right)|\frac{1}{13} \left(-45-8 \sqrt{29}\right)\right)-2 \Pi \left(-\frac{\sqrt{4-i \sqrt{13}}+\sqrt{4+i \sqrt{13}}}{\sqrt{4-i \sqrt{13}}-\sqrt{4+i \sqrt{13}}};\sin ^{-1}\left(\sqrt{\frac{i \left(\sqrt{4-i \sqrt{13}}-\sqrt{4+i \sqrt{13}}\right) x-2 i \sqrt{4+i \sqrt{13}}+2 i \sqrt{4-i \sqrt{13}}-i \sqrt{29}+\sqrt{13}+4 i}{-i \left(\sqrt{4-i \sqrt{13}}+\sqrt{4+i \sqrt{13}}\right) x-2 i \sqrt{4+i \sqrt{13}}-2 i \sqrt{4-i \sqrt{13}}+i \sqrt{29}+\sqrt{13}+4 i}}\right)|\frac{1}{13} \left(-45-8 \sqrt{29}\right)\right)\right)}{\left(\sqrt{4-i \sqrt{13}}-\sqrt{4+i \sqrt{13}}\right) \sqrt{x^4+8 x^3+16 x^2+13}}","\frac{1}{2} \log \left(x^2+\sqrt{x^4+8 x^3+16 x^2+13}+4 x\right)",1,"(2*(Sqrt[4 - I*Sqrt[13]] + Sqrt[4 + I*Sqrt[13]])*Sqrt[(Sqrt[4 - I*Sqrt[13]]*(-2 + Sqrt[4 + I*Sqrt[13]] - x))/((Sqrt[4 - I*Sqrt[13]] + Sqrt[4 + I*Sqrt[13]])*(-2 + Sqrt[4 - I*Sqrt[13]] - x))]*(2 - Sqrt[4 - I*Sqrt[13]] + x)^2*Sqrt[((-Sqrt[4 - I*Sqrt[13]] + Sqrt[4 + I*Sqrt[13]])*(2 + Sqrt[4 - I*Sqrt[13]] + x))/((Sqrt[4 - I*Sqrt[13]] + Sqrt[4 + I*Sqrt[13]])*(2 - Sqrt[4 - I*Sqrt[13]] + x))]*Sqrt[-((Sqrt[4 - I*Sqrt[13]]*(2 + Sqrt[4 + I*Sqrt[13]] + x))/((Sqrt[4 - I*Sqrt[13]] - Sqrt[4 + I*Sqrt[13]])*(-2 + Sqrt[4 - I*Sqrt[13]] - x)))]*(EllipticF[ArcSin[Sqrt[(4*I + Sqrt[13] - I*Sqrt[29] + (2*I)*Sqrt[4 - I*Sqrt[13]] - (2*I)*Sqrt[4 + I*Sqrt[13]] + I*(Sqrt[4 - I*Sqrt[13]] - Sqrt[4 + I*Sqrt[13]])*x)/(4*I + Sqrt[13] + I*Sqrt[29] - (2*I)*Sqrt[4 - I*Sqrt[13]] - (2*I)*Sqrt[4 + I*Sqrt[13]] - I*(Sqrt[4 - I*Sqrt[13]] + Sqrt[4 + I*Sqrt[13]])*x)]], (-45 - 8*Sqrt[29])/13] - 2*EllipticPi[-((Sqrt[4 - I*Sqrt[13]] + Sqrt[4 + I*Sqrt[13]])/(Sqrt[4 - I*Sqrt[13]] - Sqrt[4 + I*Sqrt[13]])), ArcSin[Sqrt[(4*I + Sqrt[13] - I*Sqrt[29] + (2*I)*Sqrt[4 - I*Sqrt[13]] - (2*I)*Sqrt[4 + I*Sqrt[13]] + I*(Sqrt[4 - I*Sqrt[13]] - Sqrt[4 + I*Sqrt[13]])*x)/(4*I + Sqrt[13] + I*Sqrt[29] - (2*I)*Sqrt[4 - I*Sqrt[13]] - (2*I)*Sqrt[4 + I*Sqrt[13]] - I*(Sqrt[4 - I*Sqrt[13]] + Sqrt[4 + I*Sqrt[13]])*x)]], (-45 - 8*Sqrt[29])/13]))/((Sqrt[4 - I*Sqrt[13]] - Sqrt[4 + I*Sqrt[13]])*Sqrt[13 + 16*x^2 + 8*x^3 + x^4])","C",0
382,1,30,31,0.0084177,"\int \frac{x}{\sqrt{b+a x^4}} \, dx","Integrate[x/Sqrt[b + a*x^4],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a} x^2}{\sqrt{a x^4+b}}\right)}{2 \sqrt{a}}","\frac{\log \left(\sqrt{a x^4+b}+\sqrt{a} x^2\right)}{2 \sqrt{a}}",1,"ArcTanh[(Sqrt[a]*x^2)/Sqrt[b + a*x^4]]/(2*Sqrt[a])","A",1
383,1,41,31,0.0183946,"\int \frac{1}{x^7 \sqrt{-1+x^6}} \, dx","Integrate[1/(x^7*Sqrt[-1 + x^6]),x]","\frac{1}{6} \sqrt{x^6-1} \left(\frac{1}{x^6}+\frac{\tanh ^{-1}\left(\sqrt{1-x^6}\right)}{\sqrt{1-x^6}}\right)","\frac{\sqrt{x^6-1}}{6 x^6}+\frac{1}{6} \tan ^{-1}\left(\sqrt{x^6-1}\right)",1,"(Sqrt[-1 + x^6]*(x^(-6) + ArcTanh[Sqrt[1 - x^6]]/Sqrt[1 - x^6]))/6","A",1
384,1,48,31,0.0100305,"\int \frac{\sqrt{-1+x^6}}{x^7} \, dx","Integrate[Sqrt[-1 + x^6]/x^7,x]","-\frac{x^6+\sqrt{1-x^6} x^6 \tanh ^{-1}\left(\sqrt{1-x^6}\right)-1}{6 x^6 \sqrt{x^6-1}}","\frac{1}{6} \tan ^{-1}\left(\sqrt{x^6-1}\right)-\frac{\sqrt{x^6-1}}{6 x^6}",1,"-1/6*(-1 + x^6 + x^6*Sqrt[1 - x^6]*ArcTanh[Sqrt[1 - x^6]])/(x^6*Sqrt[-1 + x^6])","A",1
385,1,30,31,0.0092469,"\int \frac{-1+x^6}{x^7 \sqrt{1+x^6}} \, dx","Integrate[(-1 + x^6)/(x^7*Sqrt[1 + x^6]),x]","\frac{1}{6} \left(\frac{\sqrt{x^6+1}}{x^6}-3 \tanh ^{-1}\left(\sqrt{x^6+1}\right)\right)","\frac{\sqrt{x^6+1}}{6 x^6}-\frac{1}{2} \tanh ^{-1}\left(\sqrt{x^6+1}\right)",1,"(Sqrt[1 + x^6]/x^6 - 3*ArcTanh[Sqrt[1 + x^6]])/6","A",1
386,1,44,31,0.0116681,"\int \frac{\sqrt{1+x^6}}{x^7} \, dx","Integrate[Sqrt[1 + x^6]/x^7,x]","-\frac{1}{6 x^6 \sqrt{x^6+1}}-\frac{1}{6 \sqrt{x^6+1}}-\frac{1}{6} \tanh ^{-1}\left(\sqrt{x^6+1}\right)","-\frac{\sqrt{x^6+1}}{6 x^6}-\frac{1}{6} \tanh ^{-1}\left(\sqrt{x^6+1}\right)",1,"-1/6*1/Sqrt[1 + x^6] - 1/(6*x^6*Sqrt[1 + x^6]) - ArcTanh[Sqrt[1 + x^6]]/6","A",1
387,1,168,31,0.1201438,"\int \frac{\left(2+x^6\right) \left(1-2 x^6+x^8+x^{12}\right)}{x^{10} \left(-1+x^6\right)^{3/4}} \, dx","Integrate[((2 + x^6)*(1 - 2*x^6 + x^8 + x^12))/(x^10*(-1 + x^6)^(3/4)),x]","\frac{45 \left(1-x^6\right)^{3/4} x^6 \, _2F_1\left(-\frac{1}{2},\frac{3}{4};\frac{1}{2};x^6\right)-10 \left(1-x^6\right)^{3/4} \, _2F_1\left(-\frac{3}{2},\frac{3}{4};-\frac{1}{2};x^6\right)-90 \left(1-x^6\right)^{3/4} x^8 \, _2F_1\left(-\frac{1}{6},\frac{3}{4};\frac{5}{6};x^6\right)+x^{12} \left(10 \left(1-x^6\right)^{3/4} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{3}{2};x^6\right)+9 \left(1-x^6\right)^{3/4} x^2 \, _2F_1\left(\frac{3}{4},\frac{5}{6};\frac{11}{6};x^6\right)+10 \left(x^6-1\right)\right)}{45 x^9 \left(x^6-1\right)^{3/4}}","\frac{2 \sqrt[4]{x^6-1} \left(x^{12}+9 x^8-2 x^6+1\right)}{9 x^9}",1,"(-10*(1 - x^6)^(3/4)*Hypergeometric2F1[-3/2, 3/4, -1/2, x^6] + 45*x^6*(1 - x^6)^(3/4)*Hypergeometric2F1[-1/2, 3/4, 1/2, x^6] - 90*x^8*(1 - x^6)^(3/4)*Hypergeometric2F1[-1/6, 3/4, 5/6, x^6] + x^12*(10*(-1 + x^6) + 10*(1 - x^6)^(3/4)*Hypergeometric2F1[1/2, 3/4, 3/2, x^6] + 9*x^2*(1 - x^6)^(3/4)*Hypergeometric2F1[3/4, 5/6, 11/6, x^6]))/(45*x^9*(-1 + x^6)^(3/4))","C",1
388,1,533,32,2.1544772,"\int \frac{-1+2 x+2 x^2}{\left(1-x+3 x^2\right) \sqrt{-x+x^4}} \, dx","Integrate[(-1 + 2*x + 2*x^2)/((1 - x + 3*x^2)*Sqrt[-x + x^4]),x]","-\frac{2 \sqrt{\frac{1-\frac{1}{x}}{1+\sqrt[3]{-1}}} x^2 \left(\frac{i \sqrt{11} \sqrt{\frac{1}{x^2}+\frac{1}{x}+1} \Pi \left(\frac{2 \sqrt{3}}{-2 i+\sqrt{3}-\sqrt{11}};\sin ^{-1}\left(\sqrt{\frac{1-\frac{(-1)^{2/3}}{x}}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{2 i-\sqrt{3}+\sqrt{11}}+\frac{\sqrt{\frac{1}{x^2}+\frac{1}{x}+1} \Pi \left(\frac{2 \sqrt{3}}{-2 i+\sqrt{3}-\sqrt{11}};\sin ^{-1}\left(\sqrt{-\frac{2 i+\frac{i+\sqrt{3}}{x}}{-3 i+\sqrt{3}}}\right)|\frac{1}{2} \left(1+i \sqrt{3}\right)\right)}{2 i-\sqrt{3}+\sqrt{11}}+\frac{(-1)^{5/6} \left(1+\sqrt[3]{-1}\right) \sqrt{\frac{1}{x^2}+\frac{1}{x}+1} \Pi \left(\frac{2 \sqrt{3}}{-2 i+\sqrt{3}+\sqrt{11}};\sin ^{-1}\left(\sqrt{\frac{1-\frac{(-1)^{2/3}}{x}}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{3-2 i \sqrt{3}+\sqrt{33}}+\frac{i \sqrt{11} \sqrt{\frac{1}{x^2}+\frac{1}{x}+1} \Pi \left(\frac{2 \sqrt{3}}{-2 i+\sqrt{3}+\sqrt{11}};\sin ^{-1}\left(\sqrt{\frac{1-\frac{(-1)^{2/3}}{x}}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{-2 i+\sqrt{3}+\sqrt{11}}-\frac{\left(\frac{1}{x}+\sqrt[3]{-1}\right) \sqrt{\frac{\frac{(-1)^{2/3}}{x}+\sqrt[3]{-1}}{1+\sqrt[3]{-1}}} F\left(\sin ^{-1}\left(\sqrt{\frac{1-\frac{(-1)^{2/3}}{x}}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{\sqrt{\frac{1-\frac{(-1)^{2/3}}{x}}{1+\sqrt[3]{-1}}}}\right)}{\sqrt{x \left(x^3-1\right)}}","\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{x^4-x}}{x^2+x+1}\right)",1,"(-2*Sqrt[(1 - x^(-1))/(1 + (-1)^(1/3))]*x^2*(-((((-1)^(1/3) + x^(-1))*Sqrt[((-1)^(1/3) + (-1)^(2/3)/x)/(1 + (-1)^(1/3))]*EllipticF[ArcSin[Sqrt[(1 - (-1)^(2/3)/x)/(1 + (-1)^(1/3))]], (-1)^(1/3)])/Sqrt[(1 - (-1)^(2/3)/x)/(1 + (-1)^(1/3))]) + (I*Sqrt[11]*Sqrt[1 + x^(-2) + x^(-1)]*EllipticPi[(2*Sqrt[3])/(-2*I + Sqrt[3] - Sqrt[11]), ArcSin[Sqrt[(1 - (-1)^(2/3)/x)/(1 + (-1)^(1/3))]], (-1)^(1/3)])/(2*I - Sqrt[3] + Sqrt[11]) + (Sqrt[1 + x^(-2) + x^(-1)]*EllipticPi[(2*Sqrt[3])/(-2*I + Sqrt[3] - Sqrt[11]), ArcSin[Sqrt[-((2*I + (I + Sqrt[3])/x)/(-3*I + Sqrt[3]))]], (1 + I*Sqrt[3])/2])/(2*I - Sqrt[3] + Sqrt[11]) + (I*Sqrt[11]*Sqrt[1 + x^(-2) + x^(-1)]*EllipticPi[(2*Sqrt[3])/(-2*I + Sqrt[3] + Sqrt[11]), ArcSin[Sqrt[(1 - (-1)^(2/3)/x)/(1 + (-1)^(1/3))]], (-1)^(1/3)])/(-2*I + Sqrt[3] + Sqrt[11]) + ((-1)^(5/6)*(1 + (-1)^(1/3))*Sqrt[1 + x^(-2) + x^(-1)]*EllipticPi[(2*Sqrt[3])/(-2*I + Sqrt[3] + Sqrt[11]), ArcSin[Sqrt[(1 - (-1)^(2/3)/x)/(1 + (-1)^(1/3))]], (-1)^(1/3)])/(3 - (2*I)*Sqrt[3] + Sqrt[33])))/Sqrt[x*(-1 + x^3)]","C",0
389,1,25,32,0.0126499,"\int \frac{1+x^3}{x^3 \left(-1+x^3\right) \sqrt[4]{-x+x^4}} \, dx","Integrate[(1 + x^3)/(x^3*(-1 + x^3)*(-x + x^4)^(1/4)),x]","-\frac{4 \left(7 x^3-1\right)}{9 x^2 \sqrt[4]{x \left(x^3-1\right)}}","-\frac{4 \left(7 x^3-1\right) \left(x^4-x\right)^{3/4}}{9 x^3 \left(x^3-1\right)}",1,"(-4*(-1 + 7*x^3))/(9*x^2*(x*(-1 + x^3))^(1/4))","A",1
390,1,298,32,1.239113,"\int \frac{-1-2 x+2 x^2}{\left(-1+3 x+x^2\right) \sqrt{x+x^4}} \, dx","Integrate[(-1 - 2*x + 2*x^2)/((-1 + 3*x + x^2)*Sqrt[x + x^4]),x]","-\frac{2 \sqrt{\frac{1}{x^2}-\frac{1}{x}+1} \sqrt{\frac{\frac{1}{x}+1}{1+\sqrt[3]{-1}}} x^2 \left(\frac{\sqrt{3} \left(-i \sqrt{3} x+\sqrt[3]{-1}+1\right) F\left(\sin ^{-1}\left(\sqrt{\frac{x+(-1)^{2/3}}{\left(1+\sqrt[3]{-1}\right) x}}\right)|\sqrt[3]{-1}\right)}{x+(-1)^{2/3}}-\frac{6 i \left(\left(-1+5 \sqrt[3]{-1}+\sqrt{13}+\sqrt[3]{-1} \sqrt{13}\right) \Pi \left(\frac{2 \sqrt{3}}{2 i+\sqrt{3}+i \sqrt{13}};\sin ^{-1}\left(\sqrt{\frac{x+(-1)^{2/3}}{\left(1+\sqrt[3]{-1}\right) x}}\right)|\sqrt[3]{-1}\right)-\left(1-5 \sqrt[3]{-1}+\sqrt{13}+\sqrt[3]{-1} \sqrt{13}\right) \Pi \left(\frac{2 i \sqrt{3}}{-3+2 \sqrt[3]{-1}+\sqrt{13}};\sin ^{-1}\left(\sqrt{\frac{x+(-1)^{2/3}}{\left(1+\sqrt[3]{-1}\right) x}}\right)|\sqrt[3]{-1}\right)\right)}{-12-4 i \sqrt{3}}\right)}{3 \sqrt{x^4+x}}","\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{x^4+x}}{x^2-x+1}\right)",1,"(-2*Sqrt[1 + x^(-2) - x^(-1)]*Sqrt[(1 + x^(-1))/(1 + (-1)^(1/3))]*x^2*((Sqrt[3]*(1 + (-1)^(1/3) - I*Sqrt[3]*x)*EllipticF[ArcSin[Sqrt[((-1)^(2/3) + x)/((1 + (-1)^(1/3))*x)]], (-1)^(1/3)])/((-1)^(2/3) + x) - ((6*I)*((-1 + 5*(-1)^(1/3) + Sqrt[13] + (-1)^(1/3)*Sqrt[13])*EllipticPi[(2*Sqrt[3])/(2*I + Sqrt[3] + I*Sqrt[13]), ArcSin[Sqrt[((-1)^(2/3) + x)/((1 + (-1)^(1/3))*x)]], (-1)^(1/3)] - (1 - 5*(-1)^(1/3) + Sqrt[13] + (-1)^(1/3)*Sqrt[13])*EllipticPi[((2*I)*Sqrt[3])/(-3 + 2*(-1)^(1/3) + Sqrt[13]), ArcSin[Sqrt[((-1)^(2/3) + x)/((1 + (-1)^(1/3))*x)]], (-1)^(1/3)]))/(-12 - (4*I)*Sqrt[3])))/(3*Sqrt[x + x^4])","C",1
391,1,25,32,0.0106387,"\int \frac{-1+x^2}{x^2 \left(1+x^2\right) \sqrt[4]{x^2+x^4}} \, dx","Integrate[(-1 + x^2)/(x^2*(1 + x^2)*(x^2 + x^4)^(1/4)),x]","\frac{14 x^2+2}{3 x \sqrt[4]{x^4+x^2}}","\frac{2 \left(7 x^2+1\right) \left(x^4+x^2\right)^{3/4}}{3 x^3 \left(x^2+1\right)}",1,"(2 + 14*x^2)/(3*x*(x^2 + x^4)^(1/4))","A",1
392,1,292,32,0.5419823,"\int \frac{-1+2 x}{\sqrt{-8 x+9 x^2-2 x^3+x^4}} \, dx","Integrate[(-1 + 2*x)/Sqrt[-8*x + 9*x^2 - 2*x^3 + x^4],x]","\frac{\sqrt{-\frac{i (x-1)}{\left(\sqrt{31}-15 i\right) x}} x \left(64 \sqrt{62} \sqrt{-\frac{16 i}{x}+\sqrt{31}+i} x \sqrt{\frac{x^2-x+8}{x^2}} \Pi \left(\frac{2 \sqrt{31}}{i+\sqrt{31}};\sin ^{-1}\left(\frac{\sqrt{\sqrt{31}+i-\frac{16 i}{x}}}{\sqrt{2} \sqrt[4]{31}}\right)|\frac{2 \sqrt{31}}{-15 i+\sqrt{31}}\right)+\sqrt{\frac{16 i}{x}+\sqrt{31}-i} \left(\left(-31+15 i \sqrt{31}\right) x+8 i \sqrt{31}+248\right) F\left(\sin ^{-1}\left(\frac{\sqrt{\sqrt{31}+i-\frac{16 i}{x}}}{\sqrt{2} \sqrt[4]{31}}\right)|\frac{2 \sqrt{31}}{-15 i+\sqrt{31}}\right)\right)}{\sqrt{31} \left(\sqrt{31}+i\right) \sqrt{-\frac{16 i}{x}+\sqrt{31}+i} \sqrt{x \left(x^3-2 x^2+9 x-8\right)}}","-\log \left(-x^2+\sqrt{x^4-2 x^3+9 x^2-8 x}+x-4\right)",1,"(Sqrt[((-I)*(-1 + x))/((-15*I + Sqrt[31])*x)]*x*(Sqrt[-I + Sqrt[31] + (16*I)/x]*(248 + (8*I)*Sqrt[31] + (-31 + (15*I)*Sqrt[31])*x)*EllipticF[ArcSin[Sqrt[I + Sqrt[31] - (16*I)/x]/(Sqrt[2]*31^(1/4))], (2*Sqrt[31])/(-15*I + Sqrt[31])] + 64*Sqrt[62]*Sqrt[I + Sqrt[31] - (16*I)/x]*x*Sqrt[(8 - x + x^2)/x^2]*EllipticPi[(2*Sqrt[31])/(I + Sqrt[31]), ArcSin[Sqrt[I + Sqrt[31] - (16*I)/x]/(Sqrt[2]*31^(1/4))], (2*Sqrt[31])/(-15*I + Sqrt[31])]))/(Sqrt[31]*(I + Sqrt[31])*Sqrt[I + Sqrt[31] - (16*I)/x]*Sqrt[x*(-8 + 9*x - 2*x^2 + x^3)])","C",0
393,1,33,33,0.2734321,"\int \frac{-a+2 x}{\left(-1+b-a x+x^2\right) \sqrt[4]{b-a x+x^2}} \, dx","Integrate[(-a + 2*x)/((-1 + b - a*x + x^2)*(b - a*x + x^2)^(1/4)),x]","2 \left(\tan ^{-1}\left(\sqrt[4]{-a x+b+x^2}\right)-\tanh ^{-1}\left(\sqrt[4]{-a x+b+x^2}\right)\right)","2 \tan ^{-1}\left(\sqrt[4]{-a x+b+x^2}\right)-2 \tanh ^{-1}\left(\sqrt[4]{-a x+b+x^2}\right)",1,"2*(ArcTan[(b - a*x + x^2)^(1/4)] - ArcTanh[(b - a*x + x^2)^(1/4)])","A",1
394,1,33,33,0.0097456,"\int \frac{\left(-4+x^3\right) \left(-1+x^3\right)^{2/3}}{x^{12}} \, dx","Integrate[((-4 + x^3)*(-1 + x^3)^(2/3))/x^12,x]","-\frac{\left(x^3-1\right)^{2/3} \left(39 x^9+26 x^6+95 x^3-160\right)}{440 x^{11}}","\frac{\left(x^3-1\right)^{2/3} \left(-39 x^9-26 x^6-95 x^3+160\right)}{440 x^{11}}",1,"-1/440*((-1 + x^3)^(2/3)*(-160 + 95*x^3 + 26*x^6 + 39*x^9))/x^11","A",1
395,1,290,33,0.635909,"\int \frac{-2+2 x+x^2}{\left(-1-3 x+x^2\right) \sqrt{1+x^3}} \, dx","Integrate[(-2 + 2*x + x^2)/((-1 - 3*x + x^2)*Sqrt[1 + x^3]),x]","\frac{2 \sqrt{\frac{x+1}{1+\sqrt[3]{-1}}} \sqrt{x^2-x+1} \left(-\frac{\sqrt{3} \left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1}-x\right) F\left(\sin ^{-1}\left(\sqrt{\frac{(-1)^{2/3} x+1}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{(-1)^{2/3} x+1}-\frac{6 i \left(\left(-1+5 \sqrt[3]{-1}+\sqrt{13}+\sqrt[3]{-1} \sqrt{13}\right) \Pi \left(\frac{2 \sqrt{3}}{2 i+\sqrt{3}+i \sqrt{13}};\sin ^{-1}\left(\sqrt{\frac{(-1)^{2/3} x+1}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)-\left(1-5 \sqrt[3]{-1}+\sqrt{13}+\sqrt[3]{-1} \sqrt{13}\right) \Pi \left(\frac{2 i \sqrt{3}}{-3+2 \sqrt[3]{-1}+\sqrt{13}};\sin ^{-1}\left(\sqrt{\frac{(-1)^{2/3} x+1}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)\right)}{-12-4 i \sqrt{3}}\right)}{3 \sqrt{x^3+1}}","-\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{x^3+1}}{x^2-x+1}\right)",1,"(2*Sqrt[(1 + x)/(1 + (-1)^(1/3))]*Sqrt[1 - x + x^2]*(-((Sqrt[3]*(1 + (-1)^(1/3))*((-1)^(1/3) - x)*EllipticF[ArcSin[Sqrt[(1 + (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)])/(1 + (-1)^(2/3)*x)) - ((6*I)*((-1 + 5*(-1)^(1/3) + Sqrt[13] + (-1)^(1/3)*Sqrt[13])*EllipticPi[(2*Sqrt[3])/(2*I + Sqrt[3] + I*Sqrt[13]), ArcSin[Sqrt[(1 + (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)] - (1 - 5*(-1)^(1/3) + Sqrt[13] + (-1)^(1/3)*Sqrt[13])*EllipticPi[((2*I)*Sqrt[3])/(-3 + 2*(-1)^(1/3) + Sqrt[13]), ArcSin[Sqrt[(1 + (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)]))/(-12 - (4*I)*Sqrt[3])))/(3*Sqrt[1 + x^3])","C",1
396,1,515,33,0.8669879,"\int \frac{-2+2 x+x^2}{\left(3-x+2 x^2\right) \sqrt{1+x^3}} \, dx","Integrate[(-2 + 2*x + x^2)/((3 - x + 2*x^2)*Sqrt[1 + x^3]),x]","\frac{\sqrt{\frac{x+1}{1+\sqrt[3]{-1}}} \left(\frac{2 i \sqrt{23} \sqrt{x^2-x+1} \Pi \left(-\frac{4 \sqrt{3}}{i-2 \sqrt{3}+\sqrt{23}};\sin ^{-1}\left(\sqrt{\frac{(-1)^{2/3} x+1}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{i-2 \sqrt{3}+\sqrt{23}}+\frac{10 \sqrt{x^2-x+1} \Pi \left(-\frac{4 \sqrt{3}}{i-2 \sqrt{3}+\sqrt{23}};\sin ^{-1}\left(\sqrt{\frac{\left(i+\sqrt{3}\right) x-2 i}{-3 i+\sqrt{3}}}\right)|\frac{1}{2} \left(1+i \sqrt{3}\right)\right)}{i-2 \sqrt{3}+\sqrt{23}}+\frac{10 (-1)^{5/6} \left(1+\sqrt[3]{-1}\right) \sqrt{x^2-x+1} \Pi \left(\frac{4 \sqrt{3}}{-i+2 \sqrt{3}+\sqrt{23}};\sin ^{-1}\left(\sqrt{\frac{(-1)^{2/3} x+1}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{6-i \sqrt{3}+\sqrt{69}}+\frac{2 i \sqrt{23} \sqrt{x^2-x+1} \Pi \left(\frac{4 \sqrt{3}}{-i+2 \sqrt{3}+\sqrt{23}};\sin ^{-1}\left(\sqrt{\frac{(-1)^{2/3} x+1}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{-i+2 \sqrt{3}+\sqrt{23}}-\frac{2 \left(\sqrt[3]{-1}-x\right) \sqrt{\frac{\sqrt[3]{-1}-(-1)^{2/3} x}{1+\sqrt[3]{-1}}} F\left(\sin ^{-1}\left(\sqrt{\frac{(-1)^{2/3} x+1}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{\sqrt{\frac{(-1)^{2/3} x+1}{1+\sqrt[3]{-1}}}}\right)}{2 \sqrt{x^3+1}}","-\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{x^3+1}}{\sqrt{2} \left(x^2-x+1\right)}\right)",1,"(Sqrt[(1 + x)/(1 + (-1)^(1/3))]*((-2*((-1)^(1/3) - x)*Sqrt[((-1)^(1/3) - (-1)^(2/3)*x)/(1 + (-1)^(1/3))]*EllipticF[ArcSin[Sqrt[(1 + (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)])/Sqrt[(1 + (-1)^(2/3)*x)/(1 + (-1)^(1/3))] + ((2*I)*Sqrt[23]*Sqrt[1 - x + x^2]*EllipticPi[(-4*Sqrt[3])/(I - 2*Sqrt[3] + Sqrt[23]), ArcSin[Sqrt[(1 + (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)])/(I - 2*Sqrt[3] + Sqrt[23]) + (10*Sqrt[1 - x + x^2]*EllipticPi[(-4*Sqrt[3])/(I - 2*Sqrt[3] + Sqrt[23]), ArcSin[Sqrt[(-2*I + (I + Sqrt[3])*x)/(-3*I + Sqrt[3])]], (1 + I*Sqrt[3])/2])/(I - 2*Sqrt[3] + Sqrt[23]) + ((2*I)*Sqrt[23]*Sqrt[1 - x + x^2]*EllipticPi[(4*Sqrt[3])/(-I + 2*Sqrt[3] + Sqrt[23]), ArcSin[Sqrt[(1 + (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)])/(-I + 2*Sqrt[3] + Sqrt[23]) + (10*(-1)^(5/6)*(1 + (-1)^(1/3))*Sqrt[1 - x + x^2]*EllipticPi[(4*Sqrt[3])/(-I + 2*Sqrt[3] + Sqrt[23]), ArcSin[Sqrt[(1 + (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)])/(6 - I*Sqrt[3] + Sqrt[69])))/(2*Sqrt[1 + x^3])","C",0
397,1,394,33,1.4491539,"\int \frac{-2+2 x+x^2}{\left(2-4 x+3 x^2\right) \sqrt{1+x^3}} \, dx","Integrate[(-2 + 2*x + x^2)/((2 - 4*x + 3*x^2)*Sqrt[1 + x^3]),x]","\frac{2 \sqrt{\frac{x+1}{1+\sqrt[3]{-1}}} \sqrt{x^2-x+1} \left(-\frac{\sqrt{3} \left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1}-x\right) F\left(\sin ^{-1}\left(\sqrt{\frac{(-1)^{2/3} x+1}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{(-1)^{2/3} x+1}+\frac{3 i \sqrt{2} \Pi \left(\frac{6 \sqrt{3}}{i-2 \sqrt{2}+3 \sqrt{3}};\sin ^{-1}\left(\sqrt{\frac{(-1)^{2/3} x+1}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{-2 i+3 (-1)^{5/6}+\sqrt{2}}+\frac{15 \Pi \left(\frac{6 \sqrt{3}}{i-2 \sqrt{2}+3 \sqrt{3}};\sin ^{-1}\left(\sqrt{\frac{\left(i+\sqrt{3}\right) x-2 i}{-3 i+\sqrt{3}}}\right)|\frac{1}{2} \left(1+i \sqrt{3}\right)\right)}{-2 i+3 (-1)^{5/6}+\sqrt{2}}+\frac{6 i \left(\sqrt{2}+5 i\right) \Pi \left(\frac{6 \sqrt{3}}{i+2 \sqrt{2}+3 \sqrt{3}};\sin ^{-1}\left(\sqrt{\frac{\left(i+\sqrt{3}\right) x-2 i}{-3 i+\sqrt{3}}}\right)|\frac{1}{2} \left(1+i \sqrt{3}\right)\right)}{i+2 \sqrt{2}+3 \sqrt{3}}\right)}{9 \sqrt{x^3+1}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{x^3+1}}{\sqrt{3} \left(x^2-x+1\right)}\right)}{\sqrt{3}}",1,"(2*Sqrt[(1 + x)/(1 + (-1)^(1/3))]*Sqrt[1 - x + x^2]*(-((Sqrt[3]*(1 + (-1)^(1/3))*((-1)^(1/3) - x)*EllipticF[ArcSin[Sqrt[(1 + (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)])/(1 + (-1)^(2/3)*x)) + ((3*I)*Sqrt[2]*EllipticPi[(6*Sqrt[3])/(I - 2*Sqrt[2] + 3*Sqrt[3]), ArcSin[Sqrt[(1 + (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)])/(-2*I + 3*(-1)^(5/6) + Sqrt[2]) + (15*EllipticPi[(6*Sqrt[3])/(I - 2*Sqrt[2] + 3*Sqrt[3]), ArcSin[Sqrt[(-2*I + (I + Sqrt[3])*x)/(-3*I + Sqrt[3])]], (1 + I*Sqrt[3])/2])/(-2*I + 3*(-1)^(5/6) + Sqrt[2]) + ((6*I)*(5*I + Sqrt[2])*EllipticPi[(6*Sqrt[3])/(I + 2*Sqrt[2] + 3*Sqrt[3]), ArcSin[Sqrt[(-2*I + (I + Sqrt[3])*x)/(-3*I + Sqrt[3])]], (1 + I*Sqrt[3])/2])/(I + 2*Sqrt[2] + 3*Sqrt[3])))/(9*Sqrt[1 + x^3])","C",0
398,1,28,33,0.0076362,"\int \frac{\left(-1+x^3\right) \sqrt[3]{1+x^3}}{x^{11}} \, dx","Integrate[((-1 + x^3)*(1 + x^3)^(1/3))/x^11,x]","\frac{\left(x^3+1\right)^{4/3} \left(12 x^6-16 x^3+7\right)}{70 x^{10}}","\frac{\sqrt[3]{x^3+1} \left(12 x^9-4 x^6-9 x^3+7\right)}{70 x^{10}}",1,"((1 + x^3)^(4/3)*(7 - 16*x^3 + 12*x^6))/(70*x^10)","A",1
399,1,33,33,0.0078284,"\int \frac{\sqrt[3]{-1+x^3} \left(1+x^3\right)}{x^{11}} \, dx","Integrate[((-1 + x^3)^(1/3)*(1 + x^3))/x^11,x]","\frac{\sqrt[3]{x^3-1} \left(12 x^9+4 x^6-9 x^3-7\right)}{70 x^{10}}","\frac{\sqrt[3]{x^3-1} \left(12 x^9+4 x^6-9 x^3-7\right)}{70 x^{10}}",1,"((-1 + x^3)^(1/3)*(-7 - 9*x^3 + 4*x^6 + 12*x^9))/(70*x^10)","A",1
400,1,31,33,0.0193062,"\int \frac{-1-2 x+x^2+3 x^3}{\sqrt[4]{-1+3 x-3 x^2+x^3}} \, dx","Integrate[(-1 - 2*x + x^2 + 3*x^3)/(-1 + 3*x - 3*x^2 + x^3)^(1/4),x]","\frac{4 (x-1) \left(135 x^3+245 x^2+158 x+47\right)}{585 \sqrt[4]{(x-1)^3}}","\frac{4 \left((x-1)^3\right)^{3/4} \left(135 x^3+245 x^2+158 x+47\right)}{585 (x-1)^2}",1,"(4*(-1 + x)*(47 + 158*x + 245*x^2 + 135*x^3))/(585*((-1 + x)^3)^(1/4))","A",1
401,1,31,33,0.0149048,"\int \sqrt[4]{-1+3 x-3 x^2+x^3} \left(-1-2 x+x^2+3 x^3\right) \, dx","Integrate[(-1 + 3*x - 3*x^2 + x^3)^(1/4)*(-1 - 2*x + x^2 + 3*x^3),x]","\frac{4 (x-1) \sqrt[4]{(x-1)^3} \left(693 x^3+847 x^2-182 x-731\right)}{4389}","\frac{4 \sqrt[4]{(x-1)^3} \left(693 x^4+154 x^3-1029 x^2-549 x+731\right)}{4389}",1,"(4*(-1 + x)*((-1 + x)^3)^(1/4)*(-731 - 182*x + 847*x^2 + 693*x^3))/4389","A",1
402,1,2741,33,6.2404215,"\int \frac{\left(-2 b+a x^3\right) \sqrt{b+a x^3}}{x^2 \left(b-x^2+a x^3\right)} \, dx","Integrate[((-2*b + a*x^3)*Sqrt[b + a*x^3])/(x^2*(b - x^2 + a*x^3)),x]","\text{Result too large to show}","\frac{2 \sqrt{a x^3+b}}{x}-2 \tanh ^{-1}\left(\frac{x}{\sqrt{a x^3+b}}\right)",1,"(2*Sqrt[b + a*x^3])/x + (2*Sqrt[(b^(1/3)/a^(1/3) + x)/(b^(1/3)/a^(1/3) + ((-1)^(1/3)*b^(1/3))/a^(1/3))]*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) + x)*Sqrt[(((-1)^(2/3)*b^(1/3))/a^(1/3) + x)/(((-1)^(1/3)*b^(1/3))/a^(1/3) + ((-1)^(2/3)*b^(1/3))/a^(1/3))]*EllipticF[ArcSin[Sqrt[((-1)^(1/3)*b^(1/3) - a^(1/3)*x)/(((-1)^(1/3) + (-1)^(2/3))*b^(1/3))]], (-1)^(1/3)])/(Sqrt[(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) + x)/(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) - ((-1)^(2/3)*b^(1/3))/a^(1/3))]*Sqrt[b + a*x^3]) - (4*(((-1)^(1/3)*b^(1/3))/a^(1/3) + ((-1)^(2/3)*b^(1/3))/a^(1/3))*b*Sqrt[(b^(1/3)/a^(1/3) + x)/(b^(1/3)/a^(1/3) + ((-1)^(1/3)*b^(1/3))/a^(1/3))]*Sqrt[((-(((-1)^(2/3)*b^(1/3))/a^(1/3)) - x)*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) + x))/(((-1)^(1/3)*b^(1/3))/a^(1/3) + ((-1)^(2/3)*b^(1/3))/a^(1/3))^2]*EllipticPi[((-1)^(1/3)*b^(1/3) + (-1)^(2/3)*b^(1/3))/((-1)^(1/3)*b^(1/3) - a^(1/3)*Root[b - #1^2 + a*#1^3 & , 1]), ArcSin[Sqrt[((-1)^(1/3)*b^(1/3) - a^(1/3)*x)/(((-1)^(1/3) + (-1)^(2/3))*b^(1/3))]], (-1)^(1/3)])/(a*Sqrt[b + a*x^3]*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) + Root[b - #1^2 + a*#1^3 & , 1])*(Root[b - #1^2 + a*#1^3 & , 1] - Root[b - #1^2 + a*#1^3 & , 2])*(Root[b - #1^2 + a*#1^3 & , 1] - Root[b - #1^2 + a*#1^3 & , 3])) + (2*(((-1)^(1/3)*b^(1/3))/a^(1/3) + ((-1)^(2/3)*b^(1/3))/a^(1/3))*Sqrt[(b^(1/3)/a^(1/3) + x)/(b^(1/3)/a^(1/3) + ((-1)^(1/3)*b^(1/3))/a^(1/3))]*Sqrt[((-(((-1)^(2/3)*b^(1/3))/a^(1/3)) - x)*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) + x))/(((-1)^(1/3)*b^(1/3))/a^(1/3) + ((-1)^(2/3)*b^(1/3))/a^(1/3))^2]*EllipticPi[((-1)^(1/3)*b^(1/3) + (-1)^(2/3)*b^(1/3))/((-1)^(1/3)*b^(1/3) - a^(1/3)*Root[b - #1^2 + a*#1^3 & , 1]), ArcSin[Sqrt[((-1)^(1/3)*b^(1/3) - a^(1/3)*x)/(((-1)^(1/3) + (-1)^(2/3))*b^(1/3))]], (-1)^(1/3)]*Root[b - #1^2 + a*#1^3 & , 1]^3)/(Sqrt[b + a*x^3]*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) + Root[b - #1^2 + a*#1^3 & , 1])*(Root[b - #1^2 + a*#1^3 & , 1] - Root[b - #1^2 + a*#1^3 & , 2])*(Root[b - #1^2 + a*#1^3 & , 1] - Root[b - #1^2 + a*#1^3 & , 3])) - (4*(((-1)^(1/3)*b^(1/3))/a^(1/3) + ((-1)^(2/3)*b^(1/3))/a^(1/3))*b*Sqrt[(b^(1/3)/a^(1/3) + x)/(b^(1/3)/a^(1/3) + ((-1)^(1/3)*b^(1/3))/a^(1/3))]*Sqrt[((-(((-1)^(2/3)*b^(1/3))/a^(1/3)) - x)*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) + x))/(((-1)^(1/3)*b^(1/3))/a^(1/3) + ((-1)^(2/3)*b^(1/3))/a^(1/3))^2]*EllipticPi[((-1)^(1/3)*b^(1/3) + (-1)^(2/3)*b^(1/3))/((-1)^(1/3)*b^(1/3) - a^(1/3)*Root[b - #1^2 + a*#1^3 & , 2]), ArcSin[Sqrt[((-1)^(1/3)*b^(1/3) - a^(1/3)*x)/(((-1)^(1/3) + (-1)^(2/3))*b^(1/3))]], (-1)^(1/3)])/(a*Sqrt[b + a*x^3]*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) + Root[b - #1^2 + a*#1^3 & , 2])*(-Root[b - #1^2 + a*#1^3 & , 1] + Root[b - #1^2 + a*#1^3 & , 2])*(Root[b - #1^2 + a*#1^3 & , 2] - Root[b - #1^2 + a*#1^3 & , 3])) + (2*(((-1)^(1/3)*b^(1/3))/a^(1/3) + ((-1)^(2/3)*b^(1/3))/a^(1/3))*Sqrt[(b^(1/3)/a^(1/3) + x)/(b^(1/3)/a^(1/3) + ((-1)^(1/3)*b^(1/3))/a^(1/3))]*Sqrt[((-(((-1)^(2/3)*b^(1/3))/a^(1/3)) - x)*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) + x))/(((-1)^(1/3)*b^(1/3))/a^(1/3) + ((-1)^(2/3)*b^(1/3))/a^(1/3))^2]*EllipticPi[((-1)^(1/3)*b^(1/3) + (-1)^(2/3)*b^(1/3))/((-1)^(1/3)*b^(1/3) - a^(1/3)*Root[b - #1^2 + a*#1^3 & , 2]), ArcSin[Sqrt[((-1)^(1/3)*b^(1/3) - a^(1/3)*x)/(((-1)^(1/3) + (-1)^(2/3))*b^(1/3))]], (-1)^(1/3)]*Root[b - #1^2 + a*#1^3 & , 2]^3)/(Sqrt[b + a*x^3]*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) + Root[b - #1^2 + a*#1^3 & , 2])*(-Root[b - #1^2 + a*#1^3 & , 1] + Root[b - #1^2 + a*#1^3 & , 2])*(Root[b - #1^2 + a*#1^3 & , 2] - Root[b - #1^2 + a*#1^3 & , 3])) - (4*(((-1)^(1/3)*b^(1/3))/a^(1/3) + ((-1)^(2/3)*b^(1/3))/a^(1/3))*b*Sqrt[(b^(1/3)/a^(1/3) + x)/(b^(1/3)/a^(1/3) + ((-1)^(1/3)*b^(1/3))/a^(1/3))]*Sqrt[((-(((-1)^(2/3)*b^(1/3))/a^(1/3)) - x)*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) + x))/(((-1)^(1/3)*b^(1/3))/a^(1/3) + ((-1)^(2/3)*b^(1/3))/a^(1/3))^2]*EllipticPi[((-1)^(1/3)*b^(1/3) + (-1)^(2/3)*b^(1/3))/((-1)^(1/3)*b^(1/3) - a^(1/3)*Root[b - #1^2 + a*#1^3 & , 3]), ArcSin[Sqrt[((-1)^(1/3)*b^(1/3) - a^(1/3)*x)/(((-1)^(1/3) + (-1)^(2/3))*b^(1/3))]], (-1)^(1/3)])/(a*Sqrt[b + a*x^3]*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) + Root[b - #1^2 + a*#1^3 & , 3])*(-Root[b - #1^2 + a*#1^3 & , 1] + Root[b - #1^2 + a*#1^3 & , 3])*(-Root[b - #1^2 + a*#1^3 & , 2] + Root[b - #1^2 + a*#1^3 & , 3])) + (2*(((-1)^(1/3)*b^(1/3))/a^(1/3) + ((-1)^(2/3)*b^(1/3))/a^(1/3))*Sqrt[(b^(1/3)/a^(1/3) + x)/(b^(1/3)/a^(1/3) + ((-1)^(1/3)*b^(1/3))/a^(1/3))]*Sqrt[((-(((-1)^(2/3)*b^(1/3))/a^(1/3)) - x)*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) + x))/(((-1)^(1/3)*b^(1/3))/a^(1/3) + ((-1)^(2/3)*b^(1/3))/a^(1/3))^2]*EllipticPi[((-1)^(1/3)*b^(1/3) + (-1)^(2/3)*b^(1/3))/((-1)^(1/3)*b^(1/3) - a^(1/3)*Root[b - #1^2 + a*#1^3 & , 3]), ArcSin[Sqrt[((-1)^(1/3)*b^(1/3) - a^(1/3)*x)/(((-1)^(1/3) + (-1)^(2/3))*b^(1/3))]], (-1)^(1/3)]*Root[b - #1^2 + a*#1^3 & , 3]^3)/(Sqrt[b + a*x^3]*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) + Root[b - #1^2 + a*#1^3 & , 3])*(-Root[b - #1^2 + a*#1^3 & , 1] + Root[b - #1^2 + a*#1^3 & , 3])*(-Root[b - #1^2 + a*#1^3 & , 2] + Root[b - #1^2 + a*#1^3 & , 3]))","C",0
403,1,54,33,0.0049447,"\int \frac{1}{\sqrt[4]{1+x^4}} \, dx","Integrate[(1 + x^4)^(-1/4),x]","-\frac{1}{4} \log \left(1-\frac{x}{\sqrt[4]{x^4+1}}\right)+\frac{1}{4} \log \left(\frac{x}{\sqrt[4]{x^4+1}}+1\right)+\frac{1}{2} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)","\frac{1}{2} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)+\frac{1}{2} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)",1,"ArcTan[x/(1 + x^4)^(1/4)]/2 - Log[1 - x/(1 + x^4)^(1/4)]/4 + Log[1 + x/(1 + x^4)^(1/4)]/4","A",1
404,1,287,33,1.898519,"\int \frac{-1-2 x+2 x^2}{\left(1+2 x+4 x^2\right) \sqrt{x+x^4}} \, dx","Integrate[(-1 - 2*x + 2*x^2)/((1 + 2*x + 4*x^2)*Sqrt[x + x^4]),x]","-\frac{2 \sqrt{\frac{\frac{1}{x}+1}{1+\sqrt[3]{-1}}} x^2 \left(\frac{2 \sqrt{\frac{1}{x^2}-\frac{1}{x}+1} \Pi \left(\frac{2 i}{3 i+\sqrt{3}};\sin ^{-1}\left(\sqrt{\frac{x+(-1)^{2/3}}{\left(1+\sqrt[3]{-1}\right) x}}\right)|\sqrt[3]{-1}\right)}{\sqrt{3}+3 i}-\frac{2 i \sqrt{3} \sqrt{\frac{1}{x^2}-\frac{1}{x}+1} \Pi \left(-\frac{2 \sqrt{3}}{3 i+\sqrt{3}};\sin ^{-1}\left(\sqrt{\frac{x+(-1)^{2/3}}{\left(1+\sqrt[3]{-1}\right) x}}\right)|\sqrt[3]{-1}\right)}{\sqrt{3}+3 i}+\frac{\left(\sqrt[3]{-1}-\frac{1}{x}\right) \sqrt{\frac{\sqrt[3]{-1}-\frac{(-1)^{2/3}}{x}}{1+\sqrt[3]{-1}}} F\left(\sin ^{-1}\left(\sqrt{\frac{x+(-1)^{2/3}}{\left(1+\sqrt[3]{-1}\right) x}}\right)|\sqrt[3]{-1}\right)}{\sqrt{\frac{x+(-1)^{2/3}}{\left(1+\sqrt[3]{-1}\right) x}}}\right)}{\sqrt{x^4+x}}","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{3} \sqrt{x^4+x}}{x^2-x+1}\right)}{\sqrt{3}}",1,"(-2*Sqrt[(1 + x^(-1))/(1 + (-1)^(1/3))]*x^2*((((-1)^(1/3) - x^(-1))*Sqrt[((-1)^(1/3) - (-1)^(2/3)/x)/(1 + (-1)^(1/3))]*EllipticF[ArcSin[Sqrt[((-1)^(2/3) + x)/((1 + (-1)^(1/3))*x)]], (-1)^(1/3)])/Sqrt[((-1)^(2/3) + x)/((1 + (-1)^(1/3))*x)] + (2*Sqrt[1 + x^(-2) - x^(-1)]*EllipticPi[(2*I)/(3*I + Sqrt[3]), ArcSin[Sqrt[((-1)^(2/3) + x)/((1 + (-1)^(1/3))*x)]], (-1)^(1/3)])/(3*I + Sqrt[3]) - ((2*I)*Sqrt[3]*Sqrt[1 + x^(-2) - x^(-1)]*EllipticPi[(-2*Sqrt[3])/(3*I + Sqrt[3]), ArcSin[Sqrt[((-1)^(2/3) + x)/((1 + (-1)^(1/3))*x)]], (-1)^(1/3)])/(3*I + Sqrt[3])))/Sqrt[x + x^4]","C",0
405,1,40,33,0.0224147,"\int \sqrt{x+x^4} \, dx","Integrate[Sqrt[x + x^4],x]","\frac{\sqrt{x^4+x} \left(x^{3/2}+\frac{\sinh ^{-1}\left(x^{3/2}\right)}{\sqrt{x^3+1}}\right)}{3 \sqrt{x}}","\frac{1}{3} \sqrt{x^4+x} x+\frac{1}{3} \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4+x}}\right)",1,"(Sqrt[x + x^4]*(x^(3/2) + ArcSinh[x^(3/2)]/Sqrt[1 + x^3]))/(3*Sqrt[x])","A",1
406,1,61,33,0.0141019,"\int \frac{1}{\sqrt[4]{-x^2+x^4}} \, dx","Integrate[(-x^2 + x^4)^(-1/4),x]","\frac{\sqrt{x} \sqrt[4]{x^2-1} \left(\tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2-1}}\right)+\tanh ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2-1}}\right)\right)}{\sqrt[4]{x^2 \left(x^2-1\right)}}","\tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^2}}\right)+\tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^2}}\right)",1,"(Sqrt[x]*(-1 + x^2)^(1/4)*(ArcTan[Sqrt[x]/(-1 + x^2)^(1/4)] + ArcTanh[Sqrt[x]/(-1 + x^2)^(1/4)]))/(x^2*(-1 + x^2))^(1/4)","A",1
407,0,0,33,0.2441301,"\int \frac{2 b+a x^2}{\sqrt[4]{b+a x^2} \left(-b-a x^2+x^4\right)} \, dx","Integrate[(2*b + a*x^2)/((b + a*x^2)^(1/4)*(-b - a*x^2 + x^4)),x]","\int \frac{2 b+a x^2}{\sqrt[4]{b+a x^2} \left(-b-a x^2+x^4\right)} \, dx","\tan ^{-1}\left(\frac{\sqrt[4]{a x^2+b}}{x}\right)-\tanh ^{-1}\left(\frac{x}{\sqrt[4]{a x^2+b}}\right)",1,"Integrate[(2*b + a*x^2)/((b + a*x^2)^(1/4)*(-b - a*x^2 + x^4)), x]","F",-1
408,1,702,33,3.1956972,"\int \frac{-1+2 x}{\sqrt{-2-2 x+3 x^2-2 x^3+x^4}} \, dx","Integrate[(-1 + 2*x)/Sqrt[-2 - 2*x + 3*x^2 - 2*x^3 + x^4],x]","\frac{\sqrt{4 \sqrt{3}-3} \left(-2 x+\sqrt{4 \sqrt{3}-3}+1\right)^2 \left(\frac{-2 x-i \sqrt{3+4 \sqrt{3}}+1}{\left(\sqrt{4 \sqrt{3}-3}-i \sqrt{3+4 \sqrt{3}}\right) \left(-2 x+\sqrt{4 \sqrt{3}-3}+1\right)}\right)^{3/2} \left(-2 x+i \sqrt{3+4 \sqrt{3}}+1\right) \sqrt{\frac{\left(\sqrt{4 \sqrt{3}-3}-i \sqrt{3+4 \sqrt{3}}\right) \left(2 x+\sqrt{4 \sqrt{3}-3}-1\right)}{\left(\sqrt{4 \sqrt{3}-3}+i \sqrt{3+4 \sqrt{3}}\right) \left(-2 x+\sqrt{4 \sqrt{3}-3}+1\right)}} \left(F\left(\sin ^{-1}\left(\sqrt{\frac{\left(\sqrt{-3+4 \sqrt{3}}-i \sqrt{3+4 \sqrt{3}}\right) \left(2 x+\sqrt{-3+4 \sqrt{3}}-1\right)}{\left(\sqrt{-3+4 \sqrt{3}}+i \sqrt{3+4 \sqrt{3}}\right) \left(-2 x+\sqrt{-3+4 \sqrt{3}}+1\right)}}\right)|\frac{3 i+\sqrt{39}}{3 i-\sqrt{39}}\right)-2 \Pi \left(-\frac{\sqrt{-3+4 \sqrt{3}}+i \sqrt{3+4 \sqrt{3}}}{\sqrt{-3+4 \sqrt{3}}-i \sqrt{3+4 \sqrt{3}}};\sin ^{-1}\left(\sqrt{\frac{\left(\sqrt{-3+4 \sqrt{3}}-i \sqrt{3+4 \sqrt{3}}\right) \left(2 x+\sqrt{-3+4 \sqrt{3}}-1\right)}{\left(\sqrt{-3+4 \sqrt{3}}+i \sqrt{3+4 \sqrt{3}}\right) \left(-2 x+\sqrt{-3+4 \sqrt{3}}+1\right)}}\right)|\frac{3 i+\sqrt{39}}{3 i-\sqrt{39}}\right)\right)}{\left(-2 x-i \sqrt{3+4 \sqrt{3}}+1\right) \sqrt{\frac{-2 x+i \sqrt{3+4 \sqrt{3}}+1}{\left(\sqrt{4 \sqrt{3}-3}+i \sqrt{3+4 \sqrt{3}}\right) \left(-2 x+\sqrt{4 \sqrt{3}-3}+1\right)}} \sqrt{x^4-2 x^3+3 x^2-2 x-2}}","-\log \left(-x^2+\sqrt{x^4-2 x^3+3 x^2-2 x-2}+x-1\right)",1,"(Sqrt[-3 + 4*Sqrt[3]]*(1 + Sqrt[-3 + 4*Sqrt[3]] - 2*x)^2*((1 - I*Sqrt[3 + 4*Sqrt[3]] - 2*x)/((Sqrt[-3 + 4*Sqrt[3]] - I*Sqrt[3 + 4*Sqrt[3]])*(1 + Sqrt[-3 + 4*Sqrt[3]] - 2*x)))^(3/2)*(1 + I*Sqrt[3 + 4*Sqrt[3]] - 2*x)*Sqrt[((Sqrt[-3 + 4*Sqrt[3]] - I*Sqrt[3 + 4*Sqrt[3]])*(-1 + Sqrt[-3 + 4*Sqrt[3]] + 2*x))/((Sqrt[-3 + 4*Sqrt[3]] + I*Sqrt[3 + 4*Sqrt[3]])*(1 + Sqrt[-3 + 4*Sqrt[3]] - 2*x))]*(EllipticF[ArcSin[Sqrt[((Sqrt[-3 + 4*Sqrt[3]] - I*Sqrt[3 + 4*Sqrt[3]])*(-1 + Sqrt[-3 + 4*Sqrt[3]] + 2*x))/((Sqrt[-3 + 4*Sqrt[3]] + I*Sqrt[3 + 4*Sqrt[3]])*(1 + Sqrt[-3 + 4*Sqrt[3]] - 2*x))]], (3*I + Sqrt[39])/(3*I - Sqrt[39])] - 2*EllipticPi[-((Sqrt[-3 + 4*Sqrt[3]] + I*Sqrt[3 + 4*Sqrt[3]])/(Sqrt[-3 + 4*Sqrt[3]] - I*Sqrt[3 + 4*Sqrt[3]])), ArcSin[Sqrt[((Sqrt[-3 + 4*Sqrt[3]] - I*Sqrt[3 + 4*Sqrt[3]])*(-1 + Sqrt[-3 + 4*Sqrt[3]] + 2*x))/((Sqrt[-3 + 4*Sqrt[3]] + I*Sqrt[3 + 4*Sqrt[3]])*(1 + Sqrt[-3 + 4*Sqrt[3]] - 2*x))]], (3*I + Sqrt[39])/(3*I - Sqrt[39])]))/((1 - I*Sqrt[3 + 4*Sqrt[3]] - 2*x)*Sqrt[(1 + I*Sqrt[3 + 4*Sqrt[3]] - 2*x)/((Sqrt[-3 + 4*Sqrt[3]] + I*Sqrt[3 + 4*Sqrt[3]])*(1 + Sqrt[-3 + 4*Sqrt[3]] - 2*x))]*Sqrt[-2 - 2*x + 3*x^2 - 2*x^3 + x^4])","C",0
409,1,702,33,2.9997439,"\int \frac{-1+2 x}{\sqrt{-4-4 x+5 x^2-2 x^3+x^4}} \, dx","Integrate[(-1 + 2*x)/Sqrt[-4 - 4*x + 5*x^2 - 2*x^3 + x^4],x]","\frac{\sqrt{8 \sqrt{2}-7} \left(-2 x+\sqrt{8 \sqrt{2}-7}+1\right)^2 \left(\frac{-2 x-i \sqrt{7+8 \sqrt{2}}+1}{\left(\sqrt{8 \sqrt{2}-7}-i \sqrt{7+8 \sqrt{2}}\right) \left(-2 x+\sqrt{8 \sqrt{2}-7}+1\right)}\right)^{3/2} \left(-2 x+i \sqrt{7+8 \sqrt{2}}+1\right) \sqrt{\frac{\left(\sqrt{8 \sqrt{2}-7}-i \sqrt{7+8 \sqrt{2}}\right) \left(2 x+\sqrt{8 \sqrt{2}-7}-1\right)}{\left(\sqrt{8 \sqrt{2}-7}+i \sqrt{7+8 \sqrt{2}}\right) \left(-2 x+\sqrt{8 \sqrt{2}-7}+1\right)}} \left(F\left(\sin ^{-1}\left(\sqrt{\frac{\left(\sqrt{-7+8 \sqrt{2}}-i \sqrt{7+8 \sqrt{2}}\right) \left(2 x+\sqrt{-7+8 \sqrt{2}}-1\right)}{\left(\sqrt{-7+8 \sqrt{2}}+i \sqrt{7+8 \sqrt{2}}\right) \left(-2 x+\sqrt{-7+8 \sqrt{2}}+1\right)}}\right)|\frac{7 i+\sqrt{79}}{7 i-\sqrt{79}}\right)-2 \Pi \left(-\frac{\sqrt{-7+8 \sqrt{2}}+i \sqrt{7+8 \sqrt{2}}}{\sqrt{-7+8 \sqrt{2}}-i \sqrt{7+8 \sqrt{2}}};\sin ^{-1}\left(\sqrt{\frac{\left(\sqrt{-7+8 \sqrt{2}}-i \sqrt{7+8 \sqrt{2}}\right) \left(2 x+\sqrt{-7+8 \sqrt{2}}-1\right)}{\left(\sqrt{-7+8 \sqrt{2}}+i \sqrt{7+8 \sqrt{2}}\right) \left(-2 x+\sqrt{-7+8 \sqrt{2}}+1\right)}}\right)|\frac{7 i+\sqrt{79}}{7 i-\sqrt{79}}\right)\right)}{\left(-2 x-i \sqrt{7+8 \sqrt{2}}+1\right) \sqrt{\frac{-2 x+i \sqrt{7+8 \sqrt{2}}+1}{\left(\sqrt{8 \sqrt{2}-7}+i \sqrt{7+8 \sqrt{2}}\right) \left(-2 x+\sqrt{8 \sqrt{2}-7}+1\right)}} \sqrt{x^4-2 x^3+5 x^2-4 x-4}}","-\log \left(-x^2+\sqrt{x^4-2 x^3+5 x^2-4 x-4}+x-2\right)",1,"(Sqrt[-7 + 8*Sqrt[2]]*(1 + Sqrt[-7 + 8*Sqrt[2]] - 2*x)^2*((1 - I*Sqrt[7 + 8*Sqrt[2]] - 2*x)/((Sqrt[-7 + 8*Sqrt[2]] - I*Sqrt[7 + 8*Sqrt[2]])*(1 + Sqrt[-7 + 8*Sqrt[2]] - 2*x)))^(3/2)*(1 + I*Sqrt[7 + 8*Sqrt[2]] - 2*x)*Sqrt[((Sqrt[-7 + 8*Sqrt[2]] - I*Sqrt[7 + 8*Sqrt[2]])*(-1 + Sqrt[-7 + 8*Sqrt[2]] + 2*x))/((Sqrt[-7 + 8*Sqrt[2]] + I*Sqrt[7 + 8*Sqrt[2]])*(1 + Sqrt[-7 + 8*Sqrt[2]] - 2*x))]*(EllipticF[ArcSin[Sqrt[((Sqrt[-7 + 8*Sqrt[2]] - I*Sqrt[7 + 8*Sqrt[2]])*(-1 + Sqrt[-7 + 8*Sqrt[2]] + 2*x))/((Sqrt[-7 + 8*Sqrt[2]] + I*Sqrt[7 + 8*Sqrt[2]])*(1 + Sqrt[-7 + 8*Sqrt[2]] - 2*x))]], (7*I + Sqrt[79])/(7*I - Sqrt[79])] - 2*EllipticPi[-((Sqrt[-7 + 8*Sqrt[2]] + I*Sqrt[7 + 8*Sqrt[2]])/(Sqrt[-7 + 8*Sqrt[2]] - I*Sqrt[7 + 8*Sqrt[2]])), ArcSin[Sqrt[((Sqrt[-7 + 8*Sqrt[2]] - I*Sqrt[7 + 8*Sqrt[2]])*(-1 + Sqrt[-7 + 8*Sqrt[2]] + 2*x))/((Sqrt[-7 + 8*Sqrt[2]] + I*Sqrt[7 + 8*Sqrt[2]])*(1 + Sqrt[-7 + 8*Sqrt[2]] - 2*x))]], (7*I + Sqrt[79])/(7*I - Sqrt[79])]))/((1 - I*Sqrt[7 + 8*Sqrt[2]] - 2*x)*Sqrt[(1 + I*Sqrt[7 + 8*Sqrt[2]] - 2*x)/((Sqrt[-7 + 8*Sqrt[2]] + I*Sqrt[7 + 8*Sqrt[2]])*(1 + Sqrt[-7 + 8*Sqrt[2]] - 2*x))]*Sqrt[-4 - 4*x + 5*x^2 - 2*x^3 + x^4])","C",0
410,1,33,33,0.0152261,"\int \frac{1}{x^4 \sqrt[4]{x^3+x^4}} \, dx","Integrate[1/(x^4*(x^3 + x^4)^(1/4)),x]","\frac{4 \left(x^3 (x+1)\right)^{3/4} \left(128 x^3-96 x^2+84 x-77\right)}{1155 x^6}","\frac{4 \left(128 x^3-96 x^2+84 x-77\right) \left(x^4+x^3\right)^{3/4}}{1155 x^6}",1,"(4*(x^3*(1 + x))^(3/4)*(-77 + 84*x - 96*x^2 + 128*x^3))/(1155*x^6)","A",1
411,1,32,33,0.0091613,"\int \frac{x}{\sqrt{-b+a x^4}} \, dx","Integrate[x/Sqrt[-b + a*x^4],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a} x^2}{\sqrt{a x^4-b}}\right)}{2 \sqrt{a}}","\frac{\log \left(\sqrt{a x^4-b}+\sqrt{a} x^2\right)}{2 \sqrt{a}}",1,"ArcTanh[(Sqrt[a]*x^2)/Sqrt[-b + a*x^4]]/(2*Sqrt[a])","A",1
412,1,33,33,0.0157125,"\int \frac{\left(1+x^3\right)^{2/3} \left(1-x^3+2 x^6\right)}{x^{12}} \, dx","Integrate[((1 + x^3)^(2/3)*(1 - x^3 + 2*x^6))/x^12,x]","-\frac{\left(x^3+1\right)^{2/3} \left(227 x^9+142 x^6-45 x^3+40\right)}{440 x^{11}}","\frac{\left(x^3+1\right)^{2/3} \left(-227 x^9-142 x^6+45 x^3-40\right)}{440 x^{11}}",1,"-1/440*((1 + x^3)^(2/3)*(40 - 45*x^3 + 142*x^6 + 227*x^9))/x^11","A",1
413,0,0,33,0.5626486,"\int \frac{\left(3+x^4\right) \sqrt{x-x^5}}{1-2 x^4-x^6+x^8} \, dx","Integrate[((3 + x^4)*Sqrt[x - x^5])/(1 - 2*x^4 - x^6 + x^8),x]","\int \frac{\left(3+x^4\right) \sqrt{x-x^5}}{1-2 x^4-x^6+x^8} \, dx","\tan ^{-1}\left(\frac{x^2}{\sqrt{x-x^5}}\right)+\tanh ^{-1}\left(\frac{x^2}{\sqrt{x-x^5}}\right)",1,"Integrate[((3 + x^4)*Sqrt[x - x^5])/(1 - 2*x^4 - x^6 + x^8), x]","F",-1
414,1,85,33,0.0399725,"\int \frac{-1+x^{16}}{x^8 \sqrt{-1+x^4}} \, dx","Integrate[(-1 + x^16)/(x^8*Sqrt[-1 + x^4]),x]","\frac{3 \sqrt{1-x^4} \, _2F_1\left(-\frac{7}{4},\frac{1}{2};-\frac{3}{4};x^4\right)+x^8 \left(5 \sqrt{1-x^4} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};x^4\right)+3 x^8+2 x^4-5\right)}{21 x^7 \sqrt{x^4-1}}","\frac{\sqrt{x^4-1} \left(3 x^{12}+5 x^8-5 x^4-3\right)}{21 x^7}",1,"(3*Sqrt[1 - x^4]*Hypergeometric2F1[-7/4, 1/2, -3/4, x^4] + x^8*(-5 + 2*x^4 + 3*x^8 + 5*Sqrt[1 - x^4]*Hypergeometric2F1[1/4, 1/2, 5/4, x^4]))/(21*x^7*Sqrt[-1 + x^4])","C",1
415,1,19,33,0.016952,"\int \frac{(-1+x)^{3/2}+(1+x)^{3/2}}{(-1+x)^{3/2} (1+x)^{3/2}} \, dx","Integrate[((-1 + x)^(3/2) + (1 + x)^(3/2))/((-1 + x)^(3/2)*(1 + x)^(3/2)),x]","-\frac{2}{\sqrt{x+1}}-\frac{2}{\sqrt{x-1}}","\frac{2 \sqrt{x-1}}{1-x}+\frac{2 \sqrt{x+1}}{-x-1}",1,"-2/Sqrt[-1 + x] - 2/Sqrt[1 + x]","A",1
416,1,632,34,2.2832232,"\int \frac{1+x}{(-1+x) \sqrt{x+x^2+x^3}} \, dx","Integrate[(1 + x)/((-1 + x)*Sqrt[x + x^2 + x^3]),x]","-\frac{2 (-1)^{2/3} \left(\frac{1}{x}-1\right) \sqrt{x} (x+1) \left(\sqrt[3]{-1} \left(\sqrt[3]{-1}-1\right)^2 \left(1+\sqrt[3]{-1}\right) \sqrt{1-\frac{(-1)^{2/3}}{x}} \sqrt{\frac{x+\sqrt[3]{-1}}{x}} F\left(i \sinh ^{-1}\left(\frac{(-1)^{5/6}}{\sqrt{x}}\right)|(-1)^{2/3}\right)+\frac{2 i \sqrt{3} \sqrt{\frac{\sqrt{x}-\sqrt[3]{-1}+1}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1} \sqrt{x}-1\right)}} \sqrt{\frac{(-1)^{2/3} \sqrt{x}-1}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1} \sqrt{x}-1\right)}} \sqrt{-\frac{(-1)^{2/3} \sqrt{x}+1}{\sqrt{x}+\sqrt[3]{-1}-1}} \left(\sqrt[3]{-1} \sqrt{x}-1\right)^2 \left(\left(1+\sqrt[3]{-1}\right) F\left(\left.\sin ^{-1}\left(\sqrt{\frac{\sqrt{x}-\sqrt[3]{-1}+1}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1} \sqrt{x}-1\right)}}\right)\right|-3\right)-2 \sqrt[3]{-1} \Pi \left(-1;\left.\sin ^{-1}\left(\sqrt{\frac{\sqrt{x}-\sqrt[3]{-1}+1}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1} \sqrt{x}-1\right)}}\right)\right|-3\right)\right)}{x}-\frac{2 i \sqrt{3} \sqrt{\frac{\sqrt{x}-\sqrt[3]{-1}+1}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1} \sqrt{x}-1\right)}} \sqrt{\frac{(-1)^{2/3} \sqrt{x}-1}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1} \sqrt{x}-1\right)}} \sqrt{-\frac{(-1)^{2/3} \sqrt{x}+1}{\sqrt{x}+\sqrt[3]{-1}-1}} \left(\sqrt[3]{-1} \sqrt{x}-1\right)^2 \left(\left(\sqrt[3]{-1}-1\right) F\left(\left.\sin ^{-1}\left(\sqrt{\frac{\sqrt{x}-\sqrt[3]{-1}+1}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1} \sqrt{x}-1\right)}}\right)\right|-3\right)-2 \sqrt[3]{-1} \Pi \left(3;\left.\sin ^{-1}\left(\sqrt{\frac{\sqrt{x}-\sqrt[3]{-1}+1}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1} \sqrt{x}-1\right)}}\right)\right|-3\right)\right)}{x}\right)}{\left((-1)^{2/3}-1\right) \left(\frac{1}{x^2}-1\right) \sqrt{x \left(x^2+x+1\right)}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{3} \sqrt{x^3+x^2+x}}{x^2+x+1}\right)}{\sqrt{3}}",1,"(-2*(-1)^(2/3)*(-1 + x^(-1))*Sqrt[x]*(1 + x)*((-1)^(1/3)*(-1 + (-1)^(1/3))^2*(1 + (-1)^(1/3))*Sqrt[1 - (-1)^(2/3)/x]*Sqrt[((-1)^(1/3) + x)/x]*EllipticF[I*ArcSinh[(-1)^(5/6)/Sqrt[x]], (-1)^(2/3)] + ((2*I)*Sqrt[3]*Sqrt[(1 - (-1)^(1/3) + Sqrt[x])/((1 + (-1)^(1/3))*(-1 + (-1)^(1/3)*Sqrt[x]))]*(-1 + (-1)^(1/3)*Sqrt[x])^2*Sqrt[(-1 + (-1)^(2/3)*Sqrt[x])/((1 + (-1)^(1/3))*(-1 + (-1)^(1/3)*Sqrt[x]))]*Sqrt[-((1 + (-1)^(2/3)*Sqrt[x])/(-1 + (-1)^(1/3) + Sqrt[x]))]*((1 + (-1)^(1/3))*EllipticF[ArcSin[Sqrt[(1 - (-1)^(1/3) + Sqrt[x])/((1 + (-1)^(1/3))*(-1 + (-1)^(1/3)*Sqrt[x]))]], -3] - 2*(-1)^(1/3)*EllipticPi[-1, ArcSin[Sqrt[(1 - (-1)^(1/3) + Sqrt[x])/((1 + (-1)^(1/3))*(-1 + (-1)^(1/3)*Sqrt[x]))]], -3]))/x - ((2*I)*Sqrt[3]*Sqrt[(1 - (-1)^(1/3) + Sqrt[x])/((1 + (-1)^(1/3))*(-1 + (-1)^(1/3)*Sqrt[x]))]*(-1 + (-1)^(1/3)*Sqrt[x])^2*Sqrt[(-1 + (-1)^(2/3)*Sqrt[x])/((1 + (-1)^(1/3))*(-1 + (-1)^(1/3)*Sqrt[x]))]*Sqrt[-((1 + (-1)^(2/3)*Sqrt[x])/(-1 + (-1)^(1/3) + Sqrt[x]))]*((-1 + (-1)^(1/3))*EllipticF[ArcSin[Sqrt[(1 - (-1)^(1/3) + Sqrt[x])/((1 + (-1)^(1/3))*(-1 + (-1)^(1/3)*Sqrt[x]))]], -3] - 2*(-1)^(1/3)*EllipticPi[3, ArcSin[Sqrt[(1 - (-1)^(1/3) + Sqrt[x])/((1 + (-1)^(1/3))*(-1 + (-1)^(1/3)*Sqrt[x]))]], -3]))/x))/((-1 + (-1)^(2/3))*(-1 + x^(-2))*Sqrt[x*(1 + x + x^2)])","C",0
417,1,132,34,0.9622565,"\int \frac{-1+x^2}{\left(1-x+x^2\right) \sqrt{x+x^2+x^3}} \, dx","Integrate[(-1 + x^2)/((1 - x + x^2)*Sqrt[x + x^2 + x^3]),x]","-\frac{2 (-1)^{2/3} \sqrt{\frac{\sqrt[3]{-1}}{x}+1} \sqrt{1-\frac{(-1)^{2/3}}{x}} x^{3/2} \left(-F\left(i \sinh ^{-1}\left(\frac{(-1)^{5/6}}{\sqrt{x}}\right)|(-1)^{2/3}\right)+\Pi \left(-1;i \sinh ^{-1}\left(\frac{(-1)^{5/6}}{\sqrt{x}}\right)|(-1)^{2/3}\right)+\Pi \left(-(-1)^{2/3};i \sinh ^{-1}\left(\frac{(-1)^{5/6}}{\sqrt{x}}\right)|(-1)^{2/3}\right)\right)}{\sqrt{x \left(x^2+x+1\right)}}","-\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{x^3+x^2+x}}{x^2+x+1}\right)",1,"(-2*(-1)^(2/3)*Sqrt[1 + (-1)^(1/3)/x]*Sqrt[1 - (-1)^(2/3)/x]*x^(3/2)*(-EllipticF[I*ArcSinh[(-1)^(5/6)/Sqrt[x]], (-1)^(2/3)] + EllipticPi[-1, I*ArcSinh[(-1)^(5/6)/Sqrt[x]], (-1)^(2/3)] + EllipticPi[-(-1)^(2/3), I*ArcSinh[(-1)^(5/6)/Sqrt[x]], (-1)^(2/3)]))/Sqrt[x*(1 + x + x^2)]","C",1
418,1,175,34,0.3049202,"\int \frac{-1+x}{(1+x) \sqrt{1+x^4}} \, dx","Integrate[(-1 + x)/((1 + x)*Sqrt[1 + x^4]),x]","\frac{(-1)^{3/4} \sqrt{2} \sqrt{-\frac{i \left(\sqrt{2}+(1-i) x\right)}{\sqrt{2}-(1-i) x}} \left(x^2+i\right) \left(\left(\sqrt{2}-1\right) F\left(\left.\sin ^{-1}\left(\sqrt{-\frac{i \left((1-i) x+\sqrt{2}\right)}{\sqrt{2}-(1-i) x}}\right)\right|-1\right)-2 \sqrt{2} \Pi \left(1+\sqrt{2};\left.\sin ^{-1}\left(\sqrt{-\frac{i \left((1-i) x+\sqrt{2}\right)}{\sqrt{2}-(1-i) x}}\right)\right|-1\right)\right)}{\sqrt{\frac{x^2+i}{\left(\sqrt[4]{-1}-x\right)^2}} \sqrt{x^4+1}}","-\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}+x^2+2 x+1}\right)",1,"((-1)^(3/4)*Sqrt[2]*Sqrt[((-I)*(Sqrt[2] + (1 - I)*x))/(Sqrt[2] - (1 - I)*x)]*(I + x^2)*((-1 + Sqrt[2])*EllipticF[ArcSin[Sqrt[((-I)*(Sqrt[2] + (1 - I)*x))/(Sqrt[2] - (1 - I)*x)]], -1] - 2*Sqrt[2]*EllipticPi[1 + Sqrt[2], ArcSin[Sqrt[((-I)*(Sqrt[2] + (1 - I)*x))/(Sqrt[2] - (1 - I)*x)]], -1]))/(Sqrt[(I + x^2)/((-1)^(1/4) - x)^2]*Sqrt[1 + x^4])","C",1
419,1,178,34,0.2576659,"\int \frac{1+x}{(-1+x) \sqrt{1+x^4}} \, dx","Integrate[(1 + x)/((-1 + x)*Sqrt[1 + x^4]),x]","-\frac{(-1)^{3/4} \sqrt{2} \sqrt{-\frac{i \left(\sqrt{2}+(1-i) x\right)}{\sqrt{2}-(1-i) x}} \left(x^2+i\right) \left(\left(1+\sqrt{2}\right) F\left(\left.\sin ^{-1}\left(\sqrt{-\frac{i \left((1-i) x+\sqrt{2}\right)}{\sqrt{2}-(1-i) x}}\right)\right|-1\right)-2 \sqrt{2} \Pi \left(1-\sqrt{2};\left.\sin ^{-1}\left(\sqrt{-\frac{i \left((1-i) x+\sqrt{2}\right)}{\sqrt{2}-(1-i) x}}\right)\right|-1\right)\right)}{\sqrt{\frac{x^2+i}{\left(\sqrt[4]{-1}-x\right)^2}} \sqrt{x^4+1}}","-\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}+x^2-2 x+1}\right)",1,"-(((-1)^(3/4)*Sqrt[2]*Sqrt[((-I)*(Sqrt[2] + (1 - I)*x))/(Sqrt[2] - (1 - I)*x)]*(I + x^2)*((1 + Sqrt[2])*EllipticF[ArcSin[Sqrt[((-I)*(Sqrt[2] + (1 - I)*x))/(Sqrt[2] - (1 - I)*x)]], -1] - 2*Sqrt[2]*EllipticPi[1 - Sqrt[2], ArcSin[Sqrt[((-I)*(Sqrt[2] + (1 - I)*x))/(Sqrt[2] - (1 - I)*x)]], -1]))/(Sqrt[(I + x^2)/((-1)^(1/4) - x)^2]*Sqrt[1 + x^4]))","C",1
420,1,221,34,0.4081161,"\int \frac{1+x}{(-1+x) \sqrt{1+x^2+x^4}} \, dx","Integrate[(1 + x)/((-1 + x)*Sqrt[1 + x^2 + x^4]),x]","\frac{\sqrt[6]{-1} \sqrt{6} \left(1-i \sqrt{3}\right) \left(-x+(-1)^{2/3}+1\right)^2 \sqrt{\frac{2 \sqrt{3} x+\sqrt{3}+3 i}{2 i x+\sqrt{3}-i}} \sqrt{\frac{i \left(2 \sqrt{3} x^2+\sqrt{3}+3 i\right)}{\left(\left(\sqrt{3}+i\right) x-2 i\right)^2}} \left(F\left(\left.\sin ^{-1}\left(\sqrt{\frac{-2 i x+\sqrt{3}+i}{4 i-2 \left(i+\sqrt{3}\right) x}}\right)\right|4\right)-2 \Pi \left(-2;\left.\sin ^{-1}\left(\sqrt{\frac{-2 i x+\sqrt{3}+i}{4 i-2 \left(i+\sqrt{3}\right) x}}\right)\right|4\right)\right)}{\left(1+\sqrt[3]{-1}\right) \sqrt{x^4+x^2+1}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{3} \sqrt{x^4+x^2+1}}{x^2+x+1}\right)}{\sqrt{3}}",1,"((-1)^(1/6)*Sqrt[6]*(1 - I*Sqrt[3])*(1 + (-1)^(2/3) - x)^2*Sqrt[(3*I + Sqrt[3] + 2*Sqrt[3]*x)/(-I + Sqrt[3] + (2*I)*x)]*Sqrt[(I*(3*I + Sqrt[3] + 2*Sqrt[3]*x^2))/(-2*I + (I + Sqrt[3])*x)^2]*(EllipticF[ArcSin[Sqrt[(I + Sqrt[3] - (2*I)*x)/(4*I - 2*(I + Sqrt[3])*x)]], 4] - 2*EllipticPi[-2, ArcSin[Sqrt[(I + Sqrt[3] - (2*I)*x)/(4*I - 2*(I + Sqrt[3])*x)]], 4]))/((1 + (-1)^(1/3))*Sqrt[1 + x^2 + x^4])","C",0
421,1,3217,34,1.6278215,"\int \frac{1+x^2}{\left(-1+x^2\right) \sqrt{1-x-x^2+x^3+x^4}} \, dx","Integrate[(1 + x^2)/((-1 + x^2)*Sqrt[1 - x - x^2 + x^3 + x^4]),x]","\text{Result too large to show}","2 \tanh ^{-1}\left(\frac{x}{x^2-\sqrt{x^4+x^3-x^2-x+1}-1}\right)",1,"(2*(x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])^2*Sqrt[((Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])*(x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 3, 0]))/((x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 3, 0]))]*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0])*Sqrt[((x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])*(x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))/((x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])^2*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0])^2)]*(-((EllipticF[ArcSin[Sqrt[((x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))/((x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))]], -(((Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 3, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))/((-Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 3, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0])))]*(-1 + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0]) + EllipticPi[((-1 + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))/((-1 + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0])), ArcSin[Sqrt[((x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))/((x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))]], -(((Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 3, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))/((-Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 3, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0])))]*(-Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0]))/((-1 + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0])*(-1 + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))) + (EllipticF[ArcSin[Sqrt[((x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))/((x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))]], -(((Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 3, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))/((-Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 3, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0])))]*(1 + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0]) + EllipticPi[((1 + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))/((1 + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0])), ArcSin[Sqrt[((x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))/((x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))]], -(((Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 3, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))/((-Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 3, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0])))]*(-Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0]))/((1 + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0])*(1 + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0])) + EllipticF[ArcSin[Sqrt[((x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))/((x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))]], ((Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 3, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))/((Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 3, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))]/(-Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0])))/(Sqrt[1 - x - x^2 + x^3 + x^4]*(-Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0]))","C",0
422,1,759,34,0.5590448,"\int \frac{x}{\sqrt{11-11 x-3 x^2+2 x^3+x^4}} \, dx","Integrate[x/Sqrt[11 - 11*x - 3*x^2 + 2*x^3 + x^4],x]","\frac{2 (x-1) \left(x-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2-11\&,1\right]\right) \sqrt{\frac{x-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2-11\&,2\right]}{\left(-1+\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2-11\&,2\right]\right) \left(x-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2-11\&,1\right]\right)}} \sqrt{\frac{x-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2-11\&,3\right]}{\left(-1+\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2-11\&,3\right]\right) \left(x-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2-11\&,1\right]\right)}} \left(\left(\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2-11\&,1\right]-1\right) \Pi \left(\frac{-1+\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2-11\&,3\right]}{-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2-11\&,1\right]+\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2-11\&,3\right]};\sin ^{-1}\left(\sqrt{-\frac{(x-1) \left(\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2-11\&,1\right]-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2-11\&,3\right]\right)}{\left(x-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2-11\&,1\right]\right) \left(-1+\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2-11\&,3\right]\right)}}\right)|\frac{\left(\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2-11\&,1\right]-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2-11\&,2\right]\right) \left(-1+\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2-11\&,3\right]\right)}{\left(-1+\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2-11\&,2\right]\right) \left(\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2-11\&,1\right]-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2-11\&,3\right]\right)}\right)-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2-11\&,1\right] F\left(\sin ^{-1}\left(\sqrt{-\frac{(x-1) \left(\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2-11\&,1\right]-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2-11\&,3\right]\right)}{\left(x-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2-11\&,1\right]\right) \left(-1+\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2-11\&,3\right]\right)}}\right)|\frac{\left(\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2-11\&,1\right]-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2-11\&,2\right]\right) \left(-1+\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2-11\&,3\right]\right)}{\left(-1+\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2-11\&,2\right]\right) \left(\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2-11\&,1\right]-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2-11\&,3\right]\right)}\right)\right)}{\sqrt{x^4+2 x^3-3 x^2-11 x+11} \sqrt{-\frac{(x-1) \left(\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2-11\&,1\right]-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2-11\&,3\right]\right)}{\left(-1+\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2-11\&,3\right]\right) \left(x-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2-11\&,1\right]\right)}}}","\frac{2}{3} \tanh ^{-1}\left(\frac{x^2+x-2}{\sqrt{x^4+2 x^3-3 x^2-11 x+11}}\right)",1,"(2*(-1 + x)*(x - Root[-11 + 3*#1^2 + #1^3 & , 1, 0])*(EllipticPi[(-1 + Root[-11 + 3*#1^2 + #1^3 & , 3, 0])/(-Root[-11 + 3*#1^2 + #1^3 & , 1, 0] + Root[-11 + 3*#1^2 + #1^3 & , 3, 0]), ArcSin[Sqrt[-(((-1 + x)*(Root[-11 + 3*#1^2 + #1^3 & , 1, 0] - Root[-11 + 3*#1^2 + #1^3 & , 3, 0]))/((x - Root[-11 + 3*#1^2 + #1^3 & , 1, 0])*(-1 + Root[-11 + 3*#1^2 + #1^3 & , 3, 0])))]], ((Root[-11 + 3*#1^2 + #1^3 & , 1, 0] - Root[-11 + 3*#1^2 + #1^3 & , 2, 0])*(-1 + Root[-11 + 3*#1^2 + #1^3 & , 3, 0]))/((-1 + Root[-11 + 3*#1^2 + #1^3 & , 2, 0])*(Root[-11 + 3*#1^2 + #1^3 & , 1, 0] - Root[-11 + 3*#1^2 + #1^3 & , 3, 0]))]*(-1 + Root[-11 + 3*#1^2 + #1^3 & , 1, 0]) - EllipticF[ArcSin[Sqrt[-(((-1 + x)*(Root[-11 + 3*#1^2 + #1^3 & , 1, 0] - Root[-11 + 3*#1^2 + #1^3 & , 3, 0]))/((x - Root[-11 + 3*#1^2 + #1^3 & , 1, 0])*(-1 + Root[-11 + 3*#1^2 + #1^3 & , 3, 0])))]], ((Root[-11 + 3*#1^2 + #1^3 & , 1, 0] - Root[-11 + 3*#1^2 + #1^3 & , 2, 0])*(-1 + Root[-11 + 3*#1^2 + #1^3 & , 3, 0]))/((-1 + Root[-11 + 3*#1^2 + #1^3 & , 2, 0])*(Root[-11 + 3*#1^2 + #1^3 & , 1, 0] - Root[-11 + 3*#1^2 + #1^3 & , 3, 0]))]*Root[-11 + 3*#1^2 + #1^3 & , 1, 0])*Sqrt[(x - Root[-11 + 3*#1^2 + #1^3 & , 2, 0])/((x - Root[-11 + 3*#1^2 + #1^3 & , 1, 0])*(-1 + Root[-11 + 3*#1^2 + #1^3 & , 2, 0]))]*Sqrt[(x - Root[-11 + 3*#1^2 + #1^3 & , 3, 0])/((x - Root[-11 + 3*#1^2 + #1^3 & , 1, 0])*(-1 + Root[-11 + 3*#1^2 + #1^3 & , 3, 0]))])/(Sqrt[11 - 11*x - 3*x^2 + 2*x^3 + x^4]*Sqrt[-(((-1 + x)*(Root[-11 + 3*#1^2 + #1^3 & , 1, 0] - Root[-11 + 3*#1^2 + #1^3 & , 3, 0]))/((x - Root[-11 + 3*#1^2 + #1^3 & , 1, 0])*(-1 + Root[-11 + 3*#1^2 + #1^3 & , 3, 0])))])","C",1
423,1,830,34,0.5378293,"\int \frac{1+x}{\sqrt{2-5 x-3 x^2+2 x^3+x^4}} \, dx","Integrate[(1 + x)/Sqrt[2 - 5*x - 3*x^2 + 2*x^3 + x^4],x]","-\frac{2 \sqrt{\frac{x+2}{x-\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}+1\&,1\right]}} \left(x-\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}+1\&,1\right]\right)^2 \left(\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}+1\&,1\right] F\left(\sin ^{-1}\left(\sqrt{-\frac{(x+2) \left(\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}+1\&,1\right]-\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}+1\&,3\right]\right)}{\left(x-\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}+1\&,1\right]\right) \left(2+\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}+1\&,3\right]\right)}}\right)|\frac{\left(\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}+1\&,1\right]-\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}+1\&,2\right]\right) \left(2+\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}+1\&,3\right]\right)}{\left(2+\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}+1\&,2\right]\right) \left(\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}+1\&,1\right]-\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}+1\&,3\right]\right)}\right)+F\left(\sin ^{-1}\left(\sqrt{\frac{(x+2) \left(-\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}+1\&,1\right]+\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}+1\&,3\right]\right)}{\left(x-\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}+1\&,1\right]\right) \left(2+\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}+1\&,3\right]\right)}}\right)|\frac{\left(\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}+1\&,1\right]-\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}+1\&,2\right]\right) \left(2+\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}+1\&,3\right]\right)}{\left(2+\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}+1\&,2\right]\right) \left(\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}+1\&,1\right]-\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}+1\&,3\right]\right)}\right)-\Pi \left(\frac{2+\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}+1\&,3\right]}{-\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}+1\&,1\right]+\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}+1\&,3\right]};\sin ^{-1}\left(\sqrt{-\frac{(x+2) \left(\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}+1\&,1\right]-\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}+1\&,3\right]\right)}{\left(x-\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}+1\&,1\right]\right) \left(2+\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}+1\&,3\right]\right)}}\right)|\frac{\left(\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}+1\&,1\right]-\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}+1\&,2\right]\right) \left(2+\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}+1\&,3\right]\right)}{\left(2+\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}+1\&,2\right]\right) \left(\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}+1\&,1\right]-\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}+1\&,3\right]\right)}\right) \left(2+\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}+1\&,1\right]\right)\right) \sqrt{\frac{x-\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}+1\&,2\right]}{x-\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}+1\&,1\right]}} \sqrt{\frac{x-\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}+1\&,3\right]}{x-\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}+1\&,1\right]}}}{\sqrt{x^4+2 x^3-3 x^2-5 x+2} \sqrt{\left(2+\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}+1\&,2\right]\right) \left(-\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}+1\&,1\right]+\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}+1\&,3\right]\right)}}","\frac{2}{3} \tanh ^{-1}\left(\frac{x^2+x-2}{\sqrt{x^4+2 x^3-3 x^2-5 x+2}}\right)",1,"(-2*Sqrt[(2 + x)/(x - Root[1 - 3*#1 + #1^3 & , 1, 0])]*(x - Root[1 - 3*#1 + #1^3 & , 1, 0])^2*(EllipticF[ArcSin[Sqrt[((2 + x)*(-Root[1 - 3*#1 + #1^3 & , 1, 0] + Root[1 - 3*#1 + #1^3 & , 3, 0]))/((x - Root[1 - 3*#1 + #1^3 & , 1, 0])*(2 + Root[1 - 3*#1 + #1^3 & , 3, 0]))]], ((Root[1 - 3*#1 + #1^3 & , 1, 0] - Root[1 - 3*#1 + #1^3 & , 2, 0])*(2 + Root[1 - 3*#1 + #1^3 & , 3, 0]))/((2 + Root[1 - 3*#1 + #1^3 & , 2, 0])*(Root[1 - 3*#1 + #1^3 & , 1, 0] - Root[1 - 3*#1 + #1^3 & , 3, 0]))] + EllipticF[ArcSin[Sqrt[-(((2 + x)*(Root[1 - 3*#1 + #1^3 & , 1, 0] - Root[1 - 3*#1 + #1^3 & , 3, 0]))/((x - Root[1 - 3*#1 + #1^3 & , 1, 0])*(2 + Root[1 - 3*#1 + #1^3 & , 3, 0])))]], ((Root[1 - 3*#1 + #1^3 & , 1, 0] - Root[1 - 3*#1 + #1^3 & , 2, 0])*(2 + Root[1 - 3*#1 + #1^3 & , 3, 0]))/((2 + Root[1 - 3*#1 + #1^3 & , 2, 0])*(Root[1 - 3*#1 + #1^3 & , 1, 0] - Root[1 - 3*#1 + #1^3 & , 3, 0]))]*Root[1 - 3*#1 + #1^3 & , 1, 0] - EllipticPi[(2 + Root[1 - 3*#1 + #1^3 & , 3, 0])/(-Root[1 - 3*#1 + #1^3 & , 1, 0] + Root[1 - 3*#1 + #1^3 & , 3, 0]), ArcSin[Sqrt[-(((2 + x)*(Root[1 - 3*#1 + #1^3 & , 1, 0] - Root[1 - 3*#1 + #1^3 & , 3, 0]))/((x - Root[1 - 3*#1 + #1^3 & , 1, 0])*(2 + Root[1 - 3*#1 + #1^3 & , 3, 0])))]], ((Root[1 - 3*#1 + #1^3 & , 1, 0] - Root[1 - 3*#1 + #1^3 & , 2, 0])*(2 + Root[1 - 3*#1 + #1^3 & , 3, 0]))/((2 + Root[1 - 3*#1 + #1^3 & , 2, 0])*(Root[1 - 3*#1 + #1^3 & , 1, 0] - Root[1 - 3*#1 + #1^3 & , 3, 0]))]*(2 + Root[1 - 3*#1 + #1^3 & , 1, 0]))*Sqrt[(x - Root[1 - 3*#1 + #1^3 & , 2, 0])/(x - Root[1 - 3*#1 + #1^3 & , 1, 0])]*Sqrt[(x - Root[1 - 3*#1 + #1^3 & , 3, 0])/(x - Root[1 - 3*#1 + #1^3 & , 1, 0])])/(Sqrt[2 - 5*x - 3*x^2 + 2*x^3 + x^4]*Sqrt[(2 + Root[1 - 3*#1 + #1^3 & , 2, 0])*(-Root[1 - 3*#1 + #1^3 & , 1, 0] + Root[1 - 3*#1 + #1^3 & , 3, 0])])","C",1
424,1,768,34,0.9329875,"\int \frac{x}{\sqrt{-3+3 x-3 x^2+2 x^3+x^4}} \, dx","Integrate[x/Sqrt[-3 + 3*x - 3*x^2 + 2*x^3 + x^4],x]","\frac{2 (x-1) \left(x-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+3\&,3\right]\right) \sqrt{\frac{\left(\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+3\&,1\right]-1\right) \left(x-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+3\&,2\right]\right)}{\left(-1+\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+3\&,2\right]\right) \left(x-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+3\&,1\right]\right)}} \left(\left(\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+3\&,1\right]-1\right) \Pi \left(\frac{-1+\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+3\&,3\right]}{-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+3\&,1\right]+\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+3\&,3\right]};\sin ^{-1}\left(\sqrt{-\frac{(x-1) \left(\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+3\&,1\right]-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+3\&,3\right]\right)}{\left(x-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+3\&,1\right]\right) \left(-1+\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+3\&,3\right]\right)}}\right)|\frac{\left(\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+3\&,1\right]-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+3\&,2\right]\right) \left(-1+\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+3\&,3\right]\right)}{\left(-1+\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+3\&,2\right]\right) \left(\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+3\&,1\right]-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+3\&,3\right]\right)}\right)-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+3\&,1\right] F\left(\sin ^{-1}\left(\sqrt{-\frac{(x-1) \left(\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+3\&,1\right]-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+3\&,3\right]\right)}{\left(x-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+3\&,1\right]\right) \left(-1+\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+3\&,3\right]\right)}}\right)|\frac{\left(\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+3\&,1\right]-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+3\&,2\right]\right) \left(-1+\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+3\&,3\right]\right)}{\left(-1+\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+3\&,2\right]\right) \left(\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+3\&,1\right]-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+3\&,3\right]\right)}\right)\right)}{\sqrt{x^4+2 x^3-3 x^2+3 x-3} \left(-1+\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+3\&,3\right]\right) \sqrt{-\frac{(x-1) \left(\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+3\&,1\right]-1\right) \left(\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+3\&,1\right]-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+3\&,3\right]\right) \left(x-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+3\&,3\right]\right)}{\left(-1+\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+3\&,3\right]\right)^2 \left(x-\text{Root}\left[\text{$\#$1}^3+3 \text{$\#$1}^2+3\&,1\right]\right)^2}}}","\frac{2}{3} \tanh ^{-1}\left(\frac{x^2+x-2}{\sqrt{x^4+2 x^3-3 x^2+3 x-3}}\right)",1,"(2*(-1 + x)*(EllipticPi[(-1 + Root[3 + 3*#1^2 + #1^3 & , 3, 0])/(-Root[3 + 3*#1^2 + #1^3 & , 1, 0] + Root[3 + 3*#1^2 + #1^3 & , 3, 0]), ArcSin[Sqrt[-(((-1 + x)*(Root[3 + 3*#1^2 + #1^3 & , 1, 0] - Root[3 + 3*#1^2 + #1^3 & , 3, 0]))/((x - Root[3 + 3*#1^2 + #1^3 & , 1, 0])*(-1 + Root[3 + 3*#1^2 + #1^3 & , 3, 0])))]], ((Root[3 + 3*#1^2 + #1^3 & , 1, 0] - Root[3 + 3*#1^2 + #1^3 & , 2, 0])*(-1 + Root[3 + 3*#1^2 + #1^3 & , 3, 0]))/((-1 + Root[3 + 3*#1^2 + #1^3 & , 2, 0])*(Root[3 + 3*#1^2 + #1^3 & , 1, 0] - Root[3 + 3*#1^2 + #1^3 & , 3, 0]))]*(-1 + Root[3 + 3*#1^2 + #1^3 & , 1, 0]) - EllipticF[ArcSin[Sqrt[-(((-1 + x)*(Root[3 + 3*#1^2 + #1^3 & , 1, 0] - Root[3 + 3*#1^2 + #1^3 & , 3, 0]))/((x - Root[3 + 3*#1^2 + #1^3 & , 1, 0])*(-1 + Root[3 + 3*#1^2 + #1^3 & , 3, 0])))]], ((Root[3 + 3*#1^2 + #1^3 & , 1, 0] - Root[3 + 3*#1^2 + #1^3 & , 2, 0])*(-1 + Root[3 + 3*#1^2 + #1^3 & , 3, 0]))/((-1 + Root[3 + 3*#1^2 + #1^3 & , 2, 0])*(Root[3 + 3*#1^2 + #1^3 & , 1, 0] - Root[3 + 3*#1^2 + #1^3 & , 3, 0]))]*Root[3 + 3*#1^2 + #1^3 & , 1, 0])*Sqrt[((-1 + Root[3 + 3*#1^2 + #1^3 & , 1, 0])*(x - Root[3 + 3*#1^2 + #1^3 & , 2, 0]))/((x - Root[3 + 3*#1^2 + #1^3 & , 1, 0])*(-1 + Root[3 + 3*#1^2 + #1^3 & , 2, 0]))]*(x - Root[3 + 3*#1^2 + #1^3 & , 3, 0]))/(Sqrt[-3 + 3*x - 3*x^2 + 2*x^3 + x^4]*Sqrt[-(((-1 + x)*(-1 + Root[3 + 3*#1^2 + #1^3 & , 1, 0])*(x - Root[3 + 3*#1^2 + #1^3 & , 3, 0])*(Root[3 + 3*#1^2 + #1^3 & , 1, 0] - Root[3 + 3*#1^2 + #1^3 & , 3, 0]))/((x - Root[3 + 3*#1^2 + #1^3 & , 1, 0])^2*(-1 + Root[3 + 3*#1^2 + #1^3 & , 3, 0])^2))]*(-1 + Root[3 + 3*#1^2 + #1^3 & , 3, 0]))","C",0
425,1,892,34,5.5409358,"\int \frac{\sqrt{1-x^6} \left(2+x^6\right)}{x^3 \left(-1+x^4+x^6\right)} \, dx","Integrate[(Sqrt[1 - x^6]*(2 + x^6))/(x^3*(-1 + x^4 + x^6)),x]","\frac{\sqrt{1-x^6}}{x^2}-\frac{\sqrt{\frac{1-x^2}{1+\sqrt[3]{-1}}} \sqrt{x^4+x^2+1} \left(\frac{\sqrt{3} \left(\left(1+\sqrt[3]{-1}\right) x^2+i \sqrt{3}\right) F\left(\sin ^{-1}\left(\sqrt{\frac{1-(-1)^{2/3} x^2}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{(-1)^{2/3} x^2-1}+\frac{3 i \left(\frac{\left(2+\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,1\right]^3\right) \Pi \left(\frac{i \sqrt{3}}{\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,1\right]};\sin ^{-1}\left(\sqrt{\frac{1-(-1)^{2/3} x^2}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,1\right]}+\frac{-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,2\right]^3 \left(\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,1\right]-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]\right) \left(\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]\right) \Pi \left(\frac{i \sqrt{3}}{\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,2\right]};\sin ^{-1}\left(\sqrt{\frac{1-(-1)^{2/3} x^2}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)-2 \left(\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,1\right]-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]\right) \left(\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]\right) \Pi \left(\frac{i \sqrt{3}}{\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,2\right]};\sin ^{-1}\left(\sqrt{\frac{1-(-1)^{2/3} x^2}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)+\Pi \left(\frac{i \sqrt{3}}{\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]};\sin ^{-1}\left(\sqrt{\frac{1-(-1)^{2/3} x^2}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right) \left(\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,1\right]-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,2\right]\right) \left(\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,2\right]\right) \text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]^3+2 \Pi \left(\frac{i \sqrt{3}}{\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]};\sin ^{-1}\left(\sqrt{\frac{1-(-1)^{2/3} x^2}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right) \left(\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,1\right]-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,2\right]\right) \left(\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,2\right]\right)}{\left(\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,2\right]\right) \left(\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,2\right]-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]\right) \left(\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]\right)}\right)}{\left(\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,1\right]-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,2\right]\right) \left(\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,1\right]-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]\right)}\right)}{3 \sqrt{1-x^6}}","\frac{\sqrt{1-x^6}}{x^2}-\tanh ^{-1}\left(\frac{x^2}{\sqrt{1-x^6}}\right)",1,"Sqrt[1 - x^6]/x^2 - (Sqrt[(1 - x^2)/(1 + (-1)^(1/3))]*Sqrt[1 + x^2 + x^4]*((Sqrt[3]*(I*Sqrt[3] + (1 + (-1)^(1/3))*x^2)*EllipticF[ArcSin[Sqrt[(1 - (-1)^(2/3)*x^2)/(1 + (-1)^(1/3))]], (-1)^(1/3)])/(-1 + (-1)^(2/3)*x^2) + ((3*I)*((EllipticPi[(I*Sqrt[3])/((-1)^(1/3) + Root[-1 + #1^2 + #1^3 & , 1, 0]), ArcSin[Sqrt[(1 - (-1)^(2/3)*x^2)/(1 + (-1)^(1/3))]], (-1)^(1/3)]*(2 + Root[-1 + #1^2 + #1^3 & , 1, 0]^3))/((-1)^(1/3) + Root[-1 + #1^2 + #1^3 & , 1, 0]) + (2*EllipticPi[(I*Sqrt[3])/((-1)^(1/3) + Root[-1 + #1^2 + #1^3 & , 3, 0]), ArcSin[Sqrt[(1 - (-1)^(2/3)*x^2)/(1 + (-1)^(1/3))]], (-1)^(1/3)]*(Root[-1 + #1^2 + #1^3 & , 1, 0] - Root[-1 + #1^2 + #1^3 & , 2, 0])*((-1)^(1/3) + Root[-1 + #1^2 + #1^3 & , 2, 0]) + EllipticPi[(I*Sqrt[3])/((-1)^(1/3) + Root[-1 + #1^2 + #1^3 & , 3, 0]), ArcSin[Sqrt[(1 - (-1)^(2/3)*x^2)/(1 + (-1)^(1/3))]], (-1)^(1/3)]*(Root[-1 + #1^2 + #1^3 & , 1, 0] - Root[-1 + #1^2 + #1^3 & , 2, 0])*((-1)^(1/3) + Root[-1 + #1^2 + #1^3 & , 2, 0])*Root[-1 + #1^2 + #1^3 & , 3, 0]^3 - 2*EllipticPi[(I*Sqrt[3])/((-1)^(1/3) + Root[-1 + #1^2 + #1^3 & , 2, 0]), ArcSin[Sqrt[(1 - (-1)^(2/3)*x^2)/(1 + (-1)^(1/3))]], (-1)^(1/3)]*(Root[-1 + #1^2 + #1^3 & , 1, 0] - Root[-1 + #1^2 + #1^3 & , 3, 0])*((-1)^(1/3) + Root[-1 + #1^2 + #1^3 & , 3, 0]) - EllipticPi[(I*Sqrt[3])/((-1)^(1/3) + Root[-1 + #1^2 + #1^3 & , 2, 0]), ArcSin[Sqrt[(1 - (-1)^(2/3)*x^2)/(1 + (-1)^(1/3))]], (-1)^(1/3)]*Root[-1 + #1^2 + #1^3 & , 2, 0]^3*(Root[-1 + #1^2 + #1^3 & , 1, 0] - Root[-1 + #1^2 + #1^3 & , 3, 0])*((-1)^(1/3) + Root[-1 + #1^2 + #1^3 & , 3, 0]))/(((-1)^(1/3) + Root[-1 + #1^2 + #1^3 & , 2, 0])*(Root[-1 + #1^2 + #1^3 & , 2, 0] - Root[-1 + #1^2 + #1^3 & , 3, 0])*((-1)^(1/3) + Root[-1 + #1^2 + #1^3 & , 3, 0]))))/((Root[-1 + #1^2 + #1^3 & , 1, 0] - Root[-1 + #1^2 + #1^3 & , 2, 0])*(Root[-1 + #1^2 + #1^3 & , 1, 0] - Root[-1 + #1^2 + #1^3 & , 3, 0]))))/(3*Sqrt[1 - x^6])","C",0
426,1,35,35,0.0043143,"\int \frac{\sqrt{x}}{\left(-2+x^2\right)^{3/4}} \, dx","Integrate[Sqrt[x]/(-2 + x^2)^(3/4),x]","\tanh ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2-2}}\right)-\tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2-2}}\right)","\tanh ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2-2}}\right)-\tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2-2}}\right)",1,"-ArcTan[Sqrt[x]/(-2 + x^2)^(1/4)] + ArcTanh[Sqrt[x]/(-2 + x^2)^(1/4)]","A",1
427,1,35,35,0.2714249,"\int \frac{a+x}{\left(-1+2 b+2 a x+x^2\right) \sqrt[4]{2 b+2 a x+x^2}} \, dx","Integrate[(a + x)/((-1 + 2*b + 2*a*x + x^2)*(2*b + 2*a*x + x^2)^(1/4)),x]","\tan ^{-1}\left(\sqrt[4]{2 a x+2 b+x^2}\right)-\tanh ^{-1}\left(\sqrt[4]{2 a x+2 b+x^2}\right)","\tan ^{-1}\left(\sqrt[4]{2 a x+2 b+x^2}\right)-\tanh ^{-1}\left(\sqrt[4]{2 a x+2 b+x^2}\right)",1,"ArcTan[(2*b + 2*a*x + x^2)^(1/4)] - ArcTanh[(2*b + 2*a*x + x^2)^(1/4)]","A",1
428,1,34,35,0.0323034,"\int \frac{1}{\sqrt{c+b x+a x^2}} \, dx","Integrate[1/Sqrt[c + b*x + a*x^2],x]","\frac{\log \left(2 \sqrt{a} \sqrt{a x^2+b x+c}+2 a x+b\right)}{\sqrt{a}}","-\frac{\log \left(-2 \sqrt{a} \sqrt{a x^2+b x+c}+2 a x+b\right)}{\sqrt{a}}",1,"Log[b + 2*a*x + 2*Sqrt[a]*Sqrt[c + b*x + a*x^2]]/Sqrt[a]","A",1
429,1,30,35,0.0091738,"\int x^{11} \sqrt[3]{-1+x^3} \, dx","Integrate[x^11*(-1 + x^3)^(1/3),x]","\frac{\left(x^3-1\right)^{4/3} \left(140 x^9+126 x^6+108 x^3+81\right)}{1820}","\frac{\sqrt[3]{x^3-1} \left(140 x^{12}-14 x^9-18 x^6-27 x^3-81\right)}{1820}",1,"((-1 + x^3)^(4/3)*(81 + 108*x^3 + 126*x^6 + 140*x^9))/1820","A",1
430,1,112,35,1.0360694,"\int \frac{-1-2 x+x^2}{\left(1+2 x+3 x^2\right) \sqrt{-x+x^3}} \, dx","Integrate[(-1 - 2*x + x^2)/((1 + 2*x + 3*x^2)*Sqrt[-x + x^3]),x]","-\frac{2 \sqrt{1-\frac{1}{x^2}} x^{3/2} \left(-3 F\left(\left.\sin ^{-1}\left(\frac{1}{\sqrt{x}}\right)\right|-1\right)+\left(2+i \sqrt{2}\right) \Pi \left(\frac{i}{-i+\sqrt{2}};\left.\sin ^{-1}\left(\frac{1}{\sqrt{x}}\right)\right|-1\right)+\left(2-i \sqrt{2}\right) \Pi \left(-\frac{i}{i+\sqrt{2}};\left.\sin ^{-1}\left(\frac{1}{\sqrt{x}}\right)\right|-1\right)\right)}{3 \sqrt{x \left(x^2-1\right)}}","-\frac{2 \tanh ^{-1}\left(\frac{\frac{x}{\sqrt{3}}-\frac{1}{\sqrt{3}}}{\sqrt{x^3-x}}\right)}{\sqrt{3}}",1,"(-2*Sqrt[1 - x^(-2)]*x^(3/2)*(-3*EllipticF[ArcSin[1/Sqrt[x]], -1] + (2 + I*Sqrt[2])*EllipticPi[I/(-I + Sqrt[2]), ArcSin[1/Sqrt[x]], -1] + (2 - I*Sqrt[2])*EllipticPi[(-I)/(I + Sqrt[2]), ArcSin[1/Sqrt[x]], -1]))/(3*Sqrt[x*(-1 + x^2)])","C",1
431,1,35,35,0.4724647,"\int \frac{\left(-1+x^2\right) \sqrt{-1-4 x-5 x^2-4 x^3-x^4}}{\left(1+x+x^2\right) \left(1+3 x+x^2\right)^2} \, dx","Integrate[((-1 + x^2)*Sqrt[-1 - 4*x - 5*x^2 - 4*x^3 - x^4])/((1 + x + x^2)*(1 + 3*x + x^2)^2),x]","\frac{\sqrt{-x^4-4 x^3-5 x^2-4 x-1}}{x^2+3 x+1}","\frac{\sqrt{-x^4-4 x^3-5 x^2-4 x-1}}{x^2+3 x+1}",1,"Sqrt[-1 - 4*x - 5*x^2 - 4*x^3 - x^4]/(1 + 3*x + x^2)","A",1
432,1,22,35,0.0085352,"\int \frac{-1+x^4}{x^3 \sqrt{1+x^4}} \, dx","Integrate[(-1 + x^4)/(x^3*Sqrt[1 + x^4]),x]","\frac{1}{2} \left(\sinh ^{-1}\left(x^2\right)+\frac{\sqrt{x^4+1}}{x^2}\right)","\frac{\sqrt{x^4+1}}{2 x^2}+\frac{1}{2} \log \left(\sqrt{x^4+1}+x^2\right)",1,"(Sqrt[1 + x^4]/x^2 + ArcSinh[x^2])/2","A",1
433,1,28,35,0.0124582,"\int \frac{-1+x^3}{x^6 \left(1+x^3\right) \sqrt[4]{x+x^4}} \, dx","Integrate[(-1 + x^3)/(x^6*(1 + x^3)*(x + x^4)^(1/4)),x]","\frac{-80 x^6-20 x^3+4}{21 x^5 \sqrt[4]{x^4+x}}","-\frac{4 \left(x^4+x\right)^{3/4} \left(20 x^6+5 x^3-1\right)}{21 x^6 \left(x^3+1\right)}",1,"(4 - 20*x^3 - 80*x^6)/(21*x^5*(x + x^4)^(1/4))","A",1
434,1,50,35,0.0169901,"\int \frac{\sqrt{x+x^4}}{x^3} \, dx","Integrate[Sqrt[x + x^4]/x^3,x]","\frac{2 \sqrt{x^4+x} \sinh ^{-1}\left(x^{3/2}\right)}{3 \sqrt{x} \sqrt{x^3+1}}-\frac{2 \sqrt{x^4+x}}{3 x^2}","\frac{2}{3} \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4+x}}\right)-\frac{2 \sqrt{x^4+x}}{3 x^2}",1,"(-2*Sqrt[x + x^4])/(3*x^2) + (2*Sqrt[x + x^4]*ArcSinh[x^(3/2)])/(3*Sqrt[x]*Sqrt[1 + x^3])","A",1
435,1,35,35,0.0188727,"\int \frac{1}{x^8 \sqrt[4]{x^2+x^4}} \, dx","Integrate[1/(x^8*(x^2 + x^4)^(1/4)),x]","\frac{2 \left(x^4+x^2\right)^{3/4} \left(128 x^6-96 x^4+84 x^2-77\right)}{1155 x^9}","\frac{2 \left(x^4+x^2\right)^{3/4} \left(128 x^6-96 x^4+84 x^2-77\right)}{1155 x^9}",1,"(2*(x^2 + x^4)^(3/4)*(-77 + 84*x^2 - 96*x^4 + 128*x^6))/(1155*x^9)","A",1
436,1,789,35,1.6371239,"\int \frac{1-2 x}{\sqrt{5+5 x-4 x^2-2 x^3+x^4}} \, dx","Integrate[(1 - 2*x)/Sqrt[5 + 5*x - 4*x^2 - 2*x^3 + x^4],x]","\frac{\left(-2 x+\sqrt{11-2 \sqrt{5}}+1\right)^2 \sqrt{\frac{-2 x+\sqrt{11+2 \sqrt{5}}+1}{-2 x+\sqrt{11-2 \sqrt{5}}+1}} \sqrt{-\frac{2 x+\sqrt{11+2 \sqrt{5}}-1}{\left(\sqrt{11-2 \sqrt{5}}-\sqrt{11+2 \sqrt{5}}\right) \left(-2 x+\sqrt{11-2 \sqrt{5}}+1\right)}} \left(\left(-\sqrt{11+2 \sqrt{5}} \sqrt{-\frac{2 x+\sqrt{11-2 \sqrt{5}}-1}{-2 x+\sqrt{11-2 \sqrt{5}}+1}}+\sqrt{\frac{\left(2 \sqrt{5}-11\right) \left(2 x+\sqrt{11-2 \sqrt{5}}-1\right)}{-2 x+\sqrt{11-2 \sqrt{5}}+1}}+\sqrt{2} \sqrt{\frac{\left(\sqrt{101}-11\right) \left(2 x+\sqrt{11-2 \sqrt{5}}-1\right)}{-2 x+\sqrt{11-2 \sqrt{5}}+1}}+\sqrt{2} \sqrt{-\frac{\left(2 \sqrt{5}-11\right) \left(\sqrt{101}-11\right) \left(2 x+\sqrt{11-2 \sqrt{5}}-1\right)}{-2 x+\sqrt{11-2 \sqrt{5}}+1}}\right) F\left(\sin ^{-1}\left(\sqrt{\frac{\left(\sqrt{11-2 \sqrt{5}}-\sqrt{11+2 \sqrt{5}}\right) \left(2 x+\sqrt{11-2 \sqrt{5}}-1\right)}{\left(\sqrt{11-2 \sqrt{5}}+\sqrt{11+2 \sqrt{5}}\right) \left(-2 x+\sqrt{11-2 \sqrt{5}}+1\right)}}\right)|\frac{1}{20} \left(11+\sqrt{101}\right)^2\right)-2 \sqrt{2} \sqrt{-\frac{\left(2 \sqrt{5}-11\right) \left(\sqrt{101}-11\right) \left(2 x+\sqrt{11-2 \sqrt{5}}-1\right)}{-2 x+\sqrt{11-2 \sqrt{5}}+1}} \Pi \left(-\frac{\sqrt{11-2 \sqrt{5}}+\sqrt{11+2 \sqrt{5}}}{\sqrt{11-2 \sqrt{5}}-\sqrt{11+2 \sqrt{5}}};\sin ^{-1}\left(\sqrt{\frac{\left(\sqrt{11-2 \sqrt{5}}-\sqrt{11+2 \sqrt{5}}\right) \left(2 x+\sqrt{11-2 \sqrt{5}}-1\right)}{\left(\sqrt{11-2 \sqrt{5}}+\sqrt{11+2 \sqrt{5}}\right) \left(-2 x+\sqrt{11-2 \sqrt{5}}+1\right)}}\right)|\frac{1}{20} \left(11+\sqrt{101}\right)^2\right)\right)}{\left(\sqrt{11+2 \sqrt{5}}-\sqrt{11-2 \sqrt{5}}\right)^{3/2} \sqrt{x^4-2 x^3-4 x^2+5 x+5}}","\log \left(-2 x^2+2 \sqrt{x^4-2 x^3-4 x^2+5 x+5}+2 x+5\right)",1,"((1 + Sqrt[11 - 2*Sqrt[5]] - 2*x)^2*Sqrt[(1 + Sqrt[11 + 2*Sqrt[5]] - 2*x)/(1 + Sqrt[11 - 2*Sqrt[5]] - 2*x)]*Sqrt[-((-1 + Sqrt[11 + 2*Sqrt[5]] + 2*x)/((Sqrt[11 - 2*Sqrt[5]] - Sqrt[11 + 2*Sqrt[5]])*(1 + Sqrt[11 - 2*Sqrt[5]] - 2*x)))]*((-(Sqrt[11 + 2*Sqrt[5]]*Sqrt[-((-1 + Sqrt[11 - 2*Sqrt[5]] + 2*x)/(1 + Sqrt[11 - 2*Sqrt[5]] - 2*x))]) + Sqrt[((-11 + 2*Sqrt[5])*(-1 + Sqrt[11 - 2*Sqrt[5]] + 2*x))/(1 + Sqrt[11 - 2*Sqrt[5]] - 2*x)] + Sqrt[2]*Sqrt[((-11 + Sqrt[101])*(-1 + Sqrt[11 - 2*Sqrt[5]] + 2*x))/(1 + Sqrt[11 - 2*Sqrt[5]] - 2*x)] + Sqrt[2]*Sqrt[-(((-11 + 2*Sqrt[5])*(-11 + Sqrt[101])*(-1 + Sqrt[11 - 2*Sqrt[5]] + 2*x))/(1 + Sqrt[11 - 2*Sqrt[5]] - 2*x))])*EllipticF[ArcSin[Sqrt[((Sqrt[11 - 2*Sqrt[5]] - Sqrt[11 + 2*Sqrt[5]])*(-1 + Sqrt[11 - 2*Sqrt[5]] + 2*x))/((Sqrt[11 - 2*Sqrt[5]] + Sqrt[11 + 2*Sqrt[5]])*(1 + Sqrt[11 - 2*Sqrt[5]] - 2*x))]], (11 + Sqrt[101])^2/20] - 2*Sqrt[2]*Sqrt[-(((-11 + 2*Sqrt[5])*(-11 + Sqrt[101])*(-1 + Sqrt[11 - 2*Sqrt[5]] + 2*x))/(1 + Sqrt[11 - 2*Sqrt[5]] - 2*x))]*EllipticPi[-((Sqrt[11 - 2*Sqrt[5]] + Sqrt[11 + 2*Sqrt[5]])/(Sqrt[11 - 2*Sqrt[5]] - Sqrt[11 + 2*Sqrt[5]])), ArcSin[Sqrt[((Sqrt[11 - 2*Sqrt[5]] - Sqrt[11 + 2*Sqrt[5]])*(-1 + Sqrt[11 - 2*Sqrt[5]] + 2*x))/((Sqrt[11 - 2*Sqrt[5]] + Sqrt[11 + 2*Sqrt[5]])*(1 + Sqrt[11 - 2*Sqrt[5]] - 2*x))]], (11 + Sqrt[101])^2/20]))/((-Sqrt[11 - 2*Sqrt[5]] + Sqrt[11 + 2*Sqrt[5]])^(3/2)*Sqrt[5 + 5*x - 4*x^2 - 2*x^3 + x^4])","C",0
437,1,33,35,0.0128869,"\int \frac{1}{x^4 \sqrt[4]{-x^3+x^4}} \, dx","Integrate[1/(x^4*(-x^3 + x^4)^(1/4)),x]","\frac{4 \left((x-1) x^3\right)^{3/4} \left(128 x^3+96 x^2+84 x+77\right)}{1155 x^6}","\frac{4 \left(128 x^3+96 x^2+84 x+77\right) \left(x^4-x^3\right)^{3/4}}{1155 x^6}",1,"(4*((-1 + x)*x^3)^(3/4)*(77 + 84*x + 96*x^2 + 128*x^3))/(1155*x^6)","A",1
438,1,505,35,0.9809985,"\int \frac{1+2 x}{\sqrt{-4-3 x-2 x^2+2 x^3+x^4}} \, dx","Integrate[(1 + 2*x)/Sqrt[-4 - 3*x - 2*x^2 + 2*x^3 + x^4],x]","\frac{6 \sqrt[6]{-1} \left(-2 x+\sqrt{17}-1\right) \left((-1)^{2/3}-x\right) \sqrt{\frac{i \left(2 x+\sqrt{17}+1\right)}{\left(\sqrt{17}-i \sqrt{3}\right) \left((-1)^{2/3}-x\right)}} \sqrt{\frac{-\sqrt{17} x+2 (-1)^{2/3} x+x-\sqrt[3]{-1} \sqrt{17}+\sqrt[3]{-1}-2}{\left(\sqrt{17}+i \sqrt{3}\right) \left((-1)^{2/3}-x\right)}} \left(F\left(\sin ^{-1}\left(\sqrt{\frac{2 i \sqrt{17} x+2 \sqrt{3} x-\sqrt{51}+i \sqrt{17}+\sqrt{3}+3 i}{2 i \sqrt{17} x-2 \sqrt{3} x+\sqrt{51}+i \sqrt{17}-\sqrt{3}+3 i}}\right)|\frac{7 i-\sqrt{51}}{7 i+\sqrt{51}}\right)-2 \Pi \left(-\frac{\sqrt{3}-i \sqrt{17}}{\sqrt{3}+i \sqrt{17}};\sin ^{-1}\left(\sqrt{\frac{2 i \sqrt{17} x+2 \sqrt{3} x-\sqrt{51}+i \sqrt{17}+\sqrt{3}+3 i}{2 i \sqrt{17} x-2 \sqrt{3} x+\sqrt{51}+i \sqrt{17}-\sqrt{3}+3 i}}\right)|\frac{7 i-\sqrt{51}}{7 i+\sqrt{51}}\right)\right)}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt{3}+i \sqrt{17}\right) \sqrt{\frac{-2 x+\sqrt{17}-1}{\left(\sqrt{3}-i \sqrt{17}\right) \left((-1)^{2/3}-x\right)}} \sqrt{x^4+2 x^3-2 x^2-3 x-4}}","\log \left(2 x^2+2 \sqrt{x^4+2 x^3-2 x^2-3 x-4}+2 x-3\right)",1,"(6*(-1)^(1/6)*(-1 + Sqrt[17] - 2*x)*((-1)^(2/3) - x)*Sqrt[(I*(1 + Sqrt[17] + 2*x))/(((-I)*Sqrt[3] + Sqrt[17])*((-1)^(2/3) - x))]*Sqrt[(-2 + (-1)^(1/3) - (-1)^(1/3)*Sqrt[17] + x + 2*(-1)^(2/3)*x - Sqrt[17]*x)/((I*Sqrt[3] + Sqrt[17])*((-1)^(2/3) - x))]*(EllipticF[ArcSin[Sqrt[(3*I + Sqrt[3] + I*Sqrt[17] - Sqrt[51] + 2*Sqrt[3]*x + (2*I)*Sqrt[17]*x)/(3*I - Sqrt[3] + I*Sqrt[17] + Sqrt[51] - 2*Sqrt[3]*x + (2*I)*Sqrt[17]*x)]], (7*I - Sqrt[51])/(7*I + Sqrt[51])] - 2*EllipticPi[-((Sqrt[3] - I*Sqrt[17])/(Sqrt[3] + I*Sqrt[17])), ArcSin[Sqrt[(3*I + Sqrt[3] + I*Sqrt[17] - Sqrt[51] + 2*Sqrt[3]*x + (2*I)*Sqrt[17]*x)/(3*I - Sqrt[3] + I*Sqrt[17] + Sqrt[51] - 2*Sqrt[3]*x + (2*I)*Sqrt[17]*x)]], (7*I - Sqrt[51])/(7*I + Sqrt[51])]))/((1 + (-1)^(1/3))*(Sqrt[3] + I*Sqrt[17])*Sqrt[(-1 + Sqrt[17] - 2*x)/((Sqrt[3] - I*Sqrt[17])*((-1)^(2/3) - x))]*Sqrt[-4 - 3*x - 2*x^2 + 2*x^3 + x^4])","C",0
439,0,0,35,0.2928288,"\int \frac{4 b+a x^3}{\sqrt[4]{b+a x^3} \left(-b-a x^3+x^4\right)} \, dx","Integrate[(4*b + a*x^3)/((b + a*x^3)^(1/4)*(-b - a*x^3 + x^4)),x]","\int \frac{4 b+a x^3}{\sqrt[4]{b+a x^3} \left(-b-a x^3+x^4\right)} \, dx","2 \tan ^{-1}\left(\frac{\sqrt[4]{a x^3+b}}{x}\right)-2 \tanh ^{-1}\left(\frac{x}{\sqrt[4]{a x^3+b}}\right)",1,"Integrate[(4*b + a*x^3)/((b + a*x^3)^(1/4)*(-b - a*x^3 + x^4)), x]","F",-1
440,1,32,35,0.0066352,"\int \frac{x^8}{\sqrt{-1+x^6}} \, dx","Integrate[x^8/Sqrt[-1 + x^6],x]","\frac{1}{6} \left(\sqrt{x^6-1} x^3+\tanh ^{-1}\left(\frac{x^3}{\sqrt{x^6-1}}\right)\right)","\frac{1}{6} \sqrt{x^6-1} x^3+\frac{1}{6} \log \left(\sqrt{x^6-1}+x^3\right)",1,"(x^3*Sqrt[-1 + x^6] + ArcTanh[x^3/Sqrt[-1 + x^6]])/6","A",1
441,1,36,35,0.015798,"\int \frac{\sqrt{-1+x^6}}{x^4} \, dx","Integrate[Sqrt[-1 + x^6]/x^4,x]","\frac{1}{3} \sqrt{x^6-1} \left(-\frac{1}{x^3}-\frac{\sin ^{-1}\left(x^3\right)}{\sqrt{1-x^6}}\right)","\frac{1}{3} \log \left(\sqrt{x^6-1}+x^3\right)-\frac{\sqrt{x^6-1}}{3 x^3}",1,"(Sqrt[-1 + x^6]*(-x^(-3) - ArcSin[x^3]/Sqrt[1 - x^6]))/3","A",1
442,1,42,35,0.014824,"\int x^2 \sqrt{-1+x^6} \, dx","Integrate[x^2*Sqrt[-1 + x^6],x]","\frac{\left(x^6-1\right) \left(\sin ^{-1}\left(x^3\right)+\sqrt{1-x^6} x^3\right)}{6 \sqrt{-\left(x^6-1\right)^2}}","\frac{1}{6} x^3 \sqrt{x^6-1}-\frac{1}{6} \log \left(\sqrt{x^6-1}+x^3\right)",1,"((-1 + x^6)*(x^3*Sqrt[1 - x^6] + ArcSin[x^3]))/(6*Sqrt[-(-1 + x^6)^2])","A",1
443,1,25,35,0.0052368,"\int \frac{x^8}{\sqrt{1+x^6}} \, dx","Integrate[x^8/Sqrt[1 + x^6],x]","\frac{1}{6} x^3 \sqrt{x^6+1}-\frac{1}{6} \sinh ^{-1}\left(x^3\right)","\frac{1}{6} x^3 \sqrt{x^6+1}-\frac{1}{6} \log \left(\sqrt{x^6+1}+x^3\right)",1,"(x^3*Sqrt[1 + x^6])/6 - ArcSinh[x^3]/6","A",1
444,1,25,35,0.0069397,"\int \frac{\sqrt{1+x^6}}{x^4} \, dx","Integrate[Sqrt[1 + x^6]/x^4,x]","\frac{1}{3} \sinh ^{-1}\left(x^3\right)-\frac{\sqrt{x^6+1}}{3 x^3}","\frac{1}{3} \log \left(\sqrt{x^6+1}+x^3\right)-\frac{\sqrt{x^6+1}}{3 x^3}",1,"-1/3*Sqrt[1 + x^6]/x^3 + ArcSinh[x^3]/3","A",1
445,1,28,35,0.0525964,"\int \frac{1+x^6}{x^6 \left(1+x^3\right) \sqrt[4]{x+x^4}} \, dx","Integrate[(1 + x^6)/(x^6*(1 + x^3)*(x + x^4)^(1/4)),x]","\frac{4 \left(53 x^6+8 x^3-3\right)}{63 x^5 \sqrt[4]{x^4+x}}","\frac{4 \left(x^4+x\right)^{3/4} \left(53 x^6+8 x^3-3\right)}{63 x^6 \left(x^3+1\right)}",1,"(4*(-3 + 8*x^3 + 53*x^6))/(63*x^5*(x + x^4)^(1/4))","A",1
446,1,40,35,0.0297502,"\int x \sqrt{x+x^6} \, dx","Integrate[x*Sqrt[x + x^6],x]","\frac{\sqrt{x^6+x} \left(x^{5/2}+\frac{\sinh ^{-1}\left(x^{5/2}\right)}{\sqrt{x^5+1}}\right)}{5 \sqrt{x}}","\frac{1}{5} \tanh ^{-1}\left(\frac{x^3}{\sqrt{x^6+x}}\right)+\frac{1}{5} \sqrt{x^6+x} x^2",1,"(Sqrt[x + x^6]*(x^(5/2) + ArcSinh[x^(5/2)]/Sqrt[1 + x^5]))/(5*Sqrt[x])","A",1
447,0,0,35,0.2806471,"\int \frac{-2 b c+a c x^6}{\sqrt[4]{b+a x^6} \left(b-c^4 x^4+a x^6\right)} \, dx","Integrate[(-2*b*c + a*c*x^6)/((b + a*x^6)^(1/4)*(b - c^4*x^4 + a*x^6)),x]","\int \frac{-2 b c+a c x^6}{\sqrt[4]{b+a x^6} \left(b-c^4 x^4+a x^6\right)} \, dx","-\tan ^{-1}\left(\frac{c x}{\sqrt[4]{a x^6+b}}\right)-\tanh ^{-1}\left(\frac{c x}{\sqrt[4]{a x^6+b}}\right)",1,"Integrate[(-2*b*c + a*c*x^6)/((b + a*x^6)^(1/4)*(b - c^4*x^4 + a*x^6)), x]","F",-1
448,1,35,35,0.0131675,"\int \frac{1}{\sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[1/Sqrt[x + Sqrt[1 + x^2]],x]","\sqrt{\sqrt{x^2+1}+x}-\frac{1}{3 \left(\sqrt{x^2+1}+x\right)^{3/2}}","\sqrt{\sqrt{x^2+1}+x}-\frac{1}{3 \left(\sqrt{x^2+1}+x\right)^{3/2}}",1,"-1/3*1/(x + Sqrt[1 + x^2])^(3/2) + Sqrt[x + Sqrt[1 + x^2]]","A",1
449,1,36,36,0.0066662,"\int \frac{\sqrt[4]{1+x^2}}{x} \, dx","Integrate[(1 + x^2)^(1/4)/x,x]","2 \sqrt[4]{x^2+1}-\tan ^{-1}\left(\sqrt[4]{x^2+1}\right)-\tanh ^{-1}\left(\sqrt[4]{x^2+1}\right)","2 \sqrt[4]{x^2+1}-\tan ^{-1}\left(\sqrt[4]{x^2+1}\right)-\tanh ^{-1}\left(\sqrt[4]{x^2+1}\right)",1,"2*(1 + x^2)^(1/4) - ArcTan[(1 + x^2)^(1/4)] - ArcTanh[(1 + x^2)^(1/4)]","A",1
450,1,28,36,0.0048952,"\int \frac{\sqrt{-1+x^3}}{x^7} \, dx","Integrate[Sqrt[-1 + x^3]/x^7,x]","\frac{2}{9} \left(x^3-1\right)^{3/2} \, _2F_1\left(\frac{3}{2},3;\frac{5}{2};1-x^3\right)","\frac{1}{12} \tan ^{-1}\left(\sqrt{x^3-1}\right)+\frac{\sqrt{x^3-1} \left(x^3-2\right)}{12 x^6}",1,"(2*(-1 + x^3)^(3/2)*Hypergeometric2F1[3/2, 3, 5/2, 1 - x^3])/9","C",1
451,1,214,36,1.6415037,"\int \frac{-b+a x^2}{\left(b+c x+a x^2\right) \sqrt{b x+a x^3}} \, dx","Integrate[(-b + a*x^2)/((b + c*x + a*x^2)*Sqrt[b*x + a*x^3]),x]","-\frac{2 i x^{3/2} \sqrt{\frac{b}{a x^2}+1} \left(-\Pi \left(\frac{2 i \sqrt{a} \sqrt{b}}{\sqrt{c^2-4 a b}-c};\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}}{\sqrt{x}}\right)\right|-1\right)-\Pi \left(-\frac{2 i \sqrt{a} \sqrt{b}}{c+\sqrt{c^2-4 a b}};\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}}{\sqrt{x}}\right)\right|-1\right)+F\left(\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}}{\sqrt{x}}\right)\right|-1\right)\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}} \sqrt{x \left(a x^2+b\right)}}","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a x^3+b x}}{a x^2+b}\right)}{\sqrt{c}}",1,"((-2*I)*Sqrt[1 + b/(a*x^2)]*x^(3/2)*(EllipticF[I*ArcSinh[Sqrt[(I*Sqrt[b])/Sqrt[a]]/Sqrt[x]], -1] - EllipticPi[((2*I)*Sqrt[a]*Sqrt[b])/(-c + Sqrt[-4*a*b + c^2]), I*ArcSinh[Sqrt[(I*Sqrt[b])/Sqrt[a]]/Sqrt[x]], -1] - EllipticPi[((-2*I)*Sqrt[a]*Sqrt[b])/(c + Sqrt[-4*a*b + c^2]), I*ArcSinh[Sqrt[(I*Sqrt[b])/Sqrt[a]]/Sqrt[x]], -1]))/(Sqrt[(I*Sqrt[b])/Sqrt[a]]*Sqrt[x*(b + a*x^2)])","C",1
452,1,640,36,0.8265217,"\int \frac{-1+x}{\sqrt{-2-x+6 x^2-4 x^3+x^4}} \, dx","Integrate[(-1 + x)/Sqrt[-2 - x + 6*x^2 - 4*x^3 + x^4],x]","\frac{2 \sqrt[3]{3} (x-1) \sqrt{\frac{-x+\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+3 \text{$\#$1}+2\&,2\right]}{\left(x+\sqrt[3]{3}-1\right) \left(-1+\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+3 \text{$\#$1}+2\&,2\right]\right)}} \left(x-\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+3 \text{$\#$1}+2\&,3\right]\right) \left(F\left(\sin ^{-1}\left(\sqrt{\frac{(x-1) \left(-1+\sqrt[3]{3}+\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+3 \text{$\#$1}+2\&,3\right]\right)}{\left(x+\sqrt[3]{3}-1\right) \left(-1+\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+3 \text{$\#$1}+2\&,3\right]\right)}}\right)|\frac{\left(-1+\sqrt[3]{3}+\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+3 \text{$\#$1}+2\&,2\right]\right) \left(-1+\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+3 \text{$\#$1}+2\&,3\right]\right)}{\left(-1+\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+3 \text{$\#$1}+2\&,2\right]\right) \left(-1+\sqrt[3]{3}+\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+3 \text{$\#$1}+2\&,3\right]\right)}\right)-\Pi \left(\frac{-1+\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+3 \text{$\#$1}+2\&,3\right]}{-1+\sqrt[3]{3}+\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+3 \text{$\#$1}+2\&,3\right]};\sin ^{-1}\left(\sqrt{\frac{(x-1) \left(-1+\sqrt[3]{3}+\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+3 \text{$\#$1}+2\&,3\right]\right)}{\left(x+\sqrt[3]{3}-1\right) \left(-1+\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+3 \text{$\#$1}+2\&,3\right]\right)}}\right)|\frac{\left(-1+\sqrt[3]{3}+\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+3 \text{$\#$1}+2\&,2\right]\right) \left(-1+\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+3 \text{$\#$1}+2\&,3\right]\right)}{\left(-1+\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+3 \text{$\#$1}+2\&,2\right]\right) \left(-1+\sqrt[3]{3}+\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+3 \text{$\#$1}+2\&,3\right]\right)}\right)\right)}{\sqrt{x^4-4 x^3+6 x^2-x-2} \left(-1+\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+3 \text{$\#$1}+2\&,3\right]\right) \sqrt{-\frac{(x-1) \left(\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+3 \text{$\#$1}+2\&,3\right]-1+\sqrt[3]{3}\right) \left(x-\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+3 \text{$\#$1}+2\&,3\right]\right)}{\left(x+\sqrt[3]{3}-1\right)^2 \left(-1+\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+3 \text{$\#$1}+2\&,3\right]\right)^2}}}","\frac{2}{3} \tanh ^{-1}\left(\frac{x^2-2 x+1}{\sqrt{x^4-4 x^3+6 x^2-x-2}}\right)",1,"(2*3^(1/3)*(-1 + x)*(EllipticF[ArcSin[Sqrt[((-1 + x)*(-1 + 3^(1/3) + Root[2 + 3*#1 - 3*#1^2 + #1^3 & , 3, 0]))/((-1 + 3^(1/3) + x)*(-1 + Root[2 + 3*#1 - 3*#1^2 + #1^3 & , 3, 0]))]], ((-1 + 3^(1/3) + Root[2 + 3*#1 - 3*#1^2 + #1^3 & , 2, 0])*(-1 + Root[2 + 3*#1 - 3*#1^2 + #1^3 & , 3, 0]))/((-1 + Root[2 + 3*#1 - 3*#1^2 + #1^3 & , 2, 0])*(-1 + 3^(1/3) + Root[2 + 3*#1 - 3*#1^2 + #1^3 & , 3, 0]))] - EllipticPi[(-1 + Root[2 + 3*#1 - 3*#1^2 + #1^3 & , 3, 0])/(-1 + 3^(1/3) + Root[2 + 3*#1 - 3*#1^2 + #1^3 & , 3, 0]), ArcSin[Sqrt[((-1 + x)*(-1 + 3^(1/3) + Root[2 + 3*#1 - 3*#1^2 + #1^3 & , 3, 0]))/((-1 + 3^(1/3) + x)*(-1 + Root[2 + 3*#1 - 3*#1^2 + #1^3 & , 3, 0]))]], ((-1 + 3^(1/3) + Root[2 + 3*#1 - 3*#1^2 + #1^3 & , 2, 0])*(-1 + Root[2 + 3*#1 - 3*#1^2 + #1^3 & , 3, 0]))/((-1 + Root[2 + 3*#1 - 3*#1^2 + #1^3 & , 2, 0])*(-1 + 3^(1/3) + Root[2 + 3*#1 - 3*#1^2 + #1^3 & , 3, 0]))])*Sqrt[(-x + Root[2 + 3*#1 - 3*#1^2 + #1^3 & , 2, 0])/((-1 + 3^(1/3) + x)*(-1 + Root[2 + 3*#1 - 3*#1^2 + #1^3 & , 2, 0]))]*(x - Root[2 + 3*#1 - 3*#1^2 + #1^3 & , 3, 0]))/(Sqrt[-2 - x + 6*x^2 - 4*x^3 + x^4]*(-1 + Root[2 + 3*#1 - 3*#1^2 + #1^3 & , 3, 0])*Sqrt[-(((-1 + x)*(x - Root[2 + 3*#1 - 3*#1^2 + #1^3 & , 3, 0])*(-1 + 3^(1/3) + Root[2 + 3*#1 - 3*#1^2 + #1^3 & , 3, 0]))/((-1 + 3^(1/3) + x)^2*(-1 + Root[2 + 3*#1 - 3*#1^2 + #1^3 & , 3, 0])^2))])","C",0
453,1,28,36,0.0049625,"\int \frac{\sqrt{-1+x^6}}{x^{13}} \, dx","Integrate[Sqrt[-1 + x^6]/x^13,x]","\frac{1}{9} \left(x^6-1\right)^{3/2} \, _2F_1\left(\frac{3}{2},3;\frac{5}{2};1-x^6\right)","\frac{1}{24} \tan ^{-1}\left(\sqrt{x^6-1}\right)+\frac{\sqrt{x^6-1} \left(x^6-2\right)}{24 x^{12}}",1,"((-1 + x^6)^(3/2)*Hypergeometric2F1[3/2, 3, 5/2, 1 - x^6])/9","C",1
454,0,0,36,0.2436381,"\int \frac{-1-2 x^2+2 x^4}{\left(2-3 x^2+x^4\right) \sqrt{1+x^6}} \, dx","Integrate[(-1 - 2*x^2 + 2*x^4)/((2 - 3*x^2 + x^4)*Sqrt[1 + x^6]),x]","\int \frac{-1-2 x^2+2 x^4}{\left(2-3 x^2+x^4\right) \sqrt{1+x^6}} \, dx","-\frac{\tanh ^{-1}\left(\frac{x \sqrt{x^6+1}}{\sqrt{2} \left(x^4-x^2+1\right)}\right)}{\sqrt{2}}",1,"Integrate[(-1 - 2*x^2 + 2*x^4)/((2 - 3*x^2 + x^4)*Sqrt[1 + x^6]), x]","F",-1
455,1,114,37,0.8534196,"\int \frac{-1+k x}{(1+k x) \sqrt{(1-x) x \left(1-k^2 x\right)}} \, dx","Integrate[(-1 + k*x)/((1 + k*x)*Sqrt[(1 - x)*x*(1 - k^2*x)]),x]","\frac{2 i \sqrt{\frac{1}{x-1}+1} (x-1)^{3/2} \sqrt{\frac{1-\frac{1}{k^2}}{x-1}+1} \left((k-1) F\left(i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)+2 \Pi \left(1+\frac{1}{k};i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)\right)}{(k+1) \sqrt{(x-1) x \left(k^2 x-1\right)}}","-\frac{2 \tan ^{-1}\left(\frac{(k+1) x}{\sqrt{k^2 x^3+\left(-k^2-1\right) x^2+x}}\right)}{k+1}",1,"((2*I)*Sqrt[1 + (-1 + x)^(-1)]*Sqrt[1 + (1 - k^(-2))/(-1 + x)]*(-1 + x)^(3/2)*((-1 + k)*EllipticF[I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)] + 2*EllipticPi[1 + k^(-1), I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)]))/((1 + k)*Sqrt[(-1 + x)*x*(-1 + k^2*x)])","C",1
456,1,116,37,0.7528964,"\int \frac{1+k x}{(-1+k x) \sqrt{(1-x) x \left(1-k^2 x\right)}} \, dx","Integrate[(1 + k*x)/((-1 + k*x)*Sqrt[(1 - x)*x*(1 - k^2*x)]),x]","\frac{2 i \sqrt{\frac{1}{x-1}+1} (x-1)^{3/2} \sqrt{\frac{1-\frac{1}{k^2}}{x-1}+1} \left((k+1) F\left(i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)-2 \Pi \left(\frac{k-1}{k};i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)\right)}{(k-1) \sqrt{(x-1) x \left(k^2 x-1\right)}}","-\frac{2 \tan ^{-1}\left(\frac{(k-1) x}{\sqrt{k^2 x^3+\left(-k^2-1\right) x^2+x}}\right)}{k-1}",1,"((2*I)*Sqrt[1 + (-1 + x)^(-1)]*Sqrt[1 + (1 - k^(-2))/(-1 + x)]*(-1 + x)^(3/2)*((1 + k)*EllipticF[I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)] - 2*EllipticPi[(-1 + k)/k, I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)]))/((-1 + k)*Sqrt[(-1 + x)*x*(-1 + k^2*x)])","C",1
457,1,72,37,0.1184881,"\int \frac{\left(-1+x^2\right) \sqrt{1+x^4}}{x^2 \left(1+x^2\right)} \, dx","Integrate[((-1 + x^2)*Sqrt[1 + x^4])/(x^2*(1 + x^2)),x]","\frac{1}{\sqrt{x^4+1} x}+\frac{x^3}{\sqrt{x^4+1}}+2 \sqrt[4]{-1} F\left(\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)-4 \sqrt[4]{-1} \Pi \left(-i;\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)","\frac{\sqrt{x^4+1}}{x}+\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)",1,"1/(x*Sqrt[1 + x^4]) + x^3/Sqrt[1 + x^4] + 2*(-1)^(1/4)*EllipticF[I*ArcSinh[(-1)^(1/4)*x], -1] - 4*(-1)^(1/4)*EllipticPi[-I, I*ArcSinh[(-1)^(1/4)*x], -1]","C",1
458,1,30,37,0.0141495,"\int \frac{1+x^3}{x^6 \left(-1+x^3\right) \sqrt[4]{-x+x^4}} \, dx","Integrate[(1 + x^3)/(x^6*(-1 + x^3)*(-x + x^4)^(1/4)),x]","\frac{-80 x^6+20 x^3+4}{21 x^5 \sqrt[4]{x \left(x^3-1\right)}}","-\frac{4 \left(x^4-x\right)^{3/4} \left(20 x^6-5 x^3-1\right)}{21 x^6 \left(x^3-1\right)}",1,"(4 + 20*x^3 - 80*x^6)/(21*x^5*(x*(-1 + x^3))^(1/4))","A",1
459,1,44,37,0.0212402,"\int \sqrt{-x+x^4} \, dx","Integrate[Sqrt[-x + x^4],x]","\frac{\sqrt{x \left(x^3-1\right)} \left(x^{3/2}+\frac{\sin ^{-1}\left(x^{3/2}\right)}{\sqrt{1-x^3}}\right)}{3 \sqrt{x}}","\frac{1}{3} x \sqrt{x^4-x}-\frac{1}{3} \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4-x}}\right)",1,"(Sqrt[x*(-1 + x^3)]*(x^(3/2) + ArcSin[x^(3/2)]/Sqrt[1 - x^3]))/(3*Sqrt[x])","A",1
460,1,37,37,0.0179455,"\int \frac{1}{x^8 \sqrt[4]{-x^2+x^4}} \, dx","Integrate[1/(x^8*(-x^2 + x^4)^(1/4)),x]","\frac{2 \left(x^2 \left(x^2-1\right)\right)^{3/4} \left(128 x^6+96 x^4+84 x^2+77\right)}{1155 x^9}","\frac{2 \left(x^4-x^2\right)^{3/4} \left(128 x^6+96 x^4+84 x^2+77\right)}{1155 x^9}",1,"(2*(x^2*(-1 + x^2))^(3/4)*(77 + 84*x^2 + 96*x^4 + 128*x^6))/(1155*x^9)","A",1
461,1,716,37,1.093195,"\int \frac{-1+x}{\sqrt{-1+4 x+2 x^2-4 x^3+x^4}} \, dx","Integrate[(-1 + x)/Sqrt[-1 + 4*x + 2*x^2 - 4*x^3 + x^4],x]","-\frac{2 \left(-x+\sqrt{2-\sqrt{2}}+1\right)^2 \sqrt{\frac{-x+\sqrt{2+\sqrt{2}}+1}{-x+\sqrt{2-\sqrt{2}}+1}} \sqrt{-\frac{x+\sqrt{2+\sqrt{2}}-1}{\left(\sqrt{2-\sqrt{2}}-\sqrt{2+\sqrt{2}}\right) \left(-x+\sqrt{2-\sqrt{2}}+1\right)}} \left(\left(-\sqrt{2+\sqrt{2}} \sqrt{-\frac{x+\sqrt{2-\sqrt{2}}-1}{-x+\sqrt{2-\sqrt{2}}+1}}+\sqrt{2} \sqrt{\frac{\left(\sqrt{2}-2\right) \left(x+\sqrt{2-\sqrt{2}}-1\right)}{-x+\sqrt{2-\sqrt{2}}+1}}+\sqrt{\frac{\left(\sqrt{2}-2\right) \left(x+\sqrt{2-\sqrt{2}}-1\right)}{-x+\sqrt{2-\sqrt{2}}+1}}+2 \sqrt{\frac{\left(2 \sqrt{2}-3\right) \left(x+\sqrt{2-\sqrt{2}}-1\right)}{-x+\sqrt{2-\sqrt{2}}+1}}\right) F\left(\sin ^{-1}\left(\sqrt{\frac{\left(\sqrt{2-\sqrt{2}}-\sqrt{2+\sqrt{2}}\right) \left(x+\sqrt{2-\sqrt{2}}-1\right)}{\left(\sqrt{2-\sqrt{2}}+\sqrt{2+\sqrt{2}}\right) \left(-x+\sqrt{2-\sqrt{2}}+1\right)}}\right)|3+2 \sqrt{2}\right)-4 \sqrt{\frac{\left(2 \sqrt{2}-3\right) \left(x+\sqrt{2-\sqrt{2}}-1\right)}{-x+\sqrt{2-\sqrt{2}}+1}} \Pi \left(\frac{\sqrt{2-\sqrt{2}}+\sqrt{2+\sqrt{2}}}{-\sqrt{2-\sqrt{2}}+\sqrt{2+\sqrt{2}}};\sin ^{-1}\left(\sqrt{\frac{\left(\sqrt{2-\sqrt{2}}-\sqrt{2+\sqrt{2}}\right) \left(x+\sqrt{2-\sqrt{2}}-1\right)}{\left(\sqrt{2-\sqrt{2}}+\sqrt{2+\sqrt{2}}\right) \left(-x+\sqrt{2-\sqrt{2}}+1\right)}}\right)|3+2 \sqrt{2}\right)\right)}{\left(\sqrt{2+\sqrt{2}}-\sqrt{2-\sqrt{2}}\right)^{3/2} \sqrt{x^4-4 x^3+2 x^2+4 x-1}}","-\frac{1}{2} \log \left(-x^2+\sqrt{x^4-4 x^3+2 x^2+4 x-1}+2 x+1\right)",1,"(-2*(1 + Sqrt[2 - Sqrt[2]] - x)^2*Sqrt[(1 + Sqrt[2 + Sqrt[2]] - x)/(1 + Sqrt[2 - Sqrt[2]] - x)]*Sqrt[-((-1 + Sqrt[2 + Sqrt[2]] + x)/((Sqrt[2 - Sqrt[2]] - Sqrt[2 + Sqrt[2]])*(1 + Sqrt[2 - Sqrt[2]] - x)))]*((-(Sqrt[2 + Sqrt[2]]*Sqrt[-((-1 + Sqrt[2 - Sqrt[2]] + x)/(1 + Sqrt[2 - Sqrt[2]] - x))]) + Sqrt[((-2 + Sqrt[2])*(-1 + Sqrt[2 - Sqrt[2]] + x))/(1 + Sqrt[2 - Sqrt[2]] - x)] + Sqrt[2]*Sqrt[((-2 + Sqrt[2])*(-1 + Sqrt[2 - Sqrt[2]] + x))/(1 + Sqrt[2 - Sqrt[2]] - x)] + 2*Sqrt[((-3 + 2*Sqrt[2])*(-1 + Sqrt[2 - Sqrt[2]] + x))/(1 + Sqrt[2 - Sqrt[2]] - x)])*EllipticF[ArcSin[Sqrt[((Sqrt[2 - Sqrt[2]] - Sqrt[2 + Sqrt[2]])*(-1 + Sqrt[2 - Sqrt[2]] + x))/((Sqrt[2 - Sqrt[2]] + Sqrt[2 + Sqrt[2]])*(1 + Sqrt[2 - Sqrt[2]] - x))]], 3 + 2*Sqrt[2]] - 4*Sqrt[((-3 + 2*Sqrt[2])*(-1 + Sqrt[2 - Sqrt[2]] + x))/(1 + Sqrt[2 - Sqrt[2]] - x)]*EllipticPi[(Sqrt[2 - Sqrt[2]] + Sqrt[2 + Sqrt[2]])/(-Sqrt[2 - Sqrt[2]] + Sqrt[2 + Sqrt[2]]), ArcSin[Sqrt[((Sqrt[2 - Sqrt[2]] - Sqrt[2 + Sqrt[2]])*(-1 + Sqrt[2 - Sqrt[2]] + x))/((Sqrt[2 - Sqrt[2]] + Sqrt[2 + Sqrt[2]])*(1 + Sqrt[2 - Sqrt[2]] - x))]], 3 + 2*Sqrt[2]]))/((-Sqrt[2 - Sqrt[2]] + Sqrt[2 + Sqrt[2]])^(3/2)*Sqrt[-1 + 4*x + 2*x^2 - 4*x^3 + x^4])","C",0
462,1,33,37,0.0105539,"\int \frac{\sqrt[4]{-x^3+x^4}}{(-1+x) x} \, dx","Integrate[(-x^3 + x^4)^(1/4)/((-1 + x)*x),x]","\frac{4 \sqrt[4]{(x-1) x^3} \, _2F_1\left(\frac{1}{4},\frac{1}{4};\frac{5}{4};1-x\right)}{x^{3/4}}","2 \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^3}}\right)-2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^3}}\right)",1,"(4*((-1 + x)*x^3)^(1/4)*Hypergeometric2F1[1/4, 1/4, 5/4, 1 - x])/x^(3/4)","C",1
463,1,31,37,0.0250227,"\int \frac{-2+x^3}{x \sqrt{-1+x^6}} \, dx","Integrate[(-2 + x^3)/(x*Sqrt[-1 + x^6]),x]","\frac{1}{3} \left(\tanh ^{-1}\left(\frac{x^3}{\sqrt{x^6-1}}\right)-2 \tan ^{-1}\left(\sqrt{x^6-1}\right)\right)","\frac{1}{3} \log \left(\sqrt{x^6-1}+x^3\right)-\frac{4}{3} \tan ^{-1}\left(\sqrt{x^6-1}+x^3\right)",1,"(-2*ArcTan[Sqrt[-1 + x^6]] + ArcTanh[x^3/Sqrt[-1 + x^6]])/3","A",1
464,1,29,37,0.0144116,"\int \frac{1+x^3}{x \sqrt{-1+x^6}} \, dx","Integrate[(1 + x^3)/(x*Sqrt[-1 + x^6]),x]","\frac{1}{3} \left(\tan ^{-1}\left(\sqrt{x^6-1}\right)+\tanh ^{-1}\left(\frac{x^3}{\sqrt{x^6-1}}\right)\right)","\frac{1}{3} \log \left(\sqrt{x^6-1}+x^3\right)+\frac{2}{3} \tan ^{-1}\left(\sqrt{x^6-1}+x^3\right)",1,"(ArcTan[Sqrt[-1 + x^6]] + ArcTanh[x^3/Sqrt[-1 + x^6]])/3","A",1
465,1,33,37,0.0167596,"\int \frac{-1+2 x^3}{x \sqrt{-1+x^6}} \, dx","Integrate[(-1 + 2*x^3)/(x*Sqrt[-1 + x^6]),x]","\frac{2}{3} \tanh ^{-1}\left(\frac{x^3}{\sqrt{x^6-1}}\right)-\frac{1}{3} \tan ^{-1}\left(\sqrt{x^6-1}\right)","\frac{2}{3} \log \left(\sqrt{x^6-1}+x^3\right)-\frac{2}{3} \tan ^{-1}\left(\sqrt{x^6-1}+x^3\right)",1,"-1/3*ArcTan[Sqrt[-1 + x^6]] + (2*ArcTanh[x^3/Sqrt[-1 + x^6]])/3","A",1
466,1,31,37,0.0153031,"\int \frac{1+2 x^3}{x \sqrt{-1+x^6}} \, dx","Integrate[(1 + 2*x^3)/(x*Sqrt[-1 + x^6]),x]","\frac{1}{3} \left(\tan ^{-1}\left(\sqrt{x^6-1}\right)+2 \tanh ^{-1}\left(\frac{x^3}{\sqrt{x^6-1}}\right)\right)","\frac{2}{3} \log \left(\sqrt{x^6-1}+x^3\right)+\frac{2}{3} \tan ^{-1}\left(\sqrt{x^6-1}+x^3\right)",1,"(ArcTan[Sqrt[-1 + x^6]] + 2*ArcTanh[x^3/Sqrt[-1 + x^6]])/3","A",1
467,1,31,37,0.0208773,"\int \frac{1+4 x^3}{x \sqrt{-1+x^6}} \, dx","Integrate[(1 + 4*x^3)/(x*Sqrt[-1 + x^6]),x]","\frac{1}{3} \left(\tan ^{-1}\left(\sqrt{x^6-1}\right)+4 \tanh ^{-1}\left(\frac{x^3}{\sqrt{x^6-1}}\right)\right)","\frac{4}{3} \log \left(\sqrt{x^6-1}+x^3\right)+\frac{2}{3} \tan ^{-1}\left(\sqrt{x^6-1}+x^3\right)",1,"(ArcTan[Sqrt[-1 + x^6]] + 4*ArcTanh[x^3/Sqrt[-1 + x^6]])/3","A",1
468,1,30,37,0.0539641,"\int \frac{1+x^6}{x^6 \left(-1+x^3\right) \sqrt[4]{-x+x^4}} \, dx","Integrate[(1 + x^6)/(x^6*(-1 + x^3)*(-x + x^4)^(1/4)),x]","\frac{4 \left(-53 x^6+8 x^3+3\right)}{63 x^5 \sqrt[4]{x \left(x^3-1\right)}}","-\frac{4 \left(x^4-x\right)^{3/4} \left(53 x^6-8 x^3-3\right)}{63 x^6 \left(x^3-1\right)}",1,"(4*(3 + 8*x^3 - 53*x^6))/(63*x^5*(x*(-1 + x^3))^(1/4))","A",1
469,0,0,37,0.236172,"\int \frac{x \left(8 b+5 a x^3\right)}{\sqrt[4]{b+a x^3} \left(-b-a x^3+x^8\right)} \, dx","Integrate[(x*(8*b + 5*a*x^3))/((b + a*x^3)^(1/4)*(-b - a*x^3 + x^8)),x]","\int \frac{x \left(8 b+5 a x^3\right)}{\sqrt[4]{b+a x^3} \left(-b-a x^3+x^8\right)} \, dx","2 \tan ^{-1}\left(\frac{\sqrt[4]{a x^3+b}}{x^2}\right)-2 \tanh ^{-1}\left(\frac{x^2}{\sqrt[4]{a x^3+b}}\right)",1,"Integrate[(x*(8*b + 5*a*x^3))/((b + a*x^3)^(1/4)*(-b - a*x^3 + x^8)), x]","F",-1
470,1,35,37,0.0108281,"\int \sqrt{x+\sqrt{1+x^2}} \, dx","Integrate[Sqrt[x + Sqrt[1 + x^2]],x]","\frac{2 \left(x^2+\sqrt{x^2+1} x-1\right)}{3 \sqrt{\sqrt{x^2+1}+x}}","\frac{1}{3} \left(\sqrt{x^2+1}+x\right)^{3/2}-\frac{1}{\sqrt{\sqrt{x^2+1}+x}}",1,"(2*(-1 + x^2 + x*Sqrt[1 + x^2]))/(3*Sqrt[x + Sqrt[1 + x^2]])","A",1
471,1,195,38,4.5638236,"\int \frac{a b-x^2}{\sqrt{x (-a+x) (-b+x)} \left(a b-(a+b+d) x+x^2\right)} \, dx","Integrate[(a*b - x^2)/(Sqrt[x*(-a + x)*(-b + x)]*(a*b - (a + b + d)*x + x^2)),x]","\frac{2 i x^{3/2} \sqrt{1-\frac{a}{x}} \sqrt{1-\frac{b}{x}} \left(-\Pi \left(\frac{2 b}{a+b+d-\sqrt{a^2-2 (b-d) a+(b+d)^2}};i \sinh ^{-1}\left(\frac{\sqrt{-a}}{\sqrt{x}}\right)|\frac{b}{a}\right)-\Pi \left(\frac{2 b}{a+b+d+\sqrt{a^2-2 (b-d) a+(b+d)^2}};i \sinh ^{-1}\left(\frac{\sqrt{-a}}{\sqrt{x}}\right)|\frac{b}{a}\right)+F\left(i \sinh ^{-1}\left(\frac{\sqrt{-a}}{\sqrt{x}}\right)|\frac{b}{a}\right)\right)}{\sqrt{-a} \sqrt{x (x-a) (x-b)}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{x^2 (-a-b)+a b x+x^3}}\right)}{\sqrt{d}}",1,"((2*I)*Sqrt[1 - a/x]*Sqrt[1 - b/x]*x^(3/2)*(EllipticF[I*ArcSinh[Sqrt[-a]/Sqrt[x]], b/a] - EllipticPi[(2*b)/(a + b + d - Sqrt[a^2 - 2*a*(b - d) + (b + d)^2]), I*ArcSinh[Sqrt[-a]/Sqrt[x]], b/a] - EllipticPi[(2*b)/(a + b + d + Sqrt[a^2 - 2*a*(b - d) + (b + d)^2]), I*ArcSinh[Sqrt[-a]/Sqrt[x]], b/a]))/(Sqrt[-a]*Sqrt[x*(-a + x)*(-b + x)])","C",1
472,1,210,38,5.7706571,"\int \frac{a b-x^2}{\sqrt{x (-a+x) (-b+x)} \left(a b d-(1+a d+b d) x+d x^2\right)} \, dx","Integrate[(a*b - x^2)/(Sqrt[x*(-a + x)*(-b + x)]*(a*b*d - (1 + a*d + b*d)*x + d*x^2)),x]","\frac{2 i x^{3/2} \sqrt{1-\frac{a}{x}} \sqrt{1-\frac{b}{x}} \left(-\Pi \left(\frac{2 b d}{a d+b d-\sqrt{(a d+b d+1)^2-4 a b d^2}+1};i \sinh ^{-1}\left(\frac{\sqrt{-a}}{\sqrt{x}}\right)|\frac{b}{a}\right)-\Pi \left(\frac{2 b d}{a d+b d+\sqrt{(a d+b d+1)^2-4 a b d^2}+1};i \sinh ^{-1}\left(\frac{\sqrt{-a}}{\sqrt{x}}\right)|\frac{b}{a}\right)+F\left(i \sinh ^{-1}\left(\frac{\sqrt{-a}}{\sqrt{x}}\right)|\frac{b}{a}\right)\right)}{\sqrt{-a} d \sqrt{x (x-a) (x-b)}}","\frac{2 \tanh ^{-1}\left(\frac{x}{\sqrt{d} \sqrt{x^2 (-a-b)+a b x+x^3}}\right)}{\sqrt{d}}",1,"((2*I)*Sqrt[1 - a/x]*Sqrt[1 - b/x]*x^(3/2)*(EllipticF[I*ArcSinh[Sqrt[-a]/Sqrt[x]], b/a] - EllipticPi[(2*b*d)/(1 + a*d + b*d - Sqrt[-4*a*b*d^2 + (1 + a*d + b*d)^2]), I*ArcSinh[Sqrt[-a]/Sqrt[x]], b/a] - EllipticPi[(2*b*d)/(1 + a*d + b*d + Sqrt[-4*a*b*d^2 + (1 + a*d + b*d)^2]), I*ArcSinh[Sqrt[-a]/Sqrt[x]], b/a]))/(Sqrt[-a]*d*Sqrt[x*(-a + x)*(-b + x)])","C",1
473,1,63,38,0.2649867,"\int \frac{-1+k x^2}{\left(1+k x^2\right) \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}} \, dx","Integrate[(-1 + k*x^2)/((1 + k*x^2)*Sqrt[(1 - x^2)*(1 - k^2*x^2)]),x]","\frac{\sqrt{1-x^2} \sqrt{1-k^2 x^2} \left(F\left(\sin ^{-1}(x)|k^2\right)-2 \Pi \left(-k;\sin ^{-1}(x)|k^2\right)\right)}{\sqrt{\left(x^2-1\right) \left(k^2 x^2-1\right)}}","\frac{\tan ^{-1}\left(\frac{(k+1) x}{\sqrt{k^2 x^4+\left(-k^2-1\right) x^2+1}}\right)}{-k-1}",1,"(Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*(EllipticF[ArcSin[x], k^2] - 2*EllipticPi[-k, ArcSin[x], k^2]))/Sqrt[(-1 + x^2)*(-1 + k^2*x^2)]","C",1
474,1,61,38,0.2232608,"\int \frac{1+k x^2}{\left(-1+k x^2\right) \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}} \, dx","Integrate[(1 + k*x^2)/((-1 + k*x^2)*Sqrt[(1 - x^2)*(1 - k^2*x^2)]),x]","\frac{\sqrt{1-x^2} \sqrt{1-k^2 x^2} \left(F\left(\sin ^{-1}(x)|k^2\right)-2 \Pi \left(k;\sin ^{-1}(x)|k^2\right)\right)}{\sqrt{\left(x^2-1\right) \left(k^2 x^2-1\right)}}","\frac{\tan ^{-1}\left(\frac{(k-1) x}{\sqrt{k^2 x^4+\left(-k^2-1\right) x^2+1}}\right)}{1-k}",1,"(Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*(EllipticF[ArcSin[x], k^2] - 2*EllipticPi[k, ArcSin[x], k^2]))/Sqrt[(-1 + x^2)*(-1 + k^2*x^2)]","C",1
475,1,21,38,0.2144534,"\int \frac{1-2 k^2 x+k^2 x^2}{x \sqrt{(1-x) x \left(1-k^2 x\right)} \left(-1+k^2 x\right)} \, dx","Integrate[(1 - 2*k^2*x + k^2*x^2)/(x*Sqrt[(1 - x)*x*(1 - k^2*x)]*(-1 + k^2*x)),x]","-\frac{2 (x-1)}{\sqrt{(x-1) x \left(k^2 x-1\right)}}","-\frac{2 \sqrt{k^2 x^3+\left(-k^2-1\right) x^2+x}}{x \left(k^2 x-1\right)}",1,"(-2*(-1 + x))/Sqrt[(-1 + x)*x*(-1 + k^2*x)]","A",1
476,1,28,38,0.0051019,"\int \frac{1}{x^7 \sqrt{-1+x^3}} \, dx","Integrate[1/(x^7*Sqrt[-1 + x^3]),x]","\frac{2}{3} \sqrt{x^3-1} \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};1-x^3\right)","\frac{1}{4} \tan ^{-1}\left(\sqrt{x^3-1}\right)+\frac{\sqrt{x^3-1} \left(3 x^3+2\right)}{12 x^6}",1,"(2*Sqrt[-1 + x^3]*Hypergeometric2F1[1/2, 3, 3/2, 1 - x^3])/3","C",1
477,1,26,38,0.0053113,"\int \frac{1}{x^7 \sqrt{1+x^3}} \, dx","Integrate[1/(x^7*Sqrt[1 + x^3]),x]","-\frac{2}{3} \sqrt{x^3+1} \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};x^3+1\right)","\frac{\sqrt{x^3+1} \left(3 x^3-2\right)}{12 x^6}-\frac{1}{4} \tanh ^{-1}\left(\sqrt{x^3+1}\right)",1,"(-2*Sqrt[1 + x^3]*Hypergeometric2F1[1/2, 3, 3/2, 1 + x^3])/3","C",1
478,1,26,38,0.0057988,"\int \frac{\sqrt{1+x^3}}{x^7} \, dx","Integrate[Sqrt[1 + x^3]/x^7,x]","-\frac{2}{9} \left(x^3+1\right)^{3/2} \, _2F_1\left(\frac{3}{2},3;\frac{5}{2};x^3+1\right)","\frac{1}{12} \tanh ^{-1}\left(\sqrt{x^3+1}\right)+\frac{\sqrt{x^3+1} \left(-x^3-2\right)}{12 x^6}",1,"(-2*(1 + x^3)^(3/2)*Hypergeometric2F1[3/2, 3, 5/2, 1 + x^3])/9","C",1
479,1,50,38,0.0269592,"\int \frac{1+x^3}{x^7 \sqrt{-1+x^3}} \, dx","Integrate[(1 + x^3)/(x^7*Sqrt[-1 + x^3]),x]","\frac{1}{12} \sqrt{x^3-1} \left(\frac{7 \tanh ^{-1}\left(\sqrt{1-x^3}\right)}{\sqrt{1-x^3}}+\frac{7 x^3+2}{x^6}\right)","\frac{7}{12} \tan ^{-1}\left(\sqrt{x^3-1}\right)+\frac{\sqrt{x^3-1} \left(7 x^3+2\right)}{12 x^6}",1,"(Sqrt[-1 + x^3]*((2 + 7*x^3)/x^6 + (7*ArcTanh[Sqrt[1 - x^3]])/Sqrt[1 - x^3]))/12","A",1
480,1,1701,38,6.1624332,"\int \frac{\sqrt{-1+x^3} \left(2+x^3\right)}{x^2 \left(-2-4 x^2+2 x^3\right)} \, dx","Integrate[(Sqrt[-1 + x^3]*(2 + x^3))/(x^2*(-2 - 4*x^2 + 2*x^3)),x]","\frac{2 \sqrt{\frac{x-1}{-1-\sqrt[3]{-1}}} \left(x+\sqrt[3]{-1}\right) \sqrt{\frac{x-(-1)^{2/3}}{-\sqrt[3]{-1}-(-1)^{2/3}}} F\left(\sin ^{-1}\left(\sqrt{-\frac{(-1)^{2/3} \left(x+\sqrt[3]{-1}\right)}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{\sqrt{\frac{x+\sqrt[3]{-1}}{\sqrt[3]{-1}+(-1)^{2/3}}} \sqrt{x^3-1}}+\frac{\sqrt{x^3-1}}{x}+\frac{4 \left(-\sqrt[3]{-1}-(-1)^{2/3}\right) \sqrt{\frac{x-1}{-1-\sqrt[3]{-1}}} \sqrt{\frac{\left((-1)^{2/3}-x\right) \left(x+\sqrt[3]{-1}\right)}{\left(-\sqrt[3]{-1}-(-1)^{2/3}\right)^2}} \Pi \left(\frac{\sqrt[3]{-1}+(-1)^{2/3}}{\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3-2 \text{$\#$1}^2-1\&,3\right]};\sin ^{-1}\left(\sqrt{-\frac{(-1)^{2/3} \left(x+\sqrt[3]{-1}\right)}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{\sqrt{x^3-1} \left(\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3-2 \text{$\#$1}^2-1\&,3\right]\right) \left(-\text{Root}\left[\text{$\#$1}^3-2 \text{$\#$1}^2-1\&,1\right]+\text{Root}\left[\text{$\#$1}^3-2 \text{$\#$1}^2-1\&,3\right]\right) \left(-\text{Root}\left[\text{$\#$1}^3-2 \text{$\#$1}^2-1\&,2\right]+\text{Root}\left[\text{$\#$1}^3-2 \text{$\#$1}^2-1\&,3\right]\right)}+\frac{2 \left(-\sqrt[3]{-1}-(-1)^{2/3}\right) \sqrt{\frac{x-1}{-1-\sqrt[3]{-1}}} \sqrt{\frac{\left((-1)^{2/3}-x\right) \left(x+\sqrt[3]{-1}\right)}{\left(-\sqrt[3]{-1}-(-1)^{2/3}\right)^2}} \Pi \left(\frac{\sqrt[3]{-1}+(-1)^{2/3}}{\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3-2 \text{$\#$1}^2-1\&,3\right]};\sin ^{-1}\left(\sqrt{-\frac{(-1)^{2/3} \left(x+\sqrt[3]{-1}\right)}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right) \text{Root}\left[\text{$\#$1}^3-2 \text{$\#$1}^2-1\&,3\right]^3}{\sqrt{x^3-1} \left(\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3-2 \text{$\#$1}^2-1\&,3\right]\right) \left(-\text{Root}\left[\text{$\#$1}^3-2 \text{$\#$1}^2-1\&,1\right]+\text{Root}\left[\text{$\#$1}^3-2 \text{$\#$1}^2-1\&,3\right]\right) \left(-\text{Root}\left[\text{$\#$1}^3-2 \text{$\#$1}^2-1\&,2\right]+\text{Root}\left[\text{$\#$1}^3-2 \text{$\#$1}^2-1\&,3\right]\right)}+\frac{4 \left(-\sqrt[3]{-1}-(-1)^{2/3}\right) \sqrt{\frac{x-1}{-1-\sqrt[3]{-1}}} \sqrt{\frac{\left((-1)^{2/3}-x\right) \left(x+\sqrt[3]{-1}\right)}{\left(-\sqrt[3]{-1}-(-1)^{2/3}\right)^2}} \Pi \left(\frac{\sqrt[3]{-1}+(-1)^{2/3}}{\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3-2 \text{$\#$1}^2-1\&,2\right]};\sin ^{-1}\left(\sqrt{-\frac{(-1)^{2/3} \left(x+\sqrt[3]{-1}\right)}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{\sqrt{x^3-1} \left(\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3-2 \text{$\#$1}^2-1\&,2\right]\right) \left(-\text{Root}\left[\text{$\#$1}^3-2 \text{$\#$1}^2-1\&,1\right]+\text{Root}\left[\text{$\#$1}^3-2 \text{$\#$1}^2-1\&,2\right]\right) \left(\text{Root}\left[\text{$\#$1}^3-2 \text{$\#$1}^2-1\&,2\right]-\text{Root}\left[\text{$\#$1}^3-2 \text{$\#$1}^2-1\&,3\right]\right)}+\frac{2 \left(-\sqrt[3]{-1}-(-1)^{2/3}\right) \sqrt{\frac{x-1}{-1-\sqrt[3]{-1}}} \sqrt{\frac{\left((-1)^{2/3}-x\right) \left(x+\sqrt[3]{-1}\right)}{\left(-\sqrt[3]{-1}-(-1)^{2/3}\right)^2}} \Pi \left(\frac{\sqrt[3]{-1}+(-1)^{2/3}}{\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3-2 \text{$\#$1}^2-1\&,2\right]};\sin ^{-1}\left(\sqrt{-\frac{(-1)^{2/3} \left(x+\sqrt[3]{-1}\right)}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right) \text{Root}\left[\text{$\#$1}^3-2 \text{$\#$1}^2-1\&,2\right]^3}{\sqrt{x^3-1} \left(\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3-2 \text{$\#$1}^2-1\&,2\right]\right) \left(-\text{Root}\left[\text{$\#$1}^3-2 \text{$\#$1}^2-1\&,1\right]+\text{Root}\left[\text{$\#$1}^3-2 \text{$\#$1}^2-1\&,2\right]\right) \left(\text{Root}\left[\text{$\#$1}^3-2 \text{$\#$1}^2-1\&,2\right]-\text{Root}\left[\text{$\#$1}^3-2 \text{$\#$1}^2-1\&,3\right]\right)}+\frac{4 \left(-\sqrt[3]{-1}-(-1)^{2/3}\right) \sqrt{\frac{x-1}{-1-\sqrt[3]{-1}}} \sqrt{\frac{\left((-1)^{2/3}-x\right) \left(x+\sqrt[3]{-1}\right)}{\left(-\sqrt[3]{-1}-(-1)^{2/3}\right)^2}} \Pi \left(\frac{\sqrt[3]{-1}+(-1)^{2/3}}{\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3-2 \text{$\#$1}^2-1\&,1\right]};\sin ^{-1}\left(\sqrt{-\frac{(-1)^{2/3} \left(x+\sqrt[3]{-1}\right)}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{\sqrt{x^3-1} \left(\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3-2 \text{$\#$1}^2-1\&,1\right]\right) \left(\text{Root}\left[\text{$\#$1}^3-2 \text{$\#$1}^2-1\&,1\right]-\text{Root}\left[\text{$\#$1}^3-2 \text{$\#$1}^2-1\&,2\right]\right) \left(\text{Root}\left[\text{$\#$1}^3-2 \text{$\#$1}^2-1\&,1\right]-\text{Root}\left[\text{$\#$1}^3-2 \text{$\#$1}^2-1\&,3\right]\right)}+\frac{2 \left(-\sqrt[3]{-1}-(-1)^{2/3}\right) \sqrt{\frac{x-1}{-1-\sqrt[3]{-1}}} \sqrt{\frac{\left((-1)^{2/3}-x\right) \left(x+\sqrt[3]{-1}\right)}{\left(-\sqrt[3]{-1}-(-1)^{2/3}\right)^2}} \Pi \left(\frac{\sqrt[3]{-1}+(-1)^{2/3}}{\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3-2 \text{$\#$1}^2-1\&,1\right]};\sin ^{-1}\left(\sqrt{-\frac{(-1)^{2/3} \left(x+\sqrt[3]{-1}\right)}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right) \text{Root}\left[\text{$\#$1}^3-2 \text{$\#$1}^2-1\&,1\right]^3}{\sqrt{x^3-1} \left(\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3-2 \text{$\#$1}^2-1\&,1\right]\right) \left(\text{Root}\left[\text{$\#$1}^3-2 \text{$\#$1}^2-1\&,1\right]-\text{Root}\left[\text{$\#$1}^3-2 \text{$\#$1}^2-1\&,2\right]\right) \left(\text{Root}\left[\text{$\#$1}^3-2 \text{$\#$1}^2-1\&,1\right]-\text{Root}\left[\text{$\#$1}^3-2 \text{$\#$1}^2-1\&,3\right]\right)}","\frac{\sqrt{x^3-1}}{x}-\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^3-1}}\right)",1,"Sqrt[-1 + x^3]/x + (2*Sqrt[(-1 + x)/(-1 - (-1)^(1/3))]*((-1)^(1/3) + x)*Sqrt[(-(-1)^(2/3) + x)/(-(-1)^(1/3) - (-1)^(2/3))]*EllipticF[ArcSin[Sqrt[-(((-1)^(2/3)*((-1)^(1/3) + x))/(1 + (-1)^(1/3)))]], (-1)^(1/3)])/(Sqrt[((-1)^(1/3) + x)/((-1)^(1/3) + (-1)^(2/3))]*Sqrt[-1 + x^3]) + (4*(-(-1)^(1/3) - (-1)^(2/3))*Sqrt[(-1 + x)/(-1 - (-1)^(1/3))]*Sqrt[(((-1)^(2/3) - x)*((-1)^(1/3) + x))/(-(-1)^(1/3) - (-1)^(2/3))^2]*EllipticPi[((-1)^(1/3) + (-1)^(2/3))/((-1)^(1/3) + Root[-1 - 2*#1^2 + #1^3 & , 1, 0]), ArcSin[Sqrt[-(((-1)^(2/3)*((-1)^(1/3) + x))/(1 + (-1)^(1/3)))]], (-1)^(1/3)])/(Sqrt[-1 + x^3]*((-1)^(1/3) + Root[-1 - 2*#1^2 + #1^3 & , 1, 0])*(Root[-1 - 2*#1^2 + #1^3 & , 1, 0] - Root[-1 - 2*#1^2 + #1^3 & , 2, 0])*(Root[-1 - 2*#1^2 + #1^3 & , 1, 0] - Root[-1 - 2*#1^2 + #1^3 & , 3, 0])) + (2*(-(-1)^(1/3) - (-1)^(2/3))*Sqrt[(-1 + x)/(-1 - (-1)^(1/3))]*Sqrt[(((-1)^(2/3) - x)*((-1)^(1/3) + x))/(-(-1)^(1/3) - (-1)^(2/3))^2]*EllipticPi[((-1)^(1/3) + (-1)^(2/3))/((-1)^(1/3) + Root[-1 - 2*#1^2 + #1^3 & , 1, 0]), ArcSin[Sqrt[-(((-1)^(2/3)*((-1)^(1/3) + x))/(1 + (-1)^(1/3)))]], (-1)^(1/3)]*Root[-1 - 2*#1^2 + #1^3 & , 1, 0]^3)/(Sqrt[-1 + x^3]*((-1)^(1/3) + Root[-1 - 2*#1^2 + #1^3 & , 1, 0])*(Root[-1 - 2*#1^2 + #1^3 & , 1, 0] - Root[-1 - 2*#1^2 + #1^3 & , 2, 0])*(Root[-1 - 2*#1^2 + #1^3 & , 1, 0] - Root[-1 - 2*#1^2 + #1^3 & , 3, 0])) + (4*(-(-1)^(1/3) - (-1)^(2/3))*Sqrt[(-1 + x)/(-1 - (-1)^(1/3))]*Sqrt[(((-1)^(2/3) - x)*((-1)^(1/3) + x))/(-(-1)^(1/3) - (-1)^(2/3))^2]*EllipticPi[((-1)^(1/3) + (-1)^(2/3))/((-1)^(1/3) + Root[-1 - 2*#1^2 + #1^3 & , 2, 0]), ArcSin[Sqrt[-(((-1)^(2/3)*((-1)^(1/3) + x))/(1 + (-1)^(1/3)))]], (-1)^(1/3)])/(Sqrt[-1 + x^3]*((-1)^(1/3) + Root[-1 - 2*#1^2 + #1^3 & , 2, 0])*(-Root[-1 - 2*#1^2 + #1^3 & , 1, 0] + Root[-1 - 2*#1^2 + #1^3 & , 2, 0])*(Root[-1 - 2*#1^2 + #1^3 & , 2, 0] - Root[-1 - 2*#1^2 + #1^3 & , 3, 0])) + (2*(-(-1)^(1/3) - (-1)^(2/3))*Sqrt[(-1 + x)/(-1 - (-1)^(1/3))]*Sqrt[(((-1)^(2/3) - x)*((-1)^(1/3) + x))/(-(-1)^(1/3) - (-1)^(2/3))^2]*EllipticPi[((-1)^(1/3) + (-1)^(2/3))/((-1)^(1/3) + Root[-1 - 2*#1^2 + #1^3 & , 2, 0]), ArcSin[Sqrt[-(((-1)^(2/3)*((-1)^(1/3) + x))/(1 + (-1)^(1/3)))]], (-1)^(1/3)]*Root[-1 - 2*#1^2 + #1^3 & , 2, 0]^3)/(Sqrt[-1 + x^3]*((-1)^(1/3) + Root[-1 - 2*#1^2 + #1^3 & , 2, 0])*(-Root[-1 - 2*#1^2 + #1^3 & , 1, 0] + Root[-1 - 2*#1^2 + #1^3 & , 2, 0])*(Root[-1 - 2*#1^2 + #1^3 & , 2, 0] - Root[-1 - 2*#1^2 + #1^3 & , 3, 0])) + (4*(-(-1)^(1/3) - (-1)^(2/3))*Sqrt[(-1 + x)/(-1 - (-1)^(1/3))]*Sqrt[(((-1)^(2/3) - x)*((-1)^(1/3) + x))/(-(-1)^(1/3) - (-1)^(2/3))^2]*EllipticPi[((-1)^(1/3) + (-1)^(2/3))/((-1)^(1/3) + Root[-1 - 2*#1^2 + #1^3 & , 3, 0]), ArcSin[Sqrt[-(((-1)^(2/3)*((-1)^(1/3) + x))/(1 + (-1)^(1/3)))]], (-1)^(1/3)])/(Sqrt[-1 + x^3]*((-1)^(1/3) + Root[-1 - 2*#1^2 + #1^3 & , 3, 0])*(-Root[-1 - 2*#1^2 + #1^3 & , 1, 0] + Root[-1 - 2*#1^2 + #1^3 & , 3, 0])*(-Root[-1 - 2*#1^2 + #1^3 & , 2, 0] + Root[-1 - 2*#1^2 + #1^3 & , 3, 0])) + (2*(-(-1)^(1/3) - (-1)^(2/3))*Sqrt[(-1 + x)/(-1 - (-1)^(1/3))]*Sqrt[(((-1)^(2/3) - x)*((-1)^(1/3) + x))/(-(-1)^(1/3) - (-1)^(2/3))^2]*EllipticPi[((-1)^(1/3) + (-1)^(2/3))/((-1)^(1/3) + Root[-1 - 2*#1^2 + #1^3 & , 3, 0]), ArcSin[Sqrt[-(((-1)^(2/3)*((-1)^(1/3) + x))/(1 + (-1)^(1/3)))]], (-1)^(1/3)]*Root[-1 - 2*#1^2 + #1^3 & , 3, 0]^3)/(Sqrt[-1 + x^3]*((-1)^(1/3) + Root[-1 - 2*#1^2 + #1^3 & , 3, 0])*(-Root[-1 - 2*#1^2 + #1^3 & , 1, 0] + Root[-1 - 2*#1^2 + #1^3 & , 3, 0])*(-Root[-1 - 2*#1^2 + #1^3 & , 2, 0] + Root[-1 - 2*#1^2 + #1^3 & , 3, 0]))","C",0
481,1,28,38,0.0161871,"\int x^5 \sqrt{b+a x^3} \, dx","Integrate[x^5*Sqrt[b + a*x^3],x]","\frac{2 \left(a x^3+b\right)^{3/2} \left(3 a x^3-2 b\right)}{45 a^2}","\frac{2 \sqrt{a x^3+b} \left(3 a^2 x^6+a b x^3-2 b^2\right)}{45 a^2}",1,"(2*(b + a*x^3)^(3/2)*(-2*b + 3*a*x^3))/(45*a^2)","A",1
482,1,169,38,0.1932203,"\int \frac{\left(-3+x^4\right) \sqrt[3]{1+x^4} \left(1+x^3+x^4\right)}{x^8} \, dx","Integrate[((-3 + x^4)*(1 + x^4)^(1/3)*(1 + x^3 + x^4))/x^8,x]","\frac{1}{16} \left(-9 \left(x^4+1\right)^{4/3} \, _2F_1\left(\frac{4}{3},2;\frac{7}{3};x^4+1\right)+16 x \, _2F_1\left(-\frac{1}{3},\frac{1}{4};\frac{5}{4};-x^4\right)+12 \sqrt[3]{x^4+1}+4 \log \left(1-\sqrt[3]{x^4+1}\right)-2 \log \left(\left(x^4+1\right)^{2/3}+\sqrt[3]{x^4+1}+1\right)-4 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x^4+1}+1}{\sqrt{3}}\right)\right)+\frac{3 \, _2F_1\left(-\frac{7}{4},-\frac{1}{3};-\frac{3}{4};-x^4\right)}{7 x^7}+\frac{2 \, _2F_1\left(-\frac{3}{4},-\frac{1}{3};\frac{1}{4};-x^4\right)}{3 x^3}","\frac{3 \sqrt[3]{x^4+1} \left(4 x^8+7 x^7+8 x^4+7 x^3+4\right)}{28 x^7}",1,"(3*Hypergeometric2F1[-7/4, -1/3, -3/4, -x^4])/(7*x^7) + (2*Hypergeometric2F1[-3/4, -1/3, 1/4, -x^4])/(3*x^3) + (12*(1 + x^4)^(1/3) - 4*Sqrt[3]*ArcTan[(1 + 2*(1 + x^4)^(1/3))/Sqrt[3]] + 16*x*Hypergeometric2F1[-1/3, 1/4, 5/4, -x^4] - 9*(1 + x^4)^(4/3)*Hypergeometric2F1[4/3, 2, 7/3, 1 + x^4] + 4*Log[1 - (1 + x^4)^(1/3)] - 2*Log[1 + (1 + x^4)^(1/3) + (1 + x^4)^(2/3)])/16","C",1
483,1,158,38,0.2273231,"\int \frac{\left(-3+x^4\right) \left(1+x^4\right)^{2/3} \left(1+x^3+x^4\right)}{x^9} \, dx","Integrate[((-3 + x^4)*(1 + x^4)^(2/3)*(1 + x^3 + x^4))/x^9,x]","\frac{24 \, _2F_1\left(-\frac{5}{4},-\frac{2}{3};-\frac{1}{4};-x^4\right)+x^4 \left(x \left(-12 \left(x^4+1\right)^{5/3} \, _2F_1\left(\frac{5}{3},2;\frac{8}{3};x^4+1\right)+18 \left(x^4+1\right)^{5/3} \, _2F_1\left(\frac{5}{3},3;\frac{8}{3};x^4+1\right)+5 \left(3 \left(\left(x^4+1\right)^{2/3}+\log \left(1-\sqrt[3]{x^4+1}\right)\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x^4+1}+1}{\sqrt{3}}\right)-4 \log (x)\right)\right)-40 \, _2F_1\left(-\frac{2}{3},-\frac{1}{4};\frac{3}{4};-x^4\right)\right)}{40 x^5}","\frac{3 \left(x^4+1\right)^{2/3} \left(5 x^8+8 x^7+10 x^4+8 x^3+5\right)}{40 x^8}",1,"(24*Hypergeometric2F1[-5/4, -2/3, -1/4, -x^4] + x^4*(-40*Hypergeometric2F1[-2/3, -1/4, 3/4, -x^4] + x*(-12*(1 + x^4)^(5/3)*Hypergeometric2F1[5/3, 2, 8/3, 1 + x^4] + 18*(1 + x^4)^(5/3)*Hypergeometric2F1[5/3, 3, 8/3, 1 + x^4] + 5*(2*Sqrt[3]*ArcTan[(1 + 2*(1 + x^4)^(1/3))/Sqrt[3]] - 4*Log[x] + 3*((1 + x^4)^(2/3) + Log[1 - (1 + x^4)^(1/3)])))))/(40*x^5)","C",1
484,1,155,38,0.1201398,"\int \frac{\left(-1+x^4\right)^{2/3} \left(3+x^4\right) \left(-2-x^3+2 x^4\right)}{x^9} \, dx","Integrate[((-1 + x^4)^(2/3)*(3 + x^4)*(-2 - x^3 + 2*x^4))/x^9,x]","\frac{\left(x^4-1\right)^{2/3} \left(x^4 \left(20 \, _2F_1\left(-\frac{2}{3},-\frac{1}{4};\frac{3}{4};x^4\right)+3 x \left(1-x^4\right)^{2/3} \left(-6 x^4 \, _2F_1\left(\frac{5}{3},3;\frac{8}{3};1-x^4\right)-5 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};1-x^4\right)+4 \left(x^4-1\right) \, _2F_1\left(\frac{5}{3},2;\frac{8}{3};1-x^4\right)+6 \, _2F_1\left(\frac{5}{3},3;\frac{8}{3};1-x^4\right)+5\right)\right)+12 \, _2F_1\left(-\frac{5}{4},-\frac{2}{3};-\frac{1}{4};x^4\right)\right)}{20 x^5 \left(1-x^4\right)^{2/3}}","\frac{3 \left(x^4-1\right)^{2/3} \left(5 x^8-4 x^7-10 x^4+4 x^3+5\right)}{20 x^8}",1,"((-1 + x^4)^(2/3)*(12*Hypergeometric2F1[-5/4, -2/3, -1/4, x^4] + x^4*(20*Hypergeometric2F1[-2/3, -1/4, 3/4, x^4] + 3*x*(1 - x^4)^(2/3)*(5 - 5*Hypergeometric2F1[2/3, 1, 5/3, 1 - x^4] + 4*(-1 + x^4)*Hypergeometric2F1[5/3, 2, 8/3, 1 - x^4] + 6*Hypergeometric2F1[5/3, 3, 8/3, 1 - x^4] - 6*x^4*Hypergeometric2F1[5/3, 3, 8/3, 1 - x^4]))))/(20*x^5*(1 - x^4)^(2/3))","C",1
485,1,117,38,0.0733459,"\int \frac{\left(-1+x^5\right)^{3/4} \left(4+x^5\right) \left(-1-x^4+x^5\right)}{x^{12}} \, dx","Integrate[((-1 + x^5)^(3/4)*(4 + x^5)*(-1 - x^4 + x^5))/x^12,x]","\frac{\left(x^5-1\right)^{3/4} \left(56 \, _2F_1\left(-\frac{11}{5},-\frac{3}{4};-\frac{6}{5};x^5\right)+11 x^4 \left(8 \, _2F_1\left(-\frac{7}{5},-\frac{3}{4};-\frac{2}{5};x^5\right)-7 x \left(2 x^5 \, _2F_1\left(-\frac{3}{4},-\frac{1}{5};\frac{4}{5};x^5\right)+\, _2F_1\left(-\frac{6}{5},-\frac{3}{4};-\frac{1}{5};x^5\right)-x^4 \, _2F_1\left(-\frac{3}{4},-\frac{2}{5};\frac{3}{5};x^5\right)\right)\right)\right)}{154 x^{11} \left(1-x^5\right)^{3/4}}","\frac{4 \left(x^5-1\right)^{3/4} \left(7 x^{10}-11 x^9-14 x^5+11 x^4+7\right)}{77 x^{11}}",1,"((-1 + x^5)^(3/4)*(56*Hypergeometric2F1[-11/5, -3/4, -6/5, x^5] + 11*x^4*(8*Hypergeometric2F1[-7/5, -3/4, -2/5, x^5] - 7*x*(Hypergeometric2F1[-6/5, -3/4, -1/5, x^5] - x^4*Hypergeometric2F1[-3/4, -2/5, 3/5, x^5] + 2*x^5*Hypergeometric2F1[-3/4, -1/5, 4/5, x^5]))))/(154*x^11*(1 - x^5)^(3/4))","C",1
486,1,153,38,0.2738884,"\int \frac{\left(1+x^5\right)^{2/3} \left(1+x^3+x^5\right) \left(-3+2 x^5\right)}{x^9} \, dx","Integrate[((1 + x^5)^(2/3)*(1 + x^3 + x^5)*(-3 + 2*x^5))/x^9,x]","-\frac{9}{25} \left(x^5+1\right)^{5/3} \, _2F_1\left(\frac{5}{3},2;\frac{8}{3};x^5+1\right)+\frac{3 \, _2F_1\left(-\frac{8}{5},-\frac{2}{3};-\frac{3}{5};-x^5\right)}{8 x^8}+\frac{\, _2F_1\left(-\frac{2}{3},-\frac{3}{5};\frac{2}{5};-x^5\right)}{3 x^3}+x^2 \, _2F_1\left(-\frac{2}{3},\frac{2}{5};\frac{7}{5};-x^5\right)+\frac{1}{5} \left(3 \left(x^5+1\right)^{2/3}+3 \log \left(1-\sqrt[3]{x^5+1}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x^5+1}+1}{\sqrt{3}}\right)-5 \log (x)\right)","\frac{3 \left(x^5+1\right)^{2/3} \left(5 x^{10}+8 x^8+10 x^5+8 x^3+5\right)}{40 x^8}",1,"(3*Hypergeometric2F1[-8/5, -2/3, -3/5, -x^5])/(8*x^8) + Hypergeometric2F1[-2/3, -3/5, 2/5, -x^5]/(3*x^3) + x^2*Hypergeometric2F1[-2/3, 2/5, 7/5, -x^5] - (9*(1 + x^5)^(5/3)*Hypergeometric2F1[5/3, 2, 8/3, 1 + x^5])/25 + (3*(1 + x^5)^(2/3) + 2*Sqrt[3]*ArcTan[(1 + 2*(1 + x^5)^(1/3))/Sqrt[3]] - 5*Log[x] + 3*Log[1 - (1 + x^5)^(1/3)])/5","C",1
487,1,139,38,0.1244587,"\int \frac{\left(-1+x^5\right)^{2/3} \left(-1+x^3+x^5\right) \left(3+2 x^5\right)}{x^9} \, dx","Integrate[((-1 + x^5)^(2/3)*(-1 + x^3 + x^5)*(3 + 2*x^5))/x^9,x]","\frac{\left(x^5-1\right)^{2/3} \left(225 \, _2F_1\left(-\frac{8}{5},-\frac{2}{3};-\frac{3}{5};x^5\right)+8 x^5 \left(75 x^5 \, _2F_1\left(-\frac{2}{3},\frac{2}{5};\frac{7}{5};x^5\right)-25 \, _2F_1\left(-\frac{2}{3},-\frac{3}{5};\frac{2}{5};x^5\right)+9 \left(1-x^5\right)^{2/3} x^3 \left(-5 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};1-x^5\right)+3 \left(x^5-1\right) \, _2F_1\left(\frac{5}{3},2;\frac{8}{3};1-x^5\right)+5\right)\right)\right)}{600 x^8 \left(1-x^5\right)^{2/3}}","\frac{3 \left(x^5-1\right)^{2/3} \left(5 x^{10}+8 x^8-10 x^5-8 x^3+5\right)}{40 x^8}",1,"((-1 + x^5)^(2/3)*(225*Hypergeometric2F1[-8/5, -2/3, -3/5, x^5] + 8*x^5*(-25*Hypergeometric2F1[-2/3, -3/5, 2/5, x^5] + 75*x^5*Hypergeometric2F1[-2/3, 2/5, 7/5, x^5] + 9*x^3*(1 - x^5)^(2/3)*(5 - 5*Hypergeometric2F1[2/3, 1, 5/3, 1 - x^5] + 3*(-1 + x^5)*Hypergeometric2F1[5/3, 2, 8/3, 1 - x^5]))))/(600*x^8*(1 - x^5)^(2/3))","C",1
488,1,106,38,0.0377424,"\int \frac{\left(-4+x^5\right) \left(1+x^5\right)^{3/4} \left(2-x^4+2 x^5\right)}{x^{12}} \, dx","Integrate[((-4 + x^5)*(1 + x^5)^(3/4)*(2 - x^4 + 2*x^5))/x^12,x]","-\frac{2 \, _2F_1\left(-\frac{3}{4},-\frac{1}{5};\frac{4}{5};-x^5\right)}{x}+\frac{8 \, _2F_1\left(-\frac{11}{5},-\frac{3}{4};-\frac{6}{5};-x^5\right)}{11 x^{11}}-\frac{4 \, _2F_1\left(-\frac{7}{5},-\frac{3}{4};-\frac{2}{5};-x^5\right)}{7 x^7}+\frac{\, _2F_1\left(-\frac{6}{5},-\frac{3}{4};-\frac{1}{5};-x^5\right)}{x^6}+\frac{\, _2F_1\left(-\frac{3}{4},-\frac{2}{5};\frac{3}{5};-x^5\right)}{2 x^2}","\frac{4 \left(x^5+1\right)^{3/4} \left(14 x^{10}-11 x^9+28 x^5-11 x^4+14\right)}{77 x^{11}}",1,"(8*Hypergeometric2F1[-11/5, -3/4, -6/5, -x^5])/(11*x^11) - (4*Hypergeometric2F1[-7/5, -3/4, -2/5, -x^5])/(7*x^7) + Hypergeometric2F1[-6/5, -3/4, -1/5, -x^5]/x^6 + Hypergeometric2F1[-3/4, -2/5, 3/5, -x^5]/(2*x^2) - (2*Hypergeometric2F1[-3/4, -1/5, 4/5, -x^5])/x","C",1
489,1,154,38,0.2027453,"\int \frac{\left(1+x^5\right)^{2/3} \left(-3+2 x^5\right) \left(4+3 x^3+4 x^5\right)}{x^9} \, dx","Integrate[((1 + x^5)^(2/3)*(-3 + 2*x^5)*(4 + 3*x^3 + 4*x^5))/x^9,x]","-\frac{27}{25} \left(x^5+1\right)^{5/3} \, _2F_1\left(\frac{5}{3},2;\frac{8}{3};x^5+1\right)+\frac{3 \, _2F_1\left(-\frac{8}{5},-\frac{2}{3};-\frac{3}{5};-x^5\right)}{2 x^8}+\frac{4 \, _2F_1\left(-\frac{2}{3},-\frac{3}{5};\frac{2}{5};-x^5\right)}{3 x^3}+4 x^2 \, _2F_1\left(-\frac{2}{3},\frac{2}{5};\frac{7}{5};-x^5\right)+\frac{3}{5} \left(3 \left(x^5+1\right)^{2/3}+3 \log \left(1-\sqrt[3]{x^5+1}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x^5+1}+1}{\sqrt{3}}\right)-5 \log (x)\right)","\frac{3 \left(x^5+1\right)^{2/3} \left(5 x^{10}+6 x^8+10 x^5+6 x^3+5\right)}{10 x^8}",1,"(3*Hypergeometric2F1[-8/5, -2/3, -3/5, -x^5])/(2*x^8) + (4*Hypergeometric2F1[-2/3, -3/5, 2/5, -x^5])/(3*x^3) + 4*x^2*Hypergeometric2F1[-2/3, 2/5, 7/5, -x^5] - (27*(1 + x^5)^(5/3)*Hypergeometric2F1[5/3, 2, 8/3, 1 + x^5])/25 + (3*(3*(1 + x^5)^(2/3) + 2*Sqrt[3]*ArcTan[(1 + 2*(1 + x^5)^(1/3))/Sqrt[3]] - 5*Log[x] + 3*Log[1 - (1 + x^5)^(1/3)]))/5","C",1
490,1,28,38,0.0047934,"\int \frac{1}{x^{13} \sqrt{-1+x^6}} \, dx","Integrate[1/(x^13*Sqrt[-1 + x^6]),x]","\frac{1}{3} \sqrt{x^6-1} \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};1-x^6\right)","\frac{1}{8} \tan ^{-1}\left(\sqrt{x^6-1}\right)+\frac{\sqrt{x^6-1} \left(3 x^6+2\right)}{24 x^{12}}",1,"(Sqrt[-1 + x^6]*Hypergeometric2F1[1/2, 3, 3/2, 1 - x^6])/3","C",1
491,1,37,38,0.0185739,"\int \frac{-1+x^6}{x^{13} \sqrt{1+x^6}} \, dx","Integrate[(-1 + x^6)/(x^13*Sqrt[1 + x^6]),x]","\frac{1}{24} \left(7 \tanh ^{-1}\left(\sqrt{x^6+1}\right)+\frac{\sqrt{x^6+1} \left(2-7 x^6\right)}{x^{12}}\right)","\frac{7}{24} \tanh ^{-1}\left(\sqrt{x^6+1}\right)+\frac{\sqrt{x^6+1} \left(2-7 x^6\right)}{24 x^{12}}",1,"(((2 - 7*x^6)*Sqrt[1 + x^6])/x^12 + 7*ArcTanh[Sqrt[1 + x^6]])/24","A",1
492,1,26,38,0.0052331,"\int \frac{\sqrt{1+x^6}}{x^{13}} \, dx","Integrate[Sqrt[1 + x^6]/x^13,x]","-\frac{1}{9} \left(x^6+1\right)^{3/2} \, _2F_1\left(\frac{3}{2},3;\frac{5}{2};x^6+1\right)","\frac{1}{24} \tanh ^{-1}\left(\sqrt{x^6+1}\right)+\frac{\sqrt{x^6+1} \left(-x^6-2\right)}{24 x^{12}}",1,"-1/9*((1 + x^6)^(3/2)*Hypergeometric2F1[3/2, 3, 5/2, 1 + x^6])","C",1
493,1,50,38,0.0261857,"\int \frac{1+x^6}{x^{13} \sqrt{-1+x^6}} \, dx","Integrate[(1 + x^6)/(x^13*Sqrt[-1 + x^6]),x]","\frac{1}{24} \sqrt{x^6-1} \left(\frac{7 \tanh ^{-1}\left(\sqrt{1-x^6}\right)}{\sqrt{1-x^6}}+\frac{7 x^6+2}{x^{12}}\right)","\frac{7}{24} \tan ^{-1}\left(\sqrt{x^6-1}\right)+\frac{\sqrt{x^6-1} \left(7 x^6+2\right)}{24 x^{12}}",1,"(Sqrt[-1 + x^6]*((2 + 7*x^6)/x^12 + (7*ArcTanh[Sqrt[1 - x^6]])/Sqrt[1 - x^6]))/24","A",1
494,1,100,38,0.0483037,"\int \frac{\sqrt[3]{-1+x^6} \left(1+x^6\right) \left(-1+x^3+x^6\right)}{x^8} \, dx","Integrate[((-1 + x^6)^(1/3)*(1 + x^6)*(-1 + x^3 + x^6))/x^8,x]","\frac{\sqrt[3]{x^6-1} \left(20 \, _2F_1\left(-\frac{7}{6},-\frac{1}{3};-\frac{1}{6};x^6\right)+7 x^3 \left(10 x^6 \, _2F_1\left(-\frac{1}{3},\frac{1}{3};\frac{4}{3};x^6\right)-5 \, _2F_1\left(-\frac{2}{3},-\frac{1}{3};\frac{1}{3};x^6\right)+4 x^9 \, _2F_1\left(-\frac{1}{3},\frac{5}{6};\frac{11}{6};x^6\right)\right)\right)}{140 x^7 \sqrt[3]{1-x^6}}","\frac{\sqrt[3]{x^6-1} \left(4 x^{12}+7 x^9-8 x^6-7 x^3+4\right)}{28 x^7}",1,"((-1 + x^6)^(1/3)*(20*Hypergeometric2F1[-7/6, -1/3, -1/6, x^6] + 7*x^3*(-5*Hypergeometric2F1[-2/3, -1/3, 1/3, x^6] + 10*x^6*Hypergeometric2F1[-1/3, 1/3, 4/3, x^6] + 4*x^9*Hypergeometric2F1[-1/3, 5/6, 11/6, x^6])))/(140*x^7*(1 - x^6)^(1/3))","C",1
495,1,118,38,0.0651023,"\int \frac{\left(-1+x^6\right)^{3/4} \left(2+x^6\right) \left(-1-x^4+x^6\right)}{x^{12}} \, dx","Integrate[((-1 + x^6)^(3/4)*(2 + x^6)*(-1 - x^4 + x^6))/x^12,x]","\frac{\left(x^6-1\right)^{3/4} \left(70 \, _2F_1\left(-\frac{11}{6},-\frac{3}{4};-\frac{5}{6};x^6\right)+11 x^4 \left(10 \, _2F_1\left(-\frac{7}{6},-\frac{3}{4};-\frac{1}{6};x^6\right)+35 x^6 \left(\, _2F_1\left(-\frac{3}{4},-\frac{1}{6};\frac{5}{6};x^6\right)+x^2 \, _2F_1\left(-\frac{3}{4},\frac{1}{6};\frac{7}{6};x^6\right)\right)-7 x^2 \, _2F_1\left(-\frac{5}{6},-\frac{3}{4};\frac{1}{6};x^6\right)\right)\right)}{385 x^{11} \left(1-x^6\right)^{3/4}}","\frac{2 \left(x^6-1\right)^{3/4} \left(7 x^{12}-11 x^{10}-14 x^6+11 x^4+7\right)}{77 x^{11}}",1,"((-1 + x^6)^(3/4)*(70*Hypergeometric2F1[-11/6, -3/4, -5/6, x^6] + 11*x^4*(10*Hypergeometric2F1[-7/6, -3/4, -1/6, x^6] - 7*x^2*Hypergeometric2F1[-5/6, -3/4, 1/6, x^6] + 35*x^6*(Hypergeometric2F1[-3/4, -1/6, 5/6, x^6] + x^2*Hypergeometric2F1[-3/4, 1/6, 7/6, x^6]))))/(385*x^11*(1 - x^6)^(3/4))","C",1
496,1,103,38,0.0330371,"\int \frac{\left(-2+x^6\right) \left(1+x^6\right)^{3/4} \left(1-x^4+x^6\right)}{x^{12}} \, dx","Integrate[((-2 + x^6)*(1 + x^6)^(3/4)*(1 - x^4 + x^6))/x^12,x]","\frac{\, _2F_1\left(-\frac{3}{4},-\frac{1}{6};\frac{5}{6};-x^6\right)}{x}+x \, _2F_1\left(-\frac{3}{4},\frac{1}{6};\frac{7}{6};-x^6\right)+\frac{2 \, _2F_1\left(-\frac{11}{6},-\frac{3}{4};-\frac{5}{6};-x^6\right)}{11 x^{11}}-\frac{2 \, _2F_1\left(-\frac{7}{6},-\frac{3}{4};-\frac{1}{6};-x^6\right)}{7 x^7}+\frac{\, _2F_1\left(-\frac{5}{6},-\frac{3}{4};\frac{1}{6};-x^6\right)}{5 x^5}","\frac{2 \left(x^6+1\right)^{3/4} \left(7 x^{12}-11 x^{10}+14 x^6-11 x^4+7\right)}{77 x^{11}}",1,"(2*Hypergeometric2F1[-11/6, -3/4, -5/6, -x^6])/(11*x^11) - (2*Hypergeometric2F1[-7/6, -3/4, -1/6, -x^6])/(7*x^7) + Hypergeometric2F1[-5/6, -3/4, 1/6, -x^6]/(5*x^5) + Hypergeometric2F1[-3/4, -1/6, 5/6, -x^6]/x + x*Hypergeometric2F1[-3/4, 1/6, 7/6, -x^6]","C",1
497,1,11,38,0.063231,"\int \frac{-2 x+3 x^2}{\sqrt{5-4 x^2+4 x^3+x^4-2 x^5+x^6}} \, dx","Integrate[(-2*x + 3*x^2)/Sqrt[5 - 4*x^2 + 4*x^3 + x^4 - 2*x^5 + x^6],x]","\sinh ^{-1}\left(x^3-x^2+2\right)","\log \left(x^3-x^2+\sqrt{x^6-2 x^5+x^4+4 x^3-4 x^2+5}+2\right)",1,"ArcSinh[2 - x^2 + x^3]","A",1
498,1,38,38,0.0411883,"\int \frac{-2+5 x^6}{x \sqrt{-1+x^6} \left(2+x^6\right)} \, dx","Integrate[(-2 + 5*x^6)/(x*Sqrt[-1 + x^6]*(2 + x^6)),x]","\frac{2 \tan ^{-1}\left(\frac{\sqrt{x^6-1}}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{1}{3} \tan ^{-1}\left(\sqrt{x^6-1}\right)","\frac{2 \tan ^{-1}\left(\frac{\sqrt{x^6-1}}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{1}{3} \tan ^{-1}\left(\sqrt{x^6-1}\right)",1,"-1/3*ArcTan[Sqrt[-1 + x^6]] + (2*ArcTan[Sqrt[-1 + x^6]/Sqrt[3]])/Sqrt[3]","A",1
499,1,77,38,0.0618033,"\int \frac{-1+10 x^6}{x \sqrt{-1+x^6} \left(-1+4 x^6\right)} \, dx","Integrate[(-1 + 10*x^6)/(x*Sqrt[-1 + x^6]*(-1 + 4*x^6)),x]","\frac{1}{3} \tan ^{-1}\left(\sqrt{x^6-1}\right)-\frac{\tan ^{-1}\left(\frac{2-x^3}{\sqrt{3} \sqrt{x^6-1}}\right)}{2 \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{x^3+2}{\sqrt{3} \sqrt{x^6-1}}\right)}{2 \sqrt{3}}","\frac{1}{3} \tan ^{-1}\left(\sqrt{x^6-1}\right)+\frac{\tan ^{-1}\left(\frac{2 \sqrt{x^6-1}}{\sqrt{3}}\right)}{\sqrt{3}}",1,"-1/2*ArcTan[(2 - x^3)/(Sqrt[3]*Sqrt[-1 + x^6])]/Sqrt[3] - ArcTan[(2 + x^3)/(Sqrt[3]*Sqrt[-1 + x^6])]/(2*Sqrt[3]) + ArcTan[Sqrt[-1 + x^6]]/3","B",1
500,1,39,39,0.0157297,"\int \frac{2+x+x^2}{x^2 \left(1+x^2\right)^{3/4}} \, dx","Integrate[(2 + x + x^2)/(x^2*(1 + x^2)^(3/4)),x]","-\frac{2 \sqrt[4]{x^2+1}}{x}-\tan ^{-1}\left(\sqrt[4]{x^2+1}\right)-\tanh ^{-1}\left(\sqrt[4]{x^2+1}\right)","-\frac{2 \sqrt[4]{x^2+1}}{x}-\tan ^{-1}\left(\sqrt[4]{x^2+1}\right)-\tanh ^{-1}\left(\sqrt[4]{x^2+1}\right)",1,"(-2*(1 + x^2)^(1/4))/x - ArcTan[(1 + x^2)^(1/4)] - ArcTanh[(1 + x^2)^(1/4)]","A",1
501,0,0,39,0.5414903,"\int \frac{-3+2 x}{\sqrt[4]{-x+x^2} \left(1-x+x^3\right)} \, dx","Integrate[(-3 + 2*x)/((-x + x^2)^(1/4)*(1 - x + x^3)),x]","\int \frac{-3+2 x}{\sqrt[4]{-x+x^2} \left(1-x+x^3\right)} \, dx","2 \tan ^{-1}\left(\frac{\sqrt[4]{x^2-x}}{x}\right)-2 \tanh ^{-1}\left(\frac{\left(x^2-x\right)^{3/4}}{x-1}\right)",1,"Integrate[(-3 + 2*x)/((-x + x^2)^(1/4)*(1 - x + x^3)), x]","F",-1
502,1,117,39,1.0315992,"\int \frac{\left(-1+x^2\right) \sqrt{x+x^3}}{\left(1+x^2\right) \left(1+x+x^2\right)^2} \, dx","Integrate[((-1 + x^2)*Sqrt[x + x^3])/((1 + x^2)*(1 + x + x^2)^2),x]","\sqrt{x^3+x} \left(\frac{1}{x^2+x+1}+\frac{\sqrt[4]{-1} \sqrt{\frac{1}{x^2}+1} \sqrt{x} \left(-F\left(\left.i \sinh ^{-1}\left(\frac{\sqrt[4]{-1}}{\sqrt{x}}\right)\right|-1\right)+\Pi \left(-\sqrt[6]{-1};\left.i \sinh ^{-1}\left(\frac{\sqrt[4]{-1}}{\sqrt{x}}\right)\right|-1\right)+\Pi \left(-(-1)^{5/6};\left.i \sinh ^{-1}\left(\frac{\sqrt[4]{-1}}{\sqrt{x}}\right)\right|-1\right)\right)}{x^2+1}\right)","\frac{\sqrt{x^3+x}}{x^2+x+1}-\tan ^{-1}\left(\frac{\sqrt{x^3+x}}{x^2+1}\right)",1,"Sqrt[x + x^3]*((1 + x + x^2)^(-1) + ((-1)^(1/4)*Sqrt[1 + x^(-2)]*Sqrt[x]*(-EllipticF[I*ArcSinh[(-1)^(1/4)/Sqrt[x]], -1] + EllipticPi[-(-1)^(1/6), I*ArcSinh[(-1)^(1/4)/Sqrt[x]], -1] + EllipticPi[-(-1)^(5/6), I*ArcSinh[(-1)^(1/4)/Sqrt[x]], -1]))/(1 + x^2))","C",1
503,1,10734,39,6.3415522,"\int \frac{\left(-2+x^3\right) \sqrt{2+x^2+2 x^3}}{\left(1+x^3\right) \left(1+x^2+x^3\right)} \, dx","Integrate[((-2 + x^3)*Sqrt[2 + x^2 + 2*x^3])/((1 + x^3)*(1 + x^2 + x^3)),x]","\text{Result too large to show}","-2 \tan ^{-1}\left(\frac{x}{\sqrt{2 x^3+x^2+2}}\right)-2 \tanh ^{-1}\left(\frac{x}{\sqrt{2 x^3+x^2+2}}\right)",1,"Result too large to show","C",0
504,1,204,39,1.654256,"\int \frac{b+a x^2}{\left(-b+c x+a x^2\right) \sqrt{-b x+a x^3}} \, dx","Integrate[(b + a*x^2)/((-b + c*x + a*x^2)*Sqrt[-(b*x) + a*x^3]),x]","-\frac{2 i x^{3/2} \sqrt{1-\frac{b}{a x^2}} \left(-\Pi \left(\frac{2 \sqrt{a} \sqrt{b}}{c-\sqrt{c^2+4 a b}};\left.i \sinh ^{-1}\left(\frac{\sqrt{-\frac{\sqrt{b}}{\sqrt{a}}}}{\sqrt{x}}\right)\right|-1\right)-\Pi \left(\frac{2 \sqrt{a} \sqrt{b}}{c+\sqrt{c^2+4 a b}};\left.i \sinh ^{-1}\left(\frac{\sqrt{-\frac{\sqrt{b}}{\sqrt{a}}}}{\sqrt{x}}\right)\right|-1\right)+F\left(\left.i \sinh ^{-1}\left(\frac{\sqrt{-\frac{\sqrt{b}}{\sqrt{a}}}}{\sqrt{x}}\right)\right|-1\right)\right)}{\sqrt{-\frac{\sqrt{b}}{\sqrt{a}}} \sqrt{a x^3-b x}}","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a x^3-b x}}{a x^2-b}\right)}{\sqrt{c}}",1,"((-2*I)*Sqrt[1 - b/(a*x^2)]*x^(3/2)*(EllipticF[I*ArcSinh[Sqrt[-(Sqrt[b]/Sqrt[a])]/Sqrt[x]], -1] - EllipticPi[(2*Sqrt[a]*Sqrt[b])/(c - Sqrt[4*a*b + c^2]), I*ArcSinh[Sqrt[-(Sqrt[b]/Sqrt[a])]/Sqrt[x]], -1] - EllipticPi[(2*Sqrt[a]*Sqrt[b])/(c + Sqrt[4*a*b + c^2]), I*ArcSinh[Sqrt[-(Sqrt[b]/Sqrt[a])]/Sqrt[x]], -1]))/(Sqrt[-(Sqrt[b]/Sqrt[a])]*Sqrt[-(b*x) + a*x^3])","C",1
505,1,42,39,0.0137686,"\int x \sqrt{-1+x^4} \, dx","Integrate[x*Sqrt[-1 + x^4],x]","\frac{\left(x^4-1\right) \left(\sin ^{-1}\left(x^2\right)+\sqrt{1-x^4} x^2\right)}{4 \sqrt{-\left(x^4-1\right)^2}}","\frac{1}{4} x^2 \sqrt{x^4-1}-\frac{1}{2} \tanh ^{-1}\left(\frac{\sqrt{x^4-1}}{x^2+1}\right)",1,"((-1 + x^4)*(x^2*Sqrt[1 - x^4] + ArcSin[x^2]))/(4*Sqrt[-(-1 + x^4)^2])","A",1
506,1,53,39,0.0145227,"\int \frac{\sqrt{-x+x^4}}{x^3} \, dx","Integrate[Sqrt[-x + x^4]/x^3,x]","-\frac{2 \sqrt{x \left(x^3-1\right)} \left(x^{3/2} \sin ^{-1}\left(x^{3/2}\right)+\sqrt{1-x^3}\right)}{3 x^2 \sqrt{1-x^3}}","\frac{2}{3} \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4-x}}\right)-\frac{2 \sqrt{x^4-x}}{3 x^2}",1,"(-2*Sqrt[x*(-1 + x^3)]*(Sqrt[1 - x^3] + x^(3/2)*ArcSin[x^(3/2)]))/(3*x^2*Sqrt[1 - x^3])","A",1
507,1,48,39,0.0316136,"\int x^3 \sqrt{x+x^4} \, dx","Integrate[x^3*Sqrt[x + x^4],x]","\frac{\sqrt{x^4+x} \left(2 x^{9/2}+x^{3/2}-\frac{\sinh ^{-1}\left(x^{3/2}\right)}{\sqrt{x^3+1}}\right)}{12 \sqrt{x}}","\frac{1}{12} \sqrt{x^4+x} \left(2 x^4+x\right)-\frac{1}{12} \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4+x}}\right)",1,"(Sqrt[x + x^4]*(x^(3/2) + 2*x^(9/2) - ArcSinh[x^(3/2)]/Sqrt[1 + x^3]))/(12*Sqrt[x])","A",1
508,1,2092,39,6.0784976,"\int \frac{1+x}{\sqrt{16+18 x+13 x^2+4 x^3+x^4}} \, dx","Integrate[(1 + x)/Sqrt[16 + 18*x + 13*x^2 + 4*x^3 + x^4],x]","\text{Result too large to show}","\frac{1}{2} \log \left(2 x^2+2 \sqrt{x^4+4 x^3+13 x^2+18 x+16}+4 x+9\right)",1,"(2*((-2 - I*Sqrt[2*(7 - Sqrt[17])])/2 + (2 - I*Sqrt[2*(7 + Sqrt[17])])/2)*((2 - I*Sqrt[2*(7 - Sqrt[17])])/2 + x)^2*Sqrt[(((2 - I*Sqrt[2*(7 - Sqrt[17])])/2 + (-2 + I*Sqrt[2*(7 + Sqrt[17])])/2)*((2 + I*Sqrt[2*(7 - Sqrt[17])])/2 + x))/(((2 + I*Sqrt[2*(7 - Sqrt[17])])/2 + (-2 + I*Sqrt[2*(7 + Sqrt[17])])/2)*((2 - I*Sqrt[2*(7 - Sqrt[17])])/2 + x))]*Sqrt[(((-2 + I*Sqrt[2*(7 - Sqrt[17])])/2 + (2 + I*Sqrt[2*(7 - Sqrt[17])])/2)*((2 - I*Sqrt[2*(7 + Sqrt[17])])/2 + x))/(((2 + I*Sqrt[2*(7 - Sqrt[17])])/2 + (-2 + I*Sqrt[2*(7 + Sqrt[17])])/2)*((2 - I*Sqrt[2*(7 - Sqrt[17])])/2 + x))]*Sqrt[(((-2 + I*Sqrt[2*(7 - Sqrt[17])])/2 + (2 + I*Sqrt[2*(7 - Sqrt[17])])/2)*((2 + I*Sqrt[2*(7 + Sqrt[17])])/2 + x))/(((2 + I*Sqrt[2*(7 - Sqrt[17])])/2 + (-2 - I*Sqrt[2*(7 + Sqrt[17])])/2)*((2 - I*Sqrt[2*(7 - Sqrt[17])])/2 + x))]*EllipticF[ArcSin[Sqrt[(((2 - I*Sqrt[2*(7 - Sqrt[17])])/2 + (-2 + I*Sqrt[2*(7 + Sqrt[17])])/2)*((2 + I*Sqrt[2*(7 - Sqrt[17])])/2 + x))/(((2 + I*Sqrt[2*(7 - Sqrt[17])])/2 + (-2 + I*Sqrt[2*(7 + Sqrt[17])])/2)*((2 - I*Sqrt[2*(7 - Sqrt[17])])/2 + x))]], (((-2 - I*Sqrt[2*(7 - Sqrt[17])])/2 + (2 - I*Sqrt[2*(7 + Sqrt[17])])/2)*((-2 + I*Sqrt[2*(7 - Sqrt[17])])/2 + (2 + I*Sqrt[2*(7 + Sqrt[17])])/2))/(((-2 + I*Sqrt[2*(7 - Sqrt[17])])/2 + (2 - I*Sqrt[2*(7 + Sqrt[17])])/2)*((-2 - I*Sqrt[2*(7 - Sqrt[17])])/2 + (2 + I*Sqrt[2*(7 + Sqrt[17])])/2))])/(((-2 + I*Sqrt[2*(7 - Sqrt[17])])/2 + (2 + I*Sqrt[2*(7 - Sqrt[17])])/2)*((2 - I*Sqrt[2*(7 - Sqrt[17])])/2 + (-2 + I*Sqrt[2*(7 + Sqrt[17])])/2)*Sqrt[16 + 18*x + 13*x^2 + 4*x^3 + x^4]) + (2*Sqrt[(2*(7 - Sqrt[17]))/(Sqrt[7 - Sqrt[17]] + Sqrt[7 + Sqrt[17]])]*((-2 - I*Sqrt[2*(7 - Sqrt[17])])/2 + (2 - I*Sqrt[2*(7 + Sqrt[17])])/2)*Sqrt[((Sqrt[7 - Sqrt[17]] - Sqrt[7 + Sqrt[17]])*(-2*I + Sqrt[2*(7 - Sqrt[17])] - (2*I)*x))/(2*I + Sqrt[2*(7 - Sqrt[17])] + (2*I)*x)]*((2 - I*Sqrt[2*(7 - Sqrt[17])])/2 + x)^2*Sqrt[(I*((2 - I*Sqrt[2*(7 + Sqrt[17])])/2 + x))/(((2 + I*Sqrt[2*(7 - Sqrt[17])])/2 + (-2 + I*Sqrt[2*(7 + Sqrt[17])])/2)*((2 - I*Sqrt[2*(7 - Sqrt[17])])/2 + x))]*Sqrt[(I*((2 + I*Sqrt[2*(7 + Sqrt[17])])/2 + x))/(((2 + I*Sqrt[2*(7 - Sqrt[17])])/2 + (-2 - I*Sqrt[2*(7 + Sqrt[17])])/2)*((2 - I*Sqrt[2*(7 - Sqrt[17])])/2 + x))]*(((2 - I*Sqrt[2*(7 - Sqrt[17])])*EllipticF[ArcSin[Sqrt[((Sqrt[7 - Sqrt[17]] - Sqrt[7 + Sqrt[17]])*(-2*I + Sqrt[2*(7 - Sqrt[17])] - (2*I)*x))/((Sqrt[7 - Sqrt[17]] + Sqrt[7 + Sqrt[17]])*(2*I + Sqrt[2*(7 - Sqrt[17])] + (2*I)*x))]], (Sqrt[7 - Sqrt[17]] + Sqrt[7 + Sqrt[17]])^2/(Sqrt[7 - Sqrt[17]] - Sqrt[7 + Sqrt[17]])^2])/2 + I*Sqrt[2*(7 - Sqrt[17])]*EllipticPi[((2 + I*Sqrt[2*(7 - Sqrt[17])])/2 + (-2 + I*Sqrt[2*(7 + Sqrt[17])])/2)/((2 - I*Sqrt[2*(7 - Sqrt[17])])/2 + (-2 + I*Sqrt[2*(7 + Sqrt[17])])/2), ArcSin[Sqrt[((Sqrt[7 - Sqrt[17]] - Sqrt[7 + Sqrt[17]])*(-2*I + Sqrt[2*(7 - Sqrt[17])] - (2*I)*x))/((Sqrt[7 - Sqrt[17]] + Sqrt[7 + Sqrt[17]])*(2*I + Sqrt[2*(7 - Sqrt[17])] + (2*I)*x))]], (Sqrt[7 - Sqrt[17]] + Sqrt[7 + Sqrt[17]])^2/(Sqrt[7 - Sqrt[17]] - Sqrt[7 + Sqrt[17]])^2]))/(((-2 + I*Sqrt[2*(7 - Sqrt[17])])/2 + (2 + I*Sqrt[2*(7 - Sqrt[17])])/2)*((-2 + I*Sqrt[2*(7 - Sqrt[17])])/2 + (2 - I*Sqrt[2*(7 + Sqrt[17])])/2)*Sqrt[16 + 18*x + 13*x^2 + 4*x^3 + x^4])","C",0
509,0,0,39,0.3266175,"\int \frac{\sqrt{-1+x^5} \left(2+3 x^5\right)}{x^2 \left(-1-a x^2+x^5\right)} \, dx","Integrate[(Sqrt[-1 + x^5]*(2 + 3*x^5))/(x^2*(-1 - a*x^2 + x^5)),x]","\int \frac{\sqrt{-1+x^5} \left(2+3 x^5\right)}{x^2 \left(-1-a x^2+x^5\right)} \, dx","\frac{2 \sqrt{x^5-1}}{x}-2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{x^5-1}}\right)",1,"Integrate[(Sqrt[-1 + x^5]*(2 + 3*x^5))/(x^2*(-1 - a*x^2 + x^5)), x]","F",-1
510,1,44,39,0.027714,"\int x \sqrt{-x+x^6} \, dx","Integrate[x*Sqrt[-x + x^6],x]","\frac{\sqrt{x \left(x^5-1\right)} \left(x^{5/2}+\frac{\sin ^{-1}\left(x^{5/2}\right)}{\sqrt{1-x^5}}\right)}{5 \sqrt{x}}","\frac{1}{5} x^2 \sqrt{x^6-x}-\frac{1}{5} \tanh ^{-1}\left(\frac{x^3}{\sqrt{x^6-x}}\right)",1,"(Sqrt[x*(-1 + x^5)]*(x^(5/2) + ArcSin[x^(5/2)]/Sqrt[1 - x^5]))/(5*Sqrt[x])","A",1
511,0,0,39,0.6537285,"\int \frac{\left(1+x^5\right) \left(-1+4 x^5\right)}{x \left(1-a x+x^5\right) \sqrt{x+x^6}} \, dx","Integrate[((1 + x^5)*(-1 + 4*x^5))/(x*(1 - a*x + x^5)*Sqrt[x + x^6]),x]","\int \frac{\left(1+x^5\right) \left(-1+4 x^5\right)}{x \left(1-a x+x^5\right) \sqrt{x+x^6}} \, dx","\frac{2 \sqrt{x^6+x}}{x}-2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{x^6+x}}\right)",1,"Integrate[((1 + x^5)*(-1 + 4*x^5))/(x*(1 - a*x + x^5)*Sqrt[x + x^6]), x]","F",-1
512,1,39,39,0.0178473,"\int \frac{1}{\sqrt{x-\sqrt{-1+x^2}}} \, dx","Integrate[1/Sqrt[x - Sqrt[-1 + x^2]],x]","\sqrt{x-\sqrt{x^2-1}}+\frac{1}{3 \left(x-\sqrt{x^2-1}\right)^{3/2}}","\sqrt{x-\sqrt{x^2-1}}+\frac{1}{3 \left(x-\sqrt{x^2-1}\right)^{3/2}}",1,"1/(3*(x - Sqrt[-1 + x^2])^(3/2)) + Sqrt[x - Sqrt[-1 + x^2]]","A",1
513,1,215,40,0.9662504,"\int \frac{1+x^2}{\left(-1+2 x+x^2\right) \sqrt{-x-x^2+x^3}} \, dx","Integrate[(1 + x^2)/((-1 + 2*x + x^2)*Sqrt[-x - x^2 + x^3]),x]","-\frac{2 i \sqrt{\frac{2}{\sqrt{5}-1}} \sqrt{-\frac{1}{x^2}-\frac{1}{x}+1} x^{3/2} \left(F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{1+\sqrt{5}}}}{\sqrt{x}}\right)|-\frac{3}{2}-\frac{\sqrt{5}}{2}\right)-\Pi \left(-\frac{1}{2} \left(-1+\sqrt{2}\right) \left(1+\sqrt{5}\right);i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{1+\sqrt{5}}}}{\sqrt{x}}\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)-\Pi \left(\frac{1}{2} \left(1+\sqrt{2}\right) \left(1+\sqrt{5}\right);i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{1+\sqrt{5}}}}{\sqrt{x}}\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)\right)}{\sqrt{x \left(x^2-x-1\right)}}","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{3} \sqrt{x^3-x^2-x}}{x^2-x-1}\right)}{\sqrt{3}}",1,"((-2*I)*Sqrt[2/(-1 + Sqrt[5])]*Sqrt[1 - x^(-2) - x^(-1)]*x^(3/2)*(EllipticF[I*ArcSinh[Sqrt[2/(1 + Sqrt[5])]/Sqrt[x]], -3/2 - Sqrt[5]/2] - EllipticPi[-1/2*((-1 + Sqrt[2])*(1 + Sqrt[5])), I*ArcSinh[Sqrt[2/(1 + Sqrt[5])]/Sqrt[x]], (-3 - Sqrt[5])/2] - EllipticPi[((1 + Sqrt[2])*(1 + Sqrt[5]))/2, I*ArcSinh[Sqrt[2/(1 + Sqrt[5])]/Sqrt[x]], (-3 - Sqrt[5])/2]))/Sqrt[x*(-1 - x + x^2)]","C",0
514,1,1451,40,2.9514111,"\int \frac{\left(2+x^3\right) \sqrt{-1+x^2+x^3}}{\left(-1+x^3\right)^2} \, dx","Integrate[((2 + x^3)*Sqrt[-1 + x^2 + x^3])/(-1 + x^3)^2,x]","\frac{-\frac{x \left(x^3+x^2-1\right)}{x^3-1}+\frac{F\left(\sin ^{-1}\left(\sqrt{\frac{\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]-x}{-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,2\right]+\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]}}\right)|\frac{\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,2\right]-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]}{\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,1\right]-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]}\right) \left(x-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]\right) \sqrt{\frac{\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,1\right]-x}{\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,1\right]-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]}} \sqrt{\frac{\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,2\right]-x}{\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,2\right]-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]}}}{\sqrt{\frac{x-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]}{\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,2\right]-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]}}}-\frac{2 (-1)^{2/3} \Pi \left(\frac{\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,2\right]-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]}{(-1)^{2/3}-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]};\sin ^{-1}\left(\sqrt{\frac{\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]-x}{-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,2\right]+\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]}}\right)|\frac{\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,2\right]-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]}{\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,1\right]-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]}\right) \sqrt{\frac{\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,1\right]-x}{\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,1\right]-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]}} \sqrt{-\frac{\left(x-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,2\right]\right) \left(x-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]\right)}{\left(\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,2\right]-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]\right)^2}} \left(-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,2\right]+\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]\right)}{1-i \sqrt{3}+2 \text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]}+\frac{3 (-1)^{2/3} \Pi \left(\frac{-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,2\right]+\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]}{\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]};\sin ^{-1}\left(\sqrt{\frac{\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]-x}{-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,2\right]+\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]}}\right)|\frac{\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,2\right]-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]}{\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,1\right]-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]}\right) \sqrt{\frac{\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,1\right]-x}{\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,1\right]-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]}} \sqrt{-\frac{\left(x-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,2\right]\right) \left(x-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]\right)}{\left(\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,2\right]-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]\right)^2}} \left(-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,2\right]+\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]\right)}{\left(1+\sqrt[3]{-1}\right)^2 \left(\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]\right)}-\frac{\Pi \left(\frac{-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,2\right]+\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]}{-1+\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]};\sin ^{-1}\left(\sqrt{\frac{\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]-x}{-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,2\right]+\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]}}\right)|\frac{\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,2\right]-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]}{\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,1\right]-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]}\right) \sqrt{\frac{\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,1\right]-x}{\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,1\right]-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]}} \sqrt{-\frac{\left(x-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,2\right]\right) \left(x-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]\right)}{\left(\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,2\right]-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]\right)^2}} \left(-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,2\right]+\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]\right)}{-1+\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2-1\&,3\right]}}{\sqrt{x^3+x^2-1}}","-\frac{\sqrt{x^3+x^2-1} x}{x^3-1}-\tanh ^{-1}\left(\frac{x}{\sqrt{x^3+x^2-1}}\right)",1,"(-((x*(-1 + x^2 + x^3))/(-1 + x^3)) + (EllipticF[ArcSin[Sqrt[(-x + Root[-1 + #1^2 + #1^3 & , 3, 0])/(-Root[-1 + #1^2 + #1^3 & , 2, 0] + Root[-1 + #1^2 + #1^3 & , 3, 0])]], (Root[-1 + #1^2 + #1^3 & , 2, 0] - Root[-1 + #1^2 + #1^3 & , 3, 0])/(Root[-1 + #1^2 + #1^3 & , 1, 0] - Root[-1 + #1^2 + #1^3 & , 3, 0])]*(x - Root[-1 + #1^2 + #1^3 & , 3, 0])*Sqrt[(-x + Root[-1 + #1^2 + #1^3 & , 1, 0])/(Root[-1 + #1^2 + #1^3 & , 1, 0] - Root[-1 + #1^2 + #1^3 & , 3, 0])]*Sqrt[(-x + Root[-1 + #1^2 + #1^3 & , 2, 0])/(Root[-1 + #1^2 + #1^3 & , 2, 0] - Root[-1 + #1^2 + #1^3 & , 3, 0])])/Sqrt[(x - Root[-1 + #1^2 + #1^3 & , 3, 0])/(Root[-1 + #1^2 + #1^3 & , 2, 0] - Root[-1 + #1^2 + #1^3 & , 3, 0])] - (EllipticPi[(-Root[-1 + #1^2 + #1^3 & , 2, 0] + Root[-1 + #1^2 + #1^3 & , 3, 0])/(-1 + Root[-1 + #1^2 + #1^3 & , 3, 0]), ArcSin[Sqrt[(-x + Root[-1 + #1^2 + #1^3 & , 3, 0])/(-Root[-1 + #1^2 + #1^3 & , 2, 0] + Root[-1 + #1^2 + #1^3 & , 3, 0])]], (Root[-1 + #1^2 + #1^3 & , 2, 0] - Root[-1 + #1^2 + #1^3 & , 3, 0])/(Root[-1 + #1^2 + #1^3 & , 1, 0] - Root[-1 + #1^2 + #1^3 & , 3, 0])]*Sqrt[(-x + Root[-1 + #1^2 + #1^3 & , 1, 0])/(Root[-1 + #1^2 + #1^3 & , 1, 0] - Root[-1 + #1^2 + #1^3 & , 3, 0])]*Sqrt[-(((x - Root[-1 + #1^2 + #1^3 & , 2, 0])*(x - Root[-1 + #1^2 + #1^3 & , 3, 0]))/(Root[-1 + #1^2 + #1^3 & , 2, 0] - Root[-1 + #1^2 + #1^3 & , 3, 0])^2)]*(-Root[-1 + #1^2 + #1^3 & , 2, 0] + Root[-1 + #1^2 + #1^3 & , 3, 0]))/(-1 + Root[-1 + #1^2 + #1^3 & , 3, 0]) + (3*(-1)^(2/3)*EllipticPi[(-Root[-1 + #1^2 + #1^3 & , 2, 0] + Root[-1 + #1^2 + #1^3 & , 3, 0])/((-1)^(1/3) + Root[-1 + #1^2 + #1^3 & , 3, 0]), ArcSin[Sqrt[(-x + Root[-1 + #1^2 + #1^3 & , 3, 0])/(-Root[-1 + #1^2 + #1^3 & , 2, 0] + Root[-1 + #1^2 + #1^3 & , 3, 0])]], (Root[-1 + #1^2 + #1^3 & , 2, 0] - Root[-1 + #1^2 + #1^3 & , 3, 0])/(Root[-1 + #1^2 + #1^3 & , 1, 0] - Root[-1 + #1^2 + #1^3 & , 3, 0])]*Sqrt[(-x + Root[-1 + #1^2 + #1^3 & , 1, 0])/(Root[-1 + #1^2 + #1^3 & , 1, 0] - Root[-1 + #1^2 + #1^3 & , 3, 0])]*Sqrt[-(((x - Root[-1 + #1^2 + #1^3 & , 2, 0])*(x - Root[-1 + #1^2 + #1^3 & , 3, 0]))/(Root[-1 + #1^2 + #1^3 & , 2, 0] - Root[-1 + #1^2 + #1^3 & , 3, 0])^2)]*(-Root[-1 + #1^2 + #1^3 & , 2, 0] + Root[-1 + #1^2 + #1^3 & , 3, 0]))/((1 + (-1)^(1/3))^2*((-1)^(1/3) + Root[-1 + #1^2 + #1^3 & , 3, 0])) - (2*(-1)^(2/3)*EllipticPi[(Root[-1 + #1^2 + #1^3 & , 2, 0] - Root[-1 + #1^2 + #1^3 & , 3, 0])/((-1)^(2/3) - Root[-1 + #1^2 + #1^3 & , 3, 0]), ArcSin[Sqrt[(-x + Root[-1 + #1^2 + #1^3 & , 3, 0])/(-Root[-1 + #1^2 + #1^3 & , 2, 0] + Root[-1 + #1^2 + #1^3 & , 3, 0])]], (Root[-1 + #1^2 + #1^3 & , 2, 0] - Root[-1 + #1^2 + #1^3 & , 3, 0])/(Root[-1 + #1^2 + #1^3 & , 1, 0] - Root[-1 + #1^2 + #1^3 & , 3, 0])]*Sqrt[(-x + Root[-1 + #1^2 + #1^3 & , 1, 0])/(Root[-1 + #1^2 + #1^3 & , 1, 0] - Root[-1 + #1^2 + #1^3 & , 3, 0])]*Sqrt[-(((x - Root[-1 + #1^2 + #1^3 & , 2, 0])*(x - Root[-1 + #1^2 + #1^3 & , 3, 0]))/(Root[-1 + #1^2 + #1^3 & , 2, 0] - Root[-1 + #1^2 + #1^3 & , 3, 0])^2)]*(-Root[-1 + #1^2 + #1^3 & , 2, 0] + Root[-1 + #1^2 + #1^3 & , 3, 0]))/(1 - I*Sqrt[3] + 2*Root[-1 + #1^2 + #1^3 & , 3, 0]))/Sqrt[-1 + x^2 + x^3]","C",0
515,1,173,40,0.705649,"\int \frac{2+x^2}{\left(-2+x^2\right) \sqrt{-2 x+2 x^2+x^3}} \, dx","Integrate[(2 + x^2)/((-2 + x^2)*Sqrt[-2*x + 2*x^2 + x^3]),x]","-\frac{2 i \sqrt{-\frac{2}{x^2}+\frac{2}{x}+1} x^{3/2} \left(F\left(i \sinh ^{-1}\left(\frac{\sqrt{1+\sqrt{3}}}{\sqrt{x}}\right)|-2+\sqrt{3}\right)-\Pi \left(-\sqrt{\frac{3}{2}}+\frac{1}{\sqrt{2}};i \sinh ^{-1}\left(\frac{\sqrt{1+\sqrt{3}}}{\sqrt{x}}\right)|-2+\sqrt{3}\right)-\Pi \left(\frac{-1+\sqrt{3}}{\sqrt{2}};i \sinh ^{-1}\left(\frac{\sqrt{1+\sqrt{3}}}{\sqrt{x}}\right)|-2+\sqrt{3}\right)\right)}{\sqrt{1+\sqrt{3}} \sqrt{x \left(x^2+2 x-2\right)}}","-\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{x^3+2 x^2-2 x}}{x^2+2 x-2}\right)",1,"((-2*I)*Sqrt[1 - 2/x^2 + 2/x]*x^(3/2)*(EllipticF[I*ArcSinh[Sqrt[1 + Sqrt[3]]/Sqrt[x]], -2 + Sqrt[3]] - EllipticPi[-Sqrt[3/2] + 1/Sqrt[2], I*ArcSinh[Sqrt[1 + Sqrt[3]]/Sqrt[x]], -2 + Sqrt[3]] - EllipticPi[(-1 + Sqrt[3])/Sqrt[2], I*ArcSinh[Sqrt[1 + Sqrt[3]]/Sqrt[x]], -2 + Sqrt[3]]))/(Sqrt[1 + Sqrt[3]]*Sqrt[x*(-2 + 2*x + x^2)])","C",0
516,1,1015,40,1.0520659,"\int \frac{2+x}{(-1+x) \sqrt{-1+3 x+a x^2+x^3}} \, dx","Integrate[(2 + x)/((-1 + x)*Sqrt[-1 + 3*x + a*x^2 + x^3]),x]","\frac{2 \sqrt{\frac{-x+\text{Root}\left[\text{$\#$1}^3+(a+3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}+a+3\&,1\right]+1}{\text{Root}\left[\text{$\#$1}^3+(a+3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}+a+3\&,1\right]-\text{Root}\left[\text{$\#$1}^3+(a+3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}+a+3\&,3\right]}} \left(\frac{F\left(\sin ^{-1}\left(\sqrt{\frac{-x+\text{Root}\left[\text{$\#$1}^3+(a+3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}+a+3\&,3\right]+1}{\text{Root}\left[\text{$\#$1}^3+(a+3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}+a+3\&,3\right]-\text{Root}\left[\text{$\#$1}^3+(a+3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}+a+3\&,2\right]}}\right)|\frac{\text{Root}\left[\text{$\#$1}^3+(a+3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}+a+3\&,2\right]-\text{Root}\left[\text{$\#$1}^3+(a+3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}+a+3\&,3\right]}{\text{Root}\left[\text{$\#$1}^3+(a+3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}+a+3\&,1\right]-\text{Root}\left[\text{$\#$1}^3+(a+3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}+a+3\&,3\right]}\right) \sqrt{\frac{-x+\text{Root}\left[\text{$\#$1}^3+(a+3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}+a+3\&,2\right]+1}{\text{Root}\left[\text{$\#$1}^3+(a+3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}+a+3\&,2\right]-\text{Root}\left[\text{$\#$1}^3+(a+3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}+a+3\&,3\right]}} \left(x-\text{Root}\left[\text{$\#$1}^3+(a+3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}+a+3\&,3\right]-1\right)}{\sqrt{\frac{-x+\text{Root}\left[\text{$\#$1}^3+(a+3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}+a+3\&,3\right]+1}{\text{Root}\left[\text{$\#$1}^3+(a+3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}+a+3\&,3\right]-\text{Root}\left[\text{$\#$1}^3+(a+3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}+a+3\&,2\right]}}}+\frac{3 \Pi \left(1-\frac{\text{Root}\left[\text{$\#$1}^3+(a+3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}+a+3\&,2\right]}{\text{Root}\left[\text{$\#$1}^3+(a+3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}+a+3\&,3\right]};\sin ^{-1}\left(\sqrt{\frac{-x+\text{Root}\left[\text{$\#$1}^3+(a+3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}+a+3\&,3\right]+1}{\text{Root}\left[\text{$\#$1}^3+(a+3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}+a+3\&,3\right]-\text{Root}\left[\text{$\#$1}^3+(a+3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}+a+3\&,2\right]}}\right)|\frac{\text{Root}\left[\text{$\#$1}^3+(a+3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}+a+3\&,2\right]-\text{Root}\left[\text{$\#$1}^3+(a+3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}+a+3\&,3\right]}{\text{Root}\left[\text{$\#$1}^3+(a+3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}+a+3\&,1\right]-\text{Root}\left[\text{$\#$1}^3+(a+3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}+a+3\&,3\right]}\right) \sqrt{-\frac{\left(x-\text{Root}\left[\text{$\#$1}^3+(a+3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}+a+3\&,2\right]-1\right) \left(x-\text{Root}\left[\text{$\#$1}^3+(a+3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}+a+3\&,3\right]-1\right)}{\left(\text{Root}\left[\text{$\#$1}^3+(a+3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}+a+3\&,2\right]-\text{Root}\left[\text{$\#$1}^3+(a+3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}+a+3\&,3\right]\right)^2}} \left(\text{Root}\left[\text{$\#$1}^3+(a+3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}+a+3\&,2\right]-\text{Root}\left[\text{$\#$1}^3+(a+3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}+a+3\&,3\right]\right)}{\text{Root}\left[\text{$\#$1}^3+(a+3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}+a+3\&,3\right]}\right)}{\sqrt{x^3+a x^2+3 x-1}}","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{-a-3} x}{\sqrt{a x^2+x^3+3 x-1}}\right)}{\sqrt{-a-3}}",1,"(2*Sqrt[(1 - x + Root[3 + a + (6 + 2*a)*#1 + (3 + a)*#1^2 + #1^3 & , 1])/(Root[3 + a + (6 + 2*a)*#1 + (3 + a)*#1^2 + #1^3 & , 1] - Root[3 + a + (6 + 2*a)*#1 + (3 + a)*#1^2 + #1^3 & , 3])]*((3*EllipticPi[1 - Root[3 + a + (6 + 2*a)*#1 + (3 + a)*#1^2 + #1^3 & , 2]/Root[3 + a + (6 + 2*a)*#1 + (3 + a)*#1^2 + #1^3 & , 3], ArcSin[Sqrt[(1 - x + Root[3 + a + (6 + 2*a)*#1 + (3 + a)*#1^2 + #1^3 & , 3])/(-Root[3 + a + (6 + 2*a)*#1 + (3 + a)*#1^2 + #1^3 & , 2] + Root[3 + a + (6 + 2*a)*#1 + (3 + a)*#1^2 + #1^3 & , 3])]], (Root[3 + a + (6 + 2*a)*#1 + (3 + a)*#1^2 + #1^3 & , 2] - Root[3 + a + (6 + 2*a)*#1 + (3 + a)*#1^2 + #1^3 & , 3])/(Root[3 + a + (6 + 2*a)*#1 + (3 + a)*#1^2 + #1^3 & , 1] - Root[3 + a + (6 + 2*a)*#1 + (3 + a)*#1^2 + #1^3 & , 3])]*Sqrt[-(((-1 + x - Root[3 + a + (6 + 2*a)*#1 + (3 + a)*#1^2 + #1^3 & , 2])*(-1 + x - Root[3 + a + (6 + 2*a)*#1 + (3 + a)*#1^2 + #1^3 & , 3]))/(Root[3 + a + (6 + 2*a)*#1 + (3 + a)*#1^2 + #1^3 & , 2] - Root[3 + a + (6 + 2*a)*#1 + (3 + a)*#1^2 + #1^3 & , 3])^2)]*(Root[3 + a + (6 + 2*a)*#1 + (3 + a)*#1^2 + #1^3 & , 2] - Root[3 + a + (6 + 2*a)*#1 + (3 + a)*#1^2 + #1^3 & , 3]))/Root[3 + a + (6 + 2*a)*#1 + (3 + a)*#1^2 + #1^3 & , 3] + (EllipticF[ArcSin[Sqrt[(1 - x + Root[3 + a + (6 + 2*a)*#1 + (3 + a)*#1^2 + #1^3 & , 3])/(-Root[3 + a + (6 + 2*a)*#1 + (3 + a)*#1^2 + #1^3 & , 2] + Root[3 + a + (6 + 2*a)*#1 + (3 + a)*#1^2 + #1^3 & , 3])]], (Root[3 + a + (6 + 2*a)*#1 + (3 + a)*#1^2 + #1^3 & , 2] - Root[3 + a + (6 + 2*a)*#1 + (3 + a)*#1^2 + #1^3 & , 3])/(Root[3 + a + (6 + 2*a)*#1 + (3 + a)*#1^2 + #1^3 & , 1] - Root[3 + a + (6 + 2*a)*#1 + (3 + a)*#1^2 + #1^3 & , 3])]*(-1 + x - Root[3 + a + (6 + 2*a)*#1 + (3 + a)*#1^2 + #1^3 & , 3])*Sqrt[(1 - x + Root[3 + a + (6 + 2*a)*#1 + (3 + a)*#1^2 + #1^3 & , 2])/(Root[3 + a + (6 + 2*a)*#1 + (3 + a)*#1^2 + #1^3 & , 2] - Root[3 + a + (6 + 2*a)*#1 + (3 + a)*#1^2 + #1^3 & , 3])])/Sqrt[(1 - x + Root[3 + a + (6 + 2*a)*#1 + (3 + a)*#1^2 + #1^3 & , 3])/(-Root[3 + a + (6 + 2*a)*#1 + (3 + a)*#1^2 + #1^3 & , 2] + Root[3 + a + (6 + 2*a)*#1 + (3 + a)*#1^2 + #1^3 & , 3])]))/Sqrt[-1 + 3*x + a*x^2 + x^3]","C",0
517,1,824,40,0.7611535,"\int \frac{-2+x}{(1+x) \sqrt{1+3 x+a x^2+x^3}} \, dx","Integrate[(-2 + x)/((1 + x)*Sqrt[1 + 3*x + a*x^2 + x^3]),x]","\frac{2 \sqrt{-\frac{\left(x-\text{Root}\left[\text{$\#$1}^3+(a-3) \text{$\#$1}^2+(6-2 a) \text{$\#$1}+a-3\&,2\right]+1\right) \left(x-\text{Root}\left[\text{$\#$1}^3+(a-3) \text{$\#$1}^2+(6-2 a) \text{$\#$1}+a-3\&,3\right]+1\right)}{\left(\text{Root}\left[\text{$\#$1}^3+(a-3) \text{$\#$1}^2+(6-2 a) \text{$\#$1}+a-3\&,2\right]-\text{Root}\left[\text{$\#$1}^3+(a-3) \text{$\#$1}^2+(6-2 a) \text{$\#$1}+a-3\&,3\right]\right)^2}} \left(\text{Root}\left[\text{$\#$1}^3+(a-3) \text{$\#$1}^2+(6-2 a) \text{$\#$1}+a-3\&,2\right]-\text{Root}\left[\text{$\#$1}^3+(a-3) \text{$\#$1}^2+(6-2 a) \text{$\#$1}+a-3\&,3\right]\right) \sqrt{\frac{x-\text{Root}\left[\text{$\#$1}^3+(a-3) \text{$\#$1}^2+(6-2 a) \text{$\#$1}+a-3\&,1\right]+1}{\text{Root}\left[\text{$\#$1}^3+(a-3) \text{$\#$1}^2+(6-2 a) \text{$\#$1}+a-3\&,3\right]-\text{Root}\left[\text{$\#$1}^3+(a-3) \text{$\#$1}^2+(6-2 a) \text{$\#$1}+a-3\&,1\right]}} \left(F\left(\sin ^{-1}\left(\sqrt{\frac{x-\text{Root}\left[\text{$\#$1}^3+(a-3) \text{$\#$1}^2+(6-2 a) \text{$\#$1}+a-3\&,3\right]+1}{\text{Root}\left[\text{$\#$1}^3+(a-3) \text{$\#$1}^2+(6-2 a) \text{$\#$1}+a-3\&,2\right]-\text{Root}\left[\text{$\#$1}^3+(a-3) \text{$\#$1}^2+(6-2 a) \text{$\#$1}+a-3\&,3\right]}}\right)|\frac{\text{Root}\left[\text{$\#$1}^3+(a-3) \text{$\#$1}^2+(6-2 a) \text{$\#$1}+a-3\&,2\right]-\text{Root}\left[\text{$\#$1}^3+(a-3) \text{$\#$1}^2+(6-2 a) \text{$\#$1}+a-3\&,3\right]}{\text{Root}\left[\text{$\#$1}^3+(a-3) \text{$\#$1}^2+(6-2 a) \text{$\#$1}+a-3\&,1\right]-\text{Root}\left[\text{$\#$1}^3+(a-3) \text{$\#$1}^2+(6-2 a) \text{$\#$1}+a-3\&,3\right]}\right) \text{Root}\left[\text{$\#$1}^3+(a-3) \text{$\#$1}^2+(6-2 a) \text{$\#$1}+a-3\&,3\right]-3 \Pi \left(1-\frac{\text{Root}\left[\text{$\#$1}^3+(a-3) \text{$\#$1}^2+(6-2 a) \text{$\#$1}+a-3\&,2\right]}{\text{Root}\left[\text{$\#$1}^3+(a-3) \text{$\#$1}^2+(6-2 a) \text{$\#$1}+a-3\&,3\right]};\sin ^{-1}\left(\sqrt{\frac{x-\text{Root}\left[\text{$\#$1}^3+(a-3) \text{$\#$1}^2+(6-2 a) \text{$\#$1}+a-3\&,3\right]+1}{\text{Root}\left[\text{$\#$1}^3+(a-3) \text{$\#$1}^2+(6-2 a) \text{$\#$1}+a-3\&,2\right]-\text{Root}\left[\text{$\#$1}^3+(a-3) \text{$\#$1}^2+(6-2 a) \text{$\#$1}+a-3\&,3\right]}}\right)|\frac{\text{Root}\left[\text{$\#$1}^3+(a-3) \text{$\#$1}^2+(6-2 a) \text{$\#$1}+a-3\&,2\right]-\text{Root}\left[\text{$\#$1}^3+(a-3) \text{$\#$1}^2+(6-2 a) \text{$\#$1}+a-3\&,3\right]}{\text{Root}\left[\text{$\#$1}^3+(a-3) \text{$\#$1}^2+(6-2 a) \text{$\#$1}+a-3\&,1\right]-\text{Root}\left[\text{$\#$1}^3+(a-3) \text{$\#$1}^2+(6-2 a) \text{$\#$1}+a-3\&,3\right]}\right)\right)}{\sqrt{x^3+a x^2+3 x+1} \text{Root}\left[\text{$\#$1}^3+(a-3) \text{$\#$1}^2+(6-2 a) \text{$\#$1}+a-3\&,3\right]}","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{3-a} x}{\sqrt{a x^2+x^3+3 x+1}}\right)}{\sqrt{3-a}}",1,"(2*Sqrt[-(((1 + x - Root[-3 + a + (6 - 2*a)*#1 + (-3 + a)*#1^2 + #1^3 & , 2])*(1 + x - Root[-3 + a + (6 - 2*a)*#1 + (-3 + a)*#1^2 + #1^3 & , 3]))/(Root[-3 + a + (6 - 2*a)*#1 + (-3 + a)*#1^2 + #1^3 & , 2] - Root[-3 + a + (6 - 2*a)*#1 + (-3 + a)*#1^2 + #1^3 & , 3])^2)]*(Root[-3 + a + (6 - 2*a)*#1 + (-3 + a)*#1^2 + #1^3 & , 2] - Root[-3 + a + (6 - 2*a)*#1 + (-3 + a)*#1^2 + #1^3 & , 3])*Sqrt[(1 + x - Root[-3 + a + (6 - 2*a)*#1 + (-3 + a)*#1^2 + #1^3 & , 1])/(-Root[-3 + a + (6 - 2*a)*#1 + (-3 + a)*#1^2 + #1^3 & , 1] + Root[-3 + a + (6 - 2*a)*#1 + (-3 + a)*#1^2 + #1^3 & , 3])]*(-3*EllipticPi[1 - Root[-3 + a + (6 - 2*a)*#1 + (-3 + a)*#1^2 + #1^3 & , 2]/Root[-3 + a + (6 - 2*a)*#1 + (-3 + a)*#1^2 + #1^3 & , 3], ArcSin[Sqrt[(1 + x - Root[-3 + a + (6 - 2*a)*#1 + (-3 + a)*#1^2 + #1^3 & , 3])/(Root[-3 + a + (6 - 2*a)*#1 + (-3 + a)*#1^2 + #1^3 & , 2] - Root[-3 + a + (6 - 2*a)*#1 + (-3 + a)*#1^2 + #1^3 & , 3])]], (Root[-3 + a + (6 - 2*a)*#1 + (-3 + a)*#1^2 + #1^3 & , 2] - Root[-3 + a + (6 - 2*a)*#1 + (-3 + a)*#1^2 + #1^3 & , 3])/(Root[-3 + a + (6 - 2*a)*#1 + (-3 + a)*#1^2 + #1^3 & , 1] - Root[-3 + a + (6 - 2*a)*#1 + (-3 + a)*#1^2 + #1^3 & , 3])] + EllipticF[ArcSin[Sqrt[(1 + x - Root[-3 + a + (6 - 2*a)*#1 + (-3 + a)*#1^2 + #1^3 & , 3])/(Root[-3 + a + (6 - 2*a)*#1 + (-3 + a)*#1^2 + #1^3 & , 2] - Root[-3 + a + (6 - 2*a)*#1 + (-3 + a)*#1^2 + #1^3 & , 3])]], (Root[-3 + a + (6 - 2*a)*#1 + (-3 + a)*#1^2 + #1^3 & , 2] - Root[-3 + a + (6 - 2*a)*#1 + (-3 + a)*#1^2 + #1^3 & , 3])/(Root[-3 + a + (6 - 2*a)*#1 + (-3 + a)*#1^2 + #1^3 & , 1] - Root[-3 + a + (6 - 2*a)*#1 + (-3 + a)*#1^2 + #1^3 & , 3])]*Root[-3 + a + (6 - 2*a)*#1 + (-3 + a)*#1^2 + #1^3 & , 3]))/(Sqrt[1 + 3*x + a*x^2 + x^3]*Root[-3 + a + (6 - 2*a)*#1 + (-3 + a)*#1^2 + #1^3 & , 3])","C",1
518,1,2258,40,5.4454311,"\int \frac{x \left(3 a b-2 (a+b) x+x^2\right)}{\sqrt{x (-a+x) (-b+x)} \left(-a b d+(a+b) d x-d x^2+x^3\right)} \, dx","Integrate[(x*(3*a*b - 2*(a + b)*x + x^2))/(Sqrt[x*(-a + x)*(-b + x)]*(-(a*b*d) + (a + b)*d*x - d*x^2 + x^3)),x]","\text{Result too large to show}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{x^2 (-a-b)+a b x+x^3}}{x^2}\right)}{\sqrt{d}}",1,"((2*I)*x*Sqrt[1 - x/b]*(2*a^2*d*EllipticPi[a/Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 2], I*ArcSinh[Sqrt[-(x/a)]], a/b] + a*b*d*EllipticPi[a/Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 2], I*ArcSinh[Sqrt[-(x/a)]], a/b] + 2*b^2*d*EllipticPi[a/Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 2], I*ArcSinh[Sqrt[-(x/a)]], a/b] + 3*a*b*d*EllipticPi[a/Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 3], I*ArcSinh[Sqrt[-(x/a)]], a/b] + 3*a*b*(EllipticPi[a/Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 2], I*ArcSinh[Sqrt[-(x/a)]], a/b] - 2*EllipticPi[a/Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 3], I*ArcSinh[Sqrt[-(x/a)]], a/b])*Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 2] - EllipticPi[a/Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 2], I*ArcSinh[Sqrt[-(x/a)]], a/b]*Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 1]*Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 2]^2 + 3*a*b*(2*EllipticPi[a/Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 2], I*ArcSinh[Sqrt[-(x/a)]], a/b] - EllipticPi[a/Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 3], I*ArcSinh[Sqrt[-(x/a)]], a/b])*Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 3] - 2*(a + b)*(EllipticPi[a/Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 2], I*ArcSinh[Sqrt[-(x/a)]], a/b] + EllipticPi[a/Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 3], I*ArcSinh[Sqrt[-(x/a)]], a/b])*Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 1]*Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 3] - 2*(a + b)*(2*EllipticPi[a/Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 2], I*ArcSinh[Sqrt[-(x/a)]], a/b] - EllipticPi[a/Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 3], I*ArcSinh[Sqrt[-(x/a)]], a/b])*Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 2]*Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 3] + EllipticPi[a/Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 2], I*ArcSinh[Sqrt[-(x/a)]], a/b]*Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 2]^2*Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 3] + EllipticPi[a/Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 3], I*ArcSinh[Sqrt[-(x/a)]], a/b]*Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 1]*Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 3]^2 - EllipticPi[a/Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 3], I*ArcSinh[Sqrt[-(x/a)]], a/b]*Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 2]*Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 3]^2 + EllipticF[I*ArcSinh[Sqrt[-(x/a)]], a/b]*(-(d*(-3*a*b + a*d + b*d)) + 2*Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 1]*Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 2]^2 + 2*Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 1]^2*Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 3] + 2*Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 2]*Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 3]^2) + EllipticPi[a/Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 1], I*ArcSinh[Sqrt[-(x/a)]], a/b]*(d*(-2*a^2 + a*(-7*b + d) + b*(-2*b + d)) - d*Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 2]^2 + Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 2]^3 + (-3*a*b + 4*(a + b)*Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 1] - 2*Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 1]^2)*Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 3] - Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 1]*Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 3]^2 + Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 2]*(3*a*b + 2*(a + b)*Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 3] - Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 3]^2))))/(Sqrt[x/(-a + x)]*Sqrt[x*(-a + x)*(-b + x)]*(Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 1] - Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 2])*(Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 1] - Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 3])*(Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 2] - Root[-(a*b*d) + (a*d + b*d)*#1 - d*#1^2 + #1^3 & , 3]))","C",0
519,1,1418,40,4.3026415,"\int \frac{3 a b x-2 (a+b) x^2+x^3}{\sqrt{x (-a+x) (-b+x)} \left(-a b+(a+b) x-x^2+d x^3\right)} \, dx","Integrate[(3*a*b*x - 2*(a + b)*x^2 + x^3)/(Sqrt[x*(-a + x)*(-b + x)]*(-(a*b) + (a + b)*x - x^2 + d*x^3)),x]","-\frac{2 i x \sqrt{1-\frac{x}{b}} \left(F\left(i \sinh ^{-1}\left(\sqrt{-\frac{x}{a}}\right)|\frac{a}{b}\right) \left(-2 d^2 \text{Root}\left[d \text{$\#$1}^3-\text{$\#$1}^2+(a+b) \text{$\#$1}-a b\&,3\right] \text{Root}\left[d \text{$\#$1}^3-\text{$\#$1}^2+(a+b) \text{$\#$1}-a b\&,1\right]^2-2 d^2 \text{Root}\left[d \text{$\#$1}^3-\text{$\#$1}^2+(a+b) \text{$\#$1}-a b\&,2\right]^2 \text{Root}\left[d \text{$\#$1}^3-\text{$\#$1}^2+(a+b) \text{$\#$1}-a b\&,1\right]-2 d^2 \text{Root}\left[d \text{$\#$1}^3-\text{$\#$1}^2+(a+b) \text{$\#$1}-a b\&,2\right] \text{Root}\left[d \text{$\#$1}^3-\text{$\#$1}^2+(a+b) \text{$\#$1}-a b\&,3\right]^2+a+b-3 a b d\right)-\Pi \left(\frac{a}{\text{Root}\left[d \text{$\#$1}^3-\text{$\#$1}^2+(a+b) \text{$\#$1}-a b\&,1\right]};i \sinh ^{-1}\left(\sqrt{-\frac{x}{a}}\right)|\frac{a}{b}\right) \left(d^2 \text{Root}\left[d \text{$\#$1}^3-\text{$\#$1}^2+(a+b) \text{$\#$1}-a b\&,2\right]^3-d \text{Root}\left[d \text{$\#$1}^3-\text{$\#$1}^2+(a+b) \text{$\#$1}-a b\&,2\right]^2+d^2 \left(-\text{Root}\left[d \text{$\#$1}^3-\text{$\#$1}^2+(a+b) \text{$\#$1}-a b\&,3\right]^2+2 (a+b) \text{Root}\left[d \text{$\#$1}^3-\text{$\#$1}^2+(a+b) \text{$\#$1}-a b\&,3\right]+3 a b\right) \text{Root}\left[d \text{$\#$1}^3-\text{$\#$1}^2+(a+b) \text{$\#$1}-a b\&,2\right]-d^2 \text{Root}\left[d \text{$\#$1}^3-\text{$\#$1}^2+(a+b) \text{$\#$1}-a b\&,1\right] \text{Root}\left[d \text{$\#$1}^3-\text{$\#$1}^2+(a+b) \text{$\#$1}-a b\&,3\right]^2+a+b-2 a^2 d-2 b^2 d-7 a b d+d^2 \left(-2 \text{Root}\left[d \text{$\#$1}^3-\text{$\#$1}^2+(a+b) \text{$\#$1}-a b\&,1\right]^2+4 (a+b) \text{Root}\left[d \text{$\#$1}^3-\text{$\#$1}^2+(a+b) \text{$\#$1}-a b\&,1\right]-3 a b\right) \text{Root}\left[d \text{$\#$1}^3-\text{$\#$1}^2+(a+b) \text{$\#$1}-a b\&,3\right]\right)-d \left(\Pi \left(\frac{a}{\text{Root}\left[d \text{$\#$1}^3-\text{$\#$1}^2+(a+b) \text{$\#$1}-a b\&,2\right]};i \sinh ^{-1}\left(\sqrt{-\frac{x}{a}}\right)|\frac{a}{b}\right) \left(2 a^2+b a+6 b d \text{Root}\left[d \text{$\#$1}^3-\text{$\#$1}^2+(a+b) \text{$\#$1}-a b\&,3\right] a+2 b^2-2 (a+b) d \text{Root}\left[d \text{$\#$1}^3-\text{$\#$1}^2+(a+b) \text{$\#$1}-a b\&,1\right] \text{Root}\left[d \text{$\#$1}^3-\text{$\#$1}^2+(a+b) \text{$\#$1}-a b\&,3\right]+d \text{Root}\left[d \text{$\#$1}^3-\text{$\#$1}^2+(a+b) \text{$\#$1}-a b\&,2\right]^2 \left(\text{Root}\left[d \text{$\#$1}^3-\text{$\#$1}^2+(a+b) \text{$\#$1}-a b\&,3\right]-\text{Root}\left[d \text{$\#$1}^3-\text{$\#$1}^2+(a+b) \text{$\#$1}-a b\&,1\right]\right)+d \text{Root}\left[d \text{$\#$1}^3-\text{$\#$1}^2+(a+b) \text{$\#$1}-a b\&,2\right] \left(3 a b-4 (a+b) \text{Root}\left[d \text{$\#$1}^3-\text{$\#$1}^2+(a+b) \text{$\#$1}-a b\&,3\right]\right)\right)+\Pi \left(\frac{a}{\text{Root}\left[d \text{$\#$1}^3-\text{$\#$1}^2+(a+b) \text{$\#$1}-a b\&,3\right]};i \sinh ^{-1}\left(\sqrt{-\frac{x}{a}}\right)|\frac{a}{b}\right) \left(d \text{Root}\left[d \text{$\#$1}^3-\text{$\#$1}^2+(a+b) \text{$\#$1}-a b\&,1\right] \text{Root}\left[d \text{$\#$1}^3-\text{$\#$1}^2+(a+b) \text{$\#$1}-a b\&,3\right]^2-3 a b d \text{Root}\left[d \text{$\#$1}^3-\text{$\#$1}^2+(a+b) \text{$\#$1}-a b\&,3\right]-2 (a+b) d \text{Root}\left[d \text{$\#$1}^3-\text{$\#$1}^2+(a+b) \text{$\#$1}-a b\&,1\right] \text{Root}\left[d \text{$\#$1}^3-\text{$\#$1}^2+(a+b) \text{$\#$1}-a b\&,3\right]+3 a b-d \text{Root}\left[d \text{$\#$1}^3-\text{$\#$1}^2+(a+b) \text{$\#$1}-a b\&,2\right] \left(\text{Root}\left[d \text{$\#$1}^3-\text{$\#$1}^2+(a+b) \text{$\#$1}-a b\&,3\right]^2-2 (a+b) \text{Root}\left[d \text{$\#$1}^3-\text{$\#$1}^2+(a+b) \text{$\#$1}-a b\&,3\right]+6 a b\right)\right)\right)\right)}{d^3 \sqrt{\frac{x}{x-a}} \sqrt{x (x-a) (x-b)} \left(\text{Root}\left[d \text{$\#$1}^3-\text{$\#$1}^2+(a+b) \text{$\#$1}-a b\&,1\right]-\text{Root}\left[d \text{$\#$1}^3-\text{$\#$1}^2+(a+b) \text{$\#$1}-a b\&,2\right]\right) \left(\text{Root}\left[d \text{$\#$1}^3-\text{$\#$1}^2+(a+b) \text{$\#$1}-a b\&,1\right]-\text{Root}\left[d \text{$\#$1}^3-\text{$\#$1}^2+(a+b) \text{$\#$1}-a b\&,3\right]\right) \left(\text{Root}\left[d \text{$\#$1}^3-\text{$\#$1}^2+(a+b) \text{$\#$1}-a b\&,2\right]-\text{Root}\left[d \text{$\#$1}^3-\text{$\#$1}^2+(a+b) \text{$\#$1}-a b\&,3\right]\right)}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{x^2 (-a-b)+a b x+x^3}}{\sqrt{d} x^2}\right)}{\sqrt{d}}",1,"((-2*I)*x*Sqrt[1 - x/b]*(EllipticF[I*ArcSinh[Sqrt[-(x/a)]], a/b]*(a + b - 3*a*b*d - 2*d^2*Root[-(a*b) + (a + b)*#1 - #1^2 + d*#1^3 & , 1]*Root[-(a*b) + (a + b)*#1 - #1^2 + d*#1^3 & , 2]^2 - 2*d^2*Root[-(a*b) + (a + b)*#1 - #1^2 + d*#1^3 & , 1]^2*Root[-(a*b) + (a + b)*#1 - #1^2 + d*#1^3 & , 3] - 2*d^2*Root[-(a*b) + (a + b)*#1 - #1^2 + d*#1^3 & , 2]*Root[-(a*b) + (a + b)*#1 - #1^2 + d*#1^3 & , 3]^2) - EllipticPi[a/Root[-(a*b) + (a + b)*#1 - #1^2 + d*#1^3 & , 1], I*ArcSinh[Sqrt[-(x/a)]], a/b]*(a + b - 2*a^2*d - 7*a*b*d - 2*b^2*d - d*Root[-(a*b) + (a + b)*#1 - #1^2 + d*#1^3 & , 2]^2 + d^2*Root[-(a*b) + (a + b)*#1 - #1^2 + d*#1^3 & , 2]^3 + d^2*(-3*a*b + 4*(a + b)*Root[-(a*b) + (a + b)*#1 - #1^2 + d*#1^3 & , 1] - 2*Root[-(a*b) + (a + b)*#1 - #1^2 + d*#1^3 & , 1]^2)*Root[-(a*b) + (a + b)*#1 - #1^2 + d*#1^3 & , 3] - d^2*Root[-(a*b) + (a + b)*#1 - #1^2 + d*#1^3 & , 1]*Root[-(a*b) + (a + b)*#1 - #1^2 + d*#1^3 & , 3]^2 + d^2*Root[-(a*b) + (a + b)*#1 - #1^2 + d*#1^3 & , 2]*(3*a*b + 2*(a + b)*Root[-(a*b) + (a + b)*#1 - #1^2 + d*#1^3 & , 3] - Root[-(a*b) + (a + b)*#1 - #1^2 + d*#1^3 & , 3]^2)) - d*(EllipticPi[a/Root[-(a*b) + (a + b)*#1 - #1^2 + d*#1^3 & , 2], I*ArcSinh[Sqrt[-(x/a)]], a/b]*(2*a^2 + a*b + 2*b^2 + 6*a*b*d*Root[-(a*b) + (a + b)*#1 - #1^2 + d*#1^3 & , 3] - 2*(a + b)*d*Root[-(a*b) + (a + b)*#1 - #1^2 + d*#1^3 & , 1]*Root[-(a*b) + (a + b)*#1 - #1^2 + d*#1^3 & , 3] + d*Root[-(a*b) + (a + b)*#1 - #1^2 + d*#1^3 & , 2]^2*(-Root[-(a*b) + (a + b)*#1 - #1^2 + d*#1^3 & , 1] + Root[-(a*b) + (a + b)*#1 - #1^2 + d*#1^3 & , 3]) + d*Root[-(a*b) + (a + b)*#1 - #1^2 + d*#1^3 & , 2]*(3*a*b - 4*(a + b)*Root[-(a*b) + (a + b)*#1 - #1^2 + d*#1^3 & , 3])) + EllipticPi[a/Root[-(a*b) + (a + b)*#1 - #1^2 + d*#1^3 & , 3], I*ArcSinh[Sqrt[-(x/a)]], a/b]*(3*a*b - 3*a*b*d*Root[-(a*b) + (a + b)*#1 - #1^2 + d*#1^3 & , 3] - 2*(a + b)*d*Root[-(a*b) + (a + b)*#1 - #1^2 + d*#1^3 & , 1]*Root[-(a*b) + (a + b)*#1 - #1^2 + d*#1^3 & , 3] + d*Root[-(a*b) + (a + b)*#1 - #1^2 + d*#1^3 & , 1]*Root[-(a*b) + (a + b)*#1 - #1^2 + d*#1^3 & , 3]^2 - d*Root[-(a*b) + (a + b)*#1 - #1^2 + d*#1^3 & , 2]*(6*a*b - 2*(a + b)*Root[-(a*b) + (a + b)*#1 - #1^2 + d*#1^3 & , 3] + Root[-(a*b) + (a + b)*#1 - #1^2 + d*#1^3 & , 3]^2)))))/(d^3*Sqrt[x/(-a + x)]*Sqrt[x*(-a + x)*(-b + x)]*(Root[-(a*b) + (a + b)*#1 - #1^2 + d*#1^3 & , 1] - Root[-(a*b) + (a + b)*#1 - #1^2 + d*#1^3 & , 2])*(Root[-(a*b) + (a + b)*#1 - #1^2 + d*#1^3 & , 1] - Root[-(a*b) + (a + b)*#1 - #1^2 + d*#1^3 & , 3])*(Root[-(a*b) + (a + b)*#1 - #1^2 + d*#1^3 & , 2] - Root[-(a*b) + (a + b)*#1 - #1^2 + d*#1^3 & , 3]))","C",0
520,1,58,40,0.0251304,"\int \frac{\left(-1+x^2\right) \sqrt{1+2 x^2+x^4}}{\left(1+x^2\right) \left(1+x^4\right)} \, dx","Integrate[((-1 + x^2)*Sqrt[1 + 2*x^2 + x^4])/((1 + x^2)*(1 + x^4)),x]","\frac{\sqrt{\left(x^2+1\right)^2} \left(\log \left(-x^2+\sqrt{2} x-1\right)-\log \left(x^2+\sqrt{2} x+1\right)\right)}{2 \sqrt{2} \left(x^2+1\right)}","-\frac{\sqrt{\left(x^2+1\right)^2} \tanh ^{-1}\left(\frac{\sqrt{2} x}{x^2+1}\right)}{\sqrt{2} \left(x^2+1\right)}",1,"(Sqrt[(1 + x^2)^2]*(Log[-1 + Sqrt[2]*x - x^2] - Log[1 + Sqrt[2]*x + x^2]))/(2*Sqrt[2]*(1 + x^2))","A",1
521,1,54,40,0.0158598,"\int \frac{-1+x}{\sqrt{-7+4 x+14 x^2-12 x^3+x^4}} \, dx","Integrate[(-1 + x)/Sqrt[-7 + 4*x + 14*x^2 - 12*x^3 + x^4],x]","\frac{(x-1) \sqrt{x^2-10 x-7} \log \left(-\sqrt{x^2-10 x-7}-x+5\right)}{\sqrt{(x-1)^2 \left(x^2-10 x-7\right)}}","\log (x-1)-\log \left(-x^2+\sqrt{x^4-12 x^3+14 x^2+4 x-7}+6 x-5\right)",1,"((-1 + x)*Sqrt[-7 - 10*x + x^2]*Log[5 - x - Sqrt[-7 - 10*x + x^2]])/Sqrt[(-1 + x)^2*(-7 - 10*x + x^2)]","A",1
522,1,30,40,0.142911,"\int \frac{1-2 k^2 x^2+k^2 x^4}{x^2 \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)} \left(-1+k^2 x^2\right)} \, dx","Integrate[(1 - 2*k^2*x^2 + k^2*x^4)/(x^2*Sqrt[(1 - x^2)*(1 - k^2*x^2)]*(-1 + k^2*x^2)),x]","\frac{1-x^2}{x \sqrt{\left(x^2-1\right) \left(k^2 x^2-1\right)}}","-\frac{\sqrt{k^2 x^4+\left(-k^2-1\right) x^2+1}}{x \left(k^2 x^2-1\right)}",1,"(1 - x^2)/(x*Sqrt[(-1 + x^2)*(-1 + k^2*x^2)])","A",1
523,1,40,40,0.0385184,"\int \frac{-2+x^6}{x \sqrt{-1+x^6} \left(2+x^6\right)} \, dx","Integrate[(-2 + x^6)/(x*Sqrt[-1 + x^6]*(2 + x^6)),x]","\frac{2 \tan ^{-1}\left(\frac{\sqrt{x^6-1}}{\sqrt{3}}\right)}{3 \sqrt{3}}-\frac{1}{3} \tan ^{-1}\left(\sqrt{x^6-1}\right)","\frac{2 \tan ^{-1}\left(\frac{\sqrt{x^6-1}}{\sqrt{3}}\right)}{3 \sqrt{3}}-\frac{1}{3} \tan ^{-1}\left(\sqrt{x^6-1}\right)",1,"-1/3*ArcTan[Sqrt[-1 + x^6]] + (2*ArcTan[Sqrt[-1 + x^6]/Sqrt[3]])/(3*Sqrt[3])","A",1
524,1,40,40,0.0450004,"\int \frac{\left(2+x^3\right) \left(1+x^3+x^6\right)}{x \sqrt{1+x^3}} \, dx","Integrate[((2 + x^3)*(1 + x^3 + x^6))/(x*Sqrt[1 + x^3]),x]","\frac{2}{45} \sqrt{x^3+1} \left(3 x^6+11 x^3+23\right)-\frac{4}{3} \tanh ^{-1}\left(\sqrt{x^3+1}\right)","\frac{2}{45} \sqrt{x^3+1} \left(3 x^6+11 x^3+23\right)-\frac{4}{3} \tanh ^{-1}\left(\sqrt{x^3+1}\right)",1,"(2*Sqrt[1 + x^3]*(23 + 11*x^3 + 3*x^6))/45 - (4*ArcTanh[Sqrt[1 + x^3]])/3","A",1
525,0,0,40,0.1253379,"\int \frac{4 x+3 x^2}{\sqrt{-5+4 x^2+2 x^3+4 x^4+4 x^5+x^6}} \, dx","Integrate[(4*x + 3*x^2)/Sqrt[-5 + 4*x^2 + 2*x^3 + 4*x^4 + 4*x^5 + x^6],x]","\int \frac{4 x+3 x^2}{\sqrt{-5+4 x^2+2 x^3+4 x^4+4 x^5+x^6}} \, dx","\log \left(x^3+2 x^2+\sqrt{x^6+4 x^5+4 x^4+2 x^3+4 x^2-5}+1\right)",1,"Integrate[(4*x + 3*x^2)/Sqrt[-5 + 4*x^2 + 2*x^3 + 4*x^4 + 4*x^5 + x^6], x]","F",-1
526,0,0,40,0.3688716,"\int \frac{x^2 \sqrt{q+p x^5} \left(-2 q+3 p x^5\right)}{b x^6+a \left(q+p x^5\right)^3} \, dx","Integrate[(x^2*Sqrt[q + p*x^5]*(-2*q + 3*p*x^5))/(b*x^6 + a*(q + p*x^5)^3),x]","\int \frac{x^2 \sqrt{q+p x^5} \left(-2 q+3 p x^5\right)}{b x^6+a \left(q+p x^5\right)^3} \, dx","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{b} x^3}{\sqrt{a} \left(p x^5+q\right)^{3/2}}\right)}{3 \sqrt{a} \sqrt{b}}",1,"Integrate[(x^2*Sqrt[q + p*x^5]*(-2*q + 3*p*x^5))/(b*x^6 + a*(q + p*x^5)^3), x]","F",-1
527,1,41,41,0.0210621,"\int \frac{x^8}{\sqrt{-b+a x^3}} \, dx","Integrate[x^8/Sqrt[-b + a*x^3],x]","\frac{2 \sqrt{a x^3-b} \left(3 a^2 x^6+4 a b x^3+8 b^2\right)}{45 a^3}","\frac{2 \sqrt{a x^3-b} \left(3 a^2 x^6+4 a b x^3+8 b^2\right)}{45 a^3}",1,"(2*Sqrt[-b + a*x^3]*(8*b^2 + 4*a*b*x^3 + 3*a^2*x^6))/(45*a^3)","A",1
528,1,30,41,0.0142917,"\int x^5 \sqrt{-b+a x^3} \, dx","Integrate[x^5*Sqrt[-b + a*x^3],x]","\frac{2 \left(a x^3-b\right)^{3/2} \left(3 a x^3+2 b\right)}{45 a^2}","\frac{2 \sqrt{a x^3-b} \left(3 a^2 x^6-a b x^3-2 b^2\right)}{45 a^2}",1,"(2*(-b + a*x^3)^(3/2)*(2*b + 3*a*x^3))/(45*a^2)","A",1
529,1,2865,41,6.3289459,"\int \frac{2 b+a x^3}{\sqrt{-b+a x^3} \left(-2 b-3 x^2+2 a x^3\right)} \, dx","Integrate[(2*b + a*x^3)/(Sqrt[-b + a*x^3]*(-2*b - 3*x^2 + 2*a*x^3)),x]","\text{Result too large to show}","\sqrt{\frac{2}{3}} \tanh ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x \sqrt{a x^3-b}}{b-a x^3}\right)",1,"(Sqrt[(-(b^(1/3)/a^(1/3)) + x)/(-(b^(1/3)/a^(1/3)) - ((-1)^(1/3)*b^(1/3))/a^(1/3))]*(((-1)^(1/3)*b^(1/3))/a^(1/3) + x)*Sqrt[(-(((-1)^(2/3)*b^(1/3))/a^(1/3)) + x)/(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) - ((-1)^(2/3)*b^(1/3))/a^(1/3))]*EllipticF[ArcSin[Sqrt[((-1)^(1/3)*b^(1/3) + a^(1/3)*x)/(((-1)^(1/3) + (-1)^(2/3))*b^(1/3))]], (-1)^(1/3)])/(Sqrt[(((-1)^(1/3)*b^(1/3))/a^(1/3) + x)/(((-1)^(1/3)*b^(1/3))/a^(1/3) + ((-1)^(2/3)*b^(1/3))/a^(1/3))]*Sqrt[-b + a*x^3]) + (2*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) - ((-1)^(2/3)*b^(1/3))/a^(1/3))*b*Sqrt[(-(b^(1/3)/a^(1/3)) + x)/(-(b^(1/3)/a^(1/3)) - ((-1)^(1/3)*b^(1/3))/a^(1/3))]*Sqrt[((((-1)^(2/3)*b^(1/3))/a^(1/3) - x)*(((-1)^(1/3)*b^(1/3))/a^(1/3) + x))/(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) - ((-1)^(2/3)*b^(1/3))/a^(1/3))^2]*EllipticPi[((-1)^(1/3)*b^(1/3) + (-1)^(2/3)*b^(1/3))/((-1)^(1/3)*b^(1/3) + a^(1/3)*Root[-2*b - 3*#1^2 + 2*a*#1^3 & , 1]), ArcSin[Sqrt[((-1)^(1/3)*b^(1/3) + a^(1/3)*x)/(((-1)^(1/3) + (-1)^(2/3))*b^(1/3))]], (-1)^(1/3)])/(a*Sqrt[-b + a*x^3]*(((-1)^(1/3)*b^(1/3))/a^(1/3) + Root[-2*b - 3*#1^2 + 2*a*#1^3 & , 1])*(Root[-2*b - 3*#1^2 + 2*a*#1^3 & , 1] - Root[-2*b - 3*#1^2 + 2*a*#1^3 & , 2])*(Root[-2*b - 3*#1^2 + 2*a*#1^3 & , 1] - Root[-2*b - 3*#1^2 + 2*a*#1^3 & , 3])) + ((-(((-1)^(1/3)*b^(1/3))/a^(1/3)) - ((-1)^(2/3)*b^(1/3))/a^(1/3))*Sqrt[(-(b^(1/3)/a^(1/3)) + x)/(-(b^(1/3)/a^(1/3)) - ((-1)^(1/3)*b^(1/3))/a^(1/3))]*Sqrt[((((-1)^(2/3)*b^(1/3))/a^(1/3) - x)*(((-1)^(1/3)*b^(1/3))/a^(1/3) + x))/(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) - ((-1)^(2/3)*b^(1/3))/a^(1/3))^2]*EllipticPi[((-1)^(1/3)*b^(1/3) + (-1)^(2/3)*b^(1/3))/((-1)^(1/3)*b^(1/3) + a^(1/3)*Root[-2*b - 3*#1^2 + 2*a*#1^3 & , 1]), ArcSin[Sqrt[((-1)^(1/3)*b^(1/3) + a^(1/3)*x)/(((-1)^(1/3) + (-1)^(2/3))*b^(1/3))]], (-1)^(1/3)]*Root[-2*b - 3*#1^2 + 2*a*#1^3 & , 1]^3)/(Sqrt[-b + a*x^3]*(((-1)^(1/3)*b^(1/3))/a^(1/3) + Root[-2*b - 3*#1^2 + 2*a*#1^3 & , 1])*(Root[-2*b - 3*#1^2 + 2*a*#1^3 & , 1] - Root[-2*b - 3*#1^2 + 2*a*#1^3 & , 2])*(Root[-2*b - 3*#1^2 + 2*a*#1^3 & , 1] - Root[-2*b - 3*#1^2 + 2*a*#1^3 & , 3])) + (2*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) - ((-1)^(2/3)*b^(1/3))/a^(1/3))*b*Sqrt[(-(b^(1/3)/a^(1/3)) + x)/(-(b^(1/3)/a^(1/3)) - ((-1)^(1/3)*b^(1/3))/a^(1/3))]*Sqrt[((((-1)^(2/3)*b^(1/3))/a^(1/3) - x)*(((-1)^(1/3)*b^(1/3))/a^(1/3) + x))/(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) - ((-1)^(2/3)*b^(1/3))/a^(1/3))^2]*EllipticPi[((-1)^(1/3)*b^(1/3) + (-1)^(2/3)*b^(1/3))/((-1)^(1/3)*b^(1/3) + a^(1/3)*Root[-2*b - 3*#1^2 + 2*a*#1^3 & , 2]), ArcSin[Sqrt[((-1)^(1/3)*b^(1/3) + a^(1/3)*x)/(((-1)^(1/3) + (-1)^(2/3))*b^(1/3))]], (-1)^(1/3)])/(a*Sqrt[-b + a*x^3]*(((-1)^(1/3)*b^(1/3))/a^(1/3) + Root[-2*b - 3*#1^2 + 2*a*#1^3 & , 2])*(-Root[-2*b - 3*#1^2 + 2*a*#1^3 & , 1] + Root[-2*b - 3*#1^2 + 2*a*#1^3 & , 2])*(Root[-2*b - 3*#1^2 + 2*a*#1^3 & , 2] - Root[-2*b - 3*#1^2 + 2*a*#1^3 & , 3])) + ((-(((-1)^(1/3)*b^(1/3))/a^(1/3)) - ((-1)^(2/3)*b^(1/3))/a^(1/3))*Sqrt[(-(b^(1/3)/a^(1/3)) + x)/(-(b^(1/3)/a^(1/3)) - ((-1)^(1/3)*b^(1/3))/a^(1/3))]*Sqrt[((((-1)^(2/3)*b^(1/3))/a^(1/3) - x)*(((-1)^(1/3)*b^(1/3))/a^(1/3) + x))/(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) - ((-1)^(2/3)*b^(1/3))/a^(1/3))^2]*EllipticPi[((-1)^(1/3)*b^(1/3) + (-1)^(2/3)*b^(1/3))/((-1)^(1/3)*b^(1/3) + a^(1/3)*Root[-2*b - 3*#1^2 + 2*a*#1^3 & , 2]), ArcSin[Sqrt[((-1)^(1/3)*b^(1/3) + a^(1/3)*x)/(((-1)^(1/3) + (-1)^(2/3))*b^(1/3))]], (-1)^(1/3)]*Root[-2*b - 3*#1^2 + 2*a*#1^3 & , 2]^3)/(Sqrt[-b + a*x^3]*(((-1)^(1/3)*b^(1/3))/a^(1/3) + Root[-2*b - 3*#1^2 + 2*a*#1^3 & , 2])*(-Root[-2*b - 3*#1^2 + 2*a*#1^3 & , 1] + Root[-2*b - 3*#1^2 + 2*a*#1^3 & , 2])*(Root[-2*b - 3*#1^2 + 2*a*#1^3 & , 2] - Root[-2*b - 3*#1^2 + 2*a*#1^3 & , 3])) + (2*(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) - ((-1)^(2/3)*b^(1/3))/a^(1/3))*b*Sqrt[(-(b^(1/3)/a^(1/3)) + x)/(-(b^(1/3)/a^(1/3)) - ((-1)^(1/3)*b^(1/3))/a^(1/3))]*Sqrt[((((-1)^(2/3)*b^(1/3))/a^(1/3) - x)*(((-1)^(1/3)*b^(1/3))/a^(1/3) + x))/(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) - ((-1)^(2/3)*b^(1/3))/a^(1/3))^2]*EllipticPi[((-1)^(1/3)*b^(1/3) + (-1)^(2/3)*b^(1/3))/((-1)^(1/3)*b^(1/3) + a^(1/3)*Root[-2*b - 3*#1^2 + 2*a*#1^3 & , 3]), ArcSin[Sqrt[((-1)^(1/3)*b^(1/3) + a^(1/3)*x)/(((-1)^(1/3) + (-1)^(2/3))*b^(1/3))]], (-1)^(1/3)])/(a*Sqrt[-b + a*x^3]*(((-1)^(1/3)*b^(1/3))/a^(1/3) + Root[-2*b - 3*#1^2 + 2*a*#1^3 & , 3])*(-Root[-2*b - 3*#1^2 + 2*a*#1^3 & , 1] + Root[-2*b - 3*#1^2 + 2*a*#1^3 & , 3])*(-Root[-2*b - 3*#1^2 + 2*a*#1^3 & , 2] + Root[-2*b - 3*#1^2 + 2*a*#1^3 & , 3])) + ((-(((-1)^(1/3)*b^(1/3))/a^(1/3)) - ((-1)^(2/3)*b^(1/3))/a^(1/3))*Sqrt[(-(b^(1/3)/a^(1/3)) + x)/(-(b^(1/3)/a^(1/3)) - ((-1)^(1/3)*b^(1/3))/a^(1/3))]*Sqrt[((((-1)^(2/3)*b^(1/3))/a^(1/3) - x)*(((-1)^(1/3)*b^(1/3))/a^(1/3) + x))/(-(((-1)^(1/3)*b^(1/3))/a^(1/3)) - ((-1)^(2/3)*b^(1/3))/a^(1/3))^2]*EllipticPi[((-1)^(1/3)*b^(1/3) + (-1)^(2/3)*b^(1/3))/((-1)^(1/3)*b^(1/3) + a^(1/3)*Root[-2*b - 3*#1^2 + 2*a*#1^3 & , 3]), ArcSin[Sqrt[((-1)^(1/3)*b^(1/3) + a^(1/3)*x)/(((-1)^(1/3) + (-1)^(2/3))*b^(1/3))]], (-1)^(1/3)]*Root[-2*b - 3*#1^2 + 2*a*#1^3 & , 3]^3)/(Sqrt[-b + a*x^3]*(((-1)^(1/3)*b^(1/3))/a^(1/3) + Root[-2*b - 3*#1^2 + 2*a*#1^3 & , 3])*(-Root[-2*b - 3*#1^2 + 2*a*#1^3 & , 1] + Root[-2*b - 3*#1^2 + 2*a*#1^3 & , 3])*(-Root[-2*b - 3*#1^2 + 2*a*#1^3 & , 2] + Root[-2*b - 3*#1^2 + 2*a*#1^3 & , 3]))","C",0
530,1,145,41,0.4819118,"\int \frac{\left(-1+x^4\right) \sqrt{1+x^4} \left(1+x^2+x^4\right)}{x^4 \left(1-x^2+x^4\right)} \, dx","Integrate[((-1 + x^4)*Sqrt[1 + x^4]*(1 + x^2 + x^4))/(x^4*(1 - x^2 + x^4)),x]","\frac{x^8+6 x^6+2 x^4+6 x^2-6 \sqrt[4]{-1} \sqrt{x^4+1} x^3 F\left(\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+6 \sqrt[4]{-1} \sqrt{x^4+1} x^3 \Pi \left(\sqrt[6]{-1};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+6 \sqrt[4]{-1} \sqrt{x^4+1} x^3 \Pi \left((-1)^{5/6};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+1}{3 x^3 \sqrt{x^4+1}}","\frac{\sqrt{x^4+1} \left(x^4+6 x^2+1\right)}{3 x^3}-2 \tanh ^{-1}\left(\frac{x}{\sqrt{x^4+1}}\right)",1,"(1 + 6*x^2 + 2*x^4 + 6*x^6 + x^8 - 6*(-1)^(1/4)*x^3*Sqrt[1 + x^4]*EllipticF[I*ArcSinh[(-1)^(1/4)*x], -1] + 6*(-1)^(1/4)*x^3*Sqrt[1 + x^4]*EllipticPi[(-1)^(1/6), I*ArcSinh[(-1)^(1/4)*x], -1] + 6*(-1)^(1/4)*x^3*Sqrt[1 + x^4]*EllipticPi[(-1)^(5/6), I*ArcSinh[(-1)^(1/4)*x], -1])/(3*x^3*Sqrt[1 + x^4])","C",1
531,0,0,41,0.4445813,"\int \frac{4 c+3 b x+2 a x^2}{\sqrt[4]{c+b x+a x^2} \left(-c-b x-a x^2+x^4\right)} \, dx","Integrate[(4*c + 3*b*x + 2*a*x^2)/((c + b*x + a*x^2)^(1/4)*(-c - b*x - a*x^2 + x^4)),x]","\int \frac{4 c+3 b x+2 a x^2}{\sqrt[4]{c+b x+a x^2} \left(-c-b x-a x^2+x^4\right)} \, dx","2 \tan ^{-1}\left(\frac{\sqrt[4]{a x^2+b x+c}}{x}\right)-2 \tanh ^{-1}\left(\frac{x}{\sqrt[4]{a x^2+b x+c}}\right)",1,"Integrate[(4*c + 3*b*x + 2*a*x^2)/((c + b*x + a*x^2)^(1/4)*(-c - b*x - a*x^2 + x^4)), x]","F",-1
532,1,40,41,0.0484497,"\int \frac{\left(2+x^3\right) \left(1+x^3+x^6\right)}{x^4 \sqrt{1+x^3}} \, dx","Integrate[((2 + x^3)*(1 + x^3 + x^6))/(x^4*Sqrt[1 + x^3]),x]","\frac{2}{9} \left(\frac{\sqrt{x^3+1} \left(x^6+7 x^3-3\right)}{x^3}-6 \tanh ^{-1}\left(\sqrt{x^3+1}\right)\right)","\frac{2 \sqrt{x^3+1} \left(x^6+7 x^3-3\right)}{9 x^3}-\frac{4}{3} \tanh ^{-1}\left(\sqrt{x^3+1}\right)",1,"(2*((Sqrt[1 + x^3]*(-3 + 7*x^3 + x^6))/x^3 - 6*ArcTanh[Sqrt[1 + x^3]]))/9","A",1
533,1,41,41,0.0393781,"\int \frac{\sqrt{-1+x^3} \left(-2+x^3+2 x^6\right)}{x^{10}} \, dx","Integrate[(Sqrt[-1 + x^3]*(-2 + x^3 + 2*x^6))/x^10,x]","\frac{2}{3} \tan ^{-1}\left(\sqrt{x^3-1}\right)-\frac{2 \sqrt{x^3-1} \left(3 x^6+x^3-1\right)}{9 x^9}","\frac{2}{3} \tan ^{-1}\left(\sqrt{x^3-1}\right)-\frac{2 \sqrt{x^3-1} \left(3 x^6+x^3-1\right)}{9 x^9}",1,"(-2*Sqrt[-1 + x^3]*(-1 + x^3 + 3*x^6))/(9*x^9) + (2*ArcTan[Sqrt[-1 + x^3]])/3","A",1
534,1,73,41,0.0659024,"\int \frac{-4+13 x^6}{x \sqrt{-1+x^6} \left(-1+4 x^6\right)} \, dx","Integrate[(-4 + 13*x^6)/(x*Sqrt[-1 + x^6]*(-1 + 4*x^6)),x]","\frac{1}{12} \left(16 \tan ^{-1}\left(\sqrt{x^6-1}\right)+\sqrt{3} \tan ^{-1}\left(\frac{2-x^3}{\sqrt{3} \sqrt{x^6-1}}\right)+\sqrt{3} \tan ^{-1}\left(\frac{x^3+2}{\sqrt{3} \sqrt{x^6-1}}\right)\right)","\frac{4}{3} \tan ^{-1}\left(\sqrt{x^6-1}\right)-\frac{\tan ^{-1}\left(\frac{2 \sqrt{x^6-1}}{\sqrt{3}}\right)}{2 \sqrt{3}}",1,"(Sqrt[3]*ArcTan[(2 - x^3)/(Sqrt[3]*Sqrt[-1 + x^6])] + Sqrt[3]*ArcTan[(2 + x^3)/(Sqrt[3]*Sqrt[-1 + x^6])] + 16*ArcTan[Sqrt[-1 + x^6]])/12","A",1
535,0,0,41,0.3299505,"\int \frac{-b+2 a x^3}{\left(b-x+a x^3\right) \sqrt[4]{b x^3+a x^6}} \, dx","Integrate[(-b + 2*a*x^3)/((b - x + a*x^3)*(b*x^3 + a*x^6)^(1/4)),x]","\int \frac{-b+2 a x^3}{\left(b-x+a x^3\right) \sqrt[4]{b x^3+a x^6}} \, dx","-2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{a x^6+b x^3}}\right)-2 \tanh ^{-1}\left(\frac{x}{\sqrt[4]{a x^6+b x^3}}\right)",1,"Integrate[(-b + 2*a*x^3)/((b - x + a*x^3)*(b*x^3 + a*x^6)^(1/4)), x]","F",-1
536,0,0,41,0.2493377,"\int \frac{x^3 \left(b+2 a x^5\right)}{\sqrt[4]{b x+a x^6} \left(-1+b x^5+a x^{10}\right)} \, dx","Integrate[(x^3*(b + 2*a*x^5))/((b*x + a*x^6)^(1/4)*(-1 + b*x^5 + a*x^10)),x]","\int \frac{x^3 \left(b+2 a x^5\right)}{\sqrt[4]{b x+a x^6} \left(-1+b x^5+a x^{10}\right)} \, dx","\frac{2}{5} \tan ^{-1}\left(x \sqrt[4]{a x^6+b x}\right)-\frac{2}{5} \tanh ^{-1}\left(x \sqrt[4]{a x^6+b x}\right)",1,"Integrate[(x^3*(b + 2*a*x^5))/((b*x + a*x^6)^(1/4)*(-1 + b*x^5 + a*x^10)), x]","F",-1
537,1,42,42,0.0082643,"\int \frac{\sqrt[4]{1+x^3}}{x} \, dx","Integrate[(1 + x^3)^(1/4)/x,x]","\frac{4}{3} \sqrt[4]{x^3+1}-\frac{2}{3} \tan ^{-1}\left(\sqrt[4]{x^3+1}\right)-\frac{2}{3} \tanh ^{-1}\left(\sqrt[4]{x^3+1}\right)","\frac{4}{3} \sqrt[4]{x^3+1}-\frac{2}{3} \tan ^{-1}\left(\sqrt[4]{x^3+1}\right)-\frac{2}{3} \tanh ^{-1}\left(\sqrt[4]{x^3+1}\right)",1,"(4*(1 + x^3)^(1/4))/3 - (2*ArcTan[(1 + x^3)^(1/4)])/3 - (2*ArcTanh[(1 + x^3)^(1/4)])/3","A",1
538,1,5105,42,6.7875646,"\int \frac{-2 a q+3 b p x^2+a p x^3}{\sqrt{q+p x^3} \left(b^2 c+d q+2 a b c x+a^2 c x^2+d p x^3\right)} \, dx","Integrate[(-2*a*q + 3*b*p*x^2 + a*p*x^3)/(Sqrt[q + p*x^3]*(b^2*c + d*q + 2*a*b*c*x + a^2*c*x^2 + d*p*x^3)),x]","\text{Result too large to show}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{p x^3+q}}{\sqrt{c} (a x+b)}\right)}{\sqrt{c} \sqrt{d}}",1,"Result too large to show","C",0
539,1,37,42,0.1481702,"\int \frac{\left(-1+x^3\right) \sqrt{-1+x^6}}{x^7 \left(1+x^3\right)} \, dx","Integrate[((-1 + x^3)*Sqrt[-1 + x^6])/(x^7*(1 + x^3)),x]","\frac{1}{6} \left(3 \tan ^{-1}\left(\sqrt{x^6-1}\right)+\frac{\sqrt{x^6-1} \left(1-4 x^3\right)}{x^6}\right)","\frac{\left(1-4 x^3\right) \sqrt{x^6-1}}{6 x^6}-\tan ^{-1}\left(\frac{x^3+1}{\sqrt{x^6-1}}\right)",1,"(((1 - 4*x^3)*Sqrt[-1 + x^6])/x^6 + 3*ArcTan[Sqrt[-1 + x^6]])/6","A",1
540,1,37,42,0.1189208,"\int \frac{\left(1+x^3\right) \sqrt{-1+x^6}}{x^7 \left(-1+x^3\right)} \, dx","Integrate[((1 + x^3)*Sqrt[-1 + x^6])/(x^7*(-1 + x^3)),x]","\frac{1}{6} \left(3 \tan ^{-1}\left(\sqrt{x^6-1}\right)+\frac{\sqrt{x^6-1} \left(4 x^3+1\right)}{x^6}\right)","\frac{\left(4 x^3+1\right) \sqrt{x^6-1}}{6 x^6}-\tan ^{-1}\left(\frac{x^3+1}{\sqrt{x^6-1}}\right)",1,"(((1 + 4*x^3)*Sqrt[-1 + x^6])/x^6 + 3*ArcTan[Sqrt[-1 + x^6]])/6","A",1
541,1,42,42,0.0080387,"\int \frac{\sqrt[4]{1+x^6}}{x} \, dx","Integrate[(1 + x^6)^(1/4)/x,x]","\frac{2}{3} \sqrt[4]{x^6+1}-\frac{1}{3} \tan ^{-1}\left(\sqrt[4]{x^6+1}\right)-\frac{1}{3} \tanh ^{-1}\left(\sqrt[4]{x^6+1}\right)","\frac{2}{3} \sqrt[4]{x^6+1}-\frac{1}{3} \tan ^{-1}\left(\sqrt[4]{x^6+1}\right)-\frac{1}{3} \tanh ^{-1}\left(\sqrt[4]{x^6+1}\right)",1,"(2*(1 + x^6)^(1/4))/3 - ArcTan[(1 + x^6)^(1/4)]/3 - ArcTanh[(1 + x^6)^(1/4)]/3","A",1
542,1,37,42,0.0291251,"\int \frac{1+x^{12}}{x^4 \sqrt{-1+x^6}} \, dx","Integrate[(1 + x^12)/(x^4*Sqrt[-1 + x^6]),x]","\frac{1}{6} \left(\frac{\sqrt{x^6-1} \left(x^6+2\right)}{x^3}+\tanh ^{-1}\left(\frac{x^3}{\sqrt{x^6-1}}\right)\right)","\frac{\sqrt{x^6-1} \left(x^6+2\right)}{6 x^3}+\frac{1}{3} \tanh ^{-1}\left(\frac{x^3+1}{\sqrt{x^6-1}}\right)",1,"((Sqrt[-1 + x^6]*(2 + x^6))/x^3 + ArcTanh[x^3/Sqrt[-1 + x^6]])/6","A",1
543,1,26,43,0.0047678,"\int \frac{1}{x^{10} \sqrt{1+x^3}} \, dx","Integrate[1/(x^10*Sqrt[1 + x^3]),x]","\frac{2}{3} \sqrt{x^3+1} \, _2F_1\left(\frac{1}{2},4;\frac{3}{2};x^3+1\right)","\frac{5}{24} \tanh ^{-1}\left(\sqrt{x^3+1}\right)+\frac{\sqrt{x^3+1} \left(-15 x^6+10 x^3-8\right)}{72 x^9}",1,"(2*Sqrt[1 + x^3]*Hypergeometric2F1[1/2, 4, 3/2, 1 + x^3])/3","C",1
544,1,43,43,0.0555836,"\int \frac{-1+x^3}{x^6 \sqrt[3]{x^2+x^3}} \, dx","Integrate[(-1 + x^3)/(x^6*(x^2 + x^3)^(1/3)),x]","-\frac{3 \left(x^2 (x+1)\right)^{2/3} \left(19071 x^5-12714 x^4+10595 x^3-3600 x^2+3300 x-3080\right)}{52360 x^7}","-\frac{3 \left(x^3+x^2\right)^{2/3} \left(19071 x^5-12714 x^4+10595 x^3-3600 x^2+3300 x-3080\right)}{52360 x^7}",1,"(-3*(x^2*(1 + x))^(2/3)*(-3080 + 3300*x - 3600*x^2 + 10595*x^3 - 12714*x^4 + 19071*x^5))/(52360*x^7)","A",1
545,1,1638,43,6.1750745,"\int \frac{\left(-2+x^3\right) \sqrt{1+x^3} \left(2+x^2+2 x^3\right)}{x^4 \left(1+x^2+x^3\right)} \, dx","Integrate[((-2 + x^3)*Sqrt[1 + x^3]*(2 + x^2 + 2*x^3))/(x^4*(1 + x^2 + x^3)),x]","\sqrt{x^3+1} \left(\frac{4}{3}-\frac{2}{x}+\frac{4}{3 x^3}\right)+\frac{2 \sqrt{\frac{x+1}{1+\sqrt[3]{-1}}} \left(x-\sqrt[3]{-1}\right) \sqrt{\frac{x+(-1)^{2/3}}{\sqrt[3]{-1}+(-1)^{2/3}}} F\left(\sin ^{-1}\left(\sqrt{-\frac{(-1)^{2/3} \left(\sqrt[3]{-1}-x\right)}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{\sqrt{\frac{x-\sqrt[3]{-1}}{-\sqrt[3]{-1}-(-1)^{2/3}}} \sqrt{x^3+1}}-\frac{4 \left(\sqrt[3]{-1}+(-1)^{2/3}\right) \sqrt{\frac{x+1}{1+\sqrt[3]{-1}}} \sqrt{\frac{\left(-x-(-1)^{2/3}\right) \left(x-\sqrt[3]{-1}\right)}{\left(\sqrt[3]{-1}+(-1)^{2/3}\right)^2}} \Pi \left(\frac{\sqrt[3]{-1}+(-1)^{2/3}}{\sqrt[3]{-1}-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2+1\&,3\right]};\sin ^{-1}\left(\sqrt{-\frac{(-1)^{2/3} \left(\sqrt[3]{-1}-x\right)}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{\sqrt{x^3+1} \left(-\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2+1\&,3\right]\right) \left(-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2+1\&,1\right]+\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2+1\&,3\right]\right) \left(-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2+1\&,2\right]+\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2+1\&,3\right]\right)}+\frac{2 \left(\sqrt[3]{-1}+(-1)^{2/3}\right) \sqrt{\frac{x+1}{1+\sqrt[3]{-1}}} \sqrt{\frac{\left(-x-(-1)^{2/3}\right) \left(x-\sqrt[3]{-1}\right)}{\left(\sqrt[3]{-1}+(-1)^{2/3}\right)^2}} \Pi \left(\frac{\sqrt[3]{-1}+(-1)^{2/3}}{\sqrt[3]{-1}-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2+1\&,3\right]};\sin ^{-1}\left(\sqrt{-\frac{(-1)^{2/3} \left(\sqrt[3]{-1}-x\right)}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right) \text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2+1\&,3\right]^3}{\sqrt{x^3+1} \left(-\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2+1\&,3\right]\right) \left(-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2+1\&,1\right]+\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2+1\&,3\right]\right) \left(-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2+1\&,2\right]+\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2+1\&,3\right]\right)}-\frac{4 \left(\sqrt[3]{-1}+(-1)^{2/3}\right) \sqrt{\frac{x+1}{1+\sqrt[3]{-1}}} \sqrt{\frac{\left(-x-(-1)^{2/3}\right) \left(x-\sqrt[3]{-1}\right)}{\left(\sqrt[3]{-1}+(-1)^{2/3}\right)^2}} \Pi \left(\frac{\sqrt[3]{-1}+(-1)^{2/3}}{\sqrt[3]{-1}-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2+1\&,2\right]};\sin ^{-1}\left(\sqrt{-\frac{(-1)^{2/3} \left(\sqrt[3]{-1}-x\right)}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{\sqrt{x^3+1} \left(-\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2+1\&,2\right]\right) \left(-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2+1\&,1\right]+\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2+1\&,2\right]\right) \left(\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2+1\&,2\right]-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2+1\&,3\right]\right)}+\frac{2 \left(\sqrt[3]{-1}+(-1)^{2/3}\right) \sqrt{\frac{x+1}{1+\sqrt[3]{-1}}} \sqrt{\frac{\left(-x-(-1)^{2/3}\right) \left(x-\sqrt[3]{-1}\right)}{\left(\sqrt[3]{-1}+(-1)^{2/3}\right)^2}} \Pi \left(\frac{\sqrt[3]{-1}+(-1)^{2/3}}{\sqrt[3]{-1}-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2+1\&,2\right]};\sin ^{-1}\left(\sqrt{-\frac{(-1)^{2/3} \left(\sqrt[3]{-1}-x\right)}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right) \text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2+1\&,2\right]^3}{\sqrt{x^3+1} \left(-\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2+1\&,2\right]\right) \left(-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2+1\&,1\right]+\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2+1\&,2\right]\right) \left(\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2+1\&,2\right]-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2+1\&,3\right]\right)}-\frac{4 \left(\sqrt[3]{-1}+(-1)^{2/3}\right) \sqrt{\frac{x+1}{1+\sqrt[3]{-1}}} \sqrt{\frac{\left(-x-(-1)^{2/3}\right) \left(x-\sqrt[3]{-1}\right)}{\left(\sqrt[3]{-1}+(-1)^{2/3}\right)^2}} \Pi \left(\frac{\sqrt[3]{-1}+(-1)^{2/3}}{\sqrt[3]{-1}-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2+1\&,1\right]};\sin ^{-1}\left(\sqrt{-\frac{(-1)^{2/3} \left(\sqrt[3]{-1}-x\right)}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{\sqrt{x^3+1} \left(-\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2+1\&,1\right]\right) \left(\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2+1\&,1\right]-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2+1\&,2\right]\right) \left(\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2+1\&,1\right]-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2+1\&,3\right]\right)}+\frac{2 \left(\sqrt[3]{-1}+(-1)^{2/3}\right) \sqrt{\frac{x+1}{1+\sqrt[3]{-1}}} \sqrt{\frac{\left(-x-(-1)^{2/3}\right) \left(x-\sqrt[3]{-1}\right)}{\left(\sqrt[3]{-1}+(-1)^{2/3}\right)^2}} \Pi \left(\frac{\sqrt[3]{-1}+(-1)^{2/3}}{\sqrt[3]{-1}-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2+1\&,1\right]};\sin ^{-1}\left(\sqrt{-\frac{(-1)^{2/3} \left(\sqrt[3]{-1}-x\right)}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right) \text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2+1\&,1\right]^3}{\sqrt{x^3+1} \left(-\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2+1\&,1\right]\right) \left(\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2+1\&,1\right]-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2+1\&,2\right]\right) \left(\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2+1\&,1\right]-\text{Root}\left[\text{$\#$1}^3+\text{$\#$1}^2+1\&,3\right]\right)}","\frac{2 \sqrt{x^3+1} \left(2 x^3-3 x^2+2\right)}{3 x^3}-2 \tan ^{-1}\left(\frac{x}{\sqrt{x^3+1}}\right)",1,"(4/3 + 4/(3*x^3) - 2/x)*Sqrt[1 + x^3] + (2*Sqrt[(1 + x)/(1 + (-1)^(1/3))]*(-(-1)^(1/3) + x)*Sqrt[((-1)^(2/3) + x)/((-1)^(1/3) + (-1)^(2/3))]*EllipticF[ArcSin[Sqrt[-(((-1)^(2/3)*((-1)^(1/3) - x))/(1 + (-1)^(1/3)))]], (-1)^(1/3)])/(Sqrt[(-(-1)^(1/3) + x)/(-(-1)^(1/3) - (-1)^(2/3))]*Sqrt[1 + x^3]) - (4*((-1)^(1/3) + (-1)^(2/3))*Sqrt[(1 + x)/(1 + (-1)^(1/3))]*Sqrt[((-(-1)^(2/3) - x)*(-(-1)^(1/3) + x))/((-1)^(1/3) + (-1)^(2/3))^2]*EllipticPi[((-1)^(1/3) + (-1)^(2/3))/((-1)^(1/3) - Root[1 + #1^2 + #1^3 & , 1, 0]), ArcSin[Sqrt[-(((-1)^(2/3)*((-1)^(1/3) - x))/(1 + (-1)^(1/3)))]], (-1)^(1/3)])/(Sqrt[1 + x^3]*(-(-1)^(1/3) + Root[1 + #1^2 + #1^3 & , 1, 0])*(Root[1 + #1^2 + #1^3 & , 1, 0] - Root[1 + #1^2 + #1^3 & , 2, 0])*(Root[1 + #1^2 + #1^3 & , 1, 0] - Root[1 + #1^2 + #1^3 & , 3, 0])) + (2*((-1)^(1/3) + (-1)^(2/3))*Sqrt[(1 + x)/(1 + (-1)^(1/3))]*Sqrt[((-(-1)^(2/3) - x)*(-(-1)^(1/3) + x))/((-1)^(1/3) + (-1)^(2/3))^2]*EllipticPi[((-1)^(1/3) + (-1)^(2/3))/((-1)^(1/3) - Root[1 + #1^2 + #1^3 & , 1, 0]), ArcSin[Sqrt[-(((-1)^(2/3)*((-1)^(1/3) - x))/(1 + (-1)^(1/3)))]], (-1)^(1/3)]*Root[1 + #1^2 + #1^3 & , 1, 0]^3)/(Sqrt[1 + x^3]*(-(-1)^(1/3) + Root[1 + #1^2 + #1^3 & , 1, 0])*(Root[1 + #1^2 + #1^3 & , 1, 0] - Root[1 + #1^2 + #1^3 & , 2, 0])*(Root[1 + #1^2 + #1^3 & , 1, 0] - Root[1 + #1^2 + #1^3 & , 3, 0])) - (4*((-1)^(1/3) + (-1)^(2/3))*Sqrt[(1 + x)/(1 + (-1)^(1/3))]*Sqrt[((-(-1)^(2/3) - x)*(-(-1)^(1/3) + x))/((-1)^(1/3) + (-1)^(2/3))^2]*EllipticPi[((-1)^(1/3) + (-1)^(2/3))/((-1)^(1/3) - Root[1 + #1^2 + #1^3 & , 2, 0]), ArcSin[Sqrt[-(((-1)^(2/3)*((-1)^(1/3) - x))/(1 + (-1)^(1/3)))]], (-1)^(1/3)])/(Sqrt[1 + x^3]*(-(-1)^(1/3) + Root[1 + #1^2 + #1^3 & , 2, 0])*(-Root[1 + #1^2 + #1^3 & , 1, 0] + Root[1 + #1^2 + #1^3 & , 2, 0])*(Root[1 + #1^2 + #1^3 & , 2, 0] - Root[1 + #1^2 + #1^3 & , 3, 0])) + (2*((-1)^(1/3) + (-1)^(2/3))*Sqrt[(1 + x)/(1 + (-1)^(1/3))]*Sqrt[((-(-1)^(2/3) - x)*(-(-1)^(1/3) + x))/((-1)^(1/3) + (-1)^(2/3))^2]*EllipticPi[((-1)^(1/3) + (-1)^(2/3))/((-1)^(1/3) - Root[1 + #1^2 + #1^3 & , 2, 0]), ArcSin[Sqrt[-(((-1)^(2/3)*((-1)^(1/3) - x))/(1 + (-1)^(1/3)))]], (-1)^(1/3)]*Root[1 + #1^2 + #1^3 & , 2, 0]^3)/(Sqrt[1 + x^3]*(-(-1)^(1/3) + Root[1 + #1^2 + #1^3 & , 2, 0])*(-Root[1 + #1^2 + #1^3 & , 1, 0] + Root[1 + #1^2 + #1^3 & , 2, 0])*(Root[1 + #1^2 + #1^3 & , 2, 0] - Root[1 + #1^2 + #1^3 & , 3, 0])) - (4*((-1)^(1/3) + (-1)^(2/3))*Sqrt[(1 + x)/(1 + (-1)^(1/3))]*Sqrt[((-(-1)^(2/3) - x)*(-(-1)^(1/3) + x))/((-1)^(1/3) + (-1)^(2/3))^2]*EllipticPi[((-1)^(1/3) + (-1)^(2/3))/((-1)^(1/3) - Root[1 + #1^2 + #1^3 & , 3, 0]), ArcSin[Sqrt[-(((-1)^(2/3)*((-1)^(1/3) - x))/(1 + (-1)^(1/3)))]], (-1)^(1/3)])/(Sqrt[1 + x^3]*(-(-1)^(1/3) + Root[1 + #1^2 + #1^3 & , 3, 0])*(-Root[1 + #1^2 + #1^3 & , 1, 0] + Root[1 + #1^2 + #1^3 & , 3, 0])*(-Root[1 + #1^2 + #1^3 & , 2, 0] + Root[1 + #1^2 + #1^3 & , 3, 0])) + (2*((-1)^(1/3) + (-1)^(2/3))*Sqrt[(1 + x)/(1 + (-1)^(1/3))]*Sqrt[((-(-1)^(2/3) - x)*(-(-1)^(1/3) + x))/((-1)^(1/3) + (-1)^(2/3))^2]*EllipticPi[((-1)^(1/3) + (-1)^(2/3))/((-1)^(1/3) - Root[1 + #1^2 + #1^3 & , 3, 0]), ArcSin[Sqrt[-(((-1)^(2/3)*((-1)^(1/3) - x))/(1 + (-1)^(1/3)))]], (-1)^(1/3)]*Root[1 + #1^2 + #1^3 & , 3, 0]^3)/(Sqrt[1 + x^3]*(-(-1)^(1/3) + Root[1 + #1^2 + #1^3 & , 3, 0])*(-Root[1 + #1^2 + #1^3 & , 1, 0] + Root[1 + #1^2 + #1^3 & , 3, 0])*(-Root[1 + #1^2 + #1^3 & , 2, 0] + Root[1 + #1^2 + #1^3 & , 3, 0]))","C",0
546,1,284,43,0.7873379,"\int \frac{\left(-1+x^4\right) \sqrt{1+x^2+x^4}}{\left(1+x^4\right) \left(1-x^2+x^4\right)} \, dx","Integrate[((-1 + x^4)*Sqrt[1 + x^2 + x^4])/((1 + x^4)*(1 - x^2 + x^4)),x]","\frac{\sqrt{\sqrt[3]{-1} x^2+1} \sqrt{1-(-1)^{2/3} x^2} \left(\left((-1)^{2/3}-1\right) F\left(i \sinh ^{-1}\left((-1)^{5/6} x\right)|(-1)^{2/3}\right)-2 \left(\sqrt[3]{-1}-2\right) \Pi \left(-1;i \sinh ^{-1}\left((-1)^{5/6} x\right)|(-1)^{2/3}\right)-4 (-1)^{2/3} \Pi \left(-(-1)^{2/3};i \sinh ^{-1}\left((-1)^{5/6} x\right)|(-1)^{2/3}\right)+2 \sqrt[3]{-1} \Pi \left(-(-1)^{2/3};i \sinh ^{-1}\left((-1)^{5/6} x\right)|(-1)^{2/3}\right)+(-1)^{2/3} \Pi \left(-(-1)^{5/6};i \sinh ^{-1}\left((-1)^{5/6} x\right)|(-1)^{2/3}\right)-\Pi \left(-(-1)^{5/6};i \sinh ^{-1}\left((-1)^{5/6} x\right)|(-1)^{2/3}\right)+(-1)^{2/3} \Pi \left((-1)^{5/6};i \sinh ^{-1}\left((-1)^{5/6} x\right)|(-1)^{2/3}\right)-\Pi \left((-1)^{5/6};i \sinh ^{-1}\left((-1)^{5/6} x\right)|(-1)^{2/3}\right)\right)}{\left(1+\sqrt[3]{-1}\right) \sqrt{x^4+x^2+1}}","\tanh ^{-1}\left(\frac{x}{\sqrt{x^4+x^2+1}}\right)-\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+x^2+1}}\right)",1,"(Sqrt[1 + (-1)^(1/3)*x^2]*Sqrt[1 - (-1)^(2/3)*x^2]*((-1 + (-1)^(2/3))*EllipticF[I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)] - 2*(-2 + (-1)^(1/3))*EllipticPi[-1, I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)] + 2*(-1)^(1/3)*EllipticPi[-(-1)^(2/3), I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)] - 4*(-1)^(2/3)*EllipticPi[-(-1)^(2/3), I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)] - EllipticPi[-(-1)^(5/6), I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)] + (-1)^(2/3)*EllipticPi[-(-1)^(5/6), I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)] - EllipticPi[(-1)^(5/6), I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)] + (-1)^(2/3)*EllipticPi[(-1)^(5/6), I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)]))/((1 + (-1)^(1/3))*Sqrt[1 + x^2 + x^4])","C",1
547,1,17667,43,6.2111722,"\int \frac{\sqrt{1+x+x^2+x^4} \left(-2-x+2 x^4\right)}{\left(1+x+x^4\right)^2} \, dx","Integrate[(Sqrt[1 + x + x^2 + x^4]*(-2 - x + 2*x^4))/(1 + x + x^4)^2,x]","\text{Result too large to show}","-\frac{\sqrt{x^4+x^2+x+1} x}{x^4+x+1}-\tanh ^{-1}\left(\frac{x}{\sqrt{x^4+x^2+x+1}}\right)",1,"Result too large to show","C",0
548,0,0,43,0.6684465,"\int \frac{\left(-1+x^4\right) \left(1+3 x^4\right)}{x \left(-1-a x+x^4\right) \sqrt{-x+x^5}} \, dx","Integrate[((-1 + x^4)*(1 + 3*x^4))/(x*(-1 - a*x + x^4)*Sqrt[-x + x^5]),x]","\int \frac{\left(-1+x^4\right) \left(1+3 x^4\right)}{x \left(-1-a x+x^4\right) \sqrt{-x+x^5}} \, dx","\frac{2 \sqrt{x^5-x}}{x}-2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{x^5-x}}\right)",1,"Integrate[((-1 + x^4)*(1 + 3*x^4))/(x*(-1 - a*x + x^4)*Sqrt[-x + x^5]), x]","F",-1
549,1,28,43,0.0052716,"\int \frac{1}{x^{19} \sqrt{-1+x^6}} \, dx","Integrate[1/(x^19*Sqrt[-1 + x^6]),x]","\frac{1}{3} \sqrt{x^6-1} \, _2F_1\left(\frac{1}{2},4;\frac{3}{2};1-x^6\right)","\frac{5}{48} \tan ^{-1}\left(\sqrt{x^6-1}\right)+\frac{\sqrt{x^6-1} \left(15 x^{12}+10 x^6+8\right)}{144 x^{18}}",1,"(Sqrt[-1 + x^6]*Hypergeometric2F1[1/2, 4, 3/2, 1 - x^6])/3","C",1
550,1,41,43,0.0127389,"\int \frac{x^{14}}{\sqrt{-1+x^6}} \, dx","Integrate[x^14/Sqrt[-1 + x^6],x]","\frac{1}{24} \left(\sqrt{x^6-1} \left(2 x^6+3\right) x^3+3 \tanh ^{-1}\left(\frac{x^3}{\sqrt{x^6-1}}\right)\right)","\frac{1}{8} \log \left(\sqrt{x^6-1}+x^3\right)+\frac{1}{24} \sqrt{x^6-1} \left(2 x^9+3 x^3\right)",1,"(x^3*Sqrt[-1 + x^6]*(3 + 2*x^6) + 3*ArcTanh[x^3/Sqrt[-1 + x^6]])/24","A",1
551,1,28,43,0.0052315,"\int \frac{\sqrt{-1+x^6}}{x^{19}} \, dx","Integrate[Sqrt[-1 + x^6]/x^19,x]","\frac{1}{9} \left(x^6-1\right)^{3/2} \, _2F_1\left(\frac{3}{2},4;\frac{5}{2};1-x^6\right)","\frac{1}{48} \tan ^{-1}\left(\sqrt{x^6-1}\right)+\frac{\sqrt{x^6-1} \left(3 x^{12}+2 x^6-8\right)}{144 x^{18}}",1,"((-1 + x^6)^(3/2)*Hypergeometric2F1[3/2, 4, 5/2, 1 - x^6])/9","C",1
552,1,49,43,0.0238409,"\int x^8 \sqrt{-1+x^6} \, dx","Integrate[x^8*Sqrt[-1 + x^6],x]","\frac{\left(x^6-1\right) \left(\sin ^{-1}\left(x^3\right)+\sqrt{1-x^6} \left(2 x^6-1\right) x^3\right)}{24 \sqrt{-\left(x^6-1\right)^2}}","\frac{1}{24} \sqrt{x^6-1} \left(2 x^9-x^3\right)-\frac{1}{24} \log \left(\sqrt{x^6-1}+x^3\right)",1,"((-1 + x^6)*(x^3*Sqrt[1 - x^6]*(-1 + 2*x^6) + ArcSin[x^3]))/(24*Sqrt[-(-1 + x^6)^2])","A",1
553,1,125,43,0.346619,"\int \frac{-1+x^6}{\sqrt{1+x^4} \left(1+x^6\right)} \, dx","Integrate[(-1 + x^6)/(Sqrt[1 + x^4]*(1 + x^6)),x]","\frac{(-1)^{5/12} \left(2 \left(\Pi \left(-i;\left.i \sinh ^{-1}\left(\frac{(1+i) x}{\sqrt{2}}\right)\right|-1\right)+\Pi \left(\frac{i}{2}-\frac{\sqrt{3}}{2};\left.i \sinh ^{-1}\left(\frac{(1+i) x}{\sqrt{2}}\right)\right|-1\right)+\Pi \left(\frac{1}{2} \left(i+\sqrt{3}\right);\left.i \sinh ^{-1}\left(\frac{(1+i) x}{\sqrt{2}}\right)\right|-1\right)\right)-3 F\left(\left.i \sinh ^{-1}\left(\frac{(1+i) x}{\sqrt{2}}\right)\right|-1\right)\right)}{\sqrt{3} \left(1+\sqrt[3]{-1}\right)}","-\frac{\tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{3 \sqrt{2}}-\frac{2}{3} \tanh ^{-1}\left(\frac{x}{\sqrt{x^4+1}}\right)",1,"((-1)^(5/12)*(-3*EllipticF[I*ArcSinh[((1 + I)*x)/Sqrt[2]], -1] + 2*(EllipticPi[-I, I*ArcSinh[((1 + I)*x)/Sqrt[2]], -1] + EllipticPi[I/2 - Sqrt[3]/2, I*ArcSinh[((1 + I)*x)/Sqrt[2]], -1] + EllipticPi[(I + Sqrt[3])/2, I*ArcSinh[((1 + I)*x)/Sqrt[2]], -1])))/(Sqrt[3]*(1 + (-1)^(1/3)))","C",0
554,1,31,43,0.0110425,"\int \frac{x^{14}}{\sqrt{1+x^6}} \, dx","Integrate[x^14/Sqrt[1 + x^6],x]","\frac{1}{24} \left(3 \sinh ^{-1}\left(x^3\right)+\sqrt{x^6+1} \left(2 x^6-3\right) x^3\right)","\frac{1}{8} \log \left(\sqrt{x^6+1}+x^3\right)+\frac{1}{24} \sqrt{x^6+1} \left(2 x^9-3 x^3\right)",1,"(x^3*Sqrt[1 + x^6]*(-3 + 2*x^6) + 3*ArcSinh[x^3])/24","A",1
555,1,36,43,0.0102583,"\int \frac{-1+x^6}{x^{19} \sqrt{1+x^6}} \, dx","Integrate[(-1 + x^6)/(x^19*Sqrt[1 + x^6]),x]","\frac{\sqrt{x^6+1} \left(1-11 x^{18} \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};x^6+1\right)\right)}{18 x^{18}}","\frac{\sqrt{x^6+1} \left(33 x^{12}-22 x^6+8\right)}{144 x^{18}}-\frac{11}{48} \tanh ^{-1}\left(\sqrt{x^6+1}\right)",1,"(Sqrt[1 + x^6]*(1 - 11*x^18*Hypergeometric2F1[1/2, 3, 3/2, 1 + x^6]))/(18*x^18)","C",1
556,1,114,43,0.2660198,"\int \frac{1+x^6}{\sqrt{1+x^4} \left(1-x^6\right)} \, dx","Integrate[(1 + x^6)/(Sqrt[1 + x^4]*(1 - x^6)),x]","\frac{1}{3} \sqrt[4]{-1} \left(3 F\left(\left.i \sinh ^{-1}\left(\frac{(1+i) x}{\sqrt{2}}\right)\right|-1\right)-2 \left(\Pi \left(i;\left.i \sinh ^{-1}\left(\frac{(1+i) x}{\sqrt{2}}\right)\right|-1\right)+\Pi \left(-\frac{i}{2}-\frac{\sqrt{3}}{2};\left.i \sinh ^{-1}\left(\frac{(1+i) x}{\sqrt{2}}\right)\right|-1\right)+\Pi \left(\frac{1}{2} \left(-i+\sqrt{3}\right);\left.i \sinh ^{-1}\left(\frac{(1+i) x}{\sqrt{2}}\right)\right|-1\right)\right)\right)","\frac{2}{3} \tan ^{-1}\left(\frac{x}{\sqrt{x^4+1}}\right)+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{3 \sqrt{2}}",1,"((-1)^(1/4)*(3*EllipticF[I*ArcSinh[((1 + I)*x)/Sqrt[2]], -1] - 2*(EllipticPi[I, I*ArcSinh[((1 + I)*x)/Sqrt[2]], -1] + EllipticPi[-1/2*I - Sqrt[3]/2, I*ArcSinh[((1 + I)*x)/Sqrt[2]], -1] + EllipticPi[(-I + Sqrt[3])/2, I*ArcSinh[((1 + I)*x)/Sqrt[2]], -1])))/3","C",1
557,1,114,43,0.1846981,"\int \frac{1+x^6}{\sqrt{1+x^4} \left(-1+x^6\right)} \, dx","Integrate[(1 + x^6)/(Sqrt[1 + x^4]*(-1 + x^6)),x]","\frac{1}{3} \sqrt[4]{-1} \left(2 \left(\Pi \left(i;\left.i \sinh ^{-1}\left(\frac{(1+i) x}{\sqrt{2}}\right)\right|-1\right)+\Pi \left(-\frac{i}{2}-\frac{\sqrt{3}}{2};\left.i \sinh ^{-1}\left(\frac{(1+i) x}{\sqrt{2}}\right)\right|-1\right)+\Pi \left(\frac{1}{2} \left(-i+\sqrt{3}\right);\left.i \sinh ^{-1}\left(\frac{(1+i) x}{\sqrt{2}}\right)\right|-1\right)\right)-3 F\left(\left.i \sinh ^{-1}\left(\frac{(1+i) x}{\sqrt{2}}\right)\right|-1\right)\right)","-\frac{2}{3} \tan ^{-1}\left(\frac{x}{\sqrt{x^4+1}}\right)-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{3 \sqrt{2}}",1,"((-1)^(1/4)*(-3*EllipticF[I*ArcSinh[((1 + I)*x)/Sqrt[2]], -1] + 2*(EllipticPi[I, I*ArcSinh[((1 + I)*x)/Sqrt[2]], -1] + EllipticPi[-1/2*I - Sqrt[3]/2, I*ArcSinh[((1 + I)*x)/Sqrt[2]], -1] + EllipticPi[(-I + Sqrt[3])/2, I*ArcSinh[((1 + I)*x)/Sqrt[2]], -1])))/3","C",1
558,0,0,43,0.6144061,"\int \frac{\left(-1+x^5\right) \left(1+4 x^5\right)}{x \left(-1-a x+x^5\right) \sqrt{-x+x^6}} \, dx","Integrate[((-1 + x^5)*(1 + 4*x^5))/(x*(-1 - a*x + x^5)*Sqrt[-x + x^6]),x]","\int \frac{\left(-1+x^5\right) \left(1+4 x^5\right)}{x \left(-1-a x+x^5\right) \sqrt{-x+x^6}} \, dx","\frac{2 \sqrt{x^6-x}}{x}-2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{x^6-x}}\right)",1,"Integrate[((-1 + x^5)*(1 + 4*x^5))/(x*(-1 - a*x + x^5)*Sqrt[-x + x^6]), x]","F",-1
559,1,61,43,0.064324,"\int \frac{\left(2+x^3\right) \left(1+x^3+x^6\right)}{x^7 \sqrt{1+x^3}} \, dx","Integrate[((2 + x^3)*(1 + x^3 + x^6))/(x^7*Sqrt[1 + x^3]),x]","\frac{1}{3} \left(-4 \sqrt{x^3+1} \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};x^3+1\right)+\frac{\sqrt{x^3+1} \left(2 x^3-3\right)}{x^3}-3 \tanh ^{-1}\left(\sqrt{x^3+1}\right)\right)","\frac{\sqrt{x^3+1} \left(4 x^6-3 x^3-2\right)}{6 x^6}-\frac{3}{2} \tanh ^{-1}\left(\sqrt{x^3+1}\right)",1,"((Sqrt[1 + x^3]*(-3 + 2*x^3))/x^3 - 3*ArcTanh[Sqrt[1 + x^3]] - 4*Sqrt[1 + x^3]*Hypergeometric2F1[1/2, 3, 3/2, 1 + x^3])/3","C",1
560,0,0,43,0.6412508,"\int \frac{-x+4 x^6}{\left(1+x^5\right) \left(a-x+a x^5\right) \sqrt{x+x^6}} \, dx","Integrate[(-x + 4*x^6)/((1 + x^5)*(a - x + a*x^5)*Sqrt[x + x^6]),x]","\int \frac{-x+4 x^6}{\left(1+x^5\right) \left(a-x+a x^5\right) \sqrt{x+x^6}} \, dx","\frac{2 \sqrt{x^6+x}}{x^5+1}-2 \sqrt{a} \tanh ^{-1}\left(\frac{x}{\sqrt{a} \sqrt{x^6+x}}\right)",1,"Integrate[(-x + 4*x^6)/((1 + x^5)*(a - x + a*x^5)*Sqrt[x + x^6]), x]","F",-1
561,0,0,43,0.2373457,"\int \frac{2+x^3+x^6}{x \sqrt[4]{1+x^6} \left(-4+5 x^3-4 x^6+x^9\right)} \, dx","Integrate[(2 + x^3 + x^6)/(x*(1 + x^6)^(1/4)*(-4 + 5*x^3 - 4*x^6 + x^9)),x]","\int \frac{2+x^3+x^6}{x \sqrt[4]{1+x^6} \left(-4+5 x^3-4 x^6+x^9\right)} \, dx","\frac{1}{3} \tan ^{-1}\left(\frac{1-x^3}{\sqrt[4]{x^6+1}}\right)-\frac{1}{3} \tanh ^{-1}\left(\frac{x^3-1}{\sqrt[4]{x^6+1}}\right)",1,"Integrate[(2 + x^3 + x^6)/(x*(1 + x^6)^(1/4)*(-4 + 5*x^3 - 4*x^6 + x^9)), x]","F",-1
562,1,43,43,0.0201635,"\int \sqrt[5]{243-5265 x+47250 x^2-225810 x^3+615255 x^4-954733 x^5+820340 x^6-401440 x^7+112000 x^8-16640 x^9+1024 x^{10}} \, dx","Integrate[(243 - 5265*x + 47250*x^2 - 225810*x^3 + 615255*x^4 - 954733*x^5 + 820340*x^6 - 401440*x^7 + 112000*x^8 - 16640*x^9 + 1024*x^10)^(1/5),x]","\frac{x \sqrt[5]{\left(4 x^2-13 x+3\right)^5} \left(8 x^2-39 x+18\right)}{6 \left(4 x^2-13 x+3\right)}","\frac{x \sqrt[5]{\left(4 x^2-13 x+3\right)^5} \left(8 x^2-39 x+18\right)}{6 \left(4 x^2-13 x+3\right)}",1,"(x*((3 - 13*x + 4*x^2)^5)^(1/5)*(18 - 39*x + 8*x^2))/(6*(3 - 13*x + 4*x^2))","A",1
563,0,0,43,0.2719971,"\int \frac{-b x^3+2 a x^8}{\sqrt[4]{-b x+a x^6} \left(-1-b x^5+a x^{10}\right)} \, dx","Integrate[(-(b*x^3) + 2*a*x^8)/((-(b*x) + a*x^6)^(1/4)*(-1 - b*x^5 + a*x^10)),x]","\int \frac{-b x^3+2 a x^8}{\sqrt[4]{-b x+a x^6} \left(-1-b x^5+a x^{10}\right)} \, dx","\frac{2}{5} \tan ^{-1}\left(x \sqrt[4]{a x^6-b x}\right)-\frac{2}{5} \tanh ^{-1}\left(x \sqrt[4]{a x^6-b x}\right)",1,"Integrate[(-(b*x^3) + 2*a*x^8)/((-(b*x) + a*x^6)^(1/4)*(-1 - b*x^5 + a*x^10)), x]","F",-1
564,0,0,43,0.3214711,"\int \frac{x^5 \left(-7 b+10 a x^3\right)}{\sqrt[4]{-b x^3+a x^6} \left(-1-b x^7+a x^{10}\right)} \, dx","Integrate[(x^5*(-7*b + 10*a*x^3))/((-(b*x^3) + a*x^6)^(1/4)*(-1 - b*x^7 + a*x^10)),x]","\int \frac{x^5 \left(-7 b+10 a x^3\right)}{\sqrt[4]{-b x^3+a x^6} \left(-1-b x^7+a x^{10}\right)} \, dx","2 \tan ^{-1}\left(x \sqrt[4]{a x^6-b x^3}\right)-2 \tanh ^{-1}\left(x \sqrt[4]{a x^6-b x^3}\right)",1,"Integrate[(x^5*(-7*b + 10*a*x^3))/((-(b*x^3) + a*x^6)^(1/4)*(-1 - b*x^7 + a*x^10)), x]","F",-1
565,1,72,43,0.6485345,"\int \frac{1}{x \sqrt{-\frac{a}{b^2}+\frac{a^2 x^2}{b^2}} \sqrt{a x^2+b x \sqrt{-\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}}} \, dx","Integrate[1/(x*Sqrt[-(a/b^2) + (a^2*x^2)/b^2]*Sqrt[a*x^2 + b*x*Sqrt[-(a/b^2) + (a^2*x^2)/b^2]]),x]","\frac{2 \left(b x \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x^2-1\right)}{\sqrt{\frac{a \left(a x^2-1\right)}{b^2}} \sqrt{x \left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right)}}","\frac{2 b \sqrt{b x \sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}}+a x^2}}{a x}",1,"(2*(-1 + a*x^2 + b*x*Sqrt[(a*(-1 + a*x^2))/b^2]))/(Sqrt[(a*(-1 + a*x^2))/b^2]*Sqrt[x*(a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2])])","A",1
566,1,346,44,4.8053395,"\int \frac{a b-2 a x+x^2}{\sqrt{x (-a+x) (-b+x)} \left(a d-(b+d) x+x^2\right)} \, dx","Integrate[(a*b - 2*a*x + x^2)/(Sqrt[x*(-a + x)*(-b + x)]*(a*d - (b + d)*x + x^2)),x]","-\frac{i a x^{3/2} \sqrt{1-\frac{a}{x}} \sqrt{1-\frac{b}{x}} \left(\left(-b \left(\sqrt{-4 a d+b^2+2 b d+d^2}-2 d\right)+d \left(\sqrt{-4 a d+b^2+2 b d+d^2}-4 a+d\right)+b^2\right) \Pi \left(\frac{2 d}{b+d-\sqrt{b^2+2 d b+d^2-4 a d}};i \sinh ^{-1}\left(\frac{\sqrt{-a}}{\sqrt{x}}\right)|\frac{b}{a}\right)-\left(b \left(\sqrt{-4 a d+b^2+2 b d+d^2}+2 d\right)+d \left(-\sqrt{-4 a d+b^2+2 b d+d^2}-4 a+d\right)+b^2\right) \Pi \left(\frac{2 d}{b+d+\sqrt{b^2+2 d b+d^2-4 a d}};i \sinh ^{-1}\left(\frac{\sqrt{-a}}{\sqrt{x}}\right)|\frac{b}{a}\right)+2 b \sqrt{d (d-4 a)+b^2+2 b d} F\left(i \sinh ^{-1}\left(\frac{\sqrt{-a}}{\sqrt{x}}\right)|\frac{b}{a}\right)\right)}{(-a)^{3/2} d \sqrt{d (d-4 a)+b^2+2 b d} \sqrt{x (x-a) (x-b)}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{x^2 (-a-b)+a b x+x^3}}{\sqrt{d} (a-x)}\right)}{\sqrt{d}}",1,"((-I)*a*Sqrt[1 - a/x]*Sqrt[1 - b/x]*x^(3/2)*(2*b*Sqrt[b^2 + 2*b*d + d*(-4*a + d)]*EllipticF[I*ArcSinh[Sqrt[-a]/Sqrt[x]], b/a] + (b^2 - b*(-2*d + Sqrt[b^2 - 4*a*d + 2*b*d + d^2]) + d*(-4*a + d + Sqrt[b^2 - 4*a*d + 2*b*d + d^2]))*EllipticPi[(2*d)/(b + d - Sqrt[b^2 - 4*a*d + 2*b*d + d^2]), I*ArcSinh[Sqrt[-a]/Sqrt[x]], b/a] - (b^2 + d*(-4*a + d - Sqrt[b^2 - 4*a*d + 2*b*d + d^2]) + b*(2*d + Sqrt[b^2 - 4*a*d + 2*b*d + d^2]))*EllipticPi[(2*d)/(b + d + Sqrt[b^2 - 4*a*d + 2*b*d + d^2]), I*ArcSinh[Sqrt[-a]/Sqrt[x]], b/a]))/((-a)^(3/2)*d*Sqrt[b^2 + 2*b*d + d*(-4*a + d)]*Sqrt[x*(-a + x)*(-b + x)])","C",1
567,1,238,44,7.2153476,"\int \frac{a b-2 a x+x^2}{\sqrt{x (-a+x) (-b+x)} \left(a-(1+b d) x+d x^2\right)} \, dx","Integrate[(a*b - 2*a*x + x^2)/(Sqrt[x*(-a + x)*(-b + x)]*(a - (1 + b*d)*x + d*x^2)),x]","\frac{2 i (a-x)^{3/2} \sqrt{\frac{x}{x-a}} \sqrt{\frac{b-x}{a-x}} \left(-\Pi \left(\frac{2 (a-b) d}{2 a d-b d+\sqrt{(b d+1)^2-4 a d}-1};i \sinh ^{-1}\left(\frac{\sqrt{-a}}{\sqrt{a-x}}\right)|1-\frac{b}{a}\right)-\Pi \left(-\frac{2 (a-b) d}{-2 a d+b d+\sqrt{(b d+1)^2-4 a d}+1};i \sinh ^{-1}\left(\frac{\sqrt{-a}}{\sqrt{a-x}}\right)|1-\frac{b}{a}\right)+F\left(i \sinh ^{-1}\left(\frac{\sqrt{-a}}{\sqrt{a-x}}\right)|1-\frac{b}{a}\right)\right)}{\sqrt{-a} d \sqrt{x (x-a) (x-b)}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{x^2 (-a-b)+a b x+x^3}}{a-x}\right)}{\sqrt{d}}",1,"((2*I)*(a - x)^(3/2)*Sqrt[(b - x)/(a - x)]*Sqrt[x/(-a + x)]*(EllipticF[I*ArcSinh[Sqrt[-a]/Sqrt[a - x]], 1 - b/a] - EllipticPi[(2*(a - b)*d)/(-1 + 2*a*d - b*d + Sqrt[-4*a*d + (1 + b*d)^2]), I*ArcSinh[Sqrt[-a]/Sqrt[a - x]], 1 - b/a] - EllipticPi[(-2*(a - b)*d)/(1 - 2*a*d + b*d + Sqrt[-4*a*d + (1 + b*d)^2]), I*ArcSinh[Sqrt[-a]/Sqrt[a - x]], 1 - b/a]))/(Sqrt[-a]*d*Sqrt[x*(-a + x)*(-b + x)])","C",1
568,1,1609,44,3.1271059,"\int \frac{\left(-2+x^3\right) \sqrt{1-x^2+x^3}}{\left(1+x^3\right)^2} \, dx","Integrate[((-2 + x^3)*Sqrt[1 - x^2 + x^3])/(1 + x^3)^2,x]","\frac{-\frac{x^4-x^3+x}{x^3+1}+\frac{F\left(\sin ^{-1}\left(\sqrt{\frac{\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,3\right]-x}{-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,2\right]+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,3\right]}}\right)|\frac{\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,2\right]-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,3\right]}{\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,1\right]-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,3\right]}\right) \left(x-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,3\right]\right) \sqrt{\frac{\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,1\right]-x}{\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,1\right]-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,3\right]}} \sqrt{\frac{\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,2\right]-x}{\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,2\right]-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,3\right]}}}{\sqrt{\frac{x-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,3\right]}{\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,2\right]-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,3\right]}}}+\frac{2 (-1)^{2/3} \Pi \left(\frac{-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,2\right]+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,3\right]}{(-1)^{2/3}+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,3\right]};\sin ^{-1}\left(\sqrt{\frac{\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,3\right]-x}{-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,2\right]+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,3\right]}}\right)|\frac{\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,2\right]-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,3\right]}{\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,1\right]-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,3\right]}\right) \sqrt{\frac{\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,1\right]-x}{\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,1\right]-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,3\right]}} \sqrt{-\frac{\left(x-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,2\right]\right) \left(x-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,3\right]\right)}{\left(\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,2\right]-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,3\right]\right)^2}} \left(-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,2\right]+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,3\right]\right)}{-1+i \sqrt{3}+2 \text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,3\right]}+\frac{3 (-1)^{2/3} \Pi \left(\frac{\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,2\right]-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,3\right]}{\sqrt[3]{-1}-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,3\right]};\sin ^{-1}\left(\sqrt{\frac{\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,3\right]-x}{-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,2\right]+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,3\right]}}\right)|\frac{\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,2\right]-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,3\right]}{\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,1\right]-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,3\right]}\right) \sqrt{\frac{\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,1\right]-x}{\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,1\right]-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,3\right]}} \sqrt{-\frac{\left(x-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,2\right]\right) \left(x-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,3\right]\right)}{\left(\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,2\right]-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,3\right]\right)^2}} \left(-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,2\right]+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,3\right]\right)}{\left(1+\sqrt[3]{-1}\right)^2 \left(\sqrt[3]{-1}-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,3\right]\right)}+\frac{\Pi \left(\frac{-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,2\right]+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,3\right]}{1+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,3\right]};\sin ^{-1}\left(\sqrt{\frac{\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,3\right]-x}{-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,2\right]+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,3\right]}}\right)|\frac{\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,2\right]-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,3\right]}{\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,1\right]-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,3\right]}\right) \sqrt{\frac{\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,1\right]-x}{\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,1\right]-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,3\right]}} \sqrt{-\frac{\left(x-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,2\right]\right) \left(x-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,3\right]\right)}{\left(\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,2\right]-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,3\right]\right)^2}} \left(-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,2\right]+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,3\right]\right)}{1+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+1\&,3\right]}}{\sqrt{x^3-x^2+1}}","-\frac{\sqrt{x^3-x^2+1} x}{x^3+1}-\tan ^{-1}\left(\frac{x}{\sqrt{x^3-x^2+1}}\right)",1,"(-((x - x^3 + x^4)/(1 + x^3)) + (EllipticF[ArcSin[Sqrt[(-x + Root[1 - #1^2 + #1^3 & , 3, 0])/(-Root[1 - #1^2 + #1^3 & , 2, 0] + Root[1 - #1^2 + #1^3 & , 3, 0])]], (Root[1 - #1^2 + #1^3 & , 2, 0] - Root[1 - #1^2 + #1^3 & , 3, 0])/(Root[1 - #1^2 + #1^3 & , 1, 0] - Root[1 - #1^2 + #1^3 & , 3, 0])]*(x - Root[1 - #1^2 + #1^3 & , 3, 0])*Sqrt[(-x + Root[1 - #1^2 + #1^3 & , 1, 0])/(Root[1 - #1^2 + #1^3 & , 1, 0] - Root[1 - #1^2 + #1^3 & , 3, 0])]*Sqrt[(-x + Root[1 - #1^2 + #1^3 & , 2, 0])/(Root[1 - #1^2 + #1^3 & , 2, 0] - Root[1 - #1^2 + #1^3 & , 3, 0])])/Sqrt[(x - Root[1 - #1^2 + #1^3 & , 3, 0])/(Root[1 - #1^2 + #1^3 & , 2, 0] - Root[1 - #1^2 + #1^3 & , 3, 0])] + (3*(-1)^(2/3)*EllipticPi[(Root[1 - #1^2 + #1^3 & , 2, 0] - Root[1 - #1^2 + #1^3 & , 3, 0])/((-1)^(1/3) - Root[1 - #1^2 + #1^3 & , 3, 0]), ArcSin[Sqrt[(-x + Root[1 - #1^2 + #1^3 & , 3, 0])/(-Root[1 - #1^2 + #1^3 & , 2, 0] + Root[1 - #1^2 + #1^3 & , 3, 0])]], (Root[1 - #1^2 + #1^3 & , 2, 0] - Root[1 - #1^2 + #1^3 & , 3, 0])/(Root[1 - #1^2 + #1^3 & , 1, 0] - Root[1 - #1^2 + #1^3 & , 3, 0])]*Sqrt[(-x + Root[1 - #1^2 + #1^3 & , 1, 0])/(Root[1 - #1^2 + #1^3 & , 1, 0] - Root[1 - #1^2 + #1^3 & , 3, 0])]*Sqrt[-(((x - Root[1 - #1^2 + #1^3 & , 2, 0])*(x - Root[1 - #1^2 + #1^3 & , 3, 0]))/(Root[1 - #1^2 + #1^3 & , 2, 0] - Root[1 - #1^2 + #1^3 & , 3, 0])^2)]*(-Root[1 - #1^2 + #1^3 & , 2, 0] + Root[1 - #1^2 + #1^3 & , 3, 0]))/((1 + (-1)^(1/3))^2*((-1)^(1/3) - Root[1 - #1^2 + #1^3 & , 3, 0])) + (EllipticPi[(-Root[1 - #1^2 + #1^3 & , 2, 0] + Root[1 - #1^2 + #1^3 & , 3, 0])/(1 + Root[1 - #1^2 + #1^3 & , 3, 0]), ArcSin[Sqrt[(-x + Root[1 - #1^2 + #1^3 & , 3, 0])/(-Root[1 - #1^2 + #1^3 & , 2, 0] + Root[1 - #1^2 + #1^3 & , 3, 0])]], (Root[1 - #1^2 + #1^3 & , 2, 0] - Root[1 - #1^2 + #1^3 & , 3, 0])/(Root[1 - #1^2 + #1^3 & , 1, 0] - Root[1 - #1^2 + #1^3 & , 3, 0])]*Sqrt[(-x + Root[1 - #1^2 + #1^3 & , 1, 0])/(Root[1 - #1^2 + #1^3 & , 1, 0] - Root[1 - #1^2 + #1^3 & , 3, 0])]*Sqrt[-(((x - Root[1 - #1^2 + #1^3 & , 2, 0])*(x - Root[1 - #1^2 + #1^3 & , 3, 0]))/(Root[1 - #1^2 + #1^3 & , 2, 0] - Root[1 - #1^2 + #1^3 & , 3, 0])^2)]*(-Root[1 - #1^2 + #1^3 & , 2, 0] + Root[1 - #1^2 + #1^3 & , 3, 0]))/(1 + Root[1 - #1^2 + #1^3 & , 3, 0]) + (2*(-1)^(2/3)*EllipticPi[(-Root[1 - #1^2 + #1^3 & , 2, 0] + Root[1 - #1^2 + #1^3 & , 3, 0])/((-1)^(2/3) + Root[1 - #1^2 + #1^3 & , 3, 0]), ArcSin[Sqrt[(-x + Root[1 - #1^2 + #1^3 & , 3, 0])/(-Root[1 - #1^2 + #1^3 & , 2, 0] + Root[1 - #1^2 + #1^3 & , 3, 0])]], (Root[1 - #1^2 + #1^3 & , 2, 0] - Root[1 - #1^2 + #1^3 & , 3, 0])/(Root[1 - #1^2 + #1^3 & , 1, 0] - Root[1 - #1^2 + #1^3 & , 3, 0])]*Sqrt[(-x + Root[1 - #1^2 + #1^3 & , 1, 0])/(Root[1 - #1^2 + #1^3 & , 1, 0] - Root[1 - #1^2 + #1^3 & , 3, 0])]*Sqrt[-(((x - Root[1 - #1^2 + #1^3 & , 2, 0])*(x - Root[1 - #1^2 + #1^3 & , 3, 0]))/(Root[1 - #1^2 + #1^3 & , 2, 0] - Root[1 - #1^2 + #1^3 & , 3, 0])^2)]*(-Root[1 - #1^2 + #1^3 & , 2, 0] + Root[1 - #1^2 + #1^3 & , 3, 0]))/(-1 + I*Sqrt[3] + 2*Root[1 - #1^2 + #1^3 & , 3, 0]))/Sqrt[1 - x^2 + x^3]","C",0
569,1,2730,44,4.9923709,"\int \frac{a^2 b-a (2 a-b) x-(-a+2 b) x^2+x^3}{\sqrt{x (-a+x) (-b+x)} \left(-a^3+\left(3 a^2+b d\right) x-(3 a+d) x^2+x^3\right)} \, dx","Integrate[(a^2*b - a*(2*a - b)*x - (-a + 2*b)*x^2 + x^3)/(Sqrt[x*(-a + x)*(-b + x)]*(-a^3 + (3*a^2 + b*d)*x - (3*a + d)*x^2 + x^3)),x]","\text{Result too large to show}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{x^2 (-a-b)+a b x+x^3}}{(a-x)^2}\right)}{\sqrt{d}}",1,"((-2*I)*(a - x)*Sqrt[(-b + x)/(a - b)]*(-5*a^2*d*EllipticPi[a/Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 2], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)] + 5*a*b*d*EllipticPi[a/Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 2], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)] - 2*b^2*d*EllipticPi[a/Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 2], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)] - 3*a^2*d*EllipticPi[a/Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 3], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)] + 3*a*b*d*EllipticPi[a/Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 3], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)] + 3*a*(a - b)*(EllipticPi[a/Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 2], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)] - 2*EllipticPi[a/Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 3], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)])*Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 2] - EllipticPi[a/Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 2], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)]*Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 1]*Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 2]^2 + 3*a*(a - b)*(2*EllipticPi[a/Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 2], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)] - EllipticPi[a/Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 3], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)])*Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 3] - 2*(2*a - b)*(EllipticPi[a/Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 2], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)] + EllipticPi[a/Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 3], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)])*Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 1]*Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 3] - 2*(2*a - b)*(2*EllipticPi[a/Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 2], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)] - EllipticPi[a/Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 3], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)])*Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 2]*Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 3] + EllipticPi[a/Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 2], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)]*Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 2]^2*Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 3] + EllipticPi[a/Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 3], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)]*Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 1]*Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 3]^2 - EllipticPi[a/Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 3], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)]*Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 2]*Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 3]^2 + EllipticF[I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)]*(d*(-3*a^2 + 3*a*b - 2*a*d + b*d) + 2*Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 1]*Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 2]^2 + 2*Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 1]^2*Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 3] + 2*Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 2]*Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 3]^2) + EllipticPi[a/Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 1], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)]*(d*(11*a^2 - 11*a*b + 2*b^2 + 2*a*d - b*d) + d*Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 2]^2 + Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 2]^3 + (3*a*(-a + b) + (8*a - 4*b)*Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 1] - 2*Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 1]^2)*Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 3] - Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 1]*Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 3]^2 + Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 2]*(3*a*(a - b) + (4*a - 2*b)*Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 3] - Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 3]^2))))/(Sqrt[1 - a/x]*Sqrt[x*(-a + x)*(-b + x)]*(Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 1] - Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 2])*(Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 1] - Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 3])*(Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 2] - Root[a^2*d - a*b*d + (-2*a*d + b*d)*#1 + d*#1^2 + #1^3 & , 3]))","C",0
570,1,1571,44,5.1819813,"\int \frac{a^2 b-a (2 a-b) x-(-a+2 b) x^2+x^3}{\sqrt{x (-a+x) (-b+x)} \left(-a^3 d+\left(b+3 a^2 d\right) x-(1+3 a d) x^2+d x^3\right)} \, dx","Integrate[(a^2*b - a*(2*a - b)*x - (-a + 2*b)*x^2 + x^3)/(Sqrt[x*(-a + x)*(-b + x)]*(-(a^3*d) + (b + 3*a^2*d)*x - (1 + 3*a*d)*x^2 + d*x^3)),x]","\frac{2 i (a-x) \sqrt{\frac{x-b}{a-b}} \left(F\left(i \sinh ^{-1}\left(\sqrt{\frac{x}{a}-1}\right)|\frac{a}{a-b}\right) \left(3 d a^2-3 b d a+2 a-2 d^2 \text{Root}\left[d \text{$\#$1}^3+\text{$\#$1}^2+(b-2 a) \text{$\#$1}+a^2-a b\&,1\right] \text{Root}\left[d \text{$\#$1}^3+\text{$\#$1}^2+(b-2 a) \text{$\#$1}+a^2-a b\&,2\right]^2-2 d^2 \text{Root}\left[d \text{$\#$1}^3+\text{$\#$1}^2+(b-2 a) \text{$\#$1}+a^2-a b\&,2\right] \text{Root}\left[d \text{$\#$1}^3+\text{$\#$1}^2+(b-2 a) \text{$\#$1}+a^2-a b\&,3\right]^2-b-2 d^2 \text{Root}\left[d \text{$\#$1}^3+\text{$\#$1}^2+(b-2 a) \text{$\#$1}+a^2-a b\&,1\right]^2 \text{Root}\left[d \text{$\#$1}^3+\text{$\#$1}^2+(b-2 a) \text{$\#$1}+a^2-a b\&,3\right]\right)-\Pi \left(\frac{a}{\text{Root}\left[d \text{$\#$1}^3+\text{$\#$1}^2+(b-2 a) \text{$\#$1}+a^2-a b\&,1\right]};i \sinh ^{-1}\left(\sqrt{\frac{x}{a}-1}\right)|\frac{a}{a-b}\right) \left(d^2 \text{Root}\left[d \text{$\#$1}^3+\text{$\#$1}^2+(b-2 a) \text{$\#$1}+a^2-a b\&,2\right]^3+d \text{Root}\left[d \text{$\#$1}^3+\text{$\#$1}^2+(b-2 a) \text{$\#$1}+a^2-a b\&,2\right]^2+d^2 \left(-\text{Root}\left[d \text{$\#$1}^3+\text{$\#$1}^2+(b-2 a) \text{$\#$1}+a^2-a b\&,3\right]^2+(4 a-2 b) \text{Root}\left[d \text{$\#$1}^3+\text{$\#$1}^2+(b-2 a) \text{$\#$1}+a^2-a b\&,3\right]+3 a (a-b)\right) \text{Root}\left[d \text{$\#$1}^3+\text{$\#$1}^2+(b-2 a) \text{$\#$1}+a^2-a b\&,2\right]-d^2 \text{Root}\left[d \text{$\#$1}^3+\text{$\#$1}^2+(b-2 a) \text{$\#$1}+a^2-a b\&,1\right] \text{Root}\left[d \text{$\#$1}^3+\text{$\#$1}^2+(b-2 a) \text{$\#$1}+a^2-a b\&,3\right]^2+2 a-b+11 a^2 d+2 b^2 d-11 a b d+d^2 \left(-2 \text{Root}\left[d \text{$\#$1}^3+\text{$\#$1}^2+(b-2 a) \text{$\#$1}+a^2-a b\&,1\right]^2+(8 a-4 b) \text{Root}\left[d \text{$\#$1}^3+\text{$\#$1}^2+(b-2 a) \text{$\#$1}+a^2-a b\&,1\right]+3 a (b-a)\right) \text{Root}\left[d \text{$\#$1}^3+\text{$\#$1}^2+(b-2 a) \text{$\#$1}+a^2-a b\&,3\right]\right)+d \left(\Pi \left(\frac{a}{\text{Root}\left[d \text{$\#$1}^3+\text{$\#$1}^2+(b-2 a) \text{$\#$1}+a^2-a b\&,2\right]};i \sinh ^{-1}\left(\sqrt{\frac{x}{a}-1}\right)|\frac{a}{a-b}\right) \left(5 a^2-5 b a+2 b^2+d \text{Root}\left[d \text{$\#$1}^3+\text{$\#$1}^2+(b-2 a) \text{$\#$1}+a^2-a b\&,2\right]^2 \left(\text{Root}\left[d \text{$\#$1}^3+\text{$\#$1}^2+(b-2 a) \text{$\#$1}+a^2-a b\&,1\right]-\text{Root}\left[d \text{$\#$1}^3+\text{$\#$1}^2+(b-2 a) \text{$\#$1}+a^2-a b\&,3\right]\right)-2 d \left(3 a (a-b)+(b-2 a) \text{Root}\left[d \text{$\#$1}^3+\text{$\#$1}^2+(b-2 a) \text{$\#$1}+a^2-a b\&,1\right]\right) \text{Root}\left[d \text{$\#$1}^3+\text{$\#$1}^2+(b-2 a) \text{$\#$1}+a^2-a b\&,3\right]+d \text{Root}\left[d \text{$\#$1}^3+\text{$\#$1}^2+(b-2 a) \text{$\#$1}+a^2-a b\&,2\right] \left(3 a (b-a)+(8 a-4 b) \text{Root}\left[d \text{$\#$1}^3+\text{$\#$1}^2+(b-2 a) \text{$\#$1}+a^2-a b\&,3\right]\right)\right)+\Pi \left(\frac{a}{\text{Root}\left[d \text{$\#$1}^3+\text{$\#$1}^2+(b-2 a) \text{$\#$1}+a^2-a b\&,3\right]};i \sinh ^{-1}\left(\sqrt{\frac{x}{a}-1}\right)|\frac{a}{a-b}\right) \left(-d \text{Root}\left[d \text{$\#$1}^3+\text{$\#$1}^2+(b-2 a) \text{$\#$1}+a^2-a b\&,1\right] \text{Root}\left[d \text{$\#$1}^3+\text{$\#$1}^2+(b-2 a) \text{$\#$1}+a^2-a b\&,3\right]^2+d \left(3 a (a-b)+(4 a-2 b) \text{Root}\left[d \text{$\#$1}^3+\text{$\#$1}^2+(b-2 a) \text{$\#$1}+a^2-a b\&,1\right]\right) \text{Root}\left[d \text{$\#$1}^3+\text{$\#$1}^2+(b-2 a) \text{$\#$1}+a^2-a b\&,3\right]+3 a (a-b)+d \text{Root}\left[d \text{$\#$1}^3+\text{$\#$1}^2+(b-2 a) \text{$\#$1}+a^2-a b\&,2\right] \left(\text{Root}\left[d \text{$\#$1}^3+\text{$\#$1}^2+(b-2 a) \text{$\#$1}+a^2-a b\&,3\right]^2+(2 b-4 a) \text{Root}\left[d \text{$\#$1}^3+\text{$\#$1}^2+(b-2 a) \text{$\#$1}+a^2-a b\&,3\right]+6 a (a-b)\right)\right)\right)\right)}{d^3 \sqrt{1-\frac{a}{x}} \sqrt{x (x-a) (x-b)} \left(\text{Root}\left[d \text{$\#$1}^3+\text{$\#$1}^2+(b-2 a) \text{$\#$1}+a^2-a b\&,1\right]-\text{Root}\left[d \text{$\#$1}^3+\text{$\#$1}^2+(b-2 a) \text{$\#$1}+a^2-a b\&,2\right]\right) \left(\text{Root}\left[d \text{$\#$1}^3+\text{$\#$1}^2+(b-2 a) \text{$\#$1}+a^2-a b\&,1\right]-\text{Root}\left[d \text{$\#$1}^3+\text{$\#$1}^2+(b-2 a) \text{$\#$1}+a^2-a b\&,3\right]\right) \left(\text{Root}\left[d \text{$\#$1}^3+\text{$\#$1}^2+(b-2 a) \text{$\#$1}+a^2-a b\&,2\right]-\text{Root}\left[d \text{$\#$1}^3+\text{$\#$1}^2+(b-2 a) \text{$\#$1}+a^2-a b\&,3\right]\right)}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{x^2 (-a-b)+a b x+x^3}}{\sqrt{d} (a-x)^2}\right)}{\sqrt{d}}",1,"((2*I)*(a - x)*Sqrt[(-b + x)/(a - b)]*(EllipticF[I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)]*(2*a - b + 3*a^2*d - 3*a*b*d - 2*d^2*Root[a^2 - a*b + (-2*a + b)*#1 + #1^2 + d*#1^3 & , 1]*Root[a^2 - a*b + (-2*a + b)*#1 + #1^2 + d*#1^3 & , 2]^2 - 2*d^2*Root[a^2 - a*b + (-2*a + b)*#1 + #1^2 + d*#1^3 & , 1]^2*Root[a^2 - a*b + (-2*a + b)*#1 + #1^2 + d*#1^3 & , 3] - 2*d^2*Root[a^2 - a*b + (-2*a + b)*#1 + #1^2 + d*#1^3 & , 2]*Root[a^2 - a*b + (-2*a + b)*#1 + #1^2 + d*#1^3 & , 3]^2) - EllipticPi[a/Root[a^2 - a*b + (-2*a + b)*#1 + #1^2 + d*#1^3 & , 1], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)]*(2*a - b + 11*a^2*d - 11*a*b*d + 2*b^2*d + d*Root[a^2 - a*b + (-2*a + b)*#1 + #1^2 + d*#1^3 & , 2]^2 + d^2*Root[a^2 - a*b + (-2*a + b)*#1 + #1^2 + d*#1^3 & , 2]^3 + d^2*(3*a*(-a + b) + (8*a - 4*b)*Root[a^2 - a*b + (-2*a + b)*#1 + #1^2 + d*#1^3 & , 1] - 2*Root[a^2 - a*b + (-2*a + b)*#1 + #1^2 + d*#1^3 & , 1]^2)*Root[a^2 - a*b + (-2*a + b)*#1 + #1^2 + d*#1^3 & , 3] - d^2*Root[a^2 - a*b + (-2*a + b)*#1 + #1^2 + d*#1^3 & , 1]*Root[a^2 - a*b + (-2*a + b)*#1 + #1^2 + d*#1^3 & , 3]^2 + d^2*Root[a^2 - a*b + (-2*a + b)*#1 + #1^2 + d*#1^3 & , 2]*(3*a*(a - b) + (4*a - 2*b)*Root[a^2 - a*b + (-2*a + b)*#1 + #1^2 + d*#1^3 & , 3] - Root[a^2 - a*b + (-2*a + b)*#1 + #1^2 + d*#1^3 & , 3]^2)) + d*(EllipticPi[a/Root[a^2 - a*b + (-2*a + b)*#1 + #1^2 + d*#1^3 & , 2], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)]*(5*a^2 - 5*a*b + 2*b^2 + d*Root[a^2 - a*b + (-2*a + b)*#1 + #1^2 + d*#1^3 & , 2]^2*(Root[a^2 - a*b + (-2*a + b)*#1 + #1^2 + d*#1^3 & , 1] - Root[a^2 - a*b + (-2*a + b)*#1 + #1^2 + d*#1^3 & , 3]) - 2*d*(3*a*(a - b) + (-2*a + b)*Root[a^2 - a*b + (-2*a + b)*#1 + #1^2 + d*#1^3 & , 1])*Root[a^2 - a*b + (-2*a + b)*#1 + #1^2 + d*#1^3 & , 3] + d*Root[a^2 - a*b + (-2*a + b)*#1 + #1^2 + d*#1^3 & , 2]*(3*a*(-a + b) + (8*a - 4*b)*Root[a^2 - a*b + (-2*a + b)*#1 + #1^2 + d*#1^3 & , 3])) + EllipticPi[a/Root[a^2 - a*b + (-2*a + b)*#1 + #1^2 + d*#1^3 & , 3], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)]*(3*a*(a - b) + d*(3*a*(a - b) + (4*a - 2*b)*Root[a^2 - a*b + (-2*a + b)*#1 + #1^2 + d*#1^3 & , 1])*Root[a^2 - a*b + (-2*a + b)*#1 + #1^2 + d*#1^3 & , 3] - d*Root[a^2 - a*b + (-2*a + b)*#1 + #1^2 + d*#1^3 & , 1]*Root[a^2 - a*b + (-2*a + b)*#1 + #1^2 + d*#1^3 & , 3]^2 + d*Root[a^2 - a*b + (-2*a + b)*#1 + #1^2 + d*#1^3 & , 2]*(6*a*(a - b) + (-4*a + 2*b)*Root[a^2 - a*b + (-2*a + b)*#1 + #1^2 + d*#1^3 & , 3] + Root[a^2 - a*b + (-2*a + b)*#1 + #1^2 + d*#1^3 & , 3]^2)))))/(d^3*Sqrt[1 - a/x]*Sqrt[x*(-a + x)*(-b + x)]*(Root[a^2 - a*b + (-2*a + b)*#1 + #1^2 + d*#1^3 & , 1] - Root[a^2 - a*b + (-2*a + b)*#1 + #1^2 + d*#1^3 & , 2])*(Root[a^2 - a*b + (-2*a + b)*#1 + #1^2 + d*#1^3 & , 1] - Root[a^2 - a*b + (-2*a + b)*#1 + #1^2 + d*#1^3 & , 3])*(Root[a^2 - a*b + (-2*a + b)*#1 + #1^2 + d*#1^3 & , 2] - Root[a^2 - a*b + (-2*a + b)*#1 + #1^2 + d*#1^3 & , 3]))","C",0
571,1,4253,44,4.5978358,"\int \frac{-3 x+2 x^2}{\left(-2+2 x+x^3\right) \sqrt{-2 x+2 x^2+3 x^4}} \, dx","Integrate[(-3*x + 2*x^2)/((-2 + 2*x + x^3)*Sqrt[-2*x + 2*x^2 + 3*x^4]),x]","\text{Result too large to show}","\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt{3 x^4+2 x^2-2 x}}{3 x^3+2 x-2}\right)}{\sqrt{2}}",1,"(2*(x - Root[-2 + 2*#1 + 3*#1^3 & , 1, 0])^2*(3*(Root[-2 + 2*#1 + #1^3 & , 2, 0] - Root[-2 + 2*#1 + #1^3 & , 3, 0])*(Root[-2 + 2*#1 + #1^3 & , 2, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 1, 0])*(Root[-2 + 2*#1 + #1^3 & , 3, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 1, 0])*(EllipticF[ArcSin[Sqrt[(x*(-Root[-2 + 2*#1 + 3*#1^3 & , 1, 0] + Root[-2 + 2*#1 + 3*#1^3 & , 3, 0]))/((x - Root[-2 + 2*#1 + 3*#1^3 & , 1, 0])*Root[-2 + 2*#1 + 3*#1^3 & , 3, 0])]], ((Root[-2 + 2*#1 + 3*#1^3 & , 1, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 2, 0])*Root[-2 + 2*#1 + 3*#1^3 & , 3, 0])/(Root[-2 + 2*#1 + 3*#1^3 & , 2, 0]*(Root[-2 + 2*#1 + 3*#1^3 & , 1, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 3, 0]))]*Root[-2 + 2*#1 + #1^3 & , 1, 0] - EllipticPi[-(((Root[-2 + 2*#1 + #1^3 & , 1, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 1, 0])*Root[-2 + 2*#1 + 3*#1^3 & , 3, 0])/(Root[-2 + 2*#1 + #1^3 & , 1, 0]*(Root[-2 + 2*#1 + 3*#1^3 & , 1, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 3, 0]))), ArcSin[Sqrt[(x*(-Root[-2 + 2*#1 + 3*#1^3 & , 1, 0] + Root[-2 + 2*#1 + 3*#1^3 & , 3, 0]))/((x - Root[-2 + 2*#1 + 3*#1^3 & , 1, 0])*Root[-2 + 2*#1 + 3*#1^3 & , 3, 0])]], ((Root[-2 + 2*#1 + 3*#1^3 & , 1, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 2, 0])*Root[-2 + 2*#1 + 3*#1^3 & , 3, 0])/(Root[-2 + 2*#1 + 3*#1^3 & , 2, 0]*(Root[-2 + 2*#1 + 3*#1^3 & , 1, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 3, 0]))]*Root[-2 + 2*#1 + 3*#1^3 & , 1, 0]) - 2*Root[-2 + 2*#1 + #1^3 & , 1, 0]*(Root[-2 + 2*#1 + #1^3 & , 2, 0] - Root[-2 + 2*#1 + #1^3 & , 3, 0])*(Root[-2 + 2*#1 + #1^3 & , 2, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 1, 0])*(Root[-2 + 2*#1 + #1^3 & , 3, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 1, 0])*(EllipticF[ArcSin[Sqrt[(x*(-Root[-2 + 2*#1 + 3*#1^3 & , 1, 0] + Root[-2 + 2*#1 + 3*#1^3 & , 3, 0]))/((x - Root[-2 + 2*#1 + 3*#1^3 & , 1, 0])*Root[-2 + 2*#1 + 3*#1^3 & , 3, 0])]], ((Root[-2 + 2*#1 + 3*#1^3 & , 1, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 2, 0])*Root[-2 + 2*#1 + 3*#1^3 & , 3, 0])/(Root[-2 + 2*#1 + 3*#1^3 & , 2, 0]*(Root[-2 + 2*#1 + 3*#1^3 & , 1, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 3, 0]))]*Root[-2 + 2*#1 + #1^3 & , 1, 0] - EllipticPi[-(((Root[-2 + 2*#1 + #1^3 & , 1, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 1, 0])*Root[-2 + 2*#1 + 3*#1^3 & , 3, 0])/(Root[-2 + 2*#1 + #1^3 & , 1, 0]*(Root[-2 + 2*#1 + 3*#1^3 & , 1, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 3, 0]))), ArcSin[Sqrt[(x*(-Root[-2 + 2*#1 + 3*#1^3 & , 1, 0] + Root[-2 + 2*#1 + 3*#1^3 & , 3, 0]))/((x - Root[-2 + 2*#1 + 3*#1^3 & , 1, 0])*Root[-2 + 2*#1 + 3*#1^3 & , 3, 0])]], ((Root[-2 + 2*#1 + 3*#1^3 & , 1, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 2, 0])*Root[-2 + 2*#1 + 3*#1^3 & , 3, 0])/(Root[-2 + 2*#1 + 3*#1^3 & , 2, 0]*(Root[-2 + 2*#1 + 3*#1^3 & , 1, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 3, 0]))]*Root[-2 + 2*#1 + 3*#1^3 & , 1, 0]) + 2*Root[-2 + 2*#1 + #1^3 & , 2, 0]*(Root[-2 + 2*#1 + #1^3 & , 1, 0] - Root[-2 + 2*#1 + #1^3 & , 3, 0])*(Root[-2 + 2*#1 + #1^3 & , 1, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 1, 0])*(Root[-2 + 2*#1 + #1^3 & , 3, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 1, 0])*(EllipticF[ArcSin[Sqrt[(x*(-Root[-2 + 2*#1 + 3*#1^3 & , 1, 0] + Root[-2 + 2*#1 + 3*#1^3 & , 3, 0]))/((x - Root[-2 + 2*#1 + 3*#1^3 & , 1, 0])*Root[-2 + 2*#1 + 3*#1^3 & , 3, 0])]], ((Root[-2 + 2*#1 + 3*#1^3 & , 1, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 2, 0])*Root[-2 + 2*#1 + 3*#1^3 & , 3, 0])/(Root[-2 + 2*#1 + 3*#1^3 & , 2, 0]*(Root[-2 + 2*#1 + 3*#1^3 & , 1, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 3, 0]))]*Root[-2 + 2*#1 + #1^3 & , 2, 0] - EllipticPi[-(((Root[-2 + 2*#1 + #1^3 & , 2, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 1, 0])*Root[-2 + 2*#1 + 3*#1^3 & , 3, 0])/(Root[-2 + 2*#1 + #1^3 & , 2, 0]*(Root[-2 + 2*#1 + 3*#1^3 & , 1, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 3, 0]))), ArcSin[Sqrt[(x*(-Root[-2 + 2*#1 + 3*#1^3 & , 1, 0] + Root[-2 + 2*#1 + 3*#1^3 & , 3, 0]))/((x - Root[-2 + 2*#1 + 3*#1^3 & , 1, 0])*Root[-2 + 2*#1 + 3*#1^3 & , 3, 0])]], ((Root[-2 + 2*#1 + 3*#1^3 & , 1, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 2, 0])*Root[-2 + 2*#1 + 3*#1^3 & , 3, 0])/(Root[-2 + 2*#1 + 3*#1^3 & , 2, 0]*(Root[-2 + 2*#1 + 3*#1^3 & , 1, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 3, 0]))]*Root[-2 + 2*#1 + 3*#1^3 & , 1, 0]) + 3*(Root[-2 + 2*#1 + #1^3 & , 1, 0] - Root[-2 + 2*#1 + #1^3 & , 3, 0])*(Root[-2 + 2*#1 + #1^3 & , 1, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 1, 0])*(Root[-2 + 2*#1 + #1^3 & , 3, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 1, 0])*(-(EllipticF[ArcSin[Sqrt[(x*(-Root[-2 + 2*#1 + 3*#1^3 & , 1, 0] + Root[-2 + 2*#1 + 3*#1^3 & , 3, 0]))/((x - Root[-2 + 2*#1 + 3*#1^3 & , 1, 0])*Root[-2 + 2*#1 + 3*#1^3 & , 3, 0])]], ((Root[-2 + 2*#1 + 3*#1^3 & , 1, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 2, 0])*Root[-2 + 2*#1 + 3*#1^3 & , 3, 0])/(Root[-2 + 2*#1 + 3*#1^3 & , 2, 0]*(Root[-2 + 2*#1 + 3*#1^3 & , 1, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 3, 0]))]*Root[-2 + 2*#1 + #1^3 & , 2, 0]) + EllipticPi[-(((Root[-2 + 2*#1 + #1^3 & , 2, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 1, 0])*Root[-2 + 2*#1 + 3*#1^3 & , 3, 0])/(Root[-2 + 2*#1 + #1^3 & , 2, 0]*(Root[-2 + 2*#1 + 3*#1^3 & , 1, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 3, 0]))), ArcSin[Sqrt[(x*(-Root[-2 + 2*#1 + 3*#1^3 & , 1, 0] + Root[-2 + 2*#1 + 3*#1^3 & , 3, 0]))/((x - Root[-2 + 2*#1 + 3*#1^3 & , 1, 0])*Root[-2 + 2*#1 + 3*#1^3 & , 3, 0])]], ((Root[-2 + 2*#1 + 3*#1^3 & , 1, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 2, 0])*Root[-2 + 2*#1 + 3*#1^3 & , 3, 0])/(Root[-2 + 2*#1 + 3*#1^3 & , 2, 0]*(Root[-2 + 2*#1 + 3*#1^3 & , 1, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 3, 0]))]*Root[-2 + 2*#1 + 3*#1^3 & , 1, 0]) + 3*(Root[-2 + 2*#1 + #1^3 & , 1, 0] - Root[-2 + 2*#1 + #1^3 & , 2, 0])*(Root[-2 + 2*#1 + #1^3 & , 1, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 1, 0])*(Root[-2 + 2*#1 + #1^3 & , 2, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 1, 0])*(EllipticF[ArcSin[Sqrt[(x*(-Root[-2 + 2*#1 + 3*#1^3 & , 1, 0] + Root[-2 + 2*#1 + 3*#1^3 & , 3, 0]))/((x - Root[-2 + 2*#1 + 3*#1^3 & , 1, 0])*Root[-2 + 2*#1 + 3*#1^3 & , 3, 0])]], ((Root[-2 + 2*#1 + 3*#1^3 & , 1, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 2, 0])*Root[-2 + 2*#1 + 3*#1^3 & , 3, 0])/(Root[-2 + 2*#1 + 3*#1^3 & , 2, 0]*(Root[-2 + 2*#1 + 3*#1^3 & , 1, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 3, 0]))]*Root[-2 + 2*#1 + #1^3 & , 3, 0] - EllipticPi[-(((Root[-2 + 2*#1 + #1^3 & , 3, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 1, 0])*Root[-2 + 2*#1 + 3*#1^3 & , 3, 0])/(Root[-2 + 2*#1 + #1^3 & , 3, 0]*(Root[-2 + 2*#1 + 3*#1^3 & , 1, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 3, 0]))), ArcSin[Sqrt[(x*(-Root[-2 + 2*#1 + 3*#1^3 & , 1, 0] + Root[-2 + 2*#1 + 3*#1^3 & , 3, 0]))/((x - Root[-2 + 2*#1 + 3*#1^3 & , 1, 0])*Root[-2 + 2*#1 + 3*#1^3 & , 3, 0])]], ((Root[-2 + 2*#1 + 3*#1^3 & , 1, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 2, 0])*Root[-2 + 2*#1 + 3*#1^3 & , 3, 0])/(Root[-2 + 2*#1 + 3*#1^3 & , 2, 0]*(Root[-2 + 2*#1 + 3*#1^3 & , 1, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 3, 0]))]*Root[-2 + 2*#1 + 3*#1^3 & , 1, 0]) - 2*(Root[-2 + 2*#1 + #1^3 & , 1, 0] - Root[-2 + 2*#1 + #1^3 & , 2, 0])*Root[-2 + 2*#1 + #1^3 & , 3, 0]*(Root[-2 + 2*#1 + #1^3 & , 1, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 1, 0])*(Root[-2 + 2*#1 + #1^3 & , 2, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 1, 0])*(EllipticF[ArcSin[Sqrt[(x*(-Root[-2 + 2*#1 + 3*#1^3 & , 1, 0] + Root[-2 + 2*#1 + 3*#1^3 & , 3, 0]))/((x - Root[-2 + 2*#1 + 3*#1^3 & , 1, 0])*Root[-2 + 2*#1 + 3*#1^3 & , 3, 0])]], ((Root[-2 + 2*#1 + 3*#1^3 & , 1, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 2, 0])*Root[-2 + 2*#1 + 3*#1^3 & , 3, 0])/(Root[-2 + 2*#1 + 3*#1^3 & , 2, 0]*(Root[-2 + 2*#1 + 3*#1^3 & , 1, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 3, 0]))]*Root[-2 + 2*#1 + #1^3 & , 3, 0] - EllipticPi[-(((Root[-2 + 2*#1 + #1^3 & , 3, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 1, 0])*Root[-2 + 2*#1 + 3*#1^3 & , 3, 0])/(Root[-2 + 2*#1 + #1^3 & , 3, 0]*(Root[-2 + 2*#1 + 3*#1^3 & , 1, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 3, 0]))), ArcSin[Sqrt[(x*(-Root[-2 + 2*#1 + 3*#1^3 & , 1, 0] + Root[-2 + 2*#1 + 3*#1^3 & , 3, 0]))/((x - Root[-2 + 2*#1 + 3*#1^3 & , 1, 0])*Root[-2 + 2*#1 + 3*#1^3 & , 3, 0])]], ((Root[-2 + 2*#1 + 3*#1^3 & , 1, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 2, 0])*Root[-2 + 2*#1 + 3*#1^3 & , 3, 0])/(Root[-2 + 2*#1 + 3*#1^3 & , 2, 0]*(Root[-2 + 2*#1 + 3*#1^3 & , 1, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 3, 0]))]*Root[-2 + 2*#1 + 3*#1^3 & , 1, 0]))*Sqrt[(x - Root[-2 + 2*#1 + 3*#1^3 & , 2, 0])/((x - Root[-2 + 2*#1 + 3*#1^3 & , 1, 0])*Root[-2 + 2*#1 + 3*#1^3 & , 2, 0])]*Sqrt[(x - Root[-2 + 2*#1 + 3*#1^3 & , 3, 0])/((x - Root[-2 + 2*#1 + 3*#1^3 & , 1, 0])*Root[-2 + 2*#1 + 3*#1^3 & , 3, 0])]*Root[-2 + 2*#1 + 3*#1^3 & , 3, 0]*Sqrt[(x*(-Root[-2 + 2*#1 + 3*#1^3 & , 1, 0] + Root[-2 + 2*#1 + 3*#1^3 & , 3, 0]))/((x - Root[-2 + 2*#1 + 3*#1^3 & , 1, 0])*Root[-2 + 2*#1 + 3*#1^3 & , 3, 0])])/(Sqrt[x*(-2 + 2*x + 3*x^3)]*(Root[-2 + 2*#1 + #1^3 & , 1, 0] - Root[-2 + 2*#1 + #1^3 & , 2, 0])*(Root[-2 + 2*#1 + #1^3 & , 1, 0] - Root[-2 + 2*#1 + #1^3 & , 3, 0])*(Root[-2 + 2*#1 + #1^3 & , 2, 0] - Root[-2 + 2*#1 + #1^3 & , 3, 0])*(Root[-2 + 2*#1 + #1^3 & , 1, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 1, 0])*(Root[-2 + 2*#1 + #1^3 & , 2, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 1, 0])*(Root[-2 + 2*#1 + #1^3 & , 3, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 1, 0])*(Root[-2 + 2*#1 + 3*#1^3 & , 1, 0] - Root[-2 + 2*#1 + 3*#1^3 & , 3, 0]))","C",0
572,1,8005,44,7.087869,"\int \frac{4 a q x-3 b p x^2+a p x^4}{\sqrt{q+p x^3} \left(b^2 c+d q+2 a b c x^2+d p x^3+a^2 c x^4\right)} \, dx","Integrate[(4*a*q*x - 3*b*p*x^2 + a*p*x^4)/(Sqrt[q + p*x^3]*(b^2*c + d*q + 2*a*b*c*x^2 + d*p*x^3 + a^2*c*x^4)),x]","\text{Result too large to show}","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{p x^3+q}}{\sqrt{c} \left(a x^2+b\right)}\right)}{\sqrt{c} \sqrt{d}}",1,"Result too large to show","C",0
573,1,41,44,0.0348987,"\int \frac{1+x^{12}}{x^{10} \sqrt{-1+x^6}} \, dx","Integrate[(1 + x^12)/(x^10*Sqrt[-1 + x^6]),x]","\frac{1}{9} \left(\frac{\sqrt{x^6-1} \left(2 x^6+1\right)}{x^9}+3 \tanh ^{-1}\left(\frac{x^3}{\sqrt{x^6-1}}\right)\right)","\frac{\sqrt{x^6-1} \left(2 x^6+1\right)}{9 x^9}+\frac{2}{3} \tanh ^{-1}\left(\frac{x^3+1}{\sqrt{x^6-1}}\right)",1,"((Sqrt[-1 + x^6]*(1 + 2*x^6))/x^9 + 3*ArcTanh[x^3/Sqrt[-1 + x^6]])/9","A",1
574,1,61,44,0.1073164,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt[10]{1+5 x^4+10 x^8+10 x^{12}+5 x^{16}+x^{20}}} \, dx","Integrate[(-1 + x^2)/((1 + x^2)*(1 + 5*x^4 + 10*x^8 + 10*x^12 + 5*x^16 + x^20)^(1/10)),x]","-\frac{\sqrt[4]{-1} \sqrt{x^4+1} \left(F\left(\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)-2 \Pi \left(-i;\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)\right)}{\sqrt[10]{\left(x^4+1\right)^5}}","-\frac{\left(\left(x^4+1\right)^5\right)^{9/10} \tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{\sqrt{2} \left(x^4+1\right)^{9/2}}",1,"-(((-1)^(1/4)*Sqrt[1 + x^4]*(EllipticF[I*ArcSinh[(-1)^(1/4)*x], -1] - 2*EllipticPi[-I, I*ArcSinh[(-1)^(1/4)*x], -1]))/((1 + x^4)^5)^(1/10))","C",1
575,0,0,44,0.1712385,"\int \frac{\sqrt{b+\sqrt{b^2+a x^2}}}{b^2+a x^2} \, dx","Integrate[Sqrt[b + Sqrt[b^2 + a*x^2]]/(b^2 + a*x^2),x]","\int \frac{\sqrt{b+\sqrt{b^2+a x^2}}}{b^2+a x^2} \, dx","\frac{2 \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b} \sqrt{\sqrt{a x^2+b^2}+b}}\right)}{\sqrt{a} \sqrt{b}}",1,"Integrate[Sqrt[b + Sqrt[b^2 + a*x^2]]/(b^2 + a*x^2), x]","F",-1
576,1,31,44,0.011783,"\int \frac{\sqrt{x^2+\sqrt{1+x^4}}}{\sqrt{1+x^4}} \, dx","Integrate[Sqrt[x^2 + Sqrt[1 + x^4]]/Sqrt[1 + x^4],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{\sqrt{x^4+1}+x^2}}\right)}{\sqrt{2}}","\frac{\log \left(\sqrt{x^4+1}+x^2+\sqrt{2} \sqrt{\sqrt{x^4+1}+x^2} x\right)}{\sqrt{2}}",1,"ArcTanh[(Sqrt[2]*x)/Sqrt[x^2 + Sqrt[1 + x^4]]]/Sqrt[2]","A",1
577,1,24,45,0.0048189,"\int \frac{1}{x^3 \left(1+x^2\right)^{3/4}} \, dx","Integrate[1/(x^3*(1 + x^2)^(3/4)),x]","2 \sqrt[4]{x^2+1} \, _2F_1\left(\frac{1}{4},2;\frac{5}{4};x^2+1\right)","-\frac{\sqrt[4]{x^2+1}}{2 x^2}+\frac{3}{4} \tan ^{-1}\left(\sqrt[4]{x^2+1}\right)+\frac{3}{4} \tanh ^{-1}\left(\sqrt[4]{x^2+1}\right)",1,"2*(1 + x^2)^(1/4)*Hypergeometric2F1[1/4, 2, 5/4, 1 + x^2]","C",1
578,1,26,45,0.0048508,"\int \frac{1}{x^4 \sqrt[4]{1+x^3}} \, dx","Integrate[1/(x^4*(1 + x^3)^(1/4)),x]","\frac{4}{9} \left(x^3+1\right)^{3/4} \, _2F_1\left(\frac{3}{4},2;\frac{7}{4};x^3+1\right)","-\frac{\left(x^3+1\right)^{3/4}}{3 x^3}-\frac{1}{6} \tan ^{-1}\left(\sqrt[4]{x^3+1}\right)+\frac{1}{6} \tanh ^{-1}\left(\sqrt[4]{x^3+1}\right)",1,"(4*(1 + x^3)^(3/4)*Hypergeometric2F1[3/4, 2, 7/4, 1 + x^3])/9","C",1
579,1,26,45,0.0052764,"\int \frac{\sqrt[4]{1+x^3}}{x^4} \, dx","Integrate[(1 + x^3)^(1/4)/x^4,x]","\frac{4}{15} \left(x^3+1\right)^{5/4} \, _2F_1\left(\frac{5}{4},2;\frac{9}{4};x^3+1\right)","-\frac{\sqrt[4]{x^3+1}}{3 x^3}-\frac{1}{6} \tan ^{-1}\left(\sqrt[4]{x^3+1}\right)-\frac{1}{6} \tanh ^{-1}\left(\sqrt[4]{x^3+1}\right)",1,"(4*(1 + x^3)^(5/4)*Hypergeometric2F1[5/4, 2, 9/4, 1 + x^3])/15","C",1
580,1,62,45,0.026194,"\int x^3 \sqrt{-x+x^4} \, dx","Integrate[x^3*Sqrt[-x + x^4],x]","\frac{\sqrt{x \left(x^3-1\right)} \left(\sin ^{-1}\left(x^{3/2}\right)+\sqrt{1-x^3} \left(2 x^3-1\right) x^{3/2}\right)}{12 \sqrt{x} \sqrt{1-x^3}}","\frac{1}{12} \sqrt{x^4-x} \left(2 x^4-x\right)-\frac{1}{12} \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4-x}}\right)",1,"(Sqrt[x*(-1 + x^3)]*(x^(3/2)*Sqrt[1 - x^3]*(-1 + 2*x^3) + ArcSin[x^(3/2)]))/(12*Sqrt[x]*Sqrt[1 - x^3])","A",1
581,0,0,45,0.6231112,"\int \frac{\left(1+x^4\right) \left(-1+3 x^4\right)}{x \left(1-a x+x^4\right) \sqrt{x+x^5}} \, dx","Integrate[((1 + x^4)*(-1 + 3*x^4))/(x*(1 - a*x + x^4)*Sqrt[x + x^5]),x]","\int \frac{\left(1+x^4\right) \left(-1+3 x^4\right)}{x \left(1-a x+x^4\right) \sqrt{x+x^5}} \, dx","\frac{2 \sqrt{x^5+x}}{x}-2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x^5+x}}{x^4+1}\right)",1,"Integrate[((1 + x^4)*(-1 + 3*x^4))/(x*(1 - a*x + x^4)*Sqrt[x + x^5]), x]","F",-1
582,0,0,45,0.319453,"\int \frac{\sqrt{1+x^2+x^5} \left(-2+3 x^5\right)}{\left(1+x^5\right) \left(1-x^2+x^5\right)} \, dx","Integrate[(Sqrt[1 + x^2 + x^5]*(-2 + 3*x^5))/((1 + x^5)*(1 - x^2 + x^5)),x]","\int \frac{\sqrt{1+x^2+x^5} \left(-2+3 x^5\right)}{\left(1+x^5\right) \left(1-x^2+x^5\right)} \, dx","2 \tanh ^{-1}\left(\frac{x}{\sqrt{x^5+x^2+1}}\right)-2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^5+x^2+1}}\right)",1,"Integrate[(Sqrt[1 + x^2 + x^5]*(-2 + 3*x^5))/((1 + x^5)*(1 - x^2 + x^5)), x]","F",-1
583,1,26,45,0.0054368,"\int \frac{\sqrt[4]{1+x^6}}{x^7} \, dx","Integrate[(1 + x^6)^(1/4)/x^7,x]","\frac{2}{15} \left(x^6+1\right)^{5/4} \, _2F_1\left(\frac{5}{4},2;\frac{9}{4};x^6+1\right)","-\frac{\sqrt[4]{x^6+1}}{6 x^6}-\frac{1}{12} \tan ^{-1}\left(\sqrt[4]{x^6+1}\right)-\frac{1}{12} \tanh ^{-1}\left(\sqrt[4]{x^6+1}\right)",1,"(2*(1 + x^6)^(5/4)*Hypergeometric2F1[5/4, 2, 9/4, 1 + x^6])/15","C",1
584,0,0,45,2.3386981,"\int \frac{(-1+x)^2 \left(-10-8 x+5 x^2+5 x^3\right)}{\left(\frac{1+x}{-2+x^2}\right)^{3/4} \left(-2+x^2\right) \left(-3+7 x-11 x^2+4 x^3+4 x^4-4 x^5+x^6\right)} \, dx","Integrate[((-1 + x)^2*(-10 - 8*x + 5*x^2 + 5*x^3))/(((1 + x)/(-2 + x^2))^(3/4)*(-2 + x^2)*(-3 + 7*x - 11*x^2 + 4*x^3 + 4*x^4 - 4*x^5 + x^6)),x]","\int \frac{(-1+x)^2 \left(-10-8 x+5 x^2+5 x^3\right)}{\left(\frac{1+x}{-2+x^2}\right)^{3/4} \left(-2+x^2\right) \left(-3+7 x-11 x^2+4 x^3+4 x^4-4 x^5+x^6\right)} \, dx","2 \tan ^{-1}\left(\frac{x-1}{\sqrt[4]{\frac{x+1}{x^2-2}}}\right)-2 \tanh ^{-1}\left(\frac{x-1}{\sqrt[4]{\frac{x+1}{x^2-2}}}\right)",1,"Integrate[((-1 + x)^2*(-10 - 8*x + 5*x^2 + 5*x^3))/(((1 + x)/(-2 + x^2))^(3/4)*(-2 + x^2)*(-3 + 7*x - 11*x^2 + 4*x^3 + 4*x^4 - 4*x^5 + x^6)), x]","F",-1
585,0,0,45,1.9564589,"\int \frac{x^2 (10 b+9 a x)}{\sqrt[4]{b x^2+a x^3} \left(-b-a x+x^{10}\right)} \, dx","Integrate[(x^2*(10*b + 9*a*x))/((b*x^2 + a*x^3)^(1/4)*(-b - a*x + x^10)),x]","\int \frac{x^2 (10 b+9 a x)}{\sqrt[4]{b x^2+a x^3} \left(-b-a x+x^{10}\right)} \, dx","2 \tan ^{-1}\left(\frac{\sqrt[4]{a x^3+b x^2}}{x^3}\right)-2 \tanh ^{-1}\left(\frac{x^3}{\sqrt[4]{a x^3+b x^2}}\right)",1,"Integrate[(x^2*(10*b + 9*a*x))/((b*x^2 + a*x^3)^(1/4)*(-b - a*x + x^10)), x]","F",-1
586,1,186,45,21.3360619,"\int \frac{-1+x^{16}}{\sqrt{1+x^4} \left(1+x^{16}\right)} \, dx","Integrate[(-1 + x^16)/(Sqrt[1 + x^4]*(1 + x^16)),x]","\frac{1}{4} \sqrt[4]{-1} \left(-4 F\left(\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+\Pi \left(-\sqrt[8]{-1};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+\Pi \left(\sqrt[8]{-1};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+\Pi \left(-(-1)^{3/8};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+\Pi \left((-1)^{3/8};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+\Pi \left(-(-1)^{5/8};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+\Pi \left((-1)^{5/8};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+\Pi \left(-(-1)^{7/8};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+\Pi \left((-1)^{7/8};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)\right)","\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^4+2\&,\frac{\log \left(\sqrt{x^4+1}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]",1,"((-1)^(1/4)*(-4*EllipticF[I*ArcSinh[(-1)^(1/4)*x], -1] + EllipticPi[-(-1)^(1/8), I*ArcSinh[(-1)^(1/4)*x], -1] + EllipticPi[(-1)^(1/8), I*ArcSinh[(-1)^(1/4)*x], -1] + EllipticPi[-(-1)^(3/8), I*ArcSinh[(-1)^(1/4)*x], -1] + EllipticPi[(-1)^(3/8), I*ArcSinh[(-1)^(1/4)*x], -1] + EllipticPi[-(-1)^(5/8), I*ArcSinh[(-1)^(1/4)*x], -1] + EllipticPi[(-1)^(5/8), I*ArcSinh[(-1)^(1/4)*x], -1] + EllipticPi[-(-1)^(7/8), I*ArcSinh[(-1)^(1/4)*x], -1] + EllipticPi[(-1)^(7/8), I*ArcSinh[(-1)^(1/4)*x], -1]))/4","C",1
587,1,127,45,22.2311313,"\int \frac{-1+x^{16}}{\sqrt{-1+x^4} \left(1-x^8+x^{16}\right)} \, dx","Integrate[(-1 + x^16)/(Sqrt[-1 + x^4]*(1 - x^8 + x^16)),x]","\frac{(-1)^{5/6} \sqrt{1-x^4} \left(-4 F\left(\left.\sin ^{-1}(x)\right|-1\right)+\Pi \left(-\sqrt[12]{-1};\left.\sin ^{-1}(x)\right|-1\right)+\Pi \left(\sqrt[12]{-1};\left.\sin ^{-1}(x)\right|-1\right)+\Pi \left(-(-1)^{5/12};\left.\sin ^{-1}(x)\right|-1\right)+\Pi \left((-1)^{5/12};\left.\sin ^{-1}(x)\right|-1\right)+\Pi \left(-(-1)^{7/12};\left.\sin ^{-1}(x)\right|-1\right)+\Pi \left((-1)^{7/12};\left.\sin ^{-1}(x)\right|-1\right)+\Pi \left(-(-1)^{11/12};\left.\sin ^{-1}(x)\right|-1\right)+\Pi \left((-1)^{11/12};\left.\sin ^{-1}(x)\right|-1\right)\right)}{2 \left(\sqrt{3}-i\right) \sqrt{x^4-1}}","\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8+4 \text{$\#$1}^4+1\&,\frac{\log \left(\sqrt{x^4-1}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]",1,"((-1)^(5/6)*Sqrt[1 - x^4]*(-4*EllipticF[ArcSin[x], -1] + EllipticPi[-(-1)^(1/12), ArcSin[x], -1] + EllipticPi[(-1)^(1/12), ArcSin[x], -1] + EllipticPi[-(-1)^(5/12), ArcSin[x], -1] + EllipticPi[(-1)^(5/12), ArcSin[x], -1] + EllipticPi[-(-1)^(7/12), ArcSin[x], -1] + EllipticPi[(-1)^(7/12), ArcSin[x], -1] + EllipticPi[-(-1)^(11/12), ArcSin[x], -1] + EllipticPi[(-1)^(11/12), ArcSin[x], -1]))/(2*(-I + Sqrt[3])*Sqrt[-1 + x^4])","C",1
588,1,70,45,0.0586063,"\int \frac{\sqrt{x^2+x \sqrt{-1+x^2}}}{x \sqrt{-1+x^2}} \, dx","Integrate[Sqrt[x^2 + x*Sqrt[-1 + x^2]]/(x*Sqrt[-1 + x^2]),x]","\frac{\sqrt{2} \sqrt{x \left(\sqrt{x^2-1}+x\right)} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{x}}{\sqrt{\sqrt{x^2-1}+x}}\right)}{\sqrt{x} \sqrt{\sqrt{x^2-1}+x}}","-\sqrt{2} \log \left(\sqrt{x^2-1}-\sqrt{2} \sqrt{x^2+\sqrt{x^2-1} x}+x\right)",1,"(Sqrt[2]*Sqrt[x*(x + Sqrt[-1 + x^2])]*ArcTanh[(Sqrt[2]*Sqrt[x])/Sqrt[x + Sqrt[-1 + x^2]]])/(Sqrt[x]*Sqrt[x + Sqrt[-1 + x^2]])","A",1
589,1,54,46,0.0350961,"\int x^6 \sqrt{x+x^4} \, dx","Integrate[x^6*Sqrt[x + x^4],x]","\frac{\sqrt{x^4+x} \left(\frac{3 \sinh ^{-1}\left(x^{3/2}\right)}{\sqrt{x^3+1}}+\left(8 x^6+2 x^3-3\right) x^{3/2}\right)}{72 \sqrt{x}}","\frac{1}{72} \sqrt{x^4+x} \left(8 x^7+2 x^4-3 x\right)+\frac{1}{24} \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4+x}}\right)",1,"(Sqrt[x + x^4]*(x^(3/2)*(-3 + 2*x^3 + 8*x^6) + (3*ArcSinh[x^(3/2)])/Sqrt[1 + x^3]))/(72*Sqrt[x])","A",1
590,1,709,46,5.0434149,"\int \frac{(-1+x) (1+x)^3}{\left(1+x^2\right)^2 \sqrt{1+x^2+x^4}} \, dx","Integrate[((-1 + x)*(1 + x)^3)/((1 + x^2)^2*Sqrt[1 + x^2 + x^4]),x]","\frac{2 \left(\frac{x^4+x^2+1}{x^2+1}-\frac{\sqrt[6]{-1} \sqrt{\frac{\left(\sqrt{3}-i\right) \left(x-\sqrt[3]{-1}+1\right) \left(2 x-i \sqrt{3}-1\right)}{\left(x+(-1)^{2/3}+1\right)^2}} \sqrt{\frac{2 \sqrt{3} x-\sqrt{3}+3 i}{2 \left(\sqrt{3}+i\right) x+4 i}} \left(x+(-1)^{2/3}+1\right)^2 F\left(\sin ^{-1}\left(\sqrt{\frac{i \sqrt{3} x+x+2}{x+(-1)^{2/3}+1}}\right)|\frac{1}{4}\right)}{2 \sqrt{2} \sqrt[4]{3}}+\frac{\sqrt[6]{-1} \sqrt{\frac{-2 \sqrt{3} x+\sqrt{3}+3 i}{-2 i x+\sqrt{3}-i}} \sqrt{\frac{i \sqrt{3} x+x+2}{x+(-1)^{2/3}+1}} \sqrt{\frac{2 \sqrt{3} x-\sqrt{3}+3 i}{\left(\sqrt{3}+i\right) x+2 i}} \left(x+(-1)^{2/3}+1\right)^2 \left(\left((1+2 i)-i \sqrt{3}\right) F\left(\sin ^{-1}\left(\sqrt{\frac{2 \left(-i+\sqrt{3}\right) x-4 i}{-2 i x+\sqrt{3}-i}}\right)|\frac{1}{4}\right)+2 i \sqrt{3} \Pi \left(\frac{(1+2 i)+i \sqrt{3}}{(4+2 i)-2 \sqrt{3}};\sin ^{-1}\left(\sqrt{\frac{2 \left(-i+\sqrt{3}\right) x-4 i}{-2 i x+\sqrt{3}-i}}\right)|\frac{1}{4}\right)\right)}{4 \sqrt{6}}-\frac{(-1)^{2/3} \sqrt{\frac{-2 \sqrt{3} x+\sqrt{3}+3 i}{-2 i x+\sqrt{3}-i}} \sqrt{\frac{i \sqrt{3} x+x+2}{x+(-1)^{2/3}+1}} \sqrt{\frac{2 \sqrt{3} x-\sqrt{3}+3 i}{\left(\sqrt{3}+i\right) x+2 i}} \left(x+(-1)^{2/3}+1\right)^2 \left(\left(\sqrt{3}+(2+i)\right) F\left(\sin ^{-1}\left(\sqrt{\frac{2 \left(-i+\sqrt{3}\right) x-4 i}{-2 i x+\sqrt{3}-i}}\right)|\frac{1}{4}\right)-2 \sqrt{3} \Pi \left(\frac{(1-2 i)+i \sqrt{3}}{(4-2 i)+2 \sqrt{3}};\sin ^{-1}\left(\sqrt{\frac{2 \left(-i+\sqrt{3}\right) x-4 i}{-2 i x+\sqrt{3}-i}}\right)|\frac{1}{4}\right)\right)}{4 \sqrt{6}}\right)}{\sqrt{x^4+x^2+1}}","\frac{2 \sqrt{x^4+x^2+1}}{x^2+1}-2 \tan ^{-1}\left(\frac{x}{x^2+\sqrt{x^4+x^2+1}+1}\right)",1,"(2*((1 + x^2 + x^4)/(1 + x^2) - ((-1)^(1/6)*(1 + (-1)^(2/3) + x)^2*Sqrt[((-I + Sqrt[3])*(1 - (-1)^(1/3) + x)*(-1 - I*Sqrt[3] + 2*x))/(1 + (-1)^(2/3) + x)^2]*Sqrt[(3*I - Sqrt[3] + 2*Sqrt[3]*x)/(4*I + 2*(I + Sqrt[3])*x)]*EllipticF[ArcSin[Sqrt[(2 + x + I*Sqrt[3]*x)/(1 + (-1)^(2/3) + x)]], 1/4])/(2*Sqrt[2]*3^(1/4)) + ((-1)^(1/6)*(1 + (-1)^(2/3) + x)^2*Sqrt[(3*I + Sqrt[3] - 2*Sqrt[3]*x)/(-I + Sqrt[3] - (2*I)*x)]*Sqrt[(2 + x + I*Sqrt[3]*x)/(1 + (-1)^(2/3) + x)]*Sqrt[(3*I - Sqrt[3] + 2*Sqrt[3]*x)/(2*I + (I + Sqrt[3])*x)]*(((1 + 2*I) - I*Sqrt[3])*EllipticF[ArcSin[Sqrt[(-4*I + 2*(-I + Sqrt[3])*x)/(-I + Sqrt[3] - (2*I)*x)]], 1/4] + (2*I)*Sqrt[3]*EllipticPi[((1 + 2*I) + I*Sqrt[3])/((4 + 2*I) - 2*Sqrt[3]), ArcSin[Sqrt[(-4*I + 2*(-I + Sqrt[3])*x)/(-I + Sqrt[3] - (2*I)*x)]], 1/4]))/(4*Sqrt[6]) - ((-1)^(2/3)*(1 + (-1)^(2/3) + x)^2*Sqrt[(3*I + Sqrt[3] - 2*Sqrt[3]*x)/(-I + Sqrt[3] - (2*I)*x)]*Sqrt[(2 + x + I*Sqrt[3]*x)/(1 + (-1)^(2/3) + x)]*Sqrt[(3*I - Sqrt[3] + 2*Sqrt[3]*x)/(2*I + (I + Sqrt[3])*x)]*(((2 + I) + Sqrt[3])*EllipticF[ArcSin[Sqrt[(-4*I + 2*(-I + Sqrt[3])*x)/(-I + Sqrt[3] - (2*I)*x)]], 1/4] - 2*Sqrt[3]*EllipticPi[((1 - 2*I) + I*Sqrt[3])/((4 - 2*I) + 2*Sqrt[3]), ArcSin[Sqrt[(-4*I + 2*(-I + Sqrt[3])*x)/(-I + Sqrt[3] - (2*I)*x)]], 1/4]))/(4*Sqrt[6])))/Sqrt[1 + x^2 + x^4]","C",0
591,1,3173,46,3.2168438,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{1-x-x^2-x^3+x^4}} \, dx","Integrate[(-1 + x^2)/((1 + x^2)*Sqrt[1 - x - x^2 - x^3 + x^4]),x]","\text{Result too large to show}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{3} x}{x^2-\sqrt{x^4-x^3-x^2-x+1}+1}\right)}{\sqrt{3}}",1,"(2*(1 + Sqrt[13] + Sqrt[2*(-1 + Sqrt[13])] - 4*x)^2*Sqrt[(-x + Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 3, 0])/((1 + Sqrt[13] + Sqrt[2*(-1 + Sqrt[13])] - 4*x)*(-Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 1, 0] + Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 3, 0]))]*Sqrt[-(((x - Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 1, 0])*(1 + Sqrt[13] + Sqrt[2*(-1 + Sqrt[13])] - 4*Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 4, 0]))/((1 + Sqrt[13] + Sqrt[2*(-1 + Sqrt[13])] - 4*x)*(Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 4, 0])))]*Sqrt[(-x + Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 4, 0])/((1 + Sqrt[13] + Sqrt[2*(-1 + Sqrt[13])] - 4*x)*(-Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 1, 0] + Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 4, 0]))]*(((-4*I)*((EllipticPi[(((1 - 4*I) + Sqrt[13] + Sqrt[2*(-1 + Sqrt[13])])*(Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 4, 0]))/((-I + Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 1, 0])*(1 + Sqrt[13] + Sqrt[2*(-1 + Sqrt[13])] - 4*Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 4, 0])), ArcSin[Sqrt[-(((x - Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 1, 0])*(1 + Sqrt[13] + Sqrt[2*(-1 + Sqrt[13])] - 4*Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 4, 0]))/((1 + Sqrt[13] + Sqrt[2*(-1 + Sqrt[13])] - 4*x)*(Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 4, 0])))]], -(((1 + Sqrt[13] + Sqrt[2*(-1 + Sqrt[13])] - 4*Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 3, 0])*(Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 4, 0]))/((-Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 1, 0] + Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 3, 0])*(1 + Sqrt[13] + Sqrt[2*(-1 + Sqrt[13])] - 4*Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 4, 0])))]*(1 + Sqrt[13] + Sqrt[2*(-1 + Sqrt[13])] - 4*Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 1, 0]))/4 + EllipticF[ArcSin[Sqrt[-(((x - Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 1, 0])*(1 + Sqrt[13] + Sqrt[2*(-1 + Sqrt[13])] - 4*Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 4, 0]))/((1 + Sqrt[13] + Sqrt[2*(-1 + Sqrt[13])] - 4*x)*(Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 4, 0])))]], -(((1 + Sqrt[13] + Sqrt[2*(-1 + Sqrt[13])] - 4*Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 3, 0])*(Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 4, 0]))/((-Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 1, 0] + Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 3, 0])*(1 + Sqrt[13] + Sqrt[2*(-1 + Sqrt[13])] - 4*Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 4, 0])))]*(-I + Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 1, 0]))*(Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 4, 0]))/(((1 - 4*I) + Sqrt[13] + Sqrt[2*(-1 + Sqrt[13])])*(-I + Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 1, 0])) + ((4*I)*((EllipticPi[(((1 + 4*I) + Sqrt[13] + Sqrt[2*(-1 + Sqrt[13])])*(Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 4, 0]))/((I + Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 1, 0])*(1 + Sqrt[13] + Sqrt[2*(-1 + Sqrt[13])] - 4*Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 4, 0])), ArcSin[Sqrt[-(((x - Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 1, 0])*(1 + Sqrt[13] + Sqrt[2*(-1 + Sqrt[13])] - 4*Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 4, 0]))/((1 + Sqrt[13] + Sqrt[2*(-1 + Sqrt[13])] - 4*x)*(Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 4, 0])))]], -(((1 + Sqrt[13] + Sqrt[2*(-1 + Sqrt[13])] - 4*Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 3, 0])*(Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 4, 0]))/((-Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 1, 0] + Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 3, 0])*(1 + Sqrt[13] + Sqrt[2*(-1 + Sqrt[13])] - 4*Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 4, 0])))]*(1 + Sqrt[13] + Sqrt[2*(-1 + Sqrt[13])] - 4*Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 1, 0]))/4 + EllipticF[ArcSin[Sqrt[-(((x - Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 1, 0])*(1 + Sqrt[13] + Sqrt[2*(-1 + Sqrt[13])] - 4*Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 4, 0]))/((1 + Sqrt[13] + Sqrt[2*(-1 + Sqrt[13])] - 4*x)*(Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 4, 0])))]], -(((1 + Sqrt[13] + Sqrt[2*(-1 + Sqrt[13])] - 4*Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 3, 0])*(Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 4, 0]))/((-Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 1, 0] + Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 3, 0])*(1 + Sqrt[13] + Sqrt[2*(-1 + Sqrt[13])] - 4*Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 4, 0])))]*(I + Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 1, 0]))*(Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 4, 0]))/(((1 + 4*I) + Sqrt[13] + Sqrt[2*(-1 + Sqrt[13])])*(I + Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 1, 0])) + EllipticF[ArcSin[Sqrt[-(((x - Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 1, 0])*(1 + Sqrt[13] + Sqrt[2*(-1 + Sqrt[13])] - 4*Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 4, 0]))/((1 + Sqrt[13] + Sqrt[2*(-1 + Sqrt[13])] - 4*x)*(Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 4, 0])))]], ((1 + Sqrt[13] + Sqrt[2*(-1 + Sqrt[13])] - 4*Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 3, 0])*(Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 4, 0]))/((Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 3, 0])*(1 + Sqrt[13] + Sqrt[2*(-1 + Sqrt[13])] - 4*Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 4, 0]))]*(-Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 1, 0] + Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 4, 0])))/(Sqrt[1 - x - x^2 - x^3 + x^4]*(1 + Sqrt[13] + Sqrt[2*(-1 + Sqrt[13])] - 4*Root[1 - #1 - #1^2 - #1^3 + #1^4 & , 4, 0]))","C",0
592,0,0,46,0.1645003,"\int \frac{-1-2 x+3 x^2}{\sqrt{-3-2 x-x^2+4 x^3-x^4-2 x^5+x^6}} \, dx","Integrate[(-1 - 2*x + 3*x^2)/Sqrt[-3 - 2*x - x^2 + 4*x^3 - x^4 - 2*x^5 + x^6],x]","\int \frac{-1-2 x+3 x^2}{\sqrt{-3-2 x-x^2+4 x^3-x^4-2 x^5+x^6}} \, dx","-\log \left(-x^3+x^2+\sqrt{x^6-2 x^5-x^4+4 x^3-x^2-2 x-3}+x-1\right)",1,"Integrate[(-1 - 2*x + 3*x^2)/Sqrt[-3 - 2*x - x^2 + 4*x^3 - x^4 - 2*x^5 + x^6], x]","F",-1
593,1,53,46,0.022206,"\int \frac{-x+x^2}{\sqrt{-2 x+4 x^2-2 x^3+x^4-2 x^5+x^6}} \, dx","Integrate[(-x + x^2)/Sqrt[-2*x + 4*x^2 - 2*x^3 + x^4 - 2*x^5 + x^6],x]","\frac{2 (x-1) \sqrt{x} \sqrt{x^3-2} \tanh ^{-1}\left(\frac{x^{3/2}}{\sqrt{x^3-2}}\right)}{3 \sqrt{(x-1)^2 x \left(x^3-2\right)}}","\frac{2}{3} \tanh ^{-1}\left(\frac{(x-1) \left(x^3-2\right)}{x \sqrt{x^6-2 x^5+x^4-2 x^3+4 x^2-2 x}}\right)",1,"(2*(-1 + x)*Sqrt[x]*Sqrt[-2 + x^3]*ArcTanh[x^(3/2)/Sqrt[-2 + x^3]])/(3*Sqrt[(-1 + x)^2*x*(-2 + x^3)])","A",1
594,1,38,47,0.0057626,"\int \frac{\sqrt[4]{-1+x^4}}{x^2} \, dx","Integrate[(-1 + x^4)^(1/4)/x^2,x]","-\frac{\sqrt[4]{x^4-1} \, _2F_1\left(-\frac{1}{4},-\frac{1}{4};\frac{3}{4};x^4\right)}{x \sqrt[4]{1-x^4}}","-\frac{\sqrt[4]{x^4-1}}{x}-\frac{1}{2} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-1}}\right)+\frac{1}{2} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-1}}\right)",1,"-(((-1 + x^4)^(1/4)*Hypergeometric2F1[-1/4, -1/4, 3/4, x^4])/(x*(1 - x^4)^(1/4)))","C",1
595,1,45,47,0.0189581,"\int \frac{\left(-1+x^4\right) \sqrt[4]{1+x^4}}{x} \, dx","Integrate[((-1 + x^4)*(1 + x^4)^(1/4))/x,x]","\frac{1}{10} \left(2 \sqrt[4]{x^4+1} \left(x^4-4\right)+5 \tan ^{-1}\left(\sqrt[4]{x^4+1}\right)+5 \tanh ^{-1}\left(\sqrt[4]{x^4+1}\right)\right)","\frac{1}{5} \sqrt[4]{x^4+1} \left(x^4-4\right)+\frac{1}{2} \tan ^{-1}\left(\sqrt[4]{x^4+1}\right)+\frac{1}{2} \tanh ^{-1}\left(\sqrt[4]{x^4+1}\right)",1,"(2*(-4 + x^4)*(1 + x^4)^(1/4) + 5*ArcTan[(1 + x^4)^(1/4)] + 5*ArcTanh[(1 + x^4)^(1/4)])/10","A",1
596,1,57,47,0.0243802,"\int \frac{1}{\sqrt{3+4 x+x^4}} \, dx","Integrate[1/Sqrt[3 + 4*x + x^4],x]","\frac{(x+1) \sqrt{x^2-2 x+3} \tanh ^{-1}\left(\frac{\sqrt{\frac{2}{3}} (x-2)}{\sqrt{x^2-2 x+3}}\right)}{\sqrt{6} \sqrt{x^4+4 x+3}}","\sqrt{\frac{2}{3}} \tanh ^{-1}\left(\frac{\sqrt{6} x+\sqrt{6}}{-\sqrt{x^4+4 x+3}+x^2+2 x+1}\right)",1,"((1 + x)*Sqrt[3 - 2*x + x^2]*ArcTanh[(Sqrt[2/3]*(-2 + x))/Sqrt[3 - 2*x + x^2]])/(Sqrt[6]*Sqrt[3 + 4*x + x^4])","A",1
597,1,1280,47,5.0369592,"\int \frac{\left(1+x^4\right) \sqrt{-1+2 x^2+x^4}}{\left(-1+x^4\right) \left(-1+x^2+x^4\right)} \, dx","Integrate[((1 + x^4)*Sqrt[-1 + 2*x^2 + x^4])/((-1 + x^4)*(-1 + x^2 + x^4)),x]","\frac{(x-1) (x+1) \left(x^2+1\right) \left(x^4+x^2-1\right) \left(-\frac{4 \left(\sqrt{-1+\sqrt{2}}+i \sqrt{1+\sqrt{2}}\right) \sqrt{-\frac{x+i \sqrt{1+\sqrt{2}}}{i \sqrt{1+\sqrt{2}} x-\sqrt{-1+\sqrt{2}} x+\sqrt{2}-(1+i)}} \sqrt{\frac{i \sqrt{1+\sqrt{2}}-x}{-\left(\left(\sqrt{-1+\sqrt{2}}+i \sqrt{1+\sqrt{2}}\right) x\right)+\sqrt{2}-(1-i)}} \sqrt{\frac{\left(\sqrt{-1+\sqrt{2}}-i \sqrt{1+\sqrt{2}}\right) x+\sqrt{2}-(1+i)}{-\left(\left(\sqrt{-1+\sqrt{2}}+i \sqrt{1+\sqrt{2}}\right) x\right)+\sqrt{2}-(1-i)}} \left(\sqrt{-1+\sqrt{2}} \left(\Pi \left(\frac{\left(-1+\sqrt{-1+\sqrt{2}}\right) \left(\sqrt{-1+\sqrt{2}}+i \sqrt{1+\sqrt{2}}\right)}{\left(1+\sqrt{-1+\sqrt{2}}\right) \left(\sqrt{-1+\sqrt{2}}-i \sqrt{1+\sqrt{2}}\right)};\left.\sin ^{-1}\left(\sqrt{\frac{-i \sqrt{1+\sqrt{2}} x+\sqrt{-1+\sqrt{2}} x+\sqrt{2}-(1+i)}{-\left(\left(\sqrt{-1+\sqrt{2}}+i \sqrt{1+\sqrt{2}}\right) x\right)+\sqrt{2}-(1-i)}}\right)\right|-i\right)-\Pi \left(\frac{\left(1+\sqrt{-1+\sqrt{2}}\right) \left(\sqrt{-1+\sqrt{2}}+i \sqrt{1+\sqrt{2}}\right)}{\left(-1+\sqrt{-1+\sqrt{2}}\right) \left(\sqrt{-1+\sqrt{2}}-i \sqrt{1+\sqrt{2}}\right)};\left.\sin ^{-1}\left(\sqrt{\frac{-i \sqrt{1+\sqrt{2}} x+\sqrt{-1+\sqrt{2}} x+\sqrt{2}-(1+i)}{-\left(\left(\sqrt{-1+\sqrt{2}}+i \sqrt{1+\sqrt{2}}\right) x\right)+\sqrt{2}-(1-i)}}\right)\right|-i\right)\right)-F\left(\left.\sin ^{-1}\left(\sqrt{\frac{\left(\sqrt{-1+\sqrt{2}}-i \sqrt{1+\sqrt{2}}\right) x+\sqrt{2}-(1+i)}{-\left(\left(\sqrt{-1+\sqrt{2}}+i \sqrt{1+\sqrt{2}}\right) x\right)+\sqrt{2}-(1-i)}}\right)\right|-i\right)\right) \left(\sqrt{-1+\sqrt{2}}-x\right)^2}{\left(-2+\sqrt{2}\right) \left(\sqrt{-1+\sqrt{2}}-i \sqrt{1+\sqrt{2}}\right)}-i \sqrt{1+\sqrt{2}} \sqrt{-x^4-2 x^2+1} F\left(i \sinh ^{-1}\left(\frac{x}{\sqrt{1+\sqrt{2}}}\right)|-3-2 \sqrt{2}\right)+2 i \sqrt{1+\sqrt{2}} \sqrt{-x^4-2 x^2+1} \Pi \left(1+\sqrt{2};i \sinh ^{-1}\left(\frac{x}{\sqrt{1+\sqrt{2}}}\right)|-3-2 \sqrt{2}\right)-\frac{i \sqrt{5 \left(1+\sqrt{2}\right)} \sqrt{-x^4-2 x^2+1} \Pi \left(-\frac{2 \left(1+\sqrt{2}\right)}{-1+\sqrt{5}};i \sinh ^{-1}\left(\frac{x}{\sqrt{1+\sqrt{2}}}\right)|-3-2 \sqrt{2}\right)}{-3+\sqrt{5}}+\frac{3 i \sqrt{1+\sqrt{2}} \sqrt{-x^4-2 x^2+1} \Pi \left(-\frac{2 \left(1+\sqrt{2}\right)}{-1+\sqrt{5}};i \sinh ^{-1}\left(\frac{x}{\sqrt{1+\sqrt{2}}}\right)|-3-2 \sqrt{2}\right)}{-3+\sqrt{5}}-\frac{i \sqrt{5 \left(1+\sqrt{2}\right)} \sqrt{-x^4-2 x^2+1} \Pi \left(\frac{2 \left(1+\sqrt{2}\right)}{1+\sqrt{5}};i \sinh ^{-1}\left(\frac{x}{\sqrt{1+\sqrt{2}}}\right)|-3-2 \sqrt{2}\right)}{3+\sqrt{5}}-\frac{3 i \sqrt{1+\sqrt{2}} \sqrt{-x^4-2 x^2+1} \Pi \left(\frac{2 \left(1+\sqrt{2}\right)}{1+\sqrt{5}};i \sinh ^{-1}\left(\frac{x}{\sqrt{1+\sqrt{2}}}\right)|-3-2 \sqrt{2}\right)}{3+\sqrt{5}}\right)}{\sqrt{x^4+2 x^2-1} \left(x^8+x^6-2 x^4-x^2+1\right)}","\tanh ^{-1}\left(\frac{x}{\sqrt{x^4+2 x^2-1}}\right)-\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+2 x^2-1}}\right)",1,"((-1 + x)*(1 + x)*(1 + x^2)*(-1 + x^2 + x^4)*((-I)*Sqrt[1 + Sqrt[2]]*Sqrt[1 - 2*x^2 - x^4]*EllipticF[I*ArcSinh[x/Sqrt[1 + Sqrt[2]]], -3 - 2*Sqrt[2]] + (2*I)*Sqrt[1 + Sqrt[2]]*Sqrt[1 - 2*x^2 - x^4]*EllipticPi[1 + Sqrt[2], I*ArcSinh[x/Sqrt[1 + Sqrt[2]]], -3 - 2*Sqrt[2]] + ((3*I)*Sqrt[1 + Sqrt[2]]*Sqrt[1 - 2*x^2 - x^4]*EllipticPi[(-2*(1 + Sqrt[2]))/(-1 + Sqrt[5]), I*ArcSinh[x/Sqrt[1 + Sqrt[2]]], -3 - 2*Sqrt[2]])/(-3 + Sqrt[5]) - (I*Sqrt[5*(1 + Sqrt[2])]*Sqrt[1 - 2*x^2 - x^4]*EllipticPi[(-2*(1 + Sqrt[2]))/(-1 + Sqrt[5]), I*ArcSinh[x/Sqrt[1 + Sqrt[2]]], -3 - 2*Sqrt[2]])/(-3 + Sqrt[5]) - ((3*I)*Sqrt[1 + Sqrt[2]]*Sqrt[1 - 2*x^2 - x^4]*EllipticPi[(2*(1 + Sqrt[2]))/(1 + Sqrt[5]), I*ArcSinh[x/Sqrt[1 + Sqrt[2]]], -3 - 2*Sqrt[2]])/(3 + Sqrt[5]) - (I*Sqrt[5*(1 + Sqrt[2])]*Sqrt[1 - 2*x^2 - x^4]*EllipticPi[(2*(1 + Sqrt[2]))/(1 + Sqrt[5]), I*ArcSinh[x/Sqrt[1 + Sqrt[2]]], -3 - 2*Sqrt[2]])/(3 + Sqrt[5]) - (4*(Sqrt[-1 + Sqrt[2]] + I*Sqrt[1 + Sqrt[2]])*(Sqrt[-1 + Sqrt[2]] - x)^2*Sqrt[-((I*Sqrt[1 + Sqrt[2]] + x)/((-1 - I) + Sqrt[2] - Sqrt[-1 + Sqrt[2]]*x + I*Sqrt[1 + Sqrt[2]]*x))]*Sqrt[(I*Sqrt[1 + Sqrt[2]] - x)/((-1 + I) + Sqrt[2] - (Sqrt[-1 + Sqrt[2]] + I*Sqrt[1 + Sqrt[2]])*x)]*Sqrt[((-1 - I) + Sqrt[2] + (Sqrt[-1 + Sqrt[2]] - I*Sqrt[1 + Sqrt[2]])*x)/((-1 + I) + Sqrt[2] - (Sqrt[-1 + Sqrt[2]] + I*Sqrt[1 + Sqrt[2]])*x)]*(-EllipticF[ArcSin[Sqrt[((-1 - I) + Sqrt[2] + (Sqrt[-1 + Sqrt[2]] - I*Sqrt[1 + Sqrt[2]])*x)/((-1 + I) + Sqrt[2] - (Sqrt[-1 + Sqrt[2]] + I*Sqrt[1 + Sqrt[2]])*x)]], -I] + Sqrt[-1 + Sqrt[2]]*(EllipticPi[((-1 + Sqrt[-1 + Sqrt[2]])*(Sqrt[-1 + Sqrt[2]] + I*Sqrt[1 + Sqrt[2]]))/((1 + Sqrt[-1 + Sqrt[2]])*(Sqrt[-1 + Sqrt[2]] - I*Sqrt[1 + Sqrt[2]])), ArcSin[Sqrt[((-1 - I) + Sqrt[2] + Sqrt[-1 + Sqrt[2]]*x - I*Sqrt[1 + Sqrt[2]]*x)/((-1 + I) + Sqrt[2] - (Sqrt[-1 + Sqrt[2]] + I*Sqrt[1 + Sqrt[2]])*x)]], -I] - EllipticPi[((1 + Sqrt[-1 + Sqrt[2]])*(Sqrt[-1 + Sqrt[2]] + I*Sqrt[1 + Sqrt[2]]))/((-1 + Sqrt[-1 + Sqrt[2]])*(Sqrt[-1 + Sqrt[2]] - I*Sqrt[1 + Sqrt[2]])), ArcSin[Sqrt[((-1 - I) + Sqrt[2] + Sqrt[-1 + Sqrt[2]]*x - I*Sqrt[1 + Sqrt[2]]*x)/((-1 + I) + Sqrt[2] - (Sqrt[-1 + Sqrt[2]] + I*Sqrt[1 + Sqrt[2]])*x)]], -I])))/((-2 + Sqrt[2])*(Sqrt[-1 + Sqrt[2]] - I*Sqrt[1 + Sqrt[2]]))))/(Sqrt[-1 + 2*x^2 + x^4]*(1 - x^2 - 2*x^4 + x^6 + x^8))","C",0
598,1,12187,47,6.3198125,"\int \frac{\sqrt{-1+x-x^2+x^4} \left(2-x+2 x^4\right)}{\left(-1+x+x^4\right)^2} \, dx","Integrate[(Sqrt[-1 + x - x^2 + x^4]*(2 - x + 2*x^4))/(-1 + x + x^4)^2,x]","\text{Result too large to show}","-\frac{\sqrt{x^4-x^2+x-1} x}{x^4+x-1}-\tan ^{-1}\left(\frac{x}{\sqrt{x^4-x^2+x-1}}\right)",1,"Result too large to show","C",0
599,0,0,47,1.4867292,"\int \frac{x+3 x^5}{\left(-1+x^4\right) \left(-a-x+a x^4\right) \sqrt{-x+x^5}} \, dx","Integrate[(x + 3*x^5)/((-1 + x^4)*(-a - x + a*x^4)*Sqrt[-x + x^5]),x]","\int \frac{x+3 x^5}{\left(-1+x^4\right) \left(-a-x+a x^4\right) \sqrt{-x+x^5}} \, dx","\frac{2 \sqrt{x^5-x}}{x^4-1}-2 \sqrt{a} \tanh ^{-1}\left(\frac{x}{\sqrt{a} \sqrt{x^5-x}}\right)",1,"Integrate[(x + 3*x^5)/((-1 + x^4)*(-a - x + a*x^4)*Sqrt[-x + x^5]), x]","F",-1
600,0,0,47,0.5368911,"\int \frac{\sqrt{1+x^2+x^6} \left(-1+2 x^6\right)}{\left(1+x^6\right) \left(2-x^2+2 x^6\right)} \, dx","Integrate[(Sqrt[1 + x^2 + x^6]*(-1 + 2*x^6))/((1 + x^6)*(2 - x^2 + 2*x^6)),x]","\int \frac{\sqrt{1+x^2+x^6} \left(-1+2 x^6\right)}{\left(1+x^6\right) \left(2-x^2+2 x^6\right)} \, dx","\tanh ^{-1}\left(\frac{x}{\sqrt{x^6+x^2+1}}\right)-\sqrt{\frac{3}{2}} \tanh ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt{x^6+x^2+1}}\right)",1,"Integrate[(Sqrt[1 + x^2 + x^6]*(-1 + 2*x^6))/((1 + x^6)*(2 - x^2 + 2*x^6)), x]","F",-1
601,0,0,47,1.5124175,"\int \frac{x+4 x^6}{\left(-1+x^5\right) \left(-a-x+a x^5\right) \sqrt{-x+x^6}} \, dx","Integrate[(x + 4*x^6)/((-1 + x^5)*(-a - x + a*x^5)*Sqrt[-x + x^6]),x]","\int \frac{x+4 x^6}{\left(-1+x^5\right) \left(-a-x+a x^5\right) \sqrt{-x+x^6}} \, dx","\frac{2 \sqrt{x^6-x}}{x^5-1}-2 \sqrt{a} \tanh ^{-1}\left(\frac{x}{\sqrt{a} \sqrt{x^6-x}}\right)",1,"Integrate[(x + 4*x^6)/((-1 + x^5)*(-a - x + a*x^5)*Sqrt[-x + x^6]), x]","F",-1
602,0,0,47,0.5698669,"\int \frac{\left(-1+6 x^4\right) \sqrt{x+2 x^5}}{\left(1+2 x^4\right) \left(1-x^2+4 x^4+4 x^8\right)} \, dx","Integrate[((-1 + 6*x^4)*Sqrt[x + 2*x^5])/((1 + 2*x^4)*(1 - x^2 + 4*x^4 + 4*x^8)),x]","\int \frac{\left(-1+6 x^4\right) \sqrt{x+2 x^5}}{\left(1+2 x^4\right) \left(1-x^2+4 x^4+4 x^8\right)} \, dx","\tan ^{-1}\left(\frac{\sqrt{2 x^5+x}}{2 x^4+1}\right)-\tanh ^{-1}\left(\frac{\sqrt{2 x^5+x}}{2 x^4+1}\right)",1,"Integrate[((-1 + 6*x^4)*Sqrt[x + 2*x^5])/((1 + 2*x^4)*(1 - x^2 + 4*x^4 + 4*x^8)), x]","F",-1
603,1,28,47,0.0101673,"\int \sqrt{1+\sqrt{1+x}} \, dx","Integrate[Sqrt[1 + Sqrt[1 + x]],x]","\frac{4}{15} \left(\sqrt{x+1}+1\right)^{3/2} \left(3 \sqrt{x+1}-2\right)","\frac{4}{15} \sqrt{\sqrt{x+1}+1} (3 x+1)+\frac{4}{15} \sqrt{x+1} \sqrt{\sqrt{x+1}+1}",1,"(4*(1 + Sqrt[1 + x])^(3/2)*(-2 + 3*Sqrt[1 + x]))/15","A",1
604,1,47,47,0.0397379,"\int \frac{\sqrt{1+\sqrt{1+x^2}}}{x} \, dx","Integrate[Sqrt[1 + Sqrt[1 + x^2]]/x,x]","2 \sqrt{\sqrt{x^2+1}+1}-\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+1}}{\sqrt{2}}\right)","2 \sqrt{\sqrt{x^2+1}+1}-\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+1}}{\sqrt{2}}\right)",1,"2*Sqrt[1 + Sqrt[1 + x^2]] - Sqrt[2]*ArcTanh[Sqrt[1 + Sqrt[1 + x^2]]/Sqrt[2]]","A",1
605,1,138,47,0.2362832,"\int \frac{1}{1+\sqrt[4]{9-6 x+x^2}} \, dx","Integrate[(1 + (9 - 6*x + x^2)^(1/4))^(-1),x]","\frac{\sqrt{x-3} \left(4 \left((x-3)^2\right)^{3/4}-\left(\left(-x+\sqrt{(x-3)^2}+3\right) \log (2-x)\right)-\left(x+\sqrt{(x-3)^2}-3\right) \log (4-x)\right)-2 \left(-x+\sqrt{(x-3)^2}+3\right) \sqrt[4]{(x-3)^2} \tan ^{-1}\left(\sqrt{x-3}\right)-2 \sqrt[4]{(x-3)^2} \left(x+\sqrt{(x-3)^2}-3\right) \tanh ^{-1}\left(\sqrt{x-3}\right)}{2 (x-3)^{3/2}}","\frac{\sqrt{(x-3)^2} \left(2 \sqrt[4]{x^2-6 x+9}-2 \log \left(\sqrt[4]{x^2-6 x+9}+1\right)\right)}{x-3}",1,"(-2*(3 + Sqrt[(-3 + x)^2] - x)*((-3 + x)^2)^(1/4)*ArcTan[Sqrt[-3 + x]] - 2*((-3 + x)^2)^(1/4)*(-3 + Sqrt[(-3 + x)^2] + x)*ArcTanh[Sqrt[-3 + x]] + Sqrt[-3 + x]*(4*((-3 + x)^2)^(3/4) - (3 + Sqrt[(-3 + x)^2] - x)*Log[2 - x] - (-3 + Sqrt[(-3 + x)^2] + x)*Log[4 - x]))/(2*(-3 + x)^(3/2))","B",1
606,1,48,48,0.03524,"\int \frac{x^2}{\left(-2+x^2\right) \left(-1+x^2\right)^{3/4}} \, dx","Integrate[x^2/((-2 + x^2)*(-1 + x^2)^(3/4)),x]","-\frac{x^3 \left(1-x^2\right)^{3/4} F_1\left(\frac{3}{2};\frac{3}{4},1;\frac{5}{2};x^2,\frac{x^2}{2}\right)}{6 \left(x^2-1\right)^{3/4}}","\frac{\tan ^{-1}\left(\frac{x}{\sqrt{2} \sqrt[4]{x^2-1}}\right)}{\sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{2} \sqrt[4]{x^2-1}}\right)}{\sqrt{2}}",1,"-1/6*(x^3*(1 - x^2)^(3/4)*AppellF1[3/2, 3/4, 1, 5/2, x^2, x^2/2])/(-1 + x^2)^(3/4)","C",0
607,1,68,48,0.2532714,"\int \frac{\left(-1+x^2\right) \sqrt{1+x^4}}{\left(1+x^2\right)^3} \, dx","Integrate[((-1 + x^2)*Sqrt[1 + x^4])/(1 + x^2)^3,x]","-\frac{\sqrt{x^4+1} x}{2 \left(x^2+1\right)^2}-\frac{1}{2} \sqrt[4]{-1} F\left(\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+\sqrt[4]{-1} \Pi \left(-i;\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)","-\frac{\tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{2 \sqrt{2}}-\frac{\sqrt{x^4+1} x}{2 \left(x^2+1\right)^2}",1,"-1/2*(x*Sqrt[1 + x^4])/(1 + x^2)^2 - ((-1)^(1/4)*EllipticF[I*ArcSinh[(-1)^(1/4)*x], -1])/2 + (-1)^(1/4)*EllipticPi[-I, I*ArcSinh[(-1)^(1/4)*x], -1]","C",1
608,1,196,48,0.4562466,"\int \frac{77-46 x+5 x^2}{\left(-23+82 x-23 x^2\right) \sqrt{-60+83 x-21 x^2-3 x^3+x^4}} \, dx","Integrate[(77 - 46*x + 5*x^2)/((-23 + 82*x - 23*x^2)*Sqrt[-60 + 83*x - 21*x^2 - 3*x^3 + x^4]),x]","\frac{\sqrt{\frac{x-4}{x-1}} \sqrt{\frac{x-3}{x-1}} (x-1)^2 \sqrt{\frac{x+5}{x-1}} \left(-7 F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{x+5}{x-1}}}{\sqrt{3}}\right)|\frac{3}{4}\right)+\left(5+4 \sqrt{2}\right) \Pi \left(\frac{3}{14}-\frac{3 \sqrt{2}}{7};\sin ^{-1}\left(\frac{\sqrt{\frac{x+5}{x-1}}}{\sqrt{3}}\right)|\frac{3}{4}\right)+\left(5-4 \sqrt{2}\right) \Pi \left(\frac{3}{14}+\frac{3 \sqrt{2}}{7};\sin ^{-1}\left(\frac{\sqrt{\frac{x+5}{x-1}}}{\sqrt{3}}\right)|\frac{3}{4}\right)\right)}{7 \sqrt{6} \sqrt{x^4-3 x^3-21 x^2+83 x-60}}","\frac{\tan ^{-1}\left(\frac{2 \sqrt{42} \sqrt{x^4-3 x^3-21 x^2+83 x-60}}{19 x^2-86 x+103}\right)}{\sqrt{42}}",1,"(Sqrt[(-4 + x)/(-1 + x)]*Sqrt[(-3 + x)/(-1 + x)]*(-1 + x)^2*Sqrt[(5 + x)/(-1 + x)]*(-7*EllipticF[ArcSin[Sqrt[(5 + x)/(-1 + x)]/Sqrt[3]], 3/4] + (5 + 4*Sqrt[2])*EllipticPi[3/14 - (3*Sqrt[2])/7, ArcSin[Sqrt[(5 + x)/(-1 + x)]/Sqrt[3]], 3/4] + (5 - 4*Sqrt[2])*EllipticPi[3/14 + (3*Sqrt[2])/7, ArcSin[Sqrt[(5 + x)/(-1 + x)]/Sqrt[3]], 3/4]))/(7*Sqrt[6]*Sqrt[-60 + 83*x - 21*x^2 - 3*x^3 + x^4])","C",1
609,1,45,48,0.0150479,"\int \frac{(-1+x) \sqrt[4]{x^3+x^4}}{x (1+x)} \, dx","Integrate[((-1 + x)*(x^3 + x^4)^(1/4))/(x*(1 + x)),x]","\frac{x^3 \left(-7 (x+1)^{3/4} \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};-x\right)+3 x+3\right)}{3 \left(x^3 (x+1)\right)^{3/4}}","\sqrt[4]{x^4+x^3}+\frac{7}{2} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+x^3}}\right)-\frac{7}{2} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+x^3}}\right)",1,"(x^3*(3 + 3*x - 7*(1 + x)^(3/4)*Hypergeometric2F1[3/4, 3/4, 7/4, -x]))/(3*(x^3*(1 + x))^(3/4))","C",1
610,1,38,48,0.0402686,"\int \frac{\left(-1+x^4\right) \sqrt[4]{x^3+x^4}}{x^8} \, dx","Integrate[((-1 + x^4)*(x^3 + x^4)^(1/4))/x^8,x]","\frac{4 \left(x^3 (x+1)\right)^{9/4} \left(22748 x^4-51183 x^3+39663 x^2-27183 x+13923\right)}{348075 x^{13}}","\frac{4 \sqrt[4]{x^4+x^3} \left(22748 x^6-5687 x^5-39955 x^4+960 x^3-780 x^2+663 x+13923\right)}{348075 x^7}",1,"(4*(x^3*(1 + x))^(9/4)*(13923 - 27183*x + 39663*x^2 - 51183*x^3 + 22748*x^4))/(348075*x^13)","A",1
611,1,10080,48,13.0369394,"\int \frac{-1+4 x-4 x^2+4 x^4}{\sqrt{\frac{1-2 x^2}{1+2 x^2}} \left(1+2 x^2\right) \left(-1-4 x+12 x^2-8 x^3+4 x^4\right)} \, dx","Integrate[(-1 + 4*x - 4*x^2 + 4*x^4)/(Sqrt[(1 - 2*x^2)/(1 + 2*x^2)]*(1 + 2*x^2)*(-1 - 4*x + 12*x^2 - 8*x^3 + 4*x^4)),x]","\text{Result too large to show}","\frac{\tanh ^{-1}\left(\frac{\sqrt{\frac{2}{3}} x-\sqrt{\frac{2}{3}}}{\sqrt{\frac{1-2 x^2}{2 x^2+1}}}\right)}{\sqrt{6}}",1,"Result too large to show","C",0
612,1,203,48,0.156125,"\int \frac{\left(-3+x^4\right) \left(1-2 x^3+x^4\right) \left(1-x^3+x^4\right)}{x^6 \left(1+x^4\right) \sqrt[4]{x+x^5}} \, dx","Integrate[((-3 + x^4)*(1 - 2*x^3 + x^4)*(1 - x^3 + x^4))/(x^6*(1 + x^4)*(x + x^5)^(1/4)),x]","\frac{4 \sqrt[4]{x^4+1} \left(129789 \, _2F_1\left(-\frac{21}{16},\frac{5}{4};-\frac{5}{16};-x^4\right)+x^3 \left(778734 x^4 \, _2F_1\left(\frac{7}{16},\frac{5}{4};\frac{23}{16};-x^4\right)+908523 x \, _2F_1\left(-\frac{5}{16},\frac{5}{4};\frac{11}{16};-x^4\right)-908523 \, _2F_1\left(-\frac{9}{16},\frac{5}{4};\frac{7}{16};-x^4\right)+33649 x^9 \, _2F_1\left(\frac{5}{4},\frac{27}{16};\frac{43}{16};-x^4\right)-118503 x^8 \, _2F_1\left(\frac{5}{4},\frac{23}{16};\frac{39}{16};-x^4\right)+95634 x^7 \, _2F_1\left(\frac{19}{16},\frac{5}{4};\frac{35}{16};-x^4\right)-82593 x^5 \, _2F_1\left(\frac{11}{16},\frac{5}{4};\frac{27}{16};-x^4\right)-1817046 x^3 \, _2F_1\left(\frac{3}{16},\frac{5}{4};\frac{19}{16};-x^4\right)\right)\right)}{908523 x^5 \sqrt[4]{x^5+x}}","\frac{4 \left(x^5+x\right)^{3/4} \left(x^8-7 x^7-14 x^6+2 x^4-7 x^3+1\right)}{7 x^6 \left(x^4+1\right)}",1,"(4*(1 + x^4)^(1/4)*(129789*Hypergeometric2F1[-21/16, 5/4, -5/16, -x^4] + x^3*(-908523*Hypergeometric2F1[-9/16, 5/4, 7/16, -x^4] + 908523*x*Hypergeometric2F1[-5/16, 5/4, 11/16, -x^4] - 1817046*x^3*Hypergeometric2F1[3/16, 5/4, 19/16, -x^4] + 778734*x^4*Hypergeometric2F1[7/16, 5/4, 23/16, -x^4] - 82593*x^5*Hypergeometric2F1[11/16, 5/4, 27/16, -x^4] + 95634*x^7*Hypergeometric2F1[19/16, 5/4, 35/16, -x^4] - 118503*x^8*Hypergeometric2F1[5/4, 23/16, 39/16, -x^4] + 33649*x^9*Hypergeometric2F1[5/4, 27/16, 43/16, -x^4])))/(908523*x^5*(x + x^5)^(1/4))","C",1
613,1,46,48,0.0155763,"\int \frac{x^{20}}{\sqrt{-1+x^6}} \, dx","Integrate[x^20/Sqrt[-1 + x^6],x]","\frac{1}{144} \left(15 \tanh ^{-1}\left(\frac{x^3}{\sqrt{x^6-1}}\right)+\sqrt{x^6-1} \left(8 x^{12}+10 x^6+15\right) x^3\right)","\frac{5}{48} \log \left(\sqrt{x^6-1}+x^3\right)+\frac{1}{144} \sqrt{x^6-1} \left(8 x^{15}+10 x^9+15 x^3\right)",1,"(x^3*Sqrt[-1 + x^6]*(15 + 10*x^6 + 8*x^12) + 15*ArcTanh[x^3/Sqrt[-1 + x^6]])/144","A",1
614,1,56,48,0.0311901,"\int x^{14} \sqrt{-1+x^6} \, dx","Integrate[x^14*Sqrt[-1 + x^6],x]","\frac{\left(x^6-1\right) \left(3 \sin ^{-1}\left(x^3\right)+\sqrt{1-x^6} \left(8 x^{12}-2 x^6-3\right) x^3\right)}{144 \sqrt{-\left(x^6-1\right)^2}}","\frac{1}{144} \sqrt{x^6-1} \left(8 x^{15}-2 x^9-3 x^3\right)-\frac{1}{48} \log \left(\sqrt{x^6-1}+x^3\right)",1,"((-1 + x^6)*(x^3*Sqrt[1 - x^6]*(-3 - 2*x^6 + 8*x^12) + 3*ArcSin[x^3]))/(144*Sqrt[-(-1 + x^6)^2])","A",1
615,1,36,48,0.0143738,"\int \frac{x^{20}}{\sqrt{1+x^6}} \, dx","Integrate[x^20/Sqrt[1 + x^6],x]","\frac{1}{144} \left(x^3 \sqrt{x^6+1} \left(8 x^{12}-10 x^6+15\right)-15 \sinh ^{-1}\left(x^3\right)\right)","\frac{1}{144} \sqrt{x^6+1} \left(8 x^{15}-10 x^9+15 x^3\right)-\frac{5}{48} \log \left(\sqrt{x^6+1}+x^3\right)",1,"(x^3*Sqrt[1 + x^6]*(15 - 10*x^6 + 8*x^12) - 15*ArcSinh[x^3])/144","A",1
616,0,0,48,0.4793566,"\int \frac{x-4 x^6}{\sqrt{x+x^6} \left(1-a x^2+2 x^5+x^{10}\right)} \, dx","Integrate[(x - 4*x^6)/(Sqrt[x + x^6]*(1 - a*x^2 + 2*x^5 + x^10)),x]","\int \frac{x-4 x^6}{\sqrt{x+x^6} \left(1-a x^2+2 x^5+x^{10}\right)} \, dx","\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt{x^6+x}}\right)}{a^{3/4}}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt{x^6+x}}\right)}{a^{3/4}}",1,"Integrate[(x - 4*x^6)/(Sqrt[x + x^6]*(1 - a*x^2 + 2*x^5 + x^10)), x]","F",-1
617,0,0,48,0.4857074,"\int \frac{-x+4 x^6}{\sqrt{x+x^6} \left(a-x^2+2 a x^5+a x^{10}\right)} \, dx","Integrate[(-x + 4*x^6)/(Sqrt[x + x^6]*(a - x^2 + 2*a*x^5 + a*x^10)),x]","\int \frac{-x+4 x^6}{\sqrt{x+x^6} \left(a-x^2+2 a x^5+a x^{10}\right)} \, dx","\frac{\tan ^{-1}\left(\frac{x}{\sqrt[4]{a} \sqrt{x^6+x}}\right)}{\sqrt[4]{a}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt[4]{a} \sqrt{x^6+x}}\right)}{\sqrt[4]{a}}",1,"Integrate[(-x + 4*x^6)/(Sqrt[x + x^6]*(a - x^2 + 2*a*x^5 + a*x^10)), x]","F",-1
618,1,48,48,0.0546776,"\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\sqrt{1+x^2}} \, dx","Integrate[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/Sqrt[1 + x^2],x]","4 \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)\right)","4 \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-4 \tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)",1,"4*(Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - ArcTanh[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]])","A",1
619,0,0,49,1.4816033,"\int \frac{-3 b+2 a x}{\sqrt[4]{-b x+a x^2} \left(b-a x+x^3\right)} \, dx","Integrate[(-3*b + 2*a*x)/((-(b*x) + a*x^2)^(1/4)*(b - a*x + x^3)),x]","\int \frac{-3 b+2 a x}{\sqrt[4]{-b x+a x^2} \left(b-a x+x^3\right)} \, dx","2 \tan ^{-1}\left(\frac{\sqrt[4]{a x^2-b x}}{x}\right)-2 \tanh ^{-1}\left(\frac{\left(a x^2-b x\right)^{3/4}}{a x-b}\right)",1,"Integrate[(-3*b + 2*a*x)/((-(b*x) + a*x^2)^(1/4)*(b - a*x + x^3)), x]","F",-1
620,1,5117,49,6.402655,"\int \frac{\left(-4+x^3\right) \sqrt{2-x^2+x^3}}{\left(2+x^3\right) \left(2+x^2+x^3\right)} \, dx","Integrate[((-4 + x^3)*Sqrt[2 - x^2 + x^3])/((2 + x^3)*(2 + x^2 + x^3)),x]","\text{Result too large to show}","2 \tan ^{-1}\left(\frac{x}{\sqrt{x^3-x^2+2}}\right)-2 \sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^3-x^2+2}}\right)",1,"Result too large to show","C",0
621,1,40,49,0.0056337,"\int x^2 \sqrt[4]{-1+x^4} \, dx","Integrate[x^2*(-1 + x^4)^(1/4),x]","\frac{x^3 \sqrt[4]{x^4-1} \, _2F_1\left(-\frac{1}{4},\frac{3}{4};\frac{7}{4};x^4\right)}{3 \sqrt[4]{1-x^4}}","\frac{1}{8} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-1}}\right)-\frac{1}{8} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-1}}\right)+\frac{1}{4} \sqrt[4]{x^4-1} x^3",1,"(x^3*(-1 + x^4)^(1/4)*Hypergeometric2F1[-1/4, 3/4, 7/4, x^4])/(3*(1 - x^4)^(1/4))","C",1
622,1,22,49,0.00228,"\int x^2 \sqrt[4]{1+x^4} \, dx","Integrate[x^2*(1 + x^4)^(1/4),x]","\frac{1}{3} x^3 \, _2F_1\left(-\frac{1}{4},\frac{3}{4};\frac{7}{4};-x^4\right)","-\frac{1}{8} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)+\frac{1}{8} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)+\frac{1}{4} \sqrt[4]{x^4+1} x^3",1,"(x^3*Hypergeometric2F1[-1/4, 3/4, 7/4, -x^4])/3","C",1
623,1,62,49,0.0308551,"\int \frac{\left(-b+a x^3\right) \sqrt{x+x^4}}{x^3} \, dx","Integrate[((-b + a*x^3)*Sqrt[x + x^4])/x^3,x]","\frac{\sqrt{x^4+x} \left(x^{3/2} (a-2 b) \sinh ^{-1}\left(x^{3/2}\right)+\sqrt{x^3+1} \left(a x^3+2 b\right)\right)}{3 x^2 \sqrt{x^3+1}}","\frac{1}{3} (a-2 b) \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4+x}}\right)+\frac{\sqrt{x^4+x} \left(a x^3+2 b\right)}{3 x^2}",1,"(Sqrt[x + x^4]*(Sqrt[1 + x^3]*(2*b + a*x^3) + (a - 2*b)*x^(3/2)*ArcSinh[x^(3/2)]))/(3*x^2*Sqrt[1 + x^3])","A",1
624,1,162,49,0.809387,"\int \frac{1}{\left(-2+x^4\right) \sqrt[4]{x^2+x^4}} \, dx","Integrate[1/((-2 + x^4)*(x^2 + x^4)^(1/4)),x]","-\frac{\sqrt[4]{\frac{1}{x^2}+1} x \left(-\sqrt[4]{2+\sqrt{2}} \tan ^{-1}\left(\sqrt[4]{2+\sqrt{2}} \sqrt[4]{\frac{1}{x^2}+1}\right)-\sqrt[4]{2-\sqrt{2}} \tan ^{-1}\left(\sqrt[4]{-\left(\left(\sqrt{2}-2\right) \left(\frac{1}{x^2}+1\right)\right)}\right)+\sqrt[4]{2+\sqrt{2}} \tanh ^{-1}\left(\sqrt[4]{2+\sqrt{2}} \sqrt[4]{\frac{1}{x^2}+1}\right)+\sqrt[4]{2-\sqrt{2}} \tanh ^{-1}\left(\sqrt[4]{-\left(\left(\sqrt{2}-2\right) \left(\frac{1}{x^2}+1\right)\right)}\right)\right)}{4 \sqrt[4]{x^4+x^2}}","\frac{1}{8} \text{RootSum}\left[2 \text{$\#$1}^8-4 \text{$\#$1}^4+1\&,\frac{\log \left(\sqrt[4]{x^4+x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]",1,"-1/4*((1 + x^(-2))^(1/4)*x*(-((2 + Sqrt[2])^(1/4)*ArcTan[(2 + Sqrt[2])^(1/4)*(1 + x^(-2))^(1/4)]) - (2 - Sqrt[2])^(1/4)*ArcTan[(-((-2 + Sqrt[2])*(1 + x^(-2))))^(1/4)] + (2 + Sqrt[2])^(1/4)*ArcTanh[(2 + Sqrt[2])^(1/4)*(1 + x^(-2))^(1/4)] + (2 - Sqrt[2])^(1/4)*ArcTanh[(-((-2 + Sqrt[2])*(1 + x^(-2))))^(1/4)]))/(x^2 + x^4)^(1/4)","B",1
625,0,0,49,0.2537959,"\int \frac{-4 b+a x^3}{\sqrt[4]{-b+a x^3} \left(b-a x^3+x^4\right)} \, dx","Integrate[(-4*b + a*x^3)/((-b + a*x^3)^(1/4)*(b - a*x^3 + x^4)),x]","\int \frac{-4 b+a x^3}{\sqrt[4]{-b+a x^3} \left(b-a x^3+x^4\right)} \, dx","2 \tan ^{-1}\left(\frac{\sqrt[4]{a x^3-b}}{x}\right)+2 \tanh ^{-1}\left(\frac{x \left(a x^3-b\right)^{3/4}}{b-a x^3}\right)",1,"Integrate[(-4*b + a*x^3)/((-b + a*x^3)^(1/4)*(b - a*x^3 + x^4)), x]","F",-1
626,0,0,49,0.6424841,"\int \frac{-x+3 x^5}{\left(1+x^4\right) \left(a-x+a x^4\right) \sqrt{x+x^5}} \, dx","Integrate[(-x + 3*x^5)/((1 + x^4)*(a - x + a*x^4)*Sqrt[x + x^5]),x]","\int \frac{-x+3 x^5}{\left(1+x^4\right) \left(a-x+a x^4\right) \sqrt{x+x^5}} \, dx","\frac{2 \sqrt{x^5+x}}{x^4+1}-2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{x^5+x}}{\sqrt{a} \left(x^4+1\right)}\right)",1,"Integrate[(-x + 3*x^5)/((1 + x^4)*(a - x + a*x^4)*Sqrt[x + x^5]), x]","F",-1
627,1,65,49,0.0308625,"\int \frac{\left(-1+x^3\right) \sqrt{-1+x^6}}{x^{10}} \, dx","Integrate[((-1 + x^3)*Sqrt[-1 + x^6])/x^10,x]","-\frac{x^6+\sqrt{1-x^6} x^6 \tanh ^{-1}\left(\sqrt{1-x^6}\right)-1}{6 x^6 \sqrt{x^6-1}}-\frac{\left(x^6-1\right)^{3/2}}{9 x^9}","\frac{\left(-2 x^6-3 x^3+2\right) \sqrt{x^6-1}}{18 x^9}-\frac{1}{3} \tan ^{-1}\left(\frac{x^3+1}{\sqrt{x^6-1}}\right)",1,"-1/9*(-1 + x^6)^(3/2)/x^9 - (-1 + x^6 + x^6*Sqrt[1 - x^6]*ArcTanh[Sqrt[1 - x^6]])/(6*x^6*Sqrt[-1 + x^6])","A",1
628,0,0,49,1.7143829,"\int \frac{1+x^6}{\sqrt[4]{-x^3+x^5} \left(1+x^3-x^6\right)} \, dx","Integrate[(1 + x^6)/((-x^3 + x^5)^(1/4)*(1 + x^3 - x^6)),x]","\int \frac{1+x^6}{\sqrt[4]{-x^3+x^5} \left(1+x^3-x^6\right)} \, dx","-\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^{12}+3 \text{$\#$1}^4-1\&,\frac{\log \left(\sqrt[4]{x^5-x^3}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]",1,"Integrate[(1 + x^6)/((-x^3 + x^5)^(1/4)*(1 + x^3 - x^6)), x]","F",-1
629,0,0,49,0.8146215,"\int \frac{1+x^6}{\sqrt[4]{-x^3+x^5} \left(1+x^3-x^6\right)} \, dx","Integrate[(1 + x^6)/((-x^3 + x^5)^(1/4)*(1 + x^3 - x^6)),x]","\int \frac{1+x^6}{\sqrt[4]{-x^3+x^5} \left(1+x^3-x^6\right)} \, dx","-\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^{12}+3 \text{$\#$1}^4-1\&,\frac{\log \left(\sqrt[4]{x^5-x^3}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]",1,"Integrate[(1 + x^6)/((-x^3 + x^5)^(1/4)*(1 + x^3 - x^6)), x]","F",-1
630,1,57707,49,17.6778887,"\int \frac{x (6 b+5 a x)}{\sqrt[4]{b x^2+a x^3} \left(-b-a x+x^6\right)} \, dx","Integrate[(x*(6*b + 5*a*x))/((b*x^2 + a*x^3)^(1/4)*(-b - a*x + x^6)),x]","\text{Result too large to show}","2 \tan ^{-1}\left(\frac{\sqrt[4]{a x^3+b x^2}}{x^2}\right)-2 \tanh ^{-1}\left(\frac{\left(a x^3+b x^2\right)^{3/4}}{a x+b}\right)",1,"Result too large to show","C",0
631,0,0,49,0.1699677,"\int \frac{\sqrt{-1+x^5} \left(2+3 x^5\right)}{1-a x^4-2 x^5+x^{10}} \, dx","Integrate[(Sqrt[-1 + x^5]*(2 + 3*x^5))/(1 - a*x^4 - 2*x^5 + x^10),x]","\int \frac{\sqrt{-1+x^5} \left(2+3 x^5\right)}{1-a x^4-2 x^5+x^{10}} \, dx","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt{x^5-1}}\right)}{\sqrt[4]{a}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt{x^5-1}}\right)}{\sqrt[4]{a}}",1,"Integrate[(Sqrt[-1 + x^5]*(2 + 3*x^5))/(1 - a*x^4 - 2*x^5 + x^10), x]","F",-1
632,0,0,49,0.1688241,"\int \frac{\sqrt{-1+x^5} \left(2+3 x^5\right)}{a-x^4-2 a x^5+a x^{10}} \, dx","Integrate[(Sqrt[-1 + x^5]*(2 + 3*x^5))/(a - x^4 - 2*a*x^5 + a*x^10),x]","\int \frac{\sqrt{-1+x^5} \left(2+3 x^5\right)}{a-x^4-2 a x^5+a x^{10}} \, dx","-\frac{\tan ^{-1}\left(\frac{x}{\sqrt[4]{a} \sqrt{x^5-1}}\right)}{a^{3/4}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt[4]{a} \sqrt{x^5-1}}\right)}{a^{3/4}}",1,"Integrate[(Sqrt[-1 + x^5]*(2 + 3*x^5))/(a - x^4 - 2*a*x^5 + a*x^10), x]","F",-1
633,0,0,49,0.1779662,"\int \frac{\sqrt{1+x^5} \left(-2+3 x^5\right)}{a-x^4+2 a x^5+a x^{10}} \, dx","Integrate[(Sqrt[1 + x^5]*(-2 + 3*x^5))/(a - x^4 + 2*a*x^5 + a*x^10),x]","\int \frac{\sqrt{1+x^5} \left(-2+3 x^5\right)}{a-x^4+2 a x^5+a x^{10}} \, dx","-\frac{\tan ^{-1}\left(\frac{x}{\sqrt[4]{a} \sqrt{x^5+1}}\right)}{a^{3/4}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt[4]{a} \sqrt{x^5+1}}\right)}{a^{3/4}}",1,"Integrate[(Sqrt[1 + x^5]*(-2 + 3*x^5))/(a - x^4 + 2*a*x^5 + a*x^10), x]","F",-1
634,1,106,49,0.2241768,"\int \frac{1}{\sqrt{1+\sqrt{1+x^2}}} \, dx","Integrate[1/Sqrt[1 + Sqrt[1 + x^2]],x]","\frac{\sqrt{\sqrt{x^2+1}+1} \left(-2 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{1}{2}-\frac{\sqrt{x^2+1}}{2}\right)+4 \sqrt{x^2+1}-\sqrt{2} \sqrt{\sqrt{x^2+1}-1} \tan ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}-1}}{\sqrt{2}}\right)-2\right)}{2 x}","\frac{2 x}{\sqrt{\sqrt{x^2+1}+1}}-\sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2} \sqrt{\sqrt{x^2+1}+1}}\right)",1,"(Sqrt[1 + Sqrt[1 + x^2]]*(-2 + 4*Sqrt[1 + x^2] - Sqrt[2]*Sqrt[-1 + Sqrt[1 + x^2]]*ArcTan[Sqrt[-1 + Sqrt[1 + x^2]]/Sqrt[2]] - 2*Hypergeometric2F1[-1/2, 1, 1/2, 1/2 - Sqrt[1 + x^2]/2]))/(2*x)","C",1
635,1,58,50,0.0365587,"\int x^6 \sqrt{-x+x^4} \, dx","Integrate[x^6*Sqrt[-x + x^4],x]","\frac{\sqrt{x \left(x^3-1\right)} \left(\frac{3 \sin ^{-1}\left(x^{3/2}\right)}{\sqrt{1-x^3}}+\left(8 x^6-2 x^3-3\right) x^{3/2}\right)}{72 \sqrt{x}}","\frac{1}{72} \sqrt{x^4-x} \left(8 x^7-2 x^4-3 x\right)-\frac{1}{24} \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4-x}}\right)",1,"(Sqrt[x*(-1 + x^3)]*(x^(3/2)*(-3 - 2*x^3 + 8*x^6) + (3*ArcSin[x^(3/2)])/Sqrt[1 - x^3]))/(72*Sqrt[x])","A",1
636,1,38,50,0.0187063,"\int \frac{\left(-1+x^2\right) \sqrt[4]{-x^3+x^4}}{x^8} \, dx","Integrate[((-1 + x^2)*(-x^3 + x^4)^(1/4))/x^8,x]","\frac{4 \left((x-1) x^3\right)^{9/4} \left(5248 x^4+11808 x^3+19188 x^2+27183 x+13923\right)}{348075 x^{13}}","\frac{4 \sqrt[4]{x^4-x^3} \left(5248 x^6+1312 x^5+820 x^4+615 x^3-21255 x^2-663 x+13923\right)}{348075 x^7}",1,"(4*((-1 + x)*x^3)^(9/4)*(13923 + 27183*x + 19188*x^2 + 11808*x^3 + 5248*x^4))/(348075*x^13)","A",1
637,1,55,50,0.1549017,"\int \frac{\left(-1+x^3\right) \sqrt{-1+x^6}}{x \left(1+x^3\right)} \, dx","Integrate[((-1 + x^3)*Sqrt[-1 + x^6])/(x*(1 + x^3)),x]","\frac{1}{3} \left(\tan ^{-1}\left(\sqrt{x^6-1}\right)+\frac{x^6-2 \sqrt{x^6-1} \log \left(\sqrt{x^6-1}+x^3\right)-1}{\sqrt{x^6-1}}\right)","\frac{\sqrt{x^6-1}}{3}-\frac{2}{3} \log \left(\sqrt{x^6-1}+x^3\right)+\frac{2}{3} \tan ^{-1}\left(\sqrt{x^6-1}+x^3\right)",1,"(ArcTan[Sqrt[-1 + x^6]] + (-1 + x^6 - 2*Sqrt[-1 + x^6]*Log[x^3 + Sqrt[-1 + x^6]])/Sqrt[-1 + x^6])/3","A",1
638,1,55,50,0.13188,"\int \frac{\left(1+x^3\right) \sqrt{-1+x^6}}{x \left(-1+x^3\right)} \, dx","Integrate[((1 + x^3)*Sqrt[-1 + x^6])/(x*(-1 + x^3)),x]","\frac{1}{3} \left(\tan ^{-1}\left(\sqrt{x^6-1}\right)+\frac{x^6+2 \sqrt{x^6-1} \log \left(\sqrt{x^6-1}+x^3\right)-1}{\sqrt{x^6-1}}\right)","\frac{\sqrt{x^6-1}}{3}+\frac{2}{3} \log \left(\sqrt{x^6-1}+x^3\right)+\frac{2}{3} \tan ^{-1}\left(\sqrt{x^6-1}+x^3\right)",1,"(ArcTan[Sqrt[-1 + x^6]] + (-1 + x^6 + 2*Sqrt[-1 + x^6]*Log[x^3 + Sqrt[-1 + x^6]])/Sqrt[-1 + x^6])/3","A",1
639,1,393,50,0.647262,"\int \frac{2 b+a x^4}{\sqrt[4]{b+a x^4} \left(-2 b-2 a x^4+x^8\right)} \, dx","Integrate[(2*b + a*x^4)/((b + a*x^4)^(1/4)*(-2*b - 2*a*x^4 + x^8)),x]","\frac{1}{4} \left(-\frac{\sqrt[4]{a-\sqrt{a^2+2 b}} \tan ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+2 b}+a^2+b}}{\sqrt[4]{a-\sqrt{a^2+2 b}} \sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{-a \sqrt{a^2+2 b}+a^2+b}}-\frac{\sqrt[4]{\sqrt{a^2+2 b}+a} \tan ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+2 b}+a^2+b}}{\sqrt[4]{\sqrt{a^2+2 b}+a} \sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{a \sqrt{a^2+2 b}+a^2+b}}-\frac{\sqrt[4]{a-\sqrt{a^2+2 b}} \tanh ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+2 b}+a^2+b}}{\sqrt[4]{a-\sqrt{a^2+2 b}} \sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{-a \sqrt{a^2+2 b}+a^2+b}}-\frac{\sqrt[4]{\sqrt{a^2+2 b}+a} \tanh ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+2 b}+a^2+b}}{\sqrt[4]{\sqrt{a^2+2 b}+a} \sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{a \sqrt{a^2+2 b}+a^2+b}}\right)","\frac{1}{8} \text{RootSum}\left[-2 \text{$\#$1}^8+2 \text{$\#$1}^4 a+b\&,\frac{\log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]",1,"(-(((a - Sqrt[a^2 + 2*b])^(1/4)*ArcTan[((a^2 + b - a*Sqrt[a^2 + 2*b])^(1/4)*x)/((a - Sqrt[a^2 + 2*b])^(1/4)*(b + a*x^4)^(1/4))])/(a^2 + b - a*Sqrt[a^2 + 2*b])^(1/4)) - ((a + Sqrt[a^2 + 2*b])^(1/4)*ArcTan[((a^2 + b + a*Sqrt[a^2 + 2*b])^(1/4)*x)/((a + Sqrt[a^2 + 2*b])^(1/4)*(b + a*x^4)^(1/4))])/(a^2 + b + a*Sqrt[a^2 + 2*b])^(1/4) - ((a - Sqrt[a^2 + 2*b])^(1/4)*ArcTanh[((a^2 + b - a*Sqrt[a^2 + 2*b])^(1/4)*x)/((a - Sqrt[a^2 + 2*b])^(1/4)*(b + a*x^4)^(1/4))])/(a^2 + b - a*Sqrt[a^2 + 2*b])^(1/4) - ((a + Sqrt[a^2 + 2*b])^(1/4)*ArcTanh[((a^2 + b + a*Sqrt[a^2 + 2*b])^(1/4)*x)/((a + Sqrt[a^2 + 2*b])^(1/4)*(b + a*x^4)^(1/4))])/(a^2 + b + a*Sqrt[a^2 + 2*b])^(1/4))/4","B",1
640,1,393,50,0.1120255,"\int \frac{2 b+a x^4}{\sqrt[4]{b+a x^4} \left(-2 b-2 a x^4+x^8\right)} \, dx","Integrate[(2*b + a*x^4)/((b + a*x^4)^(1/4)*(-2*b - 2*a*x^4 + x^8)),x]","\frac{1}{4} \left(-\frac{\sqrt[4]{a-\sqrt{a^2+2 b}} \tan ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+2 b}+a^2+b}}{\sqrt[4]{a-\sqrt{a^2+2 b}} \sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{-a \sqrt{a^2+2 b}+a^2+b}}-\frac{\sqrt[4]{\sqrt{a^2+2 b}+a} \tan ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+2 b}+a^2+b}}{\sqrt[4]{\sqrt{a^2+2 b}+a} \sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{a \sqrt{a^2+2 b}+a^2+b}}-\frac{\sqrt[4]{a-\sqrt{a^2+2 b}} \tanh ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+2 b}+a^2+b}}{\sqrt[4]{a-\sqrt{a^2+2 b}} \sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{-a \sqrt{a^2+2 b}+a^2+b}}-\frac{\sqrt[4]{\sqrt{a^2+2 b}+a} \tanh ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+2 b}+a^2+b}}{\sqrt[4]{\sqrt{a^2+2 b}+a} \sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{a \sqrt{a^2+2 b}+a^2+b}}\right)","\frac{1}{8} \text{RootSum}\left[-2 \text{$\#$1}^8+2 \text{$\#$1}^4 a+b\&,\frac{\log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]",1,"(-(((a - Sqrt[a^2 + 2*b])^(1/4)*ArcTan[((a^2 + b - a*Sqrt[a^2 + 2*b])^(1/4)*x)/((a - Sqrt[a^2 + 2*b])^(1/4)*(b + a*x^4)^(1/4))])/(a^2 + b - a*Sqrt[a^2 + 2*b])^(1/4)) - ((a + Sqrt[a^2 + 2*b])^(1/4)*ArcTan[((a^2 + b + a*Sqrt[a^2 + 2*b])^(1/4)*x)/((a + Sqrt[a^2 + 2*b])^(1/4)*(b + a*x^4)^(1/4))])/(a^2 + b + a*Sqrt[a^2 + 2*b])^(1/4) - ((a - Sqrt[a^2 + 2*b])^(1/4)*ArcTanh[((a^2 + b - a*Sqrt[a^2 + 2*b])^(1/4)*x)/((a - Sqrt[a^2 + 2*b])^(1/4)*(b + a*x^4)^(1/4))])/(a^2 + b - a*Sqrt[a^2 + 2*b])^(1/4) - ((a + Sqrt[a^2 + 2*b])^(1/4)*ArcTanh[((a^2 + b + a*Sqrt[a^2 + 2*b])^(1/4)*x)/((a + Sqrt[a^2 + 2*b])^(1/4)*(b + a*x^4)^(1/4))])/(a^2 + b + a*Sqrt[a^2 + 2*b])^(1/4))/4","B",1
641,0,0,50,3.7533376,"\int \frac{\left(-1+x^6\right) \left(1+x^6\right)}{\sqrt[4]{x-x^4+x^7} \left(1+3 x^6+x^{12}\right)} \, dx","Integrate[((-1 + x^6)*(1 + x^6))/((x - x^4 + x^7)^(1/4)*(1 + 3*x^6 + x^12)),x]","\int \frac{\left(-1+x^6\right) \left(1+x^6\right)}{\sqrt[4]{x-x^4+x^7} \left(1+3 x^6+x^{12}\right)} \, dx","\frac{1}{6} \text{RootSum}\left[\text{$\#$1}^8+2 \text{$\#$1}^4+2\&,\frac{\log \left(\sqrt[4]{x^7-x^4+x}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]",1,"Integrate[((-1 + x^6)*(1 + x^6))/((x - x^4 + x^7)^(1/4)*(1 + 3*x^6 + x^12)), x]","F",-1
642,1,44,50,0.0550826,"\int \sqrt{1+\sqrt{1+x^2}} \, dx","Integrate[Sqrt[1 + Sqrt[1 + x^2]],x]","\frac{2 \left(\sqrt{x^2+1}-1\right) \sqrt{\sqrt{x^2+1}+1} \left(\sqrt{x^2+1}+2\right)}{3 x}","\frac{2 \sqrt{x^2+1} x}{3 \sqrt{\sqrt{x^2+1}+1}}+\frac{4 x}{3 \sqrt{\sqrt{x^2+1}+1}}",1,"(2*(-1 + Sqrt[1 + x^2])*Sqrt[1 + Sqrt[1 + x^2]]*(2 + Sqrt[1 + x^2]))/(3*x)","A",1
643,1,78,50,0.1183123,"\int \frac{\sqrt{1+\sqrt{1+x^2}}}{x^2} \, dx","Integrate[Sqrt[1 + Sqrt[1 + x^2]]/x^2,x]","\frac{\left(\sqrt{x^2+1}-1\right) \left(\sqrt{x^2+1}+1\right)^{3/2} \left(\sqrt{2} \sqrt{\sqrt{x^2+1}-1} \tan ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}-1}}{\sqrt{2}}\right)-2\right)}{2 x^3}","\frac{\tan ^{-1}\left(\frac{x}{\sqrt{2} \sqrt{\sqrt{x^2+1}+1}}\right)}{\sqrt{2}}-\frac{\sqrt{\sqrt{x^2+1}+1}}{x}",1,"((-1 + Sqrt[1 + x^2])*(1 + Sqrt[1 + x^2])^(3/2)*(-2 + Sqrt[2]*Sqrt[-1 + Sqrt[1 + x^2]]*ArcTan[Sqrt[-1 + Sqrt[1 + x^2]]/Sqrt[2]]))/(2*x^3)","A",1
644,1,44,51,0.0118902,"\int \frac{1}{x \left(b+a x^2\right)^{3/4}} \, dx","Integrate[1/(x*(b + a*x^2)^(3/4)),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a x^2+b}}{\sqrt[4]{b}}\right)+\tanh ^{-1}\left(\frac{\sqrt[4]{a x^2+b}}{\sqrt[4]{b}}\right)}{b^{3/4}}","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a x^2+b}}{\sqrt[4]{b}}\right)}{b^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a x^2+b}}{\sqrt[4]{b}}\right)}{b^{3/4}}",1,"-((ArcTan[(b + a*x^2)^(1/4)/b^(1/4)] + ArcTanh[(b + a*x^2)^(1/4)/b^(1/4)])/b^(3/4))","A",1
645,1,131,51,0.2423446,"\int \frac{-7+x}{(-11+5 x) \sqrt{-60+83 x-21 x^2-3 x^3+x^4}} \, dx","Integrate[(-7 + x)/((-11 + 5*x)*Sqrt[-60 + 83*x - 21*x^2 - 3*x^3 + x^4]),x]","-\frac{\sqrt{\frac{x-4}{x-1}} \sqrt{\frac{x-3}{x-1}} (x-1)^2 \sqrt{\frac{x+5}{x-1}} \left(3 F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{x+5}{x-1}}}{\sqrt{3}}\right)|\frac{3}{4}\right)-2 \Pi \left(\frac{1}{2};\sin ^{-1}\left(\frac{\sqrt{\frac{x+5}{x-1}}}{\sqrt{3}}\right)|\frac{3}{4}\right)\right)}{3 \sqrt{6} \sqrt{x^4-3 x^3-21 x^2+83 x-60}}","-\frac{\tanh ^{-1}\left(\frac{6 \sqrt{6} \sqrt{x^4-3 x^3-21 x^2+83 x-60}}{29 x^2-106 x+41}\right)}{3 \sqrt{6}}",1,"-1/3*(Sqrt[(-4 + x)/(-1 + x)]*Sqrt[(-3 + x)/(-1 + x)]*(-1 + x)^2*Sqrt[(5 + x)/(-1 + x)]*(3*EllipticF[ArcSin[Sqrt[(5 + x)/(-1 + x)]/Sqrt[3]], 3/4] - 2*EllipticPi[1/2, ArcSin[Sqrt[(5 + x)/(-1 + x)]/Sqrt[3]], 3/4]))/(Sqrt[6]*Sqrt[-60 + 83*x - 21*x^2 - 3*x^3 + x^4])","C",1
646,1,47,51,0.0478147,"\int \frac{\left(-2+x^6\right) \sqrt{-1+x^6}}{x \left(2+x^6\right)} \, dx","Integrate[((-2 + x^6)*Sqrt[-1 + x^6])/(x*(2 + x^6)),x]","\frac{1}{3} \left(\sqrt{x^6-1}+\tan ^{-1}\left(\sqrt{x^6-1}\right)-2 \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{x^6-1}}{\sqrt{3}}\right)\right)","\frac{\sqrt{x^6-1}}{3}+\frac{1}{3} \tan ^{-1}\left(\sqrt{x^6-1}\right)-\frac{2 \tan ^{-1}\left(\frac{\sqrt{x^6-1}}{\sqrt{3}}\right)}{\sqrt{3}}",1,"(Sqrt[-1 + x^6] + ArcTan[Sqrt[-1 + x^6]] - 2*Sqrt[3]*ArcTan[Sqrt[-1 + x^6]/Sqrt[3]])/3","A",1
647,0,0,51,0.4372238,"\int \frac{\sqrt{-1-x^2+x^6} \left(1+2 x^6\right)}{\left(-1+x^6\right) \left(-2+x^2+2 x^6\right)} \, dx","Integrate[(Sqrt[-1 - x^2 + x^6]*(1 + 2*x^6))/((-1 + x^6)*(-2 + x^2 + 2*x^6)),x]","\int \frac{\sqrt{-1-x^2+x^6} \left(1+2 x^6\right)}{\left(-1+x^6\right) \left(-2+x^2+2 x^6\right)} \, dx","\tan ^{-1}\left(\frac{x}{\sqrt{x^6-x^2-1}}\right)-\sqrt{\frac{3}{2}} \tan ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt{x^6-x^2-1}}\right)",1,"Integrate[(Sqrt[-1 - x^2 + x^6]*(1 + 2*x^6))/((-1 + x^6)*(-2 + x^2 + 2*x^6)), x]","F",-1
648,0,0,51,0.2509499,"\int \frac{x \left(-8 b+5 a x^3\right)}{\sqrt[4]{-b+a x^3} \left(b-a x^3+x^8\right)} \, dx","Integrate[(x*(-8*b + 5*a*x^3))/((-b + a*x^3)^(1/4)*(b - a*x^3 + x^8)),x]","\int \frac{x \left(-8 b+5 a x^3\right)}{\sqrt[4]{-b+a x^3} \left(b-a x^3+x^8\right)} \, dx","2 \tan ^{-1}\left(\frac{\sqrt[4]{a x^3-b}}{x^2}\right)+2 \tanh ^{-1}\left(\frac{x^2 \left(a x^3-b\right)^{3/4}}{b-a x^3}\right)",1,"Integrate[(x*(-8*b + 5*a*x^3))/((-b + a*x^3)^(1/4)*(b - a*x^3 + x^8)), x]","F",-1
649,0,0,51,2.0794217,"\int \frac{2+16 x-x^2-9 x^3}{\sqrt[4]{\frac{1+x}{-2+x^2}} \left(-2+x^2\right) \left(-3+2 x+7 x^2-7 x^3-9 x^4+9 x^5+5 x^6-5 x^7-x^8+x^9\right)} \, dx","Integrate[(2 + 16*x - x^2 - 9*x^3)/(((1 + x)/(-2 + x^2))^(1/4)*(-2 + x^2)*(-3 + 2*x + 7*x^2 - 7*x^3 - 9*x^4 + 9*x^5 + 5*x^6 - 5*x^7 - x^8 + x^9)),x]","\int \frac{2+16 x-x^2-9 x^3}{\sqrt[4]{\frac{1+x}{-2+x^2}} \left(-2+x^2\right) \left(-3+2 x+7 x^2-7 x^3-9 x^4+9 x^5+5 x^6-5 x^7-x^8+x^9\right)} \, dx","2 \tanh ^{-1}\left(\frac{x^2-1}{\sqrt[4]{\frac{x+1}{x^2-2}}}\right)-2 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{x+1}{x^2-2}}}{x^2-1}\right)",1,"Integrate[(2 + 16*x - x^2 - 9*x^3)/(((1 + x)/(-2 + x^2))^(1/4)*(-2 + x^2)*(-3 + 2*x + 7*x^2 - 7*x^3 - 9*x^4 + 9*x^5 + 5*x^6 - 5*x^7 - x^8 + x^9)), x]","F",-1
650,0,0,51,0.5039687,"\int \frac{-1+7 x^8}{\left(1+x^8\right) \sqrt{3-x+x^2+6 x^8-x^9+3 x^{16}}} \, dx","Integrate[(-1 + 7*x^8)/((1 + x^8)*Sqrt[3 - x + x^2 + 6*x^8 - x^9 + 3*x^16]),x]","\int \frac{-1+7 x^8}{\left(1+x^8\right) \sqrt{3-x+x^2+6 x^8-x^9+3 x^{16}}} \, dx","2 \tanh ^{-1}\left(\frac{x}{\sqrt{3} x^8-\sqrt{3 x^{16}-x^9+6 x^8+x^2-x+3}+\sqrt{3}}\right)",1,"Integrate[(-1 + 7*x^8)/((1 + x^8)*Sqrt[3 - x + x^2 + 6*x^8 - x^9 + 3*x^16]), x]","F",-1
651,1,45,51,0.1126209,"\int \frac{\sqrt{1+\sqrt{1+x^2}}}{x^2 \sqrt{1+x^2}} \, dx","Integrate[Sqrt[1 + Sqrt[1 + x^2]]/(x^2*Sqrt[1 + x^2]),x]","-\frac{\sqrt{\sqrt{x^2+1}+1} \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{1}{2}-\frac{\sqrt{x^2+1}}{2}\right)}{x}","-\frac{\sqrt{\sqrt{x^2+1}+1}}{x}-\frac{\tan ^{-1}\left(\frac{x}{\sqrt{2} \sqrt{\sqrt{x^2+1}+1}}\right)}{\sqrt{2}}",1,"-((Sqrt[1 + Sqrt[1 + x^2]]*Hypergeometric2F1[-1/2, 1, 1/2, 1/2 - Sqrt[1 + x^2]/2])/x)","C",1
652,1,48,51,0.0792041,"\int \frac{x}{x+\sqrt{1+\sqrt{1+x}}} \, dx","Integrate[x/(x + Sqrt[1 + Sqrt[1 + x]]),x]","x-4 \sqrt{\sqrt{x+1}+1}+\frac{8 \tanh ^{-1}\left(\frac{2 \sqrt{\sqrt{x+1}+1}+1}{\sqrt{5}}\right)}{\sqrt{5}}","x-4 \sqrt{\sqrt{x+1}+1}+\frac{8 \tanh ^{-1}\left(\frac{2 \sqrt{\sqrt{x+1}+1}}{\sqrt{5}}+\frac{1}{\sqrt{5}}\right)}{\sqrt{5}}",1,"x - 4*Sqrt[1 + Sqrt[1 + x]] + (8*ArcTanh[(1 + 2*Sqrt[1 + Sqrt[1 + x]])/Sqrt[5]])/Sqrt[5]","A",1
653,1,45,52,0.2782968,"\int \frac{a+2 x}{\sqrt[4]{b+a x+x^2} \left(-1+2 b+2 a x+2 x^2\right)} \, dx","Integrate[(a + 2*x)/((b + a*x + x^2)^(1/4)*(-1 + 2*b + 2*a*x + 2*x^2)),x]","\sqrt[4]{2} \left(\tan ^{-1}\left(\sqrt[4]{2} \sqrt[4]{x (a+x)+b}\right)-\tanh ^{-1}\left(\sqrt[4]{2} \sqrt[4]{x (a+x)+b}\right)\right)","\sqrt[4]{2} \tan ^{-1}\left(\sqrt[4]{2} \sqrt[4]{a x+b+x^2}\right)-\sqrt[4]{2} \tanh ^{-1}\left(\sqrt[4]{2} \sqrt[4]{a x+b+x^2}\right)",1,"2^(1/4)*(ArcTan[2^(1/4)*(b + x*(a + x))^(1/4)] - ArcTanh[2^(1/4)*(b + x*(a + x))^(1/4)])","A",1
654,1,26,52,0.0050608,"\int \frac{1}{x^7 \sqrt[4]{1+x^3}} \, dx","Integrate[1/(x^7*(1 + x^3)^(1/4)),x]","-\frac{4}{9} \left(x^3+1\right)^{3/4} \, _2F_1\left(\frac{3}{4},3;\frac{7}{4};x^3+1\right)","\frac{5}{48} \tan ^{-1}\left(\sqrt[4]{x^3+1}\right)-\frac{5}{48} \tanh ^{-1}\left(\sqrt[4]{x^3+1}\right)+\frac{\left(x^3+1\right)^{3/4} \left(5 x^3-4\right)}{24 x^6}",1,"(-4*(1 + x^3)^(3/4)*Hypergeometric2F1[3/4, 3, 7/4, 1 + x^3])/9","C",1
655,1,26,52,0.0051796,"\int \frac{\sqrt[4]{1+x^3}}{x^7} \, dx","Integrate[(1 + x^3)^(1/4)/x^7,x]","-\frac{4}{15} \left(x^3+1\right)^{5/4} \, _2F_1\left(\frac{5}{4},3;\frac{9}{4};x^3+1\right)","\frac{1}{16} \tan ^{-1}\left(\sqrt[4]{x^3+1}\right)+\frac{1}{16} \tanh ^{-1}\left(\sqrt[4]{x^3+1}\right)+\frac{\sqrt[4]{x^3+1} \left(-x^3-4\right)}{24 x^6}",1,"(-4*(1 + x^3)^(5/4)*Hypergeometric2F1[5/4, 3, 9/4, 1 + x^3])/15","C",1
656,1,51,52,0.0294306,"\int \frac{\sqrt{b+a x^3} \left(2 b+a x^3\right)}{x} \, dx","Integrate[(Sqrt[b + a*x^3]*(2*b + a*x^3))/x,x]","\frac{2}{9} \left(\sqrt{a x^3+b} \left(a x^3+7 b\right)-6 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a x^3+b}}{\sqrt{b}}\right)\right)","\frac{2}{9} \sqrt{a x^3+b} \left(a x^3+7 b\right)-\frac{4}{3} b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a x^3+b}}{\sqrt{b}}\right)",1,"(2*(Sqrt[b + a*x^3]*(7*b + a*x^3) - 6*b^(3/2)*ArcTanh[Sqrt[b + a*x^3]/Sqrt[b]]))/9","A",1
657,1,47,52,0.1415552,"\int \frac{\left(1+x^3\right) \sqrt{-1+x^6}}{x^{13} \left(-1+x^3\right)} \, dx","Integrate[((1 + x^3)*Sqrt[-1 + x^6])/(x^13*(-1 + x^3)),x]","\frac{1}{72} \left(21 \tan ^{-1}\left(\sqrt{x^6-1}\right)+\frac{\sqrt{x^6-1} \left(32 x^9+21 x^6+16 x^3+6\right)}{x^{12}}\right)","\frac{7}{12} \tan ^{-1}\left(\sqrt{x^6-1}+x^3\right)+\frac{\sqrt{x^6-1} \left(32 x^9+21 x^6+16 x^3+6\right)}{72 x^{12}}",1,"((Sqrt[-1 + x^6]*(6 + 16*x^3 + 21*x^6 + 32*x^9))/x^12 + 21*ArcTan[Sqrt[-1 + x^6]])/72","A",1
658,1,65,52,0.0689016,"\int \frac{\sqrt{x+x^4} \left(-b+a x^6\right)}{x^6} \, dx","Integrate[(Sqrt[x + x^4]*(-b + a*x^6))/x^6,x]","\frac{\sqrt{x^4+x} \left(\sqrt{x^3+1} \left(3 a x^6+2 b \left(x^3+1\right)\right)+3 a x^{9/2} \sinh ^{-1}\left(x^{3/2}\right)\right)}{9 x^5 \sqrt{x^3+1}}","\frac{\sqrt{x^4+x} \left(3 a x^6+2 b x^3+2 b\right)}{9 x^5}+\frac{1}{3} a \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4+x}}\right)",1,"(Sqrt[x + x^4]*(Sqrt[1 + x^3]*(3*a*x^6 + 2*b*(1 + x^3)) + 3*a*x^(9/2)*ArcSinh[x^(3/2)]))/(9*x^5*Sqrt[1 + x^3])","A",1
659,0,0,52,0.3021632,"\int \frac{-7 b x+5 a x^3}{\sqrt[4]{-b x+a x^3} \left(b-a x^2+x^7\right)} \, dx","Integrate[(-7*b*x + 5*a*x^3)/((-(b*x) + a*x^3)^(1/4)*(b - a*x^2 + x^7)),x]","\int \frac{-7 b x+5 a x^3}{\sqrt[4]{-b x+a x^3} \left(b-a x^2+x^7\right)} \, dx","2 \tan ^{-1}\left(\frac{\sqrt[4]{a x^3-b x}}{x^2}\right)-2 \tanh ^{-1}\left(\frac{x \left(a x^3-b x\right)^{3/4}}{a x^2-b}\right)",1,"Integrate[(-7*b*x + 5*a*x^3)/((-(b*x) + a*x^3)^(1/4)*(b - a*x^2 + x^7)), x]","F",-1
660,0,0,52,0.5036047,"\int \frac{x+3 x^5}{\sqrt{-x+x^5} \left(1-a x^2-2 x^4+x^8\right)} \, dx","Integrate[(x + 3*x^5)/(Sqrt[-x + x^5]*(1 - a*x^2 - 2*x^4 + x^8)),x]","\int \frac{x+3 x^5}{\sqrt{-x+x^5} \left(1-a x^2-2 x^4+x^8\right)} \, dx","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt{x^5-x}}\right)}{a^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt{x^5-x}}\right)}{a^{3/4}}",1,"Integrate[(x + 3*x^5)/(Sqrt[-x + x^5]*(1 - a*x^2 - 2*x^4 + x^8)), x]","F",-1
661,0,0,52,0.5062325,"\int \frac{x+3 x^5}{\sqrt{-x+x^5} \left(a-x^2-2 a x^4+a x^8\right)} \, dx","Integrate[(x + 3*x^5)/(Sqrt[-x + x^5]*(a - x^2 - 2*a*x^4 + a*x^8)),x]","\int \frac{x+3 x^5}{\sqrt{-x+x^5} \left(a-x^2-2 a x^4+a x^8\right)} \, dx","\frac{\tan ^{-1}\left(\frac{x}{\sqrt[4]{a} \sqrt{x^5-x}}\right)}{\sqrt[4]{a}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt[4]{a} \sqrt{x^5-x}}\right)}{\sqrt[4]{a}}",1,"Integrate[(x + 3*x^5)/(Sqrt[-x + x^5]*(a - x^2 - 2*a*x^4 + a*x^8)), x]","F",-1
662,0,0,52,0.4934108,"\int \frac{x+4 x^6}{\sqrt{-x+x^6} \left(1-a x^2-2 x^5+x^{10}\right)} \, dx","Integrate[(x + 4*x^6)/(Sqrt[-x + x^6]*(1 - a*x^2 - 2*x^5 + x^10)),x]","\int \frac{x+4 x^6}{\sqrt{-x+x^6} \left(1-a x^2-2 x^5+x^{10}\right)} \, dx","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt{x^6-x}}\right)}{a^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt{x^6-x}}\right)}{a^{3/4}}",1,"Integrate[(x + 4*x^6)/(Sqrt[-x + x^6]*(1 - a*x^2 - 2*x^5 + x^10)), x]","F",-1
663,0,0,52,0.4954875,"\int \frac{x+4 x^6}{\sqrt{-x+x^6} \left(a-x^2-2 a x^5+a x^{10}\right)} \, dx","Integrate[(x + 4*x^6)/(Sqrt[-x + x^6]*(a - x^2 - 2*a*x^5 + a*x^10)),x]","\int \frac{x+4 x^6}{\sqrt{-x+x^6} \left(a-x^2-2 a x^5+a x^{10}\right)} \, dx","\frac{\tan ^{-1}\left(\frac{x}{\sqrt[4]{a} \sqrt{x^6-x}}\right)}{\sqrt[4]{a}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt[4]{a} \sqrt{x^6-x}}\right)}{\sqrt[4]{a}}",1,"Integrate[(x + 4*x^6)/(Sqrt[-x + x^6]*(a - x^2 - 2*a*x^5 + a*x^10)), x]","F",-1
664,1,59,53,0.0235201,"\int \frac{1}{(-5+2 x)^2 \sqrt[4]{4-4 x+x^2}} \, dx","Integrate[1/((-5 + 2*x)^2*(4 - 4*x + x^2)^(1/4)),x]","\frac{x-2}{(1-2 (x-2)) \sqrt[4]{(x-2)^2}}+\frac{\sqrt{x-2} \tanh ^{-1}\left(\sqrt{2} \sqrt{x-2}\right)}{\sqrt{2} \sqrt[4]{(x-2)^2}}","\frac{\left((x-2)^2\right)^{3/4} \left(\frac{\sqrt{x-2}}{5-2 x}+\frac{\tanh ^{-1}\left(\sqrt{2} \sqrt{x-2}\right)}{\sqrt{2}}\right)}{(x-2)^{3/2}}",1,"(-2 + x)/((1 - 2*(-2 + x))*((-2 + x)^2)^(1/4)) + (Sqrt[-2 + x]*ArcTanh[Sqrt[2]*Sqrt[-2 + x]])/(Sqrt[2]*((-2 + x)^2)^(1/4))","A",1
665,1,1719,53,6.1512737,"\int \frac{\left(-2+x^3\right) \sqrt{1+x^3} \left(2-x^2+2 x^3\right)}{x^4 \left(1-3 x^2+x^3\right)} \, dx","Integrate[((-2 + x^3)*Sqrt[1 + x^3]*(2 - x^2 + 2*x^3))/(x^4*(1 - 3*x^2 + x^3)),x]","\sqrt{x^3+1} \left(\frac{4}{3}+\frac{10}{x}+\frac{4}{3 x^3}\right)+15 \left(\frac{2 \sqrt{\frac{x+1}{1+\sqrt[3]{-1}}} \left(x-\sqrt[3]{-1}\right) \sqrt{\frac{x+(-1)^{2/3}}{\sqrt[3]{-1}+(-1)^{2/3}}} F\left(\sin ^{-1}\left(\sqrt{-\frac{(-1)^{2/3} \left(\sqrt[3]{-1}-x\right)}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{\sqrt{\frac{x-\sqrt[3]{-1}}{-\sqrt[3]{-1}-(-1)^{2/3}}} \sqrt{x^3+1}}-\frac{4 \left(\sqrt[3]{-1}+(-1)^{2/3}\right) \sqrt{\frac{x+1}{1+\sqrt[3]{-1}}} \sqrt{\frac{\left(-x-(-1)^{2/3}\right) \left(x-\sqrt[3]{-1}\right)}{\left(\sqrt[3]{-1}+(-1)^{2/3}\right)^2}} \Pi \left(\frac{\sqrt[3]{-1}+(-1)^{2/3}}{\sqrt[3]{-1}-\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+1\&,3\right]};\sin ^{-1}\left(\sqrt{-\frac{(-1)^{2/3} \left(\sqrt[3]{-1}-x\right)}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{\sqrt{x^3+1} \left(-\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+1\&,3\right]\right) \left(-\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+1\&,1\right]+\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+1\&,3\right]\right) \left(-\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+1\&,2\right]+\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+1\&,3\right]\right)}+\frac{2 \left(\sqrt[3]{-1}+(-1)^{2/3}\right) \sqrt{\frac{x+1}{1+\sqrt[3]{-1}}} \sqrt{\frac{\left(-x-(-1)^{2/3}\right) \left(x-\sqrt[3]{-1}\right)}{\left(\sqrt[3]{-1}+(-1)^{2/3}\right)^2}} \Pi \left(\frac{\sqrt[3]{-1}+(-1)^{2/3}}{\sqrt[3]{-1}-\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+1\&,3\right]};\sin ^{-1}\left(\sqrt{-\frac{(-1)^{2/3} \left(\sqrt[3]{-1}-x\right)}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right) \text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+1\&,3\right]^3}{\sqrt{x^3+1} \left(-\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+1\&,3\right]\right) \left(-\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+1\&,1\right]+\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+1\&,3\right]\right) \left(-\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+1\&,2\right]+\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+1\&,3\right]\right)}-\frac{4 \left(\sqrt[3]{-1}+(-1)^{2/3}\right) \sqrt{\frac{x+1}{1+\sqrt[3]{-1}}} \sqrt{\frac{\left(-x-(-1)^{2/3}\right) \left(x-\sqrt[3]{-1}\right)}{\left(\sqrt[3]{-1}+(-1)^{2/3}\right)^2}} \Pi \left(\frac{\sqrt[3]{-1}+(-1)^{2/3}}{\sqrt[3]{-1}-\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+1\&,2\right]};\sin ^{-1}\left(\sqrt{-\frac{(-1)^{2/3} \left(\sqrt[3]{-1}-x\right)}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{\sqrt{x^3+1} \left(-\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+1\&,2\right]\right) \left(-\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+1\&,1\right]+\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+1\&,2\right]\right) \left(\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+1\&,2\right]-\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+1\&,3\right]\right)}+\frac{2 \left(\sqrt[3]{-1}+(-1)^{2/3}\right) \sqrt{\frac{x+1}{1+\sqrt[3]{-1}}} \sqrt{\frac{\left(-x-(-1)^{2/3}\right) \left(x-\sqrt[3]{-1}\right)}{\left(\sqrt[3]{-1}+(-1)^{2/3}\right)^2}} \Pi \left(\frac{\sqrt[3]{-1}+(-1)^{2/3}}{\sqrt[3]{-1}-\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+1\&,2\right]};\sin ^{-1}\left(\sqrt{-\frac{(-1)^{2/3} \left(\sqrt[3]{-1}-x\right)}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right) \text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+1\&,2\right]^3}{\sqrt{x^3+1} \left(-\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+1\&,2\right]\right) \left(-\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+1\&,1\right]+\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+1\&,2\right]\right) \left(\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+1\&,2\right]-\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+1\&,3\right]\right)}-\frac{4 \left(\sqrt[3]{-1}+(-1)^{2/3}\right) \sqrt{\frac{x+1}{1+\sqrt[3]{-1}}} \sqrt{\frac{\left(-x-(-1)^{2/3}\right) \left(x-\sqrt[3]{-1}\right)}{\left(\sqrt[3]{-1}+(-1)^{2/3}\right)^2}} \Pi \left(\frac{\sqrt[3]{-1}+(-1)^{2/3}}{\sqrt[3]{-1}-\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+1\&,1\right]};\sin ^{-1}\left(\sqrt{-\frac{(-1)^{2/3} \left(\sqrt[3]{-1}-x\right)}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{\sqrt{x^3+1} \left(-\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+1\&,1\right]\right) \left(\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+1\&,1\right]-\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+1\&,2\right]\right) \left(\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+1\&,1\right]-\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+1\&,3\right]\right)}+\frac{2 \left(\sqrt[3]{-1}+(-1)^{2/3}\right) \sqrt{\frac{x+1}{1+\sqrt[3]{-1}}} \sqrt{\frac{\left(-x-(-1)^{2/3}\right) \left(x-\sqrt[3]{-1}\right)}{\left(\sqrt[3]{-1}+(-1)^{2/3}\right)^2}} \Pi \left(\frac{\sqrt[3]{-1}+(-1)^{2/3}}{\sqrt[3]{-1}-\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+1\&,1\right]};\sin ^{-1}\left(\sqrt{-\frac{(-1)^{2/3} \left(\sqrt[3]{-1}-x\right)}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right) \text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+1\&,1\right]^3}{\sqrt{x^3+1} \left(-\sqrt[3]{-1}+\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+1\&,1\right]\right) \left(\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+1\&,1\right]-\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+1\&,2\right]\right) \left(\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+1\&,1\right]-\text{Root}\left[\text{$\#$1}^3-3 \text{$\#$1}^2+1\&,3\right]\right)}\right)","\frac{2 \sqrt{x^3+1} \left(2 x^3+15 x^2+2\right)}{3 x^3}-10 \sqrt{3} \tanh ^{-1}\left(\frac{\sqrt{3} x}{\sqrt{x^3+1}}\right)",1,"(4/3 + 4/(3*x^3) + 10/x)*Sqrt[1 + x^3] + 15*((2*Sqrt[(1 + x)/(1 + (-1)^(1/3))]*(-(-1)^(1/3) + x)*Sqrt[((-1)^(2/3) + x)/((-1)^(1/3) + (-1)^(2/3))]*EllipticF[ArcSin[Sqrt[-(((-1)^(2/3)*((-1)^(1/3) - x))/(1 + (-1)^(1/3)))]], (-1)^(1/3)])/(Sqrt[(-(-1)^(1/3) + x)/(-(-1)^(1/3) - (-1)^(2/3))]*Sqrt[1 + x^3]) - (4*((-1)^(1/3) + (-1)^(2/3))*Sqrt[(1 + x)/(1 + (-1)^(1/3))]*Sqrt[((-(-1)^(2/3) - x)*(-(-1)^(1/3) + x))/((-1)^(1/3) + (-1)^(2/3))^2]*EllipticPi[((-1)^(1/3) + (-1)^(2/3))/((-1)^(1/3) - Root[1 - 3*#1^2 + #1^3 & , 1, 0]), ArcSin[Sqrt[-(((-1)^(2/3)*((-1)^(1/3) - x))/(1 + (-1)^(1/3)))]], (-1)^(1/3)])/(Sqrt[1 + x^3]*(-(-1)^(1/3) + Root[1 - 3*#1^2 + #1^3 & , 1, 0])*(Root[1 - 3*#1^2 + #1^3 & , 1, 0] - Root[1 - 3*#1^2 + #1^3 & , 2, 0])*(Root[1 - 3*#1^2 + #1^3 & , 1, 0] - Root[1 - 3*#1^2 + #1^3 & , 3, 0])) + (2*((-1)^(1/3) + (-1)^(2/3))*Sqrt[(1 + x)/(1 + (-1)^(1/3))]*Sqrt[((-(-1)^(2/3) - x)*(-(-1)^(1/3) + x))/((-1)^(1/3) + (-1)^(2/3))^2]*EllipticPi[((-1)^(1/3) + (-1)^(2/3))/((-1)^(1/3) - Root[1 - 3*#1^2 + #1^3 & , 1, 0]), ArcSin[Sqrt[-(((-1)^(2/3)*((-1)^(1/3) - x))/(1 + (-1)^(1/3)))]], (-1)^(1/3)]*Root[1 - 3*#1^2 + #1^3 & , 1, 0]^3)/(Sqrt[1 + x^3]*(-(-1)^(1/3) + Root[1 - 3*#1^2 + #1^3 & , 1, 0])*(Root[1 - 3*#1^2 + #1^3 & , 1, 0] - Root[1 - 3*#1^2 + #1^3 & , 2, 0])*(Root[1 - 3*#1^2 + #1^3 & , 1, 0] - Root[1 - 3*#1^2 + #1^3 & , 3, 0])) - (4*((-1)^(1/3) + (-1)^(2/3))*Sqrt[(1 + x)/(1 + (-1)^(1/3))]*Sqrt[((-(-1)^(2/3) - x)*(-(-1)^(1/3) + x))/((-1)^(1/3) + (-1)^(2/3))^2]*EllipticPi[((-1)^(1/3) + (-1)^(2/3))/((-1)^(1/3) - Root[1 - 3*#1^2 + #1^3 & , 2, 0]), ArcSin[Sqrt[-(((-1)^(2/3)*((-1)^(1/3) - x))/(1 + (-1)^(1/3)))]], (-1)^(1/3)])/(Sqrt[1 + x^3]*(-(-1)^(1/3) + Root[1 - 3*#1^2 + #1^3 & , 2, 0])*(-Root[1 - 3*#1^2 + #1^3 & , 1, 0] + Root[1 - 3*#1^2 + #1^3 & , 2, 0])*(Root[1 - 3*#1^2 + #1^3 & , 2, 0] - Root[1 - 3*#1^2 + #1^3 & , 3, 0])) + (2*((-1)^(1/3) + (-1)^(2/3))*Sqrt[(1 + x)/(1 + (-1)^(1/3))]*Sqrt[((-(-1)^(2/3) - x)*(-(-1)^(1/3) + x))/((-1)^(1/3) + (-1)^(2/3))^2]*EllipticPi[((-1)^(1/3) + (-1)^(2/3))/((-1)^(1/3) - Root[1 - 3*#1^2 + #1^3 & , 2, 0]), ArcSin[Sqrt[-(((-1)^(2/3)*((-1)^(1/3) - x))/(1 + (-1)^(1/3)))]], (-1)^(1/3)]*Root[1 - 3*#1^2 + #1^3 & , 2, 0]^3)/(Sqrt[1 + x^3]*(-(-1)^(1/3) + Root[1 - 3*#1^2 + #1^3 & , 2, 0])*(-Root[1 - 3*#1^2 + #1^3 & , 1, 0] + Root[1 - 3*#1^2 + #1^3 & , 2, 0])*(Root[1 - 3*#1^2 + #1^3 & , 2, 0] - Root[1 - 3*#1^2 + #1^3 & , 3, 0])) - (4*((-1)^(1/3) + (-1)^(2/3))*Sqrt[(1 + x)/(1 + (-1)^(1/3))]*Sqrt[((-(-1)^(2/3) - x)*(-(-1)^(1/3) + x))/((-1)^(1/3) + (-1)^(2/3))^2]*EllipticPi[((-1)^(1/3) + (-1)^(2/3))/((-1)^(1/3) - Root[1 - 3*#1^2 + #1^3 & , 3, 0]), ArcSin[Sqrt[-(((-1)^(2/3)*((-1)^(1/3) - x))/(1 + (-1)^(1/3)))]], (-1)^(1/3)])/(Sqrt[1 + x^3]*(-(-1)^(1/3) + Root[1 - 3*#1^2 + #1^3 & , 3, 0])*(-Root[1 - 3*#1^2 + #1^3 & , 1, 0] + Root[1 - 3*#1^2 + #1^3 & , 3, 0])*(-Root[1 - 3*#1^2 + #1^3 & , 2, 0] + Root[1 - 3*#1^2 + #1^3 & , 3, 0])) + (2*((-1)^(1/3) + (-1)^(2/3))*Sqrt[(1 + x)/(1 + (-1)^(1/3))]*Sqrt[((-(-1)^(2/3) - x)*(-(-1)^(1/3) + x))/((-1)^(1/3) + (-1)^(2/3))^2]*EllipticPi[((-1)^(1/3) + (-1)^(2/3))/((-1)^(1/3) - Root[1 - 3*#1^2 + #1^3 & , 3, 0]), ArcSin[Sqrt[-(((-1)^(2/3)*((-1)^(1/3) - x))/(1 + (-1)^(1/3)))]], (-1)^(1/3)]*Root[1 - 3*#1^2 + #1^3 & , 3, 0]^3)/(Sqrt[1 + x^3]*(-(-1)^(1/3) + Root[1 - 3*#1^2 + #1^3 & , 3, 0])*(-Root[1 - 3*#1^2 + #1^3 & , 1, 0] + Root[1 - 3*#1^2 + #1^3 & , 3, 0])*(-Root[1 - 3*#1^2 + #1^3 & , 2, 0] + Root[1 - 3*#1^2 + #1^3 & , 3, 0])))","C",0
666,1,52,53,0.0276714,"\int \frac{\left(-b+a x^3\right) \sqrt{b+a x^3}}{x} \, dx","Integrate[((-b + a*x^3)*Sqrt[b + a*x^3])/x,x]","\frac{1}{9} \left(6 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a x^3+b}}{\sqrt{b}}\right)+2 \left(a x^3-2 b\right) \sqrt{a x^3+b}\right)","\frac{2}{3} b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a x^3+b}}{\sqrt{b}}\right)-\frac{2}{9} \left(2 b-a x^3\right) \sqrt{a x^3+b}",1,"(2*(-2*b + a*x^3)*Sqrt[b + a*x^3] + 6*b^(3/2)*ArcTanh[Sqrt[b + a*x^3]/Sqrt[b]])/9","A",1
667,1,26,53,0.0182038,"\int \frac{x^2}{\left(-1+x^4\right) \sqrt{1+x^4}} \, dx","Integrate[x^2/((-1 + x^4)*Sqrt[1 + x^4]),x]","-\frac{1}{3} x^3 F_1\left(\frac{3}{4};\frac{1}{2},1;\frac{7}{4};-x^4,x^4\right)","\frac{\tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{4 \sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{4 \sqrt{2}}",1,"-1/3*(x^3*AppellF1[3/4, 1/2, 1, 7/4, -x^4, x^4])","C",0
668,1,108,53,0.0914354,"\int \frac{\sqrt{1+x^4}}{-1+x^4} \, dx","Integrate[Sqrt[1 + x^4]/(-1 + x^4),x]","\frac{5 x \sqrt{x^4+1} F_1\left(\frac{1}{4};-\frac{1}{2},1;\frac{5}{4};-x^4,x^4\right)}{\left(x^4-1\right) \left(2 x^4 \left(2 F_1\left(\frac{5}{4};-\frac{1}{2},2;\frac{9}{4};-x^4,x^4\right)+F_1\left(\frac{5}{4};\frac{1}{2},1;\frac{9}{4};-x^4,x^4\right)\right)+5 F_1\left(\frac{1}{4};-\frac{1}{2},1;\frac{5}{4};-x^4,x^4\right)\right)}","-\frac{\tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{2 \sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{2 \sqrt{2}}",1,"(5*x*Sqrt[1 + x^4]*AppellF1[1/4, -1/2, 1, 5/4, -x^4, x^4])/((-1 + x^4)*(5*AppellF1[1/4, -1/2, 1, 5/4, -x^4, x^4] + 2*x^4*(2*AppellF1[5/4, -1/2, 2, 9/4, -x^4, x^4] + AppellF1[5/4, 1/2, 1, 9/4, -x^4, x^4])))","C",0
669,1,58,53,0.0638028,"\int \left(b+a x^3\right) \sqrt{x+x^4} \, dx","Integrate[(b + a*x^3)*Sqrt[x + x^4],x]","\frac{\sqrt{x^4+x} \left(x^{3/2} \left(2 a x^3+a+4 b\right)-\frac{(a-4 b) \sinh ^{-1}\left(x^{3/2}\right)}{\sqrt{x^3+1}}\right)}{12 \sqrt{x}}","\frac{1}{12} \sqrt{x^4+x} \left(2 a x^4+a x+4 b x\right)+\frac{1}{12} (4 b-a) \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4+x}}\right)",1,"(Sqrt[x + x^4]*(x^(3/2)*(a + 4*b + 2*a*x^3) - ((a - 4*b)*ArcSinh[x^(3/2)])/Sqrt[1 + x^3]))/(12*Sqrt[x])","A",1
670,1,40,53,0.0061735,"\int \sqrt[4]{x^2+x^4} \, dx","Integrate[(x^2 + x^4)^(1/4),x]","\frac{2 x \sqrt[4]{x^4+x^2} \, _2F_1\left(-\frac{1}{4},\frac{3}{4};\frac{7}{4};-x^2\right)}{3 \sqrt[4]{x^2+1}}","\frac{1}{2} \sqrt[4]{x^4+x^2} x-\frac{1}{4} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+x^2}}\right)+\frac{1}{4} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+x^2}}\right)",1,"(2*x*(x^2 + x^4)^(1/4)*Hypergeometric2F1[-1/4, 3/4, 7/4, -x^2])/(3*(1 + x^2)^(1/4))","C",1
671,1,257,53,1.372429,"\int \frac{\left(-1+x^4\right) \sqrt{1+x^4}}{\left(1+3 x^2+x^4\right)^2} \, dx","Integrate[((-1 + x^4)*Sqrt[1 + x^4])/(1 + 3*x^2 + x^4)^2,x]","-\frac{x^5-\sqrt[4]{-1} \sqrt{x^4+1} x^4 \Pi \left(-\frac{2 i}{3+\sqrt{5}};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)-\sqrt[4]{-1} \sqrt{x^4+1} \Pi \left(-\frac{2 i}{3+\sqrt{5}};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+\sqrt[4]{-1} \sqrt{x^4+1} \left(x^4+3 x^2+1\right) F\left(\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)-3 \sqrt[4]{-1} \sqrt{x^4+1} x^2 \Pi \left(-\frac{2 i}{3+\sqrt{5}};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)-\sqrt[4]{-1} \sqrt{x^4+1} \left(x^4+3 x^2+1\right) \Pi \left(\frac{2 i}{-3+\sqrt{5}};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+x}{2 \sqrt{x^4+1} \left(x^4+3 x^2+1\right)}","-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{\sqrt{x^4+1}}\right)}{2 \sqrt{3}}-\frac{\sqrt{x^4+1} x}{2 \left(x^4+3 x^2+1\right)}",1,"-1/2*(x + x^5 + (-1)^(1/4)*Sqrt[1 + x^4]*(1 + 3*x^2 + x^4)*EllipticF[I*ArcSinh[(-1)^(1/4)*x], -1] - (-1)^(1/4)*Sqrt[1 + x^4]*(1 + 3*x^2 + x^4)*EllipticPi[(2*I)/(-3 + Sqrt[5]), I*ArcSinh[(-1)^(1/4)*x], -1] - (-1)^(1/4)*Sqrt[1 + x^4]*EllipticPi[(-2*I)/(3 + Sqrt[5]), I*ArcSinh[(-1)^(1/4)*x], -1] - 3*(-1)^(1/4)*x^2*Sqrt[1 + x^4]*EllipticPi[(-2*I)/(3 + Sqrt[5]), I*ArcSinh[(-1)^(1/4)*x], -1] - (-1)^(1/4)*x^4*Sqrt[1 + x^4]*EllipticPi[(-2*I)/(3 + Sqrt[5]), I*ArcSinh[(-1)^(1/4)*x], -1])/(Sqrt[1 + x^4]*(1 + 3*x^2 + x^4))","C",1
672,1,53,53,0.019539,"\int \frac{1}{x^8 \sqrt[4]{x^3+x^4}} \, dx","Integrate[1/(x^8*(x^3 + x^4)^(1/4)),x]","\frac{4 \left(x^3 (x+1)\right)^{3/4} \left(262144 x^7-196608 x^6+172032 x^5-157696 x^4+147840 x^3-140448 x^2+134596 x-129789\right)}{4023459 x^{10}}","\frac{4 \left(x^4+x^3\right)^{3/4} \left(262144 x^7-196608 x^6+172032 x^5-157696 x^4+147840 x^3-140448 x^2+134596 x-129789\right)}{4023459 x^{10}}",1,"(4*(x^3*(1 + x))^(3/4)*(-129789 + 134596*x - 140448*x^2 + 147840*x^3 - 157696*x^4 + 172032*x^5 - 196608*x^6 + 262144*x^7))/(4023459*x^10)","A",1
673,1,484,53,1.3946344,"\int \frac{1+4 x}{\sqrt{1-2 x+3 x^2+2 x^3+x^4}} \, dx","Integrate[(1 + 4*x)/Sqrt[1 - 2*x + 3*x^2 + 2*x^3 + x^4],x]","\frac{2 \left(-4 i-\sqrt{1-4 i}-\sqrt{1+4 i}\right) \left(x+\frac{1}{2} \left((1-2 i)+\sqrt{1-4 i}\right)\right)^2 \sqrt{\frac{\left(-4 i+\sqrt{1-4 i}-\sqrt{1+4 i}\right) \left(-2 x+\sqrt{1+4 i}-(1+2 i)\right)}{\sqrt{1+4 i} \left(2 x+\sqrt{1-4 i}+(1-2 i)\right)}} \sqrt{\frac{\sqrt{1-4 i} \left(-4 i+\sqrt{1-4 i}-\sqrt{1+4 i}\right) \left(-2 x+\sqrt{1-4 i}-(1-2 i)\right) \left(2 x+\sqrt{1+4 i}+(1+2 i)\right)}{\left(4 i+\sqrt{1-4 i}+\sqrt{1+4 i}\right)^2 \left(2 x+\sqrt{1-4 i}+(1-2 i)\right)^2}} \left(\left((1-4 i)+2 \sqrt{1-4 i}\right) F\left(\sin ^{-1}\left(\sqrt{2} \sqrt{\frac{\sqrt{1-4 i} \left(2 x+\sqrt{1+4 i}+(1+2 i)\right)}{\left(4 i+\sqrt{1-4 i}+\sqrt{1+4 i}\right) \left(2 x+\sqrt{1-4 i}+(1-2 i)\right)}}\right)|\frac{1}{2}+\frac{9}{2 \sqrt{17}}\right)+2 \left(4 i-\sqrt{1-4 i}+\sqrt{1+4 i}\right) \Pi \left(\frac{4 i+\sqrt{1-4 i}+\sqrt{1+4 i}}{2 \sqrt{1-4 i}};\sin ^{-1}\left(\sqrt{2} \sqrt{\frac{\sqrt{1-4 i} \left(2 x+\sqrt{1+4 i}+(1+2 i)\right)}{\left(4 i+\sqrt{1-4 i}+\sqrt{1+4 i}\right) \left(2 x+\sqrt{1-4 i}+(1-2 i)\right)}}\right)|\frac{1}{2}+\frac{9}{2 \sqrt{17}}\right)\right)}{\sqrt{1-4 i} \left(-4 i+\sqrt{1-4 i}-\sqrt{1+4 i}\right) \sqrt{x^4+2 x^3+3 x^2-2 x+1}}","-\log \left(-x^4-3 x^3-5 x^2+\left(x^2+2 x+2\right) \sqrt{x^4+2 x^3+3 x^2-2 x+1}-2 x\right)",1,"(2*(-4*I - Sqrt[1 - 4*I] - Sqrt[1 + 4*I])*(((1 - 2*I) + Sqrt[1 - 4*I])/2 + x)^2*Sqrt[((-4*I + Sqrt[1 - 4*I] - Sqrt[1 + 4*I])*((-1 - 2*I) + Sqrt[1 + 4*I] - 2*x))/(Sqrt[1 + 4*I]*((1 - 2*I) + Sqrt[1 - 4*I] + 2*x))]*Sqrt[(Sqrt[1 - 4*I]*(-4*I + Sqrt[1 - 4*I] - Sqrt[1 + 4*I])*((-1 + 2*I) + Sqrt[1 - 4*I] - 2*x)*((1 + 2*I) + Sqrt[1 + 4*I] + 2*x))/((4*I + Sqrt[1 - 4*I] + Sqrt[1 + 4*I])^2*((1 - 2*I) + Sqrt[1 - 4*I] + 2*x)^2)]*(((1 - 4*I) + 2*Sqrt[1 - 4*I])*EllipticF[ArcSin[Sqrt[2]*Sqrt[(Sqrt[1 - 4*I]*((1 + 2*I) + Sqrt[1 + 4*I] + 2*x))/((4*I + Sqrt[1 - 4*I] + Sqrt[1 + 4*I])*((1 - 2*I) + Sqrt[1 - 4*I] + 2*x))]], 1/2 + 9/(2*Sqrt[17])] + 2*(4*I - Sqrt[1 - 4*I] + Sqrt[1 + 4*I])*EllipticPi[(4*I + Sqrt[1 - 4*I] + Sqrt[1 + 4*I])/(2*Sqrt[1 - 4*I]), ArcSin[Sqrt[2]*Sqrt[(Sqrt[1 - 4*I]*((1 + 2*I) + Sqrt[1 + 4*I] + 2*x))/((4*I + Sqrt[1 - 4*I] + Sqrt[1 + 4*I])*((1 - 2*I) + Sqrt[1 - 4*I] + 2*x))]], 1/2 + 9/(2*Sqrt[17])]))/(Sqrt[1 - 4*I]*(-4*I + Sqrt[1 - 4*I] - Sqrt[1 + 4*I])*Sqrt[1 - 2*x + 3*x^2 + 2*x^3 + x^4])","C",0
674,1,44,53,0.0104284,"\int \frac{1}{\sqrt[4]{-1+x^4} \left(1+3 x^4\right)} \, dx","Integrate[1/((-1 + x^4)^(1/4)*(1 + 3*x^4)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt[4]{x^4-1}}\right)+\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt[4]{x^4-1}}\right)}{2 \sqrt{2}}","\frac{\tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt[4]{x^4-1}}\right)}{2 \sqrt{2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt[4]{x^4-1}}\right)}{2 \sqrt{2}}",1,"(ArcTan[(Sqrt[2]*x)/(-1 + x^4)^(1/4)] + ArcTanh[(Sqrt[2]*x)/(-1 + x^4)^(1/4)])/(2*Sqrt[2])","A",1
675,0,0,53,0.574007,"\int \frac{-3 b+a x^4}{\left(b-x^3+a x^4\right) \sqrt[4]{b x+a x^5}} \, dx","Integrate[(-3*b + a*x^4)/((b - x^3 + a*x^4)*(b*x + a*x^5)^(1/4)),x]","\int \frac{-3 b+a x^4}{\left(b-x^3+a x^4\right) \sqrt[4]{b x+a x^5}} \, dx","-2 \tan ^{-1}\left(\frac{\left(a x^5+b x\right)^{3/4}}{a x^4+b}\right)-2 \tanh ^{-1}\left(\frac{\left(a x^5+b x\right)^{3/4}}{a x^4+b}\right)",1,"Integrate[(-3*b + a*x^4)/((b - x^3 + a*x^4)*(b*x + a*x^5)^(1/4)), x]","F",-1
676,1,61,53,0.0335252,"\int x^{20} \sqrt{-1+x^6} \, dx","Integrate[x^20*Sqrt[-1 + x^6],x]","\frac{\left(x^6-1\right) \left(15 \sin ^{-1}\left(x^3\right)+\sqrt{1-x^6} \left(48 x^{18}-8 x^{12}-10 x^6-15\right) x^3\right)}{1152 \sqrt{-\left(x^6-1\right)^2}}","\frac{\sqrt{x^6-1} \left(48 x^{21}-8 x^{15}-10 x^9-15 x^3\right)}{1152}-\frac{5}{384} \log \left(\sqrt{x^6-1}+x^3\right)",1,"((-1 + x^6)*(x^3*Sqrt[1 - x^6]*(-15 - 10*x^6 - 8*x^12 + 48*x^18) + 15*ArcSin[x^3]))/(1152*Sqrt[-(-1 + x^6)^2])","A",1
677,1,44,53,0.1353225,"\int \frac{\left(-1+x^3\right) \sqrt{-1+x^6}}{x^4 \left(1+x^3\right)} \, dx","Integrate[((-1 + x^3)*Sqrt[-1 + x^6])/(x^4*(1 + x^3)),x]","\frac{1}{3} \left(-2 \tan ^{-1}\left(\sqrt{x^6-1}\right)+\frac{\sqrt{x^6-1}}{x^3}+\log \left(\sqrt{x^6-1}+x^3\right)\right)","\frac{\sqrt{x^6-1}}{3 x^3}+\frac{1}{3} \log \left(\sqrt{x^6-1}+x^3\right)-\frac{4}{3} \tan ^{-1}\left(\sqrt{x^6-1}+x^3\right)",1,"(Sqrt[-1 + x^6]/x^3 - 2*ArcTan[Sqrt[-1 + x^6]] + Log[x^3 + Sqrt[-1 + x^6]])/3","A",1
678,1,542,53,1.8041647,"\int \frac{1+x^6}{\sqrt{1-x^2+x^4} \left(1-x^6\right)} \, dx","Integrate[(1 + x^6)/(Sqrt[1 - x^2 + x^4]*(1 - x^6)),x]","\frac{9 \sqrt[6]{-1} \sqrt{1-\sqrt[3]{-1} x^2} \sqrt{(-1)^{2/3} x^2+1} F\left(i \sinh ^{-1}\left(\sqrt[3]{-1} x\right)|(-1)^{2/3}\right)-\frac{18 i \sqrt{1-\sqrt[3]{-1} x^2} \sqrt{(-1)^{2/3} x^2+1} \Pi \left(-1;i \sinh ^{-1}\left(\sqrt[3]{-1} x\right)|(-1)^{2/3}\right)}{\left(1+\sqrt[3]{-1}\right)^2}-6 \sqrt[6]{-1} \sqrt{1-\sqrt[3]{-1} x^2} \sqrt{(-1)^{2/3} x^2+1} \Pi \left(-(-1)^{2/3};i \sinh ^{-1}\left(\sqrt[3]{-1} x\right)|(-1)^{2/3}\right)-4 \sqrt[3]{-1} \sqrt{3} \left(1+(-1)^{2/3}\right) \sqrt{\frac{x+(-1)^{5/6}}{\left((-1)^{2/3}-1\right) \left(\sqrt[6]{-1}-x\right)}} \sqrt{\frac{2 i x+i \sqrt{3}+1}{-\sqrt{3} x+i x+2}} \sqrt{\frac{\left(\sqrt{3}+3 i\right) x+2 i \sqrt{3}}{-2+\left(\sqrt{3}-i\right) x}} \left(\sqrt[6]{-1}-x\right)^2 \left(\sqrt[6]{-1} \left(\Pi \left(-\frac{2 \left(1+(-1)^{2/3}\right)}{(3+6 i)+(2+3 i) \sqrt{3}};\sin ^{-1}\left(\sqrt{\frac{\left(3 i+\sqrt{3}\right) x+2 i \sqrt{3}}{\left(-i+\sqrt{3}\right) x-2}}\right)|-\frac{1}{3}\right)-\Pi \left(\frac{2 i \left(1+(-1)^{2/3}\right)}{(-6-3 i)+(3+2 i) \sqrt{3}};\sin ^{-1}\left(\sqrt{\frac{\left(3 i+\sqrt{3}\right) x+2 i \sqrt{3}}{\left(-i+\sqrt{3}\right) x-2}}\right)|-\frac{1}{3}\right)\right)-F\left(\sin ^{-1}\left(\sqrt{\frac{\left(3 i+\sqrt{3}\right) x+2 i \sqrt{3}}{\left(-i+\sqrt{3}\right) x-2}}\right)|-\frac{1}{3}\right)\right)}{9 \sqrt{x^4-x^2+1}}","\frac{1}{3} \sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4-x^2+1}}\right)+\frac{1}{3} \tanh ^{-1}\left(\frac{x}{\sqrt{x^4-x^2+1}}\right)",1,"(9*(-1)^(1/6)*Sqrt[1 - (-1)^(1/3)*x^2]*Sqrt[1 + (-1)^(2/3)*x^2]*EllipticF[I*ArcSinh[(-1)^(1/3)*x], (-1)^(2/3)] - ((18*I)*Sqrt[1 - (-1)^(1/3)*x^2]*Sqrt[1 + (-1)^(2/3)*x^2]*EllipticPi[-1, I*ArcSinh[(-1)^(1/3)*x], (-1)^(2/3)])/(1 + (-1)^(1/3))^2 - 6*(-1)^(1/6)*Sqrt[1 - (-1)^(1/3)*x^2]*Sqrt[1 + (-1)^(2/3)*x^2]*EllipticPi[-(-1)^(2/3), I*ArcSinh[(-1)^(1/3)*x], (-1)^(2/3)] - 4*(-1)^(1/3)*Sqrt[3]*(1 + (-1)^(2/3))*((-1)^(1/6) - x)^2*Sqrt[((-1)^(5/6) + x)/((-1 + (-1)^(2/3))*((-1)^(1/6) - x))]*Sqrt[(1 + I*Sqrt[3] + (2*I)*x)/(2 + I*x - Sqrt[3]*x)]*Sqrt[((2*I)*Sqrt[3] + (3*I + Sqrt[3])*x)/(-2 + (-I + Sqrt[3])*x)]*(-EllipticF[ArcSin[Sqrt[((2*I)*Sqrt[3] + (3*I + Sqrt[3])*x)/(-2 + (-I + Sqrt[3])*x)]], -1/3] + (-1)^(1/6)*(EllipticPi[(-2*(1 + (-1)^(2/3)))/((3 + 6*I) + (2 + 3*I)*Sqrt[3]), ArcSin[Sqrt[((2*I)*Sqrt[3] + (3*I + Sqrt[3])*x)/(-2 + (-I + Sqrt[3])*x)]], -1/3] - EllipticPi[((2*I)*(1 + (-1)^(2/3)))/((-6 - 3*I) + (3 + 2*I)*Sqrt[3]), ArcSin[Sqrt[((2*I)*Sqrt[3] + (3*I + Sqrt[3])*x)/(-2 + (-I + Sqrt[3])*x)]], -1/3])))/(9*Sqrt[1 - x^2 + x^4])","C",0
679,1,96,53,0.0664063,"\int \frac{\left(-2+x^6\right) \sqrt{-1+x^6}}{x^7 \left(2+x^6\right)} \, dx","Integrate[((-2 + x^6)*Sqrt[-1 + x^6])/(x^7*(2 + x^6)),x]","\frac{1}{6} \left(-\frac{1}{x^6 \sqrt{x^6-1}}+\frac{1}{\sqrt{x^6-1}}-2 \tan ^{-1}\left(\sqrt{x^6-1}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{x^6-1}}{\sqrt{3}}\right)+\frac{\sqrt{1-x^6} \tanh ^{-1}\left(\sqrt{1-x^6}\right)}{\sqrt{x^6-1}}\right)","\frac{\sqrt{x^6-1}}{6 x^6}-\frac{1}{2} \tan ^{-1}\left(\sqrt{x^6-1}\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{x^6-1}}{\sqrt{3}}\right)}{\sqrt{3}}",1,"(1/Sqrt[-1 + x^6] - 1/(x^6*Sqrt[-1 + x^6]) - 2*ArcTan[Sqrt[-1 + x^6]] + 2*Sqrt[3]*ArcTan[Sqrt[-1 + x^6]/Sqrt[3]] + (Sqrt[1 - x^6]*ArcTanh[Sqrt[1 - x^6]])/Sqrt[-1 + x^6])/6","A",1
680,1,58426,53,18.2255299,"\int \frac{x (-6 b+5 a x)}{\sqrt[4]{-b x^2+a x^3} \left(b-a x+x^6\right)} \, dx","Integrate[(x*(-6*b + 5*a*x))/((-(b*x^2) + a*x^3)^(1/4)*(b - a*x + x^6)),x]","\text{Result too large to show}","2 \tan ^{-1}\left(\frac{\sqrt[4]{a x^3-b x^2}}{x^2}\right)-2 \tanh ^{-1}\left(\frac{\left(a x^3-b x^2\right)^{3/4}}{a x-b}\right)",1,"Result too large to show","C",0
681,1,85,53,0.1995614,"\int \frac{\sqrt{1+x^3} \left(2+2 x^3+x^6\right)}{x \left(-1+x^6\right)} \, dx","Integrate[(Sqrt[1 + x^3]*(2 + 2*x^3 + x^6))/(x*(-1 + x^6)),x]","\frac{-4 \sqrt{\frac{1}{x^3}+1} F_1\left(\frac{3}{2};\frac{1}{2},1;\frac{5}{2};-\frac{1}{x^3},\frac{1}{x^3}\right)-9 \sqrt{x^3+1} x^6 F_1\left(1;\frac{1}{2},1;2;-x^3,x^3\right)+6 \left(x^6+x^3\right)}{9 x^3 \sqrt{x^3+1}}","\frac{2 \sqrt{x^3+1}}{3}+\frac{4}{3} \tanh ^{-1}\left(\sqrt{x^3+1}\right)-\frac{5}{3} \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{x^3+1}}{\sqrt{2}}\right)",1,"(6*(x^3 + x^6) - 9*x^6*Sqrt[1 + x^3]*AppellF1[1, 1/2, 1, 2, -x^3, x^3] - 4*Sqrt[1 + x^(-3)]*AppellF1[3/2, 1/2, 1, 5/2, -x^(-3), x^(-3)])/(9*x^3*Sqrt[1 + x^3])","C",0
682,1,106,53,0.4375463,"\int \frac{\left(-1+x^4\right) \sqrt{1+x^4}}{1+x^8} \, dx","Integrate[((-1 + x^4)*Sqrt[1 + x^4])/(1 + x^8),x]","\frac{1}{2} \sqrt[4]{-1} \left(-2 F\left(\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+\Pi \left(-\sqrt[4]{-1};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+\Pi \left(\sqrt[4]{-1};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+\Pi \left(-(-1)^{3/4};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+\Pi \left((-1)^{3/4};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)\right)","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt{x^4+1}}\right)}{2 \sqrt[4]{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt{x^4+1}}\right)}{2 \sqrt[4]{2}}",1,"((-1)^(1/4)*(-2*EllipticF[I*ArcSinh[(-1)^(1/4)*x], -1] + EllipticPi[-(-1)^(1/4), I*ArcSinh[(-1)^(1/4)*x], -1] + EllipticPi[(-1)^(1/4), I*ArcSinh[(-1)^(1/4)*x], -1] + EllipticPi[-(-1)^(3/4), I*ArcSinh[(-1)^(1/4)*x], -1] + EllipticPi[(-1)^(3/4), I*ArcSinh[(-1)^(1/4)*x], -1]))/2","C",1
683,1,106,53,0.3301614,"\int \frac{-1+x^8}{\sqrt{1+x^4} \left(1+x^8\right)} \, dx","Integrate[(-1 + x^8)/(Sqrt[1 + x^4]*(1 + x^8)),x]","\frac{1}{2} \sqrt[4]{-1} \left(-2 F\left(\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+\Pi \left(-\sqrt[4]{-1};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+\Pi \left(\sqrt[4]{-1};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+\Pi \left(-(-1)^{3/4};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+\Pi \left((-1)^{3/4};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)\right)","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt{x^4+1}}\right)}{2 \sqrt[4]{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt{x^4+1}}\right)}{2 \sqrt[4]{2}}",1,"((-1)^(1/4)*(-2*EllipticF[I*ArcSinh[(-1)^(1/4)*x], -1] + EllipticPi[-(-1)^(1/4), I*ArcSinh[(-1)^(1/4)*x], -1] + EllipticPi[(-1)^(1/4), I*ArcSinh[(-1)^(1/4)*x], -1] + EllipticPi[-(-1)^(3/4), I*ArcSinh[(-1)^(1/4)*x], -1] + EllipticPi[(-1)^(3/4), I*ArcSinh[(-1)^(1/4)*x], -1]))/2","C",1
684,1,154,53,0.2839757,"\int \frac{\sqrt{-2+x^4} \left(2+x^4\right)}{4-6 x^4+x^8} \, dx","Integrate[(Sqrt[-2 + x^4]*(2 + x^4))/(4 - 6*x^4 + x^8),x]","\frac{\sqrt{2-x^4} \left(2 F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt[4]{2}}\right)\right|-1\right)-\Pi \left(-\sqrt{\frac{2}{3+\sqrt{5}}};\left.\sin ^{-1}\left(\frac{x}{\sqrt[4]{2}}\right)\right|-1\right)-\Pi \left(\sqrt{\frac{2}{3+\sqrt{5}}};\left.\sin ^{-1}\left(\frac{x}{\sqrt[4]{2}}\right)\right|-1\right)-\Pi \left(-\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)};\left.\sin ^{-1}\left(\frac{x}{\sqrt[4]{2}}\right)\right|-1\right)-\Pi \left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)};\left.\sin ^{-1}\left(\frac{x}{\sqrt[4]{2}}\right)\right|-1\right)\right)}{2 \sqrt[4]{2} \sqrt{x^4-2}}","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt{x^4-2}}\right)}{2 \sqrt[4]{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt{x^4-2}}\right)}{2 \sqrt[4]{2}}",1,"(Sqrt[2 - x^4]*(2*EllipticF[ArcSin[x/2^(1/4)], -1] - EllipticPi[-Sqrt[2/(3 + Sqrt[5])], ArcSin[x/2^(1/4)], -1] - EllipticPi[Sqrt[2/(3 + Sqrt[5])], ArcSin[x/2^(1/4)], -1] - EllipticPi[-Sqrt[(3 + Sqrt[5])/2], ArcSin[x/2^(1/4)], -1] - EllipticPi[Sqrt[(3 + Sqrt[5])/2], ArcSin[x/2^(1/4)], -1]))/(2*2^(1/4)*Sqrt[-2 + x^4])","C",1
685,1,413,53,0.673029,"\int \frac{-2 b+a x^4}{\sqrt[4]{-b+a x^4} \left(-b+a x^4+2 x^8\right)} \, dx","Integrate[(-2*b + a*x^4)/((-b + a*x^4)^(1/4)*(-b + a*x^4 + 2*x^8)),x]","\frac{1}{2} \left(\frac{\sqrt[4]{a-\sqrt{a^2+8 b}} \tan ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+8 b}+a^2+4 b}}{\sqrt[4]{a-\sqrt{a^2+8 b}} \sqrt[4]{a x^4-b}}\right)}{\sqrt[4]{-a \sqrt{a^2+8 b}+a^2+4 b}}+\frac{\sqrt[4]{\sqrt{a^2+8 b}+a} \tan ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+8 b}+a^2+4 b}}{\sqrt[4]{\sqrt{a^2+8 b}+a} \sqrt[4]{a x^4-b}}\right)}{\sqrt[4]{a \sqrt{a^2+8 b}+a^2+4 b}}+\frac{\sqrt[4]{a-\sqrt{a^2+8 b}} \tanh ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+8 b}+a^2+4 b}}{\sqrt[4]{a-\sqrt{a^2+8 b}} \sqrt[4]{a x^4-b}}\right)}{\sqrt[4]{-a \sqrt{a^2+8 b}+a^2+4 b}}+\frac{\sqrt[4]{\sqrt{a^2+8 b}+a} \tanh ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+8 b}+a^2+4 b}}{\sqrt[4]{\sqrt{a^2+8 b}+a} \sqrt[4]{a x^4-b}}\right)}{\sqrt[4]{a \sqrt{a^2+8 b}+a^2+4 b}}\right)","-\frac{1}{4} \text{RootSum}\left[-\text{$\#$1}^8+\text{$\#$1}^4 a+2 b\&,\frac{\log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]",1,"(((a - Sqrt[a^2 + 8*b])^(1/4)*ArcTan[((a^2 + 4*b - a*Sqrt[a^2 + 8*b])^(1/4)*x)/((a - Sqrt[a^2 + 8*b])^(1/4)*(-b + a*x^4)^(1/4))])/(a^2 + 4*b - a*Sqrt[a^2 + 8*b])^(1/4) + ((a + Sqrt[a^2 + 8*b])^(1/4)*ArcTan[((a^2 + 4*b + a*Sqrt[a^2 + 8*b])^(1/4)*x)/((a + Sqrt[a^2 + 8*b])^(1/4)*(-b + a*x^4)^(1/4))])/(a^2 + 4*b + a*Sqrt[a^2 + 8*b])^(1/4) + ((a - Sqrt[a^2 + 8*b])^(1/4)*ArcTanh[((a^2 + 4*b - a*Sqrt[a^2 + 8*b])^(1/4)*x)/((a - Sqrt[a^2 + 8*b])^(1/4)*(-b + a*x^4)^(1/4))])/(a^2 + 4*b - a*Sqrt[a^2 + 8*b])^(1/4) + ((a + Sqrt[a^2 + 8*b])^(1/4)*ArcTanh[((a^2 + 4*b + a*Sqrt[a^2 + 8*b])^(1/4)*x)/((a + Sqrt[a^2 + 8*b])^(1/4)*(-b + a*x^4)^(1/4))])/(a^2 + 4*b + a*Sqrt[a^2 + 8*b])^(1/4))/2","B",1
686,1,983,53,14.556917,"\int \frac{1}{x^2 \sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[1/(x^2*Sqrt[x + Sqrt[1 + x^2]]),x]","\frac{159120 \left(x+\sqrt{x^2+1}\right)^{19/2} \left(x^2+\sqrt{x^2+1} x+1\right) \left(\frac{16}{585} \, _4F_3\left(\frac{5}{4},2,2,2;1,1,\frac{17}{4};\left(x+\sqrt{x^2+1}\right)^2\right) \left(\left(x+\sqrt{x^2+1}\right)^3+x+\sqrt{x^2+1}\right)^2+\frac{681 \left(x+\sqrt{x^2+1}\right)^6-1483 \left(x+\sqrt{x^2+1}\right)^4-6769 \left(x+\sqrt{x^2+1}\right)^2+5 \left(\left(x+\sqrt{x^2+1}\right)^8-248 \left(x+\sqrt{x^2+1}\right)^6+102 \left(x+\sqrt{x^2+1}\right)^4+1208 \left(x+\sqrt{x^2+1}\right)^2+729\right) \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\left(x+\sqrt{x^2+1}\right)^2\right)-3645}{640 \left(x+\sqrt{x^2+1}\right)^4}\right)}{x \left(\frac{x}{\sqrt{x^2+1}}+1\right) \left(\left(x+\sqrt{x^2+1}\right)^2+1\right) \left(1989 \left(54400 x^{10}+54400 \sqrt{x^2+1} x^9+107808 x^8+80608 \sqrt{x^2+1} x^7+90944 x^6+57440 \sqrt{x^2+1} x^5+42462 x^4+20418 \sqrt{x^2+1} x^3+6909 x^2+10 \left(256 x^{11}+256 \sqrt{x^2+1} x^{10}-7296 x^9-7424 \sqrt{x^2+1} x^8-15296 x^7-11552 \sqrt{x^2+1} x^6-12608 x^5-7776 \sqrt{x^2+1} x^4-5590 x^3-2672 \sqrt{x^2+1} x^2-971 x-182 \sqrt{x^2+1}\right) \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\left(x+\sqrt{x^2+1}\right)^2\right) x+967 \sqrt{x^2+1} x-140\right)+4352 x \left(26624 x^{13}+26624 \sqrt{x^2+1} x^{12}+89088 x^{11}+75776 \sqrt{x^2+1} x^{10}+115200 x^9+80640 \sqrt{x^2+1} x^8+71936 x^7+39424 \sqrt{x^2+1} x^6+22008 x^5+8680 \sqrt{x^2+1} x^4+2916 x^3+696 \sqrt{x^2+1} x^2+112 x+9 \sqrt{x^2+1}\right) \, _4F_3\left(\frac{5}{4},2,2,2;1,1,\frac{17}{4};\left(x+\sqrt{x^2+1}\right)^2\right)+40960 x \left(8192 x^{15}+8192 \sqrt{x^2+1} x^{14}+32768 x^{13}+28672 \sqrt{x^2+1} x^{12}+52736 x^{11}+39424 \sqrt{x^2+1} x^{10}+43520 x^9+26880 \sqrt{x^2+1} x^8+19392 x^7+9408 \sqrt{x^2+1} x^6+4480 x^5+1568 \sqrt{x^2+1} x^4+462 x^3+98 \sqrt{x^2+1} x^2+14 x+\sqrt{x^2+1}\right) \, _4F_3\left(\frac{9}{4},3,3,3;2,2,\frac{21}{4};\left(x+\sqrt{x^2+1}\right)^2\right)\right)}-\frac{\left(\left(x+\sqrt{x^2+1}\right)^2-1\right) \left(-2 \tan ^{-1}\left(\sqrt{x+\sqrt{x^2+1}}\right)-2 \tanh ^{-1}\left(\sqrt{x+\sqrt{x^2+1}}\right)+2 \sqrt{x+\sqrt{x^2+1}}\right)}{2 x \left(\frac{x}{\sqrt{x^2+1}}+1\right) \left(x+\sqrt{x^2+1}\right) \left(1-\frac{\left(x+\sqrt{x^2+1}\right)^2-1}{2 \left(x+\sqrt{x^2+1}\right)^2}\right)}","-\frac{1}{x \sqrt{\sqrt{x^2+1}+x}}+\tan ^{-1}\left(\sqrt{\sqrt{x^2+1}+x}\right)+\tanh ^{-1}\left(\sqrt{\sqrt{x^2+1}+x}\right)",1,"-1/2*((-1 + (x + Sqrt[1 + x^2])^2)*(2*Sqrt[x + Sqrt[1 + x^2]] - 2*ArcTan[Sqrt[x + Sqrt[1 + x^2]]] - 2*ArcTanh[Sqrt[x + Sqrt[1 + x^2]]]))/(x*(1 + x/Sqrt[1 + x^2])*(x + Sqrt[1 + x^2])*(1 - (-1 + (x + Sqrt[1 + x^2])^2)/(2*(x + Sqrt[1 + x^2])^2))) + (159120*(x + Sqrt[1 + x^2])^(19/2)*(1 + x^2 + x*Sqrt[1 + x^2])*((-3645 - 6769*(x + Sqrt[1 + x^2])^2 - 1483*(x + Sqrt[1 + x^2])^4 + 681*(x + Sqrt[1 + x^2])^6 + 5*(729 + 1208*(x + Sqrt[1 + x^2])^2 + 102*(x + Sqrt[1 + x^2])^4 - 248*(x + Sqrt[1 + x^2])^6 + (x + Sqrt[1 + x^2])^8)*Hypergeometric2F1[1/4, 1, 5/4, (x + Sqrt[1 + x^2])^2])/(640*(x + Sqrt[1 + x^2])^4) + (16*(x + Sqrt[1 + x^2] + (x + Sqrt[1 + x^2])^3)^2*HypergeometricPFQ[{5/4, 2, 2, 2}, {1, 1, 17/4}, (x + Sqrt[1 + x^2])^2])/585))/(x*(1 + x/Sqrt[1 + x^2])*(1 + (x + Sqrt[1 + x^2])^2)*(1989*(-140 + 6909*x^2 + 42462*x^4 + 90944*x^6 + 107808*x^8 + 54400*x^10 + 967*x*Sqrt[1 + x^2] + 20418*x^3*Sqrt[1 + x^2] + 57440*x^5*Sqrt[1 + x^2] + 80608*x^7*Sqrt[1 + x^2] + 54400*x^9*Sqrt[1 + x^2] + 10*x*(-971*x - 5590*x^3 - 12608*x^5 - 15296*x^7 - 7296*x^9 + 256*x^11 - 182*Sqrt[1 + x^2] - 2672*x^2*Sqrt[1 + x^2] - 7776*x^4*Sqrt[1 + x^2] - 11552*x^6*Sqrt[1 + x^2] - 7424*x^8*Sqrt[1 + x^2] + 256*x^10*Sqrt[1 + x^2])*Hypergeometric2F1[1/4, 1, 5/4, (x + Sqrt[1 + x^2])^2]) + 4352*x*(112*x + 2916*x^3 + 22008*x^5 + 71936*x^7 + 115200*x^9 + 89088*x^11 + 26624*x^13 + 9*Sqrt[1 + x^2] + 696*x^2*Sqrt[1 + x^2] + 8680*x^4*Sqrt[1 + x^2] + 39424*x^6*Sqrt[1 + x^2] + 80640*x^8*Sqrt[1 + x^2] + 75776*x^10*Sqrt[1 + x^2] + 26624*x^12*Sqrt[1 + x^2])*HypergeometricPFQ[{5/4, 2, 2, 2}, {1, 1, 17/4}, (x + Sqrt[1 + x^2])^2] + 40960*x*(14*x + 462*x^3 + 4480*x^5 + 19392*x^7 + 43520*x^9 + 52736*x^11 + 32768*x^13 + 8192*x^15 + Sqrt[1 + x^2] + 98*x^2*Sqrt[1 + x^2] + 1568*x^4*Sqrt[1 + x^2] + 9408*x^6*Sqrt[1 + x^2] + 26880*x^8*Sqrt[1 + x^2] + 39424*x^10*Sqrt[1 + x^2] + 28672*x^12*Sqrt[1 + x^2] + 8192*x^14*Sqrt[1 + x^2])*HypergeometricPFQ[{9/4, 3, 3, 3}, {2, 2, 21/4}, (x + Sqrt[1 + x^2])^2]))","C",0
687,1,209,54,0.3409123,"\int \frac{-1+\sqrt{k} x}{\left(1+\sqrt{k} x\right) \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}} \, dx","Integrate[(-1 + Sqrt[k]*x)/((1 + Sqrt[k]*x)*Sqrt[(1 - x^2)*(1 - k^2*x^2)]),x]","\frac{\sqrt{k-1} \sqrt{-((k-1) k)} \sqrt{1-x^2} \sqrt{1-k^2 x^2} F\left(\sin ^{-1}(x)|k^2\right)-2 \left(\sqrt{k} \sqrt{x^2-1} \sqrt{k^2 x^2-1} \tanh ^{-1}\left(\frac{\sqrt{-((k-1) k)} \sqrt{x^2-1}}{\sqrt{k-1} \sqrt{k^2 x^2-1}}\right)+\sqrt{k-1} \sqrt{-((k-1) k)} \sqrt{1-x^2} \sqrt{1-k^2 x^2} \Pi \left(k;\sin ^{-1}(x)|k^2\right)\right)}{\sqrt{k-1} \sqrt{-((k-1) k)} \sqrt{\left(x^2-1\right) \left(k^2 x^2-1\right)}}","-\frac{2 \tan ^{-1}\left(\frac{(k-1) x}{\sqrt{k^2 x^4+\left(-k^2-1\right) x^2+1}+k x^2+2 \sqrt{k} x+1}\right)}{k-1}",1,"(Sqrt[-1 + k]*Sqrt[-((-1 + k)*k)]*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticF[ArcSin[x], k^2] - 2*(Sqrt[k]*Sqrt[-1 + x^2]*Sqrt[-1 + k^2*x^2]*ArcTanh[(Sqrt[-((-1 + k)*k)]*Sqrt[-1 + x^2])/(Sqrt[-1 + k]*Sqrt[-1 + k^2*x^2])] + Sqrt[-1 + k]*Sqrt[-((-1 + k)*k)]*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[k, ArcSin[x], k^2]))/(Sqrt[-1 + k]*Sqrt[-((-1 + k)*k)]*Sqrt[(-1 + x^2)*(-1 + k^2*x^2)])","C",1
688,1,208,54,0.2440776,"\int \frac{1+\sqrt{k} x}{\left(-1+\sqrt{k} x\right) \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}} \, dx","Integrate[(1 + Sqrt[k]*x)/((-1 + Sqrt[k]*x)*Sqrt[(1 - x^2)*(1 - k^2*x^2)]),x]","\frac{2 \sqrt{k} \sqrt{x^2-1} \sqrt{k^2 x^2-1} \tanh ^{-1}\left(\frac{\sqrt{-((k-1) k)} \sqrt{x^2-1}}{\sqrt{k-1} \sqrt{k^2 x^2-1}}\right)+\sqrt{k-1} \sqrt{-((k-1) k)} \sqrt{1-x^2} \sqrt{1-k^2 x^2} F\left(\sin ^{-1}(x)|k^2\right)-2 \sqrt{k-1} \sqrt{-((k-1) k)} \sqrt{1-x^2} \sqrt{1-k^2 x^2} \Pi \left(k;\sin ^{-1}(x)|k^2\right)}{\sqrt{k-1} \sqrt{-((k-1) k)} \sqrt{\left(x^2-1\right) \left(k^2 x^2-1\right)}}","-\frac{2 \tan ^{-1}\left(\frac{(k-1) x}{\sqrt{k^2 x^4+\left(-k^2-1\right) x^2+1}+k x^2-2 \sqrt{k} x+1}\right)}{k-1}",1,"(2*Sqrt[k]*Sqrt[-1 + x^2]*Sqrt[-1 + k^2*x^2]*ArcTanh[(Sqrt[-((-1 + k)*k)]*Sqrt[-1 + x^2])/(Sqrt[-1 + k]*Sqrt[-1 + k^2*x^2])] + Sqrt[-1 + k]*Sqrt[-((-1 + k)*k)]*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticF[ArcSin[x], k^2] - 2*Sqrt[-1 + k]*Sqrt[-((-1 + k)*k)]*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[k, ArcSin[x], k^2])/(Sqrt[-1 + k]*Sqrt[-((-1 + k)*k)]*Sqrt[(-1 + x^2)*(-1 + k^2*x^2)])","C",1
689,1,1148,54,1.054739,"\int \frac{2+x}{(-1+x) \sqrt{-1+3 x-a x^2+x^3}} \, dx","Integrate[(2 + x)/((-1 + x)*Sqrt[-1 + 3*x - a*x^2 + x^3]),x]","\frac{2 \sqrt{\frac{-x+\text{Root}\left[\text{$\#$1}^3+(3-a) \text{$\#$1}^2+(6-2 a) \text{$\#$1}-a+3\&,1\right]+1}{\text{Root}\left[\text{$\#$1}^3+(3-a) \text{$\#$1}^2+(6-2 a) \text{$\#$1}-a+3\&,1\right]-\text{Root}\left[\text{$\#$1}^3+(3-a) \text{$\#$1}^2+(6-2 a) \text{$\#$1}-a+3\&,3\right]}} \left(\frac{F\left(\sin ^{-1}\left(\sqrt{\frac{-x+\text{Root}\left[\text{$\#$1}^3+(3-a) \text{$\#$1}^2+(6-2 a) \text{$\#$1}-a+3\&,3\right]+1}{\text{Root}\left[\text{$\#$1}^3+(3-a) \text{$\#$1}^2+(6-2 a) \text{$\#$1}-a+3\&,3\right]-\text{Root}\left[\text{$\#$1}^3+(3-a) \text{$\#$1}^2+(6-2 a) \text{$\#$1}-a+3\&,2\right]}}\right)|\frac{\text{Root}\left[\text{$\#$1}^3+(3-a) \text{$\#$1}^2+(6-2 a) \text{$\#$1}-a+3\&,2\right]-\text{Root}\left[\text{$\#$1}^3+(3-a) \text{$\#$1}^2+(6-2 a) \text{$\#$1}-a+3\&,3\right]}{\text{Root}\left[\text{$\#$1}^3+(3-a) \text{$\#$1}^2+(6-2 a) \text{$\#$1}-a+3\&,1\right]-\text{Root}\left[\text{$\#$1}^3+(3-a) \text{$\#$1}^2+(6-2 a) \text{$\#$1}-a+3\&,3\right]}\right) \sqrt{\frac{-x+\text{Root}\left[\text{$\#$1}^3+(3-a) \text{$\#$1}^2+(6-2 a) \text{$\#$1}-a+3\&,2\right]+1}{\text{Root}\left[\text{$\#$1}^3+(3-a) \text{$\#$1}^2+(6-2 a) \text{$\#$1}-a+3\&,2\right]-\text{Root}\left[\text{$\#$1}^3+(3-a) \text{$\#$1}^2+(6-2 a) \text{$\#$1}-a+3\&,3\right]}} \left(x-\text{Root}\left[\text{$\#$1}^3+(3-a) \text{$\#$1}^2+(6-2 a) \text{$\#$1}-a+3\&,3\right]-1\right)}{\sqrt{\frac{-x+\text{Root}\left[\text{$\#$1}^3+(3-a) \text{$\#$1}^2+(6-2 a) \text{$\#$1}-a+3\&,3\right]+1}{\text{Root}\left[\text{$\#$1}^3+(3-a) \text{$\#$1}^2+(6-2 a) \text{$\#$1}-a+3\&,3\right]-\text{Root}\left[\text{$\#$1}^3+(3-a) \text{$\#$1}^2+(6-2 a) \text{$\#$1}-a+3\&,2\right]}}}+\frac{3 \Pi \left(1-\frac{\text{Root}\left[\text{$\#$1}^3+(3-a) \text{$\#$1}^2+(6-2 a) \text{$\#$1}-a+3\&,2\right]}{\text{Root}\left[\text{$\#$1}^3+(3-a) \text{$\#$1}^2+(6-2 a) \text{$\#$1}-a+3\&,3\right]};\sin ^{-1}\left(\sqrt{\frac{-x+\text{Root}\left[\text{$\#$1}^3+(3-a) \text{$\#$1}^2+(6-2 a) \text{$\#$1}-a+3\&,3\right]+1}{\text{Root}\left[\text{$\#$1}^3+(3-a) \text{$\#$1}^2+(6-2 a) \text{$\#$1}-a+3\&,3\right]-\text{Root}\left[\text{$\#$1}^3+(3-a) \text{$\#$1}^2+(6-2 a) \text{$\#$1}-a+3\&,2\right]}}\right)|\frac{\text{Root}\left[\text{$\#$1}^3+(3-a) \text{$\#$1}^2+(6-2 a) \text{$\#$1}-a+3\&,2\right]-\text{Root}\left[\text{$\#$1}^3+(3-a) \text{$\#$1}^2+(6-2 a) \text{$\#$1}-a+3\&,3\right]}{\text{Root}\left[\text{$\#$1}^3+(3-a) \text{$\#$1}^2+(6-2 a) \text{$\#$1}-a+3\&,1\right]-\text{Root}\left[\text{$\#$1}^3+(3-a) \text{$\#$1}^2+(6-2 a) \text{$\#$1}-a+3\&,3\right]}\right) \sqrt{-\frac{\left(x-\text{Root}\left[\text{$\#$1}^3+(3-a) \text{$\#$1}^2+(6-2 a) \text{$\#$1}-a+3\&,2\right]-1\right) \left(x-\text{Root}\left[\text{$\#$1}^3+(3-a) \text{$\#$1}^2+(6-2 a) \text{$\#$1}-a+3\&,3\right]-1\right)}{\left(\text{Root}\left[\text{$\#$1}^3+(3-a) \text{$\#$1}^2+(6-2 a) \text{$\#$1}-a+3\&,2\right]-\text{Root}\left[\text{$\#$1}^3+(3-a) \text{$\#$1}^2+(6-2 a) \text{$\#$1}-a+3\&,3\right]\right)^2}} \left(\text{Root}\left[\text{$\#$1}^3+(3-a) \text{$\#$1}^2+(6-2 a) \text{$\#$1}-a+3\&,2\right]-\text{Root}\left[\text{$\#$1}^3+(3-a) \text{$\#$1}^2+(6-2 a) \text{$\#$1}-a+3\&,3\right]\right)}{\text{Root}\left[\text{$\#$1}^3+(3-a) \text{$\#$1}^2+(6-2 a) \text{$\#$1}-a+3\&,3\right]}\right)}{\sqrt{x^3-a x^2+3 x-1}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{a-3} x \sqrt{-a x^2+x^3+3 x-1}}{a x^2-x^3-3 x+1}\right)}{\sqrt{a-3}}",1,"(2*Sqrt[(1 - x + Root[3 - a + (6 - 2*a)*#1 + (3 - a)*#1^2 + #1^3 & , 1])/(Root[3 - a + (6 - 2*a)*#1 + (3 - a)*#1^2 + #1^3 & , 1] - Root[3 - a + (6 - 2*a)*#1 + (3 - a)*#1^2 + #1^3 & , 3])]*((3*EllipticPi[1 - Root[3 - a + (6 - 2*a)*#1 + (3 - a)*#1^2 + #1^3 & , 2]/Root[3 - a + (6 - 2*a)*#1 + (3 - a)*#1^2 + #1^3 & , 3], ArcSin[Sqrt[(1 - x + Root[3 - a + (6 - 2*a)*#1 + (3 - a)*#1^2 + #1^3 & , 3])/(-Root[3 - a + (6 - 2*a)*#1 + (3 - a)*#1^2 + #1^3 & , 2] + Root[3 - a + (6 - 2*a)*#1 + (3 - a)*#1^2 + #1^3 & , 3])]], (Root[3 - a + (6 - 2*a)*#1 + (3 - a)*#1^2 + #1^3 & , 2] - Root[3 - a + (6 - 2*a)*#1 + (3 - a)*#1^2 + #1^3 & , 3])/(Root[3 - a + (6 - 2*a)*#1 + (3 - a)*#1^2 + #1^3 & , 1] - Root[3 - a + (6 - 2*a)*#1 + (3 - a)*#1^2 + #1^3 & , 3])]*Sqrt[-(((-1 + x - Root[3 - a + (6 - 2*a)*#1 + (3 - a)*#1^2 + #1^3 & , 2])*(-1 + x - Root[3 - a + (6 - 2*a)*#1 + (3 - a)*#1^2 + #1^3 & , 3]))/(Root[3 - a + (6 - 2*a)*#1 + (3 - a)*#1^2 + #1^3 & , 2] - Root[3 - a + (6 - 2*a)*#1 + (3 - a)*#1^2 + #1^3 & , 3])^2)]*(Root[3 - a + (6 - 2*a)*#1 + (3 - a)*#1^2 + #1^3 & , 2] - Root[3 - a + (6 - 2*a)*#1 + (3 - a)*#1^2 + #1^3 & , 3]))/Root[3 - a + (6 - 2*a)*#1 + (3 - a)*#1^2 + #1^3 & , 3] + (EllipticF[ArcSin[Sqrt[(1 - x + Root[3 - a + (6 - 2*a)*#1 + (3 - a)*#1^2 + #1^3 & , 3])/(-Root[3 - a + (6 - 2*a)*#1 + (3 - a)*#1^2 + #1^3 & , 2] + Root[3 - a + (6 - 2*a)*#1 + (3 - a)*#1^2 + #1^3 & , 3])]], (Root[3 - a + (6 - 2*a)*#1 + (3 - a)*#1^2 + #1^3 & , 2] - Root[3 - a + (6 - 2*a)*#1 + (3 - a)*#1^2 + #1^3 & , 3])/(Root[3 - a + (6 - 2*a)*#1 + (3 - a)*#1^2 + #1^3 & , 1] - Root[3 - a + (6 - 2*a)*#1 + (3 - a)*#1^2 + #1^3 & , 3])]*(-1 + x - Root[3 - a + (6 - 2*a)*#1 + (3 - a)*#1^2 + #1^3 & , 3])*Sqrt[(1 - x + Root[3 - a + (6 - 2*a)*#1 + (3 - a)*#1^2 + #1^3 & , 2])/(Root[3 - a + (6 - 2*a)*#1 + (3 - a)*#1^2 + #1^3 & , 2] - Root[3 - a + (6 - 2*a)*#1 + (3 - a)*#1^2 + #1^3 & , 3])])/Sqrt[(1 - x + Root[3 - a + (6 - 2*a)*#1 + (3 - a)*#1^2 + #1^3 & , 3])/(-Root[3 - a + (6 - 2*a)*#1 + (3 - a)*#1^2 + #1^3 & , 2] + Root[3 - a + (6 - 2*a)*#1 + (3 - a)*#1^2 + #1^3 & , 3])]))/Sqrt[-1 + 3*x - a*x^2 + x^3]","C",0
690,1,933,54,0.8013307,"\int \frac{-2+x}{(1+x) \sqrt{1+3 x-a x^2+x^3}} \, dx","Integrate[(-2 + x)/((1 + x)*Sqrt[1 + 3*x - a*x^2 + x^3]),x]","\frac{2 \sqrt{-\frac{\left(x-\text{Root}\left[\text{$\#$1}^3+(-a-3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}-a-3\&,2\right]+1\right) \left(x-\text{Root}\left[\text{$\#$1}^3+(-a-3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}-a-3\&,3\right]+1\right)}{\left(\text{Root}\left[\text{$\#$1}^3+(-a-3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}-a-3\&,2\right]-\text{Root}\left[\text{$\#$1}^3+(-a-3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}-a-3\&,3\right]\right)^2}} \left(\text{Root}\left[\text{$\#$1}^3+(-a-3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}-a-3\&,2\right]-\text{Root}\left[\text{$\#$1}^3+(-a-3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}-a-3\&,3\right]\right) \sqrt{\frac{x-\text{Root}\left[\text{$\#$1}^3+(-a-3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}-a-3\&,1\right]+1}{\text{Root}\left[\text{$\#$1}^3+(-a-3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}-a-3\&,3\right]-\text{Root}\left[\text{$\#$1}^3+(-a-3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}-a-3\&,1\right]}} \left(F\left(\sin ^{-1}\left(\sqrt{\frac{x-\text{Root}\left[\text{$\#$1}^3+(-a-3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}-a-3\&,3\right]+1}{\text{Root}\left[\text{$\#$1}^3+(-a-3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}-a-3\&,2\right]-\text{Root}\left[\text{$\#$1}^3+(-a-3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}-a-3\&,3\right]}}\right)|\frac{\text{Root}\left[\text{$\#$1}^3+(-a-3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}-a-3\&,2\right]-\text{Root}\left[\text{$\#$1}^3+(-a-3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}-a-3\&,3\right]}{\text{Root}\left[\text{$\#$1}^3+(-a-3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}-a-3\&,1\right]-\text{Root}\left[\text{$\#$1}^3+(-a-3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}-a-3\&,3\right]}\right) \text{Root}\left[\text{$\#$1}^3+(-a-3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}-a-3\&,3\right]-3 \Pi \left(1-\frac{\text{Root}\left[\text{$\#$1}^3+(-a-3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}-a-3\&,2\right]}{\text{Root}\left[\text{$\#$1}^3+(-a-3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}-a-3\&,3\right]};\sin ^{-1}\left(\sqrt{\frac{x-\text{Root}\left[\text{$\#$1}^3+(-a-3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}-a-3\&,3\right]+1}{\text{Root}\left[\text{$\#$1}^3+(-a-3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}-a-3\&,2\right]-\text{Root}\left[\text{$\#$1}^3+(-a-3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}-a-3\&,3\right]}}\right)|\frac{\text{Root}\left[\text{$\#$1}^3+(-a-3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}-a-3\&,2\right]-\text{Root}\left[\text{$\#$1}^3+(-a-3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}-a-3\&,3\right]}{\text{Root}\left[\text{$\#$1}^3+(-a-3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}-a-3\&,1\right]-\text{Root}\left[\text{$\#$1}^3+(-a-3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}-a-3\&,3\right]}\right)\right)}{\sqrt{x^3-a x^2+3 x+1} \text{Root}\left[\text{$\#$1}^3+(-a-3) \text{$\#$1}^2+(2 a+6) \text{$\#$1}-a-3\&,3\right]}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{a+3} x \sqrt{-a x^2+x^3+3 x+1}}{a x^2-x^3-3 x-1}\right)}{\sqrt{a+3}}",1,"(2*Sqrt[-(((1 + x - Root[-3 - a + (6 + 2*a)*#1 + (-3 - a)*#1^2 + #1^3 & , 2])*(1 + x - Root[-3 - a + (6 + 2*a)*#1 + (-3 - a)*#1^2 + #1^3 & , 3]))/(Root[-3 - a + (6 + 2*a)*#1 + (-3 - a)*#1^2 + #1^3 & , 2] - Root[-3 - a + (6 + 2*a)*#1 + (-3 - a)*#1^2 + #1^3 & , 3])^2)]*(Root[-3 - a + (6 + 2*a)*#1 + (-3 - a)*#1^2 + #1^3 & , 2] - Root[-3 - a + (6 + 2*a)*#1 + (-3 - a)*#1^2 + #1^3 & , 3])*Sqrt[(1 + x - Root[-3 - a + (6 + 2*a)*#1 + (-3 - a)*#1^2 + #1^3 & , 1])/(-Root[-3 - a + (6 + 2*a)*#1 + (-3 - a)*#1^2 + #1^3 & , 1] + Root[-3 - a + (6 + 2*a)*#1 + (-3 - a)*#1^2 + #1^3 & , 3])]*(-3*EllipticPi[1 - Root[-3 - a + (6 + 2*a)*#1 + (-3 - a)*#1^2 + #1^3 & , 2]/Root[-3 - a + (6 + 2*a)*#1 + (-3 - a)*#1^2 + #1^3 & , 3], ArcSin[Sqrt[(1 + x - Root[-3 - a + (6 + 2*a)*#1 + (-3 - a)*#1^2 + #1^3 & , 3])/(Root[-3 - a + (6 + 2*a)*#1 + (-3 - a)*#1^2 + #1^3 & , 2] - Root[-3 - a + (6 + 2*a)*#1 + (-3 - a)*#1^2 + #1^3 & , 3])]], (Root[-3 - a + (6 + 2*a)*#1 + (-3 - a)*#1^2 + #1^3 & , 2] - Root[-3 - a + (6 + 2*a)*#1 + (-3 - a)*#1^2 + #1^3 & , 3])/(Root[-3 - a + (6 + 2*a)*#1 + (-3 - a)*#1^2 + #1^3 & , 1] - Root[-3 - a + (6 + 2*a)*#1 + (-3 - a)*#1^2 + #1^3 & , 3])] + EllipticF[ArcSin[Sqrt[(1 + x - Root[-3 - a + (6 + 2*a)*#1 + (-3 - a)*#1^2 + #1^3 & , 3])/(Root[-3 - a + (6 + 2*a)*#1 + (-3 - a)*#1^2 + #1^3 & , 2] - Root[-3 - a + (6 + 2*a)*#1 + (-3 - a)*#1^2 + #1^3 & , 3])]], (Root[-3 - a + (6 + 2*a)*#1 + (-3 - a)*#1^2 + #1^3 & , 2] - Root[-3 - a + (6 + 2*a)*#1 + (-3 - a)*#1^2 + #1^3 & , 3])/(Root[-3 - a + (6 + 2*a)*#1 + (-3 - a)*#1^2 + #1^3 & , 1] - Root[-3 - a + (6 + 2*a)*#1 + (-3 - a)*#1^2 + #1^3 & , 3])]*Root[-3 - a + (6 + 2*a)*#1 + (-3 - a)*#1^2 + #1^3 & , 3]))/(Sqrt[1 + 3*x - a*x^2 + x^3]*Root[-3 - a + (6 + 2*a)*#1 + (-3 - a)*#1^2 + #1^3 & , 3])","C",1
691,1,34,54,0.0097099,"\int \frac{\left(-1+x^4\right) \sqrt[4]{1+x^4}}{x^2} \, dx","Integrate[((-1 + x^4)*(1 + x^4)^(1/4))/x^2,x]","\frac{\left(x^4+1\right)^{5/4}}{x}-x^3 \, _2F_1\left(-\frac{1}{4},\frac{3}{4};\frac{7}{4};-x^4\right)","\frac{\sqrt[4]{x^4+1} \left(x^4+4\right)}{4 x}+\frac{3}{8} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)-\frac{3}{8} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)",1,"(1 + x^4)^(5/4)/x - x^3*Hypergeometric2F1[-1/4, 3/4, 7/4, -x^4]","C",1
692,0,0,54,0.2346758,"\int \frac{2 b+a x^2}{\sqrt[4]{b+a x^2} \left(-2 b-2 a x^2+x^4\right)} \, dx","Integrate[(2*b + a*x^2)/((b + a*x^2)^(1/4)*(-2*b - 2*a*x^2 + x^4)),x]","\int \frac{2 b+a x^2}{\sqrt[4]{b+a x^2} \left(-2 b-2 a x^2+x^4\right)} \, dx","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a x^2+b}}{x}\right)}{2^{3/4}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt[4]{2} \sqrt[4]{a x^2+b}}\right)}{2^{3/4}}",1,"Integrate[(2*b + a*x^2)/((b + a*x^2)^(1/4)*(-2*b - 2*a*x^2 + x^4)), x]","F",-1
693,1,35,54,0.0103306,"\int \frac{\sqrt[4]{-x^3+x^4}}{x} \, dx","Integrate[(-x^3 + x^4)^(1/4)/x,x]","\frac{4 \left((x-1) x^3\right)^{5/4} \, _2F_1\left(\frac{1}{4},\frac{5}{4};\frac{9}{4};1-x\right)}{5 x^{15/4}}","\sqrt[4]{x^4-x^3}+\frac{1}{2} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^3}}\right)-\frac{1}{2} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^3}}\right)",1,"(4*((-1 + x)*x^3)^(5/4)*Hypergeometric2F1[1/4, 5/4, 9/4, 1 - x])/(5*x^(15/4))","C",1
694,1,37,54,0.0213614,"\int \frac{\left(-1+x^3\right) \sqrt{-1+x^6}}{x^{13}} \, dx","Integrate[((-1 + x^3)*Sqrt[-1 + x^6])/x^13,x]","-\frac{\left(x^6-1\right)^{3/2} \left(x^9 \, _2F_1\left(\frac{3}{2},3;\frac{5}{2};1-x^6\right)-1\right)}{9 x^9}","\frac{1}{12} \tan ^{-1}\left(\frac{x^3+1}{\sqrt{x^6-1}}\right)+\frac{\sqrt{x^6-1} \left(8 x^9-3 x^6-8 x^3+6\right)}{72 x^{12}}",1,"-1/9*((-1 + x^6)^(3/2)*(-1 + x^9*Hypergeometric2F1[3/2, 3, 5/2, 1 - x^6]))/x^9","C",1
695,0,0,54,0.4131451,"\int \frac{\left(2+x^3\right) \sqrt[3]{x-x^4}}{1+x^2-2 x^3-x^4-x^5+x^6} \, dx","Integrate[((2 + x^3)*(x - x^4)^(1/3))/(1 + x^2 - 2*x^3 - x^4 - x^5 + x^6),x]","\int \frac{\left(2+x^3\right) \sqrt[3]{x-x^4}}{1+x^2-2 x^3-x^4-x^5+x^6} \, dx","-\text{RootSum}\left[\text{$\#$1}^6+\text{$\#$1}^3-1\&,\frac{\text{$\#$1} \log \left(\sqrt[3]{x-x^4}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{2 \text{$\#$1}^3+1}\&\right]",1,"Integrate[((2 + x^3)*(x - x^4)^(1/3))/(1 + x^2 - 2*x^3 - x^4 - x^5 + x^6), x]","F",-1
696,0,0,54,0.1159554,"\int \frac{\left(2+x^3\right) \sqrt[3]{x-x^4}}{1+x^2-2 x^3-x^4-x^5+x^6} \, dx","Integrate[((2 + x^3)*(x - x^4)^(1/3))/(1 + x^2 - 2*x^3 - x^4 - x^5 + x^6),x]","\int \frac{\left(2+x^3\right) \sqrt[3]{x-x^4}}{1+x^2-2 x^3-x^4-x^5+x^6} \, dx","-\text{RootSum}\left[\text{$\#$1}^6+\text{$\#$1}^3-1\&,\frac{\text{$\#$1} \log \left(\sqrt[3]{x-x^4}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{2 \text{$\#$1}^3+1}\&\right]",1,"Integrate[((2 + x^3)*(x - x^4)^(1/3))/(1 + x^2 - 2*x^3 - x^4 - x^5 + x^6), x]","F",-1
697,1,70,54,0.031868,"\int \frac{1}{\sqrt[8]{1+2 x^4+x^8}} \, dx","Integrate[(1 + 2*x^4 + x^8)^(-1/8),x]","\frac{\sqrt[4]{x^4+1} \left(-\log \left(1-\frac{x}{\sqrt[4]{x^4+1}}\right)+\log \left(\frac{x}{\sqrt[4]{x^4+1}}+1\right)+2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)\right)}{4 \sqrt[8]{\left(x^4+1\right)^2}}","\frac{\left(\left(x^4+1\right)^2\right)^{7/8} \left(\frac{1}{2} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)+\frac{1}{2} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)\right)}{\left(x^4+1\right)^{7/4}}",1,"((1 + x^4)^(1/4)*(2*ArcTan[x/(1 + x^4)^(1/4)] - Log[1 - x/(1 + x^4)^(1/4)] + Log[1 + x/(1 + x^4)^(1/4)]))/(4*((1 + x^4)^2)^(1/8))","A",1
698,1,175,54,0.9177967,"\int \frac{1}{x \sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[1/(x*Sqrt[x + Sqrt[1 + x^2]]),x]","\frac{2}{3} \sqrt{\sqrt{x^2+1}+x} \left(-\frac{\sqrt{x^2+1} \left(\sqrt{x^2+1}+x\right)^4 \left(\left(4 x^2+4 \sqrt{x^2+1} x+2\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\left(x+\sqrt{x^2+1}\right)^2\right)-x^2-\sqrt{x^2+1} x-2\right)}{16 x^6+28 x^4+13 x^2+5 \sqrt{x^2+1} x+16 \sqrt{x^2+1} x^5+20 \sqrt{x^2+1} x^3+1}+\sqrt{x^2+1}-2 x\right)","\frac{2}{\sqrt{\sqrt{x^2+1}+x}}+2 \tan ^{-1}\left(\sqrt{\sqrt{x^2+1}+x}\right)-2 \tanh ^{-1}\left(\sqrt{\sqrt{x^2+1}+x}\right)",1,"(2*Sqrt[x + Sqrt[1 + x^2]]*(-2*x + Sqrt[1 + x^2] - (Sqrt[1 + x^2]*(x + Sqrt[1 + x^2])^4*(-2 - x^2 - x*Sqrt[1 + x^2] + (2 + 4*x^2 + 4*x*Sqrt[1 + x^2])*Hypergeometric2F1[3/4, 1, 7/4, (x + Sqrt[1 + x^2])^2]))/(1 + 13*x^2 + 28*x^4 + 16*x^6 + 5*x*Sqrt[1 + x^2] + 20*x^3*Sqrt[1 + x^2] + 16*x^5*Sqrt[1 + x^2])))/3","C",1
699,1,202,55,2.9155232,"\int \frac{1-2 x+k^2 x^2}{\sqrt{(1-x) x \left(1-k^2 x\right)} \left(-1+2 x+\left(-2+k^2\right) x^2\right)} \, dx","Integrate[(1 - 2*x + k^2*x^2)/(Sqrt[(1 - x)*x*(1 - k^2*x)]*(-1 + 2*x + (-2 + k^2)*x^2)),x]","\frac{2 i \sqrt{\frac{1}{x-1}+1} (x-1)^{3/2} \sqrt{\frac{1-\frac{1}{k^2}}{x-1}+1} \left(\left(k^2-2\right) F\left(i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)+\left(\sqrt{k^2-1}+1\right) \Pi \left(\frac{k^2-1}{k^2-\sqrt{k^2-1}-1};i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)-\left(\sqrt{k^2-1}-1\right) \Pi \left(\frac{k^2-1}{k^2+\sqrt{k^2-1}-1};i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)\right)}{\left(k^2-2\right) \sqrt{(x-1) x \left(k^2 x-1\right)}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{k^2-2} \sqrt{k^2 x^3+\left(-k^2-1\right) x^2+x}}{k^2 x-1}\right)}{\sqrt{k^2-2}}",1,"((2*I)*Sqrt[1 + (-1 + x)^(-1)]*Sqrt[1 + (1 - k^(-2))/(-1 + x)]*(-1 + x)^(3/2)*((-2 + k^2)*EllipticF[I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)] + (1 + Sqrt[-1 + k^2])*EllipticPi[(-1 + k^2)/(-1 + k^2 - Sqrt[-1 + k^2]), I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)] - (-1 + Sqrt[-1 + k^2])*EllipticPi[(-1 + k^2)/(-1 + k^2 + Sqrt[-1 + k^2]), I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)]))/((-2 + k^2)*Sqrt[(-1 + x)*x*(-1 + k^2*x)])","C",1
700,1,46,55,0.01181,"\int \frac{1}{x \left(b+a x^3\right)^{3/4}} \, dx","Integrate[1/(x*(b + a*x^3)^(3/4)),x]","-\frac{2 \left(\tan ^{-1}\left(\frac{\sqrt[4]{a x^3+b}}{\sqrt[4]{b}}\right)+\tanh ^{-1}\left(\frac{\sqrt[4]{a x^3+b}}{\sqrt[4]{b}}\right)\right)}{3 b^{3/4}}","-\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{a x^3+b}}{\sqrt[4]{b}}\right)}{3 b^{3/4}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{a x^3+b}}{\sqrt[4]{b}}\right)}{3 b^{3/4}}",1,"(-2*(ArcTan[(b + a*x^3)^(1/4)/b^(1/4)] + ArcTanh[(b + a*x^3)^(1/4)/b^(1/4)]))/(3*b^(3/4))","A",1
701,1,54,55,0.0326081,"\int \frac{\left(-b+a x^3\right) \sqrt{b+a x^3}}{x^4} \, dx","Integrate[((-b + a*x^3)*Sqrt[b + a*x^3])/x^4,x]","\frac{1}{3} \left(\frac{\sqrt{a x^3+b} \left(2 a x^3+b\right)}{x^3}-a \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{a x^3+b}}{\sqrt{b}}\right)\right)","\frac{\sqrt{a x^3+b} \left(2 a x^3+b\right)}{3 x^3}-\frac{1}{3} a \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{a x^3+b}}{\sqrt{b}}\right)",1,"((Sqrt[b + a*x^3]*(b + 2*a*x^3))/x^3 - a*Sqrt[b]*ArcTanh[Sqrt[b + a*x^3]/Sqrt[b]])/3","A",1
702,1,202,55,0.7643535,"\int \frac{1-2 x+k^2 x^2}{\left(-1+2 x-2 x^2+k^2 x^2\right) \sqrt{x-x^2-k^2 x^2+k^2 x^3}} \, dx","Integrate[(1 - 2*x + k^2*x^2)/((-1 + 2*x - 2*x^2 + k^2*x^2)*Sqrt[x - x^2 - k^2*x^2 + k^2*x^3]),x]","\frac{2 i \sqrt{\frac{1}{x-1}+1} (x-1)^{3/2} \sqrt{\frac{1-\frac{1}{k^2}}{x-1}+1} \left(\left(k^2-2\right) F\left(i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)+\left(\sqrt{k^2-1}+1\right) \Pi \left(\frac{k^2-1}{k^2-\sqrt{k^2-1}-1};i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)-\left(\sqrt{k^2-1}-1\right) \Pi \left(\frac{k^2-1}{k^2+\sqrt{k^2-1}-1};i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)\right)}{\left(k^2-2\right) \sqrt{(x-1) x \left(k^2 x-1\right)}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{k^2-2} \sqrt{k^2 x^3+\left(-k^2-1\right) x^2+x}}{k^2 x-1}\right)}{\sqrt{k^2-2}}",1,"((2*I)*Sqrt[1 + (-1 + x)^(-1)]*Sqrt[1 + (1 - k^(-2))/(-1 + x)]*(-1 + x)^(3/2)*((-2 + k^2)*EllipticF[I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)] + (1 + Sqrt[-1 + k^2])*EllipticPi[(-1 + k^2)/(-1 + k^2 - Sqrt[-1 + k^2]), I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)] - (-1 + Sqrt[-1 + k^2])*EllipticPi[(-1 + k^2)/(-1 + k^2 + Sqrt[-1 + k^2]), I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)]))/((-2 + k^2)*Sqrt[(-1 + x)*x*(-1 + k^2*x)])","C",1
703,1,55,55,0.0191344,"\int \frac{2+x}{x \sqrt[4]{1+x^4}} \, dx","Integrate[(2 + x)/(x*(1 + x^4)^(1/4)),x]","\frac{1}{2} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)+\tan ^{-1}\left(\sqrt[4]{x^4+1}\right)+\frac{1}{2} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)-\tanh ^{-1}\left(\sqrt[4]{x^4+1}\right)","\frac{1}{2} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)+\tan ^{-1}\left(\sqrt[4]{x^4+1}\right)+\frac{1}{2} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)-\tanh ^{-1}\left(\sqrt[4]{x^4+1}\right)",1,"ArcTan[x/(1 + x^4)^(1/4)]/2 + ArcTan[(1 + x^4)^(1/4)] + ArcTanh[x/(1 + x^4)^(1/4)]/2 - ArcTanh[(1 + x^4)^(1/4)]","A",1
704,1,34,55,0.0087455,"\int x^6 \sqrt[4]{1+x^4} \, dx","Integrate[x^6*(1 + x^4)^(1/4),x]","\frac{1}{8} x^3 \left(\left(x^4+1\right)^{5/4}-\, _2F_1\left(-\frac{1}{4},\frac{3}{4};\frac{7}{4};-x^4\right)\right)","\frac{3}{64} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)-\frac{3}{64} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)+\frac{1}{32} \sqrt[4]{x^4+1} \left(4 x^7+x^3\right)",1,"(x^3*((1 + x^4)^(5/4) - Hypergeometric2F1[-1/4, 3/4, 7/4, -x^4]))/8","C",1
705,1,42,55,0.0083337,"\int \frac{\sqrt[4]{-x+x^4}}{x^2} \, dx","Integrate[(-x + x^4)^(1/4)/x^2,x]","-\frac{4 \sqrt[4]{x \left(x^3-1\right)} \, _2F_1\left(-\frac{1}{4},-\frac{1}{4};\frac{3}{4};x^3\right)}{3 x \sqrt[4]{1-x^3}}","-\frac{4 \sqrt[4]{x^4-x}}{3 x}-\frac{2}{3} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x}}\right)+\frac{2}{3} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x}}\right)",1,"(-4*(x*(-1 + x^3))^(1/4)*Hypergeometric2F1[-1/4, -1/4, 3/4, x^3])/(3*x*(1 - x^3)^(1/4))","C",1
706,1,42,55,0.0066241,"\int x \sqrt[4]{-x+x^4} \, dx","Integrate[x*(-x + x^4)^(1/4),x]","\frac{4 x^2 \sqrt[4]{x \left(x^3-1\right)} \, _2F_1\left(-\frac{1}{4},\frac{3}{4};\frac{7}{4};x^3\right)}{9 \sqrt[4]{1-x^3}}","\frac{1}{6} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x}}\right)-\frac{1}{6} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x}}\right)+\frac{1}{3} \sqrt[4]{x^4-x} x^2",1,"(4*x^2*(x*(-1 + x^3))^(1/4)*Hypergeometric2F1[-1/4, 3/4, 7/4, x^3])/(9*(1 - x^3)^(1/4))","C",1
707,1,68,55,0.0362606,"\int \frac{\left(-b+a x^3\right) \sqrt{-x+x^4}}{x^3} \, dx","Integrate[((-b + a*x^3)*Sqrt[-x + x^4])/x^3,x]","\frac{\sqrt{x \left(x^3-1\right)} \left(x^{3/2} (a+2 b) \sin ^{-1}\left(x^{3/2}\right)+\sqrt{1-x^3} \left(a x^3+2 b\right)\right)}{3 x^2 \sqrt{1-x^3}}","\frac{1}{3} (-a-2 b) \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4-x}}\right)+\frac{\sqrt{x^4-x} \left(a x^3+2 b\right)}{3 x^2}",1,"(Sqrt[x*(-1 + x^3)]*(Sqrt[1 - x^3]*(2*b + a*x^3) + (a + 2*b)*x^(3/2)*ArcSin[x^(3/2)]))/(3*x^2*Sqrt[1 - x^3])","A",1
708,1,35,55,0.0104473,"\int \frac{\sqrt[4]{-x^3+x^4}}{x^2} \, dx","Integrate[(-x^3 + x^4)^(1/4)/x^2,x]","\frac{4 \left((x-1) x^3\right)^{5/4} \, _2F_1\left(\frac{5}{4},\frac{5}{4};\frac{9}{4};1-x\right)}{5 x^{15/4}}","-\frac{4 \sqrt[4]{x^4-x^3}}{x}-2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^3}}\right)+2 \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^3}}\right)",1,"(4*((-1 + x)*x^3)^(5/4)*Hypergeometric2F1[5/4, 5/4, 9/4, 1 - x])/(5*x^(15/4))","C",1
709,1,1522,55,0.8806561,"\int \frac{x}{\sqrt{-17+18 x-11 x^2+6 x^3+x^4}} \, dx","Integrate[x/Sqrt[-17 + 18*x - 11*x^2 + 6*x^3 + x^4],x]","-\frac{2 \left(x-\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,1\right]\right) \left(x-\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,2\right]\right) \left(\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,2\right] F\left(\sin ^{-1}\left(\sqrt{\frac{\left(x-\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,1\right]\right) \left(\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,2\right]-\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,4\right]\right)}{\left(x-\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,2\right]\right) \left(\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,1\right]-\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,4\right]\right)}}\right)|-\frac{\left(\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,2\right]-\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,3\right]\right) \left(\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,1\right]-\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,4\right]\right)}{\left(-\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,1\right]+\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,3\right]\right) \left(\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,2\right]-\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,4\right]\right)}\right)+\Pi \left(\frac{\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,1\right]-\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,4\right]}{\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,2\right]-\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,4\right]};\sin ^{-1}\left(\sqrt{\frac{\left(x-\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,1\right]\right) \left(\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,2\right]-\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,4\right]\right)}{\left(x-\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,2\right]\right) \left(\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,1\right]-\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,4\right]\right)}}\right)|-\frac{\left(\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,2\right]-\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,3\right]\right) \left(\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,1\right]-\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,4\right]\right)}{\left(-\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,1\right]+\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,3\right]\right) \left(\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,2\right]-\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,4\right]\right)}\right) \left(\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,1\right]-\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,2\right]\right)\right) \sqrt{\frac{x-\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,3\right]}{\left(x-\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,2\right]\right) \left(-\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,1\right]+\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,3\right]\right)}} \sqrt{\frac{x-\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,4\right]}{\left(x-\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,2\right]\right) \left(-\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,1\right]+\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,4\right]\right)}}}{\sqrt{x^4+6 x^3-11 x^2+18 x-17} \sqrt{\frac{\left(x-\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,1\right]\right) \left(\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,2\right]-\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,4\right]\right)}{\left(x-\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,2\right]\right) \left(\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,1\right]-\text{Root}\left[\text{$\#$1}^4+6 \text{$\#$1}^3-11 \text{$\#$1}^2+18 \text{$\#$1}-17\&,4\right]\right)}}}","-\frac{1}{4} \log \left(-2 x^4-24 x^3-68 x^2+\left(2 x^2+18 x+34\right) \sqrt{x^4+6 x^3-11 x^2+18 x-17}-11\right)",1,"(-2*(x - Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 1, 0])*(x - Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 2, 0])*(EllipticPi[(Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 1, 0] - Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 4, 0])/(Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 2, 0] - Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 4, 0]), ArcSin[Sqrt[((x - Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 1, 0])*(Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 2, 0] - Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 4, 0]))/((x - Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 2, 0])*(Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 1, 0] - Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 4, 0]))]], -(((Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 2, 0] - Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 3, 0])*(Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 1, 0] - Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 4, 0]))/((-Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 1, 0] + Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 3, 0])*(Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 2, 0] - Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 4, 0])))]*(Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 1, 0] - Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 2, 0]) + EllipticF[ArcSin[Sqrt[((x - Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 1, 0])*(Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 2, 0] - Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 4, 0]))/((x - Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 2, 0])*(Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 1, 0] - Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 4, 0]))]], -(((Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 2, 0] - Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 3, 0])*(Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 1, 0] - Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 4, 0]))/((-Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 1, 0] + Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 3, 0])*(Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 2, 0] - Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 4, 0])))]*Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 2, 0])*Sqrt[(x - Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 3, 0])/((x - Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 2, 0])*(-Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 1, 0] + Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 3, 0]))]*Sqrt[(x - Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 4, 0])/((x - Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 2, 0])*(-Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 1, 0] + Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 4, 0]))])/(Sqrt[-17 + 18*x - 11*x^2 + 6*x^3 + x^4]*Sqrt[((x - Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 1, 0])*(Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 2, 0] - Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 4, 0]))/((x - Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 2, 0])*(Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 1, 0] - Root[-17 + 18*#1 - 11*#1^2 + 6*#1^3 + #1^4 & , 4, 0]))])","C",1
710,1,59389,55,6.6638923,"\int \frac{\sqrt{-1-x-x^2+x^4} \left(2+x+2 x^4\right)}{\left(-1-x+x^4\right) \left(-1-x+x^2+x^4\right)} \, dx","Integrate[(Sqrt[-1 - x - x^2 + x^4]*(2 + x + 2*x^4))/((-1 - x + x^4)*(-1 - x + x^2 + x^4)),x]","\text{Result too large to show}","2 \tan ^{-1}\left(\frac{x}{\sqrt{x^4-x^2-x-1}}\right)-2 \sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4-x^2-x-1}}\right)",1,"Result too large to show","C",0
711,1,46,55,0.0116221,"\int \frac{1}{x \left(b+a x^4\right)^{3/4}} \, dx","Integrate[1/(x*(b + a*x^4)^(3/4)),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a x^4+b}}{\sqrt[4]{b}}\right)+\tanh ^{-1}\left(\frac{\sqrt[4]{a x^4+b}}{\sqrt[4]{b}}\right)}{2 b^{3/4}}","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a x^4+b}}{\sqrt[4]{b}}\right)}{2 b^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a x^4+b}}{\sqrt[4]{b}}\right)}{2 b^{3/4}}",1,"-1/2*(ArcTan[(b + a*x^4)^(1/4)/b^(1/4)] + ArcTanh[(b + a*x^4)^(1/4)/b^(1/4)])/b^(3/4)","A",1
712,1,48,55,0.0064658,"\int \frac{1}{x \sqrt[4]{b+a x^4}} \, dx","Integrate[1/(x*(b + a*x^4)^(1/4)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a x^4+b}}{\sqrt[4]{b}}\right)-\tanh ^{-1}\left(\frac{\sqrt[4]{a x^4+b}}{\sqrt[4]{b}}\right)}{2 \sqrt[4]{b}}","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a x^4+b}}{\sqrt[4]{b}}\right)}{2 \sqrt[4]{b}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a x^4+b}}{\sqrt[4]{b}}\right)}{2 \sqrt[4]{b}}",1,"(ArcTan[(b + a*x^4)^(1/4)/b^(1/4)] - ArcTanh[(b + a*x^4)^(1/4)/b^(1/4)])/(2*b^(1/4))","A",1
713,1,46,55,0.0098595,"\int \frac{1}{x \left(b+a x^5\right)^{3/4}} \, dx","Integrate[1/(x*(b + a*x^5)^(3/4)),x]","-\frac{2 \left(\tan ^{-1}\left(\frac{\sqrt[4]{a x^5+b}}{\sqrt[4]{b}}\right)+\tanh ^{-1}\left(\frac{\sqrt[4]{a x^5+b}}{\sqrt[4]{b}}\right)\right)}{5 b^{3/4}}","-\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{a x^5+b}}{\sqrt[4]{b}}\right)}{5 b^{3/4}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{a x^5+b}}{\sqrt[4]{b}}\right)}{5 b^{3/4}}",1,"(-2*(ArcTan[(b + a*x^5)^(1/4)/b^(1/4)] + ArcTanh[(b + a*x^5)^(1/4)/b^(1/4)]))/(5*b^(3/4))","A",1
714,1,77,55,0.0565795,"\int \frac{\left(1+2 x^3\right) \sqrt{-1+x^6}}{x} \, dx","Integrate[((1 + 2*x^3)*Sqrt[-1 + x^6])/x,x]","\frac{-\sqrt{-\left(x^6-1\right)^2} \tan ^{-1}\left(\sqrt{x^6-1}\right)+\left(x^3-1\right) \sqrt{1-x^6} \left(x^3+1\right)^2+\left(x^6-1\right) \sin ^{-1}\left(x^3\right)}{3 \sqrt{-\left(x^6-1\right)^2}}","\frac{1}{3} \sqrt{x^6-1} \left(x^3+1\right)-\frac{1}{3} \log \left(\sqrt{x^6-1}+x^3\right)-\frac{2}{3} \tan ^{-1}\left(\sqrt{x^6-1}+x^3\right)",1,"((-1 + x^3)*(1 + x^3)^2*Sqrt[1 - x^6] + (-1 + x^6)*ArcSin[x^3] - Sqrt[-(-1 + x^6)^2]*ArcTan[Sqrt[-1 + x^6]])/(3*Sqrt[-(-1 + x^6)^2])","A",0
715,0,0,55,0.4208003,"\int \frac{\left(-2+x^3\right) \sqrt[3]{x+x^3+x^4}}{1+x^2+2 x^3+x^4+x^5+x^6} \, dx","Integrate[((-2 + x^3)*(x + x^3 + x^4)^(1/3))/(1 + x^2 + 2*x^3 + x^4 + x^5 + x^6),x]","\int \frac{\left(-2+x^3\right) \sqrt[3]{x+x^3+x^4}}{1+x^2+2 x^3+x^4+x^5+x^6} \, dx","\text{RootSum}\left[\text{$\#$1}^6-\text{$\#$1}^3+1\&,\frac{\text{$\#$1} \log \left(\sqrt[3]{x^4+x^3+x}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{2 \text{$\#$1}^3-1}\&\right]",1,"Integrate[((-2 + x^3)*(x + x^3 + x^4)^(1/3))/(1 + x^2 + 2*x^3 + x^4 + x^5 + x^6), x]","F",-1
716,0,0,55,0.1146269,"\int \frac{\left(-2+x^3\right) \sqrt[3]{x+x^3+x^4}}{1+x^2+2 x^3+x^4+x^5+x^6} \, dx","Integrate[((-2 + x^3)*(x + x^3 + x^4)^(1/3))/(1 + x^2 + 2*x^3 + x^4 + x^5 + x^6),x]","\int \frac{\left(-2+x^3\right) \sqrt[3]{x+x^3+x^4}}{1+x^2+2 x^3+x^4+x^5+x^6} \, dx","\text{RootSum}\left[\text{$\#$1}^6-\text{$\#$1}^3+1\&,\frac{\text{$\#$1} \log \left(\sqrt[3]{x^4+x^3+x}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{2 \text{$\#$1}^3-1}\&\right]",1,"Integrate[((-2 + x^3)*(x + x^3 + x^4)^(1/3))/(1 + x^2 + 2*x^3 + x^4 + x^5 + x^6), x]","F",-1
717,1,46,55,0.0118217,"\int \frac{1}{x \left(b+a x^6\right)^{3/4}} \, dx","Integrate[1/(x*(b + a*x^6)^(3/4)),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a x^6+b}}{\sqrt[4]{b}}\right)+\tanh ^{-1}\left(\frac{\sqrt[4]{a x^6+b}}{\sqrt[4]{b}}\right)}{3 b^{3/4}}","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a x^6+b}}{\sqrt[4]{b}}\right)}{3 b^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a x^6+b}}{\sqrt[4]{b}}\right)}{3 b^{3/4}}",1,"-1/3*(ArcTan[(b + a*x^6)^(1/4)/b^(1/4)] + ArcTanh[(b + a*x^6)^(1/4)/b^(1/4)])/b^(3/4)","A",1
718,1,405,55,0.6378487,"\int \frac{-2 b+a x^4}{\sqrt[4]{b+a x^4} \left(-b+a x^4+x^8\right)} \, dx","Integrate[(-2*b + a*x^4)/((b + a*x^4)^(1/4)*(-b + a*x^4 + x^8)),x]","\frac{1}{2} \left(\frac{\sqrt[4]{a-\sqrt{a^2+4 b}} \tan ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}+\frac{\sqrt[4]{\sqrt{a^2+4 b}+a} \tan ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+4 b}+a} \sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}+\frac{\sqrt[4]{a-\sqrt{a^2+4 b}} \tanh ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}+\frac{\sqrt[4]{\sqrt{a^2+4 b}+a} \tanh ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+4 b}+a} \sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}\right)","-\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4 a+2 a^2-b\&,\frac{\log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]",1,"(((a - Sqrt[a^2 + 4*b])^(1/4)*ArcTan[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a - Sqrt[a^2 + 4*b])^(1/4)*(b + a*x^4)^(1/4))])/(a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4) + ((a + Sqrt[a^2 + 4*b])^(1/4)*ArcTan[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a + Sqrt[a^2 + 4*b])^(1/4)*(b + a*x^4)^(1/4))])/(a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4) + ((a - Sqrt[a^2 + 4*b])^(1/4)*ArcTanh[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a - Sqrt[a^2 + 4*b])^(1/4)*(b + a*x^4)^(1/4))])/(a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4) + ((a + Sqrt[a^2 + 4*b])^(1/4)*ArcTanh[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a + Sqrt[a^2 + 4*b])^(1/4)*(b + a*x^4)^(1/4))])/(a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4))/2","B",1
719,1,405,55,0.1265855,"\int \frac{-2 b+a x^4}{\sqrt[4]{b+a x^4} \left(-b+a x^4+x^8\right)} \, dx","Integrate[(-2*b + a*x^4)/((b + a*x^4)^(1/4)*(-b + a*x^4 + x^8)),x]","\frac{1}{2} \left(\frac{\sqrt[4]{a-\sqrt{a^2+4 b}} \tan ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}+\frac{\sqrt[4]{\sqrt{a^2+4 b}+a} \tan ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+4 b}+a} \sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}+\frac{\sqrt[4]{a-\sqrt{a^2+4 b}} \tanh ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}+\frac{\sqrt[4]{\sqrt{a^2+4 b}+a} \tanh ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+4 b}+a} \sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}\right)","-\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4 a+2 a^2-b\&,\frac{\log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]",1,"(((a - Sqrt[a^2 + 4*b])^(1/4)*ArcTan[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a - Sqrt[a^2 + 4*b])^(1/4)*(b + a*x^4)^(1/4))])/(a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4) + ((a + Sqrt[a^2 + 4*b])^(1/4)*ArcTan[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a + Sqrt[a^2 + 4*b])^(1/4)*(b + a*x^4)^(1/4))])/(a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4) + ((a - Sqrt[a^2 + 4*b])^(1/4)*ArcTanh[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a - Sqrt[a^2 + 4*b])^(1/4)*(b + a*x^4)^(1/4))])/(a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4) + ((a + Sqrt[a^2 + 4*b])^(1/4)*ArcTanh[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a + Sqrt[a^2 + 4*b])^(1/4)*(b + a*x^4)^(1/4))])/(a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4))/2","B",1
720,0,0,55,0.1285667,"\int \frac{x^2}{\left(b+a x^4\right)^{3/4} \left(b^2+a^2 x^8\right)} \, dx","Integrate[x^2/((b + a*x^4)^(3/4)*(b^2 + a^2*x^8)),x]","\int \frac{x^2}{\left(b+a x^4\right)^{3/4} \left(b^2+a^2 x^8\right)} \, dx","-\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+2 a^2\&,\frac{\log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}^3}\&\right]}{8 b^2}",1,"Integrate[x^2/((b + a*x^4)^(3/4)*(b^2 + a^2*x^8)), x]","F",-1
721,1,67,56,0.0647273,"\int \frac{1}{(-1+x) \sqrt{-\sqrt{x}+x}} \, dx","Integrate[1/((-1 + x)*Sqrt[-Sqrt[x] + x]),x]","\frac{\sqrt{2} \sqrt{\sqrt{x}-1} \sqrt[4]{x} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x}-1}}{\sqrt{2} \sqrt[4]{x}}\right)-2 \sqrt{x}}{\sqrt{x-\sqrt{x}}}","\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{x-\sqrt{x}}}{\sqrt{2} \sqrt{x}}\right)-\frac{2 \sqrt{x-\sqrt{x}}}{\sqrt{x}-1}",1,"(-2*Sqrt[x] + Sqrt[2]*Sqrt[-1 + Sqrt[x]]*x^(1/4)*ArcTanh[Sqrt[-1 + Sqrt[x]]/(Sqrt[2]*x^(1/4))])/Sqrt[-Sqrt[x] + x]","A",1
722,1,39,56,0.0159357,"\int \frac{1}{(1+2 x) \sqrt[4]{1+2 x+2 x^2}} \, dx","Integrate[1/((1 + 2*x)*(1 + 2*x + 2*x^2)^(1/4)),x]","\frac{\tan ^{-1}\left(\sqrt[4]{4 x^2+4 x+2}\right)-\tanh ^{-1}\left(\sqrt[4]{4 x^2+4 x+2}\right)}{2^{3/4}}","\frac{\tan ^{-1}\left(\sqrt[4]{2} \sqrt[4]{2 x^2+2 x+1}\right)}{2^{3/4}}-\frac{\tanh ^{-1}\left(\sqrt[4]{2} \sqrt[4]{2 x^2+2 x+1}\right)}{2^{3/4}}",1,"(ArcTan[(2 + 4*x + 4*x^2)^(1/4)] - ArcTanh[(2 + 4*x + 4*x^2)^(1/4)])/2^(3/4)","A",1
723,1,55,56,0.0361327,"\int \frac{\sqrt{b+a x^3} \left(2 b+a x^3\right)}{x^4} \, dx","Integrate[(Sqrt[b + a*x^3]*(2*b + a*x^3))/x^4,x]","-\frac{2 \sqrt{a x^3+b} \left(b-a x^3\right)}{3 x^3}-\frac{4}{3} a \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{a x^3+b}}{\sqrt{b}}\right)","\frac{2 \left(a x^3-b\right) \sqrt{a x^3+b}}{3 x^3}-\frac{4}{3} a \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{a x^3+b}}{\sqrt{b}}\right)",1,"(-2*(b - a*x^3)*Sqrt[b + a*x^3])/(3*x^3) - (4*a*Sqrt[b]*ArcTanh[Sqrt[b + a*x^3]/Sqrt[b]])/3","A",1
724,1,2888,56,6.2930432,"\int \frac{\left(-2 q+p x^3\right) \sqrt{q+p x^3}}{x^2 \left(a q+b x^2+a p x^3\right)} \, dx","Integrate[((-2*q + p*x^3)*Sqrt[q + p*x^3])/(x^2*(a*q + b*x^2 + a*p*x^3)),x]","\text{Result too large to show}","\frac{2 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a} \sqrt{p x^3+q}}\right)}{a^{3/2}}+\frac{2 \sqrt{p x^3+q}}{a x}",1,"(2*Sqrt[q + p*x^3])/(a*x) + (b*((-2*Sqrt[(q^(1/3)/p^(1/3) + x)/(q^(1/3)/p^(1/3) + ((-1)^(1/3)*q^(1/3))/p^(1/3))]*(-(((-1)^(1/3)*q^(1/3))/p^(1/3)) + x)*Sqrt[(((-1)^(2/3)*q^(1/3))/p^(1/3) + x)/(((-1)^(1/3)*q^(1/3))/p^(1/3) + ((-1)^(2/3)*q^(1/3))/p^(1/3))]*EllipticF[ArcSin[Sqrt[((-1)^(1/3)*q^(1/3) - p^(1/3)*x)/(((-1)^(1/3) + (-1)^(2/3))*q^(1/3))]], (-1)^(1/3)])/(a*Sqrt[(-(((-1)^(1/3)*q^(1/3))/p^(1/3)) + x)/(-(((-1)^(1/3)*q^(1/3))/p^(1/3)) - ((-1)^(2/3)*q^(1/3))/p^(1/3))]*Sqrt[q + p*x^3]) + (4*(((-1)^(1/3)*q^(1/3))/p^(1/3) + ((-1)^(2/3)*q^(1/3))/p^(1/3))*q*Sqrt[(q^(1/3)/p^(1/3) + x)/(q^(1/3)/p^(1/3) + ((-1)^(1/3)*q^(1/3))/p^(1/3))]*Sqrt[((-(((-1)^(2/3)*q^(1/3))/p^(1/3)) - x)*(-(((-1)^(1/3)*q^(1/3))/p^(1/3)) + x))/(((-1)^(1/3)*q^(1/3))/p^(1/3) + ((-1)^(2/3)*q^(1/3))/p^(1/3))^2]*EllipticPi[((-1)^(1/3)*q^(1/3) + (-1)^(2/3)*q^(1/3))/((-1)^(1/3)*q^(1/3) - p^(1/3)*Root[a*q + b*#1^2 + a*p*#1^3 & , 1]), ArcSin[Sqrt[((-1)^(1/3)*q^(1/3) - p^(1/3)*x)/(((-1)^(1/3) + (-1)^(2/3))*q^(1/3))]], (-1)^(1/3)])/(a*p*Sqrt[q + p*x^3]*(-(((-1)^(1/3)*q^(1/3))/p^(1/3)) + Root[a*q + b*#1^2 + a*p*#1^3 & , 1])*(Root[a*q + b*#1^2 + a*p*#1^3 & , 1] - Root[a*q + b*#1^2 + a*p*#1^3 & , 2])*(Root[a*q + b*#1^2 + a*p*#1^3 & , 1] - Root[a*q + b*#1^2 + a*p*#1^3 & , 3])) - (2*(((-1)^(1/3)*q^(1/3))/p^(1/3) + ((-1)^(2/3)*q^(1/3))/p^(1/3))*Sqrt[(q^(1/3)/p^(1/3) + x)/(q^(1/3)/p^(1/3) + ((-1)^(1/3)*q^(1/3))/p^(1/3))]*Sqrt[((-(((-1)^(2/3)*q^(1/3))/p^(1/3)) - x)*(-(((-1)^(1/3)*q^(1/3))/p^(1/3)) + x))/(((-1)^(1/3)*q^(1/3))/p^(1/3) + ((-1)^(2/3)*q^(1/3))/p^(1/3))^2]*EllipticPi[((-1)^(1/3)*q^(1/3) + (-1)^(2/3)*q^(1/3))/((-1)^(1/3)*q^(1/3) - p^(1/3)*Root[a*q + b*#1^2 + a*p*#1^3 & , 1]), ArcSin[Sqrt[((-1)^(1/3)*q^(1/3) - p^(1/3)*x)/(((-1)^(1/3) + (-1)^(2/3))*q^(1/3))]], (-1)^(1/3)]*Root[a*q + b*#1^2 + a*p*#1^3 & , 1]^3)/(a*Sqrt[q + p*x^3]*(-(((-1)^(1/3)*q^(1/3))/p^(1/3)) + Root[a*q + b*#1^2 + a*p*#1^3 & , 1])*(Root[a*q + b*#1^2 + a*p*#1^3 & , 1] - Root[a*q + b*#1^2 + a*p*#1^3 & , 2])*(Root[a*q + b*#1^2 + a*p*#1^3 & , 1] - Root[a*q + b*#1^2 + a*p*#1^3 & , 3])) + (4*(((-1)^(1/3)*q^(1/3))/p^(1/3) + ((-1)^(2/3)*q^(1/3))/p^(1/3))*q*Sqrt[(q^(1/3)/p^(1/3) + x)/(q^(1/3)/p^(1/3) + ((-1)^(1/3)*q^(1/3))/p^(1/3))]*Sqrt[((-(((-1)^(2/3)*q^(1/3))/p^(1/3)) - x)*(-(((-1)^(1/3)*q^(1/3))/p^(1/3)) + x))/(((-1)^(1/3)*q^(1/3))/p^(1/3) + ((-1)^(2/3)*q^(1/3))/p^(1/3))^2]*EllipticPi[((-1)^(1/3)*q^(1/3) + (-1)^(2/3)*q^(1/3))/((-1)^(1/3)*q^(1/3) - p^(1/3)*Root[a*q + b*#1^2 + a*p*#1^3 & , 2]), ArcSin[Sqrt[((-1)^(1/3)*q^(1/3) - p^(1/3)*x)/(((-1)^(1/3) + (-1)^(2/3))*q^(1/3))]], (-1)^(1/3)])/(a*p*Sqrt[q + p*x^3]*(-(((-1)^(1/3)*q^(1/3))/p^(1/3)) + Root[a*q + b*#1^2 + a*p*#1^3 & , 2])*(-Root[a*q + b*#1^2 + a*p*#1^3 & , 1] + Root[a*q + b*#1^2 + a*p*#1^3 & , 2])*(Root[a*q + b*#1^2 + a*p*#1^3 & , 2] - Root[a*q + b*#1^2 + a*p*#1^3 & , 3])) - (2*(((-1)^(1/3)*q^(1/3))/p^(1/3) + ((-1)^(2/3)*q^(1/3))/p^(1/3))*Sqrt[(q^(1/3)/p^(1/3) + x)/(q^(1/3)/p^(1/3) + ((-1)^(1/3)*q^(1/3))/p^(1/3))]*Sqrt[((-(((-1)^(2/3)*q^(1/3))/p^(1/3)) - x)*(-(((-1)^(1/3)*q^(1/3))/p^(1/3)) + x))/(((-1)^(1/3)*q^(1/3))/p^(1/3) + ((-1)^(2/3)*q^(1/3))/p^(1/3))^2]*EllipticPi[((-1)^(1/3)*q^(1/3) + (-1)^(2/3)*q^(1/3))/((-1)^(1/3)*q^(1/3) - p^(1/3)*Root[a*q + b*#1^2 + a*p*#1^3 & , 2]), ArcSin[Sqrt[((-1)^(1/3)*q^(1/3) - p^(1/3)*x)/(((-1)^(1/3) + (-1)^(2/3))*q^(1/3))]], (-1)^(1/3)]*Root[a*q + b*#1^2 + a*p*#1^3 & , 2]^3)/(a*Sqrt[q + p*x^3]*(-(((-1)^(1/3)*q^(1/3))/p^(1/3)) + Root[a*q + b*#1^2 + a*p*#1^3 & , 2])*(-Root[a*q + b*#1^2 + a*p*#1^3 & , 1] + Root[a*q + b*#1^2 + a*p*#1^3 & , 2])*(Root[a*q + b*#1^2 + a*p*#1^3 & , 2] - Root[a*q + b*#1^2 + a*p*#1^3 & , 3])) + (4*(((-1)^(1/3)*q^(1/3))/p^(1/3) + ((-1)^(2/3)*q^(1/3))/p^(1/3))*q*Sqrt[(q^(1/3)/p^(1/3) + x)/(q^(1/3)/p^(1/3) + ((-1)^(1/3)*q^(1/3))/p^(1/3))]*Sqrt[((-(((-1)^(2/3)*q^(1/3))/p^(1/3)) - x)*(-(((-1)^(1/3)*q^(1/3))/p^(1/3)) + x))/(((-1)^(1/3)*q^(1/3))/p^(1/3) + ((-1)^(2/3)*q^(1/3))/p^(1/3))^2]*EllipticPi[((-1)^(1/3)*q^(1/3) + (-1)^(2/3)*q^(1/3))/((-1)^(1/3)*q^(1/3) - p^(1/3)*Root[a*q + b*#1^2 + a*p*#1^3 & , 3]), ArcSin[Sqrt[((-1)^(1/3)*q^(1/3) - p^(1/3)*x)/(((-1)^(1/3) + (-1)^(2/3))*q^(1/3))]], (-1)^(1/3)])/(a*p*Sqrt[q + p*x^3]*(-(((-1)^(1/3)*q^(1/3))/p^(1/3)) + Root[a*q + b*#1^2 + a*p*#1^3 & , 3])*(-Root[a*q + b*#1^2 + a*p*#1^3 & , 1] + Root[a*q + b*#1^2 + a*p*#1^3 & , 3])*(-Root[a*q + b*#1^2 + a*p*#1^3 & , 2] + Root[a*q + b*#1^2 + a*p*#1^3 & , 3])) - (2*(((-1)^(1/3)*q^(1/3))/p^(1/3) + ((-1)^(2/3)*q^(1/3))/p^(1/3))*Sqrt[(q^(1/3)/p^(1/3) + x)/(q^(1/3)/p^(1/3) + ((-1)^(1/3)*q^(1/3))/p^(1/3))]*Sqrt[((-(((-1)^(2/3)*q^(1/3))/p^(1/3)) - x)*(-(((-1)^(1/3)*q^(1/3))/p^(1/3)) + x))/(((-1)^(1/3)*q^(1/3))/p^(1/3) + ((-1)^(2/3)*q^(1/3))/p^(1/3))^2]*EllipticPi[((-1)^(1/3)*q^(1/3) + (-1)^(2/3)*q^(1/3))/((-1)^(1/3)*q^(1/3) - p^(1/3)*Root[a*q + b*#1^2 + a*p*#1^3 & , 3]), ArcSin[Sqrt[((-1)^(1/3)*q^(1/3) - p^(1/3)*x)/(((-1)^(1/3) + (-1)^(2/3))*q^(1/3))]], (-1)^(1/3)]*Root[a*q + b*#1^2 + a*p*#1^3 & , 3]^3)/(a*Sqrt[q + p*x^3]*(-(((-1)^(1/3)*q^(1/3))/p^(1/3)) + Root[a*q + b*#1^2 + a*p*#1^3 & , 3])*(-Root[a*q + b*#1^2 + a*p*#1^3 & , 1] + Root[a*q + b*#1^2 + a*p*#1^3 & , 3])*(-Root[a*q + b*#1^2 + a*p*#1^3 & , 2] + Root[a*q + b*#1^2 + a*p*#1^3 & , 3]))))/a","C",0
725,1,1333,56,2.1293073,"\int \frac{-1+2 x}{\sqrt{-8+4 x-3 x^2-10 x^3+x^4}} \, dx","Integrate[(-1 + 2*x)/Sqrt[-8 + 4*x - 3*x^2 - 10*x^3 + x^4],x]","\frac{2 \left(-2 x+4 \sqrt{4+\sqrt{17}}+\sqrt{17}+5\right) \left(8 \sqrt{4+\sqrt{17}} \Pi \left(\frac{5+\sqrt{17}-4 \sqrt{4+\sqrt{17}}-2 \text{Root}\left[\text{$\#$1}^4-10 \text{$\#$1}^3-3 \text{$\#$1}^2+4 \text{$\#$1}-8\&,4\right]}{5+\sqrt{17}+4 \sqrt{4+\sqrt{17}}-2 \text{Root}\left[\text{$\#$1}^4-10 \text{$\#$1}^3-3 \text{$\#$1}^2+4 \text{$\#$1}-8\&,4\right]};\sin ^{-1}\left(\sqrt{\frac{\left(-2 x-4 \sqrt{4+\sqrt{17}}+\sqrt{17}+5\right) \left(5+\sqrt{17}+4 \sqrt{4+\sqrt{17}}-2 \text{Root}\left[\text{$\#$1}^4-10 \text{$\#$1}^3-3 \text{$\#$1}^2+4 \text{$\#$1}-8\&,4\right]\right)}{\left(-2 x+4 \sqrt{4+\sqrt{17}}+\sqrt{17}+5\right) \left(5+\sqrt{17}-4 \sqrt{4+\sqrt{17}}-2 \text{Root}\left[\text{$\#$1}^4-10 \text{$\#$1}^3-3 \text{$\#$1}^2+4 \text{$\#$1}-8\&,4\right]\right)}}\right)|\frac{\left(5+\sqrt{17}+4 \sqrt{4+\sqrt{17}}-2 \text{Root}\left[\text{$\#$1}^4-10 \text{$\#$1}^3-3 \text{$\#$1}^2+4 \text{$\#$1}-8\&,3\right]\right) \left(5+\sqrt{17}-4 \sqrt{4+\sqrt{17}}-2 \text{Root}\left[\text{$\#$1}^4-10 \text{$\#$1}^3-3 \text{$\#$1}^2+4 \text{$\#$1}-8\&,4\right]\right)}{\left(5+\sqrt{17}-4 \sqrt{4+\sqrt{17}}-2 \text{Root}\left[\text{$\#$1}^4-10 \text{$\#$1}^3-3 \text{$\#$1}^2+4 \text{$\#$1}-8\&,3\right]\right) \left(5+\sqrt{17}+4 \sqrt{4+\sqrt{17}}-2 \text{Root}\left[\text{$\#$1}^4-10 \text{$\#$1}^3-3 \text{$\#$1}^2+4 \text{$\#$1}-8\&,4\right]\right)}\right)-\left(4+\sqrt{17}+4 \sqrt{4+\sqrt{17}}\right) F\left(\sin ^{-1}\left(\sqrt{\frac{\left(-2 x-4 \sqrt{4+\sqrt{17}}+\sqrt{17}+5\right) \left(5+\sqrt{17}+4 \sqrt{4+\sqrt{17}}-2 \text{Root}\left[\text{$\#$1}^4-10 \text{$\#$1}^3-3 \text{$\#$1}^2+4 \text{$\#$1}-8\&,4\right]\right)}{\left(-2 x+4 \sqrt{4+\sqrt{17}}+\sqrt{17}+5\right) \left(5+\sqrt{17}-4 \sqrt{4+\sqrt{17}}-2 \text{Root}\left[\text{$\#$1}^4-10 \text{$\#$1}^3-3 \text{$\#$1}^2+4 \text{$\#$1}-8\&,4\right]\right)}}\right)|\frac{\left(5+\sqrt{17}+4 \sqrt{4+\sqrt{17}}-2 \text{Root}\left[\text{$\#$1}^4-10 \text{$\#$1}^3-3 \text{$\#$1}^2+4 \text{$\#$1}-8\&,3\right]\right) \left(5+\sqrt{17}-4 \sqrt{4+\sqrt{17}}-2 \text{Root}\left[\text{$\#$1}^4-10 \text{$\#$1}^3-3 \text{$\#$1}^2+4 \text{$\#$1}-8\&,4\right]\right)}{\left(5+\sqrt{17}-4 \sqrt{4+\sqrt{17}}-2 \text{Root}\left[\text{$\#$1}^4-10 \text{$\#$1}^3-3 \text{$\#$1}^2+4 \text{$\#$1}-8\&,3\right]\right) \left(5+\sqrt{17}+4 \sqrt{4+\sqrt{17}}-2 \text{Root}\left[\text{$\#$1}^4-10 \text{$\#$1}^3-3 \text{$\#$1}^2+4 \text{$\#$1}-8\&,4\right]\right)}\right)\right) \sqrt{\frac{x-\text{Root}\left[\text{$\#$1}^4-10 \text{$\#$1}^3-3 \text{$\#$1}^2+4 \text{$\#$1}-8\&,3\right]}{\left(-2 x+4 \sqrt{4+\sqrt{17}}+\sqrt{17}+5\right) \left(5+\sqrt{17}-4 \sqrt{4+\sqrt{17}}-2 \text{Root}\left[\text{$\#$1}^4-10 \text{$\#$1}^3-3 \text{$\#$1}^2+4 \text{$\#$1}-8\&,3\right]\right)}} \sqrt{\frac{\left(-2 x-4 \sqrt{4+\sqrt{17}}+\sqrt{17}+5\right) \left(5+\sqrt{17}+4 \sqrt{4+\sqrt{17}}-2 \text{Root}\left[\text{$\#$1}^4-10 \text{$\#$1}^3-3 \text{$\#$1}^2+4 \text{$\#$1}-8\&,4\right]\right)}{\left(-2 x+4 \sqrt{4+\sqrt{17}}+\sqrt{17}+5\right) \left(5+\sqrt{17}-4 \sqrt{4+\sqrt{17}}-2 \text{Root}\left[\text{$\#$1}^4-10 \text{$\#$1}^3-3 \text{$\#$1}^2+4 \text{$\#$1}-8\&,4\right]\right)}} \left(x-\text{Root}\left[\text{$\#$1}^4-10 \text{$\#$1}^3-3 \text{$\#$1}^2+4 \text{$\#$1}-8\&,4\right]\right)}{\sqrt{x^4-10 x^3-3 x^2+4 x-8} \left(5+\sqrt{17}+4 \sqrt{4+\sqrt{17}}-2 \text{Root}\left[\text{$\#$1}^4-10 \text{$\#$1}^3-3 \text{$\#$1}^2+4 \text{$\#$1}-8\&,4\right]\right) \sqrt{\frac{x-\text{Root}\left[\text{$\#$1}^4-10 \text{$\#$1}^3-3 \text{$\#$1}^2+4 \text{$\#$1}-8\&,4\right]}{\left(-2 x+4 \sqrt{4+\sqrt{17}}+\sqrt{17}+5\right) \left(5+\sqrt{17}-4 \sqrt{4+\sqrt{17}}-2 \text{Root}\left[\text{$\#$1}^4-10 \text{$\#$1}^3-3 \text{$\#$1}^2+4 \text{$\#$1}-8\&,4\right]\right)}}}","-\frac{1}{2} \log \left(x^4-18 x^3+89 x^2+\left(-x^2+13 x-38\right) \sqrt{x^4-10 x^3-3 x^2+4 x-8}-76 x-90\right)",1,"(2*(5 + Sqrt[17] + 4*Sqrt[4 + Sqrt[17]] - 2*x)*(-((4 + Sqrt[17] + 4*Sqrt[4 + Sqrt[17]])*EllipticF[ArcSin[Sqrt[((5 + Sqrt[17] - 4*Sqrt[4 + Sqrt[17]] - 2*x)*(5 + Sqrt[17] + 4*Sqrt[4 + Sqrt[17]] - 2*Root[-8 + 4*#1 - 3*#1^2 - 10*#1^3 + #1^4 & , 4, 0]))/((5 + Sqrt[17] + 4*Sqrt[4 + Sqrt[17]] - 2*x)*(5 + Sqrt[17] - 4*Sqrt[4 + Sqrt[17]] - 2*Root[-8 + 4*#1 - 3*#1^2 - 10*#1^3 + #1^4 & , 4, 0]))]], ((5 + Sqrt[17] + 4*Sqrt[4 + Sqrt[17]] - 2*Root[-8 + 4*#1 - 3*#1^2 - 10*#1^3 + #1^4 & , 3, 0])*(5 + Sqrt[17] - 4*Sqrt[4 + Sqrt[17]] - 2*Root[-8 + 4*#1 - 3*#1^2 - 10*#1^3 + #1^4 & , 4, 0]))/((5 + Sqrt[17] - 4*Sqrt[4 + Sqrt[17]] - 2*Root[-8 + 4*#1 - 3*#1^2 - 10*#1^3 + #1^4 & , 3, 0])*(5 + Sqrt[17] + 4*Sqrt[4 + Sqrt[17]] - 2*Root[-8 + 4*#1 - 3*#1^2 - 10*#1^3 + #1^4 & , 4, 0]))]) + 8*Sqrt[4 + Sqrt[17]]*EllipticPi[(5 + Sqrt[17] - 4*Sqrt[4 + Sqrt[17]] - 2*Root[-8 + 4*#1 - 3*#1^2 - 10*#1^3 + #1^4 & , 4, 0])/(5 + Sqrt[17] + 4*Sqrt[4 + Sqrt[17]] - 2*Root[-8 + 4*#1 - 3*#1^2 - 10*#1^3 + #1^4 & , 4, 0]), ArcSin[Sqrt[((5 + Sqrt[17] - 4*Sqrt[4 + Sqrt[17]] - 2*x)*(5 + Sqrt[17] + 4*Sqrt[4 + Sqrt[17]] - 2*Root[-8 + 4*#1 - 3*#1^2 - 10*#1^3 + #1^4 & , 4, 0]))/((5 + Sqrt[17] + 4*Sqrt[4 + Sqrt[17]] - 2*x)*(5 + Sqrt[17] - 4*Sqrt[4 + Sqrt[17]] - 2*Root[-8 + 4*#1 - 3*#1^2 - 10*#1^3 + #1^4 & , 4, 0]))]], ((5 + Sqrt[17] + 4*Sqrt[4 + Sqrt[17]] - 2*Root[-8 + 4*#1 - 3*#1^2 - 10*#1^3 + #1^4 & , 3, 0])*(5 + Sqrt[17] - 4*Sqrt[4 + Sqrt[17]] - 2*Root[-8 + 4*#1 - 3*#1^2 - 10*#1^3 + #1^4 & , 4, 0]))/((5 + Sqrt[17] - 4*Sqrt[4 + Sqrt[17]] - 2*Root[-8 + 4*#1 - 3*#1^2 - 10*#1^3 + #1^4 & , 3, 0])*(5 + Sqrt[17] + 4*Sqrt[4 + Sqrt[17]] - 2*Root[-8 + 4*#1 - 3*#1^2 - 10*#1^3 + #1^4 & , 4, 0]))])*Sqrt[(x - Root[-8 + 4*#1 - 3*#1^2 - 10*#1^3 + #1^4 & , 3, 0])/((5 + Sqrt[17] + 4*Sqrt[4 + Sqrt[17]] - 2*x)*(5 + Sqrt[17] - 4*Sqrt[4 + Sqrt[17]] - 2*Root[-8 + 4*#1 - 3*#1^2 - 10*#1^3 + #1^4 & , 3, 0]))]*Sqrt[((5 + Sqrt[17] - 4*Sqrt[4 + Sqrt[17]] - 2*x)*(5 + Sqrt[17] + 4*Sqrt[4 + Sqrt[17]] - 2*Root[-8 + 4*#1 - 3*#1^2 - 10*#1^3 + #1^4 & , 4, 0]))/((5 + Sqrt[17] + 4*Sqrt[4 + Sqrt[17]] - 2*x)*(5 + Sqrt[17] - 4*Sqrt[4 + Sqrt[17]] - 2*Root[-8 + 4*#1 - 3*#1^2 - 10*#1^3 + #1^4 & , 4, 0]))]*(x - Root[-8 + 4*#1 - 3*#1^2 - 10*#1^3 + #1^4 & , 4, 0]))/(Sqrt[-8 + 4*x - 3*x^2 - 10*x^3 + x^4]*(5 + Sqrt[17] + 4*Sqrt[4 + Sqrt[17]] - 2*Root[-8 + 4*#1 - 3*#1^2 - 10*#1^3 + #1^4 & , 4, 0])*Sqrt[(x - Root[-8 + 4*#1 - 3*#1^2 - 10*#1^3 + #1^4 & , 4, 0])/((5 + Sqrt[17] + 4*Sqrt[4 + Sqrt[17]] - 2*x)*(5 + Sqrt[17] - 4*Sqrt[4 + Sqrt[17]] - 2*Root[-8 + 4*#1 - 3*#1^2 - 10*#1^3 + #1^4 & , 4, 0]))])","C",0
726,1,2609,56,6.0786491,"\int \frac{-1+x}{\sqrt{4-16 x+12 x^2-8 x^3+x^4}} \, dx","Integrate[(-1 + x)/Sqrt[4 - 16*x + 12*x^2 - 8*x^3 + x^4],x]","\text{Result too large to show}","-\frac{1}{4} \log \left(x^4-12 x^3+44 x^2+\left(-x^2+8 x-14\right) \sqrt{x^4-8 x^3+12 x^2-16 x+4}-56 x+36\right)",1,"(2*(x - Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 2, 0])^2*(-(EllipticF[ArcSin[Sqrt[((x - Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 1, 0])*(Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 2, 0] - Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 4, 0]))/((x - Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 2, 0])*(Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 1, 0] - Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 4, 0]))]], -(((Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 2, 0] - Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 3, 0])*(Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 1, 0] - Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 4, 0]))/((-Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 1, 0] + Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 3, 0])*(Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 2, 0] - Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 4, 0])))]*Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 2, 0]) + EllipticPi[(-Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 1, 0] + Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 4, 0])/(-Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 2, 0] + Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 4, 0]), ArcSin[Sqrt[((x - Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 1, 0])*(Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 2, 0] - Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 4, 0]))/((x - Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 2, 0])*(Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 1, 0] - Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 4, 0]))]], -(((Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 2, 0] - Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 3, 0])*(Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 1, 0] - Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 4, 0]))/((-Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 1, 0] + Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 3, 0])*(Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 2, 0] - Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 4, 0])))]*(-Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 1, 0] + Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 2, 0]))*Sqrt[(x - Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 3, 0])/((x - Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 2, 0])*(-Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 1, 0] + Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 3, 0]))]*(Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 1, 0] - Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 4, 0])*Sqrt[((x - Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 1, 0])*(Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 2, 0] - Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 4, 0]))/((x - Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 2, 0])*(Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 1, 0] - Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 4, 0]))]*Sqrt[(x - Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 4, 0])/((x - Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 2, 0])*(-Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 1, 0] + Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 4, 0]))])/(Sqrt[4 - 16*x + 12*x^2 - 8*x^3 + x^4]*(Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 2, 0] - Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 4, 0])) - (2*EllipticF[ArcSin[Sqrt[((x - Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 1, 0])*(-Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 2, 0] + Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 4, 0]))/((x - Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 2, 0])*(-Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 1, 0] + Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 4, 0]))]], ((Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 2, 0] - Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 3, 0])*(Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 1, 0] - Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 4, 0]))/((Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 1, 0] - Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 3, 0])*(Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 2, 0] - Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 4, 0]))]*(x - Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 2, 0])^2*Sqrt[(x - Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 3, 0])/((x - Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 2, 0])*(-Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 1, 0] + Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 3, 0]))]*(Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 1, 0] - Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 4, 0])*Sqrt[(x - Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 4, 0])/((x - Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 2, 0])*(-Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 1, 0] + Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 4, 0]))]*Sqrt[((x - Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 1, 0])*(-Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 2, 0] + Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 4, 0]))/((x - Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 2, 0])*(-Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 1, 0] + Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 4, 0]))])/(Sqrt[4 - 16*x + 12*x^2 - 8*x^3 + x^4]*(-Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 2, 0] + Root[4 - 16*#1 + 12*#1^2 - 8*#1^3 + #1^4 & , 4, 0]))","C",1
727,0,0,56,0.6960777,"\int \frac{\sqrt{q+p x^5} \left(-2 q+3 p x^5\right)}{x^2 \left(a q+b x^2+a p x^5\right)} \, dx","Integrate[(Sqrt[q + p*x^5]*(-2*q + 3*p*x^5))/(x^2*(a*q + b*x^2 + a*p*x^5)),x]","\int \frac{\sqrt{q+p x^5} \left(-2 q+3 p x^5\right)}{x^2 \left(a q+b x^2+a p x^5\right)} \, dx","\frac{2 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a} \sqrt{p x^5+q}}\right)}{a^{3/2}}+\frac{2 \sqrt{p x^5+q}}{a x}",1,"Integrate[(Sqrt[q + p*x^5]*(-2*q + 3*p*x^5))/(x^2*(a*q + b*x^2 + a*p*x^5)), x]","F",-1
728,0,0,56,0.7143877,"\int \frac{x^2 \left(-1+4 x^5\right)}{\left(1+x^5\right)^2 \left(a-x+a x^5\right) \sqrt{x+x^6}} \, dx","Integrate[(x^2*(-1 + 4*x^5))/((1 + x^5)^2*(a - x + a*x^5)*Sqrt[x + x^6]),x]","\int \frac{x^2 \left(-1+4 x^5\right)}{\left(1+x^5\right)^2 \left(a-x+a x^5\right) \sqrt{x+x^6}} \, dx","\frac{2 \sqrt{x^6+x} \left(3 a x^5+3 a+x\right)}{3 \left(x^5+1\right)^2}-2 a^{3/2} \tanh ^{-1}\left(\frac{x}{\sqrt{a} \sqrt{x^6+x}}\right)",1,"Integrate[(x^2*(-1 + 4*x^5))/((1 + x^5)^2*(a - x + a*x^5)*Sqrt[x + x^6]), x]","F",-1
729,1,71,56,0.0775266,"\int \frac{\sqrt{-x+x^4} \left(-b+a x^6\right)}{x^6} \, dx","Integrate[(Sqrt[-x + x^4]*(-b + a*x^6))/x^6,x]","\frac{\sqrt{x \left(x^3-1\right)} \left(\sqrt{1-x^3} \left(3 a x^6-2 b \left(x^3-1\right)\right)+3 a x^{9/2} \sin ^{-1}\left(x^{3/2}\right)\right)}{9 x^5 \sqrt{1-x^3}}","\frac{\sqrt{x^4-x} \left(3 a x^6-2 b x^3+2 b\right)}{9 x^5}-\frac{1}{3} a \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4-x}}\right)",1,"(Sqrt[x*(-1 + x^3)]*(Sqrt[1 - x^3]*(3*a*x^6 - 2*b*(-1 + x^3)) + 3*a*x^(9/2)*ArcSin[x^(3/2)]))/(9*x^5*Sqrt[1 - x^3])","A",1
730,1,2948,56,6.7949258,"\int \frac{\left(-2 q+p x^6\right) \sqrt{q+p x^6}}{x^3 \left(a q+b x^4+a p x^6\right)} \, dx","Integrate[((-2*q + p*x^6)*Sqrt[q + p*x^6])/(x^3*(a*q + b*x^4 + a*p*x^6)),x]","\text{Result too large to show}","\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a} \sqrt{p x^6+q}}\right)}{a^{3/2}}+\frac{\sqrt{p x^6+q}}{a x^2}",1,"Sqrt[q + p*x^6]/(a*x^2) + (b*((-2*Sqrt[(q^(1/3)/p^(1/3) + x^2)/(q^(1/3)/p^(1/3) + ((-1)^(1/3)*q^(1/3))/p^(1/3))]*(-(((-1)^(1/3)*q^(1/3))/p^(1/3)) + x^2)*Sqrt[(((-1)^(2/3)*q^(1/3))/p^(1/3) + x^2)/(((-1)^(1/3)*q^(1/3))/p^(1/3) + ((-1)^(2/3)*q^(1/3))/p^(1/3))]*EllipticF[ArcSin[Sqrt[((-1)^(1/3)*q^(1/3) - p^(1/3)*x^2)/(((-1)^(1/3) + (-1)^(2/3))*q^(1/3))]], (-1)^(1/3)])/(a*Sqrt[(-(((-1)^(1/3)*q^(1/3))/p^(1/3)) + x^2)/(-(((-1)^(1/3)*q^(1/3))/p^(1/3)) - ((-1)^(2/3)*q^(1/3))/p^(1/3))]*Sqrt[q + p*x^6]) + (4*(((-1)^(1/3)*q^(1/3))/p^(1/3) + ((-1)^(2/3)*q^(1/3))/p^(1/3))*q*Sqrt[(q^(1/3)/p^(1/3) + x^2)/(q^(1/3)/p^(1/3) + ((-1)^(1/3)*q^(1/3))/p^(1/3))]*Sqrt[((-(((-1)^(2/3)*q^(1/3))/p^(1/3)) - x^2)*(-(((-1)^(1/3)*q^(1/3))/p^(1/3)) + x^2))/(((-1)^(1/3)*q^(1/3))/p^(1/3) + ((-1)^(2/3)*q^(1/3))/p^(1/3))^2]*EllipticPi[((-1)^(1/3)*q^(1/3) + (-1)^(2/3)*q^(1/3))/((-1)^(1/3)*q^(1/3) - p^(1/3)*Root[a*q + b*#1^2 + a*p*#1^3 & , 1]), ArcSin[Sqrt[((-1)^(1/3)*q^(1/3) - p^(1/3)*x^2)/(((-1)^(1/3) + (-1)^(2/3))*q^(1/3))]], (-1)^(1/3)])/(a*p*Sqrt[q + p*x^6]*(-(((-1)^(1/3)*q^(1/3))/p^(1/3)) + Root[a*q + b*#1^2 + a*p*#1^3 & , 1])*(Root[a*q + b*#1^2 + a*p*#1^3 & , 1] - Root[a*q + b*#1^2 + a*p*#1^3 & , 2])*(Root[a*q + b*#1^2 + a*p*#1^3 & , 1] - Root[a*q + b*#1^2 + a*p*#1^3 & , 3])) - (2*(((-1)^(1/3)*q^(1/3))/p^(1/3) + ((-1)^(2/3)*q^(1/3))/p^(1/3))*Sqrt[(q^(1/3)/p^(1/3) + x^2)/(q^(1/3)/p^(1/3) + ((-1)^(1/3)*q^(1/3))/p^(1/3))]*Sqrt[((-(((-1)^(2/3)*q^(1/3))/p^(1/3)) - x^2)*(-(((-1)^(1/3)*q^(1/3))/p^(1/3)) + x^2))/(((-1)^(1/3)*q^(1/3))/p^(1/3) + ((-1)^(2/3)*q^(1/3))/p^(1/3))^2]*EllipticPi[((-1)^(1/3)*q^(1/3) + (-1)^(2/3)*q^(1/3))/((-1)^(1/3)*q^(1/3) - p^(1/3)*Root[a*q + b*#1^2 + a*p*#1^3 & , 1]), ArcSin[Sqrt[((-1)^(1/3)*q^(1/3) - p^(1/3)*x^2)/(((-1)^(1/3) + (-1)^(2/3))*q^(1/3))]], (-1)^(1/3)]*Root[a*q + b*#1^2 + a*p*#1^3 & , 1]^3)/(a*Sqrt[q + p*x^6]*(-(((-1)^(1/3)*q^(1/3))/p^(1/3)) + Root[a*q + b*#1^2 + a*p*#1^3 & , 1])*(Root[a*q + b*#1^2 + a*p*#1^3 & , 1] - Root[a*q + b*#1^2 + a*p*#1^3 & , 2])*(Root[a*q + b*#1^2 + a*p*#1^3 & , 1] - Root[a*q + b*#1^2 + a*p*#1^3 & , 3])) + (4*(((-1)^(1/3)*q^(1/3))/p^(1/3) + ((-1)^(2/3)*q^(1/3))/p^(1/3))*q*Sqrt[(q^(1/3)/p^(1/3) + x^2)/(q^(1/3)/p^(1/3) + ((-1)^(1/3)*q^(1/3))/p^(1/3))]*Sqrt[((-(((-1)^(2/3)*q^(1/3))/p^(1/3)) - x^2)*(-(((-1)^(1/3)*q^(1/3))/p^(1/3)) + x^2))/(((-1)^(1/3)*q^(1/3))/p^(1/3) + ((-1)^(2/3)*q^(1/3))/p^(1/3))^2]*EllipticPi[((-1)^(1/3)*q^(1/3) + (-1)^(2/3)*q^(1/3))/((-1)^(1/3)*q^(1/3) - p^(1/3)*Root[a*q + b*#1^2 + a*p*#1^3 & , 2]), ArcSin[Sqrt[((-1)^(1/3)*q^(1/3) - p^(1/3)*x^2)/(((-1)^(1/3) + (-1)^(2/3))*q^(1/3))]], (-1)^(1/3)])/(a*p*Sqrt[q + p*x^6]*(-(((-1)^(1/3)*q^(1/3))/p^(1/3)) + Root[a*q + b*#1^2 + a*p*#1^3 & , 2])*(-Root[a*q + b*#1^2 + a*p*#1^3 & , 1] + Root[a*q + b*#1^2 + a*p*#1^3 & , 2])*(Root[a*q + b*#1^2 + a*p*#1^3 & , 2] - Root[a*q + b*#1^2 + a*p*#1^3 & , 3])) - (2*(((-1)^(1/3)*q^(1/3))/p^(1/3) + ((-1)^(2/3)*q^(1/3))/p^(1/3))*Sqrt[(q^(1/3)/p^(1/3) + x^2)/(q^(1/3)/p^(1/3) + ((-1)^(1/3)*q^(1/3))/p^(1/3))]*Sqrt[((-(((-1)^(2/3)*q^(1/3))/p^(1/3)) - x^2)*(-(((-1)^(1/3)*q^(1/3))/p^(1/3)) + x^2))/(((-1)^(1/3)*q^(1/3))/p^(1/3) + ((-1)^(2/3)*q^(1/3))/p^(1/3))^2]*EllipticPi[((-1)^(1/3)*q^(1/3) + (-1)^(2/3)*q^(1/3))/((-1)^(1/3)*q^(1/3) - p^(1/3)*Root[a*q + b*#1^2 + a*p*#1^3 & , 2]), ArcSin[Sqrt[((-1)^(1/3)*q^(1/3) - p^(1/3)*x^2)/(((-1)^(1/3) + (-1)^(2/3))*q^(1/3))]], (-1)^(1/3)]*Root[a*q + b*#1^2 + a*p*#1^3 & , 2]^3)/(a*Sqrt[q + p*x^6]*(-(((-1)^(1/3)*q^(1/3))/p^(1/3)) + Root[a*q + b*#1^2 + a*p*#1^3 & , 2])*(-Root[a*q + b*#1^2 + a*p*#1^3 & , 1] + Root[a*q + b*#1^2 + a*p*#1^3 & , 2])*(Root[a*q + b*#1^2 + a*p*#1^3 & , 2] - Root[a*q + b*#1^2 + a*p*#1^3 & , 3])) + (4*(((-1)^(1/3)*q^(1/3))/p^(1/3) + ((-1)^(2/3)*q^(1/3))/p^(1/3))*q*Sqrt[(q^(1/3)/p^(1/3) + x^2)/(q^(1/3)/p^(1/3) + ((-1)^(1/3)*q^(1/3))/p^(1/3))]*Sqrt[((-(((-1)^(2/3)*q^(1/3))/p^(1/3)) - x^2)*(-(((-1)^(1/3)*q^(1/3))/p^(1/3)) + x^2))/(((-1)^(1/3)*q^(1/3))/p^(1/3) + ((-1)^(2/3)*q^(1/3))/p^(1/3))^2]*EllipticPi[((-1)^(1/3)*q^(1/3) + (-1)^(2/3)*q^(1/3))/((-1)^(1/3)*q^(1/3) - p^(1/3)*Root[a*q + b*#1^2 + a*p*#1^3 & , 3]), ArcSin[Sqrt[((-1)^(1/3)*q^(1/3) - p^(1/3)*x^2)/(((-1)^(1/3) + (-1)^(2/3))*q^(1/3))]], (-1)^(1/3)])/(a*p*Sqrt[q + p*x^6]*(-(((-1)^(1/3)*q^(1/3))/p^(1/3)) + Root[a*q + b*#1^2 + a*p*#1^3 & , 3])*(-Root[a*q + b*#1^2 + a*p*#1^3 & , 1] + Root[a*q + b*#1^2 + a*p*#1^3 & , 3])*(-Root[a*q + b*#1^2 + a*p*#1^3 & , 2] + Root[a*q + b*#1^2 + a*p*#1^3 & , 3])) - (2*(((-1)^(1/3)*q^(1/3))/p^(1/3) + ((-1)^(2/3)*q^(1/3))/p^(1/3))*Sqrt[(q^(1/3)/p^(1/3) + x^2)/(q^(1/3)/p^(1/3) + ((-1)^(1/3)*q^(1/3))/p^(1/3))]*Sqrt[((-(((-1)^(2/3)*q^(1/3))/p^(1/3)) - x^2)*(-(((-1)^(1/3)*q^(1/3))/p^(1/3)) + x^2))/(((-1)^(1/3)*q^(1/3))/p^(1/3) + ((-1)^(2/3)*q^(1/3))/p^(1/3))^2]*EllipticPi[((-1)^(1/3)*q^(1/3) + (-1)^(2/3)*q^(1/3))/((-1)^(1/3)*q^(1/3) - p^(1/3)*Root[a*q + b*#1^2 + a*p*#1^3 & , 3]), ArcSin[Sqrt[((-1)^(1/3)*q^(1/3) - p^(1/3)*x^2)/(((-1)^(1/3) + (-1)^(2/3))*q^(1/3))]], (-1)^(1/3)]*Root[a*q + b*#1^2 + a*p*#1^3 & , 3]^3)/(a*Sqrt[q + p*x^6]*(-(((-1)^(1/3)*q^(1/3))/p^(1/3)) + Root[a*q + b*#1^2 + a*p*#1^3 & , 3])*(-Root[a*q + b*#1^2 + a*p*#1^3 & , 1] + Root[a*q + b*#1^2 + a*p*#1^3 & , 3])*(-Root[a*q + b*#1^2 + a*p*#1^3 & , 2] + Root[a*q + b*#1^2 + a*p*#1^3 & , 3]))))/(2*a)","C",0
731,1,248,56,0.5798754,"\int \frac{2 \left(-2 q+p x^6\right) \sqrt{q+p x^6} \left(a q+b x^4+a p x^6\right)}{x^{11}} \, dx","Integrate[(2*(-2*q + p*x^6)*Sqrt[q + p*x^6]*(a*q + b*x^4 + a*p*x^6))/x^11,x]","\frac{5 x^4 \left(6 a p^2 x^8 \left(p x^6+q\right) \, _2F_1\left(-\frac{1}{2},\frac{1}{3};\frac{4}{3};-\frac{p x^6}{q}\right)+3 a p q x^2 \left(p x^6+q\right) \, _2F_1\left(-\frac{2}{3},-\frac{1}{2};\frac{1}{3};-\frac{p x^6}{q}\right)-4 b p \sqrt{q} x^6 \sqrt{p x^6+q} \sqrt{\frac{p x^6}{q}+1} \tanh ^{-1}\left(\frac{\sqrt{p x^6+q}}{\sqrt{q}}\right)+4 b \left(p x^6+q\right) \left(\left(p x^6+q\right) \sqrt{\frac{p x^6}{q}+1}+p x^6 \tanh ^{-1}\left(\sqrt{\frac{p x^6}{q}+1}\right)\right)\right)+12 a q^2 \left(p x^6+q\right) \, _2F_1\left(-\frac{5}{3},-\frac{1}{2};-\frac{2}{3};-\frac{p x^6}{q}\right)}{30 x^{10} \sqrt{p x^6+q} \sqrt{\frac{p x^6}{q}+1}}","\frac{2 \sqrt{p x^6+q} \left(3 a p^2 x^{12}+6 a p q x^6+3 a q^2+5 b p x^{10}+5 b q x^4\right)}{15 x^{10}}",1,"(12*a*q^2*(q + p*x^6)*Hypergeometric2F1[-5/3, -1/2, -2/3, -((p*x^6)/q)] + 5*x^4*(-4*b*p*Sqrt[q]*x^6*Sqrt[q + p*x^6]*Sqrt[1 + (p*x^6)/q]*ArcTanh[Sqrt[q + p*x^6]/Sqrt[q]] + 4*b*(q + p*x^6)*((q + p*x^6)*Sqrt[1 + (p*x^6)/q] + p*x^6*ArcTanh[Sqrt[1 + (p*x^6)/q]]) + 3*a*p*q*x^2*(q + p*x^6)*Hypergeometric2F1[-2/3, -1/2, 1/3, -((p*x^6)/q)] + 6*a*p^2*x^8*(q + p*x^6)*Hypergeometric2F1[-1/2, 1/3, 4/3, -((p*x^6)/q)]))/(30*x^10*Sqrt[q + p*x^6]*Sqrt[1 + (p*x^6)/q])","C",1
732,1,52,56,0.0371198,"\int \frac{1}{x^3 \sqrt[8]{256-256 x^2+96 x^4-16 x^6+x^8}} \, dx","Integrate[1/(x^3*(256 - 256*x^2 + 96*x^4 - 16*x^6 + x^8)^(1/8)),x]","\frac{\left(x^2-4\right) \left(\frac{2}{x^2}+\frac{\tanh ^{-1}\left(\sqrt{1-\frac{x^2}{4}}\right)}{\sqrt{4-x^2}}\right)}{16 \sqrt[8]{\left(x^2-4\right)^4}}","\frac{\left(\left(x^2-4\right)^4\right)^{7/8} \left(\frac{\sqrt{x^2-4}}{8 x^2}+\frac{1}{16} \tan ^{-1}\left(\frac{\sqrt{x^2-4}}{2}\right)\right)}{\left(x^2-4\right)^{7/2}}",1,"((-4 + x^2)*(2/x^2 + ArcTanh[Sqrt[1 - x^2/4]]/Sqrt[4 - x^2]))/(16*((-4 + x^2)^4)^(1/8))","A",1
733,0,0,56,0.338345,"\int \frac{x^3 \left(5 b+8 a x^3\right)}{\sqrt[4]{b x+a x^4} \left(-2+b x^5+a x^8\right)} \, dx","Integrate[(x^3*(5*b + 8*a*x^3))/((b*x + a*x^4)^(1/4)*(-2 + b*x^5 + a*x^8)),x]","\int \frac{x^3 \left(5 b+8 a x^3\right)}{\sqrt[4]{b x+a x^4} \left(-2+b x^5+a x^8\right)} \, dx","2^{3/4} \tan ^{-1}\left(\frac{x \sqrt[4]{a x^4+b x}}{\sqrt[4]{2}}\right)-2^{3/4} \tanh ^{-1}\left(\frac{x \sqrt[4]{a x^4+b x}}{\sqrt[4]{2}}\right)",1,"Integrate[(x^3*(5*b + 8*a*x^3))/((b*x + a*x^4)^(1/4)*(-2 + b*x^5 + a*x^8)), x]","F",-1
734,1,49,56,0.025146,"\int \sqrt{1-x^2-y^4} \, dx","Integrate[Sqrt[1 - x^2 - y^4],x]","\frac{1}{2} \left(x \sqrt{-x^2-y^4+1}-\left(y^4-1\right) \tan ^{-1}\left(\frac{x}{\sqrt{-x^2-y^4+1}}\right)\right)","\frac{1}{2} x \sqrt{-x^2-y^4+1}-\frac{1}{2} i \left(y^4-1\right) \log \left(\sqrt{-x^2-y^4+1}-i x\right)",1,"(x*Sqrt[1 - x^2 - y^4] - (-1 + y^4)*ArcTan[x/Sqrt[1 - x^2 - y^4]])/2","A",1
735,1,227,57,4.2243008,"\int \frac{1-2 k^2 x+k^2 x^2}{\sqrt{(1-x) x \left(1-k^2 x\right)} \left(-a-b x+\left(a k^2+b k^2\right) x^2\right)} \, dx","Integrate[(1 - 2*k^2*x + k^2*x^2)/(Sqrt[(1 - x)*x*(1 - k^2*x)]*(-a - b*x + (a*k^2 + b*k^2)*x^2)),x]","-\frac{2 i \sqrt{\frac{1}{x-1}+1} (x-1)^{3/2} \sqrt{\frac{1-\frac{1}{k^2}}{x-1}+1} \left(-\Pi \left(-\frac{2 (a+b) \left(k^2-1\right)}{-2 a k^2-2 b k^2+b+\sqrt{b^2+4 a k^2 b+4 a^2 k^2}};i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)-\Pi \left(\frac{2 (a+b) \left(k^2-1\right)}{2 a k^2+2 b k^2-b+\sqrt{b^2+4 a k^2 b+4 a^2 k^2}};i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)+F\left(i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)\right)}{(a+b) \sqrt{(x-1) x \left(k^2 x-1\right)}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{a+b} \sqrt{k^2 x^3+\left(-k^2-1\right) x^2+x}}{\sqrt{a} (x-1)}\right)}{\sqrt{a} \sqrt{a+b}}",1,"((-2*I)*Sqrt[1 + (-1 + x)^(-1)]*Sqrt[1 + (1 - k^(-2))/(-1 + x)]*(-1 + x)^(3/2)*(EllipticF[I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)] - EllipticPi[(-2*(a + b)*(-1 + k^2))/(b - 2*a*k^2 - 2*b*k^2 + Sqrt[b^2 + 4*a^2*k^2 + 4*a*b*k^2]), I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)] - EllipticPi[(2*(a + b)*(-1 + k^2))/(-b + 2*a*k^2 + 2*b*k^2 + Sqrt[b^2 + 4*a^2*k^2 + 4*a*b*k^2]), I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)]))/((a + b)*Sqrt[(-1 + x)*x*(-1 + k^2*x)])","C",1
736,1,8060,57,13.0298262,"\int \frac{a b c-(a+b+c) x^2+2 x^3}{\sqrt{x (-a+x) (-b+x) (-c+x)} \left(-a b c d+(-1+a b d+a c d+b c d) x-(a+b+c) d x^2+d x^3\right)} \, dx","Integrate[(a*b*c - (a + b + c)*x^2 + 2*x^3)/(Sqrt[x*(-a + x)*(-b + x)*(-c + x)]*(-(a*b*c*d) + (-1 + a*b*d + a*c*d + b*c*d)*x - (a + b + c)*d*x^2 + d*x^3)),x]","\text{Result too large to show}","-\frac{2 \tanh ^{-1}\left(\frac{x}{\sqrt{d} \sqrt{x^3 (-a-b-c)+x^2 (a b+a c+b c)-a b c x+x^4}}\right)}{\sqrt{d}}",1,"Result too large to show","C",0
737,1,54,57,0.0186601,"\int x^6 \sqrt[4]{-1+x^4} \, dx","Integrate[x^6*(-1 + x^4)^(1/4),x]","\frac{x^3 \sqrt[4]{x^4-1} \left(\, _2F_1\left(-\frac{1}{4},\frac{3}{4};\frac{7}{4};x^4\right)-\left(1-x^4\right)^{5/4}\right)}{8 \sqrt[4]{1-x^4}}","\frac{3}{64} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-1}}\right)-\frac{3}{64} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-1}}\right)+\frac{1}{32} \sqrt[4]{x^4-1} \left(4 x^7-x^3\right)",1,"(x^3*(-1 + x^4)^(1/4)*(-(1 - x^4)^(5/4) + Hypergeometric2F1[-1/4, 3/4, 7/4, x^4]))/(8*(1 - x^4)^(1/4))","C",1
738,1,47,57,0.0160176,"\int \frac{(-1+2 x) \sqrt[4]{x^3+x^4}}{x} \, dx","Integrate[((-1 + 2*x)*(x^3 + x^4)^(1/4))/x,x]","\frac{\sqrt[4]{x^3 (x+1)} \left(3 (x+1)^{5/4}-7 \, _2F_1\left(-\frac{1}{4},\frac{3}{4};\frac{7}{4};-x\right)\right)}{3 \sqrt[4]{x+1}}","\frac{1}{4} \sqrt[4]{x^4+x^3} (4 x-3)+\frac{7}{8} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+x^3}}\right)-\frac{7}{8} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+x^3}}\right)",1,"((x^3*(1 + x))^(1/4)*(3*(1 + x)^(5/4) - 7*Hypergeometric2F1[-1/4, 3/4, 7/4, -x]))/(3*(1 + x)^(1/4))","C",1
739,1,59573,57,6.6797627,"\int \frac{\sqrt{-1+x^2-2 x^3+x^4} \left(1-x^3+x^4\right)}{\left(-1-2 x^3+x^4\right) \left(-2-x^2-4 x^3+2 x^4\right)} \, dx","Integrate[(Sqrt[-1 + x^2 - 2*x^3 + x^4]*(1 - x^3 + x^4))/((-1 - 2*x^3 + x^4)*(-2 - x^2 - 4*x^3 + 2*x^4)),x]","\text{Result too large to show}","\tanh ^{-1}\left(\frac{x}{\sqrt{x^4-2 x^3+x^2-1}}\right)-\sqrt{\frac{3}{2}} \tanh ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt{x^4-2 x^3+x^2-1}}\right)",1,"Result too large to show","C",0
740,1,50,57,0.0125346,"\int \frac{x^2}{\left(b+a x^4\right)^{3/4}} \, dx","Integrate[x^2/(b + a*x^4)^(3/4),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)-\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{2 a^{3/4}}","\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{2 a^{3/4}}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{2 a^{3/4}}",1,"(-ArcTan[(a^(1/4)*x)/(b + a*x^4)^(1/4)] + ArcTanh[(a^(1/4)*x)/(b + a*x^4)^(1/4)])/(2*a^(3/4))","A",1
741,0,0,57,0.3878972,"\int \frac{1}{\sqrt[4]{b+a x^4} \left(-b+a x^8\right)} \, dx","Integrate[1/((b + a*x^4)^(1/4)*(-b + a*x^8)),x]","\int \frac{1}{\sqrt[4]{b+a x^4} \left(-b+a x^8\right)} \, dx","\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2-a b\&,\frac{\log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{8 b}",1,"Integrate[1/((b + a*x^4)^(1/4)*(-b + a*x^8)), x]","F",-1
742,0,0,57,1.1252776,"\int \frac{-b+a x^8}{\sqrt[4]{b+a x^8} \left(b-c x^4+a x^8\right)} \, dx","Integrate[(-b + a*x^8)/((b + a*x^8)^(1/4)*(b - c*x^4 + a*x^8)),x]","\int \frac{-b+a x^8}{\sqrt[4]{b+a x^8} \left(b-c x^4+a x^8\right)} \, dx","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a x^8+b}}\right)}{2 \sqrt[4]{c}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a x^8+b}}\right)}{2 \sqrt[4]{c}}",1,"Integrate[(-b + a*x^8)/((b + a*x^8)^(1/4)*(b - c*x^4 + a*x^8)), x]","F",-1
743,0,0,57,0.7095427,"\int \frac{\left(-3+2 x^5\right) \left(1+2 x^5+x^6+x^{10}\right)}{x^6 \left(1-x^3+x^5\right) \sqrt[4]{x+x^6}} \, dx","Integrate[((-3 + 2*x^5)*(1 + 2*x^5 + x^6 + x^10))/(x^6*(1 - x^3 + x^5)*(x + x^6)^(1/4)),x]","\int \frac{\left(-3+2 x^5\right) \left(1+2 x^5+x^6+x^{10}\right)}{x^6 \left(1-x^3+x^5\right) \sqrt[4]{x+x^6}} \, dx","-4 \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^6+x}}\right)-4 \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^6+x}}\right)+\frac{4 \left(x^6+x\right)^{3/4} \left(3 x^5+7 x^3+3\right)}{21 x^6}",1,"Integrate[((-3 + 2*x^5)*(1 + 2*x^5 + x^6 + x^10))/(x^6*(1 - x^3 + x^5)*(x + x^6)^(1/4)), x]","F",-1
744,1,92,57,0.1829008,"\int \sqrt{x^2+\sqrt{1+x^4}} \, dx","Integrate[Sqrt[x^2 + Sqrt[1 + x^4]],x]","\frac{2 \left(\sqrt{x^4+1}+x^2\right) x^2+\sqrt{2} \sqrt{x^2 \left(\sqrt{x^4+1}+x^2\right)} \tan ^{-1}\left(\sqrt{\left(\sqrt{x^4+1}+x^2\right)^2-1}\right)}{4 x \sqrt{\sqrt{x^4+1}+x^2}}","\frac{1}{2} \sqrt{\sqrt{x^4+1}+x^2} x+\frac{\tan ^{-1}\left(\sqrt{2} x \sqrt{\sqrt{x^4+1}+x^2}\right)}{2 \sqrt{2}}",1,"(2*x^2*(x^2 + Sqrt[1 + x^4]) + Sqrt[2]*Sqrt[x^2*(x^2 + Sqrt[1 + x^4])]*ArcTan[Sqrt[-1 + (x^2 + Sqrt[1 + x^4])^2]])/(4*x*Sqrt[x^2 + Sqrt[1 + x^4]])","A",1
745,1,95,58,0.2770395,"\int \frac{-1-x+x^2}{\left(1+x^2\right) \sqrt{-x+x^3}} \, dx","Integrate[(-1 - x + x^2)/((1 + x^2)*Sqrt[-x + x^3]),x]","\frac{2 x \sqrt{1-x^2} \left(x \left(3 x F_1\left(\frac{5}{4};\frac{1}{2},1;\frac{9}{4};x^2,-x^2\right)-5 F_1\left(\frac{3}{4};\frac{1}{2},1;\frac{7}{4};x^2,-x^2\right)\right)-15 F_1\left(\frac{1}{4};\frac{1}{2},1;\frac{5}{4};x^2,-x^2\right)\right)}{15 \sqrt{x \left(x^2-1\right)}}","-\frac{1}{4} \tan ^{-1}\left(\frac{2 \sqrt{x^3-x}}{x^2-2 x-1}\right)-\frac{3}{4} \tanh ^{-1}\left(\frac{\frac{x^2}{2}+x-\frac{1}{2}}{\sqrt{x^3-x}}\right)",1,"(2*x*Sqrt[1 - x^2]*(-15*AppellF1[1/4, 1/2, 1, 5/4, x^2, -x^2] + x*(-5*AppellF1[3/4, 1/2, 1, 7/4, x^2, -x^2] + 3*x*AppellF1[5/4, 1/2, 1, 9/4, x^2, -x^2])))/(15*Sqrt[x*(-1 + x^2)])","C",0
746,1,95,58,0.1937779,"\int \frac{-1+x+x^2}{\left(1+x^2\right) \sqrt{-x+x^3}} \, dx","Integrate[(-1 + x + x^2)/((1 + x^2)*Sqrt[-x + x^3]),x]","\frac{2 x \sqrt{1-x^2} \left(x \left(5 F_1\left(\frac{3}{4};\frac{1}{2},1;\frac{7}{4};x^2,-x^2\right)+3 x F_1\left(\frac{5}{4};\frac{1}{2},1;\frac{9}{4};x^2,-x^2\right)\right)-15 F_1\left(\frac{1}{4};\frac{1}{2},1;\frac{5}{4};x^2,-x^2\right)\right)}{15 \sqrt{x \left(x^2-1\right)}}","-\frac{3}{4} \tan ^{-1}\left(\frac{2 \sqrt{x^3-x}}{x^2-2 x-1}\right)-\frac{1}{4} \tanh ^{-1}\left(\frac{\frac{x^2}{2}+x-\frac{1}{2}}{\sqrt{x^3-x}}\right)",1,"(2*x*Sqrt[1 - x^2]*(-15*AppellF1[1/4, 1/2, 1, 5/4, x^2, -x^2] + x*(5*AppellF1[3/4, 1/2, 1, 7/4, x^2, -x^2] + 3*x*AppellF1[5/4, 1/2, 1, 9/4, x^2, -x^2])))/(15*Sqrt[x*(-1 + x^2)])","C",0
747,1,95,58,0.5255106,"\int \frac{-7+x+7 x^2}{\left(1+x^2\right) \sqrt{-x+x^3}} \, dx","Integrate[(-7 + x + 7*x^2)/((1 + x^2)*Sqrt[-x + x^3]),x]","\frac{2 x \sqrt{1-x^2} \left(x \left(5 F_1\left(\frac{3}{4};\frac{1}{2},1;\frac{7}{4};x^2,-x^2\right)+21 x F_1\left(\frac{5}{4};\frac{1}{2},1;\frac{9}{4};x^2,-x^2\right)\right)-105 F_1\left(\frac{1}{4};\frac{1}{2},1;\frac{5}{4};x^2,-x^2\right)\right)}{15 \sqrt{x \left(x^2-1\right)}}","-\frac{15}{4} \tan ^{-1}\left(\frac{2 \sqrt{x^3-x}}{x^2-2 x-1}\right)-\frac{13}{4} \tanh ^{-1}\left(\frac{\frac{x^2}{2}+x-\frac{1}{2}}{\sqrt{x^3-x}}\right)",1,"(2*x*Sqrt[1 - x^2]*(-105*AppellF1[1/4, 1/2, 1, 5/4, x^2, -x^2] + x*(5*AppellF1[3/4, 1/2, 1, 7/4, x^2, -x^2] + 21*x*AppellF1[5/4, 1/2, 1, 9/4, x^2, -x^2])))/(15*Sqrt[x*(-1 + x^2)])","C",0
748,1,40,58,0.024699,"\int \frac{1}{(-2+x) \sqrt[4]{-x^2+x^3}} \, dx","Integrate[1/((-2 + x)*(-x^2 + x^3)^(1/4)),x]","-\frac{\sqrt[4]{1-x} x F_1\left(\frac{1}{2};\frac{1}{4},1;\frac{3}{2};x,\frac{x}{2}\right)}{\sqrt[4]{(x-1) x^2}}","\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{x^3-x^2}}{x}\right)}{\sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{2} \sqrt[4]{x^3-x^2}}\right)}{\sqrt{2}}",1,"-(((1 - x)^(1/4)*x*AppellF1[1/2, 1/4, 1, 3/2, x, x/2])/((-1 + x)*x^2)^(1/4))","C",0
749,1,63,58,0.0602102,"\int \left(b+a x^3\right) \sqrt{-x+x^4} \, dx","Integrate[(b + a*x^3)*Sqrt[-x + x^4],x]","\frac{\sqrt{x \left(x^3-1\right)} \left(x^{3/2} \left(a \left(2 x^3-1\right)+4 b\right)+\frac{(a+4 b) \sin ^{-1}\left(x^{3/2}\right)}{\sqrt{1-x^3}}\right)}{12 \sqrt{x}}","\frac{1}{12} \sqrt{x^4-x} \left(2 a x^4-a x+4 b x\right)+\frac{1}{12} (-a-4 b) \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4-x}}\right)",1,"(Sqrt[x*(-1 + x^3)]*(x^(3/2)*(4*b + a*(-1 + 2*x^3)) + ((a + 4*b)*ArcSin[x^(3/2)])/Sqrt[1 - x^3]))/(12*Sqrt[x])","A",1
750,1,170,58,0.2059293,"\int \frac{-2-x+2 x^2}{\left(1+x^2\right) \sqrt{1+x^2+x^4}} \, dx","Integrate[(-2 - x + 2*x^2)/((1 + x^2)*Sqrt[1 + x^2 + x^4]),x]","\frac{1}{2} \tanh ^{-1}\left(\frac{1-x^2}{2 \sqrt{x^4+x^2+1}}\right)+\frac{2 (-1)^{2/3} \sqrt{\sqrt[3]{-1} x^2+1} \sqrt{1-(-1)^{2/3} x^2} F\left(i \sinh ^{-1}\left((-1)^{5/6} x\right)|(-1)^{2/3}\right)}{\sqrt{x^4+x^2+1}}-\frac{4 (-1)^{2/3} \sqrt{\sqrt[3]{-1} x^2+1} \sqrt{1-(-1)^{2/3} x^2} \Pi \left(\sqrt[3]{-1};i \sinh ^{-1}\left((-1)^{5/6} x\right)|(-1)^{2/3}\right)}{\sqrt{x^4+x^2+1}}","\frac{1}{2} \tanh ^{-1}\left(\frac{2 x^2}{x^4+2 x^2+\left(x^2-1\right) \sqrt{x^4+x^2+1}+1}\right)-2 \tan ^{-1}\left(\frac{x}{\sqrt{x^4+x^2+1}}\right)",1,"ArcTanh[(1 - x^2)/(2*Sqrt[1 + x^2 + x^4])]/2 + (2*(-1)^(2/3)*Sqrt[1 + (-1)^(1/3)*x^2]*Sqrt[1 - (-1)^(2/3)*x^2]*EllipticF[I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)])/Sqrt[1 + x^2 + x^4] - (4*(-1)^(2/3)*Sqrt[1 + (-1)^(1/3)*x^2]*Sqrt[1 - (-1)^(2/3)*x^2]*EllipticPi[(-1)^(1/3), I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)])/Sqrt[1 + x^2 + x^4]","C",1
751,0,0,58,0.3495887,"\int \frac{x^3 \left(-5 b+9 a x^4\right)}{\sqrt[4]{-b x+a x^5} \left(-2-b x^5+a x^9\right)} \, dx","Integrate[(x^3*(-5*b + 9*a*x^4))/((-(b*x) + a*x^5)^(1/4)*(-2 - b*x^5 + a*x^9)),x]","\int \frac{x^3 \left(-5 b+9 a x^4\right)}{\sqrt[4]{-b x+a x^5} \left(-2-b x^5+a x^9\right)} \, dx","2^{3/4} \tan ^{-1}\left(\frac{x \sqrt[4]{a x^5-b x}}{\sqrt[4]{2}}\right)-2^{3/4} \tanh ^{-1}\left(\frac{x \sqrt[4]{a x^5-b x}}{\sqrt[4]{2}}\right)",1,"Integrate[(x^3*(-5*b + 9*a*x^4))/((-(b*x) + a*x^5)^(1/4)*(-2 - b*x^5 + a*x^9)), x]","F",-1
752,1,667,59,2.3937123,"\int \frac{1+x^2}{\left(-1+x^2\right) \sqrt{x+x^2+x^3}} \, dx","Integrate[(1 + x^2)/((-1 + x^2)*Sqrt[x + x^2 + x^3]),x]","-\frac{2 (-1)^{2/3} \left(\frac{1}{x^2}-1\right) x^{7/2} \left(x^2+1\right) \left(\sqrt{1-\frac{(-1)^{2/3}}{x}} \sqrt{\frac{x+\sqrt[3]{-1}}{x}} F\left(i \sinh ^{-1}\left(\frac{(-1)^{5/6}}{\sqrt{x}}\right)|(-1)^{2/3}\right)-\sqrt{1-\frac{(-1)^{2/3}}{x}} \sqrt{\frac{x+\sqrt[3]{-1}}{x}} \Pi \left(\sqrt[3]{-1};i \sinh ^{-1}\left(\frac{(-1)^{5/6}}{\sqrt{x}}\right)|(-1)^{2/3}\right)+\frac{\sqrt{\frac{\sqrt{x}-\sqrt[3]{-1}+1}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1} \sqrt{x}-1\right)}} \sqrt{\frac{(-1)^{2/3} \sqrt{x}-1}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1} \sqrt{x}-1\right)}} \sqrt{-\frac{(-1)^{2/3} \sqrt{x}+1}{\sqrt{x}+\sqrt[3]{-1}-1}} \left(\sqrt[3]{-1} \sqrt{x}-1\right)^2 \left(\left(1+\sqrt[3]{-1}\right) F\left(\left.\sin ^{-1}\left(\sqrt{\frac{\sqrt{x}-\sqrt[3]{-1}+1}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1} \sqrt{x}-1\right)}}\right)\right|-3\right)-2 \sqrt[3]{-1} \Pi \left(-1;\left.\sin ^{-1}\left(\sqrt{\frac{\sqrt{x}-\sqrt[3]{-1}+1}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1} \sqrt{x}-1\right)}}\right)\right|-3\right)\right)}{\left(\sqrt[3]{-1}-1\right)^2 x}-\frac{\sqrt{\frac{\sqrt{x}-\sqrt[3]{-1}+1}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1} \sqrt{x}-1\right)}} \sqrt{\frac{(-1)^{2/3} \sqrt{x}-1}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1} \sqrt{x}-1\right)}} \sqrt{-\frac{(-1)^{2/3} \sqrt{x}+1}{\sqrt{x}+\sqrt[3]{-1}-1}} \left(\sqrt[3]{-1} \sqrt{x}-1\right)^2 \left(\left(\sqrt[3]{-1}-1\right) F\left(\left.\sin ^{-1}\left(\sqrt{\frac{\sqrt{x}-\sqrt[3]{-1}+1}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1} \sqrt{x}-1\right)}}\right)\right|-3\right)-2 \sqrt[3]{-1} \Pi \left(3;\left.\sin ^{-1}\left(\sqrt{\frac{\sqrt{x}-\sqrt[3]{-1}+1}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1} \sqrt{x}-1\right)}}\right)\right|-3\right)\right)}{\left(\sqrt[3]{-1}-1\right)^2 x}\right)}{\sqrt{x \left(x^2+x+1\right)} \left(x^4-1\right)}","-\tan ^{-1}\left(\frac{\sqrt{x^3+x^2+x}}{x^2+x+1}\right)-\frac{\tanh ^{-1}\left(\frac{\sqrt{3} \sqrt{x^3+x^2+x}}{x^2+x+1}\right)}{\sqrt{3}}",1,"(-2*(-1)^(2/3)*(-1 + x^(-2))*x^(7/2)*(1 + x^2)*(Sqrt[1 - (-1)^(2/3)/x]*Sqrt[((-1)^(1/3) + x)/x]*EllipticF[I*ArcSinh[(-1)^(5/6)/Sqrt[x]], (-1)^(2/3)] + (Sqrt[(1 - (-1)^(1/3) + Sqrt[x])/((1 + (-1)^(1/3))*(-1 + (-1)^(1/3)*Sqrt[x]))]*(-1 + (-1)^(1/3)*Sqrt[x])^2*Sqrt[(-1 + (-1)^(2/3)*Sqrt[x])/((1 + (-1)^(1/3))*(-1 + (-1)^(1/3)*Sqrt[x]))]*Sqrt[-((1 + (-1)^(2/3)*Sqrt[x])/(-1 + (-1)^(1/3) + Sqrt[x]))]*((1 + (-1)^(1/3))*EllipticF[ArcSin[Sqrt[(1 - (-1)^(1/3) + Sqrt[x])/((1 + (-1)^(1/3))*(-1 + (-1)^(1/3)*Sqrt[x]))]], -3] - 2*(-1)^(1/3)*EllipticPi[-1, ArcSin[Sqrt[(1 - (-1)^(1/3) + Sqrt[x])/((1 + (-1)^(1/3))*(-1 + (-1)^(1/3)*Sqrt[x]))]], -3]))/((-1 + (-1)^(1/3))^2*x) - (Sqrt[(1 - (-1)^(1/3) + Sqrt[x])/((1 + (-1)^(1/3))*(-1 + (-1)^(1/3)*Sqrt[x]))]*(-1 + (-1)^(1/3)*Sqrt[x])^2*Sqrt[(-1 + (-1)^(2/3)*Sqrt[x])/((1 + (-1)^(1/3))*(-1 + (-1)^(1/3)*Sqrt[x]))]*Sqrt[-((1 + (-1)^(2/3)*Sqrt[x])/(-1 + (-1)^(1/3) + Sqrt[x]))]*((-1 + (-1)^(1/3))*EllipticF[ArcSin[Sqrt[(1 - (-1)^(1/3) + Sqrt[x])/((1 + (-1)^(1/3))*(-1 + (-1)^(1/3)*Sqrt[x]))]], -3] - 2*(-1)^(1/3)*EllipticPi[3, ArcSin[Sqrt[(1 - (-1)^(1/3) + Sqrt[x])/((1 + (-1)^(1/3))*(-1 + (-1)^(1/3)*Sqrt[x]))]], -3]))/((-1 + (-1)^(1/3))^2*x) - Sqrt[1 - (-1)^(2/3)/x]*Sqrt[((-1)^(1/3) + x)/x]*EllipticPi[(-1)^(1/3), I*ArcSinh[(-1)^(5/6)/Sqrt[x]], (-1)^(2/3)]))/(Sqrt[x*(1 + x + x^2)]*(-1 + x^4))","C",0
753,1,6921,59,13.0975784,"\int \frac{a b c-(a+b+c) x^2+2 x^3}{\sqrt{x (-a+x) (-b+x) (-c+x)} \left(-a b c+(a b+a c+b c-d) x-(a+b+c) x^2+x^3\right)} \, dx","Integrate[(a*b*c - (a + b + c)*x^2 + 2*x^3)/(Sqrt[x*(-a + x)*(-b + x)*(-c + x)]*(-(a*b*c) + (a*b + a*c + b*c - d)*x - (a + b + c)*x^2 + x^3)),x]","\text{Result too large to show}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{x^3 (-a-b-c)+x^2 (a b+a c+b c)-a b c x+x^4}}{\sqrt{d} x}\right)}{\sqrt{d}}",1,"Result too large to show","C",0
754,1,76,59,0.0352532,"\int \frac{\left(-b+a x^3\right) \sqrt{b+a x^3}}{x^7} \, dx","Integrate[((-b + a*x^3)*Sqrt[b + a*x^3])/x^7,x]","\frac{-5 a^2 x^6 \sqrt{\frac{a x^3}{b}+1} \tanh ^{-1}\left(\sqrt{\frac{a x^3}{b}+1}\right)-3 a^2 x^6-a b x^3+2 b^2}{12 x^6 \sqrt{a x^3+b}}","\frac{\left(2 b-3 a x^3\right) \sqrt{a x^3+b}}{12 x^6}-\frac{5 a^2 \tanh ^{-1}\left(\frac{\sqrt{a x^3+b}}{\sqrt{b}}\right)}{12 \sqrt{b}}",1,"(2*b^2 - a*b*x^3 - 3*a^2*x^6 - 5*a^2*x^6*Sqrt[1 + (a*x^3)/b]*ArcTanh[Sqrt[1 + (a*x^3)/b]])/(12*x^6*Sqrt[b + a*x^3])","A",1
755,1,75,59,0.0379948,"\int \frac{\sqrt{b+a x^3} \left(2 b+a x^3\right)}{x^7} \, dx","Integrate[(Sqrt[b + a*x^3]*(2*b + a*x^3))/x^7,x]","-\frac{a^2 x^6 \sqrt{\frac{a x^3}{b}+1} \tanh ^{-1}\left(\sqrt{\frac{a x^3}{b}+1}\right)+3 a^2 x^6+5 a b x^3+2 b^2}{6 x^6 \sqrt{a x^3+b}}","\frac{\left(-3 a x^3-2 b\right) \sqrt{a x^3+b}}{6 x^6}-\frac{a^2 \tanh ^{-1}\left(\frac{\sqrt{a x^3+b}}{\sqrt{b}}\right)}{6 \sqrt{b}}",1,"-1/6*(2*b^2 + 5*a*b*x^3 + 3*a^2*x^6 + a^2*x^6*Sqrt[1 + (a*x^3)/b]*ArcTanh[Sqrt[1 + (a*x^3)/b]])/(x^6*Sqrt[b + a*x^3])","A",1
756,1,28348,59,12.6424576,"\int \frac{3 a b c x-2 (a b+a c+b c) x^2+(a+b+c) x^3}{\sqrt{x (-a+x) (-b+x) (-c+x)} \left(a b c-(a b+a c+b c) x+(a+b+c) x^2+(-1+d) x^3\right)} \, dx","Integrate[(3*a*b*c*x - 2*(a*b + a*c + b*c)*x^2 + (a + b + c)*x^3)/(Sqrt[x*(-a + x)*(-b + x)*(-c + x)]*(a*b*c - (a*b + a*c + b*c)*x + (a + b + c)*x^2 + (-1 + d)*x^3)),x]","\text{Result too large to show}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{x^3 (-a-b-c)+x^2 (a b+a c+b c)-a b c x+x^4}}{\sqrt{d} x^2}\right)}{\sqrt{d}}",1,"Result too large to show","C",0
757,1,32877,59,12.2730003,"\int \frac{x \left(3 a b c-2 (a b+a c+b c) x+(a+b+c) x^2\right)}{\sqrt{x (-a+x) (-b+x) (-c+x)} \left(-a b c d+(a b+a c+b c) d x-(a+b+c) d x^2+(-1+d) x^3\right)} \, dx","Integrate[(x*(3*a*b*c - 2*(a*b + a*c + b*c)*x + (a + b + c)*x^2))/(Sqrt[x*(-a + x)*(-b + x)*(-c + x)]*(-(a*b*c*d) + (a*b + a*c + b*c)*d*x - (a + b + c)*d*x^2 + (-1 + d)*x^3)),x]","\text{Result too large to show}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{x^3 (-a-b-c)+x^2 (a b+a c+b c)-a b c x+x^4}}{x^2}\right)}{\sqrt{d}}",1,"Result too large to show","C",0
758,1,42,59,0.0080894,"\int \sqrt[4]{-x^2+x^4} \, dx","Integrate[(-x^2 + x^4)^(1/4),x]","\frac{2 x \sqrt[4]{x^2 \left(x^2-1\right)} \, _2F_1\left(-\frac{1}{4},\frac{3}{4};\frac{7}{4};x^2\right)}{3 \sqrt[4]{1-x^2}}","\frac{1}{2} \sqrt[4]{x^4-x^2} x+\frac{1}{4} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^2}}\right)-\frac{1}{4} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^2}}\right)",1,"(2*x*(x^2*(-1 + x^2))^(1/4)*Hypergeometric2F1[-1/4, 3/4, 7/4, x^2])/(3*(1 - x^2)^(1/4))","C",1
759,1,52,59,0.0138345,"\int x^2 \sqrt[4]{x^2+x^4} \, dx","Integrate[x^2*(x^2 + x^4)^(1/4),x]","\frac{x \sqrt[4]{x^4+x^2} \left(\left(x^2+1\right)^{5/4}-\, _2F_1\left(-\frac{1}{4},\frac{3}{4};\frac{7}{4};-x^2\right)\right)}{4 \sqrt[4]{x^2+1}}","\frac{3}{32} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+x^2}}\right)-\frac{3}{32} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+x^2}}\right)+\frac{1}{16} \sqrt[4]{x^4+x^2} \left(4 x^3+x\right)",1,"(x*(x^2 + x^4)^(1/4)*((1 + x^2)^(5/4) - Hypergeometric2F1[-1/4, 3/4, 7/4, -x^2]))/(4*(1 + x^2)^(1/4))","C",1
760,1,199,59,0.8709483,"\int \frac{\left(-1+2 x^4\right) \sqrt{1+3 x^2+2 x^4}}{\left(1+2 x^2+2 x^4\right)^2} \, dx","Integrate[((-1 + 2*x^4)*Sqrt[1 + 3*x^2 + 2*x^4])/(1 + 2*x^2 + 2*x^4)^2,x]","\frac{-i \sqrt{2} \sqrt{x^2+1} \sqrt{2 x^2+1} F\left(i \sinh ^{-1}\left(\sqrt{2} x\right)|\frac{1}{2}\right)+i \sqrt{2} \sqrt{x^2+1} \sqrt{2 x^2+1} \Pi \left(\frac{1}{2}-\frac{i}{2};i \sinh ^{-1}\left(\sqrt{2} x\right)|\frac{1}{2}\right)+i \sqrt{2} \sqrt{x^2+1} \sqrt{2 x^2+1} \Pi \left(\frac{1}{2}+\frac{i}{2};i \sinh ^{-1}\left(\sqrt{2} x\right)|\frac{1}{2}\right)-\frac{2 x \left(2 x^4+3 x^2+1\right)}{2 x^4+2 x^2+1}}{4 \sqrt{2 x^4+3 x^2+1}}","-\frac{\sqrt{2 x^4+3 x^2+1} x}{2 \left(2 x^4+2 x^2+1\right)}-\frac{1}{2} \tanh ^{-1}\left(\frac{x}{\sqrt{2 x^4+3 x^2+1}}\right)",1,"((-2*x*(1 + 3*x^2 + 2*x^4))/(1 + 2*x^2 + 2*x^4) - I*Sqrt[2]*Sqrt[1 + x^2]*Sqrt[1 + 2*x^2]*EllipticF[I*ArcSinh[Sqrt[2]*x], 1/2] + I*Sqrt[2]*Sqrt[1 + x^2]*Sqrt[1 + 2*x^2]*EllipticPi[1/2 - I/2, I*ArcSinh[Sqrt[2]*x], 1/2] + I*Sqrt[2]*Sqrt[1 + x^2]*Sqrt[1 + 2*x^2]*EllipticPi[1/2 + I/2, I*ArcSinh[Sqrt[2]*x], 1/2])/(4*Sqrt[1 + 3*x^2 + 2*x^4])","C",1
761,1,109133,59,6.6776236,"\int \frac{\sqrt{-2+x^2-2 x^3+2 x^4} \left(2-x^3+2 x^4\right)}{\left(-1-x^3+x^4\right) \left(-2-x^2-2 x^3+2 x^4\right)} \, dx","Integrate[(Sqrt[-2 + x^2 - 2*x^3 + 2*x^4]*(2 - x^3 + 2*x^4))/((-1 - x^3 + x^4)*(-2 - x^2 - 2*x^3 + 2*x^4)),x]","\text{Result too large to show}","2 \tanh ^{-1}\left(\frac{x}{\sqrt{2 x^4-2 x^3+x^2-2}}\right)-2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{2 x^4-2 x^3+x^2-2}}\right)",1,"Result too large to show","C",0
762,1,95,59,0.2240825,"\int \frac{-b+a x^2}{\left(b+a x^2\right) \sqrt{b^2+a^2 x^4}} \, dx","Integrate[(-b + a*x^2)/((b + a*x^2)*Sqrt[b^2 + a^2*x^4]),x]","-\frac{i \sqrt{\frac{a^2 x^4}{b^2}+1} \left(F\left(\left.i \sinh ^{-1}\left(\sqrt{\frac{i a}{b}} x\right)\right|-1\right)-2 \Pi \left(-i;\left.i \sinh ^{-1}\left(\sqrt{\frac{i a}{b}} x\right)\right|-1\right)\right)}{\sqrt{\frac{i a}{b}} \sqrt{a^2 x^4+b^2}}","-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{b} x}{\sqrt{a^2 x^4+b^2}+a x^2+b}\right)}{\sqrt{a} \sqrt{b}}",1,"((-I)*Sqrt[1 + (a^2*x^4)/b^2]*(EllipticF[I*ArcSinh[Sqrt[(I*a)/b]*x], -1] - 2*EllipticPi[-I, I*ArcSinh[Sqrt[(I*a)/b]*x], -1]))/(Sqrt[(I*a)/b]*Sqrt[b^2 + a^2*x^4])","C",1
763,0,0,59,0.6365561,"\int \frac{3 b+a x^4}{\left(-b-x^3+a x^4\right) \sqrt[4]{-b x+a x^5}} \, dx","Integrate[(3*b + a*x^4)/((-b - x^3 + a*x^4)*(-(b*x) + a*x^5)^(1/4)),x]","\int \frac{3 b+a x^4}{\left(-b-x^3+a x^4\right) \sqrt[4]{-b x+a x^5}} \, dx","-2 \tan ^{-1}\left(\frac{\left(a x^5-b x\right)^{3/4}}{a x^4-b}\right)-2 \tanh ^{-1}\left(\frac{\left(a x^5-b x\right)^{3/4}}{a x^4-b}\right)",1,"Integrate[(3*b + a*x^4)/((-b - x^3 + a*x^4)*(-(b*x) + a*x^5)^(1/4)), x]","F",-1
764,1,80,59,0.0616843,"\int \frac{\left(-1+x^3\right) \sqrt{-1+x^6}}{x} \, dx","Integrate[((-1 + x^3)*Sqrt[-1 + x^6])/x,x]","\frac{2 \sqrt{-\left(x^6-1\right)^2} \tan ^{-1}\left(\sqrt{x^6-1}\right)+\left(x^6-1\right) \sin ^{-1}\left(x^3\right)+\sqrt{1-x^6} \left(x^9-2 x^6-x^3+2\right)}{6 \sqrt{-\left(x^6-1\right)^2}}","\frac{1}{6} \sqrt{x^6-1} \left(x^3-2\right)-\frac{2}{3} \tan ^{-1}\left(\frac{x^3+1}{\sqrt{x^6-1}}\right)-\frac{1}{3} \tanh ^{-1}\left(\frac{x^3+1}{\sqrt{x^6-1}}\right)",1,"(Sqrt[1 - x^6]*(2 - x^3 - 2*x^6 + x^9) + (-1 + x^6)*ArcSin[x^3] + 2*Sqrt[-(-1 + x^6)^2]*ArcTan[Sqrt[-1 + x^6]])/(6*Sqrt[-(-1 + x^6)^2])","A",0
765,0,0,59,0.1595423,"\int \frac{x (3+4 x) \sqrt[3]{-1-2 x+x^3}}{-2-8 x-8 x^2+x^6} \, dx","Integrate[(x*(3 + 4*x)*(-1 - 2*x + x^3)^(1/3))/(-2 - 8*x - 8*x^2 + x^6),x]","\int \frac{x (3+4 x) \sqrt[3]{-1-2 x+x^3}}{-2-8 x-8 x^2+x^6} \, dx","-\frac{1}{4} \text{RootSum}\left[2 \text{$\#$1}^6-4 \text{$\#$1}^3+1\&,\frac{\text{$\#$1} \log \left(\sqrt[3]{x^3-2 x-1}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^3-1}\&\right]",1,"Integrate[(x*(3 + 4*x)*(-1 - 2*x + x^3)^(1/3))/(-2 - 8*x - 8*x^2 + x^6), x]","F",-1
766,0,0,59,0.0700408,"\int \frac{x (3+4 x) \sqrt[3]{-1-2 x+x^3}}{-2-8 x-8 x^2+x^6} \, dx","Integrate[(x*(3 + 4*x)*(-1 - 2*x + x^3)^(1/3))/(-2 - 8*x - 8*x^2 + x^6),x]","\int \frac{x (3+4 x) \sqrt[3]{-1-2 x+x^3}}{-2-8 x-8 x^2+x^6} \, dx","-\frac{1}{4} \text{RootSum}\left[2 \text{$\#$1}^6-4 \text{$\#$1}^3+1\&,\frac{\text{$\#$1} \log \left(\sqrt[3]{x^3-2 x-1}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^3-1}\&\right]",1,"Integrate[(x*(3 + 4*x)*(-1 - 2*x + x^3)^(1/3))/(-2 - 8*x - 8*x^2 + x^6), x]","F",-1
767,0,0,59,0.1504254,"\int \frac{(3+2 x) \left(1+x+x^3\right)^{2/3}}{1+2 x+x^2+x^3+x^4+x^6} \, dx","Integrate[((3 + 2*x)*(1 + x + x^3)^(2/3))/(1 + 2*x + x^2 + x^3 + x^4 + x^6),x]","\int \frac{(3+2 x) \left(1+x+x^3\right)^{2/3}}{1+2 x+x^2+x^3+x^4+x^6} \, dx","-\text{RootSum}\left[\text{$\#$1}^6-\text{$\#$1}^3+1\&,\frac{\text{$\#$1}^2 \log \left(\sqrt[3]{x^3+x+1}-\text{$\#$1} x\right)-\text{$\#$1}^2 \log (x)}{2 \text{$\#$1}^3-1}\&\right]",1,"Integrate[((3 + 2*x)*(1 + x + x^3)^(2/3))/(1 + 2*x + x^2 + x^3 + x^4 + x^6), x]","F",-1
768,0,0,59,0.0727137,"\int \frac{(3+2 x) \left(1+x+x^3\right)^{2/3}}{1+2 x+x^2+x^3+x^4+x^6} \, dx","Integrate[((3 + 2*x)*(1 + x + x^3)^(2/3))/(1 + 2*x + x^2 + x^3 + x^4 + x^6),x]","\int \frac{(3+2 x) \left(1+x+x^3\right)^{2/3}}{1+2 x+x^2+x^3+x^4+x^6} \, dx","-\text{RootSum}\left[\text{$\#$1}^6-\text{$\#$1}^3+1\&,\frac{\text{$\#$1}^2 \log \left(\sqrt[3]{x^3+x+1}-\text{$\#$1} x\right)-\text{$\#$1}^2 \log (x)}{2 \text{$\#$1}^3-1}\&\right]",1,"Integrate[((3 + 2*x)*(1 + x + x^3)^(2/3))/(1 + 2*x + x^2 + x^3 + x^4 + x^6), x]","F",-1
769,0,0,59,0.4672839,"\int \frac{\left(2+x^3\right) \sqrt[3]{x+x^3-x^4}}{1+x^2-2 x^3+x^4-x^5+x^6} \, dx","Integrate[((2 + x^3)*(x + x^3 - x^4)^(1/3))/(1 + x^2 - 2*x^3 + x^4 - x^5 + x^6),x]","\int \frac{\left(2+x^3\right) \sqrt[3]{x+x^3-x^4}}{1+x^2-2 x^3+x^4-x^5+x^6} \, dx","-\text{RootSum}\left[\text{$\#$1}^6-\text{$\#$1}^3+1\&,\frac{\text{$\#$1} \log \left(\sqrt[3]{-x^4+x^3+x}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{2 \text{$\#$1}^3-1}\&\right]",1,"Integrate[((2 + x^3)*(x + x^3 - x^4)^(1/3))/(1 + x^2 - 2*x^3 + x^4 - x^5 + x^6), x]","F",-1
770,0,0,59,0.136341,"\int \frac{\left(2+x^3\right) \sqrt[3]{x+x^3-x^4}}{1+x^2-2 x^3+x^4-x^5+x^6} \, dx","Integrate[((2 + x^3)*(x + x^3 - x^4)^(1/3))/(1 + x^2 - 2*x^3 + x^4 - x^5 + x^6),x]","\int \frac{\left(2+x^3\right) \sqrt[3]{x+x^3-x^4}}{1+x^2-2 x^3+x^4-x^5+x^6} \, dx","-\text{RootSum}\left[\text{$\#$1}^6-\text{$\#$1}^3+1\&,\frac{\text{$\#$1} \log \left(\sqrt[3]{-x^4+x^3+x}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{2 \text{$\#$1}^3-1}\&\right]",1,"Integrate[((2 + x^3)*(x + x^3 - x^4)^(1/3))/(1 + x^2 - 2*x^3 + x^4 - x^5 + x^6), x]","F",-1
771,0,0,59,0.1787379,"\int \frac{\left(3+x^2\right) \left(1+x^2+x^3\right)^{2/3}}{-1-2 x^2+x^3-x^4+x^5+x^6} \, dx","Integrate[((3 + x^2)*(1 + x^2 + x^3)^(2/3))/(-1 - 2*x^2 + x^3 - x^4 + x^5 + x^6),x]","\int \frac{\left(3+x^2\right) \left(1+x^2+x^3\right)^{2/3}}{-1-2 x^2+x^3-x^4+x^5+x^6} \, dx","\text{RootSum}\left[\text{$\#$1}^6-3 \text{$\#$1}^3+1\&,\frac{\text{$\#$1}^2 \log \left(\sqrt[3]{x^3+x^2+1}-\text{$\#$1} x\right)-\text{$\#$1}^2 \log (x)}{2 \text{$\#$1}^3-3}\&\right]",1,"Integrate[((3 + x^2)*(1 + x^2 + x^3)^(2/3))/(-1 - 2*x^2 + x^3 - x^4 + x^5 + x^6), x]","F",-1
772,0,0,59,0.0861391,"\int \frac{\left(3+x^2\right) \left(1+x^2+x^3\right)^{2/3}}{-1-2 x^2+x^3-x^4+x^5+x^6} \, dx","Integrate[((3 + x^2)*(1 + x^2 + x^3)^(2/3))/(-1 - 2*x^2 + x^3 - x^4 + x^5 + x^6),x]","\int \frac{\left(3+x^2\right) \left(1+x^2+x^3\right)^{2/3}}{-1-2 x^2+x^3-x^4+x^5+x^6} \, dx","\text{RootSum}\left[\text{$\#$1}^6-3 \text{$\#$1}^3+1\&,\frac{\text{$\#$1}^2 \log \left(\sqrt[3]{x^3+x^2+1}-\text{$\#$1} x\right)-\text{$\#$1}^2 \log (x)}{2 \text{$\#$1}^3-3}\&\right]",1,"Integrate[((3 + x^2)*(1 + x^2 + x^3)^(2/3))/(-1 - 2*x^2 + x^3 - x^4 + x^5 + x^6), x]","F",-1
773,0,0,59,1.1591857,"\int \frac{b+a x^8}{\sqrt[4]{b-a x^8} \left(-b+c x^4+a x^8\right)} \, dx","Integrate[(b + a*x^8)/((b - a*x^8)^(1/4)*(-b + c*x^4 + a*x^8)),x]","\int \frac{b+a x^8}{\sqrt[4]{b-a x^8} \left(-b+c x^4+a x^8\right)} \, dx","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{b-a x^8}}\right)}{2 \sqrt[4]{c}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{b-a x^8}}\right)}{2 \sqrt[4]{c}}",1,"Integrate[(b + a*x^8)/((b - a*x^8)^(1/4)*(-b + c*x^4 + a*x^8)), x]","F",-1
774,0,0,59,0.1765927,"\int \frac{x \sqrt[3]{2-x^3+x^8} \left(-6+5 x^8\right)}{4+x^6+4 x^8+x^{16}} \, dx","Integrate[(x*(2 - x^3 + x^8)^(1/3)*(-6 + 5*x^8))/(4 + x^6 + 4*x^8 + x^16),x]","\int \frac{x \sqrt[3]{2-x^3+x^8} \left(-6+5 x^8\right)}{4+x^6+4 x^8+x^{16}} \, dx","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^6+2 \text{$\#$1}^3+2\&,\frac{\text{$\#$1} \log \left(\sqrt[3]{x^8-x^3+2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^3+1}\&\right]",1,"Integrate[(x*(2 - x^3 + x^8)^(1/3)*(-6 + 5*x^8))/(4 + x^6 + 4*x^8 + x^16), x]","F",-1
775,1,289,60,6.9079032,"\int \frac{a b+a c-b c-2 a x+x^2}{\sqrt{(-a+x) (-b+x) (-c+x)} \left(b c+a d-(b+c+d) x+x^2\right)} \, dx","Integrate[(a*b + a*c - b*c - 2*a*x + x^2)/(Sqrt[(-a + x)*(-b + x)*(-c + x)]*(b*c + a*d - (b + c + d)*x + x^2)),x]","-\frac{2 i (x-a)^{3/2} \sqrt{\frac{b-x}{a-x}} \sqrt{\frac{c-x}{a-x}} \left(-\Pi \left(-\frac{2 (a-c)}{-2 a+b+c+d-\sqrt{b^2-2 c b+2 d b+c^2+d^2-4 a d+2 c d}};i \sinh ^{-1}\left(\frac{\sqrt{a-b}}{\sqrt{x-a}}\right)|\frac{a-c}{a-b}\right)-\Pi \left(-\frac{2 (a-c)}{-2 a+b+c+d+\sqrt{b^2-2 c b+2 d b+c^2+d^2-4 a d+2 c d}};i \sinh ^{-1}\left(\frac{\sqrt{a-b}}{\sqrt{x-a}}\right)|\frac{a-c}{a-b}\right)+F\left(i \sinh ^{-1}\left(\frac{\sqrt{a-b}}{\sqrt{x-a}}\right)|\frac{a-c}{a-b}\right)\right)}{\sqrt{a-b} \sqrt{(x-a) (x-b) (x-c)}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{x^2 (-a-b-c)+x (a b+a c+b c)-a b c+x^3}}{\sqrt{d} (a-x)}\right)}{\sqrt{d}}",1,"((-2*I)*Sqrt[(b - x)/(a - x)]*Sqrt[(c - x)/(a - x)]*(-a + x)^(3/2)*(EllipticF[I*ArcSinh[Sqrt[a - b]/Sqrt[-a + x]], (a - c)/(a - b)] - EllipticPi[(-2*(a - c))/(-2*a + b + c + d - Sqrt[b^2 - 2*b*c + c^2 - 4*a*d + 2*b*d + 2*c*d + d^2]), I*ArcSinh[Sqrt[a - b]/Sqrt[-a + x]], (a - c)/(a - b)] - EllipticPi[(-2*(a - c))/(-2*a + b + c + d + Sqrt[b^2 - 2*b*c + c^2 - 4*a*d + 2*b*d + 2*c*d + d^2]), I*ArcSinh[Sqrt[a - b]/Sqrt[-a + x]], (a - c)/(a - b)]))/(Sqrt[a - b]*Sqrt[(-a + x)*(-b + x)*(-c + x)])","C",1
776,1,308,60,8.9648522,"\int \frac{a b+a c-b c-2 a x+x^2}{\sqrt{(-a+x) (-b+x) (-c+x)} \left(a+b c d-(1+b d+c d) x+d x^2\right)} \, dx","Integrate[(a*b + a*c - b*c - 2*a*x + x^2)/(Sqrt[(-a + x)*(-b + x)*(-c + x)]*(a + b*c*d - (1 + b*d + c*d)*x + d*x^2)),x]","-\frac{2 i (x-a)^{3/2} \sqrt{\frac{b-x}{a-x}} \sqrt{\frac{c-x}{a-x}} \left(-\Pi \left(\frac{2 (a-c) d}{2 a d-b d-c d+\sqrt{b^2 d^2-4 a d-2 b (c d-1) d+(c d+1)^2}-1};i \sinh ^{-1}\left(\frac{\sqrt{a-b}}{\sqrt{x-a}}\right)|\frac{a-c}{a-b}\right)-\Pi \left(-\frac{2 (a-c) d}{-2 a d+b d+c d+\sqrt{b^2 d^2-4 a d-2 b (c d-1) d+(c d+1)^2}+1};i \sinh ^{-1}\left(\frac{\sqrt{a-b}}{\sqrt{x-a}}\right)|\frac{a-c}{a-b}\right)+F\left(i \sinh ^{-1}\left(\frac{\sqrt{a-b}}{\sqrt{x-a}}\right)|\frac{a-c}{a-b}\right)\right)}{d \sqrt{a-b} \sqrt{(x-a) (x-b) (x-c)}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{x^2 (-a-b-c)+x (a b+a c+b c)-a b c+x^3}}{a-x}\right)}{\sqrt{d}}",1,"((-2*I)*Sqrt[(b - x)/(a - x)]*Sqrt[(c - x)/(a - x)]*(-a + x)^(3/2)*(EllipticF[I*ArcSinh[Sqrt[a - b]/Sqrt[-a + x]], (a - c)/(a - b)] - EllipticPi[(2*(a - c)*d)/(-1 + 2*a*d - b*d - c*d + Sqrt[-4*a*d + b^2*d^2 - 2*b*d*(-1 + c*d) + (1 + c*d)^2]), I*ArcSinh[Sqrt[a - b]/Sqrt[-a + x]], (a - c)/(a - b)] - EllipticPi[(-2*(a - c)*d)/(1 - 2*a*d + b*d + c*d + Sqrt[-4*a*d + b^2*d^2 - 2*b*d*(-1 + c*d) + (1 + c*d)^2]), I*ArcSinh[Sqrt[a - b]/Sqrt[-a + x]], (a - c)/(a - b)]))/(Sqrt[a - b]*d*Sqrt[(-a + x)*(-b + x)*(-c + x)])","C",1
777,1,165,60,2.4906269,"\int \frac{-1+k^2 x^2}{\sqrt{(1-x) x \left(1-k^2 x\right)} \left(1+k^2 x^2\right)} \, dx","Integrate[(-1 + k^2*x^2)/(Sqrt[(1 - x)*x*(1 - k^2*x)]*(1 + k^2*x^2)),x]","\frac{2 i \sqrt{\frac{1}{x-1}+1} (x-1)^{3/2} \sqrt{\frac{1-\frac{1}{k^2}}{x-1}+1} \left(\left(k^2-1\right) F\left(i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)+(1-i k) \Pi \left(\frac{k-i}{k};i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)+(1+i k) \Pi \left(\frac{k+i}{k};i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)\right)}{\left(k^2+1\right) \sqrt{(x-1) x \left(k^2 x-1\right)}}","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{k^2+1} \sqrt{k^2 x^3+\left(-k^2-1\right) x^2+x}}{(x-1) \left(k^2 x-1\right)}\right)}{\sqrt{k^2+1}}",1,"((2*I)*Sqrt[1 + (-1 + x)^(-1)]*Sqrt[1 + (1 - k^(-2))/(-1 + x)]*(-1 + x)^(3/2)*((-1 + k^2)*EllipticF[I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)] + (1 - I*k)*EllipticPi[(-I + k)/k, I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)] + (1 + I*k)*EllipticPi[(I + k)/k, I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)]))/((1 + k^2)*Sqrt[(-1 + x)*x*(-1 + k^2*x)])","C",1
778,1,3908,60,6.21027,"\int \frac{a (a b+a c-3 b c)+\left(-2 a^2+a b+a c+3 b c\right) x+(a-2 b-2 c) x^2+x^3}{\sqrt{(-a+x) (-b+x) (-c+x)} \left(-a^3-b c d+\left(3 a^2+b d+c d\right) x-(3 a+d) x^2+x^3\right)} \, dx","Integrate[(a*(a*b + a*c - 3*b*c) + (-2*a^2 + a*b + a*c + 3*b*c)*x + (a - 2*b - 2*c)*x^2 + x^3)/(Sqrt[(-a + x)*(-b + x)*(-c + x)]*(-a^3 - b*c*d + (3*a^2 + b*d + c*d)*x - (3*a + d)*x^2 + x^3)),x]","\text{Result too large to show}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{x^2 (-a-b-c)+x (a b+a c+b c)-a b c+x^3}}{(a-x)^2}\right)}{\sqrt{d}}",1,"((2*I)*Sqrt[(a - x)/(b - x)]*(b - x)*Sqrt[(-c + x)/(a - c)]*(3*(a - b)*(a - c)*d*(EllipticF[I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] - EllipticPi[(a - b)/Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 1], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)]) + (2*a - b - c)*d^2*(EllipticF[I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] - EllipticPi[(a - b)/Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 1], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)]) - 2*(-2*a + b + c)^2*d*(EllipticPi[(a - b)/Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 1], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] - EllipticPi[(a - b)/Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 2], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)]) - 3*(a - b)*(a - c)*d*(EllipticPi[(a - b)/Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 2], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] - EllipticPi[(a - b)/Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 3], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)]) - 3*(a - b)*(a - c)*(EllipticPi[(a - b)/Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 1], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] + EllipticPi[(a - b)/Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 2], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] - 2*EllipticPi[(a - b)/Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 3], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)])*Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 2] + (-2*EllipticF[I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] + EllipticPi[(a - b)/Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 1], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] + EllipticPi[(a - b)/Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 2], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)])*Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 1]*Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 2]^2 + 3*(a - b)*(a - c)*(EllipticPi[(a - b)/Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 1], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] - 2*EllipticPi[(a - b)/Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 2], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] + EllipticPi[(a - b)/Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 3], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)])*Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 3] - 2*(2*a - b - c)*(2*EllipticPi[(a - b)/Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 1], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] - EllipticPi[(a - b)/Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 2], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] - EllipticPi[(a - b)/Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 3], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)])*Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 1]*Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 3] - 2*(EllipticF[I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] - EllipticPi[(a - b)/Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 1], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)])*Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 1]^2*Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 3] - 2*(2*a - b - c)*(EllipticPi[(a - b)/Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 1], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] - 2*EllipticPi[(a - b)/Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 2], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] + EllipticPi[(a - b)/Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 3], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)])*Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 2]*Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 3] + (EllipticPi[(a - b)/Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 1], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] - EllipticPi[(a - b)/Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 2], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)])*Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 2]^2*Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 3] + (EllipticPi[(a - b)/Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 1], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] - EllipticPi[(a - b)/Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 3], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)])*Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 1]*Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 3]^2 + (-2*EllipticF[I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] + EllipticPi[(a - b)/Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 1], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] + EllipticPi[(a - b)/Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 3], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)])*Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 2]*Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 3]^2))/(Sqrt[(-a + x)*(-b + x)*(-c + x)]*(Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 1] - Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 2])*(Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 1] - Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 3])*(Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 2] - Root[a^2*d - a*b*d - a*c*d + b*c*d + (-2*a*d + b*d + c*d)*#1 + d*#1^2 + #1^3 & , 3]))","C",0
779,1,1788,60,4.0851992,"\int \frac{\left(-2 c+a x^3\right) \sqrt{c+b x^2+a x^3}}{\left(c+a x^3\right)^2} \, dx","Integrate[((-2*c + a*x^3)*Sqrt[c + b*x^2 + a*x^3])/(c + a*x^3)^2,x]","\frac{-\frac{x \left((b+a x) x^2+c\right)}{a x^3+c}+\frac{F\left(\sin ^{-1}\left(\sqrt{\frac{\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,3\right]-x}{\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,3\right]-\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,2\right]}}\right)|\frac{\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,2\right]-\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,3\right]}{\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,1\right]-\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,3\right]}\right) \left(x-\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,3\right]\right) \sqrt{\frac{\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,1\right]-x}{\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,1\right]-\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,3\right]}} \sqrt{\frac{\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,2\right]-x}{\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,2\right]-\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,3\right]}}}{\sqrt{\frac{x-\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,3\right]}{\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,2\right]-\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,3\right]}}}+\frac{3 (-1)^{2/3} \sqrt[3]{c} \Pi \left(\frac{\sqrt[3]{a} \left(\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,3\right]-\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,2\right]\right)}{\sqrt[3]{a} \text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,3\right]-\sqrt[3]{-1} \sqrt[3]{c}};\sin ^{-1}\left(\sqrt{\frac{\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,3\right]-x}{\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,3\right]-\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,2\right]}}\right)|\frac{\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,2\right]-\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,3\right]}{\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,1\right]-\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,3\right]}\right) \sqrt{\frac{\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,1\right]-x}{\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,1\right]-\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,3\right]}} \sqrt{-\frac{\left(x-\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,2\right]\right) \left(x-\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,3\right]\right)}{\left(\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,2\right]-\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,3\right]\right)^2}} \left(\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,3\right]-\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,2\right]\right)}{\left(1+\sqrt[3]{-1}\right)^2 \left(\sqrt[3]{-1} \sqrt[3]{c}-\sqrt[3]{a} \text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,3\right]\right)}+\frac{\sqrt[3]{c} \Pi \left(\frac{\sqrt[3]{a} \left(\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,3\right]-\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,2\right]\right)}{\sqrt[3]{a} \text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,3\right]+\sqrt[3]{c}};\sin ^{-1}\left(\sqrt{\frac{\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,3\right]-x}{\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,3\right]-\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,2\right]}}\right)|\frac{\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,2\right]-\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,3\right]}{\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,1\right]-\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,3\right]}\right) \sqrt{\frac{\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,1\right]-x}{\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,1\right]-\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,3\right]}} \sqrt{-\frac{\left(x-\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,2\right]\right) \left(x-\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,3\right]\right)}{\left(\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,2\right]-\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,3\right]\right)^2}} \left(\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,3\right]-\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,2\right]\right)}{\sqrt[3]{a} \text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,3\right]+\sqrt[3]{c}}+\frac{2 (-1)^{2/3} \sqrt[3]{c} \Pi \left(\frac{\sqrt[3]{a} \left(\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,3\right]-\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,2\right]\right)}{\sqrt[3]{a} \text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,3\right]+(-1)^{2/3} \sqrt[3]{c}};\sin ^{-1}\left(\sqrt{\frac{\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,3\right]-x}{\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,3\right]-\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,2\right]}}\right)|\frac{\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,2\right]-\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,3\right]}{\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,1\right]-\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,3\right]}\right) \sqrt{\frac{\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,1\right]-x}{\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,1\right]-\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,3\right]}} \sqrt{-\frac{\left(x-\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,2\right]\right) \left(x-\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,3\right]\right)}{\left(\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,2\right]-\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,3\right]\right)^2}} \left(\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,3\right]-\text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,2\right]\right)}{2 \sqrt[3]{a} \text{Root}\left[a \text{$\#$1}^3+b \text{$\#$1}^2+c\&,3\right]+i \left(i+\sqrt{3}\right) \sqrt[3]{c}}}{\sqrt{(b+a x) x^2+c}}","-\frac{x \sqrt{a x^3+b x^2+c}}{a x^3+c}-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x^3+b x^2+c}}\right)}{\sqrt{b}}",1,"(-((x*(c + x^2*(b + a*x)))/(c + a*x^3)) + (EllipticF[ArcSin[Sqrt[(-x + Root[c + b*#1^2 + a*#1^3 & , 3])/(-Root[c + b*#1^2 + a*#1^3 & , 2] + Root[c + b*#1^2 + a*#1^3 & , 3])]], (Root[c + b*#1^2 + a*#1^3 & , 2] - Root[c + b*#1^2 + a*#1^3 & , 3])/(Root[c + b*#1^2 + a*#1^3 & , 1] - Root[c + b*#1^2 + a*#1^3 & , 3])]*(x - Root[c + b*#1^2 + a*#1^3 & , 3])*Sqrt[(-x + Root[c + b*#1^2 + a*#1^3 & , 1])/(Root[c + b*#1^2 + a*#1^3 & , 1] - Root[c + b*#1^2 + a*#1^3 & , 3])]*Sqrt[(-x + Root[c + b*#1^2 + a*#1^3 & , 2])/(Root[c + b*#1^2 + a*#1^3 & , 2] - Root[c + b*#1^2 + a*#1^3 & , 3])])/Sqrt[(x - Root[c + b*#1^2 + a*#1^3 & , 3])/(Root[c + b*#1^2 + a*#1^3 & , 2] - Root[c + b*#1^2 + a*#1^3 & , 3])] + (3*(-1)^(2/3)*c^(1/3)*EllipticPi[(a^(1/3)*(-Root[c + b*#1^2 + a*#1^3 & , 2] + Root[c + b*#1^2 + a*#1^3 & , 3]))/(-((-1)^(1/3)*c^(1/3)) + a^(1/3)*Root[c + b*#1^2 + a*#1^3 & , 3]), ArcSin[Sqrt[(-x + Root[c + b*#1^2 + a*#1^3 & , 3])/(-Root[c + b*#1^2 + a*#1^3 & , 2] + Root[c + b*#1^2 + a*#1^3 & , 3])]], (Root[c + b*#1^2 + a*#1^3 & , 2] - Root[c + b*#1^2 + a*#1^3 & , 3])/(Root[c + b*#1^2 + a*#1^3 & , 1] - Root[c + b*#1^2 + a*#1^3 & , 3])]*Sqrt[(-x + Root[c + b*#1^2 + a*#1^3 & , 1])/(Root[c + b*#1^2 + a*#1^3 & , 1] - Root[c + b*#1^2 + a*#1^3 & , 3])]*Sqrt[-(((x - Root[c + b*#1^2 + a*#1^3 & , 2])*(x - Root[c + b*#1^2 + a*#1^3 & , 3]))/(Root[c + b*#1^2 + a*#1^3 & , 2] - Root[c + b*#1^2 + a*#1^3 & , 3])^2)]*(-Root[c + b*#1^2 + a*#1^3 & , 2] + Root[c + b*#1^2 + a*#1^3 & , 3]))/((1 + (-1)^(1/3))^2*((-1)^(1/3)*c^(1/3) - a^(1/3)*Root[c + b*#1^2 + a*#1^3 & , 3])) + (c^(1/3)*EllipticPi[(a^(1/3)*(-Root[c + b*#1^2 + a*#1^3 & , 2] + Root[c + b*#1^2 + a*#1^3 & , 3]))/(c^(1/3) + a^(1/3)*Root[c + b*#1^2 + a*#1^3 & , 3]), ArcSin[Sqrt[(-x + Root[c + b*#1^2 + a*#1^3 & , 3])/(-Root[c + b*#1^2 + a*#1^3 & , 2] + Root[c + b*#1^2 + a*#1^3 & , 3])]], (Root[c + b*#1^2 + a*#1^3 & , 2] - Root[c + b*#1^2 + a*#1^3 & , 3])/(Root[c + b*#1^2 + a*#1^3 & , 1] - Root[c + b*#1^2 + a*#1^3 & , 3])]*Sqrt[(-x + Root[c + b*#1^2 + a*#1^3 & , 1])/(Root[c + b*#1^2 + a*#1^3 & , 1] - Root[c + b*#1^2 + a*#1^3 & , 3])]*Sqrt[-(((x - Root[c + b*#1^2 + a*#1^3 & , 2])*(x - Root[c + b*#1^2 + a*#1^3 & , 3]))/(Root[c + b*#1^2 + a*#1^3 & , 2] - Root[c + b*#1^2 + a*#1^3 & , 3])^2)]*(-Root[c + b*#1^2 + a*#1^3 & , 2] + Root[c + b*#1^2 + a*#1^3 & , 3]))/(c^(1/3) + a^(1/3)*Root[c + b*#1^2 + a*#1^3 & , 3]) + (2*(-1)^(2/3)*c^(1/3)*EllipticPi[(a^(1/3)*(-Root[c + b*#1^2 + a*#1^3 & , 2] + Root[c + b*#1^2 + a*#1^3 & , 3]))/((-1)^(2/3)*c^(1/3) + a^(1/3)*Root[c + b*#1^2 + a*#1^3 & , 3]), ArcSin[Sqrt[(-x + Root[c + b*#1^2 + a*#1^3 & , 3])/(-Root[c + b*#1^2 + a*#1^3 & , 2] + Root[c + b*#1^2 + a*#1^3 & , 3])]], (Root[c + b*#1^2 + a*#1^3 & , 2] - Root[c + b*#1^2 + a*#1^3 & , 3])/(Root[c + b*#1^2 + a*#1^3 & , 1] - Root[c + b*#1^2 + a*#1^3 & , 3])]*Sqrt[(-x + Root[c + b*#1^2 + a*#1^3 & , 1])/(Root[c + b*#1^2 + a*#1^3 & , 1] - Root[c + b*#1^2 + a*#1^3 & , 3])]*Sqrt[-(((x - Root[c + b*#1^2 + a*#1^3 & , 2])*(x - Root[c + b*#1^2 + a*#1^3 & , 3]))/(Root[c + b*#1^2 + a*#1^3 & , 2] - Root[c + b*#1^2 + a*#1^3 & , 3])^2)]*(-Root[c + b*#1^2 + a*#1^3 & , 2] + Root[c + b*#1^2 + a*#1^3 & , 3]))/(I*(I + Sqrt[3])*c^(1/3) + 2*a^(1/3)*Root[c + b*#1^2 + a*#1^3 & , 3]))/Sqrt[c + x^2*(b + a*x)]","C",0
780,1,204,60,2.3070963,"\int \frac{-b+a^2 x^2}{\left(b+2 a b x+a^2 x^2\right) \sqrt{b x+a^2 x^3}} \, dx","Integrate[(-b + a^2*x^2)/((b + 2*a*b*x + a^2*x^2)*Sqrt[b*x + a^2*x^3]),x]","-\frac{2 i x^{3/2} \sqrt{\frac{b}{a^2 x^2}+1} \left(-\Pi \left(-\frac{i a \sqrt{b}}{a b-\sqrt{a^2 (b-1) b}};\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i \sqrt{b}}{a}}}{\sqrt{x}}\right)\right|-1\right)-\Pi \left(-\frac{i a \sqrt{b}}{a b+\sqrt{a^2 (b-1) b}};\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i \sqrt{b}}{a}}}{\sqrt{x}}\right)\right|-1\right)+F\left(\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i \sqrt{b}}{a}}}{\sqrt{x}}\right)\right|-1\right)\right)}{\sqrt{\frac{i \sqrt{b}}{a}} \sqrt{x \left(a^2 x^2+b\right)}}","-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{b} \sqrt{a^2 x^3+b x}}{a^2 x^2+b}\right)}{\sqrt{a} \sqrt{b}}",1,"((-2*I)*Sqrt[1 + b/(a^2*x^2)]*x^(3/2)*(EllipticF[I*ArcSinh[Sqrt[(I*Sqrt[b])/a]/Sqrt[x]], -1] - EllipticPi[((-I)*a*Sqrt[b])/(a*b - Sqrt[a^2*(-1 + b)*b]), I*ArcSinh[Sqrt[(I*Sqrt[b])/a]/Sqrt[x]], -1] - EllipticPi[((-I)*a*Sqrt[b])/(a*b + Sqrt[a^2*(-1 + b)*b]), I*ArcSinh[Sqrt[(I*Sqrt[b])/a]/Sqrt[x]], -1]))/(Sqrt[(I*Sqrt[b])/a]*Sqrt[x*(b + a^2*x^2)])","C",1
781,1,4752,60,4.9490822,"\int \frac{a (a b+a c-3 b c)+\left(-2 a^2+a b+a c+3 b c\right) x+(a-2 b-2 c) x^2+x^3}{\sqrt{(-a+x) (-b+x) (-c+x)} \left(-b c-a^3 d+\left(b+c+3 a^2 d\right) x-(1+3 a d) x^2+d x^3\right)} \, dx","Integrate[(a*(a*b + a*c - 3*b*c) + (-2*a^2 + a*b + a*c + 3*b*c)*x + (a - 2*b - 2*c)*x^2 + x^3)/(Sqrt[(-a + x)*(-b + x)*(-c + x)]*(-(b*c) - a^3*d + (b + c + 3*a^2*d)*x - (1 + 3*a*d)*x^2 + d*x^3)),x]","\text{Result too large to show}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{x^2 (-a-b-c)+x (a b+a c+b c)-a b c+x^3}}{\sqrt{d} (a-x)^2}\right)}{\sqrt{d}}",1,"((2*I)*(-a + x)*Sqrt[(-c + x)/(a - c)]*(-2*a*EllipticF[I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] + b*EllipticF[I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] + c*EllipticF[I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] - 3*a^2*d*EllipticF[I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] + 3*a*b*d*EllipticF[I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] + 3*a*c*d*EllipticF[I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] - 3*b*c*d*EllipticF[I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] + 2*a*EllipticPi[(a - b)/Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 1], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] - b*EllipticPi[(a - b)/Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 1], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] - c*EllipticPi[(a - b)/Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 1], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] + 11*a^2*d*EllipticPi[(a - b)/Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 1], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] - 11*a*b*d*EllipticPi[(a - b)/Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 1], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] + 2*b^2*d*EllipticPi[(a - b)/Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 1], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] - 11*a*c*d*EllipticPi[(a - b)/Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 1], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] + 7*b*c*d*EllipticPi[(a - b)/Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 1], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] + 2*c^2*d*EllipticPi[(a - b)/Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 1], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] - 5*a^2*d*EllipticPi[(a - b)/Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 2], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] + 5*a*b*d*EllipticPi[(a - b)/Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 2], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] - 2*b^2*d*EllipticPi[(a - b)/Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 2], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] + 5*a*c*d*EllipticPi[(a - b)/Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 2], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] - b*c*d*EllipticPi[(a - b)/Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 2], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] - 2*c^2*d*EllipticPi[(a - b)/Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 2], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] - 3*a^2*d*EllipticPi[(a - b)/Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 3], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] + 3*a*b*d*EllipticPi[(a - b)/Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 3], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] + 3*a*c*d*EllipticPi[(a - b)/Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 3], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] - 3*b*c*d*EllipticPi[(a - b)/Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 3], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] + 3*(a - b)*(a - c)*d^2*(EllipticPi[(a - b)/Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 1], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] + EllipticPi[(a - b)/Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 2], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] - 2*EllipticPi[(a - b)/Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 3], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)])*Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 2] + d^2*(2*EllipticF[I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] - EllipticPi[(a - b)/Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 1], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] - EllipticPi[(a - b)/Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 2], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)])*Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 1]*Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 2]^2 - 3*(a - b)*(a - c)*d^2*(EllipticPi[(a - b)/Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 1], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] - 2*EllipticPi[(a - b)/Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 2], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] + EllipticPi[(a - b)/Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 3], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)])*Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 3] + 2*(2*a - b - c)*d^2*(2*EllipticPi[(a - b)/Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 1], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] - EllipticPi[(a - b)/Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 2], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] - EllipticPi[(a - b)/Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 3], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)])*Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 1]*Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 3] + 2*d^2*(EllipticF[I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] - EllipticPi[(a - b)/Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 1], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)])*Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 1]^2*Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 3] + 2*(2*a - b - c)*d^2*(EllipticPi[(a - b)/Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 1], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] - 2*EllipticPi[(a - b)/Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 2], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] + EllipticPi[(a - b)/Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 3], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)])*Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 2]*Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 3] - d^2*(EllipticPi[(a - b)/Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 1], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] - EllipticPi[(a - b)/Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 2], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)])*Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 2]^2*Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 3] - d^2*(EllipticPi[(a - b)/Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 1], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] - EllipticPi[(a - b)/Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 3], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)])*Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 1]*Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 3]^2 + d^2*(2*EllipticF[I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] - EllipticPi[(a - b)/Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 1], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)] - EllipticPi[(a - b)/Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 3], I*ArcSinh[Sqrt[(-a + x)/(a - b)]], (a - b)/(a - c)])*Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 2]*Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 3]^2))/(d^3*Sqrt[(a - x)/(b - x)]*Sqrt[(-a + x)*(-b + x)*(-c + x)]*(Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 1] - Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 2])*(Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 1] - Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 3])*(Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 2] - Root[a^2 - a*b - a*c + b*c + (-2*a + b + c)*#1 + #1^2 + d*#1^3 & , 3]))","C",0
782,1,41,60,0.0721101,"\int \frac{\left(-1+x^2\right) \sqrt{1+x^4}}{x^5} \, dx","Integrate[((-1 + x^2)*Sqrt[1 + x^4])/x^5,x]","\frac{1}{4} \left(\tanh ^{-1}\left(\sqrt{x^4+1}\right)+2 \sinh ^{-1}\left(x^2\right)+\frac{\sqrt{x^4+1} \left(1-2 x^2\right)}{x^4}\right)","\frac{\sqrt{x^4+1} \left(1-2 x^2\right)}{4 x^4}+\frac{1}{2} \log \left(\sqrt{x^4+1}+x^2\right)+\frac{1}{2} \tanh ^{-1}\left(\sqrt{x^4+1}+x^2\right)",1,"(((1 - 2*x^2)*Sqrt[1 + x^4])/x^4 + 2*ArcSinh[x^2] + ArcTanh[Sqrt[1 + x^4]])/4","A",1
783,1,41,60,0.0329655,"\int \frac{\left(-1+x^2\right) \sqrt{1+x^4}}{x^3} \, dx","Integrate[((-1 + x^2)*Sqrt[1 + x^4])/x^3,x]","\frac{1}{2} \left(-\tanh ^{-1}\left(\sqrt{x^4+1}\right)-\sinh ^{-1}\left(x^2\right)+\frac{\sqrt{x^4+1} \left(x^2+1\right)}{x^2}\right)","\frac{\sqrt{x^4+1} \left(x^2+1\right)}{2 x^2}-\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)",1,"(((1 + x^2)*Sqrt[1 + x^4])/x^2 - ArcSinh[x^2] - ArcTanh[Sqrt[1 + x^4]])/2","A",1
784,1,71,60,0.0659741,"\int \frac{\left(1+2 x^3\right) \sqrt{-1+x^6}}{x^7} \, dx","Integrate[((1 + 2*x^3)*Sqrt[-1 + x^6])/x^7,x]","-\frac{\left(x^6-1\right) \left(-x^6 \tanh ^{-1}\left(\sqrt{1-x^6}\right)+\left(4 x^3+1\right) \sqrt{1-x^6}+4 x^6 \sin ^{-1}\left(x^3\right)\right)}{6 x^6 \sqrt{-\left(x^6-1\right)^2}}","\frac{\sqrt{x^6-1} \left(-4 x^3-1\right)}{6 x^6}+\frac{2}{3} \log \left(\sqrt{x^6-1}+x^3\right)+\frac{1}{3} \tan ^{-1}\left(\sqrt{x^6-1}+x^3\right)",1,"-1/6*((-1 + x^6)*((1 + 4*x^3)*Sqrt[1 - x^6] + 4*x^6*ArcSin[x^3] - x^6*ArcTanh[Sqrt[1 - x^6]]))/(x^6*Sqrt[-(-1 + x^6)^2])","A",1
785,1,63,60,0.0741034,"\int \frac{\left(1+2 x^3\right) \sqrt{-1+x^6}}{x^4} \, dx","Integrate[((1 + 2*x^3)*Sqrt[-1 + x^6])/x^4,x]","\frac{1}{3} \left(-2 \tan ^{-1}\left(\sqrt{x^6-1}\right)+\frac{\sqrt{x^6-1} \left(2 x^3-1\right)}{x^3}-\frac{\sqrt{x^6-1} \sin ^{-1}\left(x^3\right)}{\sqrt{1-x^6}}\right)","\frac{\sqrt{x^6-1} \left(2 x^3-1\right)}{3 x^3}+\frac{1}{3} \log \left(\sqrt{x^6-1}+x^3\right)-\frac{4}{3} \tan ^{-1}\left(\sqrt{x^6-1}+x^3\right)",1,"(((-1 + 2*x^3)*Sqrt[-1 + x^6])/x^3 - (Sqrt[-1 + x^6]*ArcSin[x^3])/Sqrt[1 - x^6] - 2*ArcTan[Sqrt[-1 + x^6]])/3","A",1
786,1,544,60,6.4556435,"\int \frac{b^6+a^6 x^6}{\sqrt{-b^2 x+a^2 x^3} \left(-b^6+c x^3+a^6 x^6\right)} \, dx","Integrate[(b^6 + a^6*x^6)/(Sqrt[-(b^2*x) + a^2*x^3]*(-b^6 + c*x^3 + a^6*x^6)),x]","-\frac{2 i x^{3/2} \sqrt{1-\frac{b^2}{a^2 x^2}} \left(-\Pi \left(\frac{\sqrt[3]{2} a}{b \sqrt[3]{\frac{c-\sqrt{4 a^6 b^6+c^2}}{b^6}}};\left.i \sinh ^{-1}\left(\frac{\sqrt{-\frac{b}{a}}}{\sqrt{x}}\right)\right|-1\right)-\Pi \left(\frac{\sqrt[3]{2} a}{b \sqrt[3]{\frac{c+\sqrt{4 a^6 b^6+c^2}}{b^6}}};\left.i \sinh ^{-1}\left(\frac{\sqrt{-\frac{b}{a}}}{\sqrt{x}}\right)\right|-1\right)-\Pi \left(-\frac{i \left(-i+\sqrt{3}\right) a}{2^{2/3} b \sqrt[3]{\frac{c+\sqrt{4 a^6 b^6+c^2}}{b^6}}};\left.i \sinh ^{-1}\left(\frac{\sqrt{-\frac{b}{a}}}{\sqrt{x}}\right)\right|-1\right)-\Pi \left(\frac{i \left(i+\sqrt{3}\right) a}{2^{2/3} b \sqrt[3]{\frac{c+\sqrt{4 a^6 b^6+c^2}}{b^6}}};\left.i \sinh ^{-1}\left(\frac{\sqrt{-\frac{b}{a}}}{\sqrt{x}}\right)\right|-1\right)-\Pi \left(\frac{\left(1-i \sqrt{3}\right) a b^5 \left(\frac{c-\sqrt{4 a^6 b^6+c^2}}{b^6}\right)^{2/3}}{2^{2/3} \left(\sqrt{4 a^6 b^6+c^2}-c\right)};\left.i \sinh ^{-1}\left(\frac{\sqrt{-\frac{b}{a}}}{\sqrt{x}}\right)\right|-1\right)-\Pi \left(\frac{\left(1+i \sqrt{3}\right) a b^5 \left(\frac{c-\sqrt{4 a^6 b^6+c^2}}{b^6}\right)^{2/3}}{2^{2/3} \left(\sqrt{4 a^6 b^6+c^2}-c\right)};\left.i \sinh ^{-1}\left(\frac{\sqrt{-\frac{b}{a}}}{\sqrt{x}}\right)\right|-1\right)+3 F\left(\left.i \sinh ^{-1}\left(\frac{\sqrt{-\frac{b}{a}}}{\sqrt{x}}\right)\right|-1\right)\right)}{3 \sqrt{-\frac{b}{a}} \sqrt{a^2 x^3-b^2 x}}","\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^6+3 \text{$\#$1}^2 a^2 b^2+c\&,\frac{\log \left(\sqrt{a^2 x^3-b^2 x}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]",1,"(((-2*I)/3)*Sqrt[1 - b^2/(a^2*x^2)]*x^(3/2)*(3*EllipticF[I*ArcSinh[Sqrt[-(b/a)]/Sqrt[x]], -1] - EllipticPi[(2^(1/3)*a)/(b*((c - Sqrt[4*a^6*b^6 + c^2])/b^6)^(1/3)), I*ArcSinh[Sqrt[-(b/a)]/Sqrt[x]], -1] - EllipticPi[((1 - I*Sqrt[3])*a*b^5*((c - Sqrt[4*a^6*b^6 + c^2])/b^6)^(2/3))/(2^(2/3)*(-c + Sqrt[4*a^6*b^6 + c^2])), I*ArcSinh[Sqrt[-(b/a)]/Sqrt[x]], -1] - EllipticPi[((1 + I*Sqrt[3])*a*b^5*((c - Sqrt[4*a^6*b^6 + c^2])/b^6)^(2/3))/(2^(2/3)*(-c + Sqrt[4*a^6*b^6 + c^2])), I*ArcSinh[Sqrt[-(b/a)]/Sqrt[x]], -1] - EllipticPi[(2^(1/3)*a)/(b*((c + Sqrt[4*a^6*b^6 + c^2])/b^6)^(1/3)), I*ArcSinh[Sqrt[-(b/a)]/Sqrt[x]], -1] - EllipticPi[((-I)*(-I + Sqrt[3])*a)/(2^(2/3)*b*((c + Sqrt[4*a^6*b^6 + c^2])/b^6)^(1/3)), I*ArcSinh[Sqrt[-(b/a)]/Sqrt[x]], -1] - EllipticPi[(I*(I + Sqrt[3])*a)/(2^(2/3)*b*((c + Sqrt[4*a^6*b^6 + c^2])/b^6)^(1/3)), I*ArcSinh[Sqrt[-(b/a)]/Sqrt[x]], -1]))/(Sqrt[-(b/a)]*Sqrt[-(b^2*x) + a^2*x^3])","C",1
787,1,544,60,1.4844667,"\int \frac{b^6+a^6 x^6}{\sqrt{-b^2 x+a^2 x^3} \left(-b^6+c x^3+a^6 x^6\right)} \, dx","Integrate[(b^6 + a^6*x^6)/(Sqrt[-(b^2*x) + a^2*x^3]*(-b^6 + c*x^3 + a^6*x^6)),x]","-\frac{2 i x^{3/2} \sqrt{1-\frac{b^2}{a^2 x^2}} \left(-\Pi \left(\frac{\sqrt[3]{2} a}{b \sqrt[3]{\frac{c-\sqrt{4 a^6 b^6+c^2}}{b^6}}};\left.i \sinh ^{-1}\left(\frac{\sqrt{-\frac{b}{a}}}{\sqrt{x}}\right)\right|-1\right)-\Pi \left(\frac{\sqrt[3]{2} a}{b \sqrt[3]{\frac{c+\sqrt{4 a^6 b^6+c^2}}{b^6}}};\left.i \sinh ^{-1}\left(\frac{\sqrt{-\frac{b}{a}}}{\sqrt{x}}\right)\right|-1\right)-\Pi \left(-\frac{i \left(-i+\sqrt{3}\right) a}{2^{2/3} b \sqrt[3]{\frac{c+\sqrt{4 a^6 b^6+c^2}}{b^6}}};\left.i \sinh ^{-1}\left(\frac{\sqrt{-\frac{b}{a}}}{\sqrt{x}}\right)\right|-1\right)-\Pi \left(\frac{i \left(i+\sqrt{3}\right) a}{2^{2/3} b \sqrt[3]{\frac{c+\sqrt{4 a^6 b^6+c^2}}{b^6}}};\left.i \sinh ^{-1}\left(\frac{\sqrt{-\frac{b}{a}}}{\sqrt{x}}\right)\right|-1\right)-\Pi \left(\frac{\left(1-i \sqrt{3}\right) a b^5 \left(\frac{c-\sqrt{4 a^6 b^6+c^2}}{b^6}\right)^{2/3}}{2^{2/3} \left(\sqrt{4 a^6 b^6+c^2}-c\right)};\left.i \sinh ^{-1}\left(\frac{\sqrt{-\frac{b}{a}}}{\sqrt{x}}\right)\right|-1\right)-\Pi \left(\frac{\left(1+i \sqrt{3}\right) a b^5 \left(\frac{c-\sqrt{4 a^6 b^6+c^2}}{b^6}\right)^{2/3}}{2^{2/3} \left(\sqrt{4 a^6 b^6+c^2}-c\right)};\left.i \sinh ^{-1}\left(\frac{\sqrt{-\frac{b}{a}}}{\sqrt{x}}\right)\right|-1\right)+3 F\left(\left.i \sinh ^{-1}\left(\frac{\sqrt{-\frac{b}{a}}}{\sqrt{x}}\right)\right|-1\right)\right)}{3 \sqrt{-\frac{b}{a}} \sqrt{a^2 x^3-b^2 x}}","\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^6+3 \text{$\#$1}^2 a^2 b^2+c\&,\frac{\log \left(\sqrt{a^2 x^3-b^2 x}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]",1,"(((-2*I)/3)*Sqrt[1 - b^2/(a^2*x^2)]*x^(3/2)*(3*EllipticF[I*ArcSinh[Sqrt[-(b/a)]/Sqrt[x]], -1] - EllipticPi[(2^(1/3)*a)/(b*((c - Sqrt[4*a^6*b^6 + c^2])/b^6)^(1/3)), I*ArcSinh[Sqrt[-(b/a)]/Sqrt[x]], -1] - EllipticPi[((1 - I*Sqrt[3])*a*b^5*((c - Sqrt[4*a^6*b^6 + c^2])/b^6)^(2/3))/(2^(2/3)*(-c + Sqrt[4*a^6*b^6 + c^2])), I*ArcSinh[Sqrt[-(b/a)]/Sqrt[x]], -1] - EllipticPi[((1 + I*Sqrt[3])*a*b^5*((c - Sqrt[4*a^6*b^6 + c^2])/b^6)^(2/3))/(2^(2/3)*(-c + Sqrt[4*a^6*b^6 + c^2])), I*ArcSinh[Sqrt[-(b/a)]/Sqrt[x]], -1] - EllipticPi[(2^(1/3)*a)/(b*((c + Sqrt[4*a^6*b^6 + c^2])/b^6)^(1/3)), I*ArcSinh[Sqrt[-(b/a)]/Sqrt[x]], -1] - EllipticPi[((-I)*(-I + Sqrt[3])*a)/(2^(2/3)*b*((c + Sqrt[4*a^6*b^6 + c^2])/b^6)^(1/3)), I*ArcSinh[Sqrt[-(b/a)]/Sqrt[x]], -1] - EllipticPi[(I*(I + Sqrt[3])*a)/(2^(2/3)*b*((c + Sqrt[4*a^6*b^6 + c^2])/b^6)^(1/3)), I*ArcSinh[Sqrt[-(b/a)]/Sqrt[x]], -1]))/(Sqrt[-(b/a)]*Sqrt[-(b^2*x) + a^2*x^3])","C",1
788,0,0,60,0.4922279,"\int \frac{x-3 x^5}{\sqrt{x+x^5} \left(1-a x^2+2 x^4+x^8\right)} \, dx","Integrate[(x - 3*x^5)/(Sqrt[x + x^5]*(1 - a*x^2 + 2*x^4 + x^8)),x]","\int \frac{x-3 x^5}{\sqrt{x+x^5} \left(1-a x^2+2 x^4+x^8\right)} \, dx","\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x^5+x}}{x^4+1}\right)}{a^{3/4}}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x^5+x}}{x^4+1}\right)}{a^{3/4}}",1,"Integrate[(x - 3*x^5)/(Sqrt[x + x^5]*(1 - a*x^2 + 2*x^4 + x^8)), x]","F",-1
789,1,149,60,0.3032804,"\int \frac{\sqrt{1-2 x^8} \left(-1+2 x^8\right) \left(1+2 x^8\right)}{x^7 \left(-1+x^4+2 x^8\right)} \, dx","Integrate[(Sqrt[1 - 2*x^8]*(-1 + 2*x^8)*(1 + 2*x^8))/(x^7*(-1 + x^4 + 2*x^8)),x]","-\frac{6 \sqrt{1-2 x^8} x^8 \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};2 x^8\right)+8 x^{16}-12 x^{12}-8 x^8+6 x^4-3\ 2^{3/4} \sqrt{1-2 x^8} x^6 \Pi \left(-\frac{1}{\sqrt{2}};\left.\sin ^{-1}\left(\sqrt[4]{2} x^2\right)\right|-1\right)-3\ 2^{3/4} \sqrt{1-2 x^8} x^6 \Pi \left(\sqrt{2};\left.\sin ^{-1}\left(\sqrt[4]{2} x^2\right)\right|-1\right)+2}{12 x^6 \sqrt{1-2 x^8}}","\frac{\sqrt{1-2 x^8} \left(2 x^8-3 x^4-1\right)}{6 x^6}-\frac{1}{2} \tanh ^{-1}\left(\frac{x^2 \sqrt{1-2 x^8}}{2 x^8-1}\right)",1,"-1/12*(2 + 6*x^4 - 8*x^8 - 12*x^12 + 8*x^16 - 3*2^(3/4)*x^6*Sqrt[1 - 2*x^8]*EllipticPi[-(1/Sqrt[2]), ArcSin[2^(1/4)*x^2], -1] - 3*2^(3/4)*x^6*Sqrt[1 - 2*x^8]*EllipticPi[Sqrt[2], ArcSin[2^(1/4)*x^2], -1] + 6*x^8*Sqrt[1 - 2*x^8]*Hypergeometric2F1[1/4, 1/2, 5/4, 2*x^8])/(x^6*Sqrt[1 - 2*x^8])","C",1
790,0,0,60,0.5069878,"\int \frac{-x+3 x^5}{\sqrt{x+x^5} \left(a-x^2+2 a x^4+a x^8\right)} \, dx","Integrate[(-x + 3*x^5)/(Sqrt[x + x^5]*(a - x^2 + 2*a*x^4 + a*x^8)),x]","\int \frac{-x+3 x^5}{\sqrt{x+x^5} \left(a-x^2+2 a x^4+a x^8\right)} \, dx","\frac{\tan ^{-1}\left(\frac{\sqrt{x^5+x}}{\sqrt[4]{a} \left(x^4+1\right)}\right)}{\sqrt[4]{a}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{x^5+x}}{\sqrt[4]{a} \left(x^4+1\right)}\right)}{\sqrt[4]{a}}",1,"Integrate[(-x + 3*x^5)/(Sqrt[x + x^5]*(a - x^2 + 2*a*x^4 + a*x^8)), x]","F",-1
791,0,0,60,0.2928438,"\int \frac{x^5 \left(7 b+9 a x^2\right)}{\sqrt[4]{b x^3+a x^5} \left(-2+b x^7+a x^9\right)} \, dx","Integrate[(x^5*(7*b + 9*a*x^2))/((b*x^3 + a*x^5)^(1/4)*(-2 + b*x^7 + a*x^9)),x]","\int \frac{x^5 \left(7 b+9 a x^2\right)}{\sqrt[4]{b x^3+a x^5} \left(-2+b x^7+a x^9\right)} \, dx","2^{3/4} \tan ^{-1}\left(\frac{x \sqrt[4]{a x^5+b x^3}}{\sqrt[4]{2}}\right)-2^{3/4} \tanh ^{-1}\left(\frac{x \sqrt[4]{a x^5+b x^3}}{\sqrt[4]{2}}\right)",1,"Integrate[(x^5*(7*b + 9*a*x^2))/((b*x^3 + a*x^5)^(1/4)*(-2 + b*x^7 + a*x^9)), x]","F",-1
792,1,59,60,0.0451961,"\int \frac{x^2}{\left(1+x^2\right) \sqrt[5]{243-5265 x+47250 x^2-225810 x^3+615255 x^4-954733 x^5+820340 x^6-401440 x^7+112000 x^8-16640 x^9+1024 x^{10}}} \, dx","Integrate[x^2/((1 + x^2)*(243 - 5265*x + 47250*x^2 - 225810*x^3 + 615255*x^4 - 954733*x^5 + 820340*x^6 - 401440*x^7 + 112000*x^8 - 16640*x^9 + 1024*x^10)^(1/5)),x]","\frac{\left(4 x^2-13 x+3\right) \left(-143 \log \left(x^2+1\right)-20 \log (1-4 x)+306 \log (3-x)+22 \tan ^{-1}(x)\right)}{3740 \sqrt[5]{\left(4 x^2-13 x+3\right)^5}}","\frac{(x-3) (4 x-1) \left(-\frac{13}{340} \log \left(x^2+1\right)+\frac{9}{110} \log (x-3)-\frac{1}{187} \log (4 x-1)+\frac{1}{170} \tan ^{-1}(x)\right)}{\sqrt[5]{\left(4 x^2-13 x+3\right)^5}}",1,"((3 - 13*x + 4*x^2)*(22*ArcTan[x] - 20*Log[1 - 4*x] + 306*Log[3 - x] - 143*Log[1 + x^2]))/(3740*((3 - 13*x + 4*x^2)^5)^(1/5))","A",1
793,1,75,61,0.0809969,"\int \frac{\sqrt[3]{1-2 x+x^2}}{2+x^2} \, dx","Integrate[(1 - 2*x + x^2)^(1/3)/(2 + x^2),x]","\frac{3 i \sqrt[3]{(x-1)^2} \left(\, _2F_1\left(\frac{2}{3},1;\frac{5}{3};-\frac{i (x-1)}{i+\sqrt{2}}\right)-\, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{i (x-1)}{-i+\sqrt{2}}\right)\right)}{4 \sqrt{2}}","\frac{\sqrt[3]{(x-1)^2} \text{RootSum}\left[\text{$\#$1}^6+2 \text{$\#$1}^3+3\&,\frac{\text{$\#$1}^2 \log \left(\sqrt[3]{x-1}-\text{$\#$1}\right)}{\text{$\#$1}^3+1}\&\right]}{2 (x-1)^{2/3}}",1,"(((3*I)/4)*((-1 + x)^2)^(1/3)*(-Hypergeometric2F1[2/3, 1, 5/3, (I*(-1 + x))/(-I + Sqrt[2])] + Hypergeometric2F1[2/3, 1, 5/3, ((-I)*(-1 + x))/(I + Sqrt[2])]))/Sqrt[2]","C",1
794,1,241,61,0.443401,"\int \frac{\sqrt[3]{1+2 x+x^2}}{3+x^2} \, dx","Integrate[(1 + 2*x + x^2)^(1/3)/(3 + x^2),x]","\frac{\sqrt[3]{(x+1)^2} \left(\frac{\left(3+i \sqrt{3}\right) \left(-\log \left(x+i \sqrt{3}\right)+3 \log \left(-\sqrt[3]{x+1}+\sqrt[3]{1-i \sqrt{3}}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{1+\frac{2 \sqrt[3]{x+1}}{\sqrt[3]{1-i \sqrt{3}}}}{\sqrt{3}}\right)\right)}{\sqrt[3]{1-i \sqrt{3}}}+\frac{\left(3-i \sqrt{3}\right) \left(-\log \left(\sqrt{3}+i x\right)+3 \log \left(-\sqrt[3]{x+1}+\sqrt[3]{1+i \sqrt{3}}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{1+\frac{2 \sqrt[3]{x+1}}{\sqrt[3]{1+i \sqrt{3}}}}{\sqrt{3}}\right)\right)}{\sqrt[3]{1+i \sqrt{3}}}\right)}{12 (x+1)^{2/3}}","\frac{\sqrt[3]{(x+1)^2} \text{RootSum}\left[\text{$\#$1}^6-2 \text{$\#$1}^3+4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt[3]{x+1}-\text{$\#$1}\right)}{\text{$\#$1}^3-1}\&\right]}{2 (x+1)^{2/3}}",1,"(((1 + x)^2)^(1/3)*(((3 + I*Sqrt[3])*(2*Sqrt[3]*ArcTan[(1 + (2*(1 + x)^(1/3))/(1 - I*Sqrt[3])^(1/3))/Sqrt[3]] - Log[I*Sqrt[3] + x] + 3*Log[(1 - I*Sqrt[3])^(1/3) - (1 + x)^(1/3)]))/(1 - I*Sqrt[3])^(1/3) + ((3 - I*Sqrt[3])*(2*Sqrt[3]*ArcTan[(1 + (2*(1 + x)^(1/3))/(1 + I*Sqrt[3])^(1/3))/Sqrt[3]] - Log[Sqrt[3] + I*x] + 3*Log[(1 + I*Sqrt[3])^(1/3) - (1 + x)^(1/3)]))/(1 + I*Sqrt[3])^(1/3)))/(12*(1 + x)^(2/3))","C",1
795,0,0,61,0.2748931,"\int \frac{1}{(-1+x) \sqrt[4]{x+x^3}} \, dx","Integrate[1/((-1 + x)*(x + x^3)^(1/4)),x]","\int \frac{1}{(-1+x) \sqrt[4]{x+x^3}} \, dx","\frac{\tan ^{-1}\left(\frac{2^{3/4} \sqrt[4]{x^3+x}}{x+1}\right)}{2 \sqrt[4]{2}}-\frac{\tanh ^{-1}\left(\frac{2^{3/4} \sqrt[4]{x^3+x}}{x+1}\right)}{2 \sqrt[4]{2}}",1,"Integrate[1/((-1 + x)*(x + x^3)^(1/4)), x]","F",-1
796,1,146,61,0.7956288,"\int \frac{-1+x^4}{\sqrt{x+x^3} \left(1+x^4\right)} \, dx","Integrate[(-1 + x^4)/(Sqrt[x + x^3]*(1 + x^4)),x]","\frac{\sqrt[4]{-1} \sqrt{\frac{1}{x^2}+1} x^{3/2} \left(-2 F\left(\left.i \sinh ^{-1}\left(\frac{\sqrt[4]{-1}}{\sqrt{x}}\right)\right|-1\right)+\Pi \left(-\sqrt[4]{-1};\left.i \sinh ^{-1}\left(\frac{\sqrt[4]{-1}}{\sqrt{x}}\right)\right|-1\right)+\Pi \left(\sqrt[4]{-1};\left.i \sinh ^{-1}\left(\frac{\sqrt[4]{-1}}{\sqrt{x}}\right)\right|-1\right)+\Pi \left(-(-1)^{3/4};\left.i \sinh ^{-1}\left(\frac{\sqrt[4]{-1}}{\sqrt{x}}\right)\right|-1\right)+\Pi \left((-1)^{3/4};\left.i \sinh ^{-1}\left(\frac{\sqrt[4]{-1}}{\sqrt{x}}\right)\right|-1\right)\right)}{\sqrt{x^3+x}}","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{x^3+x}}{x^2+1}\right)}{\sqrt[4]{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{x^3+x}}{x^2+1}\right)}{\sqrt[4]{2}}",1,"((-1)^(1/4)*Sqrt[1 + x^(-2)]*x^(3/2)*(-2*EllipticF[I*ArcSinh[(-1)^(1/4)/Sqrt[x]], -1] + EllipticPi[-(-1)^(1/4), I*ArcSinh[(-1)^(1/4)/Sqrt[x]], -1] + EllipticPi[(-1)^(1/4), I*ArcSinh[(-1)^(1/4)/Sqrt[x]], -1] + EllipticPi[-(-1)^(3/4), I*ArcSinh[(-1)^(1/4)/Sqrt[x]], -1] + EllipticPi[(-1)^(3/4), I*ArcSinh[(-1)^(1/4)/Sqrt[x]], -1]))/Sqrt[x + x^3]","C",1
797,1,525,61,0.6536528,"\int \frac{1+x^3}{\left(-1+x^3\right) \sqrt{1+x^4}} \, dx","Integrate[(1 + x^3)/((-1 + x^3)*Sqrt[1 + x^4]),x]","\frac{1}{18} \left(4 (-1)^{2/3} \sqrt{1-\sqrt[3]{-1}} \tanh ^{-1}\left(\frac{\sqrt[3]{-1}-x^2}{\sqrt{1+(-1)^{2/3}} \sqrt{x^4+1}}\right)+2 \sqrt[3]{-1} \sqrt{1-\sqrt[3]{-1}} \tanh ^{-1}\left(\frac{\sqrt[3]{-1}-x^2}{\sqrt{1+(-1)^{2/3}} \sqrt{x^4+1}}\right)-2 \sqrt{1-\sqrt[3]{-1}} \tanh ^{-1}\left(\frac{\sqrt[3]{-1}-x^2}{\sqrt{1+(-1)^{2/3}} \sqrt{x^4+1}}\right)+(-1)^{2/3} \sqrt{2} \tanh ^{-1}\left(\frac{x^2+1}{\sqrt{2} \sqrt{x^4+1}}\right)-\sqrt[3]{-1} \sqrt{2} \tanh ^{-1}\left(\frac{x^2+1}{\sqrt{2} \sqrt{x^4+1}}\right)-2 \sqrt{2} \tanh ^{-1}\left(\frac{x^2+1}{\sqrt{2} \sqrt{x^4+1}}\right)+2 (-1)^{2/3} \sqrt{1+(-1)^{2/3}} \tanh ^{-1}\left(\frac{x^2+(-1)^{2/3}}{\sqrt{1-\sqrt[3]{-1}} \sqrt{x^4+1}}\right)+4 \sqrt[3]{-1} \sqrt{1+(-1)^{2/3}} \tanh ^{-1}\left(\frac{x^2+(-1)^{2/3}}{\sqrt{1-\sqrt[3]{-1}} \sqrt{x^4+1}}\right)+2 \sqrt{1+(-1)^{2/3}} \tanh ^{-1}\left(\frac{x^2+(-1)^{2/3}}{\sqrt{1-\sqrt[3]{-1}} \sqrt{x^4+1}}\right)-18 \sqrt[4]{-1} F\left(\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+12 \sqrt[4]{-1} \Pi \left(i;\left.\sin ^{-1}\left((-1)^{3/4} x\right)\right|-1\right)-12 (-1)^{11/12} \Pi \left(-\sqrt[6]{-1};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+12 (-1)^{7/12} \Pi \left(-\sqrt[6]{-1};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+12 \sqrt[4]{-1} \Pi \left(-(-1)^{5/6};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)\right)","-\frac{4}{3} \tan ^{-1}\left(\frac{x}{\sqrt{x^4+1}+x^2+x+1}\right)-\frac{1}{3} \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}+x^2-2 x+1}\right)",1,"(-2*Sqrt[1 - (-1)^(1/3)]*ArcTanh[((-1)^(1/3) - x^2)/(Sqrt[1 + (-1)^(2/3)]*Sqrt[1 + x^4])] + 2*(-1)^(1/3)*Sqrt[1 - (-1)^(1/3)]*ArcTanh[((-1)^(1/3) - x^2)/(Sqrt[1 + (-1)^(2/3)]*Sqrt[1 + x^4])] + 4*(-1)^(2/3)*Sqrt[1 - (-1)^(1/3)]*ArcTanh[((-1)^(1/3) - x^2)/(Sqrt[1 + (-1)^(2/3)]*Sqrt[1 + x^4])] - 2*Sqrt[2]*ArcTanh[(1 + x^2)/(Sqrt[2]*Sqrt[1 + x^4])] - (-1)^(1/3)*Sqrt[2]*ArcTanh[(1 + x^2)/(Sqrt[2]*Sqrt[1 + x^4])] + (-1)^(2/3)*Sqrt[2]*ArcTanh[(1 + x^2)/(Sqrt[2]*Sqrt[1 + x^4])] + 2*Sqrt[1 + (-1)^(2/3)]*ArcTanh[((-1)^(2/3) + x^2)/(Sqrt[1 - (-1)^(1/3)]*Sqrt[1 + x^4])] + 4*(-1)^(1/3)*Sqrt[1 + (-1)^(2/3)]*ArcTanh[((-1)^(2/3) + x^2)/(Sqrt[1 - (-1)^(1/3)]*Sqrt[1 + x^4])] + 2*(-1)^(2/3)*Sqrt[1 + (-1)^(2/3)]*ArcTanh[((-1)^(2/3) + x^2)/(Sqrt[1 - (-1)^(1/3)]*Sqrt[1 + x^4])] - 18*(-1)^(1/4)*EllipticF[I*ArcSinh[(-1)^(1/4)*x], -1] + 12*(-1)^(1/4)*EllipticPi[I, ArcSin[(-1)^(3/4)*x], -1] + 12*(-1)^(7/12)*EllipticPi[-(-1)^(1/6), I*ArcSinh[(-1)^(1/4)*x], -1] - 12*(-1)^(11/12)*EllipticPi[-(-1)^(1/6), I*ArcSinh[(-1)^(1/4)*x], -1] + 12*(-1)^(1/4)*EllipticPi[-(-1)^(5/6), I*ArcSinh[(-1)^(1/4)*x], -1])/18","C",0
798,1,61,61,0.0170494,"\int \frac{-1+x}{x \sqrt[4]{1+x^4}} \, dx","Integrate[(-1 + x)/(x*(1 + x^4)^(1/4)),x]","\frac{1}{2} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)-\frac{1}{2} \tan ^{-1}\left(\sqrt[4]{x^4+1}\right)+\frac{1}{2} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)+\frac{1}{2} \tanh ^{-1}\left(\sqrt[4]{x^4+1}\right)","\frac{1}{2} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)-\frac{1}{2} \tan ^{-1}\left(\sqrt[4]{x^4+1}\right)+\frac{1}{2} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)+\frac{1}{2} \tanh ^{-1}\left(\sqrt[4]{x^4+1}\right)",1,"ArcTan[x/(1 + x^4)^(1/4)]/2 - ArcTan[(1 + x^4)^(1/4)]/2 + ArcTanh[x/(1 + x^4)^(1/4)]/2 + ArcTanh[(1 + x^4)^(1/4)]/2","A",1
799,1,54,61,0.0137777,"\int \frac{x^2}{\left(-b+a x^4\right)^{3/4}} \, dx","Integrate[x^2/(-b + a*x^4)^(3/4),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)-\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{2 a^{3/4}}","\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{2 a^{3/4}}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{2 a^{3/4}}",1,"(-ArcTan[(a^(1/4)*x)/(-b + a*x^4)^(1/4)] + ArcTanh[(a^(1/4)*x)/(-b + a*x^4)^(1/4)])/(2*a^(3/4))","A",1
800,0,0,61,1.9350623,"\int \frac{\left(6+x^4\right) \sqrt{-2 x+x^4+x^5}}{\left(-2+x^4\right) \left(-2-x^3+x^4\right)} \, dx","Integrate[((6 + x^4)*Sqrt[-2*x + x^4 + x^5])/((-2 + x^4)*(-2 - x^3 + x^4)),x]","\int \frac{\left(6+x^4\right) \sqrt{-2 x+x^4+x^5}}{\left(-2+x^4\right) \left(-2-x^3+x^4\right)} \, dx","2 \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^5+x^4-2 x}}\right)-2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt{x^5+x^4-2 x}}{x^4+x^3-2}\right)",1,"Integrate[((6 + x^4)*Sqrt[-2*x + x^4 + x^5])/((-2 + x^4)*(-2 - x^3 + x^4)), x]","F",-1
801,0,0,61,0.1913907,"\int \frac{\left(-3+x^2\right) \left(1-x^2+x^3\right)^{2/3}}{1-2 x^2-x^3+x^4+x^5+x^6} \, dx","Integrate[((-3 + x^2)*(1 - x^2 + x^3)^(2/3))/(1 - 2*x^2 - x^3 + x^4 + x^5 + x^6),x]","\int \frac{\left(-3+x^2\right) \left(1-x^2+x^3\right)^{2/3}}{1-2 x^2-x^3+x^4+x^5+x^6} \, dx","\text{RootSum}\left[\text{$\#$1}^6-3 \text{$\#$1}^3+3\&,\frac{\text{$\#$1}^2 \log \left(\sqrt[3]{x^3-x^2+1}-\text{$\#$1} x\right)-\text{$\#$1}^2 \log (x)}{2 \text{$\#$1}^3-3}\&\right]",1,"Integrate[((-3 + x^2)*(1 - x^2 + x^3)^(2/3))/(1 - 2*x^2 - x^3 + x^4 + x^5 + x^6), x]","F",-1
802,0,0,61,0.0886074,"\int \frac{\left(-3+x^2\right) \left(1-x^2+x^3\right)^{2/3}}{1-2 x^2-x^3+x^4+x^5+x^6} \, dx","Integrate[((-3 + x^2)*(1 - x^2 + x^3)^(2/3))/(1 - 2*x^2 - x^3 + x^4 + x^5 + x^6),x]","\int \frac{\left(-3+x^2\right) \left(1-x^2+x^3\right)^{2/3}}{1-2 x^2-x^3+x^4+x^5+x^6} \, dx","\text{RootSum}\left[\text{$\#$1}^6-3 \text{$\#$1}^3+3\&,\frac{\text{$\#$1}^2 \log \left(\sqrt[3]{x^3-x^2+1}-\text{$\#$1} x\right)-\text{$\#$1}^2 \log (x)}{2 \text{$\#$1}^3-3}\&\right]",1,"Integrate[((-3 + x^2)*(1 - x^2 + x^3)^(2/3))/(1 - 2*x^2 - x^3 + x^4 + x^5 + x^6), x]","F",-1
803,1,100,61,0.1087253,"\int \frac{\sqrt{-1+x^6} \left(-1+2 x^6\right)^2}{x \left(-1+4 x^6\right)} \, dx","Integrate[(Sqrt[-1 + x^6]*(-1 + 2*x^6)^2)/(x*(-1 + 4*x^6)),x]","\frac{1}{144} \left(16 \sqrt{x^6-1} x^6-52 \sqrt{x^6-1}+48 \tan ^{-1}\left(\sqrt{x^6-1}\right)+3 \sqrt{3} \tan ^{-1}\left(\frac{2-x^3}{\sqrt{3} \sqrt{x^6-1}}\right)+3 \sqrt{3} \tan ^{-1}\left(\frac{x^3+2}{\sqrt{3} \sqrt{x^6-1}}\right)\right)","\frac{1}{36} \sqrt{x^6-1} \left(4 x^6-13\right)+\frac{1}{3} \tan ^{-1}\left(\sqrt{x^6-1}\right)-\frac{\tan ^{-1}\left(\frac{2 \sqrt{x^6-1}}{\sqrt{3}}\right)}{8 \sqrt{3}}",1,"(-52*Sqrt[-1 + x^6] + 16*x^6*Sqrt[-1 + x^6] + 3*Sqrt[3]*ArcTan[(2 - x^3)/(Sqrt[3]*Sqrt[-1 + x^6])] + 3*Sqrt[3]*ArcTan[(2 + x^3)/(Sqrt[3]*Sqrt[-1 + x^6])] + 48*ArcTan[Sqrt[-1 + x^6]])/144","A",1
804,1,74,61,2.9285446,"\int \frac{1}{\sqrt[3]{x+x^3} \left(b+a x^6\right)} \, dx","Integrate[1/((x + x^3)^(1/3)*(b + a*x^6)),x]","-\frac{\sqrt[3]{\frac{1}{x^2}+1} x \text{RootSum}\left[\text{$\#$1}^9 b-3 \text{$\#$1}^6 b+3 \text{$\#$1}^3 b+a-b\&,\frac{\log \left(\sqrt[3]{\frac{1}{x^2}+1}-\text{$\#$1}\right)}{\text{$\#$1}}\&\right]}{6 b \sqrt[3]{x^3+x}}","-\frac{\text{RootSum}\left[\text{$\#$1}^9 b-3 \text{$\#$1}^6 b+3 \text{$\#$1}^3 b+a-b\&,\frac{\log \left(\sqrt[3]{x^3+x}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{6 b}",1,"-1/6*((1 + x^(-2))^(1/3)*x*RootSum[a - b + 3*b*#1^3 - 3*b*#1^6 + b*#1^9 & , Log[(1 + x^(-2))^(1/3) - #1]/#1 & ])/(b*(x + x^3)^(1/3))","A",1
805,1,74,61,0.353235,"\int \frac{1}{\sqrt[3]{x+x^3} \left(b+a x^6\right)} \, dx","Integrate[1/((x + x^3)^(1/3)*(b + a*x^6)),x]","-\frac{\sqrt[3]{\frac{1}{x^2}+1} x \text{RootSum}\left[\text{$\#$1}^9 b-3 \text{$\#$1}^6 b+3 \text{$\#$1}^3 b+a-b\&,\frac{\log \left(\sqrt[3]{\frac{1}{x^2}+1}-\text{$\#$1}\right)}{\text{$\#$1}}\&\right]}{6 b \sqrt[3]{x^3+x}}","-\frac{\text{RootSum}\left[\text{$\#$1}^9 b-3 \text{$\#$1}^6 b+3 \text{$\#$1}^3 b+a-b\&,\frac{\log \left(\sqrt[3]{x^3+x}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{6 b}",1,"-1/6*((1 + x^(-2))^(1/3)*x*RootSum[a - b + 3*b*#1^3 - 3*b*#1^6 + b*#1^9 & , Log[(1 + x^(-2))^(1/3) - #1]/#1 & ])/(b*(x + x^3)^(1/3))","A",1
806,0,0,61,1.8373191,"\int \frac{-b+a x^4}{\left(b-2 x^2+a x^4\right) \sqrt[4]{b x^2+a x^6}} \, dx","Integrate[(-b + a*x^4)/((b - 2*x^2 + a*x^4)*(b*x^2 + a*x^6)^(1/4)),x]","\int \frac{-b+a x^4}{\left(b-2 x^2+a x^4\right) \sqrt[4]{b x^2+a x^6}} \, dx","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{a x^6+b x^2}}\right)}{\sqrt[4]{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{a x^6+b x^2}}\right)}{\sqrt[4]{2}}",1,"Integrate[(-b + a*x^4)/((b - 2*x^2 + a*x^4)*(b*x^2 + a*x^6)^(1/4)), x]","F",-1
807,0,0,61,0.1864943,"\int \frac{\left(4+x^5\right) \sqrt{1-2 x^5+x^8+x^{10}}}{x^9} \, dx","Integrate[((4 + x^5)*Sqrt[1 - 2*x^5 + x^8 + x^10])/x^9,x]","\int \frac{\left(4+x^5\right) \sqrt{1-2 x^5+x^8+x^{10}}}{x^9} \, dx","\frac{\sqrt{x^{10}+x^8-2 x^5+1} \left(x^5-1\right)}{2 x^8}+\frac{1}{2} \log \left(x^5+\sqrt{x^{10}+x^8-2 x^5+1}-1\right)-2 \log (x)",1,"Integrate[((4 + x^5)*Sqrt[1 - 2*x^5 + x^8 + x^10])/x^9, x]","F",-1
808,0,0,61,1.2039451,"\int \frac{\left(1+x^6\right) \left(-1+x^3+x^6\right)^{2/3}}{1-x^6+x^{12}} \, dx","Integrate[((1 + x^6)*(-1 + x^3 + x^6)^(2/3))/(1 - x^6 + x^12),x]","\int \frac{\left(1+x^6\right) \left(-1+x^3+x^6\right)^{2/3}}{1-x^6+x^{12}} \, dx","\frac{1}{6} \text{RootSum}\left[\text{$\#$1}^6-2 \text{$\#$1}^3+2\&,\frac{\text{$\#$1}^2 \log \left(\sqrt[3]{x^6+x^3-1}-\text{$\#$1} x\right)-\text{$\#$1}^2 \log (x)}{\text{$\#$1}^3-1}\&\right]",1,"Integrate[((1 + x^6)*(-1 + x^3 + x^6)^(2/3))/(1 - x^6 + x^12), x]","F",-1
809,0,0,61,0.4946755,"\int \frac{\left(1+x^6\right) \left(-1+x^3+x^6\right)^{2/3}}{1-x^6+x^{12}} \, dx","Integrate[((1 + x^6)*(-1 + x^3 + x^6)^(2/3))/(1 - x^6 + x^12),x]","\int \frac{\left(1+x^6\right) \left(-1+x^3+x^6\right)^{2/3}}{1-x^6+x^{12}} \, dx","\frac{1}{6} \text{RootSum}\left[\text{$\#$1}^6-2 \text{$\#$1}^3+2\&,\frac{\text{$\#$1}^2 \log \left(\sqrt[3]{x^6+x^3-1}-\text{$\#$1} x\right)-\text{$\#$1}^2 \log (x)}{\text{$\#$1}^3-1}\&\right]",1,"Integrate[((1 + x^6)*(-1 + x^3 + x^6)^(2/3))/(1 - x^6 + x^12), x]","F",-1
810,0,0,61,0.5126128,"\int \frac{\left(-2+5 x^7\right) \sqrt[3]{2 x+x^3+2 x^8}}{4+x^4+8 x^7+4 x^{14}} \, dx","Integrate[((-2 + 5*x^7)*(2*x + x^3 + 2*x^8)^(1/3))/(4 + x^4 + 8*x^7 + 4*x^14),x]","\int \frac{\left(-2+5 x^7\right) \sqrt[3]{2 x+x^3+2 x^8}}{4+x^4+8 x^7+4 x^{14}} \, dx","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^6-2 \text{$\#$1}^3+2\&,\frac{\text{$\#$1} \log \left(\sqrt[3]{2 x^8+x^3+2 x}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^3-1}\&\right]",1,"Integrate[((-2 + 5*x^7)*(2*x + x^3 + 2*x^8)^(1/3))/(4 + x^4 + 8*x^7 + 4*x^14), x]","F",-1
811,0,0,61,0.1587477,"\int \frac{\left(-2+5 x^7\right) \sqrt[3]{2 x+x^3+2 x^8}}{4+x^4+8 x^7+4 x^{14}} \, dx","Integrate[((-2 + 5*x^7)*(2*x + x^3 + 2*x^8)^(1/3))/(4 + x^4 + 8*x^7 + 4*x^14),x]","\int \frac{\left(-2+5 x^7\right) \sqrt[3]{2 x+x^3+2 x^8}}{4+x^4+8 x^7+4 x^{14}} \, dx","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^6-2 \text{$\#$1}^3+2\&,\frac{\text{$\#$1} \log \left(\sqrt[3]{2 x^8+x^3+2 x}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^3-1}\&\right]",1,"Integrate[((-2 + 5*x^7)*(2*x + x^3 + 2*x^8)^(1/3))/(4 + x^4 + 8*x^7 + 4*x^14), x]","F",-1
812,1,57,61,0.0316039,"\int \frac{1}{\sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Integrate[1/Sqrt[a*x + Sqrt[b^2 + a^2*x^2]],x]","\frac{2 \left(3 a x \left(\sqrt{a^2 x^2+b^2}+a x\right)+b^2\right)}{3 a \left(\sqrt{a^2 x^2+b^2}+a x\right)^{3/2}}","\frac{\sqrt{\sqrt{a^2 x^2+b^2}+a x}}{a}-\frac{b^2}{3 a \left(\sqrt{a^2 x^2+b^2}+a x\right)^{3/2}}",1,"(2*(b^2 + 3*a*x*(a*x + Sqrt[b^2 + a^2*x^2])))/(3*a*(a*x + Sqrt[b^2 + a^2*x^2])^(3/2))","A",1
813,1,67,62,0.0210338,"\int x^{10} \sqrt[4]{-1+x^4} \, dx","Integrate[x^10*(-1 + x^4)^(1/4),x]","\frac{x^3 \sqrt[4]{x^4-1} \left(7 \, _2F_1\left(-\frac{1}{4},\frac{3}{4};\frac{7}{4};x^4\right)+\sqrt[4]{1-x^4} \left(8 x^8-x^4-7\right)\right)}{96 \sqrt[4]{1-x^4}}","\frac{7}{256} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-1}}\right)-\frac{7}{256} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-1}}\right)+\frac{1}{384} \sqrt[4]{x^4-1} \left(32 x^{11}-4 x^7-7 x^3\right)",1,"(x^3*(-1 + x^4)^(1/4)*((1 - x^4)^(1/4)*(-7 - x^4 + 8*x^8) + 7*Hypergeometric2F1[-1/4, 3/4, 7/4, x^4]))/(96*(1 - x^4)^(1/4))","C",1
814,1,45,62,0.0148035,"\int x^{10} \sqrt[4]{1+x^4} \, dx","Integrate[x^10*(1 + x^4)^(1/4),x]","\frac{1}{96} x^3 \left(7 \, _2F_1\left(-\frac{1}{4},\frac{3}{4};\frac{7}{4};-x^4\right)+\sqrt[4]{x^4+1} \left(8 x^8+x^4-7\right)\right)","-\frac{7}{256} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)+\frac{7}{256} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)+\frac{1}{384} \sqrt[4]{x^4+1} \left(32 x^{11}+4 x^7-7 x^3\right)",1,"(x^3*((1 + x^4)^(1/4)*(-7 + x^4 + 8*x^8) + 7*Hypergeometric2F1[-1/4, 3/4, 7/4, -x^4]))/96","C",1
815,1,72,62,0.1592612,"\int \frac{1+x^2}{\left(1-x^2+x^4\right) \sqrt[4]{x^2+x^4}} \, dx","Integrate[(1 + x^2)/((1 - x^2 + x^4)*(x^2 + x^4)^(1/4)),x]","-\frac{\left(x^4+x^2\right)^{3/4} \text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4+3\&,\frac{\text{$\#$1}^3 \log \left(\sqrt[4]{\frac{1}{x^2}+1}-\text{$\#$1}\right)}{2 \text{$\#$1}^4-3}\&\right]}{2 \left(\frac{1}{x^2}+1\right)^{3/4} x^3}","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4+3\&,\frac{\text{$\#$1}^3 \log \left(\sqrt[4]{x^4+x^2}-\text{$\#$1} x\right)-\text{$\#$1}^3 \log (x)}{2 \text{$\#$1}^4-3}\&\right]",1,"-1/2*((x^2 + x^4)^(3/4)*RootSum[3 - 3*#1^4 + #1^8 & , (Log[(1 + x^(-2))^(1/4) - #1]*#1^3)/(-3 + 2*#1^4) & ])/((1 + x^(-2))^(3/4)*x^3)","A",1
816,1,309,62,1.1823526,"\int \frac{1}{\left(-b+a x^4\right) \sqrt[4]{-b x^2+a x^4}} \, dx","Integrate[1/((-b + a*x^4)*(-(b*x^2) + a*x^4)^(1/4)),x]","-\frac{x \sqrt[4]{\frac{b}{x^2}-a} \left(-\sqrt[4]{\sqrt{b}-\sqrt{a}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{a} \sqrt[4]{-\sqrt{a}-\sqrt{b}}}\right)-\sqrt[4]{-\sqrt{a}-\sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{a} \sqrt[4]{\sqrt{b}-\sqrt{a}}}\right)+\sqrt[4]{\sqrt{b}-\sqrt{a}} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{a} \sqrt[4]{-\sqrt{a}-\sqrt{b}}}\right)+\sqrt[4]{-\sqrt{a}-\sqrt{b}} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{a} \sqrt[4]{\sqrt{b}-\sqrt{a}}}\right)\right)}{2 \sqrt[8]{a} b \sqrt[4]{-\sqrt{a}-\sqrt{b}} \sqrt[4]{\sqrt{b}-\sqrt{a}} \sqrt[4]{a x^4-b x^2}}","\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2-a b\&,\frac{\log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{4 b}",1,"-1/2*((-a + b/x^2)^(1/4)*x*(-((-Sqrt[a] + Sqrt[b])^(1/4)*ArcTan[(-a + b/x^2)^(1/4)/(a^(1/8)*(-Sqrt[a] - Sqrt[b])^(1/4))]) - (-Sqrt[a] - Sqrt[b])^(1/4)*ArcTan[(-a + b/x^2)^(1/4)/(a^(1/8)*(-Sqrt[a] + Sqrt[b])^(1/4))] + (-Sqrt[a] + Sqrt[b])^(1/4)*ArcTanh[(-a + b/x^2)^(1/4)/(a^(1/8)*(-Sqrt[a] - Sqrt[b])^(1/4))] + (-Sqrt[a] - Sqrt[b])^(1/4)*ArcTanh[(-a + b/x^2)^(1/4)/(a^(1/8)*(-Sqrt[a] + Sqrt[b])^(1/4))]))/(a^(1/8)*(-Sqrt[a] - Sqrt[b])^(1/4)*(-Sqrt[a] + Sqrt[b])^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4))","B",1
817,1,309,62,0.3135359,"\int \frac{1}{\left(-b+a x^4\right) \sqrt[4]{-b x^2+a x^4}} \, dx","Integrate[1/((-b + a*x^4)*(-(b*x^2) + a*x^4)^(1/4)),x]","-\frac{x \sqrt[4]{\frac{b}{x^2}-a} \left(-\sqrt[4]{\sqrt{b}-\sqrt{a}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{a} \sqrt[4]{-\sqrt{a}-\sqrt{b}}}\right)-\sqrt[4]{-\sqrt{a}-\sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{a} \sqrt[4]{\sqrt{b}-\sqrt{a}}}\right)+\sqrt[4]{\sqrt{b}-\sqrt{a}} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{a} \sqrt[4]{-\sqrt{a}-\sqrt{b}}}\right)+\sqrt[4]{-\sqrt{a}-\sqrt{b}} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{a} \sqrt[4]{\sqrt{b}-\sqrt{a}}}\right)\right)}{2 \sqrt[8]{a} b \sqrt[4]{-\sqrt{a}-\sqrt{b}} \sqrt[4]{\sqrt{b}-\sqrt{a}} \sqrt[4]{a x^4-b x^2}}","\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2-a b\&,\frac{\log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{4 b}",1,"-1/2*((-a + b/x^2)^(1/4)*x*(-((-Sqrt[a] + Sqrt[b])^(1/4)*ArcTan[(-a + b/x^2)^(1/4)/(a^(1/8)*(-Sqrt[a] - Sqrt[b])^(1/4))]) - (-Sqrt[a] - Sqrt[b])^(1/4)*ArcTan[(-a + b/x^2)^(1/4)/(a^(1/8)*(-Sqrt[a] + Sqrt[b])^(1/4))] + (-Sqrt[a] + Sqrt[b])^(1/4)*ArcTanh[(-a + b/x^2)^(1/4)/(a^(1/8)*(-Sqrt[a] - Sqrt[b])^(1/4))] + (-Sqrt[a] - Sqrt[b])^(1/4)*ArcTanh[(-a + b/x^2)^(1/4)/(a^(1/8)*(-Sqrt[a] + Sqrt[b])^(1/4))]))/(a^(1/8)*(-Sqrt[a] - Sqrt[b])^(1/4)*(-Sqrt[a] + Sqrt[b])^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4))","B",1
818,1,2477,62,1.8835792,"\int \frac{1-x^2}{x \sqrt{a+b x+c x^2+b x^3+a x^4}} \, dx","Integrate[(1 - x^2)/(x*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]),x]","\text{Result too large to show}","\frac{\log \left(2 \sqrt{a} \sqrt{a x^4+a+b x^3+b x+c x^2}-2 a x^2-2 a-b x\right)}{\sqrt{a}}-\frac{\log (x)}{\sqrt{a}}",1,"(2*(x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])^2*((Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(EllipticPi[(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2]*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1]*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])), ArcSin[Sqrt[((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))]], -(((Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])))] + EllipticPi[(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])/(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]), ArcSin[Sqrt[((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))]], -(((Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])))]*Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1]*Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2]) + EllipticF[ArcSin[Sqrt[((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))]], -(((Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])))]*Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1]*(-1 + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2]^2))*Sqrt[((Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3]))/((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3]))]*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])*Sqrt[((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])^2*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])^2)])/(Sqrt[x*(b + c*x + b*x^2) + a*(1 + x^4)]*Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1]*Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2]*(-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))","C",1
819,0,0,62,0.6927338,"\int \frac{x^2 \left(-1+3 x^4\right)}{\left(1+x^4\right)^2 \left(a-x+a x^4\right) \sqrt{x+x^5}} \, dx","Integrate[(x^2*(-1 + 3*x^4))/((1 + x^4)^2*(a - x + a*x^4)*Sqrt[x + x^5]),x]","\int \frac{x^2 \left(-1+3 x^4\right)}{\left(1+x^4\right)^2 \left(a-x+a x^4\right) \sqrt{x+x^5}} \, dx","\frac{2 \sqrt{x^5+x} \left(3 a x^4+3 a+x\right)}{3 \left(x^4+1\right)^2}-2 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{x^5+x}}{\sqrt{a} \left(x^4+1\right)}\right)",1,"Integrate[(x^2*(-1 + 3*x^4))/((1 + x^4)^2*(a - x + a*x^4)*Sqrt[x + x^5]), x]","F",-1
820,0,0,62,0.6312899,"\int \frac{\left(-3+x^4\right) \left(1-x^3+2 x^4-x^6-x^7+x^8\right)}{x^6 \left(1-x^3+x^4\right) \sqrt[4]{x+x^5}} \, dx","Integrate[((-3 + x^4)*(1 - x^3 + 2*x^4 - x^6 - x^7 + x^8))/(x^6*(1 - x^3 + x^4)*(x + x^5)^(1/4)),x]","\int \frac{\left(-3+x^4\right) \left(1-x^3+2 x^4-x^6-x^7+x^8\right)}{x^6 \left(1-x^3+x^4\right) \sqrt[4]{x+x^5}} \, dx","2 \tan ^{-1}\left(\frac{\left(x^5+x\right)^{3/4}}{x^4+1}\right)+2 \tanh ^{-1}\left(\frac{\left(x^5+x\right)^{3/4}}{x^4+1}\right)+\frac{4 \left(x^5+x\right)^{3/4} \left(x^4+1\right)}{7 x^6}",1,"Integrate[((-3 + x^4)*(1 - x^3 + 2*x^4 - x^6 - x^7 + x^8))/(x^6*(1 - x^3 + x^4)*(x + x^5)^(1/4)), x]","F",-1
821,1,58,62,0.0425594,"\int \frac{1+x^2}{\sqrt{1+\sqrt{1+x}}} \, dx","Integrate[(1 + x^2)/Sqrt[1 + Sqrt[1 + x]],x]","\frac{4 \sqrt{\sqrt{x+1}+1} \left(35 \left(9 \sqrt{x+1}-10\right) x^2+8 \left(5 \sqrt{x+1}+1\right) x+1091 \sqrt{x+1}-2374\right)}{3465}","\frac{4 \sqrt{x+1} \left(315 x^2+40 x+1091\right) \sqrt{\sqrt{x+1}+1}}{3465}-\frac{8 \left(175 x^2-4 x+1187\right) \sqrt{\sqrt{x+1}+1}}{3465}",1,"(4*Sqrt[1 + Sqrt[1 + x]]*(-2374 + 1091*Sqrt[1 + x] + 8*x*(1 + 5*Sqrt[1 + x]) + 35*x^2*(-10 + 9*Sqrt[1 + x])))/3465","A",1
822,0,0,62,0.3142715,"\int \frac{-1+2 x}{(1+x) \sqrt{-a^2 x^2+(1+x)^6}} \, dx","Integrate[(-1 + 2*x)/((1 + x)*Sqrt[-(a^2*x^2) + (1 + x)^6]),x]","\int \frac{-1+2 x}{(1+x) \sqrt{-a^2 x^2+(1+x)^6}} \, dx","-\frac{2 \tan ^{-1}\left(\frac{a x}{\sqrt{\left(15-a^2\right) x^2+x^6+6 x^5+15 x^4+20 x^3+6 x+1}+x^3+3 x^2+3 x+1}\right)}{a}",1,"Integrate[(-1 + 2*x)/((1 + x)*Sqrt[-(a^2*x^2) + (1 + x)^6]), x]","F",-1
823,1,510,62,2.4356659,"\int \frac{x}{\sqrt{-b+a^2 x^2} \sqrt[4]{a x+\sqrt{-b+a^2 x^2}}} \, dx","Integrate[x/(Sqrt[-b + a^2*x^2]*(a*x + Sqrt[-b + a^2*x^2])^(1/4)),x]","\frac{4 \sqrt{a^2 x^2-b} \left(20480 a^{15} x^{15}-84992 a^{13} b x^{13}+142592 a^{11} b^2 x^{11}-123392 a^9 b^3 x^9+58080 a^7 b^4 x^7-14308 a^5 b^5 x^5+1593 a^3 b^6 x^3-4 b^7 \sqrt{a^2 x^2-b}+353 a^2 b^6 x^2 \sqrt{a^2 x^2-b}+20480 a^{14} x^{14} \sqrt{a^2 x^2-b}-74752 a^{12} b x^{12} \sqrt{a^2 x^2-b}+107776 a^{10} b^2 x^{10} \sqrt{a^2 x^2-b}-77568 a^8 b^3 x^8 \sqrt{a^2 x^2-b}+28896 a^6 b^4 x^6 \sqrt{a^2 x^2-b}-5180 a^4 b^5 x^4 \sqrt{a^2 x^2-b}-53 a b^7 x\right)}{15 a^2 \left(\sqrt{a^2 x^2-b}+a x\right)^{13/4} \left(a x \left(\sqrt{a^2 x^2-b}+a x\right)-b\right) \left(a b^4 x \left(9 \sqrt{a^2 x^2-b}+41 a x\right)+256 a^9 x^9 \left(\sqrt{a^2 x^2-b}+a x\right)-64 a^7 b x^7 \left(9 \sqrt{a^2 x^2-b}+11 a x\right)+16 a^5 b^2 x^5 \left(27 \sqrt{a^2 x^2-b}+43 a x\right)-40 a^3 b^3 x^3 \left(3 \sqrt{a^2 x^2-b}+7 a x\right)-b^5\right)}","\frac{2 \left(\sqrt{a^2 x^2-b}+a x\right)^{3/4}}{3 a^2}-\frac{2 b}{5 a^2 \left(\sqrt{a^2 x^2-b}+a x\right)^{5/4}}",1,"(4*Sqrt[-b + a^2*x^2]*(-53*a*b^7*x + 1593*a^3*b^6*x^3 - 14308*a^5*b^5*x^5 + 58080*a^7*b^4*x^7 - 123392*a^9*b^3*x^9 + 142592*a^11*b^2*x^11 - 84992*a^13*b*x^13 + 20480*a^15*x^15 - 4*b^7*Sqrt[-b + a^2*x^2] + 353*a^2*b^6*x^2*Sqrt[-b + a^2*x^2] - 5180*a^4*b^5*x^4*Sqrt[-b + a^2*x^2] + 28896*a^6*b^4*x^6*Sqrt[-b + a^2*x^2] - 77568*a^8*b^3*x^8*Sqrt[-b + a^2*x^2] + 107776*a^10*b^2*x^10*Sqrt[-b + a^2*x^2] - 74752*a^12*b*x^12*Sqrt[-b + a^2*x^2] + 20480*a^14*x^14*Sqrt[-b + a^2*x^2]))/(15*a^2*(a*x + Sqrt[-b + a^2*x^2])^(13/4)*(-b + a*x*(a*x + Sqrt[-b + a^2*x^2]))*(-b^5 + 256*a^9*x^9*(a*x + Sqrt[-b + a^2*x^2]) - 40*a^3*b^3*x^3*(7*a*x + 3*Sqrt[-b + a^2*x^2]) - 64*a^7*b*x^7*(11*a*x + 9*Sqrt[-b + a^2*x^2]) + a*b^4*x*(41*a*x + 9*Sqrt[-b + a^2*x^2]) + 16*a^5*b^2*x^5*(43*a*x + 27*Sqrt[-b + a^2*x^2])))","B",1
824,1,59,62,0.0264713,"\int \sqrt{a x+\sqrt{b^2+a^2 x^2}} \, dx","Integrate[Sqrt[a*x + Sqrt[b^2 + a^2*x^2]],x]","\frac{2 a x \left(\sqrt{a^2 x^2+b^2}+a x\right)-2 b^2}{3 a \sqrt{\sqrt{a^2 x^2+b^2}+a x}}","\frac{\left(\sqrt{a^2 x^2+b^2}+a x\right)^{3/2}}{3 a}-\frac{b^2}{a \sqrt{\sqrt{a^2 x^2+b^2}+a x}}",1,"(-2*b^2 + 2*a*x*(a*x + Sqrt[b^2 + a^2*x^2]))/(3*a*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])","A",1
825,1,79,63,0.0620395,"\int \frac{1}{\left(1+\sqrt{x}\right) \sqrt{-\sqrt{x}+x}} \, dx","Integrate[1/((1 + Sqrt[x])*Sqrt[-Sqrt[x] + x]),x]","-\sqrt{2} \log \left(\sqrt{x}+1\right)+2 \log \left(-2 \sqrt{x}-2 \sqrt{x-\sqrt{x}}+1\right)+\sqrt{2} \log \left(-3 \sqrt{x}+2 \sqrt{2} \sqrt{x-\sqrt{x}}+1\right)","4 \tanh ^{-1}\left(\frac{\sqrt{x-\sqrt{x}}}{\sqrt{x}-1}\right)-2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{x-\sqrt{x}}}{\sqrt{x}-1}\right)",1,"-(Sqrt[2]*Log[1 + Sqrt[x]]) + 2*Log[1 - 2*Sqrt[x] - 2*Sqrt[-Sqrt[x] + x]] + Sqrt[2]*Log[1 - 3*Sqrt[x] + 2*Sqrt[2]*Sqrt[-Sqrt[x] + x]]","A",1
826,1,627,63,2.2775357,"\int \frac{x}{\left(-1+x^2\right) \sqrt{x+x^2+x^3}} \, dx","Integrate[x/((-1 + x^2)*Sqrt[x + x^2 + x^3]),x]","\frac{(-1)^{2/3} \sqrt{x} \left(\sqrt[3]{-1} \left(\sqrt[3]{-1}-1\right)^2 \left(1+\sqrt[3]{-1}\right) \sqrt{\sqrt[3]{-1} x+1} \sqrt{1-(-1)^{2/3} x} \Pi \left(\sqrt[3]{-1};i \sinh ^{-1}\left((-1)^{5/6} \sqrt{x}\right)|(-1)^{2/3}\right)+i \sqrt{3} \sqrt{\frac{(-1)^{2/3}-\sqrt{x}}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1}-\sqrt{x}\right)}} \sqrt{\frac{1-\left(\sqrt[3]{-1}-1\right) \sqrt{x}}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1}-\sqrt{x}\right)}} \sqrt{-\frac{\sqrt{x}+(-1)^{2/3}}{\left(\sqrt[3]{-1}-1\right) \sqrt{x}+1}} \left(\sqrt[3]{-1}-\sqrt{x}\right)^2 \left(\left(1+\sqrt[3]{-1}\right) F\left(\left.\sin ^{-1}\left(\sqrt{\frac{1-\left(-1+\sqrt[3]{-1}\right) \sqrt{x}}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1}-\sqrt{x}\right)}}\right)\right|-3\right)-2 \sqrt[3]{-1} \Pi \left(-1;\left.\sin ^{-1}\left(\sqrt{\frac{1-\left(-1+\sqrt[3]{-1}\right) \sqrt{x}}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1}-\sqrt{x}\right)}}\right)\right|-3\right)\right)-i \sqrt{3} \sqrt{\frac{(-1)^{2/3}-\sqrt{x}}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1}-\sqrt{x}\right)}} \sqrt{\frac{1-\left(\sqrt[3]{-1}-1\right) \sqrt{x}}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1}-\sqrt{x}\right)}} \sqrt{-\frac{\sqrt{x}+(-1)^{2/3}}{\left(\sqrt[3]{-1}-1\right) \sqrt{x}+1}} \left(\sqrt[3]{-1}-\sqrt{x}\right)^2 \left(\left(\sqrt[3]{-1}-1\right) F\left(\left.\sin ^{-1}\left(\sqrt{\frac{1-\left(-1+\sqrt[3]{-1}\right) \sqrt{x}}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1}-\sqrt{x}\right)}}\right)\right|-3\right)-2 \sqrt[3]{-1} \Pi \left(3;\left.\sin ^{-1}\left(\sqrt{\frac{1-\left(-1+\sqrt[3]{-1}\right) \sqrt{x}}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1}-\sqrt{x}\right)}}\right)\right|-3\right)\right)\right)}{\left(1-(-1)^{2/3}\right) \sqrt{x \left(x^2+x+1\right)}}","\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{x^3+x^2+x}}{x^2+x+1}\right)-\frac{\tanh ^{-1}\left(\frac{\sqrt{3} \sqrt{x^3+x^2+x}}{x^2+x+1}\right)}{2 \sqrt{3}}",1,"((-1)^(2/3)*Sqrt[x]*(I*Sqrt[3]*((-1)^(1/3) - Sqrt[x])^2*Sqrt[((-1)^(2/3) - Sqrt[x])/((1 + (-1)^(1/3))*((-1)^(1/3) - Sqrt[x]))]*Sqrt[(1 - (-1 + (-1)^(1/3))*Sqrt[x])/((1 + (-1)^(1/3))*((-1)^(1/3) - Sqrt[x]))]*Sqrt[-(((-1)^(2/3) + Sqrt[x])/(1 + (-1 + (-1)^(1/3))*Sqrt[x]))]*((1 + (-1)^(1/3))*EllipticF[ArcSin[Sqrt[(1 - (-1 + (-1)^(1/3))*Sqrt[x])/((1 + (-1)^(1/3))*((-1)^(1/3) - Sqrt[x]))]], -3] - 2*(-1)^(1/3)*EllipticPi[-1, ArcSin[Sqrt[(1 - (-1 + (-1)^(1/3))*Sqrt[x])/((1 + (-1)^(1/3))*((-1)^(1/3) - Sqrt[x]))]], -3]) - I*Sqrt[3]*((-1)^(1/3) - Sqrt[x])^2*Sqrt[((-1)^(2/3) - Sqrt[x])/((1 + (-1)^(1/3))*((-1)^(1/3) - Sqrt[x]))]*Sqrt[(1 - (-1 + (-1)^(1/3))*Sqrt[x])/((1 + (-1)^(1/3))*((-1)^(1/3) - Sqrt[x]))]*Sqrt[-(((-1)^(2/3) + Sqrt[x])/(1 + (-1 + (-1)^(1/3))*Sqrt[x]))]*((-1 + (-1)^(1/3))*EllipticF[ArcSin[Sqrt[(1 - (-1 + (-1)^(1/3))*Sqrt[x])/((1 + (-1)^(1/3))*((-1)^(1/3) - Sqrt[x]))]], -3] - 2*(-1)^(1/3)*EllipticPi[3, ArcSin[Sqrt[(1 - (-1 + (-1)^(1/3))*Sqrt[x])/((1 + (-1)^(1/3))*((-1)^(1/3) - Sqrt[x]))]], -3]) + (-1)^(1/3)*(-1 + (-1)^(1/3))^2*(1 + (-1)^(1/3))*Sqrt[1 + (-1)^(1/3)*x]*Sqrt[1 - (-1)^(2/3)*x]*EllipticPi[(-1)^(1/3), I*ArcSinh[(-1)^(5/6)*Sqrt[x]], (-1)^(2/3)]))/((1 - (-1)^(2/3))*Sqrt[x*(1 + x + x^2)])","C",0
827,1,8886,63,13.3258389,"\int \frac{-a b c+2 a (b+c) x-(3 a+b+c) x^2+2 x^3}{\sqrt{x (-a+x) (-b+x) (-c+x)} \left(a d+(b c-d) x-(b+c) x^2+x^3\right)} \, dx","Integrate[(-(a*b*c) + 2*a*(b + c)*x - (3*a + b + c)*x^2 + 2*x^3)/(Sqrt[x*(-a + x)*(-b + x)*(-c + x)]*(a*d + (b*c - d)*x - (b + c)*x^2 + x^3)),x]","\text{Result too large to show}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{x^3 (-a-b-c)+x^2 (a b+a c+b c)-a b c x+x^4}}{\sqrt{d} (a-x)}\right)}{\sqrt{d}}",1,"Result too large to show","C",0
828,1,60,63,0.0831575,"\int \frac{3 b+a x^3}{x \left(-b+a x^3\right) \sqrt{b+a x^3}} \, dx","Integrate[(3*b + a*x^3)/(x*(-b + a*x^3)*Sqrt[b + a*x^3]),x]","\frac{2 \left(3 \tanh ^{-1}\left(\frac{\sqrt{a x^3+b}}{\sqrt{b}}\right)-2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{a x^3+b}}{\sqrt{2} \sqrt{b}}\right)\right)}{3 \sqrt{b}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a x^3+b}}{\sqrt{b}}\right)}{\sqrt{b}}-\frac{4 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{a x^3+b}}{\sqrt{2} \sqrt{b}}\right)}{3 \sqrt{b}}",1,"(2*(3*ArcTanh[Sqrt[b + a*x^3]/Sqrt[b]] - 2*Sqrt[2]*ArcTanh[Sqrt[b + a*x^3]/(Sqrt[2]*Sqrt[b])]))/(3*Sqrt[b])","A",1
829,1,21715,63,6.9164295,"\int \frac{\left(2 c-a x^3\right) \sqrt{c+b x^2+a x^3}}{\left(c+(-3+b) x^2+a x^3\right) \left(c+(-2+b) x^2+a x^3\right)} \, dx","Integrate[((2*c - a*x^3)*Sqrt[c + b*x^2 + a*x^3])/((c + (-3 + b)*x^2 + a*x^3)*(c + (-2 + b)*x^2 + a*x^3)),x]","\text{Result too large to show}","2 \sqrt{3} \tanh ^{-1}\left(\frac{\sqrt{3} x}{\sqrt{a x^3+b x^2+c}}\right)-2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{a x^3+b x^2+c}}\right)",1,"Result too large to show","C",0
830,1,8822,63,13.3235832,"\int \frac{-a b c+2 a (b+c) x-(3 a+b+c) x^2+2 x^3}{\sqrt{x (-a+x) (-b+x) (-c+x)} \left(a+(-1+b c d) x-(b+c) d x^2+d x^3\right)} \, dx","Integrate[(-(a*b*c) + 2*a*(b + c)*x - (3*a + b + c)*x^2 + 2*x^3)/(Sqrt[x*(-a + x)*(-b + x)*(-c + x)]*(a + (-1 + b*c*d)*x - (b + c)*d*x^2 + d*x^3)),x]","\text{Result too large to show}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{x^3 (-a-b-c)+x^2 (a b+a c+b c)-a b c x+x^4}}{a-x}\right)}{\sqrt{d}}",1,"Result too large to show","C",0
831,1,525,63,0.7247316,"\int \frac{-1+x^3}{\left(1+x^3\right) \sqrt{1+x^4}} \, dx","Integrate[(-1 + x^3)/((1 + x^3)*Sqrt[1 + x^4]),x]","\frac{1}{18} \left(-4 (-1)^{2/3} \sqrt{1-\sqrt[3]{-1}} \tanh ^{-1}\left(\frac{\sqrt[3]{-1}-x^2}{\sqrt{1+(-1)^{2/3}} \sqrt{x^4+1}}\right)-2 \sqrt[3]{-1} \sqrt{1-\sqrt[3]{-1}} \tanh ^{-1}\left(\frac{\sqrt[3]{-1}-x^2}{\sqrt{1+(-1)^{2/3}} \sqrt{x^4+1}}\right)+2 \sqrt{1-\sqrt[3]{-1}} \tanh ^{-1}\left(\frac{\sqrt[3]{-1}-x^2}{\sqrt{1+(-1)^{2/3}} \sqrt{x^4+1}}\right)-(-1)^{2/3} \sqrt{2} \tanh ^{-1}\left(\frac{x^2+1}{\sqrt{2} \sqrt{x^4+1}}\right)+\sqrt[3]{-1} \sqrt{2} \tanh ^{-1}\left(\frac{x^2+1}{\sqrt{2} \sqrt{x^4+1}}\right)+2 \sqrt{2} \tanh ^{-1}\left(\frac{x^2+1}{\sqrt{2} \sqrt{x^4+1}}\right)-2 (-1)^{2/3} \sqrt{1+(-1)^{2/3}} \tanh ^{-1}\left(\frac{x^2+(-1)^{2/3}}{\sqrt{1-\sqrt[3]{-1}} \sqrt{x^4+1}}\right)-4 \sqrt[3]{-1} \sqrt{1+(-1)^{2/3}} \tanh ^{-1}\left(\frac{x^2+(-1)^{2/3}}{\sqrt{1-\sqrt[3]{-1}} \sqrt{x^4+1}}\right)-2 \sqrt{1+(-1)^{2/3}} \tanh ^{-1}\left(\frac{x^2+(-1)^{2/3}}{\sqrt{1-\sqrt[3]{-1}} \sqrt{x^4+1}}\right)-18 \sqrt[4]{-1} F\left(\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+12 \sqrt[4]{-1} \Pi \left(i;\left.\sin ^{-1}\left((-1)^{3/4} x\right)\right|-1\right)-12 (-1)^{11/12} \Pi \left(-\sqrt[6]{-1};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+12 (-1)^{7/12} \Pi \left(-\sqrt[6]{-1};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+12 \sqrt[4]{-1} \Pi \left(-(-1)^{5/6};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)\right)","-\frac{4}{3} \tan ^{-1}\left(\frac{x}{\sqrt{x^4+1}+x^2-x+1}\right)-\frac{1}{3} \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}+x^2+2 x+1}\right)",1,"(2*Sqrt[1 - (-1)^(1/3)]*ArcTanh[((-1)^(1/3) - x^2)/(Sqrt[1 + (-1)^(2/3)]*Sqrt[1 + x^4])] - 2*(-1)^(1/3)*Sqrt[1 - (-1)^(1/3)]*ArcTanh[((-1)^(1/3) - x^2)/(Sqrt[1 + (-1)^(2/3)]*Sqrt[1 + x^4])] - 4*(-1)^(2/3)*Sqrt[1 - (-1)^(1/3)]*ArcTanh[((-1)^(1/3) - x^2)/(Sqrt[1 + (-1)^(2/3)]*Sqrt[1 + x^4])] + 2*Sqrt[2]*ArcTanh[(1 + x^2)/(Sqrt[2]*Sqrt[1 + x^4])] + (-1)^(1/3)*Sqrt[2]*ArcTanh[(1 + x^2)/(Sqrt[2]*Sqrt[1 + x^4])] - (-1)^(2/3)*Sqrt[2]*ArcTanh[(1 + x^2)/(Sqrt[2]*Sqrt[1 + x^4])] - 2*Sqrt[1 + (-1)^(2/3)]*ArcTanh[((-1)^(2/3) + x^2)/(Sqrt[1 - (-1)^(1/3)]*Sqrt[1 + x^4])] - 4*(-1)^(1/3)*Sqrt[1 + (-1)^(2/3)]*ArcTanh[((-1)^(2/3) + x^2)/(Sqrt[1 - (-1)^(1/3)]*Sqrt[1 + x^4])] - 2*(-1)^(2/3)*Sqrt[1 + (-1)^(2/3)]*ArcTanh[((-1)^(2/3) + x^2)/(Sqrt[1 - (-1)^(1/3)]*Sqrt[1 + x^4])] - 18*(-1)^(1/4)*EllipticF[I*ArcSinh[(-1)^(1/4)*x], -1] + 12*(-1)^(1/4)*EllipticPi[I, ArcSin[(-1)^(3/4)*x], -1] + 12*(-1)^(7/12)*EllipticPi[-(-1)^(1/6), I*ArcSinh[(-1)^(1/4)*x], -1] - 12*(-1)^(11/12)*EllipticPi[-(-1)^(1/6), I*ArcSinh[(-1)^(1/4)*x], -1] + 12*(-1)^(1/4)*EllipticPi[-(-1)^(5/6), I*ArcSinh[(-1)^(1/4)*x], -1])/18","C",0
832,1,56,63,0.0179917,"\int x^4 \sqrt[4]{-x+x^4} \, dx","Integrate[x^4*(-x + x^4)^(1/4),x]","\frac{x^2 \sqrt[4]{x \left(x^3-1\right)} \left(\, _2F_1\left(-\frac{1}{4},\frac{3}{4};\frac{7}{4};x^3\right)-\left(1-x^3\right)^{5/4}\right)}{6 \sqrt[4]{1-x^3}}","\frac{1}{16} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x}}\right)-\frac{1}{16} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x}}\right)+\frac{1}{24} \sqrt[4]{x^4-x} \left(4 x^5-x^2\right)",1,"(x^2*(x*(-1 + x^3))^(1/4)*(-(1 - x^3)^(5/4) + Hypergeometric2F1[-1/4, 3/4, 7/4, x^3]))/(6*(1 - x^3)^(1/4))","C",1
833,1,35,63,0.0092262,"\int \sqrt[4]{-x^3+x^4} \, dx","Integrate[(-x^3 + x^4)^(1/4),x]","\frac{4 \left((x-1) x^3\right)^{5/4} \, _2F_1\left(-\frac{3}{4},\frac{5}{4};\frac{9}{4};1-x\right)}{5 x^{15/4}}","\frac{1}{8} \sqrt[4]{x^4-x^3} (4 x-1)+\frac{3}{16} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^3}}\right)-\frac{3}{16} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^3}}\right)",1,"(4*((-1 + x)*x^3)^(5/4)*Hypergeometric2F1[-3/4, 5/4, 9/4, 1 - x])/(5*x^(15/4))","C",1
834,1,61074,63,6.6276895,"\int \frac{\sqrt{2-x^3-x^4} \left(4+x^3+2 x^4\right)}{\left(-2-3 x^2+x^3+x^4\right) \left(-2-x^2+x^3+x^4\right)} \, dx","Integrate[(Sqrt[2 - x^3 - x^4]*(4 + x^3 + 2*x^4))/((-2 - 3*x^2 + x^3 + x^4)*(-2 - x^2 + x^3 + x^4)),x]","\text{Result too large to show}","-\tan ^{-1}\left(\frac{x}{\sqrt{-x^4-x^3+2}}\right)-\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x \sqrt{-x^4-x^3+2}}{x^4+x^3-2}\right)",1,"Result too large to show","C",0
835,1,392,63,11.5271089,"\int \frac{\sqrt[4]{b x^3+a x^4}}{x \left(b+a x+x^2\right)} \, dx","Integrate[(b*x^3 + a*x^4)^(1/4)/(x*(b + a*x + x^2)),x]","-\frac{\sqrt[4]{x^3 (a x+b)} \left(-\sqrt[4]{a-\sqrt{a^2-4 b}} \log \left(2^{3/4} \sqrt[4]{a-\sqrt{a^2-4 b}}-2 \sqrt[4]{a+\frac{b}{x}}\right)+\sqrt[4]{\sqrt{a^2-4 b}+a} \log \left(2^{3/4} \sqrt[4]{\sqrt{a^2-4 b}+a}-2 \sqrt[4]{a+\frac{b}{x}}\right)+\sqrt[4]{a-\sqrt{a^2-4 b}} \log \left(2^{3/4} \sqrt[4]{a-\sqrt{a^2-4 b}}+2 \sqrt[4]{a+\frac{b}{x}}\right)-\sqrt[4]{\sqrt{a^2-4 b}+a} \log \left(2^{3/4} \sqrt[4]{\sqrt{a^2-4 b}+a}+2 \sqrt[4]{a+\frac{b}{x}}\right)+2 \sqrt[4]{a-\sqrt{a^2-4 b}} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a+\frac{b}{x}}}{\sqrt[4]{a-\sqrt{a^2-4 b}}}\right)-2 \sqrt[4]{\sqrt{a^2-4 b}+a} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a+\frac{b}{x}}}{\sqrt[4]{\sqrt{a^2-4 b}+a}}\right)\right)}{\sqrt[4]{2} x \sqrt{a^2-4 b} \sqrt[4]{a+\frac{b}{x}}}","-\text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4 a+b\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{2 \text{$\#$1}^4-a}\&\right]",1,"-(((x^3*(b + a*x))^(1/4)*(2*(a - Sqrt[a^2 - 4*b])^(1/4)*ArcTan[(2^(1/4)*(a + b/x)^(1/4))/(a - Sqrt[a^2 - 4*b])^(1/4)] - 2*(a + Sqrt[a^2 - 4*b])^(1/4)*ArcTan[(2^(1/4)*(a + b/x)^(1/4))/(a + Sqrt[a^2 - 4*b])^(1/4)] - (a - Sqrt[a^2 - 4*b])^(1/4)*Log[2^(3/4)*(a - Sqrt[a^2 - 4*b])^(1/4) - 2*(a + b/x)^(1/4)] + (a + Sqrt[a^2 - 4*b])^(1/4)*Log[2^(3/4)*(a + Sqrt[a^2 - 4*b])^(1/4) - 2*(a + b/x)^(1/4)] + (a - Sqrt[a^2 - 4*b])^(1/4)*Log[2^(3/4)*(a - Sqrt[a^2 - 4*b])^(1/4) + 2*(a + b/x)^(1/4)] - (a + Sqrt[a^2 - 4*b])^(1/4)*Log[2^(3/4)*(a + Sqrt[a^2 - 4*b])^(1/4) + 2*(a + b/x)^(1/4)]))/(2^(1/4)*Sqrt[a^2 - 4*b]*(a + b/x)^(1/4)*x))","B",1
836,1,392,63,10.924639,"\int \frac{\sqrt[4]{b x^3+a x^4}}{x \left(b+a x+x^2\right)} \, dx","Integrate[(b*x^3 + a*x^4)^(1/4)/(x*(b + a*x + x^2)),x]","-\frac{\sqrt[4]{x^3 (a x+b)} \left(-\sqrt[4]{a-\sqrt{a^2-4 b}} \log \left(2^{3/4} \sqrt[4]{a-\sqrt{a^2-4 b}}-2 \sqrt[4]{a+\frac{b}{x}}\right)+\sqrt[4]{\sqrt{a^2-4 b}+a} \log \left(2^{3/4} \sqrt[4]{\sqrt{a^2-4 b}+a}-2 \sqrt[4]{a+\frac{b}{x}}\right)+\sqrt[4]{a-\sqrt{a^2-4 b}} \log \left(2^{3/4} \sqrt[4]{a-\sqrt{a^2-4 b}}+2 \sqrt[4]{a+\frac{b}{x}}\right)-\sqrt[4]{\sqrt{a^2-4 b}+a} \log \left(2^{3/4} \sqrt[4]{\sqrt{a^2-4 b}+a}+2 \sqrt[4]{a+\frac{b}{x}}\right)+2 \sqrt[4]{a-\sqrt{a^2-4 b}} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a+\frac{b}{x}}}{\sqrt[4]{a-\sqrt{a^2-4 b}}}\right)-2 \sqrt[4]{\sqrt{a^2-4 b}+a} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a+\frac{b}{x}}}{\sqrt[4]{\sqrt{a^2-4 b}+a}}\right)\right)}{\sqrt[4]{2} x \sqrt{a^2-4 b} \sqrt[4]{a+\frac{b}{x}}}","-\text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4 a+b\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{2 \text{$\#$1}^4-a}\&\right]",1,"-(((x^3*(b + a*x))^(1/4)*(2*(a - Sqrt[a^2 - 4*b])^(1/4)*ArcTan[(2^(1/4)*(a + b/x)^(1/4))/(a - Sqrt[a^2 - 4*b])^(1/4)] - 2*(a + Sqrt[a^2 - 4*b])^(1/4)*ArcTan[(2^(1/4)*(a + b/x)^(1/4))/(a + Sqrt[a^2 - 4*b])^(1/4)] - (a - Sqrt[a^2 - 4*b])^(1/4)*Log[2^(3/4)*(a - Sqrt[a^2 - 4*b])^(1/4) - 2*(a + b/x)^(1/4)] + (a + Sqrt[a^2 - 4*b])^(1/4)*Log[2^(3/4)*(a + Sqrt[a^2 - 4*b])^(1/4) - 2*(a + b/x)^(1/4)] + (a - Sqrt[a^2 - 4*b])^(1/4)*Log[2^(3/4)*(a - Sqrt[a^2 - 4*b])^(1/4) + 2*(a + b/x)^(1/4)] - (a + Sqrt[a^2 - 4*b])^(1/4)*Log[2^(3/4)*(a + Sqrt[a^2 - 4*b])^(1/4) + 2*(a + b/x)^(1/4)]))/(2^(1/4)*Sqrt[a^2 - 4*b]*(a + b/x)^(1/4)*x))","B",1
837,1,47,63,0.0653762,"\int \frac{x^2 \left(-4+x^6\right)}{\sqrt{-1+x^6} \left(2+x^6\right)} \, dx","Integrate[(x^2*(-4 + x^6))/(Sqrt[-1 + x^6]*(2 + x^6)),x]","\frac{1}{3} \left(\tanh ^{-1}\left(\frac{x^3}{\sqrt{x^6-1}}\right)-\sqrt{6} \tanh ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x^3}{\sqrt{x^6-1}}\right)\right)","\frac{1}{3} \log \left(\sqrt{x^6-1}+x^3\right)+\sqrt{\frac{2}{3}} \tanh ^{-1}\left(\frac{x^6}{\sqrt{6}}+\frac{\sqrt{x^6-1} x^3}{\sqrt{6}}+\sqrt{\frac{2}{3}}\right)",1,"(ArcTanh[x^3/Sqrt[-1 + x^6]] - Sqrt[6]*ArcTanh[(Sqrt[3/2]*x^3)/Sqrt[-1 + x^6]])/3","A",1
838,0,0,63,0.6863115,"\int \frac{\left(-1+x^5\right) \left(-1+x^3+x^5\right) \left(3+2 x^5\right)}{x^6 \left(-1-x^3+x^5\right) \sqrt[4]{-x+x^6}} \, dx","Integrate[((-1 + x^5)*(-1 + x^3 + x^5)*(3 + 2*x^5))/(x^6*(-1 - x^3 + x^5)*(-x + x^6)^(1/4)),x]","\int \frac{\left(-1+x^5\right) \left(-1+x^3+x^5\right) \left(3+2 x^5\right)}{x^6 \left(-1-x^3+x^5\right) \sqrt[4]{-x+x^6}} \, dx","-4 \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^6-x}}\right)-4 \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^6-x}}\right)+\frac{4 \left(x^6-x\right)^{3/4} \left(3 x^5+14 x^3-3\right)}{21 x^6}",1,"Integrate[((-1 + x^5)*(-1 + x^3 + x^5)*(3 + 2*x^5))/(x^6*(-1 - x^3 + x^5)*(-x + x^6)^(1/4)), x]","F",-1
839,1,84,63,0.2329741,"\int \frac{\sqrt{1+x^3} \left(2+2 x^3+x^6\right)}{x^7 \left(-1+x^6\right)} \, dx","Integrate[(Sqrt[1 + x^3]*(2 + 2*x^3 + x^6))/(x^7*(-1 + x^6)),x]","\frac{-5 \sqrt{\frac{1}{x^3}+1} x^3 F_1\left(\frac{3}{2};\frac{1}{2},1;\frac{5}{2};-\frac{1}{x^3},\frac{1}{x^3}\right)+5 x^6+7 x^3+2}{6 x^6 \sqrt{x^3+1}}-\frac{5}{12} x^3 F_1\left(1;\frac{1}{2},1;2;-x^3,x^3\right)","\frac{5}{2} \tanh ^{-1}\left(\sqrt{x^3+1}\right)-\frac{5}{3} \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{x^3+1}}{\sqrt{2}}\right)+\frac{\sqrt{x^3+1} \left(5 x^3+2\right)}{6 x^6}",1,"(-5*x^3*AppellF1[1, 1/2, 1, 2, -x^3, x^3])/12 + (2 + 7*x^3 + 5*x^6 - 5*Sqrt[1 + x^(-3)]*x^3*AppellF1[3/2, 1/2, 1, 5/2, -x^(-3), x^(-3)])/(6*x^6*Sqrt[1 + x^3])","C",0
840,0,0,63,0.1386401,"\int \frac{\sqrt{-1+x^2+x^5} \left(2+3 x^5\right)}{1+x^4-2 x^5+x^{10}} \, dx","Integrate[(Sqrt[-1 + x^2 + x^5]*(2 + 3*x^5))/(1 + x^4 - 2*x^5 + x^10),x]","\int \frac{\sqrt{-1+x^2+x^5} \left(2+3 x^5\right)}{1+x^4-2 x^5+x^{10}} \, dx","-\sqrt{1+i} \tan ^{-1}\left(\frac{\sqrt{-1-i} x}{\sqrt{x^5+x^2-1}}\right)-\sqrt{1-i} \tan ^{-1}\left(\frac{\sqrt{-1+i} x}{\sqrt{x^5+x^2-1}}\right)",1,"Integrate[(Sqrt[-1 + x^2 + x^5]*(2 + 3*x^5))/(1 + x^4 - 2*x^5 + x^10), x]","F",-1
841,1,87,63,0.5949688,"\int \frac{1}{x \sqrt{x+x^2} \sqrt{x^2+x \sqrt{x+x^2}}} \, dx","Integrate[1/(x*Sqrt[x + x^2]*Sqrt[x^2 + x*Sqrt[x + x^2]]),x]","\frac{4 \sqrt{x \left(x+\sqrt{x (x+1)}\right)} \left(x+\sqrt{x (x+1)}+1\right) \left(2 x+2 \sqrt{x (x+1)}+1\right) \left(4 x+4 \sqrt{x (x+1)}-3\right)}{15 \sqrt{x (x+1)} \left(x+\sqrt{x (x+1)}\right)^3}","\frac{4 \sqrt{x \left(\sqrt{x^2+x}+x\right)} (4 x-3)}{15 x^2}+\frac{16 \sqrt{x^2+x} \sqrt{x \left(\sqrt{x^2+x}+x\right)}}{15 x^2}",1,"(4*Sqrt[x*(x + Sqrt[x*(1 + x)])]*(1 + x + Sqrt[x*(1 + x)])*(1 + 2*x + 2*Sqrt[x*(1 + x)])*(-3 + 4*x + 4*Sqrt[x*(1 + x)]))/(15*Sqrt[x*(1 + x)]*(x + Sqrt[x*(1 + x)])^3)","A",1
842,1,41,63,0.1021705,"\int \sqrt{b+\sqrt{b^2+a x^2}} \, dx","Integrate[Sqrt[b + Sqrt[b^2 + a*x^2]],x]","\frac{2 x \left(\sqrt{a x^2+b^2}+2 b\right)}{3 \sqrt{\sqrt{a x^2+b^2}+b}}","\frac{4 b x}{3 \sqrt{\sqrt{a x^2+b^2}+b}}+\frac{2 x \sqrt{a x^2+b^2}}{3 \sqrt{\sqrt{a x^2+b^2}+b}}",1,"(2*x*(2*b + Sqrt[b^2 + a*x^2]))/(3*Sqrt[b + Sqrt[b^2 + a*x^2]])","A",1
843,1,117,63,0.1140619,"\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\sqrt{1+x^2} \sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/(Sqrt[1 + x^2]*Sqrt[x + Sqrt[1 + x^2]]),x]","-\frac{2 \left(\sqrt{x^2+1}+\sqrt{\sqrt{x^2+1}+x}+\left(\sqrt{x^2+1}+x\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+x\right)}{\left(\sqrt{x^2+1}+x\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}","-\frac{2 \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{\sqrt{\sqrt{x^2+1}+x}}-2 \tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)",1,"(-2*(x + Sqrt[1 + x^2] + Sqrt[x + Sqrt[1 + x^2]] + (x + Sqrt[1 + x^2])*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]*ArcTanh[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]]))/((x + Sqrt[1 + x^2])*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])","A",1
844,1,110,64,0.4681895,"\int \frac{-b+a x}{(b+a x) \sqrt{b^2 x+a^2 x^3}} \, dx","Integrate[(-b + a*x)/((b + a*x)*Sqrt[b^2*x + a^2*x^3]),x]","-\frac{2 i x^{3/2} \sqrt{\frac{b^2}{a^2 x^2}+1} \left(F\left(\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)-2 \Pi \left(-i;\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)\right)}{\sqrt{\frac{i b}{a}} \sqrt{x \left(a^2 x^2+b^2\right)}}","-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{b} \sqrt{a^2 x^3+b^2 x}}{a^2 x^2+b^2}\right)}{\sqrt{a} \sqrt{b}}",1,"((-2*I)*Sqrt[1 + b^2/(a^2*x^2)]*x^(3/2)*(EllipticF[I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1] - 2*EllipticPi[-I, I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1]))/(Sqrt[(I*b)/a]*Sqrt[x*(b^2 + a^2*x^2)])","C",1
845,1,110,64,0.4038307,"\int \frac{b+a x}{(-b+a x) \sqrt{b^2 x+a^2 x^3}} \, dx","Integrate[(b + a*x)/((-b + a*x)*Sqrt[b^2*x + a^2*x^3]),x]","-\frac{2 i x^{3/2} \sqrt{\frac{b^2}{a^2 x^2}+1} \left(F\left(\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)-2 \Pi \left(i;\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)\right)}{\sqrt{\frac{i b}{a}} \sqrt{x \left(a^2 x^2+b^2\right)}}","-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{b} \sqrt{a^2 x^3+b^2 x}}{a^2 x^2+b^2}\right)}{\sqrt{a} \sqrt{b}}",1,"((-2*I)*Sqrt[1 + b^2/(a^2*x^2)]*x^(3/2)*(EllipticF[I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1] - 2*EllipticPi[I, I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1]))/(Sqrt[(I*b)/a]*Sqrt[x*(b^2 + a^2*x^2)])","C",1
846,1,110,64,0.1448634,"\int \frac{-b x^2+a x^3}{\left(b x^2+a x^3\right) \sqrt{b^2 x+a^2 x^3}} \, dx","Integrate[(-(b*x^2) + a*x^3)/((b*x^2 + a*x^3)*Sqrt[b^2*x + a^2*x^3]),x]","-\frac{2 i x^{3/2} \sqrt{\frac{b^2}{a^2 x^2}+1} \left(F\left(\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)-2 \Pi \left(-i;\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)\right)}{\sqrt{\frac{i b}{a}} \sqrt{x \left(a^2 x^2+b^2\right)}}","-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{b} \sqrt{a^2 x^3+b^2 x}}{a^2 x^2+b^2}\right)}{\sqrt{a} \sqrt{b}}",1,"((-2*I)*Sqrt[1 + b^2/(a^2*x^2)]*x^(3/2)*(EllipticF[I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1] - 2*EllipticPi[-I, I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1]))/(Sqrt[(I*b)/a]*Sqrt[x*(b^2 + a^2*x^2)])","C",1
847,1,1144,64,1.1187285,"\int \frac{2+5 x}{\sqrt{-12+20 x+5 x^2+2 x^3+x^4}} \, dx","Integrate[(2 + 5*x)/Sqrt[-12 + 20*x + 5*x^2 + 2*x^3 + x^4],x]","-\frac{2 (x+3) \left(x-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,1\right]\right) \left(5 \text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,1\right] F\left(\sin ^{-1}\left(\sqrt{-\frac{(x+3) \left(\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,1\right]-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,3\right]\right)}{\left(x-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,1\right]\right) \left(3+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,3\right]\right)}}\right)|\frac{\left(\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,1\right]-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,2\right]\right) \left(3+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,3\right]\right)}{\left(3+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,2\right]\right) \left(\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,1\right]-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,3\right]\right)}\right)+2 F\left(\sin ^{-1}\left(\sqrt{\frac{(x+3) \left(-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,1\right]+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,3\right]\right)}{\left(x-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,1\right]\right) \left(3+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,3\right]\right)}}\right)|\frac{\left(\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,1\right]-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,2\right]\right) \left(3+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,3\right]\right)}{\left(3+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,2\right]\right) \left(\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,1\right]-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,3\right]\right)}\right)-5 \Pi \left(\frac{3+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,3\right]}{-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,1\right]+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,3\right]};\sin ^{-1}\left(\sqrt{-\frac{(x+3) \left(\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,1\right]-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,3\right]\right)}{\left(x-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,1\right]\right) \left(3+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,3\right]\right)}}\right)|\frac{\left(\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,1\right]-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,2\right]\right) \left(3+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,3\right]\right)}{\left(3+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,2\right]\right) \left(\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,1\right]-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,3\right]\right)}\right) \left(3+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,1\right]\right)\right) \sqrt{\frac{x-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,2\right]}{\left(x-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,1\right]\right) \left(3+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,2\right]\right)}} \sqrt{\frac{x-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,3\right]}{\left(x-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,1\right]\right) \left(3+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,3\right]\right)}}}{\sqrt{x^4+2 x^3+5 x^2+20 x-12} \sqrt{-\frac{(x+3) \left(\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,1\right]-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,3\right]\right)}{\left(x-\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,1\right]\right) \left(3+\text{Root}\left[\text{$\#$1}^3-\text{$\#$1}^2+8 \text{$\#$1}-4\&,3\right]\right)}}}","-\log \left(-x^5-3 x^4-8 x^3-24 x^2+\left(x^3+2 x^2+4 x+8\right) \sqrt{x^4+2 x^3+5 x^2+20 x-12}-16 x-16\right)",1,"(-2*(3 + x)*(x - Root[-4 + 8*#1 - #1^2 + #1^3 & , 1, 0])*(2*EllipticF[ArcSin[Sqrt[((3 + x)*(-Root[-4 + 8*#1 - #1^2 + #1^3 & , 1, 0] + Root[-4 + 8*#1 - #1^2 + #1^3 & , 3, 0]))/((x - Root[-4 + 8*#1 - #1^2 + #1^3 & , 1, 0])*(3 + Root[-4 + 8*#1 - #1^2 + #1^3 & , 3, 0]))]], ((Root[-4 + 8*#1 - #1^2 + #1^3 & , 1, 0] - Root[-4 + 8*#1 - #1^2 + #1^3 & , 2, 0])*(3 + Root[-4 + 8*#1 - #1^2 + #1^3 & , 3, 0]))/((3 + Root[-4 + 8*#1 - #1^2 + #1^3 & , 2, 0])*(Root[-4 + 8*#1 - #1^2 + #1^3 & , 1, 0] - Root[-4 + 8*#1 - #1^2 + #1^3 & , 3, 0]))] + 5*EllipticF[ArcSin[Sqrt[-(((3 + x)*(Root[-4 + 8*#1 - #1^2 + #1^3 & , 1, 0] - Root[-4 + 8*#1 - #1^2 + #1^3 & , 3, 0]))/((x - Root[-4 + 8*#1 - #1^2 + #1^3 & , 1, 0])*(3 + Root[-4 + 8*#1 - #1^2 + #1^3 & , 3, 0])))]], ((Root[-4 + 8*#1 - #1^2 + #1^3 & , 1, 0] - Root[-4 + 8*#1 - #1^2 + #1^3 & , 2, 0])*(3 + Root[-4 + 8*#1 - #1^2 + #1^3 & , 3, 0]))/((3 + Root[-4 + 8*#1 - #1^2 + #1^3 & , 2, 0])*(Root[-4 + 8*#1 - #1^2 + #1^3 & , 1, 0] - Root[-4 + 8*#1 - #1^2 + #1^3 & , 3, 0]))]*Root[-4 + 8*#1 - #1^2 + #1^3 & , 1, 0] - 5*EllipticPi[(3 + Root[-4 + 8*#1 - #1^2 + #1^3 & , 3, 0])/(-Root[-4 + 8*#1 - #1^2 + #1^3 & , 1, 0] + Root[-4 + 8*#1 - #1^2 + #1^3 & , 3, 0]), ArcSin[Sqrt[-(((3 + x)*(Root[-4 + 8*#1 - #1^2 + #1^3 & , 1, 0] - Root[-4 + 8*#1 - #1^2 + #1^3 & , 3, 0]))/((x - Root[-4 + 8*#1 - #1^2 + #1^3 & , 1, 0])*(3 + Root[-4 + 8*#1 - #1^2 + #1^3 & , 3, 0])))]], ((Root[-4 + 8*#1 - #1^2 + #1^3 & , 1, 0] - Root[-4 + 8*#1 - #1^2 + #1^3 & , 2, 0])*(3 + Root[-4 + 8*#1 - #1^2 + #1^3 & , 3, 0]))/((3 + Root[-4 + 8*#1 - #1^2 + #1^3 & , 2, 0])*(Root[-4 + 8*#1 - #1^2 + #1^3 & , 1, 0] - Root[-4 + 8*#1 - #1^2 + #1^3 & , 3, 0]))]*(3 + Root[-4 + 8*#1 - #1^2 + #1^3 & , 1, 0]))*Sqrt[(x - Root[-4 + 8*#1 - #1^2 + #1^3 & , 2, 0])/((x - Root[-4 + 8*#1 - #1^2 + #1^3 & , 1, 0])*(3 + Root[-4 + 8*#1 - #1^2 + #1^3 & , 2, 0]))]*Sqrt[(x - Root[-4 + 8*#1 - #1^2 + #1^3 & , 3, 0])/((x - Root[-4 + 8*#1 - #1^2 + #1^3 & , 1, 0])*(3 + Root[-4 + 8*#1 - #1^2 + #1^3 & , 3, 0]))])/(Sqrt[-12 + 20*x + 5*x^2 + 2*x^3 + x^4]*Sqrt[-(((3 + x)*(Root[-4 + 8*#1 - #1^2 + #1^3 & , 1, 0] - Root[-4 + 8*#1 - #1^2 + #1^3 & , 3, 0]))/((x - Root[-4 + 8*#1 - #1^2 + #1^3 & , 1, 0])*(3 + Root[-4 + 8*#1 - #1^2 + #1^3 & , 3, 0])))])","C",1
848,1,70,64,0.0407832,"\int \frac{\left(-1+x^3\right) \sqrt{-1+x^6}}{x^7} \, dx","Integrate[((-1 + x^3)*Sqrt[-1 + x^6])/x^7,x]","-\frac{\left(x^6-1\right) \left(x^6 \tanh ^{-1}\left(\sqrt{1-x^6}\right)+\left(2 x^3-1\right) \sqrt{1-x^6}+2 x^6 \sin ^{-1}\left(x^3\right)\right)}{6 x^6 \sqrt{-\left(x^6-1\right)^2}}","\frac{\sqrt{x^6-1} \left(1-2 x^3\right)}{6 x^6}+\frac{1}{3} \tan ^{-1}\left(\frac{x^3+1}{\sqrt{x^6-1}}\right)+\frac{2}{3} \tanh ^{-1}\left(\frac{x^3+1}{\sqrt{x^6-1}}\right)",1,"-1/6*((-1 + x^6)*((-1 + 2*x^3)*Sqrt[1 - x^6] + 2*x^6*ArcSin[x^3] + x^6*ArcTanh[Sqrt[1 - x^6]]))/(x^6*Sqrt[-(-1 + x^6)^2])","A",0
849,1,135,64,0.090995,"\int \frac{\sqrt{-1+x^6} \left(-1+2 x^6\right)^2}{x^7 \left(-1+4 x^6\right)} \, dx","Integrate[(Sqrt[-1 + x^6]*(-1 + 2*x^6)^2)/(x^7*(-1 + 4*x^6)),x]","\frac{4 x^{12}-2 x^6+2 \sqrt{1-x^6} x^6 \tanh ^{-1}\left(\sqrt{1-x^6}\right)-\sqrt{3} \sqrt{x^6-1} x^6 \tan ^{-1}\left(\frac{x^3-2}{\sqrt{3} \sqrt{x^6-1}}\right)+\sqrt{3} \sqrt{x^6-1} x^6 \tan ^{-1}\left(\frac{x^3+2}{\sqrt{3} \sqrt{x^6-1}}\right)-2}{12 x^6 \sqrt{x^6-1}}","\frac{\sqrt{x^6-1} \left(2 x^6+1\right)}{6 x^6}-\frac{1}{6} \tan ^{-1}\left(\sqrt{x^6-1}\right)-\frac{\tan ^{-1}\left(\frac{2 \sqrt{x^6-1}}{\sqrt{3}}\right)}{2 \sqrt{3}}",1,"(-2 - 2*x^6 + 4*x^12 - Sqrt[3]*x^6*Sqrt[-1 + x^6]*ArcTan[(-2 + x^3)/(Sqrt[3]*Sqrt[-1 + x^6])] + Sqrt[3]*x^6*Sqrt[-1 + x^6]*ArcTan[(2 + x^3)/(Sqrt[3]*Sqrt[-1 + x^6])] + 2*x^6*Sqrt[1 - x^6]*ArcTanh[Sqrt[1 - x^6]])/(12*x^6*Sqrt[-1 + x^6])","B",1
850,1,82,64,0.2204935,"\int \frac{-2+x^4}{\sqrt[4]{1+x^4} \left(-1+x^4+2 x^8\right)} \, dx","Integrate[(-2 + x^4)/((1 + x^4)^(1/4)*(-1 + x^4 + 2*x^8)),x]","\frac{x}{\sqrt[4]{x^4+1}}+\frac{-\log \left(1-\frac{\sqrt[4]{3} x}{\sqrt[4]{x^4+1}}\right)+\log \left(\frac{\sqrt[4]{3} x}{\sqrt[4]{x^4+1}}+1\right)+2 \tan ^{-1}\left(\frac{\sqrt[4]{3} x}{\sqrt[4]{x^4+1}}\right)}{4 \sqrt[4]{3}}","\frac{x}{\sqrt[4]{x^4+1}}+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{3} x}{\sqrt[4]{x^4+1}}\right)}{2 \sqrt[4]{3}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{3} x}{\sqrt[4]{x^4+1}}\right)}{2 \sqrt[4]{3}}",1,"x/(1 + x^4)^(1/4) + (2*ArcTan[(3^(1/4)*x)/(1 + x^4)^(1/4)] - Log[1 - (3^(1/4)*x)/(1 + x^4)^(1/4)] + Log[1 + (3^(1/4)*x)/(1 + x^4)^(1/4)])/(4*3^(1/4))","A",1
851,1,47,64,0.0582219,"\int \frac{-x^2+10 x^8}{\sqrt{-1+x^6} \left(-1+4 x^6\right)} \, dx","Integrate[(-x^2 + 10*x^8)/(Sqrt[-1 + x^6]*(-1 + 4*x^6)),x]","\frac{5}{6} \tanh ^{-1}\left(\frac{x^3}{\sqrt{x^6-1}}\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x^3}{\sqrt{x^6-1}}\right)}{2 \sqrt{3}}","\frac{5}{6} \log \left(\sqrt{x^6-1}+x^3\right)-\frac{\tan ^{-1}\left(-\frac{4 x^6}{\sqrt{3}}-\frac{4 \sqrt{x^6-1} x^3}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3}}",1,"-1/2*ArcTan[(Sqrt[3]*x^3)/Sqrt[-1 + x^6]]/Sqrt[3] + (5*ArcTanh[x^3/Sqrt[-1 + x^6]])/6","A",1
852,1,159,65,1.3093469,"\int \frac{1+x^2}{\left(-1+x^2\right) \left(1+2 x^2\right)^{3/2}} \, dx","Integrate[(1 + x^2)/((-1 + x^2)*(1 + 2*x^2)^(3/2)),x]","\frac{x \left(\frac{72 \left(2 x^2+1\right) x^2 \, _2F_1\left(2,2;\frac{7}{2};\frac{3 x^2}{x^2-1}\right)}{\left(x^2-1\right)^2}+\frac{10 \left(4 x^2+3\right) \left(\sqrt{\frac{6 x^2+3}{1-x^2}} x^2+\sqrt{\frac{x^2}{x^2-1}} \left(2 x^2+1\right) \sin ^{-1}\left(\sqrt{3} \sqrt{\frac{x^2}{x^2-1}}\right)\right)}{\sqrt{\frac{2 x^2+1}{3-3 x^2}} x^4}+45\right)}{45 \sqrt{2 x^2+1}}","-\frac{x}{3 \sqrt{2 x^2+1}}-\frac{2 \tanh ^{-1}\left(-\sqrt{\frac{2}{3}} x^2+\frac{\sqrt{2 x^2+1} x}{\sqrt{3}}+\sqrt{\frac{2}{3}}\right)}{3 \sqrt{3}}",1,"(x*(45 + (10*(3 + 4*x^2)*(x^2*Sqrt[(3 + 6*x^2)/(1 - x^2)] + Sqrt[x^2/(-1 + x^2)]*(1 + 2*x^2)*ArcSin[Sqrt[3]*Sqrt[x^2/(-1 + x^2)]]))/(x^4*Sqrt[(1 + 2*x^2)/(3 - 3*x^2)]) + (72*x^2*(1 + 2*x^2)*Hypergeometric2F1[2, 2, 7/2, (3*x^2)/(-1 + x^2)])/(-1 + x^2)^2))/(45*Sqrt[1 + 2*x^2])","C",0
853,1,65,65,0.0196864,"\int \frac{\left(b+a x^2\right)^{3/4}}{x} \, dx","Integrate[(b + a*x^2)^(3/4)/x,x]","b^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a x^2+b}}{\sqrt[4]{b}}\right)-b^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a x^2+b}}{\sqrt[4]{b}}\right)+\frac{2}{3} \left(a x^2+b\right)^{3/4}","b^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a x^2+b}}{\sqrt[4]{b}}\right)-b^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a x^2+b}}{\sqrt[4]{b}}\right)+\frac{2}{3} \left(a x^2+b\right)^{3/4}",1,"(2*(b + a*x^2)^(3/4))/3 + b^(3/4)*ArcTan[(b + a*x^2)^(1/4)/b^(1/4)] - b^(3/4)*ArcTanh[(b + a*x^2)^(1/4)/b^(1/4)]","A",1
854,1,177,65,0.5503057,"\int \frac{1-x+x^2}{\left(-1+x^2\right) \sqrt{x+x^3}} \, dx","Integrate[(1 - x + x^2)/((-1 + x^2)*Sqrt[x + x^3]),x]","\frac{2 \left(5 \sqrt{\frac{1}{x^2}+1} F_1\left(\frac{3}{4};\frac{1}{2},1;\frac{7}{4};-\frac{1}{x^2},\frac{1}{x^2}\right)-\frac{3 \sqrt{\frac{1}{x^2}+1} F_1\left(\frac{5}{4};\frac{1}{2},1;\frac{9}{4};-\frac{1}{x^2},\frac{1}{x^2}\right)}{x}-\frac{75 x^5 F_1\left(\frac{1}{4};\frac{1}{2},1;\frac{5}{4};-\frac{1}{x^2},\frac{1}{x^2}\right)}{\left(x^2-1\right) \left(5 x^2 F_1\left(\frac{1}{4};\frac{1}{2},1;\frac{5}{4};-\frac{1}{x^2},\frac{1}{x^2}\right)+4 F_1\left(\frac{5}{4};\frac{1}{2},2;\frac{9}{4};-\frac{1}{x^2},\frac{1}{x^2}\right)-2 F_1\left(\frac{5}{4};\frac{3}{2},1;\frac{9}{4};-\frac{1}{x^2},\frac{1}{x^2}\right)\right)}\right)}{15 \sqrt{x^3+x}}","-\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{x^3+x}}{x^2+1}\right)}{2 \sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{x^3+x}}{x^2+1}\right)}{2 \sqrt{2}}",1,"(2*(5*Sqrt[1 + x^(-2)]*AppellF1[3/4, 1/2, 1, 7/4, -x^(-2), x^(-2)] - (3*Sqrt[1 + x^(-2)]*AppellF1[5/4, 1/2, 1, 9/4, -x^(-2), x^(-2)])/x - (75*x^5*AppellF1[1/4, 1/2, 1, 5/4, -x^(-2), x^(-2)])/((-1 + x^2)*(5*x^2*AppellF1[1/4, 1/2, 1, 5/4, -x^(-2), x^(-2)] + 4*AppellF1[5/4, 1/2, 2, 9/4, -x^(-2), x^(-2)] - 2*AppellF1[5/4, 3/2, 1, 9/4, -x^(-2), x^(-2)]))))/(15*Sqrt[x + x^3])","C",0
855,1,131,65,0.196313,"\int \frac{-1+2 x^2}{\left(1+x^2\right) \sqrt{-1-x^2+x^4}} \, dx","Integrate[(-1 + 2*x^2)/((1 + x^2)*Sqrt[-1 - x^2 + x^4]),x]","-\frac{i \sqrt{\frac{2}{1+\sqrt{5}}} \sqrt{-x^4+x^2+1} \left(2 F\left(i \sinh ^{-1}\left(\sqrt{\frac{2}{-1+\sqrt{5}}} x\right)|\frac{1}{2} \left(-3+\sqrt{5}\right)\right)-3 \Pi \left(\frac{1}{2} \left(-1+\sqrt{5}\right);i \sinh ^{-1}\left(\sqrt{\frac{2}{-1+\sqrt{5}}} x\right)|\frac{1}{2} \left(-3+\sqrt{5}\right)\right)\right)}{\sqrt{x^4-x^2-1}}","-\frac{1}{2} i \log \left(\frac{-2 i x^2+\sqrt{x^4-x^2-1} x-i}{-2 i x^2-\sqrt{x^4-x^2-1} x-i}\right)",1,"((-I)*Sqrt[2/(1 + Sqrt[5])]*Sqrt[1 + x^2 - x^4]*(2*EllipticF[I*ArcSinh[Sqrt[2/(-1 + Sqrt[5])]*x], (-3 + Sqrt[5])/2] - 3*EllipticPi[(-1 + Sqrt[5])/2, I*ArcSinh[Sqrt[2/(-1 + Sqrt[5])]*x], (-3 + Sqrt[5])/2]))/Sqrt[-1 - x^2 + x^4]","C",0
856,1,350,65,1.7437567,"\int \frac{1}{\left(-2 b+a x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Integrate[1/((-2*b + a*x^4)*(b*x^2 + a*x^4)^(1/4)),x]","-\frac{x \sqrt[4]{a+\frac{b}{x^2}} \left(-\sqrt[4]{2 \sqrt{a}+\sqrt{2} \sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[8]{a} \sqrt[4]{\sqrt{a}-\frac{\sqrt{b}}{\sqrt{2}}}}\right)-\sqrt[4]{2 \sqrt{a}-\sqrt{2} \sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[8]{a} \sqrt[4]{\sqrt{a}+\frac{\sqrt{b}}{\sqrt{2}}}}\right)+\sqrt[4]{2 \sqrt{a}+\sqrt{2} \sqrt{b}} \tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[8]{a} \sqrt[4]{\sqrt{a}-\frac{\sqrt{b}}{\sqrt{2}}}}\right)+\sqrt[4]{2 \sqrt{a}-\sqrt{2} \sqrt{b}} \tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[8]{a} \sqrt[4]{\sqrt{a}+\frac{\sqrt{b}}{\sqrt{2}}}}\right)\right)}{2\ 2^{3/4} \sqrt[8]{a} b \sqrt[4]{2 \sqrt{a}-\sqrt{2} \sqrt{b}} \sqrt[4]{2 \sqrt{a}+\sqrt{2} \sqrt{b}} \sqrt[4]{x^2 \left(a x^2+b\right)}}","\frac{\text{RootSum}\left[2 \text{$\#$1}^8-4 \text{$\#$1}^4 a+2 a^2-a b\&,\frac{\log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{8 b}",1,"-1/2*((a + b/x^2)^(1/4)*x*(-((2*Sqrt[a] + Sqrt[2]*Sqrt[b])^(1/4)*ArcTan[(a + b/x^2)^(1/4)/(a^(1/8)*(Sqrt[a] - Sqrt[b]/Sqrt[2])^(1/4))]) - (2*Sqrt[a] - Sqrt[2]*Sqrt[b])^(1/4)*ArcTan[(a + b/x^2)^(1/4)/(a^(1/8)*(Sqrt[a] + Sqrt[b]/Sqrt[2])^(1/4))] + (2*Sqrt[a] + Sqrt[2]*Sqrt[b])^(1/4)*ArcTanh[(a + b/x^2)^(1/4)/(a^(1/8)*(Sqrt[a] - Sqrt[b]/Sqrt[2])^(1/4))] + (2*Sqrt[a] - Sqrt[2]*Sqrt[b])^(1/4)*ArcTanh[(a + b/x^2)^(1/4)/(a^(1/8)*(Sqrt[a] + Sqrt[b]/Sqrt[2])^(1/4))]))/(2^(3/4)*a^(1/8)*(2*Sqrt[a] - Sqrt[2]*Sqrt[b])^(1/4)*(2*Sqrt[a] + Sqrt[2]*Sqrt[b])^(1/4)*b*(x^2*(b + a*x^2))^(1/4))","B",1
857,1,350,65,0.4045218,"\int \frac{1}{\left(-2 b+a x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Integrate[1/((-2*b + a*x^4)*(b*x^2 + a*x^4)^(1/4)),x]","-\frac{x \sqrt[4]{a+\frac{b}{x^2}} \left(-\sqrt[4]{2 \sqrt{a}+\sqrt{2} \sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[8]{a} \sqrt[4]{\sqrt{a}-\frac{\sqrt{b}}{\sqrt{2}}}}\right)-\sqrt[4]{2 \sqrt{a}-\sqrt{2} \sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[8]{a} \sqrt[4]{\sqrt{a}+\frac{\sqrt{b}}{\sqrt{2}}}}\right)+\sqrt[4]{2 \sqrt{a}+\sqrt{2} \sqrt{b}} \tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[8]{a} \sqrt[4]{\sqrt{a}-\frac{\sqrt{b}}{\sqrt{2}}}}\right)+\sqrt[4]{2 \sqrt{a}-\sqrt{2} \sqrt{b}} \tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[8]{a} \sqrt[4]{\sqrt{a}+\frac{\sqrt{b}}{\sqrt{2}}}}\right)\right)}{2\ 2^{3/4} \sqrt[8]{a} b \sqrt[4]{2 \sqrt{a}-\sqrt{2} \sqrt{b}} \sqrt[4]{2 \sqrt{a}+\sqrt{2} \sqrt{b}} \sqrt[4]{x^2 \left(a x^2+b\right)}}","\frac{\text{RootSum}\left[2 \text{$\#$1}^8-4 \text{$\#$1}^4 a+2 a^2-a b\&,\frac{\log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{8 b}",1,"-1/2*((a + b/x^2)^(1/4)*x*(-((2*Sqrt[a] + Sqrt[2]*Sqrt[b])^(1/4)*ArcTan[(a + b/x^2)^(1/4)/(a^(1/8)*(Sqrt[a] - Sqrt[b]/Sqrt[2])^(1/4))]) - (2*Sqrt[a] - Sqrt[2]*Sqrt[b])^(1/4)*ArcTan[(a + b/x^2)^(1/4)/(a^(1/8)*(Sqrt[a] + Sqrt[b]/Sqrt[2])^(1/4))] + (2*Sqrt[a] + Sqrt[2]*Sqrt[b])^(1/4)*ArcTanh[(a + b/x^2)^(1/4)/(a^(1/8)*(Sqrt[a] - Sqrt[b]/Sqrt[2])^(1/4))] + (2*Sqrt[a] - Sqrt[2]*Sqrt[b])^(1/4)*ArcTanh[(a + b/x^2)^(1/4)/(a^(1/8)*(Sqrt[a] + Sqrt[b]/Sqrt[2])^(1/4))]))/(2^(3/4)*a^(1/8)*(2*Sqrt[a] - Sqrt[2]*Sqrt[b])^(1/4)*(2*Sqrt[a] + Sqrt[2]*Sqrt[b])^(1/4)*b*(x^2*(b + a*x^2))^(1/4))","B",1
858,0,0,65,0.2939394,"\int \frac{-2 b+c x^2}{\left(-b+c x^2\right) \sqrt[4]{-b+c x^2+a x^4}} \, dx","Integrate[(-2*b + c*x^2)/((-b + c*x^2)*(-b + c*x^2 + a*x^4)^(1/4)),x]","\int \frac{-2 b+c x^2}{\left(-b+c x^2\right) \sqrt[4]{-b+c x^2+a x^4}} \, dx","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b+c x^2}}\right)}{\sqrt[4]{a}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b+c x^2}}\right)}{\sqrt[4]{a}}",1,"Integrate[(-2*b + c*x^2)/((-b + c*x^2)*(-b + c*x^2 + a*x^4)^(1/4)), x]","F",-1
859,0,0,65,0.4077077,"\int \frac{-4 b+a x^3}{\left(-b+a x^3\right) \sqrt[4]{b-a x^3+c x^4}} \, dx","Integrate[(-4*b + a*x^3)/((-b + a*x^3)*(b - a*x^3 + c*x^4)^(1/4)),x]","\int \frac{-4 b+a x^3}{\left(-b+a x^3\right) \sqrt[4]{b-a x^3+c x^4}} \, dx","\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{-a x^3+b+c x^4}}\right)}{\sqrt[4]{c}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{-a x^3+b+c x^4}}\right)}{\sqrt[4]{c}}",1,"Integrate[(-4*b + a*x^3)/((-b + a*x^3)*(b - a*x^3 + c*x^4)^(1/4)), x]","F",-1
860,0,0,65,0.6440263,"\int \frac{-b+a x^6}{\left(b+a x^6\right) \sqrt[3]{-b+a^3 x^3+a x^6}} \, dx","Integrate[(-b + a*x^6)/((b + a*x^6)*(-b + a^3*x^3 + a*x^6)^(1/3)),x]","\int \frac{-b+a x^6}{\left(b+a x^6\right) \sqrt[3]{-b+a^3 x^3+a x^6}} \, dx","\frac{1}{6} \text{RootSum}\left[\text{$\#$1}^6-2 \text{$\#$1}^3 a^3+a^6+4 a b\&,\frac{\log \left(\sqrt[3]{a^3 x^3+a x^6-b}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]",1,"Integrate[(-b + a*x^6)/((b + a*x^6)*(-b + a^3*x^3 + a*x^6)^(1/3)), x]","F",-1
861,0,0,65,0.2124178,"\int \frac{-b+a x^6}{\left(b+a x^6\right) \sqrt[3]{-b+a^3 x^3+a x^6}} \, dx","Integrate[(-b + a*x^6)/((b + a*x^6)*(-b + a^3*x^3 + a*x^6)^(1/3)),x]","\int \frac{-b+a x^6}{\left(b+a x^6\right) \sqrt[3]{-b+a^3 x^3+a x^6}} \, dx","\frac{1}{6} \text{RootSum}\left[\text{$\#$1}^6-2 \text{$\#$1}^3 a^3+a^6+4 a b\&,\frac{\log \left(\sqrt[3]{a^3 x^3+a x^6-b}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]",1,"Integrate[(-b + a*x^6)/((b + a*x^6)*(-b + a^3*x^3 + a*x^6)^(1/3)), x]","F",-1
862,1,107,65,0.6289907,"\int \frac{\sqrt{1-x^4} \left(1+x^4\right)}{4-7 x^4+4 x^8} \, dx","Integrate[(Sqrt[1 - x^4]*(1 + x^4))/(4 - 7*x^4 + 4*x^8),x]","\frac{1}{8} \left(-2 F\left(\left.\sin ^{-1}(x)\right|-1\right)+\Pi \left(\frac{1}{\sqrt{\frac{7}{8}-\frac{i \sqrt{15}}{8}}};\left.\sin ^{-1}(x)\right|-1\right)+\Pi \left(\frac{1}{\sqrt{\frac{7}{8}+\frac{i \sqrt{15}}{8}}};\left.\sin ^{-1}(x)\right|-1\right)+\Pi \left(-\frac{2}{\sqrt{\frac{1}{2} \left(7-i \sqrt{15}\right)}};\left.\sin ^{-1}(x)\right|-1\right)+\Pi \left(-\frac{2}{\sqrt{\frac{1}{2} \left(7+i \sqrt{15}\right)}};\left.\sin ^{-1}(x)\right|-1\right)\right)","\frac{1}{8} \tan ^{-1}\left(\frac{x^4+\frac{x^2}{2}-1}{x \sqrt{1-x^4}}\right)-\frac{1}{8} \tanh ^{-1}\left(\frac{x^4-\frac{x^2}{2}-1}{x \sqrt{1-x^4}}\right)",1,"(-2*EllipticF[ArcSin[x], -1] + EllipticPi[1/Sqrt[7/8 - (I/8)*Sqrt[15]], ArcSin[x], -1] + EllipticPi[1/Sqrt[7/8 + (I/8)*Sqrt[15]], ArcSin[x], -1] + EllipticPi[-2/Sqrt[(7 - I*Sqrt[15])/2], ArcSin[x], -1] + EllipticPi[-2/Sqrt[(7 + I*Sqrt[15])/2], ArcSin[x], -1])/8","C",1
863,1,265,65,0.1972961,"\int \frac{x^4}{\sqrt[4]{-b+a x^4} \left(-b+a x^8\right)} \, dx","Integrate[x^4/((-b + a*x^4)^(1/4)*(-b + a*x^8)),x]","\frac{-\sqrt[4]{\sqrt{a}+\sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[8]{a} x \sqrt[4]{\sqrt{a}-\sqrt{b}}}{\sqrt[4]{a x^4-b}}\right)+\sqrt[4]{\sqrt{a}-\sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[8]{a} x \sqrt[4]{\sqrt{a}+\sqrt{b}}}{\sqrt[4]{a x^4-b}}\right)-\sqrt[4]{\sqrt{a}+\sqrt{b}} \tanh ^{-1}\left(\frac{\sqrt[8]{a} x \sqrt[4]{\sqrt{a}-\sqrt{b}}}{\sqrt[4]{a x^4-b}}\right)+\sqrt[4]{\sqrt{a}-\sqrt{b}} \tanh ^{-1}\left(\frac{\sqrt[8]{a} x \sqrt[4]{\sqrt{a}+\sqrt{b}}}{\sqrt[4]{a x^4-b}}\right)}{4 a^{5/8} \sqrt{b} \sqrt[4]{\sqrt{a}-\sqrt{b}} \sqrt[4]{\sqrt{a}+\sqrt{b}}}","\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2-a b\&,\frac{\log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1} a-\text{$\#$1}^5}\&\right]",1,"(-((Sqrt[a] + Sqrt[b])^(1/4)*ArcTan[(a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*x)/(-b + a*x^4)^(1/4)]) + (Sqrt[a] - Sqrt[b])^(1/4)*ArcTan[(a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)*x)/(-b + a*x^4)^(1/4)] - (Sqrt[a] + Sqrt[b])^(1/4)*ArcTanh[(a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*x)/(-b + a*x^4)^(1/4)] + (Sqrt[a] - Sqrt[b])^(1/4)*ArcTanh[(a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)*x)/(-b + a*x^4)^(1/4)])/(4*a^(5/8)*(Sqrt[a] - Sqrt[b])^(1/4)*(Sqrt[a] + Sqrt[b])^(1/4)*Sqrt[b])","B",1
864,0,0,65,2.4247178,"\int \frac{\sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{1+x^2} \, dx","Integrate[(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 + x^2),x]","\int \frac{\sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{1+x^2} \, dx","\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^2-1}\&\right]",1,"Integrate[(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 + x^2), x]","F",-1
865,0,0,65,0.1432439,"\int \frac{\sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{1+x^2} \, dx","Integrate[(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 + x^2),x]","\int \frac{\sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{1+x^2} \, dx","\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^2-1}\&\right]",1,"Integrate[(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 + x^2), x]","F",-1
866,1,62,66,0.0264428,"\int \frac{\sqrt{-b+a x^3}}{x \left(2 b+a x^3\right)} \, dx","Integrate[Sqrt[-b + a*x^3]/(x*(2*b + a*x^3)),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{a x^3-b}}{\sqrt{b}}\right)-\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{a x^3-b}}{\sqrt{3} \sqrt{b}}\right)}{3 \sqrt{b}}","\frac{\tan ^{-1}\left(\frac{\sqrt{a x^3-b}}{\sqrt{3} \sqrt{b}}\right)}{\sqrt{3} \sqrt{b}}-\frac{\tan ^{-1}\left(\frac{\sqrt{a x^3-b}}{\sqrt{b}}\right)}{3 \sqrt{b}}",1,"-1/3*(ArcTan[Sqrt[-b + a*x^3]/Sqrt[b]] - Sqrt[3]*ArcTan[Sqrt[-b + a*x^3]/(Sqrt[3]*Sqrt[b])])/Sqrt[b]","A",1
867,1,62,66,0.0794513,"\int \frac{-b+4 a x^3}{x \sqrt{-b+a x^3} \left(2 b+a x^3\right)} \, dx","Integrate[(-b + 4*a*x^3)/(x*Sqrt[-b + a*x^3]*(2*b + a*x^3)),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{a x^3-b}}{\sqrt{b}}\right)-3 \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{a x^3-b}}{\sqrt{3} \sqrt{b}}\right)}{3 \sqrt{b}}","\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{a x^3-b}}{\sqrt{3} \sqrt{b}}\right)}{\sqrt{b}}-\frac{\tan ^{-1}\left(\frac{\sqrt{a x^3-b}}{\sqrt{b}}\right)}{3 \sqrt{b}}",1,"-1/3*(ArcTan[Sqrt[-b + a*x^3]/Sqrt[b]] - 3*Sqrt[3]*ArcTan[Sqrt[-b + a*x^3]/(Sqrt[3]*Sqrt[b])])/Sqrt[b]","A",1
868,1,641,66,2.6917863,"\int \frac{\sqrt{1+6 x^2+x^4}}{(-1+x) (1+x)^3} \, dx","Integrate[Sqrt[1 + 6*x^2 + x^4]/((-1 + x)*(1 + x)^3),x]","\frac{\frac{x^4+6 x^2+1}{(x+1)^2}+\frac{8 \sqrt{\frac{\sqrt{3+2 \sqrt{2}}+i x}{\sqrt{3-2 \sqrt{2}}+i x}} \sqrt{-\frac{x+i \sqrt{3+2 \sqrt{2}}}{\sqrt{3+2 \sqrt{2}} x-\sqrt{3-2 \sqrt{2}} x-2 i \sqrt{2}+2 i}} \sqrt{\frac{-i \left(\sqrt{3-2 \sqrt{2}}-\sqrt{3+2 \sqrt{2}}\right) x-2 \sqrt{2}+2}{\sqrt{3-2 \sqrt{2}}+i x}} \left(\sqrt{3-2 \sqrt{2}}+i x\right)^2 \left(\left(\sqrt{3-2 \sqrt{2}}-i \left(\sqrt{2}-1\right)\right) F\left(\left.\sin ^{-1}\left(\sqrt{\frac{i \left(\sqrt{3-2 \sqrt{2}}-\sqrt{3+2 \sqrt{2}}\right) x+2 \left(-1+\sqrt{2}\right)}{2 \left(-2+\sqrt{2}\right)-i \left(\sqrt{3-2 \sqrt{2}}+\sqrt{3+2 \sqrt{2}}\right) x}}\right)\right|2\right)-2 \sqrt{3-2 \sqrt{2}} \Pi \left(\frac{\left(i+\sqrt{3-2 \sqrt{2}}\right) \left(\sqrt{3-2 \sqrt{2}}+\sqrt{3+2 \sqrt{2}}\right)}{\left(-i+\sqrt{3-2 \sqrt{2}}\right) \left(\sqrt{3-2 \sqrt{2}}-\sqrt{3+2 \sqrt{2}}\right)};\left.\sin ^{-1}\left(\sqrt{\frac{i \left(\sqrt{3-2 \sqrt{2}}-\sqrt{3+2 \sqrt{2}}\right) x+2 \left(-1+\sqrt{2}\right)}{2 \left(-2+\sqrt{2}\right)-i \left(\sqrt{3-2 \sqrt{2}}+\sqrt{3+2 \sqrt{2}}\right) x}}\right)\right|2\right)\right)}{\left(\sqrt{3-2 \sqrt{2}}-i\right) \left(\sqrt{3-2 \sqrt{2}}+i\right) \left(\sqrt{3-2 \sqrt{2}}-\sqrt{3+2 \sqrt{2}}\right)}}{4 \sqrt{x^4+6 x^2+1}}","\frac{\sqrt{x^4+6 x^2+1}}{4 (x+1)^2}-\frac{\tanh ^{-1}\left(\frac{2 \sqrt{2} x}{x^2+\sqrt{x^4+6 x^2+1}-2 x+1}\right)}{2 \sqrt{2}}",1,"((1 + 6*x^2 + x^4)/(1 + x)^2 + (8*(Sqrt[3 - 2*Sqrt[2]] + I*x)^2*Sqrt[(Sqrt[3 + 2*Sqrt[2]] + I*x)/(Sqrt[3 - 2*Sqrt[2]] + I*x)]*Sqrt[-((I*Sqrt[3 + 2*Sqrt[2]] + x)/(2*I - (2*I)*Sqrt[2] - Sqrt[3 - 2*Sqrt[2]]*x + Sqrt[3 + 2*Sqrt[2]]*x))]*Sqrt[(2 - 2*Sqrt[2] - I*(Sqrt[3 - 2*Sqrt[2]] - Sqrt[3 + 2*Sqrt[2]])*x)/(Sqrt[3 - 2*Sqrt[2]] + I*x)]*((Sqrt[3 - 2*Sqrt[2]] - I*(-1 + Sqrt[2]))*EllipticF[ArcSin[Sqrt[(2*(-1 + Sqrt[2]) + I*(Sqrt[3 - 2*Sqrt[2]] - Sqrt[3 + 2*Sqrt[2]])*x)/(2*(-2 + Sqrt[2]) - I*(Sqrt[3 - 2*Sqrt[2]] + Sqrt[3 + 2*Sqrt[2]])*x)]], 2] - 2*Sqrt[3 - 2*Sqrt[2]]*EllipticPi[((I + Sqrt[3 - 2*Sqrt[2]])*(Sqrt[3 - 2*Sqrt[2]] + Sqrt[3 + 2*Sqrt[2]]))/((-I + Sqrt[3 - 2*Sqrt[2]])*(Sqrt[3 - 2*Sqrt[2]] - Sqrt[3 + 2*Sqrt[2]])), ArcSin[Sqrt[(2*(-1 + Sqrt[2]) + I*(Sqrt[3 - 2*Sqrt[2]] - Sqrt[3 + 2*Sqrt[2]])*x)/(2*(-2 + Sqrt[2]) - I*(Sqrt[3 - 2*Sqrt[2]] + Sqrt[3 + 2*Sqrt[2]])*x)]], 2]))/((-I + Sqrt[3 - 2*Sqrt[2]])*(I + Sqrt[3 - 2*Sqrt[2]])*(Sqrt[3 - 2*Sqrt[2]] - Sqrt[3 + 2*Sqrt[2]])))/(4*Sqrt[1 + 6*x^2 + x^4])","C",0
869,1,66,66,0.014755,"\int \frac{\sqrt[4]{b+a x^4}}{x} \, dx","Integrate[(b + a*x^4)^(1/4)/x,x]","\sqrt[4]{a x^4+b}-\frac{1}{2} \sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt[4]{a x^4+b}}{\sqrt[4]{b}}\right)-\frac{1}{2} \sqrt[4]{b} \tanh ^{-1}\left(\frac{\sqrt[4]{a x^4+b}}{\sqrt[4]{b}}\right)","\sqrt[4]{a x^4+b}-\frac{1}{2} \sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt[4]{a x^4+b}}{\sqrt[4]{b}}\right)-\frac{1}{2} \sqrt[4]{b} \tanh ^{-1}\left(\frac{\sqrt[4]{a x^4+b}}{\sqrt[4]{b}}\right)",1,"(b + a*x^4)^(1/4) - (b^(1/4)*ArcTan[(b + a*x^4)^(1/4)/b^(1/4)])/2 - (b^(1/4)*ArcTanh[(b + a*x^4)^(1/4)/b^(1/4)])/2","A",1
870,1,373,66,1.7044069,"\int \frac{1}{\left(-2 b+a x^4\right) \sqrt[4]{-b x^2+a x^4}} \, dx","Integrate[1/((-2*b + a*x^4)*(-(b*x^2) + a*x^4)^(1/4)),x]","-\frac{x \sqrt[4]{\frac{b}{x^2}-a} \left(-\sqrt[4]{\sqrt{2} \sqrt{b}-2 \sqrt{a}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{2 b}{x^2}-2 a}}{\sqrt[8]{a} \sqrt[4]{-2 \sqrt{a}-\sqrt{2} \sqrt{b}}}\right)-\sqrt[4]{-2 \sqrt{a}-\sqrt{2} \sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{2 b}{x^2}-2 a}}{\sqrt[8]{a} \sqrt[4]{\sqrt{2} \sqrt{b}-2 \sqrt{a}}}\right)+\sqrt[4]{\sqrt{2} \sqrt{b}-2 \sqrt{a}} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{2 b}{x^2}-2 a}}{\sqrt[8]{a} \sqrt[4]{-2 \sqrt{a}-\sqrt{2} \sqrt{b}}}\right)+\sqrt[4]{-2 \sqrt{a}-\sqrt{2} \sqrt{b}} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{2 b}{x^2}-2 a}}{\sqrt[8]{a} \sqrt[4]{\sqrt{2} \sqrt{b}-2 \sqrt{a}}}\right)\right)}{2\ 2^{3/4} \sqrt[8]{a} b \sqrt[4]{-2 \sqrt{a}-\sqrt{2} \sqrt{b}} \sqrt[4]{\sqrt{2} \sqrt{b}-2 \sqrt{a}} \sqrt[4]{a x^4-b x^2}}","\frac{\text{RootSum}\left[2 \text{$\#$1}^8-4 \text{$\#$1}^4 a+2 a^2-a b\&,\frac{\log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{8 b}",1,"-1/2*((-a + b/x^2)^(1/4)*x*(-((-2*Sqrt[a] + Sqrt[2]*Sqrt[b])^(1/4)*ArcTan[(-2*a + (2*b)/x^2)^(1/4)/(a^(1/8)*(-2*Sqrt[a] - Sqrt[2]*Sqrt[b])^(1/4))]) - (-2*Sqrt[a] - Sqrt[2]*Sqrt[b])^(1/4)*ArcTan[(-2*a + (2*b)/x^2)^(1/4)/(a^(1/8)*(-2*Sqrt[a] + Sqrt[2]*Sqrt[b])^(1/4))] + (-2*Sqrt[a] + Sqrt[2]*Sqrt[b])^(1/4)*ArcTanh[(-2*a + (2*b)/x^2)^(1/4)/(a^(1/8)*(-2*Sqrt[a] - Sqrt[2]*Sqrt[b])^(1/4))] + (-2*Sqrt[a] - Sqrt[2]*Sqrt[b])^(1/4)*ArcTanh[(-2*a + (2*b)/x^2)^(1/4)/(a^(1/8)*(-2*Sqrt[a] + Sqrt[2]*Sqrt[b])^(1/4))]))/(2^(3/4)*a^(1/8)*(-2*Sqrt[a] - Sqrt[2]*Sqrt[b])^(1/4)*(-2*Sqrt[a] + Sqrt[2]*Sqrt[b])^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4))","B",1
871,1,373,66,0.3775283,"\int \frac{1}{\left(-2 b+a x^4\right) \sqrt[4]{-b x^2+a x^4}} \, dx","Integrate[1/((-2*b + a*x^4)*(-(b*x^2) + a*x^4)^(1/4)),x]","-\frac{x \sqrt[4]{\frac{b}{x^2}-a} \left(-\sqrt[4]{\sqrt{2} \sqrt{b}-2 \sqrt{a}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{2 b}{x^2}-2 a}}{\sqrt[8]{a} \sqrt[4]{-2 \sqrt{a}-\sqrt{2} \sqrt{b}}}\right)-\sqrt[4]{-2 \sqrt{a}-\sqrt{2} \sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{2 b}{x^2}-2 a}}{\sqrt[8]{a} \sqrt[4]{\sqrt{2} \sqrt{b}-2 \sqrt{a}}}\right)+\sqrt[4]{\sqrt{2} \sqrt{b}-2 \sqrt{a}} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{2 b}{x^2}-2 a}}{\sqrt[8]{a} \sqrt[4]{-2 \sqrt{a}-\sqrt{2} \sqrt{b}}}\right)+\sqrt[4]{-2 \sqrt{a}-\sqrt{2} \sqrt{b}} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{2 b}{x^2}-2 a}}{\sqrt[8]{a} \sqrt[4]{\sqrt{2} \sqrt{b}-2 \sqrt{a}}}\right)\right)}{2\ 2^{3/4} \sqrt[8]{a} b \sqrt[4]{-2 \sqrt{a}-\sqrt{2} \sqrt{b}} \sqrt[4]{\sqrt{2} \sqrt{b}-2 \sqrt{a}} \sqrt[4]{a x^4-b x^2}}","\frac{\text{RootSum}\left[2 \text{$\#$1}^8-4 \text{$\#$1}^4 a+2 a^2-a b\&,\frac{\log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{8 b}",1,"-1/2*((-a + b/x^2)^(1/4)*x*(-((-2*Sqrt[a] + Sqrt[2]*Sqrt[b])^(1/4)*ArcTan[(-2*a + (2*b)/x^2)^(1/4)/(a^(1/8)*(-2*Sqrt[a] - Sqrt[2]*Sqrt[b])^(1/4))]) - (-2*Sqrt[a] - Sqrt[2]*Sqrt[b])^(1/4)*ArcTan[(-2*a + (2*b)/x^2)^(1/4)/(a^(1/8)*(-2*Sqrt[a] + Sqrt[2]*Sqrt[b])^(1/4))] + (-2*Sqrt[a] + Sqrt[2]*Sqrt[b])^(1/4)*ArcTanh[(-2*a + (2*b)/x^2)^(1/4)/(a^(1/8)*(-2*Sqrt[a] - Sqrt[2]*Sqrt[b])^(1/4))] + (-2*Sqrt[a] - Sqrt[2]*Sqrt[b])^(1/4)*ArcTanh[(-2*a + (2*b)/x^2)^(1/4)/(a^(1/8)*(-2*Sqrt[a] + Sqrt[2]*Sqrt[b])^(1/4))]))/(2^(3/4)*a^(1/8)*(-2*Sqrt[a] - Sqrt[2]*Sqrt[b])^(1/4)*(-2*Sqrt[a] + Sqrt[2]*Sqrt[b])^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4))","B",1
872,0,0,66,0.1264138,"\int \frac{x^6}{\left(b+a x^4\right)^{3/4} \left(b^2+a^2 x^8\right)} \, dx","Integrate[x^6/((b + a*x^4)^(3/4)*(b^2 + a^2*x^8)),x]","\int \frac{x^6}{\left(b+a x^4\right)^{3/4} \left(b^2+a^2 x^8\right)} \, dx","\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+2 a^2\&,\frac{\log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}^3 a-\text{$\#$1}^7}\&\right]}{8 b}",1,"Integrate[x^6/((b + a*x^4)^(3/4)*(b^2 + a^2*x^8)), x]","F",-1
873,1,89,66,0.1100199,"\int \sqrt{x^3+x^2 \sqrt{-1+x^2}} \, dx","Integrate[Sqrt[x^3 + x^2*Sqrt[-1 + x^2]],x]","\frac{2 x \sqrt{x^2-1} \left(6 x^4-6 x^2-3 \sqrt{x^2-1} x+6 \sqrt{x^2-1} x^3+2\right)}{15 \sqrt{x^2 \left(\sqrt{x^2-1}+x\right)} \left(x^2+\sqrt{x^2-1} x-1\right)}","\frac{4 \left(2 x^2-1\right) \sqrt{x^2 \left(\sqrt{x^2-1}+x\right)}}{15 x}-\frac{2}{15} \sqrt{x^2-1} \sqrt{x^2 \left(\sqrt{x^2-1}+x\right)}",1,"(2*x*Sqrt[-1 + x^2]*(2 - 6*x^2 + 6*x^4 - 3*x*Sqrt[-1 + x^2] + 6*x^3*Sqrt[-1 + x^2]))/(15*Sqrt[x^2*(x + Sqrt[-1 + x^2])]*(-1 + x^2 + x*Sqrt[-1 + x^2]))","A",1
874,1,504,67,8.496816,"\int \frac{(-a+x) (-b+x) \left(-a b+x^2\right)}{x \sqrt{x (-a+x) (-b+x)} \left(a b-(a+b+d) x+x^2\right)} \, dx","Integrate[((-a + x)*(-b + x)*(-(a*b) + x^2))/(x*Sqrt[x*(-a + x)*(-b + x)]*(a*b - (a + b + d)*x + x^2)),x]","\frac{\sqrt{x (x-a) (x-b)} \left(\frac{i \left(-a \left(\sqrt{a^2-2 a (b-d)+(b+d)^2}+2 b-2 d\right)+b \sqrt{a^2-2 a (b-d)+(b+d)^2}-d \sqrt{a^2-2 a (b-d)+(b+d)^2}+a^2+b^2+2 b d+d^2\right) \sqrt{\frac{x-b}{a-b}} \Pi \left(\frac{2 a}{a-b-d+\sqrt{(-a+b+d)^2+4 a d}};i \sinh ^{-1}\left(\sqrt{\frac{x}{a}-1}\right)|\frac{a}{a-b}\right)}{\sqrt{1-\frac{a}{x}} (b-x) \sqrt{a^2-2 a (b-d)+(b+d)^2}}-\frac{i \left(a \left(\sqrt{a^2-2 a (b-d)+(b+d)^2}-2 b+2 d\right)-b \sqrt{a^2-2 a (b-d)+(b+d)^2}+d \sqrt{a^2-2 a (b-d)+(b+d)^2}+a^2+b^2+2 b d+d^2\right) \sqrt{\frac{x-b}{a-b}} \Pi \left(-\frac{2 a}{-a+b+d+\sqrt{(-a+b+d)^2+4 a d}};i \sinh ^{-1}\left(\sqrt{\frac{x}{a}-1}\right)|\frac{a}{a-b}\right)}{\sqrt{1-\frac{a}{x}} (b-x) \sqrt{a^2-2 a (b-d)+(b+d)^2}}-\frac{2 i d \sqrt{\frac{x-b}{a-b}} F\left(i \sinh ^{-1}\left(\sqrt{\frac{x}{a}-1}\right)|\frac{a}{a-b}\right)}{\sqrt{1-\frac{a}{x}} (x-b)}+2\right)}{x}","\frac{2 \sqrt{x^2 (-a-b)+a b x+x^3}}{x}-2 \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{x^2 (-a-b)+a b x+x^3}}\right)",1,"(Sqrt[x*(-a + x)*(-b + x)]*(2 - ((2*I)*d*Sqrt[(-b + x)/(a - b)]*EllipticF[I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)])/(Sqrt[1 - a/x]*(-b + x)) + (I*(a^2 + b^2 + 2*b*d + d^2 + b*Sqrt[a^2 - 2*a*(b - d) + (b + d)^2] - d*Sqrt[a^2 - 2*a*(b - d) + (b + d)^2] - a*(2*b - 2*d + Sqrt[a^2 - 2*a*(b - d) + (b + d)^2]))*Sqrt[(-b + x)/(a - b)]*EllipticPi[(2*a)/(a - b - d + Sqrt[4*a*d + (-a + b + d)^2]), I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)])/(Sqrt[a^2 - 2*a*(b - d) + (b + d)^2]*Sqrt[1 - a/x]*(b - x)) - (I*(a^2 + b^2 + 2*b*d + d^2 - b*Sqrt[a^2 - 2*a*(b - d) + (b + d)^2] + d*Sqrt[a^2 - 2*a*(b - d) + (b + d)^2] + a*(-2*b + 2*d + Sqrt[a^2 - 2*a*(b - d) + (b + d)^2]))*Sqrt[(-b + x)/(a - b)]*EllipticPi[(-2*a)/(-a + b + d + Sqrt[4*a*d + (-a + b + d)^2]), I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)])/(Sqrt[a^2 - 2*a*(b - d) + (b + d)^2]*Sqrt[1 - a/x]*(b - x))))/x","C",1
875,1,107,67,0.0953148,"\int \frac{1}{\left(b+a^3 x^2\right) \sqrt[3]{-b x^2+a^3 x^3}} \, dx","Integrate[1/((b + a^3*x^2)*(-(b*x^2) + a^3*x^3)^(1/3)),x]","\frac{3 x \left(\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(a^3-\sqrt{-a^3} \sqrt{b}\right) x}{a^3 x-b}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(a^3+\sqrt{-a^3} \sqrt{b}\right) x}{a^3 x-b}\right)\right)}{2 b \sqrt[3]{x^2 \left(a^3 x-b\right)}}","-\frac{\text{RootSum}\left[\text{$\#$1}^6-2 \text{$\#$1}^3 a^3+a^6+a^3 b\&,\frac{\log \left(\sqrt[3]{a^3 x^3-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{2 b}",1,"(3*x*(Hypergeometric2F1[1/3, 1, 4/3, ((a^3 - Sqrt[-a^3]*Sqrt[b])*x)/(-b + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, ((a^3 + Sqrt[-a^3]*Sqrt[b])*x)/(-b + a^3*x)]))/(2*b*(x^2*(-b + a^3*x))^(1/3))","A",1
876,1,107,67,0.0277901,"\int \frac{1}{\left(b+a^3 x^2\right) \sqrt[3]{-b x^2+a^3 x^3}} \, dx","Integrate[1/((b + a^3*x^2)*(-(b*x^2) + a^3*x^3)^(1/3)),x]","\frac{3 x \left(\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(a^3-\sqrt{-a^3} \sqrt{b}\right) x}{a^3 x-b}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(a^3+\sqrt{-a^3} \sqrt{b}\right) x}{a^3 x-b}\right)\right)}{2 b \sqrt[3]{x^2 \left(a^3 x-b\right)}}","-\frac{\text{RootSum}\left[\text{$\#$1}^6-2 \text{$\#$1}^3 a^3+a^6+a^3 b\&,\frac{\log \left(\sqrt[3]{a^3 x^3-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{2 b}",1,"(3*x*(Hypergeometric2F1[1/3, 1, 4/3, ((a^3 - Sqrt[-a^3]*Sqrt[b])*x)/(-b + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, ((a^3 + Sqrt[-a^3]*Sqrt[b])*x)/(-b + a^3*x)]))/(2*b*(x^2*(-b + a^3*x))^(1/3))","A",1
877,1,108,67,0.1052686,"\int \frac{\sqrt{-1+x^4}}{1+x^4} \, dx","Integrate[Sqrt[-1 + x^4]/(1 + x^4),x]","-\frac{5 x \sqrt{x^4-1} F_1\left(\frac{1}{4};-\frac{1}{2},1;\frac{5}{4};x^4,-x^4\right)}{\left(x^4+1\right) \left(2 x^4 \left(2 F_1\left(\frac{5}{4};-\frac{1}{2},2;\frac{9}{4};x^4,-x^4\right)+F_1\left(\frac{5}{4};\frac{1}{2},1;\frac{9}{4};x^4,-x^4\right)\right)-5 F_1\left(\frac{1}{4};-\frac{1}{2},1;\frac{5}{4};x^4,-x^4\right)\right)}","\frac{1}{4} \tan ^{-1}\left(\frac{\frac{x^4}{2}-x^2-\frac{1}{2}}{x \sqrt{x^4-1}}\right)-\frac{1}{4} \tanh ^{-1}\left(\frac{\frac{x^4}{2}+x^2-\frac{1}{2}}{x \sqrt{x^4-1}}\right)",1,"(-5*x*Sqrt[-1 + x^4]*AppellF1[1/4, -1/2, 1, 5/4, x^4, -x^4])/((1 + x^4)*(-5*AppellF1[1/4, -1/2, 1, 5/4, x^4, -x^4] + 2*x^4*(2*AppellF1[5/4, -1/2, 2, 9/4, x^4, -x^4] + AppellF1[5/4, 1/2, 1, 9/4, x^4, -x^4])))","C",0
878,1,56,67,0.0188021,"\int x^2 \sqrt[4]{-x^2+x^4} \, dx","Integrate[x^2*(-x^2 + x^4)^(1/4),x]","\frac{x \sqrt[4]{x^2 \left(x^2-1\right)} \left(\, _2F_1\left(-\frac{1}{4},\frac{3}{4};\frac{7}{4};x^2\right)-\left(1-x^2\right)^{5/4}\right)}{4 \sqrt[4]{1-x^2}}","\frac{3}{32} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^2}}\right)-\frac{3}{32} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^2}}\right)+\frac{1}{16} \sqrt[4]{x^4-x^2} \left(4 x^3-x\right)",1,"(x*(x^2*(-1 + x^2))^(1/4)*(-(1 - x^2)^(5/4) + Hypergeometric2F1[-1/4, 3/4, 7/4, x^2]))/(4*(1 - x^2)^(1/4))","C",1
879,1,1105,67,2.2490142,"\int \frac{x}{\sqrt{1+4 x+3 x^2-2 x^3+x^4}} \, dx","Integrate[x/Sqrt[1 + 4*x + 3*x^2 - 2*x^3 + x^4],x]","\frac{\sqrt[4]{-1} \left(-2 x+i \sqrt{3}+2 \sqrt[4]{-3}+1\right) \left(2 i x+\sqrt{3}+2 i \sqrt[4]{-3}-i\right) \left(\Pi \left(\frac{4 \sqrt[4]{-3}}{1+2 \sqrt[4]{-3}+i \sqrt{3}-2 \text{Root}\left[\text{$\#$1}^4-2 \text{$\#$1}^3+3 \text{$\#$1}^2+4 \text{$\#$1}+1\&,2\right]};\sin ^{-1}\left(\frac{\sqrt{-\frac{(-1)^{3/4} \left(2 x-i \sqrt{3}+2 \sqrt[4]{-3}-1\right) \left(1+2 \sqrt[4]{-3}+i \sqrt{3}-2 \text{Root}\left[\text{$\#$1}^4-2 \text{$\#$1}^3+3 \text{$\#$1}^2+4 \text{$\#$1}+1\&,2\right]\right)}{x-\text{Root}\left[\text{$\#$1}^4-2 \text{$\#$1}^3+3 \text{$\#$1}^2+4 \text{$\#$1}+1\&,2\right]}}}{2 \sqrt{2} \sqrt[8]{3}}\right)|-\frac{8 \sqrt[4]{-3} \left(\text{Root}\left[\text{$\#$1}^4-2 \text{$\#$1}^3+3 \text{$\#$1}^2+4 \text{$\#$1}+1\&,2\right]-\text{Root}\left[\text{$\#$1}^4-2 \text{$\#$1}^3+3 \text{$\#$1}^2+4 \text{$\#$1}+1\&,3\right]\right)}{\left(1+2 \sqrt[4]{-3}+i \sqrt{3}-2 \text{Root}\left[\text{$\#$1}^4-2 \text{$\#$1}^3+3 \text{$\#$1}^2+4 \text{$\#$1}+1\&,2\right]\right) \left(-1+2 \sqrt[4]{-3}-i \sqrt{3}+2 \text{Root}\left[\text{$\#$1}^4-2 \text{$\#$1}^3+3 \text{$\#$1}^2+4 \text{$\#$1}+1\&,3\right]\right)}\right) \left(-1+2 \sqrt[4]{-3}-i \sqrt{3}+2 \text{Root}\left[\text{$\#$1}^4-2 \text{$\#$1}^3+3 \text{$\#$1}^2+4 \text{$\#$1}+1\&,2\right]\right)-2 F\left(\sin ^{-1}\left(\frac{\sqrt{-\frac{(-1)^{3/4} \left(2 x-i \sqrt{3}+2 \sqrt[4]{-3}-1\right) \left(1+2 \sqrt[4]{-3}+i \sqrt{3}-2 \text{Root}\left[\text{$\#$1}^4-2 \text{$\#$1}^3+3 \text{$\#$1}^2+4 \text{$\#$1}+1\&,2\right]\right)}{x-\text{Root}\left[\text{$\#$1}^4-2 \text{$\#$1}^3+3 \text{$\#$1}^2+4 \text{$\#$1}+1\&,2\right]}}}{2 \sqrt{2} \sqrt[8]{3}}\right)|-\frac{8 \sqrt[4]{-3} \left(\text{Root}\left[\text{$\#$1}^4-2 \text{$\#$1}^3+3 \text{$\#$1}^2+4 \text{$\#$1}+1\&,2\right]-\text{Root}\left[\text{$\#$1}^4-2 \text{$\#$1}^3+3 \text{$\#$1}^2+4 \text{$\#$1}+1\&,3\right]\right)}{\left(1+2 \sqrt[4]{-3}+i \sqrt{3}-2 \text{Root}\left[\text{$\#$1}^4-2 \text{$\#$1}^3+3 \text{$\#$1}^2+4 \text{$\#$1}+1\&,2\right]\right) \left(-1+2 \sqrt[4]{-3}-i \sqrt{3}+2 \text{Root}\left[\text{$\#$1}^4-2 \text{$\#$1}^3+3 \text{$\#$1}^2+4 \text{$\#$1}+1\&,3\right]\right)}\right) \text{Root}\left[\text{$\#$1}^4-2 \text{$\#$1}^3+3 \text{$\#$1}^2+4 \text{$\#$1}+1\&,2\right]\right) \sqrt{\frac{\left(-1+2 \sqrt[4]{-3}-i \sqrt{3}+2 \text{Root}\left[\text{$\#$1}^4-2 \text{$\#$1}^3+3 \text{$\#$1}^2+4 \text{$\#$1}+1\&,2\right]\right) \left(x-\text{Root}\left[\text{$\#$1}^4-2 \text{$\#$1}^3+3 \text{$\#$1}^2+4 \text{$\#$1}+1\&,3\right]\right)}{\left(x-\text{Root}\left[\text{$\#$1}^4-2 \text{$\#$1}^3+3 \text{$\#$1}^2+4 \text{$\#$1}+1\&,2\right]\right) \left(-1+2 \sqrt[4]{-3}-i \sqrt{3}+2 \text{Root}\left[\text{$\#$1}^4-2 \text{$\#$1}^3+3 \text{$\#$1}^2+4 \text{$\#$1}+1\&,3\right]\right)}}}{\sqrt{x^4-2 x^3+3 x^2+4 x+1} \sqrt{\frac{\left(-2 x+i \sqrt{3}+2 \sqrt[4]{-3}+1\right) \left(2 i x+\sqrt{3}+2 i \sqrt[4]{-3}-i\right) \left(1+2 \sqrt[4]{-3}+i \sqrt{3}-2 \text{Root}\left[\text{$\#$1}^4-2 \text{$\#$1}^3+3 \text{$\#$1}^2+4 \text{$\#$1}+1\&,2\right]\right) \left(-1+2 \sqrt[4]{-3}-i \sqrt{3}+2 \text{Root}\left[\text{$\#$1}^4-2 \text{$\#$1}^3+3 \text{$\#$1}^2+4 \text{$\#$1}+1\&,2\right]\right)}{\left(x-\text{Root}\left[\text{$\#$1}^4-2 \text{$\#$1}^3+3 \text{$\#$1}^2+4 \text{$\#$1}+1\&,2\right]\right)^2}}}","\frac{1}{3} \tanh ^{-1}\left(\frac{(x+1) \sqrt{x^4-2 x^3+3 x^2+4 x+1}}{x^3}\right)+\tanh ^{-1}\left(\frac{\sqrt{x^4-2 x^3+3 x^2+4 x+1}-2 x-1}{x^2}\right)",1,"((-1)^(1/4)*(1 + 2*(-3)^(1/4) + I*Sqrt[3] - 2*x)*(-I + (2*I)*(-3)^(1/4) + Sqrt[3] + (2*I)*x)*(-2*EllipticF[ArcSin[Sqrt[-(((-1)^(3/4)*(-1 + 2*(-3)^(1/4) - I*Sqrt[3] + 2*x)*(1 + 2*(-3)^(1/4) + I*Sqrt[3] - 2*Root[1 + 4*#1 + 3*#1^2 - 2*#1^3 + #1^4 & , 2, 0]))/(x - Root[1 + 4*#1 + 3*#1^2 - 2*#1^3 + #1^4 & , 2, 0]))]/(2*Sqrt[2]*3^(1/8))], (-8*(-3)^(1/4)*(Root[1 + 4*#1 + 3*#1^2 - 2*#1^3 + #1^4 & , 2, 0] - Root[1 + 4*#1 + 3*#1^2 - 2*#1^3 + #1^4 & , 3, 0]))/((1 + 2*(-3)^(1/4) + I*Sqrt[3] - 2*Root[1 + 4*#1 + 3*#1^2 - 2*#1^3 + #1^4 & , 2, 0])*(-1 + 2*(-3)^(1/4) - I*Sqrt[3] + 2*Root[1 + 4*#1 + 3*#1^2 - 2*#1^3 + #1^4 & , 3, 0]))]*Root[1 + 4*#1 + 3*#1^2 - 2*#1^3 + #1^4 & , 2, 0] + EllipticPi[(4*(-3)^(1/4))/(1 + 2*(-3)^(1/4) + I*Sqrt[3] - 2*Root[1 + 4*#1 + 3*#1^2 - 2*#1^3 + #1^4 & , 2, 0]), ArcSin[Sqrt[-(((-1)^(3/4)*(-1 + 2*(-3)^(1/4) - I*Sqrt[3] + 2*x)*(1 + 2*(-3)^(1/4) + I*Sqrt[3] - 2*Root[1 + 4*#1 + 3*#1^2 - 2*#1^3 + #1^4 & , 2, 0]))/(x - Root[1 + 4*#1 + 3*#1^2 - 2*#1^3 + #1^4 & , 2, 0]))]/(2*Sqrt[2]*3^(1/8))], (-8*(-3)^(1/4)*(Root[1 + 4*#1 + 3*#1^2 - 2*#1^3 + #1^4 & , 2, 0] - Root[1 + 4*#1 + 3*#1^2 - 2*#1^3 + #1^4 & , 3, 0]))/((1 + 2*(-3)^(1/4) + I*Sqrt[3] - 2*Root[1 + 4*#1 + 3*#1^2 - 2*#1^3 + #1^4 & , 2, 0])*(-1 + 2*(-3)^(1/4) - I*Sqrt[3] + 2*Root[1 + 4*#1 + 3*#1^2 - 2*#1^3 + #1^4 & , 3, 0]))]*(-1 + 2*(-3)^(1/4) - I*Sqrt[3] + 2*Root[1 + 4*#1 + 3*#1^2 - 2*#1^3 + #1^4 & , 2, 0]))*Sqrt[((-1 + 2*(-3)^(1/4) - I*Sqrt[3] + 2*Root[1 + 4*#1 + 3*#1^2 - 2*#1^3 + #1^4 & , 2, 0])*(x - Root[1 + 4*#1 + 3*#1^2 - 2*#1^3 + #1^4 & , 3, 0]))/((x - Root[1 + 4*#1 + 3*#1^2 - 2*#1^3 + #1^4 & , 2, 0])*(-1 + 2*(-3)^(1/4) - I*Sqrt[3] + 2*Root[1 + 4*#1 + 3*#1^2 - 2*#1^3 + #1^4 & , 3, 0]))])/(Sqrt[1 + 4*x + 3*x^2 - 2*x^3 + x^4]*Sqrt[((1 + 2*(-3)^(1/4) + I*Sqrt[3] - 2*x)*(-I + (2*I)*(-3)^(1/4) + Sqrt[3] + (2*I)*x)*(1 + 2*(-3)^(1/4) + I*Sqrt[3] - 2*Root[1 + 4*#1 + 3*#1^2 - 2*#1^3 + #1^4 & , 2, 0])*(-1 + 2*(-3)^(1/4) - I*Sqrt[3] + 2*Root[1 + 4*#1 + 3*#1^2 - 2*#1^3 + #1^4 & , 2, 0]))/(x - Root[1 + 4*#1 + 3*#1^2 - 2*#1^3 + #1^4 & , 2, 0])^2])","C",0
880,1,1189,67,1.9658998,"\int \frac{x}{\sqrt{1-4 x+3 x^2+2 x^3+x^4}} \, dx","Integrate[x/Sqrt[1 - 4*x + 3*x^2 + 2*x^3 + x^4],x]","\frac{\sqrt[4]{-1} \left(x-\text{Root}\left[\text{$\#$1}^4+2 \text{$\#$1}^3+3 \text{$\#$1}^2-4 \text{$\#$1}+1\&,2\right]\right)^2 \sqrt{\frac{\left(-2 x-i \sqrt{3}+2 \sqrt[4]{-3}-1\right) \left(2 x+i \sqrt{3}+2 \sqrt[4]{-3}+1\right) \left(-i+2 i \sqrt[4]{-3}+\sqrt{3}-2 i \text{Root}\left[\text{$\#$1}^4+2 \text{$\#$1}^3+3 \text{$\#$1}^2-4 \text{$\#$1}+1\&,2\right]\right) \left(1+2 \sqrt[4]{-3}+i \sqrt{3}+2 \text{Root}\left[\text{$\#$1}^4+2 \text{$\#$1}^3+3 \text{$\#$1}^2-4 \text{$\#$1}+1\&,2\right]\right)}{\left(x-\text{Root}\left[\text{$\#$1}^4+2 \text{$\#$1}^3+3 \text{$\#$1}^2-4 \text{$\#$1}+1\&,2\right]\right)^2}} \left(\Pi \left(\frac{4 \sqrt[4]{-3}}{-1+2 \sqrt[4]{-3}-i \sqrt{3}-2 \text{Root}\left[\text{$\#$1}^4+2 \text{$\#$1}^3+3 \text{$\#$1}^2-4 \text{$\#$1}+1\&,2\right]};\sin ^{-1}\left(\frac{\sqrt{\frac{(-1)^{3/4} \left(x+\frac{i \sqrt{3}}{2}+\sqrt[4]{-3}+\frac{1}{2}\right) \left(\frac{1}{2}-\sqrt[4]{-3}+\frac{i \sqrt{3}}{2}+\text{Root}\left[\text{$\#$1}^4+2 \text{$\#$1}^3+3 \text{$\#$1}^2-4 \text{$\#$1}+1\&,2\right]\right)}{x-\text{Root}\left[\text{$\#$1}^4+2 \text{$\#$1}^3+3 \text{$\#$1}^2-4 \text{$\#$1}+1\&,2\right]}}}{\sqrt{2} \sqrt[8]{3}}\right)|\frac{2 \sqrt[4]{-3} \left(\text{Root}\left[\text{$\#$1}^4+2 \text{$\#$1}^3+3 \text{$\#$1}^2-4 \text{$\#$1}+1\&,2\right]-\text{Root}\left[\text{$\#$1}^4+2 \text{$\#$1}^3+3 \text{$\#$1}^2-4 \text{$\#$1}+1\&,3\right]\right)}{\left(\frac{1}{2}-\sqrt[4]{-3}+\frac{i \sqrt{3}}{2}+\text{Root}\left[\text{$\#$1}^4+2 \text{$\#$1}^3+3 \text{$\#$1}^2-4 \text{$\#$1}+1\&,2\right]\right) \left(\frac{1}{2}+\sqrt[4]{-3}+\frac{i \sqrt{3}}{2}+\text{Root}\left[\text{$\#$1}^4+2 \text{$\#$1}^3+3 \text{$\#$1}^2-4 \text{$\#$1}+1\&,3\right]\right)}\right) \left(1+2 \sqrt[4]{-3}+i \sqrt{3}+2 \text{Root}\left[\text{$\#$1}^4+2 \text{$\#$1}^3+3 \text{$\#$1}^2-4 \text{$\#$1}+1\&,2\right]\right)-2 F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{(-1)^{3/4} \left(x+\frac{i \sqrt{3}}{2}+\sqrt[4]{-3}+\frac{1}{2}\right) \left(\frac{1}{2}-\sqrt[4]{-3}+\frac{i \sqrt{3}}{2}+\text{Root}\left[\text{$\#$1}^4+2 \text{$\#$1}^3+3 \text{$\#$1}^2-4 \text{$\#$1}+1\&,2\right]\right)}{x-\text{Root}\left[\text{$\#$1}^4+2 \text{$\#$1}^3+3 \text{$\#$1}^2-4 \text{$\#$1}+1\&,2\right]}}}{\sqrt{2} \sqrt[8]{3}}\right)|\frac{2 \sqrt[4]{-3} \left(\text{Root}\left[\text{$\#$1}^4+2 \text{$\#$1}^3+3 \text{$\#$1}^2-4 \text{$\#$1}+1\&,2\right]-\text{Root}\left[\text{$\#$1}^4+2 \text{$\#$1}^3+3 \text{$\#$1}^2-4 \text{$\#$1}+1\&,3\right]\right)}{\left(\frac{1}{2}-\sqrt[4]{-3}+\frac{i \sqrt{3}}{2}+\text{Root}\left[\text{$\#$1}^4+2 \text{$\#$1}^3+3 \text{$\#$1}^2-4 \text{$\#$1}+1\&,2\right]\right) \left(\frac{1}{2}+\sqrt[4]{-3}+\frac{i \sqrt{3}}{2}+\text{Root}\left[\text{$\#$1}^4+2 \text{$\#$1}^3+3 \text{$\#$1}^2-4 \text{$\#$1}+1\&,3\right]\right)}\right) \text{Root}\left[\text{$\#$1}^4+2 \text{$\#$1}^3+3 \text{$\#$1}^2-4 \text{$\#$1}+1\&,2\right]\right) \sqrt{\frac{\left(1+2 \sqrt[4]{-3}+i \sqrt{3}+2 \text{Root}\left[\text{$\#$1}^4+2 \text{$\#$1}^3+3 \text{$\#$1}^2-4 \text{$\#$1}+1\&,2\right]\right) \left(x-\text{Root}\left[\text{$\#$1}^4+2 \text{$\#$1}^3+3 \text{$\#$1}^2-4 \text{$\#$1}+1\&,3\right]\right)}{\left(x-\text{Root}\left[\text{$\#$1}^4+2 \text{$\#$1}^3+3 \text{$\#$1}^2-4 \text{$\#$1}+1\&,2\right]\right) \left(1+2 \sqrt[4]{-3}+i \sqrt{3}+2 \text{Root}\left[\text{$\#$1}^4+2 \text{$\#$1}^3+3 \text{$\#$1}^2-4 \text{$\#$1}+1\&,3\right]\right)}}}{\sqrt{x^4+2 x^3+3 x^2-4 x+1} \left(-1+2 \sqrt[4]{-3}-i \sqrt{3}-2 \text{Root}\left[\text{$\#$1}^4+2 \text{$\#$1}^3+3 \text{$\#$1}^2-4 \text{$\#$1}+1\&,2\right]\right) \left(1+2 \sqrt[4]{-3}+i \sqrt{3}+2 \text{Root}\left[\text{$\#$1}^4+2 \text{$\#$1}^3+3 \text{$\#$1}^2-4 \text{$\#$1}+1\&,2\right]\right)}","\frac{1}{3} \tanh ^{-1}\left(\frac{(x-1) \sqrt{x^4+2 x^3+3 x^2-4 x+1}}{x^3}\right)+\tanh ^{-1}\left(\frac{\sqrt{x^4+2 x^3+3 x^2-4 x+1}+2 x-1}{x^2}\right)",1,"((-1)^(1/4)*(x - Root[1 - 4*#1 + 3*#1^2 + 2*#1^3 + #1^4 & , 2, 0])^2*Sqrt[((-1 + 2*(-3)^(1/4) - I*Sqrt[3] - 2*x)*(1 + 2*(-3)^(1/4) + I*Sqrt[3] + 2*x)*(-I + (2*I)*(-3)^(1/4) + Sqrt[3] - (2*I)*Root[1 - 4*#1 + 3*#1^2 + 2*#1^3 + #1^4 & , 2, 0])*(1 + 2*(-3)^(1/4) + I*Sqrt[3] + 2*Root[1 - 4*#1 + 3*#1^2 + 2*#1^3 + #1^4 & , 2, 0]))/(x - Root[1 - 4*#1 + 3*#1^2 + 2*#1^3 + #1^4 & , 2, 0])^2]*(-2*EllipticF[ArcSin[Sqrt[((-1)^(3/4)*(1/2 + (-3)^(1/4) + (I/2)*Sqrt[3] + x)*(1/2 - (-3)^(1/4) + (I/2)*Sqrt[3] + Root[1 - 4*#1 + 3*#1^2 + 2*#1^3 + #1^4 & , 2, 0]))/(x - Root[1 - 4*#1 + 3*#1^2 + 2*#1^3 + #1^4 & , 2, 0])]/(Sqrt[2]*3^(1/8))], (2*(-3)^(1/4)*(Root[1 - 4*#1 + 3*#1^2 + 2*#1^3 + #1^4 & , 2, 0] - Root[1 - 4*#1 + 3*#1^2 + 2*#1^3 + #1^4 & , 3, 0]))/((1/2 - (-3)^(1/4) + (I/2)*Sqrt[3] + Root[1 - 4*#1 + 3*#1^2 + 2*#1^3 + #1^4 & , 2, 0])*(1/2 + (-3)^(1/4) + (I/2)*Sqrt[3] + Root[1 - 4*#1 + 3*#1^2 + 2*#1^3 + #1^4 & , 3, 0]))]*Root[1 - 4*#1 + 3*#1^2 + 2*#1^3 + #1^4 & , 2, 0] + EllipticPi[(4*(-3)^(1/4))/(-1 + 2*(-3)^(1/4) - I*Sqrt[3] - 2*Root[1 - 4*#1 + 3*#1^2 + 2*#1^3 + #1^4 & , 2, 0]), ArcSin[Sqrt[((-1)^(3/4)*(1/2 + (-3)^(1/4) + (I/2)*Sqrt[3] + x)*(1/2 - (-3)^(1/4) + (I/2)*Sqrt[3] + Root[1 - 4*#1 + 3*#1^2 + 2*#1^3 + #1^4 & , 2, 0]))/(x - Root[1 - 4*#1 + 3*#1^2 + 2*#1^3 + #1^4 & , 2, 0])]/(Sqrt[2]*3^(1/8))], (2*(-3)^(1/4)*(Root[1 - 4*#1 + 3*#1^2 + 2*#1^3 + #1^4 & , 2, 0] - Root[1 - 4*#1 + 3*#1^2 + 2*#1^3 + #1^4 & , 3, 0]))/((1/2 - (-3)^(1/4) + (I/2)*Sqrt[3] + Root[1 - 4*#1 + 3*#1^2 + 2*#1^3 + #1^4 & , 2, 0])*(1/2 + (-3)^(1/4) + (I/2)*Sqrt[3] + Root[1 - 4*#1 + 3*#1^2 + 2*#1^3 + #1^4 & , 3, 0]))]*(1 + 2*(-3)^(1/4) + I*Sqrt[3] + 2*Root[1 - 4*#1 + 3*#1^2 + 2*#1^3 + #1^4 & , 2, 0]))*Sqrt[((1 + 2*(-3)^(1/4) + I*Sqrt[3] + 2*Root[1 - 4*#1 + 3*#1^2 + 2*#1^3 + #1^4 & , 2, 0])*(x - Root[1 - 4*#1 + 3*#1^2 + 2*#1^3 + #1^4 & , 3, 0]))/((x - Root[1 - 4*#1 + 3*#1^2 + 2*#1^3 + #1^4 & , 2, 0])*(1 + 2*(-3)^(1/4) + I*Sqrt[3] + 2*Root[1 - 4*#1 + 3*#1^2 + 2*#1^3 + #1^4 & , 3, 0]))])/(Sqrt[1 - 4*x + 3*x^2 + 2*x^3 + x^4]*(-1 + 2*(-3)^(1/4) - I*Sqrt[3] - 2*Root[1 - 4*#1 + 3*#1^2 + 2*#1^3 + #1^4 & , 2, 0])*(1 + 2*(-3)^(1/4) + I*Sqrt[3] + 2*Root[1 - 4*#1 + 3*#1^2 + 2*#1^3 + #1^4 & , 2, 0]))","C",0
881,1,119,67,0.2481729,"\int \frac{3-3 x^2+2 x^4}{\sqrt[4]{-1+x^2} \left(2-3 x^2+x^4\right)} \, dx","Integrate[(3 - 3*x^2 + 2*x^4)/((-1 + x^2)^(1/4)*(2 - 3*x^2 + x^4)),x]","\frac{2 x \left(\frac{15 F_1\left(\frac{1}{2};\frac{1}{4},1;\frac{3}{2};x^2,\frac{x^2}{2}\right)}{\left(x^2-2\right) \left(x^2 \left(2 F_1\left(\frac{3}{2};\frac{1}{4},2;\frac{5}{2};x^2,\frac{x^2}{2}\right)+F_1\left(\frac{3}{2};\frac{5}{4},1;\frac{5}{2};x^2,\frac{x^2}{2}\right)\right)+6 F_1\left(\frac{1}{2};\frac{1}{4},1;\frac{3}{2};x^2,\frac{x^2}{2}\right)\right)}+2\right)}{\sqrt[4]{x^2-1}}","\frac{4 x}{\sqrt[4]{x^2-1}}+\frac{5 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{x^2-1}}{x}\right)}{2 \sqrt{2}}-\frac{5 \tanh ^{-1}\left(\frac{x}{\sqrt{2} \sqrt[4]{x^2-1}}\right)}{2 \sqrt{2}}",1,"(2*x*(2 + (15*AppellF1[1/2, 1/4, 1, 3/2, x^2, x^2/2])/((-2 + x^2)*(6*AppellF1[1/2, 1/4, 1, 3/2, x^2, x^2/2] + x^2*(2*AppellF1[3/2, 1/4, 2, 5/2, x^2, x^2/2] + AppellF1[3/2, 5/4, 1, 5/2, x^2, x^2/2])))))/(-1 + x^2)^(1/4)","C",0
882,0,0,67,1.0664665,"\int \frac{x^2}{\left(-b+a x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Integrate[x^2/((-b + a*x^4)*(b*x^2 + a*x^4)^(1/4)),x]","\int \frac{x^2}{\left(-b+a x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","-\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2-a b\&,\frac{\log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1} a-\text{$\#$1}^5}\&\right]",1,"Integrate[x^2/((-b + a*x^4)*(b*x^2 + a*x^4)^(1/4)), x]","F",-1
883,0,0,67,0.6633001,"\int \frac{x^2}{\left(-b+a x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Integrate[x^2/((-b + a*x^4)*(b*x^2 + a*x^4)^(1/4)),x]","\int \frac{x^2}{\left(-b+a x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","-\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2-a b\&,\frac{\log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1} a-\text{$\#$1}^5}\&\right]",1,"Integrate[x^2/((-b + a*x^4)*(b*x^2 + a*x^4)^(1/4)), x]","F",-1
884,0,0,67,0.3462451,"\int \frac{4 b+x^3}{\left(b+x^3\right) \sqrt[4]{-b-x^3+a x^4}} \, dx","Integrate[(4*b + x^3)/((b + x^3)*(-b - x^3 + a*x^4)^(1/4)),x]","\int \frac{4 b+x^3}{\left(b+x^3\right) \sqrt[4]{-b-x^3+a x^4}} \, dx","\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b-x^3}}\right)}{\sqrt[4]{a}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b-x^3}}\right)}{\sqrt[4]{a}}",1,"Integrate[(4*b + x^3)/((b + x^3)*(-b - x^3 + a*x^4)^(1/4)), x]","F",-1
885,0,0,67,0.5370069,"\int \frac{4 b+a x^5}{\left(-b+a x^5\right) \sqrt[4]{-b+c x^4+a x^5}} \, dx","Integrate[(4*b + a*x^5)/((-b + a*x^5)*(-b + c*x^4 + a*x^5)^(1/4)),x]","\int \frac{4 b+a x^5}{\left(-b+a x^5\right) \sqrt[4]{-b+c x^4+a x^5}} \, dx","-\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a x^5-b+c x^4}}\right)}{\sqrt[4]{c}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a x^5-b+c x^4}}\right)}{\sqrt[4]{c}}",1,"Integrate[(4*b + a*x^5)/((-b + a*x^5)*(-b + c*x^4 + a*x^5)^(1/4)), x]","F",-1
886,0,0,67,0.3059466,"\int \frac{\sqrt{1+x^2-2 x^6} \left(1+4 x^6\right)}{\left(-1-4 x^2+2 x^6\right) \left(-1-2 x^2+2 x^6\right)} \, dx","Integrate[(Sqrt[1 + x^2 - 2*x^6]*(1 + 4*x^6))/((-1 - 4*x^2 + 2*x^6)*(-1 - 2*x^2 + 2*x^6)),x]","\int \frac{\sqrt{1+x^2-2 x^6} \left(1+4 x^6\right)}{\left(-1-4 x^2+2 x^6\right) \left(-1-2 x^2+2 x^6\right)} \, dx","-\frac{1}{2} \tan ^{-1}\left(\frac{x}{\sqrt{-2 x^6+x^2+1}}\right)-\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x \sqrt{-2 x^6+x^2+1}}{2 x^6-x^2-1}\right)",1,"Integrate[(Sqrt[1 + x^2 - 2*x^6]*(1 + 4*x^6))/((-1 - 4*x^2 + 2*x^6)*(-1 - 2*x^2 + 2*x^6)), x]","F",-1
887,1,91,67,0.1771682,"\int \frac{x^4}{\sqrt[4]{-1+x^4} \left(-1+x^8\right)} \, dx","Integrate[x^4/((-1 + x^4)^(1/4)*(-1 + x^8)),x]","\frac{-\log \left(1-\frac{\sqrt[4]{2} x}{\sqrt[4]{1-x^4}}\right)+\log \left(\frac{\sqrt[4]{2} x}{\sqrt[4]{1-x^4}}+1\right)+2 \tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{1-x^4}}\right)}{8 \sqrt[4]{2}}-\frac{x}{2 \sqrt[4]{x^4-1}}","-\frac{x}{2 \sqrt[4]{x^4-1}}+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-1}}\right)}{4 \sqrt[4]{2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-1}}\right)}{4 \sqrt[4]{2}}",1,"-1/2*x/(-1 + x^4)^(1/4) + (2*ArcTan[(2^(1/4)*x)/(1 - x^4)^(1/4)] - Log[1 - (2^(1/4)*x)/(1 - x^4)^(1/4)] + Log[1 + (2^(1/4)*x)/(1 - x^4)^(1/4)])/(8*2^(1/4))","A",0
888,1,85,67,0.248303,"\int \frac{1}{\sqrt[4]{1+x^4} \left(-1+x^8\right)} \, dx","Integrate[1/((1 + x^4)^(1/4)*(-1 + x^8)),x]","-\frac{x}{2 \sqrt[4]{x^4+1}}-\frac{-\log \left(1-\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+1}}\right)+\log \left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+1}}+1\right)+2 \tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+1}}\right)}{8 \sqrt[4]{2}}","-\frac{x}{2 \sqrt[4]{x^4+1}}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+1}}\right)}{4 \sqrt[4]{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+1}}\right)}{4 \sqrt[4]{2}}",1,"-1/2*x/(1 + x^4)^(1/4) - (2*ArcTan[(2^(1/4)*x)/(1 + x^4)^(1/4)] - Log[1 - (2^(1/4)*x)/(1 + x^4)^(1/4)] + Log[1 + (2^(1/4)*x)/(1 + x^4)^(1/4)])/(8*2^(1/4))","A",1
889,1,91,67,0.1957033,"\int \frac{-1+2 x^4}{\sqrt[4]{-1+x^4} \left(-1+x^8\right)} \, dx","Integrate[(-1 + 2*x^4)/((-1 + x^4)^(1/4)*(-1 + x^8)),x]","\frac{3 \left(-\log \left(1-\frac{\sqrt[4]{2} x}{\sqrt[4]{1-x^4}}\right)+\log \left(\frac{\sqrt[4]{2} x}{\sqrt[4]{1-x^4}}+1\right)+2 \tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{1-x^4}}\right)\right)}{8 \sqrt[4]{2}}-\frac{x}{2 \sqrt[4]{x^4-1}}","-\frac{x}{2 \sqrt[4]{x^4-1}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-1}}\right)}{4 \sqrt[4]{2}}+\frac{3 \tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-1}}\right)}{4 \sqrt[4]{2}}",1,"-1/2*x/(-1 + x^4)^(1/4) + (3*(2*ArcTan[(2^(1/4)*x)/(1 - x^4)^(1/4)] - Log[1 - (2^(1/4)*x)/(1 - x^4)^(1/4)] + Log[1 + (2^(1/4)*x)/(1 - x^4)^(1/4)]))/(8*2^(1/4))","A",0
890,1,119,67,0.2845087,"\int \frac{1+x^8}{\sqrt{1+x^4} \left(-1+x^8\right)} \, dx","Integrate[(1 + x^8)/(Sqrt[1 + x^4]*(-1 + x^8)),x]","\frac{x \left(\frac{5 \left(x^4+1\right) F_1\left(\frac{1}{4};-\frac{1}{2},1;\frac{5}{4};-x^4,x^4\right)}{\left(x^4-1\right) \left(2 x^4 \left(2 F_1\left(\frac{5}{4};-\frac{1}{2},2;\frac{9}{4};-x^4,x^4\right)+F_1\left(\frac{5}{4};\frac{1}{2},1;\frac{9}{4};-x^4,x^4\right)\right)+5 F_1\left(\frac{1}{4};-\frac{1}{2},1;\frac{5}{4};-x^4,x^4\right)\right)}-1\right)}{2 \sqrt{x^4+1}}","-\frac{x}{2 \sqrt{x^4+1}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{4 \sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{4 \sqrt{2}}",1,"(x*(-1 + (5*(1 + x^4)*AppellF1[1/4, -1/2, 1, 5/4, -x^4, x^4])/((-1 + x^4)*(5*AppellF1[1/4, -1/2, 1, 5/4, -x^4, x^4] + 2*x^4*(2*AppellF1[5/4, -1/2, 2, 9/4, -x^4, x^4] + AppellF1[5/4, 1/2, 1, 9/4, -x^4, x^4])))))/(2*Sqrt[1 + x^4])","C",0
891,1,175,67,0.8051546,"\int \frac{-1+x^{12}}{\sqrt{1+x^4} \left(1+x^{12}\right)} \, dx","Integrate[(-1 + x^12)/(Sqrt[1 + x^4]*(1 + x^12)),x]","\frac{1}{3} \left(-\frac{(-1)^{2/3} x}{\sqrt{x^4+1}}+\frac{\sqrt[3]{-1} x}{\sqrt{x^4+1}}-\frac{2 x}{\sqrt{x^4+1}}-2 \sqrt[4]{-1} F\left(\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+\sqrt[4]{-1} \Pi \left(-\sqrt[3]{-1};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+\sqrt[4]{-1} \Pi \left(\sqrt[3]{-1};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+\sqrt[4]{-1} \Pi \left(-(-1)^{2/3};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+\sqrt[4]{-1} \Pi \left((-1)^{2/3};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)\right)","-\frac{x}{3 \sqrt{x^4+1}}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{3} x}{\sqrt{x^4+1}}\right)}{3 \sqrt[4]{3}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{3} x}{\sqrt{x^4+1}}\right)}{3 \sqrt[4]{3}}",1,"((-2*x)/Sqrt[1 + x^4] + ((-1)^(1/3)*x)/Sqrt[1 + x^4] - ((-1)^(2/3)*x)/Sqrt[1 + x^4] - 2*(-1)^(1/4)*EllipticF[I*ArcSinh[(-1)^(1/4)*x], -1] + (-1)^(1/4)*EllipticPi[-(-1)^(1/3), I*ArcSinh[(-1)^(1/4)*x], -1] + (-1)^(1/4)*EllipticPi[(-1)^(1/3), I*ArcSinh[(-1)^(1/4)*x], -1] + (-1)^(1/4)*EllipticPi[-(-1)^(2/3), I*ArcSinh[(-1)^(1/4)*x], -1] + (-1)^(1/4)*EllipticPi[(-1)^(2/3), I*ArcSinh[(-1)^(1/4)*x], -1])/3","C",1
892,1,350,67,1.3211258,"\int \frac{-1+x^2}{\sqrt{1+x^2} \sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[(-1 + x^2)/(Sqrt[1 + x^2]*Sqrt[x + Sqrt[1 + x^2]]),x]","\frac{2 \left(x^2+1\right) \left(81920 x^{18}+757760 x^{16}+2336768 x^{14}+3539200 x^{12}+2978432 x^{10}+1435488 x^8+384048 x^6+51357 x^4+2660 x^2+349 \sqrt{x^2+1} x+81920 \sqrt{x^2+1} x^{17}+716800 \sqrt{x^2+1} x^{15}+1988608 \sqrt{x^2+1} x^{13}+2629376 \sqrt{x^2+1} x^{11}+1870720 \sqrt{x^2+1} x^9+730272 \sqrt{x^2+1} x^7+148176 \sqrt{x^2+1} x^5+13347 \sqrt{x^2+1} x^3+23\right)}{15 \left(\sqrt{x^2+1}+x\right)^{5/2} \left(x^2+\sqrt{x^2+1} x+1\right) \left(16 x^6+28 x^4+13 x^2+5 \sqrt{x^2+1} x+16 \sqrt{x^2+1} x^5+20 \sqrt{x^2+1} x^3+1\right) \left(64 x^8+144 x^6+104 x^4+25 x^2+7 \sqrt{x^2+1} x+64 \sqrt{x^2+1} x^7+112 \sqrt{x^2+1} x^5+56 \sqrt{x^2+1} x^3+1\right)}","\frac{2 \left(10 x^4+55 x^2+23\right)}{15 \left(\sqrt{x^2+1}+x\right)^{5/2}}+\frac{4 \sqrt{x^2+1} \left(x^3+5 x\right)}{3 \left(\sqrt{x^2+1}+x\right)^{5/2}}",1,"(2*(1 + x^2)*(23 + 2660*x^2 + 51357*x^4 + 384048*x^6 + 1435488*x^8 + 2978432*x^10 + 3539200*x^12 + 2336768*x^14 + 757760*x^16 + 81920*x^18 + 349*x*Sqrt[1 + x^2] + 13347*x^3*Sqrt[1 + x^2] + 148176*x^5*Sqrt[1 + x^2] + 730272*x^7*Sqrt[1 + x^2] + 1870720*x^9*Sqrt[1 + x^2] + 2629376*x^11*Sqrt[1 + x^2] + 1988608*x^13*Sqrt[1 + x^2] + 716800*x^15*Sqrt[1 + x^2] + 81920*x^17*Sqrt[1 + x^2]))/(15*(x + Sqrt[1 + x^2])^(5/2)*(1 + x^2 + x*Sqrt[1 + x^2])*(1 + 13*x^2 + 28*x^4 + 16*x^6 + 5*x*Sqrt[1 + x^2] + 20*x^3*Sqrt[1 + x^2] + 16*x^5*Sqrt[1 + x^2])*(1 + 25*x^2 + 104*x^4 + 144*x^6 + 64*x^8 + 7*x*Sqrt[1 + x^2] + 56*x^3*Sqrt[1 + x^2] + 112*x^5*Sqrt[1 + x^2] + 64*x^7*Sqrt[1 + x^2]))","B",1
893,1,51,67,0.026899,"\int \frac{\sqrt{1+x^2}}{\sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[Sqrt[1 + x^2]/Sqrt[x + Sqrt[1 + x^2]],x]","\frac{5 \left(\sqrt{x^2+1}+x\right)^4-30 \left(\sqrt{x^2+1}+x\right)^2-3}{30 \left(\sqrt{x^2+1}+x\right)^{5/2}}","\frac{2 \left(10 x^4-5 x^2-7\right)}{15 \left(\sqrt{x^2+1}+x\right)^{5/2}}+\frac{4 \sqrt{x^2+1} \left(x^3-x\right)}{3 \left(\sqrt{x^2+1}+x\right)^{5/2}}",1,"(-3 - 30*(x + Sqrt[1 + x^2])^2 + 5*(x + Sqrt[1 + x^2])^4)/(30*(x + Sqrt[1 + x^2])^(5/2))","A",1
894,1,102,68,0.0786386,"\int \frac{1}{\left(-b+a^3 x^2\right) \sqrt[3]{-b x^2+a^3 x^3}} \, dx","Integrate[1/((-b + a^3*x^2)*(-(b*x^2) + a^3*x^3)^(1/3)),x]","-\frac{3 x \left(\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a^{3/2} \left(a^{3/2}-\sqrt{b}\right) x}{a^3 x-b}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a^{3/2} \left(a^{3/2}+\sqrt{b}\right) x}{a^3 x-b}\right)\right)}{2 b \sqrt[3]{x^2 \left(a^3 x-b\right)}}","\frac{\text{RootSum}\left[\text{$\#$1}^6-2 \text{$\#$1}^3 a^3+a^6-a^3 b\&,\frac{\log \left(\sqrt[3]{a^3 x^3-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{2 b}",1,"(-3*x*(Hypergeometric2F1[1/3, 1, 4/3, (a^(3/2)*(a^(3/2) - Sqrt[b])*x)/(-b + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a^(3/2)*(a^(3/2) + Sqrt[b])*x)/(-b + a^3*x)]))/(2*b*(x^2*(-b + a^3*x))^(1/3))","A",1
895,1,102,68,0.0280879,"\int \frac{1}{\left(-b+a^3 x^2\right) \sqrt[3]{-b x^2+a^3 x^3}} \, dx","Integrate[1/((-b + a^3*x^2)*(-(b*x^2) + a^3*x^3)^(1/3)),x]","-\frac{3 x \left(\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a^{3/2} \left(a^{3/2}-\sqrt{b}\right) x}{a^3 x-b}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a^{3/2} \left(a^{3/2}+\sqrt{b}\right) x}{a^3 x-b}\right)\right)}{2 b \sqrt[3]{x^2 \left(a^3 x-b\right)}}","\frac{\text{RootSum}\left[\text{$\#$1}^6-2 \text{$\#$1}^3 a^3+a^6-a^3 b\&,\frac{\log \left(\sqrt[3]{a^3 x^3-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{2 b}",1,"(-3*x*(Hypergeometric2F1[1/3, 1, 4/3, (a^(3/2)*(a^(3/2) - Sqrt[b])*x)/(-b + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a^(3/2)*(a^(3/2) + Sqrt[b])*x)/(-b + a^3*x)]))/(2*b*(x^2*(-b + a^3*x))^(1/3))","A",1
896,1,103,68,0.0845615,"\int \frac{1}{\left(b+a x^2\right) \sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Integrate[1/((b + a*x^2)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","\frac{3 x \left(\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(a^3-\sqrt{-a} b^{3/2}\right) x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(a^3+\sqrt{-a} b^{3/2}\right) x}{x a^3+b^2}\right)\right)}{2 b \sqrt[3]{x^2 \left(a^3 x+b^2\right)}}","-\frac{\text{RootSum}\left[\text{$\#$1}^6-2 \text{$\#$1}^3 a^3+a^6+a b^3\&,\frac{\log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{2 b}",1,"(3*x*(Hypergeometric2F1[1/3, 1, 4/3, ((a^3 - Sqrt[-a]*b^(3/2))*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, ((a^3 + Sqrt[-a]*b^(3/2))*x)/(b^2 + a^3*x)]))/(2*b*(x^2*(b^2 + a^3*x))^(1/3))","A",1
897,1,103,68,0.0306948,"\int \frac{1}{\left(b+a x^2\right) \sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Integrate[1/((b + a*x^2)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","\frac{3 x \left(\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(a^3-\sqrt{-a} b^{3/2}\right) x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(a^3+\sqrt{-a} b^{3/2}\right) x}{x a^3+b^2}\right)\right)}{2 b \sqrt[3]{x^2 \left(a^3 x+b^2\right)}}","-\frac{\text{RootSum}\left[\text{$\#$1}^6-2 \text{$\#$1}^3 a^3+a^6+a b^3\&,\frac{\log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{2 b}",1,"(3*x*(Hypergeometric2F1[1/3, 1, 4/3, ((a^3 - Sqrt[-a]*b^(3/2))*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, ((a^3 + Sqrt[-a]*b^(3/2))*x)/(b^2 + a^3*x)]))/(2*b*(x^2*(b^2 + a^3*x))^(1/3))","A",1
898,1,69,68,0.027269,"\int x^7 \sqrt[4]{-x+x^4} \, dx","Integrate[x^7*(-x + x^4)^(1/4),x]","\frac{x^2 \sqrt[4]{x \left(x^3-1\right)} \left(7 \, _2F_1\left(-\frac{1}{4},\frac{3}{4};\frac{7}{4};x^3\right)+\sqrt[4]{1-x^3} \left(8 x^6-x^3-7\right)\right)}{72 \sqrt[4]{1-x^3}}","\frac{7}{192} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x}}\right)-\frac{7}{192} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x}}\right)+\frac{1}{288} \sqrt[4]{x^4-x} \left(32 x^8-4 x^5-7 x^2\right)",1,"(x^2*(x*(-1 + x^3))^(1/4)*((1 - x^3)^(1/4)*(-7 - x^3 + 8*x^6) + 7*Hypergeometric2F1[-1/4, 3/4, 7/4, x^3]))/(72*(1 - x^3)^(1/4))","C",1
899,0,0,68,4.9392082,"\int \frac{\left(2+x^2\right) \sqrt[4]{-1-x^2+x^4} \left(1+x^2+x^4\right)}{x^6 \left(1+x^2\right)} \, dx","Integrate[((2 + x^2)*(-1 - x^2 + x^4)^(1/4)*(1 + x^2 + x^4))/(x^6*(1 + x^2)),x]","\int \frac{\left(2+x^2\right) \sqrt[4]{-1-x^2+x^4} \left(1+x^2+x^4\right)}{x^6 \left(1+x^2\right)} \, dx","-\tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^2-1}}\right)+\tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^2-1}}\right)-\frac{2 \sqrt[4]{x^4-x^2-1} \left(4 x^4+x^2+1\right)}{5 x^5}",1,"Integrate[((2 + x^2)*(-1 - x^2 + x^4)^(1/4)*(1 + x^2 + x^4))/(x^6*(1 + x^2)), x]","F",-1
900,1,42,68,0.01866,"\int \frac{\sqrt[4]{x^3+x^4}}{x^2 \left(-1+x^2\right)} \, dx","Integrate[(x^3 + x^4)^(1/4)/(x^2*(-1 + x^2)),x]","-\frac{4 x^2 \left(x \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{2 x}{x+1}\right)-3 (x+1)\right)}{3 \left(x^3 (x+1)\right)^{3/4}}","\frac{4 \sqrt[4]{x^4+x^3}}{x}+\sqrt[4]{2} \tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+x^3}}\right)-\sqrt[4]{2} \tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+x^3}}\right)",1,"(-4*x^2*(-3*(1 + x) + x*Hypergeometric2F1[3/4, 1, 7/4, (2*x)/(1 + x)]))/(3*(x^3*(1 + x))^(3/4))","C",1
901,1,68,68,0.0371427,"\int \frac{b+2 a x^4}{x^2 \left(b+a x^4\right)^{3/4}} \, dx","Integrate[(b + 2*a*x^4)/(x^2*(b + a*x^4)^(3/4)),x]","-\frac{\sqrt[4]{a x^4+b}}{x}-\sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)+\sqrt[4]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)","-\frac{\sqrt[4]{a x^4+b}}{x}-\sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)+\sqrt[4]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)",1,"-((b + a*x^4)^(1/4)/x) - a^(1/4)*ArcTan[(a^(1/4)*x)/(b + a*x^4)^(1/4)] + a^(1/4)*ArcTanh[(a^(1/4)*x)/(b + a*x^4)^(1/4)]","A",1
902,0,0,68,0.7301191,"\int \frac{\left(1+x^2\right) \sqrt[4]{x^2+x^6}}{x^2 \left(-1+x^2\right)} \, dx","Integrate[((1 + x^2)*(x^2 + x^6)^(1/4))/(x^2*(-1 + x^2)),x]","\int \frac{\left(1+x^2\right) \sqrt[4]{x^2+x^6}}{x^2 \left(-1+x^2\right)} \, dx","\frac{2 \sqrt[4]{x^6+x^2}}{x}+\sqrt[4]{2} \tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^6+x^2}}\right)-\sqrt[4]{2} \tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^6+x^2}}\right)",1,"Integrate[((1 + x^2)*(x^2 + x^6)^(1/4))/(x^2*(-1 + x^2)), x]","F",-1
903,1,146,68,0.1846494,"\int \frac{\sqrt{-1+x^3} \left(1-x^3+x^6\right)}{x^{10} \left(2+x^3\right)} \, dx","Integrate[(Sqrt[-1 + x^3]*(1 - x^3 + x^6))/(x^10*(2 + x^3)),x]","\frac{-12 \left(x^3-1\right)^2 \, _2F_1\left(\frac{3}{2},3;\frac{5}{2};1-x^3\right)+8 \left(x^3-1\right)^2 \, _2F_1\left(\frac{3}{2},4;\frac{5}{2};1-x^3\right)+21 \left(\frac{1}{x^3}+\sqrt{x^3-1} \tan ^{-1}\left(\sqrt{x^3-1}\right)-\sqrt{3} \sqrt{x^3-1} \tan ^{-1}\left(\frac{\sqrt{x^3-1}}{\sqrt{3}}\right)-\sqrt{1-x^3} \tanh ^{-1}\left(\sqrt{1-x^3}\right)-1\right)}{72 \sqrt{x^3-1}}","\frac{13}{24} \tan ^{-1}\left(\sqrt{x^3-1}\right)-\frac{7 \tan ^{-1}\left(\frac{\sqrt{x^3-1}}{\sqrt{3}}\right)}{8 \sqrt{3}}+\frac{\sqrt{x^3-1} \left(-12 x^6+5 x^3-2\right)}{36 x^9}",1,"(21*(-1 + x^(-3) + Sqrt[-1 + x^3]*ArcTan[Sqrt[-1 + x^3]] - Sqrt[3]*Sqrt[-1 + x^3]*ArcTan[Sqrt[-1 + x^3]/Sqrt[3]] - Sqrt[1 - x^3]*ArcTanh[Sqrt[1 - x^3]]) - 12*(-1 + x^3)^2*Hypergeometric2F1[3/2, 3, 5/2, 1 - x^3] + 8*(-1 + x^3)^2*Hypergeometric2F1[3/2, 4, 5/2, 1 - x^3])/(72*Sqrt[-1 + x^3])","C",1
904,1,107,68,0.4714073,"\int \frac{\sqrt{x^2+x \sqrt{x+x^2}}}{x \sqrt{x+x^2}} \, dx","Integrate[Sqrt[x^2 + x*Sqrt[x + x^2]]/(x*Sqrt[x + x^2]),x]","\frac{2 \sqrt{2} (x+1) \sqrt{x \left(x+\sqrt{x (x+1)}\right)} \sqrt{2 x+2 \sqrt{x (x+1)}+1} \sinh ^{-1}\left(\sqrt{2} \sqrt{x+\sqrt{x (x+1)}}\right)}{\sqrt{x (x+1)} \sqrt{x+\sqrt{x (x+1)}} \left(x+\sqrt{x (x+1)}+1\right)}","\frac{2 \sqrt{2} \sqrt{\sqrt{x^2+x}-x} \sqrt{x \left(\sqrt{x^2+x}+x\right)} \tanh ^{-1}\left(\sqrt{2} \sqrt{\sqrt{x^2+x}-x}\right)}{x}",1,"(2*Sqrt[2]*(1 + x)*Sqrt[x*(x + Sqrt[x*(1 + x)])]*Sqrt[1 + 2*x + 2*Sqrt[x*(1 + x)]]*ArcSinh[Sqrt[2]*Sqrt[x + Sqrt[x*(1 + x)]]])/(Sqrt[x*(1 + x)]*Sqrt[x + Sqrt[x*(1 + x)]]*(1 + x + Sqrt[x*(1 + x)]))","A",1
905,1,102,69,0.0776944,"\int \frac{1}{\left(-b+a x^2\right) \sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Integrate[1/((-b + a*x^2)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","-\frac{3 x \left(\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a^3 x-\sqrt{a} b^{3/2} x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\sqrt{a} \left(a^{5/2}+b^{3/2}\right) x}{x a^3+b^2}\right)\right)}{2 b \sqrt[3]{x^2 \left(a^3 x+b^2\right)}}","\frac{\text{RootSum}\left[\text{$\#$1}^6-2 \text{$\#$1}^3 a^3+a^6-a b^3\&,\frac{\log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{2 b}",1,"(-3*x*(Hypergeometric2F1[1/3, 1, 4/3, (Sqrt[a]*(a^(5/2) + b^(3/2))*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a^3*x - Sqrt[a]*b^(3/2)*x)/(b^2 + a^3*x)]))/(2*b*(x^2*(b^2 + a^3*x))^(1/3))","A",1
906,1,102,69,0.0298155,"\int \frac{1}{\left(-b+a x^2\right) \sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Integrate[1/((-b + a*x^2)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","-\frac{3 x \left(\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a^3 x-\sqrt{a} b^{3/2} x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\sqrt{a} \left(a^{5/2}+b^{3/2}\right) x}{x a^3+b^2}\right)\right)}{2 b \sqrt[3]{x^2 \left(a^3 x+b^2\right)}}","\frac{\text{RootSum}\left[\text{$\#$1}^6-2 \text{$\#$1}^3 a^3+a^6-a b^3\&,\frac{\log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{2 b}",1,"(-3*x*(Hypergeometric2F1[1/3, 1, 4/3, (Sqrt[a]*(a^(5/2) + b^(3/2))*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a^3*x - Sqrt[a]*b^(3/2)*x)/(b^2 + a^3*x)]))/(2*b*(x^2*(b^2 + a^3*x))^(1/3))","A",1
907,1,4112,69,9.7194731,"\int \frac{(-a+x) (-b+x) \left(3 a b-2 (a+b) x+x^2\right)}{x^2 \sqrt{x (-a+x) (-b+x)} \left(-a b+(a+b) x-x^2+d x^3\right)} \, dx","Integrate[((-a + x)*(-b + x)*(3*a*b - 2*(a + b)*x + x^2))/(x^2*Sqrt[x*(-a + x)*(-b + x)]*(-(a*b) + (a + b)*x - x^2 + d*x^3)),x]","\text{Result too large to show}","\frac{2 \sqrt{x^2 (-a-b)+a b x+x^3}}{x^2}-2 \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{x^2 (-a-b)+a b x+x^3}}{\sqrt{d} x^2}\right)",1,"(2*Sqrt[x*(-a + x)*(-b + x)]*(1 - (I*x*Sqrt[(-b + x)/(a - b)]*(3*a^6*d^2*EllipticF[I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)] - a^3*(-1 + 3*a*d)*(-a + b + 3*a^2*d)*EllipticF[I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)] + a^3*(-a + b + 3*a^2*d)*(-1 + 2*a*d + 2*b*d)*(EllipticPi[a/Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 1], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)] - EllipticPi[a/Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 2], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)]) + a^3*(-1 + 3*a*d)*(b + 4*a^2*d + a*(-1 + b*d))*(EllipticPi[a/Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 2], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)] - EllipticPi[a/Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 3], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)]) - 3*a^5*(2*a - b)*d^2*EllipticPi[a/Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 3], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)] + a^2*(2*a - b)*(-1 + 3*a*d)*(-a + b + 3*a^2*d)*EllipticPi[a/Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 3], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)] - 2*a^2*(2*a - b)*d^2*EllipticPi[a/Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 3], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)]*Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 1]*Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 2]^2 - a^2*(2*a - b)*d^2*(EllipticPi[a/Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 2], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)] + EllipticPi[a/Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 3], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)])*Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 1]^2*Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 3] + a^2*(2*a - b)*d^2*(EllipticPi[a/Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 1], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)] - EllipticPi[a/Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 3], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)])*Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 2]^2*Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 3] - d*(b + 4*a^2*d + a*(-1 + b*d))*(EllipticPi[a/Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 1], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)] + EllipticPi[a/Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 2], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)] - 2*EllipticPi[a/Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 3], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)])*Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 1]*Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 2]^2*Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 3] + 2*d^2*EllipticF[I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)]*Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 1]^2*Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 2]^3*Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 3] + a^2*(2*a - b)*d^2*(EllipticPi[a/Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 2], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)] - EllipticPi[a/Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 3], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)])*Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 1]*Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 3]^2 - a^2*(2*a - b)*d^2*(EllipticPi[a/Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 1], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)] + EllipticPi[a/Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 3], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)])*Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 2]*Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 3]^2 + d*(b + 4*a^2*d + a*(-1 + b*d))*(EllipticPi[a/Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 1], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)] - 2*EllipticPi[a/Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 2], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)] + EllipticPi[a/Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 3], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)])*Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 1]*Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 2]*Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 3]^2 - d*(-1 + 2*a*d + 2*b*d)*(2*EllipticPi[a/Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 1], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)] - EllipticPi[a/Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 2], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)] - EllipticPi[a/Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 3], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)])*Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 1]^2*Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 2]*Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 3]^2 + 2*d^2*EllipticF[I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)]*Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 1]^3*Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 2]*Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 3]^2 - d*(-1 + 2*a*d + 2*b*d)*(EllipticPi[a/Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 1], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)] - 2*EllipticPi[a/Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 2], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)] + EllipticPi[a/Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 3], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)])*Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 1]*Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 2]^2*Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 3]^2 + 2*d^2*EllipticF[I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)]*Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 1]*Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 2]^2*Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 3]^3))/(d^2*Sqrt[1 - a/x]*(b - x)*Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 1]*(Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 1] - Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 2])*Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 2]*(Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 1] - Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 3])*(Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 2] - Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 3])*Root[-(a^3*d) + (-a + b + 3*a^2*d)*#1 + (1 - 3*a*d)*#1^2 + d*#1^3 & , 3])))/x^2","C",0
908,1,58,69,0.0126327,"\int \frac{1}{\left(1+x^3\right) \sqrt[4]{-x+x^4}} \, dx","Integrate[1/((1 + x^3)*(-x + x^4)^(1/4)),x]","\frac{4 x \sqrt[4]{1-x^3} \, _2F_1\left(\frac{1}{4},\frac{1}{4};\frac{5}{4};\frac{2 x^3}{x^3+1}\right)}{3 \sqrt[4]{x \left(x^3-1\right)} \sqrt[4]{x^3+1}}","\frac{1}{3} 2^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \left(x^4-x\right)^{3/4}}{x^3-1}\right)+\frac{1}{3} 2^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \left(x^4-x\right)^{3/4}}{x^3-1}\right)",1,"(4*x*(1 - x^3)^(1/4)*Hypergeometric2F1[1/4, 1/4, 5/4, (2*x^3)/(1 + x^3)])/(3*(x*(-1 + x^3))^(1/4)*(1 + x^3)^(1/4))","C",0
909,1,77,69,0.0394501,"\int \frac{x \sqrt{-x^2+x^4}}{-3+2 x^2} \, dx","Integrate[(x*Sqrt[-x^2 + x^4])/(-3 + 2*x^2),x]","\frac{x \sqrt{x^2-1} \left(\sqrt{x^2-1} x+2 \log \left(\sqrt{x^2-1}+x\right)-\sqrt{3} \tanh ^{-1}\left(\frac{x}{\sqrt{3} \sqrt{x^2-1}}\right)\right)}{4 \sqrt{x^2 \left(x^2-1\right)}}","\frac{1}{4} \sqrt{x^4-x^2}+\tanh ^{-1}\left(\frac{(x-1) x}{\sqrt{x^4-x^2}}\right)-\frac{1}{4} \sqrt{3} \tanh ^{-1}\left(\frac{\sqrt{3} \sqrt{x^4-x^2}}{x^2}\right)",1,"(x*Sqrt[-1 + x^2]*(x*Sqrt[-1 + x^2] - Sqrt[3]*ArcTanh[x/(Sqrt[3]*Sqrt[-1 + x^2])] + 2*Log[x + Sqrt[-1 + x^2]]))/(4*Sqrt[x^2*(-1 + x^2)])","A",1
910,1,477,69,1.8176594,"\int \frac{\left(-1+x^4\right) \left(1+x^4\right) \sqrt{-1-x^2+x^4}}{\left(-2-x^2+2 x^4\right)^2 \left(-2+x^2+2 x^4\right)} \, dx","Integrate[((-1 + x^4)*(1 + x^4)*Sqrt[-1 - x^2 + x^4])/((-2 - x^2 + 2*x^4)^2*(-2 + x^2 + 2*x^4)),x]","\frac{-2 \sqrt{1+\sqrt{5}} x^5+2 \sqrt{1+\sqrt{5}} x^3-3 i \sqrt{2} \sqrt{-x^4+x^2+1} \left(2 x^4-x^2-2\right) F\left(i \sinh ^{-1}\left(\sqrt{\frac{2}{-1+\sqrt{5}}} x\right)|\frac{1}{2} \left(-3+\sqrt{5}\right)\right)+6 i \sqrt{2} \sqrt{-x^4+x^2+1} x^4 \Pi \left(\frac{2 \left(-1+\sqrt{5}\right)}{1+\sqrt{17}};i \sinh ^{-1}\left(\sqrt{\frac{2}{-1+\sqrt{5}}} x\right)|\frac{1}{2} \left(-3+\sqrt{5}\right)\right)-3 i \sqrt{2} \sqrt{-x^4+x^2+1} x^2 \Pi \left(\frac{2 \left(-1+\sqrt{5}\right)}{1+\sqrt{17}};i \sinh ^{-1}\left(\sqrt{\frac{2}{-1+\sqrt{5}}} x\right)|\frac{1}{2} \left(-3+\sqrt{5}\right)\right)+3 i \sqrt{2} \sqrt{-x^4+x^2+1} \left(2 x^4-x^2-2\right) \Pi \left(-\frac{2 \left(-1+\sqrt{5}\right)}{-1+\sqrt{17}};i \sinh ^{-1}\left(\sqrt{\frac{2}{-1+\sqrt{5}}} x\right)|\frac{1}{2} \left(-3+\sqrt{5}\right)\right)-6 i \sqrt{2} \sqrt{-x^4+x^2+1} \Pi \left(\frac{2 \left(-1+\sqrt{5}\right)}{1+\sqrt{17}};i \sinh ^{-1}\left(\sqrt{\frac{2}{-1+\sqrt{5}}} x\right)|\frac{1}{2} \left(-3+\sqrt{5}\right)\right)+2 \sqrt{1+\sqrt{5}} x}{32 \sqrt{1+\sqrt{5}} \sqrt{x^4-x^2-1} \left(2 x^4-x^2-2\right)}","-\frac{\sqrt{x^4-x^2-1} x}{16 \left(2 x^4-x^2-2\right)}-\frac{1}{16} \sqrt{\frac{3}{2}} \tan ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt{x^4-x^2-1}}\right)",1,"(2*Sqrt[1 + Sqrt[5]]*x + 2*Sqrt[1 + Sqrt[5]]*x^3 - 2*Sqrt[1 + Sqrt[5]]*x^5 - (3*I)*Sqrt[2]*Sqrt[1 + x^2 - x^4]*(-2 - x^2 + 2*x^4)*EllipticF[I*ArcSinh[Sqrt[2/(-1 + Sqrt[5])]*x], (-3 + Sqrt[5])/2] + (3*I)*Sqrt[2]*Sqrt[1 + x^2 - x^4]*(-2 - x^2 + 2*x^4)*EllipticPi[(-2*(-1 + Sqrt[5]))/(-1 + Sqrt[17]), I*ArcSinh[Sqrt[2/(-1 + Sqrt[5])]*x], (-3 + Sqrt[5])/2] - (6*I)*Sqrt[2]*Sqrt[1 + x^2 - x^4]*EllipticPi[(2*(-1 + Sqrt[5]))/(1 + Sqrt[17]), I*ArcSinh[Sqrt[2/(-1 + Sqrt[5])]*x], (-3 + Sqrt[5])/2] - (3*I)*Sqrt[2]*x^2*Sqrt[1 + x^2 - x^4]*EllipticPi[(2*(-1 + Sqrt[5]))/(1 + Sqrt[17]), I*ArcSinh[Sqrt[2/(-1 + Sqrt[5])]*x], (-3 + Sqrt[5])/2] + (6*I)*Sqrt[2]*x^4*Sqrt[1 + x^2 - x^4]*EllipticPi[(2*(-1 + Sqrt[5]))/(1 + Sqrt[17]), I*ArcSinh[Sqrt[2/(-1 + Sqrt[5])]*x], (-3 + Sqrt[5])/2])/(32*Sqrt[1 + Sqrt[5]]*Sqrt[-1 - x^2 + x^4]*(-2 - x^2 + 2*x^4))","C",0
911,1,396,69,0.6479225,"\int \frac{b+a x^2}{\left(b+a x^2+x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Integrate[(b + a*x^2)/((b + a*x^2 + x^4)*(b*x^2 + a*x^4)^(1/4)),x]","\frac{\left(x^2 \left(a x^2+b\right)\right)^{3/4} \left(\left(a-\sqrt{a^2-4 b}\right)^{3/4} \log \left(2^{3/4} \sqrt[4]{a-\sqrt{a^2-4 b}}-2 \sqrt[4]{a+\frac{b}{x^2}}\right)-\left(\sqrt{a^2-4 b}+a\right)^{3/4} \log \left(2^{3/4} \sqrt[4]{\sqrt{a^2-4 b}+a}-2 \sqrt[4]{a+\frac{b}{x^2}}\right)-\left(a-\sqrt{a^2-4 b}\right)^{3/4} \log \left(2^{3/4} \sqrt[4]{a-\sqrt{a^2-4 b}}+2 \sqrt[4]{a+\frac{b}{x^2}}\right)+\left(\sqrt{a^2-4 b}+a\right)^{3/4} \log \left(2^{3/4} \sqrt[4]{\sqrt{a^2-4 b}+a}+2 \sqrt[4]{a+\frac{b}{x^2}}\right)+2 \left(a-\sqrt{a^2-4 b}\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a-\sqrt{a^2-4 b}}}\right)-2 \left(\sqrt{a^2-4 b}+a\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\sqrt{a^2-4 b}+a}}\right)\right)}{2\ 2^{3/4} x^3 \sqrt{a^2-4 b} \left(a+\frac{b}{x^2}\right)^{3/4}}","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4 a+b\&,\frac{\text{$\#$1}^3 \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\text{$\#$1}^3 \log (x)}{2 \text{$\#$1}^4-a}\&\right]",1,"((x^2*(b + a*x^2))^(3/4)*(2*(a - Sqrt[a^2 - 4*b])^(3/4)*ArcTan[(2^(1/4)*(a + b/x^2)^(1/4))/(a - Sqrt[a^2 - 4*b])^(1/4)] - 2*(a + Sqrt[a^2 - 4*b])^(3/4)*ArcTan[(2^(1/4)*(a + b/x^2)^(1/4))/(a + Sqrt[a^2 - 4*b])^(1/4)] + (a - Sqrt[a^2 - 4*b])^(3/4)*Log[2^(3/4)*(a - Sqrt[a^2 - 4*b])^(1/4) - 2*(a + b/x^2)^(1/4)] - (a + Sqrt[a^2 - 4*b])^(3/4)*Log[2^(3/4)*(a + Sqrt[a^2 - 4*b])^(1/4) - 2*(a + b/x^2)^(1/4)] - (a - Sqrt[a^2 - 4*b])^(3/4)*Log[2^(3/4)*(a - Sqrt[a^2 - 4*b])^(1/4) + 2*(a + b/x^2)^(1/4)] + (a + Sqrt[a^2 - 4*b])^(3/4)*Log[2^(3/4)*(a + Sqrt[a^2 - 4*b])^(1/4) + 2*(a + b/x^2)^(1/4)]))/(2*2^(3/4)*Sqrt[a^2 - 4*b]*(a + b/x^2)^(3/4)*x^3)","B",1
912,1,396,69,0.0721049,"\int \frac{b+a x^2}{\left(b+a x^2+x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Integrate[(b + a*x^2)/((b + a*x^2 + x^4)*(b*x^2 + a*x^4)^(1/4)),x]","\frac{\left(x^2 \left(a x^2+b\right)\right)^{3/4} \left(\left(a-\sqrt{a^2-4 b}\right)^{3/4} \log \left(2^{3/4} \sqrt[4]{a-\sqrt{a^2-4 b}}-2 \sqrt[4]{a+\frac{b}{x^2}}\right)-\left(\sqrt{a^2-4 b}+a\right)^{3/4} \log \left(2^{3/4} \sqrt[4]{\sqrt{a^2-4 b}+a}-2 \sqrt[4]{a+\frac{b}{x^2}}\right)-\left(a-\sqrt{a^2-4 b}\right)^{3/4} \log \left(2^{3/4} \sqrt[4]{a-\sqrt{a^2-4 b}}+2 \sqrt[4]{a+\frac{b}{x^2}}\right)+\left(\sqrt{a^2-4 b}+a\right)^{3/4} \log \left(2^{3/4} \sqrt[4]{\sqrt{a^2-4 b}+a}+2 \sqrt[4]{a+\frac{b}{x^2}}\right)+2 \left(a-\sqrt{a^2-4 b}\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a-\sqrt{a^2-4 b}}}\right)-2 \left(\sqrt{a^2-4 b}+a\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\sqrt{a^2-4 b}+a}}\right)\right)}{2\ 2^{3/4} x^3 \sqrt{a^2-4 b} \left(a+\frac{b}{x^2}\right)^{3/4}}","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4 a+b\&,\frac{\text{$\#$1}^3 \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\text{$\#$1}^3 \log (x)}{2 \text{$\#$1}^4-a}\&\right]",1,"((x^2*(b + a*x^2))^(3/4)*(2*(a - Sqrt[a^2 - 4*b])^(3/4)*ArcTan[(2^(1/4)*(a + b/x^2)^(1/4))/(a - Sqrt[a^2 - 4*b])^(1/4)] - 2*(a + Sqrt[a^2 - 4*b])^(3/4)*ArcTan[(2^(1/4)*(a + b/x^2)^(1/4))/(a + Sqrt[a^2 - 4*b])^(1/4)] + (a - Sqrt[a^2 - 4*b])^(3/4)*Log[2^(3/4)*(a - Sqrt[a^2 - 4*b])^(1/4) - 2*(a + b/x^2)^(1/4)] - (a + Sqrt[a^2 - 4*b])^(3/4)*Log[2^(3/4)*(a + Sqrt[a^2 - 4*b])^(1/4) - 2*(a + b/x^2)^(1/4)] - (a - Sqrt[a^2 - 4*b])^(3/4)*Log[2^(3/4)*(a - Sqrt[a^2 - 4*b])^(1/4) + 2*(a + b/x^2)^(1/4)] + (a + Sqrt[a^2 - 4*b])^(3/4)*Log[2^(3/4)*(a + Sqrt[a^2 - 4*b])^(1/4) + 2*(a + b/x^2)^(1/4)]))/(2*2^(3/4)*Sqrt[a^2 - 4*b]*(a + b/x^2)^(3/4)*x^3)","B",1
913,1,147,69,0.2932897,"\int \frac{\left(-b+a x^2\right) \sqrt{b^2+a^2 x^4}}{x^2 \left(b+a x^2\right)} \, dx","Integrate[((-b + a*x^2)*Sqrt[b^2 + a^2*x^4])/(x^2*(b + a*x^2)),x]","\frac{\sqrt{\frac{i a}{b}} \left(a^2 x^4+b^2\right)+2 i a b x \sqrt{\frac{a^2 x^4}{b^2}+1} F\left(\left.i \sinh ^{-1}\left(\sqrt{\frac{i a}{b}} x\right)\right|-1\right)-4 i a b x \sqrt{\frac{a^2 x^4}{b^2}+1} \Pi \left(-i;\left.i \sinh ^{-1}\left(\sqrt{\frac{i a}{b}} x\right)\right|-1\right)}{x \sqrt{\frac{i a}{b}} \sqrt{a^2 x^4+b^2}}","\frac{\sqrt{a^2 x^4+b^2}}{x}+\sqrt{2} \sqrt{a} \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{b} x}{\sqrt{a^2 x^4+b^2}}\right)",1,"(Sqrt[(I*a)/b]*(b^2 + a^2*x^4) + (2*I)*a*b*x*Sqrt[1 + (a^2*x^4)/b^2]*EllipticF[I*ArcSinh[Sqrt[(I*a)/b]*x], -1] - (4*I)*a*b*x*Sqrt[1 + (a^2*x^4)/b^2]*EllipticPi[-I, I*ArcSinh[Sqrt[(I*a)/b]*x], -1])/(Sqrt[(I*a)/b]*x*Sqrt[b^2 + a^2*x^4])","C",1
914,0,0,69,0.455856,"\int \frac{4 b+a x^3}{\left(b+a x^3\right) \sqrt[4]{-b-a x^3+c x^4}} \, dx","Integrate[(4*b + a*x^3)/((b + a*x^3)*(-b - a*x^3 + c*x^4)^(1/4)),x]","\int \frac{4 b+a x^3}{\left(b+a x^3\right) \sqrt[4]{-b-a x^3+c x^4}} \, dx","\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{-a x^3-b+c x^4}}\right)}{\sqrt[4]{c}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{-a x^3-b+c x^4}}\right)}{\sqrt[4]{c}}",1,"Integrate[(4*b + a*x^3)/((b + a*x^3)*(-b - a*x^3 + c*x^4)^(1/4)), x]","F",-1
915,0,0,69,0.462304,"\int \frac{\left(-3+x^4\right) \left(1+x^4\right) \left(1+x^3+x^4\right)}{x^6 \left(1-x^3+x^4\right) \sqrt[4]{x+x^5}} \, dx","Integrate[((-3 + x^4)*(1 + x^4)*(1 + x^3 + x^4))/(x^6*(1 - x^3 + x^4)*(x + x^5)^(1/4)),x]","\int \frac{\left(-3+x^4\right) \left(1+x^4\right) \left(1+x^3+x^4\right)}{x^6 \left(1-x^3+x^4\right) \sqrt[4]{x+x^5}} \, dx","-4 \tan ^{-1}\left(\frac{\left(x^5+x\right)^{3/4}}{x^4+1}\right)-4 \tanh ^{-1}\left(\frac{\left(x^5+x\right)^{3/4}}{x^4+1}\right)+\frac{4 \left(x^5+x\right)^{3/4} \left(3 x^4+14 x^3+3\right)}{21 x^6}",1,"Integrate[((-3 + x^4)*(1 + x^4)*(1 + x^3 + x^4))/(x^6*(1 - x^3 + x^4)*(x + x^5)^(1/4)), x]","F",-1
916,0,0,69,0.3338382,"\int \frac{\left(-3+x^4\right) \left(1+2 x^4+x^6+x^8\right)}{x^6 \left(1-x^3+x^4\right) \sqrt[4]{x+x^5}} \, dx","Integrate[((-3 + x^4)*(1 + 2*x^4 + x^6 + x^8))/(x^6*(1 - x^3 + x^4)*(x + x^5)^(1/4)),x]","\int \frac{\left(-3+x^4\right) \left(1+2 x^4+x^6+x^8\right)}{x^6 \left(1-x^3+x^4\right) \sqrt[4]{x+x^5}} \, dx","-4 \tan ^{-1}\left(\frac{\left(x^5+x\right)^{3/4}}{x^4+1}\right)-4 \tanh ^{-1}\left(\frac{\left(x^5+x\right)^{3/4}}{x^4+1}\right)+\frac{4 \left(x^5+x\right)^{3/4} \left(3 x^4+7 x^3+3\right)}{21 x^6}",1,"Integrate[((-3 + x^4)*(1 + 2*x^4 + x^6 + x^8))/(x^6*(1 - x^3 + x^4)*(x + x^5)^(1/4)), x]","F",-1
917,1,70,70,0.0210635,"\int \frac{\left(b+a x^3\right)^{3/4}}{x} \, dx","Integrate[(b + a*x^3)^(3/4)/x,x]","\frac{2}{3} b^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a x^3+b}}{\sqrt[4]{b}}\right)-\frac{2}{3} b^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a x^3+b}}{\sqrt[4]{b}}\right)+\frac{4}{9} \left(a x^3+b\right)^{3/4}","\frac{2}{3} b^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a x^3+b}}{\sqrt[4]{b}}\right)-\frac{2}{3} b^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a x^3+b}}{\sqrt[4]{b}}\right)+\frac{4}{9} \left(a x^3+b\right)^{3/4}",1,"(4*(b + a*x^3)^(3/4))/9 + (2*b^(3/4)*ArcTan[(b + a*x^3)^(1/4)/b^(1/4)])/3 - (2*b^(3/4)*ArcTanh[(b + a*x^3)^(1/4)/b^(1/4)])/3","A",1
918,1,66,70,0.0302524,"\int \frac{1+3 x+3 x^4}{x \sqrt[4]{1+x^4}} \, dx","Integrate[(1 + 3*x + 3*x^4)/(x*(1 + x^4)^(1/4)),x]","\frac{1}{2} \left(2 \left(x^4+1\right)^{3/4}+3 \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)+\tan ^{-1}\left(\sqrt[4]{x^4+1}\right)+3 \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)-\tanh ^{-1}\left(\sqrt[4]{x^4+1}\right)\right)","\left(x^4+1\right)^{3/4}+\frac{3}{2} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)+\frac{1}{2} \tan ^{-1}\left(\sqrt[4]{x^4+1}\right)+\frac{3}{2} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)-\frac{1}{2} \tanh ^{-1}\left(\sqrt[4]{x^4+1}\right)",1,"(2*(1 + x^4)^(3/4) + 3*ArcTan[x/(1 + x^4)^(1/4)] + ArcTan[(1 + x^4)^(1/4)] + 3*ArcTanh[x/(1 + x^4)^(1/4)] - ArcTanh[(1 + x^4)^(1/4)])/2","A",1
919,1,70,70,0.0190268,"\int \frac{\left(b+a x^4\right)^{3/4}}{x} \, dx","Integrate[(b + a*x^4)^(3/4)/x,x]","\frac{1}{2} b^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a x^4+b}}{\sqrt[4]{b}}\right)-\frac{1}{2} b^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a x^4+b}}{\sqrt[4]{b}}\right)+\frac{1}{3} \left(a x^4+b\right)^{3/4}","\frac{1}{2} b^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a x^4+b}}{\sqrt[4]{b}}\right)-\frac{1}{2} b^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a x^4+b}}{\sqrt[4]{b}}\right)+\frac{1}{3} \left(a x^4+b\right)^{3/4}",1,"(b + a*x^4)^(3/4)/3 + (b^(3/4)*ArcTan[(b + a*x^4)^(1/4)/b^(1/4)])/2 - (b^(3/4)*ArcTanh[(b + a*x^4)^(1/4)/b^(1/4)])/2","A",1
920,1,3600,70,2.1685303,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{a+b x+c x^2+b x^3+a x^4}} \, dx","Integrate[(-1 + x^2)/((1 + x^2)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]),x]","\text{Result too large to show}","\frac{2 \tan ^{-1}\left(\frac{x \sqrt{2 a-c}}{-\sqrt{a x^4+a+b x^3+b x+c x^2}+\sqrt{a} x^2+\sqrt{a}}\right)}{\sqrt{2 a-c}}",1,"(2*(x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])^2*Sqrt[((Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3]))/((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3]))]*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])*Sqrt[((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])^2*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])^2)]*(((-I)*(EllipticF[ArcSin[Sqrt[((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))]], -(((Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])))]*(-I + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1]) + EllipticPi[((-I + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((-I + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])), ArcSin[Sqrt[((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))]], -(((Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])))]*(-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])))/((-I + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(-I + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])) + (I*(EllipticF[ArcSin[Sqrt[((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))]], -(((Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])))]*(I + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1]) + EllipticPi[((I + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((I + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])), ArcSin[Sqrt[((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))]], -(((Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])))]*(-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])))/((I + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(I + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])) + EllipticF[ArcSin[Sqrt[((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))]], ((Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))]/(-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])))/(Sqrt[x*(b + c*x + b*x^2) + a*(1 + x^4)]*(-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2]))","C",0
921,1,147,70,0.2955038,"\int \frac{\left(b+a x^2\right) \sqrt{b^2+a^2 x^4}}{x^2 \left(-b+a x^2\right)} \, dx","Integrate[((b + a*x^2)*Sqrt[b^2 + a^2*x^4])/(x^2*(-b + a*x^2)),x]","\frac{\sqrt{\frac{i a}{b}} \left(a^2 x^4+b^2\right)-2 i a b x \sqrt{\frac{a^2 x^4}{b^2}+1} F\left(\left.i \sinh ^{-1}\left(\sqrt{\frac{i a}{b}} x\right)\right|-1\right)+4 i a b x \sqrt{\frac{a^2 x^4}{b^2}+1} \Pi \left(i;\left.i \sinh ^{-1}\left(\sqrt{\frac{i a}{b}} x\right)\right|-1\right)}{x \sqrt{\frac{i a}{b}} \sqrt{a^2 x^4+b^2}}","\frac{\sqrt{a^2 x^4+b^2}}{x}-\sqrt{2} \sqrt{a} \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{b} x}{\sqrt{a^2 x^4+b^2}}\right)",1,"(Sqrt[(I*a)/b]*(b^2 + a^2*x^4) - (2*I)*a*b*x*Sqrt[1 + (a^2*x^4)/b^2]*EllipticF[I*ArcSinh[Sqrt[(I*a)/b]*x], -1] + (4*I)*a*b*x*Sqrt[1 + (a^2*x^4)/b^2]*EllipticPi[I, I*ArcSinh[Sqrt[(I*a)/b]*x], -1])/(Sqrt[(I*a)/b]*x*Sqrt[b^2 + a^2*x^4])","C",1
922,1,70,70,0.0228312,"\int \frac{\left(b+a x^5\right)^{3/4}}{x} \, dx","Integrate[(b + a*x^5)^(3/4)/x,x]","\frac{2}{5} b^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a x^5+b}}{\sqrt[4]{b}}\right)-\frac{2}{5} b^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a x^5+b}}{\sqrt[4]{b}}\right)+\frac{4}{15} \left(a x^5+b\right)^{3/4}","\frac{2}{5} b^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a x^5+b}}{\sqrt[4]{b}}\right)-\frac{2}{5} b^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a x^5+b}}{\sqrt[4]{b}}\right)+\frac{4}{15} \left(a x^5+b\right)^{3/4}",1,"(4*(b + a*x^5)^(3/4))/15 + (2*b^(3/4)*ArcTan[(b + a*x^5)^(1/4)/b^(1/4)])/5 - (2*b^(3/4)*ArcTanh[(b + a*x^5)^(1/4)/b^(1/4)])/5","A",1
923,0,0,70,2.5520233,"\int \frac{\left(3+2 x^5\right) \sqrt{x-2 x^4-x^6}}{\left(-1+x^5\right)^2} \, dx","Integrate[((3 + 2*x^5)*Sqrt[x - 2*x^4 - x^6])/(-1 + x^5)^2,x]","\int \frac{\left(3+2 x^5\right) \sqrt{x-2 x^4-x^6}}{\left(-1+x^5\right)^2} \, dx","-\frac{\sqrt{-x^6-2 x^4+x} x}{x^5-1}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} x \sqrt{-x^6-2 x^4+x}}{x^5+2 x^3-1}\right)}{\sqrt{2}}",1,"Integrate[((3 + 2*x^5)*Sqrt[x - 2*x^4 - x^6])/(-1 + x^5)^2, x]","F",-1
924,0,0,70,0.9925874,"\int \frac{\left(-2+x^6\right) \left(1+x^6\right) \sqrt[4]{1-x^4+x^6}}{x^6 \left(1-2 x^4+x^6\right)} \, dx","Integrate[((-2 + x^6)*(1 + x^6)*(1 - x^4 + x^6)^(1/4))/(x^6*(1 - 2*x^4 + x^6)),x]","\int \frac{\left(-2+x^6\right) \left(1+x^6\right) \sqrt[4]{1-x^4+x^6}}{x^6 \left(1-2 x^4+x^6\right)} \, dx","2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^6-x^4+1}}\right)-2 \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^6-x^4+1}}\right)+\frac{2 \sqrt[4]{x^6-x^4+1} \left(x^6+9 x^4+1\right)}{5 x^5}",1,"Integrate[((-2 + x^6)*(1 + x^6)*(1 - x^4 + x^6)^(1/4))/(x^6*(1 - 2*x^4 + x^6)), x]","F",-1
925,1,70,70,0.0205532,"\int \frac{\left(b+a x^6\right)^{3/4}}{x} \, dx","Integrate[(b + a*x^6)^(3/4)/x,x]","\frac{1}{3} b^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a x^6+b}}{\sqrt[4]{b}}\right)-\frac{1}{3} b^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a x^6+b}}{\sqrt[4]{b}}\right)+\frac{2}{9} \left(a x^6+b\right)^{3/4}","\frac{1}{3} b^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a x^6+b}}{\sqrt[4]{b}}\right)-\frac{1}{3} b^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a x^6+b}}{\sqrt[4]{b}}\right)+\frac{2}{9} \left(a x^6+b\right)^{3/4}",1,"(2*(b + a*x^6)^(3/4))/9 + (b^(3/4)*ArcTan[(b + a*x^6)^(1/4)/b^(1/4)])/3 - (b^(3/4)*ArcTanh[(b + a*x^6)^(1/4)/b^(1/4)])/3","A",1
926,1,62,70,0.0419697,"\int \frac{\sqrt{1+x}}{\sqrt{x+\sqrt{1+x}}} \, dx","Integrate[Sqrt[1 + x]/Sqrt[x + Sqrt[1 + x]],x]","\frac{1}{2} \sqrt{x+\sqrt{x+1}} \left(2 \sqrt{x+1}-3\right)+\frac{7}{4} \tanh ^{-1}\left(\frac{2 \sqrt{x+1}+1}{2 \sqrt{x+\sqrt{x+1}}}\right)","\sqrt{x+1} \sqrt{x+\sqrt{x+1}}-\frac{3}{2} \sqrt{x+\sqrt{x+1}}-\frac{7}{4} \log \left(2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)",1,"(Sqrt[x + Sqrt[1 + x]]*(-3 + 2*Sqrt[1 + x]))/2 + (7*ArcTanh[(1 + 2*Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])])/4","A",1
927,1,64,70,0.025667,"\int \frac{\sqrt{x+\sqrt{1+x}}}{\sqrt{1+x}} \, dx","Integrate[Sqrt[x + Sqrt[1 + x]]/Sqrt[1 + x],x]","2 \left(\frac{1}{4} \sqrt{x+\sqrt{x+1}} \left(2 \sqrt{x+1}+1\right)-\frac{5}{8} \tanh ^{-1}\left(\frac{2 \sqrt{x+1}+1}{2 \sqrt{x+\sqrt{x+1}}}\right)\right)","\sqrt{x+1} \sqrt{x+\sqrt{x+1}}+\frac{1}{2} \sqrt{x+\sqrt{x+1}}+\frac{5}{4} \log \left(2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)",1,"2*((Sqrt[x + Sqrt[1 + x]]*(1 + 2*Sqrt[1 + x]))/4 - (5*ArcTanh[(1 + 2*Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])])/8)","A",1
928,0,0,70,0.1255971,"\int \frac{\left(-1+x^2\right) \sqrt{1+\sqrt{1+x^2}}}{1+x^2} \, dx","Integrate[((-1 + x^2)*Sqrt[1 + Sqrt[1 + x^2]])/(1 + x^2),x]","\int \frac{\left(-1+x^2\right) \sqrt{1+\sqrt{1+x^2}}}{1+x^2} \, dx","\frac{2 \sqrt{x^2+1} x}{3 \sqrt{\sqrt{x^2+1}+1}}+\frac{4 x}{3 \sqrt{\sqrt{x^2+1}+1}}-4 \tan ^{-1}\left(\frac{x}{\sqrt{\sqrt{x^2+1}+1}}\right)",1,"Integrate[((-1 + x^2)*Sqrt[1 + Sqrt[1 + x^2]])/(1 + x^2), x]","F",-1
929,1,1665,70,11.7334363,"\int \frac{1}{\sqrt{x^2+\sqrt{1+x^4}}} \, dx","Integrate[1/Sqrt[x^2 + Sqrt[1 + x^4]],x]","\frac{\sqrt{x^2+\sqrt{x^4+1}} \left(\frac{56 \left(x^2+\sqrt{x^4+1}\right)^3 \left(x^4+\sqrt{x^4+1} x^2+1\right) \left(5 \left(2 x^8+2 \sqrt{x^4+1} x^6+5 x^4+4 \sqrt{x^4+1} x^2+1\right) \, _2F_1\left(-\frac{1}{2},\frac{1}{2};\frac{5}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right)+2 \left(4 x^8+4 \sqrt{x^4+1} x^6+5 x^4+3 \sqrt{x^4+1} x^2+1\right) \, _2F_1\left(\frac{1}{2},\frac{3}{2};\frac{7}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right)+2 \left(x^4+1\right) \left(8 x^8+8 \sqrt{x^4+1} x^6+8 x^4+4 \sqrt{x^4+1} x^2+1\right) \, _3F_2\left(\frac{1}{2},\frac{3}{2},2;1,\frac{7}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right)\right) x^6}{-896 \, _2F_1\left(\frac{1}{2},\frac{3}{2};\frac{7}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^{18}+1536 \, _2F_1\left(\frac{3}{2},\frac{5}{2};\frac{9}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^{18}-896 \sqrt{x^4+1} \, _2F_1\left(\frac{1}{2},\frac{3}{2};\frac{7}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^{16}+1536 \sqrt{x^4+1} \, _2F_1\left(\frac{3}{2},\frac{5}{2};\frac{9}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^{16}+3360 \, _2F_1\left(-\frac{1}{2},\frac{1}{2};\frac{5}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^{14}-448 \, _2F_1\left(\frac{1}{2},\frac{3}{2};\frac{7}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^{14}+3456 \, _2F_1\left(\frac{3}{2},\frac{5}{2};\frac{9}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^{14}+3360 \sqrt{x^4+1} \, _2F_1\left(-\frac{1}{2},\frac{1}{2};\frac{5}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^{12}+2688 \sqrt{x^4+1} \, _2F_1\left(\frac{3}{2},\frac{5}{2};\frac{9}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^{12}+6720 \, _2F_1\left(-\frac{1}{2},\frac{1}{2};\frac{5}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^{10}+1232 \, _2F_1\left(\frac{1}{2},\frac{3}{2};\frac{7}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^{10}+2592 \, _2F_1\left(\frac{3}{2},\frac{5}{2};\frac{9}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^{10}+5040 \sqrt{x^4+1} \, _2F_1\left(-\frac{1}{2},\frac{1}{2};\frac{5}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^8+1120 \sqrt{x^4+1} \, _2F_1\left(\frac{1}{2},\frac{3}{2};\frac{7}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^8+1440 \sqrt{x^4+1} \, _2F_1\left(\frac{3}{2},\frac{5}{2};\frac{9}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^8+3990 \, _2F_1\left(-\frac{1}{2},\frac{1}{2};\frac{5}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^6+952 \, _2F_1\left(\frac{1}{2},\frac{3}{2};\frac{7}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^6+720 \, _2F_1\left(\frac{3}{2},\frac{5}{2};\frac{9}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^6+1890 \sqrt{x^4+1} \, _2F_1\left(-\frac{1}{2},\frac{1}{2};\frac{5}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^4+448 \sqrt{x^4+1} \, _2F_1\left(\frac{1}{2},\frac{3}{2};\frac{7}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^4+240 \sqrt{x^4+1} \, _2F_1\left(\frac{3}{2},\frac{5}{2};\frac{9}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^4+630 \, _2F_1\left(-\frac{1}{2},\frac{1}{2};\frac{5}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^2+140 \, _2F_1\left(\frac{1}{2},\frac{3}{2};\frac{7}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^2+54 \, _2F_1\left(\frac{3}{2},\frac{5}{2};\frac{9}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^2+105 \sqrt{x^4+1} \, _2F_1\left(-\frac{1}{2},\frac{1}{2};\frac{5}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right)+21 \sqrt{x^4+1} \, _2F_1\left(\frac{1}{2},\frac{3}{2};\frac{7}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right)+6 \sqrt{x^4+1} \, _2F_1\left(\frac{3}{2},\frac{5}{2};\frac{9}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right)+14 \left(640 x^{18}+640 \sqrt{x^4+1} x^{16}+1472 x^{14}+1152 \sqrt{x^4+1} x^{12}+1136 x^{10}+640 \sqrt{x^4+1} x^8+328 x^6+112 \sqrt{x^4+1} x^4+26 x^2+3 \sqrt{x^4+1}\right) \, _3F_2\left(\frac{1}{2},\frac{3}{2},2;1,\frac{7}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right)+12 \left(512 x^{22}+512 \sqrt{x^4+1} x^{20}+1536 x^{18}+1280 \sqrt{x^4+1} x^{16}+1696 x^{14}+1120 \sqrt{x^4+1} x^{12}+832 x^{10}+400 \sqrt{x^4+1} x^8+170 x^6+50 \sqrt{x^4+1} x^4+10 x^2+\sqrt{x^4+1}\right) \, _3F_2\left(\frac{3}{2},\frac{5}{2},3;2,\frac{9}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right)}+\frac{\sqrt{2} \sqrt{x^4+1} \sqrt{x^2 \left(x^2+\sqrt{x^4+1}\right)} \left(-x^4 \left(2 x^4+2 \sqrt{x^4+1} x^2+1\right)\right)^{3/2} \left(\sqrt{2} \sqrt{-x^2 \left(x^2+\sqrt{x^4+1}\right)} \left(-2 x^4-2 \sqrt{x^4+1} x^2+1\right)+\left(x^2+\sqrt{x^4+1}\right) \sin ^{-1}\left(x^2+\sqrt{x^4+1}\right)\right)}{16 x^{12}+16 \sqrt{x^4+1} x^{10}+28 x^8+20 \sqrt{x^4+1} x^6+13 x^4+5 \sqrt{x^4+1} x^2+1}\right)}{16 x^7}","\frac{x}{2 \sqrt{\sqrt{x^4+1}+x^2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)}{\sqrt{2}}",1,"(Sqrt[x^2 + Sqrt[1 + x^4]]*((Sqrt[2]*Sqrt[1 + x^4]*Sqrt[x^2*(x^2 + Sqrt[1 + x^4])]*(-(x^4*(1 + 2*x^4 + 2*x^2*Sqrt[1 + x^4])))^(3/2)*(Sqrt[2]*Sqrt[-(x^2*(x^2 + Sqrt[1 + x^4]))]*(1 - 2*x^4 - 2*x^2*Sqrt[1 + x^4]) + (x^2 + Sqrt[1 + x^4])*ArcSin[x^2 + Sqrt[1 + x^4]]))/(1 + 13*x^4 + 28*x^8 + 16*x^12 + 5*x^2*Sqrt[1 + x^4] + 20*x^6*Sqrt[1 + x^4] + 16*x^10*Sqrt[1 + x^4]) + (56*x^6*(x^2 + Sqrt[1 + x^4])^3*(1 + x^4 + x^2*Sqrt[1 + x^4])*(5*(1 + 5*x^4 + 2*x^8 + 4*x^2*Sqrt[1 + x^4] + 2*x^6*Sqrt[1 + x^4])*Hypergeometric2F1[-1/2, 1/2, 5/2, (x^2 + Sqrt[1 + x^4])^2] + 2*(1 + 5*x^4 + 4*x^8 + 3*x^2*Sqrt[1 + x^4] + 4*x^6*Sqrt[1 + x^4])*Hypergeometric2F1[1/2, 3/2, 7/2, (x^2 + Sqrt[1 + x^4])^2] + 2*(1 + x^4)*(1 + 8*x^4 + 8*x^8 + 4*x^2*Sqrt[1 + x^4] + 8*x^6*Sqrt[1 + x^4])*HypergeometricPFQ[{1/2, 3/2, 2}, {1, 7/2}, (x^2 + Sqrt[1 + x^4])^2]))/(630*x^2*Hypergeometric2F1[-1/2, 1/2, 5/2, (x^2 + Sqrt[1 + x^4])^2] + 3990*x^6*Hypergeometric2F1[-1/2, 1/2, 5/2, (x^2 + Sqrt[1 + x^4])^2] + 6720*x^10*Hypergeometric2F1[-1/2, 1/2, 5/2, (x^2 + Sqrt[1 + x^4])^2] + 3360*x^14*Hypergeometric2F1[-1/2, 1/2, 5/2, (x^2 + Sqrt[1 + x^4])^2] + 105*Sqrt[1 + x^4]*Hypergeometric2F1[-1/2, 1/2, 5/2, (x^2 + Sqrt[1 + x^4])^2] + 1890*x^4*Sqrt[1 + x^4]*Hypergeometric2F1[-1/2, 1/2, 5/2, (x^2 + Sqrt[1 + x^4])^2] + 5040*x^8*Sqrt[1 + x^4]*Hypergeometric2F1[-1/2, 1/2, 5/2, (x^2 + Sqrt[1 + x^4])^2] + 3360*x^12*Sqrt[1 + x^4]*Hypergeometric2F1[-1/2, 1/2, 5/2, (x^2 + Sqrt[1 + x^4])^2] + 140*x^2*Hypergeometric2F1[1/2, 3/2, 7/2, (x^2 + Sqrt[1 + x^4])^2] + 952*x^6*Hypergeometric2F1[1/2, 3/2, 7/2, (x^2 + Sqrt[1 + x^4])^2] + 1232*x^10*Hypergeometric2F1[1/2, 3/2, 7/2, (x^2 + Sqrt[1 + x^4])^2] - 448*x^14*Hypergeometric2F1[1/2, 3/2, 7/2, (x^2 + Sqrt[1 + x^4])^2] - 896*x^18*Hypergeometric2F1[1/2, 3/2, 7/2, (x^2 + Sqrt[1 + x^4])^2] + 21*Sqrt[1 + x^4]*Hypergeometric2F1[1/2, 3/2, 7/2, (x^2 + Sqrt[1 + x^4])^2] + 448*x^4*Sqrt[1 + x^4]*Hypergeometric2F1[1/2, 3/2, 7/2, (x^2 + Sqrt[1 + x^4])^2] + 1120*x^8*Sqrt[1 + x^4]*Hypergeometric2F1[1/2, 3/2, 7/2, (x^2 + Sqrt[1 + x^4])^2] - 896*x^16*Sqrt[1 + x^4]*Hypergeometric2F1[1/2, 3/2, 7/2, (x^2 + Sqrt[1 + x^4])^2] + 54*x^2*Hypergeometric2F1[3/2, 5/2, 9/2, (x^2 + Sqrt[1 + x^4])^2] + 720*x^6*Hypergeometric2F1[3/2, 5/2, 9/2, (x^2 + Sqrt[1 + x^4])^2] + 2592*x^10*Hypergeometric2F1[3/2, 5/2, 9/2, (x^2 + Sqrt[1 + x^4])^2] + 3456*x^14*Hypergeometric2F1[3/2, 5/2, 9/2, (x^2 + Sqrt[1 + x^4])^2] + 1536*x^18*Hypergeometric2F1[3/2, 5/2, 9/2, (x^2 + Sqrt[1 + x^4])^2] + 6*Sqrt[1 + x^4]*Hypergeometric2F1[3/2, 5/2, 9/2, (x^2 + Sqrt[1 + x^4])^2] + 240*x^4*Sqrt[1 + x^4]*Hypergeometric2F1[3/2, 5/2, 9/2, (x^2 + Sqrt[1 + x^4])^2] + 1440*x^8*Sqrt[1 + x^4]*Hypergeometric2F1[3/2, 5/2, 9/2, (x^2 + Sqrt[1 + x^4])^2] + 2688*x^12*Sqrt[1 + x^4]*Hypergeometric2F1[3/2, 5/2, 9/2, (x^2 + Sqrt[1 + x^4])^2] + 1536*x^16*Sqrt[1 + x^4]*Hypergeometric2F1[3/2, 5/2, 9/2, (x^2 + Sqrt[1 + x^4])^2] + 14*(26*x^2 + 328*x^6 + 1136*x^10 + 1472*x^14 + 640*x^18 + 3*Sqrt[1 + x^4] + 112*x^4*Sqrt[1 + x^4] + 640*x^8*Sqrt[1 + x^4] + 1152*x^12*Sqrt[1 + x^4] + 640*x^16*Sqrt[1 + x^4])*HypergeometricPFQ[{1/2, 3/2, 2}, {1, 7/2}, (x^2 + Sqrt[1 + x^4])^2] + 12*(10*x^2 + 170*x^6 + 832*x^10 + 1696*x^14 + 1536*x^18 + 512*x^22 + Sqrt[1 + x^4] + 50*x^4*Sqrt[1 + x^4] + 400*x^8*Sqrt[1 + x^4] + 1120*x^12*Sqrt[1 + x^4] + 1280*x^16*Sqrt[1 + x^4] + 512*x^20*Sqrt[1 + x^4])*HypergeometricPFQ[{3/2, 5/2, 3}, {2, 9/2}, (x^2 + Sqrt[1 + x^4])^2])))/(16*x^7)","C",0
930,1,82,70,0.2242113,"\int \frac{\sqrt{x^2+\sqrt{1+x^4}}}{x^2} \, dx","Integrate[Sqrt[x^2 + Sqrt[1 + x^4]]/x^2,x]","\frac{\sqrt{2} \sqrt{-x^2 \left(\sqrt{x^4+1}+x^2\right)} \sin ^{-1}\left(\sqrt{x^4+1}+x^2\right)-2 \left(\sqrt{x^4+1}+x^2\right)}{2 x \sqrt{\sqrt{x^4+1}+x^2}}","\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)-\frac{\sqrt{\sqrt{x^4+1}+x^2}}{x}",1,"(-2*(x^2 + Sqrt[1 + x^4]) + Sqrt[2]*Sqrt[-(x^2*(x^2 + Sqrt[1 + x^4]))]*ArcSin[x^2 + Sqrt[1 + x^4]])/(2*x*Sqrt[x^2 + Sqrt[1 + x^4]])","A",1
931,1,78,71,0.1028904,"\int \frac{1}{\left(\sqrt{-1+x}+2 \sqrt{x}\right)^2 \sqrt{-1+x}} \, dx","Integrate[1/((Sqrt[-1 + x] + 2*Sqrt[x])^2*Sqrt[-1 + x]),x]","\frac{-6 \sqrt{x-1}+12 \sqrt{x}+4 \sqrt{3} (3 x+1) \tan ^{-1}\left(\frac{1}{2} \sqrt{3} \sqrt{x-1}\right)-4 \sqrt{3} (3 x+1) \tan ^{-1}\left(\sqrt{3} \sqrt{x}\right)}{27 x+9}","-\frac{2 \sqrt{x-1}}{3 (3 x+1)}+\frac{4 \sqrt{x}}{3 (3 x+1)}+\frac{8 \tan ^{-1}\left(\frac{\sqrt{x-1}}{\sqrt{3}}-\frac{\sqrt{x}}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"(-6*Sqrt[-1 + x] + 12*Sqrt[x] + 4*Sqrt[3]*(1 + 3*x)*ArcTan[(Sqrt[3]*Sqrt[-1 + x])/2] - 4*Sqrt[3]*(1 + 3*x)*ArcTan[Sqrt[3]*Sqrt[x]])/(9 + 27*x)","A",1
932,1,167,71,3.2456516,"\int \frac{1}{\sqrt{-1+x^2} \left(-4+3 x^2\right)^2} \, dx","Integrate[1/(Sqrt[-1 + x^2]*(-4 + 3*x^2)^2),x]","-\frac{x \sqrt{x^2-1} \left(\frac{8 x^2 \left(x^2-1\right) \, _2F_1\left(2,3;\frac{7}{2};\frac{x^2}{4-3 x^2}\right)}{45 x^2-60}-\frac{x^2 \left(2 x^2-3\right) \sqrt{\frac{x^2-1}{3 x^2-4}} \left(2 \sqrt{\frac{x^2-x^4}{\left(4-3 x^2\right)^2}}-\sin ^{-1}\left(\sqrt{\frac{x^2}{4-3 x^2}}\right)\right)}{4 \left(\frac{x^2}{4-3 x^2}\right)^{5/2} \left(x^2-1\right)}\right)}{16 \left(1-\frac{3 x^2}{4}\right)^2}","-\frac{3 \sqrt{x^2-1} x}{8 \left(3 x^2-4\right)}+\frac{5}{32} \log \left(-x^2+\sqrt{x^2-1} x+2\right)-\frac{5}{32} \log \left(-3 x^2+3 \sqrt{x^2-1} x+2\right)",1,"-1/16*(x*Sqrt[-1 + x^2]*(-1/4*(x^2*(-3 + 2*x^2)*Sqrt[(-1 + x^2)/(-4 + 3*x^2)]*(2*Sqrt[(x^2 - x^4)/(4 - 3*x^2)^2] - ArcSin[Sqrt[x^2/(4 - 3*x^2)]]))/((x^2/(4 - 3*x^2))^(5/2)*(-1 + x^2)) + (8*x^2*(-1 + x^2)*Hypergeometric2F1[2, 3, 7/2, x^2/(4 - 3*x^2)])/(-60 + 45*x^2)))/(1 - (3*x^2)/4)^2","C",0
933,1,51,71,0.0148702,"\int \frac{1}{x \sqrt[3]{1+x^3}} \, dx","Integrate[1/(x*(1 + x^3)^(1/3)),x]","\frac{1}{2} \log \left(1-\sqrt[3]{x^3+1}\right)+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{x^3+1}+1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\log (x)}{2}","\frac{1}{3} \log \left(\sqrt[3]{x^3+1}-1\right)-\frac{1}{6} \log \left(\left(x^3+1\right)^{2/3}+\sqrt[3]{x^3+1}+1\right)+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{x^3+1}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3}}",1,"ArcTan[(1 + 2*(1 + x^3)^(1/3))/Sqrt[3]]/Sqrt[3] - Log[x]/2 + Log[1 - (1 + x^3)^(1/3)]/2","A",1
934,0,0,71,1.1436766,"\int \frac{x^2 \left(3-2 (1+k) x+k x^2\right)}{((1-x) x (1-k x))^{3/4} \left(-1+(1+k) x-k x^2+d x^3\right)} \, dx","Integrate[(x^2*(3 - 2*(1 + k)*x + k*x^2))/(((1 - x)*x*(1 - k*x))^(3/4)*(-1 + (1 + k)*x - k*x^2 + d*x^3)),x]","\int \frac{x^2 \left(3-2 (1+k) x+k x^2\right)}{((1-x) x (1-k x))^{3/4} \left(-1+(1+k) x-k x^2+d x^3\right)} \, dx","\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{k x^3+(-k-1) x^2+x}}\right)}{d^{3/4}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{k x^3+(-k-1) x^2+x}}\right)}{d^{3/4}}",1,"Integrate[(x^2*(3 - 2*(1 + k)*x + k*x^2))/(((1 - x)*x*(1 - k*x))^(3/4)*(-1 + (1 + k)*x - k*x^2 + d*x^3)), x]","F",-1
935,1,423,71,0.8098602,"\int \frac{-b+a x^2}{\left(-b+a x^2+x^4\right) \sqrt[4]{-b x^2+a x^4}} \, dx","Integrate[(-b + a*x^2)/((-b + a*x^2 + x^4)*(-(b*x^2) + a*x^4)^(1/4)),x]","\frac{\left(a x^4-b x^2\right)^{3/4} \left(-\left(-\sqrt{a^2+4 b}-a\right)^{3/4} \log \left(2^{3/4} \sqrt[4]{-\sqrt{a^2+4 b}-a}-2 \sqrt[4]{\frac{b}{x^2}-a}\right)+\left(\sqrt{a^2+4 b}-a\right)^{3/4} \log \left(2^{3/4} \sqrt[4]{\sqrt{a^2+4 b}-a}-2 \sqrt[4]{\frac{b}{x^2}-a}\right)+\left(-\sqrt{a^2+4 b}-a\right)^{3/4} \log \left(2^{3/4} \sqrt[4]{-\sqrt{a^2+4 b}-a}+2 \sqrt[4]{\frac{b}{x^2}-a}\right)-\left(\sqrt{a^2+4 b}-a\right)^{3/4} \log \left(2^{3/4} \sqrt[4]{\sqrt{a^2+4 b}-a}+2 \sqrt[4]{\frac{b}{x^2}-a}\right)-2 \left(-\sqrt{a^2+4 b}-a\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{2 b}{x^2}-2 a}}{\sqrt[4]{-\sqrt{a^2+4 b}-a}}\right)+2 \left(\sqrt{a^2+4 b}-a\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{2 b}{x^2}-2 a}}{\sqrt[4]{\sqrt{a^2+4 b}-a}}\right)\right)}{2 x^3 \sqrt{a^2+4 b} \left(\frac{2 b}{x^2}-2 a\right)^{3/4}}","-\frac{1}{2} \text{RootSum}\left[-\text{$\#$1}^8+\text{$\#$1}^4 a+b\&,\frac{\text{$\#$1}^3 \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\text{$\#$1}^3 \log (x)}{2 \text{$\#$1}^4-a}\&\right]",1,"((-(b*x^2) + a*x^4)^(3/4)*(-2*(-a - Sqrt[a^2 + 4*b])^(3/4)*ArcTan[(-2*a + (2*b)/x^2)^(1/4)/(-a - Sqrt[a^2 + 4*b])^(1/4)] + 2*(-a + Sqrt[a^2 + 4*b])^(3/4)*ArcTan[(-2*a + (2*b)/x^2)^(1/4)/(-a + Sqrt[a^2 + 4*b])^(1/4)] - (-a - Sqrt[a^2 + 4*b])^(3/4)*Log[2^(3/4)*(-a - Sqrt[a^2 + 4*b])^(1/4) - 2*(-a + b/x^2)^(1/4)] + (-a + Sqrt[a^2 + 4*b])^(3/4)*Log[2^(3/4)*(-a + Sqrt[a^2 + 4*b])^(1/4) - 2*(-a + b/x^2)^(1/4)] + (-a - Sqrt[a^2 + 4*b])^(3/4)*Log[2^(3/4)*(-a - Sqrt[a^2 + 4*b])^(1/4) + 2*(-a + b/x^2)^(1/4)] - (-a + Sqrt[a^2 + 4*b])^(3/4)*Log[2^(3/4)*(-a + Sqrt[a^2 + 4*b])^(1/4) + 2*(-a + b/x^2)^(1/4)]))/(2*Sqrt[a^2 + 4*b]*(-2*a + (2*b)/x^2)^(3/4)*x^3)","B",1
936,1,423,71,0.1115208,"\int \frac{-b+a x^2}{\left(-b+a x^2+x^4\right) \sqrt[4]{-b x^2+a x^4}} \, dx","Integrate[(-b + a*x^2)/((-b + a*x^2 + x^4)*(-(b*x^2) + a*x^4)^(1/4)),x]","\frac{\left(a x^4-b x^2\right)^{3/4} \left(-\left(-\sqrt{a^2+4 b}-a\right)^{3/4} \log \left(2^{3/4} \sqrt[4]{-\sqrt{a^2+4 b}-a}-2 \sqrt[4]{\frac{b}{x^2}-a}\right)+\left(\sqrt{a^2+4 b}-a\right)^{3/4} \log \left(2^{3/4} \sqrt[4]{\sqrt{a^2+4 b}-a}-2 \sqrt[4]{\frac{b}{x^2}-a}\right)+\left(-\sqrt{a^2+4 b}-a\right)^{3/4} \log \left(2^{3/4} \sqrt[4]{-\sqrt{a^2+4 b}-a}+2 \sqrt[4]{\frac{b}{x^2}-a}\right)-\left(\sqrt{a^2+4 b}-a\right)^{3/4} \log \left(2^{3/4} \sqrt[4]{\sqrt{a^2+4 b}-a}+2 \sqrt[4]{\frac{b}{x^2}-a}\right)-2 \left(-\sqrt{a^2+4 b}-a\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{2 b}{x^2}-2 a}}{\sqrt[4]{-\sqrt{a^2+4 b}-a}}\right)+2 \left(\sqrt{a^2+4 b}-a\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{2 b}{x^2}-2 a}}{\sqrt[4]{\sqrt{a^2+4 b}-a}}\right)\right)}{2 x^3 \sqrt{a^2+4 b} \left(\frac{2 b}{x^2}-2 a\right)^{3/4}}","-\frac{1}{2} \text{RootSum}\left[-\text{$\#$1}^8+\text{$\#$1}^4 a+b\&,\frac{\text{$\#$1}^3 \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\text{$\#$1}^3 \log (x)}{2 \text{$\#$1}^4-a}\&\right]",1,"((-(b*x^2) + a*x^4)^(3/4)*(-2*(-a - Sqrt[a^2 + 4*b])^(3/4)*ArcTan[(-2*a + (2*b)/x^2)^(1/4)/(-a - Sqrt[a^2 + 4*b])^(1/4)] + 2*(-a + Sqrt[a^2 + 4*b])^(3/4)*ArcTan[(-2*a + (2*b)/x^2)^(1/4)/(-a + Sqrt[a^2 + 4*b])^(1/4)] - (-a - Sqrt[a^2 + 4*b])^(3/4)*Log[2^(3/4)*(-a - Sqrt[a^2 + 4*b])^(1/4) - 2*(-a + b/x^2)^(1/4)] + (-a + Sqrt[a^2 + 4*b])^(3/4)*Log[2^(3/4)*(-a + Sqrt[a^2 + 4*b])^(1/4) - 2*(-a + b/x^2)^(1/4)] + (-a - Sqrt[a^2 + 4*b])^(3/4)*Log[2^(3/4)*(-a - Sqrt[a^2 + 4*b])^(1/4) + 2*(-a + b/x^2)^(1/4)] - (-a + Sqrt[a^2 + 4*b])^(3/4)*Log[2^(3/4)*(-a + Sqrt[a^2 + 4*b])^(1/4) + 2*(-a + b/x^2)^(1/4)]))/(2*Sqrt[a^2 + 4*b]*(-2*a + (2*b)/x^2)^(3/4)*x^3)","B",1
937,0,0,71,2.6530532,"\int \frac{\sqrt[3]{-x+x^3}}{b+a x^6} \, dx","Integrate[(-x + x^3)^(1/3)/(b + a*x^6),x]","\int \frac{\sqrt[3]{-x+x^3}}{b+a x^6} \, dx","\frac{\text{RootSum}\left[\text{$\#$1}^9 (-b)+3 \text{$\#$1}^6 b-3 \text{$\#$1}^3 b+a+b\&,\frac{\text{$\#$1} \log \left(\sqrt[3]{x^3-x}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^3-1}\&\right]}{6 b}",1,"Integrate[(-x + x^3)^(1/3)/(b + a*x^6), x]","F",-1
938,0,0,71,1.5797075,"\int \frac{\sqrt[3]{-x+x^3}}{b+a x^6} \, dx","Integrate[(-x + x^3)^(1/3)/(b + a*x^6),x]","\int \frac{\sqrt[3]{-x+x^3}}{b+a x^6} \, dx","\frac{\text{RootSum}\left[\text{$\#$1}^9 (-b)+3 \text{$\#$1}^6 b-3 \text{$\#$1}^3 b+a+b\&,\frac{\text{$\#$1} \log \left(\sqrt[3]{x^3-x}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^3-1}\&\right]}{6 b}",1,"Integrate[(-x + x^3)^(1/3)/(b + a*x^6), x]","F",-1
939,0,0,71,0.467135,"\int \frac{\left(-2 b+a x^6\right) \left(b+a x^6\right)^{3/4}}{x^4 \left(b-c x^4+a x^6\right)} \, dx","Integrate[((-2*b + a*x^6)*(b + a*x^6)^(3/4))/(x^4*(b - c*x^4 + a*x^6)),x]","\int \frac{\left(-2 b+a x^6\right) \left(b+a x^6\right)^{3/4}}{x^4 \left(b-c x^4+a x^6\right)} \, dx","-c^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a x^6+b}}\right)-c^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a x^6+b}}\right)+\frac{2 \left(a x^6+b\right)^{3/4}}{3 x^3}",1,"Integrate[((-2*b + a*x^6)*(b + a*x^6)^(3/4))/(x^4*(b - c*x^4 + a*x^6)), x]","F",-1
940,0,0,71,0.6190813,"\int \frac{b+a x^8}{\left(-b+a x^8\right) \sqrt[4]{-b+c x^4+a x^8}} \, dx","Integrate[(b + a*x^8)/((-b + a*x^8)*(-b + c*x^4 + a*x^8)^(1/4)),x]","\int \frac{b+a x^8}{\left(-b+a x^8\right) \sqrt[4]{-b+c x^4+a x^8}} \, dx","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a x^8-b+c x^4}}\right)}{2 \sqrt[4]{c}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a x^8-b+c x^4}}\right)}{2 \sqrt[4]{c}}",1,"Integrate[(b + a*x^8)/((-b + a*x^8)*(-b + c*x^4 + a*x^8)^(1/4)), x]","F",-1
941,0,0,71,0.1331156,"\int \frac{\sqrt{1+x^5} \left(-2+3 x^5\right)}{1+x^4+2 x^5+x^{10}} \, dx","Integrate[(Sqrt[1 + x^5]*(-2 + 3*x^5))/(1 + x^4 + 2*x^5 + x^10),x]","\int \frac{\sqrt{1+x^5} \left(-2+3 x^5\right)}{1+x^4+2 x^5+x^{10}} \, dx","-\frac{\tan ^{-1}\left(\frac{\sqrt{2} x \sqrt{x^5+1}}{x^5-x^2+1}\right)}{\sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt{x^5+1}}{x^5+x^2+1}\right)}{\sqrt{2}}",1,"Integrate[(Sqrt[1 + x^5]*(-2 + 3*x^5))/(1 + x^4 + 2*x^5 + x^10), x]","F",-1
942,1,99,71,0.1362966,"\int \frac{1}{\left(2 x+\sqrt{1+x^2}\right)^2} \, dx","Integrate[(2*x + Sqrt[1 + x^2])^(-2),x]","\frac{1}{9} \left(\frac{12 x}{1-3 x^2}-\frac{\frac{6 x^2+6}{1-3 x^2}+\sqrt{3} \sqrt{-x^2-1} \tan ^{-1}\left(\frac{1}{2} \sqrt{3} \sqrt{-x^2-1}\right)}{\sqrt{x^2+1}}-\sqrt{3} \tanh ^{-1}\left(\sqrt{3} x\right)\right)","-\frac{4 x}{3 \left(3 x^2-1\right)}+\frac{2 \sqrt{x^2+1}}{3 \left(3 x^2-1\right)}-\frac{2 \tanh ^{-1}\left(\frac{x}{\sqrt{3}}-\frac{\sqrt{x^2+1}}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"((12*x)/(1 - 3*x^2) - ((6 + 6*x^2)/(1 - 3*x^2) + Sqrt[3]*Sqrt[-1 - x^2]*ArcTan[(Sqrt[3]*Sqrt[-1 - x^2])/2])/Sqrt[1 + x^2] - Sqrt[3]*ArcTanh[Sqrt[3]*x])/9","A",1
943,1,104,71,0.1431554,"\int \frac{\sqrt{a x^2+x \sqrt{-b+a^2 x^2}}}{x \sqrt{-b+a^2 x^2}} \, dx","Integrate[Sqrt[a*x^2 + x*Sqrt[-b + a^2*x^2]]/(x*Sqrt[-b + a^2*x^2]),x]","\frac{\sqrt{2} \sqrt{x \left(\sqrt{a^2 x^2-b}+a x\right)} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x}}{\sqrt{\sqrt{a^2 x^2-b}+a x}}\right)}{\sqrt{a} \sqrt{x} \sqrt{\sqrt{a^2 x^2-b}+a x}}","-\frac{\sqrt{2} \log \left(\sqrt{a^2 x^2-b}-\sqrt{2} \sqrt{a} \sqrt{x \sqrt{a^2 x^2-b}+a x^2}+a x\right)}{\sqrt{a}}",1,"(Sqrt[2]*Sqrt[x*(a*x + Sqrt[-b + a^2*x^2])]*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[x])/Sqrt[a*x + Sqrt[-b + a^2*x^2]]])/(Sqrt[a]*Sqrt[x]*Sqrt[a*x + Sqrt[-b + a^2*x^2]])","A",1
944,1,71,71,0.1483955,"\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{1+x^2} \, dx","Integrate[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/(1 + x^2),x]","\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^4-2 \text{$\#$1}^2+1}\&\right]","\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^4-2 \text{$\#$1}^2+1}\&\right]",1,"RootSum[2 - 4*#1^2 + 6*#1^4 - 4*#1^6 + #1^8 & , (Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1)/(1 - 2*#1^2 + #1^4) & ]","A",1
945,1,71,71,0.0607563,"\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{1+x^2} \, dx","Integrate[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/(1 + x^2),x]","\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^4-2 \text{$\#$1}^2+1}\&\right]","\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^4-2 \text{$\#$1}^2+1}\&\right]",1,"RootSum[2 - 4*#1^2 + 6*#1^4 - 4*#1^6 + #1^8 & , (Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1)/(1 - 2*#1^2 + #1^4) & ]","A",1
946,1,72,72,0.0708318,"\int \frac{\sqrt[3]{1+2 x+x^2}}{4+x+x^2+x^3} \, dx","Integrate[(1 + 2*x + x^2)^(1/3)/(4 + x + x^2 + x^3),x]","\frac{\sqrt[3]{(x+1)^2} \text{RootSum}\left[\text{$\#$1}^9-2 \text{$\#$1}^6+2 \text{$\#$1}^3+3\&,\frac{\text{$\#$1}^2 \log \left(\sqrt[3]{x+1}-\text{$\#$1}\right)}{3 \text{$\#$1}^6-4 \text{$\#$1}^3+2}\&\right]}{(x+1)^{2/3}}","\frac{\sqrt[3]{(x+1)^2} \text{RootSum}\left[\text{$\#$1}^9-2 \text{$\#$1}^6+2 \text{$\#$1}^3+3\&,\frac{\text{$\#$1}^2 \log \left(\sqrt[3]{x+1}-\text{$\#$1}\right)}{3 \text{$\#$1}^6-4 \text{$\#$1}^3+2}\&\right]}{(x+1)^{2/3}}",1,"(((1 + x)^2)^(1/3)*RootSum[3 + 2*#1^3 - 2*#1^6 + #1^9 & , (Log[(1 + x)^(1/3) - #1]*#1^2)/(2 - 4*#1^3 + 3*#1^6) & ])/(1 + x)^(2/3)","A",1
947,1,350,72,1.4396288,"\int \frac{\left(-1+x^2\right) \sqrt{1+x^4}}{\left(1-x+x^2\right) \left(1+x+x^2\right)^2} \, dx","Integrate[((-1 + x^2)*Sqrt[1 + x^4])/((1 - x + x^2)*(1 + x + x^2)^2),x]","\frac{1}{8} \left(\frac{4 \sqrt{x^4+1}}{x^2+x+1}-i \sqrt{6+6 i \sqrt{3}} \tanh ^{-1}\left(\frac{2+\left(-1-i \sqrt{3}\right) x^2}{\sqrt{2+2 i \sqrt{3}} \sqrt{x^4+1}}\right)-\sqrt{2+2 i \sqrt{3}} \tanh ^{-1}\left(\frac{2+\left(-1-i \sqrt{3}\right) x^2}{\sqrt{2+2 i \sqrt{3}} \sqrt{x^4+1}}\right)+i \sqrt{6-6 i \sqrt{3}} \tanh ^{-1}\left(\frac{2+i \left(\sqrt{3}+i\right) x^2}{\sqrt{2-2 i \sqrt{3}} \sqrt{x^4+1}}\right)-\sqrt{2-2 i \sqrt{3}} \tanh ^{-1}\left(\frac{2+i \left(\sqrt{3}+i\right) x^2}{\sqrt{2-2 i \sqrt{3}} \sqrt{x^4+1}}\right)+4 \sqrt[4]{-1} \Pi \left(-\sqrt[6]{-1};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+4 \sqrt[4]{-1} \Pi \left(-(-1)^{5/6};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)\right)-\frac{1}{2} \sqrt[4]{-1} F\left(\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)","\frac{\sqrt{x^4+1}}{2 \left(x^2+x+1\right)}+\frac{1}{2} \tan ^{-1}\left(\frac{x}{\sqrt{x^4+1}+x^2-x+1}\right)-\frac{3}{2} \tan ^{-1}\left(\frac{x}{\sqrt{x^4+1}+x^2+x+1}\right)",1,"-1/2*((-1)^(1/4)*EllipticF[I*ArcSinh[(-1)^(1/4)*x], -1]) + ((4*Sqrt[1 + x^4])/(1 + x + x^2) - Sqrt[2 + (2*I)*Sqrt[3]]*ArcTanh[(2 + (-1 - I*Sqrt[3])*x^2)/(Sqrt[2 + (2*I)*Sqrt[3]]*Sqrt[1 + x^4])] - I*Sqrt[6 + (6*I)*Sqrt[3]]*ArcTanh[(2 + (-1 - I*Sqrt[3])*x^2)/(Sqrt[2 + (2*I)*Sqrt[3]]*Sqrt[1 + x^4])] - Sqrt[2 - (2*I)*Sqrt[3]]*ArcTanh[(2 + I*(I + Sqrt[3])*x^2)/(Sqrt[2 - (2*I)*Sqrt[3]]*Sqrt[1 + x^4])] + I*Sqrt[6 - (6*I)*Sqrt[3]]*ArcTanh[(2 + I*(I + Sqrt[3])*x^2)/(Sqrt[2 - (2*I)*Sqrt[3]]*Sqrt[1 + x^4])] + 4*(-1)^(1/4)*EllipticPi[-(-1)^(1/6), I*ArcSinh[(-1)^(1/4)*x], -1] + 4*(-1)^(1/4)*EllipticPi[-(-1)^(5/6), I*ArcSinh[(-1)^(1/4)*x], -1])/8","C",1
948,1,69,72,0.0267491,"\int x^4 \sqrt[4]{-x^2+x^4} \, dx","Integrate[x^4*(-x^2 + x^4)^(1/4),x]","\frac{x \sqrt[4]{x^2 \left(x^2-1\right)} \left(7 \, _2F_1\left(-\frac{1}{4},\frac{3}{4};\frac{7}{4};x^2\right)+\sqrt[4]{1-x^2} \left(8 x^4-x^2-7\right)\right)}{48 \sqrt[4]{1-x^2}}","\frac{7}{128} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^2}}\right)-\frac{7}{128} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^2}}\right)+\frac{1}{192} \sqrt[4]{x^4-x^2} \left(32 x^5-4 x^3-7 x\right)",1,"(x*(x^2*(-1 + x^2))^(1/4)*((1 - x^2)^(1/4)*(-7 - x^2 + 8*x^4) + 7*Hypergeometric2F1[-1/4, 3/4, 7/4, x^2]))/(48*(1 - x^2)^(1/4))","C",1
949,1,38,72,0.0118679,"\int \frac{x^4 \sqrt[4]{x^3+x^4}}{1+x} \, dx","Integrate[(x^4*(x^3 + x^4)^(1/4))/(1 + x),x]","\frac{4 x^8 (x+1)^{3/4} \, _2F_1\left(\frac{3}{4},\frac{23}{4};\frac{27}{4};-x\right)}{23 \left(x^3 (x+1)\right)^{3/4}}","\frac{4389 \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+x^3}}\right)}{4096}-\frac{4389 \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+x^3}}\right)}{4096}+\frac{\sqrt[4]{x^4+x^3} \left(2048 x^4-2432 x^3+3040 x^2-4180 x+7315\right)}{10240}",1,"(4*x^8*(1 + x)^(3/4)*Hypergeometric2F1[3/4, 23/4, 27/4, -x])/(23*(x^3*(1 + x))^(3/4))","C",1
950,0,0,72,0.5246585,"\int \frac{\left(4 b+a x^3\right) \left(-b-a x^3+x^4\right)}{x^4 \sqrt[4]{b+a x^3} \left(-b-a x^3+2 x^4\right)} \, dx","Integrate[((4*b + a*x^3)*(-b - a*x^3 + x^4))/(x^4*(b + a*x^3)^(1/4)*(-b - a*x^3 + 2*x^4)),x]","\int \frac{\left(4 b+a x^3\right) \left(-b-a x^3+x^4\right)}{x^4 \sqrt[4]{b+a x^3} \left(-b-a x^3+2 x^4\right)} \, dx","-\frac{4 \left(a x^3+b\right)^{3/4}}{3 x^3}-2^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a x^3+b}}{\sqrt[4]{2} x}\right)+2^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{a x^3+b}}\right)",1,"Integrate[((4*b + a*x^3)*(-b - a*x^3 + x^4))/(x^4*(b + a*x^3)^(1/4)*(-b - a*x^3 + 2*x^4)), x]","F",-1
951,1,245,72,0.8474299,"\int \frac{b+a x^2}{\left(b+a x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Integrate[(b + a*x^2)/((b + a*x^4)*(b*x^2 + a*x^4)^(1/4)),x]","-\frac{\left(x^2 \left(a x^2+b\right)\right)^{3/4} \left(\frac{\left(\sqrt{-a}+\sqrt{b}\right) \left(\tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a-\sqrt{-a} \sqrt{b}}}\right)-\tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a-\sqrt{-a} \sqrt{b}}}\right)\right)}{\sqrt[4]{a-\sqrt{-a} \sqrt{b}}}-\frac{\left(\sqrt{-a}-\sqrt{b}\right) \left(\tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\sqrt{-a} \sqrt{b}+a}}\right)-\tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\sqrt{-a} \sqrt{b}+a}}\right)\right)}{\sqrt[4]{\sqrt{-a} \sqrt{b}+a}}\right)}{2 \sqrt{b} x^3 \left(a+\frac{b}{x^2}\right)^{3/4}}","-\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{\text{$\#$1}^3 \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\text{$\#$1}^3 \log (x)}{\text{$\#$1}^4-a}\&\right]",1,"-1/2*((x^2*(b + a*x^2))^(3/4)*(((Sqrt[-a] + Sqrt[b])*(ArcTan[(a + b/x^2)^(1/4)/(a - Sqrt[-a]*Sqrt[b])^(1/4)] - ArcTanh[(a + b/x^2)^(1/4)/(a - Sqrt[-a]*Sqrt[b])^(1/4)]))/(a - Sqrt[-a]*Sqrt[b])^(1/4) - ((Sqrt[-a] - Sqrt[b])*(ArcTan[(a + b/x^2)^(1/4)/(a + Sqrt[-a]*Sqrt[b])^(1/4)] - ArcTanh[(a + b/x^2)^(1/4)/(a + Sqrt[-a]*Sqrt[b])^(1/4)]))/(a + Sqrt[-a]*Sqrt[b])^(1/4)))/(Sqrt[b]*(a + b/x^2)^(3/4)*x^3)","B",1
952,1,245,72,0.2300576,"\int \frac{b+a x^2}{\left(b+a x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Integrate[(b + a*x^2)/((b + a*x^4)*(b*x^2 + a*x^4)^(1/4)),x]","-\frac{\left(x^2 \left(a x^2+b\right)\right)^{3/4} \left(\frac{\left(\sqrt{-a}+\sqrt{b}\right) \left(\tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a-\sqrt{-a} \sqrt{b}}}\right)-\tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a-\sqrt{-a} \sqrt{b}}}\right)\right)}{\sqrt[4]{a-\sqrt{-a} \sqrt{b}}}-\frac{\left(\sqrt{-a}-\sqrt{b}\right) \left(\tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\sqrt{-a} \sqrt{b}+a}}\right)-\tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\sqrt{-a} \sqrt{b}+a}}\right)\right)}{\sqrt[4]{\sqrt{-a} \sqrt{b}+a}}\right)}{2 \sqrt{b} x^3 \left(a+\frac{b}{x^2}\right)^{3/4}}","-\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{\text{$\#$1}^3 \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\text{$\#$1}^3 \log (x)}{\text{$\#$1}^4-a}\&\right]",1,"-1/2*((x^2*(b + a*x^2))^(3/4)*(((Sqrt[-a] + Sqrt[b])*(ArcTan[(a + b/x^2)^(1/4)/(a - Sqrt[-a]*Sqrt[b])^(1/4)] - ArcTanh[(a + b/x^2)^(1/4)/(a - Sqrt[-a]*Sqrt[b])^(1/4)]))/(a - Sqrt[-a]*Sqrt[b])^(1/4) - ((Sqrt[-a] - Sqrt[b])*(ArcTan[(a + b/x^2)^(1/4)/(a + Sqrt[-a]*Sqrt[b])^(1/4)] - ArcTanh[(a + b/x^2)^(1/4)/(a + Sqrt[-a]*Sqrt[b])^(1/4)]))/(a + Sqrt[-a]*Sqrt[b])^(1/4)))/(Sqrt[b]*(a + b/x^2)^(3/4)*x^3)","B",1
953,1,72,72,0.0528426,"\int \frac{1-x}{\sqrt{3+2 x-5 x^2-4 x^3+x^4+2 x^5+x^6}} \, dx","Integrate[(1 - x)/Sqrt[3 + 2*x - 5*x^2 - 4*x^3 + x^4 + 2*x^5 + x^6],x]","-\frac{\left(x^2-1\right) \sqrt{x^2+2 x+3} \left(\log (x+1)-\log \left(\sqrt{2} \sqrt{x^2+2 x+3}+2\right)\right)}{\sqrt{2} \sqrt{\left(x^2-1\right)^2 \left(x^2+2 x+3\right)}}","-\sqrt{2} \tanh ^{-1}\left(\frac{(x+1) \left(\sqrt{2} x-\sqrt{2}\right)}{x^3+x^2-\sqrt{x^6+2 x^5+x^4-4 x^3-5 x^2+2 x+3}-x-1}\right)",1,"-(((-1 + x^2)*Sqrt[3 + 2*x + x^2]*(Log[1 + x] - Log[2 + Sqrt[2]*Sqrt[3 + 2*x + x^2]]))/(Sqrt[2]*Sqrt[(-1 + x^2)^2*(3 + 2*x + x^2)]))","A",1
954,0,0,72,0.580852,"\int \frac{\left(-1+3 x^4\right) \sqrt{1+x^2+2 x^4+x^8}}{\left(1-x+x^4\right)^2 \left(1+x+x^4\right)} \, dx","Integrate[((-1 + 3*x^4)*Sqrt[1 + x^2 + 2*x^4 + x^8])/((1 - x + x^4)^2*(1 + x + x^4)),x]","\int \frac{\left(-1+3 x^4\right) \sqrt{1+x^2+2 x^4+x^8}}{\left(1-x+x^4\right)^2 \left(1+x+x^4\right)} \, dx","-\frac{\sqrt{x^8+2 x^4+x^2+1}}{2 \left(x^4-x+1\right)}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{x^4+\sqrt{x^8+2 x^4+x^2+1}+x+1}\right)}{\sqrt{2}}",1,"Integrate[((-1 + 3*x^4)*Sqrt[1 + x^2 + 2*x^4 + x^8])/((1 - x + x^4)^2*(1 + x + x^4)), x]","F",-1
955,1,71,73,0.0774367,"\int \sqrt{c+b x+a x^2} \, dx","Integrate[Sqrt[c + b*x + a*x^2],x]","\frac{(2 a x+b) \sqrt{x (a x+b)+c}}{4 a}-\frac{\left(b^2-4 a c\right) \log \left(2 \sqrt{a} \sqrt{x (a x+b)+c}+2 a x+b\right)}{8 a^{3/2}}","\frac{\left(b^2-4 a c\right) \log \left(-2 \sqrt{a} \sqrt{a x^2+b x+c}+2 a x+b\right)}{8 a^{3/2}}+\frac{(2 a x+b) \sqrt{a x^2+b x+c}}{4 a}",1,"((b + 2*a*x)*Sqrt[c + x*(b + a*x)])/(4*a) - ((b^2 - 4*a*c)*Log[b + 2*a*x + 2*Sqrt[a]*Sqrt[c + x*(b + a*x)]])/(8*a^(3/2))","A",1
956,1,89,73,0.7979303,"\int \frac{-1+x}{\left(-1-2 x+x^2\right) \sqrt{-x+x^3}} \, dx","Integrate[(-1 + x)/((-1 - 2*x + x^2)*Sqrt[-x + x^3]),x]","-\frac{\sqrt{1-\frac{1}{x^2}} x^{3/2} \left(2 F\left(\left.\sin ^{-1}\left(\frac{1}{\sqrt{x}}\right)\right|-1\right)-\left(1+\sqrt{2}\right) \Pi \left(1-\sqrt{2};\left.\sin ^{-1}\left(\frac{1}{\sqrt{x}}\right)\right|-1\right)+\left(\sqrt{2}-1\right) \Pi \left(1+\sqrt{2};\left.\sin ^{-1}\left(\frac{1}{\sqrt{x}}\right)\right|-1\right)\right)}{\sqrt{x \left(x^2-1\right)}}","\frac{1}{4} \left(\sqrt{2}-2\right) \tanh ^{-1}\left(\frac{x-1}{\left(\sqrt{2}-1\right) \sqrt{x^3-x}}\right)+\frac{1}{4} \left(2+\sqrt{2}\right) \tanh ^{-1}\left(\frac{x-1}{\left(1+\sqrt{2}\right) \sqrt{x^3-x}}\right)",1,"-((Sqrt[1 - x^(-2)]*x^(3/2)*(2*EllipticF[ArcSin[1/Sqrt[x]], -1] - (1 + Sqrt[2])*EllipticPi[1 - Sqrt[2], ArcSin[1/Sqrt[x]], -1] + (-1 + Sqrt[2])*EllipticPi[1 + Sqrt[2], ArcSin[1/Sqrt[x]], -1]))/Sqrt[x*(-1 + x^2)])","C",1
957,1,93,73,0.6647229,"\int \frac{-2+3 x+x^2}{\left(-1-2 x+x^2\right) \sqrt{-x+x^3}} \, dx","Integrate[(-2 + 3*x + x^2)/((-1 - 2*x + x^2)*Sqrt[-x + x^3]),x]","-\frac{\sqrt{1-\frac{1}{x^2}} x^{3/2} \left(4 F\left(\left.\sin ^{-1}\left(\frac{1}{\sqrt{x}}\right)\right|-1\right)-\left(1+3 \sqrt{2}\right) \Pi \left(1-\sqrt{2};\left.\sin ^{-1}\left(\frac{1}{\sqrt{x}}\right)\right|-1\right)+\left(3 \sqrt{2}-1\right) \Pi \left(1+\sqrt{2};\left.\sin ^{-1}\left(\frac{1}{\sqrt{x}}\right)\right|-1\right)\right)}{\sqrt{x \left(x^2-1\right)}}","\frac{1}{4} \left(\sqrt{2}-6\right) \tanh ^{-1}\left(\frac{x-1}{\left(\sqrt{2}-1\right) \sqrt{x^3-x}}\right)+\frac{1}{4} \left(6+\sqrt{2}\right) \tanh ^{-1}\left(\frac{x-1}{\left(1+\sqrt{2}\right) \sqrt{x^3-x}}\right)",1,"-((Sqrt[1 - x^(-2)]*x^(3/2)*(4*EllipticF[ArcSin[1/Sqrt[x]], -1] - (1 + 3*Sqrt[2])*EllipticPi[1 - Sqrt[2], ArcSin[1/Sqrt[x]], -1] + (-1 + 3*Sqrt[2])*EllipticPi[1 + Sqrt[2], ArcSin[1/Sqrt[x]], -1]))/Sqrt[x*(-1 + x^2)])","C",1
958,0,0,73,0.1767872,"\int \frac{x \left(-3+x^2\right)}{\left(-1+x^2\right)^{2/3} \left(1-x^2+x^3\right)} \, dx","Integrate[(x*(-3 + x^2))/((-1 + x^2)^(2/3)*(1 - x^2 + x^3)),x]","\int \frac{x \left(-3+x^2\right)}{\left(-1+x^2\right)^{2/3} \left(1-x^2+x^3\right)} \, dx","\log \left(\sqrt[3]{x^2-1}-x\right)-\frac{1}{2} \log \left(x^2+\sqrt[3]{x^2-1} x+\left(x^2-1\right)^{2/3}\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^2-1}+x}\right)",1,"Integrate[(x*(-3 + x^2))/((-1 + x^2)^(2/3)*(1 - x^2 + x^3)), x]","F",-1
959,1,35,73,0.0104699,"\int x^2 \sqrt[4]{-x^3+x^4} \, dx","Integrate[x^2*(-x^3 + x^4)^(1/4),x]","\frac{4 \left((x-1) x^3\right)^{5/4} \, _2F_1\left(-\frac{11}{4},\frac{5}{4};\frac{9}{4};1-x\right)}{5 x^{15/4}}","\frac{77 \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^3}}\right)}{1024}-\frac{77 \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^3}}\right)}{1024}+\frac{\sqrt[4]{x^4-x^3} \left(384 x^3-32 x^2-44 x-77\right)}{1536}",1,"(4*((-1 + x)*x^3)^(5/4)*Hypergeometric2F1[-11/4, 5/4, 9/4, 1 - x])/(5*x^(15/4))","C",1
960,0,0,73,1.153121,"\int \frac{\left(3+x^4\right) \sqrt{x+x^4-x^5}}{\left(-1+x^4\right) \left(-1+x^3+x^4\right)} \, dx","Integrate[((3 + x^4)*Sqrt[x + x^4 - x^5])/((-1 + x^4)*(-1 + x^3 + x^4)),x]","\int \frac{\left(3+x^4\right) \sqrt{x+x^4-x^5}}{\left(-1+x^4\right) \left(-1+x^3+x^4\right)} \, dx","2 \tanh ^{-1}\left(\frac{x \sqrt{-x^5+x^4+x}}{x^4-x^3-1}\right)-2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt{-x^5+x^4+x}}{x^4-x^3-1}\right)",1,"Integrate[((3 + x^4)*Sqrt[x + x^4 - x^5])/((-1 + x^4)*(-1 + x^3 + x^4)), x]","F",-1
961,1,372,73,1.4176913,"\int \frac{\left(-b+a x^2\right) \sqrt{b x+a x^3}}{b^2 x+2 (-1+a b) x^3+a^2 x^5} \, dx","Integrate[((-b + a*x^2)*Sqrt[b*x + a*x^3])/(b^2*x + 2*(-1 + a*b)*x^3 + a^2*x^5),x]","-\frac{i x^{3/2} \sqrt{\frac{b}{a x^2}+1} \left(-\Pi \left(-\frac{i \sqrt{a}}{\sqrt{b} \sqrt{\frac{-a b+\sqrt{1-2 a b}+1}{b^2}}};\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}}{\sqrt{x}}\right)\right|-1\right)-\Pi \left(\frac{i \sqrt{a}}{\sqrt{b} \sqrt{\frac{-a b+\sqrt{1-2 a b}+1}{b^2}}};\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}}{\sqrt{x}}\right)\right|-1\right)-\Pi \left(-\frac{i \sqrt{a}}{\sqrt{b} \sqrt{-\frac{a b+\sqrt{1-2 a b}-1}{b^2}}};\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}}{\sqrt{x}}\right)\right|-1\right)-\Pi \left(\frac{i \sqrt{a}}{\sqrt{b} \sqrt{-\frac{a b+\sqrt{1-2 a b}-1}{b^2}}};\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}}{\sqrt{x}}\right)\right|-1\right)+2 F\left(\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}}{\sqrt{x}}\right)\right|-1\right)\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}} \sqrt{x \left(a x^2+b\right)}}","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{a x^3+b x}}{a x^2+b}\right)}{\sqrt[4]{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{a x^3+b x}}{a x^2+b}\right)}{\sqrt[4]{2}}",1,"((-I)*Sqrt[1 + b/(a*x^2)]*x^(3/2)*(2*EllipticF[I*ArcSinh[Sqrt[(I*Sqrt[b])/Sqrt[a]]/Sqrt[x]], -1] - EllipticPi[((-I)*Sqrt[a])/(Sqrt[b]*Sqrt[(1 - a*b + Sqrt[1 - 2*a*b])/b^2]), I*ArcSinh[Sqrt[(I*Sqrt[b])/Sqrt[a]]/Sqrt[x]], -1] - EllipticPi[(I*Sqrt[a])/(Sqrt[b]*Sqrt[(1 - a*b + Sqrt[1 - 2*a*b])/b^2]), I*ArcSinh[Sqrt[(I*Sqrt[b])/Sqrt[a]]/Sqrt[x]], -1] - EllipticPi[((-I)*Sqrt[a])/(Sqrt[b]*Sqrt[-((-1 + a*b + Sqrt[1 - 2*a*b])/b^2)]), I*ArcSinh[Sqrt[(I*Sqrt[b])/Sqrt[a]]/Sqrt[x]], -1] - EllipticPi[(I*Sqrt[a])/(Sqrt[b]*Sqrt[-((-1 + a*b + Sqrt[1 - 2*a*b])/b^2)]), I*ArcSinh[Sqrt[(I*Sqrt[b])/Sqrt[a]]/Sqrt[x]], -1]))/(Sqrt[(I*Sqrt[b])/Sqrt[a]]*Sqrt[x*(b + a*x^2)])","C",1
962,1,381,73,1.5860771,"\int \frac{\left(-2+x^3\right) \left(1+x^3\right)^{2/3}}{x^3 \left(2+x^3+x^6\right)} \, dx","Integrate[((-2 + x^3)*(1 + x^3)^(2/3))/(x^3*(2 + x^3 + x^6)),x]","\frac{\left(x^3+1\right)^{2/3}}{2 x^2}+\frac{i \left(-\frac{2 \log \left(\sqrt[3]{\sqrt{7}+i}-\frac{\sqrt[3]{\sqrt{7}-i} x}{\sqrt[3]{x^3+1}}\right)}{\sqrt[3]{\frac{\sqrt{7}-i}{\sqrt{7}+i}}}+2 \sqrt[3]{\frac{\sqrt{7}-i}{\sqrt{7}+i}} \log \left(\sqrt[3]{\sqrt{7}-i}-\frac{\sqrt[3]{\sqrt{7}+i} x}{\sqrt[3]{x^3+1}}\right)+\frac{2 \left(2 \sqrt{3} \tan ^{-1}\left(\frac{1+\frac{\left(\sqrt{7}-i\right)^{2/3} x}{\sqrt[3]{x^3+1}}}{\sqrt{3}}\right)+\log \left(\frac{2 x}{\sqrt[3]{x^3+1}}+\frac{\left(\sqrt{7}-i\right)^{2/3} x^2}{\left(x^3+1\right)^{2/3}}+\left(\sqrt{7}+i\right)^{2/3}\right)\right)}{\left(\sqrt{7}-i\right)^{2/3}}-\frac{2 \left(2 \sqrt{3} \tan ^{-1}\left(\frac{1+\frac{\left(\sqrt{7}+i\right)^{2/3} x}{\sqrt[3]{x^3+1}}}{\sqrt{3}}\right)+\log \left(\frac{2 x}{\sqrt[3]{x^3+1}}+\frac{\left(\sqrt{7}+i\right)^{2/3} x^2}{\left(x^3+1\right)^{2/3}}+\left(\sqrt{7}-i\right)^{2/3}\right)\right)}{\left(\sqrt{7}+i\right)^{2/3}}\right)}{3 \sqrt{7}}","\frac{\left(x^3+1\right)^{2/3}}{2 x^2}-\frac{2}{3} \text{RootSum}\left[2 \text{$\#$1}^6-3 \text{$\#$1}^3+2\&,\frac{\log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)-\log (x)}{4 \text{$\#$1}^4-3 \text{$\#$1}}\&\right]",1,"(1 + x^3)^(2/3)/(2*x^2) + ((I/3)*((2*(2*Sqrt[3]*ArcTan[(1 + ((-I + Sqrt[7])^(2/3)*x)/(1 + x^3)^(1/3))/Sqrt[3]] + Log[(I + Sqrt[7])^(2/3) + ((-I + Sqrt[7])^(2/3)*x^2)/(1 + x^3)^(2/3) + (2*x)/(1 + x^3)^(1/3)]))/(-I + Sqrt[7])^(2/3) - (2*(2*Sqrt[3]*ArcTan[(1 + ((I + Sqrt[7])^(2/3)*x)/(1 + x^3)^(1/3))/Sqrt[3]] + Log[(-I + Sqrt[7])^(2/3) + ((I + Sqrt[7])^(2/3)*x^2)/(1 + x^3)^(2/3) + (2*x)/(1 + x^3)^(1/3)]))/(I + Sqrt[7])^(2/3) - (2*Log[(I + Sqrt[7])^(1/3) - ((-I + Sqrt[7])^(1/3)*x)/(1 + x^3)^(1/3)])/((-I + Sqrt[7])/(I + Sqrt[7]))^(1/3) + 2*((-I + Sqrt[7])/(I + Sqrt[7]))^(1/3)*Log[(-I + Sqrt[7])^(1/3) - ((I + Sqrt[7])^(1/3)*x)/(1 + x^3)^(1/3)]))/Sqrt[7]","C",0
963,1,381,73,0.2121172,"\int \frac{\left(-2+x^3\right) \left(1+x^3\right)^{2/3}}{x^3 \left(2+x^3+x^6\right)} \, dx","Integrate[((-2 + x^3)*(1 + x^3)^(2/3))/(x^3*(2 + x^3 + x^6)),x]","\frac{\left(x^3+1\right)^{2/3}}{2 x^2}+\frac{i \left(-\frac{2 \log \left(\sqrt[3]{\sqrt{7}+i}-\frac{\sqrt[3]{\sqrt{7}-i} x}{\sqrt[3]{x^3+1}}\right)}{\sqrt[3]{\frac{\sqrt{7}-i}{\sqrt{7}+i}}}+2 \sqrt[3]{\frac{\sqrt{7}-i}{\sqrt{7}+i}} \log \left(\sqrt[3]{\sqrt{7}-i}-\frac{\sqrt[3]{\sqrt{7}+i} x}{\sqrt[3]{x^3+1}}\right)+\frac{2 \left(2 \sqrt{3} \tan ^{-1}\left(\frac{1+\frac{\left(\sqrt{7}-i\right)^{2/3} x}{\sqrt[3]{x^3+1}}}{\sqrt{3}}\right)+\log \left(\frac{2 x}{\sqrt[3]{x^3+1}}+\frac{\left(\sqrt{7}-i\right)^{2/3} x^2}{\left(x^3+1\right)^{2/3}}+\left(\sqrt{7}+i\right)^{2/3}\right)\right)}{\left(\sqrt{7}-i\right)^{2/3}}-\frac{2 \left(2 \sqrt{3} \tan ^{-1}\left(\frac{1+\frac{\left(\sqrt{7}+i\right)^{2/3} x}{\sqrt[3]{x^3+1}}}{\sqrt{3}}\right)+\log \left(\frac{2 x}{\sqrt[3]{x^3+1}}+\frac{\left(\sqrt{7}+i\right)^{2/3} x^2}{\left(x^3+1\right)^{2/3}}+\left(\sqrt{7}-i\right)^{2/3}\right)\right)}{\left(\sqrt{7}+i\right)^{2/3}}\right)}{3 \sqrt{7}}","\frac{\left(x^3+1\right)^{2/3}}{2 x^2}-\frac{2}{3} \text{RootSum}\left[2 \text{$\#$1}^6-3 \text{$\#$1}^3+2\&,\frac{\log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)-\log (x)}{4 \text{$\#$1}^4-3 \text{$\#$1}}\&\right]",1,"(1 + x^3)^(2/3)/(2*x^2) + ((I/3)*((2*(2*Sqrt[3]*ArcTan[(1 + ((-I + Sqrt[7])^(2/3)*x)/(1 + x^3)^(1/3))/Sqrt[3]] + Log[(I + Sqrt[7])^(2/3) + ((-I + Sqrt[7])^(2/3)*x^2)/(1 + x^3)^(2/3) + (2*x)/(1 + x^3)^(1/3)]))/(-I + Sqrt[7])^(2/3) - (2*(2*Sqrt[3]*ArcTan[(1 + ((I + Sqrt[7])^(2/3)*x)/(1 + x^3)^(1/3))/Sqrt[3]] + Log[(-I + Sqrt[7])^(2/3) + ((I + Sqrt[7])^(2/3)*x^2)/(1 + x^3)^(2/3) + (2*x)/(1 + x^3)^(1/3)]))/(I + Sqrt[7])^(2/3) - (2*Log[(I + Sqrt[7])^(1/3) - ((-I + Sqrt[7])^(1/3)*x)/(1 + x^3)^(1/3)])/((-I + Sqrt[7])/(I + Sqrt[7]))^(1/3) + 2*((-I + Sqrt[7])/(I + Sqrt[7]))^(1/3)*Log[(-I + Sqrt[7])^(1/3) - ((I + Sqrt[7])^(1/3)*x)/(1 + x^3)^(1/3)]))/Sqrt[7]","C",0
964,0,0,73,0.9352172,"\int \frac{\left(-3+2 x^5\right) \sqrt{x+2 x^4+x^6}}{\left(1+x^5\right) \left(1+x^3+x^5\right)} \, dx","Integrate[((-3 + 2*x^5)*Sqrt[x + 2*x^4 + x^6])/((1 + x^5)*(1 + x^3 + x^5)),x]","\int \frac{\left(-3+2 x^5\right) \sqrt{x+2 x^4+x^6}}{\left(1+x^5\right) \left(1+x^3+x^5\right)} \, dx","2 \tanh ^{-1}\left(\frac{x \sqrt{x^6+2 x^4+x}}{x^5+2 x^3+1}\right)-2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt{x^6+2 x^4+x}}{x^5+2 x^3+1}\right)",1,"Integrate[((-3 + 2*x^5)*Sqrt[x + 2*x^4 + x^6])/((1 + x^5)*(1 + x^3 + x^5)), x]","F",-1
965,0,0,73,0.232918,"\int \frac{\sqrt{-1+x^2+x^4+x^6} \left(1+x^4+2 x^6\right)}{1-x^4-2 x^6+x^8+2 x^{10}+x^{12}} \, dx","Integrate[(Sqrt[-1 + x^2 + x^4 + x^6]*(1 + x^4 + 2*x^6))/(1 - x^4 - 2*x^6 + x^8 + 2*x^10 + x^12),x]","\int \frac{\sqrt{-1+x^2+x^4+x^6} \left(1+x^4+2 x^6\right)}{1-x^4-2 x^6+x^8+2 x^{10}+x^{12}} \, dx","-\frac{1}{2} \sqrt{1+i} \tan ^{-1}\left(\frac{\sqrt{-1-i} x}{\sqrt{x^6+x^4+x^2-1}}\right)-\frac{1}{2} \sqrt{1-i} \tan ^{-1}\left(\frac{\sqrt{-1+i} x}{\sqrt{x^6+x^4+x^2-1}}\right)",1,"Integrate[(Sqrt[-1 + x^2 + x^4 + x^6]*(1 + x^4 + 2*x^6))/(1 - x^4 - 2*x^6 + x^8 + 2*x^10 + x^12), x]","F",-1
966,1,58,73,0.2078086,"\int \frac{\sqrt{x^2-x \sqrt{-x+x^2}}}{x^3} \, dx","Integrate[Sqrt[x^2 - x*Sqrt[-x + x^2]]/x^3,x]","\frac{4 x \left(4 x^2-\left(4 \sqrt{(x-1) x}+9\right) x+7 \sqrt{(x-1) x}+3\right)}{15 \left(x \left(x-\sqrt{(x-1) x}\right)\right)^{3/2}}","\frac{4 (x-3) \sqrt{-x \left(\sqrt{x^2-x}-x\right)}}{15 x^2}-\frac{4 \sqrt{x^2-x} \sqrt{-x \left(\sqrt{x^2-x}-x\right)}}{15 x^2}",1,"(4*x*(3 + 4*x^2 + 7*Sqrt[(-1 + x)*x] - x*(9 + 4*Sqrt[(-1 + x)*x])))/(15*(x*(x - Sqrt[(-1 + x)*x]))^(3/2))","A",1
967,1,73,74,0.0173711,"\int \frac{1}{x \left(1+x^2\right)^{2/3}} \, dx","Integrate[1/(x*(1 + x^2)^(2/3)),x]","\frac{1}{2} \log \left(1-\sqrt[3]{x^2+1}\right)-\frac{1}{4} \log \left(\left(x^2+1\right)^{2/3}+\sqrt[3]{x^2+1}+1\right)-\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x^2+1}+1}{\sqrt{3}}\right)","\frac{1}{2} \log \left(\sqrt[3]{x^2+1}-1\right)-\frac{1}{4} \log \left(\left(x^2+1\right)^{2/3}+\sqrt[3]{x^2+1}+1\right)-\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x^2+1}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)",1,"-1/2*(Sqrt[3]*ArcTan[(1 + 2*(1 + x^2)^(1/3))/Sqrt[3]]) + Log[1 - (1 + x^2)^(1/3)]/2 - Log[1 + (1 + x^2)^(1/3) + (1 + x^2)^(2/3)]/4","A",1
968,1,53,74,0.0073952,"\int \frac{1}{x \sqrt[3]{1+x^2}} \, dx","Integrate[1/(x*(1 + x^2)^(1/3)),x]","\frac{1}{2} \left(\frac{3}{2} \log \left(1-\sqrt[3]{x^2+1}\right)+\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x^2+1}+1}{\sqrt{3}}\right)-\log (x)\right)","\frac{1}{2} \log \left(\sqrt[3]{x^2+1}-1\right)-\frac{1}{4} \log \left(\left(x^2+1\right)^{2/3}+\sqrt[3]{x^2+1}+1\right)+\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x^2+1}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)",1,"(Sqrt[3]*ArcTan[(1 + 2*(1 + x^2)^(1/3))/Sqrt[3]] - Log[x] + (3*Log[1 - (1 + x^2)^(1/3)])/2)/2","A",1
969,1,106,74,0.8592239,"\int \frac{1}{\left(-1+x^3\right) \sqrt[3]{-x^2+x^3}} \, dx","Integrate[1/((-1 + x^3)*(-x^2 + x^3)^(1/3)),x]","\frac{x \left(\frac{\text{RootSum}\left[3 \text{$\#$1}^6-3 \text{$\#$1}^3+1\&,\frac{3 \text{$\#$1}^3 \log \left(\sqrt[3]{\frac{1}{x-1}+1}-\text{$\#$1}\right)-2 \log \left(\sqrt[3]{\frac{1}{x-1}+1}-\text{$\#$1}\right)}{2 \text{$\#$1}^5-\text{$\#$1}^2}\&\right]}{\sqrt[3]{\frac{x}{x-1}}}-9\right)}{9 \sqrt[3]{(x-1) x^2}}","\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^6-3 \text{$\#$1}^3+3\&,\frac{\log \left(\sqrt[3]{x^3-x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]+\frac{\left(x^3-x^2\right)^{2/3}}{(1-x) x}",1,"(x*(-9 + RootSum[1 - 3*#1^3 + 3*#1^6 & , (-2*Log[(1 + (-1 + x)^(-1))^(1/3) - #1] + 3*Log[(1 + (-1 + x)^(-1))^(1/3) - #1]*#1^3)/(-#1^2 + 2*#1^5) & ]/(x/(-1 + x))^(1/3)))/(9*((-1 + x)*x^2)^(1/3))","A",1
970,1,106,74,0.0460917,"\int \frac{1}{\left(-1+x^3\right) \sqrt[3]{-x^2+x^3}} \, dx","Integrate[1/((-1 + x^3)*(-x^2 + x^3)^(1/3)),x]","\frac{x \left(\frac{\text{RootSum}\left[3 \text{$\#$1}^6-3 \text{$\#$1}^3+1\&,\frac{3 \text{$\#$1}^3 \log \left(\sqrt[3]{\frac{1}{x-1}+1}-\text{$\#$1}\right)-2 \log \left(\sqrt[3]{\frac{1}{x-1}+1}-\text{$\#$1}\right)}{2 \text{$\#$1}^5-\text{$\#$1}^2}\&\right]}{\sqrt[3]{\frac{x}{x-1}}}-9\right)}{9 \sqrt[3]{(x-1) x^2}}","\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^6-3 \text{$\#$1}^3+3\&,\frac{\log \left(\sqrt[3]{x^3-x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]+\frac{\left(x^3-x^2\right)^{2/3}}{(1-x) x}",1,"(x*(-9 + RootSum[1 - 3*#1^3 + 3*#1^6 & , (-2*Log[(1 + (-1 + x)^(-1))^(1/3) - #1] + 3*Log[(1 + (-1 + x)^(-1))^(1/3) - #1]*#1^3)/(-#1^2 + 2*#1^5) & ]/(x/(-1 + x))^(1/3)))/(9*((-1 + x)*x^2)^(1/3))","A",1
971,1,1814,74,6.2203895,"\int \frac{\sqrt{-1+x^3} \left(2+x^3\right) \left(-1-x^2+x^3\right)^2}{x^6 \left(-2-3 x^2+2 x^3\right)} \, dx","Integrate[(Sqrt[-1 + x^3]*(2 + x^3)*(-1 - x^2 + x^3)^2)/(x^6*(-2 - 3*x^2 + 2*x^3)),x]","\sqrt{x^3-1} \left(\frac{x}{5}-\frac{1}{6}+\frac{1}{4 x}-\frac{2}{5 x^2}+\frac{1}{6 x^3}+\frac{1}{5 x^5}\right)+\frac{3}{8} \left(\frac{\sqrt{\frac{x-1}{-1-\sqrt[3]{-1}}} \left(x+\sqrt[3]{-1}\right) \sqrt{\frac{x-(-1)^{2/3}}{-\sqrt[3]{-1}-(-1)^{2/3}}} F\left(\sin ^{-1}\left(\sqrt{-\frac{(-1)^{2/3} \left(x+\sqrt[3]{-1}\right)}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{\sqrt{\frac{x+\sqrt[3]{-1}}{\sqrt[3]{-1}+(-1)^{2/3}}} \sqrt{x^3-1}}+\frac{2 \left(-\sqrt[3]{-1}-(-1)^{2/3}\right) \sqrt{\frac{x-1}{-1-\sqrt[3]{-1}}} \sqrt{\frac{\left((-1)^{2/3}-x\right) \left(x+\sqrt[3]{-1}\right)}{\left(-\sqrt[3]{-1}-(-1)^{2/3}\right)^2}} \Pi \left(\frac{\sqrt[3]{-1}+(-1)^{2/3}}{\sqrt[3]{-1}+\text{Root}\left[2 \text{$\#$1}^3-3 \text{$\#$1}^2-2\&,3\right]};\sin ^{-1}\left(\sqrt{-\frac{(-1)^{2/3} \left(x+\sqrt[3]{-1}\right)}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{\sqrt{x^3-1} \left(\sqrt[3]{-1}+\text{Root}\left[2 \text{$\#$1}^3-3 \text{$\#$1}^2-2\&,3\right]\right) \left(-\text{Root}\left[2 \text{$\#$1}^3-3 \text{$\#$1}^2-2\&,1\right]+\text{Root}\left[2 \text{$\#$1}^3-3 \text{$\#$1}^2-2\&,3\right]\right) \left(-\text{Root}\left[2 \text{$\#$1}^3-3 \text{$\#$1}^2-2\&,2\right]+\text{Root}\left[2 \text{$\#$1}^3-3 \text{$\#$1}^2-2\&,3\right]\right)}+\frac{\left(-\sqrt[3]{-1}-(-1)^{2/3}\right) \sqrt{\frac{x-1}{-1-\sqrt[3]{-1}}} \sqrt{\frac{\left((-1)^{2/3}-x\right) \left(x+\sqrt[3]{-1}\right)}{\left(-\sqrt[3]{-1}-(-1)^{2/3}\right)^2}} \Pi \left(\frac{\sqrt[3]{-1}+(-1)^{2/3}}{\sqrt[3]{-1}+\text{Root}\left[2 \text{$\#$1}^3-3 \text{$\#$1}^2-2\&,3\right]};\sin ^{-1}\left(\sqrt{-\frac{(-1)^{2/3} \left(x+\sqrt[3]{-1}\right)}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right) \text{Root}\left[2 \text{$\#$1}^3-3 \text{$\#$1}^2-2\&,3\right]^3}{\sqrt{x^3-1} \left(\sqrt[3]{-1}+\text{Root}\left[2 \text{$\#$1}^3-3 \text{$\#$1}^2-2\&,3\right]\right) \left(-\text{Root}\left[2 \text{$\#$1}^3-3 \text{$\#$1}^2-2\&,1\right]+\text{Root}\left[2 \text{$\#$1}^3-3 \text{$\#$1}^2-2\&,3\right]\right) \left(-\text{Root}\left[2 \text{$\#$1}^3-3 \text{$\#$1}^2-2\&,2\right]+\text{Root}\left[2 \text{$\#$1}^3-3 \text{$\#$1}^2-2\&,3\right]\right)}+\frac{2 \left(-\sqrt[3]{-1}-(-1)^{2/3}\right) \sqrt{\frac{x-1}{-1-\sqrt[3]{-1}}} \sqrt{\frac{\left((-1)^{2/3}-x\right) \left(x+\sqrt[3]{-1}\right)}{\left(-\sqrt[3]{-1}-(-1)^{2/3}\right)^2}} \Pi \left(\frac{\sqrt[3]{-1}+(-1)^{2/3}}{\sqrt[3]{-1}+\text{Root}\left[2 \text{$\#$1}^3-3 \text{$\#$1}^2-2\&,2\right]};\sin ^{-1}\left(\sqrt{-\frac{(-1)^{2/3} \left(x+\sqrt[3]{-1}\right)}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{\sqrt{x^3-1} \left(\sqrt[3]{-1}+\text{Root}\left[2 \text{$\#$1}^3-3 \text{$\#$1}^2-2\&,2\right]\right) \left(-\text{Root}\left[2 \text{$\#$1}^3-3 \text{$\#$1}^2-2\&,1\right]+\text{Root}\left[2 \text{$\#$1}^3-3 \text{$\#$1}^2-2\&,2\right]\right) \left(\text{Root}\left[2 \text{$\#$1}^3-3 \text{$\#$1}^2-2\&,2\right]-\text{Root}\left[2 \text{$\#$1}^3-3 \text{$\#$1}^2-2\&,3\right]\right)}+\frac{\left(-\sqrt[3]{-1}-(-1)^{2/3}\right) \sqrt{\frac{x-1}{-1-\sqrt[3]{-1}}} \sqrt{\frac{\left((-1)^{2/3}-x\right) \left(x+\sqrt[3]{-1}\right)}{\left(-\sqrt[3]{-1}-(-1)^{2/3}\right)^2}} \Pi \left(\frac{\sqrt[3]{-1}+(-1)^{2/3}}{\sqrt[3]{-1}+\text{Root}\left[2 \text{$\#$1}^3-3 \text{$\#$1}^2-2\&,2\right]};\sin ^{-1}\left(\sqrt{-\frac{(-1)^{2/3} \left(x+\sqrt[3]{-1}\right)}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right) \text{Root}\left[2 \text{$\#$1}^3-3 \text{$\#$1}^2-2\&,2\right]^3}{\sqrt{x^3-1} \left(\sqrt[3]{-1}+\text{Root}\left[2 \text{$\#$1}^3-3 \text{$\#$1}^2-2\&,2\right]\right) \left(-\text{Root}\left[2 \text{$\#$1}^3-3 \text{$\#$1}^2-2\&,1\right]+\text{Root}\left[2 \text{$\#$1}^3-3 \text{$\#$1}^2-2\&,2\right]\right) \left(\text{Root}\left[2 \text{$\#$1}^3-3 \text{$\#$1}^2-2\&,2\right]-\text{Root}\left[2 \text{$\#$1}^3-3 \text{$\#$1}^2-2\&,3\right]\right)}+\frac{2 \left(-\sqrt[3]{-1}-(-1)^{2/3}\right) \sqrt{\frac{x-1}{-1-\sqrt[3]{-1}}} \sqrt{\frac{\left((-1)^{2/3}-x\right) \left(x+\sqrt[3]{-1}\right)}{\left(-\sqrt[3]{-1}-(-1)^{2/3}\right)^2}} \Pi \left(\frac{\sqrt[3]{-1}+(-1)^{2/3}}{\sqrt[3]{-1}+\text{Root}\left[2 \text{$\#$1}^3-3 \text{$\#$1}^2-2\&,1\right]};\sin ^{-1}\left(\sqrt{-\frac{(-1)^{2/3} \left(x+\sqrt[3]{-1}\right)}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{\sqrt{x^3-1} \left(\sqrt[3]{-1}+\text{Root}\left[2 \text{$\#$1}^3-3 \text{$\#$1}^2-2\&,1\right]\right) \left(\text{Root}\left[2 \text{$\#$1}^3-3 \text{$\#$1}^2-2\&,1\right]-\text{Root}\left[2 \text{$\#$1}^3-3 \text{$\#$1}^2-2\&,2\right]\right) \left(\text{Root}\left[2 \text{$\#$1}^3-3 \text{$\#$1}^2-2\&,1\right]-\text{Root}\left[2 \text{$\#$1}^3-3 \text{$\#$1}^2-2\&,3\right]\right)}+\frac{\left(-\sqrt[3]{-1}-(-1)^{2/3}\right) \sqrt{\frac{x-1}{-1-\sqrt[3]{-1}}} \sqrt{\frac{\left((-1)^{2/3}-x\right) \left(x+\sqrt[3]{-1}\right)}{\left(-\sqrt[3]{-1}-(-1)^{2/3}\right)^2}} \Pi \left(\frac{\sqrt[3]{-1}+(-1)^{2/3}}{\sqrt[3]{-1}+\text{Root}\left[2 \text{$\#$1}^3-3 \text{$\#$1}^2-2\&,1\right]};\sin ^{-1}\left(\sqrt{-\frac{(-1)^{2/3} \left(x+\sqrt[3]{-1}\right)}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right) \text{Root}\left[2 \text{$\#$1}^3-3 \text{$\#$1}^2-2\&,1\right]^3}{\sqrt{x^3-1} \left(\sqrt[3]{-1}+\text{Root}\left[2 \text{$\#$1}^3-3 \text{$\#$1}^2-2\&,1\right]\right) \left(\text{Root}\left[2 \text{$\#$1}^3-3 \text{$\#$1}^2-2\&,1\right]-\text{Root}\left[2 \text{$\#$1}^3-3 \text{$\#$1}^2-2\&,2\right]\right) \left(\text{Root}\left[2 \text{$\#$1}^3-3 \text{$\#$1}^2-2\&,1\right]-\text{Root}\left[2 \text{$\#$1}^3-3 \text{$\#$1}^2-2\&,3\right]\right)}\right)","\frac{\sqrt{x^3-1} \left(12 x^6-10 x^5+15 x^4-24 x^3+10 x^2+12\right)}{60 x^5}-\frac{1}{4} \sqrt{\frac{3}{2}} \tanh ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt{x^3-1}}\right)",1,"(-1/6 + 1/(5*x^5) + 1/(6*x^3) - 2/(5*x^2) + 1/(4*x) + x/5)*Sqrt[-1 + x^3] + (3*((Sqrt[(-1 + x)/(-1 - (-1)^(1/3))]*((-1)^(1/3) + x)*Sqrt[(-(-1)^(2/3) + x)/(-(-1)^(1/3) - (-1)^(2/3))]*EllipticF[ArcSin[Sqrt[-(((-1)^(2/3)*((-1)^(1/3) + x))/(1 + (-1)^(1/3)))]], (-1)^(1/3)])/(Sqrt[((-1)^(1/3) + x)/((-1)^(1/3) + (-1)^(2/3))]*Sqrt[-1 + x^3]) + (2*(-(-1)^(1/3) - (-1)^(2/3))*Sqrt[(-1 + x)/(-1 - (-1)^(1/3))]*Sqrt[(((-1)^(2/3) - x)*((-1)^(1/3) + x))/(-(-1)^(1/3) - (-1)^(2/3))^2]*EllipticPi[((-1)^(1/3) + (-1)^(2/3))/((-1)^(1/3) + Root[-2 - 3*#1^2 + 2*#1^3 & , 1, 0]), ArcSin[Sqrt[-(((-1)^(2/3)*((-1)^(1/3) + x))/(1 + (-1)^(1/3)))]], (-1)^(1/3)])/(Sqrt[-1 + x^3]*((-1)^(1/3) + Root[-2 - 3*#1^2 + 2*#1^3 & , 1, 0])*(Root[-2 - 3*#1^2 + 2*#1^3 & , 1, 0] - Root[-2 - 3*#1^2 + 2*#1^3 & , 2, 0])*(Root[-2 - 3*#1^2 + 2*#1^3 & , 1, 0] - Root[-2 - 3*#1^2 + 2*#1^3 & , 3, 0])) + ((-(-1)^(1/3) - (-1)^(2/3))*Sqrt[(-1 + x)/(-1 - (-1)^(1/3))]*Sqrt[(((-1)^(2/3) - x)*((-1)^(1/3) + x))/(-(-1)^(1/3) - (-1)^(2/3))^2]*EllipticPi[((-1)^(1/3) + (-1)^(2/3))/((-1)^(1/3) + Root[-2 - 3*#1^2 + 2*#1^3 & , 1, 0]), ArcSin[Sqrt[-(((-1)^(2/3)*((-1)^(1/3) + x))/(1 + (-1)^(1/3)))]], (-1)^(1/3)]*Root[-2 - 3*#1^2 + 2*#1^3 & , 1, 0]^3)/(Sqrt[-1 + x^3]*((-1)^(1/3) + Root[-2 - 3*#1^2 + 2*#1^3 & , 1, 0])*(Root[-2 - 3*#1^2 + 2*#1^3 & , 1, 0] - Root[-2 - 3*#1^2 + 2*#1^3 & , 2, 0])*(Root[-2 - 3*#1^2 + 2*#1^3 & , 1, 0] - Root[-2 - 3*#1^2 + 2*#1^3 & , 3, 0])) + (2*(-(-1)^(1/3) - (-1)^(2/3))*Sqrt[(-1 + x)/(-1 - (-1)^(1/3))]*Sqrt[(((-1)^(2/3) - x)*((-1)^(1/3) + x))/(-(-1)^(1/3) - (-1)^(2/3))^2]*EllipticPi[((-1)^(1/3) + (-1)^(2/3))/((-1)^(1/3) + Root[-2 - 3*#1^2 + 2*#1^3 & , 2, 0]), ArcSin[Sqrt[-(((-1)^(2/3)*((-1)^(1/3) + x))/(1 + (-1)^(1/3)))]], (-1)^(1/3)])/(Sqrt[-1 + x^3]*((-1)^(1/3) + Root[-2 - 3*#1^2 + 2*#1^3 & , 2, 0])*(-Root[-2 - 3*#1^2 + 2*#1^3 & , 1, 0] + Root[-2 - 3*#1^2 + 2*#1^3 & , 2, 0])*(Root[-2 - 3*#1^2 + 2*#1^3 & , 2, 0] - Root[-2 - 3*#1^2 + 2*#1^3 & , 3, 0])) + ((-(-1)^(1/3) - (-1)^(2/3))*Sqrt[(-1 + x)/(-1 - (-1)^(1/3))]*Sqrt[(((-1)^(2/3) - x)*((-1)^(1/3) + x))/(-(-1)^(1/3) - (-1)^(2/3))^2]*EllipticPi[((-1)^(1/3) + (-1)^(2/3))/((-1)^(1/3) + Root[-2 - 3*#1^2 + 2*#1^3 & , 2, 0]), ArcSin[Sqrt[-(((-1)^(2/3)*((-1)^(1/3) + x))/(1 + (-1)^(1/3)))]], (-1)^(1/3)]*Root[-2 - 3*#1^2 + 2*#1^3 & , 2, 0]^3)/(Sqrt[-1 + x^3]*((-1)^(1/3) + Root[-2 - 3*#1^2 + 2*#1^3 & , 2, 0])*(-Root[-2 - 3*#1^2 + 2*#1^3 & , 1, 0] + Root[-2 - 3*#1^2 + 2*#1^3 & , 2, 0])*(Root[-2 - 3*#1^2 + 2*#1^3 & , 2, 0] - Root[-2 - 3*#1^2 + 2*#1^3 & , 3, 0])) + (2*(-(-1)^(1/3) - (-1)^(2/3))*Sqrt[(-1 + x)/(-1 - (-1)^(1/3))]*Sqrt[(((-1)^(2/3) - x)*((-1)^(1/3) + x))/(-(-1)^(1/3) - (-1)^(2/3))^2]*EllipticPi[((-1)^(1/3) + (-1)^(2/3))/((-1)^(1/3) + Root[-2 - 3*#1^2 + 2*#1^3 & , 3, 0]), ArcSin[Sqrt[-(((-1)^(2/3)*((-1)^(1/3) + x))/(1 + (-1)^(1/3)))]], (-1)^(1/3)])/(Sqrt[-1 + x^3]*((-1)^(1/3) + Root[-2 - 3*#1^2 + 2*#1^3 & , 3, 0])*(-Root[-2 - 3*#1^2 + 2*#1^3 & , 1, 0] + Root[-2 - 3*#1^2 + 2*#1^3 & , 3, 0])*(-Root[-2 - 3*#1^2 + 2*#1^3 & , 2, 0] + Root[-2 - 3*#1^2 + 2*#1^3 & , 3, 0])) + ((-(-1)^(1/3) - (-1)^(2/3))*Sqrt[(-1 + x)/(-1 - (-1)^(1/3))]*Sqrt[(((-1)^(2/3) - x)*((-1)^(1/3) + x))/(-(-1)^(1/3) - (-1)^(2/3))^2]*EllipticPi[((-1)^(1/3) + (-1)^(2/3))/((-1)^(1/3) + Root[-2 - 3*#1^2 + 2*#1^3 & , 3, 0]), ArcSin[Sqrt[-(((-1)^(2/3)*((-1)^(1/3) + x))/(1 + (-1)^(1/3)))]], (-1)^(1/3)]*Root[-2 - 3*#1^2 + 2*#1^3 & , 3, 0]^3)/(Sqrt[-1 + x^3]*((-1)^(1/3) + Root[-2 - 3*#1^2 + 2*#1^3 & , 3, 0])*(-Root[-2 - 3*#1^2 + 2*#1^3 & , 1, 0] + Root[-2 - 3*#1^2 + 2*#1^3 & , 3, 0])*(-Root[-2 - 3*#1^2 + 2*#1^3 & , 2, 0] + Root[-2 - 3*#1^2 + 2*#1^3 & , 3, 0]))))/8","C",0
972,1,74,74,0.0917684,"\int \frac{\sqrt[4]{-1+3 x-3 x^2+x^3}}{-1-2 x+x^2+3 x^3} \, dx","Integrate[(-1 + 3*x - 3*x^2 + x^3)^(1/4)/(-1 - 2*x + x^2 + 3*x^3),x]","\frac{\sqrt[4]{(x-1)^3} \text{RootSum}\left[3 \text{$\#$1}^{12}+10 \text{$\#$1}^8+9 \text{$\#$1}^4+1\&,\frac{\text{$\#$1}^3 \log \left(\sqrt[4]{x-1}-\text{$\#$1}\right)}{9 \text{$\#$1}^8+20 \text{$\#$1}^4+9}\&\right]}{(x-1)^{3/4}}","\frac{\sqrt[4]{(x-1)^3} \text{RootSum}\left[3 \text{$\#$1}^{12}+10 \text{$\#$1}^8+9 \text{$\#$1}^4+1\&,\frac{\text{$\#$1}^3 \log \left(\sqrt[4]{x-1}-\text{$\#$1}\right)}{9 \text{$\#$1}^8+20 \text{$\#$1}^4+9}\&\right]}{(x-1)^{3/4}}",1,"(((-1 + x)^3)^(1/4)*RootSum[1 + 9*#1^4 + 10*#1^8 + 3*#1^12 & , (Log[(-1 + x)^(1/4) - #1]*#1^3)/(9 + 20*#1^4 + 9*#1^8) & ])/(-1 + x)^(3/4)","A",1
973,1,1735,74,6.1748416,"\int \frac{\left(1+x+x^2\right) \left(2 x+x^2\right) \sqrt{1+2 x+x^2-x^4}}{(1+x)^4} \, dx","Integrate[((1 + x + x^2)*(2*x + x^2)*Sqrt[1 + 2*x + x^2 - x^4])/(1 + x)^4,x]","\sqrt{-x^4+x^2+2 x+1} \left(\frac{x}{3}+\frac{2}{3 (x+1)}-\frac{5}{6 (x+1)^2}+\frac{1}{3 (x+1)^3}-\frac{1}{2}\right)+\frac{(x+1) \sqrt{-x^4+x^2+2 x+1} \left(\frac{x}{2 \sqrt{-x^4+x^2+2 x+1}}-\frac{1}{2 (x+1) \sqrt{-x^4+x^2+2 x+1}}+\frac{1}{2 \sqrt{-x^4+x^2+2 x+1}}\right) \left(\frac{2 \left(-\sqrt[3]{-1}+\frac{1}{2} \left(-1-\sqrt{5}\right)\right) \sqrt{\frac{\left(-(-1)^{2/3}+\frac{1}{2} \left(1+\sqrt{5}\right)\right) \left(x+\sqrt[3]{-1}\right)}{\left(\sqrt[3]{-1}+\frac{1}{2} \left(1+\sqrt{5}\right)\right) \left(x-(-1)^{2/3}\right)}} \sqrt{\frac{\left(\sqrt[3]{-1}+(-1)^{2/3}\right) \left(x+\frac{1}{2} \left(-1-\sqrt{5}\right)\right)}{\left(\sqrt[3]{-1}+\frac{1}{2} \left(1+\sqrt{5}\right)\right) \left(x-(-1)^{2/3}\right)}} \sqrt{\frac{\left(\sqrt[3]{-1}+(-1)^{2/3}\right) \left(x+\frac{1}{2} \left(-1+\sqrt{5}\right)\right)}{\left(\sqrt[3]{-1}+\frac{1}{2} \left(1-\sqrt{5}\right)\right) \left(x-(-1)^{2/3}\right)}} F\left(\sin ^{-1}\left(\sqrt{\frac{\left(-(-1)^{2/3}+\frac{1}{2} \left(1+\sqrt{5}\right)\right) \left(x+\sqrt[3]{-1}\right)}{\left(\sqrt[3]{-1}+\frac{1}{2} \left(1+\sqrt{5}\right)\right) \left(x-(-1)^{2/3}\right)}}\right)|\frac{\left(-\sqrt[3]{-1}+\frac{1}{2} \left(-1-\sqrt{5}\right)\right) \left((-1)^{2/3}+\frac{1}{2} \left(-1+\sqrt{5}\right)\right)}{\left((-1)^{2/3}+\frac{1}{2} \left(-1-\sqrt{5}\right)\right) \left(-\sqrt[3]{-1}+\frac{1}{2} \left(-1+\sqrt{5}\right)\right)}\right) \left(x-(-1)^{2/3}\right)^2}{\left(\sqrt[3]{-1}+(-1)^{2/3}\right) \left(-(-1)^{2/3}+\frac{1}{2} \left(1+\sqrt{5}\right)\right) \sqrt{-x^4+x^2+2 x+1}}+\frac{2 \left(-\sqrt[3]{-1}+\frac{1}{2} \left(-1-\sqrt{5}\right)\right) \sqrt{\frac{\left(-1+2 (-1)^{2/3}-\sqrt{5}\right) \left(x+\sqrt[3]{-1}\right)}{\left(1+2 \sqrt[3]{-1}+\sqrt{5}\right) \left((-1)^{2/3}-x\right)}} \sqrt{\frac{\left(\sqrt[3]{-1}+(-1)^{2/3}\right) \left(x+\frac{1}{2} \left(-1-\sqrt{5}\right)\right)}{\left(\sqrt[3]{-1}+\frac{1}{2} \left(1+\sqrt{5}\right)\right) \left(x-(-1)^{2/3}\right)}} \sqrt{\frac{\left(\sqrt[3]{-1}+(-1)^{2/3}\right) \left(x+\frac{1}{2} \left(-1+\sqrt{5}\right)\right)}{\left(\sqrt[3]{-1}+\frac{1}{2} \left(1-\sqrt{5}\right)\right) \left(x-(-1)^{2/3}\right)}} \left(\left(\sqrt[3]{-1}+(-1)^{2/3}\right) \Pi \left(\frac{\sqrt[3]{-1}+\frac{1}{2} \left(1+\sqrt{5}\right)}{-(-1)^{2/3}+\frac{1}{2} \left(1+\sqrt{5}\right)};\sin ^{-1}\left(\sqrt{\frac{\left(-1+2 (-1)^{2/3}-\sqrt{5}\right) \left(x+\sqrt[3]{-1}\right)}{\left(1+2 \sqrt[3]{-1}+\sqrt{5}\right) \left((-1)^{2/3}-x\right)}}\right)|\frac{\left(1+2 \sqrt[3]{-1}+\sqrt{5}\right) \left(-1+2 (-1)^{2/3}+\sqrt{5}\right)}{\left(1+2 \sqrt[3]{-1}-\sqrt{5}\right) \left(-1+2 (-1)^{2/3}-\sqrt{5}\right)}\right)-(-1)^{2/3} F\left(\sin ^{-1}\left(\sqrt{\frac{\left(-1+2 (-1)^{2/3}-\sqrt{5}\right) \left(x+\sqrt[3]{-1}\right)}{\left(1+2 \sqrt[3]{-1}+\sqrt{5}\right) \left((-1)^{2/3}-x\right)}}\right)|\frac{\left(1+2 \sqrt[3]{-1}+\sqrt{5}\right) \left(-1+2 (-1)^{2/3}+\sqrt{5}\right)}{\left(1+2 \sqrt[3]{-1}-\sqrt{5}\right) \left(-1+2 (-1)^{2/3}-\sqrt{5}\right)}\right)\right) \left(x-(-1)^{2/3}\right)^2}{\left(\sqrt[3]{-1}+(-1)^{2/3}\right) \left((-1)^{2/3}+\frac{1}{2} \left(-1-\sqrt{5}\right)\right) \sqrt{-x^4+x^2+2 x+1}}-\frac{2 \left(\sqrt[3]{-1}+\frac{1}{2} \left(1+\sqrt{5}\right)\right) \sqrt{\frac{\left(-1+2 (-1)^{2/3}-\sqrt{5}\right) \left(x+\sqrt[3]{-1}\right)}{\left(1+2 \sqrt[3]{-1}+\sqrt{5}\right) \left((-1)^{2/3}-x\right)}} \sqrt{\frac{\left(\sqrt[3]{-1}+(-1)^{2/3}\right) \left(x+\frac{1}{2} \left(-1-\sqrt{5}\right)\right)}{\left(\sqrt[3]{-1}+\frac{1}{2} \left(1+\sqrt{5}\right)\right) \left(x-(-1)^{2/3}\right)}} \sqrt{\frac{\left(\sqrt[3]{-1}+(-1)^{2/3}\right) \left(x+\frac{1}{2} \left(-1+\sqrt{5}\right)\right)}{\left(\sqrt[3]{-1}+\frac{1}{2} \left(1-\sqrt{5}\right)\right) \left(x-(-1)^{2/3}\right)}} \left(\left(-1+\sqrt[3]{-1}\right) F\left(\sin ^{-1}\left(\sqrt{\frac{\left(-1+2 (-1)^{2/3}-\sqrt{5}\right) \left(x+\sqrt[3]{-1}\right)}{\left(1+2 \sqrt[3]{-1}+\sqrt{5}\right) \left((-1)^{2/3}-x\right)}}\right)|\frac{\left(1+2 \sqrt[3]{-1}+\sqrt{5}\right) \left(-1+2 (-1)^{2/3}+\sqrt{5}\right)}{\left(1+2 \sqrt[3]{-1}-\sqrt{5}\right) \left(-1+2 (-1)^{2/3}-\sqrt{5}\right)}\right)-\left(\sqrt[3]{-1}+(-1)^{2/3}\right) \Pi \left(\frac{\left(1+(-1)^{2/3}\right) \left(\sqrt[3]{-1}+\frac{1}{2} \left(1+\sqrt{5}\right)\right)}{\left(1-\sqrt[3]{-1}\right) \left(-(-1)^{2/3}+\frac{1}{2} \left(1+\sqrt{5}\right)\right)};\sin ^{-1}\left(\sqrt{\frac{\left(-1+2 (-1)^{2/3}-\sqrt{5}\right) \left(x+\sqrt[3]{-1}\right)}{\left(1+2 \sqrt[3]{-1}+\sqrt{5}\right) \left((-1)^{2/3}-x\right)}}\right)|\frac{\left(1+2 \sqrt[3]{-1}+\sqrt{5}\right) \left(-1+2 (-1)^{2/3}+\sqrt{5}\right)}{\left(1+2 \sqrt[3]{-1}-\sqrt{5}\right) \left(-1+2 (-1)^{2/3}-\sqrt{5}\right)}\right)\right) \left(x-(-1)^{2/3}\right)^2}{\left(1-\sqrt[3]{-1}\right) \left(-1-(-1)^{2/3}\right) \left(\sqrt[3]{-1}+(-1)^{2/3}\right) \left((-1)^{2/3}+\frac{1}{2} \left(-1-\sqrt{5}\right)\right) \sqrt{-x^4+x^2+2 x+1}}\right)}{x (x+2)}","\frac{\sqrt{-x^4+x^2+2 x+1} \left(2 x^4+3 x^3+x^2-4 x-2\right)}{6 (x+1)^3}-\tan ^{-1}\left(\frac{\sqrt{-x^4+x^2+2 x+1}}{x^2+x+1}\right)",1,"Sqrt[1 + 2*x + x^2 - x^4]*(-1/2 + x/3 + 1/(3*(1 + x)^3) - 5/(6*(1 + x)^2) + 2/(3*(1 + x))) + ((1 + x)*Sqrt[1 + 2*x + x^2 - x^4]*(1/(2*Sqrt[1 + 2*x + x^2 - x^4]) + x/(2*Sqrt[1 + 2*x + x^2 - x^4]) - 1/(2*(1 + x)*Sqrt[1 + 2*x + x^2 - x^4]))*((2*(-(-1)^(1/3) + (-1 - Sqrt[5])/2)*Sqrt[((-(-1)^(2/3) + (1 + Sqrt[5])/2)*((-1)^(1/3) + x))/(((-1)^(1/3) + (1 + Sqrt[5])/2)*(-(-1)^(2/3) + x))]*(-(-1)^(2/3) + x)^2*Sqrt[(((-1)^(1/3) + (-1)^(2/3))*((-1 - Sqrt[5])/2 + x))/(((-1)^(1/3) + (1 + Sqrt[5])/2)*(-(-1)^(2/3) + x))]*Sqrt[(((-1)^(1/3) + (-1)^(2/3))*((-1 + Sqrt[5])/2 + x))/(((-1)^(1/3) + (1 - Sqrt[5])/2)*(-(-1)^(2/3) + x))]*EllipticF[ArcSin[Sqrt[((-(-1)^(2/3) + (1 + Sqrt[5])/2)*((-1)^(1/3) + x))/(((-1)^(1/3) + (1 + Sqrt[5])/2)*(-(-1)^(2/3) + x))]], ((-(-1)^(1/3) + (-1 - Sqrt[5])/2)*((-1)^(2/3) + (-1 + Sqrt[5])/2))/(((-1)^(2/3) + (-1 - Sqrt[5])/2)*(-(-1)^(1/3) + (-1 + Sqrt[5])/2))])/(((-1)^(1/3) + (-1)^(2/3))*(-(-1)^(2/3) + (1 + Sqrt[5])/2)*Sqrt[1 + 2*x + x^2 - x^4]) + (2*(-(-1)^(1/3) + (-1 - Sqrt[5])/2)*Sqrt[((-1 + 2*(-1)^(2/3) - Sqrt[5])*((-1)^(1/3) + x))/((1 + 2*(-1)^(1/3) + Sqrt[5])*((-1)^(2/3) - x))]*(-(-1)^(2/3) + x)^2*Sqrt[(((-1)^(1/3) + (-1)^(2/3))*((-1 - Sqrt[5])/2 + x))/(((-1)^(1/3) + (1 + Sqrt[5])/2)*(-(-1)^(2/3) + x))]*Sqrt[(((-1)^(1/3) + (-1)^(2/3))*((-1 + Sqrt[5])/2 + x))/(((-1)^(1/3) + (1 - Sqrt[5])/2)*(-(-1)^(2/3) + x))]*(-((-1)^(2/3)*EllipticF[ArcSin[Sqrt[((-1 + 2*(-1)^(2/3) - Sqrt[5])*((-1)^(1/3) + x))/((1 + 2*(-1)^(1/3) + Sqrt[5])*((-1)^(2/3) - x))]], ((1 + 2*(-1)^(1/3) + Sqrt[5])*(-1 + 2*(-1)^(2/3) + Sqrt[5]))/((1 + 2*(-1)^(1/3) - Sqrt[5])*(-1 + 2*(-1)^(2/3) - Sqrt[5]))]) + ((-1)^(1/3) + (-1)^(2/3))*EllipticPi[((-1)^(1/3) + (1 + Sqrt[5])/2)/(-(-1)^(2/3) + (1 + Sqrt[5])/2), ArcSin[Sqrt[((-1 + 2*(-1)^(2/3) - Sqrt[5])*((-1)^(1/3) + x))/((1 + 2*(-1)^(1/3) + Sqrt[5])*((-1)^(2/3) - x))]], ((1 + 2*(-1)^(1/3) + Sqrt[5])*(-1 + 2*(-1)^(2/3) + Sqrt[5]))/((1 + 2*(-1)^(1/3) - Sqrt[5])*(-1 + 2*(-1)^(2/3) - Sqrt[5]))]))/(((-1)^(1/3) + (-1)^(2/3))*((-1)^(2/3) + (-1 - Sqrt[5])/2)*Sqrt[1 + 2*x + x^2 - x^4]) - (2*((-1)^(1/3) + (1 + Sqrt[5])/2)*Sqrt[((-1 + 2*(-1)^(2/3) - Sqrt[5])*((-1)^(1/3) + x))/((1 + 2*(-1)^(1/3) + Sqrt[5])*((-1)^(2/3) - x))]*(-(-1)^(2/3) + x)^2*Sqrt[(((-1)^(1/3) + (-1)^(2/3))*((-1 - Sqrt[5])/2 + x))/(((-1)^(1/3) + (1 + Sqrt[5])/2)*(-(-1)^(2/3) + x))]*Sqrt[(((-1)^(1/3) + (-1)^(2/3))*((-1 + Sqrt[5])/2 + x))/(((-1)^(1/3) + (1 - Sqrt[5])/2)*(-(-1)^(2/3) + x))]*((-1 + (-1)^(1/3))*EllipticF[ArcSin[Sqrt[((-1 + 2*(-1)^(2/3) - Sqrt[5])*((-1)^(1/3) + x))/((1 + 2*(-1)^(1/3) + Sqrt[5])*((-1)^(2/3) - x))]], ((1 + 2*(-1)^(1/3) + Sqrt[5])*(-1 + 2*(-1)^(2/3) + Sqrt[5]))/((1 + 2*(-1)^(1/3) - Sqrt[5])*(-1 + 2*(-1)^(2/3) - Sqrt[5]))] - ((-1)^(1/3) + (-1)^(2/3))*EllipticPi[((1 + (-1)^(2/3))*((-1)^(1/3) + (1 + Sqrt[5])/2))/((1 - (-1)^(1/3))*(-(-1)^(2/3) + (1 + Sqrt[5])/2)), ArcSin[Sqrt[((-1 + 2*(-1)^(2/3) - Sqrt[5])*((-1)^(1/3) + x))/((1 + 2*(-1)^(1/3) + Sqrt[5])*((-1)^(2/3) - x))]], ((1 + 2*(-1)^(1/3) + Sqrt[5])*(-1 + 2*(-1)^(2/3) + Sqrt[5]))/((1 + 2*(-1)^(1/3) - Sqrt[5])*(-1 + 2*(-1)^(2/3) - Sqrt[5]))]))/((1 - (-1)^(1/3))*(-1 - (-1)^(2/3))*((-1)^(1/3) + (-1)^(2/3))*((-1)^(2/3) + (-1 - Sqrt[5])/2)*Sqrt[1 + 2*x + x^2 - x^4])))/(x*(2 + x))","C",0
974,1,68,74,0.0323191,"\int \frac{-1-x+x^4}{x \sqrt[4]{1+x^4}} \, dx","Integrate[(-1 - x + x^4)/(x*(1 + x^4)^(1/4)),x]","\frac{1}{6} \left(2 \left(x^4+1\right)^{3/4}-3 \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)-3 \tan ^{-1}\left(\sqrt[4]{x^4+1}\right)-3 \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)+3 \tanh ^{-1}\left(\sqrt[4]{x^4+1}\right)\right)","\frac{1}{3} \left(x^4+1\right)^{3/4}-\frac{1}{2} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)-\frac{1}{2} \tan ^{-1}\left(\sqrt[4]{x^4+1}\right)-\frac{1}{2} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)+\frac{1}{2} \tanh ^{-1}\left(\sqrt[4]{x^4+1}\right)",1,"(2*(1 + x^4)^(3/4) - 3*ArcTan[x/(1 + x^4)^(1/4)] - 3*ArcTan[(1 + x^4)^(1/4)] - 3*ArcTanh[x/(1 + x^4)^(1/4)] + 3*ArcTanh[(1 + x^4)^(1/4)])/6","A",1
975,1,36,74,0.0138681,"\int \frac{\sqrt[4]{-x^3+x^4}}{x^2 \left(-1+x^2\right)} \, dx","Integrate[(-x^3 + x^4)^(1/4)/(x^2*(-1 + x^2)),x]","-\frac{2 \sqrt[4]{(x-1) x^3} \left(\, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{x-1}{2 x}\right)-2\right)}{x}","\frac{4 \sqrt[4]{x^4-x^3}}{x}+\sqrt[4]{2} \tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-x^3}}\right)-\sqrt[4]{2} \tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-x^3}}\right)",1,"(-2*((-1 + x)*x^3)^(1/4)*(-2 + Hypergeometric2F1[1/4, 1, 5/4, (-1 + x)/(2*x)]))/x","C",1
976,0,0,74,0.1432756,"\int \frac{-3+x^4}{\sqrt[3]{1+x^4} \left(1-x^3+x^4\right)} \, dx","Integrate[(-3 + x^4)/((1 + x^4)^(1/3)*(1 - x^3 + x^4)),x]","\int \frac{-3+x^4}{\sqrt[3]{1+x^4} \left(1-x^3+x^4\right)} \, dx","\log \left(\sqrt[3]{x^4+1}-x\right)-\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^4+1}+x}\right)-\frac{1}{2} \log \left(\sqrt[3]{x^4+1} x+\left(x^4+1\right)^{2/3}+x^2\right)",1,"Integrate[(-3 + x^4)/((1 + x^4)^(1/3)*(1 - x^3 + x^4)), x]","F",-1
977,1,420,74,0.6782826,"\int \frac{b+a x^2}{\left(b-a x^2+x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Integrate[(b + a*x^2)/((b - a*x^2 + x^4)*(b*x^2 + a*x^4)^(1/4)),x]","\frac{\left(x^2 \left(a x^2+b\right)\right)^{3/4} \left(\left(3 a-\sqrt{a^2-4 b}\right)^{3/4} \log \left(2^{3/4} \sqrt[4]{3 a-\sqrt{a^2-4 b}}-2 \sqrt[4]{a+\frac{b}{x^2}}\right)-\left(\sqrt{a^2-4 b}+3 a\right)^{3/4} \log \left(2^{3/4} \sqrt[4]{\sqrt{a^2-4 b}+3 a}-2 \sqrt[4]{a+\frac{b}{x^2}}\right)-\left(3 a-\sqrt{a^2-4 b}\right)^{3/4} \log \left(2^{3/4} \sqrt[4]{3 a-\sqrt{a^2-4 b}}+2 \sqrt[4]{a+\frac{b}{x^2}}\right)+\left(\sqrt{a^2-4 b}+3 a\right)^{3/4} \log \left(2^{3/4} \sqrt[4]{\sqrt{a^2-4 b}+3 a}+2 \sqrt[4]{a+\frac{b}{x^2}}\right)+2 \left(3 a-\sqrt{a^2-4 b}\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{3 a-\sqrt{a^2-4 b}}}\right)-2 \left(\sqrt{a^2-4 b}+3 a\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\sqrt{a^2-4 b}+3 a}}\right)\right)}{2\ 2^{3/4} x^3 \sqrt{a^2-4 b} \left(a+\frac{b}{x^2}\right)^{3/4}}","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4 a+2 a^2+b\&,\frac{\text{$\#$1}^3 \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\text{$\#$1}^3 \log (x)}{2 \text{$\#$1}^4-3 a}\&\right]",1,"((x^2*(b + a*x^2))^(3/4)*(2*(3*a - Sqrt[a^2 - 4*b])^(3/4)*ArcTan[(2^(1/4)*(a + b/x^2)^(1/4))/(3*a - Sqrt[a^2 - 4*b])^(1/4)] - 2*(3*a + Sqrt[a^2 - 4*b])^(3/4)*ArcTan[(2^(1/4)*(a + b/x^2)^(1/4))/(3*a + Sqrt[a^2 - 4*b])^(1/4)] + (3*a - Sqrt[a^2 - 4*b])^(3/4)*Log[2^(3/4)*(3*a - Sqrt[a^2 - 4*b])^(1/4) - 2*(a + b/x^2)^(1/4)] - (3*a + Sqrt[a^2 - 4*b])^(3/4)*Log[2^(3/4)*(3*a + Sqrt[a^2 - 4*b])^(1/4) - 2*(a + b/x^2)^(1/4)] - (3*a - Sqrt[a^2 - 4*b])^(3/4)*Log[2^(3/4)*(3*a - Sqrt[a^2 - 4*b])^(1/4) + 2*(a + b/x^2)^(1/4)] + (3*a + Sqrt[a^2 - 4*b])^(3/4)*Log[2^(3/4)*(3*a + Sqrt[a^2 - 4*b])^(1/4) + 2*(a + b/x^2)^(1/4)]))/(2*2^(3/4)*Sqrt[a^2 - 4*b]*(a + b/x^2)^(3/4)*x^3)","B",1
978,1,420,74,0.0729253,"\int \frac{b+a x^2}{\left(b-a x^2+x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Integrate[(b + a*x^2)/((b - a*x^2 + x^4)*(b*x^2 + a*x^4)^(1/4)),x]","\frac{\left(x^2 \left(a x^2+b\right)\right)^{3/4} \left(\left(3 a-\sqrt{a^2-4 b}\right)^{3/4} \log \left(2^{3/4} \sqrt[4]{3 a-\sqrt{a^2-4 b}}-2 \sqrt[4]{a+\frac{b}{x^2}}\right)-\left(\sqrt{a^2-4 b}+3 a\right)^{3/4} \log \left(2^{3/4} \sqrt[4]{\sqrt{a^2-4 b}+3 a}-2 \sqrt[4]{a+\frac{b}{x^2}}\right)-\left(3 a-\sqrt{a^2-4 b}\right)^{3/4} \log \left(2^{3/4} \sqrt[4]{3 a-\sqrt{a^2-4 b}}+2 \sqrt[4]{a+\frac{b}{x^2}}\right)+\left(\sqrt{a^2-4 b}+3 a\right)^{3/4} \log \left(2^{3/4} \sqrt[4]{\sqrt{a^2-4 b}+3 a}+2 \sqrt[4]{a+\frac{b}{x^2}}\right)+2 \left(3 a-\sqrt{a^2-4 b}\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{3 a-\sqrt{a^2-4 b}}}\right)-2 \left(\sqrt{a^2-4 b}+3 a\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\sqrt{a^2-4 b}+3 a}}\right)\right)}{2\ 2^{3/4} x^3 \sqrt{a^2-4 b} \left(a+\frac{b}{x^2}\right)^{3/4}}","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4 a+2 a^2+b\&,\frac{\text{$\#$1}^3 \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\text{$\#$1}^3 \log (x)}{2 \text{$\#$1}^4-3 a}\&\right]",1,"((x^2*(b + a*x^2))^(3/4)*(2*(3*a - Sqrt[a^2 - 4*b])^(3/4)*ArcTan[(2^(1/4)*(a + b/x^2)^(1/4))/(3*a - Sqrt[a^2 - 4*b])^(1/4)] - 2*(3*a + Sqrt[a^2 - 4*b])^(3/4)*ArcTan[(2^(1/4)*(a + b/x^2)^(1/4))/(3*a + Sqrt[a^2 - 4*b])^(1/4)] + (3*a - Sqrt[a^2 - 4*b])^(3/4)*Log[2^(3/4)*(3*a - Sqrt[a^2 - 4*b])^(1/4) - 2*(a + b/x^2)^(1/4)] - (3*a + Sqrt[a^2 - 4*b])^(3/4)*Log[2^(3/4)*(3*a + Sqrt[a^2 - 4*b])^(1/4) - 2*(a + b/x^2)^(1/4)] - (3*a - Sqrt[a^2 - 4*b])^(3/4)*Log[2^(3/4)*(3*a - Sqrt[a^2 - 4*b])^(1/4) + 2*(a + b/x^2)^(1/4)] + (3*a + Sqrt[a^2 - 4*b])^(3/4)*Log[2^(3/4)*(3*a + Sqrt[a^2 - 4*b])^(1/4) + 2*(a + b/x^2)^(1/4)]))/(2*2^(3/4)*Sqrt[a^2 - 4*b]*(a + b/x^2)^(3/4)*x^3)","B",1
979,1,74,74,0.038524,"\int \frac{-b+2 a x^4}{x^2 \left(-b+a x^4\right)^{3/4}} \, dx","Integrate[(-b + 2*a*x^4)/(x^2*(-b + a*x^4)^(3/4)),x]","-\frac{\sqrt[4]{a x^4-b}}{x}-\sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)+\sqrt[4]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)","-\frac{\sqrt[4]{a x^4-b}}{x}-\sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)+\sqrt[4]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)",1,"-((-b + a*x^4)^(1/4)/x) - a^(1/4)*ArcTan[(a^(1/4)*x)/(-b + a*x^4)^(1/4)] + a^(1/4)*ArcTanh[(a^(1/4)*x)/(-b + a*x^4)^(1/4)]","A",1
980,1,53,74,0.0144722,"\int \frac{1}{x \sqrt[3]{1+x^6}} \, dx","Integrate[1/(x*(1 + x^6)^(1/3)),x]","\frac{1}{6} \left(\frac{3}{2} \log \left(1-\sqrt[3]{x^6+1}\right)+\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x^6+1}+1}{\sqrt{3}}\right)-3 \log (x)\right)","\frac{1}{6} \log \left(\sqrt[3]{x^6+1}-1\right)-\frac{1}{12} \log \left(\left(x^6+1\right)^{2/3}+\sqrt[3]{x^6+1}+1\right)+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{x^6+1}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3}}",1,"(Sqrt[3]*ArcTan[(1 + 2*(1 + x^6)^(1/3))/Sqrt[3]] - 3*Log[x] + (3*Log[1 - (1 + x^6)^(1/3)])/2)/6","A",1
981,1,80,74,0.2453244,"\int \frac{3-9 x^4+2 x^6}{x \left(1+x^2\right)^2 \left(-1+2 x^2\right) \sqrt{\frac{1-2 x^2}{1+2 x^2}} \left(1+2 x^2\right)} \, dx","Integrate[(3 - 9*x^4 + 2*x^6)/(x*(1 + x^2)^2*(-1 + 2*x^2)*Sqrt[(1 - 2*x^2)/(1 + 2*x^2)]*(1 + 2*x^2)),x]","\frac{8 x^4-4 x^2+9 \sqrt{4-\frac{1}{x^4}} \left(x^2+1\right) x^2 \sin ^{-1}\left(\frac{1}{2 x^2}\right)-4}{6 \sqrt{\frac{1-2 x^2}{2 x^2+1}} \left(2 x^4+3 x^2+1\right)}","3 \tanh ^{-1}\left(\sqrt{\frac{1-2 x^2}{2 x^2+1}}\right)-\frac{2 \sqrt{\frac{1-2 x^2}{2 x^2+1}} \left(2 x^4-x^2-1\right)}{3 \left(2 x^4+x^2-1\right)}",1,"(-4 - 4*x^2 + 8*x^4 + 9*Sqrt[4 - x^(-4)]*x^2*(1 + x^2)*ArcSin[1/(2*x^2)])/(6*Sqrt[(1 - 2*x^2)/(1 + 2*x^2)]*(1 + 3*x^2 + 2*x^4))","A",1
982,1,92,74,0.2330009,"\int \frac{\sqrt[4]{-1+2 x^4} \left(-2+x^8\right)}{x^6 \left(-1+x^4\right)^2} \, dx","Integrate[((-1 + 2*x^4)^(1/4)*(-2 + x^8))/(x^6*(-1 + x^4)^2),x]","\frac{25 \left(1-2 x^4\right)^{3/4} \sqrt[4]{1-x^4} x^8 \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};\frac{x^4}{1-x^4}\right)+138 x^{12}-181 x^8+40 x^4+8}{20 x^5 \left(x^4-1\right) \left(2 x^4-1\right)^{3/4}}","\frac{15}{8} \tan ^{-1}\left(\frac{x}{\sqrt[4]{2 x^4-1}}\right)-\frac{15}{8} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{2 x^4-1}}\right)+\frac{\sqrt[4]{2 x^4-1} \left(69 x^8-56 x^4-8\right)}{20 x^5 \left(x^4-1\right)}",1,"(8 + 40*x^4 - 181*x^8 + 138*x^12 + 25*x^8*(1 - 2*x^4)^(3/4)*(1 - x^4)^(1/4)*Hypergeometric2F1[3/4, 3/4, 7/4, x^4/(1 - x^4)])/(20*x^5*(-1 + x^4)*(-1 + 2*x^4)^(3/4))","C",1
983,1,37,75,0.0103451,"\int \frac{\left(b+a x^2\right)^{3/4}}{x^3} \, dx","Integrate[(b + a*x^2)^(3/4)/x^3,x]","\frac{2 a \left(a x^2+b\right)^{7/4} \, _2F_1\left(\frac{7}{4},2;\frac{11}{4};\frac{a x^2}{b}+1\right)}{7 b^2}","-\frac{\left(a x^2+b\right)^{3/4}}{2 x^2}+\frac{3 a \tan ^{-1}\left(\frac{\sqrt[4]{a x^2+b}}{\sqrt[4]{b}}\right)}{4 \sqrt[4]{b}}-\frac{3 a \tanh ^{-1}\left(\frac{\sqrt[4]{a x^2+b}}{\sqrt[4]{b}}\right)}{4 \sqrt[4]{b}}",1,"(2*a*(b + a*x^2)^(7/4)*Hypergeometric2F1[7/4, 2, 11/4, 1 + (a*x^2)/b])/(7*b^2)","C",1
984,0,0,75,3.4563244,"\int \frac{3-2 (1+k) x+k x^2}{\sqrt[4]{(1-x) x (1-k x)} \left(-d+d (1+k) x-d k x^2+x^3\right)} \, dx","Integrate[(3 - 2*(1 + k)*x + k*x^2)/(((1 - x)*x*(1 - k*x))^(1/4)*(-d + d*(1 + k)*x - d*k*x^2 + x^3)),x]","\int \frac{3-2 (1+k) x+k x^2}{\sqrt[4]{(1-x) x (1-k x)} \left(-d+d (1+k) x-d k x^2+x^3\right)} \, dx","\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{k x^3+(-k-1) x^2+x}}{x}\right)}{d^{3/4}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{k x^3+(-k-1) x^2+x}}{x}\right)}{d^{3/4}}",1,"Integrate[(3 - 2*(1 + k)*x + k*x^2)/(((1 - x)*x*(1 - k*x))^(1/4)*(-d + d*(1 + k)*x - d*k*x^2 + x^3)), x]","F",-1
985,1,75,75,0.0795605,"\int \frac{1}{\sqrt[4]{-1+3 x-3 x^2+x^3} \left(-1-2 x+x^2+3 x^3\right)} \, dx","Integrate[1/((-1 + 3*x - 3*x^2 + x^3)^(1/4)*(-1 - 2*x + x^2 + 3*x^3)),x]","\frac{(x-1)^{3/4} \text{RootSum}\left[3 \text{$\#$1}^{12}+10 \text{$\#$1}^8+9 \text{$\#$1}^4+1\&,\frac{\log \left(\sqrt[4]{x-1}-\text{$\#$1}\right)}{9 \text{$\#$1}^{11}+20 \text{$\#$1}^7+9 \text{$\#$1}^3}\&\right]}{\sqrt[4]{(x-1)^3}}","\frac{\left((x-1)^3\right)^{3/4} \text{RootSum}\left[3 \text{$\#$1}^{12}+10 \text{$\#$1}^8+9 \text{$\#$1}^4+1\&,\frac{\log \left(\sqrt[4]{x-1}-\text{$\#$1}\right)}{9 \text{$\#$1}^{11}+20 \text{$\#$1}^7+9 \text{$\#$1}^3}\&\right]}{(x-1)^{9/4}}",1,"((-1 + x)^(3/4)*RootSum[1 + 9*#1^4 + 10*#1^8 + 3*#1^12 & , Log[(-1 + x)^(1/4) - #1]/(9*#1^3 + 20*#1^7 + 9*#1^11) & ])/((-1 + x)^3)^(1/4)","A",1
986,1,37,75,0.0105712,"\int \frac{\left(b+a x^3\right)^{3/4}}{x^4} \, dx","Integrate[(b + a*x^3)^(3/4)/x^4,x]","\frac{4 a \left(a x^3+b\right)^{7/4} \, _2F_1\left(\frac{7}{4},2;\frac{11}{4};\frac{a x^3}{b}+1\right)}{21 b^2}","-\frac{\left(a x^3+b\right)^{3/4}}{3 x^3}+\frac{a \tan ^{-1}\left(\frac{\sqrt[4]{a x^3+b}}{\sqrt[4]{b}}\right)}{2 \sqrt[4]{b}}-\frac{a \tanh ^{-1}\left(\frac{\sqrt[4]{a x^3+b}}{\sqrt[4]{b}}\right)}{2 \sqrt[4]{b}}",1,"(4*a*(b + a*x^3)^(7/4)*Hypergeometric2F1[7/4, 2, 11/4, 1 + (a*x^3)/b])/(21*b^2)","C",1
987,0,0,75,0.5554728,"\int \frac{\sqrt[4]{x^2+x^4}}{x^4 \left(-1+x^4\right)} \, dx","Integrate[(x^2 + x^4)^(1/4)/(x^4*(-1 + x^4)),x]","\int \frac{\sqrt[4]{x^2+x^4}}{x^4 \left(-1+x^4\right)} \, dx","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+x^2}}\right)}{2^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+x^2}}\right)}{2^{3/4}}+\frac{2 \sqrt[4]{x^4+x^2} \left(x^2+1\right)}{5 x^3}",1,"Integrate[(x^2 + x^4)^(1/4)/(x^4*(-1 + x^4)), x]","F",-1
988,0,0,75,0.1721871,"\int \frac{x \left(-3+x^4\right)}{\left(1+x^4\right)^{2/3} \left(1+x^3+x^4\right)} \, dx","Integrate[(x*(-3 + x^4))/((1 + x^4)^(2/3)*(1 + x^3 + x^4)),x]","\int \frac{x \left(-3+x^4\right)}{\left(1+x^4\right)^{2/3} \left(1+x^3+x^4\right)} \, dx","\log \left(\sqrt[3]{x^4+1}+x\right)-\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^4+1}-x}\right)-\frac{1}{2} \log \left(-\sqrt[3]{x^4+1} x+\left(x^4+1\right)^{2/3}+x^2\right)",1,"Integrate[(x*(-3 + x^4))/((1 + x^4)^(2/3)*(1 + x^3 + x^4)), x]","F",-1
989,1,2667,75,7.0381183,"\int \frac{\sqrt{2-x^2-4 x^4} \left(1+2 x^4\right)}{\left(-1+2 x^4\right) \left(-1-x^2+2 x^4\right)} \, dx","Integrate[(Sqrt[2 - x^2 - 4*x^4]*(1 + 2*x^4))/((-1 + 2*x^4)*(-1 - x^2 + 2*x^4)),x]","\text{Result too large to show}","\tan ^{-1}\left(\frac{x \sqrt{-4 x^4-x^2+2}}{4 x^4+x^2-2}\right)-\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x \sqrt{-4 x^4-x^2+2}}{4 x^4+x^2-2}\right)",1,"-(((-1 + x)*(1 + x)*(1 + 2*x^2)*Sqrt[2 - x^2 - 4*x^4]*(-1 + 2*x^4)*(Sqrt[2 - x^2 - 4*x^4]/(2*(-1 + x)) - Sqrt[2 - x^2 - 4*x^4]/(2*(1 + x)) + (2*Sqrt[2 - x^2 - 4*x^4])/(1 + 2*x^2) - (4*x^2*Sqrt[2 - x^2 - 4*x^4])/(-1 + 2*x^4))*((I*Sqrt[(1 + Sqrt[33])/2]*Sqrt[1 - (8*x^2)/(-1 - Sqrt[33])]*Sqrt[1 - (8*x^2)/(-1 + Sqrt[33])]*EllipticF[I*ArcSinh[2*Sqrt[2/(1 + Sqrt[33])]*x], (-1 - Sqrt[33])/(-1 + Sqrt[33])])/Sqrt[2 - x^2 - 4*x^4] + ((I/8)*Sqrt[1 + Sqrt[33]]*Sqrt[1 - (8*x^2)/(-1 - Sqrt[33])]*Sqrt[1 - (8*x^2)/(-1 + Sqrt[33])]*EllipticPi[-1/4*(-1 - Sqrt[33])/Sqrt[2], I*ArcSinh[2*Sqrt[2/(1 + Sqrt[33])]*x], (-1 - Sqrt[33])/(-1 + Sqrt[33])])/((-1 - 1/Sqrt[2])*(1/2 - 1/Sqrt[2])*Sqrt[2 - x^2 - 4*x^4]) - ((I/8)*Sqrt[1 + Sqrt[33]]*Sqrt[1 - (8*x^2)/(-1 - Sqrt[33])]*Sqrt[1 - (8*x^2)/(-1 + Sqrt[33])]*EllipticPi[(-1 - Sqrt[33])/(4*Sqrt[2]), I*ArcSinh[2*Sqrt[2/(1 + Sqrt[33])]*x], (-1 - Sqrt[33])/(-1 + Sqrt[33])])/((-1 + 1/Sqrt[2])*(1/2 + 1/Sqrt[2])*Sqrt[2 - x^2 - 4*x^4]) + (((3*I)/8)*Sqrt[(1 + Sqrt[33])/2]*Sqrt[1 - (8*x^2)/(-1 - Sqrt[33])]*Sqrt[1 - (8*x^2)/(-1 + Sqrt[33])]*EllipticPi[(1 + Sqrt[33])/4, I*ArcSinh[2*Sqrt[2/(1 + Sqrt[33])]*x], (-1 - Sqrt[33])/(-1 + Sqrt[33])])/((-1/2 - 1/Sqrt[2])*(-1/2 + 1/Sqrt[2])*Sqrt[2 - x^2 - 4*x^4]) - (3*(((Sqrt[(-1 + Sqrt[33])/2]/2 + (I/2)*Sqrt[(1 + Sqrt[33])/2])*(-1/2*Sqrt[(-1 + Sqrt[33])/2] + x)^2*Sqrt[((-1/2*I)*Sqrt[(1 + Sqrt[33])/2] + x)/((Sqrt[(-1 + Sqrt[33])/2]/2 + (I/2)*Sqrt[(1 + Sqrt[33])/2])*(-1/2*Sqrt[(-1 + Sqrt[33])/2] + x))]*Sqrt[((I/2)*Sqrt[(1 + Sqrt[33])/2] + x)/((Sqrt[(-1 + Sqrt[33])/2]/2 - (I/2)*Sqrt[(1 + Sqrt[33])/2])*(-1/2*Sqrt[(-1 + Sqrt[33])/2] + x))]*Sqrt[((Sqrt[-1 + Sqrt[33]] - I*Sqrt[1 + Sqrt[33]])*(Sqrt[2*(-1 + Sqrt[33])] + 4*x))/((Sqrt[-1 + Sqrt[33]] + I*Sqrt[1 + Sqrt[33]])*(Sqrt[2*(-1 + Sqrt[33])] - 4*x))]*((1 + Sqrt[(-1 + Sqrt[33])/2]/2)*EllipticF[ArcSin[Sqrt[((Sqrt[-1 + Sqrt[33]] - I*Sqrt[1 + Sqrt[33]])*(Sqrt[2*(-1 + Sqrt[33])] + 4*x))/((Sqrt[-1 + Sqrt[33]] + I*Sqrt[1 + Sqrt[33]])*(Sqrt[2*(-1 + Sqrt[33])] - 4*x))]], (Sqrt[-1 + Sqrt[33]] + I*Sqrt[1 + Sqrt[33]])^2/(Sqrt[-1 + Sqrt[33]] - I*Sqrt[1 + Sqrt[33]])^2] - Sqrt[(-1 + Sqrt[33])/2]*EllipticPi[((-1 + Sqrt[(-1 + Sqrt[33])/2]/2)*(Sqrt[(-1 + Sqrt[33])/2]/2 + (I/2)*Sqrt[(1 + Sqrt[33])/2]))/((-1 - Sqrt[(-1 + Sqrt[33])/2]/2)*(-1/2*Sqrt[(-1 + Sqrt[33])/2] + (I/2)*Sqrt[(1 + Sqrt[33])/2])), ArcSin[Sqrt[((Sqrt[-1 + Sqrt[33]] - I*Sqrt[1 + Sqrt[33]])*(Sqrt[2*(-1 + Sqrt[33])] + 4*x))/((Sqrt[-1 + Sqrt[33]] + I*Sqrt[1 + Sqrt[33]])*(Sqrt[2*(-1 + Sqrt[33])] - 4*x))]], (Sqrt[-1 + Sqrt[33]] + I*Sqrt[1 + Sqrt[33]])^2/(Sqrt[-1 + Sqrt[33]] - I*Sqrt[1 + Sqrt[33]])^2]))/((-1 - Sqrt[(-1 + Sqrt[33])/2]/2)*(1 - Sqrt[(-1 + Sqrt[33])/2]/2)*(Sqrt[(-1 + Sqrt[33])/2]/2 - (I/2)*Sqrt[(1 + Sqrt[33])/2])*Sqrt[2 - x^2 - 4*x^4]) - ((Sqrt[(-1 + Sqrt[33])/2]/2 + (I/2)*Sqrt[(1 + Sqrt[33])/2])*(-1/2*Sqrt[(-1 + Sqrt[33])/2] + x)^2*Sqrt[((-1/2*I)*Sqrt[(1 + Sqrt[33])/2] + x)/((Sqrt[(-1 + Sqrt[33])/2]/2 + (I/2)*Sqrt[(1 + Sqrt[33])/2])*(-1/2*Sqrt[(-1 + Sqrt[33])/2] + x))]*Sqrt[((I/2)*Sqrt[(1 + Sqrt[33])/2] + x)/((Sqrt[(-1 + Sqrt[33])/2]/2 - (I/2)*Sqrt[(1 + Sqrt[33])/2])*(-1/2*Sqrt[(-1 + Sqrt[33])/2] + x))]*Sqrt[((Sqrt[-1 + Sqrt[33]] - I*Sqrt[1 + Sqrt[33]])*(Sqrt[2*(-1 + Sqrt[33])] + 4*x))/((Sqrt[-1 + Sqrt[33]] + I*Sqrt[1 + Sqrt[33]])*(Sqrt[2*(-1 + Sqrt[33])] - 4*x))]*((-1 + Sqrt[(-1 + Sqrt[33])/2]/2)*EllipticF[ArcSin[Sqrt[((Sqrt[-1 + Sqrt[33]] - I*Sqrt[1 + Sqrt[33]])*(Sqrt[2*(-1 + Sqrt[33])] + 4*x))/((Sqrt[-1 + Sqrt[33]] + I*Sqrt[1 + Sqrt[33]])*(Sqrt[2*(-1 + Sqrt[33])] - 4*x))]], (Sqrt[-1 + Sqrt[33]] + I*Sqrt[1 + Sqrt[33]])^2/(Sqrt[-1 + Sqrt[33]] - I*Sqrt[1 + Sqrt[33]])^2] - Sqrt[(-1 + Sqrt[33])/2]*EllipticPi[((1 + Sqrt[(-1 + Sqrt[33])/2]/2)*(Sqrt[(-1 + Sqrt[33])/2]/2 + (I/2)*Sqrt[(1 + Sqrt[33])/2]))/((1 - Sqrt[(-1 + Sqrt[33])/2]/2)*(-1/2*Sqrt[(-1 + Sqrt[33])/2] + (I/2)*Sqrt[(1 + Sqrt[33])/2])), ArcSin[Sqrt[((Sqrt[-1 + Sqrt[33]] - I*Sqrt[1 + Sqrt[33]])*(Sqrt[2*(-1 + Sqrt[33])] + 4*x))/((Sqrt[-1 + Sqrt[33]] + I*Sqrt[1 + Sqrt[33]])*(Sqrt[2*(-1 + Sqrt[33])] - 4*x))]], (Sqrt[-1 + Sqrt[33]] + I*Sqrt[1 + Sqrt[33]])^2/(Sqrt[-1 + Sqrt[33]] - I*Sqrt[1 + Sqrt[33]])^2]))/((-1 - Sqrt[(-1 + Sqrt[33])/2]/2)*(1 - Sqrt[(-1 + Sqrt[33])/2]/2)*(Sqrt[(-1 + Sqrt[33])/2]/2 - (I/2)*Sqrt[(1 + Sqrt[33])/2])*Sqrt[2 - x^2 - 4*x^4])))/(2*(1 - 1/Sqrt[2])*(1 + 1/Sqrt[2]))))/((1 + 2*x^4)*(-2 + x^2 + 4*x^4)))","C",0
990,1,46,75,0.0101023,"\int \left(b+a x^4\right)^{3/4} \, dx","Integrate[(b + a*x^4)^(3/4),x]","\frac{x \left(a x^4+b\right)^{3/4} \, _2F_1\left(-\frac{3}{4},\frac{1}{4};\frac{5}{4};-\frac{a x^4}{b}\right)}{\left(\frac{a x^4}{b}+1\right)^{3/4}}","\frac{1}{4} x \left(a x^4+b\right)^{3/4}+\frac{3 b \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{8 \sqrt[4]{a}}+\frac{3 b \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{8 \sqrt[4]{a}}",1,"(x*(b + a*x^4)^(3/4)*Hypergeometric2F1[-3/4, 1/4, 5/4, -((a*x^4)/b)])/(1 + (a*x^4)/b)^(3/4)","C",1
991,1,51,75,0.0097172,"\int \frac{\left(b+a x^4\right)^{3/4}}{x^4} \, dx","Integrate[(b + a*x^4)^(3/4)/x^4,x]","-\frac{\left(a x^4+b\right)^{3/4} \, _2F_1\left(-\frac{3}{4},-\frac{3}{4};\frac{1}{4};-\frac{a x^4}{b}\right)}{3 x^3 \left(\frac{a x^4}{b}+1\right)^{3/4}}","\frac{1}{2} a^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)+\frac{1}{2} a^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)-\frac{\left(a x^4+b\right)^{3/4}}{3 x^3}",1,"-1/3*((b + a*x^4)^(3/4)*Hypergeometric2F1[-3/4, -3/4, 1/4, -((a*x^4)/b)])/(x^3*(1 + (a*x^4)/b)^(3/4))","C",1
992,1,37,75,0.0116742,"\int \frac{\left(b+a x^5\right)^{3/4}}{x^6} \, dx","Integrate[(b + a*x^5)^(3/4)/x^6,x]","\frac{4 a \left(a x^5+b\right)^{7/4} \, _2F_1\left(\frac{7}{4},2;\frac{11}{4};\frac{a x^5}{b}+1\right)}{35 b^2}","-\frac{\left(a x^5+b\right)^{3/4}}{5 x^5}+\frac{3 a \tan ^{-1}\left(\frac{\sqrt[4]{a x^5+b}}{\sqrt[4]{b}}\right)}{10 \sqrt[4]{b}}-\frac{3 a \tanh ^{-1}\left(\frac{\sqrt[4]{a x^5+b}}{\sqrt[4]{b}}\right)}{10 \sqrt[4]{b}}",1,"(4*a*(b + a*x^5)^(7/4)*Hypergeometric2F1[7/4, 2, 11/4, 1 + (a*x^5)/b])/(35*b^2)","C",1
993,0,0,75,0.4007004,"\int \frac{2-3 x^5}{\left(1-x^2+x^5\right) \sqrt[3]{x+x^6}} \, dx","Integrate[(2 - 3*x^5)/((1 - x^2 + x^5)*(x + x^6)^(1/3)),x]","\int \frac{2-3 x^5}{\left(1-x^2+x^5\right) \sqrt[3]{x+x^6}} \, dx","-\log \left(\sqrt[3]{x^6+x}-x\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^6+x}+x}\right)+\frac{1}{2} \log \left(\sqrt[3]{x^6+x} x+\left(x^6+x\right)^{2/3}+x^2\right)",1,"Integrate[(2 - 3*x^5)/((1 - x^2 + x^5)*(x + x^6)^(1/3)), x]","F",-1
994,1,37,75,0.0111567,"\int \frac{\left(b+a x^6\right)^{3/4}}{x^7} \, dx","Integrate[(b + a*x^6)^(3/4)/x^7,x]","\frac{2 a \left(a x^6+b\right)^{7/4} \, _2F_1\left(\frac{7}{4},2;\frac{11}{4};\frac{a x^6}{b}+1\right)}{21 b^2}","-\frac{\left(a x^6+b\right)^{3/4}}{6 x^6}+\frac{a \tan ^{-1}\left(\frac{\sqrt[4]{a x^6+b}}{\sqrt[4]{b}}\right)}{4 \sqrt[4]{b}}-\frac{a \tanh ^{-1}\left(\frac{\sqrt[4]{a x^6+b}}{\sqrt[4]{b}}\right)}{4 \sqrt[4]{b}}",1,"(2*a*(b + a*x^6)^(7/4)*Hypergeometric2F1[7/4, 2, 11/4, 1 + (a*x^6)/b])/(21*b^2)","C",1
995,0,0,75,0.299336,"\int \frac{2 b+a x^6}{\sqrt[4]{-b+a x^6} \left(-b-2 x^4+a x^6\right)} \, dx","Integrate[(2*b + a*x^6)/((-b + a*x^6)^(1/4)*(-b - 2*x^4 + a*x^6)),x]","\int \frac{2 b+a x^6}{\sqrt[4]{-b+a x^6} \left(-b-2 x^4+a x^6\right)} \, dx","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x \left(a x^6-b\right)^{3/4}}{b-a x^6}\right)}{\sqrt[4]{2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x \left(a x^6-b\right)^{3/4}}{b-a x^6}\right)}{\sqrt[4]{2}}",1,"Integrate[(2*b + a*x^6)/((-b + a*x^6)^(1/4)*(-b - 2*x^4 + a*x^6)), x]","F",-1
996,1,146,75,0.5504591,"\int \frac{\left(-1+x^4\right) \sqrt{1+x^4}}{1+3 x^4+x^8} \, dx","Integrate[((-1 + x^4)*Sqrt[1 + x^4])/(1 + 3*x^4 + x^8),x]","\frac{1}{2} \sqrt[4]{-1} \left(-2 F\left(\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+\Pi \left(-\sqrt{\frac{2}{3+\sqrt{5}}};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+\Pi \left(\sqrt{\frac{2}{3+\sqrt{5}}};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+\Pi \left(-\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+\Pi \left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)\right)","-\frac{\tan ^{-1}\left(\frac{\sqrt{2} x \sqrt{x^4+1}}{x^4-x^2+1}\right)}{2 \sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt{x^4+1}}{x^4+x^2+1}\right)}{2 \sqrt{2}}",1,"((-1)^(1/4)*(-2*EllipticF[I*ArcSinh[(-1)^(1/4)*x], -1] + EllipticPi[-Sqrt[2/(3 + Sqrt[5])], I*ArcSinh[(-1)^(1/4)*x], -1] + EllipticPi[Sqrt[2/(3 + Sqrt[5])], I*ArcSinh[(-1)^(1/4)*x], -1] + EllipticPi[-Sqrt[(3 + Sqrt[5])/2], I*ArcSinh[(-1)^(1/4)*x], -1] + EllipticPi[Sqrt[(3 + Sqrt[5])/2], I*ArcSinh[(-1)^(1/4)*x], -1]))/2","C",1
997,1,345,76,6.0418498,"\int \frac{-1+k^2 x^2}{\sqrt{(1-x) x \left(1-k^2 x\right)} \left(a+b x+a k^2 x^2\right)} \, dx","Integrate[(-1 + k^2*x^2)/(Sqrt[(1 - x)*x*(1 - k^2*x)]*(a + b*x + a*k^2*x^2)),x]","\frac{i \sqrt{\frac{1}{x-1}+1} (x-1)^{3/2} \sqrt{\frac{1-\frac{1}{k^2}}{x-1}+1} \left(2 a \left(k^2-1\right) \sqrt{b^2-4 a^2 k^2} F\left(i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)+\left(b \sqrt{b^2-4 a^2 k^2}+2 a \left(\sqrt{b^2-4 a^2 k^2}-2 a k^2\right)+b^2\right) \Pi \left(\frac{2 \left(a k^2+a+b\right)}{2 a k^2+b-\sqrt{b^2-4 a^2 k^2}};i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)+\left(b \sqrt{b^2-4 a^2 k^2}+2 a \left(\sqrt{b^2-4 a^2 k^2}+2 a k^2\right)-b^2\right) \Pi \left(\frac{2 \left(a k^2+a+b\right)}{2 a k^2+b+\sqrt{b^2-4 a^2 k^2}};i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)\right)}{a \sqrt{(x-1) x \left(k^2 x-1\right)} \left(a k^2+a+b\right) \sqrt{b^2-4 a^2 k^2}}","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{k^2 x^3+\left(-k^2-1\right) x^2+x} \sqrt{a k^2+a+b}}{\sqrt{a} (x-1) \left(k^2 x-1\right)}\right)}{\sqrt{a} \sqrt{a k^2+a+b}}",1,"(I*Sqrt[1 + (-1 + x)^(-1)]*Sqrt[1 + (1 - k^(-2))/(-1 + x)]*(-1 + x)^(3/2)*(2*a*(-1 + k^2)*Sqrt[b^2 - 4*a^2*k^2]*EllipticF[I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)] + (b^2 + b*Sqrt[b^2 - 4*a^2*k^2] + 2*a*(-2*a*k^2 + Sqrt[b^2 - 4*a^2*k^2]))*EllipticPi[(2*(a + b + a*k^2))/(b + 2*a*k^2 - Sqrt[b^2 - 4*a^2*k^2]), I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)] + (-b^2 + b*Sqrt[b^2 - 4*a^2*k^2] + 2*a*(2*a*k^2 + Sqrt[b^2 - 4*a^2*k^2]))*EllipticPi[(2*(a + b + a*k^2))/(b + 2*a*k^2 + Sqrt[b^2 - 4*a^2*k^2]), I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)]))/(a*(a + b + a*k^2)*Sqrt[b^2 - 4*a^2*k^2]*Sqrt[(-1 + x)*x*(-1 + k^2*x)])","C",1
998,1,28,76,0.0058728,"\int \frac{1}{x \sqrt[3]{-1+x^4}} \, dx","Integrate[1/(x*(-1 + x^4)^(1/3)),x]","\frac{3}{8} \left(x^4-1\right)^{2/3} \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};1-x^4\right)","-\frac{1}{4} \log \left(\sqrt[3]{x^4-1}+1\right)+\frac{1}{8} \log \left(\left(x^4-1\right)^{2/3}-\sqrt[3]{x^4-1}+1\right)-\frac{1}{4} \sqrt{3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{x^4-1}}{\sqrt{3}}\right)",1,"(3*(-1 + x^4)^(2/3)*Hypergeometric2F1[2/3, 1, 5/3, 1 - x^4])/8","C",1
999,1,360,76,0.6019631,"\int \frac{x^2 \left(-2 b+a x^2\right)}{\left(-b+a x^2\right)^{3/4} \left(4 b-4 a x^2+x^4\right)} \, dx","Integrate[(x^2*(-2*b + a*x^2))/((-b + a*x^2)^(3/4)*(4*b - 4*a*x^2 + x^4)),x]","-\frac{\sqrt[4]{-b} \sqrt{\frac{a x^2}{b}} \Pi \left(-\frac{\sqrt{b}}{\sqrt{-2 a^2-2 \sqrt{a^2-b} a+b}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{a x^2-b}}{\sqrt[4]{-b}}\right)\right|-1\right)+\sqrt[4]{-b} \sqrt{\frac{a x^2}{b}} \Pi \left(\frac{\sqrt{b}}{\sqrt{-2 a^2-2 \sqrt{a^2-b} a+b}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{a x^2-b}}{\sqrt[4]{-b}}\right)\right|-1\right)+\sqrt[4]{-b} \sqrt{\frac{a x^2}{b}} \Pi \left(-\frac{\sqrt{b}}{\sqrt{-2 a^2+2 \sqrt{a^2-b} a+b}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{a x^2-b}}{\sqrt[4]{-b}}\right)\right|-1\right)+\sqrt[4]{-b} \sqrt{\frac{a x^2}{b}} \Pi \left(\frac{\sqrt{b}}{\sqrt{-2 a^2+2 \sqrt{a^2-b} a+b}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{a x^2-b}}{\sqrt[4]{-b}}\right)\right|-1\right)-\frac{a x^2 \left(1-\frac{a x^2}{b}\right)^{3/4} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{3}{2};\frac{a x^2}{b}\right)}{\left(a x^2-b\right)^{3/4}}}{x}","\frac{\tanh ^{-1}\left(\frac{x \left(a x^2-b\right)^{3/4}}{\sqrt{2} \left(b-a x^2\right)}\right)}{\sqrt{2}}-\frac{\tan ^{-1}\left(\frac{x \left(a x^2-b\right)^{3/4}}{\sqrt{2} \left(b-a x^2\right)}\right)}{\sqrt{2}}",1,"-(((-b)^(1/4)*Sqrt[(a*x^2)/b]*EllipticPi[-(Sqrt[b]/Sqrt[-2*a^2 - 2*a*Sqrt[a^2 - b] + b]), ArcSin[(-b + a*x^2)^(1/4)/(-b)^(1/4)], -1] + (-b)^(1/4)*Sqrt[(a*x^2)/b]*EllipticPi[Sqrt[b]/Sqrt[-2*a^2 - 2*a*Sqrt[a^2 - b] + b], ArcSin[(-b + a*x^2)^(1/4)/(-b)^(1/4)], -1] + (-b)^(1/4)*Sqrt[(a*x^2)/b]*EllipticPi[-(Sqrt[b]/Sqrt[-2*a^2 + 2*a*Sqrt[a^2 - b] + b]), ArcSin[(-b + a*x^2)^(1/4)/(-b)^(1/4)], -1] + (-b)^(1/4)*Sqrt[(a*x^2)/b]*EllipticPi[Sqrt[b]/Sqrt[-2*a^2 + 2*a*Sqrt[a^2 - b] + b], ArcSin[(-b + a*x^2)^(1/4)/(-b)^(1/4)], -1] - (a*x^2*(1 - (a*x^2)/b)^(3/4)*Hypergeometric2F1[1/2, 3/4, 3/2, (a*x^2)/b])/(-b + a*x^2)^(3/4))/x)","C",1
1000,1,31019,76,15.2423053,"\int \frac{-a b x+x^3}{\sqrt{x (-a+x) (-b+x)} \left(a^2 b^2-2 a b (a+b) x+\left(a^2+4 a b+b^2-d\right) x^2-2 (a+b) x^3+x^4\right)} \, dx","Integrate[(-(a*b*x) + x^3)/(Sqrt[x*(-a + x)*(-b + x)]*(a^2*b^2 - 2*a*b*(a + b)*x + (a^2 + 4*a*b + b^2 - d)*x^2 - 2*(a + b)*x^3 + x^4)),x]","\text{Result too large to show}","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt{x^2 (-a-b)+a b x+x^3}}\right)}{d^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt{x^2 (-a-b)+a b x+x^3}}\right)}{d^{3/4}}",1,"Result too large to show","C",0
1001,1,78,76,0.0824922,"\int \frac{\sqrt[4]{-1-x^4} \left(-1+x^4\right)}{x^6 \left(1+2 x^4\right)} \, dx","Integrate[((-1 - x^4)^(1/4)*(-1 + x^4))/(x^6*(1 + 2*x^4)),x]","\frac{\frac{5 \left(x^4+1\right)^{3/4} x^8 \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};\frac{x^4}{2 x^4+1}\right)}{\left(2 x^4+1\right)^{3/4}}+14 x^8+13 x^4-1}{5 x^5 \left(-x^4-1\right)^{3/4}}","\frac{3}{2} \tan ^{-1}\left(\frac{x \left(-x^4-1\right)^{3/4}}{x^4+1}\right)-\frac{3}{2} \tanh ^{-1}\left(\frac{x \left(-x^4-1\right)^{3/4}}{x^4+1}\right)+\frac{\sqrt[4]{-x^4-1} \left(1-14 x^4\right)}{5 x^5}",1,"(-1 + 13*x^4 + 14*x^8 + (5*x^8*(1 + x^4)^(3/4)*Hypergeometric2F1[3/4, 3/4, 7/4, x^4/(1 + 2*x^4)])/(1 + 2*x^4)^(3/4))/(5*x^5*(-1 - x^4)^(3/4))","C",0
1002,1,32987,76,14.4191031,"\int \frac{a b x-x^3}{\sqrt{x (-a+x) (-b+x)} \left(a^2 b^2 d-2 a b (a+b) d x+\left(-1+a^2 d+4 a b d+b^2 d\right) x^2-2 (a+b) d x^3+d x^4\right)} \, dx","Integrate[(a*b*x - x^3)/(Sqrt[x*(-a + x)*(-b + x)]*(a^2*b^2*d - 2*a*b*(a + b)*d*x + (-1 + a^2*d + 4*a*b*d + b^2*d)*x^2 - 2*(a + b)*d*x^3 + d*x^4)),x]","\text{Result too large to show}","\frac{\tanh ^{-1}\left(\frac{x}{\sqrt[4]{d} \sqrt{x^2 (-a-b)+a b x+x^3}}\right)}{\sqrt[4]{d}}-\frac{\tan ^{-1}\left(\frac{x}{\sqrt[4]{d} \sqrt{x^2 (-a-b)+a b x+x^3}}\right)}{\sqrt[4]{d}}",1,"Result too large to show","C",0
1003,1,32986,76,6.4212866,"\int \frac{-a b x+x^3}{\sqrt{x (-a+x) (-b+x)} \left(a^2 b^2 d-2 a b (a+b) d x+\left(-1+a^2 d+4 a b d+b^2 d\right) x^2-2 (a+b) d x^3+d x^4\right)} \, dx","Integrate[(-(a*b*x) + x^3)/(Sqrt[x*(-a + x)*(-b + x)]*(a^2*b^2*d - 2*a*b*(a + b)*d*x + (-1 + a^2*d + 4*a*b*d + b^2*d)*x^2 - 2*(a + b)*d*x^3 + d*x^4)),x]","\text{Result too large to show}","\frac{\tan ^{-1}\left(\frac{x}{\sqrt[4]{d} \sqrt{x^2 (-a-b)+a b x+x^3}}\right)}{\sqrt[4]{d}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt[4]{d} \sqrt{x^2 (-a-b)+a b x+x^3}}\right)}{\sqrt[4]{d}}",1,"Result too large to show","C",0
1004,1,28,76,0.0054396,"\int \frac{1}{x \sqrt[3]{-1+x^6}} \, dx","Integrate[1/(x*(-1 + x^6)^(1/3)),x]","\frac{1}{4} \left(x^6-1\right)^{2/3} \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};1-x^6\right)","-\frac{1}{6} \log \left(\sqrt[3]{x^6-1}+1\right)+\frac{1}{12} \log \left(\left(x^6-1\right)^{2/3}-\sqrt[3]{x^6-1}+1\right)-\frac{\tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{x^6-1}}{\sqrt{3}}\right)}{2 \sqrt{3}}",1,"((-1 + x^6)^(2/3)*Hypergeometric2F1[2/3, 1, 5/3, 1 - x^6])/4","C",1
1005,1,411,76,1.7625699,"\int \frac{\left(1+x^3\right)^{2/3} \left(2+x^3+2 x^6\right)}{x^6 \left(1+x^3+x^6\right)} \, dx","Integrate[((1 + x^3)^(2/3)*(2 + x^3 + 2*x^6))/(x^6*(1 + x^3 + x^6)),x]","\frac{\left(x^3+1\right)^{2/3} \left(x^3-4\right)}{10 x^5}+\frac{i \left(-\frac{2 \log \left(\sqrt[3]{\sqrt{3}+i}-\frac{\sqrt[3]{\sqrt{3}-i} x}{\sqrt[3]{x^3+1}}\right)}{\sqrt[3]{\frac{\sqrt{3}-i}{\sqrt{3}+i}}}+2 \sqrt[3]{\frac{\sqrt{3}-i}{\sqrt{3}+i}} \log \left(\sqrt[3]{\sqrt{3}-i}-\frac{\sqrt[3]{\sqrt{3}+i} x}{\sqrt[3]{x^3+1}}\right)+\frac{2 \sqrt{3} \tan ^{-1}\left(\frac{1+\frac{\sqrt[3]{2} \left(\sqrt{3}-i\right)^{2/3} x}{\sqrt[3]{x^3+1}}}{\sqrt{3}}\right)+\log \left(\frac{2^{2/3} x}{\sqrt[3]{x^3+1}}+\frac{\left(\sqrt{3}-i\right)^{2/3} x^2}{\left(x^3+1\right)^{2/3}}+\left(\sqrt{3}+i\right)^{2/3}\right)}{\left(\frac{1}{2} \left(\sqrt{3}-i\right)\right)^{2/3}}-\frac{2 \sqrt{3} \tan ^{-1}\left(\frac{1+\frac{\sqrt[3]{2} \left(\sqrt{3}+i\right)^{2/3} x}{\sqrt[3]{x^3+1}}}{\sqrt{3}}\right)+\log \left(\frac{2^{2/3} x}{\sqrt[3]{x^3+1}}+\frac{\left(\sqrt{3}+i\right)^{2/3} x^2}{\left(x^3+1\right)^{2/3}}+\left(\sqrt{3}-i\right)^{2/3}\right)}{\left(\frac{1}{2} \left(\sqrt{3}+i\right)\right)^{2/3}}\right)}{6 \sqrt{3}}","\frac{\left(x^3-4\right) \left(x^3+1\right)^{2/3}}{10 x^5}-\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^6-\text{$\#$1}^3+1\&,\frac{\log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)-\log (x)}{2 \text{$\#$1}^4-\text{$\#$1}}\&\right]",1,"((-4 + x^3)*(1 + x^3)^(2/3))/(10*x^5) + ((I/6)*((2*Sqrt[3]*ArcTan[(1 + (2^(1/3)*(-I + Sqrt[3])^(2/3)*x)/(1 + x^3)^(1/3))/Sqrt[3]] + Log[(I + Sqrt[3])^(2/3) + ((-I + Sqrt[3])^(2/3)*x^2)/(1 + x^3)^(2/3) + (2^(2/3)*x)/(1 + x^3)^(1/3)])/((-I + Sqrt[3])/2)^(2/3) - (2*Sqrt[3]*ArcTan[(1 + (2^(1/3)*(I + Sqrt[3])^(2/3)*x)/(1 + x^3)^(1/3))/Sqrt[3]] + Log[(-I + Sqrt[3])^(2/3) + ((I + Sqrt[3])^(2/3)*x^2)/(1 + x^3)^(2/3) + (2^(2/3)*x)/(1 + x^3)^(1/3)])/((I + Sqrt[3])/2)^(2/3) - (2*Log[(I + Sqrt[3])^(1/3) - ((-I + Sqrt[3])^(1/3)*x)/(1 + x^3)^(1/3)])/((-I + Sqrt[3])/(I + Sqrt[3]))^(1/3) + 2*((-I + Sqrt[3])/(I + Sqrt[3]))^(1/3)*Log[(-I + Sqrt[3])^(1/3) - ((I + Sqrt[3])^(1/3)*x)/(1 + x^3)^(1/3)]))/Sqrt[3]","C",0
1006,1,411,76,1.4044046,"\int \frac{\left(1+x^3\right)^{2/3} \left(2+x^3+2 x^6\right)}{x^6 \left(1+x^3+x^6\right)} \, dx","Integrate[((1 + x^3)^(2/3)*(2 + x^3 + 2*x^6))/(x^6*(1 + x^3 + x^6)),x]","\frac{\left(x^3+1\right)^{2/3} \left(x^3-4\right)}{10 x^5}+\frac{i \left(-\frac{2 \log \left(\sqrt[3]{\sqrt{3}+i}-\frac{\sqrt[3]{\sqrt{3}-i} x}{\sqrt[3]{x^3+1}}\right)}{\sqrt[3]{\frac{\sqrt{3}-i}{\sqrt{3}+i}}}+2 \sqrt[3]{\frac{\sqrt{3}-i}{\sqrt{3}+i}} \log \left(\sqrt[3]{\sqrt{3}-i}-\frac{\sqrt[3]{\sqrt{3}+i} x}{\sqrt[3]{x^3+1}}\right)+\frac{2 \sqrt{3} \tan ^{-1}\left(\frac{1+\frac{\sqrt[3]{2} \left(\sqrt{3}-i\right)^{2/3} x}{\sqrt[3]{x^3+1}}}{\sqrt{3}}\right)+\log \left(\frac{2^{2/3} x}{\sqrt[3]{x^3+1}}+\frac{\left(\sqrt{3}-i\right)^{2/3} x^2}{\left(x^3+1\right)^{2/3}}+\left(\sqrt{3}+i\right)^{2/3}\right)}{\left(\frac{1}{2} \left(\sqrt{3}-i\right)\right)^{2/3}}-\frac{2 \sqrt{3} \tan ^{-1}\left(\frac{1+\frac{\sqrt[3]{2} \left(\sqrt{3}+i\right)^{2/3} x}{\sqrt[3]{x^3+1}}}{\sqrt{3}}\right)+\log \left(\frac{2^{2/3} x}{\sqrt[3]{x^3+1}}+\frac{\left(\sqrt{3}+i\right)^{2/3} x^2}{\left(x^3+1\right)^{2/3}}+\left(\sqrt{3}-i\right)^{2/3}\right)}{\left(\frac{1}{2} \left(\sqrt{3}+i\right)\right)^{2/3}}\right)}{6 \sqrt{3}}","\frac{\left(x^3-4\right) \left(x^3+1\right)^{2/3}}{10 x^5}-\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^6-\text{$\#$1}^3+1\&,\frac{\log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)-\log (x)}{2 \text{$\#$1}^4-\text{$\#$1}}\&\right]",1,"((-4 + x^3)*(1 + x^3)^(2/3))/(10*x^5) + ((I/6)*((2*Sqrt[3]*ArcTan[(1 + (2^(1/3)*(-I + Sqrt[3])^(2/3)*x)/(1 + x^3)^(1/3))/Sqrt[3]] + Log[(I + Sqrt[3])^(2/3) + ((-I + Sqrt[3])^(2/3)*x^2)/(1 + x^3)^(2/3) + (2^(2/3)*x)/(1 + x^3)^(1/3)])/((-I + Sqrt[3])/2)^(2/3) - (2*Sqrt[3]*ArcTan[(1 + (2^(1/3)*(I + Sqrt[3])^(2/3)*x)/(1 + x^3)^(1/3))/Sqrt[3]] + Log[(-I + Sqrt[3])^(2/3) + ((I + Sqrt[3])^(2/3)*x^2)/(1 + x^3)^(2/3) + (2^(2/3)*x)/(1 + x^3)^(1/3)])/((I + Sqrt[3])/2)^(2/3) - (2*Log[(I + Sqrt[3])^(1/3) - ((-I + Sqrt[3])^(1/3)*x)/(1 + x^3)^(1/3)])/((-I + Sqrt[3])/(I + Sqrt[3]))^(1/3) + 2*((-I + Sqrt[3])/(I + Sqrt[3]))^(1/3)*Log[(-I + Sqrt[3])^(1/3) - ((I + Sqrt[3])^(1/3)*x)/(1 + x^3)^(1/3)]))/Sqrt[3]","C",0
1007,1,605,76,2.5439125,"\int \frac{\left(-1+x^4\right) \left(1-x^2+x^4\right) \sqrt{4-x^2+4 x^4}}{\left(1+x^4\right) \left(4+7 x^4+4 x^8\right)} \, dx","Integrate[((-1 + x^4)*(1 - x^2 + x^4)*Sqrt[4 - x^2 + 4*x^4])/((1 + x^4)*(4 + 7*x^4 + 4*x^8)),x]","-\frac{i \sqrt{2-\frac{16 x^2}{1-3 i \sqrt{7}}} \sqrt{1-\frac{8 x^2}{1+3 i \sqrt{7}}} \left(4 F\left(i \sinh ^{-1}\left(2 \sqrt{-\frac{2}{1-3 i \sqrt{7}}} x\right)|\frac{i+3 \sqrt{7}}{i-3 \sqrt{7}}\right)+4 \Pi \left(\frac{1}{8} \left(-i-3 \sqrt{7}\right);i \sinh ^{-1}\left(2 \sqrt{-\frac{2}{1-3 i \sqrt{7}}} x\right)|\frac{i+3 \sqrt{7}}{i-3 \sqrt{7}}\right)+4 \Pi \left(\frac{1}{8} \left(i+3 \sqrt{7}\right);i \sinh ^{-1}\left(2 \sqrt{-\frac{2}{1-3 i \sqrt{7}}} x\right)|\frac{i+3 \sqrt{7}}{i-3 \sqrt{7}}\right)+\Pi \left(\frac{i+3 \sqrt{7}}{2 i-2 \sqrt{15}};i \sinh ^{-1}\left(2 \sqrt{-\frac{2}{1-3 i \sqrt{7}}} x\right)|\frac{i+3 \sqrt{7}}{i-3 \sqrt{7}}\right)-9 \Pi \left(\frac{i+3 \sqrt{7}}{2 \left(-i+\sqrt{15}\right)};i \sinh ^{-1}\left(2 \sqrt{-\frac{2}{1-3 i \sqrt{7}}} x\right)|\frac{i+3 \sqrt{7}}{i-3 \sqrt{7}}\right)-9 \Pi \left(-\frac{i+3 \sqrt{7}}{2 i+2 \sqrt{15}};i \sinh ^{-1}\left(2 \sqrt{-\frac{2}{1-3 i \sqrt{7}}} x\right)|\frac{i+3 \sqrt{7}}{i-3 \sqrt{7}}\right)+\Pi \left(\frac{i+3 \sqrt{7}}{2 i+2 \sqrt{15}};i \sinh ^{-1}\left(2 \sqrt{-\frac{2}{1-3 i \sqrt{7}}} x\right)|\frac{i+3 \sqrt{7}}{i-3 \sqrt{7}}\right)\right)}{16 \sqrt{-\frac{i}{3 \sqrt{7}+i}} \sqrt{4 x^4-x^2+4}}","\tan ^{-1}\left(\frac{x}{\sqrt{4 x^4-x^2+4}}\right)-\frac{3}{4} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{\sqrt{4 x^4-x^2+4}}\right)+\frac{1}{4} \tanh ^{-1}\left(\frac{x}{\sqrt{4 x^4-x^2+4}}\right)",1,"((-1/16*I)*Sqrt[2 - (16*x^2)/(1 - (3*I)*Sqrt[7])]*Sqrt[1 - (8*x^2)/(1 + (3*I)*Sqrt[7])]*(4*EllipticF[I*ArcSinh[2*Sqrt[-2/(1 - (3*I)*Sqrt[7])]*x], (I + 3*Sqrt[7])/(I - 3*Sqrt[7])] + 4*EllipticPi[(-I - 3*Sqrt[7])/8, I*ArcSinh[2*Sqrt[-2/(1 - (3*I)*Sqrt[7])]*x], (I + 3*Sqrt[7])/(I - 3*Sqrt[7])] + 4*EllipticPi[(I + 3*Sqrt[7])/8, I*ArcSinh[2*Sqrt[-2/(1 - (3*I)*Sqrt[7])]*x], (I + 3*Sqrt[7])/(I - 3*Sqrt[7])] + EllipticPi[(I + 3*Sqrt[7])/(2*I - 2*Sqrt[15]), I*ArcSinh[2*Sqrt[-2/(1 - (3*I)*Sqrt[7])]*x], (I + 3*Sqrt[7])/(I - 3*Sqrt[7])] - 9*EllipticPi[(I + 3*Sqrt[7])/(2*(-I + Sqrt[15])), I*ArcSinh[2*Sqrt[-2/(1 - (3*I)*Sqrt[7])]*x], (I + 3*Sqrt[7])/(I - 3*Sqrt[7])] - 9*EllipticPi[-((I + 3*Sqrt[7])/(2*I + 2*Sqrt[15])), I*ArcSinh[2*Sqrt[-2/(1 - (3*I)*Sqrt[7])]*x], (I + 3*Sqrt[7])/(I - 3*Sqrt[7])] + EllipticPi[(I + 3*Sqrt[7])/(2*I + 2*Sqrt[15]), I*ArcSinh[2*Sqrt[-2/(1 - (3*I)*Sqrt[7])]*x], (I + 3*Sqrt[7])/(I - 3*Sqrt[7])]))/(Sqrt[(-I)/(I + 3*Sqrt[7])]*Sqrt[4 - x^2 + 4*x^4])","C",1
1008,1,44,76,0.0378249,"\int \sqrt[3]{1-3 x+3 x^3-9 x^4+3 x^6-9 x^7+x^9-3 x^{10}} \, dx","Integrate[(1 - 3*x + 3*x^3 - 9*x^4 + 3*x^6 - 9*x^7 + x^9 - 3*x^10)^(1/3),x]","-\frac{\left(-\left((3 x-1) \left(x^3+1\right)^3\right)\right)^{4/3} \left(70 x^3+21 x^2+6 x+229\right)}{910 \left(x^3+1\right)^4}","\frac{\left(210 x^4-7 x^3-3 x^2+681 x-229\right) \sqrt[3]{-3 x^{10}+x^9-9 x^7+3 x^6-9 x^4+3 x^3-3 x+1}}{910 (x+1) \left(x^2-x+1\right)}",1,"-1/910*((-((-1 + 3*x)*(1 + x^3)^3))^(4/3)*(229 + 6*x + 21*x^2 + 70*x^3))/(1 + x^3)^4","A",1
1009,1,226,77,7.5987359,"\int \frac{x (-b+x) \left(a b-2 a x+x^2\right)}{(-a+x) \sqrt{x (-a+x) (-b+x)} \left(a d+(-b-d) x+x^2\right)} \, dx","Integrate[(x*(-b + x)*(a*b - 2*a*x + x^2))/((-a + x)*Sqrt[x*(-a + x)*(-b + x)]*(a*d + (-b - d)*x + x^2)),x]","\frac{2 \left(x (a-x)^2 (x-b)-\frac{i d (x-a)^3 \sqrt{\frac{x-b}{a-b}} \left(-\Pi \left(-\frac{2 a}{-2 a+b+d-\sqrt{b^2+2 d b+d^2-4 a d}};i \sinh ^{-1}\left(\sqrt{\frac{x}{a}-1}\right)|\frac{a}{a-b}\right)-\Pi \left(-\frac{2 a}{-2 a+b+d+\sqrt{b^2+2 d b+d^2-4 a d}};i \sinh ^{-1}\left(\sqrt{\frac{x}{a}-1}\right)|\frac{a}{a-b}\right)+F\left(i \sinh ^{-1}\left(\sqrt{\frac{x}{a}-1}\right)|\frac{a}{a-b}\right)\right)}{\sqrt{1-\frac{a}{x}}}\right)}{(a-x)^2 \sqrt{x (x-a) (x-b)}}","2 \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{x^2 (-a-b)+a b x+x^3}}{\sqrt{d} (a-x)}\right)-\frac{2 \sqrt{x^2 (-a-b)+a b x+x^3}}{a-x}",1,"(2*((a - x)^2*x*(-b + x) - (I*d*(-a + x)^3*Sqrt[(-b + x)/(a - b)]*(EllipticF[I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)] - EllipticPi[(-2*a)/(-2*a + b + d - Sqrt[b^2 - 4*a*d + 2*b*d + d^2]), I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)] - EllipticPi[(-2*a)/(-2*a + b + d + Sqrt[b^2 - 4*a*d + 2*b*d + d^2]), I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)]))/Sqrt[1 - a/x]))/((a - x)^2*Sqrt[x*(-a + x)*(-b + x)])","C",1
1010,1,152,77,1.7980866,"\int \frac{1+k^2 x^2}{\sqrt{(1-x) x \left(1-k^2 x\right)} \left(-1+k^2 x^2\right)} \, dx","Integrate[(1 + k^2*x^2)/(Sqrt[(1 - x)*x*(1 - k^2*x)]*(-1 + k^2*x^2)),x]","\frac{2 i \sqrt{\frac{1}{x-1}+1} (x-1)^{3/2} \sqrt{\frac{1-\frac{1}{k^2}}{x-1}+1} \left(\left(k^2+1\right) F\left(i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)+(k-1) \Pi \left(1+\frac{1}{k};i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)-(k+1) \Pi \left(\frac{k-1}{k};i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)\right)}{\left(k^2-1\right) \sqrt{(x-1) x \left(k^2 x-1\right)}}","\frac{\tan ^{-1}\left(\frac{(k-1) x}{\sqrt{k^2 x^3+\left(-k^2-1\right) x^2+x}}\right)}{1-k}+\frac{\tan ^{-1}\left(\frac{(k+1) x}{\sqrt{k^2 x^3+\left(-k^2-1\right) x^2+x}}\right)}{-k-1}",1,"((2*I)*Sqrt[1 + (-1 + x)^(-1)]*Sqrt[1 + (1 - k^(-2))/(-1 + x)]*(-1 + x)^(3/2)*((1 + k^2)*EllipticF[I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)] + (-1 + k)*EllipticPi[1 + k^(-1), I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)] - (1 + k)*EllipticPi[(-1 + k)/k, I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)]))/((-1 + k^2)*Sqrt[(-1 + x)*x*(-1 + k^2*x)])","C",1
1011,1,78,77,0.0395354,"\int \frac{1}{\sqrt[3]{1+x^3}} \, dx","Integrate[(1 + x^3)^(-1/3),x]","-\frac{1}{3} \log \left(1-\frac{x}{\sqrt[3]{x^3+1}}\right)+\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{1}{6} \log \left(\frac{x}{\sqrt[3]{x^3+1}}+\frac{x^2}{\left(x^3+1\right)^{2/3}}+1\right)","-\frac{1}{3} \log \left(\sqrt[3]{x^3+1}-x\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+1}+x}\right)}{\sqrt{3}}+\frac{1}{6} \log \left(\sqrt[3]{x^3+1} x+\left(x^3+1\right)^{2/3}+x^2\right)",1,"ArcTan[(1 + (2*x)/(1 + x^3)^(1/3))/Sqrt[3]]/Sqrt[3] - Log[1 - x/(1 + x^3)^(1/3)]/3 + Log[1 + x^2/(1 + x^3)^(2/3) + x/(1 + x^3)^(1/3)]/6","A",1
1012,1,88,77,0.8139911,"\int \frac{x+x^2}{\left(-1-2 x+x^2\right) \sqrt{-x+x^3}} \, dx","Integrate[(x + x^2)/((-1 - 2*x + x^2)*Sqrt[-x + x^3]),x]","\frac{\sqrt{x \left(x^2-1\right)} \left(-2 F\left(\left.\sin ^{-1}\left(\sqrt{x}\right)\right|-1\right)-\left(\sqrt{2}-1\right) \Pi \left(-1-\sqrt{2};\left.\sin ^{-1}\left(\sqrt{x}\right)\right|-1\right)+\left(1+\sqrt{2}\right) \Pi \left(-1+\sqrt{2};\left.\sin ^{-1}\left(\sqrt{x}\right)\right|-1\right)\right)}{\sqrt{x} \sqrt{1-x^2}}","\frac{1}{4} \left(-2-\sqrt{2}\right) \tanh ^{-1}\left(\frac{x-1}{\left(\sqrt{2}-1\right) \sqrt{x^3-x}}\right)+\frac{1}{4} \left(2-\sqrt{2}\right) \tanh ^{-1}\left(\frac{x-1}{\left(1+\sqrt{2}\right) \sqrt{x^3-x}}\right)",1,"(Sqrt[x*(-1 + x^2)]*(-2*EllipticF[ArcSin[Sqrt[x]], -1] - (-1 + Sqrt[2])*EllipticPi[-1 - Sqrt[2], ArcSin[Sqrt[x]], -1] + (1 + Sqrt[2])*EllipticPi[-1 + Sqrt[2], ArcSin[Sqrt[x]], -1]))/(Sqrt[x]*Sqrt[1 - x^2])","C",1
1013,0,0,77,1.3791336,"\int \frac{x^2 \left(3 a b-2 (a+b) x+x^2\right)}{(x (-a+x) (-b+x))^{3/4} \left(-a b+(a+b) x-x^2+d x^3\right)} \, dx","Integrate[(x^2*(3*a*b - 2*(a + b)*x + x^2))/((x*(-a + x)*(-b + x))^(3/4)*(-(a*b) + (a + b)*x - x^2 + d*x^3)),x]","\int \frac{x^2 \left(3 a b-2 (a+b) x+x^2\right)}{(x (-a+x) (-b+x))^{3/4} \left(-a b+(a+b) x-x^2+d x^3\right)} \, dx","\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{x^2 (-a-b)+a b x+x^3}}\right)}{d^{3/4}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{x^2 (-a-b)+a b x+x^3}}\right)}{d^{3/4}}",1,"Integrate[(x^2*(3*a*b - 2*(a + b)*x + x^2))/((x*(-a + x)*(-b + x))^(3/4)*(-(a*b) + (a + b)*x - x^2 + d*x^3)), x]","F",-1
1014,1,28,77,0.0058458,"\int \frac{1}{x \sqrt[4]{-1+x^4}} \, dx","Integrate[1/(x*(-1 + x^4)^(1/4)),x]","\frac{1}{3} \left(x^4-1\right)^{3/4} \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};1-x^4\right)","-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{x^4-1}}{\sqrt{x^4-1}-1}\right)}{2 \sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{x^4-1}}{\sqrt{x^4-1}+1}\right)}{2 \sqrt{2}}",1,"((-1 + x^4)^(3/4)*Hypergeometric2F1[3/4, 1, 7/4, 1 - x^4])/3","C",1
1015,1,22729,77,13.751735,"\int \frac{(-a+x) (-b+x) \left(-a b+x^2\right)}{\sqrt{x (-a+x) (-b+x)} \left(a^2 b^2-2 a b (a+b) x+\left(a^2+4 a b+b^2-d\right) x^2-2 (a+b) x^3+x^4\right)} \, dx","Integrate[((-a + x)*(-b + x)*(-(a*b) + x^2))/(Sqrt[x*(-a + x)*(-b + x)]*(a^2*b^2 - 2*a*b*(a + b)*x + (a^2 + 4*a*b + b^2 - d)*x^2 - 2*(a + b)*x^3 + x^4)),x]","\text{Result too large to show}","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt{x^2 (-a-b)+a b x+x^3}}\right)}{\sqrt[4]{d}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt{x^2 (-a-b)+a b x+x^3}}\right)}{\sqrt[4]{d}}",1,"Result too large to show","C",0
1016,1,77,77,0.0457458,"\int \frac{x^2 \left(-b+a x^4\right)}{\left(b+a x^4\right)^{3/4}} \, dx","Integrate[(x^2*(-b + a*x^4))/(b + a*x^4)^(3/4),x]","\frac{7 b \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{8 a^{3/4}}-\frac{7 b \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{8 a^{3/4}}+\frac{1}{4} x^3 \sqrt[4]{a x^4+b}","\frac{7 b \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{8 a^{3/4}}-\frac{7 b \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{8 a^{3/4}}+\frac{1}{4} x^3 \sqrt[4]{a x^4+b}",1,"(x^3*(b + a*x^4)^(1/4))/4 + (7*b*ArcTan[(a^(1/4)*x)/(b + a*x^4)^(1/4)])/(8*a^(3/4)) - (7*b*ArcTanh[(a^(1/4)*x)/(b + a*x^4)^(1/4)])/(8*a^(3/4))","A",1
1017,1,51,77,0.0127536,"\int \frac{1}{\sqrt[4]{b x+a x^4}} \, dx","Integrate[(b*x + a*x^4)^(-1/4),x]","\frac{4 x \sqrt[4]{\frac{a x^3}{b}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{4};\frac{5}{4};-\frac{a x^3}{b}\right)}{3 \sqrt[4]{x \left(a x^3+b\right)}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \left(a x^4+b x\right)^{3/4}}{a x^3+b}\right)}{3 \sqrt[4]{a}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{a} \left(a x^4+b x\right)^{3/4}}{a x^3+b}\right)}{3 \sqrt[4]{a}}",1,"(4*x*(1 + (a*x^3)/b)^(1/4)*Hypergeometric2F1[1/4, 1/4, 5/4, -((a*x^3)/b)])/(3*(x*(b + a*x^3))^(1/4))","C",1
1018,1,24546,77,13.8465447,"\int \frac{(-a+x) (-b+x) \left(-a b+x^2\right)}{\sqrt{x (-a+x) (-b+x)} \left(a^2 b^2 d-2 a b (a+b) d x+\left(-1+a^2 d+4 a b d+b^2 d\right) x^2-2 (a+b) d x^3+d x^4\right)} \, dx","Integrate[((-a + x)*(-b + x)*(-(a*b) + x^2))/(Sqrt[x*(-a + x)*(-b + x)]*(a^2*b^2*d - 2*a*b*(a + b)*d*x + (-1 + a^2*d + 4*a*b*d + b^2*d)*x^2 - 2*(a + b)*d*x^3 + d*x^4)),x]","\text{Result too large to show}","-\frac{\tan ^{-1}\left(\frac{x}{\sqrt[4]{d} \sqrt{x^2 (-a-b)+a b x+x^3}}\right)}{d^{3/4}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt[4]{d} \sqrt{x^2 (-a-b)+a b x+x^3}}\right)}{d^{3/4}}",1,"Result too large to show","C",0
1019,1,28,77,0.0054033,"\int \frac{1}{x \sqrt[4]{-1+x^6}} \, dx","Integrate[1/(x*(-1 + x^6)^(1/4)),x]","\frac{2}{9} \left(x^6-1\right)^{3/4} \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};1-x^6\right)","-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{x^6-1}}{\sqrt{x^6-1}-1}\right)}{3 \sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{x^6-1}}{\sqrt{x^6-1}+1}\right)}{3 \sqrt{2}}",1,"(2*(-1 + x^6)^(3/4)*Hypergeometric2F1[3/4, 1, 7/4, 1 - x^6])/9","C",1
1020,1,571,77,3.9602347,"\int \frac{1}{\sqrt[3]{-b x+a x^3} \left(d+c x^6\right)} \, dx","Integrate[1/((-(b*x) + a*x^3)^(1/3)*(d + c*x^6)),x]","-\frac{x \sqrt[3]{\frac{b}{x^2}-a} \left(a^2 \text{RootSum}\left[\text{$\#$1}^3 d+3 \text{$\#$1}^2 a d+3 \text{$\#$1} a^2 d+a^3 d+b^3 c\&,\frac{-\frac{\log \left(\text{$\#$1}^{2/3}+\sqrt[3]{\text{$\#$1}} \sqrt[3]{\frac{b}{x^2}-a}+\left(\frac{b}{x^2}-a\right)^{2/3}\right)}{\sqrt[3]{\text{$\#$1}}}+\frac{2 \log \left(\sqrt[3]{\text{$\#$1}}-\sqrt[3]{\frac{b}{x^2}-a}\right)}{\sqrt[3]{\text{$\#$1}}}+\frac{2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{\frac{b}{x^2}-a}}{\sqrt[3]{\text{$\#$1}}}+1}{\sqrt{3}}\right)}{\sqrt[3]{\text{$\#$1}}}}{\text{$\#$1}^2+2 \text{$\#$1} a+a^2}\&\right]+2 a \text{RootSum}\left[\text{$\#$1}^3 d+3 \text{$\#$1}^2 a d+3 \text{$\#$1} a^2 d+a^3 d+b^3 c\&,\frac{2 \text{$\#$1}^{2/3} \log \left(\sqrt[3]{\text{$\#$1}}-\sqrt[3]{\frac{b}{x^2}-a}\right)-\text{$\#$1}^{2/3} \log \left(\text{$\#$1}^{2/3}+\sqrt[3]{\text{$\#$1}} \sqrt[3]{\frac{b}{x^2}-a}+\left(\frac{b}{x^2}-a\right)^{2/3}\right)+2 \sqrt{3} \text{$\#$1}^{2/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{\frac{b}{x^2}-a}}{\sqrt[3]{\text{$\#$1}}}+1}{\sqrt{3}}\right)}{\text{$\#$1}^2+2 \text{$\#$1} a+a^2}\&\right]+\text{RootSum}\left[\text{$\#$1}^3 d+3 \text{$\#$1}^2 a d+3 \text{$\#$1} a^2 d+a^3 d+b^3 c\&,\frac{2 \text{$\#$1}^{5/3} \log \left(\sqrt[3]{\text{$\#$1}}-\sqrt[3]{\frac{b}{x^2}-a}\right)-\text{$\#$1}^{5/3} \log \left(\text{$\#$1}^{2/3}+\sqrt[3]{\text{$\#$1}} \sqrt[3]{\frac{b}{x^2}-a}+\left(\frac{b}{x^2}-a\right)^{2/3}\right)+2 \sqrt{3} \text{$\#$1}^{5/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{\frac{b}{x^2}-a}}{\sqrt[3]{\text{$\#$1}}}+1}{\sqrt{3}}\right)}{\text{$\#$1}^2+2 \text{$\#$1} a+a^2}\&\right]\right)}{12 d \sqrt[3]{a x^3-b x}}","-\frac{\text{RootSum}\left[\text{$\#$1}^9 (-d)+3 \text{$\#$1}^6 a d-3 \text{$\#$1}^3 a^2 d+a^3 d+b^3 c\&,\frac{\log \left(\sqrt[3]{a x^3-b x}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{6 d}",1,"-1/12*((-a + b/x^2)^(1/3)*x*(a^2*RootSum[b^3*c + a^3*d + 3*a^2*d*#1 + 3*a*d*#1^2 + d*#1^3 & , ((2*Sqrt[3]*ArcTan[(1 + (2*(-a + b/x^2)^(1/3))/#1^(1/3))/Sqrt[3]])/#1^(1/3) + (2*Log[-(-a + b/x^2)^(1/3) + #1^(1/3)])/#1^(1/3) - Log[(-a + b/x^2)^(2/3) + (-a + b/x^2)^(1/3)*#1^(1/3) + #1^(2/3)]/#1^(1/3))/(a^2 + 2*a*#1 + #1^2) & ] + 2*a*RootSum[b^3*c + a^3*d + 3*a^2*d*#1 + 3*a*d*#1^2 + d*#1^3 & , (2*Sqrt[3]*ArcTan[(1 + (2*(-a + b/x^2)^(1/3))/#1^(1/3))/Sqrt[3]]*#1^(2/3) + 2*Log[-(-a + b/x^2)^(1/3) + #1^(1/3)]*#1^(2/3) - Log[(-a + b/x^2)^(2/3) + (-a + b/x^2)^(1/3)*#1^(1/3) + #1^(2/3)]*#1^(2/3))/(a^2 + 2*a*#1 + #1^2) & ] + RootSum[b^3*c + a^3*d + 3*a^2*d*#1 + 3*a*d*#1^2 + d*#1^3 & , (2*Sqrt[3]*ArcTan[(1 + (2*(-a + b/x^2)^(1/3))/#1^(1/3))/Sqrt[3]]*#1^(5/3) + 2*Log[-(-a + b/x^2)^(1/3) + #1^(1/3)]*#1^(5/3) - Log[(-a + b/x^2)^(2/3) + (-a + b/x^2)^(1/3)*#1^(1/3) + #1^(2/3)]*#1^(5/3))/(a^2 + 2*a*#1 + #1^2) & ]))/(d*(-(b*x) + a*x^3)^(1/3))","B",1
1021,1,571,77,0.4922973,"\int \frac{1}{\sqrt[3]{-b x+a x^3} \left(d+c x^6\right)} \, dx","Integrate[1/((-(b*x) + a*x^3)^(1/3)*(d + c*x^6)),x]","-\frac{x \sqrt[3]{\frac{b}{x^2}-a} \left(a^2 \text{RootSum}\left[\text{$\#$1}^3 d+3 \text{$\#$1}^2 a d+3 \text{$\#$1} a^2 d+a^3 d+b^3 c\&,\frac{-\frac{\log \left(\text{$\#$1}^{2/3}+\sqrt[3]{\text{$\#$1}} \sqrt[3]{\frac{b}{x^2}-a}+\left(\frac{b}{x^2}-a\right)^{2/3}\right)}{\sqrt[3]{\text{$\#$1}}}+\frac{2 \log \left(\sqrt[3]{\text{$\#$1}}-\sqrt[3]{\frac{b}{x^2}-a}\right)}{\sqrt[3]{\text{$\#$1}}}+\frac{2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{\frac{b}{x^2}-a}}{\sqrt[3]{\text{$\#$1}}}+1}{\sqrt{3}}\right)}{\sqrt[3]{\text{$\#$1}}}}{\text{$\#$1}^2+2 \text{$\#$1} a+a^2}\&\right]+2 a \text{RootSum}\left[\text{$\#$1}^3 d+3 \text{$\#$1}^2 a d+3 \text{$\#$1} a^2 d+a^3 d+b^3 c\&,\frac{2 \text{$\#$1}^{2/3} \log \left(\sqrt[3]{\text{$\#$1}}-\sqrt[3]{\frac{b}{x^2}-a}\right)-\text{$\#$1}^{2/3} \log \left(\text{$\#$1}^{2/3}+\sqrt[3]{\text{$\#$1}} \sqrt[3]{\frac{b}{x^2}-a}+\left(\frac{b}{x^2}-a\right)^{2/3}\right)+2 \sqrt{3} \text{$\#$1}^{2/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{\frac{b}{x^2}-a}}{\sqrt[3]{\text{$\#$1}}}+1}{\sqrt{3}}\right)}{\text{$\#$1}^2+2 \text{$\#$1} a+a^2}\&\right]+\text{RootSum}\left[\text{$\#$1}^3 d+3 \text{$\#$1}^2 a d+3 \text{$\#$1} a^2 d+a^3 d+b^3 c\&,\frac{2 \text{$\#$1}^{5/3} \log \left(\sqrt[3]{\text{$\#$1}}-\sqrt[3]{\frac{b}{x^2}-a}\right)-\text{$\#$1}^{5/3} \log \left(\text{$\#$1}^{2/3}+\sqrt[3]{\text{$\#$1}} \sqrt[3]{\frac{b}{x^2}-a}+\left(\frac{b}{x^2}-a\right)^{2/3}\right)+2 \sqrt{3} \text{$\#$1}^{5/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{\frac{b}{x^2}-a}}{\sqrt[3]{\text{$\#$1}}}+1}{\sqrt{3}}\right)}{\text{$\#$1}^2+2 \text{$\#$1} a+a^2}\&\right]\right)}{12 d \sqrt[3]{a x^3-b x}}","-\frac{\text{RootSum}\left[\text{$\#$1}^9 (-d)+3 \text{$\#$1}^6 a d-3 \text{$\#$1}^3 a^2 d+a^3 d+b^3 c\&,\frac{\log \left(\sqrt[3]{a x^3-b x}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{6 d}",1,"-1/12*((-a + b/x^2)^(1/3)*x*(a^2*RootSum[b^3*c + a^3*d + 3*a^2*d*#1 + 3*a*d*#1^2 + d*#1^3 & , ((2*Sqrt[3]*ArcTan[(1 + (2*(-a + b/x^2)^(1/3))/#1^(1/3))/Sqrt[3]])/#1^(1/3) + (2*Log[-(-a + b/x^2)^(1/3) + #1^(1/3)])/#1^(1/3) - Log[(-a + b/x^2)^(2/3) + (-a + b/x^2)^(1/3)*#1^(1/3) + #1^(2/3)]/#1^(1/3))/(a^2 + 2*a*#1 + #1^2) & ] + 2*a*RootSum[b^3*c + a^3*d + 3*a^2*d*#1 + 3*a*d*#1^2 + d*#1^3 & , (2*Sqrt[3]*ArcTan[(1 + (2*(-a + b/x^2)^(1/3))/#1^(1/3))/Sqrt[3]]*#1^(2/3) + 2*Log[-(-a + b/x^2)^(1/3) + #1^(1/3)]*#1^(2/3) - Log[(-a + b/x^2)^(2/3) + (-a + b/x^2)^(1/3)*#1^(1/3) + #1^(2/3)]*#1^(2/3))/(a^2 + 2*a*#1 + #1^2) & ] + RootSum[b^3*c + a^3*d + 3*a^2*d*#1 + 3*a*d*#1^2 + d*#1^3 & , (2*Sqrt[3]*ArcTan[(1 + (2*(-a + b/x^2)^(1/3))/#1^(1/3))/Sqrt[3]]*#1^(5/3) + 2*Log[-(-a + b/x^2)^(1/3) + #1^(1/3)]*#1^(5/3) - Log[(-a + b/x^2)^(2/3) + (-a + b/x^2)^(1/3)*#1^(1/3) + #1^(2/3)]*#1^(5/3))/(a^2 + 2*a*#1 + #1^2) & ]))/(d*(-(b*x) + a*x^3)^(1/3))","B",1
1022,1,89,77,0.0568946,"\int \left(-1+x^2\right) \left(-1+x \sqrt{-1+3 x^2-x^4}\right) \, dx","Integrate[(-1 + x^2)*(-1 + x*Sqrt[-1 + 3*x^2 - x^4]),x]","\frac{1}{96} \left(-32 x^3-15 \sin ^{-1}\left(\frac{3-2 x^2}{\sqrt{5}}\right)+16 \sqrt{-x^4+3 x^2-1} x^4-36 \sqrt{-x^4+3 x^2-1} x^2-2 \sqrt{-x^4+3 x^2-1}+96 x\right)","-\frac{x^3}{3}+\frac{1}{48} \sqrt{-x^4+3 x^2-1} \left(8 x^4-18 x^2-1\right)+\frac{5}{32} i \log \left(-2 i x^2+2 \sqrt{-x^4+3 x^2-1}+3 i\right)+x",1,"(96*x - 32*x^3 - 2*Sqrt[-1 + 3*x^2 - x^4] - 36*x^2*Sqrt[-1 + 3*x^2 - x^4] + 16*x^4*Sqrt[-1 + 3*x^2 - x^4] - 15*ArcSin[(3 - 2*x^2)/Sqrt[5]])/96","A",1
1023,0,0,77,3.4382206,"\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1+x^2\right) \sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 + x^2)*Sqrt[x + Sqrt[1 + x^2]]),x]","\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1+x^2\right) \sqrt{x+\sqrt{1+x^2}}} \, dx","\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+3 \text{$\#$1}^2-1}\&\right]",1,"Integrate[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 + x^2)*Sqrt[x + Sqrt[1 + x^2]]), x]","F",-1
1024,0,0,77,0.1635869,"\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1+x^2\right) \sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 + x^2)*Sqrt[x + Sqrt[1 + x^2]]),x]","\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1+x^2\right) \sqrt{x+\sqrt{1+x^2}}} \, dx","\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+3 \text{$\#$1}^2-1}\&\right]",1,"Integrate[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 + x^2)*Sqrt[x + Sqrt[1 + x^2]]), x]","F",-1
1025,1,74,77,0.1300206,"\int \frac{\sqrt{c+\sqrt{a x+\sqrt{b+a^2 x^2}}}}{\sqrt{b+a^2 x^2}} \, dx","Integrate[Sqrt[c + Sqrt[a*x + Sqrt[b + a^2*x^2]]]/Sqrt[b + a^2*x^2],x]","\frac{4 \left(\sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}-\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}}{\sqrt{c}}\right)\right)}{a}","\frac{4 \sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}}{a}-\frac{4 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}}{\sqrt{c}}\right)}{a}",1,"(4*(Sqrt[c + Sqrt[a*x + Sqrt[b + a^2*x^2]]] - Sqrt[c]*ArcTanh[Sqrt[c + Sqrt[a*x + Sqrt[b + a^2*x^2]]]/Sqrt[c]]))/a","A",1
1026,1,59,78,0.0587061,"\int \frac{\sqrt{-1+x^2}}{(-i+x)^2} \, dx","Integrate[Sqrt[-1 + x^2]/(-I + x)^2,x]","-\frac{\sqrt{x^2-1}}{x-i}+\tanh ^{-1}\left(\frac{x}{\sqrt{x^2-1}}\right)-\frac{\tanh ^{-1}\left(\frac{x+i}{\sqrt{2} \sqrt{x^2-1}}\right)}{\sqrt{2}}","\frac{\sqrt{x^2-1}}{-x+i}-\log \left(\sqrt{x^2-1}-x\right)-\sqrt{2} \tanh ^{-1}\left(-\frac{i \sqrt{x^2-1}}{\sqrt{2}}+\frac{i x}{\sqrt{2}}+\frac{1}{\sqrt{2}}\right)",1,"-(Sqrt[-1 + x^2]/(-I + x)) + ArcTanh[x/Sqrt[-1 + x^2]] - ArcTanh[(I + x)/(Sqrt[2]*Sqrt[-1 + x^2])]/Sqrt[2]","A",1
1027,1,35,78,0.0087784,"\int \frac{1}{x^3 \left(b+a x^2\right)^{3/4}} \, dx","Integrate[1/(x^3*(b + a*x^2)^(3/4)),x]","\frac{2 a \sqrt[4]{a x^2+b} \, _2F_1\left(\frac{1}{4},2;\frac{5}{4};\frac{a x^2}{b}+1\right)}{b^2}","\frac{3 a \tan ^{-1}\left(\frac{\sqrt[4]{a x^2+b}}{\sqrt[4]{b}}\right)}{4 b^{7/4}}+\frac{3 a \tanh ^{-1}\left(\frac{\sqrt[4]{a x^2+b}}{\sqrt[4]{b}}\right)}{4 b^{7/4}}-\frac{\sqrt[4]{a x^2+b}}{2 b x^2}",1,"(2*a*(b + a*x^2)^(1/4)*Hypergeometric2F1[1/4, 2, 5/4, 1 + (a*x^2)/b])/b^2","C",1
1028,1,156,78,0.0999029,"\int \frac{\left(-1-2 x+x^2+3 x^3\right)^4}{\sqrt[4]{-1+3 x-3 x^2+x^3}} \, dx","Integrate[(-1 - 2*x + x^2 + 3*x^3)^4/(-1 + 3*x - 3*x^2 + x^3)^(1/4),x]","\frac{4 \left(\frac{81}{49} (x-1)^{49/4}+24 (x-1)^{45/4}+\frac{6372}{41} (x-1)^{41/4}+\frac{21828}{37} (x-1)^{37/4}+\frac{47854}{33} (x-1)^{33/4}+\frac{69732}{29} (x-1)^{29/4}+\frac{67882}{25} (x-1)^{25/4}+\frac{14412}{7} (x-1)^{21/4}+\frac{17205}{17} (x-1)^{17/4}+\frac{4008}{13} (x-1)^{13/4}+\frac{526}{9} (x-1)^{9/4}+\frac{36}{5} (x-1)^{5/4}+\sqrt[4]{x-1}\right) (x-1)^{3/4}}{\sqrt[4]{(x-1)^3}}","\frac{4 \left((x-1)^3\right)^{3/4} \left(1949108765175 x^{12}+4908866519700 x^{11}+609206533650 x^{10}-9283999210200 x^9-8805988591725 x^8+3131067556500 x^7+9260757242646 x^6+4070651298324 x^5-2008108342110 x^4-2834315032620 x^3-1158885626660 x^2+32327777464 x+1308401597431\right)}{1179090487575 (x-1)^2}",1,"(4*((-1 + x)^(1/4) + (36*(-1 + x)^(5/4))/5 + (526*(-1 + x)^(9/4))/9 + (4008*(-1 + x)^(13/4))/13 + (17205*(-1 + x)^(17/4))/17 + (14412*(-1 + x)^(21/4))/7 + (67882*(-1 + x)^(25/4))/25 + (69732*(-1 + x)^(29/4))/29 + (47854*(-1 + x)^(33/4))/33 + (21828*(-1 + x)^(37/4))/37 + (6372*(-1 + x)^(41/4))/41 + 24*(-1 + x)^(45/4) + (81*(-1 + x)^(49/4))/49)*(-1 + x)^(3/4))/((-1 + x)^3)^(1/4)","A",1
1029,1,37,78,0.0091907,"\int \frac{1}{x^4 \left(b+a x^3\right)^{3/4}} \, dx","Integrate[1/(x^4*(b + a*x^3)^(3/4)),x]","\frac{4 a \sqrt[4]{a x^3+b} \, _2F_1\left(\frac{1}{4},2;\frac{5}{4};\frac{a x^3}{b}+1\right)}{3 b^2}","\frac{a \tan ^{-1}\left(\frac{\sqrt[4]{a x^3+b}}{\sqrt[4]{b}}\right)}{2 b^{7/4}}+\frac{a \tanh ^{-1}\left(\frac{\sqrt[4]{a x^3+b}}{\sqrt[4]{b}}\right)}{2 b^{7/4}}-\frac{\sqrt[4]{a x^3+b}}{3 b x^3}",1,"(4*a*(b + a*x^3)^(1/4)*Hypergeometric2F1[1/4, 2, 5/4, 1 + (a*x^3)/b])/(3*b^2)","C",1
1030,1,1226,78,2.6824004,"\int \frac{x}{\sqrt{-71-96 x+10 x^2+x^4}} \, dx","Integrate[x/Sqrt[-71 - 96*x + 10*x^2 + x^4],x]","-\frac{2 \left(-x+2 \sqrt{2 \left(-1+\sqrt{3}\right)}+\sqrt{3}\right) \left(\left(\sqrt{3}+2 \sqrt{2 \left(-1+\sqrt{3}\right)}\right) F\left(\sin ^{-1}\left(\sqrt{\frac{\left(-x-2 \sqrt{2 \left(-1+\sqrt{3}\right)}+\sqrt{3}\right) \left(\sqrt{3}+2 \sqrt{2 \left(-1+\sqrt{3}\right)}-\text{Root}\left[\text{$\#$1}^4+10 \text{$\#$1}^2-96 \text{$\#$1}-71\&,4\right]\right)}{\left(-x+2 \sqrt{2 \left(-1+\sqrt{3}\right)}+\sqrt{3}\right) \left(\sqrt{3}-2 \sqrt{2 \left(-1+\sqrt{3}\right)}-\text{Root}\left[\text{$\#$1}^4+10 \text{$\#$1}^2-96 \text{$\#$1}-71\&,4\right]\right)}}\right)|\frac{\left(\sqrt{3}+2 \sqrt{2 \left(-1+\sqrt{3}\right)}-\text{Root}\left[\text{$\#$1}^4+10 \text{$\#$1}^2-96 \text{$\#$1}-71\&,3\right]\right) \left(\sqrt{3}-2 \sqrt{2 \left(-1+\sqrt{3}\right)}-\text{Root}\left[\text{$\#$1}^4+10 \text{$\#$1}^2-96 \text{$\#$1}-71\&,4\right]\right)}{\left(\sqrt{3}-2 \sqrt{2 \left(-1+\sqrt{3}\right)}-\text{Root}\left[\text{$\#$1}^4+10 \text{$\#$1}^2-96 \text{$\#$1}-71\&,3\right]\right) \left(\sqrt{3}+2 \sqrt{2 \left(-1+\sqrt{3}\right)}-\text{Root}\left[\text{$\#$1}^4+10 \text{$\#$1}^2-96 \text{$\#$1}-71\&,4\right]\right)}\right)-4 \sqrt{2 \left(-1+\sqrt{3}\right)} \Pi \left(\frac{\sqrt{3}-2 \sqrt{2 \left(-1+\sqrt{3}\right)}-\text{Root}\left[\text{$\#$1}^4+10 \text{$\#$1}^2-96 \text{$\#$1}-71\&,4\right]}{\sqrt{3}+2 \sqrt{2 \left(-1+\sqrt{3}\right)}-\text{Root}\left[\text{$\#$1}^4+10 \text{$\#$1}^2-96 \text{$\#$1}-71\&,4\right]};\sin ^{-1}\left(\sqrt{\frac{\left(-x-2 \sqrt{2 \left(-1+\sqrt{3}\right)}+\sqrt{3}\right) \left(\sqrt{3}+2 \sqrt{2 \left(-1+\sqrt{3}\right)}-\text{Root}\left[\text{$\#$1}^4+10 \text{$\#$1}^2-96 \text{$\#$1}-71\&,4\right]\right)}{\left(-x+2 \sqrt{2 \left(-1+\sqrt{3}\right)}+\sqrt{3}\right) \left(\sqrt{3}-2 \sqrt{2 \left(-1+\sqrt{3}\right)}-\text{Root}\left[\text{$\#$1}^4+10 \text{$\#$1}^2-96 \text{$\#$1}-71\&,4\right]\right)}}\right)|\frac{\left(\sqrt{3}+2 \sqrt{2 \left(-1+\sqrt{3}\right)}-\text{Root}\left[\text{$\#$1}^4+10 \text{$\#$1}^2-96 \text{$\#$1}-71\&,3\right]\right) \left(\sqrt{3}-2 \sqrt{2 \left(-1+\sqrt{3}\right)}-\text{Root}\left[\text{$\#$1}^4+10 \text{$\#$1}^2-96 \text{$\#$1}-71\&,4\right]\right)}{\left(\sqrt{3}-2 \sqrt{2 \left(-1+\sqrt{3}\right)}-\text{Root}\left[\text{$\#$1}^4+10 \text{$\#$1}^2-96 \text{$\#$1}-71\&,3\right]\right) \left(\sqrt{3}+2 \sqrt{2 \left(-1+\sqrt{3}\right)}-\text{Root}\left[\text{$\#$1}^4+10 \text{$\#$1}^2-96 \text{$\#$1}-71\&,4\right]\right)}\right)\right) \sqrt{\frac{x-\text{Root}\left[\text{$\#$1}^4+10 \text{$\#$1}^2-96 \text{$\#$1}-71\&,3\right]}{\left(-x+2 \sqrt{2 \left(-1+\sqrt{3}\right)}+\sqrt{3}\right) \left(\sqrt{3}-2 \sqrt{2 \left(-1+\sqrt{3}\right)}-\text{Root}\left[\text{$\#$1}^4+10 \text{$\#$1}^2-96 \text{$\#$1}-71\&,3\right]\right)}} \sqrt{\frac{\left(-x-2 \sqrt{2 \left(-1+\sqrt{3}\right)}+\sqrt{3}\right) \left(\sqrt{3}+2 \sqrt{2 \left(-1+\sqrt{3}\right)}-\text{Root}\left[\text{$\#$1}^4+10 \text{$\#$1}^2-96 \text{$\#$1}-71\&,4\right]\right)}{\left(-x+2 \sqrt{2 \left(-1+\sqrt{3}\right)}+\sqrt{3}\right) \left(\sqrt{3}-2 \sqrt{2 \left(-1+\sqrt{3}\right)}-\text{Root}\left[\text{$\#$1}^4+10 \text{$\#$1}^2-96 \text{$\#$1}-71\&,4\right]\right)}} \left(x-\text{Root}\left[\text{$\#$1}^4+10 \text{$\#$1}^2-96 \text{$\#$1}-71\&,4\right]\right)}{\sqrt{x^4+10 x^2-96 x-71} \left(\sqrt{3}+2 \sqrt{2 \left(-1+\sqrt{3}\right)}-\text{Root}\left[\text{$\#$1}^4+10 \text{$\#$1}^2-96 \text{$\#$1}-71\&,4\right]\right) \sqrt{\frac{x-\text{Root}\left[\text{$\#$1}^4+10 \text{$\#$1}^2-96 \text{$\#$1}-71\&,4\right]}{\left(-x+2 \sqrt{2 \left(-1+\sqrt{3}\right)}+\sqrt{3}\right) \left(\sqrt{3}-2 \sqrt{2 \left(-1+\sqrt{3}\right)}-\text{Root}\left[\text{$\#$1}^4+10 \text{$\#$1}^2-96 \text{$\#$1}-71\&,4\right]\right)}}}","-\frac{1}{8} \log \left(-x^8-20 x^6+128 x^5-54 x^4+1408 x^3-3124 x^2+\sqrt{x^4+10 x^2-96 x-71} \left(x^6+15 x^4-80 x^3+27 x^2-528 x+781\right)-10001\right)",1,"(-2*(Sqrt[3] + 2*Sqrt[2*(-1 + Sqrt[3])] - x)*((Sqrt[3] + 2*Sqrt[2*(-1 + Sqrt[3])])*EllipticF[ArcSin[Sqrt[((Sqrt[3] - 2*Sqrt[2*(-1 + Sqrt[3])] - x)*(Sqrt[3] + 2*Sqrt[2*(-1 + Sqrt[3])] - Root[-71 - 96*#1 + 10*#1^2 + #1^4 & , 4, 0]))/((Sqrt[3] + 2*Sqrt[2*(-1 + Sqrt[3])] - x)*(Sqrt[3] - 2*Sqrt[2*(-1 + Sqrt[3])] - Root[-71 - 96*#1 + 10*#1^2 + #1^4 & , 4, 0]))]], ((Sqrt[3] + 2*Sqrt[2*(-1 + Sqrt[3])] - Root[-71 - 96*#1 + 10*#1^2 + #1^4 & , 3, 0])*(Sqrt[3] - 2*Sqrt[2*(-1 + Sqrt[3])] - Root[-71 - 96*#1 + 10*#1^2 + #1^4 & , 4, 0]))/((Sqrt[3] - 2*Sqrt[2*(-1 + Sqrt[3])] - Root[-71 - 96*#1 + 10*#1^2 + #1^4 & , 3, 0])*(Sqrt[3] + 2*Sqrt[2*(-1 + Sqrt[3])] - Root[-71 - 96*#1 + 10*#1^2 + #1^4 & , 4, 0]))] - 4*Sqrt[2*(-1 + Sqrt[3])]*EllipticPi[(Sqrt[3] - 2*Sqrt[2*(-1 + Sqrt[3])] - Root[-71 - 96*#1 + 10*#1^2 + #1^4 & , 4, 0])/(Sqrt[3] + 2*Sqrt[2*(-1 + Sqrt[3])] - Root[-71 - 96*#1 + 10*#1^2 + #1^4 & , 4, 0]), ArcSin[Sqrt[((Sqrt[3] - 2*Sqrt[2*(-1 + Sqrt[3])] - x)*(Sqrt[3] + 2*Sqrt[2*(-1 + Sqrt[3])] - Root[-71 - 96*#1 + 10*#1^2 + #1^4 & , 4, 0]))/((Sqrt[3] + 2*Sqrt[2*(-1 + Sqrt[3])] - x)*(Sqrt[3] - 2*Sqrt[2*(-1 + Sqrt[3])] - Root[-71 - 96*#1 + 10*#1^2 + #1^4 & , 4, 0]))]], ((Sqrt[3] + 2*Sqrt[2*(-1 + Sqrt[3])] - Root[-71 - 96*#1 + 10*#1^2 + #1^4 & , 3, 0])*(Sqrt[3] - 2*Sqrt[2*(-1 + Sqrt[3])] - Root[-71 - 96*#1 + 10*#1^2 + #1^4 & , 4, 0]))/((Sqrt[3] - 2*Sqrt[2*(-1 + Sqrt[3])] - Root[-71 - 96*#1 + 10*#1^2 + #1^4 & , 3, 0])*(Sqrt[3] + 2*Sqrt[2*(-1 + Sqrt[3])] - Root[-71 - 96*#1 + 10*#1^2 + #1^4 & , 4, 0]))])*Sqrt[(x - Root[-71 - 96*#1 + 10*#1^2 + #1^4 & , 3, 0])/((Sqrt[3] + 2*Sqrt[2*(-1 + Sqrt[3])] - x)*(Sqrt[3] - 2*Sqrt[2*(-1 + Sqrt[3])] - Root[-71 - 96*#1 + 10*#1^2 + #1^4 & , 3, 0]))]*Sqrt[((Sqrt[3] - 2*Sqrt[2*(-1 + Sqrt[3])] - x)*(Sqrt[3] + 2*Sqrt[2*(-1 + Sqrt[3])] - Root[-71 - 96*#1 + 10*#1^2 + #1^4 & , 4, 0]))/((Sqrt[3] + 2*Sqrt[2*(-1 + Sqrt[3])] - x)*(Sqrt[3] - 2*Sqrt[2*(-1 + Sqrt[3])] - Root[-71 - 96*#1 + 10*#1^2 + #1^4 & , 4, 0]))]*(x - Root[-71 - 96*#1 + 10*#1^2 + #1^4 & , 4, 0]))/(Sqrt[-71 - 96*x + 10*x^2 + x^4]*(Sqrt[3] + 2*Sqrt[2*(-1 + Sqrt[3])] - Root[-71 - 96*#1 + 10*#1^2 + #1^4 & , 4, 0])*Sqrt[(x - Root[-71 - 96*#1 + 10*#1^2 + #1^4 & , 4, 0])/((Sqrt[3] + 2*Sqrt[2*(-1 + Sqrt[3])] - x)*(Sqrt[3] - 2*Sqrt[2*(-1 + Sqrt[3])] - Root[-71 - 96*#1 + 10*#1^2 + #1^4 & , 4, 0]))])","C",0
1031,0,0,78,0.4150286,"\int \frac{(8+3 x) \sqrt[4]{-2-x+2 x^4}}{x^2 \left(2+x+x^4\right)} \, dx","Integrate[((8 + 3*x)*(-2 - x + 2*x^4)^(1/4))/(x^2*(2 + x + x^4)),x]","\int \frac{(8+3 x) \sqrt[4]{-2-x+2 x^4}}{x^2 \left(2+x+x^4\right)} \, dx","-\frac{4 \sqrt[4]{2 x^4-x-2}}{x}-2 \sqrt[4]{3} \tan ^{-1}\left(\frac{\sqrt[4]{3} x}{\sqrt[4]{2 x^4-x-2}}\right)+2 \sqrt[4]{3} \tanh ^{-1}\left(\frac{\sqrt[4]{3} x}{\sqrt[4]{2 x^4-x-2}}\right)",1,"Integrate[((8 + 3*x)*(-2 - x + 2*x^4)^(1/4))/(x^2*(2 + x + x^4)), x]","F",-1
1032,1,34,78,0.0090779,"\int \frac{1}{x^5 \left(b+a x^4\right)^{3/4}} \, dx","Integrate[1/(x^5*(b + a*x^4)^(3/4)),x]","\frac{a \sqrt[4]{a x^4+b} \, _2F_1\left(\frac{1}{4},2;\frac{5}{4};\frac{a x^4}{b}+1\right)}{b^2}","\frac{3 a \tan ^{-1}\left(\frac{\sqrt[4]{a x^4+b}}{\sqrt[4]{b}}\right)}{8 b^{7/4}}+\frac{3 a \tanh ^{-1}\left(\frac{\sqrt[4]{a x^4+b}}{\sqrt[4]{b}}\right)}{8 b^{7/4}}-\frac{\sqrt[4]{a x^4+b}}{4 b x^4}",1,"(a*(b + a*x^4)^(1/4)*Hypergeometric2F1[1/4, 2, 5/4, 1 + (a*x^4)/b])/b^2","C",1
1033,1,37,78,0.0087992,"\int \frac{1}{x^6 \left(b+a x^5\right)^{3/4}} \, dx","Integrate[1/(x^6*(b + a*x^5)^(3/4)),x]","\frac{4 a \sqrt[4]{a x^5+b} \, _2F_1\left(\frac{1}{4},2;\frac{5}{4};\frac{a x^5}{b}+1\right)}{5 b^2}","\frac{3 a \tan ^{-1}\left(\frac{\sqrt[4]{a x^5+b}}{\sqrt[4]{b}}\right)}{10 b^{7/4}}+\frac{3 a \tanh ^{-1}\left(\frac{\sqrt[4]{a x^5+b}}{\sqrt[4]{b}}\right)}{10 b^{7/4}}-\frac{\sqrt[4]{a x^5+b}}{5 b x^5}",1,"(4*a*(b + a*x^5)^(1/4)*Hypergeometric2F1[1/4, 2, 5/4, 1 + (a*x^5)/b])/(5*b^2)","C",1
1034,1,415,78,1.938942,"\int \frac{\left(-1+x^3\right)^{2/3} \left(1-2 x^3+x^6\right)}{x^6 \left(1-x^3+x^6\right)} \, dx","Integrate[((-1 + x^3)^(2/3)*(1 - 2*x^3 + x^6))/(x^6*(1 - x^3 + x^6)),x]","\left(x^3-1\right)^{2/3} \left(\frac{7}{10 x^2}-\frac{1}{5 x^5}\right)+\frac{i \left(-\frac{2 \log \left(\sqrt[3]{\sqrt{3}+i}-\frac{\sqrt[3]{\sqrt{3}-i} x}{\sqrt[3]{x^3-1}}\right)}{\sqrt[3]{\frac{\sqrt{3}-i}{\sqrt{3}+i}}}+2 \sqrt[3]{\frac{\sqrt{3}-i}{\sqrt{3}+i}} \log \left(\sqrt[3]{\sqrt{3}-i}-\frac{\sqrt[3]{\sqrt{3}+i} x}{\sqrt[3]{x^3-1}}\right)+\frac{2 \sqrt{3} \tan ^{-1}\left(\frac{1+\frac{\sqrt[3]{2} \left(\sqrt{3}-i\right)^{2/3} x}{\sqrt[3]{x^3-1}}}{\sqrt{3}}\right)+\log \left(\frac{2^{2/3} x}{\sqrt[3]{x^3-1}}+\frac{\left(\sqrt{3}-i\right)^{2/3} x^2}{\left(x^3-1\right)^{2/3}}+\left(\sqrt{3}+i\right)^{2/3}\right)}{\left(\frac{1}{2} \left(\sqrt{3}-i\right)\right)^{2/3}}-\frac{2 \sqrt{3} \tan ^{-1}\left(\frac{1+\frac{\sqrt[3]{2} \left(\sqrt{3}+i\right)^{2/3} x}{\sqrt[3]{x^3-1}}}{\sqrt{3}}\right)+\log \left(\frac{2^{2/3} x}{\sqrt[3]{x^3-1}}+\frac{\left(\sqrt{3}+i\right)^{2/3} x^2}{\left(x^3-1\right)^{2/3}}+\left(\sqrt{3}-i\right)^{2/3}\right)}{\left(\frac{1}{2} \left(\sqrt{3}+i\right)\right)^{2/3}}\right)}{6 \sqrt{3}}","\frac{\left(x^3-1\right)^{2/3} \left(7 x^3-2\right)}{10 x^5}-\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^6-\text{$\#$1}^3+1\&,\frac{\log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)-\log (x)}{2 \text{$\#$1}^4-\text{$\#$1}}\&\right]",1,"(-1/5*1/x^5 + 7/(10*x^2))*(-1 + x^3)^(2/3) + ((I/6)*((2*Sqrt[3]*ArcTan[(1 + (2^(1/3)*(-I + Sqrt[3])^(2/3)*x)/(-1 + x^3)^(1/3))/Sqrt[3]] + Log[(I + Sqrt[3])^(2/3) + ((-I + Sqrt[3])^(2/3)*x^2)/(-1 + x^3)^(2/3) + (2^(2/3)*x)/(-1 + x^3)^(1/3)])/((-I + Sqrt[3])/2)^(2/3) - (2*Sqrt[3]*ArcTan[(1 + (2^(1/3)*(I + Sqrt[3])^(2/3)*x)/(-1 + x^3)^(1/3))/Sqrt[3]] + Log[(-I + Sqrt[3])^(2/3) + ((I + Sqrt[3])^(2/3)*x^2)/(-1 + x^3)^(2/3) + (2^(2/3)*x)/(-1 + x^3)^(1/3)])/((I + Sqrt[3])/2)^(2/3) - (2*Log[(I + Sqrt[3])^(1/3) - ((-I + Sqrt[3])^(1/3)*x)/(-1 + x^3)^(1/3)])/((-I + Sqrt[3])/(I + Sqrt[3]))^(1/3) + 2*((-I + Sqrt[3])/(I + Sqrt[3]))^(1/3)*Log[(-I + Sqrt[3])^(1/3) - ((I + Sqrt[3])^(1/3)*x)/(-1 + x^3)^(1/3)]))/Sqrt[3]","C",0
1035,1,415,78,1.1452092,"\int \frac{\left(-1+x^3\right)^{2/3} \left(1-2 x^3+x^6\right)}{x^6 \left(1-x^3+x^6\right)} \, dx","Integrate[((-1 + x^3)^(2/3)*(1 - 2*x^3 + x^6))/(x^6*(1 - x^3 + x^6)),x]","\left(x^3-1\right)^{2/3} \left(\frac{7}{10 x^2}-\frac{1}{5 x^5}\right)+\frac{i \left(-\frac{2 \log \left(\sqrt[3]{\sqrt{3}+i}-\frac{\sqrt[3]{\sqrt{3}-i} x}{\sqrt[3]{x^3-1}}\right)}{\sqrt[3]{\frac{\sqrt{3}-i}{\sqrt{3}+i}}}+2 \sqrt[3]{\frac{\sqrt{3}-i}{\sqrt{3}+i}} \log \left(\sqrt[3]{\sqrt{3}-i}-\frac{\sqrt[3]{\sqrt{3}+i} x}{\sqrt[3]{x^3-1}}\right)+\frac{2 \sqrt{3} \tan ^{-1}\left(\frac{1+\frac{\sqrt[3]{2} \left(\sqrt{3}-i\right)^{2/3} x}{\sqrt[3]{x^3-1}}}{\sqrt{3}}\right)+\log \left(\frac{2^{2/3} x}{\sqrt[3]{x^3-1}}+\frac{\left(\sqrt{3}-i\right)^{2/3} x^2}{\left(x^3-1\right)^{2/3}}+\left(\sqrt{3}+i\right)^{2/3}\right)}{\left(\frac{1}{2} \left(\sqrt{3}-i\right)\right)^{2/3}}-\frac{2 \sqrt{3} \tan ^{-1}\left(\frac{1+\frac{\sqrt[3]{2} \left(\sqrt{3}+i\right)^{2/3} x}{\sqrt[3]{x^3-1}}}{\sqrt{3}}\right)+\log \left(\frac{2^{2/3} x}{\sqrt[3]{x^3-1}}+\frac{\left(\sqrt{3}+i\right)^{2/3} x^2}{\left(x^3-1\right)^{2/3}}+\left(\sqrt{3}-i\right)^{2/3}\right)}{\left(\frac{1}{2} \left(\sqrt{3}+i\right)\right)^{2/3}}\right)}{6 \sqrt{3}}","\frac{\left(x^3-1\right)^{2/3} \left(7 x^3-2\right)}{10 x^5}-\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^6-\text{$\#$1}^3+1\&,\frac{\log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)-\log (x)}{2 \text{$\#$1}^4-\text{$\#$1}}\&\right]",1,"(-1/5*1/x^5 + 7/(10*x^2))*(-1 + x^3)^(2/3) + ((I/6)*((2*Sqrt[3]*ArcTan[(1 + (2^(1/3)*(-I + Sqrt[3])^(2/3)*x)/(-1 + x^3)^(1/3))/Sqrt[3]] + Log[(I + Sqrt[3])^(2/3) + ((-I + Sqrt[3])^(2/3)*x^2)/(-1 + x^3)^(2/3) + (2^(2/3)*x)/(-1 + x^3)^(1/3)])/((-I + Sqrt[3])/2)^(2/3) - (2*Sqrt[3]*ArcTan[(1 + (2^(1/3)*(I + Sqrt[3])^(2/3)*x)/(-1 + x^3)^(1/3))/Sqrt[3]] + Log[(-I + Sqrt[3])^(2/3) + ((I + Sqrt[3])^(2/3)*x^2)/(-1 + x^3)^(2/3) + (2^(2/3)*x)/(-1 + x^3)^(1/3)])/((I + Sqrt[3])/2)^(2/3) - (2*Log[(I + Sqrt[3])^(1/3) - ((-I + Sqrt[3])^(1/3)*x)/(-1 + x^3)^(1/3)])/((-I + Sqrt[3])/(I + Sqrt[3]))^(1/3) + 2*((-I + Sqrt[3])/(I + Sqrt[3]))^(1/3)*Log[(-I + Sqrt[3])^(1/3) - ((I + Sqrt[3])^(1/3)*x)/(-1 + x^3)^(1/3)]))/Sqrt[3]","C",0
1036,1,37,78,0.0090765,"\int \frac{1}{x^7 \left(b+a x^6\right)^{3/4}} \, dx","Integrate[1/(x^7*(b + a*x^6)^(3/4)),x]","\frac{2 a \sqrt[4]{a x^6+b} \, _2F_1\left(\frac{1}{4},2;\frac{5}{4};\frac{a x^6}{b}+1\right)}{3 b^2}","\frac{a \tan ^{-1}\left(\frac{\sqrt[4]{a x^6+b}}{\sqrt[4]{b}}\right)}{4 b^{7/4}}+\frac{a \tanh ^{-1}\left(\frac{\sqrt[4]{a x^6+b}}{\sqrt[4]{b}}\right)}{4 b^{7/4}}-\frac{\sqrt[4]{a x^6+b}}{6 b x^6}",1,"(2*a*(b + a*x^6)^(1/4)*Hypergeometric2F1[1/4, 2, 5/4, 1 + (a*x^6)/b])/(3*b^2)","C",1
1037,0,0,78,0.133153,"\int \frac{\sqrt[4]{-1+x^4} \left(-1+x^8\right)}{x^6 \left(1+x^8\right)} \, dx","Integrate[((-1 + x^4)^(1/4)*(-1 + x^8))/(x^6*(1 + x^8)),x]","\int \frac{\sqrt[4]{-1+x^4} \left(-1+x^8\right)}{x^6 \left(1+x^8\right)} \, dx","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4+2\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{x^4-1}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^4-1}\&\right]+\frac{\sqrt[4]{x^4-1} \left(1-x^4\right)}{5 x^5}",1,"Integrate[((-1 + x^4)^(1/4)*(-1 + x^8))/(x^6*(1 + x^8)), x]","F",-1
1038,0,0,78,0.3394631,"\int \frac{-1+x^8}{\sqrt[4]{1+x^4} \left(1+x^8\right)} \, dx","Integrate[(-1 + x^8)/((1 + x^4)^(1/4)*(1 + x^8)),x]","\int \frac{-1+x^8}{\sqrt[4]{1+x^4} \left(1+x^8\right)} \, dx","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4+2\&,\frac{\log \left(\sqrt[4]{x^4+1}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]+\frac{1}{2} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)+\frac{1}{2} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)",1,"Integrate[(-1 + x^8)/((1 + x^4)^(1/4)*(1 + x^8)), x]","F",-1
1039,0,0,78,0.1307882,"\int \frac{-1+x^8}{\sqrt[4]{1+x^4} \left(1+x^8\right)} \, dx","Integrate[(-1 + x^8)/((1 + x^4)^(1/4)*(1 + x^8)),x]","\int \frac{-1+x^8}{\sqrt[4]{1+x^4} \left(1+x^8\right)} \, dx","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4+2\&,\frac{\log \left(\sqrt[4]{x^4+1}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]+\frac{1}{2} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)+\frac{1}{2} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)",1,"Integrate[(-1 + x^8)/((1 + x^4)^(1/4)*(1 + x^8)), x]","F",-1
1040,0,0,78,0.2027195,"\int \frac{\sqrt[4]{-1+x^4} \left(1-x^4+x^8\right)}{x^6 \left(1+2 x^8\right)} \, dx","Integrate[((-1 + x^4)^(1/4)*(1 - x^4 + x^8))/(x^6*(1 + 2*x^8)),x]","\int \frac{\sqrt[4]{-1+x^4} \left(1-x^4+x^8\right)}{x^6 \left(1+2 x^8\right)} \, dx","\frac{\sqrt[4]{x^4-1} \left(6 x^4-1\right)}{5 x^5}-\frac{3}{8} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4+3\&,\frac{\log \left(\sqrt[4]{x^4-1}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}^7-\text{$\#$1}^3}\&\right]",1,"Integrate[((-1 + x^4)^(1/4)*(1 - x^4 + x^8))/(x^6*(1 + 2*x^8)), x]","F",-1
1041,0,0,78,0.0950152,"\int \frac{\sqrt[4]{-1+x^4} \left(1-x^4+x^8\right)}{x^6 \left(1+2 x^8\right)} \, dx","Integrate[((-1 + x^4)^(1/4)*(1 - x^4 + x^8))/(x^6*(1 + 2*x^8)),x]","\int \frac{\sqrt[4]{-1+x^4} \left(1-x^4+x^8\right)}{x^6 \left(1+2 x^8\right)} \, dx","\frac{\sqrt[4]{x^4-1} \left(6 x^4-1\right)}{5 x^5}-\frac{3}{8} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4+3\&,\frac{\log \left(\sqrt[4]{x^4-1}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}^7-\text{$\#$1}^3}\&\right]",1,"Integrate[((-1 + x^4)^(1/4)*(1 - x^4 + x^8))/(x^6*(1 + 2*x^8)), x]","F",-1
1042,1,53,78,0.0373403,"\int \frac{\left(1+2 x^4\right) \sqrt{1+2 x^8}}{x} \, dx","Integrate[((1 + 2*x^4)*Sqrt[1 + 2*x^8])/x,x]","\frac{1}{8} \left(-2 \tanh ^{-1}\left(\sqrt{2 x^8+1}\right)+\sqrt{2} \sinh ^{-1}\left(\sqrt{2} x^4\right)+2 \sqrt{2 x^8+1} \left(x^4+1\right)\right)","\frac{1}{4} \sqrt{2 x^8+1} \left(x^4+1\right)+\frac{\log \left(\sqrt{2 x^8+1}+\sqrt{2} x^4\right)}{4 \sqrt{2}}-\frac{1}{2} \tanh ^{-1}\left(\sqrt{2 x^8+1}+\sqrt{2} x^4\right)",1,"(2*(1 + x^4)*Sqrt[1 + 2*x^8] + Sqrt[2]*ArcSinh[Sqrt[2]*x^4] - 2*ArcTanh[Sqrt[1 + 2*x^8]])/8","A",1
1043,1,65,78,0.0313675,"\int \sqrt{x+\sqrt{1+x}} \, dx","Integrate[Sqrt[x + Sqrt[1 + x]],x]","\frac{1}{12} \sqrt{x+\sqrt{x+1}} \left(8 x+2 \sqrt{x+1}-3\right)+\frac{5}{8} \tanh ^{-1}\left(\frac{2 \sqrt{x+1}+1}{2 \sqrt{x+\sqrt{x+1}}}\right)","\frac{1}{12} \sqrt{x+\sqrt{x+1}} (8 x-3)+\frac{1}{6} \sqrt{x+1} \sqrt{x+\sqrt{x+1}}-\frac{5}{8} \log \left(2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)",1,"(Sqrt[x + Sqrt[1 + x]]*(-3 + 8*x + 2*Sqrt[1 + x]))/12 + (5*ArcTanh[(1 + 2*Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])])/8","A",1
1044,1,79,79,0.0388893,"\int \frac{2 b+a x^2}{x \left(b^2+a^2 x^2\right)^{3/4}} \, dx","Integrate[(2*b + a*x^2)/(x*(b^2 + a^2*x^2)^(3/4)),x]","\frac{2 \sqrt[4]{a^2 x^2+b^2}}{a}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{a^2 x^2+b^2}}{\sqrt{b}}\right)}{\sqrt{b}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{a^2 x^2+b^2}}{\sqrt{b}}\right)}{\sqrt{b}}","\frac{2 \sqrt[4]{a^2 x^2+b^2}}{a}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{a^2 x^2+b^2}}{\sqrt{b}}\right)}{\sqrt{b}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{a^2 x^2+b^2}}{\sqrt{b}}\right)}{\sqrt{b}}",1,"(2*(b^2 + a^2*x^2)^(1/4))/a - (2*ArcTan[(b^2 + a^2*x^2)^(1/4)/Sqrt[b]])/Sqrt[b] - (2*ArcTanh[(b^2 + a^2*x^2)^(1/4)/Sqrt[b]])/Sqrt[b]","A",1
1045,1,280,79,6.9568089,"\int \frac{-a b x+x^3}{(-a+x) (-b+x) \sqrt{x (-a+x) (-b+x)} \left(a b d-(1+a d+b d) x+d x^2\right)} \, dx","Integrate[(-(a*b*x) + x^3)/((-a + x)*(-b + x)*Sqrt[x*(-a + x)*(-b + x)]*(a*b*d - (1 + a*d + b*d)*x + d*x^2)),x]","\frac{2 i x^{3/2} \sqrt{1-\frac{a}{x}} \sqrt{1-\frac{b}{x}} \Pi \left(\frac{2 b d}{a d+b d-\sqrt{(a d+b d+1)^2-4 a b d^2}+1};i \sinh ^{-1}\left(\frac{\sqrt{-a}}{\sqrt{x}}\right)|\frac{b}{a}\right)+2 i x^{3/2} \sqrt{1-\frac{a}{x}} \sqrt{1-\frac{b}{x}} \Pi \left(\frac{2 b d}{a d+b d+\sqrt{(a d+b d+1)^2-4 a b d^2}+1};i \sinh ^{-1}\left(\frac{\sqrt{-a}}{\sqrt{x}}\right)|\frac{b}{a}\right)-2 i x^{3/2} \sqrt{1-\frac{a}{x}} \sqrt{1-\frac{b}{x}} F\left(i \sinh ^{-1}\left(\frac{\sqrt{-a}}{\sqrt{x}}\right)|\frac{b}{a}\right)+2 \sqrt{-a} x}{\sqrt{-a} \sqrt{x (x-a) (x-b)}}","\frac{2 \sqrt{a b x-a x^2-b x^2+x^3}}{(x-a) (x-b)}-2 \sqrt{d} \tanh ^{-1}\left(\frac{x}{\sqrt{d} \sqrt{x^2 (-a-b)+a b x+x^3}}\right)",1,"(2*Sqrt[-a]*x - (2*I)*Sqrt[1 - a/x]*Sqrt[1 - b/x]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[-a]/Sqrt[x]], b/a] + (2*I)*Sqrt[1 - a/x]*Sqrt[1 - b/x]*x^(3/2)*EllipticPi[(2*b*d)/(1 + a*d + b*d - Sqrt[-4*a*b*d^2 + (1 + a*d + b*d)^2]), I*ArcSinh[Sqrt[-a]/Sqrt[x]], b/a] + (2*I)*Sqrt[1 - a/x]*Sqrt[1 - b/x]*x^(3/2)*EllipticPi[(2*b*d)/(1 + a*d + b*d + Sqrt[-4*a*b*d^2 + (1 + a*d + b*d)^2]), I*ArcSinh[Sqrt[-a]/Sqrt[x]], b/a])/(Sqrt[-a]*Sqrt[x*(-a + x)*(-b + x)])","C",1
1046,0,0,79,3.3222377,"\int \frac{-1+2 (-1+k) x+k x^2}{\sqrt[4]{(1-x) x (1-k x)} \left(-1+(3+d) x-(3+d k) x^2+x^3\right)} \, dx","Integrate[(-1 + 2*(-1 + k)*x + k*x^2)/(((1 - x)*x*(1 - k*x))^(1/4)*(-1 + (3 + d)*x - (3 + d*k)*x^2 + x^3)),x]","\int \frac{-1+2 (-1+k) x+k x^2}{\sqrt[4]{(1-x) x (1-k x)} \left(-1+(3+d) x-(3+d k) x^2+x^3\right)} \, dx","\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{k x^3+(-k-1) x^2+x}}{x-1}\right)}{d^{3/4}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{k x^3+(-k-1) x^2+x}}{x-1}\right)}{d^{3/4}}",1,"Integrate[(-1 + 2*(-1 + k)*x + k*x^2)/(((1 - x)*x*(1 - k*x))^(1/4)*(-1 + (3 + d)*x - (3 + d*k)*x^2 + x^3)), x]","F",-1
1047,1,63,79,0.2538372,"\int \frac{1+x^4}{\sqrt{-x+x^3} \left(-1+x^4\right)} \, dx","Integrate[(1 + x^4)/(Sqrt[-x + x^3]*(-1 + x^4)),x]","\frac{x \left(x^2-1\right) F_1\left(\frac{1}{4};-\frac{1}{2},1;\frac{5}{4};x^2,-x^2\right)}{\sqrt{1-x^2} \sqrt{x \left(x^2-1\right)}}-\frac{x}{\sqrt{x \left(x^2-1\right)}}","\frac{\sqrt{x^3-x}}{1-x^2}-\frac{1}{4} \tan ^{-1}\left(\frac{2 \sqrt{x^3-x}}{x^2-2 x-1}\right)-\frac{1}{4} \tanh ^{-1}\left(\frac{\frac{x^2}{2}+x-\frac{1}{2}}{\sqrt{x^3-x}}\right)",1,"-(x/Sqrt[x*(-1 + x^2)]) + (x*(-1 + x^2)*AppellF1[1/4, -1/2, 1, 5/4, x^2, -x^2])/(Sqrt[1 - x^2]*Sqrt[x*(-1 + x^2)])","C",0
1048,1,390,79,0.9127668,"\int \frac{\left(2+x^2\right) \sqrt{4-5 x^2+x^4}}{x^2 \left(-2+2 x+x^2\right)} \, dx","Integrate[((2 + x^2)*Sqrt[4 - 5*x^2 + x^4])/(x^2*(-2 + 2*x + x^2)),x]","\frac{2 x^4-10 x^2+3 \sqrt{1-x^2} \sqrt{4-x^2} x F\left(\sin ^{-1}(x)|\frac{1}{4}\right)-3 \sqrt{1-x^2} \sqrt{4-x^2} x \Pi \left(1-\frac{\sqrt{3}}{2};\sin ^{-1}(x)|\frac{1}{4}\right)-3 \sqrt{1-x^2} \sqrt{4-x^2} x \Pi \left(1+\frac{\sqrt{3}}{2};\sin ^{-1}(x)|\frac{1}{4}\right)+2 \sqrt{x^4-5 x^2+4} x \tanh ^{-1}\left(\frac{8-5 x^2}{4 \sqrt{x^4-5 x^2+4}}\right)-2 \sqrt{x^4-5 x^2+4} x \tanh ^{-1}\left(\frac{2 x^2-5}{2 \sqrt{x^4-5 x^2+4}}\right)-\sqrt{3} \sqrt{x^4-5 x^2+4} x \tanh ^{-1}\left(\frac{2 \left(6+5 \sqrt{3}\right)-\left(3+4 \sqrt{3}\right) x^2}{2 \sqrt{6 \left(2+\sqrt{3}\right)} \sqrt{x^4-5 x^2+4}}\right)+\sqrt{3} \sqrt{x^4-5 x^2+4} x \tanh ^{-1}\left(\frac{\left(4 \sqrt{3}-3\right) x^2-10 \sqrt{3}+12}{2 \sqrt{6} \sqrt{-\left(\left(\sqrt{3}-2\right) \left(x^4-5 x^2+4\right)\right)}}\right)+8}{2 x \sqrt{x^4-5 x^2+4}}","\frac{\sqrt{x^4-5 x^2+4}}{x}-4 \tanh ^{-1}\left(\frac{x^2+x-2}{\sqrt{x^4-5 x^2+4}}\right)+2 \sqrt{3} \tanh ^{-1}\left(\frac{\sqrt{x^4-5 x^2+4}}{\sqrt{3} \left(x^2+x-2\right)}\right)",1,"(8 - 10*x^2 + 2*x^4 + 2*x*Sqrt[4 - 5*x^2 + x^4]*ArcTanh[(8 - 5*x^2)/(4*Sqrt[4 - 5*x^2 + x^4])] - 2*x*Sqrt[4 - 5*x^2 + x^4]*ArcTanh[(-5 + 2*x^2)/(2*Sqrt[4 - 5*x^2 + x^4])] - Sqrt[3]*x*Sqrt[4 - 5*x^2 + x^4]*ArcTanh[(2*(6 + 5*Sqrt[3]) - (3 + 4*Sqrt[3])*x^2)/(2*Sqrt[6*(2 + Sqrt[3])]*Sqrt[4 - 5*x^2 + x^4])] + Sqrt[3]*x*Sqrt[4 - 5*x^2 + x^4]*ArcTanh[(12 - 10*Sqrt[3] + (-3 + 4*Sqrt[3])*x^2)/(2*Sqrt[6]*Sqrt[-((-2 + Sqrt[3])*(4 - 5*x^2 + x^4))])] + 3*x*Sqrt[1 - x^2]*Sqrt[4 - x^2]*EllipticF[ArcSin[x], 1/4] - 3*x*Sqrt[1 - x^2]*Sqrt[4 - x^2]*EllipticPi[1 - Sqrt[3]/2, ArcSin[x], 1/4] - 3*x*Sqrt[1 - x^2]*Sqrt[4 - x^2]*EllipticPi[1 + Sqrt[3]/2, ArcSin[x], 1/4])/(2*x*Sqrt[4 - 5*x^2 + x^4])","C",0
1049,1,68,79,0.3188345,"\int \frac{x^2}{\left(-1+x^4\right) \sqrt[4]{x^2+x^4}} \, dx","Integrate[x^2/((-1 + x^4)*(x^2 + x^4)^(1/4)),x]","\frac{x \left(2^{3/4} \sqrt[4]{\frac{1}{x^2}+1} \left(\tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{x^2}+1}}{\sqrt[4]{2}}\right)-\tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{x^2}+1}}{\sqrt[4]{2}}\right)\right)+4\right)}{4 \sqrt[4]{x^4+x^2}}","\frac{\left(x^4+x^2\right)^{3/4}}{x \left(x^2+1\right)}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+x^2}}\right)}{2 \sqrt[4]{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+x^2}}\right)}{2 \sqrt[4]{2}}",1,"(x*(4 + 2^(3/4)*(1 + x^(-2))^(1/4)*(ArcTan[(1 + x^(-2))^(1/4)/2^(1/4)] - ArcTanh[(1 + x^(-2))^(1/4)/2^(1/4)])))/(4*(x^2 + x^4)^(1/4))","A",1
1050,1,94,79,0.0964154,"\int \frac{\left(-2+x^6\right) \sqrt{-1+x^6}}{x^4 \left(2+x^6\right)} \, dx","Integrate[((-2 + x^6)*Sqrt[-1 + x^6])/(x^4*(2 + x^6)),x]","\frac{\sqrt{1-x^6} x^{12} F_1\left(\frac{3}{2};\frac{1}{2},1;\frac{5}{2};x^6,-\frac{x^6}{2}\right)+6 x^6-4 \sqrt{6-6 x^6} x^3 \sin ^{-1}\left(\frac{\sqrt{3} x^3}{\sqrt{x^6+2}}\right)-6}{18 x^3 \sqrt{x^6-1}}","\frac{\sqrt{x^6-1}}{3 x^3}+\frac{1}{3} \log \left(\sqrt{x^6-1}+x^3\right)+\sqrt{\frac{2}{3}} \tanh ^{-1}\left(\frac{x^6}{\sqrt{6}}+\frac{\sqrt{x^6-1} x^3}{\sqrt{6}}+\sqrt{\frac{2}{3}}\right)",1,"(-6 + 6*x^6 + x^12*Sqrt[1 - x^6]*AppellF1[3/2, 1/2, 1, 5/2, x^6, -1/2*x^6] - 4*x^3*Sqrt[6 - 6*x^6]*ArcSin[(Sqrt[3]*x^3)/Sqrt[2 + x^6]])/(18*x^3*Sqrt[-1 + x^6])","C",0
1051,1,354,79,1.7000063,"\int \frac{\left(-4+x^6\right) \left(2-x^4+x^6\right)^{5/2}}{x^7 \left(2+x^6\right)^2} \, dx","Integrate[((-4 + x^6)*(2 - x^4 + x^6)^(5/2))/(x^7*(2 + x^6)^2),x]","\frac{1}{6} \sqrt{x^6-x^4+2} \left(\frac{4}{x^6}-\frac{14}{x^2}-\frac{3 x^2}{x^6+2}+2\right)+\frac{\left(\frac{1}{2}+i\right) \sqrt{i x^2+(1-i)} \sqrt{(-3-4 i) \left(x^4+i x^2-(1-i)\right)} \left(i F\left(\sin ^{-1}\left(\frac{\sqrt{(-2-i) \left(x^2-(1-i)\right)}}{\sqrt{5}}\right)|\frac{1}{2}+i\right)+\sqrt[3]{2} \left(\frac{3 \sqrt[6]{-1} \Pi \left(-\frac{2-i}{(-1+i)+\sqrt[3]{-2}};\sin ^{-1}\left(\frac{\sqrt{(-2-i) \left(x^2-(1-i)\right)}}{\sqrt{5}}\right)|\frac{1}{2}+i\right)}{\left(\sqrt[3]{-2}+(-1+i)\right) \left(1+\sqrt[3]{-1}\right)^2}-\frac{i \Pi \left(\frac{2-i}{(1-i)+\sqrt[3]{2}};\sin ^{-1}\left(\frac{\sqrt{(-2-i) \left(x^2-(1-i)\right)}}{\sqrt{5}}\right)|\frac{1}{2}+i\right)}{\sqrt[3]{2}+(1-i)}-\frac{2 \sqrt[6]{-1} \Pi \left(\frac{2-i}{(1-i)+(-1)^{2/3} \sqrt[3]{2}};\sin ^{-1}\left(\frac{\sqrt{(-2-i) \left(x^2-(1-i)\right)}}{\sqrt{5}}\right)|\frac{1}{2}+i\right)}{(-2+2 i)+\sqrt[3]{2}-i \sqrt[3]{2} \sqrt{3}}\right)\right)}{\sqrt{2} \sqrt{x^6-x^4+2}}","\frac{\sqrt{x^6-x^4+2} \left(2 x^{12}-14 x^{10}-3 x^8+8 x^6-28 x^4+8\right)}{6 x^6 \left(x^6+2\right)}-\frac{5}{2} \tan ^{-1}\left(\frac{x^2}{\sqrt{x^6-x^4+2}}\right)",1,"(Sqrt[2 - x^4 + x^6]*(2 + 4/x^6 - 14/x^2 - (3*x^2)/(2 + x^6)))/6 + ((1/2 + I)*Sqrt[(1 - I) + I*x^2]*Sqrt[(-3 - 4*I)*((-1 + I) + I*x^2 + x^4)]*(I*EllipticF[ArcSin[Sqrt[(-2 - I)*((-1 + I) + x^2)]/Sqrt[5]], 1/2 + I] + 2^(1/3)*((3*(-1)^(1/6)*EllipticPi[(-2 + I)/((-1 + I) + (-2)^(1/3)), ArcSin[Sqrt[(-2 - I)*((-1 + I) + x^2)]/Sqrt[5]], 1/2 + I])/(((-1 + I) + (-2)^(1/3))*(1 + (-1)^(1/3))^2) - (I*EllipticPi[(2 - I)/((1 - I) + 2^(1/3)), ArcSin[Sqrt[(-2 - I)*((-1 + I) + x^2)]/Sqrt[5]], 1/2 + I])/((1 - I) + 2^(1/3)) - (2*(-1)^(1/6)*EllipticPi[(2 - I)/((1 - I) + (-1)^(2/3)*2^(1/3)), ArcSin[Sqrt[(-2 - I)*((-1 + I) + x^2)]/Sqrt[5]], 1/2 + I])/((-2 + 2*I) + 2^(1/3) - I*2^(1/3)*Sqrt[3]))))/(Sqrt[2]*Sqrt[2 - x^4 + x^6])","C",1
1052,0,0,79,0.15482,"\int \frac{\left(-1+x^3\right)^{2/3} \left(2+x^3\right)}{x^6 \left(2+x^3+2 x^6\right)} \, dx","Integrate[((-1 + x^3)^(2/3)*(2 + x^3))/(x^6*(2 + x^3 + 2*x^6)),x]","\int \frac{\left(-1+x^3\right)^{2/3} \left(2+x^3\right)}{x^6 \left(2+x^3+2 x^6\right)} \, dx","\frac{\left(x^3-1\right)^{5/3}}{5 x^5}-\frac{2}{3} \text{RootSum}\left[2 \text{$\#$1}^6-5 \text{$\#$1}^3+5\&,\frac{\text{$\#$1}^2 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)-\text{$\#$1}^2 \log (x)}{4 \text{$\#$1}^3-5}\&\right]",1,"Integrate[((-1 + x^3)^(2/3)*(2 + x^3))/(x^6*(2 + x^3 + 2*x^6)), x]","F",-1
1053,0,0,79,0.0766739,"\int \frac{\left(-1+x^3\right)^{2/3} \left(2+x^3\right)}{x^6 \left(2+x^3+2 x^6\right)} \, dx","Integrate[((-1 + x^3)^(2/3)*(2 + x^3))/(x^6*(2 + x^3 + 2*x^6)),x]","\int \frac{\left(-1+x^3\right)^{2/3} \left(2+x^3\right)}{x^6 \left(2+x^3+2 x^6\right)} \, dx","\frac{\left(x^3-1\right)^{5/3}}{5 x^5}-\frac{2}{3} \text{RootSum}\left[2 \text{$\#$1}^6-5 \text{$\#$1}^3+5\&,\frac{\text{$\#$1}^2 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)-\text{$\#$1}^2 \log (x)}{4 \text{$\#$1}^3-5}\&\right]",1,"Integrate[((-1 + x^3)^(2/3)*(2 + x^3))/(x^6*(2 + x^3 + 2*x^6)), x]","F",-1
1054,0,0,79,0.1647724,"\int \frac{x+x^7}{\left(-1+x^6\right)^{2/3} \left(-1+x^3+x^6\right)} \, dx","Integrate[(x + x^7)/((-1 + x^6)^(2/3)*(-1 + x^3 + x^6)),x]","\int \frac{x+x^7}{\left(-1+x^6\right)^{2/3} \left(-1+x^3+x^6\right)} \, dx","\frac{1}{3} \log \left(\sqrt[3]{x^6-1}+x\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^6-1}-x}\right)}{\sqrt{3}}-\frac{1}{6} \log \left(-\sqrt[3]{x^6-1} x+\left(x^6-1\right)^{2/3}+x^2\right)",1,"Integrate[(x + x^7)/((-1 + x^6)^(2/3)*(-1 + x^3 + x^6)), x]","F",-1
1055,0,0,79,0.1342067,"\int \frac{\sqrt{1-x^6} \left(1+2 x^6\right)}{1+x^4-2 x^6+x^{12}} \, dx","Integrate[(Sqrt[1 - x^6]*(1 + 2*x^6))/(1 + x^4 - 2*x^6 + x^12),x]","\int \frac{\sqrt{1-x^6} \left(1+2 x^6\right)}{1+x^4-2 x^6+x^{12}} \, dx","-\frac{\tan ^{-1}\left(\frac{\sqrt{2} x \sqrt{1-x^6}}{x^6+x^2-1}\right)}{2 \sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt{1-x^6}}{x^6-x^2-1}\right)}{2 \sqrt{2}}",1,"Integrate[(Sqrt[1 - x^6]*(1 + 2*x^6))/(1 + x^4 - 2*x^6 + x^12), x]","F",-1
1056,1,111,79,0.1811761,"\int \frac{\sqrt{1+x^2}}{\sqrt{1+\sqrt{1+x^2}}} \, dx","Integrate[Sqrt[1 + x^2]/Sqrt[1 + Sqrt[1 + x^2]],x]","\frac{\sqrt{\sqrt{x^2+1}+1} \left(6 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{1}{2}-\frac{\sqrt{x^2+1}}{2}\right)+4 x^2-8 \sqrt{x^2+1}+3 \sqrt{2} \sqrt{\sqrt{x^2+1}-1} \tan ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}-1}}{\sqrt{2}}\right)+2\right)}{6 x}","\frac{2 \sqrt{x^2+1} x}{3 \sqrt{\sqrt{x^2+1}+1}}-\frac{2 x}{3 \sqrt{\sqrt{x^2+1}+1}}+\sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2} \sqrt{\sqrt{x^2+1}+1}}\right)",1,"(Sqrt[1 + Sqrt[1 + x^2]]*(2 + 4*x^2 - 8*Sqrt[1 + x^2] + 3*Sqrt[2]*Sqrt[-1 + Sqrt[1 + x^2]]*ArcTan[Sqrt[-1 + Sqrt[1 + x^2]]/Sqrt[2]] + 6*Hypergeometric2F1[-1/2, 1, 1/2, 1/2 - Sqrt[1 + x^2]/2]))/(6*x)","C",1
1057,1,66,79,0.0414315,"\int \frac{1+x^2}{\sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[(1 + x^2)/Sqrt[x + Sqrt[1 + x^2]],x]","\frac{7 \left(\sqrt{x^2+1}+x\right)^6+105 \left(\sqrt{x^2+1}+x\right)^4-35 \left(\sqrt{x^2+1}+x\right)^2-5}{140 \left(\sqrt{x^2+1}+x\right)^{7/2}}","\frac{2 \left(28 x^6+147 x^4+112 x^2+9\right)}{35 \left(\sqrt{x^2+1}+x\right)^{7/2}}+\frac{2 \sqrt{x^2+1} \left(4 x^5+19 x^3+7 x\right)}{5 \left(\sqrt{x^2+1}+x\right)^{7/2}}",1,"(-5 - 35*(x + Sqrt[1 + x^2])^2 + 105*(x + Sqrt[1 + x^2])^4 + 7*(x + Sqrt[1 + x^2])^6)/(140*(x + Sqrt[1 + x^2])^(7/2))","A",1
1058,1,194,79,3.2967931,"\int \frac{x^2}{\sqrt{x^2+\sqrt{1+x^4}}} \, dx","Integrate[x^2/Sqrt[x^2 + Sqrt[1 + x^4]],x]","\frac{\sqrt{2} x^2 \left(\sqrt{x^4+1}+x^2\right) \left(8 x^8+9 x^4+8 \sqrt{x^4+1} x^6+5 \sqrt{x^4+1} x^2+1\right)-\sqrt{x^2 \left(\sqrt{x^4+1}+x^2\right)} \left(4 x^8+5 x^4+4 \sqrt{x^4+1} x^6+3 \sqrt{x^4+1} x^2+1\right) \tan ^{-1}\left(\sqrt{\left(\sqrt{x^4+1}+x^2\right)^2-1}\right)}{8 \sqrt{2} \left(\sqrt{x^4+1}+x^2\right)^{5/2} \left(x^5+\sqrt{x^4+1} x^3+x\right)}","\frac{1}{4} \sqrt{\sqrt{x^4+1}+x^2} x-\frac{x}{8 \left(\sqrt{x^4+1}+x^2\right)^{3/2}}-\frac{\tan ^{-1}\left(\sqrt{2} x \sqrt{\sqrt{x^4+1}+x^2}\right)}{8 \sqrt{2}}",1,"(Sqrt[2]*x^2*(x^2 + Sqrt[1 + x^4])*(1 + 9*x^4 + 8*x^8 + 5*x^2*Sqrt[1 + x^4] + 8*x^6*Sqrt[1 + x^4]) - Sqrt[x^2*(x^2 + Sqrt[1 + x^4])]*(1 + 5*x^4 + 4*x^8 + 3*x^2*Sqrt[1 + x^4] + 4*x^6*Sqrt[1 + x^4])*ArcTan[Sqrt[-1 + (x^2 + Sqrt[1 + x^4])^2]])/(8*Sqrt[2]*(x^2 + Sqrt[1 + x^4])^(5/2)*(x + x^5 + x^3*Sqrt[1 + x^4]))","B",1
1059,1,200,79,0.9582421,"\int \frac{\sqrt{1+x^4}}{\sqrt{x^2+\sqrt{1+x^4}}} \, dx","Integrate[Sqrt[1 + x^4]/Sqrt[x^2 + Sqrt[1 + x^4]],x]","\frac{\sqrt{2} \left(\sqrt{x^4+1}+x^2\right) \left(16 x^8+18 x^4+16 \sqrt{x^4+1} x^6+10 \sqrt{x^4+1} x^2+3\right) x^2+5 \sqrt{x^2 \left(\sqrt{x^4+1}+x^2\right)} \left(8 x^8+8 x^4+8 \sqrt{x^4+1} x^6+4 \sqrt{x^4+1} x^2+1\right) \tan ^{-1}\left(\sqrt{\left(\sqrt{x^4+1}+x^2\right)^2-1}\right)}{8 \sqrt{2} x \sqrt{\sqrt{x^4+1}+x^2} \left(2 x^4+2 \sqrt{x^4+1} x^2+1\right)^2}","\frac{1}{4} \sqrt{\sqrt{x^4+1}+x^2} x+\frac{x}{8 \left(\sqrt{x^4+1}+x^2\right)^{3/2}}+\frac{5 \tan ^{-1}\left(\sqrt{2} x \sqrt{\sqrt{x^4+1}+x^2}\right)}{8 \sqrt{2}}",1,"(Sqrt[2]*x^2*(x^2 + Sqrt[1 + x^4])*(3 + 18*x^4 + 16*x^8 + 10*x^2*Sqrt[1 + x^4] + 16*x^6*Sqrt[1 + x^4]) + 5*Sqrt[x^2*(x^2 + Sqrt[1 + x^4])]*(1 + 8*x^4 + 8*x^8 + 4*x^2*Sqrt[1 + x^4] + 8*x^6*Sqrt[1 + x^4])*ArcTan[Sqrt[-1 + (x^2 + Sqrt[1 + x^4])^2]])/(8*Sqrt[2]*x*Sqrt[x^2 + Sqrt[1 + x^4]]*(1 + 2*x^4 + 2*x^2*Sqrt[1 + x^4])^2)","B",1
1060,0,0,80,0.1160008,"\int \frac{-3+x^2}{\sqrt[3]{-1+x^2} \left(-1+x^2+x^3\right)} \, dx","Integrate[(-3 + x^2)/((-1 + x^2)^(1/3)*(-1 + x^2 + x^3)),x]","\int \frac{-3+x^2}{\sqrt[3]{-1+x^2} \left(-1+x^2+x^3\right)} \, dx","\log \left(\sqrt[3]{x^2-1}+x\right)-\frac{1}{2} \log \left(x^2-\sqrt[3]{x^2-1} x+\left(x^2-1\right)^{2/3}\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x^2-1}}{\sqrt[3]{x^2-1}-2 x}\right)",1,"Integrate[(-3 + x^2)/((-1 + x^2)^(1/3)*(-1 + x^2 + x^3)), x]","F",-1
1061,1,277,80,4.7584306,"\int \frac{-a^2 b+a (2 a+b) x-3 a x^2+x^3}{x (-b+x) \sqrt{x (-a+x) (-b+x)} \left(a-(1+b d) x+d x^2\right)} \, dx","Integrate[(-(a^2*b) + a*(2*a + b)*x - 3*a*x^2 + x^3)/(x*(-b + x)*Sqrt[x*(-a + x)*(-b + x)]*(a - (1 + b*d)*x + d*x^2)),x]","\frac{2 (x-a) \left(i \sqrt{\frac{x}{a}} \sqrt{\frac{x-b}{a-b}} \Pi \left(\frac{2 a d}{2 a d-b d+\sqrt{(b d+1)^2-4 a d}-1};i \sinh ^{-1}\left(\sqrt{\frac{x}{a}-1}\right)|\frac{a}{a-b}\right)+i \sqrt{\frac{x}{a}} \sqrt{\frac{x-b}{a-b}} \Pi \left(-\frac{2 a d}{-2 a d+b d+\sqrt{(b d+1)^2-4 a d}+1};i \sinh ^{-1}\left(\sqrt{\frac{x}{a}-1}\right)|\frac{a}{a-b}\right)-i \sqrt{\frac{x}{a}} \sqrt{\frac{x-b}{a-b}} F\left(i \sinh ^{-1}\left(\sqrt{\frac{x}{a}-1}\right)|\frac{a}{a-b}\right)+\sqrt{\frac{x}{a}-1}\right)}{\sqrt{\frac{x}{a}-1} \sqrt{x (x-a) (x-b)}}","2 \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{x^2 (-a-b)+a b x+x^3}}{a-x}\right)+\frac{2 \sqrt{x^2 (-a-b)+a b x+x^3}}{x (x-b)}",1,"(2*(-a + x)*(Sqrt[-1 + x/a] - I*Sqrt[x/a]*Sqrt[(-b + x)/(a - b)]*EllipticF[I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)] + I*Sqrt[x/a]*Sqrt[(-b + x)/(a - b)]*EllipticPi[(2*a*d)/(-1 + 2*a*d - b*d + Sqrt[-4*a*d + (1 + b*d)^2]), I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)] + I*Sqrt[x/a]*Sqrt[(-b + x)/(a - b)]*EllipticPi[(-2*a*d)/(1 - 2*a*d + b*d + Sqrt[-4*a*d + (1 + b*d)^2]), I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)]))/(Sqrt[x*(-a + x)*(-b + x)]*Sqrt[-1 + x/a])","C",1
1062,1,129,80,0.2070741,"\int \frac{1}{\left(b+a^3 x^3\right) \sqrt[3]{-b x^2+a^3 x^3}} \, dx","Integrate[1/((b + a^3*x^3)*(-(b*x^2) + a^3*x^3)^(1/3)),x]","\frac{x \left(\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2+b^{2/3}\right) x}{a^3 x-b}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2-\sqrt[3]{-1} b^{2/3}\right) x}{a^3 x-b}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2+(-1)^{2/3} b^{2/3}\right) x}{a^3 x-b}\right)\right)}{b \sqrt[3]{x^2 \left(a^3 x-b\right)}}","-\frac{\text{RootSum}\left[-\text{$\#$1}^9+3 \text{$\#$1}^6 a^3-3 \text{$\#$1}^3 a^6+a^9+a^3 b^2\&,\frac{\log \left(\sqrt[3]{a^3 x^3-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{3 b}",1,"(x*(Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 + b^(2/3))*x)/(-b + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 - (-1)^(1/3)*b^(2/3))*x)/(-b + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 + (-1)^(2/3)*b^(2/3))*x)/(-b + a^3*x)]))/(b*(x^2*(-b + a^3*x))^(1/3))","A",1
1063,1,129,80,0.0599676,"\int \frac{1}{\left(b+a^3 x^3\right) \sqrt[3]{-b x^2+a^3 x^3}} \, dx","Integrate[1/((b + a^3*x^3)*(-(b*x^2) + a^3*x^3)^(1/3)),x]","\frac{x \left(\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2+b^{2/3}\right) x}{a^3 x-b}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2-\sqrt[3]{-1} b^{2/3}\right) x}{a^3 x-b}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2+(-1)^{2/3} b^{2/3}\right) x}{a^3 x-b}\right)\right)}{b \sqrt[3]{x^2 \left(a^3 x-b\right)}}","-\frac{\text{RootSum}\left[-\text{$\#$1}^9+3 \text{$\#$1}^6 a^3-3 \text{$\#$1}^3 a^6+a^9+a^3 b^2\&,\frac{\log \left(\sqrt[3]{a^3 x^3-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{3 b}",1,"(x*(Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 + b^(2/3))*x)/(-b + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 - (-1)^(1/3)*b^(2/3))*x)/(-b + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 + (-1)^(2/3)*b^(2/3))*x)/(-b + a^3*x)]))/(b*(x^2*(-b + a^3*x))^(1/3))","A",1
1064,0,0,80,0.1985534,"\int \frac{x^2 \left(-4+x^3\right)}{\left(-1+x^3\right)^{3/4} \left(-1+x^3+x^4\right)} \, dx","Integrate[(x^2*(-4 + x^3))/((-1 + x^3)^(3/4)*(-1 + x^3 + x^4)),x]","\int \frac{x^2 \left(-4+x^3\right)}{\left(-1+x^3\right)^{3/4} \left(-1+x^3+x^4\right)} \, dx","\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{x^3-1}}{\sqrt{x^3-1}-x^2}\right)-\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{x^3-1}}{\sqrt{x^3-1}+x^2}\right)",1,"Integrate[(x^2*(-4 + x^3))/((-1 + x^3)^(3/4)*(-1 + x^3 + x^4)), x]","F",-1
1065,1,75,80,0.022488,"\int \frac{x^6}{\left(b+a x^4\right)^{3/4}} \, dx","Integrate[x^6/(b + a*x^4)^(3/4),x]","\frac{2 a^{3/4} x^3 \sqrt[4]{a x^4+b}+3 b \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)-3 b \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{8 a^{7/4}}","\frac{3 b \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{8 a^{7/4}}-\frac{3 b \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{8 a^{7/4}}+\frac{x^3 \sqrt[4]{a x^4+b}}{4 a}",1,"(2*a^(3/4)*x^3*(b + a*x^4)^(1/4) + 3*b*ArcTan[(a^(1/4)*x)/(b + a*x^4)^(1/4)] - 3*b*ArcTanh[(a^(1/4)*x)/(b + a*x^4)^(1/4)])/(8*a^(7/4))","A",1
1066,1,53,80,0.0170666,"\int \frac{\sqrt[4]{b x^2+a x^4}}{x^2} \, dx","Integrate[(b*x^2 + a*x^4)^(1/4)/x^2,x]","-\frac{2 \sqrt[4]{x^2 \left(a x^2+b\right)} \, _2F_1\left(-\frac{1}{4},-\frac{1}{4};\frac{3}{4};-\frac{a x^2}{b}\right)}{x \sqrt[4]{\frac{a x^2}{b}+1}}","-\frac{2 \sqrt[4]{a x^4+b x^2}}{x}-\sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)+\sqrt[4]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)",1,"(-2*(x^2*(b + a*x^2))^(1/4)*Hypergeometric2F1[-1/4, -1/4, 3/4, -((a*x^2)/b)])/(x*(1 + (a*x^2)/b)^(1/4))","C",1
1067,0,0,80,6.6526871,"\int \frac{\sqrt[4]{2+x^4} \left(-4+x^8\right)}{x^6 \left(-4-2 x^4+x^8\right)} \, dx","Integrate[((2 + x^4)^(1/4)*(-4 + x^8))/(x^6*(-4 - 2*x^4 + x^8)),x]","\int \frac{\sqrt[4]{2+x^4} \left(-4+x^8\right)}{x^6 \left(-4-2 x^4+x^8\right)} \, dx","\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4-1\&,\frac{\log \left(\sqrt[4]{x^4+2}-\text{$\#$1} x\right)-\log (x)}{2 \text{$\#$1}^7-\text{$\#$1}^3}\&\right]+\frac{\sqrt[4]{x^4+2} \left(2 x^4-1\right)}{5 x^5}",1,"Integrate[((2 + x^4)^(1/4)*(-4 + x^8))/(x^6*(-4 - 2*x^4 + x^8)), x]","F",-1
1068,0,0,80,6.5834351,"\int \frac{\sqrt[4]{2+x^4} \left(-4+x^8\right)}{x^6 \left(-4-2 x^4+x^8\right)} \, dx","Integrate[((2 + x^4)^(1/4)*(-4 + x^8))/(x^6*(-4 - 2*x^4 + x^8)),x]","\int \frac{\sqrt[4]{2+x^4} \left(-4+x^8\right)}{x^6 \left(-4-2 x^4+x^8\right)} \, dx","\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4-1\&,\frac{\log \left(\sqrt[4]{x^4+2}-\text{$\#$1} x\right)-\log (x)}{2 \text{$\#$1}^7-\text{$\#$1}^3}\&\right]+\frac{\sqrt[4]{x^4+2} \left(2 x^4-1\right)}{5 x^5}",1,"Integrate[((2 + x^4)^(1/4)*(-4 + x^8))/(x^6*(-4 - 2*x^4 + x^8)), x]","F",-1
1069,0,0,80,6.6914599,"\int \frac{\sqrt[4]{-1+x^4} \left(-1+x^4+2 x^8\right)}{x^6 \left(1-x^4+x^8\right)} \, dx","Integrate[((-1 + x^4)^(1/4)*(-1 + x^4 + 2*x^8))/(x^6*(1 - x^4 + x^8)),x]","\int \frac{\sqrt[4]{-1+x^4} \left(-1+x^4+2 x^8\right)}{x^6 \left(1-x^4+x^8\right)} \, dx","\frac{3}{4} \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4+1\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{x^4-1}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{2 \text{$\#$1}^4-1}\&\right]+\frac{\sqrt[4]{x^4-1} \left(1-x^4\right)}{5 x^5}",1,"Integrate[((-1 + x^4)^(1/4)*(-1 + x^4 + 2*x^8))/(x^6*(1 - x^4 + x^8)), x]","F",-1
1070,0,0,80,6.5591095,"\int \frac{\sqrt[4]{-1+x^4} \left(-1+x^4+2 x^8\right)}{x^6 \left(1-x^4+x^8\right)} \, dx","Integrate[((-1 + x^4)^(1/4)*(-1 + x^4 + 2*x^8))/(x^6*(1 - x^4 + x^8)),x]","\int \frac{\sqrt[4]{-1+x^4} \left(-1+x^4+2 x^8\right)}{x^6 \left(1-x^4+x^8\right)} \, dx","\frac{3}{4} \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4+1\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{x^4-1}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{2 \text{$\#$1}^4-1}\&\right]+\frac{\sqrt[4]{x^4-1} \left(1-x^4\right)}{5 x^5}",1,"Integrate[((-1 + x^4)^(1/4)*(-1 + x^4 + 2*x^8))/(x^6*(1 - x^4 + x^8)), x]","F",-1
1071,0,0,81,8.4022077,"\int \frac{-2 a b+(a+b) x}{\sqrt[4]{x^2 (-a+x) (-b+x)} \left(a b d-(a+b) d x+(-1+d) x^2\right)} \, dx","Integrate[(-2*a*b + (a + b)*x)/((x^2*(-a + x)*(-b + x))^(1/4)*(a*b*d - (a + b)*d*x + (-1 + d)*x^2)),x]","\int \frac{-2 a b+(a+b) x}{\sqrt[4]{x^2 (-a+x) (-b+x)} \left(a b d-(a+b) d x+(-1+d) x^2\right)} \, dx","-\frac{2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{d} \sqrt[4]{x^3 (-a-b)+a b x^2+x^4}}\right)}{d^{3/4}}-\frac{2 \tanh ^{-1}\left(\frac{x}{\sqrt[4]{d} \sqrt[4]{x^3 (-a-b)+a b x^2+x^4}}\right)}{d^{3/4}}",1,"Integrate[(-2*a*b + (a + b)*x)/((x^2*(-a + x)*(-b + x))^(1/4)*(a*b*d - (a + b)*d*x + (-1 + d)*x^2)), x]","F",-1
1072,1,80,81,0.0195319,"\int \frac{\sqrt[3]{1+x^3}}{x} \, dx","Integrate[(1 + x^3)^(1/3)/x,x]","\sqrt[3]{x^3+1}+\frac{1}{3} \log \left(1-\sqrt[3]{x^3+1}\right)-\frac{1}{6} \log \left(\left(x^3+1\right)^{2/3}+\sqrt[3]{x^3+1}+1\right)-\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{x^3+1}+1}{\sqrt{3}}\right)}{\sqrt{3}}","\sqrt[3]{x^3+1}+\frac{1}{3} \log \left(\sqrt[3]{x^3+1}-1\right)-\frac{1}{6} \log \left(\left(x^3+1\right)^{2/3}+\sqrt[3]{x^3+1}+1\right)-\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{x^3+1}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3}}",1,"(1 + x^3)^(1/3) - ArcTan[(1 + 2*(1 + x^3)^(1/3))/Sqrt[3]]/Sqrt[3] + Log[1 - (1 + x^3)^(1/3)]/3 - Log[1 + (1 + x^3)^(1/3) + (1 + x^3)^(2/3)]/6","A",1
1073,0,0,81,2.9342515,"\int \frac{3 a b-2 (a+b) x+x^2}{\sqrt[4]{x (-a+x) (-b+x)} \left(-a b d+(a+b) d x-d x^2+x^3\right)} \, dx","Integrate[(3*a*b - 2*(a + b)*x + x^2)/((x*(-a + x)*(-b + x))^(1/4)*(-(a*b*d) + (a + b)*d*x - d*x^2 + x^3)),x]","\int \frac{3 a b-2 (a+b) x+x^2}{\sqrt[4]{x (-a+x) (-b+x)} \left(-a b d+(a+b) d x-d x^2+x^3\right)} \, dx","\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{x^2 (-a-b)+a b x+x^3}}{x}\right)}{d^{3/4}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{x^2 (-a-b)+a b x+x^3}}{x}\right)}{d^{3/4}}",1,"Integrate[(3*a*b - 2*(a + b)*x + x^2)/((x*(-a + x)*(-b + x))^(1/4)*(-(a*b*d) + (a + b)*d*x - d*x^2 + x^3)), x]","F",-1
1074,1,132,81,0.2077211,"\int \frac{1}{\left(-b+a^3 x^3\right) \sqrt[3]{-b x^2+a^3 x^3}} \, dx","Integrate[1/((-b + a^3*x^3)*(-(b*x^2) + a^3*x^3)^(1/3)),x]","-\frac{x \left(\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2-b^{2/3}\right) x}{a^3 x-b}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2+\sqrt[3]{-1} b^{2/3}\right) x}{a^3 x-b}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2-(-1)^{2/3} b^{2/3}\right) x}{a^3 x-b}\right)\right)}{b \sqrt[3]{x^2 \left(a^3 x-b\right)}}","\frac{\text{RootSum}\left[-\text{$\#$1}^9+3 \text{$\#$1}^6 a^3-3 \text{$\#$1}^3 a^6+a^9-a^3 b^2\&,\frac{\log \left(\sqrt[3]{a^3 x^3-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{3 b}",1,"-((x*(Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 - b^(2/3))*x)/(-b + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 + (-1)^(1/3)*b^(2/3))*x)/(-b + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 - (-1)^(2/3)*b^(2/3))*x)/(-b + a^3*x)]))/(b*(x^2*(-b + a^3*x))^(1/3)))","A",1
1075,1,132,81,0.0653272,"\int \frac{1}{\left(-b+a^3 x^3\right) \sqrt[3]{-b x^2+a^3 x^3}} \, dx","Integrate[1/((-b + a^3*x^3)*(-(b*x^2) + a^3*x^3)^(1/3)),x]","-\frac{x \left(\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2-b^{2/3}\right) x}{a^3 x-b}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2+\sqrt[3]{-1} b^{2/3}\right) x}{a^3 x-b}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2-(-1)^{2/3} b^{2/3}\right) x}{a^3 x-b}\right)\right)}{b \sqrt[3]{x^2 \left(a^3 x-b\right)}}","\frac{\text{RootSum}\left[-\text{$\#$1}^9+3 \text{$\#$1}^6 a^3-3 \text{$\#$1}^3 a^6+a^9-a^3 b^2\&,\frac{\log \left(\sqrt[3]{a^3 x^3-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{3 b}",1,"-((x*(Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 - b^(2/3))*x)/(-b + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 + (-1)^(1/3)*b^(2/3))*x)/(-b + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 - (-1)^(2/3)*b^(2/3))*x)/(-b + a^3*x)]))/(b*(x^2*(-b + a^3*x))^(1/3)))","A",1
1076,0,0,81,11.0678627,"\int \frac{-2 a b x^2+(a+b) x^3}{\left(x^2 (-a+x) (-b+x)\right)^{3/4} \left(-a b+(a+b) x+(-1+d) x^2\right)} \, dx","Integrate[(-2*a*b*x^2 + (a + b)*x^3)/((x^2*(-a + x)*(-b + x))^(3/4)*(-(a*b) + (a + b)*x + (-1 + d)*x^2)),x]","\int \frac{-2 a b x^2+(a+b) x^3}{\left(x^2 (-a+x) (-b+x)\right)^{3/4} \left(-a b+(a+b) x+(-1+d) x^2\right)} \, dx","\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{x^3 (-a-b)+a b x^2+x^4}}\right)}{d^{3/4}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{x^3 (-a-b)+a b x^2+x^4}}\right)}{d^{3/4}}",1,"Integrate[(-2*a*b*x^2 + (a + b)*x^3)/((x^2*(-a + x)*(-b + x))^(3/4)*(-(a*b) + (a + b)*x + (-1 + d)*x^2)), x]","F",-1
1077,1,109,81,0.1143495,"\int \frac{\left(-1+x^4\right)^{3/4}}{1+x^4} \, dx","Integrate[(-1 + x^4)^(3/4)/(1 + x^4),x]","-\frac{5 x \left(x^4-1\right)^{3/4} F_1\left(\frac{1}{4};-\frac{3}{4},1;\frac{5}{4};x^4,-x^4\right)}{\left(x^4+1\right) \left(x^4 \left(4 F_1\left(\frac{5}{4};-\frac{3}{4},2;\frac{9}{4};x^4,-x^4\right)+3 F_1\left(\frac{5}{4};\frac{1}{4},1;\frac{9}{4};x^4,-x^4\right)\right)-5 F_1\left(\frac{1}{4};-\frac{3}{4},1;\frac{5}{4};x^4,-x^4\right)\right)}","\frac{1}{2} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-1}}\right)-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-1}}\right)}{\sqrt[4]{2}}+\frac{1}{2} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-1}}\right)-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-1}}\right)}{\sqrt[4]{2}}",1,"(-5*x*(-1 + x^4)^(3/4)*AppellF1[1/4, -3/4, 1, 5/4, x^4, -x^4])/((1 + x^4)*(-5*AppellF1[1/4, -3/4, 1, 5/4, x^4, -x^4] + x^4*(4*AppellF1[5/4, -3/4, 2, 9/4, x^4, -x^4] + 3*AppellF1[5/4, 1/4, 1, 9/4, x^4, -x^4])))","C",0
1078,0,0,81,0.7046365,"\int \frac{\sqrt[4]{-x^2+x^4}}{x^4 \left(-1+x^4\right)} \, dx","Integrate[(-x^2 + x^4)^(1/4)/(x^4*(-1 + x^4)),x]","\int \frac{\sqrt[4]{-x^2+x^4}}{x^4 \left(-1+x^4\right)} \, dx","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-x^2}}\right)}{2^{3/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-x^2}}\right)}{2^{3/4}}-\frac{2 \sqrt[4]{x^4-x^2} \left(x^2-1\right)}{5 x^3}",1,"Integrate[(-x^2 + x^4)^(1/4)/(x^4*(-1 + x^4)), x]","F",-1
1079,0,0,81,0.2345422,"\int \frac{\left(1-x^2\right)^2}{\left(1+x^2\right) \left(1+6 x^2+x^4\right)^{3/4}} \, dx","Integrate[(1 - x^2)^2/((1 + x^2)*(1 + 6*x^2 + x^4)^(3/4)),x]","\int \frac{\left(1-x^2\right)^2}{\left(1+x^2\right) \left(1+6 x^2+x^4\right)^{3/4}} \, dx","-\tan ^{-1}\left(\frac{x-1}{\sqrt[4]{x^4+6 x^2+1}}\right)-\tan ^{-1}\left(\frac{x+1}{\sqrt[4]{x^4+6 x^2+1}}\right)+\tanh ^{-1}\left(\frac{x-1}{\sqrt[4]{x^4+6 x^2+1}}\right)+\tanh ^{-1}\left(\frac{x+1}{\sqrt[4]{x^4+6 x^2+1}}\right)",1,"Integrate[(1 - x^2)^2/((1 + x^2)*(1 + 6*x^2 + x^4)^(3/4)), x]","F",-1
1080,0,0,81,0.0970371,"\int \frac{1}{(1+x) \sqrt[4]{1+6 x^2+x^4}} \, dx","Integrate[1/((1 + x)*(1 + 6*x^2 + x^4)^(1/4)),x]","\int \frac{1}{(1+x) \sqrt[4]{1+6 x^2+x^4}} \, dx","\frac{\tan ^{-1}\left(\frac{\frac{x}{\sqrt[4]{2}}-\frac{1}{\sqrt[4]{2}}}{\sqrt[4]{x^4+6 x^2+1}}\right)}{2\ 2^{3/4}}+\frac{\tanh ^{-1}\left(\frac{\frac{x}{\sqrt[4]{2}}-\frac{1}{\sqrt[4]{2}}}{\sqrt[4]{x^4+6 x^2+1}}\right)}{2\ 2^{3/4}}",1,"Integrate[1/((1 + x)*(1 + 6*x^2 + x^4)^(1/4)), x]","F",-1
1081,1,76,81,0.0280846,"\int \frac{1+x}{\sqrt{-7+4 x+14 x^2-12 x^3+x^4}} \, dx","Integrate[(1 + x)/Sqrt[-7 + 4*x + 14*x^2 - 12*x^3 + x^4],x]","\frac{(x-1) \sqrt{x^2-10 x-7} \left(\tan ^{-1}\left(\frac{-x-3}{\sqrt{x^2-10 x-7}}\right)+2 \tanh ^{-1}\left(\frac{x-5}{\sqrt{x^2-10 x-7}}\right)\right)}{2 \sqrt{(x-1)^2 \left(x^2-10 x-7\right)}}","-\log \left(-x^2+\sqrt{x^4-12 x^3+14 x^2+4 x-7}+6 x-5\right)+\tan ^{-1}\left(\frac{4 x-4}{x^2-\sqrt{x^4-12 x^3+14 x^2+4 x-7}-2 x+1}\right)+\log (x-1)",1,"((-1 + x)*Sqrt[-7 - 10*x + x^2]*(ArcTan[(-3 - x)/Sqrt[-7 - 10*x + x^2]] + 2*ArcTanh[(-5 + x)/Sqrt[-7 - 10*x + x^2]]))/(2*Sqrt[(-1 + x)^2*(-7 - 10*x + x^2)])","A",1
1082,0,0,81,0.1548207,"\int \frac{3+x^4}{\sqrt[3]{-1+x^4} \left(-1-8 x^3+x^4\right)} \, dx","Integrate[(3 + x^4)/((-1 + x^4)^(1/3)*(-1 - 8*x^3 + x^4)),x]","\int \frac{3+x^4}{\sqrt[3]{-1+x^4} \left(-1-8 x^3+x^4\right)} \, dx","\frac{1}{2} \log \left(\sqrt[3]{x^4-1}-2 x\right)-\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{\sqrt[3]{x^4-1}+x}\right)-\frac{1}{4} \log \left(2 \sqrt[3]{x^4-1} x+\left(x^4-1\right)^{2/3}+4 x^2\right)",1,"Integrate[(3 + x^4)/((-1 + x^4)^(1/3)*(-1 - 8*x^3 + x^4)), x]","F",-1
1083,1,85,81,0.4664524,"\int \frac{(-3+2 x) \sqrt{-2 x+2 x^2+3 x^4}}{\left(-2+2 x+x^3\right)^2} \, dx","Integrate[((-3 + 2*x)*Sqrt[-2*x + 2*x^2 + 3*x^4])/(-2 + 2*x + x^3)^2,x]","-\frac{x^2 \left(-6 x^3+\sqrt{\frac{4}{x^3}-\frac{4}{x^2}-6} \left(x^3+2 x-2\right) \tan ^{-1}\left(\sqrt{\frac{1}{x^3}-\frac{1}{x^2}-\frac{3}{2}}\right)-4 x+4\right)}{4 \left(x^3+2 x-2\right) \sqrt{x \left(3 x^3+2 x-2\right)}}","\frac{\sqrt{3 x^4+2 x^2-2 x} x}{2 \left(x^3+2 x-2\right)}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt{3 x^4+2 x^2-2 x}}{3 x^3+2 x-2}\right)}{2 \sqrt{2}}",1,"-1/4*(x^2*(4 - 4*x - 6*x^3 + Sqrt[-6 + 4/x^3 - 4/x^2]*(-2 + 2*x + x^3)*ArcTan[Sqrt[-3/2 + x^(-3) - x^(-2)]]))/((-2 + 2*x + x^3)*Sqrt[x*(-2 + 2*x + 3*x^3)])","A",1
1084,1,81,81,0.0430188,"\int \frac{-2 b+a x^4}{x^4 \sqrt[4]{-b+a x^4}} \, dx","Integrate[(-2*b + a*x^4)/(x^4*(-b + a*x^4)^(1/4)),x]","\frac{1}{2} a^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)+\frac{1}{2} a^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)-\frac{2 \left(a x^4-b\right)^{3/4}}{3 x^3}","\frac{1}{2} a^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)+\frac{1}{2} a^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)-\frac{2 \left(a x^4-b\right)^{3/4}}{3 x^3}",1,"(-2*(-b + a*x^4)^(3/4))/(3*x^3) + (a^(3/4)*ArcTan[(a^(1/4)*x)/(-b + a*x^4)^(1/4)])/2 + (a^(3/4)*ArcTanh[(a^(1/4)*x)/(-b + a*x^4)^(1/4)])/2","A",1
1085,1,48,81,0.0112055,"\int \left(-b+a x^4\right)^{3/4} \, dx","Integrate[(-b + a*x^4)^(3/4),x]","\frac{x \left(a x^4-b\right)^{3/4} \, _2F_1\left(-\frac{3}{4},\frac{1}{4};\frac{5}{4};\frac{a x^4}{b}\right)}{\left(1-\frac{a x^4}{b}\right)^{3/4}}","\frac{1}{4} x \left(a x^4-b\right)^{3/4}-\frac{3 b \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{8 \sqrt[4]{a}}-\frac{3 b \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{8 \sqrt[4]{a}}",1,"(x*(-b + a*x^4)^(3/4)*Hypergeometric2F1[-3/4, 1/4, 5/4, (a*x^4)/b])/(1 - (a*x^4)/b)^(3/4)","C",1
1086,1,53,81,0.0115817,"\int \frac{\left(-b+a x^4\right)^{3/4}}{x^4} \, dx","Integrate[(-b + a*x^4)^(3/4)/x^4,x]","-\frac{\left(a x^4-b\right)^{3/4} \, _2F_1\left(-\frac{3}{4},-\frac{3}{4};\frac{1}{4};\frac{a x^4}{b}\right)}{3 x^3 \left(1-\frac{a x^4}{b}\right)^{3/4}}","\frac{1}{2} a^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)+\frac{1}{2} a^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)-\frac{\left(a x^4-b\right)^{3/4}}{3 x^3}",1,"-1/3*((-b + a*x^4)^(3/4)*Hypergeometric2F1[-3/4, -3/4, 1/4, (a*x^4)/b])/(x^3*(1 - (a*x^4)/b)^(3/4))","C",1
1087,1,167,81,0.2217089,"\int \frac{1}{\sqrt[3]{-b x^2+a x^3} \left(b+a x^4\right)} \, dx","Integrate[1/((-(b*x^2) + a*x^3)^(1/3)*(b + a*x^4)),x]","\frac{3 x \left(\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(a-\sqrt[4]{-a} b^{3/4}\right) x}{a x-b}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(a-i \sqrt[4]{-a} b^{3/4}\right) x}{a x-b}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(a+i \sqrt[4]{-a} b^{3/4}\right) x}{a x-b}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(a+\sqrt[4]{-a} b^{3/4}\right) x}{a x-b}\right)\right)}{4 b \sqrt[3]{x^2 (a x-b)}}","-\frac{\text{RootSum}\left[\text{$\#$1}^{12}-4 \text{$\#$1}^9 a+6 \text{$\#$1}^6 a^2-4 \text{$\#$1}^3 a^3+a^4+a b^3\&,\frac{\log \left(\sqrt[3]{a x^3-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{4 b}",1,"(3*x*(Hypergeometric2F1[1/3, 1, 4/3, ((a - (-a)^(1/4)*b^(3/4))*x)/(-b + a*x)] + Hypergeometric2F1[1/3, 1, 4/3, ((a - I*(-a)^(1/4)*b^(3/4))*x)/(-b + a*x)] + Hypergeometric2F1[1/3, 1, 4/3, ((a + I*(-a)^(1/4)*b^(3/4))*x)/(-b + a*x)] + Hypergeometric2F1[1/3, 1, 4/3, ((a + (-a)^(1/4)*b^(3/4))*x)/(-b + a*x)]))/(4*b*(x^2*(-b + a*x))^(1/3))","C",1
1088,1,167,81,0.0770267,"\int \frac{1}{\sqrt[3]{-b x^2+a x^3} \left(b+a x^4\right)} \, dx","Integrate[1/((-(b*x^2) + a*x^3)^(1/3)*(b + a*x^4)),x]","\frac{3 x \left(\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(a-\sqrt[4]{-a} b^{3/4}\right) x}{a x-b}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(a-i \sqrt[4]{-a} b^{3/4}\right) x}{a x-b}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(a+i \sqrt[4]{-a} b^{3/4}\right) x}{a x-b}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(a+\sqrt[4]{-a} b^{3/4}\right) x}{a x-b}\right)\right)}{4 b \sqrt[3]{x^2 (a x-b)}}","-\frac{\text{RootSum}\left[\text{$\#$1}^{12}-4 \text{$\#$1}^9 a+6 \text{$\#$1}^6 a^2-4 \text{$\#$1}^3 a^3+a^4+a b^3\&,\frac{\log \left(\sqrt[3]{a x^3-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{4 b}",1,"(3*x*(Hypergeometric2F1[1/3, 1, 4/3, ((a - (-a)^(1/4)*b^(3/4))*x)/(-b + a*x)] + Hypergeometric2F1[1/3, 1, 4/3, ((a - I*(-a)^(1/4)*b^(3/4))*x)/(-b + a*x)] + Hypergeometric2F1[1/3, 1, 4/3, ((a + I*(-a)^(1/4)*b^(3/4))*x)/(-b + a*x)] + Hypergeometric2F1[1/3, 1, 4/3, ((a + (-a)^(1/4)*b^(3/4))*x)/(-b + a*x)]))/(4*b*(x^2*(-b + a*x))^(1/3))","C",1
1089,1,47,81,0.0160125,"\int \frac{\sqrt[4]{b x^3+a x^4}}{x^2} \, dx","Integrate[(b*x^3 + a*x^4)^(1/4)/x^2,x]","-\frac{4 \sqrt[4]{x^3 (a x+b)} \, _2F_1\left(-\frac{1}{4},-\frac{1}{4};\frac{3}{4};-\frac{a x}{b}\right)}{x \sqrt[4]{\frac{a x}{b}+1}}","-\frac{4 \sqrt[4]{a x^4+b x^3}}{x}-2 \sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)+2 \sqrt[4]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)",1,"(-4*(x^3*(b + a*x))^(1/4)*Hypergeometric2F1[-1/4, -1/4, 3/4, -((a*x)/b)])/(x*(1 + (a*x)/b)^(1/4))","C",1
1090,0,0,81,1.945666,"\int \frac{\left(1-x^3+x^4+x^6\right)^{3/4} \left(-4+x^3+2 x^6\right)}{\left(1-x^3+x^6\right)^2} \, dx","Integrate[((1 - x^3 + x^4 + x^6)^(3/4)*(-4 + x^3 + 2*x^6))/(1 - x^3 + x^6)^2,x]","\int \frac{\left(1-x^3+x^4+x^6\right)^{3/4} \left(-4+x^3+2 x^6\right)}{\left(1-x^3+x^6\right)^2} \, dx","-\frac{\left(x^6+x^4-x^3+1\right)^{3/4} x}{x^6-x^3+1}-\frac{3}{2} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^6+x^4-x^3+1}}\right)-\frac{3}{2} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^6+x^4-x^3+1}}\right)",1,"Integrate[((1 - x^3 + x^4 + x^6)^(3/4)*(-4 + x^3 + 2*x^6))/(1 - x^3 + x^6)^2, x]","F",-1
1091,1,102,81,0.2772639,"\int \frac{1+2 x^4}{\sqrt[4]{1+x^4} \left(-2-x^4+x^8\right)} \, dx","Integrate[(1 + 2*x^4)/((1 + x^4)^(1/4)*(-2 - x^4 + x^8)),x]","\frac{x}{3 \sqrt[4]{x^4+1}}-\frac{5 \left(-\log \left(2-\frac{2^{3/4} \sqrt[4]{3} x}{\sqrt[4]{x^4+1}}\right)+\log \left(\frac{2^{3/4} \sqrt[4]{3} x}{\sqrt[4]{x^4+1}}+2\right)+2 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{3}{2}} x}{\sqrt[4]{x^4+1}}\right)\right)}{12\ 2^{3/4} \sqrt[4]{3}}","\frac{x}{3 \sqrt[4]{x^4+1}}-\frac{5 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{3}{2}} x}{\sqrt[4]{x^4+1}}\right)}{6\ 2^{3/4} \sqrt[4]{3}}-\frac{5 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{3}{2}} x}{\sqrt[4]{x^4+1}}\right)}{6\ 2^{3/4} \sqrt[4]{3}}",1,"x/(3*(1 + x^4)^(1/4)) - (5*(2*ArcTan[((3/2)^(1/4)*x)/(1 + x^4)^(1/4)] - Log[2 - (2^(3/4)*3^(1/4)*x)/(1 + x^4)^(1/4)] + Log[2 + (2^(3/4)*3^(1/4)*x)/(1 + x^4)^(1/4)]))/(12*2^(3/4)*3^(1/4))","A",1
1092,1,662,81,2.814441,"\int \frac{1}{\sqrt[4]{-b x^2+a x^4} \left(b+a x^8\right)} \, dx","Integrate[1/((-(b*x^2) + a*x^4)^(1/4)*(b + a*x^8)),x]","-\frac{x \sqrt[4]{\frac{b}{x^2}-a} \left(a^3 \text{RootSum}\left[\text{$\#$1}^4+4 \text{$\#$1}^3 a+6 \text{$\#$1}^2 a^2+4 \text{$\#$1} a^3+a^4+a b^3\&,\frac{\frac{\log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{\frac{b}{x^2}-a}\right)}{\sqrt[4]{\text{$\#$1}}}-\frac{\log \left(\sqrt[4]{\text{$\#$1}}+\sqrt[4]{\frac{b}{x^2}-a}\right)}{\sqrt[4]{\text{$\#$1}}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[4]{\text{$\#$1}}}\right)}{\sqrt[4]{\text{$\#$1}}}}{\text{$\#$1}^3+3 \text{$\#$1}^2 a+3 \text{$\#$1} a^2+a^3}\&\right]+3 a^2 \text{RootSum}\left[\text{$\#$1}^4+4 \text{$\#$1}^3 a+6 \text{$\#$1}^2 a^2+4 \text{$\#$1} a^3+a^4+a b^3\&,\frac{\text{$\#$1}^{3/4} \log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{\frac{b}{x^2}-a}\right)-\text{$\#$1}^{3/4} \log \left(\sqrt[4]{\text{$\#$1}}+\sqrt[4]{\frac{b}{x^2}-a}\right)+2 \text{$\#$1}^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[4]{\text{$\#$1}}}\right)}{\text{$\#$1}^3+3 \text{$\#$1}^2 a+3 \text{$\#$1} a^2+a^3}\&\right]+3 a \text{RootSum}\left[\text{$\#$1}^4+4 \text{$\#$1}^3 a+6 \text{$\#$1}^2 a^2+4 \text{$\#$1} a^3+a^4+a b^3\&,\frac{\text{$\#$1}^{7/4} \log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{\frac{b}{x^2}-a}\right)-\text{$\#$1}^{7/4} \log \left(\sqrt[4]{\text{$\#$1}}+\sqrt[4]{\frac{b}{x^2}-a}\right)+2 \text{$\#$1}^{7/4} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[4]{\text{$\#$1}}}\right)}{\text{$\#$1}^3+3 \text{$\#$1}^2 a+3 \text{$\#$1} a^2+a^3}\&\right]+\text{RootSum}\left[\text{$\#$1}^4+4 \text{$\#$1}^3 a+6 \text{$\#$1}^2 a^2+4 \text{$\#$1} a^3+a^4+a b^3\&,\frac{\text{$\#$1}^{11/4} \log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{\frac{b}{x^2}-a}\right)-\text{$\#$1}^{11/4} \log \left(\sqrt[4]{\text{$\#$1}}+\sqrt[4]{\frac{b}{x^2}-a}\right)+2 \text{$\#$1}^{11/4} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[4]{\text{$\#$1}}}\right)}{\text{$\#$1}^3+3 \text{$\#$1}^2 a+3 \text{$\#$1} a^2+a^3}\&\right]\right)}{8 b \sqrt[4]{a x^4-b x^2}}","-\frac{\text{RootSum}\left[\text{$\#$1}^{16}-4 \text{$\#$1}^{12} a+6 \text{$\#$1}^8 a^2-4 \text{$\#$1}^4 a^3+a^4+a b^3\&,\frac{\log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{8 b}",1,"-1/8*((-a + b/x^2)^(1/4)*x*(a^3*RootSum[a^4 + a*b^3 + 4*a^3*#1 + 6*a^2*#1^2 + 4*a*#1^3 + #1^4 & , ((2*ArcTan[(-a + b/x^2)^(1/4)/#1^(1/4)])/#1^(1/4) + Log[-(-a + b/x^2)^(1/4) + #1^(1/4)]/#1^(1/4) - Log[(-a + b/x^2)^(1/4) + #1^(1/4)]/#1^(1/4))/(a^3 + 3*a^2*#1 + 3*a*#1^2 + #1^3) & ] + 3*a^2*RootSum[a^4 + a*b^3 + 4*a^3*#1 + 6*a^2*#1^2 + 4*a*#1^3 + #1^4 & , (2*ArcTan[(-a + b/x^2)^(1/4)/#1^(1/4)]*#1^(3/4) + Log[-(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(3/4) - Log[(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(3/4))/(a^3 + 3*a^2*#1 + 3*a*#1^2 + #1^3) & ] + 3*a*RootSum[a^4 + a*b^3 + 4*a^3*#1 + 6*a^2*#1^2 + 4*a*#1^3 + #1^4 & , (2*ArcTan[(-a + b/x^2)^(1/4)/#1^(1/4)]*#1^(7/4) + Log[-(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(7/4) - Log[(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(7/4))/(a^3 + 3*a^2*#1 + 3*a*#1^2 + #1^3) & ] + RootSum[a^4 + a*b^3 + 4*a^3*#1 + 6*a^2*#1^2 + 4*a*#1^3 + #1^4 & , (2*ArcTan[(-a + b/x^2)^(1/4)/#1^(1/4)]*#1^(11/4) + Log[-(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(11/4) - Log[(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(11/4))/(a^3 + 3*a^2*#1 + 3*a*#1^2 + #1^3) & ]))/(b*(-(b*x^2) + a*x^4)^(1/4))","B",1
1093,1,662,81,0.8373853,"\int \frac{1}{\sqrt[4]{-b x^2+a x^4} \left(b+a x^8\right)} \, dx","Integrate[1/((-(b*x^2) + a*x^4)^(1/4)*(b + a*x^8)),x]","-\frac{x \sqrt[4]{\frac{b}{x^2}-a} \left(a^3 \text{RootSum}\left[\text{$\#$1}^4+4 \text{$\#$1}^3 a+6 \text{$\#$1}^2 a^2+4 \text{$\#$1} a^3+a^4+a b^3\&,\frac{\frac{\log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{\frac{b}{x^2}-a}\right)}{\sqrt[4]{\text{$\#$1}}}-\frac{\log \left(\sqrt[4]{\text{$\#$1}}+\sqrt[4]{\frac{b}{x^2}-a}\right)}{\sqrt[4]{\text{$\#$1}}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[4]{\text{$\#$1}}}\right)}{\sqrt[4]{\text{$\#$1}}}}{\text{$\#$1}^3+3 \text{$\#$1}^2 a+3 \text{$\#$1} a^2+a^3}\&\right]+3 a^2 \text{RootSum}\left[\text{$\#$1}^4+4 \text{$\#$1}^3 a+6 \text{$\#$1}^2 a^2+4 \text{$\#$1} a^3+a^4+a b^3\&,\frac{\text{$\#$1}^{3/4} \log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{\frac{b}{x^2}-a}\right)-\text{$\#$1}^{3/4} \log \left(\sqrt[4]{\text{$\#$1}}+\sqrt[4]{\frac{b}{x^2}-a}\right)+2 \text{$\#$1}^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[4]{\text{$\#$1}}}\right)}{\text{$\#$1}^3+3 \text{$\#$1}^2 a+3 \text{$\#$1} a^2+a^3}\&\right]+3 a \text{RootSum}\left[\text{$\#$1}^4+4 \text{$\#$1}^3 a+6 \text{$\#$1}^2 a^2+4 \text{$\#$1} a^3+a^4+a b^3\&,\frac{\text{$\#$1}^{7/4} \log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{\frac{b}{x^2}-a}\right)-\text{$\#$1}^{7/4} \log \left(\sqrt[4]{\text{$\#$1}}+\sqrt[4]{\frac{b}{x^2}-a}\right)+2 \text{$\#$1}^{7/4} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[4]{\text{$\#$1}}}\right)}{\text{$\#$1}^3+3 \text{$\#$1}^2 a+3 \text{$\#$1} a^2+a^3}\&\right]+\text{RootSum}\left[\text{$\#$1}^4+4 \text{$\#$1}^3 a+6 \text{$\#$1}^2 a^2+4 \text{$\#$1} a^3+a^4+a b^3\&,\frac{\text{$\#$1}^{11/4} \log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{\frac{b}{x^2}-a}\right)-\text{$\#$1}^{11/4} \log \left(\sqrt[4]{\text{$\#$1}}+\sqrt[4]{\frac{b}{x^2}-a}\right)+2 \text{$\#$1}^{11/4} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[4]{\text{$\#$1}}}\right)}{\text{$\#$1}^3+3 \text{$\#$1}^2 a+3 \text{$\#$1} a^2+a^3}\&\right]\right)}{8 b \sqrt[4]{a x^4-b x^2}}","-\frac{\text{RootSum}\left[\text{$\#$1}^{16}-4 \text{$\#$1}^{12} a+6 \text{$\#$1}^8 a^2-4 \text{$\#$1}^4 a^3+a^4+a b^3\&,\frac{\log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{8 b}",1,"-1/8*((-a + b/x^2)^(1/4)*x*(a^3*RootSum[a^4 + a*b^3 + 4*a^3*#1 + 6*a^2*#1^2 + 4*a*#1^3 + #1^4 & , ((2*ArcTan[(-a + b/x^2)^(1/4)/#1^(1/4)])/#1^(1/4) + Log[-(-a + b/x^2)^(1/4) + #1^(1/4)]/#1^(1/4) - Log[(-a + b/x^2)^(1/4) + #1^(1/4)]/#1^(1/4))/(a^3 + 3*a^2*#1 + 3*a*#1^2 + #1^3) & ] + 3*a^2*RootSum[a^4 + a*b^3 + 4*a^3*#1 + 6*a^2*#1^2 + 4*a*#1^3 + #1^4 & , (2*ArcTan[(-a + b/x^2)^(1/4)/#1^(1/4)]*#1^(3/4) + Log[-(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(3/4) - Log[(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(3/4))/(a^3 + 3*a^2*#1 + 3*a*#1^2 + #1^3) & ] + 3*a*RootSum[a^4 + a*b^3 + 4*a^3*#1 + 6*a^2*#1^2 + 4*a*#1^3 + #1^4 & , (2*ArcTan[(-a + b/x^2)^(1/4)/#1^(1/4)]*#1^(7/4) + Log[-(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(7/4) - Log[(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(7/4))/(a^3 + 3*a^2*#1 + 3*a*#1^2 + #1^3) & ] + RootSum[a^4 + a*b^3 + 4*a^3*#1 + 6*a^2*#1^2 + 4*a*#1^3 + #1^4 & , (2*ArcTan[(-a + b/x^2)^(1/4)/#1^(1/4)]*#1^(11/4) + Log[-(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(11/4) - Log[(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(11/4))/(a^3 + 3*a^2*#1 + 3*a*#1^2 + #1^3) & ]))/(b*(-(b*x^2) + a*x^4)^(1/4))","B",1
1094,1,201,81,0.8492327,"\int \frac{\left(-b^4+a^4 x^4\right) \sqrt{b^4+a^4 x^4}}{b^8+a^8 x^8} \, dx","Integrate[((-b^4 + a^4*x^4)*Sqrt[b^4 + a^4*x^4])/(b^8 + a^8*x^8),x]","-\frac{i \sqrt{\frac{a^4 x^4}{b^4}+1} \left(2 F\left(\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)-\Pi \left(-\sqrt[4]{-1};\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)-\Pi \left(\sqrt[4]{-1};\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)-\Pi \left(-(-1)^{3/4};\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)-\Pi \left((-1)^{3/4};\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)\right)}{2 \sqrt{\frac{i a^2}{b^2}} \sqrt{a^4 x^4+b^4}}","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} a b x}{\sqrt{a^4 x^4+b^4}}\right)}{2 \sqrt[4]{2} a b}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} a b x}{\sqrt{a^4 x^4+b^4}}\right)}{2 \sqrt[4]{2} a b}",1,"((-1/2*I)*Sqrt[1 + (a^4*x^4)/b^4]*(2*EllipticF[I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] - EllipticPi[-(-1)^(1/4), I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] - EllipticPi[(-1)^(1/4), I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] - EllipticPi[-(-1)^(3/4), I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] - EllipticPi[(-1)^(3/4), I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1]))/(Sqrt[(I*a^2)/b^2]*Sqrt[b^4 + a^4*x^4])","C",1
1095,1,201,81,0.5635169,"\int \frac{-b^8+a^8 x^8}{\sqrt{b^4+a^4 x^4} \left(b^8+a^8 x^8\right)} \, dx","Integrate[(-b^8 + a^8*x^8)/(Sqrt[b^4 + a^4*x^4]*(b^8 + a^8*x^8)),x]","-\frac{i \sqrt{\frac{a^4 x^4}{b^4}+1} \left(2 F\left(\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)-\Pi \left(-\sqrt[4]{-1};\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)-\Pi \left(\sqrt[4]{-1};\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)-\Pi \left(-(-1)^{3/4};\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)-\Pi \left((-1)^{3/4};\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)\right)}{2 \sqrt{\frac{i a^2}{b^2}} \sqrt{a^4 x^4+b^4}}","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} a b x}{\sqrt{a^4 x^4+b^4}}\right)}{2 \sqrt[4]{2} a b}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} a b x}{\sqrt{a^4 x^4+b^4}}\right)}{2 \sqrt[4]{2} a b}",1,"((-1/2*I)*Sqrt[1 + (a^4*x^4)/b^4]*(2*EllipticF[I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] - EllipticPi[-(-1)^(1/4), I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] - EllipticPi[(-1)^(1/4), I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] - EllipticPi[-(-1)^(3/4), I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] - EllipticPi[(-1)^(3/4), I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1]))/(Sqrt[(I*a^2)/b^2]*Sqrt[b^4 + a^4*x^4])","C",1
1096,0,0,81,0.093424,"\int \frac{\sqrt{b+\sqrt{b^2+a x^2}}}{\left(b^2+a x^2\right)^{3/2}} \, dx","Integrate[Sqrt[b + Sqrt[b^2 + a*x^2]]/(b^2 + a*x^2)^(3/2),x]","\int \frac{\sqrt{b+\sqrt{b^2+a x^2}}}{\left(b^2+a x^2\right)^{3/2}} \, dx","\frac{x}{b \sqrt{a x^2+b^2} \sqrt{\sqrt{a x^2+b^2}+b}}+\frac{\tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b} \sqrt{\sqrt{a x^2+b^2}+b}}\right)}{\sqrt{a} b^{3/2}}",1,"Integrate[Sqrt[b + Sqrt[b^2 + a*x^2]]/(b^2 + a*x^2)^(3/2), x]","F",-1
1097,1,47,81,0.024389,"\int \frac{\sqrt{a x^2+\sqrt{b+a^2 x^4}}}{\sqrt{b+a^2 x^4}} \, dx","Integrate[Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/Sqrt[b + a^2*x^4],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} x}{\sqrt{\sqrt{a^2 x^4+b}+a x^2}}\right)}{\sqrt{2} \sqrt{a}}","\frac{\log \left(i a^{3/2} x^2+i \sqrt{a} \sqrt{a^2 x^4+b}+i \sqrt{2} a x \sqrt{\sqrt{a^2 x^4+b}+a x^2}\right)}{\sqrt{2} \sqrt{a}}",1,"ArcTanh[(Sqrt[2]*Sqrt[a]*x)/Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]]/(Sqrt[2]*Sqrt[a])","A",1
1098,1,167,82,0.2100519,"\int \frac{1}{\sqrt[3]{-b x^2+a x^3} \left(-b+a x^4\right)} \, dx","Integrate[1/((-(b*x^2) + a*x^3)^(1/3)*(-b + a*x^4)),x]","-\frac{3 x \left(\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a x-\sqrt[4]{a} b^{3/4} x}{a x-b}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a x-i \sqrt[4]{a} b^{3/4} x}{a x-b}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a x+i \sqrt[4]{a} b^{3/4} x}{a x-b}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a x+\sqrt[4]{a} b^{3/4} x}{a x-b}\right)\right)}{4 b \sqrt[3]{x^2 (a x-b)}}","\frac{\text{RootSum}\left[\text{$\#$1}^{12}-4 \text{$\#$1}^9 a+6 \text{$\#$1}^6 a^2-4 \text{$\#$1}^3 a^3+a^4-a b^3\&,\frac{\log \left(\sqrt[3]{a x^3-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{4 b}",1,"(-3*x*(Hypergeometric2F1[1/3, 1, 4/3, (a*x - a^(1/4)*b^(3/4)*x)/(-b + a*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*x - I*a^(1/4)*b^(3/4)*x)/(-b + a*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*x + I*a^(1/4)*b^(3/4)*x)/(-b + a*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*x + a^(1/4)*b^(3/4)*x)/(-b + a*x)]))/(4*b*(x^2*(-b + a*x))^(1/3))","C",1
1099,1,167,82,0.0709459,"\int \frac{1}{\sqrt[3]{-b x^2+a x^3} \left(-b+a x^4\right)} \, dx","Integrate[1/((-(b*x^2) + a*x^3)^(1/3)*(-b + a*x^4)),x]","-\frac{3 x \left(\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a x-\sqrt[4]{a} b^{3/4} x}{a x-b}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a x-i \sqrt[4]{a} b^{3/4} x}{a x-b}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a x+i \sqrt[4]{a} b^{3/4} x}{a x-b}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a x+\sqrt[4]{a} b^{3/4} x}{a x-b}\right)\right)}{4 b \sqrt[3]{x^2 (a x-b)}}","\frac{\text{RootSum}\left[\text{$\#$1}^{12}-4 \text{$\#$1}^9 a+6 \text{$\#$1}^6 a^2-4 \text{$\#$1}^3 a^3+a^4-a b^3\&,\frac{\log \left(\sqrt[3]{a x^3-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{4 b}",1,"(-3*x*(Hypergeometric2F1[1/3, 1, 4/3, (a*x - a^(1/4)*b^(3/4)*x)/(-b + a*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*x - I*a^(1/4)*b^(3/4)*x)/(-b + a*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*x + I*a^(1/4)*b^(3/4)*x)/(-b + a*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*x + a^(1/4)*b^(3/4)*x)/(-b + a*x)]))/(4*b*(x^2*(-b + a*x))^(1/3))","C",1
1100,1,194,82,0.3670265,"\int \frac{\sqrt[4]{-b x^3+a x^4}}{x \left(b+a x^3\right)} \, dx","Integrate[(-(b*x^3) + a*x^4)^(1/4)/(x*(b + a*x^3)),x]","\frac{4 \sqrt[4]{x^3 (a x-b)} \left(\left(a^{2/3}+b^{2/3}\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{a x+\sqrt[3]{a} b^{2/3} x}{a x-b}\right)+\left((-1)^{2/3} a^{2/3}+b^{2/3}\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{\sqrt[3]{-1} \sqrt[3]{a} b^{2/3} x-a x}{b-a x}\right)+\left(b^{2/3}-\sqrt[3]{-1} a^{2/3}\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{a x+(-1)^{2/3} \sqrt[3]{a} b^{2/3} x}{a x-b}\right)\right)}{9 b^{2/3} (b-a x)}","\frac{1}{3} \text{RootSum}\left[-\text{$\#$1}^{12}+3 \text{$\#$1}^8 a-3 \text{$\#$1}^4 a^2+a^3+a b^2\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{a x^4-b x^3}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^4-a}\&\right]",1,"(4*(x^3*(-b + a*x))^(1/4)*((a^(2/3) + b^(2/3))*Hypergeometric2F1[3/4, 1, 7/4, (a*x + a^(1/3)*b^(2/3)*x)/(-b + a*x)] + ((-1)^(2/3)*a^(2/3) + b^(2/3))*Hypergeometric2F1[3/4, 1, 7/4, (-(a*x) + (-1)^(1/3)*a^(1/3)*b^(2/3)*x)/(b - a*x)] + (-((-1)^(1/3)*a^(2/3)) + b^(2/3))*Hypergeometric2F1[3/4, 1, 7/4, (a*x + (-1)^(2/3)*a^(1/3)*b^(2/3)*x)/(-b + a*x)]))/(9*b^(2/3)*(b - a*x))","B",1
1101,1,194,82,0.1112621,"\int \frac{\sqrt[4]{-b x^3+a x^4}}{x \left(b+a x^3\right)} \, dx","Integrate[(-(b*x^3) + a*x^4)^(1/4)/(x*(b + a*x^3)),x]","\frac{4 \sqrt[4]{x^3 (a x-b)} \left(\left(a^{2/3}+b^{2/3}\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{a x+\sqrt[3]{a} b^{2/3} x}{a x-b}\right)+\left((-1)^{2/3} a^{2/3}+b^{2/3}\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{\sqrt[3]{-1} \sqrt[3]{a} b^{2/3} x-a x}{b-a x}\right)+\left(b^{2/3}-\sqrt[3]{-1} a^{2/3}\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{a x+(-1)^{2/3} \sqrt[3]{a} b^{2/3} x}{a x-b}\right)\right)}{9 b^{2/3} (b-a x)}","\frac{1}{3} \text{RootSum}\left[-\text{$\#$1}^{12}+3 \text{$\#$1}^8 a-3 \text{$\#$1}^4 a^2+a^3+a b^2\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{a x^4-b x^3}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^4-a}\&\right]",1,"(4*(x^3*(-b + a*x))^(1/4)*((a^(2/3) + b^(2/3))*Hypergeometric2F1[3/4, 1, 7/4, (a*x + a^(1/3)*b^(2/3)*x)/(-b + a*x)] + ((-1)^(2/3)*a^(2/3) + b^(2/3))*Hypergeometric2F1[3/4, 1, 7/4, (-(a*x) + (-1)^(1/3)*a^(1/3)*b^(2/3)*x)/(b - a*x)] + (-((-1)^(1/3)*a^(2/3)) + b^(2/3))*Hypergeometric2F1[3/4, 1, 7/4, (a*x + (-1)^(2/3)*a^(1/3)*b^(2/3)*x)/(-b + a*x)]))/(9*b^(2/3)*(b - a*x))","B",1
1102,1,46,82,0.0152492,"\int \frac{\sqrt[4]{b x^3+a x^4}}{x} \, dx","Integrate[(b*x^3 + a*x^4)^(1/4)/x,x]","\frac{4 \sqrt[4]{x^3 (a x+b)} \, _2F_1\left(-\frac{1}{4},\frac{3}{4};\frac{7}{4};-\frac{a x}{b}\right)}{3 \sqrt[4]{\frac{a x}{b}+1}}","-\frac{b \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)}{2 a^{3/4}}+\frac{b \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)}{2 a^{3/4}}+\sqrt[4]{a x^4+b x^3}",1,"(4*(x^3*(b + a*x))^(1/4)*Hypergeometric2F1[-1/4, 3/4, 7/4, -((a*x)/b)])/(3*(1 + (a*x)/b)^(1/4))","C",1
1103,1,60,82,0.0290121,"\int \frac{(-b+a x) \sqrt[4]{b x^3+a x^4}}{x (b+a x)} \, dx","Integrate[((-b + a*x)*(b*x^3 + a*x^4)^(1/4))/(x*(b + a*x)),x]","\frac{x^3 \left(3 (a x+b)-7 b \left(\frac{a x}{b}+1\right)^{3/4} \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};-\frac{a x}{b}\right)\right)}{3 \left(x^3 (a x+b)\right)^{3/4}}","\frac{7 b \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)}{2 a^{3/4}}-\frac{7 b \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)}{2 a^{3/4}}+\sqrt[4]{a x^4+b x^3}",1,"(x^3*(3*(b + a*x) - 7*b*(1 + (a*x)/b)^(3/4)*Hypergeometric2F1[3/4, 3/4, 7/4, -((a*x)/b)]))/(3*(x^3*(b + a*x))^(3/4))","C",1
1104,0,0,82,0.2032759,"\int \frac{-1+3 x^4}{\left(1-x+x^4\right) \sqrt[3]{x^2+x^6}} \, dx","Integrate[(-1 + 3*x^4)/((1 - x + x^4)*(x^2 + x^6)^(1/3)),x]","\int \frac{-1+3 x^4}{\left(1-x+x^4\right) \sqrt[3]{x^2+x^6}} \, dx","\log \left(\sqrt[3]{x^6+x^2}-x\right)-\frac{1}{2} \log \left(x^2+\sqrt[3]{x^6+x^2} x+\left(x^6+x^2\right)^{2/3}\right)-\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^6+x^2}+x}\right)",1,"Integrate[(-1 + 3*x^4)/((1 - x + x^4)*(x^2 + x^6)^(1/3)), x]","F",-1
1105,1,666,82,2.4652885,"\int \frac{1}{\sqrt[4]{-b x^2+a x^4} \left(-b+a x^8\right)} \, dx","Integrate[1/((-(b*x^2) + a*x^4)^(1/4)*(-b + a*x^8)),x]","\frac{x \sqrt[4]{\frac{b}{x^2}-a} \left(a^3 \text{RootSum}\left[\text{$\#$1}^4+4 \text{$\#$1}^3 a+6 \text{$\#$1}^2 a^2+4 \text{$\#$1} a^3+a^4-a b^3\&,\frac{\frac{\log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{\frac{b}{x^2}-a}\right)}{\sqrt[4]{\text{$\#$1}}}-\frac{\log \left(\sqrt[4]{\text{$\#$1}}+\sqrt[4]{\frac{b}{x^2}-a}\right)}{\sqrt[4]{\text{$\#$1}}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[4]{\text{$\#$1}}}\right)}{\sqrt[4]{\text{$\#$1}}}}{\text{$\#$1}^3+3 \text{$\#$1}^2 a+3 \text{$\#$1} a^2+a^3}\&\right]+3 a^2 \text{RootSum}\left[\text{$\#$1}^4+4 \text{$\#$1}^3 a+6 \text{$\#$1}^2 a^2+4 \text{$\#$1} a^3+a^4-a b^3\&,\frac{\text{$\#$1}^{3/4} \log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{\frac{b}{x^2}-a}\right)-\text{$\#$1}^{3/4} \log \left(\sqrt[4]{\text{$\#$1}}+\sqrt[4]{\frac{b}{x^2}-a}\right)+2 \text{$\#$1}^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[4]{\text{$\#$1}}}\right)}{\text{$\#$1}^3+3 \text{$\#$1}^2 a+3 \text{$\#$1} a^2+a^3}\&\right]+3 a \text{RootSum}\left[\text{$\#$1}^4+4 \text{$\#$1}^3 a+6 \text{$\#$1}^2 a^2+4 \text{$\#$1} a^3+a^4-a b^3\&,\frac{\text{$\#$1}^{7/4} \log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{\frac{b}{x^2}-a}\right)-\text{$\#$1}^{7/4} \log \left(\sqrt[4]{\text{$\#$1}}+\sqrt[4]{\frac{b}{x^2}-a}\right)+2 \text{$\#$1}^{7/4} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[4]{\text{$\#$1}}}\right)}{\text{$\#$1}^3+3 \text{$\#$1}^2 a+3 \text{$\#$1} a^2+a^3}\&\right]+\text{RootSum}\left[\text{$\#$1}^4+4 \text{$\#$1}^3 a+6 \text{$\#$1}^2 a^2+4 \text{$\#$1} a^3+a^4-a b^3\&,\frac{\text{$\#$1}^{11/4} \log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{\frac{b}{x^2}-a}\right)-\text{$\#$1}^{11/4} \log \left(\sqrt[4]{\text{$\#$1}}+\sqrt[4]{\frac{b}{x^2}-a}\right)+2 \text{$\#$1}^{11/4} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[4]{\text{$\#$1}}}\right)}{\text{$\#$1}^3+3 \text{$\#$1}^2 a+3 \text{$\#$1} a^2+a^3}\&\right]\right)}{8 b \sqrt[4]{a x^4-b x^2}}","\frac{\text{RootSum}\left[\text{$\#$1}^{16}-4 \text{$\#$1}^{12} a+6 \text{$\#$1}^8 a^2-4 \text{$\#$1}^4 a^3+a^4-a b^3\&,\frac{\log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{8 b}",1,"((-a + b/x^2)^(1/4)*x*(a^3*RootSum[a^4 - a*b^3 + 4*a^3*#1 + 6*a^2*#1^2 + 4*a*#1^3 + #1^4 & , ((2*ArcTan[(-a + b/x^2)^(1/4)/#1^(1/4)])/#1^(1/4) + Log[-(-a + b/x^2)^(1/4) + #1^(1/4)]/#1^(1/4) - Log[(-a + b/x^2)^(1/4) + #1^(1/4)]/#1^(1/4))/(a^3 + 3*a^2*#1 + 3*a*#1^2 + #1^3) & ] + 3*a^2*RootSum[a^4 - a*b^3 + 4*a^3*#1 + 6*a^2*#1^2 + 4*a*#1^3 + #1^4 & , (2*ArcTan[(-a + b/x^2)^(1/4)/#1^(1/4)]*#1^(3/4) + Log[-(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(3/4) - Log[(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(3/4))/(a^3 + 3*a^2*#1 + 3*a*#1^2 + #1^3) & ] + 3*a*RootSum[a^4 - a*b^3 + 4*a^3*#1 + 6*a^2*#1^2 + 4*a*#1^3 + #1^4 & , (2*ArcTan[(-a + b/x^2)^(1/4)/#1^(1/4)]*#1^(7/4) + Log[-(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(7/4) - Log[(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(7/4))/(a^3 + 3*a^2*#1 + 3*a*#1^2 + #1^3) & ] + RootSum[a^4 - a*b^3 + 4*a^3*#1 + 6*a^2*#1^2 + 4*a*#1^3 + #1^4 & , (2*ArcTan[(-a + b/x^2)^(1/4)/#1^(1/4)]*#1^(11/4) + Log[-(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(11/4) - Log[(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(11/4))/(a^3 + 3*a^2*#1 + 3*a*#1^2 + #1^3) & ]))/(8*b*(-(b*x^2) + a*x^4)^(1/4))","B",1
1106,1,666,82,0.7284819,"\int \frac{1}{\sqrt[4]{-b x^2+a x^4} \left(-b+a x^8\right)} \, dx","Integrate[1/((-(b*x^2) + a*x^4)^(1/4)*(-b + a*x^8)),x]","\frac{x \sqrt[4]{\frac{b}{x^2}-a} \left(a^3 \text{RootSum}\left[\text{$\#$1}^4+4 \text{$\#$1}^3 a+6 \text{$\#$1}^2 a^2+4 \text{$\#$1} a^3+a^4-a b^3\&,\frac{\frac{\log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{\frac{b}{x^2}-a}\right)}{\sqrt[4]{\text{$\#$1}}}-\frac{\log \left(\sqrt[4]{\text{$\#$1}}+\sqrt[4]{\frac{b}{x^2}-a}\right)}{\sqrt[4]{\text{$\#$1}}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[4]{\text{$\#$1}}}\right)}{\sqrt[4]{\text{$\#$1}}}}{\text{$\#$1}^3+3 \text{$\#$1}^2 a+3 \text{$\#$1} a^2+a^3}\&\right]+3 a^2 \text{RootSum}\left[\text{$\#$1}^4+4 \text{$\#$1}^3 a+6 \text{$\#$1}^2 a^2+4 \text{$\#$1} a^3+a^4-a b^3\&,\frac{\text{$\#$1}^{3/4} \log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{\frac{b}{x^2}-a}\right)-\text{$\#$1}^{3/4} \log \left(\sqrt[4]{\text{$\#$1}}+\sqrt[4]{\frac{b}{x^2}-a}\right)+2 \text{$\#$1}^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[4]{\text{$\#$1}}}\right)}{\text{$\#$1}^3+3 \text{$\#$1}^2 a+3 \text{$\#$1} a^2+a^3}\&\right]+3 a \text{RootSum}\left[\text{$\#$1}^4+4 \text{$\#$1}^3 a+6 \text{$\#$1}^2 a^2+4 \text{$\#$1} a^3+a^4-a b^3\&,\frac{\text{$\#$1}^{7/4} \log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{\frac{b}{x^2}-a}\right)-\text{$\#$1}^{7/4} \log \left(\sqrt[4]{\text{$\#$1}}+\sqrt[4]{\frac{b}{x^2}-a}\right)+2 \text{$\#$1}^{7/4} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[4]{\text{$\#$1}}}\right)}{\text{$\#$1}^3+3 \text{$\#$1}^2 a+3 \text{$\#$1} a^2+a^3}\&\right]+\text{RootSum}\left[\text{$\#$1}^4+4 \text{$\#$1}^3 a+6 \text{$\#$1}^2 a^2+4 \text{$\#$1} a^3+a^4-a b^3\&,\frac{\text{$\#$1}^{11/4} \log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{\frac{b}{x^2}-a}\right)-\text{$\#$1}^{11/4} \log \left(\sqrt[4]{\text{$\#$1}}+\sqrt[4]{\frac{b}{x^2}-a}\right)+2 \text{$\#$1}^{11/4} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[4]{\text{$\#$1}}}\right)}{\text{$\#$1}^3+3 \text{$\#$1}^2 a+3 \text{$\#$1} a^2+a^3}\&\right]\right)}{8 b \sqrt[4]{a x^4-b x^2}}","\frac{\text{RootSum}\left[\text{$\#$1}^{16}-4 \text{$\#$1}^{12} a+6 \text{$\#$1}^8 a^2-4 \text{$\#$1}^4 a^3+a^4-a b^3\&,\frac{\log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{8 b}",1,"((-a + b/x^2)^(1/4)*x*(a^3*RootSum[a^4 - a*b^3 + 4*a^3*#1 + 6*a^2*#1^2 + 4*a*#1^3 + #1^4 & , ((2*ArcTan[(-a + b/x^2)^(1/4)/#1^(1/4)])/#1^(1/4) + Log[-(-a + b/x^2)^(1/4) + #1^(1/4)]/#1^(1/4) - Log[(-a + b/x^2)^(1/4) + #1^(1/4)]/#1^(1/4))/(a^3 + 3*a^2*#1 + 3*a*#1^2 + #1^3) & ] + 3*a^2*RootSum[a^4 - a*b^3 + 4*a^3*#1 + 6*a^2*#1^2 + 4*a*#1^3 + #1^4 & , (2*ArcTan[(-a + b/x^2)^(1/4)/#1^(1/4)]*#1^(3/4) + Log[-(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(3/4) - Log[(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(3/4))/(a^3 + 3*a^2*#1 + 3*a*#1^2 + #1^3) & ] + 3*a*RootSum[a^4 - a*b^3 + 4*a^3*#1 + 6*a^2*#1^2 + 4*a*#1^3 + #1^4 & , (2*ArcTan[(-a + b/x^2)^(1/4)/#1^(1/4)]*#1^(7/4) + Log[-(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(7/4) - Log[(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(7/4))/(a^3 + 3*a^2*#1 + 3*a*#1^2 + #1^3) & ] + RootSum[a^4 - a*b^3 + 4*a^3*#1 + 6*a^2*#1^2 + 4*a*#1^3 + #1^4 & , (2*ArcTan[(-a + b/x^2)^(1/4)/#1^(1/4)]*#1^(11/4) + Log[-(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(11/4) - Log[(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(11/4))/(a^3 + 3*a^2*#1 + 3*a*#1^2 + #1^3) & ]))/(8*b*(-(b*x^2) + a*x^4)^(1/4))","B",1
1107,1,82,82,0.075792,"\int \frac{-b+a x^8}{x^2 \left(b+a x^4\right)^{3/4}} \, dx","Integrate[(-b + a*x^8)/(x^2*(b + a*x^4)^(3/4)),x]","\frac{2 a^{3/4} \left(x^4+4\right) \sqrt[4]{a x^4+b}+3 b x \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)-3 b x \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{8 a^{3/4} x}","\frac{3 b \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{8 a^{3/4}}-\frac{3 b \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{8 a^{3/4}}+\frac{\left(x^4+4\right) \sqrt[4]{a x^4+b}}{4 x}",1,"(2*a^(3/4)*(4 + x^4)*(b + a*x^4)^(1/4) + 3*b*x*ArcTan[(a^(1/4)*x)/(b + a*x^4)^(1/4)] - 3*b*x*ArcTanh[(a^(1/4)*x)/(b + a*x^4)^(1/4)])/(8*a^(3/4)*x)","A",1
1108,0,0,82,0.3966417,"\int \frac{x^5 \left(-4 b+5 a x^2\right)}{\sqrt[4]{-b+a x^2} \left(b-b x^8+a x^{10}\right)} \, dx","Integrate[(x^5*(-4*b + 5*a*x^2))/((-b + a*x^2)^(1/4)*(b - b*x^8 + a*x^10)),x]","\int \frac{x^5 \left(-4 b+5 a x^2\right)}{\sqrt[4]{-b+a x^2} \left(b-b x^8+a x^{10}\right)} \, dx","\frac{1}{2} a \text{RootSum}\left[\text{$\#$1}^{20}+4 \text{$\#$1}^{16} b+6 \text{$\#$1}^{12} b^2+4 \text{$\#$1}^8 b^3+\text{$\#$1}^4 b^4+a^4 b\&,\frac{\log \left(\sqrt[4]{a x^2-b}-\text{$\#$1}\right)}{\text{$\#$1}^5+\text{$\#$1} b}\&\right]",1,"Integrate[(x^5*(-4*b + 5*a*x^2))/((-b + a*x^2)^(1/4)*(b - b*x^8 + a*x^10)), x]","F",-1
1109,1,34,83,0.0067311,"\int \frac{1}{\sqrt[3]{x^2+x^3}} \, dx","Integrate[(x^2 + x^3)^(-1/3),x]","\frac{3 x \sqrt[3]{x+1} \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};-x\right)}{\sqrt[3]{x^2 (x+1)}}","-\log \left(\sqrt[3]{x^3+x^2}-x\right)+\frac{1}{2} \log \left(x^2+\sqrt[3]{x^3+x^2} x+\left(x^3+x^2\right)^{2/3}\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+x^2}+x}\right)",1,"(3*x*(1 + x)^(1/3)*Hypergeometric2F1[1/3, 1/3, 4/3, -x])/(x^2*(1 + x))^(1/3)","C",1
1110,0,0,83,1.8396489,"\int \frac{a-3 b+2 x}{\sqrt[4]{(-a+x) (-b+x)} \left(-a^3+b d-\left(-3 a^2+d\right) x-3 a x^2+x^3\right)} \, dx","Integrate[(a - 3*b + 2*x)/(((-a + x)*(-b + x))^(1/4)*(-a^3 + b*d - (-3*a^2 + d)*x - 3*a*x^2 + x^3)),x]","\int \frac{a-3 b+2 x}{\sqrt[4]{(-a+x) (-b+x)} \left(-a^3+b d-\left(-3 a^2+d\right) x-3 a x^2+x^3\right)} \, dx","\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{x (-a-b)+a b+x^2}}{a-x}\right)}{d^{3/4}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{x (-a-b)+a b+x^2}}{a-x}\right)}{d^{3/4}}",1,"Integrate[(a - 3*b + 2*x)/(((-a + x)*(-b + x))^(1/4)*(-a^3 + b*d - (-3*a^2 + d)*x - 3*a*x^2 + x^3)), x]","F",-1
1111,0,0,83,0.774539,"\int \frac{(a-3 b+2 x) \left(a^2-2 a x+x^2\right)}{((-a+x) (-b+x))^{3/4} \left(-b+a^3 d+\left(1-3 a^2 d\right) x+3 a d x^2-d x^3\right)} \, dx","Integrate[((a - 3*b + 2*x)*(a^2 - 2*a*x + x^2))/(((-a + x)*(-b + x))^(3/4)*(-b + a^3*d + (1 - 3*a^2*d)*x + 3*a*d*x^2 - d*x^3)),x]","\int \frac{(a-3 b+2 x) \left(a^2-2 a x+x^2\right)}{((-a+x) (-b+x))^{3/4} \left(-b+a^3 d+\left(1-3 a^2 d\right) x+3 a d x^2-d x^3\right)} \, dx","\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \left(x (-a-b)+a b+x^2\right)^{3/4}}{b-x}\right)}{d^{3/4}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \left(x (-a-b)+a b+x^2\right)^{3/4}}{b-x}\right)}{d^{3/4}}",1,"Integrate[((a - 3*b + 2*x)*(a^2 - 2*a*x + x^2))/(((-a + x)*(-b + x))^(3/4)*(-b + a^3*d + (1 - 3*a^2*d)*x + 3*a*d*x^2 - d*x^3)), x]","F",-1
1112,0,0,83,3.750518,"\int \frac{-1-2 (-1+k) x+k x^2}{\sqrt[4]{(1-x) x (1-k x)} \left(-1+(d+3 k) x-\left(d+3 k^2\right) x^2+k^3 x^3\right)} \, dx","Integrate[(-1 - 2*(-1 + k)*x + k*x^2)/(((1 - x)*x*(1 - k*x))^(1/4)*(-1 + (d + 3*k)*x - (d + 3*k^2)*x^2 + k^3*x^3)),x]","\int \frac{-1-2 (-1+k) x+k x^2}{\sqrt[4]{(1-x) x (1-k x)} \left(-1+(d+3 k) x-\left(d+3 k^2\right) x^2+k^3 x^3\right)} \, dx","\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{k x^3+(-k-1) x^2+x}}{k x-1}\right)}{d^{3/4}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{k x^3+(-k-1) x^2+x}}{k x-1}\right)}{d^{3/4}}",1,"Integrate[(-1 - 2*(-1 + k)*x + k*x^2)/(((1 - x)*x*(1 - k*x))^(1/4)*(-1 + (d + 3*k)*x - (d + 3*k^2)*x^2 + k^3*x^3)), x]","F",-1
1113,1,89,83,0.0212461,"\int \frac{\sqrt{1+6 x^2+x^4}}{x \left(1+x^2\right)} \, dx","Integrate[Sqrt[1 + 6*x^2 + x^4]/(x*(1 + x^2)),x]","-\tan ^{-1}\left(\frac{4-4 x^2}{4 \sqrt{x^4+6 x^2+1}}\right)+\frac{1}{2} \tanh ^{-1}\left(\frac{2 x^2+6}{2 \sqrt{x^4+6 x^2+1}}\right)-\frac{1}{2} \tanh ^{-1}\left(\frac{6 x^2+2}{2 \sqrt{x^4+6 x^2+1}}\right)","-\frac{1}{2} \log \left(-x^2+\sqrt{x^4+6 x^2+1}+1\right)-2 \tan ^{-1}\left(\frac{x^2}{2}-\frac{1}{2} \sqrt{x^4+6 x^2+1}+\frac{1}{2}\right)-\tanh ^{-1}\left(x^2-\sqrt{x^4+6 x^2+1}+2\right)",1,"-ArcTan[(4 - 4*x^2)/(4*Sqrt[1 + 6*x^2 + x^4])] + ArcTanh[(6 + 2*x^2)/(2*Sqrt[1 + 6*x^2 + x^4])]/2 - ArcTanh[(2 + 6*x^2)/(2*Sqrt[1 + 6*x^2 + x^4])]/2","A",1
1114,0,0,83,0.4227667,"\int \frac{\left(-1+x^2\right) \sqrt[4]{-1+2 x^2+2 x^4}}{x^2 \left(-1+2 x^2\right)} \, dx","Integrate[((-1 + x^2)*(-1 + 2*x^2 + 2*x^4)^(1/4))/(x^2*(-1 + 2*x^2)),x]","\int \frac{\left(-1+x^2\right) \sqrt[4]{-1+2 x^2+2 x^4}}{x^2 \left(-1+2 x^2\right)} \, dx","-\frac{\sqrt[4]{2 x^4+2 x^2-1}}{x}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{2 x^4+2 x^2-1}}\right)}{2^{3/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{2 x^4+2 x^2-1}}\right)}{2^{3/4}}",1,"Integrate[((-1 + x^2)*(-1 + 2*x^2 + 2*x^4)^(1/4))/(x^2*(-1 + 2*x^2)), x]","F",-1
1115,1,66,83,0.0292567,"\int \frac{1}{\sqrt[4]{b+a x^4} \left(2 b+a x^4\right)} \, dx","Integrate[1/((b + a*x^4)^(1/4)*(2*b + a*x^4)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{2} \sqrt[4]{a x^4+b}}\right)+\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{2} \sqrt[4]{a x^4+b}}\right)}{2\ 2^{3/4} \sqrt[4]{a} b}","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{2} \sqrt[4]{a x^4+b}}\right)}{2\ 2^{3/4} \sqrt[4]{a} b}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{2} \sqrt[4]{a x^4+b}}\right)}{2\ 2^{3/4} \sqrt[4]{a} b}",1,"(ArcTan[(a^(1/4)*x)/(2^(1/4)*(b + a*x^4)^(1/4))] + ArcTanh[(a^(1/4)*x)/(2^(1/4)*(b + a*x^4)^(1/4))])/(2*2^(3/4)*a^(1/4)*b)","A",1
1116,1,54,83,0.0198615,"\int \frac{\sqrt[4]{-b x^2+a x^4}}{x^2} \, dx","Integrate[(-(b*x^2) + a*x^4)^(1/4)/x^2,x]","-\frac{2 \sqrt[4]{a x^4-b x^2} \, _2F_1\left(-\frac{1}{4},-\frac{1}{4};\frac{3}{4};\frac{a x^2}{b}\right)}{x \sqrt[4]{1-\frac{a x^2}{b}}}","-\frac{2 \sqrt[4]{a x^4-b x^2}}{x}-\sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)+\sqrt[4]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)",1,"(-2*(-(b*x^2) + a*x^4)^(1/4)*Hypergeometric2F1[-1/4, -1/4, 3/4, (a*x^2)/b])/(x*(1 - (a*x^2)/b)^(1/4))","C",1
1117,1,670,83,2.8482846,"\int \frac{1}{\sqrt[4]{-b x^2+a x^4} \left(a+b x^8\right)} \, dx","Integrate[1/((-(b*x^2) + a*x^4)^(1/4)*(a + b*x^8)),x]","-\frac{x \sqrt[4]{\frac{b}{x^2}-a} \left(a^3 \text{RootSum}\left[\text{$\#$1}^4 a+4 \text{$\#$1}^3 a^2+6 \text{$\#$1}^2 a^3+4 \text{$\#$1} a^4+a^5+b^5\&,\frac{\frac{\log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{\frac{b}{x^2}-a}\right)}{\sqrt[4]{\text{$\#$1}}}-\frac{\log \left(\sqrt[4]{\text{$\#$1}}+\sqrt[4]{\frac{b}{x^2}-a}\right)}{\sqrt[4]{\text{$\#$1}}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[4]{\text{$\#$1}}}\right)}{\sqrt[4]{\text{$\#$1}}}}{\text{$\#$1}^3+3 \text{$\#$1}^2 a+3 \text{$\#$1} a^2+a^3}\&\right]+3 a^2 \text{RootSum}\left[\text{$\#$1}^4 a+4 \text{$\#$1}^3 a^2+6 \text{$\#$1}^2 a^3+4 \text{$\#$1} a^4+a^5+b^5\&,\frac{\text{$\#$1}^{3/4} \log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{\frac{b}{x^2}-a}\right)-\text{$\#$1}^{3/4} \log \left(\sqrt[4]{\text{$\#$1}}+\sqrt[4]{\frac{b}{x^2}-a}\right)+2 \text{$\#$1}^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[4]{\text{$\#$1}}}\right)}{\text{$\#$1}^3+3 \text{$\#$1}^2 a+3 \text{$\#$1} a^2+a^3}\&\right]+3 a \text{RootSum}\left[\text{$\#$1}^4 a+4 \text{$\#$1}^3 a^2+6 \text{$\#$1}^2 a^3+4 \text{$\#$1} a^4+a^5+b^5\&,\frac{\text{$\#$1}^{7/4} \log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{\frac{b}{x^2}-a}\right)-\text{$\#$1}^{7/4} \log \left(\sqrt[4]{\text{$\#$1}}+\sqrt[4]{\frac{b}{x^2}-a}\right)+2 \text{$\#$1}^{7/4} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[4]{\text{$\#$1}}}\right)}{\text{$\#$1}^3+3 \text{$\#$1}^2 a+3 \text{$\#$1} a^2+a^3}\&\right]+\text{RootSum}\left[\text{$\#$1}^4 a+4 \text{$\#$1}^3 a^2+6 \text{$\#$1}^2 a^3+4 \text{$\#$1} a^4+a^5+b^5\&,\frac{\text{$\#$1}^{11/4} \log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{\frac{b}{x^2}-a}\right)-\text{$\#$1}^{11/4} \log \left(\sqrt[4]{\text{$\#$1}}+\sqrt[4]{\frac{b}{x^2}-a}\right)+2 \text{$\#$1}^{11/4} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[4]{\text{$\#$1}}}\right)}{\text{$\#$1}^3+3 \text{$\#$1}^2 a+3 \text{$\#$1} a^2+a^3}\&\right]\right)}{8 a \sqrt[4]{a x^4-b x^2}}","-\frac{\text{RootSum}\left[\text{$\#$1}^{16} a-4 \text{$\#$1}^{12} a^2+6 \text{$\#$1}^8 a^3-4 \text{$\#$1}^4 a^4+a^5+b^5\&,\frac{\log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{8 a}",1,"-1/8*((-a + b/x^2)^(1/4)*x*(a^3*RootSum[a^5 + b^5 + 4*a^4*#1 + 6*a^3*#1^2 + 4*a^2*#1^3 + a*#1^4 & , ((2*ArcTan[(-a + b/x^2)^(1/4)/#1^(1/4)])/#1^(1/4) + Log[-(-a + b/x^2)^(1/4) + #1^(1/4)]/#1^(1/4) - Log[(-a + b/x^2)^(1/4) + #1^(1/4)]/#1^(1/4))/(a^3 + 3*a^2*#1 + 3*a*#1^2 + #1^3) & ] + 3*a^2*RootSum[a^5 + b^5 + 4*a^4*#1 + 6*a^3*#1^2 + 4*a^2*#1^3 + a*#1^4 & , (2*ArcTan[(-a + b/x^2)^(1/4)/#1^(1/4)]*#1^(3/4) + Log[-(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(3/4) - Log[(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(3/4))/(a^3 + 3*a^2*#1 + 3*a*#1^2 + #1^3) & ] + 3*a*RootSum[a^5 + b^5 + 4*a^4*#1 + 6*a^3*#1^2 + 4*a^2*#1^3 + a*#1^4 & , (2*ArcTan[(-a + b/x^2)^(1/4)/#1^(1/4)]*#1^(7/4) + Log[-(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(7/4) - Log[(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(7/4))/(a^3 + 3*a^2*#1 + 3*a*#1^2 + #1^3) & ] + RootSum[a^5 + b^5 + 4*a^4*#1 + 6*a^3*#1^2 + 4*a^2*#1^3 + a*#1^4 & , (2*ArcTan[(-a + b/x^2)^(1/4)/#1^(1/4)]*#1^(11/4) + Log[-(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(11/4) - Log[(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(11/4))/(a^3 + 3*a^2*#1 + 3*a*#1^2 + #1^3) & ]))/(a*(-(b*x^2) + a*x^4)^(1/4))","B",1
1118,1,670,83,0.8920888,"\int \frac{1}{\sqrt[4]{-b x^2+a x^4} \left(a+b x^8\right)} \, dx","Integrate[1/((-(b*x^2) + a*x^4)^(1/4)*(a + b*x^8)),x]","-\frac{x \sqrt[4]{\frac{b}{x^2}-a} \left(a^3 \text{RootSum}\left[\text{$\#$1}^4 a+4 \text{$\#$1}^3 a^2+6 \text{$\#$1}^2 a^3+4 \text{$\#$1} a^4+a^5+b^5\&,\frac{\frac{\log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{\frac{b}{x^2}-a}\right)}{\sqrt[4]{\text{$\#$1}}}-\frac{\log \left(\sqrt[4]{\text{$\#$1}}+\sqrt[4]{\frac{b}{x^2}-a}\right)}{\sqrt[4]{\text{$\#$1}}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[4]{\text{$\#$1}}}\right)}{\sqrt[4]{\text{$\#$1}}}}{\text{$\#$1}^3+3 \text{$\#$1}^2 a+3 \text{$\#$1} a^2+a^3}\&\right]+3 a^2 \text{RootSum}\left[\text{$\#$1}^4 a+4 \text{$\#$1}^3 a^2+6 \text{$\#$1}^2 a^3+4 \text{$\#$1} a^4+a^5+b^5\&,\frac{\text{$\#$1}^{3/4} \log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{\frac{b}{x^2}-a}\right)-\text{$\#$1}^{3/4} \log \left(\sqrt[4]{\text{$\#$1}}+\sqrt[4]{\frac{b}{x^2}-a}\right)+2 \text{$\#$1}^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[4]{\text{$\#$1}}}\right)}{\text{$\#$1}^3+3 \text{$\#$1}^2 a+3 \text{$\#$1} a^2+a^3}\&\right]+3 a \text{RootSum}\left[\text{$\#$1}^4 a+4 \text{$\#$1}^3 a^2+6 \text{$\#$1}^2 a^3+4 \text{$\#$1} a^4+a^5+b^5\&,\frac{\text{$\#$1}^{7/4} \log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{\frac{b}{x^2}-a}\right)-\text{$\#$1}^{7/4} \log \left(\sqrt[4]{\text{$\#$1}}+\sqrt[4]{\frac{b}{x^2}-a}\right)+2 \text{$\#$1}^{7/4} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[4]{\text{$\#$1}}}\right)}{\text{$\#$1}^3+3 \text{$\#$1}^2 a+3 \text{$\#$1} a^2+a^3}\&\right]+\text{RootSum}\left[\text{$\#$1}^4 a+4 \text{$\#$1}^3 a^2+6 \text{$\#$1}^2 a^3+4 \text{$\#$1} a^4+a^5+b^5\&,\frac{\text{$\#$1}^{11/4} \log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{\frac{b}{x^2}-a}\right)-\text{$\#$1}^{11/4} \log \left(\sqrt[4]{\text{$\#$1}}+\sqrt[4]{\frac{b}{x^2}-a}\right)+2 \text{$\#$1}^{11/4} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[4]{\text{$\#$1}}}\right)}{\text{$\#$1}^3+3 \text{$\#$1}^2 a+3 \text{$\#$1} a^2+a^3}\&\right]\right)}{8 a \sqrt[4]{a x^4-b x^2}}","-\frac{\text{RootSum}\left[\text{$\#$1}^{16} a-4 \text{$\#$1}^{12} a^2+6 \text{$\#$1}^8 a^3-4 \text{$\#$1}^4 a^4+a^5+b^5\&,\frac{\log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{8 a}",1,"-1/8*((-a + b/x^2)^(1/4)*x*(a^3*RootSum[a^5 + b^5 + 4*a^4*#1 + 6*a^3*#1^2 + 4*a^2*#1^3 + a*#1^4 & , ((2*ArcTan[(-a + b/x^2)^(1/4)/#1^(1/4)])/#1^(1/4) + Log[-(-a + b/x^2)^(1/4) + #1^(1/4)]/#1^(1/4) - Log[(-a + b/x^2)^(1/4) + #1^(1/4)]/#1^(1/4))/(a^3 + 3*a^2*#1 + 3*a*#1^2 + #1^3) & ] + 3*a^2*RootSum[a^5 + b^5 + 4*a^4*#1 + 6*a^3*#1^2 + 4*a^2*#1^3 + a*#1^4 & , (2*ArcTan[(-a + b/x^2)^(1/4)/#1^(1/4)]*#1^(3/4) + Log[-(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(3/4) - Log[(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(3/4))/(a^3 + 3*a^2*#1 + 3*a*#1^2 + #1^3) & ] + 3*a*RootSum[a^5 + b^5 + 4*a^4*#1 + 6*a^3*#1^2 + 4*a^2*#1^3 + a*#1^4 & , (2*ArcTan[(-a + b/x^2)^(1/4)/#1^(1/4)]*#1^(7/4) + Log[-(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(7/4) - Log[(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(7/4))/(a^3 + 3*a^2*#1 + 3*a*#1^2 + #1^3) & ] + RootSum[a^5 + b^5 + 4*a^4*#1 + 6*a^3*#1^2 + 4*a^2*#1^3 + a*#1^4 & , (2*ArcTan[(-a + b/x^2)^(1/4)/#1^(1/4)]*#1^(11/4) + Log[-(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(11/4) - Log[(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(11/4))/(a^3 + 3*a^2*#1 + 3*a*#1^2 + #1^3) & ]))/(a*(-(b*x^2) + a*x^4)^(1/4))","B",1
1119,1,76,83,0.0768472,"\int \frac{(-1+x) \sqrt{x+\sqrt{1+x}}}{\sqrt{1+x}} \, dx","Integrate[((-1 + x)*Sqrt[x + Sqrt[1 + x]])/Sqrt[1 + x],x]","\frac{1}{192} \left(2 \sqrt{x+\sqrt{x+1}} \left(8 x \left(6 \sqrt{x+1}+1\right)-178 \sqrt{x+1}-21\right)+345 \tanh ^{-1}\left(\frac{2 \sqrt{x+1}+1}{2 \sqrt{x+\sqrt{x+1}}}\right)\right)","\frac{1}{96} \sqrt{x+\sqrt{x+1}} (8 x-21)+\frac{1}{48} \sqrt{x+1} (24 x-89) \sqrt{x+\sqrt{x+1}}-\frac{115}{64} \log \left(2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)",1,"(2*Sqrt[x + Sqrt[1 + x]]*(-21 - 178*Sqrt[1 + x] + 8*x*(1 + 6*Sqrt[1 + x])) + 345*ArcTanh[(1 + 2*Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])])/192","A",1
1120,1,76,83,0.055464,"\int \frac{x \sqrt{x+\sqrt{1+x}}}{\sqrt{1+x}} \, dx","Integrate[(x*Sqrt[x + Sqrt[1 + x]])/Sqrt[1 + x],x]","\frac{1}{96} \sqrt{x+\sqrt{x+1}} \left(8 x \left(6 \sqrt{x+1}+1\right)-82 \sqrt{x+1}+27\right)+\frac{35}{64} \tanh ^{-1}\left(\frac{2 \sqrt{x+1}+1}{2 \sqrt{x+\sqrt{x+1}}}\right)","\frac{1}{96} \sqrt{x+\sqrt{x+1}} (8 x+27)+\frac{1}{48} \sqrt{x+1} (24 x-41) \sqrt{x+\sqrt{x+1}}-\frac{35}{64} \log \left(2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)",1,"(Sqrt[x + Sqrt[1 + x]]*(27 - 82*Sqrt[1 + x] + 8*x*(1 + 6*Sqrt[1 + x])))/96 + (35*ArcTanh[(1 + 2*Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])])/64","A",1
1121,1,76,83,0.043624,"\int \sqrt{1+x} \sqrt{x+\sqrt{1+x}} \, dx","Integrate[Sqrt[1 + x]*Sqrt[x + Sqrt[1 + x]],x]","\frac{1}{96} \sqrt{x+\sqrt{x+1}} \left(8 x \left(6 \sqrt{x+1}+1\right)+14 \sqrt{x+1}+75\right)-\frac{45}{64} \tanh ^{-1}\left(\frac{2 \sqrt{x+1}+1}{2 \sqrt{x+\sqrt{x+1}}}\right)","\frac{1}{96} \sqrt{x+\sqrt{x+1}} (8 x+75)+\frac{1}{48} \sqrt{x+1} (24 x+7) \sqrt{x+\sqrt{x+1}}+\frac{45}{64} \log \left(2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)",1,"(Sqrt[x + Sqrt[1 + x]]*(75 + 14*Sqrt[1 + x] + 8*x*(1 + 6*Sqrt[1 + x])))/96 - (45*ArcTanh[(1 + 2*Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])])/64","A",1
1122,1,85,83,0.05799,"\int \frac{1+\sqrt{1+x^2}}{\sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[(1 + Sqrt[1 + x^2])/Sqrt[x + Sqrt[1 + x^2]],x]","\frac{2 \left(10 x^4+5 \left(6 \sqrt{x^2+1}-1\right) x^2-10 \left(\sqrt{x^2+1}-2\right) x+5 \sqrt{x^2+1}+10 \left(\sqrt{x^2+1}+3\right) x^3-7\right)}{15 \left(\sqrt{x^2+1}+x\right)^{5/2}}","\frac{2 \sqrt{x^2+1} \left(2 x^3+6 x^2-2 x+1\right)}{3 \left(\sqrt{x^2+1}+x\right)^{5/2}}+\frac{2 \left(10 x^4+30 x^3-5 x^2+20 x-7\right)}{15 \left(\sqrt{x^2+1}+x\right)^{5/2}}",1,"(2*(-7 + 10*x^4 + 5*Sqrt[1 + x^2] - 10*x*(-2 + Sqrt[1 + x^2]) + 10*x^3*(3 + Sqrt[1 + x^2]) + 5*x^2*(-1 + 6*Sqrt[1 + x^2])))/(15*(x + Sqrt[1 + x^2])^(5/2))","A",1
1123,1,83,83,0.0206885,"\int \frac{\sqrt{1-4 x+x^2}+\left(1-4 x+x^2\right)^{3/2}}{\sqrt{1-4 x+x^2}+\left(1-4 x+x^2\right)^{3/2}-\left(1-4 x+x^2\right)^{5/2}} \, dx","Integrate[(Sqrt[1 - 4*x + x^2] + (1 - 4*x + x^2)^(3/2))/(Sqrt[1 - 4*x + x^2] + (1 - 4*x + x^2)^(3/2) - (1 - 4*x + x^2)^(5/2)),x]","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^4-8 \text{$\#$1}^3+17 \text{$\#$1}^2-4 \text{$\#$1}-1\&,\frac{\text{$\#$1}^2 \log (x-\text{$\#$1})-4 \text{$\#$1} \log (x-\text{$\#$1})+2 \log (x-\text{$\#$1})}{2 \text{$\#$1}^3-12 \text{$\#$1}^2+17 \text{$\#$1}-2}\&\right]","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^4-8 \text{$\#$1}^3+17 \text{$\#$1}^2-4 \text{$\#$1}-1\&,\frac{\text{$\#$1}^2 \log (x-\text{$\#$1})-4 \text{$\#$1} \log (x-\text{$\#$1})+2 \log (x-\text{$\#$1})}{2 \text{$\#$1}^3-12 \text{$\#$1}^2+17 \text{$\#$1}-2}\&\right]",1,"-1/2*RootSum[-1 - 4*#1 + 17*#1^2 - 8*#1^3 + #1^4 & , (2*Log[x - #1] - 4*Log[x - #1]*#1 + Log[x - #1]*#1^2)/(-2 + 17*#1 - 12*#1^2 + 2*#1^3) & ]","A",1
1124,0,0,83,0.7483736,"\int \frac{x^2}{\sqrt{-b x+a^2 x^2} \left(a x^2+x \sqrt{-b x+a^2 x^2}\right)^{3/2}} \, dx","Integrate[x^2/(Sqrt[-(b*x) + a^2*x^2]*(a*x^2 + x*Sqrt[-(b*x) + a^2*x^2])^(3/2)),x]","\int \frac{x^2}{\sqrt{-b x+a^2 x^2} \left(a x^2+x \sqrt{-b x+a^2 x^2}\right)^{3/2}} \, dx","\frac{4 \sqrt{a^2 x^2-b x} \sqrt{x \left(\sqrt{a^2 x^2-b x}+a x\right)}}{b^2 x}-\frac{4 a \sqrt{x \left(\sqrt{a^2 x^2-b x}+a x\right)}}{b^2}",1,"Integrate[x^2/(Sqrt[-(b*x) + a^2*x^2]*(a*x^2 + x*Sqrt[-(b*x) + a^2*x^2])^(3/2)), x]","F",-1
1125,1,277,84,2.5674207,"\int \frac{a^2 b-a (2 a+b) x+3 a x^2-x^3}{x (-b+x) \sqrt{x (-a+x) (-b+x)} \left(a+(-1-b d) x+d x^2\right)} \, dx","Integrate[(a^2*b - a*(2*a + b)*x + 3*a*x^2 - x^3)/(x*(-b + x)*Sqrt[x*(-a + x)*(-b + x)]*(a + (-1 - b*d)*x + d*x^2)),x]","-\frac{2 (x-a) \left(i \sqrt{\frac{x}{a}} \sqrt{\frac{x-b}{a-b}} \Pi \left(\frac{2 a d}{2 a d-b d+\sqrt{(b d+1)^2-4 a d}-1};i \sinh ^{-1}\left(\sqrt{\frac{x}{a}-1}\right)|\frac{a}{a-b}\right)+i \sqrt{\frac{x}{a}} \sqrt{\frac{x-b}{a-b}} \Pi \left(-\frac{2 a d}{-2 a d+b d+\sqrt{(b d+1)^2-4 a d}+1};i \sinh ^{-1}\left(\sqrt{\frac{x}{a}-1}\right)|\frac{a}{a-b}\right)-i \sqrt{\frac{x}{a}} \sqrt{\frac{x-b}{a-b}} F\left(i \sinh ^{-1}\left(\sqrt{\frac{x}{a}-1}\right)|\frac{a}{a-b}\right)+\sqrt{\frac{x}{a}-1}\right)}{\sqrt{\frac{x}{a}-1} \sqrt{x (x-a) (x-b)}}","2 \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{x^2 (-a-b)+a b x+x^3}}{\sqrt{d} x (x-b)}\right)+\frac{2 \sqrt{a b x-a x^2-b x^2+x^3}}{x (b-x)}",1,"(-2*(-a + x)*(Sqrt[-1 + x/a] - I*Sqrt[x/a]*Sqrt[(-b + x)/(a - b)]*EllipticF[I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)] + I*Sqrt[x/a]*Sqrt[(-b + x)/(a - b)]*EllipticPi[(2*a*d)/(-1 + 2*a*d - b*d + Sqrt[-4*a*d + (1 + b*d)^2]), I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)] + I*Sqrt[x/a]*Sqrt[(-b + x)/(a - b)]*EllipticPi[(-2*a*d)/(1 - 2*a*d + b*d + Sqrt[-4*a*d + (1 + b*d)^2]), I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)]))/(Sqrt[x*(-a + x)*(-b + x)]*Sqrt[-1 + x/a])","C",1
1126,1,59,84,0.0250619,"\int \frac{\left(1+x^3\right)^{2/3}}{x} \, dx","Integrate[(1 + x^3)^(2/3)/x,x]","\frac{1}{2} \left(\left(x^3+1\right)^{2/3}+\log \left(1-\sqrt[3]{x^3+1}\right)-\log (x)\right)+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{x^3+1}+1}{\sqrt{3}}\right)}{\sqrt{3}}","\frac{1}{2} \left(x^3+1\right)^{2/3}+\frac{1}{3} \log \left(\sqrt[3]{x^3+1}-1\right)-\frac{1}{6} \log \left(\left(x^3+1\right)^{2/3}+\sqrt[3]{x^3+1}+1\right)+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{x^3+1}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3}}",1,"ArcTan[(1 + 2*(1 + x^3)^(1/3))/Sqrt[3]]/Sqrt[3] + ((1 + x^3)^(2/3) - Log[x] + Log[1 - (1 + x^3)^(1/3)])/2","A",1
1127,1,123,84,0.1284467,"\int \frac{\left(-b+2 a x^2\right) \sqrt[4]{b x^2+a x^4}}{b+a x^2} \, dx","Integrate[((-b + 2*a*x^2)*(b*x^2 + a*x^4)^(1/4))/(b + a*x^2),x]","\frac{x^{3/2} \left(2 a^{3/4} x^{3/2} \left(a x^2+b\right)+5 b \left(a x^2+b\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)-5 b \left(a x^2+b\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)\right)}{2 a^{3/4} \left(x^2 \left(a x^2+b\right)\right)^{3/4}}","\frac{5 b \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{2 a^{3/4}}-\frac{5 b \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{2 a^{3/4}}+x \sqrt[4]{a x^4+b x^2}",1,"(x^(3/2)*(2*a^(3/4)*x^(3/2)*(b + a*x^2) + 5*b*(b + a*x^2)^(3/4)*ArcTan[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)] - 5*b*(b + a*x^2)^(3/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)]))/(2*a^(3/4)*(x^2*(b + a*x^2))^(3/4))","A",1
1128,1,345,84,1.4560569,"\int \frac{\left(-1+x^4\right) \sqrt{1+x^2+x^4} \left(1+x^2+3 x^4+x^6+x^8\right)}{\left(1+x^4\right)^3 \left(1-x^2+x^4\right)} \, dx","Integrate[((-1 + x^4)*Sqrt[1 + x^2 + x^4]*(1 + x^2 + 3*x^4 + x^6 + x^8))/((1 + x^4)^3*(1 - x^2 + x^4)),x]","\frac{\frac{x \left(x^4+x^2+1\right) \left(9 x^4+2 x^2+9\right)}{\left(x^4+1\right)^2}+\sqrt{\sqrt[3]{-1} x^2+1} \sqrt{1-(-1)^{2/3} x^2} \left(\frac{17}{2} i \left(\sqrt{3}+i\right) F\left(i \sinh ^{-1}\left((-1)^{5/6} x\right)|(-1)^{2/3}\right)-48 \left(\sqrt[3]{-1}-1\right) \Pi \left(-1;i \sinh ^{-1}\left((-1)^{5/6} x\right)|(-1)^{2/3}\right)-96 (-1)^{2/3} \Pi \left(-(-1)^{2/3};i \sinh ^{-1}\left((-1)^{5/6} x\right)|(-1)^{2/3}\right)+48 \sqrt[3]{-1} \Pi \left(-(-1)^{2/3};i \sinh ^{-1}\left((-1)^{5/6} x\right)|(-1)^{2/3}\right)-48 \Pi \left(-(-1)^{2/3};i \sinh ^{-1}\left((-1)^{5/6} x\right)|(-1)^{2/3}\right)+31 \sqrt[3]{-1} \Pi \left(-(-1)^{5/6};i \sinh ^{-1}\left((-1)^{5/6} x\right)|(-1)^{2/3}\right)-31 \Pi \left(-(-1)^{5/6};i \sinh ^{-1}\left((-1)^{5/6} x\right)|(-1)^{2/3}\right)+31 \sqrt[3]{-1} \Pi \left((-1)^{5/6};i \sinh ^{-1}\left((-1)^{5/6} x\right)|(-1)^{2/3}\right)-31 \Pi \left((-1)^{5/6};i \sinh ^{-1}\left((-1)^{5/6} x\right)|(-1)^{2/3}\right)\right)}{8 \sqrt{x^4+x^2+1}}","\frac{31}{8} \tanh ^{-1}\left(\frac{x}{\sqrt{x^4+x^2+1}}\right)-3 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+x^2+1}}\right)+\frac{\sqrt{x^4+x^2+1} \left(9 x^5+2 x^3+9 x\right)}{8 \left(x^4+1\right)^2}",1,"((x*(1 + x^2 + x^4)*(9 + 2*x^2 + 9*x^4))/(1 + x^4)^2 + Sqrt[1 + (-1)^(1/3)*x^2]*Sqrt[1 - (-1)^(2/3)*x^2]*(((17*I)/2)*(I + Sqrt[3])*EllipticF[I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)] - 48*(-1 + (-1)^(1/3))*EllipticPi[-1, I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)] - 48*EllipticPi[-(-1)^(2/3), I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)] + 48*(-1)^(1/3)*EllipticPi[-(-1)^(2/3), I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)] - 96*(-1)^(2/3)*EllipticPi[-(-1)^(2/3), I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)] - 31*EllipticPi[-(-1)^(5/6), I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)] + 31*(-1)^(1/3)*EllipticPi[-(-1)^(5/6), I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)] - 31*EllipticPi[(-1)^(5/6), I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)] + 31*(-1)^(1/3)*EllipticPi[(-1)^(5/6), I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)]))/(8*Sqrt[1 + x^2 + x^4])","C",0
1129,0,0,84,0.4310643,"\int \frac{\left(1+x^6\right) \left(-1+x^3+x^6\right) \sqrt{1+x^{12}}}{x^7 \left(-1-x^3+x^6\right)} \, dx","Integrate[((1 + x^6)*(-1 + x^3 + x^6)*Sqrt[1 + x^12])/(x^7*(-1 - x^3 + x^6)),x]","\int \frac{\left(1+x^6\right) \left(-1+x^3+x^6\right) \sqrt{1+x^{12}}}{x^7 \left(-1-x^3+x^6\right)} \, dx","\log \left(\sqrt{x^{12}+1}+x^6-1\right)+\frac{\sqrt{x^{12}+1} \left(x^6+4 x^3-1\right)}{6 x^6}-\frac{4 \tanh ^{-1}\left(\frac{\sqrt{3} x^3}{\sqrt{x^{12}+1}+x^6-x^3-1}\right)}{\sqrt{3}}-3 \log (x)",1,"Integrate[((1 + x^6)*(-1 + x^3 + x^6)*Sqrt[1 + x^12])/(x^7*(-1 - x^3 + x^6)), x]","F",-1
1130,1,43,84,0.0295216,"\int \sqrt{d+c \sqrt{b+a x}} \, dx","Integrate[Sqrt[d + c*Sqrt[b + a*x]],x]","\frac{4 \left(c \sqrt{a x+b}+d\right)^{3/2} \left(3 c \sqrt{a x+b}-2 d\right)}{15 a c^2}","\frac{4 \left(3 a c^2 x+3 b c^2-2 d^2\right) \sqrt{c \sqrt{a x+b}+d}}{15 a c^2}+\frac{4 d \sqrt{a x+b} \sqrt{c \sqrt{a x+b}+d}}{15 a c}",1,"(4*(d + c*Sqrt[b + a*x])^(3/2)*(-2*d + 3*c*Sqrt[b + a*x]))/(15*a*c^2)","A",1
1131,1,84,85,0.0229511,"\int \frac{1+2 x^2}{x \left(1+x^2\right)^{2/3}} \, dx","Integrate[(1 + 2*x^2)/(x*(1 + x^2)^(2/3)),x]","3 \sqrt[3]{x^2+1}+\frac{1}{2} \log \left(1-\sqrt[3]{x^2+1}\right)-\frac{1}{4} \log \left(\left(x^2+1\right)^{2/3}+\sqrt[3]{x^2+1}+1\right)-\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x^2+1}+1}{\sqrt{3}}\right)","3 \sqrt[3]{x^2+1}+\frac{1}{2} \log \left(\sqrt[3]{x^2+1}-1\right)-\frac{1}{4} \log \left(\left(x^2+1\right)^{2/3}+\sqrt[3]{x^2+1}+1\right)-\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x^2+1}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)",1,"3*(1 + x^2)^(1/3) - (Sqrt[3]*ArcTan[(1 + 2*(1 + x^2)^(1/3))/Sqrt[3]])/2 + Log[1 - (1 + x^2)^(1/3)]/2 - Log[1 + (1 + x^2)^(1/3) + (1 + x^2)^(2/3)]/4","A",1
1132,1,154,85,1.3861568,"\int \frac{x}{\sqrt{(1-x) x \left(1-k^2 x\right)} \left(-1+k^2 x^2\right)} \, dx","Integrate[x/(Sqrt[(1 - x)*x*(1 - k^2*x)]*(-1 + k^2*x^2)),x]","\frac{i \sqrt{x-1} x \sqrt{\frac{1-\frac{1}{k^2}}{x-1}+1} \left(2 k F\left(i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)-(k-1) \Pi \left(1+\frac{1}{k};i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)-(k+1) \Pi \left(\frac{k-1}{k};i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)\right)}{k \left(k^2-1\right) \sqrt{\frac{1}{x-1}+1} \sqrt{(x-1) x \left(k^2 x-1\right)}}","\frac{\tan ^{-1}\left(\frac{(k+1) x}{\sqrt{k^2 x^3+\left(-k^2-1\right) x^2+x}}\right)}{2 k (k+1)}-\frac{\tan ^{-1}\left(\frac{(k-1) x}{\sqrt{k^2 x^3+\left(-k^2-1\right) x^2+x}}\right)}{2 (k-1) k}",1,"(I*Sqrt[1 + (1 - k^(-2))/(-1 + x)]*Sqrt[-1 + x]*x*(2*k*EllipticF[I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)] - (-1 + k)*EllipticPi[1 + k^(-1), I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)] - (1 + k)*EllipticPi[(-1 + k)/k, I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)]))/(k*(-1 + k^2)*Sqrt[1 + (-1 + x)^(-1)]*Sqrt[(-1 + x)*x*(-1 + k^2*x)])","C",1
1133,1,89,85,0.7829235,"\int \frac{1+x}{\left(-1+2 x+x^2\right) \sqrt{-x+x^3}} \, dx","Integrate[(1 + x)/((-1 + 2*x + x^2)*Sqrt[-x + x^3]),x]","-\frac{\sqrt{1-\frac{1}{x^2}} x^{3/2} \left(-2 F\left(\left.\sin ^{-1}\left(\frac{1}{\sqrt{x}}\right)\right|-1\right)-\left(\sqrt{2}-1\right) \Pi \left(-1-\sqrt{2};\left.\sin ^{-1}\left(\frac{1}{\sqrt{x}}\right)\right|-1\right)+\left(1+\sqrt{2}\right) \Pi \left(-1+\sqrt{2};\left.\sin ^{-1}\left(\frac{1}{\sqrt{x}}\right)\right|-1\right)\right)}{\sqrt{x \left(x^2-1\right)}}","\frac{1}{4} \left(\sqrt{2}-2\right) \tan ^{-1}\left(\frac{\sqrt{3-2 \sqrt{2}} \sqrt{x^3-x}}{x+1}\right)+\frac{1}{4} \left(2+\sqrt{2}\right) \tan ^{-1}\left(\frac{\sqrt{3+2 \sqrt{2}} \sqrt{x^3-x}}{x+1}\right)",1,"-((Sqrt[1 - x^(-2)]*x^(3/2)*(-2*EllipticF[ArcSin[1/Sqrt[x]], -1] - (-1 + Sqrt[2])*EllipticPi[-1 - Sqrt[2], ArcSin[1/Sqrt[x]], -1] + (1 + Sqrt[2])*EllipticPi[-1 + Sqrt[2], ArcSin[1/Sqrt[x]], -1]))/Sqrt[x*(-1 + x^2)])","C",1
1134,1,88,85,0.7267444,"\int \frac{-x+x^2}{\left(-1+2 x+x^2\right) \sqrt{-x+x^3}} \, dx","Integrate[(-x + x^2)/((-1 + 2*x + x^2)*Sqrt[-x + x^3]),x]","\frac{\sqrt{x} \sqrt{1-x^2} \left(2 F\left(\left.\sin ^{-1}\left(\sqrt{x}\right)\right|-1\right)-\left(1+\sqrt{2}\right) \Pi \left(1-\sqrt{2};\left.\sin ^{-1}\left(\sqrt{x}\right)\right|-1\right)+\left(\sqrt{2}-1\right) \Pi \left(1+\sqrt{2};\left.\sin ^{-1}\left(\sqrt{x}\right)\right|-1\right)\right)}{\sqrt{x \left(x^2-1\right)}}","\frac{1}{4} \left(2+\sqrt{2}\right) \tan ^{-1}\left(\frac{\sqrt{3-2 \sqrt{2}} \sqrt{x^3-x}}{x+1}\right)+\frac{1}{4} \left(\sqrt{2}-2\right) \tan ^{-1}\left(\frac{\sqrt{3+2 \sqrt{2}} \sqrt{x^3-x}}{x+1}\right)",1,"(Sqrt[x]*Sqrt[1 - x^2]*(2*EllipticF[ArcSin[Sqrt[x]], -1] - (1 + Sqrt[2])*EllipticPi[1 - Sqrt[2], ArcSin[Sqrt[x]], -1] + (-1 + Sqrt[2])*EllipticPi[1 + Sqrt[2], ArcSin[Sqrt[x]], -1]))/Sqrt[x*(-1 + x^2)]","C",1
1135,0,0,85,0.1179674,"\int \frac{3+x^2}{\sqrt[3]{1+x^2} \left(1+x^2+x^3\right)} \, dx","Integrate[(3 + x^2)/((1 + x^2)^(1/3)*(1 + x^2 + x^3)),x]","\int \frac{3+x^2}{\sqrt[3]{1+x^2} \left(1+x^2+x^3\right)} \, dx","\log \left(\sqrt[3]{x^2+1}+x\right)-\frac{1}{2} \log \left(x^2-\sqrt[3]{x^2+1} x+\left(x^2+1\right)^{2/3}\right)-\sqrt{3} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{x^2+1}}{\sqrt{3}}-\frac{2 x}{\sqrt{3}}}{\sqrt[3]{x^2+1}}\right)",1,"Integrate[(3 + x^2)/((1 + x^2)^(1/3)*(1 + x^2 + x^3)), x]","F",-1
1136,1,40,85,0.0117278,"\int \frac{x}{\left(-1+x^3\right) \left(-1+2 x^3\right)^{2/3}} \, dx","Integrate[x/((-1 + x^3)*(-1 + 2*x^3)^(2/3)),x]","-\frac{x^2 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};-\frac{x^3}{1-2 x^3}\right)}{2 \left(2 x^3-1\right)^{2/3}}","\frac{1}{3} \log \left(\sqrt[3]{2 x^3-1}-x\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{2 x^3-1}+x}\right)}{\sqrt{3}}-\frac{1}{6} \log \left(\sqrt[3]{2 x^3-1} x+\left(2 x^3-1\right)^{2/3}+x^2\right)",1,"-1/2*(x^2*Hypergeometric2F1[2/3, 1, 5/3, -(x^3/(1 - 2*x^3))])/(-1 + 2*x^3)^(2/3)","C",1
1137,0,0,85,1.0829635,"\int \frac{\left(-1-2 (-1+k) x+k x^2\right) \left(1-2 k x+k^2 x^2\right)}{((1-x) x (1-k x))^{3/4} \left(-d+(1+3 d k) x-\left(1+3 d k^2\right) x^2+d k^3 x^3\right)} \, dx","Integrate[((-1 - 2*(-1 + k)*x + k*x^2)*(1 - 2*k*x + k^2*x^2))/(((1 - x)*x*(1 - k*x))^(3/4)*(-d + (1 + 3*d*k)*x - (1 + 3*d*k^2)*x^2 + d*k^3*x^3)),x]","\int \frac{\left(-1-2 (-1+k) x+k x^2\right) \left(1-2 k x+k^2 x^2\right)}{((1-x) x (1-k x))^{3/4} \left(-d+(1+3 d k) x-\left(1+3 d k^2\right) x^2+d k^3 x^3\right)} \, dx","\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \left(k x^3+(-k-1) x^2+x\right)^{3/4}}{(x-1) x}\right)}{d^{3/4}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \left(k x^3+(-k-1) x^2+x\right)^{3/4}}{(x-1) x}\right)}{d^{3/4}}",1,"Integrate[((-1 - 2*(-1 + k)*x + k*x^2)*(1 - 2*k*x + k^2*x^2))/(((1 - x)*x*(1 - k*x))^(3/4)*(-d + (1 + 3*d*k)*x - (1 + 3*d*k^2)*x^2 + d*k^3*x^3)), x]","F",-1
1138,1,96,85,0.7247795,"\int \frac{-1+x^4}{\sqrt{-x+x^3} \left(1+x^4\right)} \, dx","Integrate[(-1 + x^4)/(Sqrt[-x + x^3]*(1 + x^4)),x]","-\frac{\sqrt{1-\frac{1}{x^2}} x^{3/2} \left(-2 F\left(\left.\sin ^{-1}\left(\frac{1}{\sqrt{x}}\right)\right|-1\right)+\Pi \left(-\sqrt[4]{-1};\left.\sin ^{-1}\left(\frac{1}{\sqrt{x}}\right)\right|-1\right)+\Pi \left(\sqrt[4]{-1};\left.\sin ^{-1}\left(\frac{1}{\sqrt{x}}\right)\right|-1\right)+\Pi \left(-(-1)^{3/4};\left.\sin ^{-1}\left(\frac{1}{\sqrt{x}}\right)\right|-1\right)+\Pi \left((-1)^{3/4};\left.\sin ^{-1}\left(\frac{1}{\sqrt{x}}\right)\right|-1\right)\right)}{\sqrt{x \left(x^2-1\right)}}","\frac{\tan ^{-1}\left(\frac{2^{3/4} \sqrt{x^3-x}}{-x^2+\sqrt{2} x+1}\right)}{2^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\frac{x^2}{2^{3/4}}+\frac{x}{\sqrt[4]{2}}-\frac{1}{2^{3/4}}}{\sqrt{x^3-x}}\right)}{2^{3/4}}",1,"-((Sqrt[1 - x^(-2)]*x^(3/2)*(-2*EllipticF[ArcSin[1/Sqrt[x]], -1] + EllipticPi[-(-1)^(1/4), ArcSin[1/Sqrt[x]], -1] + EllipticPi[(-1)^(1/4), ArcSin[1/Sqrt[x]], -1] + EllipticPi[-(-1)^(3/4), ArcSin[1/Sqrt[x]], -1] + EllipticPi[(-1)^(3/4), ArcSin[1/Sqrt[x]], -1]))/Sqrt[x*(-1 + x^2)])","C",1
1139,0,0,85,0.7649205,"\int \frac{-1+x^2}{\left(1+x+x^2\right) \sqrt[3]{x^2+x^4}} \, dx","Integrate[(-1 + x^2)/((1 + x + x^2)*(x^2 + x^4)^(1/3)),x]","\int \frac{-1+x^2}{\left(1+x+x^2\right) \sqrt[3]{x^2+x^4}} \, dx","-\log \left(\sqrt[3]{x^4+x^2}+x\right)+\frac{1}{2} \log \left(x^2-\sqrt[3]{x^4+x^2} x+\left(x^4+x^2\right)^{2/3}\right)-\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^4+x^2}-x}\right)",1,"Integrate[(-1 + x^2)/((1 + x + x^2)*(x^2 + x^4)^(1/3)), x]","F",-1
1140,1,67,85,0.0629006,"\int \frac{\left(-2 b+a x^4\right) \left(b+a x^4\right)^{3/4}}{x^8} \, dx","Integrate[((-2*b + a*x^4)*(b + a*x^4)^(3/4))/x^8,x]","\frac{\left(a x^4+b\right)^{3/4} \left(6 \left(a x^4+b\right)-\frac{7 a x^4 \, _2F_1\left(-\frac{3}{4},-\frac{3}{4};\frac{1}{4};-\frac{a x^4}{b}\right)}{\left(\frac{a x^4}{b}+1\right)^{3/4}}\right)}{21 x^7}","\frac{1}{2} a^{7/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)+\frac{1}{2} a^{7/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)+\frac{\left(6 b-a x^4\right) \left(a x^4+b\right)^{3/4}}{21 x^7}",1,"((b + a*x^4)^(3/4)*(6*(b + a*x^4) - (7*a*x^4*Hypergeometric2F1[-3/4, -3/4, 1/4, -((a*x^4)/b)])/(1 + (a*x^4)/b)^(3/4)))/(21*x^7)","C",1
1141,1,69,85,0.0856954,"\int \frac{\left(-b+a x^4\right)^{3/4} \left(-b+2 a x^4\right)}{x^8} \, dx","Integrate[((-b + a*x^4)^(3/4)*(-b + 2*a*x^4))/x^8,x]","-\frac{\left(a x^4-b\right)^{3/4} \left(\frac{14 a x^4 \, _2F_1\left(-\frac{3}{4},-\frac{3}{4};\frac{1}{4};\frac{a x^4}{b}\right)}{\left(1-\frac{a x^4}{b}\right)^{3/4}}+3 a x^4-3 b\right)}{21 x^7}","a^{7/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)+a^{7/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)+\frac{\left(3 b-17 a x^4\right) \left(a x^4-b\right)^{3/4}}{21 x^7}",1,"-1/21*((-b + a*x^4)^(3/4)*(-3*b + 3*a*x^4 + (14*a*x^4*Hypergeometric2F1[-3/4, -3/4, 1/4, (a*x^4)/b])/(1 - (a*x^4)/b)^(3/4)))/x^7","C",1
1142,1,226,85,0.2801254,"\int \frac{\left(-q+p x^2\right) \left(a q+b x+a p x^2\right) \sqrt{q^2+p^2 x^4}}{x^4} \, dx","Integrate[((-q + p*x^2)*(a*q + b*x + a*p*x^2)*Sqrt[q^2 + p^2*x^4])/x^4,x]","\frac{6 a p^2 x^4 \sqrt{p^2 x^4+q^2} \, _2F_1\left(-\frac{1}{2},\frac{1}{4};\frac{5}{4};-\frac{p^2 x^4}{q^2}\right)+2 a q^2 \sqrt{p^2 x^4+q^2} \, _2F_1\left(-\frac{3}{4},-\frac{1}{2};\frac{1}{4};-\frac{p^2 x^4}{q^2}\right)+3 b p x^3 \sqrt{\frac{p^2 x^4}{q^2}+1} \left(\sqrt{p^2 x^4+q^2}-q \tanh ^{-1}\left(\frac{\sqrt{p^2 x^4+q^2}}{q}\right)\right)+3 b x \sqrt{p^2 x^4+q^2} \left(q \sqrt{\frac{p^2 x^4}{q^2}+1}-p x^2 \sinh ^{-1}\left(\frac{p x^2}{q}\right)\right)}{6 x^3 \sqrt{\frac{p^2 x^4}{q^2}+1}}","\frac{\sqrt{p^2 x^4+q^2} \left(2 a p^2 x^4+2 a q^2+3 b p x^3+3 b q x\right)}{6 x^3}-b p q \log \left(\sqrt{p^2 x^4+q^2}+p x^2+q\right)+b p q \log (x)",1,"(3*b*x*Sqrt[q^2 + p^2*x^4]*(q*Sqrt[1 + (p^2*x^4)/q^2] - p*x^2*ArcSinh[(p*x^2)/q]) + 3*b*p*x^3*Sqrt[1 + (p^2*x^4)/q^2]*(Sqrt[q^2 + p^2*x^4] - q*ArcTanh[Sqrt[q^2 + p^2*x^4]/q]) + 2*a*q^2*Sqrt[q^2 + p^2*x^4]*Hypergeometric2F1[-3/4, -1/2, 1/4, -((p^2*x^4)/q^2)] + 6*a*p^2*x^4*Sqrt[q^2 + p^2*x^4]*Hypergeometric2F1[-1/2, 1/4, 5/4, -((p^2*x^4)/q^2)])/(6*x^3*Sqrt[1 + (p^2*x^4)/q^2])","C",1
1143,0,0,85,0.2000225,"\int \frac{-1+2 x^3}{\left(1+x+x^3\right) \sqrt[3]{x^2+x^5}} \, dx","Integrate[(-1 + 2*x^3)/((1 + x + x^3)*(x^2 + x^5)^(1/3)),x]","\int \frac{-1+2 x^3}{\left(1+x+x^3\right) \sqrt[3]{x^2+x^5}} \, dx","-\log \left(\sqrt[3]{x^5+x^2}+x\right)+\frac{1}{2} \log \left(x^2-\sqrt[3]{x^5+x^2} x+\left(x^5+x^2\right)^{2/3}\right)-\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^5+x^2}-x}\right)",1,"Integrate[(-1 + 2*x^3)/((1 + x + x^3)*(x^2 + x^5)^(1/3)), x]","F",-1
1144,0,0,85,0.384425,"\int \frac{2+3 x^5}{\left(-1+x^2+x^5\right) \sqrt[3]{-x+x^6}} \, dx","Integrate[(2 + 3*x^5)/((-1 + x^2 + x^5)*(-x + x^6)^(1/3)),x]","\int \frac{2+3 x^5}{\left(-1+x^2+x^5\right) \sqrt[3]{-x+x^6}} \, dx","-\log \left(\sqrt[3]{x^6-x}+x\right)-\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^6-x}-x}\right)+\frac{1}{2} \log \left(-\sqrt[3]{x^6-x} x+\left(x^6-x\right)^{2/3}+x^2\right)",1,"Integrate[(2 + 3*x^5)/((-1 + x^2 + x^5)*(-x + x^6)^(1/3)), x]","F",-1
1145,1,201,85,0.1812673,"\int \frac{\sqrt{-1+x^6} \left(-1+2 x^6\right)^2}{x^4 \left(-1+4 x^6\right)} \, dx","Integrate[(Sqrt[-1 + x^6]*(-1 + 2*x^6)^2)/(x^4*(-1 + 4*x^6)),x]","\frac{4 \sqrt{1-x^6} x^6-8 \sqrt{1-x^6}+4 \sqrt{1-x^6} x^{12}+12 \left(x^6-1\right) x^3 \sin ^{-1}\left(x^3\right)+\sqrt{3} \sqrt{-\left(x^6-1\right)^2} x^3 \tan ^{-1}\left(\frac{2-x^3}{\sqrt{3} \sqrt{x^6-1}}\right)-\sqrt{3} \sqrt{-\left(x^6-1\right)^2} x^3 \tan ^{-1}\left(\frac{x^3+2}{\sqrt{3} \sqrt{x^6-1}}\right)+2 \sqrt{-\left(x^6-1\right)^2} x^3 \tanh ^{-1}\left(\frac{x^3}{\sqrt{x^6-1}}\right)}{24 x^3 \sqrt{-\left(x^6-1\right)^2}}","\frac{\sqrt{x^6-1} \left(x^6+2\right)}{6 x^3}-\frac{5}{12} \log \left(\sqrt{x^6-1}+x^3\right)+\frac{\tan ^{-1}\left(-\frac{4 x^6}{\sqrt{3}}-\frac{4 \sqrt{x^6-1} x^3}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{4 \sqrt{3}}",1,"(-8*Sqrt[1 - x^6] + 4*x^6*Sqrt[1 - x^6] + 4*x^12*Sqrt[1 - x^6] + 12*x^3*(-1 + x^6)*ArcSin[x^3] + Sqrt[3]*x^3*Sqrt[-(-1 + x^6)^2]*ArcTan[(2 - x^3)/(Sqrt[3]*Sqrt[-1 + x^6])] - Sqrt[3]*x^3*Sqrt[-(-1 + x^6)^2]*ArcTan[(2 + x^3)/(Sqrt[3]*Sqrt[-1 + x^6])] + 2*x^3*Sqrt[-(-1 + x^6)^2]*ArcTanh[x^3/Sqrt[-1 + x^6]])/(24*x^3*Sqrt[-(-1 + x^6)^2])","B",1
1146,1,257,85,0.5641589,"\int \frac{1+x^4}{\sqrt[4]{-1+x^4} \left(1+x^4+x^8\right)} \, dx","Integrate[(1 + x^4)/((-1 + x^4)^(1/4)*(1 + x^4 + x^8)),x]","\frac{1}{6} \left(\frac{\tan ^{-1}\left(\frac{x}{\sqrt[4]{\frac{\sqrt{3}-i}{\sqrt{3}-3 i}} \sqrt[4]{x^4-1}}\right)}{\left(\frac{\sqrt{3}-i}{\sqrt{3}-3 i}\right)^{3/4}}+\frac{\tan ^{-1}\left(\frac{x}{\sqrt[4]{\frac{\sqrt{3}+i}{\sqrt{3}+3 i}} \sqrt[4]{x^4-1}}\right)}{\left(\frac{\sqrt{3}+i}{\sqrt{3}+3 i}\right)^{3/4}}+\frac{\tanh ^{-1}\left(\frac{x}{\sqrt[4]{\frac{\sqrt{3}-i}{\sqrt{3}-3 i}} \sqrt[4]{x^4-1}}\right)}{\left(\frac{\sqrt{3}-i}{\sqrt{3}-3 i}\right)^{3/4}}+\frac{\tanh ^{-1}\left(\frac{x}{\sqrt[4]{\frac{\sqrt{3}+i}{\sqrt{3}+3 i}} \sqrt[4]{x^4-1}}\right)}{\left(\frac{\sqrt{3}+i}{\sqrt{3}+3 i}\right)^{3/4}}\right)","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4+3\&,\frac{-\text{$\#$1}^4 \log \left(\sqrt[4]{x^4-1}-\text{$\#$1} x\right)+\text{$\#$1}^4 \log (x)+2 \log \left(\sqrt[4]{x^4-1}-\text{$\#$1} x\right)-2 \log (x)}{2 \text{$\#$1}^5-3 \text{$\#$1}}\&\right]",1,"(ArcTan[x/(((-I + Sqrt[3])/(-3*I + Sqrt[3]))^(1/4)*(-1 + x^4)^(1/4))]/((-I + Sqrt[3])/(-3*I + Sqrt[3]))^(3/4) + ArcTan[x/(((I + Sqrt[3])/(3*I + Sqrt[3]))^(1/4)*(-1 + x^4)^(1/4))]/((I + Sqrt[3])/(3*I + Sqrt[3]))^(3/4) + ArcTanh[x/(((-I + Sqrt[3])/(-3*I + Sqrt[3]))^(1/4)*(-1 + x^4)^(1/4))]/((-I + Sqrt[3])/(-3*I + Sqrt[3]))^(3/4) + ArcTanh[x/(((I + Sqrt[3])/(3*I + Sqrt[3]))^(1/4)*(-1 + x^4)^(1/4))]/((I + Sqrt[3])/(3*I + Sqrt[3]))^(3/4))/6","C",1
1147,1,192,85,0.336026,"\int \frac{-1+2 x^4}{\sqrt[4]{-1+x^4} \left(-2-x^4+2 x^8\right)} \, dx","Integrate[(-1 + 2*x^4)/((-1 + x^4)^(1/4)*(-2 - x^4 + 2*x^8)),x]","\frac{-\frac{8 \sqrt[4]{23+\sqrt{17}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{2}{5+\sqrt{17}}} x}{\sqrt[4]{x^4-1}}\right)}{1+\sqrt{17}}+\sqrt[4]{487+79 \sqrt{17}} \tan ^{-1}\left(\frac{\sqrt[4]{5+\sqrt{17}} x}{\sqrt{2} \sqrt[4]{x^4-1}}\right)-\frac{8 \sqrt[4]{23+\sqrt{17}} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{2}{5+\sqrt{17}}} x}{\sqrt[4]{x^4-1}}\right)}{1+\sqrt{17}}+\sqrt[4]{487+79 \sqrt{17}} \tanh ^{-1}\left(\frac{\sqrt[4]{5+\sqrt{17}} x}{\sqrt{2} \sqrt[4]{x^4-1}}\right)}{4 \sqrt{17}}","\frac{1}{4} \text{RootSum}\left[2 \text{$\#$1}^8-5 \text{$\#$1}^4+1\&,\frac{-\text{$\#$1}^4 \log \left(\sqrt[4]{x^4-1}-\text{$\#$1} x\right)+\text{$\#$1}^4 \log (x)-\log \left(\sqrt[4]{x^4-1}-\text{$\#$1} x\right)+\log (x)}{4 \text{$\#$1}^5-5 \text{$\#$1}}\&\right]",1,"((-8*(23 + Sqrt[17])^(1/4)*ArcTan[((2/(5 + Sqrt[17]))^(1/4)*x)/(-1 + x^4)^(1/4)])/(1 + Sqrt[17]) + (487 + 79*Sqrt[17])^(1/4)*ArcTan[((5 + Sqrt[17])^(1/4)*x)/(Sqrt[2]*(-1 + x^4)^(1/4))] - (8*(23 + Sqrt[17])^(1/4)*ArcTanh[((2/(5 + Sqrt[17]))^(1/4)*x)/(-1 + x^4)^(1/4)])/(1 + Sqrt[17]) + (487 + 79*Sqrt[17])^(1/4)*ArcTanh[((5 + Sqrt[17])^(1/4)*x)/(Sqrt[2]*(-1 + x^4)^(1/4))])/(4*Sqrt[17])","B",0
1148,1,317,85,0.5685808,"\int \frac{-1+x^4+2 x^8}{\sqrt[4]{-1+x^4} \left(1-x^4+x^8\right)} \, dx","Integrate[(-1 + x^4 + 2*x^8)/((-1 + x^4)^(1/4)*(1 - x^4 + x^8)),x]","\frac{1}{2} \left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-1}}\right)+\frac{i \sqrt{3} \tan ^{-1}\left(\frac{x}{\sqrt[4]{\frac{\sqrt{3}-i}{\sqrt{3}+i}} \sqrt[4]{x^4-1}}\right)}{\left(\frac{\sqrt{3}-i}{\sqrt{3}+i}\right)^{3/4}}-i \sqrt{3} \left(\frac{\sqrt{3}-i}{\sqrt{3}+i}\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{\sqrt{3}-i}{\sqrt{3}+i}} x}{\sqrt[4]{x^4-1}}\right)+2 \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-1}}\right)+\frac{i \sqrt{3} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{\frac{\sqrt{3}-i}{\sqrt{3}+i}} \sqrt[4]{x^4-1}}\right)}{\left(\frac{\sqrt{3}-i}{\sqrt{3}+i}\right)^{3/4}}-i \sqrt{3} \left(\frac{\sqrt{3}-i}{\sqrt{3}+i}\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{\sqrt{3}-i}{\sqrt{3}+i}} x}{\sqrt[4]{x^4-1}}\right)\right)","\frac{3}{4} \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4+1\&,\frac{\text{$\#$1}^3 \log \left(\sqrt[4]{x^4-1}-\text{$\#$1} x\right)-\text{$\#$1}^3 \log (x)}{2 \text{$\#$1}^4-1}\&\right]+\tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-1}}\right)+\tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-1}}\right)",1,"(2*ArcTan[x/(-1 + x^4)^(1/4)] + (I*Sqrt[3]*ArcTan[x/(((-I + Sqrt[3])/(I + Sqrt[3]))^(1/4)*(-1 + x^4)^(1/4))])/((-I + Sqrt[3])/(I + Sqrt[3]))^(3/4) - I*Sqrt[3]*((-I + Sqrt[3])/(I + Sqrt[3]))^(3/4)*ArcTan[(((-I + Sqrt[3])/(I + Sqrt[3]))^(1/4)*x)/(-1 + x^4)^(1/4)] + 2*ArcTanh[x/(-1 + x^4)^(1/4)] + (I*Sqrt[3]*ArcTanh[x/(((-I + Sqrt[3])/(I + Sqrt[3]))^(1/4)*(-1 + x^4)^(1/4))])/((-I + Sqrt[3])/(I + Sqrt[3]))^(3/4) - I*Sqrt[3]*((-I + Sqrt[3])/(I + Sqrt[3]))^(3/4)*ArcTanh[(((-I + Sqrt[3])/(I + Sqrt[3]))^(1/4)*x)/(-1 + x^4)^(1/4)])/2","C",1
1149,1,665,85,3.2300317,"\int \frac{1}{\sqrt[4]{b x^2+a x^4} \left(-2 b+a x^8\right)} \, dx","Integrate[1/((b*x^2 + a*x^4)^(1/4)*(-2*b + a*x^8)),x]","-\frac{x \sqrt[4]{a+\frac{b}{x^2}} \left(a^3 \text{RootSum}\left[2 \text{$\#$1}^4-8 \text{$\#$1}^3 a+12 \text{$\#$1}^2 a^2-8 \text{$\#$1} a^3+2 a^4-a b^3\&,\frac{\frac{\log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{a+\frac{b}{x^2}}\right)}{\sqrt[4]{\text{$\#$1}}}-\frac{\log \left(\sqrt[4]{\text{$\#$1}}+\sqrt[4]{a+\frac{b}{x^2}}\right)}{\sqrt[4]{\text{$\#$1}}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\text{$\#$1}}}\right)}{\sqrt[4]{\text{$\#$1}}}}{\text{$\#$1}^3-3 \text{$\#$1}^2 a+3 \text{$\#$1} a^2-a^3}\&\right]-3 a^2 \text{RootSum}\left[2 \text{$\#$1}^4-8 \text{$\#$1}^3 a+12 \text{$\#$1}^2 a^2-8 \text{$\#$1} a^3+2 a^4-a b^3\&,\frac{\text{$\#$1}^{3/4} \log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{a+\frac{b}{x^2}}\right)-\text{$\#$1}^{3/4} \log \left(\sqrt[4]{\text{$\#$1}}+\sqrt[4]{a+\frac{b}{x^2}}\right)+2 \text{$\#$1}^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\text{$\#$1}}}\right)}{\text{$\#$1}^3-3 \text{$\#$1}^2 a+3 \text{$\#$1} a^2-a^3}\&\right]+3 a \text{RootSum}\left[2 \text{$\#$1}^4-8 \text{$\#$1}^3 a+12 \text{$\#$1}^2 a^2-8 \text{$\#$1} a^3+2 a^4-a b^3\&,\frac{\text{$\#$1}^{7/4} \log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{a+\frac{b}{x^2}}\right)-\text{$\#$1}^{7/4} \log \left(\sqrt[4]{\text{$\#$1}}+\sqrt[4]{a+\frac{b}{x^2}}\right)+2 \text{$\#$1}^{7/4} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\text{$\#$1}}}\right)}{\text{$\#$1}^3-3 \text{$\#$1}^2 a+3 \text{$\#$1} a^2-a^3}\&\right]-\text{RootSum}\left[2 \text{$\#$1}^4-8 \text{$\#$1}^3 a+12 \text{$\#$1}^2 a^2-8 \text{$\#$1} a^3+2 a^4-a b^3\&,\frac{\text{$\#$1}^{11/4} \log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{a+\frac{b}{x^2}}\right)-\text{$\#$1}^{11/4} \log \left(\sqrt[4]{\text{$\#$1}}+\sqrt[4]{a+\frac{b}{x^2}}\right)+2 \text{$\#$1}^{11/4} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\text{$\#$1}}}\right)}{\text{$\#$1}^3-3 \text{$\#$1}^2 a+3 \text{$\#$1} a^2-a^3}\&\right]\right)}{16 b \sqrt[4]{x^2 \left(a x^2+b\right)}}","\frac{\text{RootSum}\left[2 \text{$\#$1}^{16}-8 \text{$\#$1}^{12} a+12 \text{$\#$1}^8 a^2-8 \text{$\#$1}^4 a^3+2 a^4-a b^3\&,\frac{\log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{16 b}",1,"-1/16*((a + b/x^2)^(1/4)*x*(a^3*RootSum[2*a^4 - a*b^3 - 8*a^3*#1 + 12*a^2*#1^2 - 8*a*#1^3 + 2*#1^4 & , ((2*ArcTan[(a + b/x^2)^(1/4)/#1^(1/4)])/#1^(1/4) + Log[-(a + b/x^2)^(1/4) + #1^(1/4)]/#1^(1/4) - Log[(a + b/x^2)^(1/4) + #1^(1/4)]/#1^(1/4))/(-a^3 + 3*a^2*#1 - 3*a*#1^2 + #1^3) & ] - 3*a^2*RootSum[2*a^4 - a*b^3 - 8*a^3*#1 + 12*a^2*#1^2 - 8*a*#1^3 + 2*#1^4 & , (2*ArcTan[(a + b/x^2)^(1/4)/#1^(1/4)]*#1^(3/4) + Log[-(a + b/x^2)^(1/4) + #1^(1/4)]*#1^(3/4) - Log[(a + b/x^2)^(1/4) + #1^(1/4)]*#1^(3/4))/(-a^3 + 3*a^2*#1 - 3*a*#1^2 + #1^3) & ] + 3*a*RootSum[2*a^4 - a*b^3 - 8*a^3*#1 + 12*a^2*#1^2 - 8*a*#1^3 + 2*#1^4 & , (2*ArcTan[(a + b/x^2)^(1/4)/#1^(1/4)]*#1^(7/4) + Log[-(a + b/x^2)^(1/4) + #1^(1/4)]*#1^(7/4) - Log[(a + b/x^2)^(1/4) + #1^(1/4)]*#1^(7/4))/(-a^3 + 3*a^2*#1 - 3*a*#1^2 + #1^3) & ] - RootSum[2*a^4 - a*b^3 - 8*a^3*#1 + 12*a^2*#1^2 - 8*a*#1^3 + 2*#1^4 & , (2*ArcTan[(a + b/x^2)^(1/4)/#1^(1/4)]*#1^(11/4) + Log[-(a + b/x^2)^(1/4) + #1^(1/4)]*#1^(11/4) - Log[(a + b/x^2)^(1/4) + #1^(1/4)]*#1^(11/4))/(-a^3 + 3*a^2*#1 - 3*a*#1^2 + #1^3) & ]))/(b*(x^2*(b + a*x^2))^(1/4))","B",1
1150,1,665,85,0.8784418,"\int \frac{1}{\sqrt[4]{b x^2+a x^4} \left(-2 b+a x^8\right)} \, dx","Integrate[1/((b*x^2 + a*x^4)^(1/4)*(-2*b + a*x^8)),x]","-\frac{x \sqrt[4]{a+\frac{b}{x^2}} \left(a^3 \text{RootSum}\left[2 \text{$\#$1}^4-8 \text{$\#$1}^3 a+12 \text{$\#$1}^2 a^2-8 \text{$\#$1} a^3+2 a^4-a b^3\&,\frac{\frac{\log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{a+\frac{b}{x^2}}\right)}{\sqrt[4]{\text{$\#$1}}}-\frac{\log \left(\sqrt[4]{\text{$\#$1}}+\sqrt[4]{a+\frac{b}{x^2}}\right)}{\sqrt[4]{\text{$\#$1}}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\text{$\#$1}}}\right)}{\sqrt[4]{\text{$\#$1}}}}{\text{$\#$1}^3-3 \text{$\#$1}^2 a+3 \text{$\#$1} a^2-a^3}\&\right]-3 a^2 \text{RootSum}\left[2 \text{$\#$1}^4-8 \text{$\#$1}^3 a+12 \text{$\#$1}^2 a^2-8 \text{$\#$1} a^3+2 a^4-a b^3\&,\frac{\text{$\#$1}^{3/4} \log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{a+\frac{b}{x^2}}\right)-\text{$\#$1}^{3/4} \log \left(\sqrt[4]{\text{$\#$1}}+\sqrt[4]{a+\frac{b}{x^2}}\right)+2 \text{$\#$1}^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\text{$\#$1}}}\right)}{\text{$\#$1}^3-3 \text{$\#$1}^2 a+3 \text{$\#$1} a^2-a^3}\&\right]+3 a \text{RootSum}\left[2 \text{$\#$1}^4-8 \text{$\#$1}^3 a+12 \text{$\#$1}^2 a^2-8 \text{$\#$1} a^3+2 a^4-a b^3\&,\frac{\text{$\#$1}^{7/4} \log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{a+\frac{b}{x^2}}\right)-\text{$\#$1}^{7/4} \log \left(\sqrt[4]{\text{$\#$1}}+\sqrt[4]{a+\frac{b}{x^2}}\right)+2 \text{$\#$1}^{7/4} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\text{$\#$1}}}\right)}{\text{$\#$1}^3-3 \text{$\#$1}^2 a+3 \text{$\#$1} a^2-a^3}\&\right]-\text{RootSum}\left[2 \text{$\#$1}^4-8 \text{$\#$1}^3 a+12 \text{$\#$1}^2 a^2-8 \text{$\#$1} a^3+2 a^4-a b^3\&,\frac{\text{$\#$1}^{11/4} \log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{a+\frac{b}{x^2}}\right)-\text{$\#$1}^{11/4} \log \left(\sqrt[4]{\text{$\#$1}}+\sqrt[4]{a+\frac{b}{x^2}}\right)+2 \text{$\#$1}^{11/4} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\text{$\#$1}}}\right)}{\text{$\#$1}^3-3 \text{$\#$1}^2 a+3 \text{$\#$1} a^2-a^3}\&\right]\right)}{16 b \sqrt[4]{x^2 \left(a x^2+b\right)}}","\frac{\text{RootSum}\left[2 \text{$\#$1}^{16}-8 \text{$\#$1}^{12} a+12 \text{$\#$1}^8 a^2-8 \text{$\#$1}^4 a^3+2 a^4-a b^3\&,\frac{\log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{16 b}",1,"-1/16*((a + b/x^2)^(1/4)*x*(a^3*RootSum[2*a^4 - a*b^3 - 8*a^3*#1 + 12*a^2*#1^2 - 8*a*#1^3 + 2*#1^4 & , ((2*ArcTan[(a + b/x^2)^(1/4)/#1^(1/4)])/#1^(1/4) + Log[-(a + b/x^2)^(1/4) + #1^(1/4)]/#1^(1/4) - Log[(a + b/x^2)^(1/4) + #1^(1/4)]/#1^(1/4))/(-a^3 + 3*a^2*#1 - 3*a*#1^2 + #1^3) & ] - 3*a^2*RootSum[2*a^4 - a*b^3 - 8*a^3*#1 + 12*a^2*#1^2 - 8*a*#1^3 + 2*#1^4 & , (2*ArcTan[(a + b/x^2)^(1/4)/#1^(1/4)]*#1^(3/4) + Log[-(a + b/x^2)^(1/4) + #1^(1/4)]*#1^(3/4) - Log[(a + b/x^2)^(1/4) + #1^(1/4)]*#1^(3/4))/(-a^3 + 3*a^2*#1 - 3*a*#1^2 + #1^3) & ] + 3*a*RootSum[2*a^4 - a*b^3 - 8*a^3*#1 + 12*a^2*#1^2 - 8*a*#1^3 + 2*#1^4 & , (2*ArcTan[(a + b/x^2)^(1/4)/#1^(1/4)]*#1^(7/4) + Log[-(a + b/x^2)^(1/4) + #1^(1/4)]*#1^(7/4) - Log[(a + b/x^2)^(1/4) + #1^(1/4)]*#1^(7/4))/(-a^3 + 3*a^2*#1 - 3*a*#1^2 + #1^3) & ] - RootSum[2*a^4 - a*b^3 - 8*a^3*#1 + 12*a^2*#1^2 - 8*a*#1^3 + 2*#1^4 & , (2*ArcTan[(a + b/x^2)^(1/4)/#1^(1/4)]*#1^(11/4) + Log[-(a + b/x^2)^(1/4) + #1^(1/4)]*#1^(11/4) - Log[(a + b/x^2)^(1/4) + #1^(1/4)]*#1^(11/4))/(-a^3 + 3*a^2*#1 - 3*a*#1^2 + #1^3) & ]))/(b*(x^2*(b + a*x^2))^(1/4))","B",1
1151,0,0,85,0.6672486,"\int \frac{\left(4+x^5\right) \sqrt[4]{-2+x^4+2 x^5} \left(2-4 x^5+x^8+2 x^{10}\right)}{x^{10} \left(-1+x^5\right)} \, dx","Integrate[((4 + x^5)*(-2 + x^4 + 2*x^5)^(1/4)*(2 - 4*x^5 + x^8 + 2*x^10))/(x^10*(-1 + x^5)),x]","\int \frac{\left(4+x^5\right) \sqrt[4]{-2+x^4+2 x^5} \left(2-4 x^5+x^8+2 x^{10}\right)}{x^{10} \left(-1+x^5\right)} \, dx","2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{2 x^5+x^4-2}}\right)-2 \tanh ^{-1}\left(\frac{x}{\sqrt[4]{2 x^5+x^4-2}}\right)+\frac{4 \sqrt[4]{2 x^5+x^4-2} \left(10 x^{10}+x^9+43 x^8-20 x^5-x^4+10\right)}{45 x^9}",1,"Integrate[((4 + x^5)*(-2 + x^4 + 2*x^5)^(1/4)*(2 - 4*x^5 + x^8 + 2*x^10))/(x^10*(-1 + x^5)), x]","F",-1
1152,1,204,85,0.9150011,"\int \frac{1+x^{12}}{\sqrt{1+x^4} \left(-1+x^{12}\right)} \, dx","Integrate[(1 + x^12)/(Sqrt[1 + x^4]*(-1 + x^12)),x]","\frac{(-1)^{5/12} \left(-3 F\left(\left.i \sinh ^{-1}\left(\frac{(1+i) x}{\sqrt{2}}\right)\right|-1\right)+\Pi \left(-i;\left.i \sinh ^{-1}\left(\frac{(1+i) x}{\sqrt{2}}\right)\right|-1\right)+\Pi \left(i;\left.i \sinh ^{-1}\left(\frac{(1+i) x}{\sqrt{2}}\right)\right|-1\right)+\Pi \left(-\frac{i}{2}-\frac{\sqrt{3}}{2};\left.i \sinh ^{-1}\left(\frac{(1+i) x}{\sqrt{2}}\right)\right|-1\right)+\Pi \left(\frac{i}{2}-\frac{\sqrt{3}}{2};\left.i \sinh ^{-1}\left(\frac{(1+i) x}{\sqrt{2}}\right)\right|-1\right)+\Pi \left(\frac{1}{2} \left(-i+\sqrt{3}\right);\left.i \sinh ^{-1}\left(\frac{(1+i) x}{\sqrt{2}}\right)\right|-1\right)+\Pi \left(\frac{1}{2} \left(i+\sqrt{3}\right);\left.i \sinh ^{-1}\left(\frac{(1+i) x}{\sqrt{2}}\right)\right|-1\right)\right)}{\sqrt{3} \left(1+\sqrt[3]{-1}\right)}","-\frac{1}{3} \tan ^{-1}\left(\frac{x}{\sqrt{x^4+1}}\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{6 \sqrt{2}}-\frac{1}{3} \tanh ^{-1}\left(\frac{x}{\sqrt{x^4+1}}\right)-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{6 \sqrt{2}}",1,"((-1)^(5/12)*(-3*EllipticF[I*ArcSinh[((1 + I)*x)/Sqrt[2]], -1] + EllipticPi[-I, I*ArcSinh[((1 + I)*x)/Sqrt[2]], -1] + EllipticPi[I, I*ArcSinh[((1 + I)*x)/Sqrt[2]], -1] + EllipticPi[-1/2*I - Sqrt[3]/2, I*ArcSinh[((1 + I)*x)/Sqrt[2]], -1] + EllipticPi[I/2 - Sqrt[3]/2, I*ArcSinh[((1 + I)*x)/Sqrt[2]], -1] + EllipticPi[(-I + Sqrt[3])/2, I*ArcSinh[((1 + I)*x)/Sqrt[2]], -1] + EllipticPi[(I + Sqrt[3])/2, I*ArcSinh[((1 + I)*x)/Sqrt[2]], -1]))/(Sqrt[3]*(1 + (-1)^(1/3)))","C",0
1153,0,0,85,0.6180292,"\int \frac{\sqrt{1-x^6} \left(1+2 x^6\right) \left(1+x^2-x^4-2 x^6-x^8+x^{12}\right)}{\left(-1+x^6\right) \left(-1+2 x^6-3 x^{12}+x^{18}\right)} \, dx","Integrate[(Sqrt[1 - x^6]*(1 + 2*x^6)*(1 + x^2 - x^4 - 2*x^6 - x^8 + x^12))/((-1 + x^6)*(-1 + 2*x^6 - 3*x^12 + x^18)),x]","\int \frac{\sqrt{1-x^6} \left(1+2 x^6\right) \left(1+x^2-x^4-2 x^6-x^8+x^{12}\right)}{\left(-1+x^6\right) \left(-1+2 x^6-3 x^{12}+x^{18}\right)} \, dx","-\frac{1}{3} \tan ^{-1}\left(\frac{x}{\sqrt{1-x^6}}\right)-\frac{1}{3} \tan ^{-1}\left(\frac{x \sqrt{1-x^6}}{x^6+x^2-1}\right)-\frac{\tanh ^{-1}\left(\frac{\sqrt{3} x \sqrt{1-x^6}}{x^6-x^2-1}\right)}{\sqrt{3}}",1,"Integrate[(Sqrt[1 - x^6]*(1 + 2*x^6)*(1 + x^2 - x^4 - 2*x^6 - x^8 + x^12))/((-1 + x^6)*(-1 + 2*x^6 - 3*x^12 + x^18)), x]","F",-1
1154,1,125,85,0.2115548,"\int \frac{x^2-\sqrt{1+x^2}}{\sqrt{1+\sqrt{1+x^2}}} \, dx","Integrate[(x^2 - Sqrt[1 + x^2])/Sqrt[1 + Sqrt[1 + x^2]],x]","\frac{\sqrt{\sqrt{x^2+1}+1} \left(-10 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{1}{2}-\frac{\sqrt{x^2+1}}{2}\right)+4 \sqrt{x^2+1} x^2-12 x^2+16 \sqrt{x^2+1}-5 \sqrt{2} \sqrt{\sqrt{x^2+1}-1} \tan ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}-1}}{\sqrt{2}}\right)-6\right)}{10 x}","\frac{2 \left(x^2+2\right) x}{5 \sqrt{\sqrt{x^2+1}+1}}-\frac{4 \sqrt{x^2+1} x}{5 \sqrt{\sqrt{x^2+1}+1}}-\sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2} \sqrt{\sqrt{x^2+1}+1}}\right)",1,"(Sqrt[1 + Sqrt[1 + x^2]]*(-6 - 12*x^2 + 16*Sqrt[1 + x^2] + 4*x^2*Sqrt[1 + x^2] - 5*Sqrt[2]*Sqrt[-1 + Sqrt[1 + x^2]]*ArcTan[Sqrt[-1 + Sqrt[1 + x^2]]/Sqrt[2]] - 10*Hypergeometric2F1[-1/2, 1, 1/2, 1/2 - Sqrt[1 + x^2]/2]))/(10*x)","C",1
1155,1,61,86,0.0205469,"\int \frac{1}{(-1+x) \sqrt[3]{2-2 x+x^2}} \, dx","Integrate[1/((-1 + x)*(2 - 2*x + x^2)^(1/3)),x]","\frac{1}{2} \left(\frac{3}{2} \log \left(1-\sqrt[3]{(x-1)^2+1}\right)-\log (1-x)+\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{(x-1)^2+1}+1}{\sqrt{3}}\right)\right)","\frac{1}{2} \log \left(\sqrt[3]{x^2-2 x+2}-1\right)-\frac{1}{4} \log \left(\left(x^2-2 x+2\right)^{2/3}+\sqrt[3]{x^2-2 x+2}+1\right)+\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x^2-2 x+2}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)",1,"(Sqrt[3]*ArcTan[(1 + 2*(1 + (-1 + x)^2)^(1/3))/Sqrt[3]] + (3*Log[1 - (1 + (-1 + x)^2)^(1/3)])/2 - Log[1 - x])/2","A",1
1156,1,59,86,0.0188078,"\int \frac{1}{(1+x) \sqrt[3]{2+2 x+x^2}} \, dx","Integrate[1/((1 + x)*(2 + 2*x + x^2)^(1/3)),x]","\frac{1}{2} \left(-\log (x+1)+\frac{3}{2} \log \left(1-\sqrt[3]{(x+1)^2+1}\right)+\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{(x+1)^2+1}+1}{\sqrt{3}}\right)\right)","\frac{1}{2} \log \left(\sqrt[3]{x^2+2 x+2}-1\right)-\frac{1}{4} \log \left(\left(x^2+2 x+2\right)^{2/3}+\sqrt[3]{x^2+2 x+2}+1\right)+\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x^2+2 x+2}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)",1,"(Sqrt[3]*ArcTan[(1 + 2*(1 + (1 + x)^2)^(1/3))/Sqrt[3]] - Log[1 + x] + (3*Log[1 - (1 + (1 + x)^2)^(1/3)])/2)/2","A",1
1157,1,30,86,0.008343,"\int \frac{\left(-1+x^3\right)^{2/3}}{x} \, dx","Integrate[(-1 + x^3)^(2/3)/x,x]","-\frac{1}{2} \left(x^3-1\right)^{2/3} \left(\, _2F_1\left(\frac{2}{3},1;\frac{5}{3};1-x^3\right)-1\right)","\frac{1}{2} \left(x^3-1\right)^{2/3}+\frac{1}{3} \log \left(\sqrt[3]{x^3-1}+1\right)-\frac{1}{6} \log \left(\left(x^3-1\right)^{2/3}-\sqrt[3]{x^3-1}+1\right)+\frac{\tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{x^3-1}}{\sqrt{3}}\right)}{\sqrt{3}}",1,"-1/2*((-1 + x^3)^(2/3)*(-1 + Hypergeometric2F1[2/3, 1, 5/3, 1 - x^3]))","C",1
1158,0,0,86,0.1233736,"\int \frac{3+x^2}{\sqrt[3]{1+x^2} \left(-1-x^2+x^3\right)} \, dx","Integrate[(3 + x^2)/((1 + x^2)^(1/3)*(-1 - x^2 + x^3)),x]","\int \frac{3+x^2}{\sqrt[3]{1+x^2} \left(-1-x^2+x^3\right)} \, dx","\log \left(\sqrt[3]{x^2+1}-x\right)-\frac{1}{2} \log \left(x^2+\sqrt[3]{x^2+1} x+\left(x^2+1\right)^{2/3}\right)-\sqrt{3} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{x^2+1}}{\sqrt{3}}+\frac{2 x}{\sqrt{3}}}{\sqrt[3]{x^2+1}}\right)",1,"Integrate[(3 + x^2)/((1 + x^2)^(1/3)*(-1 - x^2 + x^3)), x]","F",-1
1159,0,0,86,5.187866,"\int \frac{-2-(-1+k) (1+k) x+2 k^2 x^2}{\sqrt[4]{\left(1-x^2\right) \left(1-k^2 x^2\right)} \left(-1+d-(3+d) x-\left(3+d k^2\right) x^2+\left(-1+d k^2\right) x^3\right)} \, dx","Integrate[(-2 - (-1 + k)*(1 + k)*x + 2*k^2*x^2)/(((1 - x^2)*(1 - k^2*x^2))^(1/4)*(-1 + d - (3 + d)*x - (3 + d*k^2)*x^2 + (-1 + d*k^2)*x^3)),x]","\int \frac{-2-(-1+k) (1+k) x+2 k^2 x^2}{\sqrt[4]{\left(1-x^2\right) \left(1-k^2 x^2\right)} \left(-1+d-(3+d) x-\left(3+d k^2\right) x^2+\left(-1+d k^2\right) x^3\right)} \, dx","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{k^2 x^4+\left(-k^2-1\right) x^2+1}}{x+1}\right)}{d^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{k^2 x^4+\left(-k^2-1\right) x^2+1}}{x+1}\right)}{d^{3/4}}",1,"Integrate[(-2 - (-1 + k)*(1 + k)*x + 2*k^2*x^2)/(((1 - x^2)*(1 - k^2*x^2))^(1/4)*(-1 + d - (3 + d)*x - (3 + d*k^2)*x^2 + (-1 + d*k^2)*x^3)), x]","F",-1
1160,0,0,86,4.9735618,"\int \frac{-2+(-1+k) (1+k) x+2 k^2 x^2}{\sqrt[4]{\left(1-x^2\right) \left(1-k^2 x^2\right)} \left(1-d-(3+d) x+\left(3+d k^2\right) x^2+\left(-1+d k^2\right) x^3\right)} \, dx","Integrate[(-2 + (-1 + k)*(1 + k)*x + 2*k^2*x^2)/(((1 - x^2)*(1 - k^2*x^2))^(1/4)*(1 - d - (3 + d)*x + (3 + d*k^2)*x^2 + (-1 + d*k^2)*x^3)),x]","\int \frac{-2+(-1+k) (1+k) x+2 k^2 x^2}{\sqrt[4]{\left(1-x^2\right) \left(1-k^2 x^2\right)} \left(1-d-(3+d) x+\left(3+d k^2\right) x^2+\left(-1+d k^2\right) x^3\right)} \, dx","\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{k^2 x^4+\left(-k^2-1\right) x^2+1}}{x-1}\right)}{d^{3/4}}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{k^2 x^4+\left(-k^2-1\right) x^2+1}}{x-1}\right)}{d^{3/4}}",1,"Integrate[(-2 + (-1 + k)*(1 + k)*x + 2*k^2*x^2)/(((1 - x^2)*(1 - k^2*x^2))^(1/4)*(1 - d - (3 + d)*x + (3 + d*k^2)*x^2 + (-1 + d*k^2)*x^3)), x]","F",-1
1161,1,135,86,0.0301108,"\int \frac{\sqrt[4]{-1+x^4}}{x} \, dx","Integrate[(-1 + x^4)^(1/4)/x,x]","\frac{1}{8} \left(8 \sqrt[4]{x^4-1}+\sqrt{2} \log \left(\sqrt{x^4-1}-\sqrt{2} \sqrt[4]{x^4-1}+1\right)-\sqrt{2} \log \left(\sqrt{x^4-1}+\sqrt{2} \sqrt[4]{x^4-1}+1\right)+2 \sqrt{2} \tan ^{-1}\left(1-\sqrt{2} \sqrt[4]{x^4-1}\right)-2 \sqrt{2} \tan ^{-1}\left(\sqrt{2} \sqrt[4]{x^4-1}+1\right)\right)","\sqrt[4]{x^4-1}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{x^4-1}}{\sqrt{x^4-1}-1}\right)}{2 \sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{x^4-1}}{\sqrt{x^4-1}+1}\right)}{2 \sqrt{2}}",1,"(8*(-1 + x^4)^(1/4) + 2*Sqrt[2]*ArcTan[1 - Sqrt[2]*(-1 + x^4)^(1/4)] - 2*Sqrt[2]*ArcTan[1 + Sqrt[2]*(-1 + x^4)^(1/4)] + Sqrt[2]*Log[1 - Sqrt[2]*(-1 + x^4)^(1/4) + Sqrt[-1 + x^4]] - Sqrt[2]*Log[1 + Sqrt[2]*(-1 + x^4)^(1/4) + Sqrt[-1 + x^4]])/8","A",1
1162,1,52,86,0.026472,"\int \frac{\sqrt{-x+x^4}}{-b+a x^3} \, dx","Integrate[Sqrt[-x + x^4]/(-b + a*x^3),x]","-\frac{2 x \sqrt{x \left(x^3-1\right)} F_1\left(\frac{1}{2};-\frac{1}{2},1;\frac{3}{2};x^3,\frac{a x^3}{b}\right)}{3 b \sqrt{1-x^3}}","\frac{2 \sqrt{a-b} \tan ^{-1}\left(\frac{x \sqrt{x^4-x} \sqrt{a-b}}{\sqrt{b} (x-1) \left(x^2+x+1\right)}\right)}{3 a \sqrt{b}}+\frac{2 \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4-x}}\right)}{3 a}",1,"(-2*x*Sqrt[x*(-1 + x^3)]*AppellF1[1/2, -1/2, 1, 3/2, x^3, (a*x^3)/b])/(3*b*Sqrt[1 - x^3])","C",0
1163,1,69,86,0.2268656,"\int \frac{1}{\left(-1+x^4\right) \sqrt[4]{-x^2+x^4}} \, dx","Integrate[1/((-1 + x^4)*(-x^2 + x^4)^(1/4)),x]","-\frac{x \left(\sqrt[4]{1-x^2} \, _2F_1\left(\frac{1}{4},\frac{1}{4};\frac{5}{4};\frac{2 x^2}{x^2+1}\right)+\sqrt[4]{x^2+1}\right)}{\sqrt[4]{x^2 \left(x^2-1\right)} \sqrt[4]{x^2+1}}","-\frac{\left(x^4-x^2\right)^{3/4}}{x \left(x^2-1\right)}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-x^2}}\right)}{2 \sqrt[4]{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-x^2}}\right)}{2 \sqrt[4]{2}}",1,"-((x*((1 + x^2)^(1/4) + (1 - x^2)^(1/4)*Hypergeometric2F1[1/4, 1/4, 5/4, (2*x^2)/(1 + x^2)]))/((x^2*(-1 + x^2))^(1/4)*(1 + x^2)^(1/4)))","C",0
1164,1,105,86,0.1064612,"\int \frac{\sqrt[4]{-x^3+x^4}}{-1-2 x+x^2} \, dx","Integrate[(-x^3 + x^4)^(1/4)/(-1 - 2*x + x^2),x]","\frac{\sqrt[4]{(x-1) x^3} \left(4 \sqrt[4]{x} \, _2F_1\left(\frac{1}{4},\frac{1}{4};\frac{5}{4};1-x\right)+\left(\sqrt{2}-2\right) \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};-\frac{\left(-2+\sqrt{2}\right) (x-1)}{2 x}\right)-\left(2+\sqrt{2}\right) \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{\left(2+\sqrt{2}\right) (x-1)}{2 x}\right)\right)}{x}","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^4+2\&,\frac{\log \left(\sqrt[4]{x^4-x^3}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}^3}\&\right]-2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^3}}\right)+2 \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^3}}\right)",1,"(((-1 + x)*x^3)^(1/4)*(4*x^(1/4)*Hypergeometric2F1[1/4, 1/4, 5/4, 1 - x] + (-2 + Sqrt[2])*Hypergeometric2F1[1/4, 1, 5/4, -1/2*((-2 + Sqrt[2])*(-1 + x))/x] - (2 + Sqrt[2])*Hypergeometric2F1[1/4, 1, 5/4, ((2 + Sqrt[2])*(-1 + x))/(2*x)]))/x","A",1
1165,1,105,86,0.0474876,"\int \frac{\sqrt[4]{-x^3+x^4}}{-1-2 x+x^2} \, dx","Integrate[(-x^3 + x^4)^(1/4)/(-1 - 2*x + x^2),x]","\frac{\sqrt[4]{(x-1) x^3} \left(4 \sqrt[4]{x} \, _2F_1\left(\frac{1}{4},\frac{1}{4};\frac{5}{4};1-x\right)+\left(\sqrt{2}-2\right) \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};-\frac{\left(-2+\sqrt{2}\right) (x-1)}{2 x}\right)-\left(2+\sqrt{2}\right) \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{\left(2+\sqrt{2}\right) (x-1)}{2 x}\right)\right)}{x}","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^4+2\&,\frac{\log \left(\sqrt[4]{x^4-x^3}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}^3}\&\right]-2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^3}}\right)+2 \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^3}}\right)",1,"(((-1 + x)*x^3)^(1/4)*(4*x^(1/4)*Hypergeometric2F1[1/4, 1/4, 5/4, 1 - x] + (-2 + Sqrt[2])*Hypergeometric2F1[1/4, 1, 5/4, -1/2*((-2 + Sqrt[2])*(-1 + x))/x] - (2 + Sqrt[2])*Hypergeometric2F1[1/4, 1, 5/4, ((2 + Sqrt[2])*(-1 + x))/(2*x)]))/x","A",1
1166,1,81,86,0.025332,"\int \frac{x^6}{\left(-b+a x^4\right)^{3/4}} \, dx","Integrate[x^6/(-b + a*x^4)^(3/4),x]","\frac{2 a^{3/4} x^3 \sqrt[4]{a x^4-b}-3 b \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)+3 b \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{8 a^{7/4}}","-\frac{3 b \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{8 a^{7/4}}+\frac{3 b \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{8 a^{7/4}}+\frac{x^3 \sqrt[4]{a x^4-b}}{4 a}",1,"(2*a^(3/4)*x^3*(-b + a*x^4)^(1/4) - 3*b*ArcTan[(a^(1/4)*x)/(-b + a*x^4)^(1/4)] + 3*b*ArcTanh[(a^(1/4)*x)/(-b + a*x^4)^(1/4)])/(8*a^(7/4))","A",1
1167,1,61,86,0.0585454,"\int \frac{\left(-b+a x^4\right) \sqrt[4]{b+a x^4}}{x^2} \, dx","Integrate[((-b + a*x^4)*(b + a*x^4)^(1/4))/x^2,x]","\frac{\sqrt[4]{a x^4+b} \left(-\frac{a x^4 \, _2F_1\left(-\frac{1}{4},\frac{3}{4};\frac{7}{4};-\frac{a x^4}{b}\right)}{\sqrt[4]{\frac{a x^4}{b}+1}}+a x^4+b\right)}{x}","\frac{\sqrt[4]{a x^4+b} \left(a x^4+4 b\right)}{4 x}+\frac{3}{8} \sqrt[4]{a} b \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)-\frac{3}{8} \sqrt[4]{a} b \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)",1,"((b + a*x^4)^(1/4)*(b + a*x^4 - (a*x^4*Hypergeometric2F1[-1/4, 3/4, 7/4, -((a*x^4)/b)])/(1 + (a*x^4)/b)^(1/4)))/x","C",1
1168,0,0,86,0.1531719,"\int \frac{\left(-1+x^3\right)^{2/3} \left(2+x^3\right)}{x^6 \left(-4-2 x^3+x^6\right)} \, dx","Integrate[((-1 + x^3)^(2/3)*(2 + x^3))/(x^6*(-4 - 2*x^3 + x^6)),x]","\int \frac{\left(-1+x^3\right)^{2/3} \left(2+x^3\right)}{x^6 \left(-4-2 x^3+x^6\right)} \, dx","\frac{\left(1-x^3\right) \left(x^3-1\right)^{2/3}}{10 x^5}-\frac{1}{12} \text{RootSum}\left[4 \text{$\#$1}^6-10 \text{$\#$1}^3+5\&,\frac{\text{$\#$1}^2 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)-\text{$\#$1}^2 \log (x)}{4 \text{$\#$1}^3-5}\&\right]",1,"Integrate[((-1 + x^3)^(2/3)*(2 + x^3))/(x^6*(-4 - 2*x^3 + x^6)), x]","F",-1
1169,0,0,86,0.0773931,"\int \frac{\left(-1+x^3\right)^{2/3} \left(2+x^3\right)}{x^6 \left(-4-2 x^3+x^6\right)} \, dx","Integrate[((-1 + x^3)^(2/3)*(2 + x^3))/(x^6*(-4 - 2*x^3 + x^6)),x]","\int \frac{\left(-1+x^3\right)^{2/3} \left(2+x^3\right)}{x^6 \left(-4-2 x^3+x^6\right)} \, dx","\frac{\left(1-x^3\right) \left(x^3-1\right)^{2/3}}{10 x^5}-\frac{1}{12} \text{RootSum}\left[4 \text{$\#$1}^6-10 \text{$\#$1}^3+5\&,\frac{\text{$\#$1}^2 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)-\text{$\#$1}^2 \log (x)}{4 \text{$\#$1}^3-5}\&\right]",1,"Integrate[((-1 + x^3)^(2/3)*(2 + x^3))/(x^6*(-4 - 2*x^3 + x^6)), x]","F",-1
1170,0,0,86,0.1568778,"\int \frac{\left(-1+x^3\right)^{2/3} \left(4-2 x^3+x^6\right)}{x^6 \left(-8+4 x^3+x^6\right)} \, dx","Integrate[((-1 + x^3)^(2/3)*(4 - 2*x^3 + x^6))/(x^6*(-8 + 4*x^3 + x^6)),x]","\int \frac{\left(-1+x^3\right)^{2/3} \left(4-2 x^3+x^6\right)}{x^6 \left(-8+4 x^3+x^6\right)} \, dx","\frac{\left(1-x^3\right) \left(x^3-1\right)^{2/3}}{10 x^5}-\frac{1}{8} \text{RootSum}\left[8 \text{$\#$1}^6-12 \text{$\#$1}^3+3\&,\frac{\text{$\#$1}^2 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)-\text{$\#$1}^2 \log (x)}{4 \text{$\#$1}^3-3}\&\right]",1,"Integrate[((-1 + x^3)^(2/3)*(4 - 2*x^3 + x^6))/(x^6*(-8 + 4*x^3 + x^6)), x]","F",-1
1171,0,0,86,0.0798592,"\int \frac{\left(-1+x^3\right)^{2/3} \left(4-2 x^3+x^6\right)}{x^6 \left(-8+4 x^3+x^6\right)} \, dx","Integrate[((-1 + x^3)^(2/3)*(4 - 2*x^3 + x^6))/(x^6*(-8 + 4*x^3 + x^6)),x]","\int \frac{\left(-1+x^3\right)^{2/3} \left(4-2 x^3+x^6\right)}{x^6 \left(-8+4 x^3+x^6\right)} \, dx","\frac{\left(1-x^3\right) \left(x^3-1\right)^{2/3}}{10 x^5}-\frac{1}{8} \text{RootSum}\left[8 \text{$\#$1}^6-12 \text{$\#$1}^3+3\&,\frac{\text{$\#$1}^2 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)-\text{$\#$1}^2 \log (x)}{4 \text{$\#$1}^3-3}\&\right]",1,"Integrate[((-1 + x^3)^(2/3)*(4 - 2*x^3 + x^6))/(x^6*(-8 + 4*x^3 + x^6)), x]","F",-1
1172,0,0,86,0.1735823,"\int \frac{\left(-1+x^3\right)^{2/3} \left(2-2 x^3+x^6\right)}{x^6 \left(-4+4 x^3+x^6\right)} \, dx","Integrate[((-1 + x^3)^(2/3)*(2 - 2*x^3 + x^6))/(x^6*(-4 + 4*x^3 + x^6)),x]","\int \frac{\left(-1+x^3\right)^{2/3} \left(2-2 x^3+x^6\right)}{x^6 \left(-4+4 x^3+x^6\right)} \, dx","\frac{\left(1-x^3\right) \left(x^3-1\right)^{2/3}}{10 x^5}-\frac{1}{8} \text{RootSum}\left[4 \text{$\#$1}^6-4 \text{$\#$1}^3-1\&,\frac{\text{$\#$1}^2 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)-\text{$\#$1}^2 \log (x)}{2 \text{$\#$1}^3-1}\&\right]",1,"Integrate[((-1 + x^3)^(2/3)*(2 - 2*x^3 + x^6))/(x^6*(-4 + 4*x^3 + x^6)), x]","F",-1
1173,0,0,86,0.0816227,"\int \frac{\left(-1+x^3\right)^{2/3} \left(2-2 x^3+x^6\right)}{x^6 \left(-4+4 x^3+x^6\right)} \, dx","Integrate[((-1 + x^3)^(2/3)*(2 - 2*x^3 + x^6))/(x^6*(-4 + 4*x^3 + x^6)),x]","\int \frac{\left(-1+x^3\right)^{2/3} \left(2-2 x^3+x^6\right)}{x^6 \left(-4+4 x^3+x^6\right)} \, dx","\frac{\left(1-x^3\right) \left(x^3-1\right)^{2/3}}{10 x^5}-\frac{1}{8} \text{RootSum}\left[4 \text{$\#$1}^6-4 \text{$\#$1}^3-1\&,\frac{\text{$\#$1}^2 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)-\text{$\#$1}^2 \log (x)}{2 \text{$\#$1}^3-1}\&\right]",1,"Integrate[((-1 + x^3)^(2/3)*(2 - 2*x^3 + x^6))/(x^6*(-4 + 4*x^3 + x^6)), x]","F",-1
1174,0,0,86,0.390554,"\int \frac{2+x^4}{\sqrt[4]{-1+x^4} \left(-2+x^8\right)} \, dx","Integrate[(2 + x^4)/((-1 + x^4)^(1/4)*(-2 + x^8)),x]","\int \frac{2+x^4}{\sqrt[4]{-1+x^4} \left(-2+x^8\right)} \, dx","-\frac{1}{16} \text{RootSum}\left[2 \text{$\#$1}^8-4 \text{$\#$1}^4+1\&,\frac{-2 \text{$\#$1}^4 \log \left(\sqrt[4]{x^4-1}-\text{$\#$1} x\right)+2 \text{$\#$1}^4 \log (x)+3 \log \left(\sqrt[4]{x^4-1}-\text{$\#$1} x\right)-3 \log (x)}{\text{$\#$1}^5-\text{$\#$1}}\&\right]",1,"Integrate[(2 + x^4)/((-1 + x^4)^(1/4)*(-2 + x^8)), x]","F",-1
1175,1,84,86,0.1007515,"\int \frac{-b+a x^8}{x^6 \left(b+a x^4\right)^{3/4}} \, dx","Integrate[(-b + a*x^8)/(x^6*(b + a*x^4)^(3/4)),x]","\frac{1}{10} \left(-5 \sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)+5 \sqrt[4]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)+\frac{2 \sqrt[4]{a x^4+b} \left(b-4 a x^4\right)}{b x^5}\right)","-\frac{1}{2} \sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)+\frac{1}{2} \sqrt[4]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)+\frac{\sqrt[4]{a x^4+b} \left(b-4 a x^4\right)}{5 b x^5}",1,"((2*(b - 4*a*x^4)*(b + a*x^4)^(1/4))/(b*x^5) - 5*a^(1/4)*ArcTan[(a^(1/4)*x)/(b + a*x^4)^(1/4)] + 5*a^(1/4)*ArcTanh[(a^(1/4)*x)/(b + a*x^4)^(1/4)])/10","A",1
1176,1,97,87,0.0882679,"\int \frac{\sqrt{x}}{(-1+x) \sqrt{-\sqrt{x}+x}} \, dx","Integrate[Sqrt[x]/((-1 + x)*Sqrt[-Sqrt[x] + x]),x]","-\frac{\sqrt[4]{x} \left(2 \sqrt[4]{x}+4 \sqrt{1-\sqrt{x}} \sin ^{-1}\left(\sqrt{1-\sqrt{x}}\right)+\sqrt{2} \sqrt{\sqrt{x}-1} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x}-1}}{\sqrt{2} \sqrt[4]{x}}\right)\right)}{\sqrt{x-\sqrt{x}}}","-\frac{2 \sqrt{x-\sqrt{x}}}{\sqrt{x}-1}+4 \tanh ^{-1}\left(\frac{\sqrt{x-\sqrt{x}}}{\sqrt{x}-1}\right)-\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{x-\sqrt{x}}}{\sqrt{x}-1}\right)",1,"-((x^(1/4)*(2*x^(1/4) + 4*Sqrt[1 - Sqrt[x]]*ArcSin[Sqrt[1 - Sqrt[x]]] + Sqrt[2]*Sqrt[-1 + Sqrt[x]]*ArcTanh[Sqrt[-1 + Sqrt[x]]/(Sqrt[2]*x^(1/4))]))/Sqrt[-Sqrt[x] + x])","A",1
1177,1,26,87,0.0051761,"\int \frac{1}{x^3 \left(1+x^2\right)^{2/3}} \, dx","Integrate[1/(x^3*(1 + x^2)^(2/3)),x]","\frac{3}{2} \sqrt[3]{x^2+1} \, _2F_1\left(\frac{1}{3},2;\frac{4}{3};x^2+1\right)","-\frac{\sqrt[3]{x^2+1}}{2 x^2}-\frac{1}{3} \log \left(\sqrt[3]{x^2+1}-1\right)+\frac{1}{6} \log \left(\left(x^2+1\right)^{2/3}+\sqrt[3]{x^2+1}+1\right)+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{x^2+1}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3}}",1,"(3*(1 + x^2)^(1/3)*Hypergeometric2F1[1/3, 2, 4/3, 1 + x^2])/2","C",1
1178,1,26,87,0.0059126,"\int \frac{\left(1+x^2\right)^{2/3}}{x^3} \, dx","Integrate[(1 + x^2)^(2/3)/x^3,x]","\frac{3}{10} \left(x^2+1\right)^{5/3} \, _2F_1\left(\frac{5}{3},2;\frac{8}{3};x^2+1\right)","-\frac{\left(x^2+1\right)^{2/3}}{2 x^2}+\frac{1}{3} \log \left(\sqrt[3]{x^2+1}-1\right)-\frac{1}{6} \log \left(\left(x^2+1\right)^{2/3}+\sqrt[3]{x^2+1}+1\right)+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{x^2+1}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3}}",1,"(3*(1 + x^2)^(5/3)*Hypergeometric2F1[5/3, 2, 8/3, 1 + x^2])/10","C",1
1179,1,62,87,0.0238774,"\int \frac{\left(1+x^2\right)^{2/3}}{x} \, dx","Integrate[(1 + x^2)^(2/3)/x,x]","\frac{1}{4} \left(3 \left(\left(x^2+1\right)^{2/3}+\log \left(1-\sqrt[3]{x^2+1}\right)\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x^2+1}+1}{\sqrt{3}}\right)-2 \log (x)\right)","\frac{3}{4} \left(x^2+1\right)^{2/3}+\frac{1}{2} \log \left(\sqrt[3]{x^2+1}-1\right)-\frac{1}{4} \log \left(\left(x^2+1\right)^{2/3}+\sqrt[3]{x^2+1}+1\right)+\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x^2+1}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)",1,"(2*Sqrt[3]*ArcTan[(1 + 2*(1 + x^2)^(1/3))/Sqrt[3]] - 2*Log[x] + 3*((1 + x^2)^(2/3) + Log[1 - (1 + x^2)^(1/3)]))/4","A",1
1180,1,18077,87,6.6988197,"\int \frac{(3+4 x) \sqrt{x+2 x^2-2 x^4}}{(1+2 x) \left(1+2 x+x^3\right)} \, dx","Integrate[((3 + 4*x)*Sqrt[x + 2*x^2 - 2*x^4])/((1 + 2*x)*(1 + 2*x + x^3)),x]","\text{Result too large to show}","2 \sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} x \sqrt{-2 x^4+2 x^2+x}}{2 x^3-2 x-1}\right)-2 \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x \sqrt{-2 x^4+2 x^2+x}}{2 x^3-2 x-1}\right)",1,"Result too large to show","C",0
1181,1,62,87,0.0253486,"\int \frac{\left(1+x^4\right)^{2/3}}{x} \, dx","Integrate[(1 + x^4)^(2/3)/x,x]","\frac{1}{8} \left(3 \left(\left(x^4+1\right)^{2/3}+\log \left(1-\sqrt[3]{x^4+1}\right)\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x^4+1}+1}{\sqrt{3}}\right)-4 \log (x)\right)","\frac{3}{8} \left(x^4+1\right)^{2/3}+\frac{1}{4} \log \left(\sqrt[3]{x^4+1}-1\right)-\frac{1}{8} \log \left(\left(x^4+1\right)^{2/3}+\sqrt[3]{x^4+1}+1\right)+\frac{1}{4} \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x^4+1}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)",1,"(2*Sqrt[3]*ArcTan[(1 + 2*(1 + x^4)^(1/3))/Sqrt[3]] - 4*Log[x] + 3*((1 + x^4)^(2/3) + Log[1 - (1 + x^4)^(1/3)]))/8","A",1
1182,0,0,87,0.2915008,"\int \frac{\sqrt[3]{-1+x^4} \left(3+x^4\right)}{x^2 \left(-1-x^3+x^4\right)} \, dx","Integrate[((-1 + x^4)^(1/3)*(3 + x^4))/(x^2*(-1 - x^3 + x^4)),x]","\int \frac{\sqrt[3]{-1+x^4} \left(3+x^4\right)}{x^2 \left(-1-x^3+x^4\right)} \, dx","\frac{3 \sqrt[3]{x^4-1}}{x}+\log \left(\sqrt[3]{x^4-1}-x\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^4-1}+x}\right)-\frac{1}{2} \log \left(\sqrt[3]{x^4-1} x+\left(x^4-1\right)^{2/3}+x^2\right)",1,"Integrate[((-1 + x^4)^(1/3)*(3 + x^4))/(x^2*(-1 - x^3 + x^4)), x]","F",-1
1183,0,0,87,0.2113873,"\int \frac{x^2 \left(4+x^3\right)}{\left(1+x^3\right)^{3/4} \left(1+x^3+x^4\right)} \, dx","Integrate[(x^2*(4 + x^3))/((1 + x^3)^(3/4)*(1 + x^3 + x^4)),x]","\int \frac{x^2 \left(4+x^3\right)}{\left(1+x^3\right)^{3/4} \left(1+x^3+x^4\right)} \, dx","-\sqrt{2} \tan ^{-1}\left(\frac{\frac{\sqrt{x^3+1}}{\sqrt{2}}-\frac{x^2}{\sqrt{2}}}{x \sqrt[4]{x^3+1}}\right)-\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{x^3+1}}{\sqrt{x^3+1}+x^2}\right)",1,"Integrate[(x^2*(4 + x^3))/((1 + x^3)^(3/4)*(1 + x^3 + x^4)), x]","F",-1
1184,1,77,87,0.0356205,"\int \frac{x^2}{\left(-b+a x^4\right)^{3/4} \left(b+a x^4\right)} \, dx","Integrate[x^2/((-b + a*x^4)^(3/4)*(b + a*x^4)),x]","\frac{x^3 \left(1-\frac{a x^4}{b}\right)^{3/4} \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};\frac{2 a x^4}{a x^4+b}\right)}{3 b \left(a x^4-b\right)^{3/4} \left(\frac{a x^4}{b}+1\right)^{3/4}}","\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{2\ 2^{3/4} a^{3/4} b}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{2\ 2^{3/4} a^{3/4} b}",1,"(x^3*(1 - (a*x^4)/b)^(3/4)*Hypergeometric2F1[3/4, 3/4, 7/4, (2*a*x^4)/(b + a*x^4)])/(3*b*(-b + a*x^4)^(3/4)*(1 + (a*x^4)/b)^(3/4))","C",0
1185,1,70,87,0.0251698,"\int \frac{1}{\sqrt[4]{-b+a x^4} \left(b+a x^4\right)} \, dx","Integrate[1/((-b + a*x^4)^(1/4)*(b + a*x^4)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)+\tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{2 \sqrt[4]{2} \sqrt[4]{a} b}","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{2 \sqrt[4]{2} \sqrt[4]{a} b}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{2 \sqrt[4]{2} \sqrt[4]{a} b}",1,"(ArcTan[(2^(1/4)*a^(1/4)*x)/(-b + a*x^4)^(1/4)] + ArcTanh[(2^(1/4)*a^(1/4)*x)/(-b + a*x^4)^(1/4)])/(2*2^(1/4)*a^(1/4)*b)","A",1
1186,1,5341,87,8.0764255,"\int \frac{-a^2 b+a (2 a+b) x-3 a x^2+x^3}{\sqrt{x (-a+x) (-b+x)} \left(-a^2+2 a x+\left(-1+b^2 d\right) x^2-2 b d x^3+d x^4\right)} \, dx","Integrate[(-(a^2*b) + a*(2*a + b)*x - 3*a*x^2 + x^3)/(Sqrt[x*(-a + x)*(-b + x)]*(-a^2 + 2*a*x + (-1 + b^2*d)*x^2 - 2*b*d*x^3 + d*x^4)),x]","\text{Result too large to show}","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{x^2 (-a-b)+a b x+x^3}}{a-x}\right)}{\sqrt[4]{d}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{x^2 (-a-b)+a b x+x^3}}{a-x}\right)}{\sqrt[4]{d}}",1,"Result too large to show","C",0
1187,1,72,87,0.5175992,"\int \frac{1+k^2 x^4}{\sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)} \left(-1+k^2 x^4\right)} \, dx","Integrate[(1 + k^2*x^4)/(Sqrt[(1 - x^2)*(1 - k^2*x^2)]*(-1 + k^2*x^4)),x]","\frac{\sqrt{1-x^2} \sqrt{1-k^2 x^2} \left(F\left(\sin ^{-1}(x)|k^2\right)-\Pi \left(-k;\sin ^{-1}(x)|k^2\right)-\Pi \left(k;\sin ^{-1}(x)|k^2\right)\right)}{\sqrt{\left(x^2-1\right) \left(k^2 x^2-1\right)}}","\frac{\tan ^{-1}\left(\frac{(k+1) x}{\sqrt{k^2 x^4+\left(-k^2-1\right) x^2+1}+k x^2+1}\right)}{-k-1}-\frac{\tan ^{-1}\left(\frac{(k-1) x}{\sqrt{k^2 x^4+\left(-k^2-1\right) x^2+1}}\right)}{2 (k-1)}",1,"(Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*(EllipticF[ArcSin[x], k^2] - EllipticPi[-k, ArcSin[x], k^2] - EllipticPi[k, ArcSin[x], k^2]))/Sqrt[(-1 + x^2)*(-1 + k^2*x^2)]","C",1
1188,0,0,87,2.9836489,"\int \frac{x (-1+k x) (-1+(-1+2 k) x)}{\sqrt[3]{(1-x) x (1-k x)} \left(-1+(4-c) x+(-6+b+2 c+c k) x^2+(4-c-2 b k-2 c k) x^3+\left(-1+c k+b k^2\right) x^4\right)} \, dx","Integrate[(x*(-1 + k*x)*(-1 + (-1 + 2*k)*x))/(((1 - x)*x*(1 - k*x))^(1/3)*(-1 + (4 - c)*x + (-6 + b + 2*c + c*k)*x^2 + (4 - c - 2*b*k - 2*c*k)*x^3 + (-1 + c*k + b*k^2)*x^4)),x]","\int \frac{x (-1+k x) (-1+(-1+2 k) x)}{\sqrt[3]{(1-x) x (1-k x)} \left(-1+(4-c) x+(-6+b+2 c+c k) x^2+(4-c-2 b k-2 c k) x^3+\left(-1+c k+b k^2\right) x^4\right)} \, dx","\frac{1}{3} \text{RootSum}\left[-\text{$\#$1}^6-\text{$\#$1}^3 c+b\&,\frac{3 \log \left(\text{$\#$1} \sqrt[3]{k x^3+(-k-1) x^2+x}+x-1\right)-\log \left(k x^3+(-k-1) x^2+x\right)}{2 \text{$\#$1}^5+\text{$\#$1}^2 c}\&\right]",1,"Integrate[(x*(-1 + k*x)*(-1 + (-1 + 2*k)*x))/(((1 - x)*x*(1 - k*x))^(1/3)*(-1 + (4 - c)*x + (-6 + b + 2*c + c*k)*x^2 + (4 - c - 2*b*k - 2*c*k)*x^3 + (-1 + c*k + b*k^2)*x^4)), x]","F",-1
1189,1,62,87,0.0280523,"\int \frac{\left(1+x^5\right)^{2/3}}{x} \, dx","Integrate[(1 + x^5)^(2/3)/x,x]","\frac{1}{10} \left(3 \left(\left(x^5+1\right)^{2/3}+\log \left(1-\sqrt[3]{x^5+1}\right)\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x^5+1}+1}{\sqrt{3}}\right)-5 \log (x)\right)","\frac{3}{10} \left(x^5+1\right)^{2/3}+\frac{1}{5} \log \left(\sqrt[3]{x^5+1}-1\right)-\frac{1}{10} \log \left(\left(x^5+1\right)^{2/3}+\sqrt[3]{x^5+1}+1\right)+\frac{1}{5} \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x^5+1}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)",1,"(2*Sqrt[3]*ArcTan[(1 + 2*(1 + x^5)^(1/3))/Sqrt[3]] - 5*Log[x] + 3*((1 + x^5)^(2/3) + Log[1 - (1 + x^5)^(1/3)]))/10","A",1
1190,1,62,87,0.0215585,"\int \frac{\left(1+x^6\right)^{2/3}}{x} \, dx","Integrate[(1 + x^6)^(2/3)/x,x]","\frac{1}{12} \left(3 \left(\left(x^6+1\right)^{2/3}+\log \left(1-\sqrt[3]{x^6+1}\right)-2 \log (x)\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x^6+1}+1}{\sqrt{3}}\right)\right)","\frac{1}{4} \left(x^6+1\right)^{2/3}+\frac{1}{6} \log \left(\sqrt[3]{x^6+1}-1\right)-\frac{1}{12} \log \left(\left(x^6+1\right)^{2/3}+\sqrt[3]{x^6+1}+1\right)+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{x^6+1}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3}}",1,"(2*Sqrt[3]*ArcTan[(1 + 2*(1 + x^6)^(1/3))/Sqrt[3]] + 3*((1 + x^6)^(2/3) - 2*Log[x] + Log[1 - (1 + x^6)^(1/3)]))/12","A",1
1191,0,0,87,0.3906667,"\int \frac{\left(1-x^2+2 x^4\right) \sqrt{1-x^2-x^4-x^6}}{\left(-1+x^2\right) \left(1+x^2\right) \left(-1+x^4+x^6\right)} \, dx","Integrate[((1 - x^2 + 2*x^4)*Sqrt[1 - x^2 - x^4 - x^6])/((-1 + x^2)*(1 + x^2)*(-1 + x^4 + x^6)),x]","\int \frac{\left(1-x^2+2 x^4\right) \sqrt{1-x^2-x^4-x^6}}{\left(-1+x^2\right) \left(1+x^2\right) \left(-1+x^4+x^6\right)} \, dx","\tan ^{-1}\left(\frac{x \sqrt{-x^6-x^4-x^2+1}}{x^6+x^4+x^2-1}\right)-\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} x \sqrt{-x^6-x^4-x^2+1}}{x^6+x^4+x^2-1}\right)",1,"Integrate[((1 - x^2 + 2*x^4)*Sqrt[1 - x^2 - x^4 - x^6])/((-1 + x^2)*(1 + x^2)*(-1 + x^4 + x^6)), x]","F",-1
1192,0,0,87,0.2961345,"\int \frac{\sqrt[3]{-1+x^8} \left(3+5 x^8\right)}{x^2 \left(-1-x^3+x^8\right)} \, dx","Integrate[((-1 + x^8)^(1/3)*(3 + 5*x^8))/(x^2*(-1 - x^3 + x^8)),x]","\int \frac{\sqrt[3]{-1+x^8} \left(3+5 x^8\right)}{x^2 \left(-1-x^3+x^8\right)} \, dx","\frac{3 \sqrt[3]{x^8-1}}{x}+\log \left(\sqrt[3]{x^8-1}-x\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^8-1}+x}\right)-\frac{1}{2} \log \left(\sqrt[3]{x^8-1} x+\left(x^8-1\right)^{2/3}+x^2\right)",1,"Integrate[((-1 + x^8)^(1/3)*(3 + 5*x^8))/(x^2*(-1 - x^3 + x^8)), x]","F",-1
1193,1,68,87,0.0434404,"\int \frac{\left(2+x^8\right) \sqrt{4-2 x^8+x^{16}}}{x^9} \, dx","Integrate[((2 + x^8)*Sqrt[4 - 2*x^8 + x^16])/x^9,x]","\frac{1}{8} \left(\sinh ^{-1}\left(\frac{x^8-1}{\sqrt{3}}\right)+\frac{\sqrt{x^{16}-2 x^8+4} \left(x^8-2\right)}{x^8}-\tanh ^{-1}\left(\frac{4-x^8}{2 \sqrt{x^{16}-2 x^8+4}}\right)\right)","\frac{\sqrt{x^{16}-2 x^8+4} \left(x^8-2\right)}{8 x^8}-\frac{1}{8} \log \left(-x^8+\sqrt{x^{16}-2 x^8+4}+2\right)+\frac{1}{4} \tanh ^{-1}\left(\frac{2 x^8}{3}-\frac{2}{3} \sqrt{x^{16}-2 x^8+4}+\frac{1}{3}\right)",1,"(((-2 + x^8)*Sqrt[4 - 2*x^8 + x^16])/x^8 + ArcSinh[(-1 + x^8)/Sqrt[3]] - ArcTanh[(4 - x^8)/(2*Sqrt[4 - 2*x^8 + x^16])])/8","A",1
1194,1,93,87,0.0727236,"\int \frac{\sqrt{x+\sqrt{1+x}}}{1-\sqrt{1+x}} \, dx","Integrate[Sqrt[x + Sqrt[1 + x]]/(1 - Sqrt[1 + x]),x]","\frac{1}{4} \left(-2 \sqrt{x+\sqrt{x+1}} \left(2 \sqrt{x+1}+5\right)-8 \tanh ^{-1}\left(\frac{1-3 \sqrt{x+1}}{2 \sqrt{x+\sqrt{x+1}}}\right)-7 \tanh ^{-1}\left(\frac{2 \sqrt{x+1}+1}{2 \sqrt{x+\sqrt{x+1}}}\right)\right)","\frac{1}{2} \sqrt{x+\sqrt{x+1}} \left(-2 \sqrt{x+1}-5\right)+\frac{7}{4} \log \left(-2 \sqrt{x+1}+2 \sqrt{x+\sqrt{x+1}}-1\right)+4 \tanh ^{-1}\left(-\sqrt{x+1}+\sqrt{x+\sqrt{x+1}}+1\right)",1,"(-2*Sqrt[x + Sqrt[1 + x]]*(5 + 2*Sqrt[1 + x]) - 8*ArcTanh[(1 - 3*Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])] - 7*ArcTanh[(1 + 2*Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])])/4","A",1
1195,1,73,87,0.0802889,"\int \frac{\sqrt{c+\sqrt{b+a x}}}{d-\sqrt{b+a x}} \, dx","Integrate[Sqrt[c + Sqrt[b + a*x]]/(d - Sqrt[b + a*x]),x]","\frac{12 d \sqrt{c+d} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a x+b}+c}}{\sqrt{c+d}}\right)-4 \sqrt{\sqrt{a x+b}+c} \left(\sqrt{a x+b}+c+3 d\right)}{3 a}","-\frac{4 \sqrt{\sqrt{a x+b}+c} \left(\sqrt{a x+b}+c+3 d\right)}{3 a}-\frac{4 d \sqrt{-c-d} \tan ^{-1}\left(\frac{\sqrt{-c-d} \sqrt{\sqrt{a x+b}+c}}{c+d}\right)}{a}",1,"(-4*Sqrt[c + Sqrt[b + a*x]]*(c + 3*d + Sqrt[b + a*x]) + 12*d*Sqrt[c + d]*ArcTanh[Sqrt[c + Sqrt[b + a*x]]/Sqrt[c + d]])/(3*a)","A",1
1196,1,85,87,0.2054522,"\int \left(b^2+a x^2\right) \sqrt{b+\sqrt{b^2+a x^2}} \, dx","Integrate[(b^2 + a*x^2)*Sqrt[b + Sqrt[b^2 + a*x^2]],x]","\frac{2 x \left(5 a^2 x^4+24 a b^2 x^2+11 a b x^2 \sqrt{a x^2+b^2}+35 b^3 \sqrt{a x^2+b^2}+35 b^4\right)}{35 \left(\sqrt{a x^2+b^2}+b\right)^{3/2}}","\frac{2 x \sqrt{a x^2+b^2} \left(5 a x^2+13 b^2\right)}{35 \sqrt{\sqrt{a x^2+b^2}+b}}+\frac{4 x \left(3 a b x^2+11 b^3\right)}{35 \sqrt{\sqrt{a x^2+b^2}+b}}",1,"(2*x*(35*b^4 + 24*a*b^2*x^2 + 5*a^2*x^4 + 35*b^3*Sqrt[b^2 + a*x^2] + 11*a*b*x^2*Sqrt[b^2 + a*x^2]))/(35*(b + Sqrt[b^2 + a*x^2])^(3/2))","A",1
1197,0,0,87,0.2291433,"\int \frac{1}{x+\sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[(x + Sqrt[x + Sqrt[1 + x^2]])^(-1),x]","\int \frac{1}{x+\sqrt{x+\sqrt{1+x^2}}} \, dx","2 \text{RootSum}\left[\text{$\#$1}^4+2 \text{$\#$1}^3-1\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)}{2 \text{$\#$1}+3}\&\right]-\log \left(\sqrt{x^2+1}+x\right)",1,"Integrate[(x + Sqrt[x + Sqrt[1 + x^2]])^(-1), x]","F",-1
1198,0,0,87,0.1442516,"\int \frac{1}{x+\sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[(x + Sqrt[x + Sqrt[1 + x^2]])^(-1),x]","\int \frac{1}{x+\sqrt{x+\sqrt{1+x^2}}} \, dx","2 \text{RootSum}\left[\text{$\#$1}^4+2 \text{$\#$1}^3-1\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)}{2 \text{$\#$1}+3}\&\right]-\log \left(\sqrt{x^2+1}+x\right)",1,"Integrate[(x + Sqrt[x + Sqrt[1 + x^2]])^(-1), x]","F",-1
1199,1,36,88,0.0128062,"\int \frac{1}{(-2+x) \sqrt[3]{-4-4 x+x^2}} \, dx","Integrate[1/((-2 + x)*(-4 - 4*x + x^2)^(1/3)),x]","\frac{3}{32} \left((x-2)^2-8\right)^{2/3} \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{1}{8} \left(8-(x-2)^2\right)\right)","-\frac{1}{4} \log \left(\sqrt[3]{x^2-4 x-4}+2\right)+\frac{1}{8} \log \left(\left(x^2-4 x-4\right)^{2/3}-2 \sqrt[3]{x^2-4 x-4}+4\right)-\frac{1}{4} \sqrt{3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{\sqrt[3]{x^2-4 x-4}}{\sqrt{3}}\right)",1,"(3*(-8 + (-2 + x)^2)^(2/3)*Hypergeometric2F1[2/3, 1, 5/3, (8 - (-2 + x)^2)/8])/32","C",1
1200,1,169,88,1.8757902,"\int \frac{-1+k x^2}{(a+b x) \sqrt{(1-x) x (1-k x)} (b+a k x)} \, dx","Integrate[(-1 + k*x^2)/((a + b*x)*Sqrt[(1 - x)*x*(1 - k*x)]*(b + a*k*x)),x]","\frac{2 i (x-1)^{3/2} \sqrt{\frac{x}{x-1}} \sqrt{\frac{1-k x}{k-k x}} \left(a b (k-1) F\left(i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|\frac{k-1}{k}\right)+a (a k+b) \Pi \left(\frac{a+b}{b};i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|\frac{k-1}{k}\right)+b (a+b) \Pi \left(\frac{b}{a k}+1;i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|\frac{k-1}{k}\right)\right)}{a b (a+b) \sqrt{(x-1) x (k x-1)} (a k+b)}","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{a+b} \sqrt{k x^3+(-k-1) x^2+x} \sqrt{a k+b}}{\sqrt{a} \sqrt{b} (x-1) (k x-1)}\right)}{\sqrt{a} \sqrt{b} \sqrt{a+b} \sqrt{a k+b}}",1,"((2*I)*(-1 + x)^(3/2)*Sqrt[x/(-1 + x)]*Sqrt[(1 - k*x)/(k - k*x)]*(a*b*(-1 + k)*EllipticF[I*ArcSinh[1/Sqrt[-1 + x]], (-1 + k)/k] + a*(b + a*k)*EllipticPi[(a + b)/b, I*ArcSinh[1/Sqrt[-1 + x]], (-1 + k)/k] + b*(a + b)*EllipticPi[1 + b/(a*k), I*ArcSinh[1/Sqrt[-1 + x]], (-1 + k)/k]))/(a*b*(a + b)*(b + a*k)*Sqrt[(-1 + x)*x*(-1 + k*x)])","C",1
1201,1,31196,88,15.2248136,"\int \frac{x (-b+x) \left(a b-2 a x+x^2\right)}{\sqrt{x (-a+x) (-b+x)} \left(-a^2+2 a x+\left(-1+b^2 d\right) x^2-2 b d x^3+d x^4\right)} \, dx","Integrate[(x*(-b + x)*(a*b - 2*a*x + x^2))/(Sqrt[x*(-a + x)*(-b + x)]*(-a^2 + 2*a*x + (-1 + b^2*d)*x^2 - 2*b*d*x^3 + d*x^4)),x]","\text{Result too large to show}","\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{x^2 (-a-b)+a b x+x^3}}{a-x}\right)}{d^{3/4}}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{x^2 (-a-b)+a b x+x^3}}{a-x}\right)}{d^{3/4}}",1,"Result too large to show","C",0
1202,0,0,88,1.1445767,"\int \frac{1+x^4}{\left(-1-x^2+x^4\right) \sqrt[3]{-x+x^5}} \, dx","Integrate[(1 + x^4)/((-1 - x^2 + x^4)*(-x + x^5)^(1/3)),x]","\int \frac{1+x^4}{\left(-1-x^2+x^4\right) \sqrt[3]{-x+x^5}} \, dx","\frac{1}{2} \log \left(\sqrt[3]{x^5-x}-x\right)-\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^5-x}+x}\right)-\frac{1}{4} \log \left(\sqrt[3]{x^5-x} x+\left(x^5-x\right)^{2/3}+x^2\right)",1,"Integrate[(1 + x^4)/((-1 - x^2 + x^4)*(-x + x^5)^(1/3)), x]","F",-1
1203,1,35,88,0.0077419,"\int \frac{x^3}{\left(-1+x^6\right)^{2/3}} \, dx","Integrate[x^3/(-1 + x^6)^(2/3),x]","\frac{x^4 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{x^6}{x^6-1}\right)}{4 \left(x^6-1\right)^{2/3}}","-\frac{1}{6} \log \left(\sqrt[3]{x^6-1}-x^2\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x^2}{2 \sqrt[3]{x^6-1}+x^2}\right)}{2 \sqrt{3}}+\frac{1}{12} \log \left(\left(x^6-1\right)^{2/3}+x^4+\sqrt[3]{x^6-1} x^2\right)",1,"(x^4*Hypergeometric2F1[2/3, 1, 5/3, x^6/(-1 + x^6)])/(4*(-1 + x^6)^(2/3))","C",1
1204,1,83,88,0.032807,"\int \frac{x}{\sqrt[3]{-1+x^6}} \, dx","Integrate[x/(-1 + x^6)^(1/3),x]","\frac{1}{12} \left(-2 \log \left(1-\frac{x^2}{\sqrt[3]{x^6-1}}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 x^2}{\sqrt[3]{x^6-1}}+1}{\sqrt{3}}\right)+\log \left(\frac{x^4}{\left(x^6-1\right)^{2/3}}+\frac{x^2}{\sqrt[3]{x^6-1}}+1\right)\right)","-\frac{1}{6} \log \left(\sqrt[3]{x^6-1}-x^2\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x^2}{2 \sqrt[3]{x^6-1}+x^2}\right)}{2 \sqrt{3}}+\frac{1}{12} \log \left(\left(x^6-1\right)^{2/3}+x^4+\sqrt[3]{x^6-1} x^2\right)",1,"(2*Sqrt[3]*ArcTan[(1 + (2*x^2)/(-1 + x^6)^(1/3))/Sqrt[3]] - 2*Log[1 - x^2/(-1 + x^6)^(1/3)] + Log[1 + x^4/(-1 + x^6)^(2/3) + x^2/(-1 + x^6)^(1/3)])/12","A",1
1205,1,35,88,0.0070134,"\int \frac{x^3}{\left(1+x^6\right)^{2/3}} \, dx","Integrate[x^3/(1 + x^6)^(2/3),x]","\frac{x^4 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{x^6}{x^6+1}\right)}{4 \left(x^6+1\right)^{2/3}}","-\frac{1}{6} \log \left(\sqrt[3]{x^6+1}-x^2\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x^2}{2 \sqrt[3]{x^6+1}+x^2}\right)}{2 \sqrt{3}}+\frac{1}{12} \log \left(\left(x^6+1\right)^{2/3}+x^4+\sqrt[3]{x^6+1} x^2\right)",1,"(x^4*Hypergeometric2F1[2/3, 1, 5/3, x^6/(1 + x^6)])/(4*(1 + x^6)^(2/3))","C",1
1206,1,83,88,0.0309434,"\int \frac{x}{\sqrt[3]{1+x^6}} \, dx","Integrate[x/(1 + x^6)^(1/3),x]","\frac{1}{12} \left(-2 \log \left(1-\frac{x^2}{\sqrt[3]{x^6+1}}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 x^2}{\sqrt[3]{x^6+1}}+1}{\sqrt{3}}\right)+\log \left(\frac{x^4}{\left(x^6+1\right)^{2/3}}+\frac{x^2}{\sqrt[3]{x^6+1}}+1\right)\right)","-\frac{1}{6} \log \left(\sqrt[3]{x^6+1}-x^2\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x^2}{2 \sqrt[3]{x^6+1}+x^2}\right)}{2 \sqrt{3}}+\frac{1}{12} \log \left(\left(x^6+1\right)^{2/3}+x^4+\sqrt[3]{x^6+1} x^2\right)",1,"(2*Sqrt[3]*ArcTan[(1 + (2*x^2)/(1 + x^6)^(1/3))/Sqrt[3]] - 2*Log[1 - x^2/(1 + x^6)^(1/3)] + Log[1 + x^4/(1 + x^6)^(2/3) + x^2/(1 + x^6)^(1/3)])/12","A",1
1207,1,88,88,0.0763416,"\int \frac{-b+a x^8}{x^2 \left(-b+a x^4\right)^{3/4}} \, dx","Integrate[(-b + a*x^8)/(x^2*(-b + a*x^4)^(3/4)),x]","\frac{2 a^{3/4} \left(x^4-4\right) \sqrt[4]{a x^4-b}-3 b x \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)+3 b x \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{8 a^{3/4} x}","-\frac{3 b \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{8 a^{3/4}}+\frac{3 b \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{8 a^{3/4}}+\frac{\left(x^4-4\right) \sqrt[4]{a x^4-b}}{4 x}",1,"(2*a^(3/4)*(-4 + x^4)*(-b + a*x^4)^(1/4) - 3*b*x*ArcTan[(a^(1/4)*x)/(-b + a*x^4)^(1/4)] + 3*b*x*ArcTanh[(a^(1/4)*x)/(-b + a*x^4)^(1/4)])/(8*a^(3/4)*x)","A",1
1208,1,88,88,0.0837892,"\int \frac{-3 b+2 a x^8}{x^8 \sqrt[4]{-b+a x^4}} \, dx","Integrate[(-3*b + 2*a*x^8)/(x^8*(-b + a*x^4)^(1/4)),x]","a^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)+a^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)-\frac{\left(a x^4-b\right)^{3/4} \left(4 a x^4+3 b\right)}{7 b x^7}","a^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)+a^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)+\frac{\left(a x^4-b\right)^{3/4} \left(-4 a x^4-3 b\right)}{7 b x^7}",1,"-1/7*((-b + a*x^4)^(3/4)*(3*b + 4*a*x^4))/(b*x^7) + a^(3/4)*ArcTan[(a^(1/4)*x)/(-b + a*x^4)^(1/4)] + a^(3/4)*ArcTanh[(a^(1/4)*x)/(-b + a*x^4)^(1/4)]","A",1
1209,0,0,88,0.2160599,"\int \frac{-b^2+a^2 x^8}{x^2 \left(b+a x^4\right)^{3/4} \left(b^2+a^2 x^8\right)} \, dx","Integrate[(-b^2 + a^2*x^8)/(x^2*(b + a*x^4)^(3/4)*(b^2 + a^2*x^8)),x]","\int \frac{-b^2+a^2 x^8}{x^2 \left(b+a x^4\right)^{3/4} \left(b^2+a^2 x^8\right)} \, dx","\frac{a^2 \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+2 a^2\&,\frac{\log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}^3 a-\text{$\#$1}^7}\&\right]}{4 b}+\frac{\sqrt[4]{a x^4+b}}{b x}",1,"Integrate[(-b^2 + a^2*x^8)/(x^2*(b + a*x^4)^(3/4)*(b^2 + a^2*x^8)), x]","F",-1
1210,1,148,88,1.0838849,"\int \frac{\sqrt{a x^2+b x \sqrt{-\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}}}{x \sqrt{-\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}} \, dx","Integrate[Sqrt[a*x^2 + b*x*Sqrt[-(a/b^2) + (a^2*x^2)/b^2]]/(x*Sqrt[-(a/b^2) + (a^2*x^2)/b^2]),x]","\frac{\sqrt{2} x \sqrt{a x \left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right)} \left(b x \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x^2-1\right) \tanh ^{-1}\left(\frac{\sqrt{a x \left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right)}}{\sqrt{2} a x}\right)}{\sqrt{\frac{a \left(a x^2-1\right)}{b^2}} \left(x \left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right)\right)^{3/2}}","-\frac{\sqrt{2} b \log \left(b \left(-\sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}}\right)+\sqrt{2} \sqrt{a} \sqrt{b x \sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}}+a x^2}-a x\right)}{\sqrt{a}}",1,"(Sqrt[2]*x*Sqrt[a*x*(a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2])]*(-1 + a*x^2 + b*x*Sqrt[(a*(-1 + a*x^2))/b^2])*ArcTanh[Sqrt[a*x*(a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2])]/(Sqrt[2]*a*x)])/(Sqrt[(a*(-1 + a*x^2))/b^2]*(x*(a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2]))^(3/2))","A",1
1211,1,30,89,0.0065593,"\int \frac{\left(-1+x^2\right)^{2/3}}{x} \, dx","Integrate[(-1 + x^2)^(2/3)/x,x]","-\frac{3}{4} \left(x^2-1\right)^{2/3} \left(\, _2F_1\left(\frac{2}{3},1;\frac{5}{3};1-x^2\right)-1\right)","\frac{3}{4} \left(x^2-1\right)^{2/3}+\frac{1}{2} \log \left(\sqrt[3]{x^2-1}+1\right)-\frac{1}{4} \log \left(\left(x^2-1\right)^{2/3}-\sqrt[3]{x^2-1}+1\right)+\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{x^2-1}}{\sqrt{3}}\right)",1,"(-3*(-1 + x^2)^(2/3)*(-1 + Hypergeometric2F1[2/3, 1, 5/3, 1 - x^2]))/4","C",1
1212,0,0,89,0.134296,"\int \frac{-3+x}{\sqrt[3]{-1+x^2} \left(2+x+x^2\right)} \, dx","Integrate[(-3 + x)/((-1 + x^2)^(1/3)*(2 + x + x^2)),x]","\int \frac{-3+x}{\sqrt[3]{-1+x^2} \left(2+x+x^2\right)} \, dx","\log \left(\sqrt[3]{x^2-1}-x-1\right)-\frac{1}{2} \log \left(x^2+\left(x^2-1\right)^{2/3}+(x+1) \sqrt[3]{x^2-1}+2 x+1\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x^2-1}}{\sqrt[3]{x^2-1}+2 x+2}\right)",1,"Integrate[(-3 + x)/((-1 + x^2)^(1/3)*(2 + x + x^2)), x]","F",-1
1213,1,279,89,0.7971469,"\int \frac{2+x^2}{\left(-2-2 x+x^2\right) \sqrt{-1+x^3}} \, dx","Integrate[(2 + x^2)/((-2 - 2*x + x^2)*Sqrt[-1 + x^3]),x]","\frac{2 \sqrt{\frac{1-x}{1+\sqrt[3]{-1}}} \left((1+i) \left(3-i \sqrt{3}\right) \sqrt{x^2+x+1} \left(\Pi \left(\frac{2 \sqrt{3}}{-3 i+(1+2 i) \sqrt{3}};\sin ^{-1}\left(\sqrt{\frac{1-(-1)^{2/3} x}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)-i \Pi \left(\frac{2 i \sqrt{3}}{3+(2+i) \sqrt{3}};\sin ^{-1}\left(\sqrt{\frac{1-(-1)^{2/3} x}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)\right)+\frac{3 \sqrt{\frac{(-1)^{2/3} x+\sqrt[3]{-1}}{1+\sqrt[3]{-1}}} \left(\left(\sqrt{3}+i\right) x+2 i\right) F\left(\sin ^{-1}\left(\sqrt{\frac{1-(-1)^{2/3} x}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{\sqrt{\frac{1-(-1)^{2/3} x}{1+\sqrt[3]{-1}}}}\right)}{3 \left(\sqrt{3}+i\right) \sqrt{x^3-1}}","-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} \sqrt{x^3-1}}{x^2+x+1}\right)}{3^{3/4}}-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} \sqrt{x^3-1}}{x^2+x+1}\right)}{3^{3/4}}",1,"(2*Sqrt[(1 - x)/(1 + (-1)^(1/3))]*((3*Sqrt[((-1)^(1/3) + (-1)^(2/3)*x)/(1 + (-1)^(1/3))]*(2*I + (I + Sqrt[3])*x)*EllipticF[ArcSin[Sqrt[(1 - (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)])/Sqrt[(1 - (-1)^(2/3)*x)/(1 + (-1)^(1/3))] + (1 + I)*(3 - I*Sqrt[3])*Sqrt[1 + x + x^2]*(EllipticPi[(2*Sqrt[3])/(-3*I + (1 + 2*I)*Sqrt[3]), ArcSin[Sqrt[(1 - (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)] - I*EllipticPi[((2*I)*Sqrt[3])/(3 + (2 + I)*Sqrt[3]), ArcSin[Sqrt[(1 - (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)])))/(3*(I + Sqrt[3])*Sqrt[-1 + x^3])","C",0
1214,1,96,89,0.0241418,"\int \frac{\left(-1+x^3\right) \sqrt[3]{1+x^3}}{x} \, dx","Integrate[((-1 + x^3)*(1 + x^3)^(1/3))/x,x]","\frac{1}{12} \left(3 \sqrt[3]{x^3+1} x^3-9 \sqrt[3]{x^3+1}-4 \log \left(1-\sqrt[3]{x^3+1}\right)+2 \log \left(\left(x^3+1\right)^{2/3}+\sqrt[3]{x^3+1}+1\right)+4 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x^3+1}+1}{\sqrt{3}}\right)\right)","\frac{1}{4} \sqrt[3]{x^3+1} \left(x^3-3\right)-\frac{1}{3} \log \left(\sqrt[3]{x^3+1}-1\right)+\frac{1}{6} \log \left(\left(x^3+1\right)^{2/3}+\sqrt[3]{x^3+1}+1\right)+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{x^3+1}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3}}",1,"(-9*(1 + x^3)^(1/3) + 3*x^3*(1 + x^3)^(1/3) + 4*Sqrt[3]*ArcTan[(1 + 2*(1 + x^3)^(1/3))/Sqrt[3]] - 4*Log[1 - (1 + x^3)^(1/3)] + 2*Log[1 + (1 + x^3)^(1/3) + (1 + x^3)^(2/3)])/12","A",1
1215,0,0,89,3.346924,"\int \frac{-a b+2 (a-b) x+x^2}{\sqrt[4]{x (-a+x) (-b+x)} \left(-a^3+\left(3 a^2+b d\right) x-(3 a+d) x^2+x^3\right)} \, dx","Integrate[(-(a*b) + 2*(a - b)*x + x^2)/((x*(-a + x)*(-b + x))^(1/4)*(-a^3 + (3*a^2 + b*d)*x - (3*a + d)*x^2 + x^3)),x]","\int \frac{-a b+2 (a-b) x+x^2}{\sqrt[4]{x (-a+x) (-b+x)} \left(-a^3+\left(3 a^2+b d\right) x-(3 a+d) x^2+x^3\right)} \, dx","\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{x^2 (-a-b)+a b x+x^3}}{a-x}\right)}{d^{3/4}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{x^2 (-a-b)+a b x+x^3}}{a-x}\right)}{d^{3/4}}",1,"Integrate[(-(a*b) + 2*(a - b)*x + x^2)/((x*(-a + x)*(-b + x))^(1/4)*(-a^3 + (3*a^2 + b*d)*x - (3*a + d)*x^2 + x^3)), x]","F",-1
1216,0,0,89,1.0173426,"\int \frac{\left(1-2 x+x^2\right) \left(-1+2 (-1+k) x+k x^2\right)}{((1-x) x (1-k x))^{3/4} \left(-d+(1+3 d) x-(3 d+k) x^2+d x^3\right)} \, dx","Integrate[((1 - 2*x + x^2)*(-1 + 2*(-1 + k)*x + k*x^2))/(((1 - x)*x*(1 - k*x))^(3/4)*(-d + (1 + 3*d)*x - (3*d + k)*x^2 + d*x^3)),x]","\int \frac{\left(1-2 x+x^2\right) \left(-1+2 (-1+k) x+k x^2\right)}{((1-x) x (1-k x))^{3/4} \left(-d+(1+3 d) x-(3 d+k) x^2+d x^3\right)} \, dx","\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x-\sqrt[4]{d}}{\sqrt[4]{k x^3+(-k-1) x^2+x}}\right)}{d^{3/4}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} x-\sqrt[4]{d}}{\sqrt[4]{k x^3+(-k-1) x^2+x}}\right)}{d^{3/4}}",1,"Integrate[((1 - 2*x + x^2)*(-1 + 2*(-1 + k)*x + k*x^2))/(((1 - x)*x*(1 - k*x))^(3/4)*(-d + (1 + 3*d)*x - (3*d + k)*x^2 + d*x^3)), x]","F",-1
1217,1,153,89,0.6239262,"\int \frac{x^2}{\sqrt{x+x^2+x^3} \left(-1+x^4\right)} \, dx","Integrate[x^2/(Sqrt[x + x^2 + x^3]*(-1 + x^4)),x]","\frac{\sqrt[3]{-1} \sqrt{\sqrt[3]{-1} x \left(x+\sqrt[3]{-1}\right)} \sqrt{\sqrt[3]{-1} x+1} \left(\Pi \left(-\sqrt[3]{-1};\sin ^{-1}\left(\sqrt{(-1)^{2/3} x}\right)|(-1)^{2/3}\right)+\Pi \left(\sqrt[3]{-1};\sin ^{-1}\left(\sqrt{(-1)^{2/3} x}\right)|(-1)^{2/3}\right)-\Pi \left(-(-1)^{5/6};\sin ^{-1}\left(\sqrt{(-1)^{2/3} x}\right)|(-1)^{2/3}\right)-\Pi \left((-1)^{5/6};\sin ^{-1}\left(\sqrt{(-1)^{2/3} x}\right)|(-1)^{2/3}\right)\right)}{2 \sqrt{x \left(x^2+x+1\right)}}","-\frac{1}{4} \tan ^{-1}\left(\frac{\sqrt{x^3+x^2+x}}{x^2+x+1}\right)+\frac{1}{2} \tanh ^{-1}\left(\frac{\sqrt{x^3+x^2+x}}{x^2+x+1}\right)-\frac{\tanh ^{-1}\left(\frac{\sqrt{3} \sqrt{x^3+x^2+x}}{x^2+x+1}\right)}{4 \sqrt{3}}",1,"((-1)^(1/3)*Sqrt[(-1)^(1/3)*x*((-1)^(1/3) + x)]*Sqrt[1 + (-1)^(1/3)*x]*(EllipticPi[-(-1)^(1/3), ArcSin[Sqrt[(-1)^(2/3)*x]], (-1)^(2/3)] + EllipticPi[(-1)^(1/3), ArcSin[Sqrt[(-1)^(2/3)*x]], (-1)^(2/3)] - EllipticPi[-(-1)^(5/6), ArcSin[Sqrt[(-1)^(2/3)*x]], (-1)^(2/3)] - EllipticPi[(-1)^(5/6), ArcSin[Sqrt[(-1)^(2/3)*x]], (-1)^(2/3)]))/(2*Sqrt[x*(1 + x + x^2)])","C",1
1218,1,743,89,3.218104,"\int \frac{\sqrt{x+x^2+x^3}}{-1+x^4} \, dx","Integrate[Sqrt[x + x^2 + x^3]/(-1 + x^4),x]","\frac{(-1)^{2/3} \left(\sqrt{x}-1\right) \left(\sqrt{x}+1\right) \sqrt{x} (x+1) \left(x^2+1\right) \left(\sqrt{\sqrt[3]{-1} x+1} \sqrt{1-(-1)^{2/3} x} \Pi \left(\sqrt[3]{-1};i \sinh ^{-1}\left((-1)^{5/6} \sqrt{x}\right)|(-1)^{2/3}\right)+\sqrt{\sqrt[3]{-1} x+1} \sqrt{1-(-1)^{2/3} x} \Pi \left(-(-1)^{5/6};i \sinh ^{-1}\left((-1)^{5/6} \sqrt{x}\right)|(-1)^{2/3}\right)+\sqrt{\sqrt[3]{-1} x+1} \sqrt{1-(-1)^{2/3} x} \Pi \left((-1)^{5/6};i \sinh ^{-1}\left((-1)^{5/6} \sqrt{x}\right)|(-1)^{2/3}\right)+\frac{3 \sqrt{\frac{(-1)^{2/3}-\sqrt{x}}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1}-\sqrt{x}\right)}} \sqrt{\frac{1-\left(\sqrt[3]{-1}-1\right) \sqrt{x}}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1}-\sqrt{x}\right)}} \sqrt{-\frac{\sqrt{x}+(-1)^{2/3}}{\left(\sqrt[3]{-1}-1\right) \sqrt{x}+1}} \left(\sqrt[3]{-1}-\sqrt{x}\right)^2 \left(\left(1+\sqrt[3]{-1}\right) F\left(\left.\sin ^{-1}\left(\sqrt{\frac{1-\left(-1+\sqrt[3]{-1}\right) \sqrt{x}}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1}-\sqrt{x}\right)}}\right)\right|-3\right)-2 \sqrt[3]{-1} \Pi \left(-1;\left.\sin ^{-1}\left(\sqrt{\frac{1-\left(-1+\sqrt[3]{-1}\right) \sqrt{x}}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1}-\sqrt{x}\right)}}\right)\right|-3\right)\right)}{\left(\sqrt[3]{-1}-1\right)^2}-\frac{3 \sqrt{\frac{(-1)^{2/3}-\sqrt{x}}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1}-\sqrt{x}\right)}} \sqrt{\frac{1-\left(\sqrt[3]{-1}-1\right) \sqrt{x}}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1}-\sqrt{x}\right)}} \sqrt{-\frac{\sqrt{x}+(-1)^{2/3}}{\left(\sqrt[3]{-1}-1\right) \sqrt{x}+1}} \left(\sqrt[3]{-1}-\sqrt{x}\right)^2 \left(\left(\sqrt[3]{-1}-1\right) F\left(\left.\sin ^{-1}\left(\sqrt{\frac{1-\left(-1+\sqrt[3]{-1}\right) \sqrt{x}}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1}-\sqrt{x}\right)}}\right)\right|-3\right)-2 \sqrt[3]{-1} \Pi \left(3;\left.\sin ^{-1}\left(\sqrt{\frac{1-\left(-1+\sqrt[3]{-1}\right) \sqrt{x}}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1}-\sqrt{x}\right)}}\right)\right|-3\right)\right)}{\left(\sqrt[3]{-1}-1\right)^2}\right)}{2 \sqrt{x \left(x^2+x+1\right)} \left(x^4-1\right)}","\frac{1}{4} \tan ^{-1}\left(\frac{\sqrt{x^3+x^2+x}}{x^2+x+1}\right)+\frac{1}{2} \tanh ^{-1}\left(\frac{\sqrt{x^3+x^2+x}}{x^2+x+1}\right)-\frac{1}{4} \sqrt{3} \tanh ^{-1}\left(\frac{\sqrt{3} \sqrt{x^3+x^2+x}}{x^2+x+1}\right)",1,"((-1)^(2/3)*(-1 + Sqrt[x])*(1 + Sqrt[x])*Sqrt[x]*(1 + x)*(1 + x^2)*((3*((-1)^(1/3) - Sqrt[x])^2*Sqrt[((-1)^(2/3) - Sqrt[x])/((1 + (-1)^(1/3))*((-1)^(1/3) - Sqrt[x]))]*Sqrt[(1 - (-1 + (-1)^(1/3))*Sqrt[x])/((1 + (-1)^(1/3))*((-1)^(1/3) - Sqrt[x]))]*Sqrt[-(((-1)^(2/3) + Sqrt[x])/(1 + (-1 + (-1)^(1/3))*Sqrt[x]))]*((1 + (-1)^(1/3))*EllipticF[ArcSin[Sqrt[(1 - (-1 + (-1)^(1/3))*Sqrt[x])/((1 + (-1)^(1/3))*((-1)^(1/3) - Sqrt[x]))]], -3] - 2*(-1)^(1/3)*EllipticPi[-1, ArcSin[Sqrt[(1 - (-1 + (-1)^(1/3))*Sqrt[x])/((1 + (-1)^(1/3))*((-1)^(1/3) - Sqrt[x]))]], -3]))/(-1 + (-1)^(1/3))^2 - (3*((-1)^(1/3) - Sqrt[x])^2*Sqrt[((-1)^(2/3) - Sqrt[x])/((1 + (-1)^(1/3))*((-1)^(1/3) - Sqrt[x]))]*Sqrt[(1 - (-1 + (-1)^(1/3))*Sqrt[x])/((1 + (-1)^(1/3))*((-1)^(1/3) - Sqrt[x]))]*Sqrt[-(((-1)^(2/3) + Sqrt[x])/(1 + (-1 + (-1)^(1/3))*Sqrt[x]))]*((-1 + (-1)^(1/3))*EllipticF[ArcSin[Sqrt[(1 - (-1 + (-1)^(1/3))*Sqrt[x])/((1 + (-1)^(1/3))*((-1)^(1/3) - Sqrt[x]))]], -3] - 2*(-1)^(1/3)*EllipticPi[3, ArcSin[Sqrt[(1 - (-1 + (-1)^(1/3))*Sqrt[x])/((1 + (-1)^(1/3))*((-1)^(1/3) - Sqrt[x]))]], -3]))/(-1 + (-1)^(1/3))^2 + Sqrt[1 + (-1)^(1/3)*x]*Sqrt[1 - (-1)^(2/3)*x]*EllipticPi[(-1)^(1/3), I*ArcSinh[(-1)^(5/6)*Sqrt[x]], (-1)^(2/3)] + Sqrt[1 + (-1)^(1/3)*x]*Sqrt[1 - (-1)^(2/3)*x]*EllipticPi[-(-1)^(5/6), I*ArcSinh[(-1)^(5/6)*Sqrt[x]], (-1)^(2/3)] + Sqrt[1 + (-1)^(1/3)*x]*Sqrt[1 - (-1)^(2/3)*x]*EllipticPi[(-1)^(5/6), I*ArcSinh[(-1)^(5/6)*Sqrt[x]], (-1)^(2/3)]))/(2*Sqrt[x*(1 + x + x^2)]*(-1 + x^4))","C",0
1219,1,30,89,0.0071804,"\int \frac{\left(-1+x^4\right)^{2/3}}{x} \, dx","Integrate[(-1 + x^4)^(2/3)/x,x]","-\frac{3}{8} \left(x^4-1\right)^{2/3} \left(\, _2F_1\left(\frac{2}{3},1;\frac{5}{3};1-x^4\right)-1\right)","\frac{3}{8} \left(x^4-1\right)^{2/3}+\frac{1}{4} \log \left(\sqrt[3]{x^4-1}+1\right)-\frac{1}{8} \log \left(\left(x^4-1\right)^{2/3}-\sqrt[3]{x^4-1}+1\right)+\frac{1}{4} \sqrt{3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{x^4-1}}{\sqrt{3}}\right)",1,"(-3*(-1 + x^4)^(2/3)*(-1 + Hypergeometric2F1[2/3, 1, 5/3, 1 - x^4]))/8","C",1
1220,1,774,89,3.0743431,"\int \frac{1-x^2+x^4}{\sqrt{x+x^2+x^3} \left(-1+x^4\right)} \, dx","Integrate[(1 - x^2 + x^4)/(Sqrt[x + x^2 + x^3]*(-1 + x^4)),x]","-\frac{(-1)^{2/3} x^{3/2} \left(-4 \sqrt{1-\frac{(-1)^{2/3}}{x}} \sqrt{\frac{x+\sqrt[3]{-1}}{x}} F\left(i \sinh ^{-1}\left(\frac{(-1)^{5/6}}{\sqrt{x}}\right)|(-1)^{2/3}\right)+\sqrt{1-\frac{(-1)^{2/3}}{x}} \sqrt{\frac{x+\sqrt[3]{-1}}{x}} \Pi \left(\sqrt[3]{-1};i \sinh ^{-1}\left(\frac{(-1)^{5/6}}{\sqrt{x}}\right)|(-1)^{2/3}\right)+3 \sqrt{1-\frac{(-1)^{2/3}}{x}} \sqrt{\frac{x+\sqrt[3]{-1}}{x}} \Pi \left(-(-1)^{5/6};i \sinh ^{-1}\left(\frac{(-1)^{5/6}}{\sqrt{x}}\right)|(-1)^{2/3}\right)+3 \sqrt{1-\frac{(-1)^{2/3}}{x}} \sqrt{\frac{x+\sqrt[3]{-1}}{x}} \Pi \left((-1)^{5/6};i \sinh ^{-1}\left(\frac{(-1)^{5/6}}{\sqrt{x}}\right)|(-1)^{2/3}\right)-\frac{\sqrt{\frac{\sqrt{x}-\sqrt[3]{-1}+1}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1} \sqrt{x}-1\right)}} \sqrt{\frac{(-1)^{2/3} \sqrt{x}-1}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1} \sqrt{x}-1\right)}} \sqrt{-\frac{(-1)^{2/3} \sqrt{x}+1}{\sqrt{x}+\sqrt[3]{-1}-1}} \left(\sqrt[3]{-1} \sqrt{x}-1\right)^2 \left(\left(1+\sqrt[3]{-1}\right) F\left(\left.\sin ^{-1}\left(\sqrt{\frac{\sqrt{x}-\sqrt[3]{-1}+1}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1} \sqrt{x}-1\right)}}\right)\right|-3\right)-2 \sqrt[3]{-1} \Pi \left(-1;\left.\sin ^{-1}\left(\sqrt{\frac{\sqrt{x}-\sqrt[3]{-1}+1}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1} \sqrt{x}-1\right)}}\right)\right|-3\right)\right)}{\left(\sqrt[3]{-1}-1\right)^2 x}+\frac{\sqrt{\frac{\sqrt{x}-\sqrt[3]{-1}+1}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1} \sqrt{x}-1\right)}} \sqrt{\frac{(-1)^{2/3} \sqrt{x}-1}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1} \sqrt{x}-1\right)}} \sqrt{-\frac{(-1)^{2/3} \sqrt{x}+1}{\sqrt{x}+\sqrt[3]{-1}-1}} \left(\sqrt[3]{-1} \sqrt{x}-1\right)^2 \left(\left(\sqrt[3]{-1}-1\right) F\left(\left.\sin ^{-1}\left(\sqrt{\frac{\sqrt{x}-\sqrt[3]{-1}+1}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1} \sqrt{x}-1\right)}}\right)\right|-3\right)-2 \sqrt[3]{-1} \Pi \left(3;\left.\sin ^{-1}\left(\sqrt{\frac{\sqrt{x}-\sqrt[3]{-1}+1}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1} \sqrt{x}-1\right)}}\right)\right|-3\right)\right)}{\left(\sqrt[3]{-1}-1\right)^2 x}\right)}{2 \sqrt{x \left(x^2+x+1\right)}}","-\frac{1}{4} \tan ^{-1}\left(\frac{\sqrt{x^3+x^2+x}}{x^2+x+1}\right)-\frac{3}{2} \tanh ^{-1}\left(\frac{\sqrt{x^3+x^2+x}}{x^2+x+1}\right)-\frac{\tanh ^{-1}\left(\frac{\sqrt{3} \sqrt{x^3+x^2+x}}{x^2+x+1}\right)}{4 \sqrt{3}}",1,"-1/2*((-1)^(2/3)*x^(3/2)*(-4*Sqrt[1 - (-1)^(2/3)/x]*Sqrt[((-1)^(1/3) + x)/x]*EllipticF[I*ArcSinh[(-1)^(5/6)/Sqrt[x]], (-1)^(2/3)] - (Sqrt[(1 - (-1)^(1/3) + Sqrt[x])/((1 + (-1)^(1/3))*(-1 + (-1)^(1/3)*Sqrt[x]))]*(-1 + (-1)^(1/3)*Sqrt[x])^2*Sqrt[(-1 + (-1)^(2/3)*Sqrt[x])/((1 + (-1)^(1/3))*(-1 + (-1)^(1/3)*Sqrt[x]))]*Sqrt[-((1 + (-1)^(2/3)*Sqrt[x])/(-1 + (-1)^(1/3) + Sqrt[x]))]*((1 + (-1)^(1/3))*EllipticF[ArcSin[Sqrt[(1 - (-1)^(1/3) + Sqrt[x])/((1 + (-1)^(1/3))*(-1 + (-1)^(1/3)*Sqrt[x]))]], -3] - 2*(-1)^(1/3)*EllipticPi[-1, ArcSin[Sqrt[(1 - (-1)^(1/3) + Sqrt[x])/((1 + (-1)^(1/3))*(-1 + (-1)^(1/3)*Sqrt[x]))]], -3]))/((-1 + (-1)^(1/3))^2*x) + (Sqrt[(1 - (-1)^(1/3) + Sqrt[x])/((1 + (-1)^(1/3))*(-1 + (-1)^(1/3)*Sqrt[x]))]*(-1 + (-1)^(1/3)*Sqrt[x])^2*Sqrt[(-1 + (-1)^(2/3)*Sqrt[x])/((1 + (-1)^(1/3))*(-1 + (-1)^(1/3)*Sqrt[x]))]*Sqrt[-((1 + (-1)^(2/3)*Sqrt[x])/(-1 + (-1)^(1/3) + Sqrt[x]))]*((-1 + (-1)^(1/3))*EllipticF[ArcSin[Sqrt[(1 - (-1)^(1/3) + Sqrt[x])/((1 + (-1)^(1/3))*(-1 + (-1)^(1/3)*Sqrt[x]))]], -3] - 2*(-1)^(1/3)*EllipticPi[3, ArcSin[Sqrt[(1 - (-1)^(1/3) + Sqrt[x])/((1 + (-1)^(1/3))*(-1 + (-1)^(1/3)*Sqrt[x]))]], -3]))/((-1 + (-1)^(1/3))^2*x) + Sqrt[1 - (-1)^(2/3)/x]*Sqrt[((-1)^(1/3) + x)/x]*EllipticPi[(-1)^(1/3), I*ArcSinh[(-1)^(5/6)/Sqrt[x]], (-1)^(2/3)] + 3*Sqrt[1 - (-1)^(2/3)/x]*Sqrt[((-1)^(1/3) + x)/x]*EllipticPi[-(-1)^(5/6), I*ArcSinh[(-1)^(5/6)/Sqrt[x]], (-1)^(2/3)] + 3*Sqrt[1 - (-1)^(2/3)/x]*Sqrt[((-1)^(1/3) + x)/x]*EllipticPi[(-1)^(5/6), I*ArcSinh[(-1)^(5/6)/Sqrt[x]], (-1)^(2/3)]))/Sqrt[x*(1 + x + x^2)]","C",0
1221,1,743,89,1.592625,"\int \frac{1-x+x^2}{\left(-1+x^2\right) \sqrt{1-x+x^2-x^3+x^4}} \, dx","Integrate[(1 - x + x^2)/((-1 + x^2)*Sqrt[1 - x + x^2 - x^3 + x^4]),x]","-\frac{(-1)^{3/5} \sqrt{\frac{-x+(-1)^{4/5}+(-1)^{2/5}-\sqrt[5]{-1}+1}{\left(\sqrt[5]{-1}-1\right) \left(x+(-1)^{2/5}\right)}} \left(x+(-1)^{2/5}\right) \left(x+(-1)^{4/5}\right) \left(2 \left((-1)^{2/5} \sqrt{-\frac{\sqrt[5]{-1} \left(\sqrt[5]{-1}-1\right) \left(\sqrt[5]{-1}-x\right)}{\left(1-\sqrt[5]{-1}+(-1)^{2/5}\right) \left(x+(-1)^{2/5}\right)}}+2 \sqrt{-\frac{\sqrt[5]{-1} \left(\sqrt[5]{-1}-1\right) \left(\sqrt[5]{-1}-x\right)}{\left(1-\sqrt[5]{-1}+(-1)^{2/5}\right) \left(x+(-1)^{2/5}\right)}}+(-1)^{4/5} \sqrt{\frac{\sqrt[5]{-1} \left(\sqrt[5]{-1}-1\right) x-(-1)^{4/5}+\sqrt[5]{-1}-1}{\left(1-\sqrt[5]{-1}+(-1)^{2/5}\right) \left(x+(-1)^{2/5}\right)}}-\sqrt{\frac{\sqrt[5]{-1} \left(\sqrt[5]{-1}-1\right) x-(-1)^{4/5}+\sqrt[5]{-1}-1}{\left(1-\sqrt[5]{-1}+(-1)^{2/5}\right) \left(x+(-1)^{2/5}\right)}}\right) F\left(\sin ^{-1}\left(\sqrt{-\frac{\sqrt[5]{-1} \left(-1+\sqrt[5]{-1}\right) \left(\sqrt[5]{-1}-x\right)}{\left(1-\sqrt[5]{-1}+(-1)^{2/5}\right) \left(x+(-1)^{2/5}\right)}}\right)|\frac{1-\sqrt[5]{-1}+(-1)^{2/5}}{\left(-1+\sqrt[5]{-1}\right)^2}\right)+\sqrt[5]{-1} \sqrt{-\frac{\sqrt[5]{-1} \left(\sqrt[5]{-1}-1\right) \left(\sqrt[5]{-1}-x\right)}{\left(1-\sqrt[5]{-1}+(-1)^{2/5}\right) \left(x+(-1)^{2/5}\right)}} \left(\left(1+\sqrt[5]{-1}\right)^2 \Pi \left(\frac{(-1)^{4/5} \left(1+(-1)^{2/5}\right) \left(1-\sqrt[5]{-1}+(-1)^{2/5}\right)}{\left(-1+\sqrt[5]{-1}\right)^2};\sin ^{-1}\left(\sqrt{-\frac{\sqrt[5]{-1} \left(-1+\sqrt[5]{-1}\right) \left(\sqrt[5]{-1}-x\right)}{\left(1-\sqrt[5]{-1}+(-1)^{2/5}\right) \left(x+(-1)^{2/5}\right)}}\right)|\frac{1-\sqrt[5]{-1}+(-1)^{2/5}}{\left(-1+\sqrt[5]{-1}\right)^2}\right)-3 \left(1+(-1)^{2/5}\right) \Pi \left(1-\sqrt[5]{-1}+(-1)^{4/5};\sin ^{-1}\left(\sqrt{-\frac{\sqrt[5]{-1} \left(-1+\sqrt[5]{-1}\right) \left(\sqrt[5]{-1}-x\right)}{\left(1-\sqrt[5]{-1}+(-1)^{2/5}\right) \left(x+(-1)^{2/5}\right)}}\right)|\frac{1-\sqrt[5]{-1}+(-1)^{2/5}}{\left(-1+\sqrt[5]{-1}\right)^2}\right)\right)\right)}{\left((-1)^{2/5}-1\right)^2 \left(1+(-1)^{2/5}\right) \sqrt{\frac{x+(-1)^{4/5}}{\left(1-\sqrt[5]{-1}+(-1)^{2/5}\right) \left(x+(-1)^{2/5}\right)}} \sqrt{x^4-x^3+x^2-x+1}}","\frac{1}{2} \tanh ^{-1}\left(\frac{x}{x^2-\sqrt{x^4-x^3+x^2-x+1}-2 x+1}\right)+\frac{3 \tanh ^{-1}\left(\frac{\sqrt{5} x}{x^2-\sqrt{x^4-x^3+x^2-x+1}+2 x+1}\right)}{2 \sqrt{5}}",1,"-(((-1)^(3/5)*Sqrt[(1 - (-1)^(1/5) + (-1)^(2/5) + (-1)^(4/5) - x)/((-1 + (-1)^(1/5))*((-1)^(2/5) + x))]*((-1)^(2/5) + x)*((-1)^(4/5) + x)*(2*(2*Sqrt[-(((-1)^(1/5)*(-1 + (-1)^(1/5))*((-1)^(1/5) - x))/((1 - (-1)^(1/5) + (-1)^(2/5))*((-1)^(2/5) + x)))] + (-1)^(2/5)*Sqrt[-(((-1)^(1/5)*(-1 + (-1)^(1/5))*((-1)^(1/5) - x))/((1 - (-1)^(1/5) + (-1)^(2/5))*((-1)^(2/5) + x)))] - Sqrt[(-1 + (-1)^(1/5) - (-1)^(4/5) + (-1)^(1/5)*(-1 + (-1)^(1/5))*x)/((1 - (-1)^(1/5) + (-1)^(2/5))*((-1)^(2/5) + x))] + (-1)^(4/5)*Sqrt[(-1 + (-1)^(1/5) - (-1)^(4/5) + (-1)^(1/5)*(-1 + (-1)^(1/5))*x)/((1 - (-1)^(1/5) + (-1)^(2/5))*((-1)^(2/5) + x))])*EllipticF[ArcSin[Sqrt[-(((-1)^(1/5)*(-1 + (-1)^(1/5))*((-1)^(1/5) - x))/((1 - (-1)^(1/5) + (-1)^(2/5))*((-1)^(2/5) + x)))]], (1 - (-1)^(1/5) + (-1)^(2/5))/(-1 + (-1)^(1/5))^2] + (-1)^(1/5)*Sqrt[-(((-1)^(1/5)*(-1 + (-1)^(1/5))*((-1)^(1/5) - x))/((1 - (-1)^(1/5) + (-1)^(2/5))*((-1)^(2/5) + x)))]*((1 + (-1)^(1/5))^2*EllipticPi[((-1)^(4/5)*(1 + (-1)^(2/5))*(1 - (-1)^(1/5) + (-1)^(2/5)))/(-1 + (-1)^(1/5))^2, ArcSin[Sqrt[-(((-1)^(1/5)*(-1 + (-1)^(1/5))*((-1)^(1/5) - x))/((1 - (-1)^(1/5) + (-1)^(2/5))*((-1)^(2/5) + x)))]], (1 - (-1)^(1/5) + (-1)^(2/5))/(-1 + (-1)^(1/5))^2] - 3*(1 + (-1)^(2/5))*EllipticPi[1 - (-1)^(1/5) + (-1)^(4/5), ArcSin[Sqrt[-(((-1)^(1/5)*(-1 + (-1)^(1/5))*((-1)^(1/5) - x))/((1 - (-1)^(1/5) + (-1)^(2/5))*((-1)^(2/5) + x)))]], (1 - (-1)^(1/5) + (-1)^(2/5))/(-1 + (-1)^(1/5))^2])))/((-1 + (-1)^(2/5))^2*(1 + (-1)^(2/5))*Sqrt[((-1)^(4/5) + x)/((1 - (-1)^(1/5) + (-1)^(2/5))*((-1)^(2/5) + x))]*Sqrt[1 - x + x^2 - x^3 + x^4]))","C",0
1222,1,2703,89,10.4676656,"\int \frac{(-1+x)^2 \left(x-2 x^2+2 x^3\right)}{(-1+2 x) \sqrt{\frac{1-2 x}{1+2 x^2}} \left(-2+4 x+3 x^2-4 x^3+2 x^4\right)} \, dx","Integrate[((-1 + x)^2*(x - 2*x^2 + 2*x^3))/((-1 + 2*x)*Sqrt[(1 - 2*x)/(1 + 2*x^2)]*(-2 + 4*x + 3*x^2 - 4*x^3 + 2*x^4)),x]","\text{Result too large to show}","\frac{\sqrt{\frac{1-2 x}{2 x^2+1}} \left(-2 x^3+2 x^2-x+1\right)}{3 (2 x-1)}-\frac{\tanh ^{-1}\left(\frac{\frac{x}{\sqrt{3}}-\frac{1}{\sqrt{3}}}{\sqrt{\frac{1-2 x}{2 x^2+1}}}\right)}{\sqrt{3}}",1,"((1 - 2*x)^2*(1/6 - 1/(6*(-1 + 2*x))))/((-1 + 2*x)*Sqrt[(1 - 2*x)/(1 + 2*x^2)]) + ((6*I)*Sqrt[2]*Sqrt[1 + (I*(1 - 2*x))/(-I + Sqrt[2])]*Sqrt[1 - (I*(1 - 2*x))/(I + Sqrt[2])]*(1 - 2*x)^(3/2)*((Sqrt[(-I)/(I + Sqrt[2])]*Sqrt[1 - 2*x]*EllipticPi[(1 - I*Sqrt[2])/Root[3 - 20*#1 + #1^4 & , 1, 0], I*ArcSinh[Sqrt[((-I)*(1 - 2*x))/(I + Sqrt[2])]], (I + Sqrt[2])/(I - Sqrt[2])]*(-1 + Root[3 - 20*#1 + #1^4 & , 1, 0] - Root[3 - 20*#1 + #1^4 & , 1, 0]^2 + Root[3 - 20*#1 + #1^4 & , 1, 0]^3))/(Sqrt[((-I)*(1 - 2*x))/(I + Sqrt[2])]*Root[3 - 20*#1 + #1^4 & , 1, 0]*(Root[3 - 20*#1 + #1^4 & , 1, 0] - Root[3 - 20*#1 + #1^4 & , 2, 0])*(Root[3 - 20*#1 + #1^4 & , 1, 0] - Root[3 - 20*#1 + #1^4 & , 3, 0])*(Root[3 - 20*#1 + #1^4 & , 1, 0] - Root[3 - 20*#1 + #1^4 & , 4, 0])) + (-((Sqrt[(-I)/(I + Sqrt[2])]*Sqrt[1 - 2*x]*EllipticPi[(1 - I*Sqrt[2])/Root[3 - 20*#1 + #1^4 & , 2, 0], I*ArcSinh[Sqrt[((-I)*(1 - 2*x))/(I + Sqrt[2])]], (I + Sqrt[2])/(I - Sqrt[2])]*(-1 + Root[3 - 20*#1 + #1^4 & , 2, 0] - Root[3 - 20*#1 + #1^4 & , 2, 0]^2 + Root[3 - 20*#1 + #1^4 & , 2, 0]^3))/(Sqrt[((-I)*(1 - 2*x))/(I + Sqrt[2])]*(Root[3 - 20*#1 + #1^4 & , 1, 0] - Root[3 - 20*#1 + #1^4 & , 2, 0])*Root[3 - 20*#1 + #1^4 & , 2, 0])) + ((Sqrt[(-I)/(I + Sqrt[2])]*Sqrt[1 - 2*x]*EllipticPi[(1 - I*Sqrt[2])/Root[3 - 20*#1 + #1^4 & , 4, 0], I*ArcSinh[Sqrt[((-I)*(1 - 2*x))/(I + Sqrt[2])]], (I + Sqrt[2])/(I - Sqrt[2])]*(Root[3 - 20*#1 + #1^4 & , 1, 0] - Root[3 - 20*#1 + #1^4 & , 3, 0])*(Root[3 - 20*#1 + #1^4 & , 2, 0] - Root[3 - 20*#1 + #1^4 & , 3, 0])*Root[3 - 20*#1 + #1^4 & , 3, 0])/Sqrt[((-I)*(1 - 2*x))/(I + Sqrt[2])] + (Sqrt[(-I)/(I + Sqrt[2])]*Sqrt[1 - 2*x]*EllipticPi[(1 - I*Sqrt[2])/Root[3 - 20*#1 + #1^4 & , 4, 0], I*ArcSinh[Sqrt[((-I)*(1 - 2*x))/(I + Sqrt[2])]], (I + Sqrt[2])/(I - Sqrt[2])]*(Root[3 - 20*#1 + #1^4 & , 1, 0] - Root[3 - 20*#1 + #1^4 & , 3, 0])*Root[3 - 20*#1 + #1^4 & , 3, 0]*(-Root[3 - 20*#1 + #1^4 & , 2, 0] + Root[3 - 20*#1 + #1^4 & , 3, 0])*Root[3 - 20*#1 + #1^4 & , 4, 0])/Sqrt[((-I)*(1 - 2*x))/(I + Sqrt[2])] + (Sqrt[(-I)/(I + Sqrt[2])]*Sqrt[1 - 2*x]*EllipticPi[(1 - I*Sqrt[2])/Root[3 - 20*#1 + #1^4 & , 3, 0], I*ArcSinh[Sqrt[((-I)*(1 - 2*x))/(I + Sqrt[2])]], (I + Sqrt[2])/(I - Sqrt[2])]*Root[3 - 20*#1 + #1^4 & , 3, 0]*(Root[3 - 20*#1 + #1^4 & , 1, 0] - Root[3 - 20*#1 + #1^4 & , 4, 0])*(Root[3 - 20*#1 + #1^4 & , 2, 0] - Root[3 - 20*#1 + #1^4 & , 4, 0])*Root[3 - 20*#1 + #1^4 & , 4, 0])/Sqrt[((-I)*(1 - 2*x))/(I + Sqrt[2])] + (Sqrt[(-I)/(I + Sqrt[2])]*Sqrt[1 - 2*x]*EllipticPi[(1 - I*Sqrt[2])/Root[3 - 20*#1 + #1^4 & , 3, 0], I*ArcSinh[Sqrt[((-I)*(1 - 2*x))/(I + Sqrt[2])]], (I + Sqrt[2])/(I - Sqrt[2])]*Root[3 - 20*#1 + #1^4 & , 3, 0]^3*(Root[3 - 20*#1 + #1^4 & , 1, 0] - Root[3 - 20*#1 + #1^4 & , 4, 0])*(Root[3 - 20*#1 + #1^4 & , 2, 0] - Root[3 - 20*#1 + #1^4 & , 4, 0])*Root[3 - 20*#1 + #1^4 & , 4, 0])/Sqrt[((-I)*(1 - 2*x))/(I + Sqrt[2])] + (Sqrt[(-I)/(I + Sqrt[2])]*Sqrt[1 - 2*x]*EllipticPi[(1 - I*Sqrt[2])/Root[3 - 20*#1 + #1^4 & , 4, 0], I*ArcSinh[Sqrt[((-I)*(1 - 2*x))/(I + Sqrt[2])]], (I + Sqrt[2])/(I - Sqrt[2])]*(Root[3 - 20*#1 + #1^4 & , 1, 0] - Root[3 - 20*#1 + #1^4 & , 3, 0])*(Root[3 - 20*#1 + #1^4 & , 2, 0] - Root[3 - 20*#1 + #1^4 & , 3, 0])*Root[3 - 20*#1 + #1^4 & , 3, 0]*Root[3 - 20*#1 + #1^4 & , 4, 0]^2)/Sqrt[((-I)*(1 - 2*x))/(I + Sqrt[2])] + (Sqrt[(-I)/(I + Sqrt[2])]*Sqrt[1 - 2*x]*EllipticPi[(1 - I*Sqrt[2])/Root[3 - 20*#1 + #1^4 & , 4, 0], I*ArcSinh[Sqrt[((-I)*(1 - 2*x))/(I + Sqrt[2])]], (I + Sqrt[2])/(I - Sqrt[2])]*(Root[3 - 20*#1 + #1^4 & , 1, 0] - Root[3 - 20*#1 + #1^4 & , 3, 0])*Root[3 - 20*#1 + #1^4 & , 3, 0]*(-Root[3 - 20*#1 + #1^4 & , 2, 0] + Root[3 - 20*#1 + #1^4 & , 3, 0])*Root[3 - 20*#1 + #1^4 & , 4, 0]^3)/Sqrt[((-I)*(1 - 2*x))/(I + Sqrt[2])] + (Sqrt[(-I)/(I + Sqrt[2])]*Sqrt[1 - 2*x]*EllipticPi[(1 - I*Sqrt[2])/Root[3 - 20*#1 + #1^4 & , 3, 0], I*ArcSinh[Sqrt[((-I)*(1 - 2*x))/(I + Sqrt[2])]], (I + Sqrt[2])/(I - Sqrt[2])]*(Root[3 - 20*#1 + #1^4 & , 1, 0] - Root[3 - 20*#1 + #1^4 & , 4, 0])*Root[3 - 20*#1 + #1^4 & , 4, 0]*(-Root[3 - 20*#1 + #1^4 & , 2, 0] + Root[3 - 20*#1 + #1^4 & , 4, 0]))/Sqrt[((-I)*(1 - 2*x))/(I + Sqrt[2])] + (Sqrt[(-I)/(I + Sqrt[2])]*Sqrt[1 - 2*x]*EllipticPi[(1 - I*Sqrt[2])/Root[3 - 20*#1 + #1^4 & , 3, 0], I*ArcSinh[Sqrt[((-I)*(1 - 2*x))/(I + Sqrt[2])]], (I + Sqrt[2])/(I - Sqrt[2])]*Root[3 - 20*#1 + #1^4 & , 3, 0]^2*(Root[3 - 20*#1 + #1^4 & , 1, 0] - Root[3 - 20*#1 + #1^4 & , 4, 0])*Root[3 - 20*#1 + #1^4 & , 4, 0]*(-Root[3 - 20*#1 + #1^4 & , 2, 0] + Root[3 - 20*#1 + #1^4 & , 4, 0]))/Sqrt[((-I)*(1 - 2*x))/(I + Sqrt[2])])/((Root[3 - 20*#1 + #1^4 & , 1, 0] - Root[3 - 20*#1 + #1^4 & , 3, 0])*Root[3 - 20*#1 + #1^4 & , 3, 0]*(Root[3 - 20*#1 + #1^4 & , 1, 0] - Root[3 - 20*#1 + #1^4 & , 4, 0])*(Root[3 - 20*#1 + #1^4 & , 3, 0] - Root[3 - 20*#1 + #1^4 & , 4, 0])*Root[3 - 20*#1 + #1^4 & , 4, 0]))/((Root[3 - 20*#1 + #1^4 & , 2, 0] - Root[3 - 20*#1 + #1^4 & , 3, 0])*(Root[3 - 20*#1 + #1^4 & , 2, 0] - Root[3 - 20*#1 + #1^4 & , 4, 0]))))/(Sqrt[(-I)/(I + Sqrt[2])]*Sqrt[3 - 2*(1 - 2*x) + (1 - 2*x)^2]*(-1 + 2*x)*Sqrt[(1 - 2*x)/(1 + 2*x^2)]*Sqrt[1 + 2*x^2])","C",0
1223,1,30,89,0.0082822,"\int \frac{\left(-1+x^5\right)^{2/3}}{x} \, dx","Integrate[(-1 + x^5)^(2/3)/x,x]","-\frac{3}{10} \left(x^5-1\right)^{2/3} \left(\, _2F_1\left(\frac{2}{3},1;\frac{5}{3};1-x^5\right)-1\right)","\frac{3}{10} \left(x^5-1\right)^{2/3}+\frac{1}{5} \log \left(\sqrt[3]{x^5-1}+1\right)-\frac{1}{10} \log \left(\left(x^5-1\right)^{2/3}-\sqrt[3]{x^5-1}+1\right)+\frac{1}{5} \sqrt{3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{x^5-1}}{\sqrt{3}}\right)",1,"(-3*(-1 + x^5)^(2/3)*(-1 + Hypergeometric2F1[2/3, 1, 5/3, 1 - x^5]))/10","C",1
1224,1,30,89,0.009055,"\int \frac{\left(-1+x^6\right)^{2/3}}{x} \, dx","Integrate[(-1 + x^6)^(2/3)/x,x]","-\frac{1}{4} \left(x^6-1\right)^{2/3} \left(\, _2F_1\left(\frac{2}{3},1;\frac{5}{3};1-x^6\right)-1\right)","\frac{1}{4} \left(x^6-1\right)^{2/3}+\frac{1}{6} \log \left(\sqrt[3]{x^6-1}+1\right)-\frac{1}{12} \log \left(\left(x^6-1\right)^{2/3}-\sqrt[3]{x^6-1}+1\right)+\frac{\tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{x^6-1}}{\sqrt{3}}\right)}{2 \sqrt{3}}",1,"-1/4*((-1 + x^6)^(2/3)*(-1 + Hypergeometric2F1[2/3, 1, 5/3, 1 - x^6]))","C",1
1225,0,0,89,0.0374723,"\int \sqrt{a x^2+\sqrt{b+a^2 x^4}} \, dx","Integrate[Sqrt[a*x^2 + Sqrt[b + a^2*x^4]],x]","\int \sqrt{a x^2+\sqrt{b+a^2 x^4}} \, dx","\frac{1}{2} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}}{\sqrt{b}}\right)}{2 \sqrt{2} \sqrt{a}}",1,"Integrate[Sqrt[a*x^2 + Sqrt[b + a^2*x^4]], x]","F",-1
1226,1,28,90,0.0056137,"\int \frac{\left(-1+x^2\right)^{2/3}}{x^3} \, dx","Integrate[(-1 + x^2)^(2/3)/x^3,x]","\frac{3}{10} \left(x^2-1\right)^{5/3} \, _2F_1\left(\frac{5}{3},2;\frac{8}{3};1-x^2\right)","-\frac{\left(x^2-1\right)^{2/3}}{2 x^2}-\frac{1}{3} \log \left(\sqrt[3]{x^2-1}+1\right)+\frac{1}{6} \log \left(\left(x^2-1\right)^{2/3}-\sqrt[3]{x^2-1}+1\right)-\frac{\tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{x^2-1}}{\sqrt{3}}\right)}{\sqrt{3}}",1,"(3*(-1 + x^2)^(5/3)*Hypergeometric2F1[5/3, 2, 8/3, 1 - x^2])/10","C",1
1227,1,138,90,0.0489742,"\int \frac{-2+x+x^2}{x^2 \left(-1+x^2\right)^{3/4}} \, dx","Integrate[(-2 + x + x^2)/(x^2*(-1 + x^2)^(3/4)),x]","-\frac{2 \sqrt[4]{x^2-1}}{x}-\frac{\log \left(\sqrt{x^2-1}-\sqrt{2} \sqrt[4]{x^2-1}+1\right)}{2 \sqrt{2}}+\frac{\log \left(\sqrt{x^2-1}+\sqrt{2} \sqrt[4]{x^2-1}+1\right)}{2 \sqrt{2}}-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt[4]{x^2-1}\right)}{\sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt[4]{x^2-1}+1\right)}{\sqrt{2}}","-\frac{2 \sqrt[4]{x^2-1}}{x}+\frac{\tan ^{-1}\left(\frac{\frac{\sqrt{x^2-1}}{\sqrt{2}}-\frac{1}{\sqrt{2}}}{\sqrt[4]{x^2-1}}\right)}{\sqrt{2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{x^2-1}}{\sqrt{x^2-1}+1}\right)}{\sqrt{2}}",1,"(-2*(-1 + x^2)^(1/4))/x - ArcTan[1 - Sqrt[2]*(-1 + x^2)^(1/4)]/Sqrt[2] + ArcTan[1 + Sqrt[2]*(-1 + x^2)^(1/4)]/Sqrt[2] - Log[1 - Sqrt[2]*(-1 + x^2)^(1/4) + Sqrt[-1 + x^2]]/(2*Sqrt[2]) + Log[1 + Sqrt[2]*(-1 + x^2)^(1/4) + Sqrt[-1 + x^2]]/(2*Sqrt[2])","A",1
1228,1,26,90,0.0056008,"\int \frac{\sqrt[3]{1+x^3}}{x^4} \, dx","Integrate[(1 + x^3)^(1/3)/x^4,x]","\frac{1}{4} \left(x^3+1\right)^{4/3} \, _2F_1\left(\frac{4}{3},2;\frac{7}{3};x^3+1\right)","-\frac{\sqrt[3]{x^3+1}}{3 x^3}+\frac{1}{9} \log \left(\sqrt[3]{x^3+1}-1\right)-\frac{1}{18} \log \left(\left(x^3+1\right)^{2/3}+\sqrt[3]{x^3+1}+1\right)-\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{x^3+1}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"((1 + x^3)^(4/3)*Hypergeometric2F1[4/3, 2, 7/3, 1 + x^3])/4","C",1
1229,1,26,90,0.0062589,"\int \frac{\left(1+x^3\right)^{2/3}}{x^4} \, dx","Integrate[(1 + x^3)^(2/3)/x^4,x]","\frac{1}{5} \left(x^3+1\right)^{5/3} \, _2F_1\left(\frac{5}{3},2;\frac{8}{3};x^3+1\right)","-\frac{\left(x^3+1\right)^{2/3}}{3 x^3}+\frac{2}{9} \log \left(\sqrt[3]{x^3+1}-1\right)-\frac{1}{9} \log \left(\left(x^3+1\right)^{2/3}+\sqrt[3]{x^3+1}+1\right)+\frac{2 \tan ^{-1}\left(\frac{2 \sqrt[3]{x^3+1}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"((1 + x^3)^(5/3)*Hypergeometric2F1[5/3, 2, 8/3, 1 + x^3])/5","C",1
1230,0,0,90,1.5058748,"\int \frac{-2 k-(-1+k) (1+k) x+2 k x^2}{\sqrt[4]{\left(1-x^2\right) \left(1-k^2 x^2\right)} \left(-1+d+(3+d) k x-\left(d+3 k^2\right) x^2+k \left(-d+k^2\right) x^3\right)} \, dx","Integrate[(-2*k - (-1 + k)*(1 + k)*x + 2*k*x^2)/(((1 - x^2)*(1 - k^2*x^2))^(1/4)*(-1 + d + (3 + d)*k*x - (d + 3*k^2)*x^2 + k*(-d + k^2)*x^3)),x]","\int \frac{-2 k-(-1+k) (1+k) x+2 k x^2}{\sqrt[4]{\left(1-x^2\right) \left(1-k^2 x^2\right)} \left(-1+d+(3+d) k x-\left(d+3 k^2\right) x^2+k \left(-d+k^2\right) x^3\right)} \, dx","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{k^2 x^4+\left(-k^2-1\right) x^2+1}}{k x-1}\right)}{d^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{k^2 x^4+\left(-k^2-1\right) x^2+1}}{k x-1}\right)}{d^{3/4}}",1,"Integrate[(-2*k - (-1 + k)*(1 + k)*x + 2*k*x^2)/(((1 - x^2)*(1 - k^2*x^2))^(1/4)*(-1 + d + (3 + d)*k*x - (d + 3*k^2)*x^2 + k*(-d + k^2)*x^3)), x]","F",-1
1231,0,0,90,1.1727844,"\int \frac{-2 k+(-1+k) (1+k) x+2 k x^2}{\sqrt[4]{\left(1-x^2\right) \left(1-k^2 x^2\right)} \left(1-d+(3+d) k x+\left(d+3 k^2\right) x^2+k \left(-d+k^2\right) x^3\right)} \, dx","Integrate[(-2*k + (-1 + k)*(1 + k)*x + 2*k*x^2)/(((1 - x^2)*(1 - k^2*x^2))^(1/4)*(1 - d + (3 + d)*k*x + (d + 3*k^2)*x^2 + k*(-d + k^2)*x^3)),x]","\int \frac{-2 k+(-1+k) (1+k) x+2 k x^2}{\sqrt[4]{\left(1-x^2\right) \left(1-k^2 x^2\right)} \left(1-d+(3+d) k x+\left(d+3 k^2\right) x^2+k \left(-d+k^2\right) x^3\right)} \, dx","\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{k^2 x^4+\left(-k^2-1\right) x^2+1}}{k x+1}\right)}{d^{3/4}}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{k^2 x^4+\left(-k^2-1\right) x^2+1}}{k x+1}\right)}{d^{3/4}}",1,"Integrate[(-2*k + (-1 + k)*(1 + k)*x + 2*k*x^2)/(((1 - x^2)*(1 - k^2*x^2))^(1/4)*(1 - d + (3 + d)*k*x + (d + 3*k^2)*x^2 + k*(-d + k^2)*x^3)), x]","F",-1
1232,1,59,90,0.0502911,"\int \frac{\left(1+x^2\right) \sqrt{1-2 x^4}}{x^5} \, dx","Integrate[((1 + x^2)*Sqrt[1 - 2*x^4])/x^5,x]","\frac{1}{4} \left(2 \tanh ^{-1}\left(\sqrt{1-2 x^4}\right)-2 \sqrt{2} \sin ^{-1}\left(\sqrt{2} x^2\right)-\frac{\sqrt{1-2 x^4} \left(2 x^2+1\right)}{x^4}\right)","\frac{\sqrt{1-2 x^4} \left(-2 x^2-1\right)}{4 x^4}+\frac{i \log \left(\sqrt{1-2 x^4}+i \sqrt{2} x^2\right)}{\sqrt{2}}+i \tan ^{-1}\left(\sqrt{2} x^2-i \sqrt{1-2 x^4}\right)",1,"(-(((1 + 2*x^2)*Sqrt[1 - 2*x^4])/x^4) - 2*Sqrt[2]*ArcSin[Sqrt[2]*x^2] + 2*ArcTanh[Sqrt[1 - 2*x^4]])/4","A",1
1233,1,26,90,0.0059528,"\int \frac{\left(1+x^4\right)^{2/3}}{x^5} \, dx","Integrate[(1 + x^4)^(2/3)/x^5,x]","\frac{3}{20} \left(x^4+1\right)^{5/3} \, _2F_1\left(\frac{5}{3},2;\frac{8}{3};x^4+1\right)","-\frac{\left(x^4+1\right)^{2/3}}{4 x^4}+\frac{1}{6} \log \left(\sqrt[3]{x^4+1}-1\right)-\frac{1}{12} \log \left(\left(x^4+1\right)^{2/3}+\sqrt[3]{x^4+1}+1\right)+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{x^4+1}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3}}",1,"(3*(1 + x^4)^(5/3)*Hypergeometric2F1[5/3, 2, 8/3, 1 + x^4])/20","C",1
1234,0,0,90,0.2239624,"\int \frac{\left(-3+x^4\right) \left(1+x^4\right)^{2/3}}{x^3 \left(1-x^3+x^4\right)} \, dx","Integrate[((-3 + x^4)*(1 + x^4)^(2/3))/(x^3*(1 - x^3 + x^4)),x]","\int \frac{\left(-3+x^4\right) \left(1+x^4\right)^{2/3}}{x^3 \left(1-x^3+x^4\right)} \, dx","\log \left(\sqrt[3]{x^4+1}-x\right)-\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^4+1}+x}\right)+\frac{3 \left(x^4+1\right)^{2/3}}{2 x^2}-\frac{1}{2} \log \left(\sqrt[3]{x^4+1} x+\left(x^4+1\right)^{2/3}+x^2\right)",1,"Integrate[((-3 + x^4)*(1 + x^4)^(2/3))/(x^3*(1 - x^3 + x^4)), x]","F",-1
1235,0,0,90,0.3047565,"\int \frac{\sqrt[3]{-1+x^4} \left(3+x^4\right)}{x^2 \left(-1+x^3+x^4\right)} \, dx","Integrate[((-1 + x^4)^(1/3)*(3 + x^4))/(x^2*(-1 + x^3 + x^4)),x]","\int \frac{\sqrt[3]{-1+x^4} \left(3+x^4\right)}{x^2 \left(-1+x^3+x^4\right)} \, dx","\frac{3 \sqrt[3]{x^4-1}}{x}-\log \left(\sqrt[3]{x^4-1}+x\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^4-1}-x}\right)+\frac{1}{2} \log \left(-\sqrt[3]{x^4-1} x+\left(x^4-1\right)^{2/3}+x^2\right)",1,"Integrate[((-1 + x^4)^(1/3)*(3 + x^4))/(x^2*(-1 + x^3 + x^4)), x]","F",-1
1236,0,0,90,0.2353957,"\int \frac{\left(-1+x^4\right)^{2/3} \left(3+x^4\right)}{x^3 \left(-1+x^3+x^4\right)} \, dx","Integrate[((-1 + x^4)^(2/3)*(3 + x^4))/(x^3*(-1 + x^3 + x^4)),x]","\int \frac{\left(-1+x^4\right)^{2/3} \left(3+x^4\right)}{x^3 \left(-1+x^3+x^4\right)} \, dx","\log \left(\sqrt[3]{x^4-1}+x\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^4-1}-x}\right)+\frac{3 \left(x^4-1\right)^{2/3}}{2 x^2}-\frac{1}{2} \log \left(-\sqrt[3]{x^4-1} x+\left(x^4-1\right)^{2/3}+x^2\right)",1,"Integrate[((-1 + x^4)^(2/3)*(3 + x^4))/(x^3*(-1 + x^3 + x^4)), x]","F",-1
1237,0,0,90,0.2584778,"\int \frac{\left(-3+x^4\right) \sqrt[3]{1+x^4}}{x^2 \left(1+x^3+x^4\right)} \, dx","Integrate[((-3 + x^4)*(1 + x^4)^(1/3))/(x^2*(1 + x^3 + x^4)),x]","\int \frac{\left(-3+x^4\right) \sqrt[3]{1+x^4}}{x^2 \left(1+x^3+x^4\right)} \, dx","\frac{3 \sqrt[3]{x^4+1}}{x}-\log \left(\sqrt[3]{x^4+1}+x\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^4+1}-x}\right)+\frac{1}{2} \log \left(-\sqrt[3]{x^4+1} x+\left(x^4+1\right)^{2/3}+x^2\right)",1,"Integrate[((-3 + x^4)*(1 + x^4)^(1/3))/(x^2*(1 + x^3 + x^4)), x]","F",-1
1238,0,0,90,0.4667919,"\int \frac{(4+3 x) \left(-1-x+x^4\right) \sqrt[4]{-1-x+2 x^4}}{x^6 \left(1+x+x^4\right)} \, dx","Integrate[((4 + 3*x)*(-1 - x + x^4)*(-1 - x + 2*x^4)^(1/4))/(x^6*(1 + x + x^4)),x]","\int \frac{(4+3 x) \left(-1-x+x^4\right) \sqrt[4]{-1-x+2 x^4}}{x^6 \left(1+x+x^4\right)} \, dx","-4 \sqrt[4]{3} \tan ^{-1}\left(\frac{\sqrt[4]{3} x}{\sqrt[4]{2 x^4-x-1}}\right)+4 \sqrt[4]{3} \tanh ^{-1}\left(\frac{\sqrt[4]{3} x}{\sqrt[4]{2 x^4-x-1}}\right)-\frac{4 \sqrt[4]{2 x^4-x-1} \left(12 x^4-x-1\right)}{5 x^5}",1,"Integrate[((4 + 3*x)*(-1 - x + x^4)*(-1 - x + 2*x^4)^(1/4))/(x^6*(1 + x + x^4)), x]","F",-1
1239,1,120,90,0.0987644,"\int \frac{\sqrt{1+3 x^4}}{-1+3 x^4} \, dx","Integrate[Sqrt[1 + 3*x^4]/(-1 + 3*x^4),x]","\frac{5 x \sqrt{3 x^4+1} F_1\left(\frac{1}{4};-\frac{1}{2},1;\frac{5}{4};-3 x^4,3 x^4\right)}{\left(3 x^4-1\right) \left(6 x^4 \left(2 F_1\left(\frac{5}{4};-\frac{1}{2},2;\frac{9}{4};-3 x^4,3 x^4\right)+F_1\left(\frac{5}{4};\frac{1}{2},1;\frac{9}{4};-3 x^4,3 x^4\right)\right)+5 F_1\left(\frac{1}{4};-\frac{1}{2},1;\frac{5}{4};-3 x^4,3 x^4\right)\right)}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{3} x}{\sqrt{3 x^4+1}}\right)}{2 \sqrt{2} \sqrt[4]{3}}-\frac{\tan ^{-1}\left(\frac{\sqrt{3 x^4+1}}{\sqrt{3} x^2-\sqrt{2} \sqrt[4]{3} x+1}\right)}{\sqrt{2} \sqrt[4]{3}}",1,"(5*x*Sqrt[1 + 3*x^4]*AppellF1[1/4, -1/2, 1, 5/4, -3*x^4, 3*x^4])/((-1 + 3*x^4)*(5*AppellF1[1/4, -1/2, 1, 5/4, -3*x^4, 3*x^4] + 6*x^4*(2*AppellF1[5/4, -1/2, 2, 9/4, -3*x^4, 3*x^4] + AppellF1[5/4, 1/2, 1, 9/4, -3*x^4, 3*x^4])))","C",0
1240,1,125,90,0.1138127,"\int \frac{\left(b+a x^2\right) \sqrt[4]{-b x^2+a x^4}}{-b+a x^2} \, dx","Integrate[((b + a*x^2)*(-(b*x^2) + a*x^4)^(1/4))/(-b + a*x^2),x]","\frac{\sqrt[4]{a x^4-b x^2} \left(2 a^{3/4} x^{3/2} \sqrt[4]{a x^2-b}-7 b \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)+7 b \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)\right)}{4 a^{3/4} \sqrt{x} \sqrt[4]{a x^2-b}}","-\frac{7 b \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)}{4 a^{3/4}}+\frac{7 b \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)}{4 a^{3/4}}+\frac{1}{2} x \sqrt[4]{a x^4-b x^2}",1,"((-(b*x^2) + a*x^4)^(1/4)*(2*a^(3/4)*x^(3/2)*(-b + a*x^2)^(1/4) - 7*b*ArcTan[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)] + 7*b*ArcTanh[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)]))/(4*a^(3/4)*Sqrt[x]*(-b + a*x^2)^(1/4))","A",1
1241,1,66,90,0.0799771,"\int \frac{-b+2 a x^2}{\left(b+a x^2\right) \sqrt[4]{b x^2+a x^4}} \, dx","Integrate[(-b + 2*a*x^2)/((b + a*x^2)*(b*x^2 + a*x^4)^(1/4)),x]","\frac{2 x \left(2 a x^2 \sqrt[4]{\frac{a x^2}{b}+1} \, _2F_1\left(\frac{5}{4},\frac{5}{4};\frac{9}{4};-\frac{a x^2}{b}\right)-5 b\right)}{5 b \sqrt[4]{x^2 \left(a x^2+b\right)}}","-\frac{6 \left(a x^4+b x^2\right)^{3/4}}{x \left(a x^2+b\right)}+\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{\sqrt[4]{a}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{\sqrt[4]{a}}",1,"(2*x*(-5*b + 2*a*x^2*(1 + (a*x^2)/b)^(1/4)*Hypergeometric2F1[5/4, 5/4, 9/4, -((a*x^2)/b)]))/(5*b*(x^2*(b + a*x^2))^(1/4))","C",1
1242,1,26,90,0.0059202,"\int \frac{\left(1+x^5\right)^{2/3}}{x^6} \, dx","Integrate[(1 + x^5)^(2/3)/x^6,x]","\frac{3}{25} \left(x^5+1\right)^{5/3} \, _2F_1\left(\frac{5}{3},2;\frac{8}{3};x^5+1\right)","-\frac{\left(x^5+1\right)^{2/3}}{5 x^5}+\frac{2}{15} \log \left(\sqrt[3]{x^5+1}-1\right)-\frac{1}{15} \log \left(\left(x^5+1\right)^{2/3}+\sqrt[3]{x^5+1}+1\right)+\frac{2 \tan ^{-1}\left(\frac{2 \sqrt[3]{x^5+1}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{5 \sqrt{3}}",1,"(3*(1 + x^5)^(5/3)*Hypergeometric2F1[5/3, 2, 8/3, 1 + x^5])/25","C",1
1243,0,0,90,0.2830463,"\int \frac{\left(1+x^5\right)^{2/3} \left(-3+2 x^5\right)}{x^3 \left(1-x^3+x^5\right)} \, dx","Integrate[((1 + x^5)^(2/3)*(-3 + 2*x^5))/(x^3*(1 - x^3 + x^5)),x]","\int \frac{\left(1+x^5\right)^{2/3} \left(-3+2 x^5\right)}{x^3 \left(1-x^3+x^5\right)} \, dx","\log \left(\sqrt[3]{x^5+1}-x\right)-\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^5+1}+x}\right)+\frac{3 \left(x^5+1\right)^{2/3}}{2 x^2}-\frac{1}{2} \log \left(\sqrt[3]{x^5+1} x+\left(x^5+1\right)^{2/3}+x^2\right)",1,"Integrate[((1 + x^5)^(2/3)*(-3 + 2*x^5))/(x^3*(1 - x^3 + x^5)), x]","F",-1
1244,0,0,90,0.2739559,"\int \frac{\left(-1+x^5\right)^{2/3} \left(3+2 x^5\right)}{x^3 \left(-1-x^3+x^5\right)} \, dx","Integrate[((-1 + x^5)^(2/3)*(3 + 2*x^5))/(x^3*(-1 - x^3 + x^5)),x]","\int \frac{\left(-1+x^5\right)^{2/3} \left(3+2 x^5\right)}{x^3 \left(-1-x^3+x^5\right)} \, dx","\log \left(\sqrt[3]{x^5-1}-x\right)-\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^5-1}+x}\right)+\frac{3 \left(x^5-1\right)^{2/3}}{2 x^2}-\frac{1}{2} \log \left(\sqrt[3]{x^5-1} x+\left(x^5-1\right)^{2/3}+x^2\right)",1,"Integrate[((-1 + x^5)^(2/3)*(3 + 2*x^5))/(x^3*(-1 - x^3 + x^5)), x]","F",-1
1245,1,135,90,0.0300326,"\int \frac{\sqrt[4]{-1+x^6}}{x} \, dx","Integrate[(-1 + x^6)^(1/4)/x,x]","\frac{1}{12} \left(8 \sqrt[4]{x^6-1}+\sqrt{2} \log \left(\sqrt{x^6-1}-\sqrt{2} \sqrt[4]{x^6-1}+1\right)-\sqrt{2} \log \left(\sqrt{x^6-1}+\sqrt{2} \sqrt[4]{x^6-1}+1\right)+2 \sqrt{2} \tan ^{-1}\left(1-\sqrt{2} \sqrt[4]{x^6-1}\right)-2 \sqrt{2} \tan ^{-1}\left(\sqrt{2} \sqrt[4]{x^6-1}+1\right)\right)","\frac{2}{3} \sqrt[4]{x^6-1}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{x^6-1}}{\sqrt{x^6-1}-1}\right)}{3 \sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{x^6-1}}{\sqrt{x^6-1}+1}\right)}{3 \sqrt{2}}",1,"(8*(-1 + x^6)^(1/4) + 2*Sqrt[2]*ArcTan[1 - Sqrt[2]*(-1 + x^6)^(1/4)] - 2*Sqrt[2]*ArcTan[1 + Sqrt[2]*(-1 + x^6)^(1/4)] + Sqrt[2]*Log[1 - Sqrt[2]*(-1 + x^6)^(1/4) + Sqrt[-1 + x^6]] - Sqrt[2]*Log[1 + Sqrt[2]*(-1 + x^6)^(1/4) + Sqrt[-1 + x^6]])/12","A",1
1246,1,26,90,0.0057983,"\int \frac{1}{x^7 \sqrt[3]{1+x^6}} \, dx","Integrate[1/(x^7*(1 + x^6)^(1/3)),x]","\frac{1}{4} \left(x^6+1\right)^{2/3} \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};x^6+1\right)","-\frac{\left(x^6+1\right)^{2/3}}{6 x^6}-\frac{1}{18} \log \left(\sqrt[3]{x^6+1}-1\right)+\frac{1}{36} \log \left(\left(x^6+1\right)^{2/3}+\sqrt[3]{x^6+1}+1\right)-\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{x^6+1}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{6 \sqrt{3}}",1,"((1 + x^6)^(2/3)*Hypergeometric2F1[2/3, 2, 5/3, 1 + x^6])/4","C",1
1247,1,26,90,0.0061365,"\int \frac{\left(1+x^6\right)^{2/3}}{x^7} \, dx","Integrate[(1 + x^6)^(2/3)/x^7,x]","\frac{1}{10} \left(x^6+1\right)^{5/3} \, _2F_1\left(\frac{5}{3},2;\frac{8}{3};x^6+1\right)","-\frac{\left(x^6+1\right)^{2/3}}{6 x^6}+\frac{1}{9} \log \left(\sqrt[3]{x^6+1}-1\right)-\frac{1}{18} \log \left(\left(x^6+1\right)^{2/3}+\sqrt[3]{x^6+1}+1\right)+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{x^6+1}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"((1 + x^6)^(5/3)*Hypergeometric2F1[5/3, 2, 8/3, 1 + x^6])/10","C",1
1248,0,0,90,2.9107175,"\int \frac{\left(-3+k^2\right) x+2 k^2 x^3}{\sqrt[4]{\left(1-x^2\right) \left(1-k^2 x^2\right)} \left(-1+d+\left(3-d k^2\right) x^2-3 x^4+x^6\right)} \, dx","Integrate[((-3 + k^2)*x + 2*k^2*x^3)/(((1 - x^2)*(1 - k^2*x^2))^(1/4)*(-1 + d + (3 - d*k^2)*x^2 - 3*x^4 + x^6)),x]","\int \frac{\left(-3+k^2\right) x+2 k^2 x^3}{\sqrt[4]{\left(1-x^2\right) \left(1-k^2 x^2\right)} \left(-1+d+\left(3-d k^2\right) x^2-3 x^4+x^6\right)} \, dx","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{k^2 x^4+\left(-k^2-1\right) x^2+1}}{x^2-1}\right)}{d^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{k^2 x^4+\left(-k^2-1\right) x^2+1}}{x^2-1}\right)}{d^{3/4}}",1,"Integrate[((-3 + k^2)*x + 2*k^2*x^3)/(((1 - x^2)*(1 - k^2*x^2))^(1/4)*(-1 + d + (3 - d*k^2)*x^2 - 3*x^4 + x^6)), x]","F",-1
1249,0,0,90,0.2653848,"\int \frac{\left(-1+x^7\right)^{2/3} \left(3+4 x^7\right)}{x^3 \left(-1+x^3+x^7\right)} \, dx","Integrate[((-1 + x^7)^(2/3)*(3 + 4*x^7))/(x^3*(-1 + x^3 + x^7)),x]","\int \frac{\left(-1+x^7\right)^{2/3} \left(3+4 x^7\right)}{x^3 \left(-1+x^3+x^7\right)} \, dx","\log \left(\sqrt[3]{x^7-1}+x\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^7-1}-x}\right)+\frac{3 \left(x^7-1\right)^{2/3}}{2 x^2}-\frac{1}{2} \log \left(-\sqrt[3]{x^7-1} x+\left(x^7-1\right)^{2/3}+x^2\right)",1,"Integrate[((-1 + x^7)^(2/3)*(3 + 4*x^7))/(x^3*(-1 + x^3 + x^7)), x]","F",-1
1250,0,0,90,1.4270532,"\int \frac{x}{\sqrt{-b x+a^2 x^2} \left(a x^2+x \sqrt{-b x+a^2 x^2}\right)^{3/2}} \, dx","Integrate[x/(Sqrt[-(b*x) + a^2*x^2]*(a*x^2 + x*Sqrt[-(b*x) + a^2*x^2])^(3/2)),x]","\int \frac{x}{\sqrt{-b x+a^2 x^2} \left(a x^2+x \sqrt{-b x+a^2 x^2}\right)^{3/2}} \, dx","\frac{20 a \sqrt{x \left(\sqrt{a^2 x^2-b x}+a x\right)}}{3 b^2 x}-\frac{4 \sqrt{a^2 x^2-b x} \sqrt{x \left(\sqrt{a^2 x^2-b x}+a x\right)}}{3 b^2 x^2}",1,"Integrate[x/(Sqrt[-(b*x) + a^2*x^2]*(a*x^2 + x*Sqrt[-(b*x) + a^2*x^2])^(3/2)), x]","F",-1
1251,1,101,91,0.580852,"\int \frac{-\sqrt{a b}+x}{\sqrt{x (a+x) (b+x)} \left(\sqrt{a b}+x\right)} \, dx","Integrate[(-Sqrt[a*b] + x)/(Sqrt[x*(a + x)*(b + x)]*(Sqrt[a*b] + x)),x]","-\frac{2 a x^{3/2} \sqrt{\frac{a}{x}+1} \sqrt{\frac{b}{x}+1} \left(F\left(\sin ^{-1}\left(\frac{\sqrt{-a}}{\sqrt{x}}\right)|\frac{b}{a}\right)-2 \Pi \left(\frac{b}{\sqrt{a b}};\sin ^{-1}\left(\frac{\sqrt{-a}}{\sqrt{x}}\right)|\frac{b}{a}\right)\right)}{(-a)^{3/2} \sqrt{x (a+x) (b+x)}}","\frac{2 \tan ^{-1}\left(\frac{(b+x) \left(\frac{x}{\sqrt{2 \sqrt{a b}-a-b}}+\frac{a}{\sqrt{2 \sqrt{a b}-a-b}}\right)}{\sqrt{x^2 (a+b)+a b x+x^3}}\right)}{\sqrt{2 \sqrt{a b}-a-b}}",1,"(-2*a*Sqrt[1 + a/x]*Sqrt[1 + b/x]*x^(3/2)*(EllipticF[ArcSin[Sqrt[-a]/Sqrt[x]], b/a] - 2*EllipticPi[b/Sqrt[a*b], ArcSin[Sqrt[-a]/Sqrt[x]], b/a]))/((-a)^(3/2)*Sqrt[x*(a + x)*(b + x)])","C",1
1252,1,35,91,0.008973,"\int \frac{1}{\sqrt[3]{-x^2+x^3}} \, dx","Integrate[(-x^2 + x^3)^(-1/3),x]","\frac{3 \left((x-1) x^2\right)^{2/3} \, _2F_1\left(\frac{2}{3},\frac{2}{3};\frac{5}{3};1-x\right)}{2 x^{4/3}}","-\log \left(\sqrt[3]{x^3-x^2}-x\right)+\frac{1}{2} \log \left(x^2+\sqrt[3]{x^3-x^2} x+\left(x^3-x^2\right)^{2/3}\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-x^2}+x}\right)",1,"(3*((-1 + x)*x^2)^(2/3)*Hypergeometric2F1[2/3, 2/3, 5/3, 1 - x])/(2*x^(4/3))","C",1
1253,0,0,91,0.147411,"\int \frac{3-x^2}{\left(1-x^2\right) \sqrt[4]{1-6 x^2+x^4}} \, dx","Integrate[(3 - x^2)/((1 - x^2)*(1 - 6*x^2 + x^4)^(1/4)),x]","\int \frac{3-x^2}{\left(1-x^2\right) \sqrt[4]{1-6 x^2+x^4}} \, dx","\tan ^{-1}\left(\frac{x+i}{\sqrt[4]{x^4-6 x^2+1}}\right)-\tan ^{-1}\left(\frac{\sqrt[4]{x^4-6 x^2+1}}{x-i}\right)+\tanh ^{-1}\left(\frac{x+i}{\sqrt[4]{x^4-6 x^2+1}}\right)+\tanh ^{-1}\left(\frac{\sqrt[4]{x^4-6 x^2+1}}{x-i}\right)",1,"Integrate[(3 - x^2)/((1 - x^2)*(1 - 6*x^2 + x^4)^(1/4)), x]","F",-1
1254,0,0,91,1.9442671,"\int \frac{-3+x^4}{\left(1+x^4\right) \sqrt[4]{-3 x+4 x^4-3 x^5}} \, dx","Integrate[(-3 + x^4)/((1 + x^4)*(-3*x + 4*x^4 - 3*x^5)^(1/4)),x]","\int \frac{-3+x^4}{\left(1+x^4\right) \sqrt[4]{-3 x+4 x^4-3 x^5}} \, dx","\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \left(-3 x^5+4 x^4-3 x\right)^{3/4}}{3 x^4-4 x^3+3}\right)+\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} \left(-3 x^5+4 x^4-3 x\right)^{3/4}}{3 x^4-4 x^3+3}\right)",1,"Integrate[(-3 + x^4)/((1 + x^4)*(-3*x + 4*x^4 - 3*x^5)^(1/4)), x]","F",-1
1255,0,0,91,0.2576549,"\int \frac{\sqrt[3]{-1+x^6} \left(1+x^6\right)}{x^2 \left(-1+x^3+x^6\right)} \, dx","Integrate[((-1 + x^6)^(1/3)*(1 + x^6))/(x^2*(-1 + x^3 + x^6)),x]","\int \frac{\sqrt[3]{-1+x^6} \left(1+x^6\right)}{x^2 \left(-1+x^3+x^6\right)} \, dx","\frac{\sqrt[3]{x^6-1}}{x}-\frac{1}{3} \log \left(\sqrt[3]{x^6-1}+x\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^6-1}-x}\right)}{\sqrt{3}}+\frac{1}{6} \log \left(-\sqrt[3]{x^6-1} x+\left(x^6-1\right)^{2/3}+x^2\right)",1,"Integrate[((-1 + x^6)^(1/3)*(1 + x^6))/(x^2*(-1 + x^3 + x^6)), x]","F",-1
1256,1,2093,91,6.2445923,"\int \frac{\left(-1+x^4\right) \sqrt{1+x^4}}{1+x^2+3 x^4+x^6+x^8} \, dx","Integrate[((-1 + x^4)*Sqrt[1 + x^4])/(1 + x^2 + 3*x^4 + x^6 + x^8),x]","\text{Result too large to show}","-\sqrt{\frac{1}{6} \left(-1-i \sqrt{3}\right)} \tan ^{-1}\left(\frac{2 x}{\left(\sqrt{3}-i\right) \sqrt{x^4+1}}\right)-\sqrt{\frac{1}{6} \left(-1+i \sqrt{3}\right)} \tan ^{-1}\left(\frac{2 x}{\left(\sqrt{3}+i\right) \sqrt{x^4+1}}\right)",1,"-(((-1)^(1/4)*Sqrt[1 - I*x^2]*Sqrt[1 + I*x^2]*EllipticF[I*ArcSinh[(-1)^(1/4)*x], -1])/Sqrt[1 + x^4]) - ((-1)^(1/4)*Sqrt[1 - I*x^2]*Sqrt[1 + I*x^2]*EllipticPi[I/Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 1, 0], I*ArcSinh[(-1)^(1/4)*x], -1])/(Sqrt[1 + x^4]*Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 1, 0]*(Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 2, 0])*(Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 3, 0])*(Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 4, 0])) + ((-1)^(1/4)*Sqrt[1 - I*x^2]*Sqrt[1 + I*x^2]*EllipticPi[I/Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 1, 0], I*ArcSinh[(-1)^(1/4)*x], -1]*Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 1, 0]^3)/(Sqrt[1 + x^4]*(Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 2, 0])*(Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 3, 0])*(Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 4, 0])) - ((-1)^(1/4)*Sqrt[1 - I*x^2]*Sqrt[1 + I*x^2]*EllipticPi[I/Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 2, 0], I*ArcSinh[(-1)^(1/4)*x], -1])/(Sqrt[1 + x^4]*Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 2, 0]*(-Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 1, 0] + Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 2, 0])*(Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 3, 0])*(Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 4, 0])) + ((-1)^(1/4)*Sqrt[1 - I*x^2]*Sqrt[1 + I*x^2]*EllipticPi[I/Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 2, 0], I*ArcSinh[(-1)^(1/4)*x], -1]*Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 2, 0]^3)/(Sqrt[1 + x^4]*(-Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 1, 0] + Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 2, 0])*(Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 3, 0])*(Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 4, 0])) - ((-1)^(1/4)*Sqrt[1 - I*x^2]*Sqrt[1 + I*x^2]*EllipticPi[I/Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 3, 0], I*ArcSinh[(-1)^(1/4)*x], -1])/(Sqrt[1 + x^4]*Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 3, 0]*(-Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 1, 0] + Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 3, 0])*(-Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 2, 0] + Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 3, 0])*(Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 3, 0] - Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 4, 0])) + ((-1)^(1/4)*Sqrt[1 - I*x^2]*Sqrt[1 + I*x^2]*EllipticPi[I/Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 3, 0], I*ArcSinh[(-1)^(1/4)*x], -1]*Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 3, 0]^3)/(Sqrt[1 + x^4]*(-Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 1, 0] + Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 3, 0])*(-Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 2, 0] + Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 3, 0])*(Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 3, 0] - Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 4, 0])) - ((-1)^(1/4)*Sqrt[1 - I*x^2]*Sqrt[1 + I*x^2]*EllipticPi[I/Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 4, 0], I*ArcSinh[(-1)^(1/4)*x], -1])/(Sqrt[1 + x^4]*Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 4, 0]*(-Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 1, 0] + Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 4, 0])*(-Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 2, 0] + Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 4, 0])*(-Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 3, 0] + Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 4, 0])) + ((-1)^(1/4)*Sqrt[1 - I*x^2]*Sqrt[1 + I*x^2]*EllipticPi[I/Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 4, 0], I*ArcSinh[(-1)^(1/4)*x], -1]*Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 4, 0]^3)/(Sqrt[1 + x^4]*(-Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 1, 0] + Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 4, 0])*(-Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 2, 0] + Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 4, 0])*(-Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 3, 0] + Root[1 + #1 + 3*#1^2 + #1^3 + #1^4 & , 4, 0]))","C",0
1257,1,111,91,0.292869,"\int \frac{-1+2 x^8}{\sqrt[4]{1+x^4} \left(-1+x^8\right)} \, dx","Integrate[(-1 + 2*x^8)/((1 + x^4)^(1/4)*(-1 + x^8)),x]","-\frac{2}{5} x^5 F_1\left(\frac{5}{4};\frac{1}{4},1;\frac{9}{4};-x^4,x^4\right)-\frac{x}{2 \sqrt[4]{x^4+1}}+\frac{3 \left(-\log \left(1-\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+1}}\right)+\log \left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+1}}+1\right)+2 \tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+1}}\right)\right)}{8 \sqrt[4]{2}}","-\frac{x}{2 \sqrt[4]{x^4+1}}+\tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+1}}\right)}{4 \sqrt[4]{2}}+\tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+1}}\right)}{4 \sqrt[4]{2}}",1,"-1/2*x/(1 + x^4)^(1/4) - (2*x^5*AppellF1[5/4, 1/4, 1, 9/4, -x^4, x^4])/5 + (3*(2*ArcTan[(2^(1/4)*x)/(1 + x^4)^(1/4)] - Log[1 - (2^(1/4)*x)/(1 + x^4)^(1/4)] + Log[1 + (2^(1/4)*x)/(1 + x^4)^(1/4)]))/(8*2^(1/4))","C",0
1258,1,53,91,0.0159526,"\int \sqrt[4]{b x^5+a x^8} \, dx","Integrate[(b*x^5 + a*x^8)^(1/4),x]","\frac{4 x \sqrt[4]{x^5 \left(a x^3+b\right)} \, _2F_1\left(-\frac{1}{4},\frac{3}{4};\frac{7}{4};-\frac{a x^3}{b}\right)}{9 \sqrt[4]{\frac{a x^3}{b}+1}}","\frac{b \tan ^{-1}\left(\frac{\sqrt[4]{a x^8+b x^5}}{\sqrt[4]{a} x^2}\right)}{6 a^{3/4}}+\frac{b \tanh ^{-1}\left(\frac{\sqrt[4]{a x^8+b x^5}}{\sqrt[4]{a} x^2}\right)}{6 a^{3/4}}+\frac{1}{3} x \sqrt[4]{a x^8+b x^5}",1,"(4*x*(x^5*(b + a*x^3))^(1/4)*Hypergeometric2F1[-1/4, 3/4, 7/4, -((a*x^3)/b)])/(9*(1 + (a*x^3)/b)^(1/4))","C",1
1259,1,1129,91,14.1656265,"\int \frac{\sqrt{x-\sqrt{1+x^2}}}{1-\sqrt{1+x^2}} \, dx","Integrate[Sqrt[x - Sqrt[1 + x^2]]/(1 - Sqrt[1 + x^2]),x]","-\frac{159120 \left(x^2-\sqrt{x^2+1} x+1\right) \left(\frac{16}{585} \, _4F_3\left(\frac{5}{4},2,2,2;1,1,\frac{17}{4};\left(x-\sqrt{x^2+1}\right)^2\right) \left(\left(x-\sqrt{x^2+1}\right)^3+x-\sqrt{x^2+1}\right)^2+\frac{681 \left(x-\sqrt{x^2+1}\right)^6-1483 \left(x-\sqrt{x^2+1}\right)^4-6769 \left(x-\sqrt{x^2+1}\right)^2+5 \left(\left(x-\sqrt{x^2+1}\right)^8-248 \left(x-\sqrt{x^2+1}\right)^6+102 \left(x-\sqrt{x^2+1}\right)^4+1208 \left(x-\sqrt{x^2+1}\right)^2+729\right) \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\left(x-\sqrt{x^2+1}\right)^2\right)-3645}{640 \left(x-\sqrt{x^2+1}\right)^4}\right) \left(x-\sqrt{x^2+1}\right)^{23/2}}{x \left(1-\frac{x}{\sqrt{x^2+1}}\right) \left(\left(x-\sqrt{x^2+1}\right)^2+1\right) \left(1989 \left(-217600 x^{12}+217600 \sqrt{x^2+1} x^{11}-540032 x^{10}+431232 \sqrt{x^2+1} x^9-565792 x^8+377376 \sqrt{x^2+1} x^7-331584 x^6+183200 \sqrt{x^2+1} x^5-99050 x^4+36170 \sqrt{x^2+1} x^3-8563 x^2+10 \left(-1024 x^{13}+1024 \sqrt{x^2+1} x^{12}+28672 x^{11}-29184 \sqrt{x^2+1} x^{10}+75840 x^9-61120 \sqrt{x^2+1} x^8+79168 x^7-52320 \sqrt{x^2+1} x^6+44684 x^5-24300 \sqrt{x^2+1} x^4+13240 x^3-4978 \sqrt{x^2+1} x^2+1335 x-182 \sqrt{x^2+1}\right) \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\left(x-\sqrt{x^2+1}\right)^2\right) x+687 \sqrt{x^2+1} x+140\right)+4352 x \left(-106496 x^{15}+106496 \sqrt{x^2+1} x^{14}-409600 x^{13}+356352 \sqrt{x^2+1} x^{12}-632320 x^{11}+467456 \sqrt{x^2+1} x^{10}-499200 x^9+303360 \sqrt{x^2+1} x^8-212160 x^7+100800 \sqrt{x^2+1} x^6-46592 x^5+15904 \sqrt{x^2+1} x^4-4550 x^3+938 \sqrt{x^2+1} x^2-130 x+9 \sqrt{x^2+1}\right) \, _4F_3\left(\frac{5}{4},2,2,2;1,1,\frac{17}{4};\left(x-\sqrt{x^2+1}\right)^2\right)+40960 x \left(-32768 x^{17}+32768 \sqrt{x^2+1} x^{16}-147456 x^{15}+131072 \sqrt{x^2+1} x^{14}-274432 x^{13}+212992 \sqrt{x^2+1} x^{12}-272384 x^{11}+180224 \sqrt{x^2+1} x^{10}-154880 x^9+84480 \sqrt{x^2+1} x^8-50304 x^7+21504 \sqrt{x^2+1} x^6-8736 x^5+2688 \sqrt{x^2+1} x^4-688 x^3+128 \sqrt{x^2+1} x^2-16 x+\sqrt{x^2+1}\right) \, _4F_3\left(\frac{9}{4},3,3,3;2,2,\frac{21}{4};\left(x-\sqrt{x^2+1}\right)^2\right)\right)}-\frac{\left(\left(x-\sqrt{x^2+1}\right)^2-1\right)^2 \left(-\frac{2 \left(x-\sqrt{x^2+1}\right)^{3/2}}{\left(x-\sqrt{x^2+1}\right)^2-1}+\tan ^{-1}\left(\sqrt{x-\sqrt{x^2+1}}\right)-\tanh ^{-1}\left(\sqrt{x-\sqrt{x^2+1}}\right)\right)}{4 x^2 \left(1-\frac{x}{\sqrt{x^2+1}}\right) \left(1-\frac{\left(x-\sqrt{x^2+1}\right)^2-1}{2 \left(x-\sqrt{x^2+1}\right)^2}\right) \left(x-\sqrt{x^2+1}\right)^2}","\frac{2 \sqrt{x-\sqrt{x^2+1}} (-x-2)+2 \sqrt{x^2+1} \sqrt{x-\sqrt{x^2+1}}}{\sqrt{x^2+1}-x-1}-2 \tan ^{-1}\left(\sqrt{x-\sqrt{x^2+1}}\right)",1,"-1/4*((-1 + (x - Sqrt[1 + x^2])^2)^2*((-2*(x - Sqrt[1 + x^2])^(3/2))/(-1 + (x - Sqrt[1 + x^2])^2) + ArcTan[Sqrt[x - Sqrt[1 + x^2]]] - ArcTanh[Sqrt[x - Sqrt[1 + x^2]]]))/(x^2*(1 - x/Sqrt[1 + x^2])*(x - Sqrt[1 + x^2])^2*(1 - (-1 + (x - Sqrt[1 + x^2])^2)/(2*(x - Sqrt[1 + x^2])^2))) - (159120*(x - Sqrt[1 + x^2])^(23/2)*(1 + x^2 - x*Sqrt[1 + x^2])*((-3645 - 6769*(x - Sqrt[1 + x^2])^2 - 1483*(x - Sqrt[1 + x^2])^4 + 681*(x - Sqrt[1 + x^2])^6 + 5*(729 + 1208*(x - Sqrt[1 + x^2])^2 + 102*(x - Sqrt[1 + x^2])^4 - 248*(x - Sqrt[1 + x^2])^6 + (x - Sqrt[1 + x^2])^8)*Hypergeometric2F1[1/4, 1, 5/4, (x - Sqrt[1 + x^2])^2])/(640*(x - Sqrt[1 + x^2])^4) + (16*(x - Sqrt[1 + x^2] + (x - Sqrt[1 + x^2])^3)^2*HypergeometricPFQ[{5/4, 2, 2, 2}, {1, 1, 17/4}, (x - Sqrt[1 + x^2])^2])/585))/(x*(1 - x/Sqrt[1 + x^2])*(1 + (x - Sqrt[1 + x^2])^2)*(1989*(140 - 8563*x^2 - 99050*x^4 - 331584*x^6 - 565792*x^8 - 540032*x^10 - 217600*x^12 + 687*x*Sqrt[1 + x^2] + 36170*x^3*Sqrt[1 + x^2] + 183200*x^5*Sqrt[1 + x^2] + 377376*x^7*Sqrt[1 + x^2] + 431232*x^9*Sqrt[1 + x^2] + 217600*x^11*Sqrt[1 + x^2] + 10*x*(1335*x + 13240*x^3 + 44684*x^5 + 79168*x^7 + 75840*x^9 + 28672*x^11 - 1024*x^13 - 182*Sqrt[1 + x^2] - 4978*x^2*Sqrt[1 + x^2] - 24300*x^4*Sqrt[1 + x^2] - 52320*x^6*Sqrt[1 + x^2] - 61120*x^8*Sqrt[1 + x^2] - 29184*x^10*Sqrt[1 + x^2] + 1024*x^12*Sqrt[1 + x^2])*Hypergeometric2F1[1/4, 1, 5/4, (x - Sqrt[1 + x^2])^2]) + 4352*x*(-130*x - 4550*x^3 - 46592*x^5 - 212160*x^7 - 499200*x^9 - 632320*x^11 - 409600*x^13 - 106496*x^15 + 9*Sqrt[1 + x^2] + 938*x^2*Sqrt[1 + x^2] + 15904*x^4*Sqrt[1 + x^2] + 100800*x^6*Sqrt[1 + x^2] + 303360*x^8*Sqrt[1 + x^2] + 467456*x^10*Sqrt[1 + x^2] + 356352*x^12*Sqrt[1 + x^2] + 106496*x^14*Sqrt[1 + x^2])*HypergeometricPFQ[{5/4, 2, 2, 2}, {1, 1, 17/4}, (x - Sqrt[1 + x^2])^2] + 40960*x*(-16*x - 688*x^3 - 8736*x^5 - 50304*x^7 - 154880*x^9 - 272384*x^11 - 274432*x^13 - 147456*x^15 - 32768*x^17 + Sqrt[1 + x^2] + 128*x^2*Sqrt[1 + x^2] + 2688*x^4*Sqrt[1 + x^2] + 21504*x^6*Sqrt[1 + x^2] + 84480*x^8*Sqrt[1 + x^2] + 180224*x^10*Sqrt[1 + x^2] + 212992*x^12*Sqrt[1 + x^2] + 131072*x^14*Sqrt[1 + x^2] + 32768*x^16*Sqrt[1 + x^2])*HypergeometricPFQ[{9/4, 3, 3, 3}, {2, 2, 21/4}, (x - Sqrt[1 + x^2])^2]))","C",0
1260,0,0,92,0.171013,"\int \frac{(-1+x) (3+x)}{\left(-1+x^2\right)^{2/3} \left(2-x+x^2\right)} \, dx","Integrate[((-1 + x)*(3 + x))/((-1 + x^2)^(2/3)*(2 - x + x^2)),x]","\int \frac{(-1+x) (3+x)}{\left(-1+x^2\right)^{2/3} \left(2-x+x^2\right)} \, dx","-\log \left(\left(x^2-1\right)^{2/3}+x+1\right)+\frac{1}{2} \log \left(x^2+\left(x^2-1\right)^{4/3}+(-x-1) \left(x^2-1\right)^{2/3}+2 x+1\right)-\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \left(x^2-1\right)^{2/3}}{\left(x^2-1\right)^{2/3}-2 x-2}\right)",1,"Integrate[((-1 + x)*(3 + x))/((-1 + x^2)^(2/3)*(2 - x + x^2)), x]","F",-1
1261,1,28,92,0.0050753,"\int \frac{\sqrt[3]{-1+x^3}}{x^4} \, dx","Integrate[(-1 + x^3)^(1/3)/x^4,x]","\frac{1}{4} \left(x^3-1\right)^{4/3} \, _2F_1\left(\frac{4}{3},2;\frac{7}{3};1-x^3\right)","-\frac{\sqrt[3]{x^3-1}}{3 x^3}+\frac{1}{9} \log \left(\sqrt[3]{x^3-1}+1\right)-\frac{1}{18} \log \left(\left(x^3-1\right)^{2/3}-\sqrt[3]{x^3-1}+1\right)-\frac{\tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{x^3-1}}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"((-1 + x^3)^(4/3)*Hypergeometric2F1[4/3, 2, 7/3, 1 - x^3])/4","C",1
1262,1,28,92,0.0057117,"\int \frac{\left(-1+x^3\right)^{2/3}}{x^4} \, dx","Integrate[(-1 + x^3)^(2/3)/x^4,x]","\frac{1}{5} \left(x^3-1\right)^{5/3} \, _2F_1\left(\frac{5}{3},2;\frac{8}{3};1-x^3\right)","-\frac{\left(x^3-1\right)^{2/3}}{3 x^3}-\frac{2}{9} \log \left(\sqrt[3]{x^3-1}+1\right)+\frac{1}{9} \log \left(\left(x^3-1\right)^{2/3}-\sqrt[3]{x^3-1}+1\right)-\frac{2 \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{x^3-1}}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"((-1 + x^3)^(5/3)*Hypergeometric2F1[5/3, 2, 8/3, 1 - x^3])/5","C",1
1263,1,20,92,0.0022133,"\int \frac{\sqrt[3]{1+x^3}}{x^2} \, dx","Integrate[(1 + x^3)^(1/3)/x^2,x]","-\frac{\, _2F_1\left(-\frac{1}{3},-\frac{1}{3};\frac{2}{3};-x^3\right)}{x}","-\frac{\sqrt[3]{x^3+1}}{x}-\frac{1}{3} \log \left(\sqrt[3]{x^3+1}-x\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+1}+x}\right)}{\sqrt{3}}+\frac{1}{6} \log \left(\sqrt[3]{x^3+1} x+\left(x^3+1\right)^{2/3}+x^2\right)",1,"-(Hypergeometric2F1[-1/3, -1/3, 2/3, -x^3]/x)","C",1
1264,0,0,92,0.1451915,"\int \frac{-1+x}{(1+x) \sqrt[3]{2+x^3}} \, dx","Integrate[(-1 + x)/((1 + x)*(2 + x^3)^(1/3)),x]","\int \frac{-1+x}{(1+x) \sqrt[3]{2+x^3}} \, dx","-\log \left(\sqrt[3]{x^3+2}-x-2\right)-\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x^3+2}}{\sqrt[3]{x^3+2}+2 x+4}\right)+\frac{1}{2} \log \left(\left(x^3+2\right)^{2/3}+(x+2) \sqrt[3]{x^3+2}+x^2+4 x+4\right)",1,"Integrate[(-1 + x)/((1 + x)*(2 + x^3)^(1/3)), x]","F",-1
1265,1,39,92,0.0091111,"\int \frac{1}{x^7 \left(b+a x^3\right)^{3/4}} \, dx","Integrate[1/(x^7*(b + a*x^3)^(3/4)),x]","-\frac{4 a^2 \sqrt[4]{a x^3+b} \, _2F_1\left(\frac{1}{4},3;\frac{5}{4};\frac{a x^3}{b}+1\right)}{3 b^3}","-\frac{7 a^2 \tan ^{-1}\left(\frac{\sqrt[4]{a x^3+b}}{\sqrt[4]{b}}\right)}{16 b^{11/4}}-\frac{7 a^2 \tanh ^{-1}\left(\frac{\sqrt[4]{a x^3+b}}{\sqrt[4]{b}}\right)}{16 b^{11/4}}+\frac{\sqrt[4]{a x^3+b} \left(7 a x^3-4 b\right)}{24 b^2 x^6}",1,"(-4*a^2*(b + a*x^3)^(1/4)*Hypergeometric2F1[1/4, 3, 5/4, 1 + (a*x^3)/b])/(3*b^3)","C",1
1266,0,0,92,2.073777,"\int \frac{\left(1+2 x+x^2\right) \left(-2-(-1+k) (1+k) x+2 k^2 x^2\right)}{\left(\left(1-x^2\right) \left(1-k^2 x^2\right)\right)^{3/4} \left(1-d-(1+3 d) x-\left(3 d+k^2\right) x^2+\left(-d+k^2\right) x^3\right)} \, dx","Integrate[((1 + 2*x + x^2)*(-2 - (-1 + k)*(1 + k)*x + 2*k^2*x^2))/(((1 - x^2)*(1 - k^2*x^2))^(3/4)*(1 - d - (1 + 3*d)*x - (3*d + k^2)*x^2 + (-d + k^2)*x^3)),x]","\int \frac{\left(1+2 x+x^2\right) \left(-2-(-1+k) (1+k) x+2 k^2 x^2\right)}{\left(\left(1-x^2\right) \left(1-k^2 x^2\right)\right)^{3/4} \left(1-d-(1+3 d) x-\left(3 d+k^2\right) x^2+\left(-d+k^2\right) x^3\right)} \, dx","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{d} x+\sqrt[4]{d}}{\sqrt[4]{k^2 x^4+\left(-k^2-1\right) x^2+1}}\right)}{d^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{d} x+\sqrt[4]{d}}{\sqrt[4]{k^2 x^4+\left(-k^2-1\right) x^2+1}}\right)}{d^{3/4}}",1,"Integrate[((1 + 2*x + x^2)*(-2 - (-1 + k)*(1 + k)*x + 2*k^2*x^2))/(((1 - x^2)*(1 - k^2*x^2))^(3/4)*(1 - d - (1 + 3*d)*x - (3*d + k^2)*x^2 + (-d + k^2)*x^3)), x]","F",-1
1267,1,28,92,0.0047229,"\int \frac{1}{x^5 \sqrt[3]{-1+x^4}} \, dx","Integrate[1/(x^5*(-1 + x^4)^(1/3)),x]","\frac{3}{8} \left(x^4-1\right)^{2/3} \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};1-x^4\right)","\frac{\left(x^4-1\right)^{2/3}}{4 x^4}-\frac{1}{12} \log \left(\sqrt[3]{x^4-1}+1\right)+\frac{1}{24} \log \left(\left(x^4-1\right)^{2/3}-\sqrt[3]{x^4-1}+1\right)-\frac{\tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{x^4-1}}{\sqrt{3}}\right)}{4 \sqrt{3}}",1,"(3*(-1 + x^4)^(2/3)*Hypergeometric2F1[2/3, 2, 5/3, 1 - x^4])/8","C",1
1268,1,28005,92,14.4117282,"\int \frac{x (-b+x) \left(a b-2 a x+x^2\right)}{\sqrt{x (-a+x) (-b+x)} \left(-a^2 d+2 a d x+\left(b^2-d\right) x^2-2 b x^3+x^4\right)} \, dx","Integrate[(x*(-b + x)*(a*b - 2*a*x + x^2))/(Sqrt[x*(-a + x)*(-b + x)]*(-(a^2*d) + 2*a*d*x + (b^2 - d)*x^2 - 2*b*x^3 + x^4)),x]","\text{Result too large to show}","-\frac{\tan ^{-1}\left(\frac{\sqrt{x^2 (-a-b)+a b x+x^3}}{\sqrt[4]{d} (a-x)}\right)}{\sqrt[4]{d}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{x^2 (-a-b)+a b x+x^3}}{x (x-b)}\right)}{\sqrt[4]{d}}",1,"Result too large to show","C",0
1269,1,37,92,0.0083272,"\int \frac{1}{x^9 \left(b+a x^4\right)^{3/4}} \, dx","Integrate[1/(x^9*(b + a*x^4)^(3/4)),x]","-\frac{a^2 \sqrt[4]{a x^4+b} \, _2F_1\left(\frac{1}{4},3;\frac{5}{4};\frac{a x^4}{b}+1\right)}{b^3}","-\frac{21 a^2 \tan ^{-1}\left(\frac{\sqrt[4]{a x^4+b}}{\sqrt[4]{b}}\right)}{64 b^{11/4}}-\frac{21 a^2 \tanh ^{-1}\left(\frac{\sqrt[4]{a x^4+b}}{\sqrt[4]{b}}\right)}{64 b^{11/4}}+\frac{\sqrt[4]{a x^4+b} \left(7 a x^4-4 b\right)}{32 b^2 x^8}",1,"-((a^2*(b + a*x^4)^(1/4)*Hypergeometric2F1[1/4, 3, 5/4, 1 + (a*x^4)/b])/b^3)","C",1
1270,1,62,92,0.0517118,"\int x^4 \left(b+a x^4\right)^{3/4} \, dx","Integrate[x^4*(b + a*x^4)^(3/4),x]","\frac{x \left(a x^4+b\right)^{3/4} \left(-\frac{b \, _2F_1\left(-\frac{3}{4},\frac{1}{4};\frac{5}{4};-\frac{a x^4}{b}\right)}{\left(\frac{a x^4}{b}+1\right)^{3/4}}+a x^4+b\right)}{8 a}","-\frac{3 b^2 \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{64 a^{5/4}}-\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{64 a^{5/4}}+\frac{\left(a x^4+b\right)^{3/4} \left(4 a x^5+3 b x\right)}{32 a}",1,"(x*(b + a*x^4)^(3/4)*(b + a*x^4 - (b*Hypergeometric2F1[-3/4, 1/4, 5/4, -((a*x^4)/b)])/(1 + (a*x^4)/b)^(3/4)))/(8*a)","C",1
1271,1,491,92,59.3878665,"\int \frac{\sqrt[4]{-b x^3+a x^4}}{x \left(d+c x+x^2\right)} \, dx","Integrate[(-(b*x^3) + a*x^4)^(1/4)/(x*(d + c*x + x^2)),x]","\frac{\sqrt[4]{x^3 (a x-b)} \left(-\sqrt[4]{\frac{b \left(\sqrt{c^2-4 d}-c\right)}{d}-2 a} \log \left(\sqrt[4]{\frac{b \left(\sqrt{c^2-4 d}-c\right)}{2 d}-a}-\sqrt[4]{\frac{b}{x}-a}\right)+\sqrt[4]{-2 a-\frac{b \left(\sqrt{c^2-4 d}+c\right)}{d}} \log \left(\sqrt[4]{-a-\frac{b \left(\sqrt{c^2-4 d}+c\right)}{2 d}}-\sqrt[4]{\frac{b}{x}-a}\right)+\sqrt[4]{\frac{b \left(\sqrt{c^2-4 d}-c\right)}{d}-2 a} \log \left(\sqrt[4]{\frac{b \left(\sqrt{c^2-4 d}-c\right)}{2 d}-a}+\sqrt[4]{\frac{b}{x}-a}\right)-\sqrt[4]{-2 a-\frac{b \left(\sqrt{c^2-4 d}+c\right)}{d}} \log \left(\sqrt[4]{-a-\frac{b \left(\sqrt{c^2-4 d}+c\right)}{2 d}}+\sqrt[4]{\frac{b}{x}-a}\right)+2 \sqrt[4]{\frac{b \left(\sqrt{c^2-4 d}-c\right)}{d}-2 a} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{2 b}{x}-2 a}}{\sqrt[4]{\frac{b \left(\sqrt{c^2-4 d}-c\right)}{d}-2 a}}\right)-2 \sqrt[4]{-2 a-\frac{b \left(\sqrt{c^2-4 d}+c\right)}{d}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{2 b}{x}-2 a}}{\sqrt[4]{-2 a-\frac{b \left(\sqrt{c^2-4 d}+c\right)}{d}}}\right)\right)}{x \sqrt{c^2-4 d} \sqrt[4]{\frac{2 b}{x}-2 a}}","b \text{RootSum}\left[\text{$\#$1}^8 d-2 \text{$\#$1}^4 a d-\text{$\#$1}^4 b c+a^2 d+a b c+b^2\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{a x^4-b x^3}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{2 \text{$\#$1}^4 d-2 a d-b c}\&\right]",1,"((x^3*(-b + a*x))^(1/4)*(2*(-2*a + (b*(-c + Sqrt[c^2 - 4*d]))/d)^(1/4)*ArcTan[(-2*a + (2*b)/x)^(1/4)/(-2*a + (b*(-c + Sqrt[c^2 - 4*d]))/d)^(1/4)] - 2*(-2*a - (b*(c + Sqrt[c^2 - 4*d]))/d)^(1/4)*ArcTan[(-2*a + (2*b)/x)^(1/4)/(-2*a - (b*(c + Sqrt[c^2 - 4*d]))/d)^(1/4)] - (-2*a + (b*(-c + Sqrt[c^2 - 4*d]))/d)^(1/4)*Log[(-a + (b*(-c + Sqrt[c^2 - 4*d]))/(2*d))^(1/4) - (-a + b/x)^(1/4)] + (-2*a - (b*(c + Sqrt[c^2 - 4*d]))/d)^(1/4)*Log[(-a - (b*(c + Sqrt[c^2 - 4*d]))/(2*d))^(1/4) - (-a + b/x)^(1/4)] + (-2*a + (b*(-c + Sqrt[c^2 - 4*d]))/d)^(1/4)*Log[(-a + (b*(-c + Sqrt[c^2 - 4*d]))/(2*d))^(1/4) + (-a + b/x)^(1/4)] - (-2*a - (b*(c + Sqrt[c^2 - 4*d]))/d)^(1/4)*Log[(-a - (b*(c + Sqrt[c^2 - 4*d]))/(2*d))^(1/4) + (-a + b/x)^(1/4)]))/(Sqrt[c^2 - 4*d]*(-2*a + (2*b)/x)^(1/4)*x)","B",1
1272,1,491,92,58.4336306,"\int \frac{\sqrt[4]{-b x^3+a x^4}}{x \left(d+c x+x^2\right)} \, dx","Integrate[(-(b*x^3) + a*x^4)^(1/4)/(x*(d + c*x + x^2)),x]","\frac{\sqrt[4]{x^3 (a x-b)} \left(-\sqrt[4]{\frac{b \left(\sqrt{c^2-4 d}-c\right)}{d}-2 a} \log \left(\sqrt[4]{\frac{b \left(\sqrt{c^2-4 d}-c\right)}{2 d}-a}-\sqrt[4]{\frac{b}{x}-a}\right)+\sqrt[4]{-2 a-\frac{b \left(\sqrt{c^2-4 d}+c\right)}{d}} \log \left(\sqrt[4]{-a-\frac{b \left(\sqrt{c^2-4 d}+c\right)}{2 d}}-\sqrt[4]{\frac{b}{x}-a}\right)+\sqrt[4]{\frac{b \left(\sqrt{c^2-4 d}-c\right)}{d}-2 a} \log \left(\sqrt[4]{\frac{b \left(\sqrt{c^2-4 d}-c\right)}{2 d}-a}+\sqrt[4]{\frac{b}{x}-a}\right)-\sqrt[4]{-2 a-\frac{b \left(\sqrt{c^2-4 d}+c\right)}{d}} \log \left(\sqrt[4]{-a-\frac{b \left(\sqrt{c^2-4 d}+c\right)}{2 d}}+\sqrt[4]{\frac{b}{x}-a}\right)+2 \sqrt[4]{\frac{b \left(\sqrt{c^2-4 d}-c\right)}{d}-2 a} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{2 b}{x}-2 a}}{\sqrt[4]{\frac{b \left(\sqrt{c^2-4 d}-c\right)}{d}-2 a}}\right)-2 \sqrt[4]{-2 a-\frac{b \left(\sqrt{c^2-4 d}+c\right)}{d}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{2 b}{x}-2 a}}{\sqrt[4]{-2 a-\frac{b \left(\sqrt{c^2-4 d}+c\right)}{d}}}\right)\right)}{x \sqrt{c^2-4 d} \sqrt[4]{\frac{2 b}{x}-2 a}}","b \text{RootSum}\left[\text{$\#$1}^8 d-2 \text{$\#$1}^4 a d-\text{$\#$1}^4 b c+a^2 d+a b c+b^2\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{a x^4-b x^3}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{2 \text{$\#$1}^4 d-2 a d-b c}\&\right]",1,"((x^3*(-b + a*x))^(1/4)*(2*(-2*a + (b*(-c + Sqrt[c^2 - 4*d]))/d)^(1/4)*ArcTan[(-2*a + (2*b)/x)^(1/4)/(-2*a + (b*(-c + Sqrt[c^2 - 4*d]))/d)^(1/4)] - 2*(-2*a - (b*(c + Sqrt[c^2 - 4*d]))/d)^(1/4)*ArcTan[(-2*a + (2*b)/x)^(1/4)/(-2*a - (b*(c + Sqrt[c^2 - 4*d]))/d)^(1/4)] - (-2*a + (b*(-c + Sqrt[c^2 - 4*d]))/d)^(1/4)*Log[(-a + (b*(-c + Sqrt[c^2 - 4*d]))/(2*d))^(1/4) - (-a + b/x)^(1/4)] + (-2*a - (b*(c + Sqrt[c^2 - 4*d]))/d)^(1/4)*Log[(-a - (b*(c + Sqrt[c^2 - 4*d]))/(2*d))^(1/4) - (-a + b/x)^(1/4)] + (-2*a + (b*(-c + Sqrt[c^2 - 4*d]))/d)^(1/4)*Log[(-a + (b*(-c + Sqrt[c^2 - 4*d]))/(2*d))^(1/4) + (-a + b/x)^(1/4)] - (-2*a - (b*(c + Sqrt[c^2 - 4*d]))/d)^(1/4)*Log[(-a - (b*(c + Sqrt[c^2 - 4*d]))/(2*d))^(1/4) + (-a + b/x)^(1/4)]))/(Sqrt[c^2 - 4*d]*(-2*a + (2*b)/x)^(1/4)*x)","B",1
1273,1,28,92,0.0054284,"\int \frac{\left(-1+x^5\right)^{2/3}}{x^6} \, dx","Integrate[(-1 + x^5)^(2/3)/x^6,x]","\frac{3}{25} \left(x^5-1\right)^{5/3} \, _2F_1\left(\frac{5}{3},2;\frac{8}{3};1-x^5\right)","-\frac{\left(x^5-1\right)^{2/3}}{5 x^5}-\frac{2}{15} \log \left(\sqrt[3]{x^5-1}+1\right)+\frac{1}{15} \log \left(\left(x^5-1\right)^{2/3}-\sqrt[3]{x^5-1}+1\right)-\frac{2 \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{x^5-1}}{\sqrt{3}}\right)}{5 \sqrt{3}}",1,"(3*(-1 + x^5)^(5/3)*Hypergeometric2F1[5/3, 2, 8/3, 1 - x^5])/25","C",1
1274,1,39,92,0.0086572,"\int \frac{1}{x^{11} \left(b+a x^5\right)^{3/4}} \, dx","Integrate[1/(x^11*(b + a*x^5)^(3/4)),x]","-\frac{4 a^2 \sqrt[4]{a x^5+b} \, _2F_1\left(\frac{1}{4},3;\frac{5}{4};\frac{a x^5}{b}+1\right)}{5 b^3}","-\frac{21 a^2 \tan ^{-1}\left(\frac{\sqrt[4]{a x^5+b}}{\sqrt[4]{b}}\right)}{80 b^{11/4}}-\frac{21 a^2 \tanh ^{-1}\left(\frac{\sqrt[4]{a x^5+b}}{\sqrt[4]{b}}\right)}{80 b^{11/4}}+\frac{\sqrt[4]{a x^5+b} \left(7 a x^5-4 b\right)}{40 b^2 x^{10}}",1,"(-4*a^2*(b + a*x^5)^(1/4)*Hypergeometric2F1[1/4, 3, 5/4, 1 + (a*x^5)/b])/(5*b^3)","C",1
1275,1,28,92,0.0044558,"\int \frac{1}{x^7 \sqrt[3]{-1+x^6}} \, dx","Integrate[1/(x^7*(-1 + x^6)^(1/3)),x]","\frac{1}{4} \left(x^6-1\right)^{2/3} \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};1-x^6\right)","\frac{\left(x^6-1\right)^{2/3}}{6 x^6}-\frac{1}{18} \log \left(\sqrt[3]{x^6-1}+1\right)+\frac{1}{36} \log \left(\left(x^6-1\right)^{2/3}-\sqrt[3]{x^6-1}+1\right)-\frac{\tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{x^6-1}}{\sqrt{3}}\right)}{6 \sqrt{3}}",1,"((-1 + x^6)^(2/3)*Hypergeometric2F1[2/3, 2, 5/3, 1 - x^6])/4","C",1
1276,1,28,92,0.0057024,"\int \frac{\left(-1+x^6\right)^{2/3}}{x^7} \, dx","Integrate[(-1 + x^6)^(2/3)/x^7,x]","\frac{1}{10} \left(x^6-1\right)^{5/3} \, _2F_1\left(\frac{5}{3},2;\frac{8}{3};1-x^6\right)","-\frac{\left(x^6-1\right)^{2/3}}{6 x^6}-\frac{1}{9} \log \left(\sqrt[3]{x^6-1}+1\right)+\frac{1}{18} \log \left(\left(x^6-1\right)^{2/3}-\sqrt[3]{x^6-1}+1\right)-\frac{\tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{x^6-1}}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"((-1 + x^6)^(5/3)*Hypergeometric2F1[5/3, 2, 8/3, 1 - x^6])/10","C",1
1277,0,0,92,0.6059254,"\int \frac{\left(-1+x^4+2 x^6\right) \sqrt[3]{x+x^5+x^7}}{\left(1+x^4+x^6\right) \left(1-x^2+x^4+x^6\right)} \, dx","Integrate[((-1 + x^4 + 2*x^6)*(x + x^5 + x^7)^(1/3))/((1 + x^4 + x^6)*(1 - x^2 + x^4 + x^6)),x]","\int \frac{\left(-1+x^4+2 x^6\right) \sqrt[3]{x+x^5+x^7}}{\left(1+x^4+x^6\right) \left(1-x^2+x^4+x^6\right)} \, dx","\frac{1}{2} \log \left(\sqrt[3]{x^7+x^5+x}-x\right)+\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^7+x^5+x}+x}\right)-\frac{1}{4} \log \left(x^2+\sqrt[3]{x^7+x^5+x} x+\left(x^7+x^5+x\right)^{2/3}\right)",1,"Integrate[((-1 + x^4 + 2*x^6)*(x + x^5 + x^7)^(1/3))/((1 + x^4 + x^6)*(1 - x^2 + x^4 + x^6)), x]","F",-1
1278,1,125,92,0.2826516,"\int \frac{\sqrt{1+\sqrt{1+x}}}{x-\sqrt{1+x}} \, dx","Integrate[Sqrt[1 + Sqrt[1 + x]]/(x - Sqrt[1 + x]),x]","\frac{1}{5} \left(20 \sqrt{\sqrt{x+1}+1}+\sqrt{6-2 \sqrt{5}} \left(\sqrt{5}-5\right) \tanh ^{-1}\left(\sqrt{\frac{2}{3-\sqrt{5}}} \sqrt{\sqrt{x+1}+1}\right)-\sqrt{2 \left(3+\sqrt{5}\right)} \left(5+\sqrt{5}\right) \tanh ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} \sqrt{\sqrt{x+1}+1}\right)\right)","4 \sqrt{\sqrt{x+1}+1}-\frac{2}{5} \left(3 \sqrt{5}-5\right) \tanh ^{-1}\left(\frac{2 \sqrt{\sqrt{x+1}+1}}{\sqrt{5}-1}\right)-\frac{2}{5} \left(5+3 \sqrt{5}\right) \tanh ^{-1}\left(\frac{2 \sqrt{\sqrt{x+1}+1}}{1+\sqrt{5}}\right)",1,"(20*Sqrt[1 + Sqrt[1 + x]] + Sqrt[6 - 2*Sqrt[5]]*(-5 + Sqrt[5])*ArcTanh[Sqrt[2/(3 - Sqrt[5])]*Sqrt[1 + Sqrt[1 + x]]] - Sqrt[2*(3 + Sqrt[5])]*(5 + Sqrt[5])*ArcTanh[Sqrt[2/(3 + Sqrt[5])]*Sqrt[1 + Sqrt[1 + x]]])/5","A",1
1279,1,26,93,0.0044806,"\int \frac{1}{x^3 \left(-1+x^2\right)^{3/4}} \, dx","Integrate[1/(x^3*(-1 + x^2)^(3/4)),x]","2 \sqrt[4]{x^2-1} \, _2F_1\left(\frac{1}{4},2;\frac{5}{4};1-x^2\right)","\frac{\sqrt[4]{x^2-1}}{2 x^2}-\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{x^2-1}}{\sqrt{x^2-1}-1}\right)}{4 \sqrt{2}}+\frac{3 \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{x^2-1}}{\sqrt{x^2-1}+1}\right)}{4 \sqrt{2}}",1,"2*(-1 + x^2)^(1/4)*Hypergeometric2F1[1/4, 2, 5/4, 1 - x^2]","C",1
1280,1,40,93,0.006498,"\int \frac{\left(-1+x^3\right)^{2/3}}{x^3} \, dx","Integrate[(-1 + x^3)^(2/3)/x^3,x]","-\frac{\left(x^3-1\right)^{2/3} \, _2F_1\left(-\frac{2}{3},-\frac{2}{3};\frac{1}{3};x^3\right)}{2 x^2 \left(1-x^3\right)^{2/3}}","-\frac{1}{3} \log \left(\sqrt[3]{x^3-1}-x\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-1}+x}\right)}{\sqrt{3}}-\frac{\left(x^3-1\right)^{2/3}}{2 x^2}+\frac{1}{6} \log \left(\sqrt[3]{x^3-1} x+\left(x^3-1\right)^{2/3}+x^2\right)",1,"-1/2*((-1 + x^3)^(2/3)*Hypergeometric2F1[-2/3, -2/3, 1/3, x^3])/(x^2*(1 - x^3)^(2/3))","C",1
1281,1,274,93,0.7941631,"\int \frac{2+x^2}{\left(-2+2 x+x^2\right) \sqrt{1+x^3}} \, dx","Integrate[(2 + x^2)/((-2 + 2*x + x^2)*Sqrt[1 + x^3]),x]","\frac{2 \sqrt{\frac{x+1}{1+\sqrt[3]{-1}}} \left((1+i) \left(\sqrt{3}+3 i\right) \sqrt{x^2-x+1} \left(i \Pi \left(\frac{2 \sqrt{3}}{-3 i+(1+2 i) \sqrt{3}};\sin ^{-1}\left(\sqrt{\frac{(-1)^{2/3} x+1}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)+\Pi \left(\frac{2 i \sqrt{3}}{3+(2+i) \sqrt{3}};\sin ^{-1}\left(\sqrt{\frac{(-1)^{2/3} x+1}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)\right)+\frac{3 \sqrt{\frac{\sqrt[3]{-1}-(-1)^{2/3} x}{1+\sqrt[3]{-1}}} \left(\left(\sqrt{3}+i\right) x-2 i\right) F\left(\sin ^{-1}\left(\sqrt{\frac{(-1)^{2/3} x+1}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{\sqrt{\frac{(-1)^{2/3} x+1}{1+\sqrt[3]{-1}}}}\right)}{3 \left(\sqrt{3}+i\right) \sqrt{x^3+1}}","-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} \sqrt{x^3+1}}{x^2-x+1}\right)}{3^{3/4}}-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} \sqrt{x^3+1}}{x^2-x+1}\right)}{3^{3/4}}",1,"(2*Sqrt[(1 + x)/(1 + (-1)^(1/3))]*((3*Sqrt[((-1)^(1/3) - (-1)^(2/3)*x)/(1 + (-1)^(1/3))]*(-2*I + (I + Sqrt[3])*x)*EllipticF[ArcSin[Sqrt[(1 + (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)])/Sqrt[(1 + (-1)^(2/3)*x)/(1 + (-1)^(1/3))] + (1 + I)*(3*I + Sqrt[3])*Sqrt[1 - x + x^2]*(I*EllipticPi[(2*Sqrt[3])/(-3*I + (1 + 2*I)*Sqrt[3]), ArcSin[Sqrt[(1 + (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)] + EllipticPi[((2*I)*Sqrt[3])/(3 + (2 + I)*Sqrt[3]), ArcSin[Sqrt[(1 + (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)])))/(3*(I + Sqrt[3])*Sqrt[1 + x^3])","C",0
1282,1,22,93,0.0025037,"\int \frac{\left(1+x^3\right)^{2/3}}{x^3} \, dx","Integrate[(1 + x^3)^(2/3)/x^3,x]","-\frac{\, _2F_1\left(-\frac{2}{3},-\frac{2}{3};\frac{1}{3};-x^3\right)}{2 x^2}","-\frac{1}{3} \log \left(\sqrt[3]{x^3+1}-x\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+1}+x}\right)}{\sqrt{3}}-\frac{\left(x^3+1\right)^{2/3}}{2 x^2}+\frac{1}{6} \log \left(\sqrt[3]{x^3+1} x+\left(x^3+1\right)^{2/3}+x^2\right)",1,"-1/2*Hypergeometric2F1[-2/3, -2/3, 1/3, -x^3]/x^2","C",1
1283,0,0,93,4.0341607,"\int \frac{2 a b x+(-3 a+b) x^2}{\sqrt[4]{x^2 (-a+x) (-b+x)} \left(a^3-3 a^2 x+(3 a-b d) x^2+(-1+d) x^3\right)} \, dx","Integrate[(2*a*b*x + (-3*a + b)*x^2)/((x^2*(-a + x)*(-b + x))^(1/4)*(a^3 - 3*a^2*x + (3*a - b*d)*x^2 + (-1 + d)*x^3)),x]","\int \frac{2 a b x+(-3 a+b) x^2}{\sqrt[4]{x^2 (-a+x) (-b+x)} \left(a^3-3 a^2 x+(3 a-b d) x^2+(-1+d) x^3\right)} \, dx","\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{x^3 (-a-b)+a b x^2+x^4}}{a-x}\right)}{d^{3/4}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{x^3 (-a-b)+a b x^2+x^4}}{a-x}\right)}{d^{3/4}}",1,"Integrate[(2*a*b*x + (-3*a + b)*x^2)/((x^2*(-a + x)*(-b + x))^(1/4)*(a^3 - 3*a^2*x + (3*a - b*d)*x^2 + (-1 + d)*x^3)), x]","F",-1
1284,1,28,93,0.0057029,"\int \frac{\sqrt[4]{-1+x^4}}{x^5} \, dx","Integrate[(-1 + x^4)^(1/4)/x^5,x]","\frac{1}{5} \left(x^4-1\right)^{5/4} \, _2F_1\left(\frac{5}{4},2;\frac{9}{4};1-x^4\right)","-\frac{\sqrt[4]{x^4-1}}{4 x^4}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{x^4-1}}{\sqrt{x^4-1}-1}\right)}{8 \sqrt{2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{x^4-1}}{\sqrt{x^4-1}+1}\right)}{8 \sqrt{2}}",1,"((-1 + x^4)^(5/4)*Hypergeometric2F1[5/4, 2, 9/4, 1 - x^4])/5","C",1
1285,0,0,93,0.6361398,"\int \frac{1+x^2}{\left(-1+x+x^2\right) \sqrt[3]{-x^2+x^4}} \, dx","Integrate[(1 + x^2)/((-1 + x + x^2)*(-x^2 + x^4)^(1/3)),x]","\int \frac{1+x^2}{\left(-1+x+x^2\right) \sqrt[3]{-x^2+x^4}} \, dx","-\log \left(\sqrt[3]{x^4-x^2}+x\right)+\frac{1}{2} \log \left(x^2-\sqrt[3]{x^4-x^2} x+\left(x^4-x^2\right)^{2/3}\right)-\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^4-x^2}-x}\right)",1,"Integrate[(1 + x^2)/((-1 + x + x^2)*(-x^2 + x^4)^(1/3)), x]","F",-1
1286,1,88,93,0.1778186,"\int \frac{(-1+2 x) \left(2-x+x^2\right) \sqrt{-2+x^2-2 x^3+x^4}}{3-2 x+2 x^2} \, dx","Integrate[((-1 + 2*x)*(2 - x + x^2)*Sqrt[-2 + x^2 - 2*x^3 + x^4])/(3 - 2*x + 2*x^2),x]","\frac{1}{8} \left(2 \sqrt{x^4-2 x^3+x^2-2} \left(x^2-x+1\right)-7 \tanh ^{-1}\left(\frac{(x-1) x}{\sqrt{x^4-2 x^3+x^2-2}}\right)-\tanh ^{-1}\left(\frac{-3 x^2+3 x-4}{\sqrt{x^4-2 x^3+x^2-2}}\right)\right)","\frac{1}{4} \sqrt{x^4-2 x^3+x^2-2} \left(x^2-x+1\right)-\frac{7}{8} \log \left(x^2+\sqrt{x^4-2 x^3+x^2-2}-x\right)-\frac{1}{4} \tanh ^{-1}\left(2 x^2+2 \sqrt{x^4-2 x^3+x^2-2}-2 x+3\right)",1,"(2*(1 - x + x^2)*Sqrt[-2 + x^2 - 2*x^3 + x^4] - 7*ArcTanh[((-1 + x)*x)/Sqrt[-2 + x^2 - 2*x^3 + x^4]] - ArcTanh[(-4 + 3*x - 3*x^2)/Sqrt[-2 + x^2 - 2*x^3 + x^4]])/8","A",1
1287,1,58,93,0.0136652,"\int \frac{\sqrt[4]{-x^3+x^4}}{x (1+x)} \, dx","Integrate[(-x^3 + x^4)^(1/4)/(x*(1 + x)),x]","\frac{4 \sqrt[4]{(x-1) x^3} \left(\sqrt[4]{x} \, _2F_1\left(\frac{1}{4},\frac{1}{4};\frac{5}{4};1-x\right)-\, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{x-1}{2 x}\right)\right)}{x}","-2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^3}}\right)+2 \sqrt[4]{2} \tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-x^3}}\right)+2 \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^3}}\right)-2 \sqrt[4]{2} \tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-x^3}}\right)",1,"(4*((-1 + x)*x^3)^(1/4)*(x^(1/4)*Hypergeometric2F1[1/4, 1/4, 5/4, 1 - x] - Hypergeometric2F1[1/4, 1, 5/4, (-1 + x)/(2*x)]))/x","C",1
1288,0,0,93,0.1989058,"\int \frac{1+2 x^3}{\left(-1+x+x^3\right) \sqrt[3]{-x^2+x^5}} \, dx","Integrate[(1 + 2*x^3)/((-1 + x + x^3)*(-x^2 + x^5)^(1/3)),x]","\int \frac{1+2 x^3}{\left(-1+x+x^3\right) \sqrt[3]{-x^2+x^5}} \, dx","-\log \left(\sqrt[3]{x^5-x^2}+x\right)+\frac{1}{2} \log \left(x^2-\sqrt[3]{x^5-x^2} x+\left(x^5-x^2\right)^{2/3}\right)-\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^5-x^2}-x}\right)",1,"Integrate[(1 + 2*x^3)/((-1 + x + x^3)*(-x^2 + x^5)^(1/3)), x]","F",-1
1289,1,28,93,0.005275,"\int \frac{\sqrt[4]{-1+x^6}}{x^7} \, dx","Integrate[(-1 + x^6)^(1/4)/x^7,x]","\frac{2}{15} \left(x^6-1\right)^{5/4} \, _2F_1\left(\frac{5}{4},2;\frac{9}{4};1-x^6\right)","-\frac{\sqrt[4]{x^6-1}}{6 x^6}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{x^6-1}}{\sqrt{x^6-1}-1}\right)}{12 \sqrt{2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{x^6-1}}{\sqrt{x^6-1}+1}\right)}{12 \sqrt{2}}",1,"(2*(-1 + x^6)^(5/4)*Hypergeometric2F1[5/4, 2, 9/4, 1 - x^6])/15","C",1
1290,0,0,93,0.1963105,"\int \frac{1+3 x^4}{\left(-1+x+x^4\right) \sqrt[3]{-x^2+x^6}} \, dx","Integrate[(1 + 3*x^4)/((-1 + x + x^4)*(-x^2 + x^6)^(1/3)),x]","\int \frac{1+3 x^4}{\left(-1+x+x^4\right) \sqrt[3]{-x^2+x^6}} \, dx","-\log \left(\sqrt[3]{x^6-x^2}+x\right)+\frac{1}{2} \log \left(x^2-\sqrt[3]{x^6-x^2} x+\left(x^6-x^2\right)^{2/3}\right)-\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^6-x^2}-x}\right)",1,"Integrate[(1 + 3*x^4)/((-1 + x + x^4)*(-x^2 + x^6)^(1/3)), x]","F",-1
1291,1,25746,93,5.1776609,"\int \frac{\left(2+x^3\right) \sqrt{-1-x^2+x^3}}{1-x^2-2 x^3-x^4+x^5+x^6} \, dx","Integrate[((2 + x^3)*Sqrt[-1 - x^2 + x^3])/(1 - x^2 - 2*x^3 - x^4 + x^5 + x^6),x]","\text{Result too large to show}","\frac{1}{5} \left(-5-\sqrt{5}\right) \tan ^{-1}\left(\frac{\sqrt{\frac{3}{2}+\frac{\sqrt{5}}{2}} x}{\sqrt{x^3-x^2-1}}\right)+\frac{1}{5} \left(5-\sqrt{5}\right) \tan ^{-1}\left(\frac{\sqrt{\frac{2}{3+\sqrt{5}}} x}{\sqrt{x^3-x^2-1}}\right)",1,"Result too large to show","C",0
1292,1,5470,93,6.4795926,"\int \frac{\left(1+x^4\right) \sqrt{-1-x^2+x^4}}{1-x^2-3 x^4+x^6+x^8} \, dx","Integrate[((1 + x^4)*Sqrt[-1 - x^2 + x^4])/(1 - x^2 - 3*x^4 + x^6 + x^8),x]","\text{Result too large to show}","\frac{1}{10} \left(-5-\sqrt{5}\right) \tan ^{-1}\left(\frac{\sqrt{\frac{3}{2}+\frac{\sqrt{5}}{2}} x}{\sqrt{x^4-x^2-1}}\right)+\frac{1}{10} \left(5-\sqrt{5}\right) \tan ^{-1}\left(\frac{\sqrt{\frac{2}{3+\sqrt{5}}} x}{\sqrt{x^4-x^2-1}}\right)",1,"Result too large to show","C",0
1293,1,92,93,0.1093316,"\int \frac{x^2 \sqrt{x+\sqrt{1+x}}}{\sqrt{1+x}} \, dx","Integrate[(x^2*Sqrt[x + Sqrt[1 + x]])/Sqrt[1 + x],x]","\frac{2 \sqrt{x+\sqrt{x+1}} \left(128 \left(10 \sqrt{x+1}+1\right) x^2-8 \left(218 \sqrt{x+1}-41\right) x+1950 \sqrt{x+1}+563\right)-5775 \tanh ^{-1}\left(\frac{2 \sqrt{x+1}+1}{2 \sqrt{x+\sqrt{x+1}}}\right)}{7680}","\frac{\sqrt{x+\sqrt{x+1}} \left(128 x^2+328 x+563\right)}{3840}+\frac{\sqrt{x+1} \left(640 x^2-872 x+975\right) \sqrt{x+\sqrt{x+1}}}{1920}+\frac{385}{512} \log \left(2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)",1,"(2*Sqrt[x + Sqrt[1 + x]]*(563 + 1950*Sqrt[1 + x] + 128*x^2*(1 + 10*Sqrt[1 + x]) - 8*x*(-41 + 218*Sqrt[1 + x])) - 5775*ArcTanh[(1 + 2*Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])])/7680","A",1
1294,1,99,94,0.1001911,"\int \left(-1+x^3\right)^{2/3} \, dx","Integrate[(-1 + x^3)^(2/3),x]","\frac{3 (x-1) \left(x^3-1\right)^{2/3} F_1\left(\frac{5}{3};-\frac{2}{3},-\frac{2}{3};\frac{8}{3};-\frac{x-1}{1-(-1)^{2/3}},-\frac{x-1}{1+\sqrt[3]{-1}}\right)}{5 \left(\frac{x-1}{1+\sqrt[3]{-1}}+1\right)^{2/3} \left(\frac{x-1}{1-(-1)^{2/3}}+1\right)^{2/3}}","\frac{1}{3} \left(x^3-1\right)^{2/3} x+\frac{2}{9} \log \left(\sqrt[3]{x^3-1}-x\right)-\frac{2 \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-1}+x}\right)}{3 \sqrt{3}}-\frac{1}{9} \log \left(\sqrt[3]{x^3-1} x+\left(x^3-1\right)^{2/3}+x^2\right)",1,"(3*(-1 + x)*(-1 + x^3)^(2/3)*AppellF1[5/3, -2/3, -2/3, 8/3, -((-1 + x)/(1 - (-1)^(2/3))), -((-1 + x)/(1 + (-1)^(1/3)))])/(5*(1 + (-1 + x)/(1 + (-1)^(1/3)))^(2/3)*(1 + (-1 + x)/(1 - (-1)^(2/3)))^(2/3))","C",0
1295,1,99,94,0.061086,"\int \left(1+x^3\right)^{2/3} \, dx","Integrate[(1 + x^3)^(2/3),x]","\frac{3 (x+1) \left(x^3+1\right)^{2/3} F_1\left(\frac{5}{3};-\frac{2}{3},-\frac{2}{3};\frac{8}{3};-\frac{x+1}{-1+(-1)^{2/3}},-\frac{x+1}{-1-\sqrt[3]{-1}}\right)}{5 \left(\frac{x+1}{-1-\sqrt[3]{-1}}+1\right)^{2/3} \left(\frac{x+1}{(-1)^{2/3}-1}+1\right)^{2/3}}","\frac{1}{3} \left(x^3+1\right)^{2/3} x-\frac{2}{9} \log \left(\sqrt[3]{x^3+1}-x\right)+\frac{2 \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+1}+x}\right)}{3 \sqrt{3}}+\frac{1}{9} \log \left(\sqrt[3]{x^3+1} x+\left(x^3+1\right)^{2/3}+x^2\right)",1,"(3*(1 + x)*(1 + x^3)^(2/3)*AppellF1[5/3, -2/3, -2/3, 8/3, -((1 + x)/(-1 + (-1)^(2/3))), -((1 + x)/(-1 - (-1)^(1/3)))])/(5*(1 + (1 + x)/(-1 - (-1)^(1/3)))^(2/3)*(1 + (1 + x)/(-1 + (-1)^(2/3)))^(2/3))","C",0
1296,1,91,94,0.0375247,"\int \frac{-1+x^3}{\sqrt[3]{2+x^3}} \, dx","Integrate[(-1 + x^3)/(2 + x^3)^(1/3),x]","\frac{1}{18} \left(6 \left(x^3+2\right)^{2/3} x+10 \log \left(1-\frac{x}{\sqrt[3]{x^3+2}}\right)-10 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3+2}}+1}{\sqrt{3}}\right)-5 \log \left(\frac{x}{\sqrt[3]{x^3+2}}+\frac{x^2}{\left(x^3+2\right)^{2/3}}+1\right)\right)","\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)",1,"(6*x*(2 + x^3)^(2/3) - 10*Sqrt[3]*ArcTan[(1 + (2*x)/(2 + x^3)^(1/3))/Sqrt[3]] + 10*Log[1 - x/(2 + x^3)^(1/3)] - 5*Log[1 + x^2/(2 + x^3)^(2/3) + x/(2 + x^3)^(1/3)])/18","A",1
1297,1,38,94,0.007087,"\int \sqrt[3]{x+x^3} \, dx","Integrate[(x + x^3)^(1/3),x]","\frac{3 x \sqrt[3]{x^3+x} \, _2F_1\left(-\frac{1}{3},\frac{2}{3};\frac{5}{3};-x^2\right)}{4 \sqrt[3]{x^2+1}}","\frac{1}{2} \sqrt[3]{x^3+x} x-\frac{1}{6} \log \left(\sqrt[3]{x^3+x}-x\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+x}+x}\right)}{2 \sqrt{3}}+\frac{1}{12} \log \left(\sqrt[3]{x^3+x} x+\left(x^3+x\right)^{2/3}+x^2\right)",1,"(3*x*(x + x^3)^(1/3)*Hypergeometric2F1[-1/3, 2/3, 5/3, -x^2])/(4*(1 + x^2)^(1/3))","C",1
1298,0,0,94,1.8832712,"\int \frac{\left(-2 k+(-1+k) (1+k) x+2 k x^2\right) \left(1+2 k x+k^2 x^2\right)}{\left(\left(1-x^2\right) \left(1-k^2 x^2\right)\right)^{3/4} \left(-1+d+(1+3 d) k x+\left(1+3 d k^2\right) x^2+k \left(-1+d k^2\right) x^3\right)} \, dx","Integrate[((-2*k + (-1 + k)*(1 + k)*x + 2*k*x^2)*(1 + 2*k*x + k^2*x^2))/(((1 - x^2)*(1 - k^2*x^2))^(3/4)*(-1 + d + (1 + 3*d)*k*x + (1 + 3*d*k^2)*x^2 + k*(-1 + d*k^2)*x^3)),x]","\int \frac{\left(-2 k+(-1+k) (1+k) x+2 k x^2\right) \left(1+2 k x+k^2 x^2\right)}{\left(\left(1-x^2\right) \left(1-k^2 x^2\right)\right)^{3/4} \left(-1+d+(1+3 d) k x+\left(1+3 d k^2\right) x^2+k \left(-1+d k^2\right) x^3\right)} \, dx","\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{d} k x+\sqrt[4]{d}}{\sqrt[4]{k^2 x^4+\left(-k^2-1\right) x^2+1}}\right)}{d^{3/4}}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{d} k x+\sqrt[4]{d}}{\sqrt[4]{k^2 x^4+\left(-k^2-1\right) x^2+1}}\right)}{d^{3/4}}",1,"Integrate[((-2*k + (-1 + k)*(1 + k)*x + 2*k*x^2)*(1 + 2*k*x + k^2*x^2))/(((1 - x^2)*(1 - k^2*x^2))^(3/4)*(-1 + d + (1 + 3*d)*k*x + (1 + 3*d*k^2)*x^2 + k*(-1 + d*k^2)*x^3)), x]","F",-1
1299,1,118,94,0.2568975,"\int \frac{\left(-1+x^4\right)^{3/4} \left(4+x^4\right)}{x^8 \left(-4+x^4\right)} \, dx","Integrate[((-1 + x^4)^(3/4)*(4 + x^4))/(x^8*(-4 + x^4)),x]","\frac{\left(x^4-1\right)^{3/4} \left(x^4+6\right)}{42 x^7}-\frac{3^{3/4} \left(-\log \left(2-\frac{\sqrt{2} \sqrt[4]{3} x}{\sqrt[4]{1-x^4}}\right)+\log \left(\frac{\sqrt{2} \sqrt[4]{3} x}{\sqrt[4]{1-x^4}}+2\right)+2 \tan ^{-1}\left(\frac{\sqrt[4]{3} x}{\sqrt{2} \sqrt[4]{1-x^4}}\right)\right)}{16 \sqrt{2}}","-\frac{3^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{3} x}{\sqrt{2} \sqrt[4]{x^4-1}}\right)}{8 \sqrt{2}}-\frac{3^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{3} x}{\sqrt{2} \sqrt[4]{x^4-1}}\right)}{8 \sqrt{2}}+\frac{\left(x^4-1\right)^{3/4} \left(x^4+6\right)}{42 x^7}",1,"((-1 + x^4)^(3/4)*(6 + x^4))/(42*x^7) - (3^(3/4)*(2*ArcTan[(3^(1/4)*x)/(Sqrt[2]*(1 - x^4)^(1/4))] - Log[2 - (Sqrt[2]*3^(1/4)*x)/(1 - x^4)^(1/4)] + Log[2 + (Sqrt[2]*3^(1/4)*x)/(1 - x^4)^(1/4)]))/(16*Sqrt[2])","A",0
1300,0,0,94,0.2132322,"\int \frac{4 b+a x^3}{\sqrt[4]{b+a x^3} \left(b+a x^3+x^4\right)} \, dx","Integrate[(4*b + a*x^3)/((b + a*x^3)^(1/4)*(b + a*x^3 + x^4)),x]","\int \frac{4 b+a x^3}{\sqrt[4]{b+a x^3} \left(b+a x^3+x^4\right)} \, dx","\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{a x^3+b}}{\sqrt{a x^3+b}+x^2}\right)-\sqrt{2} \tan ^{-1}\left(\frac{\frac{\sqrt{a x^3+b}}{\sqrt{2}}-\frac{x^2}{\sqrt{2}}}{x \sqrt[4]{a x^3+b}}\right)",1,"Integrate[(4*b + a*x^3)/((b + a*x^3)^(1/4)*(b + a*x^3 + x^4)), x]","F",-1
1301,1,4636,94,7.4144733,"\int \frac{-a^2 b+a (2 a+b) x-3 a x^2+x^3}{\sqrt{x (-a+x) (-b+x)} \left(-a^2 d+2 a d x+\left(b^2-d\right) x^2-2 b x^3+x^4\right)} \, dx","Integrate[(-(a^2*b) + a*(2*a + b)*x - 3*a*x^2 + x^3)/(Sqrt[x*(-a + x)*(-b + x)]*(-(a^2*d) + 2*a*d*x + (b^2 - d)*x^2 - 2*b*x^3 + x^4)),x]","\text{Result too large to show}","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{x^2 (-a-b)+a b x+x^3}}{x (x-b)}\right)}{d^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{x^2 (-a-b)+a b x+x^3}}{x (x-b)}\right)}{d^{3/4}}",1,"((-2*I)*(a - x)*Sqrt[(-b + x)/(a - b)]*((EllipticPi[a/Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 1], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)]*(a*(a - b) - Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 1]^2))/((Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 1] - Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 2])*(Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 1] - Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 3])*(Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 1] - Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 4])) + ((EllipticPi[a/Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 2], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)]*(a*(-a + b) + Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 2]^2))/(Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 1] - Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 2]) + (a*b*EllipticPi[a/Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 4], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)]*(Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 1] - Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 3])*(Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 2] - Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 3]) + a^2*EllipticPi[a/Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 4], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)]*(Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 1] - Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 3])*(-Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 2] + Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 3]) + a^2*EllipticPi[a/Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 3], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)]*(Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 1] - Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 4])*(Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 2] - Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 4]) + EllipticPi[a/Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 4], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)]*(Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 1] - Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 3])*(Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 2] - Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 3])*Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 4]^2 + a*b*EllipticPi[a/Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 3], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)]*(Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 1] - Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 4])*(-Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 2] + Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 4]) + EllipticPi[a/Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 3], I*ArcSinh[Sqrt[-1 + x/a]], a/(a - b)]*Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 3]^2*(Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 1] - Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 4])*(-Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 2] + Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 4]))/((Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 1] - Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 3])*(Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 1] - Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 4])*(Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 3] - Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 4])))/((Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 2] - Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 3])*(Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 2] - Root[a^4 - 2*a^3*b + a^2*b^2 + (-4*a^3 + 6*a^2*b - 2*a*b^2)*#1 + (6*a^2 - 6*a*b + b^2 - d)*#1^2 + (-4*a + 2*b)*#1^3 + #1^4 & , 4]))))/(Sqrt[1 - a/x]*Sqrt[x*(-a + x)*(-b + x)])","C",0
1302,1,142,94,0.1469709,"\int \frac{-2 b+a x^4}{x^4 \sqrt[4]{b x^2+a x^4}} \, dx","Integrate[(-2*b + a*x^4)/(x^4*(b*x^2 + a*x^4)^(1/4)),x]","\frac{21 a^{3/4} b x^{7/2} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)+21 a^{3/4} b x^{7/2} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)-4 \left(4 a^2 x^4+a b x^2-3 b^2\right)}{21 b x^3 \sqrt[4]{x^2 \left(a x^2+b\right)}}","a^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)+a^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)-\frac{4 \left(a x^4+b x^2\right)^{3/4} \left(4 a x^2-3 b\right)}{21 b x^5}",1,"(-4*(-3*b^2 + a*b*x^2 + 4*a^2*x^4) + 21*a^(3/4)*b*x^(7/2)*(b + a*x^2)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)] + 21*a^(3/4)*b*x^(7/2)*(b + a*x^2)^(1/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(21*b*x^3*(x^2*(b + a*x^2))^(1/4))","A",1
1303,1,142,94,0.0834888,"\int \frac{2 b+a x^4}{x^4 \sqrt[4]{b x^2+a x^4}} \, dx","Integrate[(2*b + a*x^4)/(x^4*(b*x^2 + a*x^4)^(1/4)),x]","\frac{21 a^{3/4} b x^{7/2} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)+21 a^{3/4} b x^{7/2} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)+4 \left(4 a^2 x^4+a b x^2-3 b^2\right)}{21 b x^3 \sqrt[4]{x^2 \left(a x^2+b\right)}}","a^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)+a^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)+\frac{4 \left(a x^4+b x^2\right)^{3/4} \left(4 a x^2-3 b\right)}{21 b x^5}",1,"(4*(-3*b^2 + a*b*x^2 + 4*a^2*x^4) + 21*a^(3/4)*b*x^(7/2)*(b + a*x^2)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)] + 21*a^(3/4)*b*x^(7/2)*(b + a*x^2)^(1/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(21*b*x^3*(x^2*(b + a*x^2))^(1/4))","A",1
1304,1,6023,94,6.4862411,"\int \frac{-1+x}{(1+x) \sqrt{a+b x+c x^2+b x^3+a x^4}} \, dx","Integrate[(-1 + x)/((1 + x)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]),x]","\text{Result too large to show}","-\frac{2 \sqrt{-2 a+2 b-c} \tan ^{-1}\left(\frac{x \sqrt{-2 a+2 b-c}}{-\sqrt{a x^4+a+b x^3+b x+c x^2}+\sqrt{a} x^2+2 \sqrt{a} x+\sqrt{a}}\right)}{2 a-2 b+c}",1,"Result too large to show","C",1
1305,1,6023,94,6.3987601,"\int \frac{1+x}{(-1+x) \sqrt{a+b x+c x^2+b x^3+a x^4}} \, dx","Integrate[(1 + x)/((-1 + x)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]),x]","\text{Result too large to show}","-\frac{2 \sqrt{-2 a-2 b-c} \tan ^{-1}\left(\frac{x \sqrt{-2 a-2 b-c}}{-\sqrt{a x^4+a+b x^3+b x+c x^2}+\sqrt{a} x^2-2 \sqrt{a} x+\sqrt{a}}\right)}{2 a+2 b+c}",1,"Result too large to show","C",1
1306,1,70,94,0.3926774,"\int \frac{x^2}{\sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)} \left(-1+k^2 x^4\right)} \, dx","Integrate[x^2/(Sqrt[(1 - x^2)*(1 - k^2*x^2)]*(-1 + k^2*x^4)),x]","\frac{\sqrt{1-x^2} \sqrt{1-k^2 x^2} \left(\Pi \left(-k;\sin ^{-1}(x)|k^2\right)-\Pi \left(k;\sin ^{-1}(x)|k^2\right)\right)}{2 k \sqrt{\left(x^2-1\right) \left(k^2 x^2-1\right)}}","\frac{\tan ^{-1}\left(\frac{(k+1) x}{\sqrt{k^2 x^4+\left(-k^2-1\right) x^2+1}+k x^2+1}\right)}{2 k (k+1)}-\frac{\tan ^{-1}\left(\frac{(k-1) x}{\sqrt{k^2 x^4+\left(-k^2-1\right) x^2+1}}\right)}{4 (k-1) k}",1,"(Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*(EllipticPi[-k, ArcSin[x], k^2] - EllipticPi[k, ArcSin[x], k^2]))/(2*k*Sqrt[(-1 + x^2)*(-1 + k^2*x^2)])","C",1
1307,0,0,94,0.8741995,"\int \frac{\left(-1+x^6\right)^{2/3} \left(1+x^6\right)}{x^3 \left(-1-x^3+x^6\right)} \, dx","Integrate[((-1 + x^6)^(2/3)*(1 + x^6))/(x^3*(-1 - x^3 + x^6)),x]","\int \frac{\left(-1+x^6\right)^{2/3} \left(1+x^6\right)}{x^3 \left(-1-x^3+x^6\right)} \, dx","\frac{1}{3} \log \left(\sqrt[3]{x^6-1}-x\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^6-1}+x}\right)}{\sqrt{3}}+\frac{\left(x^6-1\right)^{2/3}}{2 x^2}-\frac{1}{6} \log \left(\sqrt[3]{x^6-1} x+\left(x^6-1\right)^{2/3}+x^2\right)",1,"Integrate[((-1 + x^6)^(2/3)*(1 + x^6))/(x^3*(-1 - x^3 + x^6)), x]","F",-1
1308,0,0,94,1.0913235,"\int \frac{\left(-1+x^6\right) \left(1+x^6\right)^{2/3}}{x^3 \left(1-x^3+x^6\right)} \, dx","Integrate[((-1 + x^6)*(1 + x^6)^(2/3))/(x^3*(1 - x^3 + x^6)),x]","\int \frac{\left(-1+x^6\right) \left(1+x^6\right)^{2/3}}{x^3 \left(1-x^3+x^6\right)} \, dx","\frac{1}{3} \log \left(\sqrt[3]{x^6+1}-x\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^6+1}+x}\right)}{\sqrt{3}}+\frac{\left(x^6+1\right)^{2/3}}{2 x^2}-\frac{1}{6} \log \left(\sqrt[3]{x^6+1} x+\left(x^6+1\right)^{2/3}+x^2\right)",1,"Integrate[((-1 + x^6)*(1 + x^6)^(2/3))/(x^3*(1 - x^3 + x^6)), x]","F",-1
1309,0,0,94,1.2495552,"\int \frac{-1+x^8}{\sqrt[4]{-x^2+x^4} \left(1+x^8\right)} \, dx","Integrate[(-1 + x^8)/((-x^2 + x^4)^(1/4)*(1 + x^8)),x]","\int \frac{-1+x^8}{\sqrt[4]{-x^2+x^4} \left(1+x^8\right)} \, dx","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^{16}-4 \text{$\#$1}^{12}+6 \text{$\#$1}^8-4 \text{$\#$1}^4+2\&,\frac{\log \left(\sqrt[4]{x^4-x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]+\tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^2}}\right)+\tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^2}}\right)",1,"Integrate[(-1 + x^8)/((-x^2 + x^4)^(1/4)*(1 + x^8)), x]","F",-1
1310,0,0,94,0.422877,"\int \frac{-1+x^8}{\sqrt[4]{-x^2+x^4} \left(1+x^8\right)} \, dx","Integrate[(-1 + x^8)/((-x^2 + x^4)^(1/4)*(1 + x^8)),x]","\int \frac{-1+x^8}{\sqrt[4]{-x^2+x^4} \left(1+x^8\right)} \, dx","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^{16}-4 \text{$\#$1}^{12}+6 \text{$\#$1}^8-4 \text{$\#$1}^4+2\&,\frac{\log \left(\sqrt[4]{x^4-x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]+\tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^2}}\right)+\tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^2}}\right)",1,"Integrate[(-1 + x^8)/((-x^2 + x^4)^(1/4)*(1 + x^8)), x]","F",-1
1311,0,0,94,7.1083788,"\int \frac{1+3 x^4+x^8}{x^2 \left(1+x^4\right)^{3/4} \left(1+3 x^4+3 x^8\right)} \, dx","Integrate[(1 + 3*x^4 + x^8)/(x^2*(1 + x^4)^(3/4)*(1 + 3*x^4 + 3*x^8)),x]","\int \frac{1+3 x^4+x^8}{x^2 \left(1+x^4\right)^{3/4} \left(1+3 x^4+3 x^8\right)} \, dx","-\frac{\sqrt[4]{x^4+1}}{x}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x \sqrt[4]{x^4+1}}{\sqrt{x^4+1}-x^2}\right)}{\sqrt{3}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{3} x \sqrt[4]{x^4+1}}{\sqrt{x^4+1}+x^2}\right)}{\sqrt{3}}",1,"Integrate[(1 + 3*x^4 + x^8)/(x^2*(1 + x^4)^(3/4)*(1 + 3*x^4 + 3*x^8)), x]","F",-1
1312,1,94,94,0.3648687,"\int \frac{\sqrt{c+\sqrt{a x+\sqrt{b+a^2 x^2}}}}{b+a^2 x^2} \, dx","Integrate[Sqrt[c + Sqrt[a*x + Sqrt[b + a^2*x^2]]]/(b + a^2*x^2),x]","\frac{\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6 c+6 \text{$\#$1}^4 c^2-4 \text{$\#$1}^2 c^3+b+c^4\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}-\text{$\#$1}\right)}{\text{$\#$1}^4-2 \text{$\#$1}^2 c+c^2}\&\right]}{a}","\frac{\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6 c+6 \text{$\#$1}^4 c^2-4 \text{$\#$1}^2 c^3+b+c^4\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}-\text{$\#$1}\right)}{\text{$\#$1}^4-2 \text{$\#$1}^2 c+c^2}\&\right]}{a}",1,"RootSum[b + c^4 - 4*c^3*#1^2 + 6*c^2*#1^4 - 4*c*#1^6 + #1^8 & , (Log[Sqrt[c + Sqrt[a*x + Sqrt[b + a^2*x^2]]] - #1]*#1)/(c^2 - 2*c*#1^2 + #1^4) & ]/a","A",1
1313,1,94,94,0.1399089,"\int \frac{\sqrt{c+\sqrt{a x+\sqrt{b+a^2 x^2}}}}{b+a^2 x^2} \, dx","Integrate[Sqrt[c + Sqrt[a*x + Sqrt[b + a^2*x^2]]]/(b + a^2*x^2),x]","\frac{\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6 c+6 \text{$\#$1}^4 c^2-4 \text{$\#$1}^2 c^3+b+c^4\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}-\text{$\#$1}\right)}{\text{$\#$1}^4-2 \text{$\#$1}^2 c+c^2}\&\right]}{a}","\frac{\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6 c+6 \text{$\#$1}^4 c^2-4 \text{$\#$1}^2 c^3+b+c^4\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}-\text{$\#$1}\right)}{\text{$\#$1}^4-2 \text{$\#$1}^2 c+c^2}\&\right]}{a}",1,"RootSum[b + c^4 - 4*c^3*#1^2 + 6*c^2*#1^4 - 4*c*#1^6 + #1^8 & , (Log[Sqrt[c + Sqrt[a*x + Sqrt[b + a^2*x^2]]] - #1]*#1)/(c^2 - 2*c*#1^2 + #1^4) & ]/a","A",1
1314,1,35,95,0.0224809,"\int \frac{-1+x}{x^4 \sqrt[3]{1+x^3}} \, dx","Integrate[(-1 + x)/(x^4*(1 + x^3)^(1/3)),x]","-\frac{\left(x^3+1\right)^{2/3} \left(x^2 \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};x^3+1\right)+1\right)}{2 x^2}","\frac{\left(x^3+1\right)^{2/3} (2-3 x)}{6 x^3}+\frac{1}{9} \log \left(\sqrt[3]{x^3+1}-1\right)-\frac{1}{18} \log \left(\left(x^3+1\right)^{2/3}+\sqrt[3]{x^3+1}+1\right)+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{x^3+1}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"-1/2*((1 + x^3)^(2/3)*(1 + x^2*Hypergeometric2F1[2/3, 2, 5/3, 1 + x^3]))/x^2","C",1
1315,0,0,95,0.2032247,"\int \frac{(3+2 x) \sqrt[3]{1+x+x^3}}{x^2 (1+x)} \, dx","Integrate[((3 + 2*x)*(1 + x + x^3)^(1/3))/(x^2*(1 + x)),x]","\int \frac{(3+2 x) \sqrt[3]{1+x+x^3}}{x^2 (1+x)} \, dx","-\frac{3 \sqrt[3]{x^3+x+1}}{x}-\log \left(\sqrt[3]{x^3+x+1}-x\right)-\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+x+1}+x}\right)+\frac{1}{2} \log \left(\sqrt[3]{x^3+x+1} x+\left(x^3+x+1\right)^{2/3}+x^2\right)",1,"Integrate[((3 + 2*x)*(1 + x + x^3)^(1/3))/(x^2*(1 + x)), x]","F",-1
1316,0,0,95,1.3047174,"\int \frac{\left(a^2-2 a x+x^2\right) \left(-a b+2 (a-b) x+x^2\right)}{(x (-a+x) (-b+x))^{3/4} \left(-a^3 d+\left(b+3 a^2 d\right) x-(1+3 a d) x^2+d x^3\right)} \, dx","Integrate[((a^2 - 2*a*x + x^2)*(-(a*b) + 2*(a - b)*x + x^2))/((x*(-a + x)*(-b + x))^(3/4)*(-(a^3*d) + (b + 3*a^2*d)*x - (1 + 3*a*d)*x^2 + d*x^3)),x]","\int \frac{\left(a^2-2 a x+x^2\right) \left(-a b+2 (a-b) x+x^2\right)}{(x (-a+x) (-b+x))^{3/4} \left(-a^3 d+\left(b+3 a^2 d\right) x-(1+3 a d) x^2+d x^3\right)} \, dx","\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \left(x^2 (-a-b)+a b x+x^3\right)^{3/4}}{x (x-b)}\right)}{d^{3/4}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \left(x^2 (-a-b)+a b x+x^3\right)^{3/4}}{x (x-b)}\right)}{d^{3/4}}",1,"Integrate[((a^2 - 2*a*x + x^2)*(-(a*b) + 2*(a - b)*x + x^2))/((x*(-a + x)*(-b + x))^(3/4)*(-(a^3*d) + (b + 3*a^2*d)*x - (1 + 3*a*d)*x^2 + d*x^3)), x]","F",-1
1317,0,0,95,0.2355374,"\int \frac{\left(1+x^2\right)^2}{\left(1-x^2\right) \left(1-6 x^2+x^4\right)^{3/4}} \, dx","Integrate[(1 + x^2)^2/((1 - x^2)*(1 - 6*x^2 + x^4)^(3/4)),x]","\int \frac{\left(1+x^2\right)^2}{\left(1-x^2\right) \left(1-6 x^2+x^4\right)^{3/4}} \, dx","\tan ^{-1}\left(\frac{x+i}{\sqrt[4]{x^4-6 x^2+1}}\right)-\tan ^{-1}\left(\frac{\sqrt[4]{x^4-6 x^2+1}}{x-i}\right)-\tanh ^{-1}\left(\frac{x+i}{\sqrt[4]{x^4-6 x^2+1}}\right)-\tanh ^{-1}\left(\frac{\sqrt[4]{x^4-6 x^2+1}}{x-i}\right)",1,"Integrate[(1 + x^2)^2/((1 - x^2)*(1 - 6*x^2 + x^4)^(3/4)), x]","F",-1
1318,0,0,95,0.4566488,"\int \frac{\left(-4+x^3\right) \left(1-x^3+x^4\right)}{x^2 \left(-1+x^3\right)^{3/4} \left(-1+x^3+x^4\right)} \, dx","Integrate[((-4 + x^3)*(1 - x^3 + x^4))/(x^2*(-1 + x^3)^(3/4)*(-1 + x^3 + x^4)),x]","\int \frac{\left(-4+x^3\right) \left(1-x^3+x^4\right)}{x^2 \left(-1+x^3\right)^{3/4} \left(-1+x^3+x^4\right)} \, dx","\frac{4 \sqrt[4]{x^3-1}}{x}+2 \sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{x^3-1}}{\sqrt{x^3-1}-x^2}\right)-2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{x^3-1}}{\sqrt{x^3-1}+x^2}\right)",1,"Integrate[((-4 + x^3)*(1 - x^3 + x^4))/(x^2*(-1 + x^3)^(3/4)*(-1 + x^3 + x^4)), x]","F",-1
1319,0,0,95,0.6449453,"\int \frac{\left(-1+x^4\right) \left(3+x^4\right) \left(-1-x^3+x^4\right)}{x^6 \left(-1-2 x^3+x^4\right) \sqrt[4]{-x+x^5}} \, dx","Integrate[((-1 + x^4)*(3 + x^4)*(-1 - x^3 + x^4))/(x^6*(-1 - 2*x^3 + x^4)*(-x + x^5)^(1/4)),x]","\int \frac{\left(-1+x^4\right) \left(3+x^4\right) \left(-1-x^3+x^4\right)}{x^6 \left(-1-2 x^3+x^4\right) \sqrt[4]{-x+x^5}} \, dx","-2\ 2^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \left(x^5-x\right)^{3/4}}{x^4-1}\right)-2\ 2^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \left(x^5-x\right)^{3/4}}{x^4-1}\right)+\frac{4 \left(x^5-x\right)^{3/4} \left(3 x^4+7 x^3-3\right)}{21 x^6}",1,"Integrate[((-1 + x^4)*(3 + x^4)*(-1 - x^3 + x^4))/(x^6*(-1 - 2*x^3 + x^4)*(-x + x^5)^(1/4)), x]","F",-1
1320,0,0,95,1.0385523,"\int \frac{\left(4 b+a x^5\right) \left(-b+c x^4+a x^5\right)}{x^2 \left(-b+a x^5\right)^{3/4} \left(-b-c x^4+a x^5\right)} \, dx","Integrate[((4*b + a*x^5)*(-b + c*x^4 + a*x^5))/(x^2*(-b + a*x^5)^(3/4)*(-b - c*x^4 + a*x^5)),x]","\int \frac{\left(4 b+a x^5\right) \left(-b+c x^4+a x^5\right)}{x^2 \left(-b+a x^5\right)^{3/4} \left(-b-c x^4+a x^5\right)} \, dx","-4 \sqrt[4]{c} \tan ^{-1}\left(\frac{\sqrt[4]{c} x \left(a x^5-b\right)^{3/4}}{b-a x^5}\right)+4 \sqrt[4]{c} \tanh ^{-1}\left(\frac{\sqrt[4]{c} x \left(a x^5-b\right)^{3/4}}{b-a x^5}\right)+\frac{4 \sqrt[4]{a x^5-b}}{x}",1,"Integrate[((4*b + a*x^5)*(-b + c*x^4 + a*x^5))/(x^2*(-b + a*x^5)^(3/4)*(-b - c*x^4 + a*x^5)), x]","F",-1
1321,0,0,95,0.2673434,"\int \frac{\left(-2+x^6\right) \left(1-x^4+x^6\right)}{x^4 \sqrt[4]{1+x^6} \left(1+x^4+x^6\right)} \, dx","Integrate[((-2 + x^6)*(1 - x^4 + x^6))/(x^4*(1 + x^6)^(1/4)*(1 + x^4 + x^6)),x]","\int \frac{\left(-2+x^6\right) \left(1-x^4+x^6\right)}{x^4 \sqrt[4]{1+x^6} \left(1+x^4+x^6\right)} \, dx","\frac{2 \left(x^6+1\right)^{3/4}}{3 x^3}+\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{x^6+1}}{\sqrt{x^6+1}-x^2}\right)+\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{x^6+1}}{\sqrt{x^6+1}+x^2}\right)",1,"Integrate[((-2 + x^6)*(1 - x^4 + x^6))/(x^4*(1 + x^6)^(1/4)*(1 + x^4 + x^6)), x]","F",-1
1322,0,0,95,0.7578981,"\int \frac{x^4 \left(2 b+a x^6\right)}{\sqrt[4]{-b+a x^6} \left(-b-x^4+a x^6\right)^2} \, dx","Integrate[(x^4*(2*b + a*x^6))/((-b + a*x^6)^(1/4)*(-b - x^4 + a*x^6)^2),x]","\int \frac{x^4 \left(2 b+a x^6\right)}{\sqrt[4]{-b+a x^6} \left(-b-x^4+a x^6\right)^2} \, dx","-\frac{1}{4} \tan ^{-1}\left(\frac{x \left(a x^6-b\right)^{3/4}}{b-a x^6}\right)-\frac{1}{4} \tanh ^{-1}\left(\frac{x \left(a x^6-b\right)^{3/4}}{b-a x^6}\right)-\frac{x \left(a x^6-b\right)^{3/4}}{2 \left(a x^6-b-x^4\right)}",1,"Integrate[(x^4*(2*b + a*x^6))/((-b + a*x^6)^(1/4)*(-b - x^4 + a*x^6)^2), x]","F",-1
1323,0,0,95,0.5469348,"\int \frac{\left(2 b+a x^6\right) \left(-b-x^4+a x^6\right)}{x^4 \sqrt[4]{-b+a x^6} \left(-b-2 x^4+a x^6\right)} \, dx","Integrate[((2*b + a*x^6)*(-b - x^4 + a*x^6))/(x^4*(-b + a*x^6)^(1/4)*(-b - 2*x^4 + a*x^6)),x]","\int \frac{\left(2 b+a x^6\right) \left(-b-x^4+a x^6\right)}{x^4 \sqrt[4]{-b+a x^6} \left(-b-2 x^4+a x^6\right)} \, dx","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x \left(a x^6-b\right)^{3/4}}{b-a x^6}\right)}{\sqrt[4]{2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x \left(a x^6-b\right)^{3/4}}{b-a x^6}\right)}{\sqrt[4]{2}}+\frac{2 \left(a x^6-b\right)^{3/4}}{3 x^3}",1,"Integrate[((2*b + a*x^6)*(-b - x^4 + a*x^6))/(x^4*(-b + a*x^6)^(1/4)*(-b - 2*x^4 + a*x^6)), x]","F",-1
1324,0,0,95,0.6870553,"\int \frac{\sqrt{-1-2 x^2-2 x^3-x^8} \left(-1+x^3+3 x^8\right)}{\left(1+2 x^3+x^8\right) \left(1+x^2+2 x^3+x^8\right)} \, dx","Integrate[(Sqrt[-1 - 2*x^2 - 2*x^3 - x^8]*(-1 + x^3 + 3*x^8))/((1 + 2*x^3 + x^8)*(1 + x^2 + 2*x^3 + x^8)),x]","\int \frac{\sqrt{-1-2 x^2-2 x^3-x^8} \left(-1+x^3+3 x^8\right)}{\left(1+2 x^3+x^8\right) \left(1+x^2+2 x^3+x^8\right)} \, dx","\tan ^{-1}\left(\frac{x \sqrt{-x^8-2 x^3-2 x^2-1}}{x^8+2 x^3+2 x^2+1}\right)-\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} x \sqrt{-x^8-2 x^3-2 x^2-1}}{x^8+2 x^3+2 x^2+1}\right)",1,"Integrate[(Sqrt[-1 - 2*x^2 - 2*x^3 - x^8]*(-1 + x^3 + 3*x^8))/((1 + 2*x^3 + x^8)*(1 + x^2 + 2*x^3 + x^8)), x]","F",-1
1325,0,0,95,0.1588801,"\int \frac{\left(1+x^6\right) \sqrt{-2-x^2+x^6}}{4-3 x^4-4 x^6+x^{12}} \, dx","Integrate[((1 + x^6)*Sqrt[-2 - x^2 + x^6])/(4 - 3*x^4 - 4*x^6 + x^12),x]","\int \frac{\left(1+x^6\right) \sqrt{-2-x^2+x^6}}{4-3 x^4-4 x^6+x^{12}} \, dx","-\frac{1}{4} \sqrt{\frac{1}{3} \left(1+\sqrt{3}\right)} \tan ^{-1}\left(\frac{\sqrt{1+\sqrt{3}} x}{\sqrt{x^6-x^2-2}}\right)-\frac{1}{4} \sqrt{\frac{1}{3} \left(\sqrt{3}-1\right)} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{3}-1} x}{\sqrt{x^6-x^2-2}}\right)",1,"Integrate[((1 + x^6)*Sqrt[-2 - x^2 + x^6])/(4 - 3*x^4 - 4*x^6 + x^12), x]","F",-1
1326,1,40,96,0.006213,"\int x \sqrt[3]{-1+x^3} \, dx","Integrate[x*(-1 + x^3)^(1/3),x]","\frac{x^2 \sqrt[3]{x^3-1} \, _2F_1\left(-\frac{1}{3},\frac{2}{3};\frac{5}{3};x^3\right)}{2 \sqrt[3]{1-x^3}}","\frac{1}{9} \log \left(\sqrt[3]{x^3-1}-x\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-1}+x}\right)}{3 \sqrt{3}}+\frac{1}{3} \sqrt[3]{x^3-1} x^2-\frac{1}{18} \log \left(\sqrt[3]{x^3-1} x+\left(x^3-1\right)^{2/3}+x^2\right)",1,"(x^2*(-1 + x^3)^(1/3)*Hypergeometric2F1[-1/3, 2/3, 5/3, x^3])/(2*(1 - x^3)^(1/3))","C",1
1327,1,22,96,0.0021702,"\int x \sqrt[3]{1+x^3} \, dx","Integrate[x*(1 + x^3)^(1/3),x]","\frac{1}{2} x^2 \, _2F_1\left(-\frac{1}{3},\frac{2}{3};\frac{5}{3};-x^3\right)","-\frac{1}{9} \log \left(\sqrt[3]{x^3+1}-x\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+1}+x}\right)}{3 \sqrt{3}}+\frac{1}{3} \sqrt[3]{x^3+1} x^2+\frac{1}{18} \log \left(\sqrt[3]{x^3+1} x+\left(x^3+1\right)^{2/3}+x^2\right)",1,"(x^2*Hypergeometric2F1[-1/3, 2/3, 5/3, -x^3])/2","C",1
1328,1,40,96,0.0085195,"\int \frac{\sqrt[3]{x+x^3}}{x^2} \, dx","Integrate[(x + x^3)^(1/3)/x^2,x]","-\frac{3 \sqrt[3]{x^3+x} \, _2F_1\left(-\frac{1}{3},-\frac{1}{3};\frac{2}{3};-x^2\right)}{2 x \sqrt[3]{x^2+1}}","-\frac{3 \sqrt[3]{x^3+x}}{2 x}-\frac{1}{2} \log \left(\sqrt[3]{x^3+x}-x\right)-\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+x}+x}\right)+\frac{1}{4} \log \left(\sqrt[3]{x^3+x} x+\left(x^3+x\right)^{2/3}+x^2\right)",1,"(-3*(x + x^3)^(1/3)*Hypergeometric2F1[-1/3, -1/3, 2/3, -x^2])/(2*x*(1 + x^2)^(1/3))","C",1
1329,0,0,96,1.699073,"\int \frac{(-1+x) (-1+k x) \left(3-2 (1+k) x+k x^2\right)}{x ((1-x) x (1-k x))^{3/4} \left(-1+(1+k) x-k x^2+d x^3\right)} \, dx","Integrate[((-1 + x)*(-1 + k*x)*(3 - 2*(1 + k)*x + k*x^2))/(x*((1 - x)*x*(1 - k*x))^(3/4)*(-1 + (1 + k)*x - k*x^2 + d*x^3)),x]","\int \frac{(-1+x) (-1+k x) \left(3-2 (1+k) x+k x^2\right)}{x ((1-x) x (1-k x))^{3/4} \left(-1+(1+k) x-k x^2+d x^3\right)} \, dx","2 \sqrt[4]{d} \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{k x^3+(-k-1) x^2+x}}\right)-2 \sqrt[4]{d} \tanh ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{k x^3+(-k-1) x^2+x}}\right)+\frac{4 \sqrt[4]{k x^3+(-k-1) x^2+x}}{x}",1,"Integrate[((-1 + x)*(-1 + k*x)*(3 - 2*(1 + k)*x + k*x^2))/(x*((1 - x)*x*(1 - k*x))^(3/4)*(-1 + (1 + k)*x - k*x^2 + d*x^3)), x]","F",-1
1330,0,0,96,2.1289451,"\int \frac{\left(1-2 x+x^2\right) \left(-2+(-1+k) (1+k) x+2 k^2 x^2\right)}{\left(\left(1-x^2\right) \left(1-k^2 x^2\right)\right)^{3/4} \left(-1+d-(1+3 d) x+\left(3 d+k^2\right) x^2+\left(-d+k^2\right) x^3\right)} \, dx","Integrate[((1 - 2*x + x^2)*(-2 + (-1 + k)*(1 + k)*x + 2*k^2*x^2))/(((1 - x^2)*(1 - k^2*x^2))^(3/4)*(-1 + d - (1 + 3*d)*x + (3*d + k^2)*x^2 + (-d + k^2)*x^3)),x]","\int \frac{\left(1-2 x+x^2\right) \left(-2+(-1+k) (1+k) x+2 k^2 x^2\right)}{\left(\left(1-x^2\right) \left(1-k^2 x^2\right)\right)^{3/4} \left(-1+d-(1+3 d) x+\left(3 d+k^2\right) x^2+\left(-d+k^2\right) x^3\right)} \, dx","\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{d} x-\sqrt[4]{d}}{\sqrt[4]{k^2 x^4+\left(-k^2-1\right) x^2+1}}\right)}{d^{3/4}}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{d} x-\sqrt[4]{d}}{\sqrt[4]{k^2 x^4+\left(-k^2-1\right) x^2+1}}\right)}{d^{3/4}}",1,"Integrate[((1 - 2*x + x^2)*(-2 + (-1 + k)*(1 + k)*x + 2*k^2*x^2))/(((1 - x^2)*(1 - k^2*x^2))^(3/4)*(-1 + d - (1 + 3*d)*x + (3*d + k^2)*x^2 + (-d + k^2)*x^3)), x]","F",-1
1331,1,136,96,0.1942076,"\int \frac{x^2}{\left(-b+a x^2\right) \sqrt[4]{-b x^2+a x^4}} \, dx","Integrate[x^2/((-b + a*x^2)*(-(b*x^2) + a*x^4)^(1/4)),x]","\frac{\left(a x^4-b x^2\right)^{3/4} \left(-2 \sqrt[4]{a} \sqrt{x} \left(a x^2-b\right)^{3/4}+\left(a x^2-b\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)+\left(a x^2-b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)\right)}{a^{5/4} x^{3/2} \left(a x^2-b\right)^{7/4}}","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)}{a^{5/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)}{a^{5/4}}-\frac{2 \left(a x^4-b x^2\right)^{3/4}}{a x \left(a x^2-b\right)}",1,"((-(b*x^2) + a*x^4)^(3/4)*(-2*a^(1/4)*Sqrt[x]*(-b + a*x^2)^(3/4) + (-b + a*x^2)*ArcTan[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)] + (-b + a*x^2)*ArcTanh[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)]))/(a^(5/4)*x^(3/2)*(-b + a*x^2)^(7/4))","A",1
1332,0,0,96,1.0245655,"\int \frac{\sqrt{q+p x^5} \left(-2 q+3 p x^5\right) \left(a q+b x^2+a p x^5\right)}{x^4 \left(c q+d x^2+c p x^5\right)} \, dx","Integrate[(Sqrt[q + p*x^5]*(-2*q + 3*p*x^5)*(a*q + b*x^2 + a*p*x^5))/(x^4*(c*q + d*x^2 + c*p*x^5)),x]","\int \frac{\sqrt{q+p x^5} \left(-2 q+3 p x^5\right) \left(a q+b x^2+a p x^5\right)}{x^4 \left(c q+d x^2+c p x^5\right)} \, dx","\frac{2 \left(b c \sqrt{d}-a d^{3/2}\right) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c} \sqrt{p x^5+q}}\right)}{c^{5/2}}+\frac{2 \sqrt{p x^5+q} \left(a c p x^5+a c q-3 a d x^2+3 b c x^2\right)}{3 c^2 x^3}",1,"Integrate[(Sqrt[q + p*x^5]*(-2*q + 3*p*x^5)*(a*q + b*x^2 + a*p*x^5))/(x^4*(c*q + d*x^2 + c*p*x^5)), x]","F",-1
1333,1,39,96,0.009623,"\int \frac{x}{\sqrt[3]{x^2+x^6}} \, dx","Integrate[x/(x^2 + x^6)^(1/3),x]","\frac{3 \left(x^6+x^2\right)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};-x^4\right)}{4 \left(x^4+1\right)^{2/3}}","-\frac{1}{4} \log \left(\sqrt[3]{x^6+x^2}-x^2\right)+\frac{1}{4} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x^2}{x^2+2 \sqrt[3]{x^6+x^2}}\right)+\frac{1}{8} \log \left(x^4+\sqrt[3]{x^6+x^2} x^2+\left(x^6+x^2\right)^{2/3}\right)",1,"(3*(x^2 + x^6)^(2/3)*Hypergeometric2F1[1/3, 1/3, 4/3, -x^4])/(4*(1 + x^4)^(2/3))","C",1
1334,0,0,96,1.4320133,"\int \frac{-1+x^4}{\left(1+x^2+x^4\right) \sqrt[4]{x^2+x^6}} \, dx","Integrate[(-1 + x^4)/((1 + x^2 + x^4)*(x^2 + x^6)^(1/4)),x]","\int \frac{-1+x^4}{\left(1+x^2+x^4\right) \sqrt[4]{x^2+x^6}} \, dx","-\frac{\tan ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{x^6+x^2}}{\sqrt{x^6+x^2}-x^2}\right)}{\sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{\frac{x^2}{\sqrt{2}}+\frac{\sqrt{x^6+x^2}}{\sqrt{2}}}{x \sqrt[4]{x^6+x^2}}\right)}{\sqrt{2}}",1,"Integrate[(-1 + x^4)/((1 + x^2 + x^4)*(x^2 + x^6)^(1/4)), x]","F",-1
1335,0,0,96,0.4280407,"\int \frac{-1+x^4}{\left(1+x^2+x^4\right) \sqrt[4]{x^2+x^6}} \, dx","Integrate[(-1 + x^4)/((1 + x^2 + x^4)*(x^2 + x^6)^(1/4)),x]","\int \frac{-1+x^4}{\left(1+x^2+x^4\right) \sqrt[4]{x^2+x^6}} \, dx","-\frac{\tan ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{x^6+x^2}}{\sqrt{x^6+x^2}-x^2}\right)}{\sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{\frac{x^2}{\sqrt{2}}+\frac{\sqrt{x^6+x^2}}{\sqrt{2}}}{x \sqrt[4]{x^6+x^2}}\right)}{\sqrt{2}}",1,"Integrate[(-1 + x^4)/((1 + x^2 + x^4)*(x^2 + x^6)^(1/4)), x]","F",-1
1336,0,0,96,0.399678,"\int \frac{x^2 \left(2 b+a x^6\right)}{\left(-b+a x^6\right)^{3/4} \left(-b-2 c x^4+a x^6\right)} \, dx","Integrate[(x^2*(2*b + a*x^6))/((-b + a*x^6)^(3/4)*(-b - 2*c*x^4 + a*x^6)),x]","\int \frac{x^2 \left(2 b+a x^6\right)}{\left(-b+a x^6\right)^{3/4} \left(-b-2 c x^4+a x^6\right)} \, dx","\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x \left(a x^6-b\right)^{3/4}}{b-a x^6}\right)}{2^{3/4} c^{3/4}}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x \left(a x^6-b\right)^{3/4}}{b-a x^6}\right)}{2^{3/4} c^{3/4}}",1,"Integrate[(x^2*(2*b + a*x^6))/((-b + a*x^6)^(3/4)*(-b - 2*c*x^4 + a*x^6)), x]","F",-1
1337,1,402,96,0.8599419,"\int \frac{1}{\sqrt[4]{b+a x^4} \left(-2 b-2 a x^4+x^8\right)} \, dx","Integrate[1/((b + a*x^4)^(1/4)*(-2*b - 2*a*x^4 + x^8)),x]","\frac{\frac{\tan ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+2 b}+a^2+b}}{\sqrt[4]{a-\sqrt{a^2+2 b}} \sqrt[4]{a x^4+b}}\right)}{\left(a-\sqrt{a^2+2 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+2 b}+a^2+b}}-\frac{\tan ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+2 b}+a^2+b}}{\sqrt[4]{\sqrt{a^2+2 b}+a} \sqrt[4]{a x^4+b}}\right)}{\left(\sqrt{a^2+2 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+2 b}+a^2+b}}+\frac{\tanh ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+2 b}+a^2+b}}{\sqrt[4]{a-\sqrt{a^2+2 b}} \sqrt[4]{a x^4+b}}\right)}{\left(a-\sqrt{a^2+2 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+2 b}+a^2+b}}-\frac{\tanh ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+2 b}+a^2+b}}{\sqrt[4]{\sqrt{a^2+2 b}+a} \sqrt[4]{a x^4+b}}\right)}{\left(\sqrt{a^2+2 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+2 b}+a^2+b}}}{4 \sqrt{a^2+2 b}}","-\frac{\text{RootSum}\left[-2 \text{$\#$1}^8+2 \text{$\#$1}^4 a+b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-a \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+a \log (x)}{\text{$\#$1} a-2 \text{$\#$1}^5}\&\right]}{8 b}",1,"(ArcTan[((a^2 + b - a*Sqrt[a^2 + 2*b])^(1/4)*x)/((a - Sqrt[a^2 + 2*b])^(1/4)*(b + a*x^4)^(1/4))]/((a - Sqrt[a^2 + 2*b])^(3/4)*(a^2 + b - a*Sqrt[a^2 + 2*b])^(1/4)) - ArcTan[((a^2 + b + a*Sqrt[a^2 + 2*b])^(1/4)*x)/((a + Sqrt[a^2 + 2*b])^(1/4)*(b + a*x^4)^(1/4))]/((a + Sqrt[a^2 + 2*b])^(3/4)*(a^2 + b + a*Sqrt[a^2 + 2*b])^(1/4)) + ArcTanh[((a^2 + b - a*Sqrt[a^2 + 2*b])^(1/4)*x)/((a - Sqrt[a^2 + 2*b])^(1/4)*(b + a*x^4)^(1/4))]/((a - Sqrt[a^2 + 2*b])^(3/4)*(a^2 + b - a*Sqrt[a^2 + 2*b])^(1/4)) - ArcTanh[((a^2 + b + a*Sqrt[a^2 + 2*b])^(1/4)*x)/((a + Sqrt[a^2 + 2*b])^(1/4)*(b + a*x^4)^(1/4))]/((a + Sqrt[a^2 + 2*b])^(3/4)*(a^2 + b + a*Sqrt[a^2 + 2*b])^(1/4)))/(4*Sqrt[a^2 + 2*b])","B",1
1338,1,402,96,0.0906244,"\int \frac{1}{\sqrt[4]{b+a x^4} \left(-2 b-2 a x^4+x^8\right)} \, dx","Integrate[1/((b + a*x^4)^(1/4)*(-2*b - 2*a*x^4 + x^8)),x]","\frac{\frac{\tan ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+2 b}+a^2+b}}{\sqrt[4]{a-\sqrt{a^2+2 b}} \sqrt[4]{a x^4+b}}\right)}{\left(a-\sqrt{a^2+2 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+2 b}+a^2+b}}-\frac{\tan ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+2 b}+a^2+b}}{\sqrt[4]{\sqrt{a^2+2 b}+a} \sqrt[4]{a x^4+b}}\right)}{\left(\sqrt{a^2+2 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+2 b}+a^2+b}}+\frac{\tanh ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+2 b}+a^2+b}}{\sqrt[4]{a-\sqrt{a^2+2 b}} \sqrt[4]{a x^4+b}}\right)}{\left(a-\sqrt{a^2+2 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+2 b}+a^2+b}}-\frac{\tanh ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+2 b}+a^2+b}}{\sqrt[4]{\sqrt{a^2+2 b}+a} \sqrt[4]{a x^4+b}}\right)}{\left(\sqrt{a^2+2 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+2 b}+a^2+b}}}{4 \sqrt{a^2+2 b}}","-\frac{\text{RootSum}\left[-2 \text{$\#$1}^8+2 \text{$\#$1}^4 a+b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-a \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+a \log (x)}{\text{$\#$1} a-2 \text{$\#$1}^5}\&\right]}{8 b}",1,"(ArcTan[((a^2 + b - a*Sqrt[a^2 + 2*b])^(1/4)*x)/((a - Sqrt[a^2 + 2*b])^(1/4)*(b + a*x^4)^(1/4))]/((a - Sqrt[a^2 + 2*b])^(3/4)*(a^2 + b - a*Sqrt[a^2 + 2*b])^(1/4)) - ArcTan[((a^2 + b + a*Sqrt[a^2 + 2*b])^(1/4)*x)/((a + Sqrt[a^2 + 2*b])^(1/4)*(b + a*x^4)^(1/4))]/((a + Sqrt[a^2 + 2*b])^(3/4)*(a^2 + b + a*Sqrt[a^2 + 2*b])^(1/4)) + ArcTanh[((a^2 + b - a*Sqrt[a^2 + 2*b])^(1/4)*x)/((a - Sqrt[a^2 + 2*b])^(1/4)*(b + a*x^4)^(1/4))]/((a - Sqrt[a^2 + 2*b])^(3/4)*(a^2 + b - a*Sqrt[a^2 + 2*b])^(1/4)) - ArcTanh[((a^2 + b + a*Sqrt[a^2 + 2*b])^(1/4)*x)/((a + Sqrt[a^2 + 2*b])^(1/4)*(b + a*x^4)^(1/4))]/((a + Sqrt[a^2 + 2*b])^(3/4)*(a^2 + b + a*Sqrt[a^2 + 2*b])^(1/4)))/(4*Sqrt[a^2 + 2*b])","B",1
1339,1,499,96,0.8815227,"\int \frac{-2 b+a x^4}{\sqrt[4]{b+a x^4} \left(-b-a x^4+2 x^8\right)} \, dx","Integrate[(-2*b + a*x^4)/((b + a*x^4)^(1/4)*(-b - a*x^4 + 2*x^8)),x]","-\frac{\left(a-\frac{a^2-8 b}{\sqrt{a^2+8 b}}\right) \tan ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+8 b}+a^2+4 b}}{\sqrt[4]{a-\sqrt{a^2+8 b}} \sqrt[4]{a x^4+b}}\right)}{2 \left(a-\sqrt{a^2+8 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+8 b}+a^2+4 b}}-\frac{\left(\frac{a^2-8 b}{\sqrt{a^2+8 b}}+a\right) \tan ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+8 b}+a^2+4 b}}{\sqrt[4]{\sqrt{a^2+8 b}+a} \sqrt[4]{a x^4+b}}\right)}{2 \left(\sqrt{a^2+8 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+8 b}+a^2+4 b}}-\frac{\left(a-\frac{a^2-8 b}{\sqrt{a^2+8 b}}\right) \tanh ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+8 b}+a^2+4 b}}{\sqrt[4]{a-\sqrt{a^2+8 b}} \sqrt[4]{a x^4+b}}\right)}{2 \left(a-\sqrt{a^2+8 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+8 b}+a^2+4 b}}-\frac{\left(\frac{a^2-8 b}{\sqrt{a^2+8 b}}+a\right) \tanh ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+8 b}+a^2+4 b}}{\sqrt[4]{\sqrt{a^2+8 b}+a} \sqrt[4]{a x^4+b}}\right)}{2 \left(\sqrt{a^2+8 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+8 b}+a^2+4 b}}","\frac{1}{4} \text{RootSum}\left[-\text{$\#$1}^8+\text{$\#$1}^4 a+2 b\&,\frac{2 \text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)-2 \text{$\#$1}^4 \log (x)-3 a \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+3 a \log (x)}{\text{$\#$1} a-2 \text{$\#$1}^5}\&\right]",1,"-1/2*((a - (a^2 - 8*b)/Sqrt[a^2 + 8*b])*ArcTan[((a^2 + 4*b - a*Sqrt[a^2 + 8*b])^(1/4)*x)/((a - Sqrt[a^2 + 8*b])^(1/4)*(b + a*x^4)^(1/4))])/((a - Sqrt[a^2 + 8*b])^(3/4)*(a^2 + 4*b - a*Sqrt[a^2 + 8*b])^(1/4)) - ((a + (a^2 - 8*b)/Sqrt[a^2 + 8*b])*ArcTan[((a^2 + 4*b + a*Sqrt[a^2 + 8*b])^(1/4)*x)/((a + Sqrt[a^2 + 8*b])^(1/4)*(b + a*x^4)^(1/4))])/(2*(a + Sqrt[a^2 + 8*b])^(3/4)*(a^2 + 4*b + a*Sqrt[a^2 + 8*b])^(1/4)) - ((a - (a^2 - 8*b)/Sqrt[a^2 + 8*b])*ArcTanh[((a^2 + 4*b - a*Sqrt[a^2 + 8*b])^(1/4)*x)/((a - Sqrt[a^2 + 8*b])^(1/4)*(b + a*x^4)^(1/4))])/(2*(a - Sqrt[a^2 + 8*b])^(3/4)*(a^2 + 4*b - a*Sqrt[a^2 + 8*b])^(1/4)) - ((a + (a^2 - 8*b)/Sqrt[a^2 + 8*b])*ArcTanh[((a^2 + 4*b + a*Sqrt[a^2 + 8*b])^(1/4)*x)/((a + Sqrt[a^2 + 8*b])^(1/4)*(b + a*x^4)^(1/4))])/(2*(a + Sqrt[a^2 + 8*b])^(3/4)*(a^2 + 4*b + a*Sqrt[a^2 + 8*b])^(1/4))","B",1
1340,1,169,97,2.0151644,"\int \frac{1+b x+k^2 x^2}{\sqrt{(1-x) x \left(1-k^2 x\right)} \left(-1+k^2 x^2\right)} \, dx","Integrate[(1 + b*x + k^2*x^2)/(Sqrt[(1 - x)*x*(1 - k^2*x)]*(-1 + k^2*x^2)),x]","\frac{i \sqrt{\frac{1}{x-1}+1} (x-1)^{3/2} \sqrt{\frac{1-\frac{1}{k^2}}{x-1}+1} \left(2 k \left(b+k^2+1\right) F\left(i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)-(k-1) (b-2 k) \Pi \left(1+\frac{1}{k};i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)-(k+1) (b+2 k) \Pi \left(\frac{k-1}{k};i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)\right)}{k \left(k^2-1\right) \sqrt{(x-1) x \left(k^2 x-1\right)}}","\frac{(-b-2 k) \tan ^{-1}\left(\frac{(k-1) x}{\sqrt{k^2 x^3+\left(-k^2-1\right) x^2+x}}\right)}{2 (k-1) k}+\frac{(b-2 k) \tan ^{-1}\left(\frac{(k+1) x}{\sqrt{k^2 x^3+\left(-k^2-1\right) x^2+x}}\right)}{2 k (k+1)}",1,"(I*Sqrt[1 + (-1 + x)^(-1)]*Sqrt[1 + (1 - k^(-2))/(-1 + x)]*(-1 + x)^(3/2)*(2*k*(1 + b + k^2)*EllipticF[I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)] - (b - 2*k)*(-1 + k)*EllipticPi[1 + k^(-1), I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)] - (1 + k)*(b + 2*k)*EllipticPi[(-1 + k)/k, I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)]))/(k*(-1 + k^2)*Sqrt[(-1 + x)*x*(-1 + k^2*x)])","C",1
1341,1,28,97,0.0052529,"\int \frac{\sqrt[3]{-1+x^3}}{x^7} \, dx","Integrate[(-1 + x^3)^(1/3)/x^7,x]","\frac{1}{4} \left(x^3-1\right)^{4/3} \, _2F_1\left(\frac{4}{3},3;\frac{7}{3};1-x^3\right)","\frac{1}{27} \log \left(\sqrt[3]{x^3-1}+1\right)-\frac{1}{54} \log \left(\left(x^3-1\right)^{2/3}-\sqrt[3]{x^3-1}+1\right)-\frac{\tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{x^3-1}}{\sqrt{3}}\right)}{9 \sqrt{3}}+\frac{\sqrt[3]{x^3-1} \left(x^3-3\right)}{18 x^6}",1,"((-1 + x^3)^(4/3)*Hypergeometric2F1[4/3, 3, 7/3, 1 - x^3])/4","C",1
1342,1,26,97,0.0055317,"\int \frac{\sqrt[3]{1+x^3}}{x^7} \, dx","Integrate[(1 + x^3)^(1/3)/x^7,x]","-\frac{1}{4} \left(x^3+1\right)^{4/3} \, _2F_1\left(\frac{4}{3},3;\frac{7}{3};x^3+1\right)","-\frac{1}{27} \log \left(\sqrt[3]{x^3+1}-1\right)+\frac{1}{54} \log \left(\left(x^3+1\right)^{2/3}+\sqrt[3]{x^3+1}+1\right)+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{x^3+1}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{9 \sqrt{3}}+\frac{\sqrt[3]{x^3+1} \left(-x^3-3\right)}{18 x^6}",1,"-1/4*((1 + x^3)^(4/3)*Hypergeometric2F1[4/3, 3, 7/3, 1 + x^3])","C",1
1343,1,98,97,0.034142,"\int \frac{\left(-1+x^3\right) \sqrt[3]{1+x^3}}{x^4} \, dx","Integrate[((-1 + x^3)*(1 + x^3)^(1/3))/x^4,x]","\frac{\sqrt[3]{x^3+1}}{3 x^3}+\sqrt[3]{x^3+1}+\frac{2}{9} \log \left(1-\sqrt[3]{x^3+1}\right)-\frac{1}{9} \log \left(\left(x^3+1\right)^{2/3}+\sqrt[3]{x^3+1}+1\right)-\frac{2 \tan ^{-1}\left(\frac{2 \sqrt[3]{x^3+1}+1}{\sqrt{3}}\right)}{3 \sqrt{3}}","\frac{\sqrt[3]{x^3+1} \left(3 x^3+1\right)}{3 x^3}+\frac{2}{9} \log \left(\sqrt[3]{x^3+1}-1\right)-\frac{1}{9} \log \left(\left(x^3+1\right)^{2/3}+\sqrt[3]{x^3+1}+1\right)-\frac{2 \tan ^{-1}\left(\frac{2 \sqrt[3]{x^3+1}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"(1 + x^3)^(1/3) + (1 + x^3)^(1/3)/(3*x^3) - (2*ArcTan[(1 + 2*(1 + x^3)^(1/3))/Sqrt[3]])/(3*Sqrt[3]) + (2*Log[1 - (1 + x^3)^(1/3)])/9 - Log[1 + (1 + x^3)^(1/3) + (1 + x^3)^(2/3)]/9","A",1
1344,1,481,97,0.5425167,"\int \frac{1+x}{\left(-1-x+x^3\right) \sqrt[3]{-x^2+x^3}} \, dx","Integrate[(1 + x)/((-1 - x + x^3)*(-x^2 + x^3)^(1/3)),x]","-\frac{\left(\frac{1}{x-1}+1\right)^{2/3} (x-1) \left(\text{RootSum}\left[\text{$\#$1}^3-5 \text{$\#$1}^2+4 \text{$\#$1}-1\&,\frac{-\frac{2 \log \left(\sqrt[3]{\text{$\#$1}}-\sqrt[3]{\frac{1}{x-1}+1}\right)}{\text{$\#$1}^{2/3}}+\frac{\log \left(\text{$\#$1}^{2/3}+\sqrt[3]{\text{$\#$1}} \sqrt[3]{\frac{1}{x-1}+1}+\left(\frac{1}{x-1}+1\right)^{2/3}\right)}{\text{$\#$1}^{2/3}}+\frac{2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{\frac{1}{x-1}+1}}{\sqrt[3]{\text{$\#$1}}}+1}{\sqrt{3}}\right)}{\text{$\#$1}^{2/3}}}{3 \text{$\#$1}^2-10 \text{$\#$1}+4}\&\right]-3 \text{RootSum}\left[\text{$\#$1}^3-5 \text{$\#$1}^2+4 \text{$\#$1}-1\&,\frac{\sqrt[3]{\text{$\#$1}} \log \left(\text{$\#$1}^{2/3}+\sqrt[3]{\text{$\#$1}} \sqrt[3]{\frac{1}{x-1}+1}+\left(\frac{1}{x-1}+1\right)^{2/3}\right)-2 \sqrt[3]{\text{$\#$1}} \log \left(\sqrt[3]{\text{$\#$1}}-\sqrt[3]{\frac{1}{x-1}+1}\right)+2 \sqrt{3} \sqrt[3]{\text{$\#$1}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{\frac{1}{x-1}+1}}{\sqrt[3]{\text{$\#$1}}}+1}{\sqrt{3}}\right)}{3 \text{$\#$1}^2-10 \text{$\#$1}+4}\&\right]+2 \text{RootSum}\left[\text{$\#$1}^3-5 \text{$\#$1}^2+4 \text{$\#$1}-1\&,\frac{-2 \text{$\#$1}^{4/3} \log \left(\sqrt[3]{\text{$\#$1}}-\sqrt[3]{\frac{1}{x-1}+1}\right)+\text{$\#$1}^{4/3} \log \left(\text{$\#$1}^{2/3}+\sqrt[3]{\text{$\#$1}} \sqrt[3]{\frac{1}{x-1}+1}+\left(\frac{1}{x-1}+1\right)^{2/3}\right)+2 \sqrt{3} \text{$\#$1}^{4/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{\frac{1}{x-1}+1}}{\sqrt[3]{\text{$\#$1}}}+1}{\sqrt{3}}\right)}{3 \text{$\#$1}^2-10 \text{$\#$1}+4}\&\right]\right)}{2 \sqrt[3]{(x-1) x^2}}","-\text{RootSum}\left[\text{$\#$1}^9-4 \text{$\#$1}^6+5 \text{$\#$1}^3-1\&,\frac{-\text{$\#$1}^3 \log \left(\sqrt[3]{x^3-x^2}-\text{$\#$1} x\right)+\text{$\#$1}^3 \log (x)+2 \log \left(\sqrt[3]{x^3-x^2}-\text{$\#$1} x\right)-2 \log (x)}{3 \text{$\#$1}^4-5 \text{$\#$1}}\&\right]",1,"-1/2*((1 + (-1 + x)^(-1))^(2/3)*(-1 + x)*(RootSum[-1 + 4*#1 - 5*#1^2 + #1^3 & , ((2*Sqrt[3]*ArcTan[(1 + (2*(1 + (-1 + x)^(-1))^(1/3))/#1^(1/3))/Sqrt[3]])/#1^(2/3) - (2*Log[-(1 + (-1 + x)^(-1))^(1/3) + #1^(1/3)])/#1^(2/3) + Log[(1 + (-1 + x)^(-1))^(2/3) + (1 + (-1 + x)^(-1))^(1/3)*#1^(1/3) + #1^(2/3)]/#1^(2/3))/(4 - 10*#1 + 3*#1^2) & ] - 3*RootSum[-1 + 4*#1 - 5*#1^2 + #1^3 & , (2*Sqrt[3]*ArcTan[(1 + (2*(1 + (-1 + x)^(-1))^(1/3))/#1^(1/3))/Sqrt[3]]*#1^(1/3) - 2*Log[-(1 + (-1 + x)^(-1))^(1/3) + #1^(1/3)]*#1^(1/3) + Log[(1 + (-1 + x)^(-1))^(2/3) + (1 + (-1 + x)^(-1))^(1/3)*#1^(1/3) + #1^(2/3)]*#1^(1/3))/(4 - 10*#1 + 3*#1^2) & ] + 2*RootSum[-1 + 4*#1 - 5*#1^2 + #1^3 & , (2*Sqrt[3]*ArcTan[(1 + (2*(1 + (-1 + x)^(-1))^(1/3))/#1^(1/3))/Sqrt[3]]*#1^(4/3) - 2*Log[-(1 + (-1 + x)^(-1))^(1/3) + #1^(1/3)]*#1^(4/3) + Log[(1 + (-1 + x)^(-1))^(2/3) + (1 + (-1 + x)^(-1))^(1/3)*#1^(1/3) + #1^(2/3)]*#1^(4/3))/(4 - 10*#1 + 3*#1^2) & ]))/((-1 + x)*x^2)^(1/3)","B",1
1345,1,481,97,0.103606,"\int \frac{1+x}{\left(-1-x+x^3\right) \sqrt[3]{-x^2+x^3}} \, dx","Integrate[(1 + x)/((-1 - x + x^3)*(-x^2 + x^3)^(1/3)),x]","-\frac{\left(\frac{1}{x-1}+1\right)^{2/3} (x-1) \left(\text{RootSum}\left[\text{$\#$1}^3-5 \text{$\#$1}^2+4 \text{$\#$1}-1\&,\frac{-\frac{2 \log \left(\sqrt[3]{\text{$\#$1}}-\sqrt[3]{\frac{1}{x-1}+1}\right)}{\text{$\#$1}^{2/3}}+\frac{\log \left(\text{$\#$1}^{2/3}+\sqrt[3]{\text{$\#$1}} \sqrt[3]{\frac{1}{x-1}+1}+\left(\frac{1}{x-1}+1\right)^{2/3}\right)}{\text{$\#$1}^{2/3}}+\frac{2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{\frac{1}{x-1}+1}}{\sqrt[3]{\text{$\#$1}}}+1}{\sqrt{3}}\right)}{\text{$\#$1}^{2/3}}}{3 \text{$\#$1}^2-10 \text{$\#$1}+4}\&\right]-3 \text{RootSum}\left[\text{$\#$1}^3-5 \text{$\#$1}^2+4 \text{$\#$1}-1\&,\frac{\sqrt[3]{\text{$\#$1}} \log \left(\text{$\#$1}^{2/3}+\sqrt[3]{\text{$\#$1}} \sqrt[3]{\frac{1}{x-1}+1}+\left(\frac{1}{x-1}+1\right)^{2/3}\right)-2 \sqrt[3]{\text{$\#$1}} \log \left(\sqrt[3]{\text{$\#$1}}-\sqrt[3]{\frac{1}{x-1}+1}\right)+2 \sqrt{3} \sqrt[3]{\text{$\#$1}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{\frac{1}{x-1}+1}}{\sqrt[3]{\text{$\#$1}}}+1}{\sqrt{3}}\right)}{3 \text{$\#$1}^2-10 \text{$\#$1}+4}\&\right]+2 \text{RootSum}\left[\text{$\#$1}^3-5 \text{$\#$1}^2+4 \text{$\#$1}-1\&,\frac{-2 \text{$\#$1}^{4/3} \log \left(\sqrt[3]{\text{$\#$1}}-\sqrt[3]{\frac{1}{x-1}+1}\right)+\text{$\#$1}^{4/3} \log \left(\text{$\#$1}^{2/3}+\sqrt[3]{\text{$\#$1}} \sqrt[3]{\frac{1}{x-1}+1}+\left(\frac{1}{x-1}+1\right)^{2/3}\right)+2 \sqrt{3} \text{$\#$1}^{4/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{\frac{1}{x-1}+1}}{\sqrt[3]{\text{$\#$1}}}+1}{\sqrt{3}}\right)}{3 \text{$\#$1}^2-10 \text{$\#$1}+4}\&\right]\right)}{2 \sqrt[3]{(x-1) x^2}}","-\text{RootSum}\left[\text{$\#$1}^9-4 \text{$\#$1}^6+5 \text{$\#$1}^3-1\&,\frac{-\text{$\#$1}^3 \log \left(\sqrt[3]{x^3-x^2}-\text{$\#$1} x\right)+\text{$\#$1}^3 \log (x)+2 \log \left(\sqrt[3]{x^3-x^2}-\text{$\#$1} x\right)-2 \log (x)}{3 \text{$\#$1}^4-5 \text{$\#$1}}\&\right]",1,"-1/2*((1 + (-1 + x)^(-1))^(2/3)*(-1 + x)*(RootSum[-1 + 4*#1 - 5*#1^2 + #1^3 & , ((2*Sqrt[3]*ArcTan[(1 + (2*(1 + (-1 + x)^(-1))^(1/3))/#1^(1/3))/Sqrt[3]])/#1^(2/3) - (2*Log[-(1 + (-1 + x)^(-1))^(1/3) + #1^(1/3)])/#1^(2/3) + Log[(1 + (-1 + x)^(-1))^(2/3) + (1 + (-1 + x)^(-1))^(1/3)*#1^(1/3) + #1^(2/3)]/#1^(2/3))/(4 - 10*#1 + 3*#1^2) & ] - 3*RootSum[-1 + 4*#1 - 5*#1^2 + #1^3 & , (2*Sqrt[3]*ArcTan[(1 + (2*(1 + (-1 + x)^(-1))^(1/3))/#1^(1/3))/Sqrt[3]]*#1^(1/3) - 2*Log[-(1 + (-1 + x)^(-1))^(1/3) + #1^(1/3)]*#1^(1/3) + Log[(1 + (-1 + x)^(-1))^(2/3) + (1 + (-1 + x)^(-1))^(1/3)*#1^(1/3) + #1^(2/3)]*#1^(1/3))/(4 - 10*#1 + 3*#1^2) & ] + 2*RootSum[-1 + 4*#1 - 5*#1^2 + #1^3 & , (2*Sqrt[3]*ArcTan[(1 + (2*(1 + (-1 + x)^(-1))^(1/3))/#1^(1/3))/Sqrt[3]]*#1^(4/3) - 2*Log[-(1 + (-1 + x)^(-1))^(1/3) + #1^(1/3)]*#1^(4/3) + Log[(1 + (-1 + x)^(-1))^(2/3) + (1 + (-1 + x)^(-1))^(1/3)*#1^(1/3) + #1^(2/3)]*#1^(4/3))/(4 - 10*#1 + 3*#1^2) & ]))/((-1 + x)*x^2)^(1/3)","B",1
1346,1,205,97,0.662307,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{-x-x^2+x^3}} \, dx","Integrate[(-1 + x^2)/((1 + x^2)*Sqrt[-x - x^2 + x^3]),x]","-\frac{2 i \sqrt{\frac{2}{\sqrt{5}-1}} \sqrt{-\frac{1}{x^2}-\frac{1}{x}+1} x^{3/2} \left(F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{1+\sqrt{5}}}}{\sqrt{x}}\right)|-\frac{3}{2}-\frac{\sqrt{5}}{2}\right)-\Pi \left(-\frac{1}{2} i \left(1+\sqrt{5}\right);i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{1+\sqrt{5}}}}{\sqrt{x}}\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)-\Pi \left(\frac{1}{2} i \left(1+\sqrt{5}\right);i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{1+\sqrt{5}}}}{\sqrt{x}}\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)\right)}{\sqrt{x \left(x^2-x-1\right)}}","-\sqrt{\frac{1}{5}+\frac{2 i}{5}} \tan ^{-1}\left(\frac{\sqrt{1-2 i} \sqrt{x^3-x^2-x}}{x^2-x-1}\right)-\sqrt{\frac{1}{5}-\frac{2 i}{5}} \tan ^{-1}\left(\frac{\sqrt{1+2 i} \sqrt{x^3-x^2-x}}{x^2-x-1}\right)",1,"((-2*I)*Sqrt[2/(-1 + Sqrt[5])]*Sqrt[1 - x^(-2) - x^(-1)]*x^(3/2)*(EllipticF[I*ArcSinh[Sqrt[2/(1 + Sqrt[5])]/Sqrt[x]], -3/2 - Sqrt[5]/2] - EllipticPi[(-1/2*I)*(1 + Sqrt[5]), I*ArcSinh[Sqrt[2/(1 + Sqrt[5])]/Sqrt[x]], (-3 - Sqrt[5])/2] - EllipticPi[(I/2)*(1 + Sqrt[5]), I*ArcSinh[Sqrt[2/(1 + Sqrt[5])]/Sqrt[x]], (-3 - Sqrt[5])/2]))/Sqrt[x*(-1 - x + x^2)]","C",0
1347,1,35,97,0.0075415,"\int \frac{\sqrt[3]{x^2+x^3}}{x} \, dx","Integrate[(x^2 + x^3)^(1/3)/x,x]","\frac{3 \sqrt[3]{x^2 (x+1)} \, _2F_1\left(-\frac{1}{3},\frac{2}{3};\frac{5}{3};-x\right)}{2 \sqrt[3]{x+1}}","\sqrt[3]{x^3+x^2}-\frac{1}{3} \log \left(\sqrt[3]{x^3+x^2}-x\right)+\frac{1}{6} \log \left(x^2+\sqrt[3]{x^3+x^2} x+\left(x^3+x^2\right)^{2/3}\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+x^2}+x}\right)}{\sqrt{3}}",1,"(3*(x^2*(1 + x))^(1/3)*Hypergeometric2F1[-1/3, 2/3, 5/3, -x])/(2*(1 + x)^(1/3))","C",1
1348,1,106,97,0.1142081,"\int \frac{\left(1+x^3\right)^{2/3} \left(2+x^3\right)}{x^6 \left(1+2 x^3\right)} \, dx","Integrate[((1 + x^3)^(2/3)*(2 + x^3))/(x^6*(1 + 2*x^3)),x]","3 \left(\frac{1}{3} \log \left(\frac{x}{\sqrt[3]{x^3+1}}+1\right)+\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3+1}}-1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{1}{6} \log \left(-\frac{x}{\sqrt[3]{x^3+1}}+\frac{x^2}{\left(x^3+1\right)^{2/3}}+1\right)\right)+\left(x^3+1\right)^{2/3} \left(\frac{11}{10 x^2}-\frac{2}{5 x^5}\right)","\log \left(\sqrt[3]{x^3+1}+x\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+1}-x}\right)+\frac{\left(x^3+1\right)^{2/3} \left(11 x^3-4\right)}{10 x^5}-\frac{1}{2} \log \left(-\sqrt[3]{x^3+1} x+\left(x^3+1\right)^{2/3}+x^2\right)",1,"(-2/(5*x^5) + 11/(10*x^2))*(1 + x^3)^(2/3) + 3*(ArcTan[(-1 + (2*x)/(1 + x^3)^(1/3))/Sqrt[3]]/Sqrt[3] - Log[1 + x^2/(1 + x^3)^(2/3) - x/(1 + x^3)^(1/3)]/6 + Log[1 + x/(1 + x^3)^(1/3)]/3)","A",1
1349,1,35,97,0.0102599,"\int \frac{\left(-3+x^4\right) \sqrt[3]{1+x^4}}{x^9} \, dx","Integrate[((-3 + x^4)*(1 + x^4)^(1/3))/x^9,x]","\frac{3 \left(x^4+1\right)^{4/3} \left(x^8 \, _2F_1\left(\frac{4}{3},2;\frac{7}{3};x^4+1\right)+1\right)}{8 x^8}","\frac{1}{6} \log \left(\sqrt[3]{x^4+1}-1\right)-\frac{1}{12} \log \left(\left(x^4+1\right)^{2/3}+\sqrt[3]{x^4+1}+1\right)-\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{x^4+1}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{\sqrt[3]{x^4+1} \left(3-x^4\right)}{8 x^8}",1,"(3*(1 + x^4)^(4/3)*(1 + x^8*Hypergeometric2F1[4/3, 2, 7/3, 1 + x^4]))/(8*x^8)","C",1
1350,1,66,97,0.0300854,"\int \frac{-b+a x^3}{x^3 \sqrt[4]{b x+a x^4}} \, dx","Integrate[(-b + a*x^3)/(x^3*(b*x + a*x^4)^(1/4)),x]","\frac{4 \left(3 a x^3 \sqrt[4]{\frac{a x^3}{b}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{4};\frac{5}{4};-\frac{a x^3}{b}\right)+a x^3+b\right)}{9 x^2 \sqrt[4]{x \left(a x^3+b\right)}}","\frac{2}{3} a^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} \left(a x^4+b x\right)^{3/4}}{a x^3+b}\right)+\frac{2}{3} a^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \left(a x^4+b x\right)^{3/4}}{a x^3+b}\right)+\frac{4 \left(a x^4+b x\right)^{3/4}}{9 x^3}",1,"(4*(b + a*x^3 + 3*a*x^3*(1 + (a*x^3)/b)^(1/4)*Hypergeometric2F1[1/4, 1/4, 5/4, -((a*x^3)/b)]))/(9*x^2*(x*(b + a*x^3))^(1/4))","C",1
1351,1,53,97,0.0165628,"\int \frac{b+a x^3}{x^3 \sqrt[4]{b x+a x^4}} \, dx","Integrate[(b + a*x^3)/(x^3*(b*x + a*x^4)^(1/4)),x]","-\frac{4 \left(x \left(a x^3+b\right)\right)^{3/4} \, _2F_1\left(-\frac{3}{4},-\frac{3}{4};\frac{1}{4};-\frac{a x^3}{b}\right)}{9 x^3 \left(\frac{a x^3}{b}+1\right)^{3/4}}","\frac{2}{3} a^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} \left(a x^4+b x\right)^{3/4}}{a x^3+b}\right)+\frac{2}{3} a^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \left(a x^4+b x\right)^{3/4}}{a x^3+b}\right)-\frac{4 \left(a x^4+b x\right)^{3/4}}{9 x^3}",1,"(-4*(x*(b + a*x^3))^(3/4)*Hypergeometric2F1[-3/4, -3/4, 1/4, -((a*x^3)/b)])/(9*x^3*(1 + (a*x^3)/b)^(3/4))","C",1
1352,1,26,97,0.0051416,"\int \frac{1}{x^{13} \sqrt[3]{1+x^6}} \, dx","Integrate[1/(x^13*(1 + x^6)^(1/3)),x]","-\frac{1}{4} \left(x^6+1\right)^{2/3} \, _2F_1\left(\frac{2}{3},3;\frac{5}{3};x^6+1\right)","\frac{1}{27} \log \left(\sqrt[3]{x^6+1}-1\right)-\frac{1}{54} \log \left(\left(x^6+1\right)^{2/3}+\sqrt[3]{x^6+1}+1\right)+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{x^6+1}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{9 \sqrt{3}}+\frac{\left(x^6+1\right)^{2/3} \left(4 x^6-3\right)}{36 x^{12}}",1,"-1/4*((1 + x^6)^(2/3)*Hypergeometric2F1[2/3, 3, 5/3, 1 + x^6])","C",1
1353,0,0,97,0.4027114,"\int \frac{-3+5 x^8}{\left(1+x^8\right) \sqrt[3]{1-x^3+x^8}} \, dx","Integrate[(-3 + 5*x^8)/((1 + x^8)*(1 - x^3 + x^8)^(1/3)),x]","\int \frac{-3+5 x^8}{\left(1+x^8\right) \sqrt[3]{1-x^3+x^8}} \, dx","-\log \left(\sqrt[3]{x^8-x^3+1}+x\right)-\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^8-x^3+1}-x}\right)+\frac{1}{2} \log \left(x^2-\sqrt[3]{x^8-x^3+1} x+\left(x^8-x^3+1\right)^{2/3}\right)",1,"Integrate[(-3 + 5*x^8)/((1 + x^8)*(1 - x^3 + x^8)^(1/3)), x]","F",-1
1354,1,93,97,0.0723065,"\int \frac{\sqrt{x+\sqrt{1+x}}}{1+\sqrt{1+x}} \, dx","Integrate[Sqrt[x + Sqrt[1 + x]]/(1 + Sqrt[1 + x]),x]","\frac{1}{4} \left(2 \sqrt{x+\sqrt{x+1}} \left(2 \sqrt{x+1}-3\right)+8 \tan ^{-1}\left(\frac{-\sqrt{x+1}-3}{2 \sqrt{x+\sqrt{x+1}}}\right)-\tanh ^{-1}\left(\frac{2 \sqrt{x+1}+1}{2 \sqrt{x+\sqrt{x+1}}}\right)\right)","\sqrt{x+1} \sqrt{x+\sqrt{x+1}}-\frac{3}{2} \sqrt{x+\sqrt{x+1}}+\frac{1}{4} \log \left(2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)-4 \tan ^{-1}\left(\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}+1\right)",1,"(2*Sqrt[x + Sqrt[1 + x]]*(-3 + 2*Sqrt[1 + x]) + 8*ArcTan[(-3 - Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])] - ArcTanh[(1 + 2*Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])])/4","A",1
1355,1,304,97,1.4073717,"\int \frac{x+\sqrt{1+x^2}}{1+\sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[(x + Sqrt[1 + x^2])/(1 + Sqrt[x + Sqrt[1 + x^2]]),x]","\frac{1}{12} \left(-\frac{4 \sqrt{x^2+1} \left(\sqrt{x^2+1}+x\right)^{9/2} \left(\left(4 x^2+4 \sqrt{x^2+1} x+2\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\left(x+\sqrt{x^2+1}\right)^2\right)-x^2-\sqrt{x^2+1} x-2\right)}{16 x^6+28 x^4+13 x^2+5 \sqrt{x^2+1} x+16 \sqrt{x^2+1} x^5+20 \sqrt{x^2+1} x^3+1}-4 \left(\sqrt{x^2+1}-2 x\right) \sqrt{\sqrt{x^2+1}+x}-6 \sqrt{x^2+1}+6 \log \left(\sqrt{x^2+1}+1\right)+\frac{12 \sqrt{x^2+1} \left(\sqrt{x^2+1}+x\right) \left(\sqrt{\sqrt{x^2+1}+x}-\tan ^{-1}\left(\sqrt{\sqrt{x^2+1}+x}\right)-\tanh ^{-1}\left(\sqrt{\sqrt{x^2+1}+x}\right)\right)}{x^2+\sqrt{x^2+1} x+1}-6 x-12 \log (x)\right)","\sqrt{x^2+1} \left(\frac{1}{3} \sqrt{\sqrt{x^2+1}+x}-\frac{1}{2}\right)+\frac{1}{3} (x+3) \sqrt{\sqrt{x^2+1}+x}+\frac{1}{2} \log \left(\sqrt{x^2+1}+x\right)-2 \log \left(\sqrt{\sqrt{x^2+1}+x}+1\right)-\frac{x}{2}",1,"(-6*x - 6*Sqrt[1 + x^2] - 4*(-2*x + Sqrt[1 + x^2])*Sqrt[x + Sqrt[1 + x^2]] + (12*Sqrt[1 + x^2]*(x + Sqrt[1 + x^2])*(Sqrt[x + Sqrt[1 + x^2]] - ArcTan[Sqrt[x + Sqrt[1 + x^2]]] - ArcTanh[Sqrt[x + Sqrt[1 + x^2]]]))/(1 + x^2 + x*Sqrt[1 + x^2]) - (4*Sqrt[1 + x^2]*(x + Sqrt[1 + x^2])^(9/2)*(-2 - x^2 - x*Sqrt[1 + x^2] + (2 + 4*x^2 + 4*x*Sqrt[1 + x^2])*Hypergeometric2F1[3/4, 1, 7/4, (x + Sqrt[1 + x^2])^2]))/(1 + 13*x^2 + 28*x^4 + 16*x^6 + 5*x*Sqrt[1 + x^2] + 20*x^3*Sqrt[1 + x^2] + 16*x^5*Sqrt[1 + x^2]) - 12*Log[x] + 6*Log[1 + Sqrt[1 + x^2]])/12","C",1
1356,1,68,98,0.0677273,"\int \frac{x^2}{\left(-2 b+a x^2\right) \left(-b+a x^2\right)^{3/4}} \, dx","Integrate[x^2/((-2*b + a*x^2)*(-b + a*x^2)^(3/4)),x]","-\frac{x^3 \left(1-\frac{a x^2}{b}\right)^{3/4} F_1\left(\frac{3}{2};\frac{3}{4},1;\frac{5}{2};\frac{a x^2}{b},\frac{a x^2}{2 b}\right)}{6 b \left(a x^2-b\right)^{3/4}}","\frac{\tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^2-b}}\right)}{\sqrt{2} a^{3/2} \sqrt[4]{b}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^2-b}}{\sqrt{a} x}\right)}{\sqrt{2} a^{3/2} \sqrt[4]{b}}",1,"-1/6*(x^3*(1 - (a*x^2)/b)^(3/4)*AppellF1[3/2, 3/4, 1, 5/2, (a*x^2)/b, (a*x^2)/(2*b)])/(b*(-b + a*x^2)^(3/4))","C",0
1357,0,0,98,1.7150554,"\int \frac{\left(-2 k-(-1+k) (1+k) x+2 k x^2\right) \left(1-2 k x+k^2 x^2\right)}{\left(\left(1-x^2\right) \left(1-k^2 x^2\right)\right)^{3/4} \left(1-d+(1+3 d) k x-\left(1+3 d k^2\right) x^2+k \left(-1+d k^2\right) x^3\right)} \, dx","Integrate[((-2*k - (-1 + k)*(1 + k)*x + 2*k*x^2)*(1 - 2*k*x + k^2*x^2))/(((1 - x^2)*(1 - k^2*x^2))^(3/4)*(1 - d + (1 + 3*d)*k*x - (1 + 3*d*k^2)*x^2 + k*(-1 + d*k^2)*x^3)),x]","\int \frac{\left(-2 k-(-1+k) (1+k) x+2 k x^2\right) \left(1-2 k x+k^2 x^2\right)}{\left(\left(1-x^2\right) \left(1-k^2 x^2\right)\right)^{3/4} \left(1-d+(1+3 d) k x-\left(1+3 d k^2\right) x^2+k \left(-1+d k^2\right) x^3\right)} \, dx","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{d} k x-\sqrt[4]{d}}{\sqrt[4]{k^2 x^4+\left(-k^2-1\right) x^2+1}}\right)}{d^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{d} k x-\sqrt[4]{d}}{\sqrt[4]{k^2 x^4+\left(-k^2-1\right) x^2+1}}\right)}{d^{3/4}}",1,"Integrate[((-2*k - (-1 + k)*(1 + k)*x + 2*k*x^2)*(1 - 2*k*x + k^2*x^2))/(((1 - x^2)*(1 - k^2*x^2))^(3/4)*(1 - d + (1 + 3*d)*k*x - (1 + 3*d*k^2)*x^2 + k*(-1 + d*k^2)*x^3)), x]","F",-1
1358,1,880,98,3.8612703,"\int \frac{\left(-1+x^2\right) \left(1+x^2\right) \sqrt{1+3 x^2+x^4}}{x^2 \left(1+x+x^2\right)^2} \, dx","Integrate[((-1 + x^2)*(1 + x^2)*Sqrt[1 + 3*x^2 + x^4])/(x^2*(1 + x + x^2)^2),x]","\frac{1}{2} \left(2 \sqrt{x^4+3 x^2+1} \left(\frac{1}{x^2+x+1}+\frac{1}{x}\right)+\frac{3 i \left(i+\sqrt{3}\right) \tan ^{-1}\left(\frac{\left(4-2 i \sqrt{3}\right) x^2-3 i \sqrt{3}+1}{4 \sqrt{1+i \sqrt{3}} \sqrt{x^4+3 x^2+1}}\right)}{2 \sqrt{1+i \sqrt{3}}}-\frac{3 \left(1+i \sqrt{3}\right) \tan ^{-1}\left(\frac{\left(4+2 i \sqrt{3}\right) x^2+3 i \sqrt{3}+1}{4 \sqrt{1-i \sqrt{3}} \sqrt{x^4+3 x^2+1}}\right)}{2 \sqrt{1-i \sqrt{3}}}-2 \tanh ^{-1}\left(\frac{2 x^2+3}{2 \sqrt{x^4+3 x^2+1}}\right)-2 \tanh ^{-1}\left(\frac{3 x^2+2}{2 \sqrt{x^4+3 x^2+1}}\right)-\frac{3 i \sqrt{2} \sqrt{\frac{-2 x^2+\sqrt{5}-3}{-3+\sqrt{5}}} \sqrt{2 x^2+\sqrt{5}+3} F\left(i \sinh ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} x\right)|\frac{7}{2}+\frac{3 \sqrt{5}}{2}\right)}{\sqrt{x^4+3 x^2+1}}+\frac{3 (-1)^{5/6} \sqrt{2} \sqrt{\frac{-2 x^2+\sqrt{5}-3}{-3+\sqrt{5}}} \sqrt{2 x^2+\sqrt{5}+3} \Pi \left(\frac{1}{2} \sqrt[3]{-1} \left(3+\sqrt{5}\right);i \sinh ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} x\right)|\frac{1}{2} \left(7+3 \sqrt{5}\right)\right)}{\left(1+\sqrt[3]{-1}\right) \sqrt{x^4+3 x^2+1}}+\frac{3 i \sqrt{2} \sqrt{\frac{-2 x^2+\sqrt{5}-3}{-3+\sqrt{5}}} \sqrt{2 x^2+\sqrt{5}+3} \Pi \left(\frac{1}{2} \sqrt[3]{-1} \left(3+\sqrt{5}\right);i \sinh ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} x\right)|\frac{1}{2} \left(7+3 \sqrt{5}\right)\right)}{\left(1+\sqrt[3]{-1}\right) \sqrt{x^4+3 x^2+1}}+\frac{3 (-1)^{5/6} \sqrt{2} \sqrt{\frac{-2 x^2+\sqrt{5}-3}{-3+\sqrt{5}}} \sqrt{2 x^2+\sqrt{5}+3} \Pi \left(-\frac{1}{2} (-1)^{2/3} \left(3+\sqrt{5}\right);i \sinh ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} x\right)|\frac{1}{2} \left(7+3 \sqrt{5}\right)\right)}{\left(1+\sqrt[3]{-1}\right) \sqrt{x^4+3 x^2+1}}+\frac{3 i \sqrt{2} \sqrt{\frac{-2 x^2+\sqrt{5}-3}{-3+\sqrt{5}}} \sqrt{2 x^2+\sqrt{5}+3} \Pi \left(-\frac{1}{2} (-1)^{2/3} \left(3+\sqrt{5}\right);i \sinh ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} x\right)|\frac{1}{2} \left(7+3 \sqrt{5}\right)\right)}{\left(1+\sqrt[3]{-1}\right) \sqrt{x^4+3 x^2+1}}\right)","\frac{\sqrt{x^4+3 x^2+1} \left(x^2+2 x+1\right)}{x \left(x^2+x+1\right)}-2 \log \left(x^2+\sqrt{x^4+3 x^2+1}+1\right)-3 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x}{x^2+\sqrt{x^4+3 x^2+1}+x+1}\right)+2 \log (x)",1,"(2*Sqrt[1 + 3*x^2 + x^4]*(x^(-1) + (1 + x + x^2)^(-1)) + (((3*I)/2)*(I + Sqrt[3])*ArcTan[(1 - (3*I)*Sqrt[3] + (4 - (2*I)*Sqrt[3])*x^2)/(4*Sqrt[1 + I*Sqrt[3]]*Sqrt[1 + 3*x^2 + x^4])])/Sqrt[1 + I*Sqrt[3]] - (3*(1 + I*Sqrt[3])*ArcTan[(1 + (3*I)*Sqrt[3] + (4 + (2*I)*Sqrt[3])*x^2)/(4*Sqrt[1 - I*Sqrt[3]]*Sqrt[1 + 3*x^2 + x^4])])/(2*Sqrt[1 - I*Sqrt[3]]) - 2*ArcTanh[(3 + 2*x^2)/(2*Sqrt[1 + 3*x^2 + x^4])] - 2*ArcTanh[(2 + 3*x^2)/(2*Sqrt[1 + 3*x^2 + x^4])] - ((3*I)*Sqrt[2]*Sqrt[(-3 + Sqrt[5] - 2*x^2)/(-3 + Sqrt[5])]*Sqrt[3 + Sqrt[5] + 2*x^2]*EllipticF[I*ArcSinh[Sqrt[2/(3 + Sqrt[5])]*x], 7/2 + (3*Sqrt[5])/2])/Sqrt[1 + 3*x^2 + x^4] + ((3*I)*Sqrt[2]*Sqrt[(-3 + Sqrt[5] - 2*x^2)/(-3 + Sqrt[5])]*Sqrt[3 + Sqrt[5] + 2*x^2]*EllipticPi[((-1)^(1/3)*(3 + Sqrt[5]))/2, I*ArcSinh[Sqrt[2/(3 + Sqrt[5])]*x], (7 + 3*Sqrt[5])/2])/((1 + (-1)^(1/3))*Sqrt[1 + 3*x^2 + x^4]) + (3*(-1)^(5/6)*Sqrt[2]*Sqrt[(-3 + Sqrt[5] - 2*x^2)/(-3 + Sqrt[5])]*Sqrt[3 + Sqrt[5] + 2*x^2]*EllipticPi[((-1)^(1/3)*(3 + Sqrt[5]))/2, I*ArcSinh[Sqrt[2/(3 + Sqrt[5])]*x], (7 + 3*Sqrt[5])/2])/((1 + (-1)^(1/3))*Sqrt[1 + 3*x^2 + x^4]) + ((3*I)*Sqrt[2]*Sqrt[(-3 + Sqrt[5] - 2*x^2)/(-3 + Sqrt[5])]*Sqrt[3 + Sqrt[5] + 2*x^2]*EllipticPi[-1/2*((-1)^(2/3)*(3 + Sqrt[5])), I*ArcSinh[Sqrt[2/(3 + Sqrt[5])]*x], (7 + 3*Sqrt[5])/2])/((1 + (-1)^(1/3))*Sqrt[1 + 3*x^2 + x^4]) + (3*(-1)^(5/6)*Sqrt[2]*Sqrt[(-3 + Sqrt[5] - 2*x^2)/(-3 + Sqrt[5])]*Sqrt[3 + Sqrt[5] + 2*x^2]*EllipticPi[-1/2*((-1)^(2/3)*(3 + Sqrt[5])), I*ArcSinh[Sqrt[2/(3 + Sqrt[5])]*x], (7 + 3*Sqrt[5])/2])/((1 + (-1)^(1/3))*Sqrt[1 + 3*x^2 + x^4]))/2","C",0
1359,1,105,98,0.2532552,"\int \frac{\left(2+x^2\right) \left(-4+x+2 x^2\right) \sqrt{8-7 x^2+2 x^4}}{x^4} \, dx","Integrate[((2 + x^2)*(-4 + x + 2*x^2)*Sqrt[8 - 7*x^2 + 2*x^4])/x^4,x]","\frac{\sinh ^{-1}\left(\frac{4 x^2-7}{\sqrt{15}}\right)-\tanh ^{-1}\left(\frac{16-7 x^2}{4 \sqrt{2} \sqrt{2 x^4-7 x^2+8}}\right)}{4 \sqrt{2}}+\sqrt{2 x^4-7 x^2+8} \left(\frac{8}{3 x^3}-\frac{1}{x^2}+\frac{2 x}{3}-\frac{7}{3 x}+\frac{1}{2}\right)","\frac{\log \left(\sqrt{2} x^2+\sqrt{2 x^4-7 x^2+8}-2 \sqrt{2}\right)}{2 \sqrt{2}}+\frac{\sqrt{2 x^4-7 x^2+8} \left(4 x^4+3 x^3-14 x^2-6 x+16\right)}{6 x^3}-\frac{\log (x)}{2 \sqrt{2}}",1,"(1/2 + 8/(3*x^3) - x^(-2) - 7/(3*x) + (2*x)/3)*Sqrt[8 - 7*x^2 + 2*x^4] + (ArcSinh[(-7 + 4*x^2)/Sqrt[15]] - ArcTanh[(16 - 7*x^2)/(4*Sqrt[2]*Sqrt[8 - 7*x^2 + 2*x^4])])/(4*Sqrt[2])","A",1
1360,1,65,98,0.0754992,"\int x^4 \left(-b+a x^4\right)^{3/4} \, dx","Integrate[x^4*(-b + a*x^4)^(3/4),x]","\frac{x \left(a x^4-b\right)^{3/4} \left(\frac{b \, _2F_1\left(-\frac{3}{4},\frac{1}{4};\frac{5}{4};\frac{a x^4}{b}\right)}{\left(1-\frac{a x^4}{b}\right)^{3/4}}+a x^4-b\right)}{8 a}","-\frac{3 b^2 \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{64 a^{5/4}}-\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{64 a^{5/4}}+\frac{\left(a x^4-b\right)^{3/4} \left(4 a x^5-3 b x\right)}{32 a}",1,"(x*(-b + a*x^4)^(3/4)*(-b + a*x^4 + (b*Hypergeometric2F1[-3/4, 1/4, 5/4, (a*x^4)/b])/(1 - (a*x^4)/b)^(3/4)))/(8*a)","C",1
1361,1,71,98,0.0695618,"\int \frac{\left(-2 b+a x^2\right) \sqrt[4]{b x^2+a x^4}}{x^2} \, dx","Integrate[((-2*b + a*x^2)*(b*x^2 + a*x^4)^(1/4))/x^2,x]","\frac{2 \sqrt[4]{x^2 \left(a x^2+b\right)} \left(6 \left(a x^2+b\right)-\frac{7 a x^2 \, _2F_1\left(-\frac{1}{4},\frac{3}{4};\frac{7}{4};-\frac{a x^2}{b}\right)}{\sqrt[4]{\frac{a x^2}{b}+1}}\right)}{3 x}","\frac{\sqrt[4]{a x^4+b x^2} \left(a x^2+8 b\right)}{2 x}+\frac{7}{4} \sqrt[4]{a} b \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)-\frac{7}{4} \sqrt[4]{a} b \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)",1,"(2*(x^2*(b + a*x^2))^(1/4)*(6*(b + a*x^2) - (7*a*x^2*Hypergeometric2F1[-1/4, 3/4, 7/4, -((a*x^2)/b)])/(1 + (a*x^2)/b)^(1/4)))/(3*x)","C",1
1362,1,69,98,0.0708333,"\int \frac{\left(2 b+a x^2\right) \sqrt[4]{b x^2+a x^4}}{x^2} \, dx","Integrate[((2*b + a*x^2)*(b*x^2 + a*x^4)^(1/4))/x^2,x]","\frac{2 \sqrt[4]{x^2 \left(a x^2+b\right)} \left(\frac{3 a x^2 \, _2F_1\left(-\frac{1}{4},\frac{3}{4};\frac{7}{4};-\frac{a x^2}{b}\right)}{\sqrt[4]{\frac{a x^2}{b}+1}}-2 \left(a x^2+b\right)\right)}{x}","\frac{\sqrt[4]{a x^4+b x^2} \left(a x^2-8 b\right)}{2 x}-\frac{9}{4} \sqrt[4]{a} b \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)+\frac{9}{4} \sqrt[4]{a} b \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)",1,"(2*(x^2*(b + a*x^2))^(1/4)*(-2*(b + a*x^2) + (3*a*x^2*Hypergeometric2F1[-1/4, 3/4, 7/4, -((a*x^2)/b)])/(1 + (a*x^2)/b)^(1/4)))/x","C",1
1363,0,0,98,1.9485561,"\int \frac{\left(1-3 k^2\right) x+2 k^2 x^3}{\sqrt[4]{\left(1-x^2\right) \left(1-k^2 x^2\right)} \left(-1+d+\left(-d+3 k^2\right) x^2-3 k^4 x^4+k^6 x^6\right)} \, dx","Integrate[((1 - 3*k^2)*x + 2*k^2*x^3)/(((1 - x^2)*(1 - k^2*x^2))^(1/4)*(-1 + d + (-d + 3*k^2)*x^2 - 3*k^4*x^4 + k^6*x^6)),x]","\int \frac{\left(1-3 k^2\right) x+2 k^2 x^3}{\sqrt[4]{\left(1-x^2\right) \left(1-k^2 x^2\right)} \left(-1+d+\left(-d+3 k^2\right) x^2-3 k^4 x^4+k^6 x^6\right)} \, dx","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{k^2 x^4+\left(-k^2-1\right) x^2+1}}{k^2 x^2-1}\right)}{d^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{k^2 x^4+\left(-k^2-1\right) x^2+1}}{k^2 x^2-1}\right)}{d^{3/4}}",1,"Integrate[((1 - 3*k^2)*x + 2*k^2*x^3)/(((1 - x^2)*(1 - k^2*x^2))^(1/4)*(-1 + d + (-d + 3*k^2)*x^2 - 3*k^4*x^4 + k^6*x^6)), x]","F",-1
1364,1,519,98,0.9829105,"\int \frac{-b+a x^4}{\sqrt[4]{b+a x^4} \left(b-a x^4+x^8\right)} \, dx","Integrate[(-b + a*x^4)/((b + a*x^4)^(1/4)*(b - a*x^4 + x^8)),x]","-\frac{\left(a-\frac{a^2-2 b}{\sqrt{a^2-4 b}}\right) \tan ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2-4 b}+a^2+2 b}}{\sqrt[4]{a-\sqrt{a^2-4 b}} \sqrt[4]{a x^4+b}}\right)}{2 \left(a-\sqrt{a^2-4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2-4 b}+a^2+2 b}}-\frac{\left(a \sqrt{a^2-4 b}+a^2-2 b\right) \tan ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2-4 b}+a^2+2 b}}{\sqrt[4]{\sqrt{a^2-4 b}+a} \sqrt[4]{a x^4+b}}\right)}{2 \left(\sqrt{a^2-4 b}+a\right)^{3/4} \sqrt{a^2-4 b} \sqrt[4]{a \sqrt{a^2-4 b}+a^2+2 b}}-\frac{\left(a-\frac{a^2-2 b}{\sqrt{a^2-4 b}}\right) \tanh ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2-4 b}+a^2+2 b}}{\sqrt[4]{a-\sqrt{a^2-4 b}} \sqrt[4]{a x^4+b}}\right)}{2 \left(a-\sqrt{a^2-4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2-4 b}+a^2+2 b}}-\frac{\left(a \sqrt{a^2-4 b}+a^2-2 b\right) \tanh ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2-4 b}+a^2+2 b}}{\sqrt[4]{\sqrt{a^2-4 b}+a} \sqrt[4]{a x^4+b}}\right)}{2 \left(\sqrt{a^2-4 b}+a\right)^{3/4} \sqrt{a^2-4 b} \sqrt[4]{a \sqrt{a^2-4 b}+a^2+2 b}}","-\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4 a+2 a^2+b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-2 a \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+2 a \log (x)}{3 \text{$\#$1} a-2 \text{$\#$1}^5}\&\right]",1,"-1/2*((a - (a^2 - 2*b)/Sqrt[a^2 - 4*b])*ArcTan[((a^2 - a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)*x)/((a - Sqrt[a^2 - 4*b])^(1/4)*(b + a*x^4)^(1/4))])/((a - Sqrt[a^2 - 4*b])^(3/4)*(a^2 - a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)) - ((a^2 + a*Sqrt[a^2 - 4*b] - 2*b)*ArcTan[((a^2 + a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)*x)/((a + Sqrt[a^2 - 4*b])^(1/4)*(b + a*x^4)^(1/4))])/(2*(a + Sqrt[a^2 - 4*b])^(3/4)*Sqrt[a^2 - 4*b]*(a^2 + a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)) - ((a - (a^2 - 2*b)/Sqrt[a^2 - 4*b])*ArcTanh[((a^2 - a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)*x)/((a - Sqrt[a^2 - 4*b])^(1/4)*(b + a*x^4)^(1/4))])/(2*(a - Sqrt[a^2 - 4*b])^(3/4)*(a^2 - a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)) - ((a^2 + a*Sqrt[a^2 - 4*b] - 2*b)*ArcTanh[((a^2 + a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)*x)/((a + Sqrt[a^2 - 4*b])^(1/4)*(b + a*x^4)^(1/4))])/(2*(a + Sqrt[a^2 - 4*b])^(3/4)*Sqrt[a^2 - 4*b]*(a^2 + a*Sqrt[a^2 - 4*b] + 2*b)^(1/4))","B",1
1365,1,519,98,0.248123,"\int \frac{-b+a x^4}{\sqrt[4]{b+a x^4} \left(b-a x^4+x^8\right)} \, dx","Integrate[(-b + a*x^4)/((b + a*x^4)^(1/4)*(b - a*x^4 + x^8)),x]","-\frac{\left(a-\frac{a^2-2 b}{\sqrt{a^2-4 b}}\right) \tan ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2-4 b}+a^2+2 b}}{\sqrt[4]{a-\sqrt{a^2-4 b}} \sqrt[4]{a x^4+b}}\right)}{2 \left(a-\sqrt{a^2-4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2-4 b}+a^2+2 b}}-\frac{\left(a \sqrt{a^2-4 b}+a^2-2 b\right) \tan ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2-4 b}+a^2+2 b}}{\sqrt[4]{\sqrt{a^2-4 b}+a} \sqrt[4]{a x^4+b}}\right)}{2 \left(\sqrt{a^2-4 b}+a\right)^{3/4} \sqrt{a^2-4 b} \sqrt[4]{a \sqrt{a^2-4 b}+a^2+2 b}}-\frac{\left(a-\frac{a^2-2 b}{\sqrt{a^2-4 b}}\right) \tanh ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2-4 b}+a^2+2 b}}{\sqrt[4]{a-\sqrt{a^2-4 b}} \sqrt[4]{a x^4+b}}\right)}{2 \left(a-\sqrt{a^2-4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2-4 b}+a^2+2 b}}-\frac{\left(a \sqrt{a^2-4 b}+a^2-2 b\right) \tanh ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2-4 b}+a^2+2 b}}{\sqrt[4]{\sqrt{a^2-4 b}+a} \sqrt[4]{a x^4+b}}\right)}{2 \left(\sqrt{a^2-4 b}+a\right)^{3/4} \sqrt{a^2-4 b} \sqrt[4]{a \sqrt{a^2-4 b}+a^2+2 b}}","-\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4 a+2 a^2+b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-2 a \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+2 a \log (x)}{3 \text{$\#$1} a-2 \text{$\#$1}^5}\&\right]",1,"-1/2*((a - (a^2 - 2*b)/Sqrt[a^2 - 4*b])*ArcTan[((a^2 - a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)*x)/((a - Sqrt[a^2 - 4*b])^(1/4)*(b + a*x^4)^(1/4))])/((a - Sqrt[a^2 - 4*b])^(3/4)*(a^2 - a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)) - ((a^2 + a*Sqrt[a^2 - 4*b] - 2*b)*ArcTan[((a^2 + a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)*x)/((a + Sqrt[a^2 - 4*b])^(1/4)*(b + a*x^4)^(1/4))])/(2*(a + Sqrt[a^2 - 4*b])^(3/4)*Sqrt[a^2 - 4*b]*(a^2 + a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)) - ((a - (a^2 - 2*b)/Sqrt[a^2 - 4*b])*ArcTanh[((a^2 - a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)*x)/((a - Sqrt[a^2 - 4*b])^(1/4)*(b + a*x^4)^(1/4))])/(2*(a - Sqrt[a^2 - 4*b])^(3/4)*(a^2 - a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)) - ((a^2 + a*Sqrt[a^2 - 4*b] - 2*b)*ArcTanh[((a^2 + a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)*x)/((a + Sqrt[a^2 - 4*b])^(1/4)*(b + a*x^4)^(1/4))])/(2*(a + Sqrt[a^2 - 4*b])^(3/4)*Sqrt[a^2 - 4*b]*(a^2 + a*Sqrt[a^2 - 4*b] + 2*b)^(1/4))","B",1
1366,0,0,98,1.0731013,"\int \frac{\left(4+x^5\right) \left(1-x^4-2 x^5+x^8+x^9+x^{10}\right)}{x^2 \left(-1+x^5\right)^{3/4} \left(1+x^4-2 x^5-x^8-x^9+x^{10}\right)} \, dx","Integrate[((4 + x^5)*(1 - x^4 - 2*x^5 + x^8 + x^9 + x^10))/(x^2*(-1 + x^5)^(3/4)*(1 + x^4 - 2*x^5 - x^8 - x^9 + x^10)),x]","\int \frac{\left(4+x^5\right) \left(1-x^4-2 x^5+x^8+x^9+x^{10}\right)}{x^2 \left(-1+x^5\right)^{3/4} \left(1+x^4-2 x^5-x^8-x^9+x^{10}\right)} \, dx","\frac{4 \sqrt[4]{x^5-1}}{x}-2 \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4-1\&,\frac{-\text{$\#$1}^4 \log \left(\sqrt[4]{x^5-1}-\text{$\#$1} x\right)+\text{$\#$1}^4 \log (x)-\log \left(\sqrt[4]{x^5-1}-\text{$\#$1} x\right)+\log (x)}{2 \text{$\#$1}^7-\text{$\#$1}^3}\&\right]",1,"Integrate[((4 + x^5)*(1 - x^4 - 2*x^5 + x^8 + x^9 + x^10))/(x^2*(-1 + x^5)^(3/4)*(1 + x^4 - 2*x^5 - x^8 - x^9 + x^10)), x]","F",-1
1367,0,0,98,0.7644737,"\int \frac{\left(4+x^5\right) \left(1-x^4-2 x^5+x^8+x^9+x^{10}\right)}{x^2 \left(-1+x^5\right)^{3/4} \left(1+x^4-2 x^5-x^8-x^9+x^{10}\right)} \, dx","Integrate[((4 + x^5)*(1 - x^4 - 2*x^5 + x^8 + x^9 + x^10))/(x^2*(-1 + x^5)^(3/4)*(1 + x^4 - 2*x^5 - x^8 - x^9 + x^10)),x]","\int \frac{\left(4+x^5\right) \left(1-x^4-2 x^5+x^8+x^9+x^{10}\right)}{x^2 \left(-1+x^5\right)^{3/4} \left(1+x^4-2 x^5-x^8-x^9+x^{10}\right)} \, dx","\frac{4 \sqrt[4]{x^5-1}}{x}-2 \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4-1\&,\frac{-\text{$\#$1}^4 \log \left(\sqrt[4]{x^5-1}-\text{$\#$1} x\right)+\text{$\#$1}^4 \log (x)-\log \left(\sqrt[4]{x^5-1}-\text{$\#$1} x\right)+\log (x)}{2 \text{$\#$1}^7-\text{$\#$1}^3}\&\right]",1,"Integrate[((4 + x^5)*(1 - x^4 - 2*x^5 + x^8 + x^9 + x^10))/(x^2*(-1 + x^5)^(3/4)*(1 + x^4 - 2*x^5 - x^8 - x^9 + x^10)), x]","F",-1
1368,0,0,98,0.0592772,"\int \frac{1}{\sqrt{a x^2+\sqrt{b+a^2 x^4}}} \, dx","Integrate[1/Sqrt[a*x^2 + Sqrt[b + a^2*x^4]],x]","\int \frac{1}{\sqrt{a x^2+\sqrt{b+a^2 x^4}}} \, dx","\frac{x}{2 \sqrt{\sqrt{a^2 x^4+b}+a x^2}}+\frac{\log \left(\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)}{2 \sqrt{2} \sqrt{a}}",1,"Integrate[1/Sqrt[a*x^2 + Sqrt[b + a^2*x^4]], x]","F",-1
1369,1,99,99,0.0668484,"\int \frac{\left(-3 b+2 a x^2\right) \left(b^2+a^2 x^2\right)^{3/4}}{x} \, dx","Integrate[((-3*b + 2*a*x^2)*(b^2 + a^2*x^2)^(3/4))/x,x]","\frac{2 \left(a^2 x^2+b^2\right)^{3/4} \left(2 a^2 x^2-7 a b+2 b^2\right)}{7 a}-3 b^{5/2} \tan ^{-1}\left(\frac{\sqrt[4]{a^2 x^2+b^2}}{\sqrt{b}}\right)+3 b^{5/2} \tanh ^{-1}\left(\frac{\sqrt[4]{a^2 x^2+b^2}}{\sqrt{b}}\right)","\frac{2 \left(a^2 x^2+b^2\right)^{3/4} \left(2 a^2 x^2-7 a b+2 b^2\right)}{7 a}-3 b^{5/2} \tan ^{-1}\left(\frac{\sqrt[4]{a^2 x^2+b^2}}{\sqrt{b}}\right)+3 b^{5/2} \tanh ^{-1}\left(\frac{\sqrt[4]{a^2 x^2+b^2}}{\sqrt{b}}\right)",1,"(2*(b^2 + a^2*x^2)^(3/4)*(-7*a*b + 2*b^2 + 2*a^2*x^2))/(7*a) - 3*b^(5/2)*ArcTan[(b^2 + a^2*x^2)^(1/4)/Sqrt[b]] + 3*b^(5/2)*ArcTanh[(b^2 + a^2*x^2)^(1/4)/Sqrt[b]]","A",1
1370,1,220,99,0.230102,"\int \frac{-1+x}{\left(-2-2 x+x^2\right) \sqrt{-1+x^3}} \, dx","Integrate[(-1 + x)/((-2 - 2*x + x^2)*Sqrt[-1 + x^3]),x]","-\frac{\sqrt{\frac{1-x}{1+\sqrt[3]{-1}}} \sqrt{x^2+x+1} \left(\left(3+(2+i) \sqrt{3}\right) \Pi \left(\frac{2 \sqrt{3}}{-3 i+(1+2 i) \sqrt{3}};\sin ^{-1}\left(\sqrt{-\frac{\left(i+\sqrt{3}\right) x+2 i}{-3 i+\sqrt{3}}}\right)|\frac{1}{2} \left(1+i \sqrt{3}\right)\right)+\left(3-(2-i) \sqrt{3}\right) \Pi \left(\frac{2 i \sqrt{3}}{3+(2+i) \sqrt{3}};\sin ^{-1}\left(\sqrt{-\frac{\left(i+\sqrt{3}\right) x+2 i}{-3 i+\sqrt{3}}}\right)|\frac{1}{2} \left(1+i \sqrt{3}\right)\right)\right)}{3 \left(\sqrt{3}+i\right) \sqrt{x^3-1}}","\frac{1}{6} \sqrt{3+2 \sqrt{3}} \tan ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} \sqrt{x^3-1}}{x^2+x+1}\right)-\frac{1}{6} \sqrt{2 \sqrt{3}-3} \tanh ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} \sqrt{x^3-1}}{x^2+x+1}\right)",1,"-1/3*(Sqrt[(1 - x)/(1 + (-1)^(1/3))]*Sqrt[1 + x + x^2]*((3 + (2 + I)*Sqrt[3])*EllipticPi[(2*Sqrt[3])/(-3*I + (1 + 2*I)*Sqrt[3]), ArcSin[Sqrt[-((2*I + (I + Sqrt[3])*x)/(-3*I + Sqrt[3]))]], (1 + I*Sqrt[3])/2] + (3 - (2 - I)*Sqrt[3])*EllipticPi[((2*I)*Sqrt[3])/(3 + (2 + I)*Sqrt[3]), ArcSin[Sqrt[-((2*I + (I + Sqrt[3])*x)/(-3*I + Sqrt[3]))]], (1 + I*Sqrt[3])/2]))/((I + Sqrt[3])*Sqrt[-1 + x^3])","C",1
1371,1,290,99,0.8005164,"\int \frac{3-x+x^2}{\left(-2-2 x+x^2\right) \sqrt{-1+x^3}} \, dx","Integrate[(3 - x + x^2)/((-2 - 2*x + x^2)*Sqrt[-1 + x^3]),x]","\frac{\sqrt{\frac{1-x}{1+\sqrt[3]{-1}}} \left(\sqrt{x^2+x+1} \left(\left((9+6 i)+(4-i) \sqrt{3}\right) \Pi \left(\frac{2 \sqrt{3}}{-3 i+(1+2 i) \sqrt{3}};\sin ^{-1}\left(\sqrt{\frac{1-(-1)^{2/3} x}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)-\left((-9+6 i)+(4+i) \sqrt{3}\right) \Pi \left(\frac{2 i \sqrt{3}}{3+(2+i) \sqrt{3}};\sin ^{-1}\left(\sqrt{\frac{1-(-1)^{2/3} x}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)\right)+\frac{6 \sqrt{\frac{(-1)^{2/3} x+\sqrt[3]{-1}}{1+\sqrt[3]{-1}}} \left(\left(\sqrt{3}+i\right) x+2 i\right) F\left(\sin ^{-1}\left(\sqrt{\frac{1-(-1)^{2/3} x}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{\sqrt{\frac{1-(-1)^{2/3} x}{1+\sqrt[3]{-1}}}}\right)}{3 \left(\sqrt{3}+i\right) \sqrt{x^3-1}}","-\frac{1}{6} \sqrt{15+14 \sqrt{3}} \tan ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} \sqrt{x^3-1}}{x^2+x+1}\right)-\frac{1}{6} \sqrt{14 \sqrt{3}-15} \tanh ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} \sqrt{x^3-1}}{x^2+x+1}\right)",1,"(Sqrt[(1 - x)/(1 + (-1)^(1/3))]*((6*Sqrt[((-1)^(1/3) + (-1)^(2/3)*x)/(1 + (-1)^(1/3))]*(2*I + (I + Sqrt[3])*x)*EllipticF[ArcSin[Sqrt[(1 - (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)])/Sqrt[(1 - (-1)^(2/3)*x)/(1 + (-1)^(1/3))] + Sqrt[1 + x + x^2]*(((9 + 6*I) + (4 - I)*Sqrt[3])*EllipticPi[(2*Sqrt[3])/(-3*I + (1 + 2*I)*Sqrt[3]), ArcSin[Sqrt[(1 - (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)] - ((-9 + 6*I) + (4 + I)*Sqrt[3])*EllipticPi[((2*I)*Sqrt[3])/(3 + (2 + I)*Sqrt[3]), ArcSin[Sqrt[(1 - (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)])))/(3*(I + Sqrt[3])*Sqrt[-1 + x^3])","C",0
1372,1,291,99,0.7314531,"\int \frac{2 x+x^2}{\left(-2-2 x+x^2\right) \sqrt{-1+x^3}} \, dx","Integrate[(2*x + x^2)/((-2 - 2*x + x^2)*Sqrt[-1 + x^3]),x]","\frac{2 \sqrt{\frac{1-x}{1+\sqrt[3]{-1}}} \left(\frac{3 \sqrt{\frac{(-1)^{2/3} x+\sqrt[3]{-1}}{1+\sqrt[3]{-1}}} \left(\left(\sqrt{3}+i\right) x+2 i\right) F\left(\sin ^{-1}\left(\sqrt{\frac{1-(-1)^{2/3} x}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{\sqrt{\frac{1-(-1)^{2/3} x}{1+\sqrt[3]{-1}}}}-\sqrt{x^2+x+1} \left(\left((1+2 i) \sqrt{3}-3 i\right) \Pi \left(\frac{2 \sqrt{3}}{-3 i+(1+2 i) \sqrt{3}};\sin ^{-1}\left(\sqrt{\frac{1-(-1)^{2/3} x}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)+i \left(3+(2+i) \sqrt{3}\right) \Pi \left(\frac{2 i \sqrt{3}}{3+(2+i) \sqrt{3}};\sin ^{-1}\left(\sqrt{\frac{1-(-1)^{2/3} x}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)\right)\right)}{3 \left(\sqrt{3}+i\right) \sqrt{x^3-1}}","\frac{1}{3} \sqrt{2 \sqrt{3}-3} \tan ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} \sqrt{x^3-1}}{x^2+x+1}\right)-\frac{1}{3} \sqrt{3+2 \sqrt{3}} \tanh ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} \sqrt{x^3-1}}{x^2+x+1}\right)",1,"(2*Sqrt[(1 - x)/(1 + (-1)^(1/3))]*((3*Sqrt[((-1)^(1/3) + (-1)^(2/3)*x)/(1 + (-1)^(1/3))]*(2*I + (I + Sqrt[3])*x)*EllipticF[ArcSin[Sqrt[(1 - (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)])/Sqrt[(1 - (-1)^(2/3)*x)/(1 + (-1)^(1/3))] - Sqrt[1 + x + x^2]*((-3*I + (1 + 2*I)*Sqrt[3])*EllipticPi[(2*Sqrt[3])/(-3*I + (1 + 2*I)*Sqrt[3]), ArcSin[Sqrt[(1 - (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)] + I*(3 + (2 + I)*Sqrt[3])*EllipticPi[((2*I)*Sqrt[3])/(3 + (2 + I)*Sqrt[3]), ArcSin[Sqrt[(1 - (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)])))/(3*(I + Sqrt[3])*Sqrt[-1 + x^3])","C",0
1373,1,38,99,0.0094956,"\int \frac{\sqrt[3]{-1+x^3} \left(1+x^3\right)}{x^7} \, dx","Integrate[((-1 + x^3)^(1/3)*(1 + x^3))/x^7,x]","\frac{\left(x^3-1\right)^{4/3} \left(2 x^6 \, _2F_1\left(\frac{4}{3},2;\frac{7}{3};1-x^3\right)+1\right)}{6 x^6}","\frac{4}{27} \log \left(\sqrt[3]{x^3-1}+1\right)-\frac{2}{27} \log \left(\left(x^3-1\right)^{2/3}-\sqrt[3]{x^3-1}+1\right)-\frac{4 \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{x^3-1}}{\sqrt{3}}\right)}{9 \sqrt{3}}+\frac{\sqrt[3]{x^3-1} \left(-5 x^3-3\right)}{18 x^6}",1,"((-1 + x^3)^(4/3)*(1 + 2*x^6*Hypergeometric2F1[4/3, 2, 7/3, 1 - x^3]))/(6*x^6)","C",1
1374,1,38,99,0.0088985,"\int \frac{\sqrt[3]{-1+x^3} \left(-1+2 x^3\right)}{x^7} \, dx","Integrate[((-1 + x^3)^(1/3)*(-1 + 2*x^3))/x^7,x]","\frac{\left(x^3-1\right)^{4/3} \left(5 x^6 \, _2F_1\left(\frac{4}{3},2;\frac{7}{3};1-x^3\right)-2\right)}{12 x^6}","\frac{5}{27} \log \left(\sqrt[3]{x^3-1}+1\right)-\frac{5}{54} \log \left(\left(x^3-1\right)^{2/3}-\sqrt[3]{x^3-1}+1\right)-\frac{5 \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{x^3-1}}{\sqrt{3}}\right)}{9 \sqrt{3}}+\frac{\sqrt[3]{x^3-1} \left(3-13 x^3\right)}{18 x^6}",1,"((-1 + x^3)^(4/3)*(-2 + 5*x^6*Hypergeometric2F1[4/3, 2, 7/3, 1 - x^3]))/(12*x^6)","C",1
1375,0,0,99,4.2447316,"\int \frac{\left(a^2-2 a x+x^2\right) \left(-2 a b x+(3 a-b) x^2\right)}{\left(x^2 (-a+x) (-b+x)\right)^{3/4} \left(a^3 d-3 a^2 d x+(-b+3 a d) x^2+(1-d) x^3\right)} \, dx","Integrate[((a^2 - 2*a*x + x^2)*(-2*a*b*x + (3*a - b)*x^2))/((x^2*(-a + x)*(-b + x))^(3/4)*(a^3*d - 3*a^2*d*x + (-b + 3*a*d)*x^2 + (1 - d)*x^3)),x]","\int \frac{\left(a^2-2 a x+x^2\right) \left(-2 a b x+(3 a-b) x^2\right)}{\left(x^2 (-a+x) (-b+x)\right)^{3/4} \left(a^3 d-3 a^2 d x+(-b+3 a d) x^2+(1-d) x^3\right)} \, dx","\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \left(x^3 (-a-b)+a b x^2+x^4\right)^{3/4}}{x^2 (x-b)}\right)}{d^{3/4}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \left(x^3 (-a-b)+a b x^2+x^4\right)^{3/4}}{x^2 (x-b)}\right)}{d^{3/4}}",1,"Integrate[((a^2 - 2*a*x + x^2)*(-2*a*b*x + (3*a - b)*x^2))/((x^2*(-a + x)*(-b + x))^(3/4)*(a^3*d - 3*a^2*d*x + (-b + 3*a*d)*x^2 + (1 - d)*x^3)), x]","F",-1
1376,1,11770,99,6.7182084,"\int \frac{1+x^2}{\sqrt{\frac{-2-x+2 x^2}{-1+x+x^2}} \left(1-x^2+x^4\right)} \, dx","Integrate[(1 + x^2)/(Sqrt[(-2 - x + 2*x^2)/(-1 + x + x^2)]*(1 - x^2 + x^4)),x]","\text{Result too large to show}","\sqrt{\frac{1}{5}-\frac{3 i}{5}} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{2 x^2-x-2}{x^2+x-1}}}{\sqrt{-1-3 i}}\right)+\sqrt{\frac{1}{5}+\frac{3 i}{5}} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{2 x^2-x-2}{x^2+x-1}}}{\sqrt{-1+3 i}}\right)",1,"Result too large to show","C",0
1377,1,361,99,2.9603066,"\int \frac{-2 b+a x^4}{x^4 \left(b+a x^4\right) \sqrt[4]{-b x^2+a x^4}} \, dx","Integrate[(-2*b + a*x^4)/(x^4*(b + a*x^4)*(-(b*x^2) + a*x^4)^(1/4)),x]","\frac{\sqrt{x} \left(\frac{8 \left(b-a x^2\right) \left(4 a x^2+3 b\right)}{21 b^2 x^{7/2}}+\frac{3 (-a)^{7/8} \sqrt{x} \sqrt[4]{\frac{b}{x^2}-a} \left(\sqrt[4]{\sqrt{-a}+\sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{-a} \sqrt[4]{\sqrt{-a}-\sqrt{b}}}\right)+\sqrt[4]{\sqrt{-a}-\sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{-a} \sqrt[4]{\sqrt{-a}+\sqrt{b}}}\right)-\sqrt[4]{\sqrt{-a}+\sqrt{b}} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{-a} \sqrt[4]{\sqrt{-a}-\sqrt{b}}}\right)-\sqrt[4]{\sqrt{-a}-\sqrt{b}} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{-a} \sqrt[4]{\sqrt{-a}+\sqrt{b}}}\right)\right)}{b \sqrt[4]{\sqrt{-a}-\sqrt{b}} \sqrt[4]{\sqrt{-a}+\sqrt{b}}}\right)}{2 \sqrt[4]{a x^4-b x^2}}","-\frac{3 a \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{\log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{4 b}-\frac{4 \left(a x^4-b x^2\right)^{3/4} \left(4 a x^2+3 b\right)}{21 b^2 x^5}",1,"(Sqrt[x]*((8*(b - a*x^2)*(3*b + 4*a*x^2))/(21*b^2*x^(7/2)) + (3*(-a)^(7/8)*(-a + b/x^2)^(1/4)*Sqrt[x]*((Sqrt[-a] + Sqrt[b])^(1/4)*ArcTan[(-a + b/x^2)^(1/4)/((-a)^(1/8)*(Sqrt[-a] - Sqrt[b])^(1/4))] + (Sqrt[-a] - Sqrt[b])^(1/4)*ArcTan[(-a + b/x^2)^(1/4)/((-a)^(1/8)*(Sqrt[-a] + Sqrt[b])^(1/4))] - (Sqrt[-a] + Sqrt[b])^(1/4)*ArcTanh[(-a + b/x^2)^(1/4)/((-a)^(1/8)*(Sqrt[-a] - Sqrt[b])^(1/4))] - (Sqrt[-a] - Sqrt[b])^(1/4)*ArcTanh[(-a + b/x^2)^(1/4)/((-a)^(1/8)*(Sqrt[-a] + Sqrt[b])^(1/4))]))/((Sqrt[-a] - Sqrt[b])^(1/4)*(Sqrt[-a] + Sqrt[b])^(1/4)*b)))/(2*(-(b*x^2) + a*x^4)^(1/4))","B",1
1378,1,361,99,1.4814473,"\int \frac{-2 b+a x^4}{x^4 \left(b+a x^4\right) \sqrt[4]{-b x^2+a x^4}} \, dx","Integrate[(-2*b + a*x^4)/(x^4*(b + a*x^4)*(-(b*x^2) + a*x^4)^(1/4)),x]","\frac{\sqrt{x} \left(\frac{8 \left(b-a x^2\right) \left(4 a x^2+3 b\right)}{21 b^2 x^{7/2}}+\frac{3 (-a)^{7/8} \sqrt{x} \sqrt[4]{\frac{b}{x^2}-a} \left(\sqrt[4]{\sqrt{-a}+\sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{-a} \sqrt[4]{\sqrt{-a}-\sqrt{b}}}\right)+\sqrt[4]{\sqrt{-a}-\sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{-a} \sqrt[4]{\sqrt{-a}+\sqrt{b}}}\right)-\sqrt[4]{\sqrt{-a}+\sqrt{b}} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{-a} \sqrt[4]{\sqrt{-a}-\sqrt{b}}}\right)-\sqrt[4]{\sqrt{-a}-\sqrt{b}} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{-a} \sqrt[4]{\sqrt{-a}+\sqrt{b}}}\right)\right)}{b \sqrt[4]{\sqrt{-a}-\sqrt{b}} \sqrt[4]{\sqrt{-a}+\sqrt{b}}}\right)}{2 \sqrt[4]{a x^4-b x^2}}","-\frac{3 a \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{\log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{4 b}-\frac{4 \left(a x^4-b x^2\right)^{3/4} \left(4 a x^2+3 b\right)}{21 b^2 x^5}",1,"(Sqrt[x]*((8*(b - a*x^2)*(3*b + 4*a*x^2))/(21*b^2*x^(7/2)) + (3*(-a)^(7/8)*(-a + b/x^2)^(1/4)*Sqrt[x]*((Sqrt[-a] + Sqrt[b])^(1/4)*ArcTan[(-a + b/x^2)^(1/4)/((-a)^(1/8)*(Sqrt[-a] - Sqrt[b])^(1/4))] + (Sqrt[-a] - Sqrt[b])^(1/4)*ArcTan[(-a + b/x^2)^(1/4)/((-a)^(1/8)*(Sqrt[-a] + Sqrt[b])^(1/4))] - (Sqrt[-a] + Sqrt[b])^(1/4)*ArcTanh[(-a + b/x^2)^(1/4)/((-a)^(1/8)*(Sqrt[-a] - Sqrt[b])^(1/4))] - (Sqrt[-a] - Sqrt[b])^(1/4)*ArcTanh[(-a + b/x^2)^(1/4)/((-a)^(1/8)*(Sqrt[-a] + Sqrt[b])^(1/4))]))/((Sqrt[-a] - Sqrt[b])^(1/4)*(Sqrt[-a] + Sqrt[b])^(1/4)*b)))/(2*(-(b*x^2) + a*x^4)^(1/4))","B",1
1379,1,47,99,0.014363,"\int \sqrt[4]{b x^3+a x^4} \, dx","Integrate[(b*x^3 + a*x^4)^(1/4),x]","\frac{4 x \sqrt[4]{x^3 (a x+b)} \, _2F_1\left(-\frac{1}{4},\frac{7}{4};\frac{11}{4};-\frac{a x}{b}\right)}{7 \sqrt[4]{\frac{a x}{b}+1}}","\frac{3 b^2 \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)}{16 a^{7/4}}-\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)}{16 a^{7/4}}+\frac{(4 a x+b) \sqrt[4]{a x^4+b x^3}}{8 a}",1,"(4*x*(x^3*(b + a*x))^(1/4)*Hypergeometric2F1[-1/4, 7/4, 11/4, -((a*x)/b)])/(7*(1 + (a*x)/b)^(1/4))","C",1
1380,1,28,99,0.0047446,"\int \frac{1}{x^{13} \sqrt[3]{-1+x^6}} \, dx","Integrate[1/(x^13*(-1 + x^6)^(1/3)),x]","\frac{1}{4} \left(x^6-1\right)^{2/3} \, _2F_1\left(\frac{2}{3},3;\frac{5}{3};1-x^6\right)","-\frac{1}{27} \log \left(\sqrt[3]{x^6-1}+1\right)+\frac{1}{54} \log \left(\left(x^6-1\right)^{2/3}-\sqrt[3]{x^6-1}+1\right)-\frac{\tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{x^6-1}}{\sqrt{3}}\right)}{9 \sqrt{3}}+\frac{\left(x^6-1\right)^{2/3} \left(4 x^6+3\right)}{36 x^{12}}",1,"((-1 + x^6)^(2/3)*Hypergeometric2F1[2/3, 3, 5/3, 1 - x^6])/4","C",1
1381,1,503,99,0.8886333,"\int \frac{b+2 a x^4}{\sqrt[4]{b+a x^4} \left(-2 b-a x^4+x^8\right)} \, dx","Integrate[(b + 2*a*x^4)/((b + a*x^4)^(1/4)*(-2*b - a*x^4 + x^8)),x]","-\frac{\left(a-\frac{a^2+b}{\sqrt{a^2+8 b}}\right) \tan ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+8 b}+a^2+2 b}}{\sqrt[4]{a-\sqrt{a^2+8 b}} \sqrt[4]{a x^4+b}}\right)}{\left(a-\sqrt{a^2+8 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+8 b}+a^2+2 b}}-\frac{\left(a \sqrt{a^2+8 b}+a^2+b\right) \tan ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+8 b}+a^2+2 b}}{\sqrt[4]{\sqrt{a^2+8 b}+a} \sqrt[4]{a x^4+b}}\right)}{\sqrt{a^2+8 b} \left(\sqrt{a^2+8 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+8 b}+a^2+2 b}}-\frac{\left(a-\frac{a^2+b}{\sqrt{a^2+8 b}}\right) \tanh ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+8 b}+a^2+2 b}}{\sqrt[4]{a-\sqrt{a^2+8 b}} \sqrt[4]{a x^4+b}}\right)}{\left(a-\sqrt{a^2+8 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+8 b}+a^2+2 b}}-\frac{\left(a \sqrt{a^2+8 b}+a^2+b\right) \tanh ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+8 b}+a^2+2 b}}{\sqrt[4]{\sqrt{a^2+8 b}+a} \sqrt[4]{a x^4+b}}\right)}{\sqrt{a^2+8 b} \left(\sqrt{a^2+8 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+8 b}+a^2+2 b}}","-\frac{1}{4} \text{RootSum}\left[2 \text{$\#$1}^8-3 \text{$\#$1}^4 a+a^2-b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))+a \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)-a \log (x)}{3 \text{$\#$1} a-4 \text{$\#$1}^5}\&\right]",1,"-(((a - (a^2 + b)/Sqrt[a^2 + 8*b])*ArcTan[((a^2 + 2*b - a*Sqrt[a^2 + 8*b])^(1/4)*x)/((a - Sqrt[a^2 + 8*b])^(1/4)*(b + a*x^4)^(1/4))])/((a - Sqrt[a^2 + 8*b])^(3/4)*(a^2 + 2*b - a*Sqrt[a^2 + 8*b])^(1/4))) - ((a^2 + b + a*Sqrt[a^2 + 8*b])*ArcTan[((a^2 + 2*b + a*Sqrt[a^2 + 8*b])^(1/4)*x)/((a + Sqrt[a^2 + 8*b])^(1/4)*(b + a*x^4)^(1/4))])/(Sqrt[a^2 + 8*b]*(a + Sqrt[a^2 + 8*b])^(3/4)*(a^2 + 2*b + a*Sqrt[a^2 + 8*b])^(1/4)) - ((a - (a^2 + b)/Sqrt[a^2 + 8*b])*ArcTanh[((a^2 + 2*b - a*Sqrt[a^2 + 8*b])^(1/4)*x)/((a - Sqrt[a^2 + 8*b])^(1/4)*(b + a*x^4)^(1/4))])/((a - Sqrt[a^2 + 8*b])^(3/4)*(a^2 + 2*b - a*Sqrt[a^2 + 8*b])^(1/4)) - ((a^2 + b + a*Sqrt[a^2 + 8*b])*ArcTanh[((a^2 + 2*b + a*Sqrt[a^2 + 8*b])^(1/4)*x)/((a + Sqrt[a^2 + 8*b])^(1/4)*(b + a*x^4)^(1/4))])/(Sqrt[a^2 + 8*b]*(a + Sqrt[a^2 + 8*b])^(3/4)*(a^2 + 2*b + a*Sqrt[a^2 + 8*b])^(1/4))","B",1
1382,1,782,99,3.0664133,"\int \frac{2 b+a x^4}{\sqrt[4]{b x^2+a x^4} \left(-b-a x^4+2 x^8\right)} \, dx","Integrate[(2*b + a*x^4)/((b*x^2 + a*x^4)^(1/4)*(-b - a*x^4 + 2*x^8)),x]","\frac{x \sqrt[4]{a+\frac{b}{x^2}} \left(-\left(a^2 (2 a+b) \text{RootSum}\left[\text{$\#$1}^4-4 \text{$\#$1}^3 a+6 \text{$\#$1}^2 a^2+\text{$\#$1}^2 a b-4 \text{$\#$1} a^3-2 \text{$\#$1} a^2 b+a^4+a^3 b-2 b^3\&,\frac{\frac{\log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{a+\frac{b}{x^2}}\right)}{\sqrt[4]{\text{$\#$1}}}-\frac{\log \left(\sqrt[4]{\text{$\#$1}}+\sqrt[4]{a+\frac{b}{x^2}}\right)}{\sqrt[4]{\text{$\#$1}}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\text{$\#$1}}}\right)}{\sqrt[4]{\text{$\#$1}}}}{2 \text{$\#$1}^3-6 \text{$\#$1}^2 a+6 \text{$\#$1} a^2+\text{$\#$1} a b-2 a^3-a^2 b}\&\right]\right)+a (6 a+b) \text{RootSum}\left[\text{$\#$1}^4-4 \text{$\#$1}^3 a+6 \text{$\#$1}^2 a^2+\text{$\#$1}^2 a b-4 \text{$\#$1} a^3-2 \text{$\#$1} a^2 b+a^4+a^3 b-2 b^3\&,\frac{\text{$\#$1}^{3/4} \log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{a+\frac{b}{x^2}}\right)-\text{$\#$1}^{3/4} \log \left(\sqrt[4]{\text{$\#$1}}+\sqrt[4]{a+\frac{b}{x^2}}\right)+2 \text{$\#$1}^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\text{$\#$1}}}\right)}{2 \text{$\#$1}^3-6 \text{$\#$1}^2 a+6 \text{$\#$1} a^2+\text{$\#$1} a b-2 a^3-a^2 b}\&\right]-6 a \text{RootSum}\left[\text{$\#$1}^4-4 \text{$\#$1}^3 a+6 \text{$\#$1}^2 a^2+\text{$\#$1}^2 a b-4 \text{$\#$1} a^3-2 \text{$\#$1} a^2 b+a^4+a^3 b-2 b^3\&,\frac{\text{$\#$1}^{7/4} \log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{a+\frac{b}{x^2}}\right)-\text{$\#$1}^{7/4} \log \left(\sqrt[4]{\text{$\#$1}}+\sqrt[4]{a+\frac{b}{x^2}}\right)+2 \text{$\#$1}^{7/4} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\text{$\#$1}}}\right)}{2 \text{$\#$1}^3-6 \text{$\#$1}^2 a+6 \text{$\#$1} a^2+\text{$\#$1} a b-2 a^3-a^2 b}\&\right]+2 \text{RootSum}\left[\text{$\#$1}^4-4 \text{$\#$1}^3 a+6 \text{$\#$1}^2 a^2+\text{$\#$1}^2 a b-4 \text{$\#$1} a^3-2 \text{$\#$1} a^2 b+a^4+a^3 b-2 b^3\&,\frac{\text{$\#$1}^{11/4} \log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{a+\frac{b}{x^2}}\right)-\text{$\#$1}^{11/4} \log \left(\sqrt[4]{\text{$\#$1}}+\sqrt[4]{a+\frac{b}{x^2}}\right)+2 \text{$\#$1}^{11/4} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\text{$\#$1}}}\right)}{2 \text{$\#$1}^3-6 \text{$\#$1}^2 a+6 \text{$\#$1} a^2+\text{$\#$1} a b-2 a^3-a^2 b}\&\right]\right)}{4 \sqrt[4]{x^2 \left(a x^2+b\right)}}","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^{16}-4 \text{$\#$1}^{12} a+6 \text{$\#$1}^8 a^2+\text{$\#$1}^8 a b-4 \text{$\#$1}^4 a^3-2 \text{$\#$1}^4 a^2 b+a^4+a^3 b-2 b^3\&,\frac{\log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]",1,"((a + b/x^2)^(1/4)*x*(-(a^2*(2*a + b)*RootSum[a^4 + a^3*b - 2*b^3 - 4*a^3*#1 - 2*a^2*b*#1 + 6*a^2*#1^2 + a*b*#1^2 - 4*a*#1^3 + #1^4 & , ((2*ArcTan[(a + b/x^2)^(1/4)/#1^(1/4)])/#1^(1/4) + Log[-(a + b/x^2)^(1/4) + #1^(1/4)]/#1^(1/4) - Log[(a + b/x^2)^(1/4) + #1^(1/4)]/#1^(1/4))/(-2*a^3 - a^2*b + 6*a^2*#1 + a*b*#1 - 6*a*#1^2 + 2*#1^3) & ]) + a*(6*a + b)*RootSum[a^4 + a^3*b - 2*b^3 - 4*a^3*#1 - 2*a^2*b*#1 + 6*a^2*#1^2 + a*b*#1^2 - 4*a*#1^3 + #1^4 & , (2*ArcTan[(a + b/x^2)^(1/4)/#1^(1/4)]*#1^(3/4) + Log[-(a + b/x^2)^(1/4) + #1^(1/4)]*#1^(3/4) - Log[(a + b/x^2)^(1/4) + #1^(1/4)]*#1^(3/4))/(-2*a^3 - a^2*b + 6*a^2*#1 + a*b*#1 - 6*a*#1^2 + 2*#1^3) & ] - 6*a*RootSum[a^4 + a^3*b - 2*b^3 - 4*a^3*#1 - 2*a^2*b*#1 + 6*a^2*#1^2 + a*b*#1^2 - 4*a*#1^3 + #1^4 & , (2*ArcTan[(a + b/x^2)^(1/4)/#1^(1/4)]*#1^(7/4) + Log[-(a + b/x^2)^(1/4) + #1^(1/4)]*#1^(7/4) - Log[(a + b/x^2)^(1/4) + #1^(1/4)]*#1^(7/4))/(-2*a^3 - a^2*b + 6*a^2*#1 + a*b*#1 - 6*a*#1^2 + 2*#1^3) & ] + 2*RootSum[a^4 + a^3*b - 2*b^3 - 4*a^3*#1 - 2*a^2*b*#1 + 6*a^2*#1^2 + a*b*#1^2 - 4*a*#1^3 + #1^4 & , (2*ArcTan[(a + b/x^2)^(1/4)/#1^(1/4)]*#1^(11/4) + Log[-(a + b/x^2)^(1/4) + #1^(1/4)]*#1^(11/4) - Log[(a + b/x^2)^(1/4) + #1^(1/4)]*#1^(11/4))/(-2*a^3 - a^2*b + 6*a^2*#1 + a*b*#1 - 6*a*#1^2 + 2*#1^3) & ]))/(4*(x^2*(b + a*x^2))^(1/4))","B",1
1383,1,782,99,1.5374185,"\int \frac{2 b+a x^4}{\sqrt[4]{b x^2+a x^4} \left(-b-a x^4+2 x^8\right)} \, dx","Integrate[(2*b + a*x^4)/((b*x^2 + a*x^4)^(1/4)*(-b - a*x^4 + 2*x^8)),x]","\frac{x \sqrt[4]{a+\frac{b}{x^2}} \left(-\left(a^2 (2 a+b) \text{RootSum}\left[\text{$\#$1}^4-4 \text{$\#$1}^3 a+6 \text{$\#$1}^2 a^2+\text{$\#$1}^2 a b-4 \text{$\#$1} a^3-2 \text{$\#$1} a^2 b+a^4+a^3 b-2 b^3\&,\frac{\frac{\log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{a+\frac{b}{x^2}}\right)}{\sqrt[4]{\text{$\#$1}}}-\frac{\log \left(\sqrt[4]{\text{$\#$1}}+\sqrt[4]{a+\frac{b}{x^2}}\right)}{\sqrt[4]{\text{$\#$1}}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\text{$\#$1}}}\right)}{\sqrt[4]{\text{$\#$1}}}}{2 \text{$\#$1}^3-6 \text{$\#$1}^2 a+6 \text{$\#$1} a^2+\text{$\#$1} a b-2 a^3-a^2 b}\&\right]\right)+a (6 a+b) \text{RootSum}\left[\text{$\#$1}^4-4 \text{$\#$1}^3 a+6 \text{$\#$1}^2 a^2+\text{$\#$1}^2 a b-4 \text{$\#$1} a^3-2 \text{$\#$1} a^2 b+a^4+a^3 b-2 b^3\&,\frac{\text{$\#$1}^{3/4} \log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{a+\frac{b}{x^2}}\right)-\text{$\#$1}^{3/4} \log \left(\sqrt[4]{\text{$\#$1}}+\sqrt[4]{a+\frac{b}{x^2}}\right)+2 \text{$\#$1}^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\text{$\#$1}}}\right)}{2 \text{$\#$1}^3-6 \text{$\#$1}^2 a+6 \text{$\#$1} a^2+\text{$\#$1} a b-2 a^3-a^2 b}\&\right]-6 a \text{RootSum}\left[\text{$\#$1}^4-4 \text{$\#$1}^3 a+6 \text{$\#$1}^2 a^2+\text{$\#$1}^2 a b-4 \text{$\#$1} a^3-2 \text{$\#$1} a^2 b+a^4+a^3 b-2 b^3\&,\frac{\text{$\#$1}^{7/4} \log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{a+\frac{b}{x^2}}\right)-\text{$\#$1}^{7/4} \log \left(\sqrt[4]{\text{$\#$1}}+\sqrt[4]{a+\frac{b}{x^2}}\right)+2 \text{$\#$1}^{7/4} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\text{$\#$1}}}\right)}{2 \text{$\#$1}^3-6 \text{$\#$1}^2 a+6 \text{$\#$1} a^2+\text{$\#$1} a b-2 a^3-a^2 b}\&\right]+2 \text{RootSum}\left[\text{$\#$1}^4-4 \text{$\#$1}^3 a+6 \text{$\#$1}^2 a^2+\text{$\#$1}^2 a b-4 \text{$\#$1} a^3-2 \text{$\#$1} a^2 b+a^4+a^3 b-2 b^3\&,\frac{\text{$\#$1}^{11/4} \log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{a+\frac{b}{x^2}}\right)-\text{$\#$1}^{11/4} \log \left(\sqrt[4]{\text{$\#$1}}+\sqrt[4]{a+\frac{b}{x^2}}\right)+2 \text{$\#$1}^{11/4} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\text{$\#$1}}}\right)}{2 \text{$\#$1}^3-6 \text{$\#$1}^2 a+6 \text{$\#$1} a^2+\text{$\#$1} a b-2 a^3-a^2 b}\&\right]\right)}{4 \sqrt[4]{x^2 \left(a x^2+b\right)}}","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^{16}-4 \text{$\#$1}^{12} a+6 \text{$\#$1}^8 a^2+\text{$\#$1}^8 a b-4 \text{$\#$1}^4 a^3-2 \text{$\#$1}^4 a^2 b+a^4+a^3 b-2 b^3\&,\frac{\log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]",1,"((a + b/x^2)^(1/4)*x*(-(a^2*(2*a + b)*RootSum[a^4 + a^3*b - 2*b^3 - 4*a^3*#1 - 2*a^2*b*#1 + 6*a^2*#1^2 + a*b*#1^2 - 4*a*#1^3 + #1^4 & , ((2*ArcTan[(a + b/x^2)^(1/4)/#1^(1/4)])/#1^(1/4) + Log[-(a + b/x^2)^(1/4) + #1^(1/4)]/#1^(1/4) - Log[(a + b/x^2)^(1/4) + #1^(1/4)]/#1^(1/4))/(-2*a^3 - a^2*b + 6*a^2*#1 + a*b*#1 - 6*a*#1^2 + 2*#1^3) & ]) + a*(6*a + b)*RootSum[a^4 + a^3*b - 2*b^3 - 4*a^3*#1 - 2*a^2*b*#1 + 6*a^2*#1^2 + a*b*#1^2 - 4*a*#1^3 + #1^4 & , (2*ArcTan[(a + b/x^2)^(1/4)/#1^(1/4)]*#1^(3/4) + Log[-(a + b/x^2)^(1/4) + #1^(1/4)]*#1^(3/4) - Log[(a + b/x^2)^(1/4) + #1^(1/4)]*#1^(3/4))/(-2*a^3 - a^2*b + 6*a^2*#1 + a*b*#1 - 6*a*#1^2 + 2*#1^3) & ] - 6*a*RootSum[a^4 + a^3*b - 2*b^3 - 4*a^3*#1 - 2*a^2*b*#1 + 6*a^2*#1^2 + a*b*#1^2 - 4*a*#1^3 + #1^4 & , (2*ArcTan[(a + b/x^2)^(1/4)/#1^(1/4)]*#1^(7/4) + Log[-(a + b/x^2)^(1/4) + #1^(1/4)]*#1^(7/4) - Log[(a + b/x^2)^(1/4) + #1^(1/4)]*#1^(7/4))/(-2*a^3 - a^2*b + 6*a^2*#1 + a*b*#1 - 6*a*#1^2 + 2*#1^3) & ] + 2*RootSum[a^4 + a^3*b - 2*b^3 - 4*a^3*#1 - 2*a^2*b*#1 + 6*a^2*#1^2 + a*b*#1^2 - 4*a*#1^3 + #1^4 & , (2*ArcTan[(a + b/x^2)^(1/4)/#1^(1/4)]*#1^(11/4) + Log[-(a + b/x^2)^(1/4) + #1^(1/4)]*#1^(11/4) - Log[(a + b/x^2)^(1/4) + #1^(1/4)]*#1^(11/4))/(-2*a^3 - a^2*b + 6*a^2*#1 + a*b*#1 - 6*a*#1^2 + 2*#1^3) & ]))/(4*(x^2*(b + a*x^2))^(1/4))","B",1
1384,1,64755,99,60.4853982,"\int \frac{\left(-1+2 x^2\right) \left(-1+4 x-4 x^2+4 x^4\right)}{\sqrt{\frac{1-2 x^2}{1+2 x^2}} \left(1+2 x^2\right) \left(-1-8 x+32 x^2-40 x^3+46 x^4-64 x^5+56 x^6-32 x^7+8 x^8\right)} \, dx","Integrate[((-1 + 2*x^2)*(-1 + 4*x - 4*x^2 + 4*x^4))/(Sqrt[(1 - 2*x^2)/(1 + 2*x^2)]*(1 + 2*x^2)*(-1 - 8*x + 32*x^2 - 40*x^3 + 46*x^4 - 64*x^5 + 56*x^6 - 32*x^7 + 8*x^8)),x]","\text{Result too large to show}","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{\frac{3}{2}} \sqrt{\frac{1-2 x^2}{2 x^2+1}}}{x-1}\right)}{2 \sqrt[4]{2} 3^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{\frac{3}{2}} \sqrt{\frac{1-2 x^2}{2 x^2+1}}}{x-1}\right)}{2 \sqrt[4]{2} 3^{3/4}}",1,"Result too large to show","C",0
1385,1,13664,99,15.3074716,"\int \frac{\sqrt{1+x^2}}{x^2+\sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[Sqrt[1 + x^2]/(x^2 + Sqrt[x + Sqrt[1 + x^2]]),x]","\text{Result too large to show}","\log \left(\sqrt{x^2+1}+x\right)-2 \text{RootSum}\left[\text{$\#$1}^8+4 \text{$\#$1}^5-2 \text{$\#$1}^4+1\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)-\log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)}{2 \text{$\#$1}^4+5 \text{$\#$1}-2}\&\right]",1,"Result too large to show","B",0
1386,1,13664,99,14.9290921,"\int \frac{\sqrt{1+x^2}}{x^2+\sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[Sqrt[1 + x^2]/(x^2 + Sqrt[x + Sqrt[1 + x^2]]),x]","\text{Result too large to show}","\log \left(\sqrt{x^2+1}+x\right)-2 \text{RootSum}\left[\text{$\#$1}^8+4 \text{$\#$1}^5-2 \text{$\#$1}^4+1\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)-\log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)}{2 \text{$\#$1}^4+5 \text{$\#$1}-2}\&\right]",1,"Result too large to show","B",0
1387,1,2045,100,7.487415,"\int \frac{1+k x^2}{\left(-1+c k x+k x^2\right) \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}} \, dx","Integrate[(1 + k*x^2)/((-1 + c*k*x + k*x^2)*Sqrt[(1 - x^2)*(1 - k^2*x^2)]),x]","\text{Result too large to show}","\frac{2 \sqrt{-c^2 k^2+k^2-2 k+1} \tan ^{-1}\left(\frac{x \sqrt{-c^2 k^2+k^2-2 k+1}}{c k x+\sqrt{k^2 x^4+\left(-k^2-1\right) x^2+1}+k x^2-1}\right)}{(c k-k+1) (c k+k-1)}",1,"-((-4*k^(3/2)*Sqrt[-(k*(2 + (-2 + c^2)*k + c*Sqrt[k]*Sqrt[4 + c^2*k]))]*Sqrt[-(k^2*(-2 + 2*k + c^2*k^2 + c*k^(3/2)*Sqrt[4 + c^2*k]))]*Sqrt[-1 + x^2]*Sqrt[-1 + k^2*x^2]*ArcTanh[(Sqrt[-(k^2*(-2 + 2*k + c^2*k^2 - c*k^(3/2)*Sqrt[4 + c^2*k]))]*Sqrt[-1 + x^2])/(Sqrt[-(k*(2 + (-2 + c^2)*k - c*Sqrt[k]*Sqrt[4 + c^2*k]))]*Sqrt[-1 + k^2*x^2])] - c^2*k^(5/2)*Sqrt[-(k*(2 + (-2 + c^2)*k + c*Sqrt[k]*Sqrt[4 + c^2*k]))]*Sqrt[-(k^2*(-2 + 2*k + c^2*k^2 + c*k^(3/2)*Sqrt[4 + c^2*k]))]*Sqrt[-1 + x^2]*Sqrt[-1 + k^2*x^2]*ArcTanh[(Sqrt[-(k^2*(-2 + 2*k + c^2*k^2 - c*k^(3/2)*Sqrt[4 + c^2*k]))]*Sqrt[-1 + x^2])/(Sqrt[-(k*(2 + (-2 + c^2)*k - c*Sqrt[k]*Sqrt[4 + c^2*k]))]*Sqrt[-1 + k^2*x^2])] + c*k^2*Sqrt[4 + c^2*k]*Sqrt[-(k*(2 + (-2 + c^2)*k + c*Sqrt[k]*Sqrt[4 + c^2*k]))]*Sqrt[-(k^2*(-2 + 2*k + c^2*k^2 + c*k^(3/2)*Sqrt[4 + c^2*k]))]*Sqrt[-1 + x^2]*Sqrt[-1 + k^2*x^2]*ArcTanh[(Sqrt[-(k^2*(-2 + 2*k + c^2*k^2 - c*k^(3/2)*Sqrt[4 + c^2*k]))]*Sqrt[-1 + x^2])/(Sqrt[-(k*(2 + (-2 + c^2)*k - c*Sqrt[k]*Sqrt[4 + c^2*k]))]*Sqrt[-1 + k^2*x^2])] + 4*k^(3/2)*Sqrt[-(k*(2 + (-2 + c^2)*k - c*Sqrt[k]*Sqrt[4 + c^2*k]))]*Sqrt[-(k^2*(-2 + 2*k + c^2*k^2 - c*k^(3/2)*Sqrt[4 + c^2*k]))]*Sqrt[-1 + x^2]*Sqrt[-1 + k^2*x^2]*ArcTanh[(Sqrt[-(k^2*(-2 + 2*k + c^2*k^2 + c*k^(3/2)*Sqrt[4 + c^2*k]))]*Sqrt[-1 + x^2])/(Sqrt[-(k*(2 + (-2 + c^2)*k + c*Sqrt[k]*Sqrt[4 + c^2*k]))]*Sqrt[-1 + k^2*x^2])] + c^2*k^(5/2)*Sqrt[-(k*(2 + (-2 + c^2)*k - c*Sqrt[k]*Sqrt[4 + c^2*k]))]*Sqrt[-(k^2*(-2 + 2*k + c^2*k^2 - c*k^(3/2)*Sqrt[4 + c^2*k]))]*Sqrt[-1 + x^2]*Sqrt[-1 + k^2*x^2]*ArcTanh[(Sqrt[-(k^2*(-2 + 2*k + c^2*k^2 + c*k^(3/2)*Sqrt[4 + c^2*k]))]*Sqrt[-1 + x^2])/(Sqrt[-(k*(2 + (-2 + c^2)*k + c*Sqrt[k]*Sqrt[4 + c^2*k]))]*Sqrt[-1 + k^2*x^2])] + c*k^2*Sqrt[4 + c^2*k]*Sqrt[-(k*(2 + (-2 + c^2)*k - c*Sqrt[k]*Sqrt[4 + c^2*k]))]*Sqrt[-(k^2*(-2 + 2*k + c^2*k^2 - c*k^(3/2)*Sqrt[4 + c^2*k]))]*Sqrt[-1 + x^2]*Sqrt[-1 + k^2*x^2]*ArcTanh[(Sqrt[-(k^2*(-2 + 2*k + c^2*k^2 + c*k^(3/2)*Sqrt[4 + c^2*k]))]*Sqrt[-1 + x^2])/(Sqrt[-(k*(2 + (-2 + c^2)*k + c*Sqrt[k]*Sqrt[4 + c^2*k]))]*Sqrt[-1 + k^2*x^2])] - Sqrt[4 + c^2*k]*Sqrt[-(k*(2 + (-2 + c^2)*k - c*Sqrt[k]*Sqrt[4 + c^2*k]))]*Sqrt[-(k*(2 + (-2 + c^2)*k + c*Sqrt[k]*Sqrt[4 + c^2*k]))]*Sqrt[-(k^2*(-2 + 2*k + c^2*k^2 - c*k^(3/2)*Sqrt[4 + c^2*k]))]*Sqrt[-(k^2*(-2 + 2*k + c^2*k^2 + c*k^(3/2)*Sqrt[4 + c^2*k]))]*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticF[ArcSin[x], k^2] + Sqrt[4 + c^2*k]*Sqrt[-(k*(2 + (-2 + c^2)*k - c*Sqrt[k]*Sqrt[4 + c^2*k]))]*Sqrt[-(k*(2 + (-2 + c^2)*k + c*Sqrt[k]*Sqrt[4 + c^2*k]))]*Sqrt[-(k^2*(-2 + 2*k + c^2*k^2 - c*k^(3/2)*Sqrt[4 + c^2*k]))]*Sqrt[-(k^2*(-2 + 2*k + c^2*k^2 + c*k^(3/2)*Sqrt[4 + c^2*k]))]*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[(2*k)/(2 + c^2*k - c*Sqrt[k]*Sqrt[4 + c^2*k]), ArcSin[x], k^2] + Sqrt[4 + c^2*k]*Sqrt[-(k*(2 + (-2 + c^2)*k - c*Sqrt[k]*Sqrt[4 + c^2*k]))]*Sqrt[-(k*(2 + (-2 + c^2)*k + c*Sqrt[k]*Sqrt[4 + c^2*k]))]*Sqrt[-(k^2*(-2 + 2*k + c^2*k^2 - c*k^(3/2)*Sqrt[4 + c^2*k]))]*Sqrt[-(k^2*(-2 + 2*k + c^2*k^2 + c*k^(3/2)*Sqrt[4 + c^2*k]))]*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[(2*k)/(2 + c^2*k + c*Sqrt[k]*Sqrt[4 + c^2*k]), ArcSin[x], k^2])/(Sqrt[4 + c^2*k]*Sqrt[-(k*(2 + (-2 + c^2)*k - c*Sqrt[k]*Sqrt[4 + c^2*k]))]*Sqrt[-(k*(2 + (-2 + c^2)*k + c*Sqrt[k]*Sqrt[4 + c^2*k]))]*Sqrt[-(k^2*(-2 + 2*k + c^2*k^2 - c*k^(3/2)*Sqrt[4 + c^2*k]))]*Sqrt[-(k^2*(-2 + 2*k + c^2*k^2 + c*k^(3/2)*Sqrt[4 + c^2*k]))]*Sqrt[(-1 + x^2)*(-1 + k^2*x^2)]))","C",1
1388,1,2156,100,8.3341327,"\int \frac{-1+k x^2}{\left(1+c k x+k x^2\right) \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}} \, dx","Integrate[(-1 + k*x^2)/((1 + c*k*x + k*x^2)*Sqrt[(1 - x^2)*(1 - k^2*x^2)]),x]","\text{Result too large to show}","\frac{2 \sqrt{-c^2 k^2+k^2+2 k+1} \tan ^{-1}\left(\frac{x \sqrt{-c^2 k^2+k^2+2 k+1}}{c k x+\sqrt{k^2 x^4+\left(-k^2-1\right) x^2+1}+k x^2+1}\right)}{(c k-k-1) (c k+k+1)}",1,"-((k^(3/2)*Sqrt[-1 + x^2]*Sqrt[-1 + k^2*x^2]*(((c*Sqrt[k] - Sqrt[-4 + c^2*k])*ArcTanh[(Sqrt[k^2*(2 + 2*k - c^2*k^2 + c*k^(3/2)*Sqrt[-4 + c^2*k])]*Sqrt[-1 + x^2])/(Sqrt[k*(2 - (-2 + c^2)*k + c*Sqrt[k]*Sqrt[-4 + c^2*k])]*Sqrt[-1 + k^2*x^2])])/(Sqrt[k*(2 - (-2 + c^2)*k + c*Sqrt[k]*Sqrt[-4 + c^2*k])]*Sqrt[k^2*(2 + 2*k - c^2*k^2 + c*k^(3/2)*Sqrt[-4 + c^2*k])]) + ((c*Sqrt[k] + Sqrt[-4 + c^2*k])*ArcTanh[(Sqrt[-(k^2*(-2 - 2*k + c^2*k^2 + c*k^(3/2)*Sqrt[-4 + c^2*k]))]*Sqrt[-1 + x^2])/(Sqrt[-(k*(-2 + (-2 + c^2)*k + c*Sqrt[k]*Sqrt[-4 + c^2*k]))]*Sqrt[-1 + k^2*x^2])])/(Sqrt[-(k*(-2 + (-2 + c^2)*k + c*Sqrt[k]*Sqrt[-4 + c^2*k]))]*Sqrt[-(k^2*(-2 - 2*k + c^2*k^2 + c*k^(3/2)*Sqrt[-4 + c^2*k]))])))/Sqrt[(-1 + x^2)*(-1 + k^2*x^2)]) + (Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticF[ArcSin[x], k^2])/Sqrt[(-1 + x^2)*(-1 + k^2*x^2)] - (4*c^2*k*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[(-2*k^2)/(2*k - c^2*k^2 - c*k^(3/2)*Sqrt[-4 + c^2*k]), ArcSin[x], k^2])/((2*k - c^2*k^2 - c*k^(3/2)*Sqrt[-4 + c^2*k])*(-1/2*(-2*k + c^2*k^2 - c*k^(3/2)*Sqrt[-4 + c^2*k])/k^2 + (-2*k + c^2*k^2 + c*k^(3/2)*Sqrt[-4 + c^2*k])/(2*k^2))*Sqrt[(-1 + x^2)*(-1 + k^2*x^2)]) + (c^4*k^2*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[(-2*k^2)/(2*k - c^2*k^2 - c*k^(3/2)*Sqrt[-4 + c^2*k]), ArcSin[x], k^2])/((2*k - c^2*k^2 - c*k^(3/2)*Sqrt[-4 + c^2*k])*(-1/2*(-2*k + c^2*k^2 - c*k^(3/2)*Sqrt[-4 + c^2*k])/k^2 + (-2*k + c^2*k^2 + c*k^(3/2)*Sqrt[-4 + c^2*k])/(2*k^2))*Sqrt[(-1 + x^2)*(-1 + k^2*x^2)]) - (2*c*Sqrt[k]*Sqrt[-4 + c^2*k]*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[(-2*k^2)/(2*k - c^2*k^2 - c*k^(3/2)*Sqrt[-4 + c^2*k]), ArcSin[x], k^2])/((2*k - c^2*k^2 - c*k^(3/2)*Sqrt[-4 + c^2*k])*(-1/2*(-2*k + c^2*k^2 - c*k^(3/2)*Sqrt[-4 + c^2*k])/k^2 + (-2*k + c^2*k^2 + c*k^(3/2)*Sqrt[-4 + c^2*k])/(2*k^2))*Sqrt[(-1 + x^2)*(-1 + k^2*x^2)]) + (c^3*k^(3/2)*Sqrt[-4 + c^2*k]*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[(-2*k^2)/(2*k - c^2*k^2 - c*k^(3/2)*Sqrt[-4 + c^2*k]), ArcSin[x], k^2])/((2*k - c^2*k^2 - c*k^(3/2)*Sqrt[-4 + c^2*k])*(-1/2*(-2*k + c^2*k^2 - c*k^(3/2)*Sqrt[-4 + c^2*k])/k^2 + (-2*k + c^2*k^2 + c*k^(3/2)*Sqrt[-4 + c^2*k])/(2*k^2))*Sqrt[(-1 + x^2)*(-1 + k^2*x^2)]) - (4*c^2*k*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[(-2*k^2)/(2*k - c^2*k^2 + c*k^(3/2)*Sqrt[-4 + c^2*k]), ArcSin[x], k^2])/((2*k - c^2*k^2 + c*k^(3/2)*Sqrt[-4 + c^2*k])*((-2*k + c^2*k^2 - c*k^(3/2)*Sqrt[-4 + c^2*k])/(2*k^2) - (-2*k + c^2*k^2 + c*k^(3/2)*Sqrt[-4 + c^2*k])/(2*k^2))*Sqrt[(-1 + x^2)*(-1 + k^2*x^2)]) + (c^4*k^2*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[(-2*k^2)/(2*k - c^2*k^2 + c*k^(3/2)*Sqrt[-4 + c^2*k]), ArcSin[x], k^2])/((2*k - c^2*k^2 + c*k^(3/2)*Sqrt[-4 + c^2*k])*((-2*k + c^2*k^2 - c*k^(3/2)*Sqrt[-4 + c^2*k])/(2*k^2) - (-2*k + c^2*k^2 + c*k^(3/2)*Sqrt[-4 + c^2*k])/(2*k^2))*Sqrt[(-1 + x^2)*(-1 + k^2*x^2)]) + (2*c*Sqrt[k]*Sqrt[-4 + c^2*k]*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[(-2*k^2)/(2*k - c^2*k^2 + c*k^(3/2)*Sqrt[-4 + c^2*k]), ArcSin[x], k^2])/((2*k - c^2*k^2 + c*k^(3/2)*Sqrt[-4 + c^2*k])*((-2*k + c^2*k^2 - c*k^(3/2)*Sqrt[-4 + c^2*k])/(2*k^2) - (-2*k + c^2*k^2 + c*k^(3/2)*Sqrt[-4 + c^2*k])/(2*k^2))*Sqrt[(-1 + x^2)*(-1 + k^2*x^2)]) - (c^3*k^(3/2)*Sqrt[-4 + c^2*k]*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[(-2*k^2)/(2*k - c^2*k^2 + c*k^(3/2)*Sqrt[-4 + c^2*k]), ArcSin[x], k^2])/((2*k - c^2*k^2 + c*k^(3/2)*Sqrt[-4 + c^2*k])*((-2*k + c^2*k^2 - c*k^(3/2)*Sqrt[-4 + c^2*k])/(2*k^2) - (-2*k + c^2*k^2 + c*k^(3/2)*Sqrt[-4 + c^2*k])/(2*k^2))*Sqrt[(-1 + x^2)*(-1 + k^2*x^2)])","C",1
1389,1,50,100,0.0159636,"\int x^2 \sqrt[3]{x+x^3} \, dx","Integrate[x^2*(x + x^3)^(1/3),x]","\frac{x \sqrt[3]{x^3+x} \left(\left(x^2+1\right)^{4/3}-\, _2F_1\left(-\frac{1}{3},\frac{2}{3};\frac{5}{3};-x^2\right)\right)}{4 \sqrt[3]{x^2+1}}","\frac{1}{12} \sqrt[3]{x^3+x} \left(3 x^3+x\right)+\frac{1}{18} \log \left(\sqrt[3]{x^3+x}-x\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+x}+x}\right)}{6 \sqrt{3}}-\frac{1}{36} \log \left(\sqrt[3]{x^3+x} x+\left(x^3+x\right)^{2/3}+x^2\right)",1,"(x*(x + x^3)^(1/3)*((1 + x^2)^(4/3) - Hypergeometric2F1[-1/3, 2/3, 5/3, -x^2]))/(4*(1 + x^2)^(1/3))","C",1
1390,0,0,100,0.1556112,"\int \frac{6+2 x+x^2}{\sqrt[3]{2+x^2} \left(1+3 x-2 x^2+x^3\right)} \, dx","Integrate[(6 + 2*x + x^2)/((2 + x^2)^(1/3)*(1 + 3*x - 2*x^2 + x^3)),x]","\int \frac{6+2 x+x^2}{\sqrt[3]{2+x^2} \left(1+3 x-2 x^2+x^3\right)} \, dx","\log \left(\sqrt[3]{x^2+2}+x-1\right)-\frac{1}{2} \log \left(x^2+\left(x^2+2\right)^{2/3}+(1-x) \sqrt[3]{x^2+2}-2 x+1\right)-\sqrt{3} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{x^2+2}}{\sqrt{3}}-\frac{2 x}{\sqrt{3}}+\frac{2}{\sqrt{3}}}{\sqrt[3]{x^2+2}}\right)",1,"Integrate[(6 + 2*x + x^2)/((2 + x^2)^(1/3)*(1 + 3*x - 2*x^2 + x^3)), x]","F",-1
1391,1,36,100,0.0098141,"\int \frac{\sqrt[3]{x^2+x^3}}{x^2} \, dx","Integrate[(x^2 + x^3)^(1/3)/x^2,x]","-\frac{3 \sqrt[3]{x^2 (x+1)} \, _2F_1\left(-\frac{1}{3},-\frac{1}{3};\frac{2}{3};-x\right)}{x \sqrt[3]{x+1}}","-\frac{3 \sqrt[3]{x^3+x^2}}{x}-\log \left(\sqrt[3]{x^3+x^2}-x\right)+\frac{1}{2} \log \left(x^2+\sqrt[3]{x^3+x^2} x+\left(x^3+x^2\right)^{2/3}\right)-\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+x^2}+x}\right)",1,"(-3*(x^2*(1 + x))^(1/3)*Hypergeometric2F1[-1/3, -1/3, 2/3, -x])/(x*(1 + x)^(1/3))","C",1
1392,1,35,100,0.0107102,"\int \frac{\sqrt[3]{1+x^4} \left(3+x^4\right)}{x^{13}} \, dx","Integrate[((1 + x^4)^(1/3)*(3 + x^4))/x^13,x]","\frac{\left(x^4+1\right)^{4/3} \left(x^{12} \, _2F_1\left(\frac{4}{3},3;\frac{7}{3};x^4+1\right)-2\right)}{8 x^{12}}","\frac{1}{54} \log \left(\sqrt[3]{x^4+1}-1\right)-\frac{1}{108} \log \left(\left(x^4+1\right)^{2/3}+\sqrt[3]{x^4+1}+1\right)-\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{x^4+1}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{18 \sqrt{3}}+\frac{\sqrt[3]{x^4+1} \left(x^8-6 x^4-9\right)}{36 x^{12}}",1,"((1 + x^4)^(4/3)*(-2 + x^12*Hypergeometric2F1[4/3, 3, 7/3, 1 + x^4]))/(8*x^12)","C",1
1393,0,0,100,0.3056705,"\int \frac{\left(-1+x^4\right)^{2/3} \left(3+x^4\right) \left(-1+x^3+x^4\right)}{x^6 \left(-1-x^3+x^4\right)} \, dx","Integrate[((-1 + x^4)^(2/3)*(3 + x^4)*(-1 + x^3 + x^4))/(x^6*(-1 - x^3 + x^4)),x]","\int \frac{\left(-1+x^4\right)^{2/3} \left(3+x^4\right) \left(-1+x^3+x^4\right)}{x^6 \left(-1-x^3+x^4\right)} \, dx","2 \log \left(\sqrt[3]{x^4-1}-x\right)-2 \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^4-1}+x}\right)-\log \left(\sqrt[3]{x^4-1} x+\left(x^4-1\right)^{2/3}+x^2\right)+\frac{3 \left(x^4-1\right)^{2/3} \left(x^4+5 x^3-1\right)}{5 x^5}",1,"Integrate[((-1 + x^4)^(2/3)*(3 + x^4)*(-1 + x^3 + x^4))/(x^6*(-1 - x^3 + x^4)), x]","F",-1
1394,0,0,100,0.2592873,"\int \frac{\left(-3+x^4\right) \left(1+x^4\right)^{2/3} \left(1+x^3+x^4\right)}{x^6 \left(1-x^3+x^4\right)} \, dx","Integrate[((-3 + x^4)*(1 + x^4)^(2/3)*(1 + x^3 + x^4))/(x^6*(1 - x^3 + x^4)),x]","\int \frac{\left(-3+x^4\right) \left(1+x^4\right)^{2/3} \left(1+x^3+x^4\right)}{x^6 \left(1-x^3+x^4\right)} \, dx","2 \log \left(\sqrt[3]{x^4+1}-x\right)-2 \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^4+1}+x}\right)-\log \left(\sqrt[3]{x^4+1} x+\left(x^4+1\right)^{2/3}+x^2\right)+\frac{3 \left(x^4+1\right)^{2/3} \left(x^4+5 x^3+1\right)}{5 x^5}",1,"Integrate[((-3 + x^4)*(1 + x^4)^(2/3)*(1 + x^3 + x^4))/(x^6*(1 - x^3 + x^4)), x]","F",-1
1395,1,535,100,0.9202046,"\int \frac{-b+a x^2}{\left(b+a x^2+x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Integrate[(-b + a*x^2)/((b + a*x^2 + x^4)*(b*x^2 + a*x^4)^(1/4)),x]","\frac{\sqrt{x} \sqrt[4]{a x^2+b} \left(\frac{\left(a-\frac{a^2+2 b}{\sqrt{a^2-4 b}}\right) \tan ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{-a \sqrt{a^2-4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2-4 b}} \sqrt[4]{a x^2+b}}\right)}{\left(a-\sqrt{a^2-4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2-4 b}+a^2-2 b}}+\frac{\left(\frac{a^2+2 b}{\sqrt{a^2-4 b}}+a\right) \tan ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{a \sqrt{a^2-4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2-4 b}+a} \sqrt[4]{a x^2+b}}\right)}{\left(\sqrt{a^2-4 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2-4 b}+a^2-2 b}}+\frac{\left(a-\frac{a^2+2 b}{\sqrt{a^2-4 b}}\right) \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{-a \sqrt{a^2-4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2-4 b}} \sqrt[4]{a x^2+b}}\right)}{\left(a-\sqrt{a^2-4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2-4 b}+a^2-2 b}}+\frac{\left(\frac{a^2+2 b}{\sqrt{a^2-4 b}}+a\right) \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{a \sqrt{a^2-4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2-4 b}+a} \sqrt[4]{a x^2+b}}\right)}{\left(\sqrt{a^2-4 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2-4 b}+a^2-2 b}}\right)}{\sqrt[4]{x^2 \left(a x^2+b\right)}}","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4 a+b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-2 a \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+2 a \log (x)}{\text{$\#$1} a-2 \text{$\#$1}^5}\&\right]",1,"(Sqrt[x]*(b + a*x^2)^(1/4)*(((a - (a^2 + 2*b)/Sqrt[a^2 - 4*b])*ArcTan[((a^2 - a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)*Sqrt[x])/((a - Sqrt[a^2 - 4*b])^(1/4)*(b + a*x^2)^(1/4))])/((a - Sqrt[a^2 - 4*b])^(3/4)*(a^2 - a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)) + ((a + (a^2 + 2*b)/Sqrt[a^2 - 4*b])*ArcTan[((a^2 + a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)*Sqrt[x])/((a + Sqrt[a^2 - 4*b])^(1/4)*(b + a*x^2)^(1/4))])/((a + Sqrt[a^2 - 4*b])^(3/4)*(a^2 + a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)) + ((a - (a^2 + 2*b)/Sqrt[a^2 - 4*b])*ArcTanh[((a^2 - a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)*Sqrt[x])/((a - Sqrt[a^2 - 4*b])^(1/4)*(b + a*x^2)^(1/4))])/((a - Sqrt[a^2 - 4*b])^(3/4)*(a^2 - a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)) + ((a + (a^2 + 2*b)/Sqrt[a^2 - 4*b])*ArcTanh[((a^2 + a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)*Sqrt[x])/((a + Sqrt[a^2 - 4*b])^(1/4)*(b + a*x^2)^(1/4))])/((a + Sqrt[a^2 - 4*b])^(3/4)*(a^2 + a*Sqrt[a^2 - 4*b] - 2*b)^(1/4))))/(x^2*(b + a*x^2))^(1/4)","B",1
1396,1,535,100,0.2105347,"\int \frac{-b+a x^2}{\left(b+a x^2+x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Integrate[(-b + a*x^2)/((b + a*x^2 + x^4)*(b*x^2 + a*x^4)^(1/4)),x]","\frac{\sqrt{x} \sqrt[4]{a x^2+b} \left(\frac{\left(a-\frac{a^2+2 b}{\sqrt{a^2-4 b}}\right) \tan ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{-a \sqrt{a^2-4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2-4 b}} \sqrt[4]{a x^2+b}}\right)}{\left(a-\sqrt{a^2-4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2-4 b}+a^2-2 b}}+\frac{\left(\frac{a^2+2 b}{\sqrt{a^2-4 b}}+a\right) \tan ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{a \sqrt{a^2-4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2-4 b}+a} \sqrt[4]{a x^2+b}}\right)}{\left(\sqrt{a^2-4 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2-4 b}+a^2-2 b}}+\frac{\left(a-\frac{a^2+2 b}{\sqrt{a^2-4 b}}\right) \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{-a \sqrt{a^2-4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2-4 b}} \sqrt[4]{a x^2+b}}\right)}{\left(a-\sqrt{a^2-4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2-4 b}+a^2-2 b}}+\frac{\left(\frac{a^2+2 b}{\sqrt{a^2-4 b}}+a\right) \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{a \sqrt{a^2-4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2-4 b}+a} \sqrt[4]{a x^2+b}}\right)}{\left(\sqrt{a^2-4 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2-4 b}+a^2-2 b}}\right)}{\sqrt[4]{x^2 \left(a x^2+b\right)}}","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4 a+b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-2 a \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+2 a \log (x)}{\text{$\#$1} a-2 \text{$\#$1}^5}\&\right]",1,"(Sqrt[x]*(b + a*x^2)^(1/4)*(((a - (a^2 + 2*b)/Sqrt[a^2 - 4*b])*ArcTan[((a^2 - a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)*Sqrt[x])/((a - Sqrt[a^2 - 4*b])^(1/4)*(b + a*x^2)^(1/4))])/((a - Sqrt[a^2 - 4*b])^(3/4)*(a^2 - a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)) + ((a + (a^2 + 2*b)/Sqrt[a^2 - 4*b])*ArcTan[((a^2 + a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)*Sqrt[x])/((a + Sqrt[a^2 - 4*b])^(1/4)*(b + a*x^2)^(1/4))])/((a + Sqrt[a^2 - 4*b])^(3/4)*(a^2 + a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)) + ((a - (a^2 + 2*b)/Sqrt[a^2 - 4*b])*ArcTanh[((a^2 - a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)*Sqrt[x])/((a - Sqrt[a^2 - 4*b])^(1/4)*(b + a*x^2)^(1/4))])/((a - Sqrt[a^2 - 4*b])^(3/4)*(a^2 - a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)) + ((a + (a^2 + 2*b)/Sqrt[a^2 - 4*b])*ArcTanh[((a^2 + a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)*Sqrt[x])/((a + Sqrt[a^2 - 4*b])^(1/4)*(b + a*x^2)^(1/4))])/((a + Sqrt[a^2 - 4*b])^(3/4)*(a^2 + a*Sqrt[a^2 - 4*b] - 2*b)^(1/4))))/(x^2*(b + a*x^2))^(1/4)","B",1
1397,1,342,100,0.6785641,"\int \frac{\left(-1+x^3\right) \left(1+x^3\right)^{2/3}}{x^3 \left(-1-x^3+x^6\right)} \, dx","Integrate[((-1 + x^3)*(1 + x^3)^(2/3))/(x^3*(-1 - x^3 + x^6)),x]","-\frac{\left(x^3+1\right)^{2/3}}{2 x^2}-\frac{-2 \left(\sqrt{5}-1\right)^{4/3} \log \left(\sqrt[3]{\sqrt{5}-1}-\frac{\sqrt[3]{2} x}{\sqrt[3]{x^3+1}}\right)+2 \left(1+\sqrt{5}\right)^{4/3} \log \left(\frac{\sqrt[3]{2} x}{\sqrt[3]{x^3+1}}+\sqrt[3]{1+\sqrt{5}}\right)+\left(\sqrt{5}-1\right)^{4/3} \left(2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{\frac{2}{\sqrt{5}-1}} x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)+\log \left(\frac{\sqrt[3]{2 \left(\sqrt{5}-1\right)} x}{\sqrt[3]{x^3+1}}+\frac{2^{2/3} x^2}{\left(x^3+1\right)^{2/3}}+\left(\sqrt{5}-1\right)^{2/3}\right)\right)+\left(1+\sqrt{5}\right)^{4/3} \left(2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{\frac{2}{1+\sqrt{5}}} x}{\sqrt[3]{x^3+1}}-1}{\sqrt{3}}\right)-\log \left(-\frac{\sqrt[3]{2 \left(1+\sqrt{5}\right)} x}{\sqrt[3]{x^3+1}}+\frac{2^{2/3} x^2}{\left(x^3+1\right)^{2/3}}+\left(1+\sqrt{5}\right)^{2/3}\right)\right)}{12 \sqrt[3]{2} \sqrt{5}}","-\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^6-\text{$\#$1}^3-1\&,\frac{-\text{$\#$1}^3 \log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)+\text{$\#$1}^3 \log (x)+\log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)-\log (x)}{2 \text{$\#$1}^4-\text{$\#$1}}\&\right]-\frac{\left(x^3+1\right)^{2/3}}{2 x^2}",1,"-1/2*(1 + x^3)^(2/3)/x^2 - (-2*(-1 + Sqrt[5])^(4/3)*Log[(-1 + Sqrt[5])^(1/3) - (2^(1/3)*x)/(1 + x^3)^(1/3)] + 2*(1 + Sqrt[5])^(4/3)*Log[(1 + Sqrt[5])^(1/3) + (2^(1/3)*x)/(1 + x^3)^(1/3)] + (-1 + Sqrt[5])^(4/3)*(2*Sqrt[3]*ArcTan[(1 + (2*(2/(-1 + Sqrt[5]))^(1/3)*x)/(1 + x^3)^(1/3))/Sqrt[3]] + Log[(-1 + Sqrt[5])^(2/3) + (2^(2/3)*x^2)/(1 + x^3)^(2/3) + ((2*(-1 + Sqrt[5]))^(1/3)*x)/(1 + x^3)^(1/3)]) + (1 + Sqrt[5])^(4/3)*(2*Sqrt[3]*ArcTan[(-1 + (2*(2/(1 + Sqrt[5]))^(1/3)*x)/(1 + x^3)^(1/3))/Sqrt[3]] - Log[(1 + Sqrt[5])^(2/3) + (2^(2/3)*x^2)/(1 + x^3)^(2/3) - ((2*(1 + Sqrt[5]))^(1/3)*x)/(1 + x^3)^(1/3)]))/(12*2^(1/3)*Sqrt[5])","B",1
1398,1,342,100,0.1831838,"\int \frac{\left(-1+x^3\right) \left(1+x^3\right)^{2/3}}{x^3 \left(-1-x^3+x^6\right)} \, dx","Integrate[((-1 + x^3)*(1 + x^3)^(2/3))/(x^3*(-1 - x^3 + x^6)),x]","-\frac{\left(x^3+1\right)^{2/3}}{2 x^2}-\frac{-2 \left(\sqrt{5}-1\right)^{4/3} \log \left(\sqrt[3]{\sqrt{5}-1}-\frac{\sqrt[3]{2} x}{\sqrt[3]{x^3+1}}\right)+2 \left(1+\sqrt{5}\right)^{4/3} \log \left(\frac{\sqrt[3]{2} x}{\sqrt[3]{x^3+1}}+\sqrt[3]{1+\sqrt{5}}\right)+\left(\sqrt{5}-1\right)^{4/3} \left(2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{\frac{2}{\sqrt{5}-1}} x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)+\log \left(\frac{\sqrt[3]{2 \left(\sqrt{5}-1\right)} x}{\sqrt[3]{x^3+1}}+\frac{2^{2/3} x^2}{\left(x^3+1\right)^{2/3}}+\left(\sqrt{5}-1\right)^{2/3}\right)\right)+\left(1+\sqrt{5}\right)^{4/3} \left(2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{\frac{2}{1+\sqrt{5}}} x}{\sqrt[3]{x^3+1}}-1}{\sqrt{3}}\right)-\log \left(-\frac{\sqrt[3]{2 \left(1+\sqrt{5}\right)} x}{\sqrt[3]{x^3+1}}+\frac{2^{2/3} x^2}{\left(x^3+1\right)^{2/3}}+\left(1+\sqrt{5}\right)^{2/3}\right)\right)}{12 \sqrt[3]{2} \sqrt{5}}","-\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^6-\text{$\#$1}^3-1\&,\frac{-\text{$\#$1}^3 \log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)+\text{$\#$1}^3 \log (x)+\log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)-\log (x)}{2 \text{$\#$1}^4-\text{$\#$1}}\&\right]-\frac{\left(x^3+1\right)^{2/3}}{2 x^2}",1,"-1/2*(1 + x^3)^(2/3)/x^2 - (-2*(-1 + Sqrt[5])^(4/3)*Log[(-1 + Sqrt[5])^(1/3) - (2^(1/3)*x)/(1 + x^3)^(1/3)] + 2*(1 + Sqrt[5])^(4/3)*Log[(1 + Sqrt[5])^(1/3) + (2^(1/3)*x)/(1 + x^3)^(1/3)] + (-1 + Sqrt[5])^(4/3)*(2*Sqrt[3]*ArcTan[(1 + (2*(2/(-1 + Sqrt[5]))^(1/3)*x)/(1 + x^3)^(1/3))/Sqrt[3]] + Log[(-1 + Sqrt[5])^(2/3) + (2^(2/3)*x^2)/(1 + x^3)^(2/3) + ((2*(-1 + Sqrt[5]))^(1/3)*x)/(1 + x^3)^(1/3)]) + (1 + Sqrt[5])^(4/3)*(2*Sqrt[3]*ArcTan[(-1 + (2*(2/(1 + Sqrt[5]))^(1/3)*x)/(1 + x^3)^(1/3))/Sqrt[3]] - Log[(1 + Sqrt[5])^(2/3) + (2^(2/3)*x^2)/(1 + x^3)^(2/3) - ((2*(1 + Sqrt[5]))^(1/3)*x)/(1 + x^3)^(1/3)]))/(12*2^(1/3)*Sqrt[5])","B",1
1399,0,0,100,0.325578,"\int \frac{\sqrt[3]{1+2 x^7} \left(-3+8 x^7\right)}{x^2 \left(1+x^3+2 x^7\right)} \, dx","Integrate[((1 + 2*x^7)^(1/3)*(-3 + 8*x^7))/(x^2*(1 + x^3 + 2*x^7)),x]","\int \frac{\sqrt[3]{1+2 x^7} \left(-3+8 x^7\right)}{x^2 \left(1+x^3+2 x^7\right)} \, dx","\frac{3 \sqrt[3]{2 x^7+1}}{x}-\log \left(\sqrt[3]{2 x^7+1}+x\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{2 x^7+1}-x}\right)+\frac{1}{2} \log \left(-\sqrt[3]{2 x^7+1} x+\left(2 x^7+1\right)^{2/3}+x^2\right)",1,"Integrate[((1 + 2*x^7)^(1/3)*(-3 + 8*x^7))/(x^2*(1 + x^3 + 2*x^7)), x]","F",-1
1400,1,499,100,0.898986,"\int \frac{-b+2 a x^4}{\sqrt[4]{b+a x^4} \left(-b+a x^4+x^8\right)} \, dx","Integrate[(-b + 2*a*x^4)/((b + a*x^4)^(1/4)*(-b + a*x^4 + x^8)),x]","\frac{\left(a-\frac{a^2+b}{\sqrt{a^2+4 b}}\right) \tan ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{a x^4+b}}\right)}{\left(a-\sqrt{a^2+4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}+\frac{\left(a \sqrt{a^2+4 b}+a^2+b\right) \tan ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+4 b}+a} \sqrt[4]{a x^4+b}}\right)}{\sqrt{a^2+4 b} \left(\sqrt{a^2+4 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}+\frac{\left(a-\frac{a^2+b}{\sqrt{a^2+4 b}}\right) \tanh ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{a x^4+b}}\right)}{\left(a-\sqrt{a^2+4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}+\frac{\left(a \sqrt{a^2+4 b}+a^2+b\right) \tanh ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+4 b}+a} \sqrt[4]{a x^4+b}}\right)}{\sqrt{a^2+4 b} \left(\sqrt{a^2+4 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4 a+2 a^2-b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-3 a \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+3 a \log (x)}{3 \text{$\#$1} a-2 \text{$\#$1}^5}\&\right]",1,"((a - (a^2 + b)/Sqrt[a^2 + 4*b])*ArcTan[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a - Sqrt[a^2 + 4*b])^(1/4)*(b + a*x^4)^(1/4))])/((a - Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)) + ((a^2 + b + a*Sqrt[a^2 + 4*b])*ArcTan[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a + Sqrt[a^2 + 4*b])^(1/4)*(b + a*x^4)^(1/4))])/(Sqrt[a^2 + 4*b]*(a + Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)) + ((a - (a^2 + b)/Sqrt[a^2 + 4*b])*ArcTanh[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a - Sqrt[a^2 + 4*b])^(1/4)*(b + a*x^4)^(1/4))])/((a - Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)) + ((a^2 + b + a*Sqrt[a^2 + 4*b])*ArcTanh[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a + Sqrt[a^2 + 4*b])^(1/4)*(b + a*x^4)^(1/4))])/(Sqrt[a^2 + 4*b]*(a + Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4))","B",1
1401,1,499,100,0.3465932,"\int \frac{-b+2 a x^4}{\sqrt[4]{b+a x^4} \left(-b+a x^4+x^8\right)} \, dx","Integrate[(-b + 2*a*x^4)/((b + a*x^4)^(1/4)*(-b + a*x^4 + x^8)),x]","\frac{\left(a-\frac{a^2+b}{\sqrt{a^2+4 b}}\right) \tan ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{a x^4+b}}\right)}{\left(a-\sqrt{a^2+4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}+\frac{\left(a \sqrt{a^2+4 b}+a^2+b\right) \tan ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+4 b}+a} \sqrt[4]{a x^4+b}}\right)}{\sqrt{a^2+4 b} \left(\sqrt{a^2+4 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}+\frac{\left(a-\frac{a^2+b}{\sqrt{a^2+4 b}}\right) \tanh ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{a x^4+b}}\right)}{\left(a-\sqrt{a^2+4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}+\frac{\left(a \sqrt{a^2+4 b}+a^2+b\right) \tanh ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+4 b}+a} \sqrt[4]{a x^4+b}}\right)}{\sqrt{a^2+4 b} \left(\sqrt{a^2+4 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4 a+2 a^2-b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-3 a \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+3 a \log (x)}{3 \text{$\#$1} a-2 \text{$\#$1}^5}\&\right]",1,"((a - (a^2 + b)/Sqrt[a^2 + 4*b])*ArcTan[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a - Sqrt[a^2 + 4*b])^(1/4)*(b + a*x^4)^(1/4))])/((a - Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)) + ((a^2 + b + a*Sqrt[a^2 + 4*b])*ArcTan[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a + Sqrt[a^2 + 4*b])^(1/4)*(b + a*x^4)^(1/4))])/(Sqrt[a^2 + 4*b]*(a + Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)) + ((a - (a^2 + b)/Sqrt[a^2 + 4*b])*ArcTanh[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a - Sqrt[a^2 + 4*b])^(1/4)*(b + a*x^4)^(1/4))])/((a - Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)) + ((a^2 + b + a*Sqrt[a^2 + 4*b])*ArcTanh[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a + Sqrt[a^2 + 4*b])^(1/4)*(b + a*x^4)^(1/4))])/(Sqrt[a^2 + 4*b]*(a + Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4))","B",1
1402,0,0,100,0.5828566,"\int \frac{\left(-1+3 x^4\right) \sqrt{1+x+2 x^4+x^5+x^8}}{x^2 \left(4+x+4 x^4\right)} \, dx","Integrate[((-1 + 3*x^4)*Sqrt[1 + x + 2*x^4 + x^5 + x^8])/(x^2*(4 + x + 4*x^4)),x]","\int \frac{\left(-1+3 x^4\right) \sqrt{1+x+2 x^4+x^5+x^8}}{x^2 \left(4+x+4 x^4\right)} \, dx","\frac{\sqrt{x^8+x^5+2 x^4+x+1}}{4 x}-\frac{1}{8} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt{x^8+x^5+2 x^4+x+1}}{x^4+x+1}\right)+\frac{1}{8} \tanh ^{-1}\left(\frac{\sqrt{x^8+x^5+2 x^4+x+1}}{x^4+x+1}\right)",1,"Integrate[((-1 + 3*x^4)*Sqrt[1 + x + 2*x^4 + x^5 + x^8])/(x^2*(4 + x + 4*x^4)), x]","F",-1
1403,1,99,100,0.074269,"\int \frac{-b+c x^4+a x^8}{x^2 \left(-b+a x^4\right)^{3/4}} \, dx","Integrate[(-b + c*x^4 + a*x^8)/(x^2*(-b + a*x^4)^(3/4)),x]","\frac{2 a^{3/4} \left(x^4-4\right) \sqrt[4]{a x^4-b}-x (3 b+4 c) \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)+x (3 b+4 c) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{8 a^{3/4} x}","\frac{(-3 b-4 c) \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{8 a^{3/4}}+\frac{(3 b+4 c) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{8 a^{3/4}}+\frac{\left(x^4-4\right) \sqrt[4]{a x^4-b}}{4 x}",1,"(2*a^(3/4)*(-4 + x^4)*(-b + a*x^4)^(1/4) - (3*b + 4*c)*x*ArcTan[(a^(1/4)*x)/(-b + a*x^4)^(1/4)] + (3*b + 4*c)*x*ArcTanh[(a^(1/4)*x)/(-b + a*x^4)^(1/4)])/(8*a^(3/4)*x)","A",1
1404,1,100,100,0.1472475,"\int \frac{1}{(1+x) \sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[1/((1 + x)*Sqrt[x + Sqrt[1 + x^2]]),x]","2 \left(\frac{1}{\sqrt{\sqrt{x^2+1}+x}}-\sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{1}{\sqrt{\sqrt{2}-1} \sqrt{\sqrt{x^2+1}+x}}\right)-\sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{1}{\sqrt{1+\sqrt{2}} \sqrt{\sqrt{x^2+1}+x}}\right)\right)","\frac{2}{\sqrt{\sqrt{x^2+1}+x}}+2 \sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{1+\sqrt{2}}}\right)-2 \sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{\sqrt{2}-1}}\right)",1,"2*(1/Sqrt[x + Sqrt[1 + x^2]] - Sqrt[-1 + Sqrt[2]]*ArcTan[1/(Sqrt[-1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]])] - Sqrt[1 + Sqrt[2]]*ArcTanh[1/(Sqrt[1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]])])","A",1
1405,1,204,100,2.1878002,"\int \frac{1}{x \sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Integrate[1/(x*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]),x]","\frac{2}{3} \sqrt{\sqrt{a^2 x^2+b^2}+a x} \left(\frac{\sqrt{a^2 x^2+b^2}-2 a x}{b^2}-\frac{\left(a^2 x^2+b^2\right) \left(\sqrt{a^2 x^2+b^2}+a x\right) \left(2 \left(2 a x \left(\sqrt{a^2 x^2+b^2}+a x\right)+b^2\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{\left(a x+\sqrt{b^2+a^2 x^2}\right)^2}{b^2}\right)-a x \left(\sqrt{a^2 x^2+b^2}+a x\right)-2 b^2\right)}{\left(a b x \left(\sqrt{a^2 x^2+b^2}+a x\right)+b^3\right)^2}\right)","\frac{2}{\sqrt{\sqrt{a^2 x^2+b^2}+a x}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt{\sqrt{a^2 x^2+b^2}+a x}}{\sqrt{b}}\right)}{\sqrt{b}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a^2 x^2+b^2}+a x}}{\sqrt{b}}\right)}{\sqrt{b}}",1,"(2*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]*((-2*a*x + Sqrt[b^2 + a^2*x^2])/b^2 - ((b^2 + a^2*x^2)*(a*x + Sqrt[b^2 + a^2*x^2])*(-2*b^2 - a*x*(a*x + Sqrt[b^2 + a^2*x^2]) + 2*(b^2 + 2*a*x*(a*x + Sqrt[b^2 + a^2*x^2]))*Hypergeometric2F1[3/4, 1, 7/4, (a*x + Sqrt[b^2 + a^2*x^2])^2/b^2]))/(b^3 + a*b*x*(a*x + Sqrt[b^2 + a^2*x^2]))^2))/3","C",1
1406,1,107,101,0.2132108,"\int \frac{(-3+x)^6 \left(-1-x+x^2\right)^{3/2}}{-1+x} \, dx","Integrate[((-3 + x)^6*(-1 - x + x^2)^(3/2))/(-1 + x),x]","-64 \tan ^{-1}\left(\frac{3-x}{2 \sqrt{x^2-x-1}}\right)+\frac{19451047 \tanh ^{-1}\left(\frac{1-2 x}{2 \sqrt{x^2-x-1}}\right)}{65536}+\frac{\sqrt{x^2-x-1} \left(1146880 x^8-23296000 x^7+199009280 x^6-910869760 x^5+2304529024 x^4-2700564848 x^3-508033624 x^2+4423205098 x-1245336401\right)}{10321920}","\frac{19451047 \log \left(2 \sqrt{x^2-x-1}-2 x+1\right)}{65536}+128 \tan ^{-1}\left(\sqrt{x^2-x-1}-x+1\right)+\frac{\sqrt{x^2-x-1} \left(1146880 x^8-23296000 x^7+199009280 x^6-910869760 x^5+2304529024 x^4-2700564848 x^3-508033624 x^2+4423205098 x-1245336401\right)}{10321920}",1,"(Sqrt[-1 - x + x^2]*(-1245336401 + 4423205098*x - 508033624*x^2 - 2700564848*x^3 + 2304529024*x^4 - 910869760*x^5 + 199009280*x^6 - 23296000*x^7 + 1146880*x^8))/10321920 - 64*ArcTan[(3 - x)/(2*Sqrt[-1 - x + x^2])] + (19451047*ArcTanh[(1 - 2*x)/(2*Sqrt[-1 - x + x^2])])/65536","A",1
1407,1,37,101,0.0090881,"\int \frac{\left(-1+x^3\right) \sqrt[3]{1+x^3}}{x^5} \, dx","Integrate[((-1 + x^3)*(1 + x^3)^(1/3))/x^5,x]","\frac{\left(x^3+1\right)^{4/3}}{4 x^4}-\frac{\, _2F_1\left(-\frac{1}{3},-\frac{1}{3};\frac{2}{3};-x^3\right)}{x}","-\frac{1}{3} \log \left(\sqrt[3]{x^3+1}-x\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+1}+x}\right)}{\sqrt{3}}+\frac{\sqrt[3]{x^3+1} \left(1-3 x^3\right)}{4 x^4}+\frac{1}{6} \log \left(\sqrt[3]{x^3+1} x+\left(x^3+1\right)^{2/3}+x^2\right)",1,"(1 + x^3)^(4/3)/(4*x^4) - Hypergeometric2F1[-1/3, -1/3, 2/3, -x^3]/x","C",1
1408,1,34,101,0.0095217,"\int \frac{\left(-1+x^3\right) \sqrt[3]{1+x^3}}{x^2} \, dx","Integrate[((-1 + x^3)*(1 + x^3)^(1/3))/x^2,x]","\frac{\left(x^3+1\right)^{4/3}}{x}-x^2 \, _2F_1\left(-\frac{1}{3},\frac{2}{3};\frac{5}{3};-x^3\right)","\frac{\sqrt[3]{x^3+1} \left(x^3+3\right)}{3 x}+\frac{2}{9} \log \left(\sqrt[3]{x^3+1}-x\right)+\frac{2 \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+1}+x}\right)}{3 \sqrt{3}}-\frac{1}{9} \log \left(\sqrt[3]{x^3+1} x+\left(x^3+1\right)^{2/3}+x^2\right)",1,"(1 + x^3)^(4/3)/x - x^2*Hypergeometric2F1[-1/3, 2/3, 5/3, -x^3]","C",1
1409,1,50,101,0.0219561,"\int \frac{\sqrt[3]{-1+x^3} \left(1+x^3\right)}{x^5} \, dx","Integrate[((-1 + x^3)^(1/3)*(1 + x^3))/x^5,x]","\frac{\sqrt[3]{x^3-1} \left(-\frac{4 x^3 \, _2F_1\left(-\frac{1}{3},-\frac{1}{3};\frac{2}{3};x^3\right)}{\sqrt[3]{1-x^3}}+x^3-1\right)}{4 x^4}","-\frac{1}{3} \log \left(\sqrt[3]{x^3-1}-x\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-1}+x}\right)}{\sqrt{3}}+\frac{\sqrt[3]{x^3-1} \left(-3 x^3-1\right)}{4 x^4}+\frac{1}{6} \log \left(\sqrt[3]{x^3-1} x+\left(x^3-1\right)^{2/3}+x^2\right)",1,"((-1 + x^3)^(1/3)*(-1 + x^3 - (4*x^3*Hypergeometric2F1[-1/3, -1/3, 2/3, x^3])/(1 - x^3)^(1/3)))/(4*x^4)","C",1
1410,1,152,101,0.64302,"\int \frac{x}{\left(1+x^2\right) \sqrt{-x-x^2+x^3}} \, dx","Integrate[x/((1 + x^2)*Sqrt[-x - x^2 + x^3]),x]","\frac{\sqrt{\frac{2}{1+\sqrt{5}}} \sqrt{x} \sqrt{-x^2+x+1} \left(\Pi \left(\frac{1}{2} i \left(-1+\sqrt{5}\right);i \sinh ^{-1}\left(\sqrt{\frac{2}{-1+\sqrt{5}}} \sqrt{x}\right)|\frac{1}{2} \left(-3+\sqrt{5}\right)\right)-\Pi \left(-\frac{1}{2} i \left(-1+\sqrt{5}\right);i \sinh ^{-1}\left(\sqrt{\frac{2}{-1+\sqrt{5}}} \sqrt{x}\right)|\frac{1}{2} \left(-3+\sqrt{5}\right)\right)\right)}{\sqrt{x \left(x^2-x-1\right)}}","-\frac{1}{2} \sqrt{-\frac{1}{5}-\frac{2 i}{5}} \tan ^{-1}\left(\frac{\sqrt{1-2 i} \sqrt{x^3-x^2-x}}{x^2-x-1}\right)-\frac{1}{2} \sqrt{-\frac{1}{5}+\frac{2 i}{5}} \tan ^{-1}\left(\frac{\sqrt{1+2 i} \sqrt{x^3-x^2-x}}{x^2-x-1}\right)",1,"(Sqrt[2/(1 + Sqrt[5])]*Sqrt[x]*Sqrt[1 + x - x^2]*(-EllipticPi[(-1/2*I)*(-1 + Sqrt[5]), I*ArcSinh[Sqrt[2/(-1 + Sqrt[5])]*Sqrt[x]], (-3 + Sqrt[5])/2] + EllipticPi[(I/2)*(-1 + Sqrt[5]), I*ArcSinh[Sqrt[2/(-1 + Sqrt[5])]*Sqrt[x]], (-3 + Sqrt[5])/2]))/Sqrt[x*(-1 - x + x^2)]","C",0
1411,1,211,101,0.6267929,"\int \frac{-1+x+x^2}{\left(1+x^2\right) \sqrt{-x-x^2+x^3}} \, dx","Integrate[(-1 + x + x^2)/((1 + x^2)*Sqrt[-x - x^2 + x^3]),x]","-\frac{i \sqrt{\frac{2}{\sqrt{5}-1}} \sqrt{-\frac{1}{x^2}-\frac{1}{x}+1} x^{3/2} \left(2 F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{1+\sqrt{5}}}}{\sqrt{x}}\right)|-\frac{3}{2}-\frac{\sqrt{5}}{2}\right)-(2-i) \Pi \left(-\frac{1}{2} i \left(1+\sqrt{5}\right);i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{1+\sqrt{5}}}}{\sqrt{x}}\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)-(2+i) \Pi \left(\frac{1}{2} i \left(1+\sqrt{5}\right);i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{1+\sqrt{5}}}}{\sqrt{x}}\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)\right)}{\sqrt{x \left(x^2-x-1\right)}}","-\frac{1}{2} \sqrt{\frac{11}{5}+\frac{2 i}{5}} \tan ^{-1}\left(\frac{\sqrt{1-2 i} \sqrt{x^3-x^2-x}}{x^2-x-1}\right)-\frac{1}{2} \sqrt{\frac{11}{5}-\frac{2 i}{5}} \tan ^{-1}\left(\frac{\sqrt{1+2 i} \sqrt{x^3-x^2-x}}{x^2-x-1}\right)",1,"((-I)*Sqrt[2/(-1 + Sqrt[5])]*Sqrt[1 - x^(-2) - x^(-1)]*x^(3/2)*(2*EllipticF[I*ArcSinh[Sqrt[2/(1 + Sqrt[5])]/Sqrt[x]], -3/2 - Sqrt[5]/2] - (2 - I)*EllipticPi[(-1/2*I)*(1 + Sqrt[5]), I*ArcSinh[Sqrt[2/(1 + Sqrt[5])]/Sqrt[x]], (-3 - Sqrt[5])/2] - (2 + I)*EllipticPi[(I/2)*(1 + Sqrt[5]), I*ArcSinh[Sqrt[2/(1 + Sqrt[5])]/Sqrt[x]], (-3 - Sqrt[5])/2]))/Sqrt[x*(-1 - x + x^2)]","C",0
1412,1,35,101,0.01085,"\int \frac{x}{\sqrt[3]{x^2+x^3}} \, dx","Integrate[x/(x^2 + x^3)^(1/3),x]","\frac{3 \left(x^2 (x+1)\right)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{4}{3};\frac{7}{3};-x\right)}{4 (x+1)^{2/3}}","\frac{\left(x^3+x^2\right)^{2/3}}{x}+\frac{1}{3} \log \left(\sqrt[3]{x^3+x^2}-x\right)-\frac{1}{6} \log \left(x^2+\sqrt[3]{x^3+x^2} x+\left(x^3+x^2\right)^{2/3}\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+x^2}+x}\right)}{\sqrt{3}}",1,"(3*(x^2*(1 + x))^(2/3)*Hypergeometric2F1[1/3, 4/3, 7/3, -x])/(4*(1 + x)^(2/3))","C",1
1413,1,116,101,0.3157602,"\int \frac{1}{x^6 \left(1+x^3\right) \sqrt[3]{x^2+x^3}} \, dx","Integrate[1/(x^6*(1 + x^3)*(x^2 + x^3)^(1/3)),x]","\frac{52360 x^6 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(3-i \sqrt{3}\right) x}{2 (x+1)}\right)+52360 x^6 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(3+i \sqrt{3}\right) x}{2 (x+1)}\right)+109573 x^6+19071 x^5-6357 x^4+20985 x^3-900 x^2+660 x-9240}{52360 x^5 \sqrt[3]{x^2 (x+1)}}","\frac{\left(x^3+x^2\right)^{2/3} \left(109573 x^6+19071 x^5-6357 x^4+20985 x^3-900 x^2+660 x-9240\right)}{52360 x^7 (x+1)}-\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^6-3 \text{$\#$1}^3+3\&,\frac{\log \left(\sqrt[3]{x^3+x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]",1,"(-9240 + 660*x - 900*x^2 + 20985*x^3 - 6357*x^4 + 19071*x^5 + 109573*x^6 + 52360*x^6*Hypergeometric2F1[1/3, 1, 4/3, ((3 - I*Sqrt[3])*x)/(2*(1 + x))] + 52360*x^6*Hypergeometric2F1[1/3, 1, 4/3, ((3 + I*Sqrt[3])*x)/(2*(1 + x))])/(52360*x^5*(x^2*(1 + x))^(1/3))","C",1
1414,1,116,101,0.1505829,"\int \frac{1}{x^6 \left(1+x^3\right) \sqrt[3]{x^2+x^3}} \, dx","Integrate[1/(x^6*(1 + x^3)*(x^2 + x^3)^(1/3)),x]","\frac{52360 x^6 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(3-i \sqrt{3}\right) x}{2 (x+1)}\right)+52360 x^6 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(3+i \sqrt{3}\right) x}{2 (x+1)}\right)+109573 x^6+19071 x^5-6357 x^4+20985 x^3-900 x^2+660 x-9240}{52360 x^5 \sqrt[3]{x^2 (x+1)}}","\frac{\left(x^3+x^2\right)^{2/3} \left(109573 x^6+19071 x^5-6357 x^4+20985 x^3-900 x^2+660 x-9240\right)}{52360 x^7 (x+1)}-\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^6-3 \text{$\#$1}^3+3\&,\frac{\log \left(\sqrt[3]{x^3+x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]",1,"(-9240 + 660*x - 900*x^2 + 20985*x^3 - 6357*x^4 + 19071*x^5 + 109573*x^6 + 52360*x^6*Hypergeometric2F1[1/3, 1, 4/3, ((3 - I*Sqrt[3])*x)/(2*(1 + x))] + 52360*x^6*Hypergeometric2F1[1/3, 1, 4/3, ((3 + I*Sqrt[3])*x)/(2*(1 + x))])/(52360*x^5*(x^2*(1 + x))^(1/3))","C",1
1415,1,52,101,0.0260128,"\int \frac{\sqrt[3]{-1+x^3} \left(-1+2 x^3\right)}{x^5} \, dx","Integrate[((-1 + x^3)^(1/3)*(-1 + 2*x^3))/x^5,x]","\frac{\sqrt[3]{x^3-1} \left(-\frac{8 x^3 \, _2F_1\left(-\frac{1}{3},-\frac{1}{3};\frac{2}{3};x^3\right)}{\sqrt[3]{1-x^3}}-x^3+1\right)}{4 x^4}","-\frac{2}{3} \log \left(\sqrt[3]{x^3-1}-x\right)-\frac{2 \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-1}+x}\right)}{\sqrt{3}}+\frac{\sqrt[3]{x^3-1} \left(1-9 x^3\right)}{4 x^4}+\frac{1}{3} \log \left(\sqrt[3]{x^3-1} x+\left(x^3-1\right)^{2/3}+x^2\right)",1,"((-1 + x^3)^(1/3)*(1 - x^3 - (8*x^3*Hypergeometric2F1[-1/3, -1/3, 2/3, x^3])/(1 - x^3)^(1/3)))/(4*x^4)","C",1
1416,1,111,101,0.1216478,"\int \frac{\left(-1+x^3\right)^{2/3} \left(-1+3 x^3\right)}{x^6 \left(-1+2 x^3\right)} \, dx","Integrate[((-1 + x^3)^(2/3)*(-1 + 3*x^3))/(x^6*(-1 + 2*x^3)),x]","\frac{1}{3} \log \left(\frac{x}{\sqrt[3]{1-x^3}}+1\right)+\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{1-x^3}}-1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{1}{6} \log \left(-\frac{x}{\sqrt[3]{1-x^3}}+\frac{x^2}{\left(1-x^3\right)^{2/3}}+1\right)+\left(x^3-1\right)^{2/3} \left(\frac{7}{10 x^2}-\frac{1}{5 x^5}\right)","\frac{1}{3} \log \left(\sqrt[3]{x^3-1}+x\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-1}-x}\right)}{\sqrt{3}}+\frac{\left(x^3-1\right)^{2/3} \left(7 x^3-2\right)}{10 x^5}-\frac{1}{6} \log \left(-\sqrt[3]{x^3-1} x+\left(x^3-1\right)^{2/3}+x^2\right)",1,"(-1/5*1/x^5 + 7/(10*x^2))*(-1 + x^3)^(2/3) + ArcTan[(-1 + (2*x)/(1 - x^3)^(1/3))/Sqrt[3]]/Sqrt[3] - Log[1 + x^2/(1 - x^3)^(2/3) - x/(1 - x^3)^(1/3)]/6 + Log[1 + x/(1 - x^3)^(1/3)]/3","A",0
1417,1,112,101,0.3304558,"\int \frac{x^4}{\left(-1+x^4\right)^2 \sqrt[4]{x^2+x^4}} \, dx","Integrate[x^4/((-1 + x^4)^2*(x^2 + x^4)^(1/4)),x]","\frac{x \left(-4 \left(13 x^4+2 x^2+5\right)+5\ 2^{3/4} \sqrt[4]{\frac{1}{x^2}+1} \left(x^4-1\right) \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{x^2}+1}}{\sqrt[4]{2}}\right)-5\ 2^{3/4} \sqrt[4]{\frac{1}{x^2}+1} \left(x^4-1\right) \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{x^2}+1}}{\sqrt[4]{2}}\right)\right)}{320 \left(x^4-1\right) \sqrt[4]{x^4+x^2}}","\frac{\left(x^4+x^2\right)^{3/4} \left(-13 x^4-2 x^2-5\right)}{80 x \left(x^2-1\right) \left(x^2+1\right)^2}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+x^2}}\right)}{32 \sqrt[4]{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+x^2}}\right)}{32 \sqrt[4]{2}}",1,"(x*(-4*(5 + 2*x^2 + 13*x^4) + 5*2^(3/4)*(1 + x^(-2))^(1/4)*(-1 + x^4)*ArcTan[(1 + x^(-2))^(1/4)/2^(1/4)] - 5*2^(3/4)*(1 + x^(-2))^(1/4)*(-1 + x^4)*ArcTanh[(1 + x^(-2))^(1/4)/2^(1/4)]))/(320*(-1 + x^4)*(x^2 + x^4)^(1/4))","A",1
1418,1,77,101,0.0628814,"\int \frac{\left(1+x^2\right) \sqrt[4]{x^3+x^4}}{x^2 \left(-1+x^2\right)} \, dx","Integrate[((1 + x^2)*(x^3 + x^4)^(1/4))/(x^2*(-1 + x^2)),x]","-\frac{4 \sqrt[4]{x^3 (x+1)} \left(3 (x+1) \, _2F_1\left(-\frac{1}{4},-\frac{1}{4};\frac{3}{4};-x\right)+2 \sqrt[4]{x+1} \left(x \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{2 x}{x+1}\right)-3 (x+1)\right)\right)}{3 x (x+1)^{5/4}}","\frac{4 \sqrt[4]{x^4+x^3}}{x}-2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+x^3}}\right)+2 \sqrt[4]{2} \tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+x^3}}\right)+2 \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+x^3}}\right)-2 \sqrt[4]{2} \tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+x^3}}\right)",1,"(-4*(x^3*(1 + x))^(1/4)*(3*(1 + x)*Hypergeometric2F1[-1/4, -1/4, 3/4, -x] + 2*(1 + x)^(1/4)*(-3*(1 + x) + x*Hypergeometric2F1[3/4, 1, 7/4, (2*x)/(1 + x)])))/(3*x*(1 + x)^(5/4))","C",1
1419,0,0,101,0.4528494,"\int \frac{\left(4+x^3\right) \left(-1-x^3+x^4\right)}{x^2 \left(1+x^3\right)^{3/4} \left(1+x^3+x^4\right)} \, dx","Integrate[((4 + x^3)*(-1 - x^3 + x^4))/(x^2*(1 + x^3)^(3/4)*(1 + x^3 + x^4)),x]","\int \frac{\left(4+x^3\right) \left(-1-x^3+x^4\right)}{x^2 \left(1+x^3\right)^{3/4} \left(1+x^3+x^4\right)} \, dx","\frac{4 \sqrt[4]{x^3+1}}{x}-2 \sqrt{2} \tan ^{-1}\left(\frac{\frac{\sqrt{x^3+1}}{\sqrt{2}}-\frac{x^2}{\sqrt{2}}}{x \sqrt[4]{x^3+1}}\right)-2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{x^3+1}}{\sqrt{x^3+1}+x^2}\right)",1,"Integrate[((4 + x^3)*(-1 - x^3 + x^4))/(x^2*(1 + x^3)^(3/4)*(1 + x^3 + x^4)), x]","F",-1
1420,1,127,101,0.1976942,"\int \frac{1+x^2+2 x^4}{\sqrt[4]{1+x^2} \left(2+3 x^2+x^4\right)} \, dx","Integrate[(1 + x^2 + 2*x^4)/((1 + x^2)^(1/4)*(2 + 3*x^2 + x^4)),x]","\frac{2 x \left(\frac{21 F_1\left(\frac{1}{2};\frac{1}{4},1;\frac{3}{2};-x^2,-\frac{x^2}{2}\right)}{\left(x^2+2\right) \left(x^2 \left(2 F_1\left(\frac{3}{2};\frac{1}{4},2;\frac{5}{2};-x^2,-\frac{x^2}{2}\right)+F_1\left(\frac{3}{2};\frac{5}{4},1;\frac{5}{2};-x^2,-\frac{x^2}{2}\right)\right)-6 F_1\left(\frac{1}{2};\frac{1}{4},1;\frac{3}{2};-x^2,-\frac{x^2}{2}\right)\right)}+2\right)}{\sqrt[4]{x^2+1}}","\frac{4 x}{\sqrt[4]{x^2+1}}+\frac{7}{4} \tan ^{-1}\left(\frac{\sqrt[4]{x^2+1}-x}{\sqrt[4]{x^2+1}}\right)-\frac{7}{4} \tan ^{-1}\left(\frac{\sqrt[4]{x^2+1}+x}{\sqrt[4]{x^2+1}}\right)-\frac{7}{4} \tanh ^{-1}\left(\frac{2 x \sqrt[4]{x^2+1}}{x^2+2 \sqrt{x^2+1}}\right)",1,"(2*x*(2 + (21*AppellF1[1/2, 1/4, 1, 3/2, -x^2, -1/2*x^2])/((2 + x^2)*(-6*AppellF1[1/2, 1/4, 1, 3/2, -x^2, -1/2*x^2] + x^2*(2*AppellF1[3/2, 1/4, 2, 5/2, -x^2, -1/2*x^2] + AppellF1[3/2, 5/4, 1, 5/2, -x^2, -1/2*x^2])))))/(1 + x^2)^(1/4)","C",0
1421,1,55,101,0.0223445,"\int \frac{\left(-b+a x^2\right) \sqrt[4]{-b x^2+a x^4}}{x^2} \, dx","Integrate[((-b + a*x^2)*(-(b*x^2) + a*x^4)^(1/4))/x^2,x]","\frac{2 b \sqrt[4]{a x^4-b x^2} \, _2F_1\left(-\frac{5}{4},-\frac{1}{4};\frac{3}{4};\frac{a x^2}{b}\right)}{x \sqrt[4]{1-\frac{a x^2}{b}}}","\frac{\sqrt[4]{a x^4-b x^2} \left(a x^2+4 b\right)}{2 x}+\frac{5}{4} \sqrt[4]{a} b \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)-\frac{5}{4} \sqrt[4]{a} b \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)",1,"(2*b*(-(b*x^2) + a*x^4)^(1/4)*Hypergeometric2F1[-5/4, -1/4, 3/4, (a*x^2)/b])/(x*(1 - (a*x^2)/b)^(1/4))","C",1
1422,1,390,101,4.2075246,"\int \frac{b+a x^4}{x^4 \left(2 b+a x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Integrate[(b + a*x^4)/(x^4*(2*b + a*x^4)*(b*x^2 + a*x^4)^(1/4)),x]","\frac{\sqrt{x} \left(\frac{8 \left(a x^2+b\right) \left(4 a x^2-3 b\right)}{21 b^2 x^{7/2}}-\frac{a \sqrt{x} \sqrt[4]{a+\frac{b}{x^2}} \left(\sqrt[4]{\sqrt{2} \sqrt{-a} \sqrt{b}+2 a} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a-\frac{\sqrt{-a} \sqrt{b}}{\sqrt{2}}}}\right)+\sqrt[4]{2 a-\sqrt{2} \sqrt{-a} \sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\frac{\sqrt{-a} \sqrt{b}}{\sqrt{2}}+a}}\right)-\sqrt[4]{\sqrt{2} \sqrt{-a} \sqrt{b}+2 a} \tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a-\frac{\sqrt{-a} \sqrt{b}}{\sqrt{2}}}}\right)-\sqrt[4]{2 a-\sqrt{2} \sqrt{-a} \sqrt{b}} \tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\frac{\sqrt{-a} \sqrt{b}}{\sqrt{2}}+a}}\right)\right)}{b \sqrt[4]{a-\frac{\sqrt{-a} \sqrt{b}}{\sqrt{2}}} \sqrt[4]{\sqrt{2} \sqrt{-a} \sqrt{b}+2 a}}\right)}{8 \sqrt[4]{x^2 \left(a x^2+b\right)}}","\frac{\left(4 a x^2-3 b\right) \left(a x^4+b x^2\right)^{3/4}}{21 b^2 x^5}-\frac{a \text{RootSum}\left[2 \text{$\#$1}^8-4 \text{$\#$1}^4 a+2 a^2+a b\&,\frac{\log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{16 b}",1,"(Sqrt[x]*((8*(b + a*x^2)*(-3*b + 4*a*x^2))/(21*b^2*x^(7/2)) - (a*(a + b/x^2)^(1/4)*Sqrt[x]*((2*a + Sqrt[2]*Sqrt[-a]*Sqrt[b])^(1/4)*ArcTan[(a + b/x^2)^(1/4)/(a - (Sqrt[-a]*Sqrt[b])/Sqrt[2])^(1/4)] + (2*a - Sqrt[2]*Sqrt[-a]*Sqrt[b])^(1/4)*ArcTan[(a + b/x^2)^(1/4)/(a + (Sqrt[-a]*Sqrt[b])/Sqrt[2])^(1/4)] - (2*a + Sqrt[2]*Sqrt[-a]*Sqrt[b])^(1/4)*ArcTanh[(a + b/x^2)^(1/4)/(a - (Sqrt[-a]*Sqrt[b])/Sqrt[2])^(1/4)] - (2*a - Sqrt[2]*Sqrt[-a]*Sqrt[b])^(1/4)*ArcTanh[(a + b/x^2)^(1/4)/(a + (Sqrt[-a]*Sqrt[b])/Sqrt[2])^(1/4)]))/((a - (Sqrt[-a]*Sqrt[b])/Sqrt[2])^(1/4)*(2*a + Sqrt[2]*Sqrt[-a]*Sqrt[b])^(1/4)*b)))/(8*(x^2*(b + a*x^2))^(1/4))","B",1
1423,1,390,101,2.4389029,"\int \frac{b+a x^4}{x^4 \left(2 b+a x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Integrate[(b + a*x^4)/(x^4*(2*b + a*x^4)*(b*x^2 + a*x^4)^(1/4)),x]","\frac{\sqrt{x} \left(\frac{8 \left(a x^2+b\right) \left(4 a x^2-3 b\right)}{21 b^2 x^{7/2}}-\frac{a \sqrt{x} \sqrt[4]{a+\frac{b}{x^2}} \left(\sqrt[4]{\sqrt{2} \sqrt{-a} \sqrt{b}+2 a} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a-\frac{\sqrt{-a} \sqrt{b}}{\sqrt{2}}}}\right)+\sqrt[4]{2 a-\sqrt{2} \sqrt{-a} \sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\frac{\sqrt{-a} \sqrt{b}}{\sqrt{2}}+a}}\right)-\sqrt[4]{\sqrt{2} \sqrt{-a} \sqrt{b}+2 a} \tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a-\frac{\sqrt{-a} \sqrt{b}}{\sqrt{2}}}}\right)-\sqrt[4]{2 a-\sqrt{2} \sqrt{-a} \sqrt{b}} \tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\frac{\sqrt{-a} \sqrt{b}}{\sqrt{2}}+a}}\right)\right)}{b \sqrt[4]{a-\frac{\sqrt{-a} \sqrt{b}}{\sqrt{2}}} \sqrt[4]{\sqrt{2} \sqrt{-a} \sqrt{b}+2 a}}\right)}{8 \sqrt[4]{x^2 \left(a x^2+b\right)}}","\frac{\left(4 a x^2-3 b\right) \left(a x^4+b x^2\right)^{3/4}}{21 b^2 x^5}-\frac{a \text{RootSum}\left[2 \text{$\#$1}^8-4 \text{$\#$1}^4 a+2 a^2+a b\&,\frac{\log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{16 b}",1,"(Sqrt[x]*((8*(b + a*x^2)*(-3*b + 4*a*x^2))/(21*b^2*x^(7/2)) - (a*(a + b/x^2)^(1/4)*Sqrt[x]*((2*a + Sqrt[2]*Sqrt[-a]*Sqrt[b])^(1/4)*ArcTan[(a + b/x^2)^(1/4)/(a - (Sqrt[-a]*Sqrt[b])/Sqrt[2])^(1/4)] + (2*a - Sqrt[2]*Sqrt[-a]*Sqrt[b])^(1/4)*ArcTan[(a + b/x^2)^(1/4)/(a + (Sqrt[-a]*Sqrt[b])/Sqrt[2])^(1/4)] - (2*a + Sqrt[2]*Sqrt[-a]*Sqrt[b])^(1/4)*ArcTanh[(a + b/x^2)^(1/4)/(a - (Sqrt[-a]*Sqrt[b])/Sqrt[2])^(1/4)] - (2*a - Sqrt[2]*Sqrt[-a]*Sqrt[b])^(1/4)*ArcTanh[(a + b/x^2)^(1/4)/(a + (Sqrt[-a]*Sqrt[b])/Sqrt[2])^(1/4)]))/((a - (Sqrt[-a]*Sqrt[b])/Sqrt[2])^(1/4)*(2*a + Sqrt[2]*Sqrt[-a]*Sqrt[b])^(1/4)*b)))/(8*(x^2*(b + a*x^2))^(1/4))","B",1
1424,1,3897,101,6.212417,"\int \frac{1-x^4}{x^2 \sqrt{a+b x+c x^2+b x^3+a x^4}} \, dx","Integrate[(1 - x^4)/(x^2*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]),x]","\text{Result too large to show}","-\frac{b \log \left(2 \sqrt{a} \sqrt{a x^4+a+b x^3+b x+c x^2}-2 a x^2-2 a-b x\right)}{2 a^{3/2}}+\frac{b \log (x)}{2 a^{3/2}}-\frac{\sqrt{a x^4+a+b x^3+b x+c x^2}}{a x}",1,"-((a + b*x + c*x^2 + b*x^3 + a*x^4)/(a*x*Sqrt[x*(b + c*x + b*x^2) + a*(1 + x^4)])) + (b*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]*((2*(x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])^2*(-(EllipticF[ArcSin[Sqrt[((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))]], -(((Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])))]*Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2]) + EllipticPi[(-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])/(-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]), ArcSin[Sqrt[((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))]], -(((Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])))]*(-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2]))*Sqrt[((-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3]))/((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3]))]*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])*Sqrt[((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))]*Sqrt[((-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))])/(Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]*(-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])) + (2*(x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])^2*(-(EllipticF[ArcSin[Sqrt[((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))]], -(((Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])))]*Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1]) - EllipticPi[(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2]*(-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1]*(-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])), ArcSin[Sqrt[((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))]], -(((Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])))]*(-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2]))*Sqrt[((-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3]))/((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3]))]*Sqrt[((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))]*Sqrt[((-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))]*(-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/(Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]*Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1]*Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2]*(-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))))/(2*a*Sqrt[x*(b + c*x + b*x^2) + a*(1 + x^4)])","C",1
1425,0,0,101,0.4191,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt[4]{x^2+x^6}} \, dx","Integrate[(-1 + x^2)/((1 + x^2)*(x^2 + x^6)^(1/4)),x]","\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt[4]{x^2+x^6}} \, dx","\frac{\tan ^{-1}\left(\frac{2^{3/4} x \sqrt[4]{x^6+x^2}}{\sqrt{2} x^2-\sqrt{x^6+x^2}}\right)}{2^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\frac{x^2}{\sqrt[4]{2}}+\frac{\sqrt{x^6+x^2}}{2^{3/4}}}{x \sqrt[4]{x^6+x^2}}\right)}{2^{3/4}}",1,"Integrate[(-1 + x^2)/((1 + x^2)*(x^2 + x^6)^(1/4)), x]","F",-1
1426,0,0,101,0.1110704,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt[4]{x^2+x^6}} \, dx","Integrate[(-1 + x^2)/((1 + x^2)*(x^2 + x^6)^(1/4)),x]","\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt[4]{x^2+x^6}} \, dx","\frac{\tan ^{-1}\left(\frac{2^{3/4} x \sqrt[4]{x^6+x^2}}{\sqrt{2} x^2-\sqrt{x^6+x^2}}\right)}{2^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\frac{x^2}{\sqrt[4]{2}}+\frac{\sqrt{x^6+x^2}}{2^{3/4}}}{x \sqrt[4]{x^6+x^2}}\right)}{2^{3/4}}",1,"Integrate[(-1 + x^2)/((1 + x^2)*(x^2 + x^6)^(1/4)), x]","F",-1
1427,1,47,101,0.0178598,"\int \frac{\sqrt[4]{-x^3+x^4} \left(-1+x^8\right)}{x^4} \, dx","Integrate[((-x^3 + x^4)^(1/4)*(-1 + x^8))/x^4,x]","\frac{4 (x-1)^2 \left(9 x^{9/4} \, _2F_1\left(-\frac{19}{4},\frac{5}{4};\frac{9}{4};1-x\right)-4 x-5\right)}{45 \left((x-1) x^3\right)^{3/4}}","\frac{1463 \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^3}}\right)}{32768}-\frac{1463 \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^3}}\right)}{32768}+\frac{\sqrt[4]{x^4-x^3} \left(122880 x^8-6144 x^7-7296 x^6-9120 x^5-12540 x^4-21945 x^3-262144 x^2-65536 x+327680\right)}{737280 x^3}",1,"(4*(-1 + x)^2*(-5 - 4*x + 9*x^(9/4)*Hypergeometric2F1[-19/4, 5/4, 9/4, 1 - x]))/(45*((-1 + x)*x^3)^(3/4))","C",1
1428,0,0,101,7.0318814,"\int \frac{\sqrt[4]{1+x^4} \left(2+x^4\right)}{x^2 \left(-1+2 x^4+x^8\right)} \, dx","Integrate[((1 + x^4)^(1/4)*(2 + x^4))/(x^2*(-1 + 2*x^4 + x^8)),x]","\int \frac{\sqrt[4]{1+x^4} \left(2+x^4\right)}{x^2 \left(-1+2 x^4+x^8\right)} \, dx","\frac{2 \sqrt[4]{x^4+1}}{x}-\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^4+2\&,\frac{-7 \text{$\#$1}^4 \log \left(\sqrt[4]{x^4+1}-\text{$\#$1} x\right)+7 \text{$\#$1}^4 \log (x)+4 \log \left(\sqrt[4]{x^4+1}-\text{$\#$1} x\right)-4 \log (x)}{\text{$\#$1}^7-2 \text{$\#$1}^3}\&\right]",1,"Integrate[((1 + x^4)^(1/4)*(2 + x^4))/(x^2*(-1 + 2*x^4 + x^8)), x]","F",-1
1429,0,0,101,6.9206128,"\int \frac{\sqrt[4]{1+x^4} \left(2+x^4\right)}{x^2 \left(-1+2 x^4+x^8\right)} \, dx","Integrate[((1 + x^4)^(1/4)*(2 + x^4))/(x^2*(-1 + 2*x^4 + x^8)),x]","\int \frac{\sqrt[4]{1+x^4} \left(2+x^4\right)}{x^2 \left(-1+2 x^4+x^8\right)} \, dx","\frac{2 \sqrt[4]{x^4+1}}{x}-\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^4+2\&,\frac{-7 \text{$\#$1}^4 \log \left(\sqrt[4]{x^4+1}-\text{$\#$1} x\right)+7 \text{$\#$1}^4 \log (x)+4 \log \left(\sqrt[4]{x^4+1}-\text{$\#$1} x\right)-4 \log (x)}{\text{$\#$1}^7-2 \text{$\#$1}^3}\&\right]",1,"Integrate[((1 + x^4)^(1/4)*(2 + x^4))/(x^2*(-1 + 2*x^4 + x^8)), x]","F",-1
1430,0,0,101,0.5883846,"\int \frac{-b+2 a x^4}{\sqrt[4]{-b+a x^4} \left(-b+a x^8\right)} \, dx","Integrate[(-b + 2*a*x^4)/((-b + a*x^4)^(1/4)*(-b + a*x^8)),x]","\int \frac{-b+2 a x^4}{\sqrt[4]{-b+a x^4} \left(-b+a x^8\right)} \, dx","\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2-a b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))+a \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)-a \log (x)}{\text{$\#$1} a-\text{$\#$1}^5}\&\right]",1,"Integrate[(-b + 2*a*x^4)/((-b + a*x^4)^(1/4)*(-b + a*x^8)), x]","F",-1
1431,0,0,101,0.1489889,"\int \frac{\sqrt{1+2 x^6} \left(-1+4 x^6\right)}{2+x^4+8 x^6+8 x^{12}} \, dx","Integrate[(Sqrt[1 + 2*x^6]*(-1 + 4*x^6))/(2 + x^4 + 8*x^6 + 8*x^12),x]","\int \frac{\sqrt{1+2 x^6} \left(-1+4 x^6\right)}{2+x^4+8 x^6+8 x^{12}} \, dx","-\frac{\tan ^{-1}\left(\frac{2^{3/4} x \sqrt{2 x^6+1}}{2 \sqrt{2} x^6-x^2+\sqrt{2}}\right)}{4 \sqrt[4]{2}}-\frac{\tanh ^{-1}\left(\frac{2^{3/4} x \sqrt{2 x^6+1}}{2 \sqrt{2} x^6+x^2+\sqrt{2}}\right)}{4 \sqrt[4]{2}}",1,"Integrate[(Sqrt[1 + 2*x^6]*(-1 + 4*x^6))/(2 + x^4 + 8*x^6 + 8*x^12), x]","F",-1
1432,1,281,101,0.7053163,"\int \frac{\left(-1+x^2\right) \sqrt{1+\sqrt{1+x}}}{1+x^2} \, dx","Integrate[((-1 + x^2)*Sqrt[1 + Sqrt[1 + x]])/(1 + x^2),x]","\frac{4}{15} \sqrt{\sqrt{x+1}+1} \left(3 x+\sqrt{x+1}+1\right)-\frac{(1-i)^{3/2} \left((-1+i)+\sqrt{1-i}\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x+1}+1}}{\sqrt{1-\sqrt{1-i}}}\right)}{\sqrt{1-\sqrt{1-i}}}+\frac{2 \left((1+i)+i \sqrt{1-i}\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x+1}+1}}{\sqrt{1+\sqrt{1-i}}}\right)}{\sqrt{(1-i)+(1-i)^{3/2}}}-\frac{(1+i)^{3/2} \left((-1-i)+\sqrt{1+i}\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x+1}+1}}{\sqrt{1-\sqrt{1+i}}}\right)}{\sqrt{1-\sqrt{1+i}}}-\frac{(1+i)^{3/2} \left((1+i)+\sqrt{1+i}\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x+1}+1}}{\sqrt{1+\sqrt{1+i}}}\right)}{\sqrt{1+\sqrt{1+i}}}","-\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^3-2 \text{$\#$1}}\&\right]+\frac{4}{15} \sqrt{\sqrt{x+1}+1} (3 x+1)+\frac{4}{15} \sqrt{x+1} \sqrt{\sqrt{x+1}+1}",1,"(4*Sqrt[1 + Sqrt[1 + x]]*(1 + 3*x + Sqrt[1 + x]))/15 - ((1 - I)^(3/2)*((-1 + I) + Sqrt[1 - I])*ArcTanh[Sqrt[1 + Sqrt[1 + x]]/Sqrt[1 - Sqrt[1 - I]]])/Sqrt[1 - Sqrt[1 - I]] + (2*((1 + I) + I*Sqrt[1 - I])*ArcTanh[Sqrt[1 + Sqrt[1 + x]]/Sqrt[1 + Sqrt[1 - I]]])/Sqrt[(1 - I) + (1 - I)^(3/2)] - ((1 + I)^(3/2)*((-1 - I) + Sqrt[1 + I])*ArcTanh[Sqrt[1 + Sqrt[1 + x]]/Sqrt[1 - Sqrt[1 + I]]])/Sqrt[1 - Sqrt[1 + I]] - ((1 + I)^(3/2)*((1 + I) + Sqrt[1 + I])*ArcTanh[Sqrt[1 + Sqrt[1 + x]]/Sqrt[1 + Sqrt[1 + I]]])/Sqrt[1 + Sqrt[1 + I]]","C",0
1433,1,281,101,0.1655147,"\int \frac{\left(-1+x^2\right) \sqrt{1+\sqrt{1+x}}}{1+x^2} \, dx","Integrate[((-1 + x^2)*Sqrt[1 + Sqrt[1 + x]])/(1 + x^2),x]","\frac{4}{15} \sqrt{\sqrt{x+1}+1} \left(3 x+\sqrt{x+1}+1\right)-\frac{(1-i)^{3/2} \left((-1+i)+\sqrt{1-i}\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x+1}+1}}{\sqrt{1-\sqrt{1-i}}}\right)}{\sqrt{1-\sqrt{1-i}}}+\frac{2 \left((1+i)+i \sqrt{1-i}\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x+1}+1}}{\sqrt{1+\sqrt{1-i}}}\right)}{\sqrt{(1-i)+(1-i)^{3/2}}}-\frac{(1+i)^{3/2} \left((-1-i)+\sqrt{1+i}\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x+1}+1}}{\sqrt{1-\sqrt{1+i}}}\right)}{\sqrt{1-\sqrt{1+i}}}-\frac{(1+i)^{3/2} \left((1+i)+\sqrt{1+i}\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x+1}+1}}{\sqrt{1+\sqrt{1+i}}}\right)}{\sqrt{1+\sqrt{1+i}}}","-\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^3-2 \text{$\#$1}}\&\right]+\frac{4}{15} \sqrt{\sqrt{x+1}+1} (3 x+1)+\frac{4}{15} \sqrt{x+1} \sqrt{\sqrt{x+1}+1}",1,"(4*Sqrt[1 + Sqrt[1 + x]]*(1 + 3*x + Sqrt[1 + x]))/15 - ((1 - I)^(3/2)*((-1 + I) + Sqrt[1 - I])*ArcTanh[Sqrt[1 + Sqrt[1 + x]]/Sqrt[1 - Sqrt[1 - I]]])/Sqrt[1 - Sqrt[1 - I]] + (2*((1 + I) + I*Sqrt[1 - I])*ArcTanh[Sqrt[1 + Sqrt[1 + x]]/Sqrt[1 + Sqrt[1 - I]]])/Sqrt[(1 - I) + (1 - I)^(3/2)] - ((1 + I)^(3/2)*((-1 - I) + Sqrt[1 + I])*ArcTanh[Sqrt[1 + Sqrt[1 + x]]/Sqrt[1 - Sqrt[1 + I]]])/Sqrt[1 - Sqrt[1 + I]] - ((1 + I)^(3/2)*((1 + I) + Sqrt[1 + I])*ArcTanh[Sqrt[1 + Sqrt[1 + x]]/Sqrt[1 + Sqrt[1 + I]]])/Sqrt[1 + Sqrt[1 + I]]","C",0
1434,1,250,101,0.7261019,"\int x^2 \sqrt{x^2+\sqrt{1+x^4}} \, dx","Integrate[x^2*Sqrt[x^2 + Sqrt[1 + x^4]],x]","\frac{x \sqrt{x^4+1} \sqrt{\sqrt{x^4+1}+x^2} \sqrt{x^2 \left(\sqrt{x^4+1}+x^2\right)} \left(2 x^4+2 \sqrt{x^4+1} x^2+1\right)^2 \left(\sqrt{2} \sqrt{-x^2 \left(\sqrt{x^4+1}+x^2\right)} \left(2 x^4+2 \sqrt{x^4+1} x^2-1\right)-\left(\sqrt{x^4+1}+x^2\right) \sin ^{-1}\left(\sqrt{x^4+1}+x^2\right)\right)}{8 \sqrt{2} \sqrt{-x^4 \left(2 x^4+2 \sqrt{x^4+1} x^2+1\right)} \left(16 x^{12}+28 x^8+13 x^4+16 \sqrt{x^4+1} x^{10}+20 \sqrt{x^4+1} x^6+5 \sqrt{x^4+1} x^2+1\right)}","\frac{2 \sqrt{x^4+1} x^4+\left(2 x^4-1\right) x^2}{8 x \sqrt{\sqrt{x^4+1}+x^2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)}{4 \sqrt{2}}",1,"(x*Sqrt[1 + x^4]*Sqrt[x^2 + Sqrt[1 + x^4]]*Sqrt[x^2*(x^2 + Sqrt[1 + x^4])]*(1 + 2*x^4 + 2*x^2*Sqrt[1 + x^4])^2*(Sqrt[2]*Sqrt[-(x^2*(x^2 + Sqrt[1 + x^4]))]*(-1 + 2*x^4 + 2*x^2*Sqrt[1 + x^4]) - (x^2 + Sqrt[1 + x^4])*ArcSin[x^2 + Sqrt[1 + x^4]]))/(8*Sqrt[2]*Sqrt[-(x^4*(1 + 2*x^4 + 2*x^2*Sqrt[1 + x^4]))]*(1 + 13*x^4 + 28*x^8 + 16*x^12 + 5*x^2*Sqrt[1 + x^4] + 20*x^6*Sqrt[1 + x^4] + 16*x^10*Sqrt[1 + x^4]))","B",1
1435,1,286,101,2.5605108,"\int \frac{\left(-1+x^4\right) \sqrt{x^2+\sqrt{1+x^4}}}{\sqrt{1+x^4}} \, dx","Integrate[((-1 + x^4)*Sqrt[x^2 + Sqrt[1 + x^4]])/Sqrt[1 + x^4],x]","\frac{x \left(x^4+\sqrt{x^4+1} x^2+1\right) \left(\frac{\left(2 x^4+2 \sqrt{x^4+1} x^2+1\right)^2 \, _2F_1\left(-\frac{3}{2},-\frac{1}{2};\frac{1}{2};2 x^4+2 \sqrt{x^4+1} x^2+1\right)}{\sqrt{-x^2 \left(\sqrt{x^4+1}+x^2\right)} \left(16 x^{12}+28 x^8+13 x^4+16 \sqrt{x^4+1} x^{10}+20 \sqrt{x^4+1} x^6+5 \sqrt{x^4+1} x^2+1\right)}+\frac{2 \left(\log \left(1-\frac{\sqrt{x^2 \left(\sqrt{x^4+1}+x^2\right)}}{\sqrt{2} x^2}\right)-\log \left(\frac{\sqrt{x^2 \left(\sqrt{x^4+1}+x^2\right)}}{\sqrt{2} x^2}+1\right)\right)}{\sqrt{x^4+1} \sqrt{x^2 \left(\sqrt{x^4+1}+x^2\right)}}\right)}{4 \sqrt{2} \sqrt{\sqrt{x^4+1}+x^2}}","\frac{2 \sqrt{x^4+1} x^4+\left(2 x^4+3\right) x^2}{8 x \sqrt{\sqrt{x^4+1}+x^2}}-\frac{11 \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)}{4 \sqrt{2}}",1,"(x*(1 + x^4 + x^2*Sqrt[1 + x^4])*(((1 + 2*x^4 + 2*x^2*Sqrt[1 + x^4])^2*Hypergeometric2F1[-3/2, -1/2, 1/2, 1 + 2*x^4 + 2*x^2*Sqrt[1 + x^4]])/(Sqrt[-(x^2*(x^2 + Sqrt[1 + x^4]))]*(1 + 13*x^4 + 28*x^8 + 16*x^12 + 5*x^2*Sqrt[1 + x^4] + 20*x^6*Sqrt[1 + x^4] + 16*x^10*Sqrt[1 + x^4])) + (2*(Log[1 - Sqrt[x^2*(x^2 + Sqrt[1 + x^4])]/(Sqrt[2]*x^2)] - Log[1 + Sqrt[x^2*(x^2 + Sqrt[1 + x^4])]/(Sqrt[2]*x^2)]))/(Sqrt[1 + x^4]*Sqrt[x^2*(x^2 + Sqrt[1 + x^4])])))/(4*Sqrt[2]*Sqrt[x^2 + Sqrt[1 + x^4]])","C",1
1436,1,1439,101,0.3890897,"\int \sqrt{1+x^4} \sqrt{x^2+\sqrt{1+x^4}} \, dx","Integrate[Sqrt[1 + x^4]*Sqrt[x^2 + Sqrt[1 + x^4]],x]","\frac{7 \left(x^2+\sqrt{x^4+1}\right)^{7/2} \left(x^4+\sqrt{x^4+1} x^2+1\right) \left(5 \left(2 x^8+2 \sqrt{x^4+1} x^6+5 x^4+4 \sqrt{x^4+1} x^2+1\right) \, _2F_1\left(-\frac{1}{2},\frac{1}{2};\frac{5}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right)+2 \left(4 x^8+4 \sqrt{x^4+1} x^6+5 x^4+3 \sqrt{x^4+1} x^2+1\right) \, _2F_1\left(\frac{1}{2},\frac{3}{2};\frac{7}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right)+2 \left(x^4+1\right) \left(8 x^8+8 \sqrt{x^4+1} x^6+8 x^4+4 \sqrt{x^4+1} x^2+1\right) \, _3F_2\left(\frac{1}{2},\frac{3}{2},2;1,\frac{7}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right)\right)}{2 x \left(-896 \, _2F_1\left(\frac{1}{2},\frac{3}{2};\frac{7}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^{18}+1536 \, _2F_1\left(\frac{3}{2},\frac{5}{2};\frac{9}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^{18}-896 \sqrt{x^4+1} \, _2F_1\left(\frac{1}{2},\frac{3}{2};\frac{7}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^{16}+1536 \sqrt{x^4+1} \, _2F_1\left(\frac{3}{2},\frac{5}{2};\frac{9}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^{16}+3360 \, _2F_1\left(-\frac{1}{2},\frac{1}{2};\frac{5}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^{14}-448 \, _2F_1\left(\frac{1}{2},\frac{3}{2};\frac{7}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^{14}+3456 \, _2F_1\left(\frac{3}{2},\frac{5}{2};\frac{9}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^{14}+3360 \sqrt{x^4+1} \, _2F_1\left(-\frac{1}{2},\frac{1}{2};\frac{5}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^{12}+2688 \sqrt{x^4+1} \, _2F_1\left(\frac{3}{2},\frac{5}{2};\frac{9}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^{12}+6720 \, _2F_1\left(-\frac{1}{2},\frac{1}{2};\frac{5}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^{10}+1232 \, _2F_1\left(\frac{1}{2},\frac{3}{2};\frac{7}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^{10}+2592 \, _2F_1\left(\frac{3}{2},\frac{5}{2};\frac{9}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^{10}+5040 \sqrt{x^4+1} \, _2F_1\left(-\frac{1}{2},\frac{1}{2};\frac{5}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^8+1120 \sqrt{x^4+1} \, _2F_1\left(\frac{1}{2},\frac{3}{2};\frac{7}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^8+1440 \sqrt{x^4+1} \, _2F_1\left(\frac{3}{2},\frac{5}{2};\frac{9}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^8+3990 \, _2F_1\left(-\frac{1}{2},\frac{1}{2};\frac{5}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^6+952 \, _2F_1\left(\frac{1}{2},\frac{3}{2};\frac{7}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^6+720 \, _2F_1\left(\frac{3}{2},\frac{5}{2};\frac{9}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^6+1890 \sqrt{x^4+1} \, _2F_1\left(-\frac{1}{2},\frac{1}{2};\frac{5}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^4+448 \sqrt{x^4+1} \, _2F_1\left(\frac{1}{2},\frac{3}{2};\frac{7}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^4+240 \sqrt{x^4+1} \, _2F_1\left(\frac{3}{2},\frac{5}{2};\frac{9}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^4+630 \, _2F_1\left(-\frac{1}{2},\frac{1}{2};\frac{5}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^2+140 \, _2F_1\left(\frac{1}{2},\frac{3}{2};\frac{7}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^2+54 \, _2F_1\left(\frac{3}{2},\frac{5}{2};\frac{9}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^2+105 \sqrt{x^4+1} \, _2F_1\left(-\frac{1}{2},\frac{1}{2};\frac{5}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right)+21 \sqrt{x^4+1} \, _2F_1\left(\frac{1}{2},\frac{3}{2};\frac{7}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right)+6 \sqrt{x^4+1} \, _2F_1\left(\frac{3}{2},\frac{5}{2};\frac{9}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right)+14 \left(640 x^{18}+640 \sqrt{x^4+1} x^{16}+1472 x^{14}+1152 \sqrt{x^4+1} x^{12}+1136 x^{10}+640 \sqrt{x^4+1} x^8+328 x^6+112 \sqrt{x^4+1} x^4+26 x^2+3 \sqrt{x^4+1}\right) \, _3F_2\left(\frac{1}{2},\frac{3}{2},2;1,\frac{7}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right)+12 \left(512 x^{22}+512 \sqrt{x^4+1} x^{20}+1536 x^{18}+1280 \sqrt{x^4+1} x^{16}+1696 x^{14}+1120 \sqrt{x^4+1} x^{12}+832 x^{10}+400 \sqrt{x^4+1} x^8+170 x^6+50 \sqrt{x^4+1} x^4+10 x^2+\sqrt{x^4+1}\right) \, _3F_2\left(\frac{3}{2},\frac{5}{2},3;2,\frac{9}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right)\right)}","\frac{2 \sqrt{x^4+1} x^4+\left(2 x^4+3\right) x^2}{8 x \sqrt{\sqrt{x^4+1}+x^2}}+\frac{5 \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)}{4 \sqrt{2}}",1,"(7*(x^2 + Sqrt[1 + x^4])^(7/2)*(1 + x^4 + x^2*Sqrt[1 + x^4])*(5*(1 + 5*x^4 + 2*x^8 + 4*x^2*Sqrt[1 + x^4] + 2*x^6*Sqrt[1 + x^4])*Hypergeometric2F1[-1/2, 1/2, 5/2, (x^2 + Sqrt[1 + x^4])^2] + 2*(1 + 5*x^4 + 4*x^8 + 3*x^2*Sqrt[1 + x^4] + 4*x^6*Sqrt[1 + x^4])*Hypergeometric2F1[1/2, 3/2, 7/2, (x^2 + Sqrt[1 + x^4])^2] + 2*(1 + x^4)*(1 + 8*x^4 + 8*x^8 + 4*x^2*Sqrt[1 + x^4] + 8*x^6*Sqrt[1 + x^4])*HypergeometricPFQ[{1/2, 3/2, 2}, {1, 7/2}, (x^2 + Sqrt[1 + x^4])^2]))/(2*x*(630*x^2*Hypergeometric2F1[-1/2, 1/2, 5/2, (x^2 + Sqrt[1 + x^4])^2] + 3990*x^6*Hypergeometric2F1[-1/2, 1/2, 5/2, (x^2 + Sqrt[1 + x^4])^2] + 6720*x^10*Hypergeometric2F1[-1/2, 1/2, 5/2, (x^2 + Sqrt[1 + x^4])^2] + 3360*x^14*Hypergeometric2F1[-1/2, 1/2, 5/2, (x^2 + Sqrt[1 + x^4])^2] + 105*Sqrt[1 + x^4]*Hypergeometric2F1[-1/2, 1/2, 5/2, (x^2 + Sqrt[1 + x^4])^2] + 1890*x^4*Sqrt[1 + x^4]*Hypergeometric2F1[-1/2, 1/2, 5/2, (x^2 + Sqrt[1 + x^4])^2] + 5040*x^8*Sqrt[1 + x^4]*Hypergeometric2F1[-1/2, 1/2, 5/2, (x^2 + Sqrt[1 + x^4])^2] + 3360*x^12*Sqrt[1 + x^4]*Hypergeometric2F1[-1/2, 1/2, 5/2, (x^2 + Sqrt[1 + x^4])^2] + 140*x^2*Hypergeometric2F1[1/2, 3/2, 7/2, (x^2 + Sqrt[1 + x^4])^2] + 952*x^6*Hypergeometric2F1[1/2, 3/2, 7/2, (x^2 + Sqrt[1 + x^4])^2] + 1232*x^10*Hypergeometric2F1[1/2, 3/2, 7/2, (x^2 + Sqrt[1 + x^4])^2] - 448*x^14*Hypergeometric2F1[1/2, 3/2, 7/2, (x^2 + Sqrt[1 + x^4])^2] - 896*x^18*Hypergeometric2F1[1/2, 3/2, 7/2, (x^2 + Sqrt[1 + x^4])^2] + 21*Sqrt[1 + x^4]*Hypergeometric2F1[1/2, 3/2, 7/2, (x^2 + Sqrt[1 + x^4])^2] + 448*x^4*Sqrt[1 + x^4]*Hypergeometric2F1[1/2, 3/2, 7/2, (x^2 + Sqrt[1 + x^4])^2] + 1120*x^8*Sqrt[1 + x^4]*Hypergeometric2F1[1/2, 3/2, 7/2, (x^2 + Sqrt[1 + x^4])^2] - 896*x^16*Sqrt[1 + x^4]*Hypergeometric2F1[1/2, 3/2, 7/2, (x^2 + Sqrt[1 + x^4])^2] + 54*x^2*Hypergeometric2F1[3/2, 5/2, 9/2, (x^2 + Sqrt[1 + x^4])^2] + 720*x^6*Hypergeometric2F1[3/2, 5/2, 9/2, (x^2 + Sqrt[1 + x^4])^2] + 2592*x^10*Hypergeometric2F1[3/2, 5/2, 9/2, (x^2 + Sqrt[1 + x^4])^2] + 3456*x^14*Hypergeometric2F1[3/2, 5/2, 9/2, (x^2 + Sqrt[1 + x^4])^2] + 1536*x^18*Hypergeometric2F1[3/2, 5/2, 9/2, (x^2 + Sqrt[1 + x^4])^2] + 6*Sqrt[1 + x^4]*Hypergeometric2F1[3/2, 5/2, 9/2, (x^2 + Sqrt[1 + x^4])^2] + 240*x^4*Sqrt[1 + x^4]*Hypergeometric2F1[3/2, 5/2, 9/2, (x^2 + Sqrt[1 + x^4])^2] + 1440*x^8*Sqrt[1 + x^4]*Hypergeometric2F1[3/2, 5/2, 9/2, (x^2 + Sqrt[1 + x^4])^2] + 2688*x^12*Sqrt[1 + x^4]*Hypergeometric2F1[3/2, 5/2, 9/2, (x^2 + Sqrt[1 + x^4])^2] + 1536*x^16*Sqrt[1 + x^4]*Hypergeometric2F1[3/2, 5/2, 9/2, (x^2 + Sqrt[1 + x^4])^2] + 14*(26*x^2 + 328*x^6 + 1136*x^10 + 1472*x^14 + 640*x^18 + 3*Sqrt[1 + x^4] + 112*x^4*Sqrt[1 + x^4] + 640*x^8*Sqrt[1 + x^4] + 1152*x^12*Sqrt[1 + x^4] + 640*x^16*Sqrt[1 + x^4])*HypergeometricPFQ[{1/2, 3/2, 2}, {1, 7/2}, (x^2 + Sqrt[1 + x^4])^2] + 12*(10*x^2 + 170*x^6 + 832*x^10 + 1696*x^14 + 1536*x^18 + 512*x^22 + Sqrt[1 + x^4] + 50*x^4*Sqrt[1 + x^4] + 400*x^8*Sqrt[1 + x^4] + 1120*x^12*Sqrt[1 + x^4] + 1280*x^16*Sqrt[1 + x^4] + 512*x^20*Sqrt[1 + x^4])*HypergeometricPFQ[{3/2, 5/2, 3}, {2, 9/2}, (x^2 + Sqrt[1 + x^4])^2]))","C",0
1437,1,44,102,0.0213704,"\int x^3 \left(-1+x^3\right)^{2/3} \, dx","Integrate[x^3*(-1 + x^3)^(2/3),x]","\frac{1}{6} x \left(x^3-1\right)^{2/3} \left(\frac{\, _2F_1\left(-\frac{2}{3},\frac{1}{3};\frac{4}{3};x^3\right)}{\left(1-x^3\right)^{2/3}}+x^3-1\right)","\frac{1}{27} \log \left(\sqrt[3]{x^3-1}-x\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-1}+x}\right)}{9 \sqrt{3}}+\frac{1}{18} \left(x^3-1\right)^{2/3} \left(3 x^4-2 x\right)-\frac{1}{54} \log \left(\sqrt[3]{x^3-1} x+\left(x^3-1\right)^{2/3}+x^2\right)",1,"(x*(-1 + x^3)^(2/3)*(-1 + x^3 + Hypergeometric2F1[-2/3, 1/3, 4/3, x^3]/(1 - x^3)^(2/3)))/6","C",1
1438,1,34,102,0.0097568,"\int x^4 \sqrt[3]{1+x^3} \, dx","Integrate[x^4*(1 + x^3)^(1/3),x]","\frac{1}{6} x^2 \left(\left(x^3+1\right)^{4/3}-\, _2F_1\left(-\frac{1}{3},\frac{2}{3};\frac{5}{3};-x^3\right)\right)","\frac{1}{27} \log \left(\sqrt[3]{x^3+1}-x\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+1}+x}\right)}{9 \sqrt{3}}-\frac{1}{54} \log \left(\sqrt[3]{x^3+1} x+\left(x^3+1\right)^{2/3}+x^2\right)+\frac{1}{18} \sqrt[3]{x^3+1} \left(3 x^5+x^2\right)",1,"(x^2*((1 + x^3)^(4/3) - Hypergeometric2F1[-1/3, 2/3, 5/3, -x^3]))/6","C",1
1439,1,32,102,0.0097788,"\int x^3 \left(1+x^3\right)^{2/3} \, dx","Integrate[x^3*(1 + x^3)^(2/3),x]","\frac{1}{6} x \left(\left(x^3+1\right)^{5/3}-\, _2F_1\left(-\frac{2}{3},\frac{1}{3};\frac{4}{3};-x^3\right)\right)","\frac{1}{27} \log \left(\sqrt[3]{x^3+1}-x\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+1}+x}\right)}{9 \sqrt{3}}+\frac{1}{18} \left(x^3+1\right)^{2/3} \left(3 x^4+2 x\right)-\frac{1}{54} \log \left(\sqrt[3]{x^3+1} x+\left(x^3+1\right)^{2/3}+x^2\right)",1,"(x*((1 + x^3)^(5/3) - Hypergeometric2F1[-2/3, 1/3, 4/3, -x^3]))/6","C",1
1440,1,111,102,0.1917591,"\int \frac{\left(-2+x^3\right)^{2/3} \left(4+x^3\right)}{x^6 \left(-1+x^3\right)} \, dx","Integrate[((-2 + x^3)^(2/3)*(4 + x^3))/(x^6*(-1 + x^3)),x]","\frac{\left(x^3-2\right)^{2/3} \left(21 x^3+8\right)}{10 x^5}+\frac{5}{6} \left(2 \log \left(\frac{x}{\sqrt[3]{1-2 x^3}}+1\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{1-2 x^3}}-1}{\sqrt{3}}\right)-\log \left(-\frac{x}{\sqrt[3]{1-2 x^3}}+\frac{x^2}{\left(1-2 x^3\right)^{2/3}}+1\right)\right)","\frac{5}{3} \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)}{\sqrt{3}}+\frac{\left(x^3-2\right)^{2/3} \left(21 x^3+8\right)}{10 x^5}-\frac{5}{6} \log \left(-\sqrt[3]{x^3-2} x+\left(x^3-2\right)^{2/3}+x^2\right)",1,"((-2 + x^3)^(2/3)*(8 + 21*x^3))/(10*x^5) + (5*(2*Sqrt[3]*ArcTan[(-1 + (2*x)/(1 - 2*x^3)^(1/3))/Sqrt[3]] - Log[1 + x^2/(1 - 2*x^3)^(2/3) - x/(1 - 2*x^3)^(1/3)] + 2*Log[1 + x/(1 - 2*x^3)^(1/3)]))/6","A",0
1441,0,0,102,0.5033712,"\int \frac{3 b+a x^2}{\left(b+a x^2+x^3\right) \sqrt[4]{b x+a x^3}} \, dx","Integrate[(3*b + a*x^2)/((b + a*x^2 + x^3)*(b*x + a*x^3)^(1/4)),x]","\int \frac{3 b+a x^2}{\left(b+a x^2+x^3\right) \sqrt[4]{b x+a x^3}} \, dx","\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{a x^3+b x}}{\sqrt{a x^3+b x}+x^2}\right)-\sqrt{2} \tan ^{-1}\left(\frac{\frac{\sqrt{a x^3+b x}}{\sqrt{2}}-\frac{x^2}{\sqrt{2}}}{x \sqrt[4]{a x^3+b x}}\right)",1,"Integrate[(3*b + a*x^2)/((b + a*x^2 + x^3)*(b*x + a*x^3)^(1/4)), x]","F",-1
1442,1,36,102,0.0110373,"\int \frac{\left(-3+x^4\right) \sqrt[3]{1+x^4}}{x^{13}} \, dx","Integrate[((-3 + x^4)*(1 + x^4)^(1/3))/x^13,x]","\frac{\left(x^4+1\right)^{4/3} \left(1-2 x^{12} \, _2F_1\left(\frac{4}{3},3;\frac{7}{3};x^4+1\right)\right)}{4 x^{12}}","-\frac{2}{27} \log \left(\sqrt[3]{x^4+1}-1\right)+\frac{1}{27} \log \left(\left(x^4+1\right)^{2/3}+\sqrt[3]{x^4+1}+1\right)+\frac{2 \tan ^{-1}\left(\frac{2 \sqrt[3]{x^4+1}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{9 \sqrt{3}}+\frac{\sqrt[3]{x^4+1} \left(-4 x^8-3 x^4+9\right)}{36 x^{12}}",1,"((1 + x^4)^(4/3)*(1 - 2*x^12*Hypergeometric2F1[4/3, 3, 7/3, 1 + x^4]))/(4*x^12)","C",1
1443,0,0,102,0.2154369,"\int \frac{-2 b+a x^2}{\sqrt[4]{-b+a x^2} \left(-b+a x^2+x^4\right)} \, dx","Integrate[(-2*b + a*x^2)/((-b + a*x^2)^(1/4)*(-b + a*x^2 + x^4)),x]","\int \frac{-2 b+a x^2}{\sqrt[4]{-b+a x^2} \left(-b+a x^2+x^4\right)} \, dx","\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{a x^2-b}}{\sqrt{a x^2-b}+x^2}\right)}{\sqrt{2}}-\frac{\tan ^{-1}\left(\frac{\frac{\sqrt{a x^2-b}}{\sqrt{2}}-\frac{x^2}{\sqrt{2}}}{x \sqrt[4]{a x^2-b}}\right)}{\sqrt{2}}",1,"Integrate[(-2*b + a*x^2)/((-b + a*x^2)^(1/4)*(-b + a*x^2 + x^4)), x]","F",-1
1444,0,0,102,0.2762199,"\int \frac{-4 b+a x^3}{\sqrt[4]{-b+a x^3} \left(-b+a x^3+x^4\right)} \, dx","Integrate[(-4*b + a*x^3)/((-b + a*x^3)^(1/4)*(-b + a*x^3 + x^4)),x]","\int \frac{-4 b+a x^3}{\sqrt[4]{-b+a x^3} \left(-b+a x^3+x^4\right)} \, dx","\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{a x^3-b}}{\sqrt{a x^3-b}+x^2}\right)-\sqrt{2} \tan ^{-1}\left(\frac{\frac{\sqrt{a x^3-b}}{\sqrt{2}}-\frac{x^2}{\sqrt{2}}}{x \sqrt[4]{a x^3-b}}\right)",1,"Integrate[(-4*b + a*x^3)/((-b + a*x^3)^(1/4)*(-b + a*x^3 + x^4)), x]","F",-1
1445,1,570,102,0.9800811,"\int \frac{b+a x^2}{\left(b-a x^2+x^4\right) \sqrt[4]{-b x^2+a x^4}} \, dx","Integrate[(b + a*x^2)/((b - a*x^2 + x^4)*(-(b*x^2) + a*x^4)^(1/4)),x]","\frac{\sqrt{x} \sqrt[4]{a x^2-b} \left(-\frac{\left(a-\frac{a^2+2 b}{\sqrt{a^2-4 b}}\right) \tan ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{-a \sqrt{a^2-4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2-4 b}} \sqrt[4]{a x^2-b}}\right)}{\left(a-\sqrt{a^2-4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2-4 b}+a^2-2 b}}-\frac{\left(a \sqrt{a^2-4 b}+a^2+2 b\right) \tan ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{a \sqrt{a^2-4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2-4 b}+a} \sqrt[4]{a x^2-b}}\right)}{\left(\sqrt{a^2-4 b}+a\right)^{3/4} \sqrt{a^2-4 b} \sqrt[4]{a \sqrt{a^2-4 b}+a^2-2 b}}-\frac{\left(a-\frac{a^2+2 b}{\sqrt{a^2-4 b}}\right) \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{-a \sqrt{a^2-4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2-4 b}} \sqrt[4]{a x^2-b}}\right)}{\left(a-\sqrt{a^2-4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2-4 b}+a^2-2 b}}-\frac{\left(a \sqrt{a^2-4 b}+a^2+2 b\right) \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{a \sqrt{a^2-4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2-4 b}+a} \sqrt[4]{a x^2-b}}\right)}{\left(\sqrt{a^2-4 b}+a\right)^{3/4} \sqrt{a^2-4 b} \sqrt[4]{a \sqrt{a^2-4 b}+a^2-2 b}}\right)}{\sqrt[4]{a x^4-b x^2}}","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4 a+b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-2 a \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+2 a \log (x)}{\text{$\#$1} a-2 \text{$\#$1}^5}\&\right]",1,"(Sqrt[x]*(-b + a*x^2)^(1/4)*(-(((a - (a^2 + 2*b)/Sqrt[a^2 - 4*b])*ArcTan[((a^2 - a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)*Sqrt[x])/((a - Sqrt[a^2 - 4*b])^(1/4)*(-b + a*x^2)^(1/4))])/((a - Sqrt[a^2 - 4*b])^(3/4)*(a^2 - a*Sqrt[a^2 - 4*b] - 2*b)^(1/4))) - ((a^2 + a*Sqrt[a^2 - 4*b] + 2*b)*ArcTan[((a^2 + a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)*Sqrt[x])/((a + Sqrt[a^2 - 4*b])^(1/4)*(-b + a*x^2)^(1/4))])/((a + Sqrt[a^2 - 4*b])^(3/4)*Sqrt[a^2 - 4*b]*(a^2 + a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)) - ((a - (a^2 + 2*b)/Sqrt[a^2 - 4*b])*ArcTanh[((a^2 - a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)*Sqrt[x])/((a - Sqrt[a^2 - 4*b])^(1/4)*(-b + a*x^2)^(1/4))])/((a - Sqrt[a^2 - 4*b])^(3/4)*(a^2 - a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)) - ((a^2 + a*Sqrt[a^2 - 4*b] + 2*b)*ArcTanh[((a^2 + a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)*Sqrt[x])/((a + Sqrt[a^2 - 4*b])^(1/4)*(-b + a*x^2)^(1/4))])/((a + Sqrt[a^2 - 4*b])^(3/4)*Sqrt[a^2 - 4*b]*(a^2 + a*Sqrt[a^2 - 4*b] - 2*b)^(1/4))))/(-(b*x^2) + a*x^4)^(1/4)","B",1
1446,1,570,102,0.277423,"\int \frac{b+a x^2}{\left(b-a x^2+x^4\right) \sqrt[4]{-b x^2+a x^4}} \, dx","Integrate[(b + a*x^2)/((b - a*x^2 + x^4)*(-(b*x^2) + a*x^4)^(1/4)),x]","\frac{\sqrt{x} \sqrt[4]{a x^2-b} \left(-\frac{\left(a-\frac{a^2+2 b}{\sqrt{a^2-4 b}}\right) \tan ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{-a \sqrt{a^2-4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2-4 b}} \sqrt[4]{a x^2-b}}\right)}{\left(a-\sqrt{a^2-4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2-4 b}+a^2-2 b}}-\frac{\left(a \sqrt{a^2-4 b}+a^2+2 b\right) \tan ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{a \sqrt{a^2-4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2-4 b}+a} \sqrt[4]{a x^2-b}}\right)}{\left(\sqrt{a^2-4 b}+a\right)^{3/4} \sqrt{a^2-4 b} \sqrt[4]{a \sqrt{a^2-4 b}+a^2-2 b}}-\frac{\left(a-\frac{a^2+2 b}{\sqrt{a^2-4 b}}\right) \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{-a \sqrt{a^2-4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2-4 b}} \sqrt[4]{a x^2-b}}\right)}{\left(a-\sqrt{a^2-4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2-4 b}+a^2-2 b}}-\frac{\left(a \sqrt{a^2-4 b}+a^2+2 b\right) \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{a \sqrt{a^2-4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2-4 b}+a} \sqrt[4]{a x^2-b}}\right)}{\left(\sqrt{a^2-4 b}+a\right)^{3/4} \sqrt{a^2-4 b} \sqrt[4]{a \sqrt{a^2-4 b}+a^2-2 b}}\right)}{\sqrt[4]{a x^4-b x^2}}","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4 a+b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-2 a \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+2 a \log (x)}{\text{$\#$1} a-2 \text{$\#$1}^5}\&\right]",1,"(Sqrt[x]*(-b + a*x^2)^(1/4)*(-(((a - (a^2 + 2*b)/Sqrt[a^2 - 4*b])*ArcTan[((a^2 - a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)*Sqrt[x])/((a - Sqrt[a^2 - 4*b])^(1/4)*(-b + a*x^2)^(1/4))])/((a - Sqrt[a^2 - 4*b])^(3/4)*(a^2 - a*Sqrt[a^2 - 4*b] - 2*b)^(1/4))) - ((a^2 + a*Sqrt[a^2 - 4*b] + 2*b)*ArcTan[((a^2 + a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)*Sqrt[x])/((a + Sqrt[a^2 - 4*b])^(1/4)*(-b + a*x^2)^(1/4))])/((a + Sqrt[a^2 - 4*b])^(3/4)*Sqrt[a^2 - 4*b]*(a^2 + a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)) - ((a - (a^2 + 2*b)/Sqrt[a^2 - 4*b])*ArcTanh[((a^2 - a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)*Sqrt[x])/((a - Sqrt[a^2 - 4*b])^(1/4)*(-b + a*x^2)^(1/4))])/((a - Sqrt[a^2 - 4*b])^(3/4)*(a^2 - a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)) - ((a^2 + a*Sqrt[a^2 - 4*b] + 2*b)*ArcTanh[((a^2 + a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)*Sqrt[x])/((a + Sqrt[a^2 - 4*b])^(1/4)*(-b + a*x^2)^(1/4))])/((a + Sqrt[a^2 - 4*b])^(3/4)*Sqrt[a^2 - 4*b]*(a^2 + a*Sqrt[a^2 - 4*b] - 2*b)^(1/4))))/(-(b*x^2) + a*x^4)^(1/4)","B",1
1447,1,384,102,3.6631567,"\int \frac{b+a x^4}{x^4 \left(-2 b+a x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Integrate[(b + a*x^4)/(x^4*(-2*b + a*x^4)*(b*x^2 + a*x^4)^(1/4)),x]","\frac{\sqrt{x} \left(\frac{3 a^{7/8} \sqrt{x} \sqrt[4]{a+\frac{b}{x^2}} \left(\sqrt[4]{2 \sqrt{a}+\sqrt{2} \sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[8]{a} \sqrt[4]{\sqrt{a}-\frac{\sqrt{b}}{\sqrt{2}}}}\right)+\sqrt[4]{2 \sqrt{a}-\sqrt{2} \sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[8]{a} \sqrt[4]{\sqrt{a}+\frac{\sqrt{b}}{\sqrt{2}}}}\right)-\sqrt[4]{2 \sqrt{a}+\sqrt{2} \sqrt{b}} \tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[8]{a} \sqrt[4]{\sqrt{a}-\frac{\sqrt{b}}{\sqrt{2}}}}\right)-\sqrt[4]{2 \sqrt{a}-\sqrt{2} \sqrt{b}} \tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[8]{a} \sqrt[4]{\sqrt{a}+\frac{\sqrt{b}}{\sqrt{2}}}}\right)\right)}{b \sqrt[4]{\sqrt{a}-\frac{\sqrt{b}}{\sqrt{2}}} \sqrt[4]{2 \sqrt{a}+\sqrt{2} \sqrt{b}}}+\frac{8 \left(3 b-4 a x^2\right) \left(a x^2+b\right)}{21 b^2 x^{7/2}}\right)}{8 \sqrt[4]{x^2 \left(a x^2+b\right)}}","\frac{3 a \text{RootSum}\left[2 \text{$\#$1}^8-4 \text{$\#$1}^4 a+2 a^2-a b\&,\frac{\log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{16 b}+\frac{\left(a x^4+b x^2\right)^{3/4} \left(3 b-4 a x^2\right)}{21 b^2 x^5}",1,"(Sqrt[x]*((8*(3*b - 4*a*x^2)*(b + a*x^2))/(21*b^2*x^(7/2)) + (3*a^(7/8)*(a + b/x^2)^(1/4)*Sqrt[x]*((2*Sqrt[a] + Sqrt[2]*Sqrt[b])^(1/4)*ArcTan[(a + b/x^2)^(1/4)/(a^(1/8)*(Sqrt[a] - Sqrt[b]/Sqrt[2])^(1/4))] + (2*Sqrt[a] - Sqrt[2]*Sqrt[b])^(1/4)*ArcTan[(a + b/x^2)^(1/4)/(a^(1/8)*(Sqrt[a] + Sqrt[b]/Sqrt[2])^(1/4))] - (2*Sqrt[a] + Sqrt[2]*Sqrt[b])^(1/4)*ArcTanh[(a + b/x^2)^(1/4)/(a^(1/8)*(Sqrt[a] - Sqrt[b]/Sqrt[2])^(1/4))] - (2*Sqrt[a] - Sqrt[2]*Sqrt[b])^(1/4)*ArcTanh[(a + b/x^2)^(1/4)/(a^(1/8)*(Sqrt[a] + Sqrt[b]/Sqrt[2])^(1/4))]))/((Sqrt[a] - Sqrt[b]/Sqrt[2])^(1/4)*(2*Sqrt[a] + Sqrt[2]*Sqrt[b])^(1/4)*b)))/(8*(x^2*(b + a*x^2))^(1/4))","B",1
1448,1,384,102,2.4263062,"\int \frac{b+a x^4}{x^4 \left(-2 b+a x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Integrate[(b + a*x^4)/(x^4*(-2*b + a*x^4)*(b*x^2 + a*x^4)^(1/4)),x]","\frac{\sqrt{x} \left(\frac{3 a^{7/8} \sqrt{x} \sqrt[4]{a+\frac{b}{x^2}} \left(\sqrt[4]{2 \sqrt{a}+\sqrt{2} \sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[8]{a} \sqrt[4]{\sqrt{a}-\frac{\sqrt{b}}{\sqrt{2}}}}\right)+\sqrt[4]{2 \sqrt{a}-\sqrt{2} \sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[8]{a} \sqrt[4]{\sqrt{a}+\frac{\sqrt{b}}{\sqrt{2}}}}\right)-\sqrt[4]{2 \sqrt{a}+\sqrt{2} \sqrt{b}} \tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[8]{a} \sqrt[4]{\sqrt{a}-\frac{\sqrt{b}}{\sqrt{2}}}}\right)-\sqrt[4]{2 \sqrt{a}-\sqrt{2} \sqrt{b}} \tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[8]{a} \sqrt[4]{\sqrt{a}+\frac{\sqrt{b}}{\sqrt{2}}}}\right)\right)}{b \sqrt[4]{\sqrt{a}-\frac{\sqrt{b}}{\sqrt{2}}} \sqrt[4]{2 \sqrt{a}+\sqrt{2} \sqrt{b}}}+\frac{8 \left(3 b-4 a x^2\right) \left(a x^2+b\right)}{21 b^2 x^{7/2}}\right)}{8 \sqrt[4]{x^2 \left(a x^2+b\right)}}","\frac{3 a \text{RootSum}\left[2 \text{$\#$1}^8-4 \text{$\#$1}^4 a+2 a^2-a b\&,\frac{\log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{16 b}+\frac{\left(a x^4+b x^2\right)^{3/4} \left(3 b-4 a x^2\right)}{21 b^2 x^5}",1,"(Sqrt[x]*((8*(3*b - 4*a*x^2)*(b + a*x^2))/(21*b^2*x^(7/2)) + (3*a^(7/8)*(a + b/x^2)^(1/4)*Sqrt[x]*((2*Sqrt[a] + Sqrt[2]*Sqrt[b])^(1/4)*ArcTan[(a + b/x^2)^(1/4)/(a^(1/8)*(Sqrt[a] - Sqrt[b]/Sqrt[2])^(1/4))] + (2*Sqrt[a] - Sqrt[2]*Sqrt[b])^(1/4)*ArcTan[(a + b/x^2)^(1/4)/(a^(1/8)*(Sqrt[a] + Sqrt[b]/Sqrt[2])^(1/4))] - (2*Sqrt[a] + Sqrt[2]*Sqrt[b])^(1/4)*ArcTanh[(a + b/x^2)^(1/4)/(a^(1/8)*(Sqrt[a] - Sqrt[b]/Sqrt[2])^(1/4))] - (2*Sqrt[a] - Sqrt[2]*Sqrt[b])^(1/4)*ArcTanh[(a + b/x^2)^(1/4)/(a^(1/8)*(Sqrt[a] + Sqrt[b]/Sqrt[2])^(1/4))]))/((Sqrt[a] - Sqrt[b]/Sqrt[2])^(1/4)*(2*Sqrt[a] + Sqrt[2]*Sqrt[b])^(1/4)*b)))/(8*(x^2*(b + a*x^2))^(1/4))","B",1
1449,0,0,102,1.1226525,"\int \frac{\left(-1+x^3\right) \left(1+x^3\right)^3 \left(1+x^6\right)^{2/3}}{x^6 \left(1-x^3+x^6\right)} \, dx","Integrate[((-1 + x^3)*(1 + x^3)^3*(1 + x^6)^(2/3))/(x^6*(1 - x^3 + x^6)),x]","\int \frac{\left(-1+x^3\right) \left(1+x^3\right)^3 \left(1+x^6\right)^{2/3}}{x^6 \left(1-x^3+x^6\right)} \, dx","\log \left(\sqrt[3]{x^6+1}-x\right)-\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^6+1}+x}\right)-\frac{1}{2} \log \left(\sqrt[3]{x^6+1} x+\left(x^6+1\right)^{2/3}+x^2\right)+\frac{\left(x^6+1\right)^{2/3} \left(2 x^6+15 x^3+2\right)}{10 x^5}",1,"Integrate[((-1 + x^3)*(1 + x^3)^3*(1 + x^6)^(2/3))/(x^6*(1 - x^3 + x^6)), x]","F",-1
1450,0,0,102,0.9132325,"\int \frac{\left(-1+x^6\right)^{2/3} \left(1+x^6\right) \left(-2+x^3+2 x^6\right)}{x^6 \left(-1-x^3+x^6\right)} \, dx","Integrate[((-1 + x^6)^(2/3)*(1 + x^6)*(-2 + x^3 + 2*x^6))/(x^6*(-1 - x^3 + x^6)),x]","\int \frac{\left(-1+x^6\right)^{2/3} \left(1+x^6\right) \left(-2+x^3+2 x^6\right)}{x^6 \left(-1-x^3+x^6\right)} \, dx","\log \left(\sqrt[3]{x^6-1}-x\right)-\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^6-1}+x}\right)-\frac{1}{2} \log \left(\sqrt[3]{x^6-1} x+\left(x^6-1\right)^{2/3}+x^2\right)+\frac{\left(x^6-1\right)^{2/3} \left(4 x^6+15 x^3-4\right)}{10 x^5}",1,"Integrate[((-1 + x^6)^(2/3)*(1 + x^6)*(-2 + x^3 + 2*x^6))/(x^6*(-1 - x^3 + x^6)), x]","F",-1
1451,1,415,102,0.4949532,"\int \frac{1}{\sqrt[4]{b+a x^4} \left(-b+a x^4+x^8\right)} \, dx","Integrate[1/((b + a*x^4)^(1/4)*(-b + a*x^4 + x^8)),x]","\frac{\frac{\tan ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{a x^4+b}}\right)}{\left(a-\sqrt{a^2+4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}-\frac{\tan ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+4 b}+a} \sqrt[4]{a x^4+b}}\right)}{\left(\sqrt{a^2+4 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}+\frac{\tanh ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{a x^4+b}}\right)}{\left(a-\sqrt{a^2+4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}-\frac{\tanh ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+4 b}+a} \sqrt[4]{a x^4+b}}\right)}{\left(\sqrt{a^2+4 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}}{\sqrt{a^2+4 b}}","-\frac{\text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4 a+2 a^2-b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-a \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+a \log (x)}{3 \text{$\#$1} a-2 \text{$\#$1}^5}\&\right]}{4 b}",1,"(ArcTan[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a - Sqrt[a^2 + 4*b])^(1/4)*(b + a*x^4)^(1/4))]/((a - Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)) - ArcTan[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a + Sqrt[a^2 + 4*b])^(1/4)*(b + a*x^4)^(1/4))]/((a + Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)) + ArcTanh[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a - Sqrt[a^2 + 4*b])^(1/4)*(b + a*x^4)^(1/4))]/((a - Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)) - ArcTanh[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a + Sqrt[a^2 + 4*b])^(1/4)*(b + a*x^4)^(1/4))]/((a + Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)))/Sqrt[a^2 + 4*b]","B",1
1452,1,415,102,0.0706676,"\int \frac{1}{\sqrt[4]{b+a x^4} \left(-b+a x^4+x^8\right)} \, dx","Integrate[1/((b + a*x^4)^(1/4)*(-b + a*x^4 + x^8)),x]","\frac{\frac{\tan ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{a x^4+b}}\right)}{\left(a-\sqrt{a^2+4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}-\frac{\tan ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+4 b}+a} \sqrt[4]{a x^4+b}}\right)}{\left(\sqrt{a^2+4 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}+\frac{\tanh ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{a x^4+b}}\right)}{\left(a-\sqrt{a^2+4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}-\frac{\tanh ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+4 b}+a} \sqrt[4]{a x^4+b}}\right)}{\left(\sqrt{a^2+4 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}}{\sqrt{a^2+4 b}}","-\frac{\text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4 a+2 a^2-b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-a \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+a \log (x)}{3 \text{$\#$1} a-2 \text{$\#$1}^5}\&\right]}{4 b}",1,"(ArcTan[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a - Sqrt[a^2 + 4*b])^(1/4)*(b + a*x^4)^(1/4))]/((a - Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)) - ArcTan[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a + Sqrt[a^2 + 4*b])^(1/4)*(b + a*x^4)^(1/4))]/((a + Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)) + ArcTanh[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a - Sqrt[a^2 + 4*b])^(1/4)*(b + a*x^4)^(1/4))]/((a - Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)) - ArcTanh[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a + Sqrt[a^2 + 4*b])^(1/4)*(b + a*x^4)^(1/4))]/((a + Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)))/Sqrt[a^2 + 4*b]","B",1
1453,1,804,102,3.6200871,"\int \frac{-b+a x^4}{\sqrt[4]{-b x^2+a x^4} \left(-b+2 a x^4+2 x^8\right)} \, dx","Integrate[(-b + a*x^4)/((-(b*x^2) + a*x^4)^(1/4)*(-b + 2*a*x^4 + 2*x^8)),x]","-\frac{\sqrt[4]{\frac{b}{x^2}-a} x \left((a-b) \text{RootSum}\left[a^4-2 b a^3+4 \text{$\#$1} a^3+6 \text{$\#$1}^2 a^2-4 b \text{$\#$1} a^2+4 \text{$\#$1}^3 a-2 b \text{$\#$1}^2 a+\text{$\#$1}^4-2 b^3\&,\frac{\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[4]{\text{$\#$1}}}\right)}{\sqrt[4]{\text{$\#$1}}}+\frac{\log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{\frac{b}{x^2}-a}\right)}{\sqrt[4]{\text{$\#$1}}}-\frac{\log \left(\sqrt[4]{\frac{b}{x^2}-a}+\sqrt[4]{\text{$\#$1}}\right)}{\sqrt[4]{\text{$\#$1}}}}{a^3-b a^2+3 \text{$\#$1} a^2+3 \text{$\#$1}^2 a-b \text{$\#$1} a+\text{$\#$1}^3}\&\right] a^2+(3 a-b) \text{RootSum}\left[a^4-2 b a^3+4 \text{$\#$1} a^3+6 \text{$\#$1}^2 a^2-4 b \text{$\#$1} a^2+4 \text{$\#$1}^3 a-2 b \text{$\#$1}^2 a+\text{$\#$1}^4-2 b^3\&,\frac{2 \text{$\#$1}^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[4]{\text{$\#$1}}}\right)+\log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{\frac{b}{x^2}-a}\right) \text{$\#$1}^{3/4}-\log \left(\sqrt[4]{\frac{b}{x^2}-a}+\sqrt[4]{\text{$\#$1}}\right) \text{$\#$1}^{3/4}}{a^3-b a^2+3 \text{$\#$1} a^2+3 \text{$\#$1}^2 a-b \text{$\#$1} a+\text{$\#$1}^3}\&\right] a+3 \text{RootSum}\left[a^4-2 b a^3+4 \text{$\#$1} a^3+6 \text{$\#$1}^2 a^2-4 b \text{$\#$1} a^2+4 \text{$\#$1}^3 a-2 b \text{$\#$1}^2 a+\text{$\#$1}^4-2 b^3\&,\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[4]{\text{$\#$1}}}\right) \text{$\#$1}^{7/4}+\log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{\frac{b}{x^2}-a}\right) \text{$\#$1}^{7/4}-\log \left(\sqrt[4]{\frac{b}{x^2}-a}+\sqrt[4]{\text{$\#$1}}\right) \text{$\#$1}^{7/4}}{a^3-b a^2+3 \text{$\#$1} a^2+3 \text{$\#$1}^2 a-b \text{$\#$1} a+\text{$\#$1}^3}\&\right] a+\text{RootSum}\left[a^4-2 b a^3+4 \text{$\#$1} a^3+6 \text{$\#$1}^2 a^2-4 b \text{$\#$1} a^2+4 \text{$\#$1}^3 a-2 b \text{$\#$1}^2 a+\text{$\#$1}^4-2 b^3\&,\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[4]{\text{$\#$1}}}\right) \text{$\#$1}^{11/4}+\log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{\frac{b}{x^2}-a}\right) \text{$\#$1}^{11/4}-\log \left(\sqrt[4]{\frac{b}{x^2}-a}+\sqrt[4]{\text{$\#$1}}\right) \text{$\#$1}^{11/4}}{a^3-b a^2+3 \text{$\#$1} a^2+3 \text{$\#$1}^2 a-b \text{$\#$1} a+\text{$\#$1}^3}\&\right]\right)}{8 \sqrt[4]{a x^4-b x^2}}","-\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^{16}-4 \text{$\#$1}^{12} a+6 \text{$\#$1}^8 a^2-2 \text{$\#$1}^8 a b-4 \text{$\#$1}^4 a^3+4 \text{$\#$1}^4 a^2 b+a^4-2 a^3 b-2 b^3\&,\frac{\log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]",1,"-1/8*((-a + b/x^2)^(1/4)*x*(a^2*(a - b)*RootSum[a^4 - 2*a^3*b - 2*b^3 + 4*a^3*#1 - 4*a^2*b*#1 + 6*a^2*#1^2 - 2*a*b*#1^2 + 4*a*#1^3 + #1^4 & , ((2*ArcTan[(-a + b/x^2)^(1/4)/#1^(1/4)])/#1^(1/4) + Log[-(-a + b/x^2)^(1/4) + #1^(1/4)]/#1^(1/4) - Log[(-a + b/x^2)^(1/4) + #1^(1/4)]/#1^(1/4))/(a^3 - a^2*b + 3*a^2*#1 - a*b*#1 + 3*a*#1^2 + #1^3) & ] + a*(3*a - b)*RootSum[a^4 - 2*a^3*b - 2*b^3 + 4*a^3*#1 - 4*a^2*b*#1 + 6*a^2*#1^2 - 2*a*b*#1^2 + 4*a*#1^3 + #1^4 & , (2*ArcTan[(-a + b/x^2)^(1/4)/#1^(1/4)]*#1^(3/4) + Log[-(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(3/4) - Log[(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(3/4))/(a^3 - a^2*b + 3*a^2*#1 - a*b*#1 + 3*a*#1^2 + #1^3) & ] + 3*a*RootSum[a^4 - 2*a^3*b - 2*b^3 + 4*a^3*#1 - 4*a^2*b*#1 + 6*a^2*#1^2 - 2*a*b*#1^2 + 4*a*#1^3 + #1^4 & , (2*ArcTan[(-a + b/x^2)^(1/4)/#1^(1/4)]*#1^(7/4) + Log[-(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(7/4) - Log[(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(7/4))/(a^3 - a^2*b + 3*a^2*#1 - a*b*#1 + 3*a*#1^2 + #1^3) & ] + RootSum[a^4 - 2*a^3*b - 2*b^3 + 4*a^3*#1 - 4*a^2*b*#1 + 6*a^2*#1^2 - 2*a*b*#1^2 + 4*a*#1^3 + #1^4 & , (2*ArcTan[(-a + b/x^2)^(1/4)/#1^(1/4)]*#1^(11/4) + Log[-(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(11/4) - Log[(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(11/4))/(a^3 - a^2*b + 3*a^2*#1 - a*b*#1 + 3*a*#1^2 + #1^3) & ]))/(-(b*x^2) + a*x^4)^(1/4)","B",1
1454,1,804,102,1.9609935,"\int \frac{-b+a x^4}{\sqrt[4]{-b x^2+a x^4} \left(-b+2 a x^4+2 x^8\right)} \, dx","Integrate[(-b + a*x^4)/((-(b*x^2) + a*x^4)^(1/4)*(-b + 2*a*x^4 + 2*x^8)),x]","-\frac{\sqrt[4]{\frac{b}{x^2}-a} x \left((a-b) \text{RootSum}\left[a^4-2 b a^3+4 \text{$\#$1} a^3+6 \text{$\#$1}^2 a^2-4 b \text{$\#$1} a^2+4 \text{$\#$1}^3 a-2 b \text{$\#$1}^2 a+\text{$\#$1}^4-2 b^3\&,\frac{\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[4]{\text{$\#$1}}}\right)}{\sqrt[4]{\text{$\#$1}}}+\frac{\log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{\frac{b}{x^2}-a}\right)}{\sqrt[4]{\text{$\#$1}}}-\frac{\log \left(\sqrt[4]{\frac{b}{x^2}-a}+\sqrt[4]{\text{$\#$1}}\right)}{\sqrt[4]{\text{$\#$1}}}}{a^3-b a^2+3 \text{$\#$1} a^2+3 \text{$\#$1}^2 a-b \text{$\#$1} a+\text{$\#$1}^3}\&\right] a^2+(3 a-b) \text{RootSum}\left[a^4-2 b a^3+4 \text{$\#$1} a^3+6 \text{$\#$1}^2 a^2-4 b \text{$\#$1} a^2+4 \text{$\#$1}^3 a-2 b \text{$\#$1}^2 a+\text{$\#$1}^4-2 b^3\&,\frac{2 \text{$\#$1}^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[4]{\text{$\#$1}}}\right)+\log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{\frac{b}{x^2}-a}\right) \text{$\#$1}^{3/4}-\log \left(\sqrt[4]{\frac{b}{x^2}-a}+\sqrt[4]{\text{$\#$1}}\right) \text{$\#$1}^{3/4}}{a^3-b a^2+3 \text{$\#$1} a^2+3 \text{$\#$1}^2 a-b \text{$\#$1} a+\text{$\#$1}^3}\&\right] a+3 \text{RootSum}\left[a^4-2 b a^3+4 \text{$\#$1} a^3+6 \text{$\#$1}^2 a^2-4 b \text{$\#$1} a^2+4 \text{$\#$1}^3 a-2 b \text{$\#$1}^2 a+\text{$\#$1}^4-2 b^3\&,\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[4]{\text{$\#$1}}}\right) \text{$\#$1}^{7/4}+\log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{\frac{b}{x^2}-a}\right) \text{$\#$1}^{7/4}-\log \left(\sqrt[4]{\frac{b}{x^2}-a}+\sqrt[4]{\text{$\#$1}}\right) \text{$\#$1}^{7/4}}{a^3-b a^2+3 \text{$\#$1} a^2+3 \text{$\#$1}^2 a-b \text{$\#$1} a+\text{$\#$1}^3}\&\right] a+\text{RootSum}\left[a^4-2 b a^3+4 \text{$\#$1} a^3+6 \text{$\#$1}^2 a^2-4 b \text{$\#$1} a^2+4 \text{$\#$1}^3 a-2 b \text{$\#$1}^2 a+\text{$\#$1}^4-2 b^3\&,\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[4]{\text{$\#$1}}}\right) \text{$\#$1}^{11/4}+\log \left(\sqrt[4]{\text{$\#$1}}-\sqrt[4]{\frac{b}{x^2}-a}\right) \text{$\#$1}^{11/4}-\log \left(\sqrt[4]{\frac{b}{x^2}-a}+\sqrt[4]{\text{$\#$1}}\right) \text{$\#$1}^{11/4}}{a^3-b a^2+3 \text{$\#$1} a^2+3 \text{$\#$1}^2 a-b \text{$\#$1} a+\text{$\#$1}^3}\&\right]\right)}{8 \sqrt[4]{a x^4-b x^2}}","-\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^{16}-4 \text{$\#$1}^{12} a+6 \text{$\#$1}^8 a^2-2 \text{$\#$1}^8 a b-4 \text{$\#$1}^4 a^3+4 \text{$\#$1}^4 a^2 b+a^4-2 a^3 b-2 b^3\&,\frac{\log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]",1,"-1/8*((-a + b/x^2)^(1/4)*x*(a^2*(a - b)*RootSum[a^4 - 2*a^3*b - 2*b^3 + 4*a^3*#1 - 4*a^2*b*#1 + 6*a^2*#1^2 - 2*a*b*#1^2 + 4*a*#1^3 + #1^4 & , ((2*ArcTan[(-a + b/x^2)^(1/4)/#1^(1/4)])/#1^(1/4) + Log[-(-a + b/x^2)^(1/4) + #1^(1/4)]/#1^(1/4) - Log[(-a + b/x^2)^(1/4) + #1^(1/4)]/#1^(1/4))/(a^3 - a^2*b + 3*a^2*#1 - a*b*#1 + 3*a*#1^2 + #1^3) & ] + a*(3*a - b)*RootSum[a^4 - 2*a^3*b - 2*b^3 + 4*a^3*#1 - 4*a^2*b*#1 + 6*a^2*#1^2 - 2*a*b*#1^2 + 4*a*#1^3 + #1^4 & , (2*ArcTan[(-a + b/x^2)^(1/4)/#1^(1/4)]*#1^(3/4) + Log[-(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(3/4) - Log[(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(3/4))/(a^3 - a^2*b + 3*a^2*#1 - a*b*#1 + 3*a*#1^2 + #1^3) & ] + 3*a*RootSum[a^4 - 2*a^3*b - 2*b^3 + 4*a^3*#1 - 4*a^2*b*#1 + 6*a^2*#1^2 - 2*a*b*#1^2 + 4*a*#1^3 + #1^4 & , (2*ArcTan[(-a + b/x^2)^(1/4)/#1^(1/4)]*#1^(7/4) + Log[-(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(7/4) - Log[(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(7/4))/(a^3 - a^2*b + 3*a^2*#1 - a*b*#1 + 3*a*#1^2 + #1^3) & ] + RootSum[a^4 - 2*a^3*b - 2*b^3 + 4*a^3*#1 - 4*a^2*b*#1 + 6*a^2*#1^2 - 2*a*b*#1^2 + 4*a*#1^3 + #1^4 & , (2*ArcTan[(-a + b/x^2)^(1/4)/#1^(1/4)]*#1^(11/4) + Log[-(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(11/4) - Log[(-a + b/x^2)^(1/4) + #1^(1/4)]*#1^(11/4))/(a^3 - a^2*b + 3*a^2*#1 - a*b*#1 + 3*a*#1^2 + #1^3) & ]))/(-(b*x^2) + a*x^4)^(1/4)","B",1
1455,0,0,102,0.3060559,"\int \frac{\sqrt{c x^2-x \sqrt{-b x+a x^2}}}{x^3} \, dx","Integrate[Sqrt[c*x^2 - x*Sqrt[-(b*x) + a*x^2]]/x^3,x]","\int \frac{\sqrt{c x^2-x \sqrt{-b x+a x^2}}}{x^3} \, dx","-\frac{4 \left(-3 a x+3 b+2 c^2 x\right) \sqrt{-x \left(\sqrt{a x^2-b x}-c x\right)}}{15 b x^2}-\frac{4 c \sqrt{a x^2-b x} \sqrt{-x \left(\sqrt{a x^2-b x}-c x\right)}}{15 b x^2}",1,"Integrate[Sqrt[c*x^2 - x*Sqrt[-(b*x) + a*x^2]]/x^3, x]","F",-1
1456,1,3760,102,6.9588567,"\int \frac{x}{x+\sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[x/(x + Sqrt[x + Sqrt[1 + x^2]]),x]","\text{Result too large to show}","2 \text{RootSum}\left[\text{$\#$1}^4+2 \text{$\#$1}^3-1\&,\frac{\text{$\#$1}^3 \log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)-\log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)}{2 \text{$\#$1}^3+3 \text{$\#$1}^2}\&\right]-2 \sqrt{\sqrt{x^2+1}+x}+x",1,"x + ArcSinh[x] + (Log[x - Root[-1 - 2*#1^3 + #1^4 & , 1, 0]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 1, 0]^2] - Log[2 + 2*x*Root[-1 - 2*#1^3 + #1^4 & , 1, 0] + 2*Sqrt[1 + x^2]*Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 1, 0]^2]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 1, 0]^2])/((Root[-1 - 2*#1^3 + #1^4 & , 1, 0] - Root[-1 - 2*#1^3 + #1^4 & , 2, 0])*(Root[-1 - 2*#1^3 + #1^4 & , 1, 0] - Root[-1 - 2*#1^3 + #1^4 & , 3, 0])*(Root[-1 - 2*#1^3 + #1^4 & , 1, 0] - Root[-1 - 2*#1^3 + #1^4 & , 4, 0])) + (Root[-1 - 2*#1^3 + #1^4 & , 1, 0]^2*(Log[x - Root[-1 - 2*#1^3 + #1^4 & , 1, 0]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 1, 0]^2] - Log[2 + 2*x*Root[-1 - 2*#1^3 + #1^4 & , 1, 0] + 2*Sqrt[1 + x^2]*Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 1, 0]^2]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 1, 0]^2]))/((Root[-1 - 2*#1^3 + #1^4 & , 1, 0] - Root[-1 - 2*#1^3 + #1^4 & , 2, 0])*(Root[-1 - 2*#1^3 + #1^4 & , 1, 0] - Root[-1 - 2*#1^3 + #1^4 & , 3, 0])*(Root[-1 - 2*#1^3 + #1^4 & , 1, 0] - Root[-1 - 2*#1^3 + #1^4 & , 4, 0])) + (2*Root[-1 - 2*#1^3 + #1^4 & , 1, 0]^3*(Log[x - Root[-1 - 2*#1^3 + #1^4 & , 1, 0]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 1, 0]^2] - Log[2 + 2*x*Root[-1 - 2*#1^3 + #1^4 & , 1, 0] + 2*Sqrt[1 + x^2]*Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 1, 0]^2]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 1, 0]^2]))/((Root[-1 - 2*#1^3 + #1^4 & , 1, 0] - Root[-1 - 2*#1^3 + #1^4 & , 2, 0])*(Root[-1 - 2*#1^3 + #1^4 & , 1, 0] - Root[-1 - 2*#1^3 + #1^4 & , 3, 0])*(Root[-1 - 2*#1^3 + #1^4 & , 1, 0] - Root[-1 - 2*#1^3 + #1^4 & , 4, 0])) + (Log[x - Root[-1 - 2*#1^3 + #1^4 & , 2, 0]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 2, 0]^2] - Log[2 + 2*x*Root[-1 - 2*#1^3 + #1^4 & , 2, 0] + 2*Sqrt[1 + x^2]*Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 2, 0]^2]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 2, 0]^2])/((-Root[-1 - 2*#1^3 + #1^4 & , 1, 0] + Root[-1 - 2*#1^3 + #1^4 & , 2, 0])*(Root[-1 - 2*#1^3 + #1^4 & , 2, 0] - Root[-1 - 2*#1^3 + #1^4 & , 3, 0])*(Root[-1 - 2*#1^3 + #1^4 & , 2, 0] - Root[-1 - 2*#1^3 + #1^4 & , 4, 0])) + (Root[-1 - 2*#1^3 + #1^4 & , 2, 0]^2*(Log[x - Root[-1 - 2*#1^3 + #1^4 & , 2, 0]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 2, 0]^2] - Log[2 + 2*x*Root[-1 - 2*#1^3 + #1^4 & , 2, 0] + 2*Sqrt[1 + x^2]*Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 2, 0]^2]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 2, 0]^2]))/((-Root[-1 - 2*#1^3 + #1^4 & , 1, 0] + Root[-1 - 2*#1^3 + #1^4 & , 2, 0])*(Root[-1 - 2*#1^3 + #1^4 & , 2, 0] - Root[-1 - 2*#1^3 + #1^4 & , 3, 0])*(Root[-1 - 2*#1^3 + #1^4 & , 2, 0] - Root[-1 - 2*#1^3 + #1^4 & , 4, 0])) + (2*Root[-1 - 2*#1^3 + #1^4 & , 2, 0]^3*(Log[x - Root[-1 - 2*#1^3 + #1^4 & , 2, 0]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 2, 0]^2] - Log[2 + 2*x*Root[-1 - 2*#1^3 + #1^4 & , 2, 0] + 2*Sqrt[1 + x^2]*Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 2, 0]^2]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 2, 0]^2]))/((-Root[-1 - 2*#1^3 + #1^4 & , 1, 0] + Root[-1 - 2*#1^3 + #1^4 & , 2, 0])*(Root[-1 - 2*#1^3 + #1^4 & , 2, 0] - Root[-1 - 2*#1^3 + #1^4 & , 3, 0])*(Root[-1 - 2*#1^3 + #1^4 & , 2, 0] - Root[-1 - 2*#1^3 + #1^4 & , 4, 0])) + (Log[x - Root[-1 - 2*#1^3 + #1^4 & , 3, 0]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 3, 0]^2] - Log[2 + 2*x*Root[-1 - 2*#1^3 + #1^4 & , 3, 0] + 2*Sqrt[1 + x^2]*Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 3, 0]^2]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 3, 0]^2])/((-Root[-1 - 2*#1^3 + #1^4 & , 1, 0] + Root[-1 - 2*#1^3 + #1^4 & , 3, 0])*(-Root[-1 - 2*#1^3 + #1^4 & , 2, 0] + Root[-1 - 2*#1^3 + #1^4 & , 3, 0])*(Root[-1 - 2*#1^3 + #1^4 & , 3, 0] - Root[-1 - 2*#1^3 + #1^4 & , 4, 0])) + (Root[-1 - 2*#1^3 + #1^4 & , 3, 0]^2*(Log[x - Root[-1 - 2*#1^3 + #1^4 & , 3, 0]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 3, 0]^2] - Log[2 + 2*x*Root[-1 - 2*#1^3 + #1^4 & , 3, 0] + 2*Sqrt[1 + x^2]*Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 3, 0]^2]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 3, 0]^2]))/((-Root[-1 - 2*#1^3 + #1^4 & , 1, 0] + Root[-1 - 2*#1^3 + #1^4 & , 3, 0])*(-Root[-1 - 2*#1^3 + #1^4 & , 2, 0] + Root[-1 - 2*#1^3 + #1^4 & , 3, 0])*(Root[-1 - 2*#1^3 + #1^4 & , 3, 0] - Root[-1 - 2*#1^3 + #1^4 & , 4, 0])) + (2*Root[-1 - 2*#1^3 + #1^4 & , 3, 0]^3*(Log[x - Root[-1 - 2*#1^3 + #1^4 & , 3, 0]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 3, 0]^2] - Log[2 + 2*x*Root[-1 - 2*#1^3 + #1^4 & , 3, 0] + 2*Sqrt[1 + x^2]*Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 3, 0]^2]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 3, 0]^2]))/((-Root[-1 - 2*#1^3 + #1^4 & , 1, 0] + Root[-1 - 2*#1^3 + #1^4 & , 3, 0])*(-Root[-1 - 2*#1^3 + #1^4 & , 2, 0] + Root[-1 - 2*#1^3 + #1^4 & , 3, 0])*(Root[-1 - 2*#1^3 + #1^4 & , 3, 0] - Root[-1 - 2*#1^3 + #1^4 & , 4, 0])) + (Log[x - Root[-1 - 2*#1^3 + #1^4 & , 4, 0]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 4, 0]^2] - Log[2 + 2*x*Root[-1 - 2*#1^3 + #1^4 & , 4, 0] + 2*Sqrt[1 + x^2]*Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 4, 0]^2]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 4, 0]^2])/((-Root[-1 - 2*#1^3 + #1^4 & , 1, 0] + Root[-1 - 2*#1^3 + #1^4 & , 4, 0])*(-Root[-1 - 2*#1^3 + #1^4 & , 2, 0] + Root[-1 - 2*#1^3 + #1^4 & , 4, 0])*(-Root[-1 - 2*#1^3 + #1^4 & , 3, 0] + Root[-1 - 2*#1^3 + #1^4 & , 4, 0])) + (Root[-1 - 2*#1^3 + #1^4 & , 4, 0]^2*(Log[x - Root[-1 - 2*#1^3 + #1^4 & , 4, 0]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 4, 0]^2] - Log[2 + 2*x*Root[-1 - 2*#1^3 + #1^4 & , 4, 0] + 2*Sqrt[1 + x^2]*Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 4, 0]^2]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 4, 0]^2]))/((-Root[-1 - 2*#1^3 + #1^4 & , 1, 0] + Root[-1 - 2*#1^3 + #1^4 & , 4, 0])*(-Root[-1 - 2*#1^3 + #1^4 & , 2, 0] + Root[-1 - 2*#1^3 + #1^4 & , 4, 0])*(-Root[-1 - 2*#1^3 + #1^4 & , 3, 0] + Root[-1 - 2*#1^3 + #1^4 & , 4, 0])) + (2*Root[-1 - 2*#1^3 + #1^4 & , 4, 0]^3*(Log[x - Root[-1 - 2*#1^3 + #1^4 & , 4, 0]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 4, 0]^2] - Log[2 + 2*x*Root[-1 - 2*#1^3 + #1^4 & , 4, 0] + 2*Sqrt[1 + x^2]*Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 4, 0]^2]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 4, 0]^2]))/((-Root[-1 - 2*#1^3 + #1^4 & , 1, 0] + Root[-1 - 2*#1^3 + #1^4 & , 4, 0])*(-Root[-1 - 2*#1^3 + #1^4 & , 2, 0] + Root[-1 - 2*#1^3 + #1^4 & , 4, 0])*(-Root[-1 - 2*#1^3 + #1^4 & , 3, 0] + Root[-1 - 2*#1^3 + #1^4 & , 4, 0])) + RootSum[-1 - 2*#1^3 + #1^4 & , (Log[x - #1] + Log[x - #1]*#1^3)/(-3*#1^2 + 2*#1^3) & ]/2 - ((x + Sqrt[1 + x^2])*Sqrt[2 + (x + Sqrt[1 + x^2])^(-2) + (x + Sqrt[1 + x^2])^2]*(2*RootSum[-1 - 2*#1^3 + #1^4 & , (Log[Sqrt[x + Sqrt[1 + x^2]] - #1] + Log[Sqrt[x + Sqrt[1 + x^2]] - #1]*#1^3)/(-3*#1^2 + 2*#1^3) & ] - 2*RootSum[-1 + 2*#1^3 + #1^4 & , (-Log[Sqrt[x + Sqrt[1 + x^2]] - #1] + Log[Sqrt[x + Sqrt[1 + x^2]] - #1]*#1^3)/(3*#1^2 + 2*#1^3) & ] - RootSum[1 + 4*#1^2 - 2*#1^4 + #1^8 & , (-Log[Sqrt[x + Sqrt[1 + x^2]] - #1] - 2*Log[Sqrt[x + Sqrt[1 + x^2]] - #1]*#1^2 + Log[Sqrt[x + Sqrt[1 + x^2]] - #1]*#1^4)/(#1 - #1^3 + #1^7) & ]))/(4*(1 + (x + Sqrt[1 + x^2])^2)) - 2*(Sqrt[x + Sqrt[1 + x^2]] + RootSum[-1 - 2*#1^3 + #1^4 & , (Log[Sqrt[x + Sqrt[1 + x^2]] - #1] + Log[Sqrt[x + Sqrt[1 + x^2]] - #1]*#1^3)/(-3*#1^2 + 2*#1^3) & ]/4 - RootSum[-1 + 2*#1^3 + #1^4 & , (-Log[Sqrt[x + Sqrt[1 + x^2]] - #1] + Log[Sqrt[x + Sqrt[1 + x^2]] - #1]*#1^3)/(3*#1^2 + 2*#1^3) & ]/4 + RootSum[1 + 4*#1^2 - 2*#1^4 + #1^8 & , (-Log[Sqrt[x + Sqrt[1 + x^2]] - #1] - 2*Log[Sqrt[x + Sqrt[1 + x^2]] - #1]*#1^2 + Log[Sqrt[x + Sqrt[1 + x^2]] - #1]*#1^4)/(#1 - #1^3 + #1^7) & ]/8)","B",0
1457,1,3760,102,6.7503258,"\int \frac{x}{x+\sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[x/(x + Sqrt[x + Sqrt[1 + x^2]]),x]","\text{Result too large to show}","2 \text{RootSum}\left[\text{$\#$1}^4+2 \text{$\#$1}^3-1\&,\frac{\text{$\#$1}^3 \log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)-\log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)}{2 \text{$\#$1}^3+3 \text{$\#$1}^2}\&\right]-2 \sqrt{\sqrt{x^2+1}+x}+x",1,"x + ArcSinh[x] + (Log[x - Root[-1 - 2*#1^3 + #1^4 & , 1, 0]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 1, 0]^2] - Log[2 + 2*x*Root[-1 - 2*#1^3 + #1^4 & , 1, 0] + 2*Sqrt[1 + x^2]*Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 1, 0]^2]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 1, 0]^2])/((Root[-1 - 2*#1^3 + #1^4 & , 1, 0] - Root[-1 - 2*#1^3 + #1^4 & , 2, 0])*(Root[-1 - 2*#1^3 + #1^4 & , 1, 0] - Root[-1 - 2*#1^3 + #1^4 & , 3, 0])*(Root[-1 - 2*#1^3 + #1^4 & , 1, 0] - Root[-1 - 2*#1^3 + #1^4 & , 4, 0])) + (Root[-1 - 2*#1^3 + #1^4 & , 1, 0]^2*(Log[x - Root[-1 - 2*#1^3 + #1^4 & , 1, 0]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 1, 0]^2] - Log[2 + 2*x*Root[-1 - 2*#1^3 + #1^4 & , 1, 0] + 2*Sqrt[1 + x^2]*Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 1, 0]^2]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 1, 0]^2]))/((Root[-1 - 2*#1^3 + #1^4 & , 1, 0] - Root[-1 - 2*#1^3 + #1^4 & , 2, 0])*(Root[-1 - 2*#1^3 + #1^4 & , 1, 0] - Root[-1 - 2*#1^3 + #1^4 & , 3, 0])*(Root[-1 - 2*#1^3 + #1^4 & , 1, 0] - Root[-1 - 2*#1^3 + #1^4 & , 4, 0])) + (2*Root[-1 - 2*#1^3 + #1^4 & , 1, 0]^3*(Log[x - Root[-1 - 2*#1^3 + #1^4 & , 1, 0]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 1, 0]^2] - Log[2 + 2*x*Root[-1 - 2*#1^3 + #1^4 & , 1, 0] + 2*Sqrt[1 + x^2]*Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 1, 0]^2]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 1, 0]^2]))/((Root[-1 - 2*#1^3 + #1^4 & , 1, 0] - Root[-1 - 2*#1^3 + #1^4 & , 2, 0])*(Root[-1 - 2*#1^3 + #1^4 & , 1, 0] - Root[-1 - 2*#1^3 + #1^4 & , 3, 0])*(Root[-1 - 2*#1^3 + #1^4 & , 1, 0] - Root[-1 - 2*#1^3 + #1^4 & , 4, 0])) + (Log[x - Root[-1 - 2*#1^3 + #1^4 & , 2, 0]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 2, 0]^2] - Log[2 + 2*x*Root[-1 - 2*#1^3 + #1^4 & , 2, 0] + 2*Sqrt[1 + x^2]*Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 2, 0]^2]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 2, 0]^2])/((-Root[-1 - 2*#1^3 + #1^4 & , 1, 0] + Root[-1 - 2*#1^3 + #1^4 & , 2, 0])*(Root[-1 - 2*#1^3 + #1^4 & , 2, 0] - Root[-1 - 2*#1^3 + #1^4 & , 3, 0])*(Root[-1 - 2*#1^3 + #1^4 & , 2, 0] - Root[-1 - 2*#1^3 + #1^4 & , 4, 0])) + (Root[-1 - 2*#1^3 + #1^4 & , 2, 0]^2*(Log[x - Root[-1 - 2*#1^3 + #1^4 & , 2, 0]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 2, 0]^2] - Log[2 + 2*x*Root[-1 - 2*#1^3 + #1^4 & , 2, 0] + 2*Sqrt[1 + x^2]*Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 2, 0]^2]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 2, 0]^2]))/((-Root[-1 - 2*#1^3 + #1^4 & , 1, 0] + Root[-1 - 2*#1^3 + #1^4 & , 2, 0])*(Root[-1 - 2*#1^3 + #1^4 & , 2, 0] - Root[-1 - 2*#1^3 + #1^4 & , 3, 0])*(Root[-1 - 2*#1^3 + #1^4 & , 2, 0] - Root[-1 - 2*#1^3 + #1^4 & , 4, 0])) + (2*Root[-1 - 2*#1^3 + #1^4 & , 2, 0]^3*(Log[x - Root[-1 - 2*#1^3 + #1^4 & , 2, 0]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 2, 0]^2] - Log[2 + 2*x*Root[-1 - 2*#1^3 + #1^4 & , 2, 0] + 2*Sqrt[1 + x^2]*Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 2, 0]^2]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 2, 0]^2]))/((-Root[-1 - 2*#1^3 + #1^4 & , 1, 0] + Root[-1 - 2*#1^3 + #1^4 & , 2, 0])*(Root[-1 - 2*#1^3 + #1^4 & , 2, 0] - Root[-1 - 2*#1^3 + #1^4 & , 3, 0])*(Root[-1 - 2*#1^3 + #1^4 & , 2, 0] - Root[-1 - 2*#1^3 + #1^4 & , 4, 0])) + (Log[x - Root[-1 - 2*#1^3 + #1^4 & , 3, 0]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 3, 0]^2] - Log[2 + 2*x*Root[-1 - 2*#1^3 + #1^4 & , 3, 0] + 2*Sqrt[1 + x^2]*Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 3, 0]^2]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 3, 0]^2])/((-Root[-1 - 2*#1^3 + #1^4 & , 1, 0] + Root[-1 - 2*#1^3 + #1^4 & , 3, 0])*(-Root[-1 - 2*#1^3 + #1^4 & , 2, 0] + Root[-1 - 2*#1^3 + #1^4 & , 3, 0])*(Root[-1 - 2*#1^3 + #1^4 & , 3, 0] - Root[-1 - 2*#1^3 + #1^4 & , 4, 0])) + (Root[-1 - 2*#1^3 + #1^4 & , 3, 0]^2*(Log[x - Root[-1 - 2*#1^3 + #1^4 & , 3, 0]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 3, 0]^2] - Log[2 + 2*x*Root[-1 - 2*#1^3 + #1^4 & , 3, 0] + 2*Sqrt[1 + x^2]*Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 3, 0]^2]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 3, 0]^2]))/((-Root[-1 - 2*#1^3 + #1^4 & , 1, 0] + Root[-1 - 2*#1^3 + #1^4 & , 3, 0])*(-Root[-1 - 2*#1^3 + #1^4 & , 2, 0] + Root[-1 - 2*#1^3 + #1^4 & , 3, 0])*(Root[-1 - 2*#1^3 + #1^4 & , 3, 0] - Root[-1 - 2*#1^3 + #1^4 & , 4, 0])) + (2*Root[-1 - 2*#1^3 + #1^4 & , 3, 0]^3*(Log[x - Root[-1 - 2*#1^3 + #1^4 & , 3, 0]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 3, 0]^2] - Log[2 + 2*x*Root[-1 - 2*#1^3 + #1^4 & , 3, 0] + 2*Sqrt[1 + x^2]*Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 3, 0]^2]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 3, 0]^2]))/((-Root[-1 - 2*#1^3 + #1^4 & , 1, 0] + Root[-1 - 2*#1^3 + #1^4 & , 3, 0])*(-Root[-1 - 2*#1^3 + #1^4 & , 2, 0] + Root[-1 - 2*#1^3 + #1^4 & , 3, 0])*(Root[-1 - 2*#1^3 + #1^4 & , 3, 0] - Root[-1 - 2*#1^3 + #1^4 & , 4, 0])) + (Log[x - Root[-1 - 2*#1^3 + #1^4 & , 4, 0]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 4, 0]^2] - Log[2 + 2*x*Root[-1 - 2*#1^3 + #1^4 & , 4, 0] + 2*Sqrt[1 + x^2]*Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 4, 0]^2]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 4, 0]^2])/((-Root[-1 - 2*#1^3 + #1^4 & , 1, 0] + Root[-1 - 2*#1^3 + #1^4 & , 4, 0])*(-Root[-1 - 2*#1^3 + #1^4 & , 2, 0] + Root[-1 - 2*#1^3 + #1^4 & , 4, 0])*(-Root[-1 - 2*#1^3 + #1^4 & , 3, 0] + Root[-1 - 2*#1^3 + #1^4 & , 4, 0])) + (Root[-1 - 2*#1^3 + #1^4 & , 4, 0]^2*(Log[x - Root[-1 - 2*#1^3 + #1^4 & , 4, 0]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 4, 0]^2] - Log[2 + 2*x*Root[-1 - 2*#1^3 + #1^4 & , 4, 0] + 2*Sqrt[1 + x^2]*Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 4, 0]^2]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 4, 0]^2]))/((-Root[-1 - 2*#1^3 + #1^4 & , 1, 0] + Root[-1 - 2*#1^3 + #1^4 & , 4, 0])*(-Root[-1 - 2*#1^3 + #1^4 & , 2, 0] + Root[-1 - 2*#1^3 + #1^4 & , 4, 0])*(-Root[-1 - 2*#1^3 + #1^4 & , 3, 0] + Root[-1 - 2*#1^3 + #1^4 & , 4, 0])) + (2*Root[-1 - 2*#1^3 + #1^4 & , 4, 0]^3*(Log[x - Root[-1 - 2*#1^3 + #1^4 & , 4, 0]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 4, 0]^2] - Log[2 + 2*x*Root[-1 - 2*#1^3 + #1^4 & , 4, 0] + 2*Sqrt[1 + x^2]*Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 4, 0]^2]]/Sqrt[1 + Root[-1 - 2*#1^3 + #1^4 & , 4, 0]^2]))/((-Root[-1 - 2*#1^3 + #1^4 & , 1, 0] + Root[-1 - 2*#1^3 + #1^4 & , 4, 0])*(-Root[-1 - 2*#1^3 + #1^4 & , 2, 0] + Root[-1 - 2*#1^3 + #1^4 & , 4, 0])*(-Root[-1 - 2*#1^3 + #1^4 & , 3, 0] + Root[-1 - 2*#1^3 + #1^4 & , 4, 0])) + RootSum[-1 - 2*#1^3 + #1^4 & , (Log[x - #1] + Log[x - #1]*#1^3)/(-3*#1^2 + 2*#1^3) & ]/2 - ((x + Sqrt[1 + x^2])*Sqrt[2 + (x + Sqrt[1 + x^2])^(-2) + (x + Sqrt[1 + x^2])^2]*(2*RootSum[-1 - 2*#1^3 + #1^4 & , (Log[Sqrt[x + Sqrt[1 + x^2]] - #1] + Log[Sqrt[x + Sqrt[1 + x^2]] - #1]*#1^3)/(-3*#1^2 + 2*#1^3) & ] - 2*RootSum[-1 + 2*#1^3 + #1^4 & , (-Log[Sqrt[x + Sqrt[1 + x^2]] - #1] + Log[Sqrt[x + Sqrt[1 + x^2]] - #1]*#1^3)/(3*#1^2 + 2*#1^3) & ] - RootSum[1 + 4*#1^2 - 2*#1^4 + #1^8 & , (-Log[Sqrt[x + Sqrt[1 + x^2]] - #1] - 2*Log[Sqrt[x + Sqrt[1 + x^2]] - #1]*#1^2 + Log[Sqrt[x + Sqrt[1 + x^2]] - #1]*#1^4)/(#1 - #1^3 + #1^7) & ]))/(4*(1 + (x + Sqrt[1 + x^2])^2)) - 2*(Sqrt[x + Sqrt[1 + x^2]] + RootSum[-1 - 2*#1^3 + #1^4 & , (Log[Sqrt[x + Sqrt[1 + x^2]] - #1] + Log[Sqrt[x + Sqrt[1 + x^2]] - #1]*#1^3)/(-3*#1^2 + 2*#1^3) & ]/4 - RootSum[-1 + 2*#1^3 + #1^4 & , (-Log[Sqrt[x + Sqrt[1 + x^2]] - #1] + Log[Sqrt[x + Sqrt[1 + x^2]] - #1]*#1^3)/(3*#1^2 + 2*#1^3) & ]/4 + RootSum[1 + 4*#1^2 - 2*#1^4 + #1^8 & , (-Log[Sqrt[x + Sqrt[1 + x^2]] - #1] - 2*Log[Sqrt[x + Sqrt[1 + x^2]] - #1]*#1^2 + Log[Sqrt[x + Sqrt[1 + x^2]] - #1]*#1^4)/(#1 - #1^3 + #1^7) & ]/8)","B",0
1458,1,218,103,0.2110368,"\int \frac{1+x}{\left(-2+2 x+x^2\right) \sqrt{1+x^3}} \, dx","Integrate[(1 + x)/((-2 + 2*x + x^2)*Sqrt[1 + x^3]),x]","-\frac{\sqrt{\frac{x+1}{1+\sqrt[3]{-1}}} \sqrt{x^2-x+1} \left(\left(3+(2+i) \sqrt{3}\right) \Pi \left(\frac{2 \sqrt{3}}{-3 i+(1+2 i) \sqrt{3}};\sin ^{-1}\left(\sqrt{\frac{\left(i+\sqrt{3}\right) x-2 i}{-3 i+\sqrt{3}}}\right)|\frac{1}{2} \left(1+i \sqrt{3}\right)\right)+\left(3-(2-i) \sqrt{3}\right) \Pi \left(\frac{2 i \sqrt{3}}{3+(2+i) \sqrt{3}};\sin ^{-1}\left(\sqrt{\frac{\left(i+\sqrt{3}\right) x-2 i}{-3 i+\sqrt{3}}}\right)|\frac{1}{2} \left(1+i \sqrt{3}\right)\right)\right)}{3 \left(\sqrt{3}+i\right) \sqrt{x^3+1}}","\frac{1}{6} \sqrt{2 \sqrt{3}-3} \tan ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} \sqrt{x^3+1}}{x^2-x+1}\right)-\frac{1}{6} \sqrt{3+2 \sqrt{3}} \tanh ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} \sqrt{x^3+1}}{x^2-x+1}\right)",1,"-1/3*(Sqrt[(1 + x)/(1 + (-1)^(1/3))]*Sqrt[1 - x + x^2]*((3 + (2 + I)*Sqrt[3])*EllipticPi[(2*Sqrt[3])/(-3*I + (1 + 2*I)*Sqrt[3]), ArcSin[Sqrt[(-2*I + (I + Sqrt[3])*x)/(-3*I + Sqrt[3])]], (1 + I*Sqrt[3])/2] + (3 - (2 - I)*Sqrt[3])*EllipticPi[((2*I)*Sqrt[3])/(3 + (2 + I)*Sqrt[3]), ArcSin[Sqrt[(-2*I + (I + Sqrt[3])*x)/(-3*I + Sqrt[3])]], (1 + I*Sqrt[3])/2]))/((I + Sqrt[3])*Sqrt[1 + x^3])","C",1
1459,1,286,103,0.8180155,"\int \frac{3+x+x^2}{\left(-2+2 x+x^2\right) \sqrt{1+x^3}} \, dx","Integrate[(3 + x + x^2)/((-2 + 2*x + x^2)*Sqrt[1 + x^3]),x]","\frac{\sqrt{\frac{x+1}{1+\sqrt[3]{-1}}} \left(\sqrt{x^2-x+1} \left(\left((-9-6 i)-(4-i) \sqrt{3}\right) \Pi \left(\frac{2 \sqrt{3}}{-3 i+(1+2 i) \sqrt{3}};\sin ^{-1}\left(\sqrt{\frac{(-1)^{2/3} x+1}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)+\left((-9+6 i)+(4+i) \sqrt{3}\right) \Pi \left(\frac{2 i \sqrt{3}}{3+(2+i) \sqrt{3}};\sin ^{-1}\left(\sqrt{\frac{(-1)^{2/3} x+1}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)\right)+\frac{6 \sqrt{\frac{\sqrt[3]{-1}-(-1)^{2/3} x}{1+\sqrt[3]{-1}}} \left(\left(\sqrt{3}+i\right) x-2 i\right) F\left(\sin ^{-1}\left(\sqrt{\frac{(-1)^{2/3} x+1}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{\sqrt{\frac{(-1)^{2/3} x+1}{1+\sqrt[3]{-1}}}}\right)}{3 \left(\sqrt{3}+i\right) \sqrt{x^3+1}}","-\frac{1}{6} \sqrt{14 \sqrt{3}-15} \tan ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} \sqrt{x^3+1}}{x^2-x+1}\right)-\frac{1}{6} \sqrt{15+14 \sqrt{3}} \tanh ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} \sqrt{x^3+1}}{x^2-x+1}\right)",1,"(Sqrt[(1 + x)/(1 + (-1)^(1/3))]*((6*Sqrt[((-1)^(1/3) - (-1)^(2/3)*x)/(1 + (-1)^(1/3))]*(-2*I + (I + Sqrt[3])*x)*EllipticF[ArcSin[Sqrt[(1 + (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)])/Sqrt[(1 + (-1)^(2/3)*x)/(1 + (-1)^(1/3))] + Sqrt[1 - x + x^2]*(((-9 - 6*I) - (4 - I)*Sqrt[3])*EllipticPi[(2*Sqrt[3])/(-3*I + (1 + 2*I)*Sqrt[3]), ArcSin[Sqrt[(1 + (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)] + ((-9 + 6*I) + (4 + I)*Sqrt[3])*EllipticPi[((2*I)*Sqrt[3])/(3 + (2 + I)*Sqrt[3]), ArcSin[Sqrt[(1 + (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)])))/(3*(I + Sqrt[3])*Sqrt[1 + x^3])","C",0
1460,1,286,103,0.8146774,"\int \frac{3-x+2 x^2}{\left(-2+2 x+x^2\right) \sqrt{1+x^3}} \, dx","Integrate[(3 - x + 2*x^2)/((-2 + 2*x + x^2)*Sqrt[1 + x^3]),x]","\frac{\sqrt{\frac{x+1}{1+\sqrt[3]{-1}}} \left(\sqrt{x^2-x+1} \left(\left((-9-12 i)-(2-5 i) \sqrt{3}\right) \Pi \left(\frac{2 \sqrt{3}}{-3 i+(1+2 i) \sqrt{3}};\sin ^{-1}\left(\sqrt{\frac{(-1)^{2/3} x+1}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)+\left((-9+12 i)+(2+5 i) \sqrt{3}\right) \Pi \left(\frac{2 i \sqrt{3}}{3+(2+i) \sqrt{3}};\sin ^{-1}\left(\sqrt{\frac{(-1)^{2/3} x+1}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)\right)+\frac{12 \sqrt{\frac{\sqrt[3]{-1}-(-1)^{2/3} x}{1+\sqrt[3]{-1}}} \left(\left(\sqrt{3}+i\right) x-2 i\right) F\left(\sin ^{-1}\left(\sqrt{\frac{(-1)^{2/3} x+1}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{\sqrt{\frac{(-1)^{2/3} x+1}{1+\sqrt[3]{-1}}}}\right)}{3 \left(\sqrt{3}+i\right) \sqrt{x^3+1}}","-\frac{1}{6} \sqrt{21+26 \sqrt{3}} \tan ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} \sqrt{x^3+1}}{x^2-x+1}\right)-\frac{1}{6} \sqrt{26 \sqrt{3}-21} \tanh ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} \sqrt{x^3+1}}{x^2-x+1}\right)",1,"(Sqrt[(1 + x)/(1 + (-1)^(1/3))]*((12*Sqrt[((-1)^(1/3) - (-1)^(2/3)*x)/(1 + (-1)^(1/3))]*(-2*I + (I + Sqrt[3])*x)*EllipticF[ArcSin[Sqrt[(1 + (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)])/Sqrt[(1 + (-1)^(2/3)*x)/(1 + (-1)^(1/3))] + Sqrt[1 - x + x^2]*(((-9 - 12*I) - (2 - 5*I)*Sqrt[3])*EllipticPi[(2*Sqrt[3])/(-3*I + (1 + 2*I)*Sqrt[3]), ArcSin[Sqrt[(1 + (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)] + ((-9 + 12*I) + (2 + 5*I)*Sqrt[3])*EllipticPi[((2*I)*Sqrt[3])/(3 + (2 + I)*Sqrt[3]), ArcSin[Sqrt[(1 + (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)])))/(3*(I + Sqrt[3])*Sqrt[1 + x^3])","C",0
1461,1,50,103,0.0238443,"\int \frac{\left(-1+x^3\right)^{2/3} \left(1+x^3\right)}{x^3} \, dx","Integrate[((-1 + x^3)^(2/3)*(1 + x^3))/x^3,x]","\frac{\left(x^3-1\right)^{2/3} \left(-\frac{x^3 \, _2F_1\left(-\frac{2}{3},\frac{1}{3};\frac{4}{3};x^3\right)}{\left(1-x^3\right)^{2/3}}+x^3-1\right)}{2 x^2}","-\frac{1}{9} \log \left(\sqrt[3]{x^3-1}-x\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-1}+x}\right)}{3 \sqrt{3}}+\frac{\left(x^3-1\right)^{2/3} \left(2 x^3-3\right)}{6 x^2}+\frac{1}{18} \log \left(\sqrt[3]{x^3-1} x+\left(x^3-1\right)^{2/3}+x^2\right)",1,"((-1 + x^3)^(2/3)*(-1 + x^3 - (x^3*Hypergeometric2F1[-2/3, 1/3, 4/3, x^3])/(1 - x^3)^(2/3)))/(2*x^2)","C",1
1462,1,94,103,0.0538018,"\int x^8 \left(b+a x^4\right)^{3/4} \, dx","Integrate[x^8*(b + a*x^4)^(3/4),x]","\frac{x \left(a x^4+b\right)^{3/4} \left(\left(\frac{a x^4}{b}+1\right)^{3/4} \left(8 a^2 x^8+3 a b x^4-5 b^2\right)+5 b^2 \, _2F_1\left(-\frac{3}{4},\frac{1}{4};\frac{5}{4};-\frac{a x^4}{b}\right)\right)}{96 a^2 \left(\frac{a x^4}{b}+1\right)^{3/4}}","\frac{5 b^3 \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{256 a^{9/4}}+\frac{5 b^3 \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{256 a^{9/4}}+\frac{\left(a x^4+b\right)^{3/4} \left(32 a^2 x^9+12 a b x^5-15 b^2 x\right)}{384 a^2}",1,"(x*(b + a*x^4)^(3/4)*((1 + (a*x^4)/b)^(3/4)*(-5*b^2 + 3*a*b*x^4 + 8*a^2*x^8) + 5*b^2*Hypergeometric2F1[-3/4, 1/4, 5/4, -((a*x^4)/b)]))/(96*a^2*(1 + (a*x^4)/b)^(3/4))","C",1
1463,1,44,103,0.018982,"\int \frac{1}{\left(-b+a x^3\right) \sqrt[4]{b x+a x^4}} \, dx","Integrate[1/((-b + a*x^3)*(b*x + a*x^4)^(1/4)),x]","-\frac{4 x \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{2 a x^3}{a x^3+b}\right)}{3 b \sqrt[4]{x \left(a x^3+b\right)}}","-\frac{2^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} \left(a x^4+b x\right)^{3/4}}{a x^3+b}\right)}{3 \sqrt[4]{a} b}-\frac{2^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} \left(a x^4+b x\right)^{3/4}}{a x^3+b}\right)}{3 \sqrt[4]{a} b}",1,"(-4*x*Hypergeometric2F1[1/4, 1, 5/4, (2*a*x^3)/(b + a*x^3)])/(3*b*(x*(b + a*x^3))^(1/4))","C",1
1464,1,373,103,0.7407662,"\int \frac{\left(-2+x^3\right) \left(1+x^3\right)^{2/3}}{x^3 \left(-2+x^3+2 x^6\right)} \, dx","Integrate[((-2 + x^3)*(1 + x^3)^(2/3))/(x^3*(-2 + x^3 + 2*x^6)),x]","\frac{-2 \sqrt[3]{19+5 \sqrt{17}} \log \left(\sqrt[3]{5-\sqrt{17}}-\frac{\sqrt[3]{2} x}{\sqrt[3]{x^3+1}}\right)-2 \sqrt[3]{5 \sqrt{17}-19} \log \left(\sqrt[3]{5+\sqrt{17}}-\frac{\sqrt[3]{2} x}{\sqrt[3]{x^3+1}}\right)+2 \sqrt{3} \sqrt[3]{5 \sqrt{17}-19} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{\frac{2}{5+\sqrt{17}}} x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)+2 \sqrt{3} \sqrt[3]{19+5 \sqrt{17}} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{2 \left(5+\sqrt{17}\right)} x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)+\sqrt[3]{19+5 \sqrt{17}} \log \left(\frac{\sqrt[3]{10-2 \sqrt{17}} x}{\sqrt[3]{x^3+1}}+\frac{2^{2/3} x^2}{\left(x^3+1\right)^{2/3}}+\left(5-\sqrt{17}\right)^{2/3}\right)+\sqrt[3]{5 \sqrt{17}-19} \log \left(\frac{\sqrt[3]{2 \left(5+\sqrt{17}\right)} x}{\sqrt[3]{x^3+1}}+\frac{2^{2/3} x^2}{\left(x^3+1\right)^{2/3}}+\left(5+\sqrt{17}\right)^{2/3}\right)}{6 \sqrt[3]{2} \sqrt{17}}-\frac{\left(x^3+1\right)^{2/3}}{2 x^2}","\frac{1}{3} \text{RootSum}\left[2 \text{$\#$1}^6-5 \text{$\#$1}^3+1\&,\frac{-2 \text{$\#$1}^3 \log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)+2 \text{$\#$1}^3 \log (x)+\log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)-\log (x)}{4 \text{$\#$1}^4-5 \text{$\#$1}}\&\right]-\frac{\left(x^3+1\right)^{2/3}}{2 x^2}",1,"-1/2*(1 + x^3)^(2/3)/x^2 + (2*Sqrt[3]*(-19 + 5*Sqrt[17])^(1/3)*ArcTan[(1 + (2*(2/(5 + Sqrt[17]))^(1/3)*x)/(1 + x^3)^(1/3))/Sqrt[3]] + 2*Sqrt[3]*(19 + 5*Sqrt[17])^(1/3)*ArcTan[(1 + ((2*(5 + Sqrt[17]))^(1/3)*x)/(1 + x^3)^(1/3))/Sqrt[3]] - 2*(19 + 5*Sqrt[17])^(1/3)*Log[(5 - Sqrt[17])^(1/3) - (2^(1/3)*x)/(1 + x^3)^(1/3)] - 2*(-19 + 5*Sqrt[17])^(1/3)*Log[(5 + Sqrt[17])^(1/3) - (2^(1/3)*x)/(1 + x^3)^(1/3)] + (19 + 5*Sqrt[17])^(1/3)*Log[(5 - Sqrt[17])^(2/3) + (2^(2/3)*x^2)/(1 + x^3)^(2/3) + ((10 - 2*Sqrt[17])^(1/3)*x)/(1 + x^3)^(1/3)] + (-19 + 5*Sqrt[17])^(1/3)*Log[(5 + Sqrt[17])^(2/3) + (2^(2/3)*x^2)/(1 + x^3)^(2/3) + ((2*(5 + Sqrt[17]))^(1/3)*x)/(1 + x^3)^(1/3)])/(6*2^(1/3)*Sqrt[17])","B",0
1465,1,373,103,0.5962513,"\int \frac{\left(-2+x^3\right) \left(1+x^3\right)^{2/3}}{x^3 \left(-2+x^3+2 x^6\right)} \, dx","Integrate[((-2 + x^3)*(1 + x^3)^(2/3))/(x^3*(-2 + x^3 + 2*x^6)),x]","\frac{-2 \sqrt[3]{19+5 \sqrt{17}} \log \left(\sqrt[3]{5-\sqrt{17}}-\frac{\sqrt[3]{2} x}{\sqrt[3]{x^3+1}}\right)-2 \sqrt[3]{5 \sqrt{17}-19} \log \left(\sqrt[3]{5+\sqrt{17}}-\frac{\sqrt[3]{2} x}{\sqrt[3]{x^3+1}}\right)+2 \sqrt{3} \sqrt[3]{5 \sqrt{17}-19} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{\frac{2}{5+\sqrt{17}}} x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)+2 \sqrt{3} \sqrt[3]{19+5 \sqrt{17}} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{2 \left(5+\sqrt{17}\right)} x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)+\sqrt[3]{19+5 \sqrt{17}} \log \left(\frac{\sqrt[3]{10-2 \sqrt{17}} x}{\sqrt[3]{x^3+1}}+\frac{2^{2/3} x^2}{\left(x^3+1\right)^{2/3}}+\left(5-\sqrt{17}\right)^{2/3}\right)+\sqrt[3]{5 \sqrt{17}-19} \log \left(\frac{\sqrt[3]{2 \left(5+\sqrt{17}\right)} x}{\sqrt[3]{x^3+1}}+\frac{2^{2/3} x^2}{\left(x^3+1\right)^{2/3}}+\left(5+\sqrt{17}\right)^{2/3}\right)}{6 \sqrt[3]{2} \sqrt{17}}-\frac{\left(x^3+1\right)^{2/3}}{2 x^2}","\frac{1}{3} \text{RootSum}\left[2 \text{$\#$1}^6-5 \text{$\#$1}^3+1\&,\frac{-2 \text{$\#$1}^3 \log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)+2 \text{$\#$1}^3 \log (x)+\log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)-\log (x)}{4 \text{$\#$1}^4-5 \text{$\#$1}}\&\right]-\frac{\left(x^3+1\right)^{2/3}}{2 x^2}",1,"-1/2*(1 + x^3)^(2/3)/x^2 + (2*Sqrt[3]*(-19 + 5*Sqrt[17])^(1/3)*ArcTan[(1 + (2*(2/(5 + Sqrt[17]))^(1/3)*x)/(1 + x^3)^(1/3))/Sqrt[3]] + 2*Sqrt[3]*(19 + 5*Sqrt[17])^(1/3)*ArcTan[(1 + ((2*(5 + Sqrt[17]))^(1/3)*x)/(1 + x^3)^(1/3))/Sqrt[3]] - 2*(19 + 5*Sqrt[17])^(1/3)*Log[(5 - Sqrt[17])^(1/3) - (2^(1/3)*x)/(1 + x^3)^(1/3)] - 2*(-19 + 5*Sqrt[17])^(1/3)*Log[(5 + Sqrt[17])^(1/3) - (2^(1/3)*x)/(1 + x^3)^(1/3)] + (19 + 5*Sqrt[17])^(1/3)*Log[(5 - Sqrt[17])^(2/3) + (2^(2/3)*x^2)/(1 + x^3)^(2/3) + ((10 - 2*Sqrt[17])^(1/3)*x)/(1 + x^3)^(1/3)] + (-19 + 5*Sqrt[17])^(1/3)*Log[(5 + Sqrt[17])^(2/3) + (2^(2/3)*x^2)/(1 + x^3)^(2/3) + ((2*(5 + Sqrt[17]))^(1/3)*x)/(1 + x^3)^(1/3)])/(6*2^(1/3)*Sqrt[17])","B",0
1466,0,0,103,0.162815,"\int \frac{x^2 \left(-2+x^4\right)}{\sqrt[3]{-x+x^5} \left(-1+x^4+x^8\right)} \, dx","Integrate[(x^2*(-2 + x^4))/((-x + x^5)^(1/3)*(-1 + x^4 + x^8)),x]","\int \frac{x^2 \left(-2+x^4\right)}{\sqrt[3]{-x+x^5} \left(-1+x^4+x^8\right)} \, dx","\frac{1}{4} \log \left(\sqrt[3]{x^5-x}+x^3\right)+\frac{1}{4} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x^5-x}}{\sqrt[3]{x^5-x}-2 x^3}\right)-\frac{1}{8} \log \left(x^6+\left(x^5-x\right)^{2/3}-\sqrt[3]{x^5-x} x^3\right)",1,"Integrate[(x^2*(-2 + x^4))/((-x + x^5)^(1/3)*(-1 + x^4 + x^8)), x]","F",-1
1467,1,499,103,0.7474174,"\int \frac{-b+2 a x^4}{\sqrt[4]{-b+a x^4} \left(-b-a x^4+x^8\right)} \, dx","Integrate[(-b + 2*a*x^4)/((-b + a*x^4)^(1/4)*(-b - a*x^4 + x^8)),x]","-\frac{\left(a-\frac{a^2-b}{\sqrt{a^2+4 b}}\right) \tan ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{a x^4-b}}\right)}{\left(a-\sqrt{a^2+4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}-\frac{\left(\frac{a^2-b}{\sqrt{a^2+4 b}}+a\right) \tan ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+4 b}+a} \sqrt[4]{a x^4-b}}\right)}{\left(\sqrt{a^2+4 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}-\frac{\left(a-\frac{a^2-b}{\sqrt{a^2+4 b}}\right) \tanh ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{a x^4-b}}\right)}{\left(a-\sqrt{a^2+4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}-\frac{\left(\frac{a^2-b}{\sqrt{a^2+4 b}}+a\right) \tanh ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+4 b}+a} \sqrt[4]{a x^4-b}}\right)}{\left(\sqrt{a^2+4 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4 a+2 a^2-b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))+a \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)-a \log (x)}{3 \text{$\#$1} a-2 \text{$\#$1}^5}\&\right]",1,"-(((a - (a^2 - b)/Sqrt[a^2 + 4*b])*ArcTan[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a - Sqrt[a^2 + 4*b])^(1/4)*(-b + a*x^4)^(1/4))])/((a - Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4))) - ((a + (a^2 - b)/Sqrt[a^2 + 4*b])*ArcTan[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a + Sqrt[a^2 + 4*b])^(1/4)*(-b + a*x^4)^(1/4))])/((a + Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)) - ((a - (a^2 - b)/Sqrt[a^2 + 4*b])*ArcTanh[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a - Sqrt[a^2 + 4*b])^(1/4)*(-b + a*x^4)^(1/4))])/((a - Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)) - ((a + (a^2 - b)/Sqrt[a^2 + 4*b])*ArcTanh[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a + Sqrt[a^2 + 4*b])^(1/4)*(-b + a*x^4)^(1/4))])/((a + Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4))","B",1
1468,1,491,103,0.7755424,"\int \frac{-2 b+a x^4}{\sqrt[4]{b+a x^4} \left(-2 b+a x^4+x^8\right)} \, dx","Integrate[(-2*b + a*x^4)/((b + a*x^4)^(1/4)*(-2*b + a*x^4 + x^8)),x]","\frac{1}{2} \left(\frac{\left(a-\frac{a^2+4 b}{\sqrt{a^2+8 b}}\right) \tan ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+8 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+8 b}} \sqrt[4]{a x^4+b}}\right)}{\left(a-\sqrt{a^2+8 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+8 b}+a^2-2 b}}+\frac{\left(\frac{a^2+4 b}{\sqrt{a^2+8 b}}+a\right) \tan ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+8 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+8 b}+a} \sqrt[4]{a x^4+b}}\right)}{\left(\sqrt{a^2+8 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+8 b}+a^2-2 b}}+\frac{\left(a-\frac{a^2+4 b}{\sqrt{a^2+8 b}}\right) \tanh ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+8 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+8 b}} \sqrt[4]{a x^4+b}}\right)}{\left(a-\sqrt{a^2+8 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+8 b}+a^2-2 b}}+\frac{\left(\frac{a^2+4 b}{\sqrt{a^2+8 b}}+a\right) \tanh ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+8 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+8 b}+a} \sqrt[4]{a x^4+b}}\right)}{\left(\sqrt{a^2+8 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+8 b}+a^2-2 b}}\right)","\frac{1}{4} \text{RootSum}\left[2 \text{$\#$1}^8-5 \text{$\#$1}^4 a+3 a^2-b\&,\frac{2 \text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)-2 \text{$\#$1}^4 \log (x)-3 a \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+3 a \log (x)}{5 \text{$\#$1} a-4 \text{$\#$1}^5}\&\right]",1,"(((a - (a^2 + 4*b)/Sqrt[a^2 + 8*b])*ArcTan[((a^2 - 2*b - a*Sqrt[a^2 + 8*b])^(1/4)*x)/((a - Sqrt[a^2 + 8*b])^(1/4)*(b + a*x^4)^(1/4))])/((a - Sqrt[a^2 + 8*b])^(3/4)*(a^2 - 2*b - a*Sqrt[a^2 + 8*b])^(1/4)) + ((a + (a^2 + 4*b)/Sqrt[a^2 + 8*b])*ArcTan[((a^2 - 2*b + a*Sqrt[a^2 + 8*b])^(1/4)*x)/((a + Sqrt[a^2 + 8*b])^(1/4)*(b + a*x^4)^(1/4))])/((a + Sqrt[a^2 + 8*b])^(3/4)*(a^2 - 2*b + a*Sqrt[a^2 + 8*b])^(1/4)) + ((a - (a^2 + 4*b)/Sqrt[a^2 + 8*b])*ArcTanh[((a^2 - 2*b - a*Sqrt[a^2 + 8*b])^(1/4)*x)/((a - Sqrt[a^2 + 8*b])^(1/4)*(b + a*x^4)^(1/4))])/((a - Sqrt[a^2 + 8*b])^(3/4)*(a^2 - 2*b - a*Sqrt[a^2 + 8*b])^(1/4)) + ((a + (a^2 + 4*b)/Sqrt[a^2 + 8*b])*ArcTanh[((a^2 - 2*b + a*Sqrt[a^2 + 8*b])^(1/4)*x)/((a + Sqrt[a^2 + 8*b])^(1/4)*(b + a*x^4)^(1/4))])/((a + Sqrt[a^2 + 8*b])^(3/4)*(a^2 - 2*b + a*Sqrt[a^2 + 8*b])^(1/4)))/2","B",1
1469,1,9150,103,23.0209871,"\int \frac{1}{x^2 \sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Integrate[1/(x^2*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]),x]","\text{Result too large to show}","-\frac{1}{x \sqrt{\sqrt{a^2 x^2+b^2}+a x}}+\frac{a \tan ^{-1}\left(\frac{\sqrt{\sqrt{a^2 x^2+b^2}+a x}}{\sqrt{b}}\right)}{b^{3/2}}+\frac{a \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a^2 x^2+b^2}+a x}}{\sqrt{b}}\right)}{b^{3/2}}",1,"Result too large to show","C",0
1470,1,28,104,0.0053918,"\int \frac{\sqrt[3]{-1+x^3}}{x^{10}} \, dx","Integrate[(-1 + x^3)^(1/3)/x^10,x]","\frac{1}{4} \left(x^3-1\right)^{4/3} \, _2F_1\left(\frac{4}{3},4;\frac{7}{3};1-x^3\right)","\frac{5}{243} \log \left(\sqrt[3]{x^3-1}+1\right)-\frac{5}{486} \log \left(\left(x^3-1\right)^{2/3}-\sqrt[3]{x^3-1}+1\right)-\frac{5 \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{x^3-1}}{\sqrt{3}}\right)}{81 \sqrt{3}}+\frac{\sqrt[3]{x^3-1} \left(5 x^6+3 x^3-18\right)}{162 x^9}",1,"((-1 + x^3)^(4/3)*Hypergeometric2F1[4/3, 4, 7/3, 1 - x^3])/4","C",1
1471,1,54,104,0.0169695,"\int x^4 \sqrt[3]{-1+x^3} \, dx","Integrate[x^4*(-1 + x^3)^(1/3),x]","\frac{x^2 \sqrt[3]{x^3-1} \left(\, _2F_1\left(-\frac{1}{3},\frac{2}{3};\frac{5}{3};x^3\right)-\left(1-x^3\right)^{4/3}\right)}{6 \sqrt[3]{1-x^3}}","\frac{1}{27} \log \left(\sqrt[3]{x^3-1}-x\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-1}+x}\right)}{9 \sqrt{3}}-\frac{1}{54} \log \left(\sqrt[3]{x^3-1} x+\left(x^3-1\right)^{2/3}+x^2\right)+\frac{1}{18} \sqrt[3]{x^3-1} \left(3 x^5-x^2\right)",1,"(x^2*(-1 + x^3)^(1/3)*(-(1 - x^3)^(4/3) + Hypergeometric2F1[-1/3, 2/3, 5/3, x^3]))/(6*(1 - x^3)^(1/3))","C",1
1472,1,40,104,0.0087377,"\int \sqrt[3]{-x+x^3} \, dx","Integrate[(-x + x^3)^(1/3),x]","\frac{3 x \sqrt[3]{x \left(x^2-1\right)} \, _2F_1\left(-\frac{1}{3},\frac{2}{3};\frac{5}{3};x^2\right)}{4 \sqrt[3]{1-x^2}}","\frac{1}{2} \sqrt[3]{x^3-x} x+\frac{1}{6} \log \left(\sqrt[3]{x^3-x}-x\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-x}+x}\right)}{2 \sqrt{3}}-\frac{1}{12} \log \left(\sqrt[3]{x^3-x} x+\left(x^3-x\right)^{2/3}+x^2\right)",1,"(3*x*(x*(-1 + x^2))^(1/3)*Hypergeometric2F1[-1/3, 2/3, 5/3, x^2])/(4*(1 - x^2)^(1/3))","C",1
1473,1,38,104,0.0183176,"\int \frac{\sqrt[3]{-1+x^3} \left(-1+2 x^3\right)}{x^{10}} \, dx","Integrate[((-1 + x^3)^(1/3)*(-1 + 2*x^3))/x^10,x]","\frac{\left(x^3-1\right)^{4/3} \left(13 x^9 \, _2F_1\left(\frac{4}{3},3;\frac{7}{3};1-x^3\right)-4\right)}{36 x^9}","\frac{13}{243} \log \left(\sqrt[3]{x^3-1}+1\right)-\frac{13}{486} \log \left(\left(x^3-1\right)^{2/3}-\sqrt[3]{x^3-1}+1\right)-\frac{13 \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{x^3-1}}{\sqrt{3}}\right)}{81 \sqrt{3}}+\frac{\sqrt[3]{x^3-1} \left(13 x^6-57 x^3+18\right)}{162 x^9}",1,"((-1 + x^3)^(4/3)*(-4 + 13*x^9*Hypergeometric2F1[4/3, 3, 7/3, 1 - x^3]))/(36*x^9)","C",1
1474,1,310,104,6.6189289,"\int \frac{1+k^3 x^3}{\sqrt{(1-x) x \left(1-k^2 x\right)} \left(-1+k^3 x^3\right)} \, dx","Integrate[(1 + k^3*x^3)/(Sqrt[(1 - x)*x*(1 - k^2*x)]*(-1 + k^3*x^3)),x]","-\frac{2 \sqrt{\frac{1}{x-1}+1} (x-1)^{3/2} \sqrt{\frac{1-\frac{1}{k^2}}{x-1}+1} \sqrt{k^2 x-1} \left(2 i \sqrt{3} \left(k^2+k+1\right) \Pi \left(\frac{k-1}{k};i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)+(k-1) \left(\left(\left(3-i \sqrt{3}\right) k-2 i \sqrt{3}\right) \Pi \left(\frac{2 \left(k^2+k+1\right)}{k \left(2 k-i \sqrt{3}+1\right)};i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)-i \left(2 \sqrt{3}+\left(\sqrt{3}-3 i\right) k\right) \Pi \left(\frac{2 \left(k^2+k+1\right)}{k \left(2 k+i \sqrt{3}+1\right)};i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)\right)-3 i \sqrt{3} \left(k^3+1\right) F\left(i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)\right)}{3 \left(k^3-1\right) \sqrt{(x-1) x \left(k^2 x-1\right)} \sqrt{3 k^2 x-3}}","-\frac{2 \tan ^{-1}\left(\frac{(k-1) x}{\sqrt{k^2 x^3+\left(-k^2-1\right) x^2+x}}\right)}{3 (k-1)}-\frac{4 \tan ^{-1}\left(\frac{\sqrt{k^2+k+1} \sqrt{k^2 x^3+\left(-k^2-1\right) x^2+x}}{(x-1) \left(k^2 x-1\right)}\right)}{3 \sqrt{k^2+k+1}}",1,"(-2*Sqrt[1 + (-1 + x)^(-1)]*Sqrt[1 + (1 - k^(-2))/(-1 + x)]*(-1 + x)^(3/2)*Sqrt[-1 + k^2*x]*((-3*I)*Sqrt[3]*(1 + k^3)*EllipticF[I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)] + (2*I)*Sqrt[3]*(1 + k + k^2)*EllipticPi[(-1 + k)/k, I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)] + (-1 + k)*(((-2*I)*Sqrt[3] + (3 - I*Sqrt[3])*k)*EllipticPi[(2*(1 + k + k^2))/(k*(1 - I*Sqrt[3] + 2*k)), I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)] - I*(2*Sqrt[3] + (-3*I + Sqrt[3])*k)*EllipticPi[(2*(1 + k + k^2))/(k*(1 + I*Sqrt[3] + 2*k)), I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)])))/(3*(-1 + k^3)*Sqrt[(-1 + x)*x*(-1 + k^2*x)]*Sqrt[-3 + 3*k^2*x])","C",1
1475,0,0,104,0.2648027,"\int \frac{\left(-3+x^4\right) \left(1+x^4\right)^{2/3} \left(1+2 x^3+x^4\right)}{x^6 \left(1-x^3+x^4\right)} \, dx","Integrate[((-3 + x^4)*(1 + x^4)^(2/3)*(1 + 2*x^3 + x^4))/(x^6*(1 - x^3 + x^4)),x]","\int \frac{\left(-3+x^4\right) \left(1+x^4\right)^{2/3} \left(1+2 x^3+x^4\right)}{x^6 \left(1-x^3+x^4\right)} \, dx","3 \log \left(\sqrt[3]{x^4+1}-x\right)-3 \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^4+1}+x}\right)-\frac{3}{2} \log \left(\sqrt[3]{x^4+1} x+\left(x^4+1\right)^{2/3}+x^2\right)+\frac{3 \left(x^4+1\right)^{2/3} \left(2 x^4+15 x^3+2\right)}{10 x^5}",1,"Integrate[((-3 + x^4)*(1 + x^4)^(2/3)*(1 + 2*x^3 + x^4))/(x^6*(1 - x^3 + x^4)), x]","F",-1
1476,1,77,104,0.0375237,"\int \frac{\left(b+a x^4\right)^{3/4}}{x^4 \left(2 b+a x^4\right)} \, dx","Integrate[(b + a*x^4)^(3/4)/(x^4*(2*b + a*x^4)),x]","-\frac{\left(a x^4+b\right)^{3/4} \left(\frac{a x^4}{b}+2\right)^{3/4} \, _2F_1\left(-\frac{3}{4},-\frac{3}{4};\frac{1}{4};-\frac{a x^4}{a x^4+2 b}\right)}{6 b x^3 \left(\frac{2 a x^4}{b}+2\right)^{3/4}}","\frac{a^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{2} \sqrt[4]{a x^4+b}}\right)}{4\ 2^{3/4} b}+\frac{a^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{2} \sqrt[4]{a x^4+b}}\right)}{4\ 2^{3/4} b}-\frac{\left(a x^4+b\right)^{3/4}}{6 b x^3}",1,"-1/6*((b + a*x^4)^(3/4)*(2 + (a*x^4)/b)^(3/4)*Hypergeometric2F1[-3/4, -3/4, 1/4, -((a*x^4)/(2*b + a*x^4))])/(b*x^3*(2 + (2*a*x^4)/b)^(3/4))","C",1
1477,1,54,104,0.024661,"\int \frac{-b+a x^3}{x^3 \sqrt[4]{-b x+a x^4}} \, dx","Integrate[(-b + a*x^3)/(x^3*(-(b*x) + a*x^4)^(1/4)),x]","-\frac{4 \left(a x^4-b x\right)^{3/4} \, _2F_1\left(-\frac{3}{4},-\frac{3}{4};\frac{1}{4};\frac{a x^3}{b}\right)}{9 x^3 \left(1-\frac{a x^3}{b}\right)^{3/4}}","\frac{2}{3} a^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} \left(a x^4-b x\right)^{3/4}}{a x^3-b}\right)+\frac{2}{3} a^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \left(a x^4-b x\right)^{3/4}}{a x^3-b}\right)-\frac{4 \left(a x^4-b x\right)^{3/4}}{9 x^3}",1,"(-4*(-(b*x) + a*x^4)^(3/4)*Hypergeometric2F1[-3/4, -3/4, 1/4, (a*x^3)/b])/(9*x^3*(1 - (a*x^3)/b)^(3/4))","C",1
1478,1,69,104,0.0338709,"\int \frac{b+a x^3}{x^3 \sqrt[4]{-b x+a x^4}} \, dx","Integrate[(b + a*x^3)/(x^3*(-(b*x) + a*x^4)^(1/4)),x]","\frac{4 \left(3 a x^3 \sqrt[4]{1-\frac{a x^3}{b}} \, _2F_1\left(\frac{1}{4},\frac{1}{4};\frac{5}{4};\frac{a x^3}{b}\right)+a x^3-b\right)}{9 x^2 \sqrt[4]{a x^4-b x}}","\frac{2}{3} a^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} \left(a x^4-b x\right)^{3/4}}{a x^3-b}\right)+\frac{2}{3} a^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \left(a x^4-b x\right)^{3/4}}{a x^3-b}\right)+\frac{4 \left(a x^4-b x\right)^{3/4}}{9 x^3}",1,"(4*(-b + a*x^3 + 3*a*x^3*(1 - (a*x^3)/b)^(1/4)*Hypergeometric2F1[1/4, 1/4, 5/4, (a*x^3)/b]))/(9*x^2*(-(b*x) + a*x^4)^(1/4))","C",1
1479,1,54,104,0.0152219,"\int \frac{\sqrt[4]{-b x+a x^4}}{x^2} \, dx","Integrate[(-(b*x) + a*x^4)^(1/4)/x^2,x]","-\frac{4 \sqrt[4]{a x^4-b x} \, _2F_1\left(-\frac{1}{4},-\frac{1}{4};\frac{3}{4};\frac{a x^3}{b}\right)}{3 x \sqrt[4]{1-\frac{a x^3}{b}}}","-\frac{4 \sqrt[4]{a x^4-b x}}{3 x}-\frac{2}{3} \sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt[4]{a} \left(a x^4-b x\right)^{3/4}}{a x^3-b}\right)+\frac{2}{3} \sqrt[4]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \left(a x^4-b x\right)^{3/4}}{a x^3-b}\right)",1,"(-4*(-(b*x) + a*x^4)^(1/4)*Hypergeometric2F1[-1/4, -1/4, 3/4, (a*x^3)/b])/(3*x*(1 - (a*x^3)/b)^(1/4))","C",1
1480,1,165,104,0.264345,"\int \frac{1}{\left(b-a x^2+x^4\right) \sqrt[4]{-b x^2+a x^4}} \, dx","Integrate[1/((b - a*x^2 + x^4)*(-(b*x^2) + a*x^4)^(1/4)),x]","\frac{4 x \left(\frac{\, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{\left(\frac{2}{a-\sqrt{a^2-4 b}}-\frac{a}{b}\right) b x^2}{b-a x^2}\right)}{a \sqrt{a^2-4 b}-a^2+4 b}-\frac{\, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{\left(\frac{2}{a+\sqrt{a^2-4 b}}-\frac{a}{b}\right) b x^2}{b-a x^2}\right)}{a \sqrt{a^2-4 b}+a^2-4 b}\right)}{\sqrt[4]{a x^4-b x^2}}","\frac{\text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4 a+b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-a \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+a \log (x)}{\text{$\#$1} a-2 \text{$\#$1}^5}\&\right]}{2 b}",1,"(4*x*(Hypergeometric2F1[1/4, 1, 5/4, ((2/(a - Sqrt[a^2 - 4*b]) - a/b)*b*x^2)/(b - a*x^2)]/(-a^2 + a*Sqrt[a^2 - 4*b] + 4*b) - Hypergeometric2F1[1/4, 1, 5/4, ((2/(a + Sqrt[a^2 - 4*b]) - a/b)*b*x^2)/(b - a*x^2)]/(a^2 + a*Sqrt[a^2 - 4*b] - 4*b)))/(-(b*x^2) + a*x^4)^(1/4)","A",1
1481,1,165,104,0.0690133,"\int \frac{1}{\left(b-a x^2+x^4\right) \sqrt[4]{-b x^2+a x^4}} \, dx","Integrate[1/((b - a*x^2 + x^4)*(-(b*x^2) + a*x^4)^(1/4)),x]","\frac{4 x \left(\frac{\, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{\left(\frac{2}{a-\sqrt{a^2-4 b}}-\frac{a}{b}\right) b x^2}{b-a x^2}\right)}{a \sqrt{a^2-4 b}-a^2+4 b}-\frac{\, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{\left(\frac{2}{a+\sqrt{a^2-4 b}}-\frac{a}{b}\right) b x^2}{b-a x^2}\right)}{a \sqrt{a^2-4 b}+a^2-4 b}\right)}{\sqrt[4]{a x^4-b x^2}}","\frac{\text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4 a+b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-a \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+a \log (x)}{\text{$\#$1} a-2 \text{$\#$1}^5}\&\right]}{2 b}",1,"(4*x*(Hypergeometric2F1[1/4, 1, 5/4, ((2/(a - Sqrt[a^2 - 4*b]) - a/b)*b*x^2)/(b - a*x^2)]/(-a^2 + a*Sqrt[a^2 - 4*b] + 4*b) - Hypergeometric2F1[1/4, 1, 5/4, ((2/(a + Sqrt[a^2 - 4*b]) - a/b)*b*x^2)/(b - a*x^2)]/(a^2 + a*Sqrt[a^2 - 4*b] - 4*b)))/(-(b*x^2) + a*x^4)^(1/4)","A",1
1482,1,104,104,0.0802636,"\int \frac{-b+a x^4}{x^4 \sqrt[4]{-b+2 a x^4}} \, dx","Integrate[(-b + a*x^4)/(x^4*(-b + 2*a*x^4)^(1/4)),x]","\frac{a^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x}{\sqrt[4]{2 a x^4-b}}\right)}{2 \sqrt[4]{2}}+\frac{a^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x}{\sqrt[4]{2 a x^4-b}}\right)}{2 \sqrt[4]{2}}-\frac{\left(2 a x^4-b\right)^{3/4}}{3 x^3}","\frac{a^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x}{\sqrt[4]{2 a x^4-b}}\right)}{2 \sqrt[4]{2}}+\frac{a^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x}{\sqrt[4]{2 a x^4-b}}\right)}{2 \sqrt[4]{2}}-\frac{\left(2 a x^4-b\right)^{3/4}}{3 x^3}",1,"-1/3*(-b + 2*a*x^4)^(3/4)/x^3 + (a^(3/4)*ArcTan[(2^(1/4)*a^(1/4)*x)/(-b + 2*a*x^4)^(1/4)])/(2*2^(1/4)) + (a^(3/4)*ArcTanh[(2^(1/4)*a^(1/4)*x)/(-b + 2*a*x^4)^(1/4)])/(2*2^(1/4))","A",1
1483,0,0,104,2.9746274,"\int \frac{x^4 \left(4 b+a x^5\right)}{\left(-b+a x^5\right)^2 \sqrt[4]{-b+c x^4+a x^5}} \, dx","Integrate[(x^4*(4*b + a*x^5))/((-b + a*x^5)^2*(-b + c*x^4 + a*x^5)^(1/4)),x]","\int \frac{x^4 \left(4 b+a x^5\right)}{\left(-b+a x^5\right)^2 \sqrt[4]{-b+c x^4+a x^5}} \, dx","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a x^5-b+c x^4}}\right)}{2 c^{5/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a x^5-b+c x^4}}\right)}{2 c^{5/4}}+\frac{x \left(a x^5-b+c x^4\right)^{3/4}}{c \left(b-a x^5\right)}",1,"Integrate[(x^4*(4*b + a*x^5))/((-b + a*x^5)^2*(-b + c*x^4 + a*x^5)^(1/4)), x]","F",-1
1484,1,28,104,0.0052065,"\int \frac{1}{x^{19} \sqrt[3]{-1+x^6}} \, dx","Integrate[1/(x^19*(-1 + x^6)^(1/3)),x]","\frac{1}{4} \left(x^6-1\right)^{2/3} \, _2F_1\left(\frac{2}{3},4;\frac{5}{3};1-x^6\right)","-\frac{7}{243} \log \left(\sqrt[3]{x^6-1}+1\right)+\frac{7}{486} \log \left(\left(x^6-1\right)^{2/3}-\sqrt[3]{x^6-1}+1\right)-\frac{7 \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{x^6-1}}{\sqrt{3}}\right)}{81 \sqrt{3}}+\frac{\left(x^6-1\right)^{2/3} \left(28 x^{12}+21 x^6+18\right)}{324 x^{18}}",1,"((-1 + x^6)^(2/3)*Hypergeometric2F1[2/3, 4, 5/3, 1 - x^6])/4","C",1
1485,1,97,104,0.042067,"\int \frac{x^7}{\sqrt[3]{-1+x^6}} \, dx","Integrate[x^7/(-1 + x^6)^(1/3),x]","\frac{1}{36} \left(6 \left(x^6-1\right)^{2/3} x^2-2 \log \left(1-\frac{x^2}{\sqrt[3]{x^6-1}}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 x^2}{\sqrt[3]{x^6-1}}+1}{\sqrt{3}}\right)+\log \left(\frac{x^4}{\left(x^6-1\right)^{2/3}}+\frac{x^2}{\sqrt[3]{x^6-1}}+1\right)\right)","\frac{1}{6} \left(x^6-1\right)^{2/3} x^2-\frac{1}{18} \log \left(\sqrt[3]{x^6-1}-x^2\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x^2}{2 \sqrt[3]{x^6-1}+x^2}\right)}{6 \sqrt{3}}+\frac{1}{36} \log \left(\left(x^6-1\right)^{2/3}+x^4+\sqrt[3]{x^6-1} x^2\right)",1,"(6*x^2*(-1 + x^6)^(2/3) + 2*Sqrt[3]*ArcTan[(1 + (2*x^2)/(-1 + x^6)^(1/3))/Sqrt[3]] - 2*Log[1 - x^2/(-1 + x^6)^(1/3)] + Log[1 + x^4/(-1 + x^6)^(2/3) + x^2/(-1 + x^6)^(1/3)])/36","A",1
1486,1,40,104,0.0068549,"\int x^3 \sqrt[3]{-1+x^6} \, dx","Integrate[x^3*(-1 + x^6)^(1/3),x]","\frac{x^4 \sqrt[3]{x^6-1} \, _2F_1\left(-\frac{1}{3},\frac{2}{3};\frac{5}{3};x^6\right)}{4 \sqrt[3]{1-x^6}}","\frac{1}{6} \sqrt[3]{x^6-1} x^4+\frac{1}{18} \log \left(\sqrt[3]{x^6-1}-x^2\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x^2}{2 \sqrt[3]{x^6-1}+x^2}\right)}{6 \sqrt{3}}-\frac{1}{36} \log \left(\left(x^6-1\right)^{2/3}+x^4+\sqrt[3]{x^6-1} x^2\right)",1,"(x^4*(-1 + x^6)^(1/3)*Hypergeometric2F1[-1/3, 2/3, 5/3, x^6])/(4*(1 - x^6)^(1/3))","C",1
1487,1,40,104,0.0070723,"\int x \left(-1+x^6\right)^{2/3} \, dx","Integrate[x*(-1 + x^6)^(2/3),x]","\frac{x^2 \left(x^6-1\right)^{2/3} \, _2F_1\left(-\frac{2}{3},\frac{1}{3};\frac{4}{3};x^6\right)}{2 \left(1-x^6\right)^{2/3}}","\frac{1}{6} \left(x^6-1\right)^{2/3} x^2+\frac{1}{9} \log \left(\sqrt[3]{x^6-1}-x^2\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x^2}{2 \sqrt[3]{x^6-1}+x^2}\right)}{3 \sqrt{3}}-\frac{1}{18} \log \left(\left(x^6-1\right)^{2/3}+x^4+\sqrt[3]{x^6-1} x^2\right)",1,"(x^2*(-1 + x^6)^(2/3)*Hypergeometric2F1[-2/3, 1/3, 4/3, x^6])/(2*(1 - x^6)^(2/3))","C",1
1488,1,99,104,0.0398005,"\int \frac{x^7}{\sqrt[3]{1+x^6}} \, dx","Integrate[x^7/(1 + x^6)^(1/3),x]","\frac{1}{36} \left(6 \left(x^6+1\right)^{2/3} x^2+2 \log \left(1-\frac{x^2}{\sqrt[3]{x^6+1}}\right)-2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 x^2}{\sqrt[3]{x^6+1}}+1}{\sqrt{3}}\right)-\log \left(\frac{x^4}{\left(x^6+1\right)^{2/3}}+\frac{x^2}{\sqrt[3]{x^6+1}}+1\right)\right)","\frac{1}{6} \left(x^6+1\right)^{2/3} x^2+\frac{1}{18} \log \left(\sqrt[3]{x^6+1}-x^2\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x^2}{2 \sqrt[3]{x^6+1}+x^2}\right)}{6 \sqrt{3}}-\frac{1}{36} \log \left(\left(x^6+1\right)^{2/3}+x^4+\sqrt[3]{x^6+1} x^2\right)",1,"(6*x^2*(1 + x^6)^(2/3) - 2*Sqrt[3]*ArcTan[(1 + (2*x^2)/(1 + x^6)^(1/3))/Sqrt[3]] + 2*Log[1 - x^2/(1 + x^6)^(1/3)] - Log[1 + x^4/(1 + x^6)^(2/3) + x^2/(1 + x^6)^(1/3)])/36","A",1
1489,1,22,104,0.0032176,"\int x^3 \sqrt[3]{1+x^6} \, dx","Integrate[x^3*(1 + x^6)^(1/3),x]","\frac{1}{4} x^4 \, _2F_1\left(-\frac{1}{3},\frac{2}{3};\frac{5}{3};-x^6\right)","\frac{1}{6} \sqrt[3]{x^6+1} x^4-\frac{1}{18} \log \left(\sqrt[3]{x^6+1}-x^2\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x^2}{2 \sqrt[3]{x^6+1}+x^2}\right)}{6 \sqrt{3}}+\frac{1}{36} \log \left(\left(x^6+1\right)^{2/3}+x^4+\sqrt[3]{x^6+1} x^2\right)",1,"(x^4*Hypergeometric2F1[-1/3, 2/3, 5/3, -x^6])/4","C",1
1490,1,22,104,0.0029669,"\int x \left(1+x^6\right)^{2/3} \, dx","Integrate[x*(1 + x^6)^(2/3),x]","\frac{1}{2} x^2 \, _2F_1\left(-\frac{2}{3},\frac{1}{3};\frac{4}{3};-x^6\right)","\frac{1}{6} \left(x^6+1\right)^{2/3} x^2-\frac{1}{9} \log \left(\sqrt[3]{x^6+1}-x^2\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x^2}{2 \sqrt[3]{x^6+1}+x^2}\right)}{3 \sqrt{3}}+\frac{1}{18} \log \left(\left(x^6+1\right)^{2/3}+x^4+\sqrt[3]{x^6+1} x^2\right)",1,"(x^2*Hypergeometric2F1[-2/3, 1/3, 4/3, -x^6])/2","C",1
1491,0,0,104,0.6231933,"\int \frac{\left(1-x^3+x^5\right) \left(-3+2 x^5\right)}{x^3 \left(1+x^3+x^5\right) \sqrt[4]{x+x^6}} \, dx","Integrate[((1 - x^3 + x^5)*(-3 + 2*x^5))/(x^3*(1 + x^3 + x^5)*(x + x^6)^(1/4)),x]","\int \frac{\left(1-x^3+x^5\right) \left(-3+2 x^5\right)}{x^3 \left(1+x^3+x^5\right) \sqrt[4]{x+x^6}} \, dx","\frac{4 \left(x^6+x\right)^{3/4}}{3 x^3}+2 \sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{x^6+x}}{\sqrt{x^6+x}-x^2}\right)+2 \sqrt{2} \tanh ^{-1}\left(\frac{\frac{\sqrt{x^6+x}}{\sqrt{2}}+\frac{x^2}{\sqrt{2}}}{x \sqrt[4]{x^6+x}}\right)",1,"Integrate[((1 - x^3 + x^5)*(-3 + 2*x^5))/(x^3*(1 + x^3 + x^5)*(x + x^6)^(1/4)), x]","F",-1
1492,1,44,104,0.009544,"\int \frac{x}{\sqrt[3]{-x^2+x^6}} \, dx","Integrate[x/(-x^2 + x^6)^(1/3),x]","\frac{3 x^2 \sqrt[3]{1-x^4} \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};x^4\right)}{4 \sqrt[3]{x^2 \left(x^4-1\right)}}","-\frac{1}{4} \log \left(\sqrt[3]{x^6-x^2}-x^2\right)+\frac{1}{4} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x^2}{x^2+2 \sqrt[3]{x^6-x^2}}\right)+\frac{1}{8} \log \left(x^4+\sqrt[3]{x^6-x^2} x^2+\left(x^6-x^2\right)^{2/3}\right)",1,"(3*x^2*(1 - x^4)^(1/3)*Hypergeometric2F1[1/3, 1/3, 4/3, x^4])/(4*(x^2*(-1 + x^4))^(1/3))","C",1
1493,1,387,104,0.7525958,"\int \frac{\left(-1+x^3\right)^{2/3} \left(2+x^3\right)}{x^3 \left(-4+x^3+x^6\right)} \, dx","Integrate[((-1 + x^3)^(2/3)*(2 + x^3))/(x^3*(-4 + x^3 + x^6)),x]","\frac{\left(x^3-1\right)^{2/3}}{4 x^2}+\frac{-2 \sqrt[3]{199-47 \sqrt{17}} \log \left(\sqrt[3]{7-\sqrt{17}}-\frac{2^{2/3} x}{\sqrt[3]{x^3-1}}\right)+2 \sqrt[3]{199+47 \sqrt{17}} \log \left(\sqrt[3]{7+\sqrt{17}}-\frac{2^{2/3} x}{\sqrt[3]{x^3-1}}\right)-2 \sqrt{3} \sqrt[3]{199+47 \sqrt{17}} \tan ^{-1}\left(\frac{\frac{2\ 2^{2/3} x}{\sqrt[3]{7+\sqrt{17}} \sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)+2 \sqrt{3} \sqrt[3]{199-47 \sqrt{17}} \tan ^{-1}\left(\frac{\frac{2\ 2^{2/3} x}{\sqrt[3]{-\left(\left(\sqrt{17}-7\right) \left(x^3-1\right)\right)}}+1}{\sqrt{3}}\right)+\sqrt[3]{199-47 \sqrt{17}} \log \left(\frac{2^{2/3} \sqrt[3]{7-\sqrt{17}} x}{\sqrt[3]{x^3-1}}+\frac{2 \sqrt[3]{2} x^2}{\left(x^3-1\right)^{2/3}}+\left(7-\sqrt{17}\right)^{2/3}\right)-\sqrt[3]{199+47 \sqrt{17}} \log \left(\frac{2^{2/3} \sqrt[3]{7+\sqrt{17}} x}{\sqrt[3]{x^3-1}}+\frac{2 \sqrt[3]{2} x^2}{\left(x^3-1\right)^{2/3}}+\left(7+\sqrt{17}\right)^{2/3}\right)}{24\ 2^{2/3} \sqrt{17}}","\frac{\left(x^3-1\right)^{2/3}}{4 x^2}-\frac{1}{6} \text{RootSum}\left[4 \text{$\#$1}^6-7 \text{$\#$1}^3+2\&,\frac{-\text{$\#$1}^3 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)+\text{$\#$1}^3 \log (x)+2 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)-2 \log (x)}{8 \text{$\#$1}^4-7 \text{$\#$1}}\&\right]",1,"(-1 + x^3)^(2/3)/(4*x^2) + (-2*Sqrt[3]*(199 + 47*Sqrt[17])^(1/3)*ArcTan[(1 + (2*2^(2/3)*x)/((7 + Sqrt[17])^(1/3)*(-1 + x^3)^(1/3)))/Sqrt[3]] + 2*Sqrt[3]*(199 - 47*Sqrt[17])^(1/3)*ArcTan[(1 + (2*2^(2/3)*x)/(-((-7 + Sqrt[17])*(-1 + x^3)))^(1/3))/Sqrt[3]] - 2*(199 - 47*Sqrt[17])^(1/3)*Log[(7 - Sqrt[17])^(1/3) - (2^(2/3)*x)/(-1 + x^3)^(1/3)] + 2*(199 + 47*Sqrt[17])^(1/3)*Log[(7 + Sqrt[17])^(1/3) - (2^(2/3)*x)/(-1 + x^3)^(1/3)] + (199 - 47*Sqrt[17])^(1/3)*Log[(7 - Sqrt[17])^(2/3) + (2*2^(1/3)*x^2)/(-1 + x^3)^(2/3) + (2^(2/3)*(7 - Sqrt[17])^(1/3)*x)/(-1 + x^3)^(1/3)] - (199 + 47*Sqrt[17])^(1/3)*Log[(7 + Sqrt[17])^(2/3) + (2*2^(1/3)*x^2)/(-1 + x^3)^(2/3) + (2^(2/3)*(7 + Sqrt[17])^(1/3)*x)/(-1 + x^3)^(1/3)])/(24*2^(2/3)*Sqrt[17])","B",0
1494,1,387,104,0.5191749,"\int \frac{\left(-1+x^3\right)^{2/3} \left(2+x^3\right)}{x^3 \left(-4+x^3+x^6\right)} \, dx","Integrate[((-1 + x^3)^(2/3)*(2 + x^3))/(x^3*(-4 + x^3 + x^6)),x]","\frac{\left(x^3-1\right)^{2/3}}{4 x^2}+\frac{-2 \sqrt[3]{199-47 \sqrt{17}} \log \left(\sqrt[3]{7-\sqrt{17}}-\frac{2^{2/3} x}{\sqrt[3]{x^3-1}}\right)+2 \sqrt[3]{199+47 \sqrt{17}} \log \left(\sqrt[3]{7+\sqrt{17}}-\frac{2^{2/3} x}{\sqrt[3]{x^3-1}}\right)-2 \sqrt{3} \sqrt[3]{199+47 \sqrt{17}} \tan ^{-1}\left(\frac{\frac{2\ 2^{2/3} x}{\sqrt[3]{7+\sqrt{17}} \sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)+2 \sqrt{3} \sqrt[3]{199-47 \sqrt{17}} \tan ^{-1}\left(\frac{\frac{2\ 2^{2/3} x}{\sqrt[3]{-\left(\left(\sqrt{17}-7\right) \left(x^3-1\right)\right)}}+1}{\sqrt{3}}\right)+\sqrt[3]{199-47 \sqrt{17}} \log \left(\frac{2^{2/3} \sqrt[3]{7-\sqrt{17}} x}{\sqrt[3]{x^3-1}}+\frac{2 \sqrt[3]{2} x^2}{\left(x^3-1\right)^{2/3}}+\left(7-\sqrt{17}\right)^{2/3}\right)-\sqrt[3]{199+47 \sqrt{17}} \log \left(\frac{2^{2/3} \sqrt[3]{7+\sqrt{17}} x}{\sqrt[3]{x^3-1}}+\frac{2 \sqrt[3]{2} x^2}{\left(x^3-1\right)^{2/3}}+\left(7+\sqrt{17}\right)^{2/3}\right)}{24\ 2^{2/3} \sqrt{17}}","\frac{\left(x^3-1\right)^{2/3}}{4 x^2}-\frac{1}{6} \text{RootSum}\left[4 \text{$\#$1}^6-7 \text{$\#$1}^3+2\&,\frac{-\text{$\#$1}^3 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)+\text{$\#$1}^3 \log (x)+2 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)-2 \log (x)}{8 \text{$\#$1}^4-7 \text{$\#$1}}\&\right]",1,"(-1 + x^3)^(2/3)/(4*x^2) + (-2*Sqrt[3]*(199 + 47*Sqrt[17])^(1/3)*ArcTan[(1 + (2*2^(2/3)*x)/((7 + Sqrt[17])^(1/3)*(-1 + x^3)^(1/3)))/Sqrt[3]] + 2*Sqrt[3]*(199 - 47*Sqrt[17])^(1/3)*ArcTan[(1 + (2*2^(2/3)*x)/(-((-7 + Sqrt[17])*(-1 + x^3)))^(1/3))/Sqrt[3]] - 2*(199 - 47*Sqrt[17])^(1/3)*Log[(7 - Sqrt[17])^(1/3) - (2^(2/3)*x)/(-1 + x^3)^(1/3)] + 2*(199 + 47*Sqrt[17])^(1/3)*Log[(7 + Sqrt[17])^(1/3) - (2^(2/3)*x)/(-1 + x^3)^(1/3)] + (199 - 47*Sqrt[17])^(1/3)*Log[(7 - Sqrt[17])^(2/3) + (2*2^(1/3)*x^2)/(-1 + x^3)^(2/3) + (2^(2/3)*(7 - Sqrt[17])^(1/3)*x)/(-1 + x^3)^(1/3)] - (199 + 47*Sqrt[17])^(1/3)*Log[(7 + Sqrt[17])^(2/3) + (2*2^(1/3)*x^2)/(-1 + x^3)^(2/3) + (2^(2/3)*(7 + Sqrt[17])^(1/3)*x)/(-1 + x^3)^(1/3)])/(24*2^(2/3)*Sqrt[17])","B",0
1495,0,0,104,0.1778702,"\int \frac{(-3+2 x) \left(1-x+x^3\right)^{2/3}}{1-2 x+x^2+2 x^3-2 x^4+2 x^6} \, dx","Integrate[((-3 + 2*x)*(1 - x + x^3)^(2/3))/(1 - 2*x + x^2 + 2*x^3 - 2*x^4 + 2*x^6),x]","\int \frac{(-3+2 x) \left(1-x+x^3\right)^{2/3}}{1-2 x+x^2+2 x^3-2 x^4+2 x^6} \, dx","-\tan ^{-1}\left(\frac{x}{\sqrt[3]{x^3-x+1}}\right)-\frac{1}{2} \tan ^{-1}\left(\frac{x \sqrt[3]{x^3-x+1}}{\left(x^3-x+1\right)^{2/3}-x^2}\right)-\frac{1}{2} \sqrt{3} \tanh ^{-1}\left(\frac{\sqrt{3} x \sqrt[3]{x^3-x+1}}{\left(x^3-x+1\right)^{2/3}+x^2}\right)",1,"Integrate[((-3 + 2*x)*(1 - x + x^3)^(2/3))/(1 - 2*x + x^2 + 2*x^3 - 2*x^4 + 2*x^6), x]","F",-1
1496,0,0,104,0.4916622,"\int \frac{\left(-2+x^6\right) \left(4+x^6\right) \sqrt[4]{-2+2 x^4+x^6}}{x^6 \left(-4-x^4+2 x^6\right)} \, dx","Integrate[((-2 + x^6)*(4 + x^6)*(-2 + 2*x^4 + x^6)^(1/4))/(x^6*(-4 - x^4 + 2*x^6)),x]","\int \frac{\left(-2+x^6\right) \left(4+x^6\right) \sqrt[4]{-2+2 x^4+x^6}}{x^6 \left(-4-x^4+2 x^6\right)} \, dx","\frac{1}{4} \sqrt[4]{\frac{5}{2}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{5}{2}} x}{\sqrt[4]{x^6+2 x^4-2}}\right)-\frac{1}{4} \sqrt[4]{\frac{5}{2}} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{5}{2}} x}{\sqrt[4]{x^6+2 x^4-2}}\right)+\frac{\sqrt[4]{x^6+2 x^4-2} \left(2 x^6+9 x^4-4\right)}{10 x^5}",1,"Integrate[((-2 + x^6)*(4 + x^6)*(-2 + 2*x^4 + x^6)^(1/4))/(x^6*(-4 - x^4 + 2*x^6)), x]","F",-1
1497,1,104,104,0.1229056,"\int \frac{\left(1+x^3\right)^{2/3} \left(-1+3 x^6\right)}{x^9 \left(1+2 x^3\right)} \, dx","Integrate[((1 + x^3)^(2/3)*(-1 + 3*x^6))/(x^9*(1 + 2*x^3)),x]","\frac{1}{3} \log \left(\frac{x}{\sqrt[3]{x^3+1}}+1\right)+\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3+1}}-1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{1}{6} \log \left(-\frac{x}{\sqrt[3]{x^3+1}}+\frac{x^2}{\left(x^3+1\right)^{2/3}}+1\right)+\frac{\left(x^3+1\right)^{2/3} \left(x^6-14 x^3+5\right)}{40 x^8}","\frac{1}{3} \log \left(\sqrt[3]{x^3+1}+x\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+1}-x}\right)}{\sqrt{3}}-\frac{1}{6} \log \left(-\sqrt[3]{x^3+1} x+\left(x^3+1\right)^{2/3}+x^2\right)+\frac{\left(x^3+1\right)^{2/3} \left(x^6-14 x^3+5\right)}{40 x^8}",1,"((1 + x^3)^(2/3)*(5 - 14*x^3 + x^6))/(40*x^8) + ArcTan[(-1 + (2*x)/(1 + x^3)^(1/3))/Sqrt[3]]/Sqrt[3] - Log[1 + x^2/(1 + x^3)^(2/3) - x/(1 + x^3)^(1/3)]/6 + Log[1 + x/(1 + x^3)^(1/3)]/3","A",1
1498,1,51,104,0.2333951,"\int \frac{\sqrt{1-x^4} \left(1+x^4\right)}{1-x^4+x^8} \, dx","Integrate[(Sqrt[1 - x^4]*(1 + x^4))/(1 - x^4 + x^8),x]","\frac{1}{2} \left(-2 F\left(\left.\sin ^{-1}(x)\right|-1\right)+\Pi \left(-\sqrt[6]{-1};\left.\sin ^{-1}(x)\right|-1\right)+\Pi \left(\sqrt[6]{-1};\left.\sin ^{-1}(x)\right|-1\right)+\Pi \left(-(-1)^{5/6};\left.\sin ^{-1}(x)\right|-1\right)+\Pi \left((-1)^{5/6};\left.\sin ^{-1}(x)\right|-1\right)\right)","\frac{\tan ^{-1}\left(\frac{\frac{x^4}{\sqrt{2}}+\frac{x^2}{\sqrt{2}}-\frac{1}{\sqrt{2}}}{x \sqrt{1-x^4}}\right)}{2 \sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{\frac{x^4}{\sqrt{2}}-\frac{x^2}{\sqrt{2}}-\frac{1}{\sqrt{2}}}{x \sqrt{1-x^4}}\right)}{2 \sqrt{2}}",1,"(-2*EllipticF[ArcSin[x], -1] + EllipticPi[-(-1)^(1/6), ArcSin[x], -1] + EllipticPi[(-1)^(1/6), ArcSin[x], -1] + EllipticPi[-(-1)^(5/6), ArcSin[x], -1] + EllipticPi[(-1)^(5/6), ArcSin[x], -1])/2","C",1
1499,1,93,104,0.1206248,"\int \frac{x^2}{\left(b+a x^4\right)^{3/4} \left(-b^2+a^2 x^8\right)} \, dx","Integrate[x^2/((b + a*x^4)^(3/4)*(-b^2 + a^2*x^8)),x]","-\frac{x^3 \left(\left(\frac{a x^4}{b}+1\right)^{3/4} \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};-\frac{2 a x^4}{b-a x^4}\right)+\left(1-\frac{a x^4}{b}\right)^{3/4}\right)}{6 b^2 \left(a x^4+b\right)^{3/4} \left(1-\frac{a x^4}{b}\right)^{3/4}}","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{4\ 2^{3/4} a^{3/4} b^2}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{4\ 2^{3/4} a^{3/4} b^2}-\frac{x^3}{6 b^2 \left(a x^4+b\right)^{3/4}}",1,"-1/6*(x^3*((1 - (a*x^4)/b)^(3/4) + (1 + (a*x^4)/b)^(3/4)*Hypergeometric2F1[3/4, 3/4, 7/4, (-2*a*x^4)/(b - a*x^4)]))/(b^2*(b + a*x^4)^(3/4)*(1 - (a*x^4)/b)^(3/4))","C",0
1500,1,72,104,0.1304145,"\int \frac{\sqrt{1+\sqrt{1+x^2}}}{x+\sqrt{1+x^2}} \, dx","Integrate[Sqrt[1 + Sqrt[1 + x^2]]/(x + Sqrt[1 + x^2]),x]","\frac{2 \sqrt{\sqrt{x^2+1}+1} \left(-3 x^3+\left(3 \sqrt{x^2+1}+1\right) x^2-\left(\sqrt{x^2+1}+1\right) x+7 \left(\sqrt{x^2+1}-1\right)\right)}{15 x}","-\frac{2}{15} \sqrt{\sqrt{x^2+1}+1} \left(3 x^2+1\right)+\sqrt{x^2+1} \left(\frac{8 x}{15 \sqrt{\sqrt{x^2+1}+1}}-\frac{2}{15} \sqrt{\sqrt{x^2+1}+1}\right)+\frac{2 x \left(3 x^2+11\right)}{15 \sqrt{\sqrt{x^2+1}+1}}",1,"(2*Sqrt[1 + Sqrt[1 + x^2]]*(-3*x^3 + 7*(-1 + Sqrt[1 + x^2]) - x*(1 + Sqrt[1 + x^2]) + x^2*(1 + 3*Sqrt[1 + x^2])))/(15*x)","A",1
1501,0,0,105,0.261479,"\int \frac{(2+x)^2}{x \left(4-2 x+x^2\right) \sqrt[3]{1+x+x^2}} \, dx","Integrate[(2 + x)^2/(x*(4 - 2*x + x^2)*(1 + x + x^2)^(1/3)),x]","\int \frac{(2+x)^2}{x \left(4-2 x+x^2\right) \sqrt[3]{1+x+x^2}} \, dx","\log \left(\sqrt[3]{x^2+x+1}+x-1\right)-\frac{1}{2} \log \left(x^2+\left(x^2+x+1\right)^{2/3}+(1-x) \sqrt[3]{x^2+x+1}-2 x+1\right)-\sqrt{3} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{x^2+x+1}}{\sqrt{3}}-\frac{2 x}{\sqrt{3}}+\frac{2}{\sqrt{3}}}{\sqrt[3]{x^2+x+1}}\right)",1,"Integrate[(2 + x)^2/(x*(4 - 2*x + x^2)*(1 + x + x^2)^(1/3)), x]","F",-1
1502,1,163,105,0.1534231,"\int \frac{1}{\left(-2 b+a x^2\right) \sqrt[4]{-b+a x^2}} \, dx","Integrate[1/((-2*b + a*x^2)*(-b + a*x^2)^(1/4)),x]","-\frac{6 b x F_1\left(\frac{1}{2};\frac{1}{4},1;\frac{3}{2};\frac{a x^2}{b},\frac{a x^2}{2 b}\right)}{\left(2 b-a x^2\right) \sqrt[4]{a x^2-b} \left(a x^2 \left(2 F_1\left(\frac{3}{2};\frac{1}{4},2;\frac{5}{2};\frac{a x^2}{b},\frac{a x^2}{2 b}\right)+F_1\left(\frac{3}{2};\frac{5}{4},1;\frac{5}{2};\frac{a x^2}{b},\frac{a x^2}{2 b}\right)\right)+6 b F_1\left(\frac{1}{2};\frac{1}{4},1;\frac{3}{2};\frac{a x^2}{b},\frac{a x^2}{2 b}\right)\right)}","\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^2-b}}{\sqrt{a} x}\right)}{2 \sqrt{2} \sqrt{a} b^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^2-b}}{\sqrt{a} x}\right)}{2 \sqrt{2} \sqrt{a} b^{3/4}}",1,"(-6*b*x*AppellF1[1/2, 1/4, 1, 3/2, (a*x^2)/b, (a*x^2)/(2*b)])/((2*b - a*x^2)*(-b + a*x^2)^(1/4)*(6*b*AppellF1[1/2, 1/4, 1, 3/2, (a*x^2)/b, (a*x^2)/(2*b)] + a*x^2*(2*AppellF1[3/2, 1/4, 2, 5/2, (a*x^2)/b, (a*x^2)/(2*b)] + AppellF1[3/2, 5/4, 1, 5/2, (a*x^2)/b, (a*x^2)/(2*b)])))","C",0
1503,1,41,105,0.0259837,"\int \frac{-1+x}{x^7 \sqrt[3]{1+x^3}} \, dx","Integrate[(-1 + x)/(x^7*(1 + x^3)^(1/3)),x]","\frac{\left(x^3+1\right)^{2/3} \left(5 x^5 \, _2F_1\left(\frac{2}{3},3;\frac{5}{3};x^3+1\right)+3 x^3-2\right)}{10 x^5}","-\frac{2}{27} \log \left(\sqrt[3]{x^3+1}-1\right)+\frac{1}{27} \log \left(\left(x^3+1\right)^{2/3}+\sqrt[3]{x^3+1}+1\right)-\frac{2 \tan ^{-1}\left(\frac{2 \sqrt[3]{x^3+1}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{9 \sqrt{3}}+\frac{\left(x^3+1\right)^{2/3} \left(27 x^4-20 x^3-18 x+15\right)}{90 x^6}",1,"((1 + x^3)^(2/3)*(-2 + 3*x^3 + 5*x^5*Hypergeometric2F1[2/3, 3, 5/3, 1 + x^3]))/(10*x^5)","C",1
1504,0,0,105,0.3839287,"\int \frac{3 c+2 b x+a x^2}{\sqrt[3]{c+b x+a x^2} \left(c+b x+a x^2+x^3\right)} \, dx","Integrate[(3*c + 2*b*x + a*x^2)/((c + b*x + a*x^2)^(1/3)*(c + b*x + a*x^2 + x^3)),x]","\int \frac{3 c+2 b x+a x^2}{\sqrt[3]{c+b x+a x^2} \left(c+b x+a x^2+x^3\right)} \, dx","\log \left(\sqrt[3]{a x^2+b x+c}+x\right)-\frac{1}{2} \log \left(-x \sqrt[3]{a x^2+b x+c}+\left(a x^2+b x+c\right)^{2/3}+x^2\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{a x^2+b x+c}}{\sqrt[3]{a x^2+b x+c}-2 x}\right)",1,"Integrate[(3*c + 2*b*x + a*x^2)/((c + b*x + a*x^2)^(1/3)*(c + b*x + a*x^2 + x^3)), x]","F",-1
1505,1,448,105,1.2520701,"\int \frac{-b+a x^2}{\left(b+a x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Integrate[(-b + a*x^2)/((b + a*x^4)*(b*x^2 + a*x^4)^(1/4)),x]","\frac{x \sqrt[4]{a+\frac{b}{x^2}} \left(\sqrt{b} \sqrt[4]{\sqrt{-a} \sqrt{b}+a} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a-\sqrt{-a} \sqrt{b}}}\right)-\sqrt{-a} \sqrt[4]{\sqrt{-a} \sqrt{b}+a} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a-\sqrt{-a} \sqrt{b}}}\right)+\sqrt{b} \sqrt[4]{a-\sqrt{-a} \sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\sqrt{-a} \sqrt{b}+a}}\right)+\sqrt{-a} \sqrt[4]{a-\sqrt{-a} \sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\sqrt{-a} \sqrt{b}+a}}\right)+\left(\sqrt{-a}-\sqrt{b}\right) \sqrt[4]{\sqrt{-a} \sqrt{b}+a} \tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a-\sqrt{-a} \sqrt{b}}}\right)-\left(\sqrt{-a}+\sqrt{b}\right) \sqrt[4]{a-\sqrt{-a} \sqrt{b}} \tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\sqrt{-a} \sqrt{b}+a}}\right)\right)}{2 \sqrt{b} \sqrt[4]{a-\sqrt{-a} \sqrt{b}} \sqrt[4]{\sqrt{-a} \sqrt{b}+a} \sqrt[4]{x^2 \left(a x^2+b\right)}}","-\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-2 a \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+2 a \log (x)}{\text{$\#$1} a-\text{$\#$1}^5}\&\right]",1,"((a + b/x^2)^(1/4)*x*(-(Sqrt[-a]*(a + Sqrt[-a]*Sqrt[b])^(1/4)*ArcTan[(a + b/x^2)^(1/4)/(a - Sqrt[-a]*Sqrt[b])^(1/4)]) + (a + Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[b]*ArcTan[(a + b/x^2)^(1/4)/(a - Sqrt[-a]*Sqrt[b])^(1/4)] + Sqrt[-a]*(a - Sqrt[-a]*Sqrt[b])^(1/4)*ArcTan[(a + b/x^2)^(1/4)/(a + Sqrt[-a]*Sqrt[b])^(1/4)] + (a - Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[b]*ArcTan[(a + b/x^2)^(1/4)/(a + Sqrt[-a]*Sqrt[b])^(1/4)] + (Sqrt[-a] - Sqrt[b])*(a + Sqrt[-a]*Sqrt[b])^(1/4)*ArcTanh[(a + b/x^2)^(1/4)/(a - Sqrt[-a]*Sqrt[b])^(1/4)] - (Sqrt[-a] + Sqrt[b])*(a - Sqrt[-a]*Sqrt[b])^(1/4)*ArcTanh[(a + b/x^2)^(1/4)/(a + Sqrt[-a]*Sqrt[b])^(1/4)]))/(2*(a - Sqrt[-a]*Sqrt[b])^(1/4)*(a + Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[b]*(x^2*(b + a*x^2))^(1/4))","B",1
1506,1,448,105,0.4972368,"\int \frac{-b+a x^2}{\left(b+a x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Integrate[(-b + a*x^2)/((b + a*x^4)*(b*x^2 + a*x^4)^(1/4)),x]","\frac{x \sqrt[4]{a+\frac{b}{x^2}} \left(\sqrt{b} \sqrt[4]{\sqrt{-a} \sqrt{b}+a} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a-\sqrt{-a} \sqrt{b}}}\right)-\sqrt{-a} \sqrt[4]{\sqrt{-a} \sqrt{b}+a} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a-\sqrt{-a} \sqrt{b}}}\right)+\sqrt{b} \sqrt[4]{a-\sqrt{-a} \sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\sqrt{-a} \sqrt{b}+a}}\right)+\sqrt{-a} \sqrt[4]{a-\sqrt{-a} \sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\sqrt{-a} \sqrt{b}+a}}\right)+\left(\sqrt{-a}-\sqrt{b}\right) \sqrt[4]{\sqrt{-a} \sqrt{b}+a} \tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a-\sqrt{-a} \sqrt{b}}}\right)-\left(\sqrt{-a}+\sqrt{b}\right) \sqrt[4]{a-\sqrt{-a} \sqrt{b}} \tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\sqrt{-a} \sqrt{b}+a}}\right)\right)}{2 \sqrt{b} \sqrt[4]{a-\sqrt{-a} \sqrt{b}} \sqrt[4]{\sqrt{-a} \sqrt{b}+a} \sqrt[4]{x^2 \left(a x^2+b\right)}}","-\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-2 a \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+2 a \log (x)}{\text{$\#$1} a-\text{$\#$1}^5}\&\right]",1,"((a + b/x^2)^(1/4)*x*(-(Sqrt[-a]*(a + Sqrt[-a]*Sqrt[b])^(1/4)*ArcTan[(a + b/x^2)^(1/4)/(a - Sqrt[-a]*Sqrt[b])^(1/4)]) + (a + Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[b]*ArcTan[(a + b/x^2)^(1/4)/(a - Sqrt[-a]*Sqrt[b])^(1/4)] + Sqrt[-a]*(a - Sqrt[-a]*Sqrt[b])^(1/4)*ArcTan[(a + b/x^2)^(1/4)/(a + Sqrt[-a]*Sqrt[b])^(1/4)] + (a - Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[b]*ArcTan[(a + b/x^2)^(1/4)/(a + Sqrt[-a]*Sqrt[b])^(1/4)] + (Sqrt[-a] - Sqrt[b])*(a + Sqrt[-a]*Sqrt[b])^(1/4)*ArcTanh[(a + b/x^2)^(1/4)/(a - Sqrt[-a]*Sqrt[b])^(1/4)] - (Sqrt[-a] + Sqrt[b])*(a - Sqrt[-a]*Sqrt[b])^(1/4)*ArcTanh[(a + b/x^2)^(1/4)/(a + Sqrt[-a]*Sqrt[b])^(1/4)]))/(2*(a - Sqrt[-a]*Sqrt[b])^(1/4)*(a + Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[b]*(x^2*(b + a*x^2))^(1/4))","B",1
1507,0,0,105,2.3483446,"\int \frac{\sqrt[4]{b x^2+a x^4}}{x^4 \left(b+a x^4\right)} \, dx","Integrate[(b*x^2 + a*x^4)^(1/4)/(x^4*(b + a*x^4)),x]","\int \frac{\sqrt[4]{b x^2+a x^4}}{x^4 \left(b+a x^4\right)} \, dx","\frac{a \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^4-a}\&\right]}{4 b}-\frac{2 \left(a x^2+b\right) \sqrt[4]{a x^4+b x^2}}{5 b^2 x^3}",1,"Integrate[(b*x^2 + a*x^4)^(1/4)/(x^4*(b + a*x^4)), x]","F",-1
1508,0,0,105,1.5838583,"\int \frac{\sqrt[4]{b x^2+a x^4}}{x^4 \left(b+a x^4\right)} \, dx","Integrate[(b*x^2 + a*x^4)^(1/4)/(x^4*(b + a*x^4)),x]","\int \frac{\sqrt[4]{b x^2+a x^4}}{x^4 \left(b+a x^4\right)} \, dx","\frac{a \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^4-a}\&\right]}{4 b}-\frac{2 \left(a x^2+b\right) \sqrt[4]{a x^4+b x^2}}{5 b^2 x^3}",1,"Integrate[(b*x^2 + a*x^4)^(1/4)/(x^4*(b + a*x^4)), x]","F",-1
1509,0,0,105,1.4822865,"\int \frac{\sqrt[4]{b x^2+a x^4}}{x^4 \left(b+a x^4\right)} \, dx","Integrate[(b*x^2 + a*x^4)^(1/4)/(x^4*(b + a*x^4)),x]","\int \frac{\sqrt[4]{b x^2+a x^4}}{x^4 \left(b+a x^4\right)} \, dx","\frac{a \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^4-a}\&\right]}{4 b}-\frac{2 \left(a x^2+b\right) \sqrt[4]{a x^4+b x^2}}{5 b^2 x^3}",1,"Integrate[(b*x^2 + a*x^4)^(1/4)/(x^4*(b + a*x^4)), x]","F",-1
1510,0,0,105,0.1278568,"\int \frac{x \left(3+5 x^2\right)}{\sqrt[3]{1+x^2} \left(-1+x^3+x^5\right)} \, dx","Integrate[(x*(3 + 5*x^2))/((1 + x^2)^(1/3)*(-1 + x^3 + x^5)),x]","\int \frac{x \left(3+5 x^2\right)}{\sqrt[3]{1+x^2} \left(-1+x^3+x^5\right)} \, dx","\frac{1}{2} \log \left(x^2 \left(x^2+1\right)^{2/3}\right)-\frac{1}{2} \log \left(\left(x^2+1\right)^{2/3} x^2+\sqrt[3]{x^2+1} x+1\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x \sqrt[3]{x^2+1}}{\sqrt[3]{x^2+1} x+2}\right)+2 \tanh ^{-1}\left(1-2 x \sqrt[3]{x^2+1}\right)",1,"Integrate[(x*(3 + 5*x^2))/((1 + x^2)^(1/3)*(-1 + x^3 + x^5)), x]","F",-1
1511,0,0,105,0.2877658,"\int \frac{\left(-1+x^5\right)^{2/3} \left(3+2 x^5\right) \left(-2+x^3+2 x^5\right)}{x^6 \left(-1+x^3+x^5\right)} \, dx","Integrate[((-1 + x^5)^(2/3)*(3 + 2*x^5)*(-2 + x^3 + 2*x^5))/(x^6*(-1 + x^3 + x^5)),x]","\int \frac{\left(-1+x^5\right)^{2/3} \left(3+2 x^5\right) \left(-2+x^3+2 x^5\right)}{x^6 \left(-1+x^3+x^5\right)} \, dx","-\log \left(\sqrt[3]{x^5-1}+x\right)-\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^5-1}-x}\right)+\frac{3 \left(x^5-1\right)^{2/3} \left(4 x^5-5 x^3-4\right)}{10 x^5}+\frac{1}{2} \log \left(-\sqrt[3]{x^5-1} x+\left(x^5-1\right)^{2/3}+x^2\right)",1,"Integrate[((-1 + x^5)^(2/3)*(3 + 2*x^5)*(-2 + x^3 + 2*x^5))/(x^6*(-1 + x^3 + x^5)), x]","F",-1
1512,1,50,105,0.0190358,"\int \frac{\left(1+x^3\right)^{2/3} \left(-2+x^3+x^6\right)}{x^9} \, dx","Integrate[((1 + x^3)^(2/3)*(-2 + x^3 + x^6))/x^9,x]","\frac{\left(x^3+1\right)^{2/3} \left(-7 x^6-2 x^3+5\right)-10 x^6 \, _2F_1\left(-\frac{2}{3},-\frac{2}{3};\frac{1}{3};-x^3\right)}{20 x^8}","-\frac{1}{3} \log \left(\sqrt[3]{x^3+1}-x\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+1}+x}\right)}{\sqrt{3}}+\frac{1}{6} \log \left(\sqrt[3]{x^3+1} x+\left(x^3+1\right)^{2/3}+x^2\right)+\frac{\left(x^3+1\right)^{2/3} \left(-17 x^6-2 x^3+5\right)}{20 x^8}",1,"((1 + x^3)^(2/3)*(5 - 2*x^3 - 7*x^6) - 10*x^6*Hypergeometric2F1[-2/3, -2/3, 1/3, -x^3])/(20*x^8)","C",1
1513,0,0,105,0.9260397,"\int \frac{\left(-1+x^6\right)^{2/3} \left(1+x^6\right) \left(-1-x^3+x^6\right)}{x^6 \left(-1+x^3+x^6\right)} \, dx","Integrate[((-1 + x^6)^(2/3)*(1 + x^6)*(-1 - x^3 + x^6))/(x^6*(-1 + x^3 + x^6)),x]","\int \frac{\left(-1+x^6\right)^{2/3} \left(1+x^6\right) \left(-1-x^3+x^6\right)}{x^6 \left(-1+x^3+x^6\right)} \, dx","-\frac{2}{3} \log \left(\sqrt[3]{x^6-1}+x\right)-\frac{2 \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^6-1}-x}\right)}{\sqrt{3}}+\frac{1}{3} \log \left(-\sqrt[3]{x^6-1} x+\left(x^6-1\right)^{2/3}+x^2\right)+\frac{\left(x^6-1\right)^{2/3} \left(x^6-5 x^3-1\right)}{5 x^5}",1,"Integrate[((-1 + x^6)^(2/3)*(1 + x^6)*(-1 - x^3 + x^6))/(x^6*(-1 + x^3 + x^6)), x]","F",-1
1514,1,57,105,0.0318826,"\int \frac{\left(-1+x^3\right)^{2/3} \left(-2+2 x^3+x^6\right)}{x^9} \, dx","Integrate[((-1 + x^3)^(2/3)*(-2 + 2*x^3 + x^6))/x^9,x]","\frac{\left(x^3-1\right)^{2/3} \left(\left(1-x^3\right)^{8/3}-2 x^6 \, _2F_1\left(-\frac{2}{3},-\frac{2}{3};\frac{1}{3};x^3\right)\right)}{4 x^8 \left(1-x^3\right)^{2/3}}","-\frac{1}{3} \log \left(\sqrt[3]{x^3-1}-x\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-1}+x}\right)}{\sqrt{3}}+\frac{1}{6} \log \left(\sqrt[3]{x^3-1} x+\left(x^3-1\right)^{2/3}+x^2\right)+\frac{\left(x^3-1\right)^{2/3} \left(-x^6-2 x^3+1\right)}{4 x^8}",1,"((-1 + x^3)^(2/3)*((1 - x^3)^(8/3) - 2*x^6*Hypergeometric2F1[-2/3, -2/3, 1/3, x^3]))/(4*x^8*(1 - x^3)^(2/3))","C",1
1515,1,94,105,0.0635043,"\int \frac{-2+x^4}{\sqrt[4]{1+x^4} \left(-2+x^4+x^8\right)} \, dx","Integrate[(-2 + x^4)/((1 + x^4)^(1/4)*(-2 + x^4 + x^8)),x]","\frac{4 \tan ^{-1}\left(\frac{x}{\sqrt[4]{2} \sqrt[4]{x^4+1}}\right)+\sqrt{2} \tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+1}}\right)+4 \tanh ^{-1}\left(\frac{x}{\sqrt[4]{2} \sqrt[4]{x^4+1}}\right)+\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+1}}\right)}{6\ 2^{3/4}}","\frac{1}{3} \sqrt[4]{2} \tan ^{-1}\left(\frac{x}{\sqrt[4]{2} \sqrt[4]{x^4+1}}\right)+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+1}}\right)}{6 \sqrt[4]{2}}+\frac{1}{3} \sqrt[4]{2} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{2} \sqrt[4]{x^4+1}}\right)+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+1}}\right)}{6 \sqrt[4]{2}}",1,"(4*ArcTan[x/(2^(1/4)*(1 + x^4)^(1/4))] + Sqrt[2]*ArcTan[(2^(1/4)*x)/(1 + x^4)^(1/4)] + 4*ArcTanh[x/(2^(1/4)*(1 + x^4)^(1/4))] + Sqrt[2]*ArcTanh[(2^(1/4)*x)/(1 + x^4)^(1/4)])/(6*2^(3/4))","A",1
1516,0,0,105,6.6978525,"\int \frac{\sqrt[4]{-1+x^4} \left(2+x^4\right)}{x^2 \left(2+2 x^4+x^8\right)} \, dx","Integrate[((-1 + x^4)^(1/4)*(2 + x^4))/(x^2*(2 + 2*x^4 + x^8)),x]","\int \frac{\sqrt[4]{-1+x^4} \left(2+x^4\right)}{x^2 \left(2+2 x^4+x^8\right)} \, dx","\frac{1}{8} \text{RootSum}\left[2 \text{$\#$1}^8-6 \text{$\#$1}^4+5\&,\frac{-3 \text{$\#$1}^4 \log \left(\sqrt[4]{x^4-1}-\text{$\#$1} x\right)+3 \text{$\#$1}^4 \log (x)+5 \log \left(\sqrt[4]{x^4-1}-\text{$\#$1} x\right)-5 \log (x)}{2 \text{$\#$1}^7-3 \text{$\#$1}^3}\&\right]-\frac{\sqrt[4]{x^4-1}}{x}",1,"Integrate[((-1 + x^4)^(1/4)*(2 + x^4))/(x^2*(2 + 2*x^4 + x^8)), x]","F",-1
1517,0,0,105,6.5875735,"\int \frac{\sqrt[4]{-1+x^4} \left(2+x^4\right)}{x^2 \left(2+2 x^4+x^8\right)} \, dx","Integrate[((-1 + x^4)^(1/4)*(2 + x^4))/(x^2*(2 + 2*x^4 + x^8)),x]","\int \frac{\sqrt[4]{-1+x^4} \left(2+x^4\right)}{x^2 \left(2+2 x^4+x^8\right)} \, dx","\frac{1}{8} \text{RootSum}\left[2 \text{$\#$1}^8-6 \text{$\#$1}^4+5\&,\frac{-3 \text{$\#$1}^4 \log \left(\sqrt[4]{x^4-1}-\text{$\#$1} x\right)+3 \text{$\#$1}^4 \log (x)+5 \log \left(\sqrt[4]{x^4-1}-\text{$\#$1} x\right)-5 \log (x)}{2 \text{$\#$1}^7-3 \text{$\#$1}^3}\&\right]-\frac{\sqrt[4]{x^4-1}}{x}",1,"Integrate[((-1 + x^4)^(1/4)*(2 + x^4))/(x^2*(2 + 2*x^4 + x^8)), x]","F",-1
1518,1,102,105,0.0705592,"\int \frac{-2 b-2 a x^4+x^8}{x^4 \sqrt[4]{b+a x^4}} \, dx","Integrate[(-2*b - 2*a*x^4 + x^8)/(x^4*(b + a*x^4)^(1/4)),x]","\frac{-3 x^3 \left(8 a^2+b\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)-3 x^3 \left(8 a^2+b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)+2 \sqrt[4]{a} \left(8 a+3 x^4\right) \left(a x^4+b\right)^{3/4}}{24 a^{5/4} x^3}","\frac{\left(-8 a^2-b\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{8 a^{5/4}}+\frac{\left(-8 a^2-b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{8 a^{5/4}}+\frac{\left(8 a+3 x^4\right) \left(a x^4+b\right)^{3/4}}{12 a x^3}",1,"(2*a^(1/4)*(8*a + 3*x^4)*(b + a*x^4)^(3/4) - 3*(8*a^2 + b)*x^3*ArcTan[(a^(1/4)*x)/(b + a*x^4)^(1/4)] - 3*(8*a^2 + b)*x^3*ArcTanh[(a^(1/4)*x)/(b + a*x^4)^(1/4)])/(24*a^(5/4)*x^3)","A",1
1519,1,132,105,0.3316307,"\int \frac{1-2 x^4+2 x^8}{\sqrt[4]{1+x^4} \left(-2-x^4+x^8\right)} \, dx","Integrate[(1 - 2*x^4 + 2*x^8)/((1 + x^4)^(1/4)*(-2 - x^4 + x^8)),x]","-\frac{1}{5} x^5 F_1\left(\frac{5}{4};\frac{1}{4},1;\frac{9}{4};-x^4,\frac{x^4}{2}\right)-\frac{5 x}{3 \sqrt[4]{x^4+1}}+\frac{7 \left(-\log \left(2-\frac{2^{3/4} \sqrt[4]{3} x}{\sqrt[4]{x^4+1}}\right)+\log \left(\frac{2^{3/4} \sqrt[4]{3} x}{\sqrt[4]{x^4+1}}+2\right)+2 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{3}{2}} x}{\sqrt[4]{x^4+1}}\right)\right)}{12\ 2^{3/4} \sqrt[4]{3}}","-\frac{5 x}{3 \sqrt[4]{x^4+1}}+\tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)-\frac{5 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{3}{2}} x}{\sqrt[4]{x^4+1}}\right)}{6\ 2^{3/4} \sqrt[4]{3}}+\tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)-\frac{5 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{3}{2}} x}{\sqrt[4]{x^4+1}}\right)}{6\ 2^{3/4} \sqrt[4]{3}}",1,"(-5*x)/(3*(1 + x^4)^(1/4)) - (x^5*AppellF1[5/4, 1/4, 1, 9/4, -x^4, x^4/2])/5 + (7*(2*ArcTan[((3/2)^(1/4)*x)/(1 + x^4)^(1/4)] - Log[2 - (2^(3/4)*3^(1/4)*x)/(1 + x^4)^(1/4)] + Log[2 + (2^(3/4)*3^(1/4)*x)/(1 + x^4)^(1/4)]))/(12*2^(3/4)*3^(1/4))","C",0
1520,0,0,105,0.6808626,"\int \frac{\left(1+x^3+x^8\right)^{2/3} \left(-3+5 x^8\right)}{x^3 \left(1+x^8\right)} \, dx","Integrate[((1 + x^3 + x^8)^(2/3)*(-3 + 5*x^8))/(x^3*(1 + x^8)),x]","\int \frac{\left(1+x^3+x^8\right)^{2/3} \left(-3+5 x^8\right)}{x^3 \left(1+x^8\right)} \, dx","\log \left(\sqrt[3]{x^8+x^3+1}-x\right)-\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^8+x^3+1}+x}\right)+\frac{3 \left(x^8+x^3+1\right)^{2/3}}{2 x^2}-\frac{1}{2} \log \left(x^2+\sqrt[3]{x^8+x^3+1} x+\left(x^8+x^3+1\right)^{2/3}\right)",1,"Integrate[((1 + x^3 + x^8)^(2/3)*(-3 + 5*x^8))/(x^3*(1 + x^8)), x]","F",-1
1521,0,0,105,0.4519536,"\int \frac{-b+2 a x^8}{\sqrt[4]{b+a x^4} \left(-b+a x^8\right)} \, dx","Integrate[(-b + 2*a*x^8)/((b + a*x^4)^(1/4)*(-b + a*x^8)),x]","\int \frac{-b+2 a x^8}{\sqrt[4]{b+a x^4} \left(-b+a x^8\right)} \, dx","\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2-a b\&,\frac{\log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{a}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{a}}",1,"Integrate[(-b + 2*a*x^8)/((b + a*x^4)^(1/4)*(-b + a*x^8)), x]","F",-1
1522,0,0,105,0.1697662,"\int \frac{\sqrt{-1-x^2+x^6} \left(1+2 x^6\right)}{8-x^4-16 x^6+8 x^{12}} \, dx","Integrate[(Sqrt[-1 - x^2 + x^6]*(1 + 2*x^6))/(8 - x^4 - 16*x^6 + 8*x^12),x]","\int \frac{\sqrt{-1-x^2+x^6} \left(1+2 x^6\right)}{8-x^4-16 x^6+8 x^{12}} \, dx","\frac{1}{8} \sqrt{\frac{1}{2} \left(4-\sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{4-\sqrt{2}} x}{2 \sqrt{x^6-x^2-1}}\right)-\frac{1}{8} \sqrt{\frac{1}{2} \left(4+\sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{4+\sqrt{2}} x}{2 \sqrt{x^6-x^2-1}}\right)",1,"Integrate[(Sqrt[-1 - x^2 + x^6]*(1 + 2*x^6))/(8 - x^4 - 16*x^6 + 8*x^12), x]","F",-1
1523,1,131,105,0.0377566,"\int \frac{1}{\left(1+x^2\right) \sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[1/((1 + x^2)*Sqrt[x + Sqrt[1 + x^2]]),x]","\frac{-\log \left(\sqrt{x^2+1}-\sqrt{2} \sqrt{\sqrt{x^2+1}+x}+x+1\right)+\log \left(\sqrt{x^2+1}+\sqrt{2} \sqrt{\sqrt{x^2+1}+x}+x+1\right)-2 \tan ^{-1}\left(1-\sqrt{2} \sqrt{\sqrt{x^2+1}+x}\right)+2 \tan ^{-1}\left(\sqrt{2} \sqrt{\sqrt{x^2+1}+x}+1\right)}{\sqrt{2}}","\sqrt{2} \tan ^{-1}\left(\frac{\frac{\sqrt{x^2+1}}{\sqrt{2}}+\frac{x}{\sqrt{2}}-\frac{1}{\sqrt{2}}}{\sqrt{\sqrt{x^2+1}+x}}\right)+\sqrt{2} \tanh ^{-1}\left(\frac{\frac{\sqrt{x^2+1}}{\sqrt{2}}+\frac{x}{\sqrt{2}}+\frac{1}{\sqrt{2}}}{\sqrt{\sqrt{x^2+1}+x}}\right)",1,"(-2*ArcTan[1 - Sqrt[2]*Sqrt[x + Sqrt[1 + x^2]]] + 2*ArcTan[1 + Sqrt[2]*Sqrt[x + Sqrt[1 + x^2]]] - Log[1 + x + Sqrt[1 + x^2] - Sqrt[2]*Sqrt[x + Sqrt[1 + x^2]]] + Log[1 + x + Sqrt[1 + x^2] + Sqrt[2]*Sqrt[x + Sqrt[1 + x^2]]])/Sqrt[2]","A",1
1524,0,0,105,2.2718128,"\int \frac{\sqrt{x-\sqrt{1+x^2}}}{x^2+\sqrt{1+x^2}} \, dx","Integrate[Sqrt[x - Sqrt[1 + x^2]]/(x^2 + Sqrt[1 + x^2]),x]","\int \frac{\sqrt{x-\sqrt{1+x^2}}}{x^2+\sqrt{1+x^2}} \, dx","\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^6-2 \text{$\#$1}^4-2 \text{$\#$1}^2+1\&,\frac{\text{$\#$1}^5 \log \left(\sqrt{x-\sqrt{x^2+1}}-\text{$\#$1}\right)+\text{$\#$1} \log \left(\sqrt{x-\sqrt{x^2+1}}-\text{$\#$1}\right)}{2 \text{$\#$1}^6-3 \text{$\#$1}^4-2 \text{$\#$1}^2-1}\&\right]",1,"Integrate[Sqrt[x - Sqrt[1 + x^2]]/(x^2 + Sqrt[1 + x^2]), x]","F",-1
1525,0,0,105,0.0908099,"\int \frac{\sqrt{a x^2+\sqrt{b+a^2 x^4}}}{x^2} \, dx","Integrate[Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/x^2,x]","\int \frac{\sqrt{a x^2+\sqrt{b+a^2 x^4}}}{x^2} \, dx","-\frac{\sqrt{\sqrt{a^2 x^4+b}+a x^2}}{x}+\frac{\sqrt{a} \log \left(i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)}{\sqrt{2}}",1,"Integrate[Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/x^2, x]","F",-1
1526,1,106,105,0.2162365,"\int \frac{-1+x}{(1+x) \sqrt{1+\sqrt{1+\sqrt{1+x}}}} \, dx","Integrate[(-1 + x)/((1 + x)*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]),x]","\frac{8 \left(15 x+\sqrt{x+1}-3 \sqrt{x+1} \sqrt{\sqrt{x+1}+1}+8 \sqrt{\sqrt{x+1}+1}+128\right)}{105 \sqrt{\sqrt{\sqrt{x+1}+1}+1}}+4 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{x+1}+1}+1}}{\sqrt{2}}\right)","\frac{-8 (-15 x-128)+\sqrt{x+1} \left(8-24 \sqrt{\sqrt{x+1}+1}\right)+64 \sqrt{\sqrt{x+1}+1}}{105 \sqrt{\sqrt{\sqrt{x+1}+1}+1}}+4 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{x+1}+1}+1}}{\sqrt{2}}\right)",1,"(8*(128 + 15*x + Sqrt[1 + x] + 8*Sqrt[1 + Sqrt[1 + x]] - 3*Sqrt[1 + x]*Sqrt[1 + Sqrt[1 + x]]))/(105*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]) + 4*Sqrt[2]*ArcTanh[Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]/Sqrt[2]]","A",1
1527,1,100,106,0.0477399,"\int \frac{1}{(-2+x) \sqrt[3]{1+2 x+x^2}} \, dx","Integrate[1/((-2 + x)*(1 + 2*x + x^2)^(1/3)),x]","-\frac{(x+1)^{2/3} \left(-2 \log \left(\sqrt[3]{3}-\sqrt[3]{x+1}\right)+\log \left((x+1)^{2/3}+\sqrt[3]{3} \sqrt[3]{x+1}+3^{2/3}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x+1}+\sqrt[3]{3}}{3^{5/6}}\right)\right)}{2\ 3^{2/3} \sqrt[3]{(x+1)^2}}","\frac{\left((x+1)^2\right)^{2/3} \left(\frac{\log \left(3^{2/3} \sqrt[3]{x+1}-3\right)}{3^{2/3}}-\frac{\log \left(\sqrt[3]{3} (x+1)^{2/3}+3^{2/3} \sqrt[3]{x+1}+3\right)}{2\ 3^{2/3}}-\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{x+1}}{3^{5/6}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[6]{3}}\right)}{(x+1)^{4/3}}",1,"-1/2*((1 + x)^(2/3)*(2*Sqrt[3]*ArcTan[(3^(1/3) + 2*(1 + x)^(1/3))/3^(5/6)] - 2*Log[3^(1/3) - (1 + x)^(1/3)] + Log[3^(2/3) + 3^(1/3)*(1 + x)^(1/3) + (1 + x)^(2/3)]))/(3^(2/3)*((1 + x)^2)^(1/3))","A",1
1528,1,42,106,0.0102287,"\int \frac{\sqrt[3]{-x+x^3}}{x^2} \, dx","Integrate[(-x + x^3)^(1/3)/x^2,x]","-\frac{3 \sqrt[3]{x \left(x^2-1\right)} \, _2F_1\left(-\frac{1}{3},-\frac{1}{3};\frac{2}{3};x^2\right)}{2 x \sqrt[3]{1-x^2}}","-\frac{3 \sqrt[3]{x^3-x}}{2 x}-\frac{1}{2} \log \left(\sqrt[3]{x^3-x}-x\right)-\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-x}+x}\right)+\frac{1}{4} \log \left(\sqrt[3]{x^3-x} x+\left(x^3-x\right)^{2/3}+x^2\right)",1,"(-3*(x*(-1 + x^2))^(1/3)*Hypergeometric2F1[-1/3, -1/3, 2/3, x^2])/(2*x*(1 - x^2)^(1/3))","C",1
1529,1,35,106,0.0099875,"\int \frac{\sqrt[3]{-x^2+x^3}}{x} \, dx","Integrate[(-x^2 + x^3)^(1/3)/x,x]","\frac{3 \left((x-1) x^2\right)^{4/3} \, _2F_1\left(\frac{1}{3},\frac{4}{3};\frac{7}{3};1-x\right)}{4 x^{8/3}}","\sqrt[3]{x^3-x^2}+\frac{1}{3} \log \left(\sqrt[3]{x^3-x^2}-x\right)-\frac{1}{6} \log \left(x^2+\sqrt[3]{x^3-x^2} x+\left(x^3-x^2\right)^{2/3}\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-x^2}+x}\right)}{\sqrt{3}}",1,"(3*((-1 + x)*x^2)^(4/3)*Hypergeometric2F1[1/3, 4/3, 7/3, 1 - x])/(4*x^(8/3))","C",1
1530,0,0,106,0.5895056,"\int \frac{-3 b+a x^2}{\left(-b+a x^2+x^3\right) \sqrt[4]{-b x+a x^3}} \, dx","Integrate[(-3*b + a*x^2)/((-b + a*x^2 + x^3)*(-(b*x) + a*x^3)^(1/4)),x]","\int \frac{-3 b+a x^2}{\left(-b+a x^2+x^3\right) \sqrt[4]{-b x+a x^3}} \, dx","\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{a x^3-b x}}{\sqrt{a x^3-b x}+x^2}\right)-\sqrt{2} \tan ^{-1}\left(\frac{\frac{\sqrt{a x^3-b x}}{\sqrt{2}}-\frac{x^2}{\sqrt{2}}}{x \sqrt[4]{a x^3-b x}}\right)",1,"Integrate[(-3*b + a*x^2)/((-b + a*x^2 + x^3)*(-(b*x) + a*x^3)^(1/4)), x]","F",-1
1531,1,61,106,0.0464321,"\int \frac{1}{(-2 b+a x) \sqrt[4]{-b x^2+a x^3}} \, dx","Integrate[1/((-2*b + a*x)*(-(b*x^2) + a*x^3)^(1/4)),x]","-\frac{x \sqrt[4]{\frac{b-a x}{b}} F_1\left(\frac{1}{2};\frac{1}{4},1;\frac{3}{2};\frac{a x}{b},\frac{a x}{2 b}\right)}{b \sqrt[4]{x^2 (a x-b)}}","\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^3-b x^2}}{\sqrt{a} x}\right)}{\sqrt{2} \sqrt{a} b^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^3-b x^2}}{\sqrt{a} x}\right)}{\sqrt{2} \sqrt{a} b^{3/4}}",1,"-((x*((b - a*x)/b)^(1/4)*AppellF1[1/2, 1/4, 1, 3/2, (a*x)/b, (a*x)/(2*b)])/(b*(x^2*(-b + a*x))^(1/4)))","C",0
1532,0,0,106,2.2865353,"\int \frac{\left(-b+a x^4\right) \sqrt[4]{-b x^2+a x^4}}{x^4 \left(b+a x^4\right)} \, dx","Integrate[((-b + a*x^4)*(-(b*x^2) + a*x^4)^(1/4))/(x^4*(b + a*x^4)),x]","\int \frac{\left(-b+a x^4\right) \sqrt[4]{-b x^2+a x^4}}{x^4 \left(b+a x^4\right)} \, dx","\frac{1}{2} a \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^4-a}\&\right]-\frac{2 \left(a x^2-b\right) \sqrt[4]{a x^4-b x^2}}{5 b x^3}",1,"Integrate[((-b + a*x^4)*(-(b*x^2) + a*x^4)^(1/4))/(x^4*(b + a*x^4)), x]","F",-1
1533,0,0,106,1.6339035,"\int \frac{\left(-b+a x^4\right) \sqrt[4]{-b x^2+a x^4}}{x^4 \left(b+a x^4\right)} \, dx","Integrate[((-b + a*x^4)*(-(b*x^2) + a*x^4)^(1/4))/(x^4*(b + a*x^4)),x]","\int \frac{\left(-b+a x^4\right) \sqrt[4]{-b x^2+a x^4}}{x^4 \left(b+a x^4\right)} \, dx","\frac{1}{2} a \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^4-a}\&\right]-\frac{2 \left(a x^2-b\right) \sqrt[4]{a x^4-b x^2}}{5 b x^3}",1,"Integrate[((-b + a*x^4)*(-(b*x^2) + a*x^4)^(1/4))/(x^4*(b + a*x^4)), x]","F",-1
1534,1,561,106,1.1376757,"\int \frac{-b+a x^2}{\left(b-a x^2+x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Integrate[(-b + a*x^2)/((b - a*x^2 + x^4)*(b*x^2 + a*x^4)^(1/4)),x]","\frac{\sqrt{x} \sqrt[4]{a x^2+b} \left(-\frac{\left(\frac{2 b-a^2}{\sqrt{a^2-4 b}}+a\right) \tan ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{-a \sqrt{a^2-4 b}+a^2+2 b}}{\sqrt[4]{a-\sqrt{a^2-4 b}} \sqrt[4]{a x^2+b}}\right)}{\left(a-\sqrt{a^2-4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2-4 b}+a^2+2 b}}-\frac{\left(a \sqrt{a^2-4 b}+a^2-2 b\right) \tan ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{a \sqrt{a^2-4 b}+a^2+2 b}}{\sqrt[4]{\sqrt{a^2-4 b}+a} \sqrt[4]{a x^2+b}}\right)}{\left(\sqrt{a^2-4 b}+a\right)^{3/4} \sqrt{a^2-4 b} \sqrt[4]{a \sqrt{a^2-4 b}+a^2+2 b}}-\frac{\left(\frac{2 b-a^2}{\sqrt{a^2-4 b}}+a\right) \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{-a \sqrt{a^2-4 b}+a^2+2 b}}{\sqrt[4]{a-\sqrt{a^2-4 b}} \sqrt[4]{a x^2+b}}\right)}{\left(a-\sqrt{a^2-4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2-4 b}+a^2+2 b}}-\frac{\left(a \sqrt{a^2-4 b}+a^2-2 b\right) \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{a \sqrt{a^2-4 b}+a^2+2 b}}{\sqrt[4]{\sqrt{a^2-4 b}+a} \sqrt[4]{a x^2+b}}\right)}{\left(\sqrt{a^2-4 b}+a\right)^{3/4} \sqrt{a^2-4 b} \sqrt[4]{a \sqrt{a^2-4 b}+a^2+2 b}}\right)}{\sqrt[4]{x^2 \left(a x^2+b\right)}}","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4 a+2 a^2+b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-2 a \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+2 a \log (x)}{3 \text{$\#$1} a-2 \text{$\#$1}^5}\&\right]",1,"(Sqrt[x]*(b + a*x^2)^(1/4)*(-(((a + (-a^2 + 2*b)/Sqrt[a^2 - 4*b])*ArcTan[((a^2 - a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)*Sqrt[x])/((a - Sqrt[a^2 - 4*b])^(1/4)*(b + a*x^2)^(1/4))])/((a - Sqrt[a^2 - 4*b])^(3/4)*(a^2 - a*Sqrt[a^2 - 4*b] + 2*b)^(1/4))) - ((a^2 + a*Sqrt[a^2 - 4*b] - 2*b)*ArcTan[((a^2 + a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)*Sqrt[x])/((a + Sqrt[a^2 - 4*b])^(1/4)*(b + a*x^2)^(1/4))])/((a + Sqrt[a^2 - 4*b])^(3/4)*Sqrt[a^2 - 4*b]*(a^2 + a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)) - ((a + (-a^2 + 2*b)/Sqrt[a^2 - 4*b])*ArcTanh[((a^2 - a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)*Sqrt[x])/((a - Sqrt[a^2 - 4*b])^(1/4)*(b + a*x^2)^(1/4))])/((a - Sqrt[a^2 - 4*b])^(3/4)*(a^2 - a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)) - ((a^2 + a*Sqrt[a^2 - 4*b] - 2*b)*ArcTanh[((a^2 + a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)*Sqrt[x])/((a + Sqrt[a^2 - 4*b])^(1/4)*(b + a*x^2)^(1/4))])/((a + Sqrt[a^2 - 4*b])^(3/4)*Sqrt[a^2 - 4*b]*(a^2 + a*Sqrt[a^2 - 4*b] + 2*b)^(1/4))))/(x^2*(b + a*x^2))^(1/4)","B",1
1535,1,561,106,0.2751934,"\int \frac{-b+a x^2}{\left(b-a x^2+x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Integrate[(-b + a*x^2)/((b - a*x^2 + x^4)*(b*x^2 + a*x^4)^(1/4)),x]","\frac{\sqrt{x} \sqrt[4]{a x^2+b} \left(-\frac{\left(\frac{2 b-a^2}{\sqrt{a^2-4 b}}+a\right) \tan ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{-a \sqrt{a^2-4 b}+a^2+2 b}}{\sqrt[4]{a-\sqrt{a^2-4 b}} \sqrt[4]{a x^2+b}}\right)}{\left(a-\sqrt{a^2-4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2-4 b}+a^2+2 b}}-\frac{\left(a \sqrt{a^2-4 b}+a^2-2 b\right) \tan ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{a \sqrt{a^2-4 b}+a^2+2 b}}{\sqrt[4]{\sqrt{a^2-4 b}+a} \sqrt[4]{a x^2+b}}\right)}{\left(\sqrt{a^2-4 b}+a\right)^{3/4} \sqrt{a^2-4 b} \sqrt[4]{a \sqrt{a^2-4 b}+a^2+2 b}}-\frac{\left(\frac{2 b-a^2}{\sqrt{a^2-4 b}}+a\right) \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{-a \sqrt{a^2-4 b}+a^2+2 b}}{\sqrt[4]{a-\sqrt{a^2-4 b}} \sqrt[4]{a x^2+b}}\right)}{\left(a-\sqrt{a^2-4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2-4 b}+a^2+2 b}}-\frac{\left(a \sqrt{a^2-4 b}+a^2-2 b\right) \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{a \sqrt{a^2-4 b}+a^2+2 b}}{\sqrt[4]{\sqrt{a^2-4 b}+a} \sqrt[4]{a x^2+b}}\right)}{\left(\sqrt{a^2-4 b}+a\right)^{3/4} \sqrt{a^2-4 b} \sqrt[4]{a \sqrt{a^2-4 b}+a^2+2 b}}\right)}{\sqrt[4]{x^2 \left(a x^2+b\right)}}","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4 a+2 a^2+b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-2 a \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+2 a \log (x)}{3 \text{$\#$1} a-2 \text{$\#$1}^5}\&\right]",1,"(Sqrt[x]*(b + a*x^2)^(1/4)*(-(((a + (-a^2 + 2*b)/Sqrt[a^2 - 4*b])*ArcTan[((a^2 - a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)*Sqrt[x])/((a - Sqrt[a^2 - 4*b])^(1/4)*(b + a*x^2)^(1/4))])/((a - Sqrt[a^2 - 4*b])^(3/4)*(a^2 - a*Sqrt[a^2 - 4*b] + 2*b)^(1/4))) - ((a^2 + a*Sqrt[a^2 - 4*b] - 2*b)*ArcTan[((a^2 + a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)*Sqrt[x])/((a + Sqrt[a^2 - 4*b])^(1/4)*(b + a*x^2)^(1/4))])/((a + Sqrt[a^2 - 4*b])^(3/4)*Sqrt[a^2 - 4*b]*(a^2 + a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)) - ((a + (-a^2 + 2*b)/Sqrt[a^2 - 4*b])*ArcTanh[((a^2 - a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)*Sqrt[x])/((a - Sqrt[a^2 - 4*b])^(1/4)*(b + a*x^2)^(1/4))])/((a - Sqrt[a^2 - 4*b])^(3/4)*(a^2 - a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)) - ((a^2 + a*Sqrt[a^2 - 4*b] - 2*b)*ArcTanh[((a^2 + a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)*Sqrt[x])/((a + Sqrt[a^2 - 4*b])^(1/4)*(b + a*x^2)^(1/4))])/((a + Sqrt[a^2 - 4*b])^(3/4)*Sqrt[a^2 - 4*b]*(a^2 + a*Sqrt[a^2 - 4*b] + 2*b)^(1/4))))/(x^2*(b + a*x^2))^(1/4)","B",1
1536,0,0,106,2.611685,"\int \frac{\sqrt[4]{b x^2+a x^4}}{x^4 \left(-b+a x^4\right)} \, dx","Integrate[(b*x^2 + a*x^4)^(1/4)/(x^4*(-b + a*x^4)),x]","\int \frac{\sqrt[4]{b x^2+a x^4}}{x^4 \left(-b+a x^4\right)} \, dx","\frac{a \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2-a b\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^4-a}\&\right]}{4 b}+\frac{2 \sqrt[4]{a x^4+b x^2} \left(a x^2+b\right)}{5 b^2 x^3}",1,"Integrate[(b*x^2 + a*x^4)^(1/4)/(x^4*(-b + a*x^4)), x]","F",-1
1537,0,0,106,1.494549,"\int \frac{\sqrt[4]{b x^2+a x^4}}{x^4 \left(-b+a x^4\right)} \, dx","Integrate[(b*x^2 + a*x^4)^(1/4)/(x^4*(-b + a*x^4)),x]","\int \frac{\sqrt[4]{b x^2+a x^4}}{x^4 \left(-b+a x^4\right)} \, dx","\frac{a \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2-a b\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^4-a}\&\right]}{4 b}+\frac{2 \sqrt[4]{a x^4+b x^2} \left(a x^2+b\right)}{5 b^2 x^3}",1,"Integrate[(b*x^2 + a*x^4)^(1/4)/(x^4*(-b + a*x^4)), x]","F",-1
1538,1,566,106,3.87128,"\int \frac{b^3+a^3 x^3}{\left(-b^3+a^3 x^3\right) \sqrt{b^4+a^4 x^4}} \, dx","Integrate[(b^3 + a^3*x^3)/((-b^3 + a^3*x^3)*Sqrt[b^4 + a^4*x^4]),x]","\frac{a^3 \left(18 i a \sqrt[4]{a^4} b \sqrt{\frac{a^4 x^4}{b^4}+1} F\left(\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)-12 i a \sqrt[4]{a^4} b \sqrt{\frac{a^4 x^4}{b^4}+1} \Pi \left(-\frac{i}{2}-\frac{\sqrt{3}}{2};\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)-12 i a \sqrt[4]{a^4} b \sqrt{\frac{a^4 x^4}{b^4}+1} \Pi \left(\frac{1}{2} \left(-i+\sqrt{3}\right);\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)-\frac{3}{2} \sqrt{\frac{i a^2}{b^2}} \left((4+4 i) a b \sqrt[4]{b^4} \sqrt{\frac{2 a^4 x^4}{b^4}+2} \Pi \left(\frac{i \sqrt{a^4} \sqrt{b^4}}{a^2 b^2};\left.i \sinh ^{-1}\left(\frac{(1+i) \sqrt[4]{a^4} x}{\sqrt{2} \sqrt[4]{b^4}}\right)\right|-1\right)-\sqrt[4]{a^4} \sqrt{a^4 x^4+b^4} \left(\left(1-i \sqrt{3}+\sqrt{6+6 i \sqrt{3}}\right) \tan ^{-1}\left(\frac{\left(\sqrt{3}+i\right) b^2-2 i a^2 x^2}{\sqrt{2-2 i \sqrt{3}} \sqrt{a^4 x^4+b^4}}\right)+\left(1+i \sqrt{3}+\sqrt{6-6 i \sqrt{3}}\right) \tan ^{-1}\left(\frac{2 i a^2 x^2+\left(\sqrt{3}-i\right) b^2}{\sqrt{2+2 i \sqrt{3}} \sqrt{a^4 x^4+b^4}}\right)+2 \sqrt{2} \tanh ^{-1}\left(\frac{a^2 x^2+b^2}{\sqrt{2} \sqrt{a^4 x^4+b^4}}\right)\right)\right)\right)}{18 \sqrt[4]{a^4} b^5 \left(\frac{i a^2}{b^2}\right)^{5/2} \sqrt{a^4 x^4+b^4}}","-\frac{4 \tan ^{-1}\left(\frac{a b x}{\sqrt{a^4 x^4+b^4}+a^2 x^2+a b x+b^2}\right)}{3 a b}-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} a b x}{\sqrt{a^4 x^4+b^4}+a^2 x^2-2 a b x+b^2}\right)}{3 a b}",1,"(a^3*((18*I)*a*(a^4)^(1/4)*b*Sqrt[1 + (a^4*x^4)/b^4]*EllipticF[I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] - (12*I)*a*(a^4)^(1/4)*b*Sqrt[1 + (a^4*x^4)/b^4]*EllipticPi[-1/2*I - Sqrt[3]/2, I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] - (12*I)*a*(a^4)^(1/4)*b*Sqrt[1 + (a^4*x^4)/b^4]*EllipticPi[(-I + Sqrt[3])/2, I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] - (3*Sqrt[(I*a^2)/b^2]*(-((a^4)^(1/4)*Sqrt[b^4 + a^4*x^4]*((1 - I*Sqrt[3] + Sqrt[6 + (6*I)*Sqrt[3]])*ArcTan[((I + Sqrt[3])*b^2 - (2*I)*a^2*x^2)/(Sqrt[2 - (2*I)*Sqrt[3]]*Sqrt[b^4 + a^4*x^4])] + (1 + I*Sqrt[3] + Sqrt[6 - (6*I)*Sqrt[3]])*ArcTan[((-I + Sqrt[3])*b^2 + (2*I)*a^2*x^2)/(Sqrt[2 + (2*I)*Sqrt[3]]*Sqrt[b^4 + a^4*x^4])] + 2*Sqrt[2]*ArcTanh[(b^2 + a^2*x^2)/(Sqrt[2]*Sqrt[b^4 + a^4*x^4])])) + (4 + 4*I)*a*b*(b^4)^(1/4)*Sqrt[2 + (2*a^4*x^4)/b^4]*EllipticPi[(I*Sqrt[a^4]*Sqrt[b^4])/(a^2*b^2), I*ArcSinh[((1 + I)*(a^4)^(1/4)*x)/(Sqrt[2]*(b^4)^(1/4))], -1]))/2))/(18*(a^4)^(1/4)*((I*a^2)/b^2)^(5/2)*b^5*Sqrt[b^4 + a^4*x^4])","C",0
1539,0,0,106,0.6051417,"\int \frac{\left(1+x^3\right)^{2/3} \left(1+x^3+2 x^6\right)}{x^6 \left(-1+2 x^6\right)} \, dx","Integrate[((1 + x^3)^(2/3)*(1 + x^3 + 2*x^6))/(x^6*(-1 + 2*x^6)),x]","\int \frac{\left(1+x^3\right)^{2/3} \left(1+x^3+2 x^6\right)}{x^6 \left(-1+2 x^6\right)} \, dx","\frac{\left(x^3+1\right)^{2/3} \left(7 x^3+2\right)}{10 x^5}-\frac{1}{6} \text{RootSum}\left[\text{$\#$1}^6-2 \text{$\#$1}^3-1\&,\frac{-5 \text{$\#$1}^3 \log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)+5 \text{$\#$1}^3 \log (x)-\log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)+\log (x)}{\text{$\#$1}^4-\text{$\#$1}}\&\right]",1,"Integrate[((1 + x^3)^(2/3)*(1 + x^3 + 2*x^6))/(x^6*(-1 + 2*x^6)), x]","F",-1
1540,0,0,106,0.2788198,"\int \frac{\left(1+x^3\right)^{2/3} \left(1+x^3+2 x^6\right)}{x^6 \left(-1+2 x^6\right)} \, dx","Integrate[((1 + x^3)^(2/3)*(1 + x^3 + 2*x^6))/(x^6*(-1 + 2*x^6)),x]","\int \frac{\left(1+x^3\right)^{2/3} \left(1+x^3+2 x^6\right)}{x^6 \left(-1+2 x^6\right)} \, dx","\frac{\left(x^3+1\right)^{2/3} \left(7 x^3+2\right)}{10 x^5}-\frac{1}{6} \text{RootSum}\left[\text{$\#$1}^6-2 \text{$\#$1}^3-1\&,\frac{-5 \text{$\#$1}^3 \log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)+5 \text{$\#$1}^3 \log (x)-\log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)+\log (x)}{\text{$\#$1}^4-\text{$\#$1}}\&\right]",1,"Integrate[((1 + x^3)^(2/3)*(1 + x^3 + 2*x^6))/(x^6*(-1 + 2*x^6)), x]","F",-1
1541,0,0,106,1.2604852,"\int \frac{\left(1+x^6\right) \left(-1+2 x^6\right) \left(-1+x^4+2 x^6\right)^{5/4}}{x^{10} \left(-1-x^4+2 x^6\right)} \, dx","Integrate[((1 + x^6)*(-1 + 2*x^6)*(-1 + x^4 + 2*x^6)^(5/4))/(x^10*(-1 - x^4 + 2*x^6)),x]","\int \frac{\left(1+x^6\right) \left(-1+2 x^6\right) \left(-1+x^4+2 x^6\right)^{5/4}}{x^{10} \left(-1-x^4+2 x^6\right)} \, dx","\sqrt[4]{2} \tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{2 x^6+x^4-1}}\right)-\sqrt[4]{2} \tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{2 x^6+x^4-1}}\right)+\frac{\sqrt[4]{2 x^6+x^4-1} \left(20 x^{12}+38 x^{10}+104 x^8-20 x^6-19 x^4+5\right)}{45 x^9}",1,"Integrate[((1 + x^6)*(-1 + 2*x^6)*(-1 + x^4 + 2*x^6)^(5/4))/(x^10*(-1 - x^4 + 2*x^6)), x]","F",-1
1542,1,252,106,0.4032003,"\int \frac{1}{\sqrt[3]{b^2 x^2+a^3 x^3} \left(b+a^6 x^6\right)} \, dx","Integrate[1/((b^2*x^2 + a^3*x^3)^(1/3)*(b + a^6*x^6)),x]","\frac{x \left(\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2+(-b)^{11/6}\right) x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2+\sqrt[3]{-1} (-b)^{11/6}\right) x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2+(-1)^{2/3} (-b)^{11/6}\right) x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2+(-b)^{5/6} b\right) x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2+\sqrt[3]{-1} (-b)^{5/6} b\right) x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2+(-1)^{2/3} (-b)^{5/6} b\right) x}{x a^3+b^2}\right)\right)}{2 b \sqrt[3]{x^2 \left(a^3 x+b^2\right)}}","-\frac{\text{RootSum}\left[\text{$\#$1}^{18}-6 \text{$\#$1}^{15} a^3+15 \text{$\#$1}^{12} a^6-20 \text{$\#$1}^9 a^9+15 \text{$\#$1}^6 a^{12}-6 \text{$\#$1}^3 a^{15}+a^{18}+a^6 b^{11}\&,\frac{\log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{6 b}",1,"(x*(Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 + (-b)^(11/6))*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 + (-1)^(1/3)*(-b)^(11/6))*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 + (-1)^(2/3)*(-b)^(11/6))*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 + (-b)^(5/6)*b)*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 + (-1)^(1/3)*(-b)^(5/6)*b)*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 + (-1)^(2/3)*(-b)^(5/6)*b)*x)/(b^2 + a^3*x)]))/(2*b*(x^2*(b^2 + a^3*x))^(1/3))","B",1
1543,1,252,106,0.1348768,"\int \frac{1}{\sqrt[3]{b^2 x^2+a^3 x^3} \left(b+a^6 x^6\right)} \, dx","Integrate[1/((b^2*x^2 + a^3*x^3)^(1/3)*(b + a^6*x^6)),x]","\frac{x \left(\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2+(-b)^{11/6}\right) x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2+\sqrt[3]{-1} (-b)^{11/6}\right) x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2+(-1)^{2/3} (-b)^{11/6}\right) x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2+(-b)^{5/6} b\right) x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2+\sqrt[3]{-1} (-b)^{5/6} b\right) x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2+(-1)^{2/3} (-b)^{5/6} b\right) x}{x a^3+b^2}\right)\right)}{2 b \sqrt[3]{x^2 \left(a^3 x+b^2\right)}}","-\frac{\text{RootSum}\left[\text{$\#$1}^{18}-6 \text{$\#$1}^{15} a^3+15 \text{$\#$1}^{12} a^6-20 \text{$\#$1}^9 a^9+15 \text{$\#$1}^6 a^{12}-6 \text{$\#$1}^3 a^{15}+a^{18}+a^6 b^{11}\&,\frac{\log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{6 b}",1,"(x*(Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 + (-b)^(11/6))*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 + (-1)^(1/3)*(-b)^(11/6))*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 + (-1)^(2/3)*(-b)^(11/6))*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 + (-b)^(5/6)*b)*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 + (-1)^(1/3)*(-b)^(5/6)*b)*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 + (-1)^(2/3)*(-b)^(5/6)*b)*x)/(b^2 + a^3*x)]))/(2*b*(x^2*(b^2 + a^3*x))^(1/3))","B",1
1544,0,0,106,1.023158,"\int \frac{\left(\left(1-3 k^2\right) x+2 k^2 x^3\right) \left(1-2 k^2 x^2+k^4 x^4\right)}{\left(\left(1-x^2\right) \left(1-k^2 x^2\right)\right)^{3/4} \left(1-d+\left(-1+3 d k^2\right) x^2-3 d k^4 x^4+d k^6 x^6\right)} \, dx","Integrate[(((1 - 3*k^2)*x + 2*k^2*x^3)*(1 - 2*k^2*x^2 + k^4*x^4))/(((1 - x^2)*(1 - k^2*x^2))^(3/4)*(1 - d + (-1 + 3*d*k^2)*x^2 - 3*d*k^4*x^4 + d*k^6*x^6)),x]","\int \frac{\left(\left(1-3 k^2\right) x+2 k^2 x^3\right) \left(1-2 k^2 x^2+k^4 x^4\right)}{\left(\left(1-x^2\right) \left(1-k^2 x^2\right)\right)^{3/4} \left(1-d+\left(-1+3 d k^2\right) x^2-3 d k^4 x^4+d k^6 x^6\right)} \, dx","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{d} k^2 x^2-\sqrt[4]{d}}{\sqrt[4]{k^2 x^4+\left(-k^2-1\right) x^2+1}}\right)}{d^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{d} k^2 x^2-\sqrt[4]{d}}{\sqrt[4]{k^2 x^4+\left(-k^2-1\right) x^2+1}}\right)}{d^{3/4}}",1,"Integrate[(((1 - 3*k^2)*x + 2*k^2*x^3)*(1 - 2*k^2*x^2 + k^4*x^4))/(((1 - x^2)*(1 - k^2*x^2))^(3/4)*(1 - d + (-1 + 3*d*k^2)*x^2 - 3*d*k^4*x^4 + d*k^6*x^6)), x]","F",-1
1545,1,67,106,0.1367514,"\int \frac{\sqrt[4]{-1+2 x^4} \left(-1+x^4+x^8\right)}{x^6 \left(-1+x^4\right)} \, dx","Integrate[((-1 + 2*x^4)^(1/4)*(-1 + x^4 + x^8))/(x^6*(-1 + x^4)),x]","\frac{\sqrt[4]{2 x^4-1} \left(-5 x^8 F_1\left(\frac{3}{4};-\frac{1}{4},1;\frac{7}{4};2 x^4,x^4\right)-3 \left(1-2 x^4\right)^{5/4}\right)}{15 x^5 \sqrt[4]{1-2 x^4}}","\frac{1}{2} \tan ^{-1}\left(\frac{x}{\sqrt[4]{2 x^4-1}}\right)-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{2 x^4-1}}\right)}{2^{3/4}}-\frac{1}{2} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{2 x^4-1}}\right)+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{2 x^4-1}}\right)}{2^{3/4}}+\frac{\left(2 x^4-1\right)^{5/4}}{5 x^5}",1,"((-1 + 2*x^4)^(1/4)*(-3*(1 - 2*x^4)^(5/4) - 5*x^8*AppellF1[3/4, -1/4, 1, 7/4, 2*x^4, x^4]))/(15*x^5*(1 - 2*x^4)^(1/4))","C",0
1546,1,424,106,0.4943123,"\int \frac{1}{\sqrt[4]{-b+a x^4} \left(-b-a x^4+x^8\right)} \, dx","Integrate[1/((-b + a*x^4)^(1/4)*(-b - a*x^4 + x^8)),x]","-\frac{-\frac{\tan ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{a x^4-b}}\right)}{\left(a-\sqrt{a^2+4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}+\frac{\tan ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+4 b}+a} \sqrt[4]{a x^4-b}}\right)}{\left(\sqrt{a^2+4 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}-\frac{\tanh ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{a x^4-b}}\right)}{\left(a-\sqrt{a^2+4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}+\frac{\tanh ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+4 b}+a} \sqrt[4]{a x^4-b}}\right)}{\left(\sqrt{a^2+4 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}}{\sqrt{a^2+4 b}}","-\frac{\text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4 a+2 a^2-b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-a \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+a \log (x)}{3 \text{$\#$1} a-2 \text{$\#$1}^5}\&\right]}{4 b}",1,"-((-(ArcTan[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a - Sqrt[a^2 + 4*b])^(1/4)*(-b + a*x^4)^(1/4))]/((a - Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4))) + ArcTan[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a + Sqrt[a^2 + 4*b])^(1/4)*(-b + a*x^4)^(1/4))]/((a + Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)) - ArcTanh[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a - Sqrt[a^2 + 4*b])^(1/4)*(-b + a*x^4)^(1/4))]/((a - Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)) + ArcTanh[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a + Sqrt[a^2 + 4*b])^(1/4)*(-b + a*x^4)^(1/4))]/((a + Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)))/Sqrt[a^2 + 4*b])","B",1
1547,1,424,106,0.0742145,"\int \frac{1}{\sqrt[4]{-b+a x^4} \left(-b-a x^4+x^8\right)} \, dx","Integrate[1/((-b + a*x^4)^(1/4)*(-b - a*x^4 + x^8)),x]","-\frac{-\frac{\tan ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{a x^4-b}}\right)}{\left(a-\sqrt{a^2+4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}+\frac{\tan ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+4 b}+a} \sqrt[4]{a x^4-b}}\right)}{\left(\sqrt{a^2+4 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}-\frac{\tanh ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{a x^4-b}}\right)}{\left(a-\sqrt{a^2+4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}+\frac{\tanh ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+4 b}+a} \sqrt[4]{a x^4-b}}\right)}{\left(\sqrt{a^2+4 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}}{\sqrt{a^2+4 b}}","-\frac{\text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4 a+2 a^2-b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-a \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+a \log (x)}{3 \text{$\#$1} a-2 \text{$\#$1}^5}\&\right]}{4 b}",1,"-((-(ArcTan[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a - Sqrt[a^2 + 4*b])^(1/4)*(-b + a*x^4)^(1/4))]/((a - Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4))) + ArcTan[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a + Sqrt[a^2 + 4*b])^(1/4)*(-b + a*x^4)^(1/4))]/((a + Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)) - ArcTanh[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a - Sqrt[a^2 + 4*b])^(1/4)*(-b + a*x^4)^(1/4))]/((a - Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)) + ArcTanh[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a + Sqrt[a^2 + 4*b])^(1/4)*(-b + a*x^4)^(1/4))]/((a + Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)))/Sqrt[a^2 + 4*b])","B",1
1548,1,65,107,0.0229359,"\int x^6 \left(-1+x^3\right)^{2/3} \, dx","Integrate[x^6*(-1 + x^3)^(2/3),x]","\frac{x \left(x^3-1\right)^{2/3} \left(2 \, _2F_1\left(-\frac{2}{3},\frac{1}{3};\frac{4}{3};x^3\right)+\left(1-x^3\right)^{2/3} \left(3 x^6-x^3-2\right)\right)}{27 \left(1-x^3\right)^{2/3}}","\frac{4}{243} \log \left(\sqrt[3]{x^3-1}-x\right)-\frac{4 \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-1}+x}\right)}{81 \sqrt{3}}-\frac{2}{243} \log \left(\sqrt[3]{x^3-1} x+\left(x^3-1\right)^{2/3}+x^2\right)+\frac{1}{81} \left(x^3-1\right)^{2/3} \left(9 x^7-3 x^4-4 x\right)",1,"(x*(-1 + x^3)^(2/3)*((1 - x^3)^(2/3)*(-2 - x^3 + 3*x^6) + 2*Hypergeometric2F1[-2/3, 1/3, 4/3, x^3]))/(27*(1 - x^3)^(2/3))","C",1
1549,1,43,107,0.0163261,"\int x^6 \left(1+x^3\right)^{2/3} \, dx","Integrate[x^6*(1 + x^3)^(2/3),x]","\frac{1}{27} x \left(2 \, _2F_1\left(-\frac{2}{3},\frac{1}{3};\frac{4}{3};-x^3\right)+\left(x^3+1\right)^{2/3} \left(3 x^6+x^3-2\right)\right)","-\frac{4}{243} \log \left(\sqrt[3]{x^3+1}-x\right)+\frac{4 \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+1}+x}\right)}{81 \sqrt{3}}+\frac{2}{243} \log \left(\sqrt[3]{x^3+1} x+\left(x^3+1\right)^{2/3}+x^2\right)+\frac{1}{81} \left(x^3+1\right)^{2/3} \left(9 x^7+3 x^4-4 x\right)",1,"(x*((1 + x^3)^(2/3)*(-2 + x^3 + 3*x^6) + 2*Hypergeometric2F1[-2/3, 1/3, 4/3, -x^3]))/27","C",1
1550,1,61,107,0.0230709,"\int x^4 \sqrt[3]{x+x^3} \, dx","Integrate[x^4*(x + x^3)^(1/3),x]","\frac{x \sqrt[3]{x^3+x} \left(5 \, _2F_1\left(-\frac{1}{3},\frac{2}{3};\frac{5}{3};-x^2\right)+\sqrt[3]{x^2+1} \left(6 x^4+x^2-5\right)\right)}{36 \sqrt[3]{x^2+1}}","-\frac{5}{162} \log \left(\sqrt[3]{x^3+x}-x\right)-\frac{5 \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+x}+x}\right)}{54 \sqrt{3}}+\frac{1}{108} \sqrt[3]{x^3+x} \left(18 x^5+3 x^3-5 x\right)+\frac{5}{324} \log \left(\sqrt[3]{x^3+x} x+\left(x^3+x\right)^{2/3}+x^2\right)",1,"(x*(x + x^3)^(1/3)*((1 + x^2)^(1/3)*(-5 + x^2 + 6*x^4) + 5*Hypergeometric2F1[-1/3, 2/3, 5/3, -x^2]))/(36*(1 + x^2)^(1/3))","C",1
1551,0,0,107,4.7516832,"\int \frac{x^2 \left(3 a b^2-2 b (2 a+b) x+(a+2 b) x^2\right)}{\left(x (-a+x) (-b+x)^2\right)^{3/4} \left(a b^2-b (2 a+b) x+(a+2 b) x^2+(-1+d) x^3\right)} \, dx","Integrate[(x^2*(3*a*b^2 - 2*b*(2*a + b)*x + (a + 2*b)*x^2))/((x*(-a + x)*(-b + x)^2)^(3/4)*(a*b^2 - b*(2*a + b)*x + (a + 2*b)*x^2 + (-1 + d)*x^3)),x]","\int \frac{x^2 \left(3 a b^2-2 b (2 a+b) x+(a+2 b) x^2\right)}{\left(x (-a+x) (-b+x)^2\right)^{3/4} \left(a b^2-b (2 a+b) x+(a+2 b) x^2+(-1+d) x^3\right)} \, dx","\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}}\right)}{d^{3/4}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}}\right)}{d^{3/4}}",1,"Integrate[(x^2*(3*a*b^2 - 2*b*(2*a + b)*x + (a + 2*b)*x^2))/((x*(-a + x)*(-b + x)^2)^(3/4)*(a*b^2 - b*(2*a + b)*x + (a + 2*b)*x^2 + (-1 + d)*x^3)), x]","F",-1
1552,1,35,107,0.0106113,"\int \frac{\sqrt[3]{1+x^4} \left(3+x^4\right)}{x^{17}} \, dx","Integrate[((1 + x^4)^(1/3)*(3 + x^4))/x^17,x]","-\frac{3 \left(x^4+1\right)^{4/3} \left(x^{16} \, _2F_1\left(\frac{4}{3},4;\frac{7}{3};x^4+1\right)+1\right)}{16 x^{16}}","-\frac{5}{324} \log \left(\sqrt[3]{x^4+1}-1\right)+\frac{5}{648} \log \left(\left(x^4+1\right)^{2/3}+\sqrt[3]{x^4+1}+1\right)+\frac{5 \tan ^{-1}\left(\frac{2 \sqrt[3]{x^4+1}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{108 \sqrt{3}}+\frac{\sqrt[3]{x^4+1} \left(-10 x^{12}+6 x^8-45 x^4-81\right)}{432 x^{16}}",1,"(-3*(1 + x^4)^(4/3)*(1 + x^16*Hypergeometric2F1[4/3, 4, 7/3, 1 + x^4]))/(16*x^16)","C",1
1553,1,198,107,0.2538461,"\int \frac{\left(-2+x^2\right) \sqrt[3]{x+x^3}}{x^2 \left(4-2 x^2+x^4\right)} \, dx","Integrate[((-2 + x^2)*(x + x^3)^(1/3))/(x^2*(4 - 2*x^2 + x^4)),x]","\frac{\sqrt[3]{x^3+x} \left(\left(3+i \sqrt{3}\right) \sqrt[3]{\frac{-i x^2+\sqrt{3}+i}{\sqrt{3}+i}} \, _2F_1\left(-\frac{1}{3},-\frac{1}{3};\frac{2}{3};-\frac{\left(2 i+\sqrt{3}\right) x^2}{-i x^2+\sqrt{3}+i}\right)+\left(3-i \sqrt{3}\right) \sqrt[3]{\frac{i x^2+\sqrt{3}-i}{\sqrt{3}-i}} \, _2F_1\left(-\frac{1}{3},-\frac{1}{3};\frac{2}{3};-\frac{\left(-2 i+\sqrt{3}\right) x^2}{i x^2+\sqrt{3}-i}\right)\right)}{8 x \sqrt[3]{x^2+1}}","\frac{3 \sqrt[3]{x^3+x}}{4 x}-\frac{1}{8} \text{RootSum}\left[4 \text{$\#$1}^6-10 \text{$\#$1}^3+7\&,\frac{-4 \text{$\#$1}^3 \log \left(\sqrt[3]{x^3+x}-\text{$\#$1} x\right)+4 \text{$\#$1}^3 \log (x)+7 \log \left(\sqrt[3]{x^3+x}-\text{$\#$1} x\right)-7 \log (x)}{4 \text{$\#$1}^5-5 \text{$\#$1}^2}\&\right]",1,"((x + x^3)^(1/3)*((3 + I*Sqrt[3])*((I + Sqrt[3] - I*x^2)/(I + Sqrt[3]))^(1/3)*Hypergeometric2F1[-1/3, -1/3, 2/3, -(((2*I + Sqrt[3])*x^2)/(I + Sqrt[3] - I*x^2))] + (3 - I*Sqrt[3])*((-I + Sqrt[3] + I*x^2)/(-I + Sqrt[3]))^(1/3)*Hypergeometric2F1[-1/3, -1/3, 2/3, -(((-2*I + Sqrt[3])*x^2)/(-I + Sqrt[3] + I*x^2))]))/(8*x*(1 + x^2)^(1/3))","C",0
1554,1,198,107,0.0488645,"\int \frac{\left(-2+x^2\right) \sqrt[3]{x+x^3}}{x^2 \left(4-2 x^2+x^4\right)} \, dx","Integrate[((-2 + x^2)*(x + x^3)^(1/3))/(x^2*(4 - 2*x^2 + x^4)),x]","\frac{\sqrt[3]{x^3+x} \left(\left(3+i \sqrt{3}\right) \sqrt[3]{\frac{-i x^2+\sqrt{3}+i}{\sqrt{3}+i}} \, _2F_1\left(-\frac{1}{3},-\frac{1}{3};\frac{2}{3};-\frac{\left(2 i+\sqrt{3}\right) x^2}{-i x^2+\sqrt{3}+i}\right)+\left(3-i \sqrt{3}\right) \sqrt[3]{\frac{i x^2+\sqrt{3}-i}{\sqrt{3}-i}} \, _2F_1\left(-\frac{1}{3},-\frac{1}{3};\frac{2}{3};-\frac{\left(-2 i+\sqrt{3}\right) x^2}{i x^2+\sqrt{3}-i}\right)\right)}{8 x \sqrt[3]{x^2+1}}","\frac{3 \sqrt[3]{x^3+x}}{4 x}-\frac{1}{8} \text{RootSum}\left[4 \text{$\#$1}^6-10 \text{$\#$1}^3+7\&,\frac{-4 \text{$\#$1}^3 \log \left(\sqrt[3]{x^3+x}-\text{$\#$1} x\right)+4 \text{$\#$1}^3 \log (x)+7 \log \left(\sqrt[3]{x^3+x}-\text{$\#$1} x\right)-7 \log (x)}{4 \text{$\#$1}^5-5 \text{$\#$1}^2}\&\right]",1,"((x + x^3)^(1/3)*((3 + I*Sqrt[3])*((I + Sqrt[3] - I*x^2)/(I + Sqrt[3]))^(1/3)*Hypergeometric2F1[-1/3, -1/3, 2/3, -(((2*I + Sqrt[3])*x^2)/(I + Sqrt[3] - I*x^2))] + (3 - I*Sqrt[3])*((-I + Sqrt[3] + I*x^2)/(-I + Sqrt[3]))^(1/3)*Hypergeometric2F1[-1/3, -1/3, 2/3, -(((-2*I + Sqrt[3])*x^2)/(-I + Sqrt[3] + I*x^2))]))/(8*x*(1 + x^2)^(1/3))","C",0
1555,1,92,107,0.5551926,"\int \frac{1}{\left(-1+x^4\right)^2 \sqrt[4]{-x^2+x^4}} \, dx","Integrate[1/((-1 + x^4)^2*(-x^2 + x^4)^(1/4)),x]","\frac{x^3 \left(75 \sqrt[4]{1-x^2} \left(x^4-1\right) \, _2F_1\left(\frac{1}{4},\frac{1}{4};\frac{5}{4};\frac{2 x^2}{x^2+1}\right)+\sqrt[4]{x^2+1} \left(67 x^4+2 x^2-85\right)\right)}{80 \left(x^2 \left(x^2-1\right)\right)^{5/4} \left(x^2+1\right)^{5/4}}","\frac{\left(x^4-x^2\right)^{3/4} \left(67 x^4+2 x^2-85\right)}{80 x \left(x^2-1\right)^2 \left(x^2+1\right)}+\frac{15 \tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-x^2}}\right)}{32 \sqrt[4]{2}}+\frac{15 \tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-x^2}}\right)}{32 \sqrt[4]{2}}",1,"(x^3*((1 + x^2)^(1/4)*(-85 + 2*x^2 + 67*x^4) + 75*(1 - x^2)^(1/4)*(-1 + x^4)*Hypergeometric2F1[1/4, 1/4, 5/4, (2*x^2)/(1 + x^2)]))/(80*(x^2*(-1 + x^2))^(5/4)*(1 + x^2)^(5/4))","C",0
1556,1,767,107,1.7052007,"\int \frac{\left(-1+x^2\right) \left(1-x+x^2-x^3+x^4\right)}{\left(1-x+x^2\right)^2 \left(1+x+x^2\right) \sqrt{1+3 x^2+x^4}} \, dx","Integrate[((-1 + x^2)*(1 - x + x^2 - x^3 + x^4))/((1 - x + x^2)^2*(1 + x + x^2)*Sqrt[1 + 3*x^2 + x^4]),x]","\frac{-40 i \left(1+\sqrt[3]{-1}\right) \left(x^2-x+1\right) \sqrt{2 x^2-\sqrt{5}+3} \sqrt{2 x^2+\sqrt{5}+3} F\left(i \sinh ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} x\right)|\frac{7}{2}+\frac{3 \sqrt{5}}{2}\right)+40 (-1)^{5/6} \left(x^2-x+1\right) \sqrt{2 x^2-\sqrt{5}+3} \sqrt{2 x^2+\sqrt{5}+3} \Pi \left(\frac{1}{2} \sqrt[3]{-1} \left(3+\sqrt{5}\right);i \sinh ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} x\right)|\frac{1}{2} \left(7+3 \sqrt{5}\right)\right)+40 i \left(x^2-x+1\right) \sqrt{2 x^2-\sqrt{5}+3} \sqrt{2 x^2+\sqrt{5}+3} \Pi \left(\frac{1}{2} \sqrt[3]{-1} \left(3+\sqrt{5}\right);i \sinh ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} x\right)|\frac{1}{2} \left(7+3 \sqrt{5}\right)\right)+40 (-1)^{5/6} \left(x^2-x+1\right) \sqrt{2 x^2-\sqrt{5}+3} \sqrt{2 x^2+\sqrt{5}+3} \Pi \left(-\frac{1}{2} (-1)^{2/3} \left(3+\sqrt{5}\right);i \sinh ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} x\right)|\frac{1}{2} \left(7+3 \sqrt{5}\right)\right)+40 i \left(x^2-x+1\right) \sqrt{2 x^2-\sqrt{5}+3} \sqrt{2 x^2+\sqrt{5}+3} \Pi \left(-\frac{1}{2} (-1)^{2/3} \left(3+\sqrt{5}\right);i \sinh ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} x\right)|\frac{1}{2} \left(7+3 \sqrt{5}\right)\right)+8 \left(1+\sqrt[3]{-1}\right) \sqrt{6-2 \sqrt{5}} \left(x^4+3 x^2+1\right)+3 \left(1+\sqrt[3]{-1}\right) \sqrt{6-2 \sqrt{5}} \left(x^2-x+1\right) \sqrt{x^4+3 x^2+1} \left(\left(1-i \sqrt{3}\right)^{3/2} \tan ^{-1}\left(\frac{\left(4-2 i \sqrt{3}\right) x^2-3 i \sqrt{3}+1}{4 \sqrt{1+i \sqrt{3}} \sqrt{x^4+3 x^2+1}}\right)+\left(1+i \sqrt{3}\right)^{3/2} \tan ^{-1}\left(\frac{\left(4+2 i \sqrt{3}\right) x^2+3 i \sqrt{3}+1}{4 \sqrt{1-i \sqrt{3}} \sqrt{x^4+3 x^2+1}}\right)\right)}{32 \left(1+\sqrt[3]{-1}\right) \sqrt{6-2 \sqrt{5}} \left(x^2-x+1\right) \sqrt{x^4+3 x^2+1}}","\frac{\sqrt{x^4+3 x^2+1}}{4 \left(x^2-x+1\right)}-\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x}{x^2+\sqrt{x^4+3 x^2+1}-x+1}\right)-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{x^2+\sqrt{x^4+3 x^2+1}+x+1}\right)}{2 \sqrt{2}}",1,"(8*(1 + (-1)^(1/3))*Sqrt[6 - 2*Sqrt[5]]*(1 + 3*x^2 + x^4) + 3*(1 + (-1)^(1/3))*Sqrt[6 - 2*Sqrt[5]]*(1 - x + x^2)*Sqrt[1 + 3*x^2 + x^4]*((1 - I*Sqrt[3])^(3/2)*ArcTan[(1 - (3*I)*Sqrt[3] + (4 - (2*I)*Sqrt[3])*x^2)/(4*Sqrt[1 + I*Sqrt[3]]*Sqrt[1 + 3*x^2 + x^4])] + (1 + I*Sqrt[3])^(3/2)*ArcTan[(1 + (3*I)*Sqrt[3] + (4 + (2*I)*Sqrt[3])*x^2)/(4*Sqrt[1 - I*Sqrt[3]]*Sqrt[1 + 3*x^2 + x^4])]) - (40*I)*(1 + (-1)^(1/3))*(1 - x + x^2)*Sqrt[3 - Sqrt[5] + 2*x^2]*Sqrt[3 + Sqrt[5] + 2*x^2]*EllipticF[I*ArcSinh[Sqrt[2/(3 + Sqrt[5])]*x], 7/2 + (3*Sqrt[5])/2] + (40*I)*(1 - x + x^2)*Sqrt[3 - Sqrt[5] + 2*x^2]*Sqrt[3 + Sqrt[5] + 2*x^2]*EllipticPi[((-1)^(1/3)*(3 + Sqrt[5]))/2, I*ArcSinh[Sqrt[2/(3 + Sqrt[5])]*x], (7 + 3*Sqrt[5])/2] + 40*(-1)^(5/6)*(1 - x + x^2)*Sqrt[3 - Sqrt[5] + 2*x^2]*Sqrt[3 + Sqrt[5] + 2*x^2]*EllipticPi[((-1)^(1/3)*(3 + Sqrt[5]))/2, I*ArcSinh[Sqrt[2/(3 + Sqrt[5])]*x], (7 + 3*Sqrt[5])/2] + (40*I)*(1 - x + x^2)*Sqrt[3 - Sqrt[5] + 2*x^2]*Sqrt[3 + Sqrt[5] + 2*x^2]*EllipticPi[-1/2*((-1)^(2/3)*(3 + Sqrt[5])), I*ArcSinh[Sqrt[2/(3 + Sqrt[5])]*x], (7 + 3*Sqrt[5])/2] + 40*(-1)^(5/6)*(1 - x + x^2)*Sqrt[3 - Sqrt[5] + 2*x^2]*Sqrt[3 + Sqrt[5] + 2*x^2]*EllipticPi[-1/2*((-1)^(2/3)*(3 + Sqrt[5])), I*ArcSinh[Sqrt[2/(3 + Sqrt[5])]*x], (7 + 3*Sqrt[5])/2])/(32*(1 + (-1)^(1/3))*Sqrt[6 - 2*Sqrt[5]]*(1 - x + x^2)*Sqrt[1 + 3*x^2 + x^4])","C",0
1557,1,69,107,0.0774152,"\int \frac{\left(b+a x^3\right) \left(b+2 a x^3\right)}{x^6 \sqrt[4]{b x+a x^4}} \, dx","Integrate[((b + a*x^3)*(b + 2*a*x^3))/(x^6*(b*x + a*x^4)^(1/4)),x]","\frac{4 \left(x \left(a x^3+b\right)\right)^{3/4} \left(-\frac{14 a x^3 \, _2F_1\left(-\frac{3}{4},-\frac{3}{4};\frac{1}{4};-\frac{a x^3}{b}\right)}{\left(\frac{a x^3}{b}+1\right)^{3/4}}-3 \left(a x^3+b\right)\right)}{63 x^6}","\frac{4}{3} a^{7/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} \left(a x^4+b x\right)^{3/4}}{a x^3+b}\right)+\frac{4}{3} a^{7/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \left(a x^4+b x\right)^{3/4}}{a x^3+b}\right)-\frac{4 \left(17 a x^3+3 b\right) \left(a x^4+b x\right)^{3/4}}{63 x^6}",1,"(4*(x*(b + a*x^3))^(3/4)*(-3*(b + a*x^3) - (14*a*x^3*Hypergeometric2F1[-3/4, -3/4, 1/4, -((a*x^3)/b)])/(1 + (a*x^3)/b)^(3/4)))/(63*x^6)","C",1
1558,1,562,107,3.3995864,"\int \frac{-b^3+a^3 x^3}{\left(b^3+a^3 x^3\right) \sqrt{b^4+a^4 x^4}} \, dx","Integrate[(-b^3 + a^3*x^3)/((b^3 + a^3*x^3)*Sqrt[b^4 + a^4*x^4]),x]","\frac{a^3 \left(18 i a \sqrt[4]{a^4} b \sqrt{\frac{a^4 x^4}{b^4}+1} F\left(\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)-\frac{3}{2} \left(8 i a \sqrt[4]{a^4} b \sqrt{\frac{a^4 x^4}{b^4}+1} \Pi \left(-\frac{i}{2}-\frac{\sqrt{3}}{2};\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)+8 i a \sqrt[4]{a^4} b \sqrt{\frac{a^4 x^4}{b^4}+1} \Pi \left(\frac{1}{2} \left(-i+\sqrt{3}\right);\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)+\sqrt{2} \sqrt{\frac{i a^2}{b^2}} \left((4+4 i) a b \sqrt[4]{b^4} \sqrt{\frac{a^4 x^4}{b^4}+1} \Pi \left(\frac{i \sqrt{a^4} \sqrt{b^4}}{a^2 b^2};\left.i \sinh ^{-1}\left(\frac{(1+i) \sqrt[4]{a^4} x}{\sqrt{2} \sqrt[4]{b^4}}\right)\right|-1\right)+\sqrt[4]{a^4} \sqrt{a^4 x^4+b^4} \left(\sqrt{1+i \sqrt{3}} \left(\sqrt{3}-i\right) \tan ^{-1}\left(\frac{\left(\sqrt{3}+i\right) b^2-2 i a^2 x^2}{\sqrt{2-2 i \sqrt{3}} \sqrt{a^4 x^4+b^4}}\right)+\sqrt{1-i \sqrt{3}} \left(\sqrt{3}+i\right) \tan ^{-1}\left(\frac{2 i a^2 x^2+\left(\sqrt{3}-i\right) b^2}{\sqrt{2+2 i \sqrt{3}} \sqrt{a^4 x^4+b^4}}\right)+2 \tanh ^{-1}\left(\frac{a^2 x^2+b^2}{\sqrt{2} \sqrt{a^4 x^4+b^4}}\right)\right)\right)\right)\right)}{18 \sqrt[4]{a^4} b^5 \left(\frac{i a^2}{b^2}\right)^{5/2} \sqrt{a^4 x^4+b^4}}","-\frac{4 \tan ^{-1}\left(\frac{a b x}{\sqrt{a^4 x^4+b^4}+a^2 x^2-a b x+b^2}\right)}{3 a b}-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} a b x}{\sqrt{a^4 x^4+b^4}+a^2 x^2+2 a b x+b^2}\right)}{3 a b}",1,"(a^3*((18*I)*a*(a^4)^(1/4)*b*Sqrt[1 + (a^4*x^4)/b^4]*EllipticF[I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] - (3*((8*I)*a*(a^4)^(1/4)*b*Sqrt[1 + (a^4*x^4)/b^4]*EllipticPi[-1/2*I - Sqrt[3]/2, I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] + (8*I)*a*(a^4)^(1/4)*b*Sqrt[1 + (a^4*x^4)/b^4]*EllipticPi[(-I + Sqrt[3])/2, I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] + Sqrt[2]*Sqrt[(I*a^2)/b^2]*((a^4)^(1/4)*Sqrt[b^4 + a^4*x^4]*(Sqrt[1 + I*Sqrt[3]]*(-I + Sqrt[3])*ArcTan[((I + Sqrt[3])*b^2 - (2*I)*a^2*x^2)/(Sqrt[2 - (2*I)*Sqrt[3]]*Sqrt[b^4 + a^4*x^4])] + Sqrt[1 - I*Sqrt[3]]*(I + Sqrt[3])*ArcTan[((-I + Sqrt[3])*b^2 + (2*I)*a^2*x^2)/(Sqrt[2 + (2*I)*Sqrt[3]]*Sqrt[b^4 + a^4*x^4])] + 2*ArcTanh[(b^2 + a^2*x^2)/(Sqrt[2]*Sqrt[b^4 + a^4*x^4])]) + (4 + 4*I)*a*b*(b^4)^(1/4)*Sqrt[1 + (a^4*x^4)/b^4]*EllipticPi[(I*Sqrt[a^4]*Sqrt[b^4])/(a^2*b^2), I*ArcSinh[((1 + I)*(a^4)^(1/4)*x)/(Sqrt[2]*(b^4)^(1/4))], -1])))/2))/(18*(a^4)^(1/4)*((I*a^2)/b^2)^(5/2)*b^5*Sqrt[b^4 + a^4*x^4])","C",1
1559,0,0,107,0.9412791,"\int \frac{x^4 \left(-2 b+a x^2\right)}{\left(-b+a x^2\right)^2 \sqrt[4]{-b+a x^2+c x^4}} \, dx","Integrate[(x^4*(-2*b + a*x^2))/((-b + a*x^2)^2*(-b + a*x^2 + c*x^4)^(1/4)),x]","\int \frac{x^4 \left(-2 b+a x^2\right)}{\left(-b+a x^2\right)^2 \sqrt[4]{-b+a x^2+c x^4}} \, dx","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a x^2-b+c x^4}}\right)}{4 c^{5/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a x^2-b+c x^4}}\right)}{4 c^{5/4}}-\frac{x \left(a x^2-b+c x^4\right)^{3/4}}{2 c \left(b-a x^2\right)}",1,"Integrate[(x^4*(-2*b + a*x^2))/((-b + a*x^2)^2*(-b + a*x^2 + c*x^4)^(1/4)), x]","F",-1
1560,0,0,107,0.5329979,"\int \frac{\left(-1-2 x+x^2\right) \left(-1+2 x+x^2\right)}{\left(1-x+2 x^2+x^3+x^4\right) \sqrt[3]{-x+x^5}} \, dx","Integrate[((-1 - 2*x + x^2)*(-1 + 2*x + x^2))/((1 - x + 2*x^2 + x^3 + x^4)*(-x + x^5)^(1/3)),x]","\int \frac{\left(-1-2 x+x^2\right) \left(-1+2 x+x^2\right)}{\left(1-x+2 x^2+x^3+x^4\right) \sqrt[3]{-x+x^5}} \, dx","\log \left(\sqrt[3]{x^5-x}+x^2+1\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x^5-x}}{\sqrt[3]{x^5-x}-2 x^2-2}\right)-\frac{1}{2} \log \left(\left(x^5-x\right)^{2/3}+x^4+2 x^2+\left(-x^2-1\right) \sqrt[3]{x^5-x}+1\right)",1,"Integrate[((-1 - 2*x + x^2)*(-1 + 2*x + x^2))/((1 - x + 2*x^2 + x^3 + x^4)*(-x + x^5)^(1/3)), x]","F",-1
1561,1,72,107,0.0470959,"\int \frac{-b-a x^3+x^6}{x^6 \sqrt[4]{b x+a x^4}} \, dx","Integrate[(-b - a*x^3 + x^6)/(x^6*(b*x + a*x^4)^(1/4)),x]","\frac{4 \left(7 b x^6 \sqrt[4]{\frac{a x^3}{b}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{4};\frac{5}{4};-\frac{a x^3}{b}\right)+\left(a x^3+b\right)^2\right)}{21 b x^5 \sqrt[4]{x \left(a x^3+b\right)}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \left(a x^4+b x\right)^{3/4}}{a x^3+b}\right)}{3 \sqrt[4]{a}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{a} \left(a x^4+b x\right)^{3/4}}{a x^3+b}\right)}{3 \sqrt[4]{a}}+\frac{4 \left(a x^4+b x\right)^{3/4} \left(a x^3+b\right)}{21 b x^6}",1,"(4*((b + a*x^3)^2 + 7*b*x^6*(1 + (a*x^3)/b)^(1/4)*Hypergeometric2F1[1/4, 1/4, 5/4, -((a*x^3)/b)]))/(21*b*x^5*(x*(b + a*x^3))^(1/4))","C",1
1562,1,240,107,0.3096239,"\int \frac{1}{\sqrt[3]{b^2 x^2+a^3 x^3} \left(-b+a^6 x^6\right)} \, dx","Integrate[1/((b^2*x^2 + a^3*x^3)^(1/3)*(-b + a^6*x^6)),x]","-\frac{x \left(\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2-b^{11/6}\right) x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2+b^{11/6}\right) x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2-\sqrt[3]{-1} b^{11/6}\right) x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2+\sqrt[3]{-1} b^{11/6}\right) x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2-(-1)^{2/3} b^{11/6}\right) x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2+(-1)^{2/3} b^{11/6}\right) x}{x a^3+b^2}\right)\right)}{2 b \sqrt[3]{x^2 \left(a^3 x+b^2\right)}}","\frac{\text{RootSum}\left[\text{$\#$1}^{18}-6 \text{$\#$1}^{15} a^3+15 \text{$\#$1}^{12} a^6-20 \text{$\#$1}^9 a^9+15 \text{$\#$1}^6 a^{12}-6 \text{$\#$1}^3 a^{15}+a^{18}-a^6 b^{11}\&,\frac{\log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{6 b}",1,"-1/2*(x*(Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 - b^(11/6))*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 + b^(11/6))*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 - (-1)^(1/3)*b^(11/6))*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 + (-1)^(1/3)*b^(11/6))*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 - (-1)^(2/3)*b^(11/6))*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 + (-1)^(2/3)*b^(11/6))*x)/(b^2 + a^3*x)]))/(b*(x^2*(b^2 + a^3*x))^(1/3))","B",1
1563,1,240,107,0.1051801,"\int \frac{1}{\sqrt[3]{b^2 x^2+a^3 x^3} \left(-b+a^6 x^6\right)} \, dx","Integrate[1/((b^2*x^2 + a^3*x^3)^(1/3)*(-b + a^6*x^6)),x]","-\frac{x \left(\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2-b^{11/6}\right) x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2+b^{11/6}\right) x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2-\sqrt[3]{-1} b^{11/6}\right) x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2+\sqrt[3]{-1} b^{11/6}\right) x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2-(-1)^{2/3} b^{11/6}\right) x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2+(-1)^{2/3} b^{11/6}\right) x}{x a^3+b^2}\right)\right)}{2 b \sqrt[3]{x^2 \left(a^3 x+b^2\right)}}","\frac{\text{RootSum}\left[\text{$\#$1}^{18}-6 \text{$\#$1}^{15} a^3+15 \text{$\#$1}^{12} a^6-20 \text{$\#$1}^9 a^9+15 \text{$\#$1}^6 a^{12}-6 \text{$\#$1}^3 a^{15}+a^{18}-a^6 b^{11}\&,\frac{\log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{6 b}",1,"-1/2*(x*(Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 - b^(11/6))*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 + b^(11/6))*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 - (-1)^(1/3)*b^(11/6))*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 + (-1)^(1/3)*b^(11/6))*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 - (-1)^(2/3)*b^(11/6))*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 + (-1)^(2/3)*b^(11/6))*x)/(b^2 + a^3*x)]))/(b*(x^2*(b^2 + a^3*x))^(1/3))","B",1
1564,1,271,107,0.4101861,"\int \frac{1}{\sqrt[3]{b^2 x^2+a^3 x^3} \left(-b+2 a^6 x^6\right)} \, dx","Integrate[1/((b^2*x^2 + a^3*x^3)^(1/3)*(-b + 2*a^6*x^6)),x]","-\frac{x \left(\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2-\sqrt[6]{2} b^{11/6}\right) x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2+\sqrt[6]{2} b^{11/6}\right) x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2-\sqrt[3]{-1} \sqrt[6]{2} b^{11/6}\right) x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2+\sqrt[3]{-1} \sqrt[6]{2} b^{11/6}\right) x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2-(-1)^{2/3} \sqrt[6]{2} b^{11/6}\right) x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2+(-1)^{2/3} \sqrt[6]{2} b^{11/6}\right) x}{x a^3+b^2}\right)\right)}{2 b \sqrt[3]{x^2 \left(a^3 x+b^2\right)}}","\frac{\text{RootSum}\left[\text{$\#$1}^{18}-6 \text{$\#$1}^{15} a^3+15 \text{$\#$1}^{12} a^6-20 \text{$\#$1}^9 a^9+15 \text{$\#$1}^6 a^{12}-6 \text{$\#$1}^3 a^{15}+a^{18}-2 a^6 b^{11}\&,\frac{\log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{6 b}",1,"-1/2*(x*(Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 - 2^(1/6)*b^(11/6))*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 + 2^(1/6)*b^(11/6))*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 - (-1)^(1/3)*2^(1/6)*b^(11/6))*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 + (-1)^(1/3)*2^(1/6)*b^(11/6))*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 - (-1)^(2/3)*2^(1/6)*b^(11/6))*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 + (-1)^(2/3)*2^(1/6)*b^(11/6))*x)/(b^2 + a^3*x)]))/(b*(x^2*(b^2 + a^3*x))^(1/3))","B",1
1565,1,271,107,0.1461418,"\int \frac{1}{\sqrt[3]{b^2 x^2+a^3 x^3} \left(-b+2 a^6 x^6\right)} \, dx","Integrate[1/((b^2*x^2 + a^3*x^3)^(1/3)*(-b + 2*a^6*x^6)),x]","-\frac{x \left(\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2-\sqrt[6]{2} b^{11/6}\right) x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2+\sqrt[6]{2} b^{11/6}\right) x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2-\sqrt[3]{-1} \sqrt[6]{2} b^{11/6}\right) x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2+\sqrt[3]{-1} \sqrt[6]{2} b^{11/6}\right) x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2-(-1)^{2/3} \sqrt[6]{2} b^{11/6}\right) x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2+(-1)^{2/3} \sqrt[6]{2} b^{11/6}\right) x}{x a^3+b^2}\right)\right)}{2 b \sqrt[3]{x^2 \left(a^3 x+b^2\right)}}","\frac{\text{RootSum}\left[\text{$\#$1}^{18}-6 \text{$\#$1}^{15} a^3+15 \text{$\#$1}^{12} a^6-20 \text{$\#$1}^9 a^9+15 \text{$\#$1}^6 a^{12}-6 \text{$\#$1}^3 a^{15}+a^{18}-2 a^6 b^{11}\&,\frac{\log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{6 b}",1,"-1/2*(x*(Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 - 2^(1/6)*b^(11/6))*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 + 2^(1/6)*b^(11/6))*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 - (-1)^(1/3)*2^(1/6)*b^(11/6))*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 + (-1)^(1/3)*2^(1/6)*b^(11/6))*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 - (-1)^(2/3)*2^(1/6)*b^(11/6))*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 + (-1)^(2/3)*2^(1/6)*b^(11/6))*x)/(b^2 + a^3*x)]))/(b*(x^2*(b^2 + a^3*x))^(1/3))","B",1
1566,1,283,107,0.5161964,"\int \frac{1}{\sqrt[3]{b^2 x^2+a^3 x^3} \left(b+2 a^6 x^6\right)} \, dx","Integrate[1/((b^2*x^2 + a^3*x^3)^(1/3)*(b + 2*a^6*x^6)),x]","\frac{x \left(\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2+\sqrt[6]{2} (-b)^{11/6}\right) x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2+\sqrt[3]{-1} \sqrt[6]{2} (-b)^{11/6}\right) x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2+(-1)^{2/3} \sqrt[6]{2} (-b)^{11/6}\right) x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2+\sqrt[6]{2} (-b)^{5/6} b\right) x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2+\sqrt[3]{-1} \sqrt[6]{2} (-b)^{5/6} b\right) x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2+(-1)^{2/3} \sqrt[6]{2} (-b)^{5/6} b\right) x}{x a^3+b^2}\right)\right)}{2 b \sqrt[3]{x^2 \left(a^3 x+b^2\right)}}","-\frac{\text{RootSum}\left[\text{$\#$1}^{18}-6 \text{$\#$1}^{15} a^3+15 \text{$\#$1}^{12} a^6-20 \text{$\#$1}^9 a^9+15 \text{$\#$1}^6 a^{12}-6 \text{$\#$1}^3 a^{15}+a^{18}+2 a^6 b^{11}\&,\frac{\log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{6 b}",1,"(x*(Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 + 2^(1/6)*(-b)^(11/6))*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 + (-1)^(1/3)*2^(1/6)*(-b)^(11/6))*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 + (-1)^(2/3)*2^(1/6)*(-b)^(11/6))*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 + 2^(1/6)*(-b)^(5/6)*b)*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 + (-1)^(1/3)*2^(1/6)*(-b)^(5/6)*b)*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 + (-1)^(2/3)*2^(1/6)*(-b)^(5/6)*b)*x)/(b^2 + a^3*x)]))/(2*b*(x^2*(b^2 + a^3*x))^(1/3))","B",1
1567,1,283,107,0.1398808,"\int \frac{1}{\sqrt[3]{b^2 x^2+a^3 x^3} \left(b+2 a^6 x^6\right)} \, dx","Integrate[1/((b^2*x^2 + a^3*x^3)^(1/3)*(b + 2*a^6*x^6)),x]","\frac{x \left(\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2+\sqrt[6]{2} (-b)^{11/6}\right) x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2+\sqrt[3]{-1} \sqrt[6]{2} (-b)^{11/6}\right) x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2+(-1)^{2/3} \sqrt[6]{2} (-b)^{11/6}\right) x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2+\sqrt[6]{2} (-b)^{5/6} b\right) x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2+\sqrt[3]{-1} \sqrt[6]{2} (-b)^{5/6} b\right) x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2+(-1)^{2/3} \sqrt[6]{2} (-b)^{5/6} b\right) x}{x a^3+b^2}\right)\right)}{2 b \sqrt[3]{x^2 \left(a^3 x+b^2\right)}}","-\frac{\text{RootSum}\left[\text{$\#$1}^{18}-6 \text{$\#$1}^{15} a^3+15 \text{$\#$1}^{12} a^6-20 \text{$\#$1}^9 a^9+15 \text{$\#$1}^6 a^{12}-6 \text{$\#$1}^3 a^{15}+a^{18}+2 a^6 b^{11}\&,\frac{\log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{6 b}",1,"(x*(Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 + 2^(1/6)*(-b)^(11/6))*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 + (-1)^(1/3)*2^(1/6)*(-b)^(11/6))*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 + (-1)^(2/3)*2^(1/6)*(-b)^(11/6))*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 + 2^(1/6)*(-b)^(5/6)*b)*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 + (-1)^(1/3)*2^(1/6)*(-b)^(5/6)*b)*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 + (-1)^(2/3)*2^(1/6)*(-b)^(5/6)*b)*x)/(b^2 + a^3*x)]))/(2*b*(x^2*(b^2 + a^3*x))^(1/3))","B",1
1568,0,0,107,0.2361045,"\int \frac{x^4 \left(-4+x^3\right)}{\sqrt[4]{-1+x^3} \left(-1+2 x^3-x^6+x^8\right)} \, dx","Integrate[(x^4*(-4 + x^3))/((-1 + x^3)^(1/4)*(-1 + 2*x^3 - x^6 + x^8)),x]","\int \frac{x^4 \left(-4+x^3\right)}{\sqrt[4]{-1+x^3} \left(-1+2 x^3-x^6+x^8\right)} \, dx","\tan ^{-1}\left(\frac{\sqrt[4]{x^3-1}}{x}\right)-\tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^3-1}}\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{x^3-1}}{\sqrt{x^3-1}-x^2}\right)}{\sqrt{2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{x^3-1}}{\sqrt{x^3-1}+x^2}\right)}{\sqrt{2}}",1,"Integrate[(x^4*(-4 + x^3))/((-1 + x^3)^(1/4)*(-1 + 2*x^3 - x^6 + x^8)), x]","F",-1
1569,1,97,107,0.1259893,"\int \frac{x^6}{\left(b+a x^4\right)^{3/4} \left(-b^2+a^2 x^8\right)} \, dx","Integrate[x^6/((b + a*x^4)^(3/4)*(-b^2 + a^2*x^8)),x]","\frac{x^3 \left(\left(1-\frac{a x^4}{b}\right)^{3/4}-\left(\frac{a x^4}{b}+1\right)^{3/4} \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};-\frac{2 a x^4}{b-a x^4}\right)\right)}{6 a b \left(a x^4+b\right)^{3/4} \left(1-\frac{a x^4}{b}\right)^{3/4}}","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{4\ 2^{3/4} a^{7/4} b}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{4\ 2^{3/4} a^{7/4} b}+\frac{x^3}{6 a b \left(a x^4+b\right)^{3/4}}",1,"(x^3*((1 - (a*x^4)/b)^(3/4) - (1 + (a*x^4)/b)^(3/4)*Hypergeometric2F1[3/4, 3/4, 7/4, (-2*a*x^4)/(b - a*x^4)]))/(6*a*b*(b + a*x^4)^(3/4)*(1 - (a*x^4)/b)^(3/4))","C",0
1570,0,0,107,0.2594761,"\int \frac{\left(-b^2+a x^2\right) \sqrt{b+\sqrt{b^2+a x^2}}}{b^2+a x^2} \, dx","Integrate[((-b^2 + a*x^2)*Sqrt[b + Sqrt[b^2 + a*x^2]])/(b^2 + a*x^2),x]","\int \frac{\left(-b^2+a x^2\right) \sqrt{b+\sqrt{b^2+a x^2}}}{b^2+a x^2} \, dx","\frac{4 b x}{3 \sqrt{\sqrt{a x^2+b^2}+b}}+\frac{2 x \sqrt{a x^2+b^2}}{3 \sqrt{\sqrt{a x^2+b^2}+b}}-\frac{4 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b} \sqrt{\sqrt{a x^2+b^2}+b}}\right)}{\sqrt{a}}",1,"Integrate[((-b^2 + a*x^2)*Sqrt[b + Sqrt[b^2 + a*x^2]])/(b^2 + a*x^2), x]","F",-1
1571,1,36,108,0.0065341,"\int \sqrt[3]{x^2+x^3} \, dx","Integrate[(x^2 + x^3)^(1/3),x]","\frac{3 x \sqrt[3]{x^2 (x+1)} \, _2F_1\left(-\frac{1}{3},\frac{5}{3};\frac{8}{3};-x\right)}{5 \sqrt[3]{x+1}}","\frac{1}{6} \sqrt[3]{x^3+x^2} (3 x+1)+\frac{1}{9} \log \left(\sqrt[3]{x^3+x^2}-x\right)-\frac{1}{18} \log \left(x^2+\sqrt[3]{x^3+x^2} x+\left(x^3+x^2\right)^{2/3}\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+x^2}+x}\right)}{3 \sqrt{3}}",1,"(3*x*(x^2*(1 + x))^(1/3)*Hypergeometric2F1[-1/3, 5/3, 8/3, -x])/(5*(1 + x)^(1/3))","C",1
1572,1,314,108,7.6629411,"\int \frac{-1+k^3 x^3}{\sqrt{(1-x) x \left(1-k^2 x\right)} \left(1+k^3 x^3\right)} \, dx","Integrate[(-1 + k^3*x^3)/(Sqrt[(1 - x)*x*(1 - k^2*x)]*(1 + k^3*x^3)),x]","-\frac{2 \sqrt{\frac{1}{x-1}+1} (x-1)^{3/2} \sqrt{\frac{1-\frac{1}{k^2}}{x-1}+1} \sqrt{k^2 x-1} \left(-2 i \sqrt{3} \left(k^2-k+1\right) \Pi \left(1+\frac{1}{k};i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)+(k+1) \left(\left(\left(3+i \sqrt{3}\right) k-2 i \sqrt{3}\right) \Pi \left(\frac{2 \left(k^2-k+1\right)}{k \left(2 k-i \sqrt{3}-1\right)};i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)+i \left(-2 \sqrt{3}+\left(\sqrt{3}+3 i\right) k\right) \Pi \left(\frac{2 \left(k^2-k+1\right)}{k \left(2 k+i \sqrt{3}-1\right)};i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)\right)-3 i \sqrt{3} \left(k^3-1\right) F\left(i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)\right)}{3 \left(k^3+1\right) \sqrt{(x-1) x \left(k^2 x-1\right)} \sqrt{3 k^2 x-3}}","-\frac{2 \tan ^{-1}\left(\frac{(k+1) x}{\sqrt{k^2 x^3+\left(-k^2-1\right) x^2+x}}\right)}{3 (k+1)}-\frac{4 \tan ^{-1}\left(\frac{\sqrt{k^2-k+1} \sqrt{k^2 x^3+\left(-k^2-1\right) x^2+x}}{(x-1) \left(k^2 x-1\right)}\right)}{3 \sqrt{k^2-k+1}}",1,"(-2*Sqrt[1 + (-1 + x)^(-1)]*Sqrt[1 + (1 - k^(-2))/(-1 + x)]*(-1 + x)^(3/2)*Sqrt[-1 + k^2*x]*((-3*I)*Sqrt[3]*(-1 + k^3)*EllipticF[I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)] - (2*I)*Sqrt[3]*(1 - k + k^2)*EllipticPi[1 + k^(-1), I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)] + (1 + k)*(((-2*I)*Sqrt[3] + (3 + I*Sqrt[3])*k)*EllipticPi[(2*(1 - k + k^2))/(k*(-1 - I*Sqrt[3] + 2*k)), I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)] + I*(-2*Sqrt[3] + (3*I + Sqrt[3])*k)*EllipticPi[(2*(1 - k + k^2))/(k*(-1 + I*Sqrt[3] + 2*k)), I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)])))/(3*(1 + k^3)*Sqrt[(-1 + x)*x*(-1 + k^2*x)]*Sqrt[-3 + 3*k^2*x])","C",1
1573,1,548,108,0.9884987,"\int \frac{b+a x^2}{\left(b+a x^2+x^4\right) \sqrt[4]{-b x^2+a x^4}} \, dx","Integrate[(b + a*x^2)/((b + a*x^2 + x^4)*(-(b*x^2) + a*x^4)^(1/4)),x]","\frac{\sqrt{x} \sqrt[4]{a x^2-b} \left(\frac{\left(\frac{2 b-a^2}{\sqrt{a^2-4 b}}+a\right) \tan ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{-a \sqrt{a^2-4 b}+a^2+2 b}}{\sqrt[4]{a-\sqrt{a^2-4 b}} \sqrt[4]{a x^2-b}}\right)}{\left(a-\sqrt{a^2-4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2-4 b}+a^2+2 b}}+\frac{\left(\frac{a^2-2 b}{\sqrt{a^2-4 b}}+a\right) \tan ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{a \sqrt{a^2-4 b}+a^2+2 b}}{\sqrt[4]{\sqrt{a^2-4 b}+a} \sqrt[4]{a x^2-b}}\right)}{\left(\sqrt{a^2-4 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2-4 b}+a^2+2 b}}+\frac{\left(\frac{2 b-a^2}{\sqrt{a^2-4 b}}+a\right) \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{-a \sqrt{a^2-4 b}+a^2+2 b}}{\sqrt[4]{a-\sqrt{a^2-4 b}} \sqrt[4]{a x^2-b}}\right)}{\left(a-\sqrt{a^2-4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2-4 b}+a^2+2 b}}+\frac{\left(\frac{a^2-2 b}{\sqrt{a^2-4 b}}+a\right) \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{a \sqrt{a^2-4 b}+a^2+2 b}}{\sqrt[4]{\sqrt{a^2-4 b}+a} \sqrt[4]{a x^2-b}}\right)}{\left(\sqrt{a^2-4 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2-4 b}+a^2+2 b}}\right)}{\sqrt[4]{a x^4-b x^2}}","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4 a+2 a^2+b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-2 a \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+2 a \log (x)}{3 \text{$\#$1} a-2 \text{$\#$1}^5}\&\right]",1,"(Sqrt[x]*(-b + a*x^2)^(1/4)*(((a + (-a^2 + 2*b)/Sqrt[a^2 - 4*b])*ArcTan[((a^2 - a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)*Sqrt[x])/((a - Sqrt[a^2 - 4*b])^(1/4)*(-b + a*x^2)^(1/4))])/((a - Sqrt[a^2 - 4*b])^(3/4)*(a^2 - a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)) + ((a + (a^2 - 2*b)/Sqrt[a^2 - 4*b])*ArcTan[((a^2 + a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)*Sqrt[x])/((a + Sqrt[a^2 - 4*b])^(1/4)*(-b + a*x^2)^(1/4))])/((a + Sqrt[a^2 - 4*b])^(3/4)*(a^2 + a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)) + ((a + (-a^2 + 2*b)/Sqrt[a^2 - 4*b])*ArcTanh[((a^2 - a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)*Sqrt[x])/((a - Sqrt[a^2 - 4*b])^(1/4)*(-b + a*x^2)^(1/4))])/((a - Sqrt[a^2 - 4*b])^(3/4)*(a^2 - a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)) + ((a + (a^2 - 2*b)/Sqrt[a^2 - 4*b])*ArcTanh[((a^2 + a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)*Sqrt[x])/((a + Sqrt[a^2 - 4*b])^(1/4)*(-b + a*x^2)^(1/4))])/((a + Sqrt[a^2 - 4*b])^(3/4)*(a^2 + a*Sqrt[a^2 - 4*b] + 2*b)^(1/4))))/(-(b*x^2) + a*x^4)^(1/4)","B",1
1574,1,548,108,0.2367034,"\int \frac{b+a x^2}{\left(b+a x^2+x^4\right) \sqrt[4]{-b x^2+a x^4}} \, dx","Integrate[(b + a*x^2)/((b + a*x^2 + x^4)*(-(b*x^2) + a*x^4)^(1/4)),x]","\frac{\sqrt{x} \sqrt[4]{a x^2-b} \left(\frac{\left(\frac{2 b-a^2}{\sqrt{a^2-4 b}}+a\right) \tan ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{-a \sqrt{a^2-4 b}+a^2+2 b}}{\sqrt[4]{a-\sqrt{a^2-4 b}} \sqrt[4]{a x^2-b}}\right)}{\left(a-\sqrt{a^2-4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2-4 b}+a^2+2 b}}+\frac{\left(\frac{a^2-2 b}{\sqrt{a^2-4 b}}+a\right) \tan ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{a \sqrt{a^2-4 b}+a^2+2 b}}{\sqrt[4]{\sqrt{a^2-4 b}+a} \sqrt[4]{a x^2-b}}\right)}{\left(\sqrt{a^2-4 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2-4 b}+a^2+2 b}}+\frac{\left(\frac{2 b-a^2}{\sqrt{a^2-4 b}}+a\right) \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{-a \sqrt{a^2-4 b}+a^2+2 b}}{\sqrt[4]{a-\sqrt{a^2-4 b}} \sqrt[4]{a x^2-b}}\right)}{\left(a-\sqrt{a^2-4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2-4 b}+a^2+2 b}}+\frac{\left(\frac{a^2-2 b}{\sqrt{a^2-4 b}}+a\right) \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{a \sqrt{a^2-4 b}+a^2+2 b}}{\sqrt[4]{\sqrt{a^2-4 b}+a} \sqrt[4]{a x^2-b}}\right)}{\left(\sqrt{a^2-4 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2-4 b}+a^2+2 b}}\right)}{\sqrt[4]{a x^4-b x^2}}","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4 a+2 a^2+b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-2 a \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+2 a \log (x)}{3 \text{$\#$1} a-2 \text{$\#$1}^5}\&\right]",1,"(Sqrt[x]*(-b + a*x^2)^(1/4)*(((a + (-a^2 + 2*b)/Sqrt[a^2 - 4*b])*ArcTan[((a^2 - a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)*Sqrt[x])/((a - Sqrt[a^2 - 4*b])^(1/4)*(-b + a*x^2)^(1/4))])/((a - Sqrt[a^2 - 4*b])^(3/4)*(a^2 - a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)) + ((a + (a^2 - 2*b)/Sqrt[a^2 - 4*b])*ArcTan[((a^2 + a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)*Sqrt[x])/((a + Sqrt[a^2 - 4*b])^(1/4)*(-b + a*x^2)^(1/4))])/((a + Sqrt[a^2 - 4*b])^(3/4)*(a^2 + a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)) + ((a + (-a^2 + 2*b)/Sqrt[a^2 - 4*b])*ArcTanh[((a^2 - a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)*Sqrt[x])/((a - Sqrt[a^2 - 4*b])^(1/4)*(-b + a*x^2)^(1/4))])/((a - Sqrt[a^2 - 4*b])^(3/4)*(a^2 - a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)) + ((a + (a^2 - 2*b)/Sqrt[a^2 - 4*b])*ArcTanh[((a^2 + a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)*Sqrt[x])/((a + Sqrt[a^2 - 4*b])^(1/4)*(-b + a*x^2)^(1/4))])/((a + Sqrt[a^2 - 4*b])^(3/4)*(a^2 + a*Sqrt[a^2 - 4*b] + 2*b)^(1/4))))/(-(b*x^2) + a*x^4)^(1/4)","B",1
1575,1,93,108,0.5121905,"\int \frac{c+b x^2+c k^2 x^4}{\sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)} \left(-1+k^2 x^4\right)} \, dx","Integrate[(c + b*x^2 + c*k^2*x^4)/(Sqrt[(1 - x^2)*(1 - k^2*x^2)]*(-1 + k^2*x^4)),x]","\frac{\sqrt{1-x^2} \sqrt{1-k^2 x^2} \left((b-2 c k) \Pi \left(-k;\sin ^{-1}(x)|k^2\right)-(b+2 c k) \Pi \left(k;\sin ^{-1}(x)|k^2\right)+2 c k F\left(\sin ^{-1}(x)|k^2\right)\right)}{2 k \sqrt{\left(x^2-1\right) \left(k^2 x^2-1\right)}}","\frac{(-b-2 c k) \tan ^{-1}\left(\frac{(k-1) x}{\sqrt{k^2 x^4+\left(-k^2-1\right) x^2+1}}\right)}{4 (k-1) k}+\frac{(b-2 c k) \tan ^{-1}\left(\frac{(k+1) x}{\sqrt{k^2 x^4+\left(-k^2-1\right) x^2+1}+k x^2+1}\right)}{2 k (k+1)}",1,"(Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*(2*c*k*EllipticF[ArcSin[x], k^2] + (b - 2*c*k)*EllipticPi[-k, ArcSin[x], k^2] - (b + 2*c*k)*EllipticPi[k, ArcSin[x], k^2]))/(2*k*Sqrt[(-1 + x^2)*(-1 + k^2*x^2)])","C",1
1576,0,0,108,0.6094665,"\int \frac{3 b+a x^4}{\left(-b+x^3+a x^4\right) \sqrt[4]{-b x+a x^5}} \, dx","Integrate[(3*b + a*x^4)/((-b + x^3 + a*x^4)*(-(b*x) + a*x^5)^(1/4)),x]","\int \frac{3 b+a x^4}{\left(-b+x^3+a x^4\right) \sqrt[4]{-b x+a x^5}} \, dx","-\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{a x^5-b x}}{\sqrt{a x^5-b x}-x^2}\right)-\sqrt{2} \tanh ^{-1}\left(\frac{\frac{\sqrt{a x^5-b x}}{\sqrt{2}}+\frac{x^2}{\sqrt{2}}}{x \sqrt[4]{a x^5-b x}}\right)",1,"Integrate[(3*b + a*x^4)/((-b + x^3 + a*x^4)*(-(b*x) + a*x^5)^(1/4)), x]","F",-1
1577,1,163,108,0.1066672,"\int \frac{-1+x^6}{x^6 \sqrt[3]{x+x^3}} \, dx","Integrate[(-1 + x^6)/(x^6*(x + x^3)^(1/3)),x]","\frac{27 x^6+9 x^4-3 x^2-40 \sqrt[3]{x^2+1} x^{16/3} \log \left(1-\frac{x^{2/3}}{\sqrt[3]{x^2+1}}\right)+20 \sqrt[3]{x^2+1} x^{16/3} \log \left(\frac{x^{4/3}}{\left(x^2+1\right)^{2/3}}+\frac{x^{2/3}}{\sqrt[3]{x^2+1}}+1\right)+40 \sqrt{3} \sqrt[3]{x^2+1} x^{16/3} \tan ^{-1}\left(\frac{\frac{2 x^{2/3}}{\sqrt[3]{x^2+1}}+1}{\sqrt{3}}\right)+15}{80 x^5 \sqrt[3]{x^3+x}}","-\frac{1}{2} \log \left(\sqrt[3]{x^3+x}-x\right)+\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+x}+x}\right)+\frac{1}{4} \log \left(\sqrt[3]{x^3+x} x+\left(x^3+x\right)^{2/3}+x^2\right)+\frac{3 \left(x^3+x\right)^{2/3} \left(9 x^4-6 x^2+5\right)}{80 x^6}",1,"(15 - 3*x^2 + 9*x^4 + 27*x^6 + 40*Sqrt[3]*x^(16/3)*(1 + x^2)^(1/3)*ArcTan[(1 + (2*x^(2/3))/(1 + x^2)^(1/3))/Sqrt[3]] - 40*x^(16/3)*(1 + x^2)^(1/3)*Log[1 - x^(2/3)/(1 + x^2)^(1/3)] + 20*x^(16/3)*(1 + x^2)^(1/3)*Log[1 + x^(4/3)/(1 + x^2)^(2/3) + x^(2/3)/(1 + x^2)^(1/3)])/(80*x^5*(x + x^3)^(1/3))","A",1
1578,1,52,108,0.040286,"\int \frac{\left(-1+x^3\right)^{2/3} \left(2+x^6\right)}{x^6} \, dx","Integrate[((-1 + x^3)^(2/3)*(2 + x^6))/x^6,x]","\frac{x \left(x^3-1\right)^{2/3} \, _2F_1\left(-\frac{2}{3},\frac{1}{3};\frac{4}{3};x^3\right)}{\left(1-x^3\right)^{2/3}}+\frac{2 \left(x^3-1\right)^{5/3}}{5 x^5}","\frac{2}{9} \log \left(\sqrt[3]{x^3-1}-x\right)-\frac{2 \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-1}+x}\right)}{3 \sqrt{3}}-\frac{1}{9} \log \left(\sqrt[3]{x^3-1} x+\left(x^3-1\right)^{2/3}+x^2\right)+\frac{\left(x^3-1\right)^{2/3} \left(5 x^6+6 x^3-6\right)}{15 x^5}",1,"(2*(-1 + x^3)^(5/3))/(5*x^5) + (x*(-1 + x^3)^(2/3)*Hypergeometric2F1[-2/3, 1/3, 4/3, x^3])/(1 - x^3)^(2/3)","C",1
1579,1,77,108,0.0322206,"\int \frac{\left(-1+x^3\right)^{2/3} \left(-2+x^3+x^6\right)}{x^6} \, dx","Integrate[((-1 + x^3)^(2/3)*(-2 + x^3 + x^6))/x^6,x]","\frac{\left(x^3-1\right)^{2/3} \left(-5 x^3 \, _2F_1\left(-\frac{2}{3},-\frac{2}{3};\frac{1}{3};x^3\right)+10 x^6 \, _2F_1\left(-\frac{2}{3},\frac{1}{3};\frac{4}{3};x^3\right)+4 \left(1-x^3\right)^{5/3}\right)}{10 x^5 \left(1-x^3\right)^{2/3}}","-\frac{1}{9} \log \left(\sqrt[3]{x^3-1}-x\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-1}+x}\right)}{3 \sqrt{3}}+\frac{1}{18} \log \left(\sqrt[3]{x^3-1} x+\left(x^3-1\right)^{2/3}+x^2\right)+\frac{\left(x^3-1\right)^{2/3} \left(10 x^6-27 x^3+12\right)}{30 x^5}",1,"((-1 + x^3)^(2/3)*(4*(1 - x^3)^(5/3) - 5*x^3*Hypergeometric2F1[-2/3, -2/3, 1/3, x^3] + 10*x^6*Hypergeometric2F1[-2/3, 1/3, 4/3, x^3]))/(10*x^5*(1 - x^3)^(2/3))","C",1
1580,1,35,108,0.0286069,"\int \frac{\left(1+x^3\right)^{2/3} \left(1+2 x^6\right)}{x^6} \, dx","Integrate[((1 + x^3)^(2/3)*(1 + 2*x^6))/x^6,x]","2 x \, _2F_1\left(-\frac{2}{3},\frac{1}{3};\frac{4}{3};-x^3\right)-\frac{\left(x^3+1\right)^{5/3}}{5 x^5}","-\frac{4}{9} \log \left(\sqrt[3]{x^3+1}-x\right)+\frac{4 \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+1}+x}\right)}{3 \sqrt{3}}+\frac{2}{9} \log \left(\sqrt[3]{x^3+1} x+\left(x^3+1\right)^{2/3}+x^2\right)+\frac{\left(x^3+1\right)^{2/3} \left(10 x^6-3 x^3-3\right)}{15 x^5}",1,"-1/5*(1 + x^3)^(5/3)/x^5 + 2*x*Hypergeometric2F1[-2/3, 1/3, 4/3, -x^3]","C",1
1581,0,0,108,0.6763075,"\int \frac{3 b+2 a x^5}{\left(-b+x^3+a x^5\right) \sqrt[4]{-b x+a x^6}} \, dx","Integrate[(3*b + 2*a*x^5)/((-b + x^3 + a*x^5)*(-(b*x) + a*x^6)^(1/4)),x]","\int \frac{3 b+2 a x^5}{\left(-b+x^3+a x^5\right) \sqrt[4]{-b x+a x^6}} \, dx","-\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{a x^6-b x}}{\sqrt{a x^6-b x}-x^2}\right)-\sqrt{2} \tanh ^{-1}\left(\frac{\frac{\sqrt{a x^6-b x}}{\sqrt{2}}+\frac{x^2}{\sqrt{2}}}{x \sqrt[4]{a x^6-b x}}\right)",1,"Integrate[(3*b + 2*a*x^5)/((-b + x^3 + a*x^5)*(-(b*x) + a*x^6)^(1/4)), x]","F",-1
1582,0,0,108,0.2588449,"\int \frac{\sqrt[4]{-1+x^4} \left(1+x^4+x^8\right)}{x^6 \left(-1+2 x^8\right)} \, dx","Integrate[((-1 + x^4)^(1/4)*(1 + x^4 + x^8))/(x^6*(-1 + 2*x^8)),x]","\int \frac{\sqrt[4]{-1+x^4} \left(1+x^4+x^8\right)}{x^6 \left(-1+2 x^8\right)} \, dx","\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4-1\&,\frac{-2 \text{$\#$1}^4 \log \left(\sqrt[4]{x^4-1}-\text{$\#$1} x\right)+2 \text{$\#$1}^4 \log (x)+\log \left(\sqrt[4]{x^4-1}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}^7-\text{$\#$1}^3}\&\right]+\frac{\sqrt[4]{x^4-1} \left(4 x^4+1\right)}{5 x^5}",1,"Integrate[((-1 + x^4)^(1/4)*(1 + x^4 + x^8))/(x^6*(-1 + 2*x^8)), x]","F",-1
1583,0,0,108,0.1259693,"\int \frac{\sqrt[4]{-1+x^4} \left(1+x^4+x^8\right)}{x^6 \left(-1+2 x^8\right)} \, dx","Integrate[((-1 + x^4)^(1/4)*(1 + x^4 + x^8))/(x^6*(-1 + 2*x^8)),x]","\int \frac{\sqrt[4]{-1+x^4} \left(1+x^4+x^8\right)}{x^6 \left(-1+2 x^8\right)} \, dx","\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4-1\&,\frac{-2 \text{$\#$1}^4 \log \left(\sqrt[4]{x^4-1}-\text{$\#$1} x\right)+2 \text{$\#$1}^4 \log (x)+\log \left(\sqrt[4]{x^4-1}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}^7-\text{$\#$1}^3}\&\right]+\frac{\sqrt[4]{x^4-1} \left(4 x^4+1\right)}{5 x^5}",1,"Integrate[((-1 + x^4)^(1/4)*(1 + x^4 + x^8))/(x^6*(-1 + 2*x^8)), x]","F",-1
1584,0,0,108,1.7708441,"\int \frac{\sqrt{-b x+a^2 x^2}}{\left(a x^2+x \sqrt{-b x+a^2 x^2}\right)^{3/2}} \, dx","Integrate[Sqrt[-(b*x) + a^2*x^2]/(a*x^2 + x*Sqrt[-(b*x) + a^2*x^2])^(3/2),x]","\int \frac{\sqrt{-b x+a^2 x^2}}{\left(a x^2+x \sqrt{-b x+a^2 x^2}\right)^{3/2}} \, dx","\frac{4 \left(3 a^2 x+b\right) \sqrt{a^2 x^2-b x} \sqrt{x \left(\sqrt{a^2 x^2-b x}+a x\right)}}{3 b^2 x^2}-\frac{4 \left(3 a^3 x+5 a b\right) \sqrt{x \left(\sqrt{a^2 x^2-b x}+a x\right)}}{3 b^2 x}",1,"Integrate[Sqrt[-(b*x) + a^2*x^2]/(a*x^2 + x*Sqrt[-(b*x) + a^2*x^2])^(3/2), x]","F",-1
1585,1,67,109,0.0209534,"\int x^7 \sqrt[3]{-1+x^3} \, dx","Integrate[x^7*(-1 + x^3)^(1/3),x]","\frac{x^2 \sqrt[3]{x^3-1} \left(5 \, _2F_1\left(-\frac{1}{3},\frac{2}{3};\frac{5}{3};x^3\right)+\sqrt[3]{1-x^3} \left(6 x^6-x^3-5\right)\right)}{54 \sqrt[3]{1-x^3}}","\frac{5}{243} \log \left(\sqrt[3]{x^3-1}-x\right)+\frac{5 \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-1}+x}\right)}{81 \sqrt{3}}-\frac{5}{486} \log \left(\sqrt[3]{x^3-1} x+\left(x^3-1\right)^{2/3}+x^2\right)+\frac{1}{162} \sqrt[3]{x^3-1} \left(18 x^8-3 x^5-5 x^2\right)",1,"(x^2*(-1 + x^3)^(1/3)*((1 - x^3)^(1/3)*(-5 - x^3 + 6*x^6) + 5*Hypergeometric2F1[-1/3, 2/3, 5/3, x^3]))/(54*(1 - x^3)^(1/3))","C",1
1586,1,45,109,0.0155044,"\int x^7 \sqrt[3]{1+x^3} \, dx","Integrate[x^7*(1 + x^3)^(1/3),x]","\frac{1}{54} x^2 \left(5 \, _2F_1\left(-\frac{1}{3},\frac{2}{3};\frac{5}{3};-x^3\right)+\sqrt[3]{x^3+1} \left(6 x^6+x^3-5\right)\right)","-\frac{5}{243} \log \left(\sqrt[3]{x^3+1}-x\right)-\frac{5 \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+1}+x}\right)}{81 \sqrt{3}}+\frac{5}{486} \log \left(\sqrt[3]{x^3+1} x+\left(x^3+1\right)^{2/3}+x^2\right)+\frac{1}{162} \sqrt[3]{x^3+1} \left(18 x^8+3 x^5-5 x^2\right)",1,"(x^2*((1 + x^3)^(1/3)*(-5 + x^3 + 6*x^6) + 5*Hypergeometric2F1[-1/3, 2/3, 5/3, -x^3]))/54","C",1
1587,1,38,109,0.0107727,"\int \frac{\sqrt[3]{-1+x^3} \left(1+x^3\right)}{x^{13}} \, dx","Integrate[((-1 + x^3)^(1/3)*(1 + x^3))/x^13,x]","\frac{\left(x^3-1\right)^{4/3} \left(5 x^{12} \, _2F_1\left(\frac{4}{3},4;\frac{7}{3};1-x^3\right)+1\right)}{12 x^{12}}","\frac{25}{729} \log \left(\sqrt[3]{x^3-1}+1\right)-\frac{25 \log \left(\left(x^3-1\right)^{2/3}-\sqrt[3]{x^3-1}+1\right)}{1458}-\frac{25 \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{x^3-1}}{\sqrt{3}}\right)}{243 \sqrt{3}}+\frac{\sqrt[3]{x^3-1} \left(50 x^9+30 x^6-99 x^3-81\right)}{972 x^{12}}",1,"((-1 + x^3)^(4/3)*(1 + 5*x^12*Hypergeometric2F1[4/3, 4, 7/3, 1 - x^3]))/(12*x^12)","C",1
1588,0,0,109,3.826385,"\int \frac{(-b+x) (a-3 b+2 x)}{(-a+x) ((-a+x) (-b+x))^{3/4} \left(b-a^3 d-\left(1-3 a^2 d\right) x-3 a d x^2+d x^3\right)} \, dx","Integrate[((-b + x)*(a - 3*b + 2*x))/((-a + x)*((-a + x)*(-b + x))^(3/4)*(b - a^3*d - (1 - 3*a^2*d)*x - 3*a*d*x^2 + d*x^3)),x]","\int \frac{(-b+x) (a-3 b+2 x)}{(-a+x) ((-a+x) (-b+x))^{3/4} \left(b-a^3 d-\left(1-3 a^2 d\right) x-3 a d x^2+d x^3\right)} \, dx","-2 \sqrt[4]{d} \tan ^{-1}\left(\frac{\sqrt[4]{d} \left(x (-a-b)+a b+x^2\right)^{3/4}}{b-x}\right)+2 \sqrt[4]{d} \tanh ^{-1}\left(\frac{\sqrt[4]{x (-a-b)+a b+x^2}}{\sqrt[4]{d} (a-x)}\right)-\frac{4 (b-x)}{\left(a b-a x-b x+x^2\right)^{3/4}}",1,"Integrate[((-b + x)*(a - 3*b + 2*x))/((-a + x)*((-a + x)*(-b + x))^(3/4)*(b - a^3*d - (1 - 3*a^2*d)*x - 3*a*d*x^2 + d*x^3)), x]","F",-1
1589,1,97,109,0.064382,"\int x^8 \left(-b+a x^4\right)^{3/4} \, dx","Integrate[x^8*(-b + a*x^4)^(3/4),x]","\frac{x \left(a x^4-b\right)^{3/4} \left(\left(1-\frac{a x^4}{b}\right)^{3/4} \left(8 a^2 x^8-3 a b x^4-5 b^2\right)+5 b^2 \, _2F_1\left(-\frac{3}{4},\frac{1}{4};\frac{5}{4};\frac{a x^4}{b}\right)\right)}{96 a^2 \left(1-\frac{a x^4}{b}\right)^{3/4}}","-\frac{5 b^3 \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{256 a^{9/4}}-\frac{5 b^3 \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{256 a^{9/4}}+\frac{\left(a x^4-b\right)^{3/4} \left(32 a^2 x^9-12 a b x^5-15 b^2 x\right)}{384 a^2}",1,"(x*(-b + a*x^4)^(3/4)*((1 - (a*x^4)/b)^(3/4)*(-5*b^2 - 3*a*b*x^4 + 8*a^2*x^8) + 5*b^2*Hypergeometric2F1[-3/4, 1/4, 5/4, (a*x^4)/b]))/(96*a^2*(1 - (a*x^4)/b)^(3/4))","C",1
1590,1,76,109,0.043314,"\int \frac{1}{\left(b+a x^3\right) \sqrt[4]{-b x+a x^4}} \, dx","Integrate[1/((b + a*x^3)*(-(b*x) + a*x^4)^(1/4)),x]","\frac{4 x \sqrt[4]{1-\frac{a x^3}{b}} \, _2F_1\left(\frac{1}{4},\frac{1}{4};\frac{5}{4};\frac{2 a x^3}{a x^3+b}\right)}{3 b \sqrt[4]{\frac{a x^3}{b}+1} \sqrt[4]{a x^4-b x}}","\frac{2^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} \left(a x^4-b x\right)^{3/4}}{a x^3-b}\right)}{3 \sqrt[4]{a} b}+\frac{2^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} \left(a x^4-b x\right)^{3/4}}{a x^3-b}\right)}{3 \sqrt[4]{a} b}",1,"(4*x*(1 - (a*x^3)/b)^(1/4)*Hypergeometric2F1[1/4, 1/4, 5/4, (2*a*x^3)/(b + a*x^3)])/(3*b*(1 + (a*x^3)/b)^(1/4)*(-(b*x) + a*x^4)^(1/4))","C",0
1591,0,0,109,2.8054473,"\int \frac{\sqrt[4]{-b x^2+a x^4}}{x^4 \left(-b+a x^4\right)} \, dx","Integrate[(-(b*x^2) + a*x^4)^(1/4)/(x^4*(-b + a*x^4)),x]","\int \frac{\sqrt[4]{-b x^2+a x^4}}{x^4 \left(-b+a x^4\right)} \, dx","\frac{2 \left(b-a x^2\right) \sqrt[4]{a x^4-b x^2}}{5 b^2 x^3}-\frac{a \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2-a b\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^4-a}\&\right]}{4 b}",1,"Integrate[(-(b*x^2) + a*x^4)^(1/4)/(x^4*(-b + a*x^4)), x]","F",-1
1592,0,0,109,1.646795,"\int \frac{\sqrt[4]{-b x^2+a x^4}}{x^4 \left(-b+a x^4\right)} \, dx","Integrate[(-(b*x^2) + a*x^4)^(1/4)/(x^4*(-b + a*x^4)),x]","\int \frac{\sqrt[4]{-b x^2+a x^4}}{x^4 \left(-b+a x^4\right)} \, dx","\frac{2 \left(b-a x^2\right) \sqrt[4]{a x^4-b x^2}}{5 b^2 x^3}-\frac{a \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2-a b\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^4-a}\&\right]}{4 b}",1,"Integrate[(-(b*x^2) + a*x^4)^(1/4)/(x^4*(-b + a*x^4)), x]","F",-1
1593,0,0,109,5.3309798,"\int \frac{(-2+(1+k) x) \left(1-(1+k) x+(a+k) x^2\right)}{\sqrt[3]{(1-x) x (1-k x)} \left(1-2 (1+k) x+\left(1+c+4 k+k^2\right) x^2-\left(c+2 k+c k+2 k^2\right) x^3+\left(-b+c k+k^2\right) x^4\right)} \, dx","Integrate[((-2 + (1 + k)*x)*(1 - (1 + k)*x + (a + k)*x^2))/(((1 - x)*x*(1 - k*x))^(1/3)*(1 - 2*(1 + k)*x + (1 + c + 4*k + k^2)*x^2 - (c + 2*k + c*k + 2*k^2)*x^3 + (-b + c*k + k^2)*x^4)),x]","\int \frac{(-2+(1+k) x) \left(1-(1+k) x+(a+k) x^2\right)}{\sqrt[3]{(1-x) x (1-k x)} \left(1-2 (1+k) x+\left(1+c+4 k+k^2\right) x^2-\left(c+2 k+c k+2 k^2\right) x^3+\left(-b+c k+k^2\right) x^4\right)} \, dx","-\text{RootSum}\left[-\text{$\#$1}^6-\text{$\#$1}^3 c+b\&,\frac{-\text{$\#$1}^3 \log \left(\sqrt[3]{k x^3+(-k-1) x^2+x}-\text{$\#$1} x\right)+\text{$\#$1}^3 \log (x)-a \log \left(\sqrt[3]{k x^3+(-k-1) x^2+x}-\text{$\#$1} x\right)+a \log (x)}{2 \text{$\#$1}^4+\text{$\#$1} c}\&\right]",1,"Integrate[((-2 + (1 + k)*x)*(1 - (1 + k)*x + (a + k)*x^2))/(((1 - x)*x*(1 - k*x))^(1/3)*(1 - 2*(1 + k)*x + (1 + c + 4*k + k^2)*x^2 - (c + 2*k + c*k + 2*k^2)*x^3 + (-b + c*k + k^2)*x^4)), x]","F",-1
1594,1,50,109,0.0265191,"\int \frac{\sqrt[3]{-1+x^6} \left(1+x^6\right)}{x^3} \, dx","Integrate[((-1 + x^6)^(1/3)*(1 + x^6))/x^3,x]","\frac{\sqrt[3]{x^6-1} \left(-\frac{x^6 \, _2F_1\left(-\frac{1}{3},\frac{2}{3};\frac{5}{3};x^6\right)}{\sqrt[3]{1-x^6}}+x^6-1\right)}{2 x^2}","\frac{\sqrt[3]{x^6-1} \left(x^6-3\right)}{6 x^2}-\frac{1}{9} \log \left(\sqrt[3]{x^6-1}-x^2\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x^2}{2 \sqrt[3]{x^6-1}+x^2}\right)}{3 \sqrt{3}}+\frac{1}{18} \log \left(\left(x^6-1\right)^{2/3}+x^4+\sqrt[3]{x^6-1} x^2\right)",1,"((-1 + x^6)^(1/3)*(-1 + x^6 - (x^6*Hypergeometric2F1[-1/3, 2/3, 5/3, x^6])/(1 - x^6)^(1/3)))/(2*x^2)","C",1
1595,0,0,109,0.6325677,"\int \frac{\left(1+x^3\right)^{2/3} \left(1-2 x^3+x^6\right)}{x^6 \left(-2+x^6\right)} \, dx","Integrate[((1 + x^3)^(2/3)*(1 - 2*x^3 + x^6))/(x^6*(-2 + x^6)),x]","\int \frac{\left(1+x^3\right)^{2/3} \left(1-2 x^3+x^6\right)}{x^6 \left(-2+x^6\right)} \, dx","\frac{1}{24} \text{RootSum}\left[2 \text{$\#$1}^6-4 \text{$\#$1}^3+1\&,\frac{-\text{$\#$1}^3 \log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)+\text{$\#$1}^3 \log (x)+2 \log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)-2 \log (x)}{\text{$\#$1}^4-\text{$\#$1}}\&\right]+\frac{\left(x^3+1\right)^{2/3} \left(1-4 x^3\right)}{10 x^5}",1,"Integrate[((1 + x^3)^(2/3)*(1 - 2*x^3 + x^6))/(x^6*(-2 + x^6)), x]","F",-1
1596,0,0,109,0.3379148,"\int \frac{\left(1+x^3\right)^{2/3} \left(1-2 x^3+x^6\right)}{x^6 \left(-2+x^6\right)} \, dx","Integrate[((1 + x^3)^(2/3)*(1 - 2*x^3 + x^6))/(x^6*(-2 + x^6)),x]","\int \frac{\left(1+x^3\right)^{2/3} \left(1-2 x^3+x^6\right)}{x^6 \left(-2+x^6\right)} \, dx","\frac{1}{24} \text{RootSum}\left[2 \text{$\#$1}^6-4 \text{$\#$1}^3+1\&,\frac{-\text{$\#$1}^3 \log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)+\text{$\#$1}^3 \log (x)+2 \log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)-2 \log (x)}{\text{$\#$1}^4-\text{$\#$1}}\&\right]+\frac{\left(x^3+1\right)^{2/3} \left(1-4 x^3\right)}{10 x^5}",1,"Integrate[((1 + x^3)^(2/3)*(1 - 2*x^3 + x^6))/(x^6*(-2 + x^6)), x]","F",-1
1597,1,52,109,0.0253906,"\int \frac{\sqrt[3]{-1+x^6} \left(-1+2 x^6\right)}{x^9} \, dx","Integrate[((-1 + x^6)^(1/3)*(-1 + 2*x^6))/x^9,x]","\frac{\sqrt[3]{x^6-1} \left(-\frac{8 x^6 \, _2F_1\left(-\frac{1}{3},-\frac{1}{3};\frac{2}{3};x^6\right)}{\sqrt[3]{1-x^6}}-x^6+1\right)}{8 x^8}","\frac{\sqrt[3]{x^6-1} \left(1-9 x^6\right)}{8 x^8}-\frac{1}{3} \log \left(\sqrt[3]{x^6-1}-x^2\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x^2}{2 \sqrt[3]{x^6-1}+x^2}\right)}{\sqrt{3}}+\frac{1}{6} \log \left(\left(x^6-1\right)^{2/3}+x^4+\sqrt[3]{x^6-1} x^2\right)",1,"((-1 + x^6)^(1/3)*(1 - x^6 - (8*x^6*Hypergeometric2F1[-1/3, -1/3, 2/3, x^6])/(1 - x^6)^(1/3)))/(8*x^8)","C",1
1598,1,372,109,0.6986699,"\int \frac{\left(-1+x^3\right)^{2/3} \left(-1+x^6\right)}{x^6 \left(-2+x^3+2 x^6\right)} \, dx","Integrate[((-1 + x^3)^(2/3)*(-1 + x^6))/(x^6*(-2 + x^3 + 2*x^6)),x]","\frac{-2 \sqrt[3]{43+13 \sqrt{17}} \log \left(\sqrt[3]{\sqrt{17}-3}-\frac{\sqrt[3]{2} x}{\sqrt[3]{x^3-1}}\right)-2 \sqrt[3]{13 \sqrt{17}-43} \log \left(\frac{\sqrt[3]{2} x}{\sqrt[3]{x^3-1}}+\sqrt[3]{3+\sqrt{17}}\right)+2 \sqrt{3} \sqrt[3]{43+13 \sqrt{17}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{\frac{2}{\sqrt{17}-3}} x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)+2 \sqrt{3} \sqrt[3]{13 \sqrt{17}-43} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{\frac{2}{3+\sqrt{17}}} x}{\sqrt[3]{x^3-1}}}{\sqrt{3}}\right)+\sqrt[3]{43+13 \sqrt{17}} \log \left(\frac{\sqrt[3]{2 \left(\sqrt{17}-3\right)} x}{\sqrt[3]{x^3-1}}+\frac{2^{2/3} x^2}{\left(x^3-1\right)^{2/3}}+\left(\sqrt{17}-3\right)^{2/3}\right)+\sqrt[3]{13 \sqrt{17}-43} \log \left(-\frac{\sqrt[3]{2 \left(3+\sqrt{17}\right)} x}{\sqrt[3]{x^3-1}}+\frac{2^{2/3} x^2}{\left(x^3-1\right)^{2/3}}+\left(3+\sqrt{17}\right)^{2/3}\right)}{48 \sqrt{17}}-\frac{\left(x^3-1\right)^{2/3} \left(x^3+4\right)}{40 x^5}","\frac{1}{12} \text{RootSum}\left[2 \text{$\#$1}^6-3 \text{$\#$1}^3-1\&,\frac{-\text{$\#$1}^3 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)+\text{$\#$1}^3 \log (x)-\log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)+\log (x)}{4 \text{$\#$1}^4-3 \text{$\#$1}}\&\right]+\frac{\left(x^3-1\right)^{2/3} \left(-x^3-4\right)}{40 x^5}",1,"-1/40*((-1 + x^3)^(2/3)*(4 + x^3))/x^5 + (2*Sqrt[3]*(43 + 13*Sqrt[17])^(1/3)*ArcTan[(1 + (2*(2/(-3 + Sqrt[17]))^(1/3)*x)/(-1 + x^3)^(1/3))/Sqrt[3]] + 2*Sqrt[3]*(-43 + 13*Sqrt[17])^(1/3)*ArcTan[(1 - (2*(2/(3 + Sqrt[17]))^(1/3)*x)/(-1 + x^3)^(1/3))/Sqrt[3]] - 2*(43 + 13*Sqrt[17])^(1/3)*Log[(-3 + Sqrt[17])^(1/3) - (2^(1/3)*x)/(-1 + x^3)^(1/3)] - 2*(-43 + 13*Sqrt[17])^(1/3)*Log[(3 + Sqrt[17])^(1/3) + (2^(1/3)*x)/(-1 + x^3)^(1/3)] + (43 + 13*Sqrt[17])^(1/3)*Log[(-3 + Sqrt[17])^(2/3) + (2^(2/3)*x^2)/(-1 + x^3)^(2/3) + ((2*(-3 + Sqrt[17]))^(1/3)*x)/(-1 + x^3)^(1/3)] + (-43 + 13*Sqrt[17])^(1/3)*Log[(3 + Sqrt[17])^(2/3) + (2^(2/3)*x^2)/(-1 + x^3)^(2/3) - ((2*(3 + Sqrt[17]))^(1/3)*x)/(-1 + x^3)^(1/3)])/(48*Sqrt[17])","B",0
1599,1,372,109,0.6486818,"\int \frac{\left(-1+x^3\right)^{2/3} \left(-1+x^6\right)}{x^6 \left(-2+x^3+2 x^6\right)} \, dx","Integrate[((-1 + x^3)^(2/3)*(-1 + x^6))/(x^6*(-2 + x^3 + 2*x^6)),x]","\frac{-2 \sqrt[3]{43+13 \sqrt{17}} \log \left(\sqrt[3]{\sqrt{17}-3}-\frac{\sqrt[3]{2} x}{\sqrt[3]{x^3-1}}\right)-2 \sqrt[3]{13 \sqrt{17}-43} \log \left(\frac{\sqrt[3]{2} x}{\sqrt[3]{x^3-1}}+\sqrt[3]{3+\sqrt{17}}\right)+2 \sqrt{3} \sqrt[3]{43+13 \sqrt{17}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{\frac{2}{\sqrt{17}-3}} x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)+2 \sqrt{3} \sqrt[3]{13 \sqrt{17}-43} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{\frac{2}{3+\sqrt{17}}} x}{\sqrt[3]{x^3-1}}}{\sqrt{3}}\right)+\sqrt[3]{43+13 \sqrt{17}} \log \left(\frac{\sqrt[3]{2 \left(\sqrt{17}-3\right)} x}{\sqrt[3]{x^3-1}}+\frac{2^{2/3} x^2}{\left(x^3-1\right)^{2/3}}+\left(\sqrt{17}-3\right)^{2/3}\right)+\sqrt[3]{13 \sqrt{17}-43} \log \left(-\frac{\sqrt[3]{2 \left(3+\sqrt{17}\right)} x}{\sqrt[3]{x^3-1}}+\frac{2^{2/3} x^2}{\left(x^3-1\right)^{2/3}}+\left(3+\sqrt{17}\right)^{2/3}\right)}{48 \sqrt{17}}-\frac{\left(x^3-1\right)^{2/3} \left(x^3+4\right)}{40 x^5}","\frac{1}{12} \text{RootSum}\left[2 \text{$\#$1}^6-3 \text{$\#$1}^3-1\&,\frac{-\text{$\#$1}^3 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)+\text{$\#$1}^3 \log (x)-\log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)+\log (x)}{4 \text{$\#$1}^4-3 \text{$\#$1}}\&\right]+\frac{\left(x^3-1\right)^{2/3} \left(-x^3-4\right)}{40 x^5}",1,"-1/40*((-1 + x^3)^(2/3)*(4 + x^3))/x^5 + (2*Sqrt[3]*(43 + 13*Sqrt[17])^(1/3)*ArcTan[(1 + (2*(2/(-3 + Sqrt[17]))^(1/3)*x)/(-1 + x^3)^(1/3))/Sqrt[3]] + 2*Sqrt[3]*(-43 + 13*Sqrt[17])^(1/3)*ArcTan[(1 - (2*(2/(3 + Sqrt[17]))^(1/3)*x)/(-1 + x^3)^(1/3))/Sqrt[3]] - 2*(43 + 13*Sqrt[17])^(1/3)*Log[(-3 + Sqrt[17])^(1/3) - (2^(1/3)*x)/(-1 + x^3)^(1/3)] - 2*(-43 + 13*Sqrt[17])^(1/3)*Log[(3 + Sqrt[17])^(1/3) + (2^(1/3)*x)/(-1 + x^3)^(1/3)] + (43 + 13*Sqrt[17])^(1/3)*Log[(-3 + Sqrt[17])^(2/3) + (2^(2/3)*x^2)/(-1 + x^3)^(2/3) + ((2*(-3 + Sqrt[17]))^(1/3)*x)/(-1 + x^3)^(1/3)] + (-43 + 13*Sqrt[17])^(1/3)*Log[(3 + Sqrt[17])^(2/3) + (2^(2/3)*x^2)/(-1 + x^3)^(2/3) - ((2*(3 + Sqrt[17]))^(1/3)*x)/(-1 + x^3)^(1/3)])/(48*Sqrt[17])","B",0
1600,1,97,109,0.0912708,"\int \frac{\sqrt[4]{-1+x^4} \left(2-x^4+2 x^8\right)}{x^{10} \left(-1+2 x^4\right)} \, dx","Integrate[((-1 + x^4)^(1/4)*(2 - x^4 + 2*x^8))/(x^10*(-1 + 2*x^4)),x]","\frac{-24 \sqrt[4]{1-2 x^4} \left(1-x^4\right)^{3/4} x^{12} \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};\frac{x^4}{2 x^4-1}\right)+130 x^{16}-185 x^{12}+54 x^8-x^4+2}{9 x^9 \left(x^4-1\right)^{3/4} \left(2 x^4-1\right)}","2 \sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{x^4-1}}{\sqrt{x^4-1}-x^2}\right)-2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{x^4-1}}{\sqrt{x^4-1}+x^2}\right)+\frac{\sqrt[4]{x^4-1} \left(65 x^8+5 x^4+2\right)}{9 x^9}",1,"(2 - x^4 + 54*x^8 - 185*x^12 + 130*x^16 - 24*x^12*(1 - 2*x^4)^(1/4)*(1 - x^4)^(3/4)*Hypergeometric2F1[3/4, 3/4, 7/4, x^4/(-1 + 2*x^4)])/(9*x^9*(-1 + x^4)^(3/4)*(-1 + 2*x^4))","C",0
1601,0,0,109,0.3106485,"\int \frac{\left(2+x^6\right) \left(1-2 x^6+x^8+x^{12}\right)}{x^8 \sqrt[4]{-1+x^6} \left(-1+x^4+x^6\right)} \, dx","Integrate[((2 + x^6)*(1 - 2*x^6 + x^8 + x^12))/(x^8*(-1 + x^6)^(1/4)*(-1 + x^4 + x^6)),x]","\int \frac{\left(2+x^6\right) \left(1-2 x^6+x^8+x^{12}\right)}{x^8 \sqrt[4]{-1+x^6} \left(-1+x^4+x^6\right)} \, dx","-\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{x^6-1}}{\sqrt{x^6-1}-x^2}\right)-\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{x^6-1}}{\sqrt{x^6-1}+x^2}\right)+\frac{2 \left(x^6-1\right)^{3/4} \left(3 x^6-7 x^4-3\right)}{21 x^7}",1,"Integrate[((2 + x^6)*(1 - 2*x^6 + x^8 + x^12))/(x^8*(-1 + x^6)^(1/4)*(-1 + x^4 + x^6)), x]","F",-1
1602,1,97,109,0.4770418,"\int \frac{\sqrt{x+x^2}}{x \sqrt{x^2+x \sqrt{x+x^2}}} \, dx","Integrate[Sqrt[x + x^2]/(x*Sqrt[x^2 + x*Sqrt[x + x^2]]),x]","-\frac{2 \sqrt{x (x+1)} \left(\left(x+\sqrt{x (x+1)}\right) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};1+\frac{1}{2 \left(x+\sqrt{x (x+1)}\right)}\right)+4 x+4 \sqrt{x (x+1)}+2\right)}{\sqrt{x \left(x+\sqrt{x (x+1)}\right)} \left(x+\sqrt{x (x+1)}+1\right)}","\sqrt{x \left(\sqrt{x^2+x}+x\right)} \left(\frac{\sqrt{2} \sqrt{\sqrt{x^2+x}-x} \tanh ^{-1}\left(\sqrt{2} \sqrt{\sqrt{x^2+x}-x}\right)}{x}+\frac{2 (x-2)}{x}\right)-\frac{2 \sqrt{x^2+x} \sqrt{x \left(\sqrt{x^2+x}+x\right)}}{x}",1,"(-2*Sqrt[x*(1 + x)]*(2 + 4*x + 4*Sqrt[x*(1 + x)] + (x + Sqrt[x*(1 + x)])*Hypergeometric2F1[-1/2, 1, 1/2, 1 + 1/(2*(x + Sqrt[x*(1 + x)]))]))/(Sqrt[x*(x + Sqrt[x*(1 + x)])]*(1 + x + Sqrt[x*(1 + x)]))","C",1
1603,1,140,109,0.3566739,"\int \frac{\sqrt{x^2+x \sqrt{x+x^2}}}{\sqrt{x+x^2}} \, dx","Integrate[Sqrt[x^2 + x*Sqrt[x + x^2]]/Sqrt[x + x^2],x]","\frac{(x+1) \sqrt{x \left(x+\sqrt{x (x+1)}\right)} \left(2 \sqrt{x+\sqrt{x (x+1)}} \left(2 x+2 \sqrt{x (x+1)}+3\right)-3 \sqrt{4 x+4 \sqrt{x (x+1)}+2} \sinh ^{-1}\left(\sqrt{2} \sqrt{x+\sqrt{x (x+1)}}\right)\right)}{4 \sqrt{x (x+1)} \sqrt{x+\sqrt{x (x+1)}} \left(x+\sqrt{x (x+1)}+1\right)}","\frac{3 \sqrt{x^2+x} \sqrt{x \left(\sqrt{x^2+x}+x\right)}}{2 x}+\sqrt{x \left(\sqrt{x^2+x}+x\right)} \left(-\frac{3 \sqrt{\sqrt{x^2+x}-x} \tanh ^{-1}\left(\sqrt{2} \sqrt{\sqrt{x^2+x}-x}\right)}{2 \sqrt{2} x}-\frac{1}{2}\right)",1,"((1 + x)*Sqrt[x*(x + Sqrt[x*(1 + x)])]*(2*Sqrt[x + Sqrt[x*(1 + x)]]*(3 + 2*x + 2*Sqrt[x*(1 + x)]) - 3*Sqrt[2 + 4*x + 4*Sqrt[x*(1 + x)]]*ArcSinh[Sqrt[2]*Sqrt[x + Sqrt[x*(1 + x)]]]))/(4*Sqrt[x*(1 + x)]*Sqrt[x + Sqrt[x*(1 + x)]]*(1 + x + Sqrt[x*(1 + x)]))","A",1
1604,1,149,109,0.3922741,"\int \frac{1}{\sqrt{b+\sqrt{b^2+a x^2}}} \, dx","Integrate[1/Sqrt[b + Sqrt[b^2 + a*x^2]],x]","\frac{\sqrt{\sqrt{a x^2+b^2}+b} \left(-2 b \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{b-\sqrt{b^2+a x^2}}{2 b}\right)+4 \sqrt{a x^2+b^2}-\sqrt{2} \sqrt{b} \sqrt{\sqrt{a x^2+b^2}-b} \tan ^{-1}\left(\frac{\sqrt{\sqrt{a x^2+b^2}-b}}{\sqrt{2} \sqrt{b}}\right)-2 b\right)}{2 a x}","\frac{2 x}{\sqrt{\sqrt{a x^2+b^2}+b}}-\frac{2 \sqrt{2} \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{2} \sqrt{b} \sqrt{\sqrt{a x^2+b^2}+b}}-\frac{\sqrt{\sqrt{a x^2+b^2}+b}}{\sqrt{2} \sqrt{b}}\right)}{\sqrt{a}}",1,"(Sqrt[b + Sqrt[b^2 + a*x^2]]*(-2*b + 4*Sqrt[b^2 + a*x^2] - Sqrt[2]*Sqrt[b]*Sqrt[-b + Sqrt[b^2 + a*x^2]]*ArcTan[Sqrt[-b + Sqrt[b^2 + a*x^2]]/(Sqrt[2]*Sqrt[b])] - 2*b*Hypergeometric2F1[-1/2, 1, 1/2, (b - Sqrt[b^2 + a*x^2])/(2*b)]))/(2*a*x)","C",1
1605,1,144,109,0.2881679,"\int \left(b^2+a x^2\right)^2 \sqrt{b+\sqrt{b^2+a x^2}} \, dx","Integrate[(b^2 + a*x^2)^2*Sqrt[b + Sqrt[b^2 + a*x^2]],x]","\frac{2 x \left(63 a^3 x^6 \sqrt{a x^2+b^2}+196 a^3 b x^6+914 a^2 b^3 x^4+472 a^2 b^2 x^4 \sqrt{a x^2+b^2}+1848 a b^5 x^2+1386 b^6 \sqrt{a x^2+b^2}+1155 a b^4 x^2 \sqrt{a x^2+b^2}+1386 b^7\right)}{693 \left(\sqrt{a x^2+b^2}+b\right)^{5/2}}","\frac{2 x \sqrt{a x^2+b^2} \left(63 a^2 x^4+206 a b^2 x^2+271 b^4\right)}{693 \sqrt{\sqrt{a x^2+b^2}+b}}+\frac{4 x \left(35 a^2 b x^4+118 a b^3 x^2+211 b^5\right)}{693 \sqrt{\sqrt{a x^2+b^2}+b}}",1,"(2*x*(1386*b^7 + 1848*a*b^5*x^2 + 914*a^2*b^3*x^4 + 196*a^3*b*x^6 + 1386*b^6*Sqrt[b^2 + a*x^2] + 1155*a*b^4*x^2*Sqrt[b^2 + a*x^2] + 472*a^2*b^2*x^4*Sqrt[b^2 + a*x^2] + 63*a^3*x^6*Sqrt[b^2 + a*x^2]))/(693*(b + Sqrt[b^2 + a*x^2])^(5/2))","A",1
1606,1,81,110,0.2979684,"\int \frac{1}{(1-3 x) \sqrt[3]{-x+x^3}} \, dx","Integrate[1/((1 - 3*x)*(-x + x^3)^(1/3)),x]","\frac{3 \sqrt[3]{\frac{\frac{1}{x}-1}{\frac{1}{x}-3}} \sqrt[3]{\frac{\frac{1}{x}+1}{\frac{1}{x}-3}} x F_1\left(\frac{2}{3};\frac{1}{3},\frac{1}{3};\frac{5}{3};-\frac{4}{\frac{1}{x}-3},-\frac{2}{\frac{1}{x}-3}\right)}{2 \sqrt[3]{x \left(x^2-1\right)}}","\frac{1}{4} \log \left(2 \sqrt[3]{x^3-x}+x+1\right)+\frac{1}{4} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x^3-x}}{\sqrt[3]{x^3-x}-x-1}\right)-\frac{1}{8} \log \left(4 \left(x^3-x\right)^{2/3}+(-2 x-2) \sqrt[3]{x^3-x}+x^2+2 x+1\right)",1,"(3*((-1 + x^(-1))/(-3 + x^(-1)))^(1/3)*((1 + x^(-1))/(-3 + x^(-1)))^(1/3)*x*AppellF1[2/3, 1/3, 1/3, 5/3, -4/(-3 + x^(-1)), -2/(-3 + x^(-1))])/(2*(x*(-1 + x^2))^(1/3))","C",0
1607,1,81,110,0.2654601,"\int \frac{1}{(1+3 x) \sqrt[3]{-x+x^3}} \, dx","Integrate[1/((1 + 3*x)*(-x + x^3)^(1/3)),x]","\frac{3 \sqrt[3]{\frac{\frac{1}{x}-1}{\frac{1}{x}+3}} \sqrt[3]{\frac{\frac{1}{x}+1}{\frac{1}{x}+3}} x F_1\left(\frac{2}{3};\frac{1}{3},\frac{1}{3};\frac{5}{3};\frac{2}{3+\frac{1}{x}},\frac{4}{3+\frac{1}{x}}\right)}{2 \sqrt[3]{x \left(x^2-1\right)}}","\frac{1}{4} \log \left(2 \sqrt[3]{x^3-x}+x-1\right)+\frac{1}{4} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x^3-x}}{\sqrt[3]{x^3-x}-x+1}\right)-\frac{1}{8} \log \left(4 \left(x^3-x\right)^{2/3}+(2-2 x) \sqrt[3]{x^3-x}+x^2-2 x+1\right)",1,"(3*((-1 + x^(-1))/(3 + x^(-1)))^(1/3)*((1 + x^(-1))/(3 + x^(-1)))^(1/3)*x*AppellF1[2/3, 1/3, 1/3, 5/3, 2/(3 + x^(-1)), 4/(3 + x^(-1))])/(2*(x*(-1 + x^2))^(1/3))","C",0
1608,1,35,110,0.0088703,"\int \frac{x}{\sqrt[3]{-x^2+x^3}} \, dx","Integrate[x/(-x^2 + x^3)^(1/3),x]","\frac{3 \left((x-1) x^2\right)^{2/3} \, _2F_1\left(-\frac{1}{3},\frac{2}{3};\frac{5}{3};1-x\right)}{2 x^{4/3}}","\frac{\left(x^3-x^2\right)^{2/3}}{x}-\frac{1}{3} \log \left(\sqrt[3]{x^3-x^2}-x\right)+\frac{1}{6} \log \left(x^2+\sqrt[3]{x^3-x^2} x+\left(x^3-x^2\right)^{2/3}\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-x^2}+x}\right)}{\sqrt{3}}",1,"(3*((-1 + x)*x^2)^(2/3)*Hypergeometric2F1[-1/3, 2/3, 5/3, 1 - x])/(2*x^(4/3))","C",1
1609,1,42,110,0.015792,"\int \frac{\left(1-x^3\right)^{2/3} \left(-1+x^3\right)}{x^6 \left(-1+2 x^3\right)} \, dx","Integrate[((1 - x^3)^(2/3)*(-1 + x^3))/(x^6*(-1 + 2*x^3)),x]","-\frac{\left(1-2 x^3\right)^{5/3} \, _2F_1\left(-\frac{5}{3},-\frac{5}{3};-\frac{2}{3};-\frac{x^3}{1-2 x^3}\right)}{5 x^5}","-\frac{1}{3} \log \left(\sqrt[3]{1-x^3}-x\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{1-x^3}+x}\right)}{\sqrt{3}}+\frac{\left(1-x^3\right)^{2/3} \left(-3 x^3-2\right)}{10 x^5}+\frac{1}{6} \log \left(\sqrt[3]{1-x^3} x+\left(1-x^3\right)^{2/3}+x^2\right)",1,"-1/5*((1 - 2*x^3)^(5/3)*Hypergeometric2F1[-5/3, -5/3, -2/3, -(x^3/(1 - 2*x^3))])/x^5","C",0
1610,1,585,110,7.2105757,"\int \frac{2 b+a x}{\left(b+a x+x^2\right) \sqrt[4]{b x^2+a x^3}} \, dx","Integrate[(2*b + a*x)/((b + a*x + x^2)*(b*x^2 + a*x^3)^(1/4)),x]","\frac{i \sqrt{2} a (a x+b)^{3/4} \sqrt{1-\frac{b}{a x+b}} \left(\left(a^2+\sqrt{a^4-4 a^2 b}-4 b\right) \sqrt{\frac{-a^2+\sqrt{a^4-4 a^2 b}+2 b}{b^2}} \Pi \left(-\frac{\sqrt{2}}{\sqrt{b} \sqrt{-\frac{a^2-2 b+\sqrt{a^4-4 a^2 b}}{b^2}}};\left.i \sinh ^{-1}\left(\frac{\sqrt{-\sqrt{b}}}{\sqrt[4]{b+a x}}\right)\right|-1\right)+\left(-a^2-\sqrt{a^4-4 a^2 b}+4 b\right) \sqrt{\frac{-a^2+\sqrt{a^4-4 a^2 b}+2 b}{b^2}} \Pi \left(\frac{\sqrt{2}}{\sqrt{b} \sqrt{-\frac{a^2-2 b+\sqrt{a^4-4 a^2 b}}{b^2}}};\left.i \sinh ^{-1}\left(\frac{\sqrt{-\sqrt{b}}}{\sqrt[4]{b+a x}}\right)\right|-1\right)+\sqrt{-\frac{a^2+\sqrt{a^4-4 a^2 b}-2 b}{b^2}} \left(-a^2+\sqrt{a^4-4 a^2 b}+4 b\right) \left(\Pi \left(-\frac{\sqrt{2}}{\sqrt{b} \sqrt{\frac{-a^2+2 b+\sqrt{a^4-4 a^2 b}}{b^2}}};\left.i \sinh ^{-1}\left(\frac{\sqrt{-\sqrt{b}}}{\sqrt[4]{b+a x}}\right)\right|-1\right)-\Pi \left(\frac{\sqrt{2}}{\sqrt{b} \sqrt{\frac{-a^2+2 b+\sqrt{a^4-4 a^2 b}}{b^2}}};\left.i \sinh ^{-1}\left(\frac{\sqrt{-\sqrt{b}}}{\sqrt[4]{b+a x}}\right)\right|-1\right)\right)\right)}{\sqrt{-\sqrt{b}} b \sqrt{a^4-4 a^2 b} \sqrt{-\frac{a^2+\sqrt{a^4-4 a^2 b}-2 b}{b^2}} \sqrt{\frac{-a^2+\sqrt{a^4-4 a^2 b}+2 b}{b^2}} \sqrt[4]{x^2 (a x+b)}}","\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{a x^3+b x^2}}{\sqrt{a x^3+b x^2}+x^2}\right)-\sqrt{2} \tan ^{-1}\left(\frac{\frac{\sqrt{a x^3+b x^2}}{\sqrt{2}}-\frac{x^2}{\sqrt{2}}}{x \sqrt[4]{a x^3+b x^2}}\right)",1,"(I*Sqrt[2]*a*(b + a*x)^(3/4)*Sqrt[1 - b/(b + a*x)]*((a^2 - 4*b + Sqrt[a^4 - 4*a^2*b])*Sqrt[(-a^2 + 2*b + Sqrt[a^4 - 4*a^2*b])/b^2]*EllipticPi[-(Sqrt[2]/(Sqrt[b]*Sqrt[-((a^2 - 2*b + Sqrt[a^4 - 4*a^2*b])/b^2)])), I*ArcSinh[Sqrt[-Sqrt[b]]/(b + a*x)^(1/4)], -1] + (-a^2 + 4*b - Sqrt[a^4 - 4*a^2*b])*Sqrt[(-a^2 + 2*b + Sqrt[a^4 - 4*a^2*b])/b^2]*EllipticPi[Sqrt[2]/(Sqrt[b]*Sqrt[-((a^2 - 2*b + Sqrt[a^4 - 4*a^2*b])/b^2)]), I*ArcSinh[Sqrt[-Sqrt[b]]/(b + a*x)^(1/4)], -1] + Sqrt[-((a^2 - 2*b + Sqrt[a^4 - 4*a^2*b])/b^2)]*(-a^2 + 4*b + Sqrt[a^4 - 4*a^2*b])*(EllipticPi[-(Sqrt[2]/(Sqrt[b]*Sqrt[(-a^2 + 2*b + Sqrt[a^4 - 4*a^2*b])/b^2])), I*ArcSinh[Sqrt[-Sqrt[b]]/(b + a*x)^(1/4)], -1] - EllipticPi[Sqrt[2]/(Sqrt[b]*Sqrt[(-a^2 + 2*b + Sqrt[a^4 - 4*a^2*b])/b^2]), I*ArcSinh[Sqrt[-Sqrt[b]]/(b + a*x)^(1/4)], -1])))/(Sqrt[-Sqrt[b]]*b*Sqrt[a^4 - 4*a^2*b]*Sqrt[-((a^2 - 2*b + Sqrt[a^4 - 4*a^2*b])/b^2)]*Sqrt[(-a^2 + 2*b + Sqrt[a^4 - 4*a^2*b])/b^2]*(x^2*(b + a*x))^(1/4))","C",1
1611,1,156,110,0.1949258,"\int \frac{x^3 \sqrt{x+x^4}}{-b+a x^3} \, dx","Integrate[(x^3*Sqrt[x + x^4])/(-b + a*x^3),x]","-\frac{x \sqrt{x^4+x} \left(x^3 (a+2 b) \sqrt{-\frac{x^3 (a+b)}{b}} F_1\left(\frac{3}{2};\frac{1}{2},1;\frac{5}{2};-x^3,\frac{a x^3}{b}\right)-3 b \left(\sqrt{x^3+1} \sqrt{-\frac{x^3 (a+b)}{b}}-\sin ^{-1}\left(\frac{\sqrt{-\frac{x^3 (a+b)}{b}}}{\sqrt{1-\frac{a x^3}{b}}}\right)\right)\right)}{9 a b \sqrt{x^3+1} \sqrt{-\frac{x^3 (a+b)}{b}}}","\frac{2 \sqrt{b} \sqrt{-a-b} \tan ^{-1}\left(\frac{x \sqrt{x^4+x} \sqrt{-a-b}}{\sqrt{b} (x+1) \left(x^2-x+1\right)}\right)}{3 a^2}+\frac{(a+2 b) \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4+x}}\right)}{3 a^2}+\frac{\sqrt{x^4+x} x}{3 a}",1,"-1/9*(x*Sqrt[x + x^4]*((a + 2*b)*x^3*Sqrt[-(((a + b)*x^3)/b)]*AppellF1[3/2, 1/2, 1, 5/2, -x^3, (a*x^3)/b] - 3*b*(Sqrt[-(((a + b)*x^3)/b)]*Sqrt[1 + x^3] - ArcSin[Sqrt[-(((a + b)*x^3)/b)]/Sqrt[1 - (a*x^3)/b]])))/(a*b*Sqrt[-(((a + b)*x^3)/b)]*Sqrt[1 + x^3])","C",0
1612,1,34,110,0.0112541,"\int x^9 \sqrt[3]{1+x^6} \, dx","Integrate[x^9*(1 + x^6)^(1/3),x]","\frac{1}{12} x^4 \left(\left(x^6+1\right)^{4/3}-\, _2F_1\left(-\frac{1}{3},\frac{2}{3};\frac{5}{3};-x^6\right)\right)","\frac{1}{54} \log \left(\sqrt[3]{x^6+1}-x^2\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x^2}{2 \sqrt[3]{x^6+1}+x^2}\right)}{18 \sqrt{3}}+\frac{1}{36} \sqrt[3]{x^6+1} \left(3 x^{10}+x^4\right)-\frac{1}{108} \log \left(\left(x^6+1\right)^{2/3}+x^4+\sqrt[3]{x^6+1} x^2\right)",1,"(x^4*((1 + x^6)^(4/3) - Hypergeometric2F1[-1/3, 2/3, 5/3, -x^6]))/12","C",1
1613,0,0,110,0.7418065,"\int \frac{\left(-1+x^3\right)^{2/3} \left(2+x^3\right)}{x^6 \left(4+x^6\right)} \, dx","Integrate[((-1 + x^3)^(2/3)*(2 + x^3))/(x^6*(4 + x^6)),x]","\int \frac{\left(-1+x^3\right)^{2/3} \left(2+x^3\right)}{x^6 \left(4+x^6\right)} \, dx","\frac{1}{96} \text{RootSum}\left[4 \text{$\#$1}^6-8 \text{$\#$1}^3+5\&,\frac{-6 \text{$\#$1}^3 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)+6 \text{$\#$1}^3 \log (x)+5 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)-5 \log (x)}{\text{$\#$1}^4-\text{$\#$1}}\&\right]+\frac{\left(x^3-1\right)^{2/3} \left(-x^3-4\right)}{40 x^5}",1,"Integrate[((-1 + x^3)^(2/3)*(2 + x^3))/(x^6*(4 + x^6)), x]","F",-1
1614,0,0,110,0.3413068,"\int \frac{\left(-1+x^3\right)^{2/3} \left(2+x^3\right)}{x^6 \left(4+x^6\right)} \, dx","Integrate[((-1 + x^3)^(2/3)*(2 + x^3))/(x^6*(4 + x^6)),x]","\int \frac{\left(-1+x^3\right)^{2/3} \left(2+x^3\right)}{x^6 \left(4+x^6\right)} \, dx","\frac{1}{96} \text{RootSum}\left[4 \text{$\#$1}^6-8 \text{$\#$1}^3+5\&,\frac{-6 \text{$\#$1}^3 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)+6 \text{$\#$1}^3 \log (x)+5 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)-5 \log (x)}{\text{$\#$1}^4-\text{$\#$1}}\&\right]+\frac{\left(x^3-1\right)^{2/3} \left(-x^3-4\right)}{40 x^5}",1,"Integrate[((-1 + x^3)^(2/3)*(2 + x^3))/(x^6*(4 + x^6)), x]","F",-1
1615,1,83,110,0.0490428,"\int \frac{b-a x^3+x^6}{x^6 \sqrt[4]{b x+a x^4}} \, dx","Integrate[(b - a*x^3 + x^6)/(x^6*(b*x + a*x^4)^(1/4)),x]","\frac{4 \left(11 a^2 x^6+21 b x^6 \sqrt[4]{\frac{a x^3}{b}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{4};\frac{5}{4};-\frac{a x^3}{b}\right)+8 a b x^3-3 b^2\right)}{63 b x^5 \sqrt[4]{x \left(a x^3+b\right)}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \left(a x^4+b x\right)^{3/4}}{a x^3+b}\right)}{3 \sqrt[4]{a}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{a} \left(a x^4+b x\right)^{3/4}}{a x^3+b}\right)}{3 \sqrt[4]{a}}+\frac{4 \left(a x^4+b x\right)^{3/4} \left(11 a x^3-3 b\right)}{63 b x^6}",1,"(4*(-3*b^2 + 8*a*b*x^3 + 11*a^2*x^6 + 21*b*x^6*(1 + (a*x^3)/b)^(1/4)*Hypergeometric2F1[1/4, 1/4, 5/4, -((a*x^3)/b)]))/(63*b*x^5*(x*(b + a*x^3))^(1/4))","C",1
1616,1,138,110,0.1261017,"\int \frac{-b+a x^6}{x^6 \sqrt[4]{b x+a x^4}} \, dx","Integrate[(-b + a*x^6)/(x^6*(b*x + a*x^4)^(1/4)),x]","\frac{2 \left(21 a^{3/4} b x^{21/4} \sqrt[4]{a x^3+b} \tan ^{-1}\left(\frac{\sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3+b}}\right)+21 a^{3/4} b x^{21/4} \sqrt[4]{a x^3+b} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3+b}}\right)-8 a^2 x^6-2 a b x^3+6 b^2\right)}{63 b x^5 \sqrt[4]{x \left(a x^3+b\right)}}","\frac{2}{3} a^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} \left(a x^4+b x\right)^{3/4}}{a x^3+b}\right)+\frac{2}{3} a^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \left(a x^4+b x\right)^{3/4}}{a x^3+b}\right)-\frac{4 \left(a x^4+b x\right)^{3/4} \left(4 a x^3-3 b\right)}{63 b x^6}",1,"(2*(6*b^2 - 2*a*b*x^3 - 8*a^2*x^6 + 21*a^(3/4)*b*x^(21/4)*(b + a*x^3)^(1/4)*ArcTan[(a^(1/4)*x^(3/4))/(b + a*x^3)^(1/4)] + 21*a^(3/4)*b*x^(21/4)*(b + a*x^3)^(1/4)*ArcTanh[(a^(1/4)*x^(3/4))/(b + a*x^3)^(1/4)]))/(63*b*x^5*(x*(b + a*x^3))^(1/4))","A",1
1617,1,138,110,0.0806525,"\int \frac{b+a x^6}{x^6 \sqrt[4]{b x+a x^4}} \, dx","Integrate[(b + a*x^6)/(x^6*(b*x + a*x^4)^(1/4)),x]","\frac{2 \left(21 a^{3/4} b x^{21/4} \sqrt[4]{a x^3+b} \tan ^{-1}\left(\frac{\sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3+b}}\right)+21 a^{3/4} b x^{21/4} \sqrt[4]{a x^3+b} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3+b}}\right)+8 a^2 x^6+2 a b x^3-6 b^2\right)}{63 b x^5 \sqrt[4]{x \left(a x^3+b\right)}}","\frac{2}{3} a^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} \left(a x^4+b x\right)^{3/4}}{a x^3+b}\right)+\frac{2}{3} a^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \left(a x^4+b x\right)^{3/4}}{a x^3+b}\right)+\frac{4 \left(a x^4+b x\right)^{3/4} \left(4 a x^3-3 b\right)}{63 b x^6}",1,"(2*(-6*b^2 + 2*a*b*x^3 + 8*a^2*x^6 + 21*a^(3/4)*b*x^(21/4)*(b + a*x^3)^(1/4)*ArcTan[(a^(1/4)*x^(3/4))/(b + a*x^3)^(1/4)] + 21*a^(3/4)*b*x^(21/4)*(b + a*x^3)^(1/4)*ArcTanh[(a^(1/4)*x^(3/4))/(b + a*x^3)^(1/4)]))/(63*b*x^5*(x*(b + a*x^3))^(1/4))","A",1
1618,0,0,110,0.6481133,"\int \frac{-3 b+2 a x^5}{\left(2 b+x^3+2 a x^5\right) \sqrt[4]{b x+a x^6}} \, dx","Integrate[(-3*b + 2*a*x^5)/((2*b + x^3 + 2*a*x^5)*(b*x + a*x^6)^(1/4)),x]","\int \frac{-3 b+2 a x^5}{\left(2 b+x^3+2 a x^5\right) \sqrt[4]{b x+a x^6}} \, dx","-\frac{\tan ^{-1}\left(\frac{2^{3/4} x \sqrt[4]{a x^6+b x}}{\sqrt{2} \sqrt{a x^6+b x}-x^2}\right)}{\sqrt[4]{2}}-\frac{\tanh ^{-1}\left(\frac{\frac{\sqrt{a x^6+b x}}{\sqrt[4]{2}}+\frac{x^2}{2^{3/4}}}{x \sqrt[4]{a x^6+b x}}\right)}{\sqrt[4]{2}}",1,"Integrate[(-3*b + 2*a*x^5)/((2*b + x^3 + 2*a*x^5)*(b*x + a*x^6)^(1/4)), x]","F",-1
1619,1,313,110,0.6876142,"\int \frac{1}{\sqrt[3]{b^2 x^2+a^3 x^3} \left(2 b+a^6 x^6\right)} \, dx","Integrate[1/((b^2*x^2 + a^3*x^3)^(1/3)*(2*b + a^6*x^6)),x]","\frac{x \left(\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(2 a^2+2^{5/6} (-b)^{11/6}\right) x}{2 \left(x a^3+b^2\right)}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(2 a^2+\sqrt[3]{-1} 2^{5/6} (-b)^{11/6}\right) x}{2 \left(x a^3+b^2\right)}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(2 a^2+(-1)^{2/3} 2^{5/6} (-b)^{11/6}\right) x}{2 \left(x a^3+b^2\right)}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(2 a^2+2^{5/6} (-b)^{5/6} b\right) x}{2 \left(x a^3+b^2\right)}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(2 a^2+\sqrt[3]{-1} 2^{5/6} (-b)^{5/6} b\right) x}{2 \left(x a^3+b^2\right)}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(2 a^2+(-1)^{2/3} 2^{5/6} (-b)^{5/6} b\right) x}{2 \left(x a^3+b^2\right)}\right)\right)}{4 b \sqrt[3]{x^2 \left(a^3 x+b^2\right)}}","-\frac{\text{RootSum}\left[2 \text{$\#$1}^{18}-12 \text{$\#$1}^{15} a^3+30 \text{$\#$1}^{12} a^6-40 \text{$\#$1}^9 a^9+30 \text{$\#$1}^6 a^{12}-12 \text{$\#$1}^3 a^{15}+2 a^{18}+a^6 b^{11}\&,\frac{\log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{12 b}",1,"(x*(Hypergeometric2F1[1/3, 1, 4/3, (a*(2*a^2 + 2^(5/6)*(-b)^(11/6))*x)/(2*(b^2 + a^3*x))] + Hypergeometric2F1[1/3, 1, 4/3, (a*(2*a^2 + (-1)^(1/3)*2^(5/6)*(-b)^(11/6))*x)/(2*(b^2 + a^3*x))] + Hypergeometric2F1[1/3, 1, 4/3, (a*(2*a^2 + (-1)^(2/3)*2^(5/6)*(-b)^(11/6))*x)/(2*(b^2 + a^3*x))] + Hypergeometric2F1[1/3, 1, 4/3, (a*(2*a^2 + 2^(5/6)*(-b)^(5/6)*b)*x)/(2*(b^2 + a^3*x))] + Hypergeometric2F1[1/3, 1, 4/3, (a*(2*a^2 + (-1)^(1/3)*2^(5/6)*(-b)^(5/6)*b)*x)/(2*(b^2 + a^3*x))] + Hypergeometric2F1[1/3, 1, 4/3, (a*(2*a^2 + (-1)^(2/3)*2^(5/6)*(-b)^(5/6)*b)*x)/(2*(b^2 + a^3*x))]))/(4*b*(x^2*(b^2 + a^3*x))^(1/3))","B",1
1620,1,313,110,0.2630971,"\int \frac{1}{\sqrt[3]{b^2 x^2+a^3 x^3} \left(2 b+a^6 x^6\right)} \, dx","Integrate[1/((b^2*x^2 + a^3*x^3)^(1/3)*(2*b + a^6*x^6)),x]","\frac{x \left(\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(2 a^2+2^{5/6} (-b)^{11/6}\right) x}{2 \left(x a^3+b^2\right)}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(2 a^2+\sqrt[3]{-1} 2^{5/6} (-b)^{11/6}\right) x}{2 \left(x a^3+b^2\right)}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(2 a^2+(-1)^{2/3} 2^{5/6} (-b)^{11/6}\right) x}{2 \left(x a^3+b^2\right)}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(2 a^2+2^{5/6} (-b)^{5/6} b\right) x}{2 \left(x a^3+b^2\right)}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(2 a^2+\sqrt[3]{-1} 2^{5/6} (-b)^{5/6} b\right) x}{2 \left(x a^3+b^2\right)}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(2 a^2+(-1)^{2/3} 2^{5/6} (-b)^{5/6} b\right) x}{2 \left(x a^3+b^2\right)}\right)\right)}{4 b \sqrt[3]{x^2 \left(a^3 x+b^2\right)}}","-\frac{\text{RootSum}\left[2 \text{$\#$1}^{18}-12 \text{$\#$1}^{15} a^3+30 \text{$\#$1}^{12} a^6-40 \text{$\#$1}^9 a^9+30 \text{$\#$1}^6 a^{12}-12 \text{$\#$1}^3 a^{15}+2 a^{18}+a^6 b^{11}\&,\frac{\log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{12 b}",1,"(x*(Hypergeometric2F1[1/3, 1, 4/3, (a*(2*a^2 + 2^(5/6)*(-b)^(11/6))*x)/(2*(b^2 + a^3*x))] + Hypergeometric2F1[1/3, 1, 4/3, (a*(2*a^2 + (-1)^(1/3)*2^(5/6)*(-b)^(11/6))*x)/(2*(b^2 + a^3*x))] + Hypergeometric2F1[1/3, 1, 4/3, (a*(2*a^2 + (-1)^(2/3)*2^(5/6)*(-b)^(11/6))*x)/(2*(b^2 + a^3*x))] + Hypergeometric2F1[1/3, 1, 4/3, (a*(2*a^2 + 2^(5/6)*(-b)^(5/6)*b)*x)/(2*(b^2 + a^3*x))] + Hypergeometric2F1[1/3, 1, 4/3, (a*(2*a^2 + (-1)^(1/3)*2^(5/6)*(-b)^(5/6)*b)*x)/(2*(b^2 + a^3*x))] + Hypergeometric2F1[1/3, 1, 4/3, (a*(2*a^2 + (-1)^(2/3)*2^(5/6)*(-b)^(5/6)*b)*x)/(2*(b^2 + a^3*x))]))/(4*b*(x^2*(b^2 + a^3*x))^(1/3))","B",1
1621,1,1525,110,2.2881073,"\int \frac{\left(-1+x^4\right) \left(1+x^2+3 x^4+x^6+x^8\right)}{\left(1+x^2+x^4\right)^{3/2} \left(1+3 x^2+5 x^4+3 x^6+x^8\right)} \, dx","Integrate[((-1 + x^4)*(1 + x^2 + 3*x^4 + x^6 + x^8))/((1 + x^2 + x^4)^(3/2)*(1 + 3*x^2 + 5*x^4 + 3*x^6 + x^8)),x]","\frac{-x-2 (-1)^{2/3} \sqrt{\sqrt[3]{-1} x^2+1} \sqrt{1-(-1)^{2/3} x^2} \left(-\frac{\left(-1+\text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,1\right]^2\right) \Pi \left(-\frac{\sqrt[3]{-1}}{\text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,1\right]};i \sinh ^{-1}\left((-1)^{5/6} x\right)|(-1)^{2/3}\right)}{\left(\text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,1\right]-\text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,2\right]\right) \left(\text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,1\right]-\text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,3\right]\right) \left(\text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,1\right]-\text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,4\right]\right)}+\frac{\Pi \left(-\frac{\sqrt[3]{-1}}{\text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,4\right]};i \sinh ^{-1}\left((-1)^{5/6} x\right)|(-1)^{2/3}\right)}{\left(-\text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,1\right]+\text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,4\right]\right) \left(-\text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,2\right]+\text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,4\right]\right) \left(-\text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,3\right]+\text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,4\right]\right)}-\frac{\Pi \left(-\frac{\sqrt[3]{-1}}{\text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,4\right]};i \sinh ^{-1}\left((-1)^{5/6} x\right)|(-1)^{2/3}\right) \text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,4\right]^2}{\left(-\text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,1\right]+\text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,4\right]\right) \left(-\text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,2\right]+\text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,4\right]\right) \left(-\text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,3\right]+\text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,4\right]\right)}+\frac{\Pi \left(-\frac{\sqrt[3]{-1}}{\text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,3\right]};i \sinh ^{-1}\left((-1)^{5/6} x\right)|(-1)^{2/3}\right)}{\left(-\text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,1\right]+\text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,3\right]\right) \left(-\text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,2\right]+\text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,3\right]\right) \left(\text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,3\right]-\text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,4\right]\right)}-\frac{\Pi \left(-\frac{\sqrt[3]{-1}}{\text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,3\right]};i \sinh ^{-1}\left((-1)^{5/6} x\right)|(-1)^{2/3}\right) \text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,3\right]^2}{\left(-\text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,1\right]+\text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,3\right]\right) \left(-\text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,2\right]+\text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,3\right]\right) \left(\text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,3\right]-\text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,4\right]\right)}+\frac{\Pi \left(-\frac{\sqrt[3]{-1}}{\text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,2\right]};i \sinh ^{-1}\left((-1)^{5/6} x\right)|(-1)^{2/3}\right) \left(-1+\text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,2\right]^2\right)}{\left(\text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,1\right]-\text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,2\right]\right) \left(\text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,2\right]-\text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,3\right]\right) \left(\text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,2\right]-\text{Root}\left[\text{$\#$1}^4+3 \text{$\#$1}^3+5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,4\right]\right)}\right)}{\sqrt{x^4+x^2+1}}","-\frac{x}{\sqrt{x^4+x^2+1}}+\sqrt{\frac{1}{3} \left(-2+2 i \sqrt{3}\right)} \tan ^{-1}\left(\frac{2 x}{\left(\sqrt{3}-i\right) \sqrt{x^4+x^2+1}}\right)+\sqrt{\frac{1}{3} \left(-2-2 i \sqrt{3}\right)} \tan ^{-1}\left(\frac{2 x}{\left(\sqrt{3}+i\right) \sqrt{x^4+x^2+1}}\right)",1,"(-x - 2*(-1)^(2/3)*Sqrt[1 + (-1)^(1/3)*x^2]*Sqrt[1 - (-1)^(2/3)*x^2]*(-((EllipticPi[-((-1)^(1/3)/Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 1, 0]), I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)]*(-1 + Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 1, 0]^2))/((Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 1, 0] - Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 2, 0])*(Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 1, 0] - Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 3, 0])*(Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 1, 0] - Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 4, 0]))) + (EllipticPi[-((-1)^(1/3)/Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 2, 0]), I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)]*(-1 + Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 2, 0]^2))/((Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 1, 0] - Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 2, 0])*(Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 2, 0] - Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 3, 0])*(Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 2, 0] - Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 4, 0])) + EllipticPi[-((-1)^(1/3)/Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 3, 0]), I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)]/((-Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 1, 0] + Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 3, 0])*(-Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 2, 0] + Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 3, 0])*(Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 3, 0] - Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 4, 0])) - (EllipticPi[-((-1)^(1/3)/Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 3, 0]), I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)]*Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 3, 0]^2)/((-Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 1, 0] + Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 3, 0])*(-Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 2, 0] + Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 3, 0])*(Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 3, 0] - Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 4, 0])) + EllipticPi[-((-1)^(1/3)/Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 4, 0]), I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)]/((-Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 1, 0] + Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 4, 0])*(-Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 2, 0] + Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 4, 0])*(-Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 3, 0] + Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 4, 0])) - (EllipticPi[-((-1)^(1/3)/Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 4, 0]), I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)]*Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 4, 0]^2)/((-Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 1, 0] + Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 4, 0])*(-Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 2, 0] + Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 4, 0])*(-Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 3, 0] + Root[1 + 3*#1 + 5*#1^2 + 3*#1^3 + #1^4 & , 4, 0]))))/Sqrt[1 + x^2 + x^4]","C",0
1622,0,0,110,0.4981555,"\int \frac{-b+a x^8}{\sqrt[4]{b+a x^4} \left(b+a x^8\right)} \, dx","Integrate[(-b + a*x^8)/((b + a*x^4)^(1/4)*(b + a*x^8)),x]","\int \frac{-b+a x^8}{\sqrt[4]{b+a x^4} \left(b+a x^8\right)} \, dx","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{\log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{2 \sqrt[4]{a}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{2 \sqrt[4]{a}}",1,"Integrate[(-b + a*x^8)/((b + a*x^4)^(1/4)*(b + a*x^8)), x]","F",-1
1623,0,0,110,0.2311893,"\int \frac{-b+a x^8}{\sqrt[4]{b+a x^4} \left(b+a x^8\right)} \, dx","Integrate[(-b + a*x^8)/((b + a*x^4)^(1/4)*(b + a*x^8)),x]","\int \frac{-b+a x^8}{\sqrt[4]{b+a x^4} \left(b+a x^8\right)} \, dx","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{\log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{2 \sqrt[4]{a}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{2 \sqrt[4]{a}}",1,"Integrate[(-b + a*x^8)/((b + a*x^4)^(1/4)*(b + a*x^8)), x]","F",-1
1624,0,0,110,0.675931,"\int \frac{\left(-3+2 x+2 x^5\right) \sqrt{x-x^2+x^6}}{1-2 x+x^2-x^3+x^4+2 x^5-3 x^6-x^8+x^{10}} \, dx","Integrate[((-3 + 2*x + 2*x^5)*Sqrt[x - x^2 + x^6])/(1 - 2*x + x^2 - x^3 + x^4 + 2*x^5 - 3*x^6 - x^8 + x^10),x]","\int \frac{\left(-3+2 x+2 x^5\right) \sqrt{x-x^2+x^6}}{1-2 x+x^2-x^3+x^4+2 x^5-3 x^6-x^8+x^{10}} \, dx","\sqrt{\frac{1}{5} \left(2 \sqrt{5}-2\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{1}{2}+\frac{\sqrt{5}}{2}} \sqrt{x^6-x^2+x}}{x^2}\right)-\sqrt{\frac{1}{5} \left(2+2 \sqrt{5}\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}} \sqrt{x^6-x^2+x}}{x^2}\right)",1,"Integrate[((-3 + 2*x + 2*x^5)*Sqrt[x - x^2 + x^6])/(1 - 2*x + x^2 - x^3 + x^4 + 2*x^5 - 3*x^6 - x^8 + x^10), x]","F",-1
1625,1,88,110,0.1333135,"\int \frac{\sqrt{x+\sqrt{1+x}}}{x^2 \sqrt{1+x}} \, dx","Integrate[Sqrt[x + Sqrt[1 + x]]/(x^2*Sqrt[1 + x]),x]","\frac{1}{4} \left(-\frac{4 \sqrt{x+1} \sqrt{x+\sqrt{x+1}}}{x}+3 \tan ^{-1}\left(\frac{\sqrt{x+1}+3}{2 \sqrt{x+\sqrt{x+1}}}\right)+\tanh ^{-1}\left(\frac{1-3 \sqrt{x+1}}{2 \sqrt{x+\sqrt{x+1}}}\right)\right)","-\frac{\sqrt{x+1} \sqrt{x+\sqrt{x+1}}}{x}+\frac{3}{2} \tan ^{-1}\left(\frac{\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}}{\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}+2}\right)-\frac{1}{2} \tanh ^{-1}\left(-\sqrt{x+1}+\sqrt{x+\sqrt{x+1}}+1\right)",1,"((-4*Sqrt[1 + x]*Sqrt[x + Sqrt[1 + x]])/x + 3*ArcTan[(3 + Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])] + ArcTanh[(1 - 3*Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])])/4","A",1
1626,1,90,110,0.0424741,"\int \frac{\sqrt{x+\sqrt{1+x}}}{x \sqrt{1+x}} \, dx","Integrate[Sqrt[x + Sqrt[1 + x]]/(x*Sqrt[1 + x]),x]","-\tan ^{-1}\left(\frac{\sqrt{x+1}+3}{2 \sqrt{x+\sqrt{x+1}}}\right)+\tanh ^{-1}\left(\frac{1-3 \sqrt{x+1}}{2 \sqrt{x+\sqrt{x+1}}}\right)+2 \tanh ^{-1}\left(\frac{2 \sqrt{x+1}+1}{2 \sqrt{x+\sqrt{x+1}}}\right)","-2 \log \left(2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)-2 \tan ^{-1}\left(\frac{\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}}{\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}+2}\right)-2 \tanh ^{-1}\left(-\sqrt{x+1}+\sqrt{x+\sqrt{x+1}}+1\right)",1,"-ArcTan[(3 + Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])] + ArcTanh[(1 - 3*Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])] + 2*ArcTanh[(1 + 2*Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])]","A",1
1627,1,89,110,0.0919655,"\int \frac{\sqrt{a x+\sqrt{-b+a x}}}{\sqrt{-b+a x}} \, dx","Integrate[Sqrt[a*x + Sqrt[-b + a*x]]/Sqrt[-b + a*x],x]","\frac{2 \sqrt{\sqrt{a x-b}+a x} \left(2 \sqrt{a x-b}+1\right)+(4 b-1) \tanh ^{-1}\left(\frac{2 \sqrt{a x-b}+1}{2 \sqrt{\sqrt{a x-b}+a x}}\right)}{4 a}","\frac{\sqrt{a x-b} \sqrt{\sqrt{a x-b}+a x}}{a}+\frac{\sqrt{\sqrt{a x-b}+a x}}{2 a}+\frac{(1-4 b) \log \left(2 \sqrt{a x-b}-2 \sqrt{\sqrt{a x-b}+a x}+1\right)}{4 a}",1,"(2*Sqrt[a*x + Sqrt[-b + a*x]]*(1 + 2*Sqrt[-b + a*x]) + (-1 + 4*b)*ArcTanh[(1 + 2*Sqrt[-b + a*x])/(2*Sqrt[a*x + Sqrt[-b + a*x]])])/(4*a)","A",1
1628,1,106,110,0.2146531,"\int \frac{1-a x+b \sqrt{a+b x}}{\sqrt{a+b x} \left(x+a b \sqrt{a+b x}\right)} \, dx","Integrate[(1 - a*x + b*Sqrt[a + b*x])/(Sqrt[a + b*x]*(x + a*b*Sqrt[a + b*x])),x]","-\frac{2 \left(a^3 b^3+a b^3-2\right) \tanh ^{-1}\left(\frac{-a b^2-2 \sqrt{a+b x}}{\sqrt{a} \sqrt{a b^4+4}}\right)}{\sqrt{a} \sqrt{a b^4+4}}+\left(a^2+1\right) b \log \left(a b \sqrt{a+b x}+x\right)-\frac{2 a \sqrt{a+b x}}{b}","\frac{2 \left(a^3 b^3+a b^3-2\right) \tanh ^{-1}\left(\frac{a b^2+2 \sqrt{a+b x}}{\sqrt{a} \sqrt{a b^4+4}}\right)}{\sqrt{a} \sqrt{a b^4+4}}+\left(a^2 b+b\right) \log \left(a b^2 \sqrt{a+b x}+b x\right)-\frac{2 a \sqrt{a+b x}}{b}",1,"(-2*a*Sqrt[a + b*x])/b - (2*(-2 + a*b^3 + a^3*b^3)*ArcTanh[(-(a*b^2) - 2*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[4 + a*b^4])])/(Sqrt[a]*Sqrt[4 + a*b^4]) + (1 + a^2)*b*Log[x + a*b*Sqrt[a + b*x]]","A",1
1629,1,99,110,0.2638062,"\int \frac{\sqrt{b+\sqrt{b^2+a x^2}}}{x^2} \, dx","Integrate[Sqrt[b + Sqrt[b^2 + a*x^2]]/x^2,x]","\frac{\sqrt{\sqrt{a x^2+b^2}+b} \left(\sqrt{2} \sqrt{\sqrt{a x^2+b^2}-b} \tan ^{-1}\left(\frac{\sqrt{\sqrt{a x^2+b^2}-b}}{\sqrt{2} \sqrt{b}}\right)-2 \sqrt{b}\right)}{2 \sqrt{b} x}","\frac{\sqrt{2} \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{2} \sqrt{b} \sqrt{\sqrt{a x^2+b^2}+b}}-\frac{\sqrt{\sqrt{a x^2+b^2}+b}}{\sqrt{2} \sqrt{b}}\right)}{\sqrt{b}}-\frac{\sqrt{\sqrt{a x^2+b^2}+b}}{x}",1,"(Sqrt[b + Sqrt[b^2 + a*x^2]]*(-2*Sqrt[b] + Sqrt[2]*Sqrt[-b + Sqrt[b^2 + a*x^2]]*ArcTan[Sqrt[-b + Sqrt[b^2 + a*x^2]]/(Sqrt[2]*Sqrt[b])]))/(2*Sqrt[b]*x)","A",1
1630,0,0,110,1.4179811,"\int \frac{1}{\sqrt{-b x+a^2 x^2} \left(a x^2+x \sqrt{-b x+a^2 x^2}\right)^{3/2}} \, dx","Integrate[1/(Sqrt[-(b*x) + a^2*x^2]*(a*x^2 + x*Sqrt[-(b*x) + a^2*x^2])^(3/2)),x]","\int \frac{1}{\sqrt{-b x+a^2 x^2} \left(a x^2+x \sqrt{-b x+a^2 x^2}\right)^{3/2}} \, dx","\frac{4 \left(32 a^3 x+39 a b\right) \sqrt{x \left(\sqrt{a^2 x^2-b x}+a x\right)}}{105 b^3 x^2}-\frac{4 \left(15 b-32 a^2 x\right) \sqrt{a^2 x^2-b x} \sqrt{x \left(\sqrt{a^2 x^2-b x}+a x\right)}}{105 b^3 x^3}",1,"Integrate[1/(Sqrt[-(b*x) + a^2*x^2]*(a*x^2 + x*Sqrt[-(b*x) + a^2*x^2])^(3/2)), x]","F",-1
1631,1,84,110,0.0428856,"\int \frac{1}{1+\sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[(1 + Sqrt[x + Sqrt[1 + x^2]])^(-1),x]","\sqrt{\sqrt{x^2+1}+x}+\frac{1}{\sqrt{\sqrt{x^2+1}+x}}-\frac{1}{2 \left(\sqrt{x^2+1}+x\right)}+\frac{1}{2} \log \left(\sqrt{x^2+1}+x\right)-2 \log \left(\sqrt{\sqrt{x^2+1}+x}+1\right)","\frac{\sqrt{x^2+1} \left(2 \sqrt{\sqrt{x^2+1}+x}+5\right)+(2 x+2) \sqrt{\sqrt{x^2+1}+x}+5 x-1}{2 \sqrt{x^2+1}+2 x}+\frac{1}{2} \log \left(\sqrt{x^2+1}+x\right)-2 \log \left(\sqrt{\sqrt{x^2+1}+x}+1\right)",1,"-1/2*1/(x + Sqrt[1 + x^2]) + 1/Sqrt[x + Sqrt[1 + x^2]] + Sqrt[x + Sqrt[1 + x^2]] + Log[x + Sqrt[1 + x^2]]/2 - 2*Log[1 + Sqrt[x + Sqrt[1 + x^2]]]","A",1
1632,0,0,111,0.1762802,"\int \frac{-2+x}{\left(2+x^2\right) \sqrt[3]{-1+x+2 x^2}} \, dx","Integrate[(-2 + x)/((2 + x^2)*(-1 + x + 2*x^2)^(1/3)),x]","\int \frac{-2+x}{\left(2+x^2\right) \sqrt[3]{-1+x+2 x^2}} \, dx","\frac{1}{2} \log \left(\sqrt[3]{2 x^2+x-1}-x-1\right)-\frac{1}{4} \log \left(x^2+\left(2 x^2+x-1\right)^{2/3}+(x+1) \sqrt[3]{2 x^2+x-1}+2 x+1\right)+\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{2 x^2+x-1}}{\sqrt[3]{2 x^2+x-1}+2 x+2}\right)",1,"Integrate[(-2 + x)/((2 + x^2)*(-1 + x + 2*x^2)^(1/3)), x]","F",-1
1633,0,0,111,24.6812004,"\int \frac{(-a+x) (-b+x) (-2 a b+(a+b) x)}{\left(x^2 (-a+x) (-b+x)\right)^{3/4} \left(-a b+(a+b) x+(-1+d) x^2\right)} \, dx","Integrate[((-a + x)*(-b + x)*(-2*a*b + (a + b)*x))/((x^2*(-a + x)*(-b + x))^(3/4)*(-(a*b) + (a + b)*x + (-1 + d)*x^2)),x]","\int \frac{(-a+x) (-b+x) (-2 a b+(a+b) x)}{\left(x^2 (-a+x) (-b+x)\right)^{3/4} \left(-a b+(a+b) x+(-1+d) x^2\right)} \, dx","-2 \sqrt[4]{d} \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{x^3 (-a-b)+a b x^2+x^4}}\right)+2 \sqrt[4]{d} \tanh ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{x^3 (-a-b)+a b x^2+x^4}}\right)-\frac{4 \sqrt[4]{x^3 (-a-b)+a b x^2+x^4}}{x}",1,"Integrate[((-a + x)*(-b + x)*(-2*a*b + (a + b)*x))/((x^2*(-a + x)*(-b + x))^(3/4)*(-(a*b) + (a + b)*x + (-1 + d)*x^2)), x]","F",-1
1634,1,278,111,0.9143314,"\int \frac{1-x+x^2}{\left(-2+2 x+x^2\right) \sqrt{1+x^3}} \, dx","Integrate[(1 - x + x^2)/((-2 + 2*x + x^2)*Sqrt[1 + x^3]),x]","\frac{\sqrt{\frac{x+1}{1+\sqrt[3]{-1}}} \left(i \sqrt{x^2-x+1} \left(\left(\sqrt{3}+(-2+i)\right) \Pi \left(\frac{2 \sqrt{3}}{-3 i+(1+2 i) \sqrt{3}};\sin ^{-1}\left(\sqrt{\frac{(-1)^{2/3} x+1}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)+\left(\sqrt{3}+(2+i)\right) \Pi \left(\frac{2 i \sqrt{3}}{3+(2+i) \sqrt{3}};\sin ^{-1}\left(\sqrt{\frac{(-1)^{2/3} x+1}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)\right)+\frac{2 \sqrt{\frac{\sqrt[3]{-1}-(-1)^{2/3} x}{1+\sqrt[3]{-1}}} \left(\left(\sqrt{3}+i\right) x-2 i\right) F\left(\sin ^{-1}\left(\sqrt{\frac{(-1)^{2/3} x+1}{1+\sqrt[3]{-1}}}\right)|\sqrt[3]{-1}\right)}{\sqrt{\frac{(-1)^{2/3} x+1}{1+\sqrt[3]{-1}}}}\right)}{\left(\sqrt{3}+i\right) \sqrt{x^3+1}}","-\frac{1}{2} \sqrt{\frac{1}{3} \left(3+2 \sqrt{3}\right)} \tan ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} \sqrt{x^3+1}}{x^2-x+1}\right)-\frac{1}{2} \sqrt{\frac{1}{3} \left(2 \sqrt{3}-3\right)} \tanh ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} \sqrt{x^3+1}}{x^2-x+1}\right)",1,"(Sqrt[(1 + x)/(1 + (-1)^(1/3))]*((2*Sqrt[((-1)^(1/3) - (-1)^(2/3)*x)/(1 + (-1)^(1/3))]*(-2*I + (I + Sqrt[3])*x)*EllipticF[ArcSin[Sqrt[(1 + (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)])/Sqrt[(1 + (-1)^(2/3)*x)/(1 + (-1)^(1/3))] + I*Sqrt[1 - x + x^2]*(((-2 + I) + Sqrt[3])*EllipticPi[(2*Sqrt[3])/(-3*I + (1 + 2*I)*Sqrt[3]), ArcSin[Sqrt[(1 + (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)] + ((2 + I) + Sqrt[3])*EllipticPi[((2*I)*Sqrt[3])/(3 + (2 + I)*Sqrt[3]), ArcSin[Sqrt[(1 + (-1)^(2/3)*x)/(1 + (-1)^(1/3))]], (-1)^(1/3)])))/((I + Sqrt[3])*Sqrt[1 + x^3])","C",0
1635,1,35,111,0.015409,"\int \frac{-1+x}{x \sqrt[3]{-x^2+x^3}} \, dx","Integrate[(-1 + x)/(x*(-x^2 + x^3)^(1/3)),x]","\frac{3 \left((x-1) x^2\right)^{5/3} \, _2F_1\left(\frac{5}{3},\frac{5}{3};\frac{8}{3};1-x\right)}{5 x^{10/3}}","-\frac{3 \left(x^3-x^2\right)^{2/3}}{2 x^2}-\log \left(\sqrt[3]{x^3-x^2}-x\right)+\frac{1}{2} \log \left(x^2+\sqrt[3]{x^3-x^2} x+\left(x^3-x^2\right)^{2/3}\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-x^2}+x}\right)",1,"(3*((-1 + x)*x^2)^(5/3)*Hypergeometric2F1[5/3, 5/3, 8/3, 1 - x])/(5*x^(10/3))","C",1
1636,1,41,111,0.0160691,"\int \frac{1+x}{x \sqrt[3]{-x^2+x^3}} \, dx","Integrate[(1 + x)/(x*(-x^2 + x^3)^(1/3)),x]","\frac{3 \left((x-1) x^2\right)^{2/3} \left(x^{2/3} \, _2F_1\left(\frac{2}{3},\frac{2}{3};\frac{5}{3};1-x\right)+1\right)}{2 x^2}","\frac{3 \left(x^3-x^2\right)^{2/3}}{2 x^2}-\log \left(\sqrt[3]{x^3-x^2}-x\right)+\frac{1}{2} \log \left(x^2+\sqrt[3]{x^3-x^2} x+\left(x^3-x^2\right)^{2/3}\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-x^2}+x}\right)",1,"(3*((-1 + x)*x^2)^(2/3)*(1 + x^(2/3)*Hypergeometric2F1[2/3, 2/3, 5/3, 1 - x]))/(2*x^2)","C",1
1637,1,38,111,0.0112966,"\int \frac{x^2}{\sqrt[3]{x^2+x^3}} \, dx","Integrate[x^2/(x^2 + x^3)^(1/3),x]","\frac{3 x^3 \sqrt[3]{x+1} \, _2F_1\left(\frac{1}{3},\frac{7}{3};\frac{10}{3};-x\right)}{7 \sqrt[3]{x^2 (x+1)}}","\frac{\left(x^3+x^2\right)^{2/3} (3 x-4)}{6 x}-\frac{2}{9} \log \left(\sqrt[3]{x^3+x^2}-x\right)+\frac{1}{9} \log \left(x^2+\sqrt[3]{x^3+x^2} x+\left(x^3+x^2\right)^{2/3}\right)+\frac{2 \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+x^2}+x}\right)}{3 \sqrt{3}}",1,"(3*x^3*(1 + x)^(1/3)*Hypergeometric2F1[1/3, 7/3, 10/3, -x])/(7*(x^2*(1 + x))^(1/3))","C",1
1638,0,0,111,4.7588757,"\int \frac{(a-3 b+2 x) \left(-a^3+3 a^2 x-3 a x^2+x^3\right)}{(-b+x) \sqrt[4]{(-a+x) (-b+x)} \left(-a^3+b d-\left(-3 a^2+d\right) x-3 a x^2+x^3\right)} \, dx","Integrate[((a - 3*b + 2*x)*(-a^3 + 3*a^2*x - 3*a*x^2 + x^3))/((-b + x)*((-a + x)*(-b + x))^(1/4)*(-a^3 + b*d - (-3*a^2 + d)*x - 3*a*x^2 + x^3)),x]","\int \frac{(a-3 b+2 x) \left(-a^3+3 a^2 x-3 a x^2+x^3\right)}{(-b+x) \sqrt[4]{(-a+x) (-b+x)} \left(-a^3+b d-\left(-3 a^2+d\right) x-3 a x^2+x^3\right)} \, dx","-2 \sqrt[4]{d} \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{x (-a-b)+a b+x^2}}{a-x}\right)+2 \sqrt[4]{d} \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{x (-a-b)+a b+x^2}}{a-x}\right)-\frac{4 \left(a b-a x-b x+x^2\right)^{3/4}}{b-x}",1,"Integrate[((a - 3*b + 2*x)*(-a^3 + 3*a^2*x - 3*a*x^2 + x^3))/((-b + x)*((-a + x)*(-b + x))^(1/4)*(-a^3 + b*d - (-3*a^2 + d)*x - 3*a*x^2 + x^3)), x]","F",-1
1639,0,0,111,7.8947184,"\int \frac{x^3 \left(3-2 (1+k) x+k x^2\right)}{(-1+x) \sqrt[4]{(1-x) x (1-k x)} (-1+k x) \left(-d+d (1+k) x-d k x^2+x^3\right)} \, dx","Integrate[(x^3*(3 - 2*(1 + k)*x + k*x^2))/((-1 + x)*((1 - x)*x*(1 - k*x))^(1/4)*(-1 + k*x)*(-d + d*(1 + k)*x - d*k*x^2 + x^3)),x]","\int \frac{x^3 \left(3-2 (1+k) x+k x^2\right)}{(-1+x) \sqrt[4]{(1-x) x (1-k x)} (-1+k x) \left(-d+d (1+k) x-d k x^2+x^3\right)} \, dx","2 \sqrt[4]{d} \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{k x^3+(-k-1) x^2+x}}{x}\right)-2 \sqrt[4]{d} \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{k x^3+(-k-1) x^2+x}}{x}\right)+\frac{4 \left(k x^3-k x^2-x^2+x\right)^{3/4}}{(x-1) (k x-1)}",1,"Integrate[(x^3*(3 - 2*(1 + k)*x + k*x^2))/((-1 + x)*((1 - x)*x*(1 - k*x))^(1/4)*(-1 + k*x)*(-d + d*(1 + k)*x - d*k*x^2 + x^3)), x]","F",-1
1640,1,102,111,0.2163596,"\int \frac{\left(2+x^3\right) \left(1+2 x^3\right)^{2/3}}{x^6 \left(1+x^3\right)} \, dx","Integrate[((2 + x^3)*(1 + 2*x^3)^(2/3))/(x^6*(1 + x^3)),x]","\frac{1}{30} \left(10 \log \left(1-\frac{x}{\sqrt[3]{x^3+2}}\right)-10 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3+2}}+1}{\sqrt{3}}\right)-\frac{3 \left(2 x^3+1\right)^{2/3} \left(3 x^3+4\right)}{x^5}-5 \log \left(\frac{x}{\sqrt[3]{x^3+2}}+\frac{x^2}{\left(x^3+2\right)^{2/3}}+1\right)\right)","\frac{1}{3} \log \left(\sqrt[3]{2 x^3+1}-x\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{2 x^3+1}+x}\right)}{\sqrt{3}}+\frac{\left(2 x^3+1\right)^{2/3} \left(-3 x^3-4\right)}{10 x^5}-\frac{1}{6} \log \left(\sqrt[3]{2 x^3+1} x+\left(2 x^3+1\right)^{2/3}+x^2\right)",1,"((-3*(1 + 2*x^3)^(2/3)*(4 + 3*x^3))/x^5 - 10*Sqrt[3]*ArcTan[(1 + (2*x)/(2 + x^3)^(1/3))/Sqrt[3]] + 10*Log[1 - x/(2 + x^3)^(1/3)] - 5*Log[1 + x^2/(2 + x^3)^(2/3) + x/(2 + x^3)^(1/3)])/30","A",0
1641,0,0,111,4.4097078,"\int \frac{3 a b^2-2 b (2 a+b) x+(a+2 b) x^2}{\sqrt[4]{x (-a+x) (-b+x)^2} \left(-a b^2 d+b (2 a+b) d x-(a+2 b) d x^2+(-1+d) x^3\right)} \, dx","Integrate[(3*a*b^2 - 2*b*(2*a + b)*x + (a + 2*b)*x^2)/((x*(-a + x)*(-b + x)^2)^(1/4)*(-(a*b^2*d) + b*(2*a + b)*d*x - (a + 2*b)*d*x^2 + (-1 + d)*x^3)),x]","\int \frac{3 a b^2-2 b (2 a+b) x+(a+2 b) x^2}{\sqrt[4]{x (-a+x) (-b+x)^2} \left(-a b^2 d+b (2 a+b) d x-(a+2 b) d x^2+(-1+d) x^3\right)} \, dx","\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}}{x}\right)}{d^{3/4}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}}{x}\right)}{d^{3/4}}",1,"Integrate[(3*a*b^2 - 2*b*(2*a + b)*x + (a + 2*b)*x^2)/((x*(-a + x)*(-b + x)^2)^(1/4)*(-(a*b^2*d) + b*(2*a + b)*d*x - (a + 2*b)*d*x^2 + (-1 + d)*x^3)), x]","F",-1
1642,1,87,111,0.0497969,"\int \frac{(d+c x) \sqrt[4]{-b x^3+a x^4}}{x^2} \, dx","Integrate[((d + c*x)*(-(b*x^3) + a*x^4)^(1/4))/x^2,x]","\frac{4 \sqrt[4]{x^3 (a x-b)} \left(x (b c-4 a d) \, _2F_1\left(-\frac{1}{4},\frac{3}{4};\frac{7}{4};\frac{a x}{b}\right)-3 d (b-a x) \sqrt[4]{1-\frac{a x}{b}}\right)}{3 b x \sqrt[4]{1-\frac{a x}{b}}}","\frac{(b c-4 a d) \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^3}}\right)}{2 a^{3/4}}+\frac{(4 a d-b c) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^3}}\right)}{2 a^{3/4}}+\frac{\sqrt[4]{a x^4-b x^3} (c x-4 d)}{x}",1,"(4*(x^3*(-b + a*x))^(1/4)*(-3*d*(b - a*x)*(1 - (a*x)/b)^(1/4) + (b*c - 4*a*d)*x*Hypergeometric2F1[-1/4, 3/4, 7/4, (a*x)/b]))/(3*b*x*(1 - (a*x)/b)^(1/4))","C",1
1643,0,0,111,0.5492564,"\int \frac{\left(3+x^5\right) \sqrt[3]{-2+x^3+x^5}}{x^2 \left(-2+x^5\right)} \, dx","Integrate[((3 + x^5)*(-2 + x^3 + x^5)^(1/3))/(x^2*(-2 + x^5)),x]","\int \frac{\left(3+x^5\right) \sqrt[3]{-2+x^3+x^5}}{x^2 \left(-2+x^5\right)} \, dx","\frac{3 \sqrt[3]{x^5+x^3-2}}{2 x}+\frac{1}{2} \log \left(\sqrt[3]{x^5+x^3-2}-x\right)+\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^5+x^3-2}+x}\right)-\frac{1}{4} \log \left(x^2+\sqrt[3]{x^5+x^3-2} x+\left(x^5+x^3-2\right)^{2/3}\right)",1,"Integrate[((3 + x^5)*(-2 + x^3 + x^5)^(1/3))/(x^2*(-2 + x^5)), x]","F",-1
1644,0,0,111,0.529242,"\int \frac{\left(-3+x^5\right) \left(2+x^3+x^5\right)^{2/3}}{x^3 \left(2+x^5\right)} \, dx","Integrate[((-3 + x^5)*(2 + x^3 + x^5)^(2/3))/(x^3*(2 + x^5)),x]","\int \frac{\left(-3+x^5\right) \left(2+x^3+x^5\right)^{2/3}}{x^3 \left(2+x^5\right)} \, dx","\frac{1}{2} \log \left(\sqrt[3]{x^5+x^3+2}-x\right)-\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^5+x^3+2}+x}\right)+\frac{3 \left(x^5+x^3+2\right)^{2/3}}{4 x^2}-\frac{1}{4} \log \left(x^2+\sqrt[3]{x^5+x^3+2} x+\left(x^5+x^3+2\right)^{2/3}\right)",1,"Integrate[((-3 + x^5)*(2 + x^3 + x^5)^(2/3))/(x^3*(2 + x^5)), x]","F",-1
1645,1,50,111,0.0242294,"\int \frac{\sqrt[3]{-1+x^6} \left(1+x^6\right)}{x^9} \, dx","Integrate[((-1 + x^6)^(1/3)*(1 + x^6))/x^9,x]","\frac{\sqrt[3]{x^6-1} \left(-\frac{4 x^6 \, _2F_1\left(-\frac{1}{3},-\frac{1}{3};\frac{2}{3};x^6\right)}{\sqrt[3]{1-x^6}}+x^6-1\right)}{8 x^8}","\frac{\sqrt[3]{x^6-1} \left(-3 x^6-1\right)}{8 x^8}-\frac{1}{6} \log \left(\sqrt[3]{x^6-1}-x^2\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x^2}{2 \sqrt[3]{x^6-1}+x^2}\right)}{2 \sqrt{3}}+\frac{1}{12} \log \left(\left(x^6-1\right)^{2/3}+x^4+\sqrt[3]{x^6-1} x^2\right)",1,"((-1 + x^6)^(1/3)*(-1 + x^6 - (4*x^6*Hypergeometric2F1[-1/3, -1/3, 2/3, x^6])/(1 - x^6)^(1/3)))/(8*x^8)","C",1
1646,1,301,111,0.4922339,"\int \frac{1}{\sqrt[3]{b^2 x^2+a^3 x^3} \left(-2 b+a^6 x^6\right)} \, dx","Integrate[1/((b^2*x^2 + a^3*x^3)^(1/3)*(-2*b + a^6*x^6)),x]","-\frac{x \left(\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(2 a^2-2^{5/6} b^{11/6}\right) x}{2 \left(x a^3+b^2\right)}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(2 a^2+2^{5/6} b^{11/6}\right) x}{2 \left(x a^3+b^2\right)}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(2 a^2-\sqrt[3]{-1} 2^{5/6} b^{11/6}\right) x}{2 \left(x a^3+b^2\right)}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(2 a^2+\sqrt[3]{-1} 2^{5/6} b^{11/6}\right) x}{2 \left(x a^3+b^2\right)}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(2 a^2-(-1)^{2/3} 2^{5/6} b^{11/6}\right) x}{2 \left(x a^3+b^2\right)}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(2 a^2+(-1)^{2/3} 2^{5/6} b^{11/6}\right) x}{2 \left(x a^3+b^2\right)}\right)\right)}{4 b \sqrt[3]{x^2 \left(a^3 x+b^2\right)}}","\frac{\text{RootSum}\left[2 \text{$\#$1}^{18}-12 \text{$\#$1}^{15} a^3+30 \text{$\#$1}^{12} a^6-40 \text{$\#$1}^9 a^9+30 \text{$\#$1}^6 a^{12}-12 \text{$\#$1}^3 a^{15}+2 a^{18}-a^6 b^{11}\&,\frac{\log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{12 b}",1,"-1/4*(x*(Hypergeometric2F1[1/3, 1, 4/3, (a*(2*a^2 - 2^(5/6)*b^(11/6))*x)/(2*(b^2 + a^3*x))] + Hypergeometric2F1[1/3, 1, 4/3, (a*(2*a^2 + 2^(5/6)*b^(11/6))*x)/(2*(b^2 + a^3*x))] + Hypergeometric2F1[1/3, 1, 4/3, (a*(2*a^2 - (-1)^(1/3)*2^(5/6)*b^(11/6))*x)/(2*(b^2 + a^3*x))] + Hypergeometric2F1[1/3, 1, 4/3, (a*(2*a^2 + (-1)^(1/3)*2^(5/6)*b^(11/6))*x)/(2*(b^2 + a^3*x))] + Hypergeometric2F1[1/3, 1, 4/3, (a*(2*a^2 - (-1)^(2/3)*2^(5/6)*b^(11/6))*x)/(2*(b^2 + a^3*x))] + Hypergeometric2F1[1/3, 1, 4/3, (a*(2*a^2 + (-1)^(2/3)*2^(5/6)*b^(11/6))*x)/(2*(b^2 + a^3*x))]))/(b*(x^2*(b^2 + a^3*x))^(1/3))","B",1
1647,1,301,111,0.139144,"\int \frac{1}{\sqrt[3]{b^2 x^2+a^3 x^3} \left(-2 b+a^6 x^6\right)} \, dx","Integrate[1/((b^2*x^2 + a^3*x^3)^(1/3)*(-2*b + a^6*x^6)),x]","-\frac{x \left(\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(2 a^2-2^{5/6} b^{11/6}\right) x}{2 \left(x a^3+b^2\right)}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(2 a^2+2^{5/6} b^{11/6}\right) x}{2 \left(x a^3+b^2\right)}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(2 a^2-\sqrt[3]{-1} 2^{5/6} b^{11/6}\right) x}{2 \left(x a^3+b^2\right)}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(2 a^2+\sqrt[3]{-1} 2^{5/6} b^{11/6}\right) x}{2 \left(x a^3+b^2\right)}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(2 a^2-(-1)^{2/3} 2^{5/6} b^{11/6}\right) x}{2 \left(x a^3+b^2\right)}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(2 a^2+(-1)^{2/3} 2^{5/6} b^{11/6}\right) x}{2 \left(x a^3+b^2\right)}\right)\right)}{4 b \sqrt[3]{x^2 \left(a^3 x+b^2\right)}}","\frac{\text{RootSum}\left[2 \text{$\#$1}^{18}-12 \text{$\#$1}^{15} a^3+30 \text{$\#$1}^{12} a^6-40 \text{$\#$1}^9 a^9+30 \text{$\#$1}^6 a^{12}-12 \text{$\#$1}^3 a^{15}+2 a^{18}-a^6 b^{11}\&,\frac{\log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{12 b}",1,"-1/4*(x*(Hypergeometric2F1[1/3, 1, 4/3, (a*(2*a^2 - 2^(5/6)*b^(11/6))*x)/(2*(b^2 + a^3*x))] + Hypergeometric2F1[1/3, 1, 4/3, (a*(2*a^2 + 2^(5/6)*b^(11/6))*x)/(2*(b^2 + a^3*x))] + Hypergeometric2F1[1/3, 1, 4/3, (a*(2*a^2 - (-1)^(1/3)*2^(5/6)*b^(11/6))*x)/(2*(b^2 + a^3*x))] + Hypergeometric2F1[1/3, 1, 4/3, (a*(2*a^2 + (-1)^(1/3)*2^(5/6)*b^(11/6))*x)/(2*(b^2 + a^3*x))] + Hypergeometric2F1[1/3, 1, 4/3, (a*(2*a^2 - (-1)^(2/3)*2^(5/6)*b^(11/6))*x)/(2*(b^2 + a^3*x))] + Hypergeometric2F1[1/3, 1, 4/3, (a*(2*a^2 + (-1)^(2/3)*2^(5/6)*b^(11/6))*x)/(2*(b^2 + a^3*x))]))/(b*(x^2*(b^2 + a^3*x))^(1/3))","B",1
1648,1,75,111,0.0281886,"\int \frac{1}{\sqrt[4]{-1-3 x^4-2 x^8+2 x^{12}+3 x^{16}+x^{20}}} \, dx","Integrate[(-1 - 3*x^4 - 2*x^8 + 2*x^12 + 3*x^16 + x^20)^(-1/4),x]","\frac{\sqrt[4]{x^4-1} \left(x^4+1\right) \left(\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-1}}\right)+\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-1}}\right)\right)}{2 \sqrt[4]{2} \sqrt[4]{\left(x^4-1\right) \left(x^4+1\right)^4}}","\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{x^{20}+3 x^{16}+2 x^{12}-2 x^8-3 x^4-1}}{\sqrt[4]{2} x \left(x^4+1\right)}\right)}{2 \sqrt[4]{2}}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{x^{20}+3 x^{16}+2 x^{12}-2 x^8-3 x^4-1}}{\sqrt[4]{2} x \left(x^4+1\right)}\right)}{2 \sqrt[4]{2}}",1,"((-1 + x^4)^(1/4)*(1 + x^4)*(ArcTan[(2^(1/4)*x)/(-1 + x^4)^(1/4)] + ArcTanh[(2^(1/4)*x)/(-1 + x^4)^(1/4)]))/(2*2^(1/4)*((-1 + x^4)*(1 + x^4)^4)^(1/4))","A",1
1649,1,102,111,0.1927867,"\int \frac{1+x^2}{\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","Integrate[(1 + x^2)/(Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]]),x]","\frac{4 \sqrt{\sqrt{a x+b}+c} \left(35 a^2 \left(x^2+9\right)+32 \left(-2 c^3 \left(\sqrt{a x+b}-2 c\right)+b c \left(4 \sqrt{a x+b}-9 c\right)+7 b^2\right)-8 a x \left(c \left(5 \sqrt{a x+b}-6 c\right)+7 b\right)\right)}{315 a^3}","\frac{4 \left(35 a^2 x^2+315 a^2-56 a b x+48 a c^2 x+224 b^2-288 b c^2+128 c^4\right) \sqrt{\sqrt{a x+b}+c}}{315 a^3}-\frac{32 \sqrt{a x+b} \left(5 a c x-16 b c+8 c^3\right) \sqrt{\sqrt{a x+b}+c}}{315 a^3}",1,"(4*Sqrt[c + Sqrt[b + a*x]]*(35*a^2*(9 + x^2) + 32*(7*b^2 - 2*c^3*(-2*c + Sqrt[b + a*x]) + b*c*(-9*c + 4*Sqrt[b + a*x])) - 8*a*x*(7*b + c*(-6*c + 5*Sqrt[b + a*x]))))/(315*a^3)","A",1
1650,1,629,111,2.5205575,"\int \frac{x^2}{\sqrt{-b+a^2 x^2} \sqrt[4]{a x+\sqrt{-b+a^2 x^2}}} \, dx","Integrate[x^2/(Sqrt[-b + a^2*x^2]*(a*x + Sqrt[-b + a^2*x^2])^(1/4)),x]","\frac{4 \sqrt{a^2 x^2-b} \left(294912 a^{19} x^{19}-2506752 a^{17} b x^{17}+7745536 a^{15} b^2 x^{15}-12199936 a^{13} b^3 x^{13}+10988800 a^{11} b^4 x^{11}-5854336 a^9 b^5 x^9+1812000 a^7 b^6 x^7-302768 a^5 b^7 x^5+23064 a^3 b^8 x^3-32 b^9 \sqrt{a^2 x^2-b}+4225 a^2 b^8 x^2 \sqrt{a^2 x^2-b}+294912 a^{18} x^{18} \sqrt{a^2 x^2-b}-2359296 a^{16} b x^{16} \sqrt{a^2 x^2-b}+6602752 a^{14} b^2 x^{14} \sqrt{a^2 x^2-b}-9175040 a^{12} b^3 x^{12} \sqrt{a^2 x^2-b}+7090688 a^{10} b^4 x^{10} \sqrt{a^2 x^2-b}-3127296 a^8 b^5 x^8 \sqrt{a^2 x^2-b}+760704 a^6 b^6 x^6 \sqrt{a^2 x^2-b}-91648 a^4 b^7 x^4 \sqrt{a^2 x^2-b}-520 a b^9 x\right)}{63 a^3 \left(\sqrt{a^2 x^2-b}+a x\right)^{21/4} \left(512 a^{11} x^{11}-1536 a^9 b x^9+1696 a^7 b^2 x^7-832 a^5 b^3 x^5+170 a^3 b^4 x^3-b^5 \sqrt{a^2 x^2-b}+50 a^2 b^4 x^2 \sqrt{a^2 x^2-b}+512 a^{10} x^{10} \sqrt{a^2 x^2-b}-1280 a^8 b x^8 \sqrt{a^2 x^2-b}+1120 a^6 b^2 x^6 \sqrt{a^2 x^2-b}-400 a^4 b^3 x^4 \sqrt{a^2 x^2-b}-10 a b^5 x\right) \left(a x \left(\sqrt{a^2 x^2-b}+a x\right)-b\right)}","\frac{8 \sqrt{a^2 x^2-b} \left(a^2 x^3-4 b x\right)}{7 a^2 \left(\sqrt{a^2 x^2-b}+a x\right)^{9/4}}+\frac{4 \left(18 a^4 x^4-81 a^2 b x^2+32 b^2\right)}{63 a^3 \left(\sqrt{a^2 x^2-b}+a x\right)^{9/4}}",1,"(4*Sqrt[-b + a^2*x^2]*(-520*a*b^9*x + 23064*a^3*b^8*x^3 - 302768*a^5*b^7*x^5 + 1812000*a^7*b^6*x^7 - 5854336*a^9*b^5*x^9 + 10988800*a^11*b^4*x^11 - 12199936*a^13*b^3*x^13 + 7745536*a^15*b^2*x^15 - 2506752*a^17*b*x^17 + 294912*a^19*x^19 - 32*b^9*Sqrt[-b + a^2*x^2] + 4225*a^2*b^8*x^2*Sqrt[-b + a^2*x^2] - 91648*a^4*b^7*x^4*Sqrt[-b + a^2*x^2] + 760704*a^6*b^6*x^6*Sqrt[-b + a^2*x^2] - 3127296*a^8*b^5*x^8*Sqrt[-b + a^2*x^2] + 7090688*a^10*b^4*x^10*Sqrt[-b + a^2*x^2] - 9175040*a^12*b^3*x^12*Sqrt[-b + a^2*x^2] + 6602752*a^14*b^2*x^14*Sqrt[-b + a^2*x^2] - 2359296*a^16*b*x^16*Sqrt[-b + a^2*x^2] + 294912*a^18*x^18*Sqrt[-b + a^2*x^2]))/(63*a^3*(a*x + Sqrt[-b + a^2*x^2])^(21/4)*(-10*a*b^5*x + 170*a^3*b^4*x^3 - 832*a^5*b^3*x^5 + 1696*a^7*b^2*x^7 - 1536*a^9*b*x^9 + 512*a^11*x^11 - b^5*Sqrt[-b + a^2*x^2] + 50*a^2*b^4*x^2*Sqrt[-b + a^2*x^2] - 400*a^4*b^3*x^4*Sqrt[-b + a^2*x^2] + 1120*a^6*b^2*x^6*Sqrt[-b + a^2*x^2] - 1280*a^8*b*x^8*Sqrt[-b + a^2*x^2] + 512*a^10*x^10*Sqrt[-b + a^2*x^2])*(-b + a*x*(a*x + Sqrt[-b + a^2*x^2])))","B",1
1651,1,54,112,0.019481,"\int x^2 \sqrt[3]{-x+x^3} \, dx","Integrate[x^2*(-x + x^3)^(1/3),x]","\frac{x \sqrt[3]{x \left(x^2-1\right)} \left(\, _2F_1\left(-\frac{1}{3},\frac{2}{3};\frac{5}{3};x^2\right)-\left(1-x^2\right)^{4/3}\right)}{4 \sqrt[3]{1-x^2}}","\frac{1}{12} \sqrt[3]{x^3-x} \left(3 x^3-x\right)+\frac{1}{18} \log \left(\sqrt[3]{x^3-x}-x\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-x}+x}\right)}{6 \sqrt{3}}-\frac{1}{36} \log \left(\sqrt[3]{x^3-x} x+\left(x^3-x\right)^{2/3}+x^2\right)",1,"(x*(x*(-1 + x^2))^(1/3)*(-(1 - x^2)^(4/3) + Hypergeometric2F1[-1/3, 2/3, 5/3, x^2]))/(4*(1 - x^2)^(1/3))","C",1
1652,1,68,112,0.0264708,"\int x^6 \sqrt[3]{x+x^3} \, dx","Integrate[x^6*(x + x^3)^(1/3),x]","\frac{x \sqrt[3]{x^3+x} \left(\sqrt[3]{x^2+1} \left(27 x^6+3 x^4-4 x^2+20\right)-20 \, _2F_1\left(-\frac{1}{3},\frac{2}{3};\frac{5}{3};-x^2\right)\right)}{216 \sqrt[3]{x^2+1}}","\frac{5}{243} \log \left(\sqrt[3]{x^3+x}-x\right)+\frac{5 \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+x}+x}\right)}{81 \sqrt{3}}-\frac{5}{486} \log \left(\sqrt[3]{x^3+x} x+\left(x^3+x\right)^{2/3}+x^2\right)+\frac{1}{648} \sqrt[3]{x^3+x} \left(81 x^7+9 x^5-12 x^3+20 x\right)",1,"(x*(x + x^3)^(1/3)*((1 + x^2)^(1/3)*(20 - 4*x^2 + 3*x^4 + 27*x^6) - 20*Hypergeometric2F1[-1/3, 2/3, 5/3, -x^2]))/(216*(1 + x^2)^(1/3))","C",1
1653,1,51,112,0.0275359,"\int \frac{-3+2 x}{x \sqrt[4]{-1+x^4}} \, dx","Integrate[(-3 + 2*x)/(x*(-1 + x^4)^(1/4)),x]","-\left(x^4-1\right)^{3/4} \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};1-x^4\right)+\tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-1}}\right)+\tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-1}}\right)","-\tan ^{-1}\left(\frac{\sqrt[4]{x^4-1}}{x}\right)-\frac{3 \tan ^{-1}\left(\frac{\frac{\sqrt{x^4-1}}{\sqrt{2}}-\frac{1}{\sqrt{2}}}{\sqrt[4]{x^4-1}}\right)}{2 \sqrt{2}}+\tanh ^{-1}\left(\frac{\sqrt[4]{x^4-1}}{x}\right)+\frac{3 \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{x^4-1}}{\sqrt{x^4-1}+1}\right)}{2 \sqrt{2}}",1,"ArcTan[x/(-1 + x^4)^(1/4)] + ArcTanh[x/(-1 + x^4)^(1/4)] - (-1 + x^4)^(3/4)*Hypergeometric2F1[3/4, 1, 7/4, 1 - x^4]","C",1
1654,0,0,112,0.5471539,"\int \frac{\sqrt[3]{-1+x^3-x^4} \left(-3+x^4\right)}{x^2 \left(1+x^4\right)} \, dx","Integrate[((-1 + x^3 - x^4)^(1/3)*(-3 + x^4))/(x^2*(1 + x^4)),x]","\int \frac{\sqrt[3]{-1+x^3-x^4} \left(-3+x^4\right)}{x^2 \left(1+x^4\right)} \, dx","\frac{3 \sqrt[3]{-x^4+x^3-1}}{x}+\log \left(\sqrt[3]{-x^4+x^3-1}-x\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{-x^4+x^3-1}+x}\right)-\frac{1}{2} \log \left(x^2+\sqrt[3]{-x^4+x^3-1} x+\left(-x^4+x^3-1\right)^{2/3}\right)",1,"Integrate[((-1 + x^3 - x^4)^(1/3)*(-3 + x^4))/(x^2*(1 + x^4)), x]","F",-1
1655,1,136,112,0.5351789,"\int \frac{x^3 \sqrt{-x+x^4}}{-b+a x^3} \, dx","Integrate[(x^3*Sqrt[-x + x^4])/(-b + a*x^3),x]","\frac{x^2 \left(\frac{\sqrt{1-x^3} x^3 (a-2 b) F_1\left(\frac{3}{2};\frac{1}{2},1;\frac{5}{2};x^3,\frac{a x^3}{b}\right)}{b}+\frac{3 \sqrt{1-x^3} \sin ^{-1}\left(\frac{\sqrt{\frac{x^3 (b-a)}{b}}}{\sqrt{1-\frac{a x^3}{b}}}\right)}{\sqrt{\frac{x^3 (b-a)}{b}}}+3 \left(x^3-1\right)\right)}{9 a \sqrt{x \left(x^3-1\right)}}","\frac{2 \sqrt{b} \sqrt{a-b} \tan ^{-1}\left(\frac{x \sqrt{x^4-x} \sqrt{a-b}}{\sqrt{b} (x-1) \left(x^2+x+1\right)}\right)}{3 a^2}+\frac{(2 b-a) \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4-x}}\right)}{3 a^2}+\frac{\sqrt{x^4-x} x}{3 a}",1,"(x^2*(3*(-1 + x^3) + ((a - 2*b)*x^3*Sqrt[1 - x^3]*AppellF1[3/2, 1/2, 1, 5/2, x^3, (a*x^3)/b])/b + (3*Sqrt[1 - x^3]*ArcSin[Sqrt[((-a + b)*x^3)/b]/Sqrt[1 - (a*x^3)/b]])/Sqrt[((-a + b)*x^3)/b]))/(9*a*Sqrt[x*(-1 + x^3)])","C",0
1656,1,85,112,0.4444699,"\int \frac{1+2 x^4}{\left(-1+x^4\right) \sqrt[4]{x^2+x^4}} \, dx","Integrate[(1 + 2*x^4)/((-1 + x^4)*(x^2 + x^4)^(1/4)),x]","\frac{5 \sqrt[4]{\frac{1}{x^2}+1} F_1\left(1;\frac{1}{4},1;2;-\frac{1}{x^2},\frac{1}{x^2}\right)-4 x^2 \left(4 \sqrt[4]{x^2+1} x^2 F_1\left(\frac{5}{4};\frac{1}{4},1;\frac{9}{4};-x^2,x^2\right)+15\right)}{20 x \sqrt[4]{x^4+x^2}}","-\frac{3 \left(x^4+x^2\right)^{3/4}}{x \left(x^2+1\right)}+2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+x^2}}\right)-\frac{3 \tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+x^2}}\right)}{2 \sqrt[4]{2}}+2 \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+x^2}}\right)-\frac{3 \tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+x^2}}\right)}{2 \sqrt[4]{2}}",1,"(5*(1 + x^(-2))^(1/4)*AppellF1[1, 1/4, 1, 2, -x^(-2), x^(-2)] - 4*x^2*(15 + 4*x^2*(1 + x^2)^(1/4)*AppellF1[5/4, 1/4, 1, 9/4, -x^2, x^2]))/(20*x*(x^2 + x^4)^(1/4))","C",0
1657,1,48,112,0.0310562,"\int \frac{b+a x^2}{x^2 \left(-b+a x^2\right) \sqrt[4]{b x^2+a x^4}} \, dx","Integrate[(b + a*x^2)/(x^2*(-b + a*x^2)*(b*x^2 + a*x^4)^(1/4)),x]","\frac{2 \left(x^2 \left(a x^2+b\right)\right)^{3/4} \, _2F_1\left(-\frac{3}{4},1;\frac{1}{4};\frac{2 a x^2}{a x^2+b}\right)}{3 b x^3}","-\frac{2^{3/4} a^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{b}-\frac{2^{3/4} a^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{b}+\frac{2 \left(a x^4+b x^2\right)^{3/4}}{3 b x^3}",1,"(2*(x^2*(b + a*x^2))^(3/4)*Hypergeometric2F1[-3/4, 1, 1/4, (2*a*x^2)/(b + a*x^2)])/(3*b*x^3)","C",1
1658,1,49,112,0.0161616,"\int x \sqrt[4]{b x^3+a x^4} \, dx","Integrate[x*(b*x^3 + a*x^4)^(1/4),x]","\frac{4 x^2 \sqrt[4]{x^3 (a x+b)} \, _2F_1\left(-\frac{1}{4},\frac{11}{4};\frac{15}{4};-\frac{a x}{b}\right)}{11 \sqrt[4]{\frac{a x}{b}+1}}","-\frac{7 b^3 \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)}{64 a^{11/4}}+\frac{7 b^3 \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)}{64 a^{11/4}}+\frac{\left(32 a^2 x^2+4 a b x-7 b^2\right) \sqrt[4]{a x^4+b x^3}}{96 a^2}",1,"(4*x^2*(x^3*(b + a*x))^(1/4)*Hypergeometric2F1[-1/4, 11/4, 15/4, -((a*x)/b)])/(11*(1 + (a*x)/b)^(1/4))","C",1
1659,0,0,112,0.6036058,"\int \frac{-2 b+a x^3}{\left(b+x^2+a x^3\right) \sqrt[4]{b x^2+a x^5}} \, dx","Integrate[(-2*b + a*x^3)/((b + x^2 + a*x^3)*(b*x^2 + a*x^5)^(1/4)),x]","\int \frac{-2 b+a x^3}{\left(b+x^2+a x^3\right) \sqrt[4]{b x^2+a x^5}} \, dx","-\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{a x^5+b x^2}}{\sqrt{a x^5+b x^2}-x^2}\right)-\sqrt{2} \tanh ^{-1}\left(\frac{\frac{\sqrt{a x^5+b x^2}}{\sqrt{2}}+\frac{x^2}{\sqrt{2}}}{x \sqrt[4]{a x^5+b x^2}}\right)",1,"Integrate[(-2*b + a*x^3)/((b + x^2 + a*x^3)*(b*x^2 + a*x^5)^(1/4)), x]","F",-1
1660,0,0,112,1.1345422,"\int \frac{-b+a x^2}{\left(b+x+a x^2\right) \sqrt[4]{b x^3+a x^5}} \, dx","Integrate[(-b + a*x^2)/((b + x + a*x^2)*(b*x^3 + a*x^5)^(1/4)),x]","\int \frac{-b+a x^2}{\left(b+x+a x^2\right) \sqrt[4]{b x^3+a x^5}} \, dx","-\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{a x^5+b x^3}}{\sqrt{a x^5+b x^3}-x^2}\right)-\sqrt{2} \tanh ^{-1}\left(\frac{\frac{\sqrt{a x^5+b x^3}}{\sqrt{2}}+\frac{x^2}{\sqrt{2}}}{x \sqrt[4]{a x^5+b x^3}}\right)",1,"Integrate[(-b + a*x^2)/((b + x + a*x^2)*(b*x^3 + a*x^5)^(1/4)), x]","F",-1
1661,1,113,112,0.0473349,"\int \frac{x^{13}}{\sqrt[3]{-1+x^6}} \, dx","Integrate[x^13/(-1 + x^6)^(1/3),x]","\frac{1}{108} \left(9 \left(x^6-1\right)^{2/3} x^8+12 \left(x^6-1\right)^{2/3} x^2-4 \log \left(1-\frac{x^2}{\sqrt[3]{x^6-1}}\right)+4 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 x^2}{\sqrt[3]{x^6-1}}+1}{\sqrt{3}}\right)+2 \log \left(\frac{x^4}{\left(x^6-1\right)^{2/3}}+\frac{x^2}{\sqrt[3]{x^6-1}}+1\right)\right)","-\frac{1}{27} \log \left(\sqrt[3]{x^6-1}-x^2\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x^2}{2 \sqrt[3]{x^6-1}+x^2}\right)}{9 \sqrt{3}}+\frac{1}{36} \left(x^6-1\right)^{2/3} \left(3 x^8+4 x^2\right)+\frac{1}{54} \log \left(\left(x^6-1\right)^{2/3}+x^4+\sqrt[3]{x^6-1} x^2\right)",1,"(12*x^2*(-1 + x^6)^(2/3) + 9*x^8*(-1 + x^6)^(2/3) + 4*Sqrt[3]*ArcTan[(1 + (2*x^2)/(-1 + x^6)^(1/3))/Sqrt[3]] - 4*Log[1 - x^2/(-1 + x^6)^(1/3)] + 2*Log[1 + x^4/(-1 + x^6)^(2/3) + x^2/(-1 + x^6)^(1/3)])/108","A",1
1662,1,54,112,0.0190768,"\int x^9 \sqrt[3]{-1+x^6} \, dx","Integrate[x^9*(-1 + x^6)^(1/3),x]","\frac{x^4 \sqrt[3]{x^6-1} \left(\, _2F_1\left(-\frac{1}{3},\frac{2}{3};\frac{5}{3};x^6\right)-\left(1-x^6\right)^{4/3}\right)}{12 \sqrt[3]{1-x^6}}","\frac{1}{54} \log \left(\sqrt[3]{x^6-1}-x^2\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x^2}{2 \sqrt[3]{x^6-1}+x^2}\right)}{18 \sqrt{3}}+\frac{1}{36} \sqrt[3]{x^6-1} \left(3 x^{10}-x^4\right)-\frac{1}{108} \log \left(\left(x^6-1\right)^{2/3}+x^4+\sqrt[3]{x^6-1} x^2\right)",1,"(x^4*(-1 + x^6)^(1/3)*(-(1 - x^6)^(4/3) + Hypergeometric2F1[-1/3, 2/3, 5/3, x^6]))/(12*(1 - x^6)^(1/3))","C",1
1663,1,54,112,0.0216494,"\int x^7 \left(-1+x^6\right)^{2/3} \, dx","Integrate[x^7*(-1 + x^6)^(2/3),x]","\frac{x^2 \left(x^6-1\right)^{2/3} \left(\, _2F_1\left(-\frac{2}{3},\frac{1}{3};\frac{4}{3};x^6\right)-\left(1-x^6\right)^{5/3}\right)}{12 \left(1-x^6\right)^{2/3}}","\frac{1}{54} \log \left(\sqrt[3]{x^6-1}-x^2\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x^2}{2 \sqrt[3]{x^6-1}+x^2}\right)}{18 \sqrt{3}}+\frac{1}{36} \left(x^6-1\right)^{2/3} \left(3 x^8-2 x^2\right)-\frac{1}{108} \log \left(\left(x^6-1\right)^{2/3}+x^4+\sqrt[3]{x^6-1} x^2\right)",1,"(x^2*(-1 + x^6)^(2/3)*(-(1 - x^6)^(5/3) + Hypergeometric2F1[-2/3, 1/3, 4/3, x^6]))/(12*(1 - x^6)^(2/3))","C",1
1664,1,113,112,0.0458074,"\int \frac{x^{13}}{\sqrt[3]{1+x^6}} \, dx","Integrate[x^13/(1 + x^6)^(1/3),x]","\frac{1}{108} \left(9 \left(x^6+1\right)^{2/3} x^8-12 \left(x^6+1\right)^{2/3} x^2-4 \log \left(1-\frac{x^2}{\sqrt[3]{x^6+1}}\right)+4 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 x^2}{\sqrt[3]{x^6+1}}+1}{\sqrt{3}}\right)+2 \log \left(\frac{x^4}{\left(x^6+1\right)^{2/3}}+\frac{x^2}{\sqrt[3]{x^6+1}}+1\right)\right)","-\frac{1}{27} \log \left(\sqrt[3]{x^6+1}-x^2\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x^2}{2 \sqrt[3]{x^6+1}+x^2}\right)}{9 \sqrt{3}}+\frac{1}{36} \left(x^6+1\right)^{2/3} \left(3 x^8-4 x^2\right)+\frac{1}{54} \log \left(\left(x^6+1\right)^{2/3}+x^4+\sqrt[3]{x^6+1} x^2\right)",1,"(-12*x^2*(1 + x^6)^(2/3) + 9*x^8*(1 + x^6)^(2/3) + 4*Sqrt[3]*ArcTan[(1 + (2*x^2)/(1 + x^6)^(1/3))/Sqrt[3]] - 4*Log[1 - x^2/(1 + x^6)^(1/3)] + 2*Log[1 + x^4/(1 + x^6)^(2/3) + x^2/(1 + x^6)^(1/3)])/108","A",1
1665,1,34,112,0.0136173,"\int x^7 \left(1+x^6\right)^{2/3} \, dx","Integrate[x^7*(1 + x^6)^(2/3),x]","\frac{1}{12} x^2 \left(\left(x^6+1\right)^{5/3}-\, _2F_1\left(-\frac{2}{3},\frac{1}{3};\frac{4}{3};-x^6\right)\right)","\frac{1}{54} \log \left(\sqrt[3]{x^6+1}-x^2\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x^2}{2 \sqrt[3]{x^6+1}+x^2}\right)}{18 \sqrt{3}}+\frac{1}{36} \left(x^6+1\right)^{2/3} \left(3 x^8+2 x^2\right)-\frac{1}{108} \log \left(\left(x^6+1\right)^{2/3}+x^4+\sqrt[3]{x^6+1} x^2\right)",1,"(x^2*((1 + x^6)^(5/3) - Hypergeometric2F1[-2/3, 1/3, 4/3, -x^6]))/12","C",1
1666,1,337,112,0.6759874,"\int \frac{\left(1+x^3\right)^{2/3} \left(4+x^3\right)}{x^6 \left(8-4 x^3+x^6\right)} \, dx","Integrate[((1 + x^3)^(2/3)*(4 + x^3))/(x^6*(8 - 4*x^3 + x^6)),x]","\left(x^3+1\right)^{2/3} \left(-\frac{1}{10 x^5}-\frac{23}{80 x^2}\right)+\frac{-(16-2 i) \sqrt[3]{5-i} \log \left(-\frac{\sqrt[3]{13} x}{\sqrt[3]{x^3+1}}+\sqrt[3]{10-2 i}\right)-(16+2 i) \sqrt[3]{5+i} \log \left(-\frac{\sqrt[3]{13} x}{\sqrt[3]{x^3+1}}+\sqrt[3]{10+2 i}\right)+(16-2 i) \sqrt{3} \sqrt[3]{5-i} \tan ^{-1}\left(\frac{1}{\sqrt{3}}+\frac{2^{2/3} x}{\sqrt[3]{\frac{5}{13}-\frac{i}{13}} \sqrt{3} \sqrt[3]{x^3+1}}\right)+(16+2 i) \sqrt{3} \sqrt[3]{5+i} \tan ^{-1}\left(\frac{1}{\sqrt{3}}+\frac{2^{2/3} x}{\sqrt[3]{\frac{5}{13}+\frac{i}{13}} \sqrt{3} \sqrt[3]{x^3+1}}\right)+(8-i) \sqrt[3]{5-i} \log \left(\frac{\sqrt[3]{130-26 i} x}{\sqrt[3]{x^3+1}}+\frac{13^{2/3} x^2}{\left(x^3+1\right)^{2/3}}+(10-2 i)^{2/3}\right)+(8+i) \sqrt[3]{5+i} \log \left(\frac{\sqrt[3]{130+26 i} x}{\sqrt[3]{x^3+1}}+\frac{13^{2/3} x^2}{\left(x^3+1\right)^{2/3}}+(10+2 i)^{2/3}\right)}{96\ 2^{2/3} \sqrt[3]{13}}","\frac{1}{96} \text{RootSum}\left[8 \text{$\#$1}^6-20 \text{$\#$1}^3+13\&,\frac{-32 \text{$\#$1}^3 \log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)+32 \text{$\#$1}^3 \log (x)+39 \log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)-39 \log (x)}{4 \text{$\#$1}^4-5 \text{$\#$1}}\&\right]+\frac{\left(x^3+1\right)^{2/3} \left(-23 x^3-8\right)}{80 x^5}",1,"(-1/10*1/x^5 - 23/(80*x^2))*(1 + x^3)^(2/3) + ((16 - 2*I)*Sqrt[3]*(5 - I)^(1/3)*ArcTan[1/Sqrt[3] + (2^(2/3)*x)/((5/13 - I/13)^(1/3)*Sqrt[3]*(1 + x^3)^(1/3))] + (16 + 2*I)*Sqrt[3]*(5 + I)^(1/3)*ArcTan[1/Sqrt[3] + (2^(2/3)*x)/((5/13 + I/13)^(1/3)*Sqrt[3]*(1 + x^3)^(1/3))] - (16 - 2*I)*(5 - I)^(1/3)*Log[(10 - 2*I)^(1/3) - (13^(1/3)*x)/(1 + x^3)^(1/3)] - (16 + 2*I)*(5 + I)^(1/3)*Log[(10 + 2*I)^(1/3) - (13^(1/3)*x)/(1 + x^3)^(1/3)] + (8 - I)*(5 - I)^(1/3)*Log[(10 - 2*I)^(2/3) + (13^(2/3)*x^2)/(1 + x^3)^(2/3) + ((130 - 26*I)^(1/3)*x)/(1 + x^3)^(1/3)] + (8 + I)*(5 + I)^(1/3)*Log[(10 + 2*I)^(2/3) + (13^(2/3)*x^2)/(1 + x^3)^(2/3) + ((130 + 26*I)^(1/3)*x)/(1 + x^3)^(1/3)])/(96*2^(2/3)*13^(1/3))","C",1
1667,1,337,112,0.2772163,"\int \frac{\left(1+x^3\right)^{2/3} \left(4+x^3\right)}{x^6 \left(8-4 x^3+x^6\right)} \, dx","Integrate[((1 + x^3)^(2/3)*(4 + x^3))/(x^6*(8 - 4*x^3 + x^6)),x]","\left(x^3+1\right)^{2/3} \left(-\frac{1}{10 x^5}-\frac{23}{80 x^2}\right)+\frac{-(16-2 i) \sqrt[3]{5-i} \log \left(-\frac{\sqrt[3]{13} x}{\sqrt[3]{x^3+1}}+\sqrt[3]{10-2 i}\right)-(16+2 i) \sqrt[3]{5+i} \log \left(-\frac{\sqrt[3]{13} x}{\sqrt[3]{x^3+1}}+\sqrt[3]{10+2 i}\right)+(16-2 i) \sqrt{3} \sqrt[3]{5-i} \tan ^{-1}\left(\frac{1}{\sqrt{3}}+\frac{2^{2/3} x}{\sqrt[3]{\frac{5}{13}-\frac{i}{13}} \sqrt{3} \sqrt[3]{x^3+1}}\right)+(16+2 i) \sqrt{3} \sqrt[3]{5+i} \tan ^{-1}\left(\frac{1}{\sqrt{3}}+\frac{2^{2/3} x}{\sqrt[3]{\frac{5}{13}+\frac{i}{13}} \sqrt{3} \sqrt[3]{x^3+1}}\right)+(8-i) \sqrt[3]{5-i} \log \left(\frac{\sqrt[3]{130-26 i} x}{\sqrt[3]{x^3+1}}+\frac{13^{2/3} x^2}{\left(x^3+1\right)^{2/3}}+(10-2 i)^{2/3}\right)+(8+i) \sqrt[3]{5+i} \log \left(\frac{\sqrt[3]{130+26 i} x}{\sqrt[3]{x^3+1}}+\frac{13^{2/3} x^2}{\left(x^3+1\right)^{2/3}}+(10+2 i)^{2/3}\right)}{96\ 2^{2/3} \sqrt[3]{13}}","\frac{1}{96} \text{RootSum}\left[8 \text{$\#$1}^6-20 \text{$\#$1}^3+13\&,\frac{-32 \text{$\#$1}^3 \log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)+32 \text{$\#$1}^3 \log (x)+39 \log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)-39 \log (x)}{4 \text{$\#$1}^4-5 \text{$\#$1}}\&\right]+\frac{\left(x^3+1\right)^{2/3} \left(-23 x^3-8\right)}{80 x^5}",1,"(-1/10*1/x^5 - 23/(80*x^2))*(1 + x^3)^(2/3) + ((16 - 2*I)*Sqrt[3]*(5 - I)^(1/3)*ArcTan[1/Sqrt[3] + (2^(2/3)*x)/((5/13 - I/13)^(1/3)*Sqrt[3]*(1 + x^3)^(1/3))] + (16 + 2*I)*Sqrt[3]*(5 + I)^(1/3)*ArcTan[1/Sqrt[3] + (2^(2/3)*x)/((5/13 + I/13)^(1/3)*Sqrt[3]*(1 + x^3)^(1/3))] - (16 - 2*I)*(5 - I)^(1/3)*Log[(10 - 2*I)^(1/3) - (13^(1/3)*x)/(1 + x^3)^(1/3)] - (16 + 2*I)*(5 + I)^(1/3)*Log[(10 + 2*I)^(1/3) - (13^(1/3)*x)/(1 + x^3)^(1/3)] + (8 - I)*(5 - I)^(1/3)*Log[(10 - 2*I)^(2/3) + (13^(2/3)*x^2)/(1 + x^3)^(2/3) + ((130 - 26*I)^(1/3)*x)/(1 + x^3)^(1/3)] + (8 + I)*(5 + I)^(1/3)*Log[(10 + 2*I)^(2/3) + (13^(2/3)*x^2)/(1 + x^3)^(2/3) + ((130 + 26*I)^(1/3)*x)/(1 + x^3)^(1/3)])/(96*2^(2/3)*13^(1/3))","C",1
1668,1,464,112,2.5507807,"\int \frac{\left(1+x^3\right)^{2/3} \left(2+x^3\right) \left(4+3 x^3\right)}{x^6 \left(4+2 x^3+x^6\right)} \, dx","Integrate[((1 + x^3)^(2/3)*(2 + x^3)*(4 + 3*x^3))/(x^6*(4 + 2*x^3 + x^6)),x]","\left(x^3+1\right)^{2/3} \left(-\frac{2}{5 x^5}-\frac{23}{20 x^2}\right)+\frac{1}{72} \left(-\frac{2\ 3^{2/3} \sqrt[3]{3-i \sqrt{3}} \left(3 \sqrt{3}+i\right) \log \left(-\frac{\sqrt[3]{3} x}{\sqrt[3]{x^3+1}}+\sqrt[3]{3-i \sqrt{3}}\right)}{\sqrt{3}-i}+\frac{2\ 3^{2/3} \left(-3 \sqrt{3}+i\right) \sqrt[3]{3+i \sqrt{3}} \log \left(-\frac{\sqrt[3]{3} x}{\sqrt[3]{x^3+1}}+\sqrt[3]{3+i \sqrt{3}}\right)}{\sqrt{3}+i}+\frac{\left(3 \sqrt{3}+i\right) \left(6 \tan ^{-1}\left(\frac{1}{\sqrt{3}}+\frac{2 x}{\sqrt[6]{3} \sqrt[3]{3-i \sqrt{3}} \sqrt[3]{x^3+1}}\right)+\sqrt{3} \log \left(\frac{\sqrt[3]{9-3 i \sqrt{3}} x}{\sqrt[3]{x^3+1}}+\frac{3^{2/3} x^2}{\left(x^3+1\right)^{2/3}}+\left(3-i \sqrt{3}\right)^{2/3}\right)\right)}{\left(1-\frac{i}{\sqrt{3}}\right)^{2/3}}+\frac{\sqrt[6]{3} \left(9-i \sqrt{3}\right) \left(6 \tan ^{-1}\left(\frac{1}{\sqrt{3}}+\frac{2 x}{\sqrt[6]{3} \sqrt[3]{3+i \sqrt{3}} \sqrt[3]{x^3+1}}\right)+\sqrt{3} \log \left(\frac{\sqrt[3]{9+3 i \sqrt{3}} x}{\sqrt[3]{x^3+1}}+\frac{3^{2/3} x^2}{\left(x^3+1\right)^{2/3}}+\left(3+i \sqrt{3}\right)^{2/3}\right)\right)}{\left(3+i \sqrt{3}\right)^{2/3}}\right)","\frac{1}{12} \text{RootSum}\left[4 \text{$\#$1}^6-6 \text{$\#$1}^3+3\&,\frac{-8 \text{$\#$1}^3 \log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)+8 \text{$\#$1}^3 \log (x)+9 \log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)-9 \log (x)}{4 \text{$\#$1}^4-3 \text{$\#$1}}\&\right]+\frac{\left(x^3+1\right)^{2/3} \left(-23 x^3-8\right)}{20 x^5}",1,"(-2/(5*x^5) - 23/(20*x^2))*(1 + x^3)^(2/3) + ((-2*3^(2/3)*(3 - I*Sqrt[3])^(1/3)*(I + 3*Sqrt[3])*Log[(3 - I*Sqrt[3])^(1/3) - (3^(1/3)*x)/(1 + x^3)^(1/3)])/(-I + Sqrt[3]) + (2*3^(2/3)*(I - 3*Sqrt[3])*(3 + I*Sqrt[3])^(1/3)*Log[(3 + I*Sqrt[3])^(1/3) - (3^(1/3)*x)/(1 + x^3)^(1/3)])/(I + Sqrt[3]) + ((I + 3*Sqrt[3])*(6*ArcTan[1/Sqrt[3] + (2*x)/(3^(1/6)*(3 - I*Sqrt[3])^(1/3)*(1 + x^3)^(1/3))] + Sqrt[3]*Log[(3 - I*Sqrt[3])^(2/3) + (3^(2/3)*x^2)/(1 + x^3)^(2/3) + ((9 - (3*I)*Sqrt[3])^(1/3)*x)/(1 + x^3)^(1/3)]))/(1 - I/Sqrt[3])^(2/3) + (3^(1/6)*(9 - I*Sqrt[3])*(6*ArcTan[1/Sqrt[3] + (2*x)/(3^(1/6)*(3 + I*Sqrt[3])^(1/3)*(1 + x^3)^(1/3))] + Sqrt[3]*Log[(3 + I*Sqrt[3])^(2/3) + (3^(2/3)*x^2)/(1 + x^3)^(2/3) + ((9 + (3*I)*Sqrt[3])^(1/3)*x)/(1 + x^3)^(1/3)]))/(3 + I*Sqrt[3])^(2/3))/72","C",1
1669,1,464,112,0.3435616,"\int \frac{\left(1+x^3\right)^{2/3} \left(2+x^3\right) \left(4+3 x^3\right)}{x^6 \left(4+2 x^3+x^6\right)} \, dx","Integrate[((1 + x^3)^(2/3)*(2 + x^3)*(4 + 3*x^3))/(x^6*(4 + 2*x^3 + x^6)),x]","\left(x^3+1\right)^{2/3} \left(-\frac{2}{5 x^5}-\frac{23}{20 x^2}\right)+\frac{1}{72} \left(-\frac{2\ 3^{2/3} \sqrt[3]{3-i \sqrt{3}} \left(3 \sqrt{3}+i\right) \log \left(-\frac{\sqrt[3]{3} x}{\sqrt[3]{x^3+1}}+\sqrt[3]{3-i \sqrt{3}}\right)}{\sqrt{3}-i}+\frac{2\ 3^{2/3} \left(-3 \sqrt{3}+i\right) \sqrt[3]{3+i \sqrt{3}} \log \left(-\frac{\sqrt[3]{3} x}{\sqrt[3]{x^3+1}}+\sqrt[3]{3+i \sqrt{3}}\right)}{\sqrt{3}+i}+\frac{\left(3 \sqrt{3}+i\right) \left(6 \tan ^{-1}\left(\frac{1}{\sqrt{3}}+\frac{2 x}{\sqrt[6]{3} \sqrt[3]{3-i \sqrt{3}} \sqrt[3]{x^3+1}}\right)+\sqrt{3} \log \left(\frac{\sqrt[3]{9-3 i \sqrt{3}} x}{\sqrt[3]{x^3+1}}+\frac{3^{2/3} x^2}{\left(x^3+1\right)^{2/3}}+\left(3-i \sqrt{3}\right)^{2/3}\right)\right)}{\left(1-\frac{i}{\sqrt{3}}\right)^{2/3}}+\frac{\sqrt[6]{3} \left(9-i \sqrt{3}\right) \left(6 \tan ^{-1}\left(\frac{1}{\sqrt{3}}+\frac{2 x}{\sqrt[6]{3} \sqrt[3]{3+i \sqrt{3}} \sqrt[3]{x^3+1}}\right)+\sqrt{3} \log \left(\frac{\sqrt[3]{9+3 i \sqrt{3}} x}{\sqrt[3]{x^3+1}}+\frac{3^{2/3} x^2}{\left(x^3+1\right)^{2/3}}+\left(3+i \sqrt{3}\right)^{2/3}\right)\right)}{\left(3+i \sqrt{3}\right)^{2/3}}\right)","\frac{1}{12} \text{RootSum}\left[4 \text{$\#$1}^6-6 \text{$\#$1}^3+3\&,\frac{-8 \text{$\#$1}^3 \log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)+8 \text{$\#$1}^3 \log (x)+9 \log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)-9 \log (x)}{4 \text{$\#$1}^4-3 \text{$\#$1}}\&\right]+\frac{\left(x^3+1\right)^{2/3} \left(-23 x^3-8\right)}{20 x^5}",1,"(-2/(5*x^5) - 23/(20*x^2))*(1 + x^3)^(2/3) + ((-2*3^(2/3)*(3 - I*Sqrt[3])^(1/3)*(I + 3*Sqrt[3])*Log[(3 - I*Sqrt[3])^(1/3) - (3^(1/3)*x)/(1 + x^3)^(1/3)])/(-I + Sqrt[3]) + (2*3^(2/3)*(I - 3*Sqrt[3])*(3 + I*Sqrt[3])^(1/3)*Log[(3 + I*Sqrt[3])^(1/3) - (3^(1/3)*x)/(1 + x^3)^(1/3)])/(I + Sqrt[3]) + ((I + 3*Sqrt[3])*(6*ArcTan[1/Sqrt[3] + (2*x)/(3^(1/6)*(3 - I*Sqrt[3])^(1/3)*(1 + x^3)^(1/3))] + Sqrt[3]*Log[(3 - I*Sqrt[3])^(2/3) + (3^(2/3)*x^2)/(1 + x^3)^(2/3) + ((9 - (3*I)*Sqrt[3])^(1/3)*x)/(1 + x^3)^(1/3)]))/(1 - I/Sqrt[3])^(2/3) + (3^(1/6)*(9 - I*Sqrt[3])*(6*ArcTan[1/Sqrt[3] + (2*x)/(3^(1/6)*(3 + I*Sqrt[3])^(1/3)*(1 + x^3)^(1/3))] + Sqrt[3]*Log[(3 + I*Sqrt[3])^(2/3) + (3^(2/3)*x^2)/(1 + x^3)^(2/3) + ((9 + (3*I)*Sqrt[3])^(1/3)*x)/(1 + x^3)^(1/3)]))/(3 + I*Sqrt[3])^(2/3))/72","C",1
1670,1,641,112,1.2072559,"\int \frac{\left(-1+x^3\right)^{2/3} \left(4+x^6\right)}{x^6 \left(4+2 x^3+x^6\right)} \, dx","Integrate[((-1 + x^3)^(2/3)*(4 + x^6))/(x^6*(4 + 2*x^3 + x^6)),x]","\left(x^3-1\right)^{2/3} \left(\frac{9}{20 x^2}-\frac{1}{5 x^5}\right)+\frac{1}{72} \left(\frac{2 \sqrt[3]{\frac{\sqrt{3}-i}{\sqrt{3}-2 i}} \left(5 \sqrt{3}-3 i\right) \log \left(\sqrt[3]{-\sqrt{3}+i}-\frac{\sqrt[3]{-\sqrt{3}+2 i} x}{\sqrt[3]{x^3-1}}\right)}{\sqrt{3}-i}+\frac{2 \left(5 \sqrt{3}+3 i\right) \log \left(\sqrt[3]{\sqrt{3}+i}-\frac{\sqrt[3]{\sqrt{3}+2 i} x}{\sqrt[3]{x^3-1}}\right)}{\left(\sqrt{3}+i\right)^{2/3} \sqrt[3]{\sqrt{3}+2 i}}-\frac{\left(5 \sqrt{3}+3 i\right) \left(2 \sqrt{3} \sqrt[3]{\frac{1+3 i \sqrt{3}}{\sqrt{3}+i}} \tan ^{-1}\left(\frac{1+\frac{2 \left(\sqrt{3}+2 i\right)^{2/3} x}{\sqrt[3]{1+3 i \sqrt{3}} \sqrt[3]{x^3-1}}}{\sqrt{3}}\right)+\sqrt[3]{\sqrt{3}+2 i} \log \left(\frac{\sqrt[3]{1+3 i \sqrt{3}} x}{\sqrt[3]{x^3-1}}+\frac{\left(\sqrt{3}+2 i\right)^{2/3} x^2}{\left(x^3-1\right)^{2/3}}+\left(\sqrt{3}+i\right)^{2/3}\right)\right)}{\left(1+3 i \sqrt{3}\right)^{2/3}}-\frac{\left(5 \sqrt{3}-3 i\right) \left(2 \sqrt{-3 \left(-\sqrt{3}+i\right)^{2/3}} \tanh ^{-1}\left(\frac{\sqrt[3]{-\sqrt{3}+i} \sqrt[3]{x^3-1}+2 \sqrt[3]{-\sqrt{3}+2 i} x}{\sqrt{-3 \left(-\sqrt{3}+i\right)^{2/3}} \sqrt[3]{x^3-1}}\right)+\sqrt[3]{-\sqrt{3}+i} \log \left(-\frac{\sqrt[3]{-\sqrt{3}+i} \sqrt[3]{-\sqrt{3}+2 i} x}{\sqrt[3]{x^3-1}}-\frac{\left(-\sqrt{3}+2 i\right)^{2/3} x^2}{\left(x^3-1\right)^{2/3}}-\left(-\sqrt{3}+i\right)^{2/3}\right)\right)}{\sqrt[3]{-\sqrt{3}+2 i} \left(\sqrt{3}-i\right)}\right)","\frac{\left(x^3-1\right)^{2/3} \left(9 x^3-4\right)}{20 x^5}-\frac{1}{12} \text{RootSum}\left[4 \text{$\#$1}^6-10 \text{$\#$1}^3+7\&,\frac{-6 \text{$\#$1}^3 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)+6 \text{$\#$1}^3 \log (x)+7 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)-7 \log (x)}{4 \text{$\#$1}^4-5 \text{$\#$1}}\&\right]",1,"(-1/5*1/x^5 + 9/(20*x^2))*(-1 + x^3)^(2/3) + ((2*((-I + Sqrt[3])/(-2*I + Sqrt[3]))^(1/3)*(-3*I + 5*Sqrt[3])*Log[(I - Sqrt[3])^(1/3) - ((2*I - Sqrt[3])^(1/3)*x)/(-1 + x^3)^(1/3)])/(-I + Sqrt[3]) - ((-3*I + 5*Sqrt[3])*(2*Sqrt[-3*(I - Sqrt[3])^(2/3)]*ArcTanh[(2*(2*I - Sqrt[3])^(1/3)*x + (I - Sqrt[3])^(1/3)*(-1 + x^3)^(1/3))/(Sqrt[-3*(I - Sqrt[3])^(2/3)]*(-1 + x^3)^(1/3))] + (I - Sqrt[3])^(1/3)*Log[-(I - Sqrt[3])^(2/3) - ((2*I - Sqrt[3])^(2/3)*x^2)/(-1 + x^3)^(2/3) - ((I - Sqrt[3])^(1/3)*(2*I - Sqrt[3])^(1/3)*x)/(-1 + x^3)^(1/3)]))/((2*I - Sqrt[3])^(1/3)*(-I + Sqrt[3])) - ((3*I + 5*Sqrt[3])*(2*Sqrt[3]*((1 + (3*I)*Sqrt[3])/(I + Sqrt[3]))^(1/3)*ArcTan[(1 + (2*(2*I + Sqrt[3])^(2/3)*x)/((1 + (3*I)*Sqrt[3])^(1/3)*(-1 + x^3)^(1/3)))/Sqrt[3]] + (2*I + Sqrt[3])^(1/3)*Log[(I + Sqrt[3])^(2/3) + ((2*I + Sqrt[3])^(2/3)*x^2)/(-1 + x^3)^(2/3) + ((1 + (3*I)*Sqrt[3])^(1/3)*x)/(-1 + x^3)^(1/3)]))/(1 + (3*I)*Sqrt[3])^(2/3) + (2*(3*I + 5*Sqrt[3])*Log[(I + Sqrt[3])^(1/3) - ((2*I + Sqrt[3])^(1/3)*x)/(-1 + x^3)^(1/3)])/((I + Sqrt[3])^(2/3)*(2*I + Sqrt[3])^(1/3)))/72","C",0
1671,1,641,112,0.3088026,"\int \frac{\left(-1+x^3\right)^{2/3} \left(4+x^6\right)}{x^6 \left(4+2 x^3+x^6\right)} \, dx","Integrate[((-1 + x^3)^(2/3)*(4 + x^6))/(x^6*(4 + 2*x^3 + x^6)),x]","\left(x^3-1\right)^{2/3} \left(\frac{9}{20 x^2}-\frac{1}{5 x^5}\right)+\frac{1}{72} \left(\frac{2 \sqrt[3]{\frac{\sqrt{3}-i}{\sqrt{3}-2 i}} \left(5 \sqrt{3}-3 i\right) \log \left(\sqrt[3]{-\sqrt{3}+i}-\frac{\sqrt[3]{-\sqrt{3}+2 i} x}{\sqrt[3]{x^3-1}}\right)}{\sqrt{3}-i}+\frac{2 \left(5 \sqrt{3}+3 i\right) \log \left(\sqrt[3]{\sqrt{3}+i}-\frac{\sqrt[3]{\sqrt{3}+2 i} x}{\sqrt[3]{x^3-1}}\right)}{\left(\sqrt{3}+i\right)^{2/3} \sqrt[3]{\sqrt{3}+2 i}}-\frac{\left(5 \sqrt{3}+3 i\right) \left(2 \sqrt{3} \sqrt[3]{\frac{1+3 i \sqrt{3}}{\sqrt{3}+i}} \tan ^{-1}\left(\frac{1+\frac{2 \left(\sqrt{3}+2 i\right)^{2/3} x}{\sqrt[3]{1+3 i \sqrt{3}} \sqrt[3]{x^3-1}}}{\sqrt{3}}\right)+\sqrt[3]{\sqrt{3}+2 i} \log \left(\frac{\sqrt[3]{1+3 i \sqrt{3}} x}{\sqrt[3]{x^3-1}}+\frac{\left(\sqrt{3}+2 i\right)^{2/3} x^2}{\left(x^3-1\right)^{2/3}}+\left(\sqrt{3}+i\right)^{2/3}\right)\right)}{\left(1+3 i \sqrt{3}\right)^{2/3}}-\frac{\left(5 \sqrt{3}-3 i\right) \left(2 \sqrt{-3 \left(-\sqrt{3}+i\right)^{2/3}} \tanh ^{-1}\left(\frac{\sqrt[3]{-\sqrt{3}+i} \sqrt[3]{x^3-1}+2 \sqrt[3]{-\sqrt{3}+2 i} x}{\sqrt{-3 \left(-\sqrt{3}+i\right)^{2/3}} \sqrt[3]{x^3-1}}\right)+\sqrt[3]{-\sqrt{3}+i} \log \left(-\frac{\sqrt[3]{-\sqrt{3}+i} \sqrt[3]{-\sqrt{3}+2 i} x}{\sqrt[3]{x^3-1}}-\frac{\left(-\sqrt{3}+2 i\right)^{2/3} x^2}{\left(x^3-1\right)^{2/3}}-\left(-\sqrt{3}+i\right)^{2/3}\right)\right)}{\sqrt[3]{-\sqrt{3}+2 i} \left(\sqrt{3}-i\right)}\right)","\frac{\left(x^3-1\right)^{2/3} \left(9 x^3-4\right)}{20 x^5}-\frac{1}{12} \text{RootSum}\left[4 \text{$\#$1}^6-10 \text{$\#$1}^3+7\&,\frac{-6 \text{$\#$1}^3 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)+6 \text{$\#$1}^3 \log (x)+7 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)-7 \log (x)}{4 \text{$\#$1}^4-5 \text{$\#$1}}\&\right]",1,"(-1/5*1/x^5 + 9/(20*x^2))*(-1 + x^3)^(2/3) + ((2*((-I + Sqrt[3])/(-2*I + Sqrt[3]))^(1/3)*(-3*I + 5*Sqrt[3])*Log[(I - Sqrt[3])^(1/3) - ((2*I - Sqrt[3])^(1/3)*x)/(-1 + x^3)^(1/3)])/(-I + Sqrt[3]) - ((-3*I + 5*Sqrt[3])*(2*Sqrt[-3*(I - Sqrt[3])^(2/3)]*ArcTanh[(2*(2*I - Sqrt[3])^(1/3)*x + (I - Sqrt[3])^(1/3)*(-1 + x^3)^(1/3))/(Sqrt[-3*(I - Sqrt[3])^(2/3)]*(-1 + x^3)^(1/3))] + (I - Sqrt[3])^(1/3)*Log[-(I - Sqrt[3])^(2/3) - ((2*I - Sqrt[3])^(2/3)*x^2)/(-1 + x^3)^(2/3) - ((I - Sqrt[3])^(1/3)*(2*I - Sqrt[3])^(1/3)*x)/(-1 + x^3)^(1/3)]))/((2*I - Sqrt[3])^(1/3)*(-I + Sqrt[3])) - ((3*I + 5*Sqrt[3])*(2*Sqrt[3]*((1 + (3*I)*Sqrt[3])/(I + Sqrt[3]))^(1/3)*ArcTan[(1 + (2*(2*I + Sqrt[3])^(2/3)*x)/((1 + (3*I)*Sqrt[3])^(1/3)*(-1 + x^3)^(1/3)))/Sqrt[3]] + (2*I + Sqrt[3])^(1/3)*Log[(I + Sqrt[3])^(2/3) + ((2*I + Sqrt[3])^(2/3)*x^2)/(-1 + x^3)^(2/3) + ((1 + (3*I)*Sqrt[3])^(1/3)*x)/(-1 + x^3)^(1/3)]))/(1 + (3*I)*Sqrt[3])^(2/3) + (2*(3*I + 5*Sqrt[3])*Log[(I + Sqrt[3])^(1/3) - ((2*I + Sqrt[3])^(1/3)*x)/(-1 + x^3)^(1/3)])/((I + Sqrt[3])^(2/3)*(2*I + Sqrt[3])^(1/3)))/72","C",0
1672,1,354,112,0.7993872,"\int \frac{\left(-1+x^3\right)^{2/3} \left(1-x^3+x^6\right)}{x^6 \left(-2-x^3+2 x^6\right)} \, dx","Integrate[((-1 + x^3)^(2/3)*(1 - x^3 + x^6))/(x^6*(-2 - x^3 + 2*x^6)),x]","\frac{-2 \sqrt[3]{80295+19471 \sqrt{17}} \log \left(\sqrt[3]{5-\sqrt{17}}-\frac{\sqrt[3]{2} x}{\sqrt[3]{x^3-1}}\right)+2 \sqrt[3]{80295-19471 \sqrt{17}} \log \left(\sqrt[3]{5+\sqrt{17}}-\frac{\sqrt[3]{2} x}{\sqrt[3]{x^3-1}}\right)+\sqrt[3]{80295+19471 \sqrt{17}} \left(2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{2 \left(5+\sqrt{17}\right)} x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)+\log \left(\frac{\sqrt[3]{10-2 \sqrt{17}} x}{\sqrt[3]{x^3-1}}+\frac{2^{2/3} x^2}{\left(x^3-1\right)^{2/3}}+\left(5-\sqrt{17}\right)^{2/3}\right)\right)-\sqrt[3]{80295-19471 \sqrt{17}} \left(2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{\frac{2}{5+\sqrt{17}}} x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)+\log \left(\frac{\sqrt[3]{2 \left(5+\sqrt{17}\right)} x}{\sqrt[3]{x^3-1}}+\frac{2^{2/3} x^2}{\left(x^3-1\right)^{2/3}}+\left(5+\sqrt{17}\right)^{2/3}\right)\right)}{48 \sqrt{17}}+\left(x^3-1\right)^{2/3} \left(\frac{1}{10 x^5}-\frac{19}{40 x^2}\right)","\frac{1}{12} \text{RootSum}\left[2 \text{$\#$1}^6-5 \text{$\#$1}^3+1\&,\frac{-17 \text{$\#$1}^3 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)+17 \text{$\#$1}^3 \log (x)+3 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)-3 \log (x)}{4 \text{$\#$1}^4-5 \text{$\#$1}}\&\right]+\frac{\left(x^3-1\right)^{2/3} \left(4-19 x^3\right)}{40 x^5}",1,"(1/(10*x^5) - 19/(40*x^2))*(-1 + x^3)^(2/3) + (-2*(80295 + 19471*Sqrt[17])^(1/3)*Log[(5 - Sqrt[17])^(1/3) - (2^(1/3)*x)/(-1 + x^3)^(1/3)] + 2*(80295 - 19471*Sqrt[17])^(1/3)*Log[(5 + Sqrt[17])^(1/3) - (2^(1/3)*x)/(-1 + x^3)^(1/3)] + (80295 + 19471*Sqrt[17])^(1/3)*(2*Sqrt[3]*ArcTan[(1 + ((2*(5 + Sqrt[17]))^(1/3)*x)/(-1 + x^3)^(1/3))/Sqrt[3]] + Log[(5 - Sqrt[17])^(2/3) + (2^(2/3)*x^2)/(-1 + x^3)^(2/3) + ((10 - 2*Sqrt[17])^(1/3)*x)/(-1 + x^3)^(1/3)]) - (80295 - 19471*Sqrt[17])^(1/3)*(2*Sqrt[3]*ArcTan[(1 + (2*(2/(5 + Sqrt[17]))^(1/3)*x)/(-1 + x^3)^(1/3))/Sqrt[3]] + Log[(5 + Sqrt[17])^(2/3) + (2^(2/3)*x^2)/(-1 + x^3)^(2/3) + ((2*(5 + Sqrt[17]))^(1/3)*x)/(-1 + x^3)^(1/3)]))/(48*Sqrt[17])","B",0
1673,1,354,112,0.5847567,"\int \frac{\left(-1+x^3\right)^{2/3} \left(1-x^3+x^6\right)}{x^6 \left(-2-x^3+2 x^6\right)} \, dx","Integrate[((-1 + x^3)^(2/3)*(1 - x^3 + x^6))/(x^6*(-2 - x^3 + 2*x^6)),x]","\frac{-2 \sqrt[3]{80295+19471 \sqrt{17}} \log \left(\sqrt[3]{5-\sqrt{17}}-\frac{\sqrt[3]{2} x}{\sqrt[3]{x^3-1}}\right)+2 \sqrt[3]{80295-19471 \sqrt{17}} \log \left(\sqrt[3]{5+\sqrt{17}}-\frac{\sqrt[3]{2} x}{\sqrt[3]{x^3-1}}\right)+\sqrt[3]{80295+19471 \sqrt{17}} \left(2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{2 \left(5+\sqrt{17}\right)} x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)+\log \left(\frac{\sqrt[3]{10-2 \sqrt{17}} x}{\sqrt[3]{x^3-1}}+\frac{2^{2/3} x^2}{\left(x^3-1\right)^{2/3}}+\left(5-\sqrt{17}\right)^{2/3}\right)\right)-\sqrt[3]{80295-19471 \sqrt{17}} \left(2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{\frac{2}{5+\sqrt{17}}} x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)+\log \left(\frac{\sqrt[3]{2 \left(5+\sqrt{17}\right)} x}{\sqrt[3]{x^3-1}}+\frac{2^{2/3} x^2}{\left(x^3-1\right)^{2/3}}+\left(5+\sqrt{17}\right)^{2/3}\right)\right)}{48 \sqrt{17}}+\left(x^3-1\right)^{2/3} \left(\frac{1}{10 x^5}-\frac{19}{40 x^2}\right)","\frac{1}{12} \text{RootSum}\left[2 \text{$\#$1}^6-5 \text{$\#$1}^3+1\&,\frac{-17 \text{$\#$1}^3 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)+17 \text{$\#$1}^3 \log (x)+3 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)-3 \log (x)}{4 \text{$\#$1}^4-5 \text{$\#$1}}\&\right]+\frac{\left(x^3-1\right)^{2/3} \left(4-19 x^3\right)}{40 x^5}",1,"(1/(10*x^5) - 19/(40*x^2))*(-1 + x^3)^(2/3) + (-2*(80295 + 19471*Sqrt[17])^(1/3)*Log[(5 - Sqrt[17])^(1/3) - (2^(1/3)*x)/(-1 + x^3)^(1/3)] + 2*(80295 - 19471*Sqrt[17])^(1/3)*Log[(5 + Sqrt[17])^(1/3) - (2^(1/3)*x)/(-1 + x^3)^(1/3)] + (80295 + 19471*Sqrt[17])^(1/3)*(2*Sqrt[3]*ArcTan[(1 + ((2*(5 + Sqrt[17]))^(1/3)*x)/(-1 + x^3)^(1/3))/Sqrt[3]] + Log[(5 - Sqrt[17])^(2/3) + (2^(2/3)*x^2)/(-1 + x^3)^(2/3) + ((10 - 2*Sqrt[17])^(1/3)*x)/(-1 + x^3)^(1/3)]) - (80295 - 19471*Sqrt[17])^(1/3)*(2*Sqrt[3]*ArcTan[(1 + (2*(2/(5 + Sqrt[17]))^(1/3)*x)/(-1 + x^3)^(1/3))/Sqrt[3]] + Log[(5 + Sqrt[17])^(2/3) + (2^(2/3)*x^2)/(-1 + x^3)^(2/3) + ((2*(5 + Sqrt[17]))^(1/3)*x)/(-1 + x^3)^(1/3)]))/(48*Sqrt[17])","B",0
1674,1,446,112,2.4130085,"\int \frac{\left(1+x^3\right)^{2/3} \left(4+6 x^3+3 x^6\right)}{x^6 \left(8+6 x^3+3 x^6\right)} \, dx","Integrate[((1 + x^3)^(2/3)*(4 + 6*x^3 + 3*x^6))/(x^6*(8 + 6*x^3 + 3*x^6)),x]","\left(x^3+1\right)^{2/3} \left(-\frac{1}{10 x^5}-\frac{23}{80 x^2}\right)+\frac{-\frac{6 \sqrt[3]{5-i \sqrt{15}} \left(\sqrt{15}-i\right) \log \left(-\frac{\sqrt[3]{5} x}{\sqrt[3]{x^3+1}}+\sqrt[3]{5-i \sqrt{15}}\right)}{\sqrt{15}-3 i}-\frac{6 \sqrt[3]{5+i \sqrt{15}} \left(\sqrt{15}+i\right) \log \left(-\frac{\sqrt[3]{5} x}{\sqrt[3]{x^3+1}}+\sqrt[3]{5+i \sqrt{15}}\right)}{\sqrt{15}+3 i}+\frac{\left(15-i \sqrt{15}\right) \left(2 \sqrt{3} \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{1-i \sqrt{\frac{3}{5}}} \sqrt[3]{x^3+1}}}{\sqrt{3}}\right)+\log \left(\frac{\sqrt[3]{25-5 i \sqrt{15}} x}{\sqrt[3]{x^3+1}}+\frac{5^{2/3} x^2}{\left(x^3+1\right)^{2/3}}+\left(5-i \sqrt{15}\right)^{2/3}\right)\right)}{\left(5-i \sqrt{15}\right)^{2/3}}+\frac{\left(15+i \sqrt{15}\right) \left(2 \sqrt{3} \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{1+i \sqrt{\frac{3}{5}}} \sqrt[3]{x^3+1}}}{\sqrt{3}}\right)+\log \left(\frac{\sqrt[3]{25+5 i \sqrt{15}} x}{\sqrt[3]{x^3+1}}+\frac{5^{2/3} x^2}{\left(x^3+1\right)^{2/3}}+\left(5+i \sqrt{15}\right)^{2/3}\right)\right)}{\left(5+i \sqrt{15}\right)^{2/3}}}{96 \sqrt[3]{5}}","\frac{1}{16} \text{RootSum}\left[8 \text{$\#$1}^6-10 \text{$\#$1}^3+5\&,\frac{-6 \text{$\#$1}^3 \log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)+6 \text{$\#$1}^3 \log (x)+5 \log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)-5 \log (x)}{8 \text{$\#$1}^4-5 \text{$\#$1}}\&\right]+\frac{\left(x^3+1\right)^{2/3} \left(-23 x^3-8\right)}{80 x^5}",1,"(-1/10*1/x^5 - 23/(80*x^2))*(1 + x^3)^(2/3) + ((-6*(5 - I*Sqrt[15])^(1/3)*(-I + Sqrt[15])*Log[(5 - I*Sqrt[15])^(1/3) - (5^(1/3)*x)/(1 + x^3)^(1/3)])/(-3*I + Sqrt[15]) - (6*(5 + I*Sqrt[15])^(1/3)*(I + Sqrt[15])*Log[(5 + I*Sqrt[15])^(1/3) - (5^(1/3)*x)/(1 + x^3)^(1/3)])/(3*I + Sqrt[15]) + ((15 - I*Sqrt[15])*(2*Sqrt[3]*ArcTan[(1 + (2*x)/((1 - I*Sqrt[3/5])^(1/3)*(1 + x^3)^(1/3)))/Sqrt[3]] + Log[(5 - I*Sqrt[15])^(2/3) + (5^(2/3)*x^2)/(1 + x^3)^(2/3) + ((25 - (5*I)*Sqrt[15])^(1/3)*x)/(1 + x^3)^(1/3)]))/(5 - I*Sqrt[15])^(2/3) + ((15 + I*Sqrt[15])*(2*Sqrt[3]*ArcTan[(1 + (2*x)/((1 + I*Sqrt[3/5])^(1/3)*(1 + x^3)^(1/3)))/Sqrt[3]] + Log[(5 + I*Sqrt[15])^(2/3) + (5^(2/3)*x^2)/(1 + x^3)^(2/3) + ((25 + (5*I)*Sqrt[15])^(1/3)*x)/(1 + x^3)^(1/3)]))/(5 + I*Sqrt[15])^(2/3))/(96*5^(1/3))","C",1
1675,1,446,112,1.1727178,"\int \frac{\left(1+x^3\right)^{2/3} \left(4+6 x^3+3 x^6\right)}{x^6 \left(8+6 x^3+3 x^6\right)} \, dx","Integrate[((1 + x^3)^(2/3)*(4 + 6*x^3 + 3*x^6))/(x^6*(8 + 6*x^3 + 3*x^6)),x]","\left(x^3+1\right)^{2/3} \left(-\frac{1}{10 x^5}-\frac{23}{80 x^2}\right)+\frac{-\frac{6 \sqrt[3]{5-i \sqrt{15}} \left(\sqrt{15}-i\right) \log \left(-\frac{\sqrt[3]{5} x}{\sqrt[3]{x^3+1}}+\sqrt[3]{5-i \sqrt{15}}\right)}{\sqrt{15}-3 i}-\frac{6 \sqrt[3]{5+i \sqrt{15}} \left(\sqrt{15}+i\right) \log \left(-\frac{\sqrt[3]{5} x}{\sqrt[3]{x^3+1}}+\sqrt[3]{5+i \sqrt{15}}\right)}{\sqrt{15}+3 i}+\frac{\left(15-i \sqrt{15}\right) \left(2 \sqrt{3} \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{1-i \sqrt{\frac{3}{5}}} \sqrt[3]{x^3+1}}}{\sqrt{3}}\right)+\log \left(\frac{\sqrt[3]{25-5 i \sqrt{15}} x}{\sqrt[3]{x^3+1}}+\frac{5^{2/3} x^2}{\left(x^3+1\right)^{2/3}}+\left(5-i \sqrt{15}\right)^{2/3}\right)\right)}{\left(5-i \sqrt{15}\right)^{2/3}}+\frac{\left(15+i \sqrt{15}\right) \left(2 \sqrt{3} \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{1+i \sqrt{\frac{3}{5}}} \sqrt[3]{x^3+1}}}{\sqrt{3}}\right)+\log \left(\frac{\sqrt[3]{25+5 i \sqrt{15}} x}{\sqrt[3]{x^3+1}}+\frac{5^{2/3} x^2}{\left(x^3+1\right)^{2/3}}+\left(5+i \sqrt{15}\right)^{2/3}\right)\right)}{\left(5+i \sqrt{15}\right)^{2/3}}}{96 \sqrt[3]{5}}","\frac{1}{16} \text{RootSum}\left[8 \text{$\#$1}^6-10 \text{$\#$1}^3+5\&,\frac{-6 \text{$\#$1}^3 \log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)+6 \text{$\#$1}^3 \log (x)+5 \log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)-5 \log (x)}{8 \text{$\#$1}^4-5 \text{$\#$1}}\&\right]+\frac{\left(x^3+1\right)^{2/3} \left(-23 x^3-8\right)}{80 x^5}",1,"(-1/10*1/x^5 - 23/(80*x^2))*(1 + x^3)^(2/3) + ((-6*(5 - I*Sqrt[15])^(1/3)*(-I + Sqrt[15])*Log[(5 - I*Sqrt[15])^(1/3) - (5^(1/3)*x)/(1 + x^3)^(1/3)])/(-3*I + Sqrt[15]) - (6*(5 + I*Sqrt[15])^(1/3)*(I + Sqrt[15])*Log[(5 + I*Sqrt[15])^(1/3) - (5^(1/3)*x)/(1 + x^3)^(1/3)])/(3*I + Sqrt[15]) + ((15 - I*Sqrt[15])*(2*Sqrt[3]*ArcTan[(1 + (2*x)/((1 - I*Sqrt[3/5])^(1/3)*(1 + x^3)^(1/3)))/Sqrt[3]] + Log[(5 - I*Sqrt[15])^(2/3) + (5^(2/3)*x^2)/(1 + x^3)^(2/3) + ((25 - (5*I)*Sqrt[15])^(1/3)*x)/(1 + x^3)^(1/3)]))/(5 - I*Sqrt[15])^(2/3) + ((15 + I*Sqrt[15])*(2*Sqrt[3]*ArcTan[(1 + (2*x)/((1 + I*Sqrt[3/5])^(1/3)*(1 + x^3)^(1/3)))/Sqrt[3]] + Log[(5 + I*Sqrt[15])^(2/3) + (5^(2/3)*x^2)/(1 + x^3)^(2/3) + ((25 + (5*I)*Sqrt[15])^(1/3)*x)/(1 + x^3)^(1/3)]))/(5 + I*Sqrt[15])^(2/3))/(96*5^(1/3))","C",1
1676,0,0,112,0.3675211,"\int \frac{\sqrt[3]{-1+2 x^3+x^8} \left(3+5 x^8\right)}{x^2 \left(-1+x^3+x^8\right)} \, dx","Integrate[((-1 + 2*x^3 + x^8)^(1/3)*(3 + 5*x^8))/(x^2*(-1 + x^3 + x^8)),x]","\int \frac{\sqrt[3]{-1+2 x^3+x^8} \left(3+5 x^8\right)}{x^2 \left(-1+x^3+x^8\right)} \, dx","\frac{3 \sqrt[3]{x^8+2 x^3-1}}{x}+\log \left(\sqrt[3]{x^8+2 x^3-1}-x\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^8+2 x^3-1}+x}\right)-\frac{1}{2} \log \left(x^2+\sqrt[3]{x^8+2 x^3-1} x+\left(x^8+2 x^3-1\right)^{2/3}\right)",1,"Integrate[((-1 + 2*x^3 + x^8)^(1/3)*(3 + 5*x^8))/(x^2*(-1 + x^3 + x^8)), x]","F",-1
1677,0,0,112,0.229515,"\int \frac{\left(-1+x^4\right) \sqrt{1+\sqrt{1+x^2}}}{1+x^4} \, dx","Integrate[((-1 + x^4)*Sqrt[1 + Sqrt[1 + x^2]])/(1 + x^4),x]","\int \frac{\left(-1+x^4\right) \sqrt{1+\sqrt{1+x^2}}}{1+x^4} \, dx","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8+4 \text{$\#$1}^6+4 \text{$\#$1}^4+1\&,\frac{\log \left(\frac{x}{\sqrt{\sqrt{x^2+1}+1}}-\text{$\#$1}\right)}{\text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]+\frac{2 \sqrt{x^2+1} x}{3 \sqrt{\sqrt{x^2+1}+1}}+\frac{4 x}{3 \sqrt{\sqrt{x^2+1}+1}}",1,"Integrate[((-1 + x^4)*Sqrt[1 + Sqrt[1 + x^2]])/(1 + x^4), x]","F",-1
1678,0,0,112,0.0952047,"\int \frac{\left(-1+x^4\right) \sqrt{1+\sqrt{1+x^2}}}{1+x^4} \, dx","Integrate[((-1 + x^4)*Sqrt[1 + Sqrt[1 + x^2]])/(1 + x^4),x]","\int \frac{\left(-1+x^4\right) \sqrt{1+\sqrt{1+x^2}}}{1+x^4} \, dx","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8+4 \text{$\#$1}^6+4 \text{$\#$1}^4+1\&,\frac{\log \left(\frac{x}{\sqrt{\sqrt{x^2+1}+1}}-\text{$\#$1}\right)}{\text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]+\frac{2 \sqrt{x^2+1} x}{3 \sqrt{\sqrt{x^2+1}+1}}+\frac{4 x}{3 \sqrt{\sqrt{x^2+1}+1}}",1,"Integrate[((-1 + x^4)*Sqrt[1 + Sqrt[1 + x^2]])/(1 + x^4), x]","F",-1
1679,1,93,112,0.0557406,"\int \frac{\sqrt{b^2+a^2 x^2}}{\sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Integrate[Sqrt[b^2 + a^2*x^2]/Sqrt[a*x + Sqrt[b^2 + a^2*x^2]],x]","\frac{-\frac{4 b^2}{\sqrt{\sqrt{a^2 x^2+b^2}+a x}}+\frac{2}{3} \left(\sqrt{a^2 x^2+b^2}+a x\right)^{3/2}-\frac{2 b^4}{5 \left(\sqrt{a^2 x^2+b^2}+a x\right)^{5/2}}}{4 a}","\frac{4 \sqrt{a^2 x^2+b^2} \left(a^2 x^3-b^2 x\right)}{3 \left(\sqrt{a^2 x^2+b^2}+a x\right)^{5/2}}+\frac{2 \left(10 a^4 x^4-5 a^2 b^2 x^2-7 b^4\right)}{15 a \left(\sqrt{a^2 x^2+b^2}+a x\right)^{5/2}}",1,"((-2*b^4)/(5*(a*x + Sqrt[b^2 + a^2*x^2])^(5/2)) - (4*b^2)/Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] + (2*(a*x + Sqrt[b^2 + a^2*x^2])^(3/2))/3)/(4*a)","A",1
1680,1,675,113,25.6854779,"\int \frac{-2 a+b+x}{\sqrt[4]{(-a+x) (-b+x)^2} \left(b^2+a d-(2 b+d) x+x^2\right)} \, dx","Integrate[(-2*a + b + x)/(((-a + x)*(-b + x)^2)^(1/4)*(b^2 + a*d - (2*b + d)*x + x^2)),x]","-\frac{i \sqrt{2} (x-a)^{3/4} \sqrt{\frac{b-x}{a-x}} \left(\left(\sqrt{d (-4 a+4 b+d)}+4 a-4 b-d\right) \sqrt{\frac{\sqrt{d (-4 a+4 b+d)}-2 a+2 b+d}{(a-b)^2}} \Pi \left(-\frac{\sqrt{2}}{\sqrt{b-a} \sqrt{\frac{-2 a+2 b+d-\sqrt{d (-4 a+4 b+d)}}{(a-b)^2}}};\left.i \sinh ^{-1}\left(\frac{\sqrt{-\sqrt{b-a}}}{\sqrt[4]{x-a}}\right)\right|-1\right)-\left(\sqrt{d (-4 a+4 b+d)}+4 a-4 b-d\right) \sqrt{\frac{\sqrt{d (-4 a+4 b+d)}-2 a+2 b+d}{(a-b)^2}} \Pi \left(\frac{\sqrt{2}}{\sqrt{b-a} \sqrt{\frac{-2 a+2 b+d-\sqrt{d (-4 a+4 b+d)}}{(a-b)^2}}};\left.i \sinh ^{-1}\left(\frac{\sqrt{-\sqrt{b-a}}}{\sqrt[4]{x-a}}\right)\right|-1\right)-\left(-\sqrt{d (-4 a+4 b+d)}+4 a-4 b-d\right) \sqrt{\frac{-\sqrt{d (-4 a+4 b+d)}-2 a+2 b+d}{(a-b)^2}} \left(\Pi \left(-\frac{\sqrt{2}}{\sqrt{b-a} \sqrt{\frac{-2 a+2 b+d+\sqrt{d (-4 a+4 b+d)}}{(a-b)^2}}};\left.i \sinh ^{-1}\left(\frac{\sqrt{-\sqrt{b-a}}}{\sqrt[4]{x-a}}\right)\right|-1\right)-\Pi \left(\frac{\sqrt{2}}{\sqrt{b-a} \sqrt{\frac{-2 a+2 b+d+\sqrt{d (-4 a+4 b+d)}}{(a-b)^2}}};\left.i \sinh ^{-1}\left(\frac{\sqrt{-\sqrt{b-a}}}{\sqrt[4]{x-a}}\right)\right|-1\right)\right)\right)}{(a-b) \sqrt{-\sqrt{b-a}} \sqrt{d (-4 a+4 b+d)} \sqrt{\frac{-\sqrt{d (-4 a+4 b+d)}-2 a+2 b+d}{(a-b)^2}} \sqrt{\frac{\sqrt{d (-4 a+4 b+d)}-2 a+2 b+d}{(a-b)^2}} \sqrt[4]{(x-a) (b-x)^2}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3}}{b-x}\right)}{d^{3/4}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3}}{b-x}\right)}{d^{3/4}}",1,"((-I)*Sqrt[2]*Sqrt[(b - x)/(a - x)]*(-a + x)^(3/4)*((4*a - 4*b - d + Sqrt[d*(-4*a + 4*b + d)])*Sqrt[(-2*a + 2*b + d + Sqrt[d*(-4*a + 4*b + d)])/(a - b)^2]*EllipticPi[-(Sqrt[2]/(Sqrt[-a + b]*Sqrt[(-2*a + 2*b + d - Sqrt[d*(-4*a + 4*b + d)])/(a - b)^2])), I*ArcSinh[Sqrt[-Sqrt[-a + b]]/(-a + x)^(1/4)], -1] - (4*a - 4*b - d + Sqrt[d*(-4*a + 4*b + d)])*Sqrt[(-2*a + 2*b + d + Sqrt[d*(-4*a + 4*b + d)])/(a - b)^2]*EllipticPi[Sqrt[2]/(Sqrt[-a + b]*Sqrt[(-2*a + 2*b + d - Sqrt[d*(-4*a + 4*b + d)])/(a - b)^2]), I*ArcSinh[Sqrt[-Sqrt[-a + b]]/(-a + x)^(1/4)], -1] - (4*a - 4*b - d - Sqrt[d*(-4*a + 4*b + d)])*Sqrt[(-2*a + 2*b + d - Sqrt[d*(-4*a + 4*b + d)])/(a - b)^2]*(EllipticPi[-(Sqrt[2]/(Sqrt[-a + b]*Sqrt[(-2*a + 2*b + d + Sqrt[d*(-4*a + 4*b + d)])/(a - b)^2])), I*ArcSinh[Sqrt[-Sqrt[-a + b]]/(-a + x)^(1/4)], -1] - EllipticPi[Sqrt[2]/(Sqrt[-a + b]*Sqrt[(-2*a + 2*b + d + Sqrt[d*(-4*a + 4*b + d)])/(a - b)^2]), I*ArcSinh[Sqrt[-Sqrt[-a + b]]/(-a + x)^(1/4)], -1])))/((a - b)*Sqrt[-Sqrt[-a + b]]*Sqrt[d*(-4*a + 4*b + d)]*Sqrt[(-2*a + 2*b + d - Sqrt[d*(-4*a + 4*b + d)])/(a - b)^2]*Sqrt[(-2*a + 2*b + d + Sqrt[d*(-4*a + 4*b + d)])/(a - b)^2]*((b - x)^2*(-a + x))^(1/4))","C",1
1681,1,35,113,0.0122245,"\int x \sqrt[3]{x^2+x^3} \, dx","Integrate[x*(x^2 + x^3)^(1/3),x]","\frac{3 \left(x^2 (x+1)\right)^{4/3} \, _2F_1\left(-\frac{1}{3},\frac{8}{3};\frac{11}{3};-x\right)}{8 (x+1)^{4/3}}","\frac{1}{54} \sqrt[3]{x^3+x^2} \left(18 x^2+3 x-5\right)-\frac{5}{81} \log \left(\sqrt[3]{x^3+x^2}-x\right)+\frac{5}{162} \log \left(x^2+\sqrt[3]{x^3+x^2} x+\left(x^3+x^2\right)^{2/3}\right)-\frac{5 \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+x^2}+x}\right)}{27 \sqrt{3}}",1,"(3*(x^2*(1 + x))^(4/3)*Hypergeometric2F1[-1/3, 8/3, 11/3, -x])/(8*(1 + x)^(4/3))","C",1
1682,1,2458,113,7.3377103,"\int \frac{-((2 a-3 b) b)+2 (a-2 b) x+x^2}{\sqrt[4]{(-a+x) (-b+x)^2} \left(-a^3-b^2 d+\left(3 a^2+2 b d\right) x-(3 a+d) x^2+x^3\right)} \, dx","Integrate[(-((2*a - 3*b)*b) + 2*(a - 2*b)*x + x^2)/(((-a + x)*(-b + x)^2)^(1/4)*(-a^3 - b^2*d + (3*a^2 + 2*b*d)*x - (3*a + d)*x^2 + x^3)),x]","\text{Result too large to show}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3}}{a-x}\right)}{d^{3/4}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3}}{a-x}\right)}{d^{3/4}}",1,"((-2*I)*(a - b)*(a - x)^(3/4)*Sqrt[(b - x)/(a - x)]*((-(EllipticPi[-(1/(Sqrt[a - b]*Sqrt[Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 2]])), I*ArcSinh[Sqrt[-Sqrt[a - b]]/(a - x)^(1/4)], -1]*Sqrt[Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 1]]*(1 - 4*(a - b)*Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 2] + 3*(a - b)^2*Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 2]^2)*(Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 1] - Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 3])) + EllipticPi[1/(Sqrt[a - b]*Sqrt[Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 2]]), I*ArcSinh[Sqrt[-Sqrt[a - b]]/(a - x)^(1/4)], -1]*Sqrt[Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 1]]*(1 - 4*(a - b)*Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 2] + 3*(a - b)^2*Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 2]^2)*(Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 1] - Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 3]) + (EllipticPi[-(1/(Sqrt[a - b]*Sqrt[Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 1]])), I*ArcSinh[Sqrt[-Sqrt[a - b]]/(a - x)^(1/4)], -1] - EllipticPi[1/(Sqrt[a - b]*Sqrt[Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 1]]), I*ArcSinh[Sqrt[-Sqrt[a - b]]/(a - x)^(1/4)], -1])*(1 - 4*(a - b)*Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 1] + 3*(a - b)^2*Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 1]^2)*Sqrt[Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 2]]*(Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 2] - Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 3]))*Sqrt[Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 3]] + EllipticPi[-(1/(Sqrt[a - b]*Sqrt[Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 3]])), I*ArcSinh[Sqrt[-Sqrt[a - b]]/(a - x)^(1/4)], -1]*Sqrt[Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 1]]*(Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 1] - Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 2])*Sqrt[Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 2]]*(1 - 4*(a - b)*Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 3] + 3*(a - b)^2*Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 3]^2) - EllipticPi[1/(Sqrt[a - b]*Sqrt[Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 3]]), I*ArcSinh[Sqrt[-Sqrt[a - b]]/(a - x)^(1/4)], -1]*Sqrt[Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 1]]*(Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 1] - Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 2])*Sqrt[Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 2]]*(1 - 4*(a - b)*Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 3] + 3*(a - b)^2*Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 3]^2)))/(Sqrt[-Sqrt[a - b]]*((b - x)^2*(-a + x))^(1/4)*Sqrt[Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 1]]*Sqrt[Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 2]]*Sqrt[Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 3]]*(-3*a + 3*b - 2*d + 2*(a - b)^3*d*Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 1]*Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 2]^2 + 2*(a - b)^3*d*Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 1]^2*Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 3] + 2*(a - b)^3*d*Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 2]*Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 3]^2))","C",0
1683,0,0,113,5.9634975,"\int \frac{(-1+x)^3 \left(-1+2 (-1+k) x+k x^2\right)}{x \sqrt[4]{(1-x) x (1-k x)} (-1+k x) \left(-1+(3+d) x-(3+d k) x^2+x^3\right)} \, dx","Integrate[((-1 + x)^3*(-1 + 2*(-1 + k)*x + k*x^2))/(x*((1 - x)*x*(1 - k*x))^(1/4)*(-1 + k*x)*(-1 + (3 + d)*x - (3 + d*k)*x^2 + x^3)),x]","\int \frac{(-1+x)^3 \left(-1+2 (-1+k) x+k x^2\right)}{x \sqrt[4]{(1-x) x (1-k x)} (-1+k x) \left(-1+(3+d) x-(3+d k) x^2+x^3\right)} \, dx","2 \sqrt[4]{d} \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{k x^3+(-k-1) x^2+x}}{x-1}\right)-2 \sqrt[4]{d} \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{k x^3+(-k-1) x^2+x}}{x-1}\right)+\frac{4 \left(k x^3-k x^2-x^2+x\right)^{3/4}}{x (k x-1)}",1,"Integrate[((-1 + x)^3*(-1 + 2*(-1 + k)*x + k*x^2))/(x*((1 - x)*x*(1 - k*x))^(1/4)*(-1 + k*x)*(-1 + (3 + d)*x - (3 + d*k)*x^2 + x^3)), x]","F",-1
1684,1,60,113,0.0451402,"\int \frac{b+a x^2}{\left(-b+a x^2\right) \sqrt{b x+a x^3}} \, dx","Integrate[(b + a*x^2)/((-b + a*x^2)*Sqrt[b*x + a*x^3]),x]","-\frac{2 \sqrt{x \left(a x^2+b\right)} F_1\left(\frac{1}{4};-\frac{1}{2},1;\frac{5}{4};-\frac{a x^2}{b},\frac{a x^2}{b}\right)}{b \sqrt{\frac{a x^2}{b}+1}}","-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{a x^3+b x}}{a x^2+b}\right)}{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{a x^3+b x}}{a x^2+b}\right)}{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b}}",1,"(-2*Sqrt[x*(b + a*x^2)]*AppellF1[1/4, -1/2, 1, 5/4, -((a*x^2)/b), (a*x^2)/b])/(b*Sqrt[1 + (a*x^2)/b])","C",0
1685,0,0,113,3.5486327,"\int \frac{\left(a^2-2 a x+x^2\right) \left(-((2 a-3 b) b)+2 (a-2 b) x+x^2\right)}{\left((-a+x) (-b+x)^2\right)^{3/4} \left(-b^2-a^3 d+\left(2 b+3 a^2 d\right) x-(1+3 a d) x^2+d x^3\right)} \, dx","Integrate[((a^2 - 2*a*x + x^2)*(-((2*a - 3*b)*b) + 2*(a - 2*b)*x + x^2))/(((-a + x)*(-b + x)^2)^(3/4)*(-b^2 - a^3*d + (2*b + 3*a^2*d)*x - (1 + 3*a*d)*x^2 + d*x^3)),x]","\int \frac{\left(a^2-2 a x+x^2\right) \left(-((2 a-3 b) b)+2 (a-2 b) x+x^2\right)}{\left((-a+x) (-b+x)^2\right)^{3/4} \left(-b^2-a^3 d+\left(2 b+3 a^2 d\right) x-(1+3 a d) x^2+d x^3\right)} \, dx","\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \left(x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3\right)^{3/4}}{(b-x)^2}\right)}{d^{3/4}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \left(x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3\right)^{3/4}}{(b-x)^2}\right)}{d^{3/4}}",1,"Integrate[((a^2 - 2*a*x + x^2)*(-((2*a - 3*b)*b) + 2*(a - 2*b)*x + x^2))/(((-a + x)*(-b + x)^2)^(3/4)*(-b^2 - a^3*d + (2*b + 3*a^2*d)*x - (1 + 3*a*d)*x^2 + d*x^3)), x]","F",-1
1686,1,119,113,0.220418,"\int \frac{\left(-1+x^3\right) \sqrt[4]{x^3+x^4}}{1+x^3} \, dx","Integrate[((-1 + x^3)*(x^3 + x^4)^(1/4))/(1 + x^3),x]","\frac{4 \sqrt[4]{x^3 (x+1)} \left(9 x (x+1) \, _2F_1\left(-\frac{1}{4},\frac{7}{4};\frac{11}{4};-x\right)-14 i \sqrt{3} \sqrt[4]{x+1} \left(\, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{\left(3-i \sqrt{3}\right) x}{2 (x+1)}\right)-\, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{\left(3+i \sqrt{3}\right) x}{2 (x+1)}\right)\right)\right)}{63 (x+1)^{5/4}}","2 \text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4+3\&,\frac{\log \left(\sqrt[4]{x^4+x^3}-\text{$\#$1} x\right)-\log (x)}{2 \text{$\#$1}^7-3 \text{$\#$1}^3}\&\right]+\frac{1}{8} \sqrt[4]{x^4+x^3} (4 x+1)+\frac{3}{16} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+x^3}}\right)-\frac{3}{16} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+x^3}}\right)",1,"(4*(x^3*(1 + x))^(1/4)*(9*x*(1 + x)*Hypergeometric2F1[-1/4, 7/4, 11/4, -x] - (14*I)*Sqrt[3]*(1 + x)^(1/4)*(Hypergeometric2F1[3/4, 1, 7/4, ((3 - I*Sqrt[3])*x)/(2*(1 + x))] - Hypergeometric2F1[3/4, 1, 7/4, ((3 + I*Sqrt[3])*x)/(2*(1 + x))])))/(63*(1 + x)^(5/4))","C",1
1687,1,80,113,0.0473194,"\int \frac{-b+a x^2}{x^2 \left(b+a x^2\right) \sqrt[4]{-b x^2+a x^4}} \, dx","Integrate[(-b + a*x^2)/(x^2*(b + a*x^2)*(-(b*x^2) + a*x^4)^(1/4)),x]","-\frac{2 \left(\frac{a x^2}{b}+1\right)^{3/4} \left(a x^4-b x^2\right)^{3/4} \, _2F_1\left(-\frac{3}{4},-\frac{3}{4};\frac{1}{4};\frac{2 a x^2}{a x^2+b}\right)}{3 b x^3 \left(1-\frac{a x^2}{b}\right)^{3/4}}","\frac{2^{3/4} a^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)}{b}+\frac{2^{3/4} a^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)}{b}-\frac{2 \left(a x^4-b x^2\right)^{3/4}}{3 b x^3}",1,"(-2*(1 + (a*x^2)/b)^(3/4)*(-(b*x^2) + a*x^4)^(3/4)*Hypergeometric2F1[-3/4, -3/4, 1/4, (2*a*x^2)/(b + a*x^2)])/(3*b*x^3*(1 - (a*x^2)/b)^(3/4))","C",0
1688,1,333050,113,22.590576,"\int \frac{(-b+x) (-6 a+b+5 x)}{\sqrt[4]{(-a+x) (-b+x)^2} \left(b^6+a d-\left(6 b^5+d\right) x+15 b^4 x^2-20 b^3 x^3+15 b^2 x^4-6 b x^5+x^6\right)} \, dx","Integrate[((-b + x)*(-6*a + b + 5*x))/(((-a + x)*(-b + x)^2)^(1/4)*(b^6 + a*d - (6*b^5 + d)*x + 15*b^4*x^2 - 20*b^3*x^3 + 15*b^2*x^4 - 6*b*x^5 + x^6)),x]","\text{Result too large to show}","\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3}}{(b-x)^2}\right)}{d^{3/4}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3}}{(b-x)^2}\right)}{d^{3/4}}",1,"Result too large to show","C",0
1689,0,0,113,2.3452708,"\int \frac{(-6 a+b+5 x) \left(-b^5+5 b^4 x-10 b^3 x^2+10 b^2 x^3-5 b x^4+x^5\right)}{\left((-a+x) (-b+x)^2\right)^{3/4} \left(a+b^6 d-\left(1+6 b^5 d\right) x+15 b^4 d x^2-20 b^3 d x^3+15 b^2 d x^4-6 b d x^5+d x^6\right)} \, dx","Integrate[((-6*a + b + 5*x)*(-b^5 + 5*b^4*x - 10*b^3*x^2 + 10*b^2*x^3 - 5*b*x^4 + x^5))/(((-a + x)*(-b + x)^2)^(3/4)*(a + b^6*d - (1 + 6*b^5*d)*x + 15*b^4*d*x^2 - 20*b^3*d*x^3 + 15*b^2*d*x^4 - 6*b*d*x^5 + d*x^6)),x]","\int \frac{(-6 a+b+5 x) \left(-b^5+5 b^4 x-10 b^3 x^2+10 b^2 x^3-5 b x^4+x^5\right)}{\left((-a+x) (-b+x)^2\right)^{3/4} \left(a+b^6 d-\left(1+6 b^5 d\right) x+15 b^4 d x^2-20 b^3 d x^3+15 b^2 d x^4-6 b d x^5+d x^6\right)} \, dx","\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \left(x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3\right)^{3/4}}{a-x}\right)}{d^{3/4}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \left(x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3\right)^{3/4}}{a-x}\right)}{d^{3/4}}",1,"Integrate[((-6*a + b + 5*x)*(-b^5 + 5*b^4*x - 10*b^3*x^2 + 10*b^2*x^3 - 5*b*x^4 + x^5))/(((-a + x)*(-b + x)^2)^(3/4)*(a + b^6*d - (1 + 6*b^5*d)*x + 15*b^4*d*x^2 - 20*b^3*d*x^3 + 15*b^2*d*x^4 - 6*b*d*x^5 + d*x^6)), x]","F",-1
1690,0,0,113,1.1265926,"\int \frac{x^4 \sqrt[4]{x^2+x^4}}{-1+x^8} \, dx","Integrate[(x^4*(x^2 + x^4)^(1/4))/(-1 + x^8),x]","\int \frac{x^4 \sqrt[4]{x^2+x^4}}{-1+x^8} \, dx","-\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4+2\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{x^4+x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^4-1}\&\right]+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+x^2}}\right)}{2\ 2^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+x^2}}\right)}{2\ 2^{3/4}}",1,"Integrate[(x^4*(x^2 + x^4)^(1/4))/(-1 + x^8), x]","F",-1
1691,0,0,113,0.7999622,"\int \frac{x^4 \sqrt[4]{x^2+x^4}}{-1+x^8} \, dx","Integrate[(x^4*(x^2 + x^4)^(1/4))/(-1 + x^8),x]","\int \frac{x^4 \sqrt[4]{x^2+x^4}}{-1+x^8} \, dx","-\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4+2\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{x^4+x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^4-1}\&\right]+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+x^2}}\right)}{2\ 2^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+x^2}}\right)}{2\ 2^{3/4}}",1,"Integrate[(x^4*(x^2 + x^4)^(1/4))/(-1 + x^8), x]","F",-1
1692,0,0,113,3.3588624,"\int \frac{x^4}{\sqrt[4]{x^2+x^4} \left(1+x^4+x^8\right)} \, dx","Integrate[x^4/((x^2 + x^4)^(1/4)*(1 + x^4 + x^8)),x]","\int \frac{x^4}{\sqrt[4]{x^2+x^4} \left(1+x^4+x^8\right)} \, dx","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4+1\&,\frac{\log \left(\sqrt[4]{x^4+x^2}-\text{$\#$1} x\right)-\log (x)}{2 \text{$\#$1}^5-\text{$\#$1}}\&\right]-\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4+3\&,\frac{\log \left(\sqrt[4]{x^4+x^2}-\text{$\#$1} x\right)-\log (x)}{2 \text{$\#$1}^5-3 \text{$\#$1}}\&\right]",1,"Integrate[x^4/((x^2 + x^4)^(1/4)*(1 + x^4 + x^8)), x]","F",-1
1693,0,0,113,2.2899891,"\int \frac{x^4}{\sqrt[4]{x^2+x^4} \left(1+x^4+x^8\right)} \, dx","Integrate[x^4/((x^2 + x^4)^(1/4)*(1 + x^4 + x^8)),x]","\int \frac{x^4}{\sqrt[4]{x^2+x^4} \left(1+x^4+x^8\right)} \, dx","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4+1\&,\frac{\log \left(\sqrt[4]{x^4+x^2}-\text{$\#$1} x\right)-\log (x)}{2 \text{$\#$1}^5-\text{$\#$1}}\&\right]-\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4+3\&,\frac{\log \left(\sqrt[4]{x^4+x^2}-\text{$\#$1} x\right)-\log (x)}{2 \text{$\#$1}^5-3 \text{$\#$1}}\&\right]",1,"Integrate[x^4/((x^2 + x^4)^(1/4)*(1 + x^4 + x^8)), x]","F",-1
1694,0,0,113,0.357592,"\int \frac{x^6 \left(4+x^3\right)}{\left(1+x^3\right)^{3/4} \left(-1-2 x^3-x^6+x^8\right)} \, dx","Integrate[(x^6*(4 + x^3))/((1 + x^3)^(3/4)*(-1 - 2*x^3 - x^6 + x^8)),x]","\int \frac{x^6 \left(4+x^3\right)}{\left(1+x^3\right)^{3/4} \left(-1-2 x^3-x^6+x^8\right)} \, dx","\tan ^{-1}\left(\frac{x}{\sqrt[4]{x^3+1}}\right)-\tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^3+1}}\right)-\frac{\tan ^{-1}\left(\frac{\frac{\sqrt{x^3+1}}{\sqrt{2}}-\frac{x^2}{\sqrt{2}}}{x \sqrt[4]{x^3+1}}\right)}{\sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{x^3+1}}{\sqrt{x^3+1}+x^2}\right)}{\sqrt{2}}",1,"Integrate[(x^6*(4 + x^3))/((1 + x^3)^(3/4)*(-1 - 2*x^3 - x^6 + x^8)), x]","F",-1
1695,1,72,114,0.0252243,"\int x^{10} \sqrt[3]{-1+x^3} \, dx","Integrate[x^10*(-1 + x^3)^(1/3),x]","\frac{x^2 \sqrt[3]{x^3-1} \left(20 \, _2F_1\left(-\frac{1}{3},\frac{2}{3};\frac{5}{3};x^3\right)+\sqrt[3]{1-x^3} \left(27 x^9-3 x^6-4 x^3-20\right)\right)}{324 \sqrt[3]{1-x^3}}","\frac{10}{729} \log \left(\sqrt[3]{x^3-1}-x\right)+\frac{10 \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-1}+x}\right)}{243 \sqrt{3}}-\frac{5}{729} \log \left(\sqrt[3]{x^3-1} x+\left(x^3-1\right)^{2/3}+x^2\right)+\frac{1}{972} \sqrt[3]{x^3-1} \left(81 x^{11}-9 x^8-12 x^5-20 x^2\right)",1,"(x^2*(-1 + x^3)^(1/3)*((1 - x^3)^(1/3)*(-20 - 4*x^3 - 3*x^6 + 27*x^9) + 20*Hypergeometric2F1[-1/3, 2/3, 5/3, x^3]))/(324*(1 - x^3)^(1/3))","C",1
1696,1,33,114,0.0092421,"\int \frac{x}{(-1+x) \sqrt[3]{-x^2+x^3}} \, dx","Integrate[x/((-1 + x)*(-x^2 + x^3)^(1/3)),x]","-\frac{3 x^{2/3} \, _2F_1\left(-\frac{1}{3},-\frac{1}{3};\frac{2}{3};1-x\right)}{\sqrt[3]{(x-1) x^2}}","-\frac{3 \left(x^3-x^2\right)^{2/3}}{(x-1) x}-\log \left(\sqrt[3]{x^3-x^2}-x\right)+\frac{1}{2} \log \left(x^2+\sqrt[3]{x^3-x^2} x+\left(x^3-x^2\right)^{2/3}\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-x^2}+x}\right)",1,"(-3*x^(2/3)*Hypergeometric2F1[-1/3, -1/3, 2/3, 1 - x])/((-1 + x)*x^2)^(1/3)","C",1
1697,1,36,114,0.01281,"\int \frac{1+x}{(-1+x) \sqrt[3]{-x^2+x^3}} \, dx","Integrate[(1 + x)/((-1 + x)*(-x^2 + x^3)^(1/3)),x]","-\frac{3 \left(x^{2/3} \, _2F_1\left(-\frac{1}{3},-\frac{1}{3};\frac{2}{3};1-x\right)+x\right)}{\sqrt[3]{(x-1) x^2}}","-\frac{6 \left(x^3-x^2\right)^{2/3}}{(x-1) x}-\log \left(\sqrt[3]{x^3-x^2}-x\right)+\frac{1}{2} \log \left(x^2+\sqrt[3]{x^3-x^2} x+\left(x^3-x^2\right)^{2/3}\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-x^2}+x}\right)",1,"(-3*(x + x^(2/3)*Hypergeometric2F1[-1/3, -1/3, 2/3, 1 - x]))/((-1 + x)*x^2)^(1/3)","C",1
1698,1,611,114,7.4268238,"\int \frac{-2 b+a x}{\left(-b+a x+x^2\right) \sqrt[4]{-b x^2+a x^3}} \, dx","Integrate[(-2*b + a*x)/((-b + a*x + x^2)*(-(b*x^2) + a*x^3)^(1/4)),x]","\frac{i \sqrt{2} a \sqrt{\frac{a x}{a x-b}} (a x-b)^{3/4} \left(\left(-a^2+\sqrt{a^4+4 a^2 b}-4 b\right) \sqrt{-\frac{a^2+\sqrt{a^4+4 a^2 b}+2 b}{b^2}} \Pi \left(-\frac{i \sqrt{2}}{\sqrt{b} \sqrt{\frac{-a^2-2 b+\sqrt{a^4+4 b a^2}}{b^2}}};\left.i \sinh ^{-1}\left(\frac{\sqrt{i \sqrt{b}}}{\sqrt[4]{a x-b}}\right)\right|-1\right)+\left(a^2-\sqrt{a^4+4 a^2 b}+4 b\right) \sqrt{-\frac{a^2+\sqrt{a^4+4 a^2 b}+2 b}{b^2}} \Pi \left(\frac{i \sqrt{2}}{\sqrt{b} \sqrt{\frac{-a^2-2 b+\sqrt{a^4+4 b a^2}}{b^2}}};\left.i \sinh ^{-1}\left(\frac{\sqrt{i \sqrt{b}}}{\sqrt[4]{a x-b}}\right)\right|-1\right)+\sqrt{\frac{-a^2+\sqrt{a^4+4 a^2 b}-2 b}{b^2}} \left(a^2+\sqrt{a^4+4 a^2 b}+4 b\right) \left(\Pi \left(-\frac{i \sqrt{2}}{\sqrt{b} \sqrt{-\frac{a^2+2 b+\sqrt{a^4+4 b a^2}}{b^2}}};\left.i \sinh ^{-1}\left(\frac{\sqrt{i \sqrt{b}}}{\sqrt[4]{a x-b}}\right)\right|-1\right)-\Pi \left(\frac{i \sqrt{2}}{\sqrt{b} \sqrt{-\frac{a^2+2 b+\sqrt{a^4+4 b a^2}}{b^2}}};\left.i \sinh ^{-1}\left(\frac{\sqrt{i \sqrt{b}}}{\sqrt[4]{a x-b}}\right)\right|-1\right)\right)\right)}{\left(i \sqrt{b}\right)^{5/2} \sqrt{a^4+4 a^2 b} \sqrt{\frac{-a^2+\sqrt{a^4+4 a^2 b}-2 b}{b^2}} \sqrt{-\frac{a^2+\sqrt{a^4+4 a^2 b}+2 b}{b^2}} \sqrt[4]{x^2 (a x-b)}}","\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{a x^3-b x^2}}{\sqrt{a x^3-b x^2}+x^2}\right)-\sqrt{2} \tan ^{-1}\left(\frac{\frac{\sqrt{a x^3-b x^2}}{\sqrt{2}}-\frac{x^2}{\sqrt{2}}}{x \sqrt[4]{a x^3-b x^2}}\right)",1,"(I*Sqrt[2]*a*Sqrt[(a*x)/(-b + a*x)]*(-b + a*x)^(3/4)*((-a^2 - 4*b + Sqrt[a^4 + 4*a^2*b])*Sqrt[-((a^2 + 2*b + Sqrt[a^4 + 4*a^2*b])/b^2)]*EllipticPi[((-I)*Sqrt[2])/(Sqrt[b]*Sqrt[(-a^2 - 2*b + Sqrt[a^4 + 4*a^2*b])/b^2]), I*ArcSinh[Sqrt[I*Sqrt[b]]/(-b + a*x)^(1/4)], -1] + (a^2 + 4*b - Sqrt[a^4 + 4*a^2*b])*Sqrt[-((a^2 + 2*b + Sqrt[a^4 + 4*a^2*b])/b^2)]*EllipticPi[(I*Sqrt[2])/(Sqrt[b]*Sqrt[(-a^2 - 2*b + Sqrt[a^4 + 4*a^2*b])/b^2]), I*ArcSinh[Sqrt[I*Sqrt[b]]/(-b + a*x)^(1/4)], -1] + Sqrt[(-a^2 - 2*b + Sqrt[a^4 + 4*a^2*b])/b^2]*(a^2 + 4*b + Sqrt[a^4 + 4*a^2*b])*(EllipticPi[((-I)*Sqrt[2])/(Sqrt[b]*Sqrt[-((a^2 + 2*b + Sqrt[a^4 + 4*a^2*b])/b^2)]), I*ArcSinh[Sqrt[I*Sqrt[b]]/(-b + a*x)^(1/4)], -1] - EllipticPi[(I*Sqrt[2])/(Sqrt[b]*Sqrt[-((a^2 + 2*b + Sqrt[a^4 + 4*a^2*b])/b^2)]), I*ArcSinh[Sqrt[I*Sqrt[b]]/(-b + a*x)^(1/4)], -1])))/((I*Sqrt[b])^(5/2)*Sqrt[a^4 + 4*a^2*b]*Sqrt[(-a^2 - 2*b + Sqrt[a^4 + 4*a^2*b])/b^2]*Sqrt[-((a^2 + 2*b + Sqrt[a^4 + 4*a^2*b])/b^2)]*(x^2*(-b + a*x))^(1/4))","C",1
1699,0,0,114,2.9487237,"\int \frac{\left(1+x^2\right) \sqrt[3]{-x+2 x^3}}{x^2 \left(1+x^4\right)} \, dx","Integrate[((1 + x^2)*(-x + 2*x^3)^(1/3))/(x^2*(1 + x^4)),x]","\int \frac{\left(1+x^2\right) \sqrt[3]{-x+2 x^3}}{x^2 \left(1+x^4\right)} \, dx","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^6-4 \text{$\#$1}^3+5\&,\frac{-\text{$\#$1}^3 \log \left(\sqrt[3]{2 x^3-x}-\text{$\#$1} x\right)+\text{$\#$1}^3 \log (x)+5 \log \left(\sqrt[3]{2 x^3-x}-\text{$\#$1} x\right)-5 \log (x)}{\text{$\#$1}^5-2 \text{$\#$1}^2}\&\right]-\frac{3 \sqrt[3]{2 x^3-x}}{2 x}",1,"Integrate[((1 + x^2)*(-x + 2*x^3)^(1/3))/(x^2*(1 + x^4)), x]","F",-1
1700,0,0,114,0.1293076,"\int \frac{-1+x}{\left(1+x+x^2\right) \sqrt[4]{1+x^4}} \, dx","Integrate[(-1 + x)/((1 + x + x^2)*(1 + x^4)^(1/4)),x]","\int \frac{-1+x}{\left(1+x+x^2\right) \sqrt[4]{1+x^4}} \, dx","\frac{\tan ^{-1}\left(\frac{\frac{\sqrt{x^4+1}}{\sqrt{2}}-\frac{x^2}{\sqrt{2}}-\sqrt{2} x-\frac{1}{\sqrt{2}}}{(x+1) \sqrt[4]{x^4+1}}\right)}{\sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{\left(\sqrt{2} x+\sqrt{2}\right) \sqrt[4]{x^4+1}}{\sqrt{x^4+1}+x^2+2 x+1}\right)}{\sqrt{2}}",1,"Integrate[(-1 + x)/((1 + x + x^2)*(1 + x^4)^(1/4)), x]","F",-1
1701,1,124,114,0.0712122,"\int \frac{x^2 \sqrt[4]{x^3+x^4}}{-1+x} \, dx","Integrate[(x^2*(x^3 + x^4)^(1/4))/(-1 + x),x]","\frac{4 \sqrt[4]{x^3 (x+1)} \left(21 (x+1) x^2 \, _2F_1\left(-\frac{1}{4},\frac{11}{4};\frac{15}{4};-x\right)+33 (x+1) x \, _2F_1\left(-\frac{1}{4},\frac{7}{4};\frac{11}{4};-x\right)+77 (x+1) \, _2F_1\left(-\frac{1}{4},\frac{3}{4};\frac{7}{4};-x\right)+77 (x+1) \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};-x\right)-154 \sqrt[4]{x+1} \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{2 x}{x+1}\right)\right)}{231 (x+1)^{5/4}}","-\frac{155}{64} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+x^3}}\right)+2 \sqrt[4]{2} \tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+x^3}}\right)+\frac{155}{64} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+x^3}}\right)-2 \sqrt[4]{2} \tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+x^3}}\right)+\frac{1}{96} \sqrt[4]{x^4+x^3} \left(32 x^2+52 x+101\right)",1,"(4*(x^3*(1 + x))^(1/4)*(77*(1 + x)*Hypergeometric2F1[-1/4, 3/4, 7/4, -x] + 33*x*(1 + x)*Hypergeometric2F1[-1/4, 7/4, 11/4, -x] + 21*x^2*(1 + x)*Hypergeometric2F1[-1/4, 11/4, 15/4, -x] + 77*(1 + x)*Hypergeometric2F1[3/4, 3/4, 7/4, -x] - 154*(1 + x)^(1/4)*Hypergeometric2F1[3/4, 1, 7/4, (2*x)/(1 + x)]))/(231*(1 + x)^(5/4))","C",1
1702,1,71,114,0.0882276,"\int \frac{\left(-b+a x^3\right) \left(-b+2 a x^3\right)}{x^6 \sqrt[4]{-b x+a x^4}} \, dx","Integrate[((-b + a*x^3)*(-b + 2*a*x^3))/(x^6*(-(b*x) + a*x^4)^(1/4)),x]","\frac{4 \left(a x^4-b x\right)^{3/4} \left(3 \left(b-a x^3\right)-\frac{14 a x^3 \, _2F_1\left(-\frac{3}{4},-\frac{3}{4};\frac{1}{4};\frac{a x^3}{b}\right)}{\left(1-\frac{a x^3}{b}\right)^{3/4}}\right)}{63 x^6}","\frac{4}{3} a^{7/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} \left(a x^4-b x\right)^{3/4}}{a x^3-b}\right)+\frac{4}{3} a^{7/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \left(a x^4-b x\right)^{3/4}}{a x^3-b}\right)+\frac{4 \left(3 b-17 a x^3\right) \left(a x^4-b x\right)^{3/4}}{63 x^6}",1,"(4*(-(b*x) + a*x^4)^(3/4)*(3*(b - a*x^3) - (14*a*x^3*Hypergeometric2F1[-3/4, -3/4, 1/4, (a*x^3)/b])/(1 - (a*x^3)/b)^(3/4)))/(63*x^6)","C",1
1703,1,114,114,0.1239675,"\int \frac{-b+a x^4+x^8}{x^8 \left(-b+a x^4\right) \sqrt[4]{b+a x^4}} \, dx","Integrate[(-b + a*x^4 + x^8)/(x^8*(-b + a*x^4)*(b + a*x^4)^(1/4)),x]","\frac{4 \sqrt[4]{a} \left(a x^4+b\right)^{3/4} \left(4 a x^4-3 b\right)-21\ 2^{3/4} b x^7 \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)-21\ 2^{3/4} b x^7 \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{84 \sqrt[4]{a} b^2 x^7}","\frac{\left(a x^4+b\right)^{3/4} \left(4 a x^4-3 b\right)}{21 b^2 x^7}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{2 \sqrt[4]{2} \sqrt[4]{a} b}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{2 \sqrt[4]{2} \sqrt[4]{a} b}",1,"(4*a^(1/4)*(b + a*x^4)^(3/4)*(-3*b + 4*a*x^4) - 21*2^(3/4)*b*x^7*ArcTan[(2^(1/4)*a^(1/4)*x)/(b + a*x^4)^(1/4)] - 21*2^(3/4)*b*x^7*ArcTanh[(2^(1/4)*a^(1/4)*x)/(b + a*x^4)^(1/4)])/(84*a^(1/4)*b^2*x^7)","A",1
1704,1,9486,114,24.9103195,"\int \frac{1+x^4}{x^4 \sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[(1 + x^4)/(x^4*Sqrt[x + Sqrt[1 + x^2]]),x]","\text{Result too large to show}","-\frac{1}{8} \tan ^{-1}\left(\sqrt{\sqrt{x^2+1}+x}\right)-\frac{1}{8} \tanh ^{-1}\left(\sqrt{\sqrt{x^2+1}+x}\right)+\frac{384 x^8+456 x^6+48 x^4-57 x^2+\sqrt{x^2+1} \left(384 x^7+264 x^5-36 x^3-30 x\right)-8}{24 x^3 \left(\sqrt{x^2+1}+x\right)^{9/2}}",1,"Result too large to show","C",0
1705,1,59,114,0.2357739,"\int \frac{\sqrt{b+\sqrt{b^2+a x^2}}}{x^2 \sqrt{b^2+a x^2}} \, dx","Integrate[Sqrt[b + Sqrt[b^2 + a*x^2]]/(x^2*Sqrt[b^2 + a*x^2]),x]","-\frac{\sqrt{\sqrt{a x^2+b^2}+b} \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{b-\sqrt{b^2+a x^2}}{2 b}\right)}{b x}","-\frac{\sqrt{\sqrt{a x^2+b^2}+b}}{b x}-\frac{\sqrt{2} \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{2} \sqrt{b} \sqrt{\sqrt{a x^2+b^2}+b}}-\frac{\sqrt{\sqrt{a x^2+b^2}+b}}{\sqrt{2} \sqrt{b}}\right)}{b^{3/2}}",1,"-((Sqrt[b + Sqrt[b^2 + a*x^2]]*Hypergeometric2F1[-1/2, 1, 1/2, (b - Sqrt[b^2 + a*x^2])/(2*b)])/(b*x))","C",1
1706,0,0,115,0.2296364,"\int \frac{2+x^2}{x \left(2-2 x+x^2\right) \sqrt[3]{1-x+x^2}} \, dx","Integrate[(2 + x^2)/(x*(2 - 2*x + x^2)*(1 - x + x^2)^(1/3)),x]","\int \frac{2+x^2}{x \left(2-2 x+x^2\right) \sqrt[3]{1-x+x^2}} \, dx","\log \left(\sqrt[3]{x^2-x+1}+x-1\right)-\frac{1}{2} \log \left(x^2+\left(x^2-x+1\right)^{2/3}+(1-x) \sqrt[3]{x^2-x+1}-2 x+1\right)-\sqrt{3} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{x^2-x+1}}{\sqrt{3}}-\frac{2 x}{\sqrt{3}}+\frac{2}{\sqrt{3}}}{\sqrt[3]{x^2-x+1}}\right)",1,"Integrate[(2 + x^2)/(x*(2 - 2*x + x^2)*(1 - x + x^2)^(1/3)), x]","F",-1
1707,1,46,115,0.0320418,"\int \frac{-1+x}{x^{10} \sqrt[3]{1+x^3}} \, dx","Integrate[(-1 + x)/(x^10*(1 + x^3)^(1/3)),x]","-\frac{\left(x^3+1\right)^{2/3} \left(20 x^8 \, _2F_1\left(\frac{2}{3},4;\frac{5}{3};x^3+1\right)+9 x^6-6 x^3+5\right)}{40 x^8}","\frac{14}{243} \log \left(\sqrt[3]{x^3+1}-1\right)-\frac{7}{243} \log \left(\left(x^3+1\right)^{2/3}+\sqrt[3]{x^3+1}+1\right)+\frac{14 \tan ^{-1}\left(\frac{2 \sqrt[3]{x^3+1}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{81 \sqrt{3}}+\frac{\left(x^3+1\right)^{2/3} \left(-729 x^7+560 x^6+486 x^4-420 x^3-405 x+360\right)}{3240 x^9}",1,"-1/40*((1 + x^3)^(2/3)*(5 - 6*x^3 + 9*x^6 + 20*x^8*Hypergeometric2F1[2/3, 4, 5/3, 1 + x^3]))/x^8","C",1
1708,1,70,115,0.0554373,"\int \frac{1}{x \sqrt[3]{b+a x^3}} \, dx","Integrate[1/(x*(b + a*x^3)^(1/3)),x]","\frac{3 \log \left(\sqrt[3]{b}-\sqrt[3]{a x^3+b}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a x^3+b}}{\sqrt[3]{b}}+1}{\sqrt{3}}\right)-3 \log (x)}{6 \sqrt[3]{b}}","-\frac{\log \left(\sqrt[3]{b} \sqrt[3]{a x^3+b}+\left(a x^3+b\right)^{2/3}+b^{2/3}\right)}{6 \sqrt[3]{b}}+\frac{\log \left(\sqrt[3]{a x^3+b}-\sqrt[3]{b}\right)}{3 \sqrt[3]{b}}+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{a x^3+b}}{\sqrt{3} \sqrt[3]{b}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{b}}",1,"(2*Sqrt[3]*ArcTan[(1 + (2*(b + a*x^3)^(1/3))/b^(1/3))/Sqrt[3]] - 3*Log[x] + 3*Log[b^(1/3) - (b + a*x^3)^(1/3)])/(6*b^(1/3))","A",1
1709,0,0,115,7.0854502,"\int \frac{\left(-1-2 (-1+k) x+k x^2\right) \left(-1+3 k x-3 k^2 x^2+k^3 x^3\right)}{(-1+x) x \sqrt[4]{(1-x) x (1-k x)} \left(-1+(d+3 k) x-\left(d+3 k^2\right) x^2+k^3 x^3\right)} \, dx","Integrate[((-1 - 2*(-1 + k)*x + k*x^2)*(-1 + 3*k*x - 3*k^2*x^2 + k^3*x^3))/((-1 + x)*x*((1 - x)*x*(1 - k*x))^(1/4)*(-1 + (d + 3*k)*x - (d + 3*k^2)*x^2 + k^3*x^3)),x]","\int \frac{\left(-1-2 (-1+k) x+k x^2\right) \left(-1+3 k x-3 k^2 x^2+k^3 x^3\right)}{(-1+x) x \sqrt[4]{(1-x) x (1-k x)} \left(-1+(d+3 k) x-\left(d+3 k^2\right) x^2+k^3 x^3\right)} \, dx","2 \sqrt[4]{d} \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{k x^3+(-k-1) x^2+x}}{k x-1}\right)-2 \sqrt[4]{d} \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{k x^3+(-k-1) x^2+x}}{k x-1}\right)+\frac{4 \left(k x^3-k x^2-x^2+x\right)^{3/4}}{(x-1) x}",1,"Integrate[((-1 - 2*(-1 + k)*x + k*x^2)*(-1 + 3*k*x - 3*k^2*x^2 + k^3*x^3))/((-1 + x)*x*((1 - x)*x*(1 - k*x))^(1/4)*(-1 + (d + 3*k)*x - (d + 3*k^2)*x^2 + k^3*x^3)), x]","F",-1
1710,0,0,115,0.3581118,"\int \frac{\left(3+x^4\right) \left(-1-x^3+x^4\right)^{2/3}}{x^3 \left(-1+x^4\right)} \, dx","Integrate[((3 + x^4)*(-1 - x^3 + x^4)^(2/3))/(x^3*(-1 + x^4)),x]","\int \frac{\left(3+x^4\right) \left(-1-x^3+x^4\right)^{2/3}}{x^3 \left(-1+x^4\right)} \, dx","\log \left(\sqrt[3]{x^4-x^3-1}+x\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^4-x^3-1}-x}\right)+\frac{3 \left(x^4-x^3-1\right)^{2/3}}{2 x^2}-\frac{1}{2} \log \left(x^2-\sqrt[3]{x^4-x^3-1} x+\left(x^4-x^3-1\right)^{2/3}\right)",1,"Integrate[((3 + x^4)*(-1 - x^3 + x^4)^(2/3))/(x^3*(-1 + x^4)), x]","F",-1
1711,0,0,115,3.7364382,"\int \frac{\left(1+2 x^2\right) \sqrt[3]{x+2 x^3}}{x^4 \left(1+2 x^4\right)} \, dx","Integrate[((1 + 2*x^2)*(x + 2*x^3)^(1/3))/(x^4*(1 + 2*x^4)),x]","\int \frac{\left(1+2 x^2\right) \sqrt[3]{x+2 x^3}}{x^4 \left(1+2 x^4\right)} \, dx","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^6-4 \text{$\#$1}^3+6\&,\frac{-\text{$\#$1}^3 \log \left(\sqrt[3]{2 x^3+x}-\text{$\#$1} x\right)+\text{$\#$1}^3 \log (x)+6 \log \left(\sqrt[3]{2 x^3+x}-\text{$\#$1} x\right)-6 \log (x)}{\text{$\#$1}^5-2 \text{$\#$1}^2}\&\right]-\frac{3 \left(10 x^2+1\right) \sqrt[3]{2 x^3+x}}{8 x^3}",1,"Integrate[((1 + 2*x^2)*(x + 2*x^3)^(1/3))/(x^4*(1 + 2*x^4)), x]","F",-1
1712,0,0,115,0.7360639,"\int \frac{1}{x-\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","Integrate[(x - Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]])^(-1),x]","\int \frac{1}{x-\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","4 \text{RootSum}\left[-\text{$\#$1}^4+\text{$\#$1}^3 a+2 \text{$\#$1}^2 c-\text{$\#$1} a c+b-c^2\&,\frac{\text{$\#$1}^3 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-\text{$\#$1} c \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)}{4 \text{$\#$1}^3-3 \text{$\#$1}^2 a-4 \text{$\#$1} c+a c}\&\right]",1,"Integrate[(x - Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]])^(-1), x]","F",-1
1713,0,0,115,0.4763304,"\int \frac{1}{x-\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","Integrate[(x - Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]])^(-1),x]","\int \frac{1}{x-\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","4 \text{RootSum}\left[-\text{$\#$1}^4+\text{$\#$1}^3 a+2 \text{$\#$1}^2 c-\text{$\#$1} a c+b-c^2\&,\frac{\text{$\#$1}^3 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-\text{$\#$1} c \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)}{4 \text{$\#$1}^3-3 \text{$\#$1}^2 a-4 \text{$\#$1} c+a c}\&\right]",1,"Integrate[(x - Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]])^(-1), x]","F",-1
1714,1,71,116,0.1733693,"\int \frac{2-x+x^2}{\sqrt[3]{-1+x^2} \left(3+4 x+x^2\right)} \, dx","Integrate[(2 - x + x^2)/((-1 + x^2)^(1/3)*(3 + 4*x + x^2)),x]","\frac{3 \left(x^2-1\right)^{2/3}}{x+1}-\frac{21 \left(x^2-1\right)^{2/3} F_1\left(\frac{2}{3};\frac{1}{3},1;\frac{5}{3};\frac{1-x}{2},\frac{1-x}{4}\right)}{8 \sqrt[3]{2} (x+1)^{2/3}}","\frac{3 \left(x^2-1\right)^{2/3}}{x+1}-\frac{7}{4} \log \left(2 \sqrt[3]{x^2-1}+x-1\right)+\frac{7}{8} \log \left(x^2+4 \left(x^2-1\right)^{2/3}+(2-2 x) \sqrt[3]{x^2-1}-2 x+1\right)-\frac{7}{4} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x^2-1}}{\sqrt[3]{x^2-1}-x+1}\right)",1,"(3*(-1 + x^2)^(2/3))/(1 + x) - (21*(-1 + x^2)^(2/3)*AppellF1[2/3, 1/3, 1, 5/3, (1 - x)/2, (1 - x)/4])/(8*2^(1/3)*(1 + x)^(2/3))","C",0
1715,0,0,116,3.8762617,"\int \frac{x (-1+k x) \left(-1+2 (-1+k) x+k x^2\right)}{(-1+x) ((1-x) x (1-k x))^{3/4} \left(-d+(1+3 d) x-(3 d+k) x^2+d x^3\right)} \, dx","Integrate[(x*(-1 + k*x)*(-1 + 2*(-1 + k)*x + k*x^2))/((-1 + x)*((1 - x)*x*(1 - k*x))^(3/4)*(-d + (1 + 3*d)*x - (3*d + k)*x^2 + d*x^3)),x]","\int \frac{x (-1+k x) \left(-1+2 (-1+k) x+k x^2\right)}{(-1+x) ((1-x) x (1-k x))^{3/4} \left(-d+(1+3 d) x-(3 d+k) x^2+d x^3\right)} \, dx","2 \sqrt[4]{d} \tan ^{-1}\left(\frac{\sqrt[4]{d} x-\sqrt[4]{d}}{\sqrt[4]{k x^3+(-k-1) x^2+x}}\right)-2 \sqrt[4]{d} \tanh ^{-1}\left(\frac{\sqrt[4]{d} x-\sqrt[4]{d}}{\sqrt[4]{k x^3+(-k-1) x^2+x}}\right)+\frac{4 \sqrt[4]{k x^3+(-k-1) x^2+x}}{x-1}",1,"Integrate[(x*(-1 + k*x)*(-1 + 2*(-1 + k)*x + k*x^2))/((-1 + x)*((1 - x)*x*(1 - k*x))^(3/4)*(-d + (1 + 3*d)*x - (3*d + k)*x^2 + d*x^3)), x]","F",-1
1716,0,0,116,3.9766323,"\int \frac{(-1+x) x \left(-1-2 (-1+k) x+k x^2\right)}{((1-x) x (1-k x))^{3/4} (-1+k x) \left(-d+(1+3 d k) x-\left(1+3 d k^2\right) x^2+d k^3 x^3\right)} \, dx","Integrate[((-1 + x)*x*(-1 - 2*(-1 + k)*x + k*x^2))/(((1 - x)*x*(1 - k*x))^(3/4)*(-1 + k*x)*(-d + (1 + 3*d*k)*x - (1 + 3*d*k^2)*x^2 + d*k^3*x^3)),x]","\int \frac{(-1+x) x \left(-1-2 (-1+k) x+k x^2\right)}{((1-x) x (1-k x))^{3/4} (-1+k x) \left(-d+(1+3 d k) x-\left(1+3 d k^2\right) x^2+d k^3 x^3\right)} \, dx","2 \sqrt[4]{d} \tan ^{-1}\left(\frac{\sqrt[4]{d} \left(k x^3+(-k-1) x^2+x\right)^{3/4}}{(x-1) x}\right)-2 \sqrt[4]{d} \tanh ^{-1}\left(\frac{\sqrt[4]{d} \left(k x^3+(-k-1) x^2+x\right)^{3/4}}{(x-1) x}\right)+\frac{4 \left(x^2-x\right)}{\left(k x^3-k x^2-x^2+x\right)^{3/4}}",1,"Integrate[((-1 + x)*x*(-1 - 2*(-1 + k)*x + k*x^2))/(((1 - x)*x*(1 - k*x))^(3/4)*(-1 + k*x)*(-d + (1 + 3*d*k)*x - (1 + 3*d*k^2)*x^2 + d*k^3*x^3)), x]","F",-1
1717,1,318,116,1.1265485,"\int \frac{\left(4+x^2\right) \sqrt[3]{-2 x+x^3}}{x^4 \left(-4-4 x^2+x^4\right)} \, dx","Integrate[((4 + x^2)*(-2*x + x^3)^(1/3))/(x^4*(-4 - 4*x^2 + x^4)),x]","\frac{3 \left(-\frac{\left(3+\sqrt{2}\right) \left(\left(3 \left(3 \sqrt{2}-4\right) x^2-2 \sqrt{2}+4\right) x^2 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};-\frac{\left(-2+\sqrt{2}\right) x^2}{x^2-2}\right)+3 \left(\left(3 \sqrt{2}-4\right) x^2+2 \left(\sqrt{2}-2\right)\right) x^2 \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};-\frac{\left(-2+\sqrt{2}\right) x^2}{x^2-2}\right)-2 \left(x^2-2\right) \left(3 \left(\sqrt{2}-1\right) x^2+2\right)\right)}{2+\sqrt{2}}-\left(1+\frac{1}{\sqrt{2}}\right) \left(3-\sqrt{2}\right) \left(-3 \left(\left(4+3 \sqrt{2}\right) x^2+2 \left(2+\sqrt{2}\right)\right) x^2 \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};\frac{\left(2+\sqrt{2}\right) x^2}{x^2-2}\right)+\left(2 \left(2+\sqrt{2}\right) x^2-3 \left(4+3 \sqrt{2}\right) x^4\right) \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{\left(2+\sqrt{2}\right) x^2}{x^2-2}\right)+2 \left(2-x^2\right) \left(2-3 \left(1+\sqrt{2}\right) x^2\right)\right)\right)}{128 x^2 \left(x \left(x^2-2\right)\right)^{2/3}}","\frac{1}{16} \text{RootSum}\left[\text{$\#$1}^6-4 \text{$\#$1}^3+2\&,\frac{-11 \text{$\#$1}^3 \log \left(\sqrt[3]{x^3-2 x}-\text{$\#$1} x\right)+11 \text{$\#$1}^3 \log (x)+6 \log \left(\sqrt[3]{x^3-2 x}-\text{$\#$1} x\right)-6 \log (x)}{\text{$\#$1}^5-2 \text{$\#$1}^2}\&\right]-\frac{3 \left(7 x^2-2\right) \sqrt[3]{x^3-2 x}}{16 x^3}",1,"(3*(-(((3 + Sqrt[2])*(-2*(-2 + x^2)*(2 + 3*(-1 + Sqrt[2])*x^2) + x^2*(4 - 2*Sqrt[2] + 3*(-4 + 3*Sqrt[2])*x^2)*Hypergeometric2F1[2/3, 1, 5/3, -(((-2 + Sqrt[2])*x^2)/(-2 + x^2))] + 3*x^2*(2*(-2 + Sqrt[2]) + (-4 + 3*Sqrt[2])*x^2)*Hypergeometric2F1[2/3, 2, 5/3, -(((-2 + Sqrt[2])*x^2)/(-2 + x^2))]))/(2 + Sqrt[2])) - (1 + 1/Sqrt[2])*(3 - Sqrt[2])*(2*(2 - x^2)*(2 - 3*(1 + Sqrt[2])*x^2) + (2*(2 + Sqrt[2])*x^2 - 3*(4 + 3*Sqrt[2])*x^4)*Hypergeometric2F1[2/3, 1, 5/3, ((2 + Sqrt[2])*x^2)/(-2 + x^2)] - 3*x^2*(2*(2 + Sqrt[2]) + (4 + 3*Sqrt[2])*x^2)*Hypergeometric2F1[2/3, 2, 5/3, ((2 + Sqrt[2])*x^2)/(-2 + x^2)])))/(128*x^2*(x*(-2 + x^2))^(2/3))","B",0
1718,1,318,116,0.1984097,"\int \frac{\left(4+x^2\right) \sqrt[3]{-2 x+x^3}}{x^4 \left(-4-4 x^2+x^4\right)} \, dx","Integrate[((4 + x^2)*(-2*x + x^3)^(1/3))/(x^4*(-4 - 4*x^2 + x^4)),x]","\frac{3 \left(-\frac{\left(3+\sqrt{2}\right) \left(\left(3 \left(3 \sqrt{2}-4\right) x^2-2 \sqrt{2}+4\right) x^2 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};-\frac{\left(-2+\sqrt{2}\right) x^2}{x^2-2}\right)+3 \left(\left(3 \sqrt{2}-4\right) x^2+2 \left(\sqrt{2}-2\right)\right) x^2 \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};-\frac{\left(-2+\sqrt{2}\right) x^2}{x^2-2}\right)-2 \left(x^2-2\right) \left(3 \left(\sqrt{2}-1\right) x^2+2\right)\right)}{2+\sqrt{2}}-\left(1+\frac{1}{\sqrt{2}}\right) \left(3-\sqrt{2}\right) \left(-3 \left(\left(4+3 \sqrt{2}\right) x^2+2 \left(2+\sqrt{2}\right)\right) x^2 \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};\frac{\left(2+\sqrt{2}\right) x^2}{x^2-2}\right)+\left(2 \left(2+\sqrt{2}\right) x^2-3 \left(4+3 \sqrt{2}\right) x^4\right) \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{\left(2+\sqrt{2}\right) x^2}{x^2-2}\right)+2 \left(2-x^2\right) \left(2-3 \left(1+\sqrt{2}\right) x^2\right)\right)\right)}{128 x^2 \left(x \left(x^2-2\right)\right)^{2/3}}","\frac{1}{16} \text{RootSum}\left[\text{$\#$1}^6-4 \text{$\#$1}^3+2\&,\frac{-11 \text{$\#$1}^3 \log \left(\sqrt[3]{x^3-2 x}-\text{$\#$1} x\right)+11 \text{$\#$1}^3 \log (x)+6 \log \left(\sqrt[3]{x^3-2 x}-\text{$\#$1} x\right)-6 \log (x)}{\text{$\#$1}^5-2 \text{$\#$1}^2}\&\right]-\frac{3 \left(7 x^2-2\right) \sqrt[3]{x^3-2 x}}{16 x^3}",1,"(3*(-(((3 + Sqrt[2])*(-2*(-2 + x^2)*(2 + 3*(-1 + Sqrt[2])*x^2) + x^2*(4 - 2*Sqrt[2] + 3*(-4 + 3*Sqrt[2])*x^2)*Hypergeometric2F1[2/3, 1, 5/3, -(((-2 + Sqrt[2])*x^2)/(-2 + x^2))] + 3*x^2*(2*(-2 + Sqrt[2]) + (-4 + 3*Sqrt[2])*x^2)*Hypergeometric2F1[2/3, 2, 5/3, -(((-2 + Sqrt[2])*x^2)/(-2 + x^2))]))/(2 + Sqrt[2])) - (1 + 1/Sqrt[2])*(3 - Sqrt[2])*(2*(2 - x^2)*(2 - 3*(1 + Sqrt[2])*x^2) + (2*(2 + Sqrt[2])*x^2 - 3*(4 + 3*Sqrt[2])*x^4)*Hypergeometric2F1[2/3, 1, 5/3, ((2 + Sqrt[2])*x^2)/(-2 + x^2)] - 3*x^2*(2*(2 + Sqrt[2]) + (4 + 3*Sqrt[2])*x^2)*Hypergeometric2F1[2/3, 2, 5/3, ((2 + Sqrt[2])*x^2)/(-2 + x^2)])))/(128*x^2*(x*(-2 + x^2))^(2/3))","B",0
1719,0,0,116,0.7040887,"\int \frac{2 b+a x^3}{\left(-b+x^2+a x^3\right) \sqrt[4]{-b x^2+a x^5}} \, dx","Integrate[(2*b + a*x^3)/((-b + x^2 + a*x^3)*(-(b*x^2) + a*x^5)^(1/4)),x]","\int \frac{2 b+a x^3}{\left(-b+x^2+a x^3\right) \sqrt[4]{-b x^2+a x^5}} \, dx","-\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{a x^5-b x^2}}{\sqrt{a x^5-b x^2}-x^2}\right)-\sqrt{2} \tanh ^{-1}\left(\frac{\frac{\sqrt{a x^5-b x^2}}{\sqrt{2}}+\frac{x^2}{\sqrt{2}}}{x \sqrt[4]{a x^5-b x^2}}\right)",1,"Integrate[(2*b + a*x^3)/((-b + x^2 + a*x^3)*(-(b*x^2) + a*x^5)^(1/4)), x]","F",-1
1720,0,0,116,1.2260864,"\int \frac{b+a x^2}{\left(-b+x+a x^2\right) \sqrt[4]{-b x^3+a x^5}} \, dx","Integrate[(b + a*x^2)/((-b + x + a*x^2)*(-(b*x^3) + a*x^5)^(1/4)),x]","\int \frac{b+a x^2}{\left(-b+x+a x^2\right) \sqrt[4]{-b x^3+a x^5}} \, dx","-\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{a x^5-b x^3}}{\sqrt{a x^5-b x^3}-x^2}\right)-\sqrt{2} \tanh ^{-1}\left(\frac{\frac{\sqrt{a x^5-b x^3}}{\sqrt{2}}+\frac{x^2}{\sqrt{2}}}{x \sqrt[4]{a x^5-b x^3}}\right)",1,"Integrate[(b + a*x^2)/((-b + x + a*x^2)*(-(b*x^3) + a*x^5)^(1/4)), x]","F",-1
1721,0,0,116,1.9677741,"\int \frac{b+a x^4}{\left(-b+x^2+a x^4\right) \sqrt[4]{-b x^2+a x^6}} \, dx","Integrate[(b + a*x^4)/((-b + x^2 + a*x^4)*(-(b*x^2) + a*x^6)^(1/4)),x]","\int \frac{b+a x^4}{\left(-b+x^2+a x^4\right) \sqrt[4]{-b x^2+a x^6}} \, dx","-\frac{\tan ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{a x^6-b x^2}}{\sqrt{a x^6-b x^2}-x^2}\right)}{\sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{\frac{\sqrt{a x^6-b x^2}}{\sqrt{2}}+\frac{x^2}{\sqrt{2}}}{x \sqrt[4]{a x^6-b x^2}}\right)}{\sqrt{2}}",1,"Integrate[(b + a*x^4)/((-b + x^2 + a*x^4)*(-(b*x^2) + a*x^6)^(1/4)), x]","F",-1
1722,0,0,116,0.3737829,"\int \frac{b+2 a x^3}{\left(-b+x+a x^3\right) \sqrt[4]{-b x^3+a x^6}} \, dx","Integrate[(b + 2*a*x^3)/((-b + x + a*x^3)*(-(b*x^3) + a*x^6)^(1/4)),x]","\int \frac{b+2 a x^3}{\left(-b+x+a x^3\right) \sqrt[4]{-b x^3+a x^6}} \, dx","-\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{a x^6-b x^3}}{\sqrt{a x^6-b x^3}-x^2}\right)-\sqrt{2} \tanh ^{-1}\left(\frac{\frac{\sqrt{a x^6-b x^3}}{\sqrt{2}}+\frac{x^2}{\sqrt{2}}}{x \sqrt[4]{a x^6-b x^3}}\right)",1,"Integrate[(b + 2*a*x^3)/((-b + x + a*x^3)*(-(b*x^3) + a*x^6)^(1/4)), x]","F",-1
1723,1,404,116,0.6093916,"\int \frac{1}{\sqrt[4]{-b+a x^4} \left(-b-x^4+a x^8\right)} \, dx","Integrate[1/((-b + a*x^4)^(1/4)*(-b - x^4 + a*x^8)),x]","-\frac{a^{3/4} \left(-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{-\sqrt{4 a b+1}-2 b+1}}{\sqrt[4]{1-\sqrt{4 a b+1}} \sqrt[4]{a x^4-b}}\right)}{\left(1-\sqrt{4 a b+1}\right)^{3/4} \sqrt[4]{-\sqrt{4 a b+1}-2 b+1}}+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{\sqrt{4 a b+1}-2 b+1}}{\sqrt[4]{\sqrt{4 a b+1}+1} \sqrt[4]{a x^4-b}}\right)}{\left(\sqrt{4 a b+1}+1\right)^{3/4} \sqrt[4]{\sqrt{4 a b+1}-2 b+1}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{-\sqrt{4 a b+1}-2 b+1}}{\sqrt[4]{1-\sqrt{4 a b+1}} \sqrt[4]{a x^4-b}}\right)}{\left(1-\sqrt{4 a b+1}\right)^{3/4} \sqrt[4]{-\sqrt{4 a b+1}-2 b+1}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{\sqrt{4 a b+1}-2 b+1}}{\sqrt[4]{\sqrt{4 a b+1}+1} \sqrt[4]{a x^4-b}}\right)}{\left(\sqrt{4 a b+1}+1\right)^{3/4} \sqrt[4]{\sqrt{4 a b+1}-2 b+1}}\right)}{\sqrt{4 a b+1}}","\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a-\text{$\#$1}^4+a^2-a b+a\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-a \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+a \log (x)}{2 \text{$\#$1}^5-2 \text{$\#$1} a-\text{$\#$1}}\&\right]}{4 b}",1,"-((a^(3/4)*(-(ArcTan[(a^(1/4)*(1 - 2*b - Sqrt[1 + 4*a*b])^(1/4)*x)/((1 - Sqrt[1 + 4*a*b])^(1/4)*(-b + a*x^4)^(1/4))]/((1 - Sqrt[1 + 4*a*b])^(3/4)*(1 - 2*b - Sqrt[1 + 4*a*b])^(1/4))) + ArcTan[(a^(1/4)*(1 - 2*b + Sqrt[1 + 4*a*b])^(1/4)*x)/((1 + Sqrt[1 + 4*a*b])^(1/4)*(-b + a*x^4)^(1/4))]/((1 + Sqrt[1 + 4*a*b])^(3/4)*(1 - 2*b + Sqrt[1 + 4*a*b])^(1/4)) - ArcTanh[(a^(1/4)*(1 - 2*b - Sqrt[1 + 4*a*b])^(1/4)*x)/((1 - Sqrt[1 + 4*a*b])^(1/4)*(-b + a*x^4)^(1/4))]/((1 - Sqrt[1 + 4*a*b])^(3/4)*(1 - 2*b - Sqrt[1 + 4*a*b])^(1/4)) + ArcTanh[(a^(1/4)*(1 - 2*b + Sqrt[1 + 4*a*b])^(1/4)*x)/((1 + Sqrt[1 + 4*a*b])^(1/4)*(-b + a*x^4)^(1/4))]/((1 + Sqrt[1 + 4*a*b])^(3/4)*(1 - 2*b + Sqrt[1 + 4*a*b])^(1/4))))/Sqrt[1 + 4*a*b])","B",1
1724,1,404,116,0.1515303,"\int \frac{1}{\sqrt[4]{-b+a x^4} \left(-b-x^4+a x^8\right)} \, dx","Integrate[1/((-b + a*x^4)^(1/4)*(-b - x^4 + a*x^8)),x]","-\frac{a^{3/4} \left(-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{-\sqrt{4 a b+1}-2 b+1}}{\sqrt[4]{1-\sqrt{4 a b+1}} \sqrt[4]{a x^4-b}}\right)}{\left(1-\sqrt{4 a b+1}\right)^{3/4} \sqrt[4]{-\sqrt{4 a b+1}-2 b+1}}+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{\sqrt{4 a b+1}-2 b+1}}{\sqrt[4]{\sqrt{4 a b+1}+1} \sqrt[4]{a x^4-b}}\right)}{\left(\sqrt{4 a b+1}+1\right)^{3/4} \sqrt[4]{\sqrt{4 a b+1}-2 b+1}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{-\sqrt{4 a b+1}-2 b+1}}{\sqrt[4]{1-\sqrt{4 a b+1}} \sqrt[4]{a x^4-b}}\right)}{\left(1-\sqrt{4 a b+1}\right)^{3/4} \sqrt[4]{-\sqrt{4 a b+1}-2 b+1}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{\sqrt{4 a b+1}-2 b+1}}{\sqrt[4]{\sqrt{4 a b+1}+1} \sqrt[4]{a x^4-b}}\right)}{\left(\sqrt{4 a b+1}+1\right)^{3/4} \sqrt[4]{\sqrt{4 a b+1}-2 b+1}}\right)}{\sqrt{4 a b+1}}","\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a-\text{$\#$1}^4+a^2-a b+a\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-a \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+a \log (x)}{2 \text{$\#$1}^5-2 \text{$\#$1} a-\text{$\#$1}}\&\right]}{4 b}",1,"-((a^(3/4)*(-(ArcTan[(a^(1/4)*(1 - 2*b - Sqrt[1 + 4*a*b])^(1/4)*x)/((1 - Sqrt[1 + 4*a*b])^(1/4)*(-b + a*x^4)^(1/4))]/((1 - Sqrt[1 + 4*a*b])^(3/4)*(1 - 2*b - Sqrt[1 + 4*a*b])^(1/4))) + ArcTan[(a^(1/4)*(1 - 2*b + Sqrt[1 + 4*a*b])^(1/4)*x)/((1 + Sqrt[1 + 4*a*b])^(1/4)*(-b + a*x^4)^(1/4))]/((1 + Sqrt[1 + 4*a*b])^(3/4)*(1 - 2*b + Sqrt[1 + 4*a*b])^(1/4)) - ArcTanh[(a^(1/4)*(1 - 2*b - Sqrt[1 + 4*a*b])^(1/4)*x)/((1 - Sqrt[1 + 4*a*b])^(1/4)*(-b + a*x^4)^(1/4))]/((1 - Sqrt[1 + 4*a*b])^(3/4)*(1 - 2*b - Sqrt[1 + 4*a*b])^(1/4)) + ArcTanh[(a^(1/4)*(1 - 2*b + Sqrt[1 + 4*a*b])^(1/4)*x)/((1 + Sqrt[1 + 4*a*b])^(1/4)*(-b + a*x^4)^(1/4))]/((1 + Sqrt[1 + 4*a*b])^(3/4)*(1 - 2*b + Sqrt[1 + 4*a*b])^(1/4))))/Sqrt[1 + 4*a*b])","B",1
1725,1,510,116,1.4737556,"\int \frac{b+a x^4}{\sqrt[4]{-b+a x^4} \left(b+c x^4+a x^8\right)} \, dx","Integrate[(b + a*x^4)/((-b + a*x^4)^(1/4)*(b + c*x^4 + a*x^8)),x]","\frac{1}{2} a^{3/4} \left(\frac{\left(\frac{2 b-c}{\sqrt{c^2-4 a b}}+1\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{-\sqrt{c^2-4 a b}+2 b+c}}{\sqrt[4]{c-\sqrt{c^2-4 a b}} \sqrt[4]{a x^4-b}}\right)}{\left(c-\sqrt{c^2-4 a b}\right)^{3/4} \sqrt[4]{-\sqrt{c^2-4 a b}+2 b+c}}+\frac{\left(\frac{c-2 b}{\sqrt{c^2-4 a b}}+1\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{\sqrt{c^2-4 a b}+2 b+c}}{\sqrt[4]{\sqrt{c^2-4 a b}+c} \sqrt[4]{a x^4-b}}\right)}{\left(\sqrt{c^2-4 a b}+c\right)^{3/4} \sqrt[4]{\sqrt{c^2-4 a b}+2 b+c}}+\frac{\left(\frac{2 b-c}{\sqrt{c^2-4 a b}}+1\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{-\sqrt{c^2-4 a b}+2 b+c}}{\sqrt[4]{c-\sqrt{c^2-4 a b}} \sqrt[4]{a x^4-b}}\right)}{\left(c-\sqrt{c^2-4 a b}\right)^{3/4} \sqrt[4]{-\sqrt{c^2-4 a b}+2 b+c}}+\frac{\left(\frac{c-2 b}{\sqrt{c^2-4 a b}}+1\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{\sqrt{c^2-4 a b}+2 b+c}}{\sqrt[4]{\sqrt{c^2-4 a b}+c} \sqrt[4]{a x^4-b}}\right)}{\left(\sqrt{c^2-4 a b}+c\right)^{3/4} \sqrt[4]{\sqrt{c^2-4 a b}+2 b+c}}\right)","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a-\text{$\#$1}^4 c+a^2+a b+a c\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-2 a \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+2 a \log (x)}{-2 \text{$\#$1}^5+2 \text{$\#$1} a+\text{$\#$1} c}\&\right]",1,"(a^(3/4)*(((1 + (2*b - c)/Sqrt[-4*a*b + c^2])*ArcTan[(a^(1/4)*(2*b + c - Sqrt[-4*a*b + c^2])^(1/4)*x)/((c - Sqrt[-4*a*b + c^2])^(1/4)*(-b + a*x^4)^(1/4))])/((c - Sqrt[-4*a*b + c^2])^(3/4)*(2*b + c - Sqrt[-4*a*b + c^2])^(1/4)) + ((1 + (-2*b + c)/Sqrt[-4*a*b + c^2])*ArcTan[(a^(1/4)*(2*b + c + Sqrt[-4*a*b + c^2])^(1/4)*x)/((c + Sqrt[-4*a*b + c^2])^(1/4)*(-b + a*x^4)^(1/4))])/((c + Sqrt[-4*a*b + c^2])^(3/4)*(2*b + c + Sqrt[-4*a*b + c^2])^(1/4)) + ((1 + (2*b - c)/Sqrt[-4*a*b + c^2])*ArcTanh[(a^(1/4)*(2*b + c - Sqrt[-4*a*b + c^2])^(1/4)*x)/((c - Sqrt[-4*a*b + c^2])^(1/4)*(-b + a*x^4)^(1/4))])/((c - Sqrt[-4*a*b + c^2])^(3/4)*(2*b + c - Sqrt[-4*a*b + c^2])^(1/4)) + ((1 + (-2*b + c)/Sqrt[-4*a*b + c^2])*ArcTanh[(a^(1/4)*(2*b + c + Sqrt[-4*a*b + c^2])^(1/4)*x)/((c + Sqrt[-4*a*b + c^2])^(1/4)*(-b + a*x^4)^(1/4))])/((c + Sqrt[-4*a*b + c^2])^(3/4)*(2*b + c + Sqrt[-4*a*b + c^2])^(1/4))))/2","B",1
1726,1,510,116,0.4000081,"\int \frac{b+a x^4}{\sqrt[4]{-b+a x^4} \left(b+c x^4+a x^8\right)} \, dx","Integrate[(b + a*x^4)/((-b + a*x^4)^(1/4)*(b + c*x^4 + a*x^8)),x]","\frac{1}{2} a^{3/4} \left(\frac{\left(\frac{2 b-c}{\sqrt{c^2-4 a b}}+1\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{-\sqrt{c^2-4 a b}+2 b+c}}{\sqrt[4]{c-\sqrt{c^2-4 a b}} \sqrt[4]{a x^4-b}}\right)}{\left(c-\sqrt{c^2-4 a b}\right)^{3/4} \sqrt[4]{-\sqrt{c^2-4 a b}+2 b+c}}+\frac{\left(\frac{c-2 b}{\sqrt{c^2-4 a b}}+1\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{\sqrt{c^2-4 a b}+2 b+c}}{\sqrt[4]{\sqrt{c^2-4 a b}+c} \sqrt[4]{a x^4-b}}\right)}{\left(\sqrt{c^2-4 a b}+c\right)^{3/4} \sqrt[4]{\sqrt{c^2-4 a b}+2 b+c}}+\frac{\left(\frac{2 b-c}{\sqrt{c^2-4 a b}}+1\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{-\sqrt{c^2-4 a b}+2 b+c}}{\sqrt[4]{c-\sqrt{c^2-4 a b}} \sqrt[4]{a x^4-b}}\right)}{\left(c-\sqrt{c^2-4 a b}\right)^{3/4} \sqrt[4]{-\sqrt{c^2-4 a b}+2 b+c}}+\frac{\left(\frac{c-2 b}{\sqrt{c^2-4 a b}}+1\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{\sqrt{c^2-4 a b}+2 b+c}}{\sqrt[4]{\sqrt{c^2-4 a b}+c} \sqrt[4]{a x^4-b}}\right)}{\left(\sqrt{c^2-4 a b}+c\right)^{3/4} \sqrt[4]{\sqrt{c^2-4 a b}+2 b+c}}\right)","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a-\text{$\#$1}^4 c+a^2+a b+a c\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-2 a \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+2 a \log (x)}{-2 \text{$\#$1}^5+2 \text{$\#$1} a+\text{$\#$1} c}\&\right]",1,"(a^(3/4)*(((1 + (2*b - c)/Sqrt[-4*a*b + c^2])*ArcTan[(a^(1/4)*(2*b + c - Sqrt[-4*a*b + c^2])^(1/4)*x)/((c - Sqrt[-4*a*b + c^2])^(1/4)*(-b + a*x^4)^(1/4))])/((c - Sqrt[-4*a*b + c^2])^(3/4)*(2*b + c - Sqrt[-4*a*b + c^2])^(1/4)) + ((1 + (-2*b + c)/Sqrt[-4*a*b + c^2])*ArcTan[(a^(1/4)*(2*b + c + Sqrt[-4*a*b + c^2])^(1/4)*x)/((c + Sqrt[-4*a*b + c^2])^(1/4)*(-b + a*x^4)^(1/4))])/((c + Sqrt[-4*a*b + c^2])^(3/4)*(2*b + c + Sqrt[-4*a*b + c^2])^(1/4)) + ((1 + (2*b - c)/Sqrt[-4*a*b + c^2])*ArcTanh[(a^(1/4)*(2*b + c - Sqrt[-4*a*b + c^2])^(1/4)*x)/((c - Sqrt[-4*a*b + c^2])^(1/4)*(-b + a*x^4)^(1/4))])/((c - Sqrt[-4*a*b + c^2])^(3/4)*(2*b + c - Sqrt[-4*a*b + c^2])^(1/4)) + ((1 + (-2*b + c)/Sqrt[-4*a*b + c^2])*ArcTanh[(a^(1/4)*(2*b + c + Sqrt[-4*a*b + c^2])^(1/4)*x)/((c + Sqrt[-4*a*b + c^2])^(1/4)*(-b + a*x^4)^(1/4))])/((c + Sqrt[-4*a*b + c^2])^(3/4)*(2*b + c + Sqrt[-4*a*b + c^2])^(1/4))))/2","B",1
1727,0,0,116,0.8621035,"\int \frac{\left(1+x^5\right) \sqrt[3]{1+x^3+x^5} \left(-3+2 x^5\right)}{x^2 \left(2-2 x^3+4 x^5-x^6-2 x^8+2 x^{10}\right)} \, dx","Integrate[((1 + x^5)*(1 + x^3 + x^5)^(1/3)*(-3 + 2*x^5))/(x^2*(2 - 2*x^3 + 4*x^5 - x^6 - 2*x^8 + 2*x^10)),x]","\int \frac{\left(1+x^5\right) \sqrt[3]{1+x^3+x^5} \left(-3+2 x^5\right)}{x^2 \left(2-2 x^3+4 x^5-x^6-2 x^8+2 x^{10}\right)} \, dx","\frac{3 \sqrt[3]{x^5+x^3+1}}{2 x}-\frac{1}{4} \text{RootSum}\left[2 \text{$\#$1}^6-6 \text{$\#$1}^3+3\&,\frac{-4 \text{$\#$1}^3 \log \left(\sqrt[3]{x^5+x^3+1}-\text{$\#$1} x\right)+4 \text{$\#$1}^3 \log (x)+3 \log \left(\sqrt[3]{x^5+x^3+1}-\text{$\#$1} x\right)-3 \log (x)}{2 \text{$\#$1}^5-3 \text{$\#$1}^2}\&\right]",1,"Integrate[((1 + x^5)*(1 + x^3 + x^5)^(1/3)*(-3 + 2*x^5))/(x^2*(2 - 2*x^3 + 4*x^5 - x^6 - 2*x^8 + 2*x^10)), x]","F",-1
1728,0,0,116,0.466759,"\int \frac{\left(1+x^5\right) \sqrt[3]{1+x^3+x^5} \left(-3+2 x^5\right)}{x^2 \left(2-2 x^3+4 x^5-x^6-2 x^8+2 x^{10}\right)} \, dx","Integrate[((1 + x^5)*(1 + x^3 + x^5)^(1/3)*(-3 + 2*x^5))/(x^2*(2 - 2*x^3 + 4*x^5 - x^6 - 2*x^8 + 2*x^10)),x]","\int \frac{\left(1+x^5\right) \sqrt[3]{1+x^3+x^5} \left(-3+2 x^5\right)}{x^2 \left(2-2 x^3+4 x^5-x^6-2 x^8+2 x^{10}\right)} \, dx","\frac{3 \sqrt[3]{x^5+x^3+1}}{2 x}-\frac{1}{4} \text{RootSum}\left[2 \text{$\#$1}^6-6 \text{$\#$1}^3+3\&,\frac{-4 \text{$\#$1}^3 \log \left(\sqrt[3]{x^5+x^3+1}-\text{$\#$1} x\right)+4 \text{$\#$1}^3 \log (x)+3 \log \left(\sqrt[3]{x^5+x^3+1}-\text{$\#$1} x\right)-3 \log (x)}{2 \text{$\#$1}^5-3 \text{$\#$1}^2}\&\right]",1,"Integrate[((1 + x^5)*(1 + x^3 + x^5)^(1/3)*(-3 + 2*x^5))/(x^2*(2 - 2*x^3 + 4*x^5 - x^6 - 2*x^8 + 2*x^10)), x]","F",-1
1729,1,67,117,0.0305413,"\int x^4 \sqrt[3]{-x+x^3} \, dx","Integrate[x^4*(-x + x^3)^(1/3),x]","\frac{x \sqrt[3]{x \left(x^2-1\right)} \left(5 \, _2F_1\left(-\frac{1}{3},\frac{2}{3};\frac{5}{3};x^2\right)+\sqrt[3]{1-x^2} \left(6 x^4-x^2-5\right)\right)}{36 \sqrt[3]{1-x^2}}","\frac{5}{162} \log \left(\sqrt[3]{x^3-x}-x\right)+\frac{5 \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-x}+x}\right)}{54 \sqrt{3}}+\frac{1}{108} \sqrt[3]{x^3-x} \left(18 x^5-3 x^3-5 x\right)-\frac{5}{324} \log \left(\sqrt[3]{x^3-x} x+\left(x^3-x\right)^{2/3}+x^2\right)",1,"(x*(x*(-1 + x^2))^(1/3)*((1 - x^2)^(1/3)*(-5 - x^2 + 6*x^4) + 5*Hypergeometric2F1[-1/3, 2/3, 5/3, x^2]))/(36*(1 - x^2)^(1/3))","C",1
1730,1,66,117,0.0441384,"\int \frac{x}{\left(-b+a x^2\right) \sqrt{b x+a x^3}} \, dx","Integrate[x/((-b + a*x^2)*Sqrt[b*x + a*x^3]),x]","-\frac{2 x^2 \sqrt{\frac{a x^2+b}{b}} F_1\left(\frac{3}{4};\frac{1}{2},1;\frac{7}{4};-\frac{a x^2}{b},\frac{a x^2}{b}\right)}{3 b \sqrt{x \left(a x^2+b\right)}}","\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{a x^3+b x}}{a x^2+b}\right)}{2 \sqrt{2} a^{3/4} b^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{a x^3+b x}}{a x^2+b}\right)}{2 \sqrt{2} a^{3/4} b^{3/4}}",1,"(-2*x^2*Sqrt[(b + a*x^2)/b]*AppellF1[3/4, 1/2, 1, 7/4, -((a*x^2)/b), (a*x^2)/b])/(3*b*Sqrt[x*(b + a*x^2)])","C",0
1731,1,111,117,0.9067822,"\int \frac{\sqrt{b x+a x^3}}{-b^2+a^2 x^4} \, dx","Integrate[Sqrt[b*x + a*x^3]/(-b^2 + a^2*x^4),x]","\frac{\sqrt{\frac{i \sqrt{a} x}{\sqrt{b}}} \sqrt{\frac{a x^2}{b}+1} \left(\Pi \left(i;\left.i \sinh ^{-1}\left(\sqrt{\frac{i \sqrt{a} x}{\sqrt{b}}}\right)\right|-1\right)-\Pi \left(-i;\left.i \sinh ^{-1}\left(\sqrt{\frac{i \sqrt{a} x}{\sqrt{b}}}\right)\right|-1\right)\right)}{a \sqrt{x \left(a x^2+b\right)}}","\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{a x^3+b x}}{a x^2+b}\right)}{2 \sqrt{2} a^{3/4} b^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{a x^3+b x}}{a x^2+b}\right)}{2 \sqrt{2} a^{3/4} b^{3/4}}",1,"(Sqrt[(I*Sqrt[a]*x)/Sqrt[b]]*Sqrt[1 + (a*x^2)/b]*(-EllipticPi[-I, I*ArcSinh[Sqrt[(I*Sqrt[a]*x)/Sqrt[b]]], -1] + EllipticPi[I, I*ArcSinh[Sqrt[(I*Sqrt[a]*x)/Sqrt[b]]], -1]))/(a*Sqrt[x*(b + a*x^2)])","C",1
1732,1,127,117,0.0553529,"\int \frac{x^{19}}{\sqrt[3]{-1+x^6}} \, dx","Integrate[x^19/(-1 + x^6)^(1/3),x]","\frac{1}{972} \left(54 \left(x^6-1\right)^{2/3} x^{14}+63 \left(x^6-1\right)^{2/3} x^8+84 \left(x^6-1\right)^{2/3} x^2-28 \log \left(1-\frac{x^2}{\sqrt[3]{x^6-1}}\right)+28 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 x^2}{\sqrt[3]{x^6-1}}+1}{\sqrt{3}}\right)+14 \log \left(\frac{x^4}{\left(x^6-1\right)^{2/3}}+\frac{x^2}{\sqrt[3]{x^6-1}}+1\right)\right)","-\frac{7}{243} \log \left(\sqrt[3]{x^6-1}-x^2\right)+\frac{7 \tan ^{-1}\left(\frac{\sqrt{3} x^2}{2 \sqrt[3]{x^6-1}+x^2}\right)}{81 \sqrt{3}}+\frac{7}{486} \log \left(\left(x^6-1\right)^{2/3}+x^4+\sqrt[3]{x^6-1} x^2\right)+\frac{1}{324} \left(x^6-1\right)^{2/3} \left(18 x^{14}+21 x^8+28 x^2\right)",1,"(84*x^2*(-1 + x^6)^(2/3) + 63*x^8*(-1 + x^6)^(2/3) + 54*x^14*(-1 + x^6)^(2/3) + 28*Sqrt[3]*ArcTan[(1 + (2*x^2)/(-1 + x^6)^(1/3))/Sqrt[3]] - 28*Log[1 - x^2/(-1 + x^6)^(1/3)] + 14*Log[1 + x^4/(-1 + x^6)^(2/3) + x^2/(-1 + x^6)^(1/3)])/972","A",1
1733,1,67,117,0.027703,"\int x^{15} \sqrt[3]{-1+x^6} \, dx","Integrate[x^15*(-1 + x^6)^(1/3),x]","\frac{x^4 \sqrt[3]{x^6-1} \left(5 \, _2F_1\left(-\frac{1}{3},\frac{2}{3};\frac{5}{3};x^6\right)+\sqrt[3]{1-x^6} \left(6 x^{12}-x^6-5\right)\right)}{108 \sqrt[3]{1-x^6}}","\frac{5}{486} \log \left(\sqrt[3]{x^6-1}-x^2\right)+\frac{5 \tan ^{-1}\left(\frac{\sqrt{3} x^2}{2 \sqrt[3]{x^6-1}+x^2}\right)}{162 \sqrt{3}}-\frac{5}{972} \log \left(\left(x^6-1\right)^{2/3}+x^4+\sqrt[3]{x^6-1} x^2\right)+\frac{1}{324} \sqrt[3]{x^6-1} \left(18 x^{16}-3 x^{10}-5 x^4\right)",1,"(x^4*(-1 + x^6)^(1/3)*((1 - x^6)^(1/3)*(-5 - x^6 + 6*x^12) + 5*Hypergeometric2F1[-1/3, 2/3, 5/3, x^6]))/(108*(1 - x^6)^(1/3))","C",1
1734,1,127,117,0.0529491,"\int \frac{x^{19}}{\sqrt[3]{1+x^6}} \, dx","Integrate[x^19/(1 + x^6)^(1/3),x]","\frac{1}{972} \left(54 \left(x^6+1\right)^{2/3} x^{14}-63 \left(x^6+1\right)^{2/3} x^8+84 \left(x^6+1\right)^{2/3} x^2+28 \log \left(1-\frac{x^2}{\sqrt[3]{x^6+1}}\right)-28 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 x^2}{\sqrt[3]{x^6+1}}+1}{\sqrt{3}}\right)-14 \log \left(\frac{x^4}{\left(x^6+1\right)^{2/3}}+\frac{x^2}{\sqrt[3]{x^6+1}}+1\right)\right)","\frac{7}{243} \log \left(\sqrt[3]{x^6+1}-x^2\right)-\frac{7 \tan ^{-1}\left(\frac{\sqrt{3} x^2}{2 \sqrt[3]{x^6+1}+x^2}\right)}{81 \sqrt{3}}-\frac{7}{486} \log \left(\left(x^6+1\right)^{2/3}+x^4+\sqrt[3]{x^6+1} x^2\right)+\frac{1}{324} \left(x^6+1\right)^{2/3} \left(18 x^{14}-21 x^8+28 x^2\right)",1,"(84*x^2*(1 + x^6)^(2/3) - 63*x^8*(1 + x^6)^(2/3) + 54*x^14*(1 + x^6)^(2/3) - 28*Sqrt[3]*ArcTan[(1 + (2*x^2)/(1 + x^6)^(1/3))/Sqrt[3]] + 28*Log[1 - x^2/(1 + x^6)^(1/3)] - 14*Log[1 + x^4/(1 + x^6)^(2/3) + x^2/(1 + x^6)^(1/3)])/972","A",1
1735,1,45,117,0.0163326,"\int x^{15} \sqrt[3]{1+x^6} \, dx","Integrate[x^15*(1 + x^6)^(1/3),x]","\frac{1}{108} x^4 \left(5 \, _2F_1\left(-\frac{1}{3},\frac{2}{3};\frac{5}{3};-x^6\right)+\sqrt[3]{x^6+1} \left(6 x^{12}+x^6-5\right)\right)","-\frac{5}{486} \log \left(\sqrt[3]{x^6+1}-x^2\right)-\frac{5 \tan ^{-1}\left(\frac{\sqrt{3} x^2}{2 \sqrt[3]{x^6+1}+x^2}\right)}{162 \sqrt{3}}+\frac{5}{972} \log \left(\left(x^6+1\right)^{2/3}+x^4+\sqrt[3]{x^6+1} x^2\right)+\frac{1}{324} \sqrt[3]{x^6+1} \left(18 x^{16}+3 x^{10}-5 x^4\right)",1,"(x^4*((1 + x^6)^(1/3)*(-5 + x^6 + 6*x^12) + 5*Hypergeometric2F1[-1/3, 2/3, 5/3, -x^6]))/108","C",1
1736,1,84,117,0.0661854,"\int \frac{-b-a x^3+x^6}{x^6 \sqrt[4]{-b x+a x^4}} \, dx","Integrate[(-b - a*x^3 + x^6)/(x^6*(-(b*x) + a*x^4)^(1/4)),x]","\frac{4 \left(-11 a^2 x^6+21 b x^6 \sqrt[4]{1-\frac{a x^3}{b}} \, _2F_1\left(\frac{1}{4},\frac{1}{4};\frac{5}{4};\frac{a x^3}{b}\right)+8 a b x^3+3 b^2\right)}{63 b x^5 \sqrt[4]{a x^4-b x}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \left(a x^4-b x\right)^{3/4}}{a x^3-b}\right)}{3 \sqrt[4]{a}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{a} \left(a x^4-b x\right)^{3/4}}{a x^3-b}\right)}{3 \sqrt[4]{a}}-\frac{4 \left(a x^4-b x\right)^{3/4} \left(11 a x^3+3 b\right)}{63 b x^6}",1,"(4*(3*b^2 + 8*a*b*x^3 - 11*a^2*x^6 + 21*b*x^6*(1 - (a*x^3)/b)^(1/4)*Hypergeometric2F1[1/4, 1/4, 5/4, (a*x^3)/b]))/(63*b*x^5*(-(b*x) + a*x^4)^(1/4))","C",1
1737,0,0,117,0.2455358,"\int \frac{-3-x^4+3 x^6}{\left(1-x^4+x^6\right) \sqrt[3]{1-x^3-x^4+x^6}} \, dx","Integrate[(-3 - x^4 + 3*x^6)/((1 - x^4 + x^6)*(1 - x^3 - x^4 + x^6)^(1/3)),x]","\int \frac{-3-x^4+3 x^6}{\left(1-x^4+x^6\right) \sqrt[3]{1-x^3-x^4+x^6}} \, dx","-\log \left(\sqrt[3]{x^6-x^4-x^3+1}+x\right)-\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^6-x^4-x^3+1}-x}\right)+\frac{1}{2} \log \left(x^2-\sqrt[3]{x^6-x^4-x^3+1} x+\left(x^6-x^4-x^3+1\right)^{2/3}\right)",1,"Integrate[(-3 - x^4 + 3*x^6)/((1 - x^4 + x^6)*(1 - x^3 - x^4 + x^6)^(1/3)), x]","F",-1
1738,1,147,117,0.1514991,"\int \frac{-b+a x^6}{x^6 \sqrt[4]{-b x+a x^4}} \, dx","Integrate[(-b + a*x^6)/(x^6*(-(b*x) + a*x^4)^(1/4)),x]","\frac{2 \left(21 a^{3/4} b x^{21/4} \sqrt[4]{a x^3-b} \tan ^{-1}\left(\frac{\sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3-b}}\right)+21 a^{3/4} b x^{21/4} \sqrt[4]{a x^3-b} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3-b}}\right)-8 a^2 x^6+2 a b x^3+6 b^2\right)}{63 b x^5 \sqrt[4]{a x^4-b x}}","\frac{2}{3} a^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} \left(a x^4-b x\right)^{3/4}}{a x^3-b}\right)+\frac{2}{3} a^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \left(a x^4-b x\right)^{3/4}}{a x^3-b}\right)-\frac{4 \left(a x^4-b x\right)^{3/4} \left(4 a x^3+3 b\right)}{63 b x^6}",1,"(2*(6*b^2 + 2*a*b*x^3 - 8*a^2*x^6 + 21*a^(3/4)*b*x^(21/4)*(-b + a*x^3)^(1/4)*ArcTan[(a^(1/4)*x^(3/4))/(-b + a*x^3)^(1/4)] + 21*a^(3/4)*b*x^(21/4)*(-b + a*x^3)^(1/4)*ArcTanh[(a^(1/4)*x^(3/4))/(-b + a*x^3)^(1/4)]))/(63*b*x^5*(-(b*x) + a*x^4)^(1/4))","A",1
1739,1,147,117,0.0960681,"\int \frac{b+a x^6}{x^6 \sqrt[4]{-b x+a x^4}} \, dx","Integrate[(b + a*x^6)/(x^6*(-(b*x) + a*x^4)^(1/4)),x]","\frac{2 \left(21 a^{3/4} b x^{21/4} \sqrt[4]{a x^3-b} \tan ^{-1}\left(\frac{\sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3-b}}\right)+21 a^{3/4} b x^{21/4} \sqrt[4]{a x^3-b} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3-b}}\right)+8 a^2 x^6-2 a b x^3-6 b^2\right)}{63 b x^5 \sqrt[4]{a x^4-b x}}","\frac{2}{3} a^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} \left(a x^4-b x\right)^{3/4}}{a x^3-b}\right)+\frac{2}{3} a^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \left(a x^4-b x\right)^{3/4}}{a x^3-b}\right)+\frac{4 \left(a x^4-b x\right)^{3/4} \left(4 a x^3+3 b\right)}{63 b x^6}",1,"(2*(-6*b^2 - 2*a*b*x^3 + 8*a^2*x^6 + 21*a^(3/4)*b*x^(21/4)*(-b + a*x^3)^(1/4)*ArcTan[(a^(1/4)*x^(3/4))/(-b + a*x^3)^(1/4)] + 21*a^(3/4)*b*x^(21/4)*(-b + a*x^3)^(1/4)*ArcTanh[(a^(1/4)*x^(3/4))/(-b + a*x^3)^(1/4)]))/(63*b*x^5*(-(b*x) + a*x^4)^(1/4))","A",1
1740,1,117,117,0.5915969,"\int \frac{\sqrt[4]{x^2+x^4} \left(-1-x^4+x^8\right)}{-1+x^4} \, dx","Integrate[((x^2 + x^4)^(1/4)*(-1 - x^4 + x^8))/(-1 + x^4),x]","\frac{1}{384} x \sqrt[4]{x^4+x^2} \left(64 x^4+8 x^2+\frac{3 \left(\frac{1}{x^2}+1\right)^{3/4} \left(7 \tan ^{-1}\left(\sqrt[4]{\frac{1}{x^2}+1}\right)+64 \sqrt[4]{2} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{x^2}+1}}{\sqrt[4]{2}}\right)+7 \tanh ^{-1}\left(\sqrt[4]{\frac{1}{x^2}+1}\right)+64 \sqrt[4]{2} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{x^2}+1}}{\sqrt[4]{2}}\right)\right)}{x^2+1}-14\right)","-\frac{7}{128} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+x^2}}\right)-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+x^2}}\right)}{2^{3/4}}+\frac{7}{128} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+x^2}}\right)+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+x^2}}\right)}{2^{3/4}}+\frac{1}{192} \sqrt[4]{x^4+x^2} \left(32 x^5+4 x^3-7 x\right)",1,"(x*(x^2 + x^4)^(1/4)*(-14 + 8*x^2 + 64*x^4 + (3*(1 + x^(-2))^(3/4)*(7*ArcTan[(1 + x^(-2))^(1/4)] + 64*2^(1/4)*ArcTan[(1 + x^(-2))^(1/4)/2^(1/4)] + 7*ArcTanh[(1 + x^(-2))^(1/4)] + 64*2^(1/4)*ArcTanh[(1 + x^(-2))^(1/4)/2^(1/4)]))/(1 + x^2)))/384","A",1
1741,0,0,117,0.2058066,"\int \frac{-b-a x^4+2 x^8}{\sqrt[4]{b+a x^4} \left(-b-a x^4+x^8\right)} \, dx","Integrate[(-b - a*x^4 + 2*x^8)/((b + a*x^4)^(1/4)*(-b - a*x^4 + x^8)),x]","\int \frac{-b-a x^4+2 x^8}{\sqrt[4]{b+a x^4} \left(-b-a x^4+x^8\right)} \, dx","\frac{1}{4} \text{RootSum}\left[-\text{$\#$1}^8+\text{$\#$1}^4 a+b\&,\frac{\text{$\#$1}^3 \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)-\text{$\#$1}^3 \log (x)}{2 \text{$\#$1}^4-a}\&\right]+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{a}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{a}}",1,"Integrate[(-b - a*x^4 + 2*x^8)/((b + a*x^4)^(1/4)*(-b - a*x^4 + x^8)), x]","F",-1
1742,0,0,117,0.0787201,"\int \frac{-b-a x^4+2 x^8}{\sqrt[4]{b+a x^4} \left(-b-a x^4+x^8\right)} \, dx","Integrate[(-b - a*x^4 + 2*x^8)/((b + a*x^4)^(1/4)*(-b - a*x^4 + x^8)),x]","\int \frac{-b-a x^4+2 x^8}{\sqrt[4]{b+a x^4} \left(-b-a x^4+x^8\right)} \, dx","\frac{1}{4} \text{RootSum}\left[-\text{$\#$1}^8+\text{$\#$1}^4 a+b\&,\frac{\text{$\#$1}^3 \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)-\text{$\#$1}^3 \log (x)}{2 \text{$\#$1}^4-a}\&\right]+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{a}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{a}}",1,"Integrate[(-b - a*x^4 + 2*x^8)/((b + a*x^4)^(1/4)*(-b - a*x^4 + x^8)), x]","F",-1
1743,0,0,117,1.0780983,"\int \frac{\sqrt{c x^2-x \sqrt{-b x+a x^2}}}{x^3 \sqrt{-b x+a x^2}} \, dx","Integrate[Sqrt[c*x^2 - x*Sqrt[-(b*x) + a*x^2]]/(x^3*Sqrt[-(b*x) + a*x^2]),x]","\int \frac{\sqrt{c x^2-x \sqrt{-b x+a x^2}}}{x^3 \sqrt{-b x+a x^2}} \, dx","\frac{4 \sqrt{a x^2-b x} \left(20 a x+15 b+4 c^2 x\right) \sqrt{-x \left(\sqrt{a x^2-b x}-c x\right)}}{105 b^2 x^3}-\frac{4 \left(32 a c x+3 b c-8 c^3 x\right) \sqrt{-x \left(\sqrt{a x^2-b x}-c x\right)}}{105 b^2 x^2}",1,"Integrate[Sqrt[c*x^2 - x*Sqrt[-(b*x) + a*x^2]]/(x^3*Sqrt[-(b*x) + a*x^2]), x]","F",-1
1744,1,98,118,0.0922192,"\int \frac{b+x^3}{\sqrt[3]{a+x^3}} \, dx","Integrate[(b + x^3)/(a + x^3)^(1/3),x]","\frac{1}{3} \left(x \left(a+x^3\right)^{2/3}-\frac{1}{6} (a-3 b) \left(-2 \log \left(1-\frac{x}{\sqrt[3]{a+x^3}}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{a+x^3}}+1}{\sqrt{3}}\right)+\log \left(\frac{x}{\sqrt[3]{a+x^3}}+\frac{x^2}{\left(a+x^3\right)^{2/3}}+1\right)\right)\right)","\frac{1}{9} (a-3 b) \log \left(\sqrt[3]{a+x^3}-x\right)+\frac{1}{9} \left(3 \sqrt{3} b-\sqrt{3} a\right) \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{a+x^3}+x}\right)+\frac{1}{18} (3 b-a) \log \left(x \sqrt[3]{a+x^3}+\left(a+x^3\right)^{2/3}+x^2\right)+\frac{1}{3} x \left(a+x^3\right)^{2/3}",1,"(x*(a + x^3)^(2/3) - ((a - 3*b)*(2*Sqrt[3]*ArcTan[(1 + (2*x)/(a + x^3)^(1/3))/Sqrt[3]] - 2*Log[1 - x/(a + x^3)^(1/3)] + Log[1 + x^2/(a + x^3)^(2/3) + x/(a + x^3)^(1/3)]))/6)/3","A",1
1745,1,136,118,0.2005372,"\int \frac{b+a x^2}{\sqrt[3]{x+x^3}} \, dx","Integrate[(b + a*x^2)/(x + x^3)^(1/3),x]","\frac{\sqrt[3]{x} \left(a x^{2/3} \left(x^2+1\right)-\frac{1}{6} \sqrt[3]{x^2+1} (a-3 b) \left(-2 \log \left(1-\frac{x^{2/3}}{\sqrt[3]{x^2+1}}\right)+\log \left(\frac{x^{4/3}}{\left(x^2+1\right)^{2/3}}+\frac{x^{2/3}}{\sqrt[3]{x^2+1}}+1\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 x^{2/3}}{\sqrt[3]{x^2+1}}+1}{\sqrt{3}}\right)\right)\right)}{2 \sqrt[3]{x^3+x}}","\frac{1}{6} (a-3 b) \log \left(\sqrt[3]{x^3+x}-x\right)+\frac{1}{6} \left(3 \sqrt{3} b-\sqrt{3} a\right) \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+x}+x}\right)+\frac{1}{12} (3 b-a) \log \left(\sqrt[3]{x^3+x} x+\left(x^3+x\right)^{2/3}+x^2\right)+\frac{1}{2} a \left(x^3+x\right)^{2/3}",1,"(x^(1/3)*(a*x^(2/3)*(1 + x^2) - ((a - 3*b)*(1 + x^2)^(1/3)*(2*Sqrt[3]*ArcTan[(1 + (2*x^(2/3))/(1 + x^2)^(1/3))/Sqrt[3]] - 2*Log[1 - x^(2/3)/(1 + x^2)^(1/3)] + Log[1 + x^(4/3)/(1 + x^2)^(2/3) + x^(2/3)/(1 + x^2)^(1/3)]))/6))/(2*(x + x^3)^(1/3))","A",1
1746,1,35,118,0.0104067,"\int \sqrt[3]{-x^2+x^3} \, dx","Integrate[(-x^2 + x^3)^(1/3),x]","\frac{3 \left((x-1) x^2\right)^{4/3} \, _2F_1\left(-\frac{2}{3},\frac{4}{3};\frac{7}{3};1-x\right)}{4 x^{8/3}}","\frac{1}{6} \sqrt[3]{x^3-x^2} (3 x-1)+\frac{1}{9} \log \left(\sqrt[3]{x^3-x^2}-x\right)-\frac{1}{18} \log \left(x^2+\sqrt[3]{x^3-x^2} x+\left(x^3-x^2\right)^{2/3}\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-x^2}+x}\right)}{3 \sqrt{3}}",1,"(3*((-1 + x)*x^2)^(4/3)*Hypergeometric2F1[-2/3, 4/3, 7/3, 1 - x])/(4*x^(8/3))","C",1
1747,1,38,118,0.0135017,"\int x^2 \sqrt[3]{x^2+x^3} \, dx","Integrate[x^2*(x^2 + x^3)^(1/3),x]","\frac{3 x^3 \sqrt[3]{x^2 (x+1)} \, _2F_1\left(-\frac{1}{3},\frac{11}{3};\frac{14}{3};-x\right)}{11 \sqrt[3]{x+1}}","\frac{1}{324} \sqrt[3]{x^3+x^2} \left(81 x^3+9 x^2-12 x+20\right)+\frac{10}{243} \log \left(\sqrt[3]{x^3+x^2}-x\right)-\frac{5}{243} \log \left(x^2+\sqrt[3]{x^3+x^2} x+\left(x^3+x^2\right)^{2/3}\right)+\frac{10 \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+x^2}+x}\right)}{81 \sqrt{3}}",1,"(3*x^3*(x^2*(1 + x))^(1/3)*Hypergeometric2F1[-1/3, 11/3, 14/3, -x])/(11*(1 + x)^(1/3))","C",1
1748,1,148,118,5.525396,"\int \frac{x^4}{\left(1+x^4\right)^2 \sqrt[4]{x^2+x^4}} \, dx","Integrate[x^4/((1 + x^4)^2*(x^2 + x^4)^(1/4)),x]","\frac{x \left(\frac{4 \left(x^4-1\right)}{x^4+1}+\sqrt[4]{\frac{1}{x^2}+1} \left(-(1-i)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{x^2}+1}}{\sqrt[4]{1-i}}\right)-(1+i)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{x^2}+1}}{\sqrt[4]{1+i}}\right)+(1-i)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{x^2}+1}}{\sqrt[4]{1-i}}\right)+(1+i)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{x^2}+1}}{\sqrt[4]{1+i}}\right)\right)\right)}{32 \sqrt[4]{x^4+x^2}}","\frac{1}{64} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4+2\&,\frac{-\text{$\#$1}^4 \log \left(\sqrt[4]{x^4+x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 \log (x)+2 \log \left(\sqrt[4]{x^4+x^2}-\text{$\#$1} x\right)-2 \log (x)}{\text{$\#$1}^5-\text{$\#$1}}\&\right]+\frac{\left(x^4+x^2\right)^{3/4} \left(x^2-1\right)}{8 x \left(x^4+1\right)}",1,"(x*((4*(-1 + x^4))/(1 + x^4) + (1 + x^(-2))^(1/4)*(-((1 - I)^(3/4)*ArcTan[(1 + x^(-2))^(1/4)/(1 - I)^(1/4)]) - (1 + I)^(3/4)*ArcTan[(1 + x^(-2))^(1/4)/(1 + I)^(1/4)] + (1 - I)^(3/4)*ArcTanh[(1 + x^(-2))^(1/4)/(1 - I)^(1/4)] + (1 + I)^(3/4)*ArcTanh[(1 + x^(-2))^(1/4)/(1 + I)^(1/4)])))/(32*(x^2 + x^4)^(1/4))","C",1
1749,1,148,118,5.403667,"\int \frac{x^4}{\left(1+x^4\right)^2 \sqrt[4]{x^2+x^4}} \, dx","Integrate[x^4/((1 + x^4)^2*(x^2 + x^4)^(1/4)),x]","\frac{x \left(\frac{4 \left(x^4-1\right)}{x^4+1}+\sqrt[4]{\frac{1}{x^2}+1} \left(-(1-i)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{x^2}+1}}{\sqrt[4]{1-i}}\right)-(1+i)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{x^2}+1}}{\sqrt[4]{1+i}}\right)+(1-i)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{x^2}+1}}{\sqrt[4]{1-i}}\right)+(1+i)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{x^2}+1}}{\sqrt[4]{1+i}}\right)\right)\right)}{32 \sqrt[4]{x^4+x^2}}","\frac{1}{64} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4+2\&,\frac{-\text{$\#$1}^4 \log \left(\sqrt[4]{x^4+x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 \log (x)+2 \log \left(\sqrt[4]{x^4+x^2}-\text{$\#$1} x\right)-2 \log (x)}{\text{$\#$1}^5-\text{$\#$1}}\&\right]+\frac{\left(x^4+x^2\right)^{3/4} \left(x^2-1\right)}{8 x \left(x^4+1\right)}",1,"(x*((4*(-1 + x^4))/(1 + x^4) + (1 + x^(-2))^(1/4)*(-((1 - I)^(3/4)*ArcTan[(1 + x^(-2))^(1/4)/(1 - I)^(1/4)]) - (1 + I)^(3/4)*ArcTan[(1 + x^(-2))^(1/4)/(1 + I)^(1/4)] + (1 - I)^(3/4)*ArcTanh[(1 + x^(-2))^(1/4)/(1 - I)^(1/4)] + (1 + I)^(3/4)*ArcTanh[(1 + x^(-2))^(1/4)/(1 + I)^(1/4)])))/(32*(x^2 + x^4)^(1/4))","C",1
1750,0,0,118,0.4607093,"\int \frac{\left(-3+x^4\right) \left(1-x^3+x^4\right) \left(1+x^3+x^4\right)^{2/3}}{x^6 \left(1+x^4\right)} \, dx","Integrate[((-3 + x^4)*(1 - x^3 + x^4)*(1 + x^3 + x^4)^(2/3))/(x^6*(1 + x^4)),x]","\int \frac{\left(-3+x^4\right) \left(1-x^3+x^4\right) \left(1+x^3+x^4\right)^{2/3}}{x^6 \left(1+x^4\right)} \, dx","-\log \left(\sqrt[3]{x^4+x^3+1}-x\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^4+x^3+1}+x}\right)+\frac{3 \left(x^4+x^3+1\right)^{2/3} \left(2 x^4-3 x^3+2\right)}{10 x^5}+\frac{1}{2} \log \left(x^2+\sqrt[3]{x^4+x^3+1} x+\left(x^4+x^3+1\right)^{2/3}\right)",1,"Integrate[((-3 + x^4)*(1 - x^3 + x^4)*(1 + x^3 + x^4)^(2/3))/(x^6*(1 + x^4)), x]","F",-1
1751,0,0,118,1.2278973,"\int \frac{-b+2 a x^4}{\left(b+a x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Integrate[(-b + 2*a*x^4)/((b + a*x^4)*(b*x^2 + a*x^4)^(1/4)),x]","\int \frac{-b+2 a x^4}{\left(b+a x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","\frac{3}{4} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{\log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]+\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{\sqrt[4]{a}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{\sqrt[4]{a}}",1,"Integrate[(-b + 2*a*x^4)/((b + a*x^4)*(b*x^2 + a*x^4)^(1/4)), x]","F",-1
1752,0,0,118,0.3647302,"\int \frac{-b+2 a x^4}{\left(b+a x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Integrate[(-b + 2*a*x^4)/((b + a*x^4)*(b*x^2 + a*x^4)^(1/4)),x]","\int \frac{-b+2 a x^4}{\left(b+a x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","\frac{3}{4} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{\log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]+\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{\sqrt[4]{a}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{\sqrt[4]{a}}",1,"Integrate[(-b + 2*a*x^4)/((b + a*x^4)*(b*x^2 + a*x^4)^(1/4)), x]","F",-1
1753,0,0,118,0.377992,"\int \frac{1+x^2}{\left(-1+x^2\right) \sqrt[3]{x+x^5}} \, dx","Integrate[(1 + x^2)/((-1 + x^2)*(x + x^5)^(1/3)),x]","\int \frac{1+x^2}{\left(-1+x^2\right) \sqrt[3]{x+x^5}} \, dx","\frac{\log \left(2^{2/3} \sqrt[3]{x^5+x}-2 x\right)}{2 \sqrt[3]{2}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^5+x}+x}\right)}{2 \sqrt[3]{2}}-\frac{\log \left(2^{2/3} \sqrt[3]{x^5+x} x+\sqrt[3]{2} \left(x^5+x\right)^{2/3}+2 x^2\right)}{4 \sqrt[3]{2}}",1,"Integrate[(1 + x^2)/((-1 + x^2)*(x + x^5)^(1/3)), x]","F",-1
1754,0,0,118,1.0742171,"\int \frac{\left(-1+x^2\right) \sqrt[4]{x^2+x^6}}{x^2 \left(1+x^2\right)} \, dx","Integrate[((-1 + x^2)*(x^2 + x^6)^(1/4))/(x^2*(1 + x^2)),x]","\int \frac{\left(-1+x^2\right) \sqrt[4]{x^2+x^6}}{x^2 \left(1+x^2\right)} \, dx","\frac{2 \sqrt[4]{x^6+x^2}}{x}-\frac{\tan ^{-1}\left(\frac{2^{3/4} x \sqrt[4]{x^6+x^2}}{\sqrt{2} x^2-\sqrt{x^6+x^2}}\right)}{\sqrt[4]{2}}-\frac{\tanh ^{-1}\left(\frac{\frac{x^2}{\sqrt[4]{2}}+\frac{\sqrt{x^6+x^2}}{2^{3/4}}}{x \sqrt[4]{x^6+x^2}}\right)}{\sqrt[4]{2}}",1,"Integrate[((-1 + x^2)*(x^2 + x^6)^(1/4))/(x^2*(1 + x^2)), x]","F",-1
1755,0,0,118,0.3990808,"\int \frac{\left(-1+x^2\right) \sqrt[4]{x^2+x^6}}{x^2 \left(1+x^2\right)} \, dx","Integrate[((-1 + x^2)*(x^2 + x^6)^(1/4))/(x^2*(1 + x^2)),x]","\int \frac{\left(-1+x^2\right) \sqrt[4]{x^2+x^6}}{x^2 \left(1+x^2\right)} \, dx","\frac{2 \sqrt[4]{x^6+x^2}}{x}-\frac{\tan ^{-1}\left(\frac{2^{3/4} x \sqrt[4]{x^6+x^2}}{\sqrt{2} x^2-\sqrt{x^6+x^2}}\right)}{\sqrt[4]{2}}-\frac{\tanh ^{-1}\left(\frac{\frac{x^2}{\sqrt[4]{2}}+\frac{\sqrt{x^6+x^2}}{2^{3/4}}}{x \sqrt[4]{x^6+x^2}}\right)}{\sqrt[4]{2}}",1,"Integrate[((-1 + x^2)*(x^2 + x^6)^(1/4))/(x^2*(1 + x^2)), x]","F",-1
1756,1,125,118,0.2204287,"\int \frac{\left(-1+x^3\right)^{2/3} \left(1-5 x^3+4 x^6\right)}{x^6 \left(-1+2 x^3\right)^2} \, dx","Integrate[((-1 + x^3)^(2/3)*(1 - 5*x^3 + 4*x^6))/(x^6*(-1 + 2*x^3)^2),x]","\frac{7}{18} \left(2 \log \left(\frac{x}{\sqrt[3]{1-x^3}}+1\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{1-x^3}}-1}{\sqrt{3}}\right)-\log \left(-\frac{x}{\sqrt[3]{1-x^3}}+\frac{x^2}{\left(1-x^3\right)^{2/3}}+1\right)\right)+\frac{\left(x^3-1\right)^{2/3} \left(62 x^6-33 x^3+6\right)}{30 x^5 \left(2 x^3-1\right)}","\frac{7}{9} \log \left(\sqrt[3]{x^3-1}+x\right)+\frac{7 \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-1}-x}\right)}{3 \sqrt{3}}-\frac{7}{18} \log \left(-\sqrt[3]{x^3-1} x+\left(x^3-1\right)^{2/3}+x^2\right)+\frac{\left(x^3-1\right)^{2/3} \left(62 x^6-33 x^3+6\right)}{30 x^5 \left(2 x^3-1\right)}",1,"((-1 + x^3)^(2/3)*(6 - 33*x^3 + 62*x^6))/(30*x^5*(-1 + 2*x^3)) + (7*(2*Sqrt[3]*ArcTan[(-1 + (2*x)/(1 - x^3)^(1/3))/Sqrt[3]] - Log[1 + x^2/(1 - x^3)^(2/3) - x/(1 - x^3)^(1/3)] + 2*Log[1 + x/(1 - x^3)^(1/3)]))/18","A",0
1757,1,143,118,0.255174,"\int \frac{\sqrt{1+x} \sqrt{1+\sqrt{1+x}}}{x-\sqrt{1+x}} \, dx","Integrate[(Sqrt[1 + x]*Sqrt[1 + Sqrt[1 + x]])/(x - Sqrt[1 + x]),x]","\frac{4}{3} \sqrt{\sqrt{x+1}+1} \left(\sqrt{x+1}+4\right)-\sqrt{\frac{2}{5} \left(3+\sqrt{5}\right)} \left(3 \sqrt{5}-7\right) \tanh ^{-1}\left(\sqrt{\frac{2}{3-\sqrt{5}}} \sqrt{\sqrt{x+1}+1}\right)-2 \sqrt{\frac{2}{5 \left(3+\sqrt{5}\right)}} \left(7+3 \sqrt{5}\right) \tanh ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} \sqrt{\sqrt{x+1}+1}\right)","\frac{4}{3} \sqrt{x+1} \sqrt{\sqrt{x+1}+1}+\frac{16}{3} \sqrt{\sqrt{x+1}+1}-\frac{4}{5} \left(2 \sqrt{5}-5\right) \tanh ^{-1}\left(\frac{2 \sqrt{\sqrt{x+1}+1}}{\sqrt{5}-1}\right)-\frac{4}{5} \left(5+2 \sqrt{5}\right) \tanh ^{-1}\left(\frac{2 \sqrt{\sqrt{x+1}+1}}{1+\sqrt{5}}\right)",1,"(4*Sqrt[1 + Sqrt[1 + x]]*(4 + Sqrt[1 + x]))/3 - Sqrt[(2*(3 + Sqrt[5]))/5]*(-7 + 3*Sqrt[5])*ArcTanh[Sqrt[2/(3 - Sqrt[5])]*Sqrt[1 + Sqrt[1 + x]]] - 2*Sqrt[2/(5*(3 + Sqrt[5]))]*(7 + 3*Sqrt[5])*ArcTanh[Sqrt[2/(3 + Sqrt[5])]*Sqrt[1 + Sqrt[1 + x]]]","A",0
1758,1,102,118,0.1342101,"\int \frac{\sqrt{b+a x}}{\sqrt{a b x+\sqrt{b+a x}}} \, dx","Integrate[Sqrt[b + a*x]/Sqrt[a*b*x + Sqrt[b + a*x]],x]","\frac{\left(4 b^3+3\right) \tanh ^{-1}\left(\frac{2 b \sqrt{a x+b}+1}{2 \sqrt{b} \sqrt{a b x+\sqrt{a x+b}}}\right)+2 \sqrt{b} \sqrt{a b x+\sqrt{a x+b}} \left(2 b \sqrt{a x+b}-3\right)}{4 a b^{5/2}}","\frac{\sqrt{b (a x+b)+\sqrt{a x+b}-b^2} \left(2 b \sqrt{a x+b}-3\right)}{2 a b^2}+\frac{\left(-4 b^3-3\right) \log \left(2 \sqrt{b} \sqrt{b (a x+b)+\sqrt{a x+b}-b^2}-2 b \sqrt{a x+b}-1\right)}{4 a b^{5/2}}",1,"(2*Sqrt[b]*Sqrt[a*b*x + Sqrt[b + a*x]]*(-3 + 2*b*Sqrt[b + a*x]) + (3 + 4*b^3)*ArcTanh[(1 + 2*b*Sqrt[b + a*x])/(2*Sqrt[b]*Sqrt[a*b*x + Sqrt[b + a*x]])])/(4*a*b^(5/2))","A",1
1759,0,0,118,0.1433871,"\int \frac{\sqrt{b+a^2 x^4}}{\sqrt{a x^2+\sqrt{b+a^2 x^4}}} \, dx","Integrate[Sqrt[b + a^2*x^4]/Sqrt[a*x^2 + Sqrt[b + a^2*x^4]],x]","\int \frac{\sqrt{b+a^2 x^4}}{\sqrt{a x^2+\sqrt{b+a^2 x^4}}} \, dx","\frac{1}{4} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+\frac{b x}{8 \left(\sqrt{a^2 x^4+b}+a x^2\right)^{3/2}}+\frac{5 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}}{\sqrt{b}}\right)}{8 \sqrt{2} \sqrt{a}}",1,"Integrate[Sqrt[b + a^2*x^4]/Sqrt[a*x^2 + Sqrt[b + a^2*x^4]], x]","F",-1
1760,1,388,118,24.3340331,"\int \frac{1}{(f+e x) \sqrt{d+\sqrt{c+\sqrt{b+a x}}}} \, dx","Integrate[1/((f + e*x)*Sqrt[d + Sqrt[c + Sqrt[b + a*x]]]),x]","\text{RootSum}\left[\text{$\#$1}^8 a f-\text{$\#$1}^8 b e+\text{$\#$1}^8 c^2 e-2 \text{$\#$1}^8 c d^2 e+\text{$\#$1}^8 d^4 e+4 \text{$\#$1}^6 c d e-4 \text{$\#$1}^6 d^3 e-2 \text{$\#$1}^4 c e+6 \text{$\#$1}^4 d^2 e-4 \text{$\#$1}^2 d e+e\&,\frac{\text{$\#$1}^6 d^3 \log \left(\frac{1}{\sqrt{\sqrt{\sqrt{a x+b}+c}+d}}-\text{$\#$1}\right)-\text{$\#$1}^6 c d \log \left(\frac{1}{\sqrt{\sqrt{\sqrt{a x+b}+c}+d}}-\text{$\#$1}\right)-3 \text{$\#$1}^4 d^2 \log \left(\frac{1}{\sqrt{\sqrt{\sqrt{a x+b}+c}+d}}-\text{$\#$1}\right)+\text{$\#$1}^4 c \log \left(\frac{1}{\sqrt{\sqrt{\sqrt{a x+b}+c}+d}}-\text{$\#$1}\right)+3 \text{$\#$1}^2 d \log \left(\frac{1}{\sqrt{\sqrt{\sqrt{a x+b}+c}+d}}-\text{$\#$1}\right)-\log \left(\frac{1}{\sqrt{\sqrt{\sqrt{a x+b}+c}+d}}-\text{$\#$1}\right)}{\text{$\#$1}^7 a f-\text{$\#$1}^7 b e+\text{$\#$1}^7 c^2 e-2 \text{$\#$1}^7 c d^2 e+\text{$\#$1}^7 d^4 e+3 \text{$\#$1}^5 c d e-3 \text{$\#$1}^5 d^3 e-\text{$\#$1}^3 c e+3 \text{$\#$1}^3 d^2 e-\text{$\#$1} d e}\&\right]","\frac{\text{RootSum}\left[\text{$\#$1}^8 (-e)+4 \text{$\#$1}^6 d e+2 \text{$\#$1}^4 c e-6 \text{$\#$1}^4 d^2 e-4 \text{$\#$1}^2 c d e+4 \text{$\#$1}^2 d^3 e-a f+b e-c^2 e+2 c d^2 e-d^4 e\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{a x+b}+c}+d}-\text{$\#$1}\right)}{\text{$\#$1}}\&\right]}{e}",1,"RootSum[e - 4*d*e*#1^2 - 2*c*e*#1^4 + 6*d^2*e*#1^4 + 4*c*d*e*#1^6 - 4*d^3*e*#1^6 - b*e*#1^8 + c^2*e*#1^8 - 2*c*d^2*e*#1^8 + d^4*e*#1^8 + a*f*#1^8 & , (-Log[1/Sqrt[d + Sqrt[c + Sqrt[b + a*x]]] - #1] + 3*d*Log[1/Sqrt[d + Sqrt[c + Sqrt[b + a*x]]] - #1]*#1^2 + c*Log[1/Sqrt[d + Sqrt[c + Sqrt[b + a*x]]] - #1]*#1^4 - 3*d^2*Log[1/Sqrt[d + Sqrt[c + Sqrt[b + a*x]]] - #1]*#1^4 - c*d*Log[1/Sqrt[d + Sqrt[c + Sqrt[b + a*x]]] - #1]*#1^6 + d^3*Log[1/Sqrt[d + Sqrt[c + Sqrt[b + a*x]]] - #1]*#1^6)/(-(d*e*#1) - c*e*#1^3 + 3*d^2*e*#1^3 + 3*c*d*e*#1^5 - 3*d^3*e*#1^5 - b*e*#1^7 + c^2*e*#1^7 - 2*c*d^2*e*#1^7 + d^4*e*#1^7 + a*f*#1^7) & ]","B",1
1761,0,0,119,6.9834461,"\int \frac{-a b+(-a+2 b) x}{\sqrt[4]{x (-a+x) (-b+x)^2} \left(-b^2+(2 b-a d) x+(-1+d) x^2\right)} \, dx","Integrate[(-(a*b) + (-a + 2*b)*x)/((x*(-a + x)*(-b + x)^2)^(1/4)*(-b^2 + (2*b - a*d)*x + (-1 + d)*x^2)),x]","\int \frac{-a b+(-a+2 b) x}{\sqrt[4]{x (-a+x) (-b+x)^2} \left(-b^2+(2 b-a d) x+(-1+d) x^2\right)} \, dx","\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}}{b-x}\right)}{d^{3/4}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}}{b-x}\right)}{d^{3/4}}",1,"Integrate[(-(a*b) + (-a + 2*b)*x)/((x*(-a + x)*(-b + x)^2)^(1/4)*(-b^2 + (2*b - a*d)*x + (-1 + d)*x^2)), x]","F",-1
1762,1,77,119,0.028705,"\int x^{13} \sqrt[3]{-1+x^3} \, dx","Integrate[x^13*(-1 + x^3)^(1/3),x]","\frac{x^2 \sqrt[3]{x^3-1} \left(220 \, _2F_1\left(-\frac{1}{3},\frac{2}{3};\frac{5}{3};x^3\right)+\sqrt[3]{1-x^3} \left(324 x^{12}-27 x^9-33 x^6-44 x^3-220\right)\right)}{4860 \sqrt[3]{1-x^3}}","\frac{22 \log \left(\sqrt[3]{x^3-1}-x\right)}{2187}+\frac{22 \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-1}+x}\right)}{729 \sqrt{3}}-\frac{11 \log \left(\sqrt[3]{x^3-1} x+\left(x^3-1\right)^{2/3}+x^2\right)}{2187}+\frac{\sqrt[3]{x^3-1} \left(972 x^{14}-81 x^{11}-99 x^8-132 x^5-220 x^2\right)}{14580}",1,"(x^2*(-1 + x^3)^(1/3)*((1 - x^3)^(1/3)*(-220 - 44*x^3 - 33*x^6 - 27*x^9 + 324*x^12) + 220*Hypergeometric2F1[-1/3, 2/3, 5/3, x^3]))/(4860*(1 - x^3)^(1/3))","C",1
1763,0,0,119,4.950937,"\int \frac{a b^2-2 (2 a-b) b x+(3 a-2 b) x^2}{\sqrt[4]{x (-a+x) (-b+x)^2} \left(a^3+\left(-3 a^2+b^2 d\right) x+(3 a-2 b d) x^2+(-1+d) x^3\right)} \, dx","Integrate[(a*b^2 - 2*(2*a - b)*b*x + (3*a - 2*b)*x^2)/((x*(-a + x)*(-b + x)^2)^(1/4)*(a^3 + (-3*a^2 + b^2*d)*x + (3*a - 2*b*d)*x^2 + (-1 + d)*x^3)),x]","\int \frac{a b^2-2 (2 a-b) b x+(3 a-2 b) x^2}{\sqrt[4]{x (-a+x) (-b+x)^2} \left(a^3+\left(-3 a^2+b^2 d\right) x+(3 a-2 b d) x^2+(-1+d) x^3\right)} \, dx","\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}}{a-x}\right)}{d^{3/4}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}}{a-x}\right)}{d^{3/4}}",1,"Integrate[(a*b^2 - 2*(2*a - b)*b*x + (3*a - 2*b)*x^2)/((x*(-a + x)*(-b + x)^2)^(1/4)*(a^3 + (-3*a^2 + b^2*d)*x + (3*a - 2*b*d)*x^2 + (-1 + d)*x^3)), x]","F",-1
1764,1,453,119,0.6469553,"\int \frac{\sqrt[3]{x+2 x^3} \left(-1+x^4\right)}{x^4 \left(2-x^2+x^4\right)} \, dx","Integrate[((x + 2*x^3)^(1/3)*(-1 + x^4))/(x^4*(2 - x^2 + x^4)),x]","\frac{3 \sqrt[3]{2 x^3+x} \left(\frac{\left(-5 \sqrt{7}+7 i\right) \left(\left(6 \left(2+i \sqrt{7}\right) x^2+3 i \sqrt{7}-5\right) x^2 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{2 \left(-2 i+\sqrt{7}\right) x^2}{\left(-i+\sqrt{7}\right) \left(2 x^2+1\right)}\right)+3 \left(\left(4+2 i \sqrt{7}\right) x^2-3 i \sqrt{7}+5\right) x^2 \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};\frac{2 \left(-2 i+\sqrt{7}\right) x^2}{\left(-i+\sqrt{7}\right) \left(2 x^2+1\right)}\right)+2 \left(2 x^2+1\right) \left(\left(-3-3 i \sqrt{7}\right) x^2-i \sqrt{7}+3\right)\right)}{-\sqrt{7}+5 i}+\frac{\left(5 \sqrt{7}+7 i\right) \left(-\left(\left(6 i \left(\sqrt{7}+2 i\right) x^2+3 i \sqrt{7}+5\right) x^2 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{2 \left(2 i+\sqrt{7}\right) x^2}{\left(i+\sqrt{7}\right) \left(2 x^2+1\right)}\right)\right)+3 \left(\left(4-2 i \sqrt{7}\right) x^2+3 i \sqrt{7}+5\right) x^2 \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};\frac{2 \left(2 i+\sqrt{7}\right) x^2}{\left(i+\sqrt{7}\right) \left(2 x^2+1\right)}\right)+2 \left(2 x^2+1\right) \left(3 i \left(\sqrt{7}+i\right) x^2+i \sqrt{7}+3\right)\right)}{\sqrt{7}+5 i}-28 \left(2 x^2+1\right)^2\right)}{224 x^3 \left(2 x^2+1\right)}","\frac{1}{8} \text{RootSum}\left[2 \text{$\#$1}^6-9 \text{$\#$1}^3+11\&,\frac{-\text{$\#$1}^3 \log \left(\sqrt[3]{2 x^3+x}-\text{$\#$1} x\right)+\text{$\#$1}^3 \log (x)-11 \log \left(\sqrt[3]{2 x^3+x}-\text{$\#$1} x\right)+11 \log (x)}{4 \text{$\#$1}^5-9 \text{$\#$1}^2}\&\right]+\frac{3 \sqrt[3]{2 x^3+x} \left(4 x^2+1\right)}{16 x^3}",1,"(3*(x + 2*x^3)^(1/3)*(-28*(1 + 2*x^2)^2 + ((7*I - 5*Sqrt[7])*(2*(1 + 2*x^2)*(3 - I*Sqrt[7] + (-3 - (3*I)*Sqrt[7])*x^2) + x^2*(-5 + (3*I)*Sqrt[7] + 6*(2 + I*Sqrt[7])*x^2)*Hypergeometric2F1[2/3, 1, 5/3, (2*(-2*I + Sqrt[7])*x^2)/((-I + Sqrt[7])*(1 + 2*x^2))] + 3*x^2*(5 - (3*I)*Sqrt[7] + (4 + (2*I)*Sqrt[7])*x^2)*Hypergeometric2F1[2/3, 2, 5/3, (2*(-2*I + Sqrt[7])*x^2)/((-I + Sqrt[7])*(1 + 2*x^2))]))/(5*I - Sqrt[7]) + ((7*I + 5*Sqrt[7])*(2*(1 + 2*x^2)*(3 + I*Sqrt[7] + (3*I)*(I + Sqrt[7])*x^2) - x^2*(5 + (3*I)*Sqrt[7] + (6*I)*(2*I + Sqrt[7])*x^2)*Hypergeometric2F1[2/3, 1, 5/3, (2*(2*I + Sqrt[7])*x^2)/((I + Sqrt[7])*(1 + 2*x^2))] + 3*x^2*(5 + (3*I)*Sqrt[7] + (4 - (2*I)*Sqrt[7])*x^2)*Hypergeometric2F1[2/3, 2, 5/3, (2*(2*I + Sqrt[7])*x^2)/((I + Sqrt[7])*(1 + 2*x^2))]))/(5*I + Sqrt[7])))/(224*x^3*(1 + 2*x^2))","C",0
1765,0,0,119,1.080095,"\int \frac{b+2 a x^4}{\left(-b+a x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Integrate[(b + 2*a*x^4)/((-b + a*x^4)*(b*x^2 + a*x^4)^(1/4)),x]","\int \frac{b+2 a x^4}{\left(-b+a x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","\frac{3}{4} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2-a b\&,\frac{\log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]+\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{\sqrt[4]{a}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{\sqrt[4]{a}}",1,"Integrate[(b + 2*a*x^4)/((-b + a*x^4)*(b*x^2 + a*x^4)^(1/4)), x]","F",-1
1766,0,0,119,0.3212225,"\int \frac{b+2 a x^4}{\left(-b+a x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Integrate[(b + 2*a*x^4)/((-b + a*x^4)*(b*x^2 + a*x^4)^(1/4)),x]","\int \frac{b+2 a x^4}{\left(-b+a x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","\frac{3}{4} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2-a b\&,\frac{\log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]+\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{\sqrt[4]{a}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{\sqrt[4]{a}}",1,"Integrate[(b + 2*a*x^4)/((-b + a*x^4)*(b*x^2 + a*x^4)^(1/4)), x]","F",-1
1767,0,0,119,0.5637364,"\int \frac{\left(1+x^6\right) \left(-1-x^3+x^6\right)^{2/3}}{x^3 \left(-1+x^6\right)} \, dx","Integrate[((1 + x^6)*(-1 - x^3 + x^6)^(2/3))/(x^3*(-1 + x^6)),x]","\int \frac{\left(1+x^6\right) \left(-1-x^3+x^6\right)^{2/3}}{x^3 \left(-1+x^6\right)} \, dx","\frac{1}{3} \log \left(\sqrt[3]{x^6-x^3-1}+x\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^6-x^3-1}-x}\right)}{\sqrt{3}}+\frac{\left(x^6-x^3-1\right)^{2/3}}{2 x^2}-\frac{1}{6} \log \left(x^2-\sqrt[3]{x^6-x^3-1} x+\left(x^6-x^3-1\right)^{2/3}\right)",1,"Integrate[((1 + x^6)*(-1 - x^3 + x^6)^(2/3))/(x^3*(-1 + x^6)), x]","F",-1
1768,0,0,119,0.303654,"\int \frac{\left(4+x^6\right) \sqrt[4]{-2-x^4+x^6}}{x^2 \left(-2+x^6\right)} \, dx","Integrate[((4 + x^6)*(-2 - x^4 + x^6)^(1/4))/(x^2*(-2 + x^6)),x]","\int \frac{\left(4+x^6\right) \sqrt[4]{-2-x^4+x^6}}{x^2 \left(-2+x^6\right)} \, dx","\frac{2 \sqrt[4]{x^6-x^4-2}}{x}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{x^6-x^4-2}}{\sqrt{x^6-x^4-2}-x^2}\right)}{\sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{x^6-x^4-2}}{x^2+\sqrt{x^6-x^4-2}}\right)}{\sqrt{2}}",1,"Integrate[((4 + x^6)*(-2 - x^4 + x^6)^(1/4))/(x^2*(-2 + x^6)), x]","F",-1
1769,1,47,119,0.0156694,"\int \sqrt[4]{b x^7+a x^8} \, dx","Integrate[(b*x^7 + a*x^8)^(1/4),x]","\frac{4 x \sqrt[4]{x^7 (a x+b)} \, _2F_1\left(-\frac{1}{4},\frac{11}{4};\frac{15}{4};-\frac{a x}{b}\right)}{11 \sqrt[4]{\frac{a x}{b}+1}}","\frac{7 b^3 \tan ^{-1}\left(\frac{\sqrt[4]{a x^8+b x^7}}{\sqrt[4]{a} x^2}\right)}{64 a^{11/4}}+\frac{7 b^3 \tanh ^{-1}\left(\frac{\sqrt[4]{a x^8+b x^7}}{\sqrt[4]{a} x^2}\right)}{64 a^{11/4}}+\frac{\left(32 a^2 x^2+4 a b x-7 b^2\right) \sqrt[4]{a x^8+b x^7}}{96 a^2 x}",1,"(4*x*(x^7*(b + a*x))^(1/4)*Hypergeometric2F1[-1/4, 11/4, 15/4, -((a*x)/b)])/(11*(1 + (a*x)/b)^(1/4))","C",1
1770,1,375,119,0.7602387,"\int \frac{-1+x^{10}}{\sqrt{1+x^4} \left(1+x^{10}\right)} \, dx","Integrate[(-1 + x^10)/(Sqrt[1 + x^4]*(1 + x^10)),x]","\frac{\sqrt[4]{-1} \left(\left(-4-\sqrt[5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}\right) F\left(\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+2 \left(\Pi \left(-i;\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+\left(2-\sqrt[5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}\right) \Pi \left(-\sqrt[10]{-1};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)-(-1)^{4/5} \Pi \left((-1)^{3/10};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+(-1)^{3/5} \Pi \left((-1)^{3/10};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)-(-1)^{2/5} \Pi \left((-1)^{3/10};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+\sqrt[5]{-1} \Pi \left((-1)^{3/10};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+\Pi \left((-1)^{7/10};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)-(-1)^{4/5} \Pi \left(-(-1)^{9/10};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+(-1)^{3/5} \Pi \left(-(-1)^{9/10};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)-(-1)^{2/5} \Pi \left(-(-1)^{9/10};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+\sqrt[5]{-1} \Pi \left(-(-1)^{9/10};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)\right)\right)}{4+\sqrt[5]{-1}-(-1)^{2/5}+(-1)^{3/5}-(-1)^{4/5}}","-\frac{\tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{5 \sqrt{2}}-\frac{1}{5} \sqrt{2 \left(1+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}} x}{\sqrt{x^4+1}}\right)-\frac{1}{5} \sqrt{2 \left(\sqrt{5}-1\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{2}+\frac{\sqrt{5}}{2}} x}{\sqrt{x^4+1}}\right)",1,"((-1)^(1/4)*((-4 - (-1)^(1/5) + (-1)^(2/5) - (-1)^(3/5) + (-1)^(4/5))*EllipticF[I*ArcSinh[(-1)^(1/4)*x], -1] + 2*(EllipticPi[-I, I*ArcSinh[(-1)^(1/4)*x], -1] + (2 - (-1)^(1/5) + (-1)^(2/5) - (-1)^(3/5) + (-1)^(4/5))*EllipticPi[-(-1)^(1/10), I*ArcSinh[(-1)^(1/4)*x], -1] + (-1)^(1/5)*EllipticPi[(-1)^(3/10), I*ArcSinh[(-1)^(1/4)*x], -1] - (-1)^(2/5)*EllipticPi[(-1)^(3/10), I*ArcSinh[(-1)^(1/4)*x], -1] + (-1)^(3/5)*EllipticPi[(-1)^(3/10), I*ArcSinh[(-1)^(1/4)*x], -1] - (-1)^(4/5)*EllipticPi[(-1)^(3/10), I*ArcSinh[(-1)^(1/4)*x], -1] + EllipticPi[(-1)^(7/10), I*ArcSinh[(-1)^(1/4)*x], -1] + (-1)^(1/5)*EllipticPi[-(-1)^(9/10), I*ArcSinh[(-1)^(1/4)*x], -1] - (-1)^(2/5)*EllipticPi[-(-1)^(9/10), I*ArcSinh[(-1)^(1/4)*x], -1] + (-1)^(3/5)*EllipticPi[-(-1)^(9/10), I*ArcSinh[(-1)^(1/4)*x], -1] - (-1)^(4/5)*EllipticPi[-(-1)^(9/10), I*ArcSinh[(-1)^(1/4)*x], -1])))/(4 + (-1)^(1/5) - (-1)^(2/5) + (-1)^(3/5) - (-1)^(4/5))","C",0
1771,1,371,119,0.6622558,"\int \frac{1+x^{10}}{\sqrt{1+x^4} \left(-1+x^{10}\right)} \, dx","Integrate[(1 + x^10)/(Sqrt[1 + x^4]*(-1 + x^10)),x]","\frac{\sqrt[4]{-1} \left(\left(-4-\sqrt[5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}\right) F\left(\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+2 \left(\Pi \left(i;\left.\sin ^{-1}\left((-1)^{3/4} x\right)\right|-1\right)+\left(2-\sqrt[5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}\right) \Pi \left(\sqrt[10]{-1};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)-(-1)^{4/5} \Pi \left(-(-1)^{3/10};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+(-1)^{3/5} \Pi \left(-(-1)^{3/10};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)-(-1)^{2/5} \Pi \left(-(-1)^{3/10};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+\sqrt[5]{-1} \Pi \left(-(-1)^{3/10};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+\Pi \left(-(-1)^{7/10};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)-(-1)^{4/5} \Pi \left((-1)^{9/10};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+(-1)^{3/5} \Pi \left((-1)^{9/10};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)-(-1)^{2/5} \Pi \left((-1)^{9/10};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+\sqrt[5]{-1} \Pi \left((-1)^{9/10};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)\right)\right)}{4+\sqrt[5]{-1}-(-1)^{2/5}+(-1)^{3/5}-(-1)^{4/5}}","-\frac{1}{5} \sqrt{2 \left(\sqrt{5}-1\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{1}{2}+\frac{\sqrt{5}}{2}} x}{\sqrt{x^4+1}}\right)-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{5 \sqrt{2}}-\frac{1}{5} \sqrt{2 \left(1+\sqrt{5}\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}} x}{\sqrt{x^4+1}}\right)",1,"((-1)^(1/4)*((-4 - (-1)^(1/5) + (-1)^(2/5) - (-1)^(3/5) + (-1)^(4/5))*EllipticF[I*ArcSinh[(-1)^(1/4)*x], -1] + 2*(EllipticPi[I, ArcSin[(-1)^(3/4)*x], -1] + (2 - (-1)^(1/5) + (-1)^(2/5) - (-1)^(3/5) + (-1)^(4/5))*EllipticPi[(-1)^(1/10), I*ArcSinh[(-1)^(1/4)*x], -1] + (-1)^(1/5)*EllipticPi[-(-1)^(3/10), I*ArcSinh[(-1)^(1/4)*x], -1] - (-1)^(2/5)*EllipticPi[-(-1)^(3/10), I*ArcSinh[(-1)^(1/4)*x], -1] + (-1)^(3/5)*EllipticPi[-(-1)^(3/10), I*ArcSinh[(-1)^(1/4)*x], -1] - (-1)^(4/5)*EllipticPi[-(-1)^(3/10), I*ArcSinh[(-1)^(1/4)*x], -1] + EllipticPi[-(-1)^(7/10), I*ArcSinh[(-1)^(1/4)*x], -1] + (-1)^(1/5)*EllipticPi[(-1)^(9/10), I*ArcSinh[(-1)^(1/4)*x], -1] - (-1)^(2/5)*EllipticPi[(-1)^(9/10), I*ArcSinh[(-1)^(1/4)*x], -1] + (-1)^(3/5)*EllipticPi[(-1)^(9/10), I*ArcSinh[(-1)^(1/4)*x], -1] - (-1)^(4/5)*EllipticPi[(-1)^(9/10), I*ArcSinh[(-1)^(1/4)*x], -1])))/(4 + (-1)^(1/5) - (-1)^(2/5) + (-1)^(3/5) - (-1)^(4/5))","C",0
1772,1,227,119,1.1814628,"\int \frac{1+x^{16}}{\sqrt{1+x^4} \left(-1+x^{16}\right)} \, dx","Integrate[(1 + x^16)/(Sqrt[1 + x^4]*(-1 + x^16)),x]","\left(\frac{1}{8}+\frac{i}{8}\right) \left(-\frac{(1-i) x}{\sqrt{x^4+1}}-3 \sqrt{2} F\left(\left.i \sinh ^{-1}\left(\frac{(1+i) x}{\sqrt{2}}\right)\right|-1\right)+\sqrt{2} \Pi \left(-i;\left.i \sinh ^{-1}\left(\frac{(1+i) x}{\sqrt{2}}\right)\right|-1\right)+\sqrt{2} \Pi \left(i;\left.i \sinh ^{-1}\left(\frac{(1+i) x}{\sqrt{2}}\right)\right|-1\right)+\sqrt{2} \Pi \left(-\frac{1+i}{\sqrt{2}};\left.i \sinh ^{-1}\left(\frac{(1+i) x}{\sqrt{2}}\right)\right|-1\right)+\sqrt{2} \Pi \left(-\frac{1-i}{\sqrt{2}};\left.i \sinh ^{-1}\left(\frac{(1+i) x}{\sqrt{2}}\right)\right|-1\right)+\sqrt{2} \Pi \left(\frac{1-i}{\sqrt{2}};\left.i \sinh ^{-1}\left(\frac{(1+i) x}{\sqrt{2}}\right)\right|-1\right)+\sqrt{2} \Pi \left(\frac{1+i}{\sqrt{2}};\left.i \sinh ^{-1}\left(\frac{(1+i) x}{\sqrt{2}}\right)\right|-1\right)\right)","-\frac{x}{4 \sqrt{x^4+1}}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt{x^4+1}}\right)}{4 \sqrt[4]{2}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{8 \sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt{x^4+1}}\right)}{4 \sqrt[4]{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{8 \sqrt{2}}",1,"(1/8 + I/8)*(((-1 + I)*x)/Sqrt[1 + x^4] - 3*Sqrt[2]*EllipticF[I*ArcSinh[((1 + I)*x)/Sqrt[2]], -1] + Sqrt[2]*EllipticPi[-I, I*ArcSinh[((1 + I)*x)/Sqrt[2]], -1] + Sqrt[2]*EllipticPi[I, I*ArcSinh[((1 + I)*x)/Sqrt[2]], -1] + Sqrt[2]*EllipticPi[(-1 - I)/Sqrt[2], I*ArcSinh[((1 + I)*x)/Sqrt[2]], -1] + Sqrt[2]*EllipticPi[(-1 + I)/Sqrt[2], I*ArcSinh[((1 + I)*x)/Sqrt[2]], -1] + Sqrt[2]*EllipticPi[(1 - I)/Sqrt[2], I*ArcSinh[((1 + I)*x)/Sqrt[2]], -1] + Sqrt[2]*EllipticPi[(1 + I)/Sqrt[2], I*ArcSinh[((1 + I)*x)/Sqrt[2]], -1])","C",1
1773,1,96,119,0.2009691,"\int \frac{\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}}{1-\sqrt{b+a x}} \, dx","Integrate[(Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]])/(1 - Sqrt[b + a*x]),x]","\frac{60 \sqrt{c+1} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a x+b}+c}}{\sqrt{c+1}}\right)-4 \sqrt{\sqrt{a x+b}+c} \left(c \left(\sqrt{a x+b}+5\right)+5 \sqrt{a x+b}+3 a x+3 b-2 c^2+15\right)}{15 a}","-\frac{4 \left(3 a x+3 b-2 c^2+5 c+15\right) \sqrt{\sqrt{a x+b}+c}}{15 a}-\frac{4 (c+5) \sqrt{a x+b} \sqrt{\sqrt{a x+b}+c}}{15 a}-\frac{4 \sqrt{-c-1} \tan ^{-1}\left(\frac{\sqrt{-c-1} \sqrt{\sqrt{a x+b}+c}}{c+1}\right)}{a}",1,"(-4*Sqrt[c + Sqrt[b + a*x]]*(15 + 3*b - 2*c^2 + 3*a*x + 5*Sqrt[b + a*x] + c*(5 + Sqrt[b + a*x])) + 60*Sqrt[1 + c]*ArcTanh[Sqrt[c + Sqrt[b + a*x]]/Sqrt[1 + c]])/(15*a)","A",1
1774,1,238,119,2.1193543,"\int x \sqrt{-1+x^2} \sqrt{x^2+x \sqrt{-1+x^2}} \, dx","Integrate[x*Sqrt[-1 + x^2]*Sqrt[x^2 + x*Sqrt[-1 + x^2]],x]","\frac{\sqrt{x^2-1} \left(\sqrt{x^2-1}+x\right)^4 \left(\sqrt{2} \sqrt{x \left(\sqrt{x^2-1}+x\right)} \left(192 x^6-360 x^4+212 x^2+104 \sqrt{x^2-1} x+192 \sqrt{x^2-1} x^5-264 \sqrt{x^2-1} x^3-39\right)-39 \left(4 x^3+4 \sqrt{x^2-1} x^2-\sqrt{x^2-1}-3 x\right) \sinh ^{-1}\left(\sqrt{x^2-1}+x\right)\right)}{192 \sqrt{2} \left(64 x^8-144 x^6+104 x^4-25 x^2-7 \sqrt{x^2-1} x+64 \sqrt{x^2-1} x^7-112 \sqrt{x^2-1} x^5+56 \sqrt{x^2-1} x^3+1\right)}","\frac{1}{192} \sqrt{x^2-1} \sqrt{x^2+\sqrt{x^2-1} x} \left(56 x^2-39\right)+\frac{13 \log \left(\sqrt{x^2-1}-\sqrt{2} \sqrt{x^2+\sqrt{x^2-1} x}+x\right)}{64 \sqrt{2}}+\frac{1}{192} \left(13 x-8 x^3\right) \sqrt{x^2+\sqrt{x^2-1} x}",1,"(Sqrt[-1 + x^2]*(x + Sqrt[-1 + x^2])^4*(Sqrt[2]*Sqrt[x*(x + Sqrt[-1 + x^2])]*(-39 + 212*x^2 - 360*x^4 + 192*x^6 + 104*x*Sqrt[-1 + x^2] - 264*x^3*Sqrt[-1 + x^2] + 192*x^5*Sqrt[-1 + x^2]) - 39*(-3*x + 4*x^3 - Sqrt[-1 + x^2] + 4*x^2*Sqrt[-1 + x^2])*ArcSinh[x + Sqrt[-1 + x^2]]))/(192*Sqrt[2]*(1 - 25*x^2 + 104*x^4 - 144*x^6 + 64*x^8 - 7*x*Sqrt[-1 + x^2] + 56*x^3*Sqrt[-1 + x^2] - 112*x^5*Sqrt[-1 + x^2] + 64*x^7*Sqrt[-1 + x^2]))","A",1
1775,1,354,119,0.2742082,"\int \frac{\left(-q+p x^2\right) \sqrt{q^2+p^2 x^4} \left(b x^3+a \left(q+p x^2\right)^3\right)}{x^6} \, dx","Integrate[((-q + p*x^2)*Sqrt[q^2 + p^2*x^4]*(b*x^3 + a*(q + p*x^2)^3))/x^6,x]","\frac{6 a q^4 \sqrt{p^2 x^4+q^2} \, _2F_1\left(-\frac{5}{4},-\frac{1}{2};-\frac{1}{4};-\frac{p^2 x^4}{q^2}\right)+20 a p q^3 x^2 \sqrt{p^2 x^4+q^2} \, _2F_1\left(-\frac{3}{4},-\frac{1}{2};\frac{1}{4};-\frac{p^2 x^4}{q^2}\right)+10 a p^4 x^8 \sqrt{p^2 x^4+q^2} \, _2F_1\left(-\frac{1}{2},\frac{3}{4};\frac{7}{4};-\frac{p^2 x^4}{q^2}\right)+60 a p^3 q x^6 \sqrt{p^2 x^4+q^2} \, _2F_1\left(-\frac{1}{2},\frac{1}{4};\frac{5}{4};-\frac{p^2 x^4}{q^2}\right)+15 b p x^5 \sqrt{p^2 x^4+q^2} \sqrt{\frac{p^2 x^4}{q^2}+1}-15 b p q x^5 \sqrt{\frac{p^2 x^4}{q^2}+1} \tanh ^{-1}\left(\frac{\sqrt{p^2 x^4+q^2}}{q}\right)+15 b q x^3 \sqrt{p^2 x^4+q^2} \sqrt{\frac{p^2 x^4}{q^2}+1}-15 b p x^5 \sqrt{p^2 x^4+q^2} \sinh ^{-1}\left(\frac{p x^2}{q}\right)}{30 x^5 \sqrt{\frac{p^2 x^4}{q^2}+1}}","\frac{\sqrt{p^2 x^4+q^2} \left(6 a p^4 x^8+20 a p^3 q x^6+12 a p^2 q^2 x^4+20 a p q^3 x^2+6 a q^4+15 b p x^5+15 b q x^3\right)}{30 x^5}-b p q \log \left(\sqrt{p^2 x^4+q^2}+p x^2+q\right)+b p q \log (x)",1,"(15*b*q*x^3*Sqrt[q^2 + p^2*x^4]*Sqrt[1 + (p^2*x^4)/q^2] + 15*b*p*x^5*Sqrt[q^2 + p^2*x^4]*Sqrt[1 + (p^2*x^4)/q^2] - 15*b*p*x^5*Sqrt[q^2 + p^2*x^4]*ArcSinh[(p*x^2)/q] - 15*b*p*q*x^5*Sqrt[1 + (p^2*x^4)/q^2]*ArcTanh[Sqrt[q^2 + p^2*x^4]/q] + 6*a*q^4*Sqrt[q^2 + p^2*x^4]*Hypergeometric2F1[-5/4, -1/2, -1/4, -((p^2*x^4)/q^2)] + 20*a*p*q^3*x^2*Sqrt[q^2 + p^2*x^4]*Hypergeometric2F1[-3/4, -1/2, 1/4, -((p^2*x^4)/q^2)] + 60*a*p^3*q*x^6*Sqrt[q^2 + p^2*x^4]*Hypergeometric2F1[-1/2, 1/4, 5/4, -((p^2*x^4)/q^2)] + 10*a*p^4*x^8*Sqrt[q^2 + p^2*x^4]*Hypergeometric2F1[-1/2, 3/4, 7/4, -((p^2*x^4)/q^2)])/(30*x^5*Sqrt[1 + (p^2*x^4)/q^2])","C",1
1776,1,247,119,1.7567579,"\int \frac{\left(-1+x^2\right) \sqrt{x^2+\sqrt{1+x^4}}}{\sqrt{1+x^4}} \, dx","Integrate[((-1 + x^2)*Sqrt[x^2 + Sqrt[1 + x^4]])/Sqrt[1 + x^4],x]","\frac{\sqrt{x^2 \left(\sqrt{x^4+1}+x^2\right)} \left(\left(\left(\sqrt{x^4+1}+x^2\right)^2+1\right)^2 \left(\log \left(1-\frac{\sqrt{x^2 \left(\sqrt{x^4+1}+x^2\right)}}{\sqrt{2} x^2}\right)-\log \left(\frac{\sqrt{x^2 \left(\sqrt{x^4+1}+x^2\right)}}{\sqrt{2} x^2}+1\right)\right)+4 \left(x^4+1\right) \left(2 x^4+2 \sqrt{x^4+1} x^2+1\right) \left(\sqrt{2} \sqrt{x^2 \left(\sqrt{x^4+1}+x^2\right)}-\tan ^{-1}\left(\sqrt{\left(\sqrt{x^4+1}+x^2\right)^2-1}\right)\right)\right)}{8 \sqrt{2} \sqrt{x^4+1} \left(\sqrt{x^4+1}+x^2\right)^{3/2} \left(x^5+\sqrt{x^4+1} x^3+x\right)}","\frac{1}{2} \sqrt{\sqrt{x^4+1}+x^2} x-\frac{\tan ^{-1}\left(\frac{\sqrt{2} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)}{\sqrt{2}}-\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)",1,"(Sqrt[x^2*(x^2 + Sqrt[1 + x^4])]*(4*(1 + x^4)*(1 + 2*x^4 + 2*x^2*Sqrt[1 + x^4])*(Sqrt[2]*Sqrt[x^2*(x^2 + Sqrt[1 + x^4])] - ArcTan[Sqrt[-1 + (x^2 + Sqrt[1 + x^4])^2]]) + (1 + (x^2 + Sqrt[1 + x^4])^2)^2*(Log[1 - Sqrt[x^2*(x^2 + Sqrt[1 + x^4])]/(Sqrt[2]*x^2)] - Log[1 + Sqrt[x^2*(x^2 + Sqrt[1 + x^4])]/(Sqrt[2]*x^2)])))/(8*Sqrt[2]*Sqrt[1 + x^4]*(x^2 + Sqrt[1 + x^4])^(3/2)*(x + x^5 + x^3*Sqrt[1 + x^4]))","B",1
1777,1,128,119,0.1724586,"\int \frac{x \sqrt{1+x}}{x+\sqrt{1+\sqrt{1+x}}} \, dx","Integrate[(x*Sqrt[1 + x])/(x + Sqrt[1 + Sqrt[1 + x]]),x]","\frac{1}{15} \left(10 \left(\sqrt{x+1} x+\sqrt{x+1}-2 \sqrt{x+1} \sqrt{\sqrt{x+1}+1}-2 \sqrt{\sqrt{x+1}+1}-2\right)-6 \left(\sqrt{5}-5\right) \log \left(2 \sqrt{\sqrt{x+1}+1}-\sqrt{5}+1\right)+6 \left(5+\sqrt{5}\right) \log \left(2 \sqrt{\sqrt{x+1}+1}+\sqrt{5}+1\right)\right)","\sqrt{x+1} \left(\frac{2 (x+1)}{3}-\frac{4}{3} \sqrt{\sqrt{x+1}+1}\right)-\frac{4}{3} \sqrt{\sqrt{x+1}+1}-\frac{2}{5} \left(\sqrt{5}-5\right) \log \left(-2 \sqrt{\sqrt{x+1}+1}+\sqrt{5}-1\right)+\frac{2}{5} \left(5+\sqrt{5}\right) \log \left(2 \sqrt{\sqrt{x+1}+1}+\sqrt{5}+1\right)",1,"(10*(-2 + Sqrt[1 + x] + x*Sqrt[1 + x] - 2*Sqrt[1 + Sqrt[1 + x]] - 2*Sqrt[1 + x]*Sqrt[1 + Sqrt[1 + x]]) - 6*(-5 + Sqrt[5])*Log[1 - Sqrt[5] + 2*Sqrt[1 + Sqrt[1 + x]]] + 6*(5 + Sqrt[5])*Log[1 + Sqrt[5] + 2*Sqrt[1 + Sqrt[1 + x]]])/15","A",1
1778,1,356,120,0.5726749,"\int \frac{\sqrt[3]{-x+x^3} \left(8-10 x^2+x^4\right)}{x^4 \left(4-2 x^2+x^4\right)} \, dx","Integrate[((-x + x^3)^(1/3)*(8 - 10*x^2 + x^4))/(x^4*(4 - 2*x^2 + x^4)),x]","\frac{-\left(\sqrt{3}+6 i\right) \left(\left(3 \sqrt{3} x^2+\sqrt{3}+3 i\right) x^2 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{\sqrt{3} x^2}{\left(-i+\sqrt{3}\right) \left(x^2-1\right)}\right)-3 \left(-\sqrt{3} x^2+\sqrt{3}+3 i\right) x^2 \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};\frac{\sqrt{3} x^2}{\left(-i+\sqrt{3}\right) \left(x^2-1\right)}\right)-2 \left(x^2-1\right) \left(3 \left(\sqrt{3}-i\right) x^2+2 \left(\sqrt{3}+i\right)\right)\right)-\left(-\sqrt{3}+6 i\right) \left(-\left(\left(3 \sqrt{3} x^2+\sqrt{3}-3 i\right) x^2 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{\sqrt{3} x^2}{\left(i+\sqrt{3}\right) \left(x^2-1\right)}\right)\right)-3 \left(\sqrt{3} x^2-\sqrt{3}+3 i\right) x^2 \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};\frac{\sqrt{3} x^2}{\left(i+\sqrt{3}\right) \left(x^2-1\right)}\right)+2 \left(x^2-1\right) \left(3 \left(\sqrt{3}+i\right) x^2+2 \left(\sqrt{3}-i\right)\right)\right)+24 \left(x^2-1\right)^2}{64 x^2 \left(x \left(x^2-1\right)\right)^{2/3}}","\frac{3 \left(4 x^2-1\right) \sqrt[3]{x^3-x}}{4 x^3}-\frac{1}{8} \text{RootSum}\left[4 \text{$\#$1}^6-6 \text{$\#$1}^3+3\&,\frac{-4 \text{$\#$1}^3 \log \left(\sqrt[3]{x^3-x}-\text{$\#$1} x\right)+4 \text{$\#$1}^3 \log (x)+9 \log \left(\sqrt[3]{x^3-x}-\text{$\#$1} x\right)-9 \log (x)}{4 \text{$\#$1}^5-3 \text{$\#$1}^2}\&\right]",1,"(24*(-1 + x^2)^2 - (6*I + Sqrt[3])*(-2*(-1 + x^2)*(2*(I + Sqrt[3]) + 3*(-I + Sqrt[3])*x^2) + x^2*(3*I + Sqrt[3] + 3*Sqrt[3]*x^2)*Hypergeometric2F1[2/3, 1, 5/3, (Sqrt[3]*x^2)/((-I + Sqrt[3])*(-1 + x^2))] - 3*x^2*(3*I + Sqrt[3] - Sqrt[3]*x^2)*Hypergeometric2F1[2/3, 2, 5/3, (Sqrt[3]*x^2)/((-I + Sqrt[3])*(-1 + x^2))]) - (6*I - Sqrt[3])*(2*(-1 + x^2)*(2*(-I + Sqrt[3]) + 3*(I + Sqrt[3])*x^2) - x^2*(-3*I + Sqrt[3] + 3*Sqrt[3]*x^2)*Hypergeometric2F1[2/3, 1, 5/3, (Sqrt[3]*x^2)/((I + Sqrt[3])*(-1 + x^2))] - 3*x^2*(3*I - Sqrt[3] + Sqrt[3]*x^2)*Hypergeometric2F1[2/3, 2, 5/3, (Sqrt[3]*x^2)/((I + Sqrt[3])*(-1 + x^2))]))/(64*x^2*(x*(-1 + x^2))^(2/3))","C",0
1779,1,356,120,0.227924,"\int \frac{\sqrt[3]{-x+x^3} \left(8-10 x^2+x^4\right)}{x^4 \left(4-2 x^2+x^4\right)} \, dx","Integrate[((-x + x^3)^(1/3)*(8 - 10*x^2 + x^4))/(x^4*(4 - 2*x^2 + x^4)),x]","\frac{-\left(\sqrt{3}+6 i\right) \left(\left(3 \sqrt{3} x^2+\sqrt{3}+3 i\right) x^2 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{\sqrt{3} x^2}{\left(-i+\sqrt{3}\right) \left(x^2-1\right)}\right)-3 \left(-\sqrt{3} x^2+\sqrt{3}+3 i\right) x^2 \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};\frac{\sqrt{3} x^2}{\left(-i+\sqrt{3}\right) \left(x^2-1\right)}\right)-2 \left(x^2-1\right) \left(3 \left(\sqrt{3}-i\right) x^2+2 \left(\sqrt{3}+i\right)\right)\right)-\left(-\sqrt{3}+6 i\right) \left(-\left(\left(3 \sqrt{3} x^2+\sqrt{3}-3 i\right) x^2 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{\sqrt{3} x^2}{\left(i+\sqrt{3}\right) \left(x^2-1\right)}\right)\right)-3 \left(\sqrt{3} x^2-\sqrt{3}+3 i\right) x^2 \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};\frac{\sqrt{3} x^2}{\left(i+\sqrt{3}\right) \left(x^2-1\right)}\right)+2 \left(x^2-1\right) \left(3 \left(\sqrt{3}+i\right) x^2+2 \left(\sqrt{3}-i\right)\right)\right)+24 \left(x^2-1\right)^2}{64 x^2 \left(x \left(x^2-1\right)\right)^{2/3}}","\frac{3 \left(4 x^2-1\right) \sqrt[3]{x^3-x}}{4 x^3}-\frac{1}{8} \text{RootSum}\left[4 \text{$\#$1}^6-6 \text{$\#$1}^3+3\&,\frac{-4 \text{$\#$1}^3 \log \left(\sqrt[3]{x^3-x}-\text{$\#$1} x\right)+4 \text{$\#$1}^3 \log (x)+9 \log \left(\sqrt[3]{x^3-x}-\text{$\#$1} x\right)-9 \log (x)}{4 \text{$\#$1}^5-3 \text{$\#$1}^2}\&\right]",1,"(24*(-1 + x^2)^2 - (6*I + Sqrt[3])*(-2*(-1 + x^2)*(2*(I + Sqrt[3]) + 3*(-I + Sqrt[3])*x^2) + x^2*(3*I + Sqrt[3] + 3*Sqrt[3]*x^2)*Hypergeometric2F1[2/3, 1, 5/3, (Sqrt[3]*x^2)/((-I + Sqrt[3])*(-1 + x^2))] - 3*x^2*(3*I + Sqrt[3] - Sqrt[3]*x^2)*Hypergeometric2F1[2/3, 2, 5/3, (Sqrt[3]*x^2)/((-I + Sqrt[3])*(-1 + x^2))]) - (6*I - Sqrt[3])*(2*(-1 + x^2)*(2*(-I + Sqrt[3]) + 3*(I + Sqrt[3])*x^2) - x^2*(-3*I + Sqrt[3] + 3*Sqrt[3]*x^2)*Hypergeometric2F1[2/3, 1, 5/3, (Sqrt[3]*x^2)/((I + Sqrt[3])*(-1 + x^2))] - 3*x^2*(3*I - Sqrt[3] + Sqrt[3]*x^2)*Hypergeometric2F1[2/3, 2, 5/3, (Sqrt[3]*x^2)/((I + Sqrt[3])*(-1 + x^2))]))/(64*x^2*(x*(-1 + x^2))^(2/3))","C",0
1780,1,3242,120,1.8102373,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{1-x-x^2+x^3+x^4}} \, dx","Integrate[(-1 + x^2)/((1 + x^2)*Sqrt[1 - x - x^2 + x^3 + x^4]),x]","\text{Result too large to show}","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^4+14 \text{$\#$1}^2-16 \text{$\#$1}+5\&,\frac{\text{$\#$1}^2 \log \left(-\text{$\#$1} x-x^2+\sqrt{x^4+x^3-x^2-x+1}+1\right)+\text{$\#$1}^2 (-\log (x))-\log \left(-\text{$\#$1} x-x^2+\sqrt{x^4+x^3-x^2-x+1}+1\right)+\log (x)}{\text{$\#$1}^3+7 \text{$\#$1}-4}\&\right]",1,"(2*(x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])^2*Sqrt[((Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])*(x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 3, 0]))/((x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 3, 0]))]*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0])*Sqrt[((x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])*(x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))/((x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])^2*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0])^2)]*(((-I)*(EllipticF[ArcSin[Sqrt[((x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))/((x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))]], -(((Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 3, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))/((-Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 3, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0])))]*(-I + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0]) + EllipticPi[((-I + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))/((-I + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0])), ArcSin[Sqrt[((x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))/((x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))]], -(((Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 3, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))/((-Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 3, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0])))]*(-Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])))/((-I + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0])*(-I + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0])) + (I*(EllipticF[ArcSin[Sqrt[((x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))/((x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))]], -(((Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 3, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))/((-Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 3, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0])))]*(I + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0]) + EllipticPi[((I + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))/((I + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0])), ArcSin[Sqrt[((x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))/((x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))]], -(((Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 3, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))/((-Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 3, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0])))]*(-Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])))/((I + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0])*(I + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0])) + EllipticF[ArcSin[Sqrt[((x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))/((x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))]], ((Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 3, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))/((Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 3, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))]/(-Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0])))/(Sqrt[1 - x - x^2 + x^3 + x^4]*(-Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0]))","C",0
1781,1,3242,120,1.2811573,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{1-x-x^2+x^3+x^4}} \, dx","Integrate[(-1 + x^2)/((1 + x^2)*Sqrt[1 - x - x^2 + x^3 + x^4]),x]","\text{Result too large to show}","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^4+14 \text{$\#$1}^2-16 \text{$\#$1}+5\&,\frac{\text{$\#$1}^2 \log \left(-\text{$\#$1} x-x^2+\sqrt{x^4+x^3-x^2-x+1}+1\right)+\text{$\#$1}^2 (-\log (x))-\log \left(-\text{$\#$1} x-x^2+\sqrt{x^4+x^3-x^2-x+1}+1\right)+\log (x)}{\text{$\#$1}^3+7 \text{$\#$1}-4}\&\right]",1,"(2*(x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])^2*Sqrt[((Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])*(x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 3, 0]))/((x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 3, 0]))]*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0])*Sqrt[((x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])*(x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))/((x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])^2*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0])^2)]*(((-I)*(EllipticF[ArcSin[Sqrt[((x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))/((x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))]], -(((Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 3, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))/((-Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 3, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0])))]*(-I + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0]) + EllipticPi[((-I + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))/((-I + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0])), ArcSin[Sqrt[((x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))/((x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))]], -(((Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 3, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))/((-Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 3, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0])))]*(-Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])))/((-I + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0])*(-I + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0])) + (I*(EllipticF[ArcSin[Sqrt[((x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))/((x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))]], -(((Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 3, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))/((-Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 3, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0])))]*(I + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0]) + EllipticPi[((I + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))/((I + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0])), ArcSin[Sqrt[((x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))/((x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))]], -(((Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 3, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))/((-Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 3, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0])))]*(-Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])))/((I + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0])*(I + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0])) + EllipticF[ArcSin[Sqrt[((x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))/((x - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))]], ((Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 3, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))/((Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 3, 0])*(Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] - Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0]))]/(-Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0] + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 4, 0])))/(Sqrt[1 - x - x^2 + x^3 + x^4]*(-Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 1, 0] + Root[1 - #1 - #1^2 + #1^3 + #1^4 & , 2, 0]))","C",0
1782,1,13896,120,6.3070562,"\int \frac{-1+x^4}{\left(1+x^4\right) \sqrt{1-x-x^2+x^3+x^4}} \, dx","Integrate[(-1 + x^4)/((1 + x^4)*Sqrt[1 - x - x^2 + x^3 + x^4]),x]","\text{Result too large to show}","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^4+6 \text{$\#$1}^2-8 \text{$\#$1}+3\&,\frac{\text{$\#$1}^2 \log \left(-\text{$\#$1} x-x^2+\sqrt{x^4+x^3-x^2-x+1}+1\right)+\text{$\#$1}^2 (-\log (x))-\log \left(-\text{$\#$1} x-x^2+\sqrt{x^4+x^3-x^2-x+1}+1\right)+\log (x)}{\text{$\#$1}^3+3 \text{$\#$1}-2}\&\right]",1,"Result too large to show","C",0
1783,1,13896,120,6.2961197,"\int \frac{-1+x^4}{\left(1+x^4\right) \sqrt{1-x-x^2+x^3+x^4}} \, dx","Integrate[(-1 + x^4)/((1 + x^4)*Sqrt[1 - x - x^2 + x^3 + x^4]),x]","\text{Result too large to show}","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^4+6 \text{$\#$1}^2-8 \text{$\#$1}+3\&,\frac{\text{$\#$1}^2 \log \left(-\text{$\#$1} x-x^2+\sqrt{x^4+x^3-x^2-x+1}+1\right)+\text{$\#$1}^2 (-\log (x))-\log \left(-\text{$\#$1} x-x^2+\sqrt{x^4+x^3-x^2-x+1}+1\right)+\log (x)}{\text{$\#$1}^3+3 \text{$\#$1}-2}\&\right]",1,"Result too large to show","C",0
1784,1,65,120,0.1199671,"\int \frac{b+a x^8}{x^6 \left(-b+a x^4\right) \left(b+a x^4\right)^{3/4}} \, dx","Integrate[(b + a*x^8)/(x^6*(-b + a*x^4)*(b + a*x^4)^(3/4)),x]","\frac{3 \left(a x^4+b\right)^2-5 a x^8 (a+b) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{2 a x^4}{a x^4+b}\right)}{15 b^2 x^5 \left(a x^4+b\right)^{3/4}}","\frac{\left(a^{5/4}+\sqrt[4]{a} b\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{2\ 2^{3/4} b^2}-\frac{\left(a^{5/4}+\sqrt[4]{a} b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{2\ 2^{3/4} b^2}+\frac{\left(a x^4+b\right)^{5/4}}{5 b^2 x^5}",1,"(3*(b + a*x^4)^2 - 5*a*(a + b)*x^8*Hypergeometric2F1[3/4, 1, 7/4, (2*a*x^4)/(b + a*x^4)])/(15*b^2*x^5*(b + a*x^4)^(3/4))","C",1
1785,1,527,120,1.4505817,"\int \frac{-b+2 a x^4}{\sqrt[4]{-b+a x^4} \left(-2 b-c x^4+2 a x^8\right)} \, dx","Integrate[(-b + 2*a*x^4)/((-b + a*x^4)^(1/4)*(-2*b - c*x^4 + 2*a*x^8)),x]","a^{3/4} \left(\frac{\left(\sqrt{16 a b+c^2}+2 b-c\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{\sqrt{16 a b+c^2}+4 b-c}}{\sqrt[4]{\sqrt{16 a b+c^2}-c} \sqrt[4]{a x^4-b}}\right)}{\sqrt{16 a b+c^2} \left(\sqrt{16 a b+c^2}-c\right)^{3/4} \sqrt[4]{\sqrt{16 a b+c^2}+4 b-c}}-\frac{\left(\frac{c-2 b}{\sqrt{16 a b+c^2}}+1\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{\sqrt{16 a b+c^2}-4 b+c}}{\sqrt[4]{\sqrt{16 a b+c^2}+c} \sqrt[4]{a x^4-b}}\right)}{\left(\sqrt{16 a b+c^2}+c\right)^{3/4} \sqrt[4]{\sqrt{16 a b+c^2}-4 b+c}}+\frac{\left(\sqrt{16 a b+c^2}+2 b-c\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{\sqrt{16 a b+c^2}+4 b-c}}{\sqrt[4]{\sqrt{16 a b+c^2}-c} \sqrt[4]{a x^4-b}}\right)}{\sqrt{16 a b+c^2} \left(\sqrt{16 a b+c^2}-c\right)^{3/4} \sqrt[4]{\sqrt{16 a b+c^2}+4 b-c}}-\frac{\left(\frac{c-2 b}{\sqrt{16 a b+c^2}}+1\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{\sqrt{16 a b+c^2}-4 b+c}}{\sqrt[4]{\sqrt{16 a b+c^2}+c} \sqrt[4]{a x^4-b}}\right)}{\left(\sqrt{16 a b+c^2}+c\right)^{3/4} \sqrt[4]{\sqrt{16 a b+c^2}-4 b+c}}\right)","\frac{1}{4} \text{RootSum}\left[2 \text{$\#$1}^8-4 \text{$\#$1}^4 a-\text{$\#$1}^4 c+2 a^2-2 a b+a c\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))+a \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)-a \log (x)}{-4 \text{$\#$1}^5+4 \text{$\#$1} a+\text{$\#$1} c}\&\right]",1,"a^(3/4)*(((2*b - c + Sqrt[16*a*b + c^2])*ArcTan[(a^(1/4)*(4*b - c + Sqrt[16*a*b + c^2])^(1/4)*x)/((-c + Sqrt[16*a*b + c^2])^(1/4)*(-b + a*x^4)^(1/4))])/(Sqrt[16*a*b + c^2]*(-c + Sqrt[16*a*b + c^2])^(3/4)*(4*b - c + Sqrt[16*a*b + c^2])^(1/4)) - ((1 + (-2*b + c)/Sqrt[16*a*b + c^2])*ArcTan[(a^(1/4)*(-4*b + c + Sqrt[16*a*b + c^2])^(1/4)*x)/((c + Sqrt[16*a*b + c^2])^(1/4)*(-b + a*x^4)^(1/4))])/((c + Sqrt[16*a*b + c^2])^(3/4)*(-4*b + c + Sqrt[16*a*b + c^2])^(1/4)) + ((2*b - c + Sqrt[16*a*b + c^2])*ArcTanh[(a^(1/4)*(4*b - c + Sqrt[16*a*b + c^2])^(1/4)*x)/((-c + Sqrt[16*a*b + c^2])^(1/4)*(-b + a*x^4)^(1/4))])/(Sqrt[16*a*b + c^2]*(-c + Sqrt[16*a*b + c^2])^(3/4)*(4*b - c + Sqrt[16*a*b + c^2])^(1/4)) - ((1 + (-2*b + c)/Sqrt[16*a*b + c^2])*ArcTanh[(a^(1/4)*(-4*b + c + Sqrt[16*a*b + c^2])^(1/4)*x)/((c + Sqrt[16*a*b + c^2])^(1/4)*(-b + a*x^4)^(1/4))])/((c + Sqrt[16*a*b + c^2])^(3/4)*(-4*b + c + Sqrt[16*a*b + c^2])^(1/4)))","B",1
1786,1,527,120,0.4411942,"\int \frac{-b+2 a x^4}{\sqrt[4]{-b+a x^4} \left(-2 b-c x^4+2 a x^8\right)} \, dx","Integrate[(-b + 2*a*x^4)/((-b + a*x^4)^(1/4)*(-2*b - c*x^4 + 2*a*x^8)),x]","a^{3/4} \left(\frac{\left(\sqrt{16 a b+c^2}+2 b-c\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{\sqrt{16 a b+c^2}+4 b-c}}{\sqrt[4]{\sqrt{16 a b+c^2}-c} \sqrt[4]{a x^4-b}}\right)}{\sqrt{16 a b+c^2} \left(\sqrt{16 a b+c^2}-c\right)^{3/4} \sqrt[4]{\sqrt{16 a b+c^2}+4 b-c}}-\frac{\left(\frac{c-2 b}{\sqrt{16 a b+c^2}}+1\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{\sqrt{16 a b+c^2}-4 b+c}}{\sqrt[4]{\sqrt{16 a b+c^2}+c} \sqrt[4]{a x^4-b}}\right)}{\left(\sqrt{16 a b+c^2}+c\right)^{3/4} \sqrt[4]{\sqrt{16 a b+c^2}-4 b+c}}+\frac{\left(\sqrt{16 a b+c^2}+2 b-c\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{\sqrt{16 a b+c^2}+4 b-c}}{\sqrt[4]{\sqrt{16 a b+c^2}-c} \sqrt[4]{a x^4-b}}\right)}{\sqrt{16 a b+c^2} \left(\sqrt{16 a b+c^2}-c\right)^{3/4} \sqrt[4]{\sqrt{16 a b+c^2}+4 b-c}}-\frac{\left(\frac{c-2 b}{\sqrt{16 a b+c^2}}+1\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{\sqrt{16 a b+c^2}-4 b+c}}{\sqrt[4]{\sqrt{16 a b+c^2}+c} \sqrt[4]{a x^4-b}}\right)}{\left(\sqrt{16 a b+c^2}+c\right)^{3/4} \sqrt[4]{\sqrt{16 a b+c^2}-4 b+c}}\right)","\frac{1}{4} \text{RootSum}\left[2 \text{$\#$1}^8-4 \text{$\#$1}^4 a-\text{$\#$1}^4 c+2 a^2-2 a b+a c\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))+a \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)-a \log (x)}{-4 \text{$\#$1}^5+4 \text{$\#$1} a+\text{$\#$1} c}\&\right]",1,"a^(3/4)*(((2*b - c + Sqrt[16*a*b + c^2])*ArcTan[(a^(1/4)*(4*b - c + Sqrt[16*a*b + c^2])^(1/4)*x)/((-c + Sqrt[16*a*b + c^2])^(1/4)*(-b + a*x^4)^(1/4))])/(Sqrt[16*a*b + c^2]*(-c + Sqrt[16*a*b + c^2])^(3/4)*(4*b - c + Sqrt[16*a*b + c^2])^(1/4)) - ((1 + (-2*b + c)/Sqrt[16*a*b + c^2])*ArcTan[(a^(1/4)*(-4*b + c + Sqrt[16*a*b + c^2])^(1/4)*x)/((c + Sqrt[16*a*b + c^2])^(1/4)*(-b + a*x^4)^(1/4))])/((c + Sqrt[16*a*b + c^2])^(3/4)*(-4*b + c + Sqrt[16*a*b + c^2])^(1/4)) + ((2*b - c + Sqrt[16*a*b + c^2])*ArcTanh[(a^(1/4)*(4*b - c + Sqrt[16*a*b + c^2])^(1/4)*x)/((-c + Sqrt[16*a*b + c^2])^(1/4)*(-b + a*x^4)^(1/4))])/(Sqrt[16*a*b + c^2]*(-c + Sqrt[16*a*b + c^2])^(3/4)*(4*b - c + Sqrt[16*a*b + c^2])^(1/4)) - ((1 + (-2*b + c)/Sqrt[16*a*b + c^2])*ArcTanh[(a^(1/4)*(-4*b + c + Sqrt[16*a*b + c^2])^(1/4)*x)/((c + Sqrt[16*a*b + c^2])^(1/4)*(-b + a*x^4)^(1/4))])/((c + Sqrt[16*a*b + c^2])^(3/4)*(-4*b + c + Sqrt[16*a*b + c^2])^(1/4)))","B",1
1787,0,0,121,6.8971942,"\int \frac{-a b-a c+3 b c+2 (a-b-c) x+x^2}{\sqrt[4]{(-a+x) (-b+x) (-c+x)} \left(-a^3-b c d+\left(3 a^2+b d+c d\right) x-(3 a+d) x^2+x^3\right)} \, dx","Integrate[(-(a*b) - a*c + 3*b*c + 2*(a - b - c)*x + x^2)/(((-a + x)*(-b + x)*(-c + x))^(1/4)*(-a^3 - b*c*d + (3*a^2 + b*d + c*d)*x - (3*a + d)*x^2 + x^3)),x]","\int \frac{-a b-a c+3 b c+2 (a-b-c) x+x^2}{\sqrt[4]{(-a+x) (-b+x) (-c+x)} \left(-a^3-b c d+\left(3 a^2+b d+c d\right) x-(3 a+d) x^2+x^3\right)} \, dx","\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{x^2 (-a-b-c)+x (a b+a c+b c)-a b c+x^3}}{a-x}\right)}{d^{3/4}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{x^2 (-a-b-c)+x (a b+a c+b c)-a b c+x^3}}{a-x}\right)}{d^{3/4}}",1,"Integrate[(-(a*b) - a*c + 3*b*c + 2*(a - b - c)*x + x^2)/(((-a + x)*(-b + x)*(-c + x))^(1/4)*(-a^3 - b*c*d + (3*a^2 + b*d + c*d)*x - (3*a + d)*x^2 + x^3)), x]","F",-1
1788,0,0,121,0.619537,"\int \frac{1}{(-b+a x) \sqrt[4]{b^2 x+a^2 x^3}} \, dx","Integrate[1/((-b + a*x)*(b^2*x + a^2*x^3)^(1/4)),x]","\int \frac{1}{(-b+a x) \sqrt[4]{b^2 x+a^2 x^3}} \, dx","\frac{\tan ^{-1}\left(\frac{2^{3/4} \sqrt[4]{a} \sqrt[4]{b} \sqrt[4]{a^2 x^3+b^2 x}}{a x+b}\right)}{2 \sqrt[4]{2} a^{3/4} b^{3/4}}-\frac{\tanh ^{-1}\left(\frac{2^{3/4} \sqrt[4]{a} \sqrt[4]{b} \sqrt[4]{a^2 x^3+b^2 x}}{a x+b}\right)}{2 \sqrt[4]{2} a^{3/4} b^{3/4}}",1,"Integrate[1/((-b + a*x)*(b^2*x + a^2*x^3)^(1/4)), x]","F",-1
1789,1,871,121,1.6019573,"\int \frac{\left(2+x^2\right) \left(-2-2 x+x^2\right) \sqrt{4-3 x^2+x^4}}{x^2 \left(-2+x^2\right) \left(-4+x+2 x^2\right)} \, dx","Integrate[((2 + x^2)*(-2 - 2*x + x^2)*Sqrt[4 - 3*x^2 + x^4])/(x^2*(-2 + x^2)*(-4 + x + 2*x^2)),x]","\frac{8 \sqrt{-\frac{i}{3 i+\sqrt{7}}} x^4-24 \sqrt{-\frac{i}{3 i+\sqrt{7}}} x^2+10 \sqrt{-\frac{i}{3 i+\sqrt{7}}} \sqrt{x^4-3 x^2+4} \sinh ^{-1}\left(\frac{3-2 x^2}{\sqrt{7}}\right) x+10 \sqrt{-\frac{i}{3 i+\sqrt{7}}} \sqrt{x^4-3 x^2+4} \tanh ^{-1}\left(\frac{8-3 x^2}{4 \sqrt{x^4-3 x^2+4}}\right) x+10 \sqrt{-\frac{5 i}{3 i+\sqrt{7}}} \sqrt{x^4-3 x^2+4} \tanh ^{-1}\left(\frac{2 \left(5+\sqrt{33}\right) x^2-3 \sqrt{33}+13}{2 \sqrt{10 \left(17+\sqrt{33}\right)} \sqrt{x^4-3 x^2+4}}\right) x-10 \sqrt{-\frac{5 i}{3 i+\sqrt{7}}} \sqrt{x^4-3 x^2+4} \tanh ^{-1}\left(\frac{-2 \left(-5+\sqrt{33}\right) x^2+3 \sqrt{33}+13}{2 \sqrt{10} \sqrt{-\left(\left(-17+\sqrt{33}\right) \left(x^4-3 x^2+4\right)\right)}}\right) x-9 i \sqrt{\frac{2 i x^2}{-3 i+\sqrt{7}}+1} \sqrt{2-\frac{4 i x^2}{3 i+\sqrt{7}}} F\left(i \sinh ^{-1}\left(\sqrt{-\frac{2 i}{3 i+\sqrt{7}}} x\right)|\frac{3 i+\sqrt{7}}{3 i-\sqrt{7}}\right) x-32 i \sqrt{\frac{2 i x^2}{-3 i+\sqrt{7}}+1} \sqrt{2-\frac{4 i x^2}{3 i+\sqrt{7}}} \Pi \left(\frac{3}{4}-\frac{i \sqrt{7}}{4};i \sinh ^{-1}\left(\sqrt{-\frac{2 i}{3 i+\sqrt{7}}} x\right)|\frac{3 i+\sqrt{7}}{3 i-\sqrt{7}}\right) x+25 i \sqrt{\frac{2 i x^2}{-3 i+\sqrt{7}}+1} \sqrt{2-\frac{4 i x^2}{3 i+\sqrt{7}}} \Pi \left(\frac{4 i \left(3 i+\sqrt{7}\right)}{-17+\sqrt{33}};i \sinh ^{-1}\left(\sqrt{-\frac{2 i}{3 i+\sqrt{7}}} x\right)|\frac{3 i+\sqrt{7}}{3 i-\sqrt{7}}\right) x+25 i \sqrt{\frac{2 i x^2}{-3 i+\sqrt{7}}+1} \sqrt{2-\frac{4 i x^2}{3 i+\sqrt{7}}} \Pi \left(\frac{12-4 i \sqrt{7}}{17+\sqrt{33}};i \sinh ^{-1}\left(\sqrt{-\frac{2 i}{3 i+\sqrt{7}}} x\right)|\frac{3 i+\sqrt{7}}{3 i-\sqrt{7}}\right) x+32 \sqrt{-\frac{i}{3 i+\sqrt{7}}}}{16 \sqrt{-\frac{i}{3 i+\sqrt{7}}} x \sqrt{x^4-3 x^2+4}}","\frac{\sqrt{x^4-3 x^2+4}}{2 x}-\frac{5}{4} \log \left(x^2+\sqrt{x^4-3 x^2+4}-2\right)+4 \tanh ^{-1}\left(\frac{x}{x^2+\sqrt{x^4-3 x^2+4}-2}\right)-\frac{5}{2} \sqrt{5} \tanh ^{-1}\left(\frac{\sqrt{5} x}{2 x^2+2 \sqrt{x^4-3 x^2+4}+x-4}\right)+\frac{5 \log (x)}{4}",1,"(32*Sqrt[(-I)/(3*I + Sqrt[7])] - 24*Sqrt[(-I)/(3*I + Sqrt[7])]*x^2 + 8*Sqrt[(-I)/(3*I + Sqrt[7])]*x^4 + 10*Sqrt[(-I)/(3*I + Sqrt[7])]*x*Sqrt[4 - 3*x^2 + x^4]*ArcSinh[(3 - 2*x^2)/Sqrt[7]] + 10*Sqrt[(-I)/(3*I + Sqrt[7])]*x*Sqrt[4 - 3*x^2 + x^4]*ArcTanh[(8 - 3*x^2)/(4*Sqrt[4 - 3*x^2 + x^4])] + 10*Sqrt[(-5*I)/(3*I + Sqrt[7])]*x*Sqrt[4 - 3*x^2 + x^4]*ArcTanh[(13 - 3*Sqrt[33] + 2*(5 + Sqrt[33])*x^2)/(2*Sqrt[10*(17 + Sqrt[33])]*Sqrt[4 - 3*x^2 + x^4])] - 10*Sqrt[(-5*I)/(3*I + Sqrt[7])]*x*Sqrt[4 - 3*x^2 + x^4]*ArcTanh[(13 + 3*Sqrt[33] - 2*(-5 + Sqrt[33])*x^2)/(2*Sqrt[10]*Sqrt[-((-17 + Sqrt[33])*(4 - 3*x^2 + x^4))])] - (9*I)*x*Sqrt[1 + ((2*I)*x^2)/(-3*I + Sqrt[7])]*Sqrt[2 - ((4*I)*x^2)/(3*I + Sqrt[7])]*EllipticF[I*ArcSinh[Sqrt[(-2*I)/(3*I + Sqrt[7])]*x], (3*I + Sqrt[7])/(3*I - Sqrt[7])] - (32*I)*x*Sqrt[1 + ((2*I)*x^2)/(-3*I + Sqrt[7])]*Sqrt[2 - ((4*I)*x^2)/(3*I + Sqrt[7])]*EllipticPi[3/4 - (I/4)*Sqrt[7], I*ArcSinh[Sqrt[(-2*I)/(3*I + Sqrt[7])]*x], (3*I + Sqrt[7])/(3*I - Sqrt[7])] + (25*I)*x*Sqrt[1 + ((2*I)*x^2)/(-3*I + Sqrt[7])]*Sqrt[2 - ((4*I)*x^2)/(3*I + Sqrt[7])]*EllipticPi[((4*I)*(3*I + Sqrt[7]))/(-17 + Sqrt[33]), I*ArcSinh[Sqrt[(-2*I)/(3*I + Sqrt[7])]*x], (3*I + Sqrt[7])/(3*I - Sqrt[7])] + (25*I)*x*Sqrt[1 + ((2*I)*x^2)/(-3*I + Sqrt[7])]*Sqrt[2 - ((4*I)*x^2)/(3*I + Sqrt[7])]*EllipticPi[(12 - (4*I)*Sqrt[7])/(17 + Sqrt[33]), I*ArcSinh[Sqrt[(-2*I)/(3*I + Sqrt[7])]*x], (3*I + Sqrt[7])/(3*I - Sqrt[7])])/(16*Sqrt[(-I)/(3*I + Sqrt[7])]*x*Sqrt[4 - 3*x^2 + x^4])","C",0
1790,0,0,121,0.1982959,"\int \frac{1+x}{(-1+x) \sqrt[3]{x^2+x^4}} \, dx","Integrate[(1 + x)/((-1 + x)*(x^2 + x^4)^(1/3)),x]","\int \frac{1+x}{(-1+x) \sqrt[3]{x^2+x^4}} \, dx","\frac{\log \left(2^{2/3} \sqrt[3]{x^4+x^2}-2 x\right)}{\sqrt[3]{2}}-\frac{\log \left(2 x^2+2^{2/3} \sqrt[3]{x^4+x^2} x+\sqrt[3]{2} \left(x^4+x^2\right)^{2/3}\right)}{2 \sqrt[3]{2}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^4+x^2}+x}\right)}{\sqrt[3]{2}}",1,"Integrate[(1 + x)/((-1 + x)*(x^2 + x^4)^(1/3)), x]","F",-1
1791,1,234,121,1.2931669,"\int \frac{-b^2+a^4 x^4}{\sqrt{b x+a^2 x^3} \left(b^2+a^4 x^4\right)} \, dx","Integrate[(-b^2 + a^4*x^4)/(Sqrt[b*x + a^2*x^3]*(b^2 + a^4*x^4)),x]","-\frac{i x^{3/2} \sqrt{\frac{b}{a^2 x^2}+1} \left(2 F\left(\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i \sqrt{b}}{a}}}{\sqrt{x}}\right)\right|-1\right)-\Pi \left(-\sqrt[4]{-1};\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i \sqrt{b}}{a}}}{\sqrt{x}}\right)\right|-1\right)-\Pi \left(\sqrt[4]{-1};\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i \sqrt{b}}{a}}}{\sqrt{x}}\right)\right|-1\right)-\Pi \left(-(-1)^{3/4};\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i \sqrt{b}}{a}}}{\sqrt{x}}\right)\right|-1\right)-\Pi \left((-1)^{3/4};\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i \sqrt{b}}{a}}}{\sqrt{x}}\right)\right|-1\right)\right)}{\sqrt{\frac{i \sqrt{b}}{a}} \sqrt{x \left(a^2 x^2+b\right)}}","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{a} \sqrt[4]{b} \sqrt{a^2 x^3+b x}}{a^2 x^2+b}\right)}{\sqrt[4]{2} \sqrt{a} \sqrt[4]{b}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{a} \sqrt[4]{b} \sqrt{a^2 x^3+b x}}{a^2 x^2+b}\right)}{\sqrt[4]{2} \sqrt{a} \sqrt[4]{b}}",1,"((-I)*Sqrt[1 + b/(a^2*x^2)]*x^(3/2)*(2*EllipticF[I*ArcSinh[Sqrt[(I*Sqrt[b])/a]/Sqrt[x]], -1] - EllipticPi[-(-1)^(1/4), I*ArcSinh[Sqrt[(I*Sqrt[b])/a]/Sqrt[x]], -1] - EllipticPi[(-1)^(1/4), I*ArcSinh[Sqrt[(I*Sqrt[b])/a]/Sqrt[x]], -1] - EllipticPi[-(-1)^(3/4), I*ArcSinh[Sqrt[(I*Sqrt[b])/a]/Sqrt[x]], -1] - EllipticPi[(-1)^(3/4), I*ArcSinh[Sqrt[(I*Sqrt[b])/a]/Sqrt[x]], -1]))/(Sqrt[(I*Sqrt[b])/a]*Sqrt[x*(b + a^2*x^2)])","C",1
1792,0,0,121,0.4222975,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt[3]{x+x^5}} \, dx","Integrate[(-1 + x^2)/((1 + x^2)*(x + x^5)^(1/3)),x]","\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt[3]{x+x^5}} \, dx","-\frac{\log \left(2^{2/3} \sqrt[3]{x^5+x}+2 x\right)}{2 \sqrt[3]{2}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^5+x}-x}\right)}{2 \sqrt[3]{2}}+\frac{\log \left(2^{2/3} \sqrt[3]{x^5+x} x-\sqrt[3]{2} \left(x^5+x\right)^{2/3}-2 x^2\right)}{4 \sqrt[3]{2}}",1,"Integrate[(-1 + x^2)/((1 + x^2)*(x + x^5)^(1/3)), x]","F",-1
1793,0,0,121,7.4561047,"\int \frac{\left(1+x^4\right) \sqrt[4]{-x^2+x^4}}{1+x^4+x^8} \, dx","Integrate[((1 + x^4)*(-x^2 + x^4)^(1/4))/(1 + x^4 + x^8),x]","\int \frac{\left(1+x^4\right) \sqrt[4]{-x^2+x^4}}{1+x^4+x^8} \, dx","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4+3\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{x^4-x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{2 \text{$\#$1}^4-3}\&\right]+\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4+1\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{x^4-x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{2 \text{$\#$1}^4-1}\&\right]",1,"Integrate[((1 + x^4)*(-x^2 + x^4)^(1/4))/(1 + x^4 + x^8), x]","F",-1
1794,0,0,121,2.5880695,"\int \frac{\left(1+x^4\right) \sqrt[4]{-x^2+x^4}}{1+x^4+x^8} \, dx","Integrate[((1 + x^4)*(-x^2 + x^4)^(1/4))/(1 + x^4 + x^8),x]","\int \frac{\left(1+x^4\right) \sqrt[4]{-x^2+x^4}}{1+x^4+x^8} \, dx","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4+3\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{x^4-x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{2 \text{$\#$1}^4-3}\&\right]+\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4+1\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{x^4-x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{2 \text{$\#$1}^4-1}\&\right]",1,"Integrate[((1 + x^4)*(-x^2 + x^4)^(1/4))/(1 + x^4 + x^8), x]","F",-1
1795,1,223,121,0.2968601,"\int \frac{1-2 x^4+2 x^8}{\sqrt[4]{-1+x^4} \left(-2-x^4+2 x^8\right)} \, dx","Integrate[(1 - 2*x^4 + 2*x^8)/((-1 + x^4)^(1/4)*(-2 - x^4 + 2*x^8)),x]","\frac{1}{68} \left(34 \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-1}}\right)-\sqrt{17} \sqrt[4]{2047-439 \sqrt{17}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{2}{5+\sqrt{17}}} x}{\sqrt[4]{x^4-1}}\right)-\sqrt{17} \sqrt[4]{2047+439 \sqrt{17}} \tan ^{-1}\left(\frac{\sqrt[4]{5+\sqrt{17}} x}{\sqrt{2} \sqrt[4]{x^4-1}}\right)+34 \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-1}}\right)-\sqrt{17} \sqrt[4]{2047-439 \sqrt{17}} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{2}{5+\sqrt{17}}} x}{\sqrt[4]{x^4-1}}\right)-\sqrt{17} \sqrt[4]{2047+439 \sqrt{17}} \tanh ^{-1}\left(\frac{\sqrt[4]{5+\sqrt{17}} x}{\sqrt{2} \sqrt[4]{x^4-1}}\right)\right)","-\frac{1}{4} \text{RootSum}\left[2 \text{$\#$1}^8-5 \text{$\#$1}^4+1\&,\frac{-3 \text{$\#$1}^4 \log \left(\sqrt[4]{x^4-1}-\text{$\#$1} x\right)+3 \text{$\#$1}^4 \log (x)+2 \log \left(\sqrt[4]{x^4-1}-\text{$\#$1} x\right)-2 \log (x)}{4 \text{$\#$1}^5-5 \text{$\#$1}}\&\right]+\frac{1}{2} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-1}}\right)+\frac{1}{2} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-1}}\right)",1,"(34*ArcTan[x/(-1 + x^4)^(1/4)] - Sqrt[17]*(2047 - 439*Sqrt[17])^(1/4)*ArcTan[((2/(5 + Sqrt[17]))^(1/4)*x)/(-1 + x^4)^(1/4)] - Sqrt[17]*(2047 + 439*Sqrt[17])^(1/4)*ArcTan[((5 + Sqrt[17])^(1/4)*x)/(Sqrt[2]*(-1 + x^4)^(1/4))] + 34*ArcTanh[x/(-1 + x^4)^(1/4)] - Sqrt[17]*(2047 - 439*Sqrt[17])^(1/4)*ArcTanh[((2/(5 + Sqrt[17]))^(1/4)*x)/(-1 + x^4)^(1/4)] - Sqrt[17]*(2047 + 439*Sqrt[17])^(1/4)*ArcTanh[((5 + Sqrt[17])^(1/4)*x)/(Sqrt[2]*(-1 + x^4)^(1/4))])/68","A",0
1796,1,175,121,0.8828128,"\int \frac{\sqrt{-x+x^2} \sqrt{x^2-x \sqrt{-x+x^2}}}{x^3} \, dx","Integrate[(Sqrt[-x + x^2]*Sqrt[x^2 - x*Sqrt[-x + x^2]])/x^3,x]","\frac{2 \sqrt{(x-1) x} \left(-16 x^2+16 \left(\sqrt{(x-1) x}+1\right) x-8 \sqrt{(x-1) x}+3 \sqrt{4 x-4 \sqrt{(x-1) x}-2} \left(x-\sqrt{(x-1) x}\right)^{3/2} \log \left(\sqrt{4 x-4 \sqrt{(x-1) x}-2}+2 \sqrt{x-\sqrt{(x-1) x}}\right)-2\right)}{3 \sqrt{x \left(x-\sqrt{(x-1) x}\right)} \left(\sqrt{(x-1) x}-x\right) \left(-x+\sqrt{(x-1) x}+1\right)}","\sqrt{x \left(x-\sqrt{x^2-x}\right)} \left(\frac{4}{3 x}-\frac{2 \sqrt{2} \sqrt{\sqrt{x^2-x}+x} \tanh ^{-1}\left(\sqrt{2} \sqrt{\sqrt{x^2-x}+x}\right)}{x}\right)-\frac{4 \sqrt{x^2-x} \sqrt{x \left(x-\sqrt{x^2-x}\right)}}{3 x^2}",1,"(2*Sqrt[(-1 + x)*x]*(-2 - 16*x^2 - 8*Sqrt[(-1 + x)*x] + 16*x*(1 + Sqrt[(-1 + x)*x]) + 3*Sqrt[-2 + 4*x - 4*Sqrt[(-1 + x)*x]]*(x - Sqrt[(-1 + x)*x])^(3/2)*Log[Sqrt[-2 + 4*x - 4*Sqrt[(-1 + x)*x]] + 2*Sqrt[x - Sqrt[(-1 + x)*x]]]))/(3*Sqrt[x*(x - Sqrt[(-1 + x)*x])]*(-x + Sqrt[(-1 + x)*x])*(1 - x + Sqrt[(-1 + x)*x]))","A",1
1797,0,0,122,0.6529939,"\int \frac{b+2 a x}{\sqrt[4]{c+b x+a x^2} \left(5 c+4 b x+4 a x^2\right)} \, dx","Integrate[(b + 2*a*x)/((c + b*x + a*x^2)^(1/4)*(5*c + 4*b*x + 4*a*x^2)),x]","\int \frac{b+2 a x}{\sqrt[4]{c+b x+a x^2} \left(5 c+4 b x+4 a x^2\right)} \, dx","-\frac{\tan ^{-1}\left(1-\frac{2 \sqrt[4]{a x^2+b x+c}}{\sqrt[4]{c}}\right)}{2 \sqrt[4]{c}}+\frac{\tan ^{-1}\left(\frac{2 \sqrt[4]{a x^2+b x+c}}{\sqrt[4]{c}}+1\right)}{2 \sqrt[4]{c}}-\frac{\tanh ^{-1}\left(\frac{\frac{\sqrt{a x^2+b x+c}}{\sqrt[4]{c}}+\frac{\sqrt[4]{c}}{2}}{\sqrt[4]{a x^2+b x+c}}\right)}{2 \sqrt[4]{c}}",1,"Integrate[(b + 2*a*x)/((c + b*x + a*x^2)^(1/4)*(5*c + 4*b*x + 4*a*x^2)), x]","F",-1
1798,1,72,122,0.0326172,"\int x^6 \sqrt[3]{-x+x^3} \, dx","Integrate[x^6*(-x + x^3)^(1/3),x]","\frac{x \sqrt[3]{x \left(x^2-1\right)} \left(20 \, _2F_1\left(-\frac{1}{3},\frac{2}{3};\frac{5}{3};x^2\right)+\sqrt[3]{1-x^2} \left(27 x^6-3 x^4-4 x^2-20\right)\right)}{216 \sqrt[3]{1-x^2}}","\frac{5}{243} \log \left(\sqrt[3]{x^3-x}-x\right)+\frac{5 \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-x}+x}\right)}{81 \sqrt{3}}-\frac{5}{486} \log \left(\sqrt[3]{x^3-x} x+\left(x^3-x\right)^{2/3}+x^2\right)+\frac{1}{648} \sqrt[3]{x^3-x} \left(81 x^7-9 x^5-12 x^3-20 x\right)",1,"(x*(x*(-1 + x^2))^(1/3)*((1 - x^2)^(1/3)*(-20 - 4*x^2 - 3*x^4 + 27*x^6) + 20*Hypergeometric2F1[-1/3, 2/3, 5/3, x^2]))/(216*(1 - x^2)^(1/3))","C",1
1799,1,48,122,0.0189143,"\int \frac{1}{\sqrt[3]{-1-x+x^2+x^3}} \, dx","Integrate[(-1 - x + x^2 + x^3)^(-1/3),x]","\frac{3 \left((x-1) (x+1)^2\right)^{2/3} \, _2F_1\left(\frac{2}{3},\frac{2}{3};\frac{5}{3};\frac{1-x}{2}\right)}{2\ 2^{2/3} (x+1)^{4/3}}","-\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)",1,"(3*((-1 + x)*(1 + x)^2)^(2/3)*Hypergeometric2F1[2/3, 2/3, 5/3, (1 - x)/2])/(2*2^(2/3)*(1 + x)^(4/3))","C",1
1800,1,109,122,0.3012678,"\int \frac{1+2 x^4}{\left(-1+x^4\right) \sqrt[4]{-x^2+x^4}} \, dx","Integrate[(1 + 2*x^4)/((-1 + x^4)*(-x^2 + x^4)^(1/4)),x]","\frac{x \left(4 \sqrt[4]{1-x^4} x^2 F_1\left(\frac{5}{4};\frac{1}{4},1;\frac{9}{4};x^2,-x^2\right)+5 \sqrt[4]{1-x^2} \, _2F_1\left(\frac{1}{4},\frac{1}{4};\frac{5}{4};\frac{2 x^2}{x^2+1}\right)-15 \sqrt[4]{x^2+1}\right)}{5 \sqrt[4]{x^2 \left(x^2-1\right)} \sqrt[4]{x^2+1}}","-\frac{3 \left(x^4-x^2\right)^{3/4}}{x \left(x^2-1\right)}+2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^2}}\right)-\frac{3 \tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-x^2}}\right)}{2 \sqrt[4]{2}}+2 \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^2}}\right)-\frac{3 \tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-x^2}}\right)}{2 \sqrt[4]{2}}",1,"(x*(-15*(1 + x^2)^(1/4) + 4*x^2*(1 - x^4)^(1/4)*AppellF1[5/4, 1/4, 1, 9/4, x^2, -x^2] + 5*(1 - x^2)^(1/4)*Hypergeometric2F1[1/4, 1/4, 5/4, (2*x^2)/(1 + x^2)]))/(5*(x^2*(-1 + x^2))^(1/4)*(1 + x^2)^(1/4))","C",0
1801,1,108,122,0.1545761,"\int \frac{\left(-b+a x^4\right) \sqrt[4]{b x^2+a x^4}}{x^2} \, dx","Integrate[((-b + a*x^4)*(b*x^2 + a*x^4)^(1/4))/x^2,x]","\frac{\sqrt[4]{x^2 \left(a x^2+b\right)} \left(x^2 \left(\left(a x^2+b\right) \sqrt[4]{\frac{a x^2}{b}+1}-b \, _2F_1\left(-\frac{1}{4},\frac{3}{4};\frac{7}{4};-\frac{a x^2}{b}\right)\right)+8 b \, _2F_1\left(-\frac{1}{4},-\frac{1}{4};\frac{3}{4};-\frac{a x^2}{b}\right)\right)}{4 x \sqrt[4]{\frac{a x^2}{b}+1}}","\frac{\left(32 a b+3 b^2\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{32 a^{3/4}}+\frac{\left(-32 a b-3 b^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{32 a^{3/4}}+\frac{\sqrt[4]{a x^4+b x^2} \left(4 a x^4+b x^2+32 b\right)}{16 x}",1,"((x^2*(b + a*x^2))^(1/4)*(8*b*Hypergeometric2F1[-1/4, -1/4, 3/4, -((a*x^2)/b)] + x^2*((b + a*x^2)*(1 + (a*x^2)/b)^(1/4) - b*Hypergeometric2F1[-1/4, 3/4, 7/4, -((a*x^2)/b)])))/(4*x*(1 + (a*x^2)/b)^(1/4))","C",1
1802,1,108,122,0.0827746,"\int \frac{\left(b+a x^4\right) \sqrt[4]{b x^2+a x^4}}{x^2} \, dx","Integrate[((b + a*x^4)*(b*x^2 + a*x^4)^(1/4))/x^2,x]","\frac{\sqrt[4]{x^2 \left(a x^2+b\right)} \left(x^2 \left(\left(a x^2+b\right) \sqrt[4]{\frac{a x^2}{b}+1}-b \, _2F_1\left(-\frac{1}{4},\frac{3}{4};\frac{7}{4};-\frac{a x^2}{b}\right)\right)-8 b \, _2F_1\left(-\frac{1}{4},-\frac{1}{4};\frac{3}{4};-\frac{a x^2}{b}\right)\right)}{4 x \sqrt[4]{\frac{a x^2}{b}+1}}","\frac{\left(3 b^2-32 a b\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{32 a^{3/4}}+\frac{\left(32 a b-3 b^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{32 a^{3/4}}+\frac{\sqrt[4]{a x^4+b x^2} \left(4 a x^4+b x^2-32 b\right)}{16 x}",1,"((x^2*(b + a*x^2))^(1/4)*(-8*b*Hypergeometric2F1[-1/4, -1/4, 3/4, -((a*x^2)/b)] + x^2*((b + a*x^2)*(1 + (a*x^2)/b)^(1/4) - b*Hypergeometric2F1[-1/4, 3/4, 7/4, -((a*x^2)/b)])))/(4*x*(1 + (a*x^2)/b)^(1/4))","C",1
1803,0,0,122,1.167645,"\int \frac{b+2 a x^4}{\left(-b+a x^4\right) \sqrt[4]{-b x^2+a x^4}} \, dx","Integrate[(b + 2*a*x^4)/((-b + a*x^4)*(-(b*x^2) + a*x^4)^(1/4)),x]","\int \frac{b+2 a x^4}{\left(-b+a x^4\right) \sqrt[4]{-b x^2+a x^4}} \, dx","\frac{3}{4} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2-a b\&,\frac{\log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]+\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)}{\sqrt[4]{a}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)}{\sqrt[4]{a}}",1,"Integrate[(b + 2*a*x^4)/((-b + a*x^4)*(-(b*x^2) + a*x^4)^(1/4)), x]","F",-1
1804,0,0,122,0.370059,"\int \frac{b+2 a x^4}{\left(-b+a x^4\right) \sqrt[4]{-b x^2+a x^4}} \, dx","Integrate[(b + 2*a*x^4)/((-b + a*x^4)*(-(b*x^2) + a*x^4)^(1/4)),x]","\int \frac{b+2 a x^4}{\left(-b+a x^4\right) \sqrt[4]{-b x^2+a x^4}} \, dx","\frac{3}{4} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2-a b\&,\frac{\log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]+\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)}{\sqrt[4]{a}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)}{\sqrt[4]{a}}",1,"Integrate[(b + 2*a*x^4)/((-b + a*x^4)*(-(b*x^2) + a*x^4)^(1/4)), x]","F",-1
1805,1,112,122,0.0952682,"\int \frac{-b-2 a x^4+2 x^8}{\sqrt[4]{-b+a x^4}} \, dx","Integrate[(-b - 2*a*x^4 + 2*x^8)/(-b + a*x^4)^(1/4),x]","\frac{2 \sqrt[4]{a} x \left(a x^4-b\right)^{3/4} \left(-8 a^2+4 a x^4+5 b\right)-b \left(24 a^2-5 b\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)-b \left(24 a^2-5 b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{32 a^{9/4}}","\frac{\left(a x^4-b\right)^{3/4} \left(-8 a^2 x+4 a x^5+5 b x\right)}{16 a^2}+\frac{\left(5 b^2-24 a^2 b\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{32 a^{9/4}}+\frac{\left(5 b^2-24 a^2 b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{32 a^{9/4}}",1,"(2*a^(1/4)*x*(-b + a*x^4)^(3/4)*(-8*a^2 + 5*b + 4*a*x^4) - (24*a^2 - 5*b)*b*ArcTan[(a^(1/4)*x)/(-b + a*x^4)^(1/4)] - (24*a^2 - 5*b)*b*ArcTanh[(a^(1/4)*x)/(-b + a*x^4)^(1/4)])/(32*a^(9/4))","A",1
1806,1,78,123,0.0778215,"\int \frac{-1+x}{\left(-4-2 x+x^2\right) \sqrt[3]{-2-2 x+x^2}} \, dx","Integrate[(-1 + x)/((-4 - 2*x + x^2)*(-2 - 2*x + x^2)^(1/3)),x]","\frac{-\log \left(x^2-2 x-4\right)+3 \log \left(\sqrt[3]{2}-\sqrt[3]{x^2-2 x-2}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{x^2-2 x-2}+1}{\sqrt{3}}\right)}{4 \sqrt[3]{2}}","\frac{\log \left(2^{2/3} \sqrt[3]{x^2-2 x-2}-2\right)}{2 \sqrt[3]{2}}-\frac{\log \left(\sqrt[3]{2} \left(x^2-2 x-2\right)^{2/3}+2^{2/3} \sqrt[3]{x^2-2 x-2}+2\right)}{4 \sqrt[3]{2}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{x^2-2 x-2}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt[3]{2}}",1,"(2*Sqrt[3]*ArcTan[(1 + 2^(2/3)*(-2 - 2*x + x^2)^(1/3))/Sqrt[3]] - Log[-4 - 2*x + x^2] + 3*Log[2^(1/3) - (-2 - 2*x + x^2)^(1/3)])/(4*2^(1/3))","A",1
1807,1,72,123,0.0309466,"\int \frac{1}{(1+x) \sqrt[3]{3+2 x+x^2}} \, dx","Integrate[1/((1 + x)*(3 + 2*x + x^2)^(1/3)),x]","\frac{2 \sqrt{3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{x^2+2 x+3}+1}{\sqrt{3}}\right)-2 \log (x+1)+3 \log \left(\sqrt[3]{2}-\sqrt[3]{(x+1)^2+2}\right)}{4 \sqrt[3]{2}}","\frac{\log \left(2^{2/3} \sqrt[3]{x^2+2 x+3}-2\right)}{2 \sqrt[3]{2}}-\frac{\log \left(\sqrt[3]{2} \left(x^2+2 x+3\right)^{2/3}+2^{2/3} \sqrt[3]{x^2+2 x+3}+2\right)}{4 \sqrt[3]{2}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{x^2+2 x+3}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt[3]{2}}",1,"(2*Sqrt[3]*ArcTan[(1 + 2^(2/3)*(3 + 2*x + x^2)^(1/3))/Sqrt[3]] - 2*Log[1 + x] + 3*Log[2^(1/3) - (2 + (1 + x)^2)^(1/3)])/(4*2^(1/3))","A",1
1808,1,165,123,0.0731657,"\int \frac{1}{x \left(-b+a x^2\right)^{3/4}} \, dx","Integrate[1/(x*(-b + a*x^2)^(3/4)),x]","\frac{-\log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^2-b}+\sqrt{a x^2-b}+\sqrt{b}\right)+\log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^2-b}+\sqrt{a x^2-b}+\sqrt{b}\right)-2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a x^2-b}}{\sqrt[4]{b}}\right)+2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x^2-b}}{\sqrt[4]{b}}+1\right)}{2 \sqrt{2} b^{3/4}}","\frac{\tanh ^{-1}\left(\frac{\frac{\sqrt{a x^2-b}}{\sqrt{2} \sqrt[4]{b}}+\frac{\sqrt[4]{b}}{\sqrt{2}}}{\sqrt[4]{a x^2-b}}\right)}{\sqrt{2} b^{3/4}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^2-b}}{\sqrt{a x^2-b}-\sqrt{b}}\right)}{\sqrt{2} b^{3/4}}",1,"(-2*ArcTan[1 - (Sqrt[2]*(-b + a*x^2)^(1/4))/b^(1/4)] + 2*ArcTan[1 + (Sqrt[2]*(-b + a*x^2)^(1/4))/b^(1/4)] - Log[Sqrt[b] - Sqrt[2]*b^(1/4)*(-b + a*x^2)^(1/4) + Sqrt[-b + a*x^2]] + Log[Sqrt[b] + Sqrt[2]*b^(1/4)*(-b + a*x^2)^(1/4) + Sqrt[-b + a*x^2]])/(2*Sqrt[2]*b^(3/4))","A",1
1809,1,39,123,0.0143562,"\int \frac{1}{x \sqrt[3]{-b+a x^3}} \, dx","Integrate[1/(x*(-b + a*x^3)^(1/3)),x]","\frac{\left(a x^3-b\right)^{2/3} \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};1-\frac{a x^3}{b}\right)}{2 b}","\frac{\log \left(-\sqrt[3]{b} \sqrt[3]{a x^3-b}+\left(a x^3-b\right)^{2/3}+b^{2/3}\right)}{6 \sqrt[3]{b}}-\frac{\log \left(\sqrt[3]{a x^3-b}+\sqrt[3]{b}\right)}{3 \sqrt[3]{b}}-\frac{\tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{a x^3-b}}{\sqrt{3} \sqrt[3]{b}}\right)}{\sqrt{3} \sqrt[3]{b}}",1,"((-b + a*x^3)^(2/3)*Hypergeometric2F1[2/3, 1, 5/3, 1 - (a*x^3)/b])/(2*b)","C",1
1810,1,208,123,1.2242392,"\int \frac{-b^3+a^3 x^3}{\sqrt{b^2 x+a^2 x^3} \left(b^3+a^3 x^3\right)} \, dx","Integrate[(-b^3 + a^3*x^3)/(Sqrt[b^2*x + a^2*x^3]*(b^3 + a^3*x^3)),x]","-\frac{(-1)^{5/6} x^{3/2} \sqrt{\frac{b^2}{a^2 x^2}+1} \left(\left(3-3 i \sqrt{3}\right) F\left(\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)+4 \left((-1)^{2/3} \Pi \left(-i;\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)+\left(\sqrt[3]{-1}-1\right) \Pi \left(\sqrt[6]{-1};\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)+(-1)^{2/3} \Pi \left((-1)^{5/6};\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)\right)\right)}{3 \sqrt{\frac{i b}{a}} \sqrt{x \left(a^2 x^2+b^2\right)}}","-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{b} \sqrt{a^2 x^3+b^2 x}}{a^2 x^2+b^2}\right)}{3 \sqrt{a} \sqrt{b}}-\frac{4 \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{b} \sqrt{a^2 x^3+b^2 x}}{a^2 x^2+b^2}\right)}{3 \sqrt{a} \sqrt{b}}",1,"-1/3*((-1)^(5/6)*Sqrt[1 + b^2/(a^2*x^2)]*x^(3/2)*((3 - (3*I)*Sqrt[3])*EllipticF[I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1] + 4*((-1)^(2/3)*EllipticPi[-I, I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1] + (-1 + (-1)^(1/3))*EllipticPi[(-1)^(1/6), I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1] + (-1)^(2/3)*EllipticPi[(-1)^(5/6), I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1])))/(Sqrt[(I*b)/a]*Sqrt[x*(b^2 + a^2*x^2)])","C",1
1811,1,212,123,1.058247,"\int \frac{b^3+a^3 x^3}{\sqrt{b^2 x+a^2 x^3} \left(-b^3+a^3 x^3\right)} \, dx","Integrate[(b^3 + a^3*x^3)/(Sqrt[b^2*x + a^2*x^3]*(-b^3 + a^3*x^3)),x]","-\frac{(-1)^{5/6} x^{3/2} \sqrt{\frac{b^2}{a^2 x^2}+1} \left(\left(3-3 i \sqrt{3}\right) F\left(\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)+4 \left((-1)^{2/3} \Pi \left(i;\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)+\left(\sqrt[3]{-1}-1\right) \Pi \left(-\sqrt[6]{-1};\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)+(-1)^{2/3} \Pi \left(-(-1)^{5/6};\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)\right)\right)}{3 \sqrt{\frac{i b}{a}} \sqrt{x \left(a^2 x^2+b^2\right)}}","-\frac{4 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{b} \sqrt{a^2 x^3+b^2 x}}{a^2 x^2+b^2}\right)}{3 \sqrt{a} \sqrt{b}}-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{b} \sqrt{a^2 x^3+b^2 x}}{a^2 x^2+b^2}\right)}{3 \sqrt{a} \sqrt{b}}",1,"-1/3*((-1)^(5/6)*Sqrt[1 + b^2/(a^2*x^2)]*x^(3/2)*((3 - (3*I)*Sqrt[3])*EllipticF[I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1] + 4*((-1)^(2/3)*EllipticPi[I, I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1] + (-1 + (-1)^(1/3))*EllipticPi[-(-1)^(1/6), I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1] + (-1)^(2/3)*EllipticPi[-(-1)^(5/6), I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1])))/(Sqrt[(I*b)/a]*Sqrt[x*(b^2 + a^2*x^2)])","C",1
1812,1,124,123,0.1739356,"\int \frac{\sqrt[4]{x^3+x^4}}{-2+x+2 x^2} \, dx","Integrate[(x^3 + x^4)^(1/4)/(-2 + x + 2*x^2),x]","\frac{x^3 \left(34 (x+1)^{3/4} \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};-x\right)+\left(3 \sqrt{17}-17\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{\left(-3+\sqrt{17}\right) x}{\left(1+\sqrt{17}\right) (x+1)}\right)-\left(17+3 \sqrt{17}\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{\left(3+\sqrt{17}\right) x}{\left(-1+\sqrt{17}\right) (x+1)}\right)\right)}{51 \left(x^3 (x+1)\right)^{3/4}}","-\frac{1}{2} \text{RootSum}\left[2 \text{$\#$1}^8-5 \text{$\#$1}^4+1\&,\frac{-2 \text{$\#$1}^4 \log \left(\sqrt[4]{x^4+x^3}-\text{$\#$1} x\right)+2 \text{$\#$1}^4 \log (x)+\log \left(\sqrt[4]{x^4+x^3}-\text{$\#$1} x\right)-\log (x)}{4 \text{$\#$1}^7-5 \text{$\#$1}^3}\&\right]-\tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+x^3}}\right)+\tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+x^3}}\right)",1,"(x^3*(34*(1 + x)^(3/4)*Hypergeometric2F1[3/4, 3/4, 7/4, -x] + (-17 + 3*Sqrt[17])*Hypergeometric2F1[3/4, 1, 7/4, ((-3 + Sqrt[17])*x)/((1 + Sqrt[17])*(1 + x))] - (17 + 3*Sqrt[17])*Hypergeometric2F1[3/4, 1, 7/4, ((3 + Sqrt[17])*x)/((-1 + Sqrt[17])*(1 + x))]))/(51*(x^3*(1 + x))^(3/4))","A",1
1813,0,0,123,0.6517733,"\int \frac{\left(-4 b+a x^3\right) \left(b-a x^3+x^4\right)}{x^4 \sqrt[4]{-b+a x^3} \left(-b+a x^3+x^4\right)} \, dx","Integrate[((-4*b + a*x^3)*(b - a*x^3 + x^4))/(x^4*(-b + a*x^3)^(1/4)*(-b + a*x^3 + x^4)),x]","\int \frac{\left(-4 b+a x^3\right) \left(b-a x^3+x^4\right)}{x^4 \sqrt[4]{-b+a x^3} \left(-b+a x^3+x^4\right)} \, dx","\frac{4 \left(a x^3-b\right)^{3/4}}{3 x^3}-2 \sqrt{2} \tan ^{-1}\left(\frac{\frac{\sqrt{a x^3-b}}{\sqrt{2}}-\frac{x^2}{\sqrt{2}}}{x \sqrt[4]{a x^3-b}}\right)+2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{a x^3-b}}{\sqrt{a x^3-b}+x^2}\right)",1,"Integrate[((-4*b + a*x^3)*(b - a*x^3 + x^4))/(x^4*(-b + a*x^3)^(1/4)*(-b + a*x^3 + x^4)), x]","F",-1
1814,0,0,123,0.6865028,"\int \frac{\left(-2+x^2\right) \left(-1+x^2\right) \sqrt[4]{-1+x^2+x^4}}{x^6 \left(-1+x^2+2 x^4\right)} \, dx","Integrate[((-2 + x^2)*(-1 + x^2)*(-1 + x^2 + x^4)^(1/4))/(x^6*(-1 + x^2 + 2*x^4)),x]","\int \frac{\left(-2+x^2\right) \left(-1+x^2\right) \sqrt[4]{-1+x^2+x^4}}{x^6 \left(-1+x^2+2 x^4\right)} \, dx","\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{x^4+x^2-1}}{\sqrt{x^4+x^2-1}-x^2}\right)-\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{x^4+x^2-1}}{x^2+\sqrt{x^4+x^2-1}}\right)+\frac{2 \sqrt[4]{x^4+x^2-1} \left(9 x^4-x^2+1\right)}{5 x^5}",1,"Integrate[((-2 + x^2)*(-1 + x^2)*(-1 + x^2 + x^4)^(1/4))/(x^6*(-1 + x^2 + 2*x^4)), x]","F",-1
1815,1,49,123,0.0163914,"\int x^2 \sqrt[4]{b x^3+a x^4} \, dx","Integrate[x^2*(b*x^3 + a*x^4)^(1/4),x]","\frac{4 x^3 \sqrt[4]{x^3 (a x+b)} \, _2F_1\left(-\frac{1}{4},\frac{15}{4};\frac{19}{4};-\frac{a x}{b}\right)}{15 \sqrt[4]{\frac{a x}{b}+1}}","\frac{77 b^4 \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)}{1024 a^{15/4}}-\frac{77 b^4 \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)}{1024 a^{15/4}}+\frac{\left(384 a^3 x^3+32 a^2 b x^2-44 a b^2 x+77 b^3\right) \sqrt[4]{a x^4+b x^3}}{1536 a^3}",1,"(4*x^3*(x^3*(b + a*x))^(1/4)*Hypergeometric2F1[-1/4, 15/4, 19/4, -((a*x)/b)])/(15*(1 + (a*x)/b)^(1/4))","C",1
1816,1,939,123,5.0216154,"\int \frac{1+x^6}{\sqrt{x+x^2+x^3} \left(1-x^6\right)} \, dx","Integrate[(1 + x^6)/(Sqrt[x + x^2 + x^3]*(1 - x^6)),x]","\frac{2 x \left(\sqrt{x} \left(\frac{(-1)^{2/3} \sqrt{\frac{\sqrt{x}-\sqrt[3]{-1}+1}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1} \sqrt{x}-1\right)}} \sqrt{\frac{(-1)^{2/3} \sqrt{x}-1}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1} \sqrt{x}-1\right)}} \sqrt{-\frac{(-1)^{2/3} \sqrt{x}+1}{\sqrt{x}+\sqrt[3]{-1}-1}} \left(\left(1+\sqrt[3]{-1}\right) F\left(\left.\sin ^{-1}\left(\sqrt{\frac{\sqrt{x}-\sqrt[3]{-1}+1}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1} \sqrt{x}-1\right)}}\right)\right|-3\right)-2 \sqrt[3]{-1} \Pi \left(-1;\left.\sin ^{-1}\left(\sqrt{\frac{\sqrt{x}-\sqrt[3]{-1}+1}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1} \sqrt{x}-1\right)}}\right)\right|-3\right)\right) \left(\sqrt[3]{-1} \sqrt{x}-1\right)^2}{\left(1+(-1)^{2/3}\right) x}-\frac{(-1)^{2/3} \sqrt{\frac{\sqrt{x}-\sqrt[3]{-1}+1}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1} \sqrt{x}-1\right)}} \sqrt{\frac{(-1)^{2/3} \sqrt{x}-1}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1} \sqrt{x}-1\right)}} \sqrt{-\frac{(-1)^{2/3} \sqrt{x}+1}{\sqrt{x}+\sqrt[3]{-1}-1}} \left(\left(-1+\sqrt[3]{-1}\right) F\left(\left.\sin ^{-1}\left(\sqrt{\frac{\sqrt{x}-\sqrt[3]{-1}+1}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1} \sqrt{x}-1\right)}}\right)\right|-3\right)-2 \sqrt[3]{-1} \Pi \left(3;\left.\sin ^{-1}\left(\sqrt{\frac{\sqrt{x}-\sqrt[3]{-1}+1}{\left(1+\sqrt[3]{-1}\right) \left(\sqrt[3]{-1} \sqrt{x}-1\right)}}\right)\right|-3\right)\right) \left(\sqrt[3]{-1} \sqrt{x}-1\right)^2}{\left(1+(-1)^{2/3}\right) x}-2 (-1)^{2/3} \sqrt{1-\frac{(-1)^{2/3}}{x}} \sqrt{\frac{x+\sqrt[3]{-1}}{x}} F\left(i \sinh ^{-1}\left(\frac{(-1)^{5/6}}{\sqrt{x}}\right)|(-1)^{2/3}\right)+\sqrt[3]{-1} \sqrt{1-\frac{(-1)^{2/3}}{x}} \sqrt{\frac{x+\sqrt[3]{-1}}{x}} \Pi \left(-1;i \sinh ^{-1}\left(\frac{(-1)^{5/6}}{\sqrt{x}}\right)|(-1)^{2/3}\right)-\sqrt{1-\frac{(-1)^{2/3}}{x}} \sqrt{\frac{x+\sqrt[3]{-1}}{x}} \Pi \left(-1;i \sinh ^{-1}\left(\frac{(-1)^{5/6}}{\sqrt{x}}\right)|(-1)^{2/3}\right)+(-1)^{2/3} \sqrt{1-\frac{(-1)^{2/3}}{x}} \sqrt{\frac{x+\sqrt[3]{-1}}{x}} \Pi \left(\sqrt[3]{-1};i \sinh ^{-1}\left(\frac{(-1)^{5/6}}{\sqrt{x}}\right)|(-1)^{2/3}\right)+\frac{3 (-1)^{2/3} \sqrt{1-\frac{(-1)^{2/3}}{x}} \sqrt{\frac{x+\sqrt[3]{-1}}{x}} \Pi \left(-(-1)^{2/3};i \sinh ^{-1}\left(\frac{(-1)^{5/6}}{\sqrt{x}}\right)|(-1)^{2/3}\right)}{\left(1+\sqrt[3]{-1}\right)^2}-\frac{3 \sqrt[3]{-1} \sqrt{1-\frac{(-1)^{2/3}}{x}} \sqrt{\frac{x+\sqrt[3]{-1}}{x}} \Pi \left(-(-1)^{2/3};i \sinh ^{-1}\left(\frac{(-1)^{5/6}}{\sqrt{x}}\right)|(-1)^{2/3}\right)}{\left(1+\sqrt[3]{-1}\right)^2}\right)+1\right)}{3 \sqrt{x \left(x^2+x+1\right)}}","\frac{2 \sqrt{x^3+x^2+x}}{3 \left(x^2+x+1\right)}+\frac{1}{3} \tan ^{-1}\left(\frac{\sqrt{x^3+x^2+x}}{x^2+x+1}\right)+\frac{1}{3} \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{x^3+x^2+x}}{x^2+x+1}\right)+\frac{\tanh ^{-1}\left(\frac{\sqrt{3} \sqrt{x^3+x^2+x}}{x^2+x+1}\right)}{3 \sqrt{3}}",1,"(2*x*(1 + Sqrt[x]*(-2*(-1)^(2/3)*Sqrt[1 - (-1)^(2/3)/x]*Sqrt[((-1)^(1/3) + x)/x]*EllipticF[I*ArcSinh[(-1)^(5/6)/Sqrt[x]], (-1)^(2/3)] + ((-1)^(2/3)*Sqrt[(1 - (-1)^(1/3) + Sqrt[x])/((1 + (-1)^(1/3))*(-1 + (-1)^(1/3)*Sqrt[x]))]*(-1 + (-1)^(1/3)*Sqrt[x])^2*Sqrt[(-1 + (-1)^(2/3)*Sqrt[x])/((1 + (-1)^(1/3))*(-1 + (-1)^(1/3)*Sqrt[x]))]*Sqrt[-((1 + (-1)^(2/3)*Sqrt[x])/(-1 + (-1)^(1/3) + Sqrt[x]))]*((1 + (-1)^(1/3))*EllipticF[ArcSin[Sqrt[(1 - (-1)^(1/3) + Sqrt[x])/((1 + (-1)^(1/3))*(-1 + (-1)^(1/3)*Sqrt[x]))]], -3] - 2*(-1)^(1/3)*EllipticPi[-1, ArcSin[Sqrt[(1 - (-1)^(1/3) + Sqrt[x])/((1 + (-1)^(1/3))*(-1 + (-1)^(1/3)*Sqrt[x]))]], -3]))/((1 + (-1)^(2/3))*x) - Sqrt[1 - (-1)^(2/3)/x]*Sqrt[((-1)^(1/3) + x)/x]*EllipticPi[-1, I*ArcSinh[(-1)^(5/6)/Sqrt[x]], (-1)^(2/3)] + (-1)^(1/3)*Sqrt[1 - (-1)^(2/3)/x]*Sqrt[((-1)^(1/3) + x)/x]*EllipticPi[-1, I*ArcSinh[(-1)^(5/6)/Sqrt[x]], (-1)^(2/3)] - ((-1)^(2/3)*Sqrt[(1 - (-1)^(1/3) + Sqrt[x])/((1 + (-1)^(1/3))*(-1 + (-1)^(1/3)*Sqrt[x]))]*(-1 + (-1)^(1/3)*Sqrt[x])^2*Sqrt[(-1 + (-1)^(2/3)*Sqrt[x])/((1 + (-1)^(1/3))*(-1 + (-1)^(1/3)*Sqrt[x]))]*Sqrt[-((1 + (-1)^(2/3)*Sqrt[x])/(-1 + (-1)^(1/3) + Sqrt[x]))]*((-1 + (-1)^(1/3))*EllipticF[ArcSin[Sqrt[(1 - (-1)^(1/3) + Sqrt[x])/((1 + (-1)^(1/3))*(-1 + (-1)^(1/3)*Sqrt[x]))]], -3] - 2*(-1)^(1/3)*EllipticPi[3, ArcSin[Sqrt[(1 - (-1)^(1/3) + Sqrt[x])/((1 + (-1)^(1/3))*(-1 + (-1)^(1/3)*Sqrt[x]))]], -3]))/((1 + (-1)^(2/3))*x) + (-1)^(2/3)*Sqrt[1 - (-1)^(2/3)/x]*Sqrt[((-1)^(1/3) + x)/x]*EllipticPi[(-1)^(1/3), I*ArcSinh[(-1)^(5/6)/Sqrt[x]], (-1)^(2/3)] - (3*(-1)^(1/3)*Sqrt[1 - (-1)^(2/3)/x]*Sqrt[((-1)^(1/3) + x)/x]*EllipticPi[-(-1)^(2/3), I*ArcSinh[(-1)^(5/6)/Sqrt[x]], (-1)^(2/3)])/(1 + (-1)^(1/3))^2 + (3*(-1)^(2/3)*Sqrt[1 - (-1)^(2/3)/x]*Sqrt[((-1)^(1/3) + x)/x]*EllipticPi[-(-1)^(2/3), I*ArcSinh[(-1)^(5/6)/Sqrt[x]], (-1)^(2/3)])/(1 + (-1)^(1/3))^2)))/(3*Sqrt[x*(1 + x + x^2)])","C",0
1817,1,192,123,1.3661152,"\int \frac{1-3 x^3+3 x^6}{x^6 \left(-1+2 x^3\right) \sqrt[4]{-x+x^4}} \, dx","Integrate[(1 - 3*x^3 + 3*x^6)/(x^6*(-1 + 2*x^3)*(-x + x^4)^(1/4)),x]","\frac{16 \left(1-2 x^3\right)^2 x^3 \, _3F_2\left(\frac{5}{4},2,2;1,\frac{9}{4};\frac{x^3}{1-x^3}\right)-8 x^3 \, _2F_1\left(\frac{5}{4},2;\frac{9}{4};\frac{x^3}{1-x^3}\right)+192 x^9 \, _2F_1\left(\frac{5}{4},2;\frac{9}{4};\frac{x^3}{1-x^3}\right)-80 x^6 \, _2F_1\left(\frac{5}{4},2;\frac{9}{4};\frac{x^3}{1-x^3}\right)-5 \left(128 x^9-144 x^6+13 x^3+3\right) \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{x^3}{1-x^3}\right)+150 x^9-345 x^6+240 x^3-45}{315 x^4 \left(x \left(x^3-1\right)\right)^{5/4}}","-\frac{1}{3} \sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{x^4-x}}{\sqrt{x^4-x}-x^2}\right)-\frac{1}{3} \sqrt{2} \tanh ^{-1}\left(\frac{\frac{\sqrt{x^4-x}}{\sqrt{2}}+\frac{x^2}{\sqrt{2}}}{x \sqrt[4]{x^4-x}}\right)+\frac{4 \left(x^4-x\right)^{3/4} \left(x^3-1\right)}{21 x^6}",1,"(-45 + 240*x^3 - 345*x^6 + 150*x^9 - 5*(3 + 13*x^3 - 144*x^6 + 128*x^9)*Hypergeometric2F1[1/4, 1, 5/4, x^3/(1 - x^3)] - 8*x^3*Hypergeometric2F1[5/4, 2, 9/4, x^3/(1 - x^3)] - 80*x^6*Hypergeometric2F1[5/4, 2, 9/4, x^3/(1 - x^3)] + 192*x^9*Hypergeometric2F1[5/4, 2, 9/4, x^3/(1 - x^3)] + 16*x^3*(1 - 2*x^3)^2*HypergeometricPFQ[{5/4, 2, 2}, {1, 9/4}, x^3/(1 - x^3)])/(315*x^4*(x*(-1 + x^3))^(5/4))","C",0
1818,1,73,123,0.1213203,"\int \frac{b+a x^6}{x^3 \left(b+a x^3\right) \sqrt[4]{b x+a x^4}} \, dx","Integrate[(b + a*x^6)/(x^3*(b + a*x^3)*(b*x + a*x^4)^(1/4)),x]","\frac{4 \left(3 a x^6 \sqrt[4]{\frac{a x^3}{b}+1} \, _2F_1\left(\frac{5}{4},\frac{5}{4};\frac{9}{4};-\frac{a x^3}{b}\right)-5 \left(4 a x^3+b\right)\right)}{45 b x^2 \sqrt[4]{x \left(a x^3+b\right)}}","-\frac{4 \left(a x^4+b x\right)^{3/4} \left(4 a x^3+3 b x^3+b\right)}{9 b x^3 \left(a x^3+b\right)}+\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \left(a x^4+b x\right)^{3/4}}{a x^3+b}\right)}{3 \sqrt[4]{a}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{a} \left(a x^4+b x\right)^{3/4}}{a x^3+b}\right)}{3 \sqrt[4]{a}}",1,"(4*(-5*(b + 4*a*x^3) + 3*a*x^6*(1 + (a*x^3)/b)^(1/4)*Hypergeometric2F1[5/4, 5/4, 9/4, -((a*x^3)/b)]))/(45*b*x^2*(x*(b + a*x^3))^(1/4))","C",1
1819,1,109075,123,6.8912432,"\int \frac{\left(-1-x-x^2+x^4\right) \left(2+x+2 x^4\right)}{\sqrt{-1-x+x^4} \left(4+8 x+3 x^2-x^3-7 x^4-8 x^5+x^6+4 x^8\right)} \, dx","Integrate[((-1 - x - x^2 + x^4)*(2 + x + 2*x^4))/(Sqrt[-1 - x + x^4]*(4 + 8*x + 3*x^2 - x^3 - 7*x^4 - 8*x^5 + x^6 + 4*x^8)),x]","\text{Result too large to show}","\frac{\sqrt[4]{-1} \sqrt{\sqrt{15}+7 i} \tan ^{-1}\left(\frac{\sqrt{\frac{1}{2}+\frac{i \sqrt{15}}{2}} x}{2 \sqrt{x^4-x-1}}\right)}{\sqrt{10}}-(-1)^{3/4} \sqrt{\frac{1}{10} \left(\sqrt{15}-7 i\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{1}{2}-\frac{i \sqrt{15}}{2}} x}{2 \sqrt{x^4-x-1}}\right)",1,"Result too large to show","C",0
1820,0,0,123,0.8523083,"\int \frac{\left(1+x^6\right)^2 \left(-1+2 x^6\right)}{\left(1-x^2+x^6\right)^{3/2} \left(1-x^2-x^4+2 x^6-x^8+x^{12}\right)} \, dx","Integrate[((1 + x^6)^2*(-1 + 2*x^6))/((1 - x^2 + x^6)^(3/2)*(1 - x^2 - x^4 + 2*x^6 - x^8 + x^12)),x]","\int \frac{\left(1+x^6\right)^2 \left(-1+2 x^6\right)}{\left(1-x^2+x^6\right)^{3/2} \left(1-x^2-x^4+2 x^6-x^8+x^{12}\right)} \, dx","\frac{x}{\sqrt{x^6-x^2+1}}-\sqrt{\frac{2}{145+65 \sqrt{5}}} \tan ^{-1}\left(\frac{\sqrt{\frac{1}{2}+\frac{\sqrt{5}}{2}} x}{\sqrt{x^6-x^2+1}}\right)-\sqrt{\frac{1}{10} \left(29+13 \sqrt{5}\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}} x}{\sqrt{x^6-x^2+1}}\right)",1,"Integrate[((1 + x^6)^2*(-1 + 2*x^6))/((1 - x^2 + x^6)^(3/2)*(1 - x^2 - x^4 + 2*x^6 - x^8 + x^12)), x]","F",-1
1821,1,126,123,0.1306396,"\int \frac{1}{\left(2 \sqrt{x}+\sqrt{1+x}\right)^2} \, dx","Integrate[(2*Sqrt[x] + Sqrt[1 + x])^(-2),x]","\frac{12 x^{3/2}+12 \sqrt{x}-8 \sqrt{x+1}+15 \sqrt{x+1} x \log (1-3 x)-5 \sqrt{x+1} \log (1-3 x)+10 \sqrt{-x-1} (3 x-1) \tan ^{-1}\left(\frac{2 \sqrt{x}}{\sqrt{-x-1}}\right)-8 \sqrt{x+1} (3 x-1) \sinh ^{-1}\left(\sqrt{x}\right)}{9 \sqrt{x+1} (3 x-1)}","\frac{\sqrt{x} \left(4-4 \sqrt{x+1}\right)}{3 x+\left(6 \sqrt{x+1}-6\right) \sqrt{x}-3 \sqrt{x+1}+3}-\frac{2}{9} \log \left(-\sqrt{x}+\sqrt{x+1}-1\right)-2 \log \left(\sqrt{x}+\sqrt{x+1}-1\right)+\frac{10}{9} \log \left(x+\left(2 \sqrt{x+1}-2\right) \sqrt{x}-\sqrt{x+1}+1\right)",1,"(12*Sqrt[x] + 12*x^(3/2) - 8*Sqrt[1 + x] - 8*Sqrt[1 + x]*(-1 + 3*x)*ArcSinh[Sqrt[x]] + 10*Sqrt[-1 - x]*(-1 + 3*x)*ArcTan[(2*Sqrt[x])/Sqrt[-1 - x]] - 5*Sqrt[1 + x]*Log[1 - 3*x] + 15*x*Sqrt[1 + x]*Log[1 - 3*x])/(9*Sqrt[1 + x]*(-1 + 3*x))","A",1
1822,1,98,123,4.6862354,"\int \frac{1}{x^3 \sqrt{a x^2+b x \sqrt{-\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}}} \, dx","Integrate[1/(x^3*Sqrt[a*x^2 + b*x*Sqrt[-(a/b^2) + (a^2*x^2)/b^2]]),x]","-\frac{2 \left(a x^2-1\right) \left(5 b x \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+5 a x^2-3\right)}{15 x^2 \sqrt{x \left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right)} \left(b x \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x^2-1\right)^2}","\frac{4 \left(a x^2-2\right) \sqrt{b x \sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}}+a x^2}}{15 x^2}-\frac{2 b \left(2 a x^2-3\right) \sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}} \sqrt{b x \sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}}+a x^2}}{15 a x^3}",1,"(-2*(-1 + a*x^2)*(-3 + 5*a*x^2 + 5*b*x*Sqrt[(a*(-1 + a*x^2))/b^2]))/(15*x^2*Sqrt[x*(a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2])]*(-1 + a*x^2 + b*x*Sqrt[(a*(-1 + a*x^2))/b^2])^2)","A",1
1823,1,54,124,0.0264231,"\int \frac{1}{x \sqrt[4]{-b+a x^2}} \, dx","Integrate[1/(x*(-b + a*x^2)^(1/4)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a x^2-b}}{\sqrt[4]{-b}}\right)+\tanh ^{-1}\left(\frac{b \sqrt[4]{a x^2-b}}{(-b)^{5/4}}\right)}{\sqrt[4]{-b}}","-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^2-b}}{\sqrt{a x^2-b}-\sqrt{b}}\right)}{\sqrt{2} \sqrt[4]{b}}-\frac{\tanh ^{-1}\left(\frac{\frac{\sqrt{a x^2-b}}{\sqrt{2} \sqrt[4]{b}}+\frac{\sqrt[4]{b}}{\sqrt{2}}}{\sqrt[4]{a x^2-b}}\right)}{\sqrt{2} \sqrt[4]{b}}",1,"(ArcTan[(-b + a*x^2)^(1/4)/(-b)^(1/4)] + ArcTanh[(b*(-b + a*x^2)^(1/4))/(-b)^(5/4)])/(-b)^(1/4)","A",1
1824,1,444,124,4.7896049,"\int \frac{1+k^{3/2} x^3}{\sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)} \left(-1+k^{3/2} x^3\right)} \, dx","Integrate[(1 + k^(3/2)*x^3)/(Sqrt[(1 - x^2)*(1 - k^2*x^2)]*(-1 + k^(3/2)*x^3)),x]","\frac{2 \sqrt{k} \sqrt{x^2-1} \sqrt{k^2 x^2-1} \left(-\frac{\tanh ^{-1}\left(\frac{\sqrt{(k-1) k} \sqrt{x^2-1}}{\sqrt{1-k} \sqrt{k^2 x^2-1}}\right)}{\sqrt{1-k} \sqrt{(k-1) k}}-\frac{(-1)^{2/3} \tanh ^{-1}\left(\frac{\sqrt{k \left(k+\sqrt[3]{-1}\right)} \sqrt{x^2-1}}{\sqrt{\sqrt[3]{-1} k+1} \sqrt{k^2 x^2-1}}\right)}{\sqrt{k \left(k+\sqrt[3]{-1}\right)} \sqrt{\sqrt[3]{-1} k+1}}+\frac{\sqrt[3]{-1} \tanh ^{-1}\left(\frac{\sqrt{k \left(k-(-1)^{2/3}\right)} \sqrt{x^2-1}}{\sqrt{1-(-1)^{2/3} k} \sqrt{k^2 x^2-1}}\right)}{\sqrt{k \left(k-(-1)^{2/3}\right)} \sqrt{1-(-1)^{2/3} k}}\right)+3 \sqrt{1-x^2} \sqrt{1-k^2 x^2} F\left(\sin ^{-1}(x)|k^2\right)-2 \sqrt{1-x^2} \sqrt{1-k^2 x^2} \Pi \left(k;\sin ^{-1}(x)|k^2\right)-2 \sqrt{1-x^2} \sqrt{1-k^2 x^2} \Pi \left(-\sqrt[3]{-1} k;\sin ^{-1}(x)|k^2\right)-2 \sqrt{1-x^2} \sqrt{1-k^2 x^2} \Pi \left(\frac{1}{2} i \left(i+\sqrt{3}\right) k;\sin ^{-1}(x)|k^2\right)}{3 \sqrt{\left(x^2-1\right) \left(k^2 x^2-1\right)}}","-\frac{2 \tan ^{-1}\left(\frac{(k-1) x}{\sqrt{k^2 x^4+\left(-k^2-1\right) x^2+1}+k x^2-2 \sqrt{k} x+1}\right)}{3 (k-1)}-\frac{4 \tan ^{-1}\left(\frac{\sqrt{k^2+k+1} x}{\sqrt{k^2 x^4+\left(-k^2-1\right) x^2+1}+k x^2+\sqrt{k} x+1}\right)}{3 \sqrt{k^2+k+1}}",1,"(2*Sqrt[k]*Sqrt[-1 + x^2]*Sqrt[-1 + k^2*x^2]*(-(ArcTanh[(Sqrt[(-1 + k)*k]*Sqrt[-1 + x^2])/(Sqrt[1 - k]*Sqrt[-1 + k^2*x^2])]/(Sqrt[1 - k]*Sqrt[(-1 + k)*k])) - ((-1)^(2/3)*ArcTanh[(Sqrt[k*((-1)^(1/3) + k)]*Sqrt[-1 + x^2])/(Sqrt[1 + (-1)^(1/3)*k]*Sqrt[-1 + k^2*x^2])])/(Sqrt[k*((-1)^(1/3) + k)]*Sqrt[1 + (-1)^(1/3)*k]) + ((-1)^(1/3)*ArcTanh[(Sqrt[k*(-(-1)^(2/3) + k)]*Sqrt[-1 + x^2])/(Sqrt[1 - (-1)^(2/3)*k]*Sqrt[-1 + k^2*x^2])])/(Sqrt[k*(-(-1)^(2/3) + k)]*Sqrt[1 - (-1)^(2/3)*k])) + 3*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticF[ArcSin[x], k^2] - 2*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[k, ArcSin[x], k^2] - 2*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[-((-1)^(1/3)*k), ArcSin[x], k^2] - 2*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[(I/2)*(I + Sqrt[3])*k, ArcSin[x], k^2])/(3*Sqrt[(-1 + x^2)*(-1 + k^2*x^2)])","C",1
1825,1,81,124,0.0524157,"\int \frac{(-d+2 c x) \sqrt[4]{b x^3+a x^4}}{x} \, dx","Integrate[((-d + 2*c*x)*(b*x^3 + a*x^4)^(1/4))/x,x]","\frac{\sqrt[4]{x^3 (a x+b)} \left(3 c (a x+b) \sqrt[4]{\frac{a x}{b}+1}-(4 a d+3 b c) \, _2F_1\left(-\frac{1}{4},\frac{3}{4};\frac{7}{4};-\frac{a x}{b}\right)\right)}{3 a \sqrt[4]{\frac{a x}{b}+1}}","\frac{\left(4 a b d+3 b^2 c\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)}{8 a^{7/4}}+\frac{\left(-4 a b d-3 b^2 c\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)}{8 a^{7/4}}+\frac{\sqrt[4]{a x^4+b x^3} (4 a c x-4 a d+b c)}{4 a}",1,"((x^3*(b + a*x))^(1/4)*(3*c*(b + a*x)*(1 + (a*x)/b)^(1/4) - (3*b*c + 4*a*d)*Hypergeometric2F1[-1/4, 3/4, 7/4, -((a*x)/b)]))/(3*a*(1 + (a*x)/b)^(1/4))","C",1
1826,0,0,124,0.4302006,"\int \frac{-1+x^6}{\left(1+x^6\right) \sqrt[3]{1+a^3 x^3+x^6}} \, dx","Integrate[(-1 + x^6)/((1 + x^6)*(1 + a^3*x^3 + x^6)^(1/3)),x]","\int \frac{-1+x^6}{\left(1+x^6\right) \sqrt[3]{1+a^3 x^3+x^6}} \, dx","\frac{\log \left(\sqrt[3]{a^3 x^3+x^6+1}-a x\right)}{3 a}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} a x}{2 \sqrt[3]{a^3 x^3+x^6+1}+a x}\right)}{\sqrt{3} a}-\frac{\log \left(a x \sqrt[3]{a^3 x^3+x^6+1}+\left(a^3 x^3+x^6+1\right)^{2/3}+a^2 x^2\right)}{6 a}",1,"Integrate[(-1 + x^6)/((1 + x^6)*(1 + a^3*x^3 + x^6)^(1/3)), x]","F",-1
1827,0,0,124,1.2755154,"\int \frac{\left(2+x^3+4 x^6\right) \sqrt[3]{x+2 x^3-x^4-x^7}}{\left(-1-2 x^2+x^3+x^6\right) \left(-1-x^2+x^3+x^6\right)} \, dx","Integrate[((2 + x^3 + 4*x^6)*(x + 2*x^3 - x^4 - x^7)^(1/3))/((-1 - 2*x^2 + x^3 + x^6)*(-1 - x^2 + x^3 + x^6)),x]","\int \frac{\left(2+x^3+4 x^6\right) \sqrt[3]{x+2 x^3-x^4-x^7}}{\left(-1-2 x^2+x^3+x^6\right) \left(-1-x^2+x^3+x^6\right)} \, dx","-\log \left(\sqrt[3]{-x^7-x^4+2 x^3+x}-x\right)-\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{-x^7-x^4+2 x^3+x}+x}\right)+\frac{1}{2} \log \left(x^2+\sqrt[3]{-x^7-x^4+2 x^3+x} x+\left(-x^7-x^4+2 x^3+x\right)^{2/3}\right)",1,"Integrate[((2 + x^3 + 4*x^6)*(x + 2*x^3 - x^4 - x^7)^(1/3))/((-1 - 2*x^2 + x^3 + x^6)*(-1 - x^2 + x^3 + x^6)), x]","F",-1
1828,0,0,124,0.1270969,"\int \frac{x^2}{\sqrt{a x^2+\sqrt{b+a^2 x^4}}} \, dx","Integrate[x^2/Sqrt[a*x^2 + Sqrt[b + a^2*x^4]],x]","\int \frac{x^2}{\sqrt{a x^2+\sqrt{b+a^2 x^4}}} \, dx","\frac{x \sqrt{\sqrt{a^2 x^4+b}+a x^2}}{4 a}-\frac{b x}{8 a \left(\sqrt{a^2 x^4+b}+a x^2\right)^{3/2}}-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}}{\sqrt{b}}\right)}{8 \sqrt{2} a^{3/2}}",1,"Integrate[x^2/Sqrt[a*x^2 + Sqrt[b + a^2*x^4]], x]","F",-1
1829,1,124,124,0.1871066,"\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1+x^2\right)^{3/2}} \, dx","Integrate[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/(1 + x^2)^(3/2),x]","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+3 \text{$\#$1}^3-\text{$\#$1}}\&\right]-\frac{\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{x^2+\sqrt{x^2+1} x+1}","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+3 \text{$\#$1}^3-\text{$\#$1}}\&\right]-\frac{\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{x^2+\sqrt{x^2+1} x+1}",1,"-(Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/(1 + x^2 + x*Sqrt[1 + x^2])) + RootSum[2 - 4*#1^2 + 6*#1^4 - 4*#1^6 + #1^8 & , Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]/(-#1 + 3*#1^3 - 3*#1^5 + #1^7) & ]/4","A",1
1830,1,124,124,0.0371947,"\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1+x^2\right)^{3/2}} \, dx","Integrate[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/(1 + x^2)^(3/2),x]","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+3 \text{$\#$1}^3-\text{$\#$1}}\&\right]-\frac{\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{x^2+\sqrt{x^2+1} x+1}","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+3 \text{$\#$1}^3-\text{$\#$1}}\&\right]-\frac{\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{x^2+\sqrt{x^2+1} x+1}",1,"-(Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/(1 + x^2 + x*Sqrt[1 + x^2])) + RootSum[2 - 4*#1^2 + 6*#1^4 - 4*#1^6 + #1^8 & , Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]/(-#1 + 3*#1^3 - 3*#1^5 + #1^7) & ]/4","A",1
1831,1,124,124,0.0368329,"\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1+x^2\right)^{3/2}} \, dx","Integrate[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/(1 + x^2)^(3/2),x]","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+3 \text{$\#$1}^3-\text{$\#$1}}\&\right]-\frac{\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{x^2+\sqrt{x^2+1} x+1}","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+3 \text{$\#$1}^3-\text{$\#$1}}\&\right]-\frac{\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{x^2+\sqrt{x^2+1} x+1}",1,"-(Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/(1 + x^2 + x*Sqrt[1 + x^2])) + RootSum[2 - 4*#1^2 + 6*#1^4 - 4*#1^6 + #1^8 & , Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]/(-#1 + 3*#1^3 - 3*#1^5 + #1^7) & ]/4","A",1
1832,1,36,125,0.013792,"\int \frac{1}{(-1+x) \sqrt[3]{-3-2 x+x^2}} \, dx","Integrate[1/((-1 + x)*(-3 - 2*x + x^2)^(1/3)),x]","\frac{3}{16} \left((x-1)^2-4\right)^{2/3} \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{1}{4} \left(4-(x-1)^2\right)\right)","-\frac{\log \left(\sqrt[3]{2} \sqrt[3]{x^2-2 x-3}+2\right)}{2\ 2^{2/3}}+\frac{\log \left(2^{2/3} \left(x^2-2 x-3\right)^{2/3}-2 \sqrt[3]{2} \sqrt[3]{x^2-2 x-3}+4\right)}{4\ 2^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{\sqrt[3]{2} \sqrt[3]{x^2-2 x-3}}{\sqrt{3}}\right)}{2\ 2^{2/3}}",1,"(3*(-4 + (-1 + x)^2)^(2/3)*Hypergeometric2F1[2/3, 1, 5/3, (4 - (-1 + x)^2)/4])/16","C",1
1833,1,36,125,0.0119636,"\int \frac{1}{(-1+x) \sqrt[3]{-1-2 x+x^2}} \, dx","Integrate[1/((-1 + x)*(-1 - 2*x + x^2)^(1/3)),x]","\frac{3}{8} \left((x-1)^2-2\right)^{2/3} \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{1}{2} \left(2-(x-1)^2\right)\right)","-\frac{\log \left(2^{2/3} \sqrt[3]{x^2-2 x-1}+2\right)}{2 \sqrt[3]{2}}+\frac{\log \left(-\sqrt[3]{2} \left(x^2-2 x-1\right)^{2/3}+2^{2/3} \sqrt[3]{x^2-2 x-1}-2\right)}{4 \sqrt[3]{2}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2^{2/3} \sqrt[3]{x^2-2 x-1}}{\sqrt{3}}\right)}{2 \sqrt[3]{2}}",1,"(3*(-2 + (-1 + x)^2)^(2/3)*Hypergeometric2F1[2/3, 1, 5/3, (2 - (-1 + x)^2)/2])/8","C",1
1834,1,36,125,0.0120304,"\int \frac{1}{(1+x) \sqrt[3]{-1+2 x+x^2}} \, dx","Integrate[1/((1 + x)*(-1 + 2*x + x^2)^(1/3)),x]","\frac{3}{8} \left((x+1)^2-2\right)^{2/3} \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{1}{2} \left(2-(x+1)^2\right)\right)","-\frac{\log \left(2^{2/3} \sqrt[3]{x^2+2 x-1}+2\right)}{2 \sqrt[3]{2}}+\frac{\log \left(-\sqrt[3]{2} \left(x^2+2 x-1\right)^{2/3}+2^{2/3} \sqrt[3]{x^2+2 x-1}-2\right)}{4 \sqrt[3]{2}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2^{2/3} \sqrt[3]{x^2+2 x-1}}{\sqrt{3}}\right)}{2 \sqrt[3]{2}}",1,"(3*(-2 + (1 + x)^2)^(2/3)*Hypergeometric2F1[2/3, 1, 5/3, (2 - (1 + x)^2)/2])/8","C",1
1835,0,0,125,15.030709,"\int \frac{-2 a b x^2+(a+b) x^3}{(-a+x) (-b+x) \sqrt[4]{x^2 (-a+x) (-b+x)} \left(-a b d+(a+b) d x+(1-d) x^2\right)} \, dx","Integrate[(-2*a*b*x^2 + (a + b)*x^3)/((-a + x)*(-b + x)*(x^2*(-a + x)*(-b + x))^(1/4)*(-(a*b*d) + (a + b)*d*x + (1 - d)*x^2)),x]","\int \frac{-2 a b x^2+(a+b) x^3}{(-a+x) (-b+x) \sqrt[4]{x^2 (-a+x) (-b+x)} \left(-a b d+(a+b) d x+(1-d) x^2\right)} \, dx","2 \sqrt[4]{d} \tan ^{-1}\left(\frac{x}{\sqrt[4]{d} \sqrt[4]{x^3 (-a-b)+a b x^2+x^4}}\right)+2 \sqrt[4]{d} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{d} \sqrt[4]{x^3 (-a-b)+a b x^2+x^4}}\right)-\frac{4 \left(x^3 (-a-b)+a b x^2+x^4\right)^{3/4}}{x (x-a) (x-b)}",1,"Integrate[(-2*a*b*x^2 + (a + b)*x^3)/((-a + x)*(-b + x)*(x^2*(-a + x)*(-b + x))^(1/4)*(-(a*b*d) + (a + b)*d*x + (1 - d)*x^2)), x]","F",-1
1836,0,0,125,5.4822155,"\int \frac{\left(a^2-2 a x+x^2\right) \left(a b^2-2 (2 a-b) b x+(3 a-2 b) x^2\right)}{\left(x (-a+x) (-b+x)^2\right)^{3/4} \left(a^3 d+\left(b^2-3 a^2 d\right) x+(-2 b+3 a d) x^2+(1-d) x^3\right)} \, dx","Integrate[((a^2 - 2*a*x + x^2)*(a*b^2 - 2*(2*a - b)*b*x + (3*a - 2*b)*x^2))/((x*(-a + x)*(-b + x)^2)^(3/4)*(a^3*d + (b^2 - 3*a^2*d)*x + (-2*b + 3*a*d)*x^2 + (1 - d)*x^3)),x]","\int \frac{\left(a^2-2 a x+x^2\right) \left(a b^2-2 (2 a-b) b x+(3 a-2 b) x^2\right)}{\left(x (-a+x) (-b+x)^2\right)^{3/4} \left(a^3 d+\left(b^2-3 a^2 d\right) x+(-2 b+3 a d) x^2+(1-d) x^3\right)} \, dx","\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \left(x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4\right)^{3/4}}{x (x-b)^2}\right)}{d^{3/4}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \left(x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4\right)^{3/4}}{x (x-b)^2}\right)}{d^{3/4}}",1,"Integrate[((a^2 - 2*a*x + x^2)*(a*b^2 - 2*(2*a - b)*b*x + (3*a - 2*b)*x^2))/((x*(-a + x)*(-b + x)^2)^(3/4)*(a^3*d + (b^2 - 3*a^2*d)*x + (-2*b + 3*a*d)*x^2 + (1 - d)*x^3)), x]","F",-1
1837,1,444,125,4.9227122,"\int \frac{-1+k^{3/2} x^3}{\sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)} \left(1+k^{3/2} x^3\right)} \, dx","Integrate[(-1 + k^(3/2)*x^3)/(Sqrt[(1 - x^2)*(1 - k^2*x^2)]*(1 + k^(3/2)*x^3)),x]","\frac{-2 \sqrt{k} \sqrt{x^2-1} \sqrt{k^2 x^2-1} \left(-\frac{\tanh ^{-1}\left(\frac{\sqrt{(k-1) k} \sqrt{x^2-1}}{\sqrt{1-k} \sqrt{k^2 x^2-1}}\right)}{\sqrt{1-k} \sqrt{(k-1) k}}-\frac{(-1)^{2/3} \tanh ^{-1}\left(\frac{\sqrt{k \left(k+\sqrt[3]{-1}\right)} \sqrt{x^2-1}}{\sqrt{\sqrt[3]{-1} k+1} \sqrt{k^2 x^2-1}}\right)}{\sqrt{k \left(k+\sqrt[3]{-1}\right)} \sqrt{\sqrt[3]{-1} k+1}}+\frac{\sqrt[3]{-1} \tanh ^{-1}\left(\frac{\sqrt{k \left(k-(-1)^{2/3}\right)} \sqrt{x^2-1}}{\sqrt{1-(-1)^{2/3} k} \sqrt{k^2 x^2-1}}\right)}{\sqrt{k \left(k-(-1)^{2/3}\right)} \sqrt{1-(-1)^{2/3} k}}\right)+3 \sqrt{1-x^2} \sqrt{1-k^2 x^2} F\left(\sin ^{-1}(x)|k^2\right)-2 \sqrt{1-x^2} \sqrt{1-k^2 x^2} \Pi \left(k;\sin ^{-1}(x)|k^2\right)-2 \sqrt{1-x^2} \sqrt{1-k^2 x^2} \Pi \left(-\sqrt[3]{-1} k;\sin ^{-1}(x)|k^2\right)-2 \sqrt{1-x^2} \sqrt{1-k^2 x^2} \Pi \left(\frac{1}{2} i \left(i+\sqrt{3}\right) k;\sin ^{-1}(x)|k^2\right)}{3 \sqrt{\left(x^2-1\right) \left(k^2 x^2-1\right)}}","-\frac{4 \tan ^{-1}\left(\frac{\sqrt{k^2+k+1} x}{\sqrt{k^2 x^4+\left(-k^2-1\right) x^2+1}+k x^2-\sqrt{k} x+1}\right)}{3 \sqrt{k^2+k+1}}-\frac{2 \tan ^{-1}\left(\frac{(k-1) x}{\sqrt{k^2 x^4+\left(-k^2-1\right) x^2+1}+k x^2+2 \sqrt{k} x+1}\right)}{3 (k-1)}",1,"(-2*Sqrt[k]*Sqrt[-1 + x^2]*Sqrt[-1 + k^2*x^2]*(-(ArcTanh[(Sqrt[(-1 + k)*k]*Sqrt[-1 + x^2])/(Sqrt[1 - k]*Sqrt[-1 + k^2*x^2])]/(Sqrt[1 - k]*Sqrt[(-1 + k)*k])) - ((-1)^(2/3)*ArcTanh[(Sqrt[k*((-1)^(1/3) + k)]*Sqrt[-1 + x^2])/(Sqrt[1 + (-1)^(1/3)*k]*Sqrt[-1 + k^2*x^2])])/(Sqrt[k*((-1)^(1/3) + k)]*Sqrt[1 + (-1)^(1/3)*k]) + ((-1)^(1/3)*ArcTanh[(Sqrt[k*(-(-1)^(2/3) + k)]*Sqrt[-1 + x^2])/(Sqrt[1 - (-1)^(2/3)*k]*Sqrt[-1 + k^2*x^2])])/(Sqrt[k*(-(-1)^(2/3) + k)]*Sqrt[1 - (-1)^(2/3)*k])) + 3*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticF[ArcSin[x], k^2] - 2*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[k, ArcSin[x], k^2] - 2*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[-((-1)^(1/3)*k), ArcSin[x], k^2] - 2*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[(I/2)*(I + Sqrt[3])*k, ArcSin[x], k^2])/(3*Sqrt[(-1 + x^2)*(-1 + k^2*x^2)])","C",1
1838,1,2469,125,13.0862334,"\int \frac{\sqrt{-x-x^2+x^3}}{-1+x^4} \, dx","Integrate[Sqrt[-x - x^2 + x^3]/(-1 + x^4),x]","\text{Result too large to show}","\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{x^3-x^2-x}}{x^2-x-1}\right)-\frac{1}{4} \sqrt{1-2 i} \tan ^{-1}\left(\frac{\sqrt{1-2 i} \sqrt{x^3-x^2-x}}{x^2-x-1}\right)-\frac{1}{4} \sqrt{1+2 i} \tan ^{-1}\left(\frac{\sqrt{1+2 i} \sqrt{x^3-x^2-x}}{x^2-x-1}\right)",1,"(2*(-1 + Sqrt[x])*(1 + Sqrt[x])*(1 + x)*(1 + x^2)*Sqrt[x*(-1 - x + x^2)]*(Sqrt[-1 - x + x^2]/(8*(-1 + Sqrt[x])) - Sqrt[-1 - x + x^2]/(8*(1 + Sqrt[x])) + Sqrt[-1 - x + x^2]/(4*(1 + x)) - (x*Sqrt[-1 - x + x^2])/(2*(1 + x^2)))*(((1/2 + I/4)*Sqrt[(-1 + Sqrt[5])/2]*Sqrt[1 - (2*x)/(1 - Sqrt[5])]*Sqrt[1 - (2*x)/(1 + Sqrt[5])]*EllipticPi[(-1/2*I)*(1 - Sqrt[5]), I*ArcSinh[Sqrt[2/(-1 + Sqrt[5])]*Sqrt[x]], (1 - Sqrt[5])/(1 + Sqrt[5])])/Sqrt[-1 - x + x^2] - ((1/2 - I/4)*Sqrt[(-1 + Sqrt[5])/2]*Sqrt[1 - (2*x)/(1 - Sqrt[5])]*Sqrt[1 - (2*x)/(1 + Sqrt[5])]*EllipticPi[(I/2)*(1 - Sqrt[5]), I*ArcSinh[Sqrt[2/(-1 + Sqrt[5])]*Sqrt[x]], (1 - Sqrt[5])/(1 + Sqrt[5])])/Sqrt[-1 - x + x^2] - ((I/4)*Sqrt[(-1 + Sqrt[5])/2]*Sqrt[1 - (2*x)/(1 - Sqrt[5])]*Sqrt[1 - (2*x)/(1 + Sqrt[5])]*EllipticPi[(-1 + Sqrt[5])/2, I*ArcSinh[Sqrt[2/(-1 + Sqrt[5])]*Sqrt[x]], (1 - Sqrt[5])/(1 + Sqrt[5])])/Sqrt[-1 - x + x^2] + ((I*(I*Sqrt[(-1 + Sqrt[5])/2] + Sqrt[(1 + Sqrt[5])/2])*Sqrt[((Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] - (2*I)*Sqrt[x]))/((Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] + (2*I)*Sqrt[x]))]*((-I)*Sqrt[(-1 + Sqrt[5])/2] + Sqrt[x])^2*Sqrt[(I*(-Sqrt[(1 + Sqrt[5])/2] + Sqrt[x]))/((I*Sqrt[(-1 + Sqrt[5])/2] + Sqrt[(1 + Sqrt[5])/2])*((-I)*Sqrt[(-1 + Sqrt[5])/2] + Sqrt[x]))]*Sqrt[(I*(Sqrt[(1 + Sqrt[5])/2] + Sqrt[x]))/((I*Sqrt[(-1 + Sqrt[5])/2] - Sqrt[(1 + Sqrt[5])/2])*((-I)*Sqrt[(-1 + Sqrt[5])/2] + Sqrt[x]))]*((1 + I*Sqrt[(-1 + Sqrt[5])/2])*EllipticF[ArcSin[Sqrt[((Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] - (2*I)*Sqrt[x]))/((Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] + (2*I)*Sqrt[x]))]], (Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]])^2/(Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])^2] - I*Sqrt[2*(-1 + Sqrt[5])]*EllipticPi[((-1 + I*Sqrt[(-1 + Sqrt[5])/2])*(I*Sqrt[(-1 + Sqrt[5])/2] + Sqrt[(1 + Sqrt[5])/2]))/((-1 - I*Sqrt[(-1 + Sqrt[5])/2])*((-I)*Sqrt[(-1 + Sqrt[5])/2] + Sqrt[(1 + Sqrt[5])/2])), ArcSin[Sqrt[((Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] - (2*I)*Sqrt[x]))/((Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] + (2*I)*Sqrt[x]))]], (Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]])^2/(Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])^2]))/((-1 - I*Sqrt[(-1 + Sqrt[5])/2])*(1 - I*Sqrt[(-1 + Sqrt[5])/2])*(I*Sqrt[(-1 + Sqrt[5])/2] - Sqrt[(1 + Sqrt[5])/2])*Sqrt[-1 - x + x^2]) - (I*(I*Sqrt[(-1 + Sqrt[5])/2] + Sqrt[(1 + Sqrt[5])/2])*Sqrt[((Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] - (2*I)*Sqrt[x]))/((Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] + (2*I)*Sqrt[x]))]*((-I)*Sqrt[(-1 + Sqrt[5])/2] + Sqrt[x])^2*Sqrt[(I*(-Sqrt[(1 + Sqrt[5])/2] + Sqrt[x]))/((I*Sqrt[(-1 + Sqrt[5])/2] + Sqrt[(1 + Sqrt[5])/2])*((-I)*Sqrt[(-1 + Sqrt[5])/2] + Sqrt[x]))]*Sqrt[(I*(Sqrt[(1 + Sqrt[5])/2] + Sqrt[x]))/((I*Sqrt[(-1 + Sqrt[5])/2] - Sqrt[(1 + Sqrt[5])/2])*((-I)*Sqrt[(-1 + Sqrt[5])/2] + Sqrt[x]))]*((-1 + I*Sqrt[(-1 + Sqrt[5])/2])*EllipticF[ArcSin[Sqrt[((Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] - (2*I)*Sqrt[x]))/((Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] + (2*I)*Sqrt[x]))]], (Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]])^2/(Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])^2] - I*Sqrt[2*(-1 + Sqrt[5])]*EllipticPi[((1 + I*Sqrt[(-1 + Sqrt[5])/2])*(I*Sqrt[(-1 + Sqrt[5])/2] + Sqrt[(1 + Sqrt[5])/2]))/((1 - I*Sqrt[(-1 + Sqrt[5])/2])*((-I)*Sqrt[(-1 + Sqrt[5])/2] + Sqrt[(1 + Sqrt[5])/2])), ArcSin[Sqrt[((Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] - (2*I)*Sqrt[x]))/((Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] + (2*I)*Sqrt[x]))]], (Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]])^2/(Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])^2]))/((-1 - I*Sqrt[(-1 + Sqrt[5])/2])*(1 - I*Sqrt[(-1 + Sqrt[5])/2])*(I*Sqrt[(-1 + Sqrt[5])/2] - Sqrt[(1 + Sqrt[5])/2])*Sqrt[-1 - x + x^2]))/4))/(x^(3/2)*(-1 - x + x^2))","C",0
1839,1,170,125,0.3450831,"\int \frac{\left(b+a x^3\right) \sqrt{x+x^4}}{-d+c x^3} \, dx","Integrate[((b + a*x^3)*Sqrt[x + x^4])/(-d + c*x^3),x]","-\frac{x \sqrt{x^4+x} \left(x^3 \sqrt{-\frac{x^3 (c+d)}{d}} (a (c+2 d)+2 b c) F_1\left(\frac{3}{2};\frac{1}{2},1;\frac{5}{2};-x^3,\frac{c x^3}{d}\right)+3 (a d+2 b c) \sin ^{-1}\left(\frac{\sqrt{-\frac{x^3 (c+d)}{d}}}{\sqrt{1-\frac{c x^3}{d}}}\right)-3 a d \sqrt{x^3+1} \sqrt{-\frac{x^3 (c+d)}{d}}\right)}{9 c d \sqrt{x^3+1} \sqrt{-\frac{x^3 (c+d)}{d}}}","\frac{2 \sqrt{-c-d} (a d+b c) \tan ^{-1}\left(\frac{x \sqrt{x^4+x} \sqrt{-c-d}}{\sqrt{d} (x+1) \left(x^2-x+1\right)}\right)}{3 c^2 \sqrt{d}}+\frac{\tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4+x}}\right) (a c+2 a d+2 b c)}{3 c^2}+\frac{a \sqrt{x^4+x} x}{3 c}",1,"-1/9*(x*Sqrt[x + x^4]*(-3*a*d*Sqrt[-(((c + d)*x^3)/d)]*Sqrt[1 + x^3] + (2*b*c + a*(c + 2*d))*x^3*Sqrt[-(((c + d)*x^3)/d)]*AppellF1[3/2, 1/2, 1, 5/2, -x^3, (c*x^3)/d] + 3*(2*b*c + a*d)*ArcSin[Sqrt[-(((c + d)*x^3)/d)]/Sqrt[1 - (c*x^3)/d]]))/(c*d*Sqrt[-(((c + d)*x^3)/d)]*Sqrt[1 + x^3])","C",0
1840,1,70,125,0.0361474,"\int \frac{1-2 x+2 x^4}{x \sqrt[4]{-1+x^4}} \, dx","Integrate[(1 - 2*x + 2*x^4)/(x*(-1 + x^4)^(1/4)),x]","\frac{1}{3} \left(x^4-1\right)^{3/4} \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};1-x^4\right)+\frac{2}{3} \left(x^4-1\right)^{3/4}-\tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-1}}\right)-\tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-1}}\right)","\frac{2}{3} \left(x^4-1\right)^{3/4}+\tan ^{-1}\left(\frac{\sqrt[4]{x^4-1}}{x}\right)+\frac{\tan ^{-1}\left(\frac{\frac{\sqrt{x^4-1}}{\sqrt{2}}-\frac{1}{\sqrt{2}}}{\sqrt[4]{x^4-1}}\right)}{2 \sqrt{2}}-\tanh ^{-1}\left(\frac{\sqrt[4]{x^4-1}}{x}\right)-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{x^4-1}}{\sqrt{x^4-1}+1}\right)}{2 \sqrt{2}}",1,"(2*(-1 + x^4)^(3/4))/3 - ArcTan[x/(-1 + x^4)^(1/4)] - ArcTanh[x/(-1 + x^4)^(1/4)] + ((-1 + x^4)^(3/4)*Hypergeometric2F1[3/4, 1, 7/4, 1 - x^4])/3","C",1
1841,0,0,125,0.407116,"\int \frac{x^2 \left(-4 b+a x^5\right)}{\left(b+a x^5\right)^{3/4} \left(b+c x^4+a x^5\right)} \, dx","Integrate[(x^2*(-4*b + a*x^5))/((b + a*x^5)^(3/4)*(b + c*x^4 + a*x^5)),x]","\int \frac{x^2 \left(-4 b+a x^5\right)}{\left(b+a x^5\right)^{3/4} \left(b+c x^4+a x^5\right)} \, dx","\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\frac{\sqrt{a x^5+b}}{\sqrt{2} \sqrt[4]{c}}+\frac{\sqrt[4]{c} x^2}{\sqrt{2}}}{x \sqrt[4]{a x^5+b}}\right)}{c^{3/4}}-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x \sqrt[4]{a x^5+b}}{\sqrt{a x^5+b}-\sqrt{c} x^2}\right)}{c^{3/4}}",1,"Integrate[(x^2*(-4*b + a*x^5))/((b + a*x^5)^(3/4)*(b + c*x^4 + a*x^5)), x]","F",-1
1842,1,53,125,0.0153667,"\int \frac{1}{\sqrt[6]{1+2 x-x^2-4 x^3-x^4+2 x^5+x^6}} \, dx","Integrate[(1 + 2*x - x^2 - 4*x^3 - x^4 + 2*x^5 + x^6)^(-1/6),x]","\frac{3 (x-1) (x+1)^{2/3} \, _2F_1\left(\frac{2}{3},\frac{2}{3};\frac{5}{3};\frac{1-x}{2}\right)}{2\ 2^{2/3} \sqrt[6]{(x-1)^2 (x+1)^4}}","\frac{\sqrt[3]{x-1} (x+1)^{2/3} \left(-\log \left(\sqrt[3]{x-1}-\sqrt[3]{x+1}\right)+\frac{1}{2} \log \left((x-1)^{2/3}+\sqrt[3]{x+1} \sqrt[3]{x-1}+(x+1)^{2/3}\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x+1}}{2 \sqrt[3]{x-1}+\sqrt[3]{x+1}}\right)\right)}{\sqrt[6]{(x-1)^2 (x+1)^4}}",1,"(3*(-1 + x)*(1 + x)^(2/3)*Hypergeometric2F1[2/3, 2/3, 5/3, (1 - x)/2])/(2*2^(2/3)*((-1 + x)^2*(1 + x)^4)^(1/6))","C",1
1843,0,0,125,0.3301854,"\int \frac{x^2 \left(-2 b+a x^6\right)}{\left(b+a x^6\right)^{3/4} \left(b+c x^4+a x^6\right)} \, dx","Integrate[(x^2*(-2*b + a*x^6))/((b + a*x^6)^(3/4)*(b + c*x^4 + a*x^6)),x]","\int \frac{x^2 \left(-2 b+a x^6\right)}{\left(b+a x^6\right)^{3/4} \left(b+c x^4+a x^6\right)} \, dx","\frac{\tanh ^{-1}\left(\frac{\frac{\sqrt{a x^6+b}}{\sqrt{2} \sqrt[4]{c}}+\frac{\sqrt[4]{c} x^2}{\sqrt{2}}}{x \sqrt[4]{a x^6+b}}\right)}{\sqrt{2} c^{3/4}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x \sqrt[4]{a x^6+b}}{\sqrt{a x^6+b}-\sqrt{c} x^2}\right)}{\sqrt{2} c^{3/4}}",1,"Integrate[(x^2*(-2*b + a*x^6))/((b + a*x^6)^(3/4)*(b + c*x^4 + a*x^6)), x]","F",-1
1844,0,0,125,0.4535335,"\int \frac{\left(4+x^3\right) \left(1+2 x^3+x^6+x^8\right)}{x^4 \sqrt[4]{1+x^3} \left(-1-2 x^3-x^6+x^8\right)} \, dx","Integrate[((4 + x^3)*(1 + 2*x^3 + x^6 + x^8))/(x^4*(1 + x^3)^(1/4)*(-1 - 2*x^3 - x^6 + x^8)),x]","\int \frac{\left(4+x^3\right) \left(1+2 x^3+x^6+x^8\right)}{x^4 \sqrt[4]{1+x^3} \left(-1-2 x^3-x^6+x^8\right)} \, dx","\frac{4 \left(x^3+1\right)^{3/4}}{3 x^3}-2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^3+1}}\right)-2 \tanh ^{-1}\left(\frac{\sqrt[4]{x^3+1}}{x}\right)+\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{x^3+1}}{\sqrt{x^3+1}-x^2}\right)+\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{x^3+1}}{\sqrt{x^3+1}+x^2}\right)",1,"Integrate[((4 + x^3)*(1 + 2*x^3 + x^6 + x^8))/(x^4*(1 + x^3)^(1/4)*(-1 - 2*x^3 - x^6 + x^8)), x]","F",-1
1845,1,125,125,0.1022921,"\int \frac{2-x^4+2 x^8}{\sqrt[4]{1+x^4} \left(-2+x^4+x^8\right)} \, dx","Integrate[(2 - x^4 + 2*x^8)/((1 + x^4)^(1/4)*(-2 + x^4 + x^8)),x]","\tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)-\sqrt[4]{2} \tan ^{-1}\left(\frac{x}{\sqrt[4]{2} \sqrt[4]{x^4+1}}\right)-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+1}}\right)}{2 \sqrt[4]{2}}+\tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)-\sqrt[4]{2} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{2} \sqrt[4]{x^4+1}}\right)-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+1}}\right)}{2 \sqrt[4]{2}}","\tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)-\sqrt[4]{2} \tan ^{-1}\left(\frac{x}{\sqrt[4]{2} \sqrt[4]{x^4+1}}\right)-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+1}}\right)}{2 \sqrt[4]{2}}+\tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)-\sqrt[4]{2} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{2} \sqrt[4]{x^4+1}}\right)-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+1}}\right)}{2 \sqrt[4]{2}}",1,"ArcTan[x/(1 + x^4)^(1/4)] - 2^(1/4)*ArcTan[x/(2^(1/4)*(1 + x^4)^(1/4))] - ArcTan[(2^(1/4)*x)/(1 + x^4)^(1/4)]/(2*2^(1/4)) + ArcTanh[x/(1 + x^4)^(1/4)] - 2^(1/4)*ArcTanh[x/(2^(1/4)*(1 + x^4)^(1/4))] - ArcTanh[(2^(1/4)*x)/(1 + x^4)^(1/4)]/(2*2^(1/4))","A",1
1846,0,0,125,0.3671476,"\int \frac{\sqrt{b+\sqrt{b^2+a x^2}}}{\left(b^2+a x^2\right)^2} \, dx","Integrate[Sqrt[b + Sqrt[b^2 + a*x^2]]/(b^2 + a*x^2)^2,x]","\int \frac{\sqrt{b+\sqrt{b^2+a x^2}}}{\left(b^2+a x^2\right)^2} \, dx","\frac{3 x}{4 b^2 \sqrt{a x^2+b^2} \sqrt{\sqrt{a x^2+b^2}+b}}+\frac{x}{2 b \left(a x^2+b^2\right) \sqrt{\sqrt{a x^2+b^2}+b}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b} \sqrt{\sqrt{a x^2+b^2}+b}}\right)}{4 \sqrt{a} b^{5/2}}",1,"Integrate[Sqrt[b + Sqrt[b^2 + a*x^2]]/(b^2 + a*x^2)^2, x]","F",-1
1847,1,186,126,0.60595,"\int \frac{\left(b+a x^3\right) \sqrt{-x+x^4}}{-d+c x^3} \, dx","Integrate[((b + a*x^3)*Sqrt[-x + x^4])/(-d + c*x^3),x]","\frac{\sqrt{1-x^3} x^5 \sqrt{\frac{x^3 (d-c)}{d}} (a (c-2 d)-2 b c) F_1\left(\frac{3}{2};\frac{1}{2},1;\frac{5}{2};x^3,\frac{c x^3}{d}\right)+3 x^2 \left(\sqrt{1-x^3} (a d+2 b c) \sin ^{-1}\left(\frac{\sqrt{\frac{x^3 (d-c)}{d}}}{\sqrt{1-\frac{c x^3}{d}}}\right)+a d \left(x^3-1\right) \sqrt{\frac{x^3 (d-c)}{d}}\right)}{9 c d \sqrt{x \left(x^3-1\right)} \sqrt{\frac{x^3 (d-c)}{d}}}","\frac{2 \sqrt{c-d} (a d+b c) \tan ^{-1}\left(\frac{x \sqrt{x^4-x} \sqrt{c-d}}{\sqrt{d} (x-1) \left(x^2+x+1\right)}\right)}{3 c^2 \sqrt{d}}+\frac{\tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4-x}}\right) (-a c+2 a d+2 b c)}{3 c^2}+\frac{a \sqrt{x^4-x} x}{3 c}",1,"((-2*b*c + a*(c - 2*d))*x^5*Sqrt[((-c + d)*x^3)/d]*Sqrt[1 - x^3]*AppellF1[3/2, 1/2, 1, 5/2, x^3, (c*x^3)/d] + 3*x^2*(a*d*Sqrt[((-c + d)*x^3)/d]*(-1 + x^3) + (2*b*c + a*d)*Sqrt[1 - x^3]*ArcSin[Sqrt[((-c + d)*x^3)/d]/Sqrt[1 - (c*x^3)/d]]))/(9*c*d*Sqrt[((-c + d)*x^3)/d]*Sqrt[x*(-1 + x^3)])","C",0
1848,1,46,126,0.0254093,"\int \frac{b+a x^3}{x^3 \left(-b+a x^3\right) \sqrt[4]{b x+a x^4}} \, dx","Integrate[(b + a*x^3)/(x^3*(-b + a*x^3)*(b*x + a*x^4)^(1/4)),x]","\frac{4 \left(x \left(a x^3+b\right)\right)^{3/4} \, _2F_1\left(-\frac{3}{4},1;\frac{1}{4};\frac{2 a x^3}{a x^3+b}\right)}{9 b x^3}","-\frac{2\ 2^{3/4} a^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} \left(a x^4+b x\right)^{3/4}}{a x^3+b}\right)}{3 b}-\frac{2\ 2^{3/4} a^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} \left(a x^4+b x\right)^{3/4}}{a x^3+b}\right)}{3 b}+\frac{4 \left(a x^4+b x\right)^{3/4}}{9 b x^3}",1,"(4*(x*(b + a*x^3))^(3/4)*Hypergeometric2F1[-3/4, 1, 1/4, (2*a*x^3)/(b + a*x^3)])/(9*b*x^3)","C",1
1849,0,0,126,2.6661202,"\int \frac{\left(1+2 x^6\right) \sqrt[3]{x+x^3-x^7}}{\left(-1+x^6\right)^2} \, dx","Integrate[((1 + 2*x^6)*(x + x^3 - x^7)^(1/3))/(-1 + x^6)^2,x]","\int \frac{\left(1+2 x^6\right) \sqrt[3]{x+x^3-x^7}}{\left(-1+x^6\right)^2} \, dx","-\frac{1}{6} \log \left(\sqrt[3]{-x^7+x^3+x}-x\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{-x^7+x^3+x}+x}\right)}{2 \sqrt{3}}-\frac{\sqrt[3]{-x^7+x^3+x} x}{2 \left(x^6-1\right)}+\frac{1}{12} \log \left(x^2+\sqrt[3]{-x^7+x^3+x} x+\left(-x^7+x^3+x\right)^{2/3}\right)",1,"Integrate[((1 + 2*x^6)*(x + x^3 - x^7)^(1/3))/(-1 + x^6)^2, x]","F",-1
1850,1,488,127,1.5540544,"\int \frac{-\left((2 a-b) b^2\right)+(4 a-b) b x-(2 a+b) x^2+x^3}{\left((-a+x) (-b+x)^2\right)^{3/4} \left(a+b^2 d-(1+2 b d) x+d x^2\right)} \, dx","Integrate[(-((2*a - b)*b^2) + (4*a - b)*b*x - (2*a + b)*x^2 + x^3)/(((-a + x)*(-b + x)^2)^(3/4)*(a + b^2*d - (1 + 2*b*d)*x + d*x^2)),x]","\frac{2 \sqrt[4]{(x-a) (b-x)^2} \left(\sqrt[4]{a-b} \sqrt{\frac{x-b}{a-b}} \Pi \left(-\frac{\sqrt{2} \sqrt{a-b} \sqrt{d}}{\sqrt{2 a d-2 b d-\sqrt{-4 a d+4 b d+1}-1}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{a-x}}{\sqrt[4]{a-b}}\right)\right|-1\right)+\sqrt[4]{a-b} \sqrt{\frac{x-b}{a-b}} \Pi \left(\frac{\sqrt{2} \sqrt{a-b} \sqrt{d}}{\sqrt{2 a d-2 b d-\sqrt{-4 a d+4 b d+1}-1}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{a-x}}{\sqrt[4]{a-b}}\right)\right|-1\right)+\sqrt[4]{a-b} \sqrt{\frac{x-b}{a-b}} \Pi \left(-\frac{\sqrt{2} \sqrt{a-b} \sqrt{d}}{\sqrt{2 a d-2 b d+\sqrt{-4 a d+4 b d+1}-1}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{a-x}}{\sqrt[4]{a-b}}\right)\right|-1\right)+\sqrt[4]{a-b} \sqrt{\frac{x-b}{a-b}} \Pi \left(\frac{\sqrt{2} \sqrt{a-b} \sqrt{d}}{\sqrt{2 a d-2 b d+\sqrt{-4 a d+4 b d+1}-1}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{a-x}}{\sqrt[4]{a-b}}\right)\right|-1\right)+\frac{(x-b) \left(\frac{a-x}{a-b}\right)^{3/4} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{3}{2};\frac{x-b}{a-b}\right)}{(a-x)^{3/4}}\right)}{d \sqrt[4]{a-x} (b-x)}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \left(x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3\right)^{3/4}}{(x-a) (b-x)}\right)}{d^{3/4}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \left(x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3\right)^{3/4}}{(x-a) (b-x)}\right)}{d^{3/4}}",1,"(2*((b - x)^2*(-a + x))^(1/4)*((a - b)^(1/4)*Sqrt[(-b + x)/(a - b)]*EllipticPi[-((Sqrt[2]*Sqrt[a - b]*Sqrt[d])/Sqrt[-1 + 2*a*d - 2*b*d - Sqrt[1 - 4*a*d + 4*b*d]]), ArcSin[(a - x)^(1/4)/(a - b)^(1/4)], -1] + (a - b)^(1/4)*Sqrt[(-b + x)/(a - b)]*EllipticPi[(Sqrt[2]*Sqrt[a - b]*Sqrt[d])/Sqrt[-1 + 2*a*d - 2*b*d - Sqrt[1 - 4*a*d + 4*b*d]], ArcSin[(a - x)^(1/4)/(a - b)^(1/4)], -1] + (a - b)^(1/4)*Sqrt[(-b + x)/(a - b)]*EllipticPi[-((Sqrt[2]*Sqrt[a - b]*Sqrt[d])/Sqrt[-1 + 2*a*d - 2*b*d + Sqrt[1 - 4*a*d + 4*b*d]]), ArcSin[(a - x)^(1/4)/(a - b)^(1/4)], -1] + (a - b)^(1/4)*Sqrt[(-b + x)/(a - b)]*EllipticPi[(Sqrt[2]*Sqrt[a - b]*Sqrt[d])/Sqrt[-1 + 2*a*d - 2*b*d + Sqrt[1 - 4*a*d + 4*b*d]], ArcSin[(a - x)^(1/4)/(a - b)^(1/4)], -1] + (((a - x)/(a - b))^(3/4)*(-b + x)*Hypergeometric2F1[1/2, 3/4, 3/2, (-b + x)/(a - b)])/(a - x)^(3/4)))/(d*(a - x)^(1/4)*(b - x))","C",1
1851,1,130,127,15.8837073,"\int \frac{2+x^4}{\sqrt[4]{x^2+x^4} \left(-1-x^4+2 x^8\right)} \, dx","Integrate[(2 + x^4)/((x^2 + x^4)^(1/4)*(-1 - x^4 + 2*x^8)),x]","\frac{x \left(\sqrt[4]{\frac{1}{x^2}+1} \left(2 \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4+3\&,\frac{\log \left(\sqrt[4]{\frac{1}{x^2}+1}-\text{$\#$1}\right)}{\text{$\#$1}}\&\right]+2^{3/4} \left(\log \left(2-2^{3/4} \sqrt[4]{\frac{1}{x^2}+1}\right)-\log \left(2^{3/4} \sqrt[4]{\frac{1}{x^2}+1}+2\right)+2 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{x^2}+1}}{\sqrt[4]{2}}\right)\right)\right)-8\right)}{8 \sqrt[4]{x^4+x^2}}","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4+3\&,\frac{\log \left(\sqrt[4]{x^4+x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]-\frac{\left(x^4+x^2\right)^{3/4}}{x \left(x^2+1\right)}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+x^2}}\right)}{2 \sqrt[4]{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+x^2}}\right)}{2 \sqrt[4]{2}}",1,"(x*(-8 + (1 + x^(-2))^(1/4)*(2^(3/4)*(2*ArcTan[(1 + x^(-2))^(1/4)/2^(1/4)] + Log[2 - 2^(3/4)*(1 + x^(-2))^(1/4)] - Log[2 + 2^(3/4)*(1 + x^(-2))^(1/4)]) + 2*RootSum[3 - 2*#1^4 + #1^8 & , Log[(1 + x^(-2))^(1/4) - #1]/#1 & ])))/(8*(x^2 + x^4)^(1/4))","A",1
1852,1,130,127,0.4989173,"\int \frac{2+x^4}{\sqrt[4]{x^2+x^4} \left(-1-x^4+2 x^8\right)} \, dx","Integrate[(2 + x^4)/((x^2 + x^4)^(1/4)*(-1 - x^4 + 2*x^8)),x]","\frac{x \left(\sqrt[4]{\frac{1}{x^2}+1} \left(2 \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4+3\&,\frac{\log \left(\sqrt[4]{\frac{1}{x^2}+1}-\text{$\#$1}\right)}{\text{$\#$1}}\&\right]+2^{3/4} \left(\log \left(2-2^{3/4} \sqrt[4]{\frac{1}{x^2}+1}\right)-\log \left(2^{3/4} \sqrt[4]{\frac{1}{x^2}+1}+2\right)+2 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{x^2}+1}}{\sqrt[4]{2}}\right)\right)\right)-8\right)}{8 \sqrt[4]{x^4+x^2}}","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4+3\&,\frac{\log \left(\sqrt[4]{x^4+x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]-\frac{\left(x^4+x^2\right)^{3/4}}{x \left(x^2+1\right)}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+x^2}}\right)}{2 \sqrt[4]{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+x^2}}\right)}{2 \sqrt[4]{2}}",1,"(x*(-8 + (1 + x^(-2))^(1/4)*(2^(3/4)*(2*ArcTan[(1 + x^(-2))^(1/4)/2^(1/4)] + Log[2 - 2^(3/4)*(1 + x^(-2))^(1/4)] - Log[2 + 2^(3/4)*(1 + x^(-2))^(1/4)]) + 2*RootSum[3 - 2*#1^4 + #1^8 & , Log[(1 + x^(-2))^(1/4) - #1]/#1 & ])))/(8*(x^2 + x^4)^(1/4))","A",1
1853,1,85,127,0.0522166,"\int \frac{\sqrt{x+\sqrt{1+x}}}{x^2} \, dx","Integrate[Sqrt[x + Sqrt[1 + x]]/x^2,x]","-\frac{\sqrt{x+\sqrt{x+1}}}{x}+\frac{1}{4} \tan ^{-1}\left(\frac{-\sqrt{x+1}-3}{2 \sqrt{x+\sqrt{x+1}}}\right)-\frac{3}{4} \tanh ^{-1}\left(\frac{3 \sqrt{x+1}-1}{2 \sqrt{x+\sqrt{x+1}}}\right)","-\frac{\sqrt{x+\sqrt{x+1}}}{x}-\frac{1}{4} \tan ^{-1}\left(\frac{2 x+\sqrt{x+1} \left(3-2 \sqrt{x+\sqrt{x+1}}\right)-2 \sqrt{x+\sqrt{x+1}}+1}{2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+2}\right)-\frac{3}{2} \tanh ^{-1}\left(-\sqrt{x+1}+\sqrt{x+\sqrt{x+1}}+1\right)",1,"-(Sqrt[x + Sqrt[1 + x]]/x) + ArcTan[(-3 - Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])]/4 - (3*ArcTanh[(-1 + 3*Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])])/4","A",1
1854,1,150,127,0.3381429,"\int \frac{(-1+x) \sqrt{x+\sqrt{1+x^2}}}{1+x} \, dx","Integrate[((-1 + x)*Sqrt[x + Sqrt[1 + x^2]])/(1 + x),x]","\frac{1}{3} \left(\sqrt{x^2+1}+x\right)^{3/2}-4 \sqrt{\sqrt{x^2+1}+x}-\frac{1}{\sqrt{\sqrt{x^2+1}+x}}+4 \sqrt{\sqrt{2}-1} \left(1+\sqrt{2}\right) \tan ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{1+\sqrt{2}}}\right)+4 \left(\sqrt{2}-1\right) \sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{\sqrt{2}-1}}\right)","\frac{2 \sqrt{x^2+1} (x-6)+2 \left(x^2-6 x-1\right)}{3 \sqrt{\sqrt{x^2+1}+x}}+4 \sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{1+\sqrt{2}}}\right)+4 \sqrt{\sqrt{2}-1} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{\sqrt{2}-1}}\right)",1,"-(1/Sqrt[x + Sqrt[1 + x^2]]) - 4*Sqrt[x + Sqrt[1 + x^2]] + (x + Sqrt[1 + x^2])^(3/2)/3 + 4*Sqrt[-1 + Sqrt[2]]*(1 + Sqrt[2])*ArcTan[Sqrt[x + Sqrt[1 + x^2]]/Sqrt[1 + Sqrt[2]]] + 4*(-1 + Sqrt[2])*Sqrt[1 + Sqrt[2]]*ArcTanh[Sqrt[x + Sqrt[1 + x^2]]/Sqrt[-1 + Sqrt[2]]]","A",1
1855,1,150,127,0.3053818,"\int \frac{(1+x) \sqrt{x+\sqrt{1+x^2}}}{-1+x} \, dx","Integrate[((1 + x)*Sqrt[x + Sqrt[1 + x^2]])/(-1 + x),x]","\frac{1}{3} \left(\sqrt{x^2+1}+x\right)^{3/2}+4 \sqrt{\sqrt{x^2+1}+x}-\frac{1}{\sqrt{\sqrt{x^2+1}+x}}-4 \left(\sqrt{2}-1\right) \sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{\sqrt{2}-1}}\right)-4 \sqrt{\sqrt{2}-1} \left(1+\sqrt{2}\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{1+\sqrt{2}}}\right)","\frac{2 \sqrt{x^2+1} (x+6)+2 \left(x^2+6 x-1\right)}{3 \sqrt{\sqrt{x^2+1}+x}}-4 \sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{\sqrt{2}-1}}\right)-4 \sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{1+\sqrt{2}}}\right)",1,"-(1/Sqrt[x + Sqrt[1 + x^2]]) + 4*Sqrt[x + Sqrt[1 + x^2]] + (x + Sqrt[1 + x^2])^(3/2)/3 - 4*(-1 + Sqrt[2])*Sqrt[1 + Sqrt[2]]*ArcTan[Sqrt[x + Sqrt[1 + x^2]]/Sqrt[-1 + Sqrt[2]]] - 4*Sqrt[-1 + Sqrt[2]]*(1 + Sqrt[2])*ArcTanh[Sqrt[x + Sqrt[1 + x^2]]/Sqrt[1 + Sqrt[2]]]","A",1
1856,0,0,128,0.298539,"\int \frac{6+2 x+x^2}{(1+x) \sqrt[3]{2+x+x^2} \left(2-x+2 x^2\right)} \, dx","Integrate[(6 + 2*x + x^2)/((1 + x)*(2 + x + x^2)^(1/3)*(2 - x + 2*x^2)),x]","\int \frac{6+2 x+x^2}{(1+x) \sqrt[3]{2+x+x^2} \left(2-x+2 x^2\right)} \, dx","\frac{\log \left(\sqrt[3]{x^2+x+2}+\sqrt[3]{2} x\right)}{\sqrt[3]{2}}-\frac{\log \left(2^{2/3} x^2-\sqrt[3]{2} \sqrt[3]{x^2+x+2} x+\left(x^2+x+2\right)^{2/3}\right)}{2 \sqrt[3]{2}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{x^2+x+2}}{\sqrt{3}}-\frac{2 \sqrt[3]{2} x}{\sqrt{3}}}{\sqrt[3]{x^2+x+2}}\right)}{\sqrt[3]{2}}",1,"Integrate[(6 + 2*x + x^2)/((1 + x)*(2 + x + x^2)^(1/3)*(2 - x + 2*x^2)), x]","F",-1
1857,1,165,128,0.0773542,"\int \frac{1}{x \left(-b+a x^3\right)^{3/4}} \, dx","Integrate[1/(x*(-b + a*x^3)^(3/4)),x]","\frac{-\log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^3-b}+\sqrt{a x^3-b}+\sqrt{b}\right)+\log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^3-b}+\sqrt{a x^3-b}+\sqrt{b}\right)-2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a x^3-b}}{\sqrt[4]{b}}\right)+2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x^3-b}}{\sqrt[4]{b}}+1\right)}{3 \sqrt{2} b^{3/4}}","\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\frac{\sqrt{a x^3-b}}{\sqrt{2} \sqrt[4]{b}}+\frac{\sqrt[4]{b}}{\sqrt{2}}}{\sqrt[4]{a x^3-b}}\right)}{3 b^{3/4}}-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^3-b}}{\sqrt{a x^3-b}-\sqrt{b}}\right)}{3 b^{3/4}}",1,"(-2*ArcTan[1 - (Sqrt[2]*(-b + a*x^3)^(1/4))/b^(1/4)] + 2*ArcTan[1 + (Sqrt[2]*(-b + a*x^3)^(1/4))/b^(1/4)] - Log[Sqrt[b] - Sqrt[2]*b^(1/4)*(-b + a*x^3)^(1/4) + Sqrt[-b + a*x^3]] + Log[Sqrt[b] + Sqrt[2]*b^(1/4)*(-b + a*x^3)^(1/4) + Sqrt[-b + a*x^3]])/(3*Sqrt[2]*b^(3/4))","A",1
1858,1,57,128,0.0217841,"\int \frac{1}{x \sqrt[4]{-b+a x^3}} \, dx","Integrate[1/(x*(-b + a*x^3)^(1/4)),x]","\frac{2 \left(\tan ^{-1}\left(\frac{\sqrt[4]{a x^3-b}}{\sqrt[4]{-b}}\right)+\tanh ^{-1}\left(\frac{b \sqrt[4]{a x^3-b}}{(-b)^{5/4}}\right)\right)}{3 \sqrt[4]{-b}}","-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^3-b}}{\sqrt{a x^3-b}-\sqrt{b}}\right)}{3 \sqrt[4]{b}}-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\frac{\sqrt{a x^3-b}}{\sqrt{2} \sqrt[4]{b}}+\frac{\sqrt[4]{b}}{\sqrt{2}}}{\sqrt[4]{a x^3-b}}\right)}{3 \sqrt[4]{b}}",1,"(2*(ArcTan[(-b + a*x^3)^(1/4)/(-b)^(1/4)] + ArcTanh[(b*(-b + a*x^3)^(1/4))/(-b)^(5/4)]))/(3*(-b)^(1/4))","A",1
1859,0,0,128,2.2199498,"\int \frac{\left(-3 b+a x^2\right) \left(b-a x^2+x^3\right)}{x^3 \left(-b+a x^2+x^3\right) \sqrt[4]{-b x+a x^3}} \, dx","Integrate[((-3*b + a*x^2)*(b - a*x^2 + x^3))/(x^3*(-b + a*x^2 + x^3)*(-(b*x) + a*x^3)^(1/4)),x]","\int \frac{\left(-3 b+a x^2\right) \left(b-a x^2+x^3\right)}{x^3 \left(-b+a x^2+x^3\right) \sqrt[4]{-b x+a x^3}} \, dx","\frac{4 \left(a x^3-b x\right)^{3/4}}{3 x^3}-2 \sqrt{2} \tan ^{-1}\left(\frac{\frac{\sqrt{a x^3-b x}}{\sqrt{2}}-\frac{x^2}{\sqrt{2}}}{x \sqrt[4]{a x^3-b x}}\right)+2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{a x^3-b x}}{\sqrt{a x^3-b x}+x^2}\right)",1,"Integrate[((-3*b + a*x^2)*(b - a*x^2 + x^3))/(x^3*(-b + a*x^2 + x^3)*(-(b*x) + a*x^3)^(1/4)), x]","F",-1
1860,1,165,128,0.0706918,"\int \frac{1}{x \left(-b+a x^4\right)^{3/4}} \, dx","Integrate[1/(x*(-b + a*x^4)^(3/4)),x]","\frac{-\log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^4-b}+\sqrt{a x^4-b}+\sqrt{b}\right)+\log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^4-b}+\sqrt{a x^4-b}+\sqrt{b}\right)-2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a x^4-b}}{\sqrt[4]{b}}\right)+2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x^4-b}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} b^{3/4}}","\frac{\tanh ^{-1}\left(\frac{\frac{\sqrt{a x^4-b}}{\sqrt{2} \sqrt[4]{b}}+\frac{\sqrt[4]{b}}{\sqrt{2}}}{\sqrt[4]{a x^4-b}}\right)}{2 \sqrt{2} b^{3/4}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^4-b}}{\sqrt{a x^4-b}-\sqrt{b}}\right)}{2 \sqrt{2} b^{3/4}}",1,"(-2*ArcTan[1 - (Sqrt[2]*(-b + a*x^4)^(1/4))/b^(1/4)] + 2*ArcTan[1 + (Sqrt[2]*(-b + a*x^4)^(1/4))/b^(1/4)] - Log[Sqrt[b] - Sqrt[2]*b^(1/4)*(-b + a*x^4)^(1/4) + Sqrt[-b + a*x^4]] + Log[Sqrt[b] + Sqrt[2]*b^(1/4)*(-b + a*x^4)^(1/4) + Sqrt[-b + a*x^4]])/(4*Sqrt[2]*b^(3/4))","A",1
1861,1,57,128,0.0220674,"\int \frac{1}{x \sqrt[4]{-b+a x^4}} \, dx","Integrate[1/(x*(-b + a*x^4)^(1/4)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a x^4-b}}{\sqrt[4]{-b}}\right)+\tanh ^{-1}\left(\frac{b \sqrt[4]{a x^4-b}}{(-b)^{5/4}}\right)}{2 \sqrt[4]{-b}}","-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^4-b}}{\sqrt{a x^4-b}-\sqrt{b}}\right)}{2 \sqrt{2} \sqrt[4]{b}}-\frac{\tanh ^{-1}\left(\frac{\frac{\sqrt{a x^4-b}}{\sqrt{2} \sqrt[4]{b}}+\frac{\sqrt[4]{b}}{\sqrt{2}}}{\sqrt[4]{a x^4-b}}\right)}{2 \sqrt{2} \sqrt[4]{b}}",1,"(ArcTan[(-b + a*x^4)^(1/4)/(-b)^(1/4)] + ArcTanh[(b*(-b + a*x^4)^(1/4))/(-b)^(5/4)])/(2*(-b)^(1/4))","A",1
1862,1,230,128,0.448093,"\int \frac{1-x^5}{\sqrt{a+b x} \left(1+x^5\right)} \, dx","Integrate[(1 - x^5)/(Sqrt[a + b*x]*(1 + x^5)),x]","\frac{2}{5} \left(-\frac{5 \sqrt{a+b x}}{b}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a-b}}\right)}{\sqrt{a-b}}+\frac{2 \sqrt[5]{-1} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a+\sqrt[5]{-1} b}}\right)}{\sqrt{a+\sqrt[5]{-1} b}}-\frac{2 (-1)^{2/5} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a-(-1)^{2/5} b}}\right)}{\sqrt{a-(-1)^{2/5} b}}+\frac{2 (-1)^{3/5} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a+(-1)^{3/5} b}}\right)}{\sqrt{a+(-1)^{3/5} b}}-\frac{2 (-1)^{4/5} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a-(-1)^{4/5} b}}\right)}{\sqrt{a-(-1)^{4/5} b}}\right)","\frac{2}{5} b^4 \text{RootSum}\left[-\text{$\#$1}^{10}+5 \text{$\#$1}^8 a-10 \text{$\#$1}^6 a^2+10 \text{$\#$1}^4 a^3-5 \text{$\#$1}^2 a^4+a^5-b^5\&,\frac{\log \left(\sqrt{a+b x}-\text{$\#$1}\right)}{\text{$\#$1}^9-4 \text{$\#$1}^7 a+6 \text{$\#$1}^5 a^2-4 \text{$\#$1}^3 a^3+\text{$\#$1} a^4}\&\right]-\frac{2 \sqrt{a+b x}}{b}",1,"(2*((-5*Sqrt[a + b*x])/b - (2*ArcTanh[Sqrt[a + b*x]/Sqrt[a - b]])/Sqrt[a - b] + (2*(-1)^(1/5)*ArcTanh[Sqrt[a + b*x]/Sqrt[a + (-1)^(1/5)*b]])/Sqrt[a + (-1)^(1/5)*b] - (2*(-1)^(2/5)*ArcTanh[Sqrt[a + b*x]/Sqrt[a - (-1)^(2/5)*b]])/Sqrt[a - (-1)^(2/5)*b] + (2*(-1)^(3/5)*ArcTanh[Sqrt[a + b*x]/Sqrt[a + (-1)^(3/5)*b]])/Sqrt[a + (-1)^(3/5)*b] - (2*(-1)^(4/5)*ArcTanh[Sqrt[a + b*x]/Sqrt[a - (-1)^(4/5)*b]])/Sqrt[a - (-1)^(4/5)*b]))/5","A",0
1863,1,165,128,0.072088,"\int \frac{1}{x \left(-b+a x^5\right)^{3/4}} \, dx","Integrate[1/(x*(-b + a*x^5)^(3/4)),x]","\frac{-\log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^5-b}+\sqrt{a x^5-b}+\sqrt{b}\right)+\log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^5-b}+\sqrt{a x^5-b}+\sqrt{b}\right)-2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a x^5-b}}{\sqrt[4]{b}}\right)+2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x^5-b}}{\sqrt[4]{b}}+1\right)}{5 \sqrt{2} b^{3/4}}","\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\frac{\sqrt{a x^5-b}}{\sqrt{2} \sqrt[4]{b}}+\frac{\sqrt[4]{b}}{\sqrt{2}}}{\sqrt[4]{a x^5-b}}\right)}{5 b^{3/4}}-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^5-b}}{\sqrt{a x^5-b}-\sqrt{b}}\right)}{5 b^{3/4}}",1,"(-2*ArcTan[1 - (Sqrt[2]*(-b + a*x^5)^(1/4))/b^(1/4)] + 2*ArcTan[1 + (Sqrt[2]*(-b + a*x^5)^(1/4))/b^(1/4)] - Log[Sqrt[b] - Sqrt[2]*b^(1/4)*(-b + a*x^5)^(1/4) + Sqrt[-b + a*x^5]] + Log[Sqrt[b] + Sqrt[2]*b^(1/4)*(-b + a*x^5)^(1/4) + Sqrt[-b + a*x^5]])/(5*Sqrt[2]*b^(3/4))","A",1
1864,1,165,128,0.0706837,"\int \frac{1}{x \left(-b+a x^6\right)^{3/4}} \, dx","Integrate[1/(x*(-b + a*x^6)^(3/4)),x]","\frac{-\log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^6-b}+\sqrt{a x^6-b}+\sqrt{b}\right)+\log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^6-b}+\sqrt{a x^6-b}+\sqrt{b}\right)-2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a x^6-b}}{\sqrt[4]{b}}\right)+2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x^6-b}}{\sqrt[4]{b}}+1\right)}{6 \sqrt{2} b^{3/4}}","\frac{\tanh ^{-1}\left(\frac{\frac{\sqrt{a x^6-b}}{\sqrt{2} \sqrt[4]{b}}+\frac{\sqrt[4]{b}}{\sqrt{2}}}{\sqrt[4]{a x^6-b}}\right)}{3 \sqrt{2} b^{3/4}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^6-b}}{\sqrt{a x^6-b}-\sqrt{b}}\right)}{3 \sqrt{2} b^{3/4}}",1,"(-2*ArcTan[1 - (Sqrt[2]*(-b + a*x^6)^(1/4))/b^(1/4)] + 2*ArcTan[1 + (Sqrt[2]*(-b + a*x^6)^(1/4))/b^(1/4)] - Log[Sqrt[b] - Sqrt[2]*b^(1/4)*(-b + a*x^6)^(1/4) + Sqrt[-b + a*x^6]] + Log[Sqrt[b] + Sqrt[2]*b^(1/4)*(-b + a*x^6)^(1/4) + Sqrt[-b + a*x^6]])/(6*Sqrt[2]*b^(3/4))","A",1
1865,0,0,128,0.5917136,"\int \frac{\left(1+x^4\right) \left(-1+x^2+x^4\right)^{3/2}}{\left(-1+x^4\right) \left(1+x^2-x^4-x^6+x^8\right)} \, dx","Integrate[((1 + x^4)*(-1 + x^2 + x^4)^(3/2))/((-1 + x^4)*(1 + x^2 - x^4 - x^6 + x^8)),x]","\int \frac{\left(1+x^4\right) \left(-1+x^2+x^4\right)^{3/2}}{\left(-1+x^4\right) \left(1+x^2-x^4-x^6+x^8\right)} \, dx","-\sqrt{\frac{1}{2} \left(3-i \sqrt{3}\right)} \tan ^{-1}\left(\frac{\sqrt{-\frac{3}{2}-\frac{i \sqrt{3}}{2}} x}{\sqrt{x^4+x^2-1}}\right)-\sqrt{\frac{1}{2} \left(3+i \sqrt{3}\right)} \tan ^{-1}\left(\frac{\sqrt{-\frac{3}{2}+\frac{i \sqrt{3}}{2}} x}{\sqrt{x^4+x^2-1}}\right)-\tanh ^{-1}\left(\frac{x}{\sqrt{x^4+x^2-1}}\right)",1,"Integrate[((1 + x^4)*(-1 + x^2 + x^4)^(3/2))/((-1 + x^4)*(1 + x^2 - x^4 - x^6 + x^8)), x]","F",-1
1866,0,0,128,1.2276842,"\int \frac{\left(-1+x^6\right) \left(1+x^3+x^6\right)^{2/3}}{1+x^6+x^{12}} \, dx","Integrate[((-1 + x^6)*(1 + x^3 + x^6)^(2/3))/(1 + x^6 + x^12),x]","\int \frac{\left(-1+x^6\right) \left(1+x^3+x^6\right)^{2/3}}{1+x^6+x^{12}} \, dx","\frac{\log \left(2^{2/3} \sqrt[3]{x^6+x^3+1}-2 x\right)}{3 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^6+x^3+1}+x}\right)}{\sqrt[3]{2} \sqrt{3}}-\frac{\log \left(2 x^2+2^{2/3} \sqrt[3]{x^6+x^3+1} x+\sqrt[3]{2} \left(x^6+x^3+1\right)^{2/3}\right)}{6 \sqrt[3]{2}}",1,"Integrate[((-1 + x^6)*(1 + x^3 + x^6)^(2/3))/(1 + x^6 + x^12), x]","F",-1
1867,0,0,128,1.162587,"\int \frac{\left(-1+x^3\right)^3 \left(1+x^3\right) \sqrt{2+3 x^6+2 x^{12}}}{x^7 \left(1+x^6\right)} \, dx","Integrate[((-1 + x^3)^3*(1 + x^3)*Sqrt[2 + 3*x^6 + 2*x^12])/(x^7*(1 + x^6)),x]","\int \frac{\left(-1+x^3\right)^3 \left(1+x^3\right) \sqrt{2+3 x^6+2 x^{12}}}{x^7 \left(1+x^6\right)} \, dx","-\frac{\log \left(\sqrt{2} x^6+\sqrt{2 x^{12}+3 x^6+2}+\sqrt{2}\right)}{6 \sqrt{2}}+\frac{\sqrt{2 x^{12}+3 x^6+2} \left(x^6-4 x^3+1\right)}{6 x^6}-\frac{4}{3} \tan ^{-1}\left(\frac{x^3}{\sqrt{2} x^6+\sqrt{2 x^{12}+3 x^6+2}+\sqrt{2}}\right)+\frac{\log (x)}{2 \sqrt{2}}",1,"Integrate[((-1 + x^3)^3*(1 + x^3)*Sqrt[2 + 3*x^6 + 2*x^12])/(x^7*(1 + x^6)), x]","F",-1
1868,0,0,128,3.8174825,"\int \frac{\sqrt{a x-\sqrt{b+a^2 x^2}}}{a^2 x^2+\sqrt{b+a^2 x^2}} \, dx","Integrate[Sqrt[a*x - Sqrt[b + a^2*x^2]]/(a^2*x^2 + Sqrt[b + a^2*x^2]),x]","\int \frac{\sqrt{a x-\sqrt{b+a^2 x^2}}}{a^2 x^2+\sqrt{b+a^2 x^2}} \, dx","-\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^6-2 \text{$\#$1}^4 b-2 \text{$\#$1}^2 b+b^2\&,\frac{\text{$\#$1}^5 \log \left(\sqrt{a x-\sqrt{a^2 x^2+b}}-\text{$\#$1}\right)+\text{$\#$1} b \log \left(\sqrt{a x-\sqrt{a^2 x^2+b}}-\text{$\#$1}\right)}{-2 \text{$\#$1}^6+3 \text{$\#$1}^4+2 \text{$\#$1}^2 b+b}\&\right]}{a}",1,"Integrate[Sqrt[a*x - Sqrt[b + a^2*x^2]]/(a^2*x^2 + Sqrt[b + a^2*x^2]), x]","F",-1
1869,1,1053,128,5.0938143,"\int \frac{d+c x}{\sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Integrate[(d + c*x)/Sqrt[a*x + Sqrt[b^2 + a^2*x^2]],x]","\frac{2 \left(b^2+a^2 x^2\right)^{3/2} \left(2 c b^{26}+a \left(\sqrt{b^2+a^2 x^2} (5 d+49 c x)+2 a x (65 d+302 c x)\right) b^{24}+40 a^3 x^2 \left(2 \sqrt{b^2+a^2 x^2} (21 d+62 c x)+a x (361 d+773 c x)\right) b^{22}+2288 a^5 x^4 \left(2 \sqrt{b^2+a^2 x^2} (20 d+33 c x)+a x (205 d+277 c x)\right) b^{20}+9152 a^7 x^6 \left(2 \sqrt{b^2+a^2 x^2} (105 d+118 c x)+a x (765 d+749 c x)\right) b^{18}+18304 a^9 x^8 \left(5 \sqrt{b^2+a^2 x^2} (225 d+191 c x)+a x (3175 d+2441 c x)\right) b^{16}+106496 a^{11} x^{10} \left(2 \sqrt{b^2+a^2 x^2} (605 d+414 c x)+a x (2785 d+1773 c x)\right) b^{14}+1392640 a^{13} x^{12} \left(14 \sqrt{b^2+a^2 x^2} (26 d+15 c x)+a x (707 d+387 c x)\right) b^{12}+3342336 a^{15} x^{14} \left(2 \sqrt{b^2+a^2 x^2} (195 d+98 c x)+a x (655 d+317 c x)\right) b^{10}+1245184 a^{17} x^{16} \left(3 \sqrt{b^2+a^2 x^2} (595 d+267 c x)+2 a x (1320 d+577 c x)\right) b^8+524288 a^{19} x^{18} \left(10 \sqrt{b^2+a^2 x^2} (475 d+194 c x)+a x (6275 d+2519 c x)\right) b^6+1048576 a^{21} x^{20} \left(2 \sqrt{b^2+a^2 x^2} (840 d+317 c x)+a x (2005 d+749 c x)\right) b^4+20971520 a^{23} x^{22} \left(2 \sqrt{b^2+a^2 x^2} (17 d+6 c x)+a x (37 d+13 c x)\right) b^2+41943040 a^{25} x^{24} (3 d+c x) \left(a x+\sqrt{b^2+a^2 x^2}\right)\right)}{15 a^2 \left(a x+\sqrt{b^2+a^2 x^2}\right)^{9/2} \left(512 a^{11} x^{11}+512 a^{10} \sqrt{b^2+a^2 x^2} x^{10}+1536 a^9 b^2 x^9+1280 a^8 b^2 \sqrt{b^2+a^2 x^2} x^8+1696 a^7 b^4 x^7+1120 a^6 b^4 \sqrt{b^2+a^2 x^2} x^6+832 a^5 b^6 x^5+400 a^4 b^6 \sqrt{b^2+a^2 x^2} x^4+170 a^3 b^8 x^3+50 a^2 b^8 \sqrt{b^2+a^2 x^2} x^2+10 a b^{10} x+b^{10} \sqrt{b^2+a^2 x^2}\right) \left(b^2+a x \left(a x+\sqrt{b^2+a^2 x^2}\right)\right) \left(b^{10}+a x \left(41 a x+9 \sqrt{b^2+a^2 x^2}\right) b^8+40 a^3 x^3 \left(7 a x+3 \sqrt{b^2+a^2 x^2}\right) b^6+16 a^5 x^5 \left(43 a x+27 \sqrt{b^2+a^2 x^2}\right) b^4+64 a^7 x^7 \left(11 a x+9 \sqrt{b^2+a^2 x^2}\right) b^2+256 a^9 x^9 \left(a x+\sqrt{b^2+a^2 x^2}\right)\right)}","\frac{c \left(\sqrt{a^2 x^2+b^2}+a x\right)^{3/2}}{6 a^2}-\frac{b^2 d}{3 a \left(\sqrt{a^2 x^2+b^2}+a x\right)^{3/2}}+\frac{d \sqrt{\sqrt{a^2 x^2+b^2}+a x}}{a}+\frac{b^4 c}{10 a^2 \left(\sqrt{a^2 x^2+b^2}+a x\right)^{5/2}}",1,"(2*(b^2 + a^2*x^2)^(3/2)*(2*b^26*c + 41943040*a^25*x^24*(3*d + c*x)*(a*x + Sqrt[b^2 + a^2*x^2]) + 20971520*a^23*b^2*x^22*(a*x*(37*d + 13*c*x) + 2*(17*d + 6*c*x)*Sqrt[b^2 + a^2*x^2]) + 1392640*a^13*b^12*x^12*(a*x*(707*d + 387*c*x) + 14*(26*d + 15*c*x)*Sqrt[b^2 + a^2*x^2]) + 2288*a^5*b^20*x^4*(a*x*(205*d + 277*c*x) + 2*(20*d + 33*c*x)*Sqrt[b^2 + a^2*x^2]) + a*b^24*(2*a*x*(65*d + 302*c*x) + (5*d + 49*c*x)*Sqrt[b^2 + a^2*x^2]) + 40*a^3*b^22*x^2*(a*x*(361*d + 773*c*x) + 2*(21*d + 62*c*x)*Sqrt[b^2 + a^2*x^2]) + 3342336*a^15*b^10*x^14*(a*x*(655*d + 317*c*x) + 2*(195*d + 98*c*x)*Sqrt[b^2 + a^2*x^2]) + 9152*a^7*b^18*x^6*(a*x*(765*d + 749*c*x) + 2*(105*d + 118*c*x)*Sqrt[b^2 + a^2*x^2]) + 18304*a^9*b^16*x^8*(a*x*(3175*d + 2441*c*x) + 5*(225*d + 191*c*x)*Sqrt[b^2 + a^2*x^2]) + 524288*a^19*b^6*x^18*(a*x*(6275*d + 2519*c*x) + 10*(475*d + 194*c*x)*Sqrt[b^2 + a^2*x^2]) + 1245184*a^17*b^8*x^16*(2*a*x*(1320*d + 577*c*x) + 3*(595*d + 267*c*x)*Sqrt[b^2 + a^2*x^2]) + 1048576*a^21*b^4*x^20*(a*x*(2005*d + 749*c*x) + 2*(840*d + 317*c*x)*Sqrt[b^2 + a^2*x^2]) + 106496*a^11*b^14*x^10*(a*x*(2785*d + 1773*c*x) + 2*(605*d + 414*c*x)*Sqrt[b^2 + a^2*x^2])))/(15*a^2*(a*x + Sqrt[b^2 + a^2*x^2])^(9/2)*(10*a*b^10*x + 170*a^3*b^8*x^3 + 832*a^5*b^6*x^5 + 1696*a^7*b^4*x^7 + 1536*a^9*b^2*x^9 + 512*a^11*x^11 + b^10*Sqrt[b^2 + a^2*x^2] + 50*a^2*b^8*x^2*Sqrt[b^2 + a^2*x^2] + 400*a^4*b^6*x^4*Sqrt[b^2 + a^2*x^2] + 1120*a^6*b^4*x^6*Sqrt[b^2 + a^2*x^2] + 1280*a^8*b^2*x^8*Sqrt[b^2 + a^2*x^2] + 512*a^10*x^10*Sqrt[b^2 + a^2*x^2])*(b^2 + a*x*(a*x + Sqrt[b^2 + a^2*x^2]))*(b^10 + 256*a^9*x^9*(a*x + Sqrt[b^2 + a^2*x^2]) + 40*a^3*b^6*x^3*(7*a*x + 3*Sqrt[b^2 + a^2*x^2]) + 64*a^7*b^2*x^7*(11*a*x + 9*Sqrt[b^2 + a^2*x^2]) + a*b^8*x*(41*a*x + 9*Sqrt[b^2 + a^2*x^2]) + 16*a^5*b^4*x^5*(43*a*x + 27*Sqrt[b^2 + a^2*x^2])))","B",1
1870,1,49,128,0.0333226,"\int \frac{1}{\sqrt{1+\sqrt{1+\sqrt{1+x}}}} \, dx","Integrate[1/Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]],x]","\frac{8}{105} \left(15 \sqrt{x+1}-33 \sqrt{\sqrt{x+1}+1}+37\right) \left(\sqrt{\sqrt{x+1}+1}+1\right)^{3/2}","\sqrt{x+1} \left(\frac{8}{7} \sqrt{\sqrt{x+1}+1} \sqrt{\sqrt{\sqrt{x+1}+1}+1}-\frac{48}{35} \sqrt{\sqrt{\sqrt{x+1}+1}+1}\right)+\frac{32}{105} \sqrt{\sqrt{x+1}+1} \sqrt{\sqrt{\sqrt{x+1}+1}+1}+\frac{32}{105} \sqrt{\sqrt{\sqrt{x+1}+1}+1}",1,"(8*(37 + 15*Sqrt[1 + x] - 33*Sqrt[1 + Sqrt[1 + x]])*(1 + Sqrt[1 + Sqrt[1 + x]])^(3/2))/105","A",1
1871,1,62,129,0.0242382,"\int \frac{\left(-b+a x^2\right) \sqrt[3]{x+x^3}}{x^2} \, dx","Integrate[((-b + a*x^2)*(x + x^3)^(1/3))/x^2,x]","\frac{3 \sqrt[3]{x^3+x} \left(x^2 (a-3 b) \, _2F_1\left(-\frac{1}{3},\frac{2}{3};\frac{5}{3};-x^2\right)+2 b \left(x^2+1\right)^{4/3}\right)}{4 x \sqrt[3]{x^2+1}}","\frac{1}{6} (3 b-a) \log \left(\sqrt[3]{x^3+x}-x\right)+\frac{1}{6} \left(3 \sqrt{3} b-\sqrt{3} a\right) \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+x}+x}\right)+\frac{\sqrt[3]{x^3+x} \left(a x^2+3 b\right)}{2 x}+\frac{1}{12} (a-3 b) \log \left(\sqrt[3]{x^3+x} x+\left(x^3+x\right)^{2/3}+x^2\right)",1,"(3*(x + x^3)^(1/3)*(2*b*(1 + x^2)^(4/3) + (a - 3*b)*x^2*Hypergeometric2F1[-1/3, 2/3, 5/3, -x^2]))/(4*x*(1 + x^2)^(1/3))","C",1
1872,1,228,129,0.662544,"\int \frac{1}{x^3 \sqrt[3]{-b x^2+a x^3} \left(d+c x^3\right)} \, dx","Integrate[1/(x^3*(-(b*x^2) + a*x^3)^(1/3)*(d + c*x^3)),x]","\frac{27 a^3 d x^3-9 a^2 b d x^2-40 b^3 c x^3 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};-\frac{\left(a+\frac{b \sqrt[3]{c}}{\sqrt[3]{d}}\right) x}{b-a x}\right)-40 b^3 c x^3 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(\left(1-i \sqrt{3}\right) b \sqrt[3]{c}-2 a \sqrt[3]{d}\right) x}{2 \sqrt[3]{d} (b-a x)}\right)-40 b^3 c x^3 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(\left(1+i \sqrt{3}\right) b \sqrt[3]{c}-2 a \sqrt[3]{d}\right) x}{2 \sqrt[3]{d} (b-a x)}\right)-3 a b^2 d x-15 b^3 d}{40 b^3 d^2 x^2 \sqrt[3]{x^2 (a x-b)}}","\frac{c \text{RootSum}\left[\text{$\#$1}^9 (-d)+3 \text{$\#$1}^6 a d-3 \text{$\#$1}^3 a^2 d+a^3 d+b^3 c\&,\frac{\log \left(\sqrt[3]{a x^3-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{3 d^2}+\frac{3 \left(a x^3-b x^2\right)^{2/3} \left(9 a^2 x^2+6 a b x+5 b^2\right)}{40 b^3 d x^4}",1,"(-15*b^3*d - 3*a*b^2*d*x - 9*a^2*b*d*x^2 + 27*a^3*d*x^3 - 40*b^3*c*x^3*Hypergeometric2F1[1/3, 1, 4/3, -(((a + (b*c^(1/3))/d^(1/3))*x)/(b - a*x))] - 40*b^3*c*x^3*Hypergeometric2F1[1/3, 1, 4/3, (((1 - I*Sqrt[3])*b*c^(1/3) - 2*a*d^(1/3))*x)/(2*d^(1/3)*(b - a*x))] - 40*b^3*c*x^3*Hypergeometric2F1[1/3, 1, 4/3, (((1 + I*Sqrt[3])*b*c^(1/3) - 2*a*d^(1/3))*x)/(2*d^(1/3)*(b - a*x))])/(40*b^3*d^2*x^2*(x^2*(-b + a*x))^(1/3))","C",1
1873,1,329,129,1.428038,"\int \frac{-1+x^4}{\sqrt{-x-x^2+x^3} \left(1+x^4\right)} \, dx","Integrate[(-1 + x^4)/(Sqrt[-x - x^2 + x^3]*(1 + x^4)),x]","-\frac{i \sqrt{\frac{2}{\sqrt{5}-1}} \sqrt{-\frac{1}{x^2}-\frac{1}{x}+1} x^{3/2} \left(2 F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{1+\sqrt{5}}}}{\sqrt{x}}\right)|-\frac{3}{2}-\frac{\sqrt{5}}{2}\right)-\Pi \left(-\frac{1}{2} \sqrt[4]{-1} \left(1+\sqrt{5}\right);i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{1+\sqrt{5}}}}{\sqrt{x}}\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)-\Pi \left(\frac{1}{2} \sqrt[4]{-1} \left(1+\sqrt{5}\right);i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{1+\sqrt{5}}}}{\sqrt{x}}\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)-\Pi \left(-\frac{1}{2} (-1)^{3/4} \left(1+\sqrt{5}\right);i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{1+\sqrt{5}}}}{\sqrt{x}}\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)-\Pi \left(\frac{1}{2} (-1)^{3/4} \left(1+\sqrt{5}\right);i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{1+\sqrt{5}}}}{\sqrt{x}}\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)\right)}{\sqrt{x \left(x^2-x-1\right)}}","-\sqrt{\frac{1}{3} \left(1+i \sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{1-i \sqrt{2}} \sqrt{x^3-x^2-x}}{x^2-x-1}\right)-\sqrt{\frac{1}{3} \left(1-i \sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{1+i \sqrt{2}} \sqrt{x^3-x^2-x}}{x^2-x-1}\right)",1,"((-I)*Sqrt[2/(-1 + Sqrt[5])]*Sqrt[1 - x^(-2) - x^(-1)]*x^(3/2)*(2*EllipticF[I*ArcSinh[Sqrt[2/(1 + Sqrt[5])]/Sqrt[x]], -3/2 - Sqrt[5]/2] - EllipticPi[-1/2*((-1)^(1/4)*(1 + Sqrt[5])), I*ArcSinh[Sqrt[2/(1 + Sqrt[5])]/Sqrt[x]], (-3 - Sqrt[5])/2] - EllipticPi[((-1)^(1/4)*(1 + Sqrt[5]))/2, I*ArcSinh[Sqrt[2/(1 + Sqrt[5])]/Sqrt[x]], (-3 - Sqrt[5])/2] - EllipticPi[-1/2*((-1)^(3/4)*(1 + Sqrt[5])), I*ArcSinh[Sqrt[2/(1 + Sqrt[5])]/Sqrt[x]], (-3 - Sqrt[5])/2] - EllipticPi[((-1)^(3/4)*(1 + Sqrt[5]))/2, I*ArcSinh[Sqrt[2/(1 + Sqrt[5])]/Sqrt[x]], (-3 - Sqrt[5])/2]))/Sqrt[x*(-1 - x + x^2)]","C",0
1874,1,101,129,0.0902886,"\int \sqrt{-1-11 x-36 x^2-27 x^3+16 x^4+9 x^5+x^6} \, dx","Integrate[Sqrt[-1 - 11*x - 36*x^2 - 27*x^3 + 16*x^4 + 9*x^5 + x^6],x]","\frac{\sqrt{x^2-x-1} \left(x^2+5 x+1\right) \left(325 \tanh ^{-1}\left(\frac{1-2 x}{2 \sqrt{x^2-x-1}}\right)+2 \sqrt{x^2-x-1} \left(16 x^3+104 x^2-6 x-185\right)\right)}{128 \sqrt{\left(x^2-x-1\right) \left(x^2+5 x+1\right)^2}}","-\frac{325}{128} \log \left(x^2+5 x+1\right)+\frac{\sqrt{x^6+9 x^5+16 x^4-27 x^3-36 x^2-11 x-1} \left(16 x^3+104 x^2-6 x-185\right)}{64 \left(x^2+5 x+1\right)}+\frac{325}{128} \log \left(-2 x^3-9 x^2+2 \sqrt{x^6+9 x^5+16 x^4-27 x^3-36 x^2-11 x-1}+3 x+1\right)",1,"(Sqrt[-1 - x + x^2]*(1 + 5*x + x^2)*(2*Sqrt[-1 - x + x^2]*(-185 - 6*x + 104*x^2 + 16*x^3) + 325*ArcTanh[(1 - 2*x)/(2*Sqrt[-1 - x + x^2])]))/(128*Sqrt[(-1 - x + x^2)*(1 + 5*x + x^2)^2])","A",1
1875,0,0,129,0.6145829,"\int \frac{\left(-q+2 p x^3\right) \left(a q+b x+a p x^3\right) \sqrt{q^2-2 p q x^2+2 p q x^3+p^2 x^6}}{x^4} \, dx","Integrate[((-q + 2*p*x^3)*(a*q + b*x + a*p*x^3)*Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6])/x^4,x]","\int \frac{\left(-q+2 p x^3\right) \left(a q+b x+a p x^3\right) \sqrt{q^2-2 p q x^2+2 p q x^3+p^2 x^6}}{x^4} \, dx","\frac{\sqrt{p^2 x^6+2 p q x^3-2 p q x^2+q^2} \left(2 a p^2 x^6+4 a p q x^3-4 a p q x^2+2 a q^2+3 b p x^4+3 b q x\right)}{6 x^3}-b p q \log \left(\sqrt{p^2 x^6+2 p q x^3-2 p q x^2+q^2}+p x^3+q\right)+b p q \log (x)",1,"Integrate[((-q + 2*p*x^3)*(a*q + b*x + a*p*x^3)*Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6])/x^4, x]","F",-1
1876,1,129,129,0.1072421,"\int \frac{-2-x^4+2 x^8}{\sqrt[4]{-1+x^4} \left(-2-x^4+x^8\right)} \, dx","Integrate[(-2 - x^4 + 2*x^8)/((-1 + x^4)^(1/4)*(-2 - x^4 + x^8)),x]","\tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-1}}\right)-\frac{1}{3} \sqrt[4]{2} \tan ^{-1}\left(\frac{x}{\sqrt[4]{2} \sqrt[4]{x^4-1}}\right)-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-1}}\right)}{6 \sqrt[4]{2}}+\tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-1}}\right)-\frac{1}{3} \sqrt[4]{2} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{2} \sqrt[4]{x^4-1}}\right)-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-1}}\right)}{6 \sqrt[4]{2}}","\tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-1}}\right)-\frac{1}{3} \sqrt[4]{2} \tan ^{-1}\left(\frac{x}{\sqrt[4]{2} \sqrt[4]{x^4-1}}\right)-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-1}}\right)}{6 \sqrt[4]{2}}+\tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-1}}\right)-\frac{1}{3} \sqrt[4]{2} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{2} \sqrt[4]{x^4-1}}\right)-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-1}}\right)}{6 \sqrt[4]{2}}",1,"ArcTan[x/(-1 + x^4)^(1/4)] - (2^(1/4)*ArcTan[x/(2^(1/4)*(-1 + x^4)^(1/4))])/3 - ArcTan[(2^(1/4)*x)/(-1 + x^4)^(1/4)]/(6*2^(1/4)) + ArcTanh[x/(-1 + x^4)^(1/4)] - (2^(1/4)*ArcTanh[x/(2^(1/4)*(-1 + x^4)^(1/4))])/3 - ArcTanh[(2^(1/4)*x)/(-1 + x^4)^(1/4)]/(6*2^(1/4))","A",1
1877,1,112,129,0.3484322,"\int \frac{\left(-1+x^4\right) \sqrt{1+\sqrt{1+x}}}{1+x^4} \, dx","Integrate[((-1 + x^4)*Sqrt[1 + Sqrt[1 + x]])/(1 + x^4),x]","\frac{4}{15} \sqrt{\sqrt{x+1}+1} \left(3 x+\sqrt{x+1}+1\right)-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^{16}-8 \text{$\#$1}^{14}+24 \text{$\#$1}^{12}-32 \text{$\#$1}^{10}+16 \text{$\#$1}^8+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^{11}-6 \text{$\#$1}^9+12 \text{$\#$1}^7-8 \text{$\#$1}^5}\&\right]","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^{16}-8 \text{$\#$1}^{14}+24 \text{$\#$1}^{12}-32 \text{$\#$1}^{10}+16 \text{$\#$1}^8+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^{11}-6 \text{$\#$1}^9+12 \text{$\#$1}^7-8 \text{$\#$1}^5}\&\right]+\frac{4}{15} \sqrt{\sqrt{x+1}+1} (3 x+1)+\frac{4}{15} \sqrt{x+1} \sqrt{\sqrt{x+1}+1}",1,"(4*Sqrt[1 + Sqrt[1 + x]]*(1 + 3*x + Sqrt[1 + x]))/15 - RootSum[1 + 16*#1^8 - 32*#1^10 + 24*#1^12 - 8*#1^14 + #1^16 & , Log[Sqrt[1 + Sqrt[1 + x]] - #1]/(-8*#1^5 + 12*#1^7 - 6*#1^9 + #1^11) & ]/2","A",1
1878,1,112,129,0.2032374,"\int \frac{\left(-1+x^4\right) \sqrt{1+\sqrt{1+x}}}{1+x^4} \, dx","Integrate[((-1 + x^4)*Sqrt[1 + Sqrt[1 + x]])/(1 + x^4),x]","\frac{4}{15} \sqrt{\sqrt{x+1}+1} \left(3 x+\sqrt{x+1}+1\right)-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^{16}-8 \text{$\#$1}^{14}+24 \text{$\#$1}^{12}-32 \text{$\#$1}^{10}+16 \text{$\#$1}^8+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^{11}-6 \text{$\#$1}^9+12 \text{$\#$1}^7-8 \text{$\#$1}^5}\&\right]","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^{16}-8 \text{$\#$1}^{14}+24 \text{$\#$1}^{12}-32 \text{$\#$1}^{10}+16 \text{$\#$1}^8+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^{11}-6 \text{$\#$1}^9+12 \text{$\#$1}^7-8 \text{$\#$1}^5}\&\right]+\frac{4}{15} \sqrt{\sqrt{x+1}+1} (3 x+1)+\frac{4}{15} \sqrt{x+1} \sqrt{\sqrt{x+1}+1}",1,"(4*Sqrt[1 + Sqrt[1 + x]]*(1 + 3*x + Sqrt[1 + x]))/15 - RootSum[1 + 16*#1^8 - 32*#1^10 + 24*#1^12 - 8*#1^14 + #1^16 & , Log[Sqrt[1 + Sqrt[1 + x]] - #1]/(-8*#1^5 + 12*#1^7 - 6*#1^9 + #1^11) & ]/2","A",1
1879,1,75,130,0.0721423,"\int \frac{\left(b+a x^2\right) \sqrt{b x+a x^3}}{x^2 \left(-b+a x^2\right)} \, dx","Integrate[((b + a*x^2)*Sqrt[b*x + a*x^3])/(x^2*(-b + a*x^2)),x]","\frac{6 \left(a x^2+b\right)-8 a x^2 \sqrt{\frac{a x^2}{b}+1} F_1\left(\frac{3}{4};\frac{1}{2},1;\frac{7}{4};-\frac{a x^2}{b},\frac{a x^2}{b}\right)}{3 \sqrt{x \left(a x^2+b\right)}}","\frac{2 \sqrt{a x^3+b x}}{x}+\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{a x^3+b x}}{a x^2+b}\right)-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{a x^3+b x}}{a x^2+b}\right)",1,"(6*(b + a*x^2) - 8*a*x^2*Sqrt[1 + (a*x^2)/b]*AppellF1[3/4, 1/2, 1, 7/4, -((a*x^2)/b), (a*x^2)/b])/(3*Sqrt[x*(b + a*x^2)])","C",0
1880,0,0,130,7.8607625,"\int \frac{(-2 a b+(3 a-b) x) \left(-a^3+3 a^2 x-3 a x^2+x^3\right)}{x (-b+x) \sqrt[4]{x^2 (-a+x) (-b+x)} \left(a^3-3 a^2 x+(3 a-b d) x^2+(-1+d) x^3\right)} \, dx","Integrate[((-2*a*b + (3*a - b)*x)*(-a^3 + 3*a^2*x - 3*a*x^2 + x^3))/(x*(-b + x)*(x^2*(-a + x)*(-b + x))^(1/4)*(a^3 - 3*a^2*x + (3*a - b*d)*x^2 + (-1 + d)*x^3)),x]","\int \frac{(-2 a b+(3 a-b) x) \left(-a^3+3 a^2 x-3 a x^2+x^3\right)}{x (-b+x) \sqrt[4]{x^2 (-a+x) (-b+x)} \left(a^3-3 a^2 x+(3 a-b d) x^2+(-1+d) x^3\right)} \, dx","2 \sqrt[4]{d} \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{x^3 (-a-b)+a b x^2+x^4}}{a-x}\right)-2 \sqrt[4]{d} \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{x^3 (-a-b)+a b x^2+x^4}}{a-x}\right)-\frac{4 \left(x^3 (-a-b)+a b x^2+x^4\right)^{3/4}}{x^2 (x-b)}",1,"Integrate[((-2*a*b + (3*a - b)*x)*(-a^3 + 3*a^2*x - 3*a*x^2 + x^3))/(x*(-b + x)*(x^2*(-a + x)*(-b + x))^(1/4)*(a^3 - 3*a^2*x + (3*a - b*d)*x^2 + (-1 + d)*x^3)), x]","F",-1
1881,0,0,130,0.2981372,"\int \frac{2 b+a x^2}{\sqrt[4]{b+a x^2} \left(b n+a n x^2+2 x^4\right)} \, dx","Integrate[(2*b + a*x^2)/((b + a*x^2)^(1/4)*(b*n + a*n*x^2 + 2*x^4)),x]","\int \frac{2 b+a x^2}{\sqrt[4]{b+a x^2} \left(b n+a n x^2+2 x^4\right)} \, dx","\frac{\tan ^{-1}\left(\frac{\frac{x^2}{\sqrt[4]{2} \sqrt[4]{n}}-\frac{\sqrt[4]{n} \sqrt{a x^2+b}}{2^{3/4}}}{x \sqrt[4]{a x^2+b}}\right)}{2^{3/4} n^{3/4}}+\frac{\tanh ^{-1}\left(\frac{\frac{\sqrt[4]{n} \sqrt{a x^2+b}}{2^{3/4}}+\frac{x^2}{\sqrt[4]{2} \sqrt[4]{n}}}{x \sqrt[4]{a x^2+b}}\right)}{2^{3/4} n^{3/4}}",1,"Integrate[(2*b + a*x^2)/((b + a*x^2)^(1/4)*(b*n + a*n*x^2 + 2*x^4)), x]","F",-1
1882,1,241,130,0.7078834,"\int \frac{\sqrt{1+x} \left(-1+x^2\right)}{\left(1+x^2\right) \sqrt{1+\sqrt{1+x}}} \, dx","Integrate[(Sqrt[1 + x]*(-1 + x^2))/((1 + x^2)*Sqrt[1 + Sqrt[1 + x]]),x]","-\frac{4}{15} \sqrt{\sqrt{x+1}+1} \left(-3 x+4 \sqrt{x+1}-11\right)-\frac{4 \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x+1}+1}}{\sqrt{1-\sqrt{1-i}}}\right)}{(1-i)^{3/2} \sqrt{1-\sqrt{1-i}}}+\frac{4 \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x+1}+1}}{\sqrt{1+\sqrt{1-i}}}\right)}{(1-i)^{3/2} \sqrt{1+\sqrt{1-i}}}+2 i \sqrt{\frac{1+i}{1-\sqrt{1+i}}} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x+1}+1}}{\sqrt{1-\sqrt{1+i}}}\right)+\frac{4 \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x+1}+1}}{\sqrt{1+\sqrt{1+i}}}\right)}{(1+i)^{3/2} \sqrt{1+\sqrt{1+i}}}","-\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4+1\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^5-2 \text{$\#$1}^3}\&\right]+\frac{4}{15} \sqrt{\sqrt{x+1}+1} (3 x+11)-\frac{16}{15} \sqrt{x+1} \sqrt{\sqrt{x+1}+1}",1,"(-4*Sqrt[1 + Sqrt[1 + x]]*(-11 - 3*x + 4*Sqrt[1 + x]))/15 - (4*ArcTanh[Sqrt[1 + Sqrt[1 + x]]/Sqrt[1 - Sqrt[1 - I]]])/((1 - I)^(3/2)*Sqrt[1 - Sqrt[1 - I]]) + (4*ArcTanh[Sqrt[1 + Sqrt[1 + x]]/Sqrt[1 + Sqrt[1 - I]]])/((1 - I)^(3/2)*Sqrt[1 + Sqrt[1 - I]]) + (2*I)*Sqrt[(1 + I)/(1 - Sqrt[1 + I])]*ArcTanh[Sqrt[1 + Sqrt[1 + x]]/Sqrt[1 - Sqrt[1 + I]]] + (4*ArcTanh[Sqrt[1 + Sqrt[1 + x]]/Sqrt[1 + Sqrt[1 + I]]])/((1 + I)^(3/2)*Sqrt[1 + Sqrt[1 + I]])","C",0
1883,1,241,130,0.2710977,"\int \frac{\sqrt{1+x} \left(-1+x^2\right)}{\left(1+x^2\right) \sqrt{1+\sqrt{1+x}}} \, dx","Integrate[(Sqrt[1 + x]*(-1 + x^2))/((1 + x^2)*Sqrt[1 + Sqrt[1 + x]]),x]","-\frac{4}{15} \sqrt{\sqrt{x+1}+1} \left(-3 x+4 \sqrt{x+1}-11\right)-\frac{4 \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x+1}+1}}{\sqrt{1-\sqrt{1-i}}}\right)}{(1-i)^{3/2} \sqrt{1-\sqrt{1-i}}}+\frac{4 \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x+1}+1}}{\sqrt{1+\sqrt{1-i}}}\right)}{(1-i)^{3/2} \sqrt{1+\sqrt{1-i}}}+2 i \sqrt{\frac{1+i}{1-\sqrt{1+i}}} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x+1}+1}}{\sqrt{1-\sqrt{1+i}}}\right)+\frac{4 \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x+1}+1}}{\sqrt{1+\sqrt{1+i}}}\right)}{(1+i)^{3/2} \sqrt{1+\sqrt{1+i}}}","-\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4+1\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^5-2 \text{$\#$1}^3}\&\right]+\frac{4}{15} \sqrt{\sqrt{x+1}+1} (3 x+11)-\frac{16}{15} \sqrt{x+1} \sqrt{\sqrt{x+1}+1}",1,"(-4*Sqrt[1 + Sqrt[1 + x]]*(-11 - 3*x + 4*Sqrt[1 + x]))/15 - (4*ArcTanh[Sqrt[1 + Sqrt[1 + x]]/Sqrt[1 - Sqrt[1 - I]]])/((1 - I)^(3/2)*Sqrt[1 - Sqrt[1 - I]]) + (4*ArcTanh[Sqrt[1 + Sqrt[1 + x]]/Sqrt[1 + Sqrt[1 - I]]])/((1 - I)^(3/2)*Sqrt[1 + Sqrt[1 - I]]) + (2*I)*Sqrt[(1 + I)/(1 - Sqrt[1 + I])]*ArcTanh[Sqrt[1 + Sqrt[1 + x]]/Sqrt[1 - Sqrt[1 + I]]] + (4*ArcTanh[Sqrt[1 + Sqrt[1 + x]]/Sqrt[1 + Sqrt[1 + I]]])/((1 + I)^(3/2)*Sqrt[1 + Sqrt[1 + I]])","C",0
1884,1,106,130,0.3154695,"\int \frac{\left(-1+x^4\right) \sqrt{1+\sqrt{1+x}}}{\sqrt{1+x} \left(1+x^4\right)} \, dx","Integrate[((-1 + x^4)*Sqrt[1 + Sqrt[1 + x]])/(Sqrt[1 + x]*(1 + x^4)),x]","\frac{1}{6} \left(8 \left(\sqrt{x+1}+1\right)^{3/2}-3 \text{RootSum}\left[\text{$\#$1}^{16}-8 \text{$\#$1}^{14}+24 \text{$\#$1}^{12}-32 \text{$\#$1}^{10}+16 \text{$\#$1}^8+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^{13}-7 \text{$\#$1}^{11}+18 \text{$\#$1}^9-20 \text{$\#$1}^7+8 \text{$\#$1}^5}\&\right]\right)","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^{16}-8 \text{$\#$1}^{14}+24 \text{$\#$1}^{12}-32 \text{$\#$1}^{10}+16 \text{$\#$1}^8+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^{13}-7 \text{$\#$1}^{11}+18 \text{$\#$1}^9-20 \text{$\#$1}^7+8 \text{$\#$1}^5}\&\right]+\frac{4}{3} \sqrt{x+1} \sqrt{\sqrt{x+1}+1}+\frac{4}{3} \sqrt{\sqrt{x+1}+1}",1,"(8*(1 + Sqrt[1 + x])^(3/2) - 3*RootSum[1 + 16*#1^8 - 32*#1^10 + 24*#1^12 - 8*#1^14 + #1^16 & , Log[Sqrt[1 + Sqrt[1 + x]] - #1]/(8*#1^5 - 20*#1^7 + 18*#1^9 - 7*#1^11 + #1^13) & ])/6","A",1
1885,1,106,130,0.1497323,"\int \frac{\left(-1+x^4\right) \sqrt{1+\sqrt{1+x}}}{\sqrt{1+x} \left(1+x^4\right)} \, dx","Integrate[((-1 + x^4)*Sqrt[1 + Sqrt[1 + x]])/(Sqrt[1 + x]*(1 + x^4)),x]","\frac{1}{6} \left(8 \left(\sqrt{x+1}+1\right)^{3/2}-3 \text{RootSum}\left[\text{$\#$1}^{16}-8 \text{$\#$1}^{14}+24 \text{$\#$1}^{12}-32 \text{$\#$1}^{10}+16 \text{$\#$1}^8+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^{13}-7 \text{$\#$1}^{11}+18 \text{$\#$1}^9-20 \text{$\#$1}^7+8 \text{$\#$1}^5}\&\right]\right)","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^{16}-8 \text{$\#$1}^{14}+24 \text{$\#$1}^{12}-32 \text{$\#$1}^{10}+16 \text{$\#$1}^8+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^{13}-7 \text{$\#$1}^{11}+18 \text{$\#$1}^9-20 \text{$\#$1}^7+8 \text{$\#$1}^5}\&\right]+\frac{4}{3} \sqrt{x+1} \sqrt{\sqrt{x+1}+1}+\frac{4}{3} \sqrt{\sqrt{x+1}+1}",1,"(8*(1 + Sqrt[1 + x])^(3/2) - 3*RootSum[1 + 16*#1^8 - 32*#1^10 + 24*#1^12 - 8*#1^14 + #1^16 & , Log[Sqrt[1 + Sqrt[1 + x]] - #1]/(8*#1^5 - 20*#1^7 + 18*#1^9 - 7*#1^11 + #1^13) & ])/6","A",1
1886,1,128,130,0.2441261,"\int \frac{1+a x^2}{\left(-1+a x^2\right) \sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[(1 + a*x^2)/((-1 + a*x^2)*Sqrt[x + Sqrt[1 + x^2]]),x]","-\text{RootSum}\left[\text{$\#$1}^8 a-2 \text{$\#$1}^4 a-4 \text{$\#$1}^4+a\&,\frac{\text{$\#$1}^4 \log \left(\frac{1}{\sqrt{\sqrt{x^2+1}+x}}-\text{$\#$1}\right)+\log \left(\frac{1}{\sqrt{\sqrt{x^2+1}+x}}-\text{$\#$1}\right)}{\text{$\#$1}^5 a-\text{$\#$1} a-2 \text{$\#$1}}\&\right]+\sqrt{\sqrt{x^2+1}+x}-\frac{1}{3 \left(\sqrt{x^2+1}+x\right)^{3/2}}","\text{RootSum}\left[\text{$\#$1}^8 a-2 \text{$\#$1}^4 a-4 \text{$\#$1}^4+a\&,\frac{\text{$\#$1}^4 \log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)}{\text{$\#$1}^7 a-\text{$\#$1}^3 a-2 \text{$\#$1}^3}\&\right]+\sqrt{\sqrt{x^2+1}+x}-\frac{1}{3 \left(\sqrt{x^2+1}+x\right)^{3/2}}",1,"-1/3*1/(x + Sqrt[1 + x^2])^(3/2) + Sqrt[x + Sqrt[1 + x^2]] - RootSum[a - 4*#1^4 - 2*a*#1^4 + a*#1^8 & , (Log[1/Sqrt[x + Sqrt[1 + x^2]] - #1] + Log[1/Sqrt[x + Sqrt[1 + x^2]] - #1]*#1^4)/(-2*#1 - a*#1 + a*#1^5) & ]","A",1
1887,1,137,130,0.4309686,"\int \frac{x \sqrt{x+x^2}}{\sqrt{x^2+x \sqrt{x+x^2}}} \, dx","Integrate[(x*Sqrt[x + x^2])/Sqrt[x^2 + x*Sqrt[x + x^2]],x]","\frac{\left(x+\sqrt{x (x+1)}\right)^2 \sqrt{x \left(x+\sqrt{x (x+1)}\right)} \left(x+\sqrt{x (x+1)}+1\right) \left(17 \, _2F_1\left(-\frac{5}{2},1;-\frac{3}{2};1+\frac{1}{2 \left(x+\sqrt{x (x+1)}\right)}\right)+10 \left(8 x^2+\left(8 \sqrt{x (x+1)}+11\right) x+7 \sqrt{x (x+1)}\right)\right)}{80 \sqrt{x (x+1)} \left(2 x+2 \sqrt{x (x+1)}+1\right)^3}","\frac{\sqrt{x^2+x} \sqrt{x \left(\sqrt{x^2+x}+x\right)} \left(-384 x^2-136 x+255\right)}{960 x}+\sqrt{x \left(\sqrt{x^2+x}+x\right)} \left(\frac{1}{960} \left(384 x^2+568 x-85\right)-\frac{17 \sqrt{\sqrt{x^2+x}-x} \tanh ^{-1}\left(\sqrt{2} \sqrt{\sqrt{x^2+x}-x}\right)}{64 \sqrt{2} x}\right)",1,"((x + Sqrt[x*(1 + x)])^2*Sqrt[x*(x + Sqrt[x*(1 + x)])]*(1 + x + Sqrt[x*(1 + x)])*(10*(8*x^2 + 7*Sqrt[x*(1 + x)] + x*(11 + 8*Sqrt[x*(1 + x)])) + 17*Hypergeometric2F1[-5/2, 1, -3/2, 1 + 1/(2*(x + Sqrt[x*(1 + x)]))]))/(80*Sqrt[x*(1 + x)]*(1 + 2*x + 2*Sqrt[x*(1 + x)])^3)","C",1
1888,1,170,130,0.1317001,"\int \frac{\sqrt{1+x}}{1+\sqrt{x+\sqrt{1+x}}} \, dx","Integrate[Sqrt[1 + x]/(1 + Sqrt[x + Sqrt[1 + x]]),x]","\frac{1}{12} \left(-24 \sqrt{x+1}+12 \sqrt{x+1} \sqrt{x+\sqrt{x+1}}-18 \sqrt{x+\sqrt{x+1}}-8 \log \left(1-\sqrt{x+1}\right)+32 \log \left(\sqrt{x+1}+2\right)+8 \tanh ^{-1}\left(\frac{1-3 \sqrt{x+1}}{2 \sqrt{x+\sqrt{x+1}}}\right)+45 \tanh ^{-1}\left(\frac{2 \sqrt{x+1}+1}{2 \sqrt{x+\sqrt{x+1}}}\right)-32 \tanh ^{-1}\left(\frac{3 \sqrt{x+1}+4}{2 \sqrt{x+\sqrt{x+1}}}\right)\right)","\sqrt{x+1} \left(\sqrt{x+\sqrt{x+1}}-2\right)-\frac{3}{2} \sqrt{x+\sqrt{x+1}}-\frac{23}{4} \log \left(2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)-\frac{4}{3} \log \left(\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}-2\right)+\frac{16}{3} \log \left(\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}+1\right)",1,"(-24*Sqrt[1 + x] - 18*Sqrt[x + Sqrt[1 + x]] + 12*Sqrt[1 + x]*Sqrt[x + Sqrt[1 + x]] + 8*ArcTanh[(1 - 3*Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])] + 45*ArcTanh[(1 + 2*Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])] - 32*ArcTanh[(4 + 3*Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])] - 8*Log[1 - Sqrt[1 + x]] + 32*Log[2 + Sqrt[1 + x]])/12","A",1
1889,0,0,131,1.1210184,"\int \frac{1+x}{(-1+x) (1+2 x) \sqrt[3]{-1+3 x^2}} \, dx","Integrate[(1 + x)/((-1 + x)*(1 + 2*x)*(-1 + 3*x^2)^(1/3)),x]","\int \frac{1+x}{(-1+x) (1+2 x) \sqrt[3]{-1+3 x^2}} \, dx","\frac{\log \left(\sqrt[3]{3 x^2-1}-\sqrt[3]{2} x\right)}{3 \sqrt[3]{2}}-\frac{\log \left(2^{2/3} x^2+\sqrt[3]{2} \sqrt[3]{3 x^2-1} x+\left(3 x^2-1\right)^{2/3}\right)}{6 \sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{3 x^2-1}}{\sqrt[3]{3 x^2-1}+2 \sqrt[3]{2} x}\right)}{\sqrt[3]{2} \sqrt{3}}",1,"Integrate[(1 + x)/((-1 + x)*(1 + 2*x)*(-1 + 3*x^2)^(1/3)), x]","F",-1
1890,1,160,131,0.0714761,"\int \frac{-b+a x^2}{x^2 \sqrt[3]{-x+x^3}} \, dx","Integrate[(-b + a*x^2)/(x^2*(-x + x^3)^(1/3)),x]","\frac{-2 a \sqrt[3]{x^2-1} x^{4/3} \log \left(1-\frac{x^{2/3}}{\sqrt[3]{x^2-1}}\right)+a \sqrt[3]{x^2-1} x^{4/3} \log \left(\frac{x^{4/3}}{\left(x^2-1\right)^{2/3}}+\frac{x^{2/3}}{\sqrt[3]{x^2-1}}+1\right)+2 \sqrt{3} a \sqrt[3]{x^2-1} x^{4/3} \tan ^{-1}\left(\frac{\frac{2 x^{2/3}}{\sqrt[3]{x^2-1}}+1}{\sqrt{3}}\right)-3 b x^2+3 b}{4 x \sqrt[3]{x \left(x^2-1\right)}}","\frac{1}{4} \left(a-i \sqrt{3} a\right) \log \left(-2 i \sqrt[3]{x^3-x}+\sqrt{3} x-i x\right)+\frac{1}{4} \left(a+i \sqrt{3} a\right) \log \left(2 i \sqrt[3]{x^3-x}+\sqrt{3} x+i x\right)-\frac{1}{2} a \log \left(\sqrt[3]{x^3-x}-x\right)-\frac{3 b \left(x^3-x\right)^{2/3}}{4 x^2}",1,"(3*b - 3*b*x^2 + 2*Sqrt[3]*a*x^(4/3)*(-1 + x^2)^(1/3)*ArcTan[(1 + (2*x^(2/3))/(-1 + x^2)^(1/3))/Sqrt[3]] - 2*a*x^(4/3)*(-1 + x^2)^(1/3)*Log[1 - x^(2/3)/(-1 + x^2)^(1/3)] + a*x^(4/3)*(-1 + x^2)^(1/3)*Log[1 + x^(4/3)/(-1 + x^2)^(2/3) + x^(2/3)/(-1 + x^2)^(1/3)])/(4*x*(x*(-1 + x^2))^(1/3))","A",1
1891,1,1848,131,8.7450868,"\int \frac{1+x^4}{\sqrt{-x-x^2+x^3} \left(-1+x^4\right)} \, dx","Integrate[(1 + x^4)/(Sqrt[-x - x^2 + x^3]*(-1 + x^4)),x]","-\frac{\left(\frac{1}{x^4}-1\right) x^{3/2} \left(x^4+1\right) \left(\frac{\left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right) \sqrt{\frac{i \sqrt{2 \left(1+\sqrt{5}\right)}+\frac{2}{\sqrt{x}}}{-\sqrt{10}+(1+2 i) \sqrt{2}-\frac{2 i \sqrt{1+\sqrt{5}}}{\sqrt{x}}+\frac{2 \sqrt{-1+\sqrt{5}}}{\sqrt{x}}}} \sqrt{\frac{i \sqrt{2 \left(1+\sqrt{5}\right)}-\frac{2}{\sqrt{x}}}{\sqrt{2} \left((-1+2 i)+\sqrt{5}\right)-\frac{2 \left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right)}{\sqrt{x}}}} \sqrt{\frac{\sqrt{2} \left((-1-2 i)+\sqrt{5}\right)+\frac{2 \left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right)}{\sqrt{x}}}{\sqrt{2} \left((-1+2 i)+\sqrt{5}\right)-\frac{2 \left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right)}{\sqrt{x}}}} \left(\left(2+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) F\left(\sin ^{-1}\left(\sqrt{\frac{\left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right) \left(\sqrt{2 \left(-1+\sqrt{5}\right)}+\frac{2}{\sqrt{x}}\right)}{\left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right) \left(\sqrt{2 \left(-1+\sqrt{5}\right)}-\frac{2}{\sqrt{x}}\right)}}\right)|-\frac{3}{5}-\frac{4 i}{5}\right)-2 \sqrt{2 \left(-1+\sqrt{5}\right)} \Pi \left(\frac{\left(-2+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) \left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right)}{\left(2+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) \left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right)};\sin ^{-1}\left(\sqrt{\frac{\left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right) \left(\sqrt{2 \left(-1+\sqrt{5}\right)}+\frac{2}{\sqrt{x}}\right)}{\left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right) \left(\sqrt{2 \left(-1+\sqrt{5}\right)}-\frac{2}{\sqrt{x}}\right)}}\right)|-\frac{3}{5}-\frac{4 i}{5}\right)\right) \left(\sqrt{2 \left(-1+\sqrt{5}\right)}-\frac{2}{\sqrt{x}}\right)^2}{\left(-2+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) \left(2+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) \left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right)}-\frac{\left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right) \sqrt{\frac{i \sqrt{2 \left(1+\sqrt{5}\right)}+\frac{2}{\sqrt{x}}}{-\sqrt{10}+(1+2 i) \sqrt{2}-\frac{2 i \sqrt{1+\sqrt{5}}}{\sqrt{x}}+\frac{2 \sqrt{-1+\sqrt{5}}}{\sqrt{x}}}} \sqrt{\frac{i \sqrt{2 \left(1+\sqrt{5}\right)}-\frac{2}{\sqrt{x}}}{\sqrt{2} \left((-1+2 i)+\sqrt{5}\right)-\frac{2 \left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right)}{\sqrt{x}}}} \sqrt{\frac{\sqrt{2} \left((-1-2 i)+\sqrt{5}\right)+\frac{2 \left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right)}{\sqrt{x}}}{\sqrt{2} \left((-1+2 i)+\sqrt{5}\right)-\frac{2 \left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right)}{\sqrt{x}}}} \left(\left(-2+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) F\left(\sin ^{-1}\left(\sqrt{\frac{\left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right) \left(\sqrt{2 \left(-1+\sqrt{5}\right)}+\frac{2}{\sqrt{x}}\right)}{\left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right) \left(\sqrt{2 \left(-1+\sqrt{5}\right)}-\frac{2}{\sqrt{x}}\right)}}\right)|-\frac{3}{5}-\frac{4 i}{5}\right)-2 \sqrt{2 \left(-1+\sqrt{5}\right)} \Pi \left(\frac{\left(2+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) \left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right)}{\left(-2+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) \left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right)};\sin ^{-1}\left(\sqrt{\frac{\left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right) \left(\sqrt{2 \left(-1+\sqrt{5}\right)}+\frac{2}{\sqrt{x}}\right)}{\left(\sqrt{-1+\sqrt{5}}+i \sqrt{1+\sqrt{5}}\right) \left(\sqrt{2 \left(-1+\sqrt{5}\right)}-\frac{2}{\sqrt{x}}\right)}}\right)|-\frac{3}{5}-\frac{4 i}{5}\right)\right) \left(\sqrt{2 \left(-1+\sqrt{5}\right)}-\frac{2}{\sqrt{x}}\right)^2}{\left(-2+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) \left(2+\sqrt{2 \left(-1+\sqrt{5}\right)}\right) \left(\sqrt{-1+\sqrt{5}}-i \sqrt{1+\sqrt{5}}\right)}-\frac{4 i \sqrt{1-\frac{1}{x}-\frac{1}{x^2}} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{1+\sqrt{5}}}}{\sqrt{x}}\right)|-\frac{3}{2}-\frac{\sqrt{5}}{2}\right)}{\sqrt{-1+\sqrt{5}}}+\frac{2 i \sqrt{1-\frac{1}{x}-\frac{1}{x^2}} \Pi \left(-\frac{1}{2} i \left(1+\sqrt{5}\right);i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{1+\sqrt{5}}}}{\sqrt{x}}\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{\sqrt{-1+\sqrt{5}}}+\frac{2 i \sqrt{1-\frac{1}{x}-\frac{1}{x^2}} \Pi \left(\frac{1}{2} i \left(1+\sqrt{5}\right);i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{1+\sqrt{5}}}}{\sqrt{x}}\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{\sqrt{-1+\sqrt{5}}}+\frac{2 i \sqrt{1-\frac{1}{x}-\frac{1}{x^2}} \Pi \left(\frac{1}{2} \left(1+\sqrt{5}\right);i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{1+\sqrt{5}}}}{\sqrt{x}}\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{\sqrt{-1+\sqrt{5}}}\right)}{\sqrt{2} \sqrt{x \left(x^2-x-1\right)} \left(x^4-\frac{1}{x^4}\right)}","-\tan ^{-1}\left(\frac{\sqrt{x^3-x^2-x}}{x^2-x-1}\right)-\frac{1}{2} \sqrt{\frac{1}{5}+\frac{2 i}{5}} \tan ^{-1}\left(\frac{\sqrt{1-2 i} \sqrt{x^3-x^2-x}}{x^2-x-1}\right)-\frac{1}{2} \sqrt{\frac{1}{5}-\frac{2 i}{5}} \tan ^{-1}\left(\frac{\sqrt{1+2 i} \sqrt{x^3-x^2-x}}{x^2-x-1}\right)",1,"-(((-1 + x^(-4))*x^(3/2)*(1 + x^4)*(((-4*I)*Sqrt[1 - x^(-2) - x^(-1)]*EllipticF[I*ArcSinh[Sqrt[2/(1 + Sqrt[5])]/Sqrt[x]], -3/2 - Sqrt[5]/2])/Sqrt[-1 + Sqrt[5]] + ((2*I)*Sqrt[1 - x^(-2) - x^(-1)]*EllipticPi[(-1/2*I)*(1 + Sqrt[5]), I*ArcSinh[Sqrt[2/(1 + Sqrt[5])]/Sqrt[x]], (-3 - Sqrt[5])/2])/Sqrt[-1 + Sqrt[5]] + ((2*I)*Sqrt[1 - x^(-2) - x^(-1)]*EllipticPi[(I/2)*(1 + Sqrt[5]), I*ArcSinh[Sqrt[2/(1 + Sqrt[5])]/Sqrt[x]], (-3 - Sqrt[5])/2])/Sqrt[-1 + Sqrt[5]] + ((2*I)*Sqrt[1 - x^(-2) - x^(-1)]*EllipticPi[(1 + Sqrt[5])/2, I*ArcSinh[Sqrt[2/(1 + Sqrt[5])]/Sqrt[x]], (-3 - Sqrt[5])/2])/Sqrt[-1 + Sqrt[5]] + ((Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] - 2/Sqrt[x])^2*Sqrt[(I*Sqrt[2*(1 + Sqrt[5])] + 2/Sqrt[x])/((1 + 2*I)*Sqrt[2] - Sqrt[10] + (2*Sqrt[-1 + Sqrt[5]])/Sqrt[x] - ((2*I)*Sqrt[1 + Sqrt[5]])/Sqrt[x])]*Sqrt[(I*Sqrt[2*(1 + Sqrt[5])] - 2/Sqrt[x])/(Sqrt[2]*((-1 + 2*I) + Sqrt[5]) - (2*(Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]]))/Sqrt[x])]*Sqrt[(Sqrt[2]*((-1 - 2*I) + Sqrt[5]) + (2*(Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]]))/Sqrt[x])/(Sqrt[2]*((-1 + 2*I) + Sqrt[5]) - (2*(Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]]))/Sqrt[x])]*((2 + Sqrt[2*(-1 + Sqrt[5])])*EllipticF[ArcSin[Sqrt[((Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] + 2/Sqrt[x]))/((Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] - 2/Sqrt[x]))]], -3/5 - (4*I)/5] - 2*Sqrt[2*(-1 + Sqrt[5])]*EllipticPi[((-2 + Sqrt[2*(-1 + Sqrt[5])])*(Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]]))/((2 + Sqrt[2*(-1 + Sqrt[5])])*(Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]])), ArcSin[Sqrt[((Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] + 2/Sqrt[x]))/((Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] - 2/Sqrt[x]))]], -3/5 - (4*I)/5]))/((-2 + Sqrt[2*(-1 + Sqrt[5])])*(2 + Sqrt[2*(-1 + Sqrt[5])])*(Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]])) - ((Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] - 2/Sqrt[x])^2*Sqrt[(I*Sqrt[2*(1 + Sqrt[5])] + 2/Sqrt[x])/((1 + 2*I)*Sqrt[2] - Sqrt[10] + (2*Sqrt[-1 + Sqrt[5]])/Sqrt[x] - ((2*I)*Sqrt[1 + Sqrt[5]])/Sqrt[x])]*Sqrt[(I*Sqrt[2*(1 + Sqrt[5])] - 2/Sqrt[x])/(Sqrt[2]*((-1 + 2*I) + Sqrt[5]) - (2*(Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]]))/Sqrt[x])]*Sqrt[(Sqrt[2]*((-1 - 2*I) + Sqrt[5]) + (2*(Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]]))/Sqrt[x])/(Sqrt[2]*((-1 + 2*I) + Sqrt[5]) - (2*(Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]]))/Sqrt[x])]*((-2 + Sqrt[2*(-1 + Sqrt[5])])*EllipticF[ArcSin[Sqrt[((Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] + 2/Sqrt[x]))/((Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] - 2/Sqrt[x]))]], -3/5 - (4*I)/5] - 2*Sqrt[2*(-1 + Sqrt[5])]*EllipticPi[((2 + Sqrt[2*(-1 + Sqrt[5])])*(Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]]))/((-2 + Sqrt[2*(-1 + Sqrt[5])])*(Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]])), ArcSin[Sqrt[((Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] + 2/Sqrt[x]))/((Sqrt[-1 + Sqrt[5]] + I*Sqrt[1 + Sqrt[5]])*(Sqrt[2*(-1 + Sqrt[5])] - 2/Sqrt[x]))]], -3/5 - (4*I)/5]))/((-2 + Sqrt[2*(-1 + Sqrt[5])])*(2 + Sqrt[2*(-1 + Sqrt[5])])*(Sqrt[-1 + Sqrt[5]] - I*Sqrt[1 + Sqrt[5]]))))/(Sqrt[2]*Sqrt[x*(-1 - x + x^2)]*(-x^(-4) + x^4)))","C",0
1892,0,0,131,0.3865626,"\int \frac{\left(-1+x^3\right) \sqrt[3]{1+x^6}}{x^2 \left(1+x^3\right)} \, dx","Integrate[((-1 + x^3)*(1 + x^6)^(1/3))/(x^2*(1 + x^3)),x]","\int \frac{\left(-1+x^3\right) \sqrt[3]{1+x^6}}{x^2 \left(1+x^3\right)} \, dx","\frac{\sqrt[3]{x^6+1}}{x}-\frac{1}{3} \sqrt[3]{2} \log \left(2^{2/3} \sqrt[3]{x^6+1}+2 x\right)+\frac{\sqrt[3]{2} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^6+1}-x}\right)}{\sqrt{3}}+\frac{\log \left(2^{2/3} \sqrt[3]{x^6+1} x-\sqrt[3]{2} \left(x^6+1\right)^{2/3}-2 x^2\right)}{3\ 2^{2/3}}",1,"Integrate[((-1 + x^3)*(1 + x^6)^(1/3))/(x^2*(1 + x^3)), x]","F",-1
1893,0,0,131,0.3206954,"\int \frac{\left(-2+x^6\right) \sqrt[3]{2+x^6}}{x^2 \left(2+2 x^3+x^6\right)} \, dx","Integrate[((-2 + x^6)*(2 + x^6)^(1/3))/(x^2*(2 + 2*x^3 + x^6)),x]","\int \frac{\left(-2+x^6\right) \sqrt[3]{2+x^6}}{x^2 \left(2+2 x^3+x^6\right)} \, dx","\frac{\sqrt[3]{x^6+2}}{x}-\frac{1}{3} \sqrt[3]{2} \log \left(2^{2/3} \sqrt[3]{x^6+2}+2 x\right)+\frac{\sqrt[3]{2} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^6+2}-x}\right)}{\sqrt{3}}+\frac{\log \left(2^{2/3} \sqrt[3]{x^6+2} x-\sqrt[3]{2} \left(x^6+2\right)^{2/3}-2 x^2\right)}{3\ 2^{2/3}}",1,"Integrate[((-2 + x^6)*(2 + x^6)^(1/3))/(x^2*(2 + 2*x^3 + x^6)), x]","F",-1
1894,0,0,131,0.3334486,"\int \frac{\left(1+x^3\right)^{2/3} \left(-1-2 x^3+2 x^6\right)}{x^6 \left(-1+x^3+2 x^6\right)} \, dx","Integrate[((1 + x^3)^(2/3)*(-1 - 2*x^3 + 2*x^6))/(x^6*(-1 + x^3 + 2*x^6)),x]","\int \frac{\left(1+x^3\right)^{2/3} \left(-1-2 x^3+2 x^6\right)}{x^6 \left(-1+x^3+2 x^6\right)} \, dx","-\frac{2 \log \left(3^{2/3} \sqrt[3]{x^3+1}-3 x\right)}{\sqrt[3]{3}}+2 \sqrt[6]{3} \tan ^{-1}\left(\frac{3^{5/6} x}{2 \sqrt[3]{x^3+1}+\sqrt[3]{3} x}\right)+\frac{\left(x^3+1\right)^{2/3} \left(-17 x^3-2\right)}{10 x^5}+\frac{\log \left(3^{2/3} \sqrt[3]{x^3+1} x+\sqrt[3]{3} \left(x^3+1\right)^{2/3}+3 x^2\right)}{\sqrt[3]{3}}",1,"Integrate[((1 + x^3)^(2/3)*(-1 - 2*x^3 + 2*x^6))/(x^6*(-1 + x^3 + 2*x^6)), x]","F",-1
1895,1,1192,131,3.3166724,"\int \frac{\left(1+x^3\right) \sqrt{x-x^4}}{2+4 x^3+3 x^6} \, dx","Integrate[((1 + x^3)*Sqrt[x - x^4])/(2 + 4*x^3 + 3*x^6),x]","\frac{\sqrt{x-x^4} \left(-4 \sqrt{2 \left(-5+i \sqrt{2}\right)} \sqrt{-2+i \sqrt{2}} \log \left(x^{3/2}-\sqrt{-\frac{2}{3}-\frac{i \sqrt{2}}{3}}\right)+4 \sqrt{2 \left(-5+i \sqrt{2}\right)} \sqrt{-2+i \sqrt{2}} \log \left(x^{3/2}+\sqrt{-\frac{2}{3}-\frac{i \sqrt{2}}{3}}\right)-7 i \sqrt{-5+i \sqrt{2}} \sqrt{-2+i \sqrt{2}} \log \left(3 x^{3/2}-\sqrt{-6-3 i \sqrt{2}}\right)+7 i \sqrt{-5+i \sqrt{2}} \sqrt{-2+i \sqrt{2}} \log \left(3 x^{3/2}+\sqrt{-6-3 i \sqrt{2}}\right)-4 \sqrt{-2-i \sqrt{2}} \sqrt{-10-2 i \sqrt{2}} \log \left(3 x^{3/2}-\sqrt{-6+3 i \sqrt{2}}\right)+7 i \sqrt{-5-i \sqrt{2}} \sqrt{-2-i \sqrt{2}} \log \left(3 x^{3/2}-\sqrt{-6+3 i \sqrt{2}}\right)+4 \sqrt{-2-i \sqrt{2}} \sqrt{-10-2 i \sqrt{2}} \log \left(3 x^{3/2}+\sqrt{-6+3 i \sqrt{2}}\right)-7 i \sqrt{-5-i \sqrt{2}} \sqrt{-2-i \sqrt{2}} \log \left(3 x^{3/2}+\sqrt{-6+3 i \sqrt{2}}\right)+72 \log \left(x^{3/2}+\sqrt{x^3-1}\right)-4 \sqrt{2 \left(-5+i \sqrt{2}\right)} \sqrt{-2+i \sqrt{2}} \log \left(-\sqrt{-6-3 i \sqrt{2}} x^{3/2}+\sqrt{-15-3 i \sqrt{2}} \sqrt{x^3-1}-3\right)-7 i \sqrt{-5+i \sqrt{2}} \sqrt{-2+i \sqrt{2}} \log \left(-\sqrt{-6-3 i \sqrt{2}} x^{3/2}+\sqrt{-15-3 i \sqrt{2}} \sqrt{x^3-1}-3\right)+4 \sqrt{2 \left(-5+i \sqrt{2}\right)} \sqrt{-2+i \sqrt{2}} \log \left(\sqrt{-6-3 i \sqrt{2}} x^{3/2}+\sqrt{-15-3 i \sqrt{2}} \sqrt{x^3-1}-3\right)+7 i \sqrt{-5+i \sqrt{2}} \sqrt{-2+i \sqrt{2}} \log \left(\sqrt{-6-3 i \sqrt{2}} x^{3/2}+\sqrt{-15-3 i \sqrt{2}} \sqrt{x^3-1}-3\right)-4 \sqrt{-2-i \sqrt{2}} \sqrt{-10-2 i \sqrt{2}} \log \left(-\sqrt{-6+3 i \sqrt{2}} x^{3/2}+\sqrt{3 i \left(5 i+\sqrt{2}\right)} \sqrt{x^3-1}-3\right)+7 i \sqrt{-5-i \sqrt{2}} \sqrt{-2-i \sqrt{2}} \log \left(-\sqrt{-6+3 i \sqrt{2}} x^{3/2}+\sqrt{3 i \left(5 i+\sqrt{2}\right)} \sqrt{x^3-1}-3\right)+4 \sqrt{-2-i \sqrt{2}} \sqrt{-10-2 i \sqrt{2}} \log \left(\sqrt{-6+3 i \sqrt{2}} x^{3/2}+\sqrt{3 i \left(5 i+\sqrt{2}\right)} \sqrt{x^3-1}-3\right)-7 i \sqrt{-5-i \sqrt{2}} \sqrt{-2-i \sqrt{2}} \log \left(\sqrt{-6+3 i \sqrt{2}} x^{3/2}+\sqrt{3 i \left(5 i+\sqrt{2}\right)} \sqrt{x^3-1}-3\right)\right)}{324 \sqrt{x} \sqrt{x^3-1}}","-\frac{1}{18} \sqrt{8+7 i \sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2-\frac{i}{\sqrt{2}}} x \sqrt{x-x^4}}{x^3-1}\right)-\frac{1}{18} \sqrt{8-7 i \sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2+\frac{i}{\sqrt{2}}} x \sqrt{x-x^4}}{x^3-1}\right)-\frac{2}{9} \tan ^{-1}\left(\frac{x^2}{\sqrt{x-x^4}}\right)",1,"(Sqrt[x - x^4]*(-4*Sqrt[2*(-5 + I*Sqrt[2])]*Sqrt[-2 + I*Sqrt[2]]*Log[-Sqrt[-2/3 - (I/3)*Sqrt[2]] + x^(3/2)] + 4*Sqrt[2*(-5 + I*Sqrt[2])]*Sqrt[-2 + I*Sqrt[2]]*Log[Sqrt[-2/3 - (I/3)*Sqrt[2]] + x^(3/2)] - (7*I)*Sqrt[-5 + I*Sqrt[2]]*Sqrt[-2 + I*Sqrt[2]]*Log[-Sqrt[-6 - (3*I)*Sqrt[2]] + 3*x^(3/2)] + (7*I)*Sqrt[-5 + I*Sqrt[2]]*Sqrt[-2 + I*Sqrt[2]]*Log[Sqrt[-6 - (3*I)*Sqrt[2]] + 3*x^(3/2)] + (7*I)*Sqrt[-5 - I*Sqrt[2]]*Sqrt[-2 - I*Sqrt[2]]*Log[-Sqrt[-6 + (3*I)*Sqrt[2]] + 3*x^(3/2)] - 4*Sqrt[-2 - I*Sqrt[2]]*Sqrt[-10 - (2*I)*Sqrt[2]]*Log[-Sqrt[-6 + (3*I)*Sqrt[2]] + 3*x^(3/2)] - (7*I)*Sqrt[-5 - I*Sqrt[2]]*Sqrt[-2 - I*Sqrt[2]]*Log[Sqrt[-6 + (3*I)*Sqrt[2]] + 3*x^(3/2)] + 4*Sqrt[-2 - I*Sqrt[2]]*Sqrt[-10 - (2*I)*Sqrt[2]]*Log[Sqrt[-6 + (3*I)*Sqrt[2]] + 3*x^(3/2)] + 72*Log[x^(3/2) + Sqrt[-1 + x^3]] - (7*I)*Sqrt[-5 + I*Sqrt[2]]*Sqrt[-2 + I*Sqrt[2]]*Log[-3 - Sqrt[-6 - (3*I)*Sqrt[2]]*x^(3/2) + Sqrt[-15 - (3*I)*Sqrt[2]]*Sqrt[-1 + x^3]] - 4*Sqrt[2*(-5 + I*Sqrt[2])]*Sqrt[-2 + I*Sqrt[2]]*Log[-3 - Sqrt[-6 - (3*I)*Sqrt[2]]*x^(3/2) + Sqrt[-15 - (3*I)*Sqrt[2]]*Sqrt[-1 + x^3]] + (7*I)*Sqrt[-5 + I*Sqrt[2]]*Sqrt[-2 + I*Sqrt[2]]*Log[-3 + Sqrt[-6 - (3*I)*Sqrt[2]]*x^(3/2) + Sqrt[-15 - (3*I)*Sqrt[2]]*Sqrt[-1 + x^3]] + 4*Sqrt[2*(-5 + I*Sqrt[2])]*Sqrt[-2 + I*Sqrt[2]]*Log[-3 + Sqrt[-6 - (3*I)*Sqrt[2]]*x^(3/2) + Sqrt[-15 - (3*I)*Sqrt[2]]*Sqrt[-1 + x^3]] + (7*I)*Sqrt[-5 - I*Sqrt[2]]*Sqrt[-2 - I*Sqrt[2]]*Log[-3 - Sqrt[-6 + (3*I)*Sqrt[2]]*x^(3/2) + Sqrt[(3*I)*(5*I + Sqrt[2])]*Sqrt[-1 + x^3]] - 4*Sqrt[-2 - I*Sqrt[2]]*Sqrt[-10 - (2*I)*Sqrt[2]]*Log[-3 - Sqrt[-6 + (3*I)*Sqrt[2]]*x^(3/2) + Sqrt[(3*I)*(5*I + Sqrt[2])]*Sqrt[-1 + x^3]] - (7*I)*Sqrt[-5 - I*Sqrt[2]]*Sqrt[-2 - I*Sqrt[2]]*Log[-3 + Sqrt[-6 + (3*I)*Sqrt[2]]*x^(3/2) + Sqrt[(3*I)*(5*I + Sqrt[2])]*Sqrt[-1 + x^3]] + 4*Sqrt[-2 - I*Sqrt[2]]*Sqrt[-10 - (2*I)*Sqrt[2]]*Log[-3 + Sqrt[-6 + (3*I)*Sqrt[2]]*x^(3/2) + Sqrt[(3*I)*(5*I + Sqrt[2])]*Sqrt[-1 + x^3]]))/(324*Sqrt[x]*Sqrt[-1 + x^3])","B",0
1896,1,483,131,0.7793645,"\int \frac{-2+a x^4}{\sqrt[4]{b+a x^4} \left(-b+a x^4+2 x^8\right)} \, dx","Integrate[(-2 + a*x^4)/((b + a*x^4)^(1/4)*(-b + a*x^4 + 2*x^8)),x]","\frac{1}{2} \left(\frac{\left(a-\frac{a^2+8}{\sqrt{a^2+8 b}}\right) \tan ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+8 b}+a^2-4 b}}{\sqrt[4]{a-\sqrt{a^2+8 b}} \sqrt[4]{a x^4+b}}\right)}{\left(a-\sqrt{a^2+8 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+8 b}+a^2-4 b}}+\frac{\left(\frac{a^2+8}{\sqrt{a^2+8 b}}+a\right) \tan ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+8 b}+a^2-4 b}}{\sqrt[4]{\sqrt{a^2+8 b}+a} \sqrt[4]{a x^4+b}}\right)}{\left(\sqrt{a^2+8 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+8 b}+a^2-4 b}}+\frac{\left(a-\frac{a^2+8}{\sqrt{a^2+8 b}}\right) \tanh ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+8 b}+a^2-4 b}}{\sqrt[4]{a-\sqrt{a^2+8 b}} \sqrt[4]{a x^4+b}}\right)}{\left(a-\sqrt{a^2+8 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+8 b}+a^2-4 b}}+\frac{\left(\frac{a^2+8}{\sqrt{a^2+8 b}}+a\right) \tanh ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+8 b}+a^2-4 b}}{\sqrt[4]{\sqrt{a^2+8 b}+a} \sqrt[4]{a x^4+b}}\right)}{\left(\sqrt{a^2+8 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+8 b}+a^2-4 b}}\right)","-\frac{\text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4 a+2 a^2-2 b\&,\frac{-2 \text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+2 \text{$\#$1}^4 \log (x)+2 a \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+a b \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)-a b \log (x)-2 a \log (x)}{3 \text{$\#$1} a-2 \text{$\#$1}^5}\&\right]}{4 b}",1,"(((a - (8 + a^2)/Sqrt[a^2 + 8*b])*ArcTan[((a^2 - 4*b - a*Sqrt[a^2 + 8*b])^(1/4)*x)/((a - Sqrt[a^2 + 8*b])^(1/4)*(b + a*x^4)^(1/4))])/((a - Sqrt[a^2 + 8*b])^(3/4)*(a^2 - 4*b - a*Sqrt[a^2 + 8*b])^(1/4)) + ((a + (8 + a^2)/Sqrt[a^2 + 8*b])*ArcTan[((a^2 - 4*b + a*Sqrt[a^2 + 8*b])^(1/4)*x)/((a + Sqrt[a^2 + 8*b])^(1/4)*(b + a*x^4)^(1/4))])/((a + Sqrt[a^2 + 8*b])^(3/4)*(a^2 - 4*b + a*Sqrt[a^2 + 8*b])^(1/4)) + ((a - (8 + a^2)/Sqrt[a^2 + 8*b])*ArcTanh[((a^2 - 4*b - a*Sqrt[a^2 + 8*b])^(1/4)*x)/((a - Sqrt[a^2 + 8*b])^(1/4)*(b + a*x^4)^(1/4))])/((a - Sqrt[a^2 + 8*b])^(3/4)*(a^2 - 4*b - a*Sqrt[a^2 + 8*b])^(1/4)) + ((a + (8 + a^2)/Sqrt[a^2 + 8*b])*ArcTanh[((a^2 - 4*b + a*Sqrt[a^2 + 8*b])^(1/4)*x)/((a + Sqrt[a^2 + 8*b])^(1/4)*(b + a*x^4)^(1/4))])/((a + Sqrt[a^2 + 8*b])^(3/4)*(a^2 - 4*b + a*Sqrt[a^2 + 8*b])^(1/4)))/2","B",1
1897,1,148,131,0.3647256,"\int \frac{-1+x}{(1+x) \sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[(-1 + x)/((1 + x)*Sqrt[x + Sqrt[1 + x^2]]),x]","\sqrt{\sqrt{x^2+1}+x}-\frac{4}{\sqrt{\sqrt{x^2+1}+x}}-\frac{1}{3 \left(\sqrt{x^2+1}+x\right)^{3/2}}+4 \left(\sqrt{2}-1\right) \sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{1}{\sqrt{\sqrt{2}-1} \sqrt{\sqrt{x^2+1}+x}}\right)+4 \sqrt{\sqrt{2}-1} \left(1+\sqrt{2}\right) \tanh ^{-1}\left(\frac{1}{\sqrt{1+\sqrt{2}} \sqrt{\sqrt{x^2+1}+x}}\right)","\frac{2 \sqrt{x^2+1} (3 x-6)+2 \left(3 x^2-6 x+1\right)}{3 \left(\sqrt{x^2+1}+x\right)^{3/2}}-4 \sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{1+\sqrt{2}}}\right)+4 \sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{\sqrt{2}-1}}\right)",1,"-1/3*1/(x + Sqrt[1 + x^2])^(3/2) - 4/Sqrt[x + Sqrt[1 + x^2]] + Sqrt[x + Sqrt[1 + x^2]] + 4*(-1 + Sqrt[2])*Sqrt[1 + Sqrt[2]]*ArcTan[1/(Sqrt[-1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]])] + 4*Sqrt[-1 + Sqrt[2]]*(1 + Sqrt[2])*ArcTanh[1/(Sqrt[1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]])]","A",1
1898,1,148,131,0.3573156,"\int \frac{1+x}{(-1+x) \sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[(1 + x)/((-1 + x)*Sqrt[x + Sqrt[1 + x^2]]),x]","\sqrt{\sqrt{x^2+1}+x}+\frac{4}{\sqrt{\sqrt{x^2+1}+x}}-\frac{1}{3 \left(\sqrt{x^2+1}+x\right)^{3/2}}-4 \sqrt{\sqrt{2}-1} \left(1+\sqrt{2}\right) \tan ^{-1}\left(\frac{1}{\sqrt{1+\sqrt{2}} \sqrt{\sqrt{x^2+1}+x}}\right)-4 \left(\sqrt{2}-1\right) \sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{1}{\sqrt{\sqrt{2}-1} \sqrt{\sqrt{x^2+1}+x}}\right)","\frac{2 \sqrt{x^2+1} (3 x+6)+2 \left(3 x^2+6 x+1\right)}{3 \left(\sqrt{x^2+1}+x\right)^{3/2}}+4 \sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{\sqrt{2}-1}}\right)-4 \sqrt{\sqrt{2}-1} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{1+\sqrt{2}}}\right)",1,"-1/3*1/(x + Sqrt[1 + x^2])^(3/2) + 4/Sqrt[x + Sqrt[1 + x^2]] + Sqrt[x + Sqrt[1 + x^2]] - 4*Sqrt[-1 + Sqrt[2]]*(1 + Sqrt[2])*ArcTan[1/(Sqrt[1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]])] - 4*(-1 + Sqrt[2])*Sqrt[1 + Sqrt[2]]*ArcTanh[1/(Sqrt[-1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]])]","A",1
1899,1,160,131,0.3883063,"\int \frac{\sqrt{-x+x^2}}{\sqrt{x^2-x \sqrt{-x+x^2}}} \, dx","Integrate[Sqrt[-x + x^2]/Sqrt[x^2 - x*Sqrt[-x + x^2]],x]","\frac{\sqrt{(x-1) x} \left(\sqrt{(x-1) x}-x\right) \left(9 \left(-2 x+2 \sqrt{(x-1) x}+1\right) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};1+\frac{1}{2 \left(\sqrt{(x-1) x}-x\right)}\right)-24 x^2+24 \sqrt{(x-1) x} x+22 x-10 \sqrt{(x-1) x}\right)}{12 \sqrt{x \left(x-\sqrt{(x-1) x}\right)} \left(4 x^2-\left(4 \sqrt{(x-1) x}+5\right) x+3 \sqrt{(x-1) x}+1\right)}","\frac{\sqrt{x^2-x} \sqrt{-x \left(\sqrt{x^2-x}-x\right)} (8 x-9)}{12 x}+\sqrt{x \left(x-\sqrt{x^2-x}\right)} \left(\frac{3 \sqrt{\sqrt{x^2-x}+x} \tanh ^{-1}\left(\sqrt{2} \sqrt{\sqrt{x^2-x}+x}\right)}{4 \sqrt{2} x}+\frac{1}{12} (8 x-19)\right)",1,"(Sqrt[(-1 + x)*x]*(-x + Sqrt[(-1 + x)*x])*(22*x - 24*x^2 - 10*Sqrt[(-1 + x)*x] + 24*x*Sqrt[(-1 + x)*x] + 9*(1 - 2*x + 2*Sqrt[(-1 + x)*x])*Hypergeometric2F1[-1/2, 1, 1/2, 1 + 1/(2*(-x + Sqrt[(-1 + x)*x]))]))/(12*Sqrt[x*(x - Sqrt[(-1 + x)*x])]*(1 + 4*x^2 + 3*Sqrt[(-1 + x)*x] - x*(5 + 4*Sqrt[(-1 + x)*x])))","C",1
1900,0,0,132,0.4998179,"\int \frac{6+2 x+x^2}{(2+x) \left(2+x^2\right) \sqrt[3]{2+x+x^2}} \, dx","Integrate[(6 + 2*x + x^2)/((2 + x)*(2 + x^2)*(2 + x + x^2)^(1/3)),x]","\int \frac{6+2 x+x^2}{(2+x) \left(2+x^2\right) \sqrt[3]{2+x+x^2}} \, dx","\frac{\log \left(2 \sqrt[3]{x^2+x+2}+2^{2/3} x\right)}{2^{2/3}}-\frac{\log \left(\sqrt[3]{2} x^2-2^{2/3} \sqrt[3]{x^2+x+2} x+2 \left(x^2+x+2\right)^{2/3}\right)}{2\ 2^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{x^2+x+2}}{\sqrt{3}}-\frac{2^{2/3} x}{\sqrt{3}}}{\sqrt[3]{x^2+x+2}}\right)}{2^{2/3}}",1,"Integrate[(6 + 2*x + x^2)/((2 + x)*(2 + x^2)*(2 + x + x^2)^(1/3)), x]","F",-1
1901,0,0,132,0.1018572,"\int \frac{-1+x}{x \sqrt[3]{1+2 x+2 x^2+x^3}} \, dx","Integrate[(-1 + x)/(x*(1 + 2*x + 2*x^2 + x^3)^(1/3)),x]","\int \frac{-1+x}{x \sqrt[3]{1+2 x+2 x^2+x^3}} \, dx","-\log \left(\sqrt[3]{x^3+2 x^2+2 x+1}-x-1\right)+\frac{1}{2} \log \left(x^2+\left(x^3+2 x^2+2 x+1\right)^{2/3}+(x+1) \sqrt[3]{x^3+2 x^2+2 x+1}+2 x+1\right)-\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x^3+2 x^2+2 x+1}}{\sqrt[3]{x^3+2 x^2+2 x+1}+2 x+2}\right)",1,"Integrate[(-1 + x)/(x*(1 + 2*x + 2*x^2 + x^3)^(1/3)), x]","F",-1
1902,0,0,132,0.6534532,"\int \frac{\left(-2 q+p x^3\right) \left(a q+b x^2+a p x^3\right) \sqrt{q^2+2 p q x^3-2 p q x^4+p^2 x^6}}{x^7} \, dx","Integrate[((-2*q + p*x^3)*(a*q + b*x^2 + a*p*x^3)*Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6])/x^7,x]","\int \frac{\left(-2 q+p x^3\right) \left(a q+b x^2+a p x^3\right) \sqrt{q^2+2 p q x^3-2 p q x^4+p^2 x^6}}{x^7} \, dx","\frac{\sqrt{p^2 x^6-2 p q x^4+2 p q x^3+q^2} \left(2 a p^2 x^6-4 a p q x^4+4 a p q x^3+2 a q^2+3 b p x^5+3 b q x^2\right)}{6 x^6}-b p q \log \left(\sqrt{p^2 x^6-2 p q x^4+2 p q x^3+q^2}+p x^3+q\right)+2 b p q \log (x)",1,"Integrate[((-2*q + p*x^3)*(a*q + b*x^2 + a*p*x^3)*Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6])/x^7, x]","F",-1
1903,1,159,132,0.1419377,"\int \frac{x^2}{\left(1+x^2\right) \sqrt[10]{243-5265 x+47250 x^2-225810 x^3+615255 x^4-954733 x^5+820340 x^6-401440 x^7+112000 x^8-16640 x^9+1024 x^{10}}} \, dx","Integrate[x^2/((1 + x^2)*(243 - 5265*x + 47250*x^2 - 225810*x^3 + 615255*x^4 - 954733*x^5 + 820340*x^6 - 401440*x^7 + 112000*x^8 - 16640*x^9 + 1024*x^10)^(1/10)),x]","\frac{\left(\frac{1}{340}-\frac{i}{340}\right) \sqrt{4 x^2-13 x+3} \left((7+6 i) \sqrt{1-13 i} \tan ^{-1}\left(\frac{(6+13 i)-(13+8 i) x}{2 \sqrt{1-13 i} \sqrt{4 x^2-13 x+3}}\right)-(6+7 i) \sqrt{1+13 i} \tan ^{-1}\left(\frac{(13-8 i) x-(6-13 i)}{2 \sqrt{1+13 i} \sqrt{4 x^2-13 x+3}}\right)+(85+85 i) \tanh ^{-1}\left(\frac{8 x-13}{4 \sqrt{4 x^2-13 x+3}}\right)\right)}{\sqrt[10]{\left(4 x^2-13 x+3\right)^5}}","\frac{\left(\left(4 x^2-13 x+3\right)^5\right)^{9/10} \left(32 \text{RootSum}\left[\text{$\#$1}^4-52 \text{$\#$1}^3+1174 \text{$\#$1}^2-6292 \text{$\#$1}+14641\&,\frac{\text{$\#$1} \log \left(-\text{$\#$1}+4 \sqrt{4 x^2-13 x+3}-8 x+13\right)}{\text{$\#$1}^3-39 \text{$\#$1}^2+587 \text{$\#$1}-1573}\&\right]-\frac{1}{2} \log \left(4 \sqrt{4 x^2-13 x+3}-8 x+13\right)\right)}{\left(4 x^2-13 x+3\right)^{9/2}}",1,"((1/340 - I/340)*Sqrt[3 - 13*x + 4*x^2]*((7 + 6*I)*Sqrt[1 - 13*I]*ArcTan[((6 + 13*I) - (13 + 8*I)*x)/(2*Sqrt[1 - 13*I]*Sqrt[3 - 13*x + 4*x^2])] - (6 + 7*I)*Sqrt[1 + 13*I]*ArcTan[((-6 + 13*I) + (13 - 8*I)*x)/(2*Sqrt[1 + 13*I]*Sqrt[3 - 13*x + 4*x^2])] + (85 + 85*I)*ArcTanh[(-13 + 8*x)/(4*Sqrt[3 - 13*x + 4*x^2])]))/((3 - 13*x + 4*x^2)^5)^(1/10)","C",1
1904,0,0,132,1.6244174,"\int \frac{1}{x \sqrt{-b x+a^2 x^2} \left(a x^2+x \sqrt{-b x+a^2 x^2}\right)^{3/2}} \, dx","Integrate[1/(x*Sqrt[-(b*x) + a^2*x^2]*(a*x^2 + x*Sqrt[-(b*x) + a^2*x^2])^(3/2)),x]","\int \frac{1}{x \sqrt{-b x+a^2 x^2} \left(a x^2+x \sqrt{-b x+a^2 x^2}\right)^{3/2}} \, dx","\frac{4 \left(256 a^5 x^2+32 a^3 b x+245 a b^2\right) \sqrt{x \left(\sqrt{a^2 x^2-b x}+a x\right)}}{1155 b^4 x^3}-\frac{4 \sqrt{a^2 x^2-b x} \left(-256 a^4 x^2-160 a^2 b x+105 b^2\right) \sqrt{x \left(\sqrt{a^2 x^2-b x}+a x\right)}}{1155 b^4 x^4}",1,"Integrate[1/(x*Sqrt[-(b*x) + a^2*x^2]*(a*x^2 + x*Sqrt[-(b*x) + a^2*x^2])^(3/2)), x]","F",-1
1905,0,0,132,0.1573155,"\int \frac{\sqrt{x^2+\sqrt{1+x^4}}}{\left(-1+x^2\right) \sqrt{1+x^4}} \, dx","Integrate[Sqrt[x^2 + Sqrt[1 + x^4]]/((-1 + x^2)*Sqrt[1 + x^4]),x]","\int \frac{\sqrt{x^2+\sqrt{1+x^4}}}{\left(-1+x^2\right) \sqrt{1+x^4}} \, dx","\sqrt{\frac{1}{2} \left(\sqrt{2}-1\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{2}-1\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)-\sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tanh ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)",1,"Integrate[Sqrt[x^2 + Sqrt[1 + x^4]]/((-1 + x^2)*Sqrt[1 + x^4]), x]","F",-1
1906,1,40,133,0.0120275,"\int \frac{1}{(1+2 x) \sqrt[3]{-1+4 x+4 x^2}} \, dx","Integrate[1/((1 + 2*x)*(-1 + 4*x + 4*x^2)^(1/3)),x]","\frac{3}{16} \left((2 x+1)^2-2\right)^{2/3} \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{1}{2} \left(2-(2 x+1)^2\right)\right)","-\frac{\log \left(2^{2/3} \sqrt[3]{4 x^2+4 x-1}+2\right)}{4 \sqrt[3]{2}}+\frac{\log \left(-\sqrt[3]{2} \left(4 x^2+4 x-1\right)^{2/3}+2^{2/3} \sqrt[3]{4 x^2+4 x-1}-2\right)}{8 \sqrt[3]{2}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2^{2/3} \sqrt[3]{4 x^2+4 x-1}}{\sqrt{3}}\right)}{4 \sqrt[3]{2}}",1,"(3*(-2 + (1 + 2*x)^2)^(2/3)*Hypergeometric2F1[2/3, 1, 5/3, (2 - (1 + 2*x)^2)/2])/16","C",1
1907,1,232,133,0.5664664,"\int \frac{1}{x^3 \left(-b+a x^3\right) \sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Integrate[1/(x^3*(-b + a*x^3)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","\frac{27 a^9 x^3+9 a^6 b^2 x^2-3 a^3 b^4 x-40 a b^5 x^3 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{2 x a^3+\left(-1-i \sqrt{3}\right) b^{5/3} x \sqrt[3]{a}}{2 \left(x a^3+b^2\right)}\right)-40 a b^5 x^3 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{2 x a^3+i \left(i+\sqrt{3}\right) b^{5/3} x \sqrt[3]{a}}{2 \left(x a^3+b^2\right)}\right)-40 a b^5 x^3 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\sqrt[3]{a} \left(a^{8/3}+b^{5/3}\right) x}{x a^3+b^2}\right)+15 b^6}{40 b^7 x^2 \sqrt[3]{x^2 \left(a^3 x+b^2\right)}}","\frac{a \text{RootSum}\left[-\text{$\#$1}^9+3 \text{$\#$1}^6 a^3-3 \text{$\#$1}^3 a^6+a^9+a b^5\&,\frac{\log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{3 b^2}+\frac{3 \left(a^3 x^3+b^2 x^2\right)^{2/3} \left(9 a^6 x^2-6 a^3 b^2 x+5 b^4\right)}{40 b^7 x^4}",1,"(15*b^6 - 3*a^3*b^4*x + 9*a^6*b^2*x^2 + 27*a^9*x^3 - 40*a*b^5*x^3*Hypergeometric2F1[1/3, 1, 4/3, (a^(1/3)*(a^(8/3) + b^(5/3))*x)/(b^2 + a^3*x)] - 40*a*b^5*x^3*Hypergeometric2F1[1/3, 1, 4/3, (2*a^3*x + (-1 - I*Sqrt[3])*a^(1/3)*b^(5/3)*x)/(2*(b^2 + a^3*x))] - 40*a*b^5*x^3*Hypergeometric2F1[1/3, 1, 4/3, (2*a^3*x + I*(I + Sqrt[3])*a^(1/3)*b^(5/3)*x)/(2*(b^2 + a^3*x))])/(40*b^7*x^2*(x^2*(b^2 + a^3*x))^(1/3))","C",1
1908,1,232,133,0.2324527,"\int \frac{1}{x^3 \left(-b+a x^3\right) \sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Integrate[1/(x^3*(-b + a*x^3)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","\frac{27 a^9 x^3+9 a^6 b^2 x^2-3 a^3 b^4 x-40 a b^5 x^3 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{2 x a^3+\left(-1-i \sqrt{3}\right) b^{5/3} x \sqrt[3]{a}}{2 \left(x a^3+b^2\right)}\right)-40 a b^5 x^3 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{2 x a^3+i \left(i+\sqrt{3}\right) b^{5/3} x \sqrt[3]{a}}{2 \left(x a^3+b^2\right)}\right)-40 a b^5 x^3 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\sqrt[3]{a} \left(a^{8/3}+b^{5/3}\right) x}{x a^3+b^2}\right)+15 b^6}{40 b^7 x^2 \sqrt[3]{x^2 \left(a^3 x+b^2\right)}}","\frac{a \text{RootSum}\left[-\text{$\#$1}^9+3 \text{$\#$1}^6 a^3-3 \text{$\#$1}^3 a^6+a^9+a b^5\&,\frac{\log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{3 b^2}+\frac{3 \left(a^3 x^3+b^2 x^2\right)^{2/3} \left(9 a^6 x^2-6 a^3 b^2 x+5 b^4\right)}{40 b^7 x^4}",1,"(15*b^6 - 3*a^3*b^4*x + 9*a^6*b^2*x^2 + 27*a^9*x^3 - 40*a*b^5*x^3*Hypergeometric2F1[1/3, 1, 4/3, (a^(1/3)*(a^(8/3) + b^(5/3))*x)/(b^2 + a^3*x)] - 40*a*b^5*x^3*Hypergeometric2F1[1/3, 1, 4/3, (2*a^3*x + (-1 - I*Sqrt[3])*a^(1/3)*b^(5/3)*x)/(2*(b^2 + a^3*x))] - 40*a*b^5*x^3*Hypergeometric2F1[1/3, 1, 4/3, (2*a^3*x + I*(I + Sqrt[3])*a^(1/3)*b^(5/3)*x)/(2*(b^2 + a^3*x))])/(40*b^7*x^2*(x^2*(b^2 + a^3*x))^(1/3))","C",1
1909,0,0,133,5.3419055,"\int \frac{x^3 (-b+x) (-2 a b+(3 a-b) x)}{(-a+x) \left(x^2 (-a+x) (-b+x)\right)^{3/4} \left(-a^3 d+3 a^2 d x+(b-3 a d) x^2+(-1+d) x^3\right)} \, dx","Integrate[(x^3*(-b + x)*(-2*a*b + (3*a - b)*x))/((-a + x)*(x^2*(-a + x)*(-b + x))^(3/4)*(-(a^3*d) + 3*a^2*d*x + (b - 3*a*d)*x^2 + (-1 + d)*x^3)),x]","\int \frac{x^3 (-b+x) (-2 a b+(3 a-b) x)}{(-a+x) \left(x^2 (-a+x) (-b+x)\right)^{3/4} \left(-a^3 d+3 a^2 d x+(b-3 a d) x^2+(-1+d) x^3\right)} \, dx","2 \sqrt[4]{d} \tan ^{-1}\left(\frac{\sqrt[4]{d} \left(x^3 (-a-b)+a b x^2+x^4\right)^{3/4}}{x^2 (x-b)}\right)-2 \sqrt[4]{d} \tanh ^{-1}\left(\frac{\sqrt[4]{d} \left(x^3 (-a-b)+a b x^2+x^4\right)^{3/4}}{x^2 (x-b)}\right)-\frac{4 \sqrt[4]{x^3 (-a-b)+a b x^2+x^4}}{a-x}",1,"Integrate[(x^3*(-b + x)*(-2*a*b + (3*a - b)*x))/((-a + x)*(x^2*(-a + x)*(-b + x))^(3/4)*(-(a^3*d) + 3*a^2*d*x + (b - 3*a*d)*x^2 + (-1 + d)*x^3)), x]","F",-1
1910,1,430,133,0.9235351,"\int \frac{x^2}{\sqrt{-x-x^2+x^3} \left(-1+x^4\right)} \, dx","Integrate[x^2/(Sqrt[-x - x^2 + x^3]*(-1 + x^4)),x]","\frac{(1+i) \sqrt{\frac{x}{2-2 \sqrt{5}}} \sqrt{-x^2+x+1} \left((-1+i) \sqrt{5} \Pi \left(\frac{1}{2} \left(-5-3 \sqrt{5}\right);\sin ^{-1}\left(\frac{\sqrt{2 x+\sqrt{5}-1}}{\sqrt{2} \sqrt[4]{5}}\right)|\frac{1}{2} \left(5+\sqrt{5}\right)\right)+(1-i) \left(2 \sqrt{5}-5\right) \Pi \left(\frac{1}{2} \left(5-\sqrt{5}\right);\sin ^{-1}\left(\frac{\sqrt{2 x+\sqrt{5}-1}}{\sqrt{2} \sqrt[4]{5}}\right)|\frac{1}{2} \left(5+\sqrt{5}\right)\right)+\sqrt{5} \Pi \left(\frac{2 \sqrt{5}}{(-1-2 i)+\sqrt{5}};\sin ^{-1}\left(\frac{\sqrt{2 x+\sqrt{5}-1}}{\sqrt{2} \sqrt[4]{5}}\right)|\frac{1}{2} \left(5+\sqrt{5}\right)\right)-(2+i) \Pi \left(\frac{2 \sqrt{5}}{(-1-2 i)+\sqrt{5}};\sin ^{-1}\left(\frac{\sqrt{2 x+\sqrt{5}-1}}{\sqrt{2} \sqrt[4]{5}}\right)|\frac{1}{2} \left(5+\sqrt{5}\right)\right)-i \sqrt{5} \Pi \left(\frac{2 \sqrt{5}}{(-1+2 i)+\sqrt{5}};\sin ^{-1}\left(\frac{\sqrt{2 x+\sqrt{5}-1}}{\sqrt{2} \sqrt[4]{5}}\right)|\frac{1}{2} \left(5+\sqrt{5}\right)\right)+(1+2 i) \Pi \left(\frac{2 \sqrt{5}}{(-1+2 i)+\sqrt{5}};\sin ^{-1}\left(\frac{\sqrt{2 x+\sqrt{5}-1}}{\sqrt{2} \sqrt[4]{5}}\right)|\frac{1}{2} \left(5+\sqrt{5}\right)\right)\right)}{\left(3 \sqrt{5}-5\right) \sqrt{x \left(x^2-x-1\right)}}","-\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{x^3-x^2-x}}{x^2-x-1}\right)+\frac{1}{4} \sqrt{\frac{1}{5}+\frac{2 i}{5}} \tan ^{-1}\left(\frac{\sqrt{1-2 i} \sqrt{x^3-x^2-x}}{x^2-x-1}\right)+\frac{1}{4} \sqrt{\frac{1}{5}-\frac{2 i}{5}} \tan ^{-1}\left(\frac{\sqrt{1+2 i} \sqrt{x^3-x^2-x}}{x^2-x-1}\right)",1,"((1 + I)*Sqrt[x/(2 - 2*Sqrt[5])]*Sqrt[1 + x - x^2]*((-1 + I)*Sqrt[5]*EllipticPi[(-5 - 3*Sqrt[5])/2, ArcSin[Sqrt[-1 + Sqrt[5] + 2*x]/(Sqrt[2]*5^(1/4))], (5 + Sqrt[5])/2] + (1 - I)*(-5 + 2*Sqrt[5])*EllipticPi[(5 - Sqrt[5])/2, ArcSin[Sqrt[-1 + Sqrt[5] + 2*x]/(Sqrt[2]*5^(1/4))], (5 + Sqrt[5])/2] - (2 + I)*EllipticPi[(2*Sqrt[5])/((-1 - 2*I) + Sqrt[5]), ArcSin[Sqrt[-1 + Sqrt[5] + 2*x]/(Sqrt[2]*5^(1/4))], (5 + Sqrt[5])/2] + Sqrt[5]*EllipticPi[(2*Sqrt[5])/((-1 - 2*I) + Sqrt[5]), ArcSin[Sqrt[-1 + Sqrt[5] + 2*x]/(Sqrt[2]*5^(1/4))], (5 + Sqrt[5])/2] + (1 + 2*I)*EllipticPi[(2*Sqrt[5])/((-1 + 2*I) + Sqrt[5]), ArcSin[Sqrt[-1 + Sqrt[5] + 2*x]/(Sqrt[2]*5^(1/4))], (5 + Sqrt[5])/2] - I*Sqrt[5]*EllipticPi[(2*Sqrt[5])/((-1 + 2*I) + Sqrt[5]), ArcSin[Sqrt[-1 + Sqrt[5] + 2*x]/(Sqrt[2]*5^(1/4))], (5 + Sqrt[5])/2]))/((-5 + 3*Sqrt[5])*Sqrt[x*(-1 - x + x^2)])","C",0
1911,1,4461,133,139.3735808,"\int \frac{\left(-1+x^2\right) \sqrt{1+x^2+x^4}}{\left(1+x^2\right) \left(1+x+x^2+x^3+x^4\right)} \, dx","Integrate[((-1 + x^2)*Sqrt[1 + x^2 + x^4])/((1 + x^2)*(1 + x + x^2 + x^3 + x^4)),x]","\text{Result too large to show}","-2 \tan ^{-1}\left(\frac{\sqrt{x^4+x^2+1}}{x^2-x+1}\right)+\sqrt{\frac{1}{5} \left(2+2 \sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt{x^4+x^2+1}}{\sqrt{2+\sqrt{5}} \left(x^2-x+1\right)}\right)+\sqrt{\frac{1}{5} \left(2 \sqrt{5}-2\right)} \tanh ^{-1}\left(\frac{\sqrt{x^4+x^2+1}}{\sqrt{\sqrt{5}-2} \left(x^2-x+1\right)}\right)",1,"((1 + x^2)*Sqrt[1 + x^2 + x^4]*(1 + x + x^2 + x^3 + x^4)*((-2*Sqrt[1 + x^2 + x^4])/(1 + x^2) + ((1 + 2*x + 2*x^2)*Sqrt[1 + x^2 + x^4])/(1 + x + x^2 + x^3 + x^4))*(((-1)^(2/3)*Sqrt[1 + (-1)^(1/3)*x^2]*Sqrt[1 - (-1)^(2/3)*x^2]*EllipticF[I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)])/Sqrt[1 + x^2 + x^4] + ((-1)^(1/15)*Sqrt[1 + (-1)^(1/3)*x^2]*Sqrt[1 - (-1)^(2/3)*x^2]*EllipticPi[(-1)^(2/15), I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)])/((1 - (-1)^(1/5))*(-(-1)^(1/5) - (-1)^(2/5))*(-(-1)^(1/5) + (-1)^(3/5))*(-(-1)^(1/5) - (-1)^(4/5))*Sqrt[1 + x^2 + x^4]) - ((-1)^(4/15)*Sqrt[1 + (-1)^(1/3)*x^2]*Sqrt[1 - (-1)^(2/3)*x^2]*EllipticPi[(-1)^(2/15), I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)])/((1 - (-1)^(1/5))*(-(-1)^(1/5) - (-1)^(2/5))*(-(-1)^(1/5) + (-1)^(3/5))*(-(-1)^(1/5) - (-1)^(4/5))*Sqrt[1 + x^2 + x^4]) + ((-1)^(2/3)*Sqrt[1 + (-1)^(1/3)*x^2]*Sqrt[1 - (-1)^(2/3)*x^2]*EllipticPi[(-1)^(2/15), I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)])/((1 - (-1)^(1/5))*(-(-1)^(1/5) - (-1)^(2/5))*(-(-1)^(1/5) + (-1)^(3/5))*(-(-1)^(1/5) - (-1)^(4/5))*Sqrt[1 + x^2 + x^4]) - ((-1)^(13/15)*Sqrt[1 + (-1)^(1/3)*x^2]*Sqrt[1 - (-1)^(2/3)*x^2]*EllipticPi[(-1)^(2/15), I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)])/((1 - (-1)^(1/5))*(-(-1)^(1/5) - (-1)^(2/5))*(-(-1)^(1/5) + (-1)^(3/5))*(-(-1)^(1/5) - (-1)^(4/5))*Sqrt[1 + x^2 + x^4]) - (2*(-1)^(2/3)*Sqrt[1 + (-1)^(1/3)*x^2]*Sqrt[1 - (-1)^(2/3)*x^2]*EllipticPi[(-1)^(1/3), I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)])/((-1 + (-1)^(1/5))*(-1 - (-1)^(2/5))*(-1 + (-1)^(3/5))*(-1 - (-1)^(4/5))*Sqrt[1 + x^2 + x^4]) + ((-1)^(1/15)*Sqrt[1 + (-1)^(1/3)*x^2]*Sqrt[1 - (-1)^(2/3)*x^2]*EllipticPi[(-1)^(8/15), I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)])/((1 + (-1)^(4/5))*((-1)^(1/5) + (-1)^(4/5))*(-(-1)^(2/5) + (-1)^(4/5))*((-1)^(3/5) + (-1)^(4/5))*Sqrt[1 + x^2 + x^4]) - ((-1)^(4/15)*Sqrt[1 + (-1)^(1/3)*x^2]*Sqrt[1 - (-1)^(2/3)*x^2]*EllipticPi[(-1)^(8/15), I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)])/((1 + (-1)^(4/5))*((-1)^(1/5) + (-1)^(4/5))*(-(-1)^(2/5) + (-1)^(4/5))*((-1)^(3/5) + (-1)^(4/5))*Sqrt[1 + x^2 + x^4]) - ((-1)^(7/15)*Sqrt[1 + (-1)^(1/3)*x^2]*Sqrt[1 - (-1)^(2/3)*x^2]*EllipticPi[(-1)^(8/15), I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)])/((1 + (-1)^(4/5))*((-1)^(1/5) + (-1)^(4/5))*(-(-1)^(2/5) + (-1)^(4/5))*((-1)^(3/5) + (-1)^(4/5))*Sqrt[1 + x^2 + x^4]) + ((-1)^(2/3)*Sqrt[1 + (-1)^(1/3)*x^2]*Sqrt[1 - (-1)^(2/3)*x^2]*EllipticPi[(-1)^(8/15), I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)])/((1 + (-1)^(4/5))*((-1)^(1/5) + (-1)^(4/5))*(-(-1)^(2/5) + (-1)^(4/5))*((-1)^(3/5) + (-1)^(4/5))*Sqrt[1 + x^2 + x^4]) + ((-1)^(4/15)*Sqrt[1 + (-1)^(1/3)*x^2]*Sqrt[1 - (-1)^(2/3)*x^2]*EllipticPi[-(-1)^(11/15), I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)])/((1 - (-1)^(3/5))*((-1)^(1/5) - (-1)^(3/5))*(-(-1)^(2/5) - (-1)^(3/5))*(-(-1)^(3/5) - (-1)^(4/5))*Sqrt[1 + x^2 + x^4]) + ((-1)^(7/15)*Sqrt[1 + (-1)^(1/3)*x^2]*Sqrt[1 - (-1)^(2/3)*x^2]*EllipticPi[-(-1)^(11/15), I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)])/((1 - (-1)^(3/5))*((-1)^(1/5) - (-1)^(3/5))*(-(-1)^(2/5) - (-1)^(3/5))*(-(-1)^(3/5) - (-1)^(4/5))*Sqrt[1 + x^2 + x^4]) + ((-1)^(2/3)*Sqrt[1 + (-1)^(1/3)*x^2]*Sqrt[1 - (-1)^(2/3)*x^2]*EllipticPi[-(-1)^(11/15), I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)])/((1 - (-1)^(3/5))*((-1)^(1/5) - (-1)^(3/5))*(-(-1)^(2/5) - (-1)^(3/5))*(-(-1)^(3/5) - (-1)^(4/5))*Sqrt[1 + x^2 + x^4]) + ((-1)^(13/15)*Sqrt[1 + (-1)^(1/3)*x^2]*Sqrt[1 - (-1)^(2/3)*x^2]*EllipticPi[-(-1)^(11/15), I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)])/((1 - (-1)^(3/5))*((-1)^(1/5) - (-1)^(3/5))*(-(-1)^(2/5) - (-1)^(3/5))*(-(-1)^(3/5) - (-1)^(4/5))*Sqrt[1 + x^2 + x^4]) - ((-1)^(1/15)*Sqrt[1 + (-1)^(1/3)*x^2]*Sqrt[1 - (-1)^(2/3)*x^2]*EllipticPi[(-1)^(14/15), I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)])/((1 + (-1)^(2/5))*((-1)^(1/5) + (-1)^(2/5))*((-1)^(2/5) + (-1)^(3/5))*((-1)^(2/5) - (-1)^(4/5))*Sqrt[1 + x^2 + x^4]) + ((-1)^(7/15)*Sqrt[1 + (-1)^(1/3)*x^2]*Sqrt[1 - (-1)^(2/3)*x^2]*EllipticPi[(-1)^(14/15), I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)])/((1 + (-1)^(2/5))*((-1)^(1/5) + (-1)^(2/5))*((-1)^(2/5) + (-1)^(3/5))*((-1)^(2/5) - (-1)^(4/5))*Sqrt[1 + x^2 + x^4]) + ((-1)^(2/3)*Sqrt[1 + (-1)^(1/3)*x^2]*Sqrt[1 - (-1)^(2/3)*x^2]*EllipticPi[(-1)^(14/15), I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)])/((1 + (-1)^(2/5))*((-1)^(1/5) + (-1)^(2/5))*((-1)^(2/5) + (-1)^(3/5))*((-1)^(2/5) - (-1)^(4/5))*Sqrt[1 + x^2 + x^4]) + ((-1)^(13/15)*Sqrt[1 + (-1)^(1/3)*x^2]*Sqrt[1 - (-1)^(2/3)*x^2]*EllipticPi[(-1)^(14/15), I*ArcSinh[(-1)^(5/6)*x], (-1)^(2/3)])/((1 + (-1)^(2/5))*((-1)^(1/5) + (-1)^(2/5))*((-1)^(2/5) + (-1)^(3/5))*((-1)^(2/5) - (-1)^(4/5))*Sqrt[1 + x^2 + x^4]) - ((-1)^(1/5)*((-3 + (-1)^(2/5) - 3*(-1)^(4/5))*Sqrt[6 - 5*(-1)^(1/5) + 5*(-1)^(2/5) - 6*(-1)^(3/5) + 5*(-1)^(4/5)]*Log[(-1)^(1/5) + x^2] + (4 - 5*(-1)^(1/5) + 8*(-1)^(2/5) - 8*(-1)^(3/5) + 5*(-1)^(4/5))*Sqrt[6 - 6*(-1)^(1/5) + 5*(-1)^(2/5) - 5*(-1)^(3/5) + 5*(-1)^(4/5)]*Log[-(-1)^(2/5) + x^2] + 2*Sqrt[6 - 5*(-1)^(1/5) + 5*(-1)^(2/5) - 5*(-1)^(3/5) + 6*(-1)^(4/5)]*Log[(-1)^(3/5) + x^2] - 2*(-1)^(1/5)*Sqrt[6 - 5*(-1)^(1/5) + 5*(-1)^(2/5) - 5*(-1)^(3/5) + 6*(-1)^(4/5)]*Log[(-1)^(3/5) + x^2] - (-1)^(2/5)*Sqrt[6 - 5*(-1)^(1/5) + 5*(-1)^(2/5) - 5*(-1)^(3/5) + 6*(-1)^(4/5)]*Log[(-1)^(3/5) + x^2] + 2*(-1)^(3/5)*Sqrt[6 - 5*(-1)^(1/5) + 5*(-1)^(2/5) - 5*(-1)^(3/5) + 6*(-1)^(4/5)]*Log[(-1)^(3/5) + x^2] - (-1)^(4/5)*Sqrt[6 - 5*(-1)^(1/5) + 5*(-1)^(2/5) - 5*(-1)^(3/5) + 6*(-1)^(4/5)]*Log[(-1)^(3/5) + x^2] + 3*Sqrt[6 - 5*(-1)^(1/5) + 6*(-1)^(2/5) - 5*(-1)^(3/5) + 5*(-1)^(4/5)]*Log[-(-1)^(4/5) + x^2] - 4*(-1)^(1/5)*Sqrt[6 - 5*(-1)^(1/5) + 6*(-1)^(2/5) - 5*(-1)^(3/5) + 5*(-1)^(4/5)]*Log[-(-1)^(4/5) + x^2] + 3*(-1)^(2/5)*Sqrt[6 - 5*(-1)^(1/5) + 6*(-1)^(2/5) - 5*(-1)^(3/5) + 5*(-1)^(4/5)]*Log[-(-1)^(4/5) + x^2] + 3*Sqrt[6 - 5*(-1)^(1/5) + 5*(-1)^(2/5) - 6*(-1)^(3/5) + 5*(-1)^(4/5)]*Log[2 - (-1)^(1/5) + x^2 - 2*(-1)^(1/5)*x^2 + 2*Sqrt[1 - (-1)^(1/5) + (-1)^(2/5)]*Sqrt[1 + x^2 + x^4]] - (-1)^(2/5)*Sqrt[6 - 5*(-1)^(1/5) + 5*(-1)^(2/5) - 6*(-1)^(3/5) + 5*(-1)^(4/5)]*Log[2 - (-1)^(1/5) + x^2 - 2*(-1)^(1/5)*x^2 + 2*Sqrt[1 - (-1)^(1/5) + (-1)^(2/5)]*Sqrt[1 + x^2 + x^4]] + 3*(-1)^(4/5)*Sqrt[6 - 5*(-1)^(1/5) + 5*(-1)^(2/5) - 6*(-1)^(3/5) + 5*(-1)^(4/5)]*Log[2 - (-1)^(1/5) + x^2 - 2*(-1)^(1/5)*x^2 + 2*Sqrt[1 - (-1)^(1/5) + (-1)^(2/5)]*Sqrt[1 + x^2 + x^4]] - 2*Sqrt[6 - 5*(-1)^(1/5) + 5*(-1)^(2/5) - 5*(-1)^(3/5) + 6*(-1)^(4/5)]*Log[2 - (-1)^(3/5) + x^2 - 2*(-1)^(3/5)*x^2 + 2*Sqrt[1 - (-1)^(1/5) - (-1)^(3/5)]*Sqrt[1 + x^2 + x^4]] + 2*(-1)^(1/5)*Sqrt[6 - 5*(-1)^(1/5) + 5*(-1)^(2/5) - 5*(-1)^(3/5) + 6*(-1)^(4/5)]*Log[2 - (-1)^(3/5) + x^2 - 2*(-1)^(3/5)*x^2 + 2*Sqrt[1 - (-1)^(1/5) - (-1)^(3/5)]*Sqrt[1 + x^2 + x^4]] + (-1)^(2/5)*Sqrt[6 - 5*(-1)^(1/5) + 5*(-1)^(2/5) - 5*(-1)^(3/5) + 6*(-1)^(4/5)]*Log[2 - (-1)^(3/5) + x^2 - 2*(-1)^(3/5)*x^2 + 2*Sqrt[1 - (-1)^(1/5) - (-1)^(3/5)]*Sqrt[1 + x^2 + x^4]] - 2*(-1)^(3/5)*Sqrt[6 - 5*(-1)^(1/5) + 5*(-1)^(2/5) - 5*(-1)^(3/5) + 6*(-1)^(4/5)]*Log[2 - (-1)^(3/5) + x^2 - 2*(-1)^(3/5)*x^2 + 2*Sqrt[1 - (-1)^(1/5) - (-1)^(3/5)]*Sqrt[1 + x^2 + x^4]] + (-1)^(4/5)*Sqrt[6 - 5*(-1)^(1/5) + 5*(-1)^(2/5) - 5*(-1)^(3/5) + 6*(-1)^(4/5)]*Log[2 - (-1)^(3/5) + x^2 - 2*(-1)^(3/5)*x^2 + 2*Sqrt[1 - (-1)^(1/5) - (-1)^(3/5)]*Sqrt[1 + x^2 + x^4]] - 4*Sqrt[6 - 6*(-1)^(1/5) + 5*(-1)^(2/5) - 5*(-1)^(3/5) + 5*(-1)^(4/5)]*Log[2 + (-1)^(2/5) + x^2 + 2*(-1)^(2/5)*x^2 + 2*Sqrt[1 + (-1)^(2/5) + (-1)^(4/5)]*Sqrt[1 + x^2 + x^4]] + 5*(-1)^(1/5)*Sqrt[6 - 6*(-1)^(1/5) + 5*(-1)^(2/5) - 5*(-1)^(3/5) + 5*(-1)^(4/5)]*Log[2 + (-1)^(2/5) + x^2 + 2*(-1)^(2/5)*x^2 + 2*Sqrt[1 + (-1)^(2/5) + (-1)^(4/5)]*Sqrt[1 + x^2 + x^4]] - 8*(-1)^(2/5)*Sqrt[6 - 6*(-1)^(1/5) + 5*(-1)^(2/5) - 5*(-1)^(3/5) + 5*(-1)^(4/5)]*Log[2 + (-1)^(2/5) + x^2 + 2*(-1)^(2/5)*x^2 + 2*Sqrt[1 + (-1)^(2/5) + (-1)^(4/5)]*Sqrt[1 + x^2 + x^4]] + 8*(-1)^(3/5)*Sqrt[6 - 6*(-1)^(1/5) + 5*(-1)^(2/5) - 5*(-1)^(3/5) + 5*(-1)^(4/5)]*Log[2 + (-1)^(2/5) + x^2 + 2*(-1)^(2/5)*x^2 + 2*Sqrt[1 + (-1)^(2/5) + (-1)^(4/5)]*Sqrt[1 + x^2 + x^4]] - 5*(-1)^(4/5)*Sqrt[6 - 6*(-1)^(1/5) + 5*(-1)^(2/5) - 5*(-1)^(3/5) + 5*(-1)^(4/5)]*Log[2 + (-1)^(2/5) + x^2 + 2*(-1)^(2/5)*x^2 + 2*Sqrt[1 + (-1)^(2/5) + (-1)^(4/5)]*Sqrt[1 + x^2 + x^4]] - 3*Sqrt[6 - 5*(-1)^(1/5) + 6*(-1)^(2/5) - 5*(-1)^(3/5) + 5*(-1)^(4/5)]*Log[2 + (-1)^(4/5) + x^2 + 2*(-1)^(4/5)*x^2 + 2*Sqrt[1 - (-1)^(3/5) + (-1)^(4/5)]*Sqrt[1 + x^2 + x^4]] + 4*(-1)^(1/5)*Sqrt[6 - 5*(-1)^(1/5) + 6*(-1)^(2/5) - 5*(-1)^(3/5) + 5*(-1)^(4/5)]*Log[2 + (-1)^(4/5) + x^2 + 2*(-1)^(4/5)*x^2 + 2*Sqrt[1 - (-1)^(3/5) + (-1)^(4/5)]*Sqrt[1 + x^2 + x^4]] - 3*(-1)^(2/5)*Sqrt[6 - 5*(-1)^(1/5) + 6*(-1)^(2/5) - 5*(-1)^(3/5) + 5*(-1)^(4/5)]*Log[2 + (-1)^(4/5) + x^2 + 2*(-1)^(4/5)*x^2 + 2*Sqrt[1 - (-1)^(3/5) + (-1)^(4/5)]*Sqrt[1 + x^2 + x^4]]))/(2*(-1 + (-1)^(1/5))^2*(1 + (-1)^(1/5))^4*(1 - (-1)^(1/5) + (-1)^(2/5))^(5/2)*Sqrt[6 - 5*(-1)^(1/5) + 5*(-1)^(2/5) - 6*(-1)^(3/5) + 5*(-1)^(4/5)])))/((-1 + x)*(1 + x)*(1 - x + x^2)*(1 + x + x^2))","C",0
1912,1,63,133,0.059379,"\int \frac{x^6}{\left(-b+a x^4\right) \left(b+a x^4\right)^{3/4}} \, dx","Integrate[x^6/((-b + a*x^4)*(b + a*x^4)^(3/4)),x]","-\frac{x^7 \left(\frac{a x^4}{b}+1\right)^{3/4} F_1\left(\frac{7}{4};\frac{3}{4},1;\frac{11}{4};-\frac{a x^4}{b},\frac{a x^4}{b}\right)}{7 b \left(a x^4+b\right)^{3/4}}","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{2 a^{7/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{2\ 2^{3/4} a^{7/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{2 a^{7/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{2\ 2^{3/4} a^{7/4}}",1,"-1/7*(x^7*(1 + (a*x^4)/b)^(3/4)*AppellF1[7/4, 3/4, 1, 11/4, -((a*x^4)/b), (a*x^4)/b])/(b*(b + a*x^4)^(3/4))","C",0
1913,1,78,133,0.0509265,"\int \frac{-b+a x^3}{x^3 \left(b+a x^3\right) \sqrt[4]{-b x+a x^4}} \, dx","Integrate[(-b + a*x^3)/(x^3*(b + a*x^3)*(-(b*x) + a*x^4)^(1/4)),x]","-\frac{4 \left(\frac{a x^3}{b}+1\right)^{3/4} \left(a x^4-b x\right)^{3/4} \, _2F_1\left(-\frac{3}{4},-\frac{3}{4};\frac{1}{4};\frac{2 a x^3}{a x^3+b}\right)}{9 b x^3 \left(1-\frac{a x^3}{b}\right)^{3/4}}","\frac{2\ 2^{3/4} a^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} \left(a x^4-b x\right)^{3/4}}{a x^3-b}\right)}{3 b}+\frac{2\ 2^{3/4} a^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} \left(a x^4-b x\right)^{3/4}}{a x^3-b}\right)}{3 b}-\frac{4 \left(a x^4-b x\right)^{3/4}}{9 b x^3}",1,"(-4*(1 + (a*x^3)/b)^(3/4)*(-(b*x) + a*x^4)^(3/4)*Hypergeometric2F1[-3/4, -3/4, 1/4, (2*a*x^3)/(b + a*x^3)])/(9*b*x^3*(1 - (a*x^3)/b)^(3/4))","C",0
1914,1,108,133,0.1222844,"\int \frac{-b+a x^4}{\sqrt[4]{b+a x^4} \left(-b+3 a x^4\right)} \, dx","Integrate[(-b + a*x^4)/((b + a*x^4)^(1/4)*(-b + 3*a*x^4)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)+\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)+\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)+\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{6 \sqrt[4]{a}}","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{6 \sqrt[4]{a}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{3 \sqrt{2} \sqrt[4]{a}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{6 \sqrt[4]{a}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{3 \sqrt{2} \sqrt[4]{a}}",1,"(ArcTan[(a^(1/4)*x)/(b + a*x^4)^(1/4)] + Sqrt[2]*ArcTan[(Sqrt[2]*a^(1/4)*x)/(b + a*x^4)^(1/4)] + ArcTanh[(a^(1/4)*x)/(b + a*x^4)^(1/4)] + Sqrt[2]*ArcTanh[(Sqrt[2]*a^(1/4)*x)/(b + a*x^4)^(1/4)])/(6*a^(1/4))","A",1
1915,0,0,133,0.2816757,"\int \frac{-2 b+a x^2}{\sqrt[4]{-b+a x^2} \left(-b+a x^2+c x^4\right)} \, dx","Integrate[(-2*b + a*x^2)/((-b + a*x^2)^(1/4)*(-b + a*x^2 + c*x^4)),x]","\int \frac{-2 b+a x^2}{\sqrt[4]{-b+a x^2} \left(-b+a x^2+c x^4\right)} \, dx","\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x \sqrt[4]{a x^2-b}}{\sqrt{a x^2-b}+\sqrt{c} x^2}\right)}{\sqrt{2} \sqrt[4]{c}}-\frac{\tan ^{-1}\left(\frac{\frac{\sqrt{a x^2-b}}{\sqrt{2} \sqrt[4]{c}}-\frac{\sqrt[4]{c} x^2}{\sqrt{2}}}{x \sqrt[4]{a x^2-b}}\right)}{\sqrt{2} \sqrt[4]{c}}",1,"Integrate[(-2*b + a*x^2)/((-b + a*x^2)^(1/4)*(-b + a*x^2 + c*x^4)), x]","F",-1
1916,1,3835,133,8.740567,"\int \frac{\left(-q+p x^2\right) \sqrt{q^2+p^2 x^4}}{x^2 \left(a q+b x+a p x^2\right)} \, dx","Integrate[((-q + p*x^2)*Sqrt[q^2 + p^2*x^4])/(x^2*(a*q + b*x + a*p*x^2)),x]","\text{Result too large to show}","\frac{2 \sqrt{2 a^2 p q-b^2} \tan ^{-1}\left(\frac{x \sqrt{2 a^2 p q-b^2}}{a \sqrt{p^2 x^4+q^2}+a p x^2+a q+b x}\right)}{a^2}-\frac{b \log \left(\sqrt{p^2 x^4+q^2}+p x^2+q\right)}{a^2}+\frac{b \log (x)}{a^2}+\frac{\sqrt{p^2 x^4+q^2}}{a x}",1,"Sqrt[q^2 + p^2*x^4]/(a*x) - ((b*(2*ArcTanh[(p*x^2)/Sqrt[q^2 + p^2*x^4]] + 2*ArcTanh[Sqrt[q^2 + p^2*x^4]/q] + (Sqrt[2]*Sqrt[b^2 - 2*a^2*p*q]*(b^2 - 4*a^2*p*q - b*Sqrt[b^2 - 4*a^2*p*q])*ArcTanh[(p*(b*(b - Sqrt[b^2 - 4*a^2*p*q])*x^2 + 2*a^2*q*(q - p*x^2)))/(Sqrt[2]*Sqrt[b^2 - 2*a^2*p*q]*Sqrt[b^2 - 2*a^2*p*q - b*Sqrt[b^2 - 4*a^2*p*q]]*Sqrt[q^2 + p^2*x^4])])/(b*Sqrt[b^2 - 4*a^2*p*q]*Sqrt[b^2 - 2*a^2*p*q - b*Sqrt[b^2 - 4*a^2*p*q]]) - (Sqrt[2]*Sqrt[b^2 - 2*a^2*p*q]*(b^2 - 4*a^2*p*q + b*Sqrt[b^2 - 4*a^2*p*q])*ArcTanh[(p*(b*(b + Sqrt[b^2 - 4*a^2*p*q])*x^2 + 2*a^2*q*(q - p*x^2)))/(Sqrt[2]*Sqrt[b^2 - 2*a^2*p*q]*Sqrt[b^2 - 2*a^2*p*q + b*Sqrt[b^2 - 4*a^2*p*q]]*Sqrt[q^2 + p^2*x^4])])/(b*Sqrt[b^2 - 4*a^2*p*q]*Sqrt[b^2 - 2*a^2*p*q + b*Sqrt[b^2 - 4*a^2*p*q]])))/(4*a) + (I*b^2*Sqrt[1 - (I*p*x^2)/q]*Sqrt[1 + (I*p*x^2)/q]*EllipticF[I*ArcSinh[Sqrt[(I*p)/q]*x], -1])/(a^2*Sqrt[(I*p)/q]*Sqrt[q^2 + p^2*x^4]) - ((2*I)*p*q*Sqrt[1 - (I*p*x^2)/q]*Sqrt[1 + (I*p*x^2)/q]*EllipticF[I*ArcSinh[Sqrt[(I*p)/q]*x], -1])/(Sqrt[(I*p)/q]*Sqrt[q^2 + p^2*x^4]) + (I*b^6*Sqrt[1 - (I*p*x^2)/q]*Sqrt[1 + (I*p*x^2)/q]*EllipticPi[((-2*I)*a^2*p*q)/(-b^2 + 2*a^2*p*q - Sqrt[b^4 - 4*a^2*b^2*p*q]), I*ArcSinh[Sqrt[(I*p)/q]*x], -1])/(a^4*p^2*Sqrt[(I*p)/q]*(-b^2 + 2*a^2*p*q - Sqrt[b^4 - 4*a^2*b^2*p*q])*(-1/2*(b^2 - 2*a^2*p*q - Sqrt[b^4 - 4*a^2*b^2*p*q])/(a^2*p^2) + (b^2 - 2*a^2*p*q + Sqrt[b^4 - 4*a^2*b^2*p*q])/(2*a^2*p^2))*Sqrt[q^2 + p^2*x^4]) - ((6*I)*b^4*q*Sqrt[1 - (I*p*x^2)/q]*Sqrt[1 + (I*p*x^2)/q]*EllipticPi[((-2*I)*a^2*p*q)/(-b^2 + 2*a^2*p*q - Sqrt[b^4 - 4*a^2*b^2*p*q]), I*ArcSinh[Sqrt[(I*p)/q]*x], -1])/(a^2*p*Sqrt[(I*p)/q]*(-b^2 + 2*a^2*p*q - Sqrt[b^4 - 4*a^2*b^2*p*q])*(-1/2*(b^2 - 2*a^2*p*q - Sqrt[b^4 - 4*a^2*b^2*p*q])/(a^2*p^2) + (b^2 - 2*a^2*p*q + Sqrt[b^4 - 4*a^2*b^2*p*q])/(2*a^2*p^2))*Sqrt[q^2 + p^2*x^4]) + ((8*I)*b^2*q^2*Sqrt[1 - (I*p*x^2)/q]*Sqrt[1 + (I*p*x^2)/q]*EllipticPi[((-2*I)*a^2*p*q)/(-b^2 + 2*a^2*p*q - Sqrt[b^4 - 4*a^2*b^2*p*q]), I*ArcSinh[Sqrt[(I*p)/q]*x], -1])/(Sqrt[(I*p)/q]*(-b^2 + 2*a^2*p*q - Sqrt[b^4 - 4*a^2*b^2*p*q])*(-1/2*(b^2 - 2*a^2*p*q - Sqrt[b^4 - 4*a^2*b^2*p*q])/(a^2*p^2) + (b^2 - 2*a^2*p*q + Sqrt[b^4 - 4*a^2*b^2*p*q])/(2*a^2*p^2))*Sqrt[q^2 + p^2*x^4]) + (I*b^4*Sqrt[b^4 - 4*a^2*b^2*p*q]*Sqrt[1 - (I*p*x^2)/q]*Sqrt[1 + (I*p*x^2)/q]*EllipticPi[((-2*I)*a^2*p*q)/(-b^2 + 2*a^2*p*q - Sqrt[b^4 - 4*a^2*b^2*p*q]), I*ArcSinh[Sqrt[(I*p)/q]*x], -1])/(a^4*p^2*Sqrt[(I*p)/q]*(-b^2 + 2*a^2*p*q - Sqrt[b^4 - 4*a^2*b^2*p*q])*(-1/2*(b^2 - 2*a^2*p*q - Sqrt[b^4 - 4*a^2*b^2*p*q])/(a^2*p^2) + (b^2 - 2*a^2*p*q + Sqrt[b^4 - 4*a^2*b^2*p*q])/(2*a^2*p^2))*Sqrt[q^2 + p^2*x^4]) - ((4*I)*b^2*q*Sqrt[b^4 - 4*a^2*b^2*p*q]*Sqrt[1 - (I*p*x^2)/q]*Sqrt[1 + (I*p*x^2)/q]*EllipticPi[((-2*I)*a^2*p*q)/(-b^2 + 2*a^2*p*q - Sqrt[b^4 - 4*a^2*b^2*p*q]), I*ArcSinh[Sqrt[(I*p)/q]*x], -1])/(a^2*p*Sqrt[(I*p)/q]*(-b^2 + 2*a^2*p*q - Sqrt[b^4 - 4*a^2*b^2*p*q])*(-1/2*(b^2 - 2*a^2*p*q - Sqrt[b^4 - 4*a^2*b^2*p*q])/(a^2*p^2) + (b^2 - 2*a^2*p*q + Sqrt[b^4 - 4*a^2*b^2*p*q])/(2*a^2*p^2))*Sqrt[q^2 + p^2*x^4]) + ((4*I)*q^2*Sqrt[b^4 - 4*a^2*b^2*p*q]*Sqrt[1 - (I*p*x^2)/q]*Sqrt[1 + (I*p*x^2)/q]*EllipticPi[((-2*I)*a^2*p*q)/(-b^2 + 2*a^2*p*q - Sqrt[b^4 - 4*a^2*b^2*p*q]), I*ArcSinh[Sqrt[(I*p)/q]*x], -1])/(Sqrt[(I*p)/q]*(-b^2 + 2*a^2*p*q - Sqrt[b^4 - 4*a^2*b^2*p*q])*(-1/2*(b^2 - 2*a^2*p*q - Sqrt[b^4 - 4*a^2*b^2*p*q])/(a^2*p^2) + (b^2 - 2*a^2*p*q + Sqrt[b^4 - 4*a^2*b^2*p*q])/(2*a^2*p^2))*Sqrt[q^2 + p^2*x^4]) + (I*b^6*Sqrt[1 - (I*p*x^2)/q]*Sqrt[1 + (I*p*x^2)/q]*EllipticPi[((-2*I)*a^2*p*q)/(-b^2 + 2*a^2*p*q + Sqrt[b^4 - 4*a^2*b^2*p*q]), I*ArcSinh[Sqrt[(I*p)/q]*x], -1])/(a^4*p^2*Sqrt[(I*p)/q]*(-b^2 + 2*a^2*p*q + Sqrt[b^4 - 4*a^2*b^2*p*q])*((b^2 - 2*a^2*p*q - Sqrt[b^4 - 4*a^2*b^2*p*q])/(2*a^2*p^2) - (b^2 - 2*a^2*p*q + Sqrt[b^4 - 4*a^2*b^2*p*q])/(2*a^2*p^2))*Sqrt[q^2 + p^2*x^4]) - ((6*I)*b^4*q*Sqrt[1 - (I*p*x^2)/q]*Sqrt[1 + (I*p*x^2)/q]*EllipticPi[((-2*I)*a^2*p*q)/(-b^2 + 2*a^2*p*q + Sqrt[b^4 - 4*a^2*b^2*p*q]), I*ArcSinh[Sqrt[(I*p)/q]*x], -1])/(a^2*p*Sqrt[(I*p)/q]*(-b^2 + 2*a^2*p*q + Sqrt[b^4 - 4*a^2*b^2*p*q])*((b^2 - 2*a^2*p*q - Sqrt[b^4 - 4*a^2*b^2*p*q])/(2*a^2*p^2) - (b^2 - 2*a^2*p*q + Sqrt[b^4 - 4*a^2*b^2*p*q])/(2*a^2*p^2))*Sqrt[q^2 + p^2*x^4]) + ((8*I)*b^2*q^2*Sqrt[1 - (I*p*x^2)/q]*Sqrt[1 + (I*p*x^2)/q]*EllipticPi[((-2*I)*a^2*p*q)/(-b^2 + 2*a^2*p*q + Sqrt[b^4 - 4*a^2*b^2*p*q]), I*ArcSinh[Sqrt[(I*p)/q]*x], -1])/(Sqrt[(I*p)/q]*(-b^2 + 2*a^2*p*q + Sqrt[b^4 - 4*a^2*b^2*p*q])*((b^2 - 2*a^2*p*q - Sqrt[b^4 - 4*a^2*b^2*p*q])/(2*a^2*p^2) - (b^2 - 2*a^2*p*q + Sqrt[b^4 - 4*a^2*b^2*p*q])/(2*a^2*p^2))*Sqrt[q^2 + p^2*x^4]) - (I*b^4*Sqrt[b^4 - 4*a^2*b^2*p*q]*Sqrt[1 - (I*p*x^2)/q]*Sqrt[1 + (I*p*x^2)/q]*EllipticPi[((-2*I)*a^2*p*q)/(-b^2 + 2*a^2*p*q + Sqrt[b^4 - 4*a^2*b^2*p*q]), I*ArcSinh[Sqrt[(I*p)/q]*x], -1])/(a^4*p^2*Sqrt[(I*p)/q]*(-b^2 + 2*a^2*p*q + Sqrt[b^4 - 4*a^2*b^2*p*q])*((b^2 - 2*a^2*p*q - Sqrt[b^4 - 4*a^2*b^2*p*q])/(2*a^2*p^2) - (b^2 - 2*a^2*p*q + Sqrt[b^4 - 4*a^2*b^2*p*q])/(2*a^2*p^2))*Sqrt[q^2 + p^2*x^4]) + ((4*I)*b^2*q*Sqrt[b^4 - 4*a^2*b^2*p*q]*Sqrt[1 - (I*p*x^2)/q]*Sqrt[1 + (I*p*x^2)/q]*EllipticPi[((-2*I)*a^2*p*q)/(-b^2 + 2*a^2*p*q + Sqrt[b^4 - 4*a^2*b^2*p*q]), I*ArcSinh[Sqrt[(I*p)/q]*x], -1])/(a^2*p*Sqrt[(I*p)/q]*(-b^2 + 2*a^2*p*q + Sqrt[b^4 - 4*a^2*b^2*p*q])*((b^2 - 2*a^2*p*q - Sqrt[b^4 - 4*a^2*b^2*p*q])/(2*a^2*p^2) - (b^2 - 2*a^2*p*q + Sqrt[b^4 - 4*a^2*b^2*p*q])/(2*a^2*p^2))*Sqrt[q^2 + p^2*x^4]) - ((4*I)*q^2*Sqrt[b^4 - 4*a^2*b^2*p*q]*Sqrt[1 - (I*p*x^2)/q]*Sqrt[1 + (I*p*x^2)/q]*EllipticPi[((-2*I)*a^2*p*q)/(-b^2 + 2*a^2*p*q + Sqrt[b^4 - 4*a^2*b^2*p*q]), I*ArcSinh[Sqrt[(I*p)/q]*x], -1])/(Sqrt[(I*p)/q]*(-b^2 + 2*a^2*p*q + Sqrt[b^4 - 4*a^2*b^2*p*q])*((b^2 - 2*a^2*p*q - Sqrt[b^4 - 4*a^2*b^2*p*q])/(2*a^2*p^2) - (b^2 - 2*a^2*p*q + Sqrt[b^4 - 4*a^2*b^2*p*q])/(2*a^2*p^2))*Sqrt[q^2 + p^2*x^4]))/a","C",1
1917,0,0,133,0.3649411,"\int \frac{\sqrt[3]{1+x^5} \left(-3+2 x^5\right)}{x^2 \left(2-x^3+2 x^5\right)} \, dx","Integrate[((1 + x^5)^(1/3)*(-3 + 2*x^5))/(x^2*(2 - x^3 + 2*x^5)),x]","\int \frac{\sqrt[3]{1+x^5} \left(-3+2 x^5\right)}{x^2 \left(2-x^3+2 x^5\right)} \, dx","\frac{3 \sqrt[3]{x^5+1}}{2 x}+\frac{\log \left(\sqrt[3]{2} \sqrt[3]{x^5+1}-x\right)}{2 \sqrt[3]{2}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{2} \sqrt[3]{x^5+1}+x}\right)}{2 \sqrt[3]{2}}-\frac{\log \left(\sqrt[3]{2} \sqrt[3]{x^5+1} x+2^{2/3} \left(x^5+1\right)^{2/3}+x^2\right)}{4 \sqrt[3]{2}}",1,"Integrate[((1 + x^5)^(1/3)*(-3 + 2*x^5))/(x^2*(2 - x^3 + 2*x^5)), x]","F",-1
1918,0,0,133,0.5384736,"\int \frac{x^2 \left(4 b+a x^5\right)}{\left(-b+a x^5\right)^{3/4} \left(-b+c x^4+a x^5\right)} \, dx","Integrate[(x^2*(4*b + a*x^5))/((-b + a*x^5)^(3/4)*(-b + c*x^4 + a*x^5)),x]","\int \frac{x^2 \left(4 b+a x^5\right)}{\left(-b+a x^5\right)^{3/4} \left(-b+c x^4+a x^5\right)} \, dx","\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\frac{\sqrt{a x^5-b}}{\sqrt{2} \sqrt[4]{c}}+\frac{\sqrt[4]{c} x^2}{\sqrt{2}}}{x \sqrt[4]{a x^5-b}}\right)}{c^{3/4}}-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x \sqrt[4]{a x^5-b}}{\sqrt{a x^5-b}-\sqrt{c} x^2}\right)}{c^{3/4}}",1,"Integrate[(x^2*(4*b + a*x^5))/((-b + a*x^5)^(3/4)*(-b + c*x^4 + a*x^5)), x]","F",-1
1919,0,0,133,1.401617,"\int \frac{\left(-1+x^6\right) \left(1+x^6\right)^{2/3}}{x^3 \left(2-x^3+2 x^6\right)} \, dx","Integrate[((-1 + x^6)*(1 + x^6)^(2/3))/(x^3*(2 - x^3 + 2*x^6)),x]","\int \frac{\left(-1+x^6\right) \left(1+x^6\right)^{2/3}}{x^3 \left(2-x^3+2 x^6\right)} \, dx","\frac{\log \left(\sqrt[3]{2} \sqrt[3]{x^6+1}-x\right)}{6\ 2^{2/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{2} \sqrt[3]{x^6+1}+x}\right)}{2\ 2^{2/3} \sqrt{3}}+\frac{\left(x^6+1\right)^{2/3}}{4 x^2}-\frac{\log \left(\sqrt[3]{2} \sqrt[3]{x^6+1} x+2^{2/3} \left(x^6+1\right)^{2/3}+x^2\right)}{12\ 2^{2/3}}",1,"Integrate[((-1 + x^6)*(1 + x^6)^(2/3))/(x^3*(2 - x^3 + 2*x^6)), x]","F",-1
1920,0,0,133,0.4074865,"\int \frac{x^2 \left(2 b+a x^6\right)}{\left(-b+a x^6\right)^{3/4} \left(-b+c x^4+a x^6\right)} \, dx","Integrate[(x^2*(2*b + a*x^6))/((-b + a*x^6)^(3/4)*(-b + c*x^4 + a*x^6)),x]","\int \frac{x^2 \left(2 b+a x^6\right)}{\left(-b+a x^6\right)^{3/4} \left(-b+c x^4+a x^6\right)} \, dx","\frac{\tanh ^{-1}\left(\frac{\frac{\sqrt{a x^6-b}}{\sqrt{2} \sqrt[4]{c}}+\frac{\sqrt[4]{c} x^2}{\sqrt{2}}}{x \sqrt[4]{a x^6-b}}\right)}{\sqrt{2} c^{3/4}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x \sqrt[4]{a x^6-b}}{\sqrt{a x^6-b}-\sqrt{c} x^2}\right)}{\sqrt{2} c^{3/4}}",1,"Integrate[(x^2*(2*b + a*x^6))/((-b + a*x^6)^(3/4)*(-b + c*x^4 + a*x^6)), x]","F",-1
1921,1,189,133,0.2339094,"\int x^2 \sqrt{1+x^4} \sqrt{x^2+\sqrt{1+x^4}} \, dx","Integrate[x^2*Sqrt[1 + x^4]*Sqrt[x^2 + Sqrt[1 + x^4]],x]","\frac{\sqrt{x^4+1} \sqrt{x^2 \left(\sqrt{x^4+1}+x^2\right)} \left(\sqrt{2} \sqrt{x^2 \left(\sqrt{x^4+1}+x^2\right)} \left(16 x^8+36 x^4+16 \sqrt{x^4+1} x^6+28 \sqrt{x^4+1} x^2+9\right)-9 \left(2 x^4+2 \sqrt{x^4+1} x^2+1\right) \tan ^{-1}\left(\sqrt{\left(\sqrt{x^4+1}+x^2\right)^2-1}\right)\right)}{48 \sqrt{2} \left(\sqrt{x^4+1}+x^2\right)^{3/2} \left(x^5+\sqrt{x^4+1} x^3+x\right)}","\frac{x \left(16 x^8+36 x^4+9\right) \sqrt{\sqrt{x^4+1}+x^2}+x \sqrt{x^4+1} \sqrt{\sqrt{x^4+1}+x^2} \left(16 x^6+28 x^2\right)}{48 \left(2 x^4+1\right)+96 \sqrt{x^4+1} x^2}-\frac{3 \tan ^{-1}\left(\sqrt{2} x \sqrt{\sqrt{x^4+1}+x^2}\right)}{16 \sqrt{2}}",1,"(Sqrt[1 + x^4]*Sqrt[x^2*(x^2 + Sqrt[1 + x^4])]*(Sqrt[2]*Sqrt[x^2*(x^2 + Sqrt[1 + x^4])]*(9 + 36*x^4 + 16*x^8 + 28*x^2*Sqrt[1 + x^4] + 16*x^6*Sqrt[1 + x^4]) - 9*(1 + 2*x^4 + 2*x^2*Sqrt[1 + x^4])*ArcTan[Sqrt[-1 + (x^2 + Sqrt[1 + x^4])^2]]))/(48*Sqrt[2]*(x^2 + Sqrt[1 + x^4])^(3/2)*(x + x^5 + x^3*Sqrt[1 + x^4]))","A",1
1922,1,49,133,0.0328982,"\int \sqrt{1+\sqrt{1+\sqrt{1+x}}} \, dx","Integrate[Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]],x]","\frac{8}{315} \left(35 \sqrt{x+1}-65 \sqrt{\sqrt{x+1}+1}+61\right) \left(\sqrt{\sqrt{x+1}+1}+1\right)^{5/2}","\frac{8}{315} \sqrt{\sqrt{\sqrt{x+1}+1}+1} (35 x+27)+\sqrt{x+1} \left(\frac{8}{63} \sqrt{\sqrt{x+1}+1} \sqrt{\sqrt{\sqrt{x+1}+1}+1}+\frac{8}{315} \sqrt{\sqrt{\sqrt{x+1}+1}+1}\right)-\frac{64}{315} \sqrt{\sqrt{x+1}+1} \sqrt{\sqrt{\sqrt{x+1}+1}+1}",1,"(8*(61 + 35*Sqrt[1 + x] - 65*Sqrt[1 + Sqrt[1 + x]])*(1 + Sqrt[1 + Sqrt[1 + x]])^(5/2))/315","A",1
1923,0,0,133,7.1751847,"\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right) \sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x^2)*Sqrt[x + Sqrt[1 + x^2]]),x]","\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right) \sqrt{x+\sqrt{1+x^2}}} \, dx","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^2-1}\&\right]-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^2-1}\&\right]",1,"Integrate[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x^2)*Sqrt[x + Sqrt[1 + x^2]]), x]","F",-1
1924,0,0,133,0.1959548,"\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right) \sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x^2)*Sqrt[x + Sqrt[1 + x^2]]),x]","\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right) \sqrt{x+\sqrt{1+x^2}}} \, dx","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^2-1}\&\right]-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^2-1}\&\right]",1,"Integrate[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x^2)*Sqrt[x + Sqrt[1 + x^2]]), x]","F",-1
1925,1,124,134,0.1802475,"\int \frac{\left(-2+x^3\right) \left(1+x^3\right)^{2/3}}{x^6 \left(-1+2 x^3\right)} \, dx","Integrate[((-2 + x^3)*(1 + x^3)^(2/3))/(x^6*(-1 + 2*x^3)),x]","3 \sqrt[6]{3} \tan ^{-1}\left(\frac{2 x}{\sqrt[6]{3} \sqrt[3]{x^3+1}}+\frac{1}{\sqrt{3}}\right)-\frac{\left(x^3+1\right)^{2/3} \left(19 x^3+4\right)}{10 x^5}+\frac{1}{2} 3^{2/3} \left(\log \left(\frac{\sqrt[3]{3} x}{\sqrt[3]{x^3+1}}+\frac{3^{2/3} x^2}{\left(x^3+1\right)^{2/3}}+1\right)-2 \log \left(1-\frac{\sqrt[3]{3} x}{\sqrt[3]{x^3+1}}\right)\right)","-3^{2/3} \log \left(3^{2/3} \sqrt[3]{x^3+1}-3 x\right)+3 \sqrt[6]{3} \tan ^{-1}\left(\frac{3^{5/6} x}{2 \sqrt[3]{x^3+1}+\sqrt[3]{3} x}\right)+\frac{\left(x^3+1\right)^{2/3} \left(-19 x^3-4\right)}{10 x^5}+\frac{1}{2} 3^{2/3} \log \left(3^{2/3} \sqrt[3]{x^3+1} x+\sqrt[3]{3} \left(x^3+1\right)^{2/3}+3 x^2\right)",1,"-1/10*((1 + x^3)^(2/3)*(4 + 19*x^3))/x^5 + 3*3^(1/6)*ArcTan[1/Sqrt[3] + (2*x)/(3^(1/6)*(1 + x^3)^(1/3))] + (3^(2/3)*(-2*Log[1 - (3^(1/3)*x)/(1 + x^3)^(1/3)] + Log[1 + (3^(2/3)*x^2)/(1 + x^3)^(2/3) + (3^(1/3)*x)/(1 + x^3)^(1/3)]))/2","A",1
1926,1,233,134,0.5653519,"\int \frac{1}{x^3 \left(b+a x^3\right) \sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Integrate[1/(x^3*(b + a*x^3)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","\frac{-27 a^9 x^3-9 a^6 b^2 x^2+3 a^3 b^4 x-40 a b^5 x^3 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a^3 x-\sqrt[3]{a} b^{5/3} x}{x a^3+b^2}\right)-40 a b^5 x^3 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{2 x a^3+\left(1-i \sqrt{3}\right) b^{5/3} x \sqrt[3]{a}}{2 \left(x a^3+b^2\right)}\right)-40 a b^5 x^3 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{2 x a^3+\left(1+i \sqrt{3}\right) b^{5/3} x \sqrt[3]{a}}{2 \left(x a^3+b^2\right)}\right)-15 b^6}{40 b^7 x^2 \sqrt[3]{x^2 \left(a^3 x+b^2\right)}}","\frac{a \text{RootSum}\left[-\text{$\#$1}^9+3 \text{$\#$1}^6 a^3-3 \text{$\#$1}^3 a^6+a^9-a b^5\&,\frac{\log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{3 b^2}-\frac{3 \left(9 a^6 x^2-6 a^3 b^2 x+5 b^4\right) \left(a^3 x^3+b^2 x^2\right)^{2/3}}{40 b^7 x^4}",1,"(-15*b^6 + 3*a^3*b^4*x - 9*a^6*b^2*x^2 - 27*a^9*x^3 - 40*a*b^5*x^3*Hypergeometric2F1[1/3, 1, 4/3, (a^3*x - a^(1/3)*b^(5/3)*x)/(b^2 + a^3*x)] - 40*a*b^5*x^3*Hypergeometric2F1[1/3, 1, 4/3, (2*a^3*x + (1 - I*Sqrt[3])*a^(1/3)*b^(5/3)*x)/(2*(b^2 + a^3*x))] - 40*a*b^5*x^3*Hypergeometric2F1[1/3, 1, 4/3, (2*a^3*x + (1 + I*Sqrt[3])*a^(1/3)*b^(5/3)*x)/(2*(b^2 + a^3*x))])/(40*b^7*x^2*(x^2*(b^2 + a^3*x))^(1/3))","C",1
1927,1,233,134,0.2627068,"\int \frac{1}{x^3 \left(b+a x^3\right) \sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Integrate[1/(x^3*(b + a*x^3)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","\frac{-27 a^9 x^3-9 a^6 b^2 x^2+3 a^3 b^4 x-40 a b^5 x^3 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a^3 x-\sqrt[3]{a} b^{5/3} x}{x a^3+b^2}\right)-40 a b^5 x^3 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{2 x a^3+\left(1-i \sqrt{3}\right) b^{5/3} x \sqrt[3]{a}}{2 \left(x a^3+b^2\right)}\right)-40 a b^5 x^3 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{2 x a^3+\left(1+i \sqrt{3}\right) b^{5/3} x \sqrt[3]{a}}{2 \left(x a^3+b^2\right)}\right)-15 b^6}{40 b^7 x^2 \sqrt[3]{x^2 \left(a^3 x+b^2\right)}}","\frac{a \text{RootSum}\left[-\text{$\#$1}^9+3 \text{$\#$1}^6 a^3-3 \text{$\#$1}^3 a^6+a^9-a b^5\&,\frac{\log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{3 b^2}-\frac{3 \left(9 a^6 x^2-6 a^3 b^2 x+5 b^4\right) \left(a^3 x^3+b^2 x^2\right)^{2/3}}{40 b^7 x^4}",1,"(-15*b^6 + 3*a^3*b^4*x - 9*a^6*b^2*x^2 - 27*a^9*x^3 - 40*a*b^5*x^3*Hypergeometric2F1[1/3, 1, 4/3, (a^3*x - a^(1/3)*b^(5/3)*x)/(b^2 + a^3*x)] - 40*a*b^5*x^3*Hypergeometric2F1[1/3, 1, 4/3, (2*a^3*x + (1 - I*Sqrt[3])*a^(1/3)*b^(5/3)*x)/(2*(b^2 + a^3*x))] - 40*a*b^5*x^3*Hypergeometric2F1[1/3, 1, 4/3, (2*a^3*x + (1 + I*Sqrt[3])*a^(1/3)*b^(5/3)*x)/(2*(b^2 + a^3*x))])/(40*b^7*x^2*(x^2*(b^2 + a^3*x))^(1/3))","C",1
1928,1,118,134,0.2011606,"\int \frac{\left(-1+x+x^4\right) \sqrt[4]{-x^3+x^4}}{1+x} \, dx","Integrate[((-1 + x + x^4)*(-x^3 + x^4)^(1/4))/(1 + x),x]","\frac{x^3 \left(148035 x \left(1-x^2\right)^{3/4} F_1\left(\frac{7}{4};\frac{3}{4},1;\frac{11}{4};x,-x\right)-228025 (1-x)^{3/4} \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};\frac{2 x}{x+1}\right)+7 (x+1)^{3/4} \left(6144 x^5-14208 x^4+18464 x^3-11460 x^2-31515 x+32575\right)\right)}{215040 \left((x-1) x^3\right)^{3/4} (x+1)^{3/4}}","-\frac{9869 \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^3}}\right)}{4096}+2 \sqrt[4]{2} \tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-x^3}}\right)+\frac{9869 \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^3}}\right)}{4096}-2 \sqrt[4]{2} \tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-x^3}}\right)+\frac{\sqrt[4]{x^4-x^3} \left(6144 x^4-8064 x^3+10400 x^2-1060 x-32575\right)}{30720}",1,"(x^3*(7*(1 + x)^(3/4)*(32575 - 31515*x - 11460*x^2 + 18464*x^3 - 14208*x^4 + 6144*x^5) + 148035*x*(1 - x^2)^(3/4)*AppellF1[7/4, 3/4, 1, 11/4, x, -x] - 228025*(1 - x)^(3/4)*Hypergeometric2F1[3/4, 3/4, 7/4, (2*x)/(1 + x)]))/(215040*((-1 + x)*x^3)^(3/4)*(1 + x)^(3/4))","C",0
1929,0,0,134,0.2969089,"\int \frac{\left(-3+x^4\right) \left(1+x^4\right)^{2/3}}{x^3 \left(2+x^3+2 x^4\right)} \, dx","Integrate[((-3 + x^4)*(1 + x^4)^(2/3))/(x^3*(2 + x^3 + 2*x^4)),x]","\int \frac{\left(-3+x^4\right) \left(1+x^4\right)^{2/3}}{x^3 \left(2+x^3+2 x^4\right)} \, dx","\frac{\log \left(\sqrt[3]{2} \sqrt[3]{x^4+1}+x\right)}{2\ 2^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{2} \sqrt[3]{x^4+1}-x}\right)}{2\ 2^{2/3}}+\frac{3 \left(x^4+1\right)^{2/3}}{4 x^2}-\frac{\log \left(-\sqrt[3]{2} \sqrt[3]{x^4+1} x+2^{2/3} \left(x^4+1\right)^{2/3}+x^2\right)}{4\ 2^{2/3}}",1,"Integrate[((-3 + x^4)*(1 + x^4)^(2/3))/(x^3*(2 + x^3 + 2*x^4)), x]","F",-1
1930,1,151,134,0.2608942,"\int \frac{\left(-4 b+a x^4\right) \left(b+a x^4\right)^{3/4}}{x^8 \left(4 b+a x^4\right)} \, dx","Integrate[((-4*b + a*x^4)*(b + a*x^4)^(3/4))/(x^8*(4*b + a*x^4)),x]","\frac{3^{3/4} a^{7/4} \left(-\log \left(2-\frac{\sqrt{2} \sqrt[4]{3} \sqrt[4]{a} x}{\sqrt[4]{a+b x^4}}\right)+\log \left(\frac{\sqrt{2} \sqrt[4]{3} \sqrt[4]{a} x}{\sqrt[4]{a+b x^4}}+2\right)+2 \tan ^{-1}\left(\frac{\sqrt[4]{3} \sqrt[4]{a} x}{\sqrt{2} \sqrt[4]{a+b x^4}}\right)\right)}{16 \sqrt{2} b}+\left(\frac{1}{7 x^7}-\frac{a}{42 b x^3}\right) \left(a x^4+b\right)^{3/4}","\frac{3^{3/4} a^{7/4} \tan ^{-1}\left(\frac{\sqrt[4]{3} \sqrt[4]{a} x}{\sqrt{2} \sqrt[4]{a x^4+b}}\right)}{8 \sqrt{2} b}+\frac{3^{3/4} a^{7/4} \tanh ^{-1}\left(\frac{\sqrt[4]{3} \sqrt[4]{a} x}{\sqrt{2} \sqrt[4]{a x^4+b}}\right)}{8 \sqrt{2} b}+\frac{\left(6 b-a x^4\right) \left(a x^4+b\right)^{3/4}}{42 b x^7}",1,"(1/(7*x^7) - a/(42*b*x^3))*(b + a*x^4)^(3/4) + (3^(3/4)*a^(7/4)*(2*ArcTan[(3^(1/4)*a^(1/4)*x)/(Sqrt[2]*(a + b*x^4)^(1/4))] - Log[2 - (Sqrt[2]*3^(1/4)*a^(1/4)*x)/(a + b*x^4)^(1/4)] + Log[2 + (Sqrt[2]*3^(1/4)*a^(1/4)*x)/(a + b*x^4)^(1/4)]))/(16*Sqrt[2]*b)","A",0
1931,1,151,134,0.1617417,"\int \frac{\left(b+a x^4\right)^{3/4} \left(2 b+a x^4\right)}{x^8 \left(4 b+a x^4\right)} \, dx","Integrate[((b + a*x^4)^(3/4)*(2*b + a*x^4))/(x^8*(4*b + a*x^4)),x]","\frac{3^{3/4} a^{7/4} \left(-\log \left(2-\frac{\sqrt{2} \sqrt[4]{3} \sqrt[4]{a} x}{\sqrt[4]{a+b x^4}}\right)+\log \left(\frac{\sqrt{2} \sqrt[4]{3} \sqrt[4]{a} x}{\sqrt[4]{a+b x^4}}+2\right)+2 \tan ^{-1}\left(\frac{\sqrt[4]{3} \sqrt[4]{a} x}{\sqrt{2} \sqrt[4]{a+b x^4}}\right)\right)}{64 \sqrt{2} b}+\left(-\frac{19 a}{168 b x^3}-\frac{1}{14 x^7}\right) \left(a x^4+b\right)^{3/4}","\frac{3^{3/4} a^{7/4} \tan ^{-1}\left(\frac{\sqrt[4]{3} \sqrt[4]{a} x}{\sqrt{2} \sqrt[4]{a x^4+b}}\right)}{32 \sqrt{2} b}+\frac{3^{3/4} a^{7/4} \tanh ^{-1}\left(\frac{\sqrt[4]{3} \sqrt[4]{a} x}{\sqrt{2} \sqrt[4]{a x^4+b}}\right)}{32 \sqrt{2} b}+\frac{\left(-19 a x^4-12 b\right) \left(a x^4+b\right)^{3/4}}{168 b x^7}",1,"(-1/14*1/x^7 - (19*a)/(168*b*x^3))*(b + a*x^4)^(3/4) + (3^(3/4)*a^(7/4)*(2*ArcTan[(3^(1/4)*a^(1/4)*x)/(Sqrt[2]*(a + b*x^4)^(1/4))] - Log[2 - (Sqrt[2]*3^(1/4)*a^(1/4)*x)/(a + b*x^4)^(1/4)] + Log[2 + (Sqrt[2]*3^(1/4)*a^(1/4)*x)/(a + b*x^4)^(1/4)]))/(64*Sqrt[2]*b)","A",0
1932,1,49,134,0.0235622,"\int \frac{x^4 \sqrt[4]{b x^3+a x^4}}{b+a x} \, dx","Integrate[(x^4*(b*x^3 + a*x^4)^(1/4))/(b + a*x),x]","\frac{4 x^8 \left(\frac{a x}{b}+1\right)^{3/4} \, _2F_1\left(\frac{3}{4},\frac{23}{4};\frac{27}{4};-\frac{a x}{b}\right)}{23 \left(x^3 (a x+b)\right)^{3/4}}","\frac{4389 b^5 \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)}{4096 a^{23/4}}-\frac{4389 b^5 \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)}{4096 a^{23/4}}+\frac{\sqrt[4]{a x^4+b x^3} \left(2048 a^4 x^4-2432 a^3 b x^3+3040 a^2 b^2 x^2-4180 a b^3 x+7315 b^4\right)}{10240 a^5}",1,"(4*x^8*(1 + (a*x)/b)^(3/4)*Hypergeometric2F1[3/4, 23/4, 27/4, -((a*x)/b)])/(23*(x^3*(b + a*x))^(3/4))","C",1
1933,1,95,134,0.2168061,"\int \frac{b+a x^2}{\left(-b+a x^2\right) \sqrt{b^2+a^2 x^4}} \, dx","Integrate[(b + a*x^2)/((-b + a*x^2)*Sqrt[b^2 + a^2*x^4]),x]","-\frac{i \sqrt{\frac{a^2 x^4}{b^2}+1} \left(F\left(\left.i \sinh ^{-1}\left(\sqrt{\frac{i a}{b}} x\right)\right|-1\right)-2 \Pi \left(i;\left.i \sinh ^{-1}\left(\sqrt{\frac{i a}{b}} x\right)\right|-1\right)\right)}{\sqrt{\frac{i a}{b}} \sqrt{a^2 x^4+b^2}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{6-4 \sqrt{2}} \sqrt{a} \sqrt{b} x}{\sqrt{a^2 x^4+b^2}+a x^2+b}\right)}{\sqrt{2} \sqrt{a} \sqrt{b}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{6+4 \sqrt{2}} \sqrt{a} \sqrt{b} x}{\sqrt{a^2 x^4+b^2}+a x^2+b}\right)}{\sqrt{2} \sqrt{a} \sqrt{b}}",1,"((-I)*Sqrt[1 + (a^2*x^4)/b^2]*(EllipticF[I*ArcSinh[Sqrt[(I*a)/b]*x], -1] - 2*EllipticPi[I, I*ArcSinh[Sqrt[(I*a)/b]*x], -1]))/(Sqrt[(I*a)/b]*Sqrt[b^2 + a^2*x^4])","C",1
1934,0,0,134,0.1383292,"\int \frac{\left(1+x^2\right) \sqrt{1+\sqrt{1+x^2}}}{-1+x^2} \, dx","Integrate[((1 + x^2)*Sqrt[1 + Sqrt[1 + x^2]])/(-1 + x^2),x]","\int \frac{\left(1+x^2\right) \sqrt{1+\sqrt{1+x^2}}}{-1+x^2} \, dx","\frac{2 \sqrt{x^2+1} x}{3 \sqrt{\sqrt{x^2+1}+1}}+\frac{4 x}{3 \sqrt{\sqrt{x^2+1}+1}}+2 \sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{x}{\sqrt{1+\sqrt{2}} \sqrt{\sqrt{x^2+1}+1}}\right)-2 \sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{x}{\sqrt{\sqrt{2}-1} \sqrt{\sqrt{x^2+1}+1}}\right)",1,"Integrate[((1 + x^2)*Sqrt[1 + Sqrt[1 + x^2]])/(-1 + x^2), x]","F",-1
1935,1,118,135,0.0731146,"\int \frac{1}{\sqrt[3]{-b+a x^3}} \, dx","Integrate[(-b + a*x^3)^(-1/3),x]","\frac{\log \left(\frac{a^{2/3} x^2}{\left(a x^3-b\right)^{2/3}}+\frac{\sqrt[3]{a} x}{\sqrt[3]{a x^3-b}}+1\right)-2 \log \left(1-\frac{\sqrt[3]{a} x}{\sqrt[3]{a x^3-b}}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a} x}{\sqrt[3]{a x^3-b}}+1}{\sqrt{3}}\right)}{6 \sqrt[3]{a}}","\frac{\log \left(a^{2/3} x^2+\sqrt[3]{a} x \sqrt[3]{a x^3-b}+\left(a x^3-b\right)^{2/3}\right)}{6 \sqrt[3]{a}}-\frac{\log \left(\sqrt[3]{a x^3-b}-\sqrt[3]{a} x\right)}{3 \sqrt[3]{a}}+\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{a} x}{2 \sqrt[3]{a x^3-b}+\sqrt[3]{a} x}\right)}{\sqrt{3} \sqrt[3]{a}}",1,"(2*Sqrt[3]*ArcTan[(1 + (2*a^(1/3)*x)/(-b + a*x^3)^(1/3))/Sqrt[3]] - 2*Log[1 - (a^(1/3)*x)/(-b + a*x^3)^(1/3)] + Log[1 + (a^(2/3)*x^2)/(-b + a*x^3)^(2/3) + (a^(1/3)*x)/(-b + a*x^3)^(1/3)])/(6*a^(1/3))","A",1
1936,0,0,135,1.3907775,"\int \frac{\left(a^2-2 a x+x^2\right) \left(-a b-a c+3 b c+2 (a-b-c) x+x^2\right)}{((-a+x) (-b+x) (-c+x))^{3/4} \left(-b c-a^3 d+\left(b+c+3 a^2 d\right) x-(1+3 a d) x^2+d x^3\right)} \, dx","Integrate[((a^2 - 2*a*x + x^2)*(-(a*b) - a*c + 3*b*c + 2*(a - b - c)*x + x^2))/(((-a + x)*(-b + x)*(-c + x))^(3/4)*(-(b*c) - a^3*d + (b + c + 3*a^2*d)*x - (1 + 3*a*d)*x^2 + d*x^3)),x]","\int \frac{\left(a^2-2 a x+x^2\right) \left(-a b-a c+3 b c+2 (a-b-c) x+x^2\right)}{((-a+x) (-b+x) (-c+x))^{3/4} \left(-b c-a^3 d+\left(b+c+3 a^2 d\right) x-(1+3 a d) x^2+d x^3\right)} \, dx","\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \left(x^2 (-a-b-c)+x (a b+a c+b c)-a b c+x^3\right)^{3/4}}{(b-x) (x-c)}\right)}{d^{3/4}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \left(x^2 (-a-b-c)+x (a b+a c+b c)-a b c+x^3\right)^{3/4}}{(b-x) (x-c)}\right)}{d^{3/4}}",1,"Integrate[((a^2 - 2*a*x + x^2)*(-(a*b) - a*c + 3*b*c + 2*(a - b - c)*x + x^2))/(((-a + x)*(-b + x)*(-c + x))^(3/4)*(-(b*c) - a^3*d + (b + c + 3*a^2*d)*x - (1 + 3*a*d)*x^2 + d*x^3)), x]","F",-1
1937,0,0,135,0.6494764,"\int \frac{\left(-4+x^5\right) \sqrt[4]{1-2 x^4+x^5}}{x^2 \left(1+x^5\right)} \, dx","Integrate[((-4 + x^5)*(1 - 2*x^4 + x^5)^(1/4))/(x^2*(1 + x^5)),x]","\int \frac{\left(-4+x^5\right) \sqrt[4]{1-2 x^4+x^5}}{x^2 \left(1+x^5\right)} \, dx","\frac{4 \sqrt[4]{x^5-2 x^4+1}}{x}-2^{3/4} \tan ^{-1}\left(\frac{2^{3/4} x \sqrt[4]{x^5-2 x^4+1}}{\sqrt{2} x^2-\sqrt{x^5-2 x^4+1}}\right)-2^{3/4} \tanh ^{-1}\left(\frac{2 \sqrt[4]{2} x \sqrt[4]{x^5-2 x^4+1}}{2 x^2+\sqrt{2} \sqrt{x^5-2 x^4+1}}\right)",1,"Integrate[((-4 + x^5)*(1 - 2*x^4 + x^5)^(1/4))/(x^2*(1 + x^5)), x]","F",-1
1938,1,149,135,0.1942414,"\int \frac{b+a x^6}{x^6 \sqrt[3]{x+x^3}} \, dx","Integrate[(b + a*x^6)/(x^6*(x + x^3)^(1/3)),x]","\frac{3 \sqrt[3]{x} \sqrt[3]{x^2+1} \left(\frac{1}{12} a \left(-2 \log \left(1-\frac{x^{2/3}}{\sqrt[3]{x^2+1}}\right)+\log \left(\frac{x^{4/3}}{\left(x^2+1\right)^{2/3}}+\frac{x^{2/3}}{\sqrt[3]{x^2+1}}+1\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 x^{2/3}}{\sqrt[3]{x^2+1}}+1}{\sqrt{3}}\right)\right)-\frac{b \left(x^2+1\right)^{2/3} \left(9 x^4-6 x^2+5\right)}{80 x^{16/3}}\right)}{\sqrt[3]{x^3+x}}","\frac{1}{4} \left(a-i \sqrt{3} a\right) \log \left(-2 i \sqrt[3]{x^3+x}+\sqrt{3} x-i x\right)+\frac{1}{4} \left(a+i \sqrt{3} a\right) \log \left(2 i \sqrt[3]{x^3+x}+\sqrt{3} x+i x\right)-\frac{1}{2} a \log \left(\sqrt[3]{x^3+x}-x\right)-\frac{3 b \left(x^3+x\right)^{2/3} \left(9 x^4-6 x^2+5\right)}{80 x^6}",1,"(3*x^(1/3)*(1 + x^2)^(1/3)*(-1/80*(b*(1 + x^2)^(2/3)*(5 - 6*x^2 + 9*x^4))/x^(16/3) + (a*(2*Sqrt[3]*ArcTan[(1 + (2*x^(2/3))/(1 + x^2)^(1/3))/Sqrt[3]] - 2*Log[1 - x^(2/3)/(1 + x^2)^(1/3)] + Log[1 + x^(4/3)/(1 + x^2)^(2/3) + x^(2/3)/(1 + x^2)^(1/3)]))/12))/(x + x^3)^(1/3)","A",1
1939,1,111,135,0.1255727,"\int \frac{b^2+a^2 x^2}{\sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Integrate[(b^2 + a^2*x^2)/Sqrt[a*x + Sqrt[b^2 + a^2*x^2]],x]","\frac{105 b^2 \left(\sqrt{a^2 x^2+b^2}+a x\right)^4+7 \left(\sqrt{a^2 x^2+b^2}+a x\right)^6-35 b^4 \left(\sqrt{a^2 x^2+b^2}+a x\right)^2-5 b^6}{140 a \left(\sqrt{a^2 x^2+b^2}+a x\right)^{7/2}}","\frac{2 \sqrt{a^2 x^2+b^2} \left(4 a^4 x^5+19 a^2 b^2 x^3+7 b^4 x\right)}{5 \left(\sqrt{a^2 x^2+b^2}+a x\right)^{7/2}}+\frac{2 \left(28 a^6 x^6+147 a^4 b^2 x^4+112 a^2 b^4 x^2+9 b^6\right)}{35 a \left(\sqrt{a^2 x^2+b^2}+a x\right)^{7/2}}",1,"(-5*b^6 - 35*b^4*(a*x + Sqrt[b^2 + a^2*x^2])^2 + 105*b^2*(a*x + Sqrt[b^2 + a^2*x^2])^4 + 7*(a*x + Sqrt[b^2 + a^2*x^2])^6)/(140*a*(a*x + Sqrt[b^2 + a^2*x^2])^(7/2))","A",1
1940,1,67,136,0.0588835,"\int \frac{x^2}{\left(b+a x^2\right)^{3/4} \left(2 b+a x^2\right)} \, dx","Integrate[x^2/((b + a*x^2)^(3/4)*(2*b + a*x^2)),x]","\frac{x^3 \left(\frac{a x^2+b}{b}\right)^{3/4} F_1\left(\frac{3}{2};\frac{3}{4},1;\frac{5}{2};-\frac{a x^2}{b},-\frac{a x^2}{2 b}\right)}{6 b \left(a x^2+b\right)^{3/4}}","-\frac{\tan ^{-1}\left(\frac{\frac{\sqrt[4]{b} \sqrt{a x^2+b}}{\sqrt{a}}-\frac{\sqrt{a} x^2}{2 \sqrt[4]{b}}}{x \sqrt[4]{a x^2+b}}\right)}{2 a^{3/2} \sqrt[4]{b}}-\frac{\tanh ^{-1}\left(\frac{2 \sqrt{a} \sqrt[4]{b} x \sqrt[4]{a x^2+b}}{2 \sqrt{b} \sqrt{a x^2+b}+a x^2}\right)}{2 a^{3/2} \sqrt[4]{b}}",1,"(x^3*((b + a*x^2)/b)^(3/4)*AppellF1[3/2, 3/4, 1, 5/2, -((a*x^2)/b), -1/2*(a*x^2)/b])/(6*b*(b + a*x^2)^(3/4))","C",0
1941,1,44,136,0.0124386,"\int \frac{x}{\left(-b+a x^3\right)^{2/3}} \, dx","Integrate[x/(-b + a*x^3)^(2/3),x]","\frac{x^2 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{a x^3}{a x^3-b}\right)}{2 \left(a x^3-b\right)^{2/3}}","-\frac{\log \left(\sqrt[3]{a x^3-b}-\sqrt[3]{a} x\right)}{3 a^{2/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{a} x}{2 \sqrt[3]{a x^3-b}+\sqrt[3]{a} x}\right)}{\sqrt{3} a^{2/3}}+\frac{\log \left(a^{2/3} x^2+\sqrt[3]{a} x \sqrt[3]{a x^3-b}+\left(a x^3-b\right)^{2/3}\right)}{6 a^{2/3}}",1,"(x^2*Hypergeometric2F1[2/3, 1, 5/3, (a*x^3)/(-b + a*x^3)])/(2*(-b + a*x^3)^(2/3))","C",1
1942,1,57,136,0.0274598,"\int \frac{x \sqrt[3]{x^2+x^4}}{1+2 x^2} \, dx","Integrate[(x*(x^2 + x^4)^(1/3))/(1 + 2*x^2),x]","\frac{3 \sqrt[3]{x^4+x^2} \left(\sqrt[3]{x^2+1}-F_1\left(\frac{1}{3};\frac{2}{3},1;\frac{4}{3};-x^2,-2 x^2\right)\right)}{8 \sqrt[3]{x^2+1}}","\frac{3}{8} \sqrt[3]{x^4+x^2}-\frac{\log \left(2^{2/3} \sqrt[3]{x^4+x^2}+1\right)}{8\ 2^{2/3}}+\frac{\log \left(-2 \sqrt[3]{2} \left(x^4+x^2\right)^{2/3}+2^{2/3} \sqrt[3]{x^4+x^2}-1\right)}{16\ 2^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2\ 2^{2/3} \sqrt[3]{x^4+x^2}}{\sqrt{3}}\right)}{8\ 2^{2/3}}",1,"(3*(x^2 + x^4)^(1/3)*((1 + x^2)^(1/3) - AppellF1[1/3, 2/3, 1, 4/3, -x^2, -2*x^2]))/(8*(1 + x^2)^(1/3))","C",0
1943,1,123,136,4.885402,"\int \frac{b+a x^3}{x^6 \left(-b+a x^3\right) \sqrt[4]{b x+a x^4}} \, dx","Integrate[(b + a*x^3)/(x^6*(-b + a*x^3)*(b*x + a*x^4)^(1/4)),x]","-\frac{\Gamma \left(-\frac{3}{4}\right) \left(x \left(a x^3+b\right)\right)^{7/4} \left(\left(4 a^2 x^6-7 a b x^3+3 b^2\right) \, _2F_1\left(1,1;\frac{1}{4};-\frac{2 a x^3}{b-a x^3}\right)+32 a x^3 \left(a x^3+b\right) \, _2F_1\left(2,2;\frac{5}{4};-\frac{2 a x^3}{b-a x^3}\right)\right)}{21 b^2 x^7 \Gamma \left(\frac{1}{4}\right) \left(b-a x^3\right)^2}","-\frac{2\ 2^{3/4} a^{7/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} \left(a x^4+b x\right)^{3/4}}{a x^3+b}\right)}{3 b^2}-\frac{2\ 2^{3/4} a^{7/4} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} \left(a x^4+b x\right)^{3/4}}{a x^3+b}\right)}{3 b^2}+\frac{4 \left(10 a x^3+3 b\right) \left(a x^4+b x\right)^{3/4}}{63 b^2 x^6}",1,"-1/21*((x*(b + a*x^3))^(7/4)*Gamma[-3/4]*((3*b^2 - 7*a*b*x^3 + 4*a^2*x^6)*Hypergeometric2F1[1, 1, 1/4, (-2*a*x^3)/(b - a*x^3)] + 32*a*x^3*(b + a*x^3)*Hypergeometric2F1[2, 2, 5/4, (-2*a*x^3)/(b - a*x^3)]))/(b^2*x^7*(b - a*x^3)^2*Gamma[1/4])","C",0
1944,0,0,136,0.8636075,"\int \frac{\left(-1+x^4\right) \sqrt[4]{x^2+x^6}}{1+x^4+x^8} \, dx","Integrate[((-1 + x^4)*(x^2 + x^6)^(1/4))/(1 + x^4 + x^8),x]","\int \frac{\left(-1+x^4\right) \sqrt[4]{x^2+x^6}}{1+x^4+x^8} \, dx","\frac{1}{2} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^6+x^2}}\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{x^6+x^2}}{\sqrt{x^6+x^2}-x^2}\right)}{2 \sqrt{2}}-\frac{1}{2} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^6+x^2}}\right)+\frac{\tanh ^{-1}\left(\frac{\frac{x^2}{\sqrt{2}}+\frac{\sqrt{x^6+x^2}}{\sqrt{2}}}{x \sqrt[4]{x^6+x^2}}\right)}{2 \sqrt{2}}",1,"Integrate[((-1 + x^4)*(x^2 + x^6)^(1/4))/(1 + x^4 + x^8), x]","F",-1
1945,0,0,136,0.0995671,"\int \frac{\left(-1+x^4\right) \sqrt[4]{x^2+x^6}}{1+x^4+x^8} \, dx","Integrate[((-1 + x^4)*(x^2 + x^6)^(1/4))/(1 + x^4 + x^8),x]","\int \frac{\left(-1+x^4\right) \sqrt[4]{x^2+x^6}}{1+x^4+x^8} \, dx","\frac{1}{2} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^6+x^2}}\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{x^6+x^2}}{\sqrt{x^6+x^2}-x^2}\right)}{2 \sqrt{2}}-\frac{1}{2} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^6+x^2}}\right)+\frac{\tanh ^{-1}\left(\frac{\frac{x^2}{\sqrt{2}}+\frac{\sqrt{x^6+x^2}}{\sqrt{2}}}{x \sqrt[4]{x^6+x^2}}\right)}{2 \sqrt{2}}",1,"Integrate[((-1 + x^4)*(x^2 + x^6)^(1/4))/(1 + x^4 + x^8), x]","F",-1
1946,1,132,136,0.2083863,"\int \frac{x \sqrt{a x+\sqrt{-b+a x}}}{\sqrt{-b+a x}} \, dx","Integrate[(x*Sqrt[a*x + Sqrt[-b + a*x]])/Sqrt[-b + a*x],x]","\frac{3 \left(48 b^2+8 b-5\right) \tanh ^{-1}\left(\frac{2 \sqrt{a x-b}+1}{2 \sqrt{\sqrt{a x-b}+a x}}\right)+2 \sqrt{\sqrt{a x-b}+a x} \left(12 b \left(6 \sqrt{a x-b}-1\right)+8 a \left(6 x \sqrt{a x-b}+x\right)-10 \sqrt{a x-b}+15\right)}{192 a^2}","\frac{\left(-48 b^2-8 b+5\right) \log \left(2 \sqrt{a x-b}-2 \sqrt{\sqrt{a x-b}+a x}+1\right)}{64 a^2}+\frac{\sqrt{\sqrt{a x-b}+a x} (8 a x-12 b+15)}{96 a^2}+\frac{\sqrt{a x-b} (24 a x+36 b-5) \sqrt{\sqrt{a x-b}+a x}}{48 a^2}",1,"(2*Sqrt[a*x + Sqrt[-b + a*x]]*(15 - 10*Sqrt[-b + a*x] + 12*b*(-1 + 6*Sqrt[-b + a*x]) + 8*a*(x + 6*x*Sqrt[-b + a*x])) + 3*(-5 + 8*b + 48*b^2)*ArcTanh[(1 + 2*Sqrt[-b + a*x])/(2*Sqrt[a*x + Sqrt[-b + a*x]])])/(192*a^2)","A",1
1947,1,132,136,0.1654211,"\int \frac{(-1+a x) \sqrt{a x+\sqrt{-b+a x}}}{\sqrt{-b+a x}} \, dx","Integrate[((-1 + a*x)*Sqrt[a*x + Sqrt[-b + a*x]])/Sqrt[-b + a*x],x]","\frac{3 \left(48 b^2-56 b+11\right) \tanh ^{-1}\left(\frac{2 \sqrt{a x-b}+1}{2 \sqrt{\sqrt{a x-b}+a x}}\right)+2 \sqrt{\sqrt{a x-b}+a x} \left(12 b \left(6 \sqrt{a x-b}-1\right)+8 a \left(6 x \sqrt{a x-b}+x\right)-106 \sqrt{a x-b}-33\right)}{192 a}","\frac{\left(-48 b^2+56 b-11\right) \log \left(2 \sqrt{a x-b}-2 \sqrt{\sqrt{a x-b}+a x}+1\right)}{64 a}+\frac{\sqrt{\sqrt{a x-b}+a x} (8 a x-12 b-33)}{96 a}+\frac{\sqrt{a x-b} (24 a x+36 b-53) \sqrt{\sqrt{a x-b}+a x}}{48 a}",1,"(2*Sqrt[a*x + Sqrt[-b + a*x]]*(-33 - 106*Sqrt[-b + a*x] + 12*b*(-1 + 6*Sqrt[-b + a*x]) + 8*a*(x + 6*x*Sqrt[-b + a*x])) + 3*(11 - 56*b + 48*b^2)*ArcTanh[(1 + 2*Sqrt[-b + a*x])/(2*Sqrt[a*x + Sqrt[-b + a*x]])])/(192*a)","A",1
1948,1,138,136,0.2998174,"\int \frac{-1+x^4}{\left(1+x^4\right) \sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[(-1 + x^4)/((1 + x^4)*Sqrt[x + Sqrt[1 + x^2]]),x]","2 \text{RootSum}\left[\text{$\#$1}^{16}-4 \text{$\#$1}^{12}+22 \text{$\#$1}^8-4 \text{$\#$1}^4+1\&,\frac{\text{$\#$1}^7 \log \left(\frac{1}{\sqrt{\sqrt{x^2+1}+x}}-\text{$\#$1}\right)+\text{$\#$1}^3 \log \left(\frac{1}{\sqrt{\sqrt{x^2+1}+x}}-\text{$\#$1}\right)}{\text{$\#$1}^{12}-3 \text{$\#$1}^8+11 \text{$\#$1}^4-1}\&\right]+\sqrt{\sqrt{x^2+1}+x}-\frac{1}{3 \left(\sqrt{x^2+1}+x\right)^{3/2}}","-2 \text{RootSum}\left[\text{$\#$1}^{16}-4 \text{$\#$1}^{12}+22 \text{$\#$1}^8-4 \text{$\#$1}^4+1\&,\frac{\text{$\#$1}^5 \log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)+\text{$\#$1} \log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)}{\text{$\#$1}^{12}-3 \text{$\#$1}^8+11 \text{$\#$1}^4-1}\&\right]+\sqrt{\sqrt{x^2+1}+x}-\frac{1}{3 \left(\sqrt{x^2+1}+x\right)^{3/2}}",1,"-1/3*1/(x + Sqrt[1 + x^2])^(3/2) + Sqrt[x + Sqrt[1 + x^2]] + 2*RootSum[1 - 4*#1^4 + 22*#1^8 - 4*#1^12 + #1^16 & , (Log[1/Sqrt[x + Sqrt[1 + x^2]] - #1]*#1^3 + Log[1/Sqrt[x + Sqrt[1 + x^2]] - #1]*#1^7)/(-1 + 11*#1^4 - 3*#1^8 + #1^12) & ]","A",1
1949,1,138,136,0.1142073,"\int \frac{-1+x^4}{\left(1+x^4\right) \sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[(-1 + x^4)/((1 + x^4)*Sqrt[x + Sqrt[1 + x^2]]),x]","2 \text{RootSum}\left[\text{$\#$1}^{16}-4 \text{$\#$1}^{12}+22 \text{$\#$1}^8-4 \text{$\#$1}^4+1\&,\frac{\text{$\#$1}^7 \log \left(\frac{1}{\sqrt{\sqrt{x^2+1}+x}}-\text{$\#$1}\right)+\text{$\#$1}^3 \log \left(\frac{1}{\sqrt{\sqrt{x^2+1}+x}}-\text{$\#$1}\right)}{\text{$\#$1}^{12}-3 \text{$\#$1}^8+11 \text{$\#$1}^4-1}\&\right]+\sqrt{\sqrt{x^2+1}+x}-\frac{1}{3 \left(\sqrt{x^2+1}+x\right)^{3/2}}","-2 \text{RootSum}\left[\text{$\#$1}^{16}-4 \text{$\#$1}^{12}+22 \text{$\#$1}^8-4 \text{$\#$1}^4+1\&,\frac{\text{$\#$1}^5 \log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)+\text{$\#$1} \log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)}{\text{$\#$1}^{12}-3 \text{$\#$1}^8+11 \text{$\#$1}^4-1}\&\right]+\sqrt{\sqrt{x^2+1}+x}-\frac{1}{3 \left(\sqrt{x^2+1}+x\right)^{3/2}}",1,"-1/3*1/(x + Sqrt[1 + x^2])^(3/2) + Sqrt[x + Sqrt[1 + x^2]] + 2*RootSum[1 - 4*#1^4 + 22*#1^8 - 4*#1^12 + #1^16 & , (Log[1/Sqrt[x + Sqrt[1 + x^2]] - #1]*#1^3 + Log[1/Sqrt[x + Sqrt[1 + x^2]] - #1]*#1^7)/(-1 + 11*#1^4 - 3*#1^8 + #1^12) & ]","A",1
1950,1,272,137,16.1017196,"\int \frac{1}{\sqrt[4]{-x^2+x^4} \left(-1+x^8\right)} \, dx","Integrate[1/((-x^2 + x^4)^(1/4)*(-1 + x^8)),x]","\frac{x \left(-8+\sqrt[4]{\frac{1}{x^2}-1} \left(-(-2)^{3/4} \log \left(\sqrt[4]{-2}-\sqrt[4]{\frac{1}{x^2}-1}\right)+\frac{2 \log \left(-\sqrt[4]{\frac{1}{x^2}-1}+\sqrt[4]{-1-i}\right)}{\sqrt[4]{-1-i}}+\frac{2 \log \left(-\sqrt[4]{\frac{1}{x^2}-1}+\sqrt[4]{-1+i}\right)}{\sqrt[4]{-1+i}}+(-2)^{3/4} \log \left(\sqrt[4]{\frac{1}{x^2}-1}+\sqrt[4]{-2}\right)-\frac{2 \log \left(\sqrt[4]{\frac{1}{x^2}-1}+\sqrt[4]{-1-i}\right)}{\sqrt[4]{-1-i}}-\frac{2 \log \left(\sqrt[4]{\frac{1}{x^2}-1}+\sqrt[4]{-1+i}\right)}{\sqrt[4]{-1+i}}+\frac{4 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{x^2}-1}}{\sqrt[4]{-1-i}}\right)}{\sqrt[4]{-1-i}}+\frac{4 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{x^2}-1}}{\sqrt[4]{-1+i}}\right)}{\sqrt[4]{-1+i}}-(2+2 i) \sqrt[4]{2} \tanh ^{-1}\left(\frac{(1+i) \sqrt[4]{\frac{1}{x^2}-1}}{2^{3/4}}\right)\right)\right)}{16 \sqrt[4]{x^2 \left(x^2-1\right)}}","\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4+2\&,\frac{\log \left(\sqrt[4]{x^4-x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]-\frac{\left(x^4-x^2\right)^{3/4}}{2 x \left(x^2-1\right)}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-x^2}}\right)}{4 \sqrt[4]{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-x^2}}\right)}{4 \sqrt[4]{2}}",1,"(x*(-8 + (-1 + x^(-2))^(1/4)*((4*ArcTan[(-1 + x^(-2))^(1/4)/(-1 - I)^(1/4)])/(-1 - I)^(1/4) + (4*ArcTan[(-1 + x^(-2))^(1/4)/(-1 + I)^(1/4)])/(-1 + I)^(1/4) - (2 + 2*I)*2^(1/4)*ArcTanh[((1 + I)*(-1 + x^(-2))^(1/4))/2^(3/4)] - (-2)^(3/4)*Log[(-2)^(1/4) - (-1 + x^(-2))^(1/4)] + (2*Log[(-1 - I)^(1/4) - (-1 + x^(-2))^(1/4)])/(-1 - I)^(1/4) + (2*Log[(-1 + I)^(1/4) - (-1 + x^(-2))^(1/4)])/(-1 + I)^(1/4) + (-2)^(3/4)*Log[(-2)^(1/4) + (-1 + x^(-2))^(1/4)] - (2*Log[(-1 - I)^(1/4) + (-1 + x^(-2))^(1/4)])/(-1 - I)^(1/4) - (2*Log[(-1 + I)^(1/4) + (-1 + x^(-2))^(1/4)])/(-1 + I)^(1/4))))/(16*(x^2*(-1 + x^2))^(1/4))","C",1
1951,1,272,137,0.3579326,"\int \frac{1}{\sqrt[4]{-x^2+x^4} \left(-1+x^8\right)} \, dx","Integrate[1/((-x^2 + x^4)^(1/4)*(-1 + x^8)),x]","\frac{x \left(-8+\sqrt[4]{\frac{1}{x^2}-1} \left(-(-2)^{3/4} \log \left(\sqrt[4]{-2}-\sqrt[4]{\frac{1}{x^2}-1}\right)+\frac{2 \log \left(-\sqrt[4]{\frac{1}{x^2}-1}+\sqrt[4]{-1-i}\right)}{\sqrt[4]{-1-i}}+\frac{2 \log \left(-\sqrt[4]{\frac{1}{x^2}-1}+\sqrt[4]{-1+i}\right)}{\sqrt[4]{-1+i}}+(-2)^{3/4} \log \left(\sqrt[4]{\frac{1}{x^2}-1}+\sqrt[4]{-2}\right)-\frac{2 \log \left(\sqrt[4]{\frac{1}{x^2}-1}+\sqrt[4]{-1-i}\right)}{\sqrt[4]{-1-i}}-\frac{2 \log \left(\sqrt[4]{\frac{1}{x^2}-1}+\sqrt[4]{-1+i}\right)}{\sqrt[4]{-1+i}}+\frac{4 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{x^2}-1}}{\sqrt[4]{-1-i}}\right)}{\sqrt[4]{-1-i}}+\frac{4 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{x^2}-1}}{\sqrt[4]{-1+i}}\right)}{\sqrt[4]{-1+i}}-(2+2 i) \sqrt[4]{2} \tanh ^{-1}\left(\frac{(1+i) \sqrt[4]{\frac{1}{x^2}-1}}{2^{3/4}}\right)\right)\right)}{16 \sqrt[4]{x^2 \left(x^2-1\right)}}","\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4+2\&,\frac{\log \left(\sqrt[4]{x^4-x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]-\frac{\left(x^4-x^2\right)^{3/4}}{2 x \left(x^2-1\right)}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-x^2}}\right)}{4 \sqrt[4]{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-x^2}}\right)}{4 \sqrt[4]{2}}",1,"(x*(-8 + (-1 + x^(-2))^(1/4)*((4*ArcTan[(-1 + x^(-2))^(1/4)/(-1 - I)^(1/4)])/(-1 - I)^(1/4) + (4*ArcTan[(-1 + x^(-2))^(1/4)/(-1 + I)^(1/4)])/(-1 + I)^(1/4) - (2 + 2*I)*2^(1/4)*ArcTanh[((1 + I)*(-1 + x^(-2))^(1/4))/2^(3/4)] - (-2)^(3/4)*Log[(-2)^(1/4) - (-1 + x^(-2))^(1/4)] + (2*Log[(-1 - I)^(1/4) - (-1 + x^(-2))^(1/4)])/(-1 - I)^(1/4) + (2*Log[(-1 + I)^(1/4) - (-1 + x^(-2))^(1/4)])/(-1 + I)^(1/4) + (-2)^(3/4)*Log[(-2)^(1/4) + (-1 + x^(-2))^(1/4)] - (2*Log[(-1 - I)^(1/4) + (-1 + x^(-2))^(1/4)])/(-1 - I)^(1/4) - (2*Log[(-1 + I)^(1/4) + (-1 + x^(-2))^(1/4)])/(-1 + I)^(1/4))))/(16*(x^2*(-1 + x^2))^(1/4))","C",1
1952,1,171,137,0.1178744,"\int \frac{-2+x^4}{\sqrt[4]{1+x^4} \left(-1-x^4+2 x^8\right)} \, dx","Integrate[(-2 + x^4)/((1 + x^4)^(1/4)*(-1 - x^4 + 2*x^8)),x]","\frac{2 \sqrt[4]{2} \tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+1}}\right)+2 \sqrt[4]{2} \tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+1}}\right)-5 \left(2 \tan ^{-1}\left(1-\frac{\sqrt{2} x}{\sqrt[4]{x^4+1}}\right)-2 \tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt[4]{x^4+1}}+1\right)+\log \left(-\frac{\sqrt{2} x}{\sqrt[4]{x^4+1}}+\frac{x^2}{\sqrt{x^4+1}}+1\right)-\log \left(\frac{\sqrt{2} x}{\sqrt[4]{x^4+1}}+\frac{x^2}{\sqrt{x^4+1}}+1\right)\right)}{12 \sqrt{2}}","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+1}}\right)}{6 \sqrt[4]{2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+1}}\right)}{6 \sqrt[4]{2}}+\frac{5 \tan ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{x^4+1}}{\sqrt{x^4+1}-x^2}\right)}{6 \sqrt{2}}+\frac{5 \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{x^4+1}}{\sqrt{x^4+1}+x^2}\right)}{6 \sqrt{2}}",1,"(2*2^(1/4)*ArcTan[(2^(1/4)*x)/(1 + x^4)^(1/4)] + 2*2^(1/4)*ArcTanh[(2^(1/4)*x)/(1 + x^4)^(1/4)] - 5*(2*ArcTan[1 - (Sqrt[2]*x)/(1 + x^4)^(1/4)] - 2*ArcTan[1 + (Sqrt[2]*x)/(1 + x^4)^(1/4)] + Log[1 + x^2/Sqrt[1 + x^4] - (Sqrt[2]*x)/(1 + x^4)^(1/4)] - Log[1 + x^2/Sqrt[1 + x^4] + (Sqrt[2]*x)/(1 + x^4)^(1/4)]))/(12*Sqrt[2])","A",1
1953,0,0,137,0.0944004,"\int \frac{\sqrt{b+\sqrt{b^2+a x^2}}}{\left(b^2+a x^2\right)^{5/2}} \, dx","Integrate[Sqrt[b + Sqrt[b^2 + a*x^2]]/(b^2 + a*x^2)^(5/2),x]","\int \frac{\sqrt{b+\sqrt{b^2+a x^2}}}{\left(b^2+a x^2\right)^{5/2}} \, dx","\frac{5 x}{12 b^2 \left(a x^2+b^2\right) \sqrt{\sqrt{a x^2+b^2}+b}}+\frac{5 \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b} \sqrt{\sqrt{a x^2+b^2}+b}}\right)}{8 \sqrt{a} b^{7/2}}+\frac{x \left(15 a x^2+23 b^2\right)}{24 b^3 \left(a x^2+b^2\right)^{3/2} \sqrt{\sqrt{a x^2+b^2}+b}}",1,"Integrate[Sqrt[b + Sqrt[b^2 + a*x^2]]/(b^2 + a*x^2)^(5/2), x]","F",-1
1954,1,211,138,0.0796122,"\int \frac{\sqrt[4]{-b+a x^2}}{x} \, dx","Integrate[(-b + a*x^2)^(1/4)/x,x]","2 \sqrt[4]{a x^2-b}+\frac{\sqrt[4]{b} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^2-b}+\sqrt{a x^2-b}+\sqrt{b}\right)}{2 \sqrt{2}}-\frac{\sqrt[4]{b} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^2-b}+\sqrt{a x^2-b}+\sqrt{b}\right)}{2 \sqrt{2}}+\frac{\sqrt[4]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a x^2-b}}{\sqrt[4]{b}}\right)}{\sqrt{2}}-\frac{\sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x^2-b}}{\sqrt[4]{b}}+1\right)}{\sqrt{2}}","2 \sqrt[4]{a x^2-b}+\frac{\sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^2-b}}{\sqrt{a x^2-b}-\sqrt{b}}\right)}{\sqrt{2}}-\frac{\sqrt[4]{b} \tanh ^{-1}\left(\frac{\frac{\sqrt{a x^2-b}}{\sqrt{2} \sqrt[4]{b}}+\frac{\sqrt[4]{b}}{\sqrt{2}}}{\sqrt[4]{a x^2-b}}\right)}{\sqrt{2}}",1,"2*(-b + a*x^2)^(1/4) + (b^(1/4)*ArcTan[1 - (Sqrt[2]*(-b + a*x^2)^(1/4))/b^(1/4)])/Sqrt[2] - (b^(1/4)*ArcTan[1 + (Sqrt[2]*(-b + a*x^2)^(1/4))/b^(1/4)])/Sqrt[2] + (b^(1/4)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*(-b + a*x^2)^(1/4) + Sqrt[-b + a*x^2]])/(2*Sqrt[2]) - (b^(1/4)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*(-b + a*x^2)^(1/4) + Sqrt[-b + a*x^2]])/(2*Sqrt[2])","A",1
1955,1,66,138,0.028484,"\int \frac{\left(b+a x^2\right) \sqrt[3]{-x+x^3}}{x^2} \, dx","Integrate[((b + a*x^2)*(-x + x^3)^(1/3))/x^2,x]","\frac{3 \sqrt[3]{x \left(x^2-1\right)} \left(x^2 (a-3 b) \, _2F_1\left(-\frac{1}{3},\frac{2}{3};\frac{5}{3};x^2\right)-2 b \left(1-x^2\right)^{4/3}\right)}{4 x \sqrt[3]{1-x^2}}","\frac{1}{6} (a-3 b) \log \left(\sqrt[3]{x^3-x}-x\right)+\frac{1}{6} \left(\sqrt{3} a-3 \sqrt{3} b\right) \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-x}+x}\right)+\frac{\sqrt[3]{x^3-x} \left(a x^2-3 b\right)}{2 x}+\frac{1}{12} (3 b-a) \log \left(\sqrt[3]{x^3-x} x+\left(x^3-x\right)^{2/3}+x^2\right)",1,"(3*(x*(-1 + x^2))^(1/3)*(-2*b*(1 - x^2)^(4/3) + (a - 3*b)*x^2*Hypergeometric2F1[-1/3, 2/3, 5/3, x^2]))/(4*x*(1 - x^2)^(1/3))","C",1
1956,1,169,138,0.1280939,"\int \frac{-b+a x}{x \sqrt[3]{b^3+a^3 x^3}} \, dx","Integrate[(-b + a*x)/(x*(b^3 + a^3*x^3)^(1/3)),x]","\frac{1}{6} \left(-2 \log \left(1-\frac{a x}{\sqrt[3]{a^3 x^3+b^3}}\right)-3 \log \left(b-\sqrt[3]{a^3 x^3+b^3}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 a x}{\sqrt[3]{a^3 x^3+b^3}}+1}{\sqrt{3}}\right)-2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x^3+b^3}+b}{\sqrt{3} b}\right)+\log \left(\frac{a x}{\sqrt[3]{a^3 x^3+b^3}}+\frac{a^2 x^2}{\left(a^3 x^3+b^3\right)^{2/3}}+1\right)+3 \log (x)\right)","-\log \left(\sqrt[3]{a^3 x^3+b^3}-a x-b\right)-\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{a^3 x^3+b^3}}{\sqrt[3]{a^3 x^3+b^3}+2 a x+2 b}\right)+\frac{1}{2} \log \left(\left(a^3 x^3+b^3\right)^{2/3}+(a x+b) \sqrt[3]{a^3 x^3+b^3}+a^2 x^2+2 a b x+b^2\right)",1,"(2*Sqrt[3]*ArcTan[(1 + (2*a*x)/(b^3 + a^3*x^3)^(1/3))/Sqrt[3]] - 2*Sqrt[3]*ArcTan[(b + 2*(b^3 + a^3*x^3)^(1/3))/(Sqrt[3]*b)] + 3*Log[x] - 2*Log[1 - (a*x)/(b^3 + a^3*x^3)^(1/3)] + Log[1 + (a^2*x^2)/(b^3 + a^3*x^3)^(2/3) + (a*x)/(b^3 + a^3*x^3)^(1/3)] - 3*Log[b - (b^3 + a^3*x^3)^(1/3)])/6","A",1
1957,1,124,138,0.0416213,"\int \frac{x^2 \sqrt[4]{-x^3+x^4}}{2+x} \, dx","Integrate[(x^2*(-x^3 + x^4)^(1/4))/(2 + x),x]","\frac{4 \sqrt[4]{(x-1) x^3} \left(\sqrt[4]{x} \, _2F_1\left(-\frac{11}{4},\frac{1}{4};\frac{5}{4};1-x\right)-3 \sqrt[4]{x} \, _2F_1\left(-\frac{7}{4},\frac{1}{4};\frac{5}{4};1-x\right)+6 \sqrt[4]{x} \, _2F_1\left(-\frac{3}{4},\frac{1}{4};\frac{5}{4};1-x\right)-12 \sqrt[4]{x} \, _2F_1\left(\frac{1}{4},\frac{1}{4};\frac{5}{4};1-x\right)+8 \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{2 (x-1)}{3 x}\right)\right)}{x}","\frac{1135}{64} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^3}}\right)-8\ 2^{3/4} \sqrt[4]{3} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{3}{2}} x}{\sqrt[4]{x^4-x^3}}\right)-\frac{1135}{64} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^3}}\right)+8\ 2^{3/4} \sqrt[4]{3} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{3}{2}} x}{\sqrt[4]{x^4-x^3}}\right)+\frac{1}{96} \sqrt[4]{x^4-x^3} \left(32 x^2-100 x+401\right)",1,"(4*((-1 + x)*x^3)^(1/4)*(x^(1/4)*Hypergeometric2F1[-11/4, 1/4, 5/4, 1 - x] - 3*x^(1/4)*Hypergeometric2F1[-7/4, 1/4, 5/4, 1 - x] + 6*x^(1/4)*Hypergeometric2F1[-3/4, 1/4, 5/4, 1 - x] - 12*x^(1/4)*Hypergeometric2F1[1/4, 1/4, 5/4, 1 - x] + 8*Hypergeometric2F1[1/4, 1, 5/4, (2*(-1 + x))/(3*x)]))/x","C",1
1958,0,0,138,0.6215098,"\int \frac{(-1+x) \left(-3+8 x-8 x^2+12 x^4\right)}{x \left(\frac{1-2 x^2}{1+2 x^2}\right)^{2/3} \left(1+2 x^2\right) \left(3-7 x+7 x^2-6 x^3+2 x^4\right)} \, dx","Integrate[((-1 + x)*(-3 + 8*x - 8*x^2 + 12*x^4))/(x*((1 - 2*x^2)/(1 + 2*x^2))^(2/3)*(1 + 2*x^2)*(3 - 7*x + 7*x^2 - 6*x^3 + 2*x^4)),x]","\int \frac{(-1+x) \left(-3+8 x-8 x^2+12 x^4\right)}{x \left(\frac{1-2 x^2}{1+2 x^2}\right)^{2/3} \left(1+2 x^2\right) \left(3-7 x+7 x^2-6 x^3+2 x^4\right)} \, dx","\log \left(\sqrt[3]{\frac{1-2 x^2}{2 x^2+1}}+x-1\right)-\frac{1}{2} \log \left(x^2+\left(\frac{1-2 x^2}{2 x^2+1}\right)^{2/3}+(1-x) \sqrt[3]{\frac{1-2 x^2}{2 x^2+1}}-2 x+1\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x-\sqrt{3}}{-2 \sqrt[3]{\frac{1-2 x^2}{2 x^2+1}}+x-1}\right)",1,"Integrate[((-1 + x)*(-3 + 8*x - 8*x^2 + 12*x^4))/(x*((1 - 2*x^2)/(1 + 2*x^2))^(2/3)*(1 + 2*x^2)*(3 - 7*x + 7*x^2 - 6*x^3 + 2*x^4)), x]","F",-1
1959,1,393,138,1.6426886,"\int \frac{b-a x^5}{\sqrt{a+b x} \left(a b+x^5\right)} \, dx","Integrate[(b - a*x^5)/(Sqrt[a + b*x]*(a*b + x^5)),x]","\frac{2 \left(-5 a^{19/10} \sqrt{a+b x}-\frac{\left(a^2+1\right) b^{6/5} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt[10]{a} \sqrt{a^{4/5}-b^{6/5}}}\right)}{\sqrt{a^{4/5}-b^{6/5}}}+\frac{\sqrt[5]{-1} \left(a^2+1\right) b^{6/5} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt[10]{a} \sqrt{a^{4/5}+\sqrt[5]{-1} b^{6/5}}}\right)}{\sqrt{a^{4/5}+\sqrt[5]{-1} b^{6/5}}}-\frac{(-1)^{2/5} \left(a^2+1\right) b^{6/5} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt[10]{a} \sqrt{a^{4/5}-(-1)^{2/5} b^{6/5}}}\right)}{\sqrt{a^{4/5}-(-1)^{2/5} b^{6/5}}}+\frac{(-1)^{3/5} \left(a^2+1\right) b^{6/5} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt[10]{a} \sqrt{a^{4/5}+(-1)^{3/5} b^{6/5}}}\right)}{\sqrt{a^{4/5}+(-1)^{3/5} b^{6/5}}}-\frac{(-1)^{4/5} \left(a^2+1\right) b^{6/5} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt[10]{a} \sqrt{a^{4/5}-(-1)^{4/5} b^{6/5}}}\right)}{\sqrt{a^{4/5}-(-1)^{4/5} b^{6/5}}}\right)}{5 a^{9/10} b}","\frac{1}{5} \left(a^2 b^5+b^5\right) \text{RootSum}\left[-\text{$\#$1}^{10}+5 \text{$\#$1}^8 a-10 \text{$\#$1}^6 a^2+10 \text{$\#$1}^4 a^3-5 \text{$\#$1}^2 a^4+a^5-a b^6\&,\frac{\log \left(\sqrt{a+b x}-\text{$\#$1}\right)}{\text{$\#$1}^9-4 \text{$\#$1}^7 a+6 \text{$\#$1}^5 a^2-4 \text{$\#$1}^3 a^3+\text{$\#$1} a^4}\&\right]-\frac{2 a \sqrt{a+b x}}{b}",1,"(2*(-5*a^(19/10)*Sqrt[a + b*x] - ((1 + a^2)*b^(6/5)*ArcTanh[Sqrt[a + b*x]/(a^(1/10)*Sqrt[a^(4/5) - b^(6/5)])])/Sqrt[a^(4/5) - b^(6/5)] + ((-1)^(1/5)*(1 + a^2)*b^(6/5)*ArcTanh[Sqrt[a + b*x]/(a^(1/10)*Sqrt[a^(4/5) + (-1)^(1/5)*b^(6/5)])])/Sqrt[a^(4/5) + (-1)^(1/5)*b^(6/5)] - ((-1)^(2/5)*(1 + a^2)*b^(6/5)*ArcTanh[Sqrt[a + b*x]/(a^(1/10)*Sqrt[a^(4/5) - (-1)^(2/5)*b^(6/5)])])/Sqrt[a^(4/5) - (-1)^(2/5)*b^(6/5)] + ((-1)^(3/5)*(1 + a^2)*b^(6/5)*ArcTanh[Sqrt[a + b*x]/(a^(1/10)*Sqrt[a^(4/5) + (-1)^(3/5)*b^(6/5)])])/Sqrt[a^(4/5) + (-1)^(3/5)*b^(6/5)] - ((-1)^(4/5)*(1 + a^2)*b^(6/5)*ArcTanh[Sqrt[a + b*x]/(a^(1/10)*Sqrt[a^(4/5) - (-1)^(4/5)*b^(6/5)])])/Sqrt[a^(4/5) - (-1)^(4/5)*b^(6/5)]))/(5*a^(9/10)*b)","B",0
1960,0,0,138,0.4112766,"\int \frac{\left(-1+x^3\right)^{2/3} \left(1+x^3+x^6\right)}{x^6 \left(-1+x^6\right)} \, dx","Integrate[((-1 + x^3)^(2/3)*(1 + x^3 + x^6))/(x^6*(-1 + x^6)),x]","\int \frac{\left(-1+x^3\right)^{2/3} \left(1+x^3+x^6\right)}{x^6 \left(-1+x^6\right)} \, dx","-\frac{\log \left(2^{2/3} \sqrt[3]{x^3-1}-2 x\right)}{3 \sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^3-1}+x}\right)}{\sqrt[3]{2} \sqrt{3}}+\frac{\left(x^3-1\right)^{2/3} \left(3 x^3+2\right)}{10 x^5}+\frac{\log \left(2^{2/3} \sqrt[3]{x^3-1} x+\sqrt[3]{2} \left(x^3-1\right)^{2/3}+2 x^2\right)}{6 \sqrt[3]{2}}",1,"Integrate[((-1 + x^3)^(2/3)*(1 + x^3 + x^6))/(x^6*(-1 + x^6)), x]","F",-1
1961,1,139,138,4.7560781,"\int \frac{-1+x^2}{\sqrt{1+x} \left(1+x^2\right) \sqrt{1+\sqrt{1+x}} \sqrt{1+\sqrt{1+\sqrt{1+x}}}} \, dx","Integrate[(-1 + x^2)/(Sqrt[1 + x]*(1 + x^2)*Sqrt[1 + Sqrt[1 + x]]*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]),x]","\text{RootSum}\left[2 \text{$\#$1}^{16}-8 \text{$\#$1}^{12}+8 \text{$\#$1}^{10}+14 \text{$\#$1}^8-32 \text{$\#$1}^6+24 \text{$\#$1}^4-8 \text{$\#$1}^2+1\&,\frac{\text{$\#$1}^{13} \log \left(\frac{1}{\sqrt{\sqrt{\sqrt{x+1}+1}+1}}-\text{$\#$1}\right)}{2 \text{$\#$1}^{14}-6 \text{$\#$1}^{10}+5 \text{$\#$1}^8+7 \text{$\#$1}^6-12 \text{$\#$1}^4+6 \text{$\#$1}^2-1}\&\right]+8 \sqrt{\sqrt{\sqrt{x+1}+1}+1}","8 \sqrt{\sqrt{\sqrt{x+1}+1}+1}-\text{RootSum}\left[\text{$\#$1}^{16}-8 \text{$\#$1}^{14}+24 \text{$\#$1}^{12}-32 \text{$\#$1}^{10}+14 \text{$\#$1}^8+8 \text{$\#$1}^6-8 \text{$\#$1}^4+2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x+1}+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^{15}-7 \text{$\#$1}^{13}+18 \text{$\#$1}^{11}-20 \text{$\#$1}^9+7 \text{$\#$1}^7+3 \text{$\#$1}^5-2 \text{$\#$1}^3}\&\right]",1,"8*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]] + RootSum[1 - 8*#1^2 + 24*#1^4 - 32*#1^6 + 14*#1^8 + 8*#1^10 - 8*#1^12 + 2*#1^16 & , (Log[1/Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]] - #1]*#1^13)/(-1 + 6*#1^2 - 12*#1^4 + 7*#1^6 + 5*#1^8 - 6*#1^10 + 2*#1^14) & ]","A",1
1962,1,139,138,0.7811076,"\int \frac{-1+x^2}{\sqrt{1+x} \left(1+x^2\right) \sqrt{1+\sqrt{1+x}} \sqrt{1+\sqrt{1+\sqrt{1+x}}}} \, dx","Integrate[(-1 + x^2)/(Sqrt[1 + x]*(1 + x^2)*Sqrt[1 + Sqrt[1 + x]]*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]),x]","\text{RootSum}\left[2 \text{$\#$1}^{16}-8 \text{$\#$1}^{12}+8 \text{$\#$1}^{10}+14 \text{$\#$1}^8-32 \text{$\#$1}^6+24 \text{$\#$1}^4-8 \text{$\#$1}^2+1\&,\frac{\text{$\#$1}^{13} \log \left(\frac{1}{\sqrt{\sqrt{\sqrt{x+1}+1}+1}}-\text{$\#$1}\right)}{2 \text{$\#$1}^{14}-6 \text{$\#$1}^{10}+5 \text{$\#$1}^8+7 \text{$\#$1}^6-12 \text{$\#$1}^4+6 \text{$\#$1}^2-1}\&\right]+8 \sqrt{\sqrt{\sqrt{x+1}+1}+1}","8 \sqrt{\sqrt{\sqrt{x+1}+1}+1}-\text{RootSum}\left[\text{$\#$1}^{16}-8 \text{$\#$1}^{14}+24 \text{$\#$1}^{12}-32 \text{$\#$1}^{10}+14 \text{$\#$1}^8+8 \text{$\#$1}^6-8 \text{$\#$1}^4+2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x+1}+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^{15}-7 \text{$\#$1}^{13}+18 \text{$\#$1}^{11}-20 \text{$\#$1}^9+7 \text{$\#$1}^7+3 \text{$\#$1}^5-2 \text{$\#$1}^3}\&\right]",1,"8*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]] + RootSum[1 - 8*#1^2 + 24*#1^4 - 32*#1^6 + 14*#1^8 + 8*#1^10 - 8*#1^12 + 2*#1^16 & , (Log[1/Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]] - #1]*#1^13)/(-1 + 6*#1^2 - 12*#1^4 + 7*#1^6 + 5*#1^8 - 6*#1^10 + 2*#1^14) & ]","A",1
1963,1,46,139,0.0263234,"\int \frac{x}{\left(x^2 (-a+x)\right)^{2/3} (-a d+(-1+d) x)} \, dx","Integrate[x/((x^2*(-a + x))^(2/3)*(-(a*d) + (-1 + d)*x)),x]","-\frac{3 x^2 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{x}{d (x-a)}\right)}{2 a d \left(x^2 (x-a)\right)^{2/3}}","-\frac{\log \left(d^{2/3} \left(x^3-a x^2\right)^{2/3}+\sqrt[3]{d} x \sqrt[3]{x^3-a x^2}+x^2\right)}{2 a \sqrt[3]{d}}+\frac{\log \left(x-\sqrt[3]{d} \sqrt[3]{x^3-a x^2}\right)}{a \sqrt[3]{d}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{d} \sqrt[3]{x^3-a x^2}+x}\right)}{a \sqrt[3]{d}}",1,"(-3*x^2*Hypergeometric2F1[2/3, 1, 5/3, x/(d*(-a + x))])/(2*a*d*(x^2*(-a + x))^(2/3))","C",1
1964,1,79,139,0.0274561,"\int \frac{\left(-b+a x^2\right)^{3/4}}{x} \, dx","Integrate[(-b + a*x^2)^(3/4)/x,x]","\frac{2}{3} \left(a x^2-b\right)^{3/4}+(-b)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a x^2-b}}{\sqrt[4]{-b}}\right)-(-b)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a x^2-b}}{\sqrt[4]{-b}}\right)","\frac{b^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^2-b}}{\sqrt{a x^2-b}-\sqrt{b}}\right)}{\sqrt{2}}+\frac{b^{3/4} \tanh ^{-1}\left(\frac{\frac{\sqrt{a x^2-b}}{\sqrt{2} \sqrt[4]{b}}+\frac{\sqrt[4]{b}}{\sqrt{2}}}{\sqrt[4]{a x^2-b}}\right)}{\sqrt{2}}+\frac{2}{3} \left(a x^2-b\right)^{3/4}",1,"(2*(-b + a*x^2)^(3/4))/3 + (-b)^(3/4)*ArcTan[(-b + a*x^2)^(1/4)/(-b)^(1/4)] - (-b)^(3/4)*ArcTanh[(-b + a*x^2)^(1/4)/(-b)^(1/4)]","A",1
1965,0,0,139,0.1558238,"\int \frac{-2 x+x^2}{\left(1-x+x^2\right) \sqrt[4]{1+x^4}} \, dx","Integrate[(-2*x + x^2)/((1 - x + x^2)*(1 + x^4)^(1/4)),x]","\int \frac{-2 x+x^2}{\left(1-x+x^2\right) \sqrt[4]{1+x^4}} \, dx","\frac{1}{2} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)+\frac{1}{2} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)-\frac{\tan ^{-1}\left(\frac{\left(\sqrt{2} x-\sqrt{2}\right) \sqrt[4]{x^4+1}}{\sqrt{x^4+1}-x^2+2 x-1}\right)}{\sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{\left(\sqrt{2} x-\sqrt{2}\right) \sqrt[4]{x^4+1}}{\sqrt{x^4+1}+x^2-2 x+1}\right)}{\sqrt{2}}",1,"Integrate[(-2*x + x^2)/((1 - x + x^2)*(1 + x^4)^(1/4)), x]","F",-1
1966,1,247,139,4.0553002,"\int \frac{1+k^4 x^4}{\sqrt{(1-x) x \left(1-k^2 x\right)} \left(-1+k^4 x^4\right)} \, dx","Integrate[(1 + k^4*x^4)/(Sqrt[(1 - x)*x*(1 - k^2*x)]*(-1 + k^4*x^4)),x]","\frac{i \sqrt{\frac{1}{x-1}+1} (x-1)^{3/2} \sqrt{\frac{1-\frac{1}{k^2}}{x-1}+1} \left(-(k+1) \left(\left(k^2+1\right) \Pi \left(\frac{k-1}{k};i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)+i (k-1) \left((k+i) \Pi \left(\frac{k-i}{k};i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)-(k-i) \Pi \left(\frac{k+i}{k};i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)\right)\right)+2 \left(k^4+1\right) F\left(i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)+\left(k^3-k^2+k-1\right) \Pi \left(1+\frac{1}{k};i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)\right)}{\left(k^4-1\right) \sqrt{(x-1) x \left(k^2 x-1\right)}}","-\frac{\tan ^{-1}\left(\frac{(k-1) x}{\sqrt{k^2 x^3+\left(-k^2-1\right) x^2+x}}\right)}{2 (k-1)}-\frac{\tan ^{-1}\left(\frac{(k+1) x}{\sqrt{k^2 x^3+\left(-k^2-1\right) x^2+x}}\right)}{2 (k+1)}-\frac{\tan ^{-1}\left(\frac{\sqrt{k^2+1} \sqrt{k^2 x^3+\left(-k^2-1\right) x^2+x}}{(x-1) \left(k^2 x-1\right)}\right)}{\sqrt{k^2+1}}",1,"(I*Sqrt[1 + (-1 + x)^(-1)]*Sqrt[1 + (1 - k^(-2))/(-1 + x)]*(-1 + x)^(3/2)*(2*(1 + k^4)*EllipticF[I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)] + (-1 + k - k^2 + k^3)*EllipticPi[1 + k^(-1), I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)] - (1 + k)*((1 + k^2)*EllipticPi[(-1 + k)/k, I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)] + I*(-1 + k)*((I + k)*EllipticPi[(-I + k)/k, I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)] - (-I + k)*EllipticPi[(I + k)/k, I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)]))))/((-1 + k^4)*Sqrt[(-1 + x)*x*(-1 + k^2*x)])","C",1
1967,0,0,139,2.2900679,"\int \frac{-b+a x^8}{\sqrt[4]{-b x^2+a x^4} \left(b+a x^8\right)} \, dx","Integrate[(-b + a*x^8)/((-(b*x^2) + a*x^4)^(1/4)*(b + a*x^8)),x]","\int \frac{-b+a x^8}{\sqrt[4]{-b x^2+a x^4} \left(b+a x^8\right)} \, dx","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^{16}-4 \text{$\#$1}^{12} a+6 \text{$\#$1}^8 a^2-4 \text{$\#$1}^4 a^3+a^4+a b^3\&,\frac{\log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)}{\sqrt[4]{a}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)}{\sqrt[4]{a}}",1,"Integrate[(-b + a*x^8)/((-(b*x^2) + a*x^4)^(1/4)*(b + a*x^8)), x]","F",-1
1968,0,0,139,0.81274,"\int \frac{-b+a x^8}{\sqrt[4]{-b x^2+a x^4} \left(b+a x^8\right)} \, dx","Integrate[(-b + a*x^8)/((-(b*x^2) + a*x^4)^(1/4)*(b + a*x^8)),x]","\int \frac{-b+a x^8}{\sqrt[4]{-b x^2+a x^4} \left(b+a x^8\right)} \, dx","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^{16}-4 \text{$\#$1}^{12} a+6 \text{$\#$1}^8 a^2-4 \text{$\#$1}^4 a^3+a^4+a b^3\&,\frac{\log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)}{\sqrt[4]{a}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)}{\sqrt[4]{a}}",1,"Integrate[(-b + a*x^8)/((-(b*x^2) + a*x^4)^(1/4)*(b + a*x^8)), x]","F",-1
1969,0,0,139,2.2354465,"\int \frac{\left(-1+x^8\right) \left(1+x^8\right)}{\sqrt[4]{-1-x^4+x^8} \left(1-3 x^8+x^{16}\right)} \, dx","Integrate[((-1 + x^8)*(1 + x^8))/((-1 - x^4 + x^8)^(1/4)*(1 - 3*x^8 + x^16)),x]","\int \frac{\left(-1+x^8\right) \left(1+x^8\right)}{\sqrt[4]{-1-x^4+x^8} \left(1-3 x^8+x^{16}\right)} \, dx","-\frac{x}{2 \sqrt[4]{x^8-x^4-1}}+\frac{\tan ^{-1}\left(\frac{2^{3/4} x \sqrt[4]{x^8-x^4-1}}{\sqrt{2} x^2-\sqrt{x^8-x^4-1}}\right)}{4\ 2^{3/4}}-\frac{\tanh ^{-1}\left(\frac{2 \sqrt[4]{2} x \sqrt[4]{x^8-x^4-1}}{2 x^2+\sqrt{2} \sqrt{x^8-x^4-1}}\right)}{4\ 2^{3/4}}",1,"Integrate[((-1 + x^8)*(1 + x^8))/((-1 - x^4 + x^8)^(1/4)*(1 - 3*x^8 + x^16)), x]","F",-1
1970,1,42,140,0.0270964,"\int \frac{1}{\sqrt[3]{x^2 (-a+x)} (-a d+(-1+d) x)} \, dx","Integrate[1/((x^2*(-a + x))^(1/3)*(-(a*d) + (-1 + d)*x)),x]","-\frac{3 x \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{x}{d (x-a)}\right)}{a d \sqrt[3]{x^2 (x-a)}}","\frac{\log \left(x-\sqrt[3]{d} \sqrt[3]{x^3-a x^2}\right)}{a d^{2/3}}-\frac{\log \left(d^{2/3} \left(x^3-a x^2\right)^{2/3}+\sqrt[3]{d} x \sqrt[3]{x^3-a x^2}+x^2\right)}{2 a d^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{d} \sqrt[3]{x^3-a x^2}+x}\right)}{a d^{2/3}}",1,"(-3*x*Hypergeometric2F1[1/3, 1, 4/3, x/(d*(-a + x))])/(a*d*(x^2*(-a + x))^(1/3))","C",1
1971,1,131,140,0.0574651,"\int \frac{\sqrt[3]{6+2 x+x^2}}{1+x} \, dx","Integrate[(6 + 2*x + x^2)^(1/3)/(1 + x),x]","\frac{1}{4} \left(6 \sqrt[3]{x^2+2 x+6}+2 \sqrt[3]{5} \log \left(\sqrt[3]{5}-\sqrt[3]{(x+1)^2+5}\right)-\sqrt[3]{5} \log \left(\left((x+1)^2+5\right)^{2/3}+\sqrt[3]{5} \sqrt[3]{(x+1)^2+5}+5^{2/3}\right)-2 \sqrt{3} \sqrt[3]{5} \tan ^{-1}\left(\frac{2 \sqrt[3]{(x+1)^2+5}+\sqrt[3]{5}}{\sqrt{3} \sqrt[3]{5}}\right)\right)","\frac{3}{2} \sqrt[3]{x^2+2 x+6}+\frac{1}{2} \sqrt[3]{5} \log \left(5^{2/3} \sqrt[3]{x^2+2 x+6}-5\right)-\frac{1}{4} \sqrt[3]{5} \log \left(\sqrt[3]{5} \left(x^2+2 x+6\right)^{2/3}+5^{2/3} \sqrt[3]{x^2+2 x+6}+5\right)-\frac{1}{2} \sqrt{3} \sqrt[3]{5} \tan ^{-1}\left(\frac{2 \sqrt[3]{x^2+2 x+6}}{\sqrt{3} \sqrt[3]{5}}+\frac{1}{\sqrt{3}}\right)",1,"(6*(6 + 2*x + x^2)^(1/3) - 2*Sqrt[3]*5^(1/3)*ArcTan[(5^(1/3) + 2*(5 + (1 + x)^2)^(1/3))/(Sqrt[3]*5^(1/3))] + 2*5^(1/3)*Log[5^(1/3) - (5 + (1 + x)^2)^(1/3)] - 5^(1/3)*Log[5^(2/3) + 5^(1/3)*(5 + (1 + x)^2)^(1/3) + (5 + (1 + x)^2)^(2/3)])/4","A",1
1972,1,103,140,0.0632452,"\int \frac{-1+x}{x \sqrt[3]{-1+x^3}} \, dx","Integrate[(-1 + x)/(x*(-1 + x^3)^(1/3)),x]","\frac{1}{6} \left(-3 \left(x^3-1\right)^{2/3} \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};1-x^3\right)-2 \log \left(1-\frac{x}{\sqrt[3]{x^3-1}}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)+\log \left(\frac{x}{\sqrt[3]{x^3-1}}+\frac{x^2}{\left(x^3-1\right)^{2/3}}+1\right)\right)","-\frac{1}{6} \log \left(\left(x^3-1\right)^{2/3}-\sqrt[3]{x^3-1}+1\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-1}+x}\right)}{\sqrt{3}}+\frac{\tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{x^3-1}}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{2}{3} \tanh ^{-1}\left(\frac{x+1}{-2 \sqrt[3]{x^3-1}+x-1}\right)+\frac{1}{6} \log \left(\sqrt[3]{x^3-1} x+\left(x^3-1\right)^{2/3}+x^2\right)",1,"(2*Sqrt[3]*ArcTan[(1 + (2*x)/(-1 + x^3)^(1/3))/Sqrt[3]] - 3*(-1 + x^3)^(2/3)*Hypergeometric2F1[2/3, 1, 5/3, 1 - x^3] - 2*Log[1 - x/(-1 + x^3)^(1/3)] + Log[1 + x^2/(-1 + x^3)^(2/3) + x/(-1 + x^3)^(1/3)])/6","C",1
1973,1,135,140,0.1550916,"\int \frac{\left(-1+x^3\right)^{2/3} \left(1+x^3\right)}{x^6 \left(-2+x^3\right)} \, dx","Integrate[((-1 + x^3)^(2/3)*(1 + x^3))/(x^6*(-2 + x^3)),x]","\left(\frac{1}{10 x^5}+\frac{11}{40 x^2}\right) \left(x^3-1\right)^{2/3}-\frac{-2 \log \left(2-\frac{2^{2/3} x}{\sqrt[3]{1-x^3}}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2^{2/3} x}{\sqrt[3]{1-x^3}}+1}{\sqrt{3}}\right)+\log \left(\frac{2^{2/3} x}{\sqrt[3]{1-x^3}}+\frac{\sqrt[3]{2} x^2}{\left(1-x^3\right)^{2/3}}+2\right)}{8\ 2^{2/3}}","\frac{\log \left(\sqrt[3]{2} \sqrt[3]{x^3-1}-x\right)}{4\ 2^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{2} \sqrt[3]{x^3-1}+x}\right)}{4\ 2^{2/3}}+\frac{\left(x^3-1\right)^{2/3} \left(11 x^3+4\right)}{40 x^5}-\frac{\log \left(\sqrt[3]{2} \sqrt[3]{x^3-1} x+2^{2/3} \left(x^3-1\right)^{2/3}+x^2\right)}{8\ 2^{2/3}}",1,"(1/(10*x^5) + 11/(40*x^2))*(-1 + x^3)^(2/3) - (2*Sqrt[3]*ArcTan[(1 + (2^(2/3)*x)/(1 - x^3)^(1/3))/Sqrt[3]] - 2*Log[2 - (2^(2/3)*x)/(1 - x^3)^(1/3)] + Log[2 + (2^(1/3)*x^2)/(1 - x^3)^(2/3) + (2^(2/3)*x)/(1 - x^3)^(1/3)])/(8*2^(2/3))","A",0
1974,1,102,140,0.0922365,"\int \frac{\left(-4+x^2\right) \sqrt[3]{x+x^3}}{x^4 \left(2+x^2\right)} \, dx","Integrate[((-4 + x^2)*(x + x^3)^(1/3))/(x^4*(2 + x^2)),x]","\frac{3 \sqrt[3]{x^3+x} \left(9 \left(x^2+2\right) x^2 \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};\frac{x^2}{2 x^2+2}\right)+\left(9 x^4-6 x^2\right) \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{x^2}{2 x^2+2}\right)-4 \left(11 x^4+7 x^2-4\right)\right)}{64 x^3 \left(x^2+1\right)}","-\frac{3 \log \left(\sqrt[3]{2} \sqrt[3]{x^3+x}-x\right)}{4 \sqrt[3]{2}}-\frac{3 \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{2} \sqrt[3]{x^3+x}+x}\right)}{4 \sqrt[3]{2}}-\frac{3 \sqrt[3]{x^3+x} \left(2 x^2-1\right)}{4 x^3}+\frac{3 \log \left(\sqrt[3]{2} \sqrt[3]{x^3+x} x+2^{2/3} \left(x^3+x\right)^{2/3}+x^2\right)}{8 \sqrt[3]{2}}",1,"(3*(x + x^3)^(1/3)*(-4*(-4 + 7*x^2 + 11*x^4) + (-6*x^2 + 9*x^4)*Hypergeometric2F1[2/3, 1, 5/3, x^2/(2 + 2*x^2)] + 9*x^2*(2 + x^2)*Hypergeometric2F1[2/3, 2, 5/3, x^2/(2 + 2*x^2)]))/(64*x^3*(1 + x^2))","C",0
1975,1,95,140,0.0783339,"\int \frac{2+x^2}{\left(1+x^2\right) \sqrt[3]{-x^2+x^3}} \, dx","Integrate[(2 + x^2)/((1 + x^2)*(-x^2 + x^3)^(1/3)),x]","\frac{\left(\frac{3}{8}+\frac{3 i}{8}\right) \left((x-1) x^2\right)^{2/3} \left((2-2 i) x^{2/3} \, _2F_1\left(\frac{2}{3},\frac{2}{3};\frac{5}{3};1-x\right)-i \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{\left(\frac{1}{2}-\frac{i}{2}\right) (x-1)}{x}\right)+\, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{\left(\frac{1}{2}+\frac{i}{2}\right) (x-1)}{x}\right)\right)}{x^2}","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^6-2 \text{$\#$1}^3+2\&,\frac{\log \left(\sqrt[3]{x^3-x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]-\log \left(\sqrt[3]{x^3-x^2}-x\right)+\frac{1}{2} \log \left(x^2+\sqrt[3]{x^3-x^2} x+\left(x^3-x^2\right)^{2/3}\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-x^2}+x}\right)",1,"((3/8 + (3*I)/8)*((-1 + x)*x^2)^(2/3)*((2 - 2*I)*x^(2/3)*Hypergeometric2F1[2/3, 2/3, 5/3, 1 - x] - I*Hypergeometric2F1[2/3, 1, 5/3, ((1/2 - I/2)*(-1 + x))/x] + Hypergeometric2F1[2/3, 1, 5/3, ((1/2 + I/2)*(-1 + x))/x]))/x^2","C",1
1976,1,68,140,0.045862,"\int \frac{x}{\left(b+a x^2\right) \sqrt{-b x+a x^3}} \, dx","Integrate[x/((b + a*x^2)*Sqrt[-(b*x) + a*x^3]),x]","\frac{2 x^2 \sqrt{\frac{b-a x^2}{b}} F_1\left(\frac{3}{4};\frac{1}{2},1;\frac{7}{4};\frac{a x^2}{b},-\frac{a x^2}{b}\right)}{3 b \sqrt{a x^3-b x}}","\frac{\tanh ^{-1}\left(\frac{\frac{a^{3/4} x^2}{2 \sqrt[4]{b}}-\frac{b^{3/4}}{2 \sqrt[4]{a}}+\sqrt[4]{a} \sqrt[4]{b} x}{\sqrt{a x^3-b x}}\right)}{4 a^{3/4} b^{3/4}}-\frac{\tan ^{-1}\left(\frac{2 \sqrt[4]{a} \sqrt[4]{b} \sqrt{a x^3-b x}}{-2 \sqrt{a} \sqrt{b} x+a x^2-b}\right)}{4 a^{3/4} b^{3/4}}",1,"(2*x^2*Sqrt[(b - a*x^2)/b]*AppellF1[3/4, 1/2, 1, 7/4, (a*x^2)/b, -((a*x^2)/b)])/(3*b*Sqrt[-(b*x) + a*x^3])","C",0
1977,1,62,140,0.0475127,"\int \frac{-b+a x^2}{\left(b+a x^2\right) \sqrt{-b x+a x^3}} \, dx","Integrate[(-b + a*x^2)/((b + a*x^2)*Sqrt[-(b*x) + a*x^3]),x]","\frac{2 \sqrt{a x^3-b x} F_1\left(\frac{1}{4};-\frac{1}{2},1;\frac{5}{4};\frac{a x^2}{b},-\frac{a x^2}{b}\right)}{b \sqrt{1-\frac{a x^2}{b}}}","-\frac{\tanh ^{-1}\left(\frac{\frac{a^{3/4} x^2}{2 \sqrt[4]{b}}-\frac{b^{3/4}}{2 \sqrt[4]{a}}+\sqrt[4]{a} \sqrt[4]{b} x}{\sqrt{a x^3-b x}}\right)}{2 \sqrt[4]{a} \sqrt[4]{b}}-\frac{\tan ^{-1}\left(\frac{2 \sqrt[4]{a} \sqrt[4]{b} \sqrt{a x^3-b x}}{-2 \sqrt{a} \sqrt{b} x+a x^2-b}\right)}{2 \sqrt[4]{a} \sqrt[4]{b}}",1,"(2*Sqrt[-(b*x) + a*x^3]*AppellF1[1/4, -1/2, 1, 5/4, (a*x^2)/b, -((a*x^2)/b)])/(b*Sqrt[1 - (a*x^2)/b])","C",0
1978,1,121,140,1.0261106,"\int \frac{\sqrt{-b x+a x^3}}{-b^2+a^2 x^4} \, dx","Integrate[Sqrt[-(b*x) + a*x^3]/(-b^2 + a^2*x^4),x]","\frac{\sqrt{-\frac{\sqrt{a} x}{\sqrt{b}}} \sqrt{1-\frac{a x^2}{b}} \sqrt{a x^3-b x} \left(\Pi \left(i;\left.i \sinh ^{-1}\left(\sqrt{-\frac{\sqrt{a} x}{\sqrt{b}}}\right)\right|-1\right)-\Pi \left(-i;\left.i \sinh ^{-1}\left(\sqrt{-\frac{\sqrt{a} x}{\sqrt{b}}}\right)\right|-1\right)\right)}{a x \left(a x^2-b\right)}","\frac{\tanh ^{-1}\left(\frac{\frac{a^{3/4} x^2}{2 \sqrt[4]{b}}-\frac{b^{3/4}}{2 \sqrt[4]{a}}+\sqrt[4]{a} \sqrt[4]{b} x}{\sqrt{a x^3-b x}}\right)}{4 a^{3/4} b^{3/4}}-\frac{\tan ^{-1}\left(\frac{2 \sqrt[4]{a} \sqrt[4]{b} \sqrt{a x^3-b x}}{-2 \sqrt{a} \sqrt{b} x+a x^2-b}\right)}{4 a^{3/4} b^{3/4}}",1,"(Sqrt[-((Sqrt[a]*x)/Sqrt[b])]*Sqrt[1 - (a*x^2)/b]*Sqrt[-(b*x) + a*x^3]*(-EllipticPi[-I, I*ArcSinh[Sqrt[-((Sqrt[a]*x)/Sqrt[b])]], -1] + EllipticPi[I, I*ArcSinh[Sqrt[-((Sqrt[a]*x)/Sqrt[b])]], -1]))/(a*x*(-b + a*x^2))","C",1
1979,0,0,140,0.3336664,"\int \frac{\left(1+x^5\right)^{2/3} \left(-3+2 x^5\right) \left(2+x^3+2 x^5\right)}{x^6 \left(2-x^3+2 x^5\right)} \, dx","Integrate[((1 + x^5)^(2/3)*(-3 + 2*x^5)*(2 + x^3 + 2*x^5))/(x^6*(2 - x^3 + 2*x^5)),x]","\int \frac{\left(1+x^5\right)^{2/3} \left(-3+2 x^5\right) \left(2+x^3+2 x^5\right)}{x^6 \left(2-x^3+2 x^5\right)} \, dx","\frac{\log \left(\sqrt[3]{2} \sqrt[3]{x^5+1}-x\right)}{2^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{2} \sqrt[3]{x^5+1}+x}\right)}{2^{2/3}}+\frac{3 \left(x^5+1\right)^{2/3} \left(2 x^5+5 x^3+2\right)}{10 x^5}-\frac{\log \left(\sqrt[3]{2} \sqrt[3]{x^5+1} x+2^{2/3} \left(x^5+1\right)^{2/3}+x^2\right)}{2\ 2^{2/3}}",1,"Integrate[((1 + x^5)^(2/3)*(-3 + 2*x^5)*(2 + x^3 + 2*x^5))/(x^6*(2 - x^3 + 2*x^5)), x]","F",-1
1980,0,0,140,0.6011358,"\int \frac{b+a x^6}{\left(-b+a x^6\right) \sqrt[3]{-b+a^3 x^3+a x^6}} \, dx","Integrate[(b + a*x^6)/((-b + a*x^6)*(-b + a^3*x^3 + a*x^6)^(1/3)),x]","\int \frac{b+a x^6}{\left(-b+a x^6\right) \sqrt[3]{-b+a^3 x^3+a x^6}} \, dx","\frac{\log \left(\sqrt[3]{a^3 x^3+a x^6-b}-a x\right)}{3 a}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} a x}{2 \sqrt[3]{a^3 x^3+a x^6-b}+a x}\right)}{\sqrt{3} a}-\frac{\log \left(a x \sqrt[3]{a^3 x^3+a x^6-b}+\left(a^3 x^3+a x^6-b\right)^{2/3}+a^2 x^2\right)}{6 a}",1,"Integrate[(b + a*x^6)/((-b + a*x^6)*(-b + a^3*x^3 + a*x^6)^(1/3)), x]","F",-1
1981,1,687,140,3.1559921,"\int \frac{\left(1+x^2\right) \left(1+x^8\right) \sqrt{1+x^2+x^4+x^6+x^8}}{x^7 \left(-1+x^2\right)} \, dx","Integrate[((1 + x^2)*(1 + x^8)*Sqrt[1 + x^2 + x^4 + x^6 + x^8])/(x^7*(-1 + x^2)),x]","\frac{\frac{15 (-1)^{3/5} \sqrt{-\frac{\sqrt[5]{-1} \left(\sqrt[5]{-1}-1\right) \left((-1)^{4/5}-x^2\right) \left(x^2+\sqrt[5]{-1}\right)}{\left(1-\sqrt[5]{-1}+(-1)^{2/5}\right)^2 \left((-1)^{2/5}-x^2\right)^2}} \sqrt{\frac{x^2+(-1)^{4/5}+(-1)^{2/5}-\sqrt[5]{-1}+1}{\left(\sqrt[5]{-1}-1\right) \left((-1)^{2/5}-x^2\right)}} \left((-1)^{2/5}-x^2\right)^2 \left(\left(45-32 \sqrt[5]{-1}+38 (-1)^{2/5}-32 (-1)^{3/5}+45 (-1)^{4/5}\right) F\left(\sin ^{-1}\left(\sqrt{-\frac{\sqrt[5]{-1} \left(-1+\sqrt[5]{-1}\right) \left(x^2+\sqrt[5]{-1}\right)}{\left(1-\sqrt[5]{-1}+(-1)^{2/5}\right) \left((-1)^{2/5}-x^2\right)}}\right)|\frac{1-\sqrt[5]{-1}+(-1)^{2/5}}{\left(-1+\sqrt[5]{-1}\right)^2}\right)+13 \left(1-\sqrt[5]{-1}+2 (-1)^{3/5}\right) \Pi \left(\frac{-1+\sqrt[5]{-1}-(-1)^{2/5}}{-1+\sqrt[5]{-1}};\sin ^{-1}\left(\sqrt{-\frac{\sqrt[5]{-1} \left(-1+\sqrt[5]{-1}\right) \left(x^2+\sqrt[5]{-1}\right)}{\left(1-\sqrt[5]{-1}+(-1)^{2/5}\right) \left((-1)^{2/5}-x^2\right)}}\right)|\frac{1-\sqrt[5]{-1}+(-1)^{2/5}}{\left(-1+\sqrt[5]{-1}\right)^2}\right)+\sqrt[5]{-1} \left(13 \left(2-(-1)^{2/5}+(-1)^{3/5}\right) \Pi \left(\frac{-1+\sqrt[5]{-1}-(-1)^{4/5}}{-1+\sqrt[5]{-1}};\sin ^{-1}\left(\sqrt{-\frac{\sqrt[5]{-1} \left(-1+\sqrt[5]{-1}\right) \left(x^2+\sqrt[5]{-1}\right)}{\left(1-\sqrt[5]{-1}+(-1)^{2/5}\right) \left((-1)^{2/5}-x^2\right)}}\right)|\frac{1-\sqrt[5]{-1}+(-1)^{2/5}}{\left(-1+\sqrt[5]{-1}\right)^2}\right)-64 \left(1-\sqrt[5]{-1}+(-1)^{2/5}\right) \Pi \left(1-\sqrt[5]{-1}+(-1)^{4/5};\sin ^{-1}\left(\sqrt{-\frac{\sqrt[5]{-1} \left(-1+\sqrt[5]{-1}\right) \left(x^2+\sqrt[5]{-1}\right)}{\left(1-\sqrt[5]{-1}+(-1)^{2/5}\right) \left((-1)^{2/5}-x^2\right)}}\right)|\frac{1-\sqrt[5]{-1}+(-1)^{2/5}}{\left(-1+\sqrt[5]{-1}\right)^2}\right)\right)\right)}{\left((-1)^{2/5}-1\right)^2}+\frac{\left(x^8+x^6+x^4+x^2+1\right) \left(8 x^8+26 x^6+65 x^4+26 x^2+8\right)}{x^6}}{48 \sqrt{x^8+x^6+x^4+x^2+1}}","\frac{\sqrt{x^8+x^6+x^4+x^2+1} \left(8 x^8+26 x^6+65 x^4+26 x^2+8\right)}{48 x^6}-\frac{65}{32} \log \left(-2 x^4-x^2+2 \sqrt{x^8+x^6+x^4+x^2+1}-2\right)+2 \sqrt{5} \tanh ^{-1}\left(\frac{\sqrt{5} x^2}{x^4-2 x^2-\sqrt{x^8+x^6+x^4+x^2+1}+1}\right)+\frac{65 \log (x)}{16}",1,"(((1 + x^2 + x^4 + x^6 + x^8)*(8 + 26*x^2 + 65*x^4 + 26*x^6 + 8*x^8))/x^6 + (15*(-1)^(3/5)*((-1)^(2/5) - x^2)^2*Sqrt[-(((-1)^(1/5)*(-1 + (-1)^(1/5))*((-1)^(4/5) - x^2)*((-1)^(1/5) + x^2))/((1 - (-1)^(1/5) + (-1)^(2/5))^2*((-1)^(2/5) - x^2)^2))]*Sqrt[(1 - (-1)^(1/5) + (-1)^(2/5) + (-1)^(4/5) + x^2)/((-1 + (-1)^(1/5))*((-1)^(2/5) - x^2))]*((45 - 32*(-1)^(1/5) + 38*(-1)^(2/5) - 32*(-1)^(3/5) + 45*(-1)^(4/5))*EllipticF[ArcSin[Sqrt[-(((-1)^(1/5)*(-1 + (-1)^(1/5))*((-1)^(1/5) + x^2))/((1 - (-1)^(1/5) + (-1)^(2/5))*((-1)^(2/5) - x^2)))]], (1 - (-1)^(1/5) + (-1)^(2/5))/(-1 + (-1)^(1/5))^2] + 13*(1 - (-1)^(1/5) + 2*(-1)^(3/5))*EllipticPi[(-1 + (-1)^(1/5) - (-1)^(2/5))/(-1 + (-1)^(1/5)), ArcSin[Sqrt[-(((-1)^(1/5)*(-1 + (-1)^(1/5))*((-1)^(1/5) + x^2))/((1 - (-1)^(1/5) + (-1)^(2/5))*((-1)^(2/5) - x^2)))]], (1 - (-1)^(1/5) + (-1)^(2/5))/(-1 + (-1)^(1/5))^2] + (-1)^(1/5)*(13*(2 - (-1)^(2/5) + (-1)^(3/5))*EllipticPi[(-1 + (-1)^(1/5) - (-1)^(4/5))/(-1 + (-1)^(1/5)), ArcSin[Sqrt[-(((-1)^(1/5)*(-1 + (-1)^(1/5))*((-1)^(1/5) + x^2))/((1 - (-1)^(1/5) + (-1)^(2/5))*((-1)^(2/5) - x^2)))]], (1 - (-1)^(1/5) + (-1)^(2/5))/(-1 + (-1)^(1/5))^2] - 64*(1 - (-1)^(1/5) + (-1)^(2/5))*EllipticPi[1 - (-1)^(1/5) + (-1)^(4/5), ArcSin[Sqrt[-(((-1)^(1/5)*(-1 + (-1)^(1/5))*((-1)^(1/5) + x^2))/((1 - (-1)^(1/5) + (-1)^(2/5))*((-1)^(2/5) - x^2)))]], (1 - (-1)^(1/5) + (-1)^(2/5))/(-1 + (-1)^(1/5))^2])))/(-1 + (-1)^(2/5))^2)/(48*Sqrt[1 + x^2 + x^4 + x^6 + x^8])","C",0
1982,0,0,140,1.9860945,"\int \frac{b+a x^8}{\sqrt[4]{-b x^2+a x^4} \left(-b+a x^8\right)} \, dx","Integrate[(b + a*x^8)/((-(b*x^2) + a*x^4)^(1/4)*(-b + a*x^8)),x]","\int \frac{b+a x^8}{\sqrt[4]{-b x^2+a x^4} \left(-b+a x^8\right)} \, dx","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^{16}-4 \text{$\#$1}^{12} a+6 \text{$\#$1}^8 a^2-4 \text{$\#$1}^4 a^3+a^4-a b^3\&,\frac{\log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)}{\sqrt[4]{a}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)}{\sqrt[4]{a}}",1,"Integrate[(b + a*x^8)/((-(b*x^2) + a*x^4)^(1/4)*(-b + a*x^8)), x]","F",-1
1983,0,0,140,0.7024075,"\int \frac{b+a x^8}{\sqrt[4]{-b x^2+a x^4} \left(-b+a x^8\right)} \, dx","Integrate[(b + a*x^8)/((-(b*x^2) + a*x^4)^(1/4)*(-b + a*x^8)),x]","\int \frac{b+a x^8}{\sqrt[4]{-b x^2+a x^4} \left(-b+a x^8\right)} \, dx","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^{16}-4 \text{$\#$1}^{12} a+6 \text{$\#$1}^8 a^2-4 \text{$\#$1}^4 a^3+a^4-a b^3\&,\frac{\log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)}{\sqrt[4]{a}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)}{\sqrt[4]{a}}",1,"Integrate[(b + a*x^8)/((-(b*x^2) + a*x^4)^(1/4)*(-b + a*x^8)), x]","F",-1
1984,1,140,140,0.2774789,"\int \frac{\left(-1+x^4\right) \sqrt{x+\sqrt{1+x^2}}}{1+x^4} \, dx","Integrate[((-1 + x^4)*Sqrt[x + Sqrt[1 + x^2]])/(1 + x^4),x]","-2 \text{RootSum}\left[\text{$\#$1}^{16}-4 \text{$\#$1}^{12}+22 \text{$\#$1}^8-4 \text{$\#$1}^4+1\&,\frac{\text{$\#$1}^7 \log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)+\text{$\#$1}^3 \log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)}{\text{$\#$1}^{12}-3 \text{$\#$1}^8+11 \text{$\#$1}^4-1}\&\right]+\frac{1}{3} \left(\sqrt{x^2+1}+x\right)^{3/2}-\frac{1}{\sqrt{\sqrt{x^2+1}+x}}","-2 \text{RootSum}\left[\text{$\#$1}^{16}-4 \text{$\#$1}^{12}+22 \text{$\#$1}^8-4 \text{$\#$1}^4+1\&,\frac{\text{$\#$1}^7 \log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)+\text{$\#$1}^3 \log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)}{\text{$\#$1}^{12}-3 \text{$\#$1}^8+11 \text{$\#$1}^4-1}\&\right]+\frac{1}{3} \left(\sqrt{x^2+1}+x\right)^{3/2}-\frac{1}{\sqrt{\sqrt{x^2+1}+x}}",1,"-(1/Sqrt[x + Sqrt[1 + x^2]]) + (x + Sqrt[1 + x^2])^(3/2)/3 - 2*RootSum[1 - 4*#1^4 + 22*#1^8 - 4*#1^12 + #1^16 & , (Log[Sqrt[x + Sqrt[1 + x^2]] - #1]*#1^3 + Log[Sqrt[x + Sqrt[1 + x^2]] - #1]*#1^7)/(-1 + 11*#1^4 - 3*#1^8 + #1^12) & ]","A",1
1985,1,140,140,0.0962481,"\int \frac{\left(-1+x^4\right) \sqrt{x+\sqrt{1+x^2}}}{1+x^4} \, dx","Integrate[((-1 + x^4)*Sqrt[x + Sqrt[1 + x^2]])/(1 + x^4),x]","-2 \text{RootSum}\left[\text{$\#$1}^{16}-4 \text{$\#$1}^{12}+22 \text{$\#$1}^8-4 \text{$\#$1}^4+1\&,\frac{\text{$\#$1}^7 \log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)+\text{$\#$1}^3 \log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)}{\text{$\#$1}^{12}-3 \text{$\#$1}^8+11 \text{$\#$1}^4-1}\&\right]+\frac{1}{3} \left(\sqrt{x^2+1}+x\right)^{3/2}-\frac{1}{\sqrt{\sqrt{x^2+1}+x}}","-2 \text{RootSum}\left[\text{$\#$1}^{16}-4 \text{$\#$1}^{12}+22 \text{$\#$1}^8-4 \text{$\#$1}^4+1\&,\frac{\text{$\#$1}^7 \log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)+\text{$\#$1}^3 \log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)}{\text{$\#$1}^{12}-3 \text{$\#$1}^8+11 \text{$\#$1}^4-1}\&\right]+\frac{1}{3} \left(\sqrt{x^2+1}+x\right)^{3/2}-\frac{1}{\sqrt{\sqrt{x^2+1}+x}}",1,"-(1/Sqrt[x + Sqrt[1 + x^2]]) + (x + Sqrt[1 + x^2])^(3/2)/3 - 2*RootSum[1 - 4*#1^4 + 22*#1^8 - 4*#1^12 + #1^16 & , (Log[Sqrt[x + Sqrt[1 + x^2]] - #1]*#1^3 + Log[Sqrt[x + Sqrt[1 + x^2]] - #1]*#1^7)/(-1 + 11*#1^4 - 3*#1^8 + #1^12) & ]","A",1
1986,1,139,140,0.497529,"\int \frac{x^2 \sqrt{x+x^2}}{\sqrt{x^2+x \sqrt{x+x^2}}} \, dx","Integrate[(x^2*Sqrt[x + x^2])/Sqrt[x^2 + x*Sqrt[x + x^2]],x]","\frac{\left(x+\sqrt{x (x+1)}\right)^3 \sqrt{x \left(x+\sqrt{x (x+1)}\right)} \left(x+\sqrt{x (x+1)}+1\right) \left(28 x \left(32 x^2+\left(32 \sqrt{x (x+1)}+46\right) x+30 \sqrt{x (x+1)}+11\right)-25 \, _2F_1\left(-\frac{7}{2},2;-\frac{5}{2};1+\frac{1}{2 \left(x+\sqrt{x (x+1)}\right)}\right)\right)}{672 \sqrt{x (x+1)} \left(2 x+2 \sqrt{x (x+1)}+1\right)^4}","\frac{\sqrt{x^2+x} \sqrt{x \left(\sqrt{x^2+x}+x\right)} \left(-3072 x^3-640 x^2+840 x-1575\right)}{10752 x}+\sqrt{x \left(\sqrt{x^2+x}+x\right)} \left(\frac{75 \sqrt{\sqrt{x^2+x}-x} \tanh ^{-1}\left(\sqrt{2} \sqrt{\sqrt{x^2+x}-x}\right)}{512 \sqrt{2} x}+\frac{3072 x^3+3968 x^2-120 x+525}{10752}\right)",1,"((x + Sqrt[x*(1 + x)])^3*Sqrt[x*(x + Sqrt[x*(1 + x)])]*(1 + x + Sqrt[x*(1 + x)])*(28*x*(11 + 32*x^2 + 30*Sqrt[x*(1 + x)] + x*(46 + 32*Sqrt[x*(1 + x)])) - 25*Hypergeometric2F1[-7/2, 2, -5/2, 1 + 1/(2*(x + Sqrt[x*(1 + x)]))]))/(672*Sqrt[x*(1 + x)]*(1 + 2*x + 2*Sqrt[x*(1 + x)])^4)","C",1
1987,1,135,140,0.3277452,"\int \frac{1}{\left(d+c x^2\right) \sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Integrate[1/((d + c*x^2)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]),x]","-\frac{1}{2} a \text{RootSum}\left[\text{$\#$1}^8 b^4 c+4 \text{$\#$1}^4 a^2 d-2 \text{$\#$1}^4 b^2 c+c\&,\frac{\text{$\#$1}^4 b^2 \log \left(\frac{1}{\sqrt{\sqrt{a^2 x^2+b^2}+a x}}-\text{$\#$1}\right)+\log \left(\frac{1}{\sqrt{\sqrt{a^2 x^2+b^2}+a x}}-\text{$\#$1}\right)}{\text{$\#$1}^5 b^4 c+2 \text{$\#$1} a^2 d-\text{$\#$1} b^2 c}\&\right]","\frac{1}{2} a \text{RootSum}\left[\text{$\#$1}^8 c+4 \text{$\#$1}^4 a^2 d-2 \text{$\#$1}^4 b^2 c+b^4 c\&,\frac{\text{$\#$1}^4 \left(-\log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)\right)-b^2 \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)}{\text{$\#$1}^7 (-c)-2 \text{$\#$1}^3 a^2 d+\text{$\#$1}^3 b^2 c}\&\right]",1,"-1/2*(a*RootSum[c - 2*b^2*c*#1^4 + 4*a^2*d*#1^4 + b^4*c*#1^8 & , (Log[1/Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] - #1] + b^2*Log[1/Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] - #1]*#1^4)/(-(b^2*c*#1) + 2*a^2*d*#1 + b^4*c*#1^5) & ])","A",1
1988,1,135,140,0.1093204,"\int \frac{1}{\left(d+c x^2\right) \sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Integrate[1/((d + c*x^2)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]),x]","-\frac{1}{2} a \text{RootSum}\left[\text{$\#$1}^8 b^4 c+4 \text{$\#$1}^4 a^2 d-2 \text{$\#$1}^4 b^2 c+c\&,\frac{\text{$\#$1}^4 b^2 \log \left(\frac{1}{\sqrt{\sqrt{a^2 x^2+b^2}+a x}}-\text{$\#$1}\right)+\log \left(\frac{1}{\sqrt{\sqrt{a^2 x^2+b^2}+a x}}-\text{$\#$1}\right)}{\text{$\#$1}^5 b^4 c+2 \text{$\#$1} a^2 d-\text{$\#$1} b^2 c}\&\right]","\frac{1}{2} a \text{RootSum}\left[\text{$\#$1}^8 c+4 \text{$\#$1}^4 a^2 d-2 \text{$\#$1}^4 b^2 c+b^4 c\&,\frac{\text{$\#$1}^4 \left(-\log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)\right)-b^2 \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)}{\text{$\#$1}^7 (-c)-2 \text{$\#$1}^3 a^2 d+\text{$\#$1}^3 b^2 c}\&\right]",1,"-1/2*(a*RootSum[c - 2*b^2*c*#1^4 + 4*a^2*d*#1^4 + b^4*c*#1^8 & , (Log[1/Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] - #1] + b^2*Log[1/Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] - #1]*#1^4)/(-(b^2*c*#1) + 2*a^2*d*#1 + b^4*c*#1^5) & ])","A",1
1989,1,138,140,0.3169632,"\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right) \sqrt{1+x^2}} \, dx","Integrate[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x^2)*Sqrt[1 + x^2]),x]","\frac{1}{2} \left(\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^4-2 \text{$\#$1}^2+2}\&\right]-\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^3-2 \text{$\#$1}}\&\right]\right)","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^4-2 \text{$\#$1}^2+2}\&\right]-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^3-2 \text{$\#$1}}\&\right]",1,"(-RootSum[-2 + 4*#1^4 - 4*#1^6 + #1^8 & , Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]/(-2*#1 + #1^3) & ] + RootSum[2 - 8*#1^2 + 8*#1^4 - 4*#1^6 + #1^8 & , (Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1)/(2 - 2*#1^2 + #1^4) & ])/2","A",1
1990,1,138,140,0.1013948,"\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right) \sqrt{1+x^2}} \, dx","Integrate[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x^2)*Sqrt[1 + x^2]),x]","\frac{1}{2} \left(\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^4-2 \text{$\#$1}^2+2}\&\right]-\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^3-2 \text{$\#$1}}\&\right]\right)","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^4-2 \text{$\#$1}^2+2}\&\right]-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^3-2 \text{$\#$1}}\&\right]",1,"(-RootSum[-2 + 4*#1^4 - 4*#1^6 + #1^8 & , Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]/(-2*#1 + #1^3) & ] + RootSum[2 - 8*#1^2 + 8*#1^4 - 4*#1^6 + #1^8 & , (Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1)/(2 - 2*#1^2 + #1^4) & ])/2","A",1
1991,-1,0,140,180.00184,"\int \frac{\sqrt{b+a^2 x^2}}{x^2-\sqrt[3]{a x-\sqrt{b+a^2 x^2}}} \, dx","Integrate[Sqrt[b + a^2*x^2]/(x^2 - (a*x - Sqrt[b + a^2*x^2])^(1/3)),x]","\text{\$Aborted}","3 a \text{RootSum}\left[\text{$\#$1}^{12}-4 \text{$\#$1}^7 a^2-2 \text{$\#$1}^6 b+b^2\&,\frac{\text{$\#$1} a^2 \log \left(\sqrt[3]{a x-\sqrt{a^2 x^2+b}}-\text{$\#$1}\right)+b \log \left(\sqrt[3]{a x-\sqrt{a^2 x^2+b}}-\text{$\#$1}\right)}{-3 \text{$\#$1}^6+7 \text{$\#$1} a^2+3 b}\&\right]-a \log \left(\sqrt{a^2 x^2+b}-a x\right)",1,"$Aborted","F",-1
1992,-1,0,140,180.0013392,"\int \frac{\sqrt{b+a^2 x^2}}{x^2-\sqrt{a x-\sqrt{b+a^2 x^2}}} \, dx","Integrate[Sqrt[b + a^2*x^2]/(x^2 - Sqrt[a*x - Sqrt[b + a^2*x^2]]),x]","\text{\$Aborted}","2 a \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^5 a^2-2 \text{$\#$1}^4 b+b^2\&,\frac{\text{$\#$1} a^2 \log \left(\sqrt{a x-\sqrt{a^2 x^2+b}}-\text{$\#$1}\right)+b \log \left(\sqrt{a x-\sqrt{a^2 x^2+b}}-\text{$\#$1}\right)}{-2 \text{$\#$1}^4+5 \text{$\#$1} a^2+2 b}\&\right]-a \log \left(\sqrt{a^2 x^2+b}-a x\right)",1,"$Aborted","F",-1
1993,1,129,141,0.0687188,"\int \frac{\sqrt[3]{-6-2 x+x^2}}{-1+x} \, dx","Integrate[(-6 - 2*x + x^2)^(1/3)/(-1 + x),x]","\frac{1}{4} \left(6 \sqrt[3]{x^2-2 x-6}+2 \sqrt{3} \sqrt[3]{7} \tan ^{-1}\left(\frac{7-2\ 7^{2/3} \sqrt[3]{x^2-2 x-6}}{7 \sqrt{3}}\right)-2 \sqrt[3]{7} \log \left(\sqrt[3]{(x-1)^2-7}+\sqrt[3]{7}\right)+\sqrt[3]{7} \log \left(\left((x-1)^2-7\right)^{2/3}-\sqrt[3]{7} \sqrt[3]{(x-1)^2-7}+7^{2/3}\right)\right)","\frac{3}{2} \sqrt[3]{x^2-2 x-6}-\frac{1}{2} \sqrt[3]{7} \log \left(7^{2/3} \sqrt[3]{x^2-2 x-6}+7\right)+\frac{1}{4} \sqrt[3]{7} \log \left(-\sqrt[3]{7} \left(x^2-2 x-6\right)^{2/3}+7^{2/3} \sqrt[3]{x^2-2 x-6}-7\right)+\frac{1}{2} \sqrt{3} \sqrt[3]{7} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{x^2-2 x-6}}{\sqrt{3} \sqrt[3]{7}}\right)",1,"(6*(-6 - 2*x + x^2)^(1/3) + 2*Sqrt[3]*7^(1/3)*ArcTan[(7 - 2*7^(2/3)*(-6 - 2*x + x^2)^(1/3))/(7*Sqrt[3])] - 2*7^(1/3)*Log[7^(1/3) + (-7 + (-1 + x)^2)^(1/3)] + 7^(1/3)*Log[7^(2/3) - 7^(1/3)*(-7 + (-1 + x)^2)^(1/3) + (-7 + (-1 + x)^2)^(2/3)])/4","A",1
1994,1,48,141,0.0203412,"\int \frac{-1+x}{\sqrt[3]{1-x-x^2+x^3}} \, dx","Integrate[(-1 + x)/(1 - x - x^2 + x^3)^(1/3),x]","\frac{3 \left((x-1)^2 (x+1)\right)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{4}{3};\frac{7}{3};\frac{1-x}{2}\right)}{4 \sqrt[3]{2} (x+1)^{2/3}}","\frac{(x-1)^{2/3} \sqrt[3]{x+1} \left(\sqrt[3]{x-1} (x+1)^{2/3}+\frac{2}{3} \log \left(\sqrt[3]{x-1}-\sqrt[3]{x+1}\right)-\frac{1}{3} \log \left((x-1)^{2/3}+\sqrt[3]{x+1} \sqrt[3]{x-1}+(x+1)^{2/3}\right)+\frac{2 \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x+1}}{2 \sqrt[3]{x-1}+\sqrt[3]{x+1}}\right)}{\sqrt{3}}\right)}{\sqrt[3]{(x-1)^2 (x+1)}}",1,"(3*((-1 + x)^2*(1 + x))^(2/3)*Hypergeometric2F1[1/3, 4/3, 7/3, (1 - x)/2])/(4*2^(1/3)*(1 + x)^(2/3))","C",1
1995,1,58,141,0.0192375,"\int \frac{x}{\sqrt[3]{-1-x+x^2+x^3}} \, dx","Integrate[x/(-1 - x + x^2 + x^3)^(1/3),x]","\frac{(x-1) \left(-\sqrt[3]{2} (x+1)^{2/3} \, _2F_1\left(\frac{2}{3},\frac{2}{3};\frac{5}{3};\frac{1-x}{2}\right)+4 x+4\right)}{4 \sqrt[3]{(x-1) (x+1)^2}}","\frac{\sqrt[3]{x-1} (x+1)^{2/3} \left((x-1)^{2/3} \sqrt[3]{x+1}+\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{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x+1}}{2 \sqrt[3]{x-1}+\sqrt[3]{x+1}}\right)}{\sqrt{3}}\right)}{\sqrt[3]{(x-1) (x+1)^2}}",1,"((-1 + x)*(4 + 4*x - 2^(1/3)*(1 + x)^(2/3)*Hypergeometric2F1[2/3, 2/3, 5/3, (1 - x)/2]))/(4*((-1 + x)*(1 + x)^2)^(1/3))","C",1
1996,0,0,141,0.3221795,"\int \frac{(3+2 x) \left(1+x+3 x^3\right)^{2/3}}{x^3 \left(1+x+x^3\right)} \, dx","Integrate[((3 + 2*x)*(1 + x + 3*x^3)^(2/3))/(x^3*(1 + x + x^3)),x]","\int \frac{(3+2 x) \left(1+x+3 x^3\right)^{2/3}}{x^3 \left(1+x+x^3\right)} \, dx","-2^{2/3} \log \left(2^{2/3} \sqrt[3]{3 x^3+x+1}-2 x\right)+2^{2/3} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{3 x^3+x+1}+x}\right)-\frac{3 \left(3 x^3+x+1\right)^{2/3}}{2 x^2}+\frac{\log \left(2^{2/3} \sqrt[3]{3 x^3+x+1} x+\sqrt[3]{2} \left(3 x^3+x+1\right)^{2/3}+2 x^2\right)}{\sqrt[3]{2}}",1,"Integrate[((3 + 2*x)*(1 + x + 3*x^3)^(2/3))/(x^3*(1 + x + x^3)), x]","F",-1
1997,0,0,141,4.2616578,"\int \frac{x^2 \left(-3 a b^3+2 b^2 (3 a+b) x-3 b (a+b) x^2+x^4\right)}{\left(x (-a+x) (-b+x)^3\right)^{3/4} \left(a b^3-b^2 (3 a+b) x+3 b (a+b) x^2-(a+3 b+d) x^3+x^4\right)} \, dx","Integrate[(x^2*(-3*a*b^3 + 2*b^2*(3*a + b)*x - 3*b*(a + b)*x^2 + x^4))/((x*(-a + x)*(-b + x)^3)^(3/4)*(a*b^3 - b^2*(3*a + b)*x + 3*b*(a + b)*x^2 - (a + 3*b + d)*x^3 + x^4)),x]","\int \frac{x^2 \left(-3 a b^3+2 b^2 (3 a+b) x-3 b (a+b) x^2+x^4\right)}{\left(x (-a+x) (-b+x)^3\right)^{3/4} \left(a b^3-b^2 (3 a+b) x+3 b (a+b) x^2-(a+3 b+d) x^3+x^4\right)} \, dx","\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{a b^3 x+x^3 \left(3 a b+3 b^2\right)+x^2 \left(-3 a b^2-b^3\right)+x^4 (-a-3 b)+x^5}}\right)}{d^{3/4}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{a b^3 x+x^3 \left(3 a b+3 b^2\right)+x^2 \left(-3 a b^2-b^3\right)+x^4 (-a-3 b)+x^5}}\right)}{d^{3/4}}",1,"Integrate[(x^2*(-3*a*b^3 + 2*b^2*(3*a + b)*x - 3*b*(a + b)*x^2 + x^4))/((x*(-a + x)*(-b + x)^3)^(3/4)*(a*b^3 - b^2*(3*a + b)*x + 3*b*(a + b)*x^2 - (a + 3*b + d)*x^3 + x^4)), x]","F",-1
1998,1,67,141,0.0647155,"\int \frac{x^6}{\left(-b+a x^4\right)^{3/4} \left(b+a x^4\right)} \, dx","Integrate[x^6/((-b + a*x^4)^(3/4)*(b + a*x^4)),x]","\frac{x^7 \left(\frac{b-a x^4}{b}\right)^{3/4} F_1\left(\frac{7}{4};\frac{3}{4},1;\frac{11}{4};\frac{a x^4}{b},-\frac{a x^4}{b}\right)}{7 b \left(a x^4-b\right)^{3/4}}","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{2 a^{7/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{2\ 2^{3/4} a^{7/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{2 a^{7/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{2\ 2^{3/4} a^{7/4}}",1,"(x^7*((b - a*x^4)/b)^(3/4)*AppellF1[7/4, 3/4, 1, 11/4, (a*x^4)/b, -((a*x^4)/b)])/(7*b*(-b + a*x^4)^(3/4))","C",0
1999,1,161,141,0.1816897,"\int \frac{-b+2 a x^2}{\left(-b+a x^2\right) \sqrt[4]{b x^2+a x^4}} \, dx","Integrate[(-b + 2*a*x^2)/((-b + a*x^2)*(b*x^2 + a*x^4)^(1/4)),x]","\frac{\sqrt{x} \sqrt[4]{a x^2+b} \left(4 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)-2^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)+4 \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)-2^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)\right)}{2 \sqrt[4]{a} \sqrt[4]{x^2 \left(a x^2+b\right)}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{\sqrt[4]{a}}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{\sqrt[4]{2} \sqrt[4]{a}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{\sqrt[4]{a}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{\sqrt[4]{2} \sqrt[4]{a}}",1,"(Sqrt[x]*(b + a*x^2)^(1/4)*(4*ArcTan[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)] - 2^(3/4)*ArcTan[(2^(1/4)*a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)] + 4*ArcTanh[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)] - 2^(3/4)*ArcTanh[(2^(1/4)*a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)]))/(2*a^(1/4)*(x^2*(b + a*x^2))^(1/4))","A",1
2000,1,128,141,0.1193865,"\int \frac{-3 b+2 a x^4}{\left(-2 b+a x^4\right) \sqrt[4]{b+a x^4}} \, dx","Integrate[(-3*b + 2*a*x^4)/((-2*b + a*x^4)*(b + a*x^4)^(1/4)),x]","\frac{12 \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)-\sqrt[4]{2} 3^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{3}{2}} \sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)+12 \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)-\sqrt[4]{2} 3^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{3}{2}} \sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{12 \sqrt[4]{a}}","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{a}}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{\frac{3}{2}} \sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{2\ 2^{3/4} \sqrt[4]{3} \sqrt[4]{a}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{a}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{\frac{3}{2}} \sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{2\ 2^{3/4} \sqrt[4]{3} \sqrt[4]{a}}",1,"(12*ArcTan[(a^(1/4)*x)/(b + a*x^4)^(1/4)] - 2^(1/4)*3^(3/4)*ArcTan[((3/2)^(1/4)*a^(1/4)*x)/(b + a*x^4)^(1/4)] + 12*ArcTanh[(a^(1/4)*x)/(b + a*x^4)^(1/4)] - 2^(1/4)*3^(3/4)*ArcTanh[((3/2)^(1/4)*a^(1/4)*x)/(b + a*x^4)^(1/4)])/(12*a^(1/4))","A",1
2001,1,116,141,0.0855411,"\int \frac{b+a x^4}{\sqrt[4]{-b+a x^4} \left(b+3 a x^4\right)} \, dx","Integrate[(b + a*x^4)/((-b + a*x^4)^(1/4)*(b + 3*a*x^4)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)+\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)+\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)+\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{6 \sqrt[4]{a}}","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{6 \sqrt[4]{a}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{3 \sqrt{2} \sqrt[4]{a}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{6 \sqrt[4]{a}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{3 \sqrt{2} \sqrt[4]{a}}",1,"(ArcTan[(a^(1/4)*x)/(-b + a*x^4)^(1/4)] + Sqrt[2]*ArcTan[(Sqrt[2]*a^(1/4)*x)/(-b + a*x^4)^(1/4)] + ArcTanh[(a^(1/4)*x)/(-b + a*x^4)^(1/4)] + Sqrt[2]*ArcTanh[(Sqrt[2]*a^(1/4)*x)/(-b + a*x^4)^(1/4)])/(6*a^(1/4))","A",1
2002,0,0,141,1.0293941,"\int \frac{\left(2+x^6\right) \left(-1-x^4+x^6\right)}{\sqrt[4]{1-x^4-x^6} \left(-1+x^6\right)^2} \, dx","Integrate[((2 + x^6)*(-1 - x^4 + x^6))/((1 - x^4 - x^6)^(1/4)*(-1 + x^6)^2),x]","\int \frac{\left(2+x^6\right) \left(-1-x^4+x^6\right)}{\sqrt[4]{1-x^4-x^6} \left(-1+x^6\right)^2} \, dx","-\frac{\left(-x^6-x^4+1\right)^{3/4} x}{2 \left(x^6-1\right)}-\frac{5 \tan ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{-x^6-x^4+1}}{\sqrt{-x^6-x^4+1}-x^2}\right)}{4 \sqrt{2}}-\frac{5 \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{-x^6-x^4+1}}{x^2+\sqrt{-x^6-x^4+1}}\right)}{4 \sqrt{2}}",1,"Integrate[((2 + x^6)*(-1 - x^4 + x^6))/((1 - x^4 - x^6)^(1/4)*(-1 + x^6)^2), x]","F",-1
2003,0,0,141,0.7101918,"\int \frac{\left(-2 b+a x^6\right) \left(b-c x^4+a x^6\right)}{x^2 \left(b+a x^6\right)^{3/4} \left(b+c x^4+a x^6\right)} \, dx","Integrate[((-2*b + a*x^6)*(b - c*x^4 + a*x^6))/(x^2*(b + a*x^6)^(3/4)*(b + c*x^4 + a*x^6)),x]","\int \frac{\left(-2 b+a x^6\right) \left(b-c x^4+a x^6\right)}{x^2 \left(b+a x^6\right)^{3/4} \left(b+c x^4+a x^6\right)} \, dx","\sqrt{2} \sqrt[4]{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x \sqrt[4]{a x^6+b}}{\sqrt{a x^6+b}-\sqrt{c} x^2}\right)-\sqrt{2} \sqrt[4]{c} \tanh ^{-1}\left(\frac{\frac{\sqrt{a x^6+b}}{\sqrt{2} \sqrt[4]{c}}+\frac{\sqrt[4]{c} x^2}{\sqrt{2}}}{x \sqrt[4]{a x^6+b}}\right)+\frac{2 \sqrt[4]{a x^6+b}}{x}",1,"Integrate[((-2*b + a*x^6)*(b - c*x^4 + a*x^6))/(x^2*(b + a*x^6)^(3/4)*(b + c*x^4 + a*x^6)), x]","F",-1
2004,1,99,141,0.1415982,"\int \frac{\sqrt[4]{1+2 x^4} \left(-1-x^4+2 x^8\right)}{x^6 \left(2+x^4\right)} \, dx","Integrate[((1 + 2*x^4)^(1/4)*(-1 - x^4 + 2*x^8))/(x^6*(2 + x^4)),x]","\frac{2}{7} x^7 F_1\left(\frac{7}{4};\frac{3}{4},1;\frac{11}{4};-2 x^4,-\frac{x^4}{2}\right)+\frac{5 x^3 \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};-\frac{3 x^4}{x^4+2}\right)}{12 \sqrt[4]{2} \left(x^4+2\right)^{3/4}}+\frac{\sqrt[4]{2 x^4+1} \left(9 x^4+2\right)}{20 x^5}","\frac{9}{8} \sqrt[4]{\frac{3}{2}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{3}{2}} x}{\sqrt[4]{2 x^4+1}}\right)-\sqrt[4]{2} \tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{2 x^4+1}}\right)-\frac{9}{8} \sqrt[4]{\frac{3}{2}} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{3}{2}} x}{\sqrt[4]{2 x^4+1}}\right)+\sqrt[4]{2} \tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{2 x^4+1}}\right)+\frac{\sqrt[4]{2 x^4+1} \left(9 x^4+2\right)}{20 x^5}",1,"((1 + 2*x^4)^(1/4)*(2 + 9*x^4))/(20*x^5) + (2*x^7*AppellF1[7/4, 3/4, 1, 11/4, -2*x^4, -1/2*x^4])/7 + (5*x^3*Hypergeometric2F1[3/4, 3/4, 7/4, (-3*x^4)/(2 + x^4)])/(12*2^(1/4)*(2 + x^4)^(3/4))","C",0
2005,1,671,141,1.5062891,"\int \frac{-b^8+2 a^4 x^4}{\sqrt[4]{-b^8+a^4 x^4} \left(-b^8-c x^4+a^8 x^8\right)} \, dx","Integrate[(-b^8 + 2*a^4*x^4)/((-b^8 + a^4*x^4)^(1/4)*(-b^8 - c*x^4 + a^8*x^8)),x]","a^3 \left(\frac{\left(\sqrt{4 a^8 b^8+c^2}+a^4 b^8-c\right) \tan ^{-1}\left(\frac{a x \sqrt[4]{\sqrt{4 a^8 b^8+c^2}+2 a^4 b^8-c}}{\sqrt[4]{\sqrt{4 a^8 b^8+c^2}-c} \sqrt[4]{a^4 x^4-b^8}}\right)}{\sqrt{4 a^8 b^8+c^2} \left(\sqrt{4 a^8 b^8+c^2}-c\right)^{3/4} \sqrt[4]{\sqrt{4 a^8 b^8+c^2}+2 a^4 b^8-c}}-\frac{\left(\frac{c-a^4 b^8}{\sqrt{4 a^8 b^8+c^2}}+1\right) \tan ^{-1}\left(\frac{a x \sqrt[4]{\sqrt{4 a^8 b^8+c^2}-2 a^4 b^8+c}}{\sqrt[4]{\sqrt{4 a^8 b^8+c^2}+c} \sqrt[4]{a^4 x^4-b^8}}\right)}{\left(\sqrt{4 a^8 b^8+c^2}+c\right)^{3/4} \sqrt[4]{\sqrt{4 a^8 b^8+c^2}-2 a^4 b^8+c}}+\frac{\left(\sqrt{4 a^8 b^8+c^2}+a^4 b^8-c\right) \tanh ^{-1}\left(\frac{a x \sqrt[4]{\sqrt{4 a^8 b^8+c^2}+2 a^4 b^8-c}}{\sqrt[4]{\sqrt{4 a^8 b^8+c^2}-c} \sqrt[4]{a^4 x^4-b^8}}\right)}{\sqrt{4 a^8 b^8+c^2} \left(\sqrt{4 a^8 b^8+c^2}-c\right)^{3/4} \sqrt[4]{\sqrt{4 a^8 b^8+c^2}+2 a^4 b^8-c}}-\frac{\left(\frac{c-a^4 b^8}{\sqrt{4 a^8 b^8+c^2}}+1\right) \tanh ^{-1}\left(\frac{a x \sqrt[4]{\sqrt{4 a^8 b^8+c^2}-2 a^4 b^8+c}}{\sqrt[4]{\sqrt{4 a^8 b^8+c^2}+c} \sqrt[4]{a^4 x^4-b^8}}\right)}{\left(\sqrt{4 a^8 b^8+c^2}+c\right)^{3/4} \sqrt[4]{\sqrt{4 a^8 b^8+c^2}-2 a^4 b^8+c}}\right)","\frac{1}{4} \text{RootSum}\left[-\text{$\#$1}^8+2 \text{$\#$1}^4 a^4+\text{$\#$1}^4 c+a^8 b^8-a^8-a^4 c\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a^4 x^4-b^8}-\text{$\#$1} x\right)-\text{$\#$1}^4 \log (x)+a^4 \log \left(\sqrt[4]{a^4 x^4-b^8}-\text{$\#$1} x\right)+a^4 (-\log (x))}{-2 \text{$\#$1}^5+2 \text{$\#$1} a^4+\text{$\#$1} c}\&\right]",1,"a^3*(((a^4*b^8 - c + Sqrt[4*a^8*b^8 + c^2])*ArcTan[(a*(2*a^4*b^8 - c + Sqrt[4*a^8*b^8 + c^2])^(1/4)*x)/((-c + Sqrt[4*a^8*b^8 + c^2])^(1/4)*(-b^8 + a^4*x^4)^(1/4))])/(Sqrt[4*a^8*b^8 + c^2]*(-c + Sqrt[4*a^8*b^8 + c^2])^(3/4)*(2*a^4*b^8 - c + Sqrt[4*a^8*b^8 + c^2])^(1/4)) - ((1 + (-(a^4*b^8) + c)/Sqrt[4*a^8*b^8 + c^2])*ArcTan[(a*(-2*a^4*b^8 + c + Sqrt[4*a^8*b^8 + c^2])^(1/4)*x)/((c + Sqrt[4*a^8*b^8 + c^2])^(1/4)*(-b^8 + a^4*x^4)^(1/4))])/((c + Sqrt[4*a^8*b^8 + c^2])^(3/4)*(-2*a^4*b^8 + c + Sqrt[4*a^8*b^8 + c^2])^(1/4)) + ((a^4*b^8 - c + Sqrt[4*a^8*b^8 + c^2])*ArcTanh[(a*(2*a^4*b^8 - c + Sqrt[4*a^8*b^8 + c^2])^(1/4)*x)/((-c + Sqrt[4*a^8*b^8 + c^2])^(1/4)*(-b^8 + a^4*x^4)^(1/4))])/(Sqrt[4*a^8*b^8 + c^2]*(-c + Sqrt[4*a^8*b^8 + c^2])^(3/4)*(2*a^4*b^8 - c + Sqrt[4*a^8*b^8 + c^2])^(1/4)) - ((1 + (-(a^4*b^8) + c)/Sqrt[4*a^8*b^8 + c^2])*ArcTanh[(a*(-2*a^4*b^8 + c + Sqrt[4*a^8*b^8 + c^2])^(1/4)*x)/((c + Sqrt[4*a^8*b^8 + c^2])^(1/4)*(-b^8 + a^4*x^4)^(1/4))])/((c + Sqrt[4*a^8*b^8 + c^2])^(3/4)*(-2*a^4*b^8 + c + Sqrt[4*a^8*b^8 + c^2])^(1/4)))","B",1
2006,1,180,141,0.1193545,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[(-1 + x^2)/((1 + x^2)*Sqrt[x + Sqrt[1 + x^2]]),x]","\sqrt{\sqrt{x^2+1}+x}-\frac{1}{3 \left(\sqrt{x^2+1}+x\right)^{3/2}}+\sqrt{2} \log \left(\sqrt{x^2+1}-\sqrt{2} \sqrt{\sqrt{x^2+1}+x}+x+1\right)-\sqrt{2} \log \left(\sqrt{x^2+1}+\sqrt{2} \sqrt{\sqrt{x^2+1}+x}+x+1\right)+2 \sqrt{2} \tan ^{-1}\left(1-\sqrt{2} \sqrt{\sqrt{x^2+1}+x}\right)-2 \sqrt{2} \tan ^{-1}\left(\sqrt{2} \sqrt{\sqrt{x^2+1}+x}+1\right)","\sqrt{\sqrt{x^2+1}+x}-\frac{1}{3 \left(\sqrt{x^2+1}+x\right)^{3/2}}-2 \sqrt{2} \tan ^{-1}\left(\frac{\frac{\sqrt{x^2+1}}{\sqrt{2}}+\frac{x}{\sqrt{2}}-\frac{1}{\sqrt{2}}}{\sqrt{\sqrt{x^2+1}+x}}\right)-2 \sqrt{2} \tanh ^{-1}\left(\frac{\frac{\sqrt{x^2+1}}{\sqrt{2}}+\frac{x}{\sqrt{2}}+\frac{1}{\sqrt{2}}}{\sqrt{\sqrt{x^2+1}+x}}\right)",1,"-1/3*1/(x + Sqrt[1 + x^2])^(3/2) + Sqrt[x + Sqrt[1 + x^2]] + 2*Sqrt[2]*ArcTan[1 - Sqrt[2]*Sqrt[x + Sqrt[1 + x^2]]] - 2*Sqrt[2]*ArcTan[1 + Sqrt[2]*Sqrt[x + Sqrt[1 + x^2]]] + Sqrt[2]*Log[1 + x + Sqrt[1 + x^2] - Sqrt[2]*Sqrt[x + Sqrt[1 + x^2]]] - Sqrt[2]*Log[1 + x + Sqrt[1 + x^2] + Sqrt[2]*Sqrt[x + Sqrt[1 + x^2]]]","A",1
2007,1,103,142,4.2317116,"\int \frac{\left(1+x^2\right) \sqrt[3]{x+2 x^3}}{x^4 \left(-1+x^2\right)} \, dx","Integrate[((1 + x^2)*(x + 2*x^3)^(1/3))/(x^4*(-1 + x^2)),x]","\frac{3 \left(2 x^2+1\right) \sqrt[3]{2 x^3+x} \left(2 \left(6 x^4-7 x^2+1\right) \, _2F_1\left(1,1;\frac{2}{3};\frac{3 x^2}{x^2-1}\right)+27 \left(2 x^4+x^2\right) \, _2F_1\left(2,2;\frac{5}{3};\frac{3 x^2}{x^2-1}\right)-\left(x^2-1\right)^2\right)}{8 x^3 \left(x^2-1\right)^2}","\sqrt[3]{3} \log \left(3^{2/3} \sqrt[3]{2 x^3+x}-3 x\right)+3^{5/6} \tan ^{-1}\left(\frac{3^{5/6} x}{2 \sqrt[3]{2 x^3+x}+\sqrt[3]{3} x}\right)+\frac{3 \sqrt[3]{2 x^3+x} \left(10 x^2+1\right)}{8 x^3}-\frac{1}{2} \sqrt[3]{3} \log \left(3^{2/3} \sqrt[3]{2 x^3+x} x+\sqrt[3]{3} \left(2 x^3+x\right)^{2/3}+3 x^2\right)",1,"(3*(1 + 2*x^2)*(x + 2*x^3)^(1/3)*(-(-1 + x^2)^2 + 2*(1 - 7*x^2 + 6*x^4)*Hypergeometric2F1[1, 1, 2/3, (3*x^2)/(-1 + x^2)] + 27*(x^2 + 2*x^4)*Hypergeometric2F1[2, 2, 5/3, (3*x^2)/(-1 + x^2)]))/(8*x^3*(-1 + x^2)^2)","C",0
2008,1,74,142,0.0648407,"\int \frac{\left(-b+a^3 x^3\right) \sqrt[3]{b+a^3 x^3}}{x^5} \, dx","Integrate[((-b + a^3*x^3)*(b + a^3*x^3)^(1/3))/x^5,x]","\frac{\sqrt[3]{a^3 x^3+b} \left(-\frac{4 a^3 x^3 \, _2F_1\left(-\frac{1}{3},-\frac{1}{3};\frac{2}{3};-\frac{a^3 x^3}{b}\right)}{\sqrt[3]{\frac{a^3 x^3}{b}+1}}+a^3 x^3+b\right)}{4 x^4}","\frac{\left(b-3 a^3 x^3\right) \sqrt[3]{a^3 x^3+b}}{4 x^4}-\frac{1}{3} a^4 \log \left(\sqrt[3]{a^3 x^3+b}-a x\right)-\frac{a^4 \tan ^{-1}\left(\frac{\sqrt{3} a x}{2 \sqrt[3]{a^3 x^3+b}+a x}\right)}{\sqrt{3}}+\frac{1}{6} a^4 \log \left(a x \sqrt[3]{a^3 x^3+b}+\left(a^3 x^3+b\right)^{2/3}+a^2 x^2\right)",1,"((b + a^3*x^3)^(1/3)*(b + a^3*x^3 - (4*a^3*x^3*Hypergeometric2F1[-1/3, -1/3, 2/3, -((a^3*x^3)/b)])/(1 + (a^3*x^3)/b)^(1/3)))/(4*x^4)","C",1
2009,0,0,142,0.2505466,"\int \frac{-3 b+a x^2}{\sqrt[4]{3 b-2 a x^2} \left(3 b-2 a x^2+3 x^4\right)} \, dx","Integrate[(-3*b + a*x^2)/((3*b - 2*a*x^2)^(1/4)*(3*b - 2*a*x^2 + 3*x^4)),x]","\int \frac{-3 b+a x^2}{\sqrt[4]{3 b-2 a x^2} \left(3 b-2 a x^2+3 x^4\right)} \, dx","-\frac{\tan ^{-1}\left(\frac{\frac{\sqrt[4]{3} x^2}{\sqrt{2}}-\frac{\sqrt{3 b-2 a x^2}}{\sqrt{2} \sqrt[4]{3}}}{x \sqrt[4]{3 b-2 a x^2}}\right)}{2 \sqrt{2} \sqrt[4]{3}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{3} x \sqrt[4]{3 b-2 a x^2}}{\sqrt{3 b-2 a x^2}+\sqrt{3} x^2}\right)}{2 \sqrt{2} \sqrt[4]{3}}",1,"Integrate[(-3*b + a*x^2)/((3*b - 2*a*x^2)^(1/4)*(3*b - 2*a*x^2 + 3*x^4)), x]","F",-1
2010,0,0,142,0.8615014,"\int \frac{\left(-4 b+a x^5\right) \left(b-c x^4+a x^5\right)}{x^2 \left(b+a x^5\right)^{3/4} \left(b+c x^4+a x^5\right)} \, dx","Integrate[((-4*b + a*x^5)*(b - c*x^4 + a*x^5))/(x^2*(b + a*x^5)^(3/4)*(b + c*x^4 + a*x^5)),x]","\int \frac{\left(-4 b+a x^5\right) \left(b-c x^4+a x^5\right)}{x^2 \left(b+a x^5\right)^{3/4} \left(b+c x^4+a x^5\right)} \, dx","2 \sqrt{2} \sqrt[4]{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x \sqrt[4]{a x^5+b}}{\sqrt{a x^5+b}-\sqrt{c} x^2}\right)-2 \sqrt{2} \sqrt[4]{c} \tanh ^{-1}\left(\frac{\frac{\sqrt{a x^5+b}}{\sqrt{2} \sqrt[4]{c}}+\frac{\sqrt[4]{c} x^2}{\sqrt{2}}}{x \sqrt[4]{a x^5+b}}\right)+\frac{4 \sqrt[4]{a x^5+b}}{x}",1,"Integrate[((-4*b + a*x^5)*(b - c*x^4 + a*x^5))/(x^2*(b + a*x^5)^(3/4)*(b + c*x^4 + a*x^5)), x]","F",-1
2011,0,0,142,0.3587296,"\int \frac{\left(-1+x^3\right) \left(1+x^6\right)^{2/3} \left(1-x^3+x^6\right)}{x^6 \left(1+x^3\right)} \, dx","Integrate[((-1 + x^3)*(1 + x^6)^(2/3)*(1 - x^3 + x^6))/(x^6*(1 + x^3)),x]","\int \frac{\left(-1+x^3\right) \left(1+x^6\right)^{2/3} \left(1-x^3+x^6\right)}{x^6 \left(1+x^3\right)} \, dx","-2^{2/3} \log \left(2^{2/3} \sqrt[3]{x^6+1}+2 x\right)-2^{2/3} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^6+1}-x}\right)+\frac{\log \left(2^{2/3} \sqrt[3]{x^6+1} x-\sqrt[3]{2} \left(x^6+1\right)^{2/3}-2 x^2\right)}{\sqrt[3]{2}}+\frac{\left(x^6+1\right)^{2/3} \left(2 x^6-15 x^3+2\right)}{10 x^5}",1,"Integrate[((-1 + x^3)*(1 + x^6)^(2/3)*(1 - x^3 + x^6))/(x^6*(1 + x^3)), x]","F",-1
2012,0,0,142,0.5903035,"\int \frac{\left(-b^2+a x^2\right)^2 \sqrt{b+\sqrt{b^2+a x^2}}}{\left(b^2+a x^2\right)^2} \, dx","Integrate[((-b^2 + a*x^2)^2*Sqrt[b + Sqrt[b^2 + a*x^2]])/(b^2 + a*x^2)^2,x]","\int \frac{\left(-b^2+a x^2\right)^2 \sqrt{b+\sqrt{b^2+a x^2}}}{\left(b^2+a x^2\right)^2} \, dx","\frac{x \left(2 a x^2+11 b^2\right)}{3 \sqrt{a x^2+b^2} \sqrt{\sqrt{a x^2+b^2}+b}}-\frac{5 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b} \sqrt{\sqrt{a x^2+b^2}+b}}\right)}{\sqrt{a}}+\frac{2 x \left(2 a b x^2+5 b^3\right)}{3 \left(a x^2+b^2\right) \sqrt{\sqrt{a x^2+b^2}+b}}",1,"Integrate[((-b^2 + a*x^2)^2*Sqrt[b + Sqrt[b^2 + a*x^2]])/(b^2 + a*x^2)^2, x]","F",-1
2013,1,128,143,0.2785065,"\int \frac{\left(2+x^3\right) \left(1+2 x^3\right)^{2/3}}{x^6 \left(-1+x^3\right)} \, dx","Integrate[((2 + x^3)*(1 + 2*x^3)^(2/3))/(x^6*(-1 + x^3)),x]","-3 \sqrt[6]{3} \tan ^{-1}\left(\frac{2 x}{\sqrt[6]{3} \sqrt[3]{x^3+2}}+\frac{1}{\sqrt{3}}\right)+\frac{\left(2 x^3+1\right)^{2/3} \left(23 x^3+4\right)}{10 x^5}+\frac{1}{2} 3^{2/3} \left(2 \log \left(1-\frac{\sqrt[3]{3} x}{\sqrt[3]{x^3+2}}\right)-\log \left(\frac{\sqrt[3]{3} x}{\sqrt[3]{x^3+2}}+\frac{3^{2/3} x^2}{\left(x^3+2\right)^{2/3}}+1\right)\right)","3^{2/3} \log \left(3^{2/3} \sqrt[3]{2 x^3+1}-3 x\right)-3 \sqrt[6]{3} \tan ^{-1}\left(\frac{3^{5/6} x}{2 \sqrt[3]{2 x^3+1}+\sqrt[3]{3} x}\right)+\frac{\left(2 x^3+1\right)^{2/3} \left(23 x^3+4\right)}{10 x^5}-\frac{1}{2} 3^{2/3} \log \left(3^{2/3} \sqrt[3]{2 x^3+1} x+\sqrt[3]{3} \left(2 x^3+1\right)^{2/3}+3 x^2\right)",1,"((1 + 2*x^3)^(2/3)*(4 + 23*x^3))/(10*x^5) - 3*3^(1/6)*ArcTan[1/Sqrt[3] + (2*x)/(3^(1/6)*(2 + x^3)^(1/3))] + (3^(2/3)*(2*Log[1 - (3^(1/3)*x)/(2 + x^3)^(1/3)] - Log[1 + (3^(2/3)*x^2)/(2 + x^3)^(2/3) + (3^(1/3)*x)/(2 + x^3)^(1/3)]))/2","A",0
2014,0,0,143,0.4154523,"\int \frac{\left(-4+x^2\right) \sqrt[4]{2-x^2-2 x^4}}{x^2 \left(-2+x^2\right)} \, dx","Integrate[((-4 + x^2)*(2 - x^2 - 2*x^4)^(1/4))/(x^2*(-2 + x^2)),x]","\int \frac{\left(-4+x^2\right) \sqrt[4]{2-x^2-2 x^4}}{x^2 \left(-2+x^2\right)} \, dx","-\frac{2 \sqrt[4]{-2 x^4-x^2+2}}{x}+\frac{\tan ^{-1}\left(\frac{2^{3/4} x \sqrt[4]{-2 x^4-x^2+2}}{\sqrt{2} x^2-\sqrt{-2 x^4-x^2+2}}\right)}{\sqrt[4]{2}}+\frac{\tanh ^{-1}\left(\frac{2 \sqrt[4]{2} x \sqrt[4]{-2 x^4-x^2+2}}{2 x^2+\sqrt{2} \sqrt{-2 x^4-x^2+2}}\right)}{\sqrt[4]{2}}",1,"Integrate[((-4 + x^2)*(2 - x^2 - 2*x^4)^(1/4))/(x^2*(-2 + x^2)), x]","F",-1
2015,1,121,143,0.1394042,"\int \frac{1}{(1+x) \left(-2+2 x+x^2-x^4\right)^{3/2}} \, dx","Integrate[1/((1 + x)*(-2 + 2*x + x^2 - x^4)^(3/2)),x]","\frac{7 \sqrt{5} \sqrt{x^2+2 x+2} (x-1)^2 \tanh ^{-1}\left(\frac{2 x+3}{\sqrt{5} \sqrt{x^2+2 x+2}}\right)-25 \sqrt{x^2+2 x+2} (x-1)^2 \tanh ^{-1}\left(\sqrt{(x+1)^2+1}\right)+10 \left(x^3-2 x^2-2 x+4\right)}{200 (x-1) \sqrt{-x^4+x^2+2 x-2}}","-\frac{i \sqrt{-x^4+x^2+2 x-2} \left(-\frac{1}{4} i \tanh ^{-1}\left(-\sqrt{x^2+2 x+2}+x+1\right)-\frac{7 i \tanh ^{-1}\left(\frac{\sqrt{x^2+2 x+2}}{\sqrt{5}}-\frac{x}{\sqrt{5}}+\frac{1}{\sqrt{5}}\right)}{20 \sqrt{5}}-\frac{i \left(x^3-2 x^2-2 x+4\right)}{20 (x-1)^2 \sqrt{x^2+2 x+2}}\right)}{(x-1) \sqrt{x^2+2 x+2}}",1,"(10*(4 - 2*x - 2*x^2 + x^3) + 7*Sqrt[5]*(-1 + x)^2*Sqrt[2 + 2*x + x^2]*ArcTanh[(3 + 2*x)/(Sqrt[5]*Sqrt[2 + 2*x + x^2])] - 25*(-1 + x)^2*Sqrt[2 + 2*x + x^2]*ArcTanh[Sqrt[1 + (1 + x)^2]])/(200*(-1 + x)*Sqrt[-2 + 2*x + x^2 - x^4])","A",1
2016,0,0,143,0.3293819,"\int \frac{\left(-3+2 x^4\right) \left(1+2 x^4\right)^{2/3}}{x^3 \left(2-x^3+4 x^4\right)} \, dx","Integrate[((-3 + 2*x^4)*(1 + 2*x^4)^(2/3))/(x^3*(2 - x^3 + 4*x^4)),x]","\int \frac{\left(-3+2 x^4\right) \left(1+2 x^4\right)^{2/3}}{x^3 \left(2-x^3+4 x^4\right)} \, dx","\frac{\log \left(\sqrt[3]{2} \sqrt[3]{2 x^4+1}-x\right)}{2\ 2^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{2} \sqrt[3]{2 x^4+1}+x}\right)}{2\ 2^{2/3}}+\frac{3 \left(2 x^4+1\right)^{2/3}}{4 x^2}-\frac{\log \left(\sqrt[3]{2} \sqrt[3]{2 x^4+1} x+2^{2/3} \left(2 x^4+1\right)^{2/3}+x^2\right)}{4\ 2^{2/3}}",1,"Integrate[((-3 + 2*x^4)*(1 + 2*x^4)^(2/3))/(x^3*(2 - x^3 + 4*x^4)), x]","F",-1
2017,1,132,143,0.3583228,"\int \frac{-b+a x^3}{x^6 \left(b+a x^3\right) \sqrt[4]{-b x+a x^4}} \, dx","Integrate[(-b + a*x^3)/(x^6*(b + a*x^3)*(-(b*x) + a*x^4)^(1/4)),x]","-\frac{4 \left(a x^4-b x\right)^{3/4} \left(4 a^2 x^6-6 a x^3 \left(4 a x^3-3 b\right) \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};-\frac{2 a x^3}{b-a x^3}\right)-24 a x^3 \left(a x^3+b\right) \, _2F_1\left(\frac{1}{4},2;\frac{5}{4};-\frac{2 a x^3}{b-a x^3}\right)-7 a b x^3+3 b^2\right)}{63 b^2 x^6 \left(b-a x^3\right)}","-\frac{2\ 2^{3/4} a^{7/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} \left(a x^4-b x\right)^{3/4}}{a x^3-b}\right)}{3 b^2}-\frac{2\ 2^{3/4} a^{7/4} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} \left(a x^4-b x\right)^{3/4}}{a x^3-b}\right)}{3 b^2}-\frac{4 \left(3 b-10 a x^3\right) \left(a x^4-b x\right)^{3/4}}{63 b^2 x^6}",1,"(-4*(-(b*x) + a*x^4)^(3/4)*(3*b^2 - 7*a*b*x^3 + 4*a^2*x^6 - 6*a*x^3*(-3*b + 4*a*x^3)*Hypergeometric2F1[1/4, 1, 5/4, (-2*a*x^3)/(b - a*x^3)] - 24*a*x^3*(b + a*x^3)*Hypergeometric2F1[1/4, 2, 5/4, (-2*a*x^3)/(b - a*x^3)]))/(63*b^2*x^6*(b - a*x^3))","C",0
2018,1,139,143,0.268497,"\int \frac{\left(-1+x^3\right)^{2/3} \left(4+4 x^3+x^6\right)}{x^9 \left(1+x^3\right)} \, dx","Integrate[((-1 + x^3)^(2/3)*(4 + 4*x^3 + x^6))/(x^9*(1 + x^3)),x]","\frac{1}{30} \left(5\ 2^{2/3} \left(-2 \log \left(1-\frac{\sqrt[3]{2} x}{\sqrt[3]{1-x^3}}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}+1}{\sqrt{3}}\right)+\log \left(\frac{\sqrt[3]{2} x}{\sqrt[3]{1-x^3}}+\frac{2^{2/3} x^2}{\left(1-x^3\right)^{2/3}}+1\right)\right)-\frac{3 \left(x^3-1\right)^{2/3} \left(2 x^6-2 x^3+5\right)}{x^8}\right)","-\frac{1}{3} 2^{2/3} \log \left(2^{2/3} \sqrt[3]{x^3-1}-2 x\right)+\frac{2^{2/3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^3-1}+x}\right)}{\sqrt{3}}+\frac{\log \left(2^{2/3} \sqrt[3]{x^3-1} x+\sqrt[3]{2} \left(x^3-1\right)^{2/3}+2 x^2\right)}{3 \sqrt[3]{2}}+\frac{\left(x^3-1\right)^{2/3} \left(-2 x^6+2 x^3-5\right)}{10 x^8}",1,"((-3*(-1 + x^3)^(2/3)*(5 - 2*x^3 + 2*x^6))/x^8 + 5*2^(2/3)*(2*Sqrt[3]*ArcTan[(1 + (2*2^(1/3)*x)/(1 - x^3)^(1/3))/Sqrt[3]] - 2*Log[1 - (2^(1/3)*x)/(1 - x^3)^(1/3)] + Log[1 + (2^(2/3)*x^2)/(1 - x^3)^(2/3) + (2^(1/3)*x)/(1 - x^3)^(1/3)]))/30","A",0
2019,1,131,143,0.2375443,"\int \frac{\left(1+x^3\right)^{2/3} \left(-1-2 x^3+2 x^6\right)}{x^9 \left(-1+x^3\right)} \, dx","Integrate[((1 + x^3)^(2/3)*(-1 - 2*x^3 + 2*x^6))/(x^9*(-1 + x^3)),x]","\frac{-2 \log \left(1-\frac{\sqrt[3]{2} x}{\sqrt[3]{x^3+1}}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{2} x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)+\log \left(\frac{\sqrt[3]{2} x}{\sqrt[3]{x^3+1}}+\frac{2^{2/3} x^2}{\left(x^3+1\right)^{2/3}}+1\right)}{3 \sqrt[3]{2}}-\frac{\left(x^3+1\right)^{2/3} \left(41 x^6+26 x^3+5\right)}{40 x^8}","-\frac{1}{3} 2^{2/3} \log \left(2^{2/3} \sqrt[3]{x^3+1}-2 x\right)+\frac{2^{2/3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^3+1}+x}\right)}{\sqrt{3}}+\frac{\log \left(2^{2/3} \sqrt[3]{x^3+1} x+\sqrt[3]{2} \left(x^3+1\right)^{2/3}+2 x^2\right)}{3 \sqrt[3]{2}}+\frac{\left(x^3+1\right)^{2/3} \left(-41 x^6-26 x^3-5\right)}{40 x^8}",1,"-1/40*((1 + x^3)^(2/3)*(5 + 26*x^3 + 41*x^6))/x^8 + (2*Sqrt[3]*ArcTan[(1 + (2*2^(1/3)*x)/(1 + x^3)^(1/3))/Sqrt[3]] - 2*Log[1 - (2^(1/3)*x)/(1 + x^3)^(1/3)] + Log[1 + (2^(2/3)*x^2)/(1 + x^3)^(2/3) + (2^(1/3)*x)/(1 + x^3)^(1/3)])/(3*2^(1/3))","A",1
2020,1,542,143,1.0805443,"\int \frac{1}{\sqrt[4]{-b^4+a^4 x^4} \left(-b^8-c x^4+a^8 x^8\right)} \, dx","Integrate[1/((-b^4 + a^4*x^4)^(1/4)*(-b^8 - c*x^4 + a^8*x^8)),x]","-\frac{a^7 \left(\frac{\tan ^{-1}\left(\frac{a x \sqrt[4]{\sqrt{4 a^8 b^8+c^2}+2 a^4 b^4-c}}{\sqrt[4]{\sqrt{4 a^8 b^8+c^2}-c} \sqrt[4]{a^4 x^4-b^4}}\right)}{\left(\sqrt{4 a^8 b^8+c^2}-c\right)^{3/4} \sqrt[4]{\sqrt{4 a^8 b^8+c^2}+2 a^4 b^4-c}}+\frac{\tan ^{-1}\left(\frac{a x \sqrt[4]{\sqrt{4 a^8 b^8+c^2}-2 a^4 b^4+c}}{\sqrt[4]{\sqrt{4 a^8 b^8+c^2}+c} \sqrt[4]{a^4 x^4-b^4}}\right)}{\left(\sqrt{4 a^8 b^8+c^2}+c\right)^{3/4} \sqrt[4]{\sqrt{4 a^8 b^8+c^2}-2 a^4 b^4+c}}+\frac{\tanh ^{-1}\left(\frac{a x \sqrt[4]{\sqrt{4 a^8 b^8+c^2}+2 a^4 b^4-c}}{\sqrt[4]{\sqrt{4 a^8 b^8+c^2}-c} \sqrt[4]{a^4 x^4-b^4}}\right)}{\left(\sqrt{4 a^8 b^8+c^2}-c\right)^{3/4} \sqrt[4]{\sqrt{4 a^8 b^8+c^2}+2 a^4 b^4-c}}+\frac{\tanh ^{-1}\left(\frac{a x \sqrt[4]{\sqrt{4 a^8 b^8+c^2}-2 a^4 b^4+c}}{\sqrt[4]{\sqrt{4 a^8 b^8+c^2}+c} \sqrt[4]{a^4 x^4-b^4}}\right)}{\left(\sqrt{4 a^8 b^8+c^2}+c\right)^{3/4} \sqrt[4]{\sqrt{4 a^8 b^8+c^2}-2 a^4 b^4+c}}\right)}{\sqrt{4 a^8 b^8+c^2}}","-\frac{\text{RootSum}\left[\text{$\#$1}^8 b^4-2 \text{$\#$1}^4 a^4 b^4-\text{$\#$1}^4 c+a^4 c\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a^4 x^4-b^4}-\text{$\#$1} x\right)-\text{$\#$1}^4 \log (x)-a^4 \log \left(\sqrt[4]{a^4 x^4-b^4}-\text{$\#$1} x\right)+a^4 \log (x)}{-2 \text{$\#$1}^5 b^4+2 \text{$\#$1} a^4 b^4+\text{$\#$1} c}\&\right]}{4 b^4}",1,"-((a^7*(ArcTan[(a*(2*a^4*b^4 - c + Sqrt[4*a^8*b^8 + c^2])^(1/4)*x)/((-c + Sqrt[4*a^8*b^8 + c^2])^(1/4)*(-b^4 + a^4*x^4)^(1/4))]/((-c + Sqrt[4*a^8*b^8 + c^2])^(3/4)*(2*a^4*b^4 - c + Sqrt[4*a^8*b^8 + c^2])^(1/4)) + ArcTan[(a*(-2*a^4*b^4 + c + Sqrt[4*a^8*b^8 + c^2])^(1/4)*x)/((c + Sqrt[4*a^8*b^8 + c^2])^(1/4)*(-b^4 + a^4*x^4)^(1/4))]/((c + Sqrt[4*a^8*b^8 + c^2])^(3/4)*(-2*a^4*b^4 + c + Sqrt[4*a^8*b^8 + c^2])^(1/4)) + ArcTanh[(a*(2*a^4*b^4 - c + Sqrt[4*a^8*b^8 + c^2])^(1/4)*x)/((-c + Sqrt[4*a^8*b^8 + c^2])^(1/4)*(-b^4 + a^4*x^4)^(1/4))]/((-c + Sqrt[4*a^8*b^8 + c^2])^(3/4)*(2*a^4*b^4 - c + Sqrt[4*a^8*b^8 + c^2])^(1/4)) + ArcTanh[(a*(-2*a^4*b^4 + c + Sqrt[4*a^8*b^8 + c^2])^(1/4)*x)/((c + Sqrt[4*a^8*b^8 + c^2])^(1/4)*(-b^4 + a^4*x^4)^(1/4))]/((c + Sqrt[4*a^8*b^8 + c^2])^(3/4)*(-2*a^4*b^4 + c + Sqrt[4*a^8*b^8 + c^2])^(1/4))))/Sqrt[4*a^8*b^8 + c^2])","B",1
2021,1,542,143,0.1313744,"\int \frac{1}{\sqrt[4]{-b^4+a^4 x^4} \left(-b^8-c x^4+a^8 x^8\right)} \, dx","Integrate[1/((-b^4 + a^4*x^4)^(1/4)*(-b^8 - c*x^4 + a^8*x^8)),x]","-\frac{a^7 \left(\frac{\tan ^{-1}\left(\frac{a x \sqrt[4]{\sqrt{4 a^8 b^8+c^2}+2 a^4 b^4-c}}{\sqrt[4]{\sqrt{4 a^8 b^8+c^2}-c} \sqrt[4]{a^4 x^4-b^4}}\right)}{\left(\sqrt{4 a^8 b^8+c^2}-c\right)^{3/4} \sqrt[4]{\sqrt{4 a^8 b^8+c^2}+2 a^4 b^4-c}}+\frac{\tan ^{-1}\left(\frac{a x \sqrt[4]{\sqrt{4 a^8 b^8+c^2}-2 a^4 b^4+c}}{\sqrt[4]{\sqrt{4 a^8 b^8+c^2}+c} \sqrt[4]{a^4 x^4-b^4}}\right)}{\left(\sqrt{4 a^8 b^8+c^2}+c\right)^{3/4} \sqrt[4]{\sqrt{4 a^8 b^8+c^2}-2 a^4 b^4+c}}+\frac{\tanh ^{-1}\left(\frac{a x \sqrt[4]{\sqrt{4 a^8 b^8+c^2}+2 a^4 b^4-c}}{\sqrt[4]{\sqrt{4 a^8 b^8+c^2}-c} \sqrt[4]{a^4 x^4-b^4}}\right)}{\left(\sqrt{4 a^8 b^8+c^2}-c\right)^{3/4} \sqrt[4]{\sqrt{4 a^8 b^8+c^2}+2 a^4 b^4-c}}+\frac{\tanh ^{-1}\left(\frac{a x \sqrt[4]{\sqrt{4 a^8 b^8+c^2}-2 a^4 b^4+c}}{\sqrt[4]{\sqrt{4 a^8 b^8+c^2}+c} \sqrt[4]{a^4 x^4-b^4}}\right)}{\left(\sqrt{4 a^8 b^8+c^2}+c\right)^{3/4} \sqrt[4]{\sqrt{4 a^8 b^8+c^2}-2 a^4 b^4+c}}\right)}{\sqrt{4 a^8 b^8+c^2}}","-\frac{\text{RootSum}\left[\text{$\#$1}^8 b^4-2 \text{$\#$1}^4 a^4 b^4-\text{$\#$1}^4 c+a^4 c\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a^4 x^4-b^4}-\text{$\#$1} x\right)-\text{$\#$1}^4 \log (x)-a^4 \log \left(\sqrt[4]{a^4 x^4-b^4}-\text{$\#$1} x\right)+a^4 \log (x)}{-2 \text{$\#$1}^5 b^4+2 \text{$\#$1} a^4 b^4+\text{$\#$1} c}\&\right]}{4 b^4}",1,"-((a^7*(ArcTan[(a*(2*a^4*b^4 - c + Sqrt[4*a^8*b^8 + c^2])^(1/4)*x)/((-c + Sqrt[4*a^8*b^8 + c^2])^(1/4)*(-b^4 + a^4*x^4)^(1/4))]/((-c + Sqrt[4*a^8*b^8 + c^2])^(3/4)*(2*a^4*b^4 - c + Sqrt[4*a^8*b^8 + c^2])^(1/4)) + ArcTan[(a*(-2*a^4*b^4 + c + Sqrt[4*a^8*b^8 + c^2])^(1/4)*x)/((c + Sqrt[4*a^8*b^8 + c^2])^(1/4)*(-b^4 + a^4*x^4)^(1/4))]/((c + Sqrt[4*a^8*b^8 + c^2])^(3/4)*(-2*a^4*b^4 + c + Sqrt[4*a^8*b^8 + c^2])^(1/4)) + ArcTanh[(a*(2*a^4*b^4 - c + Sqrt[4*a^8*b^8 + c^2])^(1/4)*x)/((-c + Sqrt[4*a^8*b^8 + c^2])^(1/4)*(-b^4 + a^4*x^4)^(1/4))]/((-c + Sqrt[4*a^8*b^8 + c^2])^(3/4)*(2*a^4*b^4 - c + Sqrt[4*a^8*b^8 + c^2])^(1/4)) + ArcTanh[(a*(-2*a^4*b^4 + c + Sqrt[4*a^8*b^8 + c^2])^(1/4)*x)/((c + Sqrt[4*a^8*b^8 + c^2])^(1/4)*(-b^4 + a^4*x^4)^(1/4))]/((c + Sqrt[4*a^8*b^8 + c^2])^(3/4)*(-2*a^4*b^4 + c + Sqrt[4*a^8*b^8 + c^2])^(1/4))))/Sqrt[4*a^8*b^8 + c^2])","B",1
2022,1,126,143,0.3795358,"\int \frac{x-\sqrt{1+x^2}}{\sqrt{1+\sqrt{1+x^2}}} \, dx","Integrate[(x - Sqrt[1 + x^2])/Sqrt[1 + Sqrt[1 + x^2]],x]","\frac{\sqrt{\sqrt{x^2+1}+1} \left(-6 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{1}{2}-\frac{\sqrt{x^2+1}}{2}\right)-4 x^2+4 \sqrt{x^2+1} x+8 \sqrt{x^2+1}-3 \sqrt{2} \sqrt{\sqrt{x^2+1}-1} \tan ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}-1}}{\sqrt{2}}\right)-8 x-2\right)}{6 x}","\frac{2 x}{3 \sqrt{\sqrt{x^2+1}+1}}+\sqrt{x^2+1} \left(\frac{2}{3} \sqrt{\sqrt{x^2+1}+1}-\frac{2 x}{3 \sqrt{\sqrt{x^2+1}+1}}\right)-\frac{4}{3} \sqrt{\sqrt{x^2+1}+1}-2 \sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2} \sqrt{\sqrt{x^2+1}+1}}-\frac{\sqrt{\sqrt{x^2+1}+1}}{\sqrt{2}}\right)",1,"(Sqrt[1 + Sqrt[1 + x^2]]*(-2 - 8*x - 4*x^2 + 8*Sqrt[1 + x^2] + 4*x*Sqrt[1 + x^2] - 3*Sqrt[2]*Sqrt[-1 + Sqrt[1 + x^2]]*ArcTan[Sqrt[-1 + Sqrt[1 + x^2]]/Sqrt[2]] - 6*Hypergeometric2F1[-1/2, 1, 1/2, 1/2 - Sqrt[1 + x^2]/2]))/(6*x)","C",1
2023,1,140,144,0.1941792,"\int \frac{\left(-4+x^3\right) \left(-2+x^3\right) \left(-1+x^3\right)^{2/3}}{x^9 \left(-2+3 x^3\right)} \, dx","Integrate[((-4 + x^3)*(-2 + x^3)*(-1 + x^3)^(2/3))/(x^9*(-2 + 3*x^3)),x]","\frac{5 \left(2 \log \left(\frac{2^{2/3} x}{\sqrt[3]{1-x^3}}+2\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2^{2/3} x}{\sqrt[3]{1-x^3}}-1}{\sqrt{3}}\right)-\log \left(-\frac{2^{2/3} x}{\sqrt[3]{1-x^3}}+\frac{\sqrt[3]{2} x^2}{\left(1-x^3\right)^{2/3}}+2\right)\right)}{6\ 2^{2/3}}+\frac{\left(x^3-1\right)^{2/3} \left(16 x^6+4 x^3+5\right)}{10 x^8}","\frac{5 \log \left(\sqrt[3]{2} \sqrt[3]{x^3-1}+x\right)}{3\ 2^{2/3}}+\frac{5 \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{2} \sqrt[3]{x^3-1}-x}\right)}{2^{2/3} \sqrt{3}}-\frac{5 \log \left(-\sqrt[3]{2} \sqrt[3]{x^3-1} x+2^{2/3} \left(x^3-1\right)^{2/3}+x^2\right)}{6\ 2^{2/3}}+\frac{\left(x^3-1\right)^{2/3} \left(16 x^6+4 x^3+5\right)}{10 x^8}",1,"((-1 + x^3)^(2/3)*(5 + 4*x^3 + 16*x^6))/(10*x^8) + (5*(2*Sqrt[3]*ArcTan[(-1 + (2^(2/3)*x)/(1 - x^3)^(1/3))/Sqrt[3]] - Log[2 + (2^(1/3)*x^2)/(1 - x^3)^(2/3) - (2^(2/3)*x)/(1 - x^3)^(1/3)] + 2*Log[2 + (2^(2/3)*x)/(1 - x^3)^(1/3)]))/(6*2^(2/3))","A",0
2024,1,126,144,0.0677947,"\int \frac{1}{(-1+x) \left(-2 x^2-3 x^3+x^4\right)^{3/2}} \, dx","Integrate[1/((-1 + x)*(-2*x^2 - 3*x^3 + x^4)^(3/2)),x]","\frac{-1812 x^3+6220 x^2+2023 \sqrt{2} \sqrt{x^2-3 x-2} x^2 \tan ^{-1}\left(\frac{-3 x-4}{2 \sqrt{2} \sqrt{x^2-3 x-2}}\right)-272 \sqrt{x^2-3 x-2} x^2 \tan ^{-1}\left(\frac{-x-7}{4 \sqrt{x^2-3 x-2}}\right)+952 x-544}{2176 x \sqrt{x^2 \left(x^2-3 x-2\right)}}","\frac{\sqrt{x^4-3 x^3-2 x^2} \left(-453 x^3+1555 x^2+238 x-136\right)}{544 x^3 \left(x^2-3 x-2\right)}+\frac{1}{4} \tan ^{-1}\left(\frac{\frac{x^2}{2}-\frac{1}{2} \sqrt{x^4-3 x^3-2 x^2}-\frac{x}{2}}{x}\right)-\frac{119 \tan ^{-1}\left(\frac{\frac{x^2}{\sqrt{2}}-\frac{\sqrt{x^4-3 x^3-2 x^2}}{\sqrt{2}}}{x}\right)}{32 \sqrt{2}}",1,"(-544 + 952*x + 6220*x^2 - 1812*x^3 + 2023*Sqrt[2]*x^2*Sqrt[-2 - 3*x + x^2]*ArcTan[(-4 - 3*x)/(2*Sqrt[2]*Sqrt[-2 - 3*x + x^2])] - 272*x^2*Sqrt[-2 - 3*x + x^2]*ArcTan[(-7 - x)/(4*Sqrt[-2 - 3*x + x^2])])/(2176*x*Sqrt[x^2*(-2 - 3*x + x^2)])","A",1
2025,1,75,144,0.0416514,"\int \frac{1}{\left(b+2 a x^3\right) \sqrt[4]{b x+a x^4}} \, dx","Integrate[1/((b + 2*a*x^3)*(b*x + a*x^4)^(1/4)),x]","\frac{4 x \sqrt[4]{\frac{a x^3}{b}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{4};\frac{5}{4};\frac{a x^3}{2 a x^3+b}\right)}{3 b \sqrt[4]{x \left(a x^3+b\right)} \sqrt[4]{\frac{2 a x^3}{b}+1}}","\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} x \sqrt[4]{a x^4+b x}}{\sqrt{a x^4+b x}-\sqrt{a} x^2}\right)}{3 \sqrt[4]{a} b}+\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\frac{\sqrt{a x^4+b x}}{\sqrt{2} \sqrt[4]{a}}+\frac{\sqrt[4]{a} x^2}{\sqrt{2}}}{x \sqrt[4]{a x^4+b x}}\right)}{3 \sqrt[4]{a} b}",1,"(4*x*(1 + (a*x^3)/b)^(1/4)*Hypergeometric2F1[1/4, 1/4, 5/4, (a*x^3)/(b + 2*a*x^3)])/(3*b*(x*(b + a*x^3))^(1/4)*(1 + (2*a*x^3)/b)^(1/4))","C",0
2026,0,0,144,0.4164791,"\int \frac{\sqrt[3]{1-x^7} \left(-2+x^3+2 x^7\right) \left(3+4 x^7\right)}{x^2 \left(-1+x^7\right) \left(-4+x^3+4 x^7\right)} \, dx","Integrate[((1 - x^7)^(1/3)*(-2 + x^3 + 2*x^7)*(3 + 4*x^7))/(x^2*(-1 + x^7)*(-4 + x^3 + 4*x^7)),x]","\int \frac{\sqrt[3]{1-x^7} \left(-2+x^3+2 x^7\right) \left(3+4 x^7\right)}{x^2 \left(-1+x^7\right) \left(-4+x^3+4 x^7\right)} \, dx","\frac{3 \sqrt[3]{1-x^7}}{2 x}-\frac{\log \left(2^{2/3} \sqrt[3]{1-x^7}-x\right)}{2\ 2^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2\ 2^{2/3} \sqrt[3]{1-x^7}+x}\right)}{2\ 2^{2/3}}+\frac{\log \left(2^{2/3} \sqrt[3]{1-x^7} x+2 \sqrt[3]{2} \left(1-x^7\right)^{2/3}+x^2\right)}{4\ 2^{2/3}}",1,"Integrate[((1 - x^7)^(1/3)*(-2 + x^3 + 2*x^7)*(3 + 4*x^7))/(x^2*(-1 + x^7)*(-4 + x^3 + 4*x^7)), x]","F",-1
2027,1,161,144,0.5925436,"\int \frac{\left(-1+x^2\right) \left(1+x^2\right)^3 \sqrt{1+2 x^2+x^4}}{\left(1+x^4\right) \left(1-x^2+x^4-x^6+x^8\right)} \, dx","Integrate[((-1 + x^2)*(1 + x^2)^3*Sqrt[1 + 2*x^2 + x^4])/((1 + x^4)*(1 - x^2 + x^4 - x^6 + x^8)),x]","\frac{\sqrt{\left(x^2+1\right)^2} \left(5 \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^6+\text{$\#$1}^4-\text{$\#$1}^2+1\&,\frac{\text{$\#$1}^6 \log (x-\text{$\#$1})-\text{$\#$1}^4 \log (x-\text{$\#$1})+\text{$\#$1}^2 \log (x-\text{$\#$1})-\log (x-\text{$\#$1})}{4 \text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3-\text{$\#$1}}\&\right]+2 \sqrt{2} \left(\log \left(x^2+\sqrt{2} x+1\right)-\log \left(-x^2+\sqrt{2} x-1\right)\right)\right)}{2 \left(x^2+1\right)}","\frac{\sqrt{\left(x^2+1\right)^2} \left(\frac{5}{2} \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^6+\text{$\#$1}^4-\text{$\#$1}^2+1\&,\frac{\text{$\#$1}^6 \log (x-\text{$\#$1})-\text{$\#$1}^4 \log (x-\text{$\#$1})+\text{$\#$1}^2 \log (x-\text{$\#$1})-\log (x-\text{$\#$1})}{4 \text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3-\text{$\#$1}}\&\right]+2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x}{x^2+1}\right)\right)}{x^2+1}",1,"(Sqrt[(1 + x^2)^2]*(2*Sqrt[2]*(-Log[-1 + Sqrt[2]*x - x^2] + Log[1 + Sqrt[2]*x + x^2]) + 5*RootSum[1 - #1^2 + #1^4 - #1^6 + #1^8 & , (-Log[x - #1] + Log[x - #1]*#1^2 - Log[x - #1]*#1^4 + Log[x - #1]*#1^6)/(-#1 + 2*#1^3 - 3*#1^5 + 4*#1^7) & ]))/(2*(1 + x^2))","A",1
2028,1,143,144,0.4004808,"\int \frac{1}{x^2 \sqrt{b+\sqrt{b^2+a x^2}}} \, dx","Integrate[1/(x^2*Sqrt[b + Sqrt[b^2 + a*x^2]]),x]","-\frac{\sqrt{\sqrt{a x^2+b^2}+b} \left(9 a x^2 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{b-\sqrt{b^2+a x^2}}{2 b}\right)+2 b \left(\sqrt{a x^2+b^2}+b\right) \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{b-\sqrt{b^2+a x^2}}{2 b}\right)+2 b \left(5 \sqrt{a x^2+b^2}-7 b\right)\right)}{24 a b x^3}","-\frac{\sqrt{\sqrt{a x^2+b^2}+b}}{4 b x}-\frac{1}{2 x \sqrt{\sqrt{a x^2+b^2}+b}}-\frac{\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{2} \sqrt{b} \sqrt{\sqrt{a x^2+b^2}+b}}-\frac{\sqrt{\sqrt{a x^2+b^2}+b}}{\sqrt{2} \sqrt{b}}\right)}{2 \sqrt{2} b^{3/2}}",1,"-1/24*(Sqrt[b + Sqrt[b^2 + a*x^2]]*(2*b*(-7*b + 5*Sqrt[b^2 + a*x^2]) + 2*b*(b + Sqrt[b^2 + a*x^2])*Hypergeometric2F1[-3/2, 1, -1/2, (b - Sqrt[b^2 + a*x^2])/(2*b)] + 9*a*x^2*Hypergeometric2F1[-1/2, 1, 1/2, (b - Sqrt[b^2 + a*x^2])/(2*b)]))/(a*b*x^3)","C",1
2029,1,211,145,0.0836795,"\int \frac{\sqrt[4]{-b+a x^3}}{x} \, dx","Integrate[(-b + a*x^3)^(1/4)/x,x]","\frac{1}{6} \left(8 \sqrt[4]{a x^3-b}+\sqrt{2} \sqrt[4]{b} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^3-b}+\sqrt{a x^3-b}+\sqrt{b}\right)-\sqrt{2} \sqrt[4]{b} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^3-b}+\sqrt{a x^3-b}+\sqrt{b}\right)+2 \sqrt{2} \sqrt[4]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a x^3-b}}{\sqrt[4]{b}}\right)-2 \sqrt{2} \sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x^3-b}}{\sqrt[4]{b}}+1\right)\right)","\frac{4}{3} \sqrt[4]{a x^3-b}+\frac{1}{3} \sqrt{2} \sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^3-b}}{\sqrt{a x^3-b}-\sqrt{b}}\right)-\frac{1}{3} \sqrt{2} \sqrt[4]{b} \tanh ^{-1}\left(\frac{\frac{\sqrt{a x^3-b}}{\sqrt{2} \sqrt[4]{b}}+\frac{\sqrt[4]{b}}{\sqrt{2}}}{\sqrt[4]{a x^3-b}}\right)",1,"(8*(-b + a*x^3)^(1/4) + 2*Sqrt[2]*b^(1/4)*ArcTan[1 - (Sqrt[2]*(-b + a*x^3)^(1/4))/b^(1/4)] - 2*Sqrt[2]*b^(1/4)*ArcTan[1 + (Sqrt[2]*(-b + a*x^3)^(1/4))/b^(1/4)] + Sqrt[2]*b^(1/4)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*(-b + a*x^3)^(1/4) + Sqrt[-b + a*x^3]] - Sqrt[2]*b^(1/4)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*(-b + a*x^3)^(1/4) + Sqrt[-b + a*x^3]])/6","A",1
2030,1,84,145,0.0261842,"\int \frac{\left(-b+a x^3\right)^{3/4}}{x} \, dx","Integrate[(-b + a*x^3)^(3/4)/x,x]","\frac{4}{9} \left(a x^3-b\right)^{3/4}+\frac{2}{3} (-b)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a x^3-b}}{\sqrt[4]{-b}}\right)-\frac{2}{3} (-b)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a x^3-b}}{\sqrt[4]{-b}}\right)","\frac{1}{3} \sqrt{2} b^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^3-b}}{\sqrt{a x^3-b}-\sqrt{b}}\right)+\frac{1}{3} \sqrt{2} b^{3/4} \tanh ^{-1}\left(\frac{\frac{\sqrt{a x^3-b}}{\sqrt{2} \sqrt[4]{b}}+\frac{\sqrt[4]{b}}{\sqrt{2}}}{\sqrt[4]{a x^3-b}}\right)+\frac{4}{9} \left(a x^3-b\right)^{3/4}",1,"(4*(-b + a*x^3)^(3/4))/9 + (2*(-b)^(3/4)*ArcTan[(-b + a*x^3)^(1/4)/(-b)^(1/4)])/3 - (2*(-b)^(3/4)*ArcTanh[(-b + a*x^3)^(1/4)/(-b)^(1/4)])/3","A",1
2031,0,0,145,0.396932,"\int \frac{\left(-1+x^4\right)^{2/3} \left(3+x^4\right) \left(-1-x^3+x^4\right)}{x^6 \left(-2-x^3+2 x^4\right)} \, dx","Integrate[((-1 + x^4)^(2/3)*(3 + x^4)*(-1 - x^3 + x^4))/(x^6*(-2 - x^3 + 2*x^4)),x]","\int \frac{\left(-1+x^4\right)^{2/3} \left(3+x^4\right) \left(-1-x^3+x^4\right)}{x^6 \left(-2-x^3+2 x^4\right)} \, dx","-\frac{\log \left(\sqrt[3]{2} \sqrt[3]{x^4-1}-x\right)}{4\ 2^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{2} \sqrt[3]{x^4-1}+x}\right)}{4\ 2^{2/3}}+\frac{\log \left(\sqrt[3]{2} \sqrt[3]{x^4-1} x+2^{2/3} \left(x^4-1\right)^{2/3}+x^2\right)}{8\ 2^{2/3}}+\frac{3 \left(x^4-1\right)^{2/3} \left(4 x^4-5 x^3-4\right)}{40 x^5}",1,"Integrate[((-1 + x^4)^(2/3)*(3 + x^4)*(-1 - x^3 + x^4))/(x^6*(-2 - x^3 + 2*x^4)), x]","F",-1
2032,1,84,145,0.0277086,"\int \frac{\left(-b+a x^4\right)^{3/4}}{x} \, dx","Integrate[(-b + a*x^4)^(3/4)/x,x]","\frac{1}{3} \left(a x^4-b\right)^{3/4}+\frac{1}{2} (-b)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a x^4-b}}{\sqrt[4]{-b}}\right)-\frac{1}{2} (-b)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a x^4-b}}{\sqrt[4]{-b}}\right)","\frac{b^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^4-b}}{\sqrt{a x^4-b}-\sqrt{b}}\right)}{2 \sqrt{2}}+\frac{b^{3/4} \tanh ^{-1}\left(\frac{\frac{\sqrt{a x^4-b}}{\sqrt{2} \sqrt[4]{b}}+\frac{\sqrt[4]{b}}{\sqrt{2}}}{\sqrt[4]{a x^4-b}}\right)}{2 \sqrt{2}}+\frac{1}{3} \left(a x^4-b\right)^{3/4}",1,"(-b + a*x^4)^(3/4)/3 + ((-b)^(3/4)*ArcTan[(-b + a*x^4)^(1/4)/(-b)^(1/4)])/2 - ((-b)^(3/4)*ArcTanh[(-b + a*x^4)^(1/4)/(-b)^(1/4)])/2","A",1
2033,0,0,145,2.5871245,"\int \frac{-3 a b^3+2 b^2 (3 a+b) x-3 b (a+b) x^2+x^4}{\sqrt[4]{x (-a+x) (-b+x)^3} \left(a b^3 d-b^2 (3 a+b) d x+3 b (a+b) d x^2-(1+a d+3 b d) x^3+d x^4\right)} \, dx","Integrate[(-3*a*b^3 + 2*b^2*(3*a + b)*x - 3*b*(a + b)*x^2 + x^4)/((x*(-a + x)*(-b + x)^3)^(1/4)*(a*b^3*d - b^2*(3*a + b)*d*x + 3*b*(a + b)*d*x^2 - (1 + a*d + 3*b*d)*x^3 + d*x^4)),x]","\int \frac{-3 a b^3+2 b^2 (3 a+b) x-3 b (a+b) x^2+x^4}{\sqrt[4]{x (-a+x) (-b+x)^3} \left(a b^3 d-b^2 (3 a+b) d x+3 b (a+b) d x^2-(1+a d+3 b d) x^3+d x^4\right)} \, dx","\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a b^3 x+x^3 \left(3 a b+3 b^2\right)+x^2 \left(-3 a b^2-b^3\right)+x^4 (-a-3 b)+x^5}}{x}\right)}{d^{3/4}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a b^3 x+x^3 \left(3 a b+3 b^2\right)+x^2 \left(-3 a b^2-b^3\right)+x^4 (-a-3 b)+x^5}}{x}\right)}{d^{3/4}}",1,"Integrate[(-3*a*b^3 + 2*b^2*(3*a + b)*x - 3*b*(a + b)*x^2 + x^4)/((x*(-a + x)*(-b + x)^3)^(1/4)*(a*b^3*d - b^2*(3*a + b)*d*x + 3*b*(a + b)*d*x^2 - (1 + a*d + 3*b*d)*x^3 + d*x^4)), x]","F",-1
2034,1,84,145,0.028753,"\int \frac{\left(-b+a x^5\right)^{3/4}}{x} \, dx","Integrate[(-b + a*x^5)^(3/4)/x,x]","\frac{4}{15} \left(a x^5-b\right)^{3/4}+\frac{2}{5} (-b)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a x^5-b}}{\sqrt[4]{-b}}\right)-\frac{2}{5} (-b)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a x^5-b}}{\sqrt[4]{-b}}\right)","\frac{1}{5} \sqrt{2} b^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^5-b}}{\sqrt{a x^5-b}-\sqrt{b}}\right)+\frac{1}{5} \sqrt{2} b^{3/4} \tanh ^{-1}\left(\frac{\frac{\sqrt{a x^5-b}}{\sqrt{2} \sqrt[4]{b}}+\frac{\sqrt[4]{b}}{\sqrt{2}}}{\sqrt[4]{a x^5-b}}\right)+\frac{4}{15} \left(a x^5-b\right)^{3/4}",1,"(4*(-b + a*x^5)^(3/4))/15 + (2*(-b)^(3/4)*ArcTan[(-b + a*x^5)^(1/4)/(-b)^(1/4)])/5 - (2*(-b)^(3/4)*ArcTanh[(-b + a*x^5)^(1/4)/(-b)^(1/4)])/5","A",1
2035,1,138,145,0.1813983,"\int \frac{\left(-1+x^3\right)^{2/3} \left(4+x^3+x^6\right)}{x^9 \left(-2+x^3\right)} \, dx","Integrate[((-1 + x^3)^(2/3)*(4 + x^3 + x^6))/(x^9*(-2 + x^3)),x]","\frac{\left(x^3-1\right)^{2/3} \left(7 x^6+8 x^3+10\right)}{40 x^8}-\frac{5 \left(-2 \log \left(2-\frac{2^{2/3} x}{\sqrt[3]{1-x^3}}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2^{2/3} x}{\sqrt[3]{1-x^3}}+1}{\sqrt{3}}\right)+\log \left(\frac{2^{2/3} x}{\sqrt[3]{1-x^3}}+\frac{\sqrt[3]{2} x^2}{\left(1-x^3\right)^{2/3}}+2\right)\right)}{24\ 2^{2/3}}","\frac{5 \log \left(\sqrt[3]{2} \sqrt[3]{x^3-1}-x\right)}{12\ 2^{2/3}}-\frac{5 \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{2} \sqrt[3]{x^3-1}+x}\right)}{4\ 2^{2/3} \sqrt{3}}-\frac{5 \log \left(\sqrt[3]{2} \sqrt[3]{x^3-1} x+2^{2/3} \left(x^3-1\right)^{2/3}+x^2\right)}{24\ 2^{2/3}}+\frac{\left(x^3-1\right)^{2/3} \left(7 x^6+8 x^3+10\right)}{40 x^8}",1,"((-1 + x^3)^(2/3)*(10 + 8*x^3 + 7*x^6))/(40*x^8) - (5*(2*Sqrt[3]*ArcTan[(1 + (2^(2/3)*x)/(1 - x^3)^(1/3))/Sqrt[3]] - 2*Log[2 - (2^(2/3)*x)/(1 - x^3)^(1/3)] + Log[2 + (2^(1/3)*x^2)/(1 - x^3)^(2/3) + (2^(2/3)*x)/(1 - x^3)^(1/3)]))/(24*2^(2/3))","A",0
2036,0,0,145,0.4260063,"\int \frac{-3-4 x+3 x^6}{\left(1+2 x+x^6\right) \sqrt[3]{1+2 x+2 x^3+x^6}} \, dx","Integrate[(-3 - 4*x + 3*x^6)/((1 + 2*x + x^6)*(1 + 2*x + 2*x^3 + x^6)^(1/3)),x]","\int \frac{-3-4 x+3 x^6}{\left(1+2 x+x^6\right) \sqrt[3]{1+2 x+2 x^3+x^6}} \, dx","\frac{\log \left(2^{2/3} \sqrt[3]{x^6+2 x^3+2 x+1}-2 x\right)}{\sqrt[3]{2}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^6+2 x^3+2 x+1}+x}\right)}{\sqrt[3]{2}}-\frac{\log \left(2 x^2+2^{2/3} \sqrt[3]{x^6+2 x^3+2 x+1} x+\sqrt[3]{2} \left(x^6+2 x^3+2 x+1\right)^{2/3}\right)}{2 \sqrt[3]{2}}",1,"Integrate[(-3 - 4*x + 3*x^6)/((1 + 2*x + x^6)*(1 + 2*x + 2*x^3 + x^6)^(1/3)), x]","F",-1
2037,1,84,145,0.028287,"\int \frac{\left(-b+a x^6\right)^{3/4}}{x} \, dx","Integrate[(-b + a*x^6)^(3/4)/x,x]","\frac{2}{9} \left(a x^6-b\right)^{3/4}+\frac{1}{3} (-b)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a x^6-b}}{\sqrt[4]{-b}}\right)-\frac{1}{3} (-b)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a x^6-b}}{\sqrt[4]{-b}}\right)","\frac{b^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^6-b}}{\sqrt{a x^6-b}-\sqrt{b}}\right)}{3 \sqrt{2}}+\frac{b^{3/4} \tanh ^{-1}\left(\frac{\frac{\sqrt{a x^6-b}}{\sqrt{2} \sqrt[4]{b}}+\frac{\sqrt[4]{b}}{\sqrt{2}}}{\sqrt[4]{a x^6-b}}\right)}{3 \sqrt{2}}+\frac{2}{9} \left(a x^6-b\right)^{3/4}",1,"(2*(-b + a*x^6)^(3/4))/9 + ((-b)^(3/4)*ArcTan[(-b + a*x^6)^(1/4)/(-b)^(1/4)])/3 - ((-b)^(3/4)*ArcTanh[(-b + a*x^6)^(1/4)/(-b)^(1/4)])/3","A",1
2038,1,220,145,0.150207,"\int \frac{b+a x^6}{\sqrt[3]{-x+x^3}} \, dx","Integrate[(b + a*x^6)/(-x + x^3)^(1/3),x]","\frac{\sqrt[3]{x} \sqrt[3]{x^2-1} \left(-2 (14 a+81 b) \log \left(1-\frac{x^{2/3}}{\sqrt[3]{x^2-1}}\right)+2 \sqrt{3} (14 a+81 b) \tan ^{-1}\left(\frac{\frac{2 x^{2/3}}{\sqrt[3]{x^2-1}}+1}{\sqrt{3}}\right)+54 a \left(x^2-1\right)^{2/3} x^{14/3}+63 a \left(x^2-1\right)^{2/3} x^{8/3}+84 a \left(x^2-1\right)^{2/3} x^{2/3}+14 a \log \left(\frac{x^{4/3}}{\left(x^2-1\right)^{2/3}}+\frac{x^{2/3}}{\sqrt[3]{x^2-1}}+1\right)+81 b \log \left(\frac{x^{4/3}}{\left(x^2-1\right)^{2/3}}+\frac{x^{2/3}}{\sqrt[3]{x^2-1}}+1\right)\right)}{324 \sqrt[3]{x \left(x^2-1\right)}}","\frac{1}{162} (-14 a-81 b) \log \left(\sqrt[3]{x^3-x}-x\right)+\frac{1}{162} \left(14 \sqrt{3} a+81 \sqrt{3} b\right) \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-x}+x}\right)+\frac{1}{324} (14 a+81 b) \log \left(\sqrt[3]{x^3-x} x+\left(x^3-x\right)^{2/3}+x^2\right)+\frac{1}{108} \left(x^3-x\right)^{2/3} \left(18 a x^4+21 a x^2+28 a\right)",1,"(x^(1/3)*(-1 + x^2)^(1/3)*(84*a*x^(2/3)*(-1 + x^2)^(2/3) + 63*a*x^(8/3)*(-1 + x^2)^(2/3) + 54*a*x^(14/3)*(-1 + x^2)^(2/3) + 2*Sqrt[3]*(14*a + 81*b)*ArcTan[(1 + (2*x^(2/3))/(-1 + x^2)^(1/3))/Sqrt[3]] - 2*(14*a + 81*b)*Log[1 - x^(2/3)/(-1 + x^2)^(1/3)] + 14*a*Log[1 + x^(4/3)/(-1 + x^2)^(2/3) + x^(2/3)/(-1 + x^2)^(1/3)] + 81*b*Log[1 + x^(4/3)/(-1 + x^2)^(2/3) + x^(2/3)/(-1 + x^2)^(1/3)]))/(324*(x*(-1 + x^2))^(1/3))","A",1
2039,1,231,145,1.1297493,"\int \frac{\sqrt[4]{a x^2+b x \sqrt{-\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}}}{\sqrt{-\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}} \, dx","Integrate[(a*x^2 + b*x*Sqrt[-(a/b^2) + (a^2*x^2)/b^2])^(1/4)/Sqrt[-(a/b^2) + (a^2*x^2)/b^2],x]","-\frac{a x \sqrt[4]{x \left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right)} \left(b x \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x^2-1\right) \left(-2 \sqrt[4]{2} \sqrt[4]{a x \left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right)}+\sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt[4]{\left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right)^2+a}}{\sqrt[4]{a}}\right)+\sqrt[4]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{\left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right)^2+a}}{\sqrt[4]{a}}\right)\right)}{\sqrt[4]{2} \sqrt{\frac{a \left(a x^2-1\right)}{b^2}} \left(a x \left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right)\right)^{5/4}}","\frac{2 b \sqrt[4]{b x \sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}}+a x^2}}{a}-\frac{b \tan ^{-1}\left(\sqrt[4]{2} \sqrt[4]{b x \sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}}+a x^2}\right)}{\sqrt[4]{2} a}-\frac{b \tanh ^{-1}\left(\sqrt[4]{2} \sqrt[4]{b x \sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}}+a x^2}\right)}{\sqrt[4]{2} a}",1,"-((a*x*(x*(a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2]))^(1/4)*(-1 + a*x^2 + b*x*Sqrt[(a*(-1 + a*x^2))/b^2])*(-2*2^(1/4)*(a*x*(a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2]))^(1/4) + a^(1/4)*ArcTan[(a + (a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2])^2)^(1/4)/a^(1/4)] + a^(1/4)*ArcTanh[(a + (a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2])^2)^(1/4)/a^(1/4)]))/(2^(1/4)*Sqrt[(a*(-1 + a*x^2))/b^2]*(a*x*(a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2]))^(5/4)))","A",1
2040,1,37,146,0.0216197,"\int \frac{1}{\sqrt[3]{x^2 (-a+x)} (a+(-1+d) x)} \, dx","Integrate[1/((x^2*(-a + x))^(1/3)*(a + (-1 + d)*x)),x]","\frac{3 x \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{d x}{x-a}\right)}{a \sqrt[3]{x^2 (x-a)}}","\frac{\log \left(\sqrt[3]{d} x \sqrt[3]{x^3-a x^2}+\left(x^3-a x^2\right)^{2/3}+d^{2/3} x^2\right)}{2 a \sqrt[3]{d}}-\frac{\log \left(\sqrt[3]{x^3-a x^2}-\sqrt[3]{d} x\right)}{a \sqrt[3]{d}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} x}{2 \sqrt[3]{x^3-a x^2}+\sqrt[3]{d} x}\right)}{a \sqrt[3]{d}}",1,"(3*x*Hypergeometric2F1[1/3, 1, 4/3, (d*x)/(-a + x)])/(a*(x^2*(-a + x))^(1/3))","C",1
2041,0,0,146,1.2455654,"\int \frac{\left(2+x-x^3-x^4\right)^{2/3} \left(6+2 x+x^4\right) \left(-2-x+x^3+x^4\right)}{x^6 \left(-2-x+2 x^3+x^4\right)} \, dx","Integrate[((2 + x - x^3 - x^4)^(2/3)*(6 + 2*x + x^4)*(-2 - x + x^3 + x^4))/(x^6*(-2 - x + 2*x^3 + x^4)),x]","\int \frac{\left(2+x-x^3-x^4\right)^{2/3} \left(6+2 x+x^4\right) \left(-2-x+x^3+x^4\right)}{x^6 \left(-2-x+2 x^3+x^4\right)} \, dx","-\log \left(\sqrt[3]{-x^4-x^3+x+2}-x\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{-x^4-x^3+x+2}+x}\right)+\frac{3 \left(-x^4-x^3+x+2\right)^{2/3} \left(2 x^4-3 x^3-2 x-4\right)}{10 x^5}+\frac{1}{2} \log \left(x^2+\sqrt[3]{-x^4-x^3+x+2} x+\left(-x^4-x^3+x+2\right)^{2/3}\right)",1,"Integrate[((2 + x - x^3 - x^4)^(2/3)*(6 + 2*x + x^4)*(-2 - x + x^3 + x^4))/(x^6*(-2 - x + 2*x^3 + x^4)), x]","F",-1
2042,0,0,146,0.3416955,"\int \frac{\left(-3+x^4\right) \left(1+x^4\right)^{2/3} \left(2+x^3+2 x^4\right)}{x^6 \left(4-x^3+4 x^4\right)} \, dx","Integrate[((-3 + x^4)*(1 + x^4)^(2/3)*(2 + x^3 + 2*x^4))/(x^6*(4 - x^3 + 4*x^4)),x]","\int \frac{\left(-3+x^4\right) \left(1+x^4\right)^{2/3} \left(2+x^3+2 x^4\right)}{x^6 \left(4-x^3+4 x^4\right)} \, dx","\frac{3 \log \left(2^{2/3} \sqrt[3]{x^4+1}-x\right)}{16 \sqrt[3]{2}}-\frac{3 \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2\ 2^{2/3} \sqrt[3]{x^4+1}+x}\right)}{16 \sqrt[3]{2}}-\frac{3 \log \left(2^{2/3} \sqrt[3]{x^4+1} x+2 \sqrt[3]{2} \left(x^4+1\right)^{2/3}+x^2\right)}{32 \sqrt[3]{2}}+\frac{3 \left(x^4+1\right)^{2/3} \left(8 x^4+15 x^3+8\right)}{80 x^5}",1,"Integrate[((-3 + x^4)*(1 + x^4)^(2/3)*(2 + x^3 + 2*x^4))/(x^6*(4 - x^3 + 4*x^4)), x]","F",-1
2043,0,0,146,1.1202324,"\int \frac{\left(-1-x^4+2 x^6\right) \sqrt[3]{x-x^5+x^7}}{\left(1+x^2-x^4+x^6\right)^2} \, dx","Integrate[((-1 - x^4 + 2*x^6)*(x - x^5 + x^7)^(1/3))/(1 + x^2 - x^4 + x^6)^2,x]","\int \frac{\left(-1-x^4+2 x^6\right) \sqrt[3]{x-x^5+x^7}}{\left(1+x^2-x^4+x^6\right)^2} \, dx","\frac{1}{6} \log \left(\sqrt[3]{x^7-x^5+x}+x\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x^7-x^5+x}}{\sqrt[3]{x^7-x^5+x}-2 x}\right)}{2 \sqrt{3}}-\frac{1}{12} \log \left(x^2-\sqrt[3]{x^7-x^5+x} x+\left(x^7-x^5+x\right)^{2/3}\right)-\frac{\sqrt[3]{x^7-x^5+x} x}{2 \left(x^6-x^4+x^2+1\right)}",1,"Integrate[((-1 - x^4 + 2*x^6)*(x - x^5 + x^7)^(1/3))/(1 + x^2 - x^4 + x^6)^2, x]","F",-1
2044,0,0,146,0.5134911,"\int \frac{x^4 \left(-4 b+a x^3\right)}{\sqrt[4]{-b+a x^3} \left(-b^2+2 a b x^3-a^2 x^6+x^8\right)} \, dx","Integrate[(x^4*(-4*b + a*x^3))/((-b + a*x^3)^(1/4)*(-b^2 + 2*a*b*x^3 - a^2*x^6 + x^8)),x]","\int \frac{x^4 \left(-4 b+a x^3\right)}{\sqrt[4]{-b+a x^3} \left(-b^2+2 a b x^3-a^2 x^6+x^8\right)} \, dx","\tan ^{-1}\left(\frac{\sqrt[4]{a x^3-b}}{x}\right)+\tanh ^{-1}\left(\frac{x \left(a x^3-b\right)^{3/4}}{b-a x^3}\right)-\frac{\tan ^{-1}\left(\frac{\frac{\sqrt{a x^3-b}}{\sqrt{2}}-\frac{x^2}{\sqrt{2}}}{x \sqrt[4]{a x^3-b}}\right)}{\sqrt{2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{a x^3-b}}{\sqrt{a x^3-b}+x^2}\right)}{\sqrt{2}}",1,"Integrate[(x^4*(-4*b + a*x^3))/((-b + a*x^3)^(1/4)*(-b^2 + 2*a*b*x^3 - a^2*x^6 + x^8)), x]","F",-1
2045,1,808,146,2.7178123,"\int \frac{\sqrt{-1+x^2} \sqrt{x^2+x \sqrt{-1+x^2}}}{1+x^2} \, dx","Integrate[(Sqrt[-1 + x^2]*Sqrt[x^2 + x*Sqrt[-1 + x^2]])/(1 + x^2),x]","\frac{\sqrt{x^2-1} \left(x+\sqrt{x^2-1}\right) \left(4 \sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{1+\sqrt{2}} \left(\sqrt{2} \left(x+\sqrt{x^2-1}\right)^2+3 \sqrt{2}+4\right)}{\sqrt{\left(x+\sqrt{x^2-1}\right)^2+1} \left(\left(x+\sqrt{x^2-1}\right)^2+2 \sqrt{2}+3\right)}\right)+2 \log \left(x+\sqrt{x^2-1}\right)-2 \sqrt{-1+\sqrt{2}} \log \left(\left(x+\sqrt{x^2-1}\right)^4+\left(6-4 \sqrt{2}\right) \left(x+\sqrt{x^2-1}\right)^2-12 \sqrt{2}+17\right)-2 i \sqrt{1+\sqrt{2}} \log \left(\left(x+\sqrt{x^2-1}\right)^4+\left(6+4 \sqrt{2}\right) \left(x+\sqrt{x^2-1}\right)^2+12 \sqrt{2}+17\right)+i \sqrt{1+\sqrt{2}} \log \left(\left(5+4 \sqrt{2}\right) \left(x+\sqrt{x^2-1}\right)^4-2 \sqrt{2 \left(1+\sqrt{2}\right)} \left(2+\sqrt{2}\right) \sqrt{x \left(x+\sqrt{x^2-1}\right)} \left(x+\sqrt{x^2-1}\right)^3+\left(34+24 \sqrt{2}\right) \left(x+\sqrt{x^2-1}\right)^2-\frac{2 \sqrt{2 \left(1+\sqrt{2}\right)} \left(10+7 \sqrt{2}\right) \left(x \left(x+\sqrt{x^2-1}\right)\right)^{3/2}}{x}+12 \sqrt{2}+17\right)+i \sqrt{1+\sqrt{2}} \log \left(\left(5+4 \sqrt{2}\right) \left(x+\sqrt{x^2-1}\right)^4+2 \sqrt{2 \left(1+\sqrt{2}\right)} \left(2+\sqrt{2}\right) \sqrt{x \left(x+\sqrt{x^2-1}\right)} \left(x+\sqrt{x^2-1}\right)^3+\left(34+24 \sqrt{2}\right) \left(x+\sqrt{x^2-1}\right)^2+\frac{2 \sqrt{2 \left(1+\sqrt{2}\right)} \left(10+7 \sqrt{2}\right) \left(x \left(x+\sqrt{x^2-1}\right)\right)^{3/2}}{x}+12 \sqrt{2}+17\right)-2 \log \left(\sqrt{\left(x+\sqrt{x^2-1}\right)^2+1}+1\right)+2 \sqrt{-1+\sqrt{2}} \log \left(-\left(x+\sqrt{x^2-1}\right)^4-2 \left(2 \sqrt{-1+\sqrt{2}} \sqrt{x \left(x+\sqrt{x^2-1}\right)}+1\right) \left(x+\sqrt{x^2-1}\right)^2+8 \sqrt{2 \left(-1+\sqrt{2}\right)} \sqrt{x \left(x+\sqrt{x^2-1}\right)}-12 \sqrt{-1+\sqrt{2}} \sqrt{x \left(x+\sqrt{x^2-1}\right)}-8 \sqrt{2}+11\right)+2 \sqrt{2} \sqrt{x \left(x+\sqrt{x^2-1}\right)}\right)}{2 \sqrt{2} \left(x^2+\sqrt{x^2-1} x-1\right)}","\sqrt{x^2+\sqrt{x^2-1} x}-\sqrt{2 \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{x^2+\sqrt{x^2-1} x}}{\sqrt{1+\sqrt{2}}}\right)-\frac{\tanh ^{-1}\left(\sqrt{2} \sqrt{x^2+\sqrt{x^2-1} x}\right)}{\sqrt{2}}+\sqrt{2 \left(\sqrt{2}-1\right)} \tanh ^{-1}\left(\frac{\sqrt{x^2+\sqrt{x^2-1} x}}{\sqrt{\sqrt{2}-1}}\right)",1,"(Sqrt[-1 + x^2]*(x + Sqrt[-1 + x^2])*(2*Sqrt[2]*Sqrt[x*(x + Sqrt[-1 + x^2])] + 4*Sqrt[1 + Sqrt[2]]*ArcTan[(Sqrt[1 + Sqrt[2]]*(4 + 3*Sqrt[2] + Sqrt[2]*(x + Sqrt[-1 + x^2])^2))/(Sqrt[1 + (x + Sqrt[-1 + x^2])^2]*(3 + 2*Sqrt[2] + (x + Sqrt[-1 + x^2])^2))] + 2*Log[x + Sqrt[-1 + x^2]] - 2*Sqrt[-1 + Sqrt[2]]*Log[17 - 12*Sqrt[2] + (6 - 4*Sqrt[2])*(x + Sqrt[-1 + x^2])^2 + (x + Sqrt[-1 + x^2])^4] - (2*I)*Sqrt[1 + Sqrt[2]]*Log[17 + 12*Sqrt[2] + (6 + 4*Sqrt[2])*(x + Sqrt[-1 + x^2])^2 + (x + Sqrt[-1 + x^2])^4] + I*Sqrt[1 + Sqrt[2]]*Log[17 + 12*Sqrt[2] + (34 + 24*Sqrt[2])*(x + Sqrt[-1 + x^2])^2 + (5 + 4*Sqrt[2])*(x + Sqrt[-1 + x^2])^4 - 2*Sqrt[2*(1 + Sqrt[2])]*(2 + Sqrt[2])*(x + Sqrt[-1 + x^2])^3*Sqrt[x*(x + Sqrt[-1 + x^2])] - (2*Sqrt[2*(1 + Sqrt[2])]*(10 + 7*Sqrt[2])*(x*(x + Sqrt[-1 + x^2]))^(3/2))/x] + I*Sqrt[1 + Sqrt[2]]*Log[17 + 12*Sqrt[2] + (34 + 24*Sqrt[2])*(x + Sqrt[-1 + x^2])^2 + (5 + 4*Sqrt[2])*(x + Sqrt[-1 + x^2])^4 + 2*Sqrt[2*(1 + Sqrt[2])]*(2 + Sqrt[2])*(x + Sqrt[-1 + x^2])^3*Sqrt[x*(x + Sqrt[-1 + x^2])] + (2*Sqrt[2*(1 + Sqrt[2])]*(10 + 7*Sqrt[2])*(x*(x + Sqrt[-1 + x^2]))^(3/2))/x] - 2*Log[1 + Sqrt[1 + (x + Sqrt[-1 + x^2])^2]] + 2*Sqrt[-1 + Sqrt[2]]*Log[11 - 8*Sqrt[2] - (x + Sqrt[-1 + x^2])^4 - 12*Sqrt[-1 + Sqrt[2]]*Sqrt[x*(x + Sqrt[-1 + x^2])] + 8*Sqrt[2*(-1 + Sqrt[2])]*Sqrt[x*(x + Sqrt[-1 + x^2])] - 2*(x + Sqrt[-1 + x^2])^2*(1 + 2*Sqrt[-1 + Sqrt[2]]*Sqrt[x*(x + Sqrt[-1 + x^2])])]))/(2*Sqrt[2]*(-1 + x^2 + x*Sqrt[-1 + x^2]))","C",0
2046,1,41,147,0.0200972,"\int \frac{x}{\left(x^2 (-a+x)\right)^{2/3} (a+(-1+d) x)} \, dx","Integrate[x/((x^2*(-a + x))^(2/3)*(a + (-1 + d)*x)),x]","\frac{3 x^2 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{d x}{x-a}\right)}{2 a \left(x^2 (x-a)\right)^{2/3}}","-\frac{\log \left(\sqrt[3]{x^3-a x^2}-\sqrt[3]{d} x\right)}{a d^{2/3}}+\frac{\log \left(\sqrt[3]{d} x \sqrt[3]{x^3-a x^2}+\left(x^3-a x^2\right)^{2/3}+d^{2/3} x^2\right)}{2 a d^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} x}{2 \sqrt[3]{x^3-a x^2}+\sqrt[3]{d} x}\right)}{a d^{2/3}}",1,"(3*x^2*Hypergeometric2F1[2/3, 1, 5/3, (d*x)/(-a + x)])/(2*a*(x^2*(-a + x))^(2/3))","C",1
2047,1,122,147,0.1795325,"\int \frac{2+x+x^2}{\left(3+2 x+x^2\right) \sqrt[3]{x^2+x^3}} \, dx","Integrate[(2 + x + x^2)/((3 + 2*x + x^2)*(x^2 + x^3)^(1/3)),x]","\frac{x \left(6 \sqrt[3]{x+1} \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};-x\right)+\left(-1-i \sqrt{2}\right) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{2 x}{\left(2+i \sqrt{2}\right) (x+1)}\right)+i \left(\sqrt{2}+i\right) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{2 i x}{\left(2 i+\sqrt{2}\right) (x+1)}\right)\right)}{2 \sqrt[3]{x^2 (x+1)}}","\frac{1}{2} \text{RootSum}\left[3 \text{$\#$1}^6-4 \text{$\#$1}^3+2\&,\frac{\text{$\#$1}^2 \log \left(\sqrt[3]{x^3+x^2}-\text{$\#$1} x\right)-\text{$\#$1}^2 \log (x)}{3 \text{$\#$1}^3-2}\&\right]-\log \left(\sqrt[3]{x^3+x^2}-x\right)+\frac{1}{2} \log \left(x^2+\sqrt[3]{x^3+x^2} x+\left(x^3+x^2\right)^{2/3}\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+x^2}+x}\right)",1,"(x*(6*(1 + x)^(1/3)*Hypergeometric2F1[1/3, 1/3, 4/3, -x] + (-1 - I*Sqrt[2])*Hypergeometric2F1[1/3, 1, 4/3, (2*x)/((2 + I*Sqrt[2])*(1 + x))] + I*(I + Sqrt[2])*Hypergeometric2F1[1/3, 1, 4/3, ((2*I)*x)/((2*I + Sqrt[2])*(1 + x))]))/(2*(x^2*(1 + x))^(1/3))","C",1
2048,1,122,147,0.0596603,"\int \frac{2+x+x^2}{\left(3+2 x+x^2\right) \sqrt[3]{x^2+x^3}} \, dx","Integrate[(2 + x + x^2)/((3 + 2*x + x^2)*(x^2 + x^3)^(1/3)),x]","\frac{x \left(6 \sqrt[3]{x+1} \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};-x\right)+\left(-1-i \sqrt{2}\right) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{2 x}{\left(2+i \sqrt{2}\right) (x+1)}\right)+i \left(\sqrt{2}+i\right) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{2 i x}{\left(2 i+\sqrt{2}\right) (x+1)}\right)\right)}{2 \sqrt[3]{x^2 (x+1)}}","\frac{1}{2} \text{RootSum}\left[3 \text{$\#$1}^6-4 \text{$\#$1}^3+2\&,\frac{\text{$\#$1}^2 \log \left(\sqrt[3]{x^3+x^2}-\text{$\#$1} x\right)-\text{$\#$1}^2 \log (x)}{3 \text{$\#$1}^3-2}\&\right]-\log \left(\sqrt[3]{x^3+x^2}-x\right)+\frac{1}{2} \log \left(x^2+\sqrt[3]{x^3+x^2} x+\left(x^3+x^2\right)^{2/3}\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+x^2}+x}\right)",1,"(x*(6*(1 + x)^(1/3)*Hypergeometric2F1[1/3, 1/3, 4/3, -x] + (-1 - I*Sqrt[2])*Hypergeometric2F1[1/3, 1, 4/3, (2*x)/((2 + I*Sqrt[2])*(1 + x))] + I*(I + Sqrt[2])*Hypergeometric2F1[1/3, 1, 4/3, ((2*I)*x)/((2*I + Sqrt[2])*(1 + x))]))/(2*(x^2*(1 + x))^(1/3))","C",1
2049,1,133,147,0.5143473,"\int \frac{b-c x+a x^2}{\left(-b+a x^2\right) \sqrt{b x+a x^3}} \, dx","Integrate[(b - c*x + a*x^2)/((-b + a*x^2)*Sqrt[b*x + a*x^3]),x]","-\frac{2 x \sqrt{\frac{a x^2}{b}+1} \left(x \left(3 a x F_1\left(\frac{5}{4};\frac{1}{2},1;\frac{9}{4};-\frac{a x^2}{b},\frac{a x^2}{b}\right)-5 c F_1\left(\frac{3}{4};\frac{1}{2},1;\frac{7}{4};-\frac{a x^2}{b},\frac{a x^2}{b}\right)\right)+15 b F_1\left(\frac{1}{4};\frac{1}{2},1;\frac{5}{4};-\frac{a x^2}{b},\frac{a x^2}{b}\right)\right)}{15 b \sqrt{x \left(a x^2+b\right)}}","-\frac{\left(2 \sqrt{a} \sqrt{b}+c\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{a x^3+b x}}{a x^2+b}\right)}{2 \sqrt{2} a^{3/4} b^{3/4}}-\frac{\left(2 \sqrt{a} \sqrt{b}-c\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{a x^3+b x}}{a x^2+b}\right)}{2 \sqrt{2} a^{3/4} b^{3/4}}",1,"(-2*x*Sqrt[1 + (a*x^2)/b]*(15*b*AppellF1[1/4, 1/2, 1, 5/4, -((a*x^2)/b), (a*x^2)/b] + x*(-5*c*AppellF1[3/4, 1/2, 1, 7/4, -((a*x^2)/b), (a*x^2)/b] + 3*a*x*AppellF1[5/4, 1/2, 1, 9/4, -((a*x^2)/b), (a*x^2)/b])))/(15*b*Sqrt[x*(b + a*x^2)])","C",0
2050,1,133,147,0.4288807,"\int \frac{b+c x+a x^2}{\left(-b+a x^2\right) \sqrt{b x+a x^3}} \, dx","Integrate[(b + c*x + a*x^2)/((-b + a*x^2)*Sqrt[b*x + a*x^3]),x]","-\frac{2 x \sqrt{\frac{a x^2}{b}+1} \left(x \left(5 c F_1\left(\frac{3}{4};\frac{1}{2},1;\frac{7}{4};-\frac{a x^2}{b},\frac{a x^2}{b}\right)+3 a x F_1\left(\frac{5}{4};\frac{1}{2},1;\frac{9}{4};-\frac{a x^2}{b},\frac{a x^2}{b}\right)\right)+15 b F_1\left(\frac{1}{4};\frac{1}{2},1;\frac{5}{4};-\frac{a x^2}{b},\frac{a x^2}{b}\right)\right)}{15 b \sqrt{x \left(a x^2+b\right)}}","-\frac{\left(2 \sqrt{a} \sqrt{b}-c\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{a x^3+b x}}{a x^2+b}\right)}{2 \sqrt{2} a^{3/4} b^{3/4}}-\frac{\left(2 \sqrt{a} \sqrt{b}+c\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{a x^3+b x}}{a x^2+b}\right)}{2 \sqrt{2} a^{3/4} b^{3/4}}",1,"(-2*x*Sqrt[1 + (a*x^2)/b]*(15*b*AppellF1[1/4, 1/2, 1, 5/4, -((a*x^2)/b), (a*x^2)/b] + x*(5*c*AppellF1[3/4, 1/2, 1, 7/4, -((a*x^2)/b), (a*x^2)/b] + 3*a*x*AppellF1[5/4, 1/2, 1, 9/4, -((a*x^2)/b), (a*x^2)/b])))/(15*b*Sqrt[x*(b + a*x^2)])","C",0
2051,1,133,147,0.1795315,"\int \frac{(1+x) \sqrt[4]{-x^3+x^4}}{1-x+x^2} \, dx","Integrate[((1 + x)*(-x^3 + x^4)^(1/4))/(1 - x + x^2),x]","\frac{4 \sqrt[4]{(x-1) x^3} \left(\sqrt[4]{x} \, _2F_1\left(-\frac{3}{4},\frac{1}{4};\frac{5}{4};1-x\right)+\sqrt[4]{x} \, _2F_1\left(\frac{1}{4},\frac{1}{4};\frac{5}{4};1-x\right)-\, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{\left(-i+\sqrt{3}\right) (x-1)}{\left(i+\sqrt{3}\right) x}\right)-\, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{\left(i+\sqrt{3}\right) (x-1)}{\left(-i+\sqrt{3}\right) x}\right)\right)}{x}","-\text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4+1\&,\frac{-\text{$\#$1}^4 \log \left(\sqrt[4]{x^4-x^3}-\text{$\#$1} x\right)+\text{$\#$1}^4 \log (x)+2 \log \left(\sqrt[4]{x^4-x^3}-\text{$\#$1} x\right)-2 \log (x)}{2 \text{$\#$1}^7-\text{$\#$1}^3}\&\right]+\sqrt[4]{x^4-x^3}-\frac{7}{2} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^3}}\right)+\frac{7}{2} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^3}}\right)",1,"(4*((-1 + x)*x^3)^(1/4)*(x^(1/4)*Hypergeometric2F1[-3/4, 1/4, 5/4, 1 - x] + x^(1/4)*Hypergeometric2F1[1/4, 1/4, 5/4, 1 - x] - Hypergeometric2F1[1/4, 1, 5/4, ((-I + Sqrt[3])*(-1 + x))/((I + Sqrt[3])*x)] - Hypergeometric2F1[1/4, 1, 5/4, ((I + Sqrt[3])*(-1 + x))/((-I + Sqrt[3])*x)]))/x","C",1
2052,1,133,147,0.0778888,"\int \frac{(1+x) \sqrt[4]{-x^3+x^4}}{1-x+x^2} \, dx","Integrate[((1 + x)*(-x^3 + x^4)^(1/4))/(1 - x + x^2),x]","\frac{4 \sqrt[4]{(x-1) x^3} \left(\sqrt[4]{x} \, _2F_1\left(-\frac{3}{4},\frac{1}{4};\frac{5}{4};1-x\right)+\sqrt[4]{x} \, _2F_1\left(\frac{1}{4},\frac{1}{4};\frac{5}{4};1-x\right)-\, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{\left(-i+\sqrt{3}\right) (x-1)}{\left(i+\sqrt{3}\right) x}\right)-\, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{\left(i+\sqrt{3}\right) (x-1)}{\left(-i+\sqrt{3}\right) x}\right)\right)}{x}","-\text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4+1\&,\frac{-\text{$\#$1}^4 \log \left(\sqrt[4]{x^4-x^3}-\text{$\#$1} x\right)+\text{$\#$1}^4 \log (x)+2 \log \left(\sqrt[4]{x^4-x^3}-\text{$\#$1} x\right)-2 \log (x)}{2 \text{$\#$1}^7-\text{$\#$1}^3}\&\right]+\sqrt[4]{x^4-x^3}-\frac{7}{2} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^3}}\right)+\frac{7}{2} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^3}}\right)",1,"(4*((-1 + x)*x^3)^(1/4)*(x^(1/4)*Hypergeometric2F1[-3/4, 1/4, 5/4, 1 - x] + x^(1/4)*Hypergeometric2F1[1/4, 1/4, 5/4, 1 - x] - Hypergeometric2F1[1/4, 1, 5/4, ((-I + Sqrt[3])*(-1 + x))/((I + Sqrt[3])*x)] - Hypergeometric2F1[1/4, 1, 5/4, ((I + Sqrt[3])*(-1 + x))/((-I + Sqrt[3])*x)]))/x","C",1
2053,0,0,147,0.6724187,"\int \frac{\sqrt[3]{b-a x^6} \left(b+a x^6\right)}{x^2 \left(-b+c x^3+a x^6\right)} \, dx","Integrate[((b - a*x^6)^(1/3)*(b + a*x^6))/(x^2*(-b + c*x^3 + a*x^6)),x]","\int \frac{\sqrt[3]{b-a x^6} \left(b+a x^6\right)}{x^2 \left(-b+c x^3+a x^6\right)} \, dx","-\frac{1}{6} \sqrt[3]{c} \log \left(\sqrt[3]{c} x \sqrt[3]{b-a x^6}+\left(b-a x^6\right)^{2/3}+c^{2/3} x^2\right)+\frac{1}{3} \sqrt[3]{c} \log \left(\sqrt[3]{b-a x^6}-\sqrt[3]{c} x\right)+\frac{\sqrt[3]{c} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{c} x}{2 \sqrt[3]{b-a x^6}+\sqrt[3]{c} x}\right)}{\sqrt{3}}+\frac{\sqrt[3]{b-a x^6}}{x}",1,"Integrate[((b - a*x^6)^(1/3)*(b + a*x^6))/(x^2*(-b + c*x^3 + a*x^6)), x]","F",-1
2054,0,0,147,0.2076677,"\int \frac{x^2 \left(4+7 x^3\right)}{\sqrt[3]{x+x^4} \left(-1+x^4+x^7\right)} \, dx","Integrate[(x^2*(4 + 7*x^3))/((x + x^4)^(1/3)*(-1 + x^4 + x^7)),x]","\int \frac{x^2 \left(4+7 x^3\right)}{\sqrt[3]{x+x^4} \left(-1+x^4+x^7\right)} \, dx","2 \tanh ^{-1}\left(1-2 x \sqrt[3]{x^4+x}\right)-\sqrt{3} \tan ^{-1}\left(\frac{3 \sqrt{3} x \sqrt[3]{x^4+x}-3 x^2 \sqrt[3]{x^4+x}}{-3 \sqrt[3]{x^4+x} x+\sqrt{3} \sqrt[3]{x^4+x} x^2+2 \sqrt{3} x-6}\right)-\tanh ^{-1}\left(\frac{\sqrt[3]{x^4+x} x+1}{\sqrt[3]{x^4+x} x+2 \left(x^4+x\right)^{2/3} x^2+1}\right)",1,"Integrate[(x^2*(4 + 7*x^3))/((x + x^4)^(1/3)*(-1 + x^4 + x^7)), x]","F",-1
2055,0,0,147,0.9728915,"\int \frac{2 d+c x^4}{\sqrt[4]{-b+a x^4} \left(-2 f+e x^8\right)} \, dx","Integrate[(2*d + c*x^4)/((-b + a*x^4)^(1/4)*(-2*f + e*x^8)),x]","\int \frac{2 d+c x^4}{\sqrt[4]{-b+a x^4} \left(-2 f+e x^8\right)} \, dx","\frac{\text{RootSum}\left[-2 \text{$\#$1}^8 f+4 \text{$\#$1}^4 a f-2 a^2 f+b^2 e\&,\frac{-2 \text{$\#$1}^4 d \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+2 \text{$\#$1}^4 d \log (x)+b c \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+2 a d \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)-2 a d \log (x)-b c \log (x)}{\text{$\#$1} a-\text{$\#$1}^5}\&\right]}{16 f}",1,"Integrate[(2*d + c*x^4)/((-b + a*x^4)^(1/4)*(-2*f + e*x^8)), x]","F",-1
2056,1,209,147,0.3245324,"\int \frac{\sqrt{1+x} \left(1+x^2\right)}{\left(-1+x^2\right) \sqrt{x+\sqrt{1+x}}} \, dx","Integrate[(Sqrt[1 + x]*(1 + x^2))/((-1 + x^2)*Sqrt[x + Sqrt[1 + x]]),x]","\sqrt{x+1} \sqrt{x+\sqrt{x+1}}-\frac{3}{2} \sqrt{x+\sqrt{x+1}}+\sqrt{2 \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{\left(2 \sqrt{2}-1\right) \sqrt{x+1}+\sqrt{2}+2}{2 \sqrt{\sqrt{2}-1} \sqrt{x+\sqrt{x+1}}}\right)+\frac{7}{4} \tanh ^{-1}\left(\frac{2 \sqrt{x+1}+1}{2 \sqrt{x+\sqrt{x+1}}}\right)+\sqrt{2 \left(\sqrt{2}-1\right)} \tanh ^{-1}\left(\frac{-\left(\left(1+2 \sqrt{2}\right) \sqrt{x+1}\right)-\sqrt{2}+2}{2 \sqrt{1+\sqrt{2}} \sqrt{x+\sqrt{x+1}}}\right)","-16 \text{RootSum}\left[\text{$\#$1}^4+4 \text{$\#$1}^3-18 \text{$\#$1}^2+20 \text{$\#$1}+25\&,\frac{\text{$\#$1} \log \left(\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)}{\text{$\#$1}^3+3 \text{$\#$1}^2-9 \text{$\#$1}+5}\&\right]+\sqrt{x+1} \sqrt{x+\sqrt{x+1}}-\frac{3}{2} \sqrt{x+\sqrt{x+1}}-\frac{7}{4} \log \left(2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)",1,"(-3*Sqrt[x + Sqrt[1 + x]])/2 + Sqrt[1 + x]*Sqrt[x + Sqrt[1 + x]] + Sqrt[2*(1 + Sqrt[2])]*ArcTan[(2 + Sqrt[2] + (-1 + 2*Sqrt[2])*Sqrt[1 + x])/(2*Sqrt[-1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x]])] + (7*ArcTanh[(1 + 2*Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])])/4 + Sqrt[2*(-1 + Sqrt[2])]*ArcTanh[(2 - Sqrt[2] - (1 + 2*Sqrt[2])*Sqrt[1 + x])/(2*Sqrt[1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x]])]","A",1
2057,1,209,147,0.0855045,"\int \frac{\sqrt{1+x} \left(1+x^2\right)}{\left(-1+x^2\right) \sqrt{x+\sqrt{1+x}}} \, dx","Integrate[(Sqrt[1 + x]*(1 + x^2))/((-1 + x^2)*Sqrt[x + Sqrt[1 + x]]),x]","\sqrt{x+1} \sqrt{x+\sqrt{x+1}}-\frac{3}{2} \sqrt{x+\sqrt{x+1}}+\sqrt{2 \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{\left(2 \sqrt{2}-1\right) \sqrt{x+1}+\sqrt{2}+2}{2 \sqrt{\sqrt{2}-1} \sqrt{x+\sqrt{x+1}}}\right)+\frac{7}{4} \tanh ^{-1}\left(\frac{2 \sqrt{x+1}+1}{2 \sqrt{x+\sqrt{x+1}}}\right)+\sqrt{2 \left(\sqrt{2}-1\right)} \tanh ^{-1}\left(\frac{-\left(\left(1+2 \sqrt{2}\right) \sqrt{x+1}\right)-\sqrt{2}+2}{2 \sqrt{1+\sqrt{2}} \sqrt{x+\sqrt{x+1}}}\right)","-16 \text{RootSum}\left[\text{$\#$1}^4+4 \text{$\#$1}^3-18 \text{$\#$1}^2+20 \text{$\#$1}+25\&,\frac{\text{$\#$1} \log \left(\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)}{\text{$\#$1}^3+3 \text{$\#$1}^2-9 \text{$\#$1}+5}\&\right]+\sqrt{x+1} \sqrt{x+\sqrt{x+1}}-\frac{3}{2} \sqrt{x+\sqrt{x+1}}-\frac{7}{4} \log \left(2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)",1,"(-3*Sqrt[x + Sqrt[1 + x]])/2 + Sqrt[1 + x]*Sqrt[x + Sqrt[1 + x]] + Sqrt[2*(1 + Sqrt[2])]*ArcTan[(2 + Sqrt[2] + (-1 + 2*Sqrt[2])*Sqrt[1 + x])/(2*Sqrt[-1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x]])] + (7*ArcTanh[(1 + 2*Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])])/4 + Sqrt[2*(-1 + Sqrt[2])]*ArcTanh[(2 - Sqrt[2] - (1 + 2*Sqrt[2])*Sqrt[1 + x])/(2*Sqrt[1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x]])]","A",1
2058,1,102,147,0.2332864,"\int \frac{\sqrt{x-\sqrt{-1+x^2}}}{x^2} \, dx","Integrate[Sqrt[x - Sqrt[-1 + x^2]]/x^2,x]","\frac{4 \sqrt{x^2-1} \left(x-\sqrt{x^2-1}\right)^{5/2} \left(\, _2F_1\left(\frac{3}{4},1;\frac{7}{4};-\left(x-\sqrt{x^2-1}\right)^2\right)-2 \, _2F_1\left(\frac{3}{4},2;\frac{7}{4};-\left(x-\sqrt{x^2-1}\right)^2\right)\right)}{-3 x^2+3 \sqrt{x^2-1} x+3}","\sqrt{x-\sqrt{x^2-1}} \left(\sqrt{\sqrt{x^2-1}+x} \left(-\frac{\tan ^{-1}\left(\frac{\frac{\sqrt{x^2-1}}{\sqrt{2}}+\frac{x}{\sqrt{2}}-\frac{1}{\sqrt{2}}}{\sqrt{\sqrt{x^2-1}+x}}\right)}{\sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{\frac{\sqrt{x^2-1}}{\sqrt{2}}+\frac{x}{\sqrt{2}}+\frac{1}{\sqrt{2}}}{\sqrt{\sqrt{x^2-1}+x}}\right)}{\sqrt{2}}\right)-\frac{1}{x}\right)",1,"(4*Sqrt[-1 + x^2]*(x - Sqrt[-1 + x^2])^(5/2)*(Hypergeometric2F1[3/4, 1, 7/4, -(x - Sqrt[-1 + x^2])^2] - 2*Hypergeometric2F1[3/4, 2, 7/4, -(x - Sqrt[-1 + x^2])^2]))/(3 - 3*x^2 + 3*x*Sqrt[-1 + x^2])","C",1
2059,0,0,147,1.52058,"\int \frac{\left(a x+\sqrt{-b x+a^2 x^2}\right)^{3/4}}{\sqrt{-b x+a^2 x^2}} \, dx","Integrate[(a*x + Sqrt[-(b*x) + a^2*x^2])^(3/4)/Sqrt[-(b*x) + a^2*x^2],x]","\int \frac{\left(a x+\sqrt{-b x+a^2 x^2}\right)^{3/4}}{\sqrt{-b x+a^2 x^2}} \, dx","\frac{4 \left(\sqrt{a^2 x^2-b x}+a x\right)^{3/4}}{3 a}+\frac{\sqrt[4]{2} b^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} \sqrt[4]{\sqrt{a^2 x^2-b x}+a x}}{\sqrt[4]{b}}\right)}{a^{7/4}}-\frac{\sqrt[4]{2} b^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} \sqrt[4]{\sqrt{a^2 x^2-b x}+a x}}{\sqrt[4]{b}}\right)}{a^{7/4}}",1,"Integrate[(a*x + Sqrt[-(b*x) + a^2*x^2])^(3/4)/Sqrt[-(b*x) + a^2*x^2], x]","F",-1
2060,1,117,148,0.1914135,"\int \frac{(1+x) \sqrt[4]{x^3+x^4}}{x \left(-1+x^3\right)} \, dx","Integrate[((1 + x)*(x^3 + x^4)^(1/4))/(x*(-1 + x^3)),x]","\frac{2 x^3 \left(-8 \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{2 x}{x+1}\right)+\left(1-i \sqrt{3}\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{x-i \sqrt{3} x}{2 x+2}\right)+\left(1+i \sqrt{3}\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{i \sqrt{3} x+x}{2 x+2}\right)\right)}{9 \left(x^3 (x+1)\right)^{3/4}}","\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4+1\&,\frac{-\text{$\#$1}^4 \log \left(\sqrt[4]{x^4+x^3}-\text{$\#$1} x\right)+\text{$\#$1}^4 \log (x)+2 \log \left(\sqrt[4]{x^4+x^3}-\text{$\#$1} x\right)-2 \log (x)}{2 \text{$\#$1}^7-\text{$\#$1}^3}\&\right]+\frac{4}{3} \sqrt[4]{2} \tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+x^3}}\right)-\frac{4}{3} \sqrt[4]{2} \tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+x^3}}\right)",1,"(2*x^3*(-8*Hypergeometric2F1[3/4, 1, 7/4, (2*x)/(1 + x)] + (1 - I*Sqrt[3])*Hypergeometric2F1[3/4, 1, 7/4, (x - I*Sqrt[3]*x)/(2 + 2*x)] + (1 + I*Sqrt[3])*Hypergeometric2F1[3/4, 1, 7/4, (x + I*Sqrt[3]*x)/(2 + 2*x)]))/(9*(x^3*(1 + x))^(3/4))","C",1
2061,1,237,148,0.2793945,"\int \frac{\sqrt[4]{-b x^3+a x^4} \left(-d+c x^4\right)}{x^4} \, dx","Integrate[((-(b*x^3) + a*x^4)^(1/4)*(-d + c*x^4))/x^4,x]","-\frac{4 \sqrt[4]{x^3 (a x-b)} \left(4 a^6 d x^2 \sqrt[4]{1-\frac{a x}{b}}+a^5 b d x \sqrt[4]{1-\frac{a x}{b}}-5 a^4 b^2 d \sqrt[4]{1-\frac{a x}{b}}-24 a^2 b^4 c x^2 \sqrt[4]{1-\frac{a x}{b}}+5 b^6 c \, _2F_1\left(-\frac{17}{4},-\frac{9}{4};-\frac{5}{4};\frac{a x}{b}\right)-20 b^6 c \, _2F_1\left(-\frac{13}{4},-\frac{9}{4};-\frac{5}{4};\frac{a x}{b}\right)+30 b^6 c \, _2F_1\left(-\frac{9}{4},-\frac{9}{4};-\frac{5}{4};\frac{a x}{b}\right)-15 b^6 c \sqrt[4]{1-\frac{a x}{b}}+39 a b^5 c x \sqrt[4]{1-\frac{a x}{b}}\right)}{45 a^4 b^2 x^3 \sqrt[4]{1-\frac{a x}{b}}}","\frac{3 b^2 c \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^3}}\right)}{16 a^{7/4}}-\frac{3 b^2 c \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^3}}\right)}{16 a^{7/4}}+\frac{\sqrt[4]{a x^4-b x^3} \left(-128 a^3 d x^2-32 a^2 b d x+180 a b^2 c x^4+160 a b^2 d-45 b^3 c x^3\right)}{360 a b^2 x^3}",1,"(-4*(x^3*(-b + a*x))^(1/4)*(-15*b^6*c*(1 - (a*x)/b)^(1/4) - 5*a^4*b^2*d*(1 - (a*x)/b)^(1/4) + 39*a*b^5*c*x*(1 - (a*x)/b)^(1/4) + a^5*b*d*x*(1 - (a*x)/b)^(1/4) - 24*a^2*b^4*c*x^2*(1 - (a*x)/b)^(1/4) + 4*a^6*d*x^2*(1 - (a*x)/b)^(1/4) + 5*b^6*c*Hypergeometric2F1[-17/4, -9/4, -5/4, (a*x)/b] - 20*b^6*c*Hypergeometric2F1[-13/4, -9/4, -5/4, (a*x)/b] + 30*b^6*c*Hypergeometric2F1[-9/4, -9/4, -5/4, (a*x)/b]))/(45*a^4*b^2*x^3*(1 - (a*x)/b)^(1/4))","C",1
2062,1,135,149,0.2730361,"\int \frac{\left(1+x^3\right)^{2/3} \left(2+x^3\right)}{x^6 \left(4+x^3\right)} \, dx","Integrate[((1 + x^3)^(2/3)*(2 + x^3))/(x^6*(4 + x^3)),x]","\frac{1}{192} \left(6\ 2^{2/3} \sqrt[6]{3} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{6} x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)+6^{2/3} \left(\log \left(\frac{2 \sqrt[3]{6} x}{\sqrt[3]{x^3+1}}+\frac{6^{2/3} x^2}{\left(x^3+1\right)^{2/3}}+4\right)-2 \log \left(2-\frac{\sqrt[3]{6} x}{\sqrt[3]{x^3+1}}\right)\right)\right)+\left(x^3+1\right)^{2/3} \left(-\frac{1}{10 x^5}-\frac{13}{80 x^2}\right)","-\frac{\log \left(6^{2/3} \sqrt[3]{x^3+1}-3 x\right)}{16 \sqrt[3]{6}}+\frac{\sqrt[6]{3} \tan ^{-1}\left(\frac{3^{5/6} x}{2\ 2^{2/3} \sqrt[3]{x^3+1}+\sqrt[3]{3} x}\right)}{16 \sqrt[3]{2}}+\frac{\left(x^3+1\right)^{2/3} \left(-13 x^3-8\right)}{80 x^5}+\frac{\log \left(6^{2/3} \sqrt[3]{x^3+1} x+2 \sqrt[3]{6} \left(x^3+1\right)^{2/3}+3 x^2\right)}{32 \sqrt[3]{6}}",1,"(-1/10*1/x^5 - 13/(80*x^2))*(1 + x^3)^(2/3) + (6*2^(2/3)*3^(1/6)*ArcTan[(1 + (6^(1/3)*x)/(1 + x^3)^(1/3))/Sqrt[3]] + 6^(2/3)*(-2*Log[2 - (6^(1/3)*x)/(1 + x^3)^(1/3)] + Log[4 + (6^(2/3)*x^2)/(1 + x^3)^(2/3) + (2*6^(1/3)*x)/(1 + x^3)^(1/3)]))/192","A",1
2063,1,130,149,0.2699209,"\int \frac{\left(-1+x^3\right) \left(1+3 x^3\right)^{2/3}}{x^6 \left(1+x^3\right)} \, dx","Integrate[((-1 + x^3)*(1 + 3*x^3)^(2/3))/(x^6*(1 + x^3)),x]","\frac{1}{3} 2^{2/3} \left(-2 \log \left(1-\frac{\sqrt[3]{2} x}{\sqrt[3]{x^3+3}}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{2} x}{\sqrt[3]{x^3+3}}+1}{\sqrt{3}}\right)+\log \left(\frac{\sqrt[3]{2} x}{\sqrt[3]{x^3+3}}+\frac{2^{2/3} x^2}{\left(x^3+3\right)^{2/3}}+1\right)\right)+\left(3 x^3+1\right)^{2/3} \left(\frac{1}{5 x^5}-\frac{2}{5 x^2}\right)","-\frac{2}{3} 2^{2/3} \log \left(2^{2/3} \sqrt[3]{3 x^3+1}-2 x\right)+\frac{2\ 2^{2/3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{3 x^3+1}+x}\right)}{\sqrt{3}}+\frac{\left(3 x^3+1\right)^{2/3} \left(1-2 x^3\right)}{5 x^5}+\frac{1}{3} 2^{2/3} \log \left(2^{2/3} \sqrt[3]{3 x^3+1} x+\sqrt[3]{2} \left(3 x^3+1\right)^{2/3}+2 x^2\right)",1,"(1/(5*x^5) - 2/(5*x^2))*(1 + 3*x^3)^(2/3) + (2^(2/3)*(2*Sqrt[3]*ArcTan[(1 + (2*2^(1/3)*x)/(3 + x^3)^(1/3))/Sqrt[3]] - 2*Log[1 - (2^(1/3)*x)/(3 + x^3)^(1/3)] + Log[1 + (2^(2/3)*x^2)/(3 + x^3)^(2/3) + (2^(1/3)*x)/(3 + x^3)^(1/3)]))/3","A",0
2064,0,0,149,0.6216179,"\int \frac{3-8 x+8 x^2-12 x^4}{x \sqrt[3]{\frac{1-2 x^2}{1+2 x^2}} \left(1+2 x^2\right) \left(3-7 x+7 x^2-6 x^3+2 x^4\right)} \, dx","Integrate[(3 - 8*x + 8*x^2 - 12*x^4)/(x*((1 - 2*x^2)/(1 + 2*x^2))^(1/3)*(1 + 2*x^2)*(3 - 7*x + 7*x^2 - 6*x^3 + 2*x^4)),x]","\int \frac{3-8 x+8 x^2-12 x^4}{x \sqrt[3]{\frac{1-2 x^2}{1+2 x^2}} \left(1+2 x^2\right) \left(3-7 x+7 x^2-6 x^3+2 x^4\right)} \, dx","\log \left(\sqrt[3]{\frac{1-2 x^2}{2 x^2+1}}+x-1\right)-\frac{1}{2} \log \left(x^2+\left(\frac{1-2 x^2}{2 x^2+1}\right)^{2/3}+(1-x) \sqrt[3]{\frac{1-2 x^2}{2 x^2+1}}-2 x+1\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{\frac{1-2 x^2}{2 x^2+1}}}{\sqrt[3]{\frac{1-2 x^2}{2 x^2+1}}-2 x+2}\right)",1,"Integrate[(3 - 8*x + 8*x^2 - 12*x^4)/(x*((1 - 2*x^2)/(1 + 2*x^2))^(1/3)*(1 + 2*x^2)*(3 - 7*x + 7*x^2 - 6*x^3 + 2*x^4)), x]","F",-1
2065,1,93,149,0.691941,"\int \frac{x^2}{\sqrt{b x+a x^3} \left(-b^2+a^2 x^4\right)} \, dx","Integrate[x^2/(Sqrt[b*x + a*x^3]*(-b^2 + a^2*x^4)),x]","\frac{b x \sqrt{\frac{a x^2}{b}+1}-x \left(a x^2+b\right) F_1\left(\frac{1}{4};-\frac{1}{2},1;\frac{5}{4};-\frac{a x^2}{b},\frac{a x^2}{b}\right)}{2 a b^2 \sqrt{x \left(a x^2+b\right)} \sqrt{\frac{a x^2}{b}+1}}","-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{a x^3+b x}}{a x^2+b}\right)}{4 \sqrt{2} a^{5/4} b^{5/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{a x^3+b x}}{a x^2+b}\right)}{4 \sqrt{2} a^{5/4} b^{5/4}}+\frac{\sqrt{a x^3+b x}}{2 a b \left(a x^2+b\right)}",1,"(b*x*Sqrt[1 + (a*x^2)/b] - x*(b + a*x^2)*AppellF1[1/4, -1/2, 1, 5/4, -((a*x^2)/b), (a*x^2)/b])/(2*a*b^2*Sqrt[x*(b + a*x^2)]*Sqrt[1 + (a*x^2)/b])","C",0
2066,1,97,149,5.2211479,"\int \frac{b+a x^6}{x^6 \left(-b+a x^3\right) \sqrt[4]{b x+a x^4}} \, dx","Integrate[(b + a*x^6)/(x^6*(-b + a*x^3)*(b*x + a*x^4)^(1/4)),x]","\frac{4 \left(\left(a x^3+b\right)^2-\frac{7 a x^6 (a+b) \sqrt[4]{\frac{a x^3}{b}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{4};\frac{5}{4};-\frac{2 a x^3}{b-a x^3}\right)}{\sqrt[4]{1-\frac{a x^3}{b}}}\right)}{21 b^2 x^5 \sqrt[4]{x \left(a x^3+b\right)}}","-\frac{2^{3/4} \left(a^{3/4} b+a^{7/4}\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} \left(a x^4+b x\right)^{3/4}}{a x^3+b}\right)}{3 b^2}-\frac{2^{3/4} \left(a^{3/4} b+a^{7/4}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} \left(a x^4+b x\right)^{3/4}}{a x^3+b}\right)}{3 b^2}+\frac{4 \left(a x^4+b x\right)^{3/4} \left(a x^3+b\right)}{21 b^2 x^6}",1,"(4*((b + a*x^3)^2 - (7*a*(a + b)*x^6*(1 + (a*x^3)/b)^(1/4)*Hypergeometric2F1[1/4, 1/4, 5/4, (-2*a*x^3)/(b - a*x^3)])/(1 - (a*x^3)/b)^(1/4)))/(21*b^2*x^5*(x*(b + a*x^3))^(1/4))","C",0
2067,0,0,149,0.71908,"\int \frac{\sqrt[3]{-1+2 x^3+x^8} \left(3+5 x^8\right)}{x^2 \left(-1+x^8\right)} \, dx","Integrate[((-1 + 2*x^3 + x^8)^(1/3)*(3 + 5*x^8))/(x^2*(-1 + x^8)),x]","\int \frac{\sqrt[3]{-1+2 x^3+x^8} \left(3+5 x^8\right)}{x^2 \left(-1+x^8\right)} \, dx","\frac{3 \sqrt[3]{x^8+2 x^3-1}}{x}+\sqrt[3]{2} \log \left(2^{2/3} \sqrt[3]{x^8+2 x^3-1}-2 x\right)+\sqrt[3]{2} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^8+2 x^3-1}+x}\right)-\frac{\log \left(2 x^2+2^{2/3} \sqrt[3]{x^8+2 x^3-1} x+\sqrt[3]{2} \left(x^8+2 x^3-1\right)^{2/3}\right)}{2^{2/3}}",1,"Integrate[((-1 + 2*x^3 + x^8)^(1/3)*(3 + 5*x^8))/(x^2*(-1 + x^8)), x]","F",-1
2068,1,212,149,0.4300576,"\int \frac{\sqrt{b^2+a x^2}}{\sqrt{b+\sqrt{b^2+a x^2}}} \, dx","Integrate[Sqrt[b^2 + a*x^2]/Sqrt[b + Sqrt[b^2 + a*x^2]],x]","\frac{6 b^2 \left(\sqrt{a x^2+b^2}+b\right) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{b-\sqrt{b^2+a x^2}}{2 b}\right)-6 b^2 \sqrt{a x^2+b^2}+4 a x^2 \sqrt{a x^2+b^2}+3 \sqrt{2} b^{3/2} \sqrt{\sqrt{a x^2+b^2}-b} \left(\sqrt{a x^2+b^2}+b\right) \tan ^{-1}\left(\frac{\sqrt{\sqrt{a x^2+b^2}-b}}{\sqrt{2} \sqrt{b}}\right)-4 a b x^2-6 b^3}{6 a x \sqrt{\sqrt{a x^2+b^2}+b}}","-\frac{2 b x}{3 \sqrt{\sqrt{a x^2+b^2}+b}}+\frac{2 x \sqrt{a x^2+b^2}}{3 \sqrt{\sqrt{a x^2+b^2}+b}}+\frac{2 \sqrt{2} b^{3/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{2} \sqrt{b} \sqrt{\sqrt{a x^2+b^2}+b}}-\frac{\sqrt{\sqrt{a x^2+b^2}+b}}{\sqrt{2} \sqrt{b}}\right)}{\sqrt{a}}",1,"(-6*b^3 - 4*a*b*x^2 - 6*b^2*Sqrt[b^2 + a*x^2] + 4*a*x^2*Sqrt[b^2 + a*x^2] + 3*Sqrt[2]*b^(3/2)*Sqrt[-b + Sqrt[b^2 + a*x^2]]*(b + Sqrt[b^2 + a*x^2])*ArcTan[Sqrt[-b + Sqrt[b^2 + a*x^2]]/(Sqrt[2]*Sqrt[b])] + 6*b^2*(b + Sqrt[b^2 + a*x^2])*Hypergeometric2F1[-1/2, 1, 1/2, (b - Sqrt[b^2 + a*x^2])/(2*b)])/(6*a*x*Sqrt[b + Sqrt[b^2 + a*x^2]])","C",1
2069,0,0,149,0.5372397,"\int \frac{\sqrt{b+\sqrt{b^2+a x^2}}}{\left(b^2+a x^2\right)^3} \, dx","Integrate[Sqrt[b + Sqrt[b^2 + a*x^2]]/(b^2 + a*x^2)^3,x]","\int \frac{\sqrt{b+\sqrt{b^2+a x^2}}}{\left(b^2+a x^2\right)^3} \, dx","\frac{35 \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b} \sqrt{\sqrt{a x^2+b^2}+b}}\right)}{64 \sqrt{a} b^{9/2}}+\frac{7 x \left(15 a x^2+23 b^2\right)}{192 b^4 \left(a x^2+b^2\right)^{3/2} \sqrt{\sqrt{a x^2+b^2}+b}}+\frac{x \left(35 a x^2+59 b^2\right)}{96 b^3 \left(a x^2+b^2\right)^2 \sqrt{\sqrt{a x^2+b^2}+b}}",1,"Integrate[Sqrt[b + Sqrt[b^2 + a*x^2]]/(b^2 + a*x^2)^3, x]","F",-1
2070,1,40,150,0.0144589,"\int \frac{\left(-b+a x^2\right)^{3/4}}{x^3} \, dx","Integrate[(-b + a*x^2)^(3/4)/x^3,x]","\frac{2 a \left(a x^2-b\right)^{7/4} \, _2F_1\left(\frac{7}{4},2;\frac{11}{4};1-\frac{a x^2}{b}\right)}{7 b^2}","-\frac{\left(a x^2-b\right)^{3/4}}{2 x^2}-\frac{3 a \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^2-b}}{\sqrt{a x^2-b}-\sqrt{b}}\right)}{4 \sqrt{2} \sqrt[4]{b}}-\frac{3 a \tanh ^{-1}\left(\frac{\frac{\sqrt{a x^2-b}}{\sqrt{2} \sqrt[4]{b}}+\frac{\sqrt[4]{b}}{\sqrt{2}}}{\sqrt[4]{a x^2-b}}\right)}{4 \sqrt{2} \sqrt[4]{b}}",1,"(2*a*(-b + a*x^2)^(7/4)*Hypergeometric2F1[7/4, 2, 11/4, 1 - (a*x^2)/b])/(7*b^2)","C",1
2071,1,139,150,0.1729512,"\int \frac{\left(1+x^3\right) \left(-1+2 x^3\right)^{2/3}}{x^6 \left(1+2 x^3\right)} \, dx","Integrate[((1 + x^3)*(-1 + 2*x^3)^(2/3))/(x^6*(1 + 2*x^3)),x]","\left(\frac{9}{10 x^2}-\frac{1}{5 x^5}\right) \left(2 x^3-1\right)^{2/3}-\frac{1}{3} \sqrt[3]{2} \left(-2 \log \left(1-\frac{2^{2/3} x}{\sqrt[3]{2-x^3}}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2\ 2^{2/3} x}{\sqrt[3]{2-x^3}}+1}{\sqrt{3}}\right)+\log \left(\frac{2^{2/3} x}{\sqrt[3]{2-x^3}}+\frac{2 \sqrt[3]{2} x^2}{\left(2-x^3\right)^{2/3}}+1\right)\right)","\frac{2}{3} \sqrt[3]{2} \log \left(\sqrt[3]{2} \sqrt[3]{2 x^3-1}-2 x\right)-\frac{2 \sqrt[3]{2} \tan ^{-1}\left(\frac{\sqrt{3} x}{\sqrt[3]{2} \sqrt[3]{2 x^3-1}+x}\right)}{\sqrt{3}}+\frac{\left(2 x^3-1\right)^{2/3} \left(9 x^3-2\right)}{10 x^5}-\frac{1}{3} \sqrt[3]{2} \log \left(2 \sqrt[3]{2} \sqrt[3]{2 x^3-1} x+2^{2/3} \left(2 x^3-1\right)^{2/3}+4 x^2\right)",1,"(-1/5*1/x^5 + 9/(10*x^2))*(-1 + 2*x^3)^(2/3) - (2^(1/3)*(2*Sqrt[3]*ArcTan[(1 + (2*2^(2/3)*x)/(2 - x^3)^(1/3))/Sqrt[3]] - 2*Log[1 - (2^(2/3)*x)/(2 - x^3)^(1/3)] + Log[1 + (2*2^(1/3)*x^2)/(2 - x^3)^(2/3) + (2^(2/3)*x)/(2 - x^3)^(1/3)]))/3","A",0
2072,1,129,150,0.1812741,"\int \frac{\left(1-x^3\right)^{2/3} \left(-1+4 x^3\right)}{x^6 \left(-2+3 x^3\right)} \, dx","Integrate[((1 - x^3)^(2/3)*(-1 + 4*x^3))/(x^6*(-2 + 3*x^3)),x]","\left(\frac{29}{40 x^2}-\frac{1}{10 x^5}\right) \left(1-x^3\right)^{2/3}-\frac{5 \left(-2 \log \left(2-\frac{2^{2/3} x}{\sqrt[3]{x^3-1}}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2^{2/3} x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)+\log \left(\frac{2^{2/3} x}{\sqrt[3]{x^3-1}}+\frac{\sqrt[3]{2} x^2}{\left(x^3-1\right)^{2/3}}+2\right)\right)}{24\ 2^{2/3}}","\frac{5 \log \left(\sqrt[3]{2} \sqrt[3]{1-x^3}-x\right)}{12\ 2^{2/3}}-\frac{5 \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{2} \sqrt[3]{1-x^3}+x}\right)}{4\ 2^{2/3} \sqrt{3}}+\frac{\left(1-x^3\right)^{2/3} \left(29 x^3-4\right)}{40 x^5}-\frac{5 \log \left(\sqrt[3]{2} \sqrt[3]{1-x^3} x+2^{2/3} \left(1-x^3\right)^{2/3}+x^2\right)}{24\ 2^{2/3}}",1,"(-1/10*1/x^5 + 29/(40*x^2))*(1 - x^3)^(2/3) - (5*(2*Sqrt[3]*ArcTan[(1 + (2^(2/3)*x)/(-1 + x^3)^(1/3))/Sqrt[3]] - 2*Log[2 - (2^(2/3)*x)/(-1 + x^3)^(1/3)] + Log[2 + (2^(1/3)*x^2)/(-1 + x^3)^(2/3) + (2^(2/3)*x)/(-1 + x^3)^(1/3)]))/(24*2^(2/3))","A",0
2073,1,40,150,0.0128752,"\int \frac{\sqrt[4]{-b+a x^3}}{x^4} \, dx","Integrate[(-b + a*x^3)^(1/4)/x^4,x]","\frac{4 a \left(a x^3-b\right)^{5/4} \, _2F_1\left(\frac{5}{4},2;\frac{9}{4};1-\frac{a x^3}{b}\right)}{15 b^2}","-\frac{a \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^3-b}}{\sqrt{a x^3-b}-\sqrt{b}}\right)}{6 \sqrt{2} b^{3/4}}+\frac{a \tanh ^{-1}\left(\frac{\frac{\sqrt{a x^3-b}}{\sqrt{2} \sqrt[4]{b}}+\frac{\sqrt[4]{b}}{\sqrt{2}}}{\sqrt[4]{a x^3-b}}\right)}{6 \sqrt{2} b^{3/4}}-\frac{\sqrt[4]{a x^3-b}}{3 x^3}",1,"(4*a*(-b + a*x^3)^(5/4)*Hypergeometric2F1[5/4, 2, 9/4, 1 - (a*x^3)/b])/(15*b^2)","C",1
2074,1,40,150,0.0125889,"\int \frac{\left(-b+a x^3\right)^{3/4}}{x^4} \, dx","Integrate[(-b + a*x^3)^(3/4)/x^4,x]","\frac{4 a \left(a x^3-b\right)^{7/4} \, _2F_1\left(\frac{7}{4},2;\frac{11}{4};1-\frac{a x^3}{b}\right)}{21 b^2}","-\frac{\left(a x^3-b\right)^{3/4}}{3 x^3}-\frac{a \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^3-b}}{\sqrt{a x^3-b}-\sqrt{b}}\right)}{2 \sqrt{2} \sqrt[4]{b}}-\frac{a \tanh ^{-1}\left(\frac{\frac{\sqrt{a x^3-b}}{\sqrt{2} \sqrt[4]{b}}+\frac{\sqrt[4]{b}}{\sqrt{2}}}{\sqrt[4]{a x^3-b}}\right)}{2 \sqrt{2} \sqrt[4]{b}}",1,"(4*a*(-b + a*x^3)^(7/4)*Hypergeometric2F1[7/4, 2, 11/4, 1 - (a*x^3)/b])/(21*b^2)","C",1
2075,0,0,150,7.114945,"\int \frac{(-a+x) (-3 a b+(a+2 b) x) \left(-b^3+3 b^2 x-3 b x^2+x^3\right)}{x \left(x (-a+x) (-b+x)^2\right)^{3/4} \left(a b^2-b (2 a+b) x+(a+2 b) x^2+(-1+d) x^3\right)} \, dx","Integrate[((-a + x)*(-3*a*b + (a + 2*b)*x)*(-b^3 + 3*b^2*x - 3*b*x^2 + x^3))/(x*(x*(-a + x)*(-b + x)^2)^(3/4)*(a*b^2 - b*(2*a + b)*x + (a + 2*b)*x^2 + (-1 + d)*x^3)),x]","\int \frac{(-a+x) (-3 a b+(a+2 b) x) \left(-b^3+3 b^2 x-3 b x^2+x^3\right)}{x \left(x (-a+x) (-b+x)^2\right)^{3/4} \left(a b^2-b (2 a+b) x+(a+2 b) x^2+(-1+d) x^3\right)} \, dx","-2 \sqrt[4]{d} \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}}\right)+2 \sqrt[4]{d} \tanh ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}}\right)-\frac{4 \sqrt[4]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}}{x}",1,"Integrate[((-a + x)*(-3*a*b + (a + 2*b)*x)*(-b^3 + 3*b^2*x - 3*b*x^2 + x^3))/(x*(x*(-a + x)*(-b + x)^2)^(3/4)*(a*b^2 - b*(2*a + b)*x + (a + 2*b)*x^2 + (-1 + d)*x^3)), x]","F",-1
2076,1,40,150,0.0135953,"\int \frac{\left(-b+a x^5\right)^{3/4}}{x^6} \, dx","Integrate[(-b + a*x^5)^(3/4)/x^6,x]","\frac{4 a \left(a x^5-b\right)^{7/4} \, _2F_1\left(\frac{7}{4},2;\frac{11}{4};1-\frac{a x^5}{b}\right)}{35 b^2}","-\frac{\left(a x^5-b\right)^{3/4}}{5 x^5}-\frac{3 a \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^5-b}}{\sqrt{a x^5-b}-\sqrt{b}}\right)}{10 \sqrt{2} \sqrt[4]{b}}-\frac{3 a \tanh ^{-1}\left(\frac{\frac{\sqrt{a x^5-b}}{\sqrt{2} \sqrt[4]{b}}+\frac{\sqrt[4]{b}}{\sqrt{2}}}{\sqrt[4]{a x^5-b}}\right)}{10 \sqrt{2} \sqrt[4]{b}}",1,"(4*a*(-b + a*x^5)^(7/4)*Hypergeometric2F1[7/4, 2, 11/4, 1 - (a*x^5)/b])/(35*b^2)","C",1
2077,1,40,150,0.0119239,"\int \frac{\left(-b+a x^6\right)^{3/4}}{x^7} \, dx","Integrate[(-b + a*x^6)^(3/4)/x^7,x]","\frac{2 a \left(a x^6-b\right)^{7/4} \, _2F_1\left(\frac{7}{4},2;\frac{11}{4};1-\frac{a x^6}{b}\right)}{21 b^2}","-\frac{\left(a x^6-b\right)^{3/4}}{6 x^6}-\frac{a \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^6-b}}{\sqrt{a x^6-b}-\sqrt{b}}\right)}{4 \sqrt{2} \sqrt[4]{b}}-\frac{a \tanh ^{-1}\left(\frac{\frac{\sqrt{a x^6-b}}{\sqrt{2} \sqrt[4]{b}}+\frac{\sqrt[4]{b}}{\sqrt{2}}}{\sqrt[4]{a x^6-b}}\right)}{4 \sqrt{2} \sqrt[4]{b}}",1,"(2*a*(-b + a*x^6)^(7/4)*Hypergeometric2F1[7/4, 2, 11/4, 1 - (a*x^6)/b])/(21*b^2)","C",1
2078,0,0,150,3.1536677,"\int \frac{\left(-4+5 x^7\right) \sqrt[3]{-2 x+2 x^3-x^8}}{\left(2+x^7\right) \left(2-2 x^2+x^7\right)} \, dx","Integrate[((-4 + 5*x^7)*(-2*x + 2*x^3 - x^8)^(1/3))/((2 + x^7)*(2 - 2*x^2 + x^7)),x]","\int \frac{\left(-4+5 x^7\right) \sqrt[3]{-2 x+2 x^3-x^8}}{\left(2+x^7\right) \left(2-2 x^2+x^7\right)} \, dx","-\frac{\log \left(2^{2/3} \sqrt[3]{-x^8+2 x^3-2 x}-2 x\right)}{2^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{-x^8+2 x^3-2 x}+x}\right)}{2^{2/3}}+\frac{\log \left(2 x^2+2^{2/3} \sqrt[3]{-x^8+2 x^3-2 x} x+\sqrt[3]{2} \left(-x^8+2 x^3-2 x\right)^{2/3}\right)}{2\ 2^{2/3}}",1,"Integrate[((-4 + 5*x^7)*(-2*x + 2*x^3 - x^8)^(1/3))/((2 + x^7)*(2 - 2*x^2 + x^7)), x]","F",-1
2079,1,392,150,0.916251,"\int \frac{b-2 a x^4+2 x^8}{\sqrt[4]{b+a x^4} \left(-2 b-a x^4+x^8\right)} \, dx","Integrate[(b - 2*a*x^4 + 2*x^8)/((b + a*x^4)^(1/4)*(-2*b - a*x^4 + x^8)),x]","\frac{5 b \left(\tan ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+8 b}+a^2+2 b}}{\sqrt[4]{a-\sqrt{a^2+8 b}} \sqrt[4]{a x^4+b}}\right)+\tanh ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+8 b}+a^2+2 b}}{\sqrt[4]{a-\sqrt{a^2+8 b}} \sqrt[4]{a x^4+b}}\right)\right)}{\sqrt{a^2+8 b} \left(a-\sqrt{a^2+8 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+8 b}+a^2+2 b}}-\frac{5 b \left(\tan ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+8 b}+a^2+2 b}}{\sqrt[4]{\sqrt{a^2+8 b}+a} \sqrt[4]{a x^4+b}}\right)+\tanh ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+8 b}+a^2+2 b}}{\sqrt[4]{\sqrt{a^2+8 b}+a} \sqrt[4]{a x^4+b}}\right)\right)}{\sqrt{a^2+8 b} \left(\sqrt{a^2+8 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+8 b}+a^2+2 b}}+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{a}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{a}}","-\frac{5}{4} \text{RootSum}\left[2 \text{$\#$1}^8-3 \text{$\#$1}^4 a+a^2-b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-a \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+a \log (x)}{3 \text{$\#$1} a-4 \text{$\#$1}^5}\&\right]+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{a}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{a}}",1,"ArcTan[(a^(1/4)*x)/(b + a*x^4)^(1/4)]/a^(1/4) + ArcTanh[(a^(1/4)*x)/(b + a*x^4)^(1/4)]/a^(1/4) + (5*b*(ArcTan[((a^2 + 2*b - a*Sqrt[a^2 + 8*b])^(1/4)*x)/((a - Sqrt[a^2 + 8*b])^(1/4)*(b + a*x^4)^(1/4))] + ArcTanh[((a^2 + 2*b - a*Sqrt[a^2 + 8*b])^(1/4)*x)/((a - Sqrt[a^2 + 8*b])^(1/4)*(b + a*x^4)^(1/4))]))/(Sqrt[a^2 + 8*b]*(a - Sqrt[a^2 + 8*b])^(3/4)*(a^2 + 2*b - a*Sqrt[a^2 + 8*b])^(1/4)) - (5*b*(ArcTan[((a^2 + 2*b + a*Sqrt[a^2 + 8*b])^(1/4)*x)/((a + Sqrt[a^2 + 8*b])^(1/4)*(b + a*x^4)^(1/4))] + ArcTanh[((a^2 + 2*b + a*Sqrt[a^2 + 8*b])^(1/4)*x)/((a + Sqrt[a^2 + 8*b])^(1/4)*(b + a*x^4)^(1/4))]))/(Sqrt[a^2 + 8*b]*(a + Sqrt[a^2 + 8*b])^(3/4)*(a^2 + 2*b + a*Sqrt[a^2 + 8*b])^(1/4))","B",1
2080,1,391,150,0.9617545,"\int \frac{-b+2 a x^4+2 x^8}{\sqrt[4]{b+a x^4} \left(-b+a x^4+x^8\right)} \, dx","Integrate[(-b + 2*a*x^4 + 2*x^8)/((b + a*x^4)^(1/4)*(-b + a*x^4 + x^8)),x]","\frac{b \left(\tan ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{a x^4+b}}\right)+\tanh ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{a x^4+b}}\right)\right)}{\sqrt{a^2+4 b} \left(a-\sqrt{a^2+4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}-\frac{b \left(\tan ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+4 b}+a} \sqrt[4]{a x^4+b}}\right)+\tanh ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+4 b}+a} \sqrt[4]{a x^4+b}}\right)\right)}{\sqrt{a^2+4 b} \left(\sqrt{a^2+4 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{a}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{a}}","-\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4 a+2 a^2-b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-a \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+a \log (x)}{3 \text{$\#$1} a-2 \text{$\#$1}^5}\&\right]+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{a}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{a}}",1,"ArcTan[(a^(1/4)*x)/(b + a*x^4)^(1/4)]/a^(1/4) + ArcTanh[(a^(1/4)*x)/(b + a*x^4)^(1/4)]/a^(1/4) + (b*(ArcTan[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a - Sqrt[a^2 + 4*b])^(1/4)*(b + a*x^4)^(1/4))] + ArcTanh[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a - Sqrt[a^2 + 4*b])^(1/4)*(b + a*x^4)^(1/4))]))/(Sqrt[a^2 + 4*b]*(a - Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)) - (b*(ArcTan[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a + Sqrt[a^2 + 4*b])^(1/4)*(b + a*x^4)^(1/4))] + ArcTanh[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a + Sqrt[a^2 + 4*b])^(1/4)*(b + a*x^4)^(1/4))]))/(Sqrt[a^2 + 4*b]*(a + Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4))","B",1
2081,1,391,150,0.1892032,"\int \frac{-b+2 a x^4+2 x^8}{\sqrt[4]{b+a x^4} \left(-b+a x^4+x^8\right)} \, dx","Integrate[(-b + 2*a*x^4 + 2*x^8)/((b + a*x^4)^(1/4)*(-b + a*x^4 + x^8)),x]","\frac{b \left(\tan ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{a x^4+b}}\right)+\tanh ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{a x^4+b}}\right)\right)}{\sqrt{a^2+4 b} \left(a-\sqrt{a^2+4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}-\frac{b \left(\tan ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+4 b}+a} \sqrt[4]{a x^4+b}}\right)+\tanh ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+4 b}+a} \sqrt[4]{a x^4+b}}\right)\right)}{\sqrt{a^2+4 b} \left(\sqrt{a^2+4 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{a}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{a}}","-\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4 a+2 a^2-b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-a \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+a \log (x)}{3 \text{$\#$1} a-2 \text{$\#$1}^5}\&\right]+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{a}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{a}}",1,"ArcTan[(a^(1/4)*x)/(b + a*x^4)^(1/4)]/a^(1/4) + ArcTanh[(a^(1/4)*x)/(b + a*x^4)^(1/4)]/a^(1/4) + (b*(ArcTan[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a - Sqrt[a^2 + 4*b])^(1/4)*(b + a*x^4)^(1/4))] + ArcTanh[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a - Sqrt[a^2 + 4*b])^(1/4)*(b + a*x^4)^(1/4))]))/(Sqrt[a^2 + 4*b]*(a - Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)) - (b*(ArcTan[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a + Sqrt[a^2 + 4*b])^(1/4)*(b + a*x^4)^(1/4))] + ArcTanh[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a + Sqrt[a^2 + 4*b])^(1/4)*(b + a*x^4)^(1/4))]))/(Sqrt[a^2 + 4*b]*(a + Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4))","B",1
2082,1,192,150,0.8675423,"\int \frac{\sqrt{-b^4+a^4 x^4} \left(b^4+a^4 x^4\right)}{b^8+a^8 x^8} \, dx","Integrate[(Sqrt[-b^4 + a^4*x^4]*(b^4 + a^4*x^4))/(b^8 + a^8*x^8),x]","-\frac{i \sqrt{1-\frac{a^4 x^4}{b^4}} \left(2 F\left(\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)-\Pi \left(-\sqrt[4]{-1};\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)-\Pi \left(\sqrt[4]{-1};\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)-\Pi \left(-(-1)^{3/4};\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)-\Pi \left((-1)^{3/4};\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)\right)}{2 \sqrt{-\frac{a^2}{b^2}} \sqrt{a^4 x^4-b^4}}","-\frac{\tan ^{-1}\left(\frac{-\frac{a^3 x^4}{2^{3/4} b}+\frac{b^3}{2^{3/4} a}+\frac{a b x^2}{\sqrt[4]{2}}}{x \sqrt{a^4 x^4-b^4}}\right)}{2\ 2^{3/4} a b}-\frac{\tanh ^{-1}\left(\frac{2^{3/4} a b x \sqrt{a^4 x^4-b^4}}{a^4 x^4+\sqrt{2} a^2 b^2 x^2-b^4}\right)}{2\ 2^{3/4} a b}",1,"((-1/2*I)*Sqrt[1 - (a^4*x^4)/b^4]*(2*EllipticF[I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1] - EllipticPi[-(-1)^(1/4), I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1] - EllipticPi[(-1)^(1/4), I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1] - EllipticPi[-(-1)^(3/4), I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1] - EllipticPi[(-1)^(3/4), I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1]))/(Sqrt[-(a^2/b^2)]*Sqrt[-b^4 + a^4*x^4])","C",1
2083,1,192,150,0.5988934,"\int \frac{-b^8+a^8 x^8}{\sqrt{-b^4+a^4 x^4} \left(b^8+a^8 x^8\right)} \, dx","Integrate[(-b^8 + a^8*x^8)/(Sqrt[-b^4 + a^4*x^4]*(b^8 + a^8*x^8)),x]","-\frac{i \sqrt{1-\frac{a^4 x^4}{b^4}} \left(2 F\left(\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)-\Pi \left(-\sqrt[4]{-1};\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)-\Pi \left(\sqrt[4]{-1};\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)-\Pi \left(-(-1)^{3/4};\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)-\Pi \left((-1)^{3/4};\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)\right)}{2 \sqrt{-\frac{a^2}{b^2}} \sqrt{a^4 x^4-b^4}}","-\frac{\tan ^{-1}\left(\frac{-\frac{a^3 x^4}{2^{3/4} b}+\frac{b^3}{2^{3/4} a}+\frac{a b x^2}{\sqrt[4]{2}}}{x \sqrt{a^4 x^4-b^4}}\right)}{2\ 2^{3/4} a b}-\frac{\tanh ^{-1}\left(\frac{2^{3/4} a b x \sqrt{a^4 x^4-b^4}}{a^4 x^4+\sqrt{2} a^2 b^2 x^2-b^4}\right)}{2\ 2^{3/4} a b}",1,"((-1/2*I)*Sqrt[1 - (a^4*x^4)/b^4]*(2*EllipticF[I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1] - EllipticPi[-(-1)^(1/4), I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1] - EllipticPi[(-1)^(1/4), I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1] - EllipticPi[-(-1)^(3/4), I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1] - EllipticPi[(-1)^(3/4), I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1]))/(Sqrt[-(a^2/b^2)]*Sqrt[-b^4 + a^4*x^4])","C",1
2084,1,156,150,0.5720129,"\int \frac{x^3 \sqrt{x+x^2}}{\sqrt{x^2+x \sqrt{x+x^2}}} \, dx","Integrate[(x^3*Sqrt[x + x^2])/Sqrt[x^2 + x*Sqrt[x + x^2]],x]","\frac{\left(x+\sqrt{x (x+1)}\right)^4 \sqrt{x \left(x+\sqrt{x (x+1)}\right)} \left(x+\sqrt{x (x+1)}+1\right) \left(11 \, _2F_1\left(-\frac{9}{2},3;-\frac{7}{2};1+\frac{1}{2 \left(x+\sqrt{x (x+1)}\right)}\right)+72 x \left(32 x^3+4 \left(8 \sqrt{x (x+1)}+13\right) x^2+\left(36 \sqrt{x (x+1)}+19\right) x+5 \sqrt{x (x+1)}\right)\right)}{1152 \sqrt{x (x+1)} \left(2 x+2 \sqrt{x (x+1)}+1\right)^5}","\frac{\sqrt{x^2+x} \sqrt{x \left(\sqrt{x^2+x}+x\right)} \left(-1146880 x^4-168960 x^3+201344 x^2-264264 x+495495\right)}{5160960 x}+\sqrt{x \left(\sqrt{x^2+x}+x\right)} \left(\frac{1146880 x^4+1387520 x^3-18304 x^2+37752 x-165165}{5160960}-\frac{1573 \sqrt{\sqrt{x^2+x}-x} \tanh ^{-1}\left(\sqrt{2} \sqrt{\sqrt{x^2+x}-x}\right)}{16384 \sqrt{2} x}\right)",1,"((x + Sqrt[x*(1 + x)])^4*Sqrt[x*(x + Sqrt[x*(1 + x)])]*(1 + x + Sqrt[x*(1 + x)])*(72*x*(32*x^3 + 5*Sqrt[x*(1 + x)] + 4*x^2*(13 + 8*Sqrt[x*(1 + x)]) + x*(19 + 36*Sqrt[x*(1 + x)])) + 11*Hypergeometric2F1[-9/2, 3, -7/2, 1 + 1/(2*(x + Sqrt[x*(1 + x)]))]))/(1152*Sqrt[x*(1 + x)]*(1 + 2*x + 2*Sqrt[x*(1 + x)])^5)","C",1
2085,1,91,151,0.056895,"\int \frac{\left(-b+a x^2\right)^{3/4} \left(3 b+2 a x^2\right)}{x} \, dx","Integrate[((-b + a*x^2)^(3/4)*(3*b + 2*a*x^2))/x,x]","\frac{2}{7} \left(a x^2-b\right)^{3/4} \left(2 a x^2+5 b\right)+3 b (-b)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a x^2-b}}{\sqrt[4]{-b}}\right)+3 (-b)^{7/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a x^2-b}}{\sqrt[4]{-b}}\right)","\frac{3 b^{7/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^2-b}}{\sqrt{a x^2-b}-\sqrt{b}}\right)}{\sqrt{2}}+\frac{3 b^{7/4} \tanh ^{-1}\left(\frac{\frac{\sqrt{a x^2-b}}{\sqrt{2} \sqrt[4]{b}}+\frac{\sqrt[4]{b}}{\sqrt{2}}}{\sqrt[4]{a x^2-b}}\right)}{\sqrt{2}}+\frac{2}{7} \left(a x^2-b\right)^{3/4} \left(2 a x^2+5 b\right)",1,"(2*(-b + a*x^2)^(3/4)*(5*b + 2*a*x^2))/7 + 3*(-b)^(3/4)*b*ArcTan[(-b + a*x^2)^(1/4)/(-b)^(1/4)] + 3*(-b)^(7/4)*ArcTanh[(-b + a*x^2)^(1/4)/(-b)^(1/4)]","A",1
2086,0,0,151,0.3992196,"\int \frac{\left(-6+x^2\right) \left(2-x^2+x^3\right)^{2/3}}{x^3 \left(-2+x^2+x^3\right)} \, dx","Integrate[((-6 + x^2)*(2 - x^2 + x^3)^(2/3))/(x^3*(-2 + x^2 + x^3)),x]","\int \frac{\left(-6+x^2\right) \left(2-x^2+x^3\right)^{2/3}}{x^3 \left(-2+x^2+x^3\right)} \, dx","-\frac{3 \left(x^3-x^2+2\right)^{2/3}}{2 x^2}-2^{2/3} \log \left(2^{2/3} \sqrt[3]{x^3-x^2+2}-2 x\right)+\frac{\log \left(2 x^2+2^{2/3} \sqrt[3]{x^3-x^2+2} x+\sqrt[3]{2} \left(x^3-x^2+2\right)^{2/3}\right)}{\sqrt[3]{2}}+2^{2/3} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^3-x^2+2}+x}\right)",1,"Integrate[((-6 + x^2)*(2 - x^2 + x^3)^(2/3))/(x^3*(-2 + x^2 + x^3)), x]","F",-1
2087,0,0,151,0.4695515,"\int \frac{x^3 (-4 a+3 x)}{\left(x^2 (-a+x)\right)^{2/3} \left(a d-d x+x^4\right)} \, dx","Integrate[(x^3*(-4*a + 3*x))/((x^2*(-a + x))^(2/3)*(a*d - d*x + x^4)),x]","\int \frac{x^3 (-4 a+3 x)}{\left(x^2 (-a+x)\right)^{2/3} \left(a d-d x+x^4\right)} \, dx","-\frac{\log \left(a^2 d^{2/3} \left(x^3-a x^2\right)^{2/3}+a^2 \sqrt[3]{d} x^2 \sqrt[3]{x^3-a x^2}+a^2 x^4\right)}{2 \sqrt[3]{d}}+\frac{\log \left(a x^2-a \sqrt[3]{d} \sqrt[3]{x^3-a x^2}\right)}{\sqrt[3]{d}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x^2}{2 \sqrt[3]{d} \sqrt[3]{x^3-a x^2}+x^2}\right)}{\sqrt[3]{d}}",1,"Integrate[(x^3*(-4*a + 3*x))/((x^2*(-a + x))^(2/3)*(a*d - d*x + x^4)), x]","F",-1
2088,1,10871,151,14.6048441,"\int \frac{-1+k^4 x^4}{\sqrt{(1-x) x \left(1-k^2 x\right)} \left(1+k^4 x^4\right)} \, dx","Integrate[(-1 + k^4*x^4)/(Sqrt[(1 - x)*x*(1 - k^2*x)]*(1 + k^4*x^4)),x]","\text{Result too large to show}","-\frac{\tan ^{-1}\left(\frac{\sqrt{k^2-\sqrt{2} k+1} \sqrt{k^2 x^3+\left(-k^2-1\right) x^2+x}}{(x-1) \left(k^2 x-1\right)}\right)}{\sqrt{k^2-\sqrt{2} k+1}}-\frac{\tan ^{-1}\left(\frac{\sqrt{k^2+\sqrt{2} k+1} \sqrt{k^2 x^3+\left(-k^2-1\right) x^2+x}}{(x-1) \left(k^2 x-1\right)}\right)}{\sqrt{k^2+\sqrt{2} k+1}}",1,"Result too large to show","C",0
2089,0,0,151,0.8508343,"\int \frac{1-x^4}{\left(1+x^4\right) \sqrt[4]{x^3+x^5}} \, dx","Integrate[(1 - x^4)/((1 + x^4)*(x^3 + x^5)^(1/4)),x]","\int \frac{1-x^4}{\left(1+x^4\right) \sqrt[4]{x^3+x^5}} \, dx","\frac{\tan ^{-1}\left(\frac{\sqrt[8]{2} x}{\sqrt[4]{x^5+x^3}}\right)}{\sqrt[8]{2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{2} x}{\sqrt[4]{x^5+x^3}}\right)}{\sqrt[8]{2}}-\frac{\tan ^{-1}\left(\frac{2^{5/8} x \sqrt[4]{x^5+x^3}}{\sqrt[4]{2} x^2-\sqrt{x^5+x^3}}\right)}{2^{5/8}}+\frac{\tanh ^{-1}\left(\frac{\frac{x^2}{2^{3/8}}+\frac{\sqrt{x^5+x^3}}{2^{5/8}}}{x \sqrt[4]{x^5+x^3}}\right)}{2^{5/8}}",1,"Integrate[(1 - x^4)/((1 + x^4)*(x^3 + x^5)^(1/4)), x]","F",-1
2090,1,138,151,0.5028634,"\int \frac{\left(1+x^3\right)^{2/3} \left(2+x^6\right)}{x^6 \left(-1+x^3\right)^2} \, dx","Integrate[((1 + x^3)^(2/3)*(2 + x^6))/(x^6*(-1 + x^3)^2),x]","\frac{5 \left(-2 \log \left(1-\frac{\sqrt[3]{2} x}{\sqrt[3]{x^3+1}}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{2} x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)+\log \left(\frac{\sqrt[3]{2} x}{\sqrt[3]{x^3+1}}+\frac{2^{2/3} x^2}{\left(x^3+1\right)^{2/3}}+1\right)\right)}{3 \sqrt[3]{2}}+\left(x^3+1\right)^{2/3} \left(-\frac{2}{5 x^5}-\frac{x}{x^3-1}-\frac{12}{5 x^2}\right)","-\frac{5}{3} 2^{2/3} \log \left(2^{2/3} \sqrt[3]{x^3+1}-2 x\right)+\frac{5\ 2^{2/3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^3+1}+x}\right)}{\sqrt{3}}+\frac{5 \log \left(2^{2/3} \sqrt[3]{x^3+1} x+\sqrt[3]{2} \left(x^3+1\right)^{2/3}+2 x^2\right)}{3 \sqrt[3]{2}}+\frac{\left(x^3+1\right)^{2/3} \left(-17 x^6+10 x^3+2\right)}{5 x^5 \left(x^3-1\right)}",1,"(1 + x^3)^(2/3)*(-2/(5*x^5) - 12/(5*x^2) - x/(-1 + x^3)) + (5*(2*Sqrt[3]*ArcTan[(1 + (2*2^(1/3)*x)/(1 + x^3)^(1/3))/Sqrt[3]] - 2*Log[1 - (2^(1/3)*x)/(1 + x^3)^(1/3)] + Log[1 + (2^(2/3)*x^2)/(1 + x^3)^(2/3) + (2^(1/3)*x)/(1 + x^3)^(1/3)]))/(3*2^(1/3))","A",1
2091,1,146,151,0.5917793,"\int \frac{\left(-1+x^3\right)^{2/3} \left(-2+2 x^3+x^6\right)}{x^6 \left(1+x^3\right)^2} \, dx","Integrate[((-1 + x^3)^(2/3)*(-2 + 2*x^3 + x^6))/(x^6*(1 + x^3)^2),x]","\frac{7 \left(-2 \log \left(1-\frac{\sqrt[3]{2} x}{\sqrt[3]{1-x^3}}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}+1}{\sqrt{3}}\right)+\log \left(\frac{\sqrt[3]{2} x}{\sqrt[3]{1-x^3}}+\frac{2^{2/3} x^2}{\left(1-x^3\right)^{2/3}}+1\right)\right)}{3 \sqrt[3]{2}}+\left(x^3-1\right)^{2/3} \left(\frac{2}{5 x^5}-\frac{x}{x^3+1}-\frac{17}{5 x^2}\right)","-\frac{7}{3} 2^{2/3} \log \left(2^{2/3} \sqrt[3]{x^3-1}-2 x\right)+\frac{7\ 2^{2/3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^3-1}+x}\right)}{\sqrt{3}}+\frac{7 \log \left(2^{2/3} \sqrt[3]{x^3-1} x+\sqrt[3]{2} \left(x^3-1\right)^{2/3}+2 x^2\right)}{3 \sqrt[3]{2}}+\frac{\left(x^3-1\right)^{2/3} \left(-22 x^6-15 x^3+2\right)}{5 x^5 \left(x^3+1\right)}",1,"(-1 + x^3)^(2/3)*(2/(5*x^5) - 17/(5*x^2) - x/(1 + x^3)) + (7*(2*Sqrt[3]*ArcTan[(1 + (2*2^(1/3)*x)/(1 - x^3)^(1/3))/Sqrt[3]] - 2*Log[1 - (2^(1/3)*x)/(1 - x^3)^(1/3)] + Log[1 + (2^(2/3)*x^2)/(1 - x^3)^(2/3) + (2^(1/3)*x)/(1 - x^3)^(1/3)]))/(3*2^(1/3))","A",0
2092,0,0,151,1.1023376,"\int \frac{\left(2 b+a x^6\right) \left(-b-c x^4+a x^6\right)}{x^2 \left(-b+a x^6\right)^{3/4} \left(-b+c x^4+a x^6\right)} \, dx","Integrate[((2*b + a*x^6)*(-b - c*x^4 + a*x^6))/(x^2*(-b + a*x^6)^(3/4)*(-b + c*x^4 + a*x^6)),x]","\int \frac{\left(2 b+a x^6\right) \left(-b-c x^4+a x^6\right)}{x^2 \left(-b+a x^6\right)^{3/4} \left(-b+c x^4+a x^6\right)} \, dx","\sqrt{2} \sqrt[4]{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x \sqrt[4]{a x^6-b}}{\sqrt{a x^6-b}-\sqrt{c} x^2}\right)-\sqrt{2} \sqrt[4]{c} \tanh ^{-1}\left(\frac{\frac{\sqrt{a x^6-b}}{\sqrt{2} \sqrt[4]{c}}+\frac{\sqrt[4]{c} x^2}{\sqrt{2}}}{x \sqrt[4]{a x^6-b}}\right)+\frac{2 \sqrt[4]{a x^6-b}}{x}",1,"Integrate[((2*b + a*x^6)*(-b - c*x^4 + a*x^6))/(x^2*(-b + a*x^6)^(3/4)*(-b + c*x^4 + a*x^6)), x]","F",-1
2093,1,122,151,0.2201317,"\int \frac{\sqrt{c+d \sqrt{b+a x^2}}}{x} \, dx","Integrate[Sqrt[c + d*Sqrt[b + a*x^2]]/x,x]","2 \sqrt{d \sqrt{a x^2+b}+c}-\sqrt{c-\sqrt{b} d} \tanh ^{-1}\left(\frac{\sqrt{d \sqrt{a x^2+b}+c}}{\sqrt{c-\sqrt{b} d}}\right)-\sqrt{\sqrt{b} d+c} \tanh ^{-1}\left(\frac{\sqrt{d \sqrt{a x^2+b}+c}}{\sqrt{\sqrt{b} d+c}}\right)","2 \sqrt{d \sqrt{a x^2+b}+c}+\sqrt{\sqrt{b} d-c} \tan ^{-1}\left(\frac{\sqrt{\sqrt{b} d-c} \sqrt{d \sqrt{a x^2+b}+c}}{c-\sqrt{b} d}\right)+\sqrt{-\sqrt{b} d-c} \tan ^{-1}\left(\frac{\sqrt{-\sqrt{b} d-c} \sqrt{d \sqrt{a x^2+b}+c}}{\sqrt{b} d+c}\right)",1,"2*Sqrt[c + d*Sqrt[b + a*x^2]] - Sqrt[c - Sqrt[b]*d]*ArcTanh[Sqrt[c + d*Sqrt[b + a*x^2]]/Sqrt[c - Sqrt[b]*d]] - Sqrt[c + Sqrt[b]*d]*ArcTanh[Sqrt[c + d*Sqrt[b + a*x^2]]/Sqrt[c + Sqrt[b]*d]]","A",1
2094,0,0,151,0.2922405,"\int \frac{\left(-b+a^2 x^4\right) \sqrt{a x^2+\sqrt{b+a^2 x^4}}}{\sqrt{b+a^2 x^4}} \, dx","Integrate[((-b + a^2*x^4)*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]])/Sqrt[b + a^2*x^4],x]","\int \frac{\left(-b+a^2 x^4\right) \sqrt{a x^2+\sqrt{b+a^2 x^4}}}{\sqrt{b+a^2 x^4}} \, dx","\frac{2 a^{5/2} x^6+2 a^{3/2} x^4 \sqrt{a^2 x^4+b}+3 \sqrt{a} b x^2}{8 \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}}-\frac{11 b \log \left(\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)}{8 \sqrt{2} \sqrt{a}}",1,"Integrate[((-b + a^2*x^4)*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]])/Sqrt[b + a^2*x^4], x]","F",-1
2095,0,0,151,0.0877307,"\int \sqrt{b+a^2 x^4} \sqrt{a x^2+\sqrt{b+a^2 x^4}} \, dx","Integrate[Sqrt[b + a^2*x^4]*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]],x]","\int \sqrt{b+a^2 x^4} \sqrt{a x^2+\sqrt{b+a^2 x^4}} \, dx","\frac{5 b \log \left(\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)}{8 \sqrt{2} \sqrt{a}}+\frac{2 a^{5/2} x^6+2 a^{3/2} x^4 \sqrt{a^2 x^4+b}+3 \sqrt{a} b x^2}{8 \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}}",1,"Integrate[Sqrt[b + a^2*x^4]*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]], x]","F",-1
2096,1,58,152,0.0479445,"\int \frac{1}{(2 b+a x) \sqrt[4]{b x^2+a x^3}} \, dx","Integrate[1/((2*b + a*x)*(b*x^2 + a*x^3)^(1/4)),x]","\frac{x \sqrt[4]{\frac{a x+b}{b}} F_1\left(\frac{1}{2};\frac{1}{4},1;\frac{3}{2};-\frac{a x}{b},-\frac{a x}{2 b}\right)}{b \sqrt[4]{x^2 (a x+b)}}","\frac{\tanh ^{-1}\left(\frac{2 \sqrt{a} \sqrt[4]{b} x \sqrt[4]{a x^3+b x^2}}{2 \sqrt{b} \sqrt{a x^3+b x^2}+a x^2}\right)}{2 \sqrt{a} b^{3/4}}-\frac{\tan ^{-1}\left(\frac{\frac{\sqrt[4]{b} \sqrt{a x^3+b x^2}}{\sqrt{a}}-\frac{\sqrt{a} x^2}{2 \sqrt[4]{b}}}{x \sqrt[4]{a x^3+b x^2}}\right)}{2 \sqrt{a} b^{3/4}}",1,"(x*((b + a*x)/b)^(1/4)*AppellF1[1/2, 1/4, 1, 3/2, -((a*x)/b), -1/2*(a*x)/b])/(b*(x^2*(b + a*x))^(1/4))","C",0
2097,1,646,152,1.4304211,"\int \frac{x (-4 a+3 x)}{\sqrt[3]{x^2 (-a+x)} \left(a d-d x+x^4\right)} \, dx","Integrate[(x*(-4*a + 3*x))/((x^2*(-a + x))^(1/3)*(a*d - d*x + x^4)),x]","\frac{a x \left(4 \text{RootSum}\left[\text{$\#$1}^4 \left(-a^3\right)+\text{$\#$1}^3 d-3 \text{$\#$1}^2 d+3 \text{$\#$1} d-d\&,\frac{-\sqrt[3]{\text{$\#$1}} \log \left(\text{$\#$1}^{2/3}+\sqrt[3]{\text{$\#$1}} \sqrt[3]{\frac{x}{x-a}}+\left(\frac{x}{x-a}\right)^{2/3}\right)+2 \sqrt[3]{\text{$\#$1}} \log \left(\sqrt[3]{\text{$\#$1}}-\sqrt[3]{\frac{x}{x-a}}\right)-2 \sqrt{3} \sqrt[3]{\text{$\#$1}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{\frac{x}{x-a}}}{\sqrt[3]{\text{$\#$1}}}+1}{\sqrt{3}}\right)+6 \sqrt[3]{\frac{x}{x-a}}}{4 \text{$\#$1}^3 a^3-3 \text{$\#$1}^2 d+6 \text{$\#$1} d-3 d}\&\right]+5 \text{RootSum}\left[\text{$\#$1}^4 \left(-a^3\right)+\text{$\#$1}^3 d-3 \text{$\#$1}^2 d+3 \text{$\#$1} d-d\&,\frac{-2 \text{$\#$1}^{4/3} \log \left(\sqrt[3]{\text{$\#$1}}-\sqrt[3]{\frac{x}{x-a}}\right)+\text{$\#$1}^{4/3} \log \left(\text{$\#$1}^{2/3}+\sqrt[3]{\text{$\#$1}} \sqrt[3]{\frac{x}{x-a}}+\left(\frac{x}{x-a}\right)^{2/3}\right)+2 \sqrt{3} \text{$\#$1}^{4/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{\frac{x}{x-a}}}{\sqrt[3]{\text{$\#$1}}}+1}{\sqrt{3}}\right)-6 \text{$\#$1} \sqrt[3]{\frac{x}{x-a}}}{4 \text{$\#$1}^3 a^3-3 \text{$\#$1}^2 d+6 \text{$\#$1} d-3 d}\&\right]-\text{RootSum}\left[\text{$\#$1}^4 \left(-a^3\right)+\text{$\#$1}^3 d-3 \text{$\#$1}^2 d+3 \text{$\#$1} d-d\&,\frac{-2 \text{$\#$1}^{7/3} \log \left(\sqrt[3]{\text{$\#$1}}-\sqrt[3]{\frac{x}{x-a}}\right)+\text{$\#$1}^{7/3} \log \left(\text{$\#$1}^{2/3}+\sqrt[3]{\text{$\#$1}} \sqrt[3]{\frac{x}{x-a}}+\left(\frac{x}{x-a}\right)^{2/3}\right)+2 \sqrt{3} \text{$\#$1}^{7/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{\frac{x}{x-a}}}{\sqrt[3]{\text{$\#$1}}}+1}{\sqrt{3}}\right)-6 \text{$\#$1}^2 \sqrt[3]{\frac{x}{x-a}}}{4 \text{$\#$1}^3 a^3-3 \text{$\#$1}^2 d+6 \text{$\#$1} d-3 d}\&\right]\right)}{2 \sqrt[3]{\frac{x}{x-a}} \sqrt[3]{x^2 (x-a)}}","-\frac{\log \left(a^2 d^{2/3} \left(x^3-a x^2\right)^{2/3}+a^2 \sqrt[3]{d} x^2 \sqrt[3]{x^3-a x^2}+a^2 x^4\right)}{2 d^{2/3}}+\frac{\log \left(a x^2-a \sqrt[3]{d} \sqrt[3]{x^3-a x^2}\right)}{d^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x^2}{2 \sqrt[3]{d} \sqrt[3]{x^3-a x^2}+x^2}\right)}{d^{2/3}}",1,"(a*x*(4*RootSum[-d + 3*d*#1 - 3*d*#1^2 + d*#1^3 - a^3*#1^4 & , (6*(x/(-a + x))^(1/3) - 2*Sqrt[3]*ArcTan[(1 + (2*(x/(-a + x))^(1/3))/#1^(1/3))/Sqrt[3]]*#1^(1/3) + 2*Log[-(x/(-a + x))^(1/3) + #1^(1/3)]*#1^(1/3) - Log[(x/(-a + x))^(2/3) + (x/(-a + x))^(1/3)*#1^(1/3) + #1^(2/3)]*#1^(1/3))/(-3*d + 6*d*#1 - 3*d*#1^2 + 4*a^3*#1^3) & ] + 5*RootSum[-d + 3*d*#1 - 3*d*#1^2 + d*#1^3 - a^3*#1^4 & , (-6*(x/(-a + x))^(1/3)*#1 + 2*Sqrt[3]*ArcTan[(1 + (2*(x/(-a + x))^(1/3))/#1^(1/3))/Sqrt[3]]*#1^(4/3) - 2*Log[-(x/(-a + x))^(1/3) + #1^(1/3)]*#1^(4/3) + Log[(x/(-a + x))^(2/3) + (x/(-a + x))^(1/3)*#1^(1/3) + #1^(2/3)]*#1^(4/3))/(-3*d + 6*d*#1 - 3*d*#1^2 + 4*a^3*#1^3) & ] - RootSum[-d + 3*d*#1 - 3*d*#1^2 + d*#1^3 - a^3*#1^4 & , (-6*(x/(-a + x))^(1/3)*#1^2 + 2*Sqrt[3]*ArcTan[(1 + (2*(x/(-a + x))^(1/3))/#1^(1/3))/Sqrt[3]]*#1^(7/3) - 2*Log[-(x/(-a + x))^(1/3) + #1^(1/3)]*#1^(7/3) + Log[(x/(-a + x))^(2/3) + (x/(-a + x))^(1/3)*#1^(1/3) + #1^(2/3)]*#1^(7/3))/(-3*d + 6*d*#1 - 3*d*#1^2 + 4*a^3*#1^3) & ]))/(2*(x/(-a + x))^(1/3)*(x^2*(-a + x))^(1/3))","C",1
2098,0,0,152,0.7345616,"\int \frac{\left(-b+a x^5\right)^{3/4} \left(4 b+a x^5\right)}{x^4 \left(-b+c x^4+a x^5\right)} \, dx","Integrate[((-b + a*x^5)^(3/4)*(4*b + a*x^5))/(x^4*(-b + c*x^4 + a*x^5)),x]","\int \frac{\left(-b+a x^5\right)^{3/4} \left(4 b+a x^5\right)}{x^4 \left(-b+c x^4+a x^5\right)} \, dx","\sqrt{2} c^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x \sqrt[4]{a x^5-b}}{\sqrt{a x^5-b}-\sqrt{c} x^2}\right)+\sqrt{2} c^{3/4} \tanh ^{-1}\left(\frac{\frac{\sqrt{a x^5-b}}{\sqrt{2} \sqrt[4]{c}}+\frac{\sqrt[4]{c} x^2}{\sqrt{2}}}{x \sqrt[4]{a x^5-b}}\right)+\frac{4 \left(a x^5-b\right)^{3/4}}{3 x^3}",1,"Integrate[((-b + a*x^5)^(3/4)*(4*b + a*x^5))/(x^4*(-b + c*x^4 + a*x^5)), x]","F",-1
2099,1,110,152,0.1227656,"\int \frac{\left(1+x^8\right)^{3/4}}{-1+x^8} \, dx","Integrate[(1 + x^8)^(3/4)/(-1 + x^8),x]","\frac{9 x \left(x^8+1\right)^{3/4} F_1\left(\frac{1}{8};-\frac{3}{4},1;\frac{9}{8};-x^8,x^8\right)}{\left(x^8-1\right) \left(2 x^8 \left(4 F_1\left(\frac{9}{8};-\frac{3}{4},2;\frac{17}{8};-x^8,x^8\right)+3 F_1\left(\frac{9}{8};\frac{1}{4},1;\frac{17}{8};-x^8,x^8\right)\right)+9 F_1\left(\frac{1}{8};-\frac{3}{4},1;\frac{9}{8};-x^8,x^8\right)\right)}","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^8+1}}\right)}{4 \sqrt[4]{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^8+1}}\right)}{4 \sqrt[4]{2}}+\frac{\tan ^{-1}\left(\frac{2^{3/4} x \sqrt[4]{x^8+1}}{\sqrt{2} x^2-\sqrt{x^8+1}}\right)}{4\ 2^{3/4}}-\frac{\tanh ^{-1}\left(\frac{2 \sqrt[4]{2} x \sqrt[4]{x^8+1}}{\sqrt{2} \sqrt{x^8+1}+2 x^2}\right)}{4\ 2^{3/4}}",1,"(9*x*(1 + x^8)^(3/4)*AppellF1[1/8, -3/4, 1, 9/8, -x^8, x^8])/((-1 + x^8)*(9*AppellF1[1/8, -3/4, 1, 9/8, -x^8, x^8] + 2*x^8*(4*AppellF1[9/8, -3/4, 2, 17/8, -x^8, x^8] + 3*AppellF1[9/8, 1/4, 1, 17/8, -x^8, x^8])))","C",0
2100,1,175,152,0.2548523,"\int \frac{x^4}{\sqrt[4]{-1+x^4} \left(-1+2 x^4+x^8\right)} \, dx","Integrate[x^4/((-1 + x^4)^(1/4)*(-1 + 2*x^4 + x^8)),x]","\frac{4 \tan ^{-1}\left(\frac{\sqrt[8]{2} x}{\sqrt[4]{x^4-1}}\right)+4 \tanh ^{-1}\left(\frac{\sqrt[8]{2} x}{\sqrt[4]{x^4-1}}\right)+\sqrt{2} \left(2 \tan ^{-1}\left(1-\frac{2^{5/8} x}{\sqrt[4]{x^4-1}}\right)-2 \tan ^{-1}\left(\frac{2^{5/8} x}{\sqrt[4]{x^4-1}}+1\right)+\log \left(-\frac{2^{5/8} x}{\sqrt[4]{x^4-1}}+\frac{\sqrt[4]{2} x^2}{\sqrt{x^4-1}}+1\right)-\log \left(\frac{2^{5/8} x}{\sqrt[4]{x^4-1}}+\frac{\sqrt[4]{2} x^2}{\sqrt{x^4-1}}+1\right)\right)}{16\ 2^{5/8}}","\frac{\tan ^{-1}\left(\frac{\sqrt[8]{2} x}{\sqrt[4]{x^4-1}}\right)}{4\ 2^{5/8}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{2} x}{\sqrt[4]{x^4-1}}\right)}{4\ 2^{5/8}}+\frac{\tan ^{-1}\left(\frac{2^{5/8} x \sqrt[4]{x^4-1}}{\sqrt[4]{2} x^2-\sqrt{x^4-1}}\right)}{8 \sqrt[8]{2}}-\frac{\tanh ^{-1}\left(\frac{2\ 2^{3/8} x \sqrt[4]{x^4-1}}{2^{3/4} \sqrt{x^4-1}+2 x^2}\right)}{8 \sqrt[8]{2}}",1,"(4*ArcTan[(2^(1/8)*x)/(-1 + x^4)^(1/4)] + 4*ArcTanh[(2^(1/8)*x)/(-1 + x^4)^(1/4)] + Sqrt[2]*(2*ArcTan[1 - (2^(5/8)*x)/(-1 + x^4)^(1/4)] - 2*ArcTan[1 + (2^(5/8)*x)/(-1 + x^4)^(1/4)] + Log[1 + (2^(1/4)*x^2)/Sqrt[-1 + x^4] - (2^(5/8)*x)/(-1 + x^4)^(1/4)] - Log[1 + (2^(1/4)*x^2)/Sqrt[-1 + x^4] + (2^(5/8)*x)/(-1 + x^4)^(1/4)]))/(16*2^(5/8))","A",1
2101,0,0,152,0.051083,"\int \frac{\left(-1+x^4\right)^{3/4}}{-1+2 x^4+x^8} \, dx","Integrate[(-1 + x^4)^(3/4)/(-1 + 2*x^4 + x^8),x]","\int \frac{\left(-1+x^4\right)^{3/4}}{-1+2 x^4+x^8} \, dx","\frac{\tan ^{-1}\left(\frac{\sqrt[8]{2} x}{\sqrt[4]{x^4-1}}\right)}{4 \sqrt[8]{2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{2} x}{\sqrt[4]{x^4-1}}\right)}{4 \sqrt[8]{2}}-\frac{\tan ^{-1}\left(\frac{2^{5/8} x \sqrt[4]{x^4-1}}{\sqrt[4]{2} x^2-\sqrt{x^4-1}}\right)}{4\ 2^{5/8}}+\frac{\tanh ^{-1}\left(\frac{2\ 2^{3/8} x \sqrt[4]{x^4-1}}{2^{3/4} \sqrt{x^4-1}+2 x^2}\right)}{4\ 2^{5/8}}",1,"Integrate[(-1 + x^4)^(3/4)/(-1 + 2*x^4 + x^8), x]","F",-1
2102,0,0,152,0.2571936,"\int \frac{1+x^4}{\left(-1+x^4\right) \sqrt{1+\sqrt{1+x^2}}} \, dx","Integrate[(1 + x^4)/((-1 + x^4)*Sqrt[1 + Sqrt[1 + x^2]]),x]","\int \frac{1+x^4}{\left(-1+x^4\right) \sqrt{1+\sqrt{1+x^2}}} \, dx","\frac{2 x}{\sqrt{\sqrt{x^2+1}+1}}-2 \tan ^{-1}\left(\frac{x}{\sqrt{\sqrt{x^2+1}+1}}\right)+\sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2} \sqrt{\sqrt{x^2+1}+1}}\right)-\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{x}{\sqrt{1+\sqrt{2}} \sqrt{\sqrt{x^2+1}+1}}\right)-\sqrt{\sqrt{2}-1} \tanh ^{-1}\left(\frac{x}{\sqrt{\sqrt{2}-1} \sqrt{\sqrt{x^2+1}+1}}\right)",1,"Integrate[(1 + x^4)/((-1 + x^4)*Sqrt[1 + Sqrt[1 + x^2]]), x]","F",-1
2103,1,38,153,0.0127543,"\int \frac{1}{x^3 \left(-b+a x^2\right)^{3/4}} \, dx","Integrate[1/(x^3*(-b + a*x^2)^(3/4)),x]","\frac{2 a \sqrt[4]{a x^2-b} \, _2F_1\left(\frac{1}{4},2;\frac{5}{4};1-\frac{a x^2}{b}\right)}{b^2}","-\frac{3 a \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^2-b}}{\sqrt{a x^2-b}-\sqrt{b}}\right)}{4 \sqrt{2} b^{7/4}}+\frac{3 a \tanh ^{-1}\left(\frac{\frac{\sqrt{a x^2-b}}{\sqrt{2} \sqrt[4]{b}}+\frac{\sqrt[4]{b}}{\sqrt{2}}}{\sqrt[4]{a x^2-b}}\right)}{4 \sqrt{2} b^{7/4}}+\frac{\sqrt[4]{a x^2-b}}{2 b x^2}",1,"(2*a*(-b + a*x^2)^(1/4)*Hypergeometric2F1[1/4, 2, 5/4, 1 - (a*x^2)/b])/b^2","C",1
2104,0,0,153,6.2244357,"\int \frac{a b-2 b x+x^2}{\sqrt[4]{x (-a+x) (-b+x)^3} \left(b-(1+a d) x+d x^2\right)} \, dx","Integrate[(a*b - 2*b*x + x^2)/((x*(-a + x)*(-b + x)^3)^(1/4)*(b - (1 + a*d)*x + d*x^2)),x]","\int \frac{a b-2 b x+x^2}{\sqrt[4]{x (-a+x) (-b+x)^3} \left(b-(1+a d) x+d x^2\right)} \, dx","\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a b^3 x+x^3 \left(3 a b+3 b^2\right)+x^2 \left(-3 a b^2-b^3\right)+x^4 (-a-3 b)+x^5}}{b-x}\right)}{d^{3/4}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a b^3 x+x^3 \left(3 a b+3 b^2\right)+x^2 \left(-3 a b^2-b^3\right)+x^4 (-a-3 b)+x^5}}{b-x}\right)}{d^{3/4}}",1,"Integrate[(a*b - 2*b*x + x^2)/((x*(-a + x)*(-b + x)^3)^(1/4)*(b - (1 + a*d)*x + d*x^2)), x]","F",-1
2105,1,40,153,0.0115069,"\int \frac{1}{x^4 \left(-b+a x^3\right)^{3/4}} \, dx","Integrate[1/(x^4*(-b + a*x^3)^(3/4)),x]","\frac{4 a \sqrt[4]{a x^3-b} \, _2F_1\left(\frac{1}{4},2;\frac{5}{4};1-\frac{a x^3}{b}\right)}{3 b^2}","-\frac{a \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^3-b}}{\sqrt{a x^3-b}-\sqrt{b}}\right)}{2 \sqrt{2} b^{7/4}}+\frac{a \tanh ^{-1}\left(\frac{\frac{\sqrt{a x^3-b}}{\sqrt{2} \sqrt[4]{b}}+\frac{\sqrt[4]{b}}{\sqrt{2}}}{\sqrt[4]{a x^3-b}}\right)}{2 \sqrt{2} b^{7/4}}+\frac{\sqrt[4]{a x^3-b}}{3 b x^3}",1,"(4*a*(-b + a*x^3)^(1/4)*Hypergeometric2F1[1/4, 2, 5/4, 1 - (a*x^3)/b])/(3*b^2)","C",1
2106,1,40,153,0.0091946,"\int \frac{1}{x^4 \sqrt[4]{-b+a x^3}} \, dx","Integrate[1/(x^4*(-b + a*x^3)^(1/4)),x]","\frac{4 a \left(a x^3-b\right)^{3/4} \, _2F_1\left(\frac{3}{4},2;\frac{7}{4};1-\frac{a x^3}{b}\right)}{9 b^2}","-\frac{a \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^3-b}}{\sqrt{a x^3-b}-\sqrt{b}}\right)}{6 \sqrt{2} b^{5/4}}-\frac{a \tanh ^{-1}\left(\frac{\frac{\sqrt{a x^3-b}}{\sqrt{2} \sqrt[4]{b}}+\frac{\sqrt[4]{b}}{\sqrt{2}}}{\sqrt[4]{a x^3-b}}\right)}{6 \sqrt{2} b^{5/4}}+\frac{\left(a x^3-b\right)^{3/4}}{3 b x^3}",1,"(4*a*(-b + a*x^3)^(3/4)*Hypergeometric2F1[3/4, 2, 7/4, 1 - (a*x^3)/b])/(9*b^2)","C",1
2107,1,57,153,0.7443714,"\int \frac{(2+x) \left(-1-x+x^2\right) \sqrt[4]{\frac{1+x-2 x^2}{1+x+4 x^2}}}{2 x \left(1+2 x+x^2+x^4\right)} \, dx","Integrate[((2 + x)*(-1 - x + x^2)*((1 + x - 2*x^2)/(1 + x + 4*x^2))^(1/4))/(2*x*(1 + 2*x + x^2 + x^4)),x]","\frac{1}{2} \int \frac{(x+2) \left(x^2-x-1\right) \sqrt[4]{\frac{-2 x^2+x+1}{4 x^2+x+1}}}{x \left(x^4+x^2+2 x+1\right)} \, dx","-\frac{1}{4} \text{RootSum}\left[17 \text{$\#$1}^8+14 \text{$\#$1}^4+5\&,\frac{13 \text{$\#$1}^4 \log \left(\sqrt[4]{\frac{-2 x^2+x+1}{4 x^2+x+1}}-\text{$\#$1}\right)+5 \log \left(\sqrt[4]{\frac{-2 x^2+x+1}{4 x^2+x+1}}-\text{$\#$1}\right)}{17 \text{$\#$1}^7+7 \text{$\#$1}^3}\&\right]+\tan ^{-1}\left(\sqrt[4]{\frac{-2 x^2+x+1}{4 x^2+x+1}}\right)+\tanh ^{-1}\left(\sqrt[4]{\frac{-2 x^2+x+1}{4 x^2+x+1}}\right)",1,"Integrate[((2 + x)*(-1 - x + x^2)*((1 + x - 2*x^2)/(1 + x + 4*x^2))^(1/4))/(x*(1 + 2*x + x^2 + x^4)), x]/2","A",1
2108,1,5457,153,2.3657117,"\int \frac{1+x^4}{\left(-1+x^4\right) \sqrt{1-x-x^2+x^3+x^4}} \, dx","Integrate[(1 + x^4)/((-1 + x^4)*Sqrt[1 - x - x^2 + x^3 + x^4]),x]","\text{Result too large to show}","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^4+14 \text{$\#$1}^2-16 \text{$\#$1}+5\&,\frac{\text{$\#$1}^2 \log \left(-\text{$\#$1} x-x^2+\sqrt{x^4+x^3-x^2-x+1}+1\right)+\text{$\#$1}^2 (-\log (x))-\log \left(-\text{$\#$1} x-x^2+\sqrt{x^4+x^3-x^2-x+1}+1\right)+\log (x)}{\text{$\#$1}^3+7 \text{$\#$1}-4}\&\right]+\tanh ^{-1}\left(\frac{x}{x^2-\sqrt{x^4+x^3-x^2-x+1}-1}\right)",1,"Result too large to show","C",0
2109,1,37,153,0.0140905,"\int \frac{1}{x^5 \left(-b+a x^4\right)^{3/4}} \, dx","Integrate[1/(x^5*(-b + a*x^4)^(3/4)),x]","\frac{a \sqrt[4]{a x^4-b} \, _2F_1\left(\frac{1}{4},2;\frac{5}{4};1-\frac{a x^4}{b}\right)}{b^2}","-\frac{3 a \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^4-b}}{\sqrt{a x^4-b}-\sqrt{b}}\right)}{8 \sqrt{2} b^{7/4}}+\frac{3 a \tanh ^{-1}\left(\frac{\frac{\sqrt{a x^4-b}}{\sqrt{2} \sqrt[4]{b}}+\frac{\sqrt[4]{b}}{\sqrt{2}}}{\sqrt[4]{a x^4-b}}\right)}{8 \sqrt{2} b^{7/4}}+\frac{\sqrt[4]{a x^4-b}}{4 b x^4}",1,"(a*(-b + a*x^4)^(1/4)*Hypergeometric2F1[1/4, 2, 5/4, 1 - (a*x^4)/b])/b^2","C",1
2110,0,0,153,2.6078956,"\int \frac{a b^3-2 (3 a-b) b^2 x+3 (3 a-b) b x^2-4 a x^3+x^4}{\sqrt[4]{x (-a+x) (-b+x)^3} \left(a^3-\left(3 a^2+b^3 d\right) x+3 \left(a+b^2 d\right) x^2-(1+3 b d) x^3+d x^4\right)} \, dx","Integrate[(a*b^3 - 2*(3*a - b)*b^2*x + 3*(3*a - b)*b*x^2 - 4*a*x^3 + x^4)/((x*(-a + x)*(-b + x)^3)^(1/4)*(a^3 - (3*a^2 + b^3*d)*x + 3*(a + b^2*d)*x^2 - (1 + 3*b*d)*x^3 + d*x^4)),x]","\int \frac{a b^3-2 (3 a-b) b^2 x+3 (3 a-b) b x^2-4 a x^3+x^4}{\sqrt[4]{x (-a+x) (-b+x)^3} \left(a^3-\left(3 a^2+b^3 d\right) x+3 \left(a+b^2 d\right) x^2-(1+3 b d) x^3+d x^4\right)} \, dx","\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a b^3 x+x^3 \left(3 a b+3 b^2\right)+x^2 \left(-3 a b^2-b^3\right)+x^4 (-a-3 b)+x^5}}{a-x}\right)}{d^{3/4}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a b^3 x+x^3 \left(3 a b+3 b^2\right)+x^2 \left(-3 a b^2-b^3\right)+x^4 (-a-3 b)+x^5}}{a-x}\right)}{d^{3/4}}",1,"Integrate[(a*b^3 - 2*(3*a - b)*b^2*x + 3*(3*a - b)*b*x^2 - 4*a*x^3 + x^4)/((x*(-a + x)*(-b + x)^3)^(1/4)*(a^3 - (3*a^2 + b^3*d)*x + 3*(a + b^2*d)*x^2 - (1 + 3*b*d)*x^3 + d*x^4)), x]","F",-1
2111,1,40,153,0.0113844,"\int \frac{1}{x^6 \left(-b+a x^5\right)^{3/4}} \, dx","Integrate[1/(x^6*(-b + a*x^5)^(3/4)),x]","\frac{4 a \sqrt[4]{a x^5-b} \, _2F_1\left(\frac{1}{4},2;\frac{5}{4};1-\frac{a x^5}{b}\right)}{5 b^2}","-\frac{3 a \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^5-b}}{\sqrt{a x^5-b}-\sqrt{b}}\right)}{10 \sqrt{2} b^{7/4}}+\frac{3 a \tanh ^{-1}\left(\frac{\frac{\sqrt{a x^5-b}}{\sqrt{2} \sqrt[4]{b}}+\frac{\sqrt[4]{b}}{\sqrt{2}}}{\sqrt[4]{a x^5-b}}\right)}{10 \sqrt{2} b^{7/4}}+\frac{\sqrt[4]{a x^5-b}}{5 b x^5}",1,"(4*a*(-b + a*x^5)^(1/4)*Hypergeometric2F1[1/4, 2, 5/4, 1 - (a*x^5)/b])/(5*b^2)","C",1
2112,1,40,153,0.0111164,"\int \frac{1}{x^7 \left(-b+a x^6\right)^{3/4}} \, dx","Integrate[1/(x^7*(-b + a*x^6)^(3/4)),x]","\frac{2 a \sqrt[4]{a x^6-b} \, _2F_1\left(\frac{1}{4},2;\frac{5}{4};1-\frac{a x^6}{b}\right)}{3 b^2}","-\frac{a \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^6-b}}{\sqrt{a x^6-b}-\sqrt{b}}\right)}{4 \sqrt{2} b^{7/4}}+\frac{a \tanh ^{-1}\left(\frac{\frac{\sqrt{a x^6-b}}{\sqrt{2} \sqrt[4]{b}}+\frac{\sqrt[4]{b}}{\sqrt{2}}}{\sqrt[4]{a x^6-b}}\right)}{4 \sqrt{2} b^{7/4}}+\frac{\sqrt[4]{a x^6-b}}{6 b x^6}",1,"(2*a*(-b + a*x^6)^(1/4)*Hypergeometric2F1[1/4, 2, 5/4, 1 - (a*x^6)/b])/(3*b^2)","C",1
2113,1,268,153,0.7061969,"\int \frac{b^6+a^6 x^6}{\sqrt{b^4+a^4 x^4} \left(-b^6+a^6 x^6\right)} \, dx","Integrate[(b^6 + a^6*x^6)/(Sqrt[b^4 + a^4*x^4]*(-b^6 + a^6*x^6)),x]","-\frac{i \sqrt{\frac{a^4 x^4}{b^4}+1} \left(3 \sqrt[4]{a^4} F\left(\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)-2 \sqrt[4]{a^4} \Pi \left(-\frac{i}{2}-\frac{\sqrt{3}}{2};\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)-2 \sqrt[4]{a^4} \Pi \left(\frac{1}{2} \left(-i+\sqrt{3}\right);\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)-(1-i) \sqrt{2} \sqrt[4]{b^4} \sqrt{\frac{i a^2}{b^2}} \Pi \left(\frac{i \sqrt{a^4} \sqrt{b^4}}{a^2 b^2};\left.i \sinh ^{-1}\left(\frac{(1+i) \sqrt[4]{a^4} x}{\sqrt{2} \sqrt[4]{b^4}}\right)\right|-1\right)\right)}{3 \sqrt[4]{a^4} \sqrt{\frac{i a^2}{b^2}} \sqrt{a^4 x^4+b^4}}","-\frac{2 \tan ^{-1}\left(\frac{a b x}{\sqrt{a^4 x^4+b^4}}\right)}{3 a b}+\frac{\tanh ^{-1}\left(\frac{\sqrt{6-4 \sqrt{2}} a b x}{\sqrt{a^4 x^4+b^4}+a^2 x^2+b^2}\right)}{3 \sqrt{2} a b}-\frac{\tanh ^{-1}\left(\frac{\sqrt{6+4 \sqrt{2}} a b x}{\sqrt{a^4 x^4+b^4}+a^2 x^2+b^2}\right)}{3 \sqrt{2} a b}",1,"((-1/3*I)*Sqrt[1 + (a^4*x^4)/b^4]*(3*(a^4)^(1/4)*EllipticF[I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] - 2*(a^4)^(1/4)*EllipticPi[-1/2*I - Sqrt[3]/2, I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] - 2*(a^4)^(1/4)*EllipticPi[(-I + Sqrt[3])/2, I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] - (1 - I)*Sqrt[2]*Sqrt[(I*a^2)/b^2]*(b^4)^(1/4)*EllipticPi[(I*Sqrt[a^4]*Sqrt[b^4])/(a^2*b^2), I*ArcSinh[((1 + I)*(a^4)^(1/4)*x)/(Sqrt[2]*(b^4)^(1/4))], -1]))/((a^4)^(1/4)*Sqrt[(I*a^2)/b^2]*Sqrt[b^4 + a^4*x^4])","C",1
2114,1,150,153,0.7349019,"\int \frac{\sqrt{-1+x^2} \sqrt{x^2+x \sqrt{-1+x^2}}}{1+x} \, dx","Integrate[(Sqrt[-1 + x^2]*Sqrt[x^2 + x*Sqrt[-1 + x^2]])/(1 + x),x]","\frac{\sqrt{x^2-1} \left(\sqrt{2} \sqrt{x \left(\sqrt{x^2-1}+x\right)} \left(2 x^2+2 \left(\sqrt{x^2-1}-2\right) x-4 \sqrt{x^2-1}-3\right)+3 \left(\sqrt{x^2-1}+x\right) \sinh ^{-1}\left(\sqrt{x^2-1}+x\right)+4 \left(\sqrt{x^2-1}+x\right) \tanh ^{-1}\left(\sqrt{\left(\sqrt{x^2-1}+x\right)^2+1}\right)\right)}{4 \sqrt{2} \left(x^2+\sqrt{x^2-1} x-1\right)}","\frac{1}{4} \sqrt{x^2+\sqrt{x^2-1} x} (-x-4)+\frac{3}{4} \sqrt{x^2-1} \sqrt{x^2+\sqrt{x^2-1} x}-\frac{3 \log \left(\sqrt{x^2-1}-\sqrt{2} \sqrt{x^2+\sqrt{x^2-1} x}+x\right)}{4 \sqrt{2}}-\sqrt{2} \tanh ^{-1}\left(\sqrt{x^2-1}-\sqrt{2} \sqrt{x^2+\sqrt{x^2-1} x}+x\right)",1,"(Sqrt[-1 + x^2]*(Sqrt[2]*Sqrt[x*(x + Sqrt[-1 + x^2])]*(-3 + 2*x^2 - 4*Sqrt[-1 + x^2] + 2*x*(-2 + Sqrt[-1 + x^2])) + 3*(x + Sqrt[-1 + x^2])*ArcSinh[x + Sqrt[-1 + x^2]] + 4*(x + Sqrt[-1 + x^2])*ArcTanh[Sqrt[1 + (x + Sqrt[-1 + x^2])^2]]))/(4*Sqrt[2]*(-1 + x^2 + x*Sqrt[-1 + x^2]))","A",1
2115,0,0,153,0.1895144,"\int \frac{\left(1+x^4\right) \sqrt{1+\sqrt{1+x^2}}}{-1+x^4} \, dx","Integrate[((1 + x^4)*Sqrt[1 + Sqrt[1 + x^2]])/(-1 + x^4),x]","\int \frac{\left(1+x^4\right) \sqrt{1+\sqrt{1+x^2}}}{-1+x^4} \, dx","\frac{2 \sqrt{x^2+1} x}{3 \sqrt{\sqrt{x^2+1}+1}}+\frac{4 x}{3 \sqrt{\sqrt{x^2+1}+1}}-2 \tan ^{-1}\left(\frac{x}{\sqrt{\sqrt{x^2+1}+1}}\right)+\sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{x}{\sqrt{1+\sqrt{2}} \sqrt{\sqrt{x^2+1}+1}}\right)-\sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{x}{\sqrt{\sqrt{2}-1} \sqrt{\sqrt{x^2+1}+1}}\right)",1,"Integrate[((1 + x^4)*Sqrt[1 + Sqrt[1 + x^2]])/(-1 + x^4), x]","F",-1
2116,0,0,153,0.6258126,"\int \frac{-b^2+a x^2}{\left(b^2+a x^2\right) \sqrt{b+\sqrt{b^2+a x^2}}} \, dx","Integrate[(-b^2 + a*x^2)/((b^2 + a*x^2)*Sqrt[b + Sqrt[b^2 + a*x^2]]),x]","\int \frac{-b^2+a x^2}{\left(b^2+a x^2\right) \sqrt{b+\sqrt{b^2+a x^2}}} \, dx","\frac{2 x}{\sqrt{\sqrt{a x^2+b^2}+b}}-\frac{4 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b} \sqrt{\sqrt{a x^2+b^2}+b}}\right)}{\sqrt{a}}+\frac{2 \sqrt{2} \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{2} \sqrt{b} \sqrt{\sqrt{a x^2+b^2}+b}}-\frac{\sqrt{\sqrt{a x^2+b^2}+b}}{\sqrt{2} \sqrt{b}}\right)}{\sqrt{a}}",1,"Integrate[(-b^2 + a*x^2)/((b^2 + a*x^2)*Sqrt[b + Sqrt[b^2 + a*x^2]]), x]","F",-1
2117,1,217,153,1.0550087,"\int \frac{x}{1+\sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[x/(1 + Sqrt[x + Sqrt[1 + x^2]]),x]","\frac{1}{60} \left(15 x^2-15 \sqrt{x^2+1} x-20 \left(\sqrt{x^2+1}-2 x\right) \sqrt{\sqrt{x^2+1}+x}-\frac{4 \sqrt{x^2+1} \left(6 x^4+6 x^2+3 \sqrt{x^2+1} x+6 \sqrt{x^2+1} x^3+2\right)}{\sqrt{\sqrt{x^2+1}+x} \left(x^2+\sqrt{x^2+1} x+1\right)}+\frac{4 \sqrt{\sqrt{x^2+1}+x} \left(6 x^4+21 x^2+18 \sqrt{x^2+1} x+6 \sqrt{x^2+1} x^3+7\right)}{2 x^2+2 \sqrt{x^2+1} x+1}-30 x-15 \sinh ^{-1}(x)\right)","\frac{-12 x^3-3 x^2+\sqrt{x^2+1} \left(-12 x^2+\left(8 x^2+12 x-4\right) \sqrt{\sqrt{x^2+1}+x}-3 x\right)+\left(8 x^3+12 x^2+4\right) \sqrt{\sqrt{x^2+1}+x}-6 x}{24 \sqrt{x^2+1} x+12 \left(2 x^2+1\right)}-\tanh ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}-1}{\sqrt{\sqrt{x^2+1}+x}+1}\right)",1,"(-30*x + 15*x^2 - 15*x*Sqrt[1 + x^2] - 20*(-2*x + Sqrt[1 + x^2])*Sqrt[x + Sqrt[1 + x^2]] - (4*Sqrt[1 + x^2]*(2 + 6*x^2 + 6*x^4 + 3*x*Sqrt[1 + x^2] + 6*x^3*Sqrt[1 + x^2]))/(Sqrt[x + Sqrt[1 + x^2]]*(1 + x^2 + x*Sqrt[1 + x^2])) + (4*Sqrt[x + Sqrt[1 + x^2]]*(7 + 21*x^2 + 6*x^4 + 18*x*Sqrt[1 + x^2] + 6*x^3*Sqrt[1 + x^2]))/(1 + 2*x^2 + 2*x*Sqrt[1 + x^2]) - 15*ArcSinh[x])/60","A",1
2118,0,0,154,7.1785164,"\int \frac{-2 x+(1+k) x^2}{((1-x) x (1-k x))^{2/3} \left(b-b (1+k) x+(-1+b k) x^2\right)} \, dx","Integrate[(-2*x + (1 + k)*x^2)/(((1 - x)*x*(1 - k*x))^(2/3)*(b - b*(1 + k)*x + (-1 + b*k)*x^2)),x]","\int \frac{-2 x+(1+k) x^2}{((1-x) x (1-k x))^{2/3} \left(b-b (1+k) x+(-1+b k) x^2\right)} \, dx","-\frac{\log \left(b^{2/3} \left(k x^3+(-k-1) x^2+x\right)^{2/3}+\sqrt[3]{b} x \sqrt[3]{k x^3+(-k-1) x^2+x}+x^2\right)}{2 \sqrt[3]{b}}+\frac{\log \left(x-\sqrt[3]{b} \sqrt[3]{k x^3+(-k-1) x^2+x}\right)}{\sqrt[3]{b}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{b} \sqrt[3]{k x^3+(-k-1) x^2+x}+x}\right)}{\sqrt[3]{b}}",1,"Integrate[(-2*x + (1 + k)*x^2)/(((1 - x)*x*(1 - k*x))^(2/3)*(b - b*(1 + k)*x + (-1 + b*k)*x^2)), x]","F",-1
2119,1,88,154,0.0592124,"\int \frac{\left(-b+a x^2\right) \sqrt{-b x+a x^3}}{x^2 \left(b+a x^2\right)} \, dx","Integrate[((-b + a*x^2)*Sqrt[-(b*x) + a*x^3])/(x^2*(b + a*x^2)),x]","-\frac{2 \sqrt{a x^3-b x} \left(4 a x^2 \sqrt{1-\frac{a x^2}{b}} F_1\left(\frac{3}{4};\frac{1}{2},1;\frac{7}{4};\frac{a x^2}{b},-\frac{a x^2}{b}\right)-3 a x^2+3 b\right)}{3 a x^3-3 b x}","-\sqrt[4]{a} \sqrt[4]{b} \tanh ^{-1}\left(\frac{\frac{a^{3/4} x^2}{2 \sqrt[4]{b}}-\frac{b^{3/4}}{2 \sqrt[4]{a}}+\sqrt[4]{a} \sqrt[4]{b} x}{\sqrt{a x^3-b x}}\right)+\frac{2 \sqrt{a x^3-b x}}{x}+\sqrt[4]{a} \sqrt[4]{b} \tan ^{-1}\left(\frac{2 \sqrt[4]{a} \sqrt[4]{b} \sqrt{a x^3-b x}}{-2 \sqrt{a} \sqrt{b} x+a x^2-b}\right)",1,"(-2*Sqrt[-(b*x) + a*x^3]*(3*b - 3*a*x^2 + 4*a*x^2*Sqrt[1 - (a*x^2)/b]*AppellF1[3/4, 1/2, 1, 7/4, (a*x^2)/b, -((a*x^2)/b)]))/(-3*b*x + 3*a*x^3)","C",0
2120,1,100,154,0.154726,"\int \frac{\sqrt[4]{-x^3+x^4}}{x \left(1+x^3\right)} \, dx","Integrate[(-x^3 + x^4)^(1/4)/(x*(1 + x^3)),x]","-\frac{4 \sqrt[4]{(x-1) x^3} \left((-1)^{2/3} \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{1-x}{\left(-1+\sqrt[3]{-1}\right) x}\right)+\, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{x-1}{2 x}\right)-\sqrt[3]{-1} \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{x-1}{\left(1+(-1)^{2/3}\right) x}\right)\right)}{3 x}","-\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4+1\&,\frac{-\text{$\#$1}^4 \log \left(\sqrt[4]{x^4-x^3}-\text{$\#$1} x\right)+\text{$\#$1}^4 \log (x)-\log \left(\sqrt[4]{x^4-x^3}-\text{$\#$1} x\right)+\log (x)}{2 \text{$\#$1}^7-\text{$\#$1}^3}\&\right]+\frac{2}{3} \sqrt[4]{2} \tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-x^3}}\right)-\frac{2}{3} \sqrt[4]{2} \tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-x^3}}\right)",1,"(-4*((-1 + x)*x^3)^(1/4)*((-1)^(2/3)*Hypergeometric2F1[1/4, 1, 5/4, (1 - x)/((-1 + (-1)^(1/3))*x)] + Hypergeometric2F1[1/4, 1, 5/4, (-1 + x)/(2*x)] - (-1)^(1/3)*Hypergeometric2F1[1/4, 1, 5/4, (-1 + x)/((1 + (-1)^(2/3))*x)]))/(3*x)","A",1
2121,1,100,154,0.0459695,"\int \frac{\sqrt[4]{-x^3+x^4}}{x \left(1+x^3\right)} \, dx","Integrate[(-x^3 + x^4)^(1/4)/(x*(1 + x^3)),x]","-\frac{4 \sqrt[4]{(x-1) x^3} \left((-1)^{2/3} \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{1-x}{\left(-1+\sqrt[3]{-1}\right) x}\right)+\, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{x-1}{2 x}\right)-\sqrt[3]{-1} \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{x-1}{\left(1+(-1)^{2/3}\right) x}\right)\right)}{3 x}","-\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4+1\&,\frac{-\text{$\#$1}^4 \log \left(\sqrt[4]{x^4-x^3}-\text{$\#$1} x\right)+\text{$\#$1}^4 \log (x)-\log \left(\sqrt[4]{x^4-x^3}-\text{$\#$1} x\right)+\log (x)}{2 \text{$\#$1}^7-\text{$\#$1}^3}\&\right]+\frac{2}{3} \sqrt[4]{2} \tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-x^3}}\right)-\frac{2}{3} \sqrt[4]{2} \tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-x^3}}\right)",1,"(-4*((-1 + x)*x^3)^(1/4)*((-1)^(2/3)*Hypergeometric2F1[1/4, 1, 5/4, (1 - x)/((-1 + (-1)^(1/3))*x)] + Hypergeometric2F1[1/4, 1, 5/4, (-1 + x)/(2*x)] - (-1)^(1/3)*Hypergeometric2F1[1/4, 1, 5/4, (-1 + x)/((1 + (-1)^(2/3))*x)]))/(3*x)","A",1
2122,0,0,154,0.3337195,"\int \frac{\left(-3+x^4\right) \left(1-x^3+x^4\right)^{2/3}}{x^3 \left(1+x^3+x^4\right)} \, dx","Integrate[((-3 + x^4)*(1 - x^3 + x^4)^(2/3))/(x^3*(1 + x^3 + x^4)),x]","\int \frac{\left(-3+x^4\right) \left(1-x^3+x^4\right)^{2/3}}{x^3 \left(1+x^3+x^4\right)} \, dx","2^{2/3} \log \left(2^{2/3} \sqrt[3]{x^4-x^3+1}+2 x\right)+2^{2/3} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^4-x^3+1}-x}\right)+\frac{3 \left(x^4-x^3+1\right)^{2/3}}{2 x^2}-\frac{\log \left(-2 x^2+2^{2/3} \sqrt[3]{x^4-x^3+1} x-\sqrt[3]{2} \left(x^4-x^3+1\right)^{2/3}\right)}{\sqrt[3]{2}}",1,"Integrate[((-3 + x^4)*(1 - x^3 + x^4)^(2/3))/(x^3*(1 + x^3 + x^4)), x]","F",-1
2123,0,0,154,0.5654907,"\int \frac{\left(-4 b+a x^5\right) \left(b+a x^5\right)^{3/4}}{x^4 \left(2 b+c x^4+2 a x^5\right)} \, dx","Integrate[((-4*b + a*x^5)*(b + a*x^5)^(3/4))/(x^4*(2*b + c*x^4 + 2*a*x^5)),x]","\int \frac{\left(-4 b+a x^5\right) \left(b+a x^5\right)^{3/4}}{x^4 \left(2 b+c x^4+2 a x^5\right)} \, dx","\frac{c^{3/4} \tan ^{-1}\left(\frac{2^{3/4} \sqrt[4]{c} x \sqrt[4]{a x^5+b}}{\sqrt{2} \sqrt{a x^5+b}-\sqrt{c} x^2}\right)}{2 \sqrt[4]{2}}+\frac{c^{3/4} \tanh ^{-1}\left(\frac{\frac{\sqrt{a x^5+b}}{\sqrt[4]{2} \sqrt[4]{c}}+\frac{\sqrt[4]{c} x^2}{2^{3/4}}}{x \sqrt[4]{a x^5+b}}\right)}{2 \sqrt[4]{2}}+\frac{2 \left(a x^5+b\right)^{3/4}}{3 x^3}",1,"Integrate[((-4*b + a*x^5)*(b + a*x^5)^(3/4))/(x^4*(2*b + c*x^4 + 2*a*x^5)), x]","F",-1
2124,0,0,154,1.0218096,"\int \frac{-1+x^6}{\sqrt[3]{x^2+x^4} \left(1+x^6\right)} \, dx","Integrate[(-1 + x^6)/((x^2 + x^4)^(1/3)*(1 + x^6)),x]","\int \frac{-1+x^6}{\sqrt[3]{x^2+x^4} \left(1+x^6\right)} \, dx","-\frac{\left(x^4+x^2\right)^{2/3}}{x \left(x^2+1\right)}+\frac{\tan ^{-1}\left(\frac{3^{2/3} x \sqrt[3]{x^4+x^2}}{\sqrt[3]{3} x^2-\left(x^4+x^2\right)^{2/3}}\right)}{3^{2/3}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt[6]{3} x}{\sqrt[3]{x^4+x^2}}\right)}{3 \sqrt[6]{3}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{3} x^2+\frac{\left(x^4+x^2\right)^{2/3}}{\sqrt[6]{3}}}{x \sqrt[3]{x^4+x^2}}\right)}{3 \sqrt[6]{3}}",1,"Integrate[(-1 + x^6)/((x^2 + x^4)^(1/3)*(1 + x^6)), x]","F",-1
2125,1,94,154,0.2089396,"\int \frac{\sqrt[4]{2+3 x^4} \left(4+6 x^4+x^8\right)}{x^6 \left(1+x^4\right) \left(1+2 x^4\right)} \, dx","Integrate[((2 + 3*x^4)^(1/4)*(4 + 6*x^4 + x^8))/(x^6*(1 + x^4)*(1 + 2*x^4)),x]","\frac{x^3 \left(5 \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};-\frac{x^4}{3 x^4+2}\right)-\, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{x^4}{3 x^4+2}\right)\right)}{3 \left(3 x^4+2\right)^{3/4}}+\left(\frac{24}{5 x}-\frac{4}{5 x^5}\right) \sqrt[4]{3 x^4+2}","\frac{1}{2} \tan ^{-1}\left(\frac{x}{\sqrt[4]{3 x^4+2}}\right)-\frac{1}{2} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{3 x^4+2}}\right)+\frac{4 \sqrt[4]{3 x^4+2} \left(6 x^4-1\right)}{5 x^5}+\frac{5 \tan ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{3 x^4+2}}{\sqrt{3 x^4+2}-x^2}\right)}{2 \sqrt{2}}-\frac{5 \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{3 x^4+2}}{\sqrt{3 x^4+2}+x^2}\right)}{2 \sqrt{2}}",1,"(-4/(5*x^5) + 24/(5*x))*(2 + 3*x^4)^(1/4) + (x^3*(5*Hypergeometric2F1[3/4, 1, 7/4, -(x^4/(2 + 3*x^4))] - Hypergeometric2F1[3/4, 1, 7/4, x^4/(2 + 3*x^4)]))/(3*(2 + 3*x^4)^(3/4))","C",1
2126,1,157,154,0.3049453,"\int \frac{\sqrt[8]{256-256 x^2+96 x^4-16 x^6+x^8}}{-1+x^3} \, dx","Integrate[(256 - 256*x^2 + 96*x^4 - 16*x^6 + x^8)^(1/8)/(-1 + x^3),x]","\frac{\sqrt[8]{\left(x^2-4\right)^4} \left(-\sqrt{3} \tan ^{-1}\left(\frac{x-4}{\sqrt{3} \sqrt{x^2-4}}\right)+(-1)^{2/3} \sqrt{1+4 \sqrt[3]{-1}} \tanh ^{-1}\left(\frac{4 (-1)^{2/3}-x}{\sqrt{1+4 \sqrt[3]{-1}} \sqrt{x^2-4}}\right)+\sqrt[3]{-1} \sqrt{1-4 (-1)^{2/3}} \tanh ^{-1}\left(\frac{x+4 \sqrt[3]{-1}}{\sqrt{1-4 (-1)^{2/3}} \sqrt{x^2-4}}\right)\right)}{3 \sqrt{x^2-4}}","\frac{\sqrt[8]{\left(x^2-4\right)^4} \left(\frac{2 \tan ^{-1}\left(\frac{\sqrt{x^2-4}}{\sqrt{3} (x-2)}\right)}{\sqrt{3}}-\frac{1}{3} \sqrt{2 \left(-3-5 i \sqrt{3}\right)} \tan ^{-1}\left(\frac{\sqrt{1-\frac{2 i}{\sqrt{3}}} \sqrt{x^2-4}}{x-2}\right)-\frac{1}{3} \sqrt{2 \left(-3+5 i \sqrt{3}\right)} \tan ^{-1}\left(\frac{\sqrt{1+\frac{2 i}{\sqrt{3}}} \sqrt{x^2-4}}{x-2}\right)\right)}{\sqrt{x^2-4}}",1,"(((-4 + x^2)^4)^(1/8)*(-(Sqrt[3]*ArcTan[(-4 + x)/(Sqrt[3]*Sqrt[-4 + x^2])]) + (-1)^(2/3)*Sqrt[1 + 4*(-1)^(1/3)]*ArcTanh[(4*(-1)^(2/3) - x)/(Sqrt[1 + 4*(-1)^(1/3)]*Sqrt[-4 + x^2])] + (-1)^(1/3)*Sqrt[1 - 4*(-1)^(2/3)]*ArcTanh[(4*(-1)^(1/3) + x)/(Sqrt[1 - 4*(-1)^(2/3)]*Sqrt[-4 + x^2])]))/(3*Sqrt[-4 + x^2])","A",1
2127,0,0,154,1.0742153,"\int \frac{-36-6 x^2+6 x^3+x^6}{x \left(-6+x^3\right) \sqrt[6]{\frac{6+x^3}{-6+x^3}} \left(36-90 x+122 x^2-96 x^3+51 x^4-26 x^5+15 x^6-6 x^7+x^8\right)} \, dx","Integrate[(-36 - 6*x^2 + 6*x^3 + x^6)/(x*(-6 + x^3)*((6 + x^3)/(-6 + x^3))^(1/6)*(36 - 90*x + 122*x^2 - 96*x^3 + 51*x^4 - 26*x^5 + 15*x^6 - 6*x^7 + x^8)),x]","\int \frac{-36-6 x^2+6 x^3+x^6}{x \left(-6+x^3\right) \sqrt[6]{\frac{6+x^3}{-6+x^3}} \left(36-90 x+122 x^2-96 x^3+51 x^4-26 x^5+15 x^6-6 x^7+x^8\right)} \, dx","-\frac{1}{3} \tan ^{-1}\left(\frac{\sqrt[6]{\frac{x^3+6}{x^3-6}}}{x-1}\right)-\frac{1}{6} \tan ^{-1}\left(\frac{\sqrt[3]{\frac{x^3+6}{x^3-6}}-x^2+2 x-1}{(x-1) \sqrt[6]{\frac{x^3+6}{x^3-6}}}\right)+\frac{\tanh ^{-1}\left(\frac{\left(\sqrt{3} x-\sqrt{3}\right) \sqrt[6]{\frac{x^3+6}{x^3-6}}}{\sqrt[3]{\frac{x^3+6}{x^3-6}}+x^2-2 x+1}\right)}{2 \sqrt{3}}",1,"Integrate[(-36 - 6*x^2 + 6*x^3 + x^6)/(x*(-6 + x^3)*((6 + x^3)/(-6 + x^3))^(1/6)*(36 - 90*x + 122*x^2 - 96*x^3 + 51*x^4 - 26*x^5 + 15*x^6 - 6*x^7 + x^8)), x]","F",-1
2128,1,549,154,1.0252945,"\int \frac{2 b-a x^4+2 x^8}{\sqrt[4]{b+a x^4} \left(-2 b+a x^4+x^8\right)} \, dx","Integrate[(2*b - a*x^4 + 2*x^8)/((b + a*x^4)^(1/4)*(-2*b + a*x^4 + x^8)),x]","-\frac{3 \left(a-\frac{a^2+4 b}{\sqrt{a^2+8 b}}\right) \tan ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+8 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+8 b}} \sqrt[4]{a x^4+b}}\right)}{2 \left(a-\sqrt{a^2+8 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+8 b}+a^2-2 b}}-\frac{3 \left(\frac{a^2+4 b}{\sqrt{a^2+8 b}}+a\right) \tan ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+8 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+8 b}+a} \sqrt[4]{a x^4+b}}\right)}{2 \left(\sqrt{a^2+8 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+8 b}+a^2-2 b}}-\frac{3 \left(a-\frac{a^2+4 b}{\sqrt{a^2+8 b}}\right) \tanh ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+8 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+8 b}} \sqrt[4]{a x^4+b}}\right)}{2 \left(a-\sqrt{a^2+8 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+8 b}+a^2-2 b}}-\frac{3 \left(\frac{a^2+4 b}{\sqrt{a^2+8 b}}+a\right) \tanh ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+8 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+8 b}+a} \sqrt[4]{a x^4+b}}\right)}{2 \left(\sqrt{a^2+8 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+8 b}+a^2-2 b}}+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{a}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{a}}","-\frac{3}{4} \text{RootSum}\left[2 \text{$\#$1}^8-5 \text{$\#$1}^4 a+3 a^2-b\&,\frac{2 \text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)-2 \text{$\#$1}^4 \log (x)-3 a \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+3 a \log (x)}{5 \text{$\#$1} a-4 \text{$\#$1}^5}\&\right]+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{a}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{a}}",1,"ArcTan[(a^(1/4)*x)/(b + a*x^4)^(1/4)]/a^(1/4) - (3*(a - (a^2 + 4*b)/Sqrt[a^2 + 8*b])*ArcTan[((a^2 - 2*b - a*Sqrt[a^2 + 8*b])^(1/4)*x)/((a - Sqrt[a^2 + 8*b])^(1/4)*(b + a*x^4)^(1/4))])/(2*(a - Sqrt[a^2 + 8*b])^(3/4)*(a^2 - 2*b - a*Sqrt[a^2 + 8*b])^(1/4)) - (3*(a + (a^2 + 4*b)/Sqrt[a^2 + 8*b])*ArcTan[((a^2 - 2*b + a*Sqrt[a^2 + 8*b])^(1/4)*x)/((a + Sqrt[a^2 + 8*b])^(1/4)*(b + a*x^4)^(1/4))])/(2*(a + Sqrt[a^2 + 8*b])^(3/4)*(a^2 - 2*b + a*Sqrt[a^2 + 8*b])^(1/4)) + ArcTanh[(a^(1/4)*x)/(b + a*x^4)^(1/4)]/a^(1/4) - (3*(a - (a^2 + 4*b)/Sqrt[a^2 + 8*b])*ArcTanh[((a^2 - 2*b - a*Sqrt[a^2 + 8*b])^(1/4)*x)/((a - Sqrt[a^2 + 8*b])^(1/4)*(b + a*x^4)^(1/4))])/(2*(a - Sqrt[a^2 + 8*b])^(3/4)*(a^2 - 2*b - a*Sqrt[a^2 + 8*b])^(1/4)) - (3*(a + (a^2 + 4*b)/Sqrt[a^2 + 8*b])*ArcTanh[((a^2 - 2*b + a*Sqrt[a^2 + 8*b])^(1/4)*x)/((a + Sqrt[a^2 + 8*b])^(1/4)*(b + a*x^4)^(1/4))])/(2*(a + Sqrt[a^2 + 8*b])^(3/4)*(a^2 - 2*b + a*Sqrt[a^2 + 8*b])^(1/4))","B",1
2129,1,549,154,0.3969815,"\int \frac{2 b-a x^4+2 x^8}{\sqrt[4]{b+a x^4} \left(-2 b+a x^4+x^8\right)} \, dx","Integrate[(2*b - a*x^4 + 2*x^8)/((b + a*x^4)^(1/4)*(-2*b + a*x^4 + x^8)),x]","-\frac{3 \left(a-\frac{a^2+4 b}{\sqrt{a^2+8 b}}\right) \tan ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+8 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+8 b}} \sqrt[4]{a x^4+b}}\right)}{2 \left(a-\sqrt{a^2+8 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+8 b}+a^2-2 b}}-\frac{3 \left(\frac{a^2+4 b}{\sqrt{a^2+8 b}}+a\right) \tan ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+8 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+8 b}+a} \sqrt[4]{a x^4+b}}\right)}{2 \left(\sqrt{a^2+8 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+8 b}+a^2-2 b}}-\frac{3 \left(a-\frac{a^2+4 b}{\sqrt{a^2+8 b}}\right) \tanh ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+8 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+8 b}} \sqrt[4]{a x^4+b}}\right)}{2 \left(a-\sqrt{a^2+8 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+8 b}+a^2-2 b}}-\frac{3 \left(\frac{a^2+4 b}{\sqrt{a^2+8 b}}+a\right) \tanh ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+8 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+8 b}+a} \sqrt[4]{a x^4+b}}\right)}{2 \left(\sqrt{a^2+8 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+8 b}+a^2-2 b}}+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{a}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{a}}","-\frac{3}{4} \text{RootSum}\left[2 \text{$\#$1}^8-5 \text{$\#$1}^4 a+3 a^2-b\&,\frac{2 \text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)-2 \text{$\#$1}^4 \log (x)-3 a \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+3 a \log (x)}{5 \text{$\#$1} a-4 \text{$\#$1}^5}\&\right]+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{a}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{a}}",1,"ArcTan[(a^(1/4)*x)/(b + a*x^4)^(1/4)]/a^(1/4) - (3*(a - (a^2 + 4*b)/Sqrt[a^2 + 8*b])*ArcTan[((a^2 - 2*b - a*Sqrt[a^2 + 8*b])^(1/4)*x)/((a - Sqrt[a^2 + 8*b])^(1/4)*(b + a*x^4)^(1/4))])/(2*(a - Sqrt[a^2 + 8*b])^(3/4)*(a^2 - 2*b - a*Sqrt[a^2 + 8*b])^(1/4)) - (3*(a + (a^2 + 4*b)/Sqrt[a^2 + 8*b])*ArcTan[((a^2 - 2*b + a*Sqrt[a^2 + 8*b])^(1/4)*x)/((a + Sqrt[a^2 + 8*b])^(1/4)*(b + a*x^4)^(1/4))])/(2*(a + Sqrt[a^2 + 8*b])^(3/4)*(a^2 - 2*b + a*Sqrt[a^2 + 8*b])^(1/4)) + ArcTanh[(a^(1/4)*x)/(b + a*x^4)^(1/4)]/a^(1/4) - (3*(a - (a^2 + 4*b)/Sqrt[a^2 + 8*b])*ArcTanh[((a^2 - 2*b - a*Sqrt[a^2 + 8*b])^(1/4)*x)/((a - Sqrt[a^2 + 8*b])^(1/4)*(b + a*x^4)^(1/4))])/(2*(a - Sqrt[a^2 + 8*b])^(3/4)*(a^2 - 2*b - a*Sqrt[a^2 + 8*b])^(1/4)) - (3*(a + (a^2 + 4*b)/Sqrt[a^2 + 8*b])*ArcTanh[((a^2 - 2*b + a*Sqrt[a^2 + 8*b])^(1/4)*x)/((a + Sqrt[a^2 + 8*b])^(1/4)*(b + a*x^4)^(1/4))])/(2*(a + Sqrt[a^2 + 8*b])^(3/4)*(a^2 - 2*b + a*Sqrt[a^2 + 8*b])^(1/4))","B",1
2130,0,0,154,0.6570184,"\int \frac{-b+a x^8}{\left(b+a x^8\right) \sqrt[4]{b-c x^4+a x^8}} \, dx","Integrate[(-b + a*x^8)/((b + a*x^8)*(b - c*x^4 + a*x^8)^(1/4)),x]","\int \frac{-b+a x^8}{\left(b+a x^8\right) \sqrt[4]{b-c x^4+a x^8}} \, dx","-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x \sqrt[4]{a x^8+b-c x^4}}{\sqrt{a x^8+b-c x^4}-\sqrt{c} x^2}\right)}{2 \sqrt{2} \sqrt[4]{c}}-\frac{\tanh ^{-1}\left(\frac{\frac{\sqrt{a x^8+b-c x^4}}{\sqrt{2} \sqrt[4]{c}}+\frac{\sqrt[4]{c} x^2}{\sqrt{2}}}{x \sqrt[4]{a x^8+b-c x^4}}\right)}{2 \sqrt{2} \sqrt[4]{c}}",1,"Integrate[(-b + a*x^8)/((b + a*x^8)*(b - c*x^4 + a*x^8)^(1/4)), x]","F",-1
2131,0,0,154,1.7744301,"\int \frac{1}{x^2 \sqrt{-b x+a^2 x^2} \left(a x^2+x \sqrt{-b x+a^2 x^2}\right)^{3/2}} \, dx","Integrate[1/(x^2*Sqrt[-(b*x) + a^2*x^2]*(a*x^2 + x*Sqrt[-(b*x) + a^2*x^2])^(3/2)),x]","\int \frac{1}{x^2 \sqrt{-b x+a^2 x^2} \left(a x^2+x \sqrt{-b x+a^2 x^2}\right)^{3/2}} \, dx","\frac{4 \left(8192 a^7 x^3+1024 a^5 b x^2+448 a^3 b^2 x+6699 a b^3\right) \sqrt{x \left(\sqrt{a^2 x^2-b x}+a x\right)}}{45045 b^5 x^4}-\frac{4 \sqrt{a^2 x^2-b x} \left(-8192 a^6 x^3-5120 a^4 b x^2-4032 a^2 b^2 x+3003 b^3\right) \sqrt{x \left(\sqrt{a^2 x^2-b x}+a x\right)}}{45045 b^5 x^5}",1,"Integrate[1/(x^2*Sqrt[-(b*x) + a^2*x^2]*(a*x^2 + x*Sqrt[-(b*x) + a^2*x^2])^(3/2)), x]","F",-1
2132,1,482,154,2.0751645,"\int \frac{1+\sqrt{1+x^2}}{1+\sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[(1 + Sqrt[1 + x^2])/(1 + Sqrt[x + Sqrt[1 + x^2]]),x]","-\frac{2 \sqrt{x^2+1} \left(\sqrt{x^2+1}+x\right)^{9/2} \left(\left(4 x^2+4 \sqrt{x^2+1} x+2\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\left(x+\sqrt{x^2+1}\right)^2\right)-x^2-\sqrt{x^2+1} x-2\right)}{48 x^6+84 x^4+39 x^2+15 \sqrt{x^2+1} x+48 \sqrt{x^2+1} x^5+60 \sqrt{x^2+1} x^3+3}+\frac{1}{3} \left(\sqrt{x^2+1}-2 x\right) \sqrt{\sqrt{x^2+1}+x}-\frac{x^2}{4}+\frac{1}{4} (x-4) \sqrt{x^2+1}+\log \left(\sqrt{x^2+1}+1\right)+\frac{2 \sqrt{x^2+1} \left(\sqrt{x^2+1}+x\right) \left(\sqrt{\sqrt{x^2+1}+x}-\tan ^{-1}\left(\sqrt{\sqrt{x^2+1}+x}\right)-\tanh ^{-1}\left(\sqrt{\sqrt{x^2+1}+x}\right)\right)}{x^2+\sqrt{x^2+1} x+1}-\frac{\left(6 x^4+21 x^2+18 \sqrt{x^2+1} x+6 \sqrt{x^2+1} x^3+7\right) \sqrt{\sqrt{x^2+1}+x}}{15 \left(2 x^2+2 \sqrt{x^2+1} x+1\right)}+\frac{\sqrt{x^2+1} \left(6 x^4+6 x^2+3 \sqrt{x^2+1} x+6 \sqrt{x^2+1} x^3+2\right)}{15 \left(x^2+\sqrt{x^2+1} x+1\right) \sqrt{\sqrt{x^2+1}+x}}+\frac{x}{2}-2 \log (x)+\frac{1}{4} \sinh ^{-1}(x)","\frac{5}{4} \log \left(\sqrt{x^2+1}+x\right)-4 \log \left(\sqrt{\sqrt{x^2+1}+x}+1\right)+\frac{-24 x^3+214 x^2+\sqrt{x^2+1} \left(-24 x^2+\left(16 x^2+72 x+40\right) \sqrt{\sqrt{x^2+1}+x}+214 x-24\right)+\left(16 x^3+72 x^2+48 x+40\right) \sqrt{\sqrt{x^2+1}+x}-36 x+104}{48 \sqrt{x^2+1} x+24 \left(2 x^2+1\right)}",1,"x/2 - x^2/4 + ((-4 + x)*Sqrt[1 + x^2])/4 + ((-2*x + Sqrt[1 + x^2])*Sqrt[x + Sqrt[1 + x^2]])/3 + (Sqrt[1 + x^2]*(2 + 6*x^2 + 6*x^4 + 3*x*Sqrt[1 + x^2] + 6*x^3*Sqrt[1 + x^2]))/(15*Sqrt[x + Sqrt[1 + x^2]]*(1 + x^2 + x*Sqrt[1 + x^2])) - (Sqrt[x + Sqrt[1 + x^2]]*(7 + 21*x^2 + 6*x^4 + 18*x*Sqrt[1 + x^2] + 6*x^3*Sqrt[1 + x^2]))/(15*(1 + 2*x^2 + 2*x*Sqrt[1 + x^2])) + ArcSinh[x]/4 + (2*Sqrt[1 + x^2]*(x + Sqrt[1 + x^2])*(Sqrt[x + Sqrt[1 + x^2]] - ArcTan[Sqrt[x + Sqrt[1 + x^2]]] - ArcTanh[Sqrt[x + Sqrt[1 + x^2]]]))/(1 + x^2 + x*Sqrt[1 + x^2]) - (2*Sqrt[1 + x^2]*(x + Sqrt[1 + x^2])^(9/2)*(-2 - x^2 - x*Sqrt[1 + x^2] + (2 + 4*x^2 + 4*x*Sqrt[1 + x^2])*Hypergeometric2F1[3/4, 1, 7/4, (x + Sqrt[1 + x^2])^2]))/(3 + 39*x^2 + 84*x^4 + 48*x^6 + 15*x*Sqrt[1 + x^2] + 60*x^3*Sqrt[1 + x^2] + 48*x^5*Sqrt[1 + x^2]) - 2*Log[x] + Log[1 + Sqrt[1 + x^2]]","C",1
2133,0,0,155,4.4534423,"\int \frac{-2+(1+k) x}{\sqrt[3]{(1-x) x (1-k x)} \left(b-b (1+k) x+(-1+b k) x^2\right)} \, dx","Integrate[(-2 + (1 + k)*x)/(((1 - x)*x*(1 - k*x))^(1/3)*(b - b*(1 + k)*x + (-1 + b*k)*x^2)),x]","\int \frac{-2+(1+k) x}{\sqrt[3]{(1-x) x (1-k x)} \left(b-b (1+k) x+(-1+b k) x^2\right)} \, dx","\frac{\log \left(x-\sqrt[3]{b} \sqrt[3]{k x^3+(-k-1) x^2+x}\right)}{b^{2/3}}-\frac{\log \left(b^{2/3} \left(k x^3+(-k-1) x^2+x\right)^{2/3}+\sqrt[3]{b} x \sqrt[3]{k x^3+(-k-1) x^2+x}+x^2\right)}{2 b^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{b} \sqrt[3]{k x^3+(-k-1) x^2+x}+x}\right)}{b^{2/3}}",1,"Integrate[(-2 + (1 + k)*x)/(((1 - x)*x*(1 - k*x))^(1/3)*(b - b*(1 + k)*x + (-1 + b*k)*x^2)), x]","F",-1
2134,1,129,155,0.3338889,"\int \frac{\sqrt[4]{-b+a x^4} \left(-8 b+a x^8\right)}{x^{10} \left(b+a x^4\right)} \, dx","Integrate[((-b + a*x^4)^(1/4)*(-8*b + a*x^8))/(x^10*(b + a*x^4)),x]","\frac{\left(a x^4-b\right) \left(80 a^2 x^8-a b \left(9 x^4+16\right) x^4+8 b^2\right)+\frac{6 a^2 x^{12} (b-8 a) \left(1-\frac{a x^4}{b}\right)^{3/4} \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};\frac{2 a x^4}{a x^4+b}\right)}{\left(\frac{a x^4}{b}+1\right)^{3/4}}}{9 b^2 x^9 \left(a x^4-b\right)^{3/4}}","\frac{\left(8 a^{9/4}-a^{5/4} b\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{2^{3/4} b^2}-\frac{\left(8 a^{9/4}-a^{5/4} b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{2^{3/4} b^2}+\frac{\sqrt[4]{a x^4-b} \left(80 a^2 x^8-9 a b x^8-16 a b x^4+8 b^2\right)}{9 b^2 x^9}",1,"((-b + a*x^4)*(8*b^2 + 80*a^2*x^8 - a*b*x^4*(16 + 9*x^4)) + (6*a^2*(-8*a + b)*x^12*(1 - (a*x^4)/b)^(3/4)*Hypergeometric2F1[3/4, 3/4, 7/4, (2*a*x^4)/(b + a*x^4)])/(1 + (a*x^4)/b)^(3/4))/(9*b^2*x^9*(-b + a*x^4)^(3/4))","C",0
2135,1,4996,155,14.4059495,"\int \frac{x}{x+\sqrt{x+\sqrt{1+x}}} \, dx","Integrate[x/(x + Sqrt[x + Sqrt[1 + x]]),x]","\text{Result too large to show}","4 \text{RootSum}\left[\text{$\#$1}^4+2 \text{$\#$1}^3-5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,\frac{\text{$\#$1}^3 \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)+\text{$\#$1} \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)}{4 \text{$\#$1}^3+6 \text{$\#$1}^2-10 \text{$\#$1}+3}\&\right]+x-2 \sqrt{x+\sqrt{x+1}}-\log \left(2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)",1,"x - 2*Sqrt[x + Sqrt[1 + x]] - Log[1 + 2*Sqrt[1 + x] + 2*Sqrt[x + Sqrt[1 + x]]] - (2*(1 + x)*Sqrt[(1 + (-1 + Sqrt[1 + x])/(1 + x))/(1 + x)]*((2*Sqrt[1 - (1 + x)^(-1) + 1/Sqrt[1 + x]]*(-1 + 2/Sqrt[1 + x])*(-(Log[-1 + 2/Sqrt[1 + x]]/Sqrt[5]) + Log[5 + 2*Sqrt[5]*Sqrt[1 - (1 + x)^(-1) + 1/Sqrt[1 + x]]]/Sqrt[5]))/((-2 + Sqrt[1 + x])*Sqrt[(1 + (-1 + Sqrt[1 + x])/(1 + x))/(1 + x)]) - ((1 + 2/(1 + x)^2 - (1 + x)^(-3/2) - 3/(1 + x))*Sqrt[1 - (1 + x)^(-1) + 1/Sqrt[1 + x]]*(-1 + 2/Sqrt[1 + x])*((Log[-1 + 2/Sqrt[1 + x]]/Sqrt[5] - Log[5 + 2*Sqrt[5]*Sqrt[1 - (1 + x)^(-1) + 1/Sqrt[1 + x]]]/Sqrt[5])/(2*(1/2 - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0])*(1/2 - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0])*(1/2 - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0])*(1/2 - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0])) + (Log[1/Sqrt[1 + x] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0]]/Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0]^2] - Log[2 + 1/Sqrt[1 + x] + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0] - (2*Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0])/Sqrt[1 + x] + 2*Sqrt[1 - (1 + x)^(-1) + 1/Sqrt[1 + x]]*Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0]^2]]/Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0]^2])/(4*(-1/2 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0])*(Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0])*(Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0])*(Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0])) + (Log[1/Sqrt[1 + x] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0]]/Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0]^2] - Log[2 + 1/Sqrt[1 + x] + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0] - (2*Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0])/Sqrt[1 + x] + 2*Sqrt[1 - (1 + x)^(-1) + 1/Sqrt[1 + x]]*Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0]^2]]/Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0]^2])/(4*(-1/2 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0])*(-Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0] + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0])*(Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0])*(Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0])) + (Log[1/Sqrt[1 + x] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0]]/Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0]^2] - Log[2 + 1/Sqrt[1 + x] + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0] - (2*Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0])/Sqrt[1 + x] + 2*Sqrt[1 - (1 + x)^(-1) + 1/Sqrt[1 + x]]*Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0]^2]]/Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0]^2])/(4*(-1/2 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0])*(-Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0] + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0])*(-Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0] + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0])*(Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0])) + (Log[1/Sqrt[1 + x] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0]]/Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0]^2] - Log[2 + 1/Sqrt[1 + x] + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0] - (2*Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0])/Sqrt[1 + x] + 2*Sqrt[1 - (1 + x)^(-1) + 1/Sqrt[1 + x]]*Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0]^2]]/Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0]^2])/(4*(-1/2 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0])*(-Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0] + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0])*(-Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0] + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0])*(-Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0] + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0]))))/((-1 - 2/(1 + x)^2 + (1 + x)^(-3/2) + 3/(1 + x))*(-2 + Sqrt[1 + x])*Sqrt[(1 + (-1 + Sqrt[1 + x])/(1 + x))/(1 + x)]) + ((1 + 2/(1 + x)^2 - (1 + x)^(-3/2) - 3/(1 + x))*Sqrt[1 - (1 + x)^(-1) + 1/Sqrt[1 + x]]*(-1 + 2/Sqrt[1 + x])*((Log[-1 + 2/Sqrt[1 + x]]/Sqrt[5] - Log[5 + 2*Sqrt[5]*Sqrt[1 - (1 + x)^(-1) + 1/Sqrt[1 + x]]]/Sqrt[5])/(4*(1/2 - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0])*(1/2 - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0])*(1/2 - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0])*(1/2 - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0])) + (Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0]*(Log[1/Sqrt[1 + x] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0]]/Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0]^2] - Log[2 + 1/Sqrt[1 + x] + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0] - (2*Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0])/Sqrt[1 + x] + 2*Sqrt[1 - (1 + x)^(-1) + 1/Sqrt[1 + x]]*Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0]^2]]/Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0]^2]))/(4*(-1/2 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0])*(Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0])*(Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0])*(Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0])) + (Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0]*(Log[1/Sqrt[1 + x] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0]]/Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0]^2] - Log[2 + 1/Sqrt[1 + x] + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0] - (2*Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0])/Sqrt[1 + x] + 2*Sqrt[1 - (1 + x)^(-1) + 1/Sqrt[1 + x]]*Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0]^2]]/Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0]^2]))/(4*(-1/2 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0])*(-Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0] + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0])*(Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0])*(Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0])) + (Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0]*(Log[1/Sqrt[1 + x] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0]]/Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0]^2] - Log[2 + 1/Sqrt[1 + x] + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0] - (2*Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0])/Sqrt[1 + x] + 2*Sqrt[1 - (1 + x)^(-1) + 1/Sqrt[1 + x]]*Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0]^2]]/Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0]^2]))/(4*(-1/2 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0])*(-Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0] + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0])*(-Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0] + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0])*(Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0])) + (Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0]*(Log[1/Sqrt[1 + x] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0]]/Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0]^2] - Log[2 + 1/Sqrt[1 + x] + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0] - (2*Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0])/Sqrt[1 + x] + 2*Sqrt[1 - (1 + x)^(-1) + 1/Sqrt[1 + x]]*Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0]^2]]/Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0]^2]))/(4*(-1/2 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0])*(-Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0] + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0])*(-Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0] + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0])*(-Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0] + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0]))))/((-1 - 2/(1 + x)^2 + (1 + x)^(-3/2) + 3/(1 + x))*(-2 + Sqrt[1 + x])*Sqrt[(1 + (-1 + Sqrt[1 + x])/(1 + x))/(1 + x)])))/Sqrt[(1 + x)*(1 + (-1 + Sqrt[1 + x])/(1 + x))] + 2*RootSum[2 - #1 - 3*#1^2 + #1^4 & , (-(Log[Sqrt[1 + x] - #1]*#1) + Log[Sqrt[1 + x] - #1]*#1^2 + Log[Sqrt[1 + x] - #1]*#1^3)/(-1 - 6*#1 + 4*#1^3) & ]","B",0
2136,1,4996,155,6.4122064,"\int \frac{x}{x+\sqrt{x+\sqrt{1+x}}} \, dx","Integrate[x/(x + Sqrt[x + Sqrt[1 + x]]),x]","\text{Result too large to show}","4 \text{RootSum}\left[\text{$\#$1}^4+2 \text{$\#$1}^3-5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,\frac{\text{$\#$1}^3 \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)+\text{$\#$1} \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)}{4 \text{$\#$1}^3+6 \text{$\#$1}^2-10 \text{$\#$1}+3}\&\right]+x-2 \sqrt{x+\sqrt{x+1}}-\log \left(2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)",1,"x - 2*Sqrt[x + Sqrt[1 + x]] - Log[1 + 2*Sqrt[1 + x] + 2*Sqrt[x + Sqrt[1 + x]]] - (2*(1 + x)*Sqrt[(1 + (-1 + Sqrt[1 + x])/(1 + x))/(1 + x)]*((2*Sqrt[1 - (1 + x)^(-1) + 1/Sqrt[1 + x]]*(-1 + 2/Sqrt[1 + x])*(-(Log[-1 + 2/Sqrt[1 + x]]/Sqrt[5]) + Log[5 + 2*Sqrt[5]*Sqrt[1 - (1 + x)^(-1) + 1/Sqrt[1 + x]]]/Sqrt[5]))/((-2 + Sqrt[1 + x])*Sqrt[(1 + (-1 + Sqrt[1 + x])/(1 + x))/(1 + x)]) - ((1 + 2/(1 + x)^2 - (1 + x)^(-3/2) - 3/(1 + x))*Sqrt[1 - (1 + x)^(-1) + 1/Sqrt[1 + x]]*(-1 + 2/Sqrt[1 + x])*((Log[-1 + 2/Sqrt[1 + x]]/Sqrt[5] - Log[5 + 2*Sqrt[5]*Sqrt[1 - (1 + x)^(-1) + 1/Sqrt[1 + x]]]/Sqrt[5])/(2*(1/2 - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0])*(1/2 - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0])*(1/2 - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0])*(1/2 - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0])) + (Log[1/Sqrt[1 + x] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0]]/Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0]^2] - Log[2 + 1/Sqrt[1 + x] + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0] - (2*Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0])/Sqrt[1 + x] + 2*Sqrt[1 - (1 + x)^(-1) + 1/Sqrt[1 + x]]*Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0]^2]]/Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0]^2])/(4*(-1/2 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0])*(Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0])*(Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0])*(Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0])) + (Log[1/Sqrt[1 + x] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0]]/Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0]^2] - Log[2 + 1/Sqrt[1 + x] + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0] - (2*Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0])/Sqrt[1 + x] + 2*Sqrt[1 - (1 + x)^(-1) + 1/Sqrt[1 + x]]*Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0]^2]]/Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0]^2])/(4*(-1/2 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0])*(-Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0] + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0])*(Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0])*(Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0])) + (Log[1/Sqrt[1 + x] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0]]/Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0]^2] - Log[2 + 1/Sqrt[1 + x] + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0] - (2*Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0])/Sqrt[1 + x] + 2*Sqrt[1 - (1 + x)^(-1) + 1/Sqrt[1 + x]]*Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0]^2]]/Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0]^2])/(4*(-1/2 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0])*(-Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0] + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0])*(-Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0] + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0])*(Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0])) + (Log[1/Sqrt[1 + x] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0]]/Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0]^2] - Log[2 + 1/Sqrt[1 + x] + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0] - (2*Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0])/Sqrt[1 + x] + 2*Sqrt[1 - (1 + x)^(-1) + 1/Sqrt[1 + x]]*Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0]^2]]/Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0]^2])/(4*(-1/2 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0])*(-Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0] + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0])*(-Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0] + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0])*(-Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0] + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0]))))/((-1 - 2/(1 + x)^2 + (1 + x)^(-3/2) + 3/(1 + x))*(-2 + Sqrt[1 + x])*Sqrt[(1 + (-1 + Sqrt[1 + x])/(1 + x))/(1 + x)]) + ((1 + 2/(1 + x)^2 - (1 + x)^(-3/2) - 3/(1 + x))*Sqrt[1 - (1 + x)^(-1) + 1/Sqrt[1 + x]]*(-1 + 2/Sqrt[1 + x])*((Log[-1 + 2/Sqrt[1 + x]]/Sqrt[5] - Log[5 + 2*Sqrt[5]*Sqrt[1 - (1 + x)^(-1) + 1/Sqrt[1 + x]]]/Sqrt[5])/(4*(1/2 - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0])*(1/2 - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0])*(1/2 - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0])*(1/2 - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0])) + (Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0]*(Log[1/Sqrt[1 + x] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0]]/Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0]^2] - Log[2 + 1/Sqrt[1 + x] + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0] - (2*Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0])/Sqrt[1 + x] + 2*Sqrt[1 - (1 + x)^(-1) + 1/Sqrt[1 + x]]*Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0]^2]]/Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0]^2]))/(4*(-1/2 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0])*(Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0])*(Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0])*(Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0])) + (Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0]*(Log[1/Sqrt[1 + x] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0]]/Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0]^2] - Log[2 + 1/Sqrt[1 + x] + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0] - (2*Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0])/Sqrt[1 + x] + 2*Sqrt[1 - (1 + x)^(-1) + 1/Sqrt[1 + x]]*Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0]^2]]/Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0]^2]))/(4*(-1/2 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0])*(-Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0] + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0])*(Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0])*(Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0])) + (Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0]*(Log[1/Sqrt[1 + x] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0]]/Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0]^2] - Log[2 + 1/Sqrt[1 + x] + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0] - (2*Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0])/Sqrt[1 + x] + 2*Sqrt[1 - (1 + x)^(-1) + 1/Sqrt[1 + x]]*Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0]^2]]/Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0]^2]))/(4*(-1/2 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0])*(-Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0] + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0])*(-Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0] + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0])*(Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0])) + (Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0]*(Log[1/Sqrt[1 + x] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0]]/Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0]^2] - Log[2 + 1/Sqrt[1 + x] + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0] - (2*Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0])/Sqrt[1 + x] + 2*Sqrt[1 - (1 + x)^(-1) + 1/Sqrt[1 + x]]*Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0]^2]]/Sqrt[1 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0] - Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0]^2]))/(4*(-1/2 + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0])*(-Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 1, 0] + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0])*(-Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 2, 0] + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0])*(-Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 3, 0] + Root[1 - 3*#1^2 - #1^3 + 2*#1^4 & , 4, 0]))))/((-1 - 2/(1 + x)^2 + (1 + x)^(-3/2) + 3/(1 + x))*(-2 + Sqrt[1 + x])*Sqrt[(1 + (-1 + Sqrt[1 + x])/(1 + x))/(1 + x)])))/Sqrt[(1 + x)*(1 + (-1 + Sqrt[1 + x])/(1 + x))] + 2*RootSum[2 - #1 - 3*#1^2 + #1^4 & , (-(Log[Sqrt[1 + x] - #1]*#1) + Log[Sqrt[1 + x] - #1]*#1^2 + Log[Sqrt[1 + x] - #1]*#1^3)/(-1 - 6*#1 + 4*#1^3) & ]","B",0
2137,0,0,156,0.6587466,"\int \frac{\left(-6+x^2\right) \left(-2+x^2\right) \left(2-x^2+x^3\right) \sqrt[3]{-2+x^2+2 x^3}}{x^5 \left(-2+x^2+x^3\right)^2} \, dx","Integrate[((-6 + x^2)*(-2 + x^2)*(2 - x^2 + x^3)*(-2 + x^2 + 2*x^3)^(1/3))/(x^5*(-2 + x^2 + x^3)^2),x]","\int \frac{\left(-6+x^2\right) \left(-2+x^2\right) \left(2-x^2+x^3\right) \sqrt[3]{-2+x^2+2 x^3}}{x^5 \left(-2+x^2+x^3\right)^2} \, dx","-\frac{7}{3} \log \left(\sqrt[3]{2 x^3+x^2-2}-x\right)+\frac{7}{6} \log \left(x^2+\sqrt[3]{2 x^3+x^2-2} x+\left(2 x^3+x^2-2\right)^{2/3}\right)-\frac{7 \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{2 x^3+x^2-2}+x}\right)}{\sqrt{3}}+\frac{\sqrt[3]{2 x^3+x^2-2} \left(-38 x^6-27 x^5+3 x^4+54 x^3-12 x^2+12\right)}{4 x^4 \left(x^3+x^2-2\right)}",1,"Integrate[((-6 + x^2)*(-2 + x^2)*(2 - x^2 + x^3)*(-2 + x^2 + 2*x^3)^(1/3))/(x^5*(-2 + x^2 + x^3)^2), x]","F",-1
2138,1,101,156,0.183988,"\int \frac{(-1+x) \sqrt[4]{-x^3+x^4}}{x \left(1+x^3\right)} \, dx","Integrate[((-1 + x)*(-x^3 + x^4)^(1/4))/(x*(1 + x^3)),x]","\frac{4 \sqrt[4]{(x-1) x^3} \left(2 \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{x-1}{2 x}\right)-\, _2F_1\left(\frac{1}{4},1;\frac{5}{4};-\frac{2 i (x-1)}{\left(-i+\sqrt{3}\right) x}\right)-\, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{2 i (x-1)}{\left(i+\sqrt{3}\right) x}\right)\right)}{3 x}","-\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4+1\&,\frac{-\text{$\#$1}^4 \log \left(\sqrt[4]{x^4-x^3}-\text{$\#$1} x\right)+\text{$\#$1}^4 \log (x)+2 \log \left(\sqrt[4]{x^4-x^3}-\text{$\#$1} x\right)-2 \log (x)}{2 \text{$\#$1}^7-\text{$\#$1}^3}\&\right]-\frac{4}{3} \sqrt[4]{2} \tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-x^3}}\right)+\frac{4}{3} \sqrt[4]{2} \tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-x^3}}\right)",1,"(4*((-1 + x)*x^3)^(1/4)*(2*Hypergeometric2F1[1/4, 1, 5/4, (-1 + x)/(2*x)] - Hypergeometric2F1[1/4, 1, 5/4, ((-2*I)*(-1 + x))/((-I + Sqrt[3])*x)] - Hypergeometric2F1[1/4, 1, 5/4, ((2*I)*(-1 + x))/((I + Sqrt[3])*x)]))/(3*x)","C",1
2139,1,101,156,0.0758038,"\int \frac{(-1+x) \sqrt[4]{-x^3+x^4}}{x \left(1+x^3\right)} \, dx","Integrate[((-1 + x)*(-x^3 + x^4)^(1/4))/(x*(1 + x^3)),x]","\frac{4 \sqrt[4]{(x-1) x^3} \left(2 \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{x-1}{2 x}\right)-\, _2F_1\left(\frac{1}{4},1;\frac{5}{4};-\frac{2 i (x-1)}{\left(-i+\sqrt{3}\right) x}\right)-\, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{2 i (x-1)}{\left(i+\sqrt{3}\right) x}\right)\right)}{3 x}","-\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4+1\&,\frac{-\text{$\#$1}^4 \log \left(\sqrt[4]{x^4-x^3}-\text{$\#$1} x\right)+\text{$\#$1}^4 \log (x)+2 \log \left(\sqrt[4]{x^4-x^3}-\text{$\#$1} x\right)-2 \log (x)}{2 \text{$\#$1}^7-\text{$\#$1}^3}\&\right]-\frac{4}{3} \sqrt[4]{2} \tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-x^3}}\right)+\frac{4}{3} \sqrt[4]{2} \tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-x^3}}\right)",1,"(4*((-1 + x)*x^3)^(1/4)*(2*Hypergeometric2F1[1/4, 1, 5/4, (-1 + x)/(2*x)] - Hypergeometric2F1[1/4, 1, 5/4, ((-2*I)*(-1 + x))/((-I + Sqrt[3])*x)] - Hypergeometric2F1[1/4, 1, 5/4, ((2*I)*(-1 + x))/((I + Sqrt[3])*x)]))/(3*x)","C",1
2140,0,0,156,1.4438115,"\int \frac{(1+x) \sqrt[4]{x^3+x^5}}{x \left(-1+x^3\right)} \, dx","Integrate[((1 + x)*(x^3 + x^5)^(1/4))/(x*(-1 + x^3)),x]","\int \frac{(1+x) \sqrt[4]{x^3+x^5}}{x \left(-1+x^3\right)} \, dx","\frac{2}{3} \sqrt[4]{2} \tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^5+x^3}}\right)-\frac{2}{3} \sqrt[4]{2} \tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^5+x^3}}\right)-\frac{1}{3} \sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{x^5+x^3}}{\sqrt{x^5+x^3}-x^2}\right)+\frac{1}{3} \sqrt{2} \tanh ^{-1}\left(\frac{\frac{x^2}{\sqrt{2}}+\frac{\sqrt{x^5+x^3}}{\sqrt{2}}}{x \sqrt[4]{x^5+x^3}}\right)",1,"Integrate[((1 + x)*(x^3 + x^5)^(1/4))/(x*(-1 + x^3)), x]","F",-1
2141,1,295,156,0.8092722,"\int \frac{x^3}{\sqrt[3]{-b x^2+a x^3} \left(-b^2+a^2 x^6\right)} \, dx","Integrate[x^3/((-(b*x^2) + a*x^3)^(1/3)*(-b^2 + a^2*x^6)),x]","\frac{x \left(-\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a x-\sqrt[3]{a} b^{2/3} x}{a x-b}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a x+\sqrt[3]{a} b^{2/3} x}{a x-b}\right)-\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(-1-i \sqrt{3}\right) \sqrt[3]{a} b^{2/3} x-2 a x}{2 (b-a x)}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(1-i \sqrt{3}\right) \sqrt[3]{a} b^{2/3} x-2 a x}{2 (b-a x)}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(1+i \sqrt{3}\right) \sqrt[3]{a} b^{2/3} x-2 a x}{2 (b-a x)}\right)-\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{i \left(i+\sqrt{3}\right) \sqrt[3]{a} b^{2/3} x-2 a x}{2 (b-a x)}\right)\right)}{2 a b \sqrt[3]{x^2 (a x-b)}}","\frac{\text{RootSum}\left[-\text{$\#$1}^9+3 \text{$\#$1}^6 a-3 \text{$\#$1}^3 a^2+a^3-a b^2\&,\frac{\log \left(\sqrt[3]{a x^3-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{6 a b}-\frac{\text{RootSum}\left[-\text{$\#$1}^9+3 \text{$\#$1}^6 a-3 \text{$\#$1}^3 a^2+a^3+a b^2\&,\frac{\log \left(\sqrt[3]{a x^3-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{6 a b}",1,"(x*(-Hypergeometric2F1[1/3, 1, 4/3, (a*x - a^(1/3)*b^(2/3)*x)/(-b + a*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a*x + a^(1/3)*b^(2/3)*x)/(-b + a*x)] - Hypergeometric2F1[1/3, 1, 4/3, (-2*a*x + (-1 - I*Sqrt[3])*a^(1/3)*b^(2/3)*x)/(2*(b - a*x))] + Hypergeometric2F1[1/3, 1, 4/3, (-2*a*x + (1 - I*Sqrt[3])*a^(1/3)*b^(2/3)*x)/(2*(b - a*x))] + Hypergeometric2F1[1/3, 1, 4/3, (-2*a*x + (1 + I*Sqrt[3])*a^(1/3)*b^(2/3)*x)/(2*(b - a*x))] - Hypergeometric2F1[1/3, 1, 4/3, (-2*a*x + I*(I + Sqrt[3])*a^(1/3)*b^(2/3)*x)/(2*(b - a*x))]))/(2*a*b*(x^2*(-b + a*x))^(1/3))","C",1
2142,1,302,156,0.6795139,"\int \frac{1+x^2}{\left(-1+x^2\right) \sqrt{1+\sqrt{1+\sqrt{1+x}}}} \, dx","Integrate[(1 + x^2)/((-1 + x^2)*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]),x]","8 \left(\frac{1}{8} \text{RootSum}\left[2 \text{$\#$1}^8-4 \text{$\#$1}^4+4 \text{$\#$1}^2-1\&,\frac{2 \text{$\#$1}^4 \log \left(\frac{1}{\sqrt{\sqrt{\sqrt{x+1}+1}+1}}-\text{$\#$1}\right)-3 \text{$\#$1}^2 \log \left(\frac{1}{\sqrt{\sqrt{\sqrt{x+1}+1}+1}}-\text{$\#$1}\right)+\log \left(\frac{1}{\sqrt{\sqrt{\sqrt{x+1}+1}+1}}-\text{$\#$1}\right)}{2 \text{$\#$1}^7-2 \text{$\#$1}^3+\text{$\#$1}}\&\right]+\frac{1}{7} \left(\sqrt{\sqrt{x+1}+1}+1\right)^{7/2}-\frac{3}{5} \left(\sqrt{\sqrt{x+1}+1}+1\right)^{5/2}+\frac{2}{3} \left(\sqrt{\sqrt{x+1}+1}+1\right)^{3/2}+\frac{1}{2 \sqrt{\sqrt{\sqrt{x+1}+1}+1}}-\frac{\log \left(\sqrt{2}-\frac{2}{\sqrt{\sqrt{\sqrt{x+1}+1}+1}}\right)}{4 \sqrt{2}}+\frac{\log \left(\frac{2}{\sqrt{\sqrt{\sqrt{x+1}+1}+1}}+\sqrt{2}\right)}{4 \sqrt{2}}\right)","\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x+1}+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}}\&\right]+\frac{-4 (-30 x-151)+\sqrt{x+1} \left(8-24 \sqrt{\sqrt{x+1}+1}\right)+64 \sqrt{\sqrt{x+1}+1}}{105 \sqrt{\sqrt{\sqrt{x+1}+1}+1}}+2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{x+1}+1}+1}}{\sqrt{2}}\right)",1,"8*(1/(2*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]) + (2*(1 + Sqrt[1 + Sqrt[1 + x]])^(3/2))/3 - (3*(1 + Sqrt[1 + Sqrt[1 + x]])^(5/2))/5 + (1 + Sqrt[1 + Sqrt[1 + x]])^(7/2)/7 - Log[Sqrt[2] - 2/Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]]/(4*Sqrt[2]) + Log[Sqrt[2] + 2/Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]]/(4*Sqrt[2]) + RootSum[-1 + 4*#1^2 - 4*#1^4 + 2*#1^8 & , (Log[1/Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]] - #1] - 3*Log[1/Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]] - #1]*#1^2 + 2*Log[1/Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]] - #1]*#1^4)/(#1 - 2*#1^3 + 2*#1^7) & ]/8)","A",1
2143,1,302,156,0.3558634,"\int \frac{1+x^2}{\left(-1+x^2\right) \sqrt{1+\sqrt{1+\sqrt{1+x}}}} \, dx","Integrate[(1 + x^2)/((-1 + x^2)*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]),x]","8 \left(\frac{1}{8} \text{RootSum}\left[2 \text{$\#$1}^8-4 \text{$\#$1}^4+4 \text{$\#$1}^2-1\&,\frac{2 \text{$\#$1}^4 \log \left(\frac{1}{\sqrt{\sqrt{\sqrt{x+1}+1}+1}}-\text{$\#$1}\right)-3 \text{$\#$1}^2 \log \left(\frac{1}{\sqrt{\sqrt{\sqrt{x+1}+1}+1}}-\text{$\#$1}\right)+\log \left(\frac{1}{\sqrt{\sqrt{\sqrt{x+1}+1}+1}}-\text{$\#$1}\right)}{2 \text{$\#$1}^7-2 \text{$\#$1}^3+\text{$\#$1}}\&\right]+\frac{1}{7} \left(\sqrt{\sqrt{x+1}+1}+1\right)^{7/2}-\frac{3}{5} \left(\sqrt{\sqrt{x+1}+1}+1\right)^{5/2}+\frac{2}{3} \left(\sqrt{\sqrt{x+1}+1}+1\right)^{3/2}+\frac{1}{2 \sqrt{\sqrt{\sqrt{x+1}+1}+1}}-\frac{\log \left(\sqrt{2}-\frac{2}{\sqrt{\sqrt{\sqrt{x+1}+1}+1}}\right)}{4 \sqrt{2}}+\frac{\log \left(\frac{2}{\sqrt{\sqrt{\sqrt{x+1}+1}+1}}+\sqrt{2}\right)}{4 \sqrt{2}}\right)","\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x+1}+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}}\&\right]+\frac{-4 (-30 x-151)+\sqrt{x+1} \left(8-24 \sqrt{\sqrt{x+1}+1}\right)+64 \sqrt{\sqrt{x+1}+1}}{105 \sqrt{\sqrt{\sqrt{x+1}+1}+1}}+2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{x+1}+1}+1}}{\sqrt{2}}\right)",1,"8*(1/(2*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]) + (2*(1 + Sqrt[1 + Sqrt[1 + x]])^(3/2))/3 - (3*(1 + Sqrt[1 + Sqrt[1 + x]])^(5/2))/5 + (1 + Sqrt[1 + Sqrt[1 + x]])^(7/2)/7 - Log[Sqrt[2] - 2/Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]]/(4*Sqrt[2]) + Log[Sqrt[2] + 2/Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]]/(4*Sqrt[2]) + RootSum[-1 + 4*#1^2 - 4*#1^4 + 2*#1^8 & , (Log[1/Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]] - #1] - 3*Log[1/Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]] - #1]*#1^2 + 2*Log[1/Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]] - #1]*#1^4)/(#1 - 2*#1^3 + 2*#1^7) & ]/8)","A",1
2144,0,0,157,0.4698432,"\int \frac{-1+x+x^3}{\left(1-x+x^3\right) \sqrt[3]{-x^2+x^3}} \, dx","Integrate[(-1 + x + x^3)/((1 - x + x^3)*(-x^2 + x^3)^(1/3)),x]","\int \frac{-1+x+x^3}{\left(1-x+x^3\right) \sqrt[3]{-x^2+x^3}} \, dx","2 \text{RootSum}\left[\text{$\#$1}^9-2 \text{$\#$1}^6+\text{$\#$1}^3-1\&,\frac{\text{$\#$1}^2 \log \left(\sqrt[3]{x^3-x^2}-\text{$\#$1} x\right)-\text{$\#$1}^2 \log (x)}{3 \text{$\#$1}^3-1}\&\right]-\log \left(\sqrt[3]{x^3-x^2}-x\right)+\frac{1}{2} \log \left(x^2+\sqrt[3]{x^3-x^2} x+\left(x^3-x^2\right)^{2/3}\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-x^2}+x}\right)",1,"Integrate[(-1 + x + x^3)/((1 - x + x^3)*(-x^2 + x^3)^(1/3)), x]","F",-1
2145,0,0,157,0.1172338,"\int \frac{-1+x+x^3}{\left(1-x+x^3\right) \sqrt[3]{-x^2+x^3}} \, dx","Integrate[(-1 + x + x^3)/((1 - x + x^3)*(-x^2 + x^3)^(1/3)),x]","\int \frac{-1+x+x^3}{\left(1-x+x^3\right) \sqrt[3]{-x^2+x^3}} \, dx","2 \text{RootSum}\left[\text{$\#$1}^9-2 \text{$\#$1}^6+\text{$\#$1}^3-1\&,\frac{\text{$\#$1}^2 \log \left(\sqrt[3]{x^3-x^2}-\text{$\#$1} x\right)-\text{$\#$1}^2 \log (x)}{3 \text{$\#$1}^3-1}\&\right]-\log \left(\sqrt[3]{x^3-x^2}-x\right)+\frac{1}{2} \log \left(x^2+\sqrt[3]{x^3-x^2} x+\left(x^3-x^2\right)^{2/3}\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-x^2}+x}\right)",1,"Integrate[(-1 + x + x^3)/((1 - x + x^3)*(-x^2 + x^3)^(1/3)), x]","F",-1
2146,1,71,157,0.0974397,"\int \frac{\left(1+2 x^3\right)^{4/3} \left(1+3 x^3\right)}{x^8 \left(1+4 x^3\right)} \, dx","Integrate[((1 + 2*x^3)^(4/3)*(1 + 3*x^3))/(x^8*(1 + 4*x^3)),x]","-\frac{2 x^2 \, _2F_1\left(\frac{2}{3},\frac{2}{3};\frac{5}{3};\frac{2 x^3}{4 x^3+1}\right)}{\left(4 x^3+1\right)^{2/3}}-\frac{\sqrt[3]{2 x^3+1} \left(58 x^6+9 x^3+4\right)}{28 x^7}","\frac{2}{3} \sqrt[3]{2} \log \left(2^{2/3} \sqrt[3]{2 x^3+1}+2 x\right)-\frac{2 \sqrt[3]{2} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{2 x^3+1}-x}\right)}{\sqrt{3}}-\frac{1}{3} \sqrt[3]{2} \log \left(2^{2/3} \sqrt[3]{2 x^3+1} x-\sqrt[3]{2} \left(2 x^3+1\right)^{2/3}-2 x^2\right)+\frac{\sqrt[3]{2 x^3+1} \left(-58 x^6-9 x^3-4\right)}{28 x^7}",1,"-1/28*((1 + 2*x^3)^(1/3)*(4 + 9*x^3 + 58*x^6))/x^7 - (2*x^2*Hypergeometric2F1[2/3, 2/3, 5/3, (2*x^3)/(1 + 4*x^3)])/(1 + 4*x^3)^(2/3)","C",0
2147,1,48,157,0.0253446,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt[3]{-x^2+x^4}} \, dx","Integrate[(-1 + x^2)/((1 + x^2)*(-x^2 + x^4)^(1/3)),x]","\frac{3 \left(x^2 \left(x^2-1\right)\right)^{2/3} F_1\left(\frac{1}{6};-\frac{2}{3},1;\frac{7}{6};x^2,-x^2\right)}{x \left(1-x^2\right)^{2/3}}","-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{2} x}{\sqrt[3]{x^4-x^2}}\right)}{\sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{2^{2/3} x \sqrt[3]{x^4-x^2}}{\sqrt[3]{2} \left(x^4-x^2\right)^{2/3}-2 x^2}\right)}{2 \sqrt[3]{2}}-\frac{\sqrt{3} \tanh ^{-1}\left(\frac{\frac{\sqrt[3]{2} x^2}{\sqrt{3}}+\frac{\left(x^4-x^2\right)^{2/3}}{\sqrt[3]{2} \sqrt{3}}}{x \sqrt[3]{x^4-x^2}}\right)}{2 \sqrt[3]{2}}",1,"(3*(x^2*(-1 + x^2))^(2/3)*AppellF1[1/6, -2/3, 1, 7/6, x^2, -x^2])/(x*(1 - x^2)^(2/3))","C",0
2148,1,539,157,2.4420408,"\int \frac{\sqrt[4]{-b x^2+a x^4} \left(-b+2 a x^4\right)}{b+a x^4} \, dx","Integrate[((-(b*x^2) + a*x^4)^(1/4)*(-b + 2*a*x^4))/(b + a*x^4),x]","\frac{\sqrt[4]{a x^4-b x^2} \left(\frac{12 a^{3/4} \sqrt{b} \sqrt[4]{\sqrt{-a}-\sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{-a} \sqrt[4]{\sqrt{-a}-\sqrt{b}}}\right)-12 a^{3/4} \sqrt{b} \sqrt[4]{\sqrt{-a}+\sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{-a} \sqrt[4]{\sqrt{-a}+\sqrt{b}}}\right)+12 a^{3/4} \sqrt{b} \sqrt[4]{\sqrt{-a}-\sqrt{b}} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{-a} \sqrt[4]{\sqrt{-a}-\sqrt{b}}}\right)-12 a^{3/4} \sqrt{b} \sqrt[4]{\sqrt{-a}+\sqrt{b}} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{-a} \sqrt[4]{\sqrt{-a}+\sqrt{b}}}\right)+\sqrt{2} (-a)^{3/8} b \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{\frac{b}{x^2}-a}+\sqrt{\frac{b}{x^2}-a}+\sqrt{a}\right)-\sqrt{2} (-a)^{3/8} b \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{\frac{b}{x^2}-a}+\sqrt{\frac{b}{x^2}-a}+\sqrt{a}\right)+2 \sqrt{2} (-a)^{3/8} b \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[4]{a}}\right)-2 \sqrt{2} (-a)^{3/8} b \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[4]{a}}+1\right)}{(-a)^{3/8} a^{3/4} \sqrt[4]{\frac{b}{x^2}-a}}+8 x^2\right)}{8 x}","-\frac{3}{4} b \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^4-a}\&\right]+\frac{b \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)}{2 a^{3/4}}-\frac{b \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)}{2 a^{3/4}}+x \sqrt[4]{a x^4-b x^2}",1,"((-(b*x^2) + a*x^4)^(1/4)*(8*x^2 + (2*Sqrt[2]*(-a)^(3/8)*b*ArcTan[1 - (Sqrt[2]*(-a + b/x^2)^(1/4))/a^(1/4)] - 2*Sqrt[2]*(-a)^(3/8)*b*ArcTan[1 + (Sqrt[2]*(-a + b/x^2)^(1/4))/a^(1/4)] + 12*a^(3/4)*(Sqrt[-a] - Sqrt[b])^(1/4)*Sqrt[b]*ArcTan[(-a + b/x^2)^(1/4)/((-a)^(1/8)*(Sqrt[-a] - Sqrt[b])^(1/4))] - 12*a^(3/4)*(Sqrt[-a] + Sqrt[b])^(1/4)*Sqrt[b]*ArcTan[(-a + b/x^2)^(1/4)/((-a)^(1/8)*(Sqrt[-a] + Sqrt[b])^(1/4))] + 12*a^(3/4)*(Sqrt[-a] - Sqrt[b])^(1/4)*Sqrt[b]*ArcTanh[(-a + b/x^2)^(1/4)/((-a)^(1/8)*(Sqrt[-a] - Sqrt[b])^(1/4))] - 12*a^(3/4)*(Sqrt[-a] + Sqrt[b])^(1/4)*Sqrt[b]*ArcTanh[(-a + b/x^2)^(1/4)/((-a)^(1/8)*(Sqrt[-a] + Sqrt[b])^(1/4))] + Sqrt[2]*(-a)^(3/8)*b*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*(-a + b/x^2)^(1/4) + Sqrt[-a + b/x^2]] - Sqrt[2]*(-a)^(3/8)*b*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*(-a + b/x^2)^(1/4) + Sqrt[-a + b/x^2]])/((-a)^(3/8)*a^(3/4)*(-a + b/x^2)^(1/4))))/(8*x)","B",1
2149,1,539,157,0.9867825,"\int \frac{\sqrt[4]{-b x^2+a x^4} \left(-b+2 a x^4\right)}{b+a x^4} \, dx","Integrate[((-(b*x^2) + a*x^4)^(1/4)*(-b + 2*a*x^4))/(b + a*x^4),x]","\frac{\sqrt[4]{a x^4-b x^2} \left(\frac{12 a^{3/4} \sqrt{b} \sqrt[4]{\sqrt{-a}-\sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{-a} \sqrt[4]{\sqrt{-a}-\sqrt{b}}}\right)-12 a^{3/4} \sqrt{b} \sqrt[4]{\sqrt{-a}+\sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{-a} \sqrt[4]{\sqrt{-a}+\sqrt{b}}}\right)+12 a^{3/4} \sqrt{b} \sqrt[4]{\sqrt{-a}-\sqrt{b}} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{-a} \sqrt[4]{\sqrt{-a}-\sqrt{b}}}\right)-12 a^{3/4} \sqrt{b} \sqrt[4]{\sqrt{-a}+\sqrt{b}} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{-a} \sqrt[4]{\sqrt{-a}+\sqrt{b}}}\right)+\sqrt{2} (-a)^{3/8} b \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{\frac{b}{x^2}-a}+\sqrt{\frac{b}{x^2}-a}+\sqrt{a}\right)-\sqrt{2} (-a)^{3/8} b \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{\frac{b}{x^2}-a}+\sqrt{\frac{b}{x^2}-a}+\sqrt{a}\right)+2 \sqrt{2} (-a)^{3/8} b \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[4]{a}}\right)-2 \sqrt{2} (-a)^{3/8} b \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[4]{a}}+1\right)}{(-a)^{3/8} a^{3/4} \sqrt[4]{\frac{b}{x^2}-a}}+8 x^2\right)}{8 x}","-\frac{3}{4} b \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^4-a}\&\right]+\frac{b \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)}{2 a^{3/4}}-\frac{b \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)}{2 a^{3/4}}+x \sqrt[4]{a x^4-b x^2}",1,"((-(b*x^2) + a*x^4)^(1/4)*(8*x^2 + (2*Sqrt[2]*(-a)^(3/8)*b*ArcTan[1 - (Sqrt[2]*(-a + b/x^2)^(1/4))/a^(1/4)] - 2*Sqrt[2]*(-a)^(3/8)*b*ArcTan[1 + (Sqrt[2]*(-a + b/x^2)^(1/4))/a^(1/4)] + 12*a^(3/4)*(Sqrt[-a] - Sqrt[b])^(1/4)*Sqrt[b]*ArcTan[(-a + b/x^2)^(1/4)/((-a)^(1/8)*(Sqrt[-a] - Sqrt[b])^(1/4))] - 12*a^(3/4)*(Sqrt[-a] + Sqrt[b])^(1/4)*Sqrt[b]*ArcTan[(-a + b/x^2)^(1/4)/((-a)^(1/8)*(Sqrt[-a] + Sqrt[b])^(1/4))] + 12*a^(3/4)*(Sqrt[-a] - Sqrt[b])^(1/4)*Sqrt[b]*ArcTanh[(-a + b/x^2)^(1/4)/((-a)^(1/8)*(Sqrt[-a] - Sqrt[b])^(1/4))] - 12*a^(3/4)*(Sqrt[-a] + Sqrt[b])^(1/4)*Sqrt[b]*ArcTanh[(-a + b/x^2)^(1/4)/((-a)^(1/8)*(Sqrt[-a] + Sqrt[b])^(1/4))] + Sqrt[2]*(-a)^(3/8)*b*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*(-a + b/x^2)^(1/4) + Sqrt[-a + b/x^2]] - Sqrt[2]*(-a)^(3/8)*b*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*(-a + b/x^2)^(1/4) + Sqrt[-a + b/x^2]])/((-a)^(3/8)*a^(3/4)*(-a + b/x^2)^(1/4))))/(8*x)","B",1
2150,0,0,157,0.5210919,"\int \frac{x^3 (-4 a+3 x)}{\left(x^2 (-a+x)\right)^{2/3} \left(a-x+d x^4\right)} \, dx","Integrate[(x^3*(-4*a + 3*x))/((x^2*(-a + x))^(2/3)*(a - x + d*x^4)),x]","\int \frac{x^3 (-4 a+3 x)}{\left(x^2 (-a+x)\right)^{2/3} \left(a-x+d x^4\right)} \, dx","-\frac{\log \left(a^2 d^{2/3} x^4+a^2 \sqrt[3]{d} x^2 \sqrt[3]{x^3-a x^2}+a^2 \left(x^3-a x^2\right)^{2/3}\right)}{2 d^{2/3}}+\frac{\log \left(a \sqrt[3]{x^3-a x^2}-a \sqrt[3]{d} x^2\right)}{d^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} x^2}{2 \sqrt[3]{x^3-a x^2}+\sqrt[3]{d} x^2}\right)}{d^{2/3}}",1,"Integrate[(x^3*(-4*a + 3*x))/((x^2*(-a + x))^(2/3)*(a - x + d*x^4)), x]","F",-1
2151,1,114,157,5.1816636,"\int \frac{b+a x^6}{x^6 \left(b+a x^3\right) \sqrt[4]{-b x+a x^4}} \, dx","Integrate[(b + a*x^6)/(x^6*(b + a*x^3)*(-(b*x) + a*x^4)^(1/4)),x]","\frac{28 a x^6 (a+b) \sqrt[4]{1-\frac{a x^3}{b}} \, _2F_1\left(\frac{1}{4},\frac{1}{4};\frac{5}{4};\frac{2 a x^3}{a x^3+b}\right)-4 \left(b-a x^3\right)^2 \sqrt[4]{\frac{a x^3}{b}+1}}{21 b^2 x^5 \sqrt[4]{\frac{a x^3}{b}+1} \sqrt[4]{a x^4-b x}}","\frac{2^{3/4} \left(a^{3/4} b+a^{7/4}\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} \left(a x^4-b x\right)^{3/4}}{a x^3-b}\right)}{3 b^2}+\frac{2^{3/4} \left(a^{3/4} b+a^{7/4}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} \left(a x^4-b x\right)^{3/4}}{a x^3-b}\right)}{3 b^2}+\frac{4 \left(a x^4-b x\right)^{3/4} \left(b-a x^3\right)}{21 b^2 x^6}",1,"(-4*(b - a*x^3)^2*(1 + (a*x^3)/b)^(1/4) + 28*a*(a + b)*x^6*(1 - (a*x^3)/b)^(1/4)*Hypergeometric2F1[1/4, 1/4, 5/4, (2*a*x^3)/(b + a*x^3)])/(21*b^2*x^5*(1 + (a*x^3)/b)^(1/4)*(-(b*x) + a*x^4)^(1/4))","C",0
2152,1,360,157,1.1960353,"\int \frac{-1+x^2}{\sqrt{1+x} \left(1+x^2\right) \sqrt{x+\sqrt{1+x}}} \, dx","Integrate[(-1 + x^2)/(Sqrt[1 + x]*(1 + x^2)*Sqrt[x + Sqrt[1 + x]]),x]","-\frac{i \tan ^{-1}\left(\frac{-\left(\left(1-2 \sqrt{1-i}\right) \sqrt{x+1}\right)+\sqrt{1-i}+2}{2 \sqrt{i+\sqrt{1-i}} \sqrt{x+\sqrt{x+1}}}\right)}{\sqrt{(1+i)+(1-i)^{3/2}}}+\frac{i \tan ^{-1}\left(\frac{-\left(\left(1-2 \sqrt{1+i}\right) \sqrt{x+1}\right)+\sqrt{1+i}+2}{2 \sqrt{\sqrt{1+i}-i} \sqrt{x+\sqrt{x+1}}}\right)}{\sqrt{(1-i)+(1+i)^{3/2}}}+2 \tanh ^{-1}\left(\frac{2 \sqrt{x+1}+1}{2 \sqrt{x+\sqrt{x+1}}}\right)-\frac{i \tanh ^{-1}\left(\frac{-\left(\left(1+2 \sqrt{1-i}\right) \sqrt{x+1}\right)-\sqrt{1-i}+2}{2 \sqrt{\sqrt{1-i}-i} \sqrt{x+\sqrt{x+1}}}\right)}{\sqrt{(-1-i)+(1-i)^{3/2}}}+\frac{i \tanh ^{-1}\left(\frac{-\left(\left(1+2 \sqrt{1+i}\right) \sqrt{x+1}\right)-\sqrt{1+i}+2}{2 \sqrt{i+\sqrt{1+i}} \sqrt{x+\sqrt{x+1}}}\right)}{\sqrt{(-1+i)+(1+i)^{3/2}}}","128 \text{RootSum}\left[\text{$\#$1}^8+8 \text{$\#$1}^7+12 \text{$\#$1}^6+24 \text{$\#$1}^5+470 \text{$\#$1}^4+120 \text{$\#$1}^3+300 \text{$\#$1}^2+1000 \text{$\#$1}+625\&,\frac{\text{$\#$1}^3 \log \left(\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)}{\text{$\#$1}^7+7 \text{$\#$1}^6+9 \text{$\#$1}^5+15 \text{$\#$1}^4+235 \text{$\#$1}^3+45 \text{$\#$1}^2+75 \text{$\#$1}+125}\&\right]-2 \log \left(2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)",1,"((-I)*ArcTan[(2 + Sqrt[1 - I] - (1 - 2*Sqrt[1 - I])*Sqrt[1 + x])/(2*Sqrt[I + Sqrt[1 - I]]*Sqrt[x + Sqrt[1 + x]])])/Sqrt[(1 + I) + (1 - I)^(3/2)] + (I*ArcTan[(2 + Sqrt[1 + I] - (1 - 2*Sqrt[1 + I])*Sqrt[1 + x])/(2*Sqrt[-I + Sqrt[1 + I]]*Sqrt[x + Sqrt[1 + x]])])/Sqrt[(1 - I) + (1 + I)^(3/2)] + 2*ArcTanh[(1 + 2*Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])] - (I*ArcTanh[(2 - Sqrt[1 - I] - (1 + 2*Sqrt[1 - I])*Sqrt[1 + x])/(2*Sqrt[-I + Sqrt[1 - I]]*Sqrt[x + Sqrt[1 + x]])])/Sqrt[(-1 - I) + (1 - I)^(3/2)] + (I*ArcTanh[(2 - Sqrt[1 + I] - (1 + 2*Sqrt[1 + I])*Sqrt[1 + x])/(2*Sqrt[I + Sqrt[1 + I]]*Sqrt[x + Sqrt[1 + x]])])/Sqrt[(-1 + I) + (1 + I)^(3/2)]","C",1
2153,1,360,157,0.6867718,"\int \frac{-1+x^2}{\sqrt{1+x} \left(1+x^2\right) \sqrt{x+\sqrt{1+x}}} \, dx","Integrate[(-1 + x^2)/(Sqrt[1 + x]*(1 + x^2)*Sqrt[x + Sqrt[1 + x]]),x]","-\frac{i \tan ^{-1}\left(\frac{-\left(\left(1-2 \sqrt{1-i}\right) \sqrt{x+1}\right)+\sqrt{1-i}+2}{2 \sqrt{i+\sqrt{1-i}} \sqrt{x+\sqrt{x+1}}}\right)}{\sqrt{(1+i)+(1-i)^{3/2}}}+\frac{i \tan ^{-1}\left(\frac{-\left(\left(1-2 \sqrt{1+i}\right) \sqrt{x+1}\right)+\sqrt{1+i}+2}{2 \sqrt{\sqrt{1+i}-i} \sqrt{x+\sqrt{x+1}}}\right)}{\sqrt{(1-i)+(1+i)^{3/2}}}+2 \tanh ^{-1}\left(\frac{2 \sqrt{x+1}+1}{2 \sqrt{x+\sqrt{x+1}}}\right)-\frac{i \tanh ^{-1}\left(\frac{-\left(\left(1+2 \sqrt{1-i}\right) \sqrt{x+1}\right)-\sqrt{1-i}+2}{2 \sqrt{\sqrt{1-i}-i} \sqrt{x+\sqrt{x+1}}}\right)}{\sqrt{(-1-i)+(1-i)^{3/2}}}+\frac{i \tanh ^{-1}\left(\frac{-\left(\left(1+2 \sqrt{1+i}\right) \sqrt{x+1}\right)-\sqrt{1+i}+2}{2 \sqrt{i+\sqrt{1+i}} \sqrt{x+\sqrt{x+1}}}\right)}{\sqrt{(-1+i)+(1+i)^{3/2}}}","128 \text{RootSum}\left[\text{$\#$1}^8+8 \text{$\#$1}^7+12 \text{$\#$1}^6+24 \text{$\#$1}^5+470 \text{$\#$1}^4+120 \text{$\#$1}^3+300 \text{$\#$1}^2+1000 \text{$\#$1}+625\&,\frac{\text{$\#$1}^3 \log \left(\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)}{\text{$\#$1}^7+7 \text{$\#$1}^6+9 \text{$\#$1}^5+15 \text{$\#$1}^4+235 \text{$\#$1}^3+45 \text{$\#$1}^2+75 \text{$\#$1}+125}\&\right]-2 \log \left(2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)",1,"((-I)*ArcTan[(2 + Sqrt[1 - I] - (1 - 2*Sqrt[1 - I])*Sqrt[1 + x])/(2*Sqrt[I + Sqrt[1 - I]]*Sqrt[x + Sqrt[1 + x]])])/Sqrt[(1 + I) + (1 - I)^(3/2)] + (I*ArcTan[(2 + Sqrt[1 + I] - (1 - 2*Sqrt[1 + I])*Sqrt[1 + x])/(2*Sqrt[-I + Sqrt[1 + I]]*Sqrt[x + Sqrt[1 + x]])])/Sqrt[(1 - I) + (1 + I)^(3/2)] + 2*ArcTanh[(1 + 2*Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])] - (I*ArcTanh[(2 - Sqrt[1 - I] - (1 + 2*Sqrt[1 - I])*Sqrt[1 + x])/(2*Sqrt[-I + Sqrt[1 - I]]*Sqrt[x + Sqrt[1 + x]])])/Sqrt[(-1 - I) + (1 - I)^(3/2)] + (I*ArcTanh[(2 - Sqrt[1 + I] - (1 + 2*Sqrt[1 + I])*Sqrt[1 + x])/(2*Sqrt[I + Sqrt[1 + I]]*Sqrt[x + Sqrt[1 + x]])])/Sqrt[(-1 + I) + (1 + I)^(3/2)]","C",1
2154,0,0,157,0.1001912,"\int x^2 \sqrt{a x^2+\sqrt{b+a^2 x^4}} \, dx","Integrate[x^2*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]],x]","\int x^2 \sqrt{a x^2+\sqrt{b+a^2 x^4}} \, dx","\frac{b \log \left(i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)}{8 \sqrt{2} a^{3/2}}-\frac{i \left(2 i a x^4 \sqrt{a^2 x^4+b}+i x^2 \left(2 a^2 x^4-b\right)\right)}{8 a x \sqrt{\sqrt{a^2 x^4+b}+a x^2}}",1,"Integrate[x^2*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]], x]","F",-1
2155,1,74,157,0.2581132,"\int \frac{1}{\sqrt{-b+a^2 x^2} \sqrt[3]{a x+\sqrt{-b+a^2 x^2}} \sqrt[4]{c+\sqrt[3]{a x+\sqrt{-b+a^2 x^2}}}} \, dx","Integrate[1/(Sqrt[-b + a^2*x^2]*(a*x + Sqrt[-b + a^2*x^2])^(1/3)*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^(1/4)),x]","\frac{4 \left(\sqrt[3]{\sqrt{a^2 x^2-b}+a x}+c\right)^{3/4} \, _2F_1\left(\frac{3}{4},2;\frac{7}{4};\frac{c+\sqrt[3]{a x+\sqrt{a^2 x^2-b}}}{c}\right)}{a c^2}","-\frac{3 \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt[3]{\sqrt{a^2 x^2-b}+a x}+c}}{\sqrt[4]{c}}\right)}{2 a c^{5/4}}+\frac{3 \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt[3]{\sqrt{a^2 x^2-b}+a x}+c}}{\sqrt[4]{c}}\right)}{2 a c^{5/4}}-\frac{3 \left(\sqrt[3]{\sqrt{a^2 x^2-b}+a x}+c\right)^{3/4}}{a c \sqrt[3]{\sqrt{a^2 x^2-b}+a x}}",1,"(4*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^(3/4)*Hypergeometric2F1[3/4, 2, 7/4, (c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))/c])/(a*c^2)","C",1
2156,1,2491,158,12.4822352,"\int \frac{(2 a-3 b+x) \left(-a^3+3 a^2 x-3 a x^2+x^3\right)}{(-b+x) \sqrt[4]{(-a+x) (-b+x)^2} \left(-a^3-b^2 d+\left(3 a^2+2 b d\right) x-(3 a+d) x^2+x^3\right)} \, dx","Integrate[((2*a - 3*b + x)*(-a^3 + 3*a^2*x - 3*a*x^2 + x^3))/((-b + x)*((-a + x)*(-b + x)^2)^(1/4)*(-a^3 - b^2*d + (3*a^2 + 2*b*d)*x - (3*a + d)*x^2 + x^3)),x]","\text{Result too large to show}","-2 \sqrt[4]{d} \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3}}{a-x}\right)+2 \sqrt[4]{d} \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3}}{a-x}\right)+\frac{4 \left(-a b^2+2 a b x-a x^2+b^2 x-2 b x^2+x^3\right)^{3/4}}{(b-x)^2}",1,"(4*(-a + x))/((b - x)^2*(-a + x))^(1/4) + ((2*I)*(a - b)*d*(a - x)^(7/4)*((b - x)/(a - x))^(3/2)*((-(EllipticPi[-(1/(Sqrt[a - b]*Sqrt[Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 2]])), I*ArcSinh[Sqrt[-Sqrt[a - b]]/(a - x)^(1/4)], -1]*Sqrt[Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 1]]*(1 - 4*(a - b)*Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 2] + 3*(a - b)^2*Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 2]^2)*(Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 1] - Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 3])) + EllipticPi[1/(Sqrt[a - b]*Sqrt[Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 2]]), I*ArcSinh[Sqrt[-Sqrt[a - b]]/(a - x)^(1/4)], -1]*Sqrt[Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 1]]*(1 - 4*(a - b)*Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 2] + 3*(a - b)^2*Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 2]^2)*(Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 1] - Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 3]) + (EllipticPi[-(1/(Sqrt[a - b]*Sqrt[Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 1]])), I*ArcSinh[Sqrt[-Sqrt[a - b]]/(a - x)^(1/4)], -1] - EllipticPi[1/(Sqrt[a - b]*Sqrt[Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 1]]), I*ArcSinh[Sqrt[-Sqrt[a - b]]/(a - x)^(1/4)], -1])*(1 - 4*(a - b)*Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 1] + 3*(a - b)^2*Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 1]^2)*Sqrt[Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 2]]*(Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 2] - Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 3]))*Sqrt[Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 3]] + EllipticPi[-(1/(Sqrt[a - b]*Sqrt[Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 3]])), I*ArcSinh[Sqrt[-Sqrt[a - b]]/(a - x)^(1/4)], -1]*Sqrt[Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 1]]*(Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 1] - Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 2])*Sqrt[Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 2]]*(1 - 4*(a - b)*Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 3] + 3*(a - b)^2*Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 3]^2) - EllipticPi[1/(Sqrt[a - b]*Sqrt[Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 3]]), I*ArcSinh[Sqrt[-Sqrt[a - b]]/(a - x)^(1/4)], -1]*Sqrt[Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 1]]*(Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 1] - Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 2])*Sqrt[Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 2]]*(1 - 4*(a - b)*Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 3] + 3*(a - b)^2*Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 3]^2)))/(Sqrt[-Sqrt[a - b]]*((b - x)^2*(-a + x))^(1/4)*(-b + x)*Sqrt[Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 1]]*Sqrt[Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 2]]*Sqrt[Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 3]]*(-3*a + 3*b - 2*d + 2*(a - b)^3*d*Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 1]*Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 2]^2 + 2*(a - b)^3*d*Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 1]^2*Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 3] + 2*(a - b)^3*d*Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 2]*Root[1 + d*#1 + (-2*a*d + 2*b*d)*#1^2 + (a^2*d - 2*a*b*d + b^2*d)*#1^3 & , 3]^2))","C",0
2157,1,158,158,0.234765,"\int \frac{\left(2-x+2 x^2\right) \sqrt[4]{-x^3+x^4}}{-2-2 x+x^2} \, dx","Integrate[((2 - x + 2*x^2)*(-x^3 + x^4)^(1/4))/(-2 - 2*x + x^2),x]","\frac{4 \sqrt[4]{(x-1) x^3} \left(15 \sqrt[4]{x} \, _2F_1\left(-\frac{3}{4},\frac{1}{4};\frac{5}{4};1-x\right)+2 (x-1) \sqrt[4]{x} \, _2F_1\left(-\frac{3}{4},\frac{5}{4};\frac{9}{4};1-x\right)+15 \left(3 \sqrt[4]{x} \, _2F_1\left(\frac{1}{4},\frac{1}{4};\frac{5}{4};1-x\right)+\left(\sqrt{3}-2\right) \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};-\frac{\left(-3+\sqrt{3}\right) (x-1)}{3 x}\right)-\left(2+\sqrt{3}\right) \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{\left(3+\sqrt{3}\right) (x-1)}{3 x}\right)\right)\right)}{5 x}","-9 \text{RootSum}\left[2 \text{$\#$1}^8-6 \text{$\#$1}^4+3\&,\frac{-\text{$\#$1}^4 \log \left(\sqrt[4]{x^4-x^3}-\text{$\#$1} x\right)+\text{$\#$1}^4 \log (x)+2 \log \left(\sqrt[4]{x^4-x^3}-\text{$\#$1} x\right)-2 \log (x)}{2 \text{$\#$1}^7-3 \text{$\#$1}^3}\&\right]+\frac{1}{4} \sqrt[4]{x^4-x^3} (4 x+11)-\frac{177}{8} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^3}}\right)+\frac{177}{8} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^3}}\right)",1,"(4*((-1 + x)*x^3)^(1/4)*(15*x^(1/4)*Hypergeometric2F1[-3/4, 1/4, 5/4, 1 - x] + 2*(-1 + x)*x^(1/4)*Hypergeometric2F1[-3/4, 5/4, 9/4, 1 - x] + 15*(3*x^(1/4)*Hypergeometric2F1[1/4, 1/4, 5/4, 1 - x] + (-2 + Sqrt[3])*Hypergeometric2F1[1/4, 1, 5/4, -1/3*((-3 + Sqrt[3])*(-1 + x))/x] - (2 + Sqrt[3])*Hypergeometric2F1[1/4, 1, 5/4, ((3 + Sqrt[3])*(-1 + x))/(3*x)])))/(5*x)","A",1
2158,1,158,158,0.1062734,"\int \frac{\left(2-x+2 x^2\right) \sqrt[4]{-x^3+x^4}}{-2-2 x+x^2} \, dx","Integrate[((2 - x + 2*x^2)*(-x^3 + x^4)^(1/4))/(-2 - 2*x + x^2),x]","\frac{4 \sqrt[4]{(x-1) x^3} \left(15 \sqrt[4]{x} \, _2F_1\left(-\frac{3}{4},\frac{1}{4};\frac{5}{4};1-x\right)+2 (x-1) \sqrt[4]{x} \, _2F_1\left(-\frac{3}{4},\frac{5}{4};\frac{9}{4};1-x\right)+15 \left(3 \sqrt[4]{x} \, _2F_1\left(\frac{1}{4},\frac{1}{4};\frac{5}{4};1-x\right)+\left(\sqrt{3}-2\right) \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};-\frac{\left(-3+\sqrt{3}\right) (x-1)}{3 x}\right)-\left(2+\sqrt{3}\right) \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{\left(3+\sqrt{3}\right) (x-1)}{3 x}\right)\right)\right)}{5 x}","-9 \text{RootSum}\left[2 \text{$\#$1}^8-6 \text{$\#$1}^4+3\&,\frac{-\text{$\#$1}^4 \log \left(\sqrt[4]{x^4-x^3}-\text{$\#$1} x\right)+\text{$\#$1}^4 \log (x)+2 \log \left(\sqrt[4]{x^4-x^3}-\text{$\#$1} x\right)-2 \log (x)}{2 \text{$\#$1}^7-3 \text{$\#$1}^3}\&\right]+\frac{1}{4} \sqrt[4]{x^4-x^3} (4 x+11)-\frac{177}{8} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^3}}\right)+\frac{177}{8} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^3}}\right)",1,"(4*((-1 + x)*x^3)^(1/4)*(15*x^(1/4)*Hypergeometric2F1[-3/4, 1/4, 5/4, 1 - x] + 2*(-1 + x)*x^(1/4)*Hypergeometric2F1[-3/4, 5/4, 9/4, 1 - x] + 15*(3*x^(1/4)*Hypergeometric2F1[1/4, 1/4, 5/4, 1 - x] + (-2 + Sqrt[3])*Hypergeometric2F1[1/4, 1, 5/4, -1/3*((-3 + Sqrt[3])*(-1 + x))/x] - (2 + Sqrt[3])*Hypergeometric2F1[1/4, 1, 5/4, ((3 + Sqrt[3])*(-1 + x))/(3*x)])))/(5*x)","A",1
2159,1,251,158,0.9433262,"\int \frac{\sqrt{1-3 x^2-2 x^4} \left(1+2 x^4\right)}{\left(-1+x^2+2 x^4\right) \left(-1+2 x^2+2 x^4\right)} \, dx","Integrate[(Sqrt[1 - 3*x^2 - 2*x^4]*(1 + 2*x^4))/((-1 + x^2 + 2*x^4)*(-1 + 2*x^2 + 2*x^4)),x]","i \sqrt{\frac{2}{\sqrt{17}-3}} \left(F\left(i \sinh ^{-1}\left(\frac{2 x}{\sqrt{3+\sqrt{17}}}\right)|-\frac{13}{4}-\frac{3 \sqrt{17}}{4}\right)-2 \Pi \left(-\frac{3}{2}-\frac{\sqrt{17}}{2};i \sinh ^{-1}\left(\frac{2 x}{\sqrt{3+\sqrt{17}}}\right)|-\frac{13}{4}-\frac{3 \sqrt{17}}{4}\right)-2 \Pi \left(\frac{1}{4} \left(3+\sqrt{17}\right);i \sinh ^{-1}\left(\frac{2 x}{\sqrt{3+\sqrt{17}}}\right)|\frac{1}{4} \left(-13-3 \sqrt{17}\right)\right)+\Pi \left(\frac{3+\sqrt{17}}{2-2 \sqrt{3}};i \sinh ^{-1}\left(\frac{2 x}{\sqrt{3+\sqrt{17}}}\right)|-\frac{13}{4}-\frac{3 \sqrt{17}}{4}\right)+\Pi \left(\frac{3+\sqrt{17}}{2+2 \sqrt{3}};i \sinh ^{-1}\left(\frac{2 x}{\sqrt{3+\sqrt{17}}}\right)|-\frac{13}{4}-\frac{3 \sqrt{17}}{4}\right)\right)","\tan ^{-1}\left(\frac{x \sqrt{-2 x^4-3 x^2+1}}{2 x^4+3 x^2-1}\right)-i \sqrt{2} \tanh ^{-1}\left(\frac{2 \sqrt{2} x^3-2 i \sqrt{-2 x^4-3 x^2+1} x-2 i x}{2 \sqrt{2} x^4+3 \sqrt{2} x^2-2 i \sqrt{-2 x^4-3 x^2+1} x^2-\sqrt{2} \sqrt{-2 x^4-3 x^2+1}-\sqrt{2}}\right)",1,"I*Sqrt[2/(-3 + Sqrt[17])]*(EllipticF[I*ArcSinh[(2*x)/Sqrt[3 + Sqrt[17]]], -13/4 - (3*Sqrt[17])/4] - 2*EllipticPi[-3/2 - Sqrt[17]/2, I*ArcSinh[(2*x)/Sqrt[3 + Sqrt[17]]], -13/4 - (3*Sqrt[17])/4] - 2*EllipticPi[(3 + Sqrt[17])/4, I*ArcSinh[(2*x)/Sqrt[3 + Sqrt[17]]], (-13 - 3*Sqrt[17])/4] + EllipticPi[(3 + Sqrt[17])/(2 - 2*Sqrt[3]), I*ArcSinh[(2*x)/Sqrt[3 + Sqrt[17]]], -13/4 - (3*Sqrt[17])/4] + EllipticPi[(3 + Sqrt[17])/(2 + 2*Sqrt[3]), I*ArcSinh[(2*x)/Sqrt[3 + Sqrt[17]]], -13/4 - (3*Sqrt[17])/4])","C",0
2160,1,394,158,3.044603,"\int \frac{\sqrt[4]{b x^2+a x^4} \left(-b+2 a x^4\right)}{-2 b+a x^4} \, dx","Integrate[((b*x^2 + a*x^4)^(1/4)*(-b + 2*a*x^4))/(-2*b + a*x^4),x]","\frac{\sqrt{b} x^3 \left(a+\frac{b}{x^2}\right)^{3/4} \left(3 a^{3/8} \sqrt[4]{4 \sqrt{a}-2 \sqrt{2} \sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[8]{a} \sqrt[4]{\sqrt{a}-\frac{\sqrt{b}}{\sqrt{2}}}}\right)-3 a^{3/8} \sqrt[4]{4 \sqrt{a}+2 \sqrt{2} \sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[8]{a} \sqrt[4]{\sqrt{a}+\frac{\sqrt{b}}{\sqrt{2}}}}\right)+3 a^{3/8} \sqrt[4]{4 \sqrt{a}-2 \sqrt{2} \sqrt{b}} \tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[8]{a} \sqrt[4]{\sqrt{a}-\frac{\sqrt{b}}{\sqrt{2}}}}\right)-3 a^{3/8} \sqrt[4]{4 \sqrt{a}+2 \sqrt{2} \sqrt{b}} \tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[8]{a} \sqrt[4]{\sqrt{a}+\frac{\sqrt{b}}{\sqrt{2}}}}\right)+2 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a}}\right)+2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a}}\right)\right)}{4 a^{3/4} \left(x^2 \left(a x^2+b\right)\right)^{3/4}}+x \sqrt[4]{x^2 \left(a x^2+b\right)}","\frac{3}{8} b \text{RootSum}\left[2 \text{$\#$1}^8-4 \text{$\#$1}^4 a+2 a^2-a b\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^4-a}\&\right]-\frac{b \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{2 a^{3/4}}+\frac{b \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{2 a^{3/4}}+x \sqrt[4]{a x^4+b x^2}",1,"x*(x^2*(b + a*x^2))^(1/4) + (Sqrt[b]*(a + b/x^2)^(3/4)*x^3*(2*Sqrt[b]*ArcTan[(a + b/x^2)^(1/4)/a^(1/4)] + 3*a^(3/8)*(4*Sqrt[a] - 2*Sqrt[2]*Sqrt[b])^(1/4)*ArcTan[(a + b/x^2)^(1/4)/(a^(1/8)*(Sqrt[a] - Sqrt[b]/Sqrt[2])^(1/4))] - 3*a^(3/8)*(4*Sqrt[a] + 2*Sqrt[2]*Sqrt[b])^(1/4)*ArcTan[(a + b/x^2)^(1/4)/(a^(1/8)*(Sqrt[a] + Sqrt[b]/Sqrt[2])^(1/4))] + 2*Sqrt[b]*ArcTanh[(a + b/x^2)^(1/4)/a^(1/4)] + 3*a^(3/8)*(4*Sqrt[a] - 2*Sqrt[2]*Sqrt[b])^(1/4)*ArcTanh[(a + b/x^2)^(1/4)/(a^(1/8)*(Sqrt[a] - Sqrt[b]/Sqrt[2])^(1/4))] - 3*a^(3/8)*(4*Sqrt[a] + 2*Sqrt[2]*Sqrt[b])^(1/4)*ArcTanh[(a + b/x^2)^(1/4)/(a^(1/8)*(Sqrt[a] + Sqrt[b]/Sqrt[2])^(1/4))]))/(4*a^(3/4)*(x^2*(b + a*x^2))^(3/4))","B",1
2161,1,394,158,2.008451,"\int \frac{\sqrt[4]{b x^2+a x^4} \left(-b+2 a x^4\right)}{-2 b+a x^4} \, dx","Integrate[((b*x^2 + a*x^4)^(1/4)*(-b + 2*a*x^4))/(-2*b + a*x^4),x]","\frac{\sqrt{b} x^3 \left(a+\frac{b}{x^2}\right)^{3/4} \left(3 a^{3/8} \sqrt[4]{4 \sqrt{a}-2 \sqrt{2} \sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[8]{a} \sqrt[4]{\sqrt{a}-\frac{\sqrt{b}}{\sqrt{2}}}}\right)-3 a^{3/8} \sqrt[4]{4 \sqrt{a}+2 \sqrt{2} \sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[8]{a} \sqrt[4]{\sqrt{a}+\frac{\sqrt{b}}{\sqrt{2}}}}\right)+3 a^{3/8} \sqrt[4]{4 \sqrt{a}-2 \sqrt{2} \sqrt{b}} \tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[8]{a} \sqrt[4]{\sqrt{a}-\frac{\sqrt{b}}{\sqrt{2}}}}\right)-3 a^{3/8} \sqrt[4]{4 \sqrt{a}+2 \sqrt{2} \sqrt{b}} \tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[8]{a} \sqrt[4]{\sqrt{a}+\frac{\sqrt{b}}{\sqrt{2}}}}\right)+2 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a}}\right)+2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a}}\right)\right)}{4 a^{3/4} \left(x^2 \left(a x^2+b\right)\right)^{3/4}}+x \sqrt[4]{x^2 \left(a x^2+b\right)}","\frac{3}{8} b \text{RootSum}\left[2 \text{$\#$1}^8-4 \text{$\#$1}^4 a+2 a^2-a b\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^4-a}\&\right]-\frac{b \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{2 a^{3/4}}+\frac{b \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{2 a^{3/4}}+x \sqrt[4]{a x^4+b x^2}",1,"x*(x^2*(b + a*x^2))^(1/4) + (Sqrt[b]*(a + b/x^2)^(3/4)*x^3*(2*Sqrt[b]*ArcTan[(a + b/x^2)^(1/4)/a^(1/4)] + 3*a^(3/8)*(4*Sqrt[a] - 2*Sqrt[2]*Sqrt[b])^(1/4)*ArcTan[(a + b/x^2)^(1/4)/(a^(1/8)*(Sqrt[a] - Sqrt[b]/Sqrt[2])^(1/4))] - 3*a^(3/8)*(4*Sqrt[a] + 2*Sqrt[2]*Sqrt[b])^(1/4)*ArcTan[(a + b/x^2)^(1/4)/(a^(1/8)*(Sqrt[a] + Sqrt[b]/Sqrt[2])^(1/4))] + 2*Sqrt[b]*ArcTanh[(a + b/x^2)^(1/4)/a^(1/4)] + 3*a^(3/8)*(4*Sqrt[a] - 2*Sqrt[2]*Sqrt[b])^(1/4)*ArcTanh[(a + b/x^2)^(1/4)/(a^(1/8)*(Sqrt[a] - Sqrt[b]/Sqrt[2])^(1/4))] - 3*a^(3/8)*(4*Sqrt[a] + 2*Sqrt[2]*Sqrt[b])^(1/4)*ArcTanh[(a + b/x^2)^(1/4)/(a^(1/8)*(Sqrt[a] + Sqrt[b]/Sqrt[2])^(1/4))]))/(4*a^(3/4)*(x^2*(b + a*x^2))^(3/4))","B",1
2162,1,625,158,1.1969211,"\int \frac{x (-4 a+3 x)}{\sqrt[3]{x^2 (-a+x)} \left(a-x+d x^4\right)} \, dx","Integrate[(x*(-4*a + 3*x))/((x^2*(-a + x))^(1/3)*(a - x + d*x^4)),x]","\frac{a x \left(4 \text{RootSum}\left[\text{$\#$1}^4 a^3 d-\text{$\#$1}^3+3 \text{$\#$1}^2-3 \text{$\#$1}+1\&,\frac{-\sqrt[3]{\text{$\#$1}} \log \left(\text{$\#$1}^{2/3}+\sqrt[3]{\text{$\#$1}} \sqrt[3]{\frac{x}{x-a}}+\left(\frac{x}{x-a}\right)^{2/3}\right)+2 \sqrt[3]{\text{$\#$1}} \log \left(\sqrt[3]{\text{$\#$1}}-\sqrt[3]{\frac{x}{x-a}}\right)-2 \sqrt{3} \sqrt[3]{\text{$\#$1}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{\frac{x}{x-a}}}{\sqrt[3]{\text{$\#$1}}}+1}{\sqrt{3}}\right)+6 \sqrt[3]{\frac{x}{x-a}}}{4 \text{$\#$1}^3 a^3 d-3 \text{$\#$1}^2+6 \text{$\#$1}-3}\&\right]+5 \text{RootSum}\left[\text{$\#$1}^4 a^3 d-\text{$\#$1}^3+3 \text{$\#$1}^2-3 \text{$\#$1}+1\&,\frac{-2 \text{$\#$1}^{4/3} \log \left(\sqrt[3]{\text{$\#$1}}-\sqrt[3]{\frac{x}{x-a}}\right)+\text{$\#$1}^{4/3} \log \left(\text{$\#$1}^{2/3}+\sqrt[3]{\text{$\#$1}} \sqrt[3]{\frac{x}{x-a}}+\left(\frac{x}{x-a}\right)^{2/3}\right)+2 \sqrt{3} \text{$\#$1}^{4/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{\frac{x}{x-a}}}{\sqrt[3]{\text{$\#$1}}}+1}{\sqrt{3}}\right)-6 \text{$\#$1} \sqrt[3]{\frac{x}{x-a}}}{4 \text{$\#$1}^3 a^3 d-3 \text{$\#$1}^2+6 \text{$\#$1}-3}\&\right]-\text{RootSum}\left[\text{$\#$1}^4 a^3 d-\text{$\#$1}^3+3 \text{$\#$1}^2-3 \text{$\#$1}+1\&,\frac{-2 \text{$\#$1}^{7/3} \log \left(\sqrt[3]{\text{$\#$1}}-\sqrt[3]{\frac{x}{x-a}}\right)+\text{$\#$1}^{7/3} \log \left(\text{$\#$1}^{2/3}+\sqrt[3]{\text{$\#$1}} \sqrt[3]{\frac{x}{x-a}}+\left(\frac{x}{x-a}\right)^{2/3}\right)+2 \sqrt{3} \text{$\#$1}^{7/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{\frac{x}{x-a}}}{\sqrt[3]{\text{$\#$1}}}+1}{\sqrt{3}}\right)-6 \text{$\#$1}^2 \sqrt[3]{\frac{x}{x-a}}}{4 \text{$\#$1}^3 a^3 d-3 \text{$\#$1}^2+6 \text{$\#$1}-3}\&\right]\right)}{2 \sqrt[3]{\frac{x}{x-a}} \sqrt[3]{x^2 (x-a)}}","-\frac{\log \left(a^2 d^{2/3} x^4+a^2 \sqrt[3]{d} x^2 \sqrt[3]{x^3-a x^2}+a^2 \left(x^3-a x^2\right)^{2/3}\right)}{2 \sqrt[3]{d}}+\frac{\log \left(a \sqrt[3]{x^3-a x^2}-a \sqrt[3]{d} x^2\right)}{\sqrt[3]{d}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} x^2}{2 \sqrt[3]{x^3-a x^2}+\sqrt[3]{d} x^2}\right)}{\sqrt[3]{d}}",1,"(a*x*(4*RootSum[1 - 3*#1 + 3*#1^2 - #1^3 + a^3*d*#1^4 & , (6*(x/(-a + x))^(1/3) - 2*Sqrt[3]*ArcTan[(1 + (2*(x/(-a + x))^(1/3))/#1^(1/3))/Sqrt[3]]*#1^(1/3) + 2*Log[-(x/(-a + x))^(1/3) + #1^(1/3)]*#1^(1/3) - Log[(x/(-a + x))^(2/3) + (x/(-a + x))^(1/3)*#1^(1/3) + #1^(2/3)]*#1^(1/3))/(-3 + 6*#1 - 3*#1^2 + 4*a^3*d*#1^3) & ] + 5*RootSum[1 - 3*#1 + 3*#1^2 - #1^3 + a^3*d*#1^4 & , (-6*(x/(-a + x))^(1/3)*#1 + 2*Sqrt[3]*ArcTan[(1 + (2*(x/(-a + x))^(1/3))/#1^(1/3))/Sqrt[3]]*#1^(4/3) - 2*Log[-(x/(-a + x))^(1/3) + #1^(1/3)]*#1^(4/3) + Log[(x/(-a + x))^(2/3) + (x/(-a + x))^(1/3)*#1^(1/3) + #1^(2/3)]*#1^(4/3))/(-3 + 6*#1 - 3*#1^2 + 4*a^3*d*#1^3) & ] - RootSum[1 - 3*#1 + 3*#1^2 - #1^3 + a^3*d*#1^4 & , (-6*(x/(-a + x))^(1/3)*#1^2 + 2*Sqrt[3]*ArcTan[(1 + (2*(x/(-a + x))^(1/3))/#1^(1/3))/Sqrt[3]]*#1^(7/3) - 2*Log[-(x/(-a + x))^(1/3) + #1^(1/3)]*#1^(7/3) + Log[(x/(-a + x))^(2/3) + (x/(-a + x))^(1/3)*#1^(1/3) + #1^(2/3)]*#1^(7/3))/(-3 + 6*#1 - 3*#1^2 + 4*a^3*d*#1^3) & ]))/(2*(x/(-a + x))^(1/3)*(x^2*(-a + x))^(1/3))","C",1
2163,1,403,158,0.8640146,"\int \frac{-b-2 a x^4+2 x^8}{\sqrt[4]{-b+a x^4} \left(-b-a x^4+x^8\right)} \, dx","Integrate[(-b - 2*a*x^4 + 2*x^8)/((-b + a*x^4)^(1/4)*(-b - a*x^4 + x^8)),x]","\frac{b \left(\tan ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{a x^4-b}}\right)+\tanh ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{a x^4-b}}\right)\right)}{\sqrt{a^2+4 b} \left(a-\sqrt{a^2+4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}-\frac{b \left(\tan ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+4 b}+a} \sqrt[4]{a x^4-b}}\right)+\tanh ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+4 b}+a} \sqrt[4]{a x^4-b}}\right)\right)}{\sqrt{a^2+4 b} \left(\sqrt{a^2+4 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{\sqrt[4]{a}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{\sqrt[4]{a}}","-\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4 a+2 a^2-b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-a \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+a \log (x)}{3 \text{$\#$1} a-2 \text{$\#$1}^5}\&\right]+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{\sqrt[4]{a}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{\sqrt[4]{a}}",1,"ArcTan[(a^(1/4)*x)/(-b + a*x^4)^(1/4)]/a^(1/4) + ArcTanh[(a^(1/4)*x)/(-b + a*x^4)^(1/4)]/a^(1/4) + (b*(ArcTan[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a - Sqrt[a^2 + 4*b])^(1/4)*(-b + a*x^4)^(1/4))] + ArcTanh[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a - Sqrt[a^2 + 4*b])^(1/4)*(-b + a*x^4)^(1/4))]))/(Sqrt[a^2 + 4*b]*(a - Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)) - (b*(ArcTan[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a + Sqrt[a^2 + 4*b])^(1/4)*(-b + a*x^4)^(1/4))] + ArcTanh[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a + Sqrt[a^2 + 4*b])^(1/4)*(-b + a*x^4)^(1/4))]))/(Sqrt[a^2 + 4*b]*(a + Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4))","B",1
2164,1,403,158,0.1429201,"\int \frac{-b-2 a x^4+2 x^8}{\sqrt[4]{-b+a x^4} \left(-b-a x^4+x^8\right)} \, dx","Integrate[(-b - 2*a*x^4 + 2*x^8)/((-b + a*x^4)^(1/4)*(-b - a*x^4 + x^8)),x]","\frac{b \left(\tan ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{a x^4-b}}\right)+\tanh ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{a x^4-b}}\right)\right)}{\sqrt{a^2+4 b} \left(a-\sqrt{a^2+4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}-\frac{b \left(\tan ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+4 b}+a} \sqrt[4]{a x^4-b}}\right)+\tanh ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+4 b}+a} \sqrt[4]{a x^4-b}}\right)\right)}{\sqrt{a^2+4 b} \left(\sqrt{a^2+4 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{\sqrt[4]{a}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{\sqrt[4]{a}}","-\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4 a+2 a^2-b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-a \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+a \log (x)}{3 \text{$\#$1} a-2 \text{$\#$1}^5}\&\right]+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{\sqrt[4]{a}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{\sqrt[4]{a}}",1,"ArcTan[(a^(1/4)*x)/(-b + a*x^4)^(1/4)]/a^(1/4) + ArcTanh[(a^(1/4)*x)/(-b + a*x^4)^(1/4)]/a^(1/4) + (b*(ArcTan[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a - Sqrt[a^2 + 4*b])^(1/4)*(-b + a*x^4)^(1/4))] + ArcTanh[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a - Sqrt[a^2 + 4*b])^(1/4)*(-b + a*x^4)^(1/4))]))/(Sqrt[a^2 + 4*b]*(a - Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)) - (b*(ArcTan[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a + Sqrt[a^2 + 4*b])^(1/4)*(-b + a*x^4)^(1/4))] + ArcTanh[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a + Sqrt[a^2 + 4*b])^(1/4)*(-b + a*x^4)^(1/4))]))/(Sqrt[a^2 + 4*b]*(a + Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4))","B",1
2165,1,41,159,0.014391,"\int \frac{1}{\left(-1+x^2\right) \sqrt[3]{-x^2+x^3}} \, dx","Integrate[1/((-1 + x^2)*(-x^2 + x^3)^(1/3)),x]","-\frac{3 \left((x-1) \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{x-1}{2 x}\right)+4 x\right)}{8 \sqrt[3]{(x-1) x^2}}","-\frac{3 \left(x^3-x^2\right)^{2/3}}{2 (x-1) x}+\frac{\log \left(2^{2/3} \sqrt[3]{x^3-x^2}-2 x\right)}{2 \sqrt[3]{2}}-\frac{\log \left(2 x^2+2^{2/3} \sqrt[3]{x^3-x^2} x+\sqrt[3]{2} \left(x^3-x^2\right)^{2/3}\right)}{4 \sqrt[3]{2}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^3-x^2}+x}\right)}{2 \sqrt[3]{2}}",1,"(-3*(4*x + (-1 + x)*Hypergeometric2F1[2/3, 1, 5/3, (-1 + x)/(2*x)]))/(8*((-1 + x)*x^2)^(1/3))","C",1
2166,1,396,159,1.4921866,"\int \frac{-b^2+a^2 x^4}{\sqrt{-b x+a x^3} \left(b^2+c x^2+a^2 x^4\right)} \, dx","Integrate[(-b^2 + a^2*x^4)/(Sqrt[-(b*x) + a*x^3]*(b^2 + c*x^2 + a^2*x^4)),x]","-\frac{i \sqrt{1-\frac{b}{a x^2}} \sqrt{a x^3-b x} \left(-\Pi \left(-\frac{\sqrt{2} \sqrt{a}}{\sqrt{b} \sqrt{\frac{\sqrt{c^2-4 a^2 b^2}-c}{b^2}}};\left.i \sinh ^{-1}\left(\frac{\sqrt{-\frac{\sqrt{b}}{\sqrt{a}}}}{\sqrt{x}}\right)\right|-1\right)-\Pi \left(\frac{\sqrt{2} \sqrt{a}}{\sqrt{b} \sqrt{\frac{\sqrt{c^2-4 a^2 b^2}-c}{b^2}}};\left.i \sinh ^{-1}\left(\frac{\sqrt{-\frac{\sqrt{b}}{\sqrt{a}}}}{\sqrt{x}}\right)\right|-1\right)-\Pi \left(-\frac{\sqrt{2} \sqrt{a}}{\sqrt{b} \sqrt{-\frac{c+\sqrt{c^2-4 a^2 b^2}}{b^2}}};\left.i \sinh ^{-1}\left(\frac{\sqrt{-\frac{\sqrt{b}}{\sqrt{a}}}}{\sqrt{x}}\right)\right|-1\right)-\Pi \left(\frac{\sqrt{2} \sqrt{a}}{\sqrt{b} \sqrt{-\frac{c+\sqrt{c^2-4 a^2 b^2}}{b^2}}};\left.i \sinh ^{-1}\left(\frac{\sqrt{-\frac{\sqrt{b}}{\sqrt{a}}}}{\sqrt{x}}\right)\right|-1\right)+2 F\left(\left.i \sinh ^{-1}\left(\frac{\sqrt{-\frac{\sqrt{b}}{\sqrt{a}}}}{\sqrt{x}}\right)\right|-1\right)\right)}{x^{3/2} \sqrt{-\frac{\sqrt{b}}{\sqrt{a}}} \left(a-\frac{b}{x^2}\right)}","\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{2 a b+c} \sqrt{a x^3-b x}}{x \sqrt{2 a b+c}-a x^2+b}\right)}{\sqrt{2} \sqrt[4]{2 a b+c}}-\frac{\tanh ^{-1}\left(\frac{\frac{a x^2}{\sqrt{2} \sqrt[4]{2 a b+c}}+\frac{x \sqrt[4]{2 a b+c}}{\sqrt{2}}-\frac{b}{\sqrt{2} \sqrt[4]{2 a b+c}}}{\sqrt{a x^3-b x}}\right)}{\sqrt{2} \sqrt[4]{2 a b+c}}",1,"((-I)*Sqrt[1 - b/(a*x^2)]*Sqrt[-(b*x) + a*x^3]*(2*EllipticF[I*ArcSinh[Sqrt[-(Sqrt[b]/Sqrt[a])]/Sqrt[x]], -1] - EllipticPi[-((Sqrt[2]*Sqrt[a])/(Sqrt[b]*Sqrt[(-c + Sqrt[-4*a^2*b^2 + c^2])/b^2])), I*ArcSinh[Sqrt[-(Sqrt[b]/Sqrt[a])]/Sqrt[x]], -1] - EllipticPi[(Sqrt[2]*Sqrt[a])/(Sqrt[b]*Sqrt[(-c + Sqrt[-4*a^2*b^2 + c^2])/b^2]), I*ArcSinh[Sqrt[-(Sqrt[b]/Sqrt[a])]/Sqrt[x]], -1] - EllipticPi[-((Sqrt[2]*Sqrt[a])/(Sqrt[b]*Sqrt[-((c + Sqrt[-4*a^2*b^2 + c^2])/b^2)])), I*ArcSinh[Sqrt[-(Sqrt[b]/Sqrt[a])]/Sqrt[x]], -1] - EllipticPi[(Sqrt[2]*Sqrt[a])/(Sqrt[b]*Sqrt[-((c + Sqrt[-4*a^2*b^2 + c^2])/b^2)]), I*ArcSinh[Sqrt[-(Sqrt[b]/Sqrt[a])]/Sqrt[x]], -1]))/(Sqrt[-(Sqrt[b]/Sqrt[a])]*(a - b/x^2)*x^(3/2))","C",1
2167,0,0,159,0.6706156,"\int \frac{\left(-q+2 p x^3\right) \sqrt{q^2-2 p q x^2+2 p q x^3+p^2 x^6}}{x \left(b x^2+a \left(q+p x^3\right)^2\right)} \, dx","Integrate[((-q + 2*p*x^3)*Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6])/(x*(b*x^2 + a*(q + p*x^3)^2)),x]","\int \frac{\left(-q+2 p x^3\right) \sqrt{q^2-2 p q x^2+2 p q x^3+p^2 x^6}}{x \left(b x^2+a \left(q+p x^3\right)^2\right)} \, dx","\frac{\sqrt{2 a p q+b} \tanh ^{-1}\left(\frac{\sqrt{b} x^2 \sqrt{2 a p q+b}}{\sqrt{p^2 x^6+2 p q x^3-2 p q x^2+q^2} \left(a p x^3+a q\right)+a p^2 x^6+2 a p q x^3+a q^2+b x^2}\right)}{a \sqrt{b}}+\frac{\log \left(\sqrt{p^2 x^6+2 p q x^3-2 p q x^2+q^2}+p x^3+q\right)}{a}-\frac{\log (x)}{a}",1,"Integrate[((-q + 2*p*x^3)*Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6])/(x*(b*x^2 + a*(q + p*x^3)^2)), x]","F",-1
2168,0,0,159,0.6997353,"\int \frac{\left(-2 q+p x^3\right) \sqrt{q^2+2 p q x^3-2 p q x^4+p^2 x^6}}{x \left(b x^4+a \left(q+p x^3\right)^2\right)} \, dx","Integrate[((-2*q + p*x^3)*Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6])/(x*(b*x^4 + a*(q + p*x^3)^2)),x]","\int \frac{\left(-2 q+p x^3\right) \sqrt{q^2+2 p q x^3-2 p q x^4+p^2 x^6}}{x \left(b x^4+a \left(q+p x^3\right)^2\right)} \, dx","\frac{\sqrt{2 a p q+b} \tanh ^{-1}\left(\frac{\sqrt{b} x^4 \sqrt{2 a p q+b}}{\sqrt{p^2 x^6-2 p q x^4+2 p q x^3+q^2} \left(a p x^3+a q\right)+a p^2 x^6+2 a p q x^3+a q^2+b x^4}\right)}{a \sqrt{b}}+\frac{\log \left(\sqrt{p^2 x^6-2 p q x^4+2 p q x^3+q^2}+p x^3+q\right)}{a}-\frac{2 \log (x)}{a}",1,"Integrate[((-2*q + p*x^3)*Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6])/(x*(b*x^4 + a*(q + p*x^3)^2)), x]","F",-1
2169,1,14154,159,15.8194283,"\int \frac{x^2-\sqrt{1+x^2}}{x^2+\sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[(x^2 - Sqrt[1 + x^2])/(x^2 + Sqrt[x + Sqrt[1 + x^2]]),x]","\text{Result too large to show}","-\text{RootSum}\left[\text{$\#$1}^8+4 \text{$\#$1}^5-2 \text{$\#$1}^4+1\&,\frac{\text{$\#$1}^4 \log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)-2 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)+2 \text{$\#$1} \log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)}{2 \text{$\#$1}^5+5 \text{$\#$1}^2-2 \text{$\#$1}}\&\right]-\log \left(\sqrt{x^2+1}+x\right)+x",1,"Result too large to show","B",0
2170,1,14154,159,15.2784298,"\int \frac{x^2-\sqrt{1+x^2}}{x^2+\sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[(x^2 - Sqrt[1 + x^2])/(x^2 + Sqrt[x + Sqrt[1 + x^2]]),x]","\text{Result too large to show}","-\text{RootSum}\left[\text{$\#$1}^8+4 \text{$\#$1}^5-2 \text{$\#$1}^4+1\&,\frac{\text{$\#$1}^4 \log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)-2 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)+2 \text{$\#$1} \log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)}{2 \text{$\#$1}^5+5 \text{$\#$1}^2-2 \text{$\#$1}}\&\right]-\log \left(\sqrt{x^2+1}+x\right)+x",1,"Result too large to show","B",0
2171,1,148,160,0.2568621,"\int \frac{\sqrt{1+\sqrt{1-\sqrt{1+\frac{1}{x^2}}}}}{x} \, dx","Integrate[Sqrt[1 + Sqrt[1 - Sqrt[1 + x^(-2)]]]/x,x]","-4 \sqrt{\sqrt{1-\sqrt{\frac{1}{x^2}+1}}+1}+\sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{\sqrt{\sqrt{1-\sqrt{\frac{1}{x^2}+1}}+1}}{\sqrt{\sqrt{2}-1}}\right)+2 \tanh ^{-1}\left(\sqrt{\sqrt{1-\sqrt{\frac{1}{x^2}+1}}+1}\right)+\sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{1-\sqrt{\frac{1}{x^2}+1}}+1}}{\sqrt{1+\sqrt{2}}}\right)","-4 \sqrt{\sqrt{1-\sqrt{\frac{1}{x^2}+1}}+1}+\sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{\sqrt{\sqrt{1-\sqrt{\frac{x^2+1}{x^2}}}+1}}{\sqrt{\sqrt{2}-1}}\right)+2 \tanh ^{-1}\left(\sqrt{\sqrt{1-\sqrt{\frac{x^2+1}{x^2}}}+1}\right)+\sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{1-\sqrt{\frac{x^2+1}{x^2}}}+1}}{\sqrt{1+\sqrt{2}}}\right)",1,"-4*Sqrt[1 + Sqrt[1 - Sqrt[1 + x^(-2)]]] + Sqrt[-1 + Sqrt[2]]*ArcTan[Sqrt[1 + Sqrt[1 - Sqrt[1 + x^(-2)]]]/Sqrt[-1 + Sqrt[2]]] + 2*ArcTanh[Sqrt[1 + Sqrt[1 - Sqrt[1 + x^(-2)]]]] + Sqrt[1 + Sqrt[2]]*ArcTanh[Sqrt[1 + Sqrt[1 - Sqrt[1 + x^(-2)]]]/Sqrt[1 + Sqrt[2]]]","A",1
2172,0,0,160,7.3247196,"\int \frac{-2 x+(1+k) x^2}{((1-x) x (1-k x))^{2/3} \left(1-(1+k) x+(-b+k) x^2\right)} \, dx","Integrate[(-2*x + (1 + k)*x^2)/(((1 - x)*x*(1 - k*x))^(2/3)*(1 - (1 + k)*x + (-b + k)*x^2)),x]","\int \frac{-2 x+(1+k) x^2}{((1-x) x (1-k x))^{2/3} \left(1-(1+k) x+(-b+k) x^2\right)} \, dx","\frac{\log \left(\sqrt[3]{k x^3+(-k-1) x^2+x}-\sqrt[3]{b} x\right)}{b^{2/3}}-\frac{\log \left(b^{2/3} x^2+\sqrt[3]{b} x \sqrt[3]{k x^3+(-k-1) x^2+x}+\left(k x^3+(-k-1) x^2+x\right)^{2/3}\right)}{2 b^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{b} x}{\sqrt[3]{b} x+2 \sqrt[3]{k x^3+(-k-1) x^2+x}}\right)}{b^{2/3}}",1,"Integrate[(-2*x + (1 + k)*x^2)/(((1 - x)*x*(1 - k*x))^(2/3)*(1 - (1 + k)*x + (-b + k)*x^2)), x]","F",-1
2173,0,0,161,1.6032069,"\int \frac{2-(1+k) x}{\sqrt[3]{(1-x) x (1-k x)} (1-(1+k) x)} \, dx","Integrate[(2 - (1 + k)*x)/(((1 - x)*x*(1 - k*x))^(1/3)*(1 - (1 + k)*x)),x]","\int \frac{2-(1+k) x}{\sqrt[3]{(1-x) x (1-k x)} (1-(1+k) x)} \, dx","\frac{\log \left(k^{2/3} x^2+\sqrt[3]{k} x \sqrt[3]{k x^3+(-k-1) x^2+x}+\left(k x^3+(-k-1) x^2+x\right)^{2/3}\right)}{2 \sqrt[3]{k}}-\frac{\log \left(\sqrt[3]{k x^3+(-k-1) x^2+x}-\sqrt[3]{k} x\right)}{\sqrt[3]{k}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{k} x}{2 \sqrt[3]{k x^3+(-k-1) x^2+x}+\sqrt[3]{k} x}\right)}{\sqrt[3]{k}}",1,"Integrate[(2 - (1 + k)*x)/(((1 - x)*x*(1 - k*x))^(1/3)*(1 - (1 + k)*x)), x]","F",-1
2174,0,0,161,6.5710839,"\int \frac{-2+(1+k) x}{\sqrt[3]{(1-x) x (1-k x)} \left(1-(1+k) x+(-b+k) x^2\right)} \, dx","Integrate[(-2 + (1 + k)*x)/(((1 - x)*x*(1 - k*x))^(1/3)*(1 - (1 + k)*x + (-b + k)*x^2)),x]","\int \frac{-2+(1+k) x}{\sqrt[3]{(1-x) x (1-k x)} \left(1-(1+k) x+(-b+k) x^2\right)} \, dx","-\frac{\log \left(b^{2/3} x^2+\sqrt[3]{b} x \sqrt[3]{k x^3+(-k-1) x^2+x}+\left(k x^3+(-k-1) x^2+x\right)^{2/3}\right)}{2 \sqrt[3]{b}}+\frac{\log \left(\sqrt[3]{k x^3+(-k-1) x^2+x}-\sqrt[3]{b} x\right)}{\sqrt[3]{b}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{b} x}{\sqrt[3]{b} x+2 \sqrt[3]{k x^3+(-k-1) x^2+x}}\right)}{\sqrt[3]{b}}",1,"Integrate[(-2 + (1 + k)*x)/(((1 - x)*x*(1 - k*x))^(1/3)*(1 - (1 + k)*x + (-b + k)*x^2)), x]","F",-1
2175,0,0,161,0.3766083,"\int \frac{\left(3+2 x^2\right) \left(1+2 x^2+2 x^3\right)^{2/3}}{x^3 \left(-1-2 x^2+x^3\right)} \, dx","Integrate[((3 + 2*x^2)*(1 + 2*x^2 + 2*x^3)^(2/3))/(x^3*(-1 - 2*x^2 + x^3)),x]","\int \frac{\left(3+2 x^2\right) \left(1+2 x^2+2 x^3\right)^{2/3}}{x^3 \left(-1-2 x^2+x^3\right)} \, dx","\frac{3 \left(2 x^3+2 x^2+1\right)^{2/3}}{2 x^2}+3^{2/3} \log \left(3^{2/3} \sqrt[3]{2 x^3+2 x^2+1}-3 x\right)-\frac{1}{2} 3^{2/3} \log \left(3 x^2+3^{2/3} \sqrt[3]{2 x^3+2 x^2+1} x+\sqrt[3]{3} \left(2 x^3+2 x^2+1\right)^{2/3}\right)-3 \sqrt[6]{3} \tan ^{-1}\left(\frac{3^{5/6} x}{2 \sqrt[3]{2 x^3+2 x^2+1}+\sqrt[3]{3} x}\right)",1,"Integrate[((3 + 2*x^2)*(1 + 2*x^2 + 2*x^3)^(2/3))/(x^3*(-1 - 2*x^2 + x^3)), x]","F",-1
2176,1,136,161,0.5956701,"\int \frac{-b+c x+a x^2}{\left(b+a x^2\right) \sqrt{-b x+a x^3}} \, dx","Integrate[(-b + c*x + a*x^2)/((b + a*x^2)*Sqrt[-(b*x) + a*x^3]),x]","-\frac{2 x \sqrt{1-\frac{a x^2}{b}} \left(15 b F_1\left(\frac{1}{4};\frac{1}{2},1;\frac{5}{4};\frac{a x^2}{b},-\frac{a x^2}{b}\right)-x \left(5 c F_1\left(\frac{3}{4};\frac{1}{2},1;\frac{7}{4};\frac{a x^2}{b},-\frac{a x^2}{b}\right)+3 a x F_1\left(\frac{5}{4};\frac{1}{2},1;\frac{9}{4};\frac{a x^2}{b},-\frac{a x^2}{b}\right)\right)\right)}{15 b \sqrt{a x^3-b x}}","\frac{\left(-2 \sqrt{a} \sqrt{b}-c\right) \tan ^{-1}\left(\frac{2 \sqrt[4]{a} \sqrt[4]{b} \sqrt{a x^3-b x}}{-2 \sqrt{a} \sqrt{b} x+a x^2-b}\right)}{4 a^{3/4} b^{3/4}}+\frac{\left(c-2 \sqrt{a} \sqrt{b}\right) \tanh ^{-1}\left(\frac{2 \sqrt{a} \sqrt{b} x+a x^2-b}{2 \sqrt[4]{a} \sqrt[4]{b} \sqrt{a x^3-b x}}\right)}{4 a^{3/4} b^{3/4}}",1,"(-2*x*Sqrt[1 - (a*x^2)/b]*(15*b*AppellF1[1/4, 1/2, 1, 5/4, (a*x^2)/b, -((a*x^2)/b)] - x*(5*c*AppellF1[3/4, 1/2, 1, 7/4, (a*x^2)/b, -((a*x^2)/b)] + 3*a*x*AppellF1[5/4, 1/2, 1, 9/4, (a*x^2)/b, -((a*x^2)/b)])))/(15*b*Sqrt[-(b*x) + a*x^3])","C",0
2177,0,0,161,0.5608946,"\int \frac{-4-2 x+2 x^2+x^4}{x \left(-2+x^2\right) \sqrt[4]{\frac{2+x^2}{-2+x^2}} \left(8-10 x+4 x^2+4 x^3-4 x^4+x^5\right)} \, dx","Integrate[(-4 - 2*x + 2*x^2 + x^4)/(x*(-2 + x^2)*((2 + x^2)/(-2 + x^2))^(1/4)*(8 - 10*x + 4*x^2 + 4*x^3 - 4*x^4 + x^5)),x]","\int \frac{-4-2 x+2 x^2+x^4}{x \left(-2+x^2\right) \sqrt[4]{\frac{2+x^2}{-2+x^2}} \left(8-10 x+4 x^2+4 x^3-4 x^4+x^5\right)} \, dx","\frac{\tanh ^{-1}\left(\frac{\frac{x^2}{\sqrt{2}}+\frac{\sqrt{\frac{x^2+2}{x^2-2}}}{\sqrt{2}}-\sqrt{2} x+\frac{1}{\sqrt{2}}}{(x-1) \sqrt[4]{\frac{x^2+2}{x^2-2}}}\right)}{2 \sqrt{2}}-\frac{\tan ^{-1}\left(\frac{-\frac{x^2}{\sqrt{2}}+\frac{\sqrt{\frac{x^2+2}{x^2-2}}}{\sqrt{2}}+\sqrt{2} x-\frac{1}{\sqrt{2}}}{(x-1) \sqrt[4]{\frac{x^2+2}{x^2-2}}}\right)}{2 \sqrt{2}}",1,"Integrate[(-4 - 2*x + 2*x^2 + x^4)/(x*(-2 + x^2)*((2 + x^2)/(-2 + x^2))^(1/4)*(8 - 10*x + 4*x^2 + 4*x^3 - 4*x^4 + x^5)), x]","F",-1
2178,1,153,161,0.4567344,"\int \frac{\sqrt{1+x} \left(-1+x^4\right) \sqrt{1+\sqrt{1+x}}}{1+x^4} \, dx","Integrate[(Sqrt[1 + x]*(-1 + x^4)*Sqrt[1 + Sqrt[1 + x]])/(1 + x^4),x]","\frac{4}{105} \sqrt{\sqrt{x+1}+1} \left(11 \left(\sqrt{x+1}+1\right)+3 x \left(5 \sqrt{x+1}+1\right)\right)-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^{16}-8 \text{$\#$1}^{14}+24 \text{$\#$1}^{12}-32 \text{$\#$1}^{10}+16 \text{$\#$1}^8+1\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^{11}-6 \text{$\#$1}^9+12 \text{$\#$1}^7-8 \text{$\#$1}^5}\&\right]","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^{16}-8 \text{$\#$1}^{14}+24 \text{$\#$1}^{12}-32 \text{$\#$1}^{10}+16 \text{$\#$1}^8+1\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^{11}-6 \text{$\#$1}^9+12 \text{$\#$1}^7-8 \text{$\#$1}^5}\&\right]+\frac{4}{105} \sqrt{\sqrt{x+1}+1} (3 x+11)+\frac{4}{105} \sqrt{x+1} (15 x+11) \sqrt{\sqrt{x+1}+1}",1,"(4*Sqrt[1 + Sqrt[1 + x]]*(11*(1 + Sqrt[1 + x]) + 3*x*(1 + 5*Sqrt[1 + x])))/105 - RootSum[1 + 16*#1^8 - 32*#1^10 + 24*#1^12 - 8*#1^14 + #1^16 & , (-Log[Sqrt[1 + Sqrt[1 + x]] - #1] + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2)/(-8*#1^5 + 12*#1^7 - 6*#1^9 + #1^11) & ]/2","A",1
2179,1,153,161,0.2556622,"\int \frac{\sqrt{1+x} \left(-1+x^4\right) \sqrt{1+\sqrt{1+x}}}{1+x^4} \, dx","Integrate[(Sqrt[1 + x]*(-1 + x^4)*Sqrt[1 + Sqrt[1 + x]])/(1 + x^4),x]","\frac{4}{105} \sqrt{\sqrt{x+1}+1} \left(11 \left(\sqrt{x+1}+1\right)+3 x \left(5 \sqrt{x+1}+1\right)\right)-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^{16}-8 \text{$\#$1}^{14}+24 \text{$\#$1}^{12}-32 \text{$\#$1}^{10}+16 \text{$\#$1}^8+1\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^{11}-6 \text{$\#$1}^9+12 \text{$\#$1}^7-8 \text{$\#$1}^5}\&\right]","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^{16}-8 \text{$\#$1}^{14}+24 \text{$\#$1}^{12}-32 \text{$\#$1}^{10}+16 \text{$\#$1}^8+1\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^{11}-6 \text{$\#$1}^9+12 \text{$\#$1}^7-8 \text{$\#$1}^5}\&\right]+\frac{4}{105} \sqrt{\sqrt{x+1}+1} (3 x+11)+\frac{4}{105} \sqrt{x+1} (15 x+11) \sqrt{\sqrt{x+1}+1}",1,"(4*Sqrt[1 + Sqrt[1 + x]]*(11*(1 + Sqrt[1 + x]) + 3*x*(1 + 5*Sqrt[1 + x])))/105 - RootSum[1 + 16*#1^8 - 32*#1^10 + 24*#1^12 - 8*#1^14 + #1^16 & , (-Log[Sqrt[1 + Sqrt[1 + x]] - #1] + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2)/(-8*#1^5 + 12*#1^7 - 6*#1^9 + #1^11) & ]/2","A",1
2180,1,53,162,0.0547906,"\int \frac{-d+c x}{x^4 \sqrt[3]{-b+a x^3}} \, dx","Integrate[(-d + c*x)/(x^4*(-b + a*x^3)^(1/3)),x]","\frac{\left(a x^3-b\right)^{2/3} \left(b c-a d x^2 \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};1-\frac{a x^3}{b}\right)\right)}{2 b^2 x^2}","\frac{a d \log \left(\sqrt[3]{a x^3-b}+\sqrt[3]{b}\right)}{9 b^{4/3}}-\frac{a d \log \left(-\sqrt[3]{b} \sqrt[3]{a x^3-b}+\left(a x^3-b\right)^{2/3}+b^{2/3}\right)}{18 b^{4/3}}+\frac{a d \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{a x^3-b}}{\sqrt{3} \sqrt[3]{b}}\right)}{3 \sqrt{3} b^{4/3}}+\frac{\left(a x^3-b\right)^{2/3} (3 c x-2 d)}{6 b x^3}",1,"((-b + a*x^3)^(2/3)*(b*c - a*d*x^2*Hypergeometric2F1[2/3, 2, 5/3, 1 - (a*x^3)/b]))/(2*b^2*x^2)","C",1
2181,1,167,162,0.1242285,"\int \frac{\sqrt[4]{-b x^3+a x^4} \left(-d+c x^4\right)}{x^2} \, dx","Integrate[((-(b*x^3) + a*x^4)^(1/4)*(-d + c*x^4))/x^2,x]","-\frac{4 \sqrt[4]{x^3 (a x-b)} \left(a^4 (-d) \, _2F_1\left(-\frac{1}{4},-\frac{1}{4};\frac{3}{4};\frac{a x}{b}\right)+b^4 c \, _2F_1\left(-\frac{17}{4},-\frac{1}{4};\frac{3}{4};\frac{a x}{b}\right)-4 b^4 c \, _2F_1\left(-\frac{13}{4},-\frac{1}{4};\frac{3}{4};\frac{a x}{b}\right)+6 b^4 c \, _2F_1\left(-\frac{9}{4},-\frac{1}{4};\frac{3}{4};\frac{a x}{b}\right)-4 b^4 c \, _2F_1\left(-\frac{5}{4},-\frac{1}{4};\frac{3}{4};\frac{a x}{b}\right)+b^4 c \, _2F_1\left(-\frac{1}{4},-\frac{1}{4};\frac{3}{4};\frac{a x}{b}\right)\right)}{a^4 x \sqrt[4]{1-\frac{a x}{b}}}","\frac{\left(2048 a^4 d+77 b^4 c\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^3}}\right)}{1024 a^{15/4}}+\frac{\left(-2048 a^4 d-77 b^4 c\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^3}}\right)}{1024 a^{15/4}}+\frac{\sqrt[4]{a x^4-b x^3} \left(384 a^3 c x^4+6144 a^3 d-32 a^2 b c x^3-44 a b^2 c x^2-77 b^3 c x\right)}{1536 a^3 x}",1,"(-4*(x^3*(-b + a*x))^(1/4)*(b^4*c*Hypergeometric2F1[-17/4, -1/4, 3/4, (a*x)/b] - 4*b^4*c*Hypergeometric2F1[-13/4, -1/4, 3/4, (a*x)/b] + 6*b^4*c*Hypergeometric2F1[-9/4, -1/4, 3/4, (a*x)/b] - 4*b^4*c*Hypergeometric2F1[-5/4, -1/4, 3/4, (a*x)/b] + b^4*c*Hypergeometric2F1[-1/4, -1/4, 3/4, (a*x)/b] - a^4*d*Hypergeometric2F1[-1/4, -1/4, 3/4, (a*x)/b]))/(a^4*x*(1 - (a*x)/b)^(1/4))","C",1
2182,0,0,162,1.2742177,"\int \frac{x^3 \left(5-4 (1+k) x+3 k x^2\right)}{((1-x) x (1-k x))^{2/3} \left(-b+b (1+k) x-b k x^2+x^5\right)} \, dx","Integrate[(x^3*(5 - 4*(1 + k)*x + 3*k*x^2))/(((1 - x)*x*(1 - k*x))^(2/3)*(-b + b*(1 + k)*x - b*k*x^2 + x^5)),x]","\int \frac{x^3 \left(5-4 (1+k) x+3 k x^2\right)}{((1-x) x (1-k x))^{2/3} \left(-b+b (1+k) x-b k x^2+x^5\right)} \, dx","-\frac{\log \left(b^{2/3} \left(k x^3+(-k-1) x^2+x\right)^{2/3}+\sqrt[3]{b} x^2 \sqrt[3]{k x^3+(-k-1) x^2+x}+x^4\right)}{2 \sqrt[3]{b}}+\frac{\log \left(x^2-\sqrt[3]{b} \sqrt[3]{k x^3+(-k-1) x^2+x}\right)}{\sqrt[3]{b}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x^2}{2 \sqrt[3]{b} \sqrt[3]{k x^3+(-k-1) x^2+x}+x^2}\right)}{\sqrt[3]{b}}",1,"Integrate[(x^3*(5 - 4*(1 + k)*x + 3*k*x^2))/(((1 - x)*x*(1 - k*x))^(2/3)*(-b + b*(1 + k)*x - b*k*x^2 + x^5)), x]","F",-1
2183,0,0,162,0.5145828,"\int \frac{\left(-8+x^5\right) \left(2+x^5\right) \sqrt[4]{2-3 x^4+x^5}}{x^6 \left(4-3 x^4+2 x^5\right)} \, dx","Integrate[((-8 + x^5)*(2 + x^5)*(2 - 3*x^4 + x^5)^(1/4))/(x^6*(4 - 3*x^4 + 2*x^5)),x]","\int \frac{\left(-8+x^5\right) \left(2+x^5\right) \sqrt[4]{2-3 x^4+x^5}}{x^6 \left(4-3 x^4+2 x^5\right)} \, dx","\frac{\sqrt[4]{x^5-3 x^4+2} \left(2 x^5+9 x^4+4\right)}{5 x^5}+\frac{3 \sqrt[4]{3} \tan ^{-1}\left(\frac{6^{3/4} x \sqrt[4]{x^5-3 x^4+2}}{\sqrt{6} \sqrt{x^5-3 x^4+2}-3 x^2}\right)}{2\ 2^{3/4}}-\frac{3 \sqrt[4]{3} \tanh ^{-1}\left(\frac{6^{3/4} x \sqrt[4]{x^5-3 x^4+2}}{3 x^2+\sqrt{6} \sqrt{x^5-3 x^4+2}}\right)}{2\ 2^{3/4}}",1,"Integrate[((-8 + x^5)*(2 + x^5)*(2 - 3*x^4 + x^5)^(1/4))/(x^6*(4 - 3*x^4 + 2*x^5)), x]","F",-1
2184,1,44,162,0.0278855,"\int \frac{x^2}{\left(-1+x^4\right) \sqrt[4]{x^2+x^6}} \, dx","Integrate[x^2/((-1 + x^4)*(x^2 + x^6)^(1/4)),x]","-\frac{2 x \left(x^6+x^2\right)^{3/4} F_1\left(\frac{5}{8};\frac{1}{4},1;\frac{13}{8};-x^4,x^4\right)}{5 \left(x^4+1\right)^{3/4}}","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^6+x^2}}\right)}{4 \sqrt[4]{2}}-\frac{\tan ^{-1}\left(\frac{2^{3/4} x \sqrt[4]{x^6+x^2}}{\sqrt{2} x^2-\sqrt{x^6+x^2}}\right)}{4\ 2^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^6+x^2}}\right)}{4 \sqrt[4]{2}}+\frac{\tanh ^{-1}\left(\frac{\frac{x^2}{\sqrt[4]{2}}+\frac{\sqrt{x^6+x^2}}{2^{3/4}}}{x \sqrt[4]{x^6+x^2}}\right)}{4\ 2^{3/4}}",1,"(-2*x*(x^2 + x^6)^(3/4)*AppellF1[5/8, 1/4, 1, 13/8, -x^4, x^4])/(5*(1 + x^4)^(3/4))","C",0
2185,1,44,162,0.0160236,"\int \frac{x^2}{\left(-1+x^4\right) \sqrt[4]{x^2+x^6}} \, dx","Integrate[x^2/((-1 + x^4)*(x^2 + x^6)^(1/4)),x]","-\frac{2 x \left(x^6+x^2\right)^{3/4} F_1\left(\frac{5}{8};\frac{1}{4},1;\frac{13}{8};-x^4,x^4\right)}{5 \left(x^4+1\right)^{3/4}}","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^6+x^2}}\right)}{4 \sqrt[4]{2}}-\frac{\tan ^{-1}\left(\frac{2^{3/4} x \sqrt[4]{x^6+x^2}}{\sqrt{2} x^2-\sqrt{x^6+x^2}}\right)}{4\ 2^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^6+x^2}}\right)}{4 \sqrt[4]{2}}+\frac{\tanh ^{-1}\left(\frac{\frac{x^2}{\sqrt[4]{2}}+\frac{\sqrt{x^6+x^2}}{2^{3/4}}}{x \sqrt[4]{x^6+x^2}}\right)}{4\ 2^{3/4}}",1,"(-2*x*(x^2 + x^6)^(3/4)*AppellF1[5/8, 1/4, 1, 13/8, -x^4, x^4])/(5*(1 + x^4)^(3/4))","C",0
2186,1,42,162,0.0194427,"\int \frac{1+x^4}{\left(-1+x^4\right) \sqrt[4]{x^2+x^6}} \, dx","Integrate[(1 + x^4)/((-1 + x^4)*(x^2 + x^6)^(1/4)),x]","-\frac{2 x \sqrt[4]{x^4+1} F_1\left(\frac{1}{8};-\frac{3}{4},1;\frac{9}{8};-x^4,x^4\right)}{\sqrt[4]{x^6+x^2}}","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^6+x^2}}\right)}{2 \sqrt[4]{2}}+\frac{\tan ^{-1}\left(\frac{2^{3/4} x \sqrt[4]{x^6+x^2}}{\sqrt{2} x^2-\sqrt{x^6+x^2}}\right)}{2\ 2^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^6+x^2}}\right)}{2 \sqrt[4]{2}}-\frac{\tanh ^{-1}\left(\frac{\frac{x^2}{\sqrt[4]{2}}+\frac{\sqrt{x^6+x^2}}{2^{3/4}}}{x \sqrt[4]{x^6+x^2}}\right)}{2\ 2^{3/4}}",1,"(-2*x*(1 + x^4)^(1/4)*AppellF1[1/8, -3/4, 1, 9/8, -x^4, x^4])/(x^2 + x^6)^(1/4)","C",0
2187,1,42,162,0.0108952,"\int \frac{1+x^4}{\left(-1+x^4\right) \sqrt[4]{x^2+x^6}} \, dx","Integrate[(1 + x^4)/((-1 + x^4)*(x^2 + x^6)^(1/4)),x]","-\frac{2 x \sqrt[4]{x^4+1} F_1\left(\frac{1}{8};-\frac{3}{4},1;\frac{9}{8};-x^4,x^4\right)}{\sqrt[4]{x^6+x^2}}","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^6+x^2}}\right)}{2 \sqrt[4]{2}}+\frac{\tan ^{-1}\left(\frac{2^{3/4} x \sqrt[4]{x^6+x^2}}{\sqrt{2} x^2-\sqrt{x^6+x^2}}\right)}{2\ 2^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^6+x^2}}\right)}{2 \sqrt[4]{2}}-\frac{\tanh ^{-1}\left(\frac{\frac{x^2}{\sqrt[4]{2}}+\frac{\sqrt{x^6+x^2}}{2^{3/4}}}{x \sqrt[4]{x^6+x^2}}\right)}{2\ 2^{3/4}}",1,"(-2*x*(1 + x^4)^(1/4)*AppellF1[1/8, -3/4, 1, 9/8, -x^4, x^4])/(x^2 + x^6)^(1/4)","C",0
2188,1,95,162,0.284173,"\int \frac{1-x^2+x^4}{\left(-1+x^4\right) \sqrt[4]{x^2+x^6}} \, dx","Integrate[(1 - x^2 + x^4)/((-1 + x^4)*(x^2 + x^6)^(1/4)),x]","-\frac{2 \sqrt[4]{x^4+1} \left(45 x F_1\left(\frac{1}{8};\frac{1}{4},1;\frac{9}{8};-x^4,x^4\right)+5 x^5 F_1\left(\frac{9}{8};\frac{1}{4},1;\frac{17}{8};-x^4,x^4\right)-9 x^3 F_1\left(\frac{5}{8};\frac{1}{4},1;\frac{13}{8};-x^4,x^4\right)\right)}{45 \sqrt[4]{x^6+x^2}}","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^6+x^2}}\right)}{4 \sqrt[4]{2}}+\frac{3 \tan ^{-1}\left(\frac{2^{3/4} x \sqrt[4]{x^6+x^2}}{\sqrt{2} x^2-\sqrt{x^6+x^2}}\right)}{4\ 2^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^6+x^2}}\right)}{4 \sqrt[4]{2}}-\frac{3 \tanh ^{-1}\left(\frac{\frac{x^2}{\sqrt[4]{2}}+\frac{\sqrt{x^6+x^2}}{2^{3/4}}}{x \sqrt[4]{x^6+x^2}}\right)}{4\ 2^{3/4}}",1,"(-2*(1 + x^4)^(1/4)*(45*x*AppellF1[1/8, 1/4, 1, 9/8, -x^4, x^4] - 9*x^3*AppellF1[5/8, 1/4, 1, 13/8, -x^4, x^4] + 5*x^5*AppellF1[9/8, 1/4, 1, 17/8, -x^4, x^4]))/(45*(x^2 + x^6)^(1/4))","C",0
2189,1,95,162,0.1810533,"\int \frac{1-x^2+x^4}{\left(-1+x^4\right) \sqrt[4]{x^2+x^6}} \, dx","Integrate[(1 - x^2 + x^4)/((-1 + x^4)*(x^2 + x^6)^(1/4)),x]","-\frac{2 \sqrt[4]{x^4+1} \left(45 x F_1\left(\frac{1}{8};\frac{1}{4},1;\frac{9}{8};-x^4,x^4\right)+5 x^5 F_1\left(\frac{9}{8};\frac{1}{4},1;\frac{17}{8};-x^4,x^4\right)-9 x^3 F_1\left(\frac{5}{8};\frac{1}{4},1;\frac{13}{8};-x^4,x^4\right)\right)}{45 \sqrt[4]{x^6+x^2}}","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^6+x^2}}\right)}{4 \sqrt[4]{2}}+\frac{3 \tan ^{-1}\left(\frac{2^{3/4} x \sqrt[4]{x^6+x^2}}{\sqrt{2} x^2-\sqrt{x^6+x^2}}\right)}{4\ 2^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^6+x^2}}\right)}{4 \sqrt[4]{2}}-\frac{3 \tanh ^{-1}\left(\frac{\frac{x^2}{\sqrt[4]{2}}+\frac{\sqrt{x^6+x^2}}{2^{3/4}}}{x \sqrt[4]{x^6+x^2}}\right)}{4\ 2^{3/4}}",1,"(-2*(1 + x^4)^(1/4)*(45*x*AppellF1[1/8, 1/4, 1, 9/8, -x^4, x^4] - 9*x^3*AppellF1[5/8, 1/4, 1, 13/8, -x^4, x^4] + 5*x^5*AppellF1[9/8, 1/4, 1, 17/8, -x^4, x^4]))/(45*(x^2 + x^6)^(1/4))","C",0
2190,1,95,162,0.1972967,"\int \frac{1+x^2+x^4}{\left(-1+x^4\right) \sqrt[4]{x^2+x^6}} \, dx","Integrate[(1 + x^2 + x^4)/((-1 + x^4)*(x^2 + x^6)^(1/4)),x]","-\frac{2 \sqrt[4]{x^4+1} \left(45 x F_1\left(\frac{1}{8};\frac{1}{4},1;\frac{9}{8};-x^4,x^4\right)+5 x^5 F_1\left(\frac{9}{8};\frac{1}{4},1;\frac{17}{8};-x^4,x^4\right)+9 x^3 F_1\left(\frac{5}{8};\frac{1}{4},1;\frac{13}{8};-x^4,x^4\right)\right)}{45 \sqrt[4]{x^6+x^2}}","-\frac{3 \tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^6+x^2}}\right)}{4 \sqrt[4]{2}}+\frac{\tan ^{-1}\left(\frac{2^{3/4} x \sqrt[4]{x^6+x^2}}{\sqrt{2} x^2-\sqrt{x^6+x^2}}\right)}{4\ 2^{3/4}}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^6+x^2}}\right)}{4 \sqrt[4]{2}}-\frac{\tanh ^{-1}\left(\frac{\frac{x^2}{\sqrt[4]{2}}+\frac{\sqrt{x^6+x^2}}{2^{3/4}}}{x \sqrt[4]{x^6+x^2}}\right)}{4\ 2^{3/4}}",1,"(-2*(1 + x^4)^(1/4)*(45*x*AppellF1[1/8, 1/4, 1, 9/8, -x^4, x^4] + 9*x^3*AppellF1[5/8, 1/4, 1, 13/8, -x^4, x^4] + 5*x^5*AppellF1[9/8, 1/4, 1, 17/8, -x^4, x^4]))/(45*(x^2 + x^6)^(1/4))","C",0
2191,1,95,162,0.1951939,"\int \frac{1+x^2+x^4}{\left(-1+x^4\right) \sqrt[4]{x^2+x^6}} \, dx","Integrate[(1 + x^2 + x^4)/((-1 + x^4)*(x^2 + x^6)^(1/4)),x]","-\frac{2 \sqrt[4]{x^4+1} \left(45 x F_1\left(\frac{1}{8};\frac{1}{4},1;\frac{9}{8};-x^4,x^4\right)+5 x^5 F_1\left(\frac{9}{8};\frac{1}{4},1;\frac{17}{8};-x^4,x^4\right)+9 x^3 F_1\left(\frac{5}{8};\frac{1}{4},1;\frac{13}{8};-x^4,x^4\right)\right)}{45 \sqrt[4]{x^6+x^2}}","-\frac{3 \tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^6+x^2}}\right)}{4 \sqrt[4]{2}}+\frac{\tan ^{-1}\left(\frac{2^{3/4} x \sqrt[4]{x^6+x^2}}{\sqrt{2} x^2-\sqrt{x^6+x^2}}\right)}{4\ 2^{3/4}}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^6+x^2}}\right)}{4 \sqrt[4]{2}}-\frac{\tanh ^{-1}\left(\frac{\frac{x^2}{\sqrt[4]{2}}+\frac{\sqrt{x^6+x^2}}{2^{3/4}}}{x \sqrt[4]{x^6+x^2}}\right)}{4\ 2^{3/4}}",1,"(-2*(1 + x^4)^(1/4)*(45*x*AppellF1[1/8, 1/4, 1, 9/8, -x^4, x^4] + 9*x^3*AppellF1[5/8, 1/4, 1, 13/8, -x^4, x^4] + 5*x^5*AppellF1[9/8, 1/4, 1, 17/8, -x^4, x^4]))/(45*(x^2 + x^6)^(1/4))","C",0
2192,0,0,162,0.3350608,"\int \frac{\left(-4+x^3\right) \left(-2+x^3\right) \left(-1+x^3\right)^{2/3}}{x^6 \left(-2+x^3+x^6\right)} \, dx","Integrate[((-4 + x^3)*(-2 + x^3)*(-1 + x^3)^(2/3))/(x^6*(-2 + x^3 + x^6)),x]","\int \frac{\left(-4+x^3\right) \left(-2+x^3\right) \left(-1+x^3\right)^{2/3}}{x^6 \left(-2+x^3+x^6\right)} \, dx","-\sqrt[3]{\frac{2}{3}} \log \left(\sqrt[3]{2} 3^{2/3} \sqrt[3]{x^3-1}-3 x\right)+\sqrt[3]{2} \sqrt[6]{3} \tan ^{-1}\left(\frac{3^{5/6} x}{2 \sqrt[3]{2} \sqrt[3]{x^3-1}+\sqrt[3]{3} x}\right)+\frac{\left(x^3-1\right)^{2/3} \left(8-13 x^3\right)}{10 x^5}+\frac{\log \left(\sqrt[3]{2} 3^{2/3} \sqrt[3]{x^3-1} x+2^{2/3} \sqrt[3]{3} \left(x^3-1\right)^{2/3}+3 x^2\right)}{2^{2/3} \sqrt[3]{3}}",1,"Integrate[((-4 + x^3)*(-2 + x^3)*(-1 + x^3)^(2/3))/(x^6*(-2 + x^3 + x^6)), x]","F",-1
2193,0,0,162,1.4820347,"\int \frac{\left(-1+x^4\right) \sqrt[4]{x^2+x^6}}{1+x^8} \, dx","Integrate[((-1 + x^4)*(x^2 + x^6)^(1/4))/(1 + x^8),x]","\int \frac{\left(-1+x^4\right) \sqrt[4]{x^2+x^6}}{1+x^8} \, dx","\frac{\tan ^{-1}\left(\frac{\sqrt[8]{2} x}{\sqrt[4]{x^6+x^2}}\right)}{2\ 2^{3/8}}+\frac{\tan ^{-1}\left(\frac{2^{5/8} x \sqrt[4]{x^6+x^2}}{\sqrt[4]{2} x^2-\sqrt{x^6+x^2}}\right)}{2\ 2^{7/8}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{2} x}{\sqrt[4]{x^6+x^2}}\right)}{2\ 2^{3/8}}+\frac{\tanh ^{-1}\left(\frac{\frac{x^2}{2^{3/8}}+\frac{\sqrt{x^6+x^2}}{2^{5/8}}}{x \sqrt[4]{x^6+x^2}}\right)}{2\ 2^{7/8}}",1,"Integrate[((-1 + x^4)*(x^2 + x^6)^(1/4))/(1 + x^8), x]","F",-1
2194,0,0,162,1.0285548,"\int \frac{\left(-1+x^4\right) \sqrt[4]{x^2+x^6}}{1+x^8} \, dx","Integrate[((-1 + x^4)*(x^2 + x^6)^(1/4))/(1 + x^8),x]","\int \frac{\left(-1+x^4\right) \sqrt[4]{x^2+x^6}}{1+x^8} \, dx","\frac{\tan ^{-1}\left(\frac{\sqrt[8]{2} x}{\sqrt[4]{x^6+x^2}}\right)}{2\ 2^{3/8}}+\frac{\tan ^{-1}\left(\frac{2^{5/8} x \sqrt[4]{x^6+x^2}}{\sqrt[4]{2} x^2-\sqrt{x^6+x^2}}\right)}{2\ 2^{7/8}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{2} x}{\sqrt[4]{x^6+x^2}}\right)}{2\ 2^{3/8}}+\frac{\tanh ^{-1}\left(\frac{\frac{x^2}{2^{3/8}}+\frac{\sqrt{x^6+x^2}}{2^{5/8}}}{x \sqrt[4]{x^6+x^2}}\right)}{2\ 2^{7/8}}",1,"Integrate[((-1 + x^4)*(x^2 + x^6)^(1/4))/(1 + x^8), x]","F",-1
2195,0,0,162,1.321475,"\int \frac{-1+x^8}{\sqrt[4]{x^2+x^6} \left(1+x^8\right)} \, dx","Integrate[(-1 + x^8)/((x^2 + x^6)^(1/4)*(1 + x^8)),x]","\int \frac{-1+x^8}{\sqrt[4]{x^2+x^6} \left(1+x^8\right)} \, dx","-\frac{\tan ^{-1}\left(\frac{\sqrt[8]{2} x}{\sqrt[4]{x^6+x^2}}\right)}{2 \sqrt[8]{2}}+\frac{\tan ^{-1}\left(\frac{2^{5/8} x \sqrt[4]{x^6+x^2}}{\sqrt[4]{2} x^2-\sqrt{x^6+x^2}}\right)}{2\ 2^{5/8}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{2} x}{\sqrt[4]{x^6+x^2}}\right)}{2 \sqrt[8]{2}}-\frac{\tanh ^{-1}\left(\frac{\frac{x^2}{2^{3/8}}+\frac{\sqrt{x^6+x^2}}{2^{5/8}}}{x \sqrt[4]{x^6+x^2}}\right)}{2\ 2^{5/8}}",1,"Integrate[(-1 + x^8)/((x^2 + x^6)^(1/4)*(1 + x^8)), x]","F",-1
2196,0,0,162,0.4975684,"\int \frac{-1+x^8}{\sqrt[4]{x^2+x^6} \left(1+x^8\right)} \, dx","Integrate[(-1 + x^8)/((x^2 + x^6)^(1/4)*(1 + x^8)),x]","\int \frac{-1+x^8}{\sqrt[4]{x^2+x^6} \left(1+x^8\right)} \, dx","-\frac{\tan ^{-1}\left(\frac{\sqrt[8]{2} x}{\sqrt[4]{x^6+x^2}}\right)}{2 \sqrt[8]{2}}+\frac{\tan ^{-1}\left(\frac{2^{5/8} x \sqrt[4]{x^6+x^2}}{\sqrt[4]{2} x^2-\sqrt{x^6+x^2}}\right)}{2\ 2^{5/8}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{2} x}{\sqrt[4]{x^6+x^2}}\right)}{2 \sqrt[8]{2}}-\frac{\tanh ^{-1}\left(\frac{\frac{x^2}{2^{3/8}}+\frac{\sqrt{x^6+x^2}}{2^{5/8}}}{x \sqrt[4]{x^6+x^2}}\right)}{2\ 2^{5/8}}",1,"Integrate[(-1 + x^8)/((x^2 + x^6)^(1/4)*(1 + x^8)), x]","F",-1
2197,0,0,162,0.8908562,"\int \frac{x^5 \left(8-7 (1+k) x+6 k x^2\right)}{((1-x) x (1-k x))^{2/3} \left(-b+b (1+k) x-b k x^2+x^8\right)} \, dx","Integrate[(x^5*(8 - 7*(1 + k)*x + 6*k*x^2))/(((1 - x)*x*(1 - k*x))^(2/3)*(-b + b*(1 + k)*x - b*k*x^2 + x^8)),x]","\int \frac{x^5 \left(8-7 (1+k) x+6 k x^2\right)}{((1-x) x (1-k x))^{2/3} \left(-b+b (1+k) x-b k x^2+x^8\right)} \, dx","-\frac{\log \left(b^{2/3} \left(k x^3+(-k-1) x^2+x\right)^{2/3}+\sqrt[3]{b} x^3 \sqrt[3]{k x^3+(-k-1) x^2+x}+x^6\right)}{2 \sqrt[3]{b}}+\frac{\log \left(x^3-\sqrt[3]{b} \sqrt[3]{k x^3+(-k-1) x^2+x}\right)}{\sqrt[3]{b}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x^3}{2 \sqrt[3]{b} \sqrt[3]{k x^3+(-k-1) x^2+x}+x^3}\right)}{\sqrt[3]{b}}",1,"Integrate[(x^5*(8 - 7*(1 + k)*x + 6*k*x^2))/(((1 - x)*x*(1 - k*x))^(2/3)*(-b + b*(1 + k)*x - b*k*x^2 + x^8)), x]","F",-1
2198,1,561,162,0.8647942,"\int \frac{-2 b-a x^4+2 x^8}{\sqrt[4]{-b+a x^4} \left(-2 b-a x^4+x^8\right)} \, dx","Integrate[(-2*b - a*x^4 + 2*x^8)/((-b + a*x^4)^(1/4)*(-2*b - a*x^4 + x^8)),x]","-\frac{\left(a-\frac{a^2+4 b}{\sqrt{a^2+8 b}}\right) \tan ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+8 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+8 b}} \sqrt[4]{a x^4-b}}\right)}{2 \left(a-\sqrt{a^2+8 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+8 b}+a^2-2 b}}-\frac{\left(\frac{a^2+4 b}{\sqrt{a^2+8 b}}+a\right) \tan ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+8 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+8 b}+a} \sqrt[4]{a x^4-b}}\right)}{2 \left(\sqrt{a^2+8 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+8 b}+a^2-2 b}}-\frac{\left(a-\frac{a^2+4 b}{\sqrt{a^2+8 b}}\right) \tanh ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+8 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+8 b}} \sqrt[4]{a x^4-b}}\right)}{2 \left(a-\sqrt{a^2+8 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+8 b}+a^2-2 b}}-\frac{\left(\frac{a^2+4 b}{\sqrt{a^2+8 b}}+a\right) \tanh ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+8 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+8 b}+a} \sqrt[4]{a x^4-b}}\right)}{2 \left(\sqrt{a^2+8 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+8 b}+a^2-2 b}}+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{\sqrt[4]{a}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{\sqrt[4]{a}}","-\frac{1}{4} \text{RootSum}\left[2 \text{$\#$1}^8-5 \text{$\#$1}^4 a+3 a^2-b\&,\frac{2 \text{$\#$1}^4 \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)-2 \text{$\#$1}^4 \log (x)-3 a \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+3 a \log (x)}{5 \text{$\#$1} a-4 \text{$\#$1}^5}\&\right]+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{\sqrt[4]{a}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{\sqrt[4]{a}}",1,"ArcTan[(a^(1/4)*x)/(-b + a*x^4)^(1/4)]/a^(1/4) - ((a - (a^2 + 4*b)/Sqrt[a^2 + 8*b])*ArcTan[((a^2 - 2*b - a*Sqrt[a^2 + 8*b])^(1/4)*x)/((a - Sqrt[a^2 + 8*b])^(1/4)*(-b + a*x^4)^(1/4))])/(2*(a - Sqrt[a^2 + 8*b])^(3/4)*(a^2 - 2*b - a*Sqrt[a^2 + 8*b])^(1/4)) - ((a + (a^2 + 4*b)/Sqrt[a^2 + 8*b])*ArcTan[((a^2 - 2*b + a*Sqrt[a^2 + 8*b])^(1/4)*x)/((a + Sqrt[a^2 + 8*b])^(1/4)*(-b + a*x^4)^(1/4))])/(2*(a + Sqrt[a^2 + 8*b])^(3/4)*(a^2 - 2*b + a*Sqrt[a^2 + 8*b])^(1/4)) + ArcTanh[(a^(1/4)*x)/(-b + a*x^4)^(1/4)]/a^(1/4) - ((a - (a^2 + 4*b)/Sqrt[a^2 + 8*b])*ArcTanh[((a^2 - 2*b - a*Sqrt[a^2 + 8*b])^(1/4)*x)/((a - Sqrt[a^2 + 8*b])^(1/4)*(-b + a*x^4)^(1/4))])/(2*(a - Sqrt[a^2 + 8*b])^(3/4)*(a^2 - 2*b - a*Sqrt[a^2 + 8*b])^(1/4)) - ((a + (a^2 + 4*b)/Sqrt[a^2 + 8*b])*ArcTanh[((a^2 - 2*b + a*Sqrt[a^2 + 8*b])^(1/4)*x)/((a + Sqrt[a^2 + 8*b])^(1/4)*(-b + a*x^4)^(1/4))])/(2*(a + Sqrt[a^2 + 8*b])^(3/4)*(a^2 - 2*b + a*Sqrt[a^2 + 8*b])^(1/4))","B",1
2199,1,81,162,0.1856409,"\int \frac{\sqrt{b+\sqrt{b^2+a x^2}}}{x^4} \, dx","Integrate[Sqrt[b + Sqrt[b^2 + a*x^2]]/x^4,x]","\frac{\sqrt{\sqrt{a x^2+b^2}+b} \left(\left(\sqrt{a x^2+b^2}+b\right) \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{b-\sqrt{b^2+a x^2}}{2 b}\right)-6 b\right)}{12 b x^3}","\frac{\sqrt{\sqrt{a x^2+b^2}+b} \left(\sqrt{a} \left(2 b \sqrt{a x^2+b^2}-10 b^2\right)-3 a^{3/2} x^2\right)}{24 \sqrt{a} b^2 x^3}-\frac{a^{3/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{2} \sqrt{b} \sqrt{\sqrt{a x^2+b^2}+b}}-\frac{\sqrt{\sqrt{a x^2+b^2}+b}}{\sqrt{2} \sqrt{b}}\right)}{4 \sqrt{2} b^{5/2}}",1,"(Sqrt[b + Sqrt[b^2 + a*x^2]]*(-6*b + (b + Sqrt[b^2 + a*x^2])*Hypergeometric2F1[-3/2, 1, -1/2, (b - Sqrt[b^2 + a*x^2])/(2*b)]))/(12*b*x^3)","C",1
2200,1,61,162,0.2017238,"\int \frac{\sqrt{b+\sqrt{b^2+a x^2}}}{x^4 \sqrt{b^2+a x^2}} \, dx","Integrate[Sqrt[b + Sqrt[b^2 + a*x^2]]/(x^4*Sqrt[b^2 + a*x^2]),x]","-\frac{\left(\sqrt{a x^2+b^2}+b\right)^{3/2} \, _2F_1\left(-\frac{3}{2},2;-\frac{1}{2};\frac{b-\sqrt{b^2+a x^2}}{2 b}\right)}{6 b^2 x^3}","\frac{5 a^{3/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{2} \sqrt{b} \sqrt{\sqrt{a x^2+b^2}+b}}-\frac{\sqrt{\sqrt{a x^2+b^2}+b}}{\sqrt{2} \sqrt{b}}\right)}{4 \sqrt{2} b^{7/2}}+\frac{\sqrt{\sqrt{a x^2+b^2}+b} \left(15 a^{3/2} x^2+\sqrt{a} \left(2 b^2-10 b \sqrt{a x^2+b^2}\right)\right)}{24 \sqrt{a} b^3 x^3}",1,"-1/6*((b + Sqrt[b^2 + a*x^2])^(3/2)*Hypergeometric2F1[-3/2, 2, -1/2, (b - Sqrt[b^2 + a*x^2])/(2*b)])/(b^2*x^3)","C",1
2201,1,155,163,11.3525138,"\int \frac{1}{\sqrt[3]{x+x^3} \left(-1+x^6\right)} \, dx","Integrate[1/((x + x^3)^(1/3)*(-1 + x^6)),x]","\frac{\sqrt[3]{\frac{1}{x^2}+1} x \left(4 \text{RootSum}\left[\text{$\#$1}^6-\text{$\#$1}^3+1\&,\frac{\log \left(\sqrt[3]{\frac{1}{x^2}+1}-\text{$\#$1}\right)}{\text{$\#$1}}\&\right]+2^{2/3} \left(2 \log \left(2-2^{2/3} \sqrt[3]{\frac{1}{x^2}+1}\right)-\log \left(\sqrt[3]{2} \left(\frac{1}{x^2}+1\right)^{2/3}+2^{2/3} \sqrt[3]{\frac{1}{x^2}+1}+2\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{\frac{1}{x^2}+1}+1}{\sqrt{3}}\right)\right)\right)}{24 \sqrt[3]{x^3+x}}","\frac{1}{6} \text{RootSum}\left[\text{$\#$1}^6-\text{$\#$1}^3+1\&,\frac{\log \left(\sqrt[3]{x^3+x}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]+\frac{\log \left(2^{2/3} \sqrt[3]{x^3+x}-2 x\right)}{6 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^3+x}+x}\right)}{2 \sqrt[3]{2} \sqrt{3}}-\frac{\log \left(2^{2/3} \sqrt[3]{x^3+x} x+\sqrt[3]{2} \left(x^3+x\right)^{2/3}+2 x^2\right)}{12 \sqrt[3]{2}}",1,"((1 + x^(-2))^(1/3)*x*(2^(2/3)*(2*Sqrt[3]*ArcTan[(1 + 2^(2/3)*(1 + x^(-2))^(1/3))/Sqrt[3]] + 2*Log[2 - 2^(2/3)*(1 + x^(-2))^(1/3)] - Log[2 + 2^(2/3)*(1 + x^(-2))^(1/3) + 2^(1/3)*(1 + x^(-2))^(2/3)]) + 4*RootSum[1 - #1^3 + #1^6 & , Log[(1 + x^(-2))^(1/3) - #1]/#1 & ]))/(24*(x + x^3)^(1/3))","A",1
2202,1,155,163,0.252585,"\int \frac{1}{\sqrt[3]{x+x^3} \left(-1+x^6\right)} \, dx","Integrate[1/((x + x^3)^(1/3)*(-1 + x^6)),x]","\frac{\sqrt[3]{\frac{1}{x^2}+1} x \left(4 \text{RootSum}\left[\text{$\#$1}^6-\text{$\#$1}^3+1\&,\frac{\log \left(\sqrt[3]{\frac{1}{x^2}+1}-\text{$\#$1}\right)}{\text{$\#$1}}\&\right]+2^{2/3} \left(2 \log \left(2-2^{2/3} \sqrt[3]{\frac{1}{x^2}+1}\right)-\log \left(\sqrt[3]{2} \left(\frac{1}{x^2}+1\right)^{2/3}+2^{2/3} \sqrt[3]{\frac{1}{x^2}+1}+2\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{\frac{1}{x^2}+1}+1}{\sqrt{3}}\right)\right)\right)}{24 \sqrt[3]{x^3+x}}","\frac{1}{6} \text{RootSum}\left[\text{$\#$1}^6-\text{$\#$1}^3+1\&,\frac{\log \left(\sqrt[3]{x^3+x}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]+\frac{\log \left(2^{2/3} \sqrt[3]{x^3+x}-2 x\right)}{6 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^3+x}+x}\right)}{2 \sqrt[3]{2} \sqrt{3}}-\frac{\log \left(2^{2/3} \sqrt[3]{x^3+x} x+\sqrt[3]{2} \left(x^3+x\right)^{2/3}+2 x^2\right)}{12 \sqrt[3]{2}}",1,"((1 + x^(-2))^(1/3)*x*(2^(2/3)*(2*Sqrt[3]*ArcTan[(1 + 2^(2/3)*(1 + x^(-2))^(1/3))/Sqrt[3]] + 2*Log[2 - 2^(2/3)*(1 + x^(-2))^(1/3)] - Log[2 + 2^(2/3)*(1 + x^(-2))^(1/3) + 2^(1/3)*(1 + x^(-2))^(2/3)]) + 4*RootSum[1 - #1^3 + #1^6 & , Log[(1 + x^(-2))^(1/3) - #1]/#1 & ]))/(24*(x + x^3)^(1/3))","A",1
2203,1,326,163,0.3398807,"\int \frac{\left(1+x^3\right) \sqrt{-2-x^3+x^6}}{x^4 \left(-1-2 x^3+x^6\right)} \, dx","Integrate[((1 + x^3)*Sqrt[-2 - x^3 + x^6])/(x^4*(-1 - 2*x^3 + x^6)),x]","\frac{1}{12} \left(\frac{4 \sqrt{x^6-x^3-2}}{x^3}+3 \sqrt{2} \tan ^{-1}\left(\frac{x^3+4}{2 \sqrt{2} \sqrt{x^6-x^3-2}}\right)-2\ 2^{3/4} \tan ^{-1}\left(\frac{\left(2 \sqrt{2}-1\right) x^3-\sqrt{2}+5}{2 \sqrt[4]{2} \sqrt{x^6-x^3-2}}\right)-2 \sqrt[4]{2} \tan ^{-1}\left(\frac{\left(2 \sqrt{2}-1\right) x^3-\sqrt{2}+5}{2 \sqrt[4]{2} \sqrt{x^6-x^3-2}}\right)-6 \tanh ^{-1}\left(\frac{1-2 x^3}{2 \sqrt{x^6-x^3-2}}\right)-6 \tanh ^{-1}\left(\frac{2 x^3-1}{2 \sqrt{x^6-x^3-2}}\right)+2\ 2^{3/4} \tanh ^{-1}\left(\frac{-\left(\left(1+2 \sqrt{2}\right) x^3\right)+\sqrt{2}+5}{2 \sqrt[4]{2} \sqrt{x^6-x^3-2}}\right)-2 \sqrt[4]{2} \tanh ^{-1}\left(\frac{-\left(\left(1+2 \sqrt{2}\right) x^3\right)+\sqrt{2}+5}{2 \sqrt[4]{2} \sqrt{x^6-x^3-2}}\right)\right)","\frac{\sqrt{x^6-x^3-2}}{3 x^3}-\frac{\tan ^{-1}\left(\frac{\sqrt{x^6-x^3-2}}{\sqrt{2} \left(x^3+1\right)}\right)}{\sqrt{2}}+\frac{1}{3} \sqrt{4+3 \sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{3 \sqrt{2}-4} \sqrt{x^6-x^3-2}}{x^3+1}\right)-\frac{1}{3} \sqrt{3 \sqrt{2}-4} \tanh ^{-1}\left(\frac{\sqrt{4+3 \sqrt{2}} \sqrt{x^6-x^3-2}}{x^3+1}\right)",1,"((4*Sqrt[-2 - x^3 + x^6])/x^3 + 3*Sqrt[2]*ArcTan[(4 + x^3)/(2*Sqrt[2]*Sqrt[-2 - x^3 + x^6])] - 2*2^(1/4)*ArcTan[(5 - Sqrt[2] + (-1 + 2*Sqrt[2])*x^3)/(2*2^(1/4)*Sqrt[-2 - x^3 + x^6])] - 2*2^(3/4)*ArcTan[(5 - Sqrt[2] + (-1 + 2*Sqrt[2])*x^3)/(2*2^(1/4)*Sqrt[-2 - x^3 + x^6])] - 6*ArcTanh[(1 - 2*x^3)/(2*Sqrt[-2 - x^3 + x^6])] - 6*ArcTanh[(-1 + 2*x^3)/(2*Sqrt[-2 - x^3 + x^6])] - 2*2^(1/4)*ArcTanh[(5 + Sqrt[2] - (1 + 2*Sqrt[2])*x^3)/(2*2^(1/4)*Sqrt[-2 - x^3 + x^6])] + 2*2^(3/4)*ArcTanh[(5 + Sqrt[2] - (1 + 2*Sqrt[2])*x^3)/(2*2^(1/4)*Sqrt[-2 - x^3 + x^6])])/12","A",1
2204,0,0,163,0.213556,"\int \frac{x^2 \left(-4+7 x^3\right)}{\sqrt[3]{-x+x^4} \left(-1-x^4+x^7\right)} \, dx","Integrate[(x^2*(-4 + 7*x^3))/((-x + x^4)^(1/3)*(-1 - x^4 + x^7)),x]","\int \frac{x^2 \left(-4+7 x^3\right)}{\sqrt[3]{-x+x^4} \left(-1-x^4+x^7\right)} \, dx","2 \tanh ^{-1}\left(1-2 x \sqrt[3]{x^4-x}\right)-\sqrt{3} \tan ^{-1}\left(\frac{3 \sqrt{3} x \sqrt[3]{x^4-x}-3 x^2 \sqrt[3]{x^4-x}}{-3 \sqrt[3]{x^4-x} x+\sqrt{3} \sqrt[3]{x^4-x} x^2+2 \sqrt{3} x-6}\right)-\tanh ^{-1}\left(\frac{\sqrt[3]{x^4-x} x+1}{\sqrt[3]{x^4-x} x+2 \left(x^4-x\right)^{2/3} x^2+1}\right)",1,"Integrate[(x^2*(-4 + 7*x^3))/((-x + x^4)^(1/3)*(-1 - x^4 + x^7)), x]","F",-1
2205,0,0,163,3.6065321,"\int \frac{a x^4+x^8}{\sqrt[4]{-b x^2+a x^4} \left(-b+2 a x^4+x^8\right)} \, dx","Integrate[(a*x^4 + x^8)/((-(b*x^2) + a*x^4)^(1/4)*(-b + 2*a*x^4 + x^8)),x]","\int \frac{a x^4+x^8}{\sqrt[4]{-b x^2+a x^4} \left(-b+2 a x^4+x^8\right)} \, dx","\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^{16}-4 \text{$\#$1}^{12} a+6 \text{$\#$1}^8 a^2-2 \text{$\#$1}^8 a b-4 \text{$\#$1}^4 a^3+4 \text{$\#$1}^4 a^2 b+a^4-2 a^3 b-b^3\&,\frac{\log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)}{\sqrt[4]{a}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)}{\sqrt[4]{a}}",1,"Integrate[(a*x^4 + x^8)/((-(b*x^2) + a*x^4)^(1/4)*(-b + 2*a*x^4 + x^8)), x]","F",-1
2206,0,0,163,2.7342164,"\int \frac{a x^4+x^8}{\sqrt[4]{-b x^2+a x^4} \left(-b+2 a x^4+x^8\right)} \, dx","Integrate[(a*x^4 + x^8)/((-(b*x^2) + a*x^4)^(1/4)*(-b + 2*a*x^4 + x^8)),x]","\int \frac{a x^4+x^8}{\sqrt[4]{-b x^2+a x^4} \left(-b+2 a x^4+x^8\right)} \, dx","\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^{16}-4 \text{$\#$1}^{12} a+6 \text{$\#$1}^8 a^2-2 \text{$\#$1}^8 a b-4 \text{$\#$1}^4 a^3+4 \text{$\#$1}^4 a^2 b+a^4-2 a^3 b-b^3\&,\frac{\log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)}{\sqrt[4]{a}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)}{\sqrt[4]{a}}",1,"Integrate[(a*x^4 + x^8)/((-(b*x^2) + a*x^4)^(1/4)*(-b + 2*a*x^4 + x^8)), x]","F",-1
2207,1,11852,163,7.7876038,"\int \frac{\sqrt{1+2 x^2-x^4} \left(-1+x^4\right) \left(1+x^4\right)}{\left(-1-x^2+x^4\right) \left(1+3 x^2-x^4-3 x^6+x^8\right)} \, dx","Integrate[(Sqrt[1 + 2*x^2 - x^4]*(-1 + x^4)*(1 + x^4))/((-1 - x^2 + x^4)*(1 + 3*x^2 - x^4 - 3*x^6 + x^8)),x]","\text{Result too large to show}","-\sqrt{\frac{1}{10} \left(1+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}} x \sqrt{-x^4+2 x^2+1}}{x^4-2 x^2-1}\right)-\tanh ^{-1}\left(\frac{x \sqrt{-x^4+2 x^2+1}}{x^4-2 x^2-1}\right)+\sqrt{\frac{1}{10} \left(\sqrt{5}-1\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{2}+\frac{\sqrt{5}}{2}} x \sqrt{-x^4+2 x^2+1}}{x^4-2 x^2-1}\right)",1,"Result too large to show","C",0
2208,1,198,163,0.3453015,"\int \frac{1}{\left(-1+x^2\right) \sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[1/((-1 + x^2)*Sqrt[x + Sqrt[1 + x^2]]),x]","-\frac{\frac{\left(\sqrt{2}-2\right) \tan ^{-1}\left(\frac{1}{\sqrt{\sqrt{2}-1} \sqrt{\sqrt{x^2+1}+x}}\right)}{\sqrt{\sqrt{2}-1}}+\frac{\left(2+\sqrt{2}\right) \tan ^{-1}\left(\frac{1}{\sqrt{1+\sqrt{2}} \sqrt{\sqrt{x^2+1}+x}}\right)}{\sqrt{1+\sqrt{2}}}-\frac{\left(\sqrt{2}-2\right) \tanh ^{-1}\left(\frac{1}{\sqrt{\sqrt{2}-1} \sqrt{\sqrt{x^2+1}+x}}\right)}{\sqrt{\sqrt{2}-1}}-\frac{\left(2+\sqrt{2}\right) \tanh ^{-1}\left(\frac{1}{\sqrt{1+\sqrt{2}} \sqrt{\sqrt{x^2+1}+x}}\right)}{\sqrt{1+\sqrt{2}}}}{\sqrt{2}}","\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{\sqrt{2}-1}}\right)-\sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{1+\sqrt{2}}}\right)+\sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{\sqrt{2}-1}}\right)-\sqrt{\sqrt{2}-1} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{1+\sqrt{2}}}\right)",1,"-((((-2 + Sqrt[2])*ArcTan[1/(Sqrt[-1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]])])/Sqrt[-1 + Sqrt[2]] + ((2 + Sqrt[2])*ArcTan[1/(Sqrt[1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]])])/Sqrt[1 + Sqrt[2]] - ((-2 + Sqrt[2])*ArcTanh[1/(Sqrt[-1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]])])/Sqrt[-1 + Sqrt[2]] - ((2 + Sqrt[2])*ArcTanh[1/(Sqrt[1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]])])/Sqrt[1 + Sqrt[2]])/Sqrt[2])","A",1
2209,1,11560,163,21.9214442,"\int \frac{\sqrt{-\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}}{\sqrt{a x^2+b x \sqrt{-\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}}} \, dx","Integrate[Sqrt[-(a/b^2) + (a^2*x^2)/b^2]/Sqrt[a*x^2 + b*x*Sqrt[-(a/b^2) + (a^2*x^2)/b^2]],x]","\text{Result too large to show}","\frac{1}{2} x \sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}} \sqrt{b x \sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}}+a x^2}+\frac{\left(3-2 a x^2\right) \sqrt{b x \sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}}+a x^2}}{4 b}+\frac{5 \tanh ^{-1}\left(\sqrt{2} \sqrt{b x \sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}}+a x^2}\right)}{4 \sqrt{2} b}",1,"Result too large to show","B",1
2210,1,714,163,4.602981,"\int \sqrt{-\frac{a}{b^2}+\frac{a^2 x^2}{b^2}} \sqrt{a x^2+b x \sqrt{-\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}} \, dx","Integrate[Sqrt[-(a/b^2) + (a^2*x^2)/b^2]*Sqrt[a*x^2 + b*x*Sqrt[-(a/b^2) + (a^2*x^2)/b^2]],x]","\frac{\left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right)^6 \left(b x \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x^2-1\right) \left(2 b x \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+2 a x^2-1\right)^2 \left(12 \sqrt{a} x \left(4 a^2 x^3+a x \left(4 b x \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}-3\right)-b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}\right) \tanh ^{-1}\left(\frac{\sqrt{\left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right)^2+a}}{\sqrt{a}}\right)+\sqrt{2} x \sqrt{a x \left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right)} \left(32 a^3 x^5+16 a^2 x^3 \left(2 b x \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}-5\right)-a x \left(64 b x \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}-37\right)+9 b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}\right)-3 \sqrt{x \left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right)} \sqrt{a x \left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right)} \left(2 b x \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+2 a x^2-1\right) \tanh ^{-1}\left(\sqrt{2} \sqrt{x \left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right)}\right)\right)}{24 \sqrt{2} a^2 b^2 \sqrt{\frac{a \left(a x^2-1\right)}{b^2}} \sqrt{x \left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right)} \sqrt{a x \left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right)} \left(4096 a^7 x^{13}+1024 a^6 x^{11} \left(4 b x \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}-13\right)-256 a^5 x^9 \left(44 b x \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}-65\right)+768 a^4 x^7 \left(15 b x \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}-13\right)-224 a^3 x^5 \left(24 b x \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}-13\right)+28 a^2 x^3 \left(40 b x \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}-13\right)-a x \left(84 b x \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}-13\right)+b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}\right)}","\frac{5}{12} x \sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}} \sqrt{b x \sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}}+a x^2}+\frac{\left(-2 a x^2-9\right) \sqrt{b x \sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}}+a x^2}}{24 b}+\frac{3 \tanh ^{-1}\left(\sqrt{2} \sqrt{b x \sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}}+a x^2}\right)}{8 \sqrt{2} b}",1,"((a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2])^6*(-1 + a*x^2 + b*x*Sqrt[(a*(-1 + a*x^2))/b^2])*(-1 + 2*a*x^2 + 2*b*x*Sqrt[(a*(-1 + a*x^2))/b^2])^2*(Sqrt[2]*x*Sqrt[a*x*(a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2])]*(32*a^3*x^5 + 9*b*Sqrt[(a*(-1 + a*x^2))/b^2] + 16*a^2*x^3*(-5 + 2*b*x*Sqrt[(a*(-1 + a*x^2))/b^2]) - a*x*(-37 + 64*b*x*Sqrt[(a*(-1 + a*x^2))/b^2])) - 3*Sqrt[x*(a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2])]*Sqrt[a*x*(a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2])]*(-1 + 2*a*x^2 + 2*b*x*Sqrt[(a*(-1 + a*x^2))/b^2])*ArcTanh[Sqrt[2]*Sqrt[x*(a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2])]] + 12*Sqrt[a]*x*(4*a^2*x^3 - b*Sqrt[(a*(-1 + a*x^2))/b^2] + a*x*(-3 + 4*b*x*Sqrt[(a*(-1 + a*x^2))/b^2]))*ArcTanh[Sqrt[a + (a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2])^2]/Sqrt[a]]))/(24*Sqrt[2]*a^2*b^2*Sqrt[(a*(-1 + a*x^2))/b^2]*Sqrt[x*(a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2])]*Sqrt[a*x*(a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2])]*(4096*a^7*x^13 + b*Sqrt[(a*(-1 + a*x^2))/b^2] + 1024*a^6*x^11*(-13 + 4*b*x*Sqrt[(a*(-1 + a*x^2))/b^2]) + 768*a^4*x^7*(-13 + 15*b*x*Sqrt[(a*(-1 + a*x^2))/b^2]) - 224*a^3*x^5*(-13 + 24*b*x*Sqrt[(a*(-1 + a*x^2))/b^2]) + 28*a^2*x^3*(-13 + 40*b*x*Sqrt[(a*(-1 + a*x^2))/b^2]) - 256*a^5*x^9*(-65 + 44*b*x*Sqrt[(a*(-1 + a*x^2))/b^2]) - a*x*(-13 + 84*b*x*Sqrt[(a*(-1 + a*x^2))/b^2])))","B",1
2211,0,0,164,0.3908882,"\int \frac{(-3+x) (-2+x) \left(2-x+2 x^3\right)^{2/3}}{x^6 \left(-2+x+2 x^3\right)} \, dx","Integrate[((-3 + x)*(-2 + x)*(2 - x + 2*x^3)^(2/3))/(x^6*(-2 + x + 2*x^3)),x]","\int \frac{(-3+x) (-2+x) \left(2-x+2 x^3\right)^{2/3}}{x^6 \left(-2+x+2 x^3\right)} \, dx","2 \sqrt[3]{2} \log \left(\sqrt[3]{2} \sqrt[3]{2 x^3-x+2}-2 x\right)-2 \sqrt[3]{2} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{\sqrt[3]{2} \sqrt[3]{2 x^3-x+2}+x}\right)+\frac{3 \left(2 x^3-x+2\right)^{2/3} \left(7 x^3-x+2\right)}{10 x^5}-\sqrt[3]{2} \log \left(2 \sqrt[3]{2} \sqrt[3]{2 x^3-x+2} x+2^{2/3} \left(2 x^3-x+2\right)^{2/3}+4 x^2\right)",1,"Integrate[((-3 + x)*(-2 + x)*(2 - x + 2*x^3)^(2/3))/(x^6*(-2 + x + 2*x^3)), x]","F",-1
2212,0,0,164,0.3092338,"\int \frac{\left(1+x^3\right)^{2/3} \left(2+x^3\right)}{x^6 \left(-2-x^3+x^6\right)} \, dx","Integrate[((1 + x^3)^(2/3)*(2 + x^3))/(x^6*(-2 - x^3 + x^6)),x]","\int \frac{\left(1+x^3\right)^{2/3} \left(2+x^3\right)}{x^6 \left(-2-x^3+x^6\right)} \, dx","\frac{\log \left(\sqrt[3]{2} 3^{2/3} \sqrt[3]{x^3+1}-3 x\right)}{3\ 2^{2/3} \sqrt[3]{3}}-\frac{\tan ^{-1}\left(\frac{3^{5/6} x}{2 \sqrt[3]{2} \sqrt[3]{x^3+1}+\sqrt[3]{3} x}\right)}{2^{2/3} 3^{5/6}}+\frac{\left(x^3+1\right)^{5/3}}{5 x^5}-\frac{\log \left(\sqrt[3]{2} 3^{2/3} \sqrt[3]{x^3+1} x+2^{2/3} \sqrt[3]{3} \left(x^3+1\right)^{2/3}+3 x^2\right)}{6\ 2^{2/3} \sqrt[3]{3}}",1,"Integrate[((1 + x^3)^(2/3)*(2 + x^3))/(x^6*(-2 - x^3 + x^6)), x]","F",-1
2213,0,0,164,3.1649825,"\int \frac{b+a x^6}{\sqrt[3]{x+x^3} \left(d+c x^6\right)} \, dx","Integrate[(b + a*x^6)/((x + x^3)^(1/3)*(d + c*x^6)),x]","\int \frac{b+a x^6}{\sqrt[3]{x+x^3} \left(d+c x^6\right)} \, dx","\frac{(a d-b c) \text{RootSum}\left[\text{$\#$1}^9 d-3 \text{$\#$1}^6 d+3 \text{$\#$1}^3 d+c-d\&,\frac{\log \left(\sqrt[3]{x^3+x}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{6 c d}-\frac{a \log \left(\sqrt[3]{x^3+x}-x\right)}{2 c}+\frac{\sqrt{3} a \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+x}+x}\right)}{2 c}+\frac{a \log \left(\sqrt[3]{x^3+x} x+\left(x^3+x\right)^{2/3}+x^2\right)}{4 c}",1,"Integrate[(b + a*x^6)/((x + x^3)^(1/3)*(d + c*x^6)), x]","F",-1
2214,0,0,164,0.4821742,"\int \frac{b+a x^6}{\sqrt[3]{x+x^3} \left(d+c x^6\right)} \, dx","Integrate[(b + a*x^6)/((x + x^3)^(1/3)*(d + c*x^6)),x]","\int \frac{b+a x^6}{\sqrt[3]{x+x^3} \left(d+c x^6\right)} \, dx","\frac{(a d-b c) \text{RootSum}\left[\text{$\#$1}^9 d-3 \text{$\#$1}^6 d+3 \text{$\#$1}^3 d+c-d\&,\frac{\log \left(\sqrt[3]{x^3+x}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{6 c d}-\frac{a \log \left(\sqrt[3]{x^3+x}-x\right)}{2 c}+\frac{\sqrt{3} a \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+x}+x}\right)}{2 c}+\frac{a \log \left(\sqrt[3]{x^3+x} x+\left(x^3+x\right)^{2/3}+x^2\right)}{4 c}",1,"Integrate[(b + a*x^6)/((x + x^3)^(1/3)*(d + c*x^6)), x]","F",-1
2215,1,118,165,0.0643614,"\int \frac{1}{(2+x) \sqrt[3]{1+x+x^2}} \, dx","Integrate[1/((2 + x)*(1 + x + x^2)^(1/3)),x]","-\frac{3 \sqrt[3]{\frac{2 x-i \sqrt{3}+1}{x+2}} \sqrt[3]{\frac{2 x+i \sqrt{3}+1}{x+2}} F_1\left(\frac{2}{3};\frac{1}{3},\frac{1}{3};\frac{5}{3};\frac{3-i \sqrt{3}}{2 x+4},\frac{3+i \sqrt{3}}{2 x+4}\right)}{2\ 2^{2/3} \sqrt[3]{x^2+x+1}}","\frac{\log \left(3 \sqrt[3]{x^2+x+1}+\sqrt[3]{3} x-\sqrt[3]{3}\right)}{3 \sqrt[3]{3}}-\frac{\log \left(3^{2/3} x^2+9 \left(x^2+x+1\right)^{2/3}+\left(3 \sqrt[3]{3}-3 \sqrt[3]{3} x\right) \sqrt[3]{x^2+x+1}-2\ 3^{2/3} x+3^{2/3}\right)}{6 \sqrt[3]{3}}-\frac{\tan ^{-1}\left(\frac{\frac{\sqrt[3]{x^2+x+1}}{\sqrt{3}}-\frac{2 x}{3 \sqrt[6]{3}}+\frac{2}{3 \sqrt[6]{3}}}{\sqrt[3]{x^2+x+1}}\right)}{3^{5/6}}",1,"(-3*((1 - I*Sqrt[3] + 2*x)/(2 + x))^(1/3)*((1 + I*Sqrt[3] + 2*x)/(2 + x))^(1/3)*AppellF1[2/3, 1/3, 1/3, 5/3, (3 - I*Sqrt[3])/(4 + 2*x), (3 + I*Sqrt[3])/(4 + 2*x)])/(2*2^(2/3)*(1 + x + x^2)^(1/3))","C",0
2216,0,0,165,0.325195,"\int \frac{(-3+2 x) \sqrt[3]{-1+x+x^3}}{x^2 \left(2-2 x+x^3\right)} \, dx","Integrate[((-3 + 2*x)*(-1 + x + x^3)^(1/3))/(x^2*(2 - 2*x + x^3)),x]","\int \frac{(-3+2 x) \sqrt[3]{-1+x+x^3}}{x^2 \left(2-2 x+x^3\right)} \, dx","\frac{3 \sqrt[3]{x^3+x-1}}{2 x}+\frac{1}{2} \sqrt[3]{\frac{3}{2}} \log \left(\sqrt[3]{2} 3^{2/3} \sqrt[3]{x^3+x-1}-3 x\right)+\frac{3^{5/6} \tan ^{-1}\left(\frac{3^{5/6} x}{2 \sqrt[3]{2} \sqrt[3]{x^3+x-1}+\sqrt[3]{3} x}\right)}{2 \sqrt[3]{2}}-\frac{1}{4} \sqrt[3]{\frac{3}{2}} \log \left(\sqrt[3]{2} 3^{2/3} \sqrt[3]{x^3+x-1} x+2^{2/3} \sqrt[3]{3} \left(x^3+x-1\right)^{2/3}+3 x^2\right)",1,"Integrate[((-3 + 2*x)*(-1 + x + x^3)^(1/3))/(x^2*(2 - 2*x + x^3)), x]","F",-1
2217,1,736,165,18.7312145,"\int \frac{-\left((2 a-b) b^2\right)+(4 a-b) b x-(2 a+b) x^2+x^3}{(-a+x) \sqrt[4]{(-a+x) (-b+x)^2} \left(b^2+a d-(2 b+d) x+x^2\right)} \, dx","Integrate[(-((2*a - b)*b^2) + (4*a - b)*b*x - (2*a + b)*x^2 + x^3)/((-a + x)*((-a + x)*(-b + x)^2)^(1/4)*(b^2 + a*d - (2*b + d)*x + x^2)),x]","-\frac{4 (b-x)}{\sqrt[4]{(x-a) (b-x)^2}}-\frac{i \sqrt{2} d (a-x)^{11/4} (b-x)^3 \sqrt{\frac{b}{a-x}-\frac{a}{a-x}+1} \left(\left(\sqrt{d (-4 a+4 b+d)}+4 a-4 b-d\right) \sqrt{-\frac{\sqrt{d (-4 a+4 b+d)}-2 a+2 b+d}{(a-b)^2}} \Pi \left(-\frac{\sqrt{2}}{\sqrt{a-b} \sqrt{\frac{2 a-2 b-d+\sqrt{d (-4 a+4 b+d)}}{(a-b)^2}}};\left.i \sinh ^{-1}\left(\frac{\sqrt{-\sqrt{a-b}}}{\sqrt[4]{a-x}}\right)\right|-1\right)-\left(\sqrt{d (-4 a+4 b+d)}+4 a-4 b-d\right) \sqrt{-\frac{\sqrt{d (-4 a+4 b+d)}-2 a+2 b+d}{(a-b)^2}} \Pi \left(\frac{\sqrt{2}}{\sqrt{a-b} \sqrt{\frac{2 a-2 b-d+\sqrt{d (-4 a+4 b+d)}}{(a-b)^2}}};\left.i \sinh ^{-1}\left(\frac{\sqrt{-\sqrt{a-b}}}{\sqrt[4]{a-x}}\right)\right|-1\right)-\left(-\sqrt{d (-4 a+4 b+d)}+4 a-4 b-d\right) \sqrt{\frac{\sqrt{d (-4 a+4 b+d)}+2 a-2 b-d}{(a-b)^2}} \left(\Pi \left(-\frac{\sqrt{2}}{\sqrt{a-b} \sqrt{-\frac{-2 a+2 b+d+\sqrt{d (-4 a+4 b+d)}}{(a-b)^2}}};\left.i \sinh ^{-1}\left(\frac{\sqrt{-\sqrt{a-b}}}{\sqrt[4]{a-x}}\right)\right|-1\right)-\Pi \left(\frac{\sqrt{2}}{\sqrt{a-b} \sqrt{-\frac{-2 a+2 b+d+\sqrt{d (-4 a+4 b+d)}}{(a-b)^2}}};\left.i \sinh ^{-1}\left(\frac{\sqrt{-\sqrt{a-b}}}{\sqrt[4]{a-x}}\right)\right|-1\right)\right)\right)}{\sqrt{-\sqrt{a-b}} (a-b) (x-a) (x-b) \sqrt{d (-4 a+4 b+d)} \sqrt{\frac{\sqrt{d (-4 a+4 b+d)}+2 a-2 b-d}{(a-b)^2}} \sqrt{-\frac{\sqrt{d (-4 a+4 b+d)}-2 a+2 b+d}{(a-b)^2}} \left(-\left((a-x) (b-x)^2\right)\right)^{5/4}}","-2 \sqrt[4]{d} \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3}}{b-x}\right)+2 \sqrt[4]{d} \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3}}{b-x}\right)-\frac{4 \left(-a b^2+2 a b x-a x^2+b^2 x-2 b x^2+x^3\right)^{3/4}}{(x-a) (b-x)}",1,"(-4*(b - x))/((b - x)^2*(-a + x))^(1/4) - (I*Sqrt[2]*d*Sqrt[1 - a/(a - x) + b/(a - x)]*(a - x)^(11/4)*(b - x)^3*((4*a - 4*b - d + Sqrt[d*(-4*a + 4*b + d)])*Sqrt[-((-2*a + 2*b + d + Sqrt[d*(-4*a + 4*b + d)])/(a - b)^2)]*EllipticPi[-(Sqrt[2]/(Sqrt[a - b]*Sqrt[(2*a - 2*b - d + Sqrt[d*(-4*a + 4*b + d)])/(a - b)^2])), I*ArcSinh[Sqrt[-Sqrt[a - b]]/(a - x)^(1/4)], -1] - (4*a - 4*b - d + Sqrt[d*(-4*a + 4*b + d)])*Sqrt[-((-2*a + 2*b + d + Sqrt[d*(-4*a + 4*b + d)])/(a - b)^2)]*EllipticPi[Sqrt[2]/(Sqrt[a - b]*Sqrt[(2*a - 2*b - d + Sqrt[d*(-4*a + 4*b + d)])/(a - b)^2]), I*ArcSinh[Sqrt[-Sqrt[a - b]]/(a - x)^(1/4)], -1] - (4*a - 4*b - d - Sqrt[d*(-4*a + 4*b + d)])*Sqrt[(2*a - 2*b - d + Sqrt[d*(-4*a + 4*b + d)])/(a - b)^2]*(EllipticPi[-(Sqrt[2]/(Sqrt[a - b]*Sqrt[-((-2*a + 2*b + d + Sqrt[d*(-4*a + 4*b + d)])/(a - b)^2)])), I*ArcSinh[Sqrt[-Sqrt[a - b]]/(a - x)^(1/4)], -1] - EllipticPi[Sqrt[2]/(Sqrt[a - b]*Sqrt[-((-2*a + 2*b + d + Sqrt[d*(-4*a + 4*b + d)])/(a - b)^2)]), I*ArcSinh[Sqrt[-Sqrt[a - b]]/(a - x)^(1/4)], -1])))/(Sqrt[-Sqrt[a - b]]*(a - b)*Sqrt[d*(-4*a + 4*b + d)]*Sqrt[(2*a - 2*b - d + Sqrt[d*(-4*a + 4*b + d)])/(a - b)^2]*Sqrt[-((-2*a + 2*b + d + Sqrt[d*(-4*a + 4*b + d)])/(a - b)^2)]*(-((a - x)*(b - x)^2))^(5/4)*(-a + x)*(-b + x))","C",0
2218,1,486,165,2.1719076,"\int \frac{x^4}{\left(b+a x^4\right)^2 \sqrt[4]{b x^2+a x^4}} \, dx","Integrate[x^4/((b + a*x^4)^2*(b*x^2 + a*x^4)^(1/4)),x]","\frac{x \left(\frac{4 \left(a^2 x^4-b^2\right)}{a x^4+b}-\frac{\sqrt{b} \sqrt[4]{a+\frac{b}{x^2}} \left(\sqrt{b} \sqrt[4]{\sqrt{-a} \sqrt{b}+a} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a-\sqrt{-a} \sqrt{b}}}\right)-\sqrt{-a} \sqrt[4]{\sqrt{-a} \sqrt{b}+a} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a-\sqrt{-a} \sqrt{b}}}\right)+\sqrt{b} \sqrt[4]{a-\sqrt{-a} \sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\sqrt{-a} \sqrt{b}+a}}\right)+\sqrt{-a} \sqrt[4]{a-\sqrt{-a} \sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\sqrt{-a} \sqrt{b}+a}}\right)+\left(\sqrt{-a}-\sqrt{b}\right) \sqrt[4]{\sqrt{-a} \sqrt{b}+a} \tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a-\sqrt{-a} \sqrt{b}}}\right)-\left(\sqrt{-a}+\sqrt{b}\right) \sqrt[4]{a-\sqrt{-a} \sqrt{b}} \tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\sqrt{-a} \sqrt{b}+a}}\right)\right)}{\sqrt[4]{a-\sqrt{-a} \sqrt{b}} \sqrt[4]{\sqrt{-a} \sqrt{b}+a}}\right)}{16 a b (a+b) \sqrt[4]{x^2 \left(a x^2+b\right)}}","\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-2 a \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+2 a \log (x)}{\text{$\#$1} a-\text{$\#$1}^5}\&\right]}{32 a (a+b)}+\frac{\left(a x^4+b x^2\right)^{3/4} \left(a x^2-b\right)}{4 a b x (a+b) \left(a x^4+b\right)}",1,"(x*((4*(-b^2 + a^2*x^4))/(b + a*x^4) - (Sqrt[b]*(a + b/x^2)^(1/4)*(-(Sqrt[-a]*(a + Sqrt[-a]*Sqrt[b])^(1/4)*ArcTan[(a + b/x^2)^(1/4)/(a - Sqrt[-a]*Sqrt[b])^(1/4)]) + (a + Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[b]*ArcTan[(a + b/x^2)^(1/4)/(a - Sqrt[-a]*Sqrt[b])^(1/4)] + Sqrt[-a]*(a - Sqrt[-a]*Sqrt[b])^(1/4)*ArcTan[(a + b/x^2)^(1/4)/(a + Sqrt[-a]*Sqrt[b])^(1/4)] + (a - Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[b]*ArcTan[(a + b/x^2)^(1/4)/(a + Sqrt[-a]*Sqrt[b])^(1/4)] + (Sqrt[-a] - Sqrt[b])*(a + Sqrt[-a]*Sqrt[b])^(1/4)*ArcTanh[(a + b/x^2)^(1/4)/(a - Sqrt[-a]*Sqrt[b])^(1/4)] - (Sqrt[-a] + Sqrt[b])*(a - Sqrt[-a]*Sqrt[b])^(1/4)*ArcTanh[(a + b/x^2)^(1/4)/(a + Sqrt[-a]*Sqrt[b])^(1/4)]))/((a - Sqrt[-a]*Sqrt[b])^(1/4)*(a + Sqrt[-a]*Sqrt[b])^(1/4))))/(16*a*b*(a + b)*(x^2*(b + a*x^2))^(1/4))","B",1
2219,1,486,165,0.9060307,"\int \frac{x^4}{\left(b+a x^4\right)^2 \sqrt[4]{b x^2+a x^4}} \, dx","Integrate[x^4/((b + a*x^4)^2*(b*x^2 + a*x^4)^(1/4)),x]","\frac{x \left(\frac{4 \left(a^2 x^4-b^2\right)}{a x^4+b}-\frac{\sqrt{b} \sqrt[4]{a+\frac{b}{x^2}} \left(\sqrt{b} \sqrt[4]{\sqrt{-a} \sqrt{b}+a} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a-\sqrt{-a} \sqrt{b}}}\right)-\sqrt{-a} \sqrt[4]{\sqrt{-a} \sqrt{b}+a} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a-\sqrt{-a} \sqrt{b}}}\right)+\sqrt{b} \sqrt[4]{a-\sqrt{-a} \sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\sqrt{-a} \sqrt{b}+a}}\right)+\sqrt{-a} \sqrt[4]{a-\sqrt{-a} \sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\sqrt{-a} \sqrt{b}+a}}\right)+\left(\sqrt{-a}-\sqrt{b}\right) \sqrt[4]{\sqrt{-a} \sqrt{b}+a} \tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a-\sqrt{-a} \sqrt{b}}}\right)-\left(\sqrt{-a}+\sqrt{b}\right) \sqrt[4]{a-\sqrt{-a} \sqrt{b}} \tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\sqrt{-a} \sqrt{b}+a}}\right)\right)}{\sqrt[4]{a-\sqrt{-a} \sqrt{b}} \sqrt[4]{\sqrt{-a} \sqrt{b}+a}}\right)}{16 a b (a+b) \sqrt[4]{x^2 \left(a x^2+b\right)}}","\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-2 a \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+2 a \log (x)}{\text{$\#$1} a-\text{$\#$1}^5}\&\right]}{32 a (a+b)}+\frac{\left(a x^4+b x^2\right)^{3/4} \left(a x^2-b\right)}{4 a b x (a+b) \left(a x^4+b\right)}",1,"(x*((4*(-b^2 + a^2*x^4))/(b + a*x^4) - (Sqrt[b]*(a + b/x^2)^(1/4)*(-(Sqrt[-a]*(a + Sqrt[-a]*Sqrt[b])^(1/4)*ArcTan[(a + b/x^2)^(1/4)/(a - Sqrt[-a]*Sqrt[b])^(1/4)]) + (a + Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[b]*ArcTan[(a + b/x^2)^(1/4)/(a - Sqrt[-a]*Sqrt[b])^(1/4)] + Sqrt[-a]*(a - Sqrt[-a]*Sqrt[b])^(1/4)*ArcTan[(a + b/x^2)^(1/4)/(a + Sqrt[-a]*Sqrt[b])^(1/4)] + (a - Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[b]*ArcTan[(a + b/x^2)^(1/4)/(a + Sqrt[-a]*Sqrt[b])^(1/4)] + (Sqrt[-a] - Sqrt[b])*(a + Sqrt[-a]*Sqrt[b])^(1/4)*ArcTanh[(a + b/x^2)^(1/4)/(a - Sqrt[-a]*Sqrt[b])^(1/4)] - (Sqrt[-a] + Sqrt[b])*(a - Sqrt[-a]*Sqrt[b])^(1/4)*ArcTanh[(a + b/x^2)^(1/4)/(a + Sqrt[-a]*Sqrt[b])^(1/4)]))/((a - Sqrt[-a]*Sqrt[b])^(1/4)*(a + Sqrt[-a]*Sqrt[b])^(1/4))))/(16*a*b*(a + b)*(x^2*(b + a*x^2))^(1/4))","B",1
2220,1,486,165,1.2811695,"\int \frac{x^4}{\left(b+a x^4\right)^2 \sqrt[4]{b x^2+a x^4}} \, dx","Integrate[x^4/((b + a*x^4)^2*(b*x^2 + a*x^4)^(1/4)),x]","\frac{x \left(\frac{4 \left(a^2 x^4-b^2\right)}{a x^4+b}-\frac{\sqrt{b} \sqrt[4]{a+\frac{b}{x^2}} \left(\sqrt{b} \sqrt[4]{\sqrt{-a} \sqrt{b}+a} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a-\sqrt{-a} \sqrt{b}}}\right)-\sqrt{-a} \sqrt[4]{\sqrt{-a} \sqrt{b}+a} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a-\sqrt{-a} \sqrt{b}}}\right)+\sqrt{b} \sqrt[4]{a-\sqrt{-a} \sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\sqrt{-a} \sqrt{b}+a}}\right)+\sqrt{-a} \sqrt[4]{a-\sqrt{-a} \sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\sqrt{-a} \sqrt{b}+a}}\right)+\left(\sqrt{-a}-\sqrt{b}\right) \sqrt[4]{\sqrt{-a} \sqrt{b}+a} \tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a-\sqrt{-a} \sqrt{b}}}\right)-\left(\sqrt{-a}+\sqrt{b}\right) \sqrt[4]{a-\sqrt{-a} \sqrt{b}} \tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\sqrt{-a} \sqrt{b}+a}}\right)\right)}{\sqrt[4]{a-\sqrt{-a} \sqrt{b}} \sqrt[4]{\sqrt{-a} \sqrt{b}+a}}\right)}{16 a b (a+b) \sqrt[4]{x^2 \left(a x^2+b\right)}}","\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-2 a \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+2 a \log (x)}{\text{$\#$1} a-\text{$\#$1}^5}\&\right]}{32 a (a+b)}+\frac{\left(a x^4+b x^2\right)^{3/4} \left(a x^2-b\right)}{4 a b x (a+b) \left(a x^4+b\right)}",1,"(x*((4*(-b^2 + a^2*x^4))/(b + a*x^4) - (Sqrt[b]*(a + b/x^2)^(1/4)*(-(Sqrt[-a]*(a + Sqrt[-a]*Sqrt[b])^(1/4)*ArcTan[(a + b/x^2)^(1/4)/(a - Sqrt[-a]*Sqrt[b])^(1/4)]) + (a + Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[b]*ArcTan[(a + b/x^2)^(1/4)/(a - Sqrt[-a]*Sqrt[b])^(1/4)] + Sqrt[-a]*(a - Sqrt[-a]*Sqrt[b])^(1/4)*ArcTan[(a + b/x^2)^(1/4)/(a + Sqrt[-a]*Sqrt[b])^(1/4)] + (a - Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[b]*ArcTan[(a + b/x^2)^(1/4)/(a + Sqrt[-a]*Sqrt[b])^(1/4)] + (Sqrt[-a] - Sqrt[b])*(a + Sqrt[-a]*Sqrt[b])^(1/4)*ArcTanh[(a + b/x^2)^(1/4)/(a - Sqrt[-a]*Sqrt[b])^(1/4)] - (Sqrt[-a] + Sqrt[b])*(a - Sqrt[-a]*Sqrt[b])^(1/4)*ArcTanh[(a + b/x^2)^(1/4)/(a + Sqrt[-a]*Sqrt[b])^(1/4)]))/((a - Sqrt[-a]*Sqrt[b])^(1/4)*(a + Sqrt[-a]*Sqrt[b])^(1/4))))/(16*a*b*(a + b)*(x^2*(b + a*x^2))^(1/4))","B",1
2221,1,202,165,0.2936241,"\int \frac{\left(-b+a x^4\right) \left(b+a x^4\right)^{3/4}}{x^8 \left(b+2 a x^4\right)} \, dx","Integrate[((-b + a*x^4)*(b + a*x^4)^(3/4))/(x^8*(b + 2*a*x^4)),x]","\left(\frac{1}{7 x^7}-\frac{6 a}{7 b x^3}\right) \left(a x^4+b\right)^{3/4}-\frac{3 a^{7/4} \left(-2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a} x}{\sqrt[4]{a+b x^4}}\right)+2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} x}{\sqrt[4]{a+b x^4}}+1\right)-\log \left(-\frac{\sqrt{2} \sqrt[4]{a} x}{\sqrt[4]{a+b x^4}}+\frac{\sqrt{a} x^2}{\sqrt{a+b x^4}}+1\right)+\log \left(\frac{\sqrt{2} \sqrt[4]{a} x}{\sqrt[4]{a+b x^4}}+\frac{\sqrt{a} x^2}{\sqrt{a+b x^4}}+1\right)\right)}{4 \sqrt{2} b}","-\frac{3 a^{7/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} x \sqrt[4]{a x^4+b}}{\sqrt{a x^4+b}-\sqrt{a} x^2}\right)}{2 \sqrt{2} b}-\frac{3 a^{7/4} \tanh ^{-1}\left(\frac{\frac{\sqrt{a x^4+b}}{\sqrt{2} \sqrt[4]{a}}+\frac{\sqrt[4]{a} x^2}{\sqrt{2}}}{x \sqrt[4]{a x^4+b}}\right)}{2 \sqrt{2} b}+\frac{\left(b-6 a x^4\right) \left(a x^4+b\right)^{3/4}}{7 b x^7}",1,"(1/(7*x^7) - (6*a)/(7*b*x^3))*(b + a*x^4)^(3/4) - (3*a^(7/4)*(-2*ArcTan[1 - (Sqrt[2]*a^(1/4)*x)/(a + b*x^4)^(1/4)] + 2*ArcTan[1 + (Sqrt[2]*a^(1/4)*x)/(a + b*x^4)^(1/4)] - Log[1 + (Sqrt[a]*x^2)/Sqrt[a + b*x^4] - (Sqrt[2]*a^(1/4)*x)/(a + b*x^4)^(1/4)] + Log[1 + (Sqrt[a]*x^2)/Sqrt[a + b*x^4] + (Sqrt[2]*a^(1/4)*x)/(a + b*x^4)^(1/4)]))/(4*Sqrt[2]*b)","A",0
2222,-1,0,165,180.0020588,"\int \frac{x \sqrt{b+a x}}{x+\sqrt{c+\sqrt{b+a x}}} \, dx","Integrate[(x*Sqrt[b + a*x])/(x + Sqrt[c + Sqrt[b + a*x]]),x]","\text{\$Aborted}","4 \text{RootSum}\left[-\text{$\#$1}^4+2 \text{$\#$1}^2 c-\text{$\#$1} a+b-c^2\&,\frac{\text{$\#$1}^3 a \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-\text{$\#$1}^2 b \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)}{4 \text{$\#$1}^3-4 \text{$\#$1} c+a}\&\right]-\frac{4}{3} c \sqrt{\sqrt{a x+b}+c}+\sqrt{a x+b} \left(\frac{2 (a x+b)}{3 a}-\frac{4}{3} \sqrt{\sqrt{a x+b}+c}\right)",1,"$Aborted","F",-1
2223,0,0,165,4.5621914,"\int \frac{x \sqrt{b+a x}}{x+\sqrt{c+\sqrt{b+a x}}} \, dx","Integrate[(x*Sqrt[b + a*x])/(x + Sqrt[c + Sqrt[b + a*x]]),x]","\int \frac{x \sqrt{b+a x}}{x+\sqrt{c+\sqrt{b+a x}}} \, dx","4 \text{RootSum}\left[-\text{$\#$1}^4+2 \text{$\#$1}^2 c-\text{$\#$1} a+b-c^2\&,\frac{\text{$\#$1}^3 a \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-\text{$\#$1}^2 b \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)}{4 \text{$\#$1}^3-4 \text{$\#$1} c+a}\&\right]-\frac{4}{3} c \sqrt{\sqrt{a x+b}+c}+\sqrt{a x+b} \left(\frac{2 (a x+b)}{3 a}-\frac{4}{3} \sqrt{\sqrt{a x+b}+c}\right)",1,"Integrate[(x*Sqrt[b + a*x])/(x + Sqrt[c + Sqrt[b + a*x]]), x]","F",-1
2224,1,166,166,0.2637136,"\int \frac{\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}}{x} \, dx","Integrate[Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]]/x,x]","-8 \sqrt{1-\sqrt{1-\sqrt{\frac{x-1}{x}}}}+2 \sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{\sqrt{1-\sqrt{1-\sqrt{\frac{x-1}{x}}}}}{\sqrt{\sqrt{2}-1}}\right)+4 \tanh ^{-1}\left(\sqrt{1-\sqrt{1-\sqrt{\frac{x-1}{x}}}}\right)+2 \sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt{1-\sqrt{1-\sqrt{\frac{x-1}{x}}}}}{\sqrt{1+\sqrt{2}}}\right)","-8 \sqrt{1-\sqrt{1-\sqrt{\frac{x-1}{x}}}}+2 \sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{\sqrt{1-\sqrt{1-\sqrt{\frac{x-1}{x}}}}}{\sqrt{\sqrt{2}-1}}\right)+4 \tanh ^{-1}\left(\sqrt{1-\sqrt{1-\sqrt{\frac{x-1}{x}}}}\right)+2 \sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt{1-\sqrt{1-\sqrt{\frac{x-1}{x}}}}}{\sqrt{1+\sqrt{2}}}\right)",1,"-8*Sqrt[1 - Sqrt[1 - Sqrt[(-1 + x)/x]]] + 2*Sqrt[-1 + Sqrt[2]]*ArcTan[Sqrt[1 - Sqrt[1 - Sqrt[(-1 + x)/x]]]/Sqrt[-1 + Sqrt[2]]] + 4*ArcTanh[Sqrt[1 - Sqrt[1 - Sqrt[(-1 + x)/x]]]] + 2*Sqrt[1 + Sqrt[2]]*ArcTanh[Sqrt[1 - Sqrt[1 - Sqrt[(-1 + x)/x]]]/Sqrt[1 + Sqrt[2]]]","A",1
2225,0,0,166,10.1723297,"\int \frac{-2 a b x+(a+b) x^2}{(x (-a+x) (-b+x))^{2/3} \left(a b d-(a+b) d x+(-1+d) x^2\right)} \, dx","Integrate[(-2*a*b*x + (a + b)*x^2)/((x*(-a + x)*(-b + x))^(2/3)*(a*b*d - (a + b)*d*x + (-1 + d)*x^2)),x]","\int \frac{-2 a b x+(a+b) x^2}{(x (-a+x) (-b+x))^{2/3} \left(a b d-(a+b) d x+(-1+d) x^2\right)} \, dx","-\frac{\log \left(d^{2/3} \left(x^2 (-a-b)+a b x+x^3\right)^{2/3}+\sqrt[3]{d} x \sqrt[3]{x^2 (-a-b)+a b x+x^3}+x^2\right)}{2 \sqrt[3]{d}}+\frac{\log \left(x-\sqrt[3]{d} \sqrt[3]{x^2 (-a-b)+a b x+x^3}\right)}{\sqrt[3]{d}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{d} \sqrt[3]{x^2 (-a-b)+a b x+x^3}+x}\right)}{\sqrt[3]{d}}",1,"Integrate[(-2*a*b*x + (a + b)*x^2)/((x*(-a + x)*(-b + x))^(2/3)*(a*b*d - (a + b)*d*x + (-1 + d)*x^2)), x]","F",-1
2226,1,42,166,0.0122747,"\int \frac{\sqrt[4]{-b+a x^3}}{x^7} \, dx","Integrate[(-b + a*x^3)^(1/4)/x^7,x]","\frac{4 a^2 \left(a x^3-b\right)^{5/4} \, _2F_1\left(\frac{5}{4},3;\frac{9}{4};1-\frac{a x^3}{b}\right)}{15 b^3}","-\frac{a^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^3-b}}{\sqrt{a x^3-b}-\sqrt{b}}\right)}{16 \sqrt{2} b^{7/4}}+\frac{a^2 \tanh ^{-1}\left(\frac{\frac{\sqrt{a x^3-b}}{\sqrt{2} \sqrt[4]{b}}+\frac{\sqrt[4]{b}}{\sqrt{2}}}{\sqrt[4]{a x^3-b}}\right)}{16 \sqrt{2} b^{7/4}}+\frac{\left(a x^3-4 b\right) \sqrt[4]{a x^3-b}}{24 b x^6}",1,"(4*a^2*(-b + a*x^3)^(5/4)*Hypergeometric2F1[5/4, 3, 9/4, 1 - (a*x^3)/b])/(15*b^3)","C",1
2227,1,156,166,0.290548,"\int \frac{\left(b+2 a x^2\right) \sqrt[4]{b x^2+a x^4}}{-b+a x^2} \, dx","Integrate[((b + 2*a*x^2)*(b*x^2 + a*x^4)^(1/4))/(-b + a*x^2),x]","\frac{x^3 \left(-3 a x^2 \left(1-\frac{a^2 x^4}{b^2}\right)^{3/4} F_1\left(\frac{7}{4};\frac{3}{4},1;\frac{11}{4};-\frac{a x^2}{b},\frac{a x^2}{b}\right)-5 b \left(\frac{a x^2}{b}+1\right)^{3/4} \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};-\frac{2 a x^2}{b-a x^2}\right)+3 \left(a x^2+b\right) \left(1-\frac{a x^2}{b}\right)^{3/4}\right)}{3 \left(x^2 \left(a x^2+b\right)\right)^{3/4} \left(1-\frac{a x^2}{b}\right)^{3/4}}","-\frac{7 b \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{2 a^{3/4}}+\frac{3 \sqrt[4]{2} b \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{a^{3/4}}+\frac{7 b \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{2 a^{3/4}}-\frac{3 \sqrt[4]{2} b \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{a^{3/4}}+x \sqrt[4]{a x^4+b x^2}",1,"(x^3*(3*(b + a*x^2)*(1 - (a*x^2)/b)^(3/4) - 3*a*x^2*(1 - (a^2*x^4)/b^2)^(3/4)*AppellF1[7/4, 3/4, 1, 11/4, -((a*x^2)/b), (a*x^2)/b] - 5*b*(1 + (a*x^2)/b)^(3/4)*Hypergeometric2F1[3/4, 3/4, 7/4, (-2*a*x^2)/(b - a*x^2)]))/(3*(x^2*(b + a*x^2))^(3/4)*(1 - (a*x^2)/b)^(3/4))","C",0
2228,1,204,166,1.4795088,"\int \frac{-b^4+a^4 x^4}{\sqrt{-b^2 x+a^2 x^3} \left(b^4+a^4 x^4\right)} \, dx","Integrate[(-b^4 + a^4*x^4)/(Sqrt[-(b^2*x) + a^2*x^3]*(b^4 + a^4*x^4)),x]","-\frac{i x^{3/2} \sqrt{1-\frac{b^2}{a^2 x^2}} \left(2 F\left(\left.i \sinh ^{-1}\left(\frac{\sqrt{-\frac{b}{a}}}{\sqrt{x}}\right)\right|-1\right)-\Pi \left(-\sqrt[4]{-1};\left.i \sinh ^{-1}\left(\frac{\sqrt{-\frac{b}{a}}}{\sqrt{x}}\right)\right|-1\right)-\Pi \left(\sqrt[4]{-1};\left.i \sinh ^{-1}\left(\frac{\sqrt{-\frac{b}{a}}}{\sqrt{x}}\right)\right|-1\right)-\Pi \left(-(-1)^{3/4};\left.i \sinh ^{-1}\left(\frac{\sqrt{-\frac{b}{a}}}{\sqrt{x}}\right)\right|-1\right)-\Pi \left((-1)^{3/4};\left.i \sinh ^{-1}\left(\frac{\sqrt{-\frac{b}{a}}}{\sqrt{x}}\right)\right|-1\right)\right)}{\sqrt{-\frac{b}{a}} \sqrt{a^2 x^3-b^2 x}}","\frac{\tan ^{-1}\left(\frac{2^{3/4} \sqrt{a} \sqrt{b} \sqrt{a^2 x^3-b^2 x}}{-a^2 x^2+\sqrt{2} a b x+b^2}\right)}{2^{3/4} \sqrt{a} \sqrt{b}}-\frac{\tanh ^{-1}\left(\frac{\frac{a^{3/2} x^2}{2^{3/4} \sqrt{b}}-\frac{b^{3/2}}{2^{3/4} \sqrt{a}}+\frac{\sqrt{a} \sqrt{b} x}{\sqrt[4]{2}}}{\sqrt{a^2 x^3-b^2 x}}\right)}{2^{3/4} \sqrt{a} \sqrt{b}}",1,"((-I)*Sqrt[1 - b^2/(a^2*x^2)]*x^(3/2)*(2*EllipticF[I*ArcSinh[Sqrt[-(b/a)]/Sqrt[x]], -1] - EllipticPi[-(-1)^(1/4), I*ArcSinh[Sqrt[-(b/a)]/Sqrt[x]], -1] - EllipticPi[(-1)^(1/4), I*ArcSinh[Sqrt[-(b/a)]/Sqrt[x]], -1] - EllipticPi[-(-1)^(3/4), I*ArcSinh[Sqrt[-(b/a)]/Sqrt[x]], -1] - EllipticPi[(-1)^(3/4), I*ArcSinh[Sqrt[-(b/a)]/Sqrt[x]], -1]))/(Sqrt[-(b/a)]*Sqrt[-(b^2*x) + a^2*x^3])","C",1
2229,1,841,166,8.4214479,"\int \frac{-1+x^5}{\sqrt{1+x^4} \left(1+x^5\right)} \, dx","Integrate[(-1 + x^5)/(Sqrt[1 + x^4]*(1 + x^5)),x]","\frac{\left(3 \left(1-\sqrt[5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}\right) x^8-12 \left(1-\sqrt[5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}\right) x^6+\left(16-17 \sqrt[5]{-1}+18 (-1)^{2/5}-19 (-1)^{3/5}+20 (-1)^{4/5}\right) x^4-12 \left(1-\sqrt[5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}\right) x^2+3 \left(1-\sqrt[5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}\right)\right) \left(\frac{\sqrt{2} \tanh ^{-1}\left(\frac{x^2+1}{\sqrt{2} \sqrt{x^4+1}}\right)}{-4-\sqrt[5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}}+2 \left(\frac{(-1)^{4/5} \tanh ^{-1}\left(\frac{1-\sqrt[5]{-1} x^2}{\sqrt{1+(-1)^{2/5}} \sqrt{x^4+1}}\right)}{\sqrt{1+(-1)^{2/5}} \left(1+4 \sqrt[5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}\right)}-\frac{(-1)^{2/5} \tanh ^{-1}\left(\frac{(-1)^{2/5} x^2+1}{\sqrt{1+(-1)^{4/5}} \sqrt{x^4+1}}\right)}{\left(1+\sqrt[5]{-1}\right)^4 \left(1+(-1)^{4/5}\right)^{5/2}}+\frac{\tanh ^{-1}\left(\frac{1-(-1)^{3/5} x^2}{\sqrt{1-\sqrt[5]{-1}} \sqrt{x^4+1}}\right)}{\left(1-\sqrt[5]{-1}\right)^{3/2} \left(1+\sqrt[5]{-1}\right)^4 \left(1-\sqrt[5]{-1}+(-1)^{2/5}\right)}+\frac{(-1)^{2/5} \tanh ^{-1}\left(\frac{(-1)^{4/5} x^2+1}{\sqrt{1-(-1)^{3/5}} \sqrt{x^4+1}}\right)}{\sqrt{1-(-1)^{3/5}} \left(-4-\sqrt[5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}\right)}\right)\right)}{2 \left(-1+\sqrt[5]{-1}\right)^2 \left(1+\sqrt[5]{-1}\right)^3 \left(1+(-1)^{2/5}\right) \left(1-\sqrt[5]{-1}+(-1)^{2/5}\right) x^4}-\sqrt[4]{-1} F\left(\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+\frac{2 \sqrt[4]{-1} \Pi \left(i;\left.\sin ^{-1}\left((-1)^{3/4} x\right)\right|-1\right)}{4+\sqrt[5]{-1}-(-1)^{2/5}+(-1)^{3/5}-(-1)^{4/5}}-\frac{2 (-1)^{17/20} \Pi \left(\sqrt[10]{-1};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)}{\left(-1+\sqrt[5]{-1}\right)^2 \left(1+\sqrt[5]{-1}\right)^4}+\frac{2 (-1)^{9/20} \Pi \left(-(-1)^{3/10};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)}{1+4 \sqrt[5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}}+\frac{2 \sqrt[4]{-1} \Pi \left(-(-1)^{7/10};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)}{4+\sqrt[5]{-1}-(-1)^{2/5}+(-1)^{3/5}-(-1)^{4/5}}+\frac{2 (-1)^{9/20} \Pi \left((-1)^{9/10};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)}{1+4 \sqrt[5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}}","\frac{4}{5} \text{RootSum}\left[\text{$\#$1}^4-2 \text{$\#$1}^3-4 \text{$\#$1}+4\&,\frac{\text{$\#$1}^2 \log \left(-\text{$\#$1} x+\sqrt{x^4+1}+x^2+1\right)+\text{$\#$1}^2 (-\log (x))-\text{$\#$1} \log \left(-\text{$\#$1} x+\sqrt{x^4+1}+x^2+1\right)+2 \log \left(-\text{$\#$1} x+\sqrt{x^4+1}+x^2+1\right)+\text{$\#$1} \log (x)-2 \log (x)}{2 \text{$\#$1}^3-3 \text{$\#$1}^2-2}\&\right]-\frac{1}{5} \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}+x^2+2 x+1}\right)",1,"((3*(1 - (-1)^(1/5) + (-1)^(2/5) - (-1)^(3/5) + (-1)^(4/5)) - 12*(1 - (-1)^(1/5) + (-1)^(2/5) - (-1)^(3/5) + (-1)^(4/5))*x^2 + (16 - 17*(-1)^(1/5) + 18*(-1)^(2/5) - 19*(-1)^(3/5) + 20*(-1)^(4/5))*x^4 - 12*(1 - (-1)^(1/5) + (-1)^(2/5) - (-1)^(3/5) + (-1)^(4/5))*x^6 + 3*(1 - (-1)^(1/5) + (-1)^(2/5) - (-1)^(3/5) + (-1)^(4/5))*x^8)*((Sqrt[2]*ArcTanh[(1 + x^2)/(Sqrt[2]*Sqrt[1 + x^4])])/(-4 - (-1)^(1/5) + (-1)^(2/5) - (-1)^(3/5) + (-1)^(4/5)) + 2*(((-1)^(4/5)*ArcTanh[(1 - (-1)^(1/5)*x^2)/(Sqrt[1 + (-1)^(2/5)]*Sqrt[1 + x^4])])/(Sqrt[1 + (-1)^(2/5)]*(1 + 4*(-1)^(1/5) + (-1)^(2/5) - (-1)^(3/5) + (-1)^(4/5))) - ((-1)^(2/5)*ArcTanh[(1 + (-1)^(2/5)*x^2)/(Sqrt[1 + (-1)^(4/5)]*Sqrt[1 + x^4])])/((1 + (-1)^(1/5))^4*(1 + (-1)^(4/5))^(5/2)) + ArcTanh[(1 - (-1)^(3/5)*x^2)/(Sqrt[1 - (-1)^(1/5)]*Sqrt[1 + x^4])]/((1 - (-1)^(1/5))^(3/2)*(1 + (-1)^(1/5))^4*(1 - (-1)^(1/5) + (-1)^(2/5))) + ((-1)^(2/5)*ArcTanh[(1 + (-1)^(4/5)*x^2)/(Sqrt[1 - (-1)^(3/5)]*Sqrt[1 + x^4])])/(Sqrt[1 - (-1)^(3/5)]*(-4 - (-1)^(1/5) + (-1)^(2/5) - (-1)^(3/5) + (-1)^(4/5))))))/(2*(-1 + (-1)^(1/5))^2*(1 + (-1)^(1/5))^3*(1 + (-1)^(2/5))*(1 - (-1)^(1/5) + (-1)^(2/5))*x^4) - (-1)^(1/4)*EllipticF[I*ArcSinh[(-1)^(1/4)*x], -1] + (2*(-1)^(1/4)*EllipticPi[I, ArcSin[(-1)^(3/4)*x], -1])/(4 + (-1)^(1/5) - (-1)^(2/5) + (-1)^(3/5) - (-1)^(4/5)) - (2*(-1)^(17/20)*EllipticPi[(-1)^(1/10), I*ArcSinh[(-1)^(1/4)*x], -1])/((-1 + (-1)^(1/5))^2*(1 + (-1)^(1/5))^4) + (2*(-1)^(9/20)*EllipticPi[-(-1)^(3/10), I*ArcSinh[(-1)^(1/4)*x], -1])/(1 + 4*(-1)^(1/5) + (-1)^(2/5) - (-1)^(3/5) + (-1)^(4/5)) + (2*(-1)^(1/4)*EllipticPi[-(-1)^(7/10), I*ArcSinh[(-1)^(1/4)*x], -1])/(4 + (-1)^(1/5) - (-1)^(2/5) + (-1)^(3/5) - (-1)^(4/5)) + (2*(-1)^(9/20)*EllipticPi[(-1)^(9/10), I*ArcSinh[(-1)^(1/4)*x], -1])/(1 + 4*(-1)^(1/5) + (-1)^(2/5) - (-1)^(3/5) + (-1)^(4/5))","C",0
2230,1,841,166,8.0430663,"\int \frac{-1+x^5}{\sqrt{1+x^4} \left(1+x^5\right)} \, dx","Integrate[(-1 + x^5)/(Sqrt[1 + x^4]*(1 + x^5)),x]","\frac{\left(3 \left(1-\sqrt[5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}\right) x^8-12 \left(1-\sqrt[5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}\right) x^6+\left(16-17 \sqrt[5]{-1}+18 (-1)^{2/5}-19 (-1)^{3/5}+20 (-1)^{4/5}\right) x^4-12 \left(1-\sqrt[5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}\right) x^2+3 \left(1-\sqrt[5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}\right)\right) \left(\frac{\sqrt{2} \tanh ^{-1}\left(\frac{x^2+1}{\sqrt{2} \sqrt{x^4+1}}\right)}{-4-\sqrt[5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}}+2 \left(\frac{(-1)^{4/5} \tanh ^{-1}\left(\frac{1-\sqrt[5]{-1} x^2}{\sqrt{1+(-1)^{2/5}} \sqrt{x^4+1}}\right)}{\sqrt{1+(-1)^{2/5}} \left(1+4 \sqrt[5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}\right)}-\frac{(-1)^{2/5} \tanh ^{-1}\left(\frac{(-1)^{2/5} x^2+1}{\sqrt{1+(-1)^{4/5}} \sqrt{x^4+1}}\right)}{\left(1+\sqrt[5]{-1}\right)^4 \left(1+(-1)^{4/5}\right)^{5/2}}+\frac{\tanh ^{-1}\left(\frac{1-(-1)^{3/5} x^2}{\sqrt{1-\sqrt[5]{-1}} \sqrt{x^4+1}}\right)}{\left(1-\sqrt[5]{-1}\right)^{3/2} \left(1+\sqrt[5]{-1}\right)^4 \left(1-\sqrt[5]{-1}+(-1)^{2/5}\right)}+\frac{(-1)^{2/5} \tanh ^{-1}\left(\frac{(-1)^{4/5} x^2+1}{\sqrt{1-(-1)^{3/5}} \sqrt{x^4+1}}\right)}{\sqrt{1-(-1)^{3/5}} \left(-4-\sqrt[5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}\right)}\right)\right)}{2 \left(-1+\sqrt[5]{-1}\right)^2 \left(1+\sqrt[5]{-1}\right)^3 \left(1+(-1)^{2/5}\right) \left(1-\sqrt[5]{-1}+(-1)^{2/5}\right) x^4}-\sqrt[4]{-1} F\left(\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+\frac{2 \sqrt[4]{-1} \Pi \left(i;\left.\sin ^{-1}\left((-1)^{3/4} x\right)\right|-1\right)}{4+\sqrt[5]{-1}-(-1)^{2/5}+(-1)^{3/5}-(-1)^{4/5}}-\frac{2 (-1)^{17/20} \Pi \left(\sqrt[10]{-1};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)}{\left(-1+\sqrt[5]{-1}\right)^2 \left(1+\sqrt[5]{-1}\right)^4}+\frac{2 (-1)^{9/20} \Pi \left(-(-1)^{3/10};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)}{1+4 \sqrt[5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}}+\frac{2 \sqrt[4]{-1} \Pi \left(-(-1)^{7/10};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)}{4+\sqrt[5]{-1}-(-1)^{2/5}+(-1)^{3/5}-(-1)^{4/5}}+\frac{2 (-1)^{9/20} \Pi \left((-1)^{9/10};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)}{1+4 \sqrt[5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}}","\frac{4}{5} \text{RootSum}\left[\text{$\#$1}^4-2 \text{$\#$1}^3-4 \text{$\#$1}+4\&,\frac{\text{$\#$1}^2 \log \left(-\text{$\#$1} x+\sqrt{x^4+1}+x^2+1\right)+\text{$\#$1}^2 (-\log (x))-\text{$\#$1} \log \left(-\text{$\#$1} x+\sqrt{x^4+1}+x^2+1\right)+2 \log \left(-\text{$\#$1} x+\sqrt{x^4+1}+x^2+1\right)+\text{$\#$1} \log (x)-2 \log (x)}{2 \text{$\#$1}^3-3 \text{$\#$1}^2-2}\&\right]-\frac{1}{5} \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}+x^2+2 x+1}\right)",1,"((3*(1 - (-1)^(1/5) + (-1)^(2/5) - (-1)^(3/5) + (-1)^(4/5)) - 12*(1 - (-1)^(1/5) + (-1)^(2/5) - (-1)^(3/5) + (-1)^(4/5))*x^2 + (16 - 17*(-1)^(1/5) + 18*(-1)^(2/5) - 19*(-1)^(3/5) + 20*(-1)^(4/5))*x^4 - 12*(1 - (-1)^(1/5) + (-1)^(2/5) - (-1)^(3/5) + (-1)^(4/5))*x^6 + 3*(1 - (-1)^(1/5) + (-1)^(2/5) - (-1)^(3/5) + (-1)^(4/5))*x^8)*((Sqrt[2]*ArcTanh[(1 + x^2)/(Sqrt[2]*Sqrt[1 + x^4])])/(-4 - (-1)^(1/5) + (-1)^(2/5) - (-1)^(3/5) + (-1)^(4/5)) + 2*(((-1)^(4/5)*ArcTanh[(1 - (-1)^(1/5)*x^2)/(Sqrt[1 + (-1)^(2/5)]*Sqrt[1 + x^4])])/(Sqrt[1 + (-1)^(2/5)]*(1 + 4*(-1)^(1/5) + (-1)^(2/5) - (-1)^(3/5) + (-1)^(4/5))) - ((-1)^(2/5)*ArcTanh[(1 + (-1)^(2/5)*x^2)/(Sqrt[1 + (-1)^(4/5)]*Sqrt[1 + x^4])])/((1 + (-1)^(1/5))^4*(1 + (-1)^(4/5))^(5/2)) + ArcTanh[(1 - (-1)^(3/5)*x^2)/(Sqrt[1 - (-1)^(1/5)]*Sqrt[1 + x^4])]/((1 - (-1)^(1/5))^(3/2)*(1 + (-1)^(1/5))^4*(1 - (-1)^(1/5) + (-1)^(2/5))) + ((-1)^(2/5)*ArcTanh[(1 + (-1)^(4/5)*x^2)/(Sqrt[1 - (-1)^(3/5)]*Sqrt[1 + x^4])])/(Sqrt[1 - (-1)^(3/5)]*(-4 - (-1)^(1/5) + (-1)^(2/5) - (-1)^(3/5) + (-1)^(4/5))))))/(2*(-1 + (-1)^(1/5))^2*(1 + (-1)^(1/5))^3*(1 + (-1)^(2/5))*(1 - (-1)^(1/5) + (-1)^(2/5))*x^4) - (-1)^(1/4)*EllipticF[I*ArcSinh[(-1)^(1/4)*x], -1] + (2*(-1)^(1/4)*EllipticPi[I, ArcSin[(-1)^(3/4)*x], -1])/(4 + (-1)^(1/5) - (-1)^(2/5) + (-1)^(3/5) - (-1)^(4/5)) - (2*(-1)^(17/20)*EllipticPi[(-1)^(1/10), I*ArcSinh[(-1)^(1/4)*x], -1])/((-1 + (-1)^(1/5))^2*(1 + (-1)^(1/5))^4) + (2*(-1)^(9/20)*EllipticPi[-(-1)^(3/10), I*ArcSinh[(-1)^(1/4)*x], -1])/(1 + 4*(-1)^(1/5) + (-1)^(2/5) - (-1)^(3/5) + (-1)^(4/5)) + (2*(-1)^(1/4)*EllipticPi[-(-1)^(7/10), I*ArcSinh[(-1)^(1/4)*x], -1])/(4 + (-1)^(1/5) - (-1)^(2/5) + (-1)^(3/5) - (-1)^(4/5)) + (2*(-1)^(9/20)*EllipticPi[(-1)^(9/10), I*ArcSinh[(-1)^(1/4)*x], -1])/(1 + 4*(-1)^(1/5) + (-1)^(2/5) - (-1)^(3/5) + (-1)^(4/5))","C",0
2231,1,841,166,8.2898168,"\int \frac{1+x^5}{\sqrt{1+x^4} \left(-1+x^5\right)} \, dx","Integrate[(1 + x^5)/(Sqrt[1 + x^4]*(-1 + x^5)),x]","\frac{\left(-3 \left(1-\sqrt[5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}\right) x^8+12 \left(1-\sqrt[5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}\right) x^6+\left(-16+17 \sqrt[5]{-1}-18 (-1)^{2/5}+19 (-1)^{3/5}-20 (-1)^{4/5}\right) x^4+12 \left(1-\sqrt[5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}\right) x^2-3 \left(1-\sqrt[5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}\right)\right) \left(\frac{\sqrt{2} \tanh ^{-1}\left(\frac{x^2+1}{\sqrt{2} \sqrt{x^4+1}}\right)}{-4-\sqrt[5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}}+2 \left(\frac{(-1)^{4/5} \tanh ^{-1}\left(\frac{1-\sqrt[5]{-1} x^2}{\sqrt{1+(-1)^{2/5}} \sqrt{x^4+1}}\right)}{\sqrt{1+(-1)^{2/5}} \left(1+4 \sqrt[5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}\right)}-\frac{(-1)^{2/5} \tanh ^{-1}\left(\frac{(-1)^{2/5} x^2+1}{\sqrt{1+(-1)^{4/5}} \sqrt{x^4+1}}\right)}{\left(1+\sqrt[5]{-1}\right)^4 \left(1+(-1)^{4/5}\right)^{5/2}}+\frac{\tanh ^{-1}\left(\frac{1-(-1)^{3/5} x^2}{\sqrt{1-\sqrt[5]{-1}} \sqrt{x^4+1}}\right)}{\left(1-\sqrt[5]{-1}\right)^{3/2} \left(1+\sqrt[5]{-1}\right)^4 \left(1-\sqrt[5]{-1}+(-1)^{2/5}\right)}+\frac{(-1)^{2/5} \tanh ^{-1}\left(\frac{(-1)^{4/5} x^2+1}{\sqrt{1-(-1)^{3/5}} \sqrt{x^4+1}}\right)}{\sqrt{1-(-1)^{3/5}} \left(-4-\sqrt[5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}\right)}\right)\right)}{2 \left(-1+\sqrt[5]{-1}\right)^2 \left(1+\sqrt[5]{-1}\right)^3 \left(1+(-1)^{2/5}\right) \left(1-\sqrt[5]{-1}+(-1)^{2/5}\right) x^4}-\sqrt[4]{-1} F\left(\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+\frac{2 \sqrt[4]{-1} \Pi \left(i;\left.\sin ^{-1}\left((-1)^{3/4} x\right)\right|-1\right)}{4+\sqrt[5]{-1}-(-1)^{2/5}+(-1)^{3/5}-(-1)^{4/5}}-\frac{2 (-1)^{17/20} \Pi \left(\sqrt[10]{-1};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)}{\left(-1+\sqrt[5]{-1}\right)^2 \left(1+\sqrt[5]{-1}\right)^4}+\frac{2 (-1)^{9/20} \Pi \left(-(-1)^{3/10};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)}{1+4 \sqrt[5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}}+\frac{2 \sqrt[4]{-1} \Pi \left(-(-1)^{7/10};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)}{4+\sqrt[5]{-1}-(-1)^{2/5}+(-1)^{3/5}-(-1)^{4/5}}+\frac{2 (-1)^{9/20} \Pi \left((-1)^{9/10};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)}{1+4 \sqrt[5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}}","\frac{4}{5} \text{RootSum}\left[\text{$\#$1}^4+2 \text{$\#$1}^3+4 \text{$\#$1}+4\&,\frac{\text{$\#$1}^2 \log \left(-\text{$\#$1} x+\sqrt{x^4+1}+x^2+1\right)+\text{$\#$1}^2 (-\log (x))+\text{$\#$1} \log \left(-\text{$\#$1} x+\sqrt{x^4+1}+x^2+1\right)+2 \log \left(-\text{$\#$1} x+\sqrt{x^4+1}+x^2+1\right)-\text{$\#$1} \log (x)-2 \log (x)}{2 \text{$\#$1}^3+3 \text{$\#$1}^2+2}\&\right]-\frac{1}{5} \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}+x^2-2 x+1}\right)",1,"((-3*(1 - (-1)^(1/5) + (-1)^(2/5) - (-1)^(3/5) + (-1)^(4/5)) + 12*(1 - (-1)^(1/5) + (-1)^(2/5) - (-1)^(3/5) + (-1)^(4/5))*x^2 + (-16 + 17*(-1)^(1/5) - 18*(-1)^(2/5) + 19*(-1)^(3/5) - 20*(-1)^(4/5))*x^4 + 12*(1 - (-1)^(1/5) + (-1)^(2/5) - (-1)^(3/5) + (-1)^(4/5))*x^6 - 3*(1 - (-1)^(1/5) + (-1)^(2/5) - (-1)^(3/5) + (-1)^(4/5))*x^8)*((Sqrt[2]*ArcTanh[(1 + x^2)/(Sqrt[2]*Sqrt[1 + x^4])])/(-4 - (-1)^(1/5) + (-1)^(2/5) - (-1)^(3/5) + (-1)^(4/5)) + 2*(((-1)^(4/5)*ArcTanh[(1 - (-1)^(1/5)*x^2)/(Sqrt[1 + (-1)^(2/5)]*Sqrt[1 + x^4])])/(Sqrt[1 + (-1)^(2/5)]*(1 + 4*(-1)^(1/5) + (-1)^(2/5) - (-1)^(3/5) + (-1)^(4/5))) - ((-1)^(2/5)*ArcTanh[(1 + (-1)^(2/5)*x^2)/(Sqrt[1 + (-1)^(4/5)]*Sqrt[1 + x^4])])/((1 + (-1)^(1/5))^4*(1 + (-1)^(4/5))^(5/2)) + ArcTanh[(1 - (-1)^(3/5)*x^2)/(Sqrt[1 - (-1)^(1/5)]*Sqrt[1 + x^4])]/((1 - (-1)^(1/5))^(3/2)*(1 + (-1)^(1/5))^4*(1 - (-1)^(1/5) + (-1)^(2/5))) + ((-1)^(2/5)*ArcTanh[(1 + (-1)^(4/5)*x^2)/(Sqrt[1 - (-1)^(3/5)]*Sqrt[1 + x^4])])/(Sqrt[1 - (-1)^(3/5)]*(-4 - (-1)^(1/5) + (-1)^(2/5) - (-1)^(3/5) + (-1)^(4/5))))))/(2*(-1 + (-1)^(1/5))^2*(1 + (-1)^(1/5))^3*(1 + (-1)^(2/5))*(1 - (-1)^(1/5) + (-1)^(2/5))*x^4) - (-1)^(1/4)*EllipticF[I*ArcSinh[(-1)^(1/4)*x], -1] + (2*(-1)^(1/4)*EllipticPi[I, ArcSin[(-1)^(3/4)*x], -1])/(4 + (-1)^(1/5) - (-1)^(2/5) + (-1)^(3/5) - (-1)^(4/5)) - (2*(-1)^(17/20)*EllipticPi[(-1)^(1/10), I*ArcSinh[(-1)^(1/4)*x], -1])/((-1 + (-1)^(1/5))^2*(1 + (-1)^(1/5))^4) + (2*(-1)^(9/20)*EllipticPi[-(-1)^(3/10), I*ArcSinh[(-1)^(1/4)*x], -1])/(1 + 4*(-1)^(1/5) + (-1)^(2/5) - (-1)^(3/5) + (-1)^(4/5)) + (2*(-1)^(1/4)*EllipticPi[-(-1)^(7/10), I*ArcSinh[(-1)^(1/4)*x], -1])/(4 + (-1)^(1/5) - (-1)^(2/5) + (-1)^(3/5) - (-1)^(4/5)) + (2*(-1)^(9/20)*EllipticPi[(-1)^(9/10), I*ArcSinh[(-1)^(1/4)*x], -1])/(1 + 4*(-1)^(1/5) + (-1)^(2/5) - (-1)^(3/5) + (-1)^(4/5))","C",0
2232,1,841,166,7.6251376,"\int \frac{1+x^5}{\sqrt{1+x^4} \left(-1+x^5\right)} \, dx","Integrate[(1 + x^5)/(Sqrt[1 + x^4]*(-1 + x^5)),x]","\frac{\left(-3 \left(1-\sqrt[5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}\right) x^8+12 \left(1-\sqrt[5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}\right) x^6+\left(-16+17 \sqrt[5]{-1}-18 (-1)^{2/5}+19 (-1)^{3/5}-20 (-1)^{4/5}\right) x^4+12 \left(1-\sqrt[5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}\right) x^2-3 \left(1-\sqrt[5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}\right)\right) \left(\frac{\sqrt{2} \tanh ^{-1}\left(\frac{x^2+1}{\sqrt{2} \sqrt{x^4+1}}\right)}{-4-\sqrt[5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}}+2 \left(\frac{(-1)^{4/5} \tanh ^{-1}\left(\frac{1-\sqrt[5]{-1} x^2}{\sqrt{1+(-1)^{2/5}} \sqrt{x^4+1}}\right)}{\sqrt{1+(-1)^{2/5}} \left(1+4 \sqrt[5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}\right)}-\frac{(-1)^{2/5} \tanh ^{-1}\left(\frac{(-1)^{2/5} x^2+1}{\sqrt{1+(-1)^{4/5}} \sqrt{x^4+1}}\right)}{\left(1+\sqrt[5]{-1}\right)^4 \left(1+(-1)^{4/5}\right)^{5/2}}+\frac{\tanh ^{-1}\left(\frac{1-(-1)^{3/5} x^2}{\sqrt{1-\sqrt[5]{-1}} \sqrt{x^4+1}}\right)}{\left(1-\sqrt[5]{-1}\right)^{3/2} \left(1+\sqrt[5]{-1}\right)^4 \left(1-\sqrt[5]{-1}+(-1)^{2/5}\right)}+\frac{(-1)^{2/5} \tanh ^{-1}\left(\frac{(-1)^{4/5} x^2+1}{\sqrt{1-(-1)^{3/5}} \sqrt{x^4+1}}\right)}{\sqrt{1-(-1)^{3/5}} \left(-4-\sqrt[5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}\right)}\right)\right)}{2 \left(-1+\sqrt[5]{-1}\right)^2 \left(1+\sqrt[5]{-1}\right)^3 \left(1+(-1)^{2/5}\right) \left(1-\sqrt[5]{-1}+(-1)^{2/5}\right) x^4}-\sqrt[4]{-1} F\left(\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+\frac{2 \sqrt[4]{-1} \Pi \left(i;\left.\sin ^{-1}\left((-1)^{3/4} x\right)\right|-1\right)}{4+\sqrt[5]{-1}-(-1)^{2/5}+(-1)^{3/5}-(-1)^{4/5}}-\frac{2 (-1)^{17/20} \Pi \left(\sqrt[10]{-1};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)}{\left(-1+\sqrt[5]{-1}\right)^2 \left(1+\sqrt[5]{-1}\right)^4}+\frac{2 (-1)^{9/20} \Pi \left(-(-1)^{3/10};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)}{1+4 \sqrt[5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}}+\frac{2 \sqrt[4]{-1} \Pi \left(-(-1)^{7/10};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)}{4+\sqrt[5]{-1}-(-1)^{2/5}+(-1)^{3/5}-(-1)^{4/5}}+\frac{2 (-1)^{9/20} \Pi \left((-1)^{9/10};\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)}{1+4 \sqrt[5]{-1}+(-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}}","\frac{4}{5} \text{RootSum}\left[\text{$\#$1}^4+2 \text{$\#$1}^3+4 \text{$\#$1}+4\&,\frac{\text{$\#$1}^2 \log \left(-\text{$\#$1} x+\sqrt{x^4+1}+x^2+1\right)+\text{$\#$1}^2 (-\log (x))+\text{$\#$1} \log \left(-\text{$\#$1} x+\sqrt{x^4+1}+x^2+1\right)+2 \log \left(-\text{$\#$1} x+\sqrt{x^4+1}+x^2+1\right)-\text{$\#$1} \log (x)-2 \log (x)}{2 \text{$\#$1}^3+3 \text{$\#$1}^2+2}\&\right]-\frac{1}{5} \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}+x^2-2 x+1}\right)",1,"((-3*(1 - (-1)^(1/5) + (-1)^(2/5) - (-1)^(3/5) + (-1)^(4/5)) + 12*(1 - (-1)^(1/5) + (-1)^(2/5) - (-1)^(3/5) + (-1)^(4/5))*x^2 + (-16 + 17*(-1)^(1/5) - 18*(-1)^(2/5) + 19*(-1)^(3/5) - 20*(-1)^(4/5))*x^4 + 12*(1 - (-1)^(1/5) + (-1)^(2/5) - (-1)^(3/5) + (-1)^(4/5))*x^6 - 3*(1 - (-1)^(1/5) + (-1)^(2/5) - (-1)^(3/5) + (-1)^(4/5))*x^8)*((Sqrt[2]*ArcTanh[(1 + x^2)/(Sqrt[2]*Sqrt[1 + x^4])])/(-4 - (-1)^(1/5) + (-1)^(2/5) - (-1)^(3/5) + (-1)^(4/5)) + 2*(((-1)^(4/5)*ArcTanh[(1 - (-1)^(1/5)*x^2)/(Sqrt[1 + (-1)^(2/5)]*Sqrt[1 + x^4])])/(Sqrt[1 + (-1)^(2/5)]*(1 + 4*(-1)^(1/5) + (-1)^(2/5) - (-1)^(3/5) + (-1)^(4/5))) - ((-1)^(2/5)*ArcTanh[(1 + (-1)^(2/5)*x^2)/(Sqrt[1 + (-1)^(4/5)]*Sqrt[1 + x^4])])/((1 + (-1)^(1/5))^4*(1 + (-1)^(4/5))^(5/2)) + ArcTanh[(1 - (-1)^(3/5)*x^2)/(Sqrt[1 - (-1)^(1/5)]*Sqrt[1 + x^4])]/((1 - (-1)^(1/5))^(3/2)*(1 + (-1)^(1/5))^4*(1 - (-1)^(1/5) + (-1)^(2/5))) + ((-1)^(2/5)*ArcTanh[(1 + (-1)^(4/5)*x^2)/(Sqrt[1 - (-1)^(3/5)]*Sqrt[1 + x^4])])/(Sqrt[1 - (-1)^(3/5)]*(-4 - (-1)^(1/5) + (-1)^(2/5) - (-1)^(3/5) + (-1)^(4/5))))))/(2*(-1 + (-1)^(1/5))^2*(1 + (-1)^(1/5))^3*(1 + (-1)^(2/5))*(1 - (-1)^(1/5) + (-1)^(2/5))*x^4) - (-1)^(1/4)*EllipticF[I*ArcSinh[(-1)^(1/4)*x], -1] + (2*(-1)^(1/4)*EllipticPi[I, ArcSin[(-1)^(3/4)*x], -1])/(4 + (-1)^(1/5) - (-1)^(2/5) + (-1)^(3/5) - (-1)^(4/5)) - (2*(-1)^(17/20)*EllipticPi[(-1)^(1/10), I*ArcSinh[(-1)^(1/4)*x], -1])/((-1 + (-1)^(1/5))^2*(1 + (-1)^(1/5))^4) + (2*(-1)^(9/20)*EllipticPi[-(-1)^(3/10), I*ArcSinh[(-1)^(1/4)*x], -1])/(1 + 4*(-1)^(1/5) + (-1)^(2/5) - (-1)^(3/5) + (-1)^(4/5)) + (2*(-1)^(1/4)*EllipticPi[-(-1)^(7/10), I*ArcSinh[(-1)^(1/4)*x], -1])/(4 + (-1)^(1/5) - (-1)^(2/5) + (-1)^(3/5) - (-1)^(4/5)) + (2*(-1)^(9/20)*EllipticPi[(-1)^(9/10), I*ArcSinh[(-1)^(1/4)*x], -1])/(1 + 4*(-1)^(1/5) + (-1)^(2/5) - (-1)^(3/5) + (-1)^(4/5))","C",0
2233,1,195,166,0.7106469,"\int \frac{-b^6+a^6 x^6}{\sqrt{b^4+a^4 x^4} \left(b^6+a^6 x^6\right)} \, dx","Integrate[(-b^6 + a^6*x^6)/(Sqrt[b^4 + a^4*x^4]*(b^6 + a^6*x^6)),x]","-\frac{(-1)^{5/6} \sqrt{\frac{a^4 x^4}{b^4}+1} \left(\left(3-3 i \sqrt{3}\right) F\left(\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)+4 \left((-1)^{2/3} \Pi \left(-i;\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)+\left(\sqrt[3]{-1}-1\right) \Pi \left(\sqrt[6]{-1};\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)+(-1)^{2/3} \Pi \left((-1)^{5/6};\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)\right)\right)}{6 \sqrt{\frac{i a^2}{b^2}} \sqrt{a^4 x^4+b^4}}","-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} a b x}{\sqrt{a^4 x^4+b^4}+a^2 x^2+b^2}\right)}{3 a b}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{4-2 \sqrt{3}} a b x}{\sqrt{a^4 x^4+b^4}+a^2 x^2+b^2}\right)}{3 a b}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{4+2 \sqrt{3}} a b x}{\sqrt{a^4 x^4+b^4}+a^2 x^2+b^2}\right)}{3 a b}",1,"-1/6*((-1)^(5/6)*Sqrt[1 + (a^4*x^4)/b^4]*((3 - (3*I)*Sqrt[3])*EllipticF[I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] + 4*((-1)^(2/3)*EllipticPi[-I, I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] + (-1 + (-1)^(1/3))*EllipticPi[(-1)^(1/6), I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] + (-1)^(2/3)*EllipticPi[(-1)^(5/6), I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1])))/(Sqrt[(I*a^2)/b^2]*Sqrt[b^4 + a^4*x^4])","C",1
2234,0,0,167,9.8921502,"\int \frac{-2 a b+(a+b) x}{\sqrt[3]{x (-a+x) (-b+x)} \left(a b d-(a+b) d x+(-1+d) x^2\right)} \, dx","Integrate[(-2*a*b + (a + b)*x)/((x*(-a + x)*(-b + x))^(1/3)*(a*b*d - (a + b)*d*x + (-1 + d)*x^2)),x]","\int \frac{-2 a b+(a+b) x}{\sqrt[3]{x (-a+x) (-b+x)} \left(a b d-(a+b) d x+(-1+d) x^2\right)} \, dx","\frac{\log \left(x-\sqrt[3]{d} \sqrt[3]{x^2 (-a-b)+a b x+x^3}\right)}{d^{2/3}}-\frac{\log \left(d^{2/3} \left(x^2 (-a-b)+a b x+x^3\right)^{2/3}+\sqrt[3]{d} x \sqrt[3]{x^2 (-a-b)+a b x+x^3}+x^2\right)}{2 d^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{d} \sqrt[3]{x^2 (-a-b)+a b x+x^3}+x}\right)}{d^{2/3}}",1,"Integrate[(-2*a*b + (a + b)*x)/((x*(-a + x)*(-b + x))^(1/3)*(a*b*d - (a + b)*d*x + (-1 + d)*x^2)), x]","F",-1
2235,1,42,167,0.0120102,"\int \frac{1}{x^7 \left(-b+a x^3\right)^{3/4}} \, dx","Integrate[1/(x^7*(-b + a*x^3)^(3/4)),x]","\frac{4 a^2 \sqrt[4]{a x^3-b} \, _2F_1\left(\frac{1}{4},3;\frac{5}{4};1-\frac{a x^3}{b}\right)}{3 b^3}","-\frac{7 a^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^3-b}}{\sqrt{a x^3-b}-\sqrt{b}}\right)}{16 \sqrt{2} b^{11/4}}+\frac{7 a^2 \tanh ^{-1}\left(\frac{\frac{\sqrt{a x^3-b}}{\sqrt{2} \sqrt[4]{b}}+\frac{\sqrt[4]{b}}{\sqrt{2}}}{\sqrt[4]{a x^3-b}}\right)}{16 \sqrt{2} b^{11/4}}+\frac{\sqrt[4]{a x^3-b} \left(7 a x^3+4 b\right)}{24 b^2 x^6}",1,"(4*a^2*(-b + a*x^3)^(1/4)*Hypergeometric2F1[1/4, 3, 5/4, 1 - (a*x^3)/b])/(3*b^3)","C",1
2236,1,42,167,0.0090082,"\int \frac{1}{x^7 \sqrt[4]{-b+a x^3}} \, dx","Integrate[1/(x^7*(-b + a*x^3)^(1/4)),x]","\frac{4 a^2 \left(a x^3-b\right)^{3/4} \, _2F_1\left(\frac{3}{4},3;\frac{7}{4};1-\frac{a x^3}{b}\right)}{9 b^3}","-\frac{5 a^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^3-b}}{\sqrt{a x^3-b}-\sqrt{b}}\right)}{48 \sqrt{2} b^{9/4}}-\frac{5 a^2 \tanh ^{-1}\left(\frac{\frac{\sqrt{a x^3-b}}{\sqrt{2} \sqrt[4]{b}}+\frac{\sqrt[4]{b}}{\sqrt{2}}}{\sqrt[4]{a x^3-b}}\right)}{48 \sqrt{2} b^{9/4}}+\frac{\left(a x^3-b\right)^{3/4} \left(5 a x^3+4 b\right)}{24 b^2 x^6}",1,"(4*a^2*(-b + a*x^3)^(3/4)*Hypergeometric2F1[3/4, 3, 7/4, 1 - (a*x^3)/b])/(9*b^3)","C",1
2237,0,0,167,0.0706555,"\int \frac{1+x^2}{\left(-1+x^2\right) \sqrt[3]{x^2+x^4}} \, dx","Integrate[(1 + x^2)/((-1 + x^2)*(x^2 + x^4)^(1/3)),x]","\int \frac{1+x^2}{\left(-1+x^2\right) \sqrt[3]{x^2+x^4}} \, dx","-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^4+x^2}-x}\right)}{2 \sqrt[3]{2}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^4+x^2}+x}\right)}{2 \sqrt[3]{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[3]{2} x}{\sqrt[3]{x^4+x^2}}\right)}{\sqrt[3]{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[3]{2} x^2+\frac{\left(x^4+x^2\right)^{2/3}}{\sqrt[3]{2}}}{x \sqrt[3]{x^4+x^2}}\right)}{2 \sqrt[3]{2}}",1,"Integrate[(1 + x^2)/((-1 + x^2)*(x^2 + x^4)^(1/3)), x]","F",-1
2238,0,0,167,0.3300394,"\int \frac{\left(-1+x^4\right)^{2/3} \left(3+x^4\right) \left(-2-x^3+2 x^4\right)}{x^6 \left(-2+3 x^3+2 x^4\right)} \, dx","Integrate[((-1 + x^4)^(2/3)*(3 + x^4)*(-2 - x^3 + 2*x^4))/(x^6*(-2 + 3*x^3 + 2*x^4)),x]","\int \frac{\left(-1+x^4\right)^{2/3} \left(3+x^4\right) \left(-2-x^3+2 x^4\right)}{x^6 \left(-2+3 x^3+2 x^4\right)} \, dx","-\sqrt[3]{2} 3^{2/3} \log \left(\sqrt[3]{2} 3^{2/3} \sqrt[3]{x^4-1}+3 x\right)+3 \sqrt[3]{2} \sqrt[6]{3} \tan ^{-1}\left(\frac{3^{5/6} x}{\sqrt[3]{3} x-2 \sqrt[3]{2} \sqrt[3]{x^4-1}}\right)+\left(\frac{3}{2}\right)^{2/3} \log \left(-\sqrt[3]{2} 3^{2/3} \sqrt[3]{x^4-1} x+2^{2/3} \sqrt[3]{3} \left(x^4-1\right)^{2/3}+3 x^2\right)+\frac{3 \left(x^4-1\right)^{2/3} \left(x^4-5 x^3-1\right)}{5 x^5}",1,"Integrate[((-1 + x^4)^(2/3)*(3 + x^4)*(-2 - x^3 + 2*x^4))/(x^6*(-2 + 3*x^3 + 2*x^4)), x]","F",-1
2239,1,39,167,0.0105129,"\int \frac{1}{x^9 \left(-b+a x^4\right)^{3/4}} \, dx","Integrate[1/(x^9*(-b + a*x^4)^(3/4)),x]","\frac{a^2 \sqrt[4]{a x^4-b} \, _2F_1\left(\frac{1}{4},3;\frac{5}{4};1-\frac{a x^4}{b}\right)}{b^3}","-\frac{21 a^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^4-b}}{\sqrt{a x^4-b}-\sqrt{b}}\right)}{64 \sqrt{2} b^{11/4}}+\frac{21 a^2 \tanh ^{-1}\left(\frac{\frac{\sqrt{a x^4-b}}{\sqrt{2} \sqrt[4]{b}}+\frac{\sqrt[4]{b}}{\sqrt{2}}}{\sqrt[4]{a x^4-b}}\right)}{64 \sqrt{2} b^{11/4}}+\frac{\sqrt[4]{a x^4-b} \left(7 a x^4+4 b\right)}{32 b^2 x^8}",1,"(a^2*(-b + a*x^4)^(1/4)*Hypergeometric2F1[1/4, 3, 5/4, 1 - (a*x^4)/b])/b^3","C",1
2240,1,105,167,0.7004051,"\int \frac{b^2+c x^2+a^2 x^4}{\sqrt{b x+a x^3} \left(-b^2+a^2 x^4\right)} \, dx","Integrate[(b^2 + c*x^2 + a^2*x^4)/(Sqrt[b*x + a*x^3]*(-b^2 + a^2*x^4)),x]","-\frac{x \left((2 a b+c) \left(a x^2+b\right) F_1\left(\frac{1}{4};-\frac{1}{2},1;\frac{5}{4};-\frac{a x^2}{b},\frac{a x^2}{b}\right)+b (2 a b-c) \sqrt{\frac{a x^2}{b}+1}\right)}{2 a b^2 \sqrt{x \left(a x^2+b\right)} \sqrt{\frac{a x^2}{b}+1}}","-\frac{(2 a b+c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{a x^3+b x}}{a x^2+b}\right)}{4 \sqrt{2} a^{5/4} b^{5/4}}-\frac{(2 a b+c) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{a x^3+b x}}{a x^2+b}\right)}{4 \sqrt{2} a^{5/4} b^{5/4}}+\frac{(c-2 a b) \sqrt{a x^3+b x}}{2 a b \left(a x^2+b\right)}",1,"-1/2*(x*(b*(2*a*b - c)*Sqrt[1 + (a*x^2)/b] + (2*a*b + c)*(b + a*x^2)*AppellF1[1/4, -1/2, 1, 5/4, -((a*x^2)/b), (a*x^2)/b]))/(a*b^2*Sqrt[x*(b + a*x^2)]*Sqrt[1 + (a*x^2)/b])","C",0
2241,1,42,167,0.0106606,"\int \frac{1}{x^{11} \left(-b+a x^5\right)^{3/4}} \, dx","Integrate[1/(x^11*(-b + a*x^5)^(3/4)),x]","\frac{4 a^2 \sqrt[4]{a x^5-b} \, _2F_1\left(\frac{1}{4},3;\frac{5}{4};1-\frac{a x^5}{b}\right)}{5 b^3}","-\frac{21 a^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^5-b}}{\sqrt{a x^5-b}-\sqrt{b}}\right)}{80 \sqrt{2} b^{11/4}}+\frac{21 a^2 \tanh ^{-1}\left(\frac{\frac{\sqrt{a x^5-b}}{\sqrt{2} \sqrt[4]{b}}+\frac{\sqrt[4]{b}}{\sqrt{2}}}{\sqrt[4]{a x^5-b}}\right)}{80 \sqrt{2} b^{11/4}}+\frac{\sqrt[4]{a x^5-b} \left(7 a x^5+4 b\right)}{40 b^2 x^{10}}",1,"(4*a^2*(-b + a*x^5)^(1/4)*Hypergeometric2F1[1/4, 3, 5/4, 1 - (a*x^5)/b])/(5*b^3)","C",1
2242,0,0,167,0.7763479,"\int \frac{1+x^6}{\sqrt[3]{-x^2+x^4} \left(-1+x^6\right)} \, dx","Integrate[(1 + x^6)/((-x^2 + x^4)^(1/3)*(-1 + x^6)),x]","\int \frac{1+x^6}{\sqrt[3]{-x^2+x^4} \left(-1+x^6\right)} \, dx","-\frac{\left(x^4-x^2\right)^{2/3}}{x \left(x^2-1\right)}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[6]{3} x}{\sqrt[3]{x^4-x^2}}\right)}{3 \sqrt[6]{3}}-\frac{\tan ^{-1}\left(\frac{3^{5/6} x \sqrt[3]{x^4-x^2}}{3^{2/3} \left(x^4-x^2\right)^{2/3}-3 x^2}\right)}{3 \sqrt[6]{3}}-\frac{\tanh ^{-1}\left(\frac{\frac{x^2}{\sqrt[3]{3}}+\frac{\left(x^4-x^2\right)^{2/3}}{3^{2/3}}}{x \sqrt[3]{x^4-x^2}}\right)}{3^{2/3}}",1,"Integrate[(1 + x^6)/((-x^2 + x^4)^(1/3)*(-1 + x^6)), x]","F",-1
2243,1,345,167,2.2681778,"\int \frac{-b^6+a^6 x^6}{\sqrt{b^2 x+a^2 x^3} \left(b^6+a^6 x^6\right)} \, dx","Integrate[(-b^6 + a^6*x^6)/(Sqrt[b^2*x + a^2*x^3]*(b^6 + a^6*x^6)),x]","\frac{2 \left(-x^{3/2}-\frac{i x^2 \sqrt{\frac{b^2}{a^2 x^2}+1} \left(-\Pi \left(-\frac{i \sqrt{2} a}{\sqrt{\frac{\left(1-i \sqrt{3}\right) a^2}{b^2}} b};\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)-\Pi \left(\frac{i \sqrt{2} a}{\sqrt{\frac{\left(1-i \sqrt{3}\right) a^2}{b^2}} b};\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)-\Pi \left(-\frac{i \sqrt{2} a}{\sqrt{\frac{\left(1+i \sqrt{3}\right) a^2}{b^2}} b};\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)-\Pi \left(\frac{i \sqrt{2} a}{\sqrt{\frac{\left(1+i \sqrt{3}\right) a^2}{b^2}} b};\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)+2 F\left(\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)\right)}{\sqrt{\frac{i b}{a}}}\right)}{3 \sqrt{x} \sqrt{x \left(a^2 x^2+b^2\right)}}","-\frac{2 \sqrt{a^2 x^3+b^2 x}}{3 \left(a^2 x^2+b^2\right)}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{3} \sqrt{a} \sqrt{b} \sqrt{a^2 x^3+b^2 x}}{a^2 x^2+b^2}\right)}{3 \sqrt[4]{3} \sqrt{a} \sqrt{b}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{3} \sqrt{a} \sqrt{b} \sqrt{a^2 x^3+b^2 x}}{a^2 x^2+b^2}\right)}{3 \sqrt[4]{3} \sqrt{a} \sqrt{b}}",1,"(2*(-x^(3/2) - (I*Sqrt[1 + b^2/(a^2*x^2)]*x^2*(2*EllipticF[I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1] - EllipticPi[((-I)*Sqrt[2]*a)/(Sqrt[((1 - I*Sqrt[3])*a^2)/b^2]*b), I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1] - EllipticPi[(I*Sqrt[2]*a)/(Sqrt[((1 - I*Sqrt[3])*a^2)/b^2]*b), I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1] - EllipticPi[((-I)*Sqrt[2]*a)/(Sqrt[((1 + I*Sqrt[3])*a^2)/b^2]*b), I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1] - EllipticPi[(I*Sqrt[2]*a)/(Sqrt[((1 + I*Sqrt[3])*a^2)/b^2]*b), I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1]))/Sqrt[(I*b)/a]))/(3*Sqrt[x]*Sqrt[x*(b^2 + a^2*x^2)])","C",1
2244,1,166,167,0.471123,"\int \frac{1+a x^2}{\left(-1+a x^2\right) \sqrt{a x+\sqrt{b+a^2 x^2}}} \, dx","Integrate[(1 + a*x^2)/((-1 + a*x^2)*Sqrt[a*x + Sqrt[b + a^2*x^2]]),x]","\frac{-a \text{RootSum}\left[\text{$\#$1}^8 \left(-b^2\right)+4 \text{$\#$1}^4 a+2 \text{$\#$1}^4 b-1\&,\frac{\text{$\#$1}^4 b \log \left(\frac{1}{\sqrt{\sqrt{a^2 x^2+b}+a x}}-\text{$\#$1}\right)+\log \left(\frac{1}{\sqrt{\sqrt{a^2 x^2+b}+a x}}-\text{$\#$1}\right)}{\text{$\#$1}^5 b^2-2 \text{$\#$1} a-\text{$\#$1} b}\&\right]-\frac{b}{3 \left(\sqrt{a^2 x^2+b}+a x\right)^{3/2}}+\sqrt{\sqrt{a^2 x^2+b}+a x}}{a}","\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^4 a-2 \text{$\#$1}^4 b+b^2\&,\frac{\text{$\#$1}^4 \left(-\log \left(\sqrt{\sqrt{a^2 x^2+b}+a x}-\text{$\#$1}\right)\right)-b \log \left(\sqrt{\sqrt{a^2 x^2+b}+a x}-\text{$\#$1}\right)}{-\text{$\#$1}^7+2 \text{$\#$1}^3 a+\text{$\#$1}^3 b}\&\right]-\frac{b}{3 a \left(\sqrt{a^2 x^2+b}+a x\right)^{3/2}}+\frac{\sqrt{\sqrt{a^2 x^2+b}+a x}}{a}",1,"(-1/3*b/(a*x + Sqrt[b + a^2*x^2])^(3/2) + Sqrt[a*x + Sqrt[b + a^2*x^2]] - a*RootSum[-1 + 4*a*#1^4 + 2*b*#1^4 - b^2*#1^8 & , (Log[1/Sqrt[a*x + Sqrt[b + a^2*x^2]] - #1] + b*Log[1/Sqrt[a*x + Sqrt[b + a^2*x^2]] - #1]*#1^4)/(-2*a*#1 - b*#1 + b^2*#1^5) & ])/a","A",1
2245,1,341,167,5.4060615,"\int \frac{\sqrt{-\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}}{x^2 \sqrt{a x^2+b x \sqrt{-\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}}} \, dx","Integrate[Sqrt[-(a/b^2) + (a^2*x^2)/b^2]/(x^2*Sqrt[a*x^2 + b*x*Sqrt[-(a/b^2) + (a^2*x^2)/b^2]]),x]","\frac{\frac{3 \sqrt{\frac{a \left(a x^2-1\right)}{b^2}} \left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right) \left(\, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};2 x \left(\sqrt{\frac{a \left(a x^2-1\right)}{b^2}} b+a x\right)\right)+2 b x \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+2 a x^2+3\right)}{b x \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x^2-1}-\frac{4 a \left(3 b x \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+3 a x^2-1\right)}{b x \left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right)}-\frac{3 \sqrt{2} \sqrt{a x \left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right)} \left(\sqrt{2} \sqrt{a x \left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right)}+\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{\left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right)^2+a}}{\sqrt{a}}\right)\right)}{b}}{6 \sqrt{x \left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right)}}","\frac{2 \left(2 a x^2-1\right) \sqrt{b x \sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}}+a x^2}}{3 b x^2}-\frac{4 \sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}} \sqrt{b x \sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}}+a x^2}}{3 x}-\frac{\sqrt{2} a \tanh ^{-1}\left(\sqrt{2} \sqrt{b x \sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}}+a x^2}\right)}{b}",1,"((-4*a*(-1 + 3*a*x^2 + 3*b*x*Sqrt[(a*(-1 + a*x^2))/b^2]))/(b*x*(a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2])) - (3*Sqrt[2]*Sqrt[a*x*(a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2])]*(Sqrt[2]*Sqrt[a*x*(a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2])] + Sqrt[a]*ArcTanh[Sqrt[a + (a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2])^2]/Sqrt[a]]))/b + (3*Sqrt[(a*(-1 + a*x^2))/b^2]*(a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2])*(3 + 2*a*x^2 + 2*b*x*Sqrt[(a*(-1 + a*x^2))/b^2] + Hypergeometric2F1[-1/2, 1, 1/2, 2*x*(a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2])]))/(-1 + a*x^2 + b*x*Sqrt[(a*(-1 + a*x^2))/b^2]))/(6*Sqrt[x*(a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2])])","C",1
2246,1,13567,167,6.5062866,"\int \frac{\left(-2 q+p x^3\right) \sqrt{q+p x^3}}{b x^4+a \left(q+p x^3\right)^2} \, dx","Integrate[((-2*q + p*x^3)*Sqrt[q + p*x^3])/(b*x^4 + a*(q + p*x^3)^2),x]","\text{Result too large to show}","-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x \sqrt{p x^3+q}}{\sqrt{a} p x^3+\sqrt{a} q-\sqrt{b} x^2}\right)}{\sqrt{2} a^{3/4} \sqrt[4]{b}}-\frac{\tanh ^{-1}\left(\frac{\frac{\sqrt[4]{a} p x^3}{\sqrt{2} \sqrt[4]{b}}+\frac{\sqrt[4]{a} q}{\sqrt{2} \sqrt[4]{b}}+\frac{\sqrt[4]{b} x^2}{\sqrt{2} \sqrt[4]{a}}}{x \sqrt{p x^3+q}}\right)}{\sqrt{2} a^{3/4} \sqrt[4]{b}}",1,"Result too large to show","C",0
2247,1,1550,167,7.2911636,"\int x^4 \sqrt{1+x^4} \sqrt{x^2+\sqrt{1+x^4}} \, dx","Integrate[x^4*Sqrt[1 + x^4]*Sqrt[x^2 + Sqrt[1 + x^4]],x]","\frac{5 x^3 \left(x^2+\sqrt{x^4+1}\right)^{7/2} \left(x^4+\sqrt{x^4+1} x^2+1\right) \left(-\left(\left(6 x^8+6 \sqrt{x^4+1} x^6+3 x^4-1\right) \, _2F_1\left(-\frac{3}{2},-\frac{3}{2};\frac{3}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right)\right)+6 \left(16 x^{12}+16 \sqrt{x^4+1} x^{10}+28 x^8+20 \sqrt{x^4+1} x^6+13 x^4+5 \sqrt{x^4+1} x^2+1\right) \, _2F_1\left(-\frac{1}{2},-\frac{1}{2};\frac{5}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right)-6 \left(x^4+1\right) \left(8 x^8+8 \sqrt{x^4+1} x^6+8 x^4+4 \sqrt{x^4+1} x^2+1\right) \, _3F_2\left(-\frac{1}{2},-\frac{1}{2},2;1,\frac{5}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right)\right)}{6 \left(2048 \, _2F_1\left(\frac{1}{2},\frac{1}{2};\frac{7}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^{22}+2048 \sqrt{x^4+1} \, _2F_1\left(\frac{1}{2},\frac{1}{2};\frac{7}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^{20}+5760 \, _2F_1\left(-\frac{1}{2},-\frac{1}{2};\frac{5}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^{18}+5632 \, _2F_1\left(\frac{1}{2},\frac{1}{2};\frac{7}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^{18}+5760 \sqrt{x^4+1} \, _2F_1\left(-\frac{1}{2},-\frac{1}{2};\frac{5}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^{16}+4608 \sqrt{x^4+1} \, _2F_1\left(\frac{1}{2},\frac{1}{2};\frac{7}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^{16}-160 \, _2F_1\left(-\frac{3}{2},-\frac{3}{2};\frac{3}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^{14}+13120 \, _2F_1\left(-\frac{1}{2},-\frac{1}{2};\frac{5}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^{14}+5632 \, _2F_1\left(\frac{1}{2},\frac{1}{2};\frac{7}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^{14}-160 \sqrt{x^4+1} \, _2F_1\left(-\frac{3}{2},-\frac{3}{2};\frac{3}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^{12}+10240 \sqrt{x^4+1} \, _2F_1\left(-\frac{1}{2},-\frac{1}{2};\frac{5}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^{12}+3584 \sqrt{x^4+1} \, _2F_1\left(\frac{1}{2},\frac{1}{2};\frac{7}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^{12}-320 \, _2F_1\left(-\frac{3}{2},-\frac{3}{2};\frac{3}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^{10}+10000 \, _2F_1\left(-\frac{1}{2},-\frac{1}{2};\frac{5}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^{10}+2464 \, _2F_1\left(\frac{1}{2},\frac{1}{2};\frac{7}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^{10}-240 \sqrt{x^4+1} \, _2F_1\left(-\frac{3}{2},-\frac{3}{2};\frac{3}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^8+5600 \sqrt{x^4+1} \, _2F_1\left(-\frac{1}{2},-\frac{1}{2};\frac{5}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^8+1120 \sqrt{x^4+1} \, _2F_1\left(\frac{1}{2},\frac{1}{2};\frac{7}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^8-190 \, _2F_1\left(-\frac{3}{2},-\frac{3}{2};\frac{3}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^6+2840 \, _2F_1\left(-\frac{1}{2},-\frac{1}{2};\frac{5}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^6+440 \, _2F_1\left(\frac{1}{2},\frac{1}{2};\frac{7}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^6-90 \sqrt{x^4+1} \, _2F_1\left(-\frac{3}{2},-\frac{3}{2};\frac{3}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^4+960 \sqrt{x^4+1} \, _2F_1\left(-\frac{1}{2},-\frac{1}{2};\frac{5}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^4+120 \sqrt{x^4+1} \, _2F_1\left(\frac{1}{2},\frac{1}{2};\frac{7}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^4-30 \, _2F_1\left(-\frac{3}{2},-\frac{3}{2};\frac{3}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^2+220 \, _2F_1\left(-\frac{1}{2},-\frac{1}{2};\frac{5}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^2+22 \, _2F_1\left(\frac{1}{2},\frac{1}{2};\frac{7}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right) x^2-5 \sqrt{x^4+1} \, _2F_1\left(-\frac{3}{2},-\frac{3}{2};\frac{3}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right)+25 \sqrt{x^4+1} \, _2F_1\left(-\frac{1}{2},-\frac{1}{2};\frac{5}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right)+2 \sqrt{x^4+1} \, _2F_1\left(\frac{1}{2},\frac{1}{2};\frac{7}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right)-10 \left(384 x^{18}+384 \sqrt{x^4+1} x^{16}+832 x^{14}+640 \sqrt{x^4+1} x^{12}+592 x^{10}+320 \sqrt{x^4+1} x^8+152 x^6+48 \sqrt{x^4+1} x^4+10 x^2+\sqrt{x^4+1}\right) \, _3F_2\left(-\frac{1}{2},-\frac{1}{2},2;1,\frac{5}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right)-4 \left(512 x^{22}+512 \sqrt{x^4+1} x^{20}+1536 x^{18}+1280 \sqrt{x^4+1} x^{16}+1696 x^{14}+1120 \sqrt{x^4+1} x^{12}+832 x^{10}+400 \sqrt{x^4+1} x^8+170 x^6+50 \sqrt{x^4+1} x^4+10 x^2+\sqrt{x^4+1}\right) \, _3F_2\left(\frac{1}{2},\frac{1}{2},3;2,\frac{7}{2};\left(x^2+\sqrt{x^4+1}\right)^2\right)\right)}","\frac{x \left(192 x^{12}+360 x^8+212 x^4+39\right) \sqrt{\sqrt{x^4+1}+x^2}+x \sqrt{x^4+1} \sqrt{\sqrt{x^4+1}+x^2} \left(192 x^{10}+264 x^6+104 x^2\right)}{384 \sqrt{x^4+1} \left(4 x^4+1\right)+384 \left(4 x^6+3 x^2\right)}-\frac{13 \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)}{64 \sqrt{2}}",1,"(5*x^3*(x^2 + Sqrt[1 + x^4])^(7/2)*(1 + x^4 + x^2*Sqrt[1 + x^4])*(-((-1 + 3*x^4 + 6*x^8 + 6*x^6*Sqrt[1 + x^4])*Hypergeometric2F1[-3/2, -3/2, 3/2, (x^2 + Sqrt[1 + x^4])^2]) + 6*(1 + 13*x^4 + 28*x^8 + 16*x^12 + 5*x^2*Sqrt[1 + x^4] + 20*x^6*Sqrt[1 + x^4] + 16*x^10*Sqrt[1 + x^4])*Hypergeometric2F1[-1/2, -1/2, 5/2, (x^2 + Sqrt[1 + x^4])^2] - 6*(1 + x^4)*(1 + 8*x^4 + 8*x^8 + 4*x^2*Sqrt[1 + x^4] + 8*x^6*Sqrt[1 + x^4])*HypergeometricPFQ[{-1/2, -1/2, 2}, {1, 5/2}, (x^2 + Sqrt[1 + x^4])^2]))/(6*(-30*x^2*Hypergeometric2F1[-3/2, -3/2, 3/2, (x^2 + Sqrt[1 + x^4])^2] - 190*x^6*Hypergeometric2F1[-3/2, -3/2, 3/2, (x^2 + Sqrt[1 + x^4])^2] - 320*x^10*Hypergeometric2F1[-3/2, -3/2, 3/2, (x^2 + Sqrt[1 + x^4])^2] - 160*x^14*Hypergeometric2F1[-3/2, -3/2, 3/2, (x^2 + Sqrt[1 + x^4])^2] - 5*Sqrt[1 + x^4]*Hypergeometric2F1[-3/2, -3/2, 3/2, (x^2 + Sqrt[1 + x^4])^2] - 90*x^4*Sqrt[1 + x^4]*Hypergeometric2F1[-3/2, -3/2, 3/2, (x^2 + Sqrt[1 + x^4])^2] - 240*x^8*Sqrt[1 + x^4]*Hypergeometric2F1[-3/2, -3/2, 3/2, (x^2 + Sqrt[1 + x^4])^2] - 160*x^12*Sqrt[1 + x^4]*Hypergeometric2F1[-3/2, -3/2, 3/2, (x^2 + Sqrt[1 + x^4])^2] + 220*x^2*Hypergeometric2F1[-1/2, -1/2, 5/2, (x^2 + Sqrt[1 + x^4])^2] + 2840*x^6*Hypergeometric2F1[-1/2, -1/2, 5/2, (x^2 + Sqrt[1 + x^4])^2] + 10000*x^10*Hypergeometric2F1[-1/2, -1/2, 5/2, (x^2 + Sqrt[1 + x^4])^2] + 13120*x^14*Hypergeometric2F1[-1/2, -1/2, 5/2, (x^2 + Sqrt[1 + x^4])^2] + 5760*x^18*Hypergeometric2F1[-1/2, -1/2, 5/2, (x^2 + Sqrt[1 + x^4])^2] + 25*Sqrt[1 + x^4]*Hypergeometric2F1[-1/2, -1/2, 5/2, (x^2 + Sqrt[1 + x^4])^2] + 960*x^4*Sqrt[1 + x^4]*Hypergeometric2F1[-1/2, -1/2, 5/2, (x^2 + Sqrt[1 + x^4])^2] + 5600*x^8*Sqrt[1 + x^4]*Hypergeometric2F1[-1/2, -1/2, 5/2, (x^2 + Sqrt[1 + x^4])^2] + 10240*x^12*Sqrt[1 + x^4]*Hypergeometric2F1[-1/2, -1/2, 5/2, (x^2 + Sqrt[1 + x^4])^2] + 5760*x^16*Sqrt[1 + x^4]*Hypergeometric2F1[-1/2, -1/2, 5/2, (x^2 + Sqrt[1 + x^4])^2] + 22*x^2*Hypergeometric2F1[1/2, 1/2, 7/2, (x^2 + Sqrt[1 + x^4])^2] + 440*x^6*Hypergeometric2F1[1/2, 1/2, 7/2, (x^2 + Sqrt[1 + x^4])^2] + 2464*x^10*Hypergeometric2F1[1/2, 1/2, 7/2, (x^2 + Sqrt[1 + x^4])^2] + 5632*x^14*Hypergeometric2F1[1/2, 1/2, 7/2, (x^2 + Sqrt[1 + x^4])^2] + 5632*x^18*Hypergeometric2F1[1/2, 1/2, 7/2, (x^2 + Sqrt[1 + x^4])^2] + 2048*x^22*Hypergeometric2F1[1/2, 1/2, 7/2, (x^2 + Sqrt[1 + x^4])^2] + 2*Sqrt[1 + x^4]*Hypergeometric2F1[1/2, 1/2, 7/2, (x^2 + Sqrt[1 + x^4])^2] + 120*x^4*Sqrt[1 + x^4]*Hypergeometric2F1[1/2, 1/2, 7/2, (x^2 + Sqrt[1 + x^4])^2] + 1120*x^8*Sqrt[1 + x^4]*Hypergeometric2F1[1/2, 1/2, 7/2, (x^2 + Sqrt[1 + x^4])^2] + 3584*x^12*Sqrt[1 + x^4]*Hypergeometric2F1[1/2, 1/2, 7/2, (x^2 + Sqrt[1 + x^4])^2] + 4608*x^16*Sqrt[1 + x^4]*Hypergeometric2F1[1/2, 1/2, 7/2, (x^2 + Sqrt[1 + x^4])^2] + 2048*x^20*Sqrt[1 + x^4]*Hypergeometric2F1[1/2, 1/2, 7/2, (x^2 + Sqrt[1 + x^4])^2] - 10*(10*x^2 + 152*x^6 + 592*x^10 + 832*x^14 + 384*x^18 + Sqrt[1 + x^4] + 48*x^4*Sqrt[1 + x^4] + 320*x^8*Sqrt[1 + x^4] + 640*x^12*Sqrt[1 + x^4] + 384*x^16*Sqrt[1 + x^4])*HypergeometricPFQ[{-1/2, -1/2, 2}, {1, 5/2}, (x^2 + Sqrt[1 + x^4])^2] - 4*(10*x^2 + 170*x^6 + 832*x^10 + 1696*x^14 + 1536*x^18 + 512*x^22 + Sqrt[1 + x^4] + 50*x^4*Sqrt[1 + x^4] + 400*x^8*Sqrt[1 + x^4] + 1120*x^12*Sqrt[1 + x^4] + 1280*x^16*Sqrt[1 + x^4] + 512*x^20*Sqrt[1 + x^4])*HypergeometricPFQ[{1/2, 1/2, 3}, {2, 7/2}, (x^2 + Sqrt[1 + x^4])^2]))","C",0
2248,0,0,167,0.309573,"\int \frac{\sqrt{q+p x^5} \left(-2 q+3 p x^5\right)}{b x^4+a \left(q+p x^5\right)^2} \, dx","Integrate[(Sqrt[q + p*x^5]*(-2*q + 3*p*x^5))/(b*x^4 + a*(q + p*x^5)^2),x]","\int \frac{\sqrt{q+p x^5} \left(-2 q+3 p x^5\right)}{b x^4+a \left(q+p x^5\right)^2} \, dx","-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x \sqrt{p x^5+q}}{\sqrt{a} p x^5+\sqrt{a} q-\sqrt{b} x^2}\right)}{\sqrt{2} a^{3/4} \sqrt[4]{b}}-\frac{\tanh ^{-1}\left(\frac{\frac{\sqrt[4]{a} p x^5}{\sqrt{2} \sqrt[4]{b}}+\frac{\sqrt[4]{a} q}{\sqrt{2} \sqrt[4]{b}}+\frac{\sqrt[4]{b} x^2}{\sqrt{2} \sqrt[4]{a}}}{x \sqrt{p x^5+q}}\right)}{\sqrt{2} a^{3/4} \sqrt[4]{b}}",1,"Integrate[(Sqrt[q + p*x^5]*(-2*q + 3*p*x^5))/(b*x^4 + a*(q + p*x^5)^2), x]","F",-1
2249,1,143,168,0.2197208,"\int \frac{-3+x}{\sqrt[3]{1-x^2} \left(3+x^2\right)} \, dx","Integrate[(-3 + x)/((1 - x^2)^(1/3)*(3 + x^2)),x]","\frac{1}{6} x^2 F_1\left(1;\frac{1}{3},1;2;x^2,-\frac{x^2}{3}\right)+\frac{27 x F_1\left(\frac{1}{2};\frac{1}{3},1;\frac{3}{2};x^2,-\frac{x^2}{3}\right)}{\sqrt[3]{1-x^2} \left(x^2+3\right) \left(2 x^2 \left(F_1\left(\frac{3}{2};\frac{1}{3},2;\frac{5}{2};x^2,-\frac{x^2}{3}\right)-F_1\left(\frac{3}{2};\frac{4}{3},1;\frac{5}{2};x^2,-\frac{x^2}{3}\right)\right)-9 F_1\left(\frac{1}{2};\frac{1}{3},1;\frac{3}{2};x^2,-\frac{x^2}{3}\right)\right)}","-\frac{\log \left(2 \sqrt[3]{1-x^2}+2^{2/3} x+2^{2/3}\right)}{2^{2/3}}+\frac{\log \left(-\sqrt[3]{2} x^2-2 \left(1-x^2\right)^{2/3}+\left(2^{2/3} x+2^{2/3}\right) \sqrt[3]{1-x^2}-2 \sqrt[3]{2} x-\sqrt[3]{2}\right)}{2\ 2^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{1-x^2}}{\sqrt[3]{1-x^2}-2^{2/3} x-2^{2/3}}\right)}{2^{2/3}}",1,"(x^2*AppellF1[1, 1/3, 1, 2, x^2, -1/3*x^2])/6 + (27*x*AppellF1[1/2, 1/3, 1, 3/2, x^2, -1/3*x^2])/((1 - x^2)^(1/3)*(3 + x^2)*(-9*AppellF1[1/2, 1/3, 1, 3/2, x^2, -1/3*x^2] + 2*x^2*(AppellF1[3/2, 1/3, 2, 5/2, x^2, -1/3*x^2] - AppellF1[3/2, 4/3, 1, 5/2, x^2, -1/3*x^2])))","C",0
2250,0,0,168,7.3081812,"\int \frac{x^3 (-3 a b+(a+2 b) x)}{(-a+x) (-b+x) \sqrt[4]{x (-a+x) (-b+x)^2} \left(-a b^2 d+b (2 a+b) d x-(a+2 b) d x^2+(-1+d) x^3\right)} \, dx","Integrate[(x^3*(-3*a*b + (a + 2*b)*x))/((-a + x)*(-b + x)*(x*(-a + x)*(-b + x)^2)^(1/4)*(-(a*b^2*d) + b*(2*a + b)*d*x - (a + 2*b)*d*x^2 + (-1 + d)*x^3)),x]","\int \frac{x^3 (-3 a b+(a+2 b) x)}{(-a+x) (-b+x) \sqrt[4]{x (-a+x) (-b+x)^2} \left(-a b^2 d+b (2 a+b) d x-(a+2 b) d x^2+(-1+d) x^3\right)} \, dx","2 \sqrt[4]{d} \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}}{x}\right)-2 \sqrt[4]{d} \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}}{x}\right)+\frac{4 \left(-a b^2 x+2 a b x^2-a x^3+b^2 x^2-2 b x^3+x^4\right)^{3/4}}{(x-a) (x-b)^2}",1,"Integrate[(x^3*(-3*a*b + (a + 2*b)*x))/((-a + x)*(-b + x)*(x*(-a + x)*(-b + x)^2)^(1/4)*(-(a*b^2*d) + b*(2*a + b)*d*x - (a + 2*b)*d*x^2 + (-1 + d)*x^3)), x]","F",-1
2251,1,423,168,3.7918219,"\int \frac{a x+\sqrt{b^2+a^2 x^2}}{b+\sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Integrate[(a*x + Sqrt[b^2 + a^2*x^2])/(b + Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]),x]","\frac{b \left(-2 \sqrt{a^2 x^2+b^2}+b^2 \log \left(b^2 \left(\sqrt{a^2 x^2+b^2}+a x+2\right)+\sqrt{a^2 x^2+b^2}-a x\right)-\left(b^2-1\right) \log \left(\sqrt{a^2 x^2+b^2}+a x\right)+\log \left(b^2 \left(\sqrt{a^2 x^2+b^2}+a x+2\right)+\sqrt{a^2 x^2+b^2}-a x\right)-2 \left(b^2+1\right) \log \left(2 a x-b^2+1\right)-2 a x\right)}{4 a}+\frac{a b^2 x \left(a x \left(6 \sqrt{a^2 x^2+b^2}+5\right)+3 \sqrt{a^2 x^2+b^2}+6 a^2 x^2\right)-3 \left(b^2+1\right) b \sqrt{\sqrt{a^2 x^2+b^2}+a x} \left(a x \left(\sqrt{a^2 x^2+b^2}+a x\right)+b^2\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a^2 x^2+b^2}+a x}}{b}\right)+b^4 \left(3 \sqrt{a^2 x^2+b^2}+6 a x+1\right)+4 a^3 x^3 \left(\sqrt{a^2 x^2+b^2}+a x\right)}{3 a \sqrt{\sqrt{a^2 x^2+b^2}+a x} \left(a x \left(\sqrt{a^2 x^2+b^2}+a x\right)+b^2\right)}","\sqrt{a^2 x^2+b^2} \left(\frac{\sqrt{\sqrt{a^2 x^2+b^2}+a x}}{3 a}-\frac{b}{2 a}\right)+\frac{\left(a x+3 b^2\right) \sqrt{\sqrt{a^2 x^2+b^2}+a x}}{3 a}+\frac{b \log \left(\sqrt{a^2 x^2+b^2}+a x\right)}{2 a}+\frac{\left(-b^3-b\right) \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}+b\right)}{a}-\frac{b x}{2}",1,"(4*a^3*x^3*(a*x + Sqrt[b^2 + a^2*x^2]) + b^4*(1 + 6*a*x + 3*Sqrt[b^2 + a^2*x^2]) + a*b^2*x*(6*a^2*x^2 + 3*Sqrt[b^2 + a^2*x^2] + a*x*(5 + 6*Sqrt[b^2 + a^2*x^2])) - 3*b*(1 + b^2)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]*(b^2 + a*x*(a*x + Sqrt[b^2 + a^2*x^2]))*ArcTanh[Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]/b])/(3*a*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]*(b^2 + a*x*(a*x + Sqrt[b^2 + a^2*x^2]))) + (b*(-2*a*x - 2*Sqrt[b^2 + a^2*x^2] - 2*(1 + b^2)*Log[1 - b^2 + 2*a*x] - (-1 + b^2)*Log[a*x + Sqrt[b^2 + a^2*x^2]] + Log[-(a*x) + Sqrt[b^2 + a^2*x^2] + b^2*(2 + a*x + Sqrt[b^2 + a^2*x^2])] + b^2*Log[-(a*x) + Sqrt[b^2 + a^2*x^2] + b^2*(2 + a*x + Sqrt[b^2 + a^2*x^2])]))/(4*a)","B",1
2252,1,126,169,0.0950084,"\int \frac{1}{\left(3+x^2\right) \sqrt[3]{1+3 x^2}} \, dx","Integrate[1/((3 + x^2)*(1 + 3*x^2)^(1/3)),x]","-\frac{9 x F_1\left(\frac{1}{2};\frac{1}{3},1;\frac{3}{2};-3 x^2,-\frac{x^2}{3}\right)}{\left(x^2+3\right) \sqrt[3]{3 x^2+1} \left(2 x^2 \left(F_1\left(\frac{3}{2};\frac{1}{3},2;\frac{5}{2};-3 x^2,-\frac{x^2}{3}\right)+3 F_1\left(\frac{3}{2};\frac{4}{3},1;\frac{5}{2};-3 x^2,-\frac{x^2}{3}\right)\right)-9 F_1\left(\frac{1}{2};\frac{1}{3},1;\frac{3}{2};-3 x^2,-\frac{x^2}{3}\right)\right)}","\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{3 x^2+1}+1}\right)}{4 \sqrt{3}}-\frac{i \tanh ^{-1}\left(\frac{2 i \sqrt{3} x-2 i \sqrt{3} x \sqrt[3]{3 x^2+1}}{3 x^2-4 \left(3 x^2+1\right)^{2/3}+2 \sqrt[3]{3 x^2+1}-1}\right)}{8 \sqrt{3}}+\frac{1}{8} \tanh ^{-1}\left(\frac{6 x \sqrt[3]{3 x^2+1}}{3 x^2+4 \left(3 x^2+1\right)^{2/3}-2 \sqrt[3]{3 x^2+1}+1}\right)",1,"(-9*x*AppellF1[1/2, 1/3, 1, 3/2, -3*x^2, -1/3*x^2])/((3 + x^2)*(1 + 3*x^2)^(1/3)*(-9*AppellF1[1/2, 1/3, 1, 3/2, -3*x^2, -1/3*x^2] + 2*x^2*(AppellF1[3/2, 1/3, 2, 5/2, -3*x^2, -1/3*x^2] + 3*AppellF1[3/2, 4/3, 1, 5/2, -3*x^2, -1/3*x^2])))","C",0
2253,0,0,169,0.1127924,"\int \frac{\left(1+x^2\right) \sqrt[4]{x^3+x^5}}{x^2 \left(-1+x^2\right)} \, dx","Integrate[((1 + x^2)*(x^3 + x^5)^(1/4))/(x^2*(-1 + x^2)),x]","\int \frac{\left(1+x^2\right) \sqrt[4]{x^3+x^5}}{x^2 \left(-1+x^2\right)} \, dx","\frac{4 \sqrt[4]{x^5+x^3}}{x}+\sqrt[4]{2} \tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^5+x^3}}\right)-\sqrt[4]{2} \tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^5+x^3}}\right)-\frac{\tan ^{-1}\left(\frac{2^{3/4} x \sqrt[4]{x^5+x^3}}{\sqrt{2} x^2-\sqrt{x^5+x^3}}\right)}{\sqrt[4]{2}}-\frac{\tanh ^{-1}\left(\frac{\frac{x^2}{\sqrt[4]{2}}+\frac{\sqrt{x^5+x^3}}{2^{3/4}}}{x \sqrt[4]{x^5+x^3}}\right)}{\sqrt[4]{2}}",1,"Integrate[((1 + x^2)*(x^3 + x^5)^(1/4))/(x^2*(-1 + x^2)), x]","F",-1
2254,0,0,170,0.5687507,"\int \frac{\left(4+x^2+x^5\right) \sqrt[4]{-2-x^2-2 x^4+2 x^5}}{x^2 \left(-2-x^2+2 x^5\right)} \, dx","Integrate[((4 + x^2 + x^5)*(-2 - x^2 - 2*x^4 + 2*x^5)^(1/4))/(x^2*(-2 - x^2 + 2*x^5)),x]","\int \frac{\left(4+x^2+x^5\right) \sqrt[4]{-2-x^2-2 x^4+2 x^5}}{x^2 \left(-2-x^2+2 x^5\right)} \, dx","\frac{2 \sqrt[4]{2 x^5-2 x^4-x^2-2}}{x}-\frac{\tan ^{-1}\left(\frac{2^{3/4} x \sqrt[4]{2 x^5-2 x^4-x^2-2}}{\sqrt{2} x^2-\sqrt{2 x^5-2 x^4-x^2-2}}\right)}{\sqrt[4]{2}}-\frac{\tanh ^{-1}\left(\frac{2 \sqrt[4]{2} x \sqrt[4]{2 x^5-2 x^4-x^2-2}}{2 x^2+\sqrt{2} \sqrt{2 x^5-2 x^4-x^2-2}}\right)}{\sqrt[4]{2}}",1,"Integrate[((4 + x^2 + x^5)*(-2 - x^2 - 2*x^4 + 2*x^5)^(1/4))/(x^2*(-2 - x^2 + 2*x^5)), x]","F",-1
2255,0,0,170,0.7880271,"\int \frac{\left(-1+x^4\right)^2 \sqrt{x^2+\sqrt{1+x^4}}}{\left(1+x^4\right)^2} \, dx","Integrate[((-1 + x^4)^2*Sqrt[x^2 + Sqrt[1 + x^4]])/(1 + x^4)^2,x]","\int \frac{\left(-1+x^4\right)^2 \sqrt{x^2+\sqrt{1+x^4}}}{\left(1+x^4\right)^2} \, dx","-\frac{3}{2} \tan ^{-1}\left(x \sqrt{\sqrt{x^4+1}+x^2}\right)+\frac{\tan ^{-1}\left(\sqrt{2} x \sqrt{\sqrt{x^4+1}+x^2}\right)}{2 \sqrt{2}}+\frac{x \left(2 x^8+8 x^4+4\right) \sqrt{\sqrt{x^4+1}+x^2}+x \sqrt{x^4+1} \sqrt{\sqrt{x^4+1}+x^2} \left(2 x^6+7 x^2\right)}{2 \left(2 x^8+3 x^4+1\right)+2 \sqrt{x^4+1} \left(2 x^6+2 x^2\right)}",1,"Integrate[((-1 + x^4)^2*Sqrt[x^2 + Sqrt[1 + x^4]])/(1 + x^4)^2, x]","F",-1
2256,1,191,170,0.6157518,"\int \frac{-1+x^2}{\sqrt{1+x} \left(1+x^2\right) \sqrt{1+\sqrt{1+\sqrt{1+x}}}} \, dx","Integrate[(-1 + x^2)/(Sqrt[1 + x]*(1 + x^2)*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]),x]","\frac{8}{3} \left(\sqrt{\sqrt{x+1}+1}-2\right) \sqrt{\sqrt{\sqrt{x+1}+1}+1}-\text{RootSum}\left[2 \text{$\#$1}^{16}-8 \text{$\#$1}^{12}+8 \text{$\#$1}^{10}+14 \text{$\#$1}^8-32 \text{$\#$1}^6+24 \text{$\#$1}^4-8 \text{$\#$1}^2+1\&,\frac{\text{$\#$1}^{13} \log \left(\frac{1}{\sqrt{\sqrt{\sqrt{x+1}+1}+1}}-\text{$\#$1}\right)-\text{$\#$1}^{11} \log \left(\frac{1}{\sqrt{\sqrt{\sqrt{x+1}+1}+1}}-\text{$\#$1}\right)}{2 \text{$\#$1}^{14}-6 \text{$\#$1}^{10}+5 \text{$\#$1}^8+7 \text{$\#$1}^6-12 \text{$\#$1}^4+6 \text{$\#$1}^2-1}\&\right]","-\text{RootSum}\left[\text{$\#$1}^{16}-8 \text{$\#$1}^{14}+24 \text{$\#$1}^{12}-32 \text{$\#$1}^{10}+14 \text{$\#$1}^8+8 \text{$\#$1}^6-8 \text{$\#$1}^4+2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x+1}+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^{13}-6 \text{$\#$1}^{11}+12 \text{$\#$1}^9-8 \text{$\#$1}^7-\text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]+\frac{8}{3} \sqrt{\sqrt{x+1}+1} \sqrt{\sqrt{\sqrt{x+1}+1}+1}-\frac{16}{3} \sqrt{\sqrt{\sqrt{x+1}+1}+1}",1,"(8*(-2 + Sqrt[1 + Sqrt[1 + x]])*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]])/3 - RootSum[1 - 8*#1^2 + 24*#1^4 - 32*#1^6 + 14*#1^8 + 8*#1^10 - 8*#1^12 + 2*#1^16 & , (-(Log[1/Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]] - #1]*#1^11) + Log[1/Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]] - #1]*#1^13)/(-1 + 6*#1^2 - 12*#1^4 + 7*#1^6 + 5*#1^8 - 6*#1^10 + 2*#1^14) & ]","A",1
2257,1,191,170,0.3116935,"\int \frac{-1+x^2}{\sqrt{1+x} \left(1+x^2\right) \sqrt{1+\sqrt{1+\sqrt{1+x}}}} \, dx","Integrate[(-1 + x^2)/(Sqrt[1 + x]*(1 + x^2)*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]),x]","\frac{8}{3} \left(\sqrt{\sqrt{x+1}+1}-2\right) \sqrt{\sqrt{\sqrt{x+1}+1}+1}-\text{RootSum}\left[2 \text{$\#$1}^{16}-8 \text{$\#$1}^{12}+8 \text{$\#$1}^{10}+14 \text{$\#$1}^8-32 \text{$\#$1}^6+24 \text{$\#$1}^4-8 \text{$\#$1}^2+1\&,\frac{\text{$\#$1}^{13} \log \left(\frac{1}{\sqrt{\sqrt{\sqrt{x+1}+1}+1}}-\text{$\#$1}\right)-\text{$\#$1}^{11} \log \left(\frac{1}{\sqrt{\sqrt{\sqrt{x+1}+1}+1}}-\text{$\#$1}\right)}{2 \text{$\#$1}^{14}-6 \text{$\#$1}^{10}+5 \text{$\#$1}^8+7 \text{$\#$1}^6-12 \text{$\#$1}^4+6 \text{$\#$1}^2-1}\&\right]","-\text{RootSum}\left[\text{$\#$1}^{16}-8 \text{$\#$1}^{14}+24 \text{$\#$1}^{12}-32 \text{$\#$1}^{10}+14 \text{$\#$1}^8+8 \text{$\#$1}^6-8 \text{$\#$1}^4+2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x+1}+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^{13}-6 \text{$\#$1}^{11}+12 \text{$\#$1}^9-8 \text{$\#$1}^7-\text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]+\frac{8}{3} \sqrt{\sqrt{x+1}+1} \sqrt{\sqrt{\sqrt{x+1}+1}+1}-\frac{16}{3} \sqrt{\sqrt{\sqrt{x+1}+1}+1}",1,"(8*(-2 + Sqrt[1 + Sqrt[1 + x]])*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]])/3 - RootSum[1 - 8*#1^2 + 24*#1^4 - 32*#1^6 + 14*#1^8 + 8*#1^10 - 8*#1^12 + 2*#1^16 & , (-(Log[1/Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]] - #1]*#1^11) + Log[1/Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]] - #1]*#1^13)/(-1 + 6*#1^2 - 12*#1^4 + 7*#1^6 + 5*#1^8 - 6*#1^10 + 2*#1^14) & ]","A",1
2258,1,113,171,0.0912115,"\int \left(\frac{1}{\sqrt{1-\sqrt{x}}}-\sqrt{1-\sqrt{x}-x}\right) \, dx","Integrate[1/Sqrt[1 - Sqrt[x]] - Sqrt[1 - Sqrt[x] - x],x]","2 \left(\frac{2}{3} \left(1-\sqrt{x}\right)^{3/2}-2 \sqrt{1-\sqrt{x}}\right)-2 \left(\frac{1}{2} \left(\frac{1}{4} \sqrt{-x-\sqrt{x}+1} \left(-2 \sqrt{x}-1\right)+\frac{5}{8} \sin ^{-1}\left(\frac{-2 \sqrt{x}-1}{\sqrt{5}}\right)\right)-\frac{1}{3} \left(-x-\sqrt{x}+1\right)^{3/2}\right)","\sqrt{-x-\sqrt{x}+1} \left(\frac{1}{4} \sqrt{\left(2 \sqrt{x}+1\right)^2}+\frac{2}{3}\right)-\frac{2}{3} \sqrt{-x-\sqrt{x}+1} x-\frac{8 \sqrt{1-\sqrt{x}}}{3}-\frac{4}{3} \sqrt{1-\sqrt{x}} \sqrt{x}-\frac{2}{3} \sqrt{-x-\sqrt{x}+1} \sqrt{x}+\frac{5}{8} i \log \left(-2 \sqrt{-x-\sqrt{x}+1}+i \sqrt{\left(2 \sqrt{x}+1\right)^2}\right)",1,"2*(-2*Sqrt[1 - Sqrt[x]] + (2*(1 - Sqrt[x])^(3/2))/3) - 2*(-1/3*(1 - Sqrt[x] - x)^(3/2) + (((-1 - 2*Sqrt[x])*Sqrt[1 - Sqrt[x] - x])/4 + (5*ArcSin[(-1 - 2*Sqrt[x])/Sqrt[5]])/8)/2)","A",1
2259,0,0,171,0.1682591,"\int \frac{-5+x}{\sqrt[3]{-2-x+x^2} \left(-3+4 x+x^2\right)} \, dx","Integrate[(-5 + x)/((-2 - x + x^2)^(1/3)*(-3 + 4*x + x^2)),x]","\int \frac{-5+x}{\sqrt[3]{-2-x+x^2} \left(-3+4 x+x^2\right)} \, dx","\frac{\log \left(2 \sqrt[3]{x^2-x-2}+2^{2/3} x+2^{2/3}\right)}{2^{2/3}}-\frac{\log \left(-\sqrt[3]{2} x^2-2 \left(x^2-x-2\right)^{2/3}+\left(2^{2/3} x+2^{2/3}\right) \sqrt[3]{x^2-x-2}-2 \sqrt[3]{2} x-\sqrt[3]{2}\right)}{2\ 2^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x^2-x-2}}{\sqrt[3]{x^2-x-2}-2^{2/3} x-2^{2/3}}\right)}{2^{2/3}}",1,"Integrate[(-5 + x)/((-2 - x + x^2)^(1/3)*(-3 + 4*x + x^2)), x]","F",-1
2260,1,492,171,1.6581153,"\int \frac{(-a+x) (-2 a+b+x)}{\left((-a+x) (-b+x)^2\right)^{3/4} \left(a+b^2 d-(1+2 b d) x+d x^2\right)} \, dx","Integrate[((-a + x)*(-2*a + b + x))/(((-a + x)*(-b + x)^2)^(3/4)*(a + b^2*d - (1 + 2*b*d)*x + d*x^2)),x]","\frac{2 (b-x) \left((x-a)^{3/4} \left(\sqrt[4]{b-a} \sqrt{\frac{x-b}{a-b}} \Pi \left(-\frac{\sqrt{2} \sqrt{a-b} \sqrt{d}}{\sqrt{2 a d-2 b d-\sqrt{-4 a d+4 b d+1}-1}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{x-a}}{\sqrt[4]{b-a}}\right)\right|-1\right)+\sqrt[4]{b-a} \sqrt{\frac{x-b}{a-b}} \Pi \left(\frac{\sqrt{2} \sqrt{a-b} \sqrt{d}}{\sqrt{2 a d-2 b d-\sqrt{-4 a d+4 b d+1}-1}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{x-a}}{\sqrt[4]{b-a}}\right)\right|-1\right)+\sqrt[4]{b-a} \sqrt{\frac{x-b}{a-b}} \Pi \left(-\frac{\sqrt{2} \sqrt{a-b} \sqrt{d}}{\sqrt{2 a d-2 b d+\sqrt{-4 a d+4 b d+1}-1}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{x-a}}{\sqrt[4]{b-a}}\right)\right|-1\right)+\sqrt[4]{b-a} \sqrt{\frac{x-b}{a-b}} \Pi \left(\frac{\sqrt{2} \sqrt{a-b} \sqrt{d}}{\sqrt{2 a d-2 b d+\sqrt{-4 a d+4 b d+1}-1}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{x-a}}{\sqrt[4]{b-a}}\right)\right|-1\right)+\frac{(b-x) \left(\frac{a-x}{a-b}\right)^{3/4} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{3}{2};\frac{x-b}{a-b}\right)}{(x-a)^{3/4}}\right)+2 (a-x)\right)}{\left((x-a) (b-x)^2\right)^{3/4}}","-2 \sqrt[4]{d} \tan ^{-1}\left(\frac{\sqrt[4]{d} \left(x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3\right)^{3/4}}{(x-a) (b-x)}\right)+2 \sqrt[4]{d} \tanh ^{-1}\left(\frac{\sqrt[4]{d} \left(x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3\right)^{3/4}}{(x-a) (b-x)}\right)-\frac{4 \sqrt[4]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3}}{b-x}",1,"(2*(b - x)*(2*(a - x) + (-a + x)^(3/4)*((-a + b)^(1/4)*Sqrt[(-b + x)/(a - b)]*EllipticPi[-((Sqrt[2]*Sqrt[a - b]*Sqrt[d])/Sqrt[-1 + 2*a*d - 2*b*d - Sqrt[1 - 4*a*d + 4*b*d]]), ArcSin[(-a + x)^(1/4)/(-a + b)^(1/4)], -1] + (-a + b)^(1/4)*Sqrt[(-b + x)/(a - b)]*EllipticPi[(Sqrt[2]*Sqrt[a - b]*Sqrt[d])/Sqrt[-1 + 2*a*d - 2*b*d - Sqrt[1 - 4*a*d + 4*b*d]], ArcSin[(-a + x)^(1/4)/(-a + b)^(1/4)], -1] + (-a + b)^(1/4)*Sqrt[(-b + x)/(a - b)]*EllipticPi[-((Sqrt[2]*Sqrt[a - b]*Sqrt[d])/Sqrt[-1 + 2*a*d - 2*b*d + Sqrt[1 - 4*a*d + 4*b*d]]), ArcSin[(-a + x)^(1/4)/(-a + b)^(1/4)], -1] + (-a + b)^(1/4)*Sqrt[(-b + x)/(a - b)]*EllipticPi[(Sqrt[2]*Sqrt[a - b]*Sqrt[d])/Sqrt[-1 + 2*a*d - 2*b*d + Sqrt[1 - 4*a*d + 4*b*d]], ArcSin[(-a + x)^(1/4)/(-a + b)^(1/4)], -1] + (((a - x)/(a - b))^(3/4)*(b - x)*Hypergeometric2F1[1/2, 3/4, 3/2, (-b + x)/(a - b)])/(-a + x)^(3/4))))/((b - x)^2*(-a + x))^(3/4)","C",1
2261,0,0,171,0.1902033,"\int \frac{1+x}{\left(1+4 x+x^2\right) \sqrt[3]{1-x^3}} \, dx","Integrate[(1 + x)/((1 + 4*x + x^2)*(1 - x^3)^(1/3)),x]","\int \frac{1+x}{\left(1+4 x+x^2\right) \sqrt[3]{1-x^3}} \, dx","\frac{\log \left(2 \sqrt[3]{1-x^3}+2^{2/3} x-2^{2/3}\right)}{3\ 2^{2/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{1-x^3}}{\sqrt[3]{1-x^3}-2^{2/3} x+2^{2/3}}\right)}{2^{2/3} \sqrt{3}}-\frac{\log \left(-2 \left(1-x^3\right)^{2/3}+\left(2^{2/3} x-2^{2/3}\right) \sqrt[3]{1-x^3}-\sqrt[3]{2} x^2+2 \sqrt[3]{2} x-\sqrt[3]{2}\right)}{6\ 2^{2/3}}",1,"Integrate[(1 + x)/((1 + 4*x + x^2)*(1 - x^3)^(1/3)), x]","F",-1
2262,1,445,171,2.0642375,"\int \frac{x^4}{\left(-b+a x^4\right)^2 \sqrt[4]{b x^2+a x^4}} \, dx","Integrate[x^4/((-b + a*x^4)^2*(b*x^2 + a*x^4)^(1/4)),x]","\frac{x \left(\frac{4 \sqrt[8]{a} \left(a^2 x^4-b^2\right)}{a x^4-b}+\frac{\sqrt{b} \sqrt[4]{a+\frac{b}{x^2}} \left(-\sqrt{a} \sqrt[4]{\sqrt{a}-\sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[8]{a} \sqrt[4]{\sqrt{a}+\sqrt{b}}}\right)+\sqrt{b} \sqrt[4]{\sqrt{a}-\sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[8]{a} \sqrt[4]{\sqrt{a}+\sqrt{b}}}\right)+\sqrt{b} \sqrt[4]{\sqrt{a}+\sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[8]{a} \sqrt[4]{\sqrt{a}-\sqrt{b}}}\right)+\sqrt{a} \sqrt[4]{\sqrt{a}+\sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[8]{a} \sqrt[4]{\sqrt{a}-\sqrt{b}}}\right)+\left(\sqrt{a}-\sqrt{b}\right)^{5/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[8]{a} \sqrt[4]{\sqrt{a}+\sqrt{b}}}\right)-\left(\sqrt{a}+\sqrt{b}\right)^{5/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[8]{a} \sqrt[4]{\sqrt{a}-\sqrt{b}}}\right)\right)}{\sqrt[4]{\sqrt{a}-\sqrt{b}} \sqrt[4]{\sqrt{a}+\sqrt{b}}}\right)}{16 a^{9/8} b (b-a) \sqrt[4]{x^2 \left(a x^2+b\right)}}","\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2-a b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-2 a \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+2 a \log (x)}{\text{$\#$1} a-\text{$\#$1}^5}\&\right]}{32 a (a-b)}+\frac{\left(a x^4+b x^2\right)^{3/4} \left(b-a x^2\right)}{4 a b x (a-b) \left(a x^4-b\right)}",1,"(x*((4*a^(1/8)*(-b^2 + a^2*x^4))/(-b + a*x^4) + (Sqrt[b]*(a + b/x^2)^(1/4)*(Sqrt[a]*(Sqrt[a] + Sqrt[b])^(1/4)*ArcTan[(a + b/x^2)^(1/4)/(a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4))] + (Sqrt[a] + Sqrt[b])^(1/4)*Sqrt[b]*ArcTan[(a + b/x^2)^(1/4)/(a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4))] - Sqrt[a]*(Sqrt[a] - Sqrt[b])^(1/4)*ArcTan[(a + b/x^2)^(1/4)/(a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4))] + (Sqrt[a] - Sqrt[b])^(1/4)*Sqrt[b]*ArcTan[(a + b/x^2)^(1/4)/(a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4))] - (Sqrt[a] + Sqrt[b])^(5/4)*ArcTanh[(a + b/x^2)^(1/4)/(a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4))] + (Sqrt[a] - Sqrt[b])^(5/4)*ArcTanh[(a + b/x^2)^(1/4)/(a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4))]))/((Sqrt[a] - Sqrt[b])^(1/4)*(Sqrt[a] + Sqrt[b])^(1/4))))/(16*a^(9/8)*b*(-a + b)*(x^2*(b + a*x^2))^(1/4))","B",1
2263,1,445,171,1.3621156,"\int \frac{x^4}{\left(-b+a x^4\right)^2 \sqrt[4]{b x^2+a x^4}} \, dx","Integrate[x^4/((-b + a*x^4)^2*(b*x^2 + a*x^4)^(1/4)),x]","\frac{x \left(\frac{4 \sqrt[8]{a} \left(a^2 x^4-b^2\right)}{a x^4-b}+\frac{\sqrt{b} \sqrt[4]{a+\frac{b}{x^2}} \left(-\sqrt{a} \sqrt[4]{\sqrt{a}-\sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[8]{a} \sqrt[4]{\sqrt{a}+\sqrt{b}}}\right)+\sqrt{b} \sqrt[4]{\sqrt{a}-\sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[8]{a} \sqrt[4]{\sqrt{a}+\sqrt{b}}}\right)+\sqrt{b} \sqrt[4]{\sqrt{a}+\sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[8]{a} \sqrt[4]{\sqrt{a}-\sqrt{b}}}\right)+\sqrt{a} \sqrt[4]{\sqrt{a}+\sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[8]{a} \sqrt[4]{\sqrt{a}-\sqrt{b}}}\right)+\left(\sqrt{a}-\sqrt{b}\right)^{5/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[8]{a} \sqrt[4]{\sqrt{a}+\sqrt{b}}}\right)-\left(\sqrt{a}+\sqrt{b}\right)^{5/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[8]{a} \sqrt[4]{\sqrt{a}-\sqrt{b}}}\right)\right)}{\sqrt[4]{\sqrt{a}-\sqrt{b}} \sqrt[4]{\sqrt{a}+\sqrt{b}}}\right)}{16 a^{9/8} b (b-a) \sqrt[4]{x^2 \left(a x^2+b\right)}}","\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2-a b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-2 a \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+2 a \log (x)}{\text{$\#$1} a-\text{$\#$1}^5}\&\right]}{32 a (a-b)}+\frac{\left(a x^4+b x^2\right)^{3/4} \left(b-a x^2\right)}{4 a b x (a-b) \left(a x^4-b\right)}",1,"(x*((4*a^(1/8)*(-b^2 + a^2*x^4))/(-b + a*x^4) + (Sqrt[b]*(a + b/x^2)^(1/4)*(Sqrt[a]*(Sqrt[a] + Sqrt[b])^(1/4)*ArcTan[(a + b/x^2)^(1/4)/(a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4))] + (Sqrt[a] + Sqrt[b])^(1/4)*Sqrt[b]*ArcTan[(a + b/x^2)^(1/4)/(a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4))] - Sqrt[a]*(Sqrt[a] - Sqrt[b])^(1/4)*ArcTan[(a + b/x^2)^(1/4)/(a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4))] + (Sqrt[a] - Sqrt[b])^(1/4)*Sqrt[b]*ArcTan[(a + b/x^2)^(1/4)/(a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4))] - (Sqrt[a] + Sqrt[b])^(5/4)*ArcTanh[(a + b/x^2)^(1/4)/(a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4))] + (Sqrt[a] - Sqrt[b])^(5/4)*ArcTanh[(a + b/x^2)^(1/4)/(a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4))]))/((Sqrt[a] - Sqrt[b])^(1/4)*(Sqrt[a] + Sqrt[b])^(1/4))))/(16*a^(9/8)*b*(-a + b)*(x^2*(b + a*x^2))^(1/4))","B",1
2264,1,445,171,1.1450936,"\int \frac{x^4}{\left(-b+a x^4\right)^2 \sqrt[4]{b x^2+a x^4}} \, dx","Integrate[x^4/((-b + a*x^4)^2*(b*x^2 + a*x^4)^(1/4)),x]","\frac{x \left(\frac{4 \sqrt[8]{a} \left(a^2 x^4-b^2\right)}{a x^4-b}+\frac{\sqrt{b} \sqrt[4]{a+\frac{b}{x^2}} \left(-\sqrt{a} \sqrt[4]{\sqrt{a}-\sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[8]{a} \sqrt[4]{\sqrt{a}+\sqrt{b}}}\right)+\sqrt{b} \sqrt[4]{\sqrt{a}-\sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[8]{a} \sqrt[4]{\sqrt{a}+\sqrt{b}}}\right)+\sqrt{b} \sqrt[4]{\sqrt{a}+\sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[8]{a} \sqrt[4]{\sqrt{a}-\sqrt{b}}}\right)+\sqrt{a} \sqrt[4]{\sqrt{a}+\sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[8]{a} \sqrt[4]{\sqrt{a}-\sqrt{b}}}\right)+\left(\sqrt{a}-\sqrt{b}\right)^{5/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[8]{a} \sqrt[4]{\sqrt{a}+\sqrt{b}}}\right)-\left(\sqrt{a}+\sqrt{b}\right)^{5/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[8]{a} \sqrt[4]{\sqrt{a}-\sqrt{b}}}\right)\right)}{\sqrt[4]{\sqrt{a}-\sqrt{b}} \sqrt[4]{\sqrt{a}+\sqrt{b}}}\right)}{16 a^{9/8} b (b-a) \sqrt[4]{x^2 \left(a x^2+b\right)}}","\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2-a b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-2 a \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+2 a \log (x)}{\text{$\#$1} a-\text{$\#$1}^5}\&\right]}{32 a (a-b)}+\frac{\left(a x^4+b x^2\right)^{3/4} \left(b-a x^2\right)}{4 a b x (a-b) \left(a x^4-b\right)}",1,"(x*((4*a^(1/8)*(-b^2 + a^2*x^4))/(-b + a*x^4) + (Sqrt[b]*(a + b/x^2)^(1/4)*(Sqrt[a]*(Sqrt[a] + Sqrt[b])^(1/4)*ArcTan[(a + b/x^2)^(1/4)/(a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4))] + (Sqrt[a] + Sqrt[b])^(1/4)*Sqrt[b]*ArcTan[(a + b/x^2)^(1/4)/(a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4))] - Sqrt[a]*(Sqrt[a] - Sqrt[b])^(1/4)*ArcTan[(a + b/x^2)^(1/4)/(a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4))] + (Sqrt[a] - Sqrt[b])^(1/4)*Sqrt[b]*ArcTan[(a + b/x^2)^(1/4)/(a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4))] - (Sqrt[a] + Sqrt[b])^(5/4)*ArcTanh[(a + b/x^2)^(1/4)/(a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4))] + (Sqrt[a] - Sqrt[b])^(5/4)*ArcTanh[(a + b/x^2)^(1/4)/(a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4))]))/((Sqrt[a] - Sqrt[b])^(1/4)*(Sqrt[a] + Sqrt[b])^(1/4))))/(16*a^(9/8)*b*(-a + b)*(x^2*(b + a*x^2))^(1/4))","B",1
2265,1,161,171,0.6696516,"\int \frac{x^8}{\sqrt{-1+x^4} \left(-1+x^{16}\right)} \, dx","Integrate[x^8/(Sqrt[-1 + x^4]*(-1 + x^16)),x]","-\frac{\sqrt{1-x^4} F\left(\left.\sin ^{-1}(x)\right|-1\right)+\sqrt{1-x^4} \Pi \left(-i;\left.\sin ^{-1}(x)\right|-1\right)+\sqrt{1-x^4} \Pi \left(i;\left.\sin ^{-1}(x)\right|-1\right)-\sqrt{1-x^4} \Pi \left(-\sqrt[4]{-1};\left.\sin ^{-1}(x)\right|-1\right)-\sqrt{1-x^4} \Pi \left(\sqrt[4]{-1};\left.\sin ^{-1}(x)\right|-1\right)-\sqrt{1-x^4} \Pi \left(-(-1)^{3/4};\left.\sin ^{-1}(x)\right|-1\right)-\sqrt{1-x^4} \Pi \left((-1)^{3/4};\left.\sin ^{-1}(x)\right|-1\right)+x}{8 \sqrt{x^4-1}}","-\frac{x}{8 \sqrt{x^4-1}}+\frac{1}{32} \tan ^{-1}\left(\frac{\frac{x^4}{2}-x^2-\frac{1}{2}}{x \sqrt{x^4-1}}\right)+\frac{\tan ^{-1}\left(\frac{-\frac{x^4}{2^{3/4}}+\frac{x^2}{\sqrt[4]{2}}+\frac{1}{2^{3/4}}}{x \sqrt{x^4-1}}\right)}{8\ 2^{3/4}}-\frac{1}{32} \tanh ^{-1}\left(\frac{\frac{x^4}{2}+x^2-\frac{1}{2}}{x \sqrt{x^4-1}}\right)+\frac{\tanh ^{-1}\left(\frac{2^{3/4} x \sqrt{x^4-1}}{x^4+\sqrt{2} x^2-1}\right)}{8\ 2^{3/4}}",1,"-1/8*(x + Sqrt[1 - x^4]*EllipticF[ArcSin[x], -1] + Sqrt[1 - x^4]*EllipticPi[-I, ArcSin[x], -1] + Sqrt[1 - x^4]*EllipticPi[I, ArcSin[x], -1] - Sqrt[1 - x^4]*EllipticPi[-(-1)^(1/4), ArcSin[x], -1] - Sqrt[1 - x^4]*EllipticPi[(-1)^(1/4), ArcSin[x], -1] - Sqrt[1 - x^4]*EllipticPi[-(-1)^(3/4), ArcSin[x], -1] - Sqrt[1 - x^4]*EllipticPi[(-1)^(3/4), ArcSin[x], -1])/Sqrt[-1 + x^4]","C",1
2266,0,0,171,0.6504897,"\int \frac{\sqrt{b+\sqrt{b^2+a x^2}}}{\left(b^2+a x^2\right)^4} \, dx","Integrate[Sqrt[b + Sqrt[b^2 + a*x^2]]/(b^2 + a*x^2)^4,x]","\int \frac{\sqrt{b+\sqrt{b^2+a x^2}}}{\left(b^2+a x^2\right)^4} \, dx","\frac{11 x \left(315 a^2 x^4+798 a b^2 x^2+611 b^4\right)}{7680 b^6 \left(a x^2+b^2\right)^{5/2} \sqrt{\sqrt{a x^2+b^2}+b}}+\frac{x \left(1155 a^2 x^4+3102 a b^2 x^2+2587 b^4\right)}{3840 b^5 \left(a x^2+b^2\right)^3 \sqrt{\sqrt{a x^2+b^2}+b}}+\frac{231 \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b} \sqrt{\sqrt{a x^2+b^2}+b}}\right)}{512 \sqrt{a} b^{13/2}}",1,"Integrate[Sqrt[b + Sqrt[b^2 + a*x^2]]/(b^2 + a*x^2)^4, x]","F",-1
2267,0,0,171,0.1140362,"\int \frac{\sqrt{x^2+\sqrt{1+x^4}}}{1+x^2} \, dx","Integrate[Sqrt[x^2 + Sqrt[1 + x^4]]/(1 + x^2),x]","\int \frac{\sqrt{x^2+\sqrt{1+x^4}}}{1+x^2} \, dx","\sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)+\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)-\sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{2}-1\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)",1,"Integrate[Sqrt[x^2 + Sqrt[1 + x^4]]/(1 + x^2), x]","F",-1
2268,1,164,172,0.3235397,"\int \frac{\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x^2}}}}}{x} \, dx","Integrate[Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-2)]]]/x,x]","-4 \sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x^2}}}}+\sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x^2}}}}}{\sqrt{\sqrt{2}-1}}\right)+2 \tanh ^{-1}\left(\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x^2}}}}\right)+\sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x^2}}}}}{\sqrt{1+\sqrt{2}}}\right)","-4 \sqrt{1-\sqrt{1-\sqrt{\frac{x^2-1}{x^2}}}}+\sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{\sqrt{1-\sqrt{1-\sqrt{\frac{x^2-1}{x^2}}}}}{\sqrt{\sqrt{2}-1}}\right)+2 \tanh ^{-1}\left(\sqrt{1-\sqrt{1-\sqrt{\frac{x^2-1}{x^2}}}}\right)+\sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt{1-\sqrt{1-\sqrt{\frac{x^2-1}{x^2}}}}}{\sqrt{1+\sqrt{2}}}\right)",1,"-4*Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-2)]]] + Sqrt[-1 + Sqrt[2]]*ArcTan[Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-2)]]]/Sqrt[-1 + Sqrt[2]]] + 2*ArcTanh[Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-2)]]]] + Sqrt[1 + Sqrt[2]]*ArcTanh[Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-2)]]]/Sqrt[1 + Sqrt[2]]]","A",1
2269,0,0,172,0.0806688,"\int \frac{1}{(1+x) \sqrt[3]{1-x^3}} \, dx","Integrate[1/((1 + x)*(1 - x^3)^(1/3)),x]","\int \frac{1}{(1+x) \sqrt[3]{1-x^3}} \, dx","\frac{\log \left(2 \sqrt[3]{1-x^3}+\sqrt[3]{2} x-\sqrt[3]{2}\right)}{2 \sqrt[3]{2}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{1-x^3}}{\sqrt[3]{1-x^3}-\sqrt[3]{2} x+\sqrt[3]{2}}\right)}{2 \sqrt[3]{2}}-\frac{\log \left(4 \left(1-x^3\right)^{2/3}+\left(2 \sqrt[3]{2}-2 \sqrt[3]{2} x\right) \sqrt[3]{1-x^3}+2^{2/3} x^2-2\ 2^{2/3} x+2^{2/3}\right)}{4 \sqrt[3]{2}}",1,"Integrate[1/((1 + x)*(1 - x^3)^(1/3)), x]","F",-1
2270,0,0,173,5.8167579,"\int \frac{\left(a b-2 b x+x^2\right) \left(b^2-2 b x+x^2\right)}{\left(x (-a+x) (-b+x)^3\right)^{3/4} \left(b d-(a+d) x+x^2\right)} \, dx","Integrate[((a*b - 2*b*x + x^2)*(b^2 - 2*b*x + x^2))/((x*(-a + x)*(-b + x)^3)^(3/4)*(b*d - (a + d)*x + x^2)),x]","\int \frac{\left(a b-2 b x+x^2\right) \left(b^2-2 b x+x^2\right)}{\left(x (-a+x) (-b+x)^3\right)^{3/4} \left(b d-(a+d) x+x^2\right)} \, dx","\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \left(a b^3 x+x^3 \left(3 a b+3 b^2\right)+x^2 \left(-3 a b^2-b^3\right)+x^4 (-a-3 b)+x^5\right)^{3/4}}{x (x-a) (b-x)^2}\right)}{d^{3/4}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \left(a b^3 x+x^3 \left(3 a b+3 b^2\right)+x^2 \left(-3 a b^2-b^3\right)+x^4 (-a-3 b)+x^5\right)^{3/4}}{x (x-a) (b-x)^2}\right)}{d^{3/4}}",1,"Integrate[((a*b - 2*b*x + x^2)*(b^2 - 2*b*x + x^2))/((x*(-a + x)*(-b + x)^3)^(3/4)*(b*d - (a + d)*x + x^2)), x]","F",-1
2271,0,0,173,4.9262648,"\int \frac{-2 a b+(a+b) x}{\sqrt[3]{x (-a+x) (-b+x)} \left(-a b+(a+b) x+(-1+d) x^2\right)} \, dx","Integrate[(-2*a*b + (a + b)*x)/((x*(-a + x)*(-b + x))^(1/3)*(-(a*b) + (a + b)*x + (-1 + d)*x^2)),x]","\int \frac{-2 a b+(a+b) x}{\sqrt[3]{x (-a+x) (-b+x)} \left(-a b+(a+b) x+(-1+d) x^2\right)} \, dx","\frac{\log \left(\sqrt[3]{d} x \sqrt[3]{x^2 (-a-b)+a b x+x^3}+\left(x^2 (-a-b)+a b x+x^3\right)^{2/3}+d^{2/3} x^2\right)}{2 \sqrt[3]{d}}-\frac{\log \left(\sqrt[3]{x^2 (-a-b)+a b x+x^3}-\sqrt[3]{d} x\right)}{\sqrt[3]{d}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} x}{2 \sqrt[3]{x^2 (-a-b)+a b x+x^3}+\sqrt[3]{d} x}\right)}{\sqrt[3]{d}}",1,"Integrate[(-2*a*b + (a + b)*x)/((x*(-a + x)*(-b + x))^(1/3)*(-(a*b) + (a + b)*x + (-1 + d)*x^2)), x]","F",-1
2272,1,156,173,0.2175985,"\int \frac{\left(-1+x^3\right)^{2/3} \left(1+x^3\right)}{x^6 \left(2+x^3\right)} \, dx","Integrate[((-1 + x^3)^(2/3)*(1 + x^3))/(x^6*(2 + x^3)),x]","\frac{1}{240} \left(5 \sqrt[3]{2} \sqrt[6]{3} \left(6 \tan ^{-1}\left(\frac{2^{2/3} x}{\sqrt[6]{3} \sqrt[3]{1-x^3}}+\frac{1}{\sqrt{3}}\right)+\sqrt{3} \left(\log \left(\frac{2^{2/3} \sqrt[3]{3} x}{\sqrt[3]{1-x^3}}+\frac{\sqrt[3]{2} 3^{2/3} x^2}{\left(1-x^3\right)^{2/3}}+2\right)-2 \log \left(2-\frac{2^{2/3} \sqrt[3]{3} x}{\sqrt[3]{1-x^3}}\right)\right)\right)-\frac{6 \left(x^3-1\right)^{2/3} \left(x^3+4\right)}{x^5}\right)","-\frac{\log \left(\sqrt[3]{2} 3^{2/3} \sqrt[3]{x^3-1}-3 x\right)}{4\ 2^{2/3} \sqrt[3]{3}}+\frac{\sqrt[6]{3} \tan ^{-1}\left(\frac{3^{5/6} x}{2 \sqrt[3]{2} \sqrt[3]{x^3-1}+\sqrt[3]{3} x}\right)}{4\ 2^{2/3}}+\frac{\left(x^3-1\right)^{2/3} \left(-x^3-4\right)}{40 x^5}+\frac{\log \left(\sqrt[3]{2} 3^{2/3} \sqrt[3]{x^3-1} x+2^{2/3} \sqrt[3]{3} \left(x^3-1\right)^{2/3}+3 x^2\right)}{8\ 2^{2/3} \sqrt[3]{3}}",1,"((-6*(-1 + x^3)^(2/3)*(4 + x^3))/x^5 + 5*2^(1/3)*3^(1/6)*(6*ArcTan[1/Sqrt[3] + (2^(2/3)*x)/(3^(1/6)*(1 - x^3)^(1/3))] + Sqrt[3]*(-2*Log[2 - (2^(2/3)*3^(1/3)*x)/(1 - x^3)^(1/3)] + Log[2 + (2^(1/3)*3^(2/3)*x^2)/(1 - x^3)^(2/3) + (2^(2/3)*3^(1/3)*x)/(1 - x^3)^(1/3)])))/240","A",0
2273,1,146,173,0.1532014,"\int \frac{1}{(1+x) \left(-2+3 x-2 x^2+3 x^3-2 x^4\right)^{3/2}} \, dx","Integrate[1/((1 + x)*(-2 + 3*x - 2*x^2 + 3*x^3 - 2*x^4)^(3/2)),x]","\frac{-250 \sqrt{3} \sqrt{2 x^2+x+2} (x-1)^2 \tanh ^{-1}\left(\frac{\sqrt{3} (1-x)}{2 \sqrt{2 x^2+x+2}}\right)+819 \sqrt{5} \sqrt{2 x^2+x+2} (x-1)^2 \tanh ^{-1}\left(\frac{\sqrt{5} (x+1)}{2 \sqrt{2 x^2+x+2}}\right)-30 \left(22 x^3+73 x^2-107 x-18\right)}{18000 (x-1) \sqrt{-(x-1)^2 \left(2 x^2+x+2\right)}}","\frac{i (x-1) \sqrt{2 x^2+x+2} \left(-\frac{i \tanh ^{-1}\left(-\frac{\sqrt{2 x^2+x+2}}{\sqrt{3}}+\sqrt{\frac{2}{3}} x+\sqrt{\frac{2}{3}}\right)}{12 \sqrt{3}}-\frac{91 i \tanh ^{-1}\left(\frac{\sqrt{2 x^2+x+2}}{\sqrt{5}}-\sqrt{\frac{2}{5}} x+\sqrt{\frac{2}{5}}\right)}{200 \sqrt{5}}+\frac{i \left(22 x^3+73 x^2-107 x-18\right)}{600 (x-1)^2 \sqrt{2 x^2+x+2}}\right)}{\sqrt{-(x-1)^2 \left(2 x^2+x+2\right)}}",1,"(-30*(-18 - 107*x + 73*x^2 + 22*x^3) - 250*Sqrt[3]*(-1 + x)^2*Sqrt[2 + x + 2*x^2]*ArcTanh[(Sqrt[3]*(1 - x))/(2*Sqrt[2 + x + 2*x^2])] + 819*Sqrt[5]*(-1 + x)^2*Sqrt[2 + x + 2*x^2]*ArcTanh[(Sqrt[5]*(1 + x))/(2*Sqrt[2 + x + 2*x^2])])/(18000*(-1 + x)*Sqrt[-((-1 + x)^2*(2 + x + 2*x^2))])","A",1
2274,1,221,173,0.2177241,"\int \frac{x^2 \sqrt[4]{x^3+x^4}}{-1+x^4} \, dx","Integrate[(x^2*(x^3 + x^4)^(1/4))/(-1 + x^4),x]","\frac{\sqrt[4]{x^3 (x+1)} \left(-7 \left(11 x^4 \, _2F_1\left(\frac{3}{4},\frac{15}{4};\frac{19}{4};-x\right)+11 x^3 \, _2F_1\left(\frac{3}{4},\frac{15}{4};\frac{19}{4};-x\right)-15 (x+1) x^2 \, _2F_1\left(-\frac{1}{4},\frac{11}{4};\frac{15}{4};-x\right)-165 (x+1) \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};-x\right)+(55-55 i) \sqrt[4]{x+1} \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{(1-i) x}{x+1}\right)+(55+55 i) \sqrt[4]{x+1} \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{(1+i) x}{x+1}\right)+110 \sqrt[4]{x+1} \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{2 x}{x+1}\right)\right)+385 (x+1) \, _2F_1\left(-\frac{1}{4},\frac{3}{4};\frac{7}{4};-x\right)-165 x (x+1) \, _2F_1\left(-\frac{1}{4},\frac{7}{4};\frac{11}{4};-x\right)\right)}{1155 (x+1)^{5/4}}","-\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4+2\&,\frac{-\text{$\#$1}^4 \log \left(\sqrt[4]{x^4+x^3}-\text{$\#$1} x\right)+\text{$\#$1}^4 \log (x)+2 \log \left(\sqrt[4]{x^4+x^3}-\text{$\#$1} x\right)-2 \log (x)}{\text{$\#$1}^7-\text{$\#$1}^3}\&\right]-2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+x^3}}\right)+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+x^3}}\right)}{2^{3/4}}+2 \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+x^3}}\right)-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+x^3}}\right)}{2^{3/4}}",1,"((x^3*(1 + x))^(1/4)*(385*(1 + x)*Hypergeometric2F1[-1/4, 3/4, 7/4, -x] - 165*x*(1 + x)*Hypergeometric2F1[-1/4, 7/4, 11/4, -x] - 7*(-15*x^2*(1 + x)*Hypergeometric2F1[-1/4, 11/4, 15/4, -x] - 165*(1 + x)*Hypergeometric2F1[3/4, 3/4, 7/4, -x] + (55 - 55*I)*(1 + x)^(1/4)*Hypergeometric2F1[3/4, 1, 7/4, ((1 - I)*x)/(1 + x)] + (55 + 55*I)*(1 + x)^(1/4)*Hypergeometric2F1[3/4, 1, 7/4, ((1 + I)*x)/(1 + x)] + 110*(1 + x)^(1/4)*Hypergeometric2F1[3/4, 1, 7/4, (2*x)/(1 + x)] + 11*x^3*Hypergeometric2F1[3/4, 15/4, 19/4, -x] + 11*x^4*Hypergeometric2F1[3/4, 15/4, 19/4, -x])))/(1155*(1 + x)^(5/4))","C",1
2275,1,221,173,0.0753247,"\int \frac{x^2 \sqrt[4]{x^3+x^4}}{-1+x^4} \, dx","Integrate[(x^2*(x^3 + x^4)^(1/4))/(-1 + x^4),x]","\frac{\sqrt[4]{x^3 (x+1)} \left(-7 \left(11 x^4 \, _2F_1\left(\frac{3}{4},\frac{15}{4};\frac{19}{4};-x\right)+11 x^3 \, _2F_1\left(\frac{3}{4},\frac{15}{4};\frac{19}{4};-x\right)-15 (x+1) x^2 \, _2F_1\left(-\frac{1}{4},\frac{11}{4};\frac{15}{4};-x\right)-165 (x+1) \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};-x\right)+(55-55 i) \sqrt[4]{x+1} \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{(1-i) x}{x+1}\right)+(55+55 i) \sqrt[4]{x+1} \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{(1+i) x}{x+1}\right)+110 \sqrt[4]{x+1} \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{2 x}{x+1}\right)\right)+385 (x+1) \, _2F_1\left(-\frac{1}{4},\frac{3}{4};\frac{7}{4};-x\right)-165 x (x+1) \, _2F_1\left(-\frac{1}{4},\frac{7}{4};\frac{11}{4};-x\right)\right)}{1155 (x+1)^{5/4}}","-\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4+2\&,\frac{-\text{$\#$1}^4 \log \left(\sqrt[4]{x^4+x^3}-\text{$\#$1} x\right)+\text{$\#$1}^4 \log (x)+2 \log \left(\sqrt[4]{x^4+x^3}-\text{$\#$1} x\right)-2 \log (x)}{\text{$\#$1}^7-\text{$\#$1}^3}\&\right]-2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+x^3}}\right)+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+x^3}}\right)}{2^{3/4}}+2 \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+x^3}}\right)-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+x^3}}\right)}{2^{3/4}}",1,"((x^3*(1 + x))^(1/4)*(385*(1 + x)*Hypergeometric2F1[-1/4, 3/4, 7/4, -x] - 165*x*(1 + x)*Hypergeometric2F1[-1/4, 7/4, 11/4, -x] - 7*(-15*x^2*(1 + x)*Hypergeometric2F1[-1/4, 11/4, 15/4, -x] - 165*(1 + x)*Hypergeometric2F1[3/4, 3/4, 7/4, -x] + (55 - 55*I)*(1 + x)^(1/4)*Hypergeometric2F1[3/4, 1, 7/4, ((1 - I)*x)/(1 + x)] + (55 + 55*I)*(1 + x)^(1/4)*Hypergeometric2F1[3/4, 1, 7/4, ((1 + I)*x)/(1 + x)] + 110*(1 + x)^(1/4)*Hypergeometric2F1[3/4, 1, 7/4, (2*x)/(1 + x)] + 11*x^3*Hypergeometric2F1[3/4, 15/4, 19/4, -x] + 11*x^4*Hypergeometric2F1[3/4, 15/4, 19/4, -x])))/(1155*(1 + x)^(5/4))","C",1
2276,1,153,173,11.4359441,"\int \frac{1}{\sqrt[3]{-x+x^3} \left(1+x^6\right)} \, dx","Integrate[1/((-x + x^3)^(1/3)*(1 + x^6)),x]","-\frac{\sqrt[3]{\frac{1}{x^2}-1} x \left(4 \text{RootSum}\left[\text{$\#$1}^6+\text{$\#$1}^3+1\&,\frac{\log \left(\sqrt[3]{\frac{1}{x^2}-1}-\text{$\#$1}\right)}{\text{$\#$1}}\&\right]+2^{2/3} \left(-2 \log \left(2^{2/3} \sqrt[3]{\frac{1}{x^2}-1}+2\right)+\log \left(\sqrt[3]{2} \left(\frac{1}{x^2}-1\right)^{2/3}-2^{2/3} \sqrt[3]{\frac{1}{x^2}-1}+2\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{\frac{1}{x^2}-1}-1}{\sqrt{3}}\right)\right)\right)}{24 \sqrt[3]{x \left(x^2-1\right)}}","-\frac{1}{6} \text{RootSum}\left[\text{$\#$1}^6-\text{$\#$1}^3+1\&,\frac{\log \left(\sqrt[3]{x^3-x}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]-\frac{\log \left(2^{2/3} \sqrt[3]{x^3-x}-2 x\right)}{6 \sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^3-x}+x}\right)}{2 \sqrt[3]{2} \sqrt{3}}+\frac{\log \left(2^{2/3} \sqrt[3]{x^3-x} x+\sqrt[3]{2} \left(x^3-x\right)^{2/3}+2 x^2\right)}{12 \sqrt[3]{2}}",1,"-1/24*((-1 + x^(-2))^(1/3)*x*(2^(2/3)*(2*Sqrt[3]*ArcTan[(-1 + 2^(2/3)*(-1 + x^(-2))^(1/3))/Sqrt[3]] - 2*Log[2 + 2^(2/3)*(-1 + x^(-2))^(1/3)] + Log[2 - 2^(2/3)*(-1 + x^(-2))^(1/3) + 2^(1/3)*(-1 + x^(-2))^(2/3)]) + 4*RootSum[1 + #1^3 + #1^6 & , Log[(-1 + x^(-2))^(1/3) - #1]/#1 & ]))/(x*(-1 + x^2))^(1/3)","A",1
2277,1,153,173,0.2882761,"\int \frac{1}{\sqrt[3]{-x+x^3} \left(1+x^6\right)} \, dx","Integrate[1/((-x + x^3)^(1/3)*(1 + x^6)),x]","-\frac{\sqrt[3]{\frac{1}{x^2}-1} x \left(4 \text{RootSum}\left[\text{$\#$1}^6+\text{$\#$1}^3+1\&,\frac{\log \left(\sqrt[3]{\frac{1}{x^2}-1}-\text{$\#$1}\right)}{\text{$\#$1}}\&\right]+2^{2/3} \left(-2 \log \left(2^{2/3} \sqrt[3]{\frac{1}{x^2}-1}+2\right)+\log \left(\sqrt[3]{2} \left(\frac{1}{x^2}-1\right)^{2/3}-2^{2/3} \sqrt[3]{\frac{1}{x^2}-1}+2\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{\frac{1}{x^2}-1}-1}{\sqrt{3}}\right)\right)\right)}{24 \sqrt[3]{x \left(x^2-1\right)}}","-\frac{1}{6} \text{RootSum}\left[\text{$\#$1}^6-\text{$\#$1}^3+1\&,\frac{\log \left(\sqrt[3]{x^3-x}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]-\frac{\log \left(2^{2/3} \sqrt[3]{x^3-x}-2 x\right)}{6 \sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^3-x}+x}\right)}{2 \sqrt[3]{2} \sqrt{3}}+\frac{\log \left(2^{2/3} \sqrt[3]{x^3-x} x+\sqrt[3]{2} \left(x^3-x\right)^{2/3}+2 x^2\right)}{12 \sqrt[3]{2}}",1,"-1/24*((-1 + x^(-2))^(1/3)*x*(2^(2/3)*(2*Sqrt[3]*ArcTan[(-1 + 2^(2/3)*(-1 + x^(-2))^(1/3))/Sqrt[3]] - 2*Log[2 + 2^(2/3)*(-1 + x^(-2))^(1/3)] + Log[2 - 2^(2/3)*(-1 + x^(-2))^(1/3) + 2^(1/3)*(-1 + x^(-2))^(2/3)]) + 4*RootSum[1 + #1^3 + #1^6 & , Log[(-1 + x^(-2))^(1/3) - #1]/#1 & ]))/(x*(-1 + x^2))^(1/3)","A",1
2278,1,280,173,0.2553071,"\int \frac{\sqrt{-x+x^4}}{-b+a x^6} \, dx","Integrate[Sqrt[-x + x^4]/(-b + a*x^6),x]","\frac{\sqrt{x} \sqrt{x^3-1} \left(\sqrt{\sqrt{a}-\sqrt{b}} \left(\tan ^{-1}\left(\frac{\sqrt[4]{a}-\sqrt[4]{b} x^{3/2}}{\sqrt{x^3-1} \sqrt{\sqrt{a}-\sqrt{b}}}\right)-\tan ^{-1}\left(\frac{\sqrt[4]{a}+\sqrt[4]{b} x^{3/2}}{\sqrt{x^3-1} \sqrt{\sqrt{a}-\sqrt{b}}}\right)\right)-\sqrt{\sqrt{a}+\sqrt{b}} \tanh ^{-1}\left(\frac{-\sqrt[4]{b} x^{3/2}+i \sqrt[4]{a}}{\sqrt{x^3-1} \sqrt{\sqrt{a}+\sqrt{b}}}\right)+\sqrt{\sqrt{a}+\sqrt{b}} \tanh ^{-1}\left(\frac{\sqrt[4]{b} x^{3/2}+i \sqrt[4]{a}}{\sqrt{x^3-1} \sqrt{\sqrt{a}+\sqrt{b}}}\right)\right)}{6 \sqrt{a} b^{3/4} \sqrt{x \left(x^3-1\right)}}","\frac{\sqrt{\sqrt{b} \left(\sqrt{a}-\sqrt{b}\right)} \tan ^{-1}\left(\frac{x \sqrt{x^4-x} \sqrt{\sqrt{a} \sqrt{b}-b}}{\sqrt{b} (x-1) \left(x^2+x+1\right)}\right)}{3 \sqrt{a} b}-\frac{\sqrt{-\left(\sqrt{b} \left(\sqrt{a}+\sqrt{b}\right)\right)} \tan ^{-1}\left(\frac{x \sqrt{x^4-x} \sqrt{-\sqrt{a} \sqrt{b}-b}}{\sqrt{b} (x-1) \left(x^2+x+1\right)}\right)}{3 \sqrt{a} b}",1,"(Sqrt[x]*Sqrt[-1 + x^3]*(Sqrt[Sqrt[a] - Sqrt[b]]*(ArcTan[(a^(1/4) - b^(1/4)*x^(3/2))/(Sqrt[Sqrt[a] - Sqrt[b]]*Sqrt[-1 + x^3])] - ArcTan[(a^(1/4) + b^(1/4)*x^(3/2))/(Sqrt[Sqrt[a] - Sqrt[b]]*Sqrt[-1 + x^3])]) - Sqrt[Sqrt[a] + Sqrt[b]]*ArcTanh[(I*a^(1/4) - b^(1/4)*x^(3/2))/(Sqrt[Sqrt[a] + Sqrt[b]]*Sqrt[-1 + x^3])] + Sqrt[Sqrt[a] + Sqrt[b]]*ArcTanh[(I*a^(1/4) + b^(1/4)*x^(3/2))/(Sqrt[Sqrt[a] + Sqrt[b]]*Sqrt[-1 + x^3])]))/(6*Sqrt[a]*b^(3/4)*Sqrt[x*(-1 + x^3)])","C",1
2279,0,0,173,0.3565999,"\int \frac{\left(1+2 x^8\right) \sqrt[4]{-1-2 x^4+2 x^8} \left(1-3 x^8+4 x^{16}\right)}{x^{10} \left(-1+2 x^8\right)} \, dx","Integrate[((1 + 2*x^8)*(-1 - 2*x^4 + 2*x^8)^(1/4)*(1 - 3*x^8 + 4*x^16))/(x^10*(-1 + 2*x^8)),x]","\int \frac{\left(1+2 x^8\right) \sqrt[4]{-1-2 x^4+2 x^8} \left(1-3 x^8+4 x^{16}\right)}{x^{10} \left(-1+2 x^8\right)} \, dx","-\frac{\tan ^{-1}\left(\frac{2^{3/4} x \sqrt[4]{2 x^8-2 x^4-1}}{\sqrt{2} x^2-\sqrt{2 x^8-2 x^4-1}}\right)}{2 \sqrt[4]{2}}-\frac{\tanh ^{-1}\left(\frac{2 \sqrt[4]{2} x \sqrt[4]{2 x^8-2 x^4-1}}{2 x^2+\sqrt{2} \sqrt{2 x^8-2 x^4-1}}\right)}{2 \sqrt[4]{2}}+\frac{\sqrt[4]{2 x^8-2 x^4-1} \left(20 x^{16}-4 x^{12}+9 x^8+2 x^4+5\right)}{45 x^9}",1,"Integrate[((1 + 2*x^8)*(-1 - 2*x^4 + 2*x^8)^(1/4)*(1 - 3*x^8 + 4*x^16))/(x^10*(-1 + 2*x^8)), x]","F",-1
2280,1,260,173,0.6426637,"\int \frac{\left(b^2+a x^2\right)^{3/2}}{\sqrt{b+\sqrt{b^2+a x^2}}} \, dx","Integrate[(b^2 + a*x^2)^(3/2)/Sqrt[b + Sqrt[b^2 + a*x^2]],x]","\frac{60 a^3 x^6+232 a^2 b^2 x^4+48 a^2 b x^4 \sqrt{a x^2+b^2}-210 a b^4 x^2+105 \sqrt{2} b^{7/2} \sqrt{\sqrt{a x^2+b^2}-b} \left(2 b \sqrt{a x^2+b^2}+a x^2+2 b^2\right) \tan ^{-1}\left(\frac{\sqrt{\sqrt{a x^2+b^2}-b}}{\sqrt{2} \sqrt{b}}\right)-420 b^5 \sqrt{a x^2+b^2}+210 b^4 \left(2 b \sqrt{a x^2+b^2}+a x^2+2 b^2\right) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{b-\sqrt{b^2+a x^2}}{2 b}\right)-420 b^6}{210 a x \left(\sqrt{a x^2+b^2}+b\right)^{3/2}}","\frac{2 x \sqrt{a x^2+b^2} \left(15 a x^2+46 b^2\right)}{105 \sqrt{\sqrt{a x^2+b^2}+b}}+\frac{2 \sqrt{2} b^{7/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{2} \sqrt{b} \sqrt{\sqrt{a x^2+b^2}+b}}-\frac{\sqrt{\sqrt{a x^2+b^2}+b}}{\sqrt{2} \sqrt{b}}\right)}{\sqrt{a}}-\frac{2 x \left(3 a b x^2+46 b^3\right)}{105 \sqrt{\sqrt{a x^2+b^2}+b}}",1,"(-420*b^6 - 210*a*b^4*x^2 + 232*a^2*b^2*x^4 + 60*a^3*x^6 - 420*b^5*Sqrt[b^2 + a*x^2] + 48*a^2*b*x^4*Sqrt[b^2 + a*x^2] + 105*Sqrt[2]*b^(7/2)*Sqrt[-b + Sqrt[b^2 + a*x^2]]*(2*b^2 + a*x^2 + 2*b*Sqrt[b^2 + a*x^2])*ArcTan[Sqrt[-b + Sqrt[b^2 + a*x^2]]/(Sqrt[2]*Sqrt[b])] + 210*b^4*(2*b^2 + a*x^2 + 2*b*Sqrt[b^2 + a*x^2])*Hypergeometric2F1[-1/2, 1, 1/2, (b - Sqrt[b^2 + a*x^2])/(2*b)])/(210*a*x*(b + Sqrt[b^2 + a*x^2])^(3/2))","C",1
2281,0,0,173,0.3625165,"\int \frac{x \left(-2 q+p x^6\right) \sqrt{q+p x^6}}{b x^8+a \left(q+p x^6\right)^2} \, dx","Integrate[(x*(-2*q + p*x^6)*Sqrt[q + p*x^6])/(b*x^8 + a*(q + p*x^6)^2),x]","\int \frac{x \left(-2 q+p x^6\right) \sqrt{q+p x^6}}{b x^8+a \left(q+p x^6\right)^2} \, dx","-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^2 \sqrt{p x^6+q}}{\sqrt{a} p x^6+\sqrt{a} q-\sqrt{b} x^4}\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{b}}-\frac{\tanh ^{-1}\left(\frac{\frac{\sqrt[4]{a} p x^6}{\sqrt{2} \sqrt[4]{b}}+\frac{\sqrt[4]{a} q}{\sqrt{2} \sqrt[4]{b}}+\frac{\sqrt[4]{b} x^4}{\sqrt{2} \sqrt[4]{a}}}{x^2 \sqrt{p x^6+q}}\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{b}}",1,"Integrate[(x*(-2*q + p*x^6)*Sqrt[q + p*x^6])/(b*x^8 + a*(q + p*x^6)^2), x]","F",-1
2282,1,152,174,0.1215421,"\int \frac{\sqrt[3]{-1-2 x+6 x^2}}{-1+6 x} \, dx","Integrate[(-1 - 2*x + 6*x^2)^(1/3)/(-1 + 6*x),x]","\frac{1}{4} \sqrt[3]{6 x^2-2 x-1}+\frac{\sqrt[3]{\frac{7}{2}} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{\frac{2}{7}} \sqrt[3]{6 x^2-2 x-1}}{\sqrt[6]{3}}\right)}{4\ 3^{5/6}}-\frac{1}{12} \sqrt[3]{\frac{7}{6}} \log \left(\sqrt[3]{(1-6 x)^2-7}+\sqrt[3]{7}\right)+\frac{1}{24} \sqrt[3]{\frac{7}{6}} \log \left(\left((1-6 x)^2-7\right)^{2/3}-\sqrt[3]{7} \sqrt[3]{(1-6 x)^2-7}+7^{2/3}\right)","\frac{1}{4} \sqrt[3]{6 x^2-2 x-1}-\frac{1}{12} \sqrt[3]{\frac{7}{6}} \log \left(\sqrt[3]{6} 7^{2/3} \sqrt[3]{6 x^2-2 x-1}+7\right)+\frac{1}{24} \sqrt[3]{\frac{7}{6}} \log \left(6^{2/3} \sqrt[3]{7} \left(6 x^2-2 x-1\right)^{2/3}-\sqrt[3]{6} 7^{2/3} \sqrt[3]{6 x^2-2 x-1}+7\right)+\frac{\sqrt[3]{\frac{7}{2}} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{\frac{2}{7}} \sqrt[3]{6 x^2-2 x-1}}{\sqrt[6]{3}}\right)}{4\ 3^{5/6}}",1,"(-1 - 2*x + 6*x^2)^(1/3)/4 + ((7/2)^(1/3)*ArcTan[1/Sqrt[3] - (2*(2/7)^(1/3)*(-1 - 2*x + 6*x^2)^(1/3))/3^(1/6)])/(4*3^(5/6)) - ((7/6)^(1/3)*Log[7^(1/3) + (-7 + (1 - 6*x)^2)^(1/3)])/12 + ((7/6)^(1/3)*Log[7^(2/3) - 7^(1/3)*(-7 + (1 - 6*x)^2)^(1/3) + (-7 + (1 - 6*x)^2)^(2/3)])/24","A",1
2283,0,0,174,10.7586684,"\int \frac{-2 a b x+(a+b) x^2}{(x (-a+x) (-b+x))^{2/3} \left(-a b+(a+b) x+(-1+d) x^2\right)} \, dx","Integrate[(-2*a*b*x + (a + b)*x^2)/((x*(-a + x)*(-b + x))^(2/3)*(-(a*b) + (a + b)*x + (-1 + d)*x^2)),x]","\int \frac{-2 a b x+(a+b) x^2}{(x (-a+x) (-b+x))^{2/3} \left(-a b+(a+b) x+(-1+d) x^2\right)} \, dx","-\frac{\log \left(\sqrt[3]{x^2 (-a-b)+a b x+x^3}-\sqrt[3]{d} x\right)}{d^{2/3}}+\frac{\log \left(\sqrt[3]{d} x \sqrt[3]{x^2 (-a-b)+a b x+x^3}+\left(x^2 (-a-b)+a b x+x^3\right)^{2/3}+d^{2/3} x^2\right)}{2 d^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} x}{2 \sqrt[3]{x^2 (-a-b)+a b x+x^3}+\sqrt[3]{d} x}\right)}{d^{2/3}}",1,"Integrate[(-2*a*b*x + (a + b)*x^2)/((x*(-a + x)*(-b + x))^(2/3)*(-(a*b) + (a + b)*x + (-1 + d)*x^2)), x]","F",-1
2284,0,0,174,7.423054,"\int \frac{x \left(-a b+x^2\right)}{\left(x^2 (-a+x) (-b+x)\right)^{2/3} \left(a b d-(1+a d+b d) x+d x^2\right)} \, dx","Integrate[(x*(-(a*b) + x^2))/((x^2*(-a + x)*(-b + x))^(2/3)*(a*b*d - (1 + a*d + b*d)*x + d*x^2)),x]","\int \frac{x \left(-a b+x^2\right)}{\left(x^2 (-a+x) (-b+x)\right)^{2/3} \left(a b d-(1+a d+b d) x+d x^2\right)} \, dx","-\frac{\log \left(d^{2/3} \left(x^3 (-a-b)+a b x^2+x^4\right)^{2/3}+\sqrt[3]{d} x \sqrt[3]{x^3 (-a-b)+a b x^2+x^4}+x^2\right)}{2 \sqrt[3]{d}}+\frac{\log \left(x-\sqrt[3]{d} \sqrt[3]{x^3 (-a-b)+a b x^2+x^4}\right)}{\sqrt[3]{d}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{d} \sqrt[3]{x^3 (-a-b)+a b x^2+x^4}+x}\right)}{\sqrt[3]{d}}",1,"Integrate[(x*(-(a*b) + x^2))/((x^2*(-a + x)*(-b + x))^(2/3)*(a*b*d - (1 + a*d + b*d)*x + d*x^2)), x]","F",-1
2285,1,146,174,0.2362067,"\int \frac{\left(-2+x^3\right) \left(-1+x^3\right)^{2/3}}{x^3 \left(-1+2 x^3\right)} \, dx","Integrate[((-2 + x^3)*(-1 + x^3)^(2/3))/(x^3*(-1 + 2*x^3)),x]","\frac{1}{6} \left(-2 \log \left(\frac{x}{\sqrt[3]{1-x^3}}+1\right)-2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{1-x^3}}-1}{\sqrt{3}}\right)-\frac{6 \left(x^3-1\right)^{2/3}}{x^2}+\log \left(-\frac{x}{\sqrt[3]{1-x^3}}+\frac{x^2}{\left(1-x^3\right)^{2/3}}+1\right)\right)-\frac{x^4 \sqrt[3]{1-x^3} F_1\left(\frac{4}{3};\frac{1}{3},1;\frac{7}{3};x^3,2 x^3\right)}{4 \sqrt[3]{x^3-1}}","-\frac{1}{6} \log \left(\sqrt[3]{x^3-1}-x\right)-\frac{1}{2} \log \left(\sqrt[3]{x^3-1}+x\right)-\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-1}-x}\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-1}+x}\right)}{2 \sqrt{3}}-\frac{\left(x^3-1\right)^{2/3}}{x^2}+\frac{1}{4} \log \left(-\sqrt[3]{x^3-1} x+\left(x^3-1\right)^{2/3}+x^2\right)+\frac{1}{12} \log \left(\sqrt[3]{x^3-1} x+\left(x^3-1\right)^{2/3}+x^2\right)",1,"-1/4*(x^4*(1 - x^3)^(1/3)*AppellF1[4/3, 1/3, 1, 7/3, x^3, 2*x^3])/(-1 + x^3)^(1/3) + ((-6*(-1 + x^3)^(2/3))/x^2 - 2*Sqrt[3]*ArcTan[(-1 + (2*x)/(1 - x^3)^(1/3))/Sqrt[3]] + Log[1 + x^2/(1 - x^3)^(2/3) - x/(1 - x^3)^(1/3)] - 2*Log[1 + x/(1 - x^3)^(1/3)])/6","C",0
2286,1,164,174,0.1707429,"\int \frac{\left(-b+a x^2\right) \sqrt[4]{-b x^2+a x^4}}{b+a x^2} \, dx","Integrate[((-b + a*x^2)*(-(b*x^2) + a*x^4)^(1/4))/(b + a*x^2),x]","\frac{x \sqrt[4]{a x^4-b x^2} \left(27 a x^2 \left(1-\frac{a^2 x^4}{b^2}\right)^{3/4} F_1\left(\frac{7}{4};\frac{3}{4},1;\frac{11}{4};\frac{a x^2}{b},-\frac{a x^2}{b}\right)-49 b \left(1-\frac{a x^2}{b}\right)^{3/4} \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};\frac{2 a x^2}{a x^2+b}\right)+21 \left(b-a x^2\right) \left(\frac{a x^2}{b}+1\right)^{3/4}\right)}{42 \left(b-a x^2\right) \left(\frac{a x^2}{b}+1\right)^{3/4}}","\frac{9 b \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)}{4 a^{3/4}}-\frac{2 \sqrt[4]{2} b \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)}{a^{3/4}}-\frac{9 b \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)}{4 a^{3/4}}+\frac{2 \sqrt[4]{2} b \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)}{a^{3/4}}+\frac{1}{2} x \sqrt[4]{a x^4-b x^2}",1,"(x*(-(b*x^2) + a*x^4)^(1/4)*(21*(b - a*x^2)*(1 + (a*x^2)/b)^(3/4) + 27*a*x^2*(1 - (a^2*x^4)/b^2)^(3/4)*AppellF1[7/4, 3/4, 1, 11/4, (a*x^2)/b, -((a*x^2)/b)] - 49*b*(1 - (a*x^2)/b)^(3/4)*Hypergeometric2F1[3/4, 3/4, 7/4, (2*a*x^2)/(b + a*x^2)]))/(42*(b - a*x^2)*(1 + (a*x^2)/b)^(3/4))","C",0
2287,1,5076,174,4.8908486,"\int \frac{1+x^3}{\left(-1+x^3\right) \sqrt{a+b x+c x^2+b x^3+a x^4}} \, dx","Integrate[(1 + x^3)/((-1 + x^3)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]),x]","\text{Result too large to show}","\frac{4 \tan ^{-1}\left(\frac{x \sqrt{a+b-c}}{-\sqrt{a x^4+a+b x^3+b x+c x^2}+\sqrt{a} x^2+\sqrt{a} x+\sqrt{a}}\right)}{3 \sqrt{a+b-c}}-\frac{2 \sqrt{-2 a-2 b-c} \tan ^{-1}\left(\frac{x \sqrt{-2 a-2 b-c}}{-\sqrt{a x^4+a+b x^3+b x+c x^2}+\sqrt{a} x^2-2 \sqrt{a} x+\sqrt{a}}\right)}{3 (2 a+2 b+c)}",1,"Result too large to show","C",0
2288,0,0,174,2.9280691,"\int \frac{-b+a x^6}{\sqrt[3]{-x+x^3} \left(-d+c x^6\right)} \, dx","Integrate[(-b + a*x^6)/((-x + x^3)^(1/3)*(-d + c*x^6)),x]","\int \frac{-b+a x^6}{\sqrt[3]{-x+x^3} \left(-d+c x^6\right)} \, dx","\frac{(a d-b c) \text{RootSum}\left[\text{$\#$1}^9 d-3 \text{$\#$1}^6 d+3 \text{$\#$1}^3 d+c-d\&,\frac{\log \left(\sqrt[3]{x^3-x}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{6 c d}-\frac{a \log \left(\sqrt[3]{x^3-x}-x\right)}{2 c}+\frac{\sqrt{3} a \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-x}+x}\right)}{2 c}+\frac{a \log \left(\sqrt[3]{x^3-x} x+\left(x^3-x\right)^{2/3}+x^2\right)}{4 c}",1,"Integrate[(-b + a*x^6)/((-x + x^3)^(1/3)*(-d + c*x^6)), x]","F",-1
2289,0,0,174,0.4878778,"\int \frac{-b+a x^6}{\sqrt[3]{-x+x^3} \left(-d+c x^6\right)} \, dx","Integrate[(-b + a*x^6)/((-x + x^3)^(1/3)*(-d + c*x^6)),x]","\int \frac{-b+a x^6}{\sqrt[3]{-x+x^3} \left(-d+c x^6\right)} \, dx","\frac{(a d-b c) \text{RootSum}\left[\text{$\#$1}^9 d-3 \text{$\#$1}^6 d+3 \text{$\#$1}^3 d+c-d\&,\frac{\log \left(\sqrt[3]{x^3-x}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{6 c d}-\frac{a \log \left(\sqrt[3]{x^3-x}-x\right)}{2 c}+\frac{\sqrt{3} a \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-x}+x}\right)}{2 c}+\frac{a \log \left(\sqrt[3]{x^3-x} x+\left(x^3-x\right)^{2/3}+x^2\right)}{4 c}",1,"Integrate[(-b + a*x^6)/((-x + x^3)^(1/3)*(-d + c*x^6)), x]","F",-1
2290,1,114,174,0.1438015,"\int \frac{1}{\sqrt{d+\sqrt{c+\sqrt{b+a x}}}} \, dx","Integrate[1/Sqrt[d + Sqrt[c + Sqrt[b + a*x]]],x]","\frac{8 \sqrt{\sqrt{\sqrt{a x+b}+c}+d} \left(24 d^2 \sqrt{\sqrt{a x+b}+c}-20 c \sqrt{\sqrt{a x+b}+c}+15 \sqrt{a x+b} \sqrt{\sqrt{a x+b}+c}-18 d \sqrt{a x+b}+52 c d-48 d^3\right)}{105 a}","\frac{32 \left(13 c d-12 d^3\right) \sqrt{\sqrt{\sqrt{a x+b}+c}+d}}{105 a}-\frac{32 \left(5 c-6 d^2\right) \sqrt{\sqrt{a x+b}+c} \sqrt{\sqrt{\sqrt{a x+b}+c}+d}}{105 a}+\sqrt{a x+b} \left(\frac{8 \sqrt{\sqrt{a x+b}+c} \sqrt{\sqrt{\sqrt{a x+b}+c}+d}}{7 a}-\frac{48 d \sqrt{\sqrt{\sqrt{a x+b}+c}+d}}{35 a}\right)",1,"(8*Sqrt[d + Sqrt[c + Sqrt[b + a*x]]]*(52*c*d - 48*d^3 - 18*d*Sqrt[b + a*x] - 20*c*Sqrt[c + Sqrt[b + a*x]] + 24*d^2*Sqrt[c + Sqrt[b + a*x]] + 15*Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]]))/(105*a)","A",1
2291,1,114,175,0.0529596,"\int \frac{1}{x \sqrt[3]{3+3 x+x^2}} \, dx","Integrate[1/(x*(3 + 3*x + x^2)^(1/3)),x]","-\frac{3 \sqrt[3]{\frac{2 x-i \sqrt{3}+3}{x}} \sqrt[3]{\frac{2 x+i \sqrt{3}+3}{x}} F_1\left(\frac{2}{3};\frac{1}{3},\frac{1}{3};\frac{5}{3};-\frac{3+i \sqrt{3}}{2 x},\frac{i \left(3 i+\sqrt{3}\right)}{2 x}\right)}{2\ 2^{2/3} \sqrt[3]{x^2+3 x+3}}","\frac{\log \left(-3 \sqrt[3]{x^2+3 x+3}+\sqrt[3]{3} x+3 \sqrt[3]{3}\right)}{3 \sqrt[3]{3}}-\frac{\log \left(3^{2/3} x^2+9 \left(x^2+3 x+3\right)^{2/3}+\left(3 \sqrt[3]{3} x+9 \sqrt[3]{3}\right) \sqrt[3]{x^2+3 x+3}+6\ 3^{2/3} x+9\ 3^{2/3}\right)}{6 \sqrt[3]{3}}-\frac{\tan ^{-1}\left(\frac{\frac{\sqrt[3]{x^2+3 x+3}}{\sqrt{3}}+\frac{2 x}{3 \sqrt[6]{3}}+\frac{2}{\sqrt[6]{3}}}{\sqrt[3]{x^2+3 x+3}}\right)}{3^{5/6}}",1,"(-3*((3 - I*Sqrt[3] + 2*x)/x)^(1/3)*((3 + I*Sqrt[3] + 2*x)/x)^(1/3)*AppellF1[2/3, 1/3, 1/3, 5/3, -1/2*(3 + I*Sqrt[3])/x, ((I/2)*(3*I + Sqrt[3]))/x])/(2*2^(2/3)*(3 + 3*x + x^2)^(1/3))","C",0
2292,0,0,175,14.4065549,"\int \frac{-a b+x^2}{\sqrt[3]{x^2 (-a+x) (-b+x)} \left(a b d-(1+a d+b d) x+d x^2\right)} \, dx","Integrate[(-(a*b) + x^2)/((x^2*(-a + x)*(-b + x))^(1/3)*(a*b*d - (1 + a*d + b*d)*x + d*x^2)),x]","\int \frac{-a b+x^2}{\sqrt[3]{x^2 (-a+x) (-b+x)} \left(a b d-(1+a d+b d) x+d x^2\right)} \, dx","\frac{\log \left(x-\sqrt[3]{d} \sqrt[3]{x^3 (-a-b)+a b x^2+x^4}\right)}{d^{2/3}}-\frac{\log \left(d^{2/3} \left(x^3 (-a-b)+a b x^2+x^4\right)^{2/3}+\sqrt[3]{d} x \sqrt[3]{x^3 (-a-b)+a b x^2+x^4}+x^2\right)}{2 d^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{d} \sqrt[3]{x^3 (-a-b)+a b x^2+x^4}+x}\right)}{d^{2/3}}",1,"Integrate[(-(a*b) + x^2)/((x^2*(-a + x)*(-b + x))^(1/3)*(a*b*d - (1 + a*d + b*d)*x + d*x^2)), x]","F",-1
2293,0,0,175,0.3351126,"\int \frac{(-3+2 x) \left(1-x+x^3\right)^{2/3}}{x^3 \left(-2+2 x+x^3\right)} \, dx","Integrate[((-3 + 2*x)*(1 - x + x^3)^(2/3))/(x^3*(-2 + 2*x + x^3)),x]","\int \frac{(-3+2 x) \left(1-x+x^3\right)^{2/3}}{x^3 \left(-2+2 x+x^3\right)} \, dx","-\frac{1}{2} \left(\frac{3}{2}\right)^{2/3} \log \left(\sqrt[3]{2} 3^{2/3} \sqrt[3]{x^3-x+1}-3 x\right)+\frac{3 \sqrt[6]{3} \tan ^{-1}\left(\frac{3^{5/6} x}{2 \sqrt[3]{2} \sqrt[3]{x^3-x+1}+\sqrt[3]{3} x}\right)}{2\ 2^{2/3}}-\frac{3 \left(x^3-x+1\right)^{2/3}}{4 x^2}+\frac{1}{4} \left(\frac{3}{2}\right)^{2/3} \log \left(\sqrt[3]{2} 3^{2/3} \sqrt[3]{x^3-x+1} x+2^{2/3} \sqrt[3]{3} \left(x^3-x+1\right)^{2/3}+3 x^2\right)",1,"Integrate[((-3 + 2*x)*(1 - x + x^3)^(2/3))/(x^3*(-2 + 2*x + x^3)), x]","F",-1
2294,0,0,175,0.3327848,"\int \frac{(-3+4 x) \left(-1+2 x+x^3\right)^{2/3}}{x^3 \left(2-4 x+x^3\right)} \, dx","Integrate[((-3 + 4*x)*(-1 + 2*x + x^3)^(2/3))/(x^3*(2 - 4*x + x^3)),x]","\int \frac{(-3+4 x) \left(-1+2 x+x^3\right)^{2/3}}{x^3 \left(2-4 x+x^3\right)} \, dx","\frac{1}{2} \left(\frac{3}{2}\right)^{2/3} \log \left(\sqrt[3]{2} 3^{2/3} \sqrt[3]{x^3+2 x-1}-3 x\right)-\frac{3 \sqrt[6]{3} \tan ^{-1}\left(\frac{3^{5/6} x}{2 \sqrt[3]{2} \sqrt[3]{x^3+2 x-1}+\sqrt[3]{3} x}\right)}{2\ 2^{2/3}}+\frac{3 \left(x^3+2 x-1\right)^{2/3}}{4 x^2}-\frac{1}{4} \left(\frac{3}{2}\right)^{2/3} \log \left(\sqrt[3]{2} 3^{2/3} \sqrt[3]{x^3+2 x-1} x+2^{2/3} \sqrt[3]{3} \left(x^3+2 x-1\right)^{2/3}+3 x^2\right)",1,"Integrate[((-3 + 4*x)*(-1 + 2*x + x^3)^(2/3))/(x^3*(2 - 4*x + x^3)), x]","F",-1
2295,1,161,175,0.0902685,"\int \frac{\sqrt{-81+27 x+135 x^2-150 x^3+65 x^4-13 x^5+x^6}}{-1+x} \, dx","Integrate[Sqrt[-81 + 27*x + 135*x^2 - 150*x^3 + 65*x^4 - 13*x^5 + x^6]/(-1 + x),x]","\frac{(x-3)^2 \sqrt{x^2-x-1} \left(2 \left(8 \sqrt{x^2-x-1} x^2-62 \sqrt{x^2-x-1} x+115 \sqrt{x^2-x-1}+96 \tan ^{-1}\left(\frac{3-x}{2 \sqrt{x^2-x-1}}\right)\right)-246 \tanh ^{-1}\left(\frac{1-2 x}{2 \sqrt{x^2-x-1}}\right)-15 \tanh ^{-1}\left(\frac{2 x-1}{2 \sqrt{x^2-x-1}}\right)\right)}{48 \sqrt{(x-3)^4 \left(x^2-x-1\right)}}","\frac{\sqrt{x^6-13 x^5+65 x^4-150 x^3+135 x^2+27 x-81} \left(8 x^2-62 x+115\right)}{24 (x-3)^2}-\frac{77}{16} \log \left(-2 x^3+13 x^2+2 \sqrt{x^6-13 x^5+65 x^4-150 x^3+135 x^2+27 x-81}-24 x+9\right)-8 \tan ^{-1}\left(\frac{x^2-6 x+9}{x^3-7 x^2-\sqrt{x^6-13 x^5+65 x^4-150 x^3+135 x^2+27 x-81}+15 x-9}\right)+\frac{77}{8} \log (x-3)",1,"((-3 + x)^2*Sqrt[-1 - x + x^2]*(2*(115*Sqrt[-1 - x + x^2] - 62*x*Sqrt[-1 - x + x^2] + 8*x^2*Sqrt[-1 - x + x^2] + 96*ArcTan[(3 - x)/(2*Sqrt[-1 - x + x^2])]) - 246*ArcTanh[(1 - 2*x)/(2*Sqrt[-1 - x + x^2])] - 15*ArcTanh[(-1 + 2*x)/(2*Sqrt[-1 - x + x^2])]))/(48*Sqrt[(-3 + x)^4*(-1 - x + x^2)])","A",1
2296,0,0,175,1.8496511,"\int \frac{\left(-q+2 p x^3\right) \sqrt{q^2-2 p q x^2+2 p q x^3+p^2 x^6}}{x^2 \left(a q+b x+a p x^3\right)} \, dx","Integrate[((-q + 2*p*x^3)*Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6])/(x^2*(a*q + b*x + a*p*x^3)),x]","\int \frac{\left(-q+2 p x^3\right) \sqrt{q^2-2 p q x^2+2 p q x^3+p^2 x^6}}{x^2 \left(a q+b x+a p x^3\right)} \, dx","\frac{2 \sqrt{2 a^2 p q-b^2} \tan ^{-1}\left(\frac{x \sqrt{2 a^2 p q-b^2}}{a \sqrt{p^2 x^6+2 p q x^3-2 p q x^2+q^2}+a p x^3+a q+b x}\right)}{a^2}-\frac{b \log \left(\sqrt{p^2 x^6+2 p q x^3-2 p q x^2+q^2}+p x^3+q\right)}{a^2}+\frac{b \log (x)}{a^2}+\frac{\sqrt{p^2 x^6+2 p q x^3-2 p q x^2+q^2}}{a x}",1,"Integrate[((-q + 2*p*x^3)*Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6])/(x^2*(a*q + b*x + a*p*x^3)), x]","F",-1
2297,1,193,175,0.3125491,"\int \frac{1}{x^2 \sqrt[3]{-1+5 x-7 x^2-2 x^3+10 x^4-2 x^5-5 x^6+x^7+x^8}} \, dx","Integrate[1/(x^2*(-1 + 5*x - 7*x^2 - 2*x^3 + 10*x^4 - 2*x^5 - 5*x^6 + x^7 + x^8)^(1/3)),x]","-\frac{\left(x^2+x-1\right) \left(-6 (x-1)^{2/3} x \text{RootSum}\left[\text{$\#$1}^6+3 \text{$\#$1}^3+1\&,\frac{\text{$\#$1}^3 \log \left(\sqrt[3]{x-1}-\text{$\#$1}\right)+3 \log \left(\sqrt[3]{x-1}-\text{$\#$1}\right)}{2 \text{$\#$1}^5+3 \text{$\#$1}^2}\&\right]+6 x+10 (x-1)^{2/3} x \log \left(\sqrt[3]{x-1}+1\right)-5 (x-1)^{2/3} x \log \left((x-1)^{2/3}-\sqrt[3]{x-1}+1\right)+10 \sqrt{3} (x-1)^{2/3} x \tan ^{-1}\left(\frac{2 \sqrt[3]{x-1}-1}{\sqrt{3}}\right)-6\right)}{6 x \sqrt[3]{(x-1)^2 \left(x^2+x-1\right)^3}}","\frac{(x-1)^{2/3} \left(x^2+x-1\right) \left(\text{RootSum}\left[\text{$\#$1}^6+3 \text{$\#$1}^3+1\&,\frac{\text{$\#$1}^3 \log \left(\sqrt[3]{x-1}-\text{$\#$1}\right)+3 \log \left(\sqrt[3]{x-1}-\text{$\#$1}\right)}{2 \text{$\#$1}^5+3 \text{$\#$1}^2}\&\right]-\frac{\sqrt[3]{x-1}}{x}-\frac{5}{3} \log \left(\sqrt[3]{x-1}+1\right)+\frac{5}{6} \log \left((x-1)^{2/3}-\sqrt[3]{x-1}+1\right)+\frac{5 \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{x-1}}{\sqrt{3}}\right)}{\sqrt{3}}\right)}{\sqrt[3]{(x-1)^2 \left(x^2+x-1\right)^3}}",1,"-1/6*((-1 + x + x^2)*(-6 + 6*x + 10*Sqrt[3]*(-1 + x)^(2/3)*x*ArcTan[(-1 + 2*(-1 + x)^(1/3))/Sqrt[3]] + 10*(-1 + x)^(2/3)*x*Log[1 + (-1 + x)^(1/3)] - 5*(-1 + x)^(2/3)*x*Log[1 - (-1 + x)^(1/3) + (-1 + x)^(2/3)] - 6*(-1 + x)^(2/3)*x*RootSum[1 + 3*#1^3 + #1^6 & , (3*Log[(-1 + x)^(1/3) - #1] + Log[(-1 + x)^(1/3) - #1]*#1^3)/(3*#1^2 + 2*#1^5) & ]))/(x*((-1 + x)^2*(-1 + x + x^2)^3)^(1/3))","A",1
2298,0,0,175,0.2191824,"\int \frac{\left(1+x^2\right) \sqrt{x^2+\sqrt{1+x^4}}}{\left(-1+x^2\right) \sqrt{1+x^4}} \, dx","Integrate[((1 + x^2)*Sqrt[x^2 + Sqrt[1 + x^4]])/((-1 + x^2)*Sqrt[1 + x^4]),x]","\int \frac{\left(1+x^2\right) \sqrt{x^2+\sqrt{1+x^4}}}{\left(-1+x^2\right) \sqrt{1+x^4}} \, dx","\sqrt{2 \left(\sqrt{2}-1\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{2}-1\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)+\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)-\sqrt{2 \left(1+\sqrt{2}\right)} \tanh ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)",1,"Integrate[((1 + x^2)*Sqrt[x^2 + Sqrt[1 + x^4]])/((-1 + x^2)*Sqrt[1 + x^4]), x]","F",-1
2299,0,0,176,0.3538583,"\int \frac{2+x}{(-3+x) \sqrt[4]{1-x^2} \left(1+x^2\right)} \, dx","Integrate[(2 + x)/((-3 + x)*(1 - x^2)^(1/4)*(1 + x^2)),x]","\int \frac{2+x}{(-3+x) \sqrt[4]{1-x^2} \left(1+x^2\right)} \, dx","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{1-x^2}}{\sqrt[4]{1-x^2}-\sqrt[4]{2} x+\sqrt[4]{2}}\right)}{2 \sqrt[4]{2}}+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{1-x^2}}{\sqrt[4]{1-x^2}+\sqrt[4]{2} x-\sqrt[4]{2}}\right)}{2 \sqrt[4]{2}}-\frac{\tanh ^{-1}\left(\frac{\left(2 \sqrt[4]{2} x-2 \sqrt[4]{2}\right) \sqrt[4]{1-x^2}}{\sqrt{2} x^2+2 \sqrt{1-x^2}-2 \sqrt{2} x+\sqrt{2}}\right)}{2 \sqrt[4]{2}}",1,"Integrate[(2 + x)/((-3 + x)*(1 - x^2)^(1/4)*(1 + x^2)), x]","F",-1
2300,1,194,176,0.2261303,"\int \frac{\sqrt{b^2+a^2 x^3} \left(2 b^2+c x^3+a^2 x^6\right)}{x \left(-b^2+a^2 x^6\right)} \, dx","Integrate[(Sqrt[b^2 + a^2*x^3]*(2*b^2 + c*x^3 + a^2*x^6))/(x*(-b^2 + a^2*x^6)),x]","\frac{c \sqrt{a-b} \tan ^{-1}\left(\frac{\sqrt{a^2 x^3+b^2}}{\sqrt{b} \sqrt{a-b}}\right)-\sqrt{a+b} (3 a b+c) \tanh ^{-1}\left(\frac{\sqrt{a^2 x^3+b^2}}{\sqrt{b} \sqrt{a+b}}\right)+2 a \sqrt{b} \sqrt{a^2 x^3+b^2}-3 a b \sqrt{a-b} \tan ^{-1}\left(\frac{\sqrt{a^2 x^3+b^2}}{\sqrt{b} \sqrt{a-b}}\right)+4 a b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a^2 x^3+b^2}}{b}\right)}{3 a \sqrt{b}}","\frac{\left(c \sqrt{b-a}-3 a b \sqrt{b-a}\right) \tanh ^{-1}\left(\frac{\sqrt{a^2 x^3+b^2}}{\sqrt{b} \sqrt{b-a}}\right)}{3 a \sqrt{b}}+\frac{\left(-c \sqrt{a+b}-3 a b \sqrt{a+b}\right) \tanh ^{-1}\left(\frac{\sqrt{a^2 x^3+b^2}}{\sqrt{b} \sqrt{a+b}}\right)}{3 a \sqrt{b}}+\frac{2}{3} \sqrt{a^2 x^3+b^2}+\frac{4}{3} b \tanh ^{-1}\left(\frac{\sqrt{a^2 x^3+b^2}}{b}\right)",1,"(2*a*Sqrt[b]*Sqrt[b^2 + a^2*x^3] - 3*a*Sqrt[a - b]*b*ArcTan[Sqrt[b^2 + a^2*x^3]/(Sqrt[a - b]*Sqrt[b])] + Sqrt[a - b]*c*ArcTan[Sqrt[b^2 + a^2*x^3]/(Sqrt[a - b]*Sqrt[b])] + 4*a*b^(3/2)*ArcTanh[Sqrt[b^2 + a^2*x^3]/b] - Sqrt[a + b]*(3*a*b + c)*ArcTanh[Sqrt[b^2 + a^2*x^3]/(Sqrt[b]*Sqrt[a + b])])/(3*a*Sqrt[b])","A",1
2301,0,0,176,0.1558281,"\int \frac{1-x^4+2 x^8}{\sqrt[4]{1+x^4} \left(-1-2 x^4+x^8\right)} \, dx","Integrate[(1 - x^4 + 2*x^8)/((1 + x^4)^(1/4)*(-1 - 2*x^4 + x^8)),x]","\int \frac{1-x^4+2 x^8}{\sqrt[4]{1+x^4} \left(-1-2 x^4+x^8\right)} \, dx","\tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)-\frac{3 \tan ^{-1}\left(\frac{\sqrt[8]{2} x}{\sqrt[4]{x^4+1}}\right)}{4 \sqrt[8]{2}}+\tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)-\frac{3 \tanh ^{-1}\left(\frac{\sqrt[8]{2} x}{\sqrt[4]{x^4+1}}\right)}{4 \sqrt[8]{2}}+\frac{3 \tan ^{-1}\left(\frac{2^{5/8} x \sqrt[4]{x^4+1}}{\sqrt[4]{2} x^2-\sqrt{x^4+1}}\right)}{4\ 2^{5/8}}-\frac{3 \tanh ^{-1}\left(\frac{2\ 2^{3/8} x \sqrt[4]{x^4+1}}{2^{3/4} \sqrt{x^4+1}+2 x^2}\right)}{4\ 2^{5/8}}",1,"Integrate[(1 - x^4 + 2*x^8)/((1 + x^4)^(1/4)*(-1 - 2*x^4 + x^8)), x]","F",-1
2302,0,0,176,0.2326138,"\int \frac{\left(-1+x^2\right) \sqrt{x^2+\sqrt{1+x^4}}}{\left(1+x^2\right) \sqrt{1+x^4}} \, dx","Integrate[((-1 + x^2)*Sqrt[x^2 + Sqrt[1 + x^4]])/((1 + x^2)*Sqrt[1 + x^4]),x]","\int \frac{\left(-1+x^2\right) \sqrt{x^2+\sqrt{1+x^4}}}{\left(1+x^2\right) \sqrt{1+x^4}} \, dx","-\sqrt{2 \left(\sqrt{2}-1\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)+\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)-\sqrt{2 \left(1+\sqrt{2}\right)} \tanh ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{2}-1\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)",1,"Integrate[((-1 + x^2)*Sqrt[x^2 + Sqrt[1 + x^4]])/((1 + x^2)*Sqrt[1 + x^4]), x]","F",-1
2303,-1,0,176,180.0023936,"\int \frac{x}{x+\sqrt{c+\sqrt{b+a x}}} \, dx","Integrate[x/(x + Sqrt[c + Sqrt[b + a*x]]),x]","\text{\$Aborted}","\frac{4 \text{RootSum}\left[-\text{$\#$1}^4+2 \text{$\#$1}^2 c-\text{$\#$1} a+b-c^2\&,\frac{-\text{$\#$1}^2 a c \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+\text{$\#$1} a^2 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+a c^2 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-a b \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)}{4 \text{$\#$1}^3-4 \text{$\#$1} c+a}\&\right]}{a}-4 \sqrt{\sqrt{a x+b}+c}+x",1,"$Aborted","F",-1
2304,0,0,176,4.2410695,"\int \frac{x}{x+\sqrt{c+\sqrt{b+a x}}} \, dx","Integrate[x/(x + Sqrt[c + Sqrt[b + a*x]]),x]","\int \frac{x}{x+\sqrt{c+\sqrt{b+a x}}} \, dx","\frac{4 \text{RootSum}\left[-\text{$\#$1}^4+2 \text{$\#$1}^2 c-\text{$\#$1} a+b-c^2\&,\frac{-\text{$\#$1}^2 a c \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+\text{$\#$1} a^2 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+a c^2 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-a b \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)}{4 \text{$\#$1}^3-4 \text{$\#$1} c+a}\&\right]}{a}-4 \sqrt{\sqrt{a x+b}+c}+x",1,"Integrate[x/(x + Sqrt[c + Sqrt[b + a*x]]), x]","F",-1
2305,1,120,177,0.0618285,"\int \frac{1}{(1+x) \sqrt[3]{1-x+x^2}} \, dx","Integrate[1/((1 + x)*(1 - x + x^2)^(1/3)),x]","-\frac{3 \sqrt[3]{\frac{2 x-i \sqrt{3}-1}{x+1}} \sqrt[3]{\frac{2 x+i \sqrt{3}-1}{x+1}} F_1\left(\frac{2}{3};\frac{1}{3},\frac{1}{3};\frac{5}{3};\frac{3-i \sqrt{3}}{2 x+2},\frac{3+i \sqrt{3}}{2 x+2}\right)}{2\ 2^{2/3} \sqrt[3]{x^2-x+1}}","\frac{\log \left(3 \sqrt[3]{x^2-x+1}+\sqrt[3]{3} x-2 \sqrt[3]{3}\right)}{3 \sqrt[3]{3}}-\frac{\log \left(3^{2/3} x^2+9 \left(x^2-x+1\right)^{2/3}+\left(6 \sqrt[3]{3}-3 \sqrt[3]{3} x\right) \sqrt[3]{x^2-x+1}-4\ 3^{2/3} x+4\ 3^{2/3}\right)}{6 \sqrt[3]{3}}-\frac{\tan ^{-1}\left(\frac{\frac{\sqrt[3]{x^2-x+1}}{\sqrt{3}}-\frac{2 x}{3 \sqrt[6]{3}}+\frac{4}{3 \sqrt[6]{3}}}{\sqrt[3]{x^2-x+1}}\right)}{3^{5/6}}",1,"(-3*((-1 - I*Sqrt[3] + 2*x)/(1 + x))^(1/3)*((-1 + I*Sqrt[3] + 2*x)/(1 + x))^(1/3)*AppellF1[2/3, 1/3, 1/3, 5/3, (3 - I*Sqrt[3])/(2 + 2*x), (3 + I*Sqrt[3])/(2 + 2*x)])/(2*2^(2/3)*(1 - x + x^2)^(1/3))","C",0
2306,0,0,177,0.3753394,"\int \frac{\left(1+x^4\right) \sqrt[4]{-x^3+x^4}}{x^4 \left(-1+x^4\right)} \, dx","Integrate[((1 + x^4)*(-x^3 + x^4)^(1/4))/(x^4*(-1 + x^4)),x]","\int \frac{\left(1+x^4\right) \sqrt[4]{-x^3+x^4}}{x^4 \left(-1+x^4\right)} \, dx","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4+2\&,\frac{-\text{$\#$1}^4 \log \left(\sqrt[4]{x^4-x^3}-\text{$\#$1} x\right)+\text{$\#$1}^4 \log (x)+2 \log \left(\sqrt[4]{x^4-x^3}-\text{$\#$1} x\right)-2 \log (x)}{\text{$\#$1}^7-\text{$\#$1}^3}\&\right]+\sqrt[4]{2} \tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-x^3}}\right)-\sqrt[4]{2} \tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-x^3}}\right)-\frac{4 \sqrt[4]{x^4-x^3} \left(4 x^2+x-5\right)}{45 x^3}",1,"Integrate[((1 + x^4)*(-x^3 + x^4)^(1/4))/(x^4*(-1 + x^4)), x]","F",-1
2307,0,0,177,0.1631235,"\int \frac{\left(1+x^4\right) \sqrt[4]{-x^3+x^4}}{x^4 \left(-1+x^4\right)} \, dx","Integrate[((1 + x^4)*(-x^3 + x^4)^(1/4))/(x^4*(-1 + x^4)),x]","\int \frac{\left(1+x^4\right) \sqrt[4]{-x^3+x^4}}{x^4 \left(-1+x^4\right)} \, dx","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4+2\&,\frac{-\text{$\#$1}^4 \log \left(\sqrt[4]{x^4-x^3}-\text{$\#$1} x\right)+\text{$\#$1}^4 \log (x)+2 \log \left(\sqrt[4]{x^4-x^3}-\text{$\#$1} x\right)-2 \log (x)}{\text{$\#$1}^7-\text{$\#$1}^3}\&\right]+\sqrt[4]{2} \tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-x^3}}\right)-\sqrt[4]{2} \tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-x^3}}\right)-\frac{4 \sqrt[4]{x^4-x^3} \left(4 x^2+x-5\right)}{45 x^3}",1,"Integrate[((1 + x^4)*(-x^3 + x^4)^(1/4))/(x^4*(-1 + x^4)), x]","F",-1
2308,1,69,177,0.1393953,"\int \frac{\sqrt[3]{b x+a x^3} \left(b+a x^4\right)}{x^4} \, dx","Integrate[((b*x + a*x^3)^(1/3)*(b + a*x^4))/x^4,x]","\frac{3 \sqrt[3]{x \left(a x^2+b\right)} \left(\frac{2 a x^4 \, _2F_1\left(-\frac{1}{3},\frac{2}{3};\frac{5}{3};-\frac{a x^2}{b}\right)}{\sqrt[3]{\frac{a x^2}{b}+1}}-a x^2-b\right)}{8 x^3}","\frac{1}{12} \sqrt[3]{a} b \log \left(a^{2/3} x^2+\sqrt[3]{a} x \sqrt[3]{a x^3+b x}+\left(a x^3+b x\right)^{2/3}\right)-\frac{1}{6} \sqrt[3]{a} b \log \left(\sqrt[3]{a x^3+b x}-\sqrt[3]{a} x\right)-\frac{\sqrt[3]{a} b \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{a} x}{2 \sqrt[3]{a x^3+b x}+\sqrt[3]{a} x}\right)}{2 \sqrt{3}}+\frac{\sqrt[3]{a x^3+b x} \left(4 a x^4-3 a x^2-3 b\right)}{8 x^3}",1,"(3*(x*(b + a*x^2))^(1/3)*(-b - a*x^2 + (2*a*x^4*Hypergeometric2F1[-1/3, 2/3, 5/3, -((a*x^2)/b)])/(1 + (a*x^2)/b)^(1/3)))/(8*x^3)","C",1
2309,1,73,177,0.5629147,"\int \frac{b^4+a^4 x^4}{\sqrt{-b^2 x+a^2 x^3} \left(-b^4+a^4 x^4\right)} \, dx","Integrate[(b^4 + a^4*x^4)/(Sqrt[-(b^2*x) + a^2*x^3]*(-b^4 + a^4*x^4)),x]","\frac{x \left(-\sqrt{1-\frac{a^2 x^2}{b^2}} F_1\left(\frac{1}{4};-\frac{1}{2},1;\frac{5}{4};\frac{a^2 x^2}{b^2},-\frac{a^2 x^2}{b^2}\right)-1\right)}{\sqrt{a^2 x^3-b^2 x}}","\frac{\sqrt{a^2 x^3-b^2 x}}{b^2-a^2 x^2}-\frac{\tan ^{-1}\left(\frac{2 \sqrt{a} \sqrt{b} \sqrt{a^2 x^3-b^2 x}}{a^2 x^2-2 a b x-b^2}\right)}{4 \sqrt{a} \sqrt{b}}-\frac{\tanh ^{-1}\left(\frac{\frac{a^{3/2} x^2}{2 \sqrt{b}}-\frac{b^{3/2}}{2 \sqrt{a}}+\sqrt{a} \sqrt{b} x}{\sqrt{a^2 x^3-b^2 x}}\right)}{4 \sqrt{a} \sqrt{b}}",1,"(x*(-1 - Sqrt[1 - (a^2*x^2)/b^2]*AppellF1[1/4, -1/2, 1, 5/4, (a^2*x^2)/b^2, -((a^2*x^2)/b^2)]))/Sqrt[-(b^2*x) + a^2*x^3]","C",0
2310,1,168,177,0.3160974,"\int \frac{1+x}{\left(-1+x^3\right) \sqrt[8]{256-256 x^2+96 x^4-16 x^6+x^8}} \, dx","Integrate[(1 + x)/((-1 + x^3)*(256 - 256*x^2 + 96*x^4 - 16*x^6 + x^8)^(1/8)),x]","-\frac{\sqrt{x^2-4} \left(2 \sqrt{7} \tan ^{-1}\left(\frac{4-x}{\sqrt{3} \sqrt{x^2-4}}\right)+\left(\sqrt[3]{-1}-1\right) \sqrt{1-4 (-1)^{2/3}} \tanh ^{-1}\left(\frac{4 (-1)^{2/3}-x}{\sqrt{1+4 \sqrt[3]{-1}} \sqrt{x^2-4}}\right)+\sqrt{1+4 \sqrt[3]{-1}} \left(1+(-1)^{2/3}\right) \tanh ^{-1}\left(\frac{x+4 \sqrt[3]{-1}}{\sqrt{1-4 (-1)^{2/3}} \sqrt{x^2-4}}\right)\right)}{3 \sqrt{21} \sqrt[8]{\left(x^2-4\right)^4}}","\frac{\left(\left(x^2-4\right)^4\right)^{7/8} \left(\frac{4 \tan ^{-1}\left(\frac{\sqrt{x^2-4}}{\sqrt{3}}-\frac{x}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3}}-\frac{2}{3} \text{RootSum}\left[\text{$\#$1}^4-2 \text{$\#$1}^3+12 \text{$\#$1}^2-8 \text{$\#$1}+16\&,\frac{\text{$\#$1}^2 \log \left(-\text{$\#$1}+\sqrt{x^2-4}-x\right)-\text{$\#$1} \log \left(-\text{$\#$1}+\sqrt{x^2-4}-x\right)+4 \log \left(-\text{$\#$1}+\sqrt{x^2-4}-x\right)}{2 \text{$\#$1}^3-3 \text{$\#$1}^2+12 \text{$\#$1}-4}\&\right]\right)}{\left(x^2-4\right)^{7/2}}",1,"-1/3*(Sqrt[-4 + x^2]*(2*Sqrt[7]*ArcTan[(4 - x)/(Sqrt[3]*Sqrt[-4 + x^2])] + (-1 + (-1)^(1/3))*Sqrt[1 - 4*(-1)^(2/3)]*ArcTanh[(4*(-1)^(2/3) - x)/(Sqrt[1 + 4*(-1)^(1/3)]*Sqrt[-4 + x^2])] + Sqrt[1 + 4*(-1)^(1/3)]*(1 + (-1)^(2/3))*ArcTanh[(4*(-1)^(1/3) + x)/(Sqrt[1 - 4*(-1)^(2/3)]*Sqrt[-4 + x^2])]))/(Sqrt[21]*((-4 + x^2)^4)^(1/8))","A",1
2311,0,0,177,0.2527354,"\int \frac{1}{x^2 \sqrt[3]{-1-x+5 x^2+2 x^3-10 x^4+2 x^5+7 x^6-5 x^7+x^8}} \, dx","Integrate[1/(x^2*(-1 - x + 5*x^2 + 2*x^3 - 10*x^4 + 2*x^5 + 7*x^6 - 5*x^7 + x^8)^(1/3)),x]","\int \frac{1}{x^2 \sqrt[3]{-1-x+5 x^2+2 x^3-10 x^4+2 x^5+7 x^6-5 x^7+x^8}} \, dx","\frac{(x-1)^{2/3} \left(x^2-x-1\right) \left(-\text{RootSum}\left[\text{$\#$1}^6+\text{$\#$1}^3-1\&,\frac{\text{$\#$1}^3 \log \left(\sqrt[3]{x-1}-\text{$\#$1}\right)-\log \left(\sqrt[3]{x-1}-\text{$\#$1}\right)}{2 \text{$\#$1}^5+\text{$\#$1}^2}\&\right]-\frac{\sqrt[3]{x-1}}{x}+\frac{1}{3} \log \left(\sqrt[3]{x-1}+1\right)-\frac{1}{6} \log \left((x-1)^{2/3}-\sqrt[3]{x-1}+1\right)-\frac{\tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{x-1}}{\sqrt{3}}\right)}{\sqrt{3}}\right)}{\sqrt[3]{(x-1)^2 \left(x^2-x-1\right)^3}}",1,"Integrate[1/(x^2*(-1 - x + 5*x^2 + 2*x^3 - 10*x^4 + 2*x^5 + 7*x^6 - 5*x^7 + x^8)^(1/3)), x]","F",-1
2312,1,56,177,1.2071757,"\int \frac{c x^6 \left(-4 b+a x^5\right)}{\left(b+a x^5\right)^{3/4} \left(b^2+2 a b x^5-c^2 x^8+a^2 x^{10}\right)} \, dx","Integrate[(c*x^6*(-4*b + a*x^5))/((b + a*x^5)^(3/4)*(b^2 + 2*a*b*x^5 - c^2*x^8 + a^2*x^10)),x]","c \int \frac{x^6 \left(a x^5-4 b\right)}{\left(a x^5+b\right)^{3/4} \left(a^2 x^{10}+2 a b x^5+b^2-c^2 x^8\right)} \, dx","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a x^5+b}}\right)}{c^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a x^5+b}}\right)}{c^{3/4}}-\frac{\tan ^{-1}\left(\frac{\frac{\sqrt{a x^5+b}}{\sqrt{2} \sqrt[4]{c}}-\frac{\sqrt[4]{c} x^2}{\sqrt{2}}}{x \sqrt[4]{a x^5+b}}\right)}{\sqrt{2} c^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x \sqrt[4]{a x^5+b}}{\sqrt{a x^5+b}+\sqrt{c} x^2}\right)}{\sqrt{2} c^{3/4}}",1,"c*Integrate[(x^6*(-4*b + a*x^5))/((b + a*x^5)^(3/4)*(b^2 + 2*a*b*x^5 - c^2*x^8 + a^2*x^10)), x]","F",1
2313,1,199,177,0.368681,"\int \frac{x^2 \sqrt{a x+\sqrt{-b+a x}}}{\sqrt{-b+a x}} \, dx","Integrate[(x^2*Sqrt[a*x + Sqrt[-b + a*x]])/Sqrt[-b + a*x],x]","\frac{2 \sqrt{\sqrt{a x-b}+a x} \left(128 a^2 x^2 \left(10 \sqrt{a x-b}+1\right)+400 b^2 \left(6 \sqrt{a x-b}-1\right)+8 b \left(20 a x \left(10 \sqrt{a x-b}-1\right)+30 \sqrt{a x-b}-81\right)-24 a x \left(6 \sqrt{a x-b}-7\right)-210 \sqrt{a x-b}+315\right)+15 \left(320 b^3+16 b^2+60 b-21\right) \tanh ^{-1}\left(\frac{2 \sqrt{a x-b}+1}{2 \sqrt{\sqrt{a x-b}+a x}}\right)}{7680 a^3}","\frac{\left(-320 b^3-16 b^2-60 b+21\right) \log \left(2 \sqrt{a x-b}-2 \sqrt{\sqrt{a x-b}+a x}+1\right)}{512 a^3}+\frac{\sqrt{\sqrt{a x-b}+a x} \left(128 a^2 x^2-160 a b x+168 a x-400 b^2-648 b+315\right)}{3840 a^3}+\frac{\sqrt{a x-b} \left(640 a^2 x^2+800 a b x-72 a x+1200 b^2+120 b-105\right) \sqrt{\sqrt{a x-b}+a x}}{1920 a^3}",1,"(2*Sqrt[a*x + Sqrt[-b + a*x]]*(315 - 210*Sqrt[-b + a*x] - 24*a*x*(-7 + 6*Sqrt[-b + a*x]) + 400*b^2*(-1 + 6*Sqrt[-b + a*x]) + 128*a^2*x^2*(1 + 10*Sqrt[-b + a*x]) + 8*b*(-81 + 30*Sqrt[-b + a*x] + 20*a*x*(-1 + 10*Sqrt[-b + a*x]))) + 15*(-21 + 60*b + 16*b^2 + 320*b^3)*ArcTanh[(1 + 2*Sqrt[-b + a*x])/(2*Sqrt[a*x + Sqrt[-b + a*x]])])/(7680*a^3)","A",1
2314,1,282,178,4.9998919,"\int \frac{a+b x^2+a k^4 x^4}{\sqrt{(1-x) x \left(1-k^2 x\right)} \left(-1+k^4 x^4\right)} \, dx","Integrate[(a + b*x^2 + a*k^4*x^4)/(Sqrt[(1 - x)*x*(1 - k^2*x)]*(-1 + k^4*x^4)),x]","\frac{i \sqrt{\frac{1}{x-1}+1} (x-1)^{3/2} \sqrt{\frac{1-\frac{1}{k^2}}{x-1}+1} \left(-(k+1) \left(\left(k^2+1\right) \left(2 a k^2+b\right) \Pi \left(\frac{k-1}{k};i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)+(k-1) \left(b-2 a k^2\right) \left((1-i k) \Pi \left(\frac{k-i}{k};i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)+(1+i k) \Pi \left(\frac{k+i}{k};i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)\right)\right)+4 k^2 \left(a k^4+a+b\right) F\left(i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)+\left(k^3-k^2+k-1\right) \left(2 a k^2+b\right) \Pi \left(1+\frac{1}{k};i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)\right)}{2 k^2 \left(k^4-1\right) \sqrt{(x-1) x \left(k^2 x-1\right)}}","\frac{\left(-2 a k^2-b\right) \tan ^{-1}\left(\frac{(k-1) x}{\sqrt{k^2 x^3+\left(-k^2-1\right) x^2+x}}\right)}{4 (k-1) k^2}+\frac{\left(-2 a k^2-b\right) \tan ^{-1}\left(\frac{(k+1) x}{\sqrt{k^2 x^3+\left(-k^2-1\right) x^2+x}}\right)}{4 k^2 (k+1)}+\frac{\left(b-2 a k^2\right) \tan ^{-1}\left(\frac{\sqrt{k^2+1} \sqrt{k^2 x^3+\left(-k^2-1\right) x^2+x}}{(x-1) \left(k^2 x-1\right)}\right)}{2 k^2 \sqrt{k^2+1}}",1,"((I/2)*Sqrt[1 + (-1 + x)^(-1)]*Sqrt[1 + (1 - k^(-2))/(-1 + x)]*(-1 + x)^(3/2)*(4*k^2*(a + b + a*k^4)*EllipticF[I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)] + (b + 2*a*k^2)*(-1 + k - k^2 + k^3)*EllipticPi[1 + k^(-1), I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)] - (1 + k)*((1 + k^2)*(b + 2*a*k^2)*EllipticPi[(-1 + k)/k, I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)] + (-1 + k)*(b - 2*a*k^2)*((1 - I*k)*EllipticPi[(-I + k)/k, I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)] + (1 + I*k)*EllipticPi[(I + k)/k, I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)]))))/(k^2*(-1 + k^4)*Sqrt[(-1 + x)*x*(-1 + k^2*x)])","C",1
2315,0,0,178,0.7822694,"\int \frac{\left(-2 q+p x^3\right) \sqrt{q^2+2 p q x^3-2 p q x^4+p^2 x^6} \left(a q^2+2 a p q x^3+b x^4+a p^2 x^6\right)}{x^9} \, dx","Integrate[((-2*q + p*x^3)*Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]*(a*q^2 + 2*a*p*q*x^3 + b*x^4 + a*p^2*x^6))/x^9,x]","\int \frac{\left(-2 q+p x^3\right) \sqrt{q^2+2 p q x^3-2 p q x^4+p^2 x^6} \left(a q^2+2 a p q x^3+b x^4+a p^2 x^6\right)}{x^9} \, dx","\frac{1}{2} \left(-a p^2 q^2-2 b p q\right) \log \left(\sqrt{p^2 x^6-2 p q x^4+2 p q x^3+q^2}+p x^3+q\right)+\log (x) \left(a p^2 q^2+2 b p q\right)+\frac{\sqrt{p^2 x^6-2 p q x^4+2 p q x^3+q^2} \left(a p^3 x^9-a p^2 q x^7+3 a p^2 q x^6-a p q^2 x^4+3 a p q^2 x^3+a q^3+2 b p x^7+2 b q x^4\right)}{4 x^8}",1,"Integrate[((-2*q + p*x^3)*Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]*(a*q^2 + 2*a*p*q*x^3 + b*x^4 + a*p^2*x^6))/x^9, x]","F",-1
2316,1,4912,179,3.4392523,"\int \frac{-1+x^3}{\left(1+x^3\right) \sqrt{a+b x+c x^2+b x^3+a x^4}} \, dx","Integrate[(-1 + x^3)/((1 + x^3)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]),x]","\text{Result too large to show}","\frac{4 \tan ^{-1}\left(\frac{x \sqrt{a-b-c}}{-\sqrt{a x^4+a+b x^3+b x+c x^2}+\sqrt{a} x^2-\sqrt{a} x+\sqrt{a}}\right)}{3 \sqrt{a-b-c}}-\frac{2 \sqrt{-2 a+2 b-c} \tan ^{-1}\left(\frac{x \sqrt{-2 a+2 b-c}}{-\sqrt{a x^4+a+b x^3+b x+c x^2}+\sqrt{a} x^2+2 \sqrt{a} x+\sqrt{a}}\right)}{3 (2 a-2 b+c)}",1,"(2*(x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])^2*Sqrt[((Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3]))/((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3]))]*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])*Sqrt[((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])^2*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])^2)]*((2*(-1)^(2/3)*(EllipticF[ArcSin[Sqrt[((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))]], -(((Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])))]*((-1)^(1/3) - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1]) + EllipticPi[(((-1)^(1/3) - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/(((-1)^(1/3) - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])), ArcSin[Sqrt[((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))]], -(((Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])))]*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])))/((1 + (-1)^(1/3))^2*((-1)^(1/3) - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*((-1)^(1/3) - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])) - (2*(EllipticF[ArcSin[Sqrt[((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))]], -(((Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])))]*(1 + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1]) + EllipticPi[((1 + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((1 + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])), ArcSin[Sqrt[((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))]], -(((Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])))]*(-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])))/((-1 + (-1)^(1/3))*(1 + (-1)^(1/3))^2*(1 + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(1 + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])) - (2*(-1)^(2/3)*(EllipticF[ArcSin[Sqrt[((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))]], -(((Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])))]*((-1)^(2/3) + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1]) + EllipticPi[(((-1)^(2/3) + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/(((-1)^(2/3) + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])), ArcSin[Sqrt[((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))]], -(((Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])))]*(-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])))/((-1 + (-1)^(1/3))*(1 + (-1)^(1/3))^2*((-1)^(2/3) + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*((-1)^(2/3) + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])) + EllipticF[ArcSin[Sqrt[((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))]], ((Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))]/(-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])))/(Sqrt[x*(b + c*x + b*x^2) + a*(1 + x^4)]*(-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2]))","C",0
2317,0,0,179,3.1319021,"\int \frac{5 x-4 (1+k) x^2+3 k x^3}{\sqrt[3]{(1-x) x (1-k x)} \left(-1+(1+k) x-k x^2+b x^5\right)} \, dx","Integrate[(5*x - 4*(1 + k)*x^2 + 3*k*x^3)/(((1 - x)*x*(1 - k*x))^(1/3)*(-1 + (1 + k)*x - k*x^2 + b*x^5)),x]","\int \frac{5 x-4 (1+k) x^2+3 k x^3}{\sqrt[3]{(1-x) x (1-k x)} \left(-1+(1+k) x-k x^2+b x^5\right)} \, dx","-\frac{\log \left(b^{2/3} x^4+\sqrt[3]{b} x^2 \sqrt[3]{k x^3+(-k-1) x^2+x}+\left(k x^3+(-k-1) x^2+x\right)^{2/3}\right)}{2 \sqrt[3]{b}}+\frac{\log \left(\sqrt[3]{k x^3+(-k-1) x^2+x}-\sqrt[3]{b} x^2\right)}{\sqrt[3]{b}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{k x^3+(-k-1) x^2+x}}{2 \sqrt[3]{b} x^2+\sqrt[3]{k x^3+(-k-1) x^2+x}}\right)}{\sqrt[3]{b}}",1,"Integrate[(5*x - 4*(1 + k)*x^2 + 3*k*x^3)/(((1 - x)*x*(1 - k*x))^(1/3)*(-1 + (1 + k)*x - k*x^2 + b*x^5)), x]","F",-1
2318,0,0,179,5.930876,"\int \frac{x^2 \left(8-7 (1+k) x+6 k x^2\right)}{\sqrt[3]{(1-x) x (1-k x)} \left(-1+(1+k) x-k x^2+b x^8\right)} \, dx","Integrate[(x^2*(8 - 7*(1 + k)*x + 6*k*x^2))/(((1 - x)*x*(1 - k*x))^(1/3)*(-1 + (1 + k)*x - k*x^2 + b*x^8)),x]","\int \frac{x^2 \left(8-7 (1+k) x+6 k x^2\right)}{\sqrt[3]{(1-x) x (1-k x)} \left(-1+(1+k) x-k x^2+b x^8\right)} \, dx","-\frac{\log \left(b^{2/3} x^6+\sqrt[3]{b} x^3 \sqrt[3]{k x^3+(-k-1) x^2+x}+\left(k x^3+(-k-1) x^2+x\right)^{2/3}\right)}{2 \sqrt[3]{b}}+\frac{\log \left(\sqrt[3]{k x^3+(-k-1) x^2+x}-\sqrt[3]{b} x^3\right)}{\sqrt[3]{b}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{k x^3+(-k-1) x^2+x}}{2 \sqrt[3]{b} x^3+\sqrt[3]{k x^3+(-k-1) x^2+x}}\right)}{\sqrt[3]{b}}",1,"Integrate[(x^2*(8 - 7*(1 + k)*x + 6*k*x^2))/(((1 - x)*x*(1 - k*x))^(1/3)*(-1 + (1 + k)*x - k*x^2 + b*x^8)), x]","F",-1
2319,0,0,180,5.4754197,"\int \frac{x \left(-a b+x^2\right)}{\left(x^2 (-a+x) (-b+x)\right)^{2/3} \left(a b-(a+b+d) x+x^2\right)} \, dx","Integrate[(x*(-(a*b) + x^2))/((x^2*(-a + x)*(-b + x))^(2/3)*(a*b - (a + b + d)*x + x^2)),x]","\int \frac{x \left(-a b+x^2\right)}{\left(x^2 (-a+x) (-b+x)\right)^{2/3} \left(a b-(a+b+d) x+x^2\right)} \, dx","\frac{\log \left(\sqrt[3]{x^3 (-a-b)+a b x^2+x^4}-\sqrt[3]{d} x\right)}{d^{2/3}}-\frac{\log \left(\sqrt[3]{d} x \sqrt[3]{x^3 (-a-b)+a b x^2+x^4}+\left(x^3 (-a-b)+a b x^2+x^4\right)^{2/3}+d^{2/3} x^2\right)}{2 d^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} x}{2 \sqrt[3]{x^3 (-a-b)+a b x^2+x^4}+\sqrt[3]{d} x}\right)}{d^{2/3}}",1,"Integrate[(x*(-(a*b) + x^2))/((x^2*(-a + x)*(-b + x))^(2/3)*(a*b - (a + b + d)*x + x^2)), x]","F",-1
2320,1,259,180,0.146916,"\int \frac{\left(b+x^3\right) \left(c+x^3\right)}{\sqrt[3]{a+x^3}} \, dx","Integrate[((b + x^3)*(c + x^3))/(a + x^3)^(1/3),x]","\frac{1}{54} \left(\left(-4 a^2+6 a (b+c)-18 b c\right) \log \left(1-\frac{x}{\sqrt[3]{a+x^3}}\right)+2 \sqrt{3} \left(2 a^2-3 a (b+c)+9 b c\right) \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{a+x^3}}+1}{\sqrt{3}}\right)+2 a^2 \log \left(\frac{x}{\sqrt[3]{a+x^3}}+\frac{x^2}{\left(a+x^3\right)^{2/3}}+1\right)+9 b c \log \left(\frac{x}{\sqrt[3]{a+x^3}}+\frac{x^2}{\left(a+x^3\right)^{2/3}}+1\right)+18 b x \left(a+x^3\right)^{2/3}-3 a b \log \left(\frac{x}{\sqrt[3]{a+x^3}}+\frac{x^2}{\left(a+x^3\right)^{2/3}}+1\right)+18 c x \left(a+x^3\right)^{2/3}-3 a c \log \left(\frac{x}{\sqrt[3]{a+x^3}}+\frac{x^2}{\left(a+x^3\right)^{2/3}}+1\right)-12 a x \left(a+x^3\right)^{2/3}+9 x^4 \left(a+x^3\right)^{2/3}\right)","\frac{1}{27} \left(-2 a^2+3 a b+3 a c-9 b c\right) \log \left(\sqrt[3]{a+x^3}-x\right)+\frac{1}{27} \left(2 \sqrt{3} a^2-3 \sqrt{3} a b-3 \sqrt{3} a c+9 \sqrt{3} b c\right) \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{a+x^3}+x}\right)+\frac{1}{54} \left(2 a^2-3 a b-3 a c+9 b c\right) \log \left(x \sqrt[3]{a+x^3}+\left(a+x^3\right)^{2/3}+x^2\right)+\frac{1}{18} \left(a+x^3\right)^{2/3} \left(-4 a x+6 b x+6 c x+3 x^4\right)",1,"(-12*a*x*(a + x^3)^(2/3) + 18*b*x*(a + x^3)^(2/3) + 18*c*x*(a + x^3)^(2/3) + 9*x^4*(a + x^3)^(2/3) + 2*Sqrt[3]*(2*a^2 + 9*b*c - 3*a*(b + c))*ArcTan[(1 + (2*x)/(a + x^3)^(1/3))/Sqrt[3]] + (-4*a^2 - 18*b*c + 6*a*(b + c))*Log[1 - x/(a + x^3)^(1/3)] + 2*a^2*Log[1 + x^2/(a + x^3)^(2/3) + x/(a + x^3)^(1/3)] - 3*a*b*Log[1 + x^2/(a + x^3)^(2/3) + x/(a + x^3)^(1/3)] - 3*a*c*Log[1 + x^2/(a + x^3)^(2/3) + x/(a + x^3)^(1/3)] + 9*b*c*Log[1 + x^2/(a + x^3)^(2/3) + x/(a + x^3)^(1/3)])/54","A",1
2321,1,119,180,0.153127,"\int \frac{1}{\left(1+x^3\right) \sqrt[3]{-x^2+x^3}} \, dx","Integrate[1/((1 + x^3)*(-x^2 + x^3)^(1/3)),x]","\frac{\left((x-1) x^2\right)^{2/3} \left(\, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{x-1}{2 x}\right)+\left(1-i \sqrt{3}\right) \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};-\frac{2 i (x-1)}{\left(-i+\sqrt{3}\right) x}\right)+\left(1+i \sqrt{3}\right) \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{2 i (x-1)}{\left(i+\sqrt{3}\right) x}\right)\right)}{4 x^2}","-\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^6-\text{$\#$1}^3+1\&,\frac{\log \left(\sqrt[3]{x^3-x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]-\frac{\log \left(2^{2/3} \sqrt[3]{x^3-x^2}-2 x\right)}{3 \sqrt[3]{2}}+\frac{\log \left(2 x^2+2^{2/3} \sqrt[3]{x^3-x^2} x+\sqrt[3]{2} \left(x^3-x^2\right)^{2/3}\right)}{6 \sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^3-x^2}+x}\right)}{\sqrt[3]{2} \sqrt{3}}",1,"(((-1 + x)*x^2)^(2/3)*(Hypergeometric2F1[2/3, 1, 5/3, (-1 + x)/(2*x)] + (1 - I*Sqrt[3])*Hypergeometric2F1[2/3, 1, 5/3, ((-2*I)*(-1 + x))/((-I + Sqrt[3])*x)] + (1 + I*Sqrt[3])*Hypergeometric2F1[2/3, 1, 5/3, ((2*I)*(-1 + x))/((I + Sqrt[3])*x)]))/(4*x^2)","C",1
2322,1,119,180,0.0354072,"\int \frac{1}{\left(1+x^3\right) \sqrt[3]{-x^2+x^3}} \, dx","Integrate[1/((1 + x^3)*(-x^2 + x^3)^(1/3)),x]","\frac{\left((x-1) x^2\right)^{2/3} \left(\, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{x-1}{2 x}\right)+\left(1-i \sqrt{3}\right) \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};-\frac{2 i (x-1)}{\left(-i+\sqrt{3}\right) x}\right)+\left(1+i \sqrt{3}\right) \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{2 i (x-1)}{\left(i+\sqrt{3}\right) x}\right)\right)}{4 x^2}","-\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^6-\text{$\#$1}^3+1\&,\frac{\log \left(\sqrt[3]{x^3-x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]-\frac{\log \left(2^{2/3} \sqrt[3]{x^3-x^2}-2 x\right)}{3 \sqrt[3]{2}}+\frac{\log \left(2 x^2+2^{2/3} \sqrt[3]{x^3-x^2} x+\sqrt[3]{2} \left(x^3-x^2\right)^{2/3}\right)}{6 \sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^3-x^2}+x}\right)}{\sqrt[3]{2} \sqrt{3}}",1,"(((-1 + x)*x^2)^(2/3)*(Hypergeometric2F1[2/3, 1, 5/3, (-1 + x)/(2*x)] + (1 - I*Sqrt[3])*Hypergeometric2F1[2/3, 1, 5/3, ((-2*I)*(-1 + x))/((-I + Sqrt[3])*x)] + (1 + I*Sqrt[3])*Hypergeometric2F1[2/3, 1, 5/3, ((2*I)*(-1 + x))/((I + Sqrt[3])*x)]))/(4*x^2)","C",1
2323,0,0,180,3.2698723,"\int \frac{\left(-2 q+p x^3\right) \sqrt{q^2+2 p q x^3-2 p q x^4+p^2 x^6}}{x^3 \left(a q+b x^2+a p x^3\right)} \, dx","Integrate[((-2*q + p*x^3)*Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6])/(x^3*(a*q + b*x^2 + a*p*x^3)),x]","\int \frac{\left(-2 q+p x^3\right) \sqrt{q^2+2 p q x^3-2 p q x^4+p^2 x^6}}{x^3 \left(a q+b x^2+a p x^3\right)} \, dx","\frac{2 \sqrt{2 a^2 p q-b^2} \tan ^{-1}\left(\frac{x^2 \sqrt{2 a^2 p q-b^2}}{a \sqrt{p^2 x^6-2 p q x^4+2 p q x^3+q^2}+a p x^3+a q+b x^2}\right)}{a^2}-\frac{b \log \left(\sqrt{p^2 x^6-2 p q x^4+2 p q x^3+q^2}+p x^3+q\right)}{a^2}+\frac{2 b \log (x)}{a^2}+\frac{\sqrt{p^2 x^6-2 p q x^4+2 p q x^3+q^2}}{a x^2}",1,"Integrate[((-2*q + p*x^3)*Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6])/(x^3*(a*q + b*x^2 + a*p*x^3)), x]","F",-1
2324,1,63,180,0.0837117,"\int \frac{\sqrt[4]{x^2+x^6} \left(1+x^8\right)}{x^4 \left(-1+x^4\right)} \, dx","Integrate[((x^2 + x^6)^(1/4)*(1 + x^8))/(x^4*(-1 + x^4)),x]","\frac{2 \sqrt[4]{x^6+x^2} \left(3 \left(x^4+1\right)^{5/4}-10 x^4 F_1\left(\frac{3}{8};-\frac{1}{4},1;\frac{11}{8};-x^4,x^4\right)\right)}{15 x^3 \sqrt[4]{x^4+1}}","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^6+x^2}}\right)}{2^{3/4}}+\frac{\tan ^{-1}\left(\frac{2^{3/4} x \sqrt[4]{x^6+x^2}}{\sqrt{2} x^2-\sqrt{x^6+x^2}}\right)}{2 \sqrt[4]{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^6+x^2}}\right)}{2^{3/4}}+\frac{\tanh ^{-1}\left(\frac{\frac{x^2}{\sqrt[4]{2}}+\frac{\sqrt{x^6+x^2}}{2^{3/4}}}{x \sqrt[4]{x^6+x^2}}\right)}{2 \sqrt[4]{2}}+\frac{2 \sqrt[4]{x^6+x^2} \left(x^4+1\right)}{5 x^3}",1,"(2*(x^2 + x^6)^(1/4)*(3*(1 + x^4)^(5/4) - 10*x^4*AppellF1[3/8, -1/4, 1, 11/8, -x^4, x^4]))/(15*x^3*(1 + x^4)^(1/4))","C",0
2325,1,63,180,0.0446451,"\int \frac{\sqrt[4]{x^2+x^6} \left(1+x^8\right)}{x^4 \left(-1+x^4\right)} \, dx","Integrate[((x^2 + x^6)^(1/4)*(1 + x^8))/(x^4*(-1 + x^4)),x]","\frac{2 \sqrt[4]{x^6+x^2} \left(3 \left(x^4+1\right)^{5/4}-10 x^4 F_1\left(\frac{3}{8};-\frac{1}{4},1;\frac{11}{8};-x^4,x^4\right)\right)}{15 x^3 \sqrt[4]{x^4+1}}","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^6+x^2}}\right)}{2^{3/4}}+\frac{\tan ^{-1}\left(\frac{2^{3/4} x \sqrt[4]{x^6+x^2}}{\sqrt{2} x^2-\sqrt{x^6+x^2}}\right)}{2 \sqrt[4]{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^6+x^2}}\right)}{2^{3/4}}+\frac{\tanh ^{-1}\left(\frac{\frac{x^2}{\sqrt[4]{2}}+\frac{\sqrt{x^6+x^2}}{2^{3/4}}}{x \sqrt[4]{x^6+x^2}}\right)}{2 \sqrt[4]{2}}+\frac{2 \sqrt[4]{x^6+x^2} \left(x^4+1\right)}{5 x^3}",1,"(2*(x^2 + x^6)^(1/4)*(3*(1 + x^4)^(5/4) - 10*x^4*AppellF1[3/8, -1/4, 1, 11/8, -x^4, x^4]))/(15*x^3*(1 + x^4)^(1/4))","C",0
2326,1,59,181,0.0252322,"\int \frac{1}{x \sqrt[3]{2-3 x+x^2}} \, dx","Integrate[1/(x*(2 - 3*x + x^2)^(1/3)),x]","-\frac{3 \sqrt[3]{1-\frac{2}{x}} \sqrt[3]{1-\frac{1}{x}} F_1\left(\frac{2}{3};\frac{1}{3},\frac{1}{3};\frac{5}{3};\frac{1}{x},\frac{2}{x}\right)}{2 \sqrt[3]{x^2-3 x+2}}","\frac{\log \left(2 \sqrt[3]{x^2-3 x+2}+\sqrt[3]{2} x-2 \sqrt[3]{2}\right)}{2 \sqrt[3]{2}}-\frac{\log \left(2^{2/3} x^2+4 \left(x^2-3 x+2\right)^{2/3}+\left(4 \sqrt[3]{2}-2 \sqrt[3]{2} x\right) \sqrt[3]{x^2-3 x+2}-4\ 2^{2/3} x+4\ 2^{2/3}\right)}{4 \sqrt[3]{2}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x^2-3 x+2}}{\sqrt[3]{x^2-3 x+2}-\sqrt[3]{2} x+2 \sqrt[3]{2}}\right)}{2 \sqrt[3]{2}}",1,"(-3*(1 - 2/x)^(1/3)*(1 - x^(-1))^(1/3)*AppellF1[2/3, 1/3, 1/3, 5/3, x^(-1), 2/x])/(2*(2 - 3*x + x^2)^(1/3))","C",0
2327,0,0,181,13.528414,"\int \frac{a b-x^2}{\sqrt[3]{x^2 (-a+x) (-b+x)} \left(a b-(a+b+d) x+x^2\right)} \, dx","Integrate[(a*b - x^2)/((x^2*(-a + x)*(-b + x))^(1/3)*(a*b - (a + b + d)*x + x^2)),x]","\int \frac{a b-x^2}{\sqrt[3]{x^2 (-a+x) (-b+x)} \left(a b-(a+b+d) x+x^2\right)} \, dx","\frac{\log \left(\sqrt[3]{d} x \sqrt[3]{x^3 (-a-b)+a b x^2+x^4}+\left(x^3 (-a-b)+a b x^2+x^4\right)^{2/3}+d^{2/3} x^2\right)}{2 \sqrt[3]{d}}-\frac{\log \left(\sqrt[3]{x^3 (-a-b)+a b x^2+x^4}-\sqrt[3]{d} x\right)}{\sqrt[3]{d}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} x}{2 \sqrt[3]{x^3 (-a-b)+a b x^2+x^4}+\sqrt[3]{d} x}\right)}{\sqrt[3]{d}}",1,"Integrate[(a*b - x^2)/((x^2*(-a + x)*(-b + x))^(1/3)*(a*b - (a + b + d)*x + x^2)), x]","F",-1
2328,0,0,181,0.7659883,"\int \frac{\left(-q+2 p x^3\right) \sqrt{q^2-2 p q x^2+2 p q x^3+p^2 x^6} \left(b x^2+a \left(q+p x^3\right)^2\right)}{x^5} \, dx","Integrate[((-q + 2*p*x^3)*Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6]*(b*x^2 + a*(q + p*x^3)^2))/x^5,x]","\int \frac{\left(-q+2 p x^3\right) \sqrt{q^2-2 p q x^2+2 p q x^3+p^2 x^6} \left(b x^2+a \left(q+p x^3\right)^2\right)}{x^5} \, dx","\frac{1}{2} \left(-a p^2 q^2-2 b p q\right) \log \left(\sqrt{p^2 x^6+2 p q x^3-2 p q x^2+q^2}+p x^3+q\right)+\frac{1}{2} \log (x) \left(a p^2 q^2+2 b p q\right)+\frac{\sqrt{p^2 x^6+2 p q x^3-2 p q x^2+q^2} \left(a p^3 x^9+3 a p^2 q x^6-a p^2 q x^5+3 a p q^2 x^3-a p q^2 x^2+a q^3+2 b p x^5+2 b q x^2\right)}{4 x^4}",1,"Integrate[((-q + 2*p*x^3)*Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6]*(b*x^2 + a*(q + p*x^3)^2))/x^5, x]","F",-1
2329,1,205,181,0.590325,"\int \frac{1+x}{(-1+x) \sqrt{1+\sqrt{1+\sqrt{1+x}}}} \, dx","Integrate[(1 + x)/((-1 + x)*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]),x]","8 \left(\frac{1}{4} \text{RootSum}\left[2 \text{$\#$1}^8-4 \text{$\#$1}^4+4 \text{$\#$1}^2-1\&,\frac{2 \text{$\#$1}^4 \log \left(\frac{1}{\sqrt{\sqrt{\sqrt{x+1}+1}+1}}-\text{$\#$1}\right)-3 \text{$\#$1}^2 \log \left(\frac{1}{\sqrt{\sqrt{\sqrt{x+1}+1}+1}}-\text{$\#$1}\right)+\log \left(\frac{1}{\sqrt{\sqrt{\sqrt{x+1}+1}+1}}-\text{$\#$1}\right)}{2 \text{$\#$1}^7-2 \text{$\#$1}^3+\text{$\#$1}}\&\right]+\frac{1}{7} \left(\sqrt{\sqrt{x+1}+1}+1\right)^{7/2}-\frac{3}{5} \left(\sqrt{\sqrt{x+1}+1}+1\right)^{5/2}+\frac{2}{3} \left(\sqrt{\sqrt{x+1}+1}+1\right)^{3/2}\right)","2 \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x+1}+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}}\&\right]+\sqrt{x+1} \left(\frac{8}{7} \sqrt{\sqrt{x+1}+1} \sqrt{\sqrt{\sqrt{x+1}+1}+1}-\frac{48}{35} \sqrt{\sqrt{\sqrt{x+1}+1}+1}\right)+\frac{32}{105} \sqrt{\sqrt{x+1}+1} \sqrt{\sqrt{\sqrt{x+1}+1}+1}+\frac{32}{105} \sqrt{\sqrt{\sqrt{x+1}+1}+1}",1,"8*((2*(1 + Sqrt[1 + Sqrt[1 + x]])^(3/2))/3 - (3*(1 + Sqrt[1 + Sqrt[1 + x]])^(5/2))/5 + (1 + Sqrt[1 + Sqrt[1 + x]])^(7/2)/7 + RootSum[-1 + 4*#1^2 - 4*#1^4 + 2*#1^8 & , (Log[1/Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]] - #1] - 3*Log[1/Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]] - #1]*#1^2 + 2*Log[1/Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]] - #1]*#1^4)/(#1 - 2*#1^3 + 2*#1^7) & ]/4)","A",1
2330,1,205,181,0.3350766,"\int \frac{1+x}{(-1+x) \sqrt{1+\sqrt{1+\sqrt{1+x}}}} \, dx","Integrate[(1 + x)/((-1 + x)*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]),x]","8 \left(\frac{1}{4} \text{RootSum}\left[2 \text{$\#$1}^8-4 \text{$\#$1}^4+4 \text{$\#$1}^2-1\&,\frac{2 \text{$\#$1}^4 \log \left(\frac{1}{\sqrt{\sqrt{\sqrt{x+1}+1}+1}}-\text{$\#$1}\right)-3 \text{$\#$1}^2 \log \left(\frac{1}{\sqrt{\sqrt{\sqrt{x+1}+1}+1}}-\text{$\#$1}\right)+\log \left(\frac{1}{\sqrt{\sqrt{\sqrt{x+1}+1}+1}}-\text{$\#$1}\right)}{2 \text{$\#$1}^7-2 \text{$\#$1}^3+\text{$\#$1}}\&\right]+\frac{1}{7} \left(\sqrt{\sqrt{x+1}+1}+1\right)^{7/2}-\frac{3}{5} \left(\sqrt{\sqrt{x+1}+1}+1\right)^{5/2}+\frac{2}{3} \left(\sqrt{\sqrt{x+1}+1}+1\right)^{3/2}\right)","2 \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x+1}+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}}\&\right]+\sqrt{x+1} \left(\frac{8}{7} \sqrt{\sqrt{x+1}+1} \sqrt{\sqrt{\sqrt{x+1}+1}+1}-\frac{48}{35} \sqrt{\sqrt{\sqrt{x+1}+1}+1}\right)+\frac{32}{105} \sqrt{\sqrt{x+1}+1} \sqrt{\sqrt{\sqrt{x+1}+1}+1}+\frac{32}{105} \sqrt{\sqrt{\sqrt{x+1}+1}+1}",1,"8*((2*(1 + Sqrt[1 + Sqrt[1 + x]])^(3/2))/3 - (3*(1 + Sqrt[1 + Sqrt[1 + x]])^(5/2))/5 + (1 + Sqrt[1 + Sqrt[1 + x]])^(7/2)/7 + RootSum[-1 + 4*#1^2 - 4*#1^4 + 2*#1^8 & , (Log[1/Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]] - #1] - 3*Log[1/Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]] - #1]*#1^2 + 2*Log[1/Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]] - #1]*#1^4)/(#1 - 2*#1^3 + 2*#1^7) & ]/4)","A",1
2331,0,0,183,2.2494752,"\int \frac{1}{d+c x+\sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Integrate[(d + c*x + Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])^(-1),x]","\int \frac{1}{d+c x+\sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","\frac{2 \text{RootSum}\left[\text{$\#$1}^4 (-c)-2 \text{$\#$1}^3 a-2 \text{$\#$1}^2 a d+b^2 c\&,\frac{\text{$\#$1}^2 c \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)+a d \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)+\text{$\#$1} a \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)}{2 \text{$\#$1}^2 c+3 \text{$\#$1} a+2 a d}\&\right]}{c}-\frac{\log \left(\sqrt{a^2 x^2+b^2}+a x\right)}{c}",1,"Integrate[(d + c*x + Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])^(-1), x]","F",-1
2332,0,0,183,1.5431802,"\int \frac{1}{d+c x+\sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Integrate[(d + c*x + Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])^(-1),x]","\int \frac{1}{d+c x+\sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","\frac{2 \text{RootSum}\left[\text{$\#$1}^4 (-c)-2 \text{$\#$1}^3 a-2 \text{$\#$1}^2 a d+b^2 c\&,\frac{\text{$\#$1}^2 c \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)+a d \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)+\text{$\#$1} a \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)}{2 \text{$\#$1}^2 c+3 \text{$\#$1} a+2 a d}\&\right]}{c}-\frac{\log \left(\sqrt{a^2 x^2+b^2}+a x\right)}{c}",1,"Integrate[(d + c*x + Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])^(-1), x]","F",-1
2333,1,65,184,0.0706335,"\int \frac{-d+c x}{x^7 \sqrt[3]{-b+a x^3}} \, dx","Integrate[(-d + c*x)/(x^7*(-b + a*x^3)^(1/3)),x]","\frac{\left(a x^3-b\right)^{2/3} \left(b c \left(3 a x^3+2 b\right)-5 a^2 d x^5 \, _2F_1\left(\frac{2}{3},3;\frac{5}{3};1-\frac{a x^3}{b}\right)\right)}{10 b^3 x^5}","\frac{2 a^2 d \log \left(\sqrt[3]{a x^3-b}+\sqrt[3]{b}\right)}{27 b^{7/3}}-\frac{a^2 d \log \left(-\sqrt[3]{b} \sqrt[3]{a x^3-b}+\left(a x^3-b\right)^{2/3}+b^{2/3}\right)}{27 b^{7/3}}+\frac{2 a^2 d \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{a x^3-b}}{\sqrt{3} \sqrt[3]{b}}\right)}{9 \sqrt{3} b^{7/3}}+\frac{\left(a x^3-b\right)^{2/3} \left(27 a c x^4-20 a d x^3+18 b c x-15 b d\right)}{90 b^2 x^6}",1,"((-b + a*x^3)^(2/3)*(b*c*(2*b + 3*a*x^3) - 5*a^2*d*x^5*Hypergeometric2F1[2/3, 3, 5/3, 1 - (a*x^3)/b]))/(10*b^3*x^5)","C",1
2334,0,0,184,0.5788058,"\int \frac{1+x^2+x^4}{\left(1-x^4\right) \sqrt[4]{x^3+x^5}} \, dx","Integrate[(1 + x^2 + x^4)/((1 - x^4)*(x^3 + x^5)^(1/4)),x]","\int \frac{1+x^2+x^4}{\left(1-x^4\right) \sqrt[4]{x^3+x^5}} \, dx","\frac{3 \tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^5+x^3}}\right)}{4 \sqrt[4]{2}}+\frac{3 \tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^5+x^3}}\right)}{4 \sqrt[4]{2}}+\frac{\left(x^5+x^3\right)^{3/4}}{x^2 \left(x^2+1\right)}-\frac{3 \tan ^{-1}\left(\frac{2^{3/4} x \sqrt[4]{x^5+x^3}}{\sqrt{2} x^2-\sqrt{x^5+x^3}}\right)}{4\ 2^{3/4}}+\frac{3 \tanh ^{-1}\left(\frac{\frac{x^2}{\sqrt[4]{2}}+\frac{\sqrt{x^5+x^3}}{2^{3/4}}}{x \sqrt[4]{x^5+x^3}}\right)}{4\ 2^{3/4}}",1,"Integrate[(1 + x^2 + x^4)/((1 - x^4)*(x^3 + x^5)^(1/4)), x]","F",-1
2335,1,116,184,0.6743436,"\int \frac{\sqrt{-1+2 x^4} \left(-1+2 x^8\right)}{x^7 \left(-1+2 x^4+x^8\right)} \, dx","Integrate[(Sqrt[-1 + 2*x^4]*(-1 + 2*x^8))/(x^7*(-1 + 2*x^4 + x^8)),x]","\frac{1}{8} \left(\sqrt{2+10 \sqrt{2}} \tanh ^{-1}\left(\frac{x^2}{\sqrt{\sqrt{2}-1} \sqrt{2 x^4-1}}\right)-\sqrt{10 \sqrt{2}-2} \tan ^{-1}\left(\frac{x^2}{\sqrt{1+\sqrt{2}} \sqrt{2 x^4-1}}\right)\right)+\sqrt{2 x^4-1} \left(-\frac{1}{6 x^6}-\frac{2}{3 x^2}\right)","\sqrt{2} \text{RootSum}\left[\text{$\#$1}^4+16 \text{$\#$1}^3-80 \text{$\#$1}^2+128 \text{$\#$1}-64\&,\frac{\text{$\#$1}^2 \log \left(-\text{$\#$1}+4 x^4+2 \sqrt{2} \sqrt{2 x^4-1} x^2\right)-2 \text{$\#$1} \log \left(-\text{$\#$1}+4 x^4+2 \sqrt{2} \sqrt{2 x^4-1} x^2\right)+2 \log \left(-\text{$\#$1}+4 x^4+2 \sqrt{2} \sqrt{2 x^4-1} x^2\right)}{\text{$\#$1}^3+12 \text{$\#$1}^2-40 \text{$\#$1}+32}\&\right]+\frac{\sqrt{2 x^4-1} \left(-4 x^4-1\right)}{6 x^6}",1,"(-1/6*1/x^6 - 2/(3*x^2))*Sqrt[-1 + 2*x^4] + (-(Sqrt[-2 + 10*Sqrt[2]]*ArcTan[x^2/(Sqrt[1 + Sqrt[2]]*Sqrt[-1 + 2*x^4])]) + Sqrt[2 + 10*Sqrt[2]]*ArcTanh[x^2/(Sqrt[-1 + Sqrt[2]]*Sqrt[-1 + 2*x^4])])/8","A",0
2336,1,146,184,3.5280654,"\int \frac{\sqrt{1+x} \sqrt{1+\sqrt{1+x}}}{x \sqrt{1+\sqrt{1+\sqrt{1+x}}}} \, dx","Integrate[(Sqrt[1 + x]*Sqrt[1 + Sqrt[1 + x]])/(x*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]),x]","2 \left(\frac{4}{15} \sqrt{\sqrt{\sqrt{x+1}+1}+1} \left(3 \sqrt{x+1}-4 \sqrt{\sqrt{x+1}+1}+11\right)-\sqrt{2 \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\sqrt{1+\sqrt{2}} \sqrt{\sqrt{\sqrt{x+1}+1}+1}\right)-\sqrt{2 \left(\sqrt{2}-1\right)} \tanh ^{-1}\left(\sqrt{\sqrt{2}-1} \sqrt{\sqrt{\sqrt{x+1}+1}+1}\right)\right)","\frac{8}{5} \sqrt{x+1} \sqrt{\sqrt{\sqrt{x+1}+1}+1}-\frac{32}{15} \sqrt{\sqrt{x+1}+1} \sqrt{\sqrt{\sqrt{x+1}+1}+1}+\frac{88}{15} \sqrt{\sqrt{\sqrt{x+1}+1}+1}-2 \sqrt{2 \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{x+1}+1}+1}}{\sqrt{\sqrt{2}-1}}\right)-2 \sqrt{2 \left(\sqrt{2}-1\right)} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{x+1}+1}+1}}{\sqrt{1+\sqrt{2}}}\right)",1,"2*((4*(11 + 3*Sqrt[1 + x] - 4*Sqrt[1 + Sqrt[1 + x]])*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]])/15 - Sqrt[2*(1 + Sqrt[2])]*ArcTan[Sqrt[1 + Sqrt[2]]*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]] - Sqrt[2*(-1 + Sqrt[2])]*ArcTanh[Sqrt[-1 + Sqrt[2]]*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]])","A",1
2337,0,0,185,0.5575813,"\int \frac{1+x}{(3+x) (1+2 x) \sqrt[3]{1+x^2}} \, dx","Integrate[(1 + x)/((3 + x)*(1 + 2*x)*(1 + x^2)^(1/3)),x]","\int \frac{1+x}{(3+x) (1+2 x) \sqrt[3]{1+x^2}} \, dx","\frac{\log \left(5 \sqrt[3]{x^2+1}+\sqrt[3]{10} x-2 \sqrt[3]{10}\right)}{5 \sqrt[3]{10}}-\frac{\log \left(10^{2/3} x^2+25 \left(x^2+1\right)^{2/3}+\left(10 \sqrt[3]{10}-5 \sqrt[3]{10} x\right) \sqrt[3]{x^2+1}-4\ 10^{2/3} x+4\ 10^{2/3}\right)}{10 \sqrt[3]{10}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{x^2+1}}{\sqrt{3}}-\frac{2 \sqrt[3]{2} x}{\sqrt{3} 5^{2/3}}+\frac{4 \sqrt[3]{2}}{\sqrt{3} 5^{2/3}}}{\sqrt[3]{x^2+1}}\right)}{5 \sqrt[3]{10}}",1,"Integrate[(1 + x)/((3 + x)*(1 + 2*x)*(1 + x^2)^(1/3)), x]","F",-1
2338,1,136,185,0.1510859,"\int \frac{\sqrt[3]{-x^2+x^3}}{1+x+x^2} \, dx","Integrate[(-x^2 + x^3)^(1/3)/(1 + x + x^2),x]","\frac{\sqrt[3]{(x-1) x^2} \left(6 \sqrt[3]{x} \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};1-x\right)+i \left(\sqrt{3}+3 i\right) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(-i+\sqrt{3}\right) (x-1)}{\left(-3 i+\sqrt{3}\right) x}\right)+\left(-3-i \sqrt{3}\right) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(i+\sqrt{3}\right) (x-1)}{\left(3 i+\sqrt{3}\right) x}\right)\right)}{2 x}","-\text{RootSum}\left[\text{$\#$1}^6-3 \text{$\#$1}^3+3\&,\frac{-\text{$\#$1}^3 \log \left(\sqrt[3]{x^3-x^2}-\text{$\#$1} x\right)+\text{$\#$1}^3 \log (x)+3 \log \left(\sqrt[3]{x^3-x^2}-\text{$\#$1} x\right)-3 \log (x)}{2 \text{$\#$1}^5-3 \text{$\#$1}^2}\&\right]-\log \left(\sqrt[3]{x^3-x^2}-x\right)+\frac{1}{2} \log \left(x^2+\sqrt[3]{x^3-x^2} x+\left(x^3-x^2\right)^{2/3}\right)-\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-x^2}+x}\right)",1,"(((-1 + x)*x^2)^(1/3)*(6*x^(1/3)*Hypergeometric2F1[1/3, 1/3, 4/3, 1 - x] + I*(3*I + Sqrt[3])*Hypergeometric2F1[1/3, 1, 4/3, ((-I + Sqrt[3])*(-1 + x))/((-3*I + Sqrt[3])*x)] + (-3 - I*Sqrt[3])*Hypergeometric2F1[1/3, 1, 4/3, ((I + Sqrt[3])*(-1 + x))/((3*I + Sqrt[3])*x)]))/(2*x)","C",1
2339,1,136,185,0.0621212,"\int \frac{\sqrt[3]{-x^2+x^3}}{1+x+x^2} \, dx","Integrate[(-x^2 + x^3)^(1/3)/(1 + x + x^2),x]","\frac{\sqrt[3]{(x-1) x^2} \left(6 \sqrt[3]{x} \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};1-x\right)+i \left(\sqrt{3}+3 i\right) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(-i+\sqrt{3}\right) (x-1)}{\left(-3 i+\sqrt{3}\right) x}\right)+\left(-3-i \sqrt{3}\right) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(i+\sqrt{3}\right) (x-1)}{\left(3 i+\sqrt{3}\right) x}\right)\right)}{2 x}","-\text{RootSum}\left[\text{$\#$1}^6-3 \text{$\#$1}^3+3\&,\frac{-\text{$\#$1}^3 \log \left(\sqrt[3]{x^3-x^2}-\text{$\#$1} x\right)+\text{$\#$1}^3 \log (x)+3 \log \left(\sqrt[3]{x^3-x^2}-\text{$\#$1} x\right)-3 \log (x)}{2 \text{$\#$1}^5-3 \text{$\#$1}^2}\&\right]-\log \left(\sqrt[3]{x^3-x^2}-x\right)+\frac{1}{2} \log \left(x^2+\sqrt[3]{x^3-x^2} x+\left(x^3-x^2\right)^{2/3}\right)-\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-x^2}+x}\right)",1,"(((-1 + x)*x^2)^(1/3)*(6*x^(1/3)*Hypergeometric2F1[1/3, 1/3, 4/3, 1 - x] + I*(3*I + Sqrt[3])*Hypergeometric2F1[1/3, 1, 4/3, ((-I + Sqrt[3])*(-1 + x))/((-3*I + Sqrt[3])*x)] + (-3 - I*Sqrt[3])*Hypergeometric2F1[1/3, 1, 4/3, ((I + Sqrt[3])*(-1 + x))/((3*I + Sqrt[3])*x)]))/(2*x)","C",1
2340,0,0,185,2.0680453,"\int \frac{x \left(5-4 (1+k) x+3 k x^2\right)}{\sqrt[3]{(1-x) x (1-k x)} \left(-b+(b+b k) x-b k x^2+x^5\right)} \, dx","Integrate[(x*(5 - 4*(1 + k)*x + 3*k*x^2))/(((1 - x)*x*(1 - k*x))^(1/3)*(-b + (b + b*k)*x - b*k*x^2 + x^5)),x]","\int \frac{x \left(5-4 (1+k) x+3 k x^2\right)}{\sqrt[3]{(1-x) x (1-k x)} \left(-b+(b+b k) x-b k x^2+x^5\right)} \, dx","\frac{\log \left(x^2-\sqrt[3]{b} \sqrt[3]{k x^3+(-k-1) x^2+x}\right)}{b^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{b} \sqrt[3]{k x^3+(-k-1) x^2+x}}{\sqrt[3]{b} \sqrt[3]{k x^3+(-k-1) x^2+x}+2 x^2}\right)}{b^{2/3}}-\frac{\log \left(b^{2/3} \left(k x^3+(-k-1) x^2+x\right)^{2/3}+\sqrt[3]{b} x^2 \sqrt[3]{k x^3+(-k-1) x^2+x}+x^4\right)}{2 b^{2/3}}",1,"Integrate[(x*(5 - 4*(1 + k)*x + 3*k*x^2))/(((1 - x)*x*(1 - k*x))^(1/3)*(-b + (b + b*k)*x - b*k*x^2 + x^5)), x]","F",-1
2341,0,0,185,0.5253104,"\int \frac{1+x^4}{\left(1-x^4\right) \sqrt[4]{x^3+x^5}} \, dx","Integrate[(1 + x^4)/((1 - x^4)*(x^3 + x^5)^(1/4)),x]","\int \frac{1+x^4}{\left(1-x^4\right) \sqrt[4]{x^3+x^5}} \, dx","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^5+x^3}}\right)}{2 \sqrt[4]{2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^5+x^3}}\right)}{2 \sqrt[4]{2}}+\frac{2 \left(x^5+x^3\right)^{3/4}}{x^2 \left(x^2+1\right)}-\frac{\tan ^{-1}\left(\frac{2^{3/4} x \sqrt[4]{x^5+x^3}}{\sqrt{2} x^2-\sqrt{x^5+x^3}}\right)}{2\ 2^{3/4}}+\frac{\tanh ^{-1}\left(\frac{\frac{x^2}{\sqrt[4]{2}}+\frac{\sqrt{x^5+x^3}}{2^{3/4}}}{x \sqrt[4]{x^5+x^3}}\right)}{2\ 2^{3/4}}",1,"Integrate[(1 + x^4)/((1 - x^4)*(x^3 + x^5)^(1/4)), x]","F",-1
2342,1,162,185,0.303171,"\int \frac{\left(1+x^3\right)^{2/3} \left(2+x^3+x^6\right)}{x^6 \left(-2+x^3\right)^2} \, dx","Integrate[((1 + x^3)^(2/3)*(2 + x^3 + x^6))/(x^6*(-2 + x^3)^2),x]","\frac{35 \left(6 \tan ^{-1}\left(\frac{2^{2/3} x}{\sqrt[6]{3} \sqrt[3]{x^3+1}}+\frac{1}{\sqrt{3}}\right)+\sqrt{3} \left(\log \left(\frac{2^{2/3} \sqrt[3]{3} x}{\sqrt[3]{x^3+1}}+\frac{\sqrt[3]{2} 3^{2/3} x^2}{\left(x^3+1\right)^{2/3}}+2\right)-2 \log \left(2-\frac{2^{2/3} \sqrt[3]{3} x}{\sqrt[3]{x^3+1}}\right)\right)\right)}{72\ 2^{2/3} 3^{5/6}}+\frac{\left(x^3+1\right)^{2/3} \left(-97 x^6+102 x^3+24\right)}{120 x^5 \left(x^3-2\right)}","-\frac{35 \log \left(\sqrt[3]{2} 3^{2/3} \sqrt[3]{x^3+1}-3 x\right)}{36\ 2^{2/3} \sqrt[3]{3}}+\frac{35 \tan ^{-1}\left(\frac{3^{5/6} x}{2 \sqrt[3]{2} \sqrt[3]{x^3+1}+\sqrt[3]{3} x}\right)}{12\ 2^{2/3} 3^{5/6}}+\frac{35 \log \left(\sqrt[3]{2} 3^{2/3} \sqrt[3]{x^3+1} x+2^{2/3} \sqrt[3]{3} \left(x^3+1\right)^{2/3}+3 x^2\right)}{72\ 2^{2/3} \sqrt[3]{3}}+\frac{\left(x^3+1\right)^{2/3} \left(-97 x^6+102 x^3+24\right)}{120 x^5 \left(x^3-2\right)}",1,"((1 + x^3)^(2/3)*(24 + 102*x^3 - 97*x^6))/(120*x^5*(-2 + x^3)) + (35*(6*ArcTan[1/Sqrt[3] + (2^(2/3)*x)/(3^(1/6)*(1 + x^3)^(1/3))] + Sqrt[3]*(-2*Log[2 - (2^(2/3)*3^(1/3)*x)/(1 + x^3)^(1/3)] + Log[2 + (2^(1/3)*3^(2/3)*x^2)/(1 + x^3)^(2/3) + (2^(2/3)*3^(1/3)*x)/(1 + x^3)^(1/3)])))/(72*2^(2/3)*3^(5/6))","A",1
2343,1,45,185,0.3714284,"\int \frac{1+x^8}{\sqrt[4]{x^2+x^6} \left(-1+x^8\right)} \, dx","Integrate[(1 + x^8)/((x^2 + x^6)^(1/4)*(-1 + x^8)),x]","-\frac{x \left(\sqrt[4]{x^4+1} F_1\left(\frac{1}{8};-\frac{3}{4},1;\frac{9}{8};-x^4,x^4\right)+1\right)}{\sqrt[4]{x^6+x^2}}","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^6+x^2}}\right)}{4 \sqrt[4]{2}}+\frac{\tan ^{-1}\left(\frac{2^{3/4} x \sqrt[4]{x^6+x^2}}{\sqrt{2} x^2-\sqrt{x^6+x^2}}\right)}{4\ 2^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^6+x^2}}\right)}{4 \sqrt[4]{2}}-\frac{\tanh ^{-1}\left(\frac{\frac{x^2}{\sqrt[4]{2}}+\frac{\sqrt{x^6+x^2}}{2^{3/4}}}{x \sqrt[4]{x^6+x^2}}\right)}{4\ 2^{3/4}}-\frac{\left(x^6+x^2\right)^{3/4}}{x \left(x^4+1\right)}",1,"-((x*(1 + (1 + x^4)^(1/4)*AppellF1[1/8, -3/4, 1, 9/8, -x^4, x^4]))/(x^2 + x^6)^(1/4))","C",0
2344,1,45,185,0.2931179,"\int \frac{1+x^8}{\sqrt[4]{x^2+x^6} \left(-1+x^8\right)} \, dx","Integrate[(1 + x^8)/((x^2 + x^6)^(1/4)*(-1 + x^8)),x]","-\frac{x \left(\sqrt[4]{x^4+1} F_1\left(\frac{1}{8};-\frac{3}{4},1;\frac{9}{8};-x^4,x^4\right)+1\right)}{\sqrt[4]{x^6+x^2}}","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^6+x^2}}\right)}{4 \sqrt[4]{2}}+\frac{\tan ^{-1}\left(\frac{2^{3/4} x \sqrt[4]{x^6+x^2}}{\sqrt{2} x^2-\sqrt{x^6+x^2}}\right)}{4\ 2^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^6+x^2}}\right)}{4 \sqrt[4]{2}}-\frac{\tanh ^{-1}\left(\frac{\frac{x^2}{\sqrt[4]{2}}+\frac{\sqrt{x^6+x^2}}{2^{3/4}}}{x \sqrt[4]{x^6+x^2}}\right)}{4\ 2^{3/4}}-\frac{\left(x^6+x^2\right)^{3/4}}{x \left(x^4+1\right)}",1,"-((x*(1 + (1 + x^4)^(1/4)*AppellF1[1/8, -3/4, 1, 9/8, -x^4, x^4]))/(x^2 + x^6)^(1/4))","C",0
2345,0,0,185,4.3881769,"\int \frac{x^2 \left(8-7 (1+k) x+6 k x^2\right)}{\sqrt[3]{(1-x) x (1-k x)} \left(-b+b (1+k) x-b k x^2+x^8\right)} \, dx","Integrate[(x^2*(8 - 7*(1 + k)*x + 6*k*x^2))/(((1 - x)*x*(1 - k*x))^(1/3)*(-b + b*(1 + k)*x - b*k*x^2 + x^8)),x]","\int \frac{x^2 \left(8-7 (1+k) x+6 k x^2\right)}{\sqrt[3]{(1-x) x (1-k x)} \left(-b+b (1+k) x-b k x^2+x^8\right)} \, dx","\frac{\log \left(x^3-\sqrt[3]{b} \sqrt[3]{k x^3+(-k-1) x^2+x}\right)}{b^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{b} \sqrt[3]{k x^3+(-k-1) x^2+x}}{\sqrt[3]{b} \sqrt[3]{k x^3+(-k-1) x^2+x}+2 x^3}\right)}{b^{2/3}}-\frac{\log \left(b^{2/3} \left(k x^3+(-k-1) x^2+x\right)^{2/3}+\sqrt[3]{b} x^3 \sqrt[3]{k x^3+(-k-1) x^2+x}+x^6\right)}{2 b^{2/3}}",1,"Integrate[(x^2*(8 - 7*(1 + k)*x + 6*k*x^2))/(((1 - x)*x*(1 - k*x))^(1/3)*(-b + b*(1 + k)*x - b*k*x^2 + x^8)), x]","F",-1
2346,1,220,185,0.2257184,"\int \frac{1}{\left(1+x^2\right)^2 \sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[1/((1 + x^2)^2*Sqrt[x + Sqrt[1 + x^2]]),x]","\frac{1}{16} \left(\frac{8 \sqrt{\sqrt{x^2+1}+x}}{\left(\sqrt{x^2+1}+x\right)^2+1}-\frac{8 \sqrt{\sqrt{x^2+1}+x}}{\left(x^2+\sqrt{x^2+1} x+1\right)^2}-3 \sqrt{2} \log \left(\sqrt{x^2+1}-\sqrt{2} \sqrt{\sqrt{x^2+1}+x}+x+1\right)+3 \sqrt{2} \log \left(\sqrt{x^2+1}+\sqrt{2} \sqrt{\sqrt{x^2+1}+x}+x+1\right)-6 \sqrt{2} \tan ^{-1}\left(1-\sqrt{2} \sqrt{\sqrt{x^2+1}+x}\right)+6 \sqrt{2} \tan ^{-1}\left(\sqrt{2} \sqrt{\sqrt{x^2+1}+x}+1\right)\right)","\frac{\left(\sqrt{x^2+1}+x\right)^{5/2}}{8 \left(x^2+\sqrt{x^2+1} x+1\right)^2}-\frac{3 \sqrt{\sqrt{x^2+1}+x}}{8 \left(x^2+\sqrt{x^2+1} x+1\right)^2}+\frac{3 \tan ^{-1}\left(\frac{\frac{\sqrt{x^2+1}}{\sqrt{2}}+\frac{x}{\sqrt{2}}-\frac{1}{\sqrt{2}}}{\sqrt{\sqrt{x^2+1}+x}}\right)}{4 \sqrt{2}}+\frac{3 \tanh ^{-1}\left(\frac{\frac{\sqrt{x^2+1}}{\sqrt{2}}+\frac{x}{\sqrt{2}}+\frac{1}{\sqrt{2}}}{\sqrt{\sqrt{x^2+1}+x}}\right)}{4 \sqrt{2}}",1,"((-8*Sqrt[x + Sqrt[1 + x^2]])/(1 + x^2 + x*Sqrt[1 + x^2])^2 + (8*Sqrt[x + Sqrt[1 + x^2]])/(1 + (x + Sqrt[1 + x^2])^2) - 6*Sqrt[2]*ArcTan[1 - Sqrt[2]*Sqrt[x + Sqrt[1 + x^2]]] + 6*Sqrt[2]*ArcTan[1 + Sqrt[2]*Sqrt[x + Sqrt[1 + x^2]]] - 3*Sqrt[2]*Log[1 + x + Sqrt[1 + x^2] - Sqrt[2]*Sqrt[x + Sqrt[1 + x^2]]] + 3*Sqrt[2]*Log[1 + x + Sqrt[1 + x^2] + Sqrt[2]*Sqrt[x + Sqrt[1 + x^2]]])/16","A",1
2347,0,0,186,15.4568214,"\int \frac{x (-a+x) (a b+(a-2 b) x)}{\left(x (-a+x) (-b+x)^2\right)^{3/4} \left(b^2 d+(a-2 b d) x+(-1+d) x^2\right)} \, dx","Integrate[(x*(-a + x)*(a*b + (a - 2*b)*x))/((x*(-a + x)*(-b + x)^2)^(3/4)*(b^2*d + (a - 2*b*d)*x + (-1 + d)*x^2)),x]","\int \frac{x (-a+x) (a b+(a-2 b) x)}{\left(x (-a+x) (-b+x)^2\right)^{3/4} \left(b^2 d+(a-2 b d) x+(-1+d) x^2\right)} \, dx","2 \sqrt[4]{d} \tan ^{-1}\left(\frac{\sqrt[4]{d} \left(x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4\right)^{3/4}}{x (x-a) (b-x)}\right)-2 \sqrt[4]{d} \tanh ^{-1}\left(\frac{\sqrt[4]{d} \left(x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4\right)^{3/4}}{x (x-a) (b-x)}\right)+\frac{4 \sqrt[4]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}}{b-x}",1,"Integrate[(x*(-a + x)*(a*b + (a - 2*b)*x))/((x*(-a + x)*(-b + x)^2)^(3/4)*(b^2*d + (a - 2*b*d)*x + (-1 + d)*x^2)), x]","F",-1
2348,1,26530,186,6.6626592,"\int \frac{\left(1+x^2\right) \left(1-3 x^2+x^4\right)}{x^2 \sqrt{\frac{-2+x+2 x^2}{-1+x+x^2}} \left(1-x-3 x^2+x^3+x^4\right)} \, dx","Integrate[((1 + x^2)*(1 - 3*x^2 + x^4))/(x^2*Sqrt[(-2 + x + 2*x^2)/(-1 + x + x^2)]*(1 - x - 3*x^2 + x^3 + x^4)),x]","\text{Result too large to show}","\frac{\sqrt{\frac{2 x^2+x-2}{x^2+x-1}} \left(x^2+x-1\right)}{2 x}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{\frac{2 x^2+x-2}{x^2+x-1}}}{\sqrt{2}}\right)}{2 \sqrt{2}}+\frac{1}{5} \sqrt{2 \left(5-\sqrt{5}\right)} \tanh ^{-1}\left(\sqrt{\frac{1}{2}+\frac{1}{2 \sqrt{5}}} \sqrt{\frac{2 x^2+x-2}{x^2+x-1}}\right)+\frac{1}{5} \sqrt{2 \left(5+\sqrt{5}\right)} \tanh ^{-1}\left(\sqrt{\frac{2}{5+\sqrt{5}}} \sqrt{\frac{2 x^2+x-2}{x^2+x-1}}\right)",1,"Result too large to show","C",0
2349,0,0,186,1.1748119,"\int \frac{x^3 \left(5-4 (1+k) x+3 k x^2\right)}{((1-x) x (1-k x))^{2/3} \left(-1+(1+k) x-k x^2+b x^5\right)} \, dx","Integrate[(x^3*(5 - 4*(1 + k)*x + 3*k*x^2))/(((1 - x)*x*(1 - k*x))^(2/3)*(-1 + (1 + k)*x - k*x^2 + b*x^5)),x]","\int \frac{x^3 \left(5-4 (1+k) x+3 k x^2\right)}{((1-x) x (1-k x))^{2/3} \left(-1+(1+k) x-k x^2+b x^5\right)} \, dx","\frac{\log \left(b x^2-b^{2/3} \sqrt[3]{k x^3+(-k-1) x^2+x}\right)}{b^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{k x^3+(-k-1) x^2+x}}{2 \sqrt[3]{b} x^2+\sqrt[3]{k x^3+(-k-1) x^2+x}}\right)}{b^{2/3}}-\frac{\log \left(b^{5/3} x^2 \sqrt[3]{k x^3+(-k-1) x^2+x}+b^{4/3} \left(k x^3+(-k-1) x^2+x\right)^{2/3}+b^2 x^4\right)}{2 b^{2/3}}",1,"Integrate[(x^3*(5 - 4*(1 + k)*x + 3*k*x^2))/(((1 - x)*x*(1 - k*x))^(2/3)*(-1 + (1 + k)*x - k*x^2 + b*x^5)), x]","F",-1
2350,1,166,186,0.3564268,"\int \frac{\left(-2+x^4\right) \sqrt{2+x^4}}{4+3 x^4+x^8} \, dx","Integrate[((-2 + x^4)*Sqrt[2 + x^4])/(4 + 3*x^4 + x^8),x]","\frac{1}{2} \sqrt[4]{-\frac{1}{2}} \left(-2 F\left(\left.i \sinh ^{-1}\left(\sqrt[4]{-\frac{1}{2}} x\right)\right|-1\right)+\Pi \left(-\frac{2 \sqrt{2}}{-i+\sqrt{7}};\left.i \sinh ^{-1}\left(\sqrt[4]{-\frac{1}{2}} x\right)\right|-1\right)+\Pi \left(\frac{2 \sqrt{2}}{-i+\sqrt{7}};\left.i \sinh ^{-1}\left(\sqrt[4]{-\frac{1}{2}} x\right)\right|-1\right)+\Pi \left(-\frac{2 \sqrt{2}}{i+\sqrt{7}};\left.i \sinh ^{-1}\left(\sqrt[4]{-\frac{1}{2}} x\right)\right|-1\right)+\Pi \left(\frac{2 \sqrt{2}}{i+\sqrt{7}};\left.i \sinh ^{-1}\left(\sqrt[4]{-\frac{1}{2}} x\right)\right|-1\right)\right)","-4 \sqrt[4]{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6-122 \text{$\#$1}^4-4 \text{$\#$1}^2+1\&,\frac{\text{$\#$1}^3 \left(-\log \left(-x^2+2^{3/4} x-\sqrt{2}\right)\right)+\text{$\#$1}^3 \log \left(\text{$\#$1} x^2-2^{3/4} \text{$\#$1} x+\sqrt{2} \text{$\#$1}+\sqrt{x^4+2}\right)-\text{$\#$1} \log \left(-x^2+2^{3/4} x-\sqrt{2}\right)+\text{$\#$1} \log \left(\text{$\#$1} x^2-2^{3/4} \text{$\#$1} x+\sqrt{2} \text{$\#$1}+\sqrt{x^4+2}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4-61 \text{$\#$1}^2-1}\&\right]",1,"((-1/2)^(1/4)*(-2*EllipticF[I*ArcSinh[(-1/2)^(1/4)*x], -1] + EllipticPi[(-2*Sqrt[2])/(-I + Sqrt[7]), I*ArcSinh[(-1/2)^(1/4)*x], -1] + EllipticPi[(2*Sqrt[2])/(-I + Sqrt[7]), I*ArcSinh[(-1/2)^(1/4)*x], -1] + EllipticPi[(-2*Sqrt[2])/(I + Sqrt[7]), I*ArcSinh[(-1/2)^(1/4)*x], -1] + EllipticPi[(2*Sqrt[2])/(I + Sqrt[7]), I*ArcSinh[(-1/2)^(1/4)*x], -1]))/2","C",1
2351,1,63,186,0.029282,"\int \frac{\sqrt[3]{-1-x+5 x^2+2 x^3-10 x^4+2 x^5+7 x^6-5 x^7+x^8}}{x^2} \, dx","Integrate[(-1 - x + 5*x^2 + 2*x^3 - 10*x^4 + 2*x^5 + 7*x^6 - 5*x^7 + x^8)^(1/3)/x^2,x]","\frac{\sqrt[3]{(x-1)^2 \left(x^2-x-1\right)^3} \left(5 x \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};1-x\right)+6 x^2-21 x+10\right)}{10 x \left(x^2-x-1\right)}","-\frac{\left(\sqrt[3]{x-1}+1\right) \left((x-1)^{2/3}-\sqrt[3]{x-1}+1\right)^2 (x-1)^{2/3} \sqrt[3]{(x-1)^2 \left(x^2-x-1\right)^3} \left(\frac{(x-1)^{2/3} \left(6 x^2-21 x+10\right)}{10 x}-\frac{1}{3} \log \left(\sqrt[3]{x-1}+1\right)+\frac{1}{6} \log \left((x-1)^{2/3}-\sqrt[3]{x-1}+1\right)-\frac{\tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{x-1}}{\sqrt{3}}\right)}{\sqrt{3}}\right)}{\left(-x+(x-1)^{2/3}-\sqrt[3]{x-1}+1\right) x \left(x^3-2 x^2+1\right)}",1,"(((-1 + x)^2*(-1 - x + x^2)^3)^(1/3)*(10 - 21*x + 6*x^2 + 5*x*Hypergeometric2F1[2/3, 1, 5/3, 1 - x]))/(10*x*(-1 - x + x^2))","C",1
2352,0,0,186,0.221996,"\int \frac{\left(-b+a^2 x^2\right) \sqrt{a x^2+\sqrt{b+a^2 x^4}}}{\sqrt{b+a^2 x^4}} \, dx","Integrate[((-b + a^2*x^2)*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]])/Sqrt[b + a^2*x^4],x]","\int \frac{\left(-b+a^2 x^2\right) \sqrt{a x^2+\sqrt{b+a^2 x^4}}}{\sqrt{b+a^2 x^4}} \, dx","\frac{1}{2} a x \sqrt{\sqrt{a^2 x^4+b}+a x^2}-\frac{b \log \left(\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)}{\sqrt{2} \sqrt{a}}-\frac{\sqrt{a} \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a^2 x^4+b}}{\sqrt{b}}+\frac{\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}}{\sqrt{b}}+\frac{a x^2}{\sqrt{b}}\right)}{\sqrt{2}}",1,"Integrate[((-b + a^2*x^2)*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]])/Sqrt[b + a^2*x^4], x]","F",-1
2353,1,6615,186,8.9684049,"\int \frac{\sqrt{1+x}}{x+\sqrt{x+\sqrt{1+x}}} \, dx","Integrate[Sqrt[1 + x]/(x + Sqrt[x + Sqrt[1 + x]]),x]","\text{Result too large to show}","2 \text{RootSum}\left[\text{$\#$1}^4-8 \text{$\#$1}^3-2 \text{$\#$1}^2+25\&,\frac{3 \text{$\#$1}^2 \log \left(-\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)-2 \text{$\#$1} \log \left(-\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)-5 \log \left(-\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)}{\text{$\#$1}^3-6 \text{$\#$1}^2-\text{$\#$1}}\&\right]+2 \sqrt{x+1}+2 \log \left(2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)",1,"Result too large to show","B",0
2354,1,6615,186,6.3056404,"\int \frac{\sqrt{1+x}}{x+\sqrt{x+\sqrt{1+x}}} \, dx","Integrate[Sqrt[1 + x]/(x + Sqrt[x + Sqrt[1 + x]]),x]","\text{Result too large to show}","2 \text{RootSum}\left[\text{$\#$1}^4-8 \text{$\#$1}^3-2 \text{$\#$1}^2+25\&,\frac{3 \text{$\#$1}^2 \log \left(-\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)-2 \text{$\#$1} \log \left(-\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)-5 \log \left(-\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)}{\text{$\#$1}^3-6 \text{$\#$1}^2-\text{$\#$1}}\&\right]+2 \sqrt{x+1}+2 \log \left(2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)",1,"Result too large to show","B",0
2355,1,208,187,0.3571638,"\int \frac{-i+\sqrt{k} x}{\left(i+\sqrt{k} x\right) \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}} \, dx","Integrate[(-I + Sqrt[k]*x)/((I + Sqrt[k]*x)*Sqrt[(1 - x^2)*(1 - k^2*x^2)]),x]","\frac{-2 i \sqrt{k} \sqrt{x^2-1} \sqrt{k^2 x^2-1} \tanh ^{-1}\left(\frac{\sqrt{k (k+1)} \sqrt{x^2-1}}{\sqrt{k+1} \sqrt{k^2 x^2-1}}\right)+\sqrt{k+1} \sqrt{k (k+1)} \sqrt{1-x^2} \sqrt{1-k^2 x^2} F\left(\sin ^{-1}(x)|k^2\right)-2 \sqrt{k+1} \sqrt{k (k+1)} \sqrt{1-x^2} \sqrt{1-k^2 x^2} \Pi \left(-k;\sin ^{-1}(x)|k^2\right)}{\sqrt{k+1} \sqrt{k (k+1)} \sqrt{\left(x^2-1\right) \left(k^2 x^2-1\right)}}","\frac{\tan ^{-1}\left(\frac{\left(-k-2 \sqrt{k}-1\right) x}{\sqrt{k^2 x^4+\left(-k^2-1\right) x^2+1}+k x^2-1}\right)}{k+1}+\frac{\tan ^{-1}\left(\frac{\left(-k+2 \sqrt{k}-1\right) x}{\sqrt{k^2 x^4+\left(-k^2-1\right) x^2+1}+k x^2-1}\right)}{k+1}+\frac{i \tanh ^{-1}\left(\frac{\left(2 k^{3/2}+2 \sqrt{k}\right) x^2}{k^2 x^4+\left(k x^2-1\right) \sqrt{k^2 x^4+\left(-k^2-1\right) x^2+1}+2 k x^2+1}\right)}{k+1}",1,"((-2*I)*Sqrt[k]*Sqrt[-1 + x^2]*Sqrt[-1 + k^2*x^2]*ArcTanh[(Sqrt[k*(1 + k)]*Sqrt[-1 + x^2])/(Sqrt[1 + k]*Sqrt[-1 + k^2*x^2])] + Sqrt[1 + k]*Sqrt[k*(1 + k)]*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticF[ArcSin[x], k^2] - 2*Sqrt[1 + k]*Sqrt[k*(1 + k)]*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[-k, ArcSin[x], k^2])/(Sqrt[1 + k]*Sqrt[k*(1 + k)]*Sqrt[(-1 + x^2)*(-1 + k^2*x^2)])","C",1
2356,1,208,187,0.2649944,"\int \frac{i+\sqrt{k} x}{\left(-i+\sqrt{k} x\right) \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}} \, dx","Integrate[(I + Sqrt[k]*x)/((-I + Sqrt[k]*x)*Sqrt[(1 - x^2)*(1 - k^2*x^2)]),x]","\frac{2 i \sqrt{k} \sqrt{x^2-1} \sqrt{k^2 x^2-1} \tanh ^{-1}\left(\frac{\sqrt{k (k+1)} \sqrt{x^2-1}}{\sqrt{k+1} \sqrt{k^2 x^2-1}}\right)+\sqrt{k+1} \sqrt{k (k+1)} \sqrt{1-x^2} \sqrt{1-k^2 x^2} F\left(\sin ^{-1}(x)|k^2\right)-2 \sqrt{k+1} \sqrt{k (k+1)} \sqrt{1-x^2} \sqrt{1-k^2 x^2} \Pi \left(-k;\sin ^{-1}(x)|k^2\right)}{\sqrt{k+1} \sqrt{k (k+1)} \sqrt{\left(x^2-1\right) \left(k^2 x^2-1\right)}}","\frac{\tan ^{-1}\left(\frac{\left(-k-2 \sqrt{k}-1\right) x}{\sqrt{k^2 x^4+\left(-k^2-1\right) x^2+1}+k x^2-1}\right)}{k+1}+\frac{\tan ^{-1}\left(\frac{\left(-k+2 \sqrt{k}-1\right) x}{\sqrt{k^2 x^4+\left(-k^2-1\right) x^2+1}+k x^2-1}\right)}{k+1}-\frac{i \tanh ^{-1}\left(\frac{\left(2 k^{3/2}+2 \sqrt{k}\right) x^2}{k^2 x^4+\left(k x^2-1\right) \sqrt{k^2 x^4+\left(-k^2-1\right) x^2+1}+2 k x^2+1}\right)}{k+1}",1,"((2*I)*Sqrt[k]*Sqrt[-1 + x^2]*Sqrt[-1 + k^2*x^2]*ArcTanh[(Sqrt[k*(1 + k)]*Sqrt[-1 + x^2])/(Sqrt[1 + k]*Sqrt[-1 + k^2*x^2])] + Sqrt[1 + k]*Sqrt[k*(1 + k)]*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticF[ArcSin[x], k^2] - 2*Sqrt[1 + k]*Sqrt[k*(1 + k)]*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[-k, ArcSin[x], k^2])/(Sqrt[1 + k]*Sqrt[k*(1 + k)]*Sqrt[(-1 + x^2)*(-1 + k^2*x^2)])","C",1
2357,1,186,187,0.1609293,"\int \frac{1}{\sqrt[4]{-1+3 x-3 x^2+x^3} \left(-1-2 x+x^2+3 x^3\right)^4} \, dx","Integrate[1/((-1 + 3*x - 3*x^2 + x^3)^(1/4)*(-1 - 2*x + x^2 + 3*x^3)^4),x]","\frac{(x-1)^{3/4} \left(-3 \text{RootSum}\left[3 \text{$\#$1}^{12}+10 \text{$\#$1}^8+9 \text{$\#$1}^4+1\&,\frac{566085546 \text{$\#$1}^8 \log \left(\sqrt[4]{x-1}-\text{$\#$1}\right)-234521814 \text{$\#$1}^4 \log \left(\sqrt[4]{x-1}-\text{$\#$1}\right)-41317673 \log \left(\sqrt[4]{x-1}-\text{$\#$1}\right)}{9 \text{$\#$1}^{11}+20 \text{$\#$1}^7+9 \text{$\#$1}^3}\&\right]-\frac{4 \sqrt[4]{x-1} \left(5094769914 x^8+2006712954 x^7-9762576651 x^6-5802065412 x^5+5857310139 x^4+4979849490 x^3-596630756 x^2-1357068302 x-307788101\right)}{\left(3 x^3+x^2-2 x-1\right)^3}\right)}{11439744 \sqrt[4]{(x-1)^3}}","\frac{\left((x-1)^3\right)^{3/4} \left(\frac{\sqrt[4]{x-1} \left(-5094769914 x^8-2006712954 x^7+9762576651 x^6+5802065412 x^5-5857310139 x^4-4979849490 x^3+596630756 x^2+1357068302 x+307788101\right)}{2859936 \left(3 x^3+x^2-2 x-1\right)^3}-\frac{\text{RootSum}\left[3 \text{$\#$1}^{12}+10 \text{$\#$1}^8+9 \text{$\#$1}^4+1\&,\frac{566085546 \text{$\#$1}^8 \log \left(\sqrt[4]{x-1}-\text{$\#$1}\right)-234521814 \text{$\#$1}^4 \log \left(\sqrt[4]{x-1}-\text{$\#$1}\right)-41317673 \log \left(\sqrt[4]{x-1}-\text{$\#$1}\right)}{9 \text{$\#$1}^{11}+20 \text{$\#$1}^7+9 \text{$\#$1}^3}\&\right]}{3813248}\right)}{(x-1)^{9/4}}",1,"((-1 + x)^(3/4)*((-4*(-1 + x)^(1/4)*(-307788101 - 1357068302*x - 596630756*x^2 + 4979849490*x^3 + 5857310139*x^4 - 5802065412*x^5 - 9762576651*x^6 + 2006712954*x^7 + 5094769914*x^8))/(-1 - 2*x + x^2 + 3*x^3)^3 - 3*RootSum[1 + 9*#1^4 + 10*#1^8 + 3*#1^12 & , (-41317673*Log[(-1 + x)^(1/4) - #1] - 234521814*Log[(-1 + x)^(1/4) - #1]*#1^4 + 566085546*Log[(-1 + x)^(1/4) - #1]*#1^8)/(9*#1^3 + 20*#1^7 + 9*#1^11) & ]))/(11439744*((-1 + x)^3)^(1/4))","A",1
2358,1,137,187,0.1288961,"\int \frac{\sqrt[4]{b x^3+a x^4}}{x^2 \left(-d+c x^2\right)} \, dx","Integrate[(b*x^3 + a*x^4)^(1/4)/(x^2*(-d + c*x^2)),x]","\frac{2 x^2 \left(x \left(b \sqrt{c}-a \sqrt{d}\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{\left(a-\frac{b \sqrt{c}}{\sqrt{d}}\right) x}{b+a x}\right)-x \left(a \sqrt{d}+b \sqrt{c}\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{\left(a+\frac{b \sqrt{c}}{\sqrt{d}}\right) x}{b+a x}\right)+6 \sqrt{d} (a x+b)\right)}{3 d^{3/2} \left(x^3 (a x+b)\right)^{3/4}}","\frac{\text{RootSum}\left[\text{$\#$1}^8 (-d)+2 \text{$\#$1}^4 a d-a^2 d+b^2 c\&,\frac{-\text{$\#$1}^4 a d \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)+\text{$\#$1}^4 a d \log (x)+a^2 d \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)-b^2 c \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)-a^2 d \log (x)+b^2 c \log (x)}{\text{$\#$1}^3 a-\text{$\#$1}^7}\&\right]}{2 d^2}+\frac{4 \sqrt[4]{a x^4+b x^3}}{d x}",1,"(2*x^2*(6*Sqrt[d]*(b + a*x) + (b*Sqrt[c] - a*Sqrt[d])*x*Hypergeometric2F1[3/4, 1, 7/4, ((a - (b*Sqrt[c])/Sqrt[d])*x)/(b + a*x)] - (b*Sqrt[c] + a*Sqrt[d])*x*Hypergeometric2F1[3/4, 1, 7/4, ((a + (b*Sqrt[c])/Sqrt[d])*x)/(b + a*x)]))/(3*d^(3/2)*(x^3*(b + a*x))^(3/4))","A",1
2359,1,137,187,0.0376018,"\int \frac{\sqrt[4]{b x^3+a x^4}}{x^2 \left(-d+c x^2\right)} \, dx","Integrate[(b*x^3 + a*x^4)^(1/4)/(x^2*(-d + c*x^2)),x]","\frac{2 x^2 \left(x \left(b \sqrt{c}-a \sqrt{d}\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{\left(a-\frac{b \sqrt{c}}{\sqrt{d}}\right) x}{b+a x}\right)-x \left(a \sqrt{d}+b \sqrt{c}\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{\left(a+\frac{b \sqrt{c}}{\sqrt{d}}\right) x}{b+a x}\right)+6 \sqrt{d} (a x+b)\right)}{3 d^{3/2} \left(x^3 (a x+b)\right)^{3/4}}","\frac{\text{RootSum}\left[\text{$\#$1}^8 (-d)+2 \text{$\#$1}^4 a d-a^2 d+b^2 c\&,\frac{-\text{$\#$1}^4 a d \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)+\text{$\#$1}^4 a d \log (x)+a^2 d \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)-b^2 c \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)-a^2 d \log (x)+b^2 c \log (x)}{\text{$\#$1}^3 a-\text{$\#$1}^7}\&\right]}{2 d^2}+\frac{4 \sqrt[4]{a x^4+b x^3}}{d x}",1,"(2*x^2*(6*Sqrt[d]*(b + a*x) + (b*Sqrt[c] - a*Sqrt[d])*x*Hypergeometric2F1[3/4, 1, 7/4, ((a - (b*Sqrt[c])/Sqrt[d])*x)/(b + a*x)] - (b*Sqrt[c] + a*Sqrt[d])*x*Hypergeometric2F1[3/4, 1, 7/4, ((a + (b*Sqrt[c])/Sqrt[d])*x)/(b + a*x)]))/(3*d^(3/2)*(x^3*(b + a*x))^(3/4))","A",1
2360,1,48,187,1.1280196,"\int \frac{x^4}{\sqrt[4]{x^2+x^6} \left(-1+x^8\right)} \, dx","Integrate[x^4/((x^2 + x^6)^(1/4)*(-1 + x^8)),x]","\frac{x-x \sqrt[4]{x^4+1} F_1\left(\frac{1}{8};-\frac{3}{4},1;\frac{9}{8};-x^4,x^4\right)}{2 \sqrt[4]{x^6+x^2}}","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^6+x^2}}\right)}{8 \sqrt[4]{2}}+\frac{\tan ^{-1}\left(\frac{2^{3/4} x \sqrt[4]{x^6+x^2}}{\sqrt{2} x^2-\sqrt{x^6+x^2}}\right)}{8\ 2^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^6+x^2}}\right)}{8 \sqrt[4]{2}}-\frac{\tanh ^{-1}\left(\frac{\frac{x^2}{\sqrt[4]{2}}+\frac{\sqrt{x^6+x^2}}{2^{3/4}}}{x \sqrt[4]{x^6+x^2}}\right)}{8\ 2^{3/4}}+\frac{\left(x^6+x^2\right)^{3/4}}{2 x \left(x^4+1\right)}",1,"(x - x*(1 + x^4)^(1/4)*AppellF1[1/8, -3/4, 1, 9/8, -x^4, x^4])/(2*(x^2 + x^6)^(1/4))","C",0
2361,1,48,187,0.8896282,"\int \frac{x^4}{\sqrt[4]{x^2+x^6} \left(-1+x^8\right)} \, dx","Integrate[x^4/((x^2 + x^6)^(1/4)*(-1 + x^8)),x]","\frac{x-x \sqrt[4]{x^4+1} F_1\left(\frac{1}{8};-\frac{3}{4},1;\frac{9}{8};-x^4,x^4\right)}{2 \sqrt[4]{x^6+x^2}}","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^6+x^2}}\right)}{8 \sqrt[4]{2}}+\frac{\tan ^{-1}\left(\frac{2^{3/4} x \sqrt[4]{x^6+x^2}}{\sqrt{2} x^2-\sqrt{x^6+x^2}}\right)}{8\ 2^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^6+x^2}}\right)}{8 \sqrt[4]{2}}-\frac{\tanh ^{-1}\left(\frac{\frac{x^2}{\sqrt[4]{2}}+\frac{\sqrt{x^6+x^2}}{2^{3/4}}}{x \sqrt[4]{x^6+x^2}}\right)}{8\ 2^{3/4}}+\frac{\left(x^6+x^2\right)^{3/4}}{2 x \left(x^4+1\right)}",1,"(x - x*(1 + x^4)^(1/4)*AppellF1[1/8, -3/4, 1, 9/8, -x^4, x^4])/(2*(x^2 + x^6)^(1/4))","C",0
2362,0,0,187,3.8581489,"\int \frac{\left(-1+x^4\right) \sqrt[4]{x^2+x^6}}{1-x^4+x^8} \, dx","Integrate[((-1 + x^4)*(x^2 + x^6)^(1/4))/(1 - x^4 + x^8),x]","\int \frac{\left(-1+x^4\right) \sqrt[4]{x^2+x^6}}{1-x^4+x^8} \, dx","\frac{\tan ^{-1}\left(\frac{\sqrt[8]{3} x}{\sqrt[4]{x^6+x^2}}\right)}{2\ 3^{3/8}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} 3^{7/8} x \sqrt[4]{x^6+x^2}}{3^{3/4} \sqrt{x^6+x^2}-3 x^2}\right)}{2 \sqrt{2} 3^{3/8}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{3} x}{\sqrt[4]{x^6+x^2}}\right)}{2\ 3^{3/8}}+\frac{\tanh ^{-1}\left(\frac{\frac{\sqrt[8]{3} x^2}{\sqrt{2}}+\frac{\sqrt{x^6+x^2}}{\sqrt{2} \sqrt[8]{3}}}{x \sqrt[4]{x^6+x^2}}\right)}{2 \sqrt{2} 3^{3/8}}",1,"Integrate[((-1 + x^4)*(x^2 + x^6)^(1/4))/(1 - x^4 + x^8), x]","F",-1
2363,0,0,187,0.0736154,"\int \frac{\left(-1+x^4\right) \sqrt[4]{x^2+x^6}}{1-x^4+x^8} \, dx","Integrate[((-1 + x^4)*(x^2 + x^6)^(1/4))/(1 - x^4 + x^8),x]","\int \frac{\left(-1+x^4\right) \sqrt[4]{x^2+x^6}}{1-x^4+x^8} \, dx","\frac{\tan ^{-1}\left(\frac{\sqrt[8]{3} x}{\sqrt[4]{x^6+x^2}}\right)}{2\ 3^{3/8}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} 3^{7/8} x \sqrt[4]{x^6+x^2}}{3^{3/4} \sqrt{x^6+x^2}-3 x^2}\right)}{2 \sqrt{2} 3^{3/8}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{3} x}{\sqrt[4]{x^6+x^2}}\right)}{2\ 3^{3/8}}+\frac{\tanh ^{-1}\left(\frac{\frac{\sqrt[8]{3} x^2}{\sqrt{2}}+\frac{\sqrt{x^6+x^2}}{\sqrt{2} \sqrt[8]{3}}}{x \sqrt[4]{x^6+x^2}}\right)}{2 \sqrt{2} 3^{3/8}}",1,"Integrate[((-1 + x^4)*(x^2 + x^6)^(1/4))/(1 - x^4 + x^8), x]","F",-1
2364,1,47,187,0.4252528,"\int \frac{1-x^4+x^8}{\sqrt[4]{x^2+x^6} \left(-1+x^8\right)} \, dx","Integrate[(1 - x^4 + x^8)/((x^2 + x^6)^(1/4)*(-1 + x^8)),x]","-\frac{x \left(\sqrt[4]{x^4+1} F_1\left(\frac{1}{8};-\frac{3}{4},1;\frac{9}{8};-x^4,x^4\right)+3\right)}{2 \sqrt[4]{x^6+x^2}}","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^6+x^2}}\right)}{8 \sqrt[4]{2}}+\frac{\tan ^{-1}\left(\frac{2^{3/4} x \sqrt[4]{x^6+x^2}}{\sqrt{2} x^2-\sqrt{x^6+x^2}}\right)}{8\ 2^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^6+x^2}}\right)}{8 \sqrt[4]{2}}-\frac{\tanh ^{-1}\left(\frac{\frac{x^2}{\sqrt[4]{2}}+\frac{\sqrt{x^6+x^2}}{2^{3/4}}}{x \sqrt[4]{x^6+x^2}}\right)}{8\ 2^{3/4}}-\frac{3 \left(x^6+x^2\right)^{3/4}}{2 x \left(x^4+1\right)}",1,"-1/2*(x*(3 + (1 + x^4)^(1/4)*AppellF1[1/8, -3/4, 1, 9/8, -x^4, x^4]))/(x^2 + x^6)^(1/4)","C",0
2365,1,47,187,0.2757507,"\int \frac{1-x^4+x^8}{\sqrt[4]{x^2+x^6} \left(-1+x^8\right)} \, dx","Integrate[(1 - x^4 + x^8)/((x^2 + x^6)^(1/4)*(-1 + x^8)),x]","-\frac{x \left(\sqrt[4]{x^4+1} F_1\left(\frac{1}{8};-\frac{3}{4},1;\frac{9}{8};-x^4,x^4\right)+3\right)}{2 \sqrt[4]{x^6+x^2}}","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^6+x^2}}\right)}{8 \sqrt[4]{2}}+\frac{\tan ^{-1}\left(\frac{2^{3/4} x \sqrt[4]{x^6+x^2}}{\sqrt{2} x^2-\sqrt{x^6+x^2}}\right)}{8\ 2^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^6+x^2}}\right)}{8 \sqrt[4]{2}}-\frac{\tanh ^{-1}\left(\frac{\frac{x^2}{\sqrt[4]{2}}+\frac{\sqrt{x^6+x^2}}{2^{3/4}}}{x \sqrt[4]{x^6+x^2}}\right)}{8\ 2^{3/4}}-\frac{3 \left(x^6+x^2\right)^{3/4}}{2 x \left(x^4+1\right)}",1,"-1/2*(x*(3 + (1 + x^4)^(1/4)*AppellF1[1/8, -3/4, 1, 9/8, -x^4, x^4]))/(x^2 + x^6)^(1/4)","C",0
2366,1,49,188,0.0184812,"\int \frac{1}{(-b+a x) \sqrt[4]{-x^3+x^4}} \, dx","Integrate[1/((-b + a*x)*(-x^3 + x^4)^(1/4)),x]","\frac{4 (x-1) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};-\frac{b (x-1)}{(a-b) x}\right)}{3 \sqrt[4]{(x-1) x^3} (a-b)}","\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x \sqrt[4]{x^4-x^3} \sqrt[4]{a-b}}{x^2 \sqrt{a-b}-\sqrt{b} \sqrt{x^4-x^3}}\right)}{b^{3/4} \sqrt[4]{a-b}}-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\frac{x^2 \sqrt[4]{a-b}}{\sqrt{2} \sqrt[4]{b}}+\frac{\sqrt[4]{b} \sqrt{x^4-x^3}}{\sqrt{2} \sqrt[4]{a-b}}}{x \sqrt[4]{x^4-x^3}}\right)}{b^{3/4} \sqrt[4]{a-b}}",1,"(4*(-1 + x)*Hypergeometric2F1[3/4, 1, 7/4, -((b*(-1 + x))/((a - b)*x))])/(3*(a - b)*((-1 + x)*x^3)^(1/4))","C",1
2367,1,227,189,2.2238821,"\int \frac{-x+x^2}{\sqrt{(1-x) x \left(1-k^2 x\right)} \left(1-2 x+k^2 x^2\right)} \, dx","Integrate[(-x + x^2)/(Sqrt[(1 - x)*x*(1 - k^2*x)]*(1 - 2*x + k^2*x^2)),x]","-\frac{i \sqrt{x-1} \sqrt{x} \sqrt{\frac{k^2 x-1}{k^2-1}} \left(2 \sqrt{1-k^2} F\left(i \sinh ^{-1}\left(\sqrt{x-1}\right)|\frac{k^2}{k^2-1}\right)-\left(\sqrt{1-k^2}+1\right) \Pi \left(\frac{k^2}{k^2-\sqrt{1-k^2}-1};i \sinh ^{-1}\left(\sqrt{x-1}\right)|\frac{k^2}{k^2-1}\right)-\left(\sqrt{1-k^2}-1\right) \Pi \left(\frac{k^2}{k^2+\sqrt{1-k^2}-1};i \sinh ^{-1}\left(\sqrt{x-1}\right)|\frac{k^2}{k^2-1}\right)\right)}{k^2 \sqrt{1-k^2} \sqrt{(x-1) x \left(k^2 x-1\right)}}","\frac{i \tan ^{-1}\left(\frac{\sqrt{k^2+2 i \sqrt{k^2-1}-2} \sqrt{k^2 x^3+\left(-k^2-1\right) x^2+x}}{k^2 x-1}\right)}{2 \sqrt{k^2-1} \sqrt{k^2+2 i \sqrt{k^2-1}-2}}-\frac{i \tan ^{-1}\left(\frac{\sqrt{k^2-2 i \sqrt{k^2-1}-2} \sqrt{k^2 x^3+\left(-k^2-1\right) x^2+x}}{k^2 x-1}\right)}{2 \sqrt{k^2-1} \sqrt{k^2-2 i \sqrt{k^2-1}-2}}",1,"((-I)*Sqrt[-1 + x]*Sqrt[x]*Sqrt[(-1 + k^2*x)/(-1 + k^2)]*(2*Sqrt[1 - k^2]*EllipticF[I*ArcSinh[Sqrt[-1 + x]], k^2/(-1 + k^2)] - (1 + Sqrt[1 - k^2])*EllipticPi[k^2/(-1 + k^2 - Sqrt[1 - k^2]), I*ArcSinh[Sqrt[-1 + x]], k^2/(-1 + k^2)] - (-1 + Sqrt[1 - k^2])*EllipticPi[k^2/(-1 + k^2 + Sqrt[1 - k^2]), I*ArcSinh[Sqrt[-1 + x]], k^2/(-1 + k^2)]))/(k^2*Sqrt[1 - k^2]*Sqrt[(-1 + x)*x*(-1 + k^2*x)])","C",1
2368,1,140,189,0.2119018,"\int \frac{-b+a^3 x^2}{\left(b+a^3 x^2\right) \sqrt[3]{-b x^2+a^3 x^3}} \, dx","Integrate[(-b + a^3*x^2)/((b + a^3*x^2)*(-(b*x^2) + a^3*x^3)^(1/3)),x]","\frac{3 x \left(\sqrt[3]{1-\frac{a^3 x}{b}} \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};\frac{a^3 x}{b}\right)-\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(a^3-\sqrt{-a^3} \sqrt{b}\right) x}{a^3 x-b}\right)-\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(a^3+\sqrt{-a^3} \sqrt{b}\right) x}{a^3 x-b}\right)\right)}{\sqrt[3]{x^2 \left(a^3 x-b\right)}}","\text{RootSum}\left[\text{$\#$1}^6-2 \text{$\#$1}^3 a^3+a^6+a^3 b\&,\frac{\log \left(\sqrt[3]{a^3 x^3-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]-\frac{\log \left(\sqrt[3]{a^3 x^3-b x^2}-a x\right)}{a}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} a x}{2 \sqrt[3]{a^3 x^3-b x^2}+a x}\right)}{a}+\frac{\log \left(a x \sqrt[3]{a^3 x^3-b x^2}+\left(a^3 x^3-b x^2\right)^{2/3}+a^2 x^2\right)}{2 a}",1,"(3*x*((1 - (a^3*x)/b)^(1/3)*Hypergeometric2F1[1/3, 1/3, 4/3, (a^3*x)/b] - Hypergeometric2F1[1/3, 1, 4/3, ((a^3 - Sqrt[-a^3]*Sqrt[b])*x)/(-b + a^3*x)] - Hypergeometric2F1[1/3, 1, 4/3, ((a^3 + Sqrt[-a^3]*Sqrt[b])*x)/(-b + a^3*x)]))/(x^2*(-b + a^3*x))^(1/3)","A",1
2369,1,140,189,0.0910039,"\int \frac{-b+a^3 x^2}{\left(b+a^3 x^2\right) \sqrt[3]{-b x^2+a^3 x^3}} \, dx","Integrate[(-b + a^3*x^2)/((b + a^3*x^2)*(-(b*x^2) + a^3*x^3)^(1/3)),x]","\frac{3 x \left(\sqrt[3]{1-\frac{a^3 x}{b}} \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};\frac{a^3 x}{b}\right)-\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(a^3-\sqrt{-a^3} \sqrt{b}\right) x}{a^3 x-b}\right)-\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(a^3+\sqrt{-a^3} \sqrt{b}\right) x}{a^3 x-b}\right)\right)}{\sqrt[3]{x^2 \left(a^3 x-b\right)}}","\text{RootSum}\left[\text{$\#$1}^6-2 \text{$\#$1}^3 a^3+a^6+a^3 b\&,\frac{\log \left(\sqrt[3]{a^3 x^3-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]-\frac{\log \left(\sqrt[3]{a^3 x^3-b x^2}-a x\right)}{a}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} a x}{2 \sqrt[3]{a^3 x^3-b x^2}+a x}\right)}{a}+\frac{\log \left(a x \sqrt[3]{a^3 x^3-b x^2}+\left(a^3 x^3-b x^2\right)^{2/3}+a^2 x^2\right)}{2 a}",1,"(3*x*((1 - (a^3*x)/b)^(1/3)*Hypergeometric2F1[1/3, 1/3, 4/3, (a^3*x)/b] - Hypergeometric2F1[1/3, 1, 4/3, ((a^3 - Sqrt[-a^3]*Sqrt[b])*x)/(-b + a^3*x)] - Hypergeometric2F1[1/3, 1, 4/3, ((a^3 + Sqrt[-a^3]*Sqrt[b])*x)/(-b + a^3*x)]))/(x^2*(-b + a^3*x))^(1/3)","A",1
2370,1,3575,189,2.1163032,"\int \frac{1+x^2}{\left(-1+x^2\right) \sqrt{a+b x+c x^2+b x^3+a x^4}} \, dx","Integrate[(1 + x^2)/((-1 + x^2)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]),x]","\text{Result too large to show}","-\frac{\sqrt{-2 a-2 b-c} \tan ^{-1}\left(\frac{x \sqrt{-2 a-2 b-c}}{-\sqrt{a x^4+a+b x^3+b x+c x^2}+\sqrt{a} x^2-2 \sqrt{a} x+\sqrt{a}}\right)}{2 a+2 b+c}-\frac{\sqrt{-2 a+2 b-c} \tan ^{-1}\left(\frac{x \sqrt{-2 a+2 b-c}}{-\sqrt{a x^4+a+b x^3+b x+c x^2}+\sqrt{a} x^2+2 \sqrt{a} x+\sqrt{a}}\right)}{2 a-2 b+c}",1,"(2*(x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])^2*Sqrt[((Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3]))/((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3]))]*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])*Sqrt[((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])^2*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])^2)]*(-((EllipticF[ArcSin[Sqrt[((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))]], -(((Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])))]*(-1 + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1]) + EllipticPi[((-1 + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((-1 + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])), ArcSin[Sqrt[((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))]], -(((Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])))]*(-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2]))/((-1 + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(-1 + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))) + (EllipticF[ArcSin[Sqrt[((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))]], -(((Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])))]*(1 + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1]) + EllipticPi[((1 + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((1 + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])), ArcSin[Sqrt[((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))]], -(((Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])))]*(-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2]))/((1 + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(1 + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])) + EllipticF[ArcSin[Sqrt[((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))]], ((Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))]/(-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])))/(Sqrt[x*(b + c*x + b*x^2) + a*(1 + x^4)]*(-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2]))","C",0
2371,0,0,189,4.1242917,"\int \frac{x^4 \sqrt[4]{-x^2+x^4}}{1+x^4+x^8} \, dx","Integrate[(x^4*(-x^2 + x^4)^(1/4))/(1 + x^4 + x^8),x]","\int \frac{x^4 \sqrt[4]{-x^2+x^4}}{1+x^4+x^8} \, dx","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4+3\&,\frac{-\text{$\#$1}^4 \log \left(\sqrt[4]{x^4-x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 \log (x)+3 \log \left(\sqrt[4]{x^4-x^2}-\text{$\#$1} x\right)-3 \log (x)}{2 \text{$\#$1}^7-3 \text{$\#$1}^3}\&\right]-\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4+1\&,\frac{-\text{$\#$1}^4 \log \left(\sqrt[4]{x^4-x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 \log (x)+\log \left(\sqrt[4]{x^4-x^2}-\text{$\#$1} x\right)-\log (x)}{2 \text{$\#$1}^7-\text{$\#$1}^3}\&\right]",1,"Integrate[(x^4*(-x^2 + x^4)^(1/4))/(1 + x^4 + x^8), x]","F",-1
2372,0,0,189,2.9569351,"\int \frac{x^4 \sqrt[4]{-x^2+x^4}}{1+x^4+x^8} \, dx","Integrate[(x^4*(-x^2 + x^4)^(1/4))/(1 + x^4 + x^8),x]","\int \frac{x^4 \sqrt[4]{-x^2+x^4}}{1+x^4+x^8} \, dx","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4+3\&,\frac{-\text{$\#$1}^4 \log \left(\sqrt[4]{x^4-x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 \log (x)+3 \log \left(\sqrt[4]{x^4-x^2}-\text{$\#$1} x\right)-3 \log (x)}{2 \text{$\#$1}^7-3 \text{$\#$1}^3}\&\right]-\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4+1\&,\frac{-\text{$\#$1}^4 \log \left(\sqrt[4]{x^4-x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 \log (x)+\log \left(\sqrt[4]{x^4-x^2}-\text{$\#$1} x\right)-\log (x)}{2 \text{$\#$1}^7-\text{$\#$1}^3}\&\right]",1,"Integrate[(x^4*(-x^2 + x^4)^(1/4))/(1 + x^4 + x^8), x]","F",-1
2373,1,16759,189,6.6844044,"\int \frac{\left(-2 q+p x^3\right) \sqrt{q+p x^3}}{c x^4+b x^2 \left(q+p x^3\right)+a \left(q+p x^3\right)^2} \, dx","Integrate[((-2*q + p*x^3)*Sqrt[q + p*x^3])/(c*x^4 + b*x^2*(q + p*x^3) + a*(q + p*x^3)^2),x]","\text{Result too large to show}","-\frac{\sqrt{2} \left(\sqrt{b^2-4 a c}-b\right) \tan ^{-1}\left(\frac{x \sqrt{b-\sqrt{b^2-4 a c}}}{\sqrt{2} \sqrt{a} \sqrt{p x^3+q}}\right)}{\sqrt{a} \sqrt{b^2-4 a c} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{2} \sqrt{\sqrt{b^2-4 a c}+b} \tan ^{-1}\left(\frac{x \sqrt{\sqrt{b^2-4 a c}+b}}{\sqrt{2} \sqrt{a} \sqrt{p x^3+q}}\right)}{\sqrt{a} \sqrt{b^2-4 a c}}",1,"Result too large to show","C",0
2374,0,0,189,0.7563538,"\int \frac{\left(-1+x^4\right)^2}{\left(1+x^4\right)^2 \sqrt{x^2+\sqrt{1+x^4}}} \, dx","Integrate[(-1 + x^4)^2/((1 + x^4)^2*Sqrt[x^2 + Sqrt[1 + x^4]]),x]","\int \frac{\left(-1+x^4\right)^2}{\left(1+x^4\right)^2 \sqrt{x^2+\sqrt{1+x^4}}} \, dx","-\frac{3}{2} \tanh ^{-1}\left(\frac{x}{\sqrt{\sqrt{x^4+1}+x^2}}\right)+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)}{\sqrt{2}}+\frac{\left(6 x^8+12 x^4+4\right) x^2+\sqrt{x^4+1} \left(6 x^6+9 x^2\right) x^2}{2 x \left(2 x^8+3 x^4+1\right) \sqrt{\sqrt{x^4+1}+x^2}+2 x \sqrt{x^4+1} \sqrt{\sqrt{x^4+1}+x^2} \left(2 x^6+2 x^2\right)}",1,"Integrate[(-1 + x^4)^2/((1 + x^4)^2*Sqrt[x^2 + Sqrt[1 + x^4]]), x]","F",-1
2375,0,0,189,0.2513896,"\int \frac{\sqrt{x^2+\sqrt{1+x^4}}}{\left(1+x^2\right)^2 \sqrt{1+x^4}} \, dx","Integrate[Sqrt[x^2 + Sqrt[1 + x^4]]/((1 + x^2)^2*Sqrt[1 + x^4]),x]","\int \frac{\sqrt{x^2+\sqrt{1+x^4}}}{\left(1+x^2\right)^2 \sqrt{1+x^4}} \, dx","\frac{-\left(\left(x^2-1\right) x^2\right)-\sqrt{x^4+1} x^2}{4 x \left(x^2+1\right) \sqrt{\sqrt{x^4+1}+x^2}}+\frac{1}{4} \sqrt{5 \sqrt{2}-1} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)+\frac{1}{4} \sqrt{1+5 \sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{2}-1\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)",1,"Integrate[Sqrt[x^2 + Sqrt[1 + x^4]]/((1 + x^2)^2*Sqrt[1 + x^4]), x]","F",-1
2376,0,0,189,0.4120582,"\int \frac{\sqrt{q+p x^5} \left(-2 q+3 p x^5\right)}{c x^4+b x^2 \left(q+p x^5\right)+a \left(q+p x^5\right)^2} \, dx","Integrate[(Sqrt[q + p*x^5]*(-2*q + 3*p*x^5))/(c*x^4 + b*x^2*(q + p*x^5) + a*(q + p*x^5)^2),x]","\int \frac{\sqrt{q+p x^5} \left(-2 q+3 p x^5\right)}{c x^4+b x^2 \left(q+p x^5\right)+a \left(q+p x^5\right)^2} \, dx","-\frac{\sqrt{2} \left(\sqrt{b^2-4 a c}-b\right) \tan ^{-1}\left(\frac{x \sqrt{b-\sqrt{b^2-4 a c}}}{\sqrt{2} \sqrt{a} \sqrt{p x^5+q}}\right)}{\sqrt{a} \sqrt{b^2-4 a c} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{2} \sqrt{\sqrt{b^2-4 a c}+b} \tan ^{-1}\left(\frac{x \sqrt{\sqrt{b^2-4 a c}+b}}{\sqrt{2} \sqrt{a} \sqrt{p x^5+q}}\right)}{\sqrt{a} \sqrt{b^2-4 a c}}",1,"Integrate[(Sqrt[q + p*x^5]*(-2*q + 3*p*x^5))/(c*x^4 + b*x^2*(q + p*x^5) + a*(q + p*x^5)^2), x]","F",-1
2377,0,0,189,13.0552805,"\int \frac{1}{x \sqrt{a x+\sqrt{-b+a^2 x^2}} \sqrt{c+\sqrt{a x+\sqrt{-b+a^2 x^2}}}} \, dx","Integrate[1/(x*Sqrt[a*x + Sqrt[-b + a^2*x^2]]*Sqrt[c + Sqrt[a*x + Sqrt[-b + a^2*x^2]]]),x]","\int \frac{1}{x \sqrt{a x+\sqrt{-b+a^2 x^2}} \sqrt{c+\sqrt{a x+\sqrt{-b+a^2 x^2}}}} \, dx","-\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6 c+6 \text{$\#$1}^4 c^2-4 \text{$\#$1}^2 c^3+b+c^4\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+c}-\text{$\#$1}\right)}{\text{$\#$1} c-\text{$\#$1}^3}\&\right]-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+c}}{\sqrt{c}}\right)}{c^{3/2}}+\frac{2 \sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+c}}{c \sqrt{\sqrt{a^2 x^2-b}+a x}}",1,"Integrate[1/(x*Sqrt[a*x + Sqrt[-b + a^2*x^2]]*Sqrt[c + Sqrt[a*x + Sqrt[-b + a^2*x^2]]]), x]","F",-1
2378,1,124,190,0.0916445,"\int \frac{1}{\sqrt[3]{1+x^2} \left(9+x^2\right)} \, dx","Integrate[1/((1 + x^2)^(1/3)*(9 + x^2)),x]","-\frac{27 x F_1\left(\frac{1}{2};\frac{1}{3},1;\frac{3}{2};-x^2,-\frac{x^2}{9}\right)}{\sqrt[3]{x^2+1} \left(x^2+9\right) \left(2 x^2 \left(F_1\left(\frac{3}{2};\frac{1}{3},2;\frac{5}{2};-x^2,-\frac{x^2}{9}\right)+3 F_1\left(\frac{3}{2};\frac{4}{3},1;\frac{5}{2};-x^2,-\frac{x^2}{9}\right)\right)-27 F_1\left(\frac{1}{2};\frac{1}{3},1;\frac{3}{2};-x^2,-\frac{x^2}{9}\right)\right)}","\frac{1}{12} \tan ^{-1}\left(\frac{x}{2 \sqrt[3]{x^2+1}+1}\right)+\frac{i \tan ^{-1}\left(\frac{\frac{\sqrt[3]{x^2+1}}{\sqrt{3}}-\frac{i x}{\sqrt{3}}-\frac{1}{\sqrt{3}}}{\sqrt[3]{x^2+1}}\right)}{8 \sqrt{3}}-\frac{i \tan ^{-1}\left(\frac{\frac{\sqrt[3]{x^2+1}}{\sqrt{3}}+\frac{i x}{\sqrt{3}}-\frac{1}{\sqrt{3}}}{\sqrt[3]{x^2+1}}\right)}{8 \sqrt{3}}-\frac{1}{24} i \tanh ^{-1}\left(\frac{2 i x-2 i x \sqrt[3]{x^2+1}}{x^2-4 \left(x^2+1\right)^{2/3}+2 \sqrt[3]{x^2+1}-1}\right)",1,"(-27*x*AppellF1[1/2, 1/3, 1, 3/2, -x^2, -1/9*x^2])/((1 + x^2)^(1/3)*(9 + x^2)*(-27*AppellF1[1/2, 1/3, 1, 3/2, -x^2, -1/9*x^2] + 2*x^2*(AppellF1[3/2, 1/3, 2, 5/2, -x^2, -1/9*x^2] + 3*AppellF1[3/2, 4/3, 1, 5/2, -x^2, -1/9*x^2])))","C",0
2379,1,135,190,0.1842135,"\int \frac{b+a^3 x^2}{\left(-b+a^3 x^2\right) \sqrt[3]{-b x^2+a^3 x^3}} \, dx","Integrate[(b + a^3*x^2)/((-b + a^3*x^2)*(-(b*x^2) + a^3*x^3)^(1/3)),x]","\frac{3 x \left(\sqrt[3]{1-\frac{a^3 x}{b}} \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};\frac{a^3 x}{b}\right)-\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a^{3/2} \left(a^{3/2}-\sqrt{b}\right) x}{a^3 x-b}\right)-\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a^{3/2} \left(a^{3/2}+\sqrt{b}\right) x}{a^3 x-b}\right)\right)}{\sqrt[3]{x^2 \left(a^3 x-b\right)}}","\text{RootSum}\left[\text{$\#$1}^6-2 \text{$\#$1}^3 a^3+a^6-a^3 b\&,\frac{\log \left(\sqrt[3]{a^3 x^3-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]-\frac{\log \left(\sqrt[3]{a^3 x^3-b x^2}-a x\right)}{a}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} a x}{2 \sqrt[3]{a^3 x^3-b x^2}+a x}\right)}{a}+\frac{\log \left(a x \sqrt[3]{a^3 x^3-b x^2}+\left(a^3 x^3-b x^2\right)^{2/3}+a^2 x^2\right)}{2 a}",1,"(3*x*((1 - (a^3*x)/b)^(1/3)*Hypergeometric2F1[1/3, 1/3, 4/3, (a^3*x)/b] - Hypergeometric2F1[1/3, 1, 4/3, (a^(3/2)*(a^(3/2) - Sqrt[b])*x)/(-b + a^3*x)] - Hypergeometric2F1[1/3, 1, 4/3, (a^(3/2)*(a^(3/2) + Sqrt[b])*x)/(-b + a^3*x)]))/(x^2*(-b + a^3*x))^(1/3)","A",1
2380,1,135,190,0.0854847,"\int \frac{b+a^3 x^2}{\left(-b+a^3 x^2\right) \sqrt[3]{-b x^2+a^3 x^3}} \, dx","Integrate[(b + a^3*x^2)/((-b + a^3*x^2)*(-(b*x^2) + a^3*x^3)^(1/3)),x]","\frac{3 x \left(\sqrt[3]{1-\frac{a^3 x}{b}} \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};\frac{a^3 x}{b}\right)-\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a^{3/2} \left(a^{3/2}-\sqrt{b}\right) x}{a^3 x-b}\right)-\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a^{3/2} \left(a^{3/2}+\sqrt{b}\right) x}{a^3 x-b}\right)\right)}{\sqrt[3]{x^2 \left(a^3 x-b\right)}}","\text{RootSum}\left[\text{$\#$1}^6-2 \text{$\#$1}^3 a^3+a^6-a^3 b\&,\frac{\log \left(\sqrt[3]{a^3 x^3-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]-\frac{\log \left(\sqrt[3]{a^3 x^3-b x^2}-a x\right)}{a}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} a x}{2 \sqrt[3]{a^3 x^3-b x^2}+a x}\right)}{a}+\frac{\log \left(a x \sqrt[3]{a^3 x^3-b x^2}+\left(a^3 x^3-b x^2\right)^{2/3}+a^2 x^2\right)}{2 a}",1,"(3*x*((1 - (a^3*x)/b)^(1/3)*Hypergeometric2F1[1/3, 1/3, 4/3, (a^3*x)/b] - Hypergeometric2F1[1/3, 1, 4/3, (a^(3/2)*(a^(3/2) - Sqrt[b])*x)/(-b + a^3*x)] - Hypergeometric2F1[1/3, 1, 4/3, (a^(3/2)*(a^(3/2) + Sqrt[b])*x)/(-b + a^3*x)]))/(x^2*(-b + a^3*x))^(1/3)","A",1
2381,0,0,190,3.587719,"\int \frac{-3-2 \left(1+k^2\right) x+\left(1+k^2\right) x^2+4 k^2 x^3+k^2 x^4}{\left(\left(1-x^2\right) \left(1-k^2 x^2\right)\right)^{2/3} \left(-1+d-(2+d) x-\left(1+d k^2\right) x^2+d k^2 x^3\right)} \, dx","Integrate[(-3 - 2*(1 + k^2)*x + (1 + k^2)*x^2 + 4*k^2*x^3 + k^2*x^4)/(((1 - x^2)*(1 - k^2*x^2))^(2/3)*(-1 + d - (2 + d)*x - (1 + d*k^2)*x^2 + d*k^2*x^3)),x]","\int \frac{-3-2 \left(1+k^2\right) x+\left(1+k^2\right) x^2+4 k^2 x^3+k^2 x^4}{\left(\left(1-x^2\right) \left(1-k^2 x^2\right)\right)^{2/3} \left(-1+d-(2+d) x-\left(1+d k^2\right) x^2+d k^2 x^3\right)} \, dx","-\frac{\log \left(d^{2/3} \left(k^2 x^4+\left(-k^2-1\right) x^2+1\right)^{2/3}+\left(\sqrt[3]{d} x+\sqrt[3]{d}\right) \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}+x^2+2 x+1\right)}{2 \sqrt[3]{d}}+\frac{\log \left(-\sqrt[3]{d} \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}+x+1\right)}{\sqrt[3]{d}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x+\sqrt{3}}{2 \sqrt[3]{d} \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}+x+1}\right)}{\sqrt[3]{d}}",1,"Integrate[(-3 - 2*(1 + k^2)*x + (1 + k^2)*x^2 + 4*k^2*x^3 + k^2*x^4)/(((1 - x^2)*(1 - k^2*x^2))^(2/3)*(-1 + d - (2 + d)*x - (1 + d*k^2)*x^2 + d*k^2*x^3)), x]","F",-1
2382,0,0,190,0.5527518,"\int \frac{\sqrt[4]{x^3+x^5} \left(1+x^4+x^8\right)}{x^4 \left(-1+x^4\right)} \, dx","Integrate[((x^3 + x^5)^(1/4)*(1 + x^4 + x^8))/(x^4*(-1 + x^4)),x]","\int \frac{\sqrt[4]{x^3+x^5} \left(1+x^4+x^8\right)}{x^4 \left(-1+x^4\right)} \, dx","\frac{3 \tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^5+x^3}}\right)}{2\ 2^{3/4}}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^5+x^3}}\right)}{2\ 2^{3/4}}-\frac{3 \tan ^{-1}\left(\frac{2^{3/4} x \sqrt[4]{x^5+x^3}}{\sqrt{2} x^2-\sqrt{x^5+x^3}}\right)}{4 \sqrt[4]{2}}-\frac{3 \tanh ^{-1}\left(\frac{\frac{x^2}{\sqrt[4]{2}}+\frac{\sqrt{x^5+x^3}}{2^{3/4}}}{x \sqrt[4]{x^5+x^3}}\right)}{4 \sqrt[4]{2}}+\frac{4 \sqrt[4]{x^5+x^3} \left(x^4+2 x^2+1\right)}{9 x^3}",1,"Integrate[((x^3 + x^5)^(1/4)*(1 + x^4 + x^8))/(x^4*(-1 + x^4)), x]","F",-1
2383,1,68,191,0.0292242,"\int \frac{1}{\left(b+a x^2\right) \sqrt[3]{x+x^3}} \, dx","Integrate[1/((b + a*x^2)*(x + x^3)^(1/3)),x]","\frac{3 x \sqrt[3]{x^2+1} \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};\frac{(a-b) x^2}{a x^2+b}\right)}{2 b \sqrt[3]{x^3+x} \sqrt[3]{\frac{a x^2}{b}+1}}","\frac{\log \left(x \sqrt[3]{a-b}+\sqrt[3]{b} \sqrt[3]{x^3+x}\right)}{2 b^{2/3} \sqrt[3]{a-b}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x \sqrt[3]{a-b}}{x \sqrt[3]{a-b}-2 \sqrt[3]{b} \sqrt[3]{x^3+x}}\right)}{2 b^{2/3} \sqrt[3]{a-b}}-\frac{\log \left(-\sqrt[3]{b} \sqrt[3]{x^3+x} x \sqrt[3]{a-b}+x^2 (a-b)^{2/3}+b^{2/3} \left(x^3+x\right)^{2/3}\right)}{4 b^{2/3} \sqrt[3]{a-b}}",1,"(3*x*(1 + x^2)^(1/3)*Hypergeometric2F1[1/3, 1/3, 4/3, ((a - b)*x^2)/(b + a*x^2)])/(2*b*(1 + (a*x^2)/b)^(1/3)*(x + x^3)^(1/3))","C",0
2384,1,144,191,0.136252,"\int \frac{\sqrt[4]{-b x^3+a x^4}}{x^2 \left(-d+c x^2\right)} \, dx","Integrate[(-(b*x^3) + a*x^4)^(1/4)/(x^2*(-d + c*x^2)),x]","\frac{2 x^2 \left(x \left(b \sqrt{c}-a \sqrt{d}\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};-\frac{\left(a-\frac{b \sqrt{c}}{\sqrt{d}}\right) x}{b-a x}\right)-x \left(a \sqrt{d}+b \sqrt{c}\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};-\frac{\left(a+\frac{b \sqrt{c}}{\sqrt{d}}\right) x}{b-a x}\right)-6 \sqrt{d} (b-a x)\right)}{3 d^{3/2} \left(x^3 (a x-b)\right)^{3/4}}","\frac{\text{RootSum}\left[\text{$\#$1}^8 (-d)+2 \text{$\#$1}^4 a d-a^2 d+b^2 c\&,\frac{-\text{$\#$1}^4 a d \log \left(\sqrt[4]{a x^4-b x^3}-\text{$\#$1} x\right)+\text{$\#$1}^4 a d \log (x)+a^2 d \log \left(\sqrt[4]{a x^4-b x^3}-\text{$\#$1} x\right)-b^2 c \log \left(\sqrt[4]{a x^4-b x^3}-\text{$\#$1} x\right)-a^2 d \log (x)+b^2 c \log (x)}{\text{$\#$1}^3 a-\text{$\#$1}^7}\&\right]}{2 d^2}+\frac{4 \sqrt[4]{a x^4-b x^3}}{d x}",1,"(2*x^2*(-6*Sqrt[d]*(b - a*x) + (b*Sqrt[c] - a*Sqrt[d])*x*Hypergeometric2F1[3/4, 1, 7/4, -(((a - (b*Sqrt[c])/Sqrt[d])*x)/(b - a*x))] - (b*Sqrt[c] + a*Sqrt[d])*x*Hypergeometric2F1[3/4, 1, 7/4, -(((a + (b*Sqrt[c])/Sqrt[d])*x)/(b - a*x))]))/(3*d^(3/2)*(x^3*(-b + a*x))^(3/4))","A",1
2385,1,144,191,0.0434583,"\int \frac{\sqrt[4]{-b x^3+a x^4}}{x^2 \left(-d+c x^2\right)} \, dx","Integrate[(-(b*x^3) + a*x^4)^(1/4)/(x^2*(-d + c*x^2)),x]","\frac{2 x^2 \left(x \left(b \sqrt{c}-a \sqrt{d}\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};-\frac{\left(a-\frac{b \sqrt{c}}{\sqrt{d}}\right) x}{b-a x}\right)-x \left(a \sqrt{d}+b \sqrt{c}\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};-\frac{\left(a+\frac{b \sqrt{c}}{\sqrt{d}}\right) x}{b-a x}\right)-6 \sqrt{d} (b-a x)\right)}{3 d^{3/2} \left(x^3 (a x-b)\right)^{3/4}}","\frac{\text{RootSum}\left[\text{$\#$1}^8 (-d)+2 \text{$\#$1}^4 a d-a^2 d+b^2 c\&,\frac{-\text{$\#$1}^4 a d \log \left(\sqrt[4]{a x^4-b x^3}-\text{$\#$1} x\right)+\text{$\#$1}^4 a d \log (x)+a^2 d \log \left(\sqrt[4]{a x^4-b x^3}-\text{$\#$1} x\right)-b^2 c \log \left(\sqrt[4]{a x^4-b x^3}-\text{$\#$1} x\right)-a^2 d \log (x)+b^2 c \log (x)}{\text{$\#$1}^3 a-\text{$\#$1}^7}\&\right]}{2 d^2}+\frac{4 \sqrt[4]{a x^4-b x^3}}{d x}",1,"(2*x^2*(-6*Sqrt[d]*(b - a*x) + (b*Sqrt[c] - a*Sqrt[d])*x*Hypergeometric2F1[3/4, 1, 7/4, -(((a - (b*Sqrt[c])/Sqrt[d])*x)/(b - a*x))] - (b*Sqrt[c] + a*Sqrt[d])*x*Hypergeometric2F1[3/4, 1, 7/4, -(((a + (b*Sqrt[c])/Sqrt[d])*x)/(b - a*x))]))/(3*d^(3/2)*(x^3*(-b + a*x))^(3/4))","A",1
2386,0,0,191,7.1944085,"\int \frac{\sqrt[3]{x+x^3} \left(b+a x^6\right)}{d+c x^6} \, dx","Integrate[((x + x^3)^(1/3)*(b + a*x^6))/(d + c*x^6),x]","\int \frac{\sqrt[3]{x+x^3} \left(b+a x^6\right)}{d+c x^6} \, dx","\frac{(a d-b c) \text{RootSum}\left[\text{$\#$1}^9 d-3 \text{$\#$1}^6 d+3 \text{$\#$1}^3 d+c-d\&,\frac{\text{$\#$1} \log \left(\sqrt[3]{x^3+x}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^3-1}\&\right]}{6 c d}+\frac{a \sqrt[3]{x^3+x} x}{2 c}-\frac{a \log \left(\sqrt[3]{x^3+x}-x\right)}{6 c}-\frac{a \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+x}+x}\right)}{2 \sqrt{3} c}+\frac{a \log \left(\sqrt[3]{x^3+x} x+\left(x^3+x\right)^{2/3}+x^2\right)}{12 c}",1,"Integrate[((x + x^3)^(1/3)*(b + a*x^6))/(d + c*x^6), x]","F",-1
2387,0,0,191,4.7103337,"\int \frac{\sqrt[3]{x+x^3} \left(b+a x^6\right)}{d+c x^6} \, dx","Integrate[((x + x^3)^(1/3)*(b + a*x^6))/(d + c*x^6),x]","\int \frac{\sqrt[3]{x+x^3} \left(b+a x^6\right)}{d+c x^6} \, dx","\frac{(a d-b c) \text{RootSum}\left[\text{$\#$1}^9 d-3 \text{$\#$1}^6 d+3 \text{$\#$1}^3 d+c-d\&,\frac{\text{$\#$1} \log \left(\sqrt[3]{x^3+x}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^3-1}\&\right]}{6 c d}+\frac{a \sqrt[3]{x^3+x} x}{2 c}-\frac{a \log \left(\sqrt[3]{x^3+x}-x\right)}{6 c}-\frac{a \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+x}+x}\right)}{2 \sqrt{3} c}+\frac{a \log \left(\sqrt[3]{x^3+x} x+\left(x^3+x\right)^{2/3}+x^2\right)}{12 c}",1,"Integrate[((x + x^3)^(1/3)*(b + a*x^6))/(d + c*x^6), x]","F",-1
2388,0,0,191,0.963914,"\int \frac{\left(-1+2 x^6\right) \sqrt[3]{x+x^7}}{\left(1-2 x^2+x^6\right) \left(1-x^2+x^6\right)} \, dx","Integrate[((-1 + 2*x^6)*(x + x^7)^(1/3))/((1 - 2*x^2 + x^6)*(1 - x^2 + x^6)),x]","\int \frac{\left(-1+2 x^6\right) \sqrt[3]{x+x^7}}{\left(1-2 x^2+x^6\right) \left(1-x^2+x^6\right)} \, dx","-\frac{1}{2} \log \left(\sqrt[3]{x^7+x}-x\right)+\frac{\log \left(2^{2/3} \sqrt[3]{x^7+x}-2 x\right)}{2^{2/3}}-\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^7+x}+x}\right)+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^7+x}+x}\right)}{2^{2/3}}+\frac{1}{4} \log \left(\sqrt[3]{x^7+x} x+\left(x^7+x\right)^{2/3}+x^2\right)-\frac{\log \left(2^{2/3} \sqrt[3]{x^7+x} x+\sqrt[3]{2} \left(x^7+x\right)^{2/3}+2 x^2\right)}{2\ 2^{2/3}}",1,"Integrate[((-1 + 2*x^6)*(x + x^7)^(1/3))/((1 - 2*x^2 + x^6)*(1 - x^2 + x^6)), x]","F",-1
2389,0,0,191,0.6158702,"\int \frac{\left(-q+2 p x^3\right) \sqrt{q^2-2 p q x^2+2 p q x^3+p^2 x^6} \left(b x^3+a \left(q+p x^3\right)^3\right)}{x^6} \, dx","Integrate[((-q + 2*p*x^3)*Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6]*(b*x^3 + a*(q + p*x^3)^3))/x^6,x]","\int \frac{\left(-q+2 p x^3\right) \sqrt{q^2-2 p q x^2+2 p q x^3+p^2 x^6} \left(b x^3+a \left(q+p x^3\right)^3\right)}{x^6} \, dx","\frac{\sqrt{p^2 x^6+2 p q x^3-2 p q x^2+q^2} \left(6 a p^4 x^{12}+24 a p^3 q x^9-4 a p^3 q x^8+36 a p^2 q^2 x^6-8 a p^2 q^2 x^5-16 a p^2 q^2 x^4+24 a p q^3 x^3-4 a p q^3 x^2+6 a q^4+15 b p x^6+15 b q x^3\right)}{30 x^5}-b p q \log \left(\sqrt{p^2 x^6+2 p q x^3-2 p q x^2+q^2}+p x^3+q\right)+b p q \log (x)",1,"Integrate[((-q + 2*p*x^3)*Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6]*(b*x^3 + a*(q + p*x^3)^3))/x^6, x]","F",-1
2390,0,0,192,7.5232116,"\int \frac{-1+(-1+2 k) x}{\sqrt[3]{(1-x) x (1-k x)} \left(1-(2+b) x+(1+b k) x^2\right)} \, dx","Integrate[(-1 + (-1 + 2*k)*x)/(((1 - x)*x*(1 - k*x))^(1/3)*(1 - (2 + b)*x + (1 + b*k)*x^2)),x]","\int \frac{-1+(-1+2 k) x}{\sqrt[3]{(1-x) x (1-k x)} \left(1-(2+b) x+(1+b k) x^2\right)} \, dx","\frac{\log \left(\sqrt[3]{b} \sqrt[3]{k x^3+(-k-1) x^2+x}+x-1\right)}{b^{2/3}}-\frac{\log \left(b^{2/3} \left(k x^3+(-k-1) x^2+x\right)^{2/3}+\left(\sqrt[3]{b}-\sqrt[3]{b} x\right) \sqrt[3]{k x^3+(-k-1) x^2+x}+x^2-2 x+1\right)}{2 b^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{b} \sqrt[3]{k x^3+(-k-1) x^2+x}}{\sqrt[3]{b} \sqrt[3]{k x^3+(-k-1) x^2+x}-2 x+2}\right)}{b^{2/3}}",1,"Integrate[(-1 + (-1 + 2*k)*x)/(((1 - x)*x*(1 - k*x))^(1/3)*(1 - (2 + b)*x + (1 + b*k)*x^2)), x]","F",-1
2391,0,0,192,3.5347264,"\int \frac{-3+2 \left(1+k^2\right) x+\left(1+k^2\right) x^2-4 k^2 x^3+k^2 x^4}{\left(\left(1-x^2\right) \left(1-k^2 x^2\right)\right)^{2/3} \left(1-d-(2+d) x+\left(1+d k^2\right) x^2+d k^2 x^3\right)} \, dx","Integrate[(-3 + 2*(1 + k^2)*x + (1 + k^2)*x^2 - 4*k^2*x^3 + k^2*x^4)/(((1 - x^2)*(1 - k^2*x^2))^(2/3)*(1 - d - (2 + d)*x + (1 + d*k^2)*x^2 + d*k^2*x^3)),x]","\int \frac{-3+2 \left(1+k^2\right) x+\left(1+k^2\right) x^2-4 k^2 x^3+k^2 x^4}{\left(\left(1-x^2\right) \left(1-k^2 x^2\right)\right)^{2/3} \left(1-d-(2+d) x+\left(1+d k^2\right) x^2+d k^2 x^3\right)} \, dx","-\frac{\log \left(d^{2/3} \left(k^2 x^4+\left(-k^2-1\right) x^2+1\right)^{2/3}+\left(\sqrt[3]{d}-\sqrt[3]{d} x\right) \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}+x^2-2 x+1\right)}{2 \sqrt[3]{d}}+\frac{\log \left(\sqrt[3]{d} \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}+x-1\right)}{\sqrt[3]{d}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x-\sqrt{3}}{-2 \sqrt[3]{d} \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}+x-1}\right)}{\sqrt[3]{d}}",1,"Integrate[(-3 + 2*(1 + k^2)*x + (1 + k^2)*x^2 - 4*k^2*x^3 + k^2*x^4)/(((1 - x^2)*(1 - k^2*x^2))^(2/3)*(1 - d - (2 + d)*x + (1 + d*k^2)*x^2 + d*k^2*x^3)), x]","F",-1
2392,1,244,192,0.9190032,"\int \frac{b-3 a x^3+3 x^6}{x^6 \left(-b+2 a x^3\right) \sqrt[4]{-b x+a x^4}} \, dx","Integrate[(b - 3*a*x^3 + 3*x^6)/(x^6*(-b + 2*a*x^3)*(-(b*x) + a*x^4)^(1/4)),x]","\frac{\frac{\left(2 a^2-3 b\right) \left(-16 a x^3 \left(b-2 a x^3\right)^2 \, _3F_2\left(\frac{5}{4},2,2;1,\frac{9}{4};\frac{a x^3}{b-a x^3}\right)+8 a x^3 \left(-24 a^2 x^6+10 a b x^3+b^2\right) \, _2F_1\left(\frac{5}{4},2;\frac{9}{4};\frac{a x^3}{b-a x^3}\right)+5 \left(128 a^3 x^9-144 a^2 b x^6+13 a b^2 x^3+3 b^3\right) \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{a x^3}{b-a x^3}\right)\right)}{a^2 \left(a x^3-b\right)}+15 \left(2-\frac{b}{a^2}\right) \left(b-a x^3\right) \left(4 a x^3+3 b\right)+\frac{210 b x^3 \left(a x^3-b\right)}{a}}{315 b^2 x^5 \sqrt[4]{a x^4-b x}}","\frac{\sqrt{2} \left(2 a^2-3 b\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} x \sqrt[4]{a x^4-b x}}{\sqrt{a x^4-b x}-\sqrt{a} x^2}\right)}{3 \sqrt[4]{a} b^2}+\frac{\sqrt{2} \left(2 a^2-3 b\right) \tanh ^{-1}\left(\frac{\sqrt{a x^4-b x}+\sqrt{a} x^2}{\sqrt{2} \sqrt[4]{a} x \sqrt[4]{a x^4-b x}}\right)}{3 \sqrt[4]{a} b^2}-\frac{4 \left(a x^4-b x\right)^{3/4} \left(b-a x^3\right)}{21 b^2 x^6}",1,"((210*b*x^3*(-b + a*x^3))/a + 15*(2 - b/a^2)*(b - a*x^3)*(3*b + 4*a*x^3) + ((2*a^2 - 3*b)*(5*(3*b^3 + 13*a*b^2*x^3 - 144*a^2*b*x^6 + 128*a^3*x^9)*Hypergeometric2F1[1/4, 1, 5/4, (a*x^3)/(b - a*x^3)] + 8*a*x^3*(b^2 + 10*a*b*x^3 - 24*a^2*x^6)*Hypergeometric2F1[5/4, 2, 9/4, (a*x^3)/(b - a*x^3)] - 16*a*x^3*(b - 2*a*x^3)^2*HypergeometricPFQ[{5/4, 2, 2}, {1, 9/4}, (a*x^3)/(b - a*x^3)]))/(a^2*(-b + a*x^3)))/(315*b^2*x^5*(-(b*x) + a*x^4)^(1/4))","C",0
2393,0,0,192,0.6537713,"\int \frac{\left(-2 q+p x^3\right) \sqrt{q^2+2 p q x^3-2 p q x^4+p^2 x^6} \left(b x^6+a \left(q+p x^3\right)^3\right)}{x^{11}} \, dx","Integrate[((-2*q + p*x^3)*Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]*(b*x^6 + a*(q + p*x^3)^3))/x^11,x]","\int \frac{\left(-2 q+p x^3\right) \sqrt{q^2+2 p q x^3-2 p q x^4+p^2 x^6} \left(b x^6+a \left(q+p x^3\right)^3\right)}{x^{11}} \, dx","\frac{\sqrt{p^2 x^6-2 p q x^4+2 p q x^3+q^2} \left(6 a p^4 x^{12}-4 a p^3 q x^{10}+24 a p^3 q x^9-16 a p^2 q^2 x^8-8 a p^2 q^2 x^7+36 a p^2 q^2 x^6-4 a p q^3 x^4+24 a p q^3 x^3+6 a q^4+15 b p x^9+15 b q x^6\right)}{30 x^{10}}-b p q \log \left(\sqrt{p^2 x^6-2 p q x^4+2 p q x^3+q^2}+p x^3+q\right)+2 b p q \log (x)",1,"Integrate[((-2*q + p*x^3)*Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]*(b*x^6 + a*(q + p*x^3)^3))/x^11, x]","F",-1
2394,1,6680,192,9.2230449,"\int \frac{x \sqrt{1+x}}{x+\sqrt{x+\sqrt{1+x}}} \, dx","Integrate[(x*Sqrt[1 + x])/(x + Sqrt[x + Sqrt[1 + x]]),x]","\text{Result too large to show}","4 \text{RootSum}\left[\text{$\#$1}^4+2 \text{$\#$1}^3-5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,\frac{\text{$\#$1}^3 \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)-3 \text{$\#$1}^2 \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)}{4 \text{$\#$1}^3+6 \text{$\#$1}^2-10 \text{$\#$1}+3}\&\right]+\sqrt{x+1} \left(\frac{2 (x+4)}{3}-\sqrt{x+\sqrt{x+1}}\right)-\frac{1}{2} \sqrt{x+\sqrt{x+1}}+\frac{3}{4} \log \left(2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)",1,"Result too large to show","B",0
2395,1,6680,192,6.5902709,"\int \frac{x \sqrt{1+x}}{x+\sqrt{x+\sqrt{1+x}}} \, dx","Integrate[(x*Sqrt[1 + x])/(x + Sqrt[x + Sqrt[1 + x]]),x]","\text{Result too large to show}","4 \text{RootSum}\left[\text{$\#$1}^4+2 \text{$\#$1}^3-5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,\frac{\text{$\#$1}^3 \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)-3 \text{$\#$1}^2 \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)}{4 \text{$\#$1}^3+6 \text{$\#$1}^2-10 \text{$\#$1}+3}\&\right]+\sqrt{x+1} \left(\frac{2 (x+4)}{3}-\sqrt{x+\sqrt{x+1}}\right)-\frac{1}{2} \sqrt{x+\sqrt{x+1}}+\frac{3}{4} \log \left(2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)",1,"Result too large to show","B",0
2396,1,201,193,0.4446593,"\int \frac{x^2}{\sqrt{\frac{b+a x}{d+c x}}} \, dx","Integrate[x^2/Sqrt[(b + a*x)/(d + c*x)],x]","\frac{\sqrt{c} (a x+b) \sqrt{\frac{a (c x+d)}{a d-b c}} \left(a^2 \left(8 c^2 x^2+2 c d x-3 d^2\right)-2 a b c (5 c x+2 d)+15 b^2 c^2\right)+3 \sqrt{a x+b} \sqrt{a d-b c} \left(a^2 d^2+2 a b c d+5 b^2 c^2\right) \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{a x+b}}{\sqrt{a d-b c}}\right)}{24 a^3 c^{5/2} \sqrt{\frac{a x+b}{c x+d}} \sqrt{\frac{a (c x+d)}{a d-b c}}}","\frac{\sqrt{\frac{a x+b}{c x+d}} \left(8 a^2 c^3 x^3+10 a^2 c^2 d x^2-a^2 c d^2 x-3 a^2 d^3-10 a b c^3 x^2-14 a b c^2 d x-4 a b c d^2+15 b^2 c^3 x+15 b^2 c^2 d\right)}{24 a^3 c^2}+\frac{\left(a^3 d^3+a^2 b c d^2+3 a b^2 c^2 d-5 b^3 c^3\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{a x+b}{c x+d}}}{\sqrt{a}}\right)}{8 a^{7/2} c^{5/2}}",1,"(Sqrt[c]*(b + a*x)*Sqrt[(a*(d + c*x))/(-(b*c) + a*d)]*(15*b^2*c^2 - 2*a*b*c*(2*d + 5*c*x) + a^2*(-3*d^2 + 2*c*d*x + 8*c^2*x^2)) + 3*Sqrt[-(b*c) + a*d]*(5*b^2*c^2 + 2*a*b*c*d + a^2*d^2)*Sqrt[b + a*x]*ArcSinh[(Sqrt[c]*Sqrt[b + a*x])/Sqrt[-(b*c) + a*d]])/(24*a^3*c^(5/2)*Sqrt[(b + a*x)/(d + c*x)]*Sqrt[(a*(d + c*x))/(-(b*c) + a*d)])","A",1
2397,0,0,193,0.3969159,"\int \frac{b+2 a x}{(-b+a x) (2 b+a x) \sqrt[4]{-1+b x+a x^2}} \, dx","Integrate[(b + 2*a*x)/((-b + a*x)*(2*b + a*x)*(-1 + b*x + a*x^2)^(1/4)),x]","\int \frac{b+2 a x}{(-b+a x) (2 b+a x) \sqrt[4]{-1+b x+a x^2}} \, dx","\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{a-2 b^2} \sqrt[4]{a x^2+b x-1}}{\sqrt{a-2 b^2}-\sqrt{a} \sqrt{a x^2+b x-1}}\right)}{a^{3/4} \sqrt[4]{a-2 b^2}}-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\frac{\sqrt[4]{a} \sqrt{a x^2+b x-1}}{\sqrt{2} \sqrt[4]{a-2 b^2}}+\frac{\sqrt[4]{a-2 b^2}}{\sqrt{2} \sqrt[4]{a}}}{\sqrt[4]{a x^2+b x-1}}\right)}{a^{3/4} \sqrt[4]{a-2 b^2}}",1,"Integrate[(b + 2*a*x)/((-b + a*x)*(2*b + a*x)*(-1 + b*x + a*x^2)^(1/4)), x]","F",-1
2398,1,202,193,0.4976905,"\int \frac{-1+a k x+k x^2}{\left(1+k x^2\right) \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}} \, dx","Integrate[(-1 + a*k*x + k*x^2)/((1 + k*x^2)*Sqrt[(1 - x^2)*(1 - k^2*x^2)]),x]","\frac{a k \sqrt{x^2-1} \sqrt{k^2 x^2-1} \tanh ^{-1}\left(\frac{\sqrt{k (k+1)} \sqrt{x^2-1}}{\sqrt{k+1} \sqrt{k^2 x^2-1}}\right)+\sqrt{k+1} \sqrt{k (k+1)} \sqrt{1-x^2} \sqrt{1-k^2 x^2} F\left(\sin ^{-1}(x)|k^2\right)-2 \sqrt{k+1} \sqrt{k (k+1)} \sqrt{1-x^2} \sqrt{1-k^2 x^2} \Pi \left(-k;\sin ^{-1}(x)|k^2\right)}{\sqrt{k+1} \sqrt{k (k+1)} \sqrt{\left(x^2-1\right) \left(k^2 x^2-1\right)}}","-\frac{a \sqrt{k} \tanh ^{-1}\left(\frac{\left(2 k^{3/2}+2 \sqrt{k}\right) x^2}{k^2 x^4+\left(k x^2-1\right) \sqrt{k^2 x^4+\left(-k^2-1\right) x^2+1}+2 k x^2+1}\right)}{2 (k+1)}+\frac{\tan ^{-1}\left(\frac{\left(-k-2 \sqrt{k}-1\right) x}{\sqrt{k^2 x^4+\left(-k^2-1\right) x^2+1}+k x^2-1}\right)}{k+1}+\frac{\tan ^{-1}\left(\frac{\left(-k+2 \sqrt{k}-1\right) x}{\sqrt{k^2 x^4+\left(-k^2-1\right) x^2+1}+k x^2-1}\right)}{k+1}",1,"(a*k*Sqrt[-1 + x^2]*Sqrt[-1 + k^2*x^2]*ArcTanh[(Sqrt[k*(1 + k)]*Sqrt[-1 + x^2])/(Sqrt[1 + k]*Sqrt[-1 + k^2*x^2])] + Sqrt[1 + k]*Sqrt[k*(1 + k)]*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticF[ArcSin[x], k^2] - 2*Sqrt[1 + k]*Sqrt[k*(1 + k)]*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[-k, ArcSin[x], k^2])/(Sqrt[1 + k]*Sqrt[k*(1 + k)]*Sqrt[(-1 + x^2)*(-1 + k^2*x^2)])","C",1
2399,1,192,193,0.1025605,"\int \frac{\left(-b+x^3\right) \left(b+x^3\right)}{\sqrt[3]{a x^2+x^3}} \, dx","Integrate[((-b + x^3)*(b + x^3))/(a*x^2 + x^3)^(1/3),x]","\frac{3 x \sqrt[3]{\frac{a+x}{a}} \left(a^6 \, _2F_1\left(-\frac{17}{3},\frac{1}{3};\frac{4}{3};-\frac{x}{a}\right)-6 a^6 \, _2F_1\left(-\frac{14}{3},\frac{1}{3};\frac{4}{3};-\frac{x}{a}\right)+15 a^6 \, _2F_1\left(-\frac{11}{3},\frac{1}{3};\frac{4}{3};-\frac{x}{a}\right)-20 a^6 \, _2F_1\left(-\frac{8}{3},\frac{1}{3};\frac{4}{3};-\frac{x}{a}\right)+15 a^6 \, _2F_1\left(-\frac{5}{3},\frac{1}{3};\frac{4}{3};-\frac{x}{a}\right)-6 a^6 \, _2F_1\left(-\frac{2}{3},\frac{1}{3};\frac{4}{3};-\frac{x}{a}\right)+a^6 \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};-\frac{x}{a}\right)-b^2 \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};-\frac{x}{a}\right)\right)}{\sqrt[3]{x^2 (a+x)}}","\frac{\left(6561 b^2-728 a^6\right) \log \left(\sqrt[3]{a x^2+x^3}-x\right)}{6561}+\frac{\left(728 a^6-6561 b^2\right) \log \left(x \sqrt[3]{a x^2+x^3}+\left(a x^2+x^3\right)^{2/3}+x^2\right)}{13122}+\frac{\left(728 \sqrt{3} a^6-6561 \sqrt{3} b^2\right) \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{a x^2+x^3}+x}\right)}{6561}+\frac{\left(a x^2+x^3\right)^{2/3} \left(-7280 a^5+5460 a^4 x-4680 a^3 x^2+4212 a^2 x^3-3888 a x^4+3645 x^5\right)}{21870 x}",1,"(3*x*((a + x)/a)^(1/3)*(a^6*Hypergeometric2F1[-17/3, 1/3, 4/3, -(x/a)] - 6*a^6*Hypergeometric2F1[-14/3, 1/3, 4/3, -(x/a)] + 15*a^6*Hypergeometric2F1[-11/3, 1/3, 4/3, -(x/a)] - 20*a^6*Hypergeometric2F1[-8/3, 1/3, 4/3, -(x/a)] + 15*a^6*Hypergeometric2F1[-5/3, 1/3, 4/3, -(x/a)] - 6*a^6*Hypergeometric2F1[-2/3, 1/3, 4/3, -(x/a)] + a^6*Hypergeometric2F1[1/3, 1/3, 4/3, -(x/a)] - b^2*Hypergeometric2F1[1/3, 1/3, 4/3, -(x/a)]))/(x^2*(a + x))^(1/3)","C",1
2400,1,3036,193,1.4874071,"\int \frac{x}{\left(1-x^2\right) \sqrt{a+b x+c x^2+b x^3+a x^4}} \, dx","Integrate[x/((1 - x^2)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]),x]","\text{Result too large to show}","\frac{\sqrt{-2 a-2 b-c} \tan ^{-1}\left(\frac{x \sqrt{-2 a-2 b-c}}{-\sqrt{a x^4+a+b x^3+b x+c x^2}+\sqrt{a} x^2-2 \sqrt{a} x+\sqrt{a}}\right)}{2 (2 a+2 b+c)}-\frac{\sqrt{-2 a+2 b-c} \tan ^{-1}\left(\frac{x \sqrt{-2 a+2 b-c}}{-\sqrt{a x^4+a+b x^3+b x+c x^2}+\sqrt{a} x^2+2 \sqrt{a} x+\sqrt{a}}\right)}{2 (2 a-2 b+c)}",1,"((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])^2*((-(EllipticF[ArcSin[Sqrt[((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))]], -(((Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])))]*(-1 + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])) + EllipticPi[((-1 + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((-1 + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])), ArcSin[Sqrt[((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))]], -(((Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])))]*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2]))/((-1 + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(-1 + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])) + (-(EllipticF[ArcSin[Sqrt[((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))]], -(((Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])))]*(1 + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])) + EllipticPi[((1 + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((1 + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])), ArcSin[Sqrt[((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))]], -(((Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])))]*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2]))/((1 + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(1 + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])))*Sqrt[((Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3]))/((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 3]))]*Sqrt[((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/((x - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])^2*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4])^2)]*(-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))/(Sqrt[x*(b + c*x + b*x^2) + a*(1 + x^4)]*(-Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 1] + Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2])*(Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 2] - Root[a + b*#1 + c*#1^2 + b*#1^3 + a*#1^4 & , 4]))","C",0
2401,1,214,193,0.4011407,"\int \frac{1}{\sqrt[4]{-1+x^4} \left(-1-x^4+x^8\right)} \, dx","Integrate[1/((-1 + x^4)^(1/4)*(-1 - x^4 + x^8)),x]","\frac{-\frac{\sqrt[4]{3+\sqrt{5}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3+\sqrt{5}}} x}{\sqrt[4]{x^4-1}}\right)}{1+\sqrt{5}}+\frac{\sqrt[4]{3-\sqrt{5}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x}{\sqrt[4]{x^4-1}}\right)}{1-\sqrt{5}}-\frac{\sqrt[4]{3+\sqrt{5}} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3+\sqrt{5}}} x}{\sqrt[4]{x^4-1}}\right)}{1+\sqrt{5}}+\frac{\sqrt[4]{3-\sqrt{5}} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x}{\sqrt[4]{x^4-1}}\right)}{1-\sqrt{5}}}{\sqrt[4]{2} \sqrt{5}}","-\frac{1}{2} \sqrt{\frac{1}{10} \left(\sqrt{5}-1\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}} x}{\sqrt[4]{x^4-1}}\right)-\frac{1}{2} \sqrt{\frac{1}{10} \left(1+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{1}{2}+\frac{\sqrt{5}}{2}} x}{\sqrt[4]{x^4-1}}\right)-\frac{1}{2} \sqrt{\frac{1}{10} \left(\sqrt{5}-1\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}} x}{\sqrt[4]{x^4-1}}\right)-\frac{1}{2} \sqrt{\frac{1}{10} \left(1+\sqrt{5}\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{2}+\frac{\sqrt{5}}{2}} x}{\sqrt[4]{x^4-1}}\right)",1,"(-(((3 + Sqrt[5])^(1/4)*ArcTan[((2/(3 + Sqrt[5]))^(1/4)*x)/(-1 + x^4)^(1/4)])/(1 + Sqrt[5])) + ((3 - Sqrt[5])^(1/4)*ArcTan[(((3 + Sqrt[5])/2)^(1/4)*x)/(-1 + x^4)^(1/4)])/(1 - Sqrt[5]) - ((3 + Sqrt[5])^(1/4)*ArcTanh[((2/(3 + Sqrt[5]))^(1/4)*x)/(-1 + x^4)^(1/4)])/(1 + Sqrt[5]) + ((3 - Sqrt[5])^(1/4)*ArcTanh[(((3 + Sqrt[5])/2)^(1/4)*x)/(-1 + x^4)^(1/4)])/(1 - Sqrt[5]))/(2^(1/4)*Sqrt[5])","A",1
2402,1,172,193,0.1629387,"\int \frac{-1+2 x^4}{\sqrt[4]{-1+x^4} \left(-1-x^4+x^8\right)} \, dx","Integrate[(-1 + 2*x^4)/((-1 + x^4)^(1/4)*(-1 - x^4 + x^8)),x]","\frac{-\sqrt[4]{3-\sqrt{5}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3+\sqrt{5}}} x}{\sqrt[4]{x^4-1}}\right)+\sqrt[4]{3+\sqrt{5}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x}{\sqrt[4]{x^4-1}}\right)-\sqrt[4]{3-\sqrt{5}} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3+\sqrt{5}}} x}{\sqrt[4]{x^4-1}}\right)+\sqrt[4]{3+\sqrt{5}} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x}{\sqrt[4]{x^4-1}}\right)}{2 \sqrt[4]{2}}","-\frac{1}{2} \sqrt{\frac{1}{2} \left(\sqrt{5}-1\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}} x}{\sqrt[4]{x^4-1}}\right)+\frac{1}{2} \sqrt{\frac{1}{2} \left(1+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{1}{2}+\frac{\sqrt{5}}{2}} x}{\sqrt[4]{x^4-1}}\right)-\frac{1}{2} \sqrt{\frac{1}{2} \left(\sqrt{5}-1\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}} x}{\sqrt[4]{x^4-1}}\right)+\frac{1}{2} \sqrt{\frac{1}{2} \left(1+\sqrt{5}\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{2}+\frac{\sqrt{5}}{2}} x}{\sqrt[4]{x^4-1}}\right)",1,"(-((3 - Sqrt[5])^(1/4)*ArcTan[((2/(3 + Sqrt[5]))^(1/4)*x)/(-1 + x^4)^(1/4)]) + (3 + Sqrt[5])^(1/4)*ArcTan[(((3 + Sqrt[5])/2)^(1/4)*x)/(-1 + x^4)^(1/4)] - (3 - Sqrt[5])^(1/4)*ArcTanh[((2/(3 + Sqrt[5]))^(1/4)*x)/(-1 + x^4)^(1/4)] + (3 + Sqrt[5])^(1/4)*ArcTanh[(((3 + Sqrt[5])/2)^(1/4)*x)/(-1 + x^4)^(1/4)])/(2*2^(1/4))","A",0
2403,1,214,193,0.3020355,"\int \frac{1}{\sqrt[4]{1+x^4} \left(-1+x^4+x^8\right)} \, dx","Integrate[1/((1 + x^4)^(1/4)*(-1 + x^4 + x^8)),x]","\frac{-\frac{\sqrt[4]{3+\sqrt{5}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3+\sqrt{5}}} x}{\sqrt[4]{x^4+1}}\right)}{1+\sqrt{5}}+\frac{\sqrt[4]{3-\sqrt{5}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x}{\sqrt[4]{x^4+1}}\right)}{1-\sqrt{5}}-\frac{\sqrt[4]{3+\sqrt{5}} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3+\sqrt{5}}} x}{\sqrt[4]{x^4+1}}\right)}{1+\sqrt{5}}+\frac{\sqrt[4]{3-\sqrt{5}} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x}{\sqrt[4]{x^4+1}}\right)}{1-\sqrt{5}}}{\sqrt[4]{2} \sqrt{5}}","-\frac{1}{2} \sqrt{\frac{1}{10} \left(\sqrt{5}-1\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}} x}{\sqrt[4]{x^4+1}}\right)-\frac{1}{2} \sqrt{\frac{1}{10} \left(1+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{1}{2}+\frac{\sqrt{5}}{2}} x}{\sqrt[4]{x^4+1}}\right)-\frac{1}{2} \sqrt{\frac{1}{10} \left(\sqrt{5}-1\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}} x}{\sqrt[4]{x^4+1}}\right)-\frac{1}{2} \sqrt{\frac{1}{10} \left(1+\sqrt{5}\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{2}+\frac{\sqrt{5}}{2}} x}{\sqrt[4]{x^4+1}}\right)",1,"(-(((3 + Sqrt[5])^(1/4)*ArcTan[((2/(3 + Sqrt[5]))^(1/4)*x)/(1 + x^4)^(1/4)])/(1 + Sqrt[5])) + ((3 - Sqrt[5])^(1/4)*ArcTan[(((3 + Sqrt[5])/2)^(1/4)*x)/(1 + x^4)^(1/4)])/(1 - Sqrt[5]) - ((3 + Sqrt[5])^(1/4)*ArcTanh[((2/(3 + Sqrt[5]))^(1/4)*x)/(1 + x^4)^(1/4)])/(1 + Sqrt[5]) + ((3 - Sqrt[5])^(1/4)*ArcTanh[(((3 + Sqrt[5])/2)^(1/4)*x)/(1 + x^4)^(1/4)])/(1 - Sqrt[5]))/(2^(1/4)*Sqrt[5])","A",1
2404,1,170,193,0.1165295,"\int \frac{-2+x^4}{\sqrt[4]{1+x^4} \left(-1+x^4+x^8\right)} \, dx","Integrate[(-2 + x^4)/((1 + x^4)^(1/4)*(-1 + x^4 + x^8)),x]","\frac{\sqrt[4]{3+\sqrt{5}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3+\sqrt{5}}} x}{\sqrt[4]{x^4+1}}\right)+\sqrt[4]{3-\sqrt{5}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x}{\sqrt[4]{x^4+1}}\right)+\sqrt[4]{3+\sqrt{5}} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3+\sqrt{5}}} x}{\sqrt[4]{x^4+1}}\right)+\sqrt[4]{3-\sqrt{5}} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x}{\sqrt[4]{x^4+1}}\right)}{2 \sqrt[4]{2}}","\frac{1}{2} \sqrt{\frac{1}{2} \left(1+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}} x}{\sqrt[4]{x^4+1}}\right)+\frac{1}{2} \sqrt{\frac{1}{2} \left(\sqrt{5}-1\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{1}{2}+\frac{\sqrt{5}}{2}} x}{\sqrt[4]{x^4+1}}\right)+\frac{1}{2} \sqrt{\frac{1}{2} \left(1+\sqrt{5}\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}} x}{\sqrt[4]{x^4+1}}\right)+\frac{1}{2} \sqrt{\frac{1}{2} \left(\sqrt{5}-1\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{2}+\frac{\sqrt{5}}{2}} x}{\sqrt[4]{x^4+1}}\right)",1,"((3 + Sqrt[5])^(1/4)*ArcTan[((2/(3 + Sqrt[5]))^(1/4)*x)/(1 + x^4)^(1/4)] + (3 - Sqrt[5])^(1/4)*ArcTan[(((3 + Sqrt[5])/2)^(1/4)*x)/(1 + x^4)^(1/4)] + (3 + Sqrt[5])^(1/4)*ArcTanh[((2/(3 + Sqrt[5]))^(1/4)*x)/(1 + x^4)^(1/4)] + (3 - Sqrt[5])^(1/4)*ArcTanh[(((3 + Sqrt[5])/2)^(1/4)*x)/(1 + x^4)^(1/4)])/(2*2^(1/4))","A",1
2405,1,424,193,0.4440075,"\int \frac{\sqrt[4]{b x^3+a x^4} \left(-d+c x^8\right)}{x^8} \, dx","Integrate[((b*x^3 + a*x^4)^(1/4)*(-d + c*x^8))/x^8,x]","\frac{4 \sqrt[4]{x^3 (a x+b)} \left(-8192 a^{14} d x^6 \sqrt[4]{\frac{a x}{b}+1}+2048 a^{13} b d x^5 \sqrt[4]{\frac{a x}{b}+1}-1280 a^{12} b^2 d x^4 \sqrt[4]{\frac{a x}{b}+1}+960 a^{11} b^3 d x^3 \sqrt[4]{\frac{a x}{b}+1}-780 a^{10} b^4 d x^2 \sqrt[4]{\frac{a x}{b}+1}+663 a^9 b^5 d x \sqrt[4]{\frac{a x}{b}+1}+13923 a^8 b^6 d \sqrt[4]{\frac{a x}{b}+1}+1092048 a^6 b^8 c x^6 \sqrt[4]{\frac{a x}{b}+1}+4600038 a^5 b^9 c x^5 \sqrt[4]{\frac{a x}{b}+1}+8698470 a^4 b^{10} c x^4 \sqrt[4]{\frac{a x}{b}+1}+9313560 a^3 b^{11} c x^3 \sqrt[4]{\frac{a x}{b}+1}+5833620 a^2 b^{12} c x^2 \sqrt[4]{\frac{a x}{b}+1}-13923 b^{14} c \, _2F_1\left(-\frac{33}{4},-\frac{25}{4};-\frac{21}{4};-\frac{a x}{b}\right)+111384 b^{14} c \, _2F_1\left(-\frac{29}{4},-\frac{25}{4};-\frac{21}{4};-\frac{a x}{b}\right)-389844 b^{14} c \, _2F_1\left(-\frac{25}{4},-\frac{25}{4};-\frac{21}{4};-\frac{a x}{b}\right)+292383 b^{14} c \sqrt[4]{\frac{a x}{b}+1}+2002923 a b^{13} c x \sqrt[4]{\frac{a x}{b}+1}\right)}{348075 a^8 b^6 x^7 \sqrt[4]{\frac{a x}{b}+1}}","\frac{3 b^2 c \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)}{16 a^{7/4}}-\frac{3 b^2 c \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)}{16 a^{7/4}}+\frac{\sqrt[4]{a x^4+b x^3} \left(-262144 a^7 d x^6+65536 a^6 b d x^5-40960 a^5 b^2 d x^4+30720 a^4 b^3 d x^3-24960 a^3 b^4 d x^2+21216 a^2 b^5 d x+1392300 a b^6 c x^8+445536 a b^6 d+348075 b^7 c x^7\right)}{2784600 a b^6 x^7}",1,"(4*(x^3*(b + a*x))^(1/4)*(292383*b^14*c*(1 + (a*x)/b)^(1/4) + 13923*a^8*b^6*d*(1 + (a*x)/b)^(1/4) + 2002923*a*b^13*c*x*(1 + (a*x)/b)^(1/4) + 663*a^9*b^5*d*x*(1 + (a*x)/b)^(1/4) + 5833620*a^2*b^12*c*x^2*(1 + (a*x)/b)^(1/4) - 780*a^10*b^4*d*x^2*(1 + (a*x)/b)^(1/4) + 9313560*a^3*b^11*c*x^3*(1 + (a*x)/b)^(1/4) + 960*a^11*b^3*d*x^3*(1 + (a*x)/b)^(1/4) + 8698470*a^4*b^10*c*x^4*(1 + (a*x)/b)^(1/4) - 1280*a^12*b^2*d*x^4*(1 + (a*x)/b)^(1/4) + 4600038*a^5*b^9*c*x^5*(1 + (a*x)/b)^(1/4) + 2048*a^13*b*d*x^5*(1 + (a*x)/b)^(1/4) + 1092048*a^6*b^8*c*x^6*(1 + (a*x)/b)^(1/4) - 8192*a^14*d*x^6*(1 + (a*x)/b)^(1/4) - 13923*b^14*c*Hypergeometric2F1[-33/4, -25/4, -21/4, -((a*x)/b)] + 111384*b^14*c*Hypergeometric2F1[-29/4, -25/4, -21/4, -((a*x)/b)] - 389844*b^14*c*Hypergeometric2F1[-25/4, -25/4, -21/4, -((a*x)/b)]))/(348075*a^8*b^6*x^7*(1 + (a*x)/b)^(1/4))","C",1
2406,1,158,193,0.1470686,"\int \frac{x^4 \left(2+x^5\right)}{\sqrt{1+x^5} \left(-1-x^5+a x^{10}\right)} \, dx","Integrate[(x^4*(2 + x^5))/(Sqrt[1 + x^5]*(-1 - x^5 + a*x^10)),x]","\frac{\sqrt{2 a-\sqrt{4 a+1}+1} \left(\sqrt{4 a+1}+1\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x^5+1}}{\sqrt{2 a-\sqrt{4 a+1}+1}}\right)-\left(\sqrt{4 a+1}-1\right) \sqrt{2 a+\sqrt{4 a+1}+1} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x^5+1}}{\sqrt{2 a+\sqrt{4 a+1}+1}}\right)}{5 \sqrt{2} a^{3/2}}","\frac{\sqrt{2} \left(4 a+\sqrt{4 a+1}+1\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x^5+1}}{\sqrt{-2 a-\sqrt{4 a+1}-1}}\right)}{5 \sqrt{a} \sqrt{4 a+1} \sqrt{-2 a-\sqrt{4 a+1}-1}}+\frac{\sqrt{2} \left(-4 a+\sqrt{4 a+1}-1\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x^5+1}}{\sqrt{-2 a+\sqrt{4 a+1}-1}}\right)}{5 \sqrt{a} \sqrt{4 a+1} \sqrt{-2 a+\sqrt{4 a+1}-1}}",1,"(Sqrt[1 + 2*a - Sqrt[1 + 4*a]]*(1 + Sqrt[1 + 4*a])*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[1 + x^5])/Sqrt[1 + 2*a - Sqrt[1 + 4*a]]] - (-1 + Sqrt[1 + 4*a])*Sqrt[1 + 2*a + Sqrt[1 + 4*a]]*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[1 + x^5])/Sqrt[1 + 2*a + Sqrt[1 + 4*a]]])/(5*Sqrt[2]*a^(3/2))","A",1
2407,1,158,193,0.1893421,"\int \frac{x^4 \left(-2+x^5\right)}{\sqrt{-1+x^5} \left(1-x^5+a x^{10}\right)} \, dx","Integrate[(x^4*(-2 + x^5))/(Sqrt[-1 + x^5]*(1 - x^5 + a*x^10)),x]","\frac{\left(\sqrt{1-4 a}-1\right) \sqrt{-2 a+\sqrt{1-4 a}+1} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x^5-1}}{\sqrt{-2 a+\sqrt{1-4 a}+1}}\right)-\left(\sqrt{1-4 a}+1\right) \sqrt{-2 a-\sqrt{1-4 a}+1} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x^5-1}}{\sqrt{-2 a-\sqrt{1-4 a}+1}}\right)}{5 \sqrt{2} a^{3/2}}","\frac{\sqrt{2} \left(-4 a+\sqrt{1-4 a}+1\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x^5-1}}{\sqrt{2 a-\sqrt{1-4 a}-1}}\right)}{5 \sqrt{1-4 a} \sqrt{a} \sqrt{2 a-\sqrt{1-4 a}-1}}+\frac{\sqrt{2} \left(4 a+\sqrt{1-4 a}-1\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x^5-1}}{\sqrt{2 a+\sqrt{1-4 a}-1}}\right)}{5 \sqrt{1-4 a} \sqrt{a} \sqrt{2 a+\sqrt{1-4 a}-1}}",1,"(-((1 + Sqrt[1 - 4*a])*Sqrt[1 - Sqrt[1 - 4*a] - 2*a]*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[-1 + x^5])/Sqrt[1 - Sqrt[1 - 4*a] - 2*a]]) + (-1 + Sqrt[1 - 4*a])*Sqrt[1 + Sqrt[1 - 4*a] - 2*a]*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[-1 + x^5])/Sqrt[1 + Sqrt[1 - 4*a] - 2*a]])/(5*Sqrt[2]*a^(3/2))","A",1
2408,1,158,193,0.2131067,"\int \frac{x^4 \left(3+x^5\right)}{\sqrt{1+x^5} \left(-1+a-(1+2 a) x^5+a x^{10}\right)} \, dx","Integrate[(x^4*(3 + x^5))/(Sqrt[1 + x^5]*(-1 + a - (1 + 2*a)*x^5 + a*x^10)),x]","\frac{\sqrt{4 a-\sqrt{8 a+1}+1} \left(\sqrt{8 a+1}+1\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x^5+1}}{\sqrt{4 a-\sqrt{8 a+1}+1}}\right)-\left(\sqrt{8 a+1}-1\right) \sqrt{4 a+\sqrt{8 a+1}+1} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x^5+1}}{\sqrt{4 a+\sqrt{8 a+1}+1}}\right)}{10 \sqrt{2} a^{3/2}}","\frac{\sqrt{2} \left(8 a+\sqrt{8 a+1}+1\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x^5+1}}{\sqrt{-4 a-\sqrt{8 a+1}-1}}\right)}{5 \sqrt{a} \sqrt{8 a+1} \sqrt{-4 a-\sqrt{8 a+1}-1}}+\frac{\sqrt{2} \left(-8 a+\sqrt{8 a+1}-1\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x^5+1}}{\sqrt{-4 a+\sqrt{8 a+1}-1}}\right)}{5 \sqrt{a} \sqrt{8 a+1} \sqrt{-4 a+\sqrt{8 a+1}-1}}",1,"(Sqrt[1 + 4*a - Sqrt[1 + 8*a]]*(1 + Sqrt[1 + 8*a])*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[1 + x^5])/Sqrt[1 + 4*a - Sqrt[1 + 8*a]]] - (-1 + Sqrt[1 + 8*a])*Sqrt[1 + 4*a + Sqrt[1 + 8*a]]*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[1 + x^5])/Sqrt[1 + 4*a + Sqrt[1 + 8*a]]])/(10*Sqrt[2]*a^(3/2))","A",1
2409,0,0,193,0.9638026,"\int \frac{1}{x^2-\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","Integrate[(x^2 - Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]])^(-1),x]","\int \frac{1}{x^2-\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","4 a \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6 c-2 \text{$\#$1}^4 b+6 \text{$\#$1}^4 c^2-\text{$\#$1}^3 a^2+4 \text{$\#$1}^2 b c-4 \text{$\#$1}^2 c^3+\text{$\#$1} a^2 c+b^2-2 b c^2+c^4\&,\frac{\text{$\#$1} c \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-\text{$\#$1}^3 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)}{-8 \text{$\#$1}^7+24 \text{$\#$1}^5 c+8 \text{$\#$1}^3 b-24 \text{$\#$1}^3 c^2+3 \text{$\#$1}^2 a^2-8 \text{$\#$1} b c+8 \text{$\#$1} c^3-a^2 c}\&\right]",1,"Integrate[(x^2 - Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]])^(-1), x]","F",-1
2410,0,0,193,0.6761332,"\int \frac{1}{x^2-\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","Integrate[(x^2 - Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]])^(-1),x]","\int \frac{1}{x^2-\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","4 a \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6 c-2 \text{$\#$1}^4 b+6 \text{$\#$1}^4 c^2-\text{$\#$1}^3 a^2+4 \text{$\#$1}^2 b c-4 \text{$\#$1}^2 c^3+\text{$\#$1} a^2 c+b^2-2 b c^2+c^4\&,\frac{\text{$\#$1} c \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-\text{$\#$1}^3 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)}{-8 \text{$\#$1}^7+24 \text{$\#$1}^5 c+8 \text{$\#$1}^3 b-24 \text{$\#$1}^3 c^2+3 \text{$\#$1}^2 a^2-8 \text{$\#$1} b c+8 \text{$\#$1} c^3-a^2 c}\&\right]",1,"Integrate[(x^2 - Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]])^(-1), x]","F",-1
2411,1,174,193,0.2536137,"\int \frac{1}{\sqrt{-b+a^2 x^2} \left(c+\sqrt[4]{a x+\sqrt{-b+a^2 x^2}}\right)^{2/3}} \, dx","Integrate[1/(Sqrt[-b + a^2*x^2]*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(2/3)),x]","-\frac{2 \left(\log \left(\sqrt[3]{c} \sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}+\left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{2/3}+c^{2/3}\right)-2 \log \left(\sqrt[3]{c}-\sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}}{\sqrt[3]{c}}+1}{\sqrt{3}}\right)\right)}{a c^{2/3}}","\frac{4 \log \left(\sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}-\sqrt[3]{c}\right)}{a c^{2/3}}-\frac{2 \log \left(\sqrt[3]{c} \sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}+\left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{2/3}+c^{2/3}\right)}{a c^{2/3}}-\frac{4 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}}{\sqrt{3} \sqrt[3]{c}}+\frac{1}{\sqrt{3}}\right)}{a c^{2/3}}",1,"(-2*(2*Sqrt[3]*ArcTan[(1 + (2*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(1/3))/c^(1/3))/Sqrt[3]] - 2*Log[c^(1/3) - (c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(1/3)] + Log[c^(2/3) + c^(1/3)*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(1/3) + (c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(2/3)]))/(a*c^(2/3))","A",1
2412,1,127,193,0.1101192,"\int \frac{1}{\sqrt{-b+a^2 x^2} \sqrt[3]{c+\sqrt[4]{a x+\sqrt{-b+a^2 x^2}}}} \, dx","Integrate[1/(Sqrt[-b + a^2*x^2]*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(1/3)),x]","\frac{12 \log \left(\sqrt[3]{c}-\sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}\right)+8 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}}{\sqrt[3]{c}}+1}{\sqrt{3}}\right)-\log \left(\sqrt{a^2 x^2-b}+a x\right)}{2 a \sqrt[3]{c}}","-\frac{2 \log \left(\sqrt[3]{c} \sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}+\left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{2/3}+c^{2/3}\right)}{a \sqrt[3]{c}}+\frac{4 \log \left(\sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}-\sqrt[3]{c}\right)}{a \sqrt[3]{c}}+\frac{4 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}}{\sqrt{3} \sqrt[3]{c}}+\frac{1}{\sqrt{3}}\right)}{a \sqrt[3]{c}}",1,"(8*Sqrt[3]*ArcTan[(1 + (2*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(1/3))/c^(1/3))/Sqrt[3]] - Log[a*x + Sqrt[-b + a^2*x^2]] + 12*Log[c^(1/3) - (c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(1/3)])/(2*a*c^(1/3))","A",1
2413,1,126,194,0.1011718,"\int \frac{1}{\sqrt[3]{1-3 x^2} \left(-3+x^2\right)} \, dx","Integrate[1/((1 - 3*x^2)^(1/3)*(-3 + x^2)),x]","\frac{9 x F_1\left(\frac{1}{2};\frac{1}{3},1;\frac{3}{2};3 x^2,\frac{x^2}{3}\right)}{\sqrt[3]{1-3 x^2} \left(x^2-3\right) \left(2 x^2 \left(F_1\left(\frac{3}{2};\frac{1}{3},2;\frac{5}{2};3 x^2,\frac{x^2}{3}\right)+3 F_1\left(\frac{3}{2};\frac{4}{3},1;\frac{5}{2};3 x^2,\frac{x^2}{3}\right)\right)+9 F_1\left(\frac{1}{2};\frac{1}{3},1;\frac{3}{2};3 x^2,\frac{x^2}{3}\right)\right)}","-\frac{1}{8} \tan ^{-1}\left(\frac{-\frac{\sqrt[3]{1-3 x^2}}{\sqrt{3}}+x+\frac{1}{\sqrt{3}}}{\sqrt[3]{1-3 x^2}}\right)-\frac{1}{8} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{1-3 x^2}}{\sqrt{3}}+x-\frac{1}{\sqrt{3}}}{\sqrt[3]{1-3 x^2}}\right)-\frac{\tanh ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{1-3 x^2}+1}\right)}{4 \sqrt{3}}-\frac{\tanh ^{-1}\left(\frac{2 \sqrt{3} x \sqrt[3]{1-3 x^2}-2 \sqrt{3} x}{3 x^2+4 \left(1-3 x^2\right)^{2/3}-2 \sqrt[3]{1-3 x^2}+1}\right)}{8 \sqrt{3}}",1,"(9*x*AppellF1[1/2, 1/3, 1, 3/2, 3*x^2, x^2/3])/((1 - 3*x^2)^(1/3)*(-3 + x^2)*(9*AppellF1[1/2, 1/3, 1, 3/2, 3*x^2, x^2/3] + 2*x^2*(AppellF1[3/2, 1/3, 2, 5/2, 3*x^2, x^2/3] + 3*AppellF1[3/2, 4/3, 1, 5/2, 3*x^2, x^2/3])))","C",0
2414,1,69,194,0.1515539,"\int \frac{-a+x}{\sqrt[3]{x^2 (-a+x)} \left(a^2 d-2 a d x+(-1+d) x^2\right)} \, dx","Integrate[(-a + x)/((x^2*(-a + x))^(1/3)*(a^2*d - 2*a*d*x + (-1 + d)*x^2)),x]","-\frac{3 x \left(\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{x}{\sqrt{d} (a-x)}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{x}{\sqrt{d} (x-a)}\right)\right)}{2 a d \sqrt[3]{x^2 (x-a)}}","\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{x-2 \sqrt[6]{d} \sqrt[3]{x^3-a x^2}}\right)}{2 a d^{5/6}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[6]{d} \sqrt[3]{x^3-a x^2}+x}\right)}{2 a d^{5/6}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt[6]{d} \sqrt[3]{x^3-a x^2}}\right)}{a d^{5/6}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{d} \left(x^3-a x^2\right)^{2/3}+\frac{x^2}{\sqrt[6]{d}}}{x \sqrt[3]{x^3-a x^2}}\right)}{2 a d^{5/6}}",1,"(-3*x*(Hypergeometric2F1[1/3, 1, 4/3, x/(Sqrt[d]*(a - x))] + Hypergeometric2F1[1/3, 1, 4/3, x/(Sqrt[d]*(-a + x))]))/(2*a*d*(x^2*(-a + x))^(1/3))","C",1
2415,1,221,194,0.1673528,"\int \frac{b-a x^4+2 x^8}{\sqrt[4]{-b+a x^4} \left(b+3 a x^4\right)} \, dx","Integrate[(b - a*x^4 + 2*x^8)/((-b + a*x^4)^(1/4)*(b + 3*a*x^4)),x]","\frac{-6 a^2 \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)+12 \sqrt{2} a^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)-\left(6 a^2+b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)+2 \sqrt{2} \left(6 a^2+b\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)+6 \sqrt[4]{a} x \left(a x^4-b\right)^{3/4}-b \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)+2 \sqrt{2} b \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{36 a^{9/4}}","\frac{x \left(a x^4-b\right)^{3/4}}{6 a^2}+\frac{\left(-6 a^2-b\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{36 a^{9/4}}+\frac{\left(6 a^2+b\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{9 \sqrt{2} a^{9/4}}+\frac{\left(-6 a^2-b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{36 a^{9/4}}+\frac{\left(6 a^2+b\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{9 \sqrt{2} a^{9/4}}",1,"(6*a^(1/4)*x*(-b + a*x^4)^(3/4) - 6*a^2*ArcTan[(a^(1/4)*x)/(-b + a*x^4)^(1/4)] - b*ArcTan[(a^(1/4)*x)/(-b + a*x^4)^(1/4)] + 12*Sqrt[2]*a^2*ArcTan[(Sqrt[2]*a^(1/4)*x)/(-b + a*x^4)^(1/4)] + 2*Sqrt[2]*b*ArcTan[(Sqrt[2]*a^(1/4)*x)/(-b + a*x^4)^(1/4)] - (6*a^2 + b)*ArcTanh[(a^(1/4)*x)/(-b + a*x^4)^(1/4)] + 2*Sqrt[2]*(6*a^2 + b)*ArcTanh[(Sqrt[2]*a^(1/4)*x)/(-b + a*x^4)^(1/4)])/(36*a^(9/4))","A",1
2416,1,952,194,7.3899509,"\int \frac{d+c x^2}{\sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Integrate[(d + c*x^2)/Sqrt[a*x + Sqrt[b^2 + a^2*x^2]],x]","\frac{2 \sqrt{b^2+a^2 x^2} \left(\frac{21 a^2 d \left(7 b^4+3 a x \left(7 a x+6 \sqrt{b^2+a^2 x^2}\right) b^2+6 a^3 x^3 \left(a x+\sqrt{b^2+a^2 x^2}\right)\right) \left(b^2+2 a x \left(a x+\sqrt{b^2+a^2 x^2}\right)\right)^5}{b^{10}+a x \left(41 a x+9 \sqrt{b^2+a^2 x^2}\right) b^8+40 a^3 x^3 \left(7 a x+3 \sqrt{b^2+a^2 x^2}\right) b^6+16 a^5 x^5 \left(43 a x+27 \sqrt{b^2+a^2 x^2}\right) b^4+64 a^7 x^7 \left(11 a x+9 \sqrt{b^2+a^2 x^2}\right) b^2+256 a^9 x^9 \left(a x+\sqrt{b^2+a^2 x^2}\right)}+\frac{5 c \left(a x+\sqrt{b^2+a^2 x^2}\right)^2 \left(-8 b^8-7 a x \left(7 a x+4 \sqrt{b^2+a^2 x^2}\right) b^6+7 a^3 x^3 \left(a x-4 \sqrt{b^2+a^2 x^2}\right) b^4+28 a^5 x^5 \left(4 a x+3 \sqrt{b^2+a^2 x^2}\right) b^2+56 a^7 x^7 \left(a x+\sqrt{b^2+a^2 x^2}\right)\right) \left(b^2+2 a x \left(a x+\sqrt{b^2+a^2 x^2}\right)\right)^4}{b^{12}+a x \left(61 a x+11 \sqrt{b^2+a^2 x^2}\right) b^{10}+20 a^3 x^3 \left(31 a x+11 \sqrt{b^2+a^2 x^2}\right) b^8+112 a^5 x^5 \left(21 a x+11 \sqrt{b^2+a^2 x^2}\right) b^6+256 a^7 x^7 \left(16 a x+11 \sqrt{b^2+a^2 x^2}\right) b^4+256 a^9 x^9 \left(13 a x+11 \sqrt{b^2+a^2 x^2}\right) b^2+1024 a^{11} x^{11} \left(a x+\sqrt{b^2+a^2 x^2}\right)}-\frac{21 a^2 d \left(a x+\sqrt{b^2+a^2 x^2}\right)^2 \left(2 b^4+3 a x \left(2 a x+\sqrt{b^2+a^2 x^2}\right) b^2+6 a^3 x^3 \left(a x+\sqrt{b^2+a^2 x^2}\right)\right)}{b^2+a x \left(a x+\sqrt{b^2+a^2 x^2}\right)}+\frac{c \left(16 b^8+14 a x \left(7 a x+4 \sqrt{b^2+a^2 x^2}\right) b^6+7 a^3 x^3 \left(4 a x+11 \sqrt{b^2+a^2 x^2}\right) b^4-28 a^5 x^5 \left(11 a x+6 \sqrt{b^2+a^2 x^2}\right) b^2-280 a^7 x^7 \left(a x+\sqrt{b^2+a^2 x^2}\right)\right)}{b^2+a x \left(a x+\sqrt{b^2+a^2 x^2}\right)}\right)}{315 a^3 b^2 \left(a x+\sqrt{b^2+a^2 x^2}\right)^{5/2}}","\frac{2 \sqrt{a^2 x^2+b^2} \left(12 a^4 c x^5+60 a^4 d x^3-3 a^2 b^2 c x^3+25 a^2 b^2 d x-4 b^4 c x\right)}{15 a^2 \left(\sqrt{a^2 x^2+b^2}+a x\right)^{7/2}}+\frac{2 \left(84 a^6 c x^6+420 a^6 d x^4+21 a^4 b^2 c x^4+385 a^4 b^2 d x^2-49 a^2 b^4 c x^2+35 a^2 b^4 d-8 b^6 c\right)}{105 a^3 \left(\sqrt{a^2 x^2+b^2}+a x\right)^{7/2}}",1,"(2*Sqrt[b^2 + a^2*x^2]*((-21*a^2*d*(a*x + Sqrt[b^2 + a^2*x^2])^2*(2*b^4 + 6*a^3*x^3*(a*x + Sqrt[b^2 + a^2*x^2]) + 3*a*b^2*x*(2*a*x + Sqrt[b^2 + a^2*x^2])))/(b^2 + a*x*(a*x + Sqrt[b^2 + a^2*x^2])) + (c*(16*b^8 - 280*a^7*x^7*(a*x + Sqrt[b^2 + a^2*x^2]) + 14*a*b^6*x*(7*a*x + 4*Sqrt[b^2 + a^2*x^2]) - 28*a^5*b^2*x^5*(11*a*x + 6*Sqrt[b^2 + a^2*x^2]) + 7*a^3*b^4*x^3*(4*a*x + 11*Sqrt[b^2 + a^2*x^2])))/(b^2 + a*x*(a*x + Sqrt[b^2 + a^2*x^2])) + (5*c*(a*x + Sqrt[b^2 + a^2*x^2])^2*(b^2 + 2*a*x*(a*x + Sqrt[b^2 + a^2*x^2]))^4*(-8*b^8 + 7*a^3*b^4*x^3*(a*x - 4*Sqrt[b^2 + a^2*x^2]) + 56*a^7*x^7*(a*x + Sqrt[b^2 + a^2*x^2]) + 28*a^5*b^2*x^5*(4*a*x + 3*Sqrt[b^2 + a^2*x^2]) - 7*a*b^6*x*(7*a*x + 4*Sqrt[b^2 + a^2*x^2])))/(b^12 + 1024*a^11*x^11*(a*x + Sqrt[b^2 + a^2*x^2]) + 256*a^9*b^2*x^9*(13*a*x + 11*Sqrt[b^2 + a^2*x^2]) + 256*a^7*b^4*x^7*(16*a*x + 11*Sqrt[b^2 + a^2*x^2]) + 112*a^5*b^6*x^5*(21*a*x + 11*Sqrt[b^2 + a^2*x^2]) + 20*a^3*b^8*x^3*(31*a*x + 11*Sqrt[b^2 + a^2*x^2]) + a*b^10*x*(61*a*x + 11*Sqrt[b^2 + a^2*x^2])) + (21*a^2*d*(b^2 + 2*a*x*(a*x + Sqrt[b^2 + a^2*x^2]))^5*(7*b^4 + 6*a^3*x^3*(a*x + Sqrt[b^2 + a^2*x^2]) + 3*a*b^2*x*(7*a*x + 6*Sqrt[b^2 + a^2*x^2])))/(b^10 + 256*a^9*x^9*(a*x + Sqrt[b^2 + a^2*x^2]) + 40*a^3*b^6*x^3*(7*a*x + 3*Sqrt[b^2 + a^2*x^2]) + 64*a^7*b^2*x^7*(11*a*x + 9*Sqrt[b^2 + a^2*x^2]) + a*b^8*x*(41*a*x + 9*Sqrt[b^2 + a^2*x^2]) + 16*a^5*b^4*x^5*(43*a*x + 27*Sqrt[b^2 + a^2*x^2]))))/(315*a^3*b^2*(a*x + Sqrt[b^2 + a^2*x^2])^(5/2))","B",1
2417,1,323,195,0.3576895,"\int \frac{\sqrt[4]{b x^3+a x^4} \left(-c+d x^8\right)}{x^4} \, dx","Integrate[((b*x^3 + a*x^4)^(1/4)*(-c + d*x^8))/x^4,x]","\frac{4 \sqrt[4]{x^3 (a x+b)} \left(-4 a^{10} c x^2 \sqrt[4]{\frac{a x}{b}+1}+a^9 b c x \sqrt[4]{\frac{a x}{b}+1}+5 a^8 b^2 c \sqrt[4]{\frac{a x}{b}+1}+44 a^2 b^8 d x^2 \sqrt[4]{\frac{a x}{b}+1}-5 b^{10} d \, _2F_1\left(-\frac{33}{4},-\frac{9}{4};-\frac{5}{4};-\frac{a x}{b}\right)+40 b^{10} d \, _2F_1\left(-\frac{29}{4},-\frac{9}{4};-\frac{5}{4};-\frac{a x}{b}\right)-140 b^{10} d \, _2F_1\left(-\frac{25}{4},-\frac{9}{4};-\frac{5}{4};-\frac{a x}{b}\right)+280 b^{10} d \, _2F_1\left(-\frac{21}{4},-\frac{9}{4};-\frac{5}{4};-\frac{a x}{b}\right)-350 b^{10} d \, _2F_1\left(-\frac{17}{4},-\frac{9}{4};-\frac{5}{4};-\frac{a x}{b}\right)+280 b^{10} d \, _2F_1\left(-\frac{13}{4},-\frac{9}{4};-\frac{5}{4};-\frac{a x}{b}\right)-140 b^{10} d \, _2F_1\left(-\frac{9}{4},-\frac{9}{4};-\frac{5}{4};-\frac{a x}{b}\right)+35 b^{10} d \sqrt[4]{\frac{a x}{b}+1}+79 a b^9 d x \sqrt[4]{\frac{a x}{b}+1}\right)}{45 a^8 b^2 x^3 \sqrt[4]{\frac{a x}{b}+1}}","\frac{1463 b^6 d \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)}{32768 a^{23/4}}-\frac{1463 b^6 d \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)}{32768 a^{23/4}}+\frac{\sqrt[4]{a x^4+b x^3} \left(-262144 a^7 c x^2+65536 a^6 b c x+327680 a^5 b^2 c+122880 a^5 b^2 d x^8+6144 a^4 b^3 d x^7-7296 a^3 b^4 d x^6+9120 a^2 b^5 d x^5-12540 a b^6 d x^4+21945 b^7 d x^3\right)}{737280 a^5 b^2 x^3}",1,"(4*(x^3*(b + a*x))^(1/4)*(5*a^8*b^2*c*(1 + (a*x)/b)^(1/4) + 35*b^10*d*(1 + (a*x)/b)^(1/4) + a^9*b*c*x*(1 + (a*x)/b)^(1/4) + 79*a*b^9*d*x*(1 + (a*x)/b)^(1/4) - 4*a^10*c*x^2*(1 + (a*x)/b)^(1/4) + 44*a^2*b^8*d*x^2*(1 + (a*x)/b)^(1/4) - 5*b^10*d*Hypergeometric2F1[-33/4, -9/4, -5/4, -((a*x)/b)] + 40*b^10*d*Hypergeometric2F1[-29/4, -9/4, -5/4, -((a*x)/b)] - 140*b^10*d*Hypergeometric2F1[-25/4, -9/4, -5/4, -((a*x)/b)] + 280*b^10*d*Hypergeometric2F1[-21/4, -9/4, -5/4, -((a*x)/b)] - 350*b^10*d*Hypergeometric2F1[-17/4, -9/4, -5/4, -((a*x)/b)] + 280*b^10*d*Hypergeometric2F1[-13/4, -9/4, -5/4, -((a*x)/b)] - 140*b^10*d*Hypergeometric2F1[-9/4, -9/4, -5/4, -((a*x)/b)]))/(45*a^8*b^2*x^3*(1 + (a*x)/b)^(1/4))","C",1
2418,1,388,195,0.687301,"\int \frac{\left(b^2+a x^2\right)^{5/2}}{\sqrt{b+\sqrt{b^2+a x^2}}} \, dx","Integrate[(b^2 + a*x^2)^(5/2)/Sqrt[b + Sqrt[b^2 + a*x^2]],x]","\frac{2 \left(90 a^4 x^8 \sqrt{a x^2+b^2}+170 a^4 b x^8+718 a^3 b^3 x^6+470 a^3 b^2 x^6 \sqrt{a x^2+b^2}+990 a^2 b^5 x^4+990 a^2 b^4 x^4 \sqrt{a x^2+b^2}-1485 a b^7 x^2-1980 b^8 \sqrt{a x^2+b^2}-495 a b^6 x^2 \sqrt{a x^2+b^2}-1980 b^9\right)+495 \sqrt{2} b^{11/2} \sqrt{\sqrt{a x^2+b^2}-b} \left(4 b^2 \sqrt{a x^2+b^2}+a x^2 \sqrt{a x^2+b^2}+3 a b x^2+4 b^3\right) \tan ^{-1}\left(\frac{\sqrt{\sqrt{a x^2+b^2}-b}}{\sqrt{2} \sqrt{b}}\right)+990 b^6 \left(4 b^2 \sqrt{a x^2+b^2}+a x^2 \sqrt{a x^2+b^2}+3 a b x^2+4 b^3\right) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{b-\sqrt{b^2+a x^2}}{2 b}\right)}{990 a x \left(\sqrt{a x^2+b^2}+b\right)^{5/2}}","\frac{2 x \sqrt{a x^2+b^2} \left(45 a^2 x^4+155 a b^2 x^2+247 b^4\right)}{495 \sqrt{\sqrt{a x^2+b^2}+b}}-\frac{2 x \left(5 a^2 b x^4+31 a b^3 x^2+247 b^5\right)}{495 \sqrt{\sqrt{a x^2+b^2}+b}}+\frac{2 \sqrt{2} b^{11/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{2} \sqrt{b} \sqrt{\sqrt{a x^2+b^2}+b}}-\frac{\sqrt{\sqrt{a x^2+b^2}+b}}{\sqrt{2} \sqrt{b}}\right)}{\sqrt{a}}",1,"(2*(-1980*b^9 - 1485*a*b^7*x^2 + 990*a^2*b^5*x^4 + 718*a^3*b^3*x^6 + 170*a^4*b*x^8 - 1980*b^8*Sqrt[b^2 + a*x^2] - 495*a*b^6*x^2*Sqrt[b^2 + a*x^2] + 990*a^2*b^4*x^4*Sqrt[b^2 + a*x^2] + 470*a^3*b^2*x^6*Sqrt[b^2 + a*x^2] + 90*a^4*x^8*Sqrt[b^2 + a*x^2]) + 495*Sqrt[2]*b^(11/2)*Sqrt[-b + Sqrt[b^2 + a*x^2]]*(4*b^3 + 3*a*b*x^2 + 4*b^2*Sqrt[b^2 + a*x^2] + a*x^2*Sqrt[b^2 + a*x^2])*ArcTan[Sqrt[-b + Sqrt[b^2 + a*x^2]]/(Sqrt[2]*Sqrt[b])] + 990*b^6*(4*b^3 + 3*a*b*x^2 + 4*b^2*Sqrt[b^2 + a*x^2] + a*x^2*Sqrt[b^2 + a*x^2])*Hypergeometric2F1[-1/2, 1, 1/2, (b - Sqrt[b^2 + a*x^2])/(2*b)])/(990*a*x*(b + Sqrt[b^2 + a*x^2])^(5/2))","C",1
2419,0,0,195,1.9040383,"\int \sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]],x]","\int \sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}} \, dx","\frac{\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} (6 x+16)+\sqrt{x^2+1} \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1} (60 x-8)+6 \sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\left(60 x^2-8 x-75\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{105 \sqrt{\sqrt{x^2+1}+x}}-\tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)",1,"Integrate[Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]], x]","F",-1
2420,1,43491,195,6.646286,"\int \frac{\left(x^2 c_3-c_4\right) \left(x+3 x^2 c_3+3 c_4\right)}{x \sqrt{\frac{x c_0+x^2 c_3+c_4}{x c_1+x^2 c_3+c_4}} \left(-x^2+x^4 c_3{}^2+2 x^2 c_3 c_4+c_4{}^2\right)} \, dx","Integrate[((x^2*C[3] - C[4])*(x + 3*x^2*C[3] + 3*C[4]))/(x*Sqrt[(x*C[0] + x^2*C[3] + C[4])/(x*C[1] + x^2*C[3] + C[4])]*(-x^2 + x^4*C[3]^2 + 2*x^2*C[3]*C[4] + C[4]^2)),x]","\text{Result too large to show}","-\frac{2 \sqrt{-1+c_1} \tan ^{-1}\left(\frac{\sqrt{1-c_0} \sqrt{-1+c_1} \sqrt{\frac{c_3 x^2+c_0 x+c_4}{c_3 x^2+c_1 x+c_4}}}{-1+c_0}\right)}{\sqrt{1-c_0}}-\frac{4 \sqrt{1+c_1} \tan ^{-1}\left(\frac{\sqrt{-1-c_0} \sqrt{1+c_1} \sqrt{\frac{c_3 x^2+c_0 x+c_4}{c_3 x^2+c_1 x+c_4}}}{1+c_0}\right)}{\sqrt{-1-c_0}}+6 \tanh ^{-1}\left(\sqrt{\frac{c_3 x^2+c_0 x+c_4}{c_3 x^2+c_1 x+c_4}}\right)",1,"Result too large to show","B",0
2421,0,0,196,0.846578,"\int \frac{1+x^6}{\sqrt[3]{x+x^5} \left(-1+x^6\right)} \, dx","Integrate[(1 + x^6)/((x + x^5)^(1/3)*(-1 + x^6)),x]","\int \frac{1+x^6}{\sqrt[3]{x+x^5} \left(-1+x^6\right)} \, dx","-\frac{1}{3} \log \left(\sqrt[3]{x^5+x}+x\right)+\frac{\log \left(2^{2/3} \sqrt[3]{x^5+x}-2 x\right)}{6 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^5+x}-x}\right)}{\sqrt{3}}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^5+x}+x}\right)}{2 \sqrt[3]{2} \sqrt{3}}+\frac{1}{6} \log \left(-\sqrt[3]{x^5+x} x+\left(x^5+x\right)^{2/3}+x^2\right)-\frac{\log \left(2^{2/3} \sqrt[3]{x^5+x} x+\sqrt[3]{2} \left(x^5+x\right)^{2/3}+2 x^2\right)}{12 \sqrt[3]{2}}",1,"Integrate[(1 + x^6)/((x + x^5)^(1/3)*(-1 + x^6)), x]","F",-1
2422,1,208,196,0.2632999,"\int \frac{1}{x^2 \sqrt[3]{-4-8 x+11 x^2+17 x^3-20 x^4-7 x^5+16 x^6-7 x^7+x^8}} \, dx","Integrate[1/(x^2*(-4 - 8*x + 11*x^2 + 17*x^3 - 20*x^4 - 7*x^5 + 16*x^6 - 7*x^7 + x^8)^(1/3)),x]","\frac{(x-2)^{2/3} \left(x^2-x-1\right) \left(\sqrt[3]{2} \left(2 \log \left(2^{2/3} \sqrt[3]{x-2}+2\right)-\log \left(\sqrt[3]{2} (x-2)^{2/3}-2^{2/3} \sqrt[3]{x-2}+2\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{x-2}-1}{\sqrt{3}}\right)\right)-6 \text{RootSum}\left[\text{$\#$1}^6+3 \text{$\#$1}^3+1\&,\frac{\text{$\#$1} \log \left(\sqrt[3]{x-2}-\text{$\#$1}\right)}{2 \text{$\#$1}^3+3}\&\right]\right)}{6 \sqrt[3]{(x-2)^2 \left(x^2-x-1\right)^3}}-\frac{(x-2) \left(x^2-x-1\right)}{2 x \sqrt[3]{(x-2)^2 \left(x^2-x-1\right)^3}}","\frac{(x-2)^{2/3} \left(x^2-x-1\right) \left(-\text{RootSum}\left[\text{$\#$1}^6+3 \text{$\#$1}^3+1\&,\frac{\text{$\#$1} \log \left(\sqrt[3]{x-2}-\text{$\#$1}\right)}{2 \text{$\#$1}^3+3}\&\right]-\frac{\sqrt[3]{x-2}}{2 x}+\frac{1}{3} \sqrt[3]{2} \log \left(2^{2/3} \sqrt[3]{x-2}+2\right)-\frac{\log \left(-\sqrt[3]{2} (x-2)^{2/3}+2^{2/3} \sqrt[3]{x-2}-2\right)}{3\ 2^{2/3}}-\frac{\sqrt[3]{2} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2^{2/3} \sqrt[3]{x-2}}{\sqrt{3}}\right)}{\sqrt{3}}\right)}{\sqrt[3]{(x-2)^2 \left(x^2-x-1\right)^3}}",1,"-1/2*((-2 + x)*(-1 - x + x^2))/(x*((-2 + x)^2*(-1 - x + x^2)^3)^(1/3)) + ((-2 + x)^(2/3)*(-1 - x + x^2)*(2^(1/3)*(2*Sqrt[3]*ArcTan[(-1 + 2^(2/3)*(-2 + x)^(1/3))/Sqrt[3]] + 2*Log[2 + 2^(2/3)*(-2 + x)^(1/3)] - Log[2 - 2^(2/3)*(-2 + x)^(1/3) + 2^(1/3)*(-2 + x)^(2/3)]) - 6*RootSum[1 + 3*#1^3 + #1^6 & , (Log[(-2 + x)^(1/3) - #1]*#1)/(3 + 2*#1^3) & ]))/(6*((-2 + x)^2*(-1 - x + x^2)^3)^(1/3))","A",1
2423,1,199,196,0.5820097,"\int \frac{b^8+a^8 x^8}{\sqrt{b^4+a^4 x^4} \left(-b^8+a^8 x^8\right)} \, dx","Integrate[(b^8 + a^8*x^8)/(Sqrt[b^4 + a^4*x^4]*(-b^8 + a^8*x^8)),x]","\frac{x \left(-\frac{5 \left(a^4 b^4 x^4+b^8\right) F_1\left(\frac{1}{4};-\frac{1}{2},1;\frac{5}{4};-\frac{a^4 x^4}{b^4},\frac{a^4 x^4}{b^4}\right)}{\left(b^4-a^4 x^4\right) \left(5 b^4 F_1\left(\frac{1}{4};-\frac{1}{2},1;\frac{5}{4};-\frac{a^4 x^4}{b^4},\frac{a^4 x^4}{b^4}\right)+2 a^4 x^4 \left(2 F_1\left(\frac{5}{4};-\frac{1}{2},2;\frac{9}{4};-\frac{a^4 x^4}{b^4},\frac{a^4 x^4}{b^4}\right)+F_1\left(\frac{5}{4};\frac{1}{2},1;\frac{9}{4};-\frac{a^4 x^4}{b^4},\frac{a^4 x^4}{b^4}\right)\right)\right)}-1\right)}{2 \sqrt{a^4 x^4+b^4}}","-\frac{x}{2 \sqrt{a^4 x^4+b^4}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} a b x}{\sqrt{a^4 x^4+b^4}+a^2 x^2+b^2}\right)}{2 \sqrt{2} a b}+\frac{\tanh ^{-1}\left(\frac{\sqrt{6-4 \sqrt{2}} a b x}{\sqrt{a^4 x^4+b^4}+a^2 x^2+b^2}\right)}{4 \sqrt{2} a b}-\frac{\tanh ^{-1}\left(\frac{\sqrt{6+4 \sqrt{2}} a b x}{\sqrt{a^4 x^4+b^4}+a^2 x^2+b^2}\right)}{4 \sqrt{2} a b}",1,"(x*(-1 - (5*(b^8 + a^4*b^4*x^4)*AppellF1[1/4, -1/2, 1, 5/4, -((a^4*x^4)/b^4), (a^4*x^4)/b^4])/((b^4 - a^4*x^4)*(5*b^4*AppellF1[1/4, -1/2, 1, 5/4, -((a^4*x^4)/b^4), (a^4*x^4)/b^4] + 2*a^4*x^4*(2*AppellF1[5/4, -1/2, 2, 9/4, -((a^4*x^4)/b^4), (a^4*x^4)/b^4] + AppellF1[5/4, 1/2, 1, 9/4, -((a^4*x^4)/b^4), (a^4*x^4)/b^4])))))/(2*Sqrt[b^4 + a^4*x^4])","C",0
2424,1,254,196,0.3880108,"\int \frac{\sqrt{x+\sqrt{1+x}}}{x-\sqrt{1+x}} \, dx","Integrate[Sqrt[x + Sqrt[1 + x]]/(x - Sqrt[1 + x]),x]","2 \sqrt{x+\sqrt{x+1}}+\sqrt{\sqrt{5}-1} \tan ^{-1}\left(\frac{2 \left(\sqrt{5}-2\right) \sqrt{x+1}+\sqrt{5}+3}{4 \sqrt{\sqrt{5}-1} \sqrt{x+\sqrt{x+1}}}\right)-\sqrt{\frac{1}{\sqrt{5}}-\frac{1}{5}} \tan ^{-1}\left(\frac{2 \left(\sqrt{5}-2\right) \sqrt{x+1}+\sqrt{5}+3}{4 \sqrt{\sqrt{5}-1} \sqrt{x+\sqrt{x+1}}}\right)+3 \tanh ^{-1}\left(\frac{2 \sqrt{x+1}+1}{2 \sqrt{x+\sqrt{x+1}}}\right)+\frac{1}{5} \sqrt{1+\sqrt{5}} \left(5+\sqrt{5}\right) \tanh ^{-1}\left(\frac{-2 \left(2+\sqrt{5}\right) \sqrt{x+1}-\sqrt{5}+3}{4 \sqrt{1+\sqrt{5}} \sqrt{x+\sqrt{x+1}}}\right)","-4 \text{RootSum}\left[\text{$\#$1}^4-8 \text{$\#$1}^3+6 \text{$\#$1}^2-40 \text{$\#$1}+25\&,\frac{\text{$\#$1}^2 \log \left(-\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)+2 \text{$\#$1} \log \left(-\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)+5 \log \left(-\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)}{\text{$\#$1}^3-6 \text{$\#$1}^2+3 \text{$\#$1}-10}\&\right]+2 \sqrt{x+\sqrt{x+1}}-3 \log \left(2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)",1,"2*Sqrt[x + Sqrt[1 + x]] - Sqrt[-1/5 + 1/Sqrt[5]]*ArcTan[(3 + Sqrt[5] + 2*(-2 + Sqrt[5])*Sqrt[1 + x])/(4*Sqrt[-1 + Sqrt[5]]*Sqrt[x + Sqrt[1 + x]])] + Sqrt[-1 + Sqrt[5]]*ArcTan[(3 + Sqrt[5] + 2*(-2 + Sqrt[5])*Sqrt[1 + x])/(4*Sqrt[-1 + Sqrt[5]]*Sqrt[x + Sqrt[1 + x]])] + 3*ArcTanh[(1 + 2*Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])] + (Sqrt[1 + Sqrt[5]]*(5 + Sqrt[5])*ArcTanh[(3 - Sqrt[5] - 2*(2 + Sqrt[5])*Sqrt[1 + x])/(4*Sqrt[1 + Sqrt[5]]*Sqrt[x + Sqrt[1 + x]])])/5","A",1
2425,1,254,196,0.1434536,"\int \frac{\sqrt{x+\sqrt{1+x}}}{x-\sqrt{1+x}} \, dx","Integrate[Sqrt[x + Sqrt[1 + x]]/(x - Sqrt[1 + x]),x]","2 \sqrt{x+\sqrt{x+1}}+\sqrt{\sqrt{5}-1} \tan ^{-1}\left(\frac{2 \left(\sqrt{5}-2\right) \sqrt{x+1}+\sqrt{5}+3}{4 \sqrt{\sqrt{5}-1} \sqrt{x+\sqrt{x+1}}}\right)-\sqrt{\frac{1}{\sqrt{5}}-\frac{1}{5}} \tan ^{-1}\left(\frac{2 \left(\sqrt{5}-2\right) \sqrt{x+1}+\sqrt{5}+3}{4 \sqrt{\sqrt{5}-1} \sqrt{x+\sqrt{x+1}}}\right)+3 \tanh ^{-1}\left(\frac{2 \sqrt{x+1}+1}{2 \sqrt{x+\sqrt{x+1}}}\right)+\frac{1}{5} \sqrt{1+\sqrt{5}} \left(5+\sqrt{5}\right) \tanh ^{-1}\left(\frac{-2 \left(2+\sqrt{5}\right) \sqrt{x+1}-\sqrt{5}+3}{4 \sqrt{1+\sqrt{5}} \sqrt{x+\sqrt{x+1}}}\right)","-4 \text{RootSum}\left[\text{$\#$1}^4-8 \text{$\#$1}^3+6 \text{$\#$1}^2-40 \text{$\#$1}+25\&,\frac{\text{$\#$1}^2 \log \left(-\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)+2 \text{$\#$1} \log \left(-\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)+5 \log \left(-\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)}{\text{$\#$1}^3-6 \text{$\#$1}^2+3 \text{$\#$1}-10}\&\right]+2 \sqrt{x+\sqrt{x+1}}-3 \log \left(2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)",1,"2*Sqrt[x + Sqrt[1 + x]] - Sqrt[-1/5 + 1/Sqrt[5]]*ArcTan[(3 + Sqrt[5] + 2*(-2 + Sqrt[5])*Sqrt[1 + x])/(4*Sqrt[-1 + Sqrt[5]]*Sqrt[x + Sqrt[1 + x]])] + Sqrt[-1 + Sqrt[5]]*ArcTan[(3 + Sqrt[5] + 2*(-2 + Sqrt[5])*Sqrt[1 + x])/(4*Sqrt[-1 + Sqrt[5]]*Sqrt[x + Sqrt[1 + x]])] + 3*ArcTanh[(1 + 2*Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])] + (Sqrt[1 + Sqrt[5]]*(5 + Sqrt[5])*ArcTanh[(3 - Sqrt[5] - 2*(2 + Sqrt[5])*Sqrt[1 + x])/(4*Sqrt[1 + Sqrt[5]]*Sqrt[x + Sqrt[1 + x]])])/5","A",1
2426,1,190,196,0.5178344,"\int \frac{\left(d+c x^2\right) \sqrt{a x+\sqrt{b^2+a^2 x^2}}}{-d+c x^2} \, dx","Integrate[((d + c*x^2)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(-d + c*x^2),x]","a d \text{RootSum}\left[\text{$\#$1}^8 c-4 \text{$\#$1}^4 a^2 d-2 \text{$\#$1}^4 b^2 c+b^4 c\&,\frac{\text{$\#$1}^4 \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)+b^2 \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)}{\text{$\#$1}^5 c-2 \text{$\#$1} a^2 d-\text{$\#$1} b^2 c}\&\right]-\frac{2 \left(b^2-a x \left(\sqrt{a^2 x^2+b^2}+a x\right)\right)}{3 a \sqrt{\sqrt{a^2 x^2+b^2}+a x}}","a d \text{RootSum}\left[\text{$\#$1}^8 c-4 \text{$\#$1}^4 a^2 d-2 \text{$\#$1}^4 b^2 c+b^4 c\&,\frac{\text{$\#$1}^4 \left(-\log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)\right)-b^2 \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)}{\text{$\#$1}^5 (-c)+2 \text{$\#$1} a^2 d+\text{$\#$1} b^2 c}\&\right]-\frac{b^2}{a \sqrt{\sqrt{a^2 x^2+b^2}+a x}}+\frac{\left(\sqrt{a^2 x^2+b^2}+a x\right)^{3/2}}{3 a}",1,"(-2*(b^2 - a*x*(a*x + Sqrt[b^2 + a^2*x^2])))/(3*a*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]) + a*d*RootSum[b^4*c - 2*b^2*c*#1^4 - 4*a^2*d*#1^4 + c*#1^8 & , (b^2*Log[Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] - #1] + Log[Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] - #1]*#1^4)/(-(b^2*c*#1) - 2*a^2*d*#1 + c*#1^5) & ]","A",1
2427,1,190,196,0.1288631,"\int \frac{\left(d+c x^2\right) \sqrt{a x+\sqrt{b^2+a^2 x^2}}}{-d+c x^2} \, dx","Integrate[((d + c*x^2)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(-d + c*x^2),x]","a d \text{RootSum}\left[\text{$\#$1}^8 c-4 \text{$\#$1}^4 a^2 d-2 \text{$\#$1}^4 b^2 c+b^4 c\&,\frac{\text{$\#$1}^4 \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)+b^2 \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)}{\text{$\#$1}^5 c-2 \text{$\#$1} a^2 d-\text{$\#$1} b^2 c}\&\right]-\frac{2 \left(b^2-a x \left(\sqrt{a^2 x^2+b^2}+a x\right)\right)}{3 a \sqrt{\sqrt{a^2 x^2+b^2}+a x}}","a d \text{RootSum}\left[\text{$\#$1}^8 c-4 \text{$\#$1}^4 a^2 d-2 \text{$\#$1}^4 b^2 c+b^4 c\&,\frac{\text{$\#$1}^4 \left(-\log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)\right)-b^2 \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)}{\text{$\#$1}^5 (-c)+2 \text{$\#$1} a^2 d+\text{$\#$1} b^2 c}\&\right]-\frac{b^2}{a \sqrt{\sqrt{a^2 x^2+b^2}+a x}}+\frac{\left(\sqrt{a^2 x^2+b^2}+a x\right)^{3/2}}{3 a}",1,"(-2*(b^2 - a*x*(a*x + Sqrt[b^2 + a^2*x^2])))/(3*a*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]) + a*d*RootSum[b^4*c - 2*b^2*c*#1^4 - 4*a^2*d*#1^4 + c*#1^8 & , (b^2*Log[Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] - #1] + Log[Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] - #1]*#1^4)/(-(b^2*c*#1) - 2*a^2*d*#1 + c*#1^5) & ]","A",1
2428,1,384,196,11.6636004,"\int \frac{\sqrt{-\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}}{x \sqrt{a x^2+b x \sqrt{-\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}}} \, dx","Integrate[Sqrt[-(a/b^2) + (a^2*x^2)/b^2]/(x*Sqrt[a*x^2 + b*x*Sqrt[-(a/b^2) + (a^2*x^2)/b^2]]),x]","\frac{\sqrt{x \left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right)} \left(-8 a \left(10 a^2 x^4+2 a x^2 \left(5 b x \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}-6\right)-7 b x \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+2\right)-5 \sqrt{2} \sqrt{a x \left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right)} \left(2 a^2 x^3+2 a x \left(b x \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}-1\right)-b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}\right) \tanh ^{-1}\left(\frac{\sqrt{a x \left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right)}}{\sqrt{2} a x}\right)\right)+9 \sqrt{2} a^{3/2} x \left(4 a^2 x^4+a x^2 \left(4 b x \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}-5\right)-3 b x \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+1\right) \sinh ^{-1}\left(\frac{b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x}{\sqrt{a}}\right)}{8 b x \left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right)^2 \left(b x \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x^2-1\right)}","\frac{\left(-a x^2-2\right) \sqrt{b x \sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}}+a x^2}}{b x}+\sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}} \sqrt{b x \sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}}+a x^2}-\frac{\sqrt{a} \log \left(b \left(-\sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}}\right)+\sqrt{2} \sqrt{a} \sqrt{b x \sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}}+a x^2}-a x\right)}{\sqrt{2} b}",1,"(9*Sqrt[2]*a^(3/2)*x*(1 + 4*a^2*x^4 - 3*b*x*Sqrt[(a*(-1 + a*x^2))/b^2] + a*x^2*(-5 + 4*b*x*Sqrt[(a*(-1 + a*x^2))/b^2]))*ArcSinh[(a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2])/Sqrt[a]] + Sqrt[x*(a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2])]*(-8*a*(2 + 10*a^2*x^4 - 7*b*x*Sqrt[(a*(-1 + a*x^2))/b^2] + 2*a*x^2*(-6 + 5*b*x*Sqrt[(a*(-1 + a*x^2))/b^2])) - 5*Sqrt[2]*Sqrt[a*x*(a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2])]*(2*a^2*x^3 - b*Sqrt[(a*(-1 + a*x^2))/b^2] + 2*a*x*(-1 + b*x*Sqrt[(a*(-1 + a*x^2))/b^2]))*ArcTanh[Sqrt[a*x*(a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2])]/(Sqrt[2]*a*x)]))/(8*b*x*(a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2])^2*(-1 + a*x^2 + b*x*Sqrt[(a*(-1 + a*x^2))/b^2]))","A",1
2429,0,0,196,3.6355407,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{1+\sqrt{1+x}} \sqrt{1+\sqrt{1+\sqrt{1+x}}}} \, dx","Integrate[(-1 + x^2)/((1 + x^2)*Sqrt[1 + Sqrt[1 + x]]*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]),x]","\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{1+\sqrt{1+x}} \sqrt{1+\sqrt{1+\sqrt{1+x}}}} \, dx","-\text{RootSum}\left[\text{$\#$1}^{16}-8 \text{$\#$1}^{14}+24 \text{$\#$1}^{12}-32 \text{$\#$1}^{10}+14 \text{$\#$1}^8+8 \text{$\#$1}^6-8 \text{$\#$1}^4+2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x+1}+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^{11}-5 \text{$\#$1}^9+8 \text{$\#$1}^7-4 \text{$\#$1}^5-\text{$\#$1}^3+\text{$\#$1}}\&\right]+\frac{8}{5} \sqrt{x+1} \sqrt{\sqrt{\sqrt{x+1}+1}+1}-\frac{32}{15} \sqrt{\sqrt{x+1}+1} \sqrt{\sqrt{\sqrt{x+1}+1}+1}-\frac{32}{15} \sqrt{\sqrt{\sqrt{x+1}+1}+1}",1,"Integrate[(-1 + x^2)/((1 + x^2)*Sqrt[1 + Sqrt[1 + x]]*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]), x]","F",-1
2430,0,0,196,1.0386658,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{1+\sqrt{1+x}} \sqrt{1+\sqrt{1+\sqrt{1+x}}}} \, dx","Integrate[(-1 + x^2)/((1 + x^2)*Sqrt[1 + Sqrt[1 + x]]*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]),x]","\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{1+\sqrt{1+x}} \sqrt{1+\sqrt{1+\sqrt{1+x}}}} \, dx","-\text{RootSum}\left[\text{$\#$1}^{16}-8 \text{$\#$1}^{14}+24 \text{$\#$1}^{12}-32 \text{$\#$1}^{10}+14 \text{$\#$1}^8+8 \text{$\#$1}^6-8 \text{$\#$1}^4+2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x+1}+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^{11}-5 \text{$\#$1}^9+8 \text{$\#$1}^7-4 \text{$\#$1}^5-\text{$\#$1}^3+\text{$\#$1}}\&\right]+\frac{8}{5} \sqrt{x+1} \sqrt{\sqrt{\sqrt{x+1}+1}+1}-\frac{32}{15} \sqrt{\sqrt{x+1}+1} \sqrt{\sqrt{\sqrt{x+1}+1}+1}-\frac{32}{15} \sqrt{\sqrt{\sqrt{x+1}+1}+1}",1,"Integrate[(-1 + x^2)/((1 + x^2)*Sqrt[1 + Sqrt[1 + x]]*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]), x]","F",-1
2431,1,179,196,0.2682583,"\int \sqrt{1+\sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]],x]","\frac{1}{120} \left(48 \left(\sqrt{\sqrt{x^2+1}+x}+1\right)^{5/2}-80 \left(\sqrt{\sqrt{x^2+1}+x}+1\right)^{3/2}-\frac{30 \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{\sqrt{\sqrt{x^2+1}+x}}-\frac{60 \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{\sqrt{x^2+1}+x}-15 \log \left(1-\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+15 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}+1\right)\right)","\frac{\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} (8 x-15)+\sqrt{x^2+1} \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1} (48 x-16)+8 \sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\left(48 x^2-16 x-6\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{60 \sqrt{x^2+1}+60 x}+\frac{1}{4} \tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)",1,"((-60*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(x + Sqrt[1 + x^2]) - (30*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/Sqrt[x + Sqrt[1 + x^2]] - 80*(1 + Sqrt[x + Sqrt[1 + x^2]])^(3/2) + 48*(1 + Sqrt[x + Sqrt[1 + x^2]])^(5/2) - 15*Log[1 - Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]] + 15*Log[1 + Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]])/120","A",1
2432,0,0,197,1.223357,"\int \frac{2+3 x}{\sqrt[3]{4+3 x^2} \left(-12+52 x+9 x^2\right)} \, dx","Integrate[(2 + 3*x)/((4 + 3*x^2)^(1/3)*(-12 + 52*x + 9*x^2)),x]","\int \frac{2+3 x}{\sqrt[3]{4+3 x^2} \left(-12+52 x+9 x^2\right)} \, dx","\frac{\log \left(14 \sqrt[3]{3 x^2+4}+3 \sqrt[3]{14} x-10 \sqrt[3]{14}\right)}{14 \sqrt[3]{14}}-\frac{\log \left(9\ 14^{2/3} x^2+196 \left(3 x^2+4\right)^{2/3}+\left(140 \sqrt[3]{14}-42 \sqrt[3]{14} x\right) \sqrt[3]{3 x^2+4}-60\ 14^{2/3} x+100\ 14^{2/3}\right)}{28 \sqrt[3]{14}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{3 x^2+4}}{\sqrt{3}}-\frac{\sqrt[3]{2} \sqrt{3} x}{7^{2/3}}+\frac{10 \sqrt[3]{2}}{\sqrt{3} 7^{2/3}}}{\sqrt[3]{3 x^2+4}}\right)}{14 \sqrt[3]{14}}",1,"Integrate[(2 + 3*x)/((4 + 3*x^2)^(1/3)*(-12 + 52*x + 9*x^2)), x]","F",-1
2433,1,162,197,0.6383758,"\int \left(c+b x+a x^2\right)^{5/2} \, dx","Integrate[(c + b*x + a*x^2)^(5/2),x]","\frac{\sqrt{x (a x+b)+c} \left(2 (2 a x+b) \left(32 a^2 b x \left(8 a x^2+13 c\right)+16 a^2 \left(8 a^2 x^4+26 a c x^2+33 c^2\right)-40 a b^3 x+8 a b^2 \left(11 a x^2-20 c\right)+15 b^4\right)+\frac{15 \left(b^2-4 a c\right)^{5/2} \sin ^{-1}\left(\frac{2 a x+b}{\sqrt{b^2-4 a c}}\right)}{\sqrt{\frac{a (x (a x+b)+c)}{4 a c-b^2}}}\right)}{3072 a^3}","\frac{\sqrt{a x^2+b x+c} \left(256 a^5 x^5+640 a^4 b x^4+832 a^4 c x^3+432 a^3 b^2 x^3+1248 a^3 b c x^2+1056 a^3 c^2 x+8 a^2 b^3 x^2+96 a^2 b^2 c x+528 a^2 b c^2-10 a b^4 x-160 a b^3 c+15 b^5\right)}{1536 a^3}-\frac{5 \left(64 a^3 c^3-48 a^2 b^2 c^2+12 a b^4 c-b^6\right) \log \left(-2 \sqrt{a} \sqrt{a x^2+b x+c}+2 a x+b\right)}{1024 a^{7/2}}",1,"(Sqrt[c + x*(b + a*x)]*(2*(b + 2*a*x)*(15*b^4 - 40*a*b^3*x + 32*a^2*b*x*(13*c + 8*a*x^2) + 8*a*b^2*(-20*c + 11*a*x^2) + 16*a^2*(33*c^2 + 26*a*c*x^2 + 8*a^2*x^4)) + (15*(b^2 - 4*a*c)^(5/2)*ArcSin[(b + 2*a*x)/Sqrt[b^2 - 4*a*c]])/Sqrt[(a*(c + x*(b + a*x)))/(-b^2 + 4*a*c)]))/(3072*a^3)","A",1
2434,0,0,197,7.2150123,"\int \frac{1-x^4+x^8}{x^2 \left(-1+x^4\right)^{3/4} \left(-1-x^4+x^8\right)} \, dx","Integrate[(1 - x^4 + x^8)/(x^2*(-1 + x^4)^(3/4)*(-1 - x^4 + x^8)),x]","\int \frac{1-x^4+x^8}{x^2 \left(-1+x^4\right)^{3/4} \left(-1-x^4+x^8\right)} \, dx","-\frac{\sqrt[4]{x^4-1}}{x}+\sqrt{\frac{1}{10} \left(\sqrt{5}-1\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}} x}{\sqrt[4]{x^4-1}}\right)-\sqrt{\frac{1}{10} \left(1+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{1}{2}+\frac{\sqrt{5}}{2}} x}{\sqrt[4]{x^4-1}}\right)-\sqrt{\frac{1}{10} \left(\sqrt{5}-1\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}} x}{\sqrt[4]{x^4-1}}\right)+\sqrt{\frac{1}{10} \left(1+\sqrt{5}\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{2}+\frac{\sqrt{5}}{2}} x}{\sqrt[4]{x^4-1}}\right)",1,"Integrate[(1 - x^4 + x^8)/(x^2*(-1 + x^4)^(3/4)*(-1 - x^4 + x^8)), x]","F",-1
2435,1,191,197,0.5365921,"\int \frac{\left(-d+c x^2\right) \sqrt{a x+\sqrt{b^2+a^2 x^2}}}{d+c x^2} \, dx","Integrate[((-d + c*x^2)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(d + c*x^2),x]","-a d \text{RootSum}\left[\text{$\#$1}^8 c+4 \text{$\#$1}^4 a^2 d-2 \text{$\#$1}^4 b^2 c+b^4 c\&,\frac{\text{$\#$1}^4 \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)+b^2 \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)}{\text{$\#$1}^5 c+2 \text{$\#$1} a^2 d-\text{$\#$1} b^2 c}\&\right]-\frac{2 \left(b^2-a x \left(\sqrt{a^2 x^2+b^2}+a x\right)\right)}{3 a \sqrt{\sqrt{a^2 x^2+b^2}+a x}}","-a d \text{RootSum}\left[\text{$\#$1}^8 c+4 \text{$\#$1}^4 a^2 d-2 \text{$\#$1}^4 b^2 c+b^4 c\&,\frac{\text{$\#$1}^4 \left(-\log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)\right)-b^2 \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)}{\text{$\#$1}^5 (-c)-2 \text{$\#$1} a^2 d+\text{$\#$1} b^2 c}\&\right]-\frac{b^2}{a \sqrt{\sqrt{a^2 x^2+b^2}+a x}}+\frac{\left(\sqrt{a^2 x^2+b^2}+a x\right)^{3/2}}{3 a}",1,"(-2*(b^2 - a*x*(a*x + Sqrt[b^2 + a^2*x^2])))/(3*a*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]) - a*d*RootSum[b^4*c - 2*b^2*c*#1^4 + 4*a^2*d*#1^4 + c*#1^8 & , (b^2*Log[Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] - #1] + Log[Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] - #1]*#1^4)/(-(b^2*c*#1) + 2*a^2*d*#1 + c*#1^5) & ]","A",1
2436,1,191,197,0.1287746,"\int \frac{\left(-d+c x^2\right) \sqrt{a x+\sqrt{b^2+a^2 x^2}}}{d+c x^2} \, dx","Integrate[((-d + c*x^2)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(d + c*x^2),x]","-a d \text{RootSum}\left[\text{$\#$1}^8 c+4 \text{$\#$1}^4 a^2 d-2 \text{$\#$1}^4 b^2 c+b^4 c\&,\frac{\text{$\#$1}^4 \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)+b^2 \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)}{\text{$\#$1}^5 c+2 \text{$\#$1} a^2 d-\text{$\#$1} b^2 c}\&\right]-\frac{2 \left(b^2-a x \left(\sqrt{a^2 x^2+b^2}+a x\right)\right)}{3 a \sqrt{\sqrt{a^2 x^2+b^2}+a x}}","-a d \text{RootSum}\left[\text{$\#$1}^8 c+4 \text{$\#$1}^4 a^2 d-2 \text{$\#$1}^4 b^2 c+b^4 c\&,\frac{\text{$\#$1}^4 \left(-\log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)\right)-b^2 \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)}{\text{$\#$1}^5 (-c)-2 \text{$\#$1} a^2 d+\text{$\#$1} b^2 c}\&\right]-\frac{b^2}{a \sqrt{\sqrt{a^2 x^2+b^2}+a x}}+\frac{\left(\sqrt{a^2 x^2+b^2}+a x\right)^{3/2}}{3 a}",1,"(-2*(b^2 - a*x*(a*x + Sqrt[b^2 + a^2*x^2])))/(3*a*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]) - a*d*RootSum[b^4*c - 2*b^2*c*#1^4 + 4*a^2*d*#1^4 + c*#1^8 & , (b^2*Log[Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] - #1] + Log[Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] - #1]*#1^4)/(-(b^2*c*#1) + 2*a^2*d*#1 + c*#1^5) & ]","A",1
2437,0,0,197,2.9695239,"\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/Sqrt[x + Sqrt[1 + x^2]],x]","\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\sqrt{x+\sqrt{1+x^2}}} \, dx","\frac{\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} (16 x-2)+\sqrt{x^2+1} \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1} (32 x+3)+16 \sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\left(32 x^2+3 x+8\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{24 \left(\sqrt{x^2+1}+x\right)^{3/2}}-\frac{1}{8} \tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)",1,"Integrate[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/Sqrt[x + Sqrt[1 + x^2]], x]","F",-1
2438,1,111,198,0.0562651,"\int \frac{1}{x \sqrt[3]{4-6 x+3 x^2}} \, dx","Integrate[1/(x*(4 - 6*x + 3*x^2)^(1/3)),x]","-\frac{\sqrt[3]{\frac{3 x+i \sqrt{3}-3}{x}} \sqrt[3]{\frac{9 x-3 i \sqrt{3}-9}{x}} F_1\left(\frac{2}{3};\frac{1}{3},\frac{1}{3};\frac{5}{3};\frac{3-i \sqrt{3}}{3 x},\frac{3+i \sqrt{3}}{3 x}\right)}{2 \sqrt[3]{3 x^2-6 x+4}}","\frac{\log \left(2 \sqrt[3]{3 x^2-6 x+4}+2^{2/3} x-2\ 2^{2/3}\right)}{3\ 2^{2/3}}-\frac{\log \left(-\sqrt[3]{2} x^2-2 \left(3 x^2-6 x+4\right)^{2/3}+\left(2^{2/3} x-2\ 2^{2/3}\right) \sqrt[3]{3 x^2-6 x+4}+4 \sqrt[3]{2} x-4 \sqrt[3]{2}\right)}{6\ 2^{2/3}}-\frac{\tan ^{-1}\left(\frac{\frac{\sqrt[3]{3 x^2-6 x+4}}{\sqrt{3}}-\frac{2^{2/3} x}{\sqrt{3}}+\frac{2\ 2^{2/3}}{\sqrt{3}}}{\sqrt[3]{3 x^2-6 x+4}}\right)}{2^{2/3} \sqrt{3}}",1,"-1/2*(((-3 + I*Sqrt[3] + 3*x)/x)^(1/3)*((-9 - (3*I)*Sqrt[3] + 9*x)/x)^(1/3)*AppellF1[2/3, 1/3, 1/3, 5/3, (3 - I*Sqrt[3])/(3*x), (3 + I*Sqrt[3])/(3*x)])/(4 - 6*x + 3*x^2)^(1/3)","C",0
2439,1,183,198,0.1686556,"\int \frac{x^2 \sqrt[4]{b x^3+a x^4}}{-b+a x} \, dx","Integrate[(x^2*(b*x^3 + a*x^4)^(1/4))/(-b + a*x),x]","\frac{4 x^3 \left(21 a^2 x^2 (a x+b) \, _2F_1\left(-\frac{1}{4},\frac{11}{4};\frac{15}{4};-\frac{a x}{b}\right)+77 b^2 (a x+b) \, _2F_1\left(-\frac{1}{4},\frac{3}{4};\frac{7}{4};-\frac{a x}{b}\right)+77 b^2 \left((a x+b) \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};-\frac{a x}{b}\right)-2 b \sqrt[4]{\frac{a x}{b}+1} \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{2 a x}{b+a x}\right)\right)+33 a b x (a x+b) \, _2F_1\left(-\frac{1}{4},\frac{7}{4};\frac{11}{4};-\frac{a x}{b}\right)\right)}{231 a^3 \left(x^3 (a x+b)\right)^{3/4} \sqrt[4]{\frac{a x}{b}+1}}","-\frac{155 b^3 \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)}{64 a^{15/4}}+\frac{2 \sqrt[4]{2} b^3 \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)}{a^{15/4}}+\frac{155 b^3 \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)}{64 a^{15/4}}-\frac{2 \sqrt[4]{2} b^3 \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)}{a^{15/4}}+\frac{\left(32 a^2 x^2+52 a b x+101 b^2\right) \sqrt[4]{a x^4+b x^3}}{96 a^3}",1,"(4*x^3*(77*b^2*(b + a*x)*Hypergeometric2F1[-1/4, 3/4, 7/4, -((a*x)/b)] + 33*a*b*x*(b + a*x)*Hypergeometric2F1[-1/4, 7/4, 11/4, -((a*x)/b)] + 21*a^2*x^2*(b + a*x)*Hypergeometric2F1[-1/4, 11/4, 15/4, -((a*x)/b)] + 77*b^2*((b + a*x)*Hypergeometric2F1[3/4, 3/4, 7/4, -((a*x)/b)] - 2*b*(1 + (a*x)/b)^(1/4)*Hypergeometric2F1[3/4, 1, 7/4, (2*a*x)/(b + a*x)])))/(231*a^3*(x^3*(b + a*x))^(3/4)*(1 + (a*x)/b)^(1/4))","C",1
2440,0,0,198,0.8235721,"\int \frac{-1+x^6}{\sqrt[3]{x+x^5} \left(1+x^6\right)} \, dx","Integrate[(-1 + x^6)/((x + x^5)^(1/3)*(1 + x^6)),x]","\int \frac{-1+x^6}{\sqrt[3]{x+x^5} \left(1+x^6\right)} \, dx","\frac{1}{3} \log \left(\sqrt[3]{x^5+x}-x\right)-\frac{\log \left(2^{2/3} \sqrt[3]{x^5+x}+2 x\right)}{6 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^5+x}+x}\right)}{\sqrt{3}}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^5+x}-x}\right)}{2 \sqrt[3]{2} \sqrt{3}}-\frac{1}{6} \log \left(\sqrt[3]{x^5+x} x+\left(x^5+x\right)^{2/3}+x^2\right)+\frac{\log \left(2^{2/3} \sqrt[3]{x^5+x} x-\sqrt[3]{2} \left(x^5+x\right)^{2/3}-2 x^2\right)}{12 \sqrt[3]{2}}",1,"Integrate[(-1 + x^6)/((x + x^5)^(1/3)*(1 + x^6)), x]","F",-1
2441,1,524,198,1.4433,"\int \frac{b-2 x^4+a x^8}{\sqrt[4]{-b+a x^4} \left(b-2 x^4+2 a x^8\right)} \, dx","Integrate[(b - 2*x^4 + a*x^8)/((-b + a*x^4)^(1/4)*(b - 2*x^4 + 2*a*x^8)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)+\frac{\left(\frac{a b-1}{\sqrt{1-2 a b}}+1\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{-\sqrt{1-2 a b}-2 b+1}}{\sqrt[4]{1-\sqrt{1-2 a b}} \sqrt[4]{a x^4-b}}\right)}{\left(1-\sqrt{1-2 a b}\right)^{3/4} \sqrt[4]{-\sqrt{1-2 a b}-2 b+1}}+\frac{\left(-a b+\sqrt{1-2 a b}+1\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{\sqrt{1-2 a b}-2 b+1}}{\sqrt[4]{\sqrt{1-2 a b}+1} \sqrt[4]{a x^4-b}}\right)}{\sqrt{1-2 a b} \left(\sqrt{1-2 a b}+1\right)^{3/4} \sqrt[4]{\sqrt{1-2 a b}-2 b+1}}+\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)+\frac{\left(\frac{a b-1}{\sqrt{1-2 a b}}+1\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{-\sqrt{1-2 a b}-2 b+1}}{\sqrt[4]{1-\sqrt{1-2 a b}} \sqrt[4]{a x^4-b}}\right)}{\left(1-\sqrt{1-2 a b}\right)^{3/4} \sqrt[4]{-\sqrt{1-2 a b}-2 b+1}}+\frac{\left(-a b+\sqrt{1-2 a b}+1\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{\sqrt{1-2 a b}-2 b+1}}{\sqrt[4]{\sqrt{1-2 a b}+1} \sqrt[4]{a x^4-b}}\right)}{\sqrt{1-2 a b} \left(\sqrt{1-2 a b}+1\right)^{3/4} \sqrt[4]{\sqrt{1-2 a b}-2 b+1}}}{4 \sqrt[4]{a}}","\frac{1}{16} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+2 \text{$\#$1}^4+a^2+2 a b-2 a\&,\frac{-\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+\text{$\#$1}^4 \log (x)+a \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)-2 \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)-a \log (x)+2 \log (x)}{\text{$\#$1}^5-\text{$\#$1} a+\text{$\#$1}}\&\right]+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{4 \sqrt[4]{a}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{4 \sqrt[4]{a}}",1,"(ArcTan[(a^(1/4)*x)/(-b + a*x^4)^(1/4)] + ((1 + (-1 + a*b)/Sqrt[1 - 2*a*b])*ArcTan[(a^(1/4)*(1 - 2*b - Sqrt[1 - 2*a*b])^(1/4)*x)/((1 - Sqrt[1 - 2*a*b])^(1/4)*(-b + a*x^4)^(1/4))])/((1 - Sqrt[1 - 2*a*b])^(3/4)*(1 - 2*b - Sqrt[1 - 2*a*b])^(1/4)) + ((1 - a*b + Sqrt[1 - 2*a*b])*ArcTan[(a^(1/4)*(1 - 2*b + Sqrt[1 - 2*a*b])^(1/4)*x)/((1 + Sqrt[1 - 2*a*b])^(1/4)*(-b + a*x^4)^(1/4))])/(Sqrt[1 - 2*a*b]*(1 + Sqrt[1 - 2*a*b])^(3/4)*(1 - 2*b + Sqrt[1 - 2*a*b])^(1/4)) + ArcTanh[(a^(1/4)*x)/(-b + a*x^4)^(1/4)] + ((1 + (-1 + a*b)/Sqrt[1 - 2*a*b])*ArcTanh[(a^(1/4)*(1 - 2*b - Sqrt[1 - 2*a*b])^(1/4)*x)/((1 - Sqrt[1 - 2*a*b])^(1/4)*(-b + a*x^4)^(1/4))])/((1 - Sqrt[1 - 2*a*b])^(3/4)*(1 - 2*b - Sqrt[1 - 2*a*b])^(1/4)) + ((1 - a*b + Sqrt[1 - 2*a*b])*ArcTanh[(a^(1/4)*(1 - 2*b + Sqrt[1 - 2*a*b])^(1/4)*x)/((1 + Sqrt[1 - 2*a*b])^(1/4)*(-b + a*x^4)^(1/4))])/(Sqrt[1 - 2*a*b]*(1 + Sqrt[1 - 2*a*b])^(3/4)*(1 - 2*b + Sqrt[1 - 2*a*b])^(1/4)))/(4*a^(1/4))","B",1
2442,1,524,198,0.5205331,"\int \frac{b-2 x^4+a x^8}{\sqrt[4]{-b+a x^4} \left(b-2 x^4+2 a x^8\right)} \, dx","Integrate[(b - 2*x^4 + a*x^8)/((-b + a*x^4)^(1/4)*(b - 2*x^4 + 2*a*x^8)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)+\frac{\left(\frac{a b-1}{\sqrt{1-2 a b}}+1\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{-\sqrt{1-2 a b}-2 b+1}}{\sqrt[4]{1-\sqrt{1-2 a b}} \sqrt[4]{a x^4-b}}\right)}{\left(1-\sqrt{1-2 a b}\right)^{3/4} \sqrt[4]{-\sqrt{1-2 a b}-2 b+1}}+\frac{\left(-a b+\sqrt{1-2 a b}+1\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{\sqrt{1-2 a b}-2 b+1}}{\sqrt[4]{\sqrt{1-2 a b}+1} \sqrt[4]{a x^4-b}}\right)}{\sqrt{1-2 a b} \left(\sqrt{1-2 a b}+1\right)^{3/4} \sqrt[4]{\sqrt{1-2 a b}-2 b+1}}+\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)+\frac{\left(\frac{a b-1}{\sqrt{1-2 a b}}+1\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{-\sqrt{1-2 a b}-2 b+1}}{\sqrt[4]{1-\sqrt{1-2 a b}} \sqrt[4]{a x^4-b}}\right)}{\left(1-\sqrt{1-2 a b}\right)^{3/4} \sqrt[4]{-\sqrt{1-2 a b}-2 b+1}}+\frac{\left(-a b+\sqrt{1-2 a b}+1\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{\sqrt{1-2 a b}-2 b+1}}{\sqrt[4]{\sqrt{1-2 a b}+1} \sqrt[4]{a x^4-b}}\right)}{\sqrt{1-2 a b} \left(\sqrt{1-2 a b}+1\right)^{3/4} \sqrt[4]{\sqrt{1-2 a b}-2 b+1}}}{4 \sqrt[4]{a}}","\frac{1}{16} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+2 \text{$\#$1}^4+a^2+2 a b-2 a\&,\frac{-\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+\text{$\#$1}^4 \log (x)+a \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)-2 \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)-a \log (x)+2 \log (x)}{\text{$\#$1}^5-\text{$\#$1} a+\text{$\#$1}}\&\right]+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{4 \sqrt[4]{a}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{4 \sqrt[4]{a}}",1,"(ArcTan[(a^(1/4)*x)/(-b + a*x^4)^(1/4)] + ((1 + (-1 + a*b)/Sqrt[1 - 2*a*b])*ArcTan[(a^(1/4)*(1 - 2*b - Sqrt[1 - 2*a*b])^(1/4)*x)/((1 - Sqrt[1 - 2*a*b])^(1/4)*(-b + a*x^4)^(1/4))])/((1 - Sqrt[1 - 2*a*b])^(3/4)*(1 - 2*b - Sqrt[1 - 2*a*b])^(1/4)) + ((1 - a*b + Sqrt[1 - 2*a*b])*ArcTan[(a^(1/4)*(1 - 2*b + Sqrt[1 - 2*a*b])^(1/4)*x)/((1 + Sqrt[1 - 2*a*b])^(1/4)*(-b + a*x^4)^(1/4))])/(Sqrt[1 - 2*a*b]*(1 + Sqrt[1 - 2*a*b])^(3/4)*(1 - 2*b + Sqrt[1 - 2*a*b])^(1/4)) + ArcTanh[(a^(1/4)*x)/(-b + a*x^4)^(1/4)] + ((1 + (-1 + a*b)/Sqrt[1 - 2*a*b])*ArcTanh[(a^(1/4)*(1 - 2*b - Sqrt[1 - 2*a*b])^(1/4)*x)/((1 - Sqrt[1 - 2*a*b])^(1/4)*(-b + a*x^4)^(1/4))])/((1 - Sqrt[1 - 2*a*b])^(3/4)*(1 - 2*b - Sqrt[1 - 2*a*b])^(1/4)) + ((1 - a*b + Sqrt[1 - 2*a*b])*ArcTanh[(a^(1/4)*(1 - 2*b + Sqrt[1 - 2*a*b])^(1/4)*x)/((1 + Sqrt[1 - 2*a*b])^(1/4)*(-b + a*x^4)^(1/4))])/(Sqrt[1 - 2*a*b]*(1 + Sqrt[1 - 2*a*b])^(3/4)*(1 - 2*b + Sqrt[1 - 2*a*b])^(1/4)))/(4*a^(1/4))","B",1
2443,1,594,198,1.8824622,"\int \frac{-b+c x^4+2 a x^8}{\sqrt[4]{-b+a x^4} \left(b-c x^4+a x^8\right)} \, dx","Integrate[(-b + c*x^4 + 2*a*x^8)/((-b + a*x^4)^(1/4)*(b - c*x^4 + a*x^8)),x]","\frac{\frac{3 \left(\frac{2 a b-c^2}{\sqrt{c^2-4 a b}}+c\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{\sqrt{c^2-4 a b}+2 b-c}}{\sqrt[4]{\sqrt{c^2-4 a b}-c} \sqrt[4]{a x^4-b}}\right)}{\left(\sqrt{c^2-4 a b}-c\right)^{3/4} \sqrt[4]{\sqrt{c^2-4 a b}+2 b-c}}+\frac{3 \left(2 a b-c \left(\sqrt{c^2-4 a b}+c\right)\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{\sqrt{c^2-4 a b}-2 b+c}}{\sqrt[4]{\sqrt{c^2-4 a b}+c} \sqrt[4]{a x^4-b}}\right)}{\sqrt{c^2-4 a b} \left(\sqrt{c^2-4 a b}+c\right)^{3/4} \sqrt[4]{\sqrt{c^2-4 a b}-2 b+c}}+\frac{3 \left(\frac{2 a b-c^2}{\sqrt{c^2-4 a b}}+c\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{\sqrt{c^2-4 a b}+2 b-c}}{\sqrt[4]{\sqrt{c^2-4 a b}-c} \sqrt[4]{a x^4-b}}\right)}{\left(\sqrt{c^2-4 a b}-c\right)^{3/4} \sqrt[4]{\sqrt{c^2-4 a b}+2 b-c}}+\frac{3 \left(2 a b-c \left(\sqrt{c^2-4 a b}+c\right)\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{\sqrt{c^2-4 a b}-2 b+c}}{\sqrt[4]{\sqrt{c^2-4 a b}+c} \sqrt[4]{a x^4-b}}\right)}{\sqrt{c^2-4 a b} \left(\sqrt{c^2-4 a b}+c\right)^{3/4} \sqrt[4]{\sqrt{c^2-4 a b}-2 b+c}}+2 \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)+2 \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{2 \sqrt[4]{a}}","\frac{3}{4} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+\text{$\#$1}^4 c+a^2+a b-a c\&,\frac{-\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+\text{$\#$1}^4 \log (x)-c \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+a \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)-a \log (x)+c \log (x)}{-2 \text{$\#$1}^5+2 \text{$\#$1} a-\text{$\#$1} c}\&\right]+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{\sqrt[4]{a}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{\sqrt[4]{a}}",1,"(2*ArcTan[(a^(1/4)*x)/(-b + a*x^4)^(1/4)] + (3*(c + (2*a*b - c^2)/Sqrt[-4*a*b + c^2])*ArcTan[(a^(1/4)*(2*b - c + Sqrt[-4*a*b + c^2])^(1/4)*x)/((-c + Sqrt[-4*a*b + c^2])^(1/4)*(-b + a*x^4)^(1/4))])/((-c + Sqrt[-4*a*b + c^2])^(3/4)*(2*b - c + Sqrt[-4*a*b + c^2])^(1/4)) + (3*(2*a*b - c*(c + Sqrt[-4*a*b + c^2]))*ArcTan[(a^(1/4)*(-2*b + c + Sqrt[-4*a*b + c^2])^(1/4)*x)/((c + Sqrt[-4*a*b + c^2])^(1/4)*(-b + a*x^4)^(1/4))])/(Sqrt[-4*a*b + c^2]*(c + Sqrt[-4*a*b + c^2])^(3/4)*(-2*b + c + Sqrt[-4*a*b + c^2])^(1/4)) + 2*ArcTanh[(a^(1/4)*x)/(-b + a*x^4)^(1/4)] + (3*(c + (2*a*b - c^2)/Sqrt[-4*a*b + c^2])*ArcTanh[(a^(1/4)*(2*b - c + Sqrt[-4*a*b + c^2])^(1/4)*x)/((-c + Sqrt[-4*a*b + c^2])^(1/4)*(-b + a*x^4)^(1/4))])/((-c + Sqrt[-4*a*b + c^2])^(3/4)*(2*b - c + Sqrt[-4*a*b + c^2])^(1/4)) + (3*(2*a*b - c*(c + Sqrt[-4*a*b + c^2]))*ArcTanh[(a^(1/4)*(-2*b + c + Sqrt[-4*a*b + c^2])^(1/4)*x)/((c + Sqrt[-4*a*b + c^2])^(1/4)*(-b + a*x^4)^(1/4))])/(Sqrt[-4*a*b + c^2]*(c + Sqrt[-4*a*b + c^2])^(3/4)*(-2*b + c + Sqrt[-4*a*b + c^2])^(1/4)))/(2*a^(1/4))","B",1
2444,1,594,198,0.8736835,"\int \frac{-b+c x^4+2 a x^8}{\sqrt[4]{-b+a x^4} \left(b-c x^4+a x^8\right)} \, dx","Integrate[(-b + c*x^4 + 2*a*x^8)/((-b + a*x^4)^(1/4)*(b - c*x^4 + a*x^8)),x]","\frac{\frac{3 \left(\frac{2 a b-c^2}{\sqrt{c^2-4 a b}}+c\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{\sqrt{c^2-4 a b}+2 b-c}}{\sqrt[4]{\sqrt{c^2-4 a b}-c} \sqrt[4]{a x^4-b}}\right)}{\left(\sqrt{c^2-4 a b}-c\right)^{3/4} \sqrt[4]{\sqrt{c^2-4 a b}+2 b-c}}+\frac{3 \left(2 a b-c \left(\sqrt{c^2-4 a b}+c\right)\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{\sqrt{c^2-4 a b}-2 b+c}}{\sqrt[4]{\sqrt{c^2-4 a b}+c} \sqrt[4]{a x^4-b}}\right)}{\sqrt{c^2-4 a b} \left(\sqrt{c^2-4 a b}+c\right)^{3/4} \sqrt[4]{\sqrt{c^2-4 a b}-2 b+c}}+\frac{3 \left(\frac{2 a b-c^2}{\sqrt{c^2-4 a b}}+c\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{\sqrt{c^2-4 a b}+2 b-c}}{\sqrt[4]{\sqrt{c^2-4 a b}-c} \sqrt[4]{a x^4-b}}\right)}{\left(\sqrt{c^2-4 a b}-c\right)^{3/4} \sqrt[4]{\sqrt{c^2-4 a b}+2 b-c}}+\frac{3 \left(2 a b-c \left(\sqrt{c^2-4 a b}+c\right)\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{\sqrt{c^2-4 a b}-2 b+c}}{\sqrt[4]{\sqrt{c^2-4 a b}+c} \sqrt[4]{a x^4-b}}\right)}{\sqrt{c^2-4 a b} \left(\sqrt{c^2-4 a b}+c\right)^{3/4} \sqrt[4]{\sqrt{c^2-4 a b}-2 b+c}}+2 \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)+2 \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{2 \sqrt[4]{a}}","\frac{3}{4} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+\text{$\#$1}^4 c+a^2+a b-a c\&,\frac{-\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+\text{$\#$1}^4 \log (x)-c \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+a \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)-a \log (x)+c \log (x)}{-2 \text{$\#$1}^5+2 \text{$\#$1} a-\text{$\#$1} c}\&\right]+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{\sqrt[4]{a}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{\sqrt[4]{a}}",1,"(2*ArcTan[(a^(1/4)*x)/(-b + a*x^4)^(1/4)] + (3*(c + (2*a*b - c^2)/Sqrt[-4*a*b + c^2])*ArcTan[(a^(1/4)*(2*b - c + Sqrt[-4*a*b + c^2])^(1/4)*x)/((-c + Sqrt[-4*a*b + c^2])^(1/4)*(-b + a*x^4)^(1/4))])/((-c + Sqrt[-4*a*b + c^2])^(3/4)*(2*b - c + Sqrt[-4*a*b + c^2])^(1/4)) + (3*(2*a*b - c*(c + Sqrt[-4*a*b + c^2]))*ArcTan[(a^(1/4)*(-2*b + c + Sqrt[-4*a*b + c^2])^(1/4)*x)/((c + Sqrt[-4*a*b + c^2])^(1/4)*(-b + a*x^4)^(1/4))])/(Sqrt[-4*a*b + c^2]*(c + Sqrt[-4*a*b + c^2])^(3/4)*(-2*b + c + Sqrt[-4*a*b + c^2])^(1/4)) + 2*ArcTanh[(a^(1/4)*x)/(-b + a*x^4)^(1/4)] + (3*(c + (2*a*b - c^2)/Sqrt[-4*a*b + c^2])*ArcTanh[(a^(1/4)*(2*b - c + Sqrt[-4*a*b + c^2])^(1/4)*x)/((-c + Sqrt[-4*a*b + c^2])^(1/4)*(-b + a*x^4)^(1/4))])/((-c + Sqrt[-4*a*b + c^2])^(3/4)*(2*b - c + Sqrt[-4*a*b + c^2])^(1/4)) + (3*(2*a*b - c*(c + Sqrt[-4*a*b + c^2]))*ArcTanh[(a^(1/4)*(-2*b + c + Sqrt[-4*a*b + c^2])^(1/4)*x)/((c + Sqrt[-4*a*b + c^2])^(1/4)*(-b + a*x^4)^(1/4))])/(Sqrt[-4*a*b + c^2]*(c + Sqrt[-4*a*b + c^2])^(3/4)*(-2*b + c + Sqrt[-4*a*b + c^2])^(1/4)))/(2*a^(1/4))","B",1
2445,1,325,198,0.389528,"\int \frac{\sqrt[4]{-b x^3+a x^4} \left(-d+c x^8\right)}{x^4} \, dx","Integrate[((-(b*x^3) + a*x^4)^(1/4)*(-d + c*x^8))/x^4,x]","-\frac{4 \sqrt[4]{x^3 (a x-b)} \left(4 a^{10} d x^2 \sqrt[4]{1-\frac{a x}{b}}+a^9 b d x \sqrt[4]{1-\frac{a x}{b}}-5 a^8 b^2 d \sqrt[4]{1-\frac{a x}{b}}-44 a^2 b^8 c x^2 \sqrt[4]{1-\frac{a x}{b}}+5 b^{10} c \, _2F_1\left(-\frac{33}{4},-\frac{9}{4};-\frac{5}{4};\frac{a x}{b}\right)-40 b^{10} c \, _2F_1\left(-\frac{29}{4},-\frac{9}{4};-\frac{5}{4};\frac{a x}{b}\right)+140 b^{10} c \, _2F_1\left(-\frac{25}{4},-\frac{9}{4};-\frac{5}{4};\frac{a x}{b}\right)-280 b^{10} c \, _2F_1\left(-\frac{21}{4},-\frac{9}{4};-\frac{5}{4};\frac{a x}{b}\right)+350 b^{10} c \, _2F_1\left(-\frac{17}{4},-\frac{9}{4};-\frac{5}{4};\frac{a x}{b}\right)-280 b^{10} c \, _2F_1\left(-\frac{13}{4},-\frac{9}{4};-\frac{5}{4};\frac{a x}{b}\right)+140 b^{10} c \, _2F_1\left(-\frac{9}{4},-\frac{9}{4};-\frac{5}{4};\frac{a x}{b}\right)-35 b^{10} c \sqrt[4]{1-\frac{a x}{b}}+79 a b^9 c x \sqrt[4]{1-\frac{a x}{b}}\right)}{45 a^8 b^2 x^3 \sqrt[4]{1-\frac{a x}{b}}}","\frac{1463 b^6 c \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^3}}\right)}{32768 a^{23/4}}-\frac{1463 b^6 c \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^3}}\right)}{32768 a^{23/4}}+\frac{\sqrt[4]{a x^4-b x^3} \left(-262144 a^7 d x^2-65536 a^6 b d x+122880 a^5 b^2 c x^8+327680 a^5 b^2 d-6144 a^4 b^3 c x^7-7296 a^3 b^4 c x^6-9120 a^2 b^5 c x^5-12540 a b^6 c x^4-21945 b^7 c x^3\right)}{737280 a^5 b^2 x^3}",1,"(-4*(x^3*(-b + a*x))^(1/4)*(-35*b^10*c*(1 - (a*x)/b)^(1/4) - 5*a^8*b^2*d*(1 - (a*x)/b)^(1/4) + 79*a*b^9*c*x*(1 - (a*x)/b)^(1/4) + a^9*b*d*x*(1 - (a*x)/b)^(1/4) - 44*a^2*b^8*c*x^2*(1 - (a*x)/b)^(1/4) + 4*a^10*d*x^2*(1 - (a*x)/b)^(1/4) + 5*b^10*c*Hypergeometric2F1[-33/4, -9/4, -5/4, (a*x)/b] - 40*b^10*c*Hypergeometric2F1[-29/4, -9/4, -5/4, (a*x)/b] + 140*b^10*c*Hypergeometric2F1[-25/4, -9/4, -5/4, (a*x)/b] - 280*b^10*c*Hypergeometric2F1[-21/4, -9/4, -5/4, (a*x)/b] + 350*b^10*c*Hypergeometric2F1[-17/4, -9/4, -5/4, (a*x)/b] - 280*b^10*c*Hypergeometric2F1[-13/4, -9/4, -5/4, (a*x)/b] + 140*b^10*c*Hypergeometric2F1[-9/4, -9/4, -5/4, (a*x)/b]))/(45*a^8*b^2*x^3*(1 - (a*x)/b)^(1/4))","C",1
2446,1,95,198,0.2484901,"\int \frac{\sqrt{b+\sqrt{b^2+a x^2}}}{x^6} \, dx","Integrate[Sqrt[b + Sqrt[b^2 + a*x^2]]/x^6,x]","\frac{\sqrt{\sqrt{a x^2+b^2}+b} \left(\left(2 b \sqrt{a x^2+b^2}+a x^2+2 b^2\right) \, _2F_1\left(-\frac{5}{2},2;-\frac{3}{2};\frac{b-\sqrt{b^2+a x^2}}{2 b}\right)-20 b^2\right)}{80 b^2 x^5}","\frac{7 a^{5/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{2} \sqrt{b} \sqrt{\sqrt{a x^2+b^2}+b}}-\frac{\sqrt{\sqrt{a x^2+b^2}+b}}{\sqrt{2} \sqrt{b}}\right)}{64 \sqrt{2} b^{9/2}}+\frac{\sqrt{\sqrt{a x^2+b^2}+b} \left(a^{3/2} \left(14 b^2 x^2-70 b x^2 \sqrt{a x^2+b^2}\right)+105 a^{5/2} x^4+\sqrt{a} \left(48 b^3 \sqrt{a x^2+b^2}-432 b^4\right)\right)}{1920 \sqrt{a} b^4 x^5}",1,"(Sqrt[b + Sqrt[b^2 + a*x^2]]*(-20*b^2 + (2*b^2 + a*x^2 + 2*b*Sqrt[b^2 + a*x^2])*Hypergeometric2F1[-5/2, 2, -3/2, (b - Sqrt[b^2 + a*x^2])/(2*b)]))/(80*b^2*x^5)","C",1
2447,1,81,198,0.2501244,"\int \frac{\sqrt{b+\sqrt{b^2+a x^2}}}{x^6 \sqrt{b^2+a x^2}} \, dx","Integrate[Sqrt[b + Sqrt[b^2 + a*x^2]]/(x^6*Sqrt[b^2 + a*x^2]),x]","-\frac{a^3 x \, _2F_1\left(-\frac{5}{2},3;-\frac{3}{2};\frac{b-\sqrt{b^2+a x^2}}{2 b}\right)}{20 b^3 \left(\sqrt{a x^2+b^2}-b\right)^3 \sqrt{\sqrt{a x^2+b^2}+b}}","\frac{\sqrt{\sqrt{a x^2+b^2}+b} \left(a^{3/2} \left(210 b x^2 \sqrt{a x^2+b^2}-42 b^2 x^2\right)-315 a^{5/2} x^4+\sqrt{a} \left(16 b^4-144 b^3 \sqrt{a x^2+b^2}\right)\right)}{640 \sqrt{a} b^5 x^5}-\frac{63 a^{5/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{2} \sqrt{b} \sqrt{\sqrt{a x^2+b^2}+b}}-\frac{\sqrt{\sqrt{a x^2+b^2}+b}}{\sqrt{2} \sqrt{b}}\right)}{64 \sqrt{2} b^{11/2}}",1,"-1/20*(a^3*x*Hypergeometric2F1[-5/2, 3, -3/2, (b - Sqrt[b^2 + a*x^2])/(2*b)])/(b^3*(-b + Sqrt[b^2 + a*x^2])^3*Sqrt[b + Sqrt[b^2 + a*x^2]])","C",1
2448,1,114,198,0.1255543,"\int \sqrt{d+\sqrt{c+\sqrt{b+a x}}} \, dx","Integrate[Sqrt[d + Sqrt[c + Sqrt[b + a*x]]],x]","\frac{8 \left(\sqrt{\sqrt{a x+b}+c}+d\right)^{3/2} \left(24 d^2 \sqrt{\sqrt{a x+b}+c}-28 c \sqrt{\sqrt{a x+b}+c}+35 \sqrt{a x+b} \sqrt{\sqrt{a x+b}+c}-30 d \sqrt{a x+b}+12 c d-16 d^3\right)}{315 a}","\frac{8 \left(35 a x+35 b-28 c^2+36 c d^2-16 d^4\right) \sqrt{\sqrt{\sqrt{a x+b}+c}+d}}{315 a}-\frac{64 \left(2 c d-d^3\right) \sqrt{\sqrt{a x+b}+c} \sqrt{\sqrt{\sqrt{a x+b}+c}+d}}{315 a}+\sqrt{a x+b} \left(\frac{8 \left(7 c-6 d^2\right) \sqrt{\sqrt{\sqrt{a x+b}+c}+d}}{315 a}+\frac{8 d \sqrt{\sqrt{a x+b}+c} \sqrt{\sqrt{\sqrt{a x+b}+c}+d}}{63 a}\right)",1,"(8*(d + Sqrt[c + Sqrt[b + a*x]])^(3/2)*(12*c*d - 16*d^3 - 30*d*Sqrt[b + a*x] - 28*c*Sqrt[c + Sqrt[b + a*x]] + 24*d^2*Sqrt[c + Sqrt[b + a*x]] + 35*Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]]))/(315*a)","A",1
2449,1,75,199,0.0343906,"\int \frac{1}{\left(-b+a x^2\right) \sqrt[3]{-x+x^3}} \, dx","Integrate[1/((-b + a*x^2)*(-x + x^3)^(1/3)),x]","-\frac{3 x \sqrt[3]{1-x^2} \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};\frac{(a-b) x^2}{a x^2-b}\right)}{2 b \sqrt[3]{x \left(x^2-1\right)} \sqrt[3]{1-\frac{a x^2}{b}}}","-\frac{\log \left(x \sqrt[3]{a-b}+\sqrt[3]{b} \sqrt[3]{x^3-x}\right)}{2 b^{2/3} \sqrt[3]{a-b}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x \sqrt[3]{a-b}}{x \sqrt[3]{a-b}-2 \sqrt[3]{b} \sqrt[3]{x^3-x}}\right)}{2 b^{2/3} \sqrt[3]{a-b}}+\frac{\log \left(-\sqrt[3]{b} \sqrt[3]{x^3-x} x \sqrt[3]{a-b}+x^2 (a-b)^{2/3}+b^{2/3} \left(x^3-x\right)^{2/3}\right)}{4 b^{2/3} \sqrt[3]{a-b}}",1,"(-3*x*(1 - x^2)^(1/3)*Hypergeometric2F1[1/3, 1/3, 4/3, ((a - b)*x^2)/(-b + a*x^2)])/(2*b*(x*(-1 + x^2))^(1/3)*(1 - (a*x^2)/b)^(1/3))","C",0
2450,1,120,199,0.1963722,"\int \frac{1}{x^3 \left(-1+x^3\right) \sqrt[3]{x^2+x^3}} \, dx","Integrate[1/(x^3*(-1 + x^3)*(x^2 + x^3)^(1/3)),x]","\frac{(x+1) \left(-40 x^3 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{2 x}{x+1}\right)-40 x^3 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{x-i \sqrt{3} x}{2 x+2}\right)-40 x^3 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{i \sqrt{3} x+x}{2 x+2}\right)+27 x^3+9 x^2-3 x+15\right)}{40 \left(x^2 (x+1)\right)^{4/3}}","\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^6-\text{$\#$1}^3+1\&,\frac{\log \left(\sqrt[3]{x^3+x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]+\frac{\log \left(2^{2/3} \sqrt[3]{x^3+x^2}-2 x\right)}{3 \sqrt[3]{2}}-\frac{\log \left(2 x^2+2^{2/3} \sqrt[3]{x^3+x^2} x+\sqrt[3]{2} \left(x^3+x^2\right)^{2/3}\right)}{6 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^3+x^2}+x}\right)}{\sqrt[3]{2} \sqrt{3}}+\frac{3 \left(x^3+x^2\right)^{2/3} \left(9 x^2-6 x+5\right)}{40 x^4}",1,"((1 + x)*(15 - 3*x + 9*x^2 + 27*x^3 - 40*x^3*Hypergeometric2F1[1/3, 1, 4/3, (2*x)/(1 + x)] - 40*x^3*Hypergeometric2F1[1/3, 1, 4/3, (x - I*Sqrt[3]*x)/(2 + 2*x)] - 40*x^3*Hypergeometric2F1[1/3, 1, 4/3, (x + I*Sqrt[3]*x)/(2 + 2*x)]))/(40*(x^2*(1 + x))^(4/3))","C",1
2451,1,120,199,0.0848887,"\int \frac{1}{x^3 \left(-1+x^3\right) \sqrt[3]{x^2+x^3}} \, dx","Integrate[1/(x^3*(-1 + x^3)*(x^2 + x^3)^(1/3)),x]","\frac{(x+1) \left(-40 x^3 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{2 x}{x+1}\right)-40 x^3 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{x-i \sqrt{3} x}{2 x+2}\right)-40 x^3 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{i \sqrt{3} x+x}{2 x+2}\right)+27 x^3+9 x^2-3 x+15\right)}{40 \left(x^2 (x+1)\right)^{4/3}}","\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^6-\text{$\#$1}^3+1\&,\frac{\log \left(\sqrt[3]{x^3+x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]+\frac{\log \left(2^{2/3} \sqrt[3]{x^3+x^2}-2 x\right)}{3 \sqrt[3]{2}}-\frac{\log \left(2 x^2+2^{2/3} \sqrt[3]{x^3+x^2} x+\sqrt[3]{2} \left(x^3+x^2\right)^{2/3}\right)}{6 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^3+x^2}+x}\right)}{\sqrt[3]{2} \sqrt{3}}+\frac{3 \left(x^3+x^2\right)^{2/3} \left(9 x^2-6 x+5\right)}{40 x^4}",1,"((1 + x)*(15 - 3*x + 9*x^2 + 27*x^3 - 40*x^3*Hypergeometric2F1[1/3, 1, 4/3, (2*x)/(1 + x)] - 40*x^3*Hypergeometric2F1[1/3, 1, 4/3, (x - I*Sqrt[3]*x)/(2 + 2*x)] - 40*x^3*Hypergeometric2F1[1/3, 1, 4/3, (x + I*Sqrt[3]*x)/(2 + 2*x)]))/(40*(x^2*(1 + x))^(4/3))","C",1
2452,1,313,199,0.7410824,"\int \frac{1}{x^6 \left(-b+a x^3\right) \sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Integrate[1/(x^6*(-b + a*x^3)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","\frac{-21870 a^{18} x^6-7290 a^{15} b^2 x^5+2430 a^{12} b^4 x^4+35343 a^{10} b^5 x^6-1350 a^9 b^6 x^3+11781 a^7 b^7 x^5+900 a^6 b^8 x^2-3927 a^4 b^9 x^4-660 a^3 b^{10} x-52360 a^2 b^{10} x^6 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{2 x a^3+\left(-1-i \sqrt{3}\right) b^{5/3} x \sqrt[3]{a}}{2 \left(x a^3+b^2\right)}\right)-52360 a^2 b^{10} x^6 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{2 x a^3+i \left(i+\sqrt{3}\right) b^{5/3} x \sqrt[3]{a}}{2 \left(x a^3+b^2\right)}\right)-52360 a^2 b^{10} x^6 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\sqrt[3]{a} \left(a^{8/3}+b^{5/3}\right) x}{x a^3+b^2}\right)+19635 a b^{11} x^3+9240 b^{12}}{52360 b^{13} x^5 \sqrt[3]{x^2 \left(a^3 x+b^2\right)}}","\frac{a^2 \text{RootSum}\left[-\text{$\#$1}^9+3 \text{$\#$1}^6 a^3-3 \text{$\#$1}^3 a^6+a^9+a b^5\&,\frac{\log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{3 b^3}+\frac{3 \left(a^3 x^3+b^2 x^2\right)^{2/3} \left(-7290 a^{15} x^5+4860 a^{12} b^2 x^4-4050 a^9 b^4 x^3+11781 a^7 b^5 x^5+3600 a^6 b^6 x^2-7854 a^4 b^7 x^4-3300 a^3 b^8 x+6545 a b^9 x^3+3080 b^{10}\right)}{52360 b^{13} x^7}",1,"(9240*b^12 - 660*a^3*b^10*x + 900*a^6*b^8*x^2 - 1350*a^9*b^6*x^3 + 19635*a*b^11*x^3 + 2430*a^12*b^4*x^4 - 3927*a^4*b^9*x^4 - 7290*a^15*b^2*x^5 + 11781*a^7*b^7*x^5 - 21870*a^18*x^6 + 35343*a^10*b^5*x^6 - 52360*a^2*b^10*x^6*Hypergeometric2F1[1/3, 1, 4/3, (a^(1/3)*(a^(8/3) + b^(5/3))*x)/(b^2 + a^3*x)] - 52360*a^2*b^10*x^6*Hypergeometric2F1[1/3, 1, 4/3, (2*a^3*x + (-1 - I*Sqrt[3])*a^(1/3)*b^(5/3)*x)/(2*(b^2 + a^3*x))] - 52360*a^2*b^10*x^6*Hypergeometric2F1[1/3, 1, 4/3, (2*a^3*x + I*(I + Sqrt[3])*a^(1/3)*b^(5/3)*x)/(2*(b^2 + a^3*x))])/(52360*b^13*x^5*(x^2*(b^2 + a^3*x))^(1/3))","C",1
2453,1,313,199,0.3718079,"\int \frac{1}{x^6 \left(-b+a x^3\right) \sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Integrate[1/(x^6*(-b + a*x^3)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","\frac{-21870 a^{18} x^6-7290 a^{15} b^2 x^5+2430 a^{12} b^4 x^4+35343 a^{10} b^5 x^6-1350 a^9 b^6 x^3+11781 a^7 b^7 x^5+900 a^6 b^8 x^2-3927 a^4 b^9 x^4-660 a^3 b^{10} x-52360 a^2 b^{10} x^6 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{2 x a^3+\left(-1-i \sqrt{3}\right) b^{5/3} x \sqrt[3]{a}}{2 \left(x a^3+b^2\right)}\right)-52360 a^2 b^{10} x^6 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{2 x a^3+i \left(i+\sqrt{3}\right) b^{5/3} x \sqrt[3]{a}}{2 \left(x a^3+b^2\right)}\right)-52360 a^2 b^{10} x^6 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\sqrt[3]{a} \left(a^{8/3}+b^{5/3}\right) x}{x a^3+b^2}\right)+19635 a b^{11} x^3+9240 b^{12}}{52360 b^{13} x^5 \sqrt[3]{x^2 \left(a^3 x+b^2\right)}}","\frac{a^2 \text{RootSum}\left[-\text{$\#$1}^9+3 \text{$\#$1}^6 a^3-3 \text{$\#$1}^3 a^6+a^9+a b^5\&,\frac{\log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{3 b^3}+\frac{3 \left(a^3 x^3+b^2 x^2\right)^{2/3} \left(-7290 a^{15} x^5+4860 a^{12} b^2 x^4-4050 a^9 b^4 x^3+11781 a^7 b^5 x^5+3600 a^6 b^6 x^2-7854 a^4 b^7 x^4-3300 a^3 b^8 x+6545 a b^9 x^3+3080 b^{10}\right)}{52360 b^{13} x^7}",1,"(9240*b^12 - 660*a^3*b^10*x + 900*a^6*b^8*x^2 - 1350*a^9*b^6*x^3 + 19635*a*b^11*x^3 + 2430*a^12*b^4*x^4 - 3927*a^4*b^9*x^4 - 7290*a^15*b^2*x^5 + 11781*a^7*b^7*x^5 - 21870*a^18*x^6 + 35343*a^10*b^5*x^6 - 52360*a^2*b^10*x^6*Hypergeometric2F1[1/3, 1, 4/3, (a^(1/3)*(a^(8/3) + b^(5/3))*x)/(b^2 + a^3*x)] - 52360*a^2*b^10*x^6*Hypergeometric2F1[1/3, 1, 4/3, (2*a^3*x + (-1 - I*Sqrt[3])*a^(1/3)*b^(5/3)*x)/(2*(b^2 + a^3*x))] - 52360*a^2*b^10*x^6*Hypergeometric2F1[1/3, 1, 4/3, (2*a^3*x + I*(I + Sqrt[3])*a^(1/3)*b^(5/3)*x)/(2*(b^2 + a^3*x))])/(52360*b^13*x^5*(x^2*(b^2 + a^3*x))^(1/3))","C",1
2454,1,5248,199,147.281094,"\int \frac{\left(-1+x^2\right) \left(1+x+x^2\right) \sqrt{1+3 x^2+x^4}}{\left(1+x+x^2+x^3+x^4\right)^2} \, dx","Integrate[((-1 + x^2)*(1 + x + x^2)*Sqrt[1 + 3*x^2 + x^4])/(1 + x + x^2 + x^3 + x^4)^2,x]","\text{Result too large to show}","\frac{1}{5} \text{RootSum}\left[\text{$\#$1}^4+2 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1\&,\frac{3 \text{$\#$1}^2 \log \left(-\text{$\#$1} x+x^2+\sqrt{x^4+3 x^2+1}+1\right)-3 \text{$\#$1}^2 \log (x)-2 \text{$\#$1} \log \left(-\text{$\#$1} x+x^2+\sqrt{x^4+3 x^2+1}+1\right)-3 \log \left(-\text{$\#$1} x+x^2+\sqrt{x^4+3 x^2+1}+1\right)+2 \text{$\#$1} \log (x)+3 \log (x)}{2 \text{$\#$1}^3+3 \text{$\#$1}^2-6 \text{$\#$1}-1}\&\right]+\frac{\sqrt{x^4+3 x^2+1} \left(-x^2-3 x-1\right)}{5 \left(x^4+x^3+x^2+x+1\right)}",1,"Result too large to show","C",0
2455,0,0,199,0.404776,"\int \frac{b+a x^4}{\left(-b+a x^4\right) \sqrt[4]{b^2+c x^4+a^2 x^8}} \, dx","Integrate[(b + a*x^4)/((-b + a*x^4)*(b^2 + c*x^4 + a^2*x^8)^(1/4)),x]","\int \frac{b+a x^4}{\left(-b+a x^4\right) \sqrt[4]{b^2+c x^4+a^2 x^8}} \, dx","\frac{\left(\frac{1}{4}+\frac{i}{4}\right) \tan ^{-1}\left(\frac{(1+i) x \sqrt[4]{2 a b+c} \sqrt[4]{a^2 x^8+b^2+c x^4}}{x^2 \sqrt{2 a b+c}-i \sqrt{a^2 x^8+b^2+c x^4}}\right)}{\sqrt[4]{2 a b+c}}-\frac{\left(\frac{1}{4}+\frac{i}{4}\right) \tanh ^{-1}\left(\frac{\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{a^2 x^8+b^2+c x^4}}{\sqrt[4]{2 a b+c}}+\left(\frac{1}{2}-\frac{i}{2}\right) x^2 \sqrt[4]{2 a b+c}}{x \sqrt[4]{a^2 x^8+b^2+c x^4}}\right)}{\sqrt[4]{2 a b+c}}",1,"Integrate[(b + a*x^4)/((-b + a*x^4)*(b^2 + c*x^4 + a^2*x^8)^(1/4)), x]","F",-1
2456,1,161,199,0.2725916,"\int \frac{2 x^4-x^9}{\sqrt{-1+x^5} \left(a-a x^5+x^{10}\right)} \, dx","Integrate[(2*x^4 - x^9)/(Sqrt[-1 + x^5]*(a - a*x^5 + x^10)),x]","-\frac{1}{5} \sqrt{2} \left(\frac{\left(\sqrt{\frac{a-4}{a}}+1\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{x^5-1}}{\sqrt{-a-\sqrt{a-4} \sqrt{a}+2}}\right)}{\sqrt{-a-\sqrt{a-4} \sqrt{a}+2}}-\frac{\left(\sqrt{\frac{a-4}{a}}-1\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{x^5-1}}{\sqrt{-a+\sqrt{a-4} \sqrt{a}+2}}\right)}{\sqrt{-a+\sqrt{a-4} \sqrt{a}+2}}\right)","-\frac{\sqrt{2} \left(a+\sqrt{a-4} \sqrt{a}-4\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{x^5-1}}{\sqrt{-a-\sqrt{a-4} \sqrt{a}+2}}\right)}{5 \sqrt{-a-\sqrt{a-4} \sqrt{a}+2} \sqrt{a-4} \sqrt{a}}-\frac{\sqrt{2} \left(-a+\sqrt{a-4} \sqrt{a}+4\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{x^5-1}}{\sqrt{-a+\sqrt{a-4} \sqrt{a}+2}}\right)}{5 \sqrt{-a+\sqrt{a-4} \sqrt{a}+2} \sqrt{a-4} \sqrt{a}}",1,"-1/5*(Sqrt[2]*(((1 + Sqrt[(-4 + a)/a])*ArcTan[(Sqrt[2]*Sqrt[-1 + x^5])/Sqrt[2 - Sqrt[-4 + a]*Sqrt[a] - a]])/Sqrt[2 - Sqrt[-4 + a]*Sqrt[a] - a] - ((-1 + Sqrt[(-4 + a)/a])*ArcTan[(Sqrt[2]*Sqrt[-1 + x^5])/Sqrt[2 + Sqrt[-4 + a]*Sqrt[a] - a]])/Sqrt[2 + Sqrt[-4 + a]*Sqrt[a] - a]))","A",0
2457,1,233,199,0.4563367,"\int \frac{1+x^2}{\left(-1+x^2\right) \sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[(1 + x^2)/((-1 + x^2)*Sqrt[x + Sqrt[1 + x^2]]),x]","\sqrt{\sqrt{x^2+1}+x}-\frac{1}{3 \left(\sqrt{x^2+1}+x\right)^{3/2}}-\left(\left(\sqrt{2}-2\right) \sqrt{2 \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{1}{\sqrt{\sqrt{2}-1} \sqrt{\sqrt{x^2+1}+x}}\right)\right)-\sqrt{2 \left(\sqrt{2}-1\right)} \left(2+\sqrt{2}\right) \tan ^{-1}\left(\frac{1}{\sqrt{1+\sqrt{2}} \sqrt{\sqrt{x^2+1}+x}}\right)+\left(\sqrt{2}-2\right) \sqrt{2 \left(1+\sqrt{2}\right)} \tanh ^{-1}\left(\frac{1}{\sqrt{\sqrt{2}-1} \sqrt{\sqrt{x^2+1}+x}}\right)+\sqrt{2 \left(\sqrt{2}-1\right)} \left(2+\sqrt{2}\right) \tanh ^{-1}\left(\frac{1}{\sqrt{1+\sqrt{2}} \sqrt{\sqrt{x^2+1}+x}}\right)","\sqrt{\sqrt{x^2+1}+x}-\frac{1}{3 \left(\sqrt{x^2+1}+x\right)^{3/2}}+2 \sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{\sqrt{2}-1}}\right)-2 \sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{1+\sqrt{2}}}\right)+2 \sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{\sqrt{2}-1}}\right)-2 \sqrt{\sqrt{2}-1} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{1+\sqrt{2}}}\right)",1,"-1/3*1/(x + Sqrt[1 + x^2])^(3/2) + Sqrt[x + Sqrt[1 + x^2]] - (-2 + Sqrt[2])*Sqrt[2*(1 + Sqrt[2])]*ArcTan[1/(Sqrt[-1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]])] - Sqrt[2*(-1 + Sqrt[2])]*(2 + Sqrt[2])*ArcTan[1/(Sqrt[1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]])] + (-2 + Sqrt[2])*Sqrt[2*(1 + Sqrt[2])]*ArcTanh[1/(Sqrt[-1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]])] + Sqrt[2*(-1 + Sqrt[2])]*(2 + Sqrt[2])*ArcTanh[1/(Sqrt[1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]])]","A",0
2458,1,194,199,0.5441127,"\int \frac{d+c x^2}{\left(-d+c x^2\right) \sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Integrate[(d + c*x^2)/((-d + c*x^2)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]),x]","\frac{a^2 (-d) \text{RootSum}\left[\text{$\#$1}^8 b^4 c-4 \text{$\#$1}^4 a^2 d-2 \text{$\#$1}^4 b^2 c+c\&,\frac{\text{$\#$1}^4 b^2 \log \left(\frac{1}{\sqrt{\sqrt{a^2 x^2+b^2}+a x}}-\text{$\#$1}\right)+\log \left(\frac{1}{\sqrt{\sqrt{a^2 x^2+b^2}+a x}}-\text{$\#$1}\right)}{\text{$\#$1}^5 b^4 c-2 \text{$\#$1} a^2 d-\text{$\#$1} b^2 c}\&\right]+\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\frac{b^2}{3 \left(\sqrt{a^2 x^2+b^2}+a x\right)^{3/2}}}{a}","a d \text{RootSum}\left[\text{$\#$1}^8 c-4 \text{$\#$1}^4 a^2 d-2 \text{$\#$1}^4 b^2 c+b^4 c\&,\frac{\text{$\#$1}^4 \left(-\log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)\right)-b^2 \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)}{\text{$\#$1}^7 (-c)+2 \text{$\#$1}^3 a^2 d+\text{$\#$1}^3 b^2 c}\&\right]-\frac{b^2}{3 a \left(\sqrt{a^2 x^2+b^2}+a x\right)^{3/2}}+\frac{\sqrt{\sqrt{a^2 x^2+b^2}+a x}}{a}",1,"(-1/3*b^2/(a*x + Sqrt[b^2 + a^2*x^2])^(3/2) + Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] - a^2*d*RootSum[c - 2*b^2*c*#1^4 - 4*a^2*d*#1^4 + b^4*c*#1^8 & , (Log[1/Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] - #1] + b^2*Log[1/Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] - #1]*#1^4)/(-(b^2*c*#1) - 2*a^2*d*#1 + b^4*c*#1^5) & ])/a","A",1
2459,1,194,199,0.1488828,"\int \frac{d+c x^2}{\left(-d+c x^2\right) \sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Integrate[(d + c*x^2)/((-d + c*x^2)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]),x]","\frac{a^2 (-d) \text{RootSum}\left[\text{$\#$1}^8 b^4 c-4 \text{$\#$1}^4 a^2 d-2 \text{$\#$1}^4 b^2 c+c\&,\frac{\text{$\#$1}^4 b^2 \log \left(\frac{1}{\sqrt{\sqrt{a^2 x^2+b^2}+a x}}-\text{$\#$1}\right)+\log \left(\frac{1}{\sqrt{\sqrt{a^2 x^2+b^2}+a x}}-\text{$\#$1}\right)}{\text{$\#$1}^5 b^4 c-2 \text{$\#$1} a^2 d-\text{$\#$1} b^2 c}\&\right]+\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\frac{b^2}{3 \left(\sqrt{a^2 x^2+b^2}+a x\right)^{3/2}}}{a}","a d \text{RootSum}\left[\text{$\#$1}^8 c-4 \text{$\#$1}^4 a^2 d-2 \text{$\#$1}^4 b^2 c+b^4 c\&,\frac{\text{$\#$1}^4 \left(-\log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)\right)-b^2 \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)}{\text{$\#$1}^7 (-c)+2 \text{$\#$1}^3 a^2 d+\text{$\#$1}^3 b^2 c}\&\right]-\frac{b^2}{3 a \left(\sqrt{a^2 x^2+b^2}+a x\right)^{3/2}}+\frac{\sqrt{\sqrt{a^2 x^2+b^2}+a x}}{a}",1,"(-1/3*b^2/(a*x + Sqrt[b^2 + a^2*x^2])^(3/2) + Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] - a^2*d*RootSum[c - 2*b^2*c*#1^4 - 4*a^2*d*#1^4 + b^4*c*#1^8 & , (Log[1/Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] - #1] + b^2*Log[1/Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] - #1]*#1^4)/(-(b^2*c*#1) - 2*a^2*d*#1 + b^4*c*#1^5) & ])/a","A",1
2460,1,314,200,0.731814,"\int \frac{1}{x^6 \left(b+a x^3\right) \sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Integrate[1/(x^6*(b + a*x^3)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","\frac{21870 a^{18} x^6+7290 a^{15} b^2 x^5-2430 a^{12} b^4 x^4+35343 a^{10} b^5 x^6+1350 a^9 b^6 x^3+11781 a^7 b^7 x^5-900 a^6 b^8 x^2-3927 a^4 b^9 x^4+660 a^3 b^{10} x+52360 a^2 b^{10} x^6 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a^3 x-\sqrt[3]{a} b^{5/3} x}{x a^3+b^2}\right)+52360 a^2 b^{10} x^6 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{2 x a^3+\left(1-i \sqrt{3}\right) b^{5/3} x \sqrt[3]{a}}{2 \left(x a^3+b^2\right)}\right)+52360 a^2 b^{10} x^6 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{2 x a^3+\left(1+i \sqrt{3}\right) b^{5/3} x \sqrt[3]{a}}{2 \left(x a^3+b^2\right)}\right)+19635 a b^{11} x^3-9240 b^{12}}{52360 b^{13} x^5 \sqrt[3]{x^2 \left(a^3 x+b^2\right)}}","-\frac{a^2 \text{RootSum}\left[-\text{$\#$1}^9+3 \text{$\#$1}^6 a^3-3 \text{$\#$1}^3 a^6+a^9-a b^5\&,\frac{\log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{3 b^3}-\frac{3 \left(a^3 x^3+b^2 x^2\right)^{2/3} \left(-7290 a^{15} x^5+4860 a^{12} b^2 x^4-4050 a^9 b^4 x^3-11781 a^7 b^5 x^5+3600 a^6 b^6 x^2+7854 a^4 b^7 x^4-3300 a^3 b^8 x-6545 a b^9 x^3+3080 b^{10}\right)}{52360 b^{13} x^7}",1,"(-9240*b^12 + 660*a^3*b^10*x - 900*a^6*b^8*x^2 + 1350*a^9*b^6*x^3 + 19635*a*b^11*x^3 - 2430*a^12*b^4*x^4 - 3927*a^4*b^9*x^4 + 7290*a^15*b^2*x^5 + 11781*a^7*b^7*x^5 + 21870*a^18*x^6 + 35343*a^10*b^5*x^6 + 52360*a^2*b^10*x^6*Hypergeometric2F1[1/3, 1, 4/3, (a^3*x - a^(1/3)*b^(5/3)*x)/(b^2 + a^3*x)] + 52360*a^2*b^10*x^6*Hypergeometric2F1[1/3, 1, 4/3, (2*a^3*x + (1 - I*Sqrt[3])*a^(1/3)*b^(5/3)*x)/(2*(b^2 + a^3*x))] + 52360*a^2*b^10*x^6*Hypergeometric2F1[1/3, 1, 4/3, (2*a^3*x + (1 + I*Sqrt[3])*a^(1/3)*b^(5/3)*x)/(2*(b^2 + a^3*x))])/(52360*b^13*x^5*(x^2*(b^2 + a^3*x))^(1/3))","C",1
2461,1,314,200,0.3015321,"\int \frac{1}{x^6 \left(b+a x^3\right) \sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Integrate[1/(x^6*(b + a*x^3)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","\frac{21870 a^{18} x^6+7290 a^{15} b^2 x^5-2430 a^{12} b^4 x^4+35343 a^{10} b^5 x^6+1350 a^9 b^6 x^3+11781 a^7 b^7 x^5-900 a^6 b^8 x^2-3927 a^4 b^9 x^4+660 a^3 b^{10} x+52360 a^2 b^{10} x^6 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a^3 x-\sqrt[3]{a} b^{5/3} x}{x a^3+b^2}\right)+52360 a^2 b^{10} x^6 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{2 x a^3+\left(1-i \sqrt{3}\right) b^{5/3} x \sqrt[3]{a}}{2 \left(x a^3+b^2\right)}\right)+52360 a^2 b^{10} x^6 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{2 x a^3+\left(1+i \sqrt{3}\right) b^{5/3} x \sqrt[3]{a}}{2 \left(x a^3+b^2\right)}\right)+19635 a b^{11} x^3-9240 b^{12}}{52360 b^{13} x^5 \sqrt[3]{x^2 \left(a^3 x+b^2\right)}}","-\frac{a^2 \text{RootSum}\left[-\text{$\#$1}^9+3 \text{$\#$1}^6 a^3-3 \text{$\#$1}^3 a^6+a^9-a b^5\&,\frac{\log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{3 b^3}-\frac{3 \left(a^3 x^3+b^2 x^2\right)^{2/3} \left(-7290 a^{15} x^5+4860 a^{12} b^2 x^4-4050 a^9 b^4 x^3-11781 a^7 b^5 x^5+3600 a^6 b^6 x^2+7854 a^4 b^7 x^4-3300 a^3 b^8 x-6545 a b^9 x^3+3080 b^{10}\right)}{52360 b^{13} x^7}",1,"(-9240*b^12 + 660*a^3*b^10*x - 900*a^6*b^8*x^2 + 1350*a^9*b^6*x^3 + 19635*a*b^11*x^3 - 2430*a^12*b^4*x^4 - 3927*a^4*b^9*x^4 + 7290*a^15*b^2*x^5 + 11781*a^7*b^7*x^5 + 21870*a^18*x^6 + 35343*a^10*b^5*x^6 + 52360*a^2*b^10*x^6*Hypergeometric2F1[1/3, 1, 4/3, (a^3*x - a^(1/3)*b^(5/3)*x)/(b^2 + a^3*x)] + 52360*a^2*b^10*x^6*Hypergeometric2F1[1/3, 1, 4/3, (2*a^3*x + (1 - I*Sqrt[3])*a^(1/3)*b^(5/3)*x)/(2*(b^2 + a^3*x))] + 52360*a^2*b^10*x^6*Hypergeometric2F1[1/3, 1, 4/3, (2*a^3*x + (1 + I*Sqrt[3])*a^(1/3)*b^(5/3)*x)/(2*(b^2 + a^3*x))])/(52360*b^13*x^5*(x^2*(b^2 + a^3*x))^(1/3))","C",1
2462,1,7717,200,9.1524556,"\int \frac{\left(-q+p x^2\right) \left(a q+b x+a p x^2\right) \sqrt{q^2+p^2 x^4}}{x^3 \left(c q+d x+c p x^2\right)} \, dx","Integrate[((-q + p*x^2)*(a*q + b*x + a*p*x^2)*Sqrt[q^2 + p^2*x^4])/(x^3*(c*q + d*x + c*p*x^2)),x]","\text{Result too large to show}","\frac{\sqrt{p^2 x^4+q^2} \left(a c p x^2+a c q-2 a d x+2 b c x\right)}{2 c^2 x^2}+\frac{\log \left(\sqrt{p^2 x^4+q^2}+p x^2+q\right) \left(-a c^2 p q+a d^2-b c d\right)}{c^3}-\frac{2 (a d-b c) \sqrt{2 c^2 p q-d^2} \tan ^{-1}\left(\frac{x \sqrt{2 c^2 p q-d^2}}{c \sqrt{p^2 x^4+q^2}+c p x^2+c q+d x}\right)}{c^3}+\frac{\log (x) \left(a c^2 p q-a d^2+b c d\right)}{c^3}",1,"Result too large to show","C",0
2463,0,0,200,0.1359925,"\int \frac{x \left(3+7 x^4\right)}{\sqrt[3]{1+x^4} \left(-4+x^3+x^7\right)} \, dx","Integrate[(x*(3 + 7*x^4))/((1 + x^4)^(1/3)*(-4 + x^3 + x^7)),x]","\int \frac{x \left(3+7 x^4\right)}{\sqrt[3]{1+x^4} \left(-4+x^3+x^7\right)} \, dx","\sqrt[3]{2} \tanh ^{-1}\left(1-\sqrt[3]{2} x \sqrt[3]{x^4+1}\right)-\frac{\sqrt{3} \tan ^{-1}\left(\frac{3 \sqrt{3} x \sqrt[3]{x^4+1}-6 x^2 \sqrt[3]{x^4+1}}{-3 \sqrt[3]{x^4+1} x+2 \sqrt{3} \sqrt[3]{x^4+1} x^2+4\ 2^{2/3} \sqrt{3} x-6\ 2^{2/3}}\right)}{2^{2/3}}-\frac{\tanh ^{-1}\left(\frac{2^{2/3} \sqrt[3]{x^4+1} x+2 \sqrt[3]{2}}{2^{2/3} \sqrt[3]{x^4+1} x+2 \left(x^4+1\right)^{2/3} x^2+2 \sqrt[3]{2}}\right)}{2^{2/3}}",1,"Integrate[(x*(3 + 7*x^4))/((1 + x^4)^(1/3)*(-4 + x^3 + x^7)), x]","F",-1
2464,1,191,200,0.6396441,"\int \frac{-d+c x^2}{\left(d+c x^2\right) \sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Integrate[(-d + c*x^2)/((d + c*x^2)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]),x]","a d \text{RootSum}\left[\text{$\#$1}^8 b^4 c+4 \text{$\#$1}^4 a^2 d-2 \text{$\#$1}^4 b^2 c+c\&,\frac{\text{$\#$1}^4 b^2 \log \left(\frac{1}{\sqrt{\sqrt{a^2 x^2+b^2}+a x}}-\text{$\#$1}\right)+\log \left(\frac{1}{\sqrt{\sqrt{a^2 x^2+b^2}+a x}}-\text{$\#$1}\right)}{\text{$\#$1}^5 b^4 c+2 \text{$\#$1} a^2 d-\text{$\#$1} b^2 c}\&\right]+\frac{2 \left(3 a x \left(\sqrt{a^2 x^2+b^2}+a x\right)+b^2\right)}{3 a \left(\sqrt{a^2 x^2+b^2}+a x\right)^{3/2}}","-a d \text{RootSum}\left[\text{$\#$1}^8 c+4 \text{$\#$1}^4 a^2 d-2 \text{$\#$1}^4 b^2 c+b^4 c\&,\frac{\text{$\#$1}^4 \left(-\log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)\right)-b^2 \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)}{\text{$\#$1}^7 (-c)-2 \text{$\#$1}^3 a^2 d+\text{$\#$1}^3 b^2 c}\&\right]-\frac{b^2}{3 a \left(\sqrt{a^2 x^2+b^2}+a x\right)^{3/2}}+\frac{\sqrt{\sqrt{a^2 x^2+b^2}+a x}}{a}",1,"(2*(b^2 + 3*a*x*(a*x + Sqrt[b^2 + a^2*x^2])))/(3*a*(a*x + Sqrt[b^2 + a^2*x^2])^(3/2)) + a*d*RootSum[c - 2*b^2*c*#1^4 + 4*a^2*d*#1^4 + b^4*c*#1^8 & , (Log[1/Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] - #1] + b^2*Log[1/Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] - #1]*#1^4)/(-(b^2*c*#1) + 2*a^2*d*#1 + b^4*c*#1^5) & ]","A",1
2465,1,191,200,0.2985542,"\int \frac{-d+c x^2}{\left(d+c x^2\right) \sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Integrate[(-d + c*x^2)/((d + c*x^2)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]),x]","a d \text{RootSum}\left[\text{$\#$1}^8 b^4 c+4 \text{$\#$1}^4 a^2 d-2 \text{$\#$1}^4 b^2 c+c\&,\frac{\text{$\#$1}^4 b^2 \log \left(\frac{1}{\sqrt{\sqrt{a^2 x^2+b^2}+a x}}-\text{$\#$1}\right)+\log \left(\frac{1}{\sqrt{\sqrt{a^2 x^2+b^2}+a x}}-\text{$\#$1}\right)}{\text{$\#$1}^5 b^4 c+2 \text{$\#$1} a^2 d-\text{$\#$1} b^2 c}\&\right]+\frac{2 \left(3 a x \left(\sqrt{a^2 x^2+b^2}+a x\right)+b^2\right)}{3 a \left(\sqrt{a^2 x^2+b^2}+a x\right)^{3/2}}","-a d \text{RootSum}\left[\text{$\#$1}^8 c+4 \text{$\#$1}^4 a^2 d-2 \text{$\#$1}^4 b^2 c+b^4 c\&,\frac{\text{$\#$1}^4 \left(-\log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)\right)-b^2 \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)}{\text{$\#$1}^7 (-c)-2 \text{$\#$1}^3 a^2 d+\text{$\#$1}^3 b^2 c}\&\right]-\frac{b^2}{3 a \left(\sqrt{a^2 x^2+b^2}+a x\right)^{3/2}}+\frac{\sqrt{\sqrt{a^2 x^2+b^2}+a x}}{a}",1,"(2*(b^2 + 3*a*x*(a*x + Sqrt[b^2 + a^2*x^2])))/(3*a*(a*x + Sqrt[b^2 + a^2*x^2])^(3/2)) + a*d*RootSum[c - 2*b^2*c*#1^4 + 4*a^2*d*#1^4 + b^4*c*#1^8 & , (Log[1/Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] - #1] + b^2*Log[1/Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] - #1]*#1^4)/(-(b^2*c*#1) + 2*a^2*d*#1 + b^4*c*#1^5) & ]","A",1
2466,1,205,200,1.808092,"\int \frac{\sqrt{-b x+a^2 x^2}}{\sqrt{a x^2+x \sqrt{-b x+a^2 x^2}}} \, dx","Integrate[Sqrt[-(b*x) + a^2*x^2]/Sqrt[a*x^2 + x*Sqrt[-(b*x) + a^2*x^2]],x]","\frac{b \sqrt{x \left(a^2 x-b\right)} \left(\sqrt{x \left(a^2 x-b\right)}+a x\right)^2 \left(4 \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};1-\frac{b}{2 a \left(a x+\sqrt{x \left(a^2 x-b\right)}\right)}\right)-\, _2F_1\left(-\frac{3}{2},2;-\frac{1}{2};1-\frac{b}{2 a \left(a x+\sqrt{x \left(a^2 x-b\right)}\right)}\right)-4\right)}{3 \sqrt{x \left(\sqrt{x \left(a^2 x-b\right)}+a x\right)} \left(a \left(\sqrt{x \left(a^2 x-b\right)}+a x\right)-b\right) \left(2 a \left(\sqrt{x \left(a^2 x-b\right)}+a x\right)-b\right)}","\frac{\sqrt{a^2 x^2-b x} \sqrt{x \left(\sqrt{a^2 x^2-b x}+a x\right)} \left(8 a^2 x-9 b\right)}{12 a b x}+\sqrt{x \left(\sqrt{a^2 x^2-b x}+a x\right)} \left(\frac{19 b-8 a^2 x}{12 b}+\frac{3 \sqrt{b} \sqrt{\sqrt{a^2 x^2-b x}-a x} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{\sqrt{a^2 x^2-b x}-a x}}{\sqrt{b}}\right)}{4 \sqrt{2} a^{3/2} x}\right)",1,"(b*Sqrt[x*(-b + a^2*x)]*(a*x + Sqrt[x*(-b + a^2*x)])^2*(-4 + 4*Hypergeometric2F1[-3/2, 1, -1/2, 1 - b/(2*a*(a*x + Sqrt[x*(-b + a^2*x)]))] - Hypergeometric2F1[-3/2, 2, -1/2, 1 - b/(2*a*(a*x + Sqrt[x*(-b + a^2*x)]))]))/(3*Sqrt[x*(a*x + Sqrt[x*(-b + a^2*x)])]*(-b + a*(a*x + Sqrt[x*(-b + a^2*x)]))*(-b + 2*a*(a*x + Sqrt[x*(-b + a^2*x)])))","C",1
2467,0,0,201,11.1138977,"\int \frac{a-2 b+x}{\sqrt[3]{(-a+x) (-b+x)} \left(a^2+b d-(2 a+d) x+x^2\right)} \, dx","Integrate[(a - 2*b + x)/(((-a + x)*(-b + x))^(1/3)*(a^2 + b*d - (2*a + d)*x + x^2)),x]","\int \frac{a-2 b+x}{\sqrt[3]{(-a+x) (-b+x)} \left(a^2+b d-(2 a+d) x+x^2\right)} \, dx","-\frac{\log \left(a^2+d^{2/3} \left(x (-a-b)+a b+x^2\right)^{2/3}+\sqrt[3]{x (-a-b)+a b+x^2} \left(\sqrt[3]{d} x-a \sqrt[3]{d}\right)-2 a x+x^2\right)}{2 d^{2/3}}+\frac{\log \left(\sqrt[3]{d} \sqrt[3]{x (-a-b)+a b+x^2}+a-x\right)}{d^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} \sqrt[3]{x (-a-b)+a b+x^2}}{\sqrt[3]{d} \sqrt[3]{x (-a-b)+a b+x^2}-2 a+2 x}\right)}{d^{2/3}}",1,"Integrate[(a - 2*b + x)/(((-a + x)*(-b + x))^(1/3)*(a^2 + b*d - (2*a + d)*x + x^2)), x]","F",-1
2468,0,0,201,1.0718376,"\int \frac{-a (a-2 b)-2 b x+x^2}{((-a+x) (-b+x))^{2/3} \left(b+a^2 d-(1+2 a d) x+d x^2\right)} \, dx","Integrate[(-(a*(a - 2*b)) - 2*b*x + x^2)/(((-a + x)*(-b + x))^(2/3)*(b + a^2*d - (1 + 2*a*d)*x + d*x^2)),x]","\int \frac{-a (a-2 b)-2 b x+x^2}{((-a+x) (-b+x))^{2/3} \left(b+a^2 d-(1+2 a d) x+d x^2\right)} \, dx","-\frac{\log \left(d^{2/3} \left(x (-a-b)+a b+x^2\right)^{4/3}+\left(x (-a-b)+a b+x^2\right)^{2/3} \left(\sqrt[3]{d} x-b \sqrt[3]{d}\right)+b^2-2 b x+x^2\right)}{2 d^{2/3}}+\frac{\log \left(\sqrt[3]{d} \left(x (-a-b)+a b+x^2\right)^{2/3}+b-x\right)}{d^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} \left(x (-a-b)+a b+x^2\right)^{2/3}}{\sqrt[3]{d} \left(x (-a-b)+a b+x^2\right)^{2/3}-2 b+2 x}\right)}{d^{2/3}}",1,"Integrate[(-(a*(a - 2*b)) - 2*b*x + x^2)/(((-a + x)*(-b + x))^(2/3)*(b + a^2*d - (1 + 2*a*d)*x + d*x^2)), x]","F",-1
2469,0,0,201,5.1969452,"\int \frac{-1+(2-k) x}{\sqrt[3]{(1-x) x (1-k x)} \left(1-(b+2 k) x+\left(b+k^2\right) x^2\right)} \, dx","Integrate[(-1 + (2 - k)*x)/(((1 - x)*x*(1 - k*x))^(1/3)*(1 - (b + 2*k)*x + (b + k^2)*x^2)),x]","\int \frac{-1+(2-k) x}{\sqrt[3]{(1-x) x (1-k x)} \left(1-(b+2 k) x+\left(b+k^2\right) x^2\right)} \, dx","-\frac{\log \left(b^{2/3} \left(k x^3+(-k-1) x^2+x\right)^{2/3}+\sqrt[3]{k x^3+(-k-1) x^2+x} \left(\sqrt[3]{b}-\sqrt[3]{b} k x\right)+k^2 x^2-2 k x+1\right)}{2 b^{2/3}}+\frac{\log \left(\sqrt[3]{b} \sqrt[3]{k x^3+(-k-1) x^2+x}+k x-1\right)}{b^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{b} \sqrt[3]{k x^3+(-k-1) x^2+x}}{\sqrt[3]{b} \sqrt[3]{k x^3+(-k-1) x^2+x}-2 k x+2}\right)}{b^{2/3}}",1,"Integrate[(-1 + (2 - k)*x)/(((1 - x)*x*(1 - k*x))^(1/3)*(1 - (b + 2*k)*x + (b + k^2)*x^2)), x]","F",-1
2470,0,0,201,0.5697695,"\int \frac{-3 k-2 \left(1+k^2\right) x+k \left(1+k^2\right) x^2+4 k^2 x^3+k^3 x^4}{\left(\left(1-x^2\right) \left(1-k^2 x^2\right)\right)^{2/3} \left(-1+d-(2+d) k x-\left(d+k^2\right) x^2+d k x^3\right)} \, dx","Integrate[(-3*k - 2*(1 + k^2)*x + k*(1 + k^2)*x^2 + 4*k^2*x^3 + k^3*x^4)/(((1 - x^2)*(1 - k^2*x^2))^(2/3)*(-1 + d - (2 + d)*k*x - (d + k^2)*x^2 + d*k*x^3)),x]","\int \frac{-3 k-2 \left(1+k^2\right) x+k \left(1+k^2\right) x^2+4 k^2 x^3+k^3 x^4}{\left(\left(1-x^2\right) \left(1-k^2 x^2\right)\right)^{2/3} \left(-1+d-(2+d) k x-\left(d+k^2\right) x^2+d k x^3\right)} \, dx","-\frac{\log \left(d^{2/3} \left(k^2 x^4+\left(-k^2-1\right) x^2+1\right)^{2/3}+\sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1} \left(\sqrt[3]{d} k x+\sqrt[3]{d}\right)+k^2 x^2+2 k x+1\right)}{2 \sqrt[3]{d}}+\frac{\log \left(-\sqrt[3]{d} \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}+k x+1\right)}{\sqrt[3]{d}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} k x+\sqrt{3}}{2 \sqrt[3]{d} \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}+k x+1}\right)}{\sqrt[3]{d}}",1,"Integrate[(-3*k - 2*(1 + k^2)*x + k*(1 + k^2)*x^2 + 4*k^2*x^3 + k^3*x^4)/(((1 - x^2)*(1 - k^2*x^2))^(2/3)*(-1 + d - (2 + d)*k*x - (d + k^2)*x^2 + d*k*x^3)), x]","F",-1
2471,1,181,201,0.2843264,"\int \frac{-1+2 x^4}{\sqrt[4]{1+x^4} \left(-1+x^4+x^8\right)} \, dx","Integrate[(-1 + 2*x^4)/((1 + x^4)^(1/4)*(-1 + x^4 + x^8)),x]","\frac{\sqrt[4]{123+55 \sqrt{5}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3+\sqrt{5}}} x}{\sqrt[4]{x^4+1}}\right)-\sqrt[4]{123-55 \sqrt{5}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x}{\sqrt[4]{x^4+1}}\right)+\sqrt[4]{123+55 \sqrt{5}} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3+\sqrt{5}}} x}{\sqrt[4]{x^4+1}}\right)-\sqrt[4]{123-55 \sqrt{5}} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x}{\sqrt[4]{x^4+1}}\right)}{2 \sqrt[4]{2} \sqrt{5}}","\frac{1}{2} \sqrt{\frac{1}{10} \left(11+5 \sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}} x}{\sqrt[4]{x^4+1}}\right)-\frac{1}{2} \sqrt{\frac{1}{10} \left(5 \sqrt{5}-11\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{1}{2}+\frac{\sqrt{5}}{2}} x}{\sqrt[4]{x^4+1}}\right)+\frac{1}{2} \sqrt{\frac{1}{10} \left(11+5 \sqrt{5}\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}} x}{\sqrt[4]{x^4+1}}\right)-\frac{1}{2} \sqrt{\frac{1}{10} \left(5 \sqrt{5}-11\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{2}+\frac{\sqrt{5}}{2}} x}{\sqrt[4]{x^4+1}}\right)",1,"((123 + 55*Sqrt[5])^(1/4)*ArcTan[((2/(3 + Sqrt[5]))^(1/4)*x)/(1 + x^4)^(1/4)] - (123 - 55*Sqrt[5])^(1/4)*ArcTan[(((3 + Sqrt[5])/2)^(1/4)*x)/(1 + x^4)^(1/4)] + (123 + 55*Sqrt[5])^(1/4)*ArcTanh[((2/(3 + Sqrt[5]))^(1/4)*x)/(1 + x^4)^(1/4)] - (123 - 55*Sqrt[5])^(1/4)*ArcTanh[(((3 + Sqrt[5])/2)^(1/4)*x)/(1 + x^4)^(1/4)])/(2*2^(1/4)*Sqrt[5])","A",0
2472,0,0,203,14.5645205,"\int \frac{\left(-2 x+(1+k) x^2\right) \left(a-a (1+k) x+(1+a k) x^2\right)}{(-1+x) ((1-x) x (1-k x))^{2/3} (-1+k x) \left(b-b (1+k) x+(-1+b k) x^2\right)} \, dx","Integrate[((-2*x + (1 + k)*x^2)*(a - a*(1 + k)*x + (1 + a*k)*x^2))/((-1 + x)*((1 - x)*x*(1 - k*x))^(2/3)*(-1 + k*x)*(b - b*(1 + k)*x + (-1 + b*k)*x^2)),x]","\int \frac{\left(-2 x+(1+k) x^2\right) \left(a-a (1+k) x+(1+a k) x^2\right)}{(-1+x) ((1-x) x (1-k x))^{2/3} (-1+k x) \left(b-b (1+k) x+(-1+b k) x^2\right)} \, dx","\frac{(-a-b) \log \left(b^{2/3} \left(k x^3+(-k-1) x^2+x\right)^{2/3}+\sqrt[3]{b} x \sqrt[3]{k x^3+(-k-1) x^2+x}+x^2\right)}{2 \sqrt[3]{b}}+\frac{(a+b) \log \left(x-\sqrt[3]{b} \sqrt[3]{k x^3+(-k-1) x^2+x}\right)}{\sqrt[3]{b}}+\frac{\left(\sqrt{3} a+\sqrt{3} b\right) \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{b} \sqrt[3]{k x^3+(-k-1) x^2+x}+x}\right)}{\sqrt[3]{b}}+\frac{3 x^2}{2 \left(k x^3-k x^2-x^2+x\right)^{2/3}}",1,"Integrate[((-2*x + (1 + k)*x^2)*(a - a*(1 + k)*x + (1 + a*k)*x^2))/((-1 + x)*((1 - x)*x*(1 - k*x))^(2/3)*(-1 + k*x)*(b - b*(1 + k)*x + (-1 + b*k)*x^2)), x]","F",-1
2473,0,0,203,0.5557794,"\int \frac{-3 k+2 \left(1+k^2\right) x+k \left(1+k^2\right) x^2-4 k^2 x^3+k^3 x^4}{\left(\left(1-x^2\right) \left(1-k^2 x^2\right)\right)^{2/3} \left(1-d-(2+d) k x+\left(d+k^2\right) x^2+d k x^3\right)} \, dx","Integrate[(-3*k + 2*(1 + k^2)*x + k*(1 + k^2)*x^2 - 4*k^2*x^3 + k^3*x^4)/(((1 - x^2)*(1 - k^2*x^2))^(2/3)*(1 - d - (2 + d)*k*x + (d + k^2)*x^2 + d*k*x^3)),x]","\int \frac{-3 k+2 \left(1+k^2\right) x+k \left(1+k^2\right) x^2-4 k^2 x^3+k^3 x^4}{\left(\left(1-x^2\right) \left(1-k^2 x^2\right)\right)^{2/3} \left(1-d-(2+d) k x+\left(d+k^2\right) x^2+d k x^3\right)} \, dx","-\frac{\log \left(d^{2/3} \left(k^2 x^4+\left(-k^2-1\right) x^2+1\right)^{2/3}+\sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1} \left(\sqrt[3]{d}-\sqrt[3]{d} k x\right)+k^2 x^2-2 k x+1\right)}{2 \sqrt[3]{d}}+\frac{\log \left(\sqrt[3]{d} \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}+k x-1\right)}{\sqrt[3]{d}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} k x-\sqrt{3}}{-2 \sqrt[3]{d} \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}+k x-1}\right)}{\sqrt[3]{d}}",1,"Integrate[(-3*k + 2*(1 + k^2)*x + k*(1 + k^2)*x^2 - 4*k^2*x^3 + k^3*x^4)/(((1 - x^2)*(1 - k^2*x^2))^(2/3)*(1 - d - (2 + d)*k*x + (d + k^2)*x^2 + d*k*x^3)), x]","F",-1
2474,0,0,203,6.197082,"\int \frac{\sqrt[3]{-x+x^3} \left(-b+a x^6\right)}{-d+c x^6} \, dx","Integrate[((-x + x^3)^(1/3)*(-b + a*x^6))/(-d + c*x^6),x]","\int \frac{\sqrt[3]{-x+x^3} \left(-b+a x^6\right)}{-d+c x^6} \, dx","\frac{(b c-a d) \text{RootSum}\left[\text{$\#$1}^9 d-3 \text{$\#$1}^6 d+3 \text{$\#$1}^3 d+c-d\&,\frac{\text{$\#$1} \log \left(\sqrt[3]{x^3-x}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^3-1}\&\right]}{6 c d}+\frac{a \sqrt[3]{x^3-x} x}{2 c}+\frac{a \log \left(\sqrt[3]{x^3-x}-x\right)}{6 c}+\frac{a \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-x}+x}\right)}{2 \sqrt{3} c}-\frac{a \log \left(\sqrt[3]{x^3-x} x+\left(x^3-x\right)^{2/3}+x^2\right)}{12 c}",1,"Integrate[((-x + x^3)^(1/3)*(-b + a*x^6))/(-d + c*x^6), x]","F",-1
2475,0,0,203,4.1929507,"\int \frac{\sqrt[3]{-x+x^3} \left(-b+a x^6\right)}{-d+c x^6} \, dx","Integrate[((-x + x^3)^(1/3)*(-b + a*x^6))/(-d + c*x^6),x]","\int \frac{\sqrt[3]{-x+x^3} \left(-b+a x^6\right)}{-d+c x^6} \, dx","\frac{(b c-a d) \text{RootSum}\left[\text{$\#$1}^9 d-3 \text{$\#$1}^6 d+3 \text{$\#$1}^3 d+c-d\&,\frac{\text{$\#$1} \log \left(\sqrt[3]{x^3-x}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^3-1}\&\right]}{6 c d}+\frac{a \sqrt[3]{x^3-x} x}{2 c}+\frac{a \log \left(\sqrt[3]{x^3-x}-x\right)}{6 c}+\frac{a \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-x}+x}\right)}{2 \sqrt{3} c}-\frac{a \log \left(\sqrt[3]{x^3-x} x+\left(x^3-x\right)^{2/3}+x^2\right)}{12 c}",1,"Integrate[((-x + x^3)^(1/3)*(-b + a*x^6))/(-d + c*x^6), x]","F",-1
2476,0,0,203,0.1565949,"\int \frac{1}{1-x \sqrt{c+b x+a x^2}} \, dx","Integrate[(1 - x*Sqrt[c + b*x + a*x^2])^(-1),x]","\int \frac{1}{1-x \sqrt{c+b x+a x^2}} \, dx","-2 \text{RootSum}\left[\text{$\#$1}^4 \sqrt{a}-\text{$\#$1}^3 b+4 \text{$\#$1}^2 a-4 \text{$\#$1} \sqrt{a} b+\text{$\#$1} b c-\sqrt{a} c^2+b^2\&,\frac{\text{$\#$1}^2 \sqrt{a} \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)-\text{$\#$1} b \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)+\sqrt{a} c \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)}{4 \text{$\#$1}^3 \sqrt{a}-3 \text{$\#$1}^2 b+8 \text{$\#$1} a-4 \sqrt{a} b+b c}\&\right]",1,"Integrate[(1 - x*Sqrt[c + b*x + a*x^2])^(-1), x]","F",-1
2477,1,145,204,0.2391313,"\int \frac{-b+a x^2}{\left(-b+2 a x^2\right) \sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Integrate[(-b + a*x^2)/((-b + 2*a*x^2)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","\frac{3 x \left(2 \sqrt[3]{\frac{a^3 x}{b^2}+1} \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};-\frac{a^3 x}{b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a^3 x-\sqrt{2} \sqrt{a} b^{3/2} x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{x a^3+\sqrt{2} b^{3/2} x \sqrt{a}}{x a^3+b^2}\right)\right)}{4 \sqrt[3]{x^2 \left(a^3 x+b^2\right)}}","-\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^6-2 \text{$\#$1}^3 a^3+a^6-2 a b^3\&,\frac{\log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]-\frac{\log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-a x\right)}{2 a}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} a x}{2 \sqrt[3]{a^3 x^3+b^2 x^2}+a x}\right)}{2 a}+\frac{\log \left(a x \sqrt[3]{a^3 x^3+b^2 x^2}+\left(a^3 x^3+b^2 x^2\right)^{2/3}+a^2 x^2\right)}{4 a}",1,"(3*x*(2*(1 + (a^3*x)/b^2)^(1/3)*Hypergeometric2F1[1/3, 1/3, 4/3, -((a^3*x)/b^2)] + Hypergeometric2F1[1/3, 1, 4/3, (a^3*x - Sqrt[2]*Sqrt[a]*b^(3/2)*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a^3*x + Sqrt[2]*Sqrt[a]*b^(3/2)*x)/(b^2 + a^3*x)]))/(4*(x^2*(b^2 + a^3*x))^(1/3))","A",1
2478,1,145,204,0.0979641,"\int \frac{-b+a x^2}{\left(-b+2 a x^2\right) \sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Integrate[(-b + a*x^2)/((-b + 2*a*x^2)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","\frac{3 x \left(2 \sqrt[3]{\frac{a^3 x}{b^2}+1} \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};-\frac{a^3 x}{b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a^3 x-\sqrt{2} \sqrt{a} b^{3/2} x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{x a^3+\sqrt{2} b^{3/2} x \sqrt{a}}{x a^3+b^2}\right)\right)}{4 \sqrt[3]{x^2 \left(a^3 x+b^2\right)}}","-\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^6-2 \text{$\#$1}^3 a^3+a^6-2 a b^3\&,\frac{\log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]-\frac{\log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-a x\right)}{2 a}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} a x}{2 \sqrt[3]{a^3 x^3+b^2 x^2}+a x}\right)}{2 a}+\frac{\log \left(a x \sqrt[3]{a^3 x^3+b^2 x^2}+\left(a^3 x^3+b^2 x^2\right)^{2/3}+a^2 x^2\right)}{4 a}",1,"(3*x*(2*(1 + (a^3*x)/b^2)^(1/3)*Hypergeometric2F1[1/3, 1/3, 4/3, -((a^3*x)/b^2)] + Hypergeometric2F1[1/3, 1, 4/3, (a^3*x - Sqrt[2]*Sqrt[a]*b^(3/2)*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, (a^3*x + Sqrt[2]*Sqrt[a]*b^(3/2)*x)/(b^2 + a^3*x)]))/(4*(x^2*(b^2 + a^3*x))^(1/3))","A",1
2479,1,145,204,0.204886,"\int \frac{b+a x^2}{\left(b+2 a x^2\right) \sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Integrate[(b + a*x^2)/((b + 2*a*x^2)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","\frac{3 x \left(2 \sqrt[3]{\frac{a^3 x}{b^2}+1} \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};-\frac{a^3 x}{b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(a^3-\sqrt{2} \sqrt{-a} b^{3/2}\right) x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(a^3+\sqrt{2} \sqrt{-a} b^{3/2}\right) x}{x a^3+b^2}\right)\right)}{4 \sqrt[3]{x^2 \left(a^3 x+b^2\right)}}","-\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^6-2 \text{$\#$1}^3 a^3+a^6+2 a b^3\&,\frac{\log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]-\frac{\log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-a x\right)}{2 a}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} a x}{2 \sqrt[3]{a^3 x^3+b^2 x^2}+a x}\right)}{2 a}+\frac{\log \left(a x \sqrt[3]{a^3 x^3+b^2 x^2}+\left(a^3 x^3+b^2 x^2\right)^{2/3}+a^2 x^2\right)}{4 a}",1,"(3*x*(2*(1 + (a^3*x)/b^2)^(1/3)*Hypergeometric2F1[1/3, 1/3, 4/3, -((a^3*x)/b^2)] + Hypergeometric2F1[1/3, 1, 4/3, ((a^3 - Sqrt[2]*Sqrt[-a]*b^(3/2))*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, ((a^3 + Sqrt[2]*Sqrt[-a]*b^(3/2))*x)/(b^2 + a^3*x)]))/(4*(x^2*(b^2 + a^3*x))^(1/3))","A",1
2480,1,145,204,0.0922175,"\int \frac{b+a x^2}{\left(b+2 a x^2\right) \sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Integrate[(b + a*x^2)/((b + 2*a*x^2)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","\frac{3 x \left(2 \sqrt[3]{\frac{a^3 x}{b^2}+1} \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};-\frac{a^3 x}{b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(a^3-\sqrt{2} \sqrt{-a} b^{3/2}\right) x}{x a^3+b^2}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(a^3+\sqrt{2} \sqrt{-a} b^{3/2}\right) x}{x a^3+b^2}\right)\right)}{4 \sqrt[3]{x^2 \left(a^3 x+b^2\right)}}","-\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^6-2 \text{$\#$1}^3 a^3+a^6+2 a b^3\&,\frac{\log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]-\frac{\log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-a x\right)}{2 a}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} a x}{2 \sqrt[3]{a^3 x^3+b^2 x^2}+a x}\right)}{2 a}+\frac{\log \left(a x \sqrt[3]{a^3 x^3+b^2 x^2}+\left(a^3 x^3+b^2 x^2\right)^{2/3}+a^2 x^2\right)}{4 a}",1,"(3*x*(2*(1 + (a^3*x)/b^2)^(1/3)*Hypergeometric2F1[1/3, 1/3, 4/3, -((a^3*x)/b^2)] + Hypergeometric2F1[1/3, 1, 4/3, ((a^3 - Sqrt[2]*Sqrt[-a]*b^(3/2))*x)/(b^2 + a^3*x)] + Hypergeometric2F1[1/3, 1, 4/3, ((a^3 + Sqrt[2]*Sqrt[-a]*b^(3/2))*x)/(b^2 + a^3*x)]))/(4*(x^2*(b^2 + a^3*x))^(1/3))","A",1
2481,0,0,204,3.0890208,"\int \frac{x \left(4 a b-3 (a+b) x+2 x^2\right)}{\sqrt[3]{x^2 (-a+x) (-b+x)} \left(-a b+(a+b) x-x^2+d x^4\right)} \, dx","Integrate[(x*(4*a*b - 3*(a + b)*x + 2*x^2))/((x^2*(-a + x)*(-b + x))^(1/3)*(-(a*b) + (a + b)*x - x^2 + d*x^4)),x]","\int \frac{x \left(4 a b-3 (a+b) x+2 x^2\right)}{\sqrt[3]{x^2 (-a+x) (-b+x)} \left(-a b+(a+b) x-x^2+d x^4\right)} \, dx","-\frac{\log \left(\sqrt[3]{d} x^2 \sqrt[3]{x^3 (-a-b)+a b x^2+x^4}+\left(x^3 (-a-b)+a b x^2+x^4\right)^{2/3}+d^{2/3} x^4\right)}{2 \sqrt[3]{d}}+\frac{\log \left(\sqrt[3]{x^3 (-a-b)+a b x^2+x^4}-\sqrt[3]{d} x^2\right)}{\sqrt[3]{d}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x^3 (-a-b)+a b x^2+x^4}}{\sqrt[3]{x^3 (-a-b)+a b x^2+x^4}+2 \sqrt[3]{d} x^2}\right)}{\sqrt[3]{d}}",1,"Integrate[(x*(4*a*b - 3*(a + b)*x + 2*x^2))/((x^2*(-a + x)*(-b + x))^(1/3)*(-(a*b) + (a + b)*x - x^2 + d*x^4)), x]","F",-1
2482,0,0,204,0.5156393,"\int \frac{\sqrt[4]{b+a x^4} \left(2 b+3 a x^4\right)}{x^6 \left(b+a x^8\right)} \, dx","Integrate[((b + a*x^4)^(1/4)*(2*b + 3*a*x^4))/(x^6*(b + a*x^8)),x]","\int \frac{\sqrt[4]{b+a x^4} \left(2 b+3 a x^4\right)}{x^6 \left(b+a x^8\right)} \, dx","\frac{\left(-17 a x^4-2 b\right) \sqrt[4]{a x^4+b}}{5 b x^5}-\frac{a \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{-3 \text{$\#$1}^4 a \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+2 \text{$\#$1}^4 b \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+3 \text{$\#$1}^4 a \log (x)-2 \text{$\#$1}^4 b \log (x)+3 a^2 \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+3 a b \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)-3 a^2 \log (x)-3 a b \log (x)}{\text{$\#$1}^3 a-\text{$\#$1}^7}\&\right]}{8 b}",1,"Integrate[((b + a*x^4)^(1/4)*(2*b + 3*a*x^4))/(x^6*(b + a*x^8)), x]","F",-1
2483,0,0,204,0.2621512,"\int \frac{\sqrt[4]{b+a x^4} \left(2 b+3 a x^4\right)}{x^6 \left(b+a x^8\right)} \, dx","Integrate[((b + a*x^4)^(1/4)*(2*b + 3*a*x^4))/(x^6*(b + a*x^8)),x]","\int \frac{\sqrt[4]{b+a x^4} \left(2 b+3 a x^4\right)}{x^6 \left(b+a x^8\right)} \, dx","\frac{\left(-17 a x^4-2 b\right) \sqrt[4]{a x^4+b}}{5 b x^5}-\frac{a \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{-3 \text{$\#$1}^4 a \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+2 \text{$\#$1}^4 b \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+3 \text{$\#$1}^4 a \log (x)-2 \text{$\#$1}^4 b \log (x)+3 a^2 \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+3 a b \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)-3 a^2 \log (x)-3 a b \log (x)}{\text{$\#$1}^3 a-\text{$\#$1}^7}\&\right]}{8 b}",1,"Integrate[((b + a*x^4)^(1/4)*(2*b + 3*a*x^4))/(x^6*(b + a*x^8)), x]","F",-1
2484,1,2581,204,6.3944451,"\int \frac{\sqrt{x+\sqrt{1+x}}}{1+x^2} \, dx","Integrate[Sqrt[x + Sqrt[1 + x]]/(1 + x^2),x]","\text{Result too large to show}","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^5+20 \text{$\#$1}^4-48 \text{$\#$1}^3+40 \text{$\#$1}^2-8 \text{$\#$1}+1\&,\frac{\text{$\#$1}^6 \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)-2 \text{$\#$1}^5 \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)+2 \text{$\#$1} \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)+\log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+5 \text{$\#$1}^4+10 \text{$\#$1}^3-18 \text{$\#$1}^2+10 \text{$\#$1}-1}\&\right]",1,"(((1 + I) + Sqrt[1 - I])*ArcTan[((2 - 3*I) + (3 - I)*Sqrt[1 - I] - 8*Sqrt[1 + x] - 5*Sqrt[1 - I]*Sqrt[1 + x] + (2 + 5*I)*(1 + x) + (5*I)*Sqrt[1 - I]*(1 + x) + 4*Sqrt[I - Sqrt[1 - I]]*Sqrt[x + Sqrt[1 + x]] + 2*Sqrt[1 - I]*Sqrt[I - Sqrt[1 - I]]*Sqrt[x + Sqrt[1 + x]] - (6 + 2*I)*Sqrt[I - Sqrt[1 - I]]*Sqrt[1 + x]*Sqrt[x + Sqrt[1 + x]] - (8*Sqrt[I - Sqrt[1 - I]]*Sqrt[1 + x]*Sqrt[x + Sqrt[1 + x]])/Sqrt[1 - I])/((-4 + 7*I) - (6 - 2*I)*Sqrt[1 - I] + (4 - 2*I)*Sqrt[1 + x] + (6 - 2*I)*Sqrt[1 - I]*Sqrt[1 + x] + (10 + I)*(1 + x) + (8 + 4*I)*Sqrt[1 - I]*(1 + x))])/(2*Sqrt[1 - I]*Sqrt[I - Sqrt[1 - I]]) + (((-1 - I) + Sqrt[1 - I])*ArcTan[((-2 + 3*I) + (3 - I)*Sqrt[1 - I] + 8*Sqrt[1 + x] - 5*Sqrt[1 - I]*Sqrt[1 + x] - (2 + 5*I)*(1 + x) + (5*I)*Sqrt[1 - I]*(1 + x) - 4*Sqrt[I + Sqrt[1 - I]]*Sqrt[x + Sqrt[1 + x]] + 2*Sqrt[1 - I]*Sqrt[I + Sqrt[1 - I]]*Sqrt[x + Sqrt[1 + x]] + (6 + 2*I)*Sqrt[I + Sqrt[1 - I]]*Sqrt[1 + x]*Sqrt[x + Sqrt[1 + x]] - (8*Sqrt[I + Sqrt[1 - I]]*Sqrt[1 + x]*Sqrt[x + Sqrt[1 + x]])/Sqrt[1 - I])/((4 - 7*I) - (6 - 2*I)*Sqrt[1 - I] - (4 - 2*I)*Sqrt[1 + x] + (6 - 2*I)*Sqrt[1 - I]*Sqrt[1 + x] - (10 + I)*(1 + x) + (8 + 4*I)*Sqrt[1 - I]*(1 + x))])/(2*Sqrt[1 - I]*Sqrt[I + Sqrt[1 - I]]) - ((I/2)*((-1 + I) + Sqrt[1 + I])*ArcTan[((1 + 8*I) - 5*(1 + I)^(3/2) - (16 + 8*I)*Sqrt[1 + x] + (10 + 5*I)*Sqrt[1 + I]*Sqrt[1 + x] + (9 - 8*I)*(1 + x) - (5 - 10*I)*Sqrt[1 + I]*(1 + x) - 4*Sqrt[I - Sqrt[1 + I]]*Sqrt[x + Sqrt[1 + x]] + (4 - 2*I)*Sqrt[1 + I]*Sqrt[I - Sqrt[1 + I]]*Sqrt[x + Sqrt[1 + x]] - 8*Sqrt[I - Sqrt[1 + I]]*Sqrt[1 + x]*Sqrt[x + Sqrt[1 + x]] + (8 - 4*I)*Sqrt[1 + I]*Sqrt[I - Sqrt[1 + I]]*Sqrt[1 + x]*Sqrt[x + Sqrt[1 + x]])/((9 + 20*I) - 12*(1 + I)^(3/2) - (14 + 20*I)*Sqrt[1 + x] + (22 + 12*I)*Sqrt[1 + I]*Sqrt[1 + x] + (6 - 15*I)*(1 + x) + (2 + 12*I)*Sqrt[1 + I]*(1 + x))])/(Sqrt[1 + I]*Sqrt[I - Sqrt[1 + I]]) - ((I/2)*((1 - I) + Sqrt[1 + I])*ArcTan[((-1 - 8*I) - 5*(1 + I)^(3/2) + (16 + 8*I)*Sqrt[1 + x] + (10 + 5*I)*Sqrt[1 + I]*Sqrt[1 + x] - (9 - 8*I)*(1 + x) - (5 - 10*I)*Sqrt[1 + I]*(1 + x) + 4*Sqrt[I + Sqrt[1 + I]]*Sqrt[x + Sqrt[1 + x]] + (4 - 2*I)*Sqrt[1 + I]*Sqrt[I + Sqrt[1 + I]]*Sqrt[x + Sqrt[1 + x]] + 8*Sqrt[I + Sqrt[1 + I]]*Sqrt[1 + x]*Sqrt[x + Sqrt[1 + x]] + (8 - 4*I)*Sqrt[1 + I]*Sqrt[I + Sqrt[1 + I]]*Sqrt[1 + x]*Sqrt[x + Sqrt[1 + x]])/((-9 - 20*I) - 12*(1 + I)^(3/2) + (14 + 20*I)*Sqrt[1 + x] + (22 + 12*I)*Sqrt[1 + I]*Sqrt[1 + x] - (6 - 15*I)*(1 + x) + (2 + 12*I)*Sqrt[1 + I]*(1 + x))])/(Sqrt[1 + I]*Sqrt[I + Sqrt[1 + I]]) + ((I/4)*((1 + I) + Sqrt[1 - I])*Log[(Sqrt[1 - I] - Sqrt[1 + x])^2])/(Sqrt[1 - I]*Sqrt[I - Sqrt[1 - I]]) + (((1 - I) + Sqrt[1 + I])*Log[(Sqrt[1 + I] - Sqrt[1 + x])^2])/(4*Sqrt[1 + I]*Sqrt[I + Sqrt[1 + I]]) + ((I/4)*((-1 - I) + Sqrt[1 - I])*Log[(Sqrt[1 - I] + Sqrt[1 + x])^2])/(Sqrt[1 - I]*Sqrt[I + Sqrt[1 - I]]) + (((-1 + I) + Sqrt[1 + I])*Log[(Sqrt[1 + I] + Sqrt[1 + x])^2])/(4*Sqrt[1 + I]*Sqrt[I - Sqrt[1 + I]]) - ((I/4)*((1 + I) + Sqrt[1 - I])*Log[(5 + 17*I) + (14*I)*Sqrt[1 - I] - (10 + 22*I)*Sqrt[1 + x] + (5 - 19*I)*Sqrt[1 - I]*Sqrt[1 + x] - (25 + 2*I)*(1 + x) - (15 + 9*I)*Sqrt[1 - I]*(1 + x) - (4 - 4*I)*Sqrt[I - Sqrt[1 - I]]*Sqrt[x + Sqrt[1 + x]] - (6 - 2*I)*Sqrt[1 - I]*Sqrt[I - Sqrt[1 - I]]*Sqrt[x + Sqrt[1 + x]] - (8 - 8*I)*Sqrt[I - Sqrt[1 - I]]*Sqrt[1 + x]*Sqrt[x + Sqrt[1 + x]] - (12 - 4*I)*Sqrt[1 - I]*Sqrt[I - Sqrt[1 - I]]*Sqrt[1 + x]*Sqrt[x + Sqrt[1 + x]]])/(Sqrt[1 - I]*Sqrt[I - Sqrt[1 - I]]) - ((I/4)*((-1 - I) + Sqrt[1 - I])*Log[(-5 - 17*I) + (14*I)*Sqrt[1 - I] + (10 + 22*I)*Sqrt[1 + x] + (5 - 19*I)*Sqrt[1 - I]*Sqrt[1 + x] + (25 + 2*I)*(1 + x) - (15 + 9*I)*Sqrt[1 - I]*(1 + x) + (4 - 4*I)*Sqrt[I + Sqrt[1 - I]]*Sqrt[x + Sqrt[1 + x]] - (6 - 2*I)*Sqrt[1 - I]*Sqrt[I + Sqrt[1 - I]]*Sqrt[x + Sqrt[1 + x]] + (8 - 8*I)*Sqrt[I + Sqrt[1 - I]]*Sqrt[1 + x]*Sqrt[x + Sqrt[1 + x]] - (12 - 4*I)*Sqrt[1 - I]*Sqrt[I + Sqrt[1 - I]]*Sqrt[1 + x]*Sqrt[x + Sqrt[1 + x]]])/(Sqrt[1 - I]*Sqrt[I + Sqrt[1 - I]]) - (((-1 + I) + Sqrt[1 + I])*Log[(-3 + 5*I) - (2 + 4*I)*Sqrt[1 + I] + (2 - 2*I)*Sqrt[1 + x] - (1 - 3*I)*Sqrt[1 + I]*Sqrt[1 + x] - (8 + 7*I)*(1 + x) + (9 + 3*I)*Sqrt[1 + I]*(1 + x) + (4 + 4*I)*Sqrt[I - Sqrt[1 + I]]*Sqrt[x + Sqrt[1 + x]] - 2*(1 + I)^(3/2)*Sqrt[I - Sqrt[1 + I]]*Sqrt[x + Sqrt[1 + x]] - (8 + 4*I)*Sqrt[I - Sqrt[1 + I]]*Sqrt[1 + x]*Sqrt[x + Sqrt[1 + x]] + 8*Sqrt[1 + I]*Sqrt[I - Sqrt[1 + I]]*Sqrt[1 + x]*Sqrt[x + Sqrt[1 + x]]])/(4*Sqrt[1 + I]*Sqrt[I - Sqrt[1 + I]]) - (((1 - I) + Sqrt[1 + I])*Log[(3 - 5*I) - (2 + 4*I)*Sqrt[1 + I] - (2 - 2*I)*Sqrt[1 + x] - (1 - 3*I)*Sqrt[1 + I]*Sqrt[1 + x] + (8 + 7*I)*(1 + x) + (9 + 3*I)*Sqrt[1 + I]*(1 + x) - (4 + 4*I)*Sqrt[I + Sqrt[1 + I]]*Sqrt[x + Sqrt[1 + x]] - 2*(1 + I)^(3/2)*Sqrt[I + Sqrt[1 + I]]*Sqrt[x + Sqrt[1 + x]] + (8 + 4*I)*Sqrt[I + Sqrt[1 + I]]*Sqrt[1 + x]*Sqrt[x + Sqrt[1 + x]] + 8*Sqrt[1 + I]*Sqrt[I + Sqrt[1 + I]]*Sqrt[1 + x]*Sqrt[x + Sqrt[1 + x]]])/(4*Sqrt[1 + I]*Sqrt[I + Sqrt[1 + I]])","C",0
2485,1,2581,204,6.4255108,"\int \frac{\sqrt{x+\sqrt{1+x}}}{1+x^2} \, dx","Integrate[Sqrt[x + Sqrt[1 + x]]/(1 + x^2),x]","\text{Result too large to show}","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^5+20 \text{$\#$1}^4-48 \text{$\#$1}^3+40 \text{$\#$1}^2-8 \text{$\#$1}+1\&,\frac{\text{$\#$1}^6 \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)-2 \text{$\#$1}^5 \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)+2 \text{$\#$1} \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)+\log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+5 \text{$\#$1}^4+10 \text{$\#$1}^3-18 \text{$\#$1}^2+10 \text{$\#$1}-1}\&\right]",1,"(((1 + I) + Sqrt[1 - I])*ArcTan[((2 - 3*I) + (3 - I)*Sqrt[1 - I] - 8*Sqrt[1 + x] - 5*Sqrt[1 - I]*Sqrt[1 + x] + (2 + 5*I)*(1 + x) + (5*I)*Sqrt[1 - I]*(1 + x) + 4*Sqrt[I - Sqrt[1 - I]]*Sqrt[x + Sqrt[1 + x]] + 2*Sqrt[1 - I]*Sqrt[I - Sqrt[1 - I]]*Sqrt[x + Sqrt[1 + x]] - (6 + 2*I)*Sqrt[I - Sqrt[1 - I]]*Sqrt[1 + x]*Sqrt[x + Sqrt[1 + x]] - (8*Sqrt[I - Sqrt[1 - I]]*Sqrt[1 + x]*Sqrt[x + Sqrt[1 + x]])/Sqrt[1 - I])/((-4 + 7*I) - (6 - 2*I)*Sqrt[1 - I] + (4 - 2*I)*Sqrt[1 + x] + (6 - 2*I)*Sqrt[1 - I]*Sqrt[1 + x] + (10 + I)*(1 + x) + (8 + 4*I)*Sqrt[1 - I]*(1 + x))])/(2*Sqrt[1 - I]*Sqrt[I - Sqrt[1 - I]]) + (((-1 - I) + Sqrt[1 - I])*ArcTan[((-2 + 3*I) + (3 - I)*Sqrt[1 - I] + 8*Sqrt[1 + x] - 5*Sqrt[1 - I]*Sqrt[1 + x] - (2 + 5*I)*(1 + x) + (5*I)*Sqrt[1 - I]*(1 + x) - 4*Sqrt[I + Sqrt[1 - I]]*Sqrt[x + Sqrt[1 + x]] + 2*Sqrt[1 - I]*Sqrt[I + Sqrt[1 - I]]*Sqrt[x + Sqrt[1 + x]] + (6 + 2*I)*Sqrt[I + Sqrt[1 - I]]*Sqrt[1 + x]*Sqrt[x + Sqrt[1 + x]] - (8*Sqrt[I + Sqrt[1 - I]]*Sqrt[1 + x]*Sqrt[x + Sqrt[1 + x]])/Sqrt[1 - I])/((4 - 7*I) - (6 - 2*I)*Sqrt[1 - I] - (4 - 2*I)*Sqrt[1 + x] + (6 - 2*I)*Sqrt[1 - I]*Sqrt[1 + x] - (10 + I)*(1 + x) + (8 + 4*I)*Sqrt[1 - I]*(1 + x))])/(2*Sqrt[1 - I]*Sqrt[I + Sqrt[1 - I]]) - ((I/2)*((-1 + I) + Sqrt[1 + I])*ArcTan[((1 + 8*I) - 5*(1 + I)^(3/2) - (16 + 8*I)*Sqrt[1 + x] + (10 + 5*I)*Sqrt[1 + I]*Sqrt[1 + x] + (9 - 8*I)*(1 + x) - (5 - 10*I)*Sqrt[1 + I]*(1 + x) - 4*Sqrt[I - Sqrt[1 + I]]*Sqrt[x + Sqrt[1 + x]] + (4 - 2*I)*Sqrt[1 + I]*Sqrt[I - Sqrt[1 + I]]*Sqrt[x + Sqrt[1 + x]] - 8*Sqrt[I - Sqrt[1 + I]]*Sqrt[1 + x]*Sqrt[x + Sqrt[1 + x]] + (8 - 4*I)*Sqrt[1 + I]*Sqrt[I - Sqrt[1 + I]]*Sqrt[1 + x]*Sqrt[x + Sqrt[1 + x]])/((9 + 20*I) - 12*(1 + I)^(3/2) - (14 + 20*I)*Sqrt[1 + x] + (22 + 12*I)*Sqrt[1 + I]*Sqrt[1 + x] + (6 - 15*I)*(1 + x) + (2 + 12*I)*Sqrt[1 + I]*(1 + x))])/(Sqrt[1 + I]*Sqrt[I - Sqrt[1 + I]]) - ((I/2)*((1 - I) + Sqrt[1 + I])*ArcTan[((-1 - 8*I) - 5*(1 + I)^(3/2) + (16 + 8*I)*Sqrt[1 + x] + (10 + 5*I)*Sqrt[1 + I]*Sqrt[1 + x] - (9 - 8*I)*(1 + x) - (5 - 10*I)*Sqrt[1 + I]*(1 + x) + 4*Sqrt[I + Sqrt[1 + I]]*Sqrt[x + Sqrt[1 + x]] + (4 - 2*I)*Sqrt[1 + I]*Sqrt[I + Sqrt[1 + I]]*Sqrt[x + Sqrt[1 + x]] + 8*Sqrt[I + Sqrt[1 + I]]*Sqrt[1 + x]*Sqrt[x + Sqrt[1 + x]] + (8 - 4*I)*Sqrt[1 + I]*Sqrt[I + Sqrt[1 + I]]*Sqrt[1 + x]*Sqrt[x + Sqrt[1 + x]])/((-9 - 20*I) - 12*(1 + I)^(3/2) + (14 + 20*I)*Sqrt[1 + x] + (22 + 12*I)*Sqrt[1 + I]*Sqrt[1 + x] - (6 - 15*I)*(1 + x) + (2 + 12*I)*Sqrt[1 + I]*(1 + x))])/(Sqrt[1 + I]*Sqrt[I + Sqrt[1 + I]]) + ((I/4)*((1 + I) + Sqrt[1 - I])*Log[(Sqrt[1 - I] - Sqrt[1 + x])^2])/(Sqrt[1 - I]*Sqrt[I - Sqrt[1 - I]]) + (((1 - I) + Sqrt[1 + I])*Log[(Sqrt[1 + I] - Sqrt[1 + x])^2])/(4*Sqrt[1 + I]*Sqrt[I + Sqrt[1 + I]]) + ((I/4)*((-1 - I) + Sqrt[1 - I])*Log[(Sqrt[1 - I] + Sqrt[1 + x])^2])/(Sqrt[1 - I]*Sqrt[I + Sqrt[1 - I]]) + (((-1 + I) + Sqrt[1 + I])*Log[(Sqrt[1 + I] + Sqrt[1 + x])^2])/(4*Sqrt[1 + I]*Sqrt[I - Sqrt[1 + I]]) - ((I/4)*((1 + I) + Sqrt[1 - I])*Log[(5 + 17*I) + (14*I)*Sqrt[1 - I] - (10 + 22*I)*Sqrt[1 + x] + (5 - 19*I)*Sqrt[1 - I]*Sqrt[1 + x] - (25 + 2*I)*(1 + x) - (15 + 9*I)*Sqrt[1 - I]*(1 + x) - (4 - 4*I)*Sqrt[I - Sqrt[1 - I]]*Sqrt[x + Sqrt[1 + x]] - (6 - 2*I)*Sqrt[1 - I]*Sqrt[I - Sqrt[1 - I]]*Sqrt[x + Sqrt[1 + x]] - (8 - 8*I)*Sqrt[I - Sqrt[1 - I]]*Sqrt[1 + x]*Sqrt[x + Sqrt[1 + x]] - (12 - 4*I)*Sqrt[1 - I]*Sqrt[I - Sqrt[1 - I]]*Sqrt[1 + x]*Sqrt[x + Sqrt[1 + x]]])/(Sqrt[1 - I]*Sqrt[I - Sqrt[1 - I]]) - ((I/4)*((-1 - I) + Sqrt[1 - I])*Log[(-5 - 17*I) + (14*I)*Sqrt[1 - I] + (10 + 22*I)*Sqrt[1 + x] + (5 - 19*I)*Sqrt[1 - I]*Sqrt[1 + x] + (25 + 2*I)*(1 + x) - (15 + 9*I)*Sqrt[1 - I]*(1 + x) + (4 - 4*I)*Sqrt[I + Sqrt[1 - I]]*Sqrt[x + Sqrt[1 + x]] - (6 - 2*I)*Sqrt[1 - I]*Sqrt[I + Sqrt[1 - I]]*Sqrt[x + Sqrt[1 + x]] + (8 - 8*I)*Sqrt[I + Sqrt[1 - I]]*Sqrt[1 + x]*Sqrt[x + Sqrt[1 + x]] - (12 - 4*I)*Sqrt[1 - I]*Sqrt[I + Sqrt[1 - I]]*Sqrt[1 + x]*Sqrt[x + Sqrt[1 + x]]])/(Sqrt[1 - I]*Sqrt[I + Sqrt[1 - I]]) - (((-1 + I) + Sqrt[1 + I])*Log[(-3 + 5*I) - (2 + 4*I)*Sqrt[1 + I] + (2 - 2*I)*Sqrt[1 + x] - (1 - 3*I)*Sqrt[1 + I]*Sqrt[1 + x] - (8 + 7*I)*(1 + x) + (9 + 3*I)*Sqrt[1 + I]*(1 + x) + (4 + 4*I)*Sqrt[I - Sqrt[1 + I]]*Sqrt[x + Sqrt[1 + x]] - 2*(1 + I)^(3/2)*Sqrt[I - Sqrt[1 + I]]*Sqrt[x + Sqrt[1 + x]] - (8 + 4*I)*Sqrt[I - Sqrt[1 + I]]*Sqrt[1 + x]*Sqrt[x + Sqrt[1 + x]] + 8*Sqrt[1 + I]*Sqrt[I - Sqrt[1 + I]]*Sqrt[1 + x]*Sqrt[x + Sqrt[1 + x]]])/(4*Sqrt[1 + I]*Sqrt[I - Sqrt[1 + I]]) - (((1 - I) + Sqrt[1 + I])*Log[(3 - 5*I) - (2 + 4*I)*Sqrt[1 + I] - (2 - 2*I)*Sqrt[1 + x] - (1 - 3*I)*Sqrt[1 + I]*Sqrt[1 + x] + (8 + 7*I)*(1 + x) + (9 + 3*I)*Sqrt[1 + I]*(1 + x) - (4 + 4*I)*Sqrt[I + Sqrt[1 + I]]*Sqrt[x + Sqrt[1 + x]] - 2*(1 + I)^(3/2)*Sqrt[I + Sqrt[1 + I]]*Sqrt[x + Sqrt[1 + x]] + (8 + 4*I)*Sqrt[I + Sqrt[1 + I]]*Sqrt[1 + x]*Sqrt[x + Sqrt[1 + x]] + 8*Sqrt[1 + I]*Sqrt[I + Sqrt[1 + I]]*Sqrt[1 + x]*Sqrt[x + Sqrt[1 + x]]])/(4*Sqrt[1 + I]*Sqrt[I + Sqrt[1 + I]])","C",0
2486,1,4139,204,7.1248137,"\int \frac{\sqrt{x+\sqrt{1+x}}}{x^2-\sqrt{1+x}} \, dx","Integrate[Sqrt[x + Sqrt[1 + x]]/(x^2 - Sqrt[1 + x]),x]","\text{Result too large to show}","2 \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+16 \text{$\#$1}^5-8 \text{$\#$1}^4-2 \text{$\#$1}^3+3 \text{$\#$1}^2+6 \text{$\#$1}-1\&,\frac{\text{$\#$1}^6 \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)-2 \text{$\#$1}^5 \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)+2 \text{$\#$1} \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)+\log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)}{4 \text{$\#$1}^7-12 \text{$\#$1}^5+40 \text{$\#$1}^4-16 \text{$\#$1}^3-3 \text{$\#$1}^2+3 \text{$\#$1}+3}\&\right]",1,"2*(-(((Log[Sqrt[1 + x] - Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0]] - Log[-2 + Sqrt[1 + x] + (1 + 2*Sqrt[1 + x])*Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] + 2*Sqrt[x + Sqrt[1 + x]]*Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0]^2]])*Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0])/(Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0]^2]*(Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] - Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0])*(Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] - Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0])*(Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] - Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0]))) + ((Log[Sqrt[1 + x] - Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0]] - Log[-2 + Sqrt[1 + x] + (1 + 2*Sqrt[1 + x])*Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] + 2*Sqrt[x + Sqrt[1 + x]]*Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0]^2]])*Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0]^2)/(Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0]^2]*(Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] - Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0])*(Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] - Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0])*(Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] - Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0])) + ((Log[Sqrt[1 + x] - Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0]] - Log[-2 + Sqrt[1 + x] + (1 + 2*Sqrt[1 + x])*Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] + 2*Sqrt[x + Sqrt[1 + x]]*Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0]^2]])*Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0]^3)/(Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0]^2]*(Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] - Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0])*(Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] - Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0])*(Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] - Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0])) - ((Log[Sqrt[1 + x] - Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0]] - Log[-2 + Sqrt[1 + x] + (1 + 2*Sqrt[1 + x])*Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0] + 2*Sqrt[x + Sqrt[1 + x]]*Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0]^2]])*Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0])/((-Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0])*Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0]^2]*(Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0] - Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0])*(Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0] - Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0])) + ((Log[Sqrt[1 + x] - Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0]] - Log[-2 + Sqrt[1 + x] + (1 + 2*Sqrt[1 + x])*Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0] + 2*Sqrt[x + Sqrt[1 + x]]*Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0]^2]])*Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0]^2)/((-Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0])*Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0]^2]*(Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0] - Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0])*(Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0] - Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0])) + ((Log[Sqrt[1 + x] - Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0]] - Log[-2 + Sqrt[1 + x] + (1 + 2*Sqrt[1 + x])*Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0] + 2*Sqrt[x + Sqrt[1 + x]]*Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0]^2]])*Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0]^3)/((-Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0])*Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0]^2]*(Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0] - Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0])*(Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0] - Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0])) - ((Log[Sqrt[1 + x] - Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0]] - Log[-2 + Sqrt[1 + x] + (1 + 2*Sqrt[1 + x])*Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0] + 2*Sqrt[x + Sqrt[1 + x]]*Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0]^2]])*Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0])/((-Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0])*(-Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0])*Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0]^2]*(Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0] - Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0])) + ((Log[Sqrt[1 + x] - Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0]] - Log[-2 + Sqrt[1 + x] + (1 + 2*Sqrt[1 + x])*Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0] + 2*Sqrt[x + Sqrt[1 + x]]*Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0]^2]])*Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0]^2)/((-Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0])*(-Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0])*Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0]^2]*(Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0] - Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0])) + ((Log[Sqrt[1 + x] - Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0]] - Log[-2 + Sqrt[1 + x] + (1 + 2*Sqrt[1 + x])*Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0] + 2*Sqrt[x + Sqrt[1 + x]]*Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0]^2]])*Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0]^3)/((-Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0])*(-Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0])*Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0]^2]*(Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0] - Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0])) - ((Log[Sqrt[1 + x] - Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0]] - Log[-2 + Sqrt[1 + x] + (1 + 2*Sqrt[1 + x])*Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0] + 2*Sqrt[x + Sqrt[1 + x]]*Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0]^2]])*Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0])/((-Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0])*(-Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0])*(-Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0])*Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0]^2]) + ((Log[Sqrt[1 + x] - Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0]] - Log[-2 + Sqrt[1 + x] + (1 + 2*Sqrt[1 + x])*Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0] + 2*Sqrt[x + Sqrt[1 + x]]*Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0]^2]])*Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0]^2)/((-Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0])*(-Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0])*(-Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0])*Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0]^2]) + ((Log[Sqrt[1 + x] - Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0]] - Log[-2 + Sqrt[1 + x] + (1 + 2*Sqrt[1 + x])*Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0] + 2*Sqrt[x + Sqrt[1 + x]]*Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0]^2]])*Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0]^3)/((-Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0])*(-Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0])*(-Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0])*Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0]^2]))","B",0
2487,1,4139,204,7.2256956,"\int \frac{\sqrt{x+\sqrt{1+x}}}{x^2-\sqrt{1+x}} \, dx","Integrate[Sqrt[x + Sqrt[1 + x]]/(x^2 - Sqrt[1 + x]),x]","\text{Result too large to show}","2 \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+16 \text{$\#$1}^5-8 \text{$\#$1}^4-2 \text{$\#$1}^3+3 \text{$\#$1}^2+6 \text{$\#$1}-1\&,\frac{\text{$\#$1}^6 \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)-2 \text{$\#$1}^5 \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)+2 \text{$\#$1} \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)+\log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)}{4 \text{$\#$1}^7-12 \text{$\#$1}^5+40 \text{$\#$1}^4-16 \text{$\#$1}^3-3 \text{$\#$1}^2+3 \text{$\#$1}+3}\&\right]",1,"2*(-(((Log[Sqrt[1 + x] - Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0]] - Log[-2 + Sqrt[1 + x] + (1 + 2*Sqrt[1 + x])*Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] + 2*Sqrt[x + Sqrt[1 + x]]*Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0]^2]])*Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0])/(Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0]^2]*(Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] - Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0])*(Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] - Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0])*(Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] - Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0]))) + ((Log[Sqrt[1 + x] - Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0]] - Log[-2 + Sqrt[1 + x] + (1 + 2*Sqrt[1 + x])*Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] + 2*Sqrt[x + Sqrt[1 + x]]*Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0]^2]])*Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0]^2)/(Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0]^2]*(Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] - Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0])*(Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] - Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0])*(Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] - Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0])) + ((Log[Sqrt[1 + x] - Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0]] - Log[-2 + Sqrt[1 + x] + (1 + 2*Sqrt[1 + x])*Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] + 2*Sqrt[x + Sqrt[1 + x]]*Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0]^2]])*Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0]^3)/(Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0]^2]*(Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] - Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0])*(Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] - Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0])*(Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] - Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0])) - ((Log[Sqrt[1 + x] - Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0]] - Log[-2 + Sqrt[1 + x] + (1 + 2*Sqrt[1 + x])*Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0] + 2*Sqrt[x + Sqrt[1 + x]]*Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0]^2]])*Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0])/((-Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0])*Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0]^2]*(Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0] - Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0])*(Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0] - Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0])) + ((Log[Sqrt[1 + x] - Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0]] - Log[-2 + Sqrt[1 + x] + (1 + 2*Sqrt[1 + x])*Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0] + 2*Sqrt[x + Sqrt[1 + x]]*Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0]^2]])*Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0]^2)/((-Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0])*Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0]^2]*(Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0] - Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0])*(Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0] - Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0])) + ((Log[Sqrt[1 + x] - Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0]] - Log[-2 + Sqrt[1 + x] + (1 + 2*Sqrt[1 + x])*Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0] + 2*Sqrt[x + Sqrt[1 + x]]*Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0]^2]])*Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0]^3)/((-Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0])*Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0]^2]*(Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0] - Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0])*(Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0] - Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0])) - ((Log[Sqrt[1 + x] - Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0]] - Log[-2 + Sqrt[1 + x] + (1 + 2*Sqrt[1 + x])*Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0] + 2*Sqrt[x + Sqrt[1 + x]]*Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0]^2]])*Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0])/((-Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0])*(-Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0])*Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0]^2]*(Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0] - Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0])) + ((Log[Sqrt[1 + x] - Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0]] - Log[-2 + Sqrt[1 + x] + (1 + 2*Sqrt[1 + x])*Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0] + 2*Sqrt[x + Sqrt[1 + x]]*Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0]^2]])*Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0]^2)/((-Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0])*(-Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0])*Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0]^2]*(Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0] - Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0])) + ((Log[Sqrt[1 + x] - Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0]] - Log[-2 + Sqrt[1 + x] + (1 + 2*Sqrt[1 + x])*Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0] + 2*Sqrt[x + Sqrt[1 + x]]*Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0]^2]])*Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0]^3)/((-Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0])*(-Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0])*Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0]^2]*(Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0] - Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0])) - ((Log[Sqrt[1 + x] - Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0]] - Log[-2 + Sqrt[1 + x] + (1 + 2*Sqrt[1 + x])*Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0] + 2*Sqrt[x + Sqrt[1 + x]]*Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0]^2]])*Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0])/((-Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0])*(-Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0])*(-Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0])*Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0]^2]) + ((Log[Sqrt[1 + x] - Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0]] - Log[-2 + Sqrt[1 + x] + (1 + 2*Sqrt[1 + x])*Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0] + 2*Sqrt[x + Sqrt[1 + x]]*Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0]^2]])*Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0]^2)/((-Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0])*(-Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0])*(-Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0])*Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0]^2]) + ((Log[Sqrt[1 + x] - Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0]] - Log[-2 + Sqrt[1 + x] + (1 + 2*Sqrt[1 + x])*Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0] + 2*Sqrt[x + Sqrt[1 + x]]*Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0]^2]])*Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0]^3)/((-Root[1 - #1 - 2*#1^2 + #1^4 & , 1, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0])*(-Root[1 - #1 - 2*#1^2 + #1^4 & , 2, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0])*(-Root[1 - #1 - 2*#1^2 + #1^4 & , 3, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0])*Sqrt[-1 + Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0] + Root[1 - #1 - 2*#1^2 + #1^4 & , 4, 0]^2]))","B",0
2488,1,75,205,0.1468248,"\int \frac{x^2}{\left(x^2 (-a+x)\right)^{2/3} \left(-a^2+2 a x+(-1+d) x^2\right)} \, dx","Integrate[x^2/((x^2*(-a + x))^(2/3)*(-a^2 + 2*a*x + (-1 + d)*x^2)),x]","\frac{3 x^2 \left(\, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{\sqrt{d} x}{x-a}\right)-\, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{\sqrt{d} x}{a-x}\right)\right)}{4 a \sqrt{d} \left(x^2 (x-a)\right)^{2/3}}","\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{d} x}{\sqrt[6]{d} x-2 \sqrt[3]{x^3-a x^2}}\right)}{2 a d^{5/6}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{d} x}{2 \sqrt[3]{x^3-a x^2}+\sqrt[6]{d} x}\right)}{2 a d^{5/6}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{d} x}{\sqrt[3]{x^3-a x^2}}\right)}{a d^{5/6}}+\frac{\tanh ^{-1}\left(\frac{\frac{\left(x^3-a x^2\right)^{2/3}}{\sqrt[6]{d}}+\sqrt[6]{d} x^2}{x \sqrt[3]{x^3-a x^2}}\right)}{2 a d^{5/6}}",1,"(3*x^2*(-Hypergeometric2F1[2/3, 1, 5/3, (Sqrt[d]*x)/(a - x)] + Hypergeometric2F1[2/3, 1, 5/3, (Sqrt[d]*x)/(-a + x)]))/(4*a*Sqrt[d]*(x^2*(-a + x))^(2/3))","C",1
2489,0,0,205,14.0074892,"\int \frac{(-2+(1+k) x) \left(1-(1+k) x+(a+k) x^2\right)}{x ((1-x) x (1-k x))^{2/3} \left(1-(1+k) x+(-b+k) x^2\right)} \, dx","Integrate[((-2 + (1 + k)*x)*(1 - (1 + k)*x + (a + k)*x^2))/(x*((1 - x)*x*(1 - k*x))^(2/3)*(1 - (1 + k)*x + (-b + k)*x^2)),x]","\int \frac{(-2+(1+k) x) \left(1-(1+k) x+(a+k) x^2\right)}{x ((1-x) x (1-k x))^{2/3} \left(1-(1+k) x+(-b+k) x^2\right)} \, dx","\frac{(a+b) \log \left(\sqrt[3]{k x^3+(-k-1) x^2+x}-\sqrt[3]{b} x\right)}{b^{2/3}}+\frac{(-a-b) \log \left(b^{2/3} x^2+\sqrt[3]{b} x \sqrt[3]{k x^3+(-k-1) x^2+x}+\left(k x^3+(-k-1) x^2+x\right)^{2/3}\right)}{2 b^{2/3}}+\frac{\left(\sqrt{3} a+\sqrt{3} b\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{b} x}{\sqrt[3]{b} x+2 \sqrt[3]{k x^3+(-k-1) x^2+x}}\right)}{b^{2/3}}+\frac{3 \sqrt[3]{k x^3+(-k-1) x^2+x}}{x}",1,"Integrate[((-2 + (1 + k)*x)*(1 - (1 + k)*x + (a + k)*x^2))/(x*((1 - x)*x*(1 - k*x))^(2/3)*(1 - (1 + k)*x + (-b + k)*x^2)), x]","F",-1
2490,0,0,206,4.4913723,"\int \frac{-2 a^2 b x+a (3 a+2 b) x^2-4 a x^3+x^4}{\left(x^2 (-a+x) (-b+x)\right)^{2/3} \left(-a^2+2 a x-(1+b d) x^2+d x^3\right)} \, dx","Integrate[(-2*a^2*b*x + a*(3*a + 2*b)*x^2 - 4*a*x^3 + x^4)/((x^2*(-a + x)*(-b + x))^(2/3)*(-a^2 + 2*a*x - (1 + b*d)*x^2 + d*x^3)),x]","\int \frac{-2 a^2 b x+a (3 a+2 b) x^2-4 a x^3+x^4}{\left(x^2 (-a+x) (-b+x)\right)^{2/3} \left(-a^2+2 a x-(1+b d) x^2+d x^3\right)} \, dx","-\frac{\log \left(a^2+d^{2/3} \left(x^3 (-a-b)+a b x^2+x^4\right)^{2/3}+\sqrt[3]{x^3 (-a-b)+a b x^2+x^4} \left(\sqrt[3]{d} x-a \sqrt[3]{d}\right)-2 a x+x^2\right)}{2 \sqrt[3]{d}}+\frac{\log \left(\sqrt[3]{d} \sqrt[3]{x^3 (-a-b)+a b x^2+x^4}+a-x\right)}{\sqrt[3]{d}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} a-\sqrt{3} x}{-2 \sqrt[3]{d} \sqrt[3]{x^3 (-a-b)+a b x^2+x^4}+a-x}\right)}{\sqrt[3]{d}}",1,"Integrate[(-2*a^2*b*x + a*(3*a + 2*b)*x^2 - 4*a*x^3 + x^4)/((x^2*(-a + x)*(-b + x))^(2/3)*(-a^2 + 2*a*x - (1 + b*d)*x^2 + d*x^3)), x]","F",-1
2491,1,100,206,0.0865123,"\int \frac{1}{\sqrt[3]{-8+12 x+54 x^2-135 x^3+81 x^4}} \, dx","Integrate[(-8 + 12*x + 54*x^2 - 135*x^3 + 81*x^4)^(-1/3),x]","-\frac{(3 x-2) \sqrt[3]{3 x+1} \left(\sqrt{3} \left(\log (2-3 x)-3 \log \left(\sqrt[3]{3}-\sqrt[3]{3 x+1}\right)\right)-6 \tan ^{-1}\left(\frac{2 \sqrt[3]{3 x+1}+\sqrt[3]{3}}{3^{5/6}}\right)\right)}{6\ 3^{5/6} \sqrt[3]{(3 x-2)^3 (3 x+1)}}","\frac{\log \left(3^{2/3} \sqrt[3]{81 x^4-135 x^3+54 x^2+12 x-8}-9 x+6\right)}{3 \sqrt[3]{3}}-\frac{\log \left(27 x^2+\sqrt[3]{3} \left(81 x^4-135 x^3+54 x^2+12 x-8\right)^{2/3}+\left(3\ 3^{2/3} x-2\ 3^{2/3}\right) \sqrt[3]{81 x^4-135 x^3+54 x^2+12 x-8}-36 x+12\right)}{6 \sqrt[3]{3}}-\frac{\tan ^{-1}\left(\frac{3\ 3^{5/6} x-2\ 3^{5/6}}{2 \sqrt[3]{81 x^4-135 x^3+54 x^2+12 x-8}+3 \sqrt[3]{3} x-2 \sqrt[3]{3}}\right)}{3^{5/6}}",1,"-1/6*((-2 + 3*x)*(1 + 3*x)^(1/3)*(-6*ArcTan[(3^(1/3) + 2*(1 + 3*x)^(1/3))/3^(5/6)] + Sqrt[3]*(Log[2 - 3*x] - 3*Log[3^(1/3) - (1 + 3*x)^(1/3)])))/(3^(5/6)*((-2 + 3*x)^3*(1 + 3*x))^(1/3))","A",1
2492,0,0,206,0.1992887,"\int \frac{1+x^2}{\left(-1-x+x^2\right) \sqrt[3]{-1+x^6}} \, dx","Integrate[(1 + x^2)/((-1 - x + x^2)*(-1 + x^6)^(1/3)),x]","\int \frac{1+x^2}{\left(-1-x+x^2\right) \sqrt[3]{-1+x^6}} \, dx","\frac{\log \left(-2 \sqrt[3]{x^6-1}+2^{2/3} x^2+2^{2/3} x-2^{2/3}\right)}{3\ 2^{2/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x^6-1}}{\sqrt[3]{x^6-1}+2^{2/3} x^2+2^{2/3} x-2^{2/3}}\right)}{2^{2/3} \sqrt{3}}-\frac{\log \left(2 \left(x^6-1\right)^{2/3}+\sqrt[3]{2} x^4+2 \sqrt[3]{2} x^3-\sqrt[3]{2} x^2+\left(2^{2/3} x^2+2^{2/3} x-2^{2/3}\right) \sqrt[3]{x^6-1}-2 \sqrt[3]{2} x+\sqrt[3]{2}\right)}{6\ 2^{2/3}}",1,"Integrate[(1 + x^2)/((-1 - x + x^2)*(-1 + x^6)^(1/3)), x]","F",-1
2493,0,0,206,0.0787839,"\int \frac{1+x^2}{\left(-1-x+x^2\right) \sqrt[3]{-1+x^6}} \, dx","Integrate[(1 + x^2)/((-1 - x + x^2)*(-1 + x^6)^(1/3)),x]","\int \frac{1+x^2}{\left(-1-x+x^2\right) \sqrt[3]{-1+x^6}} \, dx","\frac{\log \left(-2 \sqrt[3]{x^6-1}+2^{2/3} x^2+2^{2/3} x-2^{2/3}\right)}{3\ 2^{2/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x^6-1}}{\sqrt[3]{x^6-1}+2^{2/3} x^2+2^{2/3} x-2^{2/3}}\right)}{2^{2/3} \sqrt{3}}-\frac{\log \left(2 \left(x^6-1\right)^{2/3}+\sqrt[3]{2} x^4+2 \sqrt[3]{2} x^3-\sqrt[3]{2} x^2+\left(2^{2/3} x^2+2^{2/3} x-2^{2/3}\right) \sqrt[3]{x^6-1}-2 \sqrt[3]{2} x+\sqrt[3]{2}\right)}{6\ 2^{2/3}}",1,"Integrate[(1 + x^2)/((-1 - x + x^2)*(-1 + x^6)^(1/3)), x]","F",-1
2494,0,0,206,2.160961,"\int \frac{\left(2-2 x^4+3 x^5+4 x^6\right) \sqrt[3]{-x+2 x^3-x^5+x^6+x^7}}{\left(-1+x^2-x^4+x^5+x^6\right)^2} \, dx","Integrate[((2 - 2*x^4 + 3*x^5 + 4*x^6)*(-x + 2*x^3 - x^5 + x^6 + x^7)^(1/3))/(-1 + x^2 - x^4 + x^5 + x^6)^2,x]","\int \frac{\left(2-2 x^4+3 x^5+4 x^6\right) \sqrt[3]{-x+2 x^3-x^5+x^6+x^7}}{\left(-1+x^2-x^4+x^5+x^6\right)^2} \, dx","\frac{1}{3} \log \left(\sqrt[3]{x^7+x^6-x^5+2 x^3-x}-x\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x^7+x^6-x^5+2 x^3-x}}{\sqrt[3]{x^7+x^6-x^5+2 x^3-x}+2 x}\right)}{\sqrt{3}}-\frac{1}{6} \log \left(x^2+\sqrt[3]{x^7+x^6-x^5+2 x^3-x} x+\left(x^7+x^6-x^5+2 x^3-x\right)^{2/3}\right)-\frac{\sqrt[3]{x^7+x^6-x^5+2 x^3-x} x}{x^6+x^5-x^4+x^2-1}",1,"Integrate[((2 - 2*x^4 + 3*x^5 + 4*x^6)*(-x + 2*x^3 - x^5 + x^6 + x^7)^(1/3))/(-1 + x^2 - x^4 + x^5 + x^6)^2, x]","F",-1
2495,0,0,207,5.6613813,"\int \frac{-1+(-1+2 k) x}{\sqrt[3]{(1-x) x (1-k x)} \left(b-(1+2 b) x+(b+k) x^2\right)} \, dx","Integrate[(-1 + (-1 + 2*k)*x)/(((1 - x)*x*(1 - k*x))^(1/3)*(b - (1 + 2*b)*x + (b + k)*x^2)),x]","\int \frac{-1+(-1+2 k) x}{\sqrt[3]{(1-x) x (1-k x)} \left(b-(1+2 b) x+(b+k) x^2\right)} \, dx","-\frac{\log \left(b^{2/3} x^2-2 b^{2/3} x+b^{2/3}+\left(\sqrt[3]{b}-\sqrt[3]{b} x\right) \sqrt[3]{k x^3+(-k-1) x^2+x}+\left(k x^3+(-k-1) x^2+x\right)^{2/3}\right)}{2 \sqrt[3]{b}}+\frac{\log \left(\sqrt[3]{b} x-\sqrt[3]{b}+\sqrt[3]{k x^3+(-k-1) x^2+x}\right)}{\sqrt[3]{b}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{k x^3+(-k-1) x^2+x}}{-2 \sqrt[3]{b} x+2 \sqrt[3]{b}+\sqrt[3]{k x^3+(-k-1) x^2+x}}\right)}{\sqrt[3]{b}}",1,"Integrate[(-1 + (-1 + 2*k)*x)/(((1 - x)*x*(1 - k*x))^(1/3)*(b - (1 + 2*b)*x + (b + k)*x^2)), x]","F",-1
2496,1,321,207,1.0879299,"\int \frac{\sqrt{b^2+a^2 x^3} \left(2 b^2+c x^3+a^2 x^6\right)}{x^7 \left(-b^2+a^2 x^6\right)} \, dx","Integrate[(Sqrt[b^2 + a^2*x^3]*(2*b^2 + c*x^3 + a^2*x^6))/(x^7*(-b^2 + a^2*x^6)),x]","\frac{\frac{3 b^4 c \left(a^2 x^3 \sqrt{\frac{a^2 x^3}{b^2}+1} \tanh ^{-1}\left(\sqrt{\frac{a^2 x^3}{b^2}+1}\right)+a^2 x^3+b^2\right)}{x^3 \sqrt{a^2 x^3+b^2}}+18 a^2 b^4 \left(b \tanh ^{-1}\left(\frac{\sqrt{a^2 x^3+b^2}}{b}\right)-\sqrt{a^2 x^3+b^2}\right)-3 a b^3 (3 a b-c) \left(\sqrt{b} \sqrt{a-b} \tan ^{-1}\left(\frac{\sqrt{a^2 x^3+b^2}}{\sqrt{b} \sqrt{a-b}}\right)-\sqrt{a^2 x^3+b^2}\right)-3 a b^3 (3 a b+c) \left(\sqrt{b} \sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a^2 x^3+b^2}}{\sqrt{b} \sqrt{a+b}}\right)-\sqrt{a^2 x^3+b^2}\right)+4 a^4 \left(a^2 x^3+b^2\right)^{3/2} \, _2F_1\left(\frac{3}{2},3;\frac{5}{2};\frac{a^2 x^3}{b^2}+1\right)}{9 b^6}","\frac{\sqrt{a^2 x^3+b^2} \left(a^2 x^3+2 b^2+2 c x^3\right)}{6 b^2 x^6}-\frac{\sqrt{b-a} \left(3 a^2 b-a c\right) \tanh ^{-1}\left(\frac{\sqrt{a^2 x^3+b^2}}{\sqrt{b} \sqrt{b-a}}\right)}{3 b^{5/2}}-\frac{\sqrt{a+b} \left(3 a^2 b+a c\right) \tanh ^{-1}\left(\frac{\sqrt{a^2 x^3+b^2}}{\sqrt{b} \sqrt{a+b}}\right)}{3 b^{5/2}}+\frac{\left(-a^4+12 a^2 b^2+2 a^2 c\right) \tanh ^{-1}\left(\frac{\sqrt{a^2 x^3+b^2}}{b}\right)}{6 b^3}",1,"(-3*a*b^3*(3*a*b - c)*(-Sqrt[b^2 + a^2*x^3] + Sqrt[a - b]*Sqrt[b]*ArcTan[Sqrt[b^2 + a^2*x^3]/(Sqrt[a - b]*Sqrt[b])]) + 18*a^2*b^4*(-Sqrt[b^2 + a^2*x^3] + b*ArcTanh[Sqrt[b^2 + a^2*x^3]/b]) - 3*a*b^3*(3*a*b + c)*(-Sqrt[b^2 + a^2*x^3] + Sqrt[b]*Sqrt[a + b]*ArcTanh[Sqrt[b^2 + a^2*x^3]/(Sqrt[b]*Sqrt[a + b])]) + (3*b^4*c*(b^2 + a^2*x^3 + a^2*x^3*Sqrt[1 + (a^2*x^3)/b^2]*ArcTanh[Sqrt[1 + (a^2*x^3)/b^2]]))/(x^3*Sqrt[b^2 + a^2*x^3]) + 4*a^4*(b^2 + a^2*x^3)^(3/2)*Hypergeometric2F1[3/2, 3, 5/2, 1 + (a^2*x^3)/b^2])/(9*b^6)","C",1
2497,0,0,207,1.0124516,"\int \frac{x^7 (-4 a+3 x)}{\left(x^2 (-a+x)\right)^{2/3} \left(-a^2+2 a x-x^2+d x^8\right)} \, dx","Integrate[(x^7*(-4*a + 3*x))/((x^2*(-a + x))^(2/3)*(-a^2 + 2*a*x - x^2 + d*x^8)),x]","\int \frac{x^7 (-4 a+3 x)}{\left(x^2 (-a+x)\right)^{2/3} \left(-a^2+2 a x-x^2+d x^8\right)} \, dx","-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{d} x^2}{\sqrt[6]{d} x^2-2 \sqrt[3]{x^3-a x^2}}\right)}{2 d^{5/6}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{d} x^2}{2 \sqrt[3]{x^3-a x^2}+\sqrt[6]{d} x^2}\right)}{2 d^{5/6}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{d} \left(x^3-a x^2\right)^{2/3}}{a-x}\right)}{d^{5/6}}-\frac{\tanh ^{-1}\left(\frac{\frac{\left(x^3-a x^2\right)^{2/3}}{\sqrt[6]{d}}+\sqrt[6]{d} x^4}{x^2 \sqrt[3]{x^3-a x^2}}\right)}{2 d^{5/6}}",1,"Integrate[(x^7*(-4*a + 3*x))/((x^2*(-a + x))^(2/3)*(-a^2 + 2*a*x - x^2 + d*x^8)), x]","F",-1
2498,0,0,208,5.5004743,"\int \frac{-1+2 x+\left(-2 k+k^2\right) x^2}{((1-x) x (1-k x))^{2/3} \left(b-(1+2 b k) x+\left(1+b k^2\right) x^2\right)} \, dx","Integrate[(-1 + 2*x + (-2*k + k^2)*x^2)/(((1 - x)*x*(1 - k*x))^(2/3)*(b - (1 + 2*b*k)*x + (1 + b*k^2)*x^2)),x]","\int \frac{-1+2 x+\left(-2 k+k^2\right) x^2}{((1-x) x (1-k x))^{2/3} \left(b-(1+2 b k) x+\left(1+b k^2\right) x^2\right)} \, dx","\frac{\log \left(\sqrt[3]{b} \left(k x^3+(-k-1) x^2+x\right)^{2/3}+x^2-x\right)}{b^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{b} \left(k x^3+(-k-1) x^2+x\right)^{2/3}}{\sqrt[3]{b} \left(k x^3+(-k-1) x^2+x\right)^{2/3}-2 x^2+2 x}\right)}{b^{2/3}}-\frac{\log \left(b^{2/3} \left(k x^3+(-k-1) x^2+x\right)^{4/3}+\left(\sqrt[3]{b} x-\sqrt[3]{b} x^2\right) \left(k x^3+(-k-1) x^2+x\right)^{2/3}+x^4-2 x^3+x^2\right)}{2 b^{2/3}}",1,"Integrate[(-1 + 2*x + (-2*k + k^2)*x^2)/(((1 - x)*x*(1 - k*x))^(2/3)*(b - (1 + 2*b*k)*x + (1 + b*k^2)*x^2)), x]","F",-1
2499,1,392,208,1.1265772,"\int \frac{1}{\sqrt[3]{-x^2+x^3} \left(-1+x^4\right)} \, dx","Integrate[1/((-x^2 + x^3)^(1/3)*(-1 + x^4)),x]","\frac{x \left(-12-\frac{-\frac{4 \log \left(1-\sqrt[3]{1-i} \sqrt[3]{\frac{x}{x-1}}\right)}{\sqrt[3]{1-i}}-\frac{4 \log \left(1-\sqrt[3]{1+i} \sqrt[3]{\frac{x}{x-1}}\right)}{\sqrt[3]{1+i}}-2\ 2^{2/3} \log \left(1-\sqrt[3]{2} \sqrt[3]{\frac{x}{x-1}}\right)+\frac{2 \log \left((1-i)^{2/3} \left(\frac{x}{x-1}\right)^{2/3}+\sqrt[3]{1-i} \sqrt[3]{\frac{x}{x-1}}+1\right)}{\sqrt[3]{1-i}}+\frac{2 \log \left((1+i)^{2/3} \left(\frac{x}{x-1}\right)^{2/3}+\sqrt[3]{1+i} \sqrt[3]{\frac{x}{x-1}}+1\right)}{\sqrt[3]{1+i}}+2^{2/3} \log \left(2^{2/3} \left(\frac{x}{x-1}\right)^{2/3}+\sqrt[3]{2} \sqrt[3]{\frac{x}{x-1}}+1\right)+\frac{4 \sqrt{3} \tan ^{-1}\left(\frac{1+2 \sqrt[3]{1-i} \sqrt[3]{\frac{x}{x-1}}}{\sqrt{3}}\right)}{\sqrt[3]{1-i}}+\frac{4 \sqrt{3} \tan ^{-1}\left(\frac{1+2 \sqrt[3]{1+i} \sqrt[3]{\frac{x}{x-1}}}{\sqrt{3}}\right)}{\sqrt[3]{1+i}}+2\ 2^{2/3} \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{2} \sqrt[3]{\frac{x}{x-1}}+1}{\sqrt{3}}\right)}{\sqrt[3]{\frac{x}{x-1}}}\right)}{16 \sqrt[3]{(x-1) x^2}}","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^6-2 \text{$\#$1}^3+2\&,\frac{\log \left(\sqrt[3]{x^3-x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]-\frac{3 \left(x^3-x^2\right)^{2/3}}{4 (x-1) x}+\frac{\log \left(2^{2/3} \sqrt[3]{x^3-x^2}-2 x\right)}{4 \sqrt[3]{2}}-\frac{\log \left(2 x^2+2^{2/3} \sqrt[3]{x^3-x^2} x+\sqrt[3]{2} \left(x^3-x^2\right)^{2/3}\right)}{8 \sqrt[3]{2}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^3-x^2}+x}\right)}{4 \sqrt[3]{2}}",1,"(x*(-12 - ((4*Sqrt[3]*ArcTan[(1 + 2*(1 - I)^(1/3)*(x/(-1 + x))^(1/3))/Sqrt[3]])/(1 - I)^(1/3) + (4*Sqrt[3]*ArcTan[(1 + 2*(1 + I)^(1/3)*(x/(-1 + x))^(1/3))/Sqrt[3]])/(1 + I)^(1/3) + 2*2^(2/3)*Sqrt[3]*ArcTan[(1 + 2*2^(1/3)*(x/(-1 + x))^(1/3))/Sqrt[3]] - (4*Log[1 - (1 - I)^(1/3)*(x/(-1 + x))^(1/3)])/(1 - I)^(1/3) - (4*Log[1 - (1 + I)^(1/3)*(x/(-1 + x))^(1/3)])/(1 + I)^(1/3) - 2*2^(2/3)*Log[1 - 2^(1/3)*(x/(-1 + x))^(1/3)] + (2*Log[1 + (1 - I)^(1/3)*(x/(-1 + x))^(1/3) + (1 - I)^(2/3)*(x/(-1 + x))^(2/3)])/(1 - I)^(1/3) + (2*Log[1 + (1 + I)^(1/3)*(x/(-1 + x))^(1/3) + (1 + I)^(2/3)*(x/(-1 + x))^(2/3)])/(1 + I)^(1/3) + 2^(2/3)*Log[1 + 2^(1/3)*(x/(-1 + x))^(1/3) + 2^(2/3)*(x/(-1 + x))^(2/3)])/(x/(-1 + x))^(1/3)))/(16*((-1 + x)*x^2)^(1/3))","C",1
2500,1,392,208,0.2068152,"\int \frac{1}{\sqrt[3]{-x^2+x^3} \left(-1+x^4\right)} \, dx","Integrate[1/((-x^2 + x^3)^(1/3)*(-1 + x^4)),x]","\frac{x \left(-12-\frac{-\frac{4 \log \left(1-\sqrt[3]{1-i} \sqrt[3]{\frac{x}{x-1}}\right)}{\sqrt[3]{1-i}}-\frac{4 \log \left(1-\sqrt[3]{1+i} \sqrt[3]{\frac{x}{x-1}}\right)}{\sqrt[3]{1+i}}-2\ 2^{2/3} \log \left(1-\sqrt[3]{2} \sqrt[3]{\frac{x}{x-1}}\right)+\frac{2 \log \left((1-i)^{2/3} \left(\frac{x}{x-1}\right)^{2/3}+\sqrt[3]{1-i} \sqrt[3]{\frac{x}{x-1}}+1\right)}{\sqrt[3]{1-i}}+\frac{2 \log \left((1+i)^{2/3} \left(\frac{x}{x-1}\right)^{2/3}+\sqrt[3]{1+i} \sqrt[3]{\frac{x}{x-1}}+1\right)}{\sqrt[3]{1+i}}+2^{2/3} \log \left(2^{2/3} \left(\frac{x}{x-1}\right)^{2/3}+\sqrt[3]{2} \sqrt[3]{\frac{x}{x-1}}+1\right)+\frac{4 \sqrt{3} \tan ^{-1}\left(\frac{1+2 \sqrt[3]{1-i} \sqrt[3]{\frac{x}{x-1}}}{\sqrt{3}}\right)}{\sqrt[3]{1-i}}+\frac{4 \sqrt{3} \tan ^{-1}\left(\frac{1+2 \sqrt[3]{1+i} \sqrt[3]{\frac{x}{x-1}}}{\sqrt{3}}\right)}{\sqrt[3]{1+i}}+2\ 2^{2/3} \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{2} \sqrt[3]{\frac{x}{x-1}}+1}{\sqrt{3}}\right)}{\sqrt[3]{\frac{x}{x-1}}}\right)}{16 \sqrt[3]{(x-1) x^2}}","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^6-2 \text{$\#$1}^3+2\&,\frac{\log \left(\sqrt[3]{x^3-x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]-\frac{3 \left(x^3-x^2\right)^{2/3}}{4 (x-1) x}+\frac{\log \left(2^{2/3} \sqrt[3]{x^3-x^2}-2 x\right)}{4 \sqrt[3]{2}}-\frac{\log \left(2 x^2+2^{2/3} \sqrt[3]{x^3-x^2} x+\sqrt[3]{2} \left(x^3-x^2\right)^{2/3}\right)}{8 \sqrt[3]{2}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^3-x^2}+x}\right)}{4 \sqrt[3]{2}}",1,"(x*(-12 - ((4*Sqrt[3]*ArcTan[(1 + 2*(1 - I)^(1/3)*(x/(-1 + x))^(1/3))/Sqrt[3]])/(1 - I)^(1/3) + (4*Sqrt[3]*ArcTan[(1 + 2*(1 + I)^(1/3)*(x/(-1 + x))^(1/3))/Sqrt[3]])/(1 + I)^(1/3) + 2*2^(2/3)*Sqrt[3]*ArcTan[(1 + 2*2^(1/3)*(x/(-1 + x))^(1/3))/Sqrt[3]] - (4*Log[1 - (1 - I)^(1/3)*(x/(-1 + x))^(1/3)])/(1 - I)^(1/3) - (4*Log[1 - (1 + I)^(1/3)*(x/(-1 + x))^(1/3)])/(1 + I)^(1/3) - 2*2^(2/3)*Log[1 - 2^(1/3)*(x/(-1 + x))^(1/3)] + (2*Log[1 + (1 - I)^(1/3)*(x/(-1 + x))^(1/3) + (1 - I)^(2/3)*(x/(-1 + x))^(2/3)])/(1 - I)^(1/3) + (2*Log[1 + (1 + I)^(1/3)*(x/(-1 + x))^(1/3) + (1 + I)^(2/3)*(x/(-1 + x))^(2/3)])/(1 + I)^(1/3) + 2^(2/3)*Log[1 + 2^(1/3)*(x/(-1 + x))^(1/3) + 2^(2/3)*(x/(-1 + x))^(2/3)])/(x/(-1 + x))^(1/3)))/(16*((-1 + x)*x^2)^(1/3))","C",1
2501,1,47,208,0.0287889,"\int \frac{\sqrt[3]{-x^2+x^4}}{x \left(1+x^2\right)} \, dx","Integrate[(-x^2 + x^4)^(1/3)/(x*(1 + x^2)),x]","\frac{3 \sqrt[3]{x^2 \left(x^2-1\right)} F_1\left(\frac{1}{3};-\frac{1}{3},1;\frac{4}{3};x^2,-x^2\right)}{2 \sqrt[3]{1-x^2}}","\frac{\log \left(-2 x^2+2^{2/3} \sqrt{3} \sqrt[3]{x^4-x^2} x-\sqrt[3]{2} \left(x^4-x^2\right)^{2/3}\right)}{4\ 2^{2/3}}-\frac{\log \left(2 x^2+\sqrt[3]{2} \left(x^4-x^2\right)^{2/3}\right)}{2\ 2^{2/3}}+\frac{\log \left(2 x^2+2^{2/3} \sqrt{3} \sqrt[3]{x^4-x^2} x+\sqrt[3]{2} \left(x^4-x^2\right)^{2/3}\right)}{4\ 2^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x^2}{\sqrt[3]{2} \left(x^4-x^2\right)^{2/3}-x^2}\right)}{2\ 2^{2/3}}",1,"(3*(x^2*(-1 + x^2))^(1/3)*AppellF1[1/3, -1/3, 1, 4/3, x^2, -x^2])/(2*(1 - x^2)^(1/3))","C",0
2502,1,188,208,3.243422,"\int \frac{b+a x^6}{x^3 \left(-b+a x^3\right) \sqrt[4]{b x+a x^4}} \, dx","Integrate[(b + a*x^6)/(x^3*(-b + a*x^3)*(b*x + a*x^4)^(1/4)),x]","\frac{4 \left(\frac{4 \Gamma \left(\frac{5}{4}\right) (a+b) \left(a x^3+b\right) \left(5 \left(-4 a^2 x^6+3 a b x^3+b^2\right) \, _2F_1\left(1,1;\frac{5}{4};-\frac{2 a x^3}{b-a x^3}\right)-32 a x^3 \left(a x^3+b\right) \, _2F_1\left(2,2;\frac{9}{4};-\frac{2 a x^3}{b-a x^3}\right)\right)}{a b \Gamma \left(\frac{1}{4}\right) \left(b-a x^3\right)^2}+15 x^3 \sqrt[4]{\frac{a x^3}{b}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{4};\frac{5}{4};-\frac{a x^3}{b}\right)-\frac{5 \left(a x^3+b\right)}{a}\right)}{45 x^2 \sqrt[4]{x \left(a x^3+b\right)}}","\frac{4 \left(a x^4+b x\right)^{3/4}}{9 b x^3}+\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \left(a x^4+b x\right)^{3/4}}{a x^3+b}\right)}{3 \sqrt[4]{a}}-\frac{2^{3/4} (a+b) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} \left(a x^4+b x\right)^{3/4}}{a x^3+b}\right)}{3 \sqrt[4]{a} b}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{a} \left(a x^4+b x\right)^{3/4}}{a x^3+b}\right)}{3 \sqrt[4]{a}}-\frac{2^{3/4} (a+b) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} \left(a x^4+b x\right)^{3/4}}{a x^3+b}\right)}{3 \sqrt[4]{a} b}",1,"(4*((-5*(b + a*x^3))/a + 15*x^3*(1 + (a*x^3)/b)^(1/4)*Hypergeometric2F1[1/4, 1/4, 5/4, -((a*x^3)/b)] + (4*(a + b)*(b + a*x^3)*Gamma[5/4]*(5*(b^2 + 3*a*b*x^3 - 4*a^2*x^6)*Hypergeometric2F1[1, 1, 5/4, (-2*a*x^3)/(b - a*x^3)] - 32*a*x^3*(b + a*x^3)*Hypergeometric2F1[2, 2, 9/4, (-2*a*x^3)/(b - a*x^3)]))/(a*b*(b - a*x^3)^2*Gamma[1/4])))/(45*x^2*(x*(b + a*x^3))^(1/4))","C",0
2503,1,216,208,0.5450218,"\int \frac{\sqrt{a x+\sqrt{-b+a x}}}{x^2 \sqrt{-b+a x}} \, dx","Integrate[Sqrt[a*x + Sqrt[-b + a*x]]/(x^2*Sqrt[-b + a*x]),x]","\frac{4 b \sqrt{a x-b} \sqrt{\sqrt{a x-b}+a x}+a \left(\sqrt{-b}-2 b\right) \sqrt[4]{-b} x \tan ^{-1}\left(\frac{\left(2 \sqrt{-b}-1\right) \sqrt{a x-b}-2 b+\sqrt{-b}}{2 \sqrt[4]{-b} \sqrt{\sqrt{a x-b}+a x}}\right)+a \sqrt[4]{-b} \left(2 b+\sqrt{-b}\right) x \tanh ^{-1}\left(\frac{\left(2 \sqrt{-b}+1\right) \sqrt{a x-b}+2 b+\sqrt{-b}}{2 \sqrt[4]{-b} \sqrt{\sqrt{a x-b}+a x}}\right)}{4 b^2 x}","\frac{\sqrt{a x-b} \sqrt{\sqrt{a x-b}+a x}}{b x}-\frac{a \text{RootSum}\left[\text{$\#$1}^4+2 \text{$\#$1}^2 b-4 \text{$\#$1} b+b^2+b\&,\frac{\text{$\#$1}^2 \left(-\log \left(\text{$\#$1}+\sqrt{a x-b}-\sqrt{\sqrt{a x-b}+a x}\right)\right)+4 \text{$\#$1} b \log \left(\text{$\#$1}+\sqrt{a x-b}-\sqrt{\sqrt{a x-b}+a x}\right)-b \log \left(\text{$\#$1}+\sqrt{a x-b}-\sqrt{\sqrt{a x-b}+a x}\right)}{\text{$\#$1}^3+\text{$\#$1} b-b}\&\right]}{4 b}",1,"(4*b*Sqrt[-b + a*x]*Sqrt[a*x + Sqrt[-b + a*x]] + a*(Sqrt[-b] - 2*b)*(-b)^(1/4)*x*ArcTan[(Sqrt[-b] - 2*b + (-1 + 2*Sqrt[-b])*Sqrt[-b + a*x])/(2*(-b)^(1/4)*Sqrt[a*x + Sqrt[-b + a*x]])] + a*(-b)^(1/4)*(Sqrt[-b] + 2*b)*x*ArcTanh[(Sqrt[-b] + 2*b + (1 + 2*Sqrt[-b])*Sqrt[-b + a*x])/(2*(-b)^(1/4)*Sqrt[a*x + Sqrt[-b + a*x]])])/(4*b^2*x)","A",1
2504,0,0,209,0.223653,"\int \frac{3+x}{\sqrt[3]{-1+x^2} \left(5-x+2 x^2\right)} \, dx","Integrate[(3 + x)/((-1 + x^2)^(1/3)*(5 - x + 2*x^2)),x]","\int \frac{3+x}{\sqrt[3]{-1+x^2} \left(5-x+2 x^2\right)} \, dx","\frac{\log \left(3 \sqrt[3]{x^2-1}+\sqrt[3]{2} 3^{2/3} x-\sqrt[3]{2} 3^{2/3}\right)}{\sqrt[3]{2} 3^{2/3}}-\frac{\log \left(2^{2/3} \sqrt[3]{3} x^2+3 \left(x^2-1\right)^{2/3}+\left(\sqrt[3]{2} 3^{2/3}-\sqrt[3]{2} 3^{2/3} x\right) \sqrt[3]{x^2-1}-2\ 2^{2/3} \sqrt[3]{3} x+2^{2/3} \sqrt[3]{3}\right)}{2 \sqrt[3]{2} 3^{2/3}}+\frac{\tan ^{-1}\left(\frac{3^{5/6} \sqrt[3]{x^2-1}}{\sqrt[3]{3} \sqrt[3]{x^2-1}-2 \sqrt[3]{2} x+2 \sqrt[3]{2}}\right)}{\sqrt[3]{2} \sqrt[6]{3}}",1,"Integrate[(3 + x)/((-1 + x^2)^(1/3)*(5 - x + 2*x^2)), x]","F",-1
2505,0,0,209,12.8071881,"\int \frac{(-2+(1+k) x) \left(1-(1+k) x+(a+k) x^2\right)}{x^2 \sqrt[3]{(1-x) x (1-k x)} \left(1-(1+k) x+(-b+k) x^2\right)} \, dx","Integrate[((-2 + (1 + k)*x)*(1 - (1 + k)*x + (a + k)*x^2))/(x^2*((1 - x)*x*(1 - k*x))^(1/3)*(1 - (1 + k)*x + (-b + k)*x^2)),x]","\int \frac{(-2+(1+k) x) \left(1-(1+k) x+(a+k) x^2\right)}{x^2 \sqrt[3]{(1-x) x (1-k x)} \left(1-(1+k) x+(-b+k) x^2\right)} \, dx","\frac{(-a-b) \log \left(b^{2/3} x^2+\sqrt[3]{b} x \sqrt[3]{k x^3+(-k-1) x^2+x}+\left(k x^3+(-k-1) x^2+x\right)^{2/3}\right)}{2 \sqrt[3]{b}}+\frac{(a+b) \log \left(\sqrt[3]{k x^3+(-k-1) x^2+x}-\sqrt[3]{b} x\right)}{\sqrt[3]{b}}+\frac{\left(-\sqrt{3} a-\sqrt{3} b\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{b} x}{\sqrt[3]{b} x+2 \sqrt[3]{k x^3+(-k-1) x^2+x}}\right)}{\sqrt[3]{b}}+\frac{3 \left(k x^3+(-k-1) x^2+x\right)^{2/3}}{2 x^2}",1,"Integrate[((-2 + (1 + k)*x)*(1 - (1 + k)*x + (a + k)*x^2))/(x^2*((1 - x)*x*(1 - k*x))^(1/3)*(1 - (1 + k)*x + (-b + k)*x^2)), x]","F",-1
2506,0,0,209,2.6012861,"\int \frac{\left(-2+x^3\right) \sqrt[3]{x+x^3+x^4}}{\left(1+x^3\right) \left(1-x^2+x^3\right)} \, dx","Integrate[((-2 + x^3)*(x + x^3 + x^4)^(1/3))/((1 + x^3)*(1 - x^2 + x^3)),x]","\int \frac{\left(-2+x^3\right) \sqrt[3]{x+x^3+x^4}}{\left(1+x^3\right) \left(1-x^2+x^3\right)} \, dx","-\log \left(\sqrt[3]{x^4+x^3+x}-x\right)+\sqrt[3]{2} \log \left(2^{2/3} \sqrt[3]{x^4+x^3+x}-2 x\right)-\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^4+x^3+x}+x}\right)+\sqrt[3]{2} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^4+x^3+x}+x}\right)+\frac{1}{2} \log \left(x^2+\sqrt[3]{x^4+x^3+x} x+\left(x^4+x^3+x\right)^{2/3}\right)-\frac{\log \left(2 x^2+2^{2/3} \sqrt[3]{x^4+x^3+x} x+\sqrt[3]{2} \left(x^4+x^3+x\right)^{2/3}\right)}{2^{2/3}}",1,"Integrate[((-2 + x^3)*(x + x^3 + x^4)^(1/3))/((1 + x^3)*(1 - x^2 + x^3)), x]","F",-1
2507,0,0,209,14.654378,"\int \frac{\sqrt[4]{b x^3+a x^4}}{-2 b+a x+2 x^2} \, dx","Integrate[(b*x^3 + a*x^4)^(1/4)/(-2*b + a*x + 2*x^2),x]","\int \frac{\sqrt[4]{b x^3+a x^4}}{-2 b+a x+2 x^2} \, dx","\frac{1}{2} \text{RootSum}\left[2 \text{$\#$1}^8-5 \text{$\#$1}^4 a+3 a^2-2 b\&,\frac{-2 \text{$\#$1}^4 a \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)+2 \text{$\#$1}^4 a \log (x)+3 a^2 \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)-2 b \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)-3 a^2 \log (x)+2 b \log (x)}{5 \text{$\#$1}^3 a-4 \text{$\#$1}^7}\&\right]-\sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)+\sqrt[4]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)",1,"Integrate[(b*x^3 + a*x^4)^(1/4)/(-2*b + a*x + 2*x^2), x]","F",-1
2508,0,0,209,14.1688804,"\int \frac{\sqrt[4]{b x^3+a x^4}}{-2 b+a x+2 x^2} \, dx","Integrate[(b*x^3 + a*x^4)^(1/4)/(-2*b + a*x + 2*x^2),x]","\int \frac{\sqrt[4]{b x^3+a x^4}}{-2 b+a x+2 x^2} \, dx","\frac{1}{2} \text{RootSum}\left[2 \text{$\#$1}^8-5 \text{$\#$1}^4 a+3 a^2-2 b\&,\frac{-2 \text{$\#$1}^4 a \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)+2 \text{$\#$1}^4 a \log (x)+3 a^2 \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)-2 b \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)-3 a^2 \log (x)+2 b \log (x)}{5 \text{$\#$1}^3 a-4 \text{$\#$1}^7}\&\right]-\sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)+\sqrt[4]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)",1,"Integrate[(b*x^3 + a*x^4)^(1/4)/(-2*b + a*x + 2*x^2), x]","F",-1
2509,1,164,209,0.408575,"\int \frac{\left(1+x^3\right)^{2/3} \left(-1+2 x^6\right)}{x^6 \left(-1+2 x^3\right)} \, dx","Integrate[((1 + x^3)^(2/3)*(-1 + 2*x^6))/(x^6*(-1 + 2*x^3)),x]","\frac{1}{45} \left(-20\ 3^{2/3} \log \left(1-\frac{\sqrt[3]{3} x}{\sqrt[3]{x^3+1}}\right)+60 \sqrt[6]{3} \tan ^{-1}\left(\frac{2 x}{\sqrt[6]{3} \sqrt[3]{x^3+1}}+\frac{1}{\sqrt{3}}\right)-\frac{9 \left(x^3+1\right)^{2/3}}{x^5}-\frac{54 \left(x^3+1\right)^{2/3}}{x^2}+10\ 3^{2/3} \log \left(\frac{\sqrt[3]{3} x}{\sqrt[3]{x^3+1}}+\frac{3^{2/3} x^2}{\left(x^3+1\right)^{2/3}}+1\right)\right)-\frac{1}{2} x^4 F_1\left(\frac{4}{3};\frac{1}{3},1;\frac{7}{3};-x^3,2 x^3\right)","-\frac{1}{3} \log \left(\sqrt[3]{x^3+1}-x\right)-\frac{\log \left(3^{2/3} \sqrt[3]{x^3+1}-3 x\right)}{\sqrt[3]{3}}+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+1}+x}\right)}{\sqrt{3}}+\sqrt[6]{3} \tan ^{-1}\left(\frac{3^{5/6} x}{2 \sqrt[3]{x^3+1}+\sqrt[3]{3} x}\right)+\frac{\left(x^3+1\right)^{2/3} \left(-6 x^3-1\right)}{5 x^5}+\frac{1}{6} \log \left(\sqrt[3]{x^3+1} x+\left(x^3+1\right)^{2/3}+x^2\right)+\frac{\log \left(3^{2/3} \sqrt[3]{x^3+1} x+\sqrt[3]{3} \left(x^3+1\right)^{2/3}+3 x^2\right)}{2 \sqrt[3]{3}}",1,"-1/2*(x^4*AppellF1[4/3, 1/3, 1, 7/3, -x^3, 2*x^3]) + ((-9*(1 + x^3)^(2/3))/x^5 - (54*(1 + x^3)^(2/3))/x^2 + 60*3^(1/6)*ArcTan[1/Sqrt[3] + (2*x)/(3^(1/6)*(1 + x^3)^(1/3))] - 20*3^(2/3)*Log[1 - (3^(1/3)*x)/(1 + x^3)^(1/3)] + 10*3^(2/3)*Log[1 + (3^(2/3)*x^2)/(1 + x^3)^(2/3) + (3^(1/3)*x)/(1 + x^3)^(1/3)])/45","C",0
2510,0,0,209,0.4555747,"\int \frac{-b+a x^4}{\left(b+a x^4\right) \sqrt[4]{b^2+c x^4+a^2 x^8}} \, dx","Integrate[(-b + a*x^4)/((b + a*x^4)*(b^2 + c*x^4 + a^2*x^8)^(1/4)),x]","\int \frac{-b+a x^4}{\left(b+a x^4\right) \sqrt[4]{b^2+c x^4+a^2 x^8}} \, dx","\frac{\tan ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{2 a b-c} \sqrt[4]{a^2 x^8+b^2+c x^4}}{x^2 \sqrt{2 a b-c}-\sqrt{a^2 x^8+b^2+c x^4}}\right)}{2 \sqrt{2} \sqrt[4]{2 a b-c}}-\frac{\tanh ^{-1}\left(\frac{\frac{\sqrt{a^2 x^8+b^2+c x^4}}{\sqrt{2} \sqrt[4]{2 a b-c}}+\frac{x^2 \sqrt[4]{2 a b-c}}{\sqrt{2}}}{x \sqrt[4]{a^2 x^8+b^2+c x^4}}\right)}{2 \sqrt{2} \sqrt[4]{2 a b-c}}",1,"Integrate[(-b + a*x^4)/((b + a*x^4)*(b^2 + c*x^4 + a^2*x^8)^(1/4)), x]","F",-1
2511,1,357,209,0.6319279,"\int \frac{\sqrt{x+\sqrt{1+x}}}{\sqrt{1+x} \left(1+x^2\right)} \, dx","Integrate[Sqrt[x + Sqrt[1 + x]]/(Sqrt[1 + x]*(1 + x^2)),x]","\frac{1}{4} (1-i)^{3/2} \sqrt{i+\sqrt{1-i}} \tan ^{-1}\left(\frac{-\left(\left(1-2 \sqrt{1-i}\right) \sqrt{x+1}\right)+\sqrt{1-i}+2}{2 \sqrt{i+\sqrt{1-i}} \sqrt{x+\sqrt{x+1}}}\right)+\frac{1}{4} (1+i)^{3/2} \sqrt{\sqrt{1+i}-i} \tan ^{-1}\left(\frac{-\left(\left(1-2 \sqrt{1+i}\right) \sqrt{x+1}\right)+\sqrt{1+i}+2}{2 \sqrt{\sqrt{1+i}-i} \sqrt{x+\sqrt{x+1}}}\right)-\frac{1}{4} (1-i)^{3/2} \sqrt{\sqrt{1-i}-i} \tanh ^{-1}\left(\frac{-\left(\left(1+2 \sqrt{1-i}\right) \sqrt{x+1}\right)-\sqrt{1-i}+2}{2 \sqrt{\sqrt{1-i}-i} \sqrt{x+\sqrt{x+1}}}\right)-\frac{1}{4} (1+i)^{3/2} \sqrt{i+\sqrt{1+i}} \tanh ^{-1}\left(\frac{-\left(\left(1+2 \sqrt{1+i}\right) \sqrt{x+1}\right)-\sqrt{1+i}+2}{2 \sqrt{i+\sqrt{1+i}} \sqrt{x+\sqrt{x+1}}}\right)","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^5+20 \text{$\#$1}^4-48 \text{$\#$1}^3+40 \text{$\#$1}^2-8 \text{$\#$1}+1\&,\frac{2 \text{$\#$1}^5 \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)-5 \text{$\#$1}^4 \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)+5 \text{$\#$1}^2 \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)-\log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+5 \text{$\#$1}^4+10 \text{$\#$1}^3-18 \text{$\#$1}^2+10 \text{$\#$1}-1}\&\right]",1,"((1 - I)^(3/2)*Sqrt[I + Sqrt[1 - I]]*ArcTan[(2 + Sqrt[1 - I] - (1 - 2*Sqrt[1 - I])*Sqrt[1 + x])/(2*Sqrt[I + Sqrt[1 - I]]*Sqrt[x + Sqrt[1 + x]])])/4 + ((1 + I)^(3/2)*Sqrt[-I + Sqrt[1 + I]]*ArcTan[(2 + Sqrt[1 + I] - (1 - 2*Sqrt[1 + I])*Sqrt[1 + x])/(2*Sqrt[-I + Sqrt[1 + I]]*Sqrt[x + Sqrt[1 + x]])])/4 - ((1 - I)^(3/2)*Sqrt[-I + Sqrt[1 - I]]*ArcTanh[(2 - Sqrt[1 - I] - (1 + 2*Sqrt[1 - I])*Sqrt[1 + x])/(2*Sqrt[-I + Sqrt[1 - I]]*Sqrt[x + Sqrt[1 + x]])])/4 - ((1 + I)^(3/2)*Sqrt[I + Sqrt[1 + I]]*ArcTanh[(2 - Sqrt[1 + I] - (1 + 2*Sqrt[1 + I])*Sqrt[1 + x])/(2*Sqrt[I + Sqrt[1 + I]]*Sqrt[x + Sqrt[1 + x]])])/4","C",1
2512,1,357,209,0.2643972,"\int \frac{\sqrt{x+\sqrt{1+x}}}{\sqrt{1+x} \left(1+x^2\right)} \, dx","Integrate[Sqrt[x + Sqrt[1 + x]]/(Sqrt[1 + x]*(1 + x^2)),x]","\frac{1}{4} (1-i)^{3/2} \sqrt{i+\sqrt{1-i}} \tan ^{-1}\left(\frac{-\left(\left(1-2 \sqrt{1-i}\right) \sqrt{x+1}\right)+\sqrt{1-i}+2}{2 \sqrt{i+\sqrt{1-i}} \sqrt{x+\sqrt{x+1}}}\right)+\frac{1}{4} (1+i)^{3/2} \sqrt{\sqrt{1+i}-i} \tan ^{-1}\left(\frac{-\left(\left(1-2 \sqrt{1+i}\right) \sqrt{x+1}\right)+\sqrt{1+i}+2}{2 \sqrt{\sqrt{1+i}-i} \sqrt{x+\sqrt{x+1}}}\right)-\frac{1}{4} (1-i)^{3/2} \sqrt{\sqrt{1-i}-i} \tanh ^{-1}\left(\frac{-\left(\left(1+2 \sqrt{1-i}\right) \sqrt{x+1}\right)-\sqrt{1-i}+2}{2 \sqrt{\sqrt{1-i}-i} \sqrt{x+\sqrt{x+1}}}\right)-\frac{1}{4} (1+i)^{3/2} \sqrt{i+\sqrt{1+i}} \tanh ^{-1}\left(\frac{-\left(\left(1+2 \sqrt{1+i}\right) \sqrt{x+1}\right)-\sqrt{1+i}+2}{2 \sqrt{i+\sqrt{1+i}} \sqrt{x+\sqrt{x+1}}}\right)","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^5+20 \text{$\#$1}^4-48 \text{$\#$1}^3+40 \text{$\#$1}^2-8 \text{$\#$1}+1\&,\frac{2 \text{$\#$1}^5 \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)-5 \text{$\#$1}^4 \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)+5 \text{$\#$1}^2 \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)-\log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+5 \text{$\#$1}^4+10 \text{$\#$1}^3-18 \text{$\#$1}^2+10 \text{$\#$1}-1}\&\right]",1,"((1 - I)^(3/2)*Sqrt[I + Sqrt[1 - I]]*ArcTan[(2 + Sqrt[1 - I] - (1 - 2*Sqrt[1 - I])*Sqrt[1 + x])/(2*Sqrt[I + Sqrt[1 - I]]*Sqrt[x + Sqrt[1 + x]])])/4 + ((1 + I)^(3/2)*Sqrt[-I + Sqrt[1 + I]]*ArcTan[(2 + Sqrt[1 + I] - (1 - 2*Sqrt[1 + I])*Sqrt[1 + x])/(2*Sqrt[-I + Sqrt[1 + I]]*Sqrt[x + Sqrt[1 + x]])])/4 - ((1 - I)^(3/2)*Sqrt[-I + Sqrt[1 - I]]*ArcTanh[(2 - Sqrt[1 - I] - (1 + 2*Sqrt[1 - I])*Sqrt[1 + x])/(2*Sqrt[-I + Sqrt[1 - I]]*Sqrt[x + Sqrt[1 + x]])])/4 - ((1 + I)^(3/2)*Sqrt[I + Sqrt[1 + I]]*ArcTanh[(2 - Sqrt[1 + I] - (1 + 2*Sqrt[1 + I])*Sqrt[1 + x])/(2*Sqrt[I + Sqrt[1 + I]]*Sqrt[x + Sqrt[1 + x]])])/4","C",1
2513,0,0,210,1.8993655,"\int \frac{(2+x)^2 \sqrt[3]{-19+66 x-30 x^2+9 x^3}}{(-3+2 x)^2 \left(-5+6 x-6 x^2+x^3\right)} \, dx","Integrate[((2 + x)^2*(-19 + 66*x - 30*x^2 + 9*x^3)^(1/3))/((-3 + 2*x)^2*(-5 + 6*x - 6*x^2 + x^3)),x]","\int \frac{(2+x)^2 \sqrt[3]{-19+66 x-30 x^2+9 x^3}}{(-3+2 x)^2 \left(-5+6 x-6 x^2+x^3\right)} \, dx","\frac{\sqrt[3]{9 x^3-30 x^2+66 x-19}}{2 x-3}+\frac{1}{3} \sqrt[3]{2} \log \left(2^{2/3} \sqrt[3]{9 x^3-30 x^2+66 x-19}-4 x+6\right)-\frac{\log \left(8 x^2+\sqrt[3]{2} \left(9 x^3-30 x^2+66 x-19\right)^{2/3}+\left(2\ 2^{2/3} x-3\ 2^{2/3}\right) \sqrt[3]{9 x^3-30 x^2+66 x-19}-24 x+18\right)}{3\ 2^{2/3}}+\frac{\sqrt[3]{2} \tan ^{-1}\left(\frac{2 \sqrt{3} x-3 \sqrt{3}}{2^{2/3} \sqrt[3]{9 x^3-30 x^2+66 x-19}+2 x-3}\right)}{\sqrt{3}}",1,"Integrate[((2 + x)^2*(-19 + 66*x - 30*x^2 + 9*x^3)^(1/3))/((-3 + 2*x)^2*(-5 + 6*x - 6*x^2 + x^3)), x]","F",-1
2514,0,0,210,0.4668742,"\int \frac{1+x^3}{\left(-1+x^3\right) \sqrt[3]{x^2+x^4}} \, dx","Integrate[(1 + x^3)/((-1 + x^3)*(x^2 + x^4)^(1/3)),x]","\int \frac{1+x^3}{\left(-1+x^3\right) \sqrt[3]{x^2+x^4}} \, dx","-\frac{2}{3} \log \left(\sqrt[3]{x^4+x^2}+x\right)+\frac{\log \left(2^{2/3} \sqrt[3]{x^4+x^2}-2 x\right)}{3 \sqrt[3]{2}}+\frac{1}{3} \log \left(x^2-\sqrt[3]{x^4+x^2} x+\left(x^4+x^2\right)^{2/3}\right)-\frac{\log \left(2 x^2+2^{2/3} \sqrt[3]{x^4+x^2} x+\sqrt[3]{2} \left(x^4+x^2\right)^{2/3}\right)}{6 \sqrt[3]{2}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^4+x^2}-x}\right)}{\sqrt{3}}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^4+x^2}+x}\right)}{\sqrt[3]{2} \sqrt{3}}",1,"Integrate[(1 + x^3)/((-1 + x^3)*(x^2 + x^4)^(1/3)), x]","F",-1
2515,0,0,210,3.6111919,"\int \frac{x \left(4 a b-3 (a+b) x+2 x^2\right)}{\sqrt[3]{x^2 (-a+x) (-b+x)} \left(-a b d+(a+b) d x-d x^2+x^4\right)} \, dx","Integrate[(x*(4*a*b - 3*(a + b)*x + 2*x^2))/((x^2*(-a + x)*(-b + x))^(1/3)*(-(a*b*d) + (a + b)*d*x - d*x^2 + x^4)),x]","\int \frac{x \left(4 a b-3 (a+b) x+2 x^2\right)}{\sqrt[3]{x^2 (-a+x) (-b+x)} \left(-a b d+(a+b) d x-d x^2+x^4\right)} \, dx","\frac{\log \left(x^2-\sqrt[3]{d} \sqrt[3]{x^3 (-a-b)+a b x^2+x^4}\right)}{d^{2/3}}-\frac{\log \left(d^{2/3} \left(x^3 (-a-b)+a b x^2+x^4\right)^{2/3}+\sqrt[3]{d} x^2 \sqrt[3]{x^3 (-a-b)+a b x^2+x^4}+x^4\right)}{2 d^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} \sqrt[3]{x^3 (-a-b)+a b x^2+x^4}}{\sqrt[3]{d} \sqrt[3]{x^3 (-a-b)+a b x^2+x^4}+2 x^2}\right)}{d^{2/3}}",1,"Integrate[(x*(4*a*b - 3*(a + b)*x + 2*x^2))/((x^2*(-a + x)*(-b + x))^(1/3)*(-(a*b*d) + (a + b)*d*x - d*x^2 + x^4)), x]","F",-1
2516,1,152,210,0.2085914,"\int \frac{\sqrt{b+a x^4}}{-b+a x^4} \, dx","Integrate[Sqrt[b + a*x^4]/(-b + a*x^4),x]","-\frac{5 b x \sqrt{a x^4+b} F_1\left(\frac{1}{4};-\frac{1}{2},1;\frac{5}{4};-\frac{a x^4}{b},\frac{a x^4}{b}\right)}{\left(b-a x^4\right) \left(2 a x^4 \left(2 F_1\left(\frac{5}{4};-\frac{1}{2},2;\frac{9}{4};-\frac{a x^4}{b},\frac{a x^4}{b}\right)+F_1\left(\frac{5}{4};\frac{1}{2},1;\frac{9}{4};-\frac{a x^4}{b},\frac{a x^4}{b}\right)\right)+5 b F_1\left(\frac{1}{4};-\frac{1}{2},1;\frac{5}{4};-\frac{a x^4}{b},\frac{a x^4}{b}\right)\right)}","-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x}{\sqrt{a x^4+b}+\sqrt{a} x^2+\sqrt{b}}\right)}{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{6-4 \sqrt{2}} \sqrt[4]{a} \sqrt[4]{b} x}{\sqrt{a x^4+b}+\sqrt{a} x^2+\sqrt{b}}\right)}{2 \sqrt{2} \sqrt[4]{a} \sqrt[4]{b}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{6+4 \sqrt{2}} \sqrt[4]{a} \sqrt[4]{b} x}{\sqrt{a x^4+b}+\sqrt{a} x^2+\sqrt{b}}\right)}{2 \sqrt{2} \sqrt[4]{a} \sqrt[4]{b}}",1,"(-5*b*x*Sqrt[b + a*x^4]*AppellF1[1/4, -1/2, 1, 5/4, -((a*x^4)/b), (a*x^4)/b])/((b - a*x^4)*(5*b*AppellF1[1/4, -1/2, 1, 5/4, -((a*x^4)/b), (a*x^4)/b] + 2*a*x^4*(2*AppellF1[5/4, -1/2, 2, 9/4, -((a*x^4)/b), (a*x^4)/b] + AppellF1[5/4, 1/2, 1, 9/4, -((a*x^4)/b), (a*x^4)/b])))","C",0
2517,0,0,210,0.1769532,"\int \frac{1+x^2}{\left(-1+x+x^2\right) \sqrt[3]{-1+x^6}} \, dx","Integrate[(1 + x^2)/((-1 + x + x^2)*(-1 + x^6)^(1/3)),x]","\int \frac{1+x^2}{\left(-1+x+x^2\right) \sqrt[3]{-1+x^6}} \, dx","-\frac{\log \left(-2 \sqrt[3]{x^6-1}+2^{2/3} x^2-2^{2/3} x-2^{2/3}\right)}{3\ 2^{2/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x^6-1}}{\sqrt[3]{x^6-1}+2^{2/3} x^2-2^{2/3} x-2^{2/3}}\right)}{2^{2/3} \sqrt{3}}+\frac{\log \left(2 \left(x^6-1\right)^{2/3}+\sqrt[3]{2} x^4-2 \sqrt[3]{2} x^3-\sqrt[3]{2} x^2+\left(2^{2/3} x^2-2^{2/3} x-2^{2/3}\right) \sqrt[3]{x^6-1}+2 \sqrt[3]{2} x+\sqrt[3]{2}\right)}{6\ 2^{2/3}}",1,"Integrate[(1 + x^2)/((-1 + x + x^2)*(-1 + x^6)^(1/3)), x]","F",-1
2518,0,0,210,0.0733998,"\int \frac{1+x^2}{\left(-1+x+x^2\right) \sqrt[3]{-1+x^6}} \, dx","Integrate[(1 + x^2)/((-1 + x + x^2)*(-1 + x^6)^(1/3)),x]","\int \frac{1+x^2}{\left(-1+x+x^2\right) \sqrt[3]{-1+x^6}} \, dx","-\frac{\log \left(-2 \sqrt[3]{x^6-1}+2^{2/3} x^2-2^{2/3} x-2^{2/3}\right)}{3\ 2^{2/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x^6-1}}{\sqrt[3]{x^6-1}+2^{2/3} x^2-2^{2/3} x-2^{2/3}}\right)}{2^{2/3} \sqrt{3}}+\frac{\log \left(2 \left(x^6-1\right)^{2/3}+\sqrt[3]{2} x^4-2 \sqrt[3]{2} x^3-\sqrt[3]{2} x^2+\left(2^{2/3} x^2-2^{2/3} x-2^{2/3}\right) \sqrt[3]{x^6-1}+2 \sqrt[3]{2} x+\sqrt[3]{2}\right)}{6\ 2^{2/3}}",1,"Integrate[(1 + x^2)/((-1 + x + x^2)*(-1 + x^6)^(1/3)), x]","F",-1
2519,1,393,210,0.6111281,"\int \frac{x^3 \sqrt[3]{-x^2+x^3}}{1+x^6} \, dx","Integrate[(x^3*(-x^2 + x^3)^(1/3))/(1 + x^6),x]","\frac{\sqrt[3]{(x-1) x^2} \left(-i \left(\sqrt{3}+(-2-i)\right) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(\frac{1}{2}-\frac{i}{2}\right) (x-1)}{x}\right)+i \left(\sqrt{3}+(-2-i)\right) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(\frac{1}{2}+\frac{i}{2}\right) (x-1)}{x}\right)-\sqrt{3} \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};-\frac{2 (x-1)}{\left((-2+i)+\sqrt{3}\right) x}\right)+(2-i) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};-\frac{2 (x-1)}{\left((-2+i)+\sqrt{3}\right) x}\right)-(1+i) \sqrt{3} \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(i+\sqrt{3}\right) (x-1)}{\left((-2+i)+\sqrt{3}\right) x}\right)+(1+i) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(i+\sqrt{3}\right) (x-1)}{\left((-2+i)+\sqrt{3}\right) x}\right)+\sqrt{3} \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{2 (x-1)}{\left((2+i)+\sqrt{3}\right) x}\right)-(2-i) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{2 (x-1)}{\left((2+i)+\sqrt{3}\right) x}\right)+(1+i) \sqrt{3} \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(i+\sqrt{3}\right) (x-1)}{\left((2+i)+\sqrt{3}\right) x}\right)-(1+i) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(i+\sqrt{3}\right) (x-1)}{\left((2+i)+\sqrt{3}\right) x}\right)\right)}{4 \left(1+(-1)^{5/6}\right) x}","\frac{1}{6} \text{RootSum}\left[\text{$\#$1}^6-2 \text{$\#$1}^3+2\&,\frac{\text{$\#$1} \log \left(\sqrt[3]{x^3-x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^3-1}\&\right]-\frac{1}{6} \text{RootSum}\left[\text{$\#$1}^{12}-4 \text{$\#$1}^9+5 \text{$\#$1}^6-2 \text{$\#$1}^3+1\&,\frac{\text{$\#$1}^7 \log \left(\sqrt[3]{x^3-x^2}-\text{$\#$1} x\right)+\text{$\#$1}^7 (-\log (x))-2 \text{$\#$1}^4 \log \left(\sqrt[3]{x^3-x^2}-\text{$\#$1} x\right)+2 \text{$\#$1}^4 \log (x)-\text{$\#$1} \log \left(\sqrt[3]{x^3-x^2}-\text{$\#$1} x\right)+\text{$\#$1} \log (x)}{2 \text{$\#$1}^9-6 \text{$\#$1}^6+5 \text{$\#$1}^3-1}\&\right]",1,"(((-1 + x)*x^2)^(1/3)*((-I)*((-2 - I) + Sqrt[3])*Hypergeometric2F1[1/3, 1, 4/3, ((1/2 - I/2)*(-1 + x))/x] + I*((-2 - I) + Sqrt[3])*Hypergeometric2F1[1/3, 1, 4/3, ((1/2 + I/2)*(-1 + x))/x] + (2 - I)*Hypergeometric2F1[1/3, 1, 4/3, (-2*(-1 + x))/(((-2 + I) + Sqrt[3])*x)] - Sqrt[3]*Hypergeometric2F1[1/3, 1, 4/3, (-2*(-1 + x))/(((-2 + I) + Sqrt[3])*x)] + (1 + I)*Hypergeometric2F1[1/3, 1, 4/3, ((I + Sqrt[3])*(-1 + x))/(((-2 + I) + Sqrt[3])*x)] - (1 + I)*Sqrt[3]*Hypergeometric2F1[1/3, 1, 4/3, ((I + Sqrt[3])*(-1 + x))/(((-2 + I) + Sqrt[3])*x)] - (2 - I)*Hypergeometric2F1[1/3, 1, 4/3, (2*(-1 + x))/(((2 + I) + Sqrt[3])*x)] + Sqrt[3]*Hypergeometric2F1[1/3, 1, 4/3, (2*(-1 + x))/(((2 + I) + Sqrt[3])*x)] - (1 + I)*Hypergeometric2F1[1/3, 1, 4/3, ((I + Sqrt[3])*(-1 + x))/(((2 + I) + Sqrt[3])*x)] + (1 + I)*Sqrt[3]*Hypergeometric2F1[1/3, 1, 4/3, ((I + Sqrt[3])*(-1 + x))/(((2 + I) + Sqrt[3])*x)]))/(4*(1 + (-1)^(5/6))*x)","C",1
2520,1,586,210,1.6129651,"\int \frac{b-2 c x^4+2 a x^8}{\sqrt[4]{-b+a x^4} \left(-2 b-c x^4+2 a x^8\right)} \, dx","Integrate[(b - 2*c*x^4 + 2*a*x^8)/((-b + a*x^4)^(1/4)*(-2*b - c*x^4 + 2*a*x^8)),x]","\frac{-\frac{\left(\frac{12 a b-c^2}{\sqrt{16 a b+c^2}}+c\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{\sqrt{16 a b+c^2}+4 b-c}}{\sqrt[4]{\sqrt{16 a b+c^2}-c} \sqrt[4]{a x^4-b}}\right)}{\left(\sqrt{16 a b+c^2}-c\right)^{3/4} \sqrt[4]{\sqrt{16 a b+c^2}+4 b-c}}+\frac{\left(c \left(\sqrt{16 a b+c^2}+c\right)-12 a b\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{\sqrt{16 a b+c^2}-4 b+c}}{\sqrt[4]{\sqrt{16 a b+c^2}+c} \sqrt[4]{a x^4-b}}\right)}{\sqrt{16 a b+c^2} \left(\sqrt{16 a b+c^2}+c\right)^{3/4} \sqrt[4]{\sqrt{16 a b+c^2}-4 b+c}}-\frac{\left(\frac{12 a b-c^2}{\sqrt{16 a b+c^2}}+c\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{\sqrt{16 a b+c^2}+4 b-c}}{\sqrt[4]{\sqrt{16 a b+c^2}-c} \sqrt[4]{a x^4-b}}\right)}{\left(\sqrt{16 a b+c^2}-c\right)^{3/4} \sqrt[4]{\sqrt{16 a b+c^2}+4 b-c}}+\frac{\left(c \left(\sqrt{16 a b+c^2}+c\right)-12 a b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{\sqrt{16 a b+c^2}-4 b+c}}{\sqrt[4]{\sqrt{16 a b+c^2}+c} \sqrt[4]{a x^4-b}}\right)}{\sqrt{16 a b+c^2} \left(\sqrt{16 a b+c^2}+c\right)^{3/4} \sqrt[4]{\sqrt{16 a b+c^2}-4 b+c}}+\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)+\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{2 \sqrt[4]{a}}","\frac{1}{4} \text{RootSum}\left[2 \text{$\#$1}^8-4 \text{$\#$1}^4 a-\text{$\#$1}^4 c+2 a^2-2 a b+a c\&,\frac{-3 \text{$\#$1}^4 \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+3 \text{$\#$1}^4 \log (x)-c \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+3 a \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)-3 a \log (x)+c \log (x)}{-4 \text{$\#$1}^5+4 \text{$\#$1} a+\text{$\#$1} c}\&\right]+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{2 \sqrt[4]{a}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{2 \sqrt[4]{a}}",1,"(ArcTan[(a^(1/4)*x)/(-b + a*x^4)^(1/4)] - ((c + (12*a*b - c^2)/Sqrt[16*a*b + c^2])*ArcTan[(a^(1/4)*(4*b - c + Sqrt[16*a*b + c^2])^(1/4)*x)/((-c + Sqrt[16*a*b + c^2])^(1/4)*(-b + a*x^4)^(1/4))])/((-c + Sqrt[16*a*b + c^2])^(3/4)*(4*b - c + Sqrt[16*a*b + c^2])^(1/4)) + ((-12*a*b + c*(c + Sqrt[16*a*b + c^2]))*ArcTan[(a^(1/4)*(-4*b + c + Sqrt[16*a*b + c^2])^(1/4)*x)/((c + Sqrt[16*a*b + c^2])^(1/4)*(-b + a*x^4)^(1/4))])/(Sqrt[16*a*b + c^2]*(c + Sqrt[16*a*b + c^2])^(3/4)*(-4*b + c + Sqrt[16*a*b + c^2])^(1/4)) + ArcTanh[(a^(1/4)*x)/(-b + a*x^4)^(1/4)] - ((c + (12*a*b - c^2)/Sqrt[16*a*b + c^2])*ArcTanh[(a^(1/4)*(4*b - c + Sqrt[16*a*b + c^2])^(1/4)*x)/((-c + Sqrt[16*a*b + c^2])^(1/4)*(-b + a*x^4)^(1/4))])/((-c + Sqrt[16*a*b + c^2])^(3/4)*(4*b - c + Sqrt[16*a*b + c^2])^(1/4)) + ((-12*a*b + c*(c + Sqrt[16*a*b + c^2]))*ArcTanh[(a^(1/4)*(-4*b + c + Sqrt[16*a*b + c^2])^(1/4)*x)/((c + Sqrt[16*a*b + c^2])^(1/4)*(-b + a*x^4)^(1/4))])/(Sqrt[16*a*b + c^2]*(c + Sqrt[16*a*b + c^2])^(3/4)*(-4*b + c + Sqrt[16*a*b + c^2])^(1/4)))/(2*a^(1/4))","B",1
2521,1,586,210,0.5222243,"\int \frac{b-2 c x^4+2 a x^8}{\sqrt[4]{-b+a x^4} \left(-2 b-c x^4+2 a x^8\right)} \, dx","Integrate[(b - 2*c*x^4 + 2*a*x^8)/((-b + a*x^4)^(1/4)*(-2*b - c*x^4 + 2*a*x^8)),x]","\frac{-\frac{\left(\frac{12 a b-c^2}{\sqrt{16 a b+c^2}}+c\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{\sqrt{16 a b+c^2}+4 b-c}}{\sqrt[4]{\sqrt{16 a b+c^2}-c} \sqrt[4]{a x^4-b}}\right)}{\left(\sqrt{16 a b+c^2}-c\right)^{3/4} \sqrt[4]{\sqrt{16 a b+c^2}+4 b-c}}+\frac{\left(c \left(\sqrt{16 a b+c^2}+c\right)-12 a b\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{\sqrt{16 a b+c^2}-4 b+c}}{\sqrt[4]{\sqrt{16 a b+c^2}+c} \sqrt[4]{a x^4-b}}\right)}{\sqrt{16 a b+c^2} \left(\sqrt{16 a b+c^2}+c\right)^{3/4} \sqrt[4]{\sqrt{16 a b+c^2}-4 b+c}}-\frac{\left(\frac{12 a b-c^2}{\sqrt{16 a b+c^2}}+c\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{\sqrt{16 a b+c^2}+4 b-c}}{\sqrt[4]{\sqrt{16 a b+c^2}-c} \sqrt[4]{a x^4-b}}\right)}{\left(\sqrt{16 a b+c^2}-c\right)^{3/4} \sqrt[4]{\sqrt{16 a b+c^2}+4 b-c}}+\frac{\left(c \left(\sqrt{16 a b+c^2}+c\right)-12 a b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{\sqrt{16 a b+c^2}-4 b+c}}{\sqrt[4]{\sqrt{16 a b+c^2}+c} \sqrt[4]{a x^4-b}}\right)}{\sqrt{16 a b+c^2} \left(\sqrt{16 a b+c^2}+c\right)^{3/4} \sqrt[4]{\sqrt{16 a b+c^2}-4 b+c}}+\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)+\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{2 \sqrt[4]{a}}","\frac{1}{4} \text{RootSum}\left[2 \text{$\#$1}^8-4 \text{$\#$1}^4 a-\text{$\#$1}^4 c+2 a^2-2 a b+a c\&,\frac{-3 \text{$\#$1}^4 \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+3 \text{$\#$1}^4 \log (x)-c \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+3 a \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)-3 a \log (x)+c \log (x)}{-4 \text{$\#$1}^5+4 \text{$\#$1} a+\text{$\#$1} c}\&\right]+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{2 \sqrt[4]{a}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{2 \sqrt[4]{a}}",1,"(ArcTan[(a^(1/4)*x)/(-b + a*x^4)^(1/4)] - ((c + (12*a*b - c^2)/Sqrt[16*a*b + c^2])*ArcTan[(a^(1/4)*(4*b - c + Sqrt[16*a*b + c^2])^(1/4)*x)/((-c + Sqrt[16*a*b + c^2])^(1/4)*(-b + a*x^4)^(1/4))])/((-c + Sqrt[16*a*b + c^2])^(3/4)*(4*b - c + Sqrt[16*a*b + c^2])^(1/4)) + ((-12*a*b + c*(c + Sqrt[16*a*b + c^2]))*ArcTan[(a^(1/4)*(-4*b + c + Sqrt[16*a*b + c^2])^(1/4)*x)/((c + Sqrt[16*a*b + c^2])^(1/4)*(-b + a*x^4)^(1/4))])/(Sqrt[16*a*b + c^2]*(c + Sqrt[16*a*b + c^2])^(3/4)*(-4*b + c + Sqrt[16*a*b + c^2])^(1/4)) + ArcTanh[(a^(1/4)*x)/(-b + a*x^4)^(1/4)] - ((c + (12*a*b - c^2)/Sqrt[16*a*b + c^2])*ArcTanh[(a^(1/4)*(4*b - c + Sqrt[16*a*b + c^2])^(1/4)*x)/((-c + Sqrt[16*a*b + c^2])^(1/4)*(-b + a*x^4)^(1/4))])/((-c + Sqrt[16*a*b + c^2])^(3/4)*(4*b - c + Sqrt[16*a*b + c^2])^(1/4)) + ((-12*a*b + c*(c + Sqrt[16*a*b + c^2]))*ArcTanh[(a^(1/4)*(-4*b + c + Sqrt[16*a*b + c^2])^(1/4)*x)/((c + Sqrt[16*a*b + c^2])^(1/4)*(-b + a*x^4)^(1/4))])/(Sqrt[16*a*b + c^2]*(c + Sqrt[16*a*b + c^2])^(3/4)*(-4*b + c + Sqrt[16*a*b + c^2])^(1/4)))/(2*a^(1/4))","B",1
2522,1,173,211,0.3130507,"\int \frac{1}{x^3 \left(1+x^3\right) \sqrt[3]{-x^2+x^3}} \, dx","Integrate[1/(x^3*(1 + x^3)*(-x^2 + x^3)^(1/3)),x]","-\frac{(x-1)^2 \left(10 x^2 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{x-1}{2 x}\right)+10 \left(1-i \sqrt{3}\right) x^2 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};-\frac{2 i (x-1)}{\left(-i+\sqrt{3}\right) x}\right)+10 i \sqrt{3} x^2 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{2 i (x-1)}{\left(i+\sqrt{3}\right) x}\right)+10 x^2 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{2 i (x-1)}{\left(i+\sqrt{3}\right) x}\right)-27 x^2-18 x-15\right)}{40 \left((x-1) x^2\right)^{4/3}}","\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^6-\text{$\#$1}^3+1\&,\frac{\log \left(\sqrt[3]{x^3-x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]+\frac{\log \left(2^{2/3} \sqrt[3]{x^3-x^2}-2 x\right)}{3 \sqrt[3]{2}}-\frac{\log \left(2 x^2+2^{2/3} \sqrt[3]{x^3-x^2} x+\sqrt[3]{2} \left(x^3-x^2\right)^{2/3}\right)}{6 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^3-x^2}+x}\right)}{\sqrt[3]{2} \sqrt{3}}+\frac{3 \left(x^3-x^2\right)^{2/3} \left(9 x^2+6 x+5\right)}{40 x^4}",1,"-1/40*((-1 + x)^2*(-15 - 18*x - 27*x^2 + 10*x^2*Hypergeometric2F1[2/3, 1, 5/3, (-1 + x)/(2*x)] + 10*(1 - I*Sqrt[3])*x^2*Hypergeometric2F1[2/3, 1, 5/3, ((-2*I)*(-1 + x))/((-I + Sqrt[3])*x)] + 10*x^2*Hypergeometric2F1[2/3, 1, 5/3, ((2*I)*(-1 + x))/((I + Sqrt[3])*x)] + (10*I)*Sqrt[3]*x^2*Hypergeometric2F1[2/3, 1, 5/3, ((2*I)*(-1 + x))/((I + Sqrt[3])*x)]))/((-1 + x)*x^2)^(4/3)","C",1
2523,1,489,211,1.0122862,"\int \frac{\left(-1+x^2\right) \sqrt[4]{x^3+x^4}}{1+x^2+x^4} \, dx","Integrate[((-1 + x^2)*(x^3 + x^4)^(1/4))/(1 + x^2 + x^4),x]","\frac{\left(1-i \sqrt{3}\right) \sqrt[4]{x^3 (x+1)} \left(x^{3/4} \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};-x\right)-\frac{\left(1-\frac{1}{\sqrt{\frac{1}{2} \left(-1-i \sqrt{3}\right)}}\right) x^{3/4} \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{\left(1-i \sqrt{3}\right) x}{2 (x+1)}\right)}{(x+1)^{3/4}}\right)}{3 x^{3/4} \sqrt[4]{x+1}}+\frac{\left(1+i \sqrt{3}\right) \sqrt[4]{x^3 (x+1)} \left(x^{3/4} \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};-x\right)-\frac{\left(1-\frac{1}{\sqrt{\frac{1}{2} i \left(\sqrt{3}+i\right)}}\right) x^{3/4} \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{\left(1+i \sqrt{3}\right) x}{2 (x+1)}\right)}{(x+1)^{3/4}}\right)}{3 x^{3/4} \sqrt[4]{x+1}}+\frac{\left(1-i \sqrt{3}\right) \sqrt[4]{x^3 (x+1)} \left(2 x^{3/4} \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};-x\right)-\frac{\left(3+i \sqrt{3}\right) x^{3/4} \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{\left(1+\frac{1}{\sqrt{\frac{1}{2} \left(-1-i \sqrt{3}\right)}}\right) x}{x+1}\right)}{(x+1)^{3/4}}\right)}{6 x^{3/4} \sqrt[4]{x+1}}+\frac{\left(1+i \sqrt{3}\right) \sqrt[4]{x^3 (x+1)} \left(2 x^{3/4} \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};-x\right)-\frac{\left(3-i \sqrt{3}\right) x^{3/4} \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{\left(1+\frac{1}{\sqrt{\frac{1}{2} i \left(i+\sqrt{3}\right)}}\right) x}{x+1}\right)}{(x+1)^{3/4}}\right)}{6 x^{3/4} \sqrt[4]{x+1}}","-\frac{3}{2} \text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4+3\&,\frac{-\text{$\#$1}^4 \log \left(\sqrt[4]{x^4+x^3}-\text{$\#$1} x\right)+\text{$\#$1}^4 \log (x)+\log \left(\sqrt[4]{x^4+x^3}-\text{$\#$1} x\right)-\log (x)}{2 \text{$\#$1}^7-3 \text{$\#$1}^3}\&\right]+\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4+1\&,\frac{-\text{$\#$1}^4 \log \left(\sqrt[4]{x^4+x^3}-\text{$\#$1} x\right)+\text{$\#$1}^4 \log (x)-\log \left(\sqrt[4]{x^4+x^3}-\text{$\#$1} x\right)+\log (x)}{2 \text{$\#$1}^7-\text{$\#$1}^3}\&\right]-2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+x^3}}\right)+2 \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+x^3}}\right)",1,"((1 - I*Sqrt[3])*(x^3*(1 + x))^(1/4)*(x^(3/4)*Hypergeometric2F1[3/4, 3/4, 7/4, -x] - ((1 - 1/Sqrt[(-1 - I*Sqrt[3])/2])*x^(3/4)*Hypergeometric2F1[3/4, 1, 7/4, ((1 - I*Sqrt[3])*x)/(2*(1 + x))])/(1 + x)^(3/4)))/(3*x^(3/4)*(1 + x)^(1/4)) + ((1 + I*Sqrt[3])*(x^3*(1 + x))^(1/4)*(x^(3/4)*Hypergeometric2F1[3/4, 3/4, 7/4, -x] - ((1 - 1/Sqrt[(I/2)*(I + Sqrt[3])])*x^(3/4)*Hypergeometric2F1[3/4, 1, 7/4, ((1 + I*Sqrt[3])*x)/(2*(1 + x))])/(1 + x)^(3/4)))/(3*x^(3/4)*(1 + x)^(1/4)) + ((1 - I*Sqrt[3])*(x^3*(1 + x))^(1/4)*(2*x^(3/4)*Hypergeometric2F1[3/4, 3/4, 7/4, -x] - ((3 + I*Sqrt[3])*x^(3/4)*Hypergeometric2F1[3/4, 1, 7/4, ((1 + 1/Sqrt[(-1 - I*Sqrt[3])/2])*x)/(1 + x)])/(1 + x)^(3/4)))/(6*x^(3/4)*(1 + x)^(1/4)) + ((1 + I*Sqrt[3])*(x^3*(1 + x))^(1/4)*(2*x^(3/4)*Hypergeometric2F1[3/4, 3/4, 7/4, -x] - ((3 - I*Sqrt[3])*x^(3/4)*Hypergeometric2F1[3/4, 1, 7/4, ((1 + 1/Sqrt[(I/2)*(I + Sqrt[3])])*x)/(1 + x)])/(1 + x)^(3/4)))/(6*x^(3/4)*(1 + x)^(1/4))","C",0
2524,1,489,211,0.8020212,"\int \frac{\left(-1+x^2\right) \sqrt[4]{x^3+x^4}}{1+x^2+x^4} \, dx","Integrate[((-1 + x^2)*(x^3 + x^4)^(1/4))/(1 + x^2 + x^4),x]","\frac{\left(1-i \sqrt{3}\right) \sqrt[4]{x^3 (x+1)} \left(x^{3/4} \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};-x\right)-\frac{\left(1-\frac{1}{\sqrt{\frac{1}{2} \left(-1-i \sqrt{3}\right)}}\right) x^{3/4} \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{\left(1-i \sqrt{3}\right) x}{2 (x+1)}\right)}{(x+1)^{3/4}}\right)}{3 x^{3/4} \sqrt[4]{x+1}}+\frac{\left(1+i \sqrt{3}\right) \sqrt[4]{x^3 (x+1)} \left(x^{3/4} \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};-x\right)-\frac{\left(1-\frac{1}{\sqrt{\frac{1}{2} i \left(\sqrt{3}+i\right)}}\right) x^{3/4} \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{\left(1+i \sqrt{3}\right) x}{2 (x+1)}\right)}{(x+1)^{3/4}}\right)}{3 x^{3/4} \sqrt[4]{x+1}}+\frac{\left(1-i \sqrt{3}\right) \sqrt[4]{x^3 (x+1)} \left(2 x^{3/4} \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};-x\right)-\frac{\left(3+i \sqrt{3}\right) x^{3/4} \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{\left(1+\frac{1}{\sqrt{\frac{1}{2} \left(-1-i \sqrt{3}\right)}}\right) x}{x+1}\right)}{(x+1)^{3/4}}\right)}{6 x^{3/4} \sqrt[4]{x+1}}+\frac{\left(1+i \sqrt{3}\right) \sqrt[4]{x^3 (x+1)} \left(2 x^{3/4} \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};-x\right)-\frac{\left(3-i \sqrt{3}\right) x^{3/4} \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{\left(1+\frac{1}{\sqrt{\frac{1}{2} i \left(i+\sqrt{3}\right)}}\right) x}{x+1}\right)}{(x+1)^{3/4}}\right)}{6 x^{3/4} \sqrt[4]{x+1}}","-\frac{3}{2} \text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4+3\&,\frac{-\text{$\#$1}^4 \log \left(\sqrt[4]{x^4+x^3}-\text{$\#$1} x\right)+\text{$\#$1}^4 \log (x)+\log \left(\sqrt[4]{x^4+x^3}-\text{$\#$1} x\right)-\log (x)}{2 \text{$\#$1}^7-3 \text{$\#$1}^3}\&\right]+\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4+1\&,\frac{-\text{$\#$1}^4 \log \left(\sqrt[4]{x^4+x^3}-\text{$\#$1} x\right)+\text{$\#$1}^4 \log (x)-\log \left(\sqrt[4]{x^4+x^3}-\text{$\#$1} x\right)+\log (x)}{2 \text{$\#$1}^7-\text{$\#$1}^3}\&\right]-2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+x^3}}\right)+2 \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+x^3}}\right)",1,"((1 - I*Sqrt[3])*(x^3*(1 + x))^(1/4)*(x^(3/4)*Hypergeometric2F1[3/4, 3/4, 7/4, -x] - ((1 - 1/Sqrt[(-1 - I*Sqrt[3])/2])*x^(3/4)*Hypergeometric2F1[3/4, 1, 7/4, ((1 - I*Sqrt[3])*x)/(2*(1 + x))])/(1 + x)^(3/4)))/(3*x^(3/4)*(1 + x)^(1/4)) + ((1 + I*Sqrt[3])*(x^3*(1 + x))^(1/4)*(x^(3/4)*Hypergeometric2F1[3/4, 3/4, 7/4, -x] - ((1 - 1/Sqrt[(I/2)*(I + Sqrt[3])])*x^(3/4)*Hypergeometric2F1[3/4, 1, 7/4, ((1 + I*Sqrt[3])*x)/(2*(1 + x))])/(1 + x)^(3/4)))/(3*x^(3/4)*(1 + x)^(1/4)) + ((1 - I*Sqrt[3])*(x^3*(1 + x))^(1/4)*(2*x^(3/4)*Hypergeometric2F1[3/4, 3/4, 7/4, -x] - ((3 + I*Sqrt[3])*x^(3/4)*Hypergeometric2F1[3/4, 1, 7/4, ((1 + 1/Sqrt[(-1 - I*Sqrt[3])/2])*x)/(1 + x)])/(1 + x)^(3/4)))/(6*x^(3/4)*(1 + x)^(1/4)) + ((1 + I*Sqrt[3])*(x^3*(1 + x))^(1/4)*(2*x^(3/4)*Hypergeometric2F1[3/4, 3/4, 7/4, -x] - ((3 - I*Sqrt[3])*x^(3/4)*Hypergeometric2F1[3/4, 1, 7/4, ((1 + 1/Sqrt[(I/2)*(I + Sqrt[3])])*x)/(1 + x)])/(1 + x)^(3/4)))/(6*x^(3/4)*(1 + x)^(1/4))","C",0
2525,0,0,211,5.4085285,"\int \frac{\left(-b+a x^2\right) \sqrt[4]{-b x^2+a x^4}}{b-a x^2+x^4} \, dx","Integrate[((-b + a*x^2)*(-(b*x^2) + a*x^4)^(1/4))/(b - a*x^2 + x^4),x]","\int \frac{\left(-b+a x^2\right) \sqrt[4]{-b x^2+a x^4}}{b-a x^2+x^4} \, dx","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4 a+b\&,\frac{\text{$\#$1}^4 a^2 \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 \left(-a^2\right) \log (x)-\text{$\#$1}^4 b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 b \log (x)-a b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+a b \log (x)}{\text{$\#$1}^3 a-2 \text{$\#$1}^7}\&\right]+a^{5/4} \left(-\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)\right)+a^{5/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)",1,"Integrate[((-b + a*x^2)*(-(b*x^2) + a*x^4)^(1/4))/(b - a*x^2 + x^4), x]","F",-1
2526,0,0,211,0.0940669,"\int \frac{\left(-b+a x^2\right) \sqrt[4]{-b x^2+a x^4}}{b-a x^2+x^4} \, dx","Integrate[((-b + a*x^2)*(-(b*x^2) + a*x^4)^(1/4))/(b - a*x^2 + x^4),x]","\int \frac{\left(-b+a x^2\right) \sqrt[4]{-b x^2+a x^4}}{b-a x^2+x^4} \, dx","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4 a+b\&,\frac{\text{$\#$1}^4 a^2 \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 \left(-a^2\right) \log (x)-\text{$\#$1}^4 b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 b \log (x)-a b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+a b \log (x)}{\text{$\#$1}^3 a-2 \text{$\#$1}^7}\&\right]+a^{5/4} \left(-\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)\right)+a^{5/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)",1,"Integrate[((-b + a*x^2)*(-(b*x^2) + a*x^4)^(1/4))/(b - a*x^2 + x^4), x]","F",-1
2527,0,0,211,0.7437461,"\int \frac{\left(-b^2+a x^2\right)^2}{\left(b^2+a x^2\right)^2 \sqrt{b+\sqrt{b^2+a x^2}}} \, dx","Integrate[(-b^2 + a*x^2)^2/((b^2 + a*x^2)^2*Sqrt[b + Sqrt[b^2 + a*x^2]]),x]","\int \frac{\left(-b^2+a x^2\right)^2}{\left(b^2+a x^2\right)^2 \sqrt{b+\sqrt{b^2+a x^2}}} \, dx","\frac{2 x \left(a x^2+2 b^2\right)}{\left(a x^2+b^2\right) \sqrt{\sqrt{a x^2+b^2}+b}}-\frac{b x}{\sqrt{a x^2+b^2} \sqrt{\sqrt{a x^2+b^2}+b}}-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b} \sqrt{\sqrt{a x^2+b^2}+b}}\right)}{\sqrt{a}}-\frac{2 \sqrt{2} \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{2} \sqrt{b} \sqrt{\sqrt{a x^2+b^2}+b}}-\frac{\sqrt{\sqrt{a x^2+b^2}+b}}{\sqrt{2} \sqrt{b}}\right)}{\sqrt{a}}",1,"Integrate[(-b^2 + a*x^2)^2/((b^2 + a*x^2)^2*Sqrt[b + Sqrt[b^2 + a*x^2]]), x]","F",-1
2528,0,0,212,9.44412,"\int \frac{(-2+(1+k) x) \left(a-a (1+k) x+(1+a k) x^2\right)}{(-1+x) \sqrt[3]{(1-x) x (1-k x)} (-1+k x) \left(b-b (1+k) x+(-1+b k) x^2\right)} \, dx","Integrate[((-2 + (1 + k)*x)*(a - a*(1 + k)*x + (1 + a*k)*x^2))/((-1 + x)*((1 - x)*x*(1 - k*x))^(1/3)*(-1 + k*x)*(b - b*(1 + k)*x + (-1 + b*k)*x^2)),x]","\int \frac{(-2+(1+k) x) \left(a-a (1+k) x+(1+a k) x^2\right)}{(-1+x) \sqrt[3]{(1-x) x (1-k x)} (-1+k x) \left(b-b (1+k) x+(-1+b k) x^2\right)} \, dx","\frac{(a+b) \log \left(x-\sqrt[3]{b} \sqrt[3]{k x^3+(-k-1) x^2+x}\right)}{b^{2/3}}+\frac{(-a-b) \log \left(b^{2/3} \left(k x^3+(-k-1) x^2+x\right)^{2/3}+\sqrt[3]{b} x \sqrt[3]{k x^3+(-k-1) x^2+x}+x^2\right)}{2 b^{2/3}}+\frac{\left(-\sqrt{3} a-\sqrt{3} b\right) \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{b} \sqrt[3]{k x^3+(-k-1) x^2+x}+x}\right)}{b^{2/3}}+\frac{3 \left(k x^3-k x^2-x^2+x\right)^{2/3}}{(x-1) (k x-1)}",1,"Integrate[((-2 + (1 + k)*x)*(a - a*(1 + k)*x + (1 + a*k)*x^2))/((-1 + x)*((1 - x)*x*(1 - k*x))^(1/3)*(-1 + k*x)*(b - b*(1 + k)*x + (-1 + b*k)*x^2)), x]","F",-1
2529,1,151,212,5.1491445,"\int \frac{\left(b+x^3\right)^3}{\sqrt[3]{a+x^3}} \, dx","Integrate[(b + x^3)^3/(a + x^3)^(1/3),x]","\frac{1}{486} \left(3 x \left(a+x^3\right)^{2/3} \left(28 a^2-3 a \left(36 b+7 x^3\right)+9 \left(18 b^2+9 b x^3+2 x^6\right)\right)+\left(-14 a^3+54 a^2 b-81 a b^2+81 b^3\right) \left(-2 \log \left(1-\frac{x}{\sqrt[3]{a+x^3}}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{a+x^3}}+1}{\sqrt{3}}\right)+\log \left(\frac{x}{\sqrt[3]{a+x^3}}+\frac{x^2}{\left(a+x^3\right)^{2/3}}+1\right)\right)\right)","\frac{1}{162} \left(a+x^3\right)^{2/3} \left(28 a^2 x-108 a b x-21 a x^4+162 b^2 x+81 b x^4+18 x^7\right)+\frac{1}{243} \left(14 a^3-54 a^2 b+81 a b^2-81 b^3\right) \log \left(\sqrt[3]{a+x^3}-x\right)+\frac{1}{243} \left(-14 \sqrt{3} a^3+54 \sqrt{3} a^2 b-81 \sqrt{3} a b^2+81 \sqrt{3} b^3\right) \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{a+x^3}+x}\right)+\frac{1}{486} \left(-14 a^3+54 a^2 b-81 a b^2+81 b^3\right) \log \left(x \sqrt[3]{a+x^3}+\left(a+x^3\right)^{2/3}+x^2\right)",1,"(3*x*(a + x^3)^(2/3)*(28*a^2 - 3*a*(36*b + 7*x^3) + 9*(18*b^2 + 9*b*x^3 + 2*x^6)) + (-14*a^3 + 54*a^2*b - 81*a*b^2 + 81*b^3)*(2*Sqrt[3]*ArcTan[(1 + (2*x)/(a + x^3)^(1/3))/Sqrt[3]] - 2*Log[1 - x/(a + x^3)^(1/3)] + Log[1 + x^2/(a + x^3)^(2/3) + x/(a + x^3)^(1/3)]))/486","A",1
2530,0,0,212,0.6306557,"\int \frac{1-x^2+x^3}{\left(-1-x^2+x^3\right) \sqrt[3]{x^2+x^3}} \, dx","Integrate[(1 - x^2 + x^3)/((-1 - x^2 + x^3)*(x^2 + x^3)^(1/3)),x]","\int \frac{1-x^2+x^3}{\left(-1-x^2+x^3\right) \sqrt[3]{x^2+x^3}} \, dx","2 \text{RootSum}\left[\text{$\#$1}^9-3 \text{$\#$1}^6+4 \text{$\#$1}^3-3\&,\frac{\text{$\#$1}^6 \log \left(\sqrt[3]{x^3+x^2}-\text{$\#$1} x\right)+\text{$\#$1}^6 (-\log (x))-2 \text{$\#$1}^3 \log \left(\sqrt[3]{x^3+x^2}-\text{$\#$1} x\right)+2 \text{$\#$1}^3 \log (x)+\log \left(\sqrt[3]{x^3+x^2}-\text{$\#$1} x\right)-\log (x)}{3 \text{$\#$1}^7-6 \text{$\#$1}^4+4 \text{$\#$1}}\&\right]-\log \left(\sqrt[3]{x^3+x^2}-x\right)+\frac{1}{2} \log \left(x^2+\sqrt[3]{x^3+x^2} x+\left(x^3+x^2\right)^{2/3}\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+x^2}+x}\right)",1,"Integrate[(1 - x^2 + x^3)/((-1 - x^2 + x^3)*(x^2 + x^3)^(1/3)), x]","F",-1
2531,0,0,212,0.1017062,"\int \frac{1-x^2+x^3}{\left(-1-x^2+x^3\right) \sqrt[3]{x^2+x^3}} \, dx","Integrate[(1 - x^2 + x^3)/((-1 - x^2 + x^3)*(x^2 + x^3)^(1/3)),x]","\int \frac{1-x^2+x^3}{\left(-1-x^2+x^3\right) \sqrt[3]{x^2+x^3}} \, dx","2 \text{RootSum}\left[\text{$\#$1}^9-3 \text{$\#$1}^6+4 \text{$\#$1}^3-3\&,\frac{\text{$\#$1}^6 \log \left(\sqrt[3]{x^3+x^2}-\text{$\#$1} x\right)+\text{$\#$1}^6 (-\log (x))-2 \text{$\#$1}^3 \log \left(\sqrt[3]{x^3+x^2}-\text{$\#$1} x\right)+2 \text{$\#$1}^3 \log (x)+\log \left(\sqrt[3]{x^3+x^2}-\text{$\#$1} x\right)-\log (x)}{3 \text{$\#$1}^7-6 \text{$\#$1}^4+4 \text{$\#$1}}\&\right]-\log \left(\sqrt[3]{x^3+x^2}-x\right)+\frac{1}{2} \log \left(x^2+\sqrt[3]{x^3+x^2} x+\left(x^3+x^2\right)^{2/3}\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+x^2}+x}\right)",1,"Integrate[(1 - x^2 + x^3)/((-1 - x^2 + x^3)*(x^2 + x^3)^(1/3)), x]","F",-1
2532,0,0,212,4.0413326,"\int \frac{-3+\left(1-2 k^2\right) x+3 k^2 x^2+k^2 x^3}{\sqrt[3]{\left(1-x^2\right) \left(1-k^2 x^2\right)} \left(-1+d-(2+d) x-\left(1+d k^2\right) x^2+d k^2 x^3\right)} \, dx","Integrate[(-3 + (1 - 2*k^2)*x + 3*k^2*x^2 + k^2*x^3)/(((1 - x^2)*(1 - k^2*x^2))^(1/3)*(-1 + d - (2 + d)*x - (1 + d*k^2)*x^2 + d*k^2*x^3)),x]","\int \frac{-3+\left(1-2 k^2\right) x+3 k^2 x^2+k^2 x^3}{\sqrt[3]{\left(1-x^2\right) \left(1-k^2 x^2\right)} \left(-1+d-(2+d) x-\left(1+d k^2\right) x^2+d k^2 x^3\right)} \, dx","\frac{\log \left(-\sqrt[3]{d} \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}+x+1\right)}{d^{2/3}}-\frac{\log \left(d^{2/3} \left(k^2 x^4+\left(-k^2-1\right) x^2+1\right)^{2/3}+\left(\sqrt[3]{d} x+\sqrt[3]{d}\right) \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}+x^2+2 x+1\right)}{2 d^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}}{\sqrt[3]{d} \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}+2 x+2}\right)}{d^{2/3}}",1,"Integrate[(-3 + (1 - 2*k^2)*x + 3*k^2*x^2 + k^2*x^3)/(((1 - x^2)*(1 - k^2*x^2))^(1/3)*(-1 + d - (2 + d)*x - (1 + d*k^2)*x^2 + d*k^2*x^3)), x]","F",-1
2533,1,64,212,0.0478625,"\int \frac{x^2}{\left(-b+a x^4\right) \sqrt{b+a x^4}} \, dx","Integrate[x^2/((-b + a*x^4)*Sqrt[b + a*x^4]),x]","-\frac{x^3 \sqrt{\frac{a x^4+b}{b}} F_1\left(\frac{3}{4};\frac{1}{2},1;\frac{7}{4};-\frac{a x^4}{b},\frac{a x^4}{b}\right)}{3 b \sqrt{a x^4+b}}","\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x}{\sqrt{a x^4+b}+\sqrt{a} x^2+\sqrt{b}}\right)}{2 \sqrt{2} a^{3/4} b^{3/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{6-4 \sqrt{2}} \sqrt[4]{a} \sqrt[4]{b} x}{\sqrt{a x^4+b}+\sqrt{a} x^2+\sqrt{b}}\right)}{4 \sqrt{2} a^{3/4} b^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{6+4 \sqrt{2}} \sqrt[4]{a} \sqrt[4]{b} x}{\sqrt{a x^4+b}+\sqrt{a} x^2+\sqrt{b}}\right)}{4 \sqrt{2} a^{3/4} b^{3/4}}",1,"-1/3*(x^3*Sqrt[(b + a*x^4)/b]*AppellF1[3/4, 1/2, 1, 7/4, -((a*x^4)/b), (a*x^4)/b])/(b*Sqrt[b + a*x^4])","C",0
2534,0,0,212,4.5494098,"\int \frac{(-1+x) (-1+k x) (-2+(1+k) x)}{\sqrt[3]{(1-x) x (1-k x)} \left(b-2 (b+b k) x+\left(b+4 b k+b k^2\right) x^2-2 b k (1+k) x^3+\left(-1+b k^2\right) x^4\right)} \, dx","Integrate[((-1 + x)*(-1 + k*x)*(-2 + (1 + k)*x))/(((1 - x)*x*(1 - k*x))^(1/3)*(b - 2*(b + b*k)*x + (b + 4*b*k + b*k^2)*x^2 - 2*b*k*(1 + k)*x^3 + (-1 + b*k^2)*x^4)),x]","\int \frac{(-1+x) (-1+k x) (-2+(1+k) x)}{\sqrt[3]{(1-x) x (1-k x)} \left(b-2 (b+b k) x+\left(b+4 b k+b k^2\right) x^2-2 b k (1+k) x^3+\left(-1+b k^2\right) x^4\right)} \, dx","\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{x-2 \sqrt[6]{b} \sqrt[3]{k x^3+(-k-1) x^2+x}}\right)}{2 b^{5/6}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[6]{b} \sqrt[3]{k x^3+(-k-1) x^2+x}+x}\right)}{2 b^{5/6}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt[6]{b} \sqrt[3]{k x^3+(-k-1) x^2+x}}\right)}{b^{5/6}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{b} \left(k x^3+(-k-1) x^2+x\right)^{2/3}+\frac{x^2}{\sqrt[6]{b}}}{x \sqrt[3]{k x^3+(-k-1) x^2+x}}\right)}{2 b^{5/6}}",1,"Integrate[((-1 + x)*(-1 + k*x)*(-2 + (1 + k)*x))/(((1 - x)*x*(1 - k*x))^(1/3)*(b - 2*(b + b*k)*x + (b + 4*b*k + b*k^2)*x^2 - 2*b*k*(1 + k)*x^3 + (-1 + b*k^2)*x^4)), x]","F",-1
2535,1,180,212,1.4133139,"\int \frac{\left(-g+f x^2\right) \sqrt{c+\sqrt{b+a x}}}{e+d x^2} \, dx","Integrate[((-g + f*x^2)*Sqrt[c + Sqrt[b + a*x]])/(e + d*x^2),x]","\frac{8 d f \left(\sqrt{a x+b}+c\right)^{3/2} \left(3 \left(\sqrt{a x+b}+c\right)-5 c\right)-15 a^2 (d g+e f) \text{RootSum}\left[\text{$\#$1}^8 d-4 \text{$\#$1}^6 c d-2 \text{$\#$1}^4 b d+6 \text{$\#$1}^4 c^2 d+4 \text{$\#$1}^2 b c d-4 \text{$\#$1}^2 c^3 d+a^2 e+b^2 d-2 b c^2 d+c^4 d\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)}{\text{$\#$1}^4-2 \text{$\#$1}^2 c-b+c^2}\&\right]}{30 a d^2}","-\frac{a (d g+e f) \text{RootSum}\left[\text{$\#$1}^8 d-4 \text{$\#$1}^6 c d-2 \text{$\#$1}^4 b d+6 \text{$\#$1}^4 c^2 d+4 \text{$\#$1}^2 b c d-4 \text{$\#$1}^2 c^3 d+a^2 e+b^2 d-2 b c^2 d+c^4 d\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)}{\text{$\#$1}^4-2 \text{$\#$1}^2 c-b+c^2}\&\right]}{2 d^2}+\frac{4 f \left(3 a x+3 b-2 c^2\right) \sqrt{\sqrt{a x+b}+c}}{15 a d}+\frac{4 c f \sqrt{a x+b} \sqrt{\sqrt{a x+b}+c}}{15 a d}",1,"(8*d*f*(c + Sqrt[b + a*x])^(3/2)*(-5*c + 3*(c + Sqrt[b + a*x])) - 15*a^2*(e*f + d*g)*RootSum[b^2*d - 2*b*c^2*d + c^4*d + a^2*e + 4*b*c*d*#1^2 - 4*c^3*d*#1^2 - 2*b*d*#1^4 + 6*c^2*d*#1^4 - 4*c*d*#1^6 + d*#1^8 & , (Log[Sqrt[c + Sqrt[b + a*x]] - #1]*#1)/(-b + c^2 - 2*c*#1^2 + #1^4) & ])/(30*a*d^2)","A",1
2536,-1,0,212,180.0054116,"\int \frac{\sqrt{b^2+a^2 x^2}}{d+c x^2+\sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Integrate[Sqrt[b^2 + a^2*x^2]/(d + c*x^2 + Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]),x]","\text{\$Aborted}","\frac{a \log \left(\sqrt{a^2 x^2+b^2}+a x\right)}{c}-\frac{2 a \text{RootSum}\left[\text{$\#$1}^8 c+4 \text{$\#$1}^5 a^2+4 \text{$\#$1}^4 a^2 d-2 \text{$\#$1}^4 b^2 c+b^4 c\&,\frac{b^2 c \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)+a^2 (-d) \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)-\text{$\#$1} a^2 \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)}{-2 \text{$\#$1}^4 c-5 \text{$\#$1} a^2-4 a^2 d+2 b^2 c}\&\right]}{c}",1,"$Aborted","F",-1
2537,0,0,212,17.6649714,"\int \frac{\sqrt{b^2+a^2 x^2}}{d+c x^2+\sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Integrate[Sqrt[b^2 + a^2*x^2]/(d + c*x^2 + Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]),x]","\int \frac{\sqrt{b^2+a^2 x^2}}{d+c x^2+\sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","\frac{a \log \left(\sqrt{a^2 x^2+b^2}+a x\right)}{c}-\frac{2 a \text{RootSum}\left[\text{$\#$1}^8 c+4 \text{$\#$1}^5 a^2+4 \text{$\#$1}^4 a^2 d-2 \text{$\#$1}^4 b^2 c+b^4 c\&,\frac{b^2 c \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)+a^2 (-d) \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)-\text{$\#$1} a^2 \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)}{-2 \text{$\#$1}^4 c-5 \text{$\#$1} a^2-4 a^2 d+2 b^2 c}\&\right]}{c}",1,"Integrate[Sqrt[b^2 + a^2*x^2]/(d + c*x^2 + Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]), x]","F",-1
2538,1,67,213,0.1421934,"\int \frac{\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}}{x^2} \, dx","Integrate[Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]]/x^2,x]","\frac{8}{315} \left(1-\sqrt{1-\sqrt{\frac{x-1}{x}}}\right)^{5/2} \left(65 \sqrt{1-\sqrt{\frac{x-1}{x}}}-35 \sqrt{\frac{x-1}{x}}+61\right)","\sqrt{\frac{x-1}{x}} \left(\frac{8}{63} \sqrt{1-\sqrt{1-\sqrt{\frac{x-1}{x}}}} \sqrt{1-\sqrt{\frac{x-1}{x}}}-\frac{8}{315} \sqrt{1-\sqrt{1-\sqrt{\frac{x-1}{x}}}}\right)-\frac{64}{315} \sqrt{1-\sqrt{1-\sqrt{\frac{x-1}{x}}}}+\frac{64}{315} \sqrt{1-\sqrt{1-\sqrt{\frac{x-1}{x}}}} \sqrt{1-\sqrt{\frac{x-1}{x}}}+\frac{8 \sqrt{1-\sqrt{1-\sqrt{\frac{x-1}{x}}}} (x-1)}{9 x}",1,"(8*(1 - Sqrt[1 - Sqrt[(-1 + x)/x]])^(5/2)*(61 + 65*Sqrt[1 - Sqrt[(-1 + x)/x]] - 35*Sqrt[(-1 + x)/x]))/315","A",1
2539,1,46,213,0.0575644,"\int \frac{\sqrt[3]{x^2+x^4}}{x \left(-1+x^2\right)} \, dx","Integrate[(x^2 + x^4)^(1/3)/(x*(-1 + x^2)),x]","-\frac{3 \sqrt[3]{x^4+x^2} F_1\left(\frac{1}{3};-\frac{1}{3},1;\frac{4}{3};-\frac{1}{x^2},\frac{1}{x^2}\right)}{2 \sqrt[3]{\frac{1}{x^2}+1} x^2}","\frac{\log \left(2^{2/3} \sqrt[3]{x^4+x^2}-2 x\right)}{2\ 2^{2/3}}+\frac{\log \left(2^{2/3} \sqrt[3]{x^4+x^2}+2 x\right)}{2\ 2^{2/3}}-\frac{\log \left(-2 x^2+2^{2/3} \sqrt[3]{x^4+x^2} x-\sqrt[3]{2} \left(x^4+x^2\right)^{2/3}\right)}{4\ 2^{2/3}}-\frac{\log \left(2 x^2+2^{2/3} \sqrt[3]{x^4+x^2} x+\sqrt[3]{2} \left(x^4+x^2\right)^{2/3}\right)}{4\ 2^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x^2}{x^2+\sqrt[3]{2} \left(x^4+x^2\right)^{2/3}}\right)}{2\ 2^{2/3}}",1,"(-3*(x^2 + x^4)^(1/3)*AppellF1[1/3, -1/3, 1, 4/3, -x^(-2), x^(-2)])/(2*(1 + x^(-2))^(1/3)*x^2)","C",0
2540,1,317,213,0.7398798,"\int \frac{1}{(c+d x) \sqrt{b+a^2 x^2} \sqrt{a x-\sqrt{b+a^2 x^2}}} \, dx","Integrate[1/((c + d*x)*Sqrt[b + a^2*x^2]*Sqrt[a*x - Sqrt[b + a^2*x^2]]),x]","\frac{2 \left(a x \left(a x-\sqrt{a^2 x^2+b}\right)+b\right) \left(\left(\sqrt{a^2 c^2+b d^2}+a c\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{d}}{\sqrt{a x-\sqrt{a^2 x^2+b}} \sqrt{-\sqrt{a^2 c^2+b d^2}-a c}}\right)+\sqrt{-\sqrt{a^2 c^2+b d^2}-a c} \sqrt{\sqrt{a^2 c^2+b d^2}-a c} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{d}}{\sqrt{a x-\sqrt{a^2 x^2+b}} \sqrt{\sqrt{a^2 c^2+b d^2}-a c}}\right)\right)}{\sqrt{b} \sqrt{d} \sqrt{a^2 x^2+b} \left(a x-\sqrt{a^2 x^2+b}\right) \sqrt{a^2 c^2+b d^2} \sqrt{-\sqrt{a^2 c^2+b d^2}-a c}}","\frac{2 \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a x-\sqrt{a^2 x^2+b}}}{\sqrt{\sqrt{a^2 c^2+b d^2}+a c}}\right)}{\sqrt{a^2 c^2+b d^2} \sqrt{\sqrt{a^2 c^2+b d^2}+a c}}-\frac{2 \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a x-\sqrt{a^2 x^2+b}}}{\sqrt{a c-\sqrt{a^2 c^2+b d^2}}}\right)}{\sqrt{a^2 c^2+b d^2} \sqrt{a c-\sqrt{a^2 c^2+b d^2}}}",1,"(2*(b + a*x*(a*x - Sqrt[b + a^2*x^2]))*((a*c + Sqrt[a^2*c^2 + b*d^2])*ArcTan[(Sqrt[b]*Sqrt[d])/(Sqrt[-(a*c) - Sqrt[a^2*c^2 + b*d^2]]*Sqrt[a*x - Sqrt[b + a^2*x^2]])] + Sqrt[-(a*c) - Sqrt[a^2*c^2 + b*d^2]]*Sqrt[-(a*c) + Sqrt[a^2*c^2 + b*d^2]]*ArcTan[(Sqrt[b]*Sqrt[d])/(Sqrt[-(a*c) + Sqrt[a^2*c^2 + b*d^2]]*Sqrt[a*x - Sqrt[b + a^2*x^2]])]))/(Sqrt[b]*Sqrt[d]*Sqrt[a^2*c^2 + b*d^2]*Sqrt[-(a*c) - Sqrt[a^2*c^2 + b*d^2]]*Sqrt[b + a^2*x^2]*(a*x - Sqrt[b + a^2*x^2]))","A",1
2541,1,357,213,1.0400769,"\int \frac{\sqrt{1+x} \sqrt{1+\sqrt{1+x}}}{x^2 \sqrt{1+\sqrt{1+\sqrt{1+x}}}} \, dx","Integrate[(Sqrt[1 + x]*Sqrt[1 + Sqrt[1 + x]])/(x^2*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]),x]","\frac{1}{4} \left(\frac{\left(\sqrt{2}-1\right) \sqrt{\sqrt{\sqrt{x+1}+1}+1}}{\sqrt{2}-\sqrt{\sqrt{x+1}+1}}+\frac{\left(1+\sqrt{2}\right) \sqrt{\sqrt{\sqrt{x+1}+1}+1}}{\sqrt{\sqrt{x+1}+1}+\sqrt{2}}-\frac{2}{\sqrt{\sqrt{\sqrt{x+1}+1}+1}-1}-\frac{2}{\sqrt{\sqrt{\sqrt{x+1}+1}+1}+1}-5 \sqrt{2 \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\sqrt{1+\sqrt{2}} \sqrt{\sqrt{\sqrt{x+1}+1}+1}\right)+\frac{\tan ^{-1}\left(\sqrt{1+\sqrt{2}} \sqrt{\sqrt{\sqrt{x+1}+1}+1}\right)}{\left(\sqrt{2}-1\right)^{3/2}}+4 \tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x+1}+1}+1}\right)+\frac{\tanh ^{-1}\left(\sqrt{\sqrt{2}-1} \sqrt{\sqrt{\sqrt{x+1}+1}+1}\right)}{\left(1+\sqrt{2}\right)^{3/2}}-5 \sqrt{2 \left(\sqrt{2}-1\right)} \tanh ^{-1}\left(\sqrt{\sqrt{2}-1} \sqrt{\sqrt{\sqrt{x+1}+1}+1}\right)\right)","-\frac{\left(\sqrt{\sqrt{x+1}+1}+1\right)^{5/2}}{2 \left(\sqrt{x+1}-1\right) \sqrt{\sqrt{x+1}+1}}+\frac{5 \sqrt{\sqrt{\sqrt{x+1}+1}+1}}{2 \left(\sqrt{x+1}-1\right) \sqrt{\sqrt{x+1}+1}}-\frac{1}{4} \sqrt{17+25 \sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{x+1}+1}+1}}{\sqrt{\sqrt{2}-1}}\right)+\tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x+1}+1}+1}\right)-\frac{1}{4} \sqrt{25 \sqrt{2}-17} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{x+1}+1}+1}}{\sqrt{1+\sqrt{2}}}\right)",1,"(((-1 + Sqrt[2])*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]])/(Sqrt[2] - Sqrt[1 + Sqrt[1 + x]]) + ((1 + Sqrt[2])*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]])/(Sqrt[2] + Sqrt[1 + Sqrt[1 + x]]) - 2/(-1 + Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]) - 2/(1 + Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]) + ArcTan[Sqrt[1 + Sqrt[2]]*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]]/(-1 + Sqrt[2])^(3/2) - 5*Sqrt[2*(1 + Sqrt[2])]*ArcTan[Sqrt[1 + Sqrt[2]]*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]] + 4*ArcTanh[Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]] - 5*Sqrt[2*(-1 + Sqrt[2])]*ArcTanh[Sqrt[-1 + Sqrt[2]]*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]] + ArcTanh[Sqrt[-1 + Sqrt[2]]*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]]/(1 + Sqrt[2])^(3/2))/4","A",1
2542,0,0,214,5.7520593,"\int \frac{-1+(2-k) x}{\sqrt[3]{(1-x) x (1-k x)} \left(b-(1+2 b k) x+\left(1+b k^2\right) x^2\right)} \, dx","Integrate[(-1 + (2 - k)*x)/(((1 - x)*x*(1 - k*x))^(1/3)*(b - (1 + 2*b*k)*x + (1 + b*k^2)*x^2)),x]","\int \frac{-1+(2-k) x}{\sqrt[3]{(1-x) x (1-k x)} \left(b-(1+2 b k) x+\left(1+b k^2\right) x^2\right)} \, dx","-\frac{\log \left(b^{2/3} k^2 x^2-2 b^{2/3} k x+b^{2/3}+\sqrt[3]{k x^3+(-k-1) x^2+x} \left(\sqrt[3]{b}-\sqrt[3]{b} k x\right)+\left(k x^3+(-k-1) x^2+x\right)^{2/3}\right)}{2 \sqrt[3]{b}}+\frac{\log \left(\sqrt[3]{b} k x-\sqrt[3]{b}+\sqrt[3]{k x^3+(-k-1) x^2+x}\right)}{\sqrt[3]{b}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{k x^3+(-k-1) x^2+x}}{-2 \sqrt[3]{b} k x+2 \sqrt[3]{b}+\sqrt[3]{k x^3+(-k-1) x^2+x}}\right)}{\sqrt[3]{b}}",1,"Integrate[(-1 + (2 - k)*x)/(((1 - x)*x*(1 - k*x))^(1/3)*(b - (1 + 2*b*k)*x + (1 + b*k^2)*x^2)), x]","F",-1
2543,1,135,214,0.3725572,"\int \frac{1}{x^6 \left(-1+x^3\right) \sqrt[3]{x^2+x^3}} \, dx","Integrate[1/(x^6*(-1 + x^3)*(x^2 + x^3)^(1/3)),x]","\frac{-52360 x^6 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{2 x}{x+1}\right)-52360 x^6 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{x-i \sqrt{3} x}{2 x+2}\right)-52360 x^6 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{i \sqrt{3} x+x}{2 x+2}\right)+13473 x^6+4491 x^5-1497 x^4+18285 x^3+900 x^2-660 x+9240}{52360 x^5 \sqrt[3]{x^2 (x+1)}}","\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^6-\text{$\#$1}^3+1\&,\frac{\log \left(\sqrt[3]{x^3+x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]+\frac{\log \left(2^{2/3} \sqrt[3]{x^3+x^2}-2 x\right)}{3 \sqrt[3]{2}}-\frac{\log \left(2 x^2+2^{2/3} \sqrt[3]{x^3+x^2} x+\sqrt[3]{2} \left(x^3+x^2\right)^{2/3}\right)}{6 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^3+x^2}+x}\right)}{\sqrt[3]{2} \sqrt{3}}+\frac{3 \left(x^3+x^2\right)^{2/3} \left(4491 x^5-2994 x^4+2495 x^3+3600 x^2-3300 x+3080\right)}{52360 x^7}",1,"(9240 - 660*x + 900*x^2 + 18285*x^3 - 1497*x^4 + 4491*x^5 + 13473*x^6 - 52360*x^6*Hypergeometric2F1[1/3, 1, 4/3, (2*x)/(1 + x)] - 52360*x^6*Hypergeometric2F1[1/3, 1, 4/3, (x - I*Sqrt[3]*x)/(2 + 2*x)] - 52360*x^6*Hypergeometric2F1[1/3, 1, 4/3, (x + I*Sqrt[3]*x)/(2 + 2*x)])/(52360*x^5*(x^2*(1 + x))^(1/3))","C",1
2544,1,135,214,0.2366867,"\int \frac{1}{x^6 \left(-1+x^3\right) \sqrt[3]{x^2+x^3}} \, dx","Integrate[1/(x^6*(-1 + x^3)*(x^2 + x^3)^(1/3)),x]","\frac{-52360 x^6 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{2 x}{x+1}\right)-52360 x^6 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{x-i \sqrt{3} x}{2 x+2}\right)-52360 x^6 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{i \sqrt{3} x+x}{2 x+2}\right)+13473 x^6+4491 x^5-1497 x^4+18285 x^3+900 x^2-660 x+9240}{52360 x^5 \sqrt[3]{x^2 (x+1)}}","\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^6-\text{$\#$1}^3+1\&,\frac{\log \left(\sqrt[3]{x^3+x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]+\frac{\log \left(2^{2/3} \sqrt[3]{x^3+x^2}-2 x\right)}{3 \sqrt[3]{2}}-\frac{\log \left(2 x^2+2^{2/3} \sqrt[3]{x^3+x^2} x+\sqrt[3]{2} \left(x^3+x^2\right)^{2/3}\right)}{6 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^3+x^2}+x}\right)}{\sqrt[3]{2} \sqrt{3}}+\frac{3 \left(x^3+x^2\right)^{2/3} \left(4491 x^5-2994 x^4+2495 x^3+3600 x^2-3300 x+3080\right)}{52360 x^7}",1,"(9240 - 660*x + 900*x^2 + 18285*x^3 - 1497*x^4 + 4491*x^5 + 13473*x^6 - 52360*x^6*Hypergeometric2F1[1/3, 1, 4/3, (2*x)/(1 + x)] - 52360*x^6*Hypergeometric2F1[1/3, 1, 4/3, (x - I*Sqrt[3]*x)/(2 + 2*x)] - 52360*x^6*Hypergeometric2F1[1/3, 1, 4/3, (x + I*Sqrt[3]*x)/(2 + 2*x)])/(52360*x^5*(x^2*(1 + x))^(1/3))","C",1
2545,0,0,214,3.8724306,"\int \frac{3+\left(1-2 k^2\right) x-3 k^2 x^2+k^2 x^3}{\sqrt[3]{\left(1-x^2\right) \left(1-k^2 x^2\right)} \left(1-d-(2+d) x+\left(1+d k^2\right) x^2+d k^2 x^3\right)} \, dx","Integrate[(3 + (1 - 2*k^2)*x - 3*k^2*x^2 + k^2*x^3)/(((1 - x^2)*(1 - k^2*x^2))^(1/3)*(1 - d - (2 + d)*x + (1 + d*k^2)*x^2 + d*k^2*x^3)),x]","\int \frac{3+\left(1-2 k^2\right) x-3 k^2 x^2+k^2 x^3}{\sqrt[3]{\left(1-x^2\right) \left(1-k^2 x^2\right)} \left(1-d-(2+d) x+\left(1+d k^2\right) x^2+d k^2 x^3\right)} \, dx","-\frac{\log \left(\sqrt[3]{d} \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}+x-1\right)}{d^{2/3}}+\frac{\log \left(d^{2/3} \left(k^2 x^4+\left(-k^2-1\right) x^2+1\right)^{2/3}+\left(\sqrt[3]{d}-\sqrt[3]{d} x\right) \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}+x^2-2 x+1\right)}{2 d^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}}{\sqrt[3]{d} \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}-2 x+2}\right)}{d^{2/3}}",1,"Integrate[(3 + (1 - 2*k^2)*x - 3*k^2*x^2 + k^2*x^3)/(((1 - x^2)*(1 - k^2*x^2))^(1/3)*(1 - d - (2 + d)*x + (1 + d*k^2)*x^2 + d*k^2*x^3)), x]","F",-1
2546,1,154,214,0.2276825,"\int \frac{\left(1+x^3\right)^{2/3} \left(8-4 x^3+x^6\right)}{x^6 \left(2+x^3\right)} \, dx","Integrate[((1 + x^3)^(2/3)*(8 - 4*x^3 + x^6))/(x^6*(2 + x^3)),x]","\frac{1}{8} \left(x^4 F_1\left(\frac{4}{3};\frac{1}{3},1;\frac{7}{3};-x^3,-\frac{x^3}{2}\right)+\frac{16 \left(x^3+1\right)^{2/3} \left(3 x^3-2\right)}{5 x^5}-2 \sqrt[3]{2} \left(-2 \log \left(2-\frac{2^{2/3} x}{\sqrt[3]{x^3+1}}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2^{2/3} x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)+\log \left(\frac{2^{2/3} x}{\sqrt[3]{x^3+1}}+\frac{\sqrt[3]{2} x^2}{\left(x^3+1\right)^{2/3}}+2\right)\right)\right)","-\frac{1}{3} \log \left(\sqrt[3]{x^3+1}-x\right)+\frac{5 \log \left(\sqrt[3]{2} \sqrt[3]{x^3+1}-x\right)}{3\ 2^{2/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+1}+x}\right)}{\sqrt{3}}-\frac{5 \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{2} \sqrt[3]{x^3+1}+x}\right)}{2^{2/3} \sqrt{3}}+\frac{2 \left(x^3+1\right)^{2/3} \left(3 x^3-2\right)}{5 x^5}+\frac{1}{6} \log \left(\sqrt[3]{x^3+1} x+\left(x^3+1\right)^{2/3}+x^2\right)-\frac{5 \log \left(\sqrt[3]{2} \sqrt[3]{x^3+1} x+2^{2/3} \left(x^3+1\right)^{2/3}+x^2\right)}{6\ 2^{2/3}}",1,"((16*(1 + x^3)^(2/3)*(-2 + 3*x^3))/(5*x^5) + x^4*AppellF1[4/3, 1/3, 1, 7/3, -x^3, -1/2*x^3] - 2*2^(1/3)*(2*Sqrt[3]*ArcTan[(1 + (2^(2/3)*x)/(1 + x^3)^(1/3))/Sqrt[3]] - 2*Log[2 - (2^(2/3)*x)/(1 + x^3)^(1/3)] + Log[2 + (2^(1/3)*x^2)/(1 + x^3)^(2/3) + (2^(2/3)*x)/(1 + x^3)^(1/3)]))/8","C",0
2547,1,181,214,0.2692673,"\int \frac{\left(-1+x^3\right)^{2/3} \left(8+2 x^3+x^6\right)}{x^6 \left(-2+x^3\right)} \, dx","Integrate[((-1 + x^3)^(2/3)*(8 + 2*x^3 + x^6))/(x^6*(-2 + x^3)),x]","-\frac{\sqrt[3]{1-x^3} x^4 F_1\left(\frac{4}{3};\frac{1}{3},1;\frac{7}{3};x^3,\frac{x^3}{2}\right)}{8 \sqrt[3]{x^3-1}}+\frac{\left(x^3-1\right)^{2/3} \left(7 x^3+8\right)}{10 x^5}-\frac{-2 \log \left(2-\frac{2^{2/3} x}{\sqrt[3]{1-x^3}}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2^{2/3} x}{\sqrt[3]{1-x^3}}+1}{\sqrt{3}}\right)+\log \left(\frac{2^{2/3} x}{\sqrt[3]{1-x^3}}+\frac{\sqrt[3]{2} x^2}{\left(1-x^3\right)^{2/3}}+2\right)}{3\ 2^{2/3}}","-\frac{1}{3} \log \left(\sqrt[3]{x^3-1}-x\right)+\frac{2}{3} \sqrt[3]{2} \log \left(\sqrt[3]{2} \sqrt[3]{x^3-1}-x\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-1}+x}\right)}{\sqrt{3}}-\frac{2 \sqrt[3]{2} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{2} \sqrt[3]{x^3-1}+x}\right)}{\sqrt{3}}+\frac{\left(x^3-1\right)^{2/3} \left(7 x^3+8\right)}{10 x^5}+\frac{1}{6} \log \left(\sqrt[3]{x^3-1} x+\left(x^3-1\right)^{2/3}+x^2\right)-\frac{1}{3} \sqrt[3]{2} \log \left(\sqrt[3]{2} \sqrt[3]{x^3-1} x+2^{2/3} \left(x^3-1\right)^{2/3}+x^2\right)",1,"((-1 + x^3)^(2/3)*(8 + 7*x^3))/(10*x^5) - (x^4*(1 - x^3)^(1/3)*AppellF1[4/3, 1/3, 1, 7/3, x^3, x^3/2])/(8*(-1 + x^3)^(1/3)) - (2*Sqrt[3]*ArcTan[(1 + (2^(2/3)*x)/(1 - x^3)^(1/3))/Sqrt[3]] - 2*Log[2 - (2^(2/3)*x)/(1 - x^3)^(1/3)] + Log[2 + (2^(1/3)*x^2)/(1 - x^3)^(2/3) + (2^(2/3)*x)/(1 - x^3)^(1/3)])/(3*2^(2/3))","C",0
2548,0,0,214,1.2718169,"\int \frac{\left(-2 q+p x^3\right) \sqrt{q^2+2 p q x^3-2 p q x^4+p^2 x^6} \left(c x^4+b x^2 \left(q+p x^3\right)+a \left(q+p x^3\right)^2\right)}{x^9} \, dx","Integrate[((-2*q + p*x^3)*Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]*(c*x^4 + b*x^2*(q + p*x^3) + a*(q + p*x^3)^2))/x^9,x]","\int \frac{\left(-2 q+p x^3\right) \sqrt{q^2+2 p q x^3-2 p q x^4+p^2 x^6} \left(c x^4+b x^2 \left(q+p x^3\right)+a \left(q+p x^3\right)^2\right)}{x^9} \, dx","\frac{\sqrt{p^2 x^6-2 p q x^4+2 p q x^3+q^2} \left(3 a p^3 x^9-3 a p^2 q x^7+9 a p^2 q x^6-3 a p q^2 x^4+9 a p q^2 x^3+3 a q^3+4 b p^2 x^8-8 b p q x^6+8 b p q x^5+4 b q^2 x^2+6 c p x^7+6 c q x^4\right)}{12 x^8}+\frac{1}{2} \left(-a p^2 q^2-2 c p q\right) \log \left(\sqrt{p^2 x^6-2 p q x^4+2 p q x^3+q^2}+p x^3+q\right)+\log (x) \left(a p^2 q^2+2 c p q\right)",1,"Integrate[((-2*q + p*x^3)*Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]*(c*x^4 + b*x^2*(q + p*x^3) + a*(q + p*x^3)^2))/x^9, x]","F",-1
2549,1,119,215,0.1172368,"\int \frac{-b+a x^2}{\sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Integrate[(-b + a*x^2)/(b^2*x^2 + a^3*x^3)^(1/3),x]","\frac{3 \left(x^2 \left(a^3 x+b^2\right)\right)^{2/3} \left(b^3 \, _2F_1\left(-\frac{5}{3},\frac{1}{3};\frac{4}{3};-\frac{a^3 x}{b^2}\right)-2 b^3 \, _2F_1\left(-\frac{2}{3},\frac{1}{3};\frac{4}{3};-\frac{a^3 x}{b^2}\right)+\left(b^3-a^5\right) \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};-\frac{a^3 x}{b^2}\right)\right)}{a^5 b x \left(\frac{a^3 x}{b^2}+1\right)^{2/3}}","\frac{\left(a^3 x^3+b^2 x^2\right)^{2/3} \left(3 a^3 x-4 b^2\right)}{6 a^5 x}+\frac{\left(9 a^5 b-2 b^4\right) \log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-a x\right)}{9 a^6}-\frac{\left(9 a^5 b-2 b^4\right) \tan ^{-1}\left(\frac{\sqrt{3} a x}{2 \sqrt[3]{a^3 x^3+b^2 x^2}+a x}\right)}{3 \sqrt{3} a^6}+\frac{\left(2 b^4-9 a^5 b\right) \log \left(a x \sqrt[3]{a^3 x^3+b^2 x^2}+\left(a^3 x^3+b^2 x^2\right)^{2/3}+a^2 x^2\right)}{18 a^6}",1,"(3*(x^2*(b^2 + a^3*x))^(2/3)*(b^3*Hypergeometric2F1[-5/3, 1/3, 4/3, -((a^3*x)/b^2)] - 2*b^3*Hypergeometric2F1[-2/3, 1/3, 4/3, -((a^3*x)/b^2)] + (-a^5 + b^3)*Hypergeometric2F1[1/3, 1/3, 4/3, -((a^3*x)/b^2)]))/(a^5*b*x*(1 + (a^3*x)/b^2)^(2/3))","C",1
2550,1,117,215,0.0818717,"\int \frac{b+a x^2}{\sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Integrate[(b + a*x^2)/(b^2*x^2 + a^3*x^3)^(1/3),x]","\frac{3 \left(x^2 \left(a^3 x+b^2\right)\right)^{2/3} \left(b^3 \, _2F_1\left(-\frac{5}{3},\frac{1}{3};\frac{4}{3};-\frac{a^3 x}{b^2}\right)-2 b^3 \, _2F_1\left(-\frac{2}{3},\frac{1}{3};\frac{4}{3};-\frac{a^3 x}{b^2}\right)+\left(a^5+b^3\right) \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};-\frac{a^3 x}{b^2}\right)\right)}{a^5 b x \left(\frac{a^3 x}{b^2}+1\right)^{2/3}}","\frac{\left(a^3 x^3+b^2 x^2\right)^{2/3} \left(3 a^3 x-4 b^2\right)}{6 a^5 x}+\frac{\left(-9 a^5 b-2 b^4\right) \log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-a x\right)}{9 a^6}+\frac{\left(9 a^5 b+2 b^4\right) \tan ^{-1}\left(\frac{\sqrt{3} a x}{2 \sqrt[3]{a^3 x^3+b^2 x^2}+a x}\right)}{3 \sqrt{3} a^6}+\frac{\left(9 a^5 b+2 b^4\right) \log \left(a x \sqrt[3]{a^3 x^3+b^2 x^2}+\left(a^3 x^3+b^2 x^2\right)^{2/3}+a^2 x^2\right)}{18 a^6}",1,"(3*(x^2*(b^2 + a^3*x))^(2/3)*(b^3*Hypergeometric2F1[-5/3, 1/3, 4/3, -((a^3*x)/b^2)] - 2*b^3*Hypergeometric2F1[-2/3, 1/3, 4/3, -((a^3*x)/b^2)] + (a^5 + b^3)*Hypergeometric2F1[1/3, 1/3, 4/3, -((a^3*x)/b^2)]))/(a^5*b*x*(1 + (a^3*x)/b^2)^(2/3))","C",1
2551,0,0,215,4.0282109,"\int \frac{-a^2 b+4 a b x-(2 a+3 b) x^2+2 x^3}{\sqrt[4]{x (-a+x)^2 (-b+x)^3} \left(b+\left(-1+a^2 d\right) x-2 a d x^2+d x^3\right)} \, dx","Integrate[(-(a^2*b) + 4*a*b*x - (2*a + 3*b)*x^2 + 2*x^3)/((x*(-a + x)^2*(-b + x)^3)^(1/4)*(b + (-1 + a^2*d)*x - 2*a*d*x^2 + d*x^3)),x]","\int \frac{-a^2 b+4 a b x-(2 a+3 b) x^2+2 x^3}{\sqrt[4]{x (-a+x)^2 (-b+x)^3} \left(b+\left(-1+a^2 d\right) x-2 a d x^2+d x^3\right)} \, dx","\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{-a^2 b^3 x+x^4 \left(a^2+6 a b+3 b^2\right)+x^3 \left(-3 a^2 b-6 a b^2-b^3\right)+x^2 \left(3 a^2 b^2+2 a b^3\right)+x^5 (-2 a-3 b)+x^6}}{b-x}\right)}{d^{3/4}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{-a^2 b^3 x+x^4 \left(a^2+6 a b+3 b^2\right)+x^3 \left(-3 a^2 b-6 a b^2-b^3\right)+x^2 \left(3 a^2 b^2+2 a b^3\right)+x^5 (-2 a-3 b)+x^6}}{b-x}\right)}{d^{3/4}}",1,"Integrate[(-(a^2*b) + 4*a*b*x - (2*a + 3*b)*x^2 + 2*x^3)/((x*(-a + x)^2*(-b + x)^3)^(1/4)*(b + (-1 + a^2*d)*x - 2*a*d*x^2 + d*x^3)), x]","F",-1
2552,1,169,215,0.3708173,"\int \frac{\left(b+a x^2\right) \sqrt[4]{b x^3+a x^4}}{x^2 \left(-b+a x^2\right)} \, dx","Integrate[((b + a*x^2)*(b*x^3 + a*x^4)^(1/4))/(x^2*(-b + a*x^2)),x]","\frac{4 \sqrt[4]{x^3 (a x+b)} \left(\frac{\left(\sqrt{a} \sqrt{b} x-a x\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{a x-\sqrt{a} \sqrt{b} x}{b+a x}\right)-\left(\sqrt{a} \sqrt{b} x+a x\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{a x+\sqrt{a} \sqrt{b} x}{b+a x}\right)+6 (a x+b)}{a x+b}-\frac{3 \, _2F_1\left(-\frac{1}{4},-\frac{1}{4};\frac{3}{4};-\frac{a x}{b}\right)}{\sqrt[4]{\frac{a x}{b}+1}}\right)}{3 x}","a \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2-a b\&,\frac{-\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)+\text{$\#$1}^4 \log (x)+a \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)-b \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)-a \log (x)+b \log (x)}{\text{$\#$1}^3 a-\text{$\#$1}^7}\&\right]+\frac{4 \sqrt[4]{a x^4+b x^3}}{x}-2 \sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)+2 \sqrt[4]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)",1,"(4*(x^3*(b + a*x))^(1/4)*((-3*Hypergeometric2F1[-1/4, -1/4, 3/4, -((a*x)/b)])/(1 + (a*x)/b)^(1/4) + (6*(b + a*x) + (-(a*x) + Sqrt[a]*Sqrt[b]*x)*Hypergeometric2F1[3/4, 1, 7/4, (a*x - Sqrt[a]*Sqrt[b]*x)/(b + a*x)] - (a*x + Sqrt[a]*Sqrt[b]*x)*Hypergeometric2F1[3/4, 1, 7/4, (a*x + Sqrt[a]*Sqrt[b]*x)/(b + a*x)])/(b + a*x)))/(3*x)","A",1
2553,0,0,215,4.7411634,"\int \frac{a b^3-(6 a-b) b^2 x+9 a b x^2-(4 a+3 b) x^3+2 x^4}{\sqrt[4]{x (-a+x)^2 (-b+x)^3} \left(-a^2+\left(2 a-b^3 d\right) x+\left(-1+3 b^2 d\right) x^2-3 b d x^3+d x^4\right)} \, dx","Integrate[(a*b^3 - (6*a - b)*b^2*x + 9*a*b*x^2 - (4*a + 3*b)*x^3 + 2*x^4)/((x*(-a + x)^2*(-b + x)^3)^(1/4)*(-a^2 + (2*a - b^3*d)*x + (-1 + 3*b^2*d)*x^2 - 3*b*d*x^3 + d*x^4)),x]","\int \frac{a b^3-(6 a-b) b^2 x+9 a b x^2-(4 a+3 b) x^3+2 x^4}{\sqrt[4]{x (-a+x)^2 (-b+x)^3} \left(-a^2+\left(2 a-b^3 d\right) x+\left(-1+3 b^2 d\right) x^2-3 b d x^3+d x^4\right)} \, dx","\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{-a^2 b^3 x+x^4 \left(a^2+6 a b+3 b^2\right)+x^3 \left(-3 a^2 b-6 a b^2-b^3\right)+x^2 \left(3 a^2 b^2+2 a b^3\right)+x^5 (-2 a-3 b)+x^6}}{a-x}\right)}{d^{3/4}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{-a^2 b^3 x+x^4 \left(a^2+6 a b+3 b^2\right)+x^3 \left(-3 a^2 b-6 a b^2-b^3\right)+x^2 \left(3 a^2 b^2+2 a b^3\right)+x^5 (-2 a-3 b)+x^6}}{a-x}\right)}{d^{3/4}}",1,"Integrate[(a*b^3 - (6*a - b)*b^2*x + 9*a*b*x^2 - (4*a + 3*b)*x^3 + 2*x^4)/((x*(-a + x)^2*(-b + x)^3)^(1/4)*(-a^2 + (2*a - b^3*d)*x + (-1 + 3*b^2*d)*x^2 - 3*b*d*x^3 + d*x^4)), x]","F",-1
2554,0,0,215,0.7240193,"\int \frac{\sqrt[4]{-b+a x^4} \left(b+c x^4+a x^8\right)}{x^6 \left(b+2 a x^8\right)} \, dx","Integrate[((-b + a*x^4)^(1/4)*(b + c*x^4 + a*x^8))/(x^6*(b + 2*a*x^8)),x]","\int \frac{\sqrt[4]{-b+a x^4} \left(b+c x^4+a x^8\right)}{x^6 \left(b+2 a x^8\right)} \, dx","\frac{\sqrt[4]{a x^4-b} \left(a x^4-b-5 c x^4\right)}{5 b x^5}-\frac{a \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+2 a b\&,\frac{-\text{$\#$1}^4 c \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)-\text{$\#$1}^4 b \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+\text{$\#$1}^4 b \log (x)+\text{$\#$1}^4 c \log (x)+a c \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+2 b c \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)-a c \log (x)-2 b c \log (x)}{\text{$\#$1}^3 a-\text{$\#$1}^7}\&\right]}{8 b}",1,"Integrate[((-b + a*x^4)^(1/4)*(b + c*x^4 + a*x^8))/(x^6*(b + 2*a*x^8)), x]","F",-1
2555,0,0,215,0.3691814,"\int \frac{\sqrt[4]{-b+a x^4} \left(b+c x^4+a x^8\right)}{x^6 \left(b+2 a x^8\right)} \, dx","Integrate[((-b + a*x^4)^(1/4)*(b + c*x^4 + a*x^8))/(x^6*(b + 2*a*x^8)),x]","\int \frac{\sqrt[4]{-b+a x^4} \left(b+c x^4+a x^8\right)}{x^6 \left(b+2 a x^8\right)} \, dx","\frac{\sqrt[4]{a x^4-b} \left(a x^4-b-5 c x^4\right)}{5 b x^5}-\frac{a \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+2 a b\&,\frac{-\text{$\#$1}^4 c \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)-\text{$\#$1}^4 b \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+\text{$\#$1}^4 b \log (x)+\text{$\#$1}^4 c \log (x)+a c \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+2 b c \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)-a c \log (x)-2 b c \log (x)}{\text{$\#$1}^3 a-\text{$\#$1}^7}\&\right]}{8 b}",1,"Integrate[((-b + a*x^4)^(1/4)*(b + c*x^4 + a*x^8))/(x^6*(b + 2*a*x^8)), x]","F",-1
2556,1,333,215,0.6408771,"\int \frac{1}{(d+c x) \sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Integrate[1/((d + c*x)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]),x]","-\frac{2 \left(-\frac{\left(a d \left(\sqrt{a^2 d^2+b^2 c^2}+a d\right)+b^2 c^2\right) \tan ^{-1}\left(\frac{b \sqrt{c}}{\sqrt{\sqrt{a^2 x^2+b^2}+a x} \sqrt{-\sqrt{a^2 d^2+b^2 c^2}-a d}}\right)}{b \sqrt{a^2 d^2+b^2 c^2} \sqrt{-\sqrt{a^2 d^2+b^2 c^2}-a d}}+\frac{\left(a d \left(a d-\sqrt{a^2 d^2+b^2 c^2}\right)+b^2 c^2\right) \tan ^{-1}\left(\frac{b \sqrt{c}}{\sqrt{\sqrt{a^2 x^2+b^2}+a x} \sqrt{\sqrt{a^2 d^2+b^2 c^2}-a d}}\right)}{b \sqrt{a^2 d^2+b^2 c^2} \sqrt{\sqrt{a^2 d^2+b^2 c^2}-a d}}-\frac{\sqrt{c}}{\sqrt{\sqrt{a^2 x^2+b^2}+a x}}\right)}{c^{3/2}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{\sqrt{a^2 x^2+b^2}+a x}}{\sqrt{a d-\sqrt{a^2 d^2+b^2 c^2}}}\right)}{\sqrt{c} \sqrt{a d-\sqrt{a^2 d^2+b^2 c^2}}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{\sqrt{a^2 x^2+b^2}+a x}}{\sqrt{\sqrt{a^2 d^2+b^2 c^2}+a d}}\right)}{\sqrt{c} \sqrt{\sqrt{a^2 d^2+b^2 c^2}+a d}}+\frac{2}{c \sqrt{\sqrt{a^2 x^2+b^2}+a x}}",1,"(-2*(-(Sqrt[c]/Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]) - ((b^2*c^2 + a*d*(a*d + Sqrt[b^2*c^2 + a^2*d^2]))*ArcTan[(b*Sqrt[c])/(Sqrt[-(a*d) - Sqrt[b^2*c^2 + a^2*d^2]]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])])/(b*Sqrt[b^2*c^2 + a^2*d^2]*Sqrt[-(a*d) - Sqrt[b^2*c^2 + a^2*d^2]]) + ((b^2*c^2 + a*d*(a*d - Sqrt[b^2*c^2 + a^2*d^2]))*ArcTan[(b*Sqrt[c])/(Sqrt[-(a*d) + Sqrt[b^2*c^2 + a^2*d^2]]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])])/(b*Sqrt[b^2*c^2 + a^2*d^2]*Sqrt[-(a*d) + Sqrt[b^2*c^2 + a^2*d^2]])))/c^(3/2)","A",1
2557,0,0,215,1.1456375,"\int \frac{\left(-q+2 p x^3\right) \sqrt{q^2-2 p q x^2+2 p q x^3+p^2 x^6} \left(b q x+c x^2+b p x^4+a \left(q+p x^3\right)^2\right)}{x^5} \, dx","Integrate[((-q + 2*p*x^3)*Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6]*(b*q*x + c*x^2 + b*p*x^4 + a*(q + p*x^3)^2))/x^5,x]","\int \frac{\left(-q+2 p x^3\right) \sqrt{q^2-2 p q x^2+2 p q x^3+p^2 x^6} \left(b q x+c x^2+b p x^4+a \left(q+p x^3\right)^2\right)}{x^5} \, dx","\frac{\sqrt{p^2 x^6+2 p q x^3-2 p q x^2+q^2} \left(3 a p^3 x^9+9 a p^2 q x^6-3 a p^2 q x^5+9 a p q^2 x^3-3 a p q^2 x^2+3 a q^3+4 b p^2 x^7+8 b p q x^4-8 b p q x^3+4 b q^2 x+6 c p x^5+6 c q x^2\right)}{12 x^4}+\frac{1}{2} \left(-a p^2 q^2-2 c p q\right) \log \left(\sqrt{p^2 x^6+2 p q x^3-2 p q x^2+q^2}+p x^3+q\right)+\frac{1}{2} \log (x) \left(a p^2 q^2+2 c p q\right)",1,"Integrate[((-q + 2*p*x^3)*Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6]*(b*q*x + c*x^2 + b*p*x^4 + a*(q + p*x^3)^2))/x^5, x]","F",-1
2558,0,0,216,1.1940387,"\int \frac{-a (a-2 b)-2 b x+x^2}{((-a+x) (-b+x))^{2/3} \left(a^2+b d-(2 a+d) x+x^2\right)} \, dx","Integrate[(-(a*(a - 2*b)) - 2*b*x + x^2)/(((-a + x)*(-b + x))^(2/3)*(a^2 + b*d - (2*a + d)*x + x^2)),x]","\int \frac{-a (a-2 b)-2 b x+x^2}{((-a+x) (-b+x))^{2/3} \left(a^2+b d-(2 a+d) x+x^2\right)} \, dx","-\frac{\log \left(\left(x (-a-b)+a b+x^2\right)^{2/3} \left(d^{2/3} x-b d^{2/3}\right)+\sqrt[3]{d} \left(x (-a-b)+a b+x^2\right)^{4/3}+b^2 d-2 b d x+d x^2\right)}{2 \sqrt[3]{d}}+\frac{\log \left(\sqrt[6]{d} \left(x (-a-b)+a b+x^2\right)^{2/3}+b \sqrt{d}-\sqrt{d} x\right)}{\sqrt[3]{d}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \left(x (-a-b)+a b+x^2\right)^{2/3}}{\left(x (-a-b)+a b+x^2\right)^{2/3}-2 b \sqrt[3]{d}+2 \sqrt[3]{d} x}\right)}{\sqrt[3]{d}}",1,"Integrate[(-(a*(a - 2*b)) - 2*b*x + x^2)/(((-a + x)*(-b + x))^(2/3)*(a^2 + b*d - (2*a + d)*x + x^2)), x]","F",-1
2559,0,0,216,11.4608122,"\int \frac{a-2 b+x}{\sqrt[3]{(-a+x) (-b+x)} \left(b+a^2 d+(-1-2 a d) x+d x^2\right)} \, dx","Integrate[(a - 2*b + x)/(((-a + x)*(-b + x))^(1/3)*(b + a^2*d + (-1 - 2*a*d)*x + d*x^2)),x]","\int \frac{a-2 b+x}{\sqrt[3]{(-a+x) (-b+x)} \left(b+a^2 d+(-1-2 a d) x+d x^2\right)} \, dx","-\frac{\log \left(a^2 d^{2/3}+\sqrt[3]{x (-a-b)+a b+x^2} \left(\sqrt[3]{d} x-a \sqrt[3]{d}\right)+\left(x (-a-b)+a b+x^2\right)^{2/3}-2 a d^{2/3} x+d^{2/3} x^2\right)}{2 \sqrt[3]{d}}+\frac{\log \left(\sqrt[3]{x (-a-b)+a b+x^2}+a \sqrt[3]{d}-\sqrt[3]{d} x\right)}{\sqrt[3]{d}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x (-a-b)+a b+x^2}}{\sqrt[3]{x (-a-b)+a b+x^2}-2 a \sqrt[3]{d}+2 \sqrt[3]{d} x}\right)}{\sqrt[3]{d}}",1,"Integrate[(a - 2*b + x)/(((-a + x)*(-b + x))^(1/3)*(b + a^2*d + (-1 - 2*a*d)*x + d*x^2)), x]","F",-1
2560,0,0,216,11.0564506,"\int \frac{a-2 b+x}{\sqrt[3]{(-a+x) (-b+x)} \left(b+a^2 d-(1+2 a d) x+d x^2\right)} \, dx","Integrate[(a - 2*b + x)/(((-a + x)*(-b + x))^(1/3)*(b + a^2*d - (1 + 2*a*d)*x + d*x^2)),x]","\int \frac{a-2 b+x}{\sqrt[3]{(-a+x) (-b+x)} \left(b+a^2 d-(1+2 a d) x+d x^2\right)} \, dx","-\frac{\log \left(a^2 d^{2/3}+\sqrt[3]{x (-a-b)+a b+x^2} \left(\sqrt[3]{d} x-a \sqrt[3]{d}\right)+\left(x (-a-b)+a b+x^2\right)^{2/3}-2 a d^{2/3} x+d^{2/3} x^2\right)}{2 \sqrt[3]{d}}+\frac{\log \left(\sqrt[3]{x (-a-b)+a b+x^2}+a \sqrt[3]{d}-\sqrt[3]{d} x\right)}{\sqrt[3]{d}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x (-a-b)+a b+x^2}}{\sqrt[3]{x (-a-b)+a b+x^2}-2 a \sqrt[3]{d}+2 \sqrt[3]{d} x}\right)}{\sqrt[3]{d}}",1,"Integrate[(a - 2*b + x)/(((-a + x)*(-b + x))^(1/3)*(b + a^2*d - (1 + 2*a*d)*x + d*x^2)), x]","F",-1
2561,0,0,217,8.4019885,"\int \frac{-1+2 k x+(1-2 k) x^2}{((1-x) x (1-k x))^{2/3} \left(b-(1+2 b) x+(b+k) x^2\right)} \, dx","Integrate[(-1 + 2*k*x + (1 - 2*k)*x^2)/(((1 - x)*x*(1 - k*x))^(2/3)*(b - (1 + 2*b)*x + (b + k)*x^2)),x]","\int \frac{-1+2 k x+(1-2 k) x^2}{((1-x) x (1-k x))^{2/3} \left(b-(1+2 b) x+(b+k) x^2\right)} \, dx","-\frac{\log \left(b^{2/3} \left(k x^3+(-k-1) x^2+x\right)^{4/3}+\left(k x^3+(-k-1) x^2+x\right)^{2/3} \left(\sqrt[3]{b} x-\sqrt[3]{b} k x^2\right)+k^2 x^4-2 k x^3+x^2\right)}{2 b^{2/3}}+\frac{\log \left(\sqrt[3]{b} \left(k x^3+(-k-1) x^2+x\right)^{2/3}+k x^2-x\right)}{b^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{b} \left(k x^3+(-k-1) x^2+x\right)^{2/3}}{\sqrt[3]{b} \left(k x^3+(-k-1) x^2+x\right)^{2/3}-2 k x^2+2 x}\right)}{b^{2/3}}",1,"Integrate[(-1 + 2*k*x + (1 - 2*k)*x^2)/(((1 - x)*x*(1 - k*x))^(2/3)*(b - (1 + 2*b)*x + (b + k)*x^2)), x]","F",-1
2562,1,60,217,0.0241661,"\int \frac{-1+x}{(1+x) \sqrt[3]{-x^2+x^3}} \, dx","Integrate[(-1 + x)/((1 + x)*(-x^2 + x^3)^(1/3)),x]","\frac{3 \left((x-1) x^2\right)^{2/3} \left(x^{2/3} \, _2F_1\left(\frac{2}{3},\frac{2}{3};\frac{5}{3};1-x\right)-\, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{x-1}{2 x}\right)\right)}{2 x^2}","-\log \left(\sqrt[3]{x^3-x^2}-x\right)+2^{2/3} \log \left(2^{2/3} \sqrt[3]{x^3-x^2}-2 x\right)+\frac{1}{2} \log \left(x^2+\sqrt[3]{x^3-x^2} x+\left(x^3-x^2\right)^{2/3}\right)-\frac{\log \left(2 x^2+2^{2/3} \sqrt[3]{x^3-x^2} x+\sqrt[3]{2} \left(x^3-x^2\right)^{2/3}\right)}{\sqrt[3]{2}}+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-x^2}+x}\right)-2^{2/3} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^3-x^2}+x}\right)",1,"(3*((-1 + x)*x^2)^(2/3)*(x^(2/3)*Hypergeometric2F1[2/3, 2/3, 5/3, 1 - x] - Hypergeometric2F1[2/3, 1, 5/3, (-1 + x)/(2*x)]))/(2*x^2)","C",1
2563,0,0,217,0.6058734,"\int \frac{\left(-1+x+x^3+x^6\right)^{2/3} \left(3-2 x+3 x^6\right)}{\left(-1+x+x^6\right) \left(-1+x-x^3+x^6\right)} \, dx","Integrate[((-1 + x + x^3 + x^6)^(2/3)*(3 - 2*x + 3*x^6))/((-1 + x + x^6)*(-1 + x - x^3 + x^6)),x]","\int \frac{\left(-1+x+x^3+x^6\right)^{2/3} \left(3-2 x+3 x^6\right)}{\left(-1+x+x^6\right) \left(-1+x-x^3+x^6\right)} \, dx","-\log \left(\sqrt[3]{x^6+x^3+x-1}-x\right)+2^{2/3} \log \left(2^{2/3} \sqrt[3]{x^6+x^3+x-1}-2 x\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^6+x^3+x-1}+x}\right)-2^{2/3} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^6+x^3+x-1}+x}\right)+\frac{1}{2} \log \left(x^2+\sqrt[3]{x^6+x^3+x-1} x+\left(x^6+x^3+x-1\right)^{2/3}\right)-\frac{\log \left(2 x^2+2^{2/3} \sqrt[3]{x^6+x^3+x-1} x+\sqrt[3]{2} \left(x^6+x^3+x-1\right)^{2/3}\right)}{\sqrt[3]{2}}",1,"Integrate[((-1 + x + x^3 + x^6)^(2/3)*(3 - 2*x + 3*x^6))/((-1 + x + x^6)*(-1 + x - x^3 + x^6)), x]","F",-1
2564,1,239,217,0.5491761,"\int \frac{-1-2 x^4+2 x^8}{\sqrt[4]{-1+x^4} \left(-1-x^4+x^8\right)} \, dx","Integrate[(-1 - 2*x^4 + 2*x^8)/((-1 + x^4)^(1/4)*(-1 - x^4 + x^8)),x]","\tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-1}}\right)-\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3+\sqrt{5}}} x}{\sqrt[4]{x^4-1}}\right)}{5+\sqrt{5}}+\frac{\sqrt[4]{\frac{1}{2} \left(3-\sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x}{\sqrt[4]{x^4-1}}\right)}{\sqrt{5}-5}+\tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-1}}\right)-\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3+\sqrt{5}}} x}{\sqrt[4]{x^4-1}}\right)}{5+\sqrt{5}}+\frac{\sqrt[4]{\frac{1}{2} \left(3-\sqrt{5}\right)} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x}{\sqrt[4]{x^4-1}}\right)}{\sqrt{5}-5}","\tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-1}}\right)-\frac{1}{2} \sqrt{\frac{1}{10} \left(\sqrt{5}-1\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}} x}{\sqrt[4]{x^4-1}}\right)-\frac{1}{2} \sqrt{\frac{1}{10} \left(1+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{1}{2}+\frac{\sqrt{5}}{2}} x}{\sqrt[4]{x^4-1}}\right)+\tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-1}}\right)-\frac{1}{2} \sqrt{\frac{1}{10} \left(\sqrt{5}-1\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}} x}{\sqrt[4]{x^4-1}}\right)-\frac{1}{2} \sqrt{\frac{1}{10} \left(1+\sqrt{5}\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{2}+\frac{\sqrt{5}}{2}} x}{\sqrt[4]{x^4-1}}\right)",1,"ArcTan[x/(-1 + x^4)^(1/4)] - (((3 + Sqrt[5])/2)^(1/4)*ArcTan[((2/(3 + Sqrt[5]))^(1/4)*x)/(-1 + x^4)^(1/4)])/(5 + Sqrt[5]) + (((3 - Sqrt[5])/2)^(1/4)*ArcTan[(((3 + Sqrt[5])/2)^(1/4)*x)/(-1 + x^4)^(1/4)])/(-5 + Sqrt[5]) + ArcTanh[x/(-1 + x^4)^(1/4)] - (((3 + Sqrt[5])/2)^(1/4)*ArcTanh[((2/(3 + Sqrt[5]))^(1/4)*x)/(-1 + x^4)^(1/4)])/(5 + Sqrt[5]) + (((3 - Sqrt[5])/2)^(1/4)*ArcTanh[(((3 + Sqrt[5])/2)^(1/4)*x)/(-1 + x^4)^(1/4)])/(-5 + Sqrt[5])","A",1
2565,1,239,217,0.4920526,"\int \frac{-1+2 x^4+2 x^8}{\sqrt[4]{1+x^4} \left(-1+x^4+x^8\right)} \, dx","Integrate[(-1 + 2*x^4 + 2*x^8)/((1 + x^4)^(1/4)*(-1 + x^4 + x^8)),x]","\tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)-\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3+\sqrt{5}}} x}{\sqrt[4]{x^4+1}}\right)}{5+\sqrt{5}}+\frac{\sqrt[4]{\frac{1}{2} \left(3-\sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x}{\sqrt[4]{x^4+1}}\right)}{\sqrt{5}-5}+\tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)-\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3+\sqrt{5}}} x}{\sqrt[4]{x^4+1}}\right)}{5+\sqrt{5}}+\frac{\sqrt[4]{\frac{1}{2} \left(3-\sqrt{5}\right)} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x}{\sqrt[4]{x^4+1}}\right)}{\sqrt{5}-5}","\tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)-\frac{1}{2} \sqrt{\frac{1}{10} \left(\sqrt{5}-1\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}} x}{\sqrt[4]{x^4+1}}\right)-\frac{1}{2} \sqrt{\frac{1}{10} \left(1+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{1}{2}+\frac{\sqrt{5}}{2}} x}{\sqrt[4]{x^4+1}}\right)+\tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)-\frac{1}{2} \sqrt{\frac{1}{10} \left(\sqrt{5}-1\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}} x}{\sqrt[4]{x^4+1}}\right)-\frac{1}{2} \sqrt{\frac{1}{10} \left(1+\sqrt{5}\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{2}+\frac{\sqrt{5}}{2}} x}{\sqrt[4]{x^4+1}}\right)",1,"ArcTan[x/(1 + x^4)^(1/4)] - (((3 + Sqrt[5])/2)^(1/4)*ArcTan[((2/(3 + Sqrt[5]))^(1/4)*x)/(1 + x^4)^(1/4)])/(5 + Sqrt[5]) + (((3 - Sqrt[5])/2)^(1/4)*ArcTan[(((3 + Sqrt[5])/2)^(1/4)*x)/(1 + x^4)^(1/4)])/(-5 + Sqrt[5]) + ArcTanh[x/(1 + x^4)^(1/4)] - (((3 + Sqrt[5])/2)^(1/4)*ArcTanh[((2/(3 + Sqrt[5]))^(1/4)*x)/(1 + x^4)^(1/4)])/(5 + Sqrt[5]) + (((3 - Sqrt[5])/2)^(1/4)*ArcTanh[(((3 + Sqrt[5])/2)^(1/4)*x)/(1 + x^4)^(1/4)])/(-5 + Sqrt[5])","A",1
2566,0,0,218,6.1941422,"\int \frac{-a b+(2 a-b) x}{\sqrt[3]{x (-a+x) (-b+x)} \left(-a^2+(2 a-b d) x+(-1+d) x^2\right)} \, dx","Integrate[(-(a*b) + (2*a - b)*x)/((x*(-a + x)*(-b + x))^(1/3)*(-a^2 + (2*a - b*d)*x + (-1 + d)*x^2)),x]","\int \frac{-a b+(2 a-b) x}{\sqrt[3]{x (-a+x) (-b+x)} \left(-a^2+(2 a-b d) x+(-1+d) x^2\right)} \, dx","\frac{\log \left(a^2+d^{2/3} \left(x^2 (-a-b)+a b x+x^3\right)^{2/3}+\sqrt[3]{x^2 (-a-b)+a b x+x^3} \left(\sqrt[3]{d} x-a \sqrt[3]{d}\right)-2 a x+x^2\right)}{2 d^{2/3}}-\frac{\log \left(\sqrt[3]{d} \sqrt[3]{x^2 (-a-b)+a b x+x^3}+a-x\right)}{d^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} \sqrt[3]{x^2 (-a-b)+a b x+x^3}}{\sqrt[3]{d} \sqrt[3]{x^2 (-a-b)+a b x+x^3}-2 a+2 x}\right)}{d^{2/3}}",1,"Integrate[(-(a*b) + (2*a - b)*x)/((x*(-a + x)*(-b + x))^(1/3)*(-a^2 + (2*a - b*d)*x + (-1 + d)*x^2)), x]","F",-1
2567,0,0,218,0.8603557,"\int \frac{\left(-4 b+a x^4\right) \sqrt[4]{-b+a x^4}}{x^6 \left(-8 b+a x^8\right)} \, dx","Integrate[((-4*b + a*x^4)*(-b + a*x^4)^(1/4))/(x^6*(-8*b + a*x^8)),x]","\int \frac{\left(-4 b+a x^4\right) \sqrt[4]{-b+a x^4}}{x^6 \left(-8 b+a x^8\right)} \, dx","\frac{a \text{RootSum}\left[8 \text{$\#$1}^8-16 \text{$\#$1}^4 a+8 a^2-a b\&,\frac{-8 \text{$\#$1}^4 a \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)-4 \text{$\#$1}^4 b \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+8 \text{$\#$1}^4 a \log (x)+4 \text{$\#$1}^4 b \log (x)+8 a^2 \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)-a b \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)-8 a^2 \log (x)+a b \log (x)}{\text{$\#$1}^3 a-\text{$\#$1}^7}\&\right]}{512 b}+\frac{\sqrt[4]{a x^4-b} \left(9 a x^4-4 b\right)}{40 b x^5}",1,"Integrate[((-4*b + a*x^4)*(-b + a*x^4)^(1/4))/(x^6*(-8*b + a*x^8)), x]","F",-1
2568,0,0,218,0.4960093,"\int \frac{\left(-4 b+a x^4\right) \sqrt[4]{-b+a x^4}}{x^6 \left(-8 b+a x^8\right)} \, dx","Integrate[((-4*b + a*x^4)*(-b + a*x^4)^(1/4))/(x^6*(-8*b + a*x^8)),x]","\int \frac{\left(-4 b+a x^4\right) \sqrt[4]{-b+a x^4}}{x^6 \left(-8 b+a x^8\right)} \, dx","\frac{a \text{RootSum}\left[8 \text{$\#$1}^8-16 \text{$\#$1}^4 a+8 a^2-a b\&,\frac{-8 \text{$\#$1}^4 a \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)-4 \text{$\#$1}^4 b \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+8 \text{$\#$1}^4 a \log (x)+4 \text{$\#$1}^4 b \log (x)+8 a^2 \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)-a b \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)-8 a^2 \log (x)+a b \log (x)}{\text{$\#$1}^3 a-\text{$\#$1}^7}\&\right]}{512 b}+\frac{\sqrt[4]{a x^4-b} \left(9 a x^4-4 b\right)}{40 b x^5}",1,"Integrate[((-4*b + a*x^4)*(-b + a*x^4)^(1/4))/(x^6*(-8*b + a*x^8)), x]","F",-1
2569,1,61,219,0.0389188,"\int \frac{x}{(1+x) \sqrt[3]{-x^2+x^3}} \, dx","Integrate[x/((1 + x)*(-x^2 + x^3)^(1/3)),x]","\frac{3 \left((x-1) x^2\right)^{2/3} \left(2 x^{2/3} \, _2F_1\left(\frac{2}{3},\frac{2}{3};\frac{5}{3};1-x\right)-\, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{x-1}{2 x}\right)\right)}{4 x^2}","-\log \left(\sqrt[3]{x^3-x^2}-x\right)+\frac{\log \left(2^{2/3} \sqrt[3]{x^3-x^2}-2 x\right)}{\sqrt[3]{2}}+\frac{1}{2} \log \left(x^2+\sqrt[3]{x^3-x^2} x+\left(x^3-x^2\right)^{2/3}\right)-\frac{\log \left(2 x^2+2^{2/3} \sqrt[3]{x^3-x^2} x+\sqrt[3]{2} \left(x^3-x^2\right)^{2/3}\right)}{2 \sqrt[3]{2}}+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-x^2}+x}\right)-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^3-x^2}+x}\right)}{\sqrt[3]{2}}",1,"(3*((-1 + x)*x^2)^(2/3)*(2*x^(2/3)*Hypergeometric2F1[2/3, 2/3, 5/3, 1 - x] - Hypergeometric2F1[2/3, 1, 5/3, (-1 + x)/(2*x)]))/(4*x^2)","C",1
2570,1,61,219,0.019244,"\int \frac{\sqrt[3]{-x^2+x^3}}{-1+x^2} \, dx","Integrate[(-x^2 + x^3)^(1/3)/(-1 + x^2),x]","\frac{3 \sqrt[3]{(x-1) x^2} \left(2 \sqrt[3]{x} \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};1-x\right)-\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{x-1}{2 x}\right)\right)}{2 x}","-\log \left(\sqrt[3]{x^3-x^2}-x\right)+\frac{\log \left(2^{2/3} \sqrt[3]{x^3-x^2}-2 x\right)}{2^{2/3}}+\frac{1}{2} \log \left(x^2+\sqrt[3]{x^3-x^2} x+\left(x^3-x^2\right)^{2/3}\right)-\frac{\log \left(2 x^2+2^{2/3} \sqrt[3]{x^3-x^2} x+\sqrt[3]{2} \left(x^3-x^2\right)^{2/3}\right)}{2\ 2^{2/3}}-\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-x^2}+x}\right)+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^3-x^2}+x}\right)}{2^{2/3}}",1,"(3*((-1 + x)*x^2)^(1/3)*(2*x^(1/3)*Hypergeometric2F1[1/3, 1/3, 4/3, 1 - x] - Hypergeometric2F1[1/3, 1, 4/3, (-1 + x)/(2*x)]))/(2*x)","C",1
2571,0,0,219,0.1819303,"\int x^2 \sqrt{b+a^2 x^4} \sqrt{a x^2+\sqrt{b+a^2 x^4}} \, dx","Integrate[x^2*Sqrt[b + a^2*x^4]*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]],x]","\int x^2 \sqrt{b+a^2 x^4} \sqrt{a x^2+\sqrt{b+a^2 x^4}} \, dx","\frac{\sqrt{a} x \left(16 a^4 x^8+36 a^2 b x^4+9 b^2\right) \sqrt{\sqrt{a^2 x^4+b}+a x^2}+\sqrt{a} x \sqrt{a^2 x^4+b} \sqrt{\sqrt{a^2 x^4+b}+a x^2} \left(16 a^3 x^6+28 a b x^2\right)}{48 a^{3/2} b+96 a^{7/2} x^4+96 a^{5/2} x^2 \sqrt{a^2 x^4+b}}-\frac{3 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}}{\sqrt{b}}\right)}{16 \sqrt{2} a^{3/2}}",1,"Integrate[x^2*Sqrt[b + a^2*x^4]*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]], x]","F",-1
2572,0,0,220,0.4092429,"\int \frac{\left(-b x+a^2 x^2\right)^{3/2}}{\left(a x^2+x \sqrt{-b x+a^2 x^2}\right)^{3/2}} \, dx","Integrate[(-(b*x) + a^2*x^2)^(3/2)/(a*x^2 + x*Sqrt[-(b*x) + a^2*x^2])^(3/2),x]","\int \frac{\left(-b x+a^2 x^2\right)^{3/2}}{\left(a x^2+x \sqrt{-b x+a^2 x^2}\right)^{3/2}} \, dx","\frac{\sqrt{a^2 x^2-b x} \sqrt{x \left(\sqrt{a^2 x^2-b x}+a x\right)} \left(32 a^4 x^2-88 a^2 b x+115 b^2\right)}{40 b^2 x}+\sqrt{x \left(\sqrt{a^2 x^2-b x}+a x\right)} \left(\frac{9 \sqrt{b} \sqrt{\sqrt{a^2 x^2-b x}-a x} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{\sqrt{a^2 x^2-b x}-a x}}{\sqrt{b}}\right)}{8 \sqrt{2} \sqrt{a} x}+\frac{-32 a^5 x^2+104 a^3 b x-145 a b^2}{40 b^2}\right)",1,"Integrate[(-(b*x) + a^2*x^2)^(3/2)/(a*x^2 + x*Sqrt[-(b*x) + a^2*x^2])^(3/2), x]","F",-1
2573,0,0,221,1.8213025,"\int \frac{-3 k+\left(-2+k^2\right) x+3 k x^2+k^2 x^3}{\sqrt[3]{\left(1-x^2\right) \left(1-k^2 x^2\right)} \left(-1+d-(2+d) k x-\left(d+k^2\right) x^2+d k x^3\right)} \, dx","Integrate[(-3*k + (-2 + k^2)*x + 3*k*x^2 + k^2*x^3)/(((1 - x^2)*(1 - k^2*x^2))^(1/3)*(-1 + d - (2 + d)*k*x - (d + k^2)*x^2 + d*k*x^3)),x]","\int \frac{-3 k+\left(-2+k^2\right) x+3 k x^2+k^2 x^3}{\sqrt[3]{\left(1-x^2\right) \left(1-k^2 x^2\right)} \left(-1+d-(2+d) k x-\left(d+k^2\right) x^2+d k x^3\right)} \, dx","\frac{\log \left(-\sqrt[3]{d} \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}+k x+1\right)}{d^{2/3}}-\frac{\log \left(d^{2/3} \left(k^2 x^4+\left(-k^2-1\right) x^2+1\right)^{2/3}+\sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1} \left(\sqrt[3]{d} k x+\sqrt[3]{d}\right)+k^2 x^2+2 k x+1\right)}{2 d^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}}{\sqrt[3]{d} \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}+2 k x+2}\right)}{d^{2/3}}",1,"Integrate[(-3*k + (-2 + k^2)*x + 3*k*x^2 + k^2*x^3)/(((1 - x^2)*(1 - k^2*x^2))^(1/3)*(-1 + d - (2 + d)*k*x - (d + k^2)*x^2 + d*k*x^3)), x]","F",-1
2574,1,69,221,0.0492146,"\int \frac{a+b x}{x (-d+c x) \sqrt[4]{-x^3+x^4}} \, dx","Integrate[(a + b*x)/(x*(-d + c*x)*(-x^3 + x^4)^(1/4)),x]","-\frac{4 \left((x-1) x^3\right)^{3/4} \left((a c+b d) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{d-d x}{c x-d x}\right)+a (d-c)\right)}{3 d x^3 (d-c)}","\frac{\sqrt{2} (a c+b d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} x \sqrt[4]{x^4-x^3} \sqrt[4]{c-d}}{x^2 \sqrt{c-d}-\sqrt{d} \sqrt{x^4-x^3}}\right)}{d^{7/4} \sqrt[4]{c-d}}-\frac{\sqrt{2} (a c+b d) \tanh ^{-1}\left(\frac{x^2 \sqrt{c-d}+\sqrt{d} \sqrt{x^4-x^3}}{\sqrt{2} \sqrt[4]{d} x \sqrt[4]{x^4-x^3} \sqrt[4]{c-d}}\right)}{d^{7/4} \sqrt[4]{c-d}}-\frac{4 a \left(x^4-x^3\right)^{3/4}}{3 d x^3}",1,"(-4*((-1 + x)*x^3)^(3/4)*(a*(-c + d) + (a*c + b*d)*Hypergeometric2F1[3/4, 1, 7/4, (d - d*x)/(c*x - d*x)]))/(3*d*(-c + d)*x^3)","C",1
2575,0,0,221,0.5964284,"\int \frac{(-4+3 x) \sqrt[4]{\frac{-a+a x+b x^4}{-c+c x+d x^4}}}{(-1+x) x} \, dx","Integrate[((-4 + 3*x)*((-a + a*x + b*x^4)/(-c + c*x + d*x^4))^(1/4))/((-1 + x)*x),x]","\int \frac{(-4+3 x) \sqrt[4]{\frac{-a+a x+b x^4}{-c+c x+d x^4}}}{(-1+x) x} \, dx","-\frac{2 \sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt[4]{\frac{a x-a+b x^4}{c x-c+d x^4}}}{\sqrt[4]{a}}\right)}{\sqrt[4]{c}}+\frac{2 \sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{\frac{a x-a+b x^4}{c x-c+d x^4}}}{\sqrt[4]{b}}\right)}{\sqrt[4]{d}}-\frac{2 \sqrt[4]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt[4]{\frac{a x-a+b x^4}{c x-c+d x^4}}}{\sqrt[4]{a}}\right)}{\sqrt[4]{c}}+\frac{2 \sqrt[4]{b} \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{\frac{a x-a+b x^4}{c x-c+d x^4}}}{\sqrt[4]{b}}\right)}{\sqrt[4]{d}}",1,"Integrate[((-4 + 3*x)*((-a + a*x + b*x^4)/(-c + c*x + d*x^4))^(1/4))/((-1 + x)*x), x]","F",-1
2576,1,214,221,0.5194095,"\int \frac{\left(1+x^3\right)^{2/3} \left(1-2 x^3+2 x^6\right)}{x^6 \left(-1-x^3+2 x^6\right)} \, dx","Integrate[((1 + x^3)^(2/3)*(1 - 2*x^3 + 2*x^6))/(x^6*(-1 - x^3 + 2*x^6)),x]","\frac{1}{18} \left(-20 \log \left(\frac{x}{\sqrt[3]{x^3+1}}+1\right)+2\ 2^{2/3} \log \left(1-\frac{\sqrt[3]{2} x}{\sqrt[3]{x^3+1}}\right)+20 \sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{x^3+1}}}{\sqrt{3}}\right)-2\ 2^{2/3} \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{2} x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)+10 \log \left(-\frac{x}{\sqrt[3]{x^3+1}}+\frac{x^2}{\left(x^3+1\right)^{2/3}}+1\right)-2^{2/3} \log \left(\frac{\sqrt[3]{2} x}{\sqrt[3]{x^3+1}}+\frac{2^{2/3} x^2}{\left(x^3+1\right)^{2/3}}+1\right)\right)+\left(x^3+1\right)^{2/3} \left(\frac{1}{5 x^5}-\frac{13}{10 x^2}\right)","-\frac{10}{9} \log \left(\sqrt[3]{x^3+1}+x\right)+\frac{1}{9} 2^{2/3} \log \left(2^{2/3} \sqrt[3]{x^3+1}-2 x\right)-\frac{10 \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+1}-x}\right)}{3 \sqrt{3}}-\frac{2^{2/3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^3+1}+x}\right)}{3 \sqrt{3}}+\frac{\left(x^3+1\right)^{2/3} \left(2-13 x^3\right)}{10 x^5}+\frac{5}{9} \log \left(-\sqrt[3]{x^3+1} x+\left(x^3+1\right)^{2/3}+x^2\right)-\frac{\log \left(2^{2/3} \sqrt[3]{x^3+1} x+\sqrt[3]{2} \left(x^3+1\right)^{2/3}+2 x^2\right)}{9 \sqrt[3]{2}}",1,"(1/(5*x^5) - 13/(10*x^2))*(1 + x^3)^(2/3) + (20*Sqrt[3]*ArcTan[(1 - (2*x)/(1 + x^3)^(1/3))/Sqrt[3]] - 2*2^(2/3)*Sqrt[3]*ArcTan[(1 + (2*2^(1/3)*x)/(1 + x^3)^(1/3))/Sqrt[3]] + 10*Log[1 + x^2/(1 + x^3)^(2/3) - x/(1 + x^3)^(1/3)] - 20*Log[1 + x/(1 + x^3)^(1/3)] + 2*2^(2/3)*Log[1 - (2^(1/3)*x)/(1 + x^3)^(1/3)] - 2^(2/3)*Log[1 + (2^(2/3)*x^2)/(1 + x^3)^(2/3) + (2^(1/3)*x)/(1 + x^3)^(1/3)])/18","A",1
2577,1,40,222,0.0349257,"\int \frac{2}{(3+x) \left(2-8 x+8 x^2\right)^{2/3}} \, dx","Integrate[2/((3 + x)*(2 - 8*x + 8*x^2)^(2/3)),x]","-\frac{6 (2 x-1) \, _2F_1\left(-\frac{1}{3},1;\frac{2}{3};\frac{1}{7} (1-2 x)\right)}{7 \left(8 x^2-8 x+2\right)^{2/3}}","-\frac{3 \sqrt[3]{2} \sqrt[3]{4 x^2-4 x+1}}{7 (2 x-1)}+\frac{1}{7} \sqrt[3]{\frac{2}{7}} \log \left(\left(4 x^2-4 x+1\right)^{2/3}+2 \sqrt[3]{7} x-\sqrt[3]{7}\right)-\frac{\log \left(\left(4 x^2-4 x+1\right)^{2/3}+7^{2/3} \sqrt[3]{4 x^2-4 x+1}-2 \sqrt[3]{7} x+\sqrt[3]{7}\right)}{7\ 2^{2/3} \sqrt[3]{7}}+\frac{1}{7} \sqrt[3]{\frac{2}{7}} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \left(4 x^2-4 x+1\right)^{2/3}}{\left(4 x^2-4 x+1\right)^{2/3}-4 \sqrt[3]{7} x+2 \sqrt[3]{7}}\right)-\frac{2}{21} \sqrt[3]{\frac{2}{7}} \log (2 x-1)",1,"(-6*(-1 + 2*x)*Hypergeometric2F1[-1/3, 1, 2/3, (1 - 2*x)/7])/(7*(2 - 8*x + 8*x^2)^(2/3))","C",1
2578,0,0,222,4.3563498,"\int \frac{1-(-3+2 k) x-(4+k) x^2+3 k x^3}{\sqrt[3]{(1-x) x (1-k x)} \left(-1+(5+b) x-(10+b k) x^2+10 x^3-5 x^4+x^5\right)} \, dx","Integrate[(1 - (-3 + 2*k)*x - (4 + k)*x^2 + 3*k*x^3)/(((1 - x)*x*(1 - k*x))^(1/3)*(-1 + (5 + b)*x - (10 + b*k)*x^2 + 10*x^3 - 5*x^4 + x^5)),x]","\int \frac{1-(-3+2 k) x-(4+k) x^2+3 k x^3}{\sqrt[3]{(1-x) x (1-k x)} \left(-1+(5+b) x-(10+b k) x^2+10 x^3-5 x^4+x^5\right)} \, dx","\frac{\log \left(-\sqrt[3]{b} \sqrt[3]{k x^3+(-k-1) x^2+x}+x^2-2 x+1\right)}{b^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{b} \sqrt[3]{k x^3+(-k-1) x^2+x}}{\sqrt[3]{b} \sqrt[3]{k x^3+(-k-1) x^2+x}+2 x^2-4 x+2}\right)}{b^{2/3}}-\frac{\log \left(b^{2/3} \left(k x^3+(-k-1) x^2+x\right)^{2/3}+\left(\sqrt[3]{b} x^2-2 \sqrt[3]{b} x+\sqrt[3]{b}\right) \sqrt[3]{k x^3+(-k-1) x^2+x}+x^4-4 x^3+6 x^2-4 x+1\right)}{2 b^{2/3}}",1,"Integrate[(1 - (-3 + 2*k)*x - (4 + k)*x^2 + 3*k*x^3)/(((1 - x)*x*(1 - k*x))^(1/3)*(-1 + (5 + b)*x - (10 + b*k)*x^2 + 10*x^3 - 5*x^4 + x^5)), x]","F",-1
2579,1,55,223,0.230586,"\int \frac{1}{x \sqrt[3]{(1+x) \left(q+2 q x+x^2\right)}} \, dx","Integrate[1/(x*((1 + x)*(q + 2*q*x + x^2))^(1/3)),x]","-\frac{3 \left((x+1) \left(2 q x+q+x^2\right)\right)^{2/3} \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{x^2+2 q x+q}{q (x+1)^2}\right)}{4 q (x+1)^2}","-\frac{\log \left(q^{2/3} x^2+2 q^{2/3} x+q^{2/3}+\left((2 q+1) x^2+3 q x+q+x^3\right)^{2/3}+\left(\sqrt[3]{q} x+\sqrt[3]{q}\right) \sqrt[3]{(2 q+1) x^2+3 q x+q+x^3}\right)}{4 \sqrt[3]{q}}+\frac{\log \left(\sqrt[3]{(2 q+1) x^2+3 q x+q+x^3}-\sqrt[3]{q} x-\sqrt[3]{q}\right)}{2 \sqrt[3]{q}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{(2 q+1) x^2+3 q x+q+x^3}}{\sqrt[3]{(2 q+1) x^2+3 q x+q+x^3}+2 \sqrt[3]{q} x+2 \sqrt[3]{q}}\right)}{2 \sqrt[3]{q}}",1,"(-3*((1 + x)*(q + 2*q*x + x^2))^(2/3)*Hypergeometric2F1[2/3, 1, 5/3, (q + 2*q*x + x^2)/(q*(1 + x)^2)])/(4*q*(1 + x)^2)","C",1
2580,0,0,223,4.6709302,"\int \frac{-1+2 x+\left(-2 k+k^2\right) x^2}{((1-x) x (1-k x))^{2/3} \left(1-(b+2 k) x+\left(b+k^2\right) x^2\right)} \, dx","Integrate[(-1 + 2*x + (-2*k + k^2)*x^2)/(((1 - x)*x*(1 - k*x))^(2/3)*(1 - (b + 2*k)*x + (b + k^2)*x^2)),x]","\int \frac{-1+2 x+\left(-2 k+k^2\right) x^2}{((1-x) x (1-k x))^{2/3} \left(1-(b+2 k) x+\left(b+k^2\right) x^2\right)} \, dx","-\frac{\log \left(\left(b^{2/3} x-b^{2/3} x^2\right) \left(k x^3+(-k-1) x^2+x\right)^{2/3}+\sqrt[3]{b} \left(k x^3+(-k-1) x^2+x\right)^{4/3}+b x^4-2 b x^3+b x^2\right)}{2 \sqrt[3]{b}}+\frac{\log \left(\sqrt[6]{b} \left(k x^3+(-k-1) x^2+x\right)^{2/3}+\sqrt{b} x^2-\sqrt{b} x\right)}{\sqrt[3]{b}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \left(k x^3+(-k-1) x^2+x\right)^{2/3}}{-2 \sqrt[3]{b} x^2+2 \sqrt[3]{b} x+\left(k x^3+(-k-1) x^2+x\right)^{2/3}}\right)}{\sqrt[3]{b}}",1,"Integrate[(-1 + 2*x + (-2*k + k^2)*x^2)/(((1 - x)*x*(1 - k*x))^(2/3)*(1 - (b + 2*k)*x + (b + k^2)*x^2)), x]","F",-1
2581,0,0,223,1.5422269,"\int \frac{3 k+\left(-2+k^2\right) x-3 k x^2+k^2 x^3}{\sqrt[3]{\left(1-x^2\right) \left(1-k^2 x^2\right)} \left(1-d-(2+d) k x+\left(d+k^2\right) x^2+d k x^3\right)} \, dx","Integrate[(3*k + (-2 + k^2)*x - 3*k*x^2 + k^2*x^3)/(((1 - x^2)*(1 - k^2*x^2))^(1/3)*(1 - d - (2 + d)*k*x + (d + k^2)*x^2 + d*k*x^3)),x]","\int \frac{3 k+\left(-2+k^2\right) x-3 k x^2+k^2 x^3}{\sqrt[3]{\left(1-x^2\right) \left(1-k^2 x^2\right)} \left(1-d-(2+d) k x+\left(d+k^2\right) x^2+d k x^3\right)} \, dx","-\frac{\log \left(\sqrt[3]{d} \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}+k x-1\right)}{d^{2/3}}+\frac{\log \left(d^{2/3} \left(k^2 x^4+\left(-k^2-1\right) x^2+1\right)^{2/3}+\sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1} \left(\sqrt[3]{d}-\sqrt[3]{d} k x\right)+k^2 x^2-2 k x+1\right)}{2 d^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}}{\sqrt[3]{d} \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}-2 k x+2}\right)}{d^{2/3}}",1,"Integrate[(3*k + (-2 + k^2)*x - 3*k*x^2 + k^2*x^3)/(((1 - x^2)*(1 - k^2*x^2))^(1/3)*(1 - d - (2 + d)*k*x + (d + k^2)*x^2 + d*k*x^3)), x]","F",-1
2582,0,0,223,2.563214,"\int \frac{3+2 \left(1+k^2\right) x-\left(1+k^2\right) x^2-4 k^2 x^3-k^2 x^4}{\left(\left(1-x^2\right) \left(1-k^2 x^2\right)\right)^{2/3} \left(1-d-(1+2 d) x-\left(d+k^2\right) x^2+k^2 x^3\right)} \, dx","Integrate[(3 + 2*(1 + k^2)*x - (1 + k^2)*x^2 - 4*k^2*x^3 - k^2*x^4)/(((1 - x^2)*(1 - k^2*x^2))^(2/3)*(1 - d - (1 + 2*d)*x - (d + k^2)*x^2 + k^2*x^3)),x]","\int \frac{3+2 \left(1+k^2\right) x-\left(1+k^2\right) x^2-4 k^2 x^3-k^2 x^4}{\left(\left(1-x^2\right) \left(1-k^2 x^2\right)\right)^{2/3} \left(1-d-(1+2 d) x-\left(d+k^2\right) x^2+k^2 x^3\right)} \, dx","-\frac{\log \left(-\sqrt[3]{d} x-\sqrt[3]{d}+\sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}\right)}{d^{2/3}}+\frac{\log \left(d^{2/3} x^2+2 d^{2/3} x+d^{2/3}+\left(\sqrt[3]{d} x+\sqrt[3]{d}\right) \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}+\left(k^2 x^4+\left(-k^2-1\right) x^2+1\right)^{2/3}\right)}{2 d^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} x+\sqrt{3} \sqrt[3]{d}}{\sqrt[3]{d} x+\sqrt[3]{d}+2 \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}}\right)}{d^{2/3}}",1,"Integrate[(3 + 2*(1 + k^2)*x - (1 + k^2)*x^2 - 4*k^2*x^3 - k^2*x^4)/(((1 - x^2)*(1 - k^2*x^2))^(2/3)*(1 - d - (1 + 2*d)*x - (d + k^2)*x^2 + k^2*x^3)), x]","F",-1
2583,1,398,223,0.6015754,"\int \frac{\sqrt[4]{\frac{-1+x}{1+2 x}}-3 \left(\frac{-1+x}{1+2 x}\right)^{3/4}}{(-1+x) (1+x)^2 (-1+2 x)} \, dx","Integrate[(((-1 + x)/(1 + 2*x))^(1/4) - 3*((-1 + x)/(1 + 2*x))^(3/4))/((-1 + x)*(1 + x)^2*(-1 + 2*x)),x]","\frac{1}{18} \left(-18 \left(\frac{x-1}{2 x+1}\right)^{3/4} \, _2F_1\left(\frac{3}{4},2;\frac{7}{4};\frac{x-1}{4 x+2}\right)+\frac{3 \sqrt[4]{\frac{x-1}{2 x+1}} (2 x+1)}{x+1}+8 \sqrt[4]{2} \left(1-3 \sqrt{2}\right) \log \left(\sqrt[4]{2}-\sqrt[4]{\frac{x-1}{2 x+1}}\right)-8 i \sqrt[4]{2} \left(1+3 \sqrt{2}\right) \log \left(\sqrt[4]{2}-i \sqrt[4]{\frac{x-1}{2 x+1}}\right)+8 i \sqrt[4]{2} \left(1+3 \sqrt{2}\right) \log \left(\sqrt[4]{2}+i \sqrt[4]{\frac{x-1}{2 x+1}}\right)+8 \sqrt[4]{2} \left(3 \sqrt{2}-1\right) \log \left(\sqrt[4]{\frac{x-1}{2 x+1}}+\sqrt[4]{2}\right)-10 \log \left(2 \sqrt{\frac{x-1}{2 x+1}}-2 \sqrt[4]{\frac{x-1}{2 x+1}}+1\right)+10 \log \left(2 \sqrt{\frac{x-1}{2 x+1}}+2 \sqrt[4]{\frac{x-1}{2 x+1}}+1\right)+4 \tan ^{-1}\left(1-2 \sqrt[4]{\frac{x-1}{2 x+1}}\right)-4 \tan ^{-1}\left(2 \sqrt[4]{\frac{x-1}{2 x+1}}+1\right)+\frac{27 \left(\tan ^{-1}\left(\sqrt[4]{\frac{x-1}{4 x+2}}\right)+\tanh ^{-1}\left(\sqrt[4]{\frac{x-1}{4 x+2}}\right)\right)}{2\ 2^{3/4}}\right)","\frac{\left(\frac{x-1}{2 x+1}\right)^{3/4} (-2 x-1)}{2 (x+1)}+\frac{\sqrt[4]{\frac{x-1}{2 x+1}} (2 x+1)}{6 (x+1)}-\frac{1}{72} \sqrt{24420+55819 \sqrt{2}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{x-1}{2 x+1}}}{\sqrt[4]{2}}\right)+\frac{2}{9} \tan ^{-1}\left(\frac{2 \sqrt[4]{\frac{x-1}{2 x+1}}}{2 \sqrt{\frac{x-1}{2 x+1}}-1}\right)+\frac{1}{72} \sqrt{55819 \sqrt{2}-24420} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{x-1}{2 x+1}}}{\sqrt[4]{2}}\right)+\frac{10}{9} \tanh ^{-1}\left(\frac{2 \sqrt[4]{\frac{x-1}{2 x+1}}}{2 \sqrt{\frac{x-1}{2 x+1}}+1}\right)",1,"((3*((-1 + x)/(1 + 2*x))^(1/4)*(1 + 2*x))/(1 + x) + 4*ArcTan[1 - 2*((-1 + x)/(1 + 2*x))^(1/4)] - 4*ArcTan[1 + 2*((-1 + x)/(1 + 2*x))^(1/4)] + (27*(ArcTan[((-1 + x)/(2 + 4*x))^(1/4)] + ArcTanh[((-1 + x)/(2 + 4*x))^(1/4)]))/(2*2^(3/4)) - 18*((-1 + x)/(1 + 2*x))^(3/4)*Hypergeometric2F1[3/4, 2, 7/4, (-1 + x)/(2 + 4*x)] + 8*2^(1/4)*(1 - 3*Sqrt[2])*Log[2^(1/4) - ((-1 + x)/(1 + 2*x))^(1/4)] - (8*I)*2^(1/4)*(1 + 3*Sqrt[2])*Log[2^(1/4) - I*((-1 + x)/(1 + 2*x))^(1/4)] + (8*I)*2^(1/4)*(1 + 3*Sqrt[2])*Log[2^(1/4) + I*((-1 + x)/(1 + 2*x))^(1/4)] + 8*2^(1/4)*(-1 + 3*Sqrt[2])*Log[2^(1/4) + ((-1 + x)/(1 + 2*x))^(1/4)] - 10*Log[1 - 2*((-1 + x)/(1 + 2*x))^(1/4) + 2*Sqrt[(-1 + x)/(1 + 2*x)]] + 10*Log[1 + 2*((-1 + x)/(1 + 2*x))^(1/4) + 2*Sqrt[(-1 + x)/(1 + 2*x)]])/18","C",1
2584,1,33882,223,16.0991428,"\int \frac{\left(-q+p x^2\right) \sqrt{q^2+p^2 x^4}}{b x^3+a \left(q+p x^2\right)^3} \, dx","Integrate[((-q + p*x^2)*Sqrt[q^2 + p^2*x^4])/(b*x^3 + a*(q + p*x^2)^3),x]","\text{Result too large to show}","\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^6 a+6 \text{$\#$1}^4 a p q+8 \text{$\#$1}^3 b+12 \text{$\#$1}^2 a p^2 q^2+8 a p^3 q^3\&,\frac{\text{$\#$1}^4 \log \left(-\text{$\#$1} x+\sqrt{p^2 x^4+q^2}+p x^2+q\right)+\text{$\#$1}^4 (-\log (x))-4 \text{$\#$1}^2 p q \log \left(-\text{$\#$1} x+\sqrt{p^2 x^4+q^2}+p x^2+q\right)+4 \text{$\#$1}^2 p q \log (x)+4 p^2 q^2 \log \left(-\text{$\#$1} x+\sqrt{p^2 x^4+q^2}+p x^2+q\right)-4 p^2 q^2 \log (x)}{\text{$\#$1}^5 a+4 \text{$\#$1}^3 a p q+4 \text{$\#$1}^2 b+4 \text{$\#$1} a p^2 q^2}\&\right]",1,"Result too large to show","C",0
2585,1,33882,223,15.9610558,"\int \frac{\left(-q+p x^2\right) \sqrt{q^2+p^2 x^4}}{b x^3+a \left(q+p x^2\right)^3} \, dx","Integrate[((-q + p*x^2)*Sqrt[q^2 + p^2*x^4])/(b*x^3 + a*(q + p*x^2)^3),x]","\text{Result too large to show}","\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^6 a+6 \text{$\#$1}^4 a p q+8 \text{$\#$1}^3 b+12 \text{$\#$1}^2 a p^2 q^2+8 a p^3 q^3\&,\frac{\text{$\#$1}^4 \log \left(-\text{$\#$1} x+\sqrt{p^2 x^4+q^2}+p x^2+q\right)+\text{$\#$1}^4 (-\log (x))-4 \text{$\#$1}^2 p q \log \left(-\text{$\#$1} x+\sqrt{p^2 x^4+q^2}+p x^2+q\right)+4 \text{$\#$1}^2 p q \log (x)+4 p^2 q^2 \log \left(-\text{$\#$1} x+\sqrt{p^2 x^4+q^2}+p x^2+q\right)-4 p^2 q^2 \log (x)}{\text{$\#$1}^5 a+4 \text{$\#$1}^3 a p q+4 \text{$\#$1}^2 b+4 \text{$\#$1} a p^2 q^2}\&\right]",1,"Result too large to show","C",0
2586,0,0,223,0.5495079,"\int \frac{\left(-1+x^2\right)^2}{\left(1+x^2\right)^2 \sqrt{1+x^4} \sqrt{x^2+\sqrt{1+x^4}}} \, dx","Integrate[(-1 + x^2)^2/((1 + x^2)^2*Sqrt[1 + x^4]*Sqrt[x^2 + Sqrt[1 + x^4]]),x]","\int \frac{\left(-1+x^2\right)^2}{\left(1+x^2\right)^2 \sqrt{1+x^4} \sqrt{x^2+\sqrt{1+x^4}}} \, dx","\frac{\left(x^2+1\right) x^2+\sqrt{x^4+1} x^2}{x \left(x^2+1\right) \sqrt{\sqrt{x^4+1}+x^2}}+\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)-\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)-\sqrt{\sqrt{2}-1} \tanh ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{2}-1\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)",1,"Integrate[(-1 + x^2)^2/((1 + x^2)^2*Sqrt[1 + x^4]*Sqrt[x^2 + Sqrt[1 + x^4]]), x]","F",-1
2587,0,0,224,3.6104159,"\int \frac{-3+2 \left(1+k^2\right) x+\left(1+k^2\right) x^2-4 k^2 x^3+k^2 x^4}{\left(\left(1-x^2\right) \left(1-k^2 x^2\right)\right)^{2/3} \left(-1+d+(-1-2 d) x+\left(d+k^2\right) x^2+k^2 x^3\right)} \, dx","Integrate[(-3 + 2*(1 + k^2)*x + (1 + k^2)*x^2 - 4*k^2*x^3 + k^2*x^4)/(((1 - x^2)*(1 - k^2*x^2))^(2/3)*(-1 + d + (-1 - 2*d)*x + (d + k^2)*x^2 + k^2*x^3)),x]","\int \frac{-3+2 \left(1+k^2\right) x+\left(1+k^2\right) x^2-4 k^2 x^3+k^2 x^4}{\left(\left(1-x^2\right) \left(1-k^2 x^2\right)\right)^{2/3} \left(-1+d+(-1-2 d) x+\left(d+k^2\right) x^2+k^2 x^3\right)} \, dx","\frac{\log \left(\sqrt[3]{d} x-\sqrt[3]{d}+\sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}\right)}{d^{2/3}}-\frac{\log \left(d^{2/3} x^2-2 d^{2/3} x+d^{2/3}+\left(\sqrt[3]{d}-\sqrt[3]{d} x\right) \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}+\left(k^2 x^4+\left(-k^2-1\right) x^2+1\right)^{2/3}\right)}{2 d^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} x-\sqrt{3} \sqrt[3]{d}}{\sqrt[3]{d} x-\sqrt[3]{d}-2 \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}}\right)}{d^{2/3}}",1,"Integrate[(-3 + 2*(1 + k^2)*x + (1 + k^2)*x^2 - 4*k^2*x^3 + k^2*x^4)/(((1 - x^2)*(1 - k^2*x^2))^(2/3)*(-1 + d + (-1 - 2*d)*x + (d + k^2)*x^2 + k^2*x^3)), x]","F",-1
2588,0,0,224,1.9551179,"\int \frac{x^3 (-2+(1+k) x)}{((1-x) x (1-k x))^{2/3} \left(1-(2+2 k) x+\left(1+4 k+k^2\right) x^2-\left(2 k+2 k^2\right) x^3+\left(-b+k^2\right) x^4\right)} \, dx","Integrate[(x^3*(-2 + (1 + k)*x))/(((1 - x)*x*(1 - k*x))^(2/3)*(1 - (2 + 2*k)*x + (1 + 4*k + k^2)*x^2 - (2*k + 2*k^2)*x^3 + (-b + k^2)*x^4)),x]","\int \frac{x^3 (-2+(1+k) x)}{((1-x) x (1-k x))^{2/3} \left(1-(2+2 k) x+\left(1+4 k+k^2\right) x^2-\left(2 k+2 k^2\right) x^3+\left(-b+k^2\right) x^4\right)} \, dx","-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{b} x}{\sqrt[6]{b} x-2 \sqrt[3]{k x^3+(-k-1) x^2+x}}\right)}{2 b^{5/6}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{b} x}{\sqrt[6]{b} x+2 \sqrt[3]{k x^3+(-k-1) x^2+x}}\right)}{2 b^{5/6}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{b} x}{\sqrt[3]{k x^3+(-k-1) x^2+x}}\right)}{b^{5/6}}-\frac{\tanh ^{-1}\left(\frac{\frac{\left(k x^3+(-k-1) x^2+x\right)^{2/3}}{\sqrt[6]{b}}+\sqrt[6]{b} x^2}{x \sqrt[3]{k x^3+(-k-1) x^2+x}}\right)}{2 b^{5/6}}",1,"Integrate[(x^3*(-2 + (1 + k)*x))/(((1 - x)*x*(1 - k*x))^(2/3)*(1 - (2 + 2*k)*x + (1 + 4*k + k^2)*x^2 - (2*k + 2*k^2)*x^3 + (-b + k^2)*x^4)), x]","F",-1
2589,0,0,224,0.4181223,"\int \frac{\left(1+x^2\right)^2}{\left(-1+x^2\right)^2 \sqrt{1+x^4} \sqrt{x^2+\sqrt{1+x^4}}} \, dx","Integrate[(1 + x^2)^2/((-1 + x^2)^2*Sqrt[1 + x^4]*Sqrt[x^2 + Sqrt[1 + x^4]]),x]","\int \frac{\left(1+x^2\right)^2}{\left(-1+x^2\right)^2 \sqrt{1+x^4} \sqrt{x^2+\sqrt{1+x^4}}} \, dx","\frac{-\left(\left(x^2-1\right) x^2\right)-\sqrt{x^4+1} x^2}{x \left(x^2-1\right) \sqrt{\sqrt{x^4+1}+x^2}}+\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)-\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{2}-1\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)+\sqrt{\sqrt{2}-1} \tanh ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)",1,"Integrate[(1 + x^2)^2/((-1 + x^2)^2*Sqrt[1 + x^4]*Sqrt[x^2 + Sqrt[1 + x^4]]), x]","F",-1
2590,0,0,224,0.4700116,"\int \frac{\left(-1+x^2\right)^2 \sqrt{x^2+\sqrt{1+x^4}}}{\left(1+x^2\right)^2 \sqrt{1+x^4}} \, dx","Integrate[((-1 + x^2)^2*Sqrt[x^2 + Sqrt[1 + x^4]])/((1 + x^2)^2*Sqrt[1 + x^4]),x]","\int \frac{\left(-1+x^2\right)^2 \sqrt{x^2+\sqrt{1+x^4}}}{\left(1+x^2\right)^2 \sqrt{1+x^4}} \, dx","\frac{-\left(\left(x^2-1\right) x^2\right)-\sqrt{x^4+1} x^2}{x \left(x^2+1\right) \sqrt{\sqrt{x^4+1}+x^2}}+\sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)+\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)-\sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{2}-1\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)",1,"Integrate[((-1 + x^2)^2*Sqrt[x^2 + Sqrt[1 + x^4]])/((1 + x^2)^2*Sqrt[1 + x^4]), x]","F",-1
2591,1,257,224,0.7074036,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{1+\sqrt{1+\sqrt{1+x}}}} \, dx","Integrate[(-1 + x^2)/((1 + x^2)*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]),x]","8 \left(\frac{1}{8} \text{RootSum}\left[2 \text{$\#$1}^{16}-8 \text{$\#$1}^{12}+8 \text{$\#$1}^{10}+14 \text{$\#$1}^8-32 \text{$\#$1}^6+24 \text{$\#$1}^4-8 \text{$\#$1}^2+1\&,\frac{2 \text{$\#$1}^{11} \log \left(\frac{1}{\sqrt{\sqrt{\sqrt{x+1}+1}+1}}-\text{$\#$1}\right)-3 \text{$\#$1}^9 \log \left(\frac{1}{\sqrt{\sqrt{\sqrt{x+1}+1}+1}}-\text{$\#$1}\right)+\text{$\#$1}^7 \log \left(\frac{1}{\sqrt{\sqrt{\sqrt{x+1}+1}+1}}-\text{$\#$1}\right)}{2 \text{$\#$1}^{14}-6 \text{$\#$1}^{10}+5 \text{$\#$1}^8+7 \text{$\#$1}^6-12 \text{$\#$1}^4+6 \text{$\#$1}^2-1}\&\right]+\frac{1}{7} \left(\sqrt{\sqrt{x+1}+1}+1\right)^{7/2}-\frac{3}{5} \left(\sqrt{\sqrt{x+1}+1}+1\right)^{5/2}+\frac{2}{3} \left(\sqrt{\sqrt{x+1}+1}+1\right)^{3/2}\right)","-\text{RootSum}\left[\text{$\#$1}^{16}-8 \text{$\#$1}^{14}+24 \text{$\#$1}^{12}-32 \text{$\#$1}^{10}+14 \text{$\#$1}^8+8 \text{$\#$1}^6-8 \text{$\#$1}^4+2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x+1}+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^9-4 \text{$\#$1}^7+4 \text{$\#$1}^5-\text{$\#$1}}\&\right]+\sqrt{x+1} \left(\frac{8}{7} \sqrt{\sqrt{x+1}+1} \sqrt{\sqrt{\sqrt{x+1}+1}+1}-\frac{48}{35} \sqrt{\sqrt{\sqrt{x+1}+1}+1}\right)+\frac{32}{105} \sqrt{\sqrt{x+1}+1} \sqrt{\sqrt{\sqrt{x+1}+1}+1}+\frac{32}{105} \sqrt{\sqrt{\sqrt{x+1}+1}+1}",1,"8*((2*(1 + Sqrt[1 + Sqrt[1 + x]])^(3/2))/3 - (3*(1 + Sqrt[1 + Sqrt[1 + x]])^(5/2))/5 + (1 + Sqrt[1 + Sqrt[1 + x]])^(7/2)/7 + RootSum[1 - 8*#1^2 + 24*#1^4 - 32*#1^6 + 14*#1^8 + 8*#1^10 - 8*#1^12 + 2*#1^16 & , (Log[1/Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]] - #1]*#1^7 - 3*Log[1/Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]] - #1]*#1^9 + 2*Log[1/Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]] - #1]*#1^11)/(-1 + 6*#1^2 - 12*#1^4 + 7*#1^6 + 5*#1^8 - 6*#1^10 + 2*#1^14) & ]/8)","A",1
2592,1,257,224,0.4445121,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{1+\sqrt{1+\sqrt{1+x}}}} \, dx","Integrate[(-1 + x^2)/((1 + x^2)*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]),x]","8 \left(\frac{1}{8} \text{RootSum}\left[2 \text{$\#$1}^{16}-8 \text{$\#$1}^{12}+8 \text{$\#$1}^{10}+14 \text{$\#$1}^8-32 \text{$\#$1}^6+24 \text{$\#$1}^4-8 \text{$\#$1}^2+1\&,\frac{2 \text{$\#$1}^{11} \log \left(\frac{1}{\sqrt{\sqrt{\sqrt{x+1}+1}+1}}-\text{$\#$1}\right)-3 \text{$\#$1}^9 \log \left(\frac{1}{\sqrt{\sqrt{\sqrt{x+1}+1}+1}}-\text{$\#$1}\right)+\text{$\#$1}^7 \log \left(\frac{1}{\sqrt{\sqrt{\sqrt{x+1}+1}+1}}-\text{$\#$1}\right)}{2 \text{$\#$1}^{14}-6 \text{$\#$1}^{10}+5 \text{$\#$1}^8+7 \text{$\#$1}^6-12 \text{$\#$1}^4+6 \text{$\#$1}^2-1}\&\right]+\frac{1}{7} \left(\sqrt{\sqrt{x+1}+1}+1\right)^{7/2}-\frac{3}{5} \left(\sqrt{\sqrt{x+1}+1}+1\right)^{5/2}+\frac{2}{3} \left(\sqrt{\sqrt{x+1}+1}+1\right)^{3/2}\right)","-\text{RootSum}\left[\text{$\#$1}^{16}-8 \text{$\#$1}^{14}+24 \text{$\#$1}^{12}-32 \text{$\#$1}^{10}+14 \text{$\#$1}^8+8 \text{$\#$1}^6-8 \text{$\#$1}^4+2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x+1}+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^9-4 \text{$\#$1}^7+4 \text{$\#$1}^5-\text{$\#$1}}\&\right]+\sqrt{x+1} \left(\frac{8}{7} \sqrt{\sqrt{x+1}+1} \sqrt{\sqrt{\sqrt{x+1}+1}+1}-\frac{48}{35} \sqrt{\sqrt{\sqrt{x+1}+1}+1}\right)+\frac{32}{105} \sqrt{\sqrt{x+1}+1} \sqrt{\sqrt{\sqrt{x+1}+1}+1}+\frac{32}{105} \sqrt{\sqrt{\sqrt{x+1}+1}+1}",1,"8*((2*(1 + Sqrt[1 + Sqrt[1 + x]])^(3/2))/3 - (3*(1 + Sqrt[1 + Sqrt[1 + x]])^(5/2))/5 + (1 + Sqrt[1 + Sqrt[1 + x]])^(7/2)/7 + RootSum[1 - 8*#1^2 + 24*#1^4 - 32*#1^6 + 14*#1^8 + 8*#1^10 - 8*#1^12 + 2*#1^16 & , (Log[1/Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]] - #1]*#1^7 - 3*Log[1/Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]] - #1]*#1^9 + 2*Log[1/Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]] - #1]*#1^11)/(-1 + 6*#1^2 - 12*#1^4 + 7*#1^6 + 5*#1^8 - 6*#1^10 + 2*#1^14) & ]/8)","A",1
2593,0,0,225,1.6270665,"\int \frac{(-2+x) \sqrt[3]{x-x^2+x^3}}{(-1+x) \left(-1+x+x^2\right)} \, dx","Integrate[((-2 + x)*(x - x^2 + x^3)^(1/3))/((-1 + x)*(-1 + x + x^2)),x]","\int \frac{(-2+x) \sqrt[3]{x-x^2+x^3}}{(-1+x) \left(-1+x+x^2\right)} \, dx","-\log \left(\sqrt[3]{x^3-x^2+x}-x\right)+\sqrt[3]{2} \log \left(2^{2/3} \sqrt[3]{x^3-x^2+x}-2 x\right)+\frac{1}{2} \log \left(x^2+\sqrt[3]{x^3-x^2+x} x+\left(x^3-x^2+x\right)^{2/3}\right)-\frac{\log \left(2 x^2+2^{2/3} \sqrt[3]{x^3-x^2+x} x+\sqrt[3]{2} \left(x^3-x^2+x\right)^{2/3}\right)}{2^{2/3}}-\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-x^2+x}+x}\right)+\sqrt[3]{2} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^3-x^2+x}+x}\right)",1,"Integrate[((-2 + x)*(x - x^2 + x^3)^(1/3))/((-1 + x)*(-1 + x + x^2)), x]","F",-1
2594,1,84,225,0.0790214,"\int \frac{\left(1+x^2\right) \sqrt[3]{x^2+x^3}}{-1+x^2} \, dx","Integrate[((1 + x^2)*(x^2 + x^3)^(1/3))/(-1 + x^2),x]","\frac{3 \sqrt[3]{x^2 (x+1)} \left(x (x+1) \, _2F_1\left(-\frac{1}{3},\frac{5}{3};\frac{8}{3};-x\right)+5 (x+1) \, _2F_1\left(\frac{2}{3},\frac{2}{3};\frac{5}{3};-x\right)-5 \sqrt[3]{x+1} \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{2 x}{x+1}\right)\right)}{5 (x+1)^{4/3}}","\frac{1}{6} \sqrt[3]{x^3+x^2} (3 x+1)-\frac{17}{9} \log \left(\sqrt[3]{x^3+x^2}-x\right)+\sqrt[3]{2} \log \left(2^{2/3} \sqrt[3]{x^3+x^2}-2 x\right)+\frac{17}{18} \log \left(x^2+\sqrt[3]{x^3+x^2} x+\left(x^3+x^2\right)^{2/3}\right)-\frac{\log \left(2 x^2+2^{2/3} \sqrt[3]{x^3+x^2} x+\sqrt[3]{2} \left(x^3+x^2\right)^{2/3}\right)}{2^{2/3}}-\frac{17 \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+x^2}+x}\right)}{3 \sqrt{3}}+\sqrt[3]{2} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^3+x^2}+x}\right)",1,"(3*(x^2*(1 + x))^(1/3)*(x*(1 + x)*Hypergeometric2F1[-1/3, 5/3, 8/3, -x] + 5*(1 + x)*Hypergeometric2F1[2/3, 2/3, 5/3, -x] - 5*(1 + x)^(1/3)*Hypergeometric2F1[2/3, 1, 5/3, (2*x)/(1 + x)]))/(5*(1 + x)^(4/3))","C",1
2595,1,158,225,0.1848275,"\int \frac{-b+a x}{x \sqrt[3]{-b^3+a^3 x^3}} \, dx","Integrate[(-b + a*x)/(x*(-b^3 + a^3*x^3)^(1/3)),x]","\frac{1}{6} \left(-2 \log \left(1-\frac{a x}{\sqrt[3]{a^3 x^3-b^3}}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 a x}{\sqrt[3]{a^3 x^3-b^3}}+1}{\sqrt{3}}\right)-\frac{3 \left(a^3 x^3-b^3\right)^{2/3} \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};1-\frac{a^3 x^3}{b^3}\right)}{b^2}+\log \left(\frac{a x}{\sqrt[3]{a^3 x^3-b^3}}+\frac{a^2 x^2}{\left(a^3 x^3-b^3\right)^{2/3}}+1\right)\right)","-\frac{\tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a^3 x^3-b^3}}{\sqrt{3} a}+\frac{x}{\sqrt{3}}}{x}\right)}{\sqrt{3}}+\frac{\tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{a^3 x^3-b^3}}{\sqrt{3} b}\right)}{\sqrt{3}}-\frac{2}{3} \tanh ^{-1}\left(\frac{-a x-b}{2 \sqrt[3]{a^3 x^3-b^3}-a x+b}\right)-\frac{1}{6} \log \left(-b \sqrt[3]{a^3 x^3-b^3}+\left(a^3 x^3-b^3\right)^{2/3}+b^2\right)+\frac{1}{6} \log \left(a x \sqrt[3]{a^3 x^3-b^3}+\left(a^3 x^3-b^3\right)^{2/3}+a^2 x^2\right)",1,"(2*Sqrt[3]*ArcTan[(1 + (2*a*x)/(-b^3 + a^3*x^3)^(1/3))/Sqrt[3]] - (3*(-b^3 + a^3*x^3)^(2/3)*Hypergeometric2F1[2/3, 1, 5/3, 1 - (a^3*x^3)/b^3])/b^2 - 2*Log[1 - (a*x)/(-b^3 + a^3*x^3)^(1/3)] + Log[1 + (a^2*x^2)/(-b^3 + a^3*x^3)^(2/3) + (a*x)/(-b^3 + a^3*x^3)^(1/3)])/6","C",1
2596,0,0,225,2.5246385,"\int \frac{\left(-2+x^3\right) \sqrt[3]{x+2 x^3+x^4}}{\left(1+x^3\right) \left(1+x^2+x^3\right)} \, dx","Integrate[((-2 + x^3)*(x + 2*x^3 + x^4)^(1/3))/((1 + x^3)*(1 + x^2 + x^3)),x]","\int \frac{\left(-2+x^3\right) \sqrt[3]{x+2 x^3+x^4}}{\left(1+x^3\right) \left(1+x^2+x^3\right)} \, dx","-\log \left(\sqrt[3]{x^4+2 x^3+x}-x\right)+\sqrt[3]{2} \log \left(2^{2/3} \sqrt[3]{x^4+2 x^3+x}-2 x\right)-\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^4+2 x^3+x}+x}\right)+\sqrt[3]{2} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^4+2 x^3+x}+x}\right)+\frac{1}{2} \log \left(x^2+\sqrt[3]{x^4+2 x^3+x} x+\left(x^4+2 x^3+x\right)^{2/3}\right)-\frac{\log \left(2 x^2+2^{2/3} \sqrt[3]{x^4+2 x^3+x} x+\sqrt[3]{2} \left(x^4+2 x^3+x\right)^{2/3}\right)}{2^{2/3}}",1,"Integrate[((-2 + x^3)*(x + 2*x^3 + x^4)^(1/3))/((1 + x^3)*(1 + x^2 + x^3)), x]","F",-1
2597,1,201,225,0.1829814,"\int \frac{x^4}{\sqrt[4]{-1+x^4} \left(1-2 x^4+2 x^8\right)} \, dx","Integrate[x^4/((-1 + x^4)^(1/4)*(1 - 2*x^4 + 2*x^8)),x]","\left(\frac{1}{16}-\frac{i}{16}\right) (-1)^{5/8} \left((2+2 i) \tan ^{-1}\left(\frac{(-1)^{7/8} x}{\sqrt[4]{x^4-1}}\right)+(2+2 i) \tanh ^{-1}\left(\frac{(-1)^{7/8} x}{\sqrt[4]{x^4-1}}\right)+\sqrt[4]{-1} \left(2 \tan ^{-1}\left(1-\frac{(-1)^{7/8} \sqrt{2} x}{\sqrt[4]{x^4-1}}\right)-2 \tan ^{-1}\left(\frac{(-1)^{7/8} \sqrt{2} x}{\sqrt[4]{x^4-1}}+1\right)-\log \left(-\frac{\sqrt[8]{-1} \sqrt{2} x}{\sqrt[4]{x^4-1}}+\frac{x^2}{\sqrt{x^4-1}}+\sqrt[4]{-1}\right)+\log \left(\frac{\sqrt[8]{-1} \sqrt{2} x}{\sqrt[4]{x^4-1}}+\frac{x^2}{\sqrt{x^4-1}}+\sqrt[4]{-1}\right)\right)\right)","-\frac{1}{8} \sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}} x \sqrt[4]{x^4-1}}{\sqrt{x^4-1}-x^2}\right)+\frac{1}{8} \sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}} x \sqrt[4]{x^4-1}}{\sqrt{x^4-1}-x^2}\right)-\frac{1}{8} \sqrt{2+\sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt{2-\sqrt{2}} x \sqrt[4]{x^4-1}}{\sqrt{x^4-1}+x^2}\right)+\frac{1}{8} \sqrt{2-\sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt{2+\sqrt{2}} x \sqrt[4]{x^4-1}}{\sqrt{x^4-1}+x^2}\right)",1,"(1/16 - I/16)*(-1)^(5/8)*((2 + 2*I)*ArcTan[((-1)^(7/8)*x)/(-1 + x^4)^(1/4)] + (2 + 2*I)*ArcTanh[((-1)^(7/8)*x)/(-1 + x^4)^(1/4)] + (-1)^(1/4)*(2*ArcTan[1 - ((-1)^(7/8)*Sqrt[2]*x)/(-1 + x^4)^(1/4)] - 2*ArcTan[1 + ((-1)^(7/8)*Sqrt[2]*x)/(-1 + x^4)^(1/4)] - Log[(-1)^(1/4) + x^2/Sqrt[-1 + x^4] - ((-1)^(1/8)*Sqrt[2]*x)/(-1 + x^4)^(1/4)] + Log[(-1)^(1/4) + x^2/Sqrt[-1 + x^4] + ((-1)^(1/8)*Sqrt[2]*x)/(-1 + x^4)^(1/4)]))","C",1
2598,0,0,225,0.0441885,"\int \frac{\left(-1+x^4\right)^{3/4}}{1-2 x^4+2 x^8} \, dx","Integrate[(-1 + x^4)^(3/4)/(1 - 2*x^4 + 2*x^8),x]","\int \frac{\left(-1+x^4\right)^{3/4}}{1-2 x^4+2 x^8} \, dx","-\frac{1}{8} \sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}} x \sqrt[4]{x^4-1}}{\sqrt{x^4-1}-x^2}\right)-\frac{1}{8} \sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}} x \sqrt[4]{x^4-1}}{\sqrt{x^4-1}-x^2}\right)-\frac{1}{8} \sqrt{2-\sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt{2-\sqrt{2}} x \sqrt[4]{x^4-1}}{\sqrt{x^4-1}+x^2}\right)-\frac{1}{8} \sqrt{2+\sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt{2+\sqrt{2}} x \sqrt[4]{x^4-1}}{\sqrt{x^4-1}+x^2}\right)",1,"Integrate[(-1 + x^4)^(3/4)/(1 - 2*x^4 + 2*x^8), x]","F",-1
2599,1,201,225,0.1733955,"\int \frac{x^4}{\sqrt[4]{1+x^4} \left(1+2 x^4+2 x^8\right)} \, dx","Integrate[x^4/((1 + x^4)^(1/4)*(1 + 2*x^4 + 2*x^8)),x]","\left(-\frac{1}{16}+\frac{i}{16}\right) (-1)^{5/8} \left((2+2 i) \tan ^{-1}\left(\frac{(-1)^{7/8} x}{\sqrt[4]{x^4+1}}\right)+(2+2 i) \tanh ^{-1}\left(\frac{(-1)^{7/8} x}{\sqrt[4]{x^4+1}}\right)+\sqrt[4]{-1} \left(2 \tan ^{-1}\left(1-\frac{(-1)^{7/8} \sqrt{2} x}{\sqrt[4]{x^4+1}}\right)-2 \tan ^{-1}\left(\frac{(-1)^{7/8} \sqrt{2} x}{\sqrt[4]{x^4+1}}+1\right)-\log \left(-\frac{\sqrt[8]{-1} \sqrt{2} x}{\sqrt[4]{x^4+1}}+\frac{x^2}{\sqrt{x^4+1}}+\sqrt[4]{-1}\right)+\log \left(\frac{\sqrt[8]{-1} \sqrt{2} x}{\sqrt[4]{x^4+1}}+\frac{x^2}{\sqrt{x^4+1}}+\sqrt[4]{-1}\right)\right)\right)","\frac{1}{8} \sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}} x \sqrt[4]{x^4+1}}{\sqrt{x^4+1}-x^2}\right)-\frac{1}{8} \sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}} x \sqrt[4]{x^4+1}}{\sqrt{x^4+1}-x^2}\right)+\frac{1}{8} \sqrt{2+\sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt{2-\sqrt{2}} x \sqrt[4]{x^4+1}}{\sqrt{x^4+1}+x^2}\right)-\frac{1}{8} \sqrt{2-\sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt{2+\sqrt{2}} x \sqrt[4]{x^4+1}}{\sqrt{x^4+1}+x^2}\right)",1,"(-1/16 + I/16)*(-1)^(5/8)*((2 + 2*I)*ArcTan[((-1)^(7/8)*x)/(1 + x^4)^(1/4)] + (2 + 2*I)*ArcTanh[((-1)^(7/8)*x)/(1 + x^4)^(1/4)] + (-1)^(1/4)*(2*ArcTan[1 - ((-1)^(7/8)*Sqrt[2]*x)/(1 + x^4)^(1/4)] - 2*ArcTan[1 + ((-1)^(7/8)*Sqrt[2]*x)/(1 + x^4)^(1/4)] - Log[(-1)^(1/4) + x^2/Sqrt[1 + x^4] - ((-1)^(1/8)*Sqrt[2]*x)/(1 + x^4)^(1/4)] + Log[(-1)^(1/4) + x^2/Sqrt[1 + x^4] + ((-1)^(1/8)*Sqrt[2]*x)/(1 + x^4)^(1/4)]))","C",1
2600,0,0,225,0.0426615,"\int \frac{\left(1+x^4\right)^{3/4}}{1+2 x^4+2 x^8} \, dx","Integrate[(1 + x^4)^(3/4)/(1 + 2*x^4 + 2*x^8),x]","\int \frac{\left(1+x^4\right)^{3/4}}{1+2 x^4+2 x^8} \, dx","\frac{1}{8} \sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}} x \sqrt[4]{x^4+1}}{\sqrt{x^4+1}-x^2}\right)+\frac{1}{8} \sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}} x \sqrt[4]{x^4+1}}{\sqrt{x^4+1}-x^2}\right)+\frac{1}{8} \sqrt{2-\sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt{2-\sqrt{2}} x \sqrt[4]{x^4+1}}{\sqrt{x^4+1}+x^2}\right)+\frac{1}{8} \sqrt{2+\sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt{2+\sqrt{2}} x \sqrt[4]{x^4+1}}{\sqrt{x^4+1}+x^2}\right)",1,"Integrate[(1 + x^4)^(3/4)/(1 + 2*x^4 + 2*x^8), x]","F",-1
2601,0,0,225,1.476418,"\int \frac{x^2 \sqrt{-b x+a^2 x^2}}{\left(a x^2+x \sqrt{-b x+a^2 x^2}\right)^{3/2}} \, dx","Integrate[(x^2*Sqrt[-(b*x) + a^2*x^2])/(a*x^2 + x*Sqrt[-(b*x) + a^2*x^2])^(3/2),x]","\int \frac{x^2 \sqrt{-b x+a^2 x^2}}{\left(a x^2+x \sqrt{-b x+a^2 x^2}\right)^{3/2}} \, dx","\frac{\sqrt{a^2 x^2-b x} \sqrt{x \left(\sqrt{a^2 x^2-b x}+a x\right)} \left(96 a^4 x^2-104 a^2 b x-15 b^2\right)}{120 a^2 b^2 x}+\sqrt{x \left(\sqrt{a^2 x^2-b x}+a x\right)} \left(\frac{\sqrt{b} \sqrt{\sqrt{a^2 x^2-b x}-a x} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{\sqrt{a^2 x^2-b x}-a x}}{\sqrt{b}}\right)}{8 \sqrt{2} a^{5/2} x}+\frac{-96 a^4 x^2+152 a^2 b x+5 b^2}{120 a b^2}\right)",1,"Integrate[(x^2*Sqrt[-(b*x) + a^2*x^2])/(a*x^2 + x*Sqrt[-(b*x) + a^2*x^2])^(3/2), x]","F",-1
2602,0,0,225,0.3598611,"\int \frac{\sqrt{x^2+\sqrt{1+x^4}}}{(1+x) \sqrt{1+x^4}} \, dx","Integrate[Sqrt[x^2 + Sqrt[1 + x^4]]/((1 + x)*Sqrt[1 + x^4]),x]","\int \frac{\sqrt{x^2+\sqrt{1+x^4}}}{(1+x) \sqrt{1+x^4}} \, dx","\sqrt{\frac{1}{2} \left(\sqrt{2}-1\right)} \tan ^{-1}\left(\frac{\sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{\sqrt{2}-1}}\right)-\sqrt{\frac{1}{2} \left(\sqrt{2}-1\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{2}-1\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)-\sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{1+\sqrt{2}}}\right)+\sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tanh ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)",1,"Integrate[Sqrt[x^2 + Sqrt[1 + x^4]]/((1 + x)*Sqrt[1 + x^4]), x]","F",-1
2603,1,230,226,0.6385635,"\int \frac{-b+a x^2}{\left(-b+2 a x^3\right) \sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Integrate[(-b + a*x^2)/((-b + 2*a*x^3)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","\frac{x \left(\left(2 \sqrt[3]{b}-\sqrt[3]{2} \sqrt[3]{a}\right) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{x a^3+\sqrt[3]{2} b^{5/3} x \sqrt[3]{a}}{x a^3+b^2}\right)+\left(\sqrt[3]{-2} \sqrt[3]{a}+2 \sqrt[3]{b}\right) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\sqrt[3]{a} \left(a^{8/3}-\sqrt[3]{-2} b^{5/3}\right) x}{x a^3+b^2}\right)+\left(2 \sqrt[3]{b}-(-1)^{2/3} \sqrt[3]{2} \sqrt[3]{a}\right) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\sqrt[3]{a} \left(a^{8/3}+(-1)^{2/3} \sqrt[3]{2} b^{5/3}\right) x}{x a^3+b^2}\right)\right)}{2 \sqrt[3]{b} \sqrt[3]{x^2 \left(a^3 x+b^2\right)}}","-\frac{1}{3} \text{RootSum}\left[-\text{$\#$1}^9+3 \text{$\#$1}^6 a^3-3 \text{$\#$1}^3 a^6+a^9+2 a b^5\&,\frac{\text{$\#$1}^6 \log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)-\text{$\#$1}^6 \log (x)-2 \text{$\#$1}^3 a^3 \log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)+2 \text{$\#$1}^3 a^3 \log (x)-a b^3 \log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)+a^6 \log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)+a^6 (-\log (x))+a b^3 \log (x)}{\text{$\#$1}^7-2 \text{$\#$1}^4 a^3+\text{$\#$1} a^6}\&\right]",1,"(x*(((-2)^(1/3)*a^(1/3) + 2*b^(1/3))*Hypergeometric2F1[1/3, 1, 4/3, (a^(1/3)*(a^(8/3) - (-2)^(1/3)*b^(5/3))*x)/(b^2 + a^3*x)] + (-((-1)^(2/3)*2^(1/3)*a^(1/3)) + 2*b^(1/3))*Hypergeometric2F1[1/3, 1, 4/3, (a^(1/3)*(a^(8/3) + (-1)^(2/3)*2^(1/3)*b^(5/3))*x)/(b^2 + a^3*x)] + (-(2^(1/3)*a^(1/3)) + 2*b^(1/3))*Hypergeometric2F1[1/3, 1, 4/3, (a^3*x + 2^(1/3)*a^(1/3)*b^(5/3)*x)/(b^2 + a^3*x)]))/(2*b^(1/3)*(x^2*(b^2 + a^3*x))^(1/3))","A",1
2604,1,230,226,0.1296906,"\int \frac{-b+a x^2}{\left(-b+2 a x^3\right) \sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Integrate[(-b + a*x^2)/((-b + 2*a*x^3)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","\frac{x \left(\left(2 \sqrt[3]{b}-\sqrt[3]{2} \sqrt[3]{a}\right) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{x a^3+\sqrt[3]{2} b^{5/3} x \sqrt[3]{a}}{x a^3+b^2}\right)+\left(\sqrt[3]{-2} \sqrt[3]{a}+2 \sqrt[3]{b}\right) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\sqrt[3]{a} \left(a^{8/3}-\sqrt[3]{-2} b^{5/3}\right) x}{x a^3+b^2}\right)+\left(2 \sqrt[3]{b}-(-1)^{2/3} \sqrt[3]{2} \sqrt[3]{a}\right) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\sqrt[3]{a} \left(a^{8/3}+(-1)^{2/3} \sqrt[3]{2} b^{5/3}\right) x}{x a^3+b^2}\right)\right)}{2 \sqrt[3]{b} \sqrt[3]{x^2 \left(a^3 x+b^2\right)}}","-\frac{1}{3} \text{RootSum}\left[-\text{$\#$1}^9+3 \text{$\#$1}^6 a^3-3 \text{$\#$1}^3 a^6+a^9+2 a b^5\&,\frac{\text{$\#$1}^6 \log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)-\text{$\#$1}^6 \log (x)-2 \text{$\#$1}^3 a^3 \log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)+2 \text{$\#$1}^3 a^3 \log (x)-a b^3 \log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)+a^6 \log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)+a^6 (-\log (x))+a b^3 \log (x)}{\text{$\#$1}^7-2 \text{$\#$1}^4 a^3+\text{$\#$1} a^6}\&\right]",1,"(x*(((-2)^(1/3)*a^(1/3) + 2*b^(1/3))*Hypergeometric2F1[1/3, 1, 4/3, (a^(1/3)*(a^(8/3) - (-2)^(1/3)*b^(5/3))*x)/(b^2 + a^3*x)] + (-((-1)^(2/3)*2^(1/3)*a^(1/3)) + 2*b^(1/3))*Hypergeometric2F1[1/3, 1, 4/3, (a^(1/3)*(a^(8/3) + (-1)^(2/3)*2^(1/3)*b^(5/3))*x)/(b^2 + a^3*x)] + (-(2^(1/3)*a^(1/3)) + 2*b^(1/3))*Hypergeometric2F1[1/3, 1, 4/3, (a^3*x + 2^(1/3)*a^(1/3)*b^(5/3)*x)/(b^2 + a^3*x)]))/(2*b^(1/3)*(x^2*(b^2 + a^3*x))^(1/3))","A",1
2605,0,0,226,4.2419345,"\int \frac{2 a b x-3 a x^2+x^3}{\sqrt[3]{x^2 (-a+x) (-b+x)} \left(-a^2+2 a x-(1+b d) x^2+d x^3\right)} \, dx","Integrate[(2*a*b*x - 3*a*x^2 + x^3)/((x^2*(-a + x)*(-b + x))^(1/3)*(-a^2 + 2*a*x - (1 + b*d)*x^2 + d*x^3)),x]","\int \frac{2 a b x-3 a x^2+x^3}{\sqrt[3]{x^2 (-a+x) (-b+x)} \left(-a^2+2 a x-(1+b d) x^2+d x^3\right)} \, dx","-\frac{\log \left(a^2+d^{2/3} \left(x^3 (-a-b)+a b x^2+x^4\right)^{2/3}+\sqrt[3]{x^3 (-a-b)+a b x^2+x^4} \left(\sqrt[3]{d} x-a \sqrt[3]{d}\right)-2 a x+x^2\right)}{2 d^{2/3}}+\frac{\log \left(\sqrt[3]{d} \sqrt[3]{x^3 (-a-b)+a b x^2+x^4}+a-x\right)}{d^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} \sqrt[3]{x^3 (-a-b)+a b x^2+x^4}}{\sqrt[3]{d} \sqrt[3]{x^3 (-a-b)+a b x^2+x^4}-2 a+2 x}\right)}{d^{2/3}}",1,"Integrate[(2*a*b*x - 3*a*x^2 + x^3)/((x^2*(-a + x)*(-b + x))^(1/3)*(-a^2 + 2*a*x - (1 + b*d)*x^2 + d*x^3)), x]","F",-1
2606,0,0,226,12.421021,"\int \frac{\left(-2+k^2\right) x+k^2 x^3}{\sqrt[3]{\left(1-x^2\right) \left(1-k^2 x^2\right)} \left(1-d+\left(-2+d k^2\right) x^2+x^4\right)} \, dx","Integrate[((-2 + k^2)*x + k^2*x^3)/(((1 - x^2)*(1 - k^2*x^2))^(1/3)*(1 - d + (-2 + d*k^2)*x^2 + x^4)),x]","\int \frac{\left(-2+k^2\right) x+k^2 x^3}{\sqrt[3]{\left(1-x^2\right) \left(1-k^2 x^2\right)} \left(1-d+\left(-2+d k^2\right) x^2+x^4\right)} \, dx","\frac{\log \left(\sqrt[3]{d} \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}+x^2-1\right)}{2 d^{2/3}}-\frac{\log \left(d^{2/3} \left(k^2 x^4+\left(-k^2-1\right) x^2+1\right)^{2/3}+\left(\sqrt[3]{d}-\sqrt[3]{d} x^2\right) \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}+x^4-2 x^2+1\right)}{4 d^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}}{\sqrt[3]{d} \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}-2 x^2+2}\right)}{2 d^{2/3}}",1,"Integrate[((-2 + k^2)*x + k^2*x^3)/(((1 - x^2)*(1 - k^2*x^2))^(1/3)*(1 - d + (-2 + d*k^2)*x^2 + x^4)), x]","F",-1
2607,1,147,226,0.2482132,"\int \frac{(1+2 x) \sqrt[4]{x^3+x^4}}{-1+x+x^2} \, dx","Integrate[((1 + 2*x)*(x^3 + x^4)^(1/4))/(-1 + x + x^2),x]","\frac{2 \sqrt[4]{x^3 (x+1)} \left(4 (x+1) \, _2F_1\left(-\frac{1}{4},\frac{3}{4};\frac{7}{4};-x\right)-2 (x+1) \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};-x\right)+\sqrt[4]{x+1} \left(\left(\sqrt{5}-1\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{\left(-1+\sqrt{5}\right) x}{\left(1+\sqrt{5}\right) (x+1)}\right)-\left(1+\sqrt{5}\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{\left(1+\sqrt{5}\right) x}{\left(-1+\sqrt{5}\right) (x+1)}\right)\right)\right)}{3 (x+1)^{5/4}}","2 \sqrt[4]{x^4+x^3}+\tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+x^3}}\right)-\sqrt{2 \left(1+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}} x}{\sqrt[4]{x^4+x^3}}\right)+\sqrt{2 \left(\sqrt{5}-1\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{1}{2}+\frac{\sqrt{5}}{2}} x}{\sqrt[4]{x^4+x^3}}\right)-\tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+x^3}}\right)+\sqrt{2 \left(1+\sqrt{5}\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}} x}{\sqrt[4]{x^4+x^3}}\right)-\sqrt{2 \left(\sqrt{5}-1\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{2}+\frac{\sqrt{5}}{2}} x}{\sqrt[4]{x^4+x^3}}\right)",1,"(2*(x^3*(1 + x))^(1/4)*(4*(1 + x)*Hypergeometric2F1[-1/4, 3/4, 7/4, -x] - 2*(1 + x)*Hypergeometric2F1[3/4, 3/4, 7/4, -x] + (1 + x)^(1/4)*((-1 + Sqrt[5])*Hypergeometric2F1[3/4, 1, 7/4, ((-1 + Sqrt[5])*x)/((1 + Sqrt[5])*(1 + x))] - (1 + Sqrt[5])*Hypergeometric2F1[3/4, 1, 7/4, ((1 + Sqrt[5])*x)/((-1 + Sqrt[5])*(1 + x))])))/(3*(1 + x)^(5/4))","C",1
2608,0,0,226,1.8332334,"\int \frac{\left(-1+2 k^2\right) x-2 k^4 x^3+k^4 x^5}{\left(\left(1-x^2\right) \left(1-k^2 x^2\right)\right)^{2/3} \left(-1+d+\left(1-2 d k^2\right) x^2+d k^4 x^4\right)} \, dx","Integrate[((-1 + 2*k^2)*x - 2*k^4*x^3 + k^4*x^5)/(((1 - x^2)*(1 - k^2*x^2))^(2/3)*(-1 + d + (1 - 2*d*k^2)*x^2 + d*k^4*x^4)),x]","\int \frac{\left(-1+2 k^2\right) x-2 k^4 x^3+k^4 x^5}{\left(\left(1-x^2\right) \left(1-k^2 x^2\right)\right)^{2/3} \left(-1+d+\left(1-2 d k^2\right) x^2+d k^4 x^4\right)} \, dx","-\frac{\log \left(\sqrt[3]{d} \left(k^2 x^4+\left(-k^2-1\right) x^2+1\right)^{2/3}+x^2-1\right)}{2 d^{2/3}}+\frac{\log \left(d^{2/3} \left(k^2 x^4+\left(-k^2-1\right) x^2+1\right)^{4/3}+\left(\sqrt[3]{d}-\sqrt[3]{d} x^2\right) \left(k^2 x^4+\left(-k^2-1\right) x^2+1\right)^{2/3}+x^4-2 x^2+1\right)}{4 d^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} \left(k^2 x^4+\left(-k^2-1\right) x^2+1\right)^{2/3}}{\sqrt[3]{d} \left(k^2 x^4+\left(-k^2-1\right) x^2+1\right)^{2/3}-2 x^2+2}\right)}{2 d^{2/3}}",1,"Integrate[((-1 + 2*k^2)*x - 2*k^4*x^3 + k^4*x^5)/(((1 - x^2)*(1 - k^2*x^2))^(2/3)*(-1 + d + (1 - 2*d*k^2)*x^2 + d*k^4*x^4)), x]","F",-1
2609,0,0,227,3.711127,"\int \frac{(-a+x) (-b+x) (-2 a b+(a+b) x)}{\sqrt[3]{x (-a+x) (-b+x)} \left(a^2 b^2 d-2 a b (a+b) d x+\left(a^2+4 a b+b^2\right) d x^2-2 (a+b) d x^3+(-1+d) x^4\right)} \, dx","Integrate[((-a + x)*(-b + x)*(-2*a*b + (a + b)*x))/((x*(-a + x)*(-b + x))^(1/3)*(a^2*b^2*d - 2*a*b*(a + b)*d*x + (a^2 + 4*a*b + b^2)*d*x^2 - 2*(a + b)*d*x^3 + (-1 + d)*x^4)),x]","\int \frac{(-a+x) (-b+x) (-2 a b+(a+b) x)}{\sqrt[3]{x (-a+x) (-b+x)} \left(a^2 b^2 d-2 a b (a+b) d x+\left(a^2+4 a b+b^2\right) d x^2-2 (a+b) d x^3+(-1+d) x^4\right)} \, dx","\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{x-2 \sqrt[6]{d} \sqrt[3]{x^2 (-a-b)+a b x+x^3}}\right)}{2 d^{5/6}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[6]{d} \sqrt[3]{x^2 (-a-b)+a b x+x^3}+x}\right)}{2 d^{5/6}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt[6]{d} \sqrt[3]{x^2 (-a-b)+a b x+x^3}}\right)}{d^{5/6}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{d} \left(x^2 (-a-b)+a b x+x^3\right)^{2/3}+\frac{x^2}{\sqrt[6]{d}}}{x \sqrt[3]{x^2 (-a-b)+a b x+x^3}}\right)}{2 d^{5/6}}",1,"Integrate[((-a + x)*(-b + x)*(-2*a*b + (a + b)*x))/((x*(-a + x)*(-b + x))^(1/3)*(a^2*b^2*d - 2*a*b*(a + b)*d*x + (a^2 + 4*a*b + b^2)*d*x^2 - 2*(a + b)*d*x^3 + (-1 + d)*x^4)), x]","F",-1
2610,1,267,227,0.4427688,"\int \frac{\sqrt{b^2+a^2 x^3} \left(2 b^2+c x^3+a^2 x^6\right)}{x \left(b^2+a^2 x^6\right)} \, dx","Integrate[(Sqrt[b^2 + a^2*x^3]*(2*b^2 + c*x^3 + a^2*x^6))/(x*(b^2 + a^2*x^6)),x]","\frac{-\sqrt{-a^2} c \sqrt{\sqrt{-a^2}-b} \tan ^{-1}\left(\frac{\sqrt{a^2 x^3+b^2}}{\sqrt{b} \sqrt{\sqrt{-a^2}-b}}\right)+\sqrt{\sqrt{-a^2}+b} \left(a^2 b+\sqrt{-a^2} c\right) \tanh ^{-1}\left(\frac{\sqrt{a^2 x^3+b^2}}{\sqrt{b} \sqrt{\sqrt{-a^2}+b}}\right)+2 a^2 \sqrt{b} \sqrt{a^2 x^3+b^2}+a^2 b \sqrt{\sqrt{-a^2}-b} \tan ^{-1}\left(\frac{\sqrt{a^2 x^3+b^2}}{\sqrt{b} \sqrt{\sqrt{-a^2}-b}}\right)-4 a^2 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a^2 x^3+b^2}}{b}\right)}{3 a^2 \sqrt{b}}","\frac{\left(\sqrt[4]{-1} c \sqrt{a-i b}-(-1)^{3/4} a b \sqrt{a-i b}\right) \tan ^{-1}\left(\frac{\sqrt[4]{-1} \sqrt{a^2 x^3+b^2}}{\sqrt{b} \sqrt{a-i b}}\right)}{3 a \sqrt{b}}+\frac{\left(-\sqrt[4]{-1} c \sqrt{a+i b}-(-1)^{3/4} a b \sqrt{a+i b}\right) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a^2 x^3+b^2}}{\sqrt{2} \sqrt{b} \sqrt{a+i b}}\right)}{3 a \sqrt{b}}+\frac{2}{3} \sqrt{a^2 x^3+b^2}-\frac{4}{3} b \tanh ^{-1}\left(\frac{\sqrt{a^2 x^3+b^2}}{b}\right)",1,"(2*a^2*Sqrt[b]*Sqrt[b^2 + a^2*x^3] + a^2*Sqrt[Sqrt[-a^2] - b]*b*ArcTan[Sqrt[b^2 + a^2*x^3]/(Sqrt[Sqrt[-a^2] - b]*Sqrt[b])] - Sqrt[-a^2]*Sqrt[Sqrt[-a^2] - b]*c*ArcTan[Sqrt[b^2 + a^2*x^3]/(Sqrt[Sqrt[-a^2] - b]*Sqrt[b])] - 4*a^2*b^(3/2)*ArcTanh[Sqrt[b^2 + a^2*x^3]/b] + Sqrt[Sqrt[-a^2] + b]*(a^2*b + Sqrt[-a^2]*c)*ArcTanh[Sqrt[b^2 + a^2*x^3]/(Sqrt[b]*Sqrt[Sqrt[-a^2] + b])])/(3*a^2*Sqrt[b])","A",1
2611,1,441,227,0.7932705,"\int \frac{\sqrt{x+x^4} \left(b+a x^6\right)}{-d+c x^6} \, dx","Integrate[(Sqrt[x + x^4]*(b + a*x^6))/(-d + c*x^6),x]","\frac{\sqrt{x^4+x} \left(-\left(x^3+1\right) (a d+b c) \left(\sqrt[4]{d} \sinh ^{-1}\left(x^{3/2}\right)+\sqrt{\sqrt{c}-\sqrt{d}} \tan ^{-1}\left(\frac{-\sqrt[4]{d} x^{3/2}+i \sqrt[4]{c}}{\sqrt{x^3+1} \sqrt{\sqrt{c}-\sqrt{d}}}\right)\right)-\left(x^3+1\right) (a d+b c) \left(\sqrt[4]{d} \sinh ^{-1}\left(x^{3/2}\right)-\sqrt{\sqrt{c}-\sqrt{d}} \tan ^{-1}\left(\frac{\sqrt[4]{d} x^{3/2}+i \sqrt[4]{c}}{\sqrt{x^3+1} \sqrt{\sqrt{c}-\sqrt{d}}}\right)\right)+\left(x^3+1\right) (a d+b c) \left(\sqrt{\sqrt{c}+\sqrt{d}} \tanh ^{-1}\left(\frac{\sqrt[4]{c}-\sqrt[4]{d} x^{3/2}}{\sqrt{x^3+1} \sqrt{\sqrt{c}+\sqrt{d}}}\right)+\sqrt[4]{d} \sinh ^{-1}\left(x^{3/2}\right)\right)+\left(x^3+1\right) (a d+b c) \left(\sqrt[4]{d} \sinh ^{-1}\left(x^{3/2}\right)-\sqrt{\sqrt{c}+\sqrt{d}} \tanh ^{-1}\left(\frac{\sqrt[4]{c}+\sqrt[4]{d} x^{3/2}}{\sqrt{x^3+1} \sqrt{\sqrt{c}+\sqrt{d}}}\right)\right)+2 a \sqrt{c} d^{3/4} \left(x^{3/2} \left(x^3+1\right)^{3/2}+\left(x^3+1\right) \sinh ^{-1}\left(x^{3/2}\right)\right)\right)}{6 c^{3/2} d^{3/4} \sqrt{x} \left(x^3+1\right)^{3/2}}","\frac{\sqrt{-\left(\sqrt{d} \left(\sqrt{c}+\sqrt{d}\right)\right)} (a d+b c) \tan ^{-1}\left(\frac{x \sqrt{x^4+x} \sqrt{-\sqrt{c} \sqrt{d}-d}}{\sqrt{d} (x+1) \left(x^2-x+1\right)}\right)}{3 c^{3/2} d}-\frac{\sqrt{\sqrt{d} \left(\sqrt{c}-\sqrt{d}\right)} (a d+b c) \tan ^{-1}\left(\frac{x \sqrt{x^4+x} \sqrt{\sqrt{c} \sqrt{d}-d}}{\sqrt{d} (x+1) \left(x^2-x+1\right)}\right)}{3 c^{3/2} d}+\frac{a \sqrt{x^4+x} x}{3 c}+\frac{a \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4+x}}\right)}{3 c}",1,"(Sqrt[x + x^4]*(2*a*Sqrt[c]*d^(3/4)*(x^(3/2)*(1 + x^3)^(3/2) + (1 + x^3)*ArcSinh[x^(3/2)]) - (b*c + a*d)*(1 + x^3)*(d^(1/4)*ArcSinh[x^(3/2)] + Sqrt[Sqrt[c] - Sqrt[d]]*ArcTan[(I*c^(1/4) - d^(1/4)*x^(3/2))/(Sqrt[Sqrt[c] - Sqrt[d]]*Sqrt[1 + x^3])]) - (b*c + a*d)*(1 + x^3)*(d^(1/4)*ArcSinh[x^(3/2)] - Sqrt[Sqrt[c] - Sqrt[d]]*ArcTan[(I*c^(1/4) + d^(1/4)*x^(3/2))/(Sqrt[Sqrt[c] - Sqrt[d]]*Sqrt[1 + x^3])]) + (b*c + a*d)*(1 + x^3)*(d^(1/4)*ArcSinh[x^(3/2)] + Sqrt[Sqrt[c] + Sqrt[d]]*ArcTanh[(c^(1/4) - d^(1/4)*x^(3/2))/(Sqrt[Sqrt[c] + Sqrt[d]]*Sqrt[1 + x^3])]) + (b*c + a*d)*(1 + x^3)*(d^(1/4)*ArcSinh[x^(3/2)] - Sqrt[Sqrt[c] + Sqrt[d]]*ArcTanh[(c^(1/4) + d^(1/4)*x^(3/2))/(Sqrt[Sqrt[c] + Sqrt[d]]*Sqrt[1 + x^3])])))/(6*c^(3/2)*d^(3/4)*Sqrt[x]*(1 + x^3)^(3/2))","C",1
2612,0,0,228,3.192466,"\int \frac{x (-1+k x) \left(1-2 k x+(-1+2 k) x^2\right)}{((1-x) x (1-k x))^{2/3} \left(-1+4 x+(-6+b) x^2+(4-2 b k) x^3+\left(-1+b k^2\right) x^4\right)} \, dx","Integrate[(x*(-1 + k*x)*(1 - 2*k*x + (-1 + 2*k)*x^2))/(((1 - x)*x*(1 - k*x))^(2/3)*(-1 + 4*x + (-6 + b)*x^2 + (4 - 2*b*k)*x^3 + (-1 + b*k^2)*x^4)),x]","\int \frac{x (-1+k x) \left(1-2 k x+(-1+2 k) x^2\right)}{((1-x) x (1-k x))^{2/3} \left(-1+4 x+(-6+b) x^2+(4-2 b k) x^3+\left(-1+b k^2\right) x^4\right)} \, dx","-\frac{\log \left(-\sqrt[3]{b} \left(k x^3+(-k-1) x^2+x\right)^{2/3}+x^2-2 x+1\right)}{2 b^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{b} \left(k x^3+(-k-1) x^2+x\right)^{2/3}}{\sqrt[3]{b} \left(k x^3+(-k-1) x^2+x\right)^{2/3}+2 x^2-4 x+2}\right)}{2 b^{2/3}}+\frac{\log \left(b^{2/3} \left(k x^3+(-k-1) x^2+x\right)^{4/3}+\left(\sqrt[3]{b} x^2-2 \sqrt[3]{b} x+\sqrt[3]{b}\right) \left(k x^3+(-k-1) x^2+x\right)^{2/3}+x^4-4 x^3+6 x^2-4 x+1\right)}{4 b^{2/3}}",1,"Integrate[(x*(-1 + k*x)*(1 - 2*k*x + (-1 + 2*k)*x^2))/(((1 - x)*x*(1 - k*x))^(2/3)*(-1 + 4*x + (-6 + b)*x^2 + (4 - 2*b*k)*x^3 + (-1 + b*k^2)*x^4)), x]","F",-1
2613,0,0,228,1.7433973,"\int \frac{-3 a q+4 b p x^3+a p x^4}{\sqrt[3]{q+p x^4} \left(b^3 d+c q+3 a b^2 d x+3 a^2 b d x^2+a^3 d x^3+c p x^4\right)} \, dx","Integrate[(-3*a*q + 4*b*p*x^3 + a*p*x^4)/((q + p*x^4)^(1/3)*(b^3*d + c*q + 3*a*b^2*d*x + 3*a^2*b*d*x^2 + a^3*d*x^3 + c*p*x^4)),x]","\int \frac{-3 a q+4 b p x^3+a p x^4}{\sqrt[3]{q+p x^4} \left(b^3 d+c q+3 a b^2 d x+3 a^2 b d x^2+a^3 d x^3+c p x^4\right)} \, dx","\frac{\log \left(a^2 d^{2/3} x^2+\sqrt[3]{p x^4+q} \left(b \left(-\sqrt[3]{c}\right) \sqrt[3]{d}-a \sqrt[3]{c} \sqrt[3]{d} x\right)+2 a b d^{2/3} x+b^2 d^{2/3}+c^{2/3} \left(p x^4+q\right)^{2/3}\right)}{2 c^{2/3} \sqrt[3]{d}}-\frac{\log \left(a \sqrt[3]{d} x+b \sqrt[3]{d}+\sqrt[3]{c} \sqrt[3]{p x^4+q}\right)}{c^{2/3} \sqrt[3]{d}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{c} \sqrt[3]{p x^4+q}}{-2 a \sqrt[3]{d} x-2 b \sqrt[3]{d}+\sqrt[3]{c} \sqrt[3]{p x^4+q}}\right)}{c^{2/3} \sqrt[3]{d}}",1,"Integrate[(-3*a*q + 4*b*p*x^3 + a*p*x^4)/((q + p*x^4)^(1/3)*(b^3*d + c*q + 3*a*b^2*d*x + 3*a^2*b*d*x^2 + a^3*d*x^3 + c*p*x^4)), x]","F",-1
2614,0,0,228,2.528179,"\int \frac{x^2}{x^2-\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","Integrate[x^2/(x^2 - Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]]),x]","\int \frac{x^2}{x^2-\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","4 a \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6 c-2 \text{$\#$1}^4 b+6 \text{$\#$1}^4 c^2-\text{$\#$1}^3 a^2+4 \text{$\#$1}^2 b c-4 \text{$\#$1}^2 c^3+\text{$\#$1} a^2 c+b^2-2 b c^2+c^4\&,\frac{\text{$\#$1}^6 \left(-\log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)\right)+2 \text{$\#$1}^4 c \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-\text{$\#$1}^2 c^2 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)}{-8 \text{$\#$1}^7+24 \text{$\#$1}^5 c+8 \text{$\#$1}^3 b-24 \text{$\#$1}^3 c^2+3 \text{$\#$1}^2 a^2-8 \text{$\#$1} b c+8 \text{$\#$1} c^3-a^2 c}\&\right]+x",1,"Integrate[x^2/(x^2 - Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]]), x]","F",-1
2615,0,0,228,2.2128893,"\int \frac{x^2}{x^2-\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","Integrate[x^2/(x^2 - Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]]),x]","\int \frac{x^2}{x^2-\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","4 a \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6 c-2 \text{$\#$1}^4 b+6 \text{$\#$1}^4 c^2-\text{$\#$1}^3 a^2+4 \text{$\#$1}^2 b c-4 \text{$\#$1}^2 c^3+\text{$\#$1} a^2 c+b^2-2 b c^2+c^4\&,\frac{\text{$\#$1}^6 \left(-\log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)\right)+2 \text{$\#$1}^4 c \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-\text{$\#$1}^2 c^2 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)}{-8 \text{$\#$1}^7+24 \text{$\#$1}^5 c+8 \text{$\#$1}^3 b-24 \text{$\#$1}^3 c^2+3 \text{$\#$1}^2 a^2-8 \text{$\#$1} b c+8 \text{$\#$1} c^3-a^2 c}\&\right]+x",1,"Integrate[x^2/(x^2 - Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]]), x]","F",-1
2616,0,0,229,3.7396773,"\int \frac{3+\left(-1+2 k^2\right) x-3 k^2 x^2-k^2 x^3}{\sqrt[3]{\left(1-x^2\right) \left(1-k^2 x^2\right)} \left(1-d-(1+2 d) x-\left(d+k^2\right) x^2+k^2 x^3\right)} \, dx","Integrate[(3 + (-1 + 2*k^2)*x - 3*k^2*x^2 - k^2*x^3)/(((1 - x^2)*(1 - k^2*x^2))^(1/3)*(1 - d - (1 + 2*d)*x - (d + k^2)*x^2 + k^2*x^3)),x]","\int \frac{3+\left(-1+2 k^2\right) x-3 k^2 x^2-k^2 x^3}{\sqrt[3]{\left(1-x^2\right) \left(1-k^2 x^2\right)} \left(1-d-(1+2 d) x-\left(d+k^2\right) x^2+k^2 x^3\right)} \, dx","\frac{\log \left(d^{2/3} x^2+2 d^{2/3} x+d^{2/3}+\left(\sqrt[3]{d} x+\sqrt[3]{d}\right) \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}+\left(k^2 x^4+\left(-k^2-1\right) x^2+1\right)^{2/3}\right)}{2 \sqrt[3]{d}}-\frac{\log \left(-\sqrt[3]{d} x-\sqrt[3]{d}+\sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}\right)}{\sqrt[3]{d}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}}{2 \sqrt[3]{d} x+2 \sqrt[3]{d}+\sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}}\right)}{\sqrt[3]{d}}",1,"Integrate[(3 + (-1 + 2*k^2)*x - 3*k^2*x^2 - k^2*x^3)/(((1 - x^2)*(1 - k^2*x^2))^(1/3)*(1 - d - (1 + 2*d)*x - (d + k^2)*x^2 + k^2*x^3)), x]","F",-1
2617,0,0,229,3.7226385,"\int \frac{3+\left(1-2 k^2\right) x-3 k^2 x^2+k^2 x^3}{\sqrt[3]{\left(1-x^2\right) \left(1-k^2 x^2\right)} \left(-1+d-(1+2 d) x+\left(d+k^2\right) x^2+k^2 x^3\right)} \, dx","Integrate[(3 + (1 - 2*k^2)*x - 3*k^2*x^2 + k^2*x^3)/(((1 - x^2)*(1 - k^2*x^2))^(1/3)*(-1 + d - (1 + 2*d)*x + (d + k^2)*x^2 + k^2*x^3)),x]","\int \frac{3+\left(1-2 k^2\right) x-3 k^2 x^2+k^2 x^3}{\sqrt[3]{\left(1-x^2\right) \left(1-k^2 x^2\right)} \left(-1+d-(1+2 d) x+\left(d+k^2\right) x^2+k^2 x^3\right)} \, dx","\frac{\log \left(d^{2/3} x^2-2 d^{2/3} x+d^{2/3}+\left(\sqrt[3]{d}-\sqrt[3]{d} x\right) \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}+\left(k^2 x^4+\left(-k^2-1\right) x^2+1\right)^{2/3}\right)}{2 \sqrt[3]{d}}-\frac{\log \left(\sqrt[3]{d} x-\sqrt[3]{d}+\sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}\right)}{\sqrt[3]{d}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}}{-2 \sqrt[3]{d} x+2 \sqrt[3]{d}+\sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}}\right)}{\sqrt[3]{d}}",1,"Integrate[(3 + (1 - 2*k^2)*x - 3*k^2*x^2 + k^2*x^3)/(((1 - x^2)*(1 - k^2*x^2))^(1/3)*(-1 + d - (1 + 2*d)*x + (d + k^2)*x^2 + k^2*x^3)), x]","F",-1
2618,1,326,229,1.6387484,"\int \frac{\sqrt{-b^4+a^4 x^4} \left(b^4+a^4 x^4\right)}{b^8-c x^4+a^8 x^8} \, dx","Integrate[(Sqrt[-b^4 + a^4*x^4]*(b^4 + a^4*x^4))/(b^8 - c*x^4 + a^8*x^8),x]","-\frac{i \sqrt{1-\frac{a^4 x^4}{b^4}} \left(2 F\left(\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)-\Pi \left(-\frac{\sqrt{2} b^2}{a^2 \sqrt{\frac{c-\sqrt{c^2-4 a^8 b^8}}{a^8}}};\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)-\Pi \left(\frac{\sqrt{2} b^2}{a^2 \sqrt{\frac{c-\sqrt{c^2-4 a^8 b^8}}{a^8}}};\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)-\Pi \left(-\frac{\sqrt{2} b^2}{a^2 \sqrt{\frac{c+\sqrt{c^2-4 a^8 b^8}}{a^8}}};\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)-\Pi \left(\frac{\sqrt{2} b^2}{a^2 \sqrt{\frac{c+\sqrt{c^2-4 a^8 b^8}}{a^8}}};\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)\right)}{2 \sqrt{-\frac{a^2}{b^2}} \sqrt{a^4 x^4-b^4}}","-\frac{\tan ^{-1}\left(\frac{-\frac{a^4 x^4}{\sqrt{2} \sqrt[4]{2 a^4 b^4-c}}+\frac{x^2 \sqrt[4]{2 a^4 b^4-c}}{\sqrt{2}}+\frac{b^4}{\sqrt{2} \sqrt[4]{2 a^4 b^4-c}}}{x \sqrt{a^4 x^4-b^4}}\right)}{2 \sqrt{2} \sqrt[4]{2 a^4 b^4-c}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{2 a^4 b^4-c} \sqrt{a^4 x^4-b^4}}{x^2 \sqrt{2 a^4 b^4-c}+a^4 x^4-b^4}\right)}{2 \sqrt{2} \sqrt[4]{2 a^4 b^4-c}}",1,"((-1/2*I)*Sqrt[1 - (a^4*x^4)/b^4]*(2*EllipticF[I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1] - EllipticPi[-((Sqrt[2]*b^2)/(a^2*Sqrt[(c - Sqrt[-4*a^8*b^8 + c^2])/a^8])), I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1] - EllipticPi[(Sqrt[2]*b^2)/(a^2*Sqrt[(c - Sqrt[-4*a^8*b^8 + c^2])/a^8]), I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1] - EllipticPi[-((Sqrt[2]*b^2)/(a^2*Sqrt[(c + Sqrt[-4*a^8*b^8 + c^2])/a^8])), I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1] - EllipticPi[(Sqrt[2]*b^2)/(a^2*Sqrt[(c + Sqrt[-4*a^8*b^8 + c^2])/a^8]), I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1]))/(Sqrt[-(a^2/b^2)]*Sqrt[-b^4 + a^4*x^4])","C",1
2619,1,326,229,1.3050894,"\int \frac{-b^8+a^8 x^8}{\sqrt{-b^4+a^4 x^4} \left(b^8-c x^4+a^8 x^8\right)} \, dx","Integrate[(-b^8 + a^8*x^8)/(Sqrt[-b^4 + a^4*x^4]*(b^8 - c*x^4 + a^8*x^8)),x]","-\frac{i \sqrt{1-\frac{a^4 x^4}{b^4}} \left(2 F\left(\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)-\Pi \left(-\frac{\sqrt{2} b^2}{a^2 \sqrt{\frac{c-\sqrt{c^2-4 a^8 b^8}}{a^8}}};\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)-\Pi \left(\frac{\sqrt{2} b^2}{a^2 \sqrt{\frac{c-\sqrt{c^2-4 a^8 b^8}}{a^8}}};\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)-\Pi \left(-\frac{\sqrt{2} b^2}{a^2 \sqrt{\frac{c+\sqrt{c^2-4 a^8 b^8}}{a^8}}};\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)-\Pi \left(\frac{\sqrt{2} b^2}{a^2 \sqrt{\frac{c+\sqrt{c^2-4 a^8 b^8}}{a^8}}};\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)\right)}{2 \sqrt{-\frac{a^2}{b^2}} \sqrt{a^4 x^4-b^4}}","-\frac{\tan ^{-1}\left(\frac{-\frac{a^4 x^4}{\sqrt{2} \sqrt[4]{2 a^4 b^4-c}}+\frac{x^2 \sqrt[4]{2 a^4 b^4-c}}{\sqrt{2}}+\frac{b^4}{\sqrt{2} \sqrt[4]{2 a^4 b^4-c}}}{x \sqrt{a^4 x^4-b^4}}\right)}{2 \sqrt{2} \sqrt[4]{2 a^4 b^4-c}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{2 a^4 b^4-c} \sqrt{a^4 x^4-b^4}}{x^2 \sqrt{2 a^4 b^4-c}+a^4 x^4-b^4}\right)}{2 \sqrt{2} \sqrt[4]{2 a^4 b^4-c}}",1,"((-1/2*I)*Sqrt[1 - (a^4*x^4)/b^4]*(2*EllipticF[I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1] - EllipticPi[-((Sqrt[2]*b^2)/(a^2*Sqrt[(c - Sqrt[-4*a^8*b^8 + c^2])/a^8])), I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1] - EllipticPi[(Sqrt[2]*b^2)/(a^2*Sqrt[(c - Sqrt[-4*a^8*b^8 + c^2])/a^8]), I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1] - EllipticPi[-((Sqrt[2]*b^2)/(a^2*Sqrt[(c + Sqrt[-4*a^8*b^8 + c^2])/a^8])), I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1] - EllipticPi[(Sqrt[2]*b^2)/(a^2*Sqrt[(c + Sqrt[-4*a^8*b^8 + c^2])/a^8]), I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1]))/(Sqrt[-(a^2/b^2)]*Sqrt[-b^4 + a^4*x^4])","C",1
2620,1,204,229,0.239042,"\int \frac{\sqrt{a x+\sqrt{-b+a x}}}{x^2} \, dx","Integrate[Sqrt[a*x + Sqrt[-b + a*x]]/x^2,x]","\frac{-4 (-b)^{3/4} \sqrt{\sqrt{a x-b}+a x}+a \left(2 \sqrt{-b}-1\right) x \tan ^{-1}\left(\frac{\left(1-2 \sqrt{-b}\right) \sqrt{a x-b}+2 b-\sqrt{-b}}{2 \sqrt[4]{-b} \sqrt{\sqrt{a x-b}+a x}}\right)-a \left(2 \sqrt{-b}+1\right) x \tanh ^{-1}\left(\frac{\left(2 \sqrt{-b}+1\right) \sqrt{a x-b}+2 b+\sqrt{-b}}{2 \sqrt[4]{-b} \sqrt{\sqrt{a x-b}+a x}}\right)}{4 (-b)^{3/4} x}","-\frac{1}{4} a \text{RootSum}\left[\text{$\#$1}^4+2 \text{$\#$1}^2 b-4 \text{$\#$1} b+b^2+b\&,\frac{-2 \text{$\#$1}^2 \log \left(\text{$\#$1}+\sqrt{a x-b}-\sqrt{\sqrt{a x-b}+a x}\right)+2 \text{$\#$1} \log \left(\text{$\#$1}+\sqrt{a x-b}-\sqrt{\sqrt{a x-b}+a x}\right)+2 b \log \left(\text{$\#$1}+\sqrt{a x-b}-\sqrt{\sqrt{a x-b}+a x}\right)-\log \left(\text{$\#$1}+\sqrt{a x-b}-\sqrt{\sqrt{a x-b}+a x}\right)}{\text{$\#$1}^3+\text{$\#$1} b-b}\&\right]-\frac{\sqrt{\sqrt{a x-b}+a x}}{x}",1,"(-4*(-b)^(3/4)*Sqrt[a*x + Sqrt[-b + a*x]] + a*(-1 + 2*Sqrt[-b])*x*ArcTan[(-Sqrt[-b] + 2*b + (1 - 2*Sqrt[-b])*Sqrt[-b + a*x])/(2*(-b)^(1/4)*Sqrt[a*x + Sqrt[-b + a*x]])] - a*(1 + 2*Sqrt[-b])*x*ArcTanh[(Sqrt[-b] + 2*b + (1 + 2*Sqrt[-b])*Sqrt[-b + a*x])/(2*(-b)^(1/4)*Sqrt[a*x + Sqrt[-b + a*x]])])/(4*(-b)^(3/4)*x)","A",1
2621,0,0,230,8.5715114,"\int \frac{-1+2 k x+(1-2 k) x^2}{((1-x) x (1-k x))^{2/3} \left(1-(2+b) x+(1+b k) x^2\right)} \, dx","Integrate[(-1 + 2*k*x + (1 - 2*k)*x^2)/(((1 - x)*x*(1 - k*x))^(2/3)*(1 - (2 + b)*x + (1 + b*k)*x^2)),x]","\int \frac{-1+2 k x+(1-2 k) x^2}{((1-x) x (1-k x))^{2/3} \left(1-(2+b) x+(1+b k) x^2\right)} \, dx","-\frac{\log \left(\left(k x^3+(-k-1) x^2+x\right)^{2/3} \left(b^{2/3} x-b^{2/3} k x^2\right)+b k^2 x^4-2 b k x^3+\sqrt[3]{b} \left(k x^3+(-k-1) x^2+x\right)^{4/3}+b x^2\right)}{2 \sqrt[3]{b}}+\frac{\log \left(\sqrt{b} k x^2+\sqrt[6]{b} \left(k x^3+(-k-1) x^2+x\right)^{2/3}-\sqrt{b} x\right)}{\sqrt[3]{b}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \left(k x^3+(-k-1) x^2+x\right)^{2/3}}{-2 \sqrt[3]{b} k x^2+2 \sqrt[3]{b} x+\left(k x^3+(-k-1) x^2+x\right)^{2/3}}\right)}{\sqrt[3]{b}}",1,"Integrate[(-1 + 2*k*x + (1 - 2*k)*x^2)/(((1 - x)*x*(1 - k*x))^(2/3)*(1 - (2 + b)*x + (1 + b*k)*x^2)), x]","F",-1
2622,0,0,230,0.3534347,"\int \frac{x^3 \left(3+x^2\right)}{\left(1+x^2\right) \sqrt[3]{1+x^2-x^3} \left(1+x^2+x^3\right)} \, dx","Integrate[(x^3*(3 + x^2))/((1 + x^2)*(1 + x^2 - x^3)^(1/3)*(1 + x^2 + x^3)),x]","\int \frac{x^3 \left(3+x^2\right)}{\left(1+x^2\right) \sqrt[3]{1+x^2-x^3} \left(1+x^2+x^3\right)} \, dx","\log \left(\sqrt[3]{-x^3+x^2+1}+x\right)-\frac{\log \left(2^{2/3} \sqrt[3]{-x^3+x^2+1}+2 x\right)}{\sqrt[3]{2}}-\frac{1}{2} \log \left(x^2-\sqrt[3]{-x^3+x^2+1} x+\left(-x^3+x^2+1\right)^{2/3}\right)+\frac{\log \left(-2 x^2+2^{2/3} \sqrt[3]{-x^3+x^2+1} x-\sqrt[3]{2} \left(-x^3+x^2+1\right)^{2/3}\right)}{2 \sqrt[3]{2}}+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{-x^3+x^2+1}-x}\right)-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{-x^3+x^2+1}-x}\right)}{\sqrt[3]{2}}",1,"Integrate[(x^3*(3 + x^2))/((1 + x^2)*(1 + x^2 - x^3)^(1/3)*(1 + x^2 + x^3)), x]","F",-1
2623,1,126,230,0.1761435,"\int \frac{\left(1+x^2\right) \sqrt[4]{-x^3+x^4}}{-1+x+2 x^2} \, dx","Integrate[((1 + x^2)*(-x^3 + x^4)^(1/4))/(-1 + x + 2*x^2),x]","\frac{\sqrt[4]{(x-1) x^3} \left(-30 \sqrt[4]{x} \, _2F_1\left(-\frac{3}{4},\frac{1}{4};\frac{5}{4};1-x\right)+12 (x-1) \sqrt[4]{x} \, _2F_1\left(-\frac{3}{4},\frac{5}{4};\frac{9}{4};1-x\right)+5 \left(27 \sqrt[4]{x} \, _2F_1\left(\frac{1}{4},\frac{1}{4};\frac{5}{4};1-x\right)-5 \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{1}{x}-1\right)-16 \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{x-1}{2 x}\right)\right)\right)}{30 x}","\frac{1}{16} \sqrt[4]{x^4-x^3} (4 x-5)-\frac{57}{32} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^3}}\right)+\frac{4}{3} \sqrt[4]{2} \tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-x^3}}\right)+\frac{57}{32} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^3}}\right)-\frac{4}{3} \sqrt[4]{2} \tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-x^3}}\right)+\frac{5 \tan ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{x^4-x^3}}{\sqrt{x^4-x^3}-x^2}\right)}{12 \sqrt{2}}-\frac{5 \tanh ^{-1}\left(\frac{\frac{x^2}{\sqrt{2}}+\frac{\sqrt{x^4-x^3}}{\sqrt{2}}}{x \sqrt[4]{x^4-x^3}}\right)}{12 \sqrt{2}}",1,"(((-1 + x)*x^3)^(1/4)*(-30*x^(1/4)*Hypergeometric2F1[-3/4, 1/4, 5/4, 1 - x] + 12*(-1 + x)*x^(1/4)*Hypergeometric2F1[-3/4, 5/4, 9/4, 1 - x] + 5*(27*x^(1/4)*Hypergeometric2F1[1/4, 1/4, 5/4, 1 - x] - 5*Hypergeometric2F1[1/4, 1, 5/4, -1 + x^(-1)] - 16*Hypergeometric2F1[1/4, 1, 5/4, (-1 + x)/(2*x)])))/(30*x)","C",1
2624,1,370,230,3.0021718,"\int \frac{\sqrt[4]{b x^2+a x^4} \left(b+a x^4+x^8\right)}{b+a x^4} \, dx","Integrate[((b*x^2 + a*x^4)^(1/4)*(b + a*x^4 + x^8))/(b + a*x^4),x]","\frac{x \sqrt[4]{x^2 \left(a x^2+b\right)} \left(2 a^{3/4} \left(96 a^3+32 a^2 x^4+4 a b \left(x^2-24\right)-7 b^2\right)-\frac{3 b \left(a+\frac{b}{x^2}\right)^{3/4} \left(-64 a^{7/4} \sqrt{b} \left(\frac{\left(\sqrt{-a}+\sqrt{b}\right) \left(\tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a-\sqrt{-a} \sqrt{b}}}\right)+\tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a-\sqrt{-a} \sqrt{b}}}\right)\right)}{\left(a-\sqrt{-a} \sqrt{b}\right)^{3/4}}-\frac{\left(\sqrt{-a}-\sqrt{b}\right) \left(\tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\sqrt{-a} \sqrt{b}+a}}\right)+\tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\sqrt{-a} \sqrt{b}+a}}\right)\right)}{\left(\sqrt{-a} \sqrt{b}+a\right)^{3/4}}\right)-\left(32 a^3-32 a b+7 b^2\right) \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a}}\right)-\left(32 a^3-32 a b+7 b^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a}}\right)\right)}{a x^2+b}\right)}{384 a^{15/4}}","-\frac{b^2 \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^4-a}\&\right]}{4 a^2}+\frac{\left(-32 a^3 b+32 a b^2-7 b^3\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{128 a^{15/4}}+\frac{\left(32 a^3 b-32 a b^2+7 b^3\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{128 a^{15/4}}+\frac{\sqrt[4]{a x^4+b x^2} \left(96 a^3 x+32 a^2 x^5+4 a b x^3-96 a b x-7 b^2 x\right)}{192 a^3}",1,"(x*(x^2*(b + a*x^2))^(1/4)*(2*a^(3/4)*(96*a^3 - 7*b^2 + 32*a^2*x^4 + 4*a*b*(-24 + x^2)) - (3*b*(a + b/x^2)^(3/4)*(-((32*a^3 - 32*a*b + 7*b^2)*ArcTan[(a + b/x^2)^(1/4)/a^(1/4)]) - (32*a^3 - 32*a*b + 7*b^2)*ArcTanh[(a + b/x^2)^(1/4)/a^(1/4)] - 64*a^(7/4)*Sqrt[b]*(((Sqrt[-a] + Sqrt[b])*(ArcTan[(a + b/x^2)^(1/4)/(a - Sqrt[-a]*Sqrt[b])^(1/4)] + ArcTanh[(a + b/x^2)^(1/4)/(a - Sqrt[-a]*Sqrt[b])^(1/4)]))/(a - Sqrt[-a]*Sqrt[b])^(3/4) - ((Sqrt[-a] - Sqrt[b])*(ArcTan[(a + b/x^2)^(1/4)/(a + Sqrt[-a]*Sqrt[b])^(1/4)] + ArcTanh[(a + b/x^2)^(1/4)/(a + Sqrt[-a]*Sqrt[b])^(1/4)]))/(a + Sqrt[-a]*Sqrt[b])^(3/4))))/(b + a*x^2)))/(384*a^(15/4))","A",1
2625,1,370,230,1.2480422,"\int \frac{\sqrt[4]{b x^2+a x^4} \left(b+a x^4+x^8\right)}{b+a x^4} \, dx","Integrate[((b*x^2 + a*x^4)^(1/4)*(b + a*x^4 + x^8))/(b + a*x^4),x]","\frac{x \sqrt[4]{x^2 \left(a x^2+b\right)} \left(2 a^{3/4} \left(96 a^3+32 a^2 x^4+4 a b \left(x^2-24\right)-7 b^2\right)-\frac{3 b \left(a+\frac{b}{x^2}\right)^{3/4} \left(-64 a^{7/4} \sqrt{b} \left(\frac{\left(\sqrt{-a}+\sqrt{b}\right) \left(\tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a-\sqrt{-a} \sqrt{b}}}\right)+\tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a-\sqrt{-a} \sqrt{b}}}\right)\right)}{\left(a-\sqrt{-a} \sqrt{b}\right)^{3/4}}-\frac{\left(\sqrt{-a}-\sqrt{b}\right) \left(\tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\sqrt{-a} \sqrt{b}+a}}\right)+\tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\sqrt{-a} \sqrt{b}+a}}\right)\right)}{\left(\sqrt{-a} \sqrt{b}+a\right)^{3/4}}\right)-\left(32 a^3-32 a b+7 b^2\right) \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a}}\right)-\left(32 a^3-32 a b+7 b^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a}}\right)\right)}{a x^2+b}\right)}{384 a^{15/4}}","-\frac{b^2 \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^4-a}\&\right]}{4 a^2}+\frac{\left(-32 a^3 b+32 a b^2-7 b^3\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{128 a^{15/4}}+\frac{\left(32 a^3 b-32 a b^2+7 b^3\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{128 a^{15/4}}+\frac{\sqrt[4]{a x^4+b x^2} \left(96 a^3 x+32 a^2 x^5+4 a b x^3-96 a b x-7 b^2 x\right)}{192 a^3}",1,"(x*(x^2*(b + a*x^2))^(1/4)*(2*a^(3/4)*(96*a^3 - 7*b^2 + 32*a^2*x^4 + 4*a*b*(-24 + x^2)) - (3*b*(a + b/x^2)^(3/4)*(-((32*a^3 - 32*a*b + 7*b^2)*ArcTan[(a + b/x^2)^(1/4)/a^(1/4)]) - (32*a^3 - 32*a*b + 7*b^2)*ArcTanh[(a + b/x^2)^(1/4)/a^(1/4)] - 64*a^(7/4)*Sqrt[b]*(((Sqrt[-a] + Sqrt[b])*(ArcTan[(a + b/x^2)^(1/4)/(a - Sqrt[-a]*Sqrt[b])^(1/4)] + ArcTanh[(a + b/x^2)^(1/4)/(a - Sqrt[-a]*Sqrt[b])^(1/4)]))/(a - Sqrt[-a]*Sqrt[b])^(3/4) - ((Sqrt[-a] - Sqrt[b])*(ArcTan[(a + b/x^2)^(1/4)/(a + Sqrt[-a]*Sqrt[b])^(1/4)] + ArcTanh[(a + b/x^2)^(1/4)/(a + Sqrt[-a]*Sqrt[b])^(1/4)]))/(a + Sqrt[-a]*Sqrt[b])^(3/4))))/(b + a*x^2)))/(384*a^(15/4))","A",1
2626,1,116,231,0.1553103,"\int \frac{1}{\sqrt[3]{-1+x^2} \left(3+x^2\right)} \, dx","Integrate[1/((-1 + x^2)^(1/3)*(3 + x^2)),x]","-\frac{9 x F_1\left(\frac{1}{2};\frac{1}{3},1;\frac{3}{2};x^2,-\frac{x^2}{3}\right)}{\sqrt[3]{x^2-1} \left(x^2+3\right) \left(2 x^2 \left(F_1\left(\frac{3}{2};\frac{1}{3},2;\frac{5}{2};x^2,-\frac{x^2}{3}\right)-F_1\left(\frac{3}{2};\frac{4}{3},1;\frac{5}{2};x^2,-\frac{x^2}{3}\right)\right)-9 F_1\left(\frac{1}{2};\frac{1}{3},1;\frac{3}{2};x^2,-\frac{x^2}{3}\right)\right)}","\frac{\tan ^{-1}\left(\frac{2^{2/3} x}{2 \sqrt{3} \sqrt[3]{x^2-1}+2^{2/3} \sqrt{3}}\right)}{3\ 2^{2/3} \sqrt{3}}-\frac{\tanh ^{-1}\left(\frac{3\ 2^{2/3} x \sqrt[3]{x^2-1}}{-\sqrt[3]{2} x^2-6 \left(x^2-1\right)^{2/3}+3\ 2^{2/3} \sqrt[3]{x^2-1}-3 \sqrt[3]{2}}\right)}{6\ 2^{2/3}}-\frac{i \tanh ^{-1}\left(\frac{2 i \sqrt[3]{2} \sqrt{3} x-i 2^{2/3} \sqrt{3} x \sqrt[3]{x^2-1}}{\sqrt[3]{2} x^2-6 \left(x^2-1\right)^{2/3}+3\ 2^{2/3} \sqrt[3]{x^2-1}-3 \sqrt[3]{2}}\right)}{6\ 2^{2/3} \sqrt{3}}",1,"(-9*x*AppellF1[1/2, 1/3, 1, 3/2, x^2, -1/3*x^2])/((-1 + x^2)^(1/3)*(3 + x^2)*(-9*AppellF1[1/2, 1/3, 1, 3/2, x^2, -1/3*x^2] + 2*x^2*(AppellF1[3/2, 1/3, 2, 5/2, x^2, -1/3*x^2] - AppellF1[3/2, 4/3, 1, 5/2, x^2, -1/3*x^2])))","C",0
2627,0,0,231,0.2047882,"\int \frac{1+x}{\left(1+3 x+x^2\right) \sqrt[3]{1-x^3}} \, dx","Integrate[(1 + x)/((1 + 3*x + x^2)*(1 - x^3)^(1/3)),x]","\int \frac{1+x}{\left(1+3 x+x^2\right) \sqrt[3]{1-x^3}} \, dx","\frac{\log \left(5 \sqrt[3]{1-x^3}+\sqrt[3]{2} 5^{2/3} x-\sqrt[3]{2} 5^{2/3}\right)}{\sqrt[3]{2} 5^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{5 \sqrt{3} \sqrt[3]{1-x^3}}{5 \sqrt[3]{1-x^3}-2 \sqrt[3]{2} 5^{2/3} x+2 \sqrt[3]{2} 5^{2/3}}\right)}{\sqrt[3]{2} 5^{2/3}}-\frac{\log \left(5 \left(1-x^3\right)^{2/3}+\left(\sqrt[3]{2} 5^{2/3}-\sqrt[3]{2} 5^{2/3} x\right) \sqrt[3]{1-x^3}+2^{2/3} \sqrt[3]{5} x^2-2\ 2^{2/3} \sqrt[3]{5} x+2^{2/3} \sqrt[3]{5}\right)}{2 \sqrt[3]{2} 5^{2/3}}",1,"Integrate[(1 + x)/((1 + 3*x + x^2)*(1 - x^3)^(1/3)), x]","F",-1
2628,0,0,231,0.639494,"\int \frac{3 k+2 \left(1+k^2\right) x-k \left(1+k^2\right) x^2-4 k^2 x^3-k^3 x^4}{\left(\left(1-x^2\right) \left(1-k^2 x^2\right)\right)^{2/3} \left(1-d-(1+2 d) k x-\left(1+d k^2\right) x^2+k x^3\right)} \, dx","Integrate[(3*k + 2*(1 + k^2)*x - k*(1 + k^2)*x^2 - 4*k^2*x^3 - k^3*x^4)/(((1 - x^2)*(1 - k^2*x^2))^(2/3)*(1 - d - (1 + 2*d)*k*x - (1 + d*k^2)*x^2 + k*x^3)),x]","\int \frac{3 k+2 \left(1+k^2\right) x-k \left(1+k^2\right) x^2-4 k^2 x^3-k^3 x^4}{\left(\left(1-x^2\right) \left(1-k^2 x^2\right)\right)^{2/3} \left(1-d-(1+2 d) k x-\left(1+d k^2\right) x^2+k x^3\right)} \, dx","-\frac{\log \left(-\sqrt[3]{d} k x-\sqrt[3]{d}+\sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}\right)}{d^{2/3}}+\frac{\log \left(d^{2/3} k^2 x^2+2 d^{2/3} k x+d^{2/3}+\sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1} \left(\sqrt[3]{d} k x+\sqrt[3]{d}\right)+\left(k^2 x^4+\left(-k^2-1\right) x^2+1\right)^{2/3}\right)}{2 d^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} k x+\sqrt{3} \sqrt[3]{d}}{\sqrt[3]{d} k x+\sqrt[3]{d}+2 \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}}\right)}{d^{2/3}}",1,"Integrate[(3*k + 2*(1 + k^2)*x - k*(1 + k^2)*x^2 - 4*k^2*x^3 - k^3*x^4)/(((1 - x^2)*(1 - k^2*x^2))^(2/3)*(1 - d - (1 + 2*d)*k*x - (1 + d*k^2)*x^2 + k*x^3)), x]","F",-1
2629,1,487,231,1.5973146,"\int \frac{\sqrt{-x+x^4} \left(b+a x^6\right)}{-d+c x^6} \, dx","Integrate[(Sqrt[-x + x^4]*(b + a*x^6))/(-d + c*x^6),x]","\frac{\sqrt{x} \sqrt{x^3-1} \left(-\frac{(a d+b c) \left(\sqrt[4]{d} \tanh ^{-1}\left(\frac{x^{3/2}}{\sqrt{x^3-1}}\right)+\sqrt{\sqrt{c}+\sqrt{d}} \tanh ^{-1}\left(\frac{-\sqrt[4]{d} x^{3/2}+i \sqrt[4]{c}}{\sqrt{x^3-1} \sqrt{\sqrt{c}+\sqrt{d}}}\right)\right)}{d^{3/4}}-\frac{(a d+b c) \left(\sqrt[4]{d} \tanh ^{-1}\left(\frac{x^{3/2}}{\sqrt{x^3-1}}\right)-\sqrt{\sqrt{c}+\sqrt{d}} \tanh ^{-1}\left(\frac{\sqrt[4]{d} x^{3/2}+i \sqrt[4]{c}}{\sqrt{x^3-1} \sqrt{\sqrt{c}+\sqrt{d}}}\right)\right)}{d^{3/4}}+\frac{(a d+b c) \left(\sqrt{\sqrt{c}-\sqrt{d}} \tan ^{-1}\left(\frac{\sqrt[4]{c}-\sqrt[4]{d} x^{3/2}}{\sqrt{x^3-1} \sqrt{\sqrt{c}-\sqrt{d}}}\right)+\sqrt[4]{d} \tanh ^{-1}\left(\frac{x^{3/2}}{\sqrt{x^3-1}}\right)\right)}{d^{3/4}}+\frac{(a d+b c) \left(\sqrt[4]{d} \tanh ^{-1}\left(\frac{x^{3/2}}{\sqrt{x^3-1}}\right)-\sqrt{\sqrt{c}-\sqrt{d}} \tan ^{-1}\left(\frac{\sqrt[4]{c}+\sqrt[4]{d} x^{3/2}}{\sqrt{x^3-1} \sqrt{\sqrt{c}-\sqrt{d}}}\right)\right)}{d^{3/4}}+\frac{2 a \sqrt{c} \left(x^3-1\right) \left(\sin ^{-1}\left(x^{3/2}\right)+\sqrt{1-x^3} x^{3/2}\right)}{\sqrt{-\left(x^3-1\right)^2}}\right)}{6 c^{3/2} \sqrt{x \left(x^3-1\right)}}","-\frac{\sqrt{-\left(\sqrt{d} \left(\sqrt{c}+\sqrt{d}\right)\right)} (a d+b c) \tan ^{-1}\left(\frac{x \sqrt{x^4-x} \sqrt{-\sqrt{c} \sqrt{d}-d}}{\sqrt{d} (x-1) \left(x^2+x+1\right)}\right)}{3 c^{3/2} d}+\frac{\sqrt{\sqrt{d} \left(\sqrt{c}-\sqrt{d}\right)} (a d+b c) \tan ^{-1}\left(\frac{x \sqrt{x^4-x} \sqrt{\sqrt{c} \sqrt{d}-d}}{\sqrt{d} (x-1) \left(x^2+x+1\right)}\right)}{3 c^{3/2} d}+\frac{a \sqrt{x^4-x} x}{3 c}-\frac{a \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4-x}}\right)}{3 c}",1,"(Sqrt[x]*Sqrt[-1 + x^3]*((2*a*Sqrt[c]*(-1 + x^3)*(x^(3/2)*Sqrt[1 - x^3] + ArcSin[x^(3/2)]))/Sqrt[-(-1 + x^3)^2] + ((b*c + a*d)*(Sqrt[Sqrt[c] - Sqrt[d]]*ArcTan[(c^(1/4) - d^(1/4)*x^(3/2))/(Sqrt[Sqrt[c] - Sqrt[d]]*Sqrt[-1 + x^3])] + d^(1/4)*ArcTanh[x^(3/2)/Sqrt[-1 + x^3]]))/d^(3/4) + ((b*c + a*d)*(-(Sqrt[Sqrt[c] - Sqrt[d]]*ArcTan[(c^(1/4) + d^(1/4)*x^(3/2))/(Sqrt[Sqrt[c] - Sqrt[d]]*Sqrt[-1 + x^3])]) + d^(1/4)*ArcTanh[x^(3/2)/Sqrt[-1 + x^3]]))/d^(3/4) - ((b*c + a*d)*(d^(1/4)*ArcTanh[x^(3/2)/Sqrt[-1 + x^3]] + Sqrt[Sqrt[c] + Sqrt[d]]*ArcTanh[(I*c^(1/4) - d^(1/4)*x^(3/2))/(Sqrt[Sqrt[c] + Sqrt[d]]*Sqrt[-1 + x^3])]))/d^(3/4) - ((b*c + a*d)*(d^(1/4)*ArcTanh[x^(3/2)/Sqrt[-1 + x^3]] - Sqrt[Sqrt[c] + Sqrt[d]]*ArcTanh[(I*c^(1/4) + d^(1/4)*x^(3/2))/(Sqrt[Sqrt[c] + Sqrt[d]]*Sqrt[-1 + x^3])]))/d^(3/4)))/(6*c^(3/2)*Sqrt[x*(-1 + x^3)])","C",1
2630,0,0,232,9.0405231,"\int \frac{a^2 b-2 a^2 x+(2 a-b) x^2}{(x (-a+x) (-b+x))^{2/3} \left(a^2 d+(b-2 a d) x+(-1+d) x^2\right)} \, dx","Integrate[(a^2*b - 2*a^2*x + (2*a - b)*x^2)/((x*(-a + x)*(-b + x))^(2/3)*(a^2*d + (b - 2*a*d)*x + (-1 + d)*x^2)),x]","\int \frac{a^2 b-2 a^2 x+(2 a-b) x^2}{(x (-a+x) (-b+x))^{2/3} \left(a^2 d+(b-2 a d) x+(-1+d) x^2\right)} \, dx","-\frac{\log \left(d^{2/3} \left(x^2 (-a-b)+a b x+x^3\right)^{4/3}+\left(x^2 (-a-b)+a b x+x^3\right)^{2/3} \left(\sqrt[3]{d} x^2-b \sqrt[3]{d} x\right)+b^2 x^2-2 b x^3+x^4\right)}{2 d^{2/3}}+\frac{\log \left(\sqrt[3]{d} \left(x^2 (-a-b)+a b x+x^3\right)^{2/3}+b x-x^2\right)}{d^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} \left(x^2 (-a-b)+a b x+x^3\right)^{2/3}}{\sqrt[3]{d} \left(x^2 (-a-b)+a b x+x^3\right)^{2/3}-2 b x+2 x^2}\right)}{d^{2/3}}",1,"Integrate[(a^2*b - 2*a^2*x + (2*a - b)*x^2)/((x*(-a + x)*(-b + x))^(2/3)*(a^2*d + (b - 2*a*d)*x + (-1 + d)*x^2)), x]","F",-1
2631,0,0,232,5.2924351,"\int \frac{2 a b^2 x-b (2 a+b) x^2+x^4}{\left(x (-a+x) (-b+x)^2\right)^{2/3} \left(-a b^2+b (2 a+b) x-(a+2 b+d) x^2+x^3\right)} \, dx","Integrate[(2*a*b^2*x - b*(2*a + b)*x^2 + x^4)/((x*(-a + x)*(-b + x)^2)^(2/3)*(-(a*b^2) + b*(2*a + b)*x - (a + 2*b + d)*x^2 + x^3)),x]","\int \frac{2 a b^2 x-b (2 a+b) x^2+x^4}{\left(x (-a+x) (-b+x)^2\right)^{2/3} \left(-a b^2+b (2 a+b) x-(a+2 b+d) x^2+x^3\right)} \, dx","\frac{\log \left(\sqrt[3]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}-\sqrt[3]{d} x\right)}{d^{2/3}}-\frac{\log \left(\sqrt[3]{d} x \sqrt[3]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}+\left(x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4\right)^{2/3}+d^{2/3} x^2\right)}{2 d^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} x}{2 \sqrt[3]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}+\sqrt[3]{d} x}\right)}{d^{2/3}}",1,"Integrate[(2*a*b^2*x - b*(2*a + b)*x^2 + x^4)/((x*(-a + x)*(-b + x)^2)^(2/3)*(-(a*b^2) + b*(2*a + b)*x - (a + 2*b + d)*x^2 + x^3)), x]","F",-1
2632,0,0,232,0.6458693,"\int \frac{-3 k+2 \left(1+k^2\right) x+k \left(1+k^2\right) x^2-4 k^2 x^3+k^3 x^4}{\left(\left(1-x^2\right) \left(1-k^2 x^2\right)\right)^{2/3} \left(-1+d-(1+2 d) k x+\left(1+d k^2\right) x^2+k x^3\right)} \, dx","Integrate[(-3*k + 2*(1 + k^2)*x + k*(1 + k^2)*x^2 - 4*k^2*x^3 + k^3*x^4)/(((1 - x^2)*(1 - k^2*x^2))^(2/3)*(-1 + d - (1 + 2*d)*k*x + (1 + d*k^2)*x^2 + k*x^3)),x]","\int \frac{-3 k+2 \left(1+k^2\right) x+k \left(1+k^2\right) x^2-4 k^2 x^3+k^3 x^4}{\left(\left(1-x^2\right) \left(1-k^2 x^2\right)\right)^{2/3} \left(-1+d-(1+2 d) k x+\left(1+d k^2\right) x^2+k x^3\right)} \, dx","\frac{\log \left(\sqrt[3]{d} k x-\sqrt[3]{d}+\sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}\right)}{d^{2/3}}-\frac{\log \left(d^{2/3} k^2 x^2-2 d^{2/3} k x+d^{2/3}+\sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1} \left(\sqrt[3]{d}-\sqrt[3]{d} k x\right)+\left(k^2 x^4+\left(-k^2-1\right) x^2+1\right)^{2/3}\right)}{2 d^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} k x-\sqrt{3} \sqrt[3]{d}}{\sqrt[3]{d} k x-\sqrt[3]{d}-2 \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}}\right)}{d^{2/3}}",1,"Integrate[(-3*k + 2*(1 + k^2)*x + k*(1 + k^2)*x^2 - 4*k^2*x^3 + k^3*x^4)/(((1 - x^2)*(1 - k^2*x^2))^(2/3)*(-1 + d - (1 + 2*d)*k*x + (1 + d*k^2)*x^2 + k*x^3)), x]","F",-1
2633,1,727,232,2.4336607,"\int \frac{1-((-1+3 x) (3+4 x))^{3/2}}{1+((-1+3 x) (3+4 x))^{3/2}} \, dx","Integrate[(1 - ((-1 + 3*x)*(3 + 4*x))^(3/2))/(1 + ((-1 + 3*x)*(3 + 4*x))^(3/2)),x]","\frac{434 \sqrt{68259} \text{RootSum}\left[144 \text{$\#$1}^4+120 \text{$\#$1}^3-35 \text{$\#$1}^2-25 \text{$\#$1}+7\&,\frac{12 \text{$\#$1}^2 \log (x-\text{$\#$1})+5 \text{$\#$1} \log (x-\text{$\#$1})-\log (x-\text{$\#$1})}{576 \text{$\#$1}^3+360 \text{$\#$1}^2-70 \text{$\#$1}-25}\&\right]+2 \sqrt{14812203} \log \left(-48 \sqrt{217} \sqrt{12 x^2+5 x-3}+5208 x+169 \sqrt{217}+1085\right)-2 \sqrt{14812203} \log \left(48 \sqrt{217} \sqrt{12 x^2+5 x-3}+5208 x-169 \sqrt{217}+1085\right)+217 \sqrt{-1302+726 i \sqrt{3}} \log \left(24 \sqrt{-2-2 i \sqrt{3}} \sqrt{12 x^2+5 x-3}-24 \sqrt{145-24 i \sqrt{3}} x-5 \sqrt{145-24 i \sqrt{3}}-169\right)-217 \sqrt{-1302+726 i \sqrt{3}} \log \left(24 \sqrt{-2-2 i \sqrt{3}} \sqrt{12 x^2+5 x-3}+24 \sqrt{145-24 i \sqrt{3}} x+5 \sqrt{145-24 i \sqrt{3}}-169\right)+217 \sqrt{-1302-726 i \sqrt{3}} \log \left(24 \sqrt{-2+2 i \sqrt{3}} \sqrt{12 x^2+5 x-3}-24 \sqrt{145+24 i \sqrt{3}} x-5 \sqrt{145+24 i \sqrt{3}}-169\right)-217 \sqrt{-1302-726 i \sqrt{3}} \log \left(24 \sqrt{-2+2 i \sqrt{3}} \sqrt{12 x^2+5 x-3}+24 \sqrt{145+24 i \sqrt{3}} x+5 \sqrt{145+24 i \sqrt{3}}-169\right)-651 \sqrt{68259} x-2 \sqrt{14812203} \log \left(-24 x+\sqrt{217}-5\right)+2 \sqrt{14812203} \log \left(24 x-\sqrt{217}+5\right)+217 \sqrt{-1302+726 i \sqrt{3}} \log \left(24 x-\sqrt{145-24 i \sqrt{3}}+5\right)-217 \sqrt{-1302+726 i \sqrt{3}} \log \left(24 x+\sqrt{145-24 i \sqrt{3}}+5\right)+217 \sqrt{-1302-726 i \sqrt{3}} \log \left(24 x-\sqrt{145+24 i \sqrt{3}}+5\right)-217 \sqrt{-1302-726 i \sqrt{3}} \log \left(24 x+\sqrt{145+24 i \sqrt{3}}+5\right)}{651 \sqrt{68259}}","-\frac{4}{3} \text{RootSum}\left[\text{$\#$1}^4+13 \text{$\#$1}^3+145 \text{$\#$1}^2-156 \text{$\#$1}+144\&,\frac{\text{$\#$1}^2 \log \left(-4 \text{$\#$1} x-3 \text{$\#$1}+4 \sqrt{12 x^2+5 x-3}\right)+\text{$\#$1}^2 (-\log (4 x+3))-13 \text{$\#$1} \log \left(-4 \text{$\#$1} x-3 \text{$\#$1}+4 \sqrt{12 x^2+5 x-3}\right)-12 \log \left(-4 \text{$\#$1} x-3 \text{$\#$1}+4 \sqrt{12 x^2+5 x-3}\right)+13 \text{$\#$1} \log (4 x+3)+12 \log (4 x+3)}{4 \text{$\#$1}^3+39 \text{$\#$1}^2+290 \text{$\#$1}-156}\&\right]-\frac{8 \tanh ^{-1}\left(\frac{\frac{8 \sqrt{12 x^2+5 x-3}}{\sqrt{217}}-\frac{52 x}{\sqrt{217}}-\frac{39}{\sqrt{217}}}{4 x+3}\right)}{3 \sqrt{217}}-x",1,"(-651*Sqrt[68259]*x - 2*Sqrt[14812203]*Log[-5 + Sqrt[217] - 24*x] + 2*Sqrt[14812203]*Log[5 - Sqrt[217] + 24*x] + 217*Sqrt[-1302 + (726*I)*Sqrt[3]]*Log[5 - Sqrt[145 - (24*I)*Sqrt[3]] + 24*x] - 217*Sqrt[-1302 + (726*I)*Sqrt[3]]*Log[5 + Sqrt[145 - (24*I)*Sqrt[3]] + 24*x] + 217*Sqrt[-1302 - (726*I)*Sqrt[3]]*Log[5 - Sqrt[145 + (24*I)*Sqrt[3]] + 24*x] - 217*Sqrt[-1302 - (726*I)*Sqrt[3]]*Log[5 + Sqrt[145 + (24*I)*Sqrt[3]] + 24*x] + 2*Sqrt[14812203]*Log[1085 + 169*Sqrt[217] + 5208*x - 48*Sqrt[217]*Sqrt[-3 + 5*x + 12*x^2]] - 2*Sqrt[14812203]*Log[1085 - 169*Sqrt[217] + 5208*x + 48*Sqrt[217]*Sqrt[-3 + 5*x + 12*x^2]] + 217*Sqrt[-1302 + (726*I)*Sqrt[3]]*Log[-169 - 5*Sqrt[145 - (24*I)*Sqrt[3]] - 24*Sqrt[145 - (24*I)*Sqrt[3]]*x + 24*Sqrt[-2 - (2*I)*Sqrt[3]]*Sqrt[-3 + 5*x + 12*x^2]] - 217*Sqrt[-1302 + (726*I)*Sqrt[3]]*Log[-169 + 5*Sqrt[145 - (24*I)*Sqrt[3]] + 24*Sqrt[145 - (24*I)*Sqrt[3]]*x + 24*Sqrt[-2 - (2*I)*Sqrt[3]]*Sqrt[-3 + 5*x + 12*x^2]] + 217*Sqrt[-1302 - (726*I)*Sqrt[3]]*Log[-169 - 5*Sqrt[145 + (24*I)*Sqrt[3]] - 24*Sqrt[145 + (24*I)*Sqrt[3]]*x + 24*Sqrt[-2 + (2*I)*Sqrt[3]]*Sqrt[-3 + 5*x + 12*x^2]] - 217*Sqrt[-1302 - (726*I)*Sqrt[3]]*Log[-169 + 5*Sqrt[145 + (24*I)*Sqrt[3]] + 24*Sqrt[145 + (24*I)*Sqrt[3]]*x + 24*Sqrt[-2 + (2*I)*Sqrt[3]]*Sqrt[-3 + 5*x + 12*x^2]] + 434*Sqrt[68259]*RootSum[7 - 25*#1 - 35*#1^2 + 120*#1^3 + 144*#1^4 & , (-Log[x - #1] + 5*Log[x - #1]*#1 + 12*Log[x - #1]*#1^2)/(-25 - 70*#1 + 360*#1^2 + 576*#1^3) & ])/(651*Sqrt[68259])","C",0
2634,0,0,232,0.362031,"\int \frac{1}{\left(-b x+a^2 x^2\right)^{3/2} \left(a x^2+x \sqrt{-b x+a^2 x^2}\right)^{3/2}} \, dx","Integrate[1/((-(b*x) + a^2*x^2)^(3/2)*(a*x^2 + x*Sqrt[-(b*x) + a^2*x^2])^(3/2)),x]","\int \frac{1}{\left(-b x+a^2 x^2\right)^{3/2} \left(a x^2+x \sqrt{-b x+a^2 x^2}\right)^{3/2}} \, dx","\frac{2 \sqrt{a^2 x^2-b x} \sqrt{x \left(\sqrt{a^2 x^2-b x}+a x\right)} \left(1601 a^6 x^3-456 a^4 b x^2-200 a^2 b^2 x+210 b^3\right)}{1155 b^5 x^4 \left(b-a^2 x\right)}+\sqrt{x \left(\sqrt{a^2 x^2-b x}+a x\right)} \left(-\frac{6 a^{11/2} \sqrt{\sqrt{a^2 x^2-b x}-a x} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\sqrt{a^2 x^2-b x}-a x}}{\sqrt{b}}\right)}{b^{11/2} x}-\frac{4 \left(2533 a^5 x^2+461 a^3 b x+245 a b^2\right)}{1155 b^5 x^3}\right)",1,"Integrate[1/((-(b*x) + a^2*x^2)^(3/2)*(a*x^2 + x*Sqrt[-(b*x) + a^2*x^2])^(3/2)), x]","F",-1
2635,1,55,233,0.1885634,"\int \frac{1}{x \sqrt[3]{(-1+x) \left(q-2 q x+x^2\right)}} \, dx","Integrate[1/(x*((-1 + x)*(q - 2*q*x + x^2))^(1/3)),x]","\frac{3 \left((x-1) \left(-2 q x+q+x^2\right)\right)^{2/3} \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{x^2-2 q x+q}{q (x-1)^2}\right)}{4 q (x-1)^2}","\frac{\log \left(q^{2/3} x^2-2 q^{2/3} x+q^{2/3}+\left((-2 q-1) x^2+3 q x-q+x^3\right)^{2/3}+\left(\sqrt[3]{q} x-\sqrt[3]{q}\right) \sqrt[3]{(-2 q-1) x^2+3 q x-q+x^3}\right)}{4 \sqrt[3]{q}}-\frac{\log \left(\sqrt[3]{(-2 q-1) x^2+3 q x-q+x^3}-\sqrt[3]{q} x+\sqrt[3]{q}\right)}{2 \sqrt[3]{q}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{(-2 q-1) x^2+3 q x-q+x^3}}{\sqrt[3]{(-2 q-1) x^2+3 q x-q+x^3}+2 \sqrt[3]{q} x-2 \sqrt[3]{q}}\right)}{2 \sqrt[3]{q}}",1,"(3*((-1 + x)*(q - 2*q*x + x^2))^(2/3)*Hypergeometric2F1[2/3, 1, 5/3, (q - 2*q*x + x^2)/(q*(-1 + x)^2)])/(4*q*(-1 + x)^2)","C",1
2636,0,0,233,4.9082293,"\int \frac{a b+(-2 a+b) x}{\sqrt[3]{x (-a+x) (-b+x)} \left(a^2 d+(b-2 a d) x+(-1+d) x^2\right)} \, dx","Integrate[(a*b + (-2*a + b)*x)/((x*(-a + x)*(-b + x))^(1/3)*(a^2*d + (b - 2*a*d)*x + (-1 + d)*x^2)),x]","\int \frac{a b+(-2 a+b) x}{\sqrt[3]{x (-a+x) (-b+x)} \left(a^2 d+(b-2 a d) x+(-1+d) x^2\right)} \, dx","\frac{\log \left(a^2 d^{2/3}+\sqrt[3]{x^2 (-a-b)+a b x+x^3} \left(\sqrt[3]{d} x-a \sqrt[3]{d}\right)+\left(x^2 (-a-b)+a b x+x^3\right)^{2/3}-2 a d^{2/3} x+d^{2/3} x^2\right)}{2 \sqrt[3]{d}}-\frac{\log \left(\sqrt[3]{x^2 (-a-b)+a b x+x^3}+a \sqrt[3]{d}-\sqrt[3]{d} x\right)}{\sqrt[3]{d}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x^2 (-a-b)+a b x+x^3}}{\sqrt[3]{x^2 (-a-b)+a b x+x^3}-2 a \sqrt[3]{d}+2 \sqrt[3]{d} x}\right)}{\sqrt[3]{d}}",1,"Integrate[(a*b + (-2*a + b)*x)/((x*(-a + x)*(-b + x))^(1/3)*(a^2*d + (b - 2*a*d)*x + (-1 + d)*x^2)), x]","F",-1
2637,1,268,233,0.2862176,"\int \frac{1+x^4}{\left(-1-x^2+x^4\right) \sqrt[4]{-x^2+x^4}} \, dx","Integrate[(1 + x^4)/((-1 - x^2 + x^4)*(-x^2 + x^4)^(1/4)),x]","\frac{\sqrt{x} \sqrt[4]{x^2-1} \left(2 \tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2-1}}\right)-2^{3/4} \sqrt[4]{3+\sqrt{5}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3+\sqrt{5}}} \sqrt{x}}{\sqrt[4]{x^2-1}}\right)-2^{3/4} \sqrt[4]{3-\sqrt{5}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} \sqrt{x}}{\sqrt[4]{x^2-1}}\right)+2 \tanh ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2-1}}\right)-2^{3/4} \sqrt[4]{3+\sqrt{5}} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3+\sqrt{5}}} \sqrt{x}}{\sqrt[4]{x^2-1}}\right)-2^{3/4} \sqrt[4]{3-\sqrt{5}} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} \sqrt{x}}{\sqrt[4]{x^2-1}}\right)\right)}{2 \sqrt[4]{x^2 \left(x^2-1\right)}}","\tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^2}}\right)-\sqrt{\frac{1}{2} \left(1+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}} x}{\sqrt[4]{x^4-x^2}}\right)-\sqrt{\frac{1}{2} \left(\sqrt{5}-1\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{1}{2}+\frac{\sqrt{5}}{2}} x}{\sqrt[4]{x^4-x^2}}\right)+\tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^2}}\right)-\sqrt{\frac{1}{2} \left(1+\sqrt{5}\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}} x}{\sqrt[4]{x^4-x^2}}\right)-\sqrt{\frac{1}{2} \left(\sqrt{5}-1\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{2}+\frac{\sqrt{5}}{2}} x}{\sqrt[4]{x^4-x^2}}\right)",1,"(Sqrt[x]*(-1 + x^2)^(1/4)*(2*ArcTan[Sqrt[x]/(-1 + x^2)^(1/4)] - 2^(3/4)*(3 + Sqrt[5])^(1/4)*ArcTan[((2/(3 + Sqrt[5]))^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)] - 2^(3/4)*(3 - Sqrt[5])^(1/4)*ArcTan[(((3 + Sqrt[5])/2)^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)] + 2*ArcTanh[Sqrt[x]/(-1 + x^2)^(1/4)] - 2^(3/4)*(3 + Sqrt[5])^(1/4)*ArcTanh[((2/(3 + Sqrt[5]))^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)] - 2^(3/4)*(3 - Sqrt[5])^(1/4)*ArcTanh[(((3 + Sqrt[5])/2)^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)]))/(2*(x^2*(-1 + x^2))^(1/4))","A",1
2638,1,733,233,12.1496548,"\int \frac{x^3 \sqrt{-\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}}{\sqrt{a x^2+b x \sqrt{-\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}}} \, dx","Integrate[(x^3*Sqrt[-(a/b^2) + (a^2*x^2)/b^2])/Sqrt[a*x^2 + b*x*Sqrt[-(a/b^2) + (a^2*x^2)/b^2]],x]","\frac{b x^2 \sqrt{\frac{a \left(a x^2-1\right)}{b^2}} \left(\frac{2 x^2 \sqrt{x \left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right)} \left(-\sqrt{2} a^5 \left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right)^2 \sqrt{x \left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right)} \, _2F_1\left(-\frac{9}{2},-\frac{3}{2};-\frac{1}{2};-2 a x^2-2 b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}} x+1\right)-3 \left(\left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right)^2+a\right)^6\right)}{b}-\frac{10 \sqrt{x \left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right)} \left(\left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right)^2+a\right)^2 \left(-\sqrt{2} a^3 \left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right)^2 \sqrt{x \left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right)} \, _2F_1\left(-\frac{5}{2},-\frac{1}{2};\frac{1}{2};-2 a x^2-2 b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}} x+1\right)-\left(\left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right)^2+a\right)^4\right)}{a b}-\frac{2 \sqrt{2} a^5 x^3 \sqrt{\frac{a \left(a x^2-1\right)}{b^2}} \left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right)^2 \left(15 \left(8 a^2 x^4+8 a x^2 \left(b x \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}-1\right)-4 b x \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+1\right) \, _2F_1\left(-\frac{7}{2},-\frac{1}{2};\frac{1}{2};-2 a x^2-2 b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}} x+1\right)+3 \, _2F_1\left(-\frac{7}{2},-\frac{5}{2};-\frac{3}{2};-2 a x^2-2 b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}} x+1\right)-10 \left(2 b x \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+2 a x^2-1\right) \, _2F_1\left(-\frac{7}{2},-\frac{3}{2};-\frac{1}{2};-2 a x^2-2 b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}} x+1\right)\right)}{b x \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x^2-1}\right)}{60 a \left(b x \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x^2-1\right) \left(\left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right)^2+a\right)^5}","\frac{\left(384 a^2 x^4-136 a x^2-255\right) \sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}} \sqrt{b x \sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}}+a x^2}}{1920 a^2}+\frac{\left(-384 a^2 x^5+568 a x^3+85 x\right) \sqrt{b x \sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}}+a x^2}}{1920 a b}+\frac{17 \log \left(b \left(-\sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}}\right)+\sqrt{2} \sqrt{a} \sqrt{b x \sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}}+a x^2}-a x\right)}{128 \sqrt{2} a^{3/2} b}",1,"(b*x^2*Sqrt[(a*(-1 + a*x^2))/b^2]*((2*x^2*Sqrt[x*(a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2])]*(-3*(a + (a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2])^2)^6 - Sqrt[2]*a^5*(a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2])^2*Sqrt[x*(a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2])]*Hypergeometric2F1[-9/2, -3/2, -1/2, 1 - 2*a*x^2 - 2*b*x*Sqrt[(a*(-1 + a*x^2))/b^2]]))/b - (2*Sqrt[2]*a^5*x^3*Sqrt[(a*(-1 + a*x^2))/b^2]*(a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2])^2*(3*Hypergeometric2F1[-7/2, -5/2, -3/2, 1 - 2*a*x^2 - 2*b*x*Sqrt[(a*(-1 + a*x^2))/b^2]] - 10*(-1 + 2*a*x^2 + 2*b*x*Sqrt[(a*(-1 + a*x^2))/b^2])*Hypergeometric2F1[-7/2, -3/2, -1/2, 1 - 2*a*x^2 - 2*b*x*Sqrt[(a*(-1 + a*x^2))/b^2]] + 15*(1 + 8*a^2*x^4 - 4*b*x*Sqrt[(a*(-1 + a*x^2))/b^2] + 8*a*x^2*(-1 + b*x*Sqrt[(a*(-1 + a*x^2))/b^2]))*Hypergeometric2F1[-7/2, -1/2, 1/2, 1 - 2*a*x^2 - 2*b*x*Sqrt[(a*(-1 + a*x^2))/b^2]]))/(-1 + a*x^2 + b*x*Sqrt[(a*(-1 + a*x^2))/b^2]) - (10*Sqrt[x*(a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2])]*(a + (a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2])^2)^2*(-(a + (a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2])^2)^4 - Sqrt[2]*a^3*(a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2])^2*Sqrt[x*(a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2])]*Hypergeometric2F1[-5/2, -1/2, 1/2, 1 - 2*a*x^2 - 2*b*x*Sqrt[(a*(-1 + a*x^2))/b^2]]))/(a*b)))/(60*a*(-1 + a*x^2 + b*x*Sqrt[(a*(-1 + a*x^2))/b^2])*(a + (a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2])^2)^5)","C",1
2639,1,137,234,0.1182549,"\int \frac{\sqrt[3]{-x+x^3} \left(-2+x^4\right)}{x^4 \left(1+x^2\right)} \, dx","Integrate[((-x + x^3)^(1/3)*(-2 + x^4))/(x^4*(1 + x^2)),x]","-\frac{3 \sqrt[3]{x \left(x^2-1\right)} \left(\sqrt[3]{1-x^2} \left(\left(3 x^2-1\right) x^2 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{2 x^2}{x^2-1}\right)+3 \left(x^4+x^2\right) \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};\frac{2 x^2}{x^2-1}\right)-4 x^4+6 x^2-2\right)-4 x^2 \left(x^2-1\right) \, _2F_1\left(-\frac{1}{3},-\frac{1}{3};\frac{2}{3};x^2\right)\right)}{8 x^3 \left(1-x^2\right)^{4/3}}","-\frac{1}{2} \log \left(\sqrt[3]{x^3-x}-x\right)-\frac{\log \left(2^{2/3} \sqrt[3]{x^3-x}-2 x\right)}{2^{2/3}}-\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-x}+x}\right)-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^3-x}+x}\right)}{2^{2/3}}-\frac{3 \sqrt[3]{x^3-x} \left(5 x^2-1\right)}{4 x^3}+\frac{1}{4} \log \left(\sqrt[3]{x^3-x} x+\left(x^3-x\right)^{2/3}+x^2\right)+\frac{\log \left(2^{2/3} \sqrt[3]{x^3-x} x+\sqrt[3]{2} \left(x^3-x\right)^{2/3}+2 x^2\right)}{2\ 2^{2/3}}",1,"(-3*(x*(-1 + x^2))^(1/3)*(-4*x^2*(-1 + x^2)*Hypergeometric2F1[-1/3, -1/3, 2/3, x^2] + (1 - x^2)^(1/3)*(-2 + 6*x^2 - 4*x^4 + x^2*(-1 + 3*x^2)*Hypergeometric2F1[2/3, 1, 5/3, (2*x^2)/(-1 + x^2)] + 3*(x^2 + x^4)*Hypergeometric2F1[2/3, 2, 5/3, (2*x^2)/(-1 + x^2)])))/(8*x^3*(1 - x^2)^(4/3))","C",0
2640,1,79,234,2.2000452,"\int \frac{2 \left(3 a q x-2 b p x^3+a p x^5\right)}{\sqrt[3]{q+p x^4} \left(b^3 d+c q+3 a b^2 d x^2+\left(3 a^2 b d+c p\right) x^4+a^3 d x^6\right)} \, dx","Integrate[(2*(3*a*q*x - 2*b*p*x^3 + a*p*x^5))/((q + p*x^4)^(1/3)*(b^3*d + c*q + 3*a*b^2*d*x^2 + (3*a^2*b*d + c*p)*x^4 + a^3*d*x^6)),x]","2 \int \frac{a p x^5+3 a q x-2 b p x^3}{\sqrt[3]{p x^4+q} \left(a^3 d x^6+x^4 \left(3 a^2 b d+c p\right)+3 a b^2 d x^2+b^3 d+c q\right)} \, dx","-\frac{\log \left(a^2 d^{2/3} x^4+\sqrt[3]{p x^4+q} \left(-a \sqrt[3]{c} \sqrt[3]{d} x^2-b \sqrt[3]{c} \sqrt[3]{d}\right)+2 a b d^{2/3} x^2+b^2 d^{2/3}+c^{2/3} \left(p x^4+q\right)^{2/3}\right)}{2 c^{2/3} \sqrt[3]{d}}+\frac{\log \left(a \sqrt[3]{d} x^2+b \sqrt[3]{d}+\sqrt[3]{c} \sqrt[3]{p x^4+q}\right)}{c^{2/3} \sqrt[3]{d}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{c} \sqrt[3]{p x^4+q}}{-2 a \sqrt[3]{d} x^2-2 b \sqrt[3]{d}+\sqrt[3]{c} \sqrt[3]{p x^4+q}}\right)}{c^{2/3} \sqrt[3]{d}}",1,"2*Integrate[(3*a*q*x - 2*b*p*x^3 + a*p*x^5)/((q + p*x^4)^(1/3)*(b^3*d + c*q + 3*a*b^2*d*x^2 + (3*a^2*b*d + c*p)*x^4 + a^3*d*x^6)), x]","F",1
2641,0,0,235,3.995057,"\int \frac{\left(b^2-2 b x+x^2\right) \left(-a^2 b+4 a b x-(2 a+3 b) x^2+2 x^3\right)}{\left(x (-a+x)^2 (-b+x)^3\right)^{3/4} \left(b d+\left(a^2-d\right) x-2 a x^2+x^3\right)} \, dx","Integrate[((b^2 - 2*b*x + x^2)*(-(a^2*b) + 4*a*b*x - (2*a + 3*b)*x^2 + 2*x^3))/((x*(-a + x)^2*(-b + x)^3)^(3/4)*(b*d + (a^2 - d)*x - 2*a*x^2 + x^3)),x]","\int \frac{\left(b^2-2 b x+x^2\right) \left(-a^2 b+4 a b x-(2 a+3 b) x^2+2 x^3\right)}{\left(x (-a+x)^2 (-b+x)^3\right)^{3/4} \left(b d+\left(a^2-d\right) x-2 a x^2+x^3\right)} \, dx","\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \left(-a^2 b^3 x+x^4 \left(a^2+6 a b+3 b^2\right)+x^3 \left(-3 a^2 b-6 a b^2-b^3\right)+x^2 \left(3 a^2 b^2+2 a b^3\right)+x^5 (-2 a-3 b)+x^6\right)^{3/4}}{x (x-a)^2 (b-x)^2}\right)}{d^{3/4}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \left(-a^2 b^3 x+x^4 \left(a^2+6 a b+3 b^2\right)+x^3 \left(-3 a^2 b-6 a b^2-b^3\right)+x^2 \left(3 a^2 b^2+2 a b^3\right)+x^5 (-2 a-3 b)+x^6\right)^{3/4}}{x (x-a)^2 (b-x)^2}\right)}{d^{3/4}}",1,"Integrate[((b^2 - 2*b*x + x^2)*(-(a^2*b) + 4*a*b*x - (2*a + 3*b)*x^2 + 2*x^3))/((x*(-a + x)^2*(-b + x)^3)^(3/4)*(b*d + (a^2 - d)*x - 2*a*x^2 + x^3)), x]","F",-1
2642,0,0,235,8.2324467,"\int \frac{(-2+(1+k) x) \left(1-2 (1+k) x+\left(1+4 k+k^2\right) x^2-2 \left(k+k^2\right) x^3+\left(a+k^2\right) x^4\right)}{x^3 ((1-x) x (1-k x))^{2/3} \left(1-(1+k) x+(-b+k) x^2\right)} \, dx","Integrate[((-2 + (1 + k)*x)*(1 - 2*(1 + k)*x + (1 + 4*k + k^2)*x^2 - 2*(k + k^2)*x^3 + (a + k^2)*x^4))/(x^3*((1 - x)*x*(1 - k*x))^(2/3)*(1 - (1 + k)*x + (-b + k)*x^2)),x]","\int \frac{(-2+(1+k) x) \left(1-2 (1+k) x+\left(1+4 k+k^2\right) x^2-2 \left(k+k^2\right) x^3+\left(a+k^2\right) x^4\right)}{x^3 ((1-x) x (1-k x))^{2/3} \left(1-(1+k) x+(-b+k) x^2\right)} \, dx","\frac{\left(a+b^2\right) \log \left(\sqrt[3]{k x^3+(-k-1) x^2+x}-\sqrt[3]{b} x\right)}{b^{2/3}}+\frac{\left(-a-b^2\right) \log \left(b^{2/3} x^2+\sqrt[3]{b} x \sqrt[3]{k x^3+(-k-1) x^2+x}+\left(k x^3+(-k-1) x^2+x\right)^{2/3}\right)}{2 b^{2/3}}+\frac{\left(\sqrt{3} a+\sqrt{3} b^2\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{b} x}{\sqrt[3]{b} x+2 \sqrt[3]{k x^3+(-k-1) x^2+x}}\right)}{b^{2/3}}+\frac{3 \sqrt[3]{k x^3-k x^2-x^2+x} \left(4 b x^2+k x^2-k x-x+1\right)}{4 x^3}",1,"Integrate[((-2 + (1 + k)*x)*(1 - 2*(1 + k)*x + (1 + 4*k + k^2)*x^2 - 2*(k + k^2)*x^3 + (a + k^2)*x^4))/(x^3*((1 - x)*x*(1 - k*x))^(2/3)*(1 - (1 + k)*x + (-b + k)*x^2)), x]","F",-1
2643,1,302,235,0.4662981,"\int \frac{\left(1+x^3\right) \sqrt[3]{-x^2+x^3}}{1+x^6} \, dx","Integrate[((1 + x^3)*(-x^2 + x^3)^(1/3))/(1 + x^6),x]","\frac{\left(\frac{1}{4}+\frac{i}{4}\right) \sqrt[3]{(x-1) x^2} \left(-\left(\left(\sqrt{3}+i\right) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(\frac{1}{2}-\frac{i}{2}\right) (x-1)}{x}\right)\right)+\left(1-i \sqrt{3}\right) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(\frac{1}{2}+\frac{i}{2}\right) (x-1)}{x}\right)+\sqrt{3} \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};-\frac{2 (x-1)}{\left((-2+i)+\sqrt{3}\right) x}\right)-i \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};-\frac{2 (x-1)}{\left((-2+i)+\sqrt{3}\right) x}\right)-2 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(i+\sqrt{3}\right) (x-1)}{\left((-2+i)+\sqrt{3}\right) x}\right)+i \sqrt{3} \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{2 (x-1)}{\left((2+i)+\sqrt{3}\right) x}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{2 (x-1)}{\left((2+i)+\sqrt{3}\right) x}\right)+2 i \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(i+\sqrt{3}\right) (x-1)}{\left((2+i)+\sqrt{3}\right) x}\right)\right)}{\left(\sqrt[3]{-1}-1\right) x}","\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^6-2 \text{$\#$1}^3+2\&,\frac{\log \left(\sqrt[3]{x^3-x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}^2}\&\right]-\frac{1}{6} \text{RootSum}\left[\text{$\#$1}^{12}-4 \text{$\#$1}^9+5 \text{$\#$1}^6-2 \text{$\#$1}^3+1\&,\frac{2 \text{$\#$1}^9 \log \left(\sqrt[3]{x^3-x^2}-\text{$\#$1} x\right)-2 \text{$\#$1}^9 \log (x)-3 \text{$\#$1}^6 \log \left(\sqrt[3]{x^3-x^2}-\text{$\#$1} x\right)+3 \text{$\#$1}^6 \log (x)-\text{$\#$1}^3 \log \left(\sqrt[3]{x^3-x^2}-\text{$\#$1} x\right)+\text{$\#$1}^3 \log (x)-\log \left(\sqrt[3]{x^3-x^2}-\text{$\#$1} x\right)+\log (x)}{2 \text{$\#$1}^{11}-6 \text{$\#$1}^8+5 \text{$\#$1}^5-\text{$\#$1}^2}\&\right]",1,"((1/4 + I/4)*((-1 + x)*x^2)^(1/3)*(-((I + Sqrt[3])*Hypergeometric2F1[1/3, 1, 4/3, ((1/2 - I/2)*(-1 + x))/x]) + (1 - I*Sqrt[3])*Hypergeometric2F1[1/3, 1, 4/3, ((1/2 + I/2)*(-1 + x))/x] - I*Hypergeometric2F1[1/3, 1, 4/3, (-2*(-1 + x))/(((-2 + I) + Sqrt[3])*x)] + Sqrt[3]*Hypergeometric2F1[1/3, 1, 4/3, (-2*(-1 + x))/(((-2 + I) + Sqrt[3])*x)] - 2*Hypergeometric2F1[1/3, 1, 4/3, ((I + Sqrt[3])*(-1 + x))/(((-2 + I) + Sqrt[3])*x)] + Hypergeometric2F1[1/3, 1, 4/3, (2*(-1 + x))/(((2 + I) + Sqrt[3])*x)] + I*Sqrt[3]*Hypergeometric2F1[1/3, 1, 4/3, (2*(-1 + x))/(((2 + I) + Sqrt[3])*x)] + (2*I)*Hypergeometric2F1[1/3, 1, 4/3, ((I + Sqrt[3])*(-1 + x))/(((2 + I) + Sqrt[3])*x)]))/((-1 + (-1)^(1/3))*x)","C",1
2644,0,0,235,0.362469,"\int \frac{\sqrt{a x^2+\sqrt{b+a^2 x^4}}}{\left(d+c x^2\right) \sqrt{b+a^2 x^4}} \, dx","Integrate[Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/((d + c*x^2)*Sqrt[b + a^2*x^4]),x]","\int \frac{\sqrt{a x^2+\sqrt{b+a^2 x^4}}}{\left(d+c x^2\right) \sqrt{b+a^2 x^4}} \, dx","-\frac{i \sqrt{a} \text{RootSum}\left[\text{$\#$1}^4 c+4 i \text{$\#$1}^3 a d+2 \text{$\#$1}^2 b c-4 i \text{$\#$1} a b d+b^2 c\&,\frac{b \log \left(-\text{$\#$1}+i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)-\text{$\#$1}^2 \log \left(-\text{$\#$1}+i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)}{\text{$\#$1}^3 c+3 i \text{$\#$1}^2 a d+\text{$\#$1} b c-i a b d}\&\right]}{\sqrt{2}}",1,"Integrate[Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/((d + c*x^2)*Sqrt[b + a^2*x^4]), x]","F",-1
2645,0,0,235,0.1595488,"\int \frac{\sqrt{a x^2+\sqrt{b+a^2 x^4}}}{\left(d+c x^2\right) \sqrt{b+a^2 x^4}} \, dx","Integrate[Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/((d + c*x^2)*Sqrt[b + a^2*x^4]),x]","\int \frac{\sqrt{a x^2+\sqrt{b+a^2 x^4}}}{\left(d+c x^2\right) \sqrt{b+a^2 x^4}} \, dx","-\frac{i \sqrt{a} \text{RootSum}\left[\text{$\#$1}^4 c+4 i \text{$\#$1}^3 a d+2 \text{$\#$1}^2 b c-4 i \text{$\#$1} a b d+b^2 c\&,\frac{b \log \left(-\text{$\#$1}+i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)-\text{$\#$1}^2 \log \left(-\text{$\#$1}+i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)}{\text{$\#$1}^3 c+3 i \text{$\#$1}^2 a d+\text{$\#$1} b c-i a b d}\&\right]}{\sqrt{2}}",1,"Integrate[Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/((d + c*x^2)*Sqrt[b + a^2*x^4]), x]","F",-1
2646,0,0,235,11.7626911,"\int \frac{\sqrt{a x+\sqrt{b+a^2 x^2}} \sqrt{c+\sqrt{a x+\sqrt{b+a^2 x^2}}}}{\left(b+a^2 x^2\right)^{3/2}} \, dx","Integrate[(Sqrt[a*x + Sqrt[b + a^2*x^2]]*Sqrt[c + Sqrt[a*x + Sqrt[b + a^2*x^2]]])/(b + a^2*x^2)^(3/2),x]","\int \frac{\sqrt{a x+\sqrt{b+a^2 x^2}} \sqrt{c+\sqrt{a x+\sqrt{b+a^2 x^2}}}}{\left(b+a^2 x^2\right)^{3/2}} \, dx","-\frac{\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6 c+6 \text{$\#$1}^4 c^2-4 \text{$\#$1}^2 c^3+b+c^4\&,\frac{3 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}-\text{$\#$1}\right)-c \log \left(\sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}-\text{$\#$1}\right)}{-\text{$\#$1}^7+3 \text{$\#$1}^5 c-3 \text{$\#$1}^3 c^2+\text{$\#$1} c^3}\&\right]}{4 a}-\frac{\sqrt{\sqrt{a^2 x^2+b}+a x} \sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}}{a^2 x \sqrt{a^2 x^2+b}+a \left(a^2 x^2+b\right)}",1,"Integrate[(Sqrt[a*x + Sqrt[b + a^2*x^2]]*Sqrt[c + Sqrt[a*x + Sqrt[b + a^2*x^2]]])/(b + a^2*x^2)^(3/2), x]","F",-1
2647,0,0,235,0.2066961,"\int \frac{\sqrt{a x+\sqrt{b+a^2 x^2}} \sqrt{c+\sqrt{a x+\sqrt{b+a^2 x^2}}}}{\left(b+a^2 x^2\right)^{3/2}} \, dx","Integrate[(Sqrt[a*x + Sqrt[b + a^2*x^2]]*Sqrt[c + Sqrt[a*x + Sqrt[b + a^2*x^2]]])/(b + a^2*x^2)^(3/2),x]","\int \frac{\sqrt{a x+\sqrt{b+a^2 x^2}} \sqrt{c+\sqrt{a x+\sqrt{b+a^2 x^2}}}}{\left(b+a^2 x^2\right)^{3/2}} \, dx","-\frac{\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6 c+6 \text{$\#$1}^4 c^2-4 \text{$\#$1}^2 c^3+b+c^4\&,\frac{3 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}-\text{$\#$1}\right)-c \log \left(\sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}-\text{$\#$1}\right)}{-\text{$\#$1}^7+3 \text{$\#$1}^5 c-3 \text{$\#$1}^3 c^2+\text{$\#$1} c^3}\&\right]}{4 a}-\frac{\sqrt{\sqrt{a^2 x^2+b}+a x} \sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}}{a^2 x \sqrt{a^2 x^2+b}+a \left(a^2 x^2+b\right)}",1,"Integrate[(Sqrt[a*x + Sqrt[b + a^2*x^2]]*Sqrt[c + Sqrt[a*x + Sqrt[b + a^2*x^2]]])/(b + a^2*x^2)^(3/2), x]","F",-1
2648,1,204,236,0.4633311,"\int \frac{1+a k x+k x^2}{\left(-1+k x^2\right) \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}} \, dx","Integrate[(1 + a*k*x + k*x^2)/((-1 + k*x^2)*Sqrt[(1 - x^2)*(1 - k^2*x^2)]),x]","\frac{a k \sqrt{x^2-1} \sqrt{k^2 x^2-1} \tanh ^{-1}\left(\frac{\sqrt{-((k-1) k)} \sqrt{x^2-1}}{\sqrt{k-1} \sqrt{k^2 x^2-1}}\right)+\sqrt{k-1} \sqrt{-((k-1) k)} \sqrt{1-x^2} \sqrt{1-k^2 x^2} F\left(\sin ^{-1}(x)|k^2\right)-2 \sqrt{k-1} \sqrt{-((k-1) k)} \sqrt{1-x^2} \sqrt{1-k^2 x^2} \Pi \left(k;\sin ^{-1}(x)|k^2\right)}{\sqrt{k-1} \sqrt{-((k-1) k)} \sqrt{\left(x^2-1\right) \left(k^2 x^2-1\right)}}","\frac{a \sqrt{k} \tan ^{-1}\left(\frac{\left(2 \sqrt{k}-2 k^{3/2}\right) x^2}{k^2 x^4+\left(k x^2+1\right) \sqrt{k^2 x^4+\left(-k^2-1\right) x^2+1}-2 k x^2+1}\right)}{2 \left(\sqrt{k}-1\right) \left(\sqrt{k}+1\right)}+\frac{\tan ^{-1}\left(\frac{\left(-k-2 i \sqrt{k}+1\right) x}{\sqrt{k^2 x^4+\left(-k^2-1\right) x^2+1}+k x^2+1}\right)}{\left(\sqrt{k}-1\right) \left(\sqrt{k}+1\right)}+\frac{\tan ^{-1}\left(\frac{\left(-k+2 i \sqrt{k}+1\right) x}{\sqrt{k^2 x^4+\left(-k^2-1\right) x^2+1}+k x^2+1}\right)}{\left(\sqrt{k}-1\right) \left(\sqrt{k}+1\right)}",1,"(a*k*Sqrt[-1 + x^2]*Sqrt[-1 + k^2*x^2]*ArcTanh[(Sqrt[-((-1 + k)*k)]*Sqrt[-1 + x^2])/(Sqrt[-1 + k]*Sqrt[-1 + k^2*x^2])] + Sqrt[-1 + k]*Sqrt[-((-1 + k)*k)]*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticF[ArcSin[x], k^2] - 2*Sqrt[-1 + k]*Sqrt[-((-1 + k)*k)]*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[k, ArcSin[x], k^2])/(Sqrt[-1 + k]*Sqrt[-((-1 + k)*k)]*Sqrt[(-1 + x^2)*(-1 + k^2*x^2)])","C",1
2649,0,0,236,1.3304972,"\int \frac{3 k+\left(2-k^2\right) x-3 k x^2-k^2 x^3}{\sqrt[3]{\left(1-x^2\right) \left(1-k^2 x^2\right)} \left(1-d-(1+2 d) k x+\left(-1-d k^2\right) x^2+k x^3\right)} \, dx","Integrate[(3*k + (2 - k^2)*x - 3*k*x^2 - k^2*x^3)/(((1 - x^2)*(1 - k^2*x^2))^(1/3)*(1 - d - (1 + 2*d)*k*x + (-1 - d*k^2)*x^2 + k*x^3)),x]","\int \frac{3 k+\left(2-k^2\right) x-3 k x^2-k^2 x^3}{\sqrt[3]{\left(1-x^2\right) \left(1-k^2 x^2\right)} \left(1-d-(1+2 d) k x+\left(-1-d k^2\right) x^2+k x^3\right)} \, dx","\frac{\log \left(d^{2/3} k^2 x^2+2 d^{2/3} k x+d^{2/3}+\sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1} \left(\sqrt[3]{d} k x+\sqrt[3]{d}\right)+\left(k^2 x^4+\left(-k^2-1\right) x^2+1\right)^{2/3}\right)}{2 \sqrt[3]{d}}-\frac{\log \left(-\sqrt[3]{d} k x-\sqrt[3]{d}+\sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}\right)}{\sqrt[3]{d}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}}{2 \sqrt[3]{d} k x+2 \sqrt[3]{d}+\sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}}\right)}{\sqrt[3]{d}}",1,"Integrate[(3*k + (2 - k^2)*x - 3*k*x^2 - k^2*x^3)/(((1 - x^2)*(1 - k^2*x^2))^(1/3)*(1 - d - (1 + 2*d)*k*x + (-1 - d*k^2)*x^2 + k*x^3)), x]","F",-1
2650,0,0,236,1.3543895,"\int \frac{3 k+\left(-2+k^2\right) x-3 k x^2+k^2 x^3}{\sqrt[3]{\left(1-x^2\right) \left(1-k^2 x^2\right)} \left(-1+d-(1+2 d) k x+\left(1+d k^2\right) x^2+k x^3\right)} \, dx","Integrate[(3*k + (-2 + k^2)*x - 3*k*x^2 + k^2*x^3)/(((1 - x^2)*(1 - k^2*x^2))^(1/3)*(-1 + d - (1 + 2*d)*k*x + (1 + d*k^2)*x^2 + k*x^3)),x]","\int \frac{3 k+\left(-2+k^2\right) x-3 k x^2+k^2 x^3}{\sqrt[3]{\left(1-x^2\right) \left(1-k^2 x^2\right)} \left(-1+d-(1+2 d) k x+\left(1+d k^2\right) x^2+k x^3\right)} \, dx","\frac{\log \left(d^{2/3} k^2 x^2-2 d^{2/3} k x+d^{2/3}+\sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1} \left(\sqrt[3]{d}-\sqrt[3]{d} k x\right)+\left(k^2 x^4+\left(-k^2-1\right) x^2+1\right)^{2/3}\right)}{2 \sqrt[3]{d}}-\frac{\log \left(\sqrt[3]{d} k x-\sqrt[3]{d}+\sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}\right)}{\sqrt[3]{d}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}}{-2 \sqrt[3]{d} k x+2 \sqrt[3]{d}+\sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}}\right)}{\sqrt[3]{d}}",1,"Integrate[(3*k + (-2 + k^2)*x - 3*k*x^2 + k^2*x^3)/(((1 - x^2)*(1 - k^2*x^2))^(1/3)*(-1 + d - (1 + 2*d)*k*x + (1 + d*k^2)*x^2 + k*x^3)), x]","F",-1
2651,1,182,236,0.2397328,"\int \frac{\sqrt[4]{-b x^3+a x^4}}{d+c x^2} \, dx","Integrate[(-(b*x^3) + a*x^4)^(1/4)/(d + c*x^2),x]","-\frac{2 \sqrt[4]{x^3 (a x-b)} \left(\left(b \sqrt{-c}-a \sqrt{d}\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};-\frac{\left(a-\frac{b \sqrt{-c}}{\sqrt{d}}\right) x}{b-a x}\right)-\left(a \sqrt{d}+b \sqrt{-c}\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};-\frac{\left(a+\frac{b \sqrt{-c}}{\sqrt{d}}\right) x}{b-a x}\right)+2 a \sqrt{d} \left(1-\frac{a x}{b}\right)^{3/4} \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};\frac{a x}{b}\right)\right)}{3 c \sqrt{d} (b-a x)}","\frac{\text{RootSum}\left[\text{$\#$1}^8 d-2 \text{$\#$1}^4 a d+a^2 d+b^2 c\&,\frac{-\text{$\#$1}^4 a d \log \left(\sqrt[4]{a x^4-b x^3}-\text{$\#$1} x\right)+\text{$\#$1}^4 a d \log (x)+a^2 d \log \left(\sqrt[4]{a x^4-b x^3}-\text{$\#$1} x\right)+b^2 c \log \left(\sqrt[4]{a x^4-b x^3}-\text{$\#$1} x\right)-a^2 d \log (x)-b^2 c \log (x)}{\text{$\#$1}^3 a-\text{$\#$1}^7}\&\right]}{2 c d}-\frac{2 \sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^3}}\right)}{c}+\frac{2 \sqrt[4]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^3}}\right)}{c}",1,"(-2*(x^3*(-b + a*x))^(1/4)*(2*a*Sqrt[d]*(1 - (a*x)/b)^(3/4)*Hypergeometric2F1[3/4, 3/4, 7/4, (a*x)/b] + (b*Sqrt[-c] - a*Sqrt[d])*Hypergeometric2F1[3/4, 1, 7/4, -(((a - (b*Sqrt[-c])/Sqrt[d])*x)/(b - a*x))] - (b*Sqrt[-c] + a*Sqrt[d])*Hypergeometric2F1[3/4, 1, 7/4, -(((a + (b*Sqrt[-c])/Sqrt[d])*x)/(b - a*x))]))/(3*c*Sqrt[d]*(b - a*x))","A",1
2652,1,182,236,0.1188463,"\int \frac{\sqrt[4]{-b x^3+a x^4}}{d+c x^2} \, dx","Integrate[(-(b*x^3) + a*x^4)^(1/4)/(d + c*x^2),x]","-\frac{2 \sqrt[4]{x^3 (a x-b)} \left(\left(b \sqrt{-c}-a \sqrt{d}\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};-\frac{\left(a-\frac{b \sqrt{-c}}{\sqrt{d}}\right) x}{b-a x}\right)-\left(a \sqrt{d}+b \sqrt{-c}\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};-\frac{\left(a+\frac{b \sqrt{-c}}{\sqrt{d}}\right) x}{b-a x}\right)+2 a \sqrt{d} \left(1-\frac{a x}{b}\right)^{3/4} \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};\frac{a x}{b}\right)\right)}{3 c \sqrt{d} (b-a x)}","\frac{\text{RootSum}\left[\text{$\#$1}^8 d-2 \text{$\#$1}^4 a d+a^2 d+b^2 c\&,\frac{-\text{$\#$1}^4 a d \log \left(\sqrt[4]{a x^4-b x^3}-\text{$\#$1} x\right)+\text{$\#$1}^4 a d \log (x)+a^2 d \log \left(\sqrt[4]{a x^4-b x^3}-\text{$\#$1} x\right)+b^2 c \log \left(\sqrt[4]{a x^4-b x^3}-\text{$\#$1} x\right)-a^2 d \log (x)-b^2 c \log (x)}{\text{$\#$1}^3 a-\text{$\#$1}^7}\&\right]}{2 c d}-\frac{2 \sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^3}}\right)}{c}+\frac{2 \sqrt[4]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^3}}\right)}{c}",1,"(-2*(x^3*(-b + a*x))^(1/4)*(2*a*Sqrt[d]*(1 - (a*x)/b)^(3/4)*Hypergeometric2F1[3/4, 3/4, 7/4, (a*x)/b] + (b*Sqrt[-c] - a*Sqrt[d])*Hypergeometric2F1[3/4, 1, 7/4, -(((a - (b*Sqrt[-c])/Sqrt[d])*x)/(b - a*x))] - (b*Sqrt[-c] + a*Sqrt[d])*Hypergeometric2F1[3/4, 1, 7/4, -(((a + (b*Sqrt[-c])/Sqrt[d])*x)/(b - a*x))]))/(3*c*Sqrt[d]*(b - a*x))","A",1
2653,1,915,236,8.0415951,"\int \frac{d+c x^4}{x \sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Integrate[(d + c*x^4)/(x*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]),x]","\frac{2 \left(-1155 d \left(2 a x-\sqrt{b^2+a^2 x^2}\right) \left(a x+\sqrt{b^2+a^2 x^2}\right) a^4-\frac{1155 d \left(b^2+a^2 x^2\right) \left(a x+\sqrt{b^2+a^2 x^2}\right)^2 \left(-2 b^2-a x \left(a x+\sqrt{b^2+a^2 x^2}\right)+2 \left(b^2+2 a x \left(a x+\sqrt{b^2+a^2 x^2}\right)\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{\left(a x+\sqrt{b^2+a^2 x^2}\right)^2}{b^2}\right)\right) a^4}{\left(b^2+a x \left(a x+\sqrt{b^2+a^2 x^2}\right)\right)^2}+\frac{c \sqrt{b^2+a^2 x^2} \left(128 b^{10}+144 a x \left(9 a x+4 \sqrt{b^2+a^2 x^2}\right) b^8+195 a^3 x^3 \left(9 a x+8 \sqrt{b^2+a^2 x^2}\right) b^6-15 a^5 x^5 \left(97 a x+\sqrt{b^2+a^2 x^2}\right) b^4-180 a^7 x^7 \left(37 a x+23 \sqrt{b^2+a^2 x^2}\right) b^2-5040 a^9 x^9 \left(a x+\sqrt{b^2+a^2 x^2}\right)\right)}{\left(a x+\sqrt{b^2+a^2 x^2}\right)^3 \left(b^2+a x \left(a x+\sqrt{b^2+a^2 x^2}\right)\right)}+\frac{c \sqrt{b^2+a^2 x^2} \left(b^2+2 a x \left(a x+\sqrt{b^2+a^2 x^2}\right)\right)^4 \left(-304 b^{10}-342 a x \left(9 a x+4 \sqrt{b^2+a^2 x^2}\right) b^8-15 a^3 x^3 \left(249 a x+247 \sqrt{b^2+a^2 x^2}\right) b^6+15 a^5 x^5 \left(317 a x+89 \sqrt{b^2+a^2 x^2}\right) b^4+180 a^7 x^7 \left(59 a x+45 \sqrt{b^2+a^2 x^2}\right) b^2+5040 a^9 x^9 \left(a x+\sqrt{b^2+a^2 x^2}\right)\right)}{2048 a^{13} x^{13}+2048 a^{12} \sqrt{b^2+a^2 x^2} x^{12}+7168 a^{11} b^2 x^{11}+6144 a^{10} b^2 \sqrt{b^2+a^2 x^2} x^{10}+9728 a^9 b^4 x^9+6912 a^8 b^4 \sqrt{b^2+a^2 x^2} x^8+6400 a^7 b^6 x^7+3584 a^6 b^6 \sqrt{b^2+a^2 x^2} x^6+2072 a^5 b^8 x^5+840 a^4 b^8 \sqrt{b^2+a^2 x^2} x^4+292 a^3 b^{10} x^3+72 a^2 b^{10} \sqrt{b^2+a^2 x^2} x^2+12 a b^{12} x+b^{12} \sqrt{b^2+a^2 x^2}}\right)}{3465 a^4 b^2 \sqrt{a x+\sqrt{b^2+a^2 x^2}}}","\frac{2 d}{\sqrt{\sqrt{a^2 x^2+b^2}+a x}}+\frac{2 d \tan ^{-1}\left(\frac{\sqrt{\sqrt{a^2 x^2+b^2}+a x}}{\sqrt{b}}\right)}{\sqrt{b}}-\frac{2 d \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a^2 x^2+b^2}+a x}}{\sqrt{b}}\right)}{\sqrt{b}}-\frac{b^2 c \left(\sqrt{a^2 x^2+b^2}+a x\right)^{3/2}}{12 a^4}+\frac{c \left(\sqrt{a^2 x^2+b^2}+a x\right)^{7/2}}{56 a^4}+\frac{b^8 c}{72 a^4 \left(\sqrt{a^2 x^2+b^2}+a x\right)^{9/2}}-\frac{b^6 c}{20 a^4 \left(\sqrt{a^2 x^2+b^2}+a x\right)^{5/2}}",1,"(2*(-1155*a^4*d*(2*a*x - Sqrt[b^2 + a^2*x^2])*(a*x + Sqrt[b^2 + a^2*x^2]) + (c*Sqrt[b^2 + a^2*x^2]*(128*b^10 - 5040*a^9*x^9*(a*x + Sqrt[b^2 + a^2*x^2]) - 15*a^5*b^4*x^5*(97*a*x + Sqrt[b^2 + a^2*x^2]) + 144*a*b^8*x*(9*a*x + 4*Sqrt[b^2 + a^2*x^2]) + 195*a^3*b^6*x^3*(9*a*x + 8*Sqrt[b^2 + a^2*x^2]) - 180*a^7*b^2*x^7*(37*a*x + 23*Sqrt[b^2 + a^2*x^2])))/((a*x + Sqrt[b^2 + a^2*x^2])^3*(b^2 + a*x*(a*x + Sqrt[b^2 + a^2*x^2]))) + (c*Sqrt[b^2 + a^2*x^2]*(b^2 + 2*a*x*(a*x + Sqrt[b^2 + a^2*x^2]))^4*(-304*b^10 + 5040*a^9*x^9*(a*x + Sqrt[b^2 + a^2*x^2]) - 342*a*b^8*x*(9*a*x + 4*Sqrt[b^2 + a^2*x^2]) + 180*a^7*b^2*x^7*(59*a*x + 45*Sqrt[b^2 + a^2*x^2]) + 15*a^5*b^4*x^5*(317*a*x + 89*Sqrt[b^2 + a^2*x^2]) - 15*a^3*b^6*x^3*(249*a*x + 247*Sqrt[b^2 + a^2*x^2])))/(12*a*b^12*x + 292*a^3*b^10*x^3 + 2072*a^5*b^8*x^5 + 6400*a^7*b^6*x^7 + 9728*a^9*b^4*x^9 + 7168*a^11*b^2*x^11 + 2048*a^13*x^13 + b^12*Sqrt[b^2 + a^2*x^2] + 72*a^2*b^10*x^2*Sqrt[b^2 + a^2*x^2] + 840*a^4*b^8*x^4*Sqrt[b^2 + a^2*x^2] + 3584*a^6*b^6*x^6*Sqrt[b^2 + a^2*x^2] + 6912*a^8*b^4*x^8*Sqrt[b^2 + a^2*x^2] + 6144*a^10*b^2*x^10*Sqrt[b^2 + a^2*x^2] + 2048*a^12*x^12*Sqrt[b^2 + a^2*x^2]) - (1155*a^4*d*(b^2 + a^2*x^2)*(a*x + Sqrt[b^2 + a^2*x^2])^2*(-2*b^2 - a*x*(a*x + Sqrt[b^2 + a^2*x^2]) + 2*(b^2 + 2*a*x*(a*x + Sqrt[b^2 + a^2*x^2]))*Hypergeometric2F1[3/4, 1, 7/4, (a*x + Sqrt[b^2 + a^2*x^2])^2/b^2]))/(b^2 + a*x*(a*x + Sqrt[b^2 + a^2*x^2]))^2))/(3465*a^4*b^2*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])","C",1
2654,0,0,236,4.5109672,"\int \frac{\sqrt{1+x^2} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[(Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/Sqrt[x + Sqrt[1 + x^2]],x]","\int \frac{\sqrt{1+x^2} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\sqrt{x+\sqrt{1+x^2}}} \, dx","\frac{\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(3072 x^3+4096 x^2+1814 x+1712\right)+\sqrt{x^2+1} \left(\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(3072 x^2+4096 x+278\right)+\left(30720 x^3-4096 x^2-36930 x-632\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\left(30720 x^4-4096 x^3-21570 x^2-2680 x-24993\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{26880 \left(\sqrt{x^2+1}+x\right)^{5/2}}-\frac{263}{256} \tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)",1,"Integrate[(Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/Sqrt[x + Sqrt[1 + x^2]], x]","F",-1
2655,0,0,236,2.7413551,"\int \sqrt{1+x^2} \sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[Sqrt[1 + x^2]*Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]],x]","\int \sqrt{1+x^2} \sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}} \, dx","\frac{\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(2240 x^3+1536 x^2+40688 x-1542\right)+\sqrt{x^2+1} \left(\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(2240 x^2+1536 x+39568\right)+\left(40320 x^3-2560 x^2+92032 x+2825\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\left(40320 x^4-2560 x^3+112192 x^2+1545 x+31736\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{55440 \left(\sqrt{x^2+1}+x\right)^{3/2}}-\frac{1}{16} \tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)",1,"Integrate[Sqrt[1 + x^2]*Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]], x]","F",-1
2656,1,68,237,0.0218128,"\int \frac{\sqrt[4]{-x^3+x^4}}{x (-b+a x)} \, dx","Integrate[(-x^3 + x^4)^(1/4)/(x*(-b + a*x)),x]","\frac{4 \sqrt[4]{(x-1) x^3} \left(\sqrt[4]{x} \, _2F_1\left(\frac{1}{4},\frac{1}{4};\frac{5}{4};1-x\right)-\, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{b-b x}{a x-b x}\right)\right)}{a x}","-\frac{\sqrt{2} \sqrt[4]{a-b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x \sqrt[4]{x^4-x^3} \sqrt[4]{a-b}}{x^2 \sqrt{a-b}-\sqrt{b} \sqrt{x^4-x^3}}\right)}{a \sqrt[4]{b}}-\frac{\sqrt{2} \sqrt[4]{a-b} \tanh ^{-1}\left(\frac{\frac{x^2 \sqrt[4]{a-b}}{\sqrt{2} \sqrt[4]{b}}+\frac{\sqrt[4]{b} \sqrt{x^4-x^3}}{\sqrt{2} \sqrt[4]{a-b}}}{x \sqrt[4]{x^4-x^3}}\right)}{a \sqrt[4]{b}}-\frac{2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^3}}\right)}{a}+\frac{2 \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^3}}\right)}{a}",1,"(4*((-1 + x)*x^3)^(1/4)*(x^(1/4)*Hypergeometric2F1[1/4, 1/4, 5/4, 1 - x] - Hypergeometric2F1[1/4, 1, 5/4, (b - b*x)/(a*x - b*x)]))/(a*x)","C",1
2657,0,0,237,0.6199369,"\int \frac{x^3 (-2 a b+(a+b) x)}{(x (-a+x) (-b+x))^{2/3} \left(-a^2 b^2+2 a b (a+b) x-\left(a^2+4 a b+b^2\right) x^2+2 (a+b) x^3+(-1+d) x^4\right)} \, dx","Integrate[(x^3*(-2*a*b + (a + b)*x))/((x*(-a + x)*(-b + x))^(2/3)*(-(a^2*b^2) + 2*a*b*(a + b)*x - (a^2 + 4*a*b + b^2)*x^2 + 2*(a + b)*x^3 + (-1 + d)*x^4)),x]","\int \frac{x^3 (-2 a b+(a+b) x)}{(x (-a+x) (-b+x))^{2/3} \left(-a^2 b^2+2 a b (a+b) x-\left(a^2+4 a b+b^2\right) x^2+2 (a+b) x^3+(-1+d) x^4\right)} \, dx","\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{d} x}{\sqrt[6]{d} x-2 \sqrt[3]{x^2 (-a-b)+a b x+x^3}}\right)}{2 d^{5/6}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{d} x}{2 \sqrt[3]{x^2 (-a-b)+a b x+x^3}+\sqrt[6]{d} x}\right)}{2 d^{5/6}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{d} x}{\sqrt[3]{x^2 (-a-b)+a b x+x^3}}\right)}{d^{5/6}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{d} x \sqrt[3]{x^2 (-a-b)+a b x+x^3}}{\left(x^2 (-a-b)+a b x+x^3\right)^{2/3}+\sqrt[3]{d} x^2}\right)}{2 d^{5/6}}",1,"Integrate[(x^3*(-2*a*b + (a + b)*x))/((x*(-a + x)*(-b + x))^(2/3)*(-(a^2*b^2) + 2*a*b*(a + b)*x - (a^2 + 4*a*b + b^2)*x^2 + 2*(a + b)*x^3 + (-1 + d)*x^4)), x]","F",-1
2658,0,0,237,0.8467744,"\int \frac{1+2 x^6}{\sqrt[3]{x+x^3} \left(-1+x^6\right)} \, dx","Integrate[(1 + 2*x^6)/((x + x^3)^(1/3)*(-1 + x^6)),x]","\int \frac{1+2 x^6}{\sqrt[3]{x+x^3} \left(-1+x^6\right)} \, dx","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^6-\text{$\#$1}^3+1\&,\frac{\log \left(\sqrt[3]{x^3+x}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]-\log \left(\sqrt[3]{x^3+x}-x\right)+\frac{\log \left(2^{2/3} \sqrt[3]{x^3+x}-2 x\right)}{2 \sqrt[3]{2}}+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+x}+x}\right)-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^3+x}+x}\right)}{2 \sqrt[3]{2}}+\frac{1}{2} \log \left(\sqrt[3]{x^3+x} x+\left(x^3+x\right)^{2/3}+x^2\right)-\frac{\log \left(2^{2/3} \sqrt[3]{x^3+x} x+\sqrt[3]{2} \left(x^3+x\right)^{2/3}+2 x^2\right)}{4 \sqrt[3]{2}}",1,"Integrate[(1 + 2*x^6)/((x + x^3)^(1/3)*(-1 + x^6)), x]","F",-1
2659,0,0,237,0.2631942,"\int \frac{1+2 x^6}{\sqrt[3]{x+x^3} \left(-1+x^6\right)} \, dx","Integrate[(1 + 2*x^6)/((x + x^3)^(1/3)*(-1 + x^6)),x]","\int \frac{1+2 x^6}{\sqrt[3]{x+x^3} \left(-1+x^6\right)} \, dx","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^6-\text{$\#$1}^3+1\&,\frac{\log \left(\sqrt[3]{x^3+x}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]-\log \left(\sqrt[3]{x^3+x}-x\right)+\frac{\log \left(2^{2/3} \sqrt[3]{x^3+x}-2 x\right)}{2 \sqrt[3]{2}}+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+x}+x}\right)-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^3+x}+x}\right)}{2 \sqrt[3]{2}}+\frac{1}{2} \log \left(\sqrt[3]{x^3+x} x+\left(x^3+x\right)^{2/3}+x^2\right)-\frac{\log \left(2^{2/3} \sqrt[3]{x^3+x} x+\sqrt[3]{2} \left(x^3+x\right)^{2/3}+2 x^2\right)}{4 \sqrt[3]{2}}",1,"Integrate[(1 + 2*x^6)/((x + x^3)^(1/3)*(-1 + x^6)), x]","F",-1
2660,1,108,238,0.2429293,"\int \frac{\left(-4 b+a x^3\right) \sqrt[3]{b+a x^3}}{x^5 \left(-2 b+a x^3\right)} \, dx","Integrate[((-4*b + a*x^3)*(b + a*x^3)^(1/3))/(x^5*(-2*b + a*x^3)),x]","\frac{\frac{3 a^2 x^6 \left(\frac{2 a x^3}{b}+2\right)^{2/3} \, _2F_1\left(\frac{2}{3},\frac{2}{3};\frac{5}{3};\frac{3 a x^3}{a x^3-2 b}\right)}{\left(2-\frac{a x^3}{b}\right)^{2/3}}-4 \left(2 a^2 x^6+3 a b x^3+b^2\right)}{8 b x^4 \left(a x^3+b\right)^{2/3}}","-\frac{a^{4/3} \log \left(\sqrt[3]{2} 3^{2/3} \sqrt[3]{a x^3+b}-3 \sqrt[3]{a} x\right)}{2 \sqrt[3]{2} 3^{2/3} b}-\frac{a^{4/3} \tan ^{-1}\left(\frac{3^{5/6} \sqrt[3]{a} x}{2 \sqrt[3]{2} \sqrt[3]{a x^3+b}+\sqrt[3]{3} \sqrt[3]{a} x}\right)}{2 \sqrt[3]{2} \sqrt[6]{3} b}+\frac{a^{4/3} \log \left(3 a^{2/3} x^2+\sqrt[3]{2} 3^{2/3} \sqrt[3]{a} x \sqrt[3]{a x^3+b}+2^{2/3} \sqrt[3]{3} \left(a x^3+b\right)^{2/3}\right)}{4 \sqrt[3]{2} 3^{2/3} b}+\frac{\left(-2 a x^3-b\right) \sqrt[3]{a x^3+b}}{2 b x^4}",1,"(-4*(b^2 + 3*a*b*x^3 + 2*a^2*x^6) + (3*a^2*x^6*(2 + (2*a*x^3)/b)^(2/3)*Hypergeometric2F1[2/3, 2/3, 5/3, (3*a*x^3)/(-2*b + a*x^3)])/(2 - (a*x^3)/b)^(2/3))/(8*b*x^4*(b + a*x^3)^(2/3))","C",0
2661,0,0,238,4.1571616,"\int \frac{-2 a^2 b x+a (3 a+2 b) x^2-4 a x^3+x^4}{\left(x^2 (-a+x) (-b+x)\right)^{2/3} \left(-a^2 d+2 a d x-(b+d) x^2+x^3\right)} \, dx","Integrate[(-2*a^2*b*x + a*(3*a + 2*b)*x^2 - 4*a*x^3 + x^4)/((x^2*(-a + x)*(-b + x))^(2/3)*(-(a^2*d) + 2*a*d*x - (b + d)*x^2 + x^3)),x]","\int \frac{-2 a^2 b x+a (3 a+2 b) x^2-4 a x^3+x^4}{\left(x^2 (-a+x) (-b+x)\right)^{2/3} \left(-a^2 d+2 a d x-(b+d) x^2+x^3\right)} \, dx","-\frac{\log \left(a^2 d^{2/3}+\sqrt[3]{x^3 (-a-b)+a b x^2+x^4} \left(\sqrt[3]{d} x-a \sqrt[3]{d}\right)+\left(x^3 (-a-b)+a b x^2+x^4\right)^{2/3}-2 a d^{2/3} x+d^{2/3} x^2\right)}{2 d^{2/3}}+\frac{\log \left(\sqrt[3]{x^3 (-a-b)+a b x^2+x^4}+a \sqrt[3]{d}-\sqrt[3]{d} x\right)}{d^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} a \sqrt[3]{d}-\sqrt{3} \sqrt[3]{d} x}{-2 \sqrt[3]{x^3 (-a-b)+a b x^2+x^4}+a \sqrt[3]{d}-\sqrt[3]{d} x}\right)}{d^{2/3}}",1,"Integrate[(-2*a^2*b*x + a*(3*a + 2*b)*x^2 - 4*a*x^3 + x^4)/((x^2*(-a + x)*(-b + x))^(2/3)*(-(a^2*d) + 2*a*d*x - (b + d)*x^2 + x^3)), x]","F",-1
2662,0,0,238,6.6143196,"\int \frac{(-2+(1+k) x) \left(1-2 (1+k) x+\left(1+4 k+k^2\right) x^2-2 \left(k+k^2\right) x^3+\left(a+k^2\right) x^4\right)}{x^4 \sqrt[3]{(1-x) x (1-k x)} \left(1-(1+k) x+(-b+k) x^2\right)} \, dx","Integrate[((-2 + (1 + k)*x)*(1 - 2*(1 + k)*x + (1 + 4*k + k^2)*x^2 - 2*(k + k^2)*x^3 + (a + k^2)*x^4))/(x^4*((1 - x)*x*(1 - k*x))^(1/3)*(1 - (1 + k)*x + (-b + k)*x^2)),x]","\int \frac{(-2+(1+k) x) \left(1-2 (1+k) x+\left(1+4 k+k^2\right) x^2-2 \left(k+k^2\right) x^3+\left(a+k^2\right) x^4\right)}{x^4 \sqrt[3]{(1-x) x (1-k x)} \left(1-(1+k) x+(-b+k) x^2\right)} \, dx","\frac{\left(a+b^2\right) \log \left(\sqrt[3]{k x^3+(-k-1) x^2+x}-\sqrt[3]{b} x\right)}{\sqrt[3]{b}}+\frac{\left(-\sqrt{3} a-\sqrt{3} b^2\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{b} x}{\sqrt[3]{b} x+2 \sqrt[3]{k x^3+(-k-1) x^2+x}}\right)}{\sqrt[3]{b}}+\frac{\left(-a-b^2\right) \log \left(b^{2/3} x^2+\sqrt[3]{b} x \sqrt[3]{k x^3+(-k-1) x^2+x}+\left(k x^3+(-k-1) x^2+x\right)^{2/3}\right)}{2 \sqrt[3]{b}}+\frac{3 \left(k x^3-k x^2-x^2+x\right)^{2/3} \left(5 b x^2+2 k x^2-2 k x-2 x+2\right)}{10 x^4}",1,"Integrate[((-2 + (1 + k)*x)*(1 - 2*(1 + k)*x + (1 + 4*k + k^2)*x^2 - 2*(k + k^2)*x^3 + (a + k^2)*x^4))/(x^4*((1 - x)*x*(1 - k*x))^(1/3)*(1 - (1 + k)*x + (-b + k)*x^2)), x]","F",-1
2663,1,176,238,2.7927842,"\int \frac{x^6 \sqrt{x+x^4}}{b+a x^6} \, dx","Integrate[(x^6*Sqrt[x + x^4])/(b + a*x^6),x]","\frac{x \sqrt{x^4+x} \left(\frac{\sqrt{\frac{1}{x^3}+1} \left(\sqrt[4]{b} \left(\sqrt{\sqrt{-a}-\sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{\frac{1}{x^3}+1}}{\sqrt{\sqrt{-a}-\sqrt{b}}}\right)-\sqrt{\sqrt{-a}+\sqrt{b}} \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{\frac{1}{x^3}+1}}{\sqrt{\sqrt{-a}+\sqrt{b}}}\right)\right)+\sqrt{-a} \tanh ^{-1}\left(\sqrt{\frac{1}{x^3}+1}\right)\right)}{\sqrt{-a} \left(x^3+1\right)}+1\right)}{3 a}","\frac{\sqrt[4]{-1} \sqrt{\sqrt{b} \left(\sqrt{a}-i \sqrt{b}\right)} \tan ^{-1}\left(\frac{(1+i) \sqrt{x^4+x} \sqrt{\sqrt{a} \sqrt{b}-i b}}{\sqrt{2} x^2 \left(\sqrt{a}-i \sqrt{b}\right)}\right)}{3 a^{3/2}}+\frac{(-1)^{3/4} \sqrt{\sqrt{b} \left(\sqrt{a}+i \sqrt{b}\right)} \tan ^{-1}\left(\frac{(1+i) x \sqrt{x^4+x} \sqrt{\sqrt{a} \sqrt{b}+i b}}{\sqrt{2} \sqrt{b} (x+1) \left(x^2-x+1\right)}\right)}{3 a^{3/2}}+\frac{\sqrt{x^4+x} x}{3 a}+\frac{\tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4+x}}\right)}{3 a}",1,"(x*Sqrt[x + x^4]*(1 + (Sqrt[1 + x^(-3)]*(Sqrt[-a]*ArcTanh[Sqrt[1 + x^(-3)]] + b^(1/4)*(Sqrt[Sqrt[-a] - Sqrt[b]]*ArcTan[(b^(1/4)*Sqrt[1 + x^(-3)])/Sqrt[Sqrt[-a] - Sqrt[b]]] - Sqrt[Sqrt[-a] + Sqrt[b]]*ArcTanh[(b^(1/4)*Sqrt[1 + x^(-3)])/Sqrt[Sqrt[-a] + Sqrt[b]]])))/(Sqrt[-a]*(1 + x^3))))/(3*a)","A",1
2664,0,0,238,2.3518632,"\int \frac{\sqrt[4]{b x^2+a x^4} \left(-b-a x^4+x^8\right)}{-b+a x^4} \, dx","Integrate[((b*x^2 + a*x^4)^(1/4)*(-b - a*x^4 + x^8))/(-b + a*x^4),x]","\int \frac{\sqrt[4]{b x^2+a x^4} \left(-b-a x^4+x^8\right)}{-b+a x^4} \, dx","\frac{\left(b^2-2 a^2 b\right) \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2-a b\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^4-a}\&\right]}{4 a^2}+\frac{\left(32 a^3 b-32 a b^2-7 b^3\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{128 a^{15/4}}+\frac{\left(-32 a^3 b+32 a b^2+7 b^3\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{128 a^{15/4}}+\frac{\sqrt[4]{a x^4+b x^2} \left(-96 a^3 x+32 a^2 x^5+4 a b x^3+96 a b x-7 b^2 x\right)}{192 a^3}",1,"Integrate[((b*x^2 + a*x^4)^(1/4)*(-b - a*x^4 + x^8))/(-b + a*x^4), x]","F",-1
2665,0,0,238,1.0675276,"\int \frac{\sqrt[4]{b x^2+a x^4} \left(-b-a x^4+x^8\right)}{-b+a x^4} \, dx","Integrate[((b*x^2 + a*x^4)^(1/4)*(-b - a*x^4 + x^8))/(-b + a*x^4),x]","\int \frac{\sqrt[4]{b x^2+a x^4} \left(-b-a x^4+x^8\right)}{-b+a x^4} \, dx","\frac{\left(b^2-2 a^2 b\right) \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2-a b\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^4-a}\&\right]}{4 a^2}+\frac{\left(32 a^3 b-32 a b^2-7 b^3\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{128 a^{15/4}}+\frac{\left(-32 a^3 b+32 a b^2+7 b^3\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{128 a^{15/4}}+\frac{\sqrt[4]{a x^4+b x^2} \left(-96 a^3 x+32 a^2 x^5+4 a b x^3+96 a b x-7 b^2 x\right)}{192 a^3}",1,"Integrate[((b*x^2 + a*x^4)^(1/4)*(-b - a*x^4 + x^8))/(-b + a*x^4), x]","F",-1
2666,0,0,238,1.1048132,"\int \frac{\left(-2+2 x^4+5 x^7\right) \sqrt[3]{x-x^3+x^5+x^8}}{\left(2+x^2+2 x^4+2 x^7\right)^2} \, dx","Integrate[((-2 + 2*x^4 + 5*x^7)*(x - x^3 + x^5 + x^8)^(1/3))/(2 + x^2 + 2*x^4 + 2*x^7)^2,x]","\int \frac{\left(-2+2 x^4+5 x^7\right) \sqrt[3]{x-x^3+x^5+x^8}}{\left(2+x^2+2 x^4+2 x^7\right)^2} \, dx","\frac{\log \left(2 \sqrt[3]{x^8+x^5-x^3+x}+2^{2/3} \sqrt[3]{3} x\right)}{6 \sqrt[3]{2} 3^{2/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x^8+x^5-x^3+x}}{2^{2/3} \sqrt[3]{3} x-\sqrt[3]{x^8+x^5-x^3+x}}\right)}{6 \sqrt[3]{2} \sqrt[6]{3}}-\frac{\log \left(\sqrt[3]{2} 3^{2/3} x^2-2^{2/3} \sqrt[3]{3} \sqrt[3]{x^8+x^5-x^3+x} x+2 \left(x^8+x^5-x^3+x\right)^{2/3}\right)}{12 \sqrt[3]{2} 3^{2/3}}-\frac{\sqrt[3]{x^8+x^5-x^3+x} x}{2 \left(2 x^7+2 x^4+x^2+2\right)}",1,"Integrate[((-2 + 2*x^4 + 5*x^7)*(x - x^3 + x^5 + x^8)^(1/3))/(2 + x^2 + 2*x^4 + 2*x^7)^2, x]","F",-1
2667,1,574,239,2.1757912,"\int \frac{-b^5+a^5 x^5}{\sqrt{b^2 x+a^2 x^3} \left(b^5+a^5 x^5\right)} \, dx","Integrate[(-b^5 + a^5*x^5)/(Sqrt[b^2*x + a^2*x^3]*(b^5 + a^5*x^5)),x]","\frac{2 \sqrt[10]{-1} x^{3/2} \sqrt{\frac{b^2}{a^2 x^2}+1} \left(\left(1+\sqrt[5]{-1}\right)^2 \left(1-3 \sqrt[5]{-1}+(-1)^{2/5}\right) F\left(\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)+2 \left((-1)^{2/5} \Pi \left(-i;\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)+\left(1-\sqrt[5]{-1}+2 (-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}\right) \Pi \left(-\sqrt[10]{-1};\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)-(-1)^{4/5} \Pi \left((-1)^{3/10};\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)+(-1)^{3/5} \Pi \left((-1)^{3/10};\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)+\sqrt[5]{-1} \Pi \left((-1)^{3/10};\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)-\Pi \left((-1)^{3/10};\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)+(-1)^{2/5} \Pi \left((-1)^{7/10};\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)-(-1)^{4/5} \Pi \left(-(-1)^{9/10};\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)+(-1)^{3/5} \Pi \left(-(-1)^{9/10};\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)+\sqrt[5]{-1} \Pi \left(-(-1)^{9/10};\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)-\Pi \left(-(-1)^{9/10};\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)\right)\right)}{\left(\sqrt[5]{-1}-1\right)^2 \left(1+\sqrt[5]{-1}\right)^4 \left(1+(-1)^{2/5}\right) \left(1-\sqrt[5]{-1}+(-1)^{2/5}\right) \sqrt{\frac{i b}{a}} \sqrt{x \left(a^2 x^2+b^2\right)}}","-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{b} \sqrt{a^2 x^3+b^2 x}}{a^2 x^2+b^2}\right)}{5 \sqrt{a} \sqrt{b}}-\frac{2 \sqrt{2 \left(1+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}} \sqrt{a} \sqrt{b} \sqrt{a^2 x^3+b^2 x}}{a^2 x^2+b^2}\right)}{5 \sqrt{a} \sqrt{b}}-\frac{2 \sqrt{2 \left(\sqrt{5}-1\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{2}+\frac{\sqrt{5}}{2}} \sqrt{a} \sqrt{b} \sqrt{a^2 x^3+b^2 x}}{a^2 x^2+b^2}\right)}{5 \sqrt{a} \sqrt{b}}",1,"(2*(-1)^(1/10)*Sqrt[1 + b^2/(a^2*x^2)]*x^(3/2)*((1 + (-1)^(1/5))^2*(1 - 3*(-1)^(1/5) + (-1)^(2/5))*EllipticF[I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1] + 2*((-1)^(2/5)*EllipticPi[-I, I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1] + (1 - (-1)^(1/5) + 2*(-1)^(2/5) - (-1)^(3/5) + (-1)^(4/5))*EllipticPi[-(-1)^(1/10), I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1] - EllipticPi[(-1)^(3/10), I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1] + (-1)^(1/5)*EllipticPi[(-1)^(3/10), I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1] + (-1)^(3/5)*EllipticPi[(-1)^(3/10), I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1] - (-1)^(4/5)*EllipticPi[(-1)^(3/10), I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1] + (-1)^(2/5)*EllipticPi[(-1)^(7/10), I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1] - EllipticPi[-(-1)^(9/10), I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1] + (-1)^(1/5)*EllipticPi[-(-1)^(9/10), I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1] + (-1)^(3/5)*EllipticPi[-(-1)^(9/10), I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1] - (-1)^(4/5)*EllipticPi[-(-1)^(9/10), I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1])))/((-1 + (-1)^(1/5))^2*(1 + (-1)^(1/5))^4*(1 + (-1)^(2/5))*(1 - (-1)^(1/5) + (-1)^(2/5))*Sqrt[(I*b)/a]*Sqrt[x*(b^2 + a^2*x^2)])","C",0
2668,1,574,239,1.9213542,"\int \frac{b^5+a^5 x^5}{\sqrt{b^2 x+a^2 x^3} \left(-b^5+a^5 x^5\right)} \, dx","Integrate[(b^5 + a^5*x^5)/(Sqrt[b^2*x + a^2*x^3]*(-b^5 + a^5*x^5)),x]","\frac{2 \sqrt[10]{-1} x^{3/2} \sqrt{\frac{b^2}{a^2 x^2}+1} \left(\left(1+\sqrt[5]{-1}\right)^2 \left(1-3 \sqrt[5]{-1}+(-1)^{2/5}\right) F\left(\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)+2 \left((-1)^{2/5} \Pi \left(i;\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)+\left(1-\sqrt[5]{-1}+2 (-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}\right) \Pi \left(\sqrt[10]{-1};\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)-(-1)^{4/5} \Pi \left(-(-1)^{3/10};\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)+(-1)^{3/5} \Pi \left(-(-1)^{3/10};\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)+\sqrt[5]{-1} \Pi \left(-(-1)^{3/10};\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)-\Pi \left(-(-1)^{3/10};\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)+(-1)^{2/5} \Pi \left(-(-1)^{7/10};\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)-(-1)^{4/5} \Pi \left((-1)^{9/10};\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)+(-1)^{3/5} \Pi \left((-1)^{9/10};\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)+\sqrt[5]{-1} \Pi \left((-1)^{9/10};\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)-\Pi \left((-1)^{9/10};\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)\right)\right)}{\left(\sqrt[5]{-1}-1\right)^2 \left(1+\sqrt[5]{-1}\right)^4 \left(1+(-1)^{2/5}\right) \left(1-\sqrt[5]{-1}+(-1)^{2/5}\right) \sqrt{\frac{i b}{a}} \sqrt{x \left(a^2 x^2+b^2\right)}}","-\frac{2 \sqrt{2 \left(\sqrt{5}-1\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{1}{2}+\frac{\sqrt{5}}{2}} \sqrt{a} \sqrt{b} \sqrt{a^2 x^3+b^2 x}}{a^2 x^2+b^2}\right)}{5 \sqrt{a} \sqrt{b}}-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{b} \sqrt{a^2 x^3+b^2 x}}{a^2 x^2+b^2}\right)}{5 \sqrt{a} \sqrt{b}}-\frac{2 \sqrt{2 \left(1+\sqrt{5}\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}} \sqrt{a} \sqrt{b} \sqrt{a^2 x^3+b^2 x}}{a^2 x^2+b^2}\right)}{5 \sqrt{a} \sqrt{b}}",1,"(2*(-1)^(1/10)*Sqrt[1 + b^2/(a^2*x^2)]*x^(3/2)*((1 + (-1)^(1/5))^2*(1 - 3*(-1)^(1/5) + (-1)^(2/5))*EllipticF[I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1] + 2*((-1)^(2/5)*EllipticPi[I, I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1] + (1 - (-1)^(1/5) + 2*(-1)^(2/5) - (-1)^(3/5) + (-1)^(4/5))*EllipticPi[(-1)^(1/10), I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1] - EllipticPi[-(-1)^(3/10), I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1] + (-1)^(1/5)*EllipticPi[-(-1)^(3/10), I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1] + (-1)^(3/5)*EllipticPi[-(-1)^(3/10), I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1] - (-1)^(4/5)*EllipticPi[-(-1)^(3/10), I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1] + (-1)^(2/5)*EllipticPi[-(-1)^(7/10), I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1] - EllipticPi[(-1)^(9/10), I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1] + (-1)^(1/5)*EllipticPi[(-1)^(9/10), I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1] + (-1)^(3/5)*EllipticPi[(-1)^(9/10), I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1] - (-1)^(4/5)*EllipticPi[(-1)^(9/10), I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1])))/((-1 + (-1)^(1/5))^2*(1 + (-1)^(1/5))^4*(1 + (-1)^(2/5))*(1 - (-1)^(1/5) + (-1)^(2/5))*Sqrt[(I*b)/a]*Sqrt[x*(b^2 + a^2*x^2)])","C",0
2669,1,292,239,0.3146841,"\int \frac{-2 b-a x^4+2 x^8}{x^4 \sqrt[4]{-b+a x^4} \left(-b+2 a x^4\right)} \, dx","Integrate[(-2*b - a*x^4 + 2*x^8)/(x^4*(-b + a*x^4)^(1/4)*(-b + 2*a*x^4)),x]","\frac{16 a^{5/4} \left(a x^4-b\right)^{3/4}-6 \sqrt{2} x^3 \left(5 a^2-b\right) \left(\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)-\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}+1\right)\right)-3 \sqrt{2} x^3 \left(5 a^2-b\right) \left(\log \left(-\frac{\sqrt{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}+\frac{\sqrt{a} x^2}{\sqrt{a x^4-b}}+1\right)-\log \left(\frac{\sqrt{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}+\frac{\sqrt{a} x^2}{\sqrt{a x^4-b}}+1\right)\right)+12 b x^3 \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)+12 b x^3 \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{24 a^{5/4} b x^3}","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{2 a^{5/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{2 a^{5/4}}+\frac{\left(5 a^2-b\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} x \sqrt[4]{a x^4-b}}{\sqrt{a x^4-b}-\sqrt{a} x^2}\right)}{2 \sqrt{2} a^{5/4} b}+\frac{\left(5 a^2-b\right) \tanh ^{-1}\left(\frac{\sqrt{a x^4-b}+\sqrt{a} x^2}{\sqrt{2} \sqrt[4]{a} x \sqrt[4]{a x^4-b}}\right)}{2 \sqrt{2} a^{5/4} b}+\frac{2 \left(a x^4-b\right)^{3/4}}{3 b x^3}",1,"(16*a^(5/4)*(-b + a*x^4)^(3/4) + 12*b*x^3*ArcTan[(a^(1/4)*x)/(-b + a*x^4)^(1/4)] - 6*Sqrt[2]*(5*a^2 - b)*x^3*(ArcTan[1 - (Sqrt[2]*a^(1/4)*x)/(-b + a*x^4)^(1/4)] - ArcTan[1 + (Sqrt[2]*a^(1/4)*x)/(-b + a*x^4)^(1/4)]) + 12*b*x^3*ArcTanh[(a^(1/4)*x)/(-b + a*x^4)^(1/4)] - 3*Sqrt[2]*(5*a^2 - b)*x^3*(Log[1 + (Sqrt[a]*x^2)/Sqrt[-b + a*x^4] - (Sqrt[2]*a^(1/4)*x)/(-b + a*x^4)^(1/4)] - Log[1 + (Sqrt[a]*x^2)/Sqrt[-b + a*x^4] + (Sqrt[2]*a^(1/4)*x)/(-b + a*x^4)^(1/4)]))/(24*a^(5/4)*b*x^3)","A",1
2670,1,195,239,2.7514489,"\int \frac{-1+x^{16}}{\sqrt{-1+x^4} \left(1+x^8+x^{16}\right)} \, dx","Integrate[(-1 + x^16)/(Sqrt[-1 + x^4]*(1 + x^8 + x^16)),x]","\frac{\sqrt{1-x^4} \left(4 F\left(\left.\sin ^{-1}(x)\right|-1\right)-\Pi \left(-\frac{i}{2}-\frac{\sqrt{3}}{2};\left.\sin ^{-1}(x)\right|-1\right)-\Pi \left(\frac{i}{2}-\frac{\sqrt{3}}{2};\left.\sin ^{-1}(x)\right|-1\right)-\Pi \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2};\left.\sin ^{-1}(x)\right|-1\right)-\Pi \left(\frac{1}{2}-\frac{i \sqrt{3}}{2};\left.\sin ^{-1}(x)\right|-1\right)-\Pi \left(\frac{1}{2}+\frac{i \sqrt{3}}{2};\left.\sin ^{-1}(x)\right|-1\right)-\Pi \left(\frac{1}{2} \left(-i+\sqrt{3}\right);\left.\sin ^{-1}(x)\right|-1\right)-\Pi \left(\frac{1}{2} i \left(i+\sqrt{3}\right);\left.\sin ^{-1}(x)\right|-1\right)-\Pi \left(\frac{1}{2} \left(i+\sqrt{3}\right);\left.\sin ^{-1}(x)\right|-1\right)\right)}{4 \sqrt{x^4-1}}","\frac{\tan ^{-1}\left(\frac{\frac{x^4}{\sqrt{2}}-\frac{x^2}{\sqrt{2}}-\frac{1}{\sqrt{2}}}{x \sqrt{x^4-1}}\right)}{4 \sqrt{2}}+\frac{\tan ^{-1}\left(\frac{\frac{x^4}{\sqrt{2} \sqrt[4]{3}}-\frac{\sqrt[4]{3} x^2}{\sqrt{2}}-\frac{1}{\sqrt{2} \sqrt[4]{3}}}{x \sqrt{x^4-1}}\right)}{4 \sqrt{2} \sqrt[4]{3}}-\frac{\tanh ^{-1}\left(\frac{\frac{x^4}{\sqrt{2}}+\frac{x^2}{\sqrt{2}}-\frac{1}{\sqrt{2}}}{x \sqrt{x^4-1}}\right)}{4 \sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{\frac{x^4}{\sqrt{2} \sqrt[4]{3}}+\frac{\sqrt[4]{3} x^2}{\sqrt{2}}-\frac{1}{\sqrt{2} \sqrt[4]{3}}}{x \sqrt{x^4-1}}\right)}{4 \sqrt{2} \sqrt[4]{3}}",1,"(Sqrt[1 - x^4]*(4*EllipticF[ArcSin[x], -1] - EllipticPi[-1/2*I - Sqrt[3]/2, ArcSin[x], -1] - EllipticPi[I/2 - Sqrt[3]/2, ArcSin[x], -1] - EllipticPi[-1/2 - (I/2)*Sqrt[3], ArcSin[x], -1] - EllipticPi[1/2 - (I/2)*Sqrt[3], ArcSin[x], -1] - EllipticPi[1/2 + (I/2)*Sqrt[3], ArcSin[x], -1] - EllipticPi[(-I + Sqrt[3])/2, ArcSin[x], -1] - EllipticPi[(I/2)*(I + Sqrt[3]), ArcSin[x], -1] - EllipticPi[(I + Sqrt[3])/2, ArcSin[x], -1]))/(4*Sqrt[-1 + x^4])","C",1
2671,0,0,241,3.2921624,"\int \frac{2 a b x-3 a x^2+x^3}{\sqrt[3]{x^2 (-a+x) (-b+x)} \left(-a^2 d+2 a d x-(b+d) x^2+x^3\right)} \, dx","Integrate[(2*a*b*x - 3*a*x^2 + x^3)/((x^2*(-a + x)*(-b + x))^(1/3)*(-(a^2*d) + 2*a*d*x - (b + d)*x^2 + x^3)),x]","\int \frac{2 a b x-3 a x^2+x^3}{\sqrt[3]{x^2 (-a+x) (-b+x)} \left(-a^2 d+2 a d x-(b+d) x^2+x^3\right)} \, dx","-\frac{\log \left(a^2 d^{2/3}+\sqrt[3]{x^3 (-a-b)+a b x^2+x^4} \left(\sqrt[3]{d} x-a \sqrt[3]{d}\right)+\left(x^3 (-a-b)+a b x^2+x^4\right)^{2/3}-2 a d^{2/3} x+d^{2/3} x^2\right)}{2 \sqrt[3]{d}}+\frac{\log \left(\sqrt[3]{x^3 (-a-b)+a b x^2+x^4}+a \sqrt[3]{d}-\sqrt[3]{d} x\right)}{\sqrt[3]{d}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x^3 (-a-b)+a b x^2+x^4}}{\sqrt[3]{x^3 (-a-b)+a b x^2+x^4}-2 a \sqrt[3]{d}+2 \sqrt[3]{d} x}\right)}{\sqrt[3]{d}}",1,"Integrate[(2*a*b*x - 3*a*x^2 + x^3)/((x^2*(-a + x)*(-b + x))^(1/3)*(-(a^2*d) + 2*a*d*x - (b + d)*x^2 + x^3)), x]","F",-1
2672,1,177,241,0.3270383,"\int \frac{\left(d+c x^2\right) \sqrt[4]{b x^3+a x^4}}{x^2 \left(-d+c x^2\right)} \, dx","Integrate[((d + c*x^2)*(b*x^3 + a*x^4)^(1/4))/(x^2*(-d + c*x^2)),x]","\frac{4 \sqrt[4]{x^3 (a x+b)} \left(\frac{x \left(b \sqrt{c}-a \sqrt{d}\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{\left(a-\frac{b \sqrt{c}}{\sqrt{d}}\right) x}{b+a x}\right)-x \left(a \sqrt{d}+b \sqrt{c}\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{\left(a+\frac{b \sqrt{c}}{\sqrt{d}}\right) x}{b+a x}\right)+6 \sqrt{d} (a x+b)}{\sqrt{d} (a x+b)}-\frac{3 \, _2F_1\left(-\frac{1}{4},-\frac{1}{4};\frac{3}{4};-\frac{a x}{b}\right)}{\sqrt[4]{\frac{a x}{b}+1}}\right)}{3 x}","\frac{\text{RootSum}\left[\text{$\#$1}^8 (-d)+2 \text{$\#$1}^4 a d-a^2 d+b^2 c\&,\frac{-\text{$\#$1}^4 a d \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)+\text{$\#$1}^4 a d \log (x)+a^2 d \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)-b^2 c \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)-a^2 d \log (x)+b^2 c \log (x)}{\text{$\#$1}^3 a-\text{$\#$1}^7}\&\right]}{d}+\frac{4 \sqrt[4]{a x^4+b x^3}}{x}-2 \sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)+2 \sqrt[4]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)",1,"(4*(x^3*(b + a*x))^(1/4)*((-3*Hypergeometric2F1[-1/4, -1/4, 3/4, -((a*x)/b)])/(1 + (a*x)/b)^(1/4) + (6*Sqrt[d]*(b + a*x) + (b*Sqrt[c] - a*Sqrt[d])*x*Hypergeometric2F1[3/4, 1, 7/4, ((a - (b*Sqrt[c])/Sqrt[d])*x)/(b + a*x)] - (b*Sqrt[c] + a*Sqrt[d])*x*Hypergeometric2F1[3/4, 1, 7/4, ((a + (b*Sqrt[c])/Sqrt[d])*x)/(b + a*x)])/(Sqrt[d]*(b + a*x))))/(3*x)","A",1
2673,1,177,241,0.0916304,"\int \frac{\left(d+c x^2\right) \sqrt[4]{b x^3+a x^4}}{x^2 \left(-d+c x^2\right)} \, dx","Integrate[((d + c*x^2)*(b*x^3 + a*x^4)^(1/4))/(x^2*(-d + c*x^2)),x]","\frac{4 \sqrt[4]{x^3 (a x+b)} \left(\frac{x \left(b \sqrt{c}-a \sqrt{d}\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{\left(a-\frac{b \sqrt{c}}{\sqrt{d}}\right) x}{b+a x}\right)-x \left(a \sqrt{d}+b \sqrt{c}\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{\left(a+\frac{b \sqrt{c}}{\sqrt{d}}\right) x}{b+a x}\right)+6 \sqrt{d} (a x+b)}{\sqrt{d} (a x+b)}-\frac{3 \, _2F_1\left(-\frac{1}{4},-\frac{1}{4};\frac{3}{4};-\frac{a x}{b}\right)}{\sqrt[4]{\frac{a x}{b}+1}}\right)}{3 x}","\frac{\text{RootSum}\left[\text{$\#$1}^8 (-d)+2 \text{$\#$1}^4 a d-a^2 d+b^2 c\&,\frac{-\text{$\#$1}^4 a d \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)+\text{$\#$1}^4 a d \log (x)+a^2 d \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)-b^2 c \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)-a^2 d \log (x)+b^2 c \log (x)}{\text{$\#$1}^3 a-\text{$\#$1}^7}\&\right]}{d}+\frac{4 \sqrt[4]{a x^4+b x^3}}{x}-2 \sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)+2 \sqrt[4]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)",1,"(4*(x^3*(b + a*x))^(1/4)*((-3*Hypergeometric2F1[-1/4, -1/4, 3/4, -((a*x)/b)])/(1 + (a*x)/b)^(1/4) + (6*Sqrt[d]*(b + a*x) + (b*Sqrt[c] - a*Sqrt[d])*x*Hypergeometric2F1[3/4, 1, 7/4, ((a - (b*Sqrt[c])/Sqrt[d])*x)/(b + a*x)] - (b*Sqrt[c] + a*Sqrt[d])*x*Hypergeometric2F1[3/4, 1, 7/4, ((a + (b*Sqrt[c])/Sqrt[d])*x)/(b + a*x)])/(Sqrt[d]*(b + a*x))))/(3*x)","A",1
2674,1,15389,241,6.560009,"\int \frac{-1+x^4}{\left(1+x^4\right) \sqrt{a+b x+c x^2+b x^3+a x^4}} \, dx","Integrate[(-1 + x^4)/((1 + x^4)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]),x]","\text{Result too large to show}","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^4-4 \text{$\#$1}^2 a-2 \text{$\#$1}^2 c+8 \text{$\#$1} \sqrt{a} b+4 a^2-4 a c-2 b^2+c^2\&,\frac{\text{$\#$1}^2 \log \left(-\text{$\#$1} x+\sqrt{a x^4+a+b x^3+b x+c x^2}+\sqrt{a} \left(-x^2-1\right)\right)+\text{$\#$1}^2 (-\log (x))+2 a \log \left(-\text{$\#$1} x+\sqrt{a x^4+a+b x^3+b x+c x^2}+\sqrt{a} \left(-x^2-1\right)\right)-c \log \left(-\text{$\#$1} x+\sqrt{a x^4+a+b x^3+b x+c x^2}+\sqrt{a} \left(-x^2-1\right)\right)-2 a \log (x)+c \log (x)}{-\text{$\#$1}^3+2 \text{$\#$1} a+\text{$\#$1} c-2 \sqrt{a} b}\&\right]",1,"Result too large to show","C",0
2675,0,0,241,11.8037256,"\int \frac{\left(-2+k^2\right) x+k^2 x^3}{\sqrt[3]{\left(1-x^2\right) \left(1-k^2 x^2\right)} \left(-1+d+\left(-2 d+k^2\right) x^2+d x^4\right)} \, dx","Integrate[((-2 + k^2)*x + k^2*x^3)/(((1 - x^2)*(1 - k^2*x^2))^(1/3)*(-1 + d + (-2*d + k^2)*x^2 + d*x^4)),x]","\int \frac{\left(-2+k^2\right) x+k^2 x^3}{\sqrt[3]{\left(1-x^2\right) \left(1-k^2 x^2\right)} \left(-1+d+\left(-2 d+k^2\right) x^2+d x^4\right)} \, dx","-\frac{\log \left(d^{2/3} x^4-2 d^{2/3} x^2+d^{2/3}+\left(\sqrt[3]{d}-\sqrt[3]{d} x^2\right) \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}+\left(k^2 x^4+\left(-k^2-1\right) x^2+1\right)^{2/3}\right)}{4 \sqrt[3]{d}}+\frac{\log \left(\sqrt[3]{d} x^2-\sqrt[3]{d}+\sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}\right)}{2 \sqrt[3]{d}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}}{-2 \sqrt[3]{d} x^2+2 \sqrt[3]{d}+\sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}}\right)}{2 \sqrt[3]{d}}",1,"Integrate[((-2 + k^2)*x + k^2*x^3)/(((1 - x^2)*(1 - k^2*x^2))^(1/3)*(-1 + d + (-2*d + k^2)*x^2 + d*x^4)), x]","F",-1
2676,0,0,241,1.8910805,"\int \frac{\left(-1+2 k^2\right) x-2 k^4 x^3+k^4 x^5}{\left(\left(1-x^2\right) \left(1-k^2 x^2\right)\right)^{2/3} \left(1-d+\left(d-2 k^2\right) x^2+k^4 x^4\right)} \, dx","Integrate[((-1 + 2*k^2)*x - 2*k^4*x^3 + k^4*x^5)/(((1 - x^2)*(1 - k^2*x^2))^(2/3)*(1 - d + (d - 2*k^2)*x^2 + k^4*x^4)),x]","\int \frac{\left(-1+2 k^2\right) x-2 k^4 x^3+k^4 x^5}{\left(\left(1-x^2\right) \left(1-k^2 x^2\right)\right)^{2/3} \left(1-d+\left(d-2 k^2\right) x^2+k^4 x^4\right)} \, dx","\frac{\log \left(d^{2/3} x^4-2 d^{2/3} x^2+d^{2/3}+\left(\sqrt[3]{d}-\sqrt[3]{d} x^2\right) \left(k^2 x^4+\left(-k^2-1\right) x^2+1\right)^{2/3}+\left(k^2 x^4+\left(-k^2-1\right) x^2+1\right)^{4/3}\right)}{4 \sqrt[3]{d}}-\frac{\log \left(\sqrt[3]{d} x^2-\sqrt[3]{d}+\left(k^2 x^4+\left(-k^2-1\right) x^2+1\right)^{2/3}\right)}{2 \sqrt[3]{d}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \left(k^2 x^4+\left(-k^2-1\right) x^2+1\right)^{2/3}}{-2 \sqrt[3]{d} x^2+2 \sqrt[3]{d}+\left(k^2 x^4+\left(-k^2-1\right) x^2+1\right)^{2/3}}\right)}{2 \sqrt[3]{d}}",1,"Integrate[((-1 + 2*k^2)*x - 2*k^4*x^3 + k^4*x^5)/(((1 - x^2)*(1 - k^2*x^2))^(2/3)*(1 - d + (d - 2*k^2)*x^2 + k^4*x^4)), x]","F",-1
2677,0,0,241,0.3466269,"\int \frac{\left(-2+x^6\right) \left(1-x^4+x^6\right)}{\sqrt[4]{1+x^6} \left(1+2 x^6+x^8+x^{12}\right)} \, dx","Integrate[((-2 + x^6)*(1 - x^4 + x^6))/((1 + x^6)^(1/4)*(1 + 2*x^6 + x^8 + x^12)),x]","\int \frac{\left(-2+x^6\right) \left(1-x^4+x^6\right)}{\sqrt[4]{1+x^6} \left(1+2 x^6+x^8+x^{12}\right)} \, dx","\frac{1}{2} \sqrt{\frac{1}{2} \left(2-\sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}} x \sqrt[4]{x^6+1}}{\sqrt{x^6+1}-x^2}\right)-\frac{1}{2} \sqrt{\frac{1}{2} \left(2+\sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}} x \sqrt[4]{x^6+1}}{\sqrt{x^6+1}-x^2}\right)+\frac{1}{2} \sqrt{\frac{1}{2} \left(2-\sqrt{2}\right)} \tanh ^{-1}\left(\frac{\sqrt{2-\sqrt{2}} x \sqrt[4]{x^6+1}}{\sqrt{x^6+1}+x^2}\right)-\frac{1}{2} \sqrt{\frac{1}{2} \left(2+\sqrt{2}\right)} \tanh ^{-1}\left(\frac{\sqrt{2+\sqrt{2}} x \sqrt[4]{x^6+1}}{\sqrt{x^6+1}+x^2}\right)",1,"Integrate[((-2 + x^6)*(1 - x^4 + x^6))/((1 + x^6)^(1/4)*(1 + 2*x^6 + x^8 + x^12)), x]","F",-1
2678,0,0,242,2.3235582,"\int \frac{\left(-q+2 p x^3\right) \left(a q+b x+a p x^3\right) \sqrt{q^2-2 p q x^2+2 p q x^3+p^2 x^6}}{x^3 \left(c q+d x+c p x^3\right)} \, dx","Integrate[((-q + 2*p*x^3)*(a*q + b*x + a*p*x^3)*Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6])/(x^3*(c*q + d*x + c*p*x^3)),x]","\int \frac{\left(-q+2 p x^3\right) \left(a q+b x+a p x^3\right) \sqrt{q^2-2 p q x^2+2 p q x^3+p^2 x^6}}{x^3 \left(c q+d x+c p x^3\right)} \, dx","\frac{\sqrt{p^2 x^6+2 p q x^3-2 p q x^2+q^2} \left(a c p x^3+a c q-2 a d x+2 b c x\right)}{2 c^2 x^2}+\frac{\log \left(\sqrt{p^2 x^6+2 p q x^3-2 p q x^2+q^2}+p x^3+q\right) \left(-a c^2 p q+a d^2-b c d\right)}{c^3}-\frac{2 (a d-b c) \sqrt{2 c^2 p q-d^2} \tan ^{-1}\left(\frac{x \sqrt{2 c^2 p q-d^2}}{c \sqrt{p^2 x^6+2 p q x^3-2 p q x^2+q^2}+c p x^3+c q+d x}\right)}{c^3}+\frac{\log (x) \left(a c^2 p q-a d^2+b c d\right)}{c^3}",1,"Integrate[((-q + 2*p*x^3)*(a*q + b*x + a*p*x^3)*Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6])/(x^3*(c*q + d*x + c*p*x^3)), x]","F",-1
2679,0,0,242,0.2529306,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{x^2+\sqrt{1+x^4}}} \, dx","Integrate[(-1 + x^2)/((1 + x^2)*Sqrt[x^2 + Sqrt[1 + x^4]]),x]","\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{x^2+\sqrt{1+x^4}}} \, dx","\frac{x}{2 \sqrt{\sqrt{x^4+1}+x^2}}+2 \sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)-2 \sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)}{\sqrt{2}}-2 \sqrt{\sqrt{2}-1} \tanh ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{2}-1\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)",1,"Integrate[(-1 + x^2)/((1 + x^2)*Sqrt[x^2 + Sqrt[1 + x^4]]), x]","F",-1
2680,0,0,242,0.1495834,"\int \frac{\left(-1+x^2\right) \sqrt{x^2+\sqrt{1+x^4}}}{1+x^2} \, dx","Integrate[((-1 + x^2)*Sqrt[x^2 + Sqrt[1 + x^4]])/(1 + x^2),x]","\int \frac{\left(-1+x^2\right) \sqrt{x^2+\sqrt{1+x^4}}}{1+x^2} \, dx","\frac{1}{2} \sqrt{\sqrt{x^4+1}+x^2} x+\frac{\tan ^{-1}\left(\frac{\sqrt{2} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)}{\sqrt{2}}-2 \sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)-2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)+2 \sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{2}-1\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)",1,"Integrate[((-1 + x^2)*Sqrt[x^2 + Sqrt[1 + x^4]])/(1 + x^2), x]","F",-1
2681,1,373,242,0.6461237,"\int \sqrt{1+x^2} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]],x]","\frac{\left(x^2+\sqrt{x^2+1} x+1\right) \left(79065 \left(2 x^2+2 \sqrt{x^2+1} x+1\right) \log \left(1-\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)-79065 \left(2 x^2+2 \sqrt{x^2+1} x+1\right) \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}+1\right)+2 \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(35840 x^4+512 \left(5 \sqrt{\sqrt{x^2+1}+x} \sqrt{x^2+1}-6 \sqrt{x^2+1}+4 \sqrt{\sqrt{x^2+1}+x}+377\right) x^2+\left(2048 \sqrt{\sqrt{x^2+1}+x} \sqrt{x^2+1}+175104 \sqrt{x^2+1}+345 \sqrt{\sqrt{x^2+1}+x}-1254\right) x+282 \sqrt{x^2+1}-935 \sqrt{x^2+1} \sqrt{\sqrt{x^2+1}+x}+184 \sqrt{\sqrt{x^2+1}+x}+512 \left(70 \sqrt{x^2+1}+5 \sqrt{\sqrt{x^2+1}+x}-6\right) x^3+78032\right)\right)}{80640 \sqrt{x^2+1} \left(\sqrt{x^2+1}+x\right)^3}","\frac{\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(2560 x^3+2048 x^2+345 x+184\right)+\sqrt{x^2+1} \left(\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(2560 x^2+2048 x-935\right)+\left(35840 x^3-3072 x^2+175104 x+282\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\left(35840 x^4-3072 x^3+193024 x^2-1254 x+78032\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{80640 \sqrt{x^2+1} x+40320 \left(2 x^2+1\right)}-\frac{251}{128} \tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)",1,"((1 + x^2 + x*Sqrt[1 + x^2])*(2*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]*(78032 + 35840*x^4 + 282*Sqrt[1 + x^2] + 184*Sqrt[x + Sqrt[1 + x^2]] - 935*Sqrt[1 + x^2]*Sqrt[x + Sqrt[1 + x^2]] + 512*x^3*(-6 + 70*Sqrt[1 + x^2] + 5*Sqrt[x + Sqrt[1 + x^2]]) + 512*x^2*(377 - 6*Sqrt[1 + x^2] + 4*Sqrt[x + Sqrt[1 + x^2]] + 5*Sqrt[1 + x^2]*Sqrt[x + Sqrt[1 + x^2]]) + x*(-1254 + 175104*Sqrt[1 + x^2] + 345*Sqrt[x + Sqrt[1 + x^2]] + 2048*Sqrt[1 + x^2]*Sqrt[x + Sqrt[1 + x^2]])) + 79065*(1 + 2*x^2 + 2*x*Sqrt[1 + x^2])*Log[1 - Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]] - 79065*(1 + 2*x^2 + 2*x*Sqrt[1 + x^2])*Log[1 + Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]]))/(80640*Sqrt[1 + x^2]*(x + Sqrt[1 + x^2])^3)","A",1
2682,1,71,243,0.1770726,"\int \frac{x (-a+x)}{\left(x^2 (-a+x)\right)^{2/3} \left(a^2 d-2 a d x+(-1+d) x^2\right)} \, dx","Integrate[(x*(-a + x))/((x^2*(-a + x))^(2/3)*(a^2*d - 2*a*d*x + (-1 + d)*x^2)),x]","-\frac{3 x^2 \left(\, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{x}{\sqrt{d} (a-x)}\right)+\, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{x}{\sqrt{d} (x-a)}\right)\right)}{4 a d \left(x^2 (x-a)\right)^{2/3}}","\frac{\log \left(x-\sqrt[6]{d} \sqrt[3]{x^3-a x^2}\right)}{2 a d^{2/3}}+\frac{\log \left(\sqrt[6]{d} \sqrt[3]{x^3-a x^2}+x\right)}{2 a d^{2/3}}-\frac{\log \left(-\sqrt[6]{d} x \sqrt[3]{x^3-a x^2}+\sqrt[3]{d} \left(x^3-a x^2\right)^{2/3}+x^2\right)}{4 a d^{2/3}}-\frac{\log \left(\sqrt[6]{d} x \sqrt[3]{x^3-a x^2}+\sqrt[3]{d} \left(x^3-a x^2\right)^{2/3}+x^2\right)}{4 a d^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x^2}{2 \sqrt[3]{d} \left(x^3-a x^2\right)^{2/3}+x^2}\right)}{2 a d^{2/3}}",1,"(-3*x^2*(Hypergeometric2F1[2/3, 1, 5/3, x/(Sqrt[d]*(a - x))] + Hypergeometric2F1[2/3, 1, 5/3, x/(Sqrt[d]*(-a + x))]))/(4*a*d*(x^2*(-a + x))^(2/3))","C",1
2683,1,73,243,0.1251866,"\int \frac{x}{\sqrt[3]{x^2 (-a+x)} \left(a^2 d-2 a d x+(-1+d) x^2\right)} \, dx","Integrate[x/((x^2*(-a + x))^(1/3)*(a^2*d - 2*a*d*x + (-1 + d)*x^2)),x]","\frac{3 x \left(\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{x}{\sqrt{d} (a-x)}\right)-\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{x}{\sqrt{d} (x-a)}\right)\right)}{2 a \sqrt{d} \sqrt[3]{x^2 (x-a)}}","\frac{\log \left(x-\sqrt[6]{d} \sqrt[3]{x^3-a x^2}\right)}{2 a \sqrt[3]{d}}+\frac{\log \left(\sqrt[6]{d} \sqrt[3]{x^3-a x^2}+x\right)}{2 a \sqrt[3]{d}}-\frac{\log \left(-\sqrt[6]{d} x \sqrt[3]{x^3-a x^2}+\sqrt[3]{d} \left(x^3-a x^2\right)^{2/3}+x^2\right)}{4 a \sqrt[3]{d}}-\frac{\log \left(\sqrt[6]{d} x \sqrt[3]{x^3-a x^2}+\sqrt[3]{d} \left(x^3-a x^2\right)^{2/3}+x^2\right)}{4 a \sqrt[3]{d}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x^2}{2 \sqrt[3]{d} \left(x^3-a x^2\right)^{2/3}+x^2}\right)}{2 a \sqrt[3]{d}}",1,"(3*x*(Hypergeometric2F1[1/3, 1, 4/3, x/(Sqrt[d]*(a - x))] - Hypergeometric2F1[1/3, 1, 4/3, x/(Sqrt[d]*(-a + x))]))/(2*a*Sqrt[d]*(x^2*(-a + x))^(1/3))","C",1
2684,1,71,243,0.1169207,"\int \frac{-a x+x^2}{\left(x^2 (-a+x)\right)^{2/3} \left(a^2 d-2 a d x+(-1+d) x^2\right)} \, dx","Integrate[(-(a*x) + x^2)/((x^2*(-a + x))^(2/3)*(a^2*d - 2*a*d*x + (-1 + d)*x^2)),x]","-\frac{3 x^2 \left(\, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{x}{\sqrt{d} (a-x)}\right)+\, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{x}{\sqrt{d} (x-a)}\right)\right)}{4 a d \left(x^2 (x-a)\right)^{2/3}}","\frac{\log \left(x-\sqrt[6]{d} \sqrt[3]{x^3-a x^2}\right)}{2 a d^{2/3}}+\frac{\log \left(\sqrt[6]{d} \sqrt[3]{x^3-a x^2}+x\right)}{2 a d^{2/3}}-\frac{\log \left(-\sqrt[6]{d} x \sqrt[3]{x^3-a x^2}+\sqrt[3]{d} \left(x^3-a x^2\right)^{2/3}+x^2\right)}{4 a d^{2/3}}-\frac{\log \left(\sqrt[6]{d} x \sqrt[3]{x^3-a x^2}+\sqrt[3]{d} \left(x^3-a x^2\right)^{2/3}+x^2\right)}{4 a d^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x^2}{2 \sqrt[3]{d} \left(x^3-a x^2\right)^{2/3}+x^2}\right)}{2 a d^{2/3}}",1,"(-3*x^2*(Hypergeometric2F1[2/3, 1, 5/3, x/(Sqrt[d]*(a - x))] + Hypergeometric2F1[2/3, 1, 5/3, x/(Sqrt[d]*(-a + x))]))/(4*a*d*(x^2*(-a + x))^(2/3))","C",1
2685,0,0,243,0.1884607,"\int \frac{-1+x}{(1+x) \sqrt[3]{-1+x^3}} \, dx","Integrate[(-1 + x)/((1 + x)*(-1 + x^3)^(1/3)),x]","\int \frac{-1+x}{(1+x) \sqrt[3]{-1+x^3}} \, dx","\frac{\log \left(-2 \sqrt[3]{x^3-1}+\sqrt[3]{2} x-\sqrt[3]{2}\right)}{\sqrt[3]{2}}-\frac{1}{3} \log \left(\sqrt[3]{x^3-1}-x\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-1}+x}\right)}{\sqrt{3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{x^3-1}}{\sqrt{3}}+\frac{\sqrt[3]{2} x}{\sqrt{3}}-\frac{\sqrt[3]{2}}{\sqrt{3}}}{\sqrt[3]{x^3-1}}\right)}{\sqrt[3]{2}}+\frac{1}{6} \log \left(\sqrt[3]{x^3-1} x+\left(x^3-1\right)^{2/3}+x^2\right)-\frac{\log \left(4 \left(x^3-1\right)^{2/3}+\left(2 \sqrt[3]{2} x-2 \sqrt[3]{2}\right) \sqrt[3]{x^3-1}+2^{2/3} x^2-2\ 2^{2/3} x+2^{2/3}\right)}{2 \sqrt[3]{2}}",1,"Integrate[(-1 + x)/((1 + x)*(-1 + x^3)^(1/3)), x]","F",-1
2686,1,85,243,0.0818424,"\int \frac{\left(1+x^2\right) \sqrt[3]{-x^2+x^3}}{-1+x^2} \, dx","Integrate[((1 + x^2)*(-x^2 + x^3)^(1/3))/(-1 + x^2),x]","\frac{3 \sqrt[3]{(x-1) x^2} \left((x-1) \sqrt[3]{x} \, _2F_1\left(-\frac{2}{3},\frac{4}{3};\frac{7}{3};1-x\right)+8 \sqrt[3]{x} \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};1-x\right)-4 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{x-1}{2 x}\right)\right)}{4 x}","\frac{1}{6} \sqrt[3]{x^3-x^2} (3 x-1)-\frac{17}{9} \log \left(\sqrt[3]{x^3-x^2}-x\right)+\sqrt[3]{2} \log \left(2^{2/3} \sqrt[3]{x^3-x^2}-2 x\right)+\frac{17}{18} \log \left(x^2+\sqrt[3]{x^3-x^2} x+\left(x^3-x^2\right)^{2/3}\right)-\frac{\log \left(2 x^2+2^{2/3} \sqrt[3]{x^3-x^2} x+\sqrt[3]{2} \left(x^3-x^2\right)^{2/3}\right)}{2^{2/3}}-\frac{17 \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-x^2}+x}\right)}{3 \sqrt{3}}+\sqrt[3]{2} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^3-x^2}+x}\right)",1,"(3*((-1 + x)*x^2)^(1/3)*((-1 + x)*x^(1/3)*Hypergeometric2F1[-2/3, 4/3, 7/3, 1 - x] + 8*x^(1/3)*Hypergeometric2F1[1/3, 1/3, 4/3, 1 - x] - 4*Hypergeometric2F1[1/3, 1, 4/3, (-1 + x)/(2*x)]))/(4*x)","C",1
2687,1,656,243,1.9955015,"\int \frac{b+a x^4}{\left(-b-a x^2+x^4\right) \sqrt[4]{-b x^2+a x^4}} \, dx","Integrate[(b + a*x^4)/((-b - a*x^2 + x^4)*(-(b*x^2) + a*x^4)^(1/4)),x]","\frac{\sqrt{x} \sqrt[4]{a x^2-b} \left(a^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)+a^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)-\frac{\left(a^2-\frac{a^3+2 a b+2 b}{\sqrt{a^2+4 b}}\right) \tan ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{a x^2-b}}\right)}{\left(a-\sqrt{a^2+4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}-\frac{\left(a^3+a^2 \sqrt{a^2+4 b}+2 a b+2 b\right) \tan ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+4 b}+a} \sqrt[4]{a x^2-b}}\right)}{\sqrt{a^2+4 b} \left(\sqrt{a^2+4 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}-\frac{\left(a^2-\frac{a^3+2 a b+2 b}{\sqrt{a^2+4 b}}\right) \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{a x^2-b}}\right)}{\left(a-\sqrt{a^2+4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}-\frac{\left(a^3+a^2 \sqrt{a^2+4 b}+2 a b+2 b\right) \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+4 b}+a} \sqrt[4]{a x^2-b}}\right)}{\sqrt{a^2+4 b} \left(\sqrt{a^2+4 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}\right)}{\sqrt[4]{a x^4-b x^2}}","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4 a+2 a^2-b\&,\frac{-\text{$\#$1}^4 a \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 a \log (x)+\text{$\#$1}^4 \log (x)+2 a^2 \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+a \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-2 a^2 \log (x)-a \log (x)}{3 \text{$\#$1} a-2 \text{$\#$1}^5}\&\right]+a^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)+a^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)",1,"(Sqrt[x]*(-b + a*x^2)^(1/4)*(a^(3/4)*ArcTan[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)] - ((a^2 - (a^3 + 2*b + 2*a*b)/Sqrt[a^2 + 4*b])*ArcTan[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*Sqrt[x])/((a - Sqrt[a^2 + 4*b])^(1/4)*(-b + a*x^2)^(1/4))])/((a - Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)) - ((a^3 + 2*b + 2*a*b + a^2*Sqrt[a^2 + 4*b])*ArcTan[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*Sqrt[x])/((a + Sqrt[a^2 + 4*b])^(1/4)*(-b + a*x^2)^(1/4))])/(Sqrt[a^2 + 4*b]*(a + Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)) + a^(3/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)] - ((a^2 - (a^3 + 2*b + 2*a*b)/Sqrt[a^2 + 4*b])*ArcTanh[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*Sqrt[x])/((a - Sqrt[a^2 + 4*b])^(1/4)*(-b + a*x^2)^(1/4))])/((a - Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)) - ((a^3 + 2*b + 2*a*b + a^2*Sqrt[a^2 + 4*b])*ArcTanh[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*Sqrt[x])/((a + Sqrt[a^2 + 4*b])^(1/4)*(-b + a*x^2)^(1/4))])/(Sqrt[a^2 + 4*b]*(a + Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4))))/(-(b*x^2) + a*x^4)^(1/4)","B",1
2688,1,656,243,0.8737576,"\int \frac{b+a x^4}{\left(-b-a x^2+x^4\right) \sqrt[4]{-b x^2+a x^4}} \, dx","Integrate[(b + a*x^4)/((-b - a*x^2 + x^4)*(-(b*x^2) + a*x^4)^(1/4)),x]","\frac{\sqrt{x} \sqrt[4]{a x^2-b} \left(a^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)+a^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)-\frac{\left(a^2-\frac{a^3+2 a b+2 b}{\sqrt{a^2+4 b}}\right) \tan ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{a x^2-b}}\right)}{\left(a-\sqrt{a^2+4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}-\frac{\left(a^3+a^2 \sqrt{a^2+4 b}+2 a b+2 b\right) \tan ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+4 b}+a} \sqrt[4]{a x^2-b}}\right)}{\sqrt{a^2+4 b} \left(\sqrt{a^2+4 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}-\frac{\left(a^2-\frac{a^3+2 a b+2 b}{\sqrt{a^2+4 b}}\right) \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{a x^2-b}}\right)}{\left(a-\sqrt{a^2+4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}-\frac{\left(a^3+a^2 \sqrt{a^2+4 b}+2 a b+2 b\right) \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+4 b}+a} \sqrt[4]{a x^2-b}}\right)}{\sqrt{a^2+4 b} \left(\sqrt{a^2+4 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}\right)}{\sqrt[4]{a x^4-b x^2}}","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4 a+2 a^2-b\&,\frac{-\text{$\#$1}^4 a \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 a \log (x)+\text{$\#$1}^4 \log (x)+2 a^2 \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+a \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-2 a^2 \log (x)-a \log (x)}{3 \text{$\#$1} a-2 \text{$\#$1}^5}\&\right]+a^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)+a^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)",1,"(Sqrt[x]*(-b + a*x^2)^(1/4)*(a^(3/4)*ArcTan[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)] - ((a^2 - (a^3 + 2*b + 2*a*b)/Sqrt[a^2 + 4*b])*ArcTan[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*Sqrt[x])/((a - Sqrt[a^2 + 4*b])^(1/4)*(-b + a*x^2)^(1/4))])/((a - Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)) - ((a^3 + 2*b + 2*a*b + a^2*Sqrt[a^2 + 4*b])*ArcTan[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*Sqrt[x])/((a + Sqrt[a^2 + 4*b])^(1/4)*(-b + a*x^2)^(1/4))])/(Sqrt[a^2 + 4*b]*(a + Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)) + a^(3/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)] - ((a^2 - (a^3 + 2*b + 2*a*b)/Sqrt[a^2 + 4*b])*ArcTanh[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*Sqrt[x])/((a - Sqrt[a^2 + 4*b])^(1/4)*(-b + a*x^2)^(1/4))])/((a - Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)) - ((a^3 + 2*b + 2*a*b + a^2*Sqrt[a^2 + 4*b])*ArcTanh[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*Sqrt[x])/((a + Sqrt[a^2 + 4*b])^(1/4)*(-b + a*x^2)^(1/4))])/(Sqrt[a^2 + 4*b]*(a + Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4))))/(-(b*x^2) + a*x^4)^(1/4)","B",1
2689,0,0,243,13.1360745,"\int \frac{\left(1-2 k^2\right) x+k^2 x^3}{\sqrt[3]{\left(1-x^2\right) \left(1-k^2 x^2\right)} \left(1-d+\left(d-2 k^2\right) x^2+k^4 x^4\right)} \, dx","Integrate[((1 - 2*k^2)*x + k^2*x^3)/(((1 - x^2)*(1 - k^2*x^2))^(1/3)*(1 - d + (d - 2*k^2)*x^2 + k^4*x^4)),x]","\int \frac{\left(1-2 k^2\right) x+k^2 x^3}{\sqrt[3]{\left(1-x^2\right) \left(1-k^2 x^2\right)} \left(1-d+\left(d-2 k^2\right) x^2+k^4 x^4\right)} \, dx","\frac{\log \left(\sqrt[3]{d} \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}+k^2 x^2-1\right)}{2 d^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}}{\sqrt[3]{d} \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}-2 k^2 x^2+2}\right)}{2 d^{2/3}}-\frac{\log \left(d^{2/3} \left(k^2 x^4+\left(-k^2-1\right) x^2+1\right)^{2/3}+\sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1} \left(\sqrt[3]{d}-\sqrt[3]{d} k^2 x^2\right)+k^4 x^4-2 k^2 x^2+1\right)}{4 d^{2/3}}",1,"Integrate[((1 - 2*k^2)*x + k^2*x^3)/(((1 - x^2)*(1 - k^2*x^2))^(1/3)*(1 - d + (d - 2*k^2)*x^2 + k^4*x^4)), x]","F",-1
2690,0,0,243,1.8815516,"\int \frac{\left(2-k^2\right) x-2 x^3+k^2 x^5}{\left(\left(1-x^2\right) \left(1-k^2 x^2\right)\right)^{2/3} \left(-1+d+\left(-2 d+k^2\right) x^2+d x^4\right)} \, dx","Integrate[((2 - k^2)*x - 2*x^3 + k^2*x^5)/(((1 - x^2)*(1 - k^2*x^2))^(2/3)*(-1 + d + (-2*d + k^2)*x^2 + d*x^4)),x]","\int \frac{\left(2-k^2\right) x-2 x^3+k^2 x^5}{\left(\left(1-x^2\right) \left(1-k^2 x^2\right)\right)^{2/3} \left(-1+d+\left(-2 d+k^2\right) x^2+d x^4\right)} \, dx","-\frac{\log \left(\sqrt[3]{d} \left(k^2 x^4+\left(-k^2-1\right) x^2+1\right)^{2/3}+k^2 x^2-1\right)}{2 d^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} \left(k^2 x^4+\left(-k^2-1\right) x^2+1\right)^{2/3}}{\sqrt[3]{d} \left(k^2 x^4+\left(-k^2-1\right) x^2+1\right)^{2/3}-2 k^2 x^2+2}\right)}{2 d^{2/3}}+\frac{\log \left(d^{2/3} \left(k^2 x^4+\left(-k^2-1\right) x^2+1\right)^{4/3}+\left(k^2 x^4+\left(-k^2-1\right) x^2+1\right)^{2/3} \left(\sqrt[3]{d}-\sqrt[3]{d} k^2 x^2\right)+k^4 x^4-2 k^2 x^2+1\right)}{4 d^{2/3}}",1,"Integrate[((2 - k^2)*x - 2*x^3 + k^2*x^5)/(((1 - x^2)*(1 - k^2*x^2))^(2/3)*(-1 + d + (-2*d + k^2)*x^2 + d*x^4)), x]","F",-1
2691,1,196,243,0.6063196,"\int \frac{1}{x^4 \sqrt{b+\sqrt{b^2+a x^2}}} \, dx","Integrate[1/(x^4*Sqrt[b + Sqrt[b^2 + a*x^2]]),x]","\frac{a^2 x \left(17 \left(2 b \sqrt{a x^2+b^2}+a x^2+2 b^2\right) \, _2F_1\left(-\frac{5}{2},1;-\frac{3}{2};\frac{b-\sqrt{b^2+a x^2}}{2 b}\right)-2 \left(\left(2 b \sqrt{a x^2+b^2}+a x^2+2 b^2\right) \, _2F_1\left(-\frac{5}{2},2;-\frac{3}{2};\frac{b-\sqrt{b^2+a x^2}}{2 b}\right)+5 b \left(7 \sqrt{a x^2+b^2}-b\right)\right)\right)}{160 b \left(\sqrt{a x^2+b^2}-b\right)^3 \left(\sqrt{a x^2+b^2}+b\right)^{5/2}}","\frac{5 a^{3/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{2} \sqrt{b} \sqrt{\sqrt{a x^2+b^2}+b}}-\frac{\sqrt{\sqrt{a x^2+b^2}+b}}{\sqrt{2} \sqrt{b}}\right)}{32 \sqrt{2} b^{7/2}}+\frac{a^{5/2} \left(15 x^2 \sqrt{a x^2+b^2}+5 b x^2\right)+a^{3/2} \left(-8 b^2 \sqrt{a x^2+b^2}-56 b^3\right)}{\frac{384 a^{3/2} b^4 x^3 \sqrt{a x^2+b^2}}{\left(\sqrt{a x^2+b^2}+b\right)^{3/2}}+\frac{192 a^{3/2} b^3 x^3 \left(a x^2+2 b^2\right)}{\left(\sqrt{a x^2+b^2}+b\right)^{3/2}}}",1,"(a^2*x*(17*(2*b^2 + a*x^2 + 2*b*Sqrt[b^2 + a*x^2])*Hypergeometric2F1[-5/2, 1, -3/2, (b - Sqrt[b^2 + a*x^2])/(2*b)] - 2*(5*b*(-b + 7*Sqrt[b^2 + a*x^2]) + (2*b^2 + a*x^2 + 2*b*Sqrt[b^2 + a*x^2])*Hypergeometric2F1[-5/2, 2, -3/2, (b - Sqrt[b^2 + a*x^2])/(2*b)])))/(160*b*(-b + Sqrt[b^2 + a*x^2])^3*(b + Sqrt[b^2 + a*x^2])^(5/2))","C",1
2692,0,0,244,3.8696117,"\int \frac{-a (a-5 b)-(3 a+5 b) x+4 x^2}{\sqrt[3]{(-a+x) (-b+x)} \left(-a^5+b d-\left(-5 a^4+d\right) x-10 a^3 x^2+10 a^2 x^3-5 a x^4+x^5\right)} \, dx","Integrate[(-(a*(a - 5*b)) - (3*a + 5*b)*x + 4*x^2)/(((-a + x)*(-b + x))^(1/3)*(-a^5 + b*d - (-5*a^4 + d)*x - 10*a^3*x^2 + 10*a^2*x^3 - 5*a*x^4 + x^5)),x]","\int \frac{-a (a-5 b)-(3 a+5 b) x+4 x^2}{\sqrt[3]{(-a+x) (-b+x)} \left(-a^5+b d-\left(-5 a^4+d\right) x-10 a^3 x^2+10 a^2 x^3-5 a x^4+x^5\right)} \, dx","\frac{\log \left(a^2-\sqrt[3]{d} \sqrt[3]{x (-a-b)+a b+x^2}-2 a x+x^2\right)}{d^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} \sqrt[3]{x (-a-b)+a b+x^2}}{2 a^2+\sqrt[3]{d} \sqrt[3]{x (-a-b)+a b+x^2}-4 a x+2 x^2}\right)}{d^{2/3}}-\frac{\log \left(a^4-4 a^3 x+\sqrt[3]{x (-a-b)+a b+x^2} \left(a^2 \sqrt[3]{d}-2 a \sqrt[3]{d} x+\sqrt[3]{d} x^2\right)+6 a^2 x^2+d^{2/3} \left(x (-a-b)+a b+x^2\right)^{2/3}-4 a x^3+x^4\right)}{2 d^{2/3}}",1,"Integrate[(-(a*(a - 5*b)) - (3*a + 5*b)*x + 4*x^2)/(((-a + x)*(-b + x))^(1/3)*(-a^5 + b*d - (-5*a^4 + d)*x - 10*a^3*x^2 + 10*a^2*x^3 - 5*a*x^4 + x^5)), x]","F",-1
2693,1,181,244,3.4954449,"\int \frac{x^6 \sqrt{-x+x^4}}{b+a x^6} \, dx","Integrate[(x^6*Sqrt[-x + x^4])/(b + a*x^6),x]","\frac{x \sqrt{x \left(x^3-1\right)} \left(\frac{\sqrt{\frac{1}{x^3}-1} \left(-\sqrt[4]{b} \sqrt{\sqrt{-a}+\sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{\frac{1}{x^3}-1}}{\sqrt{\sqrt{-a}+\sqrt{b}}}\right)+\sqrt[4]{b} \sqrt{\sqrt{-a}-\sqrt{b}} \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{\frac{1}{x^3}-1}}{\sqrt{\sqrt{-a}-\sqrt{b}}}\right)+\sqrt{-a} \tan ^{-1}\left(\sqrt{\frac{1}{x^3}-1}\right)\right)}{\sqrt{-a} \left(x^3-1\right)}+1\right)}{3 a}","-\frac{\sqrt[4]{-1} \sqrt{\sqrt{b} \left(\sqrt{a}-i \sqrt{b}\right)} \tan ^{-1}\left(\frac{(1+i) \sqrt{x^4-x} \sqrt{\sqrt{a} \sqrt{b}-i b}}{\sqrt{2} x^2 \left(\sqrt{a}-i \sqrt{b}\right)}\right)}{3 a^{3/2}}-\frac{(-1)^{3/4} \sqrt{\sqrt{b} \left(\sqrt{a}+i \sqrt{b}\right)} \tan ^{-1}\left(\frac{(1+i) x \sqrt{x^4-x} \sqrt{\sqrt{a} \sqrt{b}+i b}}{\sqrt{2} \sqrt{b} (x-1) \left(x^2+x+1\right)}\right)}{3 a^{3/2}}+\frac{\sqrt{x^4-x} x}{3 a}-\frac{\tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4-x}}\right)}{3 a}",1,"(x*Sqrt[x*(-1 + x^3)]*(1 + (Sqrt[-1 + x^(-3)]*(Sqrt[-a]*ArcTan[Sqrt[-1 + x^(-3)]] - Sqrt[Sqrt[-a] + Sqrt[b]]*b^(1/4)*ArcTan[(b^(1/4)*Sqrt[-1 + x^(-3)])/Sqrt[Sqrt[-a] + Sqrt[b]]] + Sqrt[Sqrt[-a] - Sqrt[b]]*b^(1/4)*ArcTanh[(b^(1/4)*Sqrt[-1 + x^(-3)])/Sqrt[Sqrt[-a] - Sqrt[b]]]))/(Sqrt[-a]*(-1 + x^3))))/(3*a)","A",1
2694,1,255,244,2.1099904,"\int \frac{b^6+a^6 x^6}{\sqrt{-b^2 x+a^2 x^3} \left(-b^6+a^6 x^6\right)} \, dx","Integrate[(b^6 + a^6*x^6)/(Sqrt[-(b^2*x) + a^2*x^3]*(-b^6 + a^6*x^6)),x]","\frac{2 \left(-x^{3/2}-\frac{i x^2 \sqrt{1-\frac{b^2}{a^2 x^2}} \left(2 F\left(\left.i \sinh ^{-1}\left(\frac{\sqrt{-\frac{b}{a}}}{\sqrt{x}}\right)\right|-1\right)-\Pi \left(-\frac{2 i}{-i+\sqrt{3}};\left.i \sinh ^{-1}\left(\frac{\sqrt{-\frac{b}{a}}}{\sqrt{x}}\right)\right|-1\right)-\Pi \left(\frac{2 i}{-i+\sqrt{3}};\left.i \sinh ^{-1}\left(\frac{\sqrt{-\frac{b}{a}}}{\sqrt{x}}\right)\right|-1\right)-\Pi \left(-\frac{2 i}{i+\sqrt{3}};\left.i \sinh ^{-1}\left(\frac{\sqrt{-\frac{b}{a}}}{\sqrt{x}}\right)\right|-1\right)-\Pi \left(\frac{2 i}{i+\sqrt{3}};\left.i \sinh ^{-1}\left(\frac{\sqrt{-\frac{b}{a}}}{\sqrt{x}}\right)\right|-1\right)\right)}{\sqrt{-\frac{b}{a}}}\right)}{3 \sqrt{x} \sqrt{a^2 x^3-b^2 x}}","\frac{2 \sqrt{a^2 x^3-b^2 x}}{3 \left(b^2-a^2 x^2\right)}-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} 3^{3/4} \sqrt{a} \sqrt{b} \sqrt{a^2 x^3-b^2 x}}{\sqrt{3} a^2 x^2-3 a b x-\sqrt{3} b^2}\right)}{3 \sqrt[4]{3} \sqrt{a} \sqrt{b}}-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\frac{a^{3/2} x^2}{\sqrt{2} \sqrt[4]{3} \sqrt{b}}-\frac{b^{3/2}}{\sqrt{2} \sqrt[4]{3} \sqrt{a}}+\frac{\sqrt[4]{3} \sqrt{a} \sqrt{b} x}{\sqrt{2}}}{\sqrt{a^2 x^3-b^2 x}}\right)}{3 \sqrt[4]{3} \sqrt{a} \sqrt{b}}",1,"(2*(-x^(3/2) - (I*Sqrt[1 - b^2/(a^2*x^2)]*x^2*(2*EllipticF[I*ArcSinh[Sqrt[-(b/a)]/Sqrt[x]], -1] - EllipticPi[(-2*I)/(-I + Sqrt[3]), I*ArcSinh[Sqrt[-(b/a)]/Sqrt[x]], -1] - EllipticPi[(2*I)/(-I + Sqrt[3]), I*ArcSinh[Sqrt[-(b/a)]/Sqrt[x]], -1] - EllipticPi[(-2*I)/(I + Sqrt[3]), I*ArcSinh[Sqrt[-(b/a)]/Sqrt[x]], -1] - EllipticPi[(2*I)/(I + Sqrt[3]), I*ArcSinh[Sqrt[-(b/a)]/Sqrt[x]], -1]))/Sqrt[-(b/a)]))/(3*Sqrt[x]*Sqrt[-(b^2*x) + a^2*x^3])","C",1
2695,0,0,245,9.8445525,"\int \frac{a^2 b-2 a^2 x+(2 a-b) x^2}{(x (-a+x) (-b+x))^{2/3} \left(a^2+(-2 a+b d) x+(1-d) x^2\right)} \, dx","Integrate[(a^2*b - 2*a^2*x + (2*a - b)*x^2)/((x*(-a + x)*(-b + x))^(2/3)*(a^2 + (-2*a + b*d)*x + (1 - d)*x^2)),x]","\int \frac{a^2 b-2 a^2 x+(2 a-b) x^2}{(x (-a+x) (-b+x))^{2/3} \left(a^2+(-2 a+b d) x+(1-d) x^2\right)} \, dx","-\frac{\log \left(\left(x^2 (-a-b)+a b x+x^3\right)^{2/3} \left(d^{2/3} x^2-b d^{2/3} x\right)+\sqrt[3]{d} \left(x^2 (-a-b)+a b x+x^3\right)^{4/3}+b^2 d x^2-2 b d x^3+d x^4\right)}{2 \sqrt[3]{d}}+\frac{\log \left(\sqrt[6]{d} \left(x^2 (-a-b)+a b x+x^3\right)^{2/3}+b \sqrt{d} x-\sqrt{d} x^2\right)}{\sqrt[3]{d}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \left(x^2 (-a-b)+a b x+x^3\right)^{2/3}}{\left(x^2 (-a-b)+a b x+x^3\right)^{2/3}-2 b \sqrt[3]{d} x+2 \sqrt[3]{d} x^2}\right)}{\sqrt[3]{d}}",1,"Integrate[(a^2*b - 2*a^2*x + (2*a - b)*x^2)/((x*(-a + x)*(-b + x))^(2/3)*(a^2 + (-2*a + b*d)*x + (1 - d)*x^2)), x]","F",-1
2696,1,296,245,2.6151809,"\int \frac{b^6+a^6 x^6}{\sqrt{b^2 x+a^2 x^3} \left(-b^6+a^6 x^6\right)} \, dx","Integrate[(b^6 + a^6*x^6)/(Sqrt[b^2*x + a^2*x^3]*(-b^6 + a^6*x^6)),x]","\frac{2 i x^{3/2} \sqrt{\frac{b^2}{a^2 x^2}+1} \left(-3 F\left(\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)+\Pi \left(-i;\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)+\Pi \left(i;\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)+\Pi \left(-\frac{i}{2}-\frac{\sqrt{3}}{2};\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)+\Pi \left(\frac{i}{2}-\frac{\sqrt{3}}{2};\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)+\Pi \left(\frac{1}{2} \left(-i+\sqrt{3}\right);\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)+\Pi \left(\frac{1}{2} \left(i+\sqrt{3}\right);\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i b}{a}}}{\sqrt{x}}\right)\right|-1\right)\right)}{3 \sqrt{\frac{i b}{a}} \sqrt{x \left(a^2 x^2+b^2\right)}}","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{b} \sqrt{a^2 x^3+b^2 x}}{a^2 x^2+b^2}\right)}{3 \sqrt{a} \sqrt{b}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{b} \sqrt{a^2 x^3+b^2 x}}{a^2 x^2+b^2}\right)}{3 \sqrt{2} \sqrt{a} \sqrt{b}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{b} \sqrt{a^2 x^3+b^2 x}}{a^2 x^2+b^2}\right)}{3 \sqrt{a} \sqrt{b}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{b} \sqrt{a^2 x^3+b^2 x}}{a^2 x^2+b^2}\right)}{3 \sqrt{2} \sqrt{a} \sqrt{b}}",1,"(((2*I)/3)*Sqrt[1 + b^2/(a^2*x^2)]*x^(3/2)*(-3*EllipticF[I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1] + EllipticPi[-I, I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1] + EllipticPi[I, I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1] + EllipticPi[-1/2*I - Sqrt[3]/2, I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1] + EllipticPi[I/2 - Sqrt[3]/2, I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1] + EllipticPi[(-I + Sqrt[3])/2, I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1] + EllipticPi[(I + Sqrt[3])/2, I*ArcSinh[Sqrt[(I*b)/a]/Sqrt[x]], -1]))/(Sqrt[(I*b)/a]*Sqrt[x*(b^2 + a^2*x^2)])","C",1
2697,-1,0,245,180.0892051,"\int \frac{\left(2+5 x^7\right) \sqrt[3]{-x-x^3+x^8}}{\left(-1+x^7\right) \left(-1+x^2+x^7\right)} \, dx","Integrate[((2 + 5*x^7)*(-x - x^3 + x^8)^(1/3))/((-1 + x^7)*(-1 + x^2 + x^7)),x]","\text{\$Aborted}","-\log \left(\sqrt[3]{x^8-x^3-x}+x\right)+\sqrt[3]{2} \log \left(2^{2/3} \sqrt[3]{x^8-x^3-x}+2 x\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^8-x^3-x}-x}\right)-\sqrt[3]{2} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^8-x^3-x}-x}\right)+\frac{1}{2} \log \left(x^2-\sqrt[3]{x^8-x^3-x} x+\left(x^8-x^3-x\right)^{2/3}\right)-\frac{\log \left(-2 x^2+2^{2/3} \sqrt[3]{x^8-x^3-x} x-\sqrt[3]{2} \left(x^8-x^3-x\right)^{2/3}\right)}{2^{2/3}}",1,"$Aborted","F",-1
2698,0,0,245,0.2898712,"\int \frac{x^6 \left(-4+x^3\right)}{\left(-1+x^3\right)^{3/4} \left(1-2 x^3+x^6+x^8\right)} \, dx","Integrate[(x^6*(-4 + x^3))/((-1 + x^3)^(3/4)*(1 - 2*x^3 + x^6 + x^8)),x]","\int \frac{x^6 \left(-4+x^3\right)}{\left(-1+x^3\right)^{3/4} \left(1-2 x^3+x^6+x^8\right)} \, dx","\frac{1}{2} \sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}} x \sqrt[4]{x^3-1}}{\sqrt{x^3-1}-x^2}\right)-\frac{1}{2} \sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{\left(\sqrt{\frac{2}{2-\sqrt{2}}}-\frac{2}{\sqrt{2-\sqrt{2}}}\right) x \sqrt[4]{x^3-1}}{\sqrt{x^3-1}-x^2}\right)-\frac{1}{2} \sqrt{2-\sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt{2-\sqrt{2}} x \sqrt[4]{x^3-1}}{\sqrt{x^3-1}+x^2}\right)-\frac{1}{2} \sqrt{2+\sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt{2+\sqrt{2}} x \sqrt[4]{x^3-1}}{\sqrt{x^3-1}+x^2}\right)",1,"Integrate[(x^6*(-4 + x^3))/((-1 + x^3)^(3/4)*(1 - 2*x^3 + x^6 + x^8)), x]","F",-1
2699,0,0,245,0.2786372,"\int \frac{x^6 \left(4+x^5\right)}{\left(-1+x^5\right)^{3/4} \left(1-2 x^5+x^8+x^{10}\right)} \, dx","Integrate[(x^6*(4 + x^5))/((-1 + x^5)^(3/4)*(1 - 2*x^5 + x^8 + x^10)),x]","\int \frac{x^6 \left(4+x^5\right)}{\left(-1+x^5\right)^{3/4} \left(1-2 x^5+x^8+x^{10}\right)} \, dx","-\frac{1}{2} \sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}} x \sqrt[4]{x^5-1}}{\sqrt{x^5-1}-x^2}\right)+\frac{1}{2} \sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{\left(\sqrt{\frac{2}{2-\sqrt{2}}}-\frac{2}{\sqrt{2-\sqrt{2}}}\right) x \sqrt[4]{x^5-1}}{\sqrt{x^5-1}-x^2}\right)+\frac{1}{2} \sqrt{2-\sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt{2-\sqrt{2}} x \sqrt[4]{x^5-1}}{\sqrt{x^5-1}+x^2}\right)+\frac{1}{2} \sqrt{2+\sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt{2+\sqrt{2}} x \sqrt[4]{x^5-1}}{\sqrt{x^5-1}+x^2}\right)",1,"Integrate[(x^6*(4 + x^5))/((-1 + x^5)^(3/4)*(1 - 2*x^5 + x^8 + x^10)), x]","F",-1
2700,1,373,245,27.3680543,"\int \frac{\sqrt{b+a x} \left(-g+f x^2\right)}{\left(e+d x^2\right) \sqrt{c+\sqrt{b+a x}}} \, dx","Integrate[(Sqrt[b + a*x]*(-g + f*x^2))/((e + d*x^2)*Sqrt[c + Sqrt[b + a*x]]),x]","-\frac{\left(\sqrt{a x+b}+c\right)^{7/2} \left(\frac{c}{\sqrt{a x+b}+c}-1\right) \left(\frac{15 a^2 (d g+e f) \text{RootSum}\left[\text{$\#$1}^8 a^2 e+\text{$\#$1}^8 b^2 d-2 \text{$\#$1}^8 b c^2 d+\text{$\#$1}^8 c^4 d+4 \text{$\#$1}^6 b c d-4 \text{$\#$1}^6 c^3 d-2 \text{$\#$1}^4 b d+6 \text{$\#$1}^4 c^2 d-4 \text{$\#$1}^2 c d+d\&,\frac{\text{$\#$1}^5 c^2 \log \left(\frac{1}{\sqrt{\sqrt{a x+b}+c}}-\text{$\#$1}\right)-2 \text{$\#$1}^3 c \log \left(\frac{1}{\sqrt{\sqrt{a x+b}+c}}-\text{$\#$1}\right)+\text{$\#$1} \log \left(\frac{1}{\sqrt{\sqrt{a x+b}+c}}-\text{$\#$1}\right)}{\text{$\#$1}^6 a^2 e+\text{$\#$1}^6 b^2 d-2 \text{$\#$1}^6 b c^2 d+\text{$\#$1}^6 c^4 d+3 \text{$\#$1}^4 b c d-3 \text{$\#$1}^4 c^3 d-\text{$\#$1}^2 b d+3 \text{$\#$1}^2 c^2 d-c d}\&\right]}{\left(\sqrt{a x+b}+c\right)^{5/2}}+\frac{8 f \left(-4 c \sqrt{a x+b}+3 a x+3 b+8 c^2\right)}{\left(\sqrt{a x+b}+c\right)^2}\right)}{30 a d \sqrt{a x+b}}","-\frac{a (d g+e f) \text{RootSum}\left[\text{$\#$1}^8 d-4 \text{$\#$1}^6 c d-2 \text{$\#$1}^4 b d+6 \text{$\#$1}^4 c^2 d+4 \text{$\#$1}^2 b c d-4 \text{$\#$1}^2 c^3 d+a^2 e+b^2 d-2 b c^2 d+c^4 d\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-c \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)}{\text{$\#$1}^5-2 \text{$\#$1}^3 c-\text{$\#$1} b+\text{$\#$1} c^2}\&\right]}{2 d^2}+\frac{4 f \left(3 a x+3 b+8 c^2\right) \sqrt{\sqrt{a x+b}+c}}{15 a d}-\frac{16 c f \sqrt{a x+b} \sqrt{\sqrt{a x+b}+c}}{15 a d}",1,"-1/30*((c + Sqrt[b + a*x])^(7/2)*(-1 + c/(c + Sqrt[b + a*x]))*((8*f*(3*b + 8*c^2 + 3*a*x - 4*c*Sqrt[b + a*x]))/(c + Sqrt[b + a*x])^2 + (15*a^2*(e*f + d*g)*RootSum[d - 4*c*d*#1^2 - 2*b*d*#1^4 + 6*c^2*d*#1^4 + 4*b*c*d*#1^6 - 4*c^3*d*#1^6 + b^2*d*#1^8 - 2*b*c^2*d*#1^8 + c^4*d*#1^8 + a^2*e*#1^8 & , (Log[1/Sqrt[c + Sqrt[b + a*x]] - #1]*#1 - 2*c*Log[1/Sqrt[c + Sqrt[b + a*x]] - #1]*#1^3 + c^2*Log[1/Sqrt[c + Sqrt[b + a*x]] - #1]*#1^5)/(-(c*d) - b*d*#1^2 + 3*c^2*d*#1^2 + 3*b*c*d*#1^4 - 3*c^3*d*#1^4 + b^2*d*#1^6 - 2*b*c^2*d*#1^6 + c^4*d*#1^6 + a^2*e*#1^6) & ])/(c + Sqrt[b + a*x])^(5/2)))/(a*d*Sqrt[b + a*x])","A",1
2701,0,0,245,0.1822413,"\int \frac{\sqrt{1+x^4} \sqrt{x^2+\sqrt{1+x^4}}}{1+x^2} \, dx","Integrate[(Sqrt[1 + x^4]*Sqrt[x^2 + Sqrt[1 + x^4]])/(1 + x^2),x]","\int \frac{\sqrt{1+x^4} \sqrt{x^2+\sqrt{1+x^4}}}{1+x^2} \, dx","\frac{1}{2} \sqrt{\sqrt{x^4+1}+x^2} x-\frac{\tan ^{-1}\left(\frac{\sqrt{2} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)}{\sqrt{2}}+\sqrt{2 \left(\sqrt{2}-1\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)-\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)+\sqrt{2 \left(1+\sqrt{2}\right)} \tanh ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{2}-1\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)",1,"Integrate[(Sqrt[1 + x^4]*Sqrt[x^2 + Sqrt[1 + x^4]])/(1 + x^2), x]","F",-1
2702,1,1881,245,4.910663,"\int \frac{x}{x^2-\sqrt{1+x} \sqrt{1+\sqrt{1+x}}} \, dx","Integrate[x/(x^2 - Sqrt[1 + x]*Sqrt[1 + Sqrt[1 + x]]),x]","\frac{1}{55} \left(-2 \left(-4+\sqrt{5}\right) \sqrt{10 \left(3+\sqrt{5}\right)} \tanh ^{-1}\left(\sqrt{\frac{2}{3-\sqrt{5}}} \sqrt{\sqrt{x+1}+1}\right)-4 \sqrt{\frac{10}{3+\sqrt{5}}} \left(4+\sqrt{5}\right) \tanh ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} \sqrt{\sqrt{x+1}+1}\right)-2 \sqrt{5} \tanh ^{-1}\left(\frac{2 \sqrt{x+1}-1}{\sqrt{5}}\right)+15 \log \left(\sqrt{x+1}-x\right)+10 \text{RootSum}\left[\text{$\#$1}^5-2 \text{$\#$1}^3+\text{$\#$1}^2+2 \text{$\#$1}-1\&,\frac{8 \log \left(\sqrt{x+1}-\text{$\#$1}\right) \text{$\#$1}^4-2 \log \left(\sqrt{x+1}-\text{$\#$1}\right) \text{$\#$1}^3-10 \log \left(\sqrt{x+1}-\text{$\#$1}\right) \text{$\#$1}^2+5 \log \left(\sqrt{x+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{x+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4-6 \text{$\#$1}^2+2 \text{$\#$1}+2}\&\right]+20 \text{RootSum}\left[\text{$\#$1}^5-\text{$\#$1}^4-2 \text{$\#$1}^3+\text{$\#$1}^2+\text{$\#$1}+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2+3 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4-4 \text{$\#$1}^3-6 \text{$\#$1}^2+2 \text{$\#$1}+1}\&\right]-50 \left(\text{RootSum}\left[\text{$\#$1}^5-\text{$\#$1}^4-2 \text{$\#$1}^3+\text{$\#$1}^2+\text{$\#$1}+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2+2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4-4 \text{$\#$1}^3-6 \text{$\#$1}^2+2 \text{$\#$1}+1}\&\right]-\text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1}\&\right]\right)+80 \left(\text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1}\&\right]-\text{RootSum}\left[\text{$\#$1}^5-\text{$\#$1}^4-2 \text{$\#$1}^3+\text{$\#$1}^2+\text{$\#$1}+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4-4 \text{$\#$1}^3-6 \text{$\#$1}^2+2 \text{$\#$1}+1}\&\right]\right)+30 \left(\text{RootSum}\left[\text{$\#$1}^5-\text{$\#$1}^4-2 \text{$\#$1}^3+\text{$\#$1}^2+\text{$\#$1}+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4-4 \text{$\#$1}^3-6 \text{$\#$1}^2+2 \text{$\#$1}+1}\&\right]-\text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1}\&\right]\right)-20 \text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4+2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2-3 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1}\&\right]-70 \left(\text{RootSum}\left[\text{$\#$1}^5-\text{$\#$1}^4+\text{$\#$1}^3+2 \text{$\#$1}^2-\text{$\#$1}-1\&,\frac{\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}^3-\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}^2-\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}}{5 \text{$\#$1}^4-4 \text{$\#$1}^3+3 \text{$\#$1}^2+4 \text{$\#$1}-1}\&\right]+\text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4+\text{$\#$1}^3-2 \text{$\#$1}^2-\text{$\#$1}+1\&,\frac{\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}^3+\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}^2-\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}}{5 \text{$\#$1}^4+4 \text{$\#$1}^3+3 \text{$\#$1}^2-4 \text{$\#$1}-1}\&\right]\right)\right)","\frac{4}{11} \text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{8 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)+6 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-12 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-5 \text{$\#$1} \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1}\&\right]+\frac{2}{55} \left(15+\sqrt{5}\right) \log \left(-2 \sqrt{\sqrt{x+1}+1}+\sqrt{5}+1\right)-\frac{2}{55} \left(\sqrt{5}-15\right) \log \left(2 \sqrt{\sqrt{x+1}+1}+\sqrt{5}-1\right)",1,"(-2*(-4 + Sqrt[5])*Sqrt[10*(3 + Sqrt[5])]*ArcTanh[Sqrt[2/(3 - Sqrt[5])]*Sqrt[1 + Sqrt[1 + x]]] - 4*Sqrt[10/(3 + Sqrt[5])]*(4 + Sqrt[5])*ArcTanh[Sqrt[2/(3 + Sqrt[5])]*Sqrt[1 + Sqrt[1 + x]]] - 2*Sqrt[5]*ArcTanh[(-1 + 2*Sqrt[1 + x])/Sqrt[5]] + 15*Log[-x + Sqrt[1 + x]] + 10*RootSum[-1 + 2*#1 + #1^2 - 2*#1^3 + #1^5 & , (Log[Sqrt[1 + x] - #1] + 5*Log[Sqrt[1 + x] - #1]*#1 - 10*Log[Sqrt[1 + x] - #1]*#1^2 - 2*Log[Sqrt[1 + x] - #1]*#1^3 + 8*Log[Sqrt[1 + x] - #1]*#1^4)/(2 + 2*#1 - 6*#1^2 + 5*#1^4) & ] + 20*RootSum[1 + #1 + #1^2 - 2*#1^3 - #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] + 3*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 + 2*#1 - 6*#1^2 - 4*#1^3 + 5*#1^4) & ] - 50*(RootSum[1 + #1 + #1^2 - 2*#1^3 - #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] + 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 + 2*#1 - 6*#1^2 - 4*#1^3 + 5*#1^4) & ] - RootSum[-1 + #1 - #1^2 - 2*#1^3 + #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 - 2*#1 - 6*#1^2 + 4*#1^3 + 5*#1^4) & ]) + 80*(-RootSum[1 + #1 + #1^2 - 2*#1^3 - #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 + 2*#1 - 6*#1^2 - 4*#1^3 + 5*#1^4) & ] + RootSum[-1 + #1 - #1^2 - 2*#1^3 + #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 - 2*#1 - 6*#1^2 + 4*#1^3 + 5*#1^4) & ]) + 30*(RootSum[1 + #1 + #1^2 - 2*#1^3 - #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 + 2*#1 - 6*#1^2 - 4*#1^3 + 5*#1^4) & ] - RootSum[-1 + #1 - #1^2 - 2*#1^3 + #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 - 2*#1 - 6*#1^2 + 4*#1^3 + 5*#1^4) & ]) - 20*RootSum[-1 + #1 - #1^2 - 2*#1^3 + #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] - 3*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 - 2*#1 - 6*#1^2 + 4*#1^3 + 5*#1^4) & ] - 70*(RootSum[-1 - #1 + 2*#1^2 + #1^3 - #1^4 + #1^5 & , (-(Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1) - Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3)/(-1 + 4*#1 + 3*#1^2 - 4*#1^3 + 5*#1^4) & ] + RootSum[1 - #1 - 2*#1^2 + #1^3 + #1^4 + #1^5 & , (-(Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1) + Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3)/(-1 - 4*#1 + 3*#1^2 + 4*#1^3 + 5*#1^4) & ]))/55","B",0
2703,1,1881,245,3.7407045,"\int \frac{x}{x^2-\sqrt{1+x} \sqrt{1+\sqrt{1+x}}} \, dx","Integrate[x/(x^2 - Sqrt[1 + x]*Sqrt[1 + Sqrt[1 + x]]),x]","\frac{1}{55} \left(-2 \left(-4+\sqrt{5}\right) \sqrt{10 \left(3+\sqrt{5}\right)} \tanh ^{-1}\left(\sqrt{\frac{2}{3-\sqrt{5}}} \sqrt{\sqrt{x+1}+1}\right)-4 \sqrt{\frac{10}{3+\sqrt{5}}} \left(4+\sqrt{5}\right) \tanh ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} \sqrt{\sqrt{x+1}+1}\right)-2 \sqrt{5} \tanh ^{-1}\left(\frac{2 \sqrt{x+1}-1}{\sqrt{5}}\right)+15 \log \left(\sqrt{x+1}-x\right)+10 \text{RootSum}\left[\text{$\#$1}^5-2 \text{$\#$1}^3+\text{$\#$1}^2+2 \text{$\#$1}-1\&,\frac{8 \log \left(\sqrt{x+1}-\text{$\#$1}\right) \text{$\#$1}^4-2 \log \left(\sqrt{x+1}-\text{$\#$1}\right) \text{$\#$1}^3-10 \log \left(\sqrt{x+1}-\text{$\#$1}\right) \text{$\#$1}^2+5 \log \left(\sqrt{x+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{x+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4-6 \text{$\#$1}^2+2 \text{$\#$1}+2}\&\right]+20 \text{RootSum}\left[\text{$\#$1}^5-\text{$\#$1}^4-2 \text{$\#$1}^3+\text{$\#$1}^2+\text{$\#$1}+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2+3 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4-4 \text{$\#$1}^3-6 \text{$\#$1}^2+2 \text{$\#$1}+1}\&\right]-50 \left(\text{RootSum}\left[\text{$\#$1}^5-\text{$\#$1}^4-2 \text{$\#$1}^3+\text{$\#$1}^2+\text{$\#$1}+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2+2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4-4 \text{$\#$1}^3-6 \text{$\#$1}^2+2 \text{$\#$1}+1}\&\right]-\text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1}\&\right]\right)+80 \left(\text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1}\&\right]-\text{RootSum}\left[\text{$\#$1}^5-\text{$\#$1}^4-2 \text{$\#$1}^3+\text{$\#$1}^2+\text{$\#$1}+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4-4 \text{$\#$1}^3-6 \text{$\#$1}^2+2 \text{$\#$1}+1}\&\right]\right)+30 \left(\text{RootSum}\left[\text{$\#$1}^5-\text{$\#$1}^4-2 \text{$\#$1}^3+\text{$\#$1}^2+\text{$\#$1}+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4-4 \text{$\#$1}^3-6 \text{$\#$1}^2+2 \text{$\#$1}+1}\&\right]-\text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1}\&\right]\right)-20 \text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4+2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2-3 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1}\&\right]-70 \left(\text{RootSum}\left[\text{$\#$1}^5-\text{$\#$1}^4+\text{$\#$1}^3+2 \text{$\#$1}^2-\text{$\#$1}-1\&,\frac{\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}^3-\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}^2-\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}}{5 \text{$\#$1}^4-4 \text{$\#$1}^3+3 \text{$\#$1}^2+4 \text{$\#$1}-1}\&\right]+\text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4+\text{$\#$1}^3-2 \text{$\#$1}^2-\text{$\#$1}+1\&,\frac{\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}^3+\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}^2-\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}}{5 \text{$\#$1}^4+4 \text{$\#$1}^3+3 \text{$\#$1}^2-4 \text{$\#$1}-1}\&\right]\right)\right)","\frac{4}{11} \text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{8 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)+6 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-12 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-5 \text{$\#$1} \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1}\&\right]+\frac{2}{55} \left(15+\sqrt{5}\right) \log \left(-2 \sqrt{\sqrt{x+1}+1}+\sqrt{5}+1\right)-\frac{2}{55} \left(\sqrt{5}-15\right) \log \left(2 \sqrt{\sqrt{x+1}+1}+\sqrt{5}-1\right)",1,"(-2*(-4 + Sqrt[5])*Sqrt[10*(3 + Sqrt[5])]*ArcTanh[Sqrt[2/(3 - Sqrt[5])]*Sqrt[1 + Sqrt[1 + x]]] - 4*Sqrt[10/(3 + Sqrt[5])]*(4 + Sqrt[5])*ArcTanh[Sqrt[2/(3 + Sqrt[5])]*Sqrt[1 + Sqrt[1 + x]]] - 2*Sqrt[5]*ArcTanh[(-1 + 2*Sqrt[1 + x])/Sqrt[5]] + 15*Log[-x + Sqrt[1 + x]] + 10*RootSum[-1 + 2*#1 + #1^2 - 2*#1^3 + #1^5 & , (Log[Sqrt[1 + x] - #1] + 5*Log[Sqrt[1 + x] - #1]*#1 - 10*Log[Sqrt[1 + x] - #1]*#1^2 - 2*Log[Sqrt[1 + x] - #1]*#1^3 + 8*Log[Sqrt[1 + x] - #1]*#1^4)/(2 + 2*#1 - 6*#1^2 + 5*#1^4) & ] + 20*RootSum[1 + #1 + #1^2 - 2*#1^3 - #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] + 3*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 + 2*#1 - 6*#1^2 - 4*#1^3 + 5*#1^4) & ] - 50*(RootSum[1 + #1 + #1^2 - 2*#1^3 - #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] + 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 + 2*#1 - 6*#1^2 - 4*#1^3 + 5*#1^4) & ] - RootSum[-1 + #1 - #1^2 - 2*#1^3 + #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 - 2*#1 - 6*#1^2 + 4*#1^3 + 5*#1^4) & ]) + 80*(-RootSum[1 + #1 + #1^2 - 2*#1^3 - #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 + 2*#1 - 6*#1^2 - 4*#1^3 + 5*#1^4) & ] + RootSum[-1 + #1 - #1^2 - 2*#1^3 + #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 - 2*#1 - 6*#1^2 + 4*#1^3 + 5*#1^4) & ]) + 30*(RootSum[1 + #1 + #1^2 - 2*#1^3 - #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 + 2*#1 - 6*#1^2 - 4*#1^3 + 5*#1^4) & ] - RootSum[-1 + #1 - #1^2 - 2*#1^3 + #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 - 2*#1 - 6*#1^2 + 4*#1^3 + 5*#1^4) & ]) - 20*RootSum[-1 + #1 - #1^2 - 2*#1^3 + #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] - 3*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 - 2*#1 - 6*#1^2 + 4*#1^3 + 5*#1^4) & ] - 70*(RootSum[-1 - #1 + 2*#1^2 + #1^3 - #1^4 + #1^5 & , (-(Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1) - Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3)/(-1 + 4*#1 + 3*#1^2 - 4*#1^3 + 5*#1^4) & ] + RootSum[1 - #1 - 2*#1^2 + #1^3 + #1^4 + #1^5 & , (-(Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1) + Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3)/(-1 - 4*#1 + 3*#1^2 + 4*#1^3 + 5*#1^4) & ]))/55","B",0
2704,0,0,246,5.0157819,"\int \frac{\sqrt{b+a x} \sqrt{1+\sqrt{b+a x}}}{x^2 \sqrt{1+\sqrt{1+\sqrt{b+a x}}}} \, dx","Integrate[(Sqrt[b + a*x]*Sqrt[1 + Sqrt[b + a*x]])/(x^2*Sqrt[1 + Sqrt[1 + Sqrt[b + a*x]]]),x]","\int \frac{\sqrt{b+a x} \sqrt{1+\sqrt{b+a x}}}{x^2 \sqrt{1+\sqrt{1+\sqrt{b+a x}}}} \, dx","\frac{1}{8} a \text{RootSum}\left[-\text{$\#$1}^8+4 \text{$\#$1}^6-4 \text{$\#$1}^4+b\&,\frac{5 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{a x+b}+1}+1}-\text{$\#$1}\right)-9 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{a x+b}+1}+1}-\text{$\#$1}\right)+2 \log \left(\sqrt{\sqrt{\sqrt{a x+b}+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]-\frac{\sqrt{a x+b} \sqrt{\sqrt{\sqrt{a x+b}+1}+1}}{x}+\frac{\sqrt{\sqrt{a x+b}+1} \sqrt{\sqrt{\sqrt{a x+b}+1}+1}}{x}-\frac{\sqrt{\sqrt{\sqrt{a x+b}+1}+1}}{x}",1,"Integrate[(Sqrt[b + a*x]*Sqrt[1 + Sqrt[b + a*x]])/(x^2*Sqrt[1 + Sqrt[1 + Sqrt[b + a*x]]]), x]","F",-1
2705,0,0,246,1.6402891,"\int \frac{\sqrt{b+a x} \sqrt{1+\sqrt{b+a x}}}{x^2 \sqrt{1+\sqrt{1+\sqrt{b+a x}}}} \, dx","Integrate[(Sqrt[b + a*x]*Sqrt[1 + Sqrt[b + a*x]])/(x^2*Sqrt[1 + Sqrt[1 + Sqrt[b + a*x]]]),x]","\int \frac{\sqrt{b+a x} \sqrt{1+\sqrt{b+a x}}}{x^2 \sqrt{1+\sqrt{1+\sqrt{b+a x}}}} \, dx","\frac{1}{8} a \text{RootSum}\left[-\text{$\#$1}^8+4 \text{$\#$1}^6-4 \text{$\#$1}^4+b\&,\frac{5 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{a x+b}+1}+1}-\text{$\#$1}\right)-9 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{a x+b}+1}+1}-\text{$\#$1}\right)+2 \log \left(\sqrt{\sqrt{\sqrt{a x+b}+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]-\frac{\sqrt{a x+b} \sqrt{\sqrt{\sqrt{a x+b}+1}+1}}{x}+\frac{\sqrt{\sqrt{a x+b}+1} \sqrt{\sqrt{\sqrt{a x+b}+1}+1}}{x}-\frac{\sqrt{\sqrt{\sqrt{a x+b}+1}+1}}{x}",1,"Integrate[(Sqrt[b + a*x]*Sqrt[1 + Sqrt[b + a*x]])/(x^2*Sqrt[1 + Sqrt[1 + Sqrt[b + a*x]]]), x]","F",-1
2706,1,367,247,2.2850276,"\int \frac{x^4 \sqrt[4]{b x^2+a x^4}}{b+a x^2+x^4} \, dx","Integrate[(x^4*(b*x^2 + a*x^4)^(1/4))/(b + a*x^2 + x^4),x]","\frac{\sqrt[4]{x^2 \left(a x^2+b\right)} \left(3 \sqrt{a^2-4 b} \left(4 a^2-b\right) \left(a x^2+b\right) \left(\tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)-\tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)\right)-4 a^{3/4} x^{3/2} \left(a^3-a^2 \sqrt{a^2-4 b}+b \sqrt{a^2-4 b}-3 a b\right) \sqrt[4]{a x^2+b} \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};-\frac{\left(\frac{2}{a-\sqrt{a^2-4 b}}-\frac{a}{b}\right) b x^2}{a x^2+b}\right)+4 a^{3/4} x^{3/2} \left(a^3+a^2 \sqrt{a^2-4 b}-b \sqrt{a^2-4 b}-3 a b\right) \sqrt[4]{a x^2+b} \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};-\frac{\left(\frac{2}{a+\sqrt{a^2-4 b}}-\frac{a}{b}\right) b x^2}{a x^2+b}\right)\right)}{12 a^{3/4} \sqrt{x} \sqrt{a^2-4 b} \left(a x^2+b\right)^{5/4}}+\frac{1}{2} x \sqrt[4]{x^2 \left(a x^2+b\right)}","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4 a+b\&,\frac{\text{$\#$1}^4 a^2 \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 \left(-a^2\right) \log (x)-\text{$\#$1}^4 b \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 b \log (x)-a b \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+a b \log (x)}{\text{$\#$1}^3 a-2 \text{$\#$1}^7}\&\right]+\frac{\left(4 a^2-b\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{4 a^{3/4}}+\frac{\left(b-4 a^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{4 a^{3/4}}+\frac{1}{2} x \sqrt[4]{a x^4+b x^2}",1,"(x*(x^2*(b + a*x^2))^(1/4))/2 + ((x^2*(b + a*x^2))^(1/4)*(3*Sqrt[a^2 - 4*b]*(4*a^2 - b)*(b + a*x^2)*(ArcTan[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)] - ArcTanh[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)]) - 4*a^(3/4)*(a^3 - a^2*Sqrt[a^2 - 4*b] - 3*a*b + Sqrt[a^2 - 4*b]*b)*x^(3/2)*(b + a*x^2)^(1/4)*Hypergeometric2F1[3/4, 1, 7/4, -(((2/(a - Sqrt[a^2 - 4*b]) - a/b)*b*x^2)/(b + a*x^2))] + 4*a^(3/4)*(a^3 + a^2*Sqrt[a^2 - 4*b] - 3*a*b - Sqrt[a^2 - 4*b]*b)*x^(3/2)*(b + a*x^2)^(1/4)*Hypergeometric2F1[3/4, 1, 7/4, -(((2/(a + Sqrt[a^2 - 4*b]) - a/b)*b*x^2)/(b + a*x^2))]))/(12*a^(3/4)*Sqrt[a^2 - 4*b]*Sqrt[x]*(b + a*x^2)^(5/4))","A",1
2707,1,367,247,0.4584184,"\int \frac{x^4 \sqrt[4]{b x^2+a x^4}}{b+a x^2+x^4} \, dx","Integrate[(x^4*(b*x^2 + a*x^4)^(1/4))/(b + a*x^2 + x^4),x]","\frac{\sqrt[4]{x^2 \left(a x^2+b\right)} \left(3 \sqrt{a^2-4 b} \left(4 a^2-b\right) \left(a x^2+b\right) \left(\tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)-\tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)\right)-4 a^{3/4} x^{3/2} \left(a^3-a^2 \sqrt{a^2-4 b}+b \sqrt{a^2-4 b}-3 a b\right) \sqrt[4]{a x^2+b} \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};-\frac{\left(\frac{2}{a-\sqrt{a^2-4 b}}-\frac{a}{b}\right) b x^2}{a x^2+b}\right)+4 a^{3/4} x^{3/2} \left(a^3+a^2 \sqrt{a^2-4 b}-b \sqrt{a^2-4 b}-3 a b\right) \sqrt[4]{a x^2+b} \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};-\frac{\left(\frac{2}{a+\sqrt{a^2-4 b}}-\frac{a}{b}\right) b x^2}{a x^2+b}\right)\right)}{12 a^{3/4} \sqrt{x} \sqrt{a^2-4 b} \left(a x^2+b\right)^{5/4}}+\frac{1}{2} x \sqrt[4]{x^2 \left(a x^2+b\right)}","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4 a+b\&,\frac{\text{$\#$1}^4 a^2 \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 \left(-a^2\right) \log (x)-\text{$\#$1}^4 b \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 b \log (x)-a b \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+a b \log (x)}{\text{$\#$1}^3 a-2 \text{$\#$1}^7}\&\right]+\frac{\left(4 a^2-b\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{4 a^{3/4}}+\frac{\left(b-4 a^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{4 a^{3/4}}+\frac{1}{2} x \sqrt[4]{a x^4+b x^2}",1,"(x*(x^2*(b + a*x^2))^(1/4))/2 + ((x^2*(b + a*x^2))^(1/4)*(3*Sqrt[a^2 - 4*b]*(4*a^2 - b)*(b + a*x^2)*(ArcTan[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)] - ArcTanh[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)]) - 4*a^(3/4)*(a^3 - a^2*Sqrt[a^2 - 4*b] - 3*a*b + Sqrt[a^2 - 4*b]*b)*x^(3/2)*(b + a*x^2)^(1/4)*Hypergeometric2F1[3/4, 1, 7/4, -(((2/(a - Sqrt[a^2 - 4*b]) - a/b)*b*x^2)/(b + a*x^2))] + 4*a^(3/4)*(a^3 + a^2*Sqrt[a^2 - 4*b] - 3*a*b - Sqrt[a^2 - 4*b]*b)*x^(3/2)*(b + a*x^2)^(1/4)*Hypergeometric2F1[3/4, 1, 7/4, -(((2/(a + Sqrt[a^2 - 4*b]) - a/b)*b*x^2)/(b + a*x^2))]))/(12*a^(3/4)*Sqrt[a^2 - 4*b]*Sqrt[x]*(b + a*x^2)^(5/4))","A",1
2708,0,0,247,2.1330346,"\int \frac{(b+a x) \left(-3 a q+4 b p x^3+a p x^4\right)}{\left(q+p x^4\right)^{2/3} \left(b^3 c+d q+3 a b^2 c x+3 a^2 b c x^2+a^3 c x^3+d p x^4\right)} \, dx","Integrate[((b + a*x)*(-3*a*q + 4*b*p*x^3 + a*p*x^4))/((q + p*x^4)^(2/3)*(b^3*c + d*q + 3*a*b^2*c*x + 3*a^2*b*c*x^2 + a^3*c*x^3 + d*p*x^4)),x]","\int \frac{(b+a x) \left(-3 a q+4 b p x^3+a p x^4\right)}{\left(q+p x^4\right)^{2/3} \left(b^3 c+d q+3 a b^2 c x+3 a^2 b c x^2+a^3 c x^3+d p x^4\right)} \, dx","\frac{\log \left(a^2 \sqrt[3]{c} x+a b \sqrt[3]{c}+a \sqrt[3]{d} \sqrt[3]{p x^4+q}\right)}{c^{2/3} \sqrt[3]{d}}-\frac{\log \left(a^4 c^{2/3} x^2+2 a^3 b c^{2/3} x+a^2 b^2 c^{2/3}+a^2 d^{2/3} \left(p x^4+q\right)^{2/3}+\sqrt[3]{p x^4+q} \left(a^3 \left(-\sqrt[3]{c}\right) \sqrt[3]{d} x-a^2 b \sqrt[3]{c} \sqrt[3]{d}\right)\right)}{2 c^{2/3} \sqrt[3]{d}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} a \sqrt[3]{c} x+\sqrt{3} b \sqrt[3]{c}}{a \sqrt[3]{c} x+b \sqrt[3]{c}-2 \sqrt[3]{d} \sqrt[3]{p x^4+q}}\right)}{c^{2/3} \sqrt[3]{d}}",1,"Integrate[((b + a*x)*(-3*a*q + 4*b*p*x^3 + a*p*x^4))/((q + p*x^4)^(2/3)*(b^3*c + d*q + 3*a*b^2*c*x + 3*a^2*b*c*x^2 + a^3*c*x^3 + d*p*x^4)), x]","F",-1
2709,1,442,247,0.8127958,"\int \frac{\sqrt{b^2+a^2 x^3} \left(2 b^2+c x^3+a^2 x^6\right)}{x^7 \left(b^2+a^2 x^6\right)} \, dx","Integrate[(Sqrt[b^2 + a^2*x^3]*(2*b^2 + c*x^3 + a^2*x^6))/(x^7*(b^2 + a^2*x^6)),x]","\frac{-3 b^{7/2} \left(-\sqrt{-a^2} c x^3 \sqrt{\sqrt{-a^2}-b} \sqrt{a^2 x^3+b^2} \tan ^{-1}\left(\frac{\sqrt{a^2 x^3+b^2}}{\sqrt{b} \sqrt{\sqrt{-a^2}-b}}\right)+x^3 \sqrt{\sqrt{-a^2}+b} \left(a^2 b+\sqrt{-a^2} c\right) \sqrt{a^2 x^3+b^2} \tanh ^{-1}\left(\frac{\sqrt{a^2 x^3+b^2}}{\sqrt{b} \sqrt{\sqrt{-a^2}+b}}\right)+a^2 \sqrt{b} c x^3 \sqrt{\frac{a^2 x^3}{b^2}+1} \tanh ^{-1}\left(\sqrt{\frac{a^2 x^3}{b^2}+1}\right)+a^2 b x^3 \sqrt{\sqrt{-a^2}-b} \sqrt{a^2 x^3+b^2} \tan ^{-1}\left(\frac{\sqrt{a^2 x^3+b^2}}{\sqrt{b} \sqrt{\sqrt{-a^2}-b}}\right)-2 a^2 b^{3/2} x^3 \sqrt{a^2 x^3+b^2} \tanh ^{-1}\left(\frac{\sqrt{a^2 x^3+b^2}}{b}\right)+a^2 \sqrt{b} c x^3+b^{5/2} c\right)-4 a^4 x^3 \left(a^2 x^3+b^2\right)^2 \, _2F_1\left(\frac{3}{2},3;\frac{5}{2};\frac{a^2 x^3}{b^2}+1\right)}{9 b^6 x^3 \sqrt{a^2 x^3+b^2}}","\frac{\sqrt{a^2 x^3+b^2} \left(-a^2 x^3-2 b^2-2 c x^3\right)}{6 b^2 x^6}+\frac{\sqrt{a-i b} \left((-1)^{3/4} a^2 b-\sqrt[4]{-1} a c\right) \tan ^{-1}\left(\frac{\sqrt[4]{-1} \sqrt{a^2 x^3+b^2}}{\sqrt{b} \sqrt{a-i b}}\right)}{3 b^{5/2}}-\frac{\sqrt{a+i b} \left((-1)^{3/4} a c-\sqrt[4]{-1} a^2 b\right) \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a^2 x^3+b^2}}{\sqrt{b} \sqrt{a+i b}}\right)}{3 b^{5/2}}+\frac{\left(a^4+4 a^2 b^2-2 a^2 c\right) \tanh ^{-1}\left(\frac{\sqrt{a^2 x^3+b^2}}{b}\right)}{6 b^3}",1,"(-3*b^(7/2)*(b^(5/2)*c + a^2*Sqrt[b]*c*x^3 + a^2*Sqrt[Sqrt[-a^2] - b]*b*x^3*Sqrt[b^2 + a^2*x^3]*ArcTan[Sqrt[b^2 + a^2*x^3]/(Sqrt[Sqrt[-a^2] - b]*Sqrt[b])] - Sqrt[-a^2]*Sqrt[Sqrt[-a^2] - b]*c*x^3*Sqrt[b^2 + a^2*x^3]*ArcTan[Sqrt[b^2 + a^2*x^3]/(Sqrt[Sqrt[-a^2] - b]*Sqrt[b])] - 2*a^2*b^(3/2)*x^3*Sqrt[b^2 + a^2*x^3]*ArcTanh[Sqrt[b^2 + a^2*x^3]/b] + Sqrt[Sqrt[-a^2] + b]*(a^2*b + Sqrt[-a^2]*c)*x^3*Sqrt[b^2 + a^2*x^3]*ArcTanh[Sqrt[b^2 + a^2*x^3]/(Sqrt[b]*Sqrt[Sqrt[-a^2] + b])] + a^2*Sqrt[b]*c*x^3*Sqrt[1 + (a^2*x^3)/b^2]*ArcTanh[Sqrt[1 + (a^2*x^3)/b^2]]) - 4*a^4*x^3*(b^2 + a^2*x^3)^2*Hypergeometric2F1[3/2, 3, 5/2, 1 + (a^2*x^3)/b^2])/(9*b^6*x^3*Sqrt[b^2 + a^2*x^3])","C",1
2710,1,148,248,0.8864872,"\int \frac{\left(-2+x^4\right) \sqrt{2+x^4}}{\left(2+x^2+x^4\right) \left(2+2 x^2+x^4\right)} \, dx","Integrate[((-2 + x^4)*Sqrt[2 + x^4])/((2 + x^2 + x^4)*(2 + 2*x^2 + x^4)),x]","-\sqrt[4]{-\frac{1}{2}} \left(F\left(\left.i \sinh ^{-1}\left(\sqrt[4]{-\frac{1}{2}} x\right)\right|-1\right)-2 \Pi \left(-\frac{1+i}{\sqrt{2}};\left.i \sinh ^{-1}\left(\sqrt[4]{-\frac{1}{2}} x\right)\right|-1\right)-2 \Pi \left(\frac{1-i}{\sqrt{2}};\left.i \sinh ^{-1}\left(\sqrt[4]{-\frac{1}{2}} x\right)\right|-1\right)+\Pi \left(-\frac{2 \sqrt{2}}{-i+\sqrt{7}};\left.i \sinh ^{-1}\left(\sqrt[4]{-\frac{1}{2}} x\right)\right|-1\right)+\Pi \left(\frac{2 \sqrt{2}}{i+\sqrt{7}};\left.i \sinh ^{-1}\left(\sqrt[4]{-\frac{1}{2}} x\right)\right|-1\right)\right)","2 \sqrt[4]{2} \text{RootSum}\left[\text{$\#$1}^8+12 \sqrt{2} \text{$\#$1}^6-4 \text{$\#$1}^6-24 \sqrt{2} \text{$\#$1}^4+70 \text{$\#$1}^4+12 \sqrt{2} \text{$\#$1}^2-4 \text{$\#$1}^2+1\&,\frac{\text{$\#$1}^3 \left(-\log \left(-x^2+2^{3/4} x-\sqrt{2}\right)\right)+\text{$\#$1}^3 \log \left(\text{$\#$1} x^2-2^{3/4} \text{$\#$1} x+\sqrt{2} \text{$\#$1}+\sqrt{x^4+2}\right)-\text{$\#$1} \log \left(-x^2+2^{3/4} x-\sqrt{2}\right)+\text{$\#$1} \log \left(\text{$\#$1} x^2-2^{3/4} \text{$\#$1} x+\sqrt{2} \text{$\#$1}+\sqrt{x^4+2}\right)}{\text{$\#$1}^6+9 \sqrt{2} \text{$\#$1}^4-3 \text{$\#$1}^4-12 \sqrt{2} \text{$\#$1}^2+35 \text{$\#$1}^2+3 \sqrt{2}-1}\&\right]",1,"-((-1/2)^(1/4)*(EllipticF[I*ArcSinh[(-1/2)^(1/4)*x], -1] - 2*EllipticPi[(-1 - I)/Sqrt[2], I*ArcSinh[(-1/2)^(1/4)*x], -1] - 2*EllipticPi[(1 - I)/Sqrt[2], I*ArcSinh[(-1/2)^(1/4)*x], -1] + EllipticPi[(-2*Sqrt[2])/(-I + Sqrt[7]), I*ArcSinh[(-1/2)^(1/4)*x], -1] + EllipticPi[(2*Sqrt[2])/(I + Sqrt[7]), I*ArcSinh[(-1/2)^(1/4)*x], -1]))","C",1
2711,0,0,248,0.3104671,"\int \frac{x^2 \left(-2+x^8\right) \sqrt[4]{2-2 x^4+x^8}}{\left(2+x^8\right) \left(4-x^4+2 x^8\right)} \, dx","Integrate[(x^2*(-2 + x^8)*(2 - 2*x^4 + x^8)^(1/4))/((2 + x^8)*(4 - x^4 + 2*x^8)),x]","\int \frac{x^2 \left(-2+x^8\right) \sqrt[4]{2-2 x^4+x^8}}{\left(2+x^8\right) \left(4-x^4+2 x^8\right)} \, dx","\frac{\tan ^{-1}\left(\frac{2^{3/4} x \sqrt[4]{x^8-2 x^4+2}}{\sqrt{2} x^2-\sqrt{x^8-2 x^4+2}}\right)}{2 \sqrt[4]{2}}+\frac{\sqrt[4]{3} \tan ^{-1}\left(\frac{6^{3/4} x \sqrt[4]{x^8-2 x^4+2}}{\sqrt{6} \sqrt{x^8-2 x^4+2}-3 x^2}\right)}{2\ 2^{3/4}}+\frac{\tanh ^{-1}\left(\frac{2 \sqrt[4]{2} x \sqrt[4]{x^8-2 x^4+2}}{2 x^2+\sqrt{2} \sqrt{x^8-2 x^4+2}}\right)}{2 \sqrt[4]{2}}-\frac{\sqrt[4]{3} \tanh ^{-1}\left(\frac{6^{3/4} x \sqrt[4]{x^8-2 x^4+2}}{3 x^2+\sqrt{6} \sqrt{x^8-2 x^4+2}}\right)}{2\ 2^{3/4}}",1,"Integrate[(x^2*(-2 + x^8)*(2 - 2*x^4 + x^8)^(1/4))/((2 + x^8)*(4 - x^4 + 2*x^8)), x]","F",-1
2712,1,554,248,1.4519699,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{x+\sqrt{1+x}}} \, dx","Integrate[(-1 + x^2)/((1 + x^2)*Sqrt[x + Sqrt[1 + x]]),x]","\frac{1}{2} \left(4 \sqrt{x+\sqrt{x+1}}+\frac{2 i \log \left(-\sqrt{x+1}+\sqrt{1+i}\right)}{\sqrt{i+\sqrt{1+i}}}+\frac{2 i \log \left(\sqrt{x+1}+\sqrt{1+i}\right)}{\sqrt{i-\sqrt{1+i}}}+\frac{\log \left(x-2 \sqrt{1-i} \sqrt{x+1}+(2-i)\right)}{\sqrt{i-\sqrt{1-i}}}-\frac{\log \left(-x+2 \sqrt{1-i} \sqrt{x+1}-(2-i)\right)}{\sqrt{i-\sqrt{1-i}}}-2 \log \left(2 \sqrt{x+1}+2 \sqrt{x+\sqrt{x+1}}+1\right)-\frac{2 i \log \left(2 \sqrt{1+i} \sqrt{x+1}-\sqrt{x+1}-2 \sqrt{i-\sqrt{1+i}} \sqrt{x+\sqrt{x+1}}+\sqrt{1+i}+2\right)}{\sqrt{i-\sqrt{1+i}}}-\frac{2 i \log \left(-2 \sqrt{1+i} \sqrt{x+1}-\sqrt{x+1}-2 \sqrt{i+\sqrt{1+i}} \sqrt{x+\sqrt{x+1}}-\sqrt{1+i}+2\right)}{\sqrt{i+\sqrt{1+i}}}-\frac{2 i \tan ^{-1}\left(\frac{2 \sqrt{i+\sqrt{1-i}} \sqrt{x+\sqrt{x+1}}}{2 \sqrt{1-i} \sqrt{x+1}-\sqrt{x+1}+\sqrt{1-i}+2}\right)}{\sqrt{i+\sqrt{1-i}}}+\frac{2 i \tan ^{-1}\left(\frac{2 \sqrt{i-\sqrt{1-i}} \sqrt{x+\sqrt{x+1}}}{2 \sqrt{1-i} \sqrt{x+1}+\sqrt{x+1}+\sqrt{1-i}-2}\right)}{\sqrt{i-\sqrt{1-i}}}\right)","32 \text{RootSum}\left[\text{$\#$1}^8-8 \text{$\#$1}^7+12 \text{$\#$1}^6-24 \text{$\#$1}^5+470 \text{$\#$1}^4-120 \text{$\#$1}^3+300 \text{$\#$1}^2-1000 \text{$\#$1}+625\&,\frac{\text{$\#$1}^4 \log \left(-\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)-2 \text{$\#$1}^3 \log \left(-\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)+5 \text{$\#$1}^2 \log \left(-\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)}{\text{$\#$1}^7-7 \text{$\#$1}^6+9 \text{$\#$1}^5-15 \text{$\#$1}^4+235 \text{$\#$1}^3-45 \text{$\#$1}^2+75 \text{$\#$1}-125}\&\right]+2 \sqrt{x+\sqrt{x+1}}+\log \left(2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)",1,"(4*Sqrt[x + Sqrt[1 + x]] - ((2*I)*ArcTan[(2*Sqrt[I + Sqrt[1 - I]]*Sqrt[x + Sqrt[1 + x]])/(2 + Sqrt[1 - I] - Sqrt[1 + x] + 2*Sqrt[1 - I]*Sqrt[1 + x])])/Sqrt[I + Sqrt[1 - I]] + ((2*I)*ArcTan[(2*Sqrt[I - Sqrt[1 - I]]*Sqrt[x + Sqrt[1 + x]])/(-2 + Sqrt[1 - I] + Sqrt[1 + x] + 2*Sqrt[1 - I]*Sqrt[1 + x])])/Sqrt[I - Sqrt[1 - I]] + ((2*I)*Log[Sqrt[1 + I] - Sqrt[1 + x]])/Sqrt[I + Sqrt[1 + I]] + ((2*I)*Log[Sqrt[1 + I] + Sqrt[1 + x]])/Sqrt[I - Sqrt[1 + I]] + Log[(2 - I) + x - 2*Sqrt[1 - I]*Sqrt[1 + x]]/Sqrt[I - Sqrt[1 - I]] - Log[(-2 + I) - x + 2*Sqrt[1 - I]*Sqrt[1 + x]]/Sqrt[I - Sqrt[1 - I]] - 2*Log[1 + 2*Sqrt[1 + x] + 2*Sqrt[x + Sqrt[1 + x]]] - ((2*I)*Log[2 + Sqrt[1 + I] - Sqrt[1 + x] + 2*Sqrt[1 + I]*Sqrt[1 + x] - 2*Sqrt[I - Sqrt[1 + I]]*Sqrt[x + Sqrt[1 + x]]])/Sqrt[I - Sqrt[1 + I]] - ((2*I)*Log[2 - Sqrt[1 + I] - Sqrt[1 + x] - 2*Sqrt[1 + I]*Sqrt[1 + x] - 2*Sqrt[I + Sqrt[1 + I]]*Sqrt[x + Sqrt[1 + x]]])/Sqrt[I + Sqrt[1 + I]])/2","C",1
2713,1,554,248,0.1839997,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{x+\sqrt{1+x}}} \, dx","Integrate[(-1 + x^2)/((1 + x^2)*Sqrt[x + Sqrt[1 + x]]),x]","\frac{1}{2} \left(4 \sqrt{x+\sqrt{x+1}}+\frac{2 i \log \left(-\sqrt{x+1}+\sqrt{1+i}\right)}{\sqrt{i+\sqrt{1+i}}}+\frac{2 i \log \left(\sqrt{x+1}+\sqrt{1+i}\right)}{\sqrt{i-\sqrt{1+i}}}+\frac{\log \left(x-2 \sqrt{1-i} \sqrt{x+1}+(2-i)\right)}{\sqrt{i-\sqrt{1-i}}}-\frac{\log \left(-x+2 \sqrt{1-i} \sqrt{x+1}-(2-i)\right)}{\sqrt{i-\sqrt{1-i}}}-2 \log \left(2 \sqrt{x+1}+2 \sqrt{x+\sqrt{x+1}}+1\right)-\frac{2 i \log \left(2 \sqrt{1+i} \sqrt{x+1}-\sqrt{x+1}-2 \sqrt{i-\sqrt{1+i}} \sqrt{x+\sqrt{x+1}}+\sqrt{1+i}+2\right)}{\sqrt{i-\sqrt{1+i}}}-\frac{2 i \log \left(-2 \sqrt{1+i} \sqrt{x+1}-\sqrt{x+1}-2 \sqrt{i+\sqrt{1+i}} \sqrt{x+\sqrt{x+1}}-\sqrt{1+i}+2\right)}{\sqrt{i+\sqrt{1+i}}}-\frac{2 i \tan ^{-1}\left(\frac{2 \sqrt{i+\sqrt{1-i}} \sqrt{x+\sqrt{x+1}}}{2 \sqrt{1-i} \sqrt{x+1}-\sqrt{x+1}+\sqrt{1-i}+2}\right)}{\sqrt{i+\sqrt{1-i}}}+\frac{2 i \tan ^{-1}\left(\frac{2 \sqrt{i-\sqrt{1-i}} \sqrt{x+\sqrt{x+1}}}{2 \sqrt{1-i} \sqrt{x+1}+\sqrt{x+1}+\sqrt{1-i}-2}\right)}{\sqrt{i-\sqrt{1-i}}}\right)","32 \text{RootSum}\left[\text{$\#$1}^8-8 \text{$\#$1}^7+12 \text{$\#$1}^6-24 \text{$\#$1}^5+470 \text{$\#$1}^4-120 \text{$\#$1}^3+300 \text{$\#$1}^2-1000 \text{$\#$1}+625\&,\frac{\text{$\#$1}^4 \log \left(-\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)-2 \text{$\#$1}^3 \log \left(-\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)+5 \text{$\#$1}^2 \log \left(-\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)}{\text{$\#$1}^7-7 \text{$\#$1}^6+9 \text{$\#$1}^5-15 \text{$\#$1}^4+235 \text{$\#$1}^3-45 \text{$\#$1}^2+75 \text{$\#$1}-125}\&\right]+2 \sqrt{x+\sqrt{x+1}}+\log \left(2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)",1,"(4*Sqrt[x + Sqrt[1 + x]] - ((2*I)*ArcTan[(2*Sqrt[I + Sqrt[1 - I]]*Sqrt[x + Sqrt[1 + x]])/(2 + Sqrt[1 - I] - Sqrt[1 + x] + 2*Sqrt[1 - I]*Sqrt[1 + x])])/Sqrt[I + Sqrt[1 - I]] + ((2*I)*ArcTan[(2*Sqrt[I - Sqrt[1 - I]]*Sqrt[x + Sqrt[1 + x]])/(-2 + Sqrt[1 - I] + Sqrt[1 + x] + 2*Sqrt[1 - I]*Sqrt[1 + x])])/Sqrt[I - Sqrt[1 - I]] + ((2*I)*Log[Sqrt[1 + I] - Sqrt[1 + x]])/Sqrt[I + Sqrt[1 + I]] + ((2*I)*Log[Sqrt[1 + I] + Sqrt[1 + x]])/Sqrt[I - Sqrt[1 + I]] + Log[(2 - I) + x - 2*Sqrt[1 - I]*Sqrt[1 + x]]/Sqrt[I - Sqrt[1 - I]] - Log[(-2 + I) - x + 2*Sqrt[1 - I]*Sqrt[1 + x]]/Sqrt[I - Sqrt[1 - I]] - 2*Log[1 + 2*Sqrt[1 + x] + 2*Sqrt[x + Sqrt[1 + x]]] - ((2*I)*Log[2 + Sqrt[1 + I] - Sqrt[1 + x] + 2*Sqrt[1 + I]*Sqrt[1 + x] - 2*Sqrt[I - Sqrt[1 + I]]*Sqrt[x + Sqrt[1 + x]]])/Sqrt[I - Sqrt[1 + I]] - ((2*I)*Log[2 - Sqrt[1 + I] - Sqrt[1 + x] - 2*Sqrt[1 + I]*Sqrt[1 + x] - 2*Sqrt[I + Sqrt[1 + I]]*Sqrt[x + Sqrt[1 + x]]])/Sqrt[I + Sqrt[1 + I]])/2","C",1
2714,1,225,248,13.6484272,"\int \frac{1}{\sqrt{-b+a^2 x^2} \sqrt[3]{a x^2+x \sqrt{-b+a^2 x^2}}} \, dx","Integrate[1/(Sqrt[-b + a^2*x^2]*(a*x^2 + x*Sqrt[-b + a^2*x^2])^(1/3)),x]","\frac{\sqrt{a^2 x^2-b} \left(a x \left(\sqrt{a^2 x^2-b}+a x\right)\right)^{4/3} \left(-2 \log \left(\sqrt{a^2 x^2-b}+a x\right)+3 \log \left(\sqrt[3]{b}-\sqrt[3]{\left(\sqrt{a^2 x^2-b}+a x\right)^2+b}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{\left(\sqrt{a^2 x^2-b}+a x\right)^2+b}}{\sqrt[3]{b}}+1}{\sqrt{3}}\right)\right)}{2\ 2^{2/3} a^2 \sqrt[3]{b} x \sqrt[3]{x \left(\sqrt{a^2 x^2-b}+a x\right)} \left(a x \left(\sqrt{a^2 x^2-b}+a x\right)-b\right)}","-\frac{\log \left(\frac{\sqrt[3]{2} \sqrt[3]{a} \sqrt[3]{x \sqrt{a^2 x^2-b}+a x^2}}{\sqrt[3]{b}}+\frac{2^{2/3} a^{2/3} \left(x \sqrt{a^2 x^2-b}+a x^2\right)^{2/3}}{b^{2/3}}+1\right)}{2\ 2^{2/3} a^{2/3} \sqrt[3]{b}}+\frac{\log \left(\frac{\sqrt[3]{2} \sqrt[3]{a} \sqrt[3]{x \sqrt{a^2 x^2-b}+a x^2}}{\sqrt[3]{b}}-1\right)}{2^{2/3} a^{2/3} \sqrt[3]{b}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{2} \sqrt[3]{a} \sqrt[3]{x \sqrt{a^2 x^2-b}+a x^2}}{\sqrt{3} \sqrt[3]{b}}+\frac{1}{\sqrt{3}}\right)}{2^{2/3} a^{2/3} \sqrt[3]{b}}",1,"(Sqrt[-b + a^2*x^2]*(a*x*(a*x + Sqrt[-b + a^2*x^2]))^(4/3)*(2*Sqrt[3]*ArcTan[(1 + (2*(b + (a*x + Sqrt[-b + a^2*x^2])^2)^(1/3))/b^(1/3))/Sqrt[3]] - 2*Log[a*x + Sqrt[-b + a^2*x^2]] + 3*Log[b^(1/3) - (b + (a*x + Sqrt[-b + a^2*x^2])^2)^(1/3)]))/(2*2^(2/3)*a^2*b^(1/3)*x*(x*(a*x + Sqrt[-b + a^2*x^2]))^(1/3)*(-b + a*x*(a*x + Sqrt[-b + a^2*x^2])))","A",1
2715,1,503,248,0.7930743,"\int \frac{\sqrt{-b+a x}}{1+\sqrt{a x+\sqrt{-b+a x}}} \, dx","Integrate[Sqrt[-b + a*x]/(1 + Sqrt[a*x + Sqrt[-b + a*x]]),x]","\frac{-8 \sqrt{5-4 b} \sqrt{a x-b}-6 \sqrt{5-4 b} \sqrt{\sqrt{a x-b}+a x}+4 \sqrt{5-4 b} \sqrt{a x-b} \sqrt{\sqrt{a x-b}+a x}+4 \sqrt{5-4 b} \log \left(-\sqrt{a x-b}-a x+1\right)-8 (2 b-3) \tanh ^{-1}\left(\frac{2 \sqrt{a x-b}+1}{\sqrt{5-4 b}}\right)-\sqrt{5-4 b} (4 b-11) \tanh ^{-1}\left(\frac{2 \sqrt{a x-b}+1}{2 \sqrt{\sqrt{a x-b}+a x}}\right)-4 \left(2 b+\sqrt{5-4 b}-3\right) \tanh ^{-1}\left(\frac{-2 \sqrt{5-4 b} \sqrt{a x-b}-4 b-\sqrt{5-4 b}+1}{4 \sqrt{\sqrt{a x-b}+a x}}\right)+8 b \tanh ^{-1}\left(\frac{2 \sqrt{5-4 b} \sqrt{a x-b}-4 b+\sqrt{5-4 b}+1}{4 \sqrt{\sqrt{a x-b}+a x}}\right)-4 \sqrt{5-4 b} \tanh ^{-1}\left(\frac{2 \sqrt{5-4 b} \sqrt{a x-b}-4 b+\sqrt{5-4 b}+1}{4 \sqrt{\sqrt{a x-b}+a x}}\right)-12 \tanh ^{-1}\left(\frac{2 \sqrt{5-4 b} \sqrt{a x-b}-4 b+\sqrt{5-4 b}+1}{4 \sqrt{\sqrt{a x-b}+a x}}\right)}{4 a \sqrt{5-4 b}}","\sqrt{a x-b} \left(\frac{\sqrt{\sqrt{a x-b}+a x}}{a}-\frac{2}{a}\right)-\frac{3 \sqrt{\sqrt{a x-b}+a x}}{2 a}+\frac{(4 b-19) \log \left(2 \sqrt{a x-b}-2 \sqrt{\sqrt{a x-b}+a x}+1\right)}{4 a}+\frac{2 \log \left(2 \sqrt{a x-b} \sqrt{\sqrt{a x-b}+a x}-\sqrt{\sqrt{a x-b}+a x}-2 a x+1\right)}{a}-\frac{4 (2 b-3) \tan ^{-1}\left(\frac{-2 \sqrt{a x-b}+2 \sqrt{\sqrt{a x-b}+a x}+1}{\sqrt{4 b-5}}\right)}{a \sqrt{4 b-5}}",1,"(-8*Sqrt[5 - 4*b]*Sqrt[-b + a*x] - 6*Sqrt[5 - 4*b]*Sqrt[a*x + Sqrt[-b + a*x]] + 4*Sqrt[5 - 4*b]*Sqrt[-b + a*x]*Sqrt[a*x + Sqrt[-b + a*x]] - 8*(-3 + 2*b)*ArcTanh[(1 + 2*Sqrt[-b + a*x])/Sqrt[5 - 4*b]] - Sqrt[5 - 4*b]*(-11 + 4*b)*ArcTanh[(1 + 2*Sqrt[-b + a*x])/(2*Sqrt[a*x + Sqrt[-b + a*x]])] - 4*(-3 + Sqrt[5 - 4*b] + 2*b)*ArcTanh[(1 - Sqrt[5 - 4*b] - 4*b - 2*Sqrt[5 - 4*b]*Sqrt[-b + a*x])/(4*Sqrt[a*x + Sqrt[-b + a*x]])] - 12*ArcTanh[(1 + Sqrt[5 - 4*b] - 4*b + 2*Sqrt[5 - 4*b]*Sqrt[-b + a*x])/(4*Sqrt[a*x + Sqrt[-b + a*x]])] - 4*Sqrt[5 - 4*b]*ArcTanh[(1 + Sqrt[5 - 4*b] - 4*b + 2*Sqrt[5 - 4*b]*Sqrt[-b + a*x])/(4*Sqrt[a*x + Sqrt[-b + a*x]])] + 8*b*ArcTanh[(1 + Sqrt[5 - 4*b] - 4*b + 2*Sqrt[5 - 4*b]*Sqrt[-b + a*x])/(4*Sqrt[a*x + Sqrt[-b + a*x]])] + 4*Sqrt[5 - 4*b]*Log[1 - a*x - Sqrt[-b + a*x]])/(4*a*Sqrt[5 - 4*b])","B",1
2716,1,86,249,0.0991678,"\int x \sqrt{1+\sqrt{2}+\sqrt{2} x+x^2} \, dx","Integrate[x*Sqrt[1 + Sqrt[2] + Sqrt[2]*x + x^2],x]","\frac{1}{24} \left(2 \sqrt{x^2+\sqrt{2} x+\sqrt{2}+1} \left(4 x^2+\sqrt{2} x+4 \sqrt{2}+1\right)-3 \left(4+\sqrt{2}\right) \sinh ^{-1}\left(\sqrt{\frac{1}{14} \left(2 \sqrt{2}-1\right)} \left(2 x+\sqrt{2}\right)\right)\right)","\left(\frac{1}{2}+\frac{1}{4 \sqrt{2}}\right) \log \left(-2 \sqrt{x^2+\sqrt{2} x+\sqrt{2}+1}+2 x+\sqrt{2}\right)+\frac{4150400378441530192773231110852 x^{10}+24945598143999361560228474400848 x^9+105092569428910116088968496479929 x^8+287852425478772976908575001303368 x^7+628530823497779895944692654279120 x^6+1027228435068267876872457367335328 x^5+1378491402159939739304774333547654 x^4+1387443210853276135686753647625176 x^3+1129650644023239063399012556878492 x^2+\sqrt{2} \left(2934776252235219007085702870688 x^{10}+17639201608376503319286232221121 x^9+74311668495500397843180232944316 x^8+203542402037035701060244675374692 x^7+444438407480045173855448430747052 x^6+726360192264417334196307996315058 x^5+974740618274645593869948214329596 x^4+981070502905588448116241178725596 x^3+798783630760582994655573305295524 x^2+424011909556064190889798701120701 x+165915436694475540805635728313976\right)+599643393101900122105957184226864 x+234639860780381988229271893709089}{12 \sqrt{2} \left(733694063058804751771425717672 x^4+2075200189220765096386615555426 x^3+5009976441455984103472318426114 x^2+5009976441455984103472318426114 x+4276282378397179351700892708442\right) \left(x^2+\sqrt{2} x+\sqrt{2}+1\right)^{3/2}+12 \left(1037600094610382548193307777713 x^4+2934776252235219007085702870688 x^3+7085176630676749199858933981540 x^2+7085176630676749199858933981540 x+6047576536066366651665626203827\right) \left(x^2+\sqrt{2} x+\sqrt{2}+1\right)^{3/2}}",1,"(2*Sqrt[1 + Sqrt[2] + Sqrt[2]*x + x^2]*(1 + 4*Sqrt[2] + Sqrt[2]*x + 4*x^2) - 3*(4 + Sqrt[2])*ArcSinh[Sqrt[(-1 + 2*Sqrt[2])/14]*(Sqrt[2] + 2*x)])/24","A",1
2717,1,68,249,0.1747756,"\int \frac{-a x+x^2}{\left(x^2 (-a+x)\right)^{2/3} \left(a^2-2 a x+(1-d) x^2\right)} \, dx","Integrate[(-(a*x) + x^2)/((x^2*(-a + x))^(2/3)*(a^2 - 2*a*x + (1 - d)*x^2)),x]","-\frac{3 x^2 \left(\, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{\sqrt{d} x}{a-x}\right)+\, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{\sqrt{d} x}{x-a}\right)\right)}{4 a \left(x^2 (x-a)\right)^{2/3}}","\frac{\log \left(\sqrt[3]{x^3-a x^2}-\sqrt[6]{d} x\right)}{2 a \sqrt[3]{d}}+\frac{\log \left(\sqrt[3]{x^3-a x^2}+\sqrt[6]{d} x\right)}{2 a \sqrt[3]{d}}-\frac{\log \left(-\sqrt[6]{d} x \sqrt[3]{x^3-a x^2}+\left(x^3-a x^2\right)^{2/3}+\sqrt[3]{d} x^2\right)}{4 a \sqrt[3]{d}}-\frac{\log \left(\sqrt[6]{d} x \sqrt[3]{x^3-a x^2}+\left(x^3-a x^2\right)^{2/3}+\sqrt[3]{d} x^2\right)}{4 a \sqrt[3]{d}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} x^2}{2 \left(x^3-a x^2\right)^{2/3}+\sqrt[3]{d} x^2}\right)}{2 a \sqrt[3]{d}}",1,"(-3*x^2*(Hypergeometric2F1[2/3, 1, 5/3, (Sqrt[d]*x)/(a - x)] + Hypergeometric2F1[2/3, 1, 5/3, (Sqrt[d]*x)/(-a + x)]))/(4*a*(x^2*(-a + x))^(2/3))","C",1
2718,1,73,249,0.1084254,"\int \frac{x}{\sqrt[3]{x^2 (-a+x)} \left(-a^2+2 a x+(-1+d) x^2\right)} \, dx","Integrate[x/((x^2*(-a + x))^(1/3)*(-a^2 + 2*a*x + (-1 + d)*x^2)),x]","\frac{3 x \left(\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\sqrt{d} x}{x-a}\right)-\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\sqrt{d} x}{a-x}\right)\right)}{2 a \sqrt{d} \sqrt[3]{x^2 (x-a)}}","-\frac{\log \left(\sqrt[3]{x^3-a x^2}-\sqrt[6]{d} x\right)}{2 a d^{2/3}}-\frac{\log \left(\sqrt[3]{x^3-a x^2}+\sqrt[6]{d} x\right)}{2 a d^{2/3}}+\frac{\log \left(-\sqrt[6]{d} x \sqrt[3]{x^3-a x^2}+\left(x^3-a x^2\right)^{2/3}+\sqrt[3]{d} x^2\right)}{4 a d^{2/3}}+\frac{\log \left(\sqrt[6]{d} x \sqrt[3]{x^3-a x^2}+\left(x^3-a x^2\right)^{2/3}+\sqrt[3]{d} x^2\right)}{4 a d^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} x^2}{2 \left(x^3-a x^2\right)^{2/3}+\sqrt[3]{d} x^2}\right)}{2 a d^{2/3}}",1,"(3*x*(-Hypergeometric2F1[1/3, 1, 4/3, (Sqrt[d]*x)/(a - x)] + Hypergeometric2F1[1/3, 1, 4/3, (Sqrt[d]*x)/(-a + x)]))/(2*a*Sqrt[d]*(x^2*(-a + x))^(1/3))","C",1
2719,0,0,249,3.2514203,"\int \frac{-a b x^2+x^4}{\left(x^2 (-a+x) (-b+x)\right)^{2/3} \left(a^2 b^2-2 a b (a+b) x+\left(a^2+4 a b+b^2-d\right) x^2-2 (a+b) x^3+x^4\right)} \, dx","Integrate[(-(a*b*x^2) + x^4)/((x^2*(-a + x)*(-b + x))^(2/3)*(a^2*b^2 - 2*a*b*(a + b)*x + (a^2 + 4*a*b + b^2 - d)*x^2 - 2*(a + b)*x^3 + x^4)),x]","\int \frac{-a b x^2+x^4}{\left(x^2 (-a+x) (-b+x)\right)^{2/3} \left(a^2 b^2-2 a b (a+b) x+\left(a^2+4 a b+b^2-d\right) x^2-2 (a+b) x^3+x^4\right)} \, dx","-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{d} x}{\sqrt[6]{d} x-2 \sqrt[3]{x^3 (-a-b)+a b x^2+x^4}}\right)}{2 d^{5/6}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{d} x}{2 \sqrt[3]{x^3 (-a-b)+a b x^2+x^4}+\sqrt[6]{d} x}\right)}{2 d^{5/6}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{d} x}{\sqrt[3]{x^3 (-a-b)+a b x^2+x^4}}\right)}{d^{5/6}}-\frac{\tanh ^{-1}\left(\frac{\frac{\left(x^3 (-a-b)+a b x^2+x^4\right)^{2/3}}{\sqrt[6]{d}}+\sqrt[6]{d} x^2}{x \sqrt[3]{x^3 (-a-b)+a b x^2+x^4}}\right)}{2 d^{5/6}}",1,"Integrate[(-(a*b*x^2) + x^4)/((x^2*(-a + x)*(-b + x))^(2/3)*(a^2*b^2 - 2*a*b*(a + b)*x + (a^2 + 4*a*b + b^2 - d)*x^2 - 2*(a + b)*x^3 + x^4)), x]","F",-1
2720,1,84,249,0.049315,"\int \frac{\sqrt[4]{\frac{1+4 x^2+a x^2+6 x^4+4 a x^4+4 x^6+6 a x^6+x^8+4 a x^8+a x^{10}}{x^2}}}{x} \, dx","Integrate[((1 + 4*x^2 + a*x^2 + 6*x^4 + 4*a*x^4 + 4*x^6 + 6*a*x^6 + x^8 + 4*a*x^8 + a*x^10)/x^2)^(1/4)/x,x]","-\frac{2 \sqrt[4]{\frac{\left(x^2+1\right)^4 \left(a x^2+1\right)}{x^2}} \left(3 \left(a x^2+1\right)^{5/4}-(4 a+1) x^2 \, _2F_1\left(-\frac{1}{4},\frac{3}{4};\frac{7}{4};-a x^2\right)\right)}{3 \left(x^2+1\right) \sqrt[4]{a x^2+1}}","\frac{\sqrt[4]{\frac{a x^{10}+4 a x^8+6 a x^6+4 a x^4+a x^2+x^8+4 x^6+6 x^4+4 x^2+1}{x^2}} \left(\frac{\sqrt{x} \tan ^{-1}\left(\frac{\sqrt[4]{a x^2+1}}{\sqrt[4]{a} \sqrt{x}}\right)}{4 a^{3/4}}+\frac{\sqrt{x} \tanh ^{-1}\left(\frac{\sqrt[4]{a x^2+1}}{\sqrt[4]{a} \sqrt{x}}\right)}{4 a^{3/4}}+\frac{1}{2} x^2 \sqrt[4]{a x^2+1}-2 \sqrt[4]{a x^2+1}+\sqrt[4]{a} \sqrt{x} \tan ^{-1}\left(\frac{\sqrt[4]{a x^2+1}}{\sqrt[4]{a} \sqrt{x}}\right)+\sqrt[4]{a} \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt[4]{a x^2+1}}{\sqrt[4]{a} \sqrt{x}}\right)\right)}{\left(x^2+1\right) \sqrt[4]{a x^2+1}}",1,"(-2*(((1 + x^2)^4*(1 + a*x^2))/x^2)^(1/4)*(3*(1 + a*x^2)^(5/4) - (1 + 4*a)*x^2*Hypergeometric2F1[-1/4, 3/4, 7/4, -(a*x^2)]))/(3*(1 + x^2)*(1 + a*x^2)^(1/4))","C",1
2721,1,37,250,0.0382106,"\int \frac{\sqrt[3]{2-8 x+8 x^2}}{3+x} \, dx","Integrate[(2 - 8*x + 8*x^2)^(1/3)/(3 + x),x]","-\frac{3 \sqrt[3]{(1-2 x)^2} \left(\, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{1}{7} (1-2 x)\right)-1\right)}{2^{2/3}}","-\frac{\sqrt[3]{(1-2 x)^2} \left(7^{2/3} \sqrt[3]{2 x-1}+7\right) \left(\sqrt[3]{7} (2 x-1)^{2/3}-7^{2/3} \sqrt[3]{2 x-1}+7\right)^2 \left(\frac{3 (2 x-1)^{2/3}}{2^{2/3}}+\sqrt[3]{2} 7^{2/3} \log \left(7^{2/3} \sqrt[3]{2 x-1}+7\right)-\left(\frac{7}{2}\right)^{2/3} \log \left(-\sqrt[3]{7} (2 x-1)^{2/3}+7^{2/3} \sqrt[3]{2 x-1}-7\right)+\sqrt[3]{2} \sqrt{3} 7^{2/3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{2 x-1}}{\sqrt{3} \sqrt[3]{7}}\right)\right)}{14 (x+3) \sqrt[3]{2 x-1} \left(-2 \sqrt[3]{7} x+(14 x-7)^{2/3}-7 \sqrt[3]{2 x-1}+\sqrt[3]{7}\right)}",1,"(-3*((1 - 2*x)^2)^(1/3)*(-1 + Hypergeometric2F1[2/3, 1, 5/3, (1 - 2*x)/7]))/2^(2/3)","C",1
2722,0,0,250,1.5356506,"\int \frac{(b+a x) \left(-a q+b p x^2\right)}{\left(q+p x^3\right)^{2/3} \left(b^3 c+d q+3 a b^2 c x+3 a^2 b c x^2+\left(a^3 c+d p\right) x^3\right)} \, dx","Integrate[((b + a*x)*(-(a*q) + b*p*x^2))/((q + p*x^3)^(2/3)*(b^3*c + d*q + 3*a*b^2*c*x + 3*a^2*b*c*x^2 + (a^3*c + d*p)*x^3)),x]","\int \frac{(b+a x) \left(-a q+b p x^2\right)}{\left(q+p x^3\right)^{2/3} \left(b^3 c+d q+3 a b^2 c x+3 a^2 b c x^2+\left(a^3 c+d p\right) x^3\right)} \, dx","-\frac{\log \left(a^2 b^2 c^{2/3} x^2+2 a b^3 c^{2/3} x+\sqrt[3]{p x^3+q} \left(b^3 \left(-\sqrt[3]{c}\right) \sqrt[3]{d}-a b^2 \sqrt[3]{c} \sqrt[3]{d} x\right)+b^4 c^{2/3}+b^2 d^{2/3} \left(p x^3+q\right)^{2/3}\right)}{6 c^{2/3} \sqrt[3]{d}}+\frac{\log \left(a b \sqrt[3]{c} x+b^2 \sqrt[3]{c}+b \sqrt[3]{d} \sqrt[3]{p x^3+q}\right)}{3 c^{2/3} \sqrt[3]{d}}+\frac{\tan ^{-1}\left(\frac{\sqrt{3} a \sqrt[3]{c} x+\sqrt{3} b \sqrt[3]{c}}{a \sqrt[3]{c} x+b \sqrt[3]{c}-2 \sqrt[3]{d} \sqrt[3]{p x^3+q}}\right)}{\sqrt{3} c^{2/3} \sqrt[3]{d}}",1,"Integrate[((b + a*x)*(-(a*q) + b*p*x^2))/((q + p*x^3)^(2/3)*(b^3*c + d*q + 3*a*b^2*c*x + 3*a^2*b*c*x^2 + (a^3*c + d*p)*x^3)), x]","F",-1
2723,0,0,250,1.9056086,"\int \frac{(-b+x) \left(-a (a-2 b)-2 b x+x^2\right)}{((-a+x) (-b+x))^{2/3} \left(a^4-b^2 d-2 \left(2 a^3-b d\right) x+\left(6 a^2-d\right) x^2-4 a x^3+x^4\right)} \, dx","Integrate[((-b + x)*(-(a*(a - 2*b)) - 2*b*x + x^2))/(((-a + x)*(-b + x))^(2/3)*(a^4 - b^2*d - 2*(2*a^3 - b*d)*x + (6*a^2 - d)*x^2 - 4*a*x^3 + x^4)),x]","\int \frac{(-b+x) \left(-a (a-2 b)-2 b x+x^2\right)}{((-a+x) (-b+x))^{2/3} \left(a^4-b^2 d-2 \left(2 a^3-b d\right) x+\left(6 a^2-d\right) x^2-4 a x^3+x^4\right)} \, dx","\frac{\log \left(a^2-\sqrt[3]{d} \left(x (-a-b)+a b+x^2\right)^{2/3}-2 a x+x^2\right)}{2 d^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} \left(x (-a-b)+a b+x^2\right)^{2/3}}{2 a^2+\sqrt[3]{d} \left(x (-a-b)+a b+x^2\right)^{2/3}-4 a x+2 x^2}\right)}{2 d^{2/3}}-\frac{\log \left(a^4-4 a^3 x+\left(x (-a-b)+a b+x^2\right)^{2/3} \left(a^2 \sqrt[3]{d}-2 a \sqrt[3]{d} x+\sqrt[3]{d} x^2\right)+6 a^2 x^2+d^{2/3} \left(x (-a-b)+a b+x^2\right)^{4/3}-4 a x^3+x^4\right)}{4 d^{2/3}}",1,"Integrate[((-b + x)*(-(a*(a - 2*b)) - 2*b*x + x^2))/(((-a + x)*(-b + x))^(2/3)*(a^4 - b^2*d - 2*(2*a^3 - b*d)*x + (6*a^2 - d)*x^2 - 4*a*x^3 + x^4)), x]","F",-1
2724,1,204,250,0.4381482,"\int \frac{\sqrt{1+x^5} \left(2+x^5\right)}{x^6 \left(-1-x^5+a x^{10}\right)} \, dx","Integrate[(Sqrt[1 + x^5]*(2 + x^5))/(x^6*(-1 - x^5 + a*x^10)),x]","\frac{\sqrt{4 a-2 \sqrt{4 a+1}+2} \left(4 a+\sqrt{4 a+1}+1\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x^5+1}}{\sqrt{2 a-\sqrt{4 a+1}+1}}\right)}{10 \sqrt{a} \sqrt{4 a+1}}+\frac{\left(-4 a+\sqrt{4 a+1}-1\right) \sqrt{2 a+\sqrt{4 a+1}+1} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x^5+1}}{\sqrt{2 a+\sqrt{4 a+1}+1}}\right)}{5 \sqrt{2} \sqrt{a} \sqrt{4 a+1}}+\frac{2 \sqrt{x^5+1}}{5 x^5}","\frac{\left(4 \sqrt{2} a^{3/2}+\sqrt{2} \sqrt{4 a+1} \sqrt{a}+\sqrt{2} \sqrt{a}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x^5+1}}{\sqrt{-2 a-\sqrt{4 a+1}-1}}\right)}{5 \sqrt{4 a+1} \sqrt{-2 a-\sqrt{4 a+1}-1}}+\frac{\left(-4 \sqrt{2} a^{3/2}+\sqrt{2} \sqrt{4 a+1} \sqrt{a}-\sqrt{2} \sqrt{a}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x^5+1}}{\sqrt{-2 a+\sqrt{4 a+1}-1}}\right)}{5 \sqrt{4 a+1} \sqrt{-2 a+\sqrt{4 a+1}-1}}+\frac{2 \sqrt{x^5+1}}{5 x^5}",1,"(2*Sqrt[1 + x^5])/(5*x^5) + (Sqrt[2 + 4*a - 2*Sqrt[1 + 4*a]]*(1 + 4*a + Sqrt[1 + 4*a])*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[1 + x^5])/Sqrt[1 + 2*a - Sqrt[1 + 4*a]]])/(10*Sqrt[a]*Sqrt[1 + 4*a]) + ((-1 - 4*a + Sqrt[1 + 4*a])*Sqrt[1 + 2*a + Sqrt[1 + 4*a]]*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[1 + x^5])/Sqrt[1 + 2*a + Sqrt[1 + 4*a]]])/(5*Sqrt[2]*Sqrt[a]*Sqrt[1 + 4*a])","A",1
2725,1,238,250,0.7513593,"\int \frac{\left(-2+x^5\right) \sqrt{-1+x^5}}{x^6 \left(1-x^5+a x^{10}\right)} \, dx","Integrate[((-2 + x^5)*Sqrt[-1 + x^5])/(x^6*(1 - x^5 + a*x^10)),x]","\frac{2}{5} \left(-\frac{\sqrt{a} \left(4 a+\sqrt{1-4 a}-1\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x^5-1}}{\sqrt{-2 a-\sqrt{1-4 a}+1}}\right)}{\sqrt{2-8 a} \sqrt{-2 a-\sqrt{1-4 a}+1}}-\frac{\left(-4 a+\sqrt{1-4 a}+1\right) \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x^5-1}}{\sqrt{-2 a+\sqrt{1-4 a}+1}}\right)}{\sqrt{2-8 a} \sqrt{-2 a+\sqrt{1-4 a}+1}}+\tan ^{-1}\left(\sqrt{x^5-1}\right)+\frac{x^5+\sqrt{1-x^5} x^5 \tanh ^{-1}\left(\sqrt{1-x^5}\right)-1}{x^5 \sqrt{x^5-1}}\right)","\frac{\left(-4 \sqrt{2} a^{3/2}+\sqrt{2} \sqrt{1-4 a} \sqrt{a}+\sqrt{2} \sqrt{a}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x^5-1}}{\sqrt{2 a-\sqrt{1-4 a}-1}}\right)}{5 \sqrt{1-4 a} \sqrt{2 a-\sqrt{1-4 a}-1}}+\frac{\left(4 \sqrt{2} a^{3/2}+\sqrt{2} \sqrt{1-4 a} \sqrt{a}-\sqrt{2} \sqrt{a}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x^5-1}}{\sqrt{2 a+\sqrt{1-4 a}-1}}\right)}{5 \sqrt{1-4 a} \sqrt{2 a+\sqrt{1-4 a}-1}}+\frac{2 \sqrt{x^5-1}}{5 x^5}",1,"(2*(ArcTan[Sqrt[-1 + x^5]] + (-1 + x^5 + x^5*Sqrt[1 - x^5]*ArcTanh[Sqrt[1 - x^5]])/(x^5*Sqrt[-1 + x^5]) - (Sqrt[a]*(-1 + Sqrt[1 - 4*a] + 4*a)*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[-1 + x^5])/Sqrt[1 - Sqrt[1 - 4*a] - 2*a]])/(Sqrt[2 - 8*a]*Sqrt[1 - Sqrt[1 - 4*a] - 2*a]) - ((1 + Sqrt[1 - 4*a] - 4*a)*Sqrt[a]*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[-1 + x^5])/Sqrt[1 + Sqrt[1 - 4*a] - 2*a]])/(Sqrt[2 - 8*a]*Sqrt[1 + Sqrt[1 - 4*a] - 2*a])))/5","A",1
2726,1,1883,250,4.2325724,"\int \frac{1}{x^2-\sqrt{1+x} \sqrt{1+\sqrt{1+x}}} \, dx","Integrate[(x^2 - Sqrt[1 + x]*Sqrt[1 + Sqrt[1 + x]])^(-1),x]","\frac{1}{55} \left(-\sqrt{10 \left(3+\sqrt{5}\right)} \left(-1+3 \sqrt{5}\right) \tanh ^{-1}\left(\sqrt{\frac{2}{3-\sqrt{5}}} \sqrt{\sqrt{x+1}+1}\right)-2 \sqrt{\frac{10}{3+\sqrt{5}}} \left(1+3 \sqrt{5}\right) \tanh ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} \sqrt{\sqrt{x+1}+1}\right)-14 \sqrt{5} \tanh ^{-1}\left(\frac{2 \sqrt{x+1}-1}{\sqrt{5}}\right)-5 \log \left(\sqrt{x+1}-x\right)+10 \text{RootSum}\left[\text{$\#$1}^5-2 \text{$\#$1}^3+\text{$\#$1}^2+2 \text{$\#$1}-1\&,\frac{\log \left(\sqrt{x+1}-\text{$\#$1}\right) \text{$\#$1}^4-3 \log \left(\sqrt{x+1}-\text{$\#$1}\right) \text{$\#$1}^3+7 \log \left(\sqrt{x+1}-\text{$\#$1}\right) \text{$\#$1}^2+2 \log \left(\sqrt{x+1}-\text{$\#$1}\right) \text{$\#$1}-4 \log \left(\sqrt{x+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4-6 \text{$\#$1}^2+2 \text{$\#$1}+2}\&\right]+10 \left(3 \text{RootSum}\left[\text{$\#$1}^5-\text{$\#$1}^4-2 \text{$\#$1}^3+\text{$\#$1}^2+\text{$\#$1}+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2+3 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4-4 \text{$\#$1}^3-6 \text{$\#$1}^2+2 \text{$\#$1}+1}\&\right]-\text{RootSum}\left[\text{$\#$1}^5-\text{$\#$1}^4-2 \text{$\#$1}^3+\text{$\#$1}^2+\text{$\#$1}+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4-4 \text{$\#$1}^3-6 \text{$\#$1}^2+2 \text{$\#$1}+1}\&\right]-2 \text{RootSum}\left[\text{$\#$1}^5-\text{$\#$1}^4-2 \text{$\#$1}^3+\text{$\#$1}^2+\text{$\#$1}+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2+2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4-4 \text{$\#$1}^3-6 \text{$\#$1}^2+2 \text{$\#$1}+1}\&\right]-\text{RootSum}\left[\text{$\#$1}^5-\text{$\#$1}^4-2 \text{$\#$1}^3+\text{$\#$1}^2+\text{$\#$1}+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4-4 \text{$\#$1}^3-6 \text{$\#$1}^2+2 \text{$\#$1}+1}\&\right]+6 \text{RootSum}\left[\text{$\#$1}^5-\text{$\#$1}^4+\text{$\#$1}^3+2 \text{$\#$1}^2-\text{$\#$1}-1\&,\frac{\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}^3-\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}^2-\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}}{5 \text{$\#$1}^4-4 \text{$\#$1}^3+3 \text{$\#$1}^2+4 \text{$\#$1}-1}\&\right]+2 \text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1}\&\right]+\text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1}\&\right]+\text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1}\&\right]-3 \text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4+2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2-3 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1}\&\right]+6 \text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4+\text{$\#$1}^3-2 \text{$\#$1}^2-\text{$\#$1}+1\&,\frac{\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}^3+\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}^2-\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}}{5 \text{$\#$1}^4+4 \text{$\#$1}^3+3 \text{$\#$1}^2-4 \text{$\#$1}-1}\&\right]\right)\right)","\frac{4}{11} \text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{\text{$\#$1}^4 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-2 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-7 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-2 \text{$\#$1} \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)+7 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1}\&\right]+\frac{2}{55} \left(7 \sqrt{5}-5\right) \log \left(-2 \sqrt{\sqrt{x+1}+1}+\sqrt{5}+1\right)-\frac{2}{55} \left(5+7 \sqrt{5}\right) \log \left(2 \sqrt{\sqrt{x+1}+1}+\sqrt{5}-1\right)",1,"(-(Sqrt[10*(3 + Sqrt[5])]*(-1 + 3*Sqrt[5])*ArcTanh[Sqrt[2/(3 - Sqrt[5])]*Sqrt[1 + Sqrt[1 + x]]]) - 2*Sqrt[10/(3 + Sqrt[5])]*(1 + 3*Sqrt[5])*ArcTanh[Sqrt[2/(3 + Sqrt[5])]*Sqrt[1 + Sqrt[1 + x]]] - 14*Sqrt[5]*ArcTanh[(-1 + 2*Sqrt[1 + x])/Sqrt[5]] - 5*Log[-x + Sqrt[1 + x]] + 10*RootSum[-1 + 2*#1 + #1^2 - 2*#1^3 + #1^5 & , (-4*Log[Sqrt[1 + x] - #1] + 2*Log[Sqrt[1 + x] - #1]*#1 + 7*Log[Sqrt[1 + x] - #1]*#1^2 - 3*Log[Sqrt[1 + x] - #1]*#1^3 + Log[Sqrt[1 + x] - #1]*#1^4)/(2 + 2*#1 - 6*#1^2 + 5*#1^4) & ] + 10*(3*RootSum[1 + #1 + #1^2 - 2*#1^3 - #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] + 3*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 + 2*#1 - 6*#1^2 - 4*#1^3 + 5*#1^4) & ] - RootSum[1 + #1 + #1^2 - 2*#1^3 - #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 + 2*#1 - 6*#1^2 - 4*#1^3 + 5*#1^4) & ] - 2*RootSum[1 + #1 + #1^2 - 2*#1^3 - #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] + 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 + 2*#1 - 6*#1^2 - 4*#1^3 + 5*#1^4) & ] - RootSum[1 + #1 + #1^2 - 2*#1^3 - #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 + 2*#1 - 6*#1^2 - 4*#1^3 + 5*#1^4) & ] + 6*RootSum[-1 - #1 + 2*#1^2 + #1^3 - #1^4 + #1^5 & , (-(Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1) - Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3)/(-1 + 4*#1 + 3*#1^2 - 4*#1^3 + 5*#1^4) & ] + 2*RootSum[-1 + #1 - #1^2 - 2*#1^3 + #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 - 2*#1 - 6*#1^2 + 4*#1^3 + 5*#1^4) & ] + RootSum[-1 + #1 - #1^2 - 2*#1^3 + #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 - 2*#1 - 6*#1^2 + 4*#1^3 + 5*#1^4) & ] + RootSum[-1 + #1 - #1^2 - 2*#1^3 + #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 - 2*#1 - 6*#1^2 + 4*#1^3 + 5*#1^4) & ] - 3*RootSum[-1 + #1 - #1^2 - 2*#1^3 + #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] - 3*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 - 2*#1 - 6*#1^2 + 4*#1^3 + 5*#1^4) & ] + 6*RootSum[1 - #1 - 2*#1^2 + #1^3 + #1^4 + #1^5 & , (-(Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1) + Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3)/(-1 - 4*#1 + 3*#1^2 + 4*#1^3 + 5*#1^4) & ]))/55","B",0
2727,1,1883,250,3.5619189,"\int \frac{1}{x^2-\sqrt{1+x} \sqrt{1+\sqrt{1+x}}} \, dx","Integrate[(x^2 - Sqrt[1 + x]*Sqrt[1 + Sqrt[1 + x]])^(-1),x]","\frac{1}{55} \left(-\sqrt{10 \left(3+\sqrt{5}\right)} \left(-1+3 \sqrt{5}\right) \tanh ^{-1}\left(\sqrt{\frac{2}{3-\sqrt{5}}} \sqrt{\sqrt{x+1}+1}\right)-2 \sqrt{\frac{10}{3+\sqrt{5}}} \left(1+3 \sqrt{5}\right) \tanh ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} \sqrt{\sqrt{x+1}+1}\right)-14 \sqrt{5} \tanh ^{-1}\left(\frac{2 \sqrt{x+1}-1}{\sqrt{5}}\right)-5 \log \left(\sqrt{x+1}-x\right)+10 \text{RootSum}\left[\text{$\#$1}^5-2 \text{$\#$1}^3+\text{$\#$1}^2+2 \text{$\#$1}-1\&,\frac{\log \left(\sqrt{x+1}-\text{$\#$1}\right) \text{$\#$1}^4-3 \log \left(\sqrt{x+1}-\text{$\#$1}\right) \text{$\#$1}^3+7 \log \left(\sqrt{x+1}-\text{$\#$1}\right) \text{$\#$1}^2+2 \log \left(\sqrt{x+1}-\text{$\#$1}\right) \text{$\#$1}-4 \log \left(\sqrt{x+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4-6 \text{$\#$1}^2+2 \text{$\#$1}+2}\&\right]+10 \left(3 \text{RootSum}\left[\text{$\#$1}^5-\text{$\#$1}^4-2 \text{$\#$1}^3+\text{$\#$1}^2+\text{$\#$1}+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2+3 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4-4 \text{$\#$1}^3-6 \text{$\#$1}^2+2 \text{$\#$1}+1}\&\right]-\text{RootSum}\left[\text{$\#$1}^5-\text{$\#$1}^4-2 \text{$\#$1}^3+\text{$\#$1}^2+\text{$\#$1}+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4-4 \text{$\#$1}^3-6 \text{$\#$1}^2+2 \text{$\#$1}+1}\&\right]-2 \text{RootSum}\left[\text{$\#$1}^5-\text{$\#$1}^4-2 \text{$\#$1}^3+\text{$\#$1}^2+\text{$\#$1}+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2+2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4-4 \text{$\#$1}^3-6 \text{$\#$1}^2+2 \text{$\#$1}+1}\&\right]-\text{RootSum}\left[\text{$\#$1}^5-\text{$\#$1}^4-2 \text{$\#$1}^3+\text{$\#$1}^2+\text{$\#$1}+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4-4 \text{$\#$1}^3-6 \text{$\#$1}^2+2 \text{$\#$1}+1}\&\right]+6 \text{RootSum}\left[\text{$\#$1}^5-\text{$\#$1}^4+\text{$\#$1}^3+2 \text{$\#$1}^2-\text{$\#$1}-1\&,\frac{\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}^3-\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}^2-\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}}{5 \text{$\#$1}^4-4 \text{$\#$1}^3+3 \text{$\#$1}^2+4 \text{$\#$1}-1}\&\right]+2 \text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1}\&\right]+\text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1}\&\right]+\text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1}\&\right]-3 \text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4+2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2-3 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1}\&\right]+6 \text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4+\text{$\#$1}^3-2 \text{$\#$1}^2-\text{$\#$1}+1\&,\frac{\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}^3+\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}^2-\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}}{5 \text{$\#$1}^4+4 \text{$\#$1}^3+3 \text{$\#$1}^2-4 \text{$\#$1}-1}\&\right]\right)\right)","\frac{4}{11} \text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{\text{$\#$1}^4 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-2 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-7 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-2 \text{$\#$1} \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)+7 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1}\&\right]+\frac{2}{55} \left(7 \sqrt{5}-5\right) \log \left(-2 \sqrt{\sqrt{x+1}+1}+\sqrt{5}+1\right)-\frac{2}{55} \left(5+7 \sqrt{5}\right) \log \left(2 \sqrt{\sqrt{x+1}+1}+\sqrt{5}-1\right)",1,"(-(Sqrt[10*(3 + Sqrt[5])]*(-1 + 3*Sqrt[5])*ArcTanh[Sqrt[2/(3 - Sqrt[5])]*Sqrt[1 + Sqrt[1 + x]]]) - 2*Sqrt[10/(3 + Sqrt[5])]*(1 + 3*Sqrt[5])*ArcTanh[Sqrt[2/(3 + Sqrt[5])]*Sqrt[1 + Sqrt[1 + x]]] - 14*Sqrt[5]*ArcTanh[(-1 + 2*Sqrt[1 + x])/Sqrt[5]] - 5*Log[-x + Sqrt[1 + x]] + 10*RootSum[-1 + 2*#1 + #1^2 - 2*#1^3 + #1^5 & , (-4*Log[Sqrt[1 + x] - #1] + 2*Log[Sqrt[1 + x] - #1]*#1 + 7*Log[Sqrt[1 + x] - #1]*#1^2 - 3*Log[Sqrt[1 + x] - #1]*#1^3 + Log[Sqrt[1 + x] - #1]*#1^4)/(2 + 2*#1 - 6*#1^2 + 5*#1^4) & ] + 10*(3*RootSum[1 + #1 + #1^2 - 2*#1^3 - #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] + 3*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 + 2*#1 - 6*#1^2 - 4*#1^3 + 5*#1^4) & ] - RootSum[1 + #1 + #1^2 - 2*#1^3 - #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 + 2*#1 - 6*#1^2 - 4*#1^3 + 5*#1^4) & ] - 2*RootSum[1 + #1 + #1^2 - 2*#1^3 - #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] + 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 + 2*#1 - 6*#1^2 - 4*#1^3 + 5*#1^4) & ] - RootSum[1 + #1 + #1^2 - 2*#1^3 - #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 + 2*#1 - 6*#1^2 - 4*#1^3 + 5*#1^4) & ] + 6*RootSum[-1 - #1 + 2*#1^2 + #1^3 - #1^4 + #1^5 & , (-(Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1) - Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3)/(-1 + 4*#1 + 3*#1^2 - 4*#1^3 + 5*#1^4) & ] + 2*RootSum[-1 + #1 - #1^2 - 2*#1^3 + #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 - 2*#1 - 6*#1^2 + 4*#1^3 + 5*#1^4) & ] + RootSum[-1 + #1 - #1^2 - 2*#1^3 + #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 - 2*#1 - 6*#1^2 + 4*#1^3 + 5*#1^4) & ] + RootSum[-1 + #1 - #1^2 - 2*#1^3 + #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 - 2*#1 - 6*#1^2 + 4*#1^3 + 5*#1^4) & ] - 3*RootSum[-1 + #1 - #1^2 - 2*#1^3 + #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] - 3*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 - 2*#1 - 6*#1^2 + 4*#1^3 + 5*#1^4) & ] + 6*RootSum[1 - #1 - 2*#1^2 + #1^3 + #1^4 + #1^5 & , (-(Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1) + Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3)/(-1 - 4*#1 + 3*#1^2 + 4*#1^3 + 5*#1^4) & ]))/55","B",0
2728,1,57413,250,6.8510598,"\int \frac{x \left(x^2 c_3-c_4\right)}{\sqrt{\frac{x c_0+x^2 c_3+c_4}{x c_1+x^2 c_3+c_4}} \left(x+3 x^2 c_3+3 c_4\right) \left(-x^2+x^4 c_3{}^2+2 x^2 c_3 c_4+c_4{}^2\right)} \, dx","Integrate[(x*(x^2*C[3] - C[4]))/(Sqrt[(x*C[0] + x^2*C[3] + C[4])/(x*C[1] + x^2*C[3] + C[4])]*(x + 3*x^2*C[3] + 3*C[4])*(-x^2 + x^4*C[3]^2 + 2*x^2*C[3]*C[4] + C[4]^2)),x]","\text{Result too large to show}","-\frac{\sqrt{-1+c_1} \tan ^{-1}\left(\frac{\sqrt{1-c_0} \sqrt{-1+c_1} \sqrt{\frac{c_3 x^2+c_0 x+c_4}{c_3 x^2+c_1 x+c_4}}}{-1+c_0}\right)}{2 \sqrt{1-c_0}}-\frac{\sqrt{1+c_1} \tan ^{-1}\left(\frac{\sqrt{-1-c_0} \sqrt{1+c_1} \sqrt{\frac{c_3 x^2+c_0 x+c_4}{c_3 x^2+c_1 x+c_4}}}{1+c_0}\right)}{4 \sqrt{-1-c_0}}+\frac{3 \sqrt{-1+3 c_1} \tan ^{-1}\left(\frac{\sqrt{1-3 c_0} \sqrt{-1+3 c_1} \sqrt{\frac{c_3 x^2+c_0 x+c_4}{c_3 x^2+c_1 x+c_4}}}{-1+3 c_0}\right)}{4 \sqrt{1-3 c_0}}",1,"Result too large to show","B",0
2729,1,644,251,2.506175,"\int \frac{1}{\left(-b+a x^4\right)^2 \sqrt[4]{-b x^2+a x^4}} \, dx","Integrate[1/((-b + a*x^4)^2*(-(b*x^2) + a*x^4)^(1/4)),x]","\frac{\left(a x^2-b\right) \left(\frac{7 b \sqrt[4]{\sqrt{b}-\sqrt{a}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{a} \sqrt[4]{-\sqrt{a}-\sqrt{b}}}\right)+\sqrt{a} \sqrt{b} \sqrt[4]{\sqrt{b}-\sqrt{a}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{a} \sqrt[4]{-\sqrt{a}-\sqrt{b}}}\right)-8 a \sqrt[4]{\sqrt{b}-\sqrt{a}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{a} \sqrt[4]{-\sqrt{a}-\sqrt{b}}}\right)+7 b \sqrt[4]{-\sqrt{a}-\sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{a} \sqrt[4]{\sqrt{b}-\sqrt{a}}}\right)-\sqrt{a} \sqrt{b} \sqrt[4]{-\sqrt{a}-\sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{a} \sqrt[4]{\sqrt{b}-\sqrt{a}}}\right)-8 a \sqrt[4]{-\sqrt{a}-\sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{a} \sqrt[4]{\sqrt{b}-\sqrt{a}}}\right)+\sqrt[4]{\sqrt{b}-\sqrt{a}} \left(-\sqrt{a} \sqrt{b}+8 a-7 b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{a} \sqrt[4]{-\sqrt{a}-\sqrt{b}}}\right)+\sqrt[4]{-\sqrt{a}-\sqrt{b}} \left(\sqrt{a} \sqrt{b}+8 a-7 b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{a} \sqrt[4]{\sqrt{b}-\sqrt{a}}}\right)}{\sqrt[8]{a} \sqrt[4]{-\sqrt{a}-\sqrt{b}} \sqrt[4]{\sqrt{b}-\sqrt{a}} \left(\frac{b}{x^2}-a\right)^{3/4}}+\frac{4 x^2 \left(a x^2+b\right)}{a x^4-b}\right)}{16 b^2 x (b-a) \sqrt[4]{a x^4-b x^2}}","\frac{\left(-a x^2-b\right) \left(a x^4-b x^2\right)^{3/4}}{4 b^2 x (b-a) \left(b-a x^4\right)}-\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2-a b\&,\frac{-8 \text{$\#$1}^4 a \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+7 \text{$\#$1}^4 b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+8 \text{$\#$1}^4 a \log (x)-7 \text{$\#$1}^4 b \log (x)+8 a^2 \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-6 a b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-8 a^2 \log (x)+6 a b \log (x)}{\text{$\#$1} a-\text{$\#$1}^5}\&\right]}{32 b^2 (a-b)}",1,"((-b + a*x^2)*((4*x^2*(b + a*x^2))/(-b + a*x^4) + (-8*a*(-Sqrt[a] + Sqrt[b])^(1/4)*ArcTan[(-a + b/x^2)^(1/4)/(a^(1/8)*(-Sqrt[a] - Sqrt[b])^(1/4))] + Sqrt[a]*(-Sqrt[a] + Sqrt[b])^(1/4)*Sqrt[b]*ArcTan[(-a + b/x^2)^(1/4)/(a^(1/8)*(-Sqrt[a] - Sqrt[b])^(1/4))] + 7*(-Sqrt[a] + Sqrt[b])^(1/4)*b*ArcTan[(-a + b/x^2)^(1/4)/(a^(1/8)*(-Sqrt[a] - Sqrt[b])^(1/4))] - 8*a*(-Sqrt[a] - Sqrt[b])^(1/4)*ArcTan[(-a + b/x^2)^(1/4)/(a^(1/8)*(-Sqrt[a] + Sqrt[b])^(1/4))] - Sqrt[a]*(-Sqrt[a] - Sqrt[b])^(1/4)*Sqrt[b]*ArcTan[(-a + b/x^2)^(1/4)/(a^(1/8)*(-Sqrt[a] + Sqrt[b])^(1/4))] + 7*(-Sqrt[a] - Sqrt[b])^(1/4)*b*ArcTan[(-a + b/x^2)^(1/4)/(a^(1/8)*(-Sqrt[a] + Sqrt[b])^(1/4))] + (-Sqrt[a] + Sqrt[b])^(1/4)*(8*a - Sqrt[a]*Sqrt[b] - 7*b)*ArcTanh[(-a + b/x^2)^(1/4)/(a^(1/8)*(-Sqrt[a] - Sqrt[b])^(1/4))] + (-Sqrt[a] - Sqrt[b])^(1/4)*(8*a + Sqrt[a]*Sqrt[b] - 7*b)*ArcTanh[(-a + b/x^2)^(1/4)/(a^(1/8)*(-Sqrt[a] + Sqrt[b])^(1/4))])/(a^(1/8)*(-Sqrt[a] - Sqrt[b])^(1/4)*(-Sqrt[a] + Sqrt[b])^(1/4)*(-a + b/x^2)^(3/4))))/(16*b^2*(-a + b)*x*(-(b*x^2) + a*x^4)^(1/4))","B",1
2730,1,644,251,1.7961348,"\int \frac{1}{\left(-b+a x^4\right)^2 \sqrt[4]{-b x^2+a x^4}} \, dx","Integrate[1/((-b + a*x^4)^2*(-(b*x^2) + a*x^4)^(1/4)),x]","\frac{\left(a x^2-b\right) \left(\frac{7 b \sqrt[4]{\sqrt{b}-\sqrt{a}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{a} \sqrt[4]{-\sqrt{a}-\sqrt{b}}}\right)+\sqrt{a} \sqrt{b} \sqrt[4]{\sqrt{b}-\sqrt{a}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{a} \sqrt[4]{-\sqrt{a}-\sqrt{b}}}\right)-8 a \sqrt[4]{\sqrt{b}-\sqrt{a}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{a} \sqrt[4]{-\sqrt{a}-\sqrt{b}}}\right)+7 b \sqrt[4]{-\sqrt{a}-\sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{a} \sqrt[4]{\sqrt{b}-\sqrt{a}}}\right)-\sqrt{a} \sqrt{b} \sqrt[4]{-\sqrt{a}-\sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{a} \sqrt[4]{\sqrt{b}-\sqrt{a}}}\right)-8 a \sqrt[4]{-\sqrt{a}-\sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{a} \sqrt[4]{\sqrt{b}-\sqrt{a}}}\right)+\sqrt[4]{\sqrt{b}-\sqrt{a}} \left(-\sqrt{a} \sqrt{b}+8 a-7 b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{a} \sqrt[4]{-\sqrt{a}-\sqrt{b}}}\right)+\sqrt[4]{-\sqrt{a}-\sqrt{b}} \left(\sqrt{a} \sqrt{b}+8 a-7 b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{a} \sqrt[4]{\sqrt{b}-\sqrt{a}}}\right)}{\sqrt[8]{a} \sqrt[4]{-\sqrt{a}-\sqrt{b}} \sqrt[4]{\sqrt{b}-\sqrt{a}} \left(\frac{b}{x^2}-a\right)^{3/4}}+\frac{4 x^2 \left(a x^2+b\right)}{a x^4-b}\right)}{16 b^2 x (b-a) \sqrt[4]{a x^4-b x^2}}","\frac{\left(-a x^2-b\right) \left(a x^4-b x^2\right)^{3/4}}{4 b^2 x (b-a) \left(b-a x^4\right)}-\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2-a b\&,\frac{-8 \text{$\#$1}^4 a \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+7 \text{$\#$1}^4 b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+8 \text{$\#$1}^4 a \log (x)-7 \text{$\#$1}^4 b \log (x)+8 a^2 \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-6 a b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-8 a^2 \log (x)+6 a b \log (x)}{\text{$\#$1} a-\text{$\#$1}^5}\&\right]}{32 b^2 (a-b)}",1,"((-b + a*x^2)*((4*x^2*(b + a*x^2))/(-b + a*x^4) + (-8*a*(-Sqrt[a] + Sqrt[b])^(1/4)*ArcTan[(-a + b/x^2)^(1/4)/(a^(1/8)*(-Sqrt[a] - Sqrt[b])^(1/4))] + Sqrt[a]*(-Sqrt[a] + Sqrt[b])^(1/4)*Sqrt[b]*ArcTan[(-a + b/x^2)^(1/4)/(a^(1/8)*(-Sqrt[a] - Sqrt[b])^(1/4))] + 7*(-Sqrt[a] + Sqrt[b])^(1/4)*b*ArcTan[(-a + b/x^2)^(1/4)/(a^(1/8)*(-Sqrt[a] - Sqrt[b])^(1/4))] - 8*a*(-Sqrt[a] - Sqrt[b])^(1/4)*ArcTan[(-a + b/x^2)^(1/4)/(a^(1/8)*(-Sqrt[a] + Sqrt[b])^(1/4))] - Sqrt[a]*(-Sqrt[a] - Sqrt[b])^(1/4)*Sqrt[b]*ArcTan[(-a + b/x^2)^(1/4)/(a^(1/8)*(-Sqrt[a] + Sqrt[b])^(1/4))] + 7*(-Sqrt[a] - Sqrt[b])^(1/4)*b*ArcTan[(-a + b/x^2)^(1/4)/(a^(1/8)*(-Sqrt[a] + Sqrt[b])^(1/4))] + (-Sqrt[a] + Sqrt[b])^(1/4)*(8*a - Sqrt[a]*Sqrt[b] - 7*b)*ArcTanh[(-a + b/x^2)^(1/4)/(a^(1/8)*(-Sqrt[a] - Sqrt[b])^(1/4))] + (-Sqrt[a] - Sqrt[b])^(1/4)*(8*a + Sqrt[a]*Sqrt[b] - 7*b)*ArcTanh[(-a + b/x^2)^(1/4)/(a^(1/8)*(-Sqrt[a] + Sqrt[b])^(1/4))])/(a^(1/8)*(-Sqrt[a] - Sqrt[b])^(1/4)*(-Sqrt[a] + Sqrt[b])^(1/4)*(-a + b/x^2)^(3/4))))/(16*b^2*(-a + b)*x*(-(b*x^2) + a*x^4)^(1/4))","B",1
2731,0,0,251,4.4211764,"\int \frac{\left(-2 q+p x^3\right) \left(a q+b x^2+a p x^3\right) \sqrt{q^2+2 p q x^3-2 p q x^4+p^2 x^6}}{x^5 \left(c q+d x^2+c p x^3\right)} \, dx","Integrate[((-2*q + p*x^3)*(a*q + b*x^2 + a*p*x^3)*Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6])/(x^5*(c*q + d*x^2 + c*p*x^3)),x]","\int \frac{\left(-2 q+p x^3\right) \left(a q+b x^2+a p x^3\right) \sqrt{q^2+2 p q x^3-2 p q x^4+p^2 x^6}}{x^5 \left(c q+d x^2+c p x^3\right)} \, dx","\frac{\sqrt{p^2 x^6-2 p q x^4+2 p q x^3+q^2} \left(a c p x^3+a c q-2 a d x^2+2 b c x^2\right)}{2 c^2 x^4}+\frac{\log \left(\sqrt{p^2 x^6-2 p q x^4+2 p q x^3+q^2}+p x^3+q\right) \left(-a c^2 p q+a d^2-b c d\right)}{c^3}-\frac{2 (a d-b c) \sqrt{2 c^2 p q-d^2} \tan ^{-1}\left(\frac{x^2 \sqrt{2 c^2 p q-d^2}}{c \sqrt{p^2 x^6-2 p q x^4+2 p q x^3+q^2}+c p x^3+c q+d x^2}\right)}{c^3}+\frac{2 \log (x) \left(a c^2 p q-a d^2+b c d\right)}{c^3}",1,"Integrate[((-2*q + p*x^3)*(a*q + b*x^2 + a*p*x^3)*Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6])/(x^5*(c*q + d*x^2 + c*p*x^3)), x]","F",-1
2732,1,87,252,3.6177831,"\int -\frac{(-1+x) x \left(-1+2 x+\left(-2 k+k^2\right) x^2\right)}{((1-x) x (1-k x))^{2/3} \left(1-4 k x+\left(-b+6 k^2\right) x^2+\left(2 b-4 k^3\right) x^3+\left(-b+k^4\right) x^4\right)} \, dx","Integrate[-(((-1 + x)*x*(-1 + 2*x + (-2*k + k^2)*x^2))/(((1 - x)*x*(1 - k*x))^(2/3)*(1 - 4*k*x + (-b + 6*k^2)*x^2 + (2*b - 4*k^3)*x^3 + (-b + k^4)*x^4))),x]","-\int \frac{(x-1) x \left(\left(k^2-2 k\right) x^2+2 x-1\right)}{((1-x) x (1-k x))^{2/3} \left(x^4 \left(k^4-b\right)+x^3 \left(2 b-4 k^3\right)+x^2 \left(6 k^2-b\right)-4 k x+1\right)} \, dx","\frac{\log \left(-\sqrt[3]{b} \left(k x^3+(-k-1) x^2+x\right)^{2/3}+k^2 x^2-2 k x+1\right)}{2 b^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{b} \left(k x^3+(-k-1) x^2+x\right)^{2/3}}{\sqrt[3]{b} \left(k x^3+(-k-1) x^2+x\right)^{2/3}+2 k^2 x^2-4 k x+2}\right)}{2 b^{2/3}}-\frac{\log \left(b^{2/3} \left(k x^3+(-k-1) x^2+x\right)^{4/3}+\left(k x^3+(-k-1) x^2+x\right)^{2/3} \left(\sqrt[3]{b} k^2 x^2-2 \sqrt[3]{b} k x+\sqrt[3]{b}\right)+k^4 x^4-4 k^3 x^3+6 k^2 x^2-4 k x+1\right)}{4 b^{2/3}}",1,"-Integrate[((-1 + x)*x*(-1 + 2*x + (-2*k + k^2)*x^2))/(((1 - x)*x*(1 - k*x))^(2/3)*(1 - 4*k*x + (-b + 6*k^2)*x^2 + (2*b - 4*k^3)*x^3 + (-b + k^4)*x^4)), x]","F",1
2733,0,0,252,0.9879012,"\int \frac{\left(-2 q+p x^3\right) \sqrt{q^2+2 p q x^3-2 p q x^4+p^2 x^6} \left(b x^8+a \left(q+p x^3\right)^4\right)}{x^{13}} \, dx","Integrate[((-2*q + p*x^3)*Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]*(b*x^8 + a*(q + p*x^3)^4))/x^13,x]","\int \frac{\left(-2 q+p x^3\right) \sqrt{q^2+2 p q x^3-2 p q x^4+p^2 x^6} \left(b x^8+a \left(q+p x^3\right)^4\right)}{x^{13}} \, dx","\log (x) \left(a p^3 q^3+2 b p q\right)+\frac{1}{2} \left(-a p^3 q^3-2 b p q\right) \log \left(\sqrt{p^2 x^6-2 p q x^4+2 p q x^3+q^2}+p x^3+q\right)+\frac{\sqrt{p^2 x^6-2 p q x^4+2 p q x^3+q^2} \left(2 a p^5 x^{15}-a p^4 q x^{13}+10 a p^4 q x^{12}-3 a p^3 q^2 x^{11}-3 a p^3 q^2 x^{10}+20 a p^3 q^2 x^9-3 a p^2 q^3 x^8-3 a p^2 q^3 x^7+20 a p^2 q^3 x^6-a p q^4 x^4+10 a p q^4 x^3+2 a q^5+6 b p x^{11}+6 b q x^8\right)}{12 x^{12}}",1,"Integrate[((-2*q + p*x^3)*Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]*(b*x^8 + a*(q + p*x^3)^4))/x^13, x]","F",-1
2734,1,1887,252,4.0618429,"\int \frac{x^2}{x^2-\sqrt{1+x} \sqrt{1+\sqrt{1+x}}} \, dx","Integrate[x^2/(x^2 - Sqrt[1 + x]*Sqrt[1 + Sqrt[1 + x]]),x]","\frac{1}{55} \left(55 x-\sqrt{10 \left(3+\sqrt{5}\right)} \left(-9+5 \sqrt{5}\right) \tanh ^{-1}\left(\sqrt{\frac{2}{3-\sqrt{5}}} \sqrt{\sqrt{x+1}+1}\right)-2 \sqrt{\frac{10}{3+\sqrt{5}}} \left(9+5 \sqrt{5}\right) \tanh ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} \sqrt{\sqrt{x+1}+1}\right)-16 \sqrt{5} \tanh ^{-1}\left(\frac{2 \sqrt{x+1}-1}{\sqrt{5}}\right)+10 \log \left(\sqrt{x+1}-x\right)-10 \text{RootSum}\left[\text{$\#$1}^5-2 \text{$\#$1}^3+\text{$\#$1}^2+2 \text{$\#$1}-1\&,\frac{2 \log \left(\sqrt{x+1}-\text{$\#$1}\right) \text{$\#$1}^4+5 \log \left(\sqrt{x+1}-\text{$\#$1}\right) \text{$\#$1}^3+3 \log \left(\sqrt{x+1}-\text{$\#$1}\right) \text{$\#$1}^2-7 \log \left(\sqrt{x+1}-\text{$\#$1}\right) \text{$\#$1}+3 \log \left(\sqrt{x+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4-6 \text{$\#$1}^2+2 \text{$\#$1}+2}\&\right]-10 \left(6 \text{RootSum}\left[\text{$\#$1}^5-\text{$\#$1}^4-2 \text{$\#$1}^3+\text{$\#$1}^2+\text{$\#$1}+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2+3 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4-4 \text{$\#$1}^3-6 \text{$\#$1}^2+2 \text{$\#$1}+1}\&\right]-2 \text{RootSum}\left[\text{$\#$1}^5-\text{$\#$1}^4-2 \text{$\#$1}^3+\text{$\#$1}^2+\text{$\#$1}+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4-4 \text{$\#$1}^3-6 \text{$\#$1}^2+2 \text{$\#$1}+1}\&\right]-4 \text{RootSum}\left[\text{$\#$1}^5-\text{$\#$1}^4-2 \text{$\#$1}^3+\text{$\#$1}^2+\text{$\#$1}+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2+2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4-4 \text{$\#$1}^3-6 \text{$\#$1}^2+2 \text{$\#$1}+1}\&\right]-2 \text{RootSum}\left[\text{$\#$1}^5-\text{$\#$1}^4-2 \text{$\#$1}^3+\text{$\#$1}^2+\text{$\#$1}+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4-4 \text{$\#$1}^3-6 \text{$\#$1}^2+2 \text{$\#$1}+1}\&\right]+\text{RootSum}\left[\text{$\#$1}^5-\text{$\#$1}^4+\text{$\#$1}^3+2 \text{$\#$1}^2-\text{$\#$1}-1\&,\frac{\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}^3-\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}^2-\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}}{5 \text{$\#$1}^4-4 \text{$\#$1}^3+3 \text{$\#$1}^2+4 \text{$\#$1}-1}\&\right]+4 \text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1}\&\right]+2 \text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1}\&\right]+2 \text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1}\&\right]-6 \text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4+2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2-3 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1}\&\right]+\text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4+\text{$\#$1}^3-2 \text{$\#$1}^2-\text{$\#$1}+1\&,\frac{\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}^3+\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}^2-\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}}{5 \text{$\#$1}^4+4 \text{$\#$1}^3+3 \text{$\#$1}^2-4 \text{$\#$1}-1}\&\right]\right)\right)","-\frac{4}{11} \text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{2 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-4 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-3 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)+7 \text{$\#$1} \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)+3 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1}\&\right]+x+\frac{4}{55} \left(5+4 \sqrt{5}\right) \log \left(-2 \sqrt{\sqrt{x+1}+1}+\sqrt{5}+1\right)-\frac{4}{55} \left(4 \sqrt{5}-5\right) \log \left(2 \sqrt{\sqrt{x+1}+1}+\sqrt{5}-1\right)",1,"(55*x - Sqrt[10*(3 + Sqrt[5])]*(-9 + 5*Sqrt[5])*ArcTanh[Sqrt[2/(3 - Sqrt[5])]*Sqrt[1 + Sqrt[1 + x]]] - 2*Sqrt[10/(3 + Sqrt[5])]*(9 + 5*Sqrt[5])*ArcTanh[Sqrt[2/(3 + Sqrt[5])]*Sqrt[1 + Sqrt[1 + x]]] - 16*Sqrt[5]*ArcTanh[(-1 + 2*Sqrt[1 + x])/Sqrt[5]] + 10*Log[-x + Sqrt[1 + x]] - 10*RootSum[-1 + 2*#1 + #1^2 - 2*#1^3 + #1^5 & , (3*Log[Sqrt[1 + x] - #1] - 7*Log[Sqrt[1 + x] - #1]*#1 + 3*Log[Sqrt[1 + x] - #1]*#1^2 + 5*Log[Sqrt[1 + x] - #1]*#1^3 + 2*Log[Sqrt[1 + x] - #1]*#1^4)/(2 + 2*#1 - 6*#1^2 + 5*#1^4) & ] - 10*(6*RootSum[1 + #1 + #1^2 - 2*#1^3 - #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] + 3*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 + 2*#1 - 6*#1^2 - 4*#1^3 + 5*#1^4) & ] - 2*RootSum[1 + #1 + #1^2 - 2*#1^3 - #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 + 2*#1 - 6*#1^2 - 4*#1^3 + 5*#1^4) & ] - 4*RootSum[1 + #1 + #1^2 - 2*#1^3 - #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] + 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 + 2*#1 - 6*#1^2 - 4*#1^3 + 5*#1^4) & ] - 2*RootSum[1 + #1 + #1^2 - 2*#1^3 - #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 + 2*#1 - 6*#1^2 - 4*#1^3 + 5*#1^4) & ] + RootSum[-1 - #1 + 2*#1^2 + #1^3 - #1^4 + #1^5 & , (-(Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1) - Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3)/(-1 + 4*#1 + 3*#1^2 - 4*#1^3 + 5*#1^4) & ] + 4*RootSum[-1 + #1 - #1^2 - 2*#1^3 + #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 - 2*#1 - 6*#1^2 + 4*#1^3 + 5*#1^4) & ] + 2*RootSum[-1 + #1 - #1^2 - 2*#1^3 + #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 - 2*#1 - 6*#1^2 + 4*#1^3 + 5*#1^4) & ] + 2*RootSum[-1 + #1 - #1^2 - 2*#1^3 + #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 - 2*#1 - 6*#1^2 + 4*#1^3 + 5*#1^4) & ] - 6*RootSum[-1 + #1 - #1^2 - 2*#1^3 + #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] - 3*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 - 2*#1 - 6*#1^2 + 4*#1^3 + 5*#1^4) & ] + RootSum[1 - #1 - 2*#1^2 + #1^3 + #1^4 + #1^5 & , (-(Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1) + Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3)/(-1 - 4*#1 + 3*#1^2 + 4*#1^3 + 5*#1^4) & ]))/55","B",0
2735,1,1887,252,3.1483812,"\int \frac{x^2}{x^2-\sqrt{1+x} \sqrt{1+\sqrt{1+x}}} \, dx","Integrate[x^2/(x^2 - Sqrt[1 + x]*Sqrt[1 + Sqrt[1 + x]]),x]","\frac{1}{55} \left(55 x-\sqrt{10 \left(3+\sqrt{5}\right)} \left(-9+5 \sqrt{5}\right) \tanh ^{-1}\left(\sqrt{\frac{2}{3-\sqrt{5}}} \sqrt{\sqrt{x+1}+1}\right)-2 \sqrt{\frac{10}{3+\sqrt{5}}} \left(9+5 \sqrt{5}\right) \tanh ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} \sqrt{\sqrt{x+1}+1}\right)-16 \sqrt{5} \tanh ^{-1}\left(\frac{2 \sqrt{x+1}-1}{\sqrt{5}}\right)+10 \log \left(\sqrt{x+1}-x\right)-10 \text{RootSum}\left[\text{$\#$1}^5-2 \text{$\#$1}^3+\text{$\#$1}^2+2 \text{$\#$1}-1\&,\frac{2 \log \left(\sqrt{x+1}-\text{$\#$1}\right) \text{$\#$1}^4+5 \log \left(\sqrt{x+1}-\text{$\#$1}\right) \text{$\#$1}^3+3 \log \left(\sqrt{x+1}-\text{$\#$1}\right) \text{$\#$1}^2-7 \log \left(\sqrt{x+1}-\text{$\#$1}\right) \text{$\#$1}+3 \log \left(\sqrt{x+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4-6 \text{$\#$1}^2+2 \text{$\#$1}+2}\&\right]-10 \left(6 \text{RootSum}\left[\text{$\#$1}^5-\text{$\#$1}^4-2 \text{$\#$1}^3+\text{$\#$1}^2+\text{$\#$1}+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2+3 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4-4 \text{$\#$1}^3-6 \text{$\#$1}^2+2 \text{$\#$1}+1}\&\right]-2 \text{RootSum}\left[\text{$\#$1}^5-\text{$\#$1}^4-2 \text{$\#$1}^3+\text{$\#$1}^2+\text{$\#$1}+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4-4 \text{$\#$1}^3-6 \text{$\#$1}^2+2 \text{$\#$1}+1}\&\right]-4 \text{RootSum}\left[\text{$\#$1}^5-\text{$\#$1}^4-2 \text{$\#$1}^3+\text{$\#$1}^2+\text{$\#$1}+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2+2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4-4 \text{$\#$1}^3-6 \text{$\#$1}^2+2 \text{$\#$1}+1}\&\right]-2 \text{RootSum}\left[\text{$\#$1}^5-\text{$\#$1}^4-2 \text{$\#$1}^3+\text{$\#$1}^2+\text{$\#$1}+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4-4 \text{$\#$1}^3-6 \text{$\#$1}^2+2 \text{$\#$1}+1}\&\right]+\text{RootSum}\left[\text{$\#$1}^5-\text{$\#$1}^4+\text{$\#$1}^3+2 \text{$\#$1}^2-\text{$\#$1}-1\&,\frac{\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}^3-\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}^2-\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}}{5 \text{$\#$1}^4-4 \text{$\#$1}^3+3 \text{$\#$1}^2+4 \text{$\#$1}-1}\&\right]+4 \text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1}\&\right]+2 \text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1}\&\right]+2 \text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1}\&\right]-6 \text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4+2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2-3 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1}\&\right]+\text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4+\text{$\#$1}^3-2 \text{$\#$1}^2-\text{$\#$1}+1\&,\frac{\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}^3+\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}^2-\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}}{5 \text{$\#$1}^4+4 \text{$\#$1}^3+3 \text{$\#$1}^2-4 \text{$\#$1}-1}\&\right]\right)\right)","-\frac{4}{11} \text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{2 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-4 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-3 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)+7 \text{$\#$1} \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)+3 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1}\&\right]+x+\frac{4}{55} \left(5+4 \sqrt{5}\right) \log \left(-2 \sqrt{\sqrt{x+1}+1}+\sqrt{5}+1\right)-\frac{4}{55} \left(4 \sqrt{5}-5\right) \log \left(2 \sqrt{\sqrt{x+1}+1}+\sqrt{5}-1\right)",1,"(55*x - Sqrt[10*(3 + Sqrt[5])]*(-9 + 5*Sqrt[5])*ArcTanh[Sqrt[2/(3 - Sqrt[5])]*Sqrt[1 + Sqrt[1 + x]]] - 2*Sqrt[10/(3 + Sqrt[5])]*(9 + 5*Sqrt[5])*ArcTanh[Sqrt[2/(3 + Sqrt[5])]*Sqrt[1 + Sqrt[1 + x]]] - 16*Sqrt[5]*ArcTanh[(-1 + 2*Sqrt[1 + x])/Sqrt[5]] + 10*Log[-x + Sqrt[1 + x]] - 10*RootSum[-1 + 2*#1 + #1^2 - 2*#1^3 + #1^5 & , (3*Log[Sqrt[1 + x] - #1] - 7*Log[Sqrt[1 + x] - #1]*#1 + 3*Log[Sqrt[1 + x] - #1]*#1^2 + 5*Log[Sqrt[1 + x] - #1]*#1^3 + 2*Log[Sqrt[1 + x] - #1]*#1^4)/(2 + 2*#1 - 6*#1^2 + 5*#1^4) & ] - 10*(6*RootSum[1 + #1 + #1^2 - 2*#1^3 - #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] + 3*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 + 2*#1 - 6*#1^2 - 4*#1^3 + 5*#1^4) & ] - 2*RootSum[1 + #1 + #1^2 - 2*#1^3 - #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 + 2*#1 - 6*#1^2 - 4*#1^3 + 5*#1^4) & ] - 4*RootSum[1 + #1 + #1^2 - 2*#1^3 - #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] + 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 + 2*#1 - 6*#1^2 - 4*#1^3 + 5*#1^4) & ] - 2*RootSum[1 + #1 + #1^2 - 2*#1^3 - #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 + 2*#1 - 6*#1^2 - 4*#1^3 + 5*#1^4) & ] + RootSum[-1 - #1 + 2*#1^2 + #1^3 - #1^4 + #1^5 & , (-(Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1) - Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3)/(-1 + 4*#1 + 3*#1^2 - 4*#1^3 + 5*#1^4) & ] + 4*RootSum[-1 + #1 - #1^2 - 2*#1^3 + #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 - 2*#1 - 6*#1^2 + 4*#1^3 + 5*#1^4) & ] + 2*RootSum[-1 + #1 - #1^2 - 2*#1^3 + #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 - 2*#1 - 6*#1^2 + 4*#1^3 + 5*#1^4) & ] + 2*RootSum[-1 + #1 - #1^2 - 2*#1^3 + #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 - 2*#1 - 6*#1^2 + 4*#1^3 + 5*#1^4) & ] - 6*RootSum[-1 + #1 - #1^2 - 2*#1^3 + #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] - 3*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 - 2*#1 - 6*#1^2 + 4*#1^3 + 5*#1^4) & ] + RootSum[1 - #1 - 2*#1^2 + #1^3 + #1^4 + #1^5 & , (-(Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1) + Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3)/(-1 - 4*#1 + 3*#1^2 + 4*#1^3 + 5*#1^4) & ]))/55","B",0
2736,1,27,253,0.0107593,"\int \frac{1}{x \sqrt[5]{1-4 x+6 x^2-4 x^3+x^4}} \, dx","Integrate[1/(x*(1 - 4*x + 6*x^2 - 4*x^3 + x^4)^(1/5)),x]","\frac{5 (x-1) \, _2F_1\left(\frac{1}{5},1;\frac{6}{5};1-x\right)}{\sqrt[5]{(x-1)^4}}","\frac{(x-1)^{4/5} \left(\log \left(\sqrt[5]{x-1}+1\right)+\frac{1}{4} \left(-1-\sqrt{5}\right) \log \left(2 (x-1)^{2/5}+\left(-1-\sqrt{5}\right) \sqrt[5]{x-1}+2\right)+\frac{1}{4} \left(\sqrt{5}-1\right) \log \left(2 (x-1)^{2/5}+\left(\sqrt{5}-1\right) \sqrt[5]{x-1}+2\right)-\sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(-\frac{4 \sqrt[5]{x-1}}{\sqrt{10-2 \sqrt{5}}}+\frac{1}{\sqrt{10-2 \sqrt{5}}}+\sqrt{\frac{5}{10-2 \sqrt{5}}}\right)+\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{4 \sqrt[5]{x-1}}{\sqrt{10+2 \sqrt{5}}}-\frac{1}{\sqrt{10+2 \sqrt{5}}}+\sqrt{\frac{5}{10+2 \sqrt{5}}}\right)\right)}{\sqrt[5]{(x-1)^4}}",1,"(5*(-1 + x)*Hypergeometric2F1[1/5, 1, 6/5, 1 - x])/((-1 + x)^4)^(1/5)","C",1
2737,0,0,254,0.3315283,"\int \frac{1-x+x^2}{\left(-1+x^2\right) \sqrt[3]{x^2+x^4}} \, dx","Integrate[(1 - x + x^2)/((-1 + x^2)*(x^2 + x^4)^(1/3)),x]","\int \frac{1-x+x^2}{\left(-1+x^2\right) \sqrt[3]{x^2+x^4}} \, dx","\frac{\log \left(2^{2/3} \sqrt[3]{x^4+x^2}-2 x\right)}{4 \sqrt[3]{2}}-\frac{3 \log \left(2^{2/3} \sqrt[3]{x^4+x^2}+2 x\right)}{4 \sqrt[3]{2}}+\frac{3 \log \left(-2 x^2+2^{2/3} \sqrt[3]{x^4+x^2} x-\sqrt[3]{2} \left(x^4+x^2\right)^{2/3}\right)}{8 \sqrt[3]{2}}-\frac{\log \left(2 x^2+2^{2/3} \sqrt[3]{x^4+x^2} x+\sqrt[3]{2} \left(x^4+x^2\right)^{2/3}\right)}{8 \sqrt[3]{2}}-\frac{3 \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^4+x^2}-x}\right)}{4 \sqrt[3]{2}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^4+x^2}+x}\right)}{4 \sqrt[3]{2}}",1,"Integrate[(1 - x + x^2)/((-1 + x^2)*(x^2 + x^4)^(1/3)), x]","F",-1
2738,0,0,254,0.1936006,"\int \frac{1+x+x^2}{\left(-1+x^2\right) \sqrt[3]{x^2+x^4}} \, dx","Integrate[(1 + x + x^2)/((-1 + x^2)*(x^2 + x^4)^(1/3)),x]","\int \frac{1+x+x^2}{\left(-1+x^2\right) \sqrt[3]{x^2+x^4}} \, dx","\frac{3 \log \left(2^{2/3} \sqrt[3]{x^4+x^2}-2 x\right)}{4 \sqrt[3]{2}}-\frac{\log \left(2^{2/3} \sqrt[3]{x^4+x^2}+2 x\right)}{4 \sqrt[3]{2}}+\frac{\log \left(-2 x^2+2^{2/3} \sqrt[3]{x^4+x^2} x-\sqrt[3]{2} \left(x^4+x^2\right)^{2/3}\right)}{8 \sqrt[3]{2}}-\frac{3 \log \left(2 x^2+2^{2/3} \sqrt[3]{x^4+x^2} x+\sqrt[3]{2} \left(x^4+x^2\right)^{2/3}\right)}{8 \sqrt[3]{2}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^4+x^2}-x}\right)}{4 \sqrt[3]{2}}-\frac{3 \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^4+x^2}+x}\right)}{4 \sqrt[3]{2}}",1,"Integrate[(1 + x + x^2)/((-1 + x^2)*(x^2 + x^4)^(1/3)), x]","F",-1
2739,1,8085,254,6.1749449,"\int \frac{\left(-1+x^2\right) \sqrt{1-x-x^2+x^3+x^4}}{x^2 \left(1+x^2\right)} \, dx","Integrate[((-1 + x^2)*Sqrt[1 - x - x^2 + x^3 + x^4])/(x^2*(1 + x^2)),x]","\text{Result too large to show}","\text{RootSum}\left[\text{$\#$1}^4-4 \text{$\#$1}^3+62 \text{$\#$1}^2+12 \text{$\#$1}+9\&,\frac{3 \text{$\#$1}^2 \log \left(\text{$\#$1} x-2 x^2+2 \sqrt{x^4+x^3-x^2-x+1}-x+2\right)-3 \text{$\#$1}^2 \log (x)+10 \text{$\#$1} \log \left(\text{$\#$1} x-2 x^2+2 \sqrt{x^4+x^3-x^2-x+1}-x+2\right)-9 \log \left(\text{$\#$1} x-2 x^2+2 \sqrt{x^4+x^3-x^2-x+1}-x+2\right)-10 \text{$\#$1} \log (x)+9 \log (x)}{\text{$\#$1}^3-3 \text{$\#$1}^2+31 \text{$\#$1}+3}\&\right]+\frac{\sqrt{x^4+x^3-x^2-x+1}}{x}-\frac{1}{2} \log \left(-2 x^2+2 \sqrt{x^4+x^3-x^2-x+1}-x+2\right)+\frac{\log (x)}{2}",1,"Result too large to show","C",0
2740,1,8085,254,6.1541384,"\int \frac{\left(-1+x^2\right) \sqrt{1-x-x^2+x^3+x^4}}{x^2 \left(1+x^2\right)} \, dx","Integrate[((-1 + x^2)*Sqrt[1 - x - x^2 + x^3 + x^4])/(x^2*(1 + x^2)),x]","\text{Result too large to show}","\text{RootSum}\left[\text{$\#$1}^4-4 \text{$\#$1}^3+62 \text{$\#$1}^2+12 \text{$\#$1}+9\&,\frac{3 \text{$\#$1}^2 \log \left(\text{$\#$1} x-2 x^2+2 \sqrt{x^4+x^3-x^2-x+1}-x+2\right)-3 \text{$\#$1}^2 \log (x)+10 \text{$\#$1} \log \left(\text{$\#$1} x-2 x^2+2 \sqrt{x^4+x^3-x^2-x+1}-x+2\right)-9 \log \left(\text{$\#$1} x-2 x^2+2 \sqrt{x^4+x^3-x^2-x+1}-x+2\right)-10 \text{$\#$1} \log (x)+9 \log (x)}{\text{$\#$1}^3-3 \text{$\#$1}^2+31 \text{$\#$1}+3}\&\right]+\frac{\sqrt{x^4+x^3-x^2-x+1}}{x}-\frac{1}{2} \log \left(-2 x^2+2 \sqrt{x^4+x^3-x^2-x+1}-x+2\right)+\frac{\log (x)}{2}",1,"Result too large to show","C",0
2741,1,236,254,0.5029699,"\int \frac{\left(-1+x^3\right)^{2/3} \left(4+x^3\right)}{x^6 \left(-2-x^3+x^6\right)} \, dx","Integrate[((-1 + x^3)^(2/3)*(4 + x^3))/(x^6*(-2 - x^3 + x^6)),x]","\frac{2 \log \left(\sqrt[3]{2}-\frac{x}{\sqrt[3]{x^3-1}}\right)-8 \sqrt[3]{2} \log \left(1-\frac{\sqrt[3]{2} x}{\sqrt[3]{x^3-1}}\right)+8 \sqrt[3]{2} \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{2} x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)-2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2^{2/3} x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)-\log \left(\frac{\sqrt[3]{2} x}{\sqrt[3]{x^3-1}}+\frac{x^2}{\left(x^3-1\right)^{2/3}}+2^{2/3}\right)+4 \sqrt[3]{2} \log \left(\frac{\sqrt[3]{2} x}{\sqrt[3]{x^3-1}}+\frac{2^{2/3} x^2}{\left(x^3-1\right)^{2/3}}+1\right)}{12\ 2^{2/3}}+\left(x^3-1\right)^{2/3} \left(\frac{2}{5 x^5}-\frac{13}{20 x^2}\right)","\frac{\log \left(\sqrt[3]{2} \sqrt[3]{x^3-1}-x\right)}{6\ 2^{2/3}}-\frac{1}{3} 2^{2/3} \log \left(2^{2/3} \sqrt[3]{x^3-1}-2 x\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{2} \sqrt[3]{x^3-1}+x}\right)}{2\ 2^{2/3} \sqrt{3}}+\frac{2^{2/3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^3-1}+x}\right)}{\sqrt{3}}+\frac{\left(x^3-1\right)^{2/3} \left(8-13 x^3\right)}{20 x^5}+\frac{\log \left(2^{2/3} \sqrt[3]{x^3-1} x+\sqrt[3]{2} \left(x^3-1\right)^{2/3}+2 x^2\right)}{3 \sqrt[3]{2}}-\frac{\log \left(\sqrt[3]{2} \sqrt[3]{x^3-1} x+2^{2/3} \left(x^3-1\right)^{2/3}+x^2\right)}{12\ 2^{2/3}}",1,"(2/(5*x^5) - 13/(20*x^2))*(-1 + x^3)^(2/3) + (8*2^(1/3)*Sqrt[3]*ArcTan[(1 + (2*2^(1/3)*x)/(-1 + x^3)^(1/3))/Sqrt[3]] - 2*Sqrt[3]*ArcTan[(1 + (2^(2/3)*x)/(-1 + x^3)^(1/3))/Sqrt[3]] + 2*Log[2^(1/3) - x/(-1 + x^3)^(1/3)] - 8*2^(1/3)*Log[1 - (2^(1/3)*x)/(-1 + x^3)^(1/3)] - Log[2^(2/3) + x^2/(-1 + x^3)^(2/3) + (2^(1/3)*x)/(-1 + x^3)^(1/3)] + 4*2^(1/3)*Log[1 + (2^(2/3)*x^2)/(-1 + x^3)^(2/3) + (2^(1/3)*x)/(-1 + x^3)^(1/3)])/(12*2^(2/3))","A",1
2742,1,74,254,0.3441146,"\int \frac{\sqrt[3]{c+\sqrt[4]{a x+\sqrt{-b+a^2 x^2}}}}{\sqrt{-b+a^2 x^2} \sqrt[4]{a x+\sqrt{-b+a^2 x^2}}} \, dx","Integrate[(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(1/3)/(Sqrt[-b + a^2*x^2]*(a*x + Sqrt[-b + a^2*x^2])^(1/4)),x]","\frac{3 \left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{4/3} \, _2F_1\left(\frac{4}{3},2;\frac{7}{3};\frac{c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}{c}\right)}{a c^2}","\frac{4 \log \left(\sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}-\sqrt[3]{c}\right)}{3 a c^{2/3}}-\frac{2 \log \left(\sqrt[3]{c} \sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}+\left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{2/3}+c^{2/3}\right)}{3 a c^{2/3}}-\frac{4 \tan ^{-1}\left(\frac{2 \sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}}{\sqrt{3} \sqrt[3]{c}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} a c^{2/3}}-\frac{4 \sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}}{a \sqrt[4]{\sqrt{a^2 x^2-b}+a x}}",1,"(3*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(4/3)*Hypergeometric2F1[4/3, 2, 7/3, (c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))/c])/(a*c^2)","C",1
2743,1,186,255,0.4330124,"\int \frac{\left(x+x^2\right) \sqrt[4]{x^3+x^4}}{-1+x+x^2} \, dx","Integrate[((x + x^2)*(x^3 + x^4)^(1/4))/(-1 + x + x^2),x]","\frac{4}{15} \sqrt[4]{x^3 (x+1)} \left(\frac{5 \, _2F_1\left(-\frac{5}{4},\frac{3}{4};\frac{7}{4};-x\right)}{\sqrt[4]{x+1}}-\frac{5 \, _2F_1\left(-\frac{1}{4},\frac{3}{4};\frac{7}{4};-x\right)}{\sqrt[4]{x+1}}+\frac{5 \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};-x\right)}{\sqrt[4]{x+1}}-\frac{2 \sqrt{5} \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{\left(-1+\sqrt{5}\right) x}{\left(1+\sqrt{5}\right) (x+1)}\right)}{\left(1+\sqrt{5}\right) (x+1)}-\frac{2 \sqrt{5} \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{\left(1+\sqrt{5}\right) x}{\left(-1+\sqrt{5}\right) (x+1)}\right)}{\left(\sqrt{5}-1\right) (x+1)}\right)","\frac{1}{8} \sqrt[4]{x^4+x^3} (4 x+1)-\frac{29}{16} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+x^3}}\right)+\sqrt{\frac{1}{5} \left(2+2 \sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}} x}{\sqrt[4]{x^4+x^3}}\right)+\sqrt{\frac{1}{5} \left(2 \sqrt{5}-2\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{1}{2}+\frac{\sqrt{5}}{2}} x}{\sqrt[4]{x^4+x^3}}\right)+\frac{29}{16} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+x^3}}\right)-\sqrt{\frac{1}{5} \left(2+2 \sqrt{5}\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}} x}{\sqrt[4]{x^4+x^3}}\right)-\sqrt{\frac{1}{5} \left(2 \sqrt{5}-2\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{2}+\frac{\sqrt{5}}{2}} x}{\sqrt[4]{x^4+x^3}}\right)",1,"(4*(x^3*(1 + x))^(1/4)*((5*Hypergeometric2F1[-5/4, 3/4, 7/4, -x])/(1 + x)^(1/4) - (5*Hypergeometric2F1[-1/4, 3/4, 7/4, -x])/(1 + x)^(1/4) + (5*Hypergeometric2F1[3/4, 3/4, 7/4, -x])/(1 + x)^(1/4) - (2*Sqrt[5]*Hypergeometric2F1[3/4, 1, 7/4, ((-1 + Sqrt[5])*x)/((1 + Sqrt[5])*(1 + x))])/((1 + Sqrt[5])*(1 + x)) - (2*Sqrt[5]*Hypergeometric2F1[3/4, 1, 7/4, ((1 + Sqrt[5])*x)/((-1 + Sqrt[5])*(1 + x))])/((-1 + Sqrt[5])*(1 + x))))/15","C",1
2744,1,77,255,0.1381226,"\int \frac{\left(b+x^4\right)^2}{\sqrt[4]{a b^4+4 a b^3 x^4+b^4 x^4+6 a b^2 x^8+4 b^3 x^8+4 a b x^{12}+6 b^2 x^{12}+a x^{16}+4 b x^{16}+x^{20}}} \, dx","Integrate[(b + x^4)^2/(a*b^4 + 4*a*b^3*x^4 + b^4*x^4 + 6*a*b^2*x^8 + 4*b^3*x^8 + 4*a*b*x^12 + 6*b^2*x^12 + a*x^16 + 4*b*x^16 + x^20)^(1/4),x]","\frac{\left(b+x^4\right) \left(x \left(a+x^4\right)-\frac{1}{2} (a-4 b) \sqrt[4]{a+x^4} \left(\tan ^{-1}\left(\frac{x}{\sqrt[4]{a+x^4}}\right)+\tanh ^{-1}\left(\frac{x}{\sqrt[4]{a+x^4}}\right)\right)\right)}{4 \sqrt[4]{\left(a+x^4\right) \left(b+x^4\right)^4}}","\frac{x \left(a b^4+x^{12} \left(4 a b+6 b^2\right)+x^4 \left(4 a b^3+b^4\right)+x^8 \left(6 a b^2+4 b^3\right)+x^{16} (a+4 b)+x^{20}\right)^{3/4}}{4 \left(b+x^4\right)^3}+\frac{1}{8} (a-4 b) \tan ^{-1}\left(\frac{\sqrt[4]{a b^4+x^{12} \left(4 a b+6 b^2\right)+x^4 \left(4 a b^3+b^4\right)+x^8 \left(6 a b^2+4 b^3\right)+x^{16} (a+4 b)+x^{20}}}{x \left(b+x^4\right)}\right)+\frac{1}{8} (4 b-a) \tanh ^{-1}\left(\frac{\sqrt[4]{a b^4+x^{12} \left(4 a b+6 b^2\right)+x^4 \left(4 a b^3+b^4\right)+x^8 \left(6 a b^2+4 b^3\right)+x^{16} (a+4 b)+x^{20}}}{x \left(b+x^4\right)}\right)",1,"((b + x^4)*(x*(a + x^4) - ((a - 4*b)*(a + x^4)^(1/4)*(ArcTan[x/(a + x^4)^(1/4)] + ArcTanh[x/(a + x^4)^(1/4)]))/2))/(4*((a + x^4)*(b + x^4)^4)^(1/4))","A",1
2745,0,0,255,1.3615988,"\int \frac{\left(-q+2 p x^3\right) \sqrt{q^2-2 p q x^2+2 p q x^3+p^2 x^6} \left(b x^4+a \left(q+p x^3\right)^4\right)}{x^7} \, dx","Integrate[((-q + 2*p*x^3)*Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6]*(b*x^4 + a*(q + p*x^3)^4))/x^7,x]","\int \frac{\left(-q+2 p x^3\right) \sqrt{q^2-2 p q x^2+2 p q x^3+p^2 x^6} \left(b x^4+a \left(q+p x^3\right)^4\right)}{x^7} \, dx","\frac{1}{2} \log (x) \left(a p^3 q^3+2 b p q\right)+\frac{1}{2} \left(-a p^3 q^3-2 b p q\right) \log \left(\sqrt{p^2 x^6+2 p q x^3-2 p q x^2+q^2}+p x^3+q\right)+\frac{\sqrt{p^2 x^6+2 p q x^3-2 p q x^2+q^2} \left(2 a p^5 x^{15}+10 a p^4 q x^{12}-a p^4 q x^{11}+20 a p^3 q^2 x^9-3 a p^3 q^2 x^8-3 a p^3 q^2 x^7+20 a p^2 q^3 x^6-3 a p^2 q^3 x^5-3 a p^2 q^3 x^4+10 a p q^4 x^3-a p q^4 x^2+2 a q^5+6 b p x^7+6 b q x^4\right)}{12 x^6}",1,"Integrate[((-q + 2*p*x^3)*Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6]*(b*x^4 + a*(q + p*x^3)^4))/x^7, x]","F",-1
2746,1,777,255,4.1606251,"\int \frac{1-\sqrt{x-\sqrt{1+x^2}}}{x^4-2 x^2 \sqrt{1+x^2}} \, dx","Integrate[(1 - Sqrt[x - Sqrt[1 + x^2]])/(x^4 - 2*x^2*Sqrt[1 + x^2]),x]","\frac{\left(x^2-2 \sqrt{x^2+1}\right) x^2 \left(-2 \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6-2 \text{$\#$1}^4-4 \text{$\#$1}^2+1\&,\frac{\text{$\#$1}^3 \log \left(\sqrt{x-\sqrt{x^2+1}}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4-\text{$\#$1}^2-1}\&\right]+2 \text{RootSum}\left[\text{$\#$1}^8+4 \text{$\#$1}^6-2 \text{$\#$1}^4+4 \text{$\#$1}^2+1\&,\frac{\text{$\#$1}^3 \log \left(\sqrt{x-\sqrt{x^2+1}}-\text{$\#$1}\right)}{\text{$\#$1}^6+3 \text{$\#$1}^4-\text{$\#$1}^2+1}\&\right]+\frac{2 \sqrt{x^2+1} \left(\sqrt{x^2+1}-x\right) \left(\left(\sqrt{x^2+1}-x\right) x \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6-2 \text{$\#$1}^4-4 \text{$\#$1}^2+1\&,\frac{\text{$\#$1}^3 \log \left(\sqrt{x-\sqrt{x^2+1}}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4-\text{$\#$1}^2-1}\&\right]+\left(\sqrt{x^2+1}-x\right) x \text{RootSum}\left[\text{$\#$1}^8+4 \text{$\#$1}^6-2 \text{$\#$1}^4+4 \text{$\#$1}^2+1\&,\frac{\text{$\#$1}^3 \log \left(\sqrt{x-\sqrt{x^2+1}}-\text{$\#$1}\right)}{\text{$\#$1}^6+3 \text{$\#$1}^4-\text{$\#$1}^2+1}\&\right]-2 \sqrt{x-\sqrt{x^2+1}}+x^2 \log \left(1-\sqrt{x-\sqrt{x^2+1}}\right)-x^2 \log \left(\sqrt{x-\sqrt{x^2+1}}+1\right)-\sqrt{x^2+1} x \log \left(1-\sqrt{x-\sqrt{x^2+1}}\right)+\sqrt{x^2+1} x \log \left(\sqrt{x-\sqrt{x^2+1}}+1\right)-2 x^2 \tan ^{-1}\left(\sqrt{x-\sqrt{x^2+1}}\right)+2 \sqrt{x^2+1} x \tan ^{-1}\left(\sqrt{x-\sqrt{x^2+1}}\right)\right)}{x \left(-2 x^3+2 \sqrt{x^2+1} x^2+\sqrt{x^2+1}-2 x\right)}+\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{x}{\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{x^2+1}}\right)-\sqrt{\sqrt{2}-1} \tanh ^{-1}\left(\frac{x}{\sqrt{2 \left(\sqrt{2}-1\right)} \sqrt{x^2+1}}\right)-\frac{\tan ^{-1}\left(\frac{x}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{\sqrt{\sqrt{2}-1}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{2 \left(1+\sqrt{2}\right)}}\right)}{\sqrt{1+\sqrt{2}}}\right)}{8 \left(x^4-2 x^2 \sqrt{x^2+1}\right)}+\frac{\sqrt{x^2+1}}{2 x}","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-8 \text{$\#$1}^7+32 \text{$\#$1}^6-80 \text{$\#$1}^5+128 \text{$\#$1}^4-128 \text{$\#$1}^3+80 \text{$\#$1}^2-32 \text{$\#$1}+8\&,\frac{\text{$\#$1}^3 \log \left(\text{$\#$1}+\sqrt{x-\sqrt{x^2+1}}-1\right)-2 \text{$\#$1}^2 \log \left(\text{$\#$1}+\sqrt{x-\sqrt{x^2+1}}-1\right)+\text{$\#$1} \log \left(\text{$\#$1}+\sqrt{x-\sqrt{x^2+1}}-1\right)}{\text{$\#$1}^6-6 \text{$\#$1}^5+18 \text{$\#$1}^4-32 \text{$\#$1}^3+32 \text{$\#$1}^2-16 \text{$\#$1}+4}\&\right]-\frac{1}{\left(\sqrt{x^2+1}-x-1\right) \left(\sqrt{x-\sqrt{x^2+1}}+1\right)}+\frac{1}{2} \tan ^{-1}\left(\sqrt{x-\sqrt{x^2+1}}\right)+\frac{1}{2} \tanh ^{-1}\left(\sqrt{x-\sqrt{x^2+1}}\right)",1,"Sqrt[1 + x^2]/(2*x) + (x^2*(x^2 - 2*Sqrt[1 + x^2])*(-(ArcTan[x/Sqrt[2*(-1 + Sqrt[2])]]/Sqrt[-1 + Sqrt[2]]) + Sqrt[1 + Sqrt[2]]*ArcTan[x/(Sqrt[2*(1 + Sqrt[2])]*Sqrt[1 + x^2])] - ArcTanh[x/Sqrt[2*(1 + Sqrt[2])]]/Sqrt[1 + Sqrt[2]] - Sqrt[-1 + Sqrt[2]]*ArcTanh[x/(Sqrt[2*(-1 + Sqrt[2])]*Sqrt[1 + x^2])] - 2*RootSum[1 - 4*#1^2 - 2*#1^4 - 4*#1^6 + #1^8 & , (Log[Sqrt[x - Sqrt[1 + x^2]] - #1]*#1^3)/(-1 - #1^2 - 3*#1^4 + #1^6) & ] + 2*RootSum[1 + 4*#1^2 - 2*#1^4 + 4*#1^6 + #1^8 & , (Log[Sqrt[x - Sqrt[1 + x^2]] - #1]*#1^3)/(1 - #1^2 + 3*#1^4 + #1^6) & ] + (2*Sqrt[1 + x^2]*(-x + Sqrt[1 + x^2])*(-2*Sqrt[x - Sqrt[1 + x^2]] - 2*x^2*ArcTan[Sqrt[x - Sqrt[1 + x^2]]] + 2*x*Sqrt[1 + x^2]*ArcTan[Sqrt[x - Sqrt[1 + x^2]]] + x^2*Log[1 - Sqrt[x - Sqrt[1 + x^2]]] - x*Sqrt[1 + x^2]*Log[1 - Sqrt[x - Sqrt[1 + x^2]]] - x^2*Log[1 + Sqrt[x - Sqrt[1 + x^2]]] + x*Sqrt[1 + x^2]*Log[1 + Sqrt[x - Sqrt[1 + x^2]]] + x*(-x + Sqrt[1 + x^2])*RootSum[1 - 4*#1^2 - 2*#1^4 - 4*#1^6 + #1^8 & , (Log[Sqrt[x - Sqrt[1 + x^2]] - #1]*#1^3)/(-1 - #1^2 - 3*#1^4 + #1^6) & ] + x*(-x + Sqrt[1 + x^2])*RootSum[1 + 4*#1^2 - 2*#1^4 + 4*#1^6 + #1^8 & , (Log[Sqrt[x - Sqrt[1 + x^2]] - #1]*#1^3)/(1 - #1^2 + 3*#1^4 + #1^6) & ]))/(x*(-2*x - 2*x^3 + Sqrt[1 + x^2] + 2*x^2*Sqrt[1 + x^2]))))/(8*(x^4 - 2*x^2*Sqrt[1 + x^2]))","B",1
2747,1,298,255,0.5187423,"\int \frac{1}{\sqrt{-b+a^2 x^2} \sqrt[6]{c+\sqrt[4]{a x+\sqrt{-b+a^2 x^2}}}} \, dx","Integrate[1/(Sqrt[-b + a^2*x^2]*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(1/6)),x]","-\frac{2 \left(-\log \left(-\sqrt[6]{c} \sqrt[6]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}+\sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}+\sqrt[3]{c}\right)+\log \left(\sqrt[6]{c} \sqrt[6]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}+\sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}+\sqrt[3]{c}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[6]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}}{\sqrt[6]{c}}}{\sqrt{3}}\right)-2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[6]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}}{\sqrt[6]{c}}+1}{\sqrt{3}}\right)+4 \tanh ^{-1}\left(\frac{\sqrt[6]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}}{\sqrt[6]{c}}\right)\right)}{a \sqrt[6]{c}}","-\frac{4 \sqrt{3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}}{\sqrt{3} \sqrt[6]{c}}\right)}{a \sqrt[6]{c}}+\frac{4 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[6]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}}{\sqrt{3} \sqrt[6]{c}}+\frac{1}{\sqrt{3}}\right)}{a \sqrt[6]{c}}-\frac{8 \tanh ^{-1}\left(\frac{\sqrt[6]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}}{\sqrt[6]{c}}\right)}{a \sqrt[6]{c}}-\frac{4 \tanh ^{-1}\left(\frac{\frac{\sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}}{\sqrt[6]{c}}+\sqrt[6]{c}}{\sqrt[6]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}}\right)}{a \sqrt[6]{c}}",1,"(-2*(2*Sqrt[3]*ArcTan[(1 - (2*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(1/6))/c^(1/6))/Sqrt[3]] - 2*Sqrt[3]*ArcTan[(1 + (2*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(1/6))/c^(1/6))/Sqrt[3]] + 4*ArcTanh[(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(1/6)/c^(1/6)] - Log[c^(1/3) - c^(1/6)*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(1/6) + (c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(1/3)] + Log[c^(1/3) + c^(1/6)*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(1/6) + (c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(1/3)]))/(a*c^(1/6))","A",1
2748,0,0,256,14.2709328,"\int \frac{\left(1-2 k^2\right) x+k^2 x^3}{\sqrt[3]{\left(1-x^2\right) \left(1-k^2 x^2\right)} \left(-1+d+\left(1-2 d k^2\right) x^2+d k^4 x^4\right)} \, dx","Integrate[((1 - 2*k^2)*x + k^2*x^3)/(((1 - x^2)*(1 - k^2*x^2))^(1/3)*(-1 + d + (1 - 2*d*k^2)*x^2 + d*k^4*x^4)),x]","\int \frac{\left(1-2 k^2\right) x+k^2 x^3}{\sqrt[3]{\left(1-x^2\right) \left(1-k^2 x^2\right)} \left(-1+d+\left(1-2 d k^2\right) x^2+d k^4 x^4\right)} \, dx","-\frac{\log \left(d^{2/3} k^4 x^4-2 d^{2/3} k^2 x^2+d^{2/3}+\sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1} \left(\sqrt[3]{d}-\sqrt[3]{d} k^2 x^2\right)+\left(k^2 x^4+\left(-k^2-1\right) x^2+1\right)^{2/3}\right)}{4 \sqrt[3]{d}}+\frac{\log \left(\sqrt[3]{d} k^2 x^2-\sqrt[3]{d}+\sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}\right)}{2 \sqrt[3]{d}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}}{-2 \sqrt[3]{d} k^2 x^2+2 \sqrt[3]{d}+\sqrt[3]{k^2 x^4+\left(-k^2-1\right) x^2+1}}\right)}{2 \sqrt[3]{d}}",1,"Integrate[((1 - 2*k^2)*x + k^2*x^3)/(((1 - x^2)*(1 - k^2*x^2))^(1/3)*(-1 + d + (1 - 2*d*k^2)*x^2 + d*k^4*x^4)), x]","F",-1
2749,0,0,256,2.5020132,"\int \frac{\left(2-k^2\right) x-2 x^3+k^2 x^5}{\left(\left(1-x^2\right) \left(1-k^2 x^2\right)\right)^{2/3} \left(1-d+\left(-2+d k^2\right) x^2+x^4\right)} \, dx","Integrate[((2 - k^2)*x - 2*x^3 + k^2*x^5)/(((1 - x^2)*(1 - k^2*x^2))^(2/3)*(1 - d + (-2 + d*k^2)*x^2 + x^4)),x]","\int \frac{\left(2-k^2\right) x-2 x^3+k^2 x^5}{\left(\left(1-x^2\right) \left(1-k^2 x^2\right)\right)^{2/3} \left(1-d+\left(-2+d k^2\right) x^2+x^4\right)} \, dx","\frac{\log \left(d^{2/3} k^4 x^4-2 d^{2/3} k^2 x^2+d^{2/3}+\left(k^2 x^4+\left(-k^2-1\right) x^2+1\right)^{2/3} \left(\sqrt[3]{d}-\sqrt[3]{d} k^2 x^2\right)+\left(k^2 x^4+\left(-k^2-1\right) x^2+1\right)^{4/3}\right)}{4 \sqrt[3]{d}}-\frac{\log \left(\sqrt[3]{d} k^2 x^2-\sqrt[3]{d}+\left(k^2 x^4+\left(-k^2-1\right) x^2+1\right)^{2/3}\right)}{2 \sqrt[3]{d}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \left(k^2 x^4+\left(-k^2-1\right) x^2+1\right)^{2/3}}{-2 \sqrt[3]{d} k^2 x^2+2 \sqrt[3]{d}+\left(k^2 x^4+\left(-k^2-1\right) x^2+1\right)^{2/3}}\right)}{2 \sqrt[3]{d}}",1,"Integrate[((2 - k^2)*x - 2*x^3 + k^2*x^5)/(((1 - x^2)*(1 - k^2*x^2))^(2/3)*(1 - d + (-2 + d*k^2)*x^2 + x^4)), x]","F",-1
2750,1,231,257,2.0681666,"\int \frac{\left(-1+x^4\right) \sqrt[4]{-x^2+x^4}}{-1-x^2+x^4} \, dx","Integrate[((-1 + x^4)*(-x^2 + x^4)^(1/4))/(-1 - x^2 + x^4),x]","\frac{\sqrt[4]{x^2 \left(x^2-1\right)} \left(\frac{4 \left(\sqrt{5}-1\right)^{3/4} \left(5+\sqrt{5}\right) x^{3/2} \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};\frac{\left(1+\sqrt{5}\right) x^2}{2 x^2+\sqrt{5}-1}\right)}{\sqrt[4]{1-x^2} \left(2 x^2+\sqrt{5}-1\right)^{3/4}}+\frac{4 \left(\sqrt{5}-5\right) x^{3/2} \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{\left(-1+\sqrt{5}\right) x^2}{\left(1+\sqrt{5}\right) \left(x^2-1\right)}\right)}{x^2-1}-\frac{45 \left(\tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2-1}}\right)-\tanh ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2-1}}\right)\right)}{\sqrt[4]{x^2-1}}\right)}{60 \sqrt{x}}+\frac{1}{2} \sqrt[4]{x^2 \left(x^2-1\right)} x","\frac{1}{2} \sqrt[4]{x^4-x^2} x-\frac{3}{4} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^2}}\right)+\sqrt{\frac{1}{10} \left(1+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}} x}{\sqrt[4]{x^4-x^2}}\right)+\sqrt{\frac{1}{10} \left(\sqrt{5}-1\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{1}{2}+\frac{\sqrt{5}}{2}} x}{\sqrt[4]{x^4-x^2}}\right)+\frac{3}{4} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^2}}\right)-\sqrt{\frac{1}{10} \left(1+\sqrt{5}\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}} x}{\sqrt[4]{x^4-x^2}}\right)-\sqrt{\frac{1}{10} \left(\sqrt{5}-1\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{2}+\frac{\sqrt{5}}{2}} x}{\sqrt[4]{x^4-x^2}}\right)",1,"(x*(x^2*(-1 + x^2))^(1/4))/2 + ((x^2*(-1 + x^2))^(1/4)*((-45*(ArcTan[Sqrt[x]/(-1 + x^2)^(1/4)] - ArcTanh[Sqrt[x]/(-1 + x^2)^(1/4)]))/(-1 + x^2)^(1/4) + (4*(-1 + Sqrt[5])^(3/4)*(5 + Sqrt[5])*x^(3/2)*Hypergeometric2F1[3/4, 3/4, 7/4, ((1 + Sqrt[5])*x^2)/(-1 + Sqrt[5] + 2*x^2)])/((1 - x^2)^(1/4)*(-1 + Sqrt[5] + 2*x^2)^(3/4)) + (4*(-5 + Sqrt[5])*x^(3/2)*Hypergeometric2F1[3/4, 1, 7/4, ((-1 + Sqrt[5])*x^2)/((1 + Sqrt[5])*(-1 + x^2))])/(-1 + x^2)))/(60*Sqrt[x])","C",0
2751,0,0,257,8.8003739,"\int \frac{1+(3-2 k) x-(4+k) x^2+3 k x^3}{\sqrt[3]{(1-x) x (1-k x)} \left(-b+(1+5 b) x-(10 b+k) x^2+10 b x^3-5 b x^4+b x^5\right)} \, dx","Integrate[(1 + (3 - 2*k)*x - (4 + k)*x^2 + 3*k*x^3)/(((1 - x)*x*(1 - k*x))^(1/3)*(-b + (1 + 5*b)*x - (10*b + k)*x^2 + 10*b*x^3 - 5*b*x^4 + b*x^5)),x]","\int \frac{1+(3-2 k) x-(4+k) x^2+3 k x^3}{\sqrt[3]{(1-x) x (1-k x)} \left(-b+(1+5 b) x-(10 b+k) x^2+10 b x^3-5 b x^4+b x^5\right)} \, dx","-\frac{\log \left(b^{2/3} x^4-4 b^{2/3} x^3+6 b^{2/3} x^2-4 b^{2/3} x+b^{2/3}+\left(\sqrt[3]{b} x^2-2 \sqrt[3]{b} x+\sqrt[3]{b}\right) \sqrt[3]{k x^3+(-k-1) x^2+x}+\left(k x^3+(-k-1) x^2+x\right)^{2/3}\right)}{2 \sqrt[3]{b}}+\frac{\log \left(-\sqrt[3]{b} x^2+2 \sqrt[3]{b} x-\sqrt[3]{b}+\sqrt[3]{k x^3+(-k-1) x^2+x}\right)}{\sqrt[3]{b}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{k x^3+(-k-1) x^2+x}}{2 \sqrt[3]{b} x^2-4 \sqrt[3]{b} x+2 \sqrt[3]{b}+\sqrt[3]{k x^3+(-k-1) x^2+x}}\right)}{\sqrt[3]{b}}",1,"Integrate[(1 + (3 - 2*k)*x - (4 + k)*x^2 + 3*k*x^3)/(((1 - x)*x*(1 - k*x))^(1/3)*(-b + (1 + 5*b)*x - (10*b + k)*x^2 + 10*b*x^3 - 5*b*x^4 + b*x^5)), x]","F",-1
2752,1,928,257,4.738395,"\int \frac{x^3}{\sqrt[3]{-x^2+x^3} \left(-1+x^6\right)} \, dx","Integrate[x^3/((-x^2 + x^3)^(1/3)*(-1 + x^6)),x]","\frac{x \left(\frac{2^{2/3} \left(6 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{2} \sqrt[3]{\frac{x}{x-1}}+1}{\sqrt{3}}\right)+6 \sqrt{3} \sqrt[3]{1-i \sqrt{3}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{2} \sqrt[3]{\frac{x}{x-1}}}{\sqrt[3]{1-i \sqrt{3}}}+1}{\sqrt{3}}\right)-6 \sqrt[6]{3} \sqrt[3]{3-i \sqrt{3}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{6} \sqrt[3]{\frac{x}{x-1}}}{\sqrt[3]{3-i \sqrt{3}}}+1}{\sqrt{3}}\right)+6 \sqrt{3} \sqrt[3]{1+i \sqrt{3}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{2} \sqrt[3]{\frac{x}{x-1}}}{\sqrt[3]{1+i \sqrt{3}}}+1}{\sqrt{3}}\right)-6 \sqrt[6]{3} \sqrt[3]{3+i \sqrt{3}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{6} \sqrt[3]{\frac{x}{x-1}}}{\sqrt[3]{3+i \sqrt{3}}}+1}{\sqrt{3}}\right)-6 \log \left(1-\sqrt[3]{2} \sqrt[3]{\frac{x}{x-1}}\right)-6 \sqrt[3]{1-i \sqrt{3}} \log \left(\sqrt[3]{1-i \sqrt{3}}-\sqrt[3]{2} \sqrt[3]{\frac{x}{x-1}}\right)-6 \sqrt[3]{1+i \sqrt{3}} \log \left(\sqrt[3]{1+i \sqrt{3}}-\sqrt[3]{2} \sqrt[3]{\frac{x}{x-1}}\right)+2\ 3^{2/3} \sqrt[3]{3-i \sqrt{3}} \log \left(\sqrt[3]{3-i \sqrt{3}}-\sqrt[3]{6} \sqrt[3]{\frac{x}{x-1}}\right)+2\ 3^{2/3} \sqrt[3]{3+i \sqrt{3}} \log \left(\sqrt[3]{3+i \sqrt{3}}-\sqrt[3]{6} \sqrt[3]{\frac{x}{x-1}}\right)+3 \log \left(2^{2/3} \left(\frac{x}{x-1}\right)^{2/3}+\sqrt[3]{2} \sqrt[3]{\frac{x}{x-1}}+1\right)+3 \sqrt[3]{1-i \sqrt{3}} \log \left(2^{2/3} \left(\frac{x}{x-1}\right)^{2/3}+\sqrt[3]{2-2 i \sqrt{3}} \sqrt[3]{\frac{x}{x-1}}+\left(1-i \sqrt{3}\right)^{2/3}\right)+3 \sqrt[3]{1+i \sqrt{3}} \log \left(2^{2/3} \left(\frac{x}{x-1}\right)^{2/3}+\sqrt[3]{2+2 i \sqrt{3}} \sqrt[3]{\frac{x}{x-1}}+\left(1+i \sqrt{3}\right)^{2/3}\right)-3^{2/3} \sqrt[3]{3-i \sqrt{3}} \log \left(6^{2/3} \left(\frac{x}{x-1}\right)^{2/3}+\sqrt[3]{18-6 i \sqrt{3}} \sqrt[3]{\frac{x}{x-1}}+\left(3-i \sqrt{3}\right)^{2/3}\right)-3^{2/3} \sqrt[3]{3+i \sqrt{3}} \log \left(6^{2/3} \left(\frac{x}{x-1}\right)^{2/3}+\sqrt[3]{18+6 i \sqrt{3}} \sqrt[3]{\frac{x}{x-1}}+\left(3+i \sqrt{3}\right)^{2/3}\right)\right)}{\sqrt[3]{\frac{x}{x-1}}}-36\right)}{72 \sqrt[3]{(x-1) x^2}}","\frac{1}{6} \text{RootSum}\left[\text{$\#$1}^6-3 \text{$\#$1}^3+3\&,\frac{\log \left(\sqrt[3]{x^3-x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]-\frac{1}{6} \text{RootSum}\left[\text{$\#$1}^6-\text{$\#$1}^3+1\&,\frac{\log \left(\sqrt[3]{x^3-x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]-\frac{\left(x^3-x^2\right)^{2/3}}{2 (x-1) x}-\frac{\log \left(2^{2/3} \sqrt[3]{x^3-x^2}-2 x\right)}{6 \sqrt[3]{2}}+\frac{\log \left(2 x^2+2^{2/3} \sqrt[3]{x^3-x^2} x+\sqrt[3]{2} \left(x^3-x^2\right)^{2/3}\right)}{12 \sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^3-x^2}+x}\right)}{2 \sqrt[3]{2} \sqrt{3}}",1,"(x*(-36 + (2^(2/3)*(6*Sqrt[3]*ArcTan[(1 + 2*2^(1/3)*(x/(-1 + x))^(1/3))/Sqrt[3]] + 6*Sqrt[3]*(1 - I*Sqrt[3])^(1/3)*ArcTan[(1 + (2*2^(1/3)*(x/(-1 + x))^(1/3))/(1 - I*Sqrt[3])^(1/3))/Sqrt[3]] - 6*3^(1/6)*(3 - I*Sqrt[3])^(1/3)*ArcTan[(1 + (2*6^(1/3)*(x/(-1 + x))^(1/3))/(3 - I*Sqrt[3])^(1/3))/Sqrt[3]] + 6*Sqrt[3]*(1 + I*Sqrt[3])^(1/3)*ArcTan[(1 + (2*2^(1/3)*(x/(-1 + x))^(1/3))/(1 + I*Sqrt[3])^(1/3))/Sqrt[3]] - 6*3^(1/6)*(3 + I*Sqrt[3])^(1/3)*ArcTan[(1 + (2*6^(1/3)*(x/(-1 + x))^(1/3))/(3 + I*Sqrt[3])^(1/3))/Sqrt[3]] - 6*Log[1 - 2^(1/3)*(x/(-1 + x))^(1/3)] - 6*(1 - I*Sqrt[3])^(1/3)*Log[(1 - I*Sqrt[3])^(1/3) - 2^(1/3)*(x/(-1 + x))^(1/3)] - 6*(1 + I*Sqrt[3])^(1/3)*Log[(1 + I*Sqrt[3])^(1/3) - 2^(1/3)*(x/(-1 + x))^(1/3)] + 2*3^(2/3)*(3 - I*Sqrt[3])^(1/3)*Log[(3 - I*Sqrt[3])^(1/3) - 6^(1/3)*(x/(-1 + x))^(1/3)] + 2*3^(2/3)*(3 + I*Sqrt[3])^(1/3)*Log[(3 + I*Sqrt[3])^(1/3) - 6^(1/3)*(x/(-1 + x))^(1/3)] + 3*Log[1 + 2^(1/3)*(x/(-1 + x))^(1/3) + 2^(2/3)*(x/(-1 + x))^(2/3)] + 3*(1 - I*Sqrt[3])^(1/3)*Log[(1 - I*Sqrt[3])^(2/3) + (2 - (2*I)*Sqrt[3])^(1/3)*(x/(-1 + x))^(1/3) + 2^(2/3)*(x/(-1 + x))^(2/3)] + 3*(1 + I*Sqrt[3])^(1/3)*Log[(1 + I*Sqrt[3])^(2/3) + (2 + (2*I)*Sqrt[3])^(1/3)*(x/(-1 + x))^(1/3) + 2^(2/3)*(x/(-1 + x))^(2/3)] - 3^(2/3)*(3 - I*Sqrt[3])^(1/3)*Log[(3 - I*Sqrt[3])^(2/3) + (18 - (6*I)*Sqrt[3])^(1/3)*(x/(-1 + x))^(1/3) + 6^(2/3)*(x/(-1 + x))^(2/3)] - 3^(2/3)*(3 + I*Sqrt[3])^(1/3)*Log[(3 + I*Sqrt[3])^(2/3) + (18 + (6*I)*Sqrt[3])^(1/3)*(x/(-1 + x))^(1/3) + 6^(2/3)*(x/(-1 + x))^(2/3)]))/(x/(-1 + x))^(1/3)))/(72*((-1 + x)*x^2)^(1/3))","C",1
2753,0,0,257,4.6654027,"\int \frac{\sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{1-x^2} \, dx","Integrate[(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2),x]","\int \frac{\sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{1-x^2} \, dx","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^5-3 \text{$\#$1}^3+2 \text{$\#$1}}\&\right]-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\text{$\#$1}^5 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+4 \text{$\#$1}^2-2}\&\right]",1,"Integrate[(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2), x]","F",-1
2754,0,0,257,0.2295833,"\int \frac{\sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{1-x^2} \, dx","Integrate[(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2),x]","\int \frac{\sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{1-x^2} \, dx","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^5-3 \text{$\#$1}^3+2 \text{$\#$1}}\&\right]-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\text{$\#$1}^5 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+4 \text{$\#$1}^2-2}\&\right]",1,"Integrate[(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2), x]","F",-1
2755,1,74,257,0.2955645,"\int \frac{1}{\sqrt{-b+a^2 x^2} \sqrt[4]{a x+\sqrt{-b+a^2 x^2}} \sqrt[3]{c+\sqrt[4]{a x+\sqrt{-b+a^2 x^2}}}} \, dx","Integrate[1/(Sqrt[-b + a^2*x^2]*(a*x + Sqrt[-b + a^2*x^2])^(1/4)*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(1/3)),x]","\frac{6 \left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{2/3} \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};\frac{c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}{c}\right)}{a c^2}","-\frac{4 \log \left(\sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}-\sqrt[3]{c}\right)}{3 a c^{4/3}}+\frac{2 \log \left(\sqrt[3]{c} \sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}+\left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{2/3}+c^{2/3}\right)}{3 a c^{4/3}}-\frac{4 \tan ^{-1}\left(\frac{2 \sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}}{\sqrt{3} \sqrt[3]{c}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} a c^{4/3}}-\frac{4 \left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{2/3}}{a c \sqrt[4]{\sqrt{a^2 x^2-b}+a x}}",1,"(6*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(2/3)*Hypergeometric2F1[2/3, 2, 5/3, (c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))/c])/(a*c^2)","C",1
2756,0,0,258,7.3038367,"\int \frac{(-b+x) \left(a b-2 b x+x^2\right)}{\left(x (-a+x) (-b+x)^2\right)^{2/3} \left(b-(1+a d) x+d x^2\right)} \, dx","Integrate[((-b + x)*(a*b - 2*b*x + x^2))/((x*(-a + x)*(-b + x)^2)^(2/3)*(b - (1 + a*d)*x + d*x^2)),x]","\int \frac{(-b+x) \left(a b-2 b x+x^2\right)}{\left(x (-a+x) (-b+x)^2\right)^{2/3} \left(b-(1+a d) x+d x^2\right)} \, dx","-\frac{\log \left(d^{2/3} \left(x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4\right)^{2/3}+\sqrt[3]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4} \left(\sqrt[3]{d} x-b \sqrt[3]{d}\right)+b^2-2 b x+x^2\right)}{2 \sqrt[3]{d}}+\frac{\log \left(\sqrt[3]{d} \sqrt[3]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}+b-x\right)}{\sqrt[3]{d}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} b-\sqrt{3} x}{-2 \sqrt[3]{d} \sqrt[3]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}+b-x}\right)}{\sqrt[3]{d}}",1,"Integrate[((-b + x)*(a*b - 2*b*x + x^2))/((x*(-a + x)*(-b + x)^2)^(2/3)*(b - (1 + a*d)*x + d*x^2)), x]","F",-1
2757,0,0,258,1.2637359,"\int \frac{(a-5 b+4 x) \left(-a^3+3 a^2 x-3 a x^2+x^3\right)}{((-a+x) (-b+x))^{2/3} \left(-a^5+b d-\left(-5 a^4+d\right) x-10 a^3 x^2+10 a^2 x^3-5 a x^4+x^5\right)} \, dx","Integrate[((a - 5*b + 4*x)*(-a^3 + 3*a^2*x - 3*a*x^2 + x^3))/(((-a + x)*(-b + x))^(2/3)*(-a^5 + b*d - (-5*a^4 + d)*x - 10*a^3*x^2 + 10*a^2*x^3 - 5*a*x^4 + x^5)),x]","\int \frac{(a-5 b+4 x) \left(-a^3+3 a^2 x-3 a x^2+x^3\right)}{((-a+x) (-b+x))^{2/3} \left(-a^5+b d-\left(-5 a^4+d\right) x-10 a^3 x^2+10 a^2 x^3-5 a x^4+x^5\right)} \, dx","\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} a^2-2 \sqrt{3} a x+\sqrt{3} x^2}{a^2+2 \sqrt[3]{d} \sqrt[3]{x (-a-b)+a b+x^2}-2 a x+x^2}\right)}{\sqrt[3]{d}}+\frac{\log \left(a^3-2 a^2 x-a \sqrt[3]{d} \sqrt[3]{x (-a-b)+a b+x^2}+a x^2\right)}{\sqrt[3]{d}}-\frac{\log \left(a^6-4 a^5 x+6 a^4 x^2-4 a^3 x^3+a^2 d^{2/3} \left(x (-a-b)+a b+x^2\right)^{2/3}+a^2 x^4+\sqrt[3]{x (-a-b)+a b+x^2} \left(a^4 \sqrt[3]{d}-2 a^3 \sqrt[3]{d} x+a^2 \sqrt[3]{d} x^2\right)\right)}{2 \sqrt[3]{d}}",1,"Integrate[((a - 5*b + 4*x)*(-a^3 + 3*a^2*x - 3*a*x^2 + x^3))/(((-a + x)*(-b + x))^(2/3)*(-a^5 + b*d - (-5*a^4 + d)*x - 10*a^3*x^2 + 10*a^2*x^3 - 5*a*x^4 + x^5)), x]","F",-1
2758,1,314,258,10.0986141,"\int \frac{1-x^3 \sqrt[3]{5+4 x}-x^3 (5+4 x)^{2/3}}{1-x \sqrt{5+4 x}} \, dx","Integrate[(1 - x^3*(5 + 4*x)^(1/3) - x^3*(5 + 4*x)^(2/3))/(1 - x*Sqrt[5 + 4*x]),x]","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^6-\text{$\#$1}^3-4\&,\frac{2 \text{$\#$1}^5 \log \left(\sqrt[6]{4 x+5}-\text{$\#$1}\right)-\text{$\#$1}^4 \log \left(\sqrt[6]{4 x+5}-\text{$\#$1}\right)+2 \text{$\#$1}^3 \log \left(\sqrt[6]{4 x+5}-\text{$\#$1}\right)-8 \text{$\#$1}^2 \log \left(\sqrt[6]{4 x+5}-\text{$\#$1}\right)+3 \text{$\#$1} \log \left(\sqrt[6]{4 x+5}-\text{$\#$1}\right)-4 \log \left(\sqrt[6]{4 x+5}-\text{$\#$1}\right)}{2 \text{$\#$1}^5-\text{$\#$1}^2}\&\right]+\frac{3}{608} (4 x+5)^{19/6}+\frac{3}{544} (4 x+5)^{17/6}-\frac{15}{208} (4 x+5)^{13/6}-\frac{15}{176} (4 x+5)^{11/6}+\frac{3}{80} (4 x+5)^{5/3}+\frac{3}{64} (4 x+5)^{4/3}+\frac{75}{224} (4 x+5)^{7/6}+\frac{15}{32} (4 x+5)^{5/6}-\frac{15}{32} (4 x+5)^{2/3}-\frac{15}{16} \sqrt[3]{4 x+5}+\frac{3}{2} \sqrt[6]{4 x+5}-3 \log \left(\sqrt[6]{4 x+5}+1\right)","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^6-\text{$\#$1}^3-4\&,\frac{2 \text{$\#$1}^5 \log \left(\sqrt[6]{4 x+5}-\text{$\#$1}\right)-\text{$\#$1}^4 \log \left(\sqrt[6]{4 x+5}-\text{$\#$1}\right)+2 \text{$\#$1}^3 \log \left(\sqrt[6]{4 x+5}-\text{$\#$1}\right)-8 \text{$\#$1}^2 \log \left(\sqrt[6]{4 x+5}-\text{$\#$1}\right)+3 \text{$\#$1} \log \left(\sqrt[6]{4 x+5}-\text{$\#$1}\right)-4 \log \left(\sqrt[6]{4 x+5}-\text{$\#$1}\right)}{2 \text{$\#$1}^5-\text{$\#$1}^2}\&\right]+\frac{3}{748} (4 x+5)^{5/6} \left(22 x^2-30 x+45\right)+\frac{3 \sqrt[6]{4 x+5} \left(728 x^3+70 x^2-150 x+4583\right)}{6916}+\frac{3}{64} \sqrt[3]{4 x+5} (4 x-15)+\frac{3}{160} (4 x+5)^{2/3} (8 x-15)-3 \log \left(\sqrt[6]{4 x+5}+1\right)",1,"(3*(5 + 4*x)^(1/6))/2 - (15*(5 + 4*x)^(1/3))/16 - (15*(5 + 4*x)^(2/3))/32 + (15*(5 + 4*x)^(5/6))/32 + (75*(5 + 4*x)^(7/6))/224 + (3*(5 + 4*x)^(4/3))/64 + (3*(5 + 4*x)^(5/3))/80 - (15*(5 + 4*x)^(11/6))/176 - (15*(5 + 4*x)^(13/6))/208 + (3*(5 + 4*x)^(17/6))/544 + (3*(5 + 4*x)^(19/6))/608 - 3*Log[1 + (5 + 4*x)^(1/6)] + RootSum[-4 - #1^3 + #1^6 & , (-4*Log[(5 + 4*x)^(1/6) - #1] + 3*Log[(5 + 4*x)^(1/6) - #1]*#1 - 8*Log[(5 + 4*x)^(1/6) - #1]*#1^2 + 2*Log[(5 + 4*x)^(1/6) - #1]*#1^3 - Log[(5 + 4*x)^(1/6) - #1]*#1^4 + 2*Log[(5 + 4*x)^(1/6) - #1]*#1^5)/(-#1^2 + 2*#1^5) & ]/2","A",1
2759,0,0,259,0.6077247,"\int \frac{x^3 \left(x^3 c_3-2 c_4\right) \sqrt{\frac{x^2 c_0+x^3 c_3+c_4}{x^2 c_1+x^3 c_3+c_4}}}{\left(x^2+2 x^3 c_3+2 c_4\right) \left(-x^4+x^6 c_3{}^2+2 x^3 c_3 c_4+c_4{}^2\right)} \, dx","Integrate[(x^3*(x^3*C[3] - 2*C[4])*Sqrt[(x^2*C[0] + x^3*C[3] + C[4])/(x^2*C[1] + x^3*C[3] + C[4])])/((x^2 + 2*x^3*C[3] + 2*C[4])*(-x^4 + x^6*C[3]^2 + 2*x^3*C[3]*C[4] + C[4]^2)),x]","\int \frac{x^3 \left(x^3 c_3-2 c_4\right) \sqrt{\frac{x^2 c_0+x^3 c_3+c_4}{x^2 c_1+x^3 c_3+c_4}}}{\left(x^2+2 x^3 c_3+2 c_4\right) \left(-x^4+x^6 c_3{}^2+2 x^3 c_3 c_4+c_4{}^2\right)} \, dx","\frac{\sqrt{1-c_0} \tan ^{-1}\left(\frac{\sqrt{1-c_0} \sqrt{-1+c_1} \sqrt{\frac{c_3 x^3+c_0 x^2+c_4}{c_3 x^3+c_1 x^2+c_4}}}{-1+c_0}\right)}{\sqrt{-1+c_1}}+\frac{\sqrt{-1-c_0} \tan ^{-1}\left(\frac{\sqrt{-1-c_0} \sqrt{1+c_1} \sqrt{\frac{c_3 x^3+c_0 x^2+c_4}{c_3 x^3+c_1 x^2+c_4}}}{1+c_0}\right)}{3 \sqrt{1+c_1}}-\frac{4 \sqrt{1-2 c_0} \tan ^{-1}\left(\frac{\sqrt{1-2 c_0} \sqrt{-1+2 c_1} \sqrt{\frac{c_3 x^3+c_0 x^2+c_4}{c_3 x^3+c_1 x^2+c_4}}}{-1+2 c_0}\right)}{3 \sqrt{-1+2 c_1}}",1,"Integrate[(x^3*(x^3*C[3] - 2*C[4])*Sqrt[(x^2*C[0] + x^3*C[3] + C[4])/(x^2*C[1] + x^3*C[3] + C[4])])/((x^2 + 2*x^3*C[3] + 2*C[4])*(-x^4 + x^6*C[3]^2 + 2*x^3*C[3]*C[4] + C[4]^2)), x]","F",-1
2760,0,0,259,0.6428092,"\int \frac{x^5 \left(2 x^5 c_3-3 c_4\right) \sqrt{\frac{x^3 c_0+x^5 c_3+c_4}{x^3 c_1+x^5 c_3+c_4}}}{\left(x^3+2 x^5 c_3+2 c_4\right) \left(-x^6+x^{10} c_3{}^2+2 x^5 c_3 c_4+c_4{}^2\right)} \, dx","Integrate[(x^5*(2*x^5*C[3] - 3*C[4])*Sqrt[(x^3*C[0] + x^5*C[3] + C[4])/(x^3*C[1] + x^5*C[3] + C[4])])/((x^3 + 2*x^5*C[3] + 2*C[4])*(-x^6 + x^10*C[3]^2 + 2*x^5*C[3]*C[4] + C[4]^2)),x]","\int \frac{x^5 \left(2 x^5 c_3-3 c_4\right) \sqrt{\frac{x^3 c_0+x^5 c_3+c_4}{x^3 c_1+x^5 c_3+c_4}}}{\left(x^3+2 x^5 c_3+2 c_4\right) \left(-x^6+x^{10} c_3{}^2+2 x^5 c_3 c_4+c_4{}^2\right)} \, dx","\frac{\sqrt{1-c_0} \tan ^{-1}\left(\frac{\sqrt{1-c_0} \sqrt{-1+c_1} \sqrt{\frac{c_3 x^5+c_0 x^3+c_4}{c_3 x^5+c_1 x^3+c_4}}}{-1+c_0}\right)}{\sqrt{-1+c_1}}+\frac{\sqrt{-1-c_0} \tan ^{-1}\left(\frac{\sqrt{-1-c_0} \sqrt{1+c_1} \sqrt{\frac{c_3 x^5+c_0 x^3+c_4}{c_3 x^5+c_1 x^3+c_4}}}{1+c_0}\right)}{3 \sqrt{1+c_1}}-\frac{4 \sqrt{1-2 c_0} \tan ^{-1}\left(\frac{\sqrt{1-2 c_0} \sqrt{-1+2 c_1} \sqrt{\frac{c_3 x^5+c_0 x^3+c_4}{c_3 x^5+c_1 x^3+c_4}}}{-1+2 c_0}\right)}{3 \sqrt{-1+2 c_1}}",1,"Integrate[(x^5*(2*x^5*C[3] - 3*C[4])*Sqrt[(x^3*C[0] + x^5*C[3] + C[4])/(x^3*C[1] + x^5*C[3] + C[4])])/((x^3 + 2*x^5*C[3] + 2*C[4])*(-x^6 + x^10*C[3]^2 + 2*x^5*C[3]*C[4] + C[4]^2)), x]","F",-1
2761,1,5697,260,7.4778607,"\int \frac{\left(-1+x^2\right)^2 \left(x+x^3\right)}{\sqrt{1+x^4} \left(1-2 x^2+4 x^4-2 x^6+x^8\right)} \, dx","Integrate[((-1 + x^2)^2*(x + x^3))/(Sqrt[1 + x^4]*(1 - 2*x^2 + 4*x^4 - 2*x^6 + x^8)),x]","\text{Result too large to show}","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^7+12 \text{$\#$1}^6-4 \text{$\#$1}^5-10 \text{$\#$1}^4+4 \text{$\#$1}^3+12 \text{$\#$1}^2+4 \text{$\#$1}+1\&,\frac{\text{$\#$1}^6 \log \left(-\text{$\#$1}+\sqrt{x^4+1}+x^2\right)-2 \text{$\#$1}^5 \log \left(-\text{$\#$1}+\sqrt{x^4+1}+x^2\right)-7 \text{$\#$1}^4 \log \left(-\text{$\#$1}+\sqrt{x^4+1}+x^2\right)+12 \text{$\#$1}^3 \log \left(-\text{$\#$1}+\sqrt{x^4+1}+x^2\right)+7 \text{$\#$1}^2 \log \left(-\text{$\#$1}+\sqrt{x^4+1}+x^2\right)-2 \text{$\#$1} \log \left(-\text{$\#$1}+\sqrt{x^4+1}+x^2\right)-\log \left(-\text{$\#$1}+\sqrt{x^4+1}+x^2\right)}{2 \text{$\#$1}^7-7 \text{$\#$1}^6+18 \text{$\#$1}^5-5 \text{$\#$1}^4-10 \text{$\#$1}^3+3 \text{$\#$1}^2+6 \text{$\#$1}+1}\&\right]",1,"Result too large to show","C",0
2762,1,168,261,0.2580782,"\int \frac{\left(-1+x+2 x^2\right) \sqrt[4]{-x^3+x^4}}{-1-x+x^2} \, dx","Integrate[((-1 + x + 2*x^2)*(-x^3 + x^4)^(1/4))/(-1 - x + x^2),x]","\frac{4 \sqrt[4]{(x-1) x^3} \left(15 \sqrt[4]{x} \, _2F_1\left(-\frac{3}{4},\frac{1}{4};\frac{5}{4};1-x\right)+2 (x-1) \sqrt[4]{x} \, _2F_1\left(-\frac{3}{4},\frac{5}{4};\frac{9}{4};1-x\right)+5 \sqrt[4]{x} \, _2F_1\left(\frac{1}{4},\frac{1}{4};\frac{5}{4};1-x\right)+5 \left(\sqrt{5}-2\right) \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{\left(-1+\sqrt{5}\right) (x-1)}{\left(1+\sqrt{5}\right) x}\right)-5 \left(2+\sqrt{5}\right) \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{\left(1+\sqrt{5}\right) (x-1)}{\left(-1+\sqrt{5}\right) x}\right)\right)}{5 x}","\frac{1}{4} \sqrt[4]{x^4-x^3} (4 x+11)-\frac{49}{8} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^3}}\right)+\sqrt{2 \left(11+5 \sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}} x}{\sqrt[4]{x^4-x^3}}\right)-\sqrt{2 \left(5 \sqrt{5}-11\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{1}{2}+\frac{\sqrt{5}}{2}} x}{\sqrt[4]{x^4-x^3}}\right)+\frac{49}{8} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^3}}\right)-\sqrt{2 \left(11+5 \sqrt{5}\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}} x}{\sqrt[4]{x^4-x^3}}\right)+\sqrt{2 \left(5 \sqrt{5}-11\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{2}+\frac{\sqrt{5}}{2}} x}{\sqrt[4]{x^4-x^3}}\right)",1,"(4*((-1 + x)*x^3)^(1/4)*(15*x^(1/4)*Hypergeometric2F1[-3/4, 1/4, 5/4, 1 - x] + 2*(-1 + x)*x^(1/4)*Hypergeometric2F1[-3/4, 5/4, 9/4, 1 - x] + 5*x^(1/4)*Hypergeometric2F1[1/4, 1/4, 5/4, 1 - x] + 5*(-2 + Sqrt[5])*Hypergeometric2F1[1/4, 1, 5/4, ((-1 + Sqrt[5])*(-1 + x))/((1 + Sqrt[5])*x)] - 5*(2 + Sqrt[5])*Hypergeometric2F1[1/4, 1, 5/4, ((1 + Sqrt[5])*(-1 + x))/((-1 + Sqrt[5])*x)]))/(5*x)","C",1
2763,0,0,261,0.307812,"\int \frac{\left(2+x^6\right) \left(-1+x^4+x^6\right)}{\sqrt[4]{-1+x^6} \left(1-2 x^6+x^8+x^{12}\right)} \, dx","Integrate[((2 + x^6)*(-1 + x^4 + x^6))/((-1 + x^6)^(1/4)*(1 - 2*x^6 + x^8 + x^12)),x]","\int \frac{\left(2+x^6\right) \left(-1+x^4+x^6\right)}{\sqrt[4]{-1+x^6} \left(1-2 x^6+x^8+x^{12}\right)} \, dx","-\frac{1}{2} \sqrt{\frac{1}{2} \left(2-\sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}} x \sqrt[4]{x^6-1}}{\sqrt{x^6-1}-x^2}\right)+\frac{1}{2} \sqrt{\frac{1}{2} \left(2+\sqrt{2}\right)} \tan ^{-1}\left(\frac{\left(\sqrt{\frac{2}{2-\sqrt{2}}}-\frac{2}{\sqrt{2-\sqrt{2}}}\right) x \sqrt[4]{x^6-1}}{\sqrt{x^6-1}-x^2}\right)-\frac{1}{2} \sqrt{\frac{1}{2} \left(2+\sqrt{2}\right)} \tanh ^{-1}\left(\frac{\sqrt{2-\sqrt{2}} x \sqrt[4]{x^6-1}}{\sqrt{x^6-1}+x^2}\right)-\frac{1}{2} \sqrt{\frac{1}{2} \left(2-\sqrt{2}\right)} \tanh ^{-1}\left(\frac{\sqrt{2+\sqrt{2}} x \sqrt[4]{x^6-1}}{\sqrt{x^6-1}+x^2}\right)",1,"Integrate[((2 + x^6)*(-1 + x^4 + x^6))/((-1 + x^6)^(1/4)*(1 - 2*x^6 + x^8 + x^12)), x]","F",-1
2764,1,273,261,0.8870442,"\int \frac{1}{(d+c x)^2 \sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Integrate[1/((d + c*x)^2*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]),x]","-\frac{a \left(-\frac{\sqrt{-\sqrt{a^2 d^2+b^2 c^2}-a d} \tan ^{-1}\left(\frac{b \sqrt{c}}{\sqrt{\sqrt{a^2 x^2+b^2}+a x} \sqrt{-\sqrt{a^2 d^2+b^2 c^2}-a d}}\right)}{b \sqrt{a^2 d^2+b^2 c^2}}+\frac{\sqrt{\sqrt{a^2 d^2+b^2 c^2}-a d} \tan ^{-1}\left(\frac{b \sqrt{c}}{\sqrt{\sqrt{a^2 x^2+b^2}+a x} \sqrt{\sqrt{a^2 d^2+b^2 c^2}-a d}}\right)}{b \sqrt{a^2 d^2+b^2 c^2}}+\frac{\sqrt{c}}{\sqrt{\sqrt{a^2 x^2+b^2}+a x} (a c x+a d)}\right)}{c^{3/2}}","-\frac{a \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{\sqrt{a^2 x^2+b^2}+a x}}{\sqrt{a d-\sqrt{a^2 d^2+b^2 c^2}}}\right)}{\sqrt{c} \sqrt{a^2 d^2+b^2 c^2} \sqrt{a d-\sqrt{a^2 d^2+b^2 c^2}}}+\frac{a \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{\sqrt{a^2 x^2+b^2}+a x}}{\sqrt{\sqrt{a^2 d^2+b^2 c^2}+a d}}\right)}{\sqrt{c} \sqrt{a^2 d^2+b^2 c^2} \sqrt{\sqrt{a^2 d^2+b^2 c^2}+a d}}-\frac{1}{c \sqrt{\sqrt{a^2 x^2+b^2}+a x} (c x+d)}",1,"-((a*(Sqrt[c]/((a*d + a*c*x)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]) - (Sqrt[-(a*d) - Sqrt[b^2*c^2 + a^2*d^2]]*ArcTan[(b*Sqrt[c])/(Sqrt[-(a*d) - Sqrt[b^2*c^2 + a^2*d^2]]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])])/(b*Sqrt[b^2*c^2 + a^2*d^2]) + (Sqrt[-(a*d) + Sqrt[b^2*c^2 + a^2*d^2]]*ArcTan[(b*Sqrt[c])/(Sqrt[-(a*d) + Sqrt[b^2*c^2 + a^2*d^2]]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])])/(b*Sqrt[b^2*c^2 + a^2*d^2])))/c^(3/2))","A",1
2765,0,0,261,0.3019962,"\int \frac{\left(1+x^2\right)^2}{\left(-1+x^2\right)^2 \sqrt{x^2+\sqrt{1+x^4}}} \, dx","Integrate[(1 + x^2)^2/((-1 + x^2)^2*Sqrt[x^2 + Sqrt[1 + x^4]]),x]","\int \frac{\left(1+x^2\right)^2}{\left(-1+x^2\right)^2 \sqrt{x^2+\sqrt{1+x^4}}} \, dx","\frac{x \left(x^2-5\right)}{2 \left(x^2-1\right) \sqrt{\sqrt{x^4+1}+x^2}}-4 \sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)+\sqrt{2 \left(7+5 \sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{2}-1\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)}{\sqrt{2}}-\sqrt{2 \left(5 \sqrt{2}-7\right)} \tanh ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)",1,"Integrate[(1 + x^2)^2/((-1 + x^2)^2*Sqrt[x^2 + Sqrt[1 + x^4]]), x]","F",-1
2766,0,0,262,3.504087,"\int \frac{a (a b+a c-2 b c)-2 \left(a^2-b c\right) x+(2 a-b-c) x^2}{((-a+x) (-b+x) (-c+x))^{2/3} \left(a^2-b c d+(-2 a+b d+c d) x+(1-d) x^2\right)} \, dx","Integrate[(a*(a*b + a*c - 2*b*c) - 2*(a^2 - b*c)*x + (2*a - b - c)*x^2)/(((-a + x)*(-b + x)*(-c + x))^(2/3)*(a^2 - b*c*d + (-2*a + b*d + c*d)*x + (1 - d)*x^2)),x]","\int \frac{a (a b+a c-2 b c)-2 \left(a^2-b c\right) x+(2 a-b-c) x^2}{((-a+x) (-b+x) (-c+x))^{2/3} \left(a^2-b c d+(-2 a+b d+c d) x+(1-d) x^2\right)} \, dx","-\frac{\log \left(a^2+d^{2/3} \left(x^2 (-a-b-c)+x (a b+a c+b c)-a b c+x^3\right)^{2/3}+\left(\sqrt[3]{d} x-a \sqrt[3]{d}\right) \sqrt[3]{x^2 (-a-b-c)+x (a b+a c+b c)-a b c+x^3}-2 a x+x^2\right)}{2 \sqrt[3]{d}}+\frac{\log \left(\sqrt[3]{d} \sqrt[3]{x^2 (-a-b-c)+x (a b+a c+b c)-a b c+x^3}+a-x\right)}{\sqrt[3]{d}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} a-\sqrt{3} x}{-2 \sqrt[3]{d} \sqrt[3]{x^2 (-a-b-c)+x (a b+a c+b c)-a b c+x^3}+a-x}\right)}{\sqrt[3]{d}}",1,"Integrate[(a*(a*b + a*c - 2*b*c) - 2*(a^2 - b*c)*x + (2*a - b - c)*x^2)/(((-a + x)*(-b + x)*(-c + x))^(2/3)*(a^2 - b*c*d + (-2*a + b*d + c*d)*x + (1 - d)*x^2)), x]","F",-1
2767,1,6061,262,3.1362001,"\int \frac{1+x^4}{\left(-1+x^4\right) \sqrt{a+b x+c x^2+b x^3+a x^4}} \, dx","Integrate[(1 + x^4)/((-1 + x^4)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]),x]","\text{Result too large to show}","\frac{\tan ^{-1}\left(\frac{x \sqrt{2 a-c}}{-\sqrt{a x^4+a+b x^3+b x+c x^2}+\sqrt{a} x^2+\sqrt{a}}\right)}{\sqrt{2 a-c}}-\frac{\sqrt{-2 a-2 b-c} \tan ^{-1}\left(\frac{x \sqrt{-2 a-2 b-c}}{-\sqrt{a x^4+a+b x^3+b x+c x^2}+\sqrt{a} x^2-2 \sqrt{a} x+\sqrt{a}}\right)}{2 (2 a+2 b+c)}-\frac{\sqrt{-2 a+2 b-c} \tan ^{-1}\left(\frac{x \sqrt{-2 a+2 b-c}}{-\sqrt{a x^4+a+b x^3+b x+c x^2}+\sqrt{a} x^2+2 \sqrt{a} x+\sqrt{a}}\right)}{2 (2 a-2 b+c)}",1,"Result too large to show","C",0
2768,0,0,262,0.3402969,"\int \frac{\left(-1+x^2\right)^2}{\left(1+x^2\right)^2 \sqrt{x^2+\sqrt{1+x^4}}} \, dx","Integrate[(-1 + x^2)^2/((1 + x^2)^2*Sqrt[x^2 + Sqrt[1 + x^4]]),x]","\int \frac{\left(-1+x^2\right)^2}{\left(1+x^2\right)^2 \sqrt{x^2+\sqrt{1+x^4}}} \, dx","\frac{x \left(x^2+5\right)}{2 \left(x^2+1\right) \sqrt{\sqrt{x^4+1}+x^2}}+4 \sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)-\sqrt{2 \left(7+5 \sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)}{\sqrt{2}}-\sqrt{2 \left(5 \sqrt{2}-7\right)} \tanh ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{2}-1\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)",1,"Integrate[(-1 + x^2)^2/((1 + x^2)^2*Sqrt[x^2 + Sqrt[1 + x^4]]), x]","F",-1
2769,0,0,263,3.6009042,"\int \frac{2 a b^2-b (2 a+b) x+x^3}{\sqrt[3]{x (-a+x) (-b+x)^2} \left(-a b^2+b (2 a+b) x-(a+2 b+d) x^2+x^3\right)} \, dx","Integrate[(2*a*b^2 - b*(2*a + b)*x + x^3)/((x*(-a + x)*(-b + x)^2)^(1/3)*(-(a*b^2) + b*(2*a + b)*x - (a + 2*b + d)*x^2 + x^3)),x]","\int \frac{2 a b^2-b (2 a+b) x+x^3}{\sqrt[3]{x (-a+x) (-b+x)^2} \left(-a b^2+b (2 a+b) x-(a+2 b+d) x^2+x^3\right)} \, dx","-\frac{\log \left(\sqrt[3]{d} x \sqrt[3]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}+\left(x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4\right)^{2/3}+d^{2/3} x^2\right)}{2 \sqrt[3]{d}}+\frac{\log \left(\sqrt[3]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}-\sqrt[3]{d} x\right)}{\sqrt[3]{d}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}}{\sqrt[3]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}+2 \sqrt[3]{d} x}\right)}{\sqrt[3]{d}}",1,"Integrate[(2*a*b^2 - b*(2*a + b)*x + x^3)/((x*(-a + x)*(-b + x)^2)^(1/3)*(-(a*b^2) + b*(2*a + b)*x - (a + 2*b + d)*x^2 + x^3)), x]","F",-1
2770,1,159,263,0.176777,"\int \frac{-d+c x}{x \sqrt[3]{-b+a x^3}} \, dx","Integrate[(-d + c*x)/(x*(-b + a*x^3)^(1/3)),x]","\frac{1}{6} \left(\frac{c \left(\log \left(\frac{a^{2/3} x^2}{\left(a x^3-b\right)^{2/3}}+\frac{\sqrt[3]{a} x}{\sqrt[3]{a x^3-b}}+1\right)-2 \log \left(1-\frac{\sqrt[3]{a} x}{\sqrt[3]{a x^3-b}}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a} x}{\sqrt[3]{a x^3-b}}+1}{\sqrt{3}}\right)\right)}{\sqrt[3]{a}}-\frac{3 d \left(a x^3-b\right)^{2/3} \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};1-\frac{a x^3}{b}\right)}{b}\right)","\frac{c \log \left(a^{2/3} x^2+\sqrt[3]{a} x \sqrt[3]{a x^3-b}+\left(a x^3-b\right)^{2/3}\right)}{6 \sqrt[3]{a}}-\frac{d \log \left(-\sqrt[3]{b} \sqrt[3]{a x^3-b}+\left(a x^3-b\right)^{2/3}+b^{2/3}\right)}{6 \sqrt[3]{b}}-\frac{c \log \left(\sqrt[3]{a x^3-b}-\sqrt[3]{a} x\right)}{3 \sqrt[3]{a}}-\frac{c \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a x^3-b}}{\sqrt{3} \sqrt[3]{a}}+\frac{x}{\sqrt{3}}}{x}\right)}{\sqrt{3} \sqrt[3]{a}}+\frac{d \log \left(\sqrt[3]{a x^3-b}+\sqrt[3]{b}\right)}{3 \sqrt[3]{b}}+\frac{d \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{a x^3-b}}{\sqrt{3} \sqrt[3]{b}}\right)}{\sqrt{3} \sqrt[3]{b}}",1,"((-3*d*(-b + a*x^3)^(2/3)*Hypergeometric2F1[2/3, 1, 5/3, 1 - (a*x^3)/b])/b + (c*(2*Sqrt[3]*ArcTan[(1 + (2*a^(1/3)*x)/(-b + a*x^3)^(1/3))/Sqrt[3]] - 2*Log[1 - (a^(1/3)*x)/(-b + a*x^3)^(1/3)] + Log[1 + (a^(2/3)*x^2)/(-b + a*x^3)^(2/3) + (a^(1/3)*x)/(-b + a*x^3)^(1/3)]))/a^(1/3))/6","C",1
2771,1,305,263,0.646194,"\int \frac{-b^4+c^2 x^2+a^4 x^4}{\sqrt{-b^4+a^4 x^4} \left(b^4+a^4 x^4\right)} \, dx","Integrate[(-b^4 + c^2*x^2 + a^4*x^4)/(Sqrt[-b^4 + a^4*x^4]*(b^4 + a^4*x^4)),x]","\frac{x \left(5 c^2 x^2 \sqrt{1-\frac{a^4 x^4}{b^4}} F_1\left(\frac{3}{4};\frac{1}{2},1;\frac{7}{4};\frac{a^4 x^4}{b^4},-\frac{a^4 x^4}{b^4}\right)+3 a^4 x^4 \sqrt{1-\frac{a^4 x^4}{b^4}} F_1\left(\frac{5}{4};\frac{1}{2},1;\frac{9}{4};\frac{a^4 x^4}{b^4},-\frac{a^4 x^4}{b^4}\right)-\frac{75 b^{12} F_1\left(\frac{1}{4};\frac{1}{2},1;\frac{5}{4};\frac{a^4 x^4}{b^4},-\frac{a^4 x^4}{b^4}\right)}{\left(a^4 x^4+b^4\right) \left(5 b^4 F_1\left(\frac{1}{4};\frac{1}{2},1;\frac{5}{4};\frac{a^4 x^4}{b^4},-\frac{a^4 x^4}{b^4}\right)+2 a^4 x^4 \left(F_1\left(\frac{5}{4};\frac{3}{2},1;\frac{9}{4};\frac{a^4 x^4}{b^4},-\frac{a^4 x^4}{b^4}\right)-2 F_1\left(\frac{5}{4};\frac{1}{2},2;\frac{9}{4};\frac{a^4 x^4}{b^4},-\frac{a^4 x^4}{b^4}\right)\right)\right)}\right)}{15 b^4 \sqrt{a^4 x^4-b^4}}","-\frac{\left(\frac{1}{4}-\frac{i}{4}\right) \left(2 a^2 b^2+i c^2\right) \tan ^{-1}\left(\frac{(1+i) a b x}{\sqrt{a^4 x^4-b^4}+a^2 x^2+i b^2}\right)}{a^3 b^3}+\frac{\left(\frac{1}{8}-\frac{i}{8}\right) \left(2 a^2 b^2-i c^2\right) \tanh ^{-1}\left(\frac{(1-i) \sqrt{a^4 x^4-b^4}+(1-i) a^2 x^2+(1+i) b^2}{2 \sqrt{3-2 \sqrt{2}} a b x}\right)}{a^3 b^3}+\frac{\left(\frac{1}{8}+\frac{i}{8}\right) \left(c^2+2 i a^2 b^2\right) \tanh ^{-1}\left(\frac{(1-i) \sqrt{a^4 x^4-b^4}+(1-i) a^2 x^2+(1+i) b^2}{2 \sqrt{3+2 \sqrt{2}} a b x}\right)}{a^3 b^3}",1,"(x*(5*c^2*x^2*Sqrt[1 - (a^4*x^4)/b^4]*AppellF1[3/4, 1/2, 1, 7/4, (a^4*x^4)/b^4, -((a^4*x^4)/b^4)] + 3*a^4*x^4*Sqrt[1 - (a^4*x^4)/b^4]*AppellF1[5/4, 1/2, 1, 9/4, (a^4*x^4)/b^4, -((a^4*x^4)/b^4)] - (75*b^12*AppellF1[1/4, 1/2, 1, 5/4, (a^4*x^4)/b^4, -((a^4*x^4)/b^4)])/((b^4 + a^4*x^4)*(5*b^4*AppellF1[1/4, 1/2, 1, 5/4, (a^4*x^4)/b^4, -((a^4*x^4)/b^4)] + 2*a^4*x^4*(-2*AppellF1[5/4, 1/2, 2, 9/4, (a^4*x^4)/b^4, -((a^4*x^4)/b^4)] + AppellF1[5/4, 3/2, 1, 9/4, (a^4*x^4)/b^4, -((a^4*x^4)/b^4)])))))/(15*b^4*Sqrt[-b^4 + a^4*x^4])","C",0
2772,1,5410,265,2.6912786,"\int \frac{x^2}{\left(1-x^4\right) \sqrt{a+b x+c x^2+b x^3+a x^4}} \, dx","Integrate[x^2/((1 - x^4)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]),x]","\text{Result too large to show}","\frac{\tan ^{-1}\left(\frac{x \sqrt{2 a-c}}{-\sqrt{a x^4+a+b x^3+b x+c x^2}+\sqrt{a} x^2+\sqrt{a}}\right)}{2 \sqrt{2 a-c}}+\frac{\sqrt{-2 a-2 b-c} \tan ^{-1}\left(\frac{x \sqrt{-2 a-2 b-c}}{-\sqrt{a x^4+a+b x^3+b x+c x^2}+\sqrt{a} x^2-2 \sqrt{a} x+\sqrt{a}}\right)}{4 (2 a+2 b+c)}+\frac{\sqrt{-2 a+2 b-c} \tan ^{-1}\left(\frac{x \sqrt{-2 a+2 b-c}}{-\sqrt{a x^4+a+b x^3+b x+c x^2}+\sqrt{a} x^2+2 \sqrt{a} x+\sqrt{a}}\right)}{4 (2 a-2 b+c)}",1,"Result too large to show","C",0
2773,0,0,265,1.9287594,"\int \frac{x (-b+x) \left(-a^2 b+2 a^2 x+(-2 a+b) x^2\right)}{(x (-a+x) (-b+x))^{2/3} \left(-a^4+4 a^3 x+\left(-6 a^2+b^2 d\right) x^2+2 (2 a-b d) x^3+(-1+d) x^4\right)} \, dx","Integrate[(x*(-b + x)*(-(a^2*b) + 2*a^2*x + (-2*a + b)*x^2))/((x*(-a + x)*(-b + x))^(2/3)*(-a^4 + 4*a^3*x + (-6*a^2 + b^2*d)*x^2 + 2*(2*a - b*d)*x^3 + (-1 + d)*x^4)),x]","\int \frac{x (-b+x) \left(-a^2 b+2 a^2 x+(-2 a+b) x^2\right)}{(x (-a+x) (-b+x))^{2/3} \left(-a^4+4 a^3 x+\left(-6 a^2+b^2 d\right) x^2+2 (2 a-b d) x^3+(-1+d) x^4\right)} \, dx","\frac{\log \left(a^2-\sqrt[3]{d} \left(x^2 (-a-b)+a b x+x^3\right)^{2/3}-2 a x+x^2\right)}{2 d^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} \left(x^2 (-a-b)+a b x+x^3\right)^{2/3}}{2 a^2+\sqrt[3]{d} \left(x^2 (-a-b)+a b x+x^3\right)^{2/3}-4 a x+2 x^2}\right)}{2 d^{2/3}}-\frac{\log \left(a^4-4 a^3 x+\left(x^2 (-a-b)+a b x+x^3\right)^{2/3} \left(a^2 \sqrt[3]{d}-2 a \sqrt[3]{d} x+\sqrt[3]{d} x^2\right)+6 a^2 x^2+d^{2/3} \left(x^2 (-a-b)+a b x+x^3\right)^{4/3}-4 a x^3+x^4\right)}{4 d^{2/3}}",1,"Integrate[(x*(-b + x)*(-(a^2*b) + 2*a^2*x + (-2*a + b)*x^2))/((x*(-a + x)*(-b + x))^(2/3)*(-a^4 + 4*a^3*x + (-6*a^2 + b^2*d)*x^2 + 2*(2*a - b*d)*x^3 + (-1 + d)*x^4)), x]","F",-1
2774,1,259,265,0.4080589,"\int \frac{\left(-1+x^3\right)^{2/3} \left(8-8 x^3+x^6\right)}{x^6 \left(-4+x^3\right) \left(-2+x^3\right)} \, dx","Integrate[((-1 + x^3)^(2/3)*(8 - 8*x^3 + x^6))/(x^6*(-4 + x^3)*(-2 + x^3)),x]","\frac{1}{96} \left(8 \sqrt[3]{2} \log \left(\sqrt[3]{2}-\frac{x}{\sqrt[3]{x^3-1}}\right)-2\ 6^{2/3} \log \left(2^{2/3}-\frac{\sqrt[3]{3} x}{\sqrt[3]{x^3-1}}\right)-8 \sqrt[3]{2} \sqrt{3} \tan ^{-1}\left(\frac{\frac{2^{2/3} x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)+6\ 2^{2/3} \sqrt[6]{3} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{6} x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)-4 \sqrt[3]{2} \log \left(\frac{\sqrt[3]{2} x}{\sqrt[3]{x^3-1}}+\frac{x^2}{\left(x^3-1\right)^{2/3}}+2^{2/3}\right)+6^{2/3} \log \left(\frac{2^{2/3} \sqrt[3]{3} x}{\sqrt[3]{x^3-1}}+\frac{3^{2/3} x^2}{\left(x^3-1\right)^{2/3}}+2 \sqrt[3]{2}\right)\right)+\left(x^3-1\right)^{2/3} \left(\frac{13}{40 x^2}-\frac{1}{5 x^5}\right)","\frac{\log \left(\sqrt[3]{2} \sqrt[3]{x^3-1}-x\right)}{6\ 2^{2/3}}-\frac{\log \left(6^{2/3} \sqrt[3]{x^3-1}-3 x\right)}{8 \sqrt[3]{6}}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{2} \sqrt[3]{x^3-1}+x}\right)}{2\ 2^{2/3} \sqrt{3}}+\frac{\sqrt[6]{3} \tan ^{-1}\left(\frac{3^{5/6} x}{2\ 2^{2/3} \sqrt[3]{x^3-1}+\sqrt[3]{3} x}\right)}{8 \sqrt[3]{2}}+\frac{\left(x^3-1\right)^{2/3} \left(13 x^3-8\right)}{40 x^5}-\frac{\log \left(\sqrt[3]{2} \sqrt[3]{x^3-1} x+2^{2/3} \left(x^3-1\right)^{2/3}+x^2\right)}{12\ 2^{2/3}}+\frac{\log \left(6^{2/3} \sqrt[3]{x^3-1} x+2 \sqrt[3]{6} \left(x^3-1\right)^{2/3}+3 x^2\right)}{16 \sqrt[3]{6}}",1,"(-1/5*1/x^5 + 13/(40*x^2))*(-1 + x^3)^(2/3) + (-8*2^(1/3)*Sqrt[3]*ArcTan[(1 + (2^(2/3)*x)/(-1 + x^3)^(1/3))/Sqrt[3]] + 6*2^(2/3)*3^(1/6)*ArcTan[(1 + (6^(1/3)*x)/(-1 + x^3)^(1/3))/Sqrt[3]] + 8*2^(1/3)*Log[2^(1/3) - x/(-1 + x^3)^(1/3)] - 4*2^(1/3)*Log[2^(2/3) + x^2/(-1 + x^3)^(2/3) + (2^(1/3)*x)/(-1 + x^3)^(1/3)] - 2*6^(2/3)*Log[2^(2/3) - (3^(1/3)*x)/(-1 + x^3)^(1/3)] + 6^(2/3)*Log[2*2^(1/3) + (3^(2/3)*x^2)/(-1 + x^3)^(2/3) + (2^(2/3)*3^(1/3)*x)/(-1 + x^3)^(1/3)])/96","A",1
2775,1,199,265,0.3566072,"\int \frac{\left(c+\left(a x+\sqrt{-b+a^2 x^2}\right)^{3/4}\right)^{4/3}}{\sqrt{-b+a^2 x^2}} \, dx","Integrate[(c + (a*x + Sqrt[-b + a^2*x^2])^(3/4))^(4/3)/Sqrt[-b + a^2*x^2],x]","\frac{-2 c^2 \left(\frac{c \sqrt[4]{\sqrt{a^2 x^2-b}+a x}+\sqrt{a^2 x^2-b}+a x}{\sqrt{a^2 x^2-b}+a x}\right)^{2/3} \, _2F_1\left(\frac{2}{3},\frac{2}{3};\frac{5}{3};-\frac{c}{\left(a x+\sqrt{a^2 x^2-b}\right)^{3/4}}\right)+6 c \left(\sqrt{a^2 x^2-b}+a x\right)^{3/4}+\left(\sqrt{a^2 x^2-b}+a x\right)^{3/2}+5 c^2}{a \left(\left(\sqrt{a^2 x^2-b}+a x\right)^{3/4}+c\right)^{2/3}}","\frac{4 c^{4/3} \log \left(\sqrt[3]{\left(\sqrt{a^2 x^2-b}+a x\right)^{3/4}+c}-\sqrt[3]{c}\right)}{3 a}-\frac{2 c^{4/3} \log \left(\sqrt[3]{c} \sqrt[3]{\left(\sqrt{a^2 x^2-b}+a x\right)^{3/4}+c}+\left(\left(\sqrt{a^2 x^2-b}+a x\right)^{3/4}+c\right)^{2/3}+c^{2/3}\right)}{3 a}-\frac{4 c^{4/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{\left(\sqrt{a^2 x^2-b}+a x\right)^{3/4}+c}}{\sqrt{3} \sqrt[3]{c}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} a}+\frac{4 c \sqrt[3]{\left(\sqrt{a^2 x^2-b}+a x\right)^{3/4}+c}}{a}+\frac{\left(\left(\sqrt{a^2 x^2-b}+a x\right)^{3/4}+c\right)^{4/3}}{a}",1,"(5*c^2 + 6*c*(a*x + Sqrt[-b + a^2*x^2])^(3/4) + (a*x + Sqrt[-b + a^2*x^2])^(3/2) - 2*c^2*((a*x + Sqrt[-b + a^2*x^2] + c*(a*x + Sqrt[-b + a^2*x^2])^(1/4))/(a*x + Sqrt[-b + a^2*x^2]))^(2/3)*Hypergeometric2F1[2/3, 2/3, 5/3, -(c/(a*x + Sqrt[-b + a^2*x^2])^(3/4))])/(a*(c + (a*x + Sqrt[-b + a^2*x^2])^(3/4))^(2/3))","C",1
2776,0,0,266,0.1036454,"\int \frac{1}{(-b+a x) \sqrt[3]{b^3+a^3 x^3}} \, dx","Integrate[1/((-b + a*x)*(b^3 + a^3*x^3)^(1/3)),x]","\int \frac{1}{(-b+a x) \sqrt[3]{b^3+a^3 x^3}} \, dx","\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{a^3 x^3+b^3}}{\sqrt[3]{a^3 x^3+b^3}+\sqrt[3]{2} a x+\sqrt[3]{2} b}\right)}{2 \sqrt[3]{2} a b}+\frac{\log \left(\sqrt[3]{2} a^{3/2} \sqrt{b} x-2 \sqrt{a} \sqrt{b} \sqrt[3]{a^3 x^3+b^3}+\sqrt[3]{2} \sqrt{a} b^{3/2}\right)}{2 \sqrt[3]{2} a b}-\frac{\log \left(4 a b \left(a^3 x^3+b^3\right)^{2/3}+2^{2/3} a^3 b x^2+2\ 2^{2/3} a^2 b^2 x+\left(2 \sqrt[3]{2} a^2 b x+2 \sqrt[3]{2} a b^2\right) \sqrt[3]{a^3 x^3+b^3}+2^{2/3} a b^3\right)}{4 \sqrt[3]{2} a b}",1,"Integrate[1/((-b + a*x)*(b^3 + a^3*x^3)^(1/3)), x]","F",-1
2777,1,331,266,1.4383896,"\int \frac{\sqrt[3]{a x^2+b x \sqrt{-\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}}}{\sqrt{-\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}} \, dx","Integrate[(a*x^2 + b*x*Sqrt[-(a/b^2) + (a^2*x^2)/b^2])^(1/3)/Sqrt[-(a/b^2) + (a^2*x^2)/b^2],x]","\frac{a x \sqrt[3]{x \left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right)} \left(b x \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x^2-1\right) \left(-\sqrt[3]{a} \log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{\left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right)^2+a}+\left(\left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right)^2+a\right)^{2/3}\right)+6 \sqrt[3]{2} \sqrt[3]{a x \left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right)}+2 \sqrt[3]{a} \log \left(\sqrt[3]{a}-\sqrt[3]{\left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right)^2+a}\right)-2 \sqrt{3} \sqrt[3]{a} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{\left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right)^2+a}}{\sqrt[3]{a}}+1}{\sqrt{3}}\right)\right)}{4 \sqrt[3]{2} \sqrt{\frac{a \left(a x^2-1\right)}{b^2}} \left(a x \left(b \sqrt{\frac{a \left(a x^2-1\right)}{b^2}}+a x\right)\right)^{4/3}}","\frac{3 b \sqrt[3]{b x \sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}}+a x^2}}{2 a}+\frac{b \log \left(\sqrt[3]{2} \sqrt[3]{b x \sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}}+a x^2}-1\right)}{2 \sqrt[3]{2} a}-\frac{b \log \left(2^{2/3} \left(b x \sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}}+a x^2\right)^{2/3}+\sqrt[3]{2} \sqrt[3]{b x \sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}}+a x^2}+1\right)}{4 \sqrt[3]{2} a}-\frac{\sqrt{3} b \tan ^{-1}\left(\frac{2 \sqrt[3]{2} \sqrt[3]{b x \sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}}+a x^2}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt[3]{2} a}",1,"(a*x*(x*(a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2]))^(1/3)*(-1 + a*x^2 + b*x*Sqrt[(a*(-1 + a*x^2))/b^2])*(6*2^(1/3)*(a*x*(a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2]))^(1/3) - 2*Sqrt[3]*a^(1/3)*ArcTan[(1 + (2*(a + (a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2])^2)^(1/3))/a^(1/3))/Sqrt[3]] + 2*a^(1/3)*Log[a^(1/3) - (a + (a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2])^2)^(1/3)] - a^(1/3)*Log[a^(2/3) + a^(1/3)*(a + (a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2])^2)^(1/3) + (a + (a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2])^2)^(2/3)]))/(4*2^(1/3)*Sqrt[(a*(-1 + a*x^2))/b^2]*(a*x*(a*x + b*Sqrt[(a*(-1 + a*x^2))/b^2]))^(4/3))","A",1
2778,1,211,266,0.4614926,"\int \frac{\sqrt{1+x^2} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{1-x^2} \, dx","Integrate[(Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2),x]","-\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^3-2 \text{$\#$1}}\&\right]+\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^4-2 \text{$\#$1}^2+2}\&\right]-4 \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-2 \log \left(1-\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}+1\right)","-\text{RootSum}\left[\text{$\#$1}^8+8 \text{$\#$1}^7+24 \text{$\#$1}^6+32 \text{$\#$1}^5+14 \text{$\#$1}^4-8 \text{$\#$1}^3-8 \text{$\#$1}^2-1\&,\frac{\log \left(-\text{$\#$1}+\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-1\right)}{\text{$\#$1}^3+3 \text{$\#$1}^2+\text{$\#$1}-1}\&\right]+\text{RootSum}\left[\text{$\#$1}^8+8 \text{$\#$1}^7+24 \text{$\#$1}^6+32 \text{$\#$1}^5+18 \text{$\#$1}^4+8 \text{$\#$1}^3+8 \text{$\#$1}^2-1\&,\frac{\text{$\#$1} \log \left(-\text{$\#$1}+\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-1\right)+\log \left(-\text{$\#$1}+\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-1\right)}{\text{$\#$1}^4+4 \text{$\#$1}^3+4 \text{$\#$1}^2+1}\&\right]-4 \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}+4 \tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)",1,"-4*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - 2*Log[1 - Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]] + 2*Log[1 + Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]] - RootSum[-2 + 4*#1^4 - 4*#1^6 + #1^8 & , Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]/(-2*#1 + #1^3) & ] + RootSum[2 - 8*#1^2 + 8*#1^4 - 4*#1^6 + #1^8 & , (Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1)/(2 - 2*#1^2 + #1^4) & ]","A",1
2779,1,211,266,0.1524183,"\int \frac{\sqrt{1+x^2} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{1-x^2} \, dx","Integrate[(Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2),x]","-\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^3-2 \text{$\#$1}}\&\right]+\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^4-2 \text{$\#$1}^2+2}\&\right]-4 \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-2 \log \left(1-\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}+1\right)","-\text{RootSum}\left[\text{$\#$1}^8+8 \text{$\#$1}^7+24 \text{$\#$1}^6+32 \text{$\#$1}^5+14 \text{$\#$1}^4-8 \text{$\#$1}^3-8 \text{$\#$1}^2-1\&,\frac{\log \left(-\text{$\#$1}+\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-1\right)}{\text{$\#$1}^3+3 \text{$\#$1}^2+\text{$\#$1}-1}\&\right]+\text{RootSum}\left[\text{$\#$1}^8+8 \text{$\#$1}^7+24 \text{$\#$1}^6+32 \text{$\#$1}^5+18 \text{$\#$1}^4+8 \text{$\#$1}^3+8 \text{$\#$1}^2-1\&,\frac{\text{$\#$1} \log \left(-\text{$\#$1}+\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-1\right)+\log \left(-\text{$\#$1}+\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-1\right)}{\text{$\#$1}^4+4 \text{$\#$1}^3+4 \text{$\#$1}^2+1}\&\right]-4 \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}+4 \tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)",1,"-4*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - 2*Log[1 - Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]] + 2*Log[1 + Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]] - RootSum[-2 + 4*#1^4 - 4*#1^6 + #1^8 & , Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]/(-2*#1 + #1^3) & ] + RootSum[2 - 8*#1^2 + 8*#1^4 - 4*#1^6 + #1^8 & , (Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1)/(2 - 2*#1^2 + #1^4) & ]","A",1
2780,1,62,267,0.0637217,"\int \frac{-b+x}{\left((-a+x) (-b+x)^2\right)^{2/3} (b-a d+(-1+d) x)} \, dx","Integrate[(-b + x)/(((-a + x)*(-b + x)^2)^(2/3)*(b - a*d + (-1 + d)*x)),x]","-\frac{3 (b-x)^2 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{b-x}{a d-d x}\right)}{2 d (a-b) \left((x-a) (b-x)^2\right)^{2/3}}","-\frac{\log \left(d^{2/3} \left(x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3\right)^{2/3}+\sqrt[3]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3} \left(\sqrt[3]{d} x-b \sqrt[3]{d}\right)+b^2-2 b x+x^2\right)}{2 \sqrt[3]{d} (a-b)}+\frac{\log \left(\sqrt[3]{d} \sqrt[3]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3}+b-x\right)}{\sqrt[3]{d} (a-b)}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} b-\sqrt{3} x}{-2 \sqrt[3]{d} \sqrt[3]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3}+b-x}\right)}{\sqrt[3]{d} (a-b)}",1,"(-3*(b - x)^2*Hypergeometric2F1[2/3, 1, 5/3, (b - x)/(a*d - d*x)])/(2*(a - b)*d*((b - x)^2*(-a + x))^(2/3))","C",1
2781,1,573,267,1.4603115,"\int \frac{-a q x+b p x^3}{\sqrt{q+p x^4} \left(b^2 c+d q+2 a b c x^2+\left(a^2 c+d p\right) x^4\right)} \, dx","Integrate[(-(a*q*x) + b*p*x^3)/(Sqrt[q + p*x^4]*(b^2*c + d*q + 2*a*b*c*x^2 + (a^2*c + d*p)*x^4)),x]","\frac{\sqrt{c} \left(\frac{\left(a^3 c q-b \sqrt{d} p \sqrt{b^2 (-c) p-q \left(a^2 c+d p\right)}+a p \left(b^2 c+d q\right)\right) \tanh ^{-1}\left(\frac{\sqrt{d} p x^2 \sqrt{b^2 (-c) p-q \left(a^2 c+d p\right)}+a^2 c q-a b c p x^2+d p q}{\sqrt{c} \sqrt{p x^4+q} \sqrt{a^4 c q+a^2 p \left(b^2 c+d q\right)-2 a b \sqrt{d} p \sqrt{b^2 (-c) p-q \left(a^2 c+d p\right)}-b^2 d p^2}}\right)}{2 c \sqrt{a^4 c q+a^2 p \left(b^2 c+d q\right)-2 a b \sqrt{d} p \sqrt{b^2 (-c) p-q \left(a^2 c+d p\right)}-b^2 d p^2}}-\frac{\left(a^3 c q+b \sqrt{d} p \sqrt{b^2 (-c) p-q \left(a^2 c+d p\right)}+a p \left(b^2 c+d q\right)\right) \tanh ^{-1}\left(\frac{-\sqrt{d} p x^2 \sqrt{b^2 (-c) p-q \left(a^2 c+d p\right)}+a^2 c q-a b c p x^2+d p q}{\sqrt{c} \sqrt{p x^4+q} \sqrt{a^4 c q+a^2 p \left(b^2 c+d q\right)+2 a b \sqrt{d} p \sqrt{b^2 (-c) p-q \left(a^2 c+d p\right)}-b^2 d p^2}}\right)}{2 c \sqrt{a^4 c q+a^2 p \left(b^2 c+d q\right)+2 a b \sqrt{d} p \sqrt{b^2 (-c) p-q \left(a^2 c+d p\right)}-b^2 d p^2}}\right)}{2 \sqrt{d} \sqrt{b^2 (-c) p-q \left(a^2 c+d p\right)}}","-\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^4 a^2 c+\text{$\#$1}^4 d p+4 \text{$\#$1}^3 a b c \sqrt{p}-2 \text{$\#$1}^2 a^2 c q+4 \text{$\#$1}^2 b^2 c p+2 \text{$\#$1}^2 d p q-4 \text{$\#$1} a b c \sqrt{p} q+a^2 c q^2+d p q^2\&,\frac{\text{$\#$1}^2 (-b) p \log \left(-\text{$\#$1}+\sqrt{p x^4+q}+\sqrt{p} x^2\right)+2 \text{$\#$1} a \sqrt{p} q \log \left(-\text{$\#$1}+\sqrt{p x^4+q}+\sqrt{p} x^2\right)+b p q \log \left(-\text{$\#$1}+\sqrt{p x^4+q}+\sqrt{p} x^2\right)}{\text{$\#$1}^3 a^2 c+\text{$\#$1}^3 d p+3 \text{$\#$1}^2 a b c \sqrt{p}-\text{$\#$1} a^2 c q+2 \text{$\#$1} b^2 c p+\text{$\#$1} d p q-a b c \sqrt{p} q}\&\right]",1,"(Sqrt[c]*(-1/2*((a^3*c*q + a*p*(b^2*c + d*q) + b*Sqrt[d]*p*Sqrt[-(b^2*c*p) - (a^2*c + d*p)*q])*ArcTanh[(a^2*c*q + d*p*q - a*b*c*p*x^2 - Sqrt[d]*p*Sqrt[-(b^2*c*p) - (a^2*c + d*p)*q]*x^2)/(Sqrt[c]*Sqrt[-(b^2*d*p^2) + a^4*c*q + a^2*p*(b^2*c + d*q) + 2*a*b*Sqrt[d]*p*Sqrt[-(b^2*c*p) - (a^2*c + d*p)*q]]*Sqrt[q + p*x^4])])/(c*Sqrt[-(b^2*d*p^2) + a^4*c*q + a^2*p*(b^2*c + d*q) + 2*a*b*Sqrt[d]*p*Sqrt[-(b^2*c*p) - (a^2*c + d*p)*q]]) + ((a^3*c*q + a*p*(b^2*c + d*q) - b*Sqrt[d]*p*Sqrt[-(b^2*c*p) - (a^2*c + d*p)*q])*ArcTanh[(a^2*c*q + d*p*q - a*b*c*p*x^2 + Sqrt[d]*p*Sqrt[-(b^2*c*p) - (a^2*c + d*p)*q]*x^2)/(Sqrt[c]*Sqrt[-(b^2*d*p^2) + a^4*c*q + a^2*p*(b^2*c + d*q) - 2*a*b*Sqrt[d]*p*Sqrt[-(b^2*c*p) - (a^2*c + d*p)*q]]*Sqrt[q + p*x^4])])/(2*c*Sqrt[-(b^2*d*p^2) + a^4*c*q + a^2*p*(b^2*c + d*q) - 2*a*b*Sqrt[d]*p*Sqrt[-(b^2*c*p) - (a^2*c + d*p)*q]])))/(2*Sqrt[d]*Sqrt[-(b^2*c*p) - (a^2*c + d*p)*q])","B",1
2782,1,52549,267,7.3955193,"\int \frac{(b+a x)^2 \left(-2 a q+3 b p x^2+a p x^3\right)}{\sqrt{q+p x^3} \left(b^4 c+d q^2+4 a b^3 c x+6 a^2 b^2 c x^2+\left(4 a^3 b c+2 d p q\right) x^3+a^4 c x^4+d p^2 x^6\right)} \, dx","Integrate[((b + a*x)^2*(-2*a*q + 3*b*p*x^2 + a*p*x^3))/(Sqrt[q + p*x^3]*(b^4*c + d*q^2 + 4*a*b^3*c*x + 6*a^2*b^2*c*x^2 + (4*a^3*b*c + 2*d*p*q)*x^3 + a^4*c*x^4 + d*p^2*x^6)),x]","\text{Result too large to show}","\frac{\tanh ^{-1}\left(\frac{\sqrt{p x^3+q} \left(\sqrt{2} a \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{2} b \sqrt[4]{c} \sqrt[4]{d}\right)}{a^2 \sqrt{c} x^2+2 a b \sqrt{c} x+b^2 \sqrt{c}+\sqrt{d} p x^3+\sqrt{d} q}\right)}{\sqrt{2} c^{3/4} \sqrt[4]{d}}+\frac{\tan ^{-1}\left(\frac{a \sqrt[4]{c} x+b \sqrt[4]{c}}{a \sqrt[4]{c} x+b \sqrt[4]{c}-\sqrt{2} \sqrt[4]{d} \sqrt{p x^3+q}}\right)}{\sqrt{2} c^{3/4} \sqrt[4]{d}}-\frac{\tan ^{-1}\left(\frac{a \sqrt[4]{c} x+b \sqrt[4]{c}}{a \sqrt[4]{c} x+b \sqrt[4]{c}+\sqrt{2} \sqrt[4]{d} \sqrt{p x^3+q}}\right)}{\sqrt{2} c^{3/4} \sqrt[4]{d}}",1,"Result too large to show","C",0
2783,0,0,267,9.3362806,"\int \frac{\left(1+x^2\right) \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2 \sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[((1 + x^2)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/((1 - x^2)^2*Sqrt[x + Sqrt[1 + x^2]]),x]","\int \frac{\left(1+x^2\right) \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2 \sqrt{x+\sqrt{1+x^2}}} \, dx","-\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]-\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+4 \text{$\#$1}^3-2 \text{$\#$1}}\&\right]-\frac{\sqrt{\sqrt{\sqrt{x^2+1}+x}+1} x}{\left(x^2-1\right) \sqrt{\sqrt{x^2+1}+x}}",1,"Integrate[((1 + x^2)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/((1 - x^2)^2*Sqrt[x + Sqrt[1 + x^2]]), x]","F",-1
2784,0,0,267,0.2442521,"\int \frac{\left(1+x^2\right) \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2 \sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[((1 + x^2)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/((1 - x^2)^2*Sqrt[x + Sqrt[1 + x^2]]),x]","\int \frac{\left(1+x^2\right) \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2 \sqrt{x+\sqrt{1+x^2}}} \, dx","-\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]-\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+4 \text{$\#$1}^3-2 \text{$\#$1}}\&\right]-\frac{\sqrt{\sqrt{\sqrt{x^2+1}+x}+1} x}{\left(x^2-1\right) \sqrt{\sqrt{x^2+1}+x}}",1,"Integrate[((1 + x^2)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/((1 - x^2)^2*Sqrt[x + Sqrt[1 + x^2]]), x]","F",-1
2785,1,13957,268,18.6690498,"\int \frac{-1+k^4 x^4}{\sqrt{(1-x) x \left(1-k^2 x\right)} \left(a+b x^2+a k^4 x^4\right)} \, dx","Integrate[(-1 + k^4*x^4)/(Sqrt[(1 - x)*x*(1 - k^2*x)]*(a + b*x^2 + a*k^4*x^4)),x]","\text{Result too large to show}","-\frac{\tan ^{-1}\left(\frac{\sqrt{k^2 x^3+\left(-k^2-1\right) x^2+x} \sqrt{-\sqrt{a} \sqrt{2 a k^2-b}+a k^2+a}}{\sqrt{a} (x-1) \left(k^2 x-1\right)}\right)}{\sqrt{a} \sqrt{-\sqrt{a} \sqrt{2 a k^2-b}+a k^2+a}}-\frac{\sqrt{\sqrt{a} \left(\sqrt{2 a k^2-b}+\sqrt{a} k^2+\sqrt{a}\right)} \tan ^{-1}\left(\frac{\sqrt{k^2 x^3+\left(-k^2-1\right) x^2+x} \sqrt{\sqrt{a} \sqrt{2 a k^2-b}+a k^2+a}}{\sqrt{a} (x-1) \left(k^2 x-1\right)}\right)}{a \left(\sqrt{2 a k^2-b}+\sqrt{a} k^2+\sqrt{a}\right)}",1,"Result too large to show","C",0
2786,1,738,268,1.8834408,"\int \frac{x^5 (-4 a+3 x)}{\sqrt[3]{x^2 (-a+x)} \left(-a^2+2 a x-x^2+d x^8\right)} \, dx","Integrate[(x^5*(-4*a + 3*x))/((x^2*(-a + x))^(1/3)*(-a^2 + 2*a*x - x^2 + d*x^8)),x]","-\frac{a^4 x \left(4 \text{RootSum}\left[\text{$\#$1}^8 a^6 d-\text{$\#$1}^6+6 \text{$\#$1}^5-15 \text{$\#$1}^4+20 \text{$\#$1}^3-15 \text{$\#$1}^2+6 \text{$\#$1}-1\&,\frac{-2 \text{$\#$1}^{13/3} \log \left(\sqrt[3]{\text{$\#$1}}-\sqrt[3]{\frac{x}{x-a}}\right)+\text{$\#$1}^{13/3} \log \left(\text{$\#$1}^{2/3}+\sqrt[3]{\text{$\#$1}} \sqrt[3]{\frac{x}{x-a}}+\left(\frac{x}{x-a}\right)^{2/3}\right)+2 \sqrt{3} \text{$\#$1}^{13/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{\frac{x}{x-a}}}{\sqrt[3]{\text{$\#$1}}}+1}{\sqrt{3}}\right)-6 \text{$\#$1}^4 \sqrt[3]{\frac{x}{x-a}}}{4 \text{$\#$1}^7 a^6 d-3 \text{$\#$1}^5+15 \text{$\#$1}^4-30 \text{$\#$1}^3+30 \text{$\#$1}^2-15 \text{$\#$1}+3}\&\right]-5 \text{RootSum}\left[\text{$\#$1}^8 a^6 d-\text{$\#$1}^6+6 \text{$\#$1}^5-15 \text{$\#$1}^4+20 \text{$\#$1}^3-15 \text{$\#$1}^2+6 \text{$\#$1}-1\&,\frac{-2 \text{$\#$1}^{16/3} \log \left(\sqrt[3]{\text{$\#$1}}-\sqrt[3]{\frac{x}{x-a}}\right)+\text{$\#$1}^{16/3} \log \left(\text{$\#$1}^{2/3}+\sqrt[3]{\text{$\#$1}} \sqrt[3]{\frac{x}{x-a}}+\left(\frac{x}{x-a}\right)^{2/3}\right)+2 \sqrt{3} \text{$\#$1}^{16/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{\frac{x}{x-a}}}{\sqrt[3]{\text{$\#$1}}}+1}{\sqrt{3}}\right)-6 \text{$\#$1}^5 \sqrt[3]{\frac{x}{x-a}}}{4 \text{$\#$1}^7 a^6 d-3 \text{$\#$1}^5+15 \text{$\#$1}^4-30 \text{$\#$1}^3+30 \text{$\#$1}^2-15 \text{$\#$1}+3}\&\right]+\text{RootSum}\left[\text{$\#$1}^8 a^6 d-\text{$\#$1}^6+6 \text{$\#$1}^5-15 \text{$\#$1}^4+20 \text{$\#$1}^3-15 \text{$\#$1}^2+6 \text{$\#$1}-1\&,\frac{-2 \text{$\#$1}^{19/3} \log \left(\sqrt[3]{\text{$\#$1}}-\sqrt[3]{\frac{x}{x-a}}\right)+\text{$\#$1}^{19/3} \log \left(\text{$\#$1}^{2/3}+\sqrt[3]{\text{$\#$1}} \sqrt[3]{\frac{x}{x-a}}+\left(\frac{x}{x-a}\right)^{2/3}\right)+2 \sqrt{3} \text{$\#$1}^{19/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{\frac{x}{x-a}}}{\sqrt[3]{\text{$\#$1}}}+1}{\sqrt{3}}\right)-6 \text{$\#$1}^6 \sqrt[3]{\frac{x}{x-a}}}{4 \text{$\#$1}^7 a^6 d-3 \text{$\#$1}^5+15 \text{$\#$1}^4-30 \text{$\#$1}^3+30 \text{$\#$1}^2-15 \text{$\#$1}+3}\&\right]\right)}{4 \sqrt[3]{\frac{x}{x-a}} \sqrt[3]{x^2 (x-a)}}","-\frac{\log \left(a^2 \sqrt[3]{d} x^4-a^2 \sqrt[6]{d} x^2 \sqrt[3]{x^3-a x^2}+a^2 \left(x^3-a x^2\right)^{2/3}\right)}{4 d^{2/3}}-\frac{\log \left(a^2 \sqrt[3]{d} x^4+a^2 \sqrt[6]{d} x^2 \sqrt[3]{x^3-a x^2}+a^2 \left(x^3-a x^2\right)^{2/3}\right)}{4 d^{2/3}}+\frac{\log \left(a \sqrt[3]{x^3-a x^2}-a \sqrt[6]{d} x^2\right)}{2 d^{2/3}}+\frac{\log \left(a \sqrt[6]{d} x^2+a \sqrt[3]{x^3-a x^2}\right)}{2 d^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} x^4}{2 \left(x^3-a x^2\right)^{2/3}+\sqrt[3]{d} x^4}\right)}{2 d^{2/3}}",1,"-1/4*(a^4*x*(4*RootSum[-1 + 6*#1 - 15*#1^2 + 20*#1^3 - 15*#1^4 + 6*#1^5 - #1^6 + a^6*d*#1^8 & , (-6*(x/(-a + x))^(1/3)*#1^4 + 2*Sqrt[3]*ArcTan[(1 + (2*(x/(-a + x))^(1/3))/#1^(1/3))/Sqrt[3]]*#1^(13/3) - 2*Log[-(x/(-a + x))^(1/3) + #1^(1/3)]*#1^(13/3) + Log[(x/(-a + x))^(2/3) + (x/(-a + x))^(1/3)*#1^(1/3) + #1^(2/3)]*#1^(13/3))/(3 - 15*#1 + 30*#1^2 - 30*#1^3 + 15*#1^4 - 3*#1^5 + 4*a^6*d*#1^7) & ] - 5*RootSum[-1 + 6*#1 - 15*#1^2 + 20*#1^3 - 15*#1^4 + 6*#1^5 - #1^6 + a^6*d*#1^8 & , (-6*(x/(-a + x))^(1/3)*#1^5 + 2*Sqrt[3]*ArcTan[(1 + (2*(x/(-a + x))^(1/3))/#1^(1/3))/Sqrt[3]]*#1^(16/3) - 2*Log[-(x/(-a + x))^(1/3) + #1^(1/3)]*#1^(16/3) + Log[(x/(-a + x))^(2/3) + (x/(-a + x))^(1/3)*#1^(1/3) + #1^(2/3)]*#1^(16/3))/(3 - 15*#1 + 30*#1^2 - 30*#1^3 + 15*#1^4 - 3*#1^5 + 4*a^6*d*#1^7) & ] + RootSum[-1 + 6*#1 - 15*#1^2 + 20*#1^3 - 15*#1^4 + 6*#1^5 - #1^6 + a^6*d*#1^8 & , (-6*(x/(-a + x))^(1/3)*#1^6 + 2*Sqrt[3]*ArcTan[(1 + (2*(x/(-a + x))^(1/3))/#1^(1/3))/Sqrt[3]]*#1^(19/3) - 2*Log[-(x/(-a + x))^(1/3) + #1^(1/3)]*#1^(19/3) + Log[(x/(-a + x))^(2/3) + (x/(-a + x))^(1/3)*#1^(1/3) + #1^(2/3)]*#1^(19/3))/(3 - 15*#1 + 30*#1^2 - 30*#1^3 + 15*#1^4 - 3*#1^5 + 4*a^6*d*#1^7) & ]))/((x/(-a + x))^(1/3)*(x^2*(-a + x))^(1/3))","C",1
2787,1,23,269,0.0130873,"\int \frac{\sqrt{1-x}}{8 (1+x)^{7/2}} \, dx","Integrate[Sqrt[1 - x]/(8*(1 + x)^(7/2)),x]","-\frac{(1-x)^{3/2} (x+4)}{120 (x+1)^{5/2}}","\frac{\left(\frac{1}{960}-\frac{\sqrt{1-x}}{960}\right) \left(\sqrt{x+1}-1\right)^9 \left(\frac{15 \left(\sqrt{1-x}-1\right)^8}{\left(\sqrt{x+1}-1\right)^8}-\frac{30 \left(\sqrt{1-x}-1\right)^7}{\left(\sqrt{x+1}-1\right)^7}+\frac{40 \left(\sqrt{1-x}-1\right)^6}{\left(\sqrt{x+1}-1\right)^6}+\frac{50 \left(\sqrt{1-x}-1\right)^5}{\left(\sqrt{x+1}-1\right)^5}-\frac{46 \left(\sqrt{1-x}-1\right)^4}{\left(\sqrt{x+1}-1\right)^4}-\frac{50 \left(\sqrt{1-x}-1\right)^3}{\left(\sqrt{x+1}-1\right)^3}+\frac{40 \left(\sqrt{1-x}-1\right)^2}{\left(\sqrt{x+1}-1\right)^2}+\frac{30 \sqrt{1-x}-30}{\sqrt{x+1}-1}+15\right)}{\left(x+\sqrt{1-x} \sqrt{x+1}-2 \sqrt{x+1}+1\right)^5}",1,"-1/120*((1 - x)^(3/2)*(4 + x))/(1 + x)^(5/2)","A",1
2788,0,0,269,3.3892511,"\int \frac{2 a b^2-b (2 a+b) x+x^3}{\sqrt[3]{x (-a+x) (-b+x)^2} \left(-a b^2 d+b (2 a+b) d x-(1+a d+2 b d) x^2+d x^3\right)} \, dx","Integrate[(2*a*b^2 - b*(2*a + b)*x + x^3)/((x*(-a + x)*(-b + x)^2)^(1/3)*(-(a*b^2*d) + b*(2*a + b)*d*x - (1 + a*d + 2*b*d)*x^2 + d*x^3)),x]","\int \frac{2 a b^2-b (2 a+b) x+x^3}{\sqrt[3]{x (-a+x) (-b+x)^2} \left(-a b^2 d+b (2 a+b) d x-(1+a d+2 b d) x^2+d x^3\right)} \, dx","\frac{\log \left(x-\sqrt[3]{d} \sqrt[3]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}\right)}{d^{2/3}}-\frac{\log \left(d^{2/3} \left(x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4\right)^{2/3}+\sqrt[3]{d} x \sqrt[3]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}+x^2\right)}{2 d^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} \sqrt[3]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}}{\sqrt[3]{d} \sqrt[3]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}+2 x}\right)}{d^{2/3}}",1,"Integrate[(2*a*b^2 - b*(2*a + b)*x + x^3)/((x*(-a + x)*(-b + x)^2)^(1/3)*(-(a*b^2*d) + b*(2*a + b)*d*x - (1 + a*d + 2*b*d)*x^2 + d*x^3)), x]","F",-1
2789,1,226,269,0.190397,"\int \frac{\left(-x+x^2\right) \sqrt[4]{-x^3+x^4}}{-1-x+x^2} \, dx","Integrate[((-x + x^2)*(-x^3 + x^4)^(1/4))/(-1 - x + x^2),x]","\frac{2 \sqrt[4]{(x-1) x^3} \left(10 \sqrt[4]{x} \, _2F_1\left(-\frac{7}{4},\frac{1}{4};\frac{5}{4};1-x\right)-10 \sqrt[4]{x} \, _2F_1\left(-\frac{3}{4},\frac{1}{4};\frac{5}{4};1-x\right)+10 \sqrt[4]{x} \, _2F_1\left(\frac{1}{4},\frac{1}{4};\frac{5}{4};1-x\right)+\sqrt{5} \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{\left(-1+\sqrt{5}\right) (x-1)}{\left(1+\sqrt{5}\right) x}\right)-5 \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{\left(-1+\sqrt{5}\right) (x-1)}{\left(1+\sqrt{5}\right) x}\right)-\sqrt{5} \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{\left(1+\sqrt{5}\right) (x-1)}{\left(-1+\sqrt{5}\right) x}\right)-5 \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{\left(1+\sqrt{5}\right) (x-1)}{\left(-1+\sqrt{5}\right) x}\right)\right)}{5 x}","\frac{1}{8} \sqrt[4]{x^4-x^3} (4 x-1)-\frac{29}{16} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^3}}\right)+\sqrt{\frac{1}{5} \left(2+2 \sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}} x}{\sqrt[4]{x^4-x^3}}\right)+\sqrt{\frac{1}{5} \left(2 \sqrt{5}-2\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{1}{2}+\frac{\sqrt{5}}{2}} x}{\sqrt[4]{x^4-x^3}}\right)+\frac{29}{16} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^3}}\right)-\sqrt{\frac{1}{5} \left(2+2 \sqrt{5}\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}} x}{\sqrt[4]{x^4-x^3}}\right)-\sqrt{\frac{1}{5} \left(2 \sqrt{5}-2\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{2}+\frac{\sqrt{5}}{2}} x}{\sqrt[4]{x^4-x^3}}\right)",1,"(2*((-1 + x)*x^3)^(1/4)*(10*x^(1/4)*Hypergeometric2F1[-7/4, 1/4, 5/4, 1 - x] - 10*x^(1/4)*Hypergeometric2F1[-3/4, 1/4, 5/4, 1 - x] + 10*x^(1/4)*Hypergeometric2F1[1/4, 1/4, 5/4, 1 - x] - 5*Hypergeometric2F1[1/4, 1, 5/4, ((-1 + Sqrt[5])*(-1 + x))/((1 + Sqrt[5])*x)] + Sqrt[5]*Hypergeometric2F1[1/4, 1, 5/4, ((-1 + Sqrt[5])*(-1 + x))/((1 + Sqrt[5])*x)] - 5*Hypergeometric2F1[1/4, 1, 5/4, ((1 + Sqrt[5])*(-1 + x))/((-1 + Sqrt[5])*x)] - Sqrt[5]*Hypergeometric2F1[1/4, 1, 5/4, ((1 + Sqrt[5])*(-1 + x))/((-1 + Sqrt[5])*x)]))/(5*x)","C",1
2790,0,0,269,9.0372842,"\int \frac{\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}}{x \sqrt{d+\sqrt{c+\sqrt{b+a x}}}} \, dx","Integrate[(Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]])/(x*Sqrt[d + Sqrt[c + Sqrt[b + a*x]]]),x]","\int \frac{\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}}{x \sqrt{d+\sqrt{c+\sqrt{b+a x}}}} \, dx","-b \text{RootSum}\left[-\text{$\#$1}^8+4 \text{$\#$1}^6 d+2 \text{$\#$1}^4 c-6 \text{$\#$1}^4 d^2-4 \text{$\#$1}^2 c d+4 \text{$\#$1}^2 d^3+b-c^2+2 c d^2-d^4\&,\frac{d \log \left(\sqrt{\sqrt{\sqrt{a x+b}+c}+d}-\text{$\#$1}\right)-\text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{a x+b}+c}+d}-\text{$\#$1}\right)}{\text{$\#$1}^5-2 \text{$\#$1}^3 d-\text{$\#$1} c+\text{$\#$1} d^2}\&\right]+\frac{8}{15} \left(3 c+8 d^2\right) \sqrt{\sqrt{\sqrt{a x+b}+c}+d}-\frac{32}{15} d \sqrt{\sqrt{a x+b}+c} \sqrt{\sqrt{\sqrt{a x+b}+c}+d}+\frac{8}{5} \sqrt{a x+b} \sqrt{\sqrt{\sqrt{a x+b}+c}+d}",1,"Integrate[(Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]])/(x*Sqrt[d + Sqrt[c + Sqrt[b + a*x]]]), x]","F",-1
2791,0,0,269,1.8272957,"\int \frac{\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}}{x \sqrt{d+\sqrt{c+\sqrt{b+a x}}}} \, dx","Integrate[(Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]])/(x*Sqrt[d + Sqrt[c + Sqrt[b + a*x]]]),x]","\int \frac{\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}}{x \sqrt{d+\sqrt{c+\sqrt{b+a x}}}} \, dx","-b \text{RootSum}\left[-\text{$\#$1}^8+4 \text{$\#$1}^6 d+2 \text{$\#$1}^4 c-6 \text{$\#$1}^4 d^2-4 \text{$\#$1}^2 c d+4 \text{$\#$1}^2 d^3+b-c^2+2 c d^2-d^4\&,\frac{d \log \left(\sqrt{\sqrt{\sqrt{a x+b}+c}+d}-\text{$\#$1}\right)-\text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{a x+b}+c}+d}-\text{$\#$1}\right)}{\text{$\#$1}^5-2 \text{$\#$1}^3 d-\text{$\#$1} c+\text{$\#$1} d^2}\&\right]+\frac{8}{15} \left(3 c+8 d^2\right) \sqrt{\sqrt{\sqrt{a x+b}+c}+d}-\frac{32}{15} d \sqrt{\sqrt{a x+b}+c} \sqrt{\sqrt{\sqrt{a x+b}+c}+d}+\frac{8}{5} \sqrt{a x+b} \sqrt{\sqrt{\sqrt{a x+b}+c}+d}",1,"Integrate[(Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]])/(x*Sqrt[d + Sqrt[c + Sqrt[b + a*x]]]), x]","F",-1
2792,1,188,269,1.2285143,"\int \frac{1}{\sqrt{1+\sqrt{a x+\sqrt{-b+a^2 x^2}}}} \, dx","Integrate[1/Sqrt[1 + Sqrt[a*x + Sqrt[-b + a^2*x^2]]],x]","\frac{2 \sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+1} \left(-\frac{9 b}{\sqrt{\sqrt{a^2 x^2-b}+a x}}+\frac{6 b}{\sqrt{a^2 x^2-b}+a x}+8 \sqrt{\sqrt{a^2 x^2-b}+a x}-16\right)-9 b \log \left(1-\frac{1}{\sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+1}}\right)+9 b \log \left(\frac{1}{\sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+1}}+1\right)}{24 a}","\frac{\sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+1} (6 b-16 a x)+\sqrt{a^2 x^2-b} \left(8 \sqrt{\sqrt{a^2 x^2-b}+a x} \sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+1}-16 \sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+1}\right)+(8 a x-9 b) \sqrt{\sqrt{a^2 x^2-b}+a x} \sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+1}}{12 a \sqrt{a^2 x^2-b}+12 a^2 x}+\frac{3 b \tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+1}\right)}{4 a}",1,"(2*Sqrt[1 + Sqrt[a*x + Sqrt[-b + a^2*x^2]]]*(-16 + (6*b)/(a*x + Sqrt[-b + a^2*x^2]) - (9*b)/Sqrt[a*x + Sqrt[-b + a^2*x^2]] + 8*Sqrt[a*x + Sqrt[-b + a^2*x^2]]) - 9*b*Log[1 - 1/Sqrt[1 + Sqrt[a*x + Sqrt[-b + a^2*x^2]]]] + 9*b*Log[1 + 1/Sqrt[1 + Sqrt[a*x + Sqrt[-b + a^2*x^2]]]])/(24*a)","A",1
2793,0,0,270,3.9043757,"\int \frac{(-1+x) (-1+k x) \left(-2 x+(1+k) x^2\right)}{((1-x) x (1-k x))^{2/3} \left(b-2 b (1+k) x+\left(b+4 b k+b k^2\right) x^2-2 b k (1+k) x^3+\left(-1+b k^2\right) x^4\right)} \, dx","Integrate[((-1 + x)*(-1 + k*x)*(-2*x + (1 + k)*x^2))/(((1 - x)*x*(1 - k*x))^(2/3)*(b - 2*b*(1 + k)*x + (b + 4*b*k + b*k^2)*x^2 - 2*b*k*(1 + k)*x^3 + (-1 + b*k^2)*x^4)),x]","\int \frac{(-1+x) (-1+k x) \left(-2 x+(1+k) x^2\right)}{((1-x) x (1-k x))^{2/3} \left(b-2 b (1+k) x+\left(b+4 b k+b k^2\right) x^2-2 b k (1+k) x^3+\left(-1+b k^2\right) x^4\right)} \, dx","\frac{\log \left(x-\sqrt[6]{b} \sqrt[3]{k x^3+(-k-1) x^2+x}\right)}{2 b^{2/3}}+\frac{\log \left(\sqrt[6]{b} \sqrt[3]{k x^3+(-k-1) x^2+x}+x\right)}{2 b^{2/3}}-\frac{\log \left(-\sqrt[6]{b} x \sqrt[3]{k x^3+(-k-1) x^2+x}+\sqrt[3]{b} \left(k x^3+(-k-1) x^2+x\right)^{2/3}+x^2\right)}{4 b^{2/3}}-\frac{\log \left(\sqrt[6]{b} x \sqrt[3]{k x^3+(-k-1) x^2+x}+\sqrt[3]{b} \left(k x^3+(-k-1) x^2+x\right)^{2/3}+x^2\right)}{4 b^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x^2}{2 \sqrt[3]{b} \left(k x^3+(-k-1) x^2+x\right)^{2/3}+x^2}\right)}{2 b^{2/3}}",1,"Integrate[((-1 + x)*(-1 + k*x)*(-2*x + (1 + k)*x^2))/(((1 - x)*x*(1 - k*x))^(2/3)*(b - 2*b*(1 + k)*x + (b + 4*b*k + b*k^2)*x^2 - 2*b*k*(1 + k)*x^3 + (-1 + b*k^2)*x^4)), x]","F",-1
2794,0,0,270,1.5479046,"\int \frac{\left(-1+2 (-2+k) x+3 k x^2\right) \left(-1+3 x-3 x^2+x^3\right)}{((1-x) x (1-k x))^{2/3} \left(-b+(1+5 b) x-(10 b+k) x^2+10 b x^3-5 b x^4+b x^5\right)} \, dx","Integrate[((-1 + 2*(-2 + k)*x + 3*k*x^2)*(-1 + 3*x - 3*x^2 + x^3))/(((1 - x)*x*(1 - k*x))^(2/3)*(-b + (1 + 5*b)*x - (10*b + k)*x^2 + 10*b*x^3 - 5*b*x^4 + b*x^5)),x]","\int \frac{\left(-1+2 (-2+k) x+3 k x^2\right) \left(-1+3 x-3 x^2+x^3\right)}{((1-x) x (1-k x))^{2/3} \left(-b+(1+5 b) x-(10 b+k) x^2+10 b x^3-5 b x^4+b x^5\right)} \, dx","\frac{\log \left(-\sqrt[3]{b} x^2+2 \sqrt[3]{b} x-\sqrt[3]{b}+\sqrt[3]{k x^3+(-k-1) x^2+x}\right)}{b^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{b} x^2-2 \sqrt{3} \sqrt[3]{b} x+\sqrt{3} \sqrt[3]{b}}{\sqrt[3]{b} x^2-2 \sqrt[3]{b} x+\sqrt[3]{b}+2 \sqrt[3]{k x^3+(-k-1) x^2+x}}\right)}{b^{2/3}}-\frac{\log \left(b^{2/3} x^4-4 b^{2/3} x^3+6 b^{2/3} x^2-4 b^{2/3} x+b^{2/3}+\left(\sqrt[3]{b} x^2-2 \sqrt[3]{b} x+\sqrt[3]{b}\right) \sqrt[3]{k x^3+(-k-1) x^2+x}+\left(k x^3+(-k-1) x^2+x\right)^{2/3}\right)}{2 b^{2/3}}",1,"Integrate[((-1 + 2*(-2 + k)*x + 3*k*x^2)*(-1 + 3*x - 3*x^2 + x^3))/(((1 - x)*x*(1 - k*x))^(2/3)*(-b + (1 + 5*b)*x - (10*b + k)*x^2 + 10*b*x^3 - 5*b*x^4 + b*x^5)), x]","F",-1
2795,0,0,270,10.2010389,"\int \frac{\sqrt[4]{2 b+a x^4} \left(-4 b+a x^8\right)}{x^6 \left(-4 b+c x^4+a x^8\right)} \, dx","Integrate[((2*b + a*x^4)^(1/4)*(-4*b + a*x^8))/(x^6*(-4*b + c*x^4 + a*x^8)),x]","\int \frac{\sqrt[4]{2 b+a x^4} \left(-4 b+a x^8\right)}{x^6 \left(-4 b+c x^4+a x^8\right)} \, dx","\frac{\sqrt[4]{a x^4+2 b} \left(-2 a x^4-4 b-5 c x^4\right)}{20 b x^5}-\frac{c \text{RootSum}\left[2 \text{$\#$1}^8-4 \text{$\#$1}^4 a-\text{$\#$1}^4 c+2 a^2-2 a b+a c\&,\frac{-\text{$\#$1}^4 c \log \left(\sqrt[4]{a x^4+2 b}-\text{$\#$1} x\right)-2 \text{$\#$1}^4 a \log \left(\sqrt[4]{a x^4+2 b}-\text{$\#$1} x\right)+2 \text{$\#$1}^4 a \log (x)+\text{$\#$1}^4 c \log (x)+2 a^2 \log \left(\sqrt[4]{a x^4+2 b}-\text{$\#$1} x\right)+a c \log \left(\sqrt[4]{a x^4+2 b}-\text{$\#$1} x\right)-2 a b \log \left(\sqrt[4]{a x^4+2 b}-\text{$\#$1} x\right)-2 a^2 \log (x)+2 a b \log (x)-a c \log (x)}{-4 \text{$\#$1}^7+4 \text{$\#$1}^3 a+\text{$\#$1}^3 c}\&\right]}{16 b}",1,"Integrate[((2*b + a*x^4)^(1/4)*(-4*b + a*x^8))/(x^6*(-4*b + c*x^4 + a*x^8)), x]","F",-1
2796,0,0,270,9.8061771,"\int \frac{\sqrt[4]{2 b+a x^4} \left(-4 b+a x^8\right)}{x^6 \left(-4 b+c x^4+a x^8\right)} \, dx","Integrate[((2*b + a*x^4)^(1/4)*(-4*b + a*x^8))/(x^6*(-4*b + c*x^4 + a*x^8)),x]","\int \frac{\sqrt[4]{2 b+a x^4} \left(-4 b+a x^8\right)}{x^6 \left(-4 b+c x^4+a x^8\right)} \, dx","\frac{\sqrt[4]{a x^4+2 b} \left(-2 a x^4-4 b-5 c x^4\right)}{20 b x^5}-\frac{c \text{RootSum}\left[2 \text{$\#$1}^8-4 \text{$\#$1}^4 a-\text{$\#$1}^4 c+2 a^2-2 a b+a c\&,\frac{-\text{$\#$1}^4 c \log \left(\sqrt[4]{a x^4+2 b}-\text{$\#$1} x\right)-2 \text{$\#$1}^4 a \log \left(\sqrt[4]{a x^4+2 b}-\text{$\#$1} x\right)+2 \text{$\#$1}^4 a \log (x)+\text{$\#$1}^4 c \log (x)+2 a^2 \log \left(\sqrt[4]{a x^4+2 b}-\text{$\#$1} x\right)+a c \log \left(\sqrt[4]{a x^4+2 b}-\text{$\#$1} x\right)-2 a b \log \left(\sqrt[4]{a x^4+2 b}-\text{$\#$1} x\right)-2 a^2 \log (x)+2 a b \log (x)-a c \log (x)}{-4 \text{$\#$1}^7+4 \text{$\#$1}^3 a+\text{$\#$1}^3 c}\&\right]}{16 b}",1,"Integrate[((2*b + a*x^4)^(1/4)*(-4*b + a*x^8))/(x^6*(-4*b + c*x^4 + a*x^8)), x]","F",-1
2797,1,276,270,1.7985282,"\int \frac{-b^{12}+a^{12} x^{12}}{\sqrt{-b^4+a^4 x^4} \left(b^{12}+a^{12} x^{12}\right)} \, dx","Integrate[(-b^12 + a^12*x^12)/(Sqrt[-b^4 + a^4*x^4]*(b^12 + a^12*x^12)),x]","-\frac{i \sqrt{1-\frac{a^4 x^4}{b^4}} \left(3 F\left(\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)-\Pi \left(-i;\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)-\Pi \left(i;\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)-\Pi \left(-\frac{i}{2}-\frac{\sqrt{3}}{2};\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)-\Pi \left(\frac{i}{2}-\frac{\sqrt{3}}{2};\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)-\Pi \left(\frac{1}{2} \left(-i+\sqrt{3}\right);\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)-\Pi \left(\frac{1}{2} \left(i+\sqrt{3}\right);\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)\right)}{3 \sqrt{-\frac{a^2}{b^2}} \sqrt{a^4 x^4-b^4}}","-\frac{\tan ^{-1}\left(\frac{-\frac{a^3 x^4}{2 b}+\frac{b^3}{2 a}+a b x^2}{x \sqrt{a^4 x^4-b^4}}\right)}{12 a b}+\frac{\tanh ^{-1}\left(\frac{-\frac{a^3 x^4}{2 b}+\frac{b^3}{2 a}-a b x^2}{x \sqrt{a^4 x^4-b^4}}\right)}{12 a b}+\frac{\tanh ^{-1}\left(\frac{-\frac{a^3 x^4}{\sqrt{2} b}+\frac{b^3}{\sqrt{2} a}-\frac{a b x^2}{\sqrt{2}}}{x \sqrt{a^4 x^4-b^4}}\right)}{3 \sqrt{2} a b}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} a b x \sqrt{a^4 x^4-b^4}}{-a^4 x^4+a^2 b^2 x^2+b^4}\right)}{3 \sqrt{2} a b}",1,"((-1/3*I)*Sqrt[1 - (a^4*x^4)/b^4]*(3*EllipticF[I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1] - EllipticPi[-I, I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1] - EllipticPi[I, I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1] - EllipticPi[-1/2*I - Sqrt[3]/2, I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1] - EllipticPi[I/2 - Sqrt[3]/2, I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1] - EllipticPi[(-I + Sqrt[3])/2, I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1] - EllipticPi[(I + Sqrt[3])/2, I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1]))/(Sqrt[-(a^2/b^2)]*Sqrt[-b^4 + a^4*x^4])","C",1
2798,0,0,270,0.4074269,"\int \frac{1}{1-(1+x) \sqrt{c+b x+a x^2}} \, dx","Integrate[(1 - (1 + x)*Sqrt[c + b*x + a*x^2])^(-1),x]","\int \frac{1}{1-(1+x) \sqrt{c+b x+a x^2}} \, dx","2 \text{RootSum}\left[\text{$\#$1}^4 \left(-\sqrt{a}\right)+2 \text{$\#$1}^3 a+\text{$\#$1}^3 b-3 \text{$\#$1}^2 \sqrt{a} b-4 \text{$\#$1}^2 a+4 \text{$\#$1} \sqrt{a} b+2 \text{$\#$1} a c+\text{$\#$1} b^2-\text{$\#$1} b c-\sqrt{a} b c+\sqrt{a} c^2-b^2\&,\frac{\text{$\#$1}^2 \sqrt{a} \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)-\text{$\#$1} b \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)+\sqrt{a} c \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)}{-4 \text{$\#$1}^3 \sqrt{a}+6 \text{$\#$1}^2 a+3 \text{$\#$1}^2 b-6 \text{$\#$1} \sqrt{a} b-8 \text{$\#$1} a+4 \sqrt{a} b+2 a c+b^2-b c}\&\right]",1,"Integrate[(1 - (1 + x)*Sqrt[c + b*x + a*x^2])^(-1), x]","F",-1
2799,1,135,271,0.238218,"\int \frac{\left(1-x^4\right) \sqrt[4]{1-x-4 x^2+4 x^3+6 x^4-6 x^5-4 x^6+4 x^7+x^8-x^9}}{1+x^4} \, dx","Integrate[((1 - x^4)*(1 - x - 4*x^2 + 4*x^3 + 6*x^4 - 6*x^5 - 4*x^6 + 4*x^7 + x^8 - x^9)^(1/4))/(1 + x^4),x]","-\frac{\sqrt[4]{-(x-1)^5 (x+1)^4} \left(8 (x-1)^{9/4} (9 x+17)-117 \text{RootSum}\left[\text{$\#$1}^{16}+4 \text{$\#$1}^{12}+6 \text{$\#$1}^8+4 \text{$\#$1}^4+2\&,\frac{\text{$\#$1}^9 \log \left(\sqrt[4]{x-1}-\text{$\#$1}\right)+2 \text{$\#$1}^5 \log \left(\sqrt[4]{x-1}-\text{$\#$1}\right)}{\text{$\#$1}^{12}+3 \text{$\#$1}^8+3 \text{$\#$1}^4+1}\&\right]\right)}{234 (x-1)^{5/4} (x+1)}","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^{16}-4 \text{$\#$1}^{12}+6 \text{$\#$1}^8-4 \text{$\#$1}^4+2\&,\frac{\text{$\#$1}^9 \left(-\log \left(x^2-1\right)\right)+\text{$\#$1}^9 \log \left(-\text{$\#$1} x^2+\text{$\#$1}+\sqrt[4]{-x^9+x^8+4 x^7-4 x^6-6 x^5+6 x^4+4 x^3-4 x^2-x+1}\right)+2 \text{$\#$1}^5 \log \left(x^2-1\right)-2 \text{$\#$1}^5 \log \left(-\text{$\#$1} x^2+\text{$\#$1}+\sqrt[4]{-x^9+x^8+4 x^7-4 x^6-6 x^5+6 x^4+4 x^3-4 x^2-x+1}\right)}{\text{$\#$1}^{12}-3 \text{$\#$1}^8+3 \text{$\#$1}^4-1}\&\right]-\frac{4 \sqrt[4]{-x^9+x^8+4 x^7-4 x^6-6 x^5+6 x^4+4 x^3-4 x^2-x+1} \left(9 x^2+8 x-17\right)}{117 (x+1)}",1,"-1/234*((-((-1 + x)^5*(1 + x)^4))^(1/4)*(8*(-1 + x)^(9/4)*(17 + 9*x) - 117*RootSum[2 + 4*#1^4 + 6*#1^8 + 4*#1^12 + #1^16 & , (2*Log[(-1 + x)^(1/4) - #1]*#1^5 + Log[(-1 + x)^(1/4) - #1]*#1^9)/(1 + 3*#1^4 + 3*#1^8 + #1^12) & ]))/((-1 + x)^(5/4)*(1 + x))","A",1
2800,0,0,272,4.3522946,"\int \frac{-a (a-5 b)-(3 a+5 b) x+4 x^2}{\sqrt[3]{(-a+x) (-b+x)} \left(b-a^5 d-\left(1-5 a^4 d\right) x-10 a^3 d x^2+10 a^2 d x^3-5 a d x^4+d x^5\right)} \, dx","Integrate[(-(a*(a - 5*b)) - (3*a + 5*b)*x + 4*x^2)/(((-a + x)*(-b + x))^(1/3)*(b - a^5*d - (1 - 5*a^4*d)*x - 10*a^3*d*x^2 + 10*a^2*d*x^3 - 5*a*d*x^4 + d*x^5)),x]","\int \frac{-a (a-5 b)-(3 a+5 b) x+4 x^2}{\sqrt[3]{(-a+x) (-b+x)} \left(b-a^5 d-\left(1-5 a^4 d\right) x-10 a^3 d x^2+10 a^2 d x^3-5 a d x^4+d x^5\right)} \, dx","\frac{\log \left(a^2 \sqrt{d}-\sqrt[6]{d} \sqrt[3]{x (-a-b)+a b+x^2}-2 a \sqrt{d} x+\sqrt{d} x^2\right)}{\sqrt[3]{d}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x (-a-b)+a b+x^2}}{2 a^2 \sqrt[3]{d}+\sqrt[3]{x (-a-b)+a b+x^2}-4 a \sqrt[3]{d} x+2 \sqrt[3]{d} x^2}\right)}{\sqrt[3]{d}}-\frac{\log \left(a^4 d-4 a^3 d x+\sqrt[3]{x (-a-b)+a b+x^2} \left(a^2 d^{2/3}-2 a d^{2/3} x+d^{2/3} x^2\right)+6 a^2 d x^2+\sqrt[3]{d} \left(x (-a-b)+a b+x^2\right)^{2/3}-4 a d x^3+d x^4\right)}{2 \sqrt[3]{d}}",1,"Integrate[(-(a*(a - 5*b)) - (3*a + 5*b)*x + 4*x^2)/(((-a + x)*(-b + x))^(1/3)*(b - a^5*d - (1 - 5*a^4*d)*x - 10*a^3*d*x^2 + 10*a^2*d*x^3 - 5*a*d*x^4 + d*x^5)), x]","F",-1
2801,0,0,272,1.4679852,"\int \frac{1+x^8}{\sqrt[4]{-x^2+x^4} \left(-1+x^8\right)} \, dx","Integrate[(1 + x^8)/((-x^2 + x^4)^(1/4)*(-1 + x^8)),x]","\int \frac{1+x^8}{\sqrt[4]{-x^2+x^4} \left(-1+x^8\right)} \, dx","\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4+2\&,\frac{-3 \text{$\#$1}^4 \log \left(\sqrt[4]{x^4-x^2}-\text{$\#$1} x\right)+3 \text{$\#$1}^4 \log (x)-2 \log \left(\sqrt[4]{x^4-x^2}-\text{$\#$1} x\right)+2 \log (x)}{\text{$\#$1}^5-\text{$\#$1}}\&\right]+\frac{5}{8} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4+2\&,\frac{\text{$\#$1}^3 \log \left(\sqrt[4]{x^4-x^2}-\text{$\#$1} x\right)-\text{$\#$1}^3 \log (x)}{\text{$\#$1}^4-1}\&\right]-\frac{\left(x^4-x^2\right)^{3/4}}{x \left(x^2-1\right)}+\tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^2}}\right)-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-x^2}}\right)}{2 \sqrt[4]{2}}+\tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^2}}\right)-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-x^2}}\right)}{2 \sqrt[4]{2}}",1,"Integrate[(1 + x^8)/((-x^2 + x^4)^(1/4)*(-1 + x^8)), x]","F",-1
2802,0,0,272,0.6914313,"\int \frac{1+x^8}{\sqrt[4]{-x^2+x^4} \left(-1+x^8\right)} \, dx","Integrate[(1 + x^8)/((-x^2 + x^4)^(1/4)*(-1 + x^8)),x]","\int \frac{1+x^8}{\sqrt[4]{-x^2+x^4} \left(-1+x^8\right)} \, dx","\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4+2\&,\frac{-3 \text{$\#$1}^4 \log \left(\sqrt[4]{x^4-x^2}-\text{$\#$1} x\right)+3 \text{$\#$1}^4 \log (x)-2 \log \left(\sqrt[4]{x^4-x^2}-\text{$\#$1} x\right)+2 \log (x)}{\text{$\#$1}^5-\text{$\#$1}}\&\right]+\frac{5}{8} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4+2\&,\frac{\text{$\#$1}^3 \log \left(\sqrt[4]{x^4-x^2}-\text{$\#$1} x\right)-\text{$\#$1}^3 \log (x)}{\text{$\#$1}^4-1}\&\right]-\frac{\left(x^4-x^2\right)^{3/4}}{x \left(x^2-1\right)}+\tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^2}}\right)-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-x^2}}\right)}{2 \sqrt[4]{2}}+\tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^2}}\right)-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-x^2}}\right)}{2 \sqrt[4]{2}}",1,"Integrate[(1 + x^8)/((-x^2 + x^4)^(1/4)*(-1 + x^8)), x]","F",-1
2803,1,88,273,0.2793488,"\int \frac{a b-(a+b) x+x^2}{\left((-a+x) (-b+x)^2\right)^{2/3} \left(a^2-b^2 d-2 (a-b d) x+(1-d) x^2\right)} \, dx","Integrate[(a*b - (a + b)*x + x^2)/(((-a + x)*(-b + x)^2)^(2/3)*(a^2 - b^2*d - 2*(a - b*d)*x + (1 - d)*x^2)),x]","-\frac{3 \sqrt[3]{(x-a) (b-x)^2} \left(\, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{\sqrt{d} (b-x)}{x-a}\right)+\, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{\sqrt{d} (x-b)}{x-a}\right)\right)}{4 (a-b) (x-a)}","-\frac{\log \left(a^2+d^{2/3} \left(x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3\right)^{2/3}+\sqrt[3]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3} \left(\sqrt[3]{d} x-a \sqrt[3]{d}\right)-2 a x+x^2\right)}{4 \sqrt[3]{d} (a-b)}+\frac{\log \left(\sqrt[3]{d} \sqrt[3]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3}+a-x\right)}{2 \sqrt[3]{d} (a-b)}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} a-\sqrt{3} x}{-2 \sqrt[3]{d} \sqrt[3]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3}+a-x}\right)}{2 \sqrt[3]{d} (a-b)}",1,"(-3*((b - x)^2*(-a + x))^(1/3)*(Hypergeometric2F1[2/3, 1, 5/3, (Sqrt[d]*(b - x))/(-a + x)] + Hypergeometric2F1[2/3, 1, 5/3, (Sqrt[d]*(-b + x))/(-a + x)]))/(4*(a - b)*(-a + x))","C",1
2804,0,0,273,0.2427246,"\int \frac{\sqrt{x^2+\sqrt{1+x^4}}}{\left(-1+x^4\right) \sqrt{1+x^4}} \, dx","Integrate[Sqrt[x^2 + Sqrt[1 + x^4]]/((-1 + x^4)*Sqrt[1 + x^4]),x]","\int \frac{\sqrt{x^2+\sqrt{1+x^4}}}{\left(-1+x^4\right) \sqrt{1+x^4}} \, dx","\frac{1}{2} \sqrt{\frac{1}{2} \left(\sqrt{2}-1\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{2}-1\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)-\frac{1}{2} \sqrt{\frac{1}{2} \left(\sqrt{2}-1\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)-\frac{1}{2} \sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tanh ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{2}-1\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)-\frac{1}{2} \sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tanh ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)",1,"Integrate[Sqrt[x^2 + Sqrt[1 + x^4]]/((-1 + x^4)*Sqrt[1 + x^4]), x]","F",-1
2805,0,0,274,0.886872,"\int \frac{-1+x^6}{\sqrt[3]{-x^2+x^4} \left(1+x^6\right)} \, dx","Integrate[(-1 + x^6)/((-x^2 + x^4)^(1/3)*(1 + x^6)),x]","\int \frac{-1+x^6}{\sqrt[3]{-x^2+x^4} \left(1+x^6\right)} \, dx","-\frac{2}{3} \tan ^{-1}\left(\frac{x}{\sqrt[3]{x^4-x^2}}\right)-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{2} x}{\sqrt[3]{x^4-x^2}}\right)}{3 \sqrt[3]{2}}-\frac{1}{3} \tan ^{-1}\left(\frac{x \sqrt[3]{x^4-x^2}}{\left(x^4-x^2\right)^{2/3}-x^2}\right)-\frac{\tan ^{-1}\left(\frac{2^{2/3} x \sqrt[3]{x^4-x^2}}{\sqrt[3]{2} \left(x^4-x^2\right)^{2/3}-2 x^2}\right)}{6 \sqrt[3]{2}}-\frac{\tanh ^{-1}\left(\frac{\frac{x^2}{\sqrt{3}}+\frac{\left(x^4-x^2\right)^{2/3}}{\sqrt{3}}}{x \sqrt[3]{x^4-x^2}}\right)}{\sqrt{3}}-\frac{\tanh ^{-1}\left(\frac{\frac{\sqrt[3]{2} x^2}{\sqrt{3}}+\frac{\left(x^4-x^2\right)^{2/3}}{\sqrt[3]{2} \sqrt{3}}}{x \sqrt[3]{x^4-x^2}}\right)}{2 \sqrt[3]{2} \sqrt{3}}",1,"Integrate[(-1 + x^6)/((-x^2 + x^4)^(1/3)*(1 + x^6)), x]","F",-1
2806,0,0,274,0.1763392,"\int \frac{\sqrt{x^2+\sqrt{1+x^4}}}{1+x} \, dx","Integrate[Sqrt[x^2 + Sqrt[1 + x^4]]/(1 + x),x]","\int \frac{\sqrt{x^2+\sqrt{1+x^4}}}{1+x} \, dx","\sqrt{\sqrt{x^4+1}+x^2}-\sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{\sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{\sqrt{2}-1}}\right)+\sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{2}-1\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)-\sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{1+\sqrt{2}}}\right)-\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)+\sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)",1,"Integrate[Sqrt[x^2 + Sqrt[1 + x^4]]/(1 + x), x]","F",-1
2807,1,65,275,0.0514033,"\int \frac{b+a x^2}{\left(b-a x^2\right) \sqrt[4]{b x^3+a x^5}} \, dx","Integrate[(b + a*x^2)/((b - a*x^2)*(b*x^3 + a*x^5)^(1/4)),x]","\frac{4 \left(x^3 \left(a x^2+b\right)\right)^{3/4} F_1\left(\frac{1}{8};-\frac{3}{4},1;\frac{9}{8};-\frac{a x^2}{b},\frac{a x^2}{b}\right)}{b x^2 \left(\frac{a x^2}{b}+1\right)^{3/4}}","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[8]{a} \sqrt[8]{b} x}{\sqrt[4]{a x^5+b x^3}}\right)}{\sqrt[4]{2} \sqrt[8]{a} \sqrt[8]{b}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[8]{a} \sqrt[8]{b} x}{\sqrt[4]{a x^5+b x^3}}\right)}{\sqrt[4]{2} \sqrt[8]{a} \sqrt[8]{b}}-\frac{\tan ^{-1}\left(\frac{2^{3/4} \sqrt[8]{a} \sqrt[8]{b} x \sqrt[4]{a x^5+b x^3}}{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^2-\sqrt{a x^5+b x^3}}\right)}{2^{3/4} \sqrt[8]{a} \sqrt[8]{b}}+\frac{\tanh ^{-1}\left(\frac{\frac{\sqrt[8]{a} \sqrt[8]{b} x^2}{\sqrt[4]{2}}+\frac{\sqrt{a x^5+b x^3}}{2^{3/4} \sqrt[8]{a} \sqrt[8]{b}}}{x \sqrt[4]{a x^5+b x^3}}\right)}{2^{3/4} \sqrt[8]{a} \sqrt[8]{b}}",1,"(4*(x^3*(b + a*x^2))^(3/4)*AppellF1[1/8, -3/4, 1, 9/8, -((a*x^2)/b), (a*x^2)/b])/(b*x^2*(1 + (a*x^2)/b)^(3/4))","C",0
2808,0,0,275,0.2480568,"\int \frac{\left(4+x^3\right) \left(1+x^3+x^4\right)}{\sqrt[4]{1+x^3} \left(1+2 x^3+x^6+x^8\right)} \, dx","Integrate[((4 + x^3)*(1 + x^3 + x^4))/((1 + x^3)^(1/4)*(1 + 2*x^3 + x^6 + x^8)),x]","\int \frac{\left(4+x^3\right) \left(1+x^3+x^4\right)}{\sqrt[4]{1+x^3} \left(1+2 x^3+x^6+x^8\right)} \, dx","-\sqrt{\frac{1}{2} \left(2+\sqrt{2}\right)} \tan ^{-1}\left(\frac{\frac{\sqrt{2-\sqrt{2}} x^2}{\sqrt{2}-2}-\frac{\sqrt{2-\sqrt{2}} \sqrt{x^3+1}}{\sqrt{2}-2}}{x \sqrt[4]{x^3+1}}\right)-\sqrt{\frac{1}{2} \left(2-\sqrt{2}\right)} \tan ^{-1}\left(\frac{\frac{\sqrt{x^3+1}}{\sqrt{2+\sqrt{2}}}-\frac{x^2}{\sqrt{2+\sqrt{2}}}}{x \sqrt[4]{x^3+1}}\right)+\sqrt{\frac{1}{2} \left(2+\sqrt{2}\right)} \tanh ^{-1}\left(\frac{\sqrt{2-\sqrt{2}} x \sqrt[4]{x^3+1}}{\sqrt{x^3+1}+x^2}\right)+\sqrt{\frac{1}{2} \left(2-\sqrt{2}\right)} \tanh ^{-1}\left(\frac{\sqrt{2+\sqrt{2}} x \sqrt[4]{x^3+1}}{\sqrt{x^3+1}+x^2}\right)",1,"Integrate[((4 + x^3)*(1 + x^3 + x^4))/((1 + x^3)^(1/4)*(1 + 2*x^3 + x^6 + x^8)), x]","F",-1
2809,1,1912,275,4.1699218,"\int \frac{x^2 \sqrt{1+x}}{x^2-\sqrt{1+x} \sqrt{1+\sqrt{1+x}}} \, dx","Integrate[(x^2*Sqrt[1 + x])/(x^2 - Sqrt[1 + x]*Sqrt[1 + Sqrt[1 + x]]),x]","\frac{1}{165} \left(110 (x+1)^{3/2}-3 \sqrt{10 \left(3+\sqrt{5}\right)} \left(-17+7 \sqrt{5}\right) \tanh ^{-1}\left(\sqrt{\frac{2}{3-\sqrt{5}}} \sqrt{\sqrt{x+1}+1}\right)-6 \sqrt{\frac{10}{3+\sqrt{5}}} \left(17+7 \sqrt{5}\right) \tanh ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} \sqrt{\sqrt{x+1}+1}\right)-54 \sqrt{5} \tanh ^{-1}\left(\frac{2 \sqrt{x+1}-1}{\sqrt{5}}\right)+75 \log \left(\sqrt{x+1}-x\right)-30 \text{RootSum}\left[\text{$\#$1}^5-2 \text{$\#$1}^3+\text{$\#$1}^2+2 \text{$\#$1}-1\&,\frac{5 \log \left(\sqrt{x+1}-\text{$\#$1}\right) \text{$\#$1}^4+7 \log \left(\sqrt{x+1}-\text{$\#$1}\right) \text{$\#$1}^3-9 \log \left(\sqrt{x+1}-\text{$\#$1}\right) \text{$\#$1}^2-\log \left(\sqrt{x+1}-\text{$\#$1}\right) \text{$\#$1}+2 \log \left(\sqrt{x+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4-6 \text{$\#$1}^2+2 \text{$\#$1}+2}\&\right]+30 \left(-4 \text{RootSum}\left[\text{$\#$1}^5-\text{$\#$1}^4-2 \text{$\#$1}^3+\text{$\#$1}^2+\text{$\#$1}+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2+3 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4-4 \text{$\#$1}^3-6 \text{$\#$1}^2+2 \text{$\#$1}+1}\&\right]+5 \text{RootSum}\left[\text{$\#$1}^5-\text{$\#$1}^4-2 \text{$\#$1}^3+\text{$\#$1}^2+\text{$\#$1}+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4-4 \text{$\#$1}^3-6 \text{$\#$1}^2+2 \text{$\#$1}+1}\&\right]+10 \text{RootSum}\left[\text{$\#$1}^5-\text{$\#$1}^4-2 \text{$\#$1}^3+\text{$\#$1}^2+\text{$\#$1}+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2+2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4-4 \text{$\#$1}^3-6 \text{$\#$1}^2+2 \text{$\#$1}+1}\&\right]-6 \text{RootSum}\left[\text{$\#$1}^5-\text{$\#$1}^4-2 \text{$\#$1}^3+\text{$\#$1}^2+\text{$\#$1}+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4-4 \text{$\#$1}^3-6 \text{$\#$1}^2+2 \text{$\#$1}+1}\&\right]+14 \text{RootSum}\left[\text{$\#$1}^5-\text{$\#$1}^4+\text{$\#$1}^3+2 \text{$\#$1}^2-\text{$\#$1}-1\&,\frac{\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}^3-\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}^2-\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}}{5 \text{$\#$1}^4-4 \text{$\#$1}^3+3 \text{$\#$1}^2+4 \text{$\#$1}-1}\&\right]-10 \text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1}\&\right]-5 \text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1}\&\right]+6 \text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1}\&\right]+4 \text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4+2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2-3 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1}\&\right]+14 \text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4+\text{$\#$1}^3-2 \text{$\#$1}^2-\text{$\#$1}+1\&,\frac{\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}^3+\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}^2-\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}}{5 \text{$\#$1}^4+4 \text{$\#$1}^3+3 \text{$\#$1}^2-4 \text{$\#$1}-1}\&\right]\right)+660 \sqrt{\sqrt{x+1}+1}\right)","-\frac{4}{11} \text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{5 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)+\text{$\#$1}^3 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-2 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)+\text{$\#$1} \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-9 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1}\&\right]+\frac{2}{3} (x+1)^{3/2}+4 \sqrt{\sqrt{x+1}+1}+\frac{2}{55} \left(25+9 \sqrt{5}\right) \log \left(-2 \sqrt{\sqrt{x+1}+1}+\sqrt{5}+1\right)-\frac{2}{55} \left(9 \sqrt{5}-25\right) \log \left(2 \sqrt{\sqrt{x+1}+1}+\sqrt{5}-1\right)",1,"(110*(1 + x)^(3/2) + 660*Sqrt[1 + Sqrt[1 + x]] - 3*Sqrt[10*(3 + Sqrt[5])]*(-17 + 7*Sqrt[5])*ArcTanh[Sqrt[2/(3 - Sqrt[5])]*Sqrt[1 + Sqrt[1 + x]]] - 6*Sqrt[10/(3 + Sqrt[5])]*(17 + 7*Sqrt[5])*ArcTanh[Sqrt[2/(3 + Sqrt[5])]*Sqrt[1 + Sqrt[1 + x]]] - 54*Sqrt[5]*ArcTanh[(-1 + 2*Sqrt[1 + x])/Sqrt[5]] + 75*Log[-x + Sqrt[1 + x]] - 30*RootSum[-1 + 2*#1 + #1^2 - 2*#1^3 + #1^5 & , (2*Log[Sqrt[1 + x] - #1] - Log[Sqrt[1 + x] - #1]*#1 - 9*Log[Sqrt[1 + x] - #1]*#1^2 + 7*Log[Sqrt[1 + x] - #1]*#1^3 + 5*Log[Sqrt[1 + x] - #1]*#1^4)/(2 + 2*#1 - 6*#1^2 + 5*#1^4) & ] + 30*(-4*RootSum[1 + #1 + #1^2 - 2*#1^3 - #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] + 3*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 + 2*#1 - 6*#1^2 - 4*#1^3 + 5*#1^4) & ] + 5*RootSum[1 + #1 + #1^2 - 2*#1^3 - #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 + 2*#1 - 6*#1^2 - 4*#1^3 + 5*#1^4) & ] + 10*RootSum[1 + #1 + #1^2 - 2*#1^3 - #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] + 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 + 2*#1 - 6*#1^2 - 4*#1^3 + 5*#1^4) & ] - 6*RootSum[1 + #1 + #1^2 - 2*#1^3 - #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 + 2*#1 - 6*#1^2 - 4*#1^3 + 5*#1^4) & ] + 14*RootSum[-1 - #1 + 2*#1^2 + #1^3 - #1^4 + #1^5 & , (-(Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1) - Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3)/(-1 + 4*#1 + 3*#1^2 - 4*#1^3 + 5*#1^4) & ] - 10*RootSum[-1 + #1 - #1^2 - 2*#1^3 + #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 - 2*#1 - 6*#1^2 + 4*#1^3 + 5*#1^4) & ] - 5*RootSum[-1 + #1 - #1^2 - 2*#1^3 + #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 - 2*#1 - 6*#1^2 + 4*#1^3 + 5*#1^4) & ] + 6*RootSum[-1 + #1 - #1^2 - 2*#1^3 + #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 - 2*#1 - 6*#1^2 + 4*#1^3 + 5*#1^4) & ] + 4*RootSum[-1 + #1 - #1^2 - 2*#1^3 + #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] - 3*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 - 2*#1 - 6*#1^2 + 4*#1^3 + 5*#1^4) & ] + 14*RootSum[1 - #1 - 2*#1^2 + #1^3 + #1^4 + #1^5 & , (-(Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1) + Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3)/(-1 - 4*#1 + 3*#1^2 + 4*#1^3 + 5*#1^4) & ]))/165","B",0
2810,1,1912,275,3.287049,"\int \frac{x^2 \sqrt{1+x}}{x^2-\sqrt{1+x} \sqrt{1+\sqrt{1+x}}} \, dx","Integrate[(x^2*Sqrt[1 + x])/(x^2 - Sqrt[1 + x]*Sqrt[1 + Sqrt[1 + x]]),x]","\frac{1}{165} \left(110 (x+1)^{3/2}-3 \sqrt{10 \left(3+\sqrt{5}\right)} \left(-17+7 \sqrt{5}\right) \tanh ^{-1}\left(\sqrt{\frac{2}{3-\sqrt{5}}} \sqrt{\sqrt{x+1}+1}\right)-6 \sqrt{\frac{10}{3+\sqrt{5}}} \left(17+7 \sqrt{5}\right) \tanh ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} \sqrt{\sqrt{x+1}+1}\right)-54 \sqrt{5} \tanh ^{-1}\left(\frac{2 \sqrt{x+1}-1}{\sqrt{5}}\right)+75 \log \left(\sqrt{x+1}-x\right)-30 \text{RootSum}\left[\text{$\#$1}^5-2 \text{$\#$1}^3+\text{$\#$1}^2+2 \text{$\#$1}-1\&,\frac{5 \log \left(\sqrt{x+1}-\text{$\#$1}\right) \text{$\#$1}^4+7 \log \left(\sqrt{x+1}-\text{$\#$1}\right) \text{$\#$1}^3-9 \log \left(\sqrt{x+1}-\text{$\#$1}\right) \text{$\#$1}^2-\log \left(\sqrt{x+1}-\text{$\#$1}\right) \text{$\#$1}+2 \log \left(\sqrt{x+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4-6 \text{$\#$1}^2+2 \text{$\#$1}+2}\&\right]+30 \left(-4 \text{RootSum}\left[\text{$\#$1}^5-\text{$\#$1}^4-2 \text{$\#$1}^3+\text{$\#$1}^2+\text{$\#$1}+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2+3 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4-4 \text{$\#$1}^3-6 \text{$\#$1}^2+2 \text{$\#$1}+1}\&\right]+5 \text{RootSum}\left[\text{$\#$1}^5-\text{$\#$1}^4-2 \text{$\#$1}^3+\text{$\#$1}^2+\text{$\#$1}+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4-4 \text{$\#$1}^3-6 \text{$\#$1}^2+2 \text{$\#$1}+1}\&\right]+10 \text{RootSum}\left[\text{$\#$1}^5-\text{$\#$1}^4-2 \text{$\#$1}^3+\text{$\#$1}^2+\text{$\#$1}+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2+2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4-4 \text{$\#$1}^3-6 \text{$\#$1}^2+2 \text{$\#$1}+1}\&\right]-6 \text{RootSum}\left[\text{$\#$1}^5-\text{$\#$1}^4-2 \text{$\#$1}^3+\text{$\#$1}^2+\text{$\#$1}+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4-4 \text{$\#$1}^3-6 \text{$\#$1}^2+2 \text{$\#$1}+1}\&\right]+14 \text{RootSum}\left[\text{$\#$1}^5-\text{$\#$1}^4+\text{$\#$1}^3+2 \text{$\#$1}^2-\text{$\#$1}-1\&,\frac{\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}^3-\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}^2-\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}}{5 \text{$\#$1}^4-4 \text{$\#$1}^3+3 \text{$\#$1}^2+4 \text{$\#$1}-1}\&\right]-10 \text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1}\&\right]-5 \text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1}\&\right]+6 \text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1}\&\right]+4 \text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^4+2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^3-2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}^2-3 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right) \text{$\#$1}+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1}\&\right]+14 \text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4+\text{$\#$1}^3-2 \text{$\#$1}^2-\text{$\#$1}+1\&,\frac{\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}^3+\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}^2-\log \left(\frac{1}{\sqrt{\sqrt{x+1}+1}}-\text{$\#$1}\right) \text{$\#$1}}{5 \text{$\#$1}^4+4 \text{$\#$1}^3+3 \text{$\#$1}^2-4 \text{$\#$1}-1}\&\right]\right)+660 \sqrt{\sqrt{x+1}+1}\right)","-\frac{4}{11} \text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{5 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)+\text{$\#$1}^3 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-2 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)+\text{$\#$1} \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-9 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1}\&\right]+\frac{2}{3} (x+1)^{3/2}+4 \sqrt{\sqrt{x+1}+1}+\frac{2}{55} \left(25+9 \sqrt{5}\right) \log \left(-2 \sqrt{\sqrt{x+1}+1}+\sqrt{5}+1\right)-\frac{2}{55} \left(9 \sqrt{5}-25\right) \log \left(2 \sqrt{\sqrt{x+1}+1}+\sqrt{5}-1\right)",1,"(110*(1 + x)^(3/2) + 660*Sqrt[1 + Sqrt[1 + x]] - 3*Sqrt[10*(3 + Sqrt[5])]*(-17 + 7*Sqrt[5])*ArcTanh[Sqrt[2/(3 - Sqrt[5])]*Sqrt[1 + Sqrt[1 + x]]] - 6*Sqrt[10/(3 + Sqrt[5])]*(17 + 7*Sqrt[5])*ArcTanh[Sqrt[2/(3 + Sqrt[5])]*Sqrt[1 + Sqrt[1 + x]]] - 54*Sqrt[5]*ArcTanh[(-1 + 2*Sqrt[1 + x])/Sqrt[5]] + 75*Log[-x + Sqrt[1 + x]] - 30*RootSum[-1 + 2*#1 + #1^2 - 2*#1^3 + #1^5 & , (2*Log[Sqrt[1 + x] - #1] - Log[Sqrt[1 + x] - #1]*#1 - 9*Log[Sqrt[1 + x] - #1]*#1^2 + 7*Log[Sqrt[1 + x] - #1]*#1^3 + 5*Log[Sqrt[1 + x] - #1]*#1^4)/(2 + 2*#1 - 6*#1^2 + 5*#1^4) & ] + 30*(-4*RootSum[1 + #1 + #1^2 - 2*#1^3 - #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] + 3*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 + 2*#1 - 6*#1^2 - 4*#1^3 + 5*#1^4) & ] + 5*RootSum[1 + #1 + #1^2 - 2*#1^3 - #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 + 2*#1 - 6*#1^2 - 4*#1^3 + 5*#1^4) & ] + 10*RootSum[1 + #1 + #1^2 - 2*#1^3 - #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] + 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 + 2*#1 - 6*#1^2 - 4*#1^3 + 5*#1^4) & ] - 6*RootSum[1 + #1 + #1^2 - 2*#1^3 - #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 + 2*#1 - 6*#1^2 - 4*#1^3 + 5*#1^4) & ] + 14*RootSum[-1 - #1 + 2*#1^2 + #1^3 - #1^4 + #1^5 & , (-(Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1) - Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3)/(-1 + 4*#1 + 3*#1^2 - 4*#1^3 + 5*#1^4) & ] - 10*RootSum[-1 + #1 - #1^2 - 2*#1^3 + #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 - 2*#1 - 6*#1^2 + 4*#1^3 + 5*#1^4) & ] - 5*RootSum[-1 + #1 - #1^2 - 2*#1^3 + #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 - 2*#1 - 6*#1^2 + 4*#1^3 + 5*#1^4) & ] + 6*RootSum[-1 + #1 - #1^2 - 2*#1^3 + #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] - Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 - 2*#1 - 6*#1^2 + 4*#1^3 + 5*#1^4) & ] + 4*RootSum[-1 + #1 - #1^2 - 2*#1^3 + #1^4 + #1^5 & , (Log[Sqrt[1 + Sqrt[1 + x]] - #1] - 3*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1 - 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + 2*Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[1 + x]] - #1]*#1^4)/(1 - 2*#1 - 6*#1^2 + 4*#1^3 + 5*#1^4) & ] + 14*RootSum[1 - #1 - 2*#1^2 + #1^3 + #1^4 + #1^5 & , (-(Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1) + Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1^2 + Log[1/Sqrt[1 + Sqrt[1 + x]] - #1]*#1^3)/(-1 - 4*#1 + 3*#1^2 + 4*#1^3 + 5*#1^4) & ]))/165","B",0
2811,1,232,276,0.7503021,"\int \frac{\left(-b-a x+x^4\right) \sqrt[4]{b x^3+a x^4}}{-b+a x} \, dx","Integrate[((-b - a*x + x^4)*(b*x^3 + a*x^4)^(1/4))/(-b + a*x),x]","\frac{x^3 \left(35 b^2 \left(13056 a^4-6541 b^3\right) \left(\frac{a x}{b}+1\right)^{3/4} \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};-\frac{2 a x}{b-a x}\right)+15 a b x \left(19712 a^4-9843 b^3\right) \left(1-\frac{a^2 x^2}{b^2}\right)^{3/4} F_1\left(\frac{7}{4};\frac{3}{4},1;\frac{11}{4};-\frac{a x}{b},\frac{a x}{b}\right)+7 \left(1-\frac{a x}{b}\right)^{3/4} \left(-15360 a^6 x^2+768 a^5 \left(8 x^5-105 b x\right)-384 a^4 b \left(170 b-37 x^4\right)+18464 a^3 b^2 x^3+26820 a^2 b^3 x^2+49125 a b^4 x+32705 b^5\right)\right)}{215040 a^5 \left(x^3 (a x+b)\right)^{3/4} \left(1-\frac{a x}{b}\right)^{3/4}}","\frac{\left(19712 a^4 b^2-9843 b^5\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)}{4096 a^{23/4}}-\frac{2 \sqrt[4]{2} \left(2 a^4 b^2-b^5\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)}{a^{23/4}}+\frac{\left(9843 b^5-19712 a^4 b^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)}{4096 a^{23/4}}+\frac{2 \sqrt[4]{2} \left(2 a^4 b^2-b^5\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)}{a^{23/4}}+\frac{\sqrt[4]{a x^4+b x^3} \left(-15360 a^5 x-65280 a^4 b+6144 a^4 x^4+8064 a^3 b x^3+10400 a^2 b^2 x^2+16420 a b^3 x+32705 b^4\right)}{30720 a^5}",1,"(x^3*(7*(1 - (a*x)/b)^(3/4)*(32705*b^5 + 49125*a*b^4*x - 15360*a^6*x^2 + 26820*a^2*b^3*x^2 + 18464*a^3*b^2*x^3 - 384*a^4*b*(170*b - 37*x^4) + 768*a^5*(-105*b*x + 8*x^5)) + 15*a*b*(19712*a^4 - 9843*b^3)*x*(1 - (a^2*x^2)/b^2)^(3/4)*AppellF1[7/4, 3/4, 1, 11/4, -((a*x)/b), (a*x)/b] + 35*b^2*(13056*a^4 - 6541*b^3)*(1 + (a*x)/b)^(3/4)*Hypergeometric2F1[3/4, 3/4, 7/4, (-2*a*x)/(b - a*x)]))/(215040*a^5*(x^3*(b + a*x))^(3/4)*(1 - (a*x)/b)^(3/4))","C",0
2812,0,0,276,2.8449362,"\int \frac{(-4 a+b+3 x) \left(-b^3+3 b^2 x-3 b x^2+x^3\right)}{\left((-a+x) (-b+x)^2\right)^{2/3} \left(a+b^4 d-\left(1+4 b^3 d\right) x+6 b^2 d x^2-4 b d x^3+d x^4\right)} \, dx","Integrate[((-4*a + b + 3*x)*(-b^3 + 3*b^2*x - 3*b*x^2 + x^3))/(((-a + x)*(-b + x)^2)^(2/3)*(a + b^4*d - (1 + 4*b^3*d)*x + 6*b^2*d*x^2 - 4*b*d*x^3 + d*x^4)),x]","\int \frac{(-4 a+b+3 x) \left(-b^3+3 b^2 x-3 b x^2+x^3\right)}{\left((-a+x) (-b+x)^2\right)^{2/3} \left(a+b^4 d-\left(1+4 b^3 d\right) x+6 b^2 d x^2-4 b d x^3+d x^4\right)} \, dx","-\frac{\log \left(a^2+d^{2/3} \left(x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3\right)^{4/3}+\left(x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3\right)^{2/3} \left(\sqrt[3]{d} x-a \sqrt[3]{d}\right)-2 a x+x^2\right)}{2 d^{2/3}}+\frac{\log \left(\sqrt[3]{d} \left(x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3\right)^{2/3}+a-x\right)}{d^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} \left(x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3\right)^{2/3}}{\sqrt[3]{d} \left(x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3\right)^{2/3}-2 a+2 x}\right)}{d^{2/3}}",1,"Integrate[((-4*a + b + 3*x)*(-b^3 + 3*b^2*x - 3*b*x^2 + x^3))/(((-a + x)*(-b + x)^2)^(2/3)*(a + b^4*d - (1 + 4*b^3*d)*x + 6*b^2*d*x^2 - 4*b*d*x^3 + d*x^4)), x]","F",-1
2813,0,0,276,5.415737,"\int \frac{x^2 (-2+(1+k) x)}{\sqrt[3]{(1-x) x (1-k x)} \left(1-(2+2 k) x+\left(1+4 k+k^2\right) x^2-\left(2 k+2 k^2\right) x^3+\left(-b+k^2\right) x^4\right)} \, dx","Integrate[(x^2*(-2 + (1 + k)*x))/(((1 - x)*x*(1 - k*x))^(1/3)*(1 - (2 + 2*k)*x + (1 + 4*k + k^2)*x^2 - (2*k + 2*k^2)*x^3 + (-b + k^2)*x^4)),x]","\int \frac{x^2 (-2+(1+k) x)}{\sqrt[3]{(1-x) x (1-k x)} \left(1-(2+2 k) x+\left(1+4 k+k^2\right) x^2-\left(2 k+2 k^2\right) x^3+\left(-b+k^2\right) x^4\right)} \, dx","\frac{\log \left(\sqrt[3]{k x^3+(-k-1) x^2+x}-\sqrt[6]{b} x\right)}{2 b^{2/3}}+\frac{\log \left(\sqrt[6]{b} x+\sqrt[3]{k x^3+(-k-1) x^2+x}\right)}{2 b^{2/3}}-\frac{\log \left(-\sqrt[6]{b} x \sqrt[3]{k x^3+(-k-1) x^2+x}+\sqrt[3]{b} x^2+\left(k x^3+(-k-1) x^2+x\right)^{2/3}\right)}{4 b^{2/3}}-\frac{\log \left(\sqrt[6]{b} x \sqrt[3]{k x^3+(-k-1) x^2+x}+\sqrt[3]{b} x^2+\left(k x^3+(-k-1) x^2+x\right)^{2/3}\right)}{4 b^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{b} x^2}{\sqrt[3]{b} x^2+2 \left(k x^3+(-k-1) x^2+x\right)^{2/3}}\right)}{2 b^{2/3}}",1,"Integrate[(x^2*(-2 + (1 + k)*x))/(((1 - x)*x*(1 - k*x))^(1/3)*(1 - (2 + 2*k)*x + (1 + 4*k + k^2)*x^2 - (2*k + 2*k^2)*x^3 + (-b + k^2)*x^4)), x]","F",-1
2814,1,157,276,0.1866775,"\int \frac{1}{c+\sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Integrate[(c + Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])^(-1),x]","\frac{\frac{b^2 \log \left(\sqrt{a^2 x^2+b^2}+a x\right)}{2 c^3}+\frac{b^2}{c^2 \sqrt{\sqrt{a^2 x^2+b^2}+a x}}-\frac{\left(b^2+c^4\right) \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}+c\right)}{c^3}-\frac{b^2}{2 c \left(\sqrt{a^2 x^2+b^2}+a x\right)}+\sqrt{\sqrt{a^2 x^2+b^2}+a x}}{a}","\frac{b^2 \log \left(\sqrt{a^2 x^2+b^2}+a x\right)}{2 a c^3}-\frac{b^2 \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}+c\right)}{a c^3}+\frac{\sqrt{a^2 x^2+b^2} \left(\left(3 b^2+2 c^4\right) \sqrt{\sqrt{a^2 x^2+b^2}+a x}+4 a c^3 x+2 b^2 c\right)+\sqrt{\sqrt{a^2 x^2+b^2}+a x} \left(3 a b^2 x+2 a c^4 x-b^2 c^2\right)+4 a^2 c^3 x^2+2 a b^2 c x+2 b^2 c^3}{2 a c^3 \left(\sqrt{a^2 x^2+b^2}+a x\right)^{3/2}}-\frac{c \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}+c\right)}{a}",1,"(-1/2*b^2/(c*(a*x + Sqrt[b^2 + a^2*x^2])) + b^2/(c^2*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]) + Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] + (b^2*Log[a*x + Sqrt[b^2 + a^2*x^2]])/(2*c^3) - ((b^2 + c^4)*Log[c + Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]])/c^3)/a","A",1
2815,1,56,278,0.0311883,"\int \frac{(-7+x) \sqrt[3]{1+x-5 x^2+3 x^3}}{(-5+x) (-1+x)^3} \, dx","Integrate[((-7 + x)*(1 + x - 5*x^2 + 3*x^3)^(1/3))/((-5 + x)*(-1 + x)^3),x]","\frac{3 \left(8 (x-1)^2 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{4 (x-1)}{3 x+1}\right)-39 x^2-10 x+1\right)}{32 \left((x-1)^2 (3 x+1)\right)^{2/3}}","\frac{(x-1)^{4/3} (3 x+1)^{2/3} \left(-\frac{21 \sqrt[3]{3} \left(7 (3 x+1)^{4/3}-16 \sqrt[3]{3 x+1}\right)}{64 (3 x-3)^{4/3}}+\frac{3 \sqrt[3]{3} \left(23 (3 x+1)^{4/3}-80 \sqrt[3]{3 x+1}\right)}{64 (3 x-3)^{4/3}}-\frac{\log \left(6^{2/3} \sqrt[3]{3 x-3}-3 \sqrt[3]{3 x+1}\right)}{4 \sqrt[3]{2}}+\frac{\log \left(2 \sqrt[3]{6} (3 x-3)^{2/3}+6^{2/3} \sqrt[3]{3 x+1} \sqrt[3]{3 x-3}+3 (3 x+1)^{2/3}\right)}{8 \sqrt[3]{2}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{3^{5/6} \sqrt[3]{3 x+1}}{2\ 2^{2/3} \sqrt[3]{3 x-3}+\sqrt[3]{3} \sqrt[3]{3 x+1}}\right)}{4 \sqrt[3]{2}}\right)}{\left((x-1)^2 (3 x+1)\right)^{2/3}}",1,"(3*(1 - 10*x - 39*x^2 + 8*(-1 + x)^2*Hypergeometric2F1[2/3, 1, 5/3, (4*(-1 + x))/(1 + 3*x)]))/(32*((-1 + x)^2*(1 + 3*x))^(2/3))","C",1
2816,1,156,278,0.8774338,"\int \frac{b^2+a^2 x^2}{\left(-b^2+a^2 x^2\right)^3 \sqrt[3]{-b x^2+a x^3}} \, dx","Integrate[(b^2 + a^2*x^2)/((-b^2 + a^2*x^2)^3*(-(b*x^2) + a*x^3)^(1/3)),x]","\frac{x \sqrt[3]{\frac{a x}{b}+1} \left(-625 a^4 x^4-67 a^3 b x^3+1503 a^2 b^2 x^2+91 a b^3 x-1190 b^4\right)-826 x \sqrt[3]{1-\frac{a x}{b}} \left(b^2-a^2 x^2\right)^2 \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};\frac{2 a x}{b+a x}\right)}{672 b^4 (b-a x)^2 \sqrt[3]{x^2 (a x-b)} (a x+b)^2 \sqrt[3]{\frac{a x}{b}+1}}","-\frac{59 \log \left(2 a^{2/3} x^2+2^{2/3} \sqrt[3]{a} x \sqrt[3]{a x^3-b x^2}+\sqrt[3]{2} \left(a x^3-b x^2\right)^{2/3}\right)}{288 \sqrt[3]{2} \sqrt[3]{a} b^4}-\frac{\left(a x^3-b x^2\right)^{2/3} \left(-625 a^4 x^4-67 a^3 b x^3+1503 a^2 b^2 x^2+91 a b^3 x-1190 b^4\right)}{672 b^4 x (b-a x)^3 (a x+b)^2}+\frac{59 \log \left(2^{2/3} \sqrt[3]{a x^3-b x^2}-2 \sqrt[3]{a} x\right)}{144 \sqrt[3]{2} \sqrt[3]{a} b^4}-\frac{59 \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{a} x}{2^{2/3} \sqrt[3]{a x^3-b x^2}+\sqrt[3]{a} x}\right)}{48 \sqrt[3]{2} \sqrt{3} \sqrt[3]{a} b^4}",1,"(x*(1 + (a*x)/b)^(1/3)*(-1190*b^4 + 91*a*b^3*x + 1503*a^2*b^2*x^2 - 67*a^3*b*x^3 - 625*a^4*x^4) - 826*x*(1 - (a*x)/b)^(1/3)*(b^2 - a^2*x^2)^2*Hypergeometric2F1[1/3, 1/3, 4/3, (2*a*x)/(b + a*x)])/(672*b^4*(b - a*x)^2*(x^2*(-b + a*x))^(1/3)*(b + a*x)^2*(1 + (a*x)/b)^(1/3))","C",0
2817,1,374,278,1.2750556,"\int \frac{d+c x}{(-d+c x) \sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Integrate[(d + c*x)/((-d + c*x)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]),x]","\frac{\frac{12 a d \left(a d \left(a d-\sqrt{a^2 d^2+b^2 c^2}\right)+b^2 c^2\right) \tan ^{-1}\left(\frac{b \sqrt{c}}{\sqrt{\sqrt{a^2 x^2+b^2}+a x} \sqrt{a d-\sqrt{a^2 d^2+b^2 c^2}}}\right)}{b \sqrt{a^2 d^2+b^2 c^2} \sqrt{a d-\sqrt{a^2 d^2+b^2 c^2}}}-\frac{12 a d \left(a d \left(\sqrt{a^2 d^2+b^2 c^2}+a d\right)+b^2 c^2\right) \tan ^{-1}\left(\frac{b \sqrt{c}}{\sqrt{\sqrt{a^2 x^2+b^2}+a x} \sqrt{\sqrt{a^2 d^2+b^2 c^2}+a d}}\right)}{b \sqrt{a^2 d^2+b^2 c^2} \sqrt{\sqrt{a^2 d^2+b^2 c^2}+a d}}+\frac{\sqrt{c} \left(6 a \left(\sqrt{a^2 x^2+b^2}+a x\right) (c x+2 d)+2 b^2 c\right)}{\left(\sqrt{a^2 x^2+b^2}+a x\right)^{3/2}}}{3 a c^{3/2}}","\frac{4 d \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{\sqrt{a^2 x^2+b^2}+a x}}{\sqrt{-\sqrt{a^2 d^2+b^2 c^2}-a d}}\right)}{\sqrt{c} \sqrt{-\sqrt{a^2 d^2+b^2 c^2}-a d}}+\frac{4 d \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{\sqrt{a^2 x^2+b^2}+a x}}{\sqrt{\sqrt{a^2 d^2+b^2 c^2}-a d}}\right)}{\sqrt{c} \sqrt{\sqrt{a^2 d^2+b^2 c^2}-a d}}+\frac{2 \sqrt{a^2 x^2+b^2} (3 a c x+6 a d)+2 \left(3 a^2 c x^2+6 a^2 d x+b^2 c\right)}{3 a c \left(\sqrt{a^2 x^2+b^2}+a x\right)^{3/2}}",1,"((Sqrt[c]*(2*b^2*c + 6*a*(2*d + c*x)*(a*x + Sqrt[b^2 + a^2*x^2])))/(a*x + Sqrt[b^2 + a^2*x^2])^(3/2) + (12*a*d*(b^2*c^2 + a*d*(a*d - Sqrt[b^2*c^2 + a^2*d^2]))*ArcTan[(b*Sqrt[c])/(Sqrt[a*d - Sqrt[b^2*c^2 + a^2*d^2]]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])])/(b*Sqrt[b^2*c^2 + a^2*d^2]*Sqrt[a*d - Sqrt[b^2*c^2 + a^2*d^2]]) - (12*a*d*(b^2*c^2 + a*d*(a*d + Sqrt[b^2*c^2 + a^2*d^2]))*ArcTan[(b*Sqrt[c])/(Sqrt[a*d + Sqrt[b^2*c^2 + a^2*d^2]]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])])/(b*Sqrt[b^2*c^2 + a^2*d^2]*Sqrt[a*d + Sqrt[b^2*c^2 + a^2*d^2]]))/(3*a*c^(3/2))","A",1
2818,0,0,279,61.0705735,"\int \frac{\sqrt[4]{-b x^3+a x^4}}{-d-2 c x+x^2} \, dx","Integrate[(-(b*x^3) + a*x^4)^(1/4)/(-d - 2*c*x + x^2),x]","\int \frac{\sqrt[4]{-b x^3+a x^4}}{-d-2 c x+x^2} \, dx","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8 (-d)+2 \text{$\#$1}^4 a d+2 \text{$\#$1}^4 b c-a^2 d-2 a b c+b^2\&,\frac{-\text{$\#$1}^4 a d \log \left(\sqrt[4]{a x^4-b x^3}-\text{$\#$1} x\right)+\text{$\#$1}^4 a d \log (x)+a^2 d \log \left(\sqrt[4]{a x^4-b x^3}-\text{$\#$1} x\right)-b^2 \log \left(\sqrt[4]{a x^4-b x^3}-\text{$\#$1} x\right)+2 a b c \log \left(\sqrt[4]{a x^4-b x^3}-\text{$\#$1} x\right)-a^2 d \log (x)-2 a b c \log (x)+b^2 \log (x)}{\text{$\#$1}^7 (-d)+\text{$\#$1}^3 a d+\text{$\#$1}^3 b c}\&\right]-2 \sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^3}}\right)+2 \sqrt[4]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^3}}\right)",1,"Integrate[(-(b*x^3) + a*x^4)^(1/4)/(-d - 2*c*x + x^2), x]","F",-1
2819,0,0,279,60.694357,"\int \frac{\sqrt[4]{-b x^3+a x^4}}{-d-2 c x+x^2} \, dx","Integrate[(-(b*x^3) + a*x^4)^(1/4)/(-d - 2*c*x + x^2),x]","\int \frac{\sqrt[4]{-b x^3+a x^4}}{-d-2 c x+x^2} \, dx","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8 (-d)+2 \text{$\#$1}^4 a d+2 \text{$\#$1}^4 b c-a^2 d-2 a b c+b^2\&,\frac{-\text{$\#$1}^4 a d \log \left(\sqrt[4]{a x^4-b x^3}-\text{$\#$1} x\right)+\text{$\#$1}^4 a d \log (x)+a^2 d \log \left(\sqrt[4]{a x^4-b x^3}-\text{$\#$1} x\right)-b^2 \log \left(\sqrt[4]{a x^4-b x^3}-\text{$\#$1} x\right)+2 a b c \log \left(\sqrt[4]{a x^4-b x^3}-\text{$\#$1} x\right)-a^2 d \log (x)-2 a b c \log (x)+b^2 \log (x)}{\text{$\#$1}^7 (-d)+\text{$\#$1}^3 a d+\text{$\#$1}^3 b c}\&\right]-2 \sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^3}}\right)+2 \sqrt[4]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^3}}\right)",1,"Integrate[(-(b*x^3) + a*x^4)^(1/4)/(-d - 2*c*x + x^2), x]","F",-1
2820,0,0,279,4.4090685,"\int \frac{x (-1+k x) (-1+(-1+2 k) x)}{\sqrt[3]{(1-x) x (1-k x)} \left(-1+4 x+(-6+b) x^2+(4-2 b k) x^3+\left(-1+b k^2\right) x^4\right)} \, dx","Integrate[(x*(-1 + k*x)*(-1 + (-1 + 2*k)*x))/(((1 - x)*x*(1 - k*x))^(1/3)*(-1 + 4*x + (-6 + b)*x^2 + (4 - 2*b*k)*x^3 + (-1 + b*k^2)*x^4)),x]","\int \frac{x (-1+k x) (-1+(-1+2 k) x)}{\sqrt[3]{(1-x) x (1-k x)} \left(-1+4 x+(-6+b) x^2+(4-2 b k) x^3+\left(-1+b k^2\right) x^4\right)} \, dx","\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{b} \sqrt[3]{k x^3+(-k-1) x^2+x}}{\sqrt[6]{b} \sqrt[3]{k x^3+(-k-1) x^2+x}-2 x+2}\right)}{2 b^{5/6}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{b} \sqrt[3]{k x^3+(-k-1) x^2+x}}{\sqrt[6]{b} \sqrt[3]{k x^3+(-k-1) x^2+x}+2 x-2}\right)}{2 b^{5/6}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{b} \sqrt[3]{k x^3+(-k-1) x^2+x}}{x-1}\right)}{b^{5/6}}+\frac{\tanh ^{-1}\left(\frac{\left(\sqrt[6]{b} x-\sqrt[6]{b}\right) \sqrt[3]{k x^3+(-k-1) x^2+x}}{\sqrt[3]{b} \left(k x^3+(-k-1) x^2+x\right)^{2/3}+x^2-2 x+1}\right)}{2 b^{5/6}}",1,"Integrate[(x*(-1 + k*x)*(-1 + (-1 + 2*k)*x))/(((1 - x)*x*(1 - k*x))^(1/3)*(-1 + 4*x + (-6 + b)*x^2 + (4 - 2*b*k)*x^3 + (-1 + b*k^2)*x^4)), x]","F",-1
2821,0,0,279,5.4988586,"\int \frac{1+(-2+3 k) x-\left(k+4 k^2\right) x^2+3 k^2 x^3}{\sqrt[3]{(1-x) x (1-k x)} \left(-b+(1+5 b k) x-\left(1+10 b k^2\right) x^2+10 b k^3 x^3-5 b k^4 x^4+b k^5 x^5\right)} \, dx","Integrate[(1 + (-2 + 3*k)*x - (k + 4*k^2)*x^2 + 3*k^2*x^3)/(((1 - x)*x*(1 - k*x))^(1/3)*(-b + (1 + 5*b*k)*x - (1 + 10*b*k^2)*x^2 + 10*b*k^3*x^3 - 5*b*k^4*x^4 + b*k^5*x^5)),x]","\int \frac{1+(-2+3 k) x-\left(k+4 k^2\right) x^2+3 k^2 x^3}{\sqrt[3]{(1-x) x (1-k x)} \left(-b+(1+5 b k) x-\left(1+10 b k^2\right) x^2+10 b k^3 x^3-5 b k^4 x^4+b k^5 x^5\right)} \, dx","-\frac{\log \left(b^{2/3} k^4 x^4-4 b^{2/3} k^3 x^3+6 b^{2/3} k^2 x^2-4 b^{2/3} k x+b^{2/3}+\sqrt[3]{k x^3+(-k-1) x^2+x} \left(\sqrt[3]{b} k^2 x^2-2 \sqrt[3]{b} k x+\sqrt[3]{b}\right)+\left(k x^3+(-k-1) x^2+x\right)^{2/3}\right)}{2 \sqrt[3]{b}}+\frac{\log \left(-\sqrt[3]{b} k^2 x^2+2 \sqrt[3]{b} k x-\sqrt[3]{b}+\sqrt[3]{k x^3+(-k-1) x^2+x}\right)}{\sqrt[3]{b}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{k x^3+(-k-1) x^2+x}}{2 \sqrt[3]{b} k^2 x^2-4 \sqrt[3]{b} k x+2 \sqrt[3]{b}+\sqrt[3]{k x^3+(-k-1) x^2+x}}\right)}{\sqrt[3]{b}}",1,"Integrate[(1 + (-2 + 3*k)*x - (k + 4*k^2)*x^2 + 3*k^2*x^3)/(((1 - x)*x*(1 - k*x))^(1/3)*(-b + (1 + 5*b*k)*x - (1 + 10*b*k^2)*x^2 + 10*b*k^3*x^3 - 5*b*k^4*x^4 + b*k^5*x^5)), x]","F",-1
2822,1,1949,282,7.6461061,"\int \frac{(d+c x)^2}{\sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Integrate[(d + c*x)^2/Sqrt[a*x + Sqrt[b^2 + a^2*x^2]],x]","-\frac{\left(a^2\right)^{3/2} c^2 \left(45 b^8-210 \left(a x+\sqrt{b^2+a^2 x^2}\right)^2 b^6-126 \left(a x+\sqrt{b^2+a^2 x^2}\right)^6 b^2+35 \left(a x+\sqrt{b^2+a^2 x^2}\right)^8\right) x^3}{315 b^2 \left(\frac{a}{\sqrt{a^2}}+\frac{\sqrt{a^2} x}{\sqrt{b^2+a^2 x^2}}\right) \sqrt{a x+\sqrt{b^2+a^2 x^2}} \left(\sqrt{a^2} \left(a x+\sqrt{b^2+a^2 x^2}\right)^2-\sqrt{a^2} b^2\right)^3 \left(\frac{\sqrt{a^2}}{a}-\frac{\sqrt{a^2} \left(a x+\sqrt{b^2+a^2 x^2}\right)^2-\sqrt{a^2} b^2}{2 a \left(a x+\sqrt{b^2+a^2 x^2}\right)^2}\right)}-\frac{2 a^2 c d \left(-21 b^6+105 \left(a x+\sqrt{b^2+a^2 x^2}\right)^2 b^4-35 \left(a x+\sqrt{b^2+a^2 x^2}\right)^4 b^2+15 \left(a x+\sqrt{b^2+a^2 x^2}\right)^6\right) x^2}{105 b^2 \left(\frac{a}{\sqrt{a^2}}+\frac{\sqrt{a^2} x}{\sqrt{b^2+a^2 x^2}}\right) \sqrt{a x+\sqrt{b^2+a^2 x^2}} \left(\sqrt{a^2} \left(a x+\sqrt{b^2+a^2 x^2}\right)^2-\sqrt{a^2} b^2\right)^2 \left(\frac{\sqrt{a^2}}{a}-\frac{\sqrt{a^2} \left(a x+\sqrt{b^2+a^2 x^2}\right)^2-\sqrt{a^2} b^2}{2 a \left(a x+\sqrt{b^2+a^2 x^2}\right)^2}\right)}-\frac{\sqrt{a^2} d^2 \left(a x+\sqrt{b^2+a^2 x^2}\right) \left(\frac{2 b^4}{3 \left(a x+\sqrt{b^2+a^2 x^2}\right)^{3/2}}+\frac{2}{5} \left(a x+\sqrt{b^2+a^2 x^2}\right)^{5/2}\right) x}{2 b^2 \left(\frac{a}{\sqrt{a^2}}+\frac{\sqrt{a^2} x}{\sqrt{b^2+a^2 x^2}}\right) \left(\sqrt{a^2} \left(a x+\sqrt{b^2+a^2 x^2}\right)^2-\sqrt{a^2} b^2\right) \left(\frac{\sqrt{a^2}}{a}-\frac{\sqrt{a^2} \left(a x+\sqrt{b^2+a^2 x^2}\right)^2-\sqrt{a^2} b^2}{2 a \left(a x+\sqrt{b^2+a^2 x^2}\right)^2}\right)}+\frac{2 d^2 \sqrt{b^2+a^2 x^2} \left(2 x \sqrt{b^2+a^2 x^2} a^2+\left(b^2+2 a^2 x^2\right) a\right) \left(6 x \sqrt{b^2+a^2 x^2} \left(3 b^2+a^2 x^2\right) a^2+\left(7 b^4+21 a^2 x^2 b^2+6 a^4 x^4\right) a\right) \left(\sqrt{a^2} b^2+2 \sqrt{a^2} x \left(x a^2+\sqrt{b^2+a^2 x^2} a\right)\right)^3}{15 a^4 \sqrt{a^2} b^2 \sqrt{a x+\sqrt{b^2+a^2 x^2}} \left(x \sqrt{b^2+a^2 x^2} \left(9 b^8+120 a^2 x^2 b^6+432 a^4 x^4 b^4+576 a^6 x^6 b^2+256 a^8 x^8\right) a^2+\left(b^{10}+41 a^2 x^2 b^8+280 a^4 x^4 b^6+688 a^6 x^6 b^4+704 a^8 x^8 b^2+256 a^{10} x^{10}\right) a\right)}+\frac{4 c d \sqrt{b^2+a^2 x^2} \left(2 x \sqrt{b^2+a^2 x^2} a^2+\left(b^2+2 a^2 x^2\right) a\right) \left(5 x \sqrt{b^2+a^2 x^2} \left(11 b^4+19 a^2 x^2 b^2+12 a^4 x^4\right) a^2+\left(22 b^6+95 a^2 x^2 b^4+125 a^4 x^4 b^2+60 a^6 x^6\right) a\right) \left(\sqrt{a^2} b^2+2 \sqrt{a^2} x \left(x a^2+\sqrt{b^2+a^2 x^2} a\right)\right)^3}{105 a^6 b^2 \sqrt{a x+\sqrt{b^2+a^2 x^2}} \left(\sqrt{a^2} \sqrt{b^2+a^2 x^2} \left(b^{10}+50 a^2 x^2 b^8+400 a^4 x^4 b^6+1120 a^6 x^6 b^4+1280 a^8 x^8 b^2+512 a^{10} x^{10}\right)+2 a \left(256 \left(a^2\right)^{11/2} x^{11}+768 \left(a^2\right)^{9/2} b^2 x^9+848 \left(a^2\right)^{7/2} b^4 x^7+416 \left(a^2\right)^{5/2} b^6 x^5+85 \left(a^2\right)^{3/2} b^8 x^3+5 \sqrt{a^2} b^{10} x\right)\right)}+\frac{2 c^2 \sqrt{b^2+a^2 x^2} \left(2 x \sqrt{b^2+a^2 x^2} a^2+\left(b^2+2 a^2 x^2\right) a\right) \left(28 x \sqrt{b^2+a^2 x^2} \left(-b^6-a^2 x^2 b^4+3 a^4 x^4 b^2+2 a^6 x^6\right) a^2+\left(-8 b^8-49 a^2 x^2 b^6+7 a^4 x^4 b^4+112 a^6 x^6 b^2+56 a^8 x^8\right) a\right) \left(\sqrt{a^2} b^2+2 \sqrt{a^2} x \left(x a^2+\sqrt{b^2+a^2 x^2} a\right)\right)^3}{63 a^6 \sqrt{a^2} b^2 \sqrt{a x+\sqrt{b^2+a^2 x^2}} \left(x \sqrt{b^2+a^2 x^2} \left(11 b^{10}+220 a^2 x^2 b^8+1232 a^4 x^4 b^6+2816 a^6 x^6 b^4+2816 a^8 x^8 b^2+1024 a^{10} x^{10}\right) a^2+\left(b^{12}+61 a^2 x^2 b^{10}+620 a^4 x^4 b^8+2352 a^6 x^6 b^6+4096 a^8 x^8 b^4+3328 a^{10} x^{10} b^2+1024 a^{12} x^{12}\right) a\right)}","\frac{2 \sqrt{a^2 x^2+b^2} \left(12 a^4 c^2 x^5+40 a^4 c d x^4+60 a^4 d^2 x^3-3 a^2 b^2 c^2 x^3+30 a^2 b^2 c d x^2+25 a^2 b^2 d^2 x-4 b^4 c^2 x+4 b^4 c d\right)}{15 a^2 \left(\sqrt{a^2 x^2+b^2}+a x\right)^{7/2}}+\frac{2 \left(84 a^6 c^2 x^6+280 a^6 c d x^5+420 a^6 d^2 x^4+21 a^4 b^2 c^2 x^4+350 a^4 b^2 c d x^3+385 a^4 b^2 d^2 x^2-49 a^2 b^4 c^2 x^2+98 a^2 b^4 c d x+35 a^2 b^4 d^2-8 b^6 c^2\right)}{105 a^3 \left(\sqrt{a^2 x^2+b^2}+a x\right)^{7/2}}",1,"(2*d^2*Sqrt[b^2 + a^2*x^2]*(2*a^2*x*Sqrt[b^2 + a^2*x^2] + a*(b^2 + 2*a^2*x^2))*(6*a^2*x*Sqrt[b^2 + a^2*x^2]*(3*b^2 + a^2*x^2) + a*(7*b^4 + 21*a^2*b^2*x^2 + 6*a^4*x^4))*(Sqrt[a^2]*b^2 + 2*Sqrt[a^2]*x*(a^2*x + a*Sqrt[b^2 + a^2*x^2]))^3)/(15*a^4*Sqrt[a^2]*b^2*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]*(a^2*x*Sqrt[b^2 + a^2*x^2]*(9*b^8 + 120*a^2*b^6*x^2 + 432*a^4*b^4*x^4 + 576*a^6*b^2*x^6 + 256*a^8*x^8) + a*(b^10 + 41*a^2*b^8*x^2 + 280*a^4*b^6*x^4 + 688*a^6*b^4*x^6 + 704*a^8*b^2*x^8 + 256*a^10*x^10))) + (4*c*d*Sqrt[b^2 + a^2*x^2]*(2*a^2*x*Sqrt[b^2 + a^2*x^2] + a*(b^2 + 2*a^2*x^2))*(5*a^2*x*Sqrt[b^2 + a^2*x^2]*(11*b^4 + 19*a^2*b^2*x^2 + 12*a^4*x^4) + a*(22*b^6 + 95*a^2*b^4*x^2 + 125*a^4*b^2*x^4 + 60*a^6*x^6))*(Sqrt[a^2]*b^2 + 2*Sqrt[a^2]*x*(a^2*x + a*Sqrt[b^2 + a^2*x^2]))^3)/(105*a^6*b^2*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]*(Sqrt[a^2]*Sqrt[b^2 + a^2*x^2]*(b^10 + 50*a^2*b^8*x^2 + 400*a^4*b^6*x^4 + 1120*a^6*b^4*x^6 + 1280*a^8*b^2*x^8 + 512*a^10*x^10) + 2*a*(5*Sqrt[a^2]*b^10*x + 85*(a^2)^(3/2)*b^8*x^3 + 416*(a^2)^(5/2)*b^6*x^5 + 848*(a^2)^(7/2)*b^4*x^7 + 768*(a^2)^(9/2)*b^2*x^9 + 256*(a^2)^(11/2)*x^11))) + (2*c^2*Sqrt[b^2 + a^2*x^2]*(2*a^2*x*Sqrt[b^2 + a^2*x^2] + a*(b^2 + 2*a^2*x^2))*(28*a^2*x*Sqrt[b^2 + a^2*x^2]*(-b^6 - a^2*b^4*x^2 + 3*a^4*b^2*x^4 + 2*a^6*x^6) + a*(-8*b^8 - 49*a^2*b^6*x^2 + 7*a^4*b^4*x^4 + 112*a^6*b^2*x^6 + 56*a^8*x^8))*(Sqrt[a^2]*b^2 + 2*Sqrt[a^2]*x*(a^2*x + a*Sqrt[b^2 + a^2*x^2]))^3)/(63*a^6*Sqrt[a^2]*b^2*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]*(a^2*x*Sqrt[b^2 + a^2*x^2]*(11*b^10 + 220*a^2*b^8*x^2 + 1232*a^4*b^6*x^4 + 2816*a^6*b^4*x^6 + 2816*a^8*b^2*x^8 + 1024*a^10*x^10) + a*(b^12 + 61*a^2*b^10*x^2 + 620*a^4*b^8*x^4 + 2352*a^6*b^6*x^6 + 4096*a^8*b^4*x^8 + 3328*a^10*b^2*x^10 + 1024*a^12*x^12))) - (Sqrt[a^2]*d^2*x*(a*x + Sqrt[b^2 + a^2*x^2])*((2*b^4)/(3*(a*x + Sqrt[b^2 + a^2*x^2])^(3/2)) + (2*(a*x + Sqrt[b^2 + a^2*x^2])^(5/2))/5))/(2*b^2*(a/Sqrt[a^2] + (Sqrt[a^2]*x)/Sqrt[b^2 + a^2*x^2])*(-(Sqrt[a^2]*b^2) + Sqrt[a^2]*(a*x + Sqrt[b^2 + a^2*x^2])^2)*(Sqrt[a^2]/a - (-(Sqrt[a^2]*b^2) + Sqrt[a^2]*(a*x + Sqrt[b^2 + a^2*x^2])^2)/(2*a*(a*x + Sqrt[b^2 + a^2*x^2])^2))) - (2*a^2*c*d*x^2*(-21*b^6 + 105*b^4*(a*x + Sqrt[b^2 + a^2*x^2])^2 - 35*b^2*(a*x + Sqrt[b^2 + a^2*x^2])^4 + 15*(a*x + Sqrt[b^2 + a^2*x^2])^6))/(105*b^2*(a/Sqrt[a^2] + (Sqrt[a^2]*x)/Sqrt[b^2 + a^2*x^2])*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]*(-(Sqrt[a^2]*b^2) + Sqrt[a^2]*(a*x + Sqrt[b^2 + a^2*x^2])^2)^2*(Sqrt[a^2]/a - (-(Sqrt[a^2]*b^2) + Sqrt[a^2]*(a*x + Sqrt[b^2 + a^2*x^2])^2)/(2*a*(a*x + Sqrt[b^2 + a^2*x^2])^2))) - ((a^2)^(3/2)*c^2*x^3*(45*b^8 - 210*b^6*(a*x + Sqrt[b^2 + a^2*x^2])^2 - 126*b^2*(a*x + Sqrt[b^2 + a^2*x^2])^6 + 35*(a*x + Sqrt[b^2 + a^2*x^2])^8))/(315*b^2*(a/Sqrt[a^2] + (Sqrt[a^2]*x)/Sqrt[b^2 + a^2*x^2])*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]*(-(Sqrt[a^2]*b^2) + Sqrt[a^2]*(a*x + Sqrt[b^2 + a^2*x^2])^2)^3*(Sqrt[a^2]/a - (-(Sqrt[a^2]*b^2) + Sqrt[a^2]*(a*x + Sqrt[b^2 + a^2*x^2])^2)/(2*a*(a*x + Sqrt[b^2 + a^2*x^2])^2)))","B",1
2823,1,1433,282,8.8011798,"\int \frac{1-\sqrt[3]{1-3 x+3 x^3-9 x^4+3 x^6-9 x^7+x^9-3 x^{10}}}{x^2+\sqrt[3]{1-3 x+3 x^3-9 x^4+3 x^6-9 x^7+x^9-3 x^{10}}} \, dx","Integrate[(1 - (1 - 3*x + 3*x^3 - 9*x^4 + 3*x^6 - 9*x^7 + x^9 - 3*x^10)^(1/3))/(x^2 + (1 - 3*x + 3*x^3 - 9*x^4 + 3*x^6 - 9*x^7 + x^9 - 3*x^10)^(1/3)),x]","-x-\frac{\left(-\left((3 x-1) \left(x^3+1\right)^3\right)\right)^{2/3} \text{RootSum}\left[\text{$\#$1}^{10}+3 \text{$\#$1}^7-3 \text{$\#$1}^6+3 \text{$\#$1}^4-6 \text{$\#$1}^3+28 \text{$\#$1}-3\&,\frac{\log \left(\sqrt[3]{3 x-1}-\text{$\#$1}\right) \text{$\#$1}^8+2 \log \left(\sqrt[3]{3 x-1}-\text{$\#$1}\right) \text{$\#$1}^5+10 \log \left(\sqrt[3]{3 x-1}-\text{$\#$1}\right) \text{$\#$1}^2}{10 \text{$\#$1}^9+21 \text{$\#$1}^6-18 \text{$\#$1}^5+12 \text{$\#$1}^3-18 \text{$\#$1}^2+28}\&\right]}{(3 x-1)^{2/3} \left(x^3+1\right)^2}-\frac{1}{3} \text{RootSum}\left[3 \text{$\#$1}^{10}-\text{$\#$1}^9+9 \text{$\#$1}^7-4 \text{$\#$1}^6+9 \text{$\#$1}^4-3 \text{$\#$1}^3+3 \text{$\#$1}-1\&,\frac{\log (x-\text{$\#$1}) \text{$\#$1}^6+\log (x-\text{$\#$1}) \text{$\#$1}^4}{10 \text{$\#$1}^9-3 \text{$\#$1}^8+21 \text{$\#$1}^6-8 \text{$\#$1}^5+12 \text{$\#$1}^3-3 \text{$\#$1}^2+1}\&\right]-\frac{\left(-\left((3 x-1) \left(x^3+1\right)^3\right)\right)^{2/3} \text{RootSum}\left[\text{$\#$1}^{20}+6 \text{$\#$1}^{17}+3 \text{$\#$1}^{16}+15 \text{$\#$1}^{14}+15 \text{$\#$1}^{13}+9 \text{$\#$1}^{12}+74 \text{$\#$1}^{11}+30 \text{$\#$1}^{10}+36 \text{$\#$1}^9+177 \text{$\#$1}^8+111 \text{$\#$1}^7+54 \text{$\#$1}^6+168 \text{$\#$1}^5+177 \text{$\#$1}^4+36 \text{$\#$1}^3+784 \text{$\#$1}^2+84 \text{$\#$1}+9\&,\frac{2 \log \left(\sqrt[3]{3 x-1}-\text{$\#$1}\right) \text{$\#$1}^{18}+10 \log \left(\sqrt[3]{3 x-1}-\text{$\#$1}\right) \text{$\#$1}^{15}+3 \log \left(\sqrt[3]{3 x-1}-\text{$\#$1}\right) \text{$\#$1}^{14}+38 \log \left(\sqrt[3]{3 x-1}-\text{$\#$1}\right) \text{$\#$1}^{12}+12 \log \left(\sqrt[3]{3 x-1}-\text{$\#$1}\right) \text{$\#$1}^{11}+128 \log \left(\sqrt[3]{3 x-1}-\text{$\#$1}\right) \text{$\#$1}^9+45 \log \left(\sqrt[3]{3 x-1}-\text{$\#$1}\right) \text{$\#$1}^8+172 \log \left(\sqrt[3]{3 x-1}-\text{$\#$1}\right) \text{$\#$1}^6+66 \log \left(\sqrt[3]{3 x-1}-\text{$\#$1}\right) \text{$\#$1}^5+560 \log \left(\sqrt[3]{3 x-1}-\text{$\#$1}\right) \text{$\#$1}^3+30 \log \left(\sqrt[3]{3 x-1}-\text{$\#$1}\right) \text{$\#$1}^2}{20 \text{$\#$1}^{19}+102 \text{$\#$1}^{16}+48 \text{$\#$1}^{15}+210 \text{$\#$1}^{13}+195 \text{$\#$1}^{12}+108 \text{$\#$1}^{11}+814 \text{$\#$1}^{10}+300 \text{$\#$1}^9+324 \text{$\#$1}^8+1416 \text{$\#$1}^7+777 \text{$\#$1}^6+324 \text{$\#$1}^5+840 \text{$\#$1}^4+708 \text{$\#$1}^3+108 \text{$\#$1}^2+1568 \text{$\#$1}+84}\&\right]}{(3 x-1)^{2/3} \left(x^3+1\right)^2}+\frac{\sqrt[3]{-\left((3 x-1) \left(x^3+1\right)^3\right)} \left(x^4+x^2\right) \text{RootSum}\left[\text{$\#$1}^{10}+3 \text{$\#$1}^7-3 \text{$\#$1}^6+3 \text{$\#$1}^4-6 \text{$\#$1}^3+28 \text{$\#$1}-3\&,\frac{\log \left(\sqrt[3]{3 x-1}-\text{$\#$1}\right) \text{$\#$1}^8+2 \log \left(\sqrt[3]{3 x-1}-\text{$\#$1}\right) \text{$\#$1}^5+10 \log \left(\sqrt[3]{3 x-1}-\text{$\#$1}\right) \text{$\#$1}^2}{10 \text{$\#$1}^9+21 \text{$\#$1}^6-18 \text{$\#$1}^5+12 \text{$\#$1}^3-18 \text{$\#$1}^2+28}\&\right]}{\sqrt[3]{3 x-1} \left(x^2+1\right) \left(x^3+1\right) x^2}-\frac{\sqrt[3]{-\left((3 x-1) \left(x^3+1\right)^3\right)} \left(x^4+x^2\right) \text{RootSum}\left[\text{$\#$1}^{20}+6 \text{$\#$1}^{17}+3 \text{$\#$1}^{16}+15 \text{$\#$1}^{14}+15 \text{$\#$1}^{13}+9 \text{$\#$1}^{12}+74 \text{$\#$1}^{11}+30 \text{$\#$1}^{10}+36 \text{$\#$1}^9+177 \text{$\#$1}^8+111 \text{$\#$1}^7+54 \text{$\#$1}^6+168 \text{$\#$1}^5+177 \text{$\#$1}^4+36 \text{$\#$1}^3+784 \text{$\#$1}^2+84 \text{$\#$1}+9\&,\frac{\log \left(\sqrt[3]{3 x-1}-\text{$\#$1}\right) \text{$\#$1}^{18}+5 \log \left(\sqrt[3]{3 x-1}-\text{$\#$1}\right) \text{$\#$1}^{15}-3 \log \left(\sqrt[3]{3 x-1}-\text{$\#$1}\right) \text{$\#$1}^{14}+19 \log \left(\sqrt[3]{3 x-1}-\text{$\#$1}\right) \text{$\#$1}^{12}-12 \log \left(\sqrt[3]{3 x-1}-\text{$\#$1}\right) \text{$\#$1}^{11}+64 \log \left(\sqrt[3]{3 x-1}-\text{$\#$1}\right) \text{$\#$1}^9-45 \log \left(\sqrt[3]{3 x-1}-\text{$\#$1}\right) \text{$\#$1}^8+86 \log \left(\sqrt[3]{3 x-1}-\text{$\#$1}\right) \text{$\#$1}^6-66 \log \left(\sqrt[3]{3 x-1}-\text{$\#$1}\right) \text{$\#$1}^5+280 \log \left(\sqrt[3]{3 x-1}-\text{$\#$1}\right) \text{$\#$1}^3-30 \log \left(\sqrt[3]{3 x-1}-\text{$\#$1}\right) \text{$\#$1}^2}{20 \text{$\#$1}^{19}+102 \text{$\#$1}^{16}+48 \text{$\#$1}^{15}+210 \text{$\#$1}^{13}+195 \text{$\#$1}^{12}+108 \text{$\#$1}^{11}+814 \text{$\#$1}^{10}+300 \text{$\#$1}^9+324 \text{$\#$1}^8+1416 \text{$\#$1}^7+777 \text{$\#$1}^6+324 \text{$\#$1}^5+840 \text{$\#$1}^4+708 \text{$\#$1}^3+108 \text{$\#$1}^2+1568 \text{$\#$1}+84}\&\right]}{\sqrt[3]{3 x-1} \left(x^2+1\right) \left(x^3+1\right) x^2}","3 \text{RootSum}\left[\text{$\#$1}^{10}-3 \text{$\#$1}^7-3 \text{$\#$1}^6+3 \text{$\#$1}^4+6 \text{$\#$1}^3-28 \text{$\#$1}-3\&,\frac{\text{$\#$1}^8 \left(-\log \left(x^3+1\right)\right)+\text{$\#$1}^8 \log \left(-\text{$\#$1} x^3-\text{$\#$1}+\sqrt[3]{-3 x^{10}+x^9-9 x^7+3 x^6-9 x^4+3 x^3-3 x+1}\right)+2 \text{$\#$1}^5 \log \left(x^3+1\right)-2 \text{$\#$1}^5 \log \left(-\text{$\#$1} x^3-\text{$\#$1}+\sqrt[3]{-3 x^{10}+x^9-9 x^7+3 x^6-9 x^4+3 x^3-3 x+1}\right)-10 \text{$\#$1}^2 \log \left(x^3+1\right)+10 \text{$\#$1}^2 \log \left(-\text{$\#$1} x^3-\text{$\#$1}+\sqrt[3]{-3 x^{10}+x^9-9 x^7+3 x^6-9 x^4+3 x^3-3 x+1}\right)}{10 \text{$\#$1}^9-21 \text{$\#$1}^6-18 \text{$\#$1}^5+12 \text{$\#$1}^3+18 \text{$\#$1}^2-28}\&\right]-x",1,"-x - ((-((-1 + 3*x)*(1 + x^3)^3))^(2/3)*RootSum[-3 + 28*#1 - 6*#1^3 + 3*#1^4 - 3*#1^6 + 3*#1^7 + #1^10 & , (10*Log[(-1 + 3*x)^(1/3) - #1]*#1^2 + 2*Log[(-1 + 3*x)^(1/3) - #1]*#1^5 + Log[(-1 + 3*x)^(1/3) - #1]*#1^8)/(28 - 18*#1^2 + 12*#1^3 - 18*#1^5 + 21*#1^6 + 10*#1^9) & ])/((-1 + 3*x)^(2/3)*(1 + x^3)^2) + ((-((-1 + 3*x)*(1 + x^3)^3))^(1/3)*(x^2 + x^4)*RootSum[-3 + 28*#1 - 6*#1^3 + 3*#1^4 - 3*#1^6 + 3*#1^7 + #1^10 & , (10*Log[(-1 + 3*x)^(1/3) - #1]*#1^2 + 2*Log[(-1 + 3*x)^(1/3) - #1]*#1^5 + Log[(-1 + 3*x)^(1/3) - #1]*#1^8)/(28 - 18*#1^2 + 12*#1^3 - 18*#1^5 + 21*#1^6 + 10*#1^9) & ])/(x^2*(-1 + 3*x)^(1/3)*(1 + x^2)*(1 + x^3)) - RootSum[-1 + 3*#1 - 3*#1^3 + 9*#1^4 - 4*#1^6 + 9*#1^7 - #1^9 + 3*#1^10 & , (Log[x - #1]*#1^4 + Log[x - #1]*#1^6)/(1 - 3*#1^2 + 12*#1^3 - 8*#1^5 + 21*#1^6 - 3*#1^8 + 10*#1^9) & ]/3 - ((-((-1 + 3*x)*(1 + x^3)^3))^(1/3)*(x^2 + x^4)*RootSum[9 + 84*#1 + 784*#1^2 + 36*#1^3 + 177*#1^4 + 168*#1^5 + 54*#1^6 + 111*#1^7 + 177*#1^8 + 36*#1^9 + 30*#1^10 + 74*#1^11 + 9*#1^12 + 15*#1^13 + 15*#1^14 + 3*#1^16 + 6*#1^17 + #1^20 & , (-30*Log[(-1 + 3*x)^(1/3) - #1]*#1^2 + 280*Log[(-1 + 3*x)^(1/3) - #1]*#1^3 - 66*Log[(-1 + 3*x)^(1/3) - #1]*#1^5 + 86*Log[(-1 + 3*x)^(1/3) - #1]*#1^6 - 45*Log[(-1 + 3*x)^(1/3) - #1]*#1^8 + 64*Log[(-1 + 3*x)^(1/3) - #1]*#1^9 - 12*Log[(-1 + 3*x)^(1/3) - #1]*#1^11 + 19*Log[(-1 + 3*x)^(1/3) - #1]*#1^12 - 3*Log[(-1 + 3*x)^(1/3) - #1]*#1^14 + 5*Log[(-1 + 3*x)^(1/3) - #1]*#1^15 + Log[(-1 + 3*x)^(1/3) - #1]*#1^18)/(84 + 1568*#1 + 108*#1^2 + 708*#1^3 + 840*#1^4 + 324*#1^5 + 777*#1^6 + 1416*#1^7 + 324*#1^8 + 300*#1^9 + 814*#1^10 + 108*#1^11 + 195*#1^12 + 210*#1^13 + 48*#1^15 + 102*#1^16 + 20*#1^19) & ])/(x^2*(-1 + 3*x)^(1/3)*(1 + x^2)*(1 + x^3)) - ((-((-1 + 3*x)*(1 + x^3)^3))^(2/3)*RootSum[9 + 84*#1 + 784*#1^2 + 36*#1^3 + 177*#1^4 + 168*#1^5 + 54*#1^6 + 111*#1^7 + 177*#1^8 + 36*#1^9 + 30*#1^10 + 74*#1^11 + 9*#1^12 + 15*#1^13 + 15*#1^14 + 3*#1^16 + 6*#1^17 + #1^20 & , (30*Log[(-1 + 3*x)^(1/3) - #1]*#1^2 + 560*Log[(-1 + 3*x)^(1/3) - #1]*#1^3 + 66*Log[(-1 + 3*x)^(1/3) - #1]*#1^5 + 172*Log[(-1 + 3*x)^(1/3) - #1]*#1^6 + 45*Log[(-1 + 3*x)^(1/3) - #1]*#1^8 + 128*Log[(-1 + 3*x)^(1/3) - #1]*#1^9 + 12*Log[(-1 + 3*x)^(1/3) - #1]*#1^11 + 38*Log[(-1 + 3*x)^(1/3) - #1]*#1^12 + 3*Log[(-1 + 3*x)^(1/3) - #1]*#1^14 + 10*Log[(-1 + 3*x)^(1/3) - #1]*#1^15 + 2*Log[(-1 + 3*x)^(1/3) - #1]*#1^18)/(84 + 1568*#1 + 108*#1^2 + 708*#1^3 + 840*#1^4 + 324*#1^5 + 777*#1^6 + 1416*#1^7 + 324*#1^8 + 300*#1^9 + 814*#1^10 + 108*#1^11 + 195*#1^12 + 210*#1^13 + 48*#1^15 + 102*#1^16 + 20*#1^19) & ])/((-1 + 3*x)^(2/3)*(1 + x^3)^2)","B",1
2824,0,0,285,0.6583013,"\int \frac{1-k x}{(1+(-2+k) x) ((1-x) x (1-k x))^{2/3}} \, dx","Integrate[(1 - k*x)/((1 + (-2 + k)*x)*((1 - x)*x*(1 - k*x))^(2/3)),x]","\int \frac{1-k x}{(1+(-2+k) x) ((1-x) x (1-k x))^{2/3}} \, dx","-\frac{(-1)^{2/3} \log \left(k^2 x^2+2 (-1)^{2/3} \sqrt[3]{2} (k-1)^{2/3} \left(k x^3+(-k-1) x^2+x\right)^{2/3}+\left(\sqrt[3]{-1} 2^{2/3} \sqrt[3]{k-1}-\sqrt[3]{-1} 2^{2/3} \sqrt[3]{k-1} k x\right) \sqrt[3]{k x^3+(-k-1) x^2+x}-2 k x+1\right)}{2\ 2^{2/3} \sqrt[3]{k-1}}+\frac{(-1)^{2/3} \log \left(\sqrt[3]{-1} 2^{2/3} \sqrt[3]{k-1} \sqrt[3]{k x^3+(-k-1) x^2+x}+k x-1\right)}{2^{2/3} \sqrt[3]{k-1}}+\frac{(-1)^{2/3} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} k x-\sqrt{3}}{-2 \sqrt[3]{-1} 2^{2/3} \sqrt[3]{k-1} \sqrt[3]{k x^3+(-k-1) x^2+x}+k x-1}\right)}{2^{2/3} \sqrt[3]{k-1}}",1,"Integrate[(1 - k*x)/((1 + (-2 + k)*x)*((1 - x)*x*(1 - k*x))^(2/3)), x]","F",-1
2825,0,0,285,0.458477,"\int \frac{1+x^2+x^3}{\left(-1+x^2+x^3\right) \sqrt[3]{x^2+x^3}} \, dx","Integrate[(1 + x^2 + x^3)/((-1 + x^2 + x^3)*(x^2 + x^3)^(1/3)),x]","\int \frac{1+x^2+x^3}{\left(-1+x^2+x^3\right) \sqrt[3]{x^2+x^3}} \, dx","2 \text{RootSum}\left[\text{$\#$1}^3-\text{$\#$1}-1\&,\frac{\text{$\#$1} \log \left(\sqrt[3]{x^3+x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{3 \text{$\#$1}^2-1}\&\right]+2 \text{RootSum}\left[\text{$\#$1}^6+\text{$\#$1}^4-2 \text{$\#$1}^3+\text{$\#$1}^2-\text{$\#$1}+1\&,\frac{2 \text{$\#$1}^4 \log \left(\sqrt[3]{x^3+x^2}-\text{$\#$1} x\right)-2 \text{$\#$1}^4 \log (x)+\text{$\#$1}^2 \log \left(\sqrt[3]{x^3+x^2}-\text{$\#$1} x\right)-\text{$\#$1}^2 \log (x)-2 \text{$\#$1} \log \left(\sqrt[3]{x^3+x^2}-\text{$\#$1} x\right)+2 \text{$\#$1} \log (x)}{6 \text{$\#$1}^5+4 \text{$\#$1}^3-6 \text{$\#$1}^2+2 \text{$\#$1}-1}\&\right]-\log \left(\sqrt[3]{x^3+x^2}-x\right)+\frac{1}{2} \log \left(x^2+\sqrt[3]{x^3+x^2} x+\left(x^3+x^2\right)^{2/3}\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+x^2}+x}\right)",1,"Integrate[(1 + x^2 + x^3)/((-1 + x^2 + x^3)*(x^2 + x^3)^(1/3)), x]","F",-1
2826,0,0,285,0.0769903,"\int \frac{1+x^2+x^3}{\left(-1+x^2+x^3\right) \sqrt[3]{x^2+x^3}} \, dx","Integrate[(1 + x^2 + x^3)/((-1 + x^2 + x^3)*(x^2 + x^3)^(1/3)),x]","\int \frac{1+x^2+x^3}{\left(-1+x^2+x^3\right) \sqrt[3]{x^2+x^3}} \, dx","2 \text{RootSum}\left[\text{$\#$1}^3-\text{$\#$1}-1\&,\frac{\text{$\#$1} \log \left(\sqrt[3]{x^3+x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{3 \text{$\#$1}^2-1}\&\right]+2 \text{RootSum}\left[\text{$\#$1}^6+\text{$\#$1}^4-2 \text{$\#$1}^3+\text{$\#$1}^2-\text{$\#$1}+1\&,\frac{2 \text{$\#$1}^4 \log \left(\sqrt[3]{x^3+x^2}-\text{$\#$1} x\right)-2 \text{$\#$1}^4 \log (x)+\text{$\#$1}^2 \log \left(\sqrt[3]{x^3+x^2}-\text{$\#$1} x\right)-\text{$\#$1}^2 \log (x)-2 \text{$\#$1} \log \left(\sqrt[3]{x^3+x^2}-\text{$\#$1} x\right)+2 \text{$\#$1} \log (x)}{6 \text{$\#$1}^5+4 \text{$\#$1}^3-6 \text{$\#$1}^2+2 \text{$\#$1}-1}\&\right]-\log \left(\sqrt[3]{x^3+x^2}-x\right)+\frac{1}{2} \log \left(x^2+\sqrt[3]{x^3+x^2} x+\left(x^3+x^2\right)^{2/3}\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+x^2}+x}\right)",1,"Integrate[(1 + x^2 + x^3)/((-1 + x^2 + x^3)*(x^2 + x^3)^(1/3)), x]","F",-1
2827,1,182,286,0.2681442,"\int \frac{\sqrt{a x+\sqrt{-b+a x}}}{x \sqrt{-b+a x}} \, dx","Integrate[Sqrt[a*x + Sqrt[-b + a*x]]/(x*Sqrt[-b + a*x]),x]","2 \tanh ^{-1}\left(\frac{2 \sqrt{a x-b}+1}{2 \sqrt{\sqrt{a x-b}+a x}}\right)-\frac{\tan ^{-1}\left(\frac{\left(2 \sqrt{-b}-1\right) \sqrt{a x-b}-2 b+\sqrt{-b}}{2 \sqrt[4]{-b} \sqrt{\sqrt{a x-b}+a x}}\right)+\tanh ^{-1}\left(\frac{\left(2 \sqrt{-b}+1\right) \sqrt{a x-b}+2 b+\sqrt{-b}}{2 \sqrt[4]{-b} \sqrt{\sqrt{a x-b}+a x}}\right)}{\sqrt[4]{-b}}","-2 \text{RootSum}\left[\text{$\#$1}^4+4 \text{$\#$1}^3+8 \text{$\#$1}^2 b+6 \text{$\#$1}^2-16 \text{$\#$1} b+4 \text{$\#$1}+16 b^2-8 b+1\&,\frac{\text{$\#$1}^2 \left(-\log \left(\text{$\#$1}+2 \sqrt{a x-b}-2 \sqrt{\sqrt{a x-b}+a x}+1\right)\right)-2 \text{$\#$1} \log \left(\text{$\#$1}+2 \sqrt{a x-b}-2 \sqrt{\sqrt{a x-b}+a x}+1\right)+4 b \log \left(\text{$\#$1}+2 \sqrt{a x-b}-2 \sqrt{\sqrt{a x-b}+a x}+1\right)-\log \left(\text{$\#$1}+2 \sqrt{a x-b}-2 \sqrt{\sqrt{a x-b}+a x}+1\right)}{\text{$\#$1}^3+3 \text{$\#$1}^2+4 \text{$\#$1} b+3 \text{$\#$1}-4 b+1}\&\right]-2 \log \left(2 \sqrt{a x-b}-2 \sqrt{\sqrt{a x-b}+a x}+1\right)",1,"2*ArcTanh[(1 + 2*Sqrt[-b + a*x])/(2*Sqrt[a*x + Sqrt[-b + a*x]])] - (ArcTan[(Sqrt[-b] - 2*b + (-1 + 2*Sqrt[-b])*Sqrt[-b + a*x])/(2*(-b)^(1/4)*Sqrt[a*x + Sqrt[-b + a*x]])] + ArcTanh[(Sqrt[-b] + 2*b + (1 + 2*Sqrt[-b])*Sqrt[-b + a*x])/(2*(-b)^(1/4)*Sqrt[a*x + Sqrt[-b + a*x]])])/(-b)^(1/4)","A",1
2828,0,0,286,9.2663133,"\int \sqrt{a x+\sqrt{b+a^2 x^2}} \sqrt{c+\sqrt{a x+\sqrt{b+a^2 x^2}}} \, dx","Integrate[Sqrt[a*x + Sqrt[b + a^2*x^2]]*Sqrt[c + Sqrt[a*x + Sqrt[b + a^2*x^2]]],x]","\int \sqrt{a x+\sqrt{b+a^2 x^2}} \sqrt{c+\sqrt{a x+\sqrt{b+a^2 x^2}}} \, dx","\frac{\sqrt{\sqrt{a^2 x^2+b}+a x} \left(6 a c x+16 c^3\right) \sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}+\sqrt{a^2 x^2+b} \left(\left(60 a x-8 c^2\right) \sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}+6 c \sqrt{\sqrt{a^2 x^2+b}+a x} \sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}\right)+\left(60 a^2 x^2-8 a c^2 x-75 b\right) \sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}}{105 a \sqrt{\sqrt{a^2 x^2+b}+a x}}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}}{\sqrt{c}}\right)}{a \sqrt{c}}",1,"Integrate[Sqrt[a*x + Sqrt[b + a^2*x^2]]*Sqrt[c + Sqrt[a*x + Sqrt[b + a^2*x^2]]], x]","F",-1
2829,0,0,287,0.1436132,"\int x^4 \sqrt{b+a^2 x^4} \sqrt{a x^2+\sqrt{b+a^2 x^4}} \, dx","Integrate[x^4*Sqrt[b + a^2*x^4]*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]],x]","\int x^4 \sqrt{b+a^2 x^4} \sqrt{a x^2+\sqrt{b+a^2 x^4}} \, dx","\frac{\sqrt{a} x \left(192 a^6 x^{12}+360 a^4 b x^8+212 a^2 b^2 x^4+39 b^3\right) \sqrt{\sqrt{a^2 x^4+b}+a x^2}+\sqrt{a} x \sqrt{a^2 x^4+b} \sqrt{\sqrt{a^2 x^4+b}+a x^2} \left(192 a^5 x^{10}+264 a^3 b x^6+104 a b^2 x^2\right)}{1152 a^{7/2} b x^2+1536 a^{11/2} x^6+1536 a^{9/2} x^4 \sqrt{a^2 x^4+b}+384 a^{5/2} b \sqrt{a^2 x^4+b}}-\frac{13 b^2 \log \left(i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)}{128 \sqrt{2} a^{5/2}}",1,"Integrate[x^4*Sqrt[b + a^2*x^4]*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]], x]","F",-1
2830,0,0,287,14.522971,"\int \frac{\sqrt{c+\sqrt{a x+\sqrt{b+a^2 x^2}}}}{\left(b+a^2 x^2\right)^{3/2} \sqrt{a x+\sqrt{b+a^2 x^2}}} \, dx","Integrate[Sqrt[c + Sqrt[a*x + Sqrt[b + a^2*x^2]]]/((b + a^2*x^2)^(3/2)*Sqrt[a*x + Sqrt[b + a^2*x^2]]),x]","\int \frac{\sqrt{c+\sqrt{a x+\sqrt{b+a^2 x^2}}}}{\left(b+a^2 x^2\right)^{3/2} \sqrt{a x+\sqrt{b+a^2 x^2}}} \, dx","\frac{\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6 c+6 \text{$\#$1}^4 c^2-4 \text{$\#$1}^2 c^3+b+c^4\&,\frac{\text{$\#$1}^2 \left(-\log \left(\sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}-\text{$\#$1}\right)\right)-c \log \left(\sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}-\text{$\#$1}\right)}{\text{$\#$1} c-\text{$\#$1}^3}\&\right]}{4 a b}+\frac{a x \sqrt{\sqrt{a^2 x^2+b}+a x} \sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}+\sqrt{a^2 x^2+b} \sqrt{\sqrt{a^2 x^2+b}+a x} \sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}}{a^2 b x \sqrt{a^2 x^2+b}+a b \left(a^2 x^2+b\right)}",1,"Integrate[Sqrt[c + Sqrt[a*x + Sqrt[b + a^2*x^2]]]/((b + a^2*x^2)^(3/2)*Sqrt[a*x + Sqrt[b + a^2*x^2]]), x]","F",-1
2831,0,0,287,0.2594784,"\int \frac{\sqrt{c+\sqrt{a x+\sqrt{b+a^2 x^2}}}}{\left(b+a^2 x^2\right)^{3/2} \sqrt{a x+\sqrt{b+a^2 x^2}}} \, dx","Integrate[Sqrt[c + Sqrt[a*x + Sqrt[b + a^2*x^2]]]/((b + a^2*x^2)^(3/2)*Sqrt[a*x + Sqrt[b + a^2*x^2]]),x]","\int \frac{\sqrt{c+\sqrt{a x+\sqrt{b+a^2 x^2}}}}{\left(b+a^2 x^2\right)^{3/2} \sqrt{a x+\sqrt{b+a^2 x^2}}} \, dx","\frac{\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6 c+6 \text{$\#$1}^4 c^2-4 \text{$\#$1}^2 c^3+b+c^4\&,\frac{\text{$\#$1}^2 \left(-\log \left(\sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}-\text{$\#$1}\right)\right)-c \log \left(\sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}-\text{$\#$1}\right)}{\text{$\#$1} c-\text{$\#$1}^3}\&\right]}{4 a b}+\frac{a x \sqrt{\sqrt{a^2 x^2+b}+a x} \sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}+\sqrt{a^2 x^2+b} \sqrt{\sqrt{a^2 x^2+b}+a x} \sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}}{a^2 b x \sqrt{a^2 x^2+b}+a b \left(a^2 x^2+b\right)}",1,"Integrate[Sqrt[c + Sqrt[a*x + Sqrt[b + a^2*x^2]]]/((b + a^2*x^2)^(3/2)*Sqrt[a*x + Sqrt[b + a^2*x^2]]), x]","F",-1
2832,1,53,288,0.0410904,"\int \frac{x^2}{\left(b+a x^2\right) \sqrt[3]{x+x^3}} \, dx","Integrate[x^2/((b + a*x^2)*(x + x^3)^(1/3)),x]","\frac{3 x^3 \sqrt[3]{x^2+1} F_1\left(\frac{4}{3};\frac{1}{3},1;\frac{7}{3};-x^2,-\frac{a x^2}{b}\right)}{8 b \sqrt[3]{x^3+x}}","\frac{\sqrt[3]{b} \log \left(-\sqrt[3]{b} \sqrt[3]{x^3+x} x \sqrt[3]{a-b}+x^2 (a-b)^{2/3}+b^{2/3} \left(x^3+x\right)^{2/3}\right)}{4 a \sqrt[3]{a-b}}-\frac{\sqrt[3]{b} \log \left(x \sqrt[3]{a-b}+\sqrt[3]{b} \sqrt[3]{x^3+x}\right)}{2 a \sqrt[3]{a-b}}+\frac{\sqrt{3} \sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt{3} x \sqrt[3]{a-b}}{x \sqrt[3]{a-b}-2 \sqrt[3]{b} \sqrt[3]{x^3+x}}\right)}{2 a \sqrt[3]{a-b}}-\frac{\log \left(\sqrt[3]{x^3+x}-x\right)}{2 a}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+x}+x}\right)}{2 a}+\frac{\log \left(\sqrt[3]{x^3+x} x+\left(x^3+x\right)^{2/3}+x^2\right)}{4 a}",1,"(3*x^3*(1 + x^2)^(1/3)*AppellF1[4/3, 1/3, 1, 7/3, -x^2, -((a*x^2)/b)])/(8*b*(x + x^3)^(1/3))","C",0
2833,0,0,288,0.7230831,"\int \frac{1+x^6}{\sqrt[3]{x^2+x^4} \left(-1+x^6\right)} \, dx","Integrate[(1 + x^6)/((x^2 + x^4)^(1/3)*(-1 + x^6)),x]","\int \frac{1+x^6}{\sqrt[3]{x^2+x^4} \left(-1+x^6\right)} \, dx","-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^4+x^2}-x}\right)}{\sqrt{3}}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^4+x^2}+x}\right)}{\sqrt{3}}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^4+x^2}-x}\right)}{2 \sqrt[3]{2} \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^4+x^2}+x}\right)}{2 \sqrt[3]{2} \sqrt{3}}-\frac{2}{3} \tanh ^{-1}\left(\frac{x}{\sqrt[3]{x^4+x^2}}\right)-\frac{\tanh ^{-1}\left(\frac{\sqrt[3]{2} x}{\sqrt[3]{x^4+x^2}}\right)}{3 \sqrt[3]{2}}-\frac{1}{3} \tanh ^{-1}\left(\frac{x^2+\left(x^4+x^2\right)^{2/3}}{x \sqrt[3]{x^4+x^2}}\right)-\frac{\tanh ^{-1}\left(\frac{\sqrt[3]{2} x^2+\frac{\left(x^4+x^2\right)^{2/3}}{\sqrt[3]{2}}}{x \sqrt[3]{x^4+x^2}}\right)}{6 \sqrt[3]{2}}",1,"Integrate[(1 + x^6)/((x^2 + x^4)^(1/3)*(-1 + x^6)), x]","F",-1
2834,1,182,288,5.308274,"\int \frac{\sqrt{-2+3 x^4} \left(-1+3 x^4\right)}{x^3 \left(1-3 x^4+3 x^8\right)} \, dx","Integrate[(Sqrt[-2 + 3*x^4]*(-1 + 3*x^4))/(x^3*(1 - 3*x^4 + 3*x^8)),x]","\frac{\sqrt{3 x^4-2}}{2 x^2}+\frac{3 i \left(\tan ^{-1}\left(\frac{\sqrt{-\frac{3 \left(\sqrt{3}-i\right)}{\sqrt{3}+3 i}} x^2}{\sqrt{3 x^4-2}}\right)+\sqrt{-\sqrt{3}+i} \sqrt{-\frac{1}{\sqrt{3}+i}} \tan ^{-1}\left(\frac{x^2}{\sqrt{\frac{-\sqrt{3}+3 i}{3 \sqrt{3}+3 i}} \sqrt{3 x^4-2}}\right)\right)}{\left(\sqrt{3}-3 i\right) \sqrt{\frac{-3 \sqrt{3}+3 i}{\sqrt{3}+3 i}}}","\frac{1}{2} \sqrt{3} \text{RootSum}\left[\text{$\#$1}^4-2 \text{$\#$1}^3+4 \text{$\#$1}+4\&,\frac{\text{$\#$1}^2 \log \left(-\text{$\#$1}+\sqrt{3 x^4-2}+\sqrt{3} x^2\right)-\text{$\#$1} \log \left(-\text{$\#$1}+\sqrt{3 x^4-2}+\sqrt{3} x^2\right)-2 \log \left(-\text{$\#$1}+\sqrt{3 x^4-2}+\sqrt{3} x^2\right)}{2 \text{$\#$1}^3-3 \text{$\#$1}^2+2}\&\right]-\frac{1}{2} \sqrt{3} \text{RootSum}\left[\text{$\#$1}^4+2 \text{$\#$1}^3-4 \text{$\#$1}+4\&,\frac{\text{$\#$1}^2 \log \left(-\text{$\#$1}+\sqrt{3 x^4-2}+\sqrt{3} x^2\right)+\text{$\#$1} \log \left(-\text{$\#$1}+\sqrt{3 x^4-2}+\sqrt{3} x^2\right)-2 \log \left(-\text{$\#$1}+\sqrt{3 x^4-2}+\sqrt{3} x^2\right)}{2 \text{$\#$1}^3+3 \text{$\#$1}^2-2}\&\right]+\frac{\sqrt{3 x^4-2}}{2 x^2}",1,"Sqrt[-2 + 3*x^4]/(2*x^2) + ((3*I)*(ArcTan[(Sqrt[(-3*(-I + Sqrt[3]))/(3*I + Sqrt[3])]*x^2)/Sqrt[-2 + 3*x^4]] + Sqrt[I - Sqrt[3]]*Sqrt[-(I + Sqrt[3])^(-1)]*ArcTan[x^2/(Sqrt[(3*I - Sqrt[3])/(3*I + 3*Sqrt[3])]*Sqrt[-2 + 3*x^4])]))/((-3*I + Sqrt[3])*Sqrt[(3*I - 3*Sqrt[3])/(3*I + Sqrt[3])])","C",0
2835,0,0,288,0.4363752,"\int \frac{1}{\left(-b x+a^2 x^2\right)^{5/2} \left(a x^2+x \sqrt{-b x+a^2 x^2}\right)^{3/2}} \, dx","Integrate[1/((-(b*x) + a^2*x^2)^(5/2)*(a*x^2 + x*Sqrt[-(b*x) + a^2*x^2])^(3/2)),x]","\int \frac{1}{\left(-b x+a^2 x^2\right)^{5/2} \left(a x^2+x \sqrt{-b x+a^2 x^2}\right)^{3/2}} \, dx","\frac{\sqrt{a^2 x^2-b x} \sqrt{x \left(\sqrt{a^2 x^2-b x}+a x\right)} \left(121339 a^{10} x^5-148243 a^8 b x^4+12416 a^6 b^2 x^3+5248 a^4 b^3 x^2+2688 a^2 b^4 x-4368 b^5\right)}{16380 b^7 x^5 \left(b-a^2 x\right)^2}+\sqrt{x \left(\sqrt{a^2 x^2-b x}+a x\right)} \left(\frac{109 a^{15/2} \sqrt{\sqrt{a^2 x^2-b x}-a x} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\sqrt{a^2 x^2-b x}-a x}}{\sqrt{b}}\right)}{4 b^{15/2} x}-\frac{283847 a^9 x^4-229768 a^7 b x^3-24840 a^5 b^2 x^2-9352 a^3 b^3 x-4872 a b^4}{8190 b^7 x^4 \left(b-a^2 x\right)}\right)",1,"Integrate[1/((-(b*x) + a^2*x^2)^(5/2)*(a*x^2 + x*Sqrt[-(b*x) + a^2*x^2])^(3/2)), x]","F",-1
2836,0,0,289,2.5797063,"\int \frac{(a-2 b+x) (-b+x)}{\sqrt[3]{(-a+x) (-b+x)} \left(a^4-b^2 d-2 \left(2 a^3-b d\right) x+\left(6 a^2-d\right) x^2-4 a x^3+x^4\right)} \, dx","Integrate[((a - 2*b + x)*(-b + x))/(((-a + x)*(-b + x))^(1/3)*(a^4 - b^2*d - 2*(2*a^3 - b*d)*x + (6*a^2 - d)*x^2 - 4*a*x^3 + x^4)),x]","\int \frac{(a-2 b+x) (-b+x)}{\sqrt[3]{(-a+x) (-b+x)} \left(a^4-b^2 d-2 \left(2 a^3-b d\right) x+\left(6 a^2-d\right) x^2-4 a x^3+x^4\right)} \, dx","\frac{\tanh ^{-1}\left(\frac{\sqrt[3]{x (-a-b)+a b+x^2} \left(a \sqrt[6]{d}-\sqrt[6]{d} x\right)}{a^2+\sqrt[3]{d} \left(x (-a-b)+a b+x^2\right)^{2/3}-2 a x+x^2}\right)}{2 d^{5/6}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{d} \sqrt[3]{x (-a-b)+a b+x^2}}{\sqrt[6]{d} \sqrt[3]{x (-a-b)+a b+x^2}+2 a-2 x}\right)}{2 d^{5/6}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{d} \sqrt[3]{x (-a-b)+a b+x^2}}{\sqrt[6]{d} \sqrt[3]{x (-a-b)+a b+x^2}-2 a+2 x}\right)}{2 d^{5/6}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[3]{x (-a-b)+a b+x^2}}{a-x}\right)}{d^{5/6}}",1,"Integrate[((a - 2*b + x)*(-b + x))/(((-a + x)*(-b + x))^(1/3)*(a^4 - b^2*d - 2*(2*a^3 - b*d)*x + (6*a^2 - d)*x^2 - 4*a*x^3 + x^4)), x]","F",-1
2837,0,0,289,4.8566934,"\int \frac{(-1+x) x (1+(-2+k) x)}{\sqrt[3]{(1-x) x (1-k x)} \left(1-4 k x+\left(-b+6 k^2\right) x^2+\left(2 b-4 k^3\right) x^3+\left(-b+k^4\right) x^4\right)} \, dx","Integrate[((-1 + x)*x*(1 + (-2 + k)*x))/(((1 - x)*x*(1 - k*x))^(1/3)*(1 - 4*k*x + (-b + 6*k^2)*x^2 + (2*b - 4*k^3)*x^3 + (-b + k^4)*x^4)),x]","\int \frac{(-1+x) x (1+(-2+k) x)}{\sqrt[3]{(1-x) x (1-k x)} \left(1-4 k x+\left(-b+6 k^2\right) x^2+\left(2 b-4 k^3\right) x^3+\left(-b+k^4\right) x^4\right)} \, dx","\frac{\tanh ^{-1}\left(\frac{\sqrt[3]{k x^3+(-k-1) x^2+x} \left(\sqrt[6]{b} k x-\sqrt[6]{b}\right)}{\sqrt[3]{b} \left(k x^3+(-k-1) x^2+x\right)^{2/3}+k^2 x^2-2 k x+1}\right)}{2 b^{5/6}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{b} \sqrt[3]{k x^3+(-k-1) x^2+x}}{\sqrt[6]{b} \sqrt[3]{k x^3+(-k-1) x^2+x}-2 k x+2}\right)}{2 b^{5/6}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{b} \sqrt[3]{k x^3+(-k-1) x^2+x}}{\sqrt[6]{b} \sqrt[3]{k x^3+(-k-1) x^2+x}+2 k x-2}\right)}{2 b^{5/6}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{b} \sqrt[3]{k x^3+(-k-1) x^2+x}}{k x-1}\right)}{b^{5/6}}",1,"Integrate[((-1 + x)*x*(1 + (-2 + k)*x))/(((1 - x)*x*(1 - k*x))^(1/3)*(1 - 4*k*x + (-b + 6*k^2)*x^2 + (2*b - 4*k^3)*x^3 + (-b + k^4)*x^4)), x]","F",-1
2838,0,0,289,0.3473877,"\int \frac{\left(-1+x^3\right)^{2/3} \left(4+x^6\right)}{x^6 \left(-4+x^6\right)} \, dx","Integrate[((-1 + x^3)^(2/3)*(4 + x^6))/(x^6*(-4 + x^6)),x]","\int \frac{\left(-1+x^3\right)^{2/3} \left(4+x^6\right)}{x^6 \left(-4+x^6\right)} \, dx","\frac{\log \left(\sqrt[3]{2} \sqrt[3]{x^3-1}-x\right)}{6\ 2^{2/3}}-\frac{\log \left(\sqrt[3]{2} 3^{2/3} \sqrt[3]{x^3-1}-3 x\right)}{2\ 2^{2/3} \sqrt[3]{3}}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{2} \sqrt[3]{x^3-1}+x}\right)}{2\ 2^{2/3} \sqrt{3}}+\frac{\sqrt[6]{3} \tan ^{-1}\left(\frac{3^{5/6} x}{2 \sqrt[3]{2} \sqrt[3]{x^3-1}+\sqrt[3]{3} x}\right)}{2\ 2^{2/3}}+\frac{\left(x^3-1\right)^{2/3} \left(1-x^3\right)}{5 x^5}-\frac{\log \left(\sqrt[3]{2} \sqrt[3]{x^3-1} x+2^{2/3} \left(x^3-1\right)^{2/3}+x^2\right)}{12\ 2^{2/3}}+\frac{\log \left(\sqrt[3]{2} 3^{2/3} \sqrt[3]{x^3-1} x+2^{2/3} \sqrt[3]{3} \left(x^3-1\right)^{2/3}+3 x^2\right)}{4\ 2^{2/3} \sqrt[3]{3}}",1,"Integrate[((-1 + x^3)^(2/3)*(4 + x^6))/(x^6*(-4 + x^6)), x]","F",-1
2839,1,73,289,0.1827195,"\int \frac{\sqrt[6]{c+\sqrt[4]{a x+\sqrt{-b+a^2 x^2}}}}{\sqrt{-b+a^2 x^2}} \, dx","Integrate[(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(1/6)/Sqrt[-b + a^2*x^2],x]","-\frac{24 \sqrt[6]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c} \left(\, _2F_1\left(\frac{1}{6},1;\frac{7}{6};\frac{c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}{c}\right)-1\right)}{a}","\frac{24 \sqrt[6]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}}{a}+\frac{4 \sqrt{3} \sqrt[6]{c} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}}{\sqrt{3} \sqrt[6]{c}}\right)}{a}-\frac{4 \sqrt{3} \sqrt[6]{c} \tan ^{-1}\left(\frac{2 \sqrt[6]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}}{\sqrt{3} \sqrt[6]{c}}+\frac{1}{\sqrt{3}}\right)}{a}-\frac{8 \sqrt[6]{c} \tanh ^{-1}\left(\frac{\sqrt[6]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}}{\sqrt[6]{c}}\right)}{a}-\frac{4 \sqrt[6]{c} \tanh ^{-1}\left(\frac{\frac{\sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}}{\sqrt[6]{c}}+\sqrt[6]{c}}{\sqrt[6]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}}\right)}{a}",1,"(-24*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(1/6)*(-1 + Hypergeometric2F1[1/6, 1, 7/6, (c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))/c]))/a","C",1
2840,0,0,290,7.2957636,"\int \frac{(-b+x) \left(a b-2 b x+x^2\right)}{\left(x (-a+x) (-b+x)^2\right)^{2/3} \left(b d-(a+d) x+x^2\right)} \, dx","Integrate[((-b + x)*(a*b - 2*b*x + x^2))/((x*(-a + x)*(-b + x)^2)^(2/3)*(b*d - (a + d)*x + x^2)),x]","\int \frac{(-b+x) \left(a b-2 b x+x^2\right)}{\left(x (-a+x) (-b+x)^2\right)^{2/3} \left(b d-(a+d) x+x^2\right)} \, dx","\frac{\log \left(\sqrt[3]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}+b \sqrt[3]{d}-\sqrt[3]{d} x\right)}{d^{2/3}}-\frac{\log \left(\sqrt[3]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4} \left(\sqrt[3]{d} x-b \sqrt[3]{d}\right)+\left(x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4\right)^{2/3}+b^2 d^{2/3}-2 b d^{2/3} x+d^{2/3} x^2\right)}{2 d^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} b \sqrt[3]{d}-\sqrt{3} \sqrt[3]{d} x}{-2 \sqrt[3]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}+b \sqrt[3]{d}-\sqrt[3]{d} x}\right)}{d^{2/3}}",1,"Integrate[((-b + x)*(a*b - 2*b*x + x^2))/((x*(-a + x)*(-b + x)^2)^(2/3)*(b*d - (a + d)*x + x^2)), x]","F",-1
2841,1,184,290,0.2648187,"\int \frac{-d+c x^4}{x \sqrt[3]{-b+a x^3}} \, dx","Integrate[(-d + c*x^4)/(x*(-b + a*x^3)^(1/3)),x]","\frac{1}{18} \left(\frac{c \left(b \log \left(\frac{a^{2/3} x^2}{\left(a x^3-b\right)^{2/3}}+\frac{\sqrt[3]{a} x}{\sqrt[3]{a x^3-b}}+1\right)+6 \sqrt[3]{a} x \left(a x^3-b\right)^{2/3}-2 b \log \left(1-\frac{\sqrt[3]{a} x}{\sqrt[3]{a x^3-b}}\right)+2 \sqrt{3} b \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a} x}{\sqrt[3]{a x^3-b}}+1}{\sqrt{3}}\right)\right)}{a^{4/3}}-\frac{9 d \left(a x^3-b\right)^{2/3} \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};1-\frac{a x^3}{b}\right)}{b}\right)","-\frac{b c \log \left(\sqrt[3]{a x^3-b}-\sqrt[3]{a} x\right)}{9 a^{4/3}}-\frac{b c \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a x^3-b}}{\sqrt{3} \sqrt[3]{a}}+\frac{x}{\sqrt{3}}}{x}\right)}{3 \sqrt{3} a^{4/3}}+\frac{b c \log \left(a^{2/3} x^2+\sqrt[3]{a} x \sqrt[3]{a x^3-b}+\left(a x^3-b\right)^{2/3}\right)}{18 a^{4/3}}-\frac{d \log \left(-\sqrt[3]{b} \sqrt[3]{a x^3-b}+\left(a x^3-b\right)^{2/3}+b^{2/3}\right)}{6 \sqrt[3]{b}}+\frac{c x \left(a x^3-b\right)^{2/3}}{3 a}+\frac{d \log \left(\sqrt[3]{a x^3-b}+\sqrt[3]{b}\right)}{3 \sqrt[3]{b}}+\frac{d \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{a x^3-b}}{\sqrt{3} \sqrt[3]{b}}\right)}{\sqrt{3} \sqrt[3]{b}}",1,"((-9*d*(-b + a*x^3)^(2/3)*Hypergeometric2F1[2/3, 1, 5/3, 1 - (a*x^3)/b])/b + (c*(6*a^(1/3)*x*(-b + a*x^3)^(2/3) + 2*Sqrt[3]*b*ArcTan[(1 + (2*a^(1/3)*x)/(-b + a*x^3)^(1/3))/Sqrt[3]] - 2*b*Log[1 - (a^(1/3)*x)/(-b + a*x^3)^(1/3)] + b*Log[1 + (a^(2/3)*x^2)/(-b + a*x^3)^(2/3) + (a^(1/3)*x)/(-b + a*x^3)^(1/3)]))/a^(4/3))/18","C",1
2842,0,0,291,5.768235,"\int \frac{a b-2 b x+x^2}{\sqrt[3]{x (-a+x) (-b+x)^2} \left(b-(1+a d) x+d x^2\right)} \, dx","Integrate[(a*b - 2*b*x + x^2)/((x*(-a + x)*(-b + x)^2)^(1/3)*(b - (1 + a*d)*x + d*x^2)),x]","\int \frac{a b-2 b x+x^2}{\sqrt[3]{x (-a+x) (-b+x)^2} \left(b-(1+a d) x+d x^2\right)} \, dx","\frac{\log \left(\sqrt[3]{d} \sqrt[3]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}+b-x\right)}{d^{2/3}}-\frac{\log \left(d^{2/3} \left(x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4\right)^{2/3}+\sqrt[3]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4} \left(\sqrt[3]{d} x-b \sqrt[3]{d}\right)+b^2-2 b x+x^2\right)}{2 d^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} \sqrt[3]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}}{\sqrt[3]{d} \sqrt[3]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}-2 b+2 x}\right)}{d^{2/3}}",1,"Integrate[(a*b - 2*b*x + x^2)/((x*(-a + x)*(-b + x)^2)^(1/3)*(b - (1 + a*d)*x + d*x^2)), x]","F",-1
2843,0,0,291,3.6341098,"\int \frac{-a b^2+(4 a-b) b x-3 a x^2+x^3}{\sqrt[3]{x (-a+x) (-b+x)^2} \left(-a^2+\left(2 a+b^2 d\right) x-(1+2 b d) x^2+d x^3\right)} \, dx","Integrate[(-(a*b^2) + (4*a - b)*b*x - 3*a*x^2 + x^3)/((x*(-a + x)*(-b + x)^2)^(1/3)*(-a^2 + (2*a + b^2*d)*x - (1 + 2*b*d)*x^2 + d*x^3)),x]","\int \frac{-a b^2+(4 a-b) b x-3 a x^2+x^3}{\sqrt[3]{x (-a+x) (-b+x)^2} \left(-a^2+\left(2 a+b^2 d\right) x-(1+2 b d) x^2+d x^3\right)} \, dx","-\frac{\log \left(a^2+d^{2/3} \left(x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4\right)^{2/3}+\sqrt[3]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4} \left(\sqrt[3]{d} x-a \sqrt[3]{d}\right)-2 a x+x^2\right)}{2 d^{2/3}}+\frac{\log \left(\sqrt[3]{d} \sqrt[3]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}+a-x\right)}{d^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} \sqrt[3]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}}{\sqrt[3]{d} \sqrt[3]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}-2 a+2 x}\right)}{d^{2/3}}",1,"Integrate[(-(a*b^2) + (4*a - b)*b*x - 3*a*x^2 + x^3)/((x*(-a + x)*(-b + x)^2)^(1/3)*(-a^2 + (2*a + b^2*d)*x - (1 + 2*b*d)*x^2 + d*x^3)), x]","F",-1
2844,0,0,291,2.8788558,"\int \frac{(-4 a+b+3 x) \left(-b^3+3 b^2 x-3 b x^2+x^3\right)}{\left((-a+x) (-b+x)^2\right)^{2/3} \left(b^4+a d-\left(4 b^3+d\right) x+6 b^2 x^2-4 b x^3+x^4\right)} \, dx","Integrate[((-4*a + b + 3*x)*(-b^3 + 3*b^2*x - 3*b*x^2 + x^3))/(((-a + x)*(-b + x)^2)^(2/3)*(b^4 + a*d - (4*b^3 + d)*x + 6*b^2*x^2 - 4*b*x^3 + x^4)),x]","\int \frac{(-4 a+b+3 x) \left(-b^3+3 b^2 x-3 b x^2+x^3\right)}{\left((-a+x) (-b+x)^2\right)^{2/3} \left(b^4+a d-\left(4 b^3+d\right) x+6 b^2 x^2-4 b x^3+x^4\right)} \, dx","-\frac{\log \left(a^2 d+\left(x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3\right)^{2/3} \left(d^{2/3} x-a d^{2/3}\right)+\sqrt[3]{d} \left(x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3\right)^{4/3}-2 a d x+d x^2\right)}{2 \sqrt[3]{d}}+\frac{\log \left(\sqrt[6]{d} \left(x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3\right)^{2/3}+a \sqrt{d}-\sqrt{d} x\right)}{\sqrt[3]{d}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \left(x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3\right)^{2/3}}{\left(x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3\right)^{2/3}-2 a \sqrt[3]{d}+2 \sqrt[3]{d} x}\right)}{\sqrt[3]{d}}",1,"Integrate[((-4*a + b + 3*x)*(-b^3 + 3*b^2*x - 3*b*x^2 + x^3))/(((-a + x)*(-b + x)^2)^(2/3)*(b^4 + a*d - (4*b^3 + d)*x + 6*b^2*x^2 - 4*b*x^3 + x^4)), x]","F",-1
2845,1,105,291,0.0658288,"\int \frac{\sqrt[4]{-b x^3+a x^4}}{x (-d+c x)} \, dx","Integrate[(-(b*x^3) + a*x^4)^(1/4)/(x*(-d + c*x)),x]","-\frac{4 \sqrt[4]{x^3 (a x-b)} \left((b c-a d) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{b c x-a d x}{b d-a d x}\right)+a d \left(1-\frac{a x}{b}\right)^{3/4} \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};\frac{a x}{b}\right)\right)}{3 c d (b-a x)}","-\frac{(1-i) \sqrt[4]{a d-b c} \tan ^{-1}\left(\frac{(1+i) \sqrt[4]{d} x \sqrt[4]{a x^4-b x^3} \sqrt[4]{a d-b c}}{x^2 \sqrt{a d-b c}-i \sqrt{d} \sqrt{a x^4-b x^3}}\right)}{c \sqrt[4]{d}}-\frac{(1-i) \sqrt[4]{a d-b c} \tanh ^{-1}\left(\frac{\frac{\left(\frac{1}{2}-\frac{i}{2}\right) x^2 \sqrt[4]{a d-b c}}{\sqrt[4]{d}}+\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt[4]{d} \sqrt{a x^4-b x^3}}{\sqrt[4]{a d-b c}}}{x \sqrt[4]{a x^4-b x^3}}\right)}{c \sqrt[4]{d}}-\frac{2 \sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^3}}\right)}{c}+\frac{2 \sqrt[4]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^3}}\right)}{c}",1,"(-4*(x^3*(-b + a*x))^(1/4)*(a*d*(1 - (a*x)/b)^(3/4)*Hypergeometric2F1[3/4, 3/4, 7/4, (a*x)/b] + (b*c - a*d)*Hypergeometric2F1[3/4, 1, 7/4, (b*c*x - a*d*x)/(b*d - a*d*x)]))/(3*c*d*(b - a*x))","C",1
2846,0,0,291,1.8629063,"\int \frac{(-a+x) (-b+x) \left(-2 a b x+(a+b) x^2\right)}{(x (-a+x) (-b+x))^{2/3} \left(a^2 b^2 d-2 a b (a+b) d x+\left(a^2+4 a b+b^2\right) d x^2-2 (a+b) d x^3+(-1+d) x^4\right)} \, dx","Integrate[((-a + x)*(-b + x)*(-2*a*b*x + (a + b)*x^2))/((x*(-a + x)*(-b + x))^(2/3)*(a^2*b^2*d - 2*a*b*(a + b)*d*x + (a^2 + 4*a*b + b^2)*d*x^2 - 2*(a + b)*d*x^3 + (-1 + d)*x^4)),x]","\int \frac{(-a+x) (-b+x) \left(-2 a b x+(a+b) x^2\right)}{(x (-a+x) (-b+x))^{2/3} \left(a^2 b^2 d-2 a b (a+b) d x+\left(a^2+4 a b+b^2\right) d x^2-2 (a+b) d x^3+(-1+d) x^4\right)} \, dx","\frac{\log \left(x-\sqrt[6]{d} \sqrt[3]{x^2 (-a-b)+a b x+x^3}\right)}{2 d^{2/3}}+\frac{\log \left(\sqrt[6]{d} \sqrt[3]{x^2 (-a-b)+a b x+x^3}+x\right)}{2 d^{2/3}}-\frac{\log \left(-\sqrt[6]{d} x \sqrt[3]{x^2 (-a-b)+a b x+x^3}+\sqrt[3]{d} \left(x^2 (-a-b)+a b x+x^3\right)^{2/3}+x^2\right)}{4 d^{2/3}}-\frac{\log \left(\sqrt[6]{d} x \sqrt[3]{x^2 (-a-b)+a b x+x^3}+\sqrt[3]{d} \left(x^2 (-a-b)+a b x+x^3\right)^{2/3}+x^2\right)}{4 d^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x^2}{2 \sqrt[3]{d} \left(x^2 (-a-b)+a b x+x^3\right)^{2/3}+x^2}\right)}{2 d^{2/3}}",1,"Integrate[((-a + x)*(-b + x)*(-2*a*b*x + (a + b)*x^2))/((x*(-a + x)*(-b + x))^(2/3)*(a^2*b^2*d - 2*a*b*(a + b)*d*x + (a^2 + 4*a*b + b^2)*d*x^2 - 2*(a + b)*d*x^3 + (-1 + d)*x^4)), x]","F",-1
2847,0,0,291,0.9956804,"\int \frac{1+x^3+x^6}{\sqrt[4]{x^3+x^5} \left(1-x^6\right)} \, dx","Integrate[(1 + x^3 + x^6)/((x^3 + x^5)^(1/4)*(1 - x^6)),x]","\int \frac{1+x^3+x^6}{\sqrt[4]{x^3+x^5} \left(1-x^6\right)} \, dx","\frac{1}{3} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^5+x^3}}\right)+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^5+x^3}}\right)}{2 \sqrt[4]{2}}+\frac{1}{3} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^5+x^3}}\right)+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^5+x^3}}\right)}{2 \sqrt[4]{2}}-\frac{\tan ^{-1}\left(\frac{2^{3/4} x \sqrt[4]{x^5+x^3}}{\sqrt{2} x^2-\sqrt{x^5+x^3}}\right)}{6\ 2^{3/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{x^5+x^3}}{\sqrt{x^5+x^3}-x^2}\right)}{\sqrt{2}}+\frac{\tanh ^{-1}\left(\frac{\frac{x^2}{\sqrt[4]{2}}+\frac{\sqrt{x^5+x^3}}{2^{3/4}}}{x \sqrt[4]{x^5+x^3}}\right)}{6\ 2^{3/4}}+\frac{\tanh ^{-1}\left(\frac{\frac{x^2}{\sqrt{2}}+\frac{\sqrt{x^5+x^3}}{\sqrt{2}}}{x \sqrt[4]{x^5+x^3}}\right)}{\sqrt{2}}",1,"Integrate[(1 + x^3 + x^6)/((x^3 + x^5)^(1/4)*(1 - x^6)), x]","F",-1
2848,1,244,293,2.8130176,"\int \frac{-a-b x+\left(b+a k^2\right) x^2}{\sqrt{(1-x) x \left(1-k^2 x\right)} \left(1-2 x+k^2 x^2\right)} \, dx","Integrate[(-a - b*x + (b + a*k^2)*x^2)/(Sqrt[(1 - x)*x*(1 - k^2*x)]*(1 - 2*x + k^2*x^2)),x]","\frac{i \sqrt{\frac{1}{x-1}+1} (x-1)^{3/2} \sqrt{\frac{1-\frac{1}{k^2}}{x-1}+1} \left(\left(b \left(\sqrt{1-k^2}-1\right)-2 a k^2\right) \Pi \left(\frac{k^2-1}{k^2-\sqrt{1-k^2}-1};i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)+\left(2 a k^2+b \sqrt{1-k^2}+b\right) \Pi \left(\frac{k^2-1}{k^2+\sqrt{1-k^2}-1};i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)+2 a \sqrt{1-k^2} k^2 F\left(i \sinh ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)|1-\frac{1}{k^2}\right)\right)}{k^2 \sqrt{1-k^2} \sqrt{(x-1) x \left(k^2 x-1\right)}}","\frac{\left(2 i a k^2-2 a \sqrt{k^2-1} k^2-i b k^2-2 b \sqrt{k^2-1}+2 i b\right) \tan ^{-1}\left(\frac{\sqrt{k^2-2 i \sqrt{k^2-1}-2} \sqrt{k^2 x^3+\left(-k^2-1\right) x^2+x}}{k^2 (x-1) x}\right)}{2 k^2 \sqrt{k^2-1} \sqrt{k^2-2 i \sqrt{k^2-1}-2}}+\frac{\left(-2 i a k^2-2 a \sqrt{k^2-1} k^2+i b k^2-2 b \sqrt{k^2-1}-2 i b\right) \tan ^{-1}\left(\frac{\sqrt{k^2+2 i \sqrt{k^2-1}-2} \sqrt{k^2 x^3+\left(-k^2-1\right) x^2+x}}{k^2 (x-1) x}\right)}{2 k^2 \sqrt{k^2-1} \sqrt{k^2+2 i \sqrt{k^2-1}-2}}",1,"(I*Sqrt[1 + (-1 + x)^(-1)]*Sqrt[1 + (1 - k^(-2))/(-1 + x)]*(-1 + x)^(3/2)*(2*a*k^2*Sqrt[1 - k^2]*EllipticF[I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)] + (-2*a*k^2 + b*(-1 + Sqrt[1 - k^2]))*EllipticPi[(-1 + k^2)/(-1 + k^2 - Sqrt[1 - k^2]), I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)] + (b + 2*a*k^2 + b*Sqrt[1 - k^2])*EllipticPi[(-1 + k^2)/(-1 + k^2 + Sqrt[1 - k^2]), I*ArcSinh[1/Sqrt[-1 + x]], 1 - k^(-2)]))/(k^2*Sqrt[1 - k^2]*Sqrt[(-1 + x)*x*(-1 + k^2*x)])","C",1
2849,0,0,293,0.0659194,"\int \frac{1-2 x^4+x^8}{\sqrt[4]{-1+x^4} \left(1-2 x^4+2 x^8\right)} \, dx","Integrate[(1 - 2*x^4 + x^8)/((-1 + x^4)^(1/4)*(1 - 2*x^4 + 2*x^8)),x]","\int \frac{1-2 x^4+x^8}{\sqrt[4]{-1+x^4} \left(1-2 x^4+2 x^8\right)} \, dx","\frac{1}{4} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-1}}\right)+\frac{1}{4} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-1}}\right)+\frac{1}{8} \sqrt{\frac{1}{2} \left(2-\sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}} x \sqrt[4]{x^4-1}}{\sqrt{x^4-1}-x^2}\right)-\frac{1}{8} \sqrt{\frac{1}{2} \left(2+\sqrt{2}\right)} \tan ^{-1}\left(\frac{\left(\sqrt{\frac{2}{2-\sqrt{2}}}-\frac{2}{\sqrt{2-\sqrt{2}}}\right) x \sqrt[4]{x^4-1}}{\sqrt{x^4-1}-x^2}\right)+\frac{1}{8} \sqrt{\frac{1}{2} \left(2+\sqrt{2}\right)} \tanh ^{-1}\left(\frac{\sqrt{2-\sqrt{2}} x \sqrt[4]{x^4-1}}{\sqrt{x^4-1}+x^2}\right)+\frac{1}{8} \sqrt{\frac{1}{2} \left(2-\sqrt{2}\right)} \tanh ^{-1}\left(\frac{\sqrt{2+\sqrt{2}} x \sqrt[4]{x^4-1}}{\sqrt{x^4-1}+x^2}\right)",1,"Integrate[(1 - 2*x^4 + x^8)/((-1 + x^4)^(1/4)*(1 - 2*x^4 + 2*x^8)), x]","F",-1
2850,1,220,293,0.5912763,"\int \sqrt{c+\sqrt{a x+\sqrt{b+a^2 x^2}}} \, dx","Integrate[Sqrt[c + Sqrt[a*x + Sqrt[b + a^2*x^2]]],x]","-\frac{2 \left(-\frac{b \tanh ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}}{\sqrt{c}}\right)}{8 c^{3/2}}-\frac{1}{5} \left(\sqrt{\sqrt{a^2 x^2+b}+a x}+c\right)^{5/2}+\frac{1}{3} c \left(\sqrt{\sqrt{a^2 x^2+b}+a x}+c\right)^{3/2}+\frac{b \sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}}{8 c \sqrt{\sqrt{a^2 x^2+b}+a x}}+\frac{b \sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}}{4 \left(\sqrt{a^2 x^2+b}+a x\right)}\right)}{a}","\frac{b \tanh ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}}{\sqrt{c}}\right)}{4 a c^{3/2}}+\frac{\left(48 a^2 c x^2-16 a c^3 x-6 b c\right) \sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}+\sqrt{\sqrt{a^2 x^2+b}+a x} \sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c} \left(8 a c^2 x-15 b\right)+\sqrt{a^2 x^2+b} \left(\left(48 a c x-16 c^3\right) \sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}+8 c^2 \sqrt{\sqrt{a^2 x^2+b}+a x} \sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}\right)}{60 a c \sqrt{a^2 x^2+b}+60 a^2 c x}",1,"(-2*((b*Sqrt[c + Sqrt[a*x + Sqrt[b + a^2*x^2]]])/(4*(a*x + Sqrt[b + a^2*x^2])) + (b*Sqrt[c + Sqrt[a*x + Sqrt[b + a^2*x^2]]])/(8*c*Sqrt[a*x + Sqrt[b + a^2*x^2]]) + (c*(c + Sqrt[a*x + Sqrt[b + a^2*x^2]])^(3/2))/3 - (c + Sqrt[a*x + Sqrt[b + a^2*x^2]])^(5/2)/5 - (b*ArcTanh[Sqrt[c + Sqrt[a*x + Sqrt[b + a^2*x^2]]]/Sqrt[c]])/(8*c^(3/2))))/a","A",1
2851,1,219,294,0.7016878,"\int \frac{x^3}{\sqrt[3]{x^2 (-a+x)} \left(-a^4+4 a^3 x-6 a^2 x^2+4 a x^3+(-1+d) x^4\right)} \, dx","Integrate[x^3/((x^2*(-a + x))^(1/3)*(-a^4 + 4*a^3*x - 6*a^2*x^2 + 4*a*x^3 + (-1 + d)*x^4)),x]","\frac{x \left(-\log \left(\sqrt[3]{d} \left(\frac{x}{x-a}\right)^{4/3}-\sqrt[6]{d} \left(\frac{x}{x-a}\right)^{2/3}+1\right)+\log \left(\sqrt[3]{d} \left(\frac{x}{x-a}\right)^{4/3}+\sqrt[6]{d} \left(\frac{x}{x-a}\right)^{2/3}+1\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{1-2 \sqrt[6]{d} \left(\frac{x}{x-a}\right)^{2/3}}{\sqrt{3}}\right)-2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \left(\frac{x}{x-a}\right)^{2/3}+1}{\sqrt{3}}\right)+4 \tanh ^{-1}\left(\sqrt[6]{d} \left(\frac{x}{x-a}\right)^{2/3}\right)\right)}{8 a d^{5/6} \sqrt[3]{\frac{x}{x-a}} \sqrt[3]{x^2 (x-a)}}","-\frac{\log \left(\sqrt[3]{x^3-a x^2}-\sqrt[12]{d} x\right)}{4 a d^{5/6}}-\frac{\log \left(\sqrt[3]{x^3-a x^2}+\sqrt[12]{d} x\right)}{4 a d^{5/6}}+\frac{\log \left(\left(x^3-a x^2\right)^{2/3}+\sqrt[6]{d} x^2\right)}{4 a d^{5/6}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{d} x^2}{\sqrt[6]{d} x^2-2 \left(x^3-a x^2\right)^{2/3}}\right)}{4 a d^{5/6}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{d} x^2}{2 \left(x^3-a x^2\right)^{2/3}+\sqrt[6]{d} x^2}\right)}{4 a d^{5/6}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{d} \left(x^3-a x^2\right)^{2/3}}{(x-a) \sqrt[3]{x^3-a x^2}+\sqrt[3]{d} x^2}\right)}{4 a d^{5/6}}",1,"(x*(2*Sqrt[3]*ArcTan[(1 - 2*d^(1/6)*(x/(-a + x))^(2/3))/Sqrt[3]] - 2*Sqrt[3]*ArcTan[(1 + 2*d^(1/6)*(x/(-a + x))^(2/3))/Sqrt[3]] + 4*ArcTanh[d^(1/6)*(x/(-a + x))^(2/3)] - Log[1 - d^(1/6)*(x/(-a + x))^(2/3) + d^(1/3)*(x/(-a + x))^(4/3)] + Log[1 + d^(1/6)*(x/(-a + x))^(2/3) + d^(1/3)*(x/(-a + x))^(4/3)]))/(8*a*d^(5/6)*(x/(-a + x))^(1/3)*(x^2*(-a + x))^(1/3))","A",1
2852,0,0,294,0.2802743,"\int \frac{\sqrt{c+\sqrt{a x^2+x \sqrt{-b+a^2 x^2}}}}{\sqrt{-b+a^2 x^2}} \, dx","Integrate[Sqrt[c + Sqrt[a*x^2 + x*Sqrt[-b + a^2*x^2]]]/Sqrt[-b + a^2*x^2],x]","\int \frac{\sqrt{c+\sqrt{a x^2+x \sqrt{-b+a^2 x^2}}}}{\sqrt{-b+a^2 x^2}} \, dx","\frac{2 \sqrt{\sqrt{x \left(\sqrt{a^2 x^2-b}+a x\right)}+c}}{a}-\frac{\sqrt{\sqrt{2} \sqrt{b}-2 \sqrt{a} c} \left(\sqrt{2} \sqrt{a} c-\sqrt{b}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt{\sqrt{x \left(\sqrt{a^2 x^2-b}+a x\right)}+c}}{\sqrt{\sqrt{2} \sqrt{b}-2 \sqrt{a} c}}\right)}{a^{5/4} \left(2 \sqrt{a} c-\sqrt{2} \sqrt{b}\right)}-\frac{\left(\sqrt{2} \sqrt{a} c+\sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt{\sqrt{x \left(\sqrt{a^2 x^2-b}+a x\right)}+c}}{\sqrt{2 \sqrt{a} c+\sqrt{2} \sqrt{b}}}\right)}{a^{5/4} \sqrt{2 \sqrt{a} c+\sqrt{2} \sqrt{b}}}",1,"Integrate[Sqrt[c + Sqrt[a*x^2 + x*Sqrt[-b + a^2*x^2]]]/Sqrt[-b + a^2*x^2], x]","F",-1
2853,0,0,296,3.2894182,"\int \frac{-a (a b+a c-2 b c)+2 \left(a^2-b c\right) x+(-2 a+b+c) x^2}{((-a+x) (-b+x) (-c+x))^{2/3} \left(-b c+a^2 d+(b+c-2 a d) x+(-1+d) x^2\right)} \, dx","Integrate[(-(a*(a*b + a*c - 2*b*c)) + 2*(a^2 - b*c)*x + (-2*a + b + c)*x^2)/(((-a + x)*(-b + x)*(-c + x))^(2/3)*(-(b*c) + a^2*d + (b + c - 2*a*d)*x + (-1 + d)*x^2)),x]","\int \frac{-a (a b+a c-2 b c)+2 \left(a^2-b c\right) x+(-2 a+b+c) x^2}{((-a+x) (-b+x) (-c+x))^{2/3} \left(-b c+a^2 d+(b+c-2 a d) x+(-1+d) x^2\right)} \, dx","\frac{\log \left(a^2 d^{2/3}+\left(\sqrt[3]{d} x-a \sqrt[3]{d}\right) \sqrt[3]{x^2 (-a-b-c)+x (a b+a c+b c)-a b c+x^3}+\left(x^2 (-a-b-c)+x (a b+a c+b c)-a b c+x^3\right)^{2/3}-2 a d^{2/3} x+d^{2/3} x^2\right)}{2 d^{2/3}}-\frac{\log \left(\sqrt[3]{x^2 (-a-b-c)+x (a b+a c+b c)-a b c+x^3}+a \sqrt[3]{d}-\sqrt[3]{d} x\right)}{d^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} a \sqrt[3]{d}-\sqrt{3} \sqrt[3]{d} x}{-2 \sqrt[3]{x^2 (-a-b-c)+x (a b+a c+b c)-a b c+x^3}+a \sqrt[3]{d}-\sqrt[3]{d} x}\right)}{d^{2/3}}",1,"Integrate[(-(a*(a*b + a*c - 2*b*c)) + 2*(a^2 - b*c)*x + (-2*a + b + c)*x^2)/(((-a + x)*(-b + x)*(-c + x))^(2/3)*(-(b*c) + a^2*d + (b + c - 2*a*d)*x + (-1 + d)*x^2)), x]","F",-1
2854,0,0,297,2.6592078,"\int \frac{x^2 (-2 a b+(a+b) x)}{\sqrt[3]{x (-a+x) (-b+x)} \left(-a^2 b^2+2 a b (a+b) x-\left(a^2+4 a b+b^2\right) x^2+2 (a+b) x^3+(-1+d) x^4\right)} \, dx","Integrate[(x^2*(-2*a*b + (a + b)*x))/((x*(-a + x)*(-b + x))^(1/3)*(-(a^2*b^2) + 2*a*b*(a + b)*x - (a^2 + 4*a*b + b^2)*x^2 + 2*(a + b)*x^3 + (-1 + d)*x^4)),x]","\int \frac{x^2 (-2 a b+(a+b) x)}{\sqrt[3]{x (-a+x) (-b+x)} \left(-a^2 b^2+2 a b (a+b) x-\left(a^2+4 a b+b^2\right) x^2+2 (a+b) x^3+(-1+d) x^4\right)} \, dx","-\frac{\log \left(\sqrt[3]{x^2 (-a-b)+a b x+x^3}-\sqrt[6]{d} x\right)}{2 d^{2/3}}-\frac{\log \left(\sqrt[3]{x^2 (-a-b)+a b x+x^3}+\sqrt[6]{d} x\right)}{2 d^{2/3}}+\frac{\log \left(-\sqrt[6]{d} x \sqrt[3]{x^2 (-a-b)+a b x+x^3}+\left(x^2 (-a-b)+a b x+x^3\right)^{2/3}+\sqrt[3]{d} x^2\right)}{4 d^{2/3}}+\frac{\log \left(\sqrt[6]{d} x \sqrt[3]{x^2 (-a-b)+a b x+x^3}+\left(x^2 (-a-b)+a b x+x^3\right)^{2/3}+\sqrt[3]{d} x^2\right)}{4 d^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} x^2}{2 \left(x^2 (-a-b)+a b x+x^3\right)^{2/3}+\sqrt[3]{d} x^2}\right)}{2 d^{2/3}}",1,"Integrate[(x^2*(-2*a*b + (a + b)*x))/((x*(-a + x)*(-b + x))^(1/3)*(-(a^2*b^2) + 2*a*b*(a + b)*x - (a^2 + 4*a*b + b^2)*x^2 + 2*(a + b)*x^3 + (-1 + d)*x^4)), x]","F",-1
2855,0,0,297,0.8826291,"\int \frac{1+x^6}{\sqrt[4]{x^3+x^5} \left(1-x^6\right)} \, dx","Integrate[(1 + x^6)/((x^3 + x^5)^(1/4)*(1 - x^6)),x]","\int \frac{1+x^6}{\sqrt[4]{x^3+x^5} \left(1-x^6\right)} \, dx","\frac{2}{3} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^5+x^3}}\right)+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^5+x^3}}\right)}{3 \sqrt[4]{2}}+\frac{2}{3} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^5+x^3}}\right)+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^5+x^3}}\right)}{3 \sqrt[4]{2}}-\frac{\tan ^{-1}\left(\frac{2^{3/4} x \sqrt[4]{x^5+x^3}}{\sqrt{2} x^2-\sqrt{x^5+x^3}}\right)}{3\ 2^{3/4}}+\frac{1}{3} \sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} x \sqrt[4]{x^5+x^3}}{\sqrt{x^5+x^3}-x^2}\right)+\frac{\tanh ^{-1}\left(\frac{\frac{x^2}{\sqrt[4]{2}}+\frac{\sqrt{x^5+x^3}}{2^{3/4}}}{x \sqrt[4]{x^5+x^3}}\right)}{3\ 2^{3/4}}+\frac{1}{3} \sqrt{2} \tanh ^{-1}\left(\frac{\frac{x^2}{\sqrt{2}}+\frac{\sqrt{x^5+x^3}}{\sqrt{2}}}{x \sqrt[4]{x^5+x^3}}\right)",1,"Integrate[(1 + x^6)/((x^3 + x^5)^(1/4)*(1 - x^6)), x]","F",-1
2856,1,373,297,1.3213455,"\int \frac{b^{16}+a^{16} x^{16}}{\sqrt{-b^4+a^4 x^4} \left(-b^{16}+a^{16} x^{16}\right)} \, dx","Integrate[(b^16 + a^16*x^16)/(Sqrt[-b^4 + a^4*x^4]*(-b^16 + a^16*x^16)),x]","\frac{x \left(-\sqrt{-\frac{a^2}{b^2}}\right)-3 i \sqrt{1-\frac{a^4 x^4}{b^4}} F\left(\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)+i \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(-i;\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)+i \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(i;\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)+i \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(-\sqrt[4]{-1};\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)+i \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(\sqrt[4]{-1};\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)+i \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(-(-1)^{3/4};\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)+i \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left((-1)^{3/4};\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)}{4 \sqrt{-\frac{a^2}{b^2}} \sqrt{a^4 x^4-b^4}}","-\frac{x}{4 \sqrt{a^4 x^4-b^4}}-\frac{\tan ^{-1}\left(\frac{-\frac{a^3 x^4}{2 b}+\frac{b^3}{2 a}+a b x^2}{x \sqrt{a^4 x^4-b^4}}\right)}{16 a b}+\frac{\tanh ^{-1}\left(\frac{-\frac{a^3 x^4}{2 b}+\frac{b^3}{2 a}-a b x^2}{x \sqrt{a^4 x^4-b^4}}\right)}{16 a b}+\frac{\tanh ^{-1}\left(\frac{-\frac{a^3 x^4}{2^{3/4} b}+\frac{b^3}{2^{3/4} a}-\frac{a b x^2}{\sqrt[4]{2}}}{x \sqrt{a^4 x^4-b^4}}\right)}{4\ 2^{3/4} a b}+\frac{\tan ^{-1}\left(\frac{2^{3/4} a b x \sqrt{a^4 x^4-b^4}}{-a^4 x^4+\sqrt{2} a^2 b^2 x^2+b^4}\right)}{4\ 2^{3/4} a b}",1,"(-(Sqrt[-(a^2/b^2)]*x) - (3*I)*Sqrt[1 - (a^4*x^4)/b^4]*EllipticF[I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1] + I*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[-I, I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1] + I*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[I, I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1] + I*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[-(-1)^(1/4), I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1] + I*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[(-1)^(1/4), I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1] + I*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[-(-1)^(3/4), I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1] + I*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[(-1)^(3/4), I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1])/(4*Sqrt[-(a^2/b^2)]*Sqrt[-b^4 + a^4*x^4])","C",1
2857,1,188,299,0.3404393,"\int \frac{\sqrt[3]{-b^2 x^2+a^3 x^3}}{b+a x^2} \, dx","Integrate[(-(b^2*x^2) + a^3*x^3)^(1/3)/(b + a*x^2),x]","\frac{3 x^2 \left(2 (-a)^{5/2} \left(1-\frac{a^3 x}{b^2}\right)^{2/3} \, _2F_1\left(\frac{2}{3},\frac{2}{3};\frac{5}{3};\frac{a^3 x}{b^2}\right)-\left((-a)^{5/2}+b^{3/2}\right) \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{\left(a^3-\sqrt{-a} b^{3/2}\right) x}{a^3 x-b^2}\right)+\left(a (-a)^{3/2}+b^{3/2}\right) \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{\left(a^3+\sqrt{-a} b^{3/2}\right) x}{a^3 x-b^2}\right)\right)}{4 \sqrt{-a} \left(x^2 \left(a^3 x-b^2\right)\right)^{2/3}}","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^6-2 \text{$\#$1}^3 a^3+a^6+a b^3\&,\frac{\text{$\#$1}^3 a^2 \log (x)-\text{$\#$1}^3 a^2 \log \left(\sqrt[3]{a^3 x^3-b^2 x^2}-\text{$\#$1} x\right)+b^3 \log \left(\sqrt[3]{a^3 x^3-b^2 x^2}-\text{$\#$1} x\right)+a^5 \log \left(\sqrt[3]{a^3 x^3-b^2 x^2}-\text{$\#$1} x\right)+a^5 (-\log (x))-b^3 \log (x)}{\text{$\#$1}^2 a^3-\text{$\#$1}^5}\&\right]-\log \left(\sqrt[3]{a^3 x^3-b^2 x^2}-a x\right)-\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} a x}{2 \sqrt[3]{a^3 x^3-b^2 x^2}+a x}\right)+\frac{1}{2} \log \left(a x \sqrt[3]{a^3 x^3-b^2 x^2}+\left(a^3 x^3-b^2 x^2\right)^{2/3}+a^2 x^2\right)",1,"(3*x^2*(2*(-a)^(5/2)*(1 - (a^3*x)/b^2)^(2/3)*Hypergeometric2F1[2/3, 2/3, 5/3, (a^3*x)/b^2] - ((-a)^(5/2) + b^(3/2))*Hypergeometric2F1[2/3, 1, 5/3, ((a^3 - Sqrt[-a]*b^(3/2))*x)/(-b^2 + a^3*x)] + ((-a)^(3/2)*a + b^(3/2))*Hypergeometric2F1[2/3, 1, 5/3, ((a^3 + Sqrt[-a]*b^(3/2))*x)/(-b^2 + a^3*x)]))/(4*Sqrt[-a]*(x^2*(-b^2 + a^3*x))^(2/3))","A",1
2858,1,188,299,0.1047219,"\int \frac{\sqrt[3]{-b^2 x^2+a^3 x^3}}{b+a x^2} \, dx","Integrate[(-(b^2*x^2) + a^3*x^3)^(1/3)/(b + a*x^2),x]","\frac{3 x^2 \left(2 (-a)^{5/2} \left(1-\frac{a^3 x}{b^2}\right)^{2/3} \, _2F_1\left(\frac{2}{3},\frac{2}{3};\frac{5}{3};\frac{a^3 x}{b^2}\right)-\left((-a)^{5/2}+b^{3/2}\right) \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{\left(a^3-\sqrt{-a} b^{3/2}\right) x}{a^3 x-b^2}\right)+\left(a (-a)^{3/2}+b^{3/2}\right) \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{\left(a^3+\sqrt{-a} b^{3/2}\right) x}{a^3 x-b^2}\right)\right)}{4 \sqrt{-a} \left(x^2 \left(a^3 x-b^2\right)\right)^{2/3}}","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^6-2 \text{$\#$1}^3 a^3+a^6+a b^3\&,\frac{\text{$\#$1}^3 a^2 \log (x)-\text{$\#$1}^3 a^2 \log \left(\sqrt[3]{a^3 x^3-b^2 x^2}-\text{$\#$1} x\right)+b^3 \log \left(\sqrt[3]{a^3 x^3-b^2 x^2}-\text{$\#$1} x\right)+a^5 \log \left(\sqrt[3]{a^3 x^3-b^2 x^2}-\text{$\#$1} x\right)+a^5 (-\log (x))-b^3 \log (x)}{\text{$\#$1}^2 a^3-\text{$\#$1}^5}\&\right]-\log \left(\sqrt[3]{a^3 x^3-b^2 x^2}-a x\right)-\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} a x}{2 \sqrt[3]{a^3 x^3-b^2 x^2}+a x}\right)+\frac{1}{2} \log \left(a x \sqrt[3]{a^3 x^3-b^2 x^2}+\left(a^3 x^3-b^2 x^2\right)^{2/3}+a^2 x^2\right)",1,"(3*x^2*(2*(-a)^(5/2)*(1 - (a^3*x)/b^2)^(2/3)*Hypergeometric2F1[2/3, 2/3, 5/3, (a^3*x)/b^2] - ((-a)^(5/2) + b^(3/2))*Hypergeometric2F1[2/3, 1, 5/3, ((a^3 - Sqrt[-a]*b^(3/2))*x)/(-b^2 + a^3*x)] + ((-a)^(3/2)*a + b^(3/2))*Hypergeometric2F1[2/3, 1, 5/3, ((a^3 + Sqrt[-a]*b^(3/2))*x)/(-b^2 + a^3*x)]))/(4*Sqrt[-a]*(x^2*(-b^2 + a^3*x))^(2/3))","A",1
2859,1,221,299,0.743499,"\int \frac{b^8+x^4+a^8 x^8}{\sqrt{-b^4+a^4 x^4} \left(-b^8+a^8 x^8\right)} \, dx","Integrate[(b^8 + x^4 + a^8*x^8)/(Sqrt[-b^4 + a^4*x^4]*(-b^8 + a^8*x^8)),x]","\frac{x \left(\frac{5 \left(2 a^4 b^4-1\right) \left(a^4 x^4-b^4\right) F_1\left(\frac{1}{4};-\frac{1}{2},1;\frac{5}{4};\frac{a^4 x^4}{b^4},-\frac{a^4 x^4}{b^4}\right)}{\left(a^4 x^4+b^4\right) \left(5 b^4 F_1\left(\frac{1}{4};-\frac{1}{2},1;\frac{5}{4};\frac{a^4 x^4}{b^4},-\frac{a^4 x^4}{b^4}\right)-2 a^4 x^4 \left(2 F_1\left(\frac{5}{4};-\frac{1}{2},2;\frac{9}{4};\frac{a^4 x^4}{b^4},-\frac{a^4 x^4}{b^4}\right)+F_1\left(\frac{5}{4};\frac{1}{2},1;\frac{9}{4};\frac{a^4 x^4}{b^4},-\frac{a^4 x^4}{b^4}\right)\right)\right)}-2 a^4-\frac{1}{b^4}\right)}{4 a^4 \sqrt{a^4 x^4-b^4}}","\frac{x \left(2 a^4 b^4+1\right) \sqrt{a^4 x^4-b^4}}{4 a^4 b^4 \left(b^4-a^4 x^4\right)}-\frac{\left(\frac{1}{8}-\frac{i}{8}\right) \left(2 a^4 b^4-1\right) \tan ^{-1}\left(\frac{(1+i) a b x}{\sqrt{a^4 x^4-b^4}+a^2 x^2+i b^2}\right)}{a^5 b^5}+\frac{\left(\frac{1}{16}-\frac{i}{16}\right) \left(2 a^4 b^4-1\right) \tanh ^{-1}\left(\frac{(1-i) \sqrt{a^4 x^4-b^4}+(1-i) a^2 x^2+(1+i) b^2}{2 \sqrt{3-2 \sqrt{2}} a b x}\right)}{a^5 b^5}-\frac{\left(\frac{1}{16}-\frac{i}{16}\right) \left(2 a^4 b^4-1\right) \tanh ^{-1}\left(\frac{(1-i) \sqrt{a^4 x^4-b^4}+(1-i) a^2 x^2+(1+i) b^2}{2 \sqrt{3+2 \sqrt{2}} a b x}\right)}{a^5 b^5}",1,"(x*(-2*a^4 - b^(-4) + (5*(-1 + 2*a^4*b^4)*(-b^4 + a^4*x^4)*AppellF1[1/4, -1/2, 1, 5/4, (a^4*x^4)/b^4, -((a^4*x^4)/b^4)])/((b^4 + a^4*x^4)*(5*b^4*AppellF1[1/4, -1/2, 1, 5/4, (a^4*x^4)/b^4, -((a^4*x^4)/b^4)] - 2*a^4*x^4*(2*AppellF1[5/4, -1/2, 2, 9/4, (a^4*x^4)/b^4, -((a^4*x^4)/b^4)] + AppellF1[5/4, 1/2, 1, 9/4, (a^4*x^4)/b^4, -((a^4*x^4)/b^4)])))))/(4*a^4*Sqrt[-b^4 + a^4*x^4])","C",0
2860,1,179,300,0.2213642,"\int \frac{\sqrt[3]{-b^2 x^2+a^3 x^3}}{-b+a x^2} \, dx","Integrate[(-(b^2*x^2) + a^3*x^3)^(1/3)/(-b + a*x^2),x]","\frac{3 x^2 \left(2 a^{5/2} \left(1-\frac{a^3 x}{b^2}\right)^{2/3} \, _2F_1\left(\frac{2}{3},\frac{2}{3};\frac{5}{3};\frac{a^3 x}{b^2}\right)+\left(b^{3/2}-a^{5/2}\right) \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{\sqrt{a} \left(a^{5/2}-b^{3/2}\right) x}{a^3 x-b^2}\right)-\left(a^{5/2}+b^{3/2}\right) \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{\sqrt{a} \left(a^{5/2}+b^{3/2}\right) x}{a^3 x-b^2}\right)\right)}{4 \sqrt{a} \left(x^2 \left(a^3 x-b^2\right)\right)^{2/3}}","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^6-2 \text{$\#$1}^3 a^3+a^6-a b^3\&,\frac{\text{$\#$1}^3 a^2 \log (x)-\text{$\#$1}^3 a^2 \log \left(\sqrt[3]{a^3 x^3-b^2 x^2}-\text{$\#$1} x\right)-b^3 \log \left(\sqrt[3]{a^3 x^3-b^2 x^2}-\text{$\#$1} x\right)+a^5 \log \left(\sqrt[3]{a^3 x^3-b^2 x^2}-\text{$\#$1} x\right)+a^5 (-\log (x))+b^3 \log (x)}{\text{$\#$1}^2 a^3-\text{$\#$1}^5}\&\right]-\log \left(\sqrt[3]{a^3 x^3-b^2 x^2}-a x\right)-\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} a x}{2 \sqrt[3]{a^3 x^3-b^2 x^2}+a x}\right)+\frac{1}{2} \log \left(a x \sqrt[3]{a^3 x^3-b^2 x^2}+\left(a^3 x^3-b^2 x^2\right)^{2/3}+a^2 x^2\right)",1,"(3*x^2*(2*a^(5/2)*(1 - (a^3*x)/b^2)^(2/3)*Hypergeometric2F1[2/3, 2/3, 5/3, (a^3*x)/b^2] + (-a^(5/2) + b^(3/2))*Hypergeometric2F1[2/3, 1, 5/3, (Sqrt[a]*(a^(5/2) - b^(3/2))*x)/(-b^2 + a^3*x)] - (a^(5/2) + b^(3/2))*Hypergeometric2F1[2/3, 1, 5/3, (Sqrt[a]*(a^(5/2) + b^(3/2))*x)/(-b^2 + a^3*x)]))/(4*Sqrt[a]*(x^2*(-b^2 + a^3*x))^(2/3))","A",1
2861,1,179,300,0.0893528,"\int \frac{\sqrt[3]{-b^2 x^2+a^3 x^3}}{-b+a x^2} \, dx","Integrate[(-(b^2*x^2) + a^3*x^3)^(1/3)/(-b + a*x^2),x]","\frac{3 x^2 \left(2 a^{5/2} \left(1-\frac{a^3 x}{b^2}\right)^{2/3} \, _2F_1\left(\frac{2}{3},\frac{2}{3};\frac{5}{3};\frac{a^3 x}{b^2}\right)+\left(b^{3/2}-a^{5/2}\right) \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{\sqrt{a} \left(a^{5/2}-b^{3/2}\right) x}{a^3 x-b^2}\right)-\left(a^{5/2}+b^{3/2}\right) \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{\sqrt{a} \left(a^{5/2}+b^{3/2}\right) x}{a^3 x-b^2}\right)\right)}{4 \sqrt{a} \left(x^2 \left(a^3 x-b^2\right)\right)^{2/3}}","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^6-2 \text{$\#$1}^3 a^3+a^6-a b^3\&,\frac{\text{$\#$1}^3 a^2 \log (x)-\text{$\#$1}^3 a^2 \log \left(\sqrt[3]{a^3 x^3-b^2 x^2}-\text{$\#$1} x\right)-b^3 \log \left(\sqrt[3]{a^3 x^3-b^2 x^2}-\text{$\#$1} x\right)+a^5 \log \left(\sqrt[3]{a^3 x^3-b^2 x^2}-\text{$\#$1} x\right)+a^5 (-\log (x))+b^3 \log (x)}{\text{$\#$1}^2 a^3-\text{$\#$1}^5}\&\right]-\log \left(\sqrt[3]{a^3 x^3-b^2 x^2}-a x\right)-\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} a x}{2 \sqrt[3]{a^3 x^3-b^2 x^2}+a x}\right)+\frac{1}{2} \log \left(a x \sqrt[3]{a^3 x^3-b^2 x^2}+\left(a^3 x^3-b^2 x^2\right)^{2/3}+a^2 x^2\right)",1,"(3*x^2*(2*a^(5/2)*(1 - (a^3*x)/b^2)^(2/3)*Hypergeometric2F1[2/3, 2/3, 5/3, (a^3*x)/b^2] + (-a^(5/2) + b^(3/2))*Hypergeometric2F1[2/3, 1, 5/3, (Sqrt[a]*(a^(5/2) - b^(3/2))*x)/(-b^2 + a^3*x)] - (a^(5/2) + b^(3/2))*Hypergeometric2F1[2/3, 1, 5/3, (Sqrt[a]*(a^(5/2) + b^(3/2))*x)/(-b^2 + a^3*x)]))/(4*Sqrt[a]*(x^2*(-b^2 + a^3*x))^(2/3))","A",1
2862,1,57,301,0.0623484,"\int \frac{-b+x}{\left((-a+x) (-b+x)^2\right)^{2/3} (a-b d+(-1+d) x)} \, dx","Integrate[(-b + x)/(((-a + x)*(-b + x)^2)^(2/3)*(a - b*d + (-1 + d)*x)),x]","\frac{3 (b-x)^2 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{d (b-x)}{a-x}\right)}{2 (a-b) \left((x-a) (b-x)^2\right)^{2/3}}","-\frac{\log \left(\sqrt[3]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3}+b \sqrt[3]{d}-\sqrt[3]{d} x\right)}{d^{2/3} (a-b)}+\frac{\log \left(\sqrt[3]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3} \left(\sqrt[3]{d} x-b \sqrt[3]{d}\right)+\left(x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3\right)^{2/3}+b^2 d^{2/3}-2 b d^{2/3} x+d^{2/3} x^2\right)}{2 d^{2/3} (a-b)}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} b \sqrt[3]{d}-\sqrt{3} \sqrt[3]{d} x}{-2 \sqrt[3]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3}+b \sqrt[3]{d}-\sqrt[3]{d} x}\right)}{d^{2/3} (a-b)}",1,"(3*(b - x)^2*Hypergeometric2F1[2/3, 1, 5/3, (d*(b - x))/(a - x)])/(2*(a - b)*((b - x)^2*(-a + x))^(2/3))","C",1
2863,1,524,301,8.6275392,"\int \frac{\sqrt{-b+x^2} \left(c+x^4\right) \sqrt{x+\sqrt{-b+x^2}}}{x} \, dx","Integrate[(Sqrt[-b + x^2]*(c + x^4)*Sqrt[x + Sqrt[-b + x^2]])/x,x]","\frac{1}{6} c \left(-3 \sqrt{2} b^{3/4} \log \left(\sqrt{x^2-b}-\sqrt{2} \sqrt[4]{b} \sqrt{\sqrt{x^2-b}+x}+\sqrt{b}+x\right)+3 \sqrt{2} b^{3/4} \log \left(\sqrt{x^2-b}+\sqrt{2} \sqrt[4]{b} \sqrt{\sqrt{x^2-b}+x}+\sqrt{b}+x\right)+6 \sqrt{2} b^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{\sqrt{x^2-b}+x}}{\sqrt[4]{b}}\right)-6 \sqrt{2} b^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{\sqrt{x^2-b}+x}}{\sqrt[4]{b}}+1\right)+\frac{4 x \left(\sqrt{x^2-b}+x\right)-8 b}{\sqrt{\sqrt{x^2-b}+x}}\right)+\frac{2 \sqrt{x^2-b} \left(304 b^5-342 b^4 x \left(4 \sqrt{x^2-b}+9 x\right)+15 b^3 x^3 \left(247 \sqrt{x^2-b}+249 x\right)+15 b^2 x^5 \left(89 \sqrt{x^2-b}+317 x\right)+5040 x^9 \left(\sqrt{x^2-b}+x\right)-180 b x^7 \left(45 \sqrt{x^2-b}+59 x\right)\right) \left(\sqrt{x^2-b}+x\right)^{9/2}}{3465 \left(-b^5+b^4 x \left(9 \sqrt{x^2-b}+41 x\right)-40 b^3 x^3 \left(3 \sqrt{x^2-b}+7 x\right)+16 b^2 x^5 \left(27 \sqrt{x^2-b}+43 x\right)+256 x^9 \left(\sqrt{x^2-b}+x\right)-64 b x^7 \left(9 \sqrt{x^2-b}+11 x\right)\right)}","\sqrt{2} b^{3/4} c \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{\sqrt{x^2-b}+x}}{\sqrt{x^2-b}-\sqrt{b}+x}\right)+\sqrt{2} b^{3/4} c \tanh ^{-1}\left(\frac{\frac{\sqrt{x^2-b}}{\sqrt{2} \sqrt[4]{b}}+\frac{x}{\sqrt{2} \sqrt[4]{b}}+\frac{\sqrt[4]{b}}{\sqrt{2}}}{\sqrt{\sqrt{x^2-b}+x}}\right)+\frac{2 \sqrt{x^2-b} \left(-1368 b^4 x+3705 b^3 x^3+10395 b^2 c x+1335 b^2 x^5-32340 b c x^3-8100 b x^7+18480 c x^5+5040 x^9\right)+2 \left(304 b^5-3078 b^4 x^2-2310 b^3 c+3735 b^3 x^4+24255 b^2 c x^2+4755 b^2 x^6-41580 b c x^4-10620 b x^8+18480 c x^6+5040 x^{10}\right)}{3465 \left(\sqrt{x^2-b}+x\right)^{9/2}}",1,"(2*Sqrt[-b + x^2]*(x + Sqrt[-b + x^2])^(9/2)*(304*b^5 + 5040*x^9*(x + Sqrt[-b + x^2]) - 342*b^4*x*(9*x + 4*Sqrt[-b + x^2]) - 180*b*x^7*(59*x + 45*Sqrt[-b + x^2]) + 15*b^2*x^5*(317*x + 89*Sqrt[-b + x^2]) + 15*b^3*x^3*(249*x + 247*Sqrt[-b + x^2])))/(3465*(-b^5 + 256*x^9*(x + Sqrt[-b + x^2]) - 40*b^3*x^3*(7*x + 3*Sqrt[-b + x^2]) - 64*b*x^7*(11*x + 9*Sqrt[-b + x^2]) + b^4*x*(41*x + 9*Sqrt[-b + x^2]) + 16*b^2*x^5*(43*x + 27*Sqrt[-b + x^2]))) + (c*((-8*b + 4*x*(x + Sqrt[-b + x^2]))/Sqrt[x + Sqrt[-b + x^2]] + 6*Sqrt[2]*b^(3/4)*ArcTan[1 - (Sqrt[2]*Sqrt[x + Sqrt[-b + x^2]])/b^(1/4)] - 6*Sqrt[2]*b^(3/4)*ArcTan[1 + (Sqrt[2]*Sqrt[x + Sqrt[-b + x^2]])/b^(1/4)] - 3*Sqrt[2]*b^(3/4)*Log[Sqrt[b] + x + Sqrt[-b + x^2] - Sqrt[2]*b^(1/4)*Sqrt[x + Sqrt[-b + x^2]]] + 3*Sqrt[2]*b^(3/4)*Log[Sqrt[b] + x + Sqrt[-b + x^2] + Sqrt[2]*b^(1/4)*Sqrt[x + Sqrt[-b + x^2]]]))/6","A",1
2864,1,379,303,1.4036008,"\int \frac{x^8}{\sqrt{-b^4+a^4 x^4} \left(-b^{16}+a^{16} x^{16}\right)} \, dx","Integrate[x^8/(Sqrt[-b^4 + a^4*x^4]*(-b^16 + a^16*x^16)),x]","\frac{x \left(-\sqrt{-\frac{a^2}{b^2}}\right)+i \sqrt{1-\frac{a^4 x^4}{b^4}} F\left(\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)+i \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(-i;\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)+i \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(i;\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)-i \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(-\sqrt[4]{-1};\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)-i \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(\sqrt[4]{-1};\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)-i \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(-(-1)^{3/4};\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)-i \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left((-1)^{3/4};\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)}{8 a^8 b^8 \sqrt{-\frac{a^2}{b^2}} \sqrt{a^4 x^4-b^4}}","-\frac{x}{8 a^8 b^8 \sqrt{a^4 x^4-b^4}}-\frac{\tan ^{-1}\left(\frac{-\frac{a^3 x^4}{2 b}+\frac{b^3}{2 a}+a b x^2}{x \sqrt{a^4 x^4-b^4}}\right)}{32 a^9 b^9}+\frac{\tanh ^{-1}\left(\frac{-\frac{a^3 x^4}{2 b}+\frac{b^3}{2 a}-a b x^2}{x \sqrt{a^4 x^4-b^4}}\right)}{32 a^9 b^9}-\frac{\tanh ^{-1}\left(\frac{-\frac{a^3 x^4}{2^{3/4} b}+\frac{b^3}{2^{3/4} a}-\frac{a b x^2}{\sqrt[4]{2}}}{x \sqrt{a^4 x^4-b^4}}\right)}{8\ 2^{3/4} a^9 b^9}-\frac{\tan ^{-1}\left(\frac{2^{3/4} a b x \sqrt{a^4 x^4-b^4}}{-a^4 x^4+\sqrt{2} a^2 b^2 x^2+b^4}\right)}{8\ 2^{3/4} a^9 b^9}",1,"(-(Sqrt[-(a^2/b^2)]*x) + I*Sqrt[1 - (a^4*x^4)/b^4]*EllipticF[I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1] + I*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[-I, I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1] + I*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[I, I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1] - I*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[-(-1)^(1/4), I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1] - I*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[(-1)^(1/4), I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1] - I*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[-(-1)^(3/4), I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1] - I*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[(-1)^(3/4), I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1])/(8*a^8*Sqrt[-(a^2/b^2)]*b^8*Sqrt[-b^4 + a^4*x^4])","C",1
2865,1,54,304,0.0432798,"\int \frac{x^2}{\left(-b+a x^2\right) \sqrt[3]{-x+x^3}} \, dx","Integrate[x^2/((-b + a*x^2)*(-x + x^3)^(1/3)),x]","-\frac{3 x^3 \sqrt[3]{1-x^2} F_1\left(\frac{4}{3};\frac{1}{3},1;\frac{7}{3};x^2,\frac{a x^2}{b}\right)}{8 b \sqrt[3]{x \left(x^2-1\right)}}","\frac{\sqrt[3]{b} \log \left(-\sqrt[3]{b} \sqrt[3]{x^3-x} x \sqrt[3]{a-b}+x^2 (a-b)^{2/3}+b^{2/3} \left(x^3-x\right)^{2/3}\right)}{4 a \sqrt[3]{a-b}}-\frac{\sqrt[3]{b} \log \left(x \sqrt[3]{a-b}+\sqrt[3]{b} \sqrt[3]{x^3-x}\right)}{2 a \sqrt[3]{a-b}}+\frac{\sqrt{3} \sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt{3} x \sqrt[3]{a-b}}{x \sqrt[3]{a-b}-2 \sqrt[3]{b} \sqrt[3]{x^3-x}}\right)}{2 a \sqrt[3]{a-b}}-\frac{\log \left(\sqrt[3]{x^3-x}-x\right)}{2 a}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-x}+x}\right)}{2 a}+\frac{\log \left(\sqrt[3]{x^3-x} x+\left(x^3-x\right)^{2/3}+x^2\right)}{4 a}",1,"(-3*x^3*(1 - x^2)^(1/3)*AppellF1[4/3, 1/3, 1, 7/3, x^2, (a*x^2)/b])/(8*b*(x*(-1 + x^2))^(1/3))","C",0
2866,1,379,304,1.0797238,"\int \frac{\left(1+x^4\right) \sqrt{x+\sqrt{1+x^2}}}{-1+x^4} \, dx","Integrate[((1 + x^4)*Sqrt[x + Sqrt[1 + x^2]])/(-1 + x^4),x]","\frac{1}{3} \left(\sqrt{x^2+1}+x\right)^{3/2}-\frac{1}{\sqrt{\sqrt{x^2+1}+x}}-\frac{\log \left(\sqrt{x^2+1}-\sqrt{2} \sqrt{\sqrt{x^2+1}+x}+x+1\right)}{\sqrt{2}}+\frac{\log \left(\sqrt{x^2+1}+\sqrt{2} \sqrt{\sqrt{x^2+1}+x}+x+1\right)}{\sqrt{2}}+\frac{\left(\sqrt{2}-2\right) \tan ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{\sqrt{2}-1}}\right)}{\sqrt{2 \left(\sqrt{2}-1\right)}}+\frac{\left(2+\sqrt{2}\right) \tan ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{1+\sqrt{2}}}\right)}{\sqrt{2 \left(1+\sqrt{2}\right)}}+\sqrt{2} \tan ^{-1}\left(1-\sqrt{2} \sqrt{\sqrt{x^2+1}+x}\right)-\sqrt{2} \tan ^{-1}\left(\sqrt{2} \sqrt{\sqrt{x^2+1}+x}+1\right)-\frac{\left(\sqrt{2}-2\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{\sqrt{2}-1}}\right)}{\sqrt{2 \left(\sqrt{2}-1\right)}}-\frac{\left(2+\sqrt{2}\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{1+\sqrt{2}}}\right)}{\sqrt{2 \left(1+\sqrt{2}\right)}}","\frac{1}{3} \left(\sqrt{x^2+1}+x\right)^{3/2}-\frac{1}{\sqrt{\sqrt{x^2+1}+x}}-\sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{\sqrt{2}-1}}\right)+\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{1+\sqrt{2}}}\right)-\sqrt{2} \tan ^{-1}\left(\frac{\frac{\sqrt{x^2+1}}{\sqrt{2}}+\frac{x}{\sqrt{2}}-\frac{1}{\sqrt{2}}}{\sqrt{\sqrt{x^2+1}+x}}\right)+\sqrt{\sqrt{2}-1} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{\sqrt{2}-1}}\right)-\sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{1+\sqrt{2}}}\right)+\sqrt{2} \tanh ^{-1}\left(\frac{\frac{\sqrt{x^2+1}}{\sqrt{2}}+\frac{x}{\sqrt{2}}+\frac{1}{\sqrt{2}}}{\sqrt{\sqrt{x^2+1}+x}}\right)",1,"-(1/Sqrt[x + Sqrt[1 + x^2]]) + (x + Sqrt[1 + x^2])^(3/2)/3 + ((-2 + Sqrt[2])*ArcTan[Sqrt[x + Sqrt[1 + x^2]]/Sqrt[-1 + Sqrt[2]]])/Sqrt[2*(-1 + Sqrt[2])] + ((2 + Sqrt[2])*ArcTan[Sqrt[x + Sqrt[1 + x^2]]/Sqrt[1 + Sqrt[2]]])/Sqrt[2*(1 + Sqrt[2])] + Sqrt[2]*ArcTan[1 - Sqrt[2]*Sqrt[x + Sqrt[1 + x^2]]] - Sqrt[2]*ArcTan[1 + Sqrt[2]*Sqrt[x + Sqrt[1 + x^2]]] - ((-2 + Sqrt[2])*ArcTanh[Sqrt[x + Sqrt[1 + x^2]]/Sqrt[-1 + Sqrt[2]]])/Sqrt[2*(-1 + Sqrt[2])] - ((2 + Sqrt[2])*ArcTanh[Sqrt[x + Sqrt[1 + x^2]]/Sqrt[1 + Sqrt[2]]])/Sqrt[2*(1 + Sqrt[2])] - Log[1 + x + Sqrt[1 + x^2] - Sqrt[2]*Sqrt[x + Sqrt[1 + x^2]]]/Sqrt[2] + Log[1 + x + Sqrt[1 + x^2] + Sqrt[2]*Sqrt[x + Sqrt[1 + x^2]]]/Sqrt[2]","A",1
2867,1,91,305,0.4062244,"\int \frac{(-a+x) (-b+x)}{\left((-a+x) (-b+x)^2\right)^{2/3} \left(-b^2+a^2 d+2 (b-a d) x+(-1+d) x^2\right)} \, dx","Integrate[((-a + x)*(-b + x))/(((-a + x)*(-b + x)^2)^(2/3)*(-b^2 + a^2*d + 2*(b - a*d)*x + (-1 + d)*x^2)),x]","-\frac{3 (b-x)^2 \left(\, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{b-x}{\sqrt{d} (x-a)}\right)+\, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{x-b}{\sqrt{d} (x-a)}\right)\right)}{4 d (a-b) \left((x-a) (b-x)^2\right)^{2/3}}","-\frac{\log \left(a^2 d^{2/3}+\sqrt[3]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3} \left(\sqrt[3]{d} x-a \sqrt[3]{d}\right)+\left(x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3\right)^{2/3}-2 a d^{2/3} x+d^{2/3} x^2\right)}{4 d^{2/3} (a-b)}+\frac{\log \left(\sqrt[3]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3}+a \sqrt[3]{d}-\sqrt[3]{d} x\right)}{2 d^{2/3} (a-b)}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} a \sqrt[3]{d}-\sqrt{3} \sqrt[3]{d} x}{-2 \sqrt[3]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3}+a \sqrt[3]{d}-\sqrt[3]{d} x}\right)}{2 d^{2/3} (a-b)}",1,"(-3*(b - x)^2*(Hypergeometric2F1[2/3, 1, 5/3, (b - x)/(Sqrt[d]*(-a + x))] + Hypergeometric2F1[2/3, 1, 5/3, (-b + x)/(Sqrt[d]*(-a + x))]))/(4*(a - b)*d*((b - x)^2*(-a + x))^(2/3))","C",1
2868,1,91,305,0.2697873,"\int \frac{a b-(a+b) x+x^2}{\left((-a+x) (-b+x)^2\right)^{2/3} \left(-b^2+a^2 d+2 (b-a d) x+(-1+d) x^2\right)} \, dx","Integrate[(a*b - (a + b)*x + x^2)/(((-a + x)*(-b + x)^2)^(2/3)*(-b^2 + a^2*d + 2*(b - a*d)*x + (-1 + d)*x^2)),x]","-\frac{3 \sqrt[3]{(x-a) (b-x)^2} \left(\, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{b-x}{\sqrt{d} (x-a)}\right)+\, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{x-b}{\sqrt{d} (x-a)}\right)\right)}{4 d (a-b) (x-a)}","-\frac{\log \left(a^2 d^{2/3}+\sqrt[3]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3} \left(\sqrt[3]{d} x-a \sqrt[3]{d}\right)+\left(x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3\right)^{2/3}-2 a d^{2/3} x+d^{2/3} x^2\right)}{4 d^{2/3} (a-b)}+\frac{\log \left(\sqrt[3]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3}+a \sqrt[3]{d}-\sqrt[3]{d} x\right)}{2 d^{2/3} (a-b)}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} a \sqrt[3]{d}-\sqrt{3} \sqrt[3]{d} x}{-2 \sqrt[3]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3}+a \sqrt[3]{d}-\sqrt[3]{d} x}\right)}{2 d^{2/3} (a-b)}",1,"(-3*((b - x)^2*(-a + x))^(1/3)*(Hypergeometric2F1[2/3, 1, 5/3, (b - x)/(Sqrt[d]*(-a + x))] + Hypergeometric2F1[2/3, 1, 5/3, (-b + x)/(Sqrt[d]*(-a + x))]))/(4*(a - b)*d*(-a + x))","C",1
2869,0,0,305,1.9636555,"\int \frac{x}{x^2-\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","Integrate[x/(x^2 - Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]]),x]","\int \frac{x}{x^2-\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","-4 \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6 c-2 \text{$\#$1}^4 b+6 \text{$\#$1}^4 c^2-\text{$\#$1}^3 a^2+4 \text{$\#$1}^2 b c-4 \text{$\#$1}^2 c^3+\text{$\#$1} a^2 c+b^2-2 b c^2+c^4\&,\frac{\text{$\#$1}^7 \left(-\log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)\right)+3 \text{$\#$1}^5 c \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-3 \text{$\#$1}^3 c^2 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+\text{$\#$1}^3 b \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+\text{$\#$1} c^3 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-\text{$\#$1} b c \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)}{8 \text{$\#$1}^7-24 \text{$\#$1}^5 c-8 \text{$\#$1}^3 b+24 \text{$\#$1}^3 c^2-3 \text{$\#$1}^2 a^2+8 \text{$\#$1} b c-8 \text{$\#$1} c^3+a^2 c}\&\right]",1,"Integrate[x/(x^2 - Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]]), x]","F",-1
2870,0,0,305,1.3915815,"\int \frac{x}{x^2-\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","Integrate[x/(x^2 - Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]]),x]","\int \frac{x}{x^2-\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","-4 \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6 c-2 \text{$\#$1}^4 b+6 \text{$\#$1}^4 c^2-\text{$\#$1}^3 a^2+4 \text{$\#$1}^2 b c-4 \text{$\#$1}^2 c^3+\text{$\#$1} a^2 c+b^2-2 b c^2+c^4\&,\frac{\text{$\#$1}^7 \left(-\log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)\right)+3 \text{$\#$1}^5 c \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-3 \text{$\#$1}^3 c^2 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+\text{$\#$1}^3 b \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+\text{$\#$1} c^3 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-\text{$\#$1} b c \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)}{8 \text{$\#$1}^7-24 \text{$\#$1}^5 c-8 \text{$\#$1}^3 b+24 \text{$\#$1}^3 c^2-3 \text{$\#$1}^2 a^2+8 \text{$\#$1} b c-8 \text{$\#$1} c^3+a^2 c}\&\right]",1,"Integrate[x/(x^2 - Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]]), x]","F",-1
2871,0,0,306,8.1665907,"\int \frac{a b-2 b x+x^2}{\sqrt[3]{x (-a+x) (-b+x)^2} \left(b d-(a+d) x+x^2\right)} \, dx","Integrate[(a*b - 2*b*x + x^2)/((x*(-a + x)*(-b + x)^2)^(1/3)*(b*d - (a + d)*x + x^2)),x]","\int \frac{a b-2 b x+x^2}{\sqrt[3]{x (-a+x) (-b+x)^2} \left(b d-(a+d) x+x^2\right)} \, dx","-\frac{\log \left(\sqrt[3]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4} \left(d^{2/3} x-b d^{2/3}\right)+\sqrt[3]{d} \left(x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4\right)^{2/3}+b^2 d-2 b d x+d x^2\right)}{2 \sqrt[3]{d}}+\frac{\log \left(\sqrt[6]{d} \sqrt[3]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}+b \sqrt{d}-\sqrt{d} x\right)}{\sqrt[3]{d}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}}{\sqrt[3]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}-2 b \sqrt[3]{d}+2 \sqrt[3]{d} x}\right)}{\sqrt[3]{d}}",1,"Integrate[(a*b - 2*b*x + x^2)/((x*(-a + x)*(-b + x)^2)^(1/3)*(b*d - (a + d)*x + x^2)), x]","F",-1
2872,0,0,306,3.5432267,"\int \frac{-a b^2+(4 a-b) b x-3 a x^2+x^3}{\sqrt[3]{x (-a+x) (-b+x)^2} \left(-a^2 d+\left(b^2+2 a d\right) x-(2 b+d) x^2+x^3\right)} \, dx","Integrate[(-(a*b^2) + (4*a - b)*b*x - 3*a*x^2 + x^3)/((x*(-a + x)*(-b + x)^2)^(1/3)*(-(a^2*d) + (b^2 + 2*a*d)*x - (2*b + d)*x^2 + x^3)),x]","\int \frac{-a b^2+(4 a-b) b x-3 a x^2+x^3}{\sqrt[3]{x (-a+x) (-b+x)^2} \left(-a^2 d+\left(b^2+2 a d\right) x-(2 b+d) x^2+x^3\right)} \, dx","-\frac{\log \left(a^2 d^{2/3}+\sqrt[3]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4} \left(\sqrt[3]{d} x-a \sqrt[3]{d}\right)+\left(x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4\right)^{2/3}-2 a d^{2/3} x+d^{2/3} x^2\right)}{2 \sqrt[3]{d}}+\frac{\log \left(\sqrt[3]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}+a \sqrt[3]{d}-\sqrt[3]{d} x\right)}{\sqrt[3]{d}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}}{\sqrt[3]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}-2 a \sqrt[3]{d}+2 \sqrt[3]{d} x}\right)}{\sqrt[3]{d}}",1,"Integrate[(-(a*b^2) + (4*a - b)*b*x - 3*a*x^2 + x^3)/((x*(-a + x)*(-b + x)^2)^(1/3)*(-(a^2*d) + (b^2 + 2*a*d)*x - (2*b + d)*x^2 + x^3)), x]","F",-1
2873,1,216,306,0.2974379,"\int \frac{-d+c x^7}{x \sqrt[3]{-b+a x^3}} \, dx","Integrate[(-d + c*x^7)/(x*(-b + a*x^3)^(1/3)),x]","\frac{c \left(2 b^2 \log \left(\frac{a^{2/3} x^2}{\left(a x^3-b\right)^{2/3}}+\frac{\sqrt[3]{a} x}{\sqrt[3]{a x^3-b}}+1\right)+9 a^{4/3} x^4 \left(a x^3-b\right)^{2/3}-4 b^2 \log \left(1-\frac{\sqrt[3]{a} x}{\sqrt[3]{a x^3-b}}\right)+4 \sqrt{3} b^2 \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a} x}{\sqrt[3]{a x^3-b}}+1}{\sqrt{3}}\right)+12 \sqrt[3]{a} b x \left(a x^3-b\right)^{2/3}\right)}{54 a^{7/3}}-\frac{d \left(a x^3-b\right)^{2/3} \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};1-\frac{a x^3}{b}\right)}{2 b}","-\frac{2 b^2 c \log \left(\sqrt[3]{a x^3-b}-\sqrt[3]{a} x\right)}{27 a^{7/3}}-\frac{2 b^2 c \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a x^3-b}}{\sqrt{3} \sqrt[3]{a}}+\frac{x}{\sqrt{3}}}{x}\right)}{9 \sqrt{3} a^{7/3}}+\frac{b^2 c \log \left(a^{2/3} x^2+\sqrt[3]{a} x \sqrt[3]{a x^3-b}+\left(a x^3-b\right)^{2/3}\right)}{27 a^{7/3}}+\frac{c \left(a x^3-b\right)^{2/3} \left(3 a x^4+4 b x\right)}{18 a^2}-\frac{d \log \left(-\sqrt[3]{b} \sqrt[3]{a x^3-b}+\left(a x^3-b\right)^{2/3}+b^{2/3}\right)}{6 \sqrt[3]{b}}+\frac{d \log \left(\sqrt[3]{a x^3-b}+\sqrt[3]{b}\right)}{3 \sqrt[3]{b}}+\frac{d \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{a x^3-b}}{\sqrt{3} \sqrt[3]{b}}\right)}{\sqrt{3} \sqrt[3]{b}}",1,"-1/2*(d*(-b + a*x^3)^(2/3)*Hypergeometric2F1[2/3, 1, 5/3, 1 - (a*x^3)/b])/b + (c*(12*a^(1/3)*b*x*(-b + a*x^3)^(2/3) + 9*a^(4/3)*x^4*(-b + a*x^3)^(2/3) + 4*Sqrt[3]*b^2*ArcTan[(1 + (2*a^(1/3)*x)/(-b + a*x^3)^(1/3))/Sqrt[3]] - 4*b^2*Log[1 - (a^(1/3)*x)/(-b + a*x^3)^(1/3)] + 2*b^2*Log[1 + (a^(2/3)*x^2)/(-b + a*x^3)^(2/3) + (a^(1/3)*x)/(-b + a*x^3)^(1/3)]))/(54*a^(7/3))","C",1
2874,1,255,306,0.4573831,"\int \frac{\sqrt{c+\sqrt{b+a x}}}{x-\sqrt{b+a x}} \, dx","Integrate[Sqrt[c + Sqrt[b + a*x]]/(x - Sqrt[b + a*x]),x]","\frac{2 \sqrt{2} \left(a \left(c-\sqrt{a^2+4 b}\right)-c \sqrt{a^2+4 b}+a^2+2 b\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\sqrt{a x+b}+c}}{\sqrt{-\sqrt{a^2+4 b}+a+2 c}}\right)}{\sqrt{a^2+4 b} \sqrt{-\sqrt{a^2+4 b}+a+2 c}}-\frac{2 \sqrt{2} \left(a \left(\sqrt{a^2+4 b}+c\right)+c \sqrt{a^2+4 b}+a^2+2 b\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\sqrt{a x+b}+c}}{\sqrt{\sqrt{a^2+4 b}+a+2 c}}\right)}{\sqrt{a^2+4 b} \sqrt{\sqrt{a^2+4 b}+a+2 c}}+4 \sqrt{\sqrt{a x+b}+c}","\frac{2 \left(\sqrt{2} c \sqrt{a^2+4 b}+\sqrt{2} a \sqrt{a^2+4 b}+\sqrt{2} a^2+\sqrt{2} a c+2 \sqrt{2} b\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{\sqrt{a x+b}+c}}{\sqrt{-\sqrt{a^2+4 b}-a-2 c}}\right)}{\sqrt{a^2+4 b} \sqrt{-\sqrt{a^2+4 b}-a-2 c}}+\frac{2 \left(\sqrt{2} c \sqrt{a^2+4 b}+\sqrt{2} a \sqrt{a^2+4 b}-\sqrt{2} a^2-\sqrt{2} a c-2 \sqrt{2} b\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{\sqrt{a x+b}+c}}{\sqrt{\sqrt{a^2+4 b}-a-2 c}}\right)}{\sqrt{a^2+4 b} \sqrt{\sqrt{a^2+4 b}-a-2 c}}+4 \sqrt{\sqrt{a x+b}+c}",1,"4*Sqrt[c + Sqrt[b + a*x]] + (2*Sqrt[2]*(a^2 + 2*b - Sqrt[a^2 + 4*b]*c + a*(-Sqrt[a^2 + 4*b] + c))*ArcTanh[(Sqrt[2]*Sqrt[c + Sqrt[b + a*x]])/Sqrt[a - Sqrt[a^2 + 4*b] + 2*c]])/(Sqrt[a^2 + 4*b]*Sqrt[a - Sqrt[a^2 + 4*b] + 2*c]) - (2*Sqrt[2]*(a^2 + 2*b + Sqrt[a^2 + 4*b]*c + a*(Sqrt[a^2 + 4*b] + c))*ArcTanh[(Sqrt[2]*Sqrt[c + Sqrt[b + a*x]])/Sqrt[a + Sqrt[a^2 + 4*b] + 2*c]])/(Sqrt[a^2 + 4*b]*Sqrt[a + Sqrt[a^2 + 4*b] + 2*c])","A",1
2875,0,0,308,0.2411569,"\int \frac{1+x}{(1+2 x) \sqrt[3]{27+27 x+36 x^2+28 x^3+9 x^4+x^5}} \, dx","Integrate[(1 + x)/((1 + 2*x)*(27 + 27*x + 36*x^2 + 28*x^3 + 9*x^4 + x^5)^(1/3)),x]","\int \frac{1+x}{(1+2 x) \sqrt[3]{27+27 x+36 x^2+28 x^3+9 x^4+x^5}} \, dx","\frac{\log \left(\sqrt[3]{10} x^2+5 \sqrt[3]{x^5+9 x^4+28 x^3+36 x^2+27 x+27}+\sqrt[3]{10} x-6 \sqrt[3]{10}\right)}{5 \sqrt[3]{10}}-\frac{\log \left(10^{2/3} x^4+2\ 10^{2/3} x^3-11\ 10^{2/3} x^2+25 \left(x^5+9 x^4+28 x^3+36 x^2+27 x+27\right)^{2/3}+\left(-5 \sqrt[3]{10} x^2-5 \sqrt[3]{10} x+30 \sqrt[3]{10}\right) \sqrt[3]{x^5+9 x^4+28 x^3+36 x^2+27 x+27}-12\ 10^{2/3} x+36\ 10^{2/3}\right)}{10 \sqrt[3]{10}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{5 \sqrt{3} \sqrt[3]{x^5+9 x^4+28 x^3+36 x^2+27 x+27}}{-2 \sqrt[3]{10} x^2+5 \sqrt[3]{x^5+9 x^4+28 x^3+36 x^2+27 x+27}-2 \sqrt[3]{10} x+12 \sqrt[3]{10}}\right)}{5 \sqrt[3]{10}}",1,"Integrate[(1 + x)/((1 + 2*x)*(27 + 27*x + 36*x^2 + 28*x^3 + 9*x^4 + x^5)^(1/3)), x]","F",-1
2876,1,268,310,0.7050937,"\int \frac{-b x+a x^3}{\left(-b+2 a x^3\right) \sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Integrate[(-(b*x) + a*x^3)/((-b + 2*a*x^3)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","\frac{3 \sqrt[3]{a} x \sqrt[3]{\frac{a^3 x}{b^2}+1} \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};-\frac{a^3 x}{b^2}\right)-x \left(\left(\sqrt[3]{a}-2^{2/3} \sqrt[3]{b}\right) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{x a^3+\sqrt[3]{2} b^{5/3} x \sqrt[3]{a}}{x a^3+b^2}\right)+\left(\sqrt[3]{a}-(-2)^{2/3} \sqrt[3]{b}\right) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\sqrt[3]{a} \left(a^{8/3}-\sqrt[3]{-2} b^{5/3}\right) x}{x a^3+b^2}\right)+\left(\sqrt[3]{a}+\sqrt[3]{-1} 2^{2/3} \sqrt[3]{b}\right) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\sqrt[3]{a} \left(a^{8/3}+(-1)^{2/3} \sqrt[3]{2} b^{5/3}\right) x}{x a^3+b^2}\right)\right)}{2 \sqrt[3]{a} \sqrt[3]{x^2 \left(a^3 x+b^2\right)}}","\frac{1}{6} \text{RootSum}\left[-\text{$\#$1}^9+3 \text{$\#$1}^6 a^3-3 \text{$\#$1}^3 a^6+a^9+2 a b^5\&,\frac{-\text{$\#$1}^3 \log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)+\text{$\#$1}^3 \log (x)+a^3 \log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)+2 b^2 \log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)+a^3 (-\log (x))-2 b^2 \log (x)}{\text{$\#$1} a^3-\text{$\#$1}^4}\&\right]-\frac{\log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-a x\right)}{2 a}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} a x}{2 \sqrt[3]{a^3 x^3+b^2 x^2}+a x}\right)}{2 a}+\frac{\log \left(a x \sqrt[3]{a^3 x^3+b^2 x^2}+\left(a^3 x^3+b^2 x^2\right)^{2/3}+a^2 x^2\right)}{4 a}",1,"(3*a^(1/3)*x*(1 + (a^3*x)/b^2)^(1/3)*Hypergeometric2F1[1/3, 1/3, 4/3, -((a^3*x)/b^2)] - x*((a^(1/3) - (-2)^(2/3)*b^(1/3))*Hypergeometric2F1[1/3, 1, 4/3, (a^(1/3)*(a^(8/3) - (-2)^(1/3)*b^(5/3))*x)/(b^2 + a^3*x)] + (a^(1/3) + (-1)^(1/3)*2^(2/3)*b^(1/3))*Hypergeometric2F1[1/3, 1, 4/3, (a^(1/3)*(a^(8/3) + (-1)^(2/3)*2^(1/3)*b^(5/3))*x)/(b^2 + a^3*x)] + (a^(1/3) - 2^(2/3)*b^(1/3))*Hypergeometric2F1[1/3, 1, 4/3, (a^3*x + 2^(1/3)*a^(1/3)*b^(5/3)*x)/(b^2 + a^3*x)]))/(2*a^(1/3)*(x^2*(b^2 + a^3*x))^(1/3))","A",1
2877,1,268,310,0.2208042,"\int \frac{-b x+a x^3}{\left(-b+2 a x^3\right) \sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Integrate[(-(b*x) + a*x^3)/((-b + 2*a*x^3)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","\frac{3 \sqrt[3]{a} x \sqrt[3]{\frac{a^3 x}{b^2}+1} \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};-\frac{a^3 x}{b^2}\right)-x \left(\left(\sqrt[3]{a}-2^{2/3} \sqrt[3]{b}\right) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{x a^3+\sqrt[3]{2} b^{5/3} x \sqrt[3]{a}}{x a^3+b^2}\right)+\left(\sqrt[3]{a}-(-2)^{2/3} \sqrt[3]{b}\right) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\sqrt[3]{a} \left(a^{8/3}-\sqrt[3]{-2} b^{5/3}\right) x}{x a^3+b^2}\right)+\left(\sqrt[3]{a}+\sqrt[3]{-1} 2^{2/3} \sqrt[3]{b}\right) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\sqrt[3]{a} \left(a^{8/3}+(-1)^{2/3} \sqrt[3]{2} b^{5/3}\right) x}{x a^3+b^2}\right)\right)}{2 \sqrt[3]{a} \sqrt[3]{x^2 \left(a^3 x+b^2\right)}}","\frac{1}{6} \text{RootSum}\left[-\text{$\#$1}^9+3 \text{$\#$1}^6 a^3-3 \text{$\#$1}^3 a^6+a^9+2 a b^5\&,\frac{-\text{$\#$1}^3 \log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)+\text{$\#$1}^3 \log (x)+a^3 \log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)+2 b^2 \log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)+a^3 (-\log (x))-2 b^2 \log (x)}{\text{$\#$1} a^3-\text{$\#$1}^4}\&\right]-\frac{\log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-a x\right)}{2 a}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} a x}{2 \sqrt[3]{a^3 x^3+b^2 x^2}+a x}\right)}{2 a}+\frac{\log \left(a x \sqrt[3]{a^3 x^3+b^2 x^2}+\left(a^3 x^3+b^2 x^2\right)^{2/3}+a^2 x^2\right)}{4 a}",1,"(3*a^(1/3)*x*(1 + (a^3*x)/b^2)^(1/3)*Hypergeometric2F1[1/3, 1/3, 4/3, -((a^3*x)/b^2)] - x*((a^(1/3) - (-2)^(2/3)*b^(1/3))*Hypergeometric2F1[1/3, 1, 4/3, (a^(1/3)*(a^(8/3) - (-2)^(1/3)*b^(5/3))*x)/(b^2 + a^3*x)] + (a^(1/3) + (-1)^(1/3)*2^(2/3)*b^(1/3))*Hypergeometric2F1[1/3, 1, 4/3, (a^(1/3)*(a^(8/3) + (-1)^(2/3)*2^(1/3)*b^(5/3))*x)/(b^2 + a^3*x)] + (a^(1/3) - 2^(2/3)*b^(1/3))*Hypergeometric2F1[1/3, 1, 4/3, (a^3*x + 2^(1/3)*a^(1/3)*b^(5/3)*x)/(b^2 + a^3*x)]))/(2*a^(1/3)*(x^2*(b^2 + a^3*x))^(1/3))","A",1
2878,1,268,310,0.6581897,"\int \frac{b x+a x^3}{\left(b+2 a x^3\right) \sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Integrate[(b*x + a*x^3)/((b + 2*a*x^3)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","\frac{3 \sqrt[3]{a} x \sqrt[3]{\frac{a^3 x}{b^2}+1} \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};-\frac{a^3 x}{b^2}\right)-x \left(\left(\sqrt[3]{a}+2^{2/3} \sqrt[3]{b}\right) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a^3 x-\sqrt[3]{2} \sqrt[3]{a} b^{5/3} x}{x a^3+b^2}\right)+\left(\sqrt[3]{a}+(-2)^{2/3} \sqrt[3]{b}\right) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\sqrt[3]{a} \left(a^{8/3}+\sqrt[3]{-2} b^{5/3}\right) x}{x a^3+b^2}\right)+\left(\sqrt[3]{a}-\sqrt[3]{-1} 2^{2/3} \sqrt[3]{b}\right) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\sqrt[3]{a} \left(a^{8/3}-(-1)^{2/3} \sqrt[3]{2} b^{5/3}\right) x}{x a^3+b^2}\right)\right)}{2 \sqrt[3]{a} \sqrt[3]{x^2 \left(a^3 x+b^2\right)}}","\frac{1}{6} \text{RootSum}\left[-\text{$\#$1}^9+3 \text{$\#$1}^6 a^3-3 \text{$\#$1}^3 a^6+a^9-2 a b^5\&,\frac{-\text{$\#$1}^3 \log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)+\text{$\#$1}^3 \log (x)+a^3 \log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)+2 b^2 \log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)+a^3 (-\log (x))-2 b^2 \log (x)}{\text{$\#$1} a^3-\text{$\#$1}^4}\&\right]-\frac{\log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-a x\right)}{2 a}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} a x}{2 \sqrt[3]{a^3 x^3+b^2 x^2}+a x}\right)}{2 a}+\frac{\log \left(a x \sqrt[3]{a^3 x^3+b^2 x^2}+\left(a^3 x^3+b^2 x^2\right)^{2/3}+a^2 x^2\right)}{4 a}",1,"(3*a^(1/3)*x*(1 + (a^3*x)/b^2)^(1/3)*Hypergeometric2F1[1/3, 1/3, 4/3, -((a^3*x)/b^2)] - x*((a^(1/3) + (-2)^(2/3)*b^(1/3))*Hypergeometric2F1[1/3, 1, 4/3, (a^(1/3)*(a^(8/3) + (-2)^(1/3)*b^(5/3))*x)/(b^2 + a^3*x)] + (a^(1/3) - (-1)^(1/3)*2^(2/3)*b^(1/3))*Hypergeometric2F1[1/3, 1, 4/3, (a^(1/3)*(a^(8/3) - (-1)^(2/3)*2^(1/3)*b^(5/3))*x)/(b^2 + a^3*x)] + (a^(1/3) + 2^(2/3)*b^(1/3))*Hypergeometric2F1[1/3, 1, 4/3, (a^3*x - 2^(1/3)*a^(1/3)*b^(5/3)*x)/(b^2 + a^3*x)]))/(2*a^(1/3)*(x^2*(b^2 + a^3*x))^(1/3))","A",1
2879,0,0,310,3.3622643,"\int \frac{x (-b+x) (a b+(-2 a+b) x)}{\sqrt[3]{x (-a+x) (-b+x)} \left(-a^4+4 a^3 x+\left(-6 a^2+b^2 d\right) x^2+2 (2 a-b d) x^3+(-1+d) x^4\right)} \, dx","Integrate[(x*(-b + x)*(a*b + (-2*a + b)*x))/((x*(-a + x)*(-b + x))^(1/3)*(-a^4 + 4*a^3*x + (-6*a^2 + b^2*d)*x^2 + 2*(2*a - b*d)*x^3 + (-1 + d)*x^4)),x]","\int \frac{x (-b+x) (a b+(-2 a+b) x)}{\sqrt[3]{x (-a+x) (-b+x)} \left(-a^4+4 a^3 x+\left(-6 a^2+b^2 d\right) x^2+2 (2 a-b d) x^3+(-1+d) x^4\right)} \, dx","\frac{\tanh ^{-1}\left(\frac{\sqrt[3]{x^2 (-a-b)+a b x+x^3} \left(a \sqrt[6]{d}-\sqrt[6]{d} x\right)}{a^2+\sqrt[3]{d} \left(x^2 (-a-b)+a b x+x^3\right)^{2/3}-2 a x+x^2}\right)}{2 d^{5/6}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{d} \sqrt[3]{x^2 (-a-b)+a b x+x^3}}{\sqrt[6]{d} \sqrt[3]{x^2 (-a-b)+a b x+x^3}+2 a-2 x}\right)}{2 d^{5/6}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{d} \sqrt[3]{x^2 (-a-b)+a b x+x^3}}{\sqrt[6]{d} \sqrt[3]{x^2 (-a-b)+a b x+x^3}-2 a+2 x}\right)}{2 d^{5/6}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[3]{x^2 (-a-b)+a b x+x^3}}{a-x}\right)}{d^{5/6}}",1,"Integrate[(x*(-b + x)*(a*b + (-2*a + b)*x))/((x*(-a + x)*(-b + x))^(1/3)*(-a^4 + 4*a^3*x + (-6*a^2 + b^2*d)*x^2 + 2*(2*a - b*d)*x^3 + (-1 + d)*x^4)), x]","F",-1
2880,0,0,311,9.1243596,"\int \frac{-a b-a c+2 b c+(2 a-b-c) x}{\sqrt[3]{(-a+x) (-b+x) (-c+x)} \left(-b c+a^2 d+(b+c-2 a d) x+(-1+d) x^2\right)} \, dx","Integrate[(-(a*b) - a*c + 2*b*c + (2*a - b - c)*x)/(((-a + x)*(-b + x)*(-c + x))^(1/3)*(-(b*c) + a^2*d + (b + c - 2*a*d)*x + (-1 + d)*x^2)),x]","\int \frac{-a b-a c+2 b c+(2 a-b-c) x}{\sqrt[3]{(-a+x) (-b+x) (-c+x)} \left(-b c+a^2 d+(b+c-2 a d) x+(-1+d) x^2\right)} \, dx","-\frac{\log \left(a^2 d^{2/3}+\left(\sqrt[3]{d} x-a \sqrt[3]{d}\right) \sqrt[3]{x^2 (-a-b-c)+x (a b+a c+b c)-a b c+x^3}+\left(x^2 (-a-b-c)+x (a b+a c+b c)-a b c+x^3\right)^{2/3}-2 a d^{2/3} x+d^{2/3} x^2\right)}{2 \sqrt[3]{d}}+\frac{\log \left(\sqrt[3]{x^2 (-a-b-c)+x (a b+a c+b c)-a b c+x^3}+a \sqrt[3]{d}-\sqrt[3]{d} x\right)}{\sqrt[3]{d}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x^2 (-a-b-c)+x (a b+a c+b c)-a b c+x^3}}{\sqrt[3]{x^2 (-a-b-c)+x (a b+a c+b c)-a b c+x^3}-2 a \sqrt[3]{d}+2 \sqrt[3]{d} x}\right)}{\sqrt[3]{d}}",1,"Integrate[(-(a*b) - a*c + 2*b*c + (2*a - b - c)*x)/(((-a + x)*(-b + x)*(-c + x))^(1/3)*(-(b*c) + a^2*d + (b + c - 2*a*d)*x + (-1 + d)*x^2)), x]","F",-1
2881,0,0,311,3.1622519,"\int \frac{x \left(-a b+x^2\right)}{\sqrt[3]{x^2 (-a+x) (-b+x)} \left(a^2 b^2-2 a b (a+b) x+\left(a^2+4 a b+b^2-d\right) x^2-2 (a+b) x^3+x^4\right)} \, dx","Integrate[(x*(-(a*b) + x^2))/((x^2*(-a + x)*(-b + x))^(1/3)*(a^2*b^2 - 2*a*b*(a + b)*x + (a^2 + 4*a*b + b^2 - d)*x^2 - 2*(a + b)*x^3 + x^4)),x]","\int \frac{x \left(-a b+x^2\right)}{\sqrt[3]{x^2 (-a+x) (-b+x)} \left(a^2 b^2-2 a b (a+b) x+\left(a^2+4 a b+b^2-d\right) x^2-2 (a+b) x^3+x^4\right)} \, dx","\frac{\log \left(\sqrt[3]{x^3 (-a-b)+a b x^2+x^4}-\sqrt[6]{d} x\right)}{2 d^{2/3}}+\frac{\log \left(\sqrt[3]{x^3 (-a-b)+a b x^2+x^4}+\sqrt[6]{d} x\right)}{2 d^{2/3}}-\frac{\log \left(-\sqrt[6]{d} x \sqrt[3]{x^3 (-a-b)+a b x^2+x^4}+\left(x^3 (-a-b)+a b x^2+x^4\right)^{2/3}+\sqrt[3]{d} x^2\right)}{4 d^{2/3}}-\frac{\log \left(\sqrt[6]{d} x \sqrt[3]{x^3 (-a-b)+a b x^2+x^4}+\left(x^3 (-a-b)+a b x^2+x^4\right)^{2/3}+\sqrt[3]{d} x^2\right)}{4 d^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} x^2}{2 \left(x^3 (-a-b)+a b x^2+x^4\right)^{2/3}+\sqrt[3]{d} x^2}\right)}{2 d^{2/3}}",1,"Integrate[(x*(-(a*b) + x^2))/((x^2*(-a + x)*(-b + x))^(1/3)*(a^2*b^2 - 2*a*b*(a + b)*x + (a^2 + 4*a*b + b^2 - d)*x^2 - 2*(a + b)*x^3 + x^4)), x]","F",-1
2882,1,294,311,3.0594258,"\int \frac{-b^6+a^6 x^6}{\sqrt{-b^2 x+a^2 x^3} \left(b^6+a^6 x^6\right)} \, dx","Integrate[(-b^6 + a^6*x^6)/(Sqrt[-(b^2*x) + a^2*x^3]*(b^6 + a^6*x^6)),x]","-\frac{2 i x^{3/2} \sqrt{1-\frac{b^2}{a^2 x^2}} \left(3 F\left(\left.i \sinh ^{-1}\left(\frac{\sqrt{-\frac{b}{a}}}{\sqrt{x}}\right)\right|-1\right)-\Pi \left(-i;\left.i \sinh ^{-1}\left(\frac{\sqrt{-\frac{b}{a}}}{\sqrt{x}}\right)\right|-1\right)-\Pi \left(i;\left.i \sinh ^{-1}\left(\frac{\sqrt{-\frac{b}{a}}}{\sqrt{x}}\right)\right|-1\right)-\Pi \left(-\frac{i}{2}-\frac{\sqrt{3}}{2};\left.i \sinh ^{-1}\left(\frac{\sqrt{-\frac{b}{a}}}{\sqrt{x}}\right)\right|-1\right)-\Pi \left(\frac{i}{2}-\frac{\sqrt{3}}{2};\left.i \sinh ^{-1}\left(\frac{\sqrt{-\frac{b}{a}}}{\sqrt{x}}\right)\right|-1\right)-\Pi \left(\frac{1}{2} \left(-i+\sqrt{3}\right);\left.i \sinh ^{-1}\left(\frac{\sqrt{-\frac{b}{a}}}{\sqrt{x}}\right)\right|-1\right)-\Pi \left(\frac{1}{2} \left(i+\sqrt{3}\right);\left.i \sinh ^{-1}\left(\frac{\sqrt{-\frac{b}{a}}}{\sqrt{x}}\right)\right|-1\right)\right)}{3 \sqrt{-\frac{b}{a}} \sqrt{a^2 x^3-b^2 x}}","-\frac{\tan ^{-1}\left(\frac{2 \sqrt{a} \sqrt{b} \sqrt{a^2 x^3-b^2 x}}{a^2 x^2-2 a b x-b^2}\right)}{6 \sqrt{a} \sqrt{b}}-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{b} \sqrt{a^2 x^3-b^2 x}}{a^2 x^2-a b x-b^2}\right)}{3 \sqrt{a} \sqrt{b}}-\frac{\tanh ^{-1}\left(\frac{\frac{a^{3/2} x^2}{2 \sqrt{b}}-\frac{b^{3/2}}{2 \sqrt{a}}+\sqrt{a} \sqrt{b} x}{\sqrt{a^2 x^3-b^2 x}}\right)}{6 \sqrt{a} \sqrt{b}}-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\frac{a^{3/2} x^2}{\sqrt{2} \sqrt{b}}-\frac{b^{3/2}}{\sqrt{2} \sqrt{a}}+\frac{\sqrt{a} \sqrt{b} x}{\sqrt{2}}}{\sqrt{a^2 x^3-b^2 x}}\right)}{3 \sqrt{a} \sqrt{b}}",1,"(((-2*I)/3)*Sqrt[1 - b^2/(a^2*x^2)]*x^(3/2)*(3*EllipticF[I*ArcSinh[Sqrt[-(b/a)]/Sqrt[x]], -1] - EllipticPi[-I, I*ArcSinh[Sqrt[-(b/a)]/Sqrt[x]], -1] - EllipticPi[I, I*ArcSinh[Sqrt[-(b/a)]/Sqrt[x]], -1] - EllipticPi[-1/2*I - Sqrt[3]/2, I*ArcSinh[Sqrt[-(b/a)]/Sqrt[x]], -1] - EllipticPi[I/2 - Sqrt[3]/2, I*ArcSinh[Sqrt[-(b/a)]/Sqrt[x]], -1] - EllipticPi[(-I + Sqrt[3])/2, I*ArcSinh[Sqrt[-(b/a)]/Sqrt[x]], -1] - EllipticPi[(I + Sqrt[3])/2, I*ArcSinh[Sqrt[-(b/a)]/Sqrt[x]], -1]))/(Sqrt[-(b/a)]*Sqrt[-(b^2*x) + a^2*x^3])","C",1
2883,0,0,311,0.2731536,"\int \frac{\sqrt{1+x^4} \sqrt{x^2+\sqrt{1+x^4}}}{-1+x^4} \, dx","Integrate[(Sqrt[1 + x^4]*Sqrt[x^2 + Sqrt[1 + x^4]])/(-1 + x^4),x]","\int \frac{\sqrt{1+x^4} \sqrt{x^2+\sqrt{1+x^4}}}{-1+x^4} \, dx","\sqrt{\frac{1}{2} \left(\sqrt{2}-1\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{2}-1\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)-\sqrt{\frac{1}{2} \left(\sqrt{2}-1\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)+\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)-\sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tanh ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{2}-1\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)-\sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tanh ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)",1,"Integrate[(Sqrt[1 + x^4]*Sqrt[x^2 + Sqrt[1 + x^4]])/(-1 + x^4), x]","F",-1
2884,1,19036,311,17.5856677,"\int \frac{x^4}{1-x \sqrt{1+x^2} \sqrt{x-\sqrt{1+x^2}}} \, dx","Integrate[x^4/(1 - x*Sqrt[1 + x^2]*Sqrt[x - Sqrt[1 + x^2]]),x]","\text{Result too large to show}","-\text{RootSum}\left[\text{$\#$1}^8+4 \text{$\#$1}^3-1\&,\frac{\text{$\#$1}^6 \log \left(\sqrt{x-\sqrt{x^2+1}}-\text{$\#$1}\right)-\text{$\#$1}^5 \log \left(\sqrt{x-\sqrt{x^2+1}}-\text{$\#$1}\right)-\text{$\#$1}^2 \log \left(\sqrt{x-\sqrt{x^2+1}}-\text{$\#$1}\right)+3 \text{$\#$1} \log \left(\sqrt{x-\sqrt{x^2+1}}-\text{$\#$1}\right)-4 \log \left(\sqrt{x-\sqrt{x^2+1}}-\text{$\#$1}\right)}{2 \text{$\#$1}^6+3 \text{$\#$1}}\&\right]+\frac{1}{20} \left(x-\sqrt{x^2+1}\right)^{5/2}-\frac{3}{4} \sqrt{x-\sqrt{x^2+1}}+\frac{1}{4 \left(\sqrt{x^2+1}-x\right)^2}+\frac{4}{\sqrt{x-\sqrt{x^2+1}}}-\frac{1}{4 \left(x-\sqrt{x^2+1}\right)^{3/2}}+\frac{1}{28 \left(x-\sqrt{x^2+1}\right)^{7/2}}+\frac{3}{2} \log \left(\sqrt{x^2+1}-x\right)",1,"Result too large to show","B",0
2885,0,0,312,0.2662865,"\int \frac{\sqrt{x^2+\sqrt{1+x^4}}}{(1+x)^2 \sqrt{1+x^4}} \, dx","Integrate[Sqrt[x^2 + Sqrt[1 + x^4]]/((1 + x)^2*Sqrt[1 + x^4]),x]","\int \frac{\sqrt{x^2+\sqrt{1+x^4}}}{(1+x)^2 \sqrt{1+x^4}} \, dx","\frac{2 x^4+x^2+\left(-x^2-1\right) \left(\sqrt{x^4+1}+x^2\right) x+\sqrt{x^4+1} \left(2 x^2-\left(\sqrt{x^4+1}+x^2\right) x+1\right)+1}{2 \left(x^2-1\right) \left(\sqrt{x^4+1}+x^2\right)^{3/2}}+\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{\sqrt{2}-1}}\right)}{2 \sqrt{\sqrt{2}-1}}-\frac{1}{2} \sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{2}-1\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)-\frac{\tanh ^{-1}\left(\frac{\sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{1+\sqrt{2}}}\right)}{2 \sqrt{1+\sqrt{2}}}+\frac{1}{2} \sqrt{\sqrt{2}-1} \tanh ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)",1,"Integrate[Sqrt[x^2 + Sqrt[1 + x^4]]/((1 + x)^2*Sqrt[1 + x^4]), x]","F",-1
2886,0,0,313,3.5659386,"\int \frac{(-b+x) \left(a b-2 b x+x^2\right)}{\sqrt[3]{x (-a+x) (-b+x)^2} \left(-b^2 d+2 b d x-\left(-a^2+d\right) x^2-2 a x^3+x^4\right)} \, dx","Integrate[((-b + x)*(a*b - 2*b*x + x^2))/((x*(-a + x)*(-b + x)^2)^(1/3)*(-(b^2*d) + 2*b*d*x - (-a^2 + d)*x^2 - 2*a*x^3 + x^4)),x]","\int \frac{(-b+x) \left(a b-2 b x+x^2\right)}{\sqrt[3]{x (-a+x) (-b+x)^2} \left(-b^2 d+2 b d x-\left(-a^2+d\right) x^2-2 a x^3+x^4\right)} \, dx","-\frac{\log \left(a^2 x^2+d^{2/3} \left(x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4\right)^{2/3}+\sqrt[3]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4} \left(\sqrt[3]{d} x^2-a \sqrt[3]{d} x\right)-2 a x^3+x^4\right)}{4 d^{2/3}}+\frac{\log \left(\sqrt[3]{d} \sqrt[3]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}+a x-x^2\right)}{2 d^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} \sqrt[3]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}}{\sqrt[3]{d} \sqrt[3]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}-2 a x+2 x^2}\right)}{2 d^{2/3}}",1,"Integrate[((-b + x)*(a*b - 2*b*x + x^2))/((x*(-a + x)*(-b + x)^2)^(1/3)*(-(b^2*d) + 2*b*d*x - (-a^2 + d)*x^2 - 2*a*x^3 + x^4)), x]","F",-1
2887,1,201,313,0.6321894,"\int \frac{b^8+a^8 x^8}{\sqrt{-b^4+a^4 x^4} \left(-b^8+a^8 x^8\right)} \, dx","Integrate[(b^8 + a^8*x^8)/(Sqrt[-b^4 + a^4*x^4]*(-b^8 + a^8*x^8)),x]","\frac{x \left(-\frac{5 \left(b^8-a^4 b^4 x^4\right) F_1\left(\frac{1}{4};-\frac{1}{2},1;\frac{5}{4};\frac{a^4 x^4}{b^4},-\frac{a^4 x^4}{b^4}\right)}{\left(a^4 x^4+b^4\right) \left(5 b^4 F_1\left(\frac{1}{4};-\frac{1}{2},1;\frac{5}{4};\frac{a^4 x^4}{b^4},-\frac{a^4 x^4}{b^4}\right)-2 a^4 x^4 \left(2 F_1\left(\frac{5}{4};-\frac{1}{2},2;\frac{9}{4};\frac{a^4 x^4}{b^4},-\frac{a^4 x^4}{b^4}\right)+F_1\left(\frac{5}{4};\frac{1}{2},1;\frac{9}{4};\frac{a^4 x^4}{b^4},-\frac{a^4 x^4}{b^4}\right)\right)\right)}-1\right)}{2 \sqrt{a^4 x^4-b^4}}","-\frac{x}{2 \sqrt{a^4 x^4-b^4}}+\frac{\left(\frac{1}{8}-\frac{i}{8}\right) \tanh ^{-1}\left(\frac{\frac{\left(\frac{1}{2}-\frac{i}{2}\right) \sqrt{a^4 x^4-b^4}}{\sqrt{3-2 \sqrt{2}} a b}+\frac{\left(\frac{1}{2}-\frac{i}{2}\right) a x^2}{\sqrt{3-2 \sqrt{2}} b}+\frac{\left(\frac{1}{2}+\frac{i}{2}\right) b}{\sqrt{3-2 \sqrt{2}} a}}{x}\right)}{a b}-\frac{\left(\frac{1}{8}-\frac{i}{8}\right) \tanh ^{-1}\left(\frac{\frac{\left(\frac{1}{2}-\frac{i}{2}\right) \sqrt{a^4 x^4-b^4}}{\sqrt{3+2 \sqrt{2}} a b}+\frac{\left(\frac{1}{2}-\frac{i}{2}\right) a x^2}{\sqrt{3+2 \sqrt{2}} b}+\frac{\left(\frac{1}{2}+\frac{i}{2}\right) b}{\sqrt{3+2 \sqrt{2}} a}}{x}\right)}{a b}-\frac{\left(\frac{1}{4}-\frac{i}{4}\right) \tan ^{-1}\left(\frac{(1+i) a b x}{\sqrt{a^4 x^4-b^4}+a^2 x^2+i b^2}\right)}{a b}",1,"(x*(-1 - (5*(b^8 - a^4*b^4*x^4)*AppellF1[1/4, -1/2, 1, 5/4, (a^4*x^4)/b^4, -((a^4*x^4)/b^4)])/((b^4 + a^4*x^4)*(5*b^4*AppellF1[1/4, -1/2, 1, 5/4, (a^4*x^4)/b^4, -((a^4*x^4)/b^4)] - 2*a^4*x^4*(2*AppellF1[5/4, -1/2, 2, 9/4, (a^4*x^4)/b^4, -((a^4*x^4)/b^4)] + AppellF1[5/4, 1/2, 1, 9/4, (a^4*x^4)/b^4, -((a^4*x^4)/b^4)])))))/(2*Sqrt[-b^4 + a^4*x^4])","C",0
2888,1,340,313,0.8081274,"\int \frac{1}{\sqrt{-1+x^2} \left(\sqrt{x}+\sqrt{-1+x^2}\right)^2} \, dx","Integrate[1/(Sqrt[-1 + x^2]*(Sqrt[x] + Sqrt[-1 + x^2])^2),x]","\frac{2}{5} \left(\frac{\sqrt{x} (1-2 x)}{-x^2+x+1}+\frac{\sqrt{x^2-1} (1-2 x)}{x^2-x-1}-\frac{1}{2} \sqrt{\frac{5}{2} \left(1+\sqrt{5}\right)} \tan ^{-1}\left(\frac{-\sqrt{5} x+x-2}{\sqrt{2 \left(\sqrt{5}-1\right)} \sqrt{x^2-1}}\right)-\sqrt{\sqrt{5}-\frac{2}{5}} \tan ^{-1}\left(\frac{\left(\sqrt{5}-1\right) x+2}{\sqrt{2 \left(\sqrt{5}-1\right)} \sqrt{x^2-1}}\right)-\sqrt{\frac{5}{2 \left(1+\sqrt{5}\right)}} \tanh ^{-1}\left(\frac{\sqrt{5} x+x-2}{\sqrt{2 \left(1+\sqrt{5}\right)} \sqrt{x^2-1}}\right)-\sqrt{\frac{2}{5}+\sqrt{5}} \tanh ^{-1}\left(\frac{2-\left(1+\sqrt{5}\right) x}{\sqrt{2 \left(1+\sqrt{5}\right)} \sqrt{x^2-1}}\right)+\sqrt{\frac{1}{10} \left(5 \sqrt{5}-11\right)} \tan ^{-1}\left(\sqrt{\frac{2}{\sqrt{5}-1}} \sqrt{x}\right)-\sqrt{\frac{1}{10} \left(11+5 \sqrt{5}\right)} \tanh ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} \sqrt{x}\right)\right)","-\frac{1}{5} \sqrt{2 \sqrt{5}-\frac{22}{5}} \tan ^{-1}\left(\frac{\sqrt{x^2-1}}{\sqrt{2+\sqrt{5}} (x+1)}\right)+\frac{1}{5} \sqrt{\frac{22}{5}+2 \sqrt{5}} \tanh ^{-1}\left(\frac{\sqrt{x^2-1}}{\sqrt{\sqrt{5}-2} (x+1)}\right)+\frac{4 x^{3/2}-4 \sqrt{x^2-1} x+2 \sqrt{x^2-1}-2 \sqrt{x}}{5 \left(x^2-x-1\right)}-\frac{4}{5} \sqrt{\frac{2}{5 \sqrt{5}-5}} \tan ^{-1}\left(\sqrt{\frac{2}{\sqrt{5}-1}} \sqrt{x}\right)+\frac{2}{5} \sqrt{\frac{2}{\sqrt{5}-1}} \tan ^{-1}\left(\sqrt{\frac{2}{\sqrt{5}-1}} \sqrt{x}\right)-\frac{4}{5} \sqrt{\frac{2}{5+5 \sqrt{5}}} \tanh ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} \sqrt{x}\right)-\frac{2}{5} \sqrt{\frac{2}{1+\sqrt{5}}} \tanh ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} \sqrt{x}\right)",1,"(2*(((1 - 2*x)*Sqrt[x])/(1 + x - x^2) + ((1 - 2*x)*Sqrt[-1 + x^2])/(-1 - x + x^2) + Sqrt[(-11 + 5*Sqrt[5])/10]*ArcTan[Sqrt[2/(-1 + Sqrt[5])]*Sqrt[x]] - (Sqrt[(5*(1 + Sqrt[5]))/2]*ArcTan[(-2 + x - Sqrt[5]*x)/(Sqrt[2*(-1 + Sqrt[5])]*Sqrt[-1 + x^2])])/2 - Sqrt[-2/5 + Sqrt[5]]*ArcTan[(2 + (-1 + Sqrt[5])*x)/(Sqrt[2*(-1 + Sqrt[5])]*Sqrt[-1 + x^2])] - Sqrt[(11 + 5*Sqrt[5])/10]*ArcTanh[Sqrt[2/(1 + Sqrt[5])]*Sqrt[x]] - Sqrt[5/(2*(1 + Sqrt[5]))]*ArcTanh[(-2 + x + Sqrt[5]*x)/(Sqrt[2*(1 + Sqrt[5])]*Sqrt[-1 + x^2])] - Sqrt[2/5 + Sqrt[5]]*ArcTanh[(2 - (1 + Sqrt[5])*x)/(Sqrt[2*(1 + Sqrt[5])]*Sqrt[-1 + x^2])]))/5","A",0
2889,1,308,315,0.5944008,"\int \frac{b+a x^2}{\left(d+c x^2\right) \sqrt[3]{x+x^3}} \, dx","Integrate[(b + a*x^2)/((d + c*x^2)*(x + x^3)^(1/3)),x]","\frac{\sqrt[3]{x} \sqrt[3]{x^2+1} \left(\frac{2 (b c-a d) \log \left(\frac{x^{2/3} \sqrt[3]{c-d}}{\sqrt[3]{x^2+1}}+\sqrt[3]{d}\right)}{d^{2/3} \sqrt[3]{c-d}}-\frac{(b c-a d) \left(\log \left(\frac{x^{4/3} (c-d)^{2/3}}{\left(x^2+1\right)^{2/3}}-\frac{\sqrt[3]{d} x^{2/3} \sqrt[3]{c-d}}{\sqrt[3]{x^2+1}}+d^{2/3}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 x^{2/3} \sqrt[3]{c-d}}{\sqrt[3]{d} \sqrt[3]{x^2+1}}}{\sqrt{3}}\right)\right)}{d^{2/3} \sqrt[3]{c-d}}-2 a \log \left(1-\frac{x^{2/3}}{\sqrt[3]{x^2+1}}\right)+a \left(\log \left(\frac{x^{4/3}}{\left(x^2+1\right)^{2/3}}+\frac{x^{2/3}}{\sqrt[3]{x^2+1}}+1\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 x^{2/3}}{\sqrt[3]{x^2+1}}+1}{\sqrt{3}}\right)\right)\right)}{4 c \sqrt[3]{x^3+x}}","\frac{(b c-a d) \log \left(x \sqrt[3]{c-d}+\sqrt[3]{d} \sqrt[3]{x^3+x}\right)}{2 c d^{2/3} \sqrt[3]{c-d}}-\frac{\sqrt{3} (b c-a d) \tan ^{-1}\left(\frac{\sqrt{3} x \sqrt[3]{c-d}}{x \sqrt[3]{c-d}-2 \sqrt[3]{d} \sqrt[3]{x^3+x}}\right)}{2 c d^{2/3} \sqrt[3]{c-d}}+\frac{(a d-b c) \log \left(-\sqrt[3]{d} \sqrt[3]{x^3+x} x \sqrt[3]{c-d}+x^2 (c-d)^{2/3}+d^{2/3} \left(x^3+x\right)^{2/3}\right)}{4 c d^{2/3} \sqrt[3]{c-d}}-\frac{a \log \left(\sqrt[3]{x^3+x}-x\right)}{2 c}+\frac{\sqrt{3} a \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+x}+x}\right)}{2 c}+\frac{a \log \left(\sqrt[3]{x^3+x} x+\left(x^3+x\right)^{2/3}+x^2\right)}{4 c}",1,"(x^(1/3)*(1 + x^2)^(1/3)*(-2*a*Log[1 - x^(2/3)/(1 + x^2)^(1/3)] + a*(2*Sqrt[3]*ArcTan[(1 + (2*x^(2/3))/(1 + x^2)^(1/3))/Sqrt[3]] + Log[1 + x^(4/3)/(1 + x^2)^(2/3) + x^(2/3)/(1 + x^2)^(1/3)]) + (2*(b*c - a*d)*Log[d^(1/3) + ((c - d)^(1/3)*x^(2/3))/(1 + x^2)^(1/3)])/((c - d)^(1/3)*d^(2/3)) - ((b*c - a*d)*(2*Sqrt[3]*ArcTan[(1 - (2*(c - d)^(1/3)*x^(2/3))/(d^(1/3)*(1 + x^2)^(1/3)))/Sqrt[3]] + Log[d^(2/3) + ((c - d)^(2/3)*x^(4/3))/(1 + x^2)^(2/3) - ((c - d)^(1/3)*d^(1/3)*x^(2/3))/(1 + x^2)^(1/3)]))/((c - d)^(1/3)*d^(2/3))))/(4*c*(x + x^3)^(1/3))","A",1
2890,0,0,315,3.3782147,"\int \frac{x^3 \left(4 a b-3 (a+b) x+2 x^2\right)}{\left(x^2 (-a+x) (-b+x)\right)^{2/3} \left(-a b+(a+b) x-x^2+d x^4\right)} \, dx","Integrate[(x^3*(4*a*b - 3*(a + b)*x + 2*x^2))/((x^2*(-a + x)*(-b + x))^(2/3)*(-(a*b) + (a + b)*x - x^2 + d*x^4)),x]","\int \frac{x^3 \left(4 a b-3 (a+b) x+2 x^2\right)}{\left(x^2 (-a+x) (-b+x)\right)^{2/3} \left(-a b+(a+b) x-x^2+d x^4\right)} \, dx","-\frac{\log \left(a^2 b^2-2 a^2 b x+a^2 x^2-2 a b^2 x+d^{2/3} \left(x^3 (-a-b)+a b x^2+x^4\right)^{4/3}+\left(x^3 (-a-b)+a b x^2+x^4\right)^{2/3} \left(a b \sqrt[3]{d}-a \sqrt[3]{d} x-b \sqrt[3]{d} x+\sqrt[3]{d} x^2\right)+4 a b x^2-2 a x^3+b^2 x^2-2 b x^3+x^4\right)}{2 d^{2/3}}+\frac{\log \left(-\sqrt[3]{d} \left(x^3 (-a-b)+a b x^2+x^4\right)^{2/3}+a b-a x-b x+x^2\right)}{d^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} \left(x^3 (-a-b)+a b x^2+x^4\right)^{2/3}}{\sqrt[3]{d} \left(x^3 (-a-b)+a b x^2+x^4\right)^{2/3}+2 a b-2 a x-2 b x+2 x^2}\right)}{d^{2/3}}",1,"Integrate[(x^3*(4*a*b - 3*(a + b)*x + 2*x^2))/((x^2*(-a + x)*(-b + x))^(2/3)*(-(a*b) + (a + b)*x - x^2 + d*x^4)), x]","F",-1
2891,1,268,316,0.6755228,"\int \frac{b x+a x^3}{\left(b+2 a x^3\right) \sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Integrate[(b*x + a*x^3)/((b + 2*a*x^3)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","\frac{3 \sqrt[3]{a} x \sqrt[3]{\frac{a^3 x}{b^2}+1} \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};-\frac{a^3 x}{b^2}\right)-x \left(\left(\sqrt[3]{a}+2^{2/3} \sqrt[3]{b}\right) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a^3 x-\sqrt[3]{2} \sqrt[3]{a} b^{5/3} x}{x a^3+b^2}\right)+\left(\sqrt[3]{a}+(-2)^{2/3} \sqrt[3]{b}\right) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\sqrt[3]{a} \left(a^{8/3}+\sqrt[3]{-2} b^{5/3}\right) x}{x a^3+b^2}\right)+\left(\sqrt[3]{a}-\sqrt[3]{-1} 2^{2/3} \sqrt[3]{b}\right) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\sqrt[3]{a} \left(a^{8/3}-(-1)^{2/3} \sqrt[3]{2} b^{5/3}\right) x}{x a^3+b^2}\right)\right)}{2 \sqrt[3]{a} \sqrt[3]{x^2 \left(a^3 x+b^2\right)}}","\frac{1}{6} \text{RootSum}\left[-\text{$\#$1}^9+3 \text{$\#$1}^6 a^3-3 \text{$\#$1}^3 a^6+a^9-2 a b^5\&,\frac{-\text{$\#$1}^3 \log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)+\text{$\#$1}^3 \log (x)+a^3 \log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)+2 b^2 \log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-\text{$\#$1} x\right)+a^3 (-\log (x))-2 b^2 \log (x)}{\text{$\#$1} a^3-\text{$\#$1}^4}\&\right]-\frac{\log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-a x\right)}{2 a}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a^3 x^3+b^2 x^2}}{\sqrt{3} a}+\frac{x}{\sqrt{3}}}{x}\right)}{2 a}+\frac{\log \left(a x \sqrt[3]{a^3 x^3+b^2 x^2}+\left(a^3 x^3+b^2 x^2\right)^{2/3}+a^2 x^2\right)}{4 a}",1,"(3*a^(1/3)*x*(1 + (a^3*x)/b^2)^(1/3)*Hypergeometric2F1[1/3, 1/3, 4/3, -((a^3*x)/b^2)] - x*((a^(1/3) + (-2)^(2/3)*b^(1/3))*Hypergeometric2F1[1/3, 1, 4/3, (a^(1/3)*(a^(8/3) + (-2)^(1/3)*b^(5/3))*x)/(b^2 + a^3*x)] + (a^(1/3) - (-1)^(1/3)*2^(2/3)*b^(1/3))*Hypergeometric2F1[1/3, 1, 4/3, (a^(1/3)*(a^(8/3) - (-1)^(2/3)*2^(1/3)*b^(5/3))*x)/(b^2 + a^3*x)] + (a^(1/3) + 2^(2/3)*b^(1/3))*Hypergeometric2F1[1/3, 1, 4/3, (a^3*x - 2^(1/3)*a^(1/3)*b^(5/3)*x)/(b^2 + a^3*x)]))/(2*a^(1/3)*(x^2*(b^2 + a^3*x))^(1/3))","A",1
2892,0,0,316,0.525939,"\int \frac{1}{\sqrt{-1+2 x} (4+3 x)+(1+x) \sqrt{-3+4 x}} \, dx","Integrate[(Sqrt[-1 + 2*x]*(4 + 3*x) + (1 + x)*Sqrt[-3 + 4*x])^(-1),x]","\int \frac{1}{\sqrt{-1+2 x} (4+3 x)+(1+x) \sqrt{-3+4 x}} \, dx","-\text{RootSum}\left[40 \text{$\#$1}^6-40 \text{$\#$1}^5+12 \text{$\#$1}^4-4 \text{$\#$1}^3+6 \text{$\#$1}^2-10 \text{$\#$1}+5\&,\frac{-4 \text{$\#$1}^4 \log \left(\sqrt{4 x-3}-1\right)+4 \text{$\#$1}^4 \log \left(\text{$\#$1} \left(-\sqrt{4 x-3}\right)+\text{$\#$1}+\sqrt{2 x-1}-1\right)+12 \text{$\#$1}^3 \log \left(\sqrt{4 x-3}-1\right)-12 \text{$\#$1}^3 \log \left(\text{$\#$1} \left(-\sqrt{4 x-3}\right)+\text{$\#$1}+\sqrt{2 x-1}-1\right)-12 \text{$\#$1}^2 \log \left(\sqrt{4 x-3}-1\right)+12 \text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{4 x-3}\right)+\text{$\#$1}+\sqrt{2 x-1}-1\right)+6 \text{$\#$1} \log \left(\sqrt{4 x-3}-1\right)-6 \text{$\#$1} \log \left(\text{$\#$1} \left(-\sqrt{4 x-3}\right)+\text{$\#$1}+\sqrt{2 x-1}-1\right)+\log \left(\text{$\#$1} \left(-\sqrt{4 x-3}\right)+\text{$\#$1}+\sqrt{2 x-1}-1\right)-\log \left(\sqrt{4 x-3}-1\right)}{120 \text{$\#$1}^5-100 \text{$\#$1}^4+24 \text{$\#$1}^3-6 \text{$\#$1}^2+6 \text{$\#$1}-5}\&\right]",1,"Integrate[(Sqrt[-1 + 2*x]*(4 + 3*x) + (1 + x)*Sqrt[-3 + 4*x])^(-1), x]","F",-1
2893,1,519,316,102.5450178,"\int \frac{f+e x}{(h+g x) \sqrt{d+\sqrt{c+\sqrt{b+a x}}}} \, dx","Integrate[(f + e*x)/((h + g*x)*Sqrt[d + Sqrt[c + Sqrt[b + a*x]]]),x]","\frac{(f g-e h) \text{RootSum}\left[\text{$\#$1}^8 a h-\text{$\#$1}^8 b g+\text{$\#$1}^8 c^2 g-2 \text{$\#$1}^8 c d^2 g+\text{$\#$1}^8 d^4 g+4 \text{$\#$1}^6 c d g-4 \text{$\#$1}^6 d^3 g-2 \text{$\#$1}^4 c g+6 \text{$\#$1}^4 d^2 g-4 \text{$\#$1}^2 d g+g\&,\frac{\text{$\#$1}^6 d^3 \log \left(\frac{1}{\sqrt{\sqrt{\sqrt{a x+b}+c}+d}}-\text{$\#$1}\right)-\text{$\#$1}^6 c d \log \left(\frac{1}{\sqrt{\sqrt{\sqrt{a x+b}+c}+d}}-\text{$\#$1}\right)-3 \text{$\#$1}^4 d^2 \log \left(\frac{1}{\sqrt{\sqrt{\sqrt{a x+b}+c}+d}}-\text{$\#$1}\right)+\text{$\#$1}^4 c \log \left(\frac{1}{\sqrt{\sqrt{\sqrt{a x+b}+c}+d}}-\text{$\#$1}\right)+3 \text{$\#$1}^2 d \log \left(\frac{1}{\sqrt{\sqrt{\sqrt{a x+b}+c}+d}}-\text{$\#$1}\right)-\log \left(\frac{1}{\sqrt{\sqrt{\sqrt{a x+b}+c}+d}}-\text{$\#$1}\right)}{\text{$\#$1}^7 a h-\text{$\#$1}^7 b g+\text{$\#$1}^7 c^2 g-2 \text{$\#$1}^7 c d^2 g+\text{$\#$1}^7 d^4 g+3 \text{$\#$1}^5 c d g-3 \text{$\#$1}^5 d^3 g-\text{$\#$1}^3 c g+3 \text{$\#$1}^3 d^2 g-\text{$\#$1} d g}\&\right]}{g}+\frac{8 e \sqrt{\sqrt{\sqrt{a x+b}+c}+d} \left(24 d^2 \sqrt{\sqrt{a x+b}+c}-20 c \sqrt{\sqrt{a x+b}+c}+15 \sqrt{a x+b} \sqrt{\sqrt{a x+b}+c}-18 d \sqrt{a x+b}+52 c d-48 d^3\right)}{105 a g}","\frac{(f g-e h) \text{RootSum}\left[\text{$\#$1}^8 (-g)+4 \text{$\#$1}^6 d g+2 \text{$\#$1}^4 c g-6 \text{$\#$1}^4 d^2 g-4 \text{$\#$1}^2 c d g+4 \text{$\#$1}^2 d^3 g-a h+b g-c^2 g+2 c d^2 g-d^4 g\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{a x+b}+c}+d}-\text{$\#$1}\right)}{\text{$\#$1}}\&\right]}{g^2}+\frac{32 e \left(13 c d-12 d^3\right) \sqrt{\sqrt{\sqrt{a x+b}+c}+d}}{105 a g}-\frac{32 e \left(5 c-6 d^2\right) \sqrt{\sqrt{a x+b}+c} \sqrt{\sqrt{\sqrt{a x+b}+c}+d}}{105 a g}+\sqrt{a x+b} \left(\frac{8 e \sqrt{\sqrt{a x+b}+c} \sqrt{\sqrt{\sqrt{a x+b}+c}+d}}{7 a g}-\frac{48 d e \sqrt{\sqrt{\sqrt{a x+b}+c}+d}}{35 a g}\right)",1,"(8*e*Sqrt[d + Sqrt[c + Sqrt[b + a*x]]]*(52*c*d - 48*d^3 - 18*d*Sqrt[b + a*x] - 20*c*Sqrt[c + Sqrt[b + a*x]] + 24*d^2*Sqrt[c + Sqrt[b + a*x]] + 15*Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]]))/(105*a*g) + ((f*g - e*h)*RootSum[g - 4*d*g*#1^2 - 2*c*g*#1^4 + 6*d^2*g*#1^4 + 4*c*d*g*#1^6 - 4*d^3*g*#1^6 - b*g*#1^8 + c^2*g*#1^8 - 2*c*d^2*g*#1^8 + d^4*g*#1^8 + a*h*#1^8 & , (-Log[1/Sqrt[d + Sqrt[c + Sqrt[b + a*x]]] - #1] + 3*d*Log[1/Sqrt[d + Sqrt[c + Sqrt[b + a*x]]] - #1]*#1^2 + c*Log[1/Sqrt[d + Sqrt[c + Sqrt[b + a*x]]] - #1]*#1^4 - 3*d^2*Log[1/Sqrt[d + Sqrt[c + Sqrt[b + a*x]]] - #1]*#1^4 - c*d*Log[1/Sqrt[d + Sqrt[c + Sqrt[b + a*x]]] - #1]*#1^6 + d^3*Log[1/Sqrt[d + Sqrt[c + Sqrt[b + a*x]]] - #1]*#1^6)/(-(d*g*#1) - c*g*#1^3 + 3*d^2*g*#1^3 + 3*c*d*g*#1^5 - 3*d^3*g*#1^5 - b*g*#1^7 + c^2*g*#1^7 - 2*c*d^2*g*#1^7 + d^4*g*#1^7 + a*h*#1^7) & ])/g","A",1
2894,0,0,316,5.1897867,"\int \left(1+x^2\right)^{3/2} \sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[(1 + x^2)^(3/2)*Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]],x]","\int \left(1+x^2\right)^{3/2} \sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}} \, dx","\frac{\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(1968046080 x^7+1130364928 x^6+10550149120 x^5+6568280064 x^4+96561463296 x^3+1984342244 x^2+66830366096 x-1176816782\right)+\sqrt{x^2+1} \left(\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(1968046080 x^6+1130364928 x^5+9566126080 x^4+6003097600 x^3+92024406016 x^2-875910940 x+21890925968\right)+\left(66913566720 x^7-2099249152 x^6+214715203584 x^5-10745282560 x^4+308588576768 x^3+3694527828 x^2+88760534448 x+2167822549\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\left(66913566720 x^8-2099249152 x^7+248171986944 x^6-11794907136 x^5+407581982720 x^4-1415707308 x^3+220397520304 x^2+5227043711 x+15903121112\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{39729930240 \left(\sqrt{x^2+1}+x\right)^{7/2}}-\frac{545 \tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)}{8192}",1,"Integrate[(1 + x^2)^(3/2)*Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]], x]","F",-1
2895,0,0,317,1.2766114,"\int \frac{(a-5 b+4 x) \left(-a^3+3 a^2 x-3 a x^2+x^3\right)}{((-a+x) (-b+x))^{2/3} \left(b-a^5 d-\left(1-5 a^4 d\right) x-10 a^3 d x^2+10 a^2 d x^3-5 a d x^4+d x^5\right)} \, dx","Integrate[((a - 5*b + 4*x)*(-a^3 + 3*a^2*x - 3*a*x^2 + x^3))/(((-a + x)*(-b + x))^(2/3)*(b - a^5*d - (1 - 5*a^4*d)*x - 10*a^3*d*x^2 + 10*a^2*d*x^3 - 5*a*d*x^4 + d*x^5)),x]","\int \frac{(a-5 b+4 x) \left(-a^3+3 a^2 x-3 a x^2+x^3\right)}{((-a+x) (-b+x))^{2/3} \left(b-a^5 d-\left(1-5 a^4 d\right) x-10 a^3 d x^2+10 a^2 d x^3-5 a d x^4+d x^5\right)} \, dx","\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} a^2 \sqrt[3]{d}-2 \sqrt{3} a \sqrt[3]{d} x+\sqrt{3} \sqrt[3]{d} x^2}{a^2 \sqrt[3]{d}+2 \sqrt[3]{x (-a-b)+a b+x^2}-2 a \sqrt[3]{d} x+\sqrt[3]{d} x^2}\right)}{d^{2/3}}+\frac{\log \left(a^3 \sqrt[3]{d}-2 a^2 \sqrt[3]{d} x-a \sqrt[3]{x (-a-b)+a b+x^2}+a \sqrt[3]{d} x^2\right)}{d^{2/3}}-\frac{\log \left(a^6 d^{2/3}-4 a^5 d^{2/3} x+6 a^4 d^{2/3} x^2-4 a^3 d^{2/3} x^3+a^2 \left(x (-a-b)+a b+x^2\right)^{2/3}+a^2 d^{2/3} x^4+\sqrt[3]{x (-a-b)+a b+x^2} \left(a^4 \sqrt[3]{d}-2 a^3 \sqrt[3]{d} x+a^2 \sqrt[3]{d} x^2\right)\right)}{2 d^{2/3}}",1,"Integrate[((a - 5*b + 4*x)*(-a^3 + 3*a^2*x - 3*a*x^2 + x^3))/(((-a + x)*(-b + x))^(2/3)*(b - a^5*d - (1 - 5*a^4*d)*x - 10*a^3*d*x^2 + 10*a^2*d*x^3 - 5*a*d*x^4 + d*x^5)), x]","F",-1
2896,0,0,318,1.9283427,"\int \frac{\left(2-2 x+2 x^2-3 x^3+3 x^4\right) \sqrt[3]{-x-x^3-x^4+x^6}}{(1+x) \left(-1+2 x-2 x^2+x^3\right) \left(-1-x^3+x^5\right)} \, dx","Integrate[((2 - 2*x + 2*x^2 - 3*x^3 + 3*x^4)*(-x - x^3 - x^4 + x^6)^(1/3))/((1 + x)*(-1 + 2*x - 2*x^2 + x^3)*(-1 - x^3 + x^5)),x]","\int \frac{\left(2-2 x+2 x^2-3 x^3+3 x^4\right) \sqrt[3]{-x-x^3-x^4+x^6}}{(1+x) \left(-1+2 x-2 x^2+x^3\right) \left(-1-x^3+x^5\right)} \, dx","-\log \left(\sqrt[3]{x^6-x^4-x^3-x}+x\right)+\sqrt[3]{2} \log \left(\sqrt[3]{x^6-x^4-x^3-x}+\sqrt[3]{2} x\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x^6-x^4-x^3-x}}{\sqrt[3]{x^6-x^4-x^3-x}-2 x}\right)-\sqrt[3]{2} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x^6-x^4-x^3-x}}{\sqrt[3]{x^6-x^4-x^3-x}-2 \sqrt[3]{2} x}\right)+\frac{1}{2} \log \left(x^2-\sqrt[3]{x^6-x^4-x^3-x} x+\left(x^6-x^4-x^3-x\right)^{2/3}\right)-\frac{\log \left(2^{2/3} x^2-\sqrt[3]{2} \sqrt[3]{x^6-x^4-x^3-x} x+\left(x^6-x^4-x^3-x\right)^{2/3}\right)}{2^{2/3}}",1,"Integrate[((2 - 2*x + 2*x^2 - 3*x^3 + 3*x^4)*(-x - x^3 - x^4 + x^6)^(1/3))/((1 + x)*(-1 + 2*x - 2*x^2 + x^3)*(-1 - x^3 + x^5)), x]","F",-1
2897,1,56,319,0.0315573,"\int \frac{1}{(-b+a x) \sqrt[3]{-b^2 x^2+a^3 x^3}} \, dx","Integrate[1/((-b + a*x)*(-(b^2*x^2) + a^3*x^3)^(1/3)),x]","-\frac{3 x \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(a^3-a b\right) x}{a^3 x-b^2}\right)}{b \sqrt[3]{x^2 \left(a^3 x-b^2\right)}}","-\frac{i \left(\sqrt{3}-i\right) \log \left(\sqrt[3]{-1} \sqrt[3]{a^3 x^3-b^2 x^2}+\sqrt[3]{a} x \sqrt[3]{a^2-b}\right)}{2 \sqrt[3]{a} b \sqrt[3]{a^2-b}}+\frac{\sqrt{-3+3 i \sqrt{3}} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{a} x \sqrt[3]{a^2-b}}{\sqrt[3]{a} x \sqrt[3]{a^2-b}-2 \sqrt[3]{-1} \sqrt[3]{a^3 x^3-b^2 x^2}}\right)}{\sqrt{2} \sqrt[3]{a} b \sqrt[3]{a^2-b}}+\frac{\left(1+i \sqrt{3}\right) \log \left((-1)^{2/3} \left(a^3 x^3-b^2 x^2\right)^{2/3}+a^{2/3} x^2 \left(a^2-b\right)^{2/3}-\sqrt[3]{-1} \sqrt[3]{a} x \sqrt[3]{a^2-b} \sqrt[3]{a^3 x^3-b^2 x^2}\right)}{4 \sqrt[3]{a} b \sqrt[3]{a^2-b}}",1,"(-3*x*Hypergeometric2F1[1/3, 1, 4/3, ((a^3 - a*b)*x)/(-b^2 + a^3*x)])/(b*(x^2*(-b^2 + a^3*x))^(1/3))","C",1
2898,1,893,319,1.7580615,"\int \frac{(-b+x) (-4 a+b+3 x)}{\sqrt[3]{(-a+x) (-b+x)^2} \left(b^4+a d-\left(4 b^3+d\right) x+6 b^2 x^2-4 b x^3+x^4\right)} \, dx","Integrate[((-b + x)*(-4*a + b + 3*x))/(((-a + x)*(-b + x)^2)^(1/3)*(b^4 + a*d - (4*b^3 + d)*x + 6*b^2*x^2 - 4*b*x^3 + x^4)),x]","\frac{(a-b) \left(\frac{b-x}{a-x}\right)^{2/3} (x-a) \left(4 \text{RootSum}\left[-a^3 \text{$\#$1}^4+b^3 \text{$\#$1}^4-3 a b^2 \text{$\#$1}^4+3 a^2 b \text{$\#$1}^4+d \text{$\#$1}^3-3 d \text{$\#$1}^2+3 d \text{$\#$1}-d\&,\frac{-2 \sqrt{3} \sqrt[3]{\text{$\#$1}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{\frac{b-x}{a-x}}}{\sqrt[3]{\text{$\#$1}}}+1}{\sqrt{3}}\right)+6 \sqrt[3]{\frac{x-b}{x-a}}+2 \log \left(\sqrt[3]{\text{$\#$1}}-\sqrt[3]{\frac{x-b}{x-a}}\right) \sqrt[3]{\text{$\#$1}}-\log \left(\left(\frac{x-b}{x-a}\right)^{2/3}+\sqrt[3]{\text{$\#$1}} \sqrt[3]{\frac{x-b}{x-a}}+\text{$\#$1}^{2/3}\right) \sqrt[3]{\text{$\#$1}}}{4 a^3 \text{$\#$1}^3-4 b^3 \text{$\#$1}^3+12 a b^2 \text{$\#$1}^3-12 a^2 b \text{$\#$1}^3-3 d \text{$\#$1}^2+6 d \text{$\#$1}-3 d}\&\right]+5 \text{RootSum}\left[-a^3 \text{$\#$1}^4+b^3 \text{$\#$1}^4-3 a b^2 \text{$\#$1}^4+3 a^2 b \text{$\#$1}^4+d \text{$\#$1}^3-3 d \text{$\#$1}^2+3 d \text{$\#$1}-d\&,\frac{2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{\frac{b-x}{a-x}}}{\sqrt[3]{\text{$\#$1}}}+1}{\sqrt{3}}\right) \text{$\#$1}^{4/3}-2 \log \left(\sqrt[3]{\text{$\#$1}}-\sqrt[3]{\frac{x-b}{x-a}}\right) \text{$\#$1}^{4/3}+\log \left(\left(\frac{x-b}{x-a}\right)^{2/3}+\sqrt[3]{\text{$\#$1}} \sqrt[3]{\frac{x-b}{x-a}}+\text{$\#$1}^{2/3}\right) \text{$\#$1}^{4/3}-6 \sqrt[3]{\frac{x-b}{x-a}} \text{$\#$1}}{4 a^3 \text{$\#$1}^3-4 b^3 \text{$\#$1}^3+12 a b^2 \text{$\#$1}^3-12 a^2 b \text{$\#$1}^3-3 d \text{$\#$1}^2+6 d \text{$\#$1}-3 d}\&\right]-\text{RootSum}\left[-a^3 \text{$\#$1}^4+b^3 \text{$\#$1}^4-3 a b^2 \text{$\#$1}^4+3 a^2 b \text{$\#$1}^4+d \text{$\#$1}^3-3 d \text{$\#$1}^2+3 d \text{$\#$1}-d\&,\frac{2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{\frac{b-x}{a-x}}}{\sqrt[3]{\text{$\#$1}}}+1}{\sqrt{3}}\right) \text{$\#$1}^{7/3}-2 \log \left(\sqrt[3]{\text{$\#$1}}-\sqrt[3]{\frac{x-b}{x-a}}\right) \text{$\#$1}^{7/3}+\log \left(\left(\frac{x-b}{x-a}\right)^{2/3}+\sqrt[3]{\text{$\#$1}} \sqrt[3]{\frac{x-b}{x-a}}+\text{$\#$1}^{2/3}\right) \text{$\#$1}^{7/3}-6 \sqrt[3]{\frac{x-b}{x-a}} \text{$\#$1}^2}{4 a^3 \text{$\#$1}^3-4 b^3 \text{$\#$1}^3+12 a b^2 \text{$\#$1}^3-12 a^2 b \text{$\#$1}^3-3 d \text{$\#$1}^2+6 d \text{$\#$1}-3 d}\&\right]\right)}{2 \sqrt[3]{(b-x)^2 (x-a)}}","\frac{\log \left(-\sqrt[3]{d} \sqrt[3]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3}+b^2-2 b x+x^2\right)}{d^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} \sqrt[3]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3}}{\sqrt[3]{d} \sqrt[3]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3}+2 b^2-4 b x+2 x^2}\right)}{d^{2/3}}-\frac{\log \left(d^{2/3} \left(x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3\right)^{2/3}+\sqrt[3]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3} \left(b^2 \sqrt[3]{d}-2 b \sqrt[3]{d} x+\sqrt[3]{d} x^2\right)+b^4-4 b^3 x+6 b^2 x^2-4 b x^3+x^4\right)}{2 d^{2/3}}",1,"((a - b)*((b - x)/(a - x))^(2/3)*(-a + x)*(4*RootSum[-d + 3*d*#1 - 3*d*#1^2 + d*#1^3 - a^3*#1^4 + 3*a^2*b*#1^4 - 3*a*b^2*#1^4 + b^3*#1^4 & , (6*((-b + x)/(-a + x))^(1/3) - 2*Sqrt[3]*ArcTan[(1 + (2*((b - x)/(a - x))^(1/3))/#1^(1/3))/Sqrt[3]]*#1^(1/3) + 2*Log[-((-b + x)/(-a + x))^(1/3) + #1^(1/3)]*#1^(1/3) - Log[((-b + x)/(-a + x))^(2/3) + ((-b + x)/(-a + x))^(1/3)*#1^(1/3) + #1^(2/3)]*#1^(1/3))/(-3*d + 6*d*#1 - 3*d*#1^2 + 4*a^3*#1^3 - 12*a^2*b*#1^3 + 12*a*b^2*#1^3 - 4*b^3*#1^3) & ] + 5*RootSum[-d + 3*d*#1 - 3*d*#1^2 + d*#1^3 - a^3*#1^4 + 3*a^2*b*#1^4 - 3*a*b^2*#1^4 + b^3*#1^4 & , (-6*((-b + x)/(-a + x))^(1/3)*#1 + 2*Sqrt[3]*ArcTan[(1 + (2*((b - x)/(a - x))^(1/3))/#1^(1/3))/Sqrt[3]]*#1^(4/3) - 2*Log[-((-b + x)/(-a + x))^(1/3) + #1^(1/3)]*#1^(4/3) + Log[((-b + x)/(-a + x))^(2/3) + ((-b + x)/(-a + x))^(1/3)*#1^(1/3) + #1^(2/3)]*#1^(4/3))/(-3*d + 6*d*#1 - 3*d*#1^2 + 4*a^3*#1^3 - 12*a^2*b*#1^3 + 12*a*b^2*#1^3 - 4*b^3*#1^3) & ] - RootSum[-d + 3*d*#1 - 3*d*#1^2 + d*#1^3 - a^3*#1^4 + 3*a^2*b*#1^4 - 3*a*b^2*#1^4 + b^3*#1^4 & , (-6*((-b + x)/(-a + x))^(1/3)*#1^2 + 2*Sqrt[3]*ArcTan[(1 + (2*((b - x)/(a - x))^(1/3))/#1^(1/3))/Sqrt[3]]*#1^(7/3) - 2*Log[-((-b + x)/(-a + x))^(1/3) + #1^(1/3)]*#1^(7/3) + Log[((-b + x)/(-a + x))^(2/3) + ((-b + x)/(-a + x))^(1/3)*#1^(1/3) + #1^(2/3)]*#1^(7/3))/(-3*d + 6*d*#1 - 3*d*#1^2 + 4*a^3*#1^3 - 12*a^2*b*#1^3 + 12*a*b^2*#1^3 - 4*b^3*#1^3) & ]))/(2*((b - x)^2*(-a + x))^(1/3))","C",1
2899,1,205,319,0.4716001,"\int \frac{x^4}{\sqrt{-b^4+a^4 x^4} \left(-b^8+a^8 x^8\right)} \, dx","Integrate[x^4/(Sqrt[-b^4 + a^4*x^4]*(-b^8 + a^8*x^8)),x]","\frac{x \left(\frac{5 \left(b^4-a^4 x^4\right) F_1\left(\frac{1}{4};-\frac{1}{2},1;\frac{5}{4};\frac{a^4 x^4}{b^4},-\frac{a^4 x^4}{b^4}\right)}{\left(a^4 x^4+b^4\right) \left(5 b^4 F_1\left(\frac{1}{4};-\frac{1}{2},1;\frac{5}{4};\frac{a^4 x^4}{b^4},-\frac{a^4 x^4}{b^4}\right)-2 a^4 x^4 \left(2 F_1\left(\frac{5}{4};-\frac{1}{2},2;\frac{9}{4};\frac{a^4 x^4}{b^4},-\frac{a^4 x^4}{b^4}\right)+F_1\left(\frac{5}{4};\frac{1}{2},1;\frac{9}{4};\frac{a^4 x^4}{b^4},-\frac{a^4 x^4}{b^4}\right)\right)\right)}-\frac{1}{b^4}\right)}{4 a^4 \sqrt{a^4 x^4-b^4}}","-\frac{x}{4 a^4 b^4 \sqrt{a^4 x^4-b^4}}-\frac{\left(\frac{1}{16}-\frac{i}{16}\right) \tanh ^{-1}\left(\frac{\frac{\left(\frac{1}{2}-\frac{i}{2}\right) \sqrt{a^4 x^4-b^4}}{\sqrt{3-2 \sqrt{2}} a b}+\frac{\left(\frac{1}{2}-\frac{i}{2}\right) a x^2}{\sqrt{3-2 \sqrt{2}} b}+\frac{\left(\frac{1}{2}+\frac{i}{2}\right) b}{\sqrt{3-2 \sqrt{2}} a}}{x}\right)}{a^5 b^5}+\frac{\left(\frac{1}{16}-\frac{i}{16}\right) \tanh ^{-1}\left(\frac{\frac{\left(\frac{1}{2}-\frac{i}{2}\right) \sqrt{a^4 x^4-b^4}}{\sqrt{3+2 \sqrt{2}} a b}+\frac{\left(\frac{1}{2}-\frac{i}{2}\right) a x^2}{\sqrt{3+2 \sqrt{2}} b}+\frac{\left(\frac{1}{2}+\frac{i}{2}\right) b}{\sqrt{3+2 \sqrt{2}} a}}{x}\right)}{a^5 b^5}+\frac{\left(\frac{1}{8}-\frac{i}{8}\right) \tan ^{-1}\left(\frac{(1+i) a b x}{\sqrt{a^4 x^4-b^4}+a^2 x^2+i b^2}\right)}{a^5 b^5}",1,"(x*(-b^(-4) + (5*(b^4 - a^4*x^4)*AppellF1[1/4, -1/2, 1, 5/4, (a^4*x^4)/b^4, -((a^4*x^4)/b^4)])/((b^4 + a^4*x^4)*(5*b^4*AppellF1[1/4, -1/2, 1, 5/4, (a^4*x^4)/b^4, -((a^4*x^4)/b^4)] - 2*a^4*x^4*(2*AppellF1[5/4, -1/2, 2, 9/4, (a^4*x^4)/b^4, -((a^4*x^4)/b^4)] + AppellF1[5/4, 1/2, 1, 9/4, (a^4*x^4)/b^4, -((a^4*x^4)/b^4)])))))/(4*a^4*Sqrt[-b^4 + a^4*x^4])","C",0
2900,1,74,319,0.3056221,"\int \frac{1}{\sqrt{-b+a^2 x^2} \sqrt{a x+\sqrt{-b+a^2 x^2}} \sqrt[3]{c+\sqrt[4]{a x+\sqrt{-b+a^2 x^2}}}} \, dx","Integrate[1/(Sqrt[-b + a^2*x^2]*Sqrt[a*x + Sqrt[-b + a^2*x^2]]*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(1/3)),x]","-\frac{6 \left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{2/3} \, _2F_1\left(\frac{2}{3},3;\frac{5}{3};\frac{c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}{c}\right)}{a c^3}","\frac{8 \log \left(\sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}-\sqrt[3]{c}\right)}{9 a c^{7/3}}-\frac{4 \log \left(\sqrt[3]{c} \sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}+\left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{2/3}+c^{2/3}\right)}{9 a c^{7/3}}+\frac{8 \tan ^{-1}\left(\frac{2 \sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}}{\sqrt{3} \sqrt[3]{c}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3} a c^{7/3}}+\frac{8 \sqrt[4]{\sqrt{a^2 x^2-b}+a x} \left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{2/3}-6 c \left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{2/3}}{3 a c^2 \sqrt{\sqrt{a^2 x^2-b}+a x}}",1,"(-6*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(2/3)*Hypergeometric2F1[2/3, 3, 5/3, (c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))/c])/(a*c^3)","C",1
2901,0,0,321,0.8595584,"\int \frac{\left(1+x^2\right)^2 \sqrt{x^2+\sqrt{1+x^4}}}{\sqrt{1+x^4} \left(-1+x^2+x^4\right)} \, dx","Integrate[((1 + x^2)^2*Sqrt[x^2 + Sqrt[1 + x^4]])/(Sqrt[1 + x^4]*(-1 + x^2 + x^4)),x]","\int \frac{\left(1+x^2\right)^2 \sqrt{x^2+\sqrt{1+x^4}}}{\sqrt{1+x^4} \left(-1+x^2+x^4\right)} \, dx","\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)-\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^6-6 \text{$\#$1}^4+2 \text{$\#$1}^2+1\&,\frac{\text{$\#$1}^6 \left(-\log \left(\sqrt{x^4+1}+x^2-1\right)\right)+\text{$\#$1}^6 \log \left(\text{$\#$1} \sqrt{x^4+1}+\text{$\#$1} x^2-\text{$\#$1}+\sqrt{2} \sqrt{\sqrt{x^4+1}+x^2} x\right)-2 \text{$\#$1}^4 \log \left(\sqrt{x^4+1}+x^2-1\right)+2 \text{$\#$1}^4 \log \left(\text{$\#$1} \sqrt{x^4+1}+\text{$\#$1} x^2-\text{$\#$1}+\sqrt{2} \sqrt{\sqrt{x^4+1}+x^2} x\right)-\log \left(\text{$\#$1} \sqrt{x^4+1}+\text{$\#$1} x^2-\text{$\#$1}+\sqrt{2} \sqrt{\sqrt{x^4+1}+x^2} x\right)+\log \left(\sqrt{x^4+1}+x^2-1\right)}{2 \text{$\#$1}^7-3 \text{$\#$1}^5-6 \text{$\#$1}^3+\text{$\#$1}}\&\right]}{\sqrt{2}}",1,"Integrate[((1 + x^2)^2*Sqrt[x^2 + Sqrt[1 + x^4]])/(Sqrt[1 + x^4]*(-1 + x^2 + x^4)), x]","F",-1
2902,0,0,321,0.3724215,"\int \frac{\left(1+x^2\right)^2 \sqrt{x^2+\sqrt{1+x^4}}}{\sqrt{1+x^4} \left(-1+x^2+x^4\right)} \, dx","Integrate[((1 + x^2)^2*Sqrt[x^2 + Sqrt[1 + x^4]])/(Sqrt[1 + x^4]*(-1 + x^2 + x^4)),x]","\int \frac{\left(1+x^2\right)^2 \sqrt{x^2+\sqrt{1+x^4}}}{\sqrt{1+x^4} \left(-1+x^2+x^4\right)} \, dx","\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)-\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^6-6 \text{$\#$1}^4+2 \text{$\#$1}^2+1\&,\frac{\text{$\#$1}^6 \left(-\log \left(\sqrt{x^4+1}+x^2-1\right)\right)+\text{$\#$1}^6 \log \left(\text{$\#$1} \sqrt{x^4+1}+\text{$\#$1} x^2-\text{$\#$1}+\sqrt{2} \sqrt{\sqrt{x^4+1}+x^2} x\right)-2 \text{$\#$1}^4 \log \left(\sqrt{x^4+1}+x^2-1\right)+2 \text{$\#$1}^4 \log \left(\text{$\#$1} \sqrt{x^4+1}+\text{$\#$1} x^2-\text{$\#$1}+\sqrt{2} \sqrt{\sqrt{x^4+1}+x^2} x\right)-\log \left(\text{$\#$1} \sqrt{x^4+1}+\text{$\#$1} x^2-\text{$\#$1}+\sqrt{2} \sqrt{\sqrt{x^4+1}+x^2} x\right)+\log \left(\sqrt{x^4+1}+x^2-1\right)}{2 \text{$\#$1}^7-3 \text{$\#$1}^5-6 \text{$\#$1}^3+\text{$\#$1}}\&\right]}{\sqrt{2}}",1,"Integrate[((1 + x^2)^2*Sqrt[x^2 + Sqrt[1 + x^4]])/(Sqrt[1 + x^4]*(-1 + x^2 + x^4)), x]","F",-1
2903,1,359,323,0.542899,"\int \frac{x^2 \sqrt[4]{b x^3+a x^4}}{-b+a x^4} \, dx","Integrate[(x^2*(b*x^3 + a*x^4)^(1/4))/(-b + a*x^4),x]","\frac{x^3 \left(\left(b^{3/4}-a^{3/4}\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{a x-\sqrt[4]{a} b^{3/4} x}{b+a x}\right)-a^{3/4} \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{a x-i \sqrt[4]{a} b^{3/4} x}{b+a x}\right)-a^{3/4} \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{a x+i \sqrt[4]{a} b^{3/4} x}{b+a x}\right)-a^{3/4} \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{a x+\sqrt[4]{a} b^{3/4} x}{b+a x}\right)+4 a^{3/4} \left(\frac{a x}{b}+1\right)^{3/4} \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};-\frac{a x}{b}\right)+i b^{3/4} \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{a x-i \sqrt[4]{a} b^{3/4} x}{b+a x}\right)-i b^{3/4} \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{a x+i \sqrt[4]{a} b^{3/4} x}{b+a x}\right)-b^{3/4} \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{a x+\sqrt[4]{a} b^{3/4} x}{b+a x}\right)\right)}{3 a^{3/4} \left(x^3 (a x+b)\right)^{3/4}}","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^{16}-4 \text{$\#$1}^{12} a+6 \text{$\#$1}^8 a^2-4 \text{$\#$1}^4 a^3+a^4-a b^3\&,\frac{-\text{$\#$1}^{12} \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)+\text{$\#$1}^{12} \log (x)+3 \text{$\#$1}^8 a \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)-3 \text{$\#$1}^8 a \log (x)-3 \text{$\#$1}^4 a^2 \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)+3 \text{$\#$1}^4 a^2 \log (x)+a^3 \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)-b^3 \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)-a^3 \log (x)+b^3 \log (x)}{-\text{$\#$1}^{15}+3 \text{$\#$1}^{11} a-3 \text{$\#$1}^7 a^2+\text{$\#$1}^3 a^3}\&\right]-\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)}{a^{3/4}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)}{a^{3/4}}",1,"(x^3*(4*a^(3/4)*(1 + (a*x)/b)^(3/4)*Hypergeometric2F1[3/4, 3/4, 7/4, -((a*x)/b)] + (-a^(3/4) + b^(3/4))*Hypergeometric2F1[3/4, 1, 7/4, (a*x - a^(1/4)*b^(3/4)*x)/(b + a*x)] - a^(3/4)*Hypergeometric2F1[3/4, 1, 7/4, (a*x - I*a^(1/4)*b^(3/4)*x)/(b + a*x)] + I*b^(3/4)*Hypergeometric2F1[3/4, 1, 7/4, (a*x - I*a^(1/4)*b^(3/4)*x)/(b + a*x)] - a^(3/4)*Hypergeometric2F1[3/4, 1, 7/4, (a*x + I*a^(1/4)*b^(3/4)*x)/(b + a*x)] - I*b^(3/4)*Hypergeometric2F1[3/4, 1, 7/4, (a*x + I*a^(1/4)*b^(3/4)*x)/(b + a*x)] - a^(3/4)*Hypergeometric2F1[3/4, 1, 7/4, (a*x + a^(1/4)*b^(3/4)*x)/(b + a*x)] - b^(3/4)*Hypergeometric2F1[3/4, 1, 7/4, (a*x + a^(1/4)*b^(3/4)*x)/(b + a*x)]))/(3*a^(3/4)*(x^3*(b + a*x))^(3/4))","C",1
2904,1,359,323,0.3120193,"\int \frac{x^2 \sqrt[4]{b x^3+a x^4}}{-b+a x^4} \, dx","Integrate[(x^2*(b*x^3 + a*x^4)^(1/4))/(-b + a*x^4),x]","\frac{x^3 \left(\left(b^{3/4}-a^{3/4}\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{a x-\sqrt[4]{a} b^{3/4} x}{b+a x}\right)-a^{3/4} \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{a x-i \sqrt[4]{a} b^{3/4} x}{b+a x}\right)-a^{3/4} \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{a x+i \sqrt[4]{a} b^{3/4} x}{b+a x}\right)-a^{3/4} \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{a x+\sqrt[4]{a} b^{3/4} x}{b+a x}\right)+4 a^{3/4} \left(\frac{a x}{b}+1\right)^{3/4} \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};-\frac{a x}{b}\right)+i b^{3/4} \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{a x-i \sqrt[4]{a} b^{3/4} x}{b+a x}\right)-i b^{3/4} \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{a x+i \sqrt[4]{a} b^{3/4} x}{b+a x}\right)-b^{3/4} \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{a x+\sqrt[4]{a} b^{3/4} x}{b+a x}\right)\right)}{3 a^{3/4} \left(x^3 (a x+b)\right)^{3/4}}","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^{16}-4 \text{$\#$1}^{12} a+6 \text{$\#$1}^8 a^2-4 \text{$\#$1}^4 a^3+a^4-a b^3\&,\frac{-\text{$\#$1}^{12} \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)+\text{$\#$1}^{12} \log (x)+3 \text{$\#$1}^8 a \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)-3 \text{$\#$1}^8 a \log (x)-3 \text{$\#$1}^4 a^2 \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)+3 \text{$\#$1}^4 a^2 \log (x)+a^3 \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)-b^3 \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)-a^3 \log (x)+b^3 \log (x)}{-\text{$\#$1}^{15}+3 \text{$\#$1}^{11} a-3 \text{$\#$1}^7 a^2+\text{$\#$1}^3 a^3}\&\right]-\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)}{a^{3/4}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)}{a^{3/4}}",1,"(x^3*(4*a^(3/4)*(1 + (a*x)/b)^(3/4)*Hypergeometric2F1[3/4, 3/4, 7/4, -((a*x)/b)] + (-a^(3/4) + b^(3/4))*Hypergeometric2F1[3/4, 1, 7/4, (a*x - a^(1/4)*b^(3/4)*x)/(b + a*x)] - a^(3/4)*Hypergeometric2F1[3/4, 1, 7/4, (a*x - I*a^(1/4)*b^(3/4)*x)/(b + a*x)] + I*b^(3/4)*Hypergeometric2F1[3/4, 1, 7/4, (a*x - I*a^(1/4)*b^(3/4)*x)/(b + a*x)] - a^(3/4)*Hypergeometric2F1[3/4, 1, 7/4, (a*x + I*a^(1/4)*b^(3/4)*x)/(b + a*x)] - I*b^(3/4)*Hypergeometric2F1[3/4, 1, 7/4, (a*x + I*a^(1/4)*b^(3/4)*x)/(b + a*x)] - a^(3/4)*Hypergeometric2F1[3/4, 1, 7/4, (a*x + a^(1/4)*b^(3/4)*x)/(b + a*x)] - b^(3/4)*Hypergeometric2F1[3/4, 1, 7/4, (a*x + a^(1/4)*b^(3/4)*x)/(b + a*x)]))/(3*a^(3/4)*(x^3*(b + a*x))^(3/4))","C",1
2905,0,0,323,7.4749853,"\int \frac{\left(1+x^2\right) \sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","Integrate[((1 + x^2)*Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2)^2,x]","\int \frac{\left(1+x^2\right) \sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{3 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-4 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^5-2 \text{$\#$1}^3}\&\right]+\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{3 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-4 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^5-2 \text{$\#$1}^3+2 \text{$\#$1}}\&\right]-\frac{\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} x}{x^2-1}",1,"Integrate[((1 + x^2)*Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2)^2, x]","F",-1
2906,0,0,323,0.237644,"\int \frac{\left(1+x^2\right) \sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","Integrate[((1 + x^2)*Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2)^2,x]","\int \frac{\left(1+x^2\right) \sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{3 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-4 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^5-2 \text{$\#$1}^3}\&\right]+\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{3 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-4 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^5-2 \text{$\#$1}^3+2 \text{$\#$1}}\&\right]-\frac{\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} x}{x^2-1}",1,"Integrate[((1 + x^2)*Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2)^2, x]","F",-1
2907,0,0,324,3.3367579,"\int \frac{x^3 (-b+x) \left(2 a b-3 a x+x^2\right)}{\sqrt[3]{x^2 (-a+x) (-b+x)} \left(-a^4+4 a^3 x-6 a^2 x^2+4 a x^3+\left(-1+b^2 d\right) x^4-2 b d x^5+d x^6\right)} \, dx","Integrate[(x^3*(-b + x)*(2*a*b - 3*a*x + x^2))/((x^2*(-a + x)*(-b + x))^(1/3)*(-a^4 + 4*a^3*x - 6*a^2*x^2 + 4*a*x^3 + (-1 + b^2*d)*x^4 - 2*b*d*x^5 + d*x^6)),x]","\int \frac{x^3 (-b+x) \left(2 a b-3 a x+x^2\right)}{\sqrt[3]{x^2 (-a+x) (-b+x)} \left(-a^4+4 a^3 x-6 a^2 x^2+4 a x^3+\left(-1+b^2 d\right) x^4-2 b d x^5+d x^6\right)} \, dx","\frac{\tanh ^{-1}\left(\frac{\sqrt[3]{x^3 (-a-b)+a b x^2+x^4} \left(a \sqrt[6]{d}-\sqrt[6]{d} x\right)}{a^2+\sqrt[3]{d} \left(x^3 (-a-b)+a b x^2+x^4\right)^{2/3}-2 a x+x^2}\right)}{2 d^{5/6}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{d} \sqrt[3]{x^3 (-a-b)+a b x^2+x^4}}{\sqrt[6]{d} \sqrt[3]{x^3 (-a-b)+a b x^2+x^4}+2 a-2 x}\right)}{2 d^{5/6}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{d} \sqrt[3]{x^3 (-a-b)+a b x^2+x^4}}{\sqrt[6]{d} \sqrt[3]{x^3 (-a-b)+a b x^2+x^4}-2 a+2 x}\right)}{2 d^{5/6}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[3]{x^3 (-a-b)+a b x^2+x^4}}{a-x}\right)}{d^{5/6}}",1,"Integrate[(x^3*(-b + x)*(2*a*b - 3*a*x + x^2))/((x^2*(-a + x)*(-b + x))^(1/3)*(-a^4 + 4*a^3*x - 6*a^2*x^2 + 4*a*x^3 + (-1 + b^2*d)*x^4 - 2*b*d*x^5 + d*x^6)), x]","F",-1
2908,1,265,325,0.7515774,"\int \frac{\left(1+x^3\right)^{2/3} \left(-1+x^6\right)}{x^6 \left(-1-2 x^3+2 x^6\right)} \, dx","Integrate[((1 + x^3)^(2/3)*(-1 + x^6))/(x^6*(-1 - 2*x^3 + 2*x^6)),x]","\frac{-12 \left(\sqrt{3}-2\right) \log \left(1-\frac{\sqrt[6]{3} x}{\sqrt[3]{x^3+1}}\right)+12 \left(2+\sqrt{3}\right) \log \left(\frac{\sqrt[6]{3} x}{\sqrt[3]{x^3+1}}+1\right)-\left(1+\sqrt{3}\right) \left(3+\sqrt{3}\right) \left(6 \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 x}{\sqrt[3]{3} \sqrt[3]{x^3+1}}\right)+\sqrt{3} \log \left(-\frac{\sqrt[6]{3} x}{\sqrt[3]{x^3+1}}+\frac{\sqrt[3]{3} x^2}{\left(x^3+1\right)^{2/3}}+1\right)\right)+\left(\sqrt{3}-3\right) \left(\sqrt{3}-1\right) \left(6 \tan ^{-1}\left(\frac{2 x}{\sqrt[3]{3} \sqrt[3]{x^3+1}}+\frac{1}{\sqrt{3}}\right)+\sqrt{3} \log \left(\frac{\sqrt[6]{3} x}{\sqrt[3]{x^3+1}}+\frac{\sqrt[3]{3} x^2}{\left(x^3+1\right)^{2/3}}+1\right)\right)}{24\ 3^{2/3}}+\left(x^3+1\right)^{2/3} \left(\frac{4}{5 x^2}-\frac{1}{5 x^5}\right)","\frac{\log \left(3^{5/6} \sqrt[3]{x^3+1}-3 x\right)}{2\ 3^{2/3} \sqrt[3]{26+15 \sqrt{3}}}+\frac{\sqrt[3]{26+15 \sqrt{3}} \log \left(3^{5/6} \sqrt[3]{x^3+1}+3 x\right)}{2\ 3^{2/3}}-\frac{1}{2} \sqrt[3]{\frac{1}{3} \left(45+26 \sqrt{3}\right)} \tan ^{-1}\left(\frac{3^{2/3} x}{\sqrt[6]{3} x-2 \sqrt[3]{x^3+1}}\right)-\frac{\tan ^{-1}\left(\frac{3^{2/3} x}{2 \sqrt[3]{x^3+1}+\sqrt[6]{3} x}\right)}{2 \sqrt[3]{45+26 \sqrt{3}}}+\frac{\left(x^3+1\right)^{2/3} \left(4 x^3-1\right)}{5 x^5}-\frac{\sqrt[3]{26+15 \sqrt{3}} \log \left(3^{5/6} \sqrt[3]{x^3+1} x-3^{2/3} \left(x^3+1\right)^{2/3}-3 x^2\right)}{4\ 3^{2/3}}-\frac{\log \left(3^{5/6} \sqrt[3]{x^3+1} x+3^{2/3} \left(x^3+1\right)^{2/3}+3 x^2\right)}{4\ 3^{2/3} \sqrt[3]{26+15 \sqrt{3}}}",1,"(-1/5*1/x^5 + 4/(5*x^2))*(1 + x^3)^(2/3) + (-12*(-2 + Sqrt[3])*Log[1 - (3^(1/6)*x)/(1 + x^3)^(1/3)] - (1 + Sqrt[3])*(3 + Sqrt[3])*(6*ArcTan[1/Sqrt[3] - (2*x)/(3^(1/3)*(1 + x^3)^(1/3))] + Sqrt[3]*Log[1 + (3^(1/3)*x^2)/(1 + x^3)^(2/3) - (3^(1/6)*x)/(1 + x^3)^(1/3)]) + 12*(2 + Sqrt[3])*Log[1 + (3^(1/6)*x)/(1 + x^3)^(1/3)] + (-3 + Sqrt[3])*(-1 + Sqrt[3])*(6*ArcTan[1/Sqrt[3] + (2*x)/(3^(1/3)*(1 + x^3)^(1/3))] + Sqrt[3]*Log[1 + (3^(1/3)*x^2)/(1 + x^3)^(2/3) + (3^(1/6)*x)/(1 + x^3)^(1/3)]))/(24*3^(2/3))","A",1
2909,1,383,326,0.9604893,"\int \frac{1+x^4}{\left(-1+x^4\right) \sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[(1 + x^4)/((-1 + x^4)*Sqrt[x + Sqrt[1 + x^2]]),x]","\sqrt{\sqrt{x^2+1}+x}-\frac{1}{3 \left(\sqrt{x^2+1}+x\right)^{3/2}}+\frac{\log \left(-\frac{\sqrt{2}}{\sqrt{\sqrt{x^2+1}+x}}+\frac{1}{\sqrt{x^2+1}+x}+1\right)}{\sqrt{2}}-\frac{\log \left(\frac{\sqrt{2}}{\sqrt{\sqrt{x^2+1}+x}}+\frac{1}{\sqrt{x^2+1}+x}+1\right)}{\sqrt{2}}-\frac{\left(\sqrt{2}-2\right) \tan ^{-1}\left(\frac{1}{\sqrt{\sqrt{2}-1} \sqrt{\sqrt{x^2+1}+x}}\right)}{\sqrt{2 \left(\sqrt{2}-1\right)}}-\frac{\left(2+\sqrt{2}\right) \tan ^{-1}\left(\frac{1}{\sqrt{1+\sqrt{2}} \sqrt{\sqrt{x^2+1}+x}}\right)}{\sqrt{2 \left(1+\sqrt{2}\right)}}-\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2}}{\sqrt{\sqrt{x^2+1}+x}}\right)+\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2}}{\sqrt{\sqrt{x^2+1}+x}}+1\right)+\frac{\left(\sqrt{2}-2\right) \tanh ^{-1}\left(\frac{1}{\sqrt{\sqrt{2}-1} \sqrt{\sqrt{x^2+1}+x}}\right)}{\sqrt{2 \left(\sqrt{2}-1\right)}}+\frac{\left(2+\sqrt{2}\right) \tanh ^{-1}\left(\frac{1}{\sqrt{1+\sqrt{2}} \sqrt{\sqrt{x^2+1}+x}}\right)}{\sqrt{2 \left(1+\sqrt{2}\right)}}","\frac{4}{3} \sqrt{\sqrt{x^2+1}-x} x+\frac{2}{3} \sqrt{x^2+1} \sqrt{\sqrt{x^2+1}-x}+\sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}-x}}{\sqrt{\sqrt{2}-1}}\right)-\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}-x}}{\sqrt{1+\sqrt{2}}}\right)+\sqrt{2} \tan ^{-1}\left(\frac{\frac{\sqrt{x^2+1}}{\sqrt{2}}-\frac{x}{\sqrt{2}}-\frac{1}{\sqrt{2}}}{\sqrt{\sqrt{x^2+1}-x}}\right)-\sqrt{\sqrt{2}-1} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}-x}}{\sqrt{\sqrt{2}-1}}\right)+\sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}-x}}{\sqrt{1+\sqrt{2}}}\right)-\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\sqrt{x^2+1}-x}}{\sqrt{x^2+1}-x+1}\right)",1,"-1/3*1/(x + Sqrt[1 + x^2])^(3/2) + Sqrt[x + Sqrt[1 + x^2]] - ((-2 + Sqrt[2])*ArcTan[1/(Sqrt[-1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]])])/Sqrt[2*(-1 + Sqrt[2])] - ((2 + Sqrt[2])*ArcTan[1/(Sqrt[1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]])])/Sqrt[2*(1 + Sqrt[2])] - Sqrt[2]*ArcTan[1 - Sqrt[2]/Sqrt[x + Sqrt[1 + x^2]]] + Sqrt[2]*ArcTan[1 + Sqrt[2]/Sqrt[x + Sqrt[1 + x^2]]] + ((-2 + Sqrt[2])*ArcTanh[1/(Sqrt[-1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]])])/Sqrt[2*(-1 + Sqrt[2])] + ((2 + Sqrt[2])*ArcTanh[1/(Sqrt[1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]])])/Sqrt[2*(1 + Sqrt[2])] + Log[1 + (x + Sqrt[1 + x^2])^(-1) - Sqrt[2]/Sqrt[x + Sqrt[1 + x^2]]]/Sqrt[2] - Log[1 + (x + Sqrt[1 + x^2])^(-1) + Sqrt[2]/Sqrt[x + Sqrt[1 + x^2]]]/Sqrt[2]","A",1
2910,1,320,327,14.8769284,"\int \frac{(b+2 a x) \sqrt[4]{b x^3+a x^4}}{-b+a x+x^2} \, dx","Integrate[((b + 2*a*x)*(b*x^3 + a*x^4)^(1/4))/(-b + a*x + x^2),x]","\frac{3 \sqrt[4]{a} x^{9/4} \left(4 a^2-3 b\right) (a x+b)^{3/4} \left(\tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)-\tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)\right)+\frac{4 x^3 \left(2 a^4-a^2 b+\frac{-2 a^5-3 a^3 b+5 a b^2}{\sqrt{a^2+4 b}}+b^2\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{b \left(\frac{a}{b}+\frac{2}{\sqrt{a^2+4 b}-a}\right) x}{b+a x}\right)}{a-\sqrt{a^2+4 b}}+\frac{4 x^3 \left(2 a^4-a^2 b+\frac{2 a^5+3 a^3 b-5 a b^2}{\sqrt{a^2+4 b}}+b^2\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{b \left(\frac{a}{b}-\frac{2}{a+\sqrt{a^2+4 b}}\right) x}{b+a x}\right)}{\sqrt{a^2+4 b}+a}+6 a x^3 (a x+b)}{3 \left(x^3 (a x+b)\right)^{3/4}}","-\text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4 a+2 a^2-b\&,\frac{-2 \text{$\#$1}^4 a^3 \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)+2 \text{$\#$1}^4 a^3 \log (x)+3 \text{$\#$1}^4 a b \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)-3 \text{$\#$1}^4 a b \log (x)+4 a^4 \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)-4 a^2 b \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)+b^2 \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)-4 a^4 \log (x)+4 a^2 b \log (x)-b^2 \log (x)}{3 \text{$\#$1}^3 a-2 \text{$\#$1}^7}\&\right]+\left(4 a^{9/4}-3 \sqrt[4]{a} b\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)+\left(3 \sqrt[4]{a} b-4 a^{9/4}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)+2 a \sqrt[4]{a x^4+b x^3}",1,"(6*a*x^3*(b + a*x) + 3*a^(1/4)*(4*a^2 - 3*b)*x^(9/4)*(b + a*x)^(3/4)*(ArcTan[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)] - ArcTanh[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)]) + (4*(2*a^4 - a^2*b + b^2 + (-2*a^5 - 3*a^3*b + 5*a*b^2)/Sqrt[a^2 + 4*b])*x^3*Hypergeometric2F1[3/4, 1, 7/4, (b*(a/b + 2/(-a + Sqrt[a^2 + 4*b]))*x)/(b + a*x)])/(a - Sqrt[a^2 + 4*b]) + (4*(2*a^4 - a^2*b + b^2 + (2*a^5 + 3*a^3*b - 5*a*b^2)/Sqrt[a^2 + 4*b])*x^3*Hypergeometric2F1[3/4, 1, 7/4, (b*(a/b - 2/(a + Sqrt[a^2 + 4*b]))*x)/(b + a*x)])/(a + Sqrt[a^2 + 4*b]))/(3*(x^3*(b + a*x))^(3/4))","A",1
2911,1,320,327,14.1533119,"\int \frac{(b+2 a x) \sqrt[4]{b x^3+a x^4}}{-b+a x+x^2} \, dx","Integrate[((b + 2*a*x)*(b*x^3 + a*x^4)^(1/4))/(-b + a*x + x^2),x]","\frac{3 \sqrt[4]{a} x^{9/4} \left(4 a^2-3 b\right) (a x+b)^{3/4} \left(\tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)-\tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)\right)+\frac{4 x^3 \left(2 a^4-a^2 b+\frac{-2 a^5-3 a^3 b+5 a b^2}{\sqrt{a^2+4 b}}+b^2\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{b \left(\frac{a}{b}+\frac{2}{\sqrt{a^2+4 b}-a}\right) x}{b+a x}\right)}{a-\sqrt{a^2+4 b}}+\frac{4 x^3 \left(2 a^4-a^2 b+\frac{2 a^5+3 a^3 b-5 a b^2}{\sqrt{a^2+4 b}}+b^2\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{b \left(\frac{a}{b}-\frac{2}{a+\sqrt{a^2+4 b}}\right) x}{b+a x}\right)}{\sqrt{a^2+4 b}+a}+6 a x^3 (a x+b)}{3 \left(x^3 (a x+b)\right)^{3/4}}","-\text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4 a+2 a^2-b\&,\frac{-2 \text{$\#$1}^4 a^3 \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)+2 \text{$\#$1}^4 a^3 \log (x)+3 \text{$\#$1}^4 a b \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)-3 \text{$\#$1}^4 a b \log (x)+4 a^4 \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)-4 a^2 b \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)+b^2 \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)-4 a^4 \log (x)+4 a^2 b \log (x)-b^2 \log (x)}{3 \text{$\#$1}^3 a-2 \text{$\#$1}^7}\&\right]+\left(4 a^{9/4}-3 \sqrt[4]{a} b\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)+\left(3 \sqrt[4]{a} b-4 a^{9/4}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)+2 a \sqrt[4]{a x^4+b x^3}",1,"(6*a*x^3*(b + a*x) + 3*a^(1/4)*(4*a^2 - 3*b)*x^(9/4)*(b + a*x)^(3/4)*(ArcTan[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)] - ArcTanh[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)]) + (4*(2*a^4 - a^2*b + b^2 + (-2*a^5 - 3*a^3*b + 5*a*b^2)/Sqrt[a^2 + 4*b])*x^3*Hypergeometric2F1[3/4, 1, 7/4, (b*(a/b + 2/(-a + Sqrt[a^2 + 4*b]))*x)/(b + a*x)])/(a - Sqrt[a^2 + 4*b]) + (4*(2*a^4 - a^2*b + b^2 + (2*a^5 + 3*a^3*b - 5*a*b^2)/Sqrt[a^2 + 4*b])*x^3*Hypergeometric2F1[3/4, 1, 7/4, (b*(a/b - 2/(a + Sqrt[a^2 + 4*b]))*x)/(b + a*x)])/(a + Sqrt[a^2 + 4*b]))/(3*(x^3*(b + a*x))^(3/4))","A",1
2912,0,0,328,1.7901114,"\int \frac{x^3}{\sqrt[3]{-x^2+x^4} \left(1+x^6\right)} \, dx","Integrate[x^3/((-x^2 + x^4)^(1/3)*(1 + x^6)),x]","\int \frac{x^3}{\sqrt[3]{-x^2+x^4} \left(1+x^6\right)} \, dx","\frac{1}{6} \log \left(x^2+\left(x^4-x^2\right)^{2/3}\right)-\frac{1}{12} i \left(\sqrt{3}-i\right) \log \left(-i \sqrt{3} x^2-x^2+2 \left(x^4-x^2\right)^{2/3}\right)+\frac{1}{12} i \left(\sqrt{3}+i\right) \log \left(i \sqrt{3} x^2-x^2+2 \left(x^4-x^2\right)^{2/3}\right)+\frac{\log \left(-2 x^2+2^{2/3} \sqrt{3} \sqrt[3]{x^4-x^2} x-\sqrt[3]{2} \left(x^4-x^2\right)^{2/3}\right)}{24 \sqrt[3]{2}}-\frac{\log \left(2 x^2+\sqrt[3]{2} \left(x^4-x^2\right)^{2/3}\right)}{12 \sqrt[3]{2}}+\frac{\log \left(2 x^2+2^{2/3} \sqrt{3} \sqrt[3]{x^4-x^2} x+\sqrt[3]{2} \left(x^4-x^2\right)^{2/3}\right)}{24 \sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x^2}{\sqrt[3]{2} \left(x^4-x^2\right)^{2/3}-x^2}\right)}{4 \sqrt[3]{2} \sqrt{3}}",1,"Integrate[x^3/((-x^2 + x^4)^(1/3)*(1 + x^6)), x]","F",-1
2913,-1,0,328,180.0034807,"\int \frac{x^4 \sqrt{b+a^2 x^2}}{x^2-\sqrt{a x-\sqrt{b+a^2 x^2}}} \, dx","Integrate[(x^4*Sqrt[b + a^2*x^2])/(x^2 - Sqrt[a*x - Sqrt[b + a^2*x^2]]),x]","\text{\$Aborted}","\frac{2 \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^5 a^2-2 \text{$\#$1}^4 b+b^2\&,\frac{\text{$\#$1}^3 a^6 \log \left(\sqrt{a x-\sqrt{a^2 x^2+b}}-\text{$\#$1}\right)+\text{$\#$1}^2 a^4 b \log \left(\sqrt{a x-\sqrt{a^2 x^2+b}}-\text{$\#$1}\right)}{-2 \text{$\#$1}^4+5 \text{$\#$1} a^2+2 b}\&\right]}{a^3}+\frac{b^2}{6 a \left(a x-\sqrt{a^2 x^2+b}\right)^{3/2}}-\frac{b \sqrt{a x-\sqrt{a^2 x^2+b}}}{a}-\frac{\left(a x-\sqrt{a^2 x^2+b}\right)^{5/2}}{10 a}+a \sqrt{a^2 x^2+b}-a^2 x+\frac{b^4}{64 a^3 \left(\sqrt{a^2 x^2+b}-a x\right)^4}+\frac{b^2 \log \left(\sqrt{a^2 x^2+b}-a x\right)}{8 a^3}-\frac{\left(\sqrt{a^2 x^2+b}-a x\right)^4}{64 a^3}",1,"$Aborted","F",-1
2914,1,171,329,0.1711256,"\int \frac{-1+x^2}{\sqrt[4]{\frac{b+a x}{d+c x}}} \, dx","Integrate[(-1 + x^2)/((b + a*x)/(d + c*x))^(1/4),x]","\frac{4 (c x+d) \left(\frac{a x+b}{c x+d}\right)^{3/4} \left(a \left(a \left(d^2-c^2\right) \, _2F_1\left(-\frac{1}{4},\frac{3}{4};\frac{7}{4};\frac{c (b+a x)}{b c-a d}\right)+2 d (b c-a d) \, _2F_1\left(-\frac{5}{4},\frac{3}{4};\frac{7}{4};\frac{c (b+a x)}{b c-a d}\right)\right)+(b c-a d)^2 \, _2F_1\left(-\frac{9}{4},\frac{3}{4};\frac{7}{4};\frac{c (b+a x)}{b c-a d}\right)\right)}{3 a^3 c^2 \sqrt[4]{\frac{a (c x+d)}{a d-b c}}}","\frac{\left(\frac{a x+b}{c x+d}\right)^{3/4} \left(32 a^2 c^3 x^3-96 a^2 c^3 x+36 a^2 c^2 d x^2-96 a^2 c^2 d-3 a^2 c d^2 x-7 a^2 d^3-36 a b c^3 x^2-42 a b c^2 d x-6 a b c d^2+45 b^2 c^3 x+45 b^2 c^2 d\right)}{96 a^3 c^2}+\frac{\left(32 a^3 c^2 d-7 a^3 d^3-32 a^2 b c^3-3 a^2 b c d^2-5 a b^2 c^2 d+15 b^3 c^3\right) \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt[4]{\frac{a x+b}{c x+d}}}{\sqrt[4]{a}}\right)}{64 a^{13/4} c^{11/4}}+\frac{\left(-32 a^3 c^2 d+7 a^3 d^3+32 a^2 b c^3+3 a^2 b c d^2+5 a b^2 c^2 d-15 b^3 c^3\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt[4]{\frac{a x+b}{c x+d}}}{\sqrt[4]{a}}\right)}{64 a^{13/4} c^{11/4}}",1,"(4*((b + a*x)/(d + c*x))^(3/4)*(d + c*x)*((b*c - a*d)^2*Hypergeometric2F1[-9/4, 3/4, 7/4, (c*(b + a*x))/(b*c - a*d)] + a*(2*d*(b*c - a*d)*Hypergeometric2F1[-5/4, 3/4, 7/4, (c*(b + a*x))/(b*c - a*d)] + a*(-c^2 + d^2)*Hypergeometric2F1[-1/4, 3/4, 7/4, (c*(b + a*x))/(b*c - a*d)])))/(3*a^3*c^2*((a*(d + c*x))/(-(b*c) + a*d))^(1/4))","C",1
2915,1,199,329,0.9547394,"\int \frac{-b+a x^4}{\sqrt{b+a x^4} \left(b-c^2 x^2+a x^4\right)} \, dx","Integrate[(-b + a*x^4)/(Sqrt[b + a*x^4]*(b - c^2*x^2 + a*x^4)),x]","-\frac{i \sqrt{\frac{a x^4}{b}+1} \left(-\Pi \left(\frac{2 i \sqrt{a} \sqrt{b}}{c^2-\sqrt{c^4-4 a b}};\left.i \sinh ^{-1}\left(\sqrt{\frac{i \sqrt{a}}{\sqrt{b}}} x\right)\right|-1\right)-\Pi \left(\frac{2 i \sqrt{a} \sqrt{b}}{c^2+\sqrt{c^4-4 a b}};\left.i \sinh ^{-1}\left(\sqrt{\frac{i \sqrt{a}}{\sqrt{b}}} x\right)\right|-1\right)+F\left(\left.i \sinh ^{-1}\left(\sqrt{\frac{i \sqrt{a}}{\sqrt{b}}} x\right)\right|-1\right)\right)}{\sqrt{\frac{i \sqrt{a}}{\sqrt{b}}} \sqrt{a x^4+b}}","-\frac{\left(\sqrt{2 \sqrt{a} \sqrt{b}+c^2}+c\right) \sqrt{c \sqrt{2 \sqrt{a} \sqrt{b}+c^2}-\sqrt{a} \sqrt{b}-c^2} \tan ^{-1}\left(\frac{\sqrt{2} x \sqrt{c \sqrt{2 \sqrt{a} \sqrt{b}+c^2}-\sqrt{a} \sqrt{b}-c^2}}{\sqrt{a x^4+b}+\sqrt{a} x^2+\sqrt{b}}\right)}{\sqrt{2} \sqrt{a} \sqrt{b} c}-\frac{\left(\sqrt{2 \sqrt{a} \sqrt{b}+c^2}-c\right) \sqrt{c \sqrt{2 \sqrt{a} \sqrt{b}+c^2}+\sqrt{a} \sqrt{b}+c^2} \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt{c \sqrt{2 \sqrt{a} \sqrt{b}+c^2}+\sqrt{a} \sqrt{b}+c^2}}{\sqrt{a x^4+b}+\sqrt{a} x^2+\sqrt{b}}\right)}{\sqrt{2} \sqrt{a} \sqrt{b} c}",1,"((-I)*Sqrt[1 + (a*x^4)/b]*(EllipticF[I*ArcSinh[Sqrt[(I*Sqrt[a])/Sqrt[b]]*x], -1] - EllipticPi[((2*I)*Sqrt[a]*Sqrt[b])/(c^2 - Sqrt[-4*a*b + c^4]), I*ArcSinh[Sqrt[(I*Sqrt[a])/Sqrt[b]]*x], -1] - EllipticPi[((2*I)*Sqrt[a]*Sqrt[b])/(c^2 + Sqrt[-4*a*b + c^4]), I*ArcSinh[Sqrt[(I*Sqrt[a])/Sqrt[b]]*x], -1]))/(Sqrt[(I*Sqrt[a])/Sqrt[b]]*Sqrt[b + a*x^4])","C",1
2916,1,188,330,0.1145888,"\int \frac{\left(1+x^2\right) \sqrt[3]{-1-x^2+x^4+x^6}}{x} \, dx","Integrate[((1 + x^2)*(-1 - x^2 + x^4 + x^6)^(1/3))/x,x]","-\frac{3 \sqrt[3]{\left(x^2-1\right) \left(x^2+1\right)^2} \left(2^{2/3} x^2 \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};\frac{1}{2} \left(1-x^2\right)\right)-4\ 2^{2/3} \left(x^2+1\right) \, _2F_1\left(-\frac{5}{3},\frac{1}{3};\frac{4}{3};\frac{1}{2} \left(1-x^2\right)\right)+2\ 2^{2/3} \left(x^2+1\right) \, _2F_1\left(-\frac{2}{3},\frac{1}{3};\frac{4}{3};\frac{1}{2} \left(1-x^2\right)\right)+2^{2/3} \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};\frac{1}{2} \left(1-x^2\right)\right)+2 \left(x^2+1\right)^{2/3} \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{1-x^2}{x^2+1}\right)\right)}{4 \left(x^2+1\right)^{5/3}}","\frac{\left(x^2-1\right)^{2/3} \left(x^2+1\right)^{4/3} \left(\frac{1}{12} \sqrt[3]{x^2-1} \left(3 \left(x^2+1\right)^{5/3}-2 \left(x^2+1\right)^{2/3}\right)+\frac{1}{2} \sqrt[3]{x^2-1} \left(x^2+1\right)^{2/3}+\frac{1}{18} \log \left(\sqrt[3]{x^2-1}-\sqrt[3]{x^2+1}\right)-\frac{1}{2} \log \left(\sqrt[3]{x^2-1}+\sqrt[3]{x^2+1}\right)+\frac{1}{4} \log \left(\left(x^2-1\right)^{2/3}-\sqrt[3]{x^2+1} \sqrt[3]{x^2-1}+\left(x^2+1\right)^{2/3}\right)-\frac{1}{36} \log \left(\left(x^2-1\right)^{2/3}+\sqrt[3]{x^2+1} \sqrt[3]{x^2-1}+\left(x^2+1\right)^{2/3}\right)+\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x^2+1}}{2 \sqrt[3]{x^2-1}-\sqrt[3]{x^2+1}}\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x^2+1}}{2 \sqrt[3]{x^2-1}+\sqrt[3]{x^2+1}}\right)}{6 \sqrt{3}}\right)}{\left(\left(x^2-1\right) \left(x^2+1\right)^2\right)^{2/3}}",1,"(-3*((-1 + x^2)*(1 + x^2)^2)^(1/3)*(-4*2^(2/3)*(1 + x^2)*Hypergeometric2F1[-5/3, 1/3, 4/3, (1 - x^2)/2] + 2*2^(2/3)*(1 + x^2)*Hypergeometric2F1[-2/3, 1/3, 4/3, (1 - x^2)/2] + 2^(2/3)*Hypergeometric2F1[1/3, 1/3, 4/3, (1 - x^2)/2] + 2^(2/3)*x^2*Hypergeometric2F1[1/3, 1/3, 4/3, (1 - x^2)/2] + 2*(1 + x^2)^(2/3)*Hypergeometric2F1[1/3, 1, 4/3, (1 - x^2)/(1 + x^2)]))/(4*(1 + x^2)^(5/3))","C",1
2917,1,10907,330,20.8435114,"\int \sqrt{-\frac{a}{b^2}+\frac{a^2 x^2}{b^2}} \sqrt[3]{a x^2+b x \sqrt{-\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}} \, dx","Integrate[Sqrt[-(a/b^2) + (a^2*x^2)/b^2]*(a*x^2 + b*x*Sqrt[-(a/b^2) + (a^2*x^2)/b^2])^(1/3),x]","\text{Result too large to show}","\frac{7}{16} x \sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}} \sqrt[3]{b x \sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}}+a x^2}+\frac{\left(-a x^2-10\right) \sqrt[3]{b x \sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}}+a x^2}}{16 b}-\frac{5 \log \left(\sqrt[3]{2} \sqrt[3]{b x \sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}}+a x^2}-1\right)}{24 \sqrt[3]{2} b}+\frac{5 \log \left(2^{2/3} \left(b x \sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}}+a x^2\right)^{2/3}+\sqrt[3]{2} \sqrt[3]{b x \sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}}+a x^2}+1\right)}{48 \sqrt[3]{2} b}+\frac{5 \tan ^{-1}\left(\frac{2 \sqrt[3]{2} \sqrt[3]{b x \sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}}+a x^2}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{8 \sqrt[3]{2} \sqrt{3} b}",1,"Result too large to show","C",0
2918,1,310,331,0.6019434,"\int \frac{-b+a x^2}{\left(-d+c x^2\right) \sqrt[3]{-x+x^3}} \, dx","Integrate[(-b + a*x^2)/((-d + c*x^2)*(-x + x^3)^(1/3)),x]","\frac{\sqrt[3]{x} \sqrt[3]{x^2-1} \left(\frac{2 (b c-a d) \log \left(\frac{x^{2/3} \sqrt[3]{c-d}}{\sqrt[3]{x^2-1}}+\sqrt[3]{d}\right)}{d^{2/3} \sqrt[3]{c-d}}-\frac{(b c-a d) \left(\log \left(\frac{x^{4/3} (c-d)^{2/3}}{\left(x^2-1\right)^{2/3}}-\frac{\sqrt[3]{d} x^{2/3} \sqrt[3]{c-d}}{\sqrt[3]{x^2-1}}+d^{2/3}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 x^{2/3} \sqrt[3]{c-d}}{\sqrt[3]{d} \sqrt[3]{x^2-1}}}{\sqrt{3}}\right)\right)}{d^{2/3} \sqrt[3]{c-d}}-2 a \log \left(1-\frac{x^{2/3}}{\sqrt[3]{x^2-1}}\right)+a \left(\log \left(\frac{x^{4/3}}{\left(x^2-1\right)^{2/3}}+\frac{x^{2/3}}{\sqrt[3]{x^2-1}}+1\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 x^{2/3}}{\sqrt[3]{x^2-1}}+1}{\sqrt{3}}\right)\right)\right)}{4 c \sqrt[3]{x \left(x^2-1\right)}}","\frac{(b c-a d) \log \left(x \sqrt[3]{c-d}+\sqrt[3]{d} \sqrt[3]{x^3-x}\right)}{2 c d^{2/3} \sqrt[3]{c-d}}-\frac{\sqrt{3} (b c-a d) \tan ^{-1}\left(\frac{\sqrt{3} x \sqrt[3]{c-d}}{x \sqrt[3]{c-d}-2 \sqrt[3]{d} \sqrt[3]{x^3-x}}\right)}{2 c d^{2/3} \sqrt[3]{c-d}}+\frac{(a d-b c) \log \left(-\sqrt[3]{d} \sqrt[3]{x^3-x} x \sqrt[3]{c-d}+x^2 (c-d)^{2/3}+d^{2/3} \left(x^3-x\right)^{2/3}\right)}{4 c d^{2/3} \sqrt[3]{c-d}}-\frac{a \log \left(\sqrt[3]{x^3-x}-x\right)}{2 c}+\frac{\sqrt{3} a \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-x}+x}\right)}{2 c}+\frac{a \log \left(\sqrt[3]{x^3-x} x+\left(x^3-x\right)^{2/3}+x^2\right)}{4 c}",1,"(x^(1/3)*(-1 + x^2)^(1/3)*(-2*a*Log[1 - x^(2/3)/(-1 + x^2)^(1/3)] + a*(2*Sqrt[3]*ArcTan[(1 + (2*x^(2/3))/(-1 + x^2)^(1/3))/Sqrt[3]] + Log[1 + x^(4/3)/(-1 + x^2)^(2/3) + x^(2/3)/(-1 + x^2)^(1/3)]) + (2*(b*c - a*d)*Log[d^(1/3) + ((c - d)^(1/3)*x^(2/3))/(-1 + x^2)^(1/3)])/((c - d)^(1/3)*d^(2/3)) - ((b*c - a*d)*(2*Sqrt[3]*ArcTan[(1 - (2*(c - d)^(1/3)*x^(2/3))/(d^(1/3)*(-1 + x^2)^(1/3)))/Sqrt[3]] + Log[d^(2/3) + ((c - d)^(2/3)*x^(4/3))/(-1 + x^2)^(2/3) - ((c - d)^(1/3)*d^(1/3)*x^(2/3))/(-1 + x^2)^(1/3)]))/((c - d)^(1/3)*d^(2/3))))/(4*c*(x*(-1 + x^2))^(1/3))","A",1
2919,0,0,332,0.0849417,"\int \frac{1}{(b+a x) \sqrt[3]{-b^3+a^3 x^3}} \, dx","Integrate[1/((b + a*x)*(-b^3 + a^3*x^3)^(1/3)),x]","\int \frac{1}{(b+a x) \sqrt[3]{-b^3+a^3 x^3}} \, dx","\frac{(-1)^{5/6} \sqrt{3} \tanh ^{-1}\left(\frac{\frac{i \sqrt[3]{a^3 x^3-b^3}}{\sqrt{3}}+\frac{\left(-\sqrt{3} a-i a\right) x}{2^{2/3} \sqrt{3}}+\frac{\sqrt{3} b+i b}{2^{2/3} \sqrt{3}}}{\sqrt[3]{a^3 x^3-b^3}}\right)}{2 \sqrt[3]{2} a b}+\frac{\sqrt[3]{-\frac{1}{2}} \log \left((-1)^{2/3} a^{3/2} \sqrt{b} x-2^{2/3} \sqrt{a} \sqrt{b} \sqrt[3]{a^3 x^3-b^3}-(-1)^{2/3} \sqrt{a} b^{3/2}\right)}{2 a b}-\frac{\sqrt[3]{-\frac{1}{2}} \log \left(-2 \sqrt[3]{2} a b \left(a^3 x^3-b^3\right)^{2/3}+\sqrt[3]{-1} a^3 b x^2-2 \sqrt[3]{-1} a^2 b^2 x+\left((-2)^{2/3} a b^2-(-2)^{2/3} a^2 b x\right) \sqrt[3]{a^3 x^3-b^3}+\sqrt[3]{-1} a b^3\right)}{4 a b}",1,"Integrate[1/((b + a*x)*(-b^3 + a^3*x^3)^(1/3)), x]","F",-1
2920,1,408,333,1.7873139,"\int \frac{-b^{12}+a^{12} x^{12}}{\sqrt{b^4+a^4 x^4} \left(b^{12}+a^{12} x^{12}\right)} \, dx","Integrate[(-b^12 + a^12*x^12)/(Sqrt[b^4 + a^4*x^4]*(b^12 + a^12*x^12)),x]","-\frac{i \left(-i x \sqrt{\frac{i a^2}{b^2}}+2 \sqrt{\frac{a^4 x^4}{b^4}+1} F\left(\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)-\sqrt{\frac{a^4 x^4}{b^4}+1} \Pi \left(-\frac{i \sqrt{2} b^2}{a^2 \sqrt{\frac{\left(1-i \sqrt{3}\right) b^4}{a^4}}};\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)-\sqrt{\frac{a^4 x^4}{b^4}+1} \Pi \left(\frac{i \sqrt{2} b^2}{a^2 \sqrt{\frac{\left(1-i \sqrt{3}\right) b^4}{a^4}}};\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)-\sqrt{\frac{a^4 x^4}{b^4}+1} \Pi \left(-\frac{i \sqrt{2} b^2}{a^2 \sqrt{\frac{\left(1+i \sqrt{3}\right) b^4}{a^4}}};\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)-\sqrt{\frac{a^4 x^4}{b^4}+1} \Pi \left(\frac{i \sqrt{2} b^2}{a^2 \sqrt{\frac{\left(1+i \sqrt{3}\right) b^4}{a^4}}};\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)\right)}{3 \sqrt{\frac{i a^2}{b^2}} \sqrt{a^4 x^4+b^4}}","\frac{1}{6} \text{RootSum}\left[\text{$\#$1}^8-8 \text{$\#$1}^6 a^2 b^2-24 \text{$\#$1}^4 a^4 b^4-32 \text{$\#$1}^2 a^6 b^6+16 a^8 b^8\&,\frac{-\text{$\#$1}^6 \log \left(-\text{$\#$1} x+\sqrt{a^4 x^4+b^4}+a^2 x^2+b^2\right)+\text{$\#$1}^6 \log (x)-2 \text{$\#$1}^4 a^2 b^2 \log (x)+2 \text{$\#$1}^4 a^2 b^2 \log \left(-\text{$\#$1} x+\sqrt{a^4 x^4+b^4}+a^2 x^2+b^2\right)-4 \text{$\#$1}^2 a^4 b^4 \log (x)+4 \text{$\#$1}^2 a^4 b^4 \log \left(-\text{$\#$1} x+\sqrt{a^4 x^4+b^4}+a^2 x^2+b^2\right)-8 a^6 b^6 \log \left(-\text{$\#$1} x+\sqrt{a^4 x^4+b^4}+a^2 x^2+b^2\right)+8 a^6 b^6 \log (x)}{-\text{$\#$1}^7+6 \text{$\#$1}^5 a^2 b^2+12 \text{$\#$1}^3 a^4 b^4+8 \text{$\#$1} a^6 b^6}\&\right]-\frac{x}{3 \sqrt{a^4 x^4+b^4}}",1,"((-1/3*I)*((-I)*Sqrt[(I*a^2)/b^2]*x + 2*Sqrt[1 + (a^4*x^4)/b^4]*EllipticF[I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] - Sqrt[1 + (a^4*x^4)/b^4]*EllipticPi[((-I)*Sqrt[2]*b^2)/(a^2*Sqrt[((1 - I*Sqrt[3])*b^4)/a^4]), I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] - Sqrt[1 + (a^4*x^4)/b^4]*EllipticPi[(I*Sqrt[2]*b^2)/(a^2*Sqrt[((1 - I*Sqrt[3])*b^4)/a^4]), I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] - Sqrt[1 + (a^4*x^4)/b^4]*EllipticPi[((-I)*Sqrt[2]*b^2)/(a^2*Sqrt[((1 + I*Sqrt[3])*b^4)/a^4]), I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] - Sqrt[1 + (a^4*x^4)/b^4]*EllipticPi[(I*Sqrt[2]*b^2)/(a^2*Sqrt[((1 + I*Sqrt[3])*b^4)/a^4]), I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1]))/(Sqrt[(I*a^2)/b^2]*Sqrt[b^4 + a^4*x^4])","C",1
2921,1,275,334,0.5309077,"\int \frac{\left(c+b x+a x^2\right)^{5/2}}{c+b x} \, dx","Integrate[(c + b*x + a*x^2)^(5/2)/(c + b*x),x]","\frac{-3840 a^5 c^5 \tanh ^{-1}\left(\frac{-2 a c x+b^2 x+b c}{2 \sqrt{a} c \sqrt{x (a x+b)+c}}\right)+15 \left(-256 a^5 c^5+80 a^2 b^6 c^2-30 a b^8 c+3 b^{10}\right) \tanh ^{-1}\left(\frac{2 a x+b}{2 \sqrt{a} \sqrt{x (a x+b)+c}}\right)+2 \sqrt{a} b \sqrt{x (a x+b)+c} \left(-960 a^4 b c^3 x+1920 a^4 c^4-80 a^3 b^3 c x \left(6 a x^2+c\right)+160 a^3 b^2 c^2 \left(4 a x^2+c\right)+12 a^2 b^5 x \left(84 a x^2+109 c\right)+24 a^2 b^4 \left(16 a^2 x^4+2 a c x^2+c^2\right)+30 a b^7 x+6 a b^6 \left(124 a x^2+65 c\right)-45 b^8\right)}{3840 a^{5/2} b^6}","-\frac{a^{5/2} c^5 \log \left(\sqrt{a x^2+b x+c}-\sqrt{a} x\right)}{b^6}+\frac{a^{5/2} c^5 \log \left(-b \sqrt{a x^2+b x+c}+\sqrt{a} b x+2 \sqrt{a} c\right)}{b^6}+\frac{\left(256 a^5 c^5-80 a^2 b^6 c^2+30 a b^8 c-3 b^{10}\right) \log \left(-2 \sqrt{a} \sqrt{a x^2+b x+c}+2 a x+b\right)}{256 a^{5/2} b^6}+\frac{\sqrt{a x^2+b x+c} \left(384 a^4 b^4 x^4-480 a^4 b^3 c x^3+640 a^4 b^2 c^2 x^2-960 a^4 b c^3 x+1920 a^4 c^4+1008 a^3 b^5 x^3+48 a^3 b^4 c x^2-80 a^3 b^3 c^2 x+160 a^3 b^2 c^3+744 a^2 b^6 x^2+1308 a^2 b^5 c x+24 a^2 b^4 c^2+30 a b^7 x+390 a b^6 c-45 b^8\right)}{1920 a^2 b^5}",1,"(2*Sqrt[a]*b*Sqrt[c + x*(b + a*x)]*(-45*b^8 + 1920*a^4*c^4 + 30*a*b^7*x - 960*a^4*b*c^3*x + 160*a^3*b^2*c^2*(c + 4*a*x^2) - 80*a^3*b^3*c*x*(c + 6*a*x^2) + 12*a^2*b^5*x*(109*c + 84*a*x^2) + 6*a*b^6*(65*c + 124*a*x^2) + 24*a^2*b^4*(c^2 + 2*a*c*x^2 + 16*a^2*x^4)) + 15*(3*b^10 - 30*a*b^8*c + 80*a^2*b^6*c^2 - 256*a^5*c^5)*ArcTanh[(b + 2*a*x)/(2*Sqrt[a]*Sqrt[c + x*(b + a*x)])] - 3840*a^5*c^5*ArcTanh[(b*c + b^2*x - 2*a*c*x)/(2*Sqrt[a]*c*Sqrt[c + x*(b + a*x)])])/(3840*a^(5/2)*b^6)","A",1
2922,1,606,334,3.3343018,"\int \frac{\left(-b-a x^2+x^4\right) \sqrt[4]{b x^2+a x^4}}{b+a x^4} \, dx","Integrate[((-b - a*x^2 + x^4)*(b*x^2 + a*x^4)^(1/4))/(b + a*x^4),x]","\frac{x \sqrt[4]{x^2 \left(a x^2+b\right)} \left(2-\frac{\left(a+\frac{b}{x^2}\right)^{3/4} \left(\frac{2 \left(a^2-a b-b\right) \left(\frac{\left(\sqrt{-a}-\sqrt{b}\right) \left(\tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\sqrt{-a} \sqrt{b}+a}}\right)+\tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\sqrt{-a} \sqrt{b}+a}}\right)\right)}{\left(\sqrt{-a} \sqrt{b}+a\right)^{3/4}}-\frac{\left(\sqrt{-a}+\sqrt{b}\right) \left(\tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a-\sqrt{-a} \sqrt{b}}}\right)+\tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a-\sqrt{-a} \sqrt{b}}}\right)\right)}{\left(a-\sqrt{-a} \sqrt{b}\right)^{3/4}}\right)}{\sqrt{b}}+\frac{\left(4 a^2-b\right) \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a}}\right)}{a^{3/4}}+\frac{\left(4 a^2-b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a}}\right)}{a^{3/4}}+\frac{2 (-a)^{3/2} (a+b) \left(-\left(\sqrt{-a} \sqrt{b}+a\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a-\sqrt{-a} \sqrt{b}}}\right)+\left(a-\sqrt{-a} \sqrt{b}\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\sqrt{-a} \sqrt{b}+a}}\right)-\left(\sqrt{-a} \sqrt{b}+a\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a-\sqrt{-a} \sqrt{b}}}\right)+\left(a-\sqrt{-a} \sqrt{b}\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\sqrt{-a} \sqrt{b}+a}}\right)\right)}{\sqrt{b} \left(a-\sqrt{-a} \sqrt{b}\right)^{3/4} \left(\sqrt{-a} \sqrt{b}+a\right)^{3/4}}\right)}{a x^2+b}\right)}{4 a}","-\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{-\text{$\#$1}^4 a^2 \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 a^2 \log (x)+\text{$\#$1}^4 a b \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 b \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\text{$\#$1}^4 a b \log (x)-\text{$\#$1}^4 b \log (x)+a^3 \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+a^2 b \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-a^3 \log (x)-a^2 b \log (x)}{\text{$\#$1}^3 a-\text{$\#$1}^7}\&\right]}{4 a}+\frac{\left(4 a^2-b\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{4 a^{7/4}}+\frac{\left(b-4 a^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{4 a^{7/4}}+\frac{x \sqrt[4]{a x^4+b x^2}}{2 a}",1,"(x*(x^2*(b + a*x^2))^(1/4)*(2 - ((a + b/x^2)^(3/4)*(((4*a^2 - b)*ArcTan[(a + b/x^2)^(1/4)/a^(1/4)])/a^(3/4) + ((4*a^2 - b)*ArcTanh[(a + b/x^2)^(1/4)/a^(1/4)])/a^(3/4) + (2*(-a)^(3/2)*(a + b)*(-((a + Sqrt[-a]*Sqrt[b])^(3/4)*ArcTan[(a + b/x^2)^(1/4)/(a - Sqrt[-a]*Sqrt[b])^(1/4)]) + (a - Sqrt[-a]*Sqrt[b])^(3/4)*ArcTan[(a + b/x^2)^(1/4)/(a + Sqrt[-a]*Sqrt[b])^(1/4)] - (a + Sqrt[-a]*Sqrt[b])^(3/4)*ArcTanh[(a + b/x^2)^(1/4)/(a - Sqrt[-a]*Sqrt[b])^(1/4)] + (a - Sqrt[-a]*Sqrt[b])^(3/4)*ArcTanh[(a + b/x^2)^(1/4)/(a + Sqrt[-a]*Sqrt[b])^(1/4)]))/((a - Sqrt[-a]*Sqrt[b])^(3/4)*(a + Sqrt[-a]*Sqrt[b])^(3/4)*Sqrt[b]) + (2*(a^2 - b - a*b)*(-(((Sqrt[-a] + Sqrt[b])*(ArcTan[(a + b/x^2)^(1/4)/(a - Sqrt[-a]*Sqrt[b])^(1/4)] + ArcTanh[(a + b/x^2)^(1/4)/(a - Sqrt[-a]*Sqrt[b])^(1/4)]))/(a - Sqrt[-a]*Sqrt[b])^(3/4)) + ((Sqrt[-a] - Sqrt[b])*(ArcTan[(a + b/x^2)^(1/4)/(a + Sqrt[-a]*Sqrt[b])^(1/4)] + ArcTanh[(a + b/x^2)^(1/4)/(a + Sqrt[-a]*Sqrt[b])^(1/4)]))/(a + Sqrt[-a]*Sqrt[b])^(3/4)))/Sqrt[b]))/(b + a*x^2)))/(4*a)","A",1
2923,1,606,334,1.8888004,"\int \frac{\left(-b-a x^2+x^4\right) \sqrt[4]{b x^2+a x^4}}{b+a x^4} \, dx","Integrate[((-b - a*x^2 + x^4)*(b*x^2 + a*x^4)^(1/4))/(b + a*x^4),x]","\frac{x \sqrt[4]{x^2 \left(a x^2+b\right)} \left(2-\frac{\left(a+\frac{b}{x^2}\right)^{3/4} \left(\frac{2 \left(a^2-a b-b\right) \left(\frac{\left(\sqrt{-a}-\sqrt{b}\right) \left(\tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\sqrt{-a} \sqrt{b}+a}}\right)+\tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\sqrt{-a} \sqrt{b}+a}}\right)\right)}{\left(\sqrt{-a} \sqrt{b}+a\right)^{3/4}}-\frac{\left(\sqrt{-a}+\sqrt{b}\right) \left(\tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a-\sqrt{-a} \sqrt{b}}}\right)+\tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a-\sqrt{-a} \sqrt{b}}}\right)\right)}{\left(a-\sqrt{-a} \sqrt{b}\right)^{3/4}}\right)}{\sqrt{b}}+\frac{\left(4 a^2-b\right) \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a}}\right)}{a^{3/4}}+\frac{\left(4 a^2-b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a}}\right)}{a^{3/4}}+\frac{2 (-a)^{3/2} (a+b) \left(-\left(\sqrt{-a} \sqrt{b}+a\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a-\sqrt{-a} \sqrt{b}}}\right)+\left(a-\sqrt{-a} \sqrt{b}\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\sqrt{-a} \sqrt{b}+a}}\right)-\left(\sqrt{-a} \sqrt{b}+a\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{a-\sqrt{-a} \sqrt{b}}}\right)+\left(a-\sqrt{-a} \sqrt{b}\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a+\frac{b}{x^2}}}{\sqrt[4]{\sqrt{-a} \sqrt{b}+a}}\right)\right)}{\sqrt{b} \left(a-\sqrt{-a} \sqrt{b}\right)^{3/4} \left(\sqrt{-a} \sqrt{b}+a\right)^{3/4}}\right)}{a x^2+b}\right)}{4 a}","-\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{-\text{$\#$1}^4 a^2 \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 a^2 \log (x)+\text{$\#$1}^4 a b \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 b \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\text{$\#$1}^4 a b \log (x)-\text{$\#$1}^4 b \log (x)+a^3 \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+a^2 b \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-a^3 \log (x)-a^2 b \log (x)}{\text{$\#$1}^3 a-\text{$\#$1}^7}\&\right]}{4 a}+\frac{\left(4 a^2-b\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{4 a^{7/4}}+\frac{\left(b-4 a^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{4 a^{7/4}}+\frac{x \sqrt[4]{a x^4+b x^2}}{2 a}",1,"(x*(x^2*(b + a*x^2))^(1/4)*(2 - ((a + b/x^2)^(3/4)*(((4*a^2 - b)*ArcTan[(a + b/x^2)^(1/4)/a^(1/4)])/a^(3/4) + ((4*a^2 - b)*ArcTanh[(a + b/x^2)^(1/4)/a^(1/4)])/a^(3/4) + (2*(-a)^(3/2)*(a + b)*(-((a + Sqrt[-a]*Sqrt[b])^(3/4)*ArcTan[(a + b/x^2)^(1/4)/(a - Sqrt[-a]*Sqrt[b])^(1/4)]) + (a - Sqrt[-a]*Sqrt[b])^(3/4)*ArcTan[(a + b/x^2)^(1/4)/(a + Sqrt[-a]*Sqrt[b])^(1/4)] - (a + Sqrt[-a]*Sqrt[b])^(3/4)*ArcTanh[(a + b/x^2)^(1/4)/(a - Sqrt[-a]*Sqrt[b])^(1/4)] + (a - Sqrt[-a]*Sqrt[b])^(3/4)*ArcTanh[(a + b/x^2)^(1/4)/(a + Sqrt[-a]*Sqrt[b])^(1/4)]))/((a - Sqrt[-a]*Sqrt[b])^(3/4)*(a + Sqrt[-a]*Sqrt[b])^(3/4)*Sqrt[b]) + (2*(a^2 - b - a*b)*(-(((Sqrt[-a] + Sqrt[b])*(ArcTan[(a + b/x^2)^(1/4)/(a - Sqrt[-a]*Sqrt[b])^(1/4)] + ArcTanh[(a + b/x^2)^(1/4)/(a - Sqrt[-a]*Sqrt[b])^(1/4)]))/(a - Sqrt[-a]*Sqrt[b])^(3/4)) + ((Sqrt[-a] - Sqrt[b])*(ArcTan[(a + b/x^2)^(1/4)/(a + Sqrt[-a]*Sqrt[b])^(1/4)] + ArcTanh[(a + b/x^2)^(1/4)/(a + Sqrt[-a]*Sqrt[b])^(1/4)]))/(a + Sqrt[-a]*Sqrt[b])^(3/4)))/Sqrt[b]))/(b + a*x^2)))/(4*a)","A",1
2924,1,400,337,1.0834283,"\int \frac{\sqrt{1+x} \left(-1+x^2\right)}{\left(1+x^2\right) \sqrt{x+\sqrt{1+x}}} \, dx","Integrate[(Sqrt[1 + x]*(-1 + x^2))/((1 + x^2)*Sqrt[x + Sqrt[1 + x]]),x]","\sqrt{x+1} \sqrt{x+\sqrt{x+1}}-\frac{3}{2} \sqrt{x+\sqrt{x+1}}-\frac{(1+i) \tan ^{-1}\left(\frac{-\left(\left(1-2 \sqrt{1-i}\right) \sqrt{x+1}\right)+\sqrt{1-i}+2}{2 \sqrt{i+\sqrt{1-i}} \sqrt{x+\sqrt{x+1}}}\right)}{\sqrt{(1+i)+(1-i)^{3/2}}}-\frac{(1-i) \tan ^{-1}\left(\frac{-\left(\left(1-2 \sqrt{1+i}\right) \sqrt{x+1}\right)+\sqrt{1+i}+2}{2 \sqrt{\sqrt{1+i}-i} \sqrt{x+\sqrt{x+1}}}\right)}{\sqrt{(1-i)+(1+i)^{3/2}}}+\frac{7}{4} \tanh ^{-1}\left(\frac{2 \sqrt{x+1}+1}{2 \sqrt{x+\sqrt{x+1}}}\right)-\frac{(1+i) \tanh ^{-1}\left(\frac{-\left(\left(1+2 \sqrt{1-i}\right) \sqrt{x+1}\right)-\sqrt{1-i}+2}{2 \sqrt{\sqrt{1-i}-i} \sqrt{x+\sqrt{x+1}}}\right)}{\sqrt{(-1-i)+(1-i)^{3/2}}}-\frac{(1-i) \tanh ^{-1}\left(\frac{-\left(\left(1+2 \sqrt{1+i}\right) \sqrt{x+1}\right)-\sqrt{1+i}+2}{2 \sqrt{i+\sqrt{1+i}} \sqrt{x+\sqrt{x+1}}}\right)}{\sqrt{(-1+i)+(1+i)^{3/2}}}","8 \text{RootSum}\left[\text{$\#$1}^8+8 \text{$\#$1}^7+12 \text{$\#$1}^6+24 \text{$\#$1}^5+470 \text{$\#$1}^4+120 \text{$\#$1}^3+300 \text{$\#$1}^2+1000 \text{$\#$1}+625\&,\frac{\text{$\#$1}^5 \log \left(\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)+4 \text{$\#$1}^4 \log \left(\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)+14 \text{$\#$1}^3 \log \left(\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)+20 \text{$\#$1}^2 \log \left(\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)+25 \text{$\#$1} \log \left(\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)}{\text{$\#$1}^7+7 \text{$\#$1}^6+9 \text{$\#$1}^5+15 \text{$\#$1}^4+235 \text{$\#$1}^3+45 \text{$\#$1}^2+75 \text{$\#$1}+125}\&\right]+\sqrt{x+1} \sqrt{x+\sqrt{x+1}}-\frac{3}{2} \sqrt{x+\sqrt{x+1}}-\frac{7}{4} \log \left(2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)",1,"(-3*Sqrt[x + Sqrt[1 + x]])/2 + Sqrt[1 + x]*Sqrt[x + Sqrt[1 + x]] - ((1 + I)*ArcTan[(2 + Sqrt[1 - I] - (1 - 2*Sqrt[1 - I])*Sqrt[1 + x])/(2*Sqrt[I + Sqrt[1 - I]]*Sqrt[x + Sqrt[1 + x]])])/Sqrt[(1 + I) + (1 - I)^(3/2)] - ((1 - I)*ArcTan[(2 + Sqrt[1 + I] - (1 - 2*Sqrt[1 + I])*Sqrt[1 + x])/(2*Sqrt[-I + Sqrt[1 + I]]*Sqrt[x + Sqrt[1 + x]])])/Sqrt[(1 - I) + (1 + I)^(3/2)] + (7*ArcTanh[(1 + 2*Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])])/4 - ((1 + I)*ArcTanh[(2 - Sqrt[1 - I] - (1 + 2*Sqrt[1 - I])*Sqrt[1 + x])/(2*Sqrt[-I + Sqrt[1 - I]]*Sqrt[x + Sqrt[1 + x]])])/Sqrt[(-1 - I) + (1 - I)^(3/2)] - ((1 - I)*ArcTanh[(2 - Sqrt[1 + I] - (1 + 2*Sqrt[1 + I])*Sqrt[1 + x])/(2*Sqrt[I + Sqrt[1 + I]]*Sqrt[x + Sqrt[1 + x]])])/Sqrt[(-1 + I) + (1 + I)^(3/2)]","C",1
2925,1,400,337,0.2821128,"\int \frac{\sqrt{1+x} \left(-1+x^2\right)}{\left(1+x^2\right) \sqrt{x+\sqrt{1+x}}} \, dx","Integrate[(Sqrt[1 + x]*(-1 + x^2))/((1 + x^2)*Sqrt[x + Sqrt[1 + x]]),x]","\sqrt{x+1} \sqrt{x+\sqrt{x+1}}-\frac{3}{2} \sqrt{x+\sqrt{x+1}}-\frac{(1+i) \tan ^{-1}\left(\frac{-\left(\left(1-2 \sqrt{1-i}\right) \sqrt{x+1}\right)+\sqrt{1-i}+2}{2 \sqrt{i+\sqrt{1-i}} \sqrt{x+\sqrt{x+1}}}\right)}{\sqrt{(1+i)+(1-i)^{3/2}}}-\frac{(1-i) \tan ^{-1}\left(\frac{-\left(\left(1-2 \sqrt{1+i}\right) \sqrt{x+1}\right)+\sqrt{1+i}+2}{2 \sqrt{\sqrt{1+i}-i} \sqrt{x+\sqrt{x+1}}}\right)}{\sqrt{(1-i)+(1+i)^{3/2}}}+\frac{7}{4} \tanh ^{-1}\left(\frac{2 \sqrt{x+1}+1}{2 \sqrt{x+\sqrt{x+1}}}\right)-\frac{(1+i) \tanh ^{-1}\left(\frac{-\left(\left(1+2 \sqrt{1-i}\right) \sqrt{x+1}\right)-\sqrt{1-i}+2}{2 \sqrt{\sqrt{1-i}-i} \sqrt{x+\sqrt{x+1}}}\right)}{\sqrt{(-1-i)+(1-i)^{3/2}}}-\frac{(1-i) \tanh ^{-1}\left(\frac{-\left(\left(1+2 \sqrt{1+i}\right) \sqrt{x+1}\right)-\sqrt{1+i}+2}{2 \sqrt{i+\sqrt{1+i}} \sqrt{x+\sqrt{x+1}}}\right)}{\sqrt{(-1+i)+(1+i)^{3/2}}}","8 \text{RootSum}\left[\text{$\#$1}^8+8 \text{$\#$1}^7+12 \text{$\#$1}^6+24 \text{$\#$1}^5+470 \text{$\#$1}^4+120 \text{$\#$1}^3+300 \text{$\#$1}^2+1000 \text{$\#$1}+625\&,\frac{\text{$\#$1}^5 \log \left(\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)+4 \text{$\#$1}^4 \log \left(\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)+14 \text{$\#$1}^3 \log \left(\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)+20 \text{$\#$1}^2 \log \left(\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)+25 \text{$\#$1} \log \left(\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)}{\text{$\#$1}^7+7 \text{$\#$1}^6+9 \text{$\#$1}^5+15 \text{$\#$1}^4+235 \text{$\#$1}^3+45 \text{$\#$1}^2+75 \text{$\#$1}+125}\&\right]+\sqrt{x+1} \sqrt{x+\sqrt{x+1}}-\frac{3}{2} \sqrt{x+\sqrt{x+1}}-\frac{7}{4} \log \left(2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)",1,"(-3*Sqrt[x + Sqrt[1 + x]])/2 + Sqrt[1 + x]*Sqrt[x + Sqrt[1 + x]] - ((1 + I)*ArcTan[(2 + Sqrt[1 - I] - (1 - 2*Sqrt[1 - I])*Sqrt[1 + x])/(2*Sqrt[I + Sqrt[1 - I]]*Sqrt[x + Sqrt[1 + x]])])/Sqrt[(1 + I) + (1 - I)^(3/2)] - ((1 - I)*ArcTan[(2 + Sqrt[1 + I] - (1 - 2*Sqrt[1 + I])*Sqrt[1 + x])/(2*Sqrt[-I + Sqrt[1 + I]]*Sqrt[x + Sqrt[1 + x]])])/Sqrt[(1 - I) + (1 + I)^(3/2)] + (7*ArcTanh[(1 + 2*Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])])/4 - ((1 + I)*ArcTanh[(2 - Sqrt[1 - I] - (1 + 2*Sqrt[1 - I])*Sqrt[1 + x])/(2*Sqrt[-I + Sqrt[1 - I]]*Sqrt[x + Sqrt[1 + x]])])/Sqrt[(-1 - I) + (1 - I)^(3/2)] - ((1 - I)*ArcTanh[(2 - Sqrt[1 + I] - (1 + 2*Sqrt[1 + I])*Sqrt[1 + x])/(2*Sqrt[I + Sqrt[1 + I]]*Sqrt[x + Sqrt[1 + x]])])/Sqrt[(-1 + I) + (1 + I)^(3/2)]","C",1
2926,1,3855,337,7.1415345,"\int \frac{-x^2+\sqrt{1+2 x^2}+\left(1+2 x^2\right)^{5/2}}{x^2-x \left(1+2 x^2\right)^{3/2}} \, dx","Integrate[(-x^2 + Sqrt[1 + 2*x^2] + (1 + 2*x^2)^(5/2))/(x^2 - x*(1 + 2*x^2)^(3/2)),x]","\text{Result too large to show}","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^6+2 \sqrt{2} \text{$\#$1}^4+3 \text{$\#$1}^4-2 \sqrt{2} \text{$\#$1}^2+3 \text{$\#$1}^2+1\&,\frac{2 \text{$\#$1}^5 \log \left(-\text{$\#$1}+\sqrt{2 x^2+1}-\sqrt{2} x\right)+\text{$\#$1}^4 \log \left(-\text{$\#$1}+\sqrt{2 x^2+1}-\sqrt{2} x\right)+4 \sqrt{2} \text{$\#$1}^3 \log \left(-\text{$\#$1}+\sqrt{2 x^2+1}-\sqrt{2} x\right)+2 \text{$\#$1}^3 \log \left(-\text{$\#$1}+\sqrt{2 x^2+1}-\sqrt{2} x\right)+4 \text{$\#$1} \log \left(-\text{$\#$1}+\sqrt{2 x^2+1}-\sqrt{2} x\right)-\log \left(-\text{$\#$1}+\sqrt{2 x^2+1}-\sqrt{2} x\right)}{3 \text{$\#$1}^5+4 \sqrt{2} \text{$\#$1}^3+6 \text{$\#$1}^3-2 \sqrt{2} \text{$\#$1}+3 \text{$\#$1}}\&\right]-x^2+\frac{1}{2} \left(2+\sqrt{2}\right) \log \left(\sqrt{2 x^2+1}-\sqrt{2} x\right)-2 \log \left(\sqrt{2} x \sqrt{2 x^2+1}-2 x^2\right)",1,"(x^3*(-x + (1 + 2*x^2)^(3/2)))/(x^2 - x*(1 + 2*x^2)^(3/2)) + (x*(-x + (1 + 2*x^2)^(3/2))*ArcSinh[Sqrt[2]*x])/(Sqrt[2]*(x^2 - x*(1 + 2*x^2)^(3/2))) + (x*(-x + (1 + 2*x^2)^(3/2))*ArcTan[x])/(5*(x^2 - x*(1 + 2*x^2)^(3/2))) - ((1/5 + I/10)*x*(-x + (1 + 2*x^2)^(3/2))*ArcTan[(2*x)/Sqrt[1 - I]])/(Sqrt[1 - I]*(x^2 - x*(1 + 2*x^2)^(3/2))) - ((1/5 - I/10)*x*(-x + (1 + 2*x^2)^(3/2))*ArcTan[(2*x)/Sqrt[1 + I]])/(Sqrt[1 + I]*(x^2 - x*(1 + 2*x^2)^(3/2))) + ((1/5 - (3*I)/20)*x*(-x + (1 + 2*x^2)^(3/2))*ArcTan[(2*x^2)/(1 + 2*x^2)])/(x^2 - x*(1 + 2*x^2)^(3/2)) - ((1/5 + (3*I)/20)*x*(-x + (1 + 2*x^2)^(3/2))*ArcTan[(1 + 2*x^2)/(2*x^2)])/(x^2 - x*(1 + 2*x^2)^(3/2)) + ((1/40 + (3*I)/40)*((4 + 2*I) + Sqrt[-2 - 2*I])*x*(-x + (1 + 2*x^2)^(3/2))*ArcTan[((-7 - 10*I) - 2*(-1 - I)^(3/2)*Sqrt[2] - (36 + 20*I)*x + (75 + 19*I)*Sqrt[-2 - 2*I]*x + (330 + 266*I)*x^2 + (116 + 64*I)*Sqrt[-2 - 2*I]*x^2 + (176 + 320*I)*x^3 - (300 + 104*I)*Sqrt[-2 - 2*I]*x^3 - (192 + 160*I)*x^4 + 88*(-1 - I)^(3/2)*Sqrt[2]*x^4)/((49 + 40*I) - 21*(-1 - I)^(3/2)*Sqrt[2] + (92 + 260*I)*x - (170 + 68*I)*Sqrt[-2 - 2*I]*x - (410 + 402*I)*x^2 - (232 + 268*I)*Sqrt[-2 - 2*I]*x^2 - (192 + 560*I)*x^3 + (280 + 88*I)*Sqrt[-2 - 2*I]*x^3 + (144 + 80*I)*x^4 - 96*(-1 - I)^(3/2)*Sqrt[2]*x^4)])/(Sqrt[-1 - I]*Sqrt[1 + I]*(x^2 - x*(1 + 2*x^2)^(3/2))) + ((1/40 + (3*I)/40)*((-4 - 2*I) + Sqrt[-2 - 2*I])*x*(-x + (1 + 2*x^2)^(3/2))*ArcTan[((7 + 10*I) - 2*(-1 - I)^(3/2)*Sqrt[2] + (36 + 20*I)*x + (75 + 19*I)*Sqrt[-2 - 2*I]*x - (330 + 266*I)*x^2 + (116 + 64*I)*Sqrt[-2 - 2*I]*x^2 - (176 + 320*I)*x^3 - (300 + 104*I)*Sqrt[-2 - 2*I]*x^3 + (192 + 160*I)*x^4 + 88*(-1 - I)^(3/2)*Sqrt[2]*x^4)/((-49 - 40*I) - 21*(-1 - I)^(3/2)*Sqrt[2] - (92 + 260*I)*x - (170 + 68*I)*Sqrt[-2 - 2*I]*x + (410 + 402*I)*x^2 - (232 + 268*I)*Sqrt[-2 - 2*I]*x^2 + (192 + 560*I)*x^3 + (280 + 88*I)*Sqrt[-2 - 2*I]*x^3 - (144 + 80*I)*x^4 - 96*(-1 - I)^(3/2)*Sqrt[2]*x^4)])/(Sqrt[-1 - I]*Sqrt[1 + I]*(x^2 - x*(1 + 2*x^2)^(3/2))) - ((1/10 + I/5)*x*(-x + (1 + 2*x^2)^(3/2))*ArcTan[(-4 - 4*x^2 - 5*Sqrt[1 + 2*x^2])/(-3 + 2*x^2)])/(x^2 - x*(1 + 2*x^2)^(3/2)) - ((1/10 - I/5)*x*(-x + (1 + 2*x^2)^(3/2))*ArcTan[(4 + 4*x^2 - 5*Sqrt[1 + 2*x^2])/(-3 + 2*x^2)])/(x^2 - x*(1 + 2*x^2)^(3/2)) - ((1/20 - I/40)*((-2 - 4*I) + Sqrt[2 - 2*I])*x*(-x + (1 + 2*x^2)^(3/2))*ArcTan[((10 + 7*I) - 22/Sqrt[1/2 - I/2] + (52 + 36*I)*x - (47 + 21*I)*Sqrt[2 - 2*I]*x + (214 + 166*I)*x^2 - (60 + 96*I)*Sqrt[2 - 2*I]*x^2 + (32 + 176*I)*x^3 - (52 + 136*I)*Sqrt[2 - 2*I]*x^3 + (160 + 192*I)*x^4 - (32*x^4)/Sqrt[1/2 - I/2] - (110 - 10*I)*x*Sqrt[1 + 2*x^2] + 20*Sqrt[2 - 2*I]*x*Sqrt[1 + 2*x^2] - 80*x^2*Sqrt[1 + 2*x^2] + (120 + 100*I)*Sqrt[2 - 2*I]*x^2*Sqrt[1 + 2*x^2] - (240 + 200*I)*x^3*Sqrt[1 + 2*x^2] + (80*Sqrt[2]*x^3*Sqrt[1 + 2*x^2])/Sqrt[1 - I])/((-10 - I) + 6/Sqrt[1/2 - I/2] - (56 - 32*I)*x + (26 + 8*I)*Sqrt[2 - 2*I]*x - (22 + 58*I)*x^2 + (80 + 68*I)*Sqrt[2 - 2*I]*x^2 - (176 + 48*I)*x^3 + (36 + 68*I)*Sqrt[2 - 2*I]*x^3 + (120 - 296*I)*x^4 + (48 + 128*I)*Sqrt[2 - 2*I]*x^4)])/(x^2 - x*(1 + 2*x^2)^(3/2)) - ((1/40 + I/20)*((2 + 4*I) + Sqrt[2 - 2*I])*x*(-x + (1 + 2*x^2)^(3/2))*ArcTanh[((-7 + 10*I) - 11*(1 - I)^(3/2)*Sqrt[2] - (36 - 52*I)*x - (21 - 47*I)*Sqrt[2 - 2*I]*x - (166 - 214*I)*x^2 - (96 - 60*I)*Sqrt[2 - 2*I]*x^2 - (176 - 32*I)*x^3 - (136 - 52*I)*Sqrt[2 - 2*I]*x^3 - (192 - 160*I)*x^4 - 16*(1 - I)^(3/2)*Sqrt[2]*x^4 + (10 + 110*I)*x*Sqrt[1 + 2*x^2] + (20*I)*Sqrt[2 - 2*I]*x*Sqrt[1 + 2*x^2] + (80*I)*x^2*Sqrt[1 + 2*x^2] - (100 - 120*I)*Sqrt[2 - 2*I]*x^2*Sqrt[1 + 2*x^2] - (200 - 240*I)*x^3*Sqrt[1 + 2*x^2] - 40*(1 - I)^(3/2)*Sqrt[2]*x^3*Sqrt[1 + 2*x^2])/((10 + I) + 6/Sqrt[1/2 - I/2] + (56 - 32*I)*x + (26 + 8*I)*Sqrt[2 - 2*I]*x + (22 + 58*I)*x^2 + (80 + 68*I)*Sqrt[2 - 2*I]*x^2 + (176 + 48*I)*x^3 + (36 + 68*I)*Sqrt[2 - 2*I]*x^3 - (120 - 296*I)*x^4 + (48 + 128*I)*Sqrt[2 - 2*I]*x^4)])/(x^2 - x*(1 + 2*x^2)^(3/2)) - ((3/80 - I/80)*((-4 - 2*I) + Sqrt[-2 - 2*I])*x*(-x + (1 + 2*x^2)^(3/2))*Log[(Sqrt[-2 - 2*I] - (2 + 2*I)*x)^2*(Sqrt[-2 - 2*I] - (2 - 2*I)*x)^2])/(Sqrt[-1 - I]*Sqrt[1 + I]*(x^2 - x*(1 + 2*x^2)^(3/2))) - ((1/80 + I/40)*((-2 - 4*I) + Sqrt[2 - 2*I])*x*(-x + (1 + 2*x^2)^(3/2))*Log[(Sqrt[2 - 2*I] - (2 + 2*I)*x)^2*(Sqrt[2 - 2*I] - (2 - 2*I)*x)^2])/(x^2 - x*(1 + 2*x^2)^(3/2)) + (2*x*(-x + (1 + 2*x^2)^(3/2))*Log[x])/(x^2 - x*(1 + 2*x^2)^(3/2)) - ((I/10)*x*(-x + (1 + 2*x^2)^(3/2))*Log[(-I + x)*(I + x)])/(x^2 - x*(1 + 2*x^2)^(3/2)) - ((3/80 - I/80)*((4 + 2*I) + Sqrt[-2 - 2*I])*x*(-x + (1 + 2*x^2)^(3/2))*Log[(Sqrt[-2 - 2*I] + (2 - 2*I)*x)^2*(Sqrt[-2 - 2*I] + (2 + 2*I)*x)^2])/(Sqrt[-1 - I]*Sqrt[1 + I]*(x^2 - x*(1 + 2*x^2)^(3/2))) - ((1/80 + I/40)*((2 + 4*I) + Sqrt[2 - 2*I])*x*(-x + (1 + 2*x^2)^(3/2))*Log[(Sqrt[2 - 2*I] + (2 - 2*I)*x)^2*(Sqrt[2 - 2*I] + (2 + 2*I)*x)^2])/(x^2 - x*(1 + 2*x^2)^(3/2)) - (x*(-x + (1 + 2*x^2)^(3/2))*Log[1 + x^2])/(5*(x^2 - x*(1 + 2*x^2)^(3/2))) - (3*x*(-x + (1 + 2*x^2)^(3/2))*Log[1 + 4*x^2 + 8*x^4])/(20*(x^2 - x*(1 + 2*x^2)^(3/2))) + ((1/10 + I/20)*x*(-x + (1 + 2*x^2)^(3/2))*Log[1 + 3*x^2 - 2*x*Sqrt[1 + 2*x^2]])/(x^2 - x*(1 + 2*x^2)^(3/2)) - ((1/10 - I/20)*x*(-x + (1 + 2*x^2)^(3/2))*Log[1 + 3*x^2 + 2*x*Sqrt[1 + 2*x^2]])/(x^2 - x*(1 + 2*x^2)^(3/2)) + ((1/80 + I/40)*((-2 - 4*I) + Sqrt[2 - 2*I])*x*(-x + (1 + 2*x^2)^(3/2))*Log[(7 + 16*I) - (1 + 3*I)*Sqrt[2 - 2*I] + (4 + 12*I)*x + (9 - 23*I)*Sqrt[2 - 2*I]*x - (16 - 68*I)*x^2 + (4 - 12*I)*Sqrt[2 - 2*I]*x^2 + (16*I)*x^3 + (20 - 24*I)*Sqrt[2 - 2*I]*x^3 - (40 - 48*I)*x^4 + 8*(1 - I)^(3/2)*Sqrt[2]*x^4 - (4 + 4*I)*Sqrt[1 + 2*x^2] + (1 + 11*I)*Sqrt[2 - 2*I]*Sqrt[1 + 2*x^2] - (4 + 44*I)*x*Sqrt[1 + 2*x^2] + (8*I)*Sqrt[2 - 2*I]*x*Sqrt[1 + 2*x^2] - (16*I)*x^2*Sqrt[1 + 2*x^2] - (20 - 24*I)*Sqrt[2 - 2*I]*x^2*Sqrt[1 + 2*x^2]])/(x^2 - x*(1 + 2*x^2)^(3/2)) + ((1/80 + I/40)*((2 + 4*I) + Sqrt[2 - 2*I])*x*(-x + (1 + 2*x^2)^(3/2))*Log[(7 + 16*I) + (1 + 3*I)*Sqrt[2 - 2*I] + (4 + 12*I)*x - (9 - 23*I)*Sqrt[2 - 2*I]*x - (16 - 68*I)*x^2 - (4 - 12*I)*Sqrt[2 - 2*I]*x^2 + (16*I)*x^3 - (20 - 24*I)*Sqrt[2 - 2*I]*x^3 - (40 - 48*I)*x^4 - 8*(1 - I)^(3/2)*Sqrt[2]*x^4 + (4 + 4*I)*Sqrt[1 + 2*x^2] + (1 + 11*I)*Sqrt[2 - 2*I]*Sqrt[1 + 2*x^2] + (4 + 44*I)*x*Sqrt[1 + 2*x^2] + (8*I)*Sqrt[2 - 2*I]*x*Sqrt[1 + 2*x^2] + (16*I)*x^2*Sqrt[1 + 2*x^2] - (20 - 24*I)*Sqrt[2 - 2*I]*x^2*Sqrt[1 + 2*x^2]])/(x^2 - x*(1 + 2*x^2)^(3/2)) + ((3/80 - I/80)*((-4 - 2*I) + Sqrt[-2 - 2*I])*x*(-x + (1 + 2*x^2)^(3/2))*Log[(14 + 3*I) - (6 + 2*I)*Sqrt[-2 - 2*I] + (40 + 8*I)*x + (25 - 21*I)*Sqrt[-2 - 2*I]*x - (64 - 80*I)*x^2 - (64*x^2)/Sqrt[-1/2 - I/2] - (32 - 64*I)*x^3 + (24 + 52*I)*Sqrt[-2 - 2*I]*x^3 - (40 + 32*I)*x^4 - 16*(-1 - I)^(3/2)*Sqrt[2]*x^4 - 8*Sqrt[-1 - I]*Sqrt[1 + I]*Sqrt[1 + 2*x^2] + (9 - I)*Sqrt[2 + 2*I]*Sqrt[1 + 2*x^2] + (24 - 30*I)*Sqrt[-1 - I]*Sqrt[1 + I]*x*Sqrt[1 + 2*x^2] + 24*Sqrt[2 + 2*I]*x*Sqrt[1 + 2*x^2] - (64*Sqrt[1 + I]*x^2*Sqrt[1 + 2*x^2])/Sqrt[-1 - I] - (32 - 40*I)*Sqrt[2 + 2*I]*x^2*Sqrt[1 + 2*x^2] + (4 + 36*I)*Sqrt[-1 - I]*Sqrt[1 + I]*x^3*Sqrt[1 + 2*x^2] - (32*Sqrt[2]*x^3*Sqrt[1 + 2*x^2])/Sqrt[1 + I]])/(Sqrt[-1 - I]*Sqrt[1 + I]*(x^2 - x*(1 + 2*x^2)^(3/2))) + ((3/80 - I/80)*((4 + 2*I) + Sqrt[-2 - 2*I])*x*(-x + (1 + 2*x^2)^(3/2))*Log[(-14 - 3*I) - (6 + 2*I)*Sqrt[-2 - 2*I] - (40 + 8*I)*x + (25 - 21*I)*Sqrt[-2 - 2*I]*x + (64 - 80*I)*x^2 - (64*x^2)/Sqrt[-1/2 - I/2] + (32 - 64*I)*x^3 + (24 + 52*I)*Sqrt[-2 - 2*I]*x^3 + (40 + 32*I)*x^4 - 16*(-1 - I)^(3/2)*Sqrt[2]*x^4 - 8*Sqrt[-1 - I]*Sqrt[1 + I]*Sqrt[1 + 2*x^2] - (9 - I)*Sqrt[2 + 2*I]*Sqrt[1 + 2*x^2] + (24 - 30*I)*Sqrt[-1 - I]*Sqrt[1 + I]*x*Sqrt[1 + 2*x^2] - 24*Sqrt[2 + 2*I]*x*Sqrt[1 + 2*x^2] - (64*Sqrt[1 + I]*x^2*Sqrt[1 + 2*x^2])/Sqrt[-1 - I] + (32 - 40*I)*Sqrt[2 + 2*I]*x^2*Sqrt[1 + 2*x^2] + (4 + 36*I)*Sqrt[-1 - I]*Sqrt[1 + I]*x^3*Sqrt[1 + 2*x^2] + (32*Sqrt[2]*x^3*Sqrt[1 + 2*x^2])/Sqrt[1 + I]])/(Sqrt[-1 - I]*Sqrt[1 + I]*(x^2 - x*(1 + 2*x^2)^(3/2)))","C",0
2927,1,319,339,0.2815474,"\int \frac{\left(-b+x^3\right) \left(b+x^3\right) \left(-c+x^3\right)}{\sqrt[3]{a x^2+x^3}} \, dx","Integrate[((-b + x^3)*(b + x^3)*(-c + x^3))/(a*x^2 + x^3)^(1/3),x]","\frac{3 x \sqrt[3]{\frac{a+x}{a}} \left(a^9 \, _2F_1\left(-\frac{26}{3},\frac{1}{3};\frac{4}{3};-\frac{x}{a}\right)-9 a^9 \, _2F_1\left(-\frac{23}{3},\frac{1}{3};\frac{4}{3};-\frac{x}{a}\right)+36 a^9 \, _2F_1\left(-\frac{20}{3},\frac{1}{3};\frac{4}{3};-\frac{x}{a}\right)+a^3 \left(84 a^6+20 a^3 c-b^2\right) \, _2F_1\left(-\frac{8}{3},\frac{1}{3};\frac{4}{3};-\frac{x}{a}\right)-3 a^3 \left(12 a^6+5 a^3 c-b^2\right) \, _2F_1\left(-\frac{5}{3},\frac{1}{3};\frac{4}{3};-\frac{x}{a}\right)+3 a^3 \left(3 a^6+2 a^3 c-b^2\right) \, _2F_1\left(-\frac{2}{3},\frac{1}{3};\frac{4}{3};-\frac{x}{a}\right)-\left(a^6-b^2\right) \left(a^3+c\right) \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};-\frac{x}{a}\right)-a^6 \left(84 a^3+c\right) \, _2F_1\left(-\frac{17}{3},\frac{1}{3};\frac{4}{3};-\frac{x}{a}\right)+6 a^6 \left(21 a^3+c\right) \, _2F_1\left(-\frac{14}{3},\frac{1}{3};\frac{4}{3};-\frac{x}{a}\right)-3 a^6 \left(42 a^3+5 c\right) \, _2F_1\left(-\frac{11}{3},\frac{1}{3};\frac{4}{3};-\frac{x}{a}\right)\right)}{\sqrt[3]{x^2 (a+x)}}","\frac{\left(135850 a^9+176904 a^6 c-275562 a^3 b^2-1594323 b^2 c\right) \log \left(\sqrt[3]{a x^2+x^3}-x\right)}{1594323}+\frac{\left(-135850 a^9-176904 a^6 c+275562 a^3 b^2+1594323 b^2 c\right) \log \left(x \sqrt[3]{a x^2+x^3}+\left(a x^2+x^3\right)^{2/3}+x^2\right)}{3188646}+\frac{\left(-135850 \sqrt{3} a^9-176904 \sqrt{3} a^6 c+275562 \sqrt{3} a^3 b^2+1594323 \sqrt{3} b^2 c\right) \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{a x^2+x^3}+x}\right)}{1594323}+\frac{\left(a x^2+x^3\right)^{2/3} \left(38038000 a^8-28528500 a^7 x+24453000 a^6 x^2+49533120 a^5 c-22007700 a^5 x^3-37149840 a^4 c x+20314800 a^4 x^4+31842720 a^3 c x^2-19045125 a^3 x^5-77157360 a^2 b^2-28658448 a^2 c x^3+18042750 a^2 x^6+57868020 a b^2 x+26453952 a c x^4-17222625 a x^7-49601160 b^2 x^2-24800580 c x^5+16533720 x^8\right)}{148803480 x}",1,"(3*x*((a + x)/a)^(1/3)*(a^9*Hypergeometric2F1[-26/3, 1/3, 4/3, -(x/a)] - 9*a^9*Hypergeometric2F1[-23/3, 1/3, 4/3, -(x/a)] + 36*a^9*Hypergeometric2F1[-20/3, 1/3, 4/3, -(x/a)] - a^6*(84*a^3 + c)*Hypergeometric2F1[-17/3, 1/3, 4/3, -(x/a)] + 6*a^6*(21*a^3 + c)*Hypergeometric2F1[-14/3, 1/3, 4/3, -(x/a)] - 3*a^6*(42*a^3 + 5*c)*Hypergeometric2F1[-11/3, 1/3, 4/3, -(x/a)] + a^3*(84*a^6 - b^2 + 20*a^3*c)*Hypergeometric2F1[-8/3, 1/3, 4/3, -(x/a)] - 3*a^3*(12*a^6 - b^2 + 5*a^3*c)*Hypergeometric2F1[-5/3, 1/3, 4/3, -(x/a)] + 3*a^3*(3*a^6 - b^2 + 2*a^3*c)*Hypergeometric2F1[-2/3, 1/3, 4/3, -(x/a)] - (a^6 - b^2)*(a^3 + c)*Hypergeometric2F1[1/3, 1/3, 4/3, -(x/a)]))/(x^2*(a + x))^(1/3)","C",1
2928,0,0,340,3.3654062,"\int \frac{x (-a+x) (-b+x) \left(a b-2 b x+x^2\right)}{\left(x (-a+x) (-b+x)^2\right)^{2/3} \left(-b^2+2 b x-\left(1-a^2 d\right) x^2-2 a d x^3+d x^4\right)} \, dx","Integrate[(x*(-a + x)*(-b + x)*(a*b - 2*b*x + x^2))/((x*(-a + x)*(-b + x)^2)^(2/3)*(-b^2 + 2*b*x - (1 - a^2*d)*x^2 - 2*a*d*x^3 + d*x^4)),x]","\int \frac{x (-a+x) (-b+x) \left(a b-2 b x+x^2\right)}{\left(x (-a+x) (-b+x)^2\right)^{2/3} \left(-b^2+2 b x-\left(1-a^2 d\right) x^2-2 a d x^3+d x^4\right)} \, dx","\frac{\log \left(-\sqrt[3]{d} \left(x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4\right)^{2/3}+b^2-2 b x+x^2\right)}{2 d^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} \left(x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4\right)^{2/3}}{\sqrt[3]{d} \left(x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4\right)^{2/3}+2 b^2-4 b x+2 x^2}\right)}{2 d^{2/3}}-\frac{\log \left(d^{2/3} \left(x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4\right)^{4/3}+\left(x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4\right)^{2/3} \left(b^2 \sqrt[3]{d}-2 b \sqrt[3]{d} x+\sqrt[3]{d} x^2\right)+b^4-4 b^3 x+6 b^2 x^2-4 b x^3+x^4\right)}{4 d^{2/3}}",1,"Integrate[(x*(-a + x)*(-b + x)*(a*b - 2*b*x + x^2))/((x*(-a + x)*(-b + x)^2)^(2/3)*(-b^2 + 2*b*x - (1 - a^2*d)*x^2 - 2*a*d*x^3 + d*x^4)), x]","F",-1
2929,1,756,342,4.021735,"\int \frac{\left(-b-a x^2+x^4\right) \sqrt[4]{-b x^2+a x^4}}{b+a x^4} \, dx","Integrate[((-b - a*x^2 + x^4)*(-(b*x^2) + a*x^4)^(1/4))/(b + a*x^4),x]","\frac{x \sqrt[4]{a x^4-b x^2} \left(8-\frac{\left(\frac{b}{x^2}-a\right)^{3/4} \left(\frac{8 \left(a^2+a b+b\right) \left(\sqrt[4]{\sqrt{-a}-\sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{-a} \sqrt[4]{\sqrt{-a}-\sqrt{b}}}\right)-\sqrt[4]{\sqrt{-a}+\sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{-a} \sqrt[4]{\sqrt{-a}+\sqrt{b}}}\right)+\sqrt[4]{\sqrt{-a}-\sqrt{b}} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{-a} \sqrt[4]{\sqrt{-a}-\sqrt{b}}}\right)-\sqrt[4]{\sqrt{-a}+\sqrt{b}} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{-a} \sqrt[4]{\sqrt{-a}+\sqrt{b}}}\right)\right)}{(-a)^{3/8} \sqrt{b}}+\frac{\sqrt{2} \left(4 a^2+b\right) \left(\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{\frac{b}{x^2}-a}+\sqrt{\frac{b}{x^2}-a}+\sqrt{a}\right)-\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{\frac{b}{x^2}-a}+\sqrt{\frac{b}{x^2}-a}+\sqrt{a}\right)\right)}{a^{3/4}}+\frac{2 \sqrt{2} \left(4 a^2+b\right) \left(\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[4]{a}}\right)-\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[4]{a}}+1\right)\right)}{a^{3/4}}+\frac{8 (-a)^{9/8} (a+b) \left(\left(\sqrt{-a}+\sqrt{b}\right)^{3/4} \left(\tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{-a} \sqrt[4]{\sqrt{-a}-\sqrt{b}}}\right)+\tanh ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{-a} \sqrt[4]{\sqrt{-a}-\sqrt{b}}}\right)\right)-\left(\sqrt{-a}-\sqrt{b}\right)^{3/4} \left(\tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{-a} \sqrt[4]{\sqrt{-a}+\sqrt{b}}}\right)+\tanh ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{-a} \sqrt[4]{\sqrt{-a}+\sqrt{b}}}\right)\right)\right)}{\sqrt{b} \left(\sqrt{-a}-\sqrt{b}\right)^{3/4} \left(\sqrt{-a}+\sqrt{b}\right)^{3/4}}\right)}{a x^2-b}\right)}{16 a}","-\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{-\text{$\#$1}^4 a^2 \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 a^2 \log (x)-\text{$\#$1}^4 a b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\text{$\#$1}^4 b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 a b \log (x)+\text{$\#$1}^4 b \log (x)+a^3 \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+a^2 b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-a^3 \log (x)-a^2 b \log (x)}{\text{$\#$1}^3 a-\text{$\#$1}^7}\&\right]}{4 a}+\frac{\left(4 a^2+b\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)}{4 a^{7/4}}+\frac{\left(-4 a^2-b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)}{4 a^{7/4}}+\frac{x \sqrt[4]{a x^4-b x^2}}{2 a}",1,"(x*(-(b*x^2) + a*x^4)^(1/4)*(8 - ((-a + b/x^2)^(3/4)*((2*Sqrt[2]*(4*a^2 + b)*(ArcTan[1 - (Sqrt[2]*(-a + b/x^2)^(1/4))/a^(1/4)] - ArcTan[1 + (Sqrt[2]*(-a + b/x^2)^(1/4))/a^(1/4)]))/a^(3/4) + (8*(a^2 + b + a*b)*((Sqrt[-a] - Sqrt[b])^(1/4)*ArcTan[(-a + b/x^2)^(1/4)/((-a)^(1/8)*(Sqrt[-a] - Sqrt[b])^(1/4))] - (Sqrt[-a] + Sqrt[b])^(1/4)*ArcTan[(-a + b/x^2)^(1/4)/((-a)^(1/8)*(Sqrt[-a] + Sqrt[b])^(1/4))] + (Sqrt[-a] - Sqrt[b])^(1/4)*ArcTanh[(-a + b/x^2)^(1/4)/((-a)^(1/8)*(Sqrt[-a] - Sqrt[b])^(1/4))] - (Sqrt[-a] + Sqrt[b])^(1/4)*ArcTanh[(-a + b/x^2)^(1/4)/((-a)^(1/8)*(Sqrt[-a] + Sqrt[b])^(1/4))]))/((-a)^(3/8)*Sqrt[b]) + (8*(-a)^(9/8)*(a + b)*((Sqrt[-a] + Sqrt[b])^(3/4)*(ArcTan[(-a + b/x^2)^(1/4)/((-a)^(1/8)*(Sqrt[-a] - Sqrt[b])^(1/4))] + ArcTanh[(-a + b/x^2)^(1/4)/((-a)^(1/8)*(Sqrt[-a] - Sqrt[b])^(1/4))]) - (Sqrt[-a] - Sqrt[b])^(3/4)*(ArcTan[(-a + b/x^2)^(1/4)/((-a)^(1/8)*(Sqrt[-a] + Sqrt[b])^(1/4))] + ArcTanh[(-a + b/x^2)^(1/4)/((-a)^(1/8)*(Sqrt[-a] + Sqrt[b])^(1/4))])))/((Sqrt[-a] - Sqrt[b])^(3/4)*(Sqrt[-a] + Sqrt[b])^(3/4)*Sqrt[b]) + (Sqrt[2]*(4*a^2 + b)*(Log[Sqrt[a] - Sqrt[2]*a^(1/4)*(-a + b/x^2)^(1/4) + Sqrt[-a + b/x^2]] - Log[Sqrt[a] + Sqrt[2]*a^(1/4)*(-a + b/x^2)^(1/4) + Sqrt[-a + b/x^2]]))/a^(3/4)))/(-b + a*x^2)))/(16*a)","B",1
2930,1,756,342,2.4926887,"\int \frac{\left(-b-a x^2+x^4\right) \sqrt[4]{-b x^2+a x^4}}{b+a x^4} \, dx","Integrate[((-b - a*x^2 + x^4)*(-(b*x^2) + a*x^4)^(1/4))/(b + a*x^4),x]","\frac{x \sqrt[4]{a x^4-b x^2} \left(8-\frac{\left(\frac{b}{x^2}-a\right)^{3/4} \left(\frac{8 \left(a^2+a b+b\right) \left(\sqrt[4]{\sqrt{-a}-\sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{-a} \sqrt[4]{\sqrt{-a}-\sqrt{b}}}\right)-\sqrt[4]{\sqrt{-a}+\sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{-a} \sqrt[4]{\sqrt{-a}+\sqrt{b}}}\right)+\sqrt[4]{\sqrt{-a}-\sqrt{b}} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{-a} \sqrt[4]{\sqrt{-a}-\sqrt{b}}}\right)-\sqrt[4]{\sqrt{-a}+\sqrt{b}} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{-a} \sqrt[4]{\sqrt{-a}+\sqrt{b}}}\right)\right)}{(-a)^{3/8} \sqrt{b}}+\frac{\sqrt{2} \left(4 a^2+b\right) \left(\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{\frac{b}{x^2}-a}+\sqrt{\frac{b}{x^2}-a}+\sqrt{a}\right)-\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{\frac{b}{x^2}-a}+\sqrt{\frac{b}{x^2}-a}+\sqrt{a}\right)\right)}{a^{3/4}}+\frac{2 \sqrt{2} \left(4 a^2+b\right) \left(\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[4]{a}}\right)-\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[4]{a}}+1\right)\right)}{a^{3/4}}+\frac{8 (-a)^{9/8} (a+b) \left(\left(\sqrt{-a}+\sqrt{b}\right)^{3/4} \left(\tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{-a} \sqrt[4]{\sqrt{-a}-\sqrt{b}}}\right)+\tanh ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{-a} \sqrt[4]{\sqrt{-a}-\sqrt{b}}}\right)\right)-\left(\sqrt{-a}-\sqrt{b}\right)^{3/4} \left(\tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{-a} \sqrt[4]{\sqrt{-a}+\sqrt{b}}}\right)+\tanh ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{-a} \sqrt[4]{\sqrt{-a}+\sqrt{b}}}\right)\right)\right)}{\sqrt{b} \left(\sqrt{-a}-\sqrt{b}\right)^{3/4} \left(\sqrt{-a}+\sqrt{b}\right)^{3/4}}\right)}{a x^2-b}\right)}{16 a}","-\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{-\text{$\#$1}^4 a^2 \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 a^2 \log (x)-\text{$\#$1}^4 a b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\text{$\#$1}^4 b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 a b \log (x)+\text{$\#$1}^4 b \log (x)+a^3 \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+a^2 b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-a^3 \log (x)-a^2 b \log (x)}{\text{$\#$1}^3 a-\text{$\#$1}^7}\&\right]}{4 a}+\frac{\left(4 a^2+b\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)}{4 a^{7/4}}+\frac{\left(-4 a^2-b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)}{4 a^{7/4}}+\frac{x \sqrt[4]{a x^4-b x^2}}{2 a}",1,"(x*(-(b*x^2) + a*x^4)^(1/4)*(8 - ((-a + b/x^2)^(3/4)*((2*Sqrt[2]*(4*a^2 + b)*(ArcTan[1 - (Sqrt[2]*(-a + b/x^2)^(1/4))/a^(1/4)] - ArcTan[1 + (Sqrt[2]*(-a + b/x^2)^(1/4))/a^(1/4)]))/a^(3/4) + (8*(a^2 + b + a*b)*((Sqrt[-a] - Sqrt[b])^(1/4)*ArcTan[(-a + b/x^2)^(1/4)/((-a)^(1/8)*(Sqrt[-a] - Sqrt[b])^(1/4))] - (Sqrt[-a] + Sqrt[b])^(1/4)*ArcTan[(-a + b/x^2)^(1/4)/((-a)^(1/8)*(Sqrt[-a] + Sqrt[b])^(1/4))] + (Sqrt[-a] - Sqrt[b])^(1/4)*ArcTanh[(-a + b/x^2)^(1/4)/((-a)^(1/8)*(Sqrt[-a] - Sqrt[b])^(1/4))] - (Sqrt[-a] + Sqrt[b])^(1/4)*ArcTanh[(-a + b/x^2)^(1/4)/((-a)^(1/8)*(Sqrt[-a] + Sqrt[b])^(1/4))]))/((-a)^(3/8)*Sqrt[b]) + (8*(-a)^(9/8)*(a + b)*((Sqrt[-a] + Sqrt[b])^(3/4)*(ArcTan[(-a + b/x^2)^(1/4)/((-a)^(1/8)*(Sqrt[-a] - Sqrt[b])^(1/4))] + ArcTanh[(-a + b/x^2)^(1/4)/((-a)^(1/8)*(Sqrt[-a] - Sqrt[b])^(1/4))]) - (Sqrt[-a] - Sqrt[b])^(3/4)*(ArcTan[(-a + b/x^2)^(1/4)/((-a)^(1/8)*(Sqrt[-a] + Sqrt[b])^(1/4))] + ArcTanh[(-a + b/x^2)^(1/4)/((-a)^(1/8)*(Sqrt[-a] + Sqrt[b])^(1/4))])))/((Sqrt[-a] - Sqrt[b])^(3/4)*(Sqrt[-a] + Sqrt[b])^(3/4)*Sqrt[b]) + (Sqrt[2]*(4*a^2 + b)*(Log[Sqrt[a] - Sqrt[2]*a^(1/4)*(-a + b/x^2)^(1/4) + Sqrt[-a + b/x^2]] - Log[Sqrt[a] + Sqrt[2]*a^(1/4)*(-a + b/x^2)^(1/4) + Sqrt[-a + b/x^2]]))/a^(3/4)))/(-b + a*x^2)))/(16*a)","B",1
2931,1,375,343,0.8235331,"\int \frac{a b c-b^2 x+a^2 x^2}{\sqrt{c+b x+a x^2} \left(c+b x^2\right)} \, dx","Integrate[(a*b*c - b^2*x + a^2*x^2)/(Sqrt[c + b*x + a*x^2]*(c + b*x^2)),x]","\frac{1}{2} \left(\frac{2 a^{3/2} \tanh ^{-1}\left(\frac{2 a x+b}{2 \sqrt{a} \sqrt{x (a x+b)+c}}\right)}{b}+\frac{\left(-a^2 \sqrt{c}+a b^2 \sqrt{c}+(-b)^{5/2}\right) \tan ^{-1}\left(\frac{2 a \sqrt{-b} \sqrt{c} x+b^2 (-x)-2 b c+\sqrt{-b} b \sqrt{c}}{2 \sqrt[4]{c} \sqrt{b \left(a \sqrt{c}+b \left(\sqrt{-b}-\sqrt{c}\right)\right)} \sqrt{x (a x+b)+c}}\right)}{\sqrt{-b} \sqrt[4]{c} \sqrt{b \left(a \sqrt{c}+b \left(\sqrt{-b}-\sqrt{c}\right)\right)}}+\frac{\left(a^2 \sqrt{c}-a b^2 \sqrt{c}+(-b)^{5/2}\right) \tanh ^{-1}\left(\frac{2 a \sqrt{-b} \sqrt{c} x+b^2 x+2 b c+\sqrt{-b} b \sqrt{c}}{2 \sqrt[4]{c} \sqrt{b \left(b \left(\sqrt{-b}+\sqrt{c}\right)-a \sqrt{c}\right)} \sqrt{x (a x+b)+c}}\right)}{\sqrt{-b} \sqrt[4]{c} \sqrt{b \left(b \left(\sqrt{-b}+\sqrt{c}\right)-a \sqrt{c}\right)}}\right)","\frac{\text{RootSum}\left[\text{$\#$1}^4 b+4 \text{$\#$1}^2 a c-2 \text{$\#$1}^2 b c-4 \text{$\#$1} \sqrt{a} b c+b^2 c+b c^2\&,\frac{\text{$\#$1}^2 b^3 \left(-\log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)\right)-2 \text{$\#$1} a^{3/2} b^2 c \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)+2 \text{$\#$1} a^{5/2} c \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)-a^2 b c \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)+a b^3 c \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)+b^3 c \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)}{\text{$\#$1}^3 b+2 \text{$\#$1} a c-\text{$\#$1} b c-\sqrt{a} b c}\&\right]}{2 b}-\frac{a^{3/2} \log \left(-2 \sqrt{a} \sqrt{a x^2+b x+c}+2 a x+b\right)}{b}",1,"((((-b)^(5/2) - a^2*Sqrt[c] + a*b^2*Sqrt[c])*ArcTan[(Sqrt[-b]*b*Sqrt[c] - 2*b*c - b^2*x + 2*a*Sqrt[-b]*Sqrt[c]*x)/(2*Sqrt[b*(b*(Sqrt[-b] - Sqrt[c]) + a*Sqrt[c])]*c^(1/4)*Sqrt[c + x*(b + a*x)])])/(Sqrt[-b]*Sqrt[b*(b*(Sqrt[-b] - Sqrt[c]) + a*Sqrt[c])]*c^(1/4)) + (2*a^(3/2)*ArcTanh[(b + 2*a*x)/(2*Sqrt[a]*Sqrt[c + x*(b + a*x)])])/b + (((-b)^(5/2) + a^2*Sqrt[c] - a*b^2*Sqrt[c])*ArcTanh[(Sqrt[-b]*b*Sqrt[c] + 2*b*c + b^2*x + 2*a*Sqrt[-b]*Sqrt[c]*x)/(2*Sqrt[b*(b*(Sqrt[-b] + Sqrt[c]) - a*Sqrt[c])]*c^(1/4)*Sqrt[c + x*(b + a*x)])])/(Sqrt[-b]*Sqrt[b*(b*(Sqrt[-b] + Sqrt[c]) - a*Sqrt[c])]*c^(1/4)))/2","A",1
2932,1,736,343,3.8502709,"\int \frac{\left(b+a x^2+x^4\right) \sqrt[4]{-b x^2+a x^4}}{-b+a x^4} \, dx","Integrate[((b + a*x^2 + x^4)*(-(b*x^2) + a*x^4)^(1/4))/(-b + a*x^4),x]","\frac{x \sqrt[4]{a x^4-b x^2} \left(8 a^{7/8}-\frac{\left(\frac{b}{x^2}-a\right)^{3/4} \left(-\sqrt{2} \sqrt[8]{a} \left(4 a^2-b\right) \left(\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{\frac{b}{x^2}-a}+\sqrt{\frac{b}{x^2}-a}+\sqrt{a}\right)-\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{\frac{b}{x^2}-a}+\sqrt{\frac{b}{x^2}-a}+\sqrt{a}\right)\right)-2 \sqrt{2} \sqrt[8]{a} \left(4 a^2-b\right) \left(\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[4]{a}}\right)-\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[4]{a}}+1\right)\right)-\frac{8 \left(a^2 (a-b) \left(\left(\sqrt{b}-\sqrt{a}\right)^{3/4} \left(\tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{a} \sqrt[4]{-\sqrt{a}-\sqrt{b}}}\right)+\tanh ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{a} \sqrt[4]{-\sqrt{a}-\sqrt{b}}}\right)\right)-\left(-\sqrt{a}-\sqrt{b}\right)^{3/4} \left(\tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{a} \sqrt[4]{\sqrt{b}-\sqrt{a}}}\right)+\tanh ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{a} \sqrt[4]{\sqrt{b}-\sqrt{a}}}\right)\right)\right)-\sqrt{a} \left(a^2-a b-b\right) \left(\left(\sqrt{b}-\sqrt{a}\right)^{3/4} \left(\sqrt{a}+\sqrt{b}\right) \left(\tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{a} \sqrt[4]{-\sqrt{a}-\sqrt{b}}}\right)+\tanh ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{a} \sqrt[4]{-\sqrt{a}-\sqrt{b}}}\right)\right)-\left(-\sqrt{a}-\sqrt{b}\right)^{3/4} \left(\sqrt{a}-\sqrt{b}\right) \left(\tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{a} \sqrt[4]{\sqrt{b}-\sqrt{a}}}\right)+\tanh ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{a} \sqrt[4]{\sqrt{b}-\sqrt{a}}}\right)\right)\right)\right)}{\sqrt{b} \left(-\sqrt{a}-\sqrt{b}\right)^{3/4} \left(\sqrt{b}-\sqrt{a}\right)^{3/4}}\right)}{a x^2-b}\right)}{16 a^{15/8}}","\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2-a b\&,\frac{-\text{$\#$1}^4 a^2 \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 a^2 \log (x)+\text{$\#$1}^4 a b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\text{$\#$1}^4 a b \log (x)-\text{$\#$1}^4 b \log (x)+a^3 \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-a^2 b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-a^3 \log (x)+a^2 b \log (x)}{\text{$\#$1}^3 a-\text{$\#$1}^7}\&\right]}{4 a}+\frac{\left(b-4 a^2\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)}{4 a^{7/4}}+\frac{\left(4 a^2-b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)}{4 a^{7/4}}+\frac{x \sqrt[4]{a x^4-b x^2}}{2 a}",1,"(x*(-(b*x^2) + a*x^4)^(1/4)*(8*a^(7/8) - ((-a + b/x^2)^(3/4)*(-2*Sqrt[2]*a^(1/8)*(4*a^2 - b)*(ArcTan[1 - (Sqrt[2]*(-a + b/x^2)^(1/4))/a^(1/4)] - ArcTan[1 + (Sqrt[2]*(-a + b/x^2)^(1/4))/a^(1/4)]) - (8*(a^2*(a - b)*((-Sqrt[a] + Sqrt[b])^(3/4)*(ArcTan[(-a + b/x^2)^(1/4)/(a^(1/8)*(-Sqrt[a] - Sqrt[b])^(1/4))] + ArcTanh[(-a + b/x^2)^(1/4)/(a^(1/8)*(-Sqrt[a] - Sqrt[b])^(1/4))]) - (-Sqrt[a] - Sqrt[b])^(3/4)*(ArcTan[(-a + b/x^2)^(1/4)/(a^(1/8)*(-Sqrt[a] + Sqrt[b])^(1/4))] + ArcTanh[(-a + b/x^2)^(1/4)/(a^(1/8)*(-Sqrt[a] + Sqrt[b])^(1/4))])) - Sqrt[a]*(a^2 - b - a*b)*((-Sqrt[a] + Sqrt[b])^(3/4)*(Sqrt[a] + Sqrt[b])*(ArcTan[(-a + b/x^2)^(1/4)/(a^(1/8)*(-Sqrt[a] - Sqrt[b])^(1/4))] + ArcTanh[(-a + b/x^2)^(1/4)/(a^(1/8)*(-Sqrt[a] - Sqrt[b])^(1/4))]) - (-Sqrt[a] - Sqrt[b])^(3/4)*(Sqrt[a] - Sqrt[b])*(ArcTan[(-a + b/x^2)^(1/4)/(a^(1/8)*(-Sqrt[a] + Sqrt[b])^(1/4))] + ArcTanh[(-a + b/x^2)^(1/4)/(a^(1/8)*(-Sqrt[a] + Sqrt[b])^(1/4))]))))/((-Sqrt[a] - Sqrt[b])^(3/4)*(-Sqrt[a] + Sqrt[b])^(3/4)*Sqrt[b]) - Sqrt[2]*a^(1/8)*(4*a^2 - b)*(Log[Sqrt[a] - Sqrt[2]*a^(1/4)*(-a + b/x^2)^(1/4) + Sqrt[-a + b/x^2]] - Log[Sqrt[a] + Sqrt[2]*a^(1/4)*(-a + b/x^2)^(1/4) + Sqrt[-a + b/x^2]])))/(-b + a*x^2)))/(16*a^(15/8))","B",1
2933,1,736,343,1.5137888,"\int \frac{\left(b+a x^2+x^4\right) \sqrt[4]{-b x^2+a x^4}}{-b+a x^4} \, dx","Integrate[((b + a*x^2 + x^4)*(-(b*x^2) + a*x^4)^(1/4))/(-b + a*x^4),x]","\frac{x \sqrt[4]{a x^4-b x^2} \left(8 a^{7/8}-\frac{\left(\frac{b}{x^2}-a\right)^{3/4} \left(-\sqrt{2} \sqrt[8]{a} \left(4 a^2-b\right) \left(\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{\frac{b}{x^2}-a}+\sqrt{\frac{b}{x^2}-a}+\sqrt{a}\right)-\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{\frac{b}{x^2}-a}+\sqrt{\frac{b}{x^2}-a}+\sqrt{a}\right)\right)-2 \sqrt{2} \sqrt[8]{a} \left(4 a^2-b\right) \left(\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[4]{a}}\right)-\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[4]{a}}+1\right)\right)-\frac{8 \left(a^2 (a-b) \left(\left(\sqrt{b}-\sqrt{a}\right)^{3/4} \left(\tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{a} \sqrt[4]{-\sqrt{a}-\sqrt{b}}}\right)+\tanh ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{a} \sqrt[4]{-\sqrt{a}-\sqrt{b}}}\right)\right)-\left(-\sqrt{a}-\sqrt{b}\right)^{3/4} \left(\tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{a} \sqrt[4]{\sqrt{b}-\sqrt{a}}}\right)+\tanh ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{a} \sqrt[4]{\sqrt{b}-\sqrt{a}}}\right)\right)\right)-\sqrt{a} \left(a^2-a b-b\right) \left(\left(\sqrt{b}-\sqrt{a}\right)^{3/4} \left(\sqrt{a}+\sqrt{b}\right) \left(\tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{a} \sqrt[4]{-\sqrt{a}-\sqrt{b}}}\right)+\tanh ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{a} \sqrt[4]{-\sqrt{a}-\sqrt{b}}}\right)\right)-\left(-\sqrt{a}-\sqrt{b}\right)^{3/4} \left(\sqrt{a}-\sqrt{b}\right) \left(\tan ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{a} \sqrt[4]{\sqrt{b}-\sqrt{a}}}\right)+\tanh ^{-1}\left(\frac{\sqrt[4]{\frac{b}{x^2}-a}}{\sqrt[8]{a} \sqrt[4]{\sqrt{b}-\sqrt{a}}}\right)\right)\right)\right)}{\sqrt{b} \left(-\sqrt{a}-\sqrt{b}\right)^{3/4} \left(\sqrt{b}-\sqrt{a}\right)^{3/4}}\right)}{a x^2-b}\right)}{16 a^{15/8}}","\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2-a b\&,\frac{-\text{$\#$1}^4 a^2 \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 a^2 \log (x)+\text{$\#$1}^4 a b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\text{$\#$1}^4 a b \log (x)-\text{$\#$1}^4 b \log (x)+a^3 \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-a^2 b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-a^3 \log (x)+a^2 b \log (x)}{\text{$\#$1}^3 a-\text{$\#$1}^7}\&\right]}{4 a}+\frac{\left(b-4 a^2\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)}{4 a^{7/4}}+\frac{\left(4 a^2-b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)}{4 a^{7/4}}+\frac{x \sqrt[4]{a x^4-b x^2}}{2 a}",1,"(x*(-(b*x^2) + a*x^4)^(1/4)*(8*a^(7/8) - ((-a + b/x^2)^(3/4)*(-2*Sqrt[2]*a^(1/8)*(4*a^2 - b)*(ArcTan[1 - (Sqrt[2]*(-a + b/x^2)^(1/4))/a^(1/4)] - ArcTan[1 + (Sqrt[2]*(-a + b/x^2)^(1/4))/a^(1/4)]) - (8*(a^2*(a - b)*((-Sqrt[a] + Sqrt[b])^(3/4)*(ArcTan[(-a + b/x^2)^(1/4)/(a^(1/8)*(-Sqrt[a] - Sqrt[b])^(1/4))] + ArcTanh[(-a + b/x^2)^(1/4)/(a^(1/8)*(-Sqrt[a] - Sqrt[b])^(1/4))]) - (-Sqrt[a] - Sqrt[b])^(3/4)*(ArcTan[(-a + b/x^2)^(1/4)/(a^(1/8)*(-Sqrt[a] + Sqrt[b])^(1/4))] + ArcTanh[(-a + b/x^2)^(1/4)/(a^(1/8)*(-Sqrt[a] + Sqrt[b])^(1/4))])) - Sqrt[a]*(a^2 - b - a*b)*((-Sqrt[a] + Sqrt[b])^(3/4)*(Sqrt[a] + Sqrt[b])*(ArcTan[(-a + b/x^2)^(1/4)/(a^(1/8)*(-Sqrt[a] - Sqrt[b])^(1/4))] + ArcTanh[(-a + b/x^2)^(1/4)/(a^(1/8)*(-Sqrt[a] - Sqrt[b])^(1/4))]) - (-Sqrt[a] - Sqrt[b])^(3/4)*(Sqrt[a] - Sqrt[b])*(ArcTan[(-a + b/x^2)^(1/4)/(a^(1/8)*(-Sqrt[a] + Sqrt[b])^(1/4))] + ArcTanh[(-a + b/x^2)^(1/4)/(a^(1/8)*(-Sqrt[a] + Sqrt[b])^(1/4))]))))/((-Sqrt[a] - Sqrt[b])^(3/4)*(-Sqrt[a] + Sqrt[b])^(3/4)*Sqrt[b]) - Sqrt[2]*a^(1/8)*(4*a^2 - b)*(Log[Sqrt[a] - Sqrt[2]*a^(1/4)*(-a + b/x^2)^(1/4) + Sqrt[-a + b/x^2]] - Log[Sqrt[a] + Sqrt[2]*a^(1/4)*(-a + b/x^2)^(1/4) + Sqrt[-a + b/x^2]])))/(-b + a*x^2)))/(16*a^(15/8))","B",1
2934,0,0,343,4.5892219,"\int \frac{(-1+(-1+2 k) x) \left(1-2 x+x^2\right)}{\sqrt[3]{(1-x) x (1-k x)} \left(-b+4 b x+(1-6 b) x^2+(4 b-2 k) x^3+\left(-b+k^2\right) x^4\right)} \, dx","Integrate[((-1 + (-1 + 2*k)*x)*(1 - 2*x + x^2))/(((1 - x)*x*(1 - k*x))^(1/3)*(-b + 4*b*x + (1 - 6*b)*x^2 + (4*b - 2*k)*x^3 + (-b + k^2)*x^4)),x]","\int \frac{(-1+(-1+2 k) x) \left(1-2 x+x^2\right)}{\sqrt[3]{(1-x) x (1-k x)} \left(-b+4 b x+(1-6 b) x^2+(4 b-2 k) x^3+\left(-b+k^2\right) x^4\right)} \, dx","-\frac{\log \left(-\sqrt[6]{b} x+\sqrt[6]{b}+\sqrt[3]{k x^3+(-k-1) x^2+x}\right)}{2 b^{2/3}}-\frac{\log \left(\sqrt[6]{b} x-\sqrt[6]{b}+\sqrt[3]{k x^3+(-k-1) x^2+x}\right)}{2 b^{2/3}}+\frac{\log \left(\left(\sqrt[6]{b}-\sqrt[6]{b} x\right) \sqrt[3]{k x^3+(-k-1) x^2+x}+\sqrt[3]{b} x^2-2 \sqrt[3]{b} x+\sqrt[3]{b}+\left(k x^3+(-k-1) x^2+x\right)^{2/3}\right)}{4 b^{2/3}}+\frac{\log \left(\left(\sqrt[6]{b} x-\sqrt[6]{b}\right) \sqrt[3]{k x^3+(-k-1) x^2+x}+\sqrt[3]{b} x^2-2 \sqrt[3]{b} x+\sqrt[3]{b}+\left(k x^3+(-k-1) x^2+x\right)^{2/3}\right)}{4 b^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \left(k x^3+(-k-1) x^2+x\right)^{2/3}}{\sqrt{3} \sqrt[3]{b}}+\frac{x^2}{\sqrt{3}}-\frac{2 x}{\sqrt{3}}+\frac{1}{\sqrt{3}}}{(x-1)^2}\right)}{2 b^{2/3}}",1,"Integrate[((-1 + (-1 + 2*k)*x)*(1 - 2*x + x^2))/(((1 - x)*x*(1 - k*x))^(1/3)*(-b + 4*b*x + (1 - 6*b)*x^2 + (4*b - 2*k)*x^3 + (-b + k^2)*x^4)), x]","F",-1
2935,0,0,345,0.8272748,"\int \frac{1}{(b+a x) \sqrt[4]{b^2 x+a^2 x^3}} \, dx","Integrate[1/((b + a*x)*(b^2*x + a^2*x^3)^(1/4)),x]","\int \frac{1}{(b+a x) \sqrt[4]{b^2 x+a^2 x^3}} \, dx","\frac{\tan ^{-1}\left(\frac{2 \sqrt[4]{a} \sqrt[4]{b} \sqrt[4]{a^2 x^3+b^2 x}}{2 \sqrt[4]{a} \sqrt[4]{b} \sqrt[4]{a^2 x^3+b^2 x}-2^{3/4} a x+2^{3/4} b}\right)}{2\ 2^{3/4} a^{3/4} b^{3/4}}-\frac{\tan ^{-1}\left(\frac{2 \sqrt[4]{a} \sqrt[4]{b} \sqrt[4]{a^2 x^3+b^2 x}}{2 \sqrt[4]{a} \sqrt[4]{b} \sqrt[4]{a^2 x^3+b^2 x}+2^{3/4} a x-2^{3/4} b}\right)}{2\ 2^{3/4} a^{3/4} b^{3/4}}-\frac{\tanh ^{-1}\left(\frac{-2 \sqrt[4]{2} \sqrt{a} \sqrt{b} \sqrt{a^2 x^3+b^2 x}-\frac{a^2 x^2}{\sqrt[4]{2}}+2^{3/4} a b x-\frac{b^2}{\sqrt[4]{2}}}{2 a^{5/4} \sqrt[4]{b} x \sqrt[4]{a^2 x^3+b^2 x}-2 \sqrt[4]{a} b^{5/4} \sqrt[4]{a^2 x^3+b^2 x}}\right)}{2\ 2^{3/4} a^{3/4} b^{3/4}}",1,"Integrate[1/((b + a*x)*(b^2*x + a^2*x^3)^(1/4)), x]","F",-1
2936,1,447,346,2.7483256,"\int \frac{\left(-b+a x^4\right) \sqrt[4]{-b x^2+a x^4}}{-b-a x^2+x^4} \, dx","Integrate[((-b + a*x^4)*(-(b*x^2) + a*x^4)^(1/4))/(-b - a*x^2 + x^4),x]","\frac{\sqrt[4]{a x^4-b x^2} \left(4 a^3 x^5+(4-3 a) b^2 x+a b x^3 \left(a-x^2-4\right)\right) \left(\frac{3 \sqrt[4]{a} \left(4 a^2-b\right) \left(\tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)-\tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)\right)}{x^{3/2} \sqrt[4]{a x^2-b}}+\frac{8 \left(a^4+\frac{-a^5-2 a^3 b+a^2 b+2 a b^2-2 b^2}{\sqrt{a^2+4 b}}-a b\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};-\frac{b \left(\frac{a}{b}+\frac{2}{\sqrt{a^2+4 b}-a}\right) x^2}{b-a x^2}\right)}{\left(a-\sqrt{a^2+4 b}\right) \left(a x^2-b\right)}+\frac{8 \left(a^4+\frac{a^5+2 a^3 b-a^2 b-2 a b^2+2 b^2}{\sqrt{a^2+4 b}}-a b\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};-\frac{b \left(\frac{a}{b}-\frac{2}{a+\sqrt{a^2+4 b}}\right) x^2}{b-a x^2}\right)}{\left(\sqrt{a^2+4 b}+a\right) \left(a x^2-b\right)}\right)}{12 \left(-4 a^3 x^4+(3 a-4) b^2+a b x^2 \left(-a+x^2+4\right)\right)}+\frac{1}{2} a x \sqrt[4]{a x^4-b x^2}","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4 a+2 a^2-b\&,\frac{-\text{$\#$1}^4 a^3 \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 a^3 \log (x)+\text{$\#$1}^4 a b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\text{$\#$1}^4 b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\text{$\#$1}^4 a b \log (x)+\text{$\#$1}^4 b \log (x)+2 a^4 \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-a^2 b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-2 a^4 \log (x)+a^2 b \log (x)}{3 \text{$\#$1}^3 a-2 \text{$\#$1}^7}\&\right]+\frac{1}{4} \left(\sqrt[4]{a} b-4 a^{9/4}\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)+\frac{1}{4} \left(4 a^{9/4}-\sqrt[4]{a} b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)+\frac{1}{2} a x \sqrt[4]{a x^4-b x^2}",1,"(a*x*(-(b*x^2) + a*x^4)^(1/4))/2 + ((-(b*x^2) + a*x^4)^(1/4)*((4 - 3*a)*b^2*x + 4*a^3*x^5 + a*b*x^3*(-4 + a - x^2))*((3*a^(1/4)*(4*a^2 - b)*(ArcTan[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)] - ArcTanh[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)]))/(x^(3/2)*(-b + a*x^2)^(1/4)) + (8*(a^4 - a*b + (-a^5 + a^2*b - 2*a^3*b - 2*b^2 + 2*a*b^2)/Sqrt[a^2 + 4*b])*Hypergeometric2F1[3/4, 1, 7/4, -((b*(a/b + 2/(-a + Sqrt[a^2 + 4*b]))*x^2)/(b - a*x^2))])/((a - Sqrt[a^2 + 4*b])*(-b + a*x^2)) + (8*(a^4 - a*b + (a^5 - a^2*b + 2*a^3*b + 2*b^2 - 2*a*b^2)/Sqrt[a^2 + 4*b])*Hypergeometric2F1[3/4, 1, 7/4, -((b*(a/b - 2/(a + Sqrt[a^2 + 4*b]))*x^2)/(b - a*x^2))])/((a + Sqrt[a^2 + 4*b])*(-b + a*x^2))))/(12*((-4 + 3*a)*b^2 - 4*a^3*x^4 + a*b*x^2*(4 - a + x^2)))","A",1
2937,1,447,346,0.7199206,"\int \frac{\left(-b+a x^4\right) \sqrt[4]{-b x^2+a x^4}}{-b-a x^2+x^4} \, dx","Integrate[((-b + a*x^4)*(-(b*x^2) + a*x^4)^(1/4))/(-b - a*x^2 + x^4),x]","\frac{\sqrt[4]{a x^4-b x^2} \left(4 a^3 x^5+(4-3 a) b^2 x+a b x^3 \left(a-x^2-4\right)\right) \left(\frac{3 \sqrt[4]{a} \left(4 a^2-b\right) \left(\tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)-\tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)\right)}{x^{3/2} \sqrt[4]{a x^2-b}}+\frac{8 \left(a^4+\frac{-a^5-2 a^3 b+a^2 b+2 a b^2-2 b^2}{\sqrt{a^2+4 b}}-a b\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};-\frac{b \left(\frac{a}{b}+\frac{2}{\sqrt{a^2+4 b}-a}\right) x^2}{b-a x^2}\right)}{\left(a-\sqrt{a^2+4 b}\right) \left(a x^2-b\right)}+\frac{8 \left(a^4+\frac{a^5+2 a^3 b-a^2 b-2 a b^2+2 b^2}{\sqrt{a^2+4 b}}-a b\right) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};-\frac{b \left(\frac{a}{b}-\frac{2}{a+\sqrt{a^2+4 b}}\right) x^2}{b-a x^2}\right)}{\left(\sqrt{a^2+4 b}+a\right) \left(a x^2-b\right)}\right)}{12 \left(-4 a^3 x^4+(3 a-4) b^2+a b x^2 \left(-a+x^2+4\right)\right)}+\frac{1}{2} a x \sqrt[4]{a x^4-b x^2}","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4 a+2 a^2-b\&,\frac{-\text{$\#$1}^4 a^3 \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 a^3 \log (x)+\text{$\#$1}^4 a b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\text{$\#$1}^4 b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\text{$\#$1}^4 a b \log (x)+\text{$\#$1}^4 b \log (x)+2 a^4 \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-a^2 b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-2 a^4 \log (x)+a^2 b \log (x)}{3 \text{$\#$1}^3 a-2 \text{$\#$1}^7}\&\right]+\frac{1}{4} \left(\sqrt[4]{a} b-4 a^{9/4}\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)+\frac{1}{4} \left(4 a^{9/4}-\sqrt[4]{a} b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)+\frac{1}{2} a x \sqrt[4]{a x^4-b x^2}",1,"(a*x*(-(b*x^2) + a*x^4)^(1/4))/2 + ((-(b*x^2) + a*x^4)^(1/4)*((4 - 3*a)*b^2*x + 4*a^3*x^5 + a*b*x^3*(-4 + a - x^2))*((3*a^(1/4)*(4*a^2 - b)*(ArcTan[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)] - ArcTanh[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)]))/(x^(3/2)*(-b + a*x^2)^(1/4)) + (8*(a^4 - a*b + (-a^5 + a^2*b - 2*a^3*b - 2*b^2 + 2*a*b^2)/Sqrt[a^2 + 4*b])*Hypergeometric2F1[3/4, 1, 7/4, -((b*(a/b + 2/(-a + Sqrt[a^2 + 4*b]))*x^2)/(b - a*x^2))])/((a - Sqrt[a^2 + 4*b])*(-b + a*x^2)) + (8*(a^4 - a*b + (a^5 - a^2*b + 2*a^3*b + 2*b^2 - 2*a*b^2)/Sqrt[a^2 + 4*b])*Hypergeometric2F1[3/4, 1, 7/4, -((b*(a/b - 2/(a + Sqrt[a^2 + 4*b]))*x^2)/(b - a*x^2))])/((a + Sqrt[a^2 + 4*b])*(-b + a*x^2))))/(12*((-4 + 3*a)*b^2 - 4*a^3*x^4 + a*b*x^2*(4 - a + x^2)))","A",1
2938,0,0,347,2.3048463,"\int \frac{(-b+x) (-4 a+b+3 x)}{\sqrt[3]{(-a+x) (-b+x)^2} \left(a+b^4 d-\left(1+4 b^3 d\right) x+6 b^2 d x^2-4 b d x^3+d x^4\right)} \, dx","Integrate[((-b + x)*(-4*a + b + 3*x))/(((-a + x)*(-b + x)^2)^(1/3)*(a + b^4*d - (1 + 4*b^3*d)*x + 6*b^2*d*x^2 - 4*b*d*x^3 + d*x^4)),x]","\int \frac{(-b+x) (-4 a+b+3 x)}{\sqrt[3]{(-a+x) (-b+x)^2} \left(a+b^4 d-\left(1+4 b^3 d\right) x+6 b^2 d x^2-4 b d x^3+d x^4\right)} \, dx","\frac{\log \left(-\sqrt[6]{d} \sqrt[3]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3}+b^2 \sqrt{d}-2 b \sqrt{d} x+\sqrt{d} x^2\right)}{\sqrt[3]{d}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3}}{\sqrt[3]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3}+2 b^2 \sqrt[3]{d}-4 b \sqrt[3]{d} x+2 \sqrt[3]{d} x^2}\right)}{\sqrt[3]{d}}-\frac{\log \left(\sqrt[3]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3} \left(b^2 d^{2/3}-2 b d^{2/3} x+d^{2/3} x^2\right)+\sqrt[3]{d} \left(x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3\right)^{2/3}+b^4 d-4 b^3 d x+6 b^2 d x^2-4 b d x^3+d x^4\right)}{2 \sqrt[3]{d}}",1,"Integrate[((-b + x)*(-4*a + b + 3*x))/(((-a + x)*(-b + x)^2)^(1/3)*(a + b^4*d - (1 + 4*b^3*d)*x + 6*b^2*d*x^2 - 4*b*d*x^3 + d*x^4)), x]","F",-1
2939,1,205,348,0.7200626,"\int \frac{\left(d+c x^2\right) \sqrt{a x+\sqrt{b^2+a^2 x^2}}}{f+e x^2} \, dx","Integrate[((d + c*x^2)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(f + e*x^2),x]","\frac{3 a (d e-c f) \text{RootSum}\left[\text{$\#$1}^8 e+4 \text{$\#$1}^4 a^2 f-2 \text{$\#$1}^4 b^2 e+b^4 e\&,\frac{\text{$\#$1}^4 \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)+b^2 \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)}{\text{$\#$1}^5 e+2 \text{$\#$1} a^2 f-\text{$\#$1} b^2 e}\&\right]+\frac{4 c \left(a x \left(\sqrt{a^2 x^2+b^2}+a x\right)-b^2\right)}{a \sqrt{\sqrt{a^2 x^2+b^2}+a x}}}{6 e}","-\frac{a c f \text{RootSum}\left[\text{$\#$1}^8 e+4 \text{$\#$1}^4 a^2 f-2 \text{$\#$1}^4 b^2 e+b^4 e\&,\frac{\text{$\#$1}^4 \left(-\log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)\right)-b^2 \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)}{\text{$\#$1}^5 (-e)-2 \text{$\#$1} a^2 f+\text{$\#$1} b^2 e}\&\right]}{2 e}+\frac{1}{2} a d \text{RootSum}\left[\text{$\#$1}^8 e+4 \text{$\#$1}^4 a^2 f-2 \text{$\#$1}^4 b^2 e+b^4 e\&,\frac{\text{$\#$1}^4 \left(-\log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)\right)-b^2 \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)}{\text{$\#$1}^5 (-e)-2 \text{$\#$1} a^2 f+\text{$\#$1} b^2 e}\&\right]-\frac{b^2 c}{a e \sqrt{\sqrt{a^2 x^2+b^2}+a x}}+\frac{c \left(\sqrt{a^2 x^2+b^2}+a x\right)^{3/2}}{3 a e}",1,"((4*c*(-b^2 + a*x*(a*x + Sqrt[b^2 + a^2*x^2])))/(a*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]) + 3*a*(d*e - c*f)*RootSum[b^4*e - 2*b^2*e*#1^4 + 4*a^2*f*#1^4 + e*#1^8 & , (b^2*Log[Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] - #1] + Log[Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] - #1]*#1^4)/(-(b^2*e*#1) + 2*a^2*f*#1 + e*#1^5) & ])/(6*e)","A",1
2940,0,0,349,0.747554,"\int \frac{\left(1+x^2\right) \sqrt{x^2+\sqrt{1+x^4}}}{\sqrt{1+x^4} \left(-1+x^2+x^4\right)} \, dx","Integrate[((1 + x^2)*Sqrt[x^2 + Sqrt[1 + x^4]])/(Sqrt[1 + x^4]*(-1 + x^2 + x^4)),x]","\int \frac{\left(1+x^2\right) \sqrt{x^2+\sqrt{1+x^4}}}{\sqrt{1+x^4} \left(-1+x^2+x^4\right)} \, dx","-\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^6-6 \text{$\#$1}^4+2 \text{$\#$1}^2+1\&,\frac{\text{$\#$1}^6 \left(-\log \left(\sqrt{x^4+1}+x^2-1\right)\right)+\text{$\#$1}^6 \log \left(\text{$\#$1} \sqrt{x^4+1}+\text{$\#$1} x^2-\text{$\#$1}+\sqrt{2} \sqrt{\sqrt{x^4+1}+x^2} x\right)-3 \text{$\#$1}^4 \log \left(\sqrt{x^4+1}+x^2-1\right)+3 \text{$\#$1}^4 \log \left(\text{$\#$1} \sqrt{x^4+1}+\text{$\#$1} x^2-\text{$\#$1}+\sqrt{2} \sqrt{\sqrt{x^4+1}+x^2} x\right)-\text{$\#$1}^2 \log \left(\sqrt{x^4+1}+x^2-1\right)+\text{$\#$1}^2 \log \left(\text{$\#$1} \sqrt{x^4+1}+\text{$\#$1} x^2-\text{$\#$1}+\sqrt{2} \sqrt{\sqrt{x^4+1}+x^2} x\right)-\log \left(\text{$\#$1} \sqrt{x^4+1}+\text{$\#$1} x^2-\text{$\#$1}+\sqrt{2} \sqrt{\sqrt{x^4+1}+x^2} x\right)+\log \left(\sqrt{x^4+1}+x^2-1\right)}{2 \text{$\#$1}^7-3 \text{$\#$1}^5-6 \text{$\#$1}^3+\text{$\#$1}}\&\right]}{2 \sqrt{2}}",1,"Integrate[((1 + x^2)*Sqrt[x^2 + Sqrt[1 + x^4]])/(Sqrt[1 + x^4]*(-1 + x^2 + x^4)), x]","F",-1
2941,0,0,349,0.3618986,"\int \frac{\left(1+x^2\right) \sqrt{x^2+\sqrt{1+x^4}}}{\sqrt{1+x^4} \left(-1+x^2+x^4\right)} \, dx","Integrate[((1 + x^2)*Sqrt[x^2 + Sqrt[1 + x^4]])/(Sqrt[1 + x^4]*(-1 + x^2 + x^4)),x]","\int \frac{\left(1+x^2\right) \sqrt{x^2+\sqrt{1+x^4}}}{\sqrt{1+x^4} \left(-1+x^2+x^4\right)} \, dx","-\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^6-6 \text{$\#$1}^4+2 \text{$\#$1}^2+1\&,\frac{\text{$\#$1}^6 \left(-\log \left(\sqrt{x^4+1}+x^2-1\right)\right)+\text{$\#$1}^6 \log \left(\text{$\#$1} \sqrt{x^4+1}+\text{$\#$1} x^2-\text{$\#$1}+\sqrt{2} \sqrt{\sqrt{x^4+1}+x^2} x\right)-3 \text{$\#$1}^4 \log \left(\sqrt{x^4+1}+x^2-1\right)+3 \text{$\#$1}^4 \log \left(\text{$\#$1} \sqrt{x^4+1}+\text{$\#$1} x^2-\text{$\#$1}+\sqrt{2} \sqrt{\sqrt{x^4+1}+x^2} x\right)-\text{$\#$1}^2 \log \left(\sqrt{x^4+1}+x^2-1\right)+\text{$\#$1}^2 \log \left(\text{$\#$1} \sqrt{x^4+1}+\text{$\#$1} x^2-\text{$\#$1}+\sqrt{2} \sqrt{\sqrt{x^4+1}+x^2} x\right)-\log \left(\text{$\#$1} \sqrt{x^4+1}+\text{$\#$1} x^2-\text{$\#$1}+\sqrt{2} \sqrt{\sqrt{x^4+1}+x^2} x\right)+\log \left(\sqrt{x^4+1}+x^2-1\right)}{2 \text{$\#$1}^7-3 \text{$\#$1}^5-6 \text{$\#$1}^3+\text{$\#$1}}\&\right]}{2 \sqrt{2}}",1,"Integrate[((1 + x^2)*Sqrt[x^2 + Sqrt[1 + x^4]])/(Sqrt[1 + x^4]*(-1 + x^2 + x^4)), x]","F",-1
2942,0,0,351,0.2485967,"\int \frac{1-x^4}{\left(1+x^2+x^4\right) \sqrt[4]{-x^3+x^5}} \, dx","Integrate[(1 - x^4)/((1 + x^2 + x^4)*(-x^3 + x^5)^(1/4)),x]","\int \frac{1-x^4}{\left(1+x^2+x^4\right) \sqrt[4]{-x^3+x^5}} \, dx","\frac{\tan ^{-1}\left(\frac{3^{7/8} \sqrt{2-\sqrt{2}} x \sqrt[4]{x^5-x^3}}{3^{3/4} \sqrt{x^5-x^3}-3 x^2}\right)}{2^{3/4} \sqrt[8]{3 \left(17+12 \sqrt{2}\right)}}+\frac{\sqrt[8]{\frac{1}{3} \left(17+12 \sqrt{2}\right)} \tan ^{-1}\left(\frac{3^{7/8} \sqrt{2+\sqrt{2}} x \sqrt[4]{x^5-x^3}}{3^{3/4} \sqrt{x^5-x^3}-3 x^2}\right)}{2^{3/4}}+\frac{\tanh ^{-1}\left(\frac{\frac{\sqrt[8]{3} x^2}{\sqrt{2-\sqrt{2}}}+\frac{\sqrt{x^5-x^3}}{\sqrt[8]{3} \sqrt{2-\sqrt{2}}}}{x \sqrt[4]{x^5-x^3}}\right)}{2^{3/4} \sqrt[8]{3 \left(17+12 \sqrt{2}\right)}}+\frac{\sqrt[8]{\frac{1}{3} \left(17+12 \sqrt{2}\right)} \tanh ^{-1}\left(\frac{\frac{\sqrt[8]{3} x^2}{\sqrt{2+\sqrt{2}}}+\frac{\sqrt{x^5-x^3}}{\sqrt[8]{3} \sqrt{2+\sqrt{2}}}}{x \sqrt[4]{x^5-x^3}}\right)}{2^{3/4}}",1,"Integrate[(1 - x^4)/((1 + x^2 + x^4)*(-x^3 + x^5)^(1/4)), x]","F",-1
2943,1,12131,351,24.9069211,"\int \frac{\sqrt{-b+a^2 x^2}}{\sqrt[3]{a x^2+x \sqrt{-b+a^2 x^2}}} \, dx","Integrate[Sqrt[-b + a^2*x^2]/(a*x^2 + x*Sqrt[-b + a^2*x^2])^(1/3),x]","\text{Result too large to show}","\frac{a x \sqrt{a^2 x^2-b} \left(x \sqrt{a^2 x^2-b}+a x^2\right)^{2/3}}{2 b}+\frac{\left(5 b-4 a^2 x^2\right) \left(x \sqrt{a^2 x^2-b}+a x^2\right)^{2/3}}{8 b}-\frac{7 b^{2/3} \log \left(\frac{\sqrt[3]{2} \sqrt[3]{a} \sqrt[3]{x \sqrt{a^2 x^2-b}+a x^2}}{\sqrt[3]{b}}-1\right)}{12\ 2^{2/3} a^{2/3}}+\frac{7 b^{2/3} \log \left(\frac{\sqrt[3]{2} \sqrt[3]{a} \sqrt[3]{x \sqrt{a^2 x^2-b}+a x^2}}{\sqrt[3]{b}}+\frac{2^{2/3} a^{2/3} \left(x \sqrt{a^2 x^2-b}+a x^2\right)^{2/3}}{b^{2/3}}+1\right)}{24\ 2^{2/3} a^{2/3}}-\frac{7 b^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{2} \sqrt[3]{a} \sqrt[3]{x \sqrt{a^2 x^2-b}+a x^2}}{\sqrt{3} \sqrt[3]{b}}+\frac{1}{\sqrt{3}}\right)}{4\ 2^{2/3} \sqrt{3} a^{2/3}}",1,"Result too large to show","C",0
2944,0,0,351,0.6310277,"\int \frac{\left(b+a^2 x^2\right) \sqrt{a x^2+\sqrt{b+a^2 x^4}}}{\left(-b+a^2 x^2\right) \sqrt{b+a^2 x^4}} \, dx","Integrate[((b + a^2*x^2)*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]])/((-b + a^2*x^2)*Sqrt[b + a^2*x^4]),x]","\int \frac{\left(b+a^2 x^2\right) \sqrt{a x^2+\sqrt{b+a^2 x^4}}}{\left(-b+a^2 x^2\right) \sqrt{b+a^2 x^4}} \, dx","\frac{\log \left(i a^{3/2} x^2+i \sqrt{a} \sqrt{a^2 x^4+b}+i \sqrt{2} a x \sqrt{\sqrt{a^2 x^4+b}+a x^2}\right)}{\sqrt{2} \sqrt{a}}-\frac{i \sqrt{2} \text{RootSum}\left[\text{$\#$1}^4 \sqrt{a}-4 i \text{$\#$1}^3 b+2 \text{$\#$1}^2 a^{3/2} b+4 i \text{$\#$1} a b^2+a^{5/2} b^2\&,\frac{a b^2 \log \left(-\text{$\#$1}+i a^{3/2} x^2+i \sqrt{a} \sqrt{a^2 x^4+b}+i \sqrt{2} a x \sqrt{\sqrt{a^2 x^4+b}+a x^2}\right)-\text{$\#$1}^2 b \log \left(-\text{$\#$1}+i a^{3/2} x^2+i \sqrt{a} \sqrt{a^2 x^4+b}+i \sqrt{2} a x \sqrt{\sqrt{a^2 x^4+b}+a x^2}\right)}{\text{$\#$1}^3 \sqrt{a}-3 i \text{$\#$1}^2 b+\text{$\#$1} a^{3/2} b+i a b^2}\&\right]}{\sqrt{a}}",1,"Integrate[((b + a^2*x^2)*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]])/((-b + a^2*x^2)*Sqrt[b + a^2*x^4]), x]","F",-1
2945,0,0,351,0.1977656,"\int \frac{\left(b+a^2 x^2\right) \sqrt{a x^2+\sqrt{b+a^2 x^4}}}{\left(-b+a^2 x^2\right) \sqrt{b+a^2 x^4}} \, dx","Integrate[((b + a^2*x^2)*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]])/((-b + a^2*x^2)*Sqrt[b + a^2*x^4]),x]","\int \frac{\left(b+a^2 x^2\right) \sqrt{a x^2+\sqrt{b+a^2 x^4}}}{\left(-b+a^2 x^2\right) \sqrt{b+a^2 x^4}} \, dx","\frac{\log \left(i a^{3/2} x^2+i \sqrt{a} \sqrt{a^2 x^4+b}+i \sqrt{2} a x \sqrt{\sqrt{a^2 x^4+b}+a x^2}\right)}{\sqrt{2} \sqrt{a}}-\frac{i \sqrt{2} \text{RootSum}\left[\text{$\#$1}^4 \sqrt{a}-4 i \text{$\#$1}^3 b+2 \text{$\#$1}^2 a^{3/2} b+4 i \text{$\#$1} a b^2+a^{5/2} b^2\&,\frac{a b^2 \log \left(-\text{$\#$1}+i a^{3/2} x^2+i \sqrt{a} \sqrt{a^2 x^4+b}+i \sqrt{2} a x \sqrt{\sqrt{a^2 x^4+b}+a x^2}\right)-\text{$\#$1}^2 b \log \left(-\text{$\#$1}+i a^{3/2} x^2+i \sqrt{a} \sqrt{a^2 x^4+b}+i \sqrt{2} a x \sqrt{\sqrt{a^2 x^4+b}+a x^2}\right)}{\text{$\#$1}^3 \sqrt{a}-3 i \text{$\#$1}^2 b+\text{$\#$1} a^{3/2} b+i a b^2}\&\right]}{\sqrt{a}}",1,"Integrate[((b + a^2*x^2)*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]])/((-b + a^2*x^2)*Sqrt[b + a^2*x^4]), x]","F",-1
2946,1,12183,352,7.1392349,"\int \frac{x^3}{\sqrt{a+b x+c x^2+b x^3+a x^4} \left(1-x^6\right)} \, dx","Integrate[x^3/(Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]*(1 - x^6)),x]","\text{Result too large to show}","\frac{\sqrt{-2 a-2 b-c} \tan ^{-1}\left(\frac{x \sqrt{-2 a-2 b-c}}{-\sqrt{a x^4+a+b x^3+b x+c x^2}+\sqrt{a} x^2-2 \sqrt{a} x+\sqrt{a}}\right)}{6 (2 a+2 b+c)}+\frac{\tan ^{-1}\left(\frac{x \sqrt{a-b-c}}{-\sqrt{a x^4+a+b x^3+b x+c x^2}+\sqrt{a} x^2-\sqrt{a} x+\sqrt{a}}\right)}{3 \sqrt{a-b-c}}-\frac{\tan ^{-1}\left(\frac{x \sqrt{a+b-c}}{-\sqrt{a x^4+a+b x^3+b x+c x^2}+\sqrt{a} x^2+\sqrt{a} x+\sqrt{a}}\right)}{3 \sqrt{a+b-c}}-\frac{\sqrt{-2 a+2 b-c} \tan ^{-1}\left(\frac{x \sqrt{-2 a+2 b-c}}{-\sqrt{a x^4+a+b x^3+b x+c x^2}+\sqrt{a} x^2+2 \sqrt{a} x+\sqrt{a}}\right)}{6 (2 a-2 b+c)}",1,"Result too large to show","C",0
2947,0,0,352,1.2480556,"\int \frac{\left(-q+2 p x^3\right) \sqrt{q^2-2 p q x^2+2 p q x^3+p^2 x^6} \left(b x^6+a \left(q+p x^3\right)^6\right)}{x^9} \, dx","Integrate[((-q + 2*p*x^3)*Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6]*(b*x^6 + a*(q + p*x^3)^6))/x^9,x]","\int \frac{\left(-q+2 p x^3\right) \sqrt{q^2-2 p q x^2+2 p q x^3+p^2 x^6} \left(b x^6+a \left(q+p x^3\right)^6\right)}{x^9} \, dx","\frac{1}{8} \log (x) \left(5 a p^4 q^4+8 b p q\right)+\frac{1}{8} \left(-5 a p^4 q^4-8 b p q\right) \log \left(\sqrt{p^2 x^6+2 p q x^3-2 p q x^2+q^2}+p x^3+q\right)+\frac{\sqrt{p^2 x^6+2 p q x^3-2 p q x^2+q^2} \left(6 a p^7 x^{21}+42 a p^6 q x^{18}-2 a p^6 q x^{17}+126 a p^5 q^2 x^{15}-10 a p^5 q^2 x^{14}-5 a p^5 q^2 x^{13}+210 a p^4 q^3 x^{12}-20 a p^4 q^3 x^{11}-15 a p^4 q^3 x^{10}-15 a p^4 q^3 x^9+210 a p^3 q^4 x^9-20 a p^3 q^4 x^8-15 a p^3 q^4 x^7-15 a p^3 q^4 x^6+126 a p^2 q^5 x^6-10 a p^2 q^5 x^5-5 a p^2 q^5 x^4+42 a p q^6 x^3-2 a p q^6 x^2+6 a q^7+24 b p x^9+24 b q x^6\right)}{48 x^8}",1,"Integrate[((-q + 2*p*x^3)*Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6]*(b*x^6 + a*(q + p*x^3)^6))/x^9, x]","F",-1
2948,0,0,352,1.2845227,"\int \frac{\left(-2 q+p x^3\right) \sqrt{q^2+2 p q x^3-2 p q x^4+p^2 x^6} \left(b x^{12}+a \left(q+p x^3\right)^6\right)}{x^{17}} \, dx","Integrate[((-2*q + p*x^3)*Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]*(b*x^12 + a*(q + p*x^3)^6))/x^17,x]","\int \frac{\left(-2 q+p x^3\right) \sqrt{q^2+2 p q x^3-2 p q x^4+p^2 x^6} \left(b x^{12}+a \left(q+p x^3\right)^6\right)}{x^{17}} \, dx","\frac{1}{4} \log (x) \left(5 a p^4 q^4+8 b p q\right)+\frac{1}{8} \left(-5 a p^4 q^4-8 b p q\right) \log \left(\sqrt{p^2 x^6-2 p q x^4+2 p q x^3+q^2}+p x^3+q\right)+\frac{\sqrt{p^2 x^6-2 p q x^4+2 p q x^3+q^2} \left(6 a p^7 x^{21}-2 a p^6 q x^{19}+42 a p^6 q x^{18}-5 a p^5 q^2 x^{17}-10 a p^5 q^2 x^{16}+126 a p^5 q^2 x^{15}-15 a p^4 q^3 x^{15}-15 a p^4 q^3 x^{14}-20 a p^4 q^3 x^{13}+210 a p^4 q^3 x^{12}-15 a p^3 q^4 x^{12}-15 a p^3 q^4 x^{11}-20 a p^3 q^4 x^{10}+210 a p^3 q^4 x^9-5 a p^2 q^5 x^8-10 a p^2 q^5 x^7+126 a p^2 q^5 x^6-2 a p q^6 x^4+42 a p q^6 x^3+6 a q^7+24 b p x^{15}+24 b q x^{12}\right)}{48 x^{16}}",1,"Integrate[((-2*q + p*x^3)*Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]*(b*x^12 + a*(q + p*x^3)^6))/x^17, x]","F",-1
2949,1,420,352,1.9296302,"\int \frac{\left(-q+p x^4\right) \sqrt{q+p x^4}}{b x^4+a \left(q+p x^4\right)^2} \, dx","Integrate[((-q + p*x^4)*Sqrt[q + p*x^4])/(b*x^4 + a*(q + p*x^4)^2),x]","-\frac{i \sqrt{\frac{p x^4}{q}+1} \left(-\Pi \left(-\frac{i \sqrt{2} \sqrt{q}}{\sqrt{p} \sqrt{-\frac{b-\sqrt{b+4 a p q} \sqrt{b}+2 a p q}{a p^2}}};\left.i \sinh ^{-1}\left(\sqrt{\frac{i \sqrt{p}}{\sqrt{q}}} x\right)\right|-1\right)-\Pi \left(\frac{i \sqrt{2} \sqrt{q}}{\sqrt{p} \sqrt{-\frac{b-\sqrt{b+4 a p q} \sqrt{b}+2 a p q}{a p^2}}};\left.i \sinh ^{-1}\left(\sqrt{\frac{i \sqrt{p}}{\sqrt{q}}} x\right)\right|-1\right)-\Pi \left(-\frac{i \sqrt{2} \sqrt{q}}{\sqrt{p} \sqrt{-\frac{b+\sqrt{b+4 a p q} \sqrt{b}+2 a p q}{a p^2}}};\left.i \sinh ^{-1}\left(\sqrt{\frac{i \sqrt{p}}{\sqrt{q}}} x\right)\right|-1\right)-\Pi \left(\frac{i \sqrt{2} \sqrt{q}}{\sqrt{p} \sqrt{-\frac{b+\sqrt{b+4 a p q} \sqrt{b}+2 a p q}{a p^2}}};\left.i \sinh ^{-1}\left(\sqrt{\frac{i \sqrt{p}}{\sqrt{q}}} x\right)\right|-1\right)+2 F\left(\left.i \sinh ^{-1}\left(\sqrt{\frac{i \sqrt{p}}{\sqrt{q}}} x\right)\right|-1\right)\right)}{2 a \sqrt{\frac{i \sqrt{p}}{\sqrt{q}}} \sqrt{p x^4+q}}","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8 a-8 \text{$\#$1}^6 a \sqrt{p} \sqrt{q}+24 \text{$\#$1}^4 a p q+16 \text{$\#$1}^4 b-32 \text{$\#$1}^2 a p^{3/2} q^{3/2}+16 a p^2 q^2\&,\frac{-\text{$\#$1}^6 \log \left(-\text{$\#$1} x+\sqrt{p x^4+q}+\sqrt{p} x^2+\sqrt{q}\right)+\text{$\#$1}^6 \log (x)+2 \text{$\#$1}^4 \sqrt{p} \sqrt{q} \log \left(-\text{$\#$1} x+\sqrt{p x^4+q}+\sqrt{p} x^2+\sqrt{q}\right)-2 \text{$\#$1}^4 \sqrt{p} \sqrt{q} \log (x)+4 \text{$\#$1}^2 p q \log \left(-\text{$\#$1} x+\sqrt{p x^4+q}+\sqrt{p} x^2+\sqrt{q}\right)-4 \text{$\#$1}^2 p q \log (x)-8 p^{3/2} q^{3/2} \log \left(-\text{$\#$1} x+\sqrt{p x^4+q}+\sqrt{p} x^2+\sqrt{q}\right)+8 p^{3/2} q^{3/2} \log (x)}{\text{$\#$1}^7 (-a)+6 \text{$\#$1}^5 a \sqrt{p} \sqrt{q}-12 \text{$\#$1}^3 a p q-8 \text{$\#$1}^3 b+8 \text{$\#$1} a p^{3/2} q^{3/2}}\&\right]",1,"((-1/2*I)*Sqrt[1 + (p*x^4)/q]*(2*EllipticF[I*ArcSinh[Sqrt[(I*Sqrt[p])/Sqrt[q]]*x], -1] - EllipticPi[((-I)*Sqrt[2]*Sqrt[q])/(Sqrt[p]*Sqrt[-((b + 2*a*p*q - Sqrt[b]*Sqrt[b + 4*a*p*q])/(a*p^2))]), I*ArcSinh[Sqrt[(I*Sqrt[p])/Sqrt[q]]*x], -1] - EllipticPi[(I*Sqrt[2]*Sqrt[q])/(Sqrt[p]*Sqrt[-((b + 2*a*p*q - Sqrt[b]*Sqrt[b + 4*a*p*q])/(a*p^2))]), I*ArcSinh[Sqrt[(I*Sqrt[p])/Sqrt[q]]*x], -1] - EllipticPi[((-I)*Sqrt[2]*Sqrt[q])/(Sqrt[p]*Sqrt[-((b + 2*a*p*q + Sqrt[b]*Sqrt[b + 4*a*p*q])/(a*p^2))]), I*ArcSinh[Sqrt[(I*Sqrt[p])/Sqrt[q]]*x], -1] - EllipticPi[(I*Sqrt[2]*Sqrt[q])/(Sqrt[p]*Sqrt[-((b + 2*a*p*q + Sqrt[b]*Sqrt[b + 4*a*p*q])/(a*p^2))]), I*ArcSinh[Sqrt[(I*Sqrt[p])/Sqrt[q]]*x], -1]))/(a*Sqrt[(I*Sqrt[p])/Sqrt[q]]*Sqrt[q + p*x^4])","C",1
2950,1,250,354,0.4689221,"\int \frac{-3 b+a x}{\sqrt[3]{b^2-a^2 x^2} \left(3 b^2+a^2 x^2\right)} \, dx","Integrate[(-3*b + a*x)/((b^2 - a^2*x^2)^(1/3)*(3*b^2 + a^2*x^2)),x]","\frac{x \left(a x \sqrt[3]{1-\frac{a^2 x^2}{b^2}} F_1\left(1;\frac{1}{3},1;2;\frac{a^2 x^2}{b^2},-\frac{a^2 x^2}{3 b^2}\right)-\frac{162 b^5 F_1\left(\frac{1}{2};\frac{1}{3},1;\frac{3}{2};\frac{a^2 x^2}{b^2},-\frac{a^2 x^2}{3 b^2}\right)}{\left(a^2 x^2+3 b^2\right) \left(9 b^2 F_1\left(\frac{1}{2};\frac{1}{3},1;\frac{3}{2};\frac{a^2 x^2}{b^2},-\frac{a^2 x^2}{3 b^2}\right)+2 a^2 x^2 \left(F_1\left(\frac{3}{2};\frac{4}{3},1;\frac{5}{2};\frac{a^2 x^2}{b^2},-\frac{a^2 x^2}{3 b^2}\right)-F_1\left(\frac{3}{2};\frac{1}{3},2;\frac{5}{2};\frac{a^2 x^2}{b^2},-\frac{a^2 x^2}{3 b^2}\right)\right)\right)}\right)}{6 b^2 \sqrt[3]{b^2-a^2 x^2}}","\frac{\log \left(\sqrt[3]{b} \sqrt[3]{b^2-a^2 x^2}\right)}{2^{2/3} a b^{2/3}}-\frac{\log \left(b^{2/3} \left(b^2-a^2 x^2\right)^{2/3}\right)}{2\ 2^{2/3} a b^{2/3}}-\frac{\log \left(2 \sqrt[3]{b} \sqrt[3]{b^2-a^2 x^2}+2^{2/3} a x+2^{2/3} b\right)}{2^{2/3} a b^{2/3}}+\frac{\log \left(-2^{2/3} a \sqrt[3]{b} x \sqrt[3]{b^2-a^2 x^2}-2^{2/3} b^{4/3} \sqrt[3]{b^2-a^2 x^2}+2 b^{2/3} \left(b^2-a^2 x^2\right)^{2/3}+\sqrt[3]{2} a^2 x^2+2 \sqrt[3]{2} a b x+\sqrt[3]{2} b^2\right)}{2\ 2^{2/3} a b^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{b} \sqrt[3]{b^2-a^2 x^2}}{\sqrt[3]{b} \sqrt[3]{b^2-a^2 x^2}-2^{2/3} a x-2^{2/3} b}\right)}{2^{2/3} a b^{2/3}}",1,"(x*(a*x*(1 - (a^2*x^2)/b^2)^(1/3)*AppellF1[1, 1/3, 1, 2, (a^2*x^2)/b^2, -1/3*(a^2*x^2)/b^2] - (162*b^5*AppellF1[1/2, 1/3, 1, 3/2, (a^2*x^2)/b^2, -1/3*(a^2*x^2)/b^2])/((3*b^2 + a^2*x^2)*(9*b^2*AppellF1[1/2, 1/3, 1, 3/2, (a^2*x^2)/b^2, -1/3*(a^2*x^2)/b^2] + 2*a^2*x^2*(-AppellF1[3/2, 1/3, 2, 5/2, (a^2*x^2)/b^2, -1/3*(a^2*x^2)/b^2] + AppellF1[3/2, 4/3, 1, 5/2, (a^2*x^2)/b^2, -1/3*(a^2*x^2)/b^2])))))/(6*b^2*(b^2 - a^2*x^2)^(1/3))","C",0
2951,1,418,354,2.3429788,"\int \frac{x+\sqrt{1+4 x+7 x^2+8 x^3+5 x^4+2 x^5}}{1-\sqrt{1+4 x+7 x^2+8 x^3+5 x^4+2 x^5}} \, dx","Integrate[(x + Sqrt[1 + 4*x + 7*x^2 + 8*x^3 + 5*x^4 + 2*x^5])/(1 - Sqrt[1 + 4*x + 7*x^2 + 8*x^3 + 5*x^4 + 2*x^5]),x]","\frac{\sqrt{2 x+1} \left(x^2+x+1\right) \left(\text{RootSum}\left[\text{$\#$1}^4+\text{$\#$1}^3+\text{$\#$1}^2+\text{$\#$1}+4\&,\frac{\text{$\#$1}^3 \log \left(\sqrt{2 x+1}-\text{$\#$1}\right)-2 \text{$\#$1}^2 \log \left(\sqrt{2 x+1}-\text{$\#$1}\right)-\text{$\#$1} \log \left(\sqrt{2 x+1}-\text{$\#$1}\right)-4 \log \left(\sqrt{2 x+1}-\text{$\#$1}\right)}{4 \text{$\#$1}^3+3 \text{$\#$1}^2+2 \text{$\#$1}+1}\&\right]-\text{RootSum}\left[\text{$\#$1}^4-\text{$\#$1}^3+\text{$\#$1}^2-\text{$\#$1}+4\&,\frac{\text{$\#$1}^3 \log \left(\sqrt{2 x+1}-\text{$\#$1}\right)+2 \text{$\#$1}^2 \log \left(\sqrt{2 x+1}-\text{$\#$1}\right)-\text{$\#$1} \log \left(\sqrt{2 x+1}-\text{$\#$1}\right)+4 \log \left(\sqrt{2 x+1}-\text{$\#$1}\right)}{4 \text{$\#$1}^3-3 \text{$\#$1}^2+2 \text{$\#$1}-1}\&\right]\right)}{4 \sqrt{(2 x+1) \left(x^2+x+1\right)^2}}+\frac{1}{4} \left(\text{RootSum}\left[2 \text{$\#$1}^4+5 \text{$\#$1}^3+8 \text{$\#$1}^2+7 \text{$\#$1}+4\&,\frac{2 \text{$\#$1}^3 \log (x-\text{$\#$1})+5 \text{$\#$1}^2 \log (x-\text{$\#$1})+8 \text{$\#$1} \log (x-\text{$\#$1})+3 \log (x-\text{$\#$1})}{8 \text{$\#$1}^3+15 \text{$\#$1}^2+16 \text{$\#$1}+7}\&\right]+2 \tanh ^{-1}\left(\frac{\sqrt{(2 x+1) \left(x^2+x+1\right)^2}}{x^2+x+1}\right)-4 x-\log (x)\right)","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^4+\text{$\#$1}^3+\text{$\#$1}^2+\text{$\#$1}+4\&,\frac{\text{$\#$1}^3 \left(-\log \left(x^2+x+1\right)\right)+\text{$\#$1}^3 \log \left(-\text{$\#$1} x^2-\text{$\#$1} x-\text{$\#$1}+\sqrt{2 x^5+5 x^4+8 x^3+7 x^2+4 x+1}\right)+2 \text{$\#$1}^2 \log \left(x^2+x+1\right)-2 \text{$\#$1}^2 \log \left(-\text{$\#$1} x^2-\text{$\#$1} x-\text{$\#$1}+\sqrt{2 x^5+5 x^4+8 x^3+7 x^2+4 x+1}\right)+\text{$\#$1} \log \left(x^2+x+1\right)-\text{$\#$1} \log \left(-\text{$\#$1} x^2-\text{$\#$1} x-\text{$\#$1}+\sqrt{2 x^5+5 x^4+8 x^3+7 x^2+4 x+1}\right)-4 \log \left(-\text{$\#$1} x^2-\text{$\#$1} x-\text{$\#$1}+\sqrt{2 x^5+5 x^4+8 x^3+7 x^2+4 x+1}\right)+4 \log \left(x^2+x+1\right)}{4 \text{$\#$1}^3+3 \text{$\#$1}^2+2 \text{$\#$1}+1}\&\right]+\frac{1}{2} \log \left(x^2+x+1\right)-\frac{1}{2} \log \left(-x^2+\sqrt{2 x^5+5 x^4+8 x^3+7 x^2+4 x+1}-x-1\right)-x",1,"(Sqrt[1 + 2*x]*(1 + x + x^2)*(-RootSum[4 - #1 + #1^2 - #1^3 + #1^4 & , (4*Log[Sqrt[1 + 2*x] - #1] - Log[Sqrt[1 + 2*x] - #1]*#1 + 2*Log[Sqrt[1 + 2*x] - #1]*#1^2 + Log[Sqrt[1 + 2*x] - #1]*#1^3)/(-1 + 2*#1 - 3*#1^2 + 4*#1^3) & ] + RootSum[4 + #1 + #1^2 + #1^3 + #1^4 & , (-4*Log[Sqrt[1 + 2*x] - #1] - Log[Sqrt[1 + 2*x] - #1]*#1 - 2*Log[Sqrt[1 + 2*x] - #1]*#1^2 + Log[Sqrt[1 + 2*x] - #1]*#1^3)/(1 + 2*#1 + 3*#1^2 + 4*#1^3) & ]))/(4*Sqrt[(1 + 2*x)*(1 + x + x^2)^2]) + (-4*x + 2*ArcTanh[Sqrt[(1 + 2*x)*(1 + x + x^2)^2]/(1 + x + x^2)] - Log[x] + RootSum[4 + 7*#1 + 8*#1^2 + 5*#1^3 + 2*#1^4 & , (3*Log[x - #1] + 8*Log[x - #1]*#1 + 5*Log[x - #1]*#1^2 + 2*Log[x - #1]*#1^3)/(7 + 16*#1 + 15*#1^2 + 8*#1^3) & ])/4","A",1
2952,0,0,355,3.4811658,"\int \frac{x^3 \left(4 a b-3 (a+b) x+2 x^2\right)}{\left(x^2 (-a+x) (-b+x)\right)^{2/3} \left(-a b d+(a+b) d x-d x^2+x^4\right)} \, dx","Integrate[(x^3*(4*a*b - 3*(a + b)*x + 2*x^2))/((x^2*(-a + x)*(-b + x))^(2/3)*(-(a*b*d) + (a + b)*d*x - d*x^2 + x^4)),x]","\int \frac{x^3 \left(4 a b-3 (a+b) x+2 x^2\right)}{\left(x^2 (-a+x) (-b+x)\right)^{2/3} \left(-a b d+(a+b) d x-d x^2+x^4\right)} \, dx","-\frac{\log \left(a^2 b^2 d-2 a^2 b d x+a^2 d x^2-2 a b^2 d x+\left(x^3 (-a-b)+a b x^2+x^4\right)^{2/3} \left(a b d^{2/3}-a d^{2/3} x-b d^{2/3} x+d^{2/3} x^2\right)+4 a b d x^2+\sqrt[3]{d} \left(x^3 (-a-b)+a b x^2+x^4\right)^{4/3}-2 a d x^3+b^2 d x^2-2 b d x^3+d x^4\right)}{2 \sqrt[3]{d}}+\frac{\log \left(\sqrt[6]{d} \left(x^3 (-a-b)+a b x^2+x^4\right)^{2/3}-a b \sqrt{d}+a \sqrt{d} x+b \sqrt{d} x-\sqrt{d} x^2\right)}{\sqrt[3]{d}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \left(x^3 (-a-b)+a b x^2+x^4\right)^{2/3}}{x \left(-2 a \sqrt[3]{d}-2 b \sqrt[3]{d}\right)+2 a b \sqrt[3]{d}+\left(x^3 (-a-b)+a b x^2+x^4\right)^{2/3}+2 \sqrt[3]{d} x^2}\right)}{\sqrt[3]{d}}",1,"Integrate[(x^3*(4*a*b - 3*(a + b)*x + 2*x^2))/((x^2*(-a + x)*(-b + x))^(2/3)*(-(a*b*d) + (a + b)*d*x - d*x^2 + x^4)), x]","F",-1
2953,0,0,356,1.3425,"\int \frac{x^3}{\sqrt[3]{x^2+x^4} \left(-1+x^6\right)} \, dx","Integrate[x^3/((x^2 + x^4)^(1/3)*(-1 + x^6)),x]","\int \frac{x^3}{\sqrt[3]{x^2+x^4} \left(-1+x^6\right)} \, dx","-\frac{1}{6} \log \left(\sqrt[3]{x^4+x^2}-x\right)-\frac{1}{6} \log \left(\sqrt[3]{x^4+x^2}+x\right)+\frac{\log \left(2^{2/3} \sqrt[3]{x^4+x^2}-2 x\right)}{12 \sqrt[3]{2}}+\frac{\log \left(2^{2/3} \sqrt[3]{x^4+x^2}+2 x\right)}{12 \sqrt[3]{2}}+\frac{1}{12} \log \left(x^2-\sqrt[3]{x^4+x^2} x+\left(x^4+x^2\right)^{2/3}\right)+\frac{1}{12} \log \left(x^2+\sqrt[3]{x^4+x^2} x+\left(x^4+x^2\right)^{2/3}\right)-\frac{\log \left(-2 x^2+2^{2/3} \sqrt[3]{x^4+x^2} x-\sqrt[3]{2} \left(x^4+x^2\right)^{2/3}\right)}{24 \sqrt[3]{2}}-\frac{\log \left(2 x^2+2^{2/3} \sqrt[3]{x^4+x^2} x+\sqrt[3]{2} \left(x^4+x^2\right)^{2/3}\right)}{24 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x^2}{x^2+2 \left(x^4+x^2\right)^{2/3}}\right)}{2 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x^2}{x^2+\sqrt[3]{2} \left(x^4+x^2\right)^{2/3}}\right)}{4 \sqrt[3]{2} \sqrt{3}}",1,"Integrate[x^3/((x^2 + x^4)^(1/3)*(-1 + x^6)), x]","F",-1
2954,1,365,357,0.6947297,"\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2 \sqrt{1+x^2}} \, dx","Integrate[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x^2)^2*Sqrt[1 + x^2]),x]","\frac{\left(x^2+\sqrt{x^2+1} x+1\right) \left(\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{11 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-10 \text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+4 \text{$\#$1}^2-2}\&\right]-\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{11 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-10 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]-\frac{8 \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(3 x^2+3 \sqrt{x^2+1} x+1\right)}{\left(x^2-1\right) \left(2 x^2+2 \sqrt{x^2+1} x+1\right)}\right)}{32 \sqrt{x^2+1} \left(\sqrt{x^2+1}+x\right)}","\frac{1}{32} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{11 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-10 \text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+4 \text{$\#$1}^2-2}\&\right]-\frac{1}{32} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{11 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-10 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]+\frac{\left(-3 x^2-1\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-3 x \sqrt{x^2+1} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{4 \left(2 x^2+1\right) \left(x^2-1\right)+8 x \sqrt{x^2+1} \left(x^2-1\right)}",1,"((1 + x^2 + x*Sqrt[1 + x^2])*((-8*(1 + 3*x^2 + 3*x*Sqrt[1 + x^2])*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/((-1 + x^2)*(1 + 2*x^2 + 2*x*Sqrt[1 + x^2])) - RootSum[-2 + 4*#1^4 - 4*#1^6 + #1^8 & , (-2*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1] - 10*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^2 + 11*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^4)/(2*#1^3 - 3*#1^5 + #1^7) & ] + RootSum[2 - 8*#1^2 + 8*#1^4 - 4*#1^6 + #1^8 & , (-10*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1 + 11*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^3)/(-2 + 4*#1^2 - 3*#1^4 + #1^6) & ]))/(32*Sqrt[1 + x^2]*(x + Sqrt[1 + x^2]))","A",1
2955,1,365,357,0.2527155,"\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2 \sqrt{1+x^2}} \, dx","Integrate[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x^2)^2*Sqrt[1 + x^2]),x]","\frac{\left(x^2+\sqrt{x^2+1} x+1\right) \left(\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{11 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-10 \text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+4 \text{$\#$1}^2-2}\&\right]-\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{11 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-10 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]-\frac{8 \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(3 x^2+3 \sqrt{x^2+1} x+1\right)}{\left(x^2-1\right) \left(2 x^2+2 \sqrt{x^2+1} x+1\right)}\right)}{32 \sqrt{x^2+1} \left(\sqrt{x^2+1}+x\right)}","\frac{1}{32} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{11 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-10 \text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+4 \text{$\#$1}^2-2}\&\right]-\frac{1}{32} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{11 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-10 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]+\frac{\left(-3 x^2-1\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-3 x \sqrt{x^2+1} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{4 \left(2 x^2+1\right) \left(x^2-1\right)+8 x \sqrt{x^2+1} \left(x^2-1\right)}",1,"((1 + x^2 + x*Sqrt[1 + x^2])*((-8*(1 + 3*x^2 + 3*x*Sqrt[1 + x^2])*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/((-1 + x^2)*(1 + 2*x^2 + 2*x*Sqrt[1 + x^2])) - RootSum[-2 + 4*#1^4 - 4*#1^6 + #1^8 & , (-2*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1] - 10*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^2 + 11*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^4)/(2*#1^3 - 3*#1^5 + #1^7) & ] + RootSum[2 - 8*#1^2 + 8*#1^4 - 4*#1^6 + #1^8 & , (-10*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1 + 11*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^3)/(-2 + 4*#1^2 - 3*#1^4 + #1^6) & ]))/(32*Sqrt[1 + x^2]*(x + Sqrt[1 + x^2]))","A",1
2956,1,365,357,0.5834381,"\int \frac{\sqrt{1+x^2} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","Integrate[(Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2)^2,x]","\frac{\left(x^2+\sqrt{x^2+1} x+1\right) \left(\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{3 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+4 \text{$\#$1}^2-2}\&\right]-\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{3 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]-\frac{8 \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(3 x^2+3 \sqrt{x^2+1} x+1\right)}{\left(x^2-1\right) \left(2 x^2+2 \sqrt{x^2+1} x+1\right)}\right)}{16 \sqrt{x^2+1} \left(\sqrt{x^2+1}+x\right)}","\frac{1}{16} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{3 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+4 \text{$\#$1}^2-2}\&\right]-\frac{1}{16} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{3 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]+\frac{\left(-3 x^2-1\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-3 x \sqrt{x^2+1} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{2 \left(2 x^2+1\right) \left(x^2-1\right)+4 x \sqrt{x^2+1} \left(x^2-1\right)}",1,"((1 + x^2 + x*Sqrt[1 + x^2])*((-8*(1 + 3*x^2 + 3*x*Sqrt[1 + x^2])*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/((-1 + x^2)*(1 + 2*x^2 + 2*x*Sqrt[1 + x^2])) - RootSum[-2 + 4*#1^4 - 4*#1^6 + #1^8 & , (-2*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1] - 2*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^2 + 3*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^4)/(2*#1^3 - 3*#1^5 + #1^7) & ] + RootSum[2 - 8*#1^2 + 8*#1^4 - 4*#1^6 + #1^8 & , (-2*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1 + 3*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^3)/(-2 + 4*#1^2 - 3*#1^4 + #1^6) & ]))/(16*Sqrt[1 + x^2]*(x + Sqrt[1 + x^2]))","A",1
2957,1,365,357,0.2313576,"\int \frac{\sqrt{1+x^2} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","Integrate[(Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2)^2,x]","\frac{\left(x^2+\sqrt{x^2+1} x+1\right) \left(\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{3 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+4 \text{$\#$1}^2-2}\&\right]-\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{3 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]-\frac{8 \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(3 x^2+3 \sqrt{x^2+1} x+1\right)}{\left(x^2-1\right) \left(2 x^2+2 \sqrt{x^2+1} x+1\right)}\right)}{16 \sqrt{x^2+1} \left(\sqrt{x^2+1}+x\right)}","\frac{1}{16} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{3 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+4 \text{$\#$1}^2-2}\&\right]-\frac{1}{16} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{3 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]+\frac{\left(-3 x^2-1\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-3 x \sqrt{x^2+1} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{2 \left(2 x^2+1\right) \left(x^2-1\right)+4 x \sqrt{x^2+1} \left(x^2-1\right)}",1,"((1 + x^2 + x*Sqrt[1 + x^2])*((-8*(1 + 3*x^2 + 3*x*Sqrt[1 + x^2])*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/((-1 + x^2)*(1 + 2*x^2 + 2*x*Sqrt[1 + x^2])) - RootSum[-2 + 4*#1^4 - 4*#1^6 + #1^8 & , (-2*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1] - 2*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^2 + 3*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^4)/(2*#1^3 - 3*#1^5 + #1^7) & ] + RootSum[2 - 8*#1^2 + 8*#1^4 - 4*#1^6 + #1^8 & , (-2*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1 + 3*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^3)/(-2 + 4*#1^2 - 3*#1^4 + #1^6) & ]))/(16*Sqrt[1 + x^2]*(x + Sqrt[1 + x^2]))","A",1
2958,1,365,357,0.1939173,"\int \frac{\sqrt{1+x^2} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","Integrate[(Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2)^2,x]","\frac{\left(x^2+\sqrt{x^2+1} x+1\right) \left(\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{3 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+4 \text{$\#$1}^2-2}\&\right]-\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{3 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]-\frac{8 \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(3 x^2+3 \sqrt{x^2+1} x+1\right)}{\left(x^2-1\right) \left(2 x^2+2 \sqrt{x^2+1} x+1\right)}\right)}{16 \sqrt{x^2+1} \left(\sqrt{x^2+1}+x\right)}","\frac{1}{16} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{3 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+4 \text{$\#$1}^2-2}\&\right]-\frac{1}{16} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{3 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]+\frac{\left(-3 x^2-1\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-3 x \sqrt{x^2+1} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{2 \left(2 x^2+1\right) \left(x^2-1\right)+4 x \sqrt{x^2+1} \left(x^2-1\right)}",1,"((1 + x^2 + x*Sqrt[1 + x^2])*((-8*(1 + 3*x^2 + 3*x*Sqrt[1 + x^2])*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/((-1 + x^2)*(1 + 2*x^2 + 2*x*Sqrt[1 + x^2])) - RootSum[-2 + 4*#1^4 - 4*#1^6 + #1^8 & , (-2*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1] - 2*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^2 + 3*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^4)/(2*#1^3 - 3*#1^5 + #1^7) & ] + RootSum[2 - 8*#1^2 + 8*#1^4 - 4*#1^6 + #1^8 & , (-2*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1 + 3*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^3)/(-2 + 4*#1^2 - 3*#1^4 + #1^6) & ]))/(16*Sqrt[1 + x^2]*(x + Sqrt[1 + x^2]))","A",1
2959,1,271,362,0.6349538,"\int \frac{\left(c+b x+a x^2\right)^{5/2}}{(c+b x)^2} \, dx","Integrate[(c + b*x + a*x^2)^(5/2)/(c + b*x)^2,x]","\frac{5 \left(64 a^3 c^3 \left(2 a c-b^2\right) \tanh ^{-1}\left(\frac{-2 a c x+b^2 x+b c}{2 \sqrt{a} c \sqrt{x (a x+b)+c}}\right)-\left(-128 a^4 c^4+64 a^3 b^2 c^3-8 a b^6 c+b^8\right) \tanh ^{-1}\left(\frac{2 a x+b}{2 \sqrt{a} \sqrt{x (a x+b)+c}}\right)+2 \sqrt{a} b \left(32 a^3 b c^2 x-64 a^3 c^3-8 a^2 b^3 c x+48 a^2 b^2 c^2+2 a b^5 x-4 a b^4 c+b^6\right) \sqrt{x (a x+b)+c}\right)}{128 a^{3/2} b^6}+\frac{5 \left(6 a b x-8 a c+7 b^2\right) (x (a x+b)+c)^{3/2}}{24 b^3}-\frac{(x (a x+b)+c)^{5/2}}{b (b x+c)}","\frac{5 \left(2 a^{5/2} c^4-a^{3/2} b^2 c^3\right) \log \left(\sqrt{a x^2+b x+c}-\sqrt{a} x\right)}{2 b^6}-\frac{5 \left(2 a^{5/2} c^4-a^{3/2} b^2 c^3\right) \log \left(\sqrt{a} (b x+2 c)-b \sqrt{a x^2+b x+c}\right)}{2 b^6}+\frac{\sqrt{a x^2+b x+c} \left(48 a^3 b^4 x^4-80 a^3 b^3 c x^3+160 a^3 b^2 c^2 x^2-480 a^3 b c^3 x-960 a^3 c^4+136 a^2 b^5 x^3-64 a^2 b^4 c x^2+200 a^2 b^3 c^2 x+400 a^2 b^2 c^3+118 a b^6 x^2+146 a b^5 c x+28 a b^4 c^2+15 b^7 x+15 b^6 c\right)}{192 a b^5 (b x+c)}-\frac{5 \left(128 a^4 c^4-64 a^3 b^2 c^3+8 a b^6 c-b^8\right) \log \left(-2 \sqrt{a} \sqrt{a x^2+b x+c}+2 a x+b\right)}{128 a^{3/2} b^6}",1,"(5*(7*b^2 - 8*a*c + 6*a*b*x)*(c + x*(b + a*x))^(3/2))/(24*b^3) - (c + x*(b + a*x))^(5/2)/(b*(c + b*x)) + (5*(2*Sqrt[a]*b*(b^6 - 4*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3 + 2*a*b^5*x - 8*a^2*b^3*c*x + 32*a^3*b*c^2*x)*Sqrt[c + x*(b + a*x)] - (b^8 - 8*a*b^6*c + 64*a^3*b^2*c^3 - 128*a^4*c^4)*ArcTanh[(b + 2*a*x)/(2*Sqrt[a]*Sqrt[c + x*(b + a*x)])] + 64*a^3*c^3*(-b^2 + 2*a*c)*ArcTanh[(b*c + b^2*x - 2*a*c*x)/(2*Sqrt[a]*c*Sqrt[c + x*(b + a*x)])]))/(128*a^(3/2)*b^6)","A",1
2960,0,0,362,0.5298935,"\int \frac{\left(1+x^4\right)^2}{\left(-1+x^4\right)^2 \sqrt{x^2+\sqrt{1+x^4}}} \, dx","Integrate[(1 + x^4)^2/((-1 + x^4)^2*Sqrt[x^2 + Sqrt[1 + x^4]]),x]","\int \frac{\left(1+x^4\right)^2}{\left(-1+x^4\right)^2 \sqrt{x^2+\sqrt{1+x^4}}} \, dx","\frac{x \left(x^4-3\right)}{2 \left(x^4-1\right) \sqrt{\sqrt{x^4+1}+x^2}}+\frac{1}{2} \sqrt{\frac{1}{2} \left(7+5 \sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{2}-1\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)-\frac{1}{2} \sqrt{\frac{1}{2} \left(7+5 \sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)}{\sqrt{2}}-\frac{1}{2} \sqrt{\frac{1}{2} \left(5 \sqrt{2}-7\right)} \tanh ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{2}-1\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)-\frac{1}{2} \sqrt{\frac{1}{2} \left(5 \sqrt{2}-7\right)} \tanh ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)",1,"Integrate[(1 + x^4)^2/((-1 + x^4)^2*Sqrt[x^2 + Sqrt[1 + x^4]]), x]","F",-1
2961,1,143,363,0.1946175,"\int \frac{\sqrt{a x+\sqrt{-b+a x}}}{1+\sqrt{-b+a x}} \, dx","Integrate[Sqrt[a*x + Sqrt[-b + a*x]]/(1 + Sqrt[-b + a*x]),x]","\frac{2 \sqrt{\sqrt{a x-b}+a x} \left(2 \sqrt{a x-b}-3\right)+8 \sqrt{b} \tanh ^{-1}\left(\frac{-\sqrt{a x-b}+2 b-1}{2 \sqrt{b} \sqrt{\sqrt{a x-b}+a x}}\right)+(4 b+3) \tanh ^{-1}\left(\frac{2 \sqrt{a x-b}+1}{2 \sqrt{\sqrt{a x-b}+a x}}\right)}{4 a}","\frac{\sqrt{\frac{\sqrt{a x-b}+a x}{\left(\sqrt{a x-b}+1\right)^2}} (2 a x-2 b-3)}{2 a}-\frac{\sqrt{a x-b} \sqrt{\frac{\sqrt{a x-b}+a x}{\left(\sqrt{a x-b}+1\right)^2}}}{2 a}+\frac{2 \sqrt{b} \log \left(\sqrt{a x-b}+1\right)}{a}-\frac{2 \sqrt{b} \log \left(2 \sqrt{b} \sqrt{\frac{\sqrt{a x-b}+a x}{\left(\sqrt{a x-b}+1\right)^2}}+\sqrt{a x-b} \left(2 \sqrt{b} \sqrt{\frac{\sqrt{a x-b}+a x}{\left(\sqrt{a x-b}+1\right)^2}}+1\right)-2 b+1\right)}{a}+\frac{(-4 b-3) \tanh ^{-1}\left(\frac{-\sqrt{a x-b} \sqrt{\frac{\sqrt{a x-b}+a x}{\left(\sqrt{a x-b}+1\right)^2}}-\sqrt{\frac{\sqrt{a x-b}+a x}{\left(\sqrt{a x-b}+1\right)^2}}+\sqrt{b}}{\sqrt{a x-b}+1}\right)}{2 a}",1,"(2*Sqrt[a*x + Sqrt[-b + a*x]]*(-3 + 2*Sqrt[-b + a*x]) + 8*Sqrt[b]*ArcTanh[(-1 + 2*b - Sqrt[-b + a*x])/(2*Sqrt[b]*Sqrt[a*x + Sqrt[-b + a*x]])] + (3 + 4*b)*ArcTanh[(1 + 2*Sqrt[-b + a*x])/(2*Sqrt[a*x + Sqrt[-b + a*x]])])/(4*a)","A",1
2962,0,0,366,13.7221655,"\int \frac{\left(b x+a x^2\right) \sqrt[4]{b x^3+a x^4}}{-b+a x+x^2} \, dx","Integrate[((b*x + a*x^2)*(b*x^3 + a*x^4)^(1/4))/(-b + a*x + x^2),x]","\int \frac{\left(b x+a x^2\right) \sqrt[4]{b x^3+a x^4}}{-b+a x+x^2} \, dx","\text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4 a+2 a^2-b\&,\frac{-\text{$\#$1}^4 a^4 \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)+\text{$\#$1}^4 a^4 \log (x)+\text{$\#$1}^4 a^2 b \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)-\text{$\#$1}^4 a^2 b \log (x)-\text{$\#$1}^4 b^2 \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)+\text{$\#$1}^4 b^2 \log (x)+2 a^5 \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)-a^3 b \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)-2 a^5 \log (x)+a^3 b \log (x)}{3 \text{$\#$1}^3 a-2 \text{$\#$1}^7}\&\right]+\frac{1}{8} \sqrt[4]{a x^4+b x^3} \left(-8 a^2+4 a x+9 b\right)+\frac{\left(-32 a^4+8 a^2 b-5 b^2\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)}{16 a^{3/4}}+\frac{\left(32 a^4-8 a^2 b+5 b^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)}{16 a^{3/4}}",1,"Integrate[((b*x + a*x^2)*(b*x^3 + a*x^4)^(1/4))/(-b + a*x + x^2), x]","F",-1
2963,0,0,366,13.5030044,"\int \frac{\left(b x+a x^2\right) \sqrt[4]{b x^3+a x^4}}{-b+a x+x^2} \, dx","Integrate[((b*x + a*x^2)*(b*x^3 + a*x^4)^(1/4))/(-b + a*x + x^2),x]","\int \frac{\left(b x+a x^2\right) \sqrt[4]{b x^3+a x^4}}{-b+a x+x^2} \, dx","\text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4 a+2 a^2-b\&,\frac{-\text{$\#$1}^4 a^4 \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)+\text{$\#$1}^4 a^4 \log (x)+\text{$\#$1}^4 a^2 b \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)-\text{$\#$1}^4 a^2 b \log (x)-\text{$\#$1}^4 b^2 \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)+\text{$\#$1}^4 b^2 \log (x)+2 a^5 \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)-a^3 b \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)-2 a^5 \log (x)+a^3 b \log (x)}{3 \text{$\#$1}^3 a-2 \text{$\#$1}^7}\&\right]+\frac{1}{8} \sqrt[4]{a x^4+b x^3} \left(-8 a^2+4 a x+9 b\right)+\frac{\left(-32 a^4+8 a^2 b-5 b^2\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)}{16 a^{3/4}}+\frac{\left(32 a^4-8 a^2 b+5 b^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)}{16 a^{3/4}}",1,"Integrate[((b*x + a*x^2)*(b*x^3 + a*x^4)^(1/4))/(-b + a*x + x^2), x]","F",-1
2964,1,544,366,1.3396235,"\int \frac{-b^{10}+a^{10} x^{10}}{\sqrt{b^4+a^4 x^4} \left(b^{10}+a^{10} x^{10}\right)} \, dx","Integrate[(-b^10 + a^10*x^10)/(Sqrt[b^4 + a^4*x^4]*(b^10 + a^10*x^10)),x]","\frac{\sqrt[10]{-1} \sqrt{\frac{a^4 x^4}{b^4}+1} \left(\left(1+\sqrt[5]{-1}\right)^2 \left(1-3 \sqrt[5]{-1}+(-1)^{2/5}\right) F\left(\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)+2 \left((-1)^{2/5} \Pi \left(-i;\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)+\left(1-\sqrt[5]{-1}+2 (-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}\right) \Pi \left(-\sqrt[10]{-1};\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)-(-1)^{4/5} \Pi \left((-1)^{3/10};\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)+(-1)^{3/5} \Pi \left((-1)^{3/10};\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)+\sqrt[5]{-1} \Pi \left((-1)^{3/10};\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)-\Pi \left((-1)^{3/10};\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)+(-1)^{2/5} \Pi \left((-1)^{7/10};\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)-(-1)^{4/5} \Pi \left(-(-1)^{9/10};\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)+(-1)^{3/5} \Pi \left(-(-1)^{9/10};\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)+\sqrt[5]{-1} \Pi \left(-(-1)^{9/10};\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)-\Pi \left(-(-1)^{9/10};\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)\right)\right)}{\left(\sqrt[5]{-1}-1\right)^2 \left(1+\sqrt[5]{-1}\right)^4 \left(1+(-1)^{2/5}\right) \left(1-\sqrt[5]{-1}+(-1)^{2/5}\right) \sqrt{\frac{i a^2}{b^2}} \sqrt{a^4 x^4+b^4}}","\frac{1}{5} \text{RootSum}\left[\text{$\#$1}^8-12 \text{$\#$1}^6 a^2 b^2+24 \text{$\#$1}^4 a^4 b^4-48 \text{$\#$1}^2 a^6 b^6+16 a^8 b^8\&,\frac{-\text{$\#$1}^6 \log \left(-\text{$\#$1} x+\sqrt{a^4 x^4+b^4}+a^2 x^2+b^2\right)+\text{$\#$1}^6 \log (x)-4 \text{$\#$1}^4 a^2 b^2 \log (x)+4 \text{$\#$1}^4 a^2 b^2 \log \left(-\text{$\#$1} x+\sqrt{a^4 x^4+b^4}+a^2 x^2+b^2\right)-8 \text{$\#$1}^2 a^4 b^4 \log (x)+8 \text{$\#$1}^2 a^4 b^4 \log \left(-\text{$\#$1} x+\sqrt{a^4 x^4+b^4}+a^2 x^2+b^2\right)-8 a^6 b^6 \log \left(-\text{$\#$1} x+\sqrt{a^4 x^4+b^4}+a^2 x^2+b^2\right)+8 a^6 b^6 \log (x)}{-\text{$\#$1}^7+9 \text{$\#$1}^5 a^2 b^2-12 \text{$\#$1}^3 a^4 b^4+12 \text{$\#$1} a^6 b^6}\&\right]-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} a b x}{\sqrt{a^4 x^4+b^4}+a^2 x^2+b^2}\right)}{5 a b}",1,"((-1)^(1/10)*Sqrt[1 + (a^4*x^4)/b^4]*((1 + (-1)^(1/5))^2*(1 - 3*(-1)^(1/5) + (-1)^(2/5))*EllipticF[I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] + 2*((-1)^(2/5)*EllipticPi[-I, I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] + (1 - (-1)^(1/5) + 2*(-1)^(2/5) - (-1)^(3/5) + (-1)^(4/5))*EllipticPi[-(-1)^(1/10), I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] - EllipticPi[(-1)^(3/10), I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] + (-1)^(1/5)*EllipticPi[(-1)^(3/10), I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] + (-1)^(3/5)*EllipticPi[(-1)^(3/10), I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] - (-1)^(4/5)*EllipticPi[(-1)^(3/10), I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] + (-1)^(2/5)*EllipticPi[(-1)^(7/10), I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] - EllipticPi[-(-1)^(9/10), I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] + (-1)^(1/5)*EllipticPi[-(-1)^(9/10), I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] + (-1)^(3/5)*EllipticPi[-(-1)^(9/10), I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] - (-1)^(4/5)*EllipticPi[-(-1)^(9/10), I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1])))/((-1 + (-1)^(1/5))^2*(1 + (-1)^(1/5))^4*(1 + (-1)^(2/5))*(1 - (-1)^(1/5) + (-1)^(2/5))*Sqrt[(I*a^2)/b^2]*Sqrt[b^4 + a^4*x^4])","C",0
2965,1,544,366,1.155577,"\int \frac{-b^{10}+a^{10} x^{10}}{\sqrt{b^4+a^4 x^4} \left(b^{10}+a^{10} x^{10}\right)} \, dx","Integrate[(-b^10 + a^10*x^10)/(Sqrt[b^4 + a^4*x^4]*(b^10 + a^10*x^10)),x]","\frac{\sqrt[10]{-1} \sqrt{\frac{a^4 x^4}{b^4}+1} \left(\left(1+\sqrt[5]{-1}\right)^2 \left(1-3 \sqrt[5]{-1}+(-1)^{2/5}\right) F\left(\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)+2 \left((-1)^{2/5} \Pi \left(-i;\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)+\left(1-\sqrt[5]{-1}+2 (-1)^{2/5}-(-1)^{3/5}+(-1)^{4/5}\right) \Pi \left(-\sqrt[10]{-1};\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)-(-1)^{4/5} \Pi \left((-1)^{3/10};\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)+(-1)^{3/5} \Pi \left((-1)^{3/10};\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)+\sqrt[5]{-1} \Pi \left((-1)^{3/10};\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)-\Pi \left((-1)^{3/10};\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)+(-1)^{2/5} \Pi \left((-1)^{7/10};\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)-(-1)^{4/5} \Pi \left(-(-1)^{9/10};\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)+(-1)^{3/5} \Pi \left(-(-1)^{9/10};\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)+\sqrt[5]{-1} \Pi \left(-(-1)^{9/10};\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)-\Pi \left(-(-1)^{9/10};\left.i \sinh ^{-1}\left(\sqrt{\frac{i a^2}{b^2}} x\right)\right|-1\right)\right)\right)}{\left(\sqrt[5]{-1}-1\right)^2 \left(1+\sqrt[5]{-1}\right)^4 \left(1+(-1)^{2/5}\right) \left(1-\sqrt[5]{-1}+(-1)^{2/5}\right) \sqrt{\frac{i a^2}{b^2}} \sqrt{a^4 x^4+b^4}}","\frac{1}{5} \text{RootSum}\left[\text{$\#$1}^8-12 \text{$\#$1}^6 a^2 b^2+24 \text{$\#$1}^4 a^4 b^4-48 \text{$\#$1}^2 a^6 b^6+16 a^8 b^8\&,\frac{-\text{$\#$1}^6 \log \left(-\text{$\#$1} x+\sqrt{a^4 x^4+b^4}+a^2 x^2+b^2\right)+\text{$\#$1}^6 \log (x)-4 \text{$\#$1}^4 a^2 b^2 \log (x)+4 \text{$\#$1}^4 a^2 b^2 \log \left(-\text{$\#$1} x+\sqrt{a^4 x^4+b^4}+a^2 x^2+b^2\right)-8 \text{$\#$1}^2 a^4 b^4 \log (x)+8 \text{$\#$1}^2 a^4 b^4 \log \left(-\text{$\#$1} x+\sqrt{a^4 x^4+b^4}+a^2 x^2+b^2\right)-8 a^6 b^6 \log \left(-\text{$\#$1} x+\sqrt{a^4 x^4+b^4}+a^2 x^2+b^2\right)+8 a^6 b^6 \log (x)}{-\text{$\#$1}^7+9 \text{$\#$1}^5 a^2 b^2-12 \text{$\#$1}^3 a^4 b^4+12 \text{$\#$1} a^6 b^6}\&\right]-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} a b x}{\sqrt{a^4 x^4+b^4}+a^2 x^2+b^2}\right)}{5 a b}",1,"((-1)^(1/10)*Sqrt[1 + (a^4*x^4)/b^4]*((1 + (-1)^(1/5))^2*(1 - 3*(-1)^(1/5) + (-1)^(2/5))*EllipticF[I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] + 2*((-1)^(2/5)*EllipticPi[-I, I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] + (1 - (-1)^(1/5) + 2*(-1)^(2/5) - (-1)^(3/5) + (-1)^(4/5))*EllipticPi[-(-1)^(1/10), I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] - EllipticPi[(-1)^(3/10), I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] + (-1)^(1/5)*EllipticPi[(-1)^(3/10), I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] + (-1)^(3/5)*EllipticPi[(-1)^(3/10), I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] - (-1)^(4/5)*EllipticPi[(-1)^(3/10), I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] + (-1)^(2/5)*EllipticPi[(-1)^(7/10), I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] - EllipticPi[-(-1)^(9/10), I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] + (-1)^(1/5)*EllipticPi[-(-1)^(9/10), I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] + (-1)^(3/5)*EllipticPi[-(-1)^(9/10), I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1] - (-1)^(4/5)*EllipticPi[-(-1)^(9/10), I*ArcSinh[Sqrt[(I*a^2)/b^2]*x], -1])))/((-1 + (-1)^(1/5))^2*(1 + (-1)^(1/5))^4*(1 + (-1)^(2/5))*(1 - (-1)^(1/5) + (-1)^(2/5))*Sqrt[(I*a^2)/b^2]*Sqrt[b^4 + a^4*x^4])","C",0
2966,1,168,367,0.255377,"\int \frac{\left(b+a x^2\right) \sqrt[3]{x+x^3}}{d+c x^2} \, dx","Integrate[((b + a*x^2)*(x + x^3)^(1/3))/(d + c*x^2),x]","\frac{x \sqrt[3]{x^3+x} \left(2 x^2 \left(\frac{c x^2}{d}+1\right)^{2/3} (a (c-3 d)+3 b c) F_1\left(\frac{5}{3};\frac{2}{3},1;\frac{8}{3};-x^2,-\frac{c x^2}{d}\right)+5 \left((3 b c-2 a d) \, _2F_1\left(\frac{2}{3},\frac{2}{3};\frac{5}{3};\frac{(c-d) x^2}{c x^2+d}\right)+2 a d \sqrt[3]{x^2+1} \left(\frac{c x^2}{d}+1\right)^{2/3}\right)\right)}{20 c d \sqrt[3]{x^2+1} \left(\frac{c x^2}{d}+1\right)^{2/3}}","\frac{\sqrt[3]{c-d} (b c-a d) \log \left(-\sqrt[3]{d} \sqrt[3]{x^3+x} x \sqrt[3]{c-d}+x^2 (c-d)^{2/3}+d^{2/3} \left(x^3+x\right)^{2/3}\right)}{4 c^2 \sqrt[3]{d}}+\frac{\log \left(\sqrt[3]{x^3+x}-x\right) (-a c+3 a d-3 b c)}{6 c^2}-\frac{\sqrt[3]{c-d} (b c-a d) \log \left(x \sqrt[3]{c-d}+\sqrt[3]{d} \sqrt[3]{x^3+x}\right)}{2 c^2 \sqrt[3]{d}}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+x}+x}\right) (a c-3 a d+3 b c)}{2 \sqrt{3} c^2}-\frac{\sqrt{3} \sqrt[3]{c-d} (b c-a d) \tan ^{-1}\left(\frac{\sqrt{3} x \sqrt[3]{c-d}}{x \sqrt[3]{c-d}-2 \sqrt[3]{d} \sqrt[3]{x^3+x}}\right)}{2 c^2 \sqrt[3]{d}}+\frac{\log \left(\sqrt[3]{x^3+x} x+\left(x^3+x\right)^{2/3}+x^2\right) (a c-3 a d+3 b c)}{12 c^2}+\frac{a \sqrt[3]{x^3+x} x}{2 c}",1,"(x*(x + x^3)^(1/3)*(2*(3*b*c + a*(c - 3*d))*x^2*(1 + (c*x^2)/d)^(2/3)*AppellF1[5/3, 2/3, 1, 8/3, -x^2, -((c*x^2)/d)] + 5*(2*a*d*(1 + x^2)^(1/3)*(1 + (c*x^2)/d)^(2/3) + (3*b*c - 2*a*d)*Hypergeometric2F1[2/3, 2/3, 5/3, ((c - d)*x^2)/(d + c*x^2)])))/(20*c*d*(1 + x^2)^(1/3)*(1 + (c*x^2)/d)^(2/3))","C",0
2967,1,923,367,2.190159,"\int \frac{x^2 \left(b+a x^3\right) \left(-b p+3 a q+2 a p x^3\right)}{\left(q+p x^3\right)^{2/3} \left(b^3 c+d q+\left(3 a b^2 c+d p\right) x^3+3 a^2 b c x^6+a^3 c x^9\right)} \, dx","Integrate[(x^2*(b + a*x^3)*(-(b*p) + 3*a*q + 2*a*p*x^3))/((q + p*x^3)^(2/3)*(b^3*c + d*q + (3*a*b^2*c + d*p)*x^3 + 3*a^2*b*c*x^6 + a^3*c*x^9)),x]","\frac{1}{6} p \left(\text{RootSum}\left[-c q^3 a^3+c \text{$\#$1}^3 a^3-3 c q \text{$\#$1}^2 a^3+3 c q^2 \text{$\#$1} a^3+3 b c p q^2 a^2+3 b c p \text{$\#$1}^2 a^2-6 b c p q \text{$\#$1} a^2-3 b^2 c p^2 q a+3 b^2 c p^2 \text{$\#$1} a+b^3 c p^3+d p^3 \text{$\#$1}\&,\frac{\frac{2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{p x^3+q}}{\sqrt[3]{\text{$\#$1}}}+1}{\sqrt{3}}\right)}{\text{$\#$1}^{2/3}}-\frac{2 \log \left(\sqrt[3]{\text{$\#$1}}-\sqrt[3]{p x^3+q}\right)}{\text{$\#$1}^{2/3}}+\frac{\log \left(\left(p x^3+q\right)^{2/3}+\sqrt[3]{\text{$\#$1}} \sqrt[3]{p x^3+q}+\text{$\#$1}^{2/3}\right)}{\text{$\#$1}^{2/3}}}{3 c q^2 a^3+3 c \text{$\#$1}^2 a^3-6 c q \text{$\#$1} a^3-6 b c p q a^2+6 b c p \text{$\#$1} a^2+3 b^2 c p^2 a+d p^3}\&\right] (b p-a q)^2+a \left((a q-b p) \text{RootSum}\left[-c q^3 a^3+c \text{$\#$1}^3 a^3-3 c q \text{$\#$1}^2 a^3+3 c q^2 \text{$\#$1} a^3+3 b c p q^2 a^2+3 b c p \text{$\#$1}^2 a^2-6 b c p q \text{$\#$1} a^2-3 b^2 c p^2 q a+3 b^2 c p^2 \text{$\#$1} a+b^3 c p^3+d p^3 \text{$\#$1}\&,\frac{2 \sqrt{3} \sqrt[3]{\text{$\#$1}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{p x^3+q}}{\sqrt[3]{\text{$\#$1}}}+1}{\sqrt{3}}\right)-2 \log \left(\sqrt[3]{\text{$\#$1}}-\sqrt[3]{p x^3+q}\right) \sqrt[3]{\text{$\#$1}}+\log \left(\left(p x^3+q\right)^{2/3}+\sqrt[3]{\text{$\#$1}} \sqrt[3]{p x^3+q}+\text{$\#$1}^{2/3}\right) \sqrt[3]{\text{$\#$1}}}{3 c q^2 a^3+3 c \text{$\#$1}^2 a^3-6 c q \text{$\#$1} a^3-6 b c p q a^2+6 b c p \text{$\#$1} a^2+3 b^2 c p^2 a+d p^3}\&\right]-2 a \text{RootSum}\left[-c q^3 a^3+c \text{$\#$1}^3 a^3-3 c q \text{$\#$1}^2 a^3+3 c q^2 \text{$\#$1} a^3+3 b c p q^2 a^2+3 b c p \text{$\#$1}^2 a^2-6 b c p q \text{$\#$1} a^2-3 b^2 c p^2 q a+3 b^2 c p^2 \text{$\#$1} a+b^3 c p^3+d p^3 \text{$\#$1}\&,\frac{2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{p x^3+q}}{\sqrt[3]{\text{$\#$1}}}+1}{\sqrt{3}}\right) \text{$\#$1}^{4/3}-2 \log \left(\sqrt[3]{\text{$\#$1}}-\sqrt[3]{p x^3+q}\right) \text{$\#$1}^{4/3}+\log \left(\left(p x^3+q\right)^{2/3}+\sqrt[3]{\text{$\#$1}} \sqrt[3]{p x^3+q}+\text{$\#$1}^{2/3}\right) \text{$\#$1}^{4/3}}{3 c q^2 a^3+3 c \text{$\#$1}^2 a^3-6 c q \text{$\#$1} a^3-6 b c p q a^2+6 b c p \text{$\#$1} a^2+3 b^2 c p^2 a+d p^3}\&\right]\right)\right)","\frac{1}{3} p \text{RootSum}\left[\text{$\#$1}^9 a^3 c-3 \text{$\#$1}^6 a^3 c q+3 \text{$\#$1}^6 a^2 b c p+3 \text{$\#$1}^3 a^3 c q^2-6 \text{$\#$1}^3 a^2 b c p q+3 \text{$\#$1}^3 a b^2 c p^2+\text{$\#$1}^3 d p^3-a^3 c q^3+3 a^2 b c p q^2-3 a b^2 c p^2 q+b^3 c p^3\&,\frac{2 \text{$\#$1}^6 a^2 \log \left(\sqrt[3]{p x^3+q}-\text{$\#$1}\right)-\text{$\#$1}^3 a^2 q \log \left(\sqrt[3]{p x^3+q}-\text{$\#$1}\right)+\text{$\#$1}^3 a b p \log \left(\sqrt[3]{p x^3+q}-\text{$\#$1}\right)-a^2 q^2 \log \left(\sqrt[3]{p x^3+q}-\text{$\#$1}\right)+2 a b p q \log \left(\sqrt[3]{p x^3+q}-\text{$\#$1}\right)-b^2 p^2 \log \left(\sqrt[3]{p x^3+q}-\text{$\#$1}\right)}{3 \text{$\#$1}^8 a^3 c-6 \text{$\#$1}^5 a^3 c q+6 \text{$\#$1}^5 a^2 b c p+3 \text{$\#$1}^2 a^3 c q^2-6 \text{$\#$1}^2 a^2 b c p q+3 \text{$\#$1}^2 a b^2 c p^2+\text{$\#$1}^2 d p^3}\&\right]",1,"(p*((b*p - a*q)^2*RootSum[b^3*c*p^3 - 3*a*b^2*c*p^2*q + 3*a^2*b*c*p*q^2 - a^3*c*q^3 + 3*a*b^2*c*p^2*#1 + d*p^3*#1 - 6*a^2*b*c*p*q*#1 + 3*a^3*c*q^2*#1 + 3*a^2*b*c*p*#1^2 - 3*a^3*c*q*#1^2 + a^3*c*#1^3 & , ((2*Sqrt[3]*ArcTan[(1 + (2*(q + p*x^3)^(1/3))/#1^(1/3))/Sqrt[3]])/#1^(2/3) - (2*Log[-(q + p*x^3)^(1/3) + #1^(1/3)])/#1^(2/3) + Log[(q + p*x^3)^(2/3) + (q + p*x^3)^(1/3)*#1^(1/3) + #1^(2/3)]/#1^(2/3))/(3*a*b^2*c*p^2 + d*p^3 - 6*a^2*b*c*p*q + 3*a^3*c*q^2 + 6*a^2*b*c*p*#1 - 6*a^3*c*q*#1 + 3*a^3*c*#1^2) & ] + a*((-(b*p) + a*q)*RootSum[b^3*c*p^3 - 3*a*b^2*c*p^2*q + 3*a^2*b*c*p*q^2 - a^3*c*q^3 + 3*a*b^2*c*p^2*#1 + d*p^3*#1 - 6*a^2*b*c*p*q*#1 + 3*a^3*c*q^2*#1 + 3*a^2*b*c*p*#1^2 - 3*a^3*c*q*#1^2 + a^3*c*#1^3 & , (2*Sqrt[3]*ArcTan[(1 + (2*(q + p*x^3)^(1/3))/#1^(1/3))/Sqrt[3]]*#1^(1/3) - 2*Log[-(q + p*x^3)^(1/3) + #1^(1/3)]*#1^(1/3) + Log[(q + p*x^3)^(2/3) + (q + p*x^3)^(1/3)*#1^(1/3) + #1^(2/3)]*#1^(1/3))/(3*a*b^2*c*p^2 + d*p^3 - 6*a^2*b*c*p*q + 3*a^3*c*q^2 + 6*a^2*b*c*p*#1 - 6*a^3*c*q*#1 + 3*a^3*c*#1^2) & ] - 2*a*RootSum[b^3*c*p^3 - 3*a*b^2*c*p^2*q + 3*a^2*b*c*p*q^2 - a^3*c*q^3 + 3*a*b^2*c*p^2*#1 + d*p^3*#1 - 6*a^2*b*c*p*q*#1 + 3*a^3*c*q^2*#1 + 3*a^2*b*c*p*#1^2 - 3*a^3*c*q*#1^2 + a^3*c*#1^3 & , (2*Sqrt[3]*ArcTan[(1 + (2*(q + p*x^3)^(1/3))/#1^(1/3))/Sqrt[3]]*#1^(4/3) - 2*Log[-(q + p*x^3)^(1/3) + #1^(1/3)]*#1^(4/3) + Log[(q + p*x^3)^(2/3) + (q + p*x^3)^(1/3)*#1^(1/3) + #1^(2/3)]*#1^(4/3))/(3*a*b^2*c*p^2 + d*p^3 - 6*a^2*b*c*p*q + 3*a^3*c*q^2 + 6*a^2*b*c*p*#1 - 6*a^3*c*q*#1 + 3*a^3*c*#1^2) & ])))/6","B",1
2968,0,0,369,9.9294272,"\int \frac{a b+a c-2 b c+(-2 a+b+c) x}{\sqrt[3]{(-a+x) (-b+x) (-c+x)} \left(a^2-b c d+(-2 a+b d+c d) x+(1-d) x^2\right)} \, dx","Integrate[(a*b + a*c - 2*b*c + (-2*a + b + c)*x)/(((-a + x)*(-b + x)*(-c + x))^(1/3)*(a^2 - b*c*d + (-2*a + b*d + c*d)*x + (1 - d)*x^2)),x]","\int \frac{a b+a c-2 b c+(-2 a+b+c) x}{\sqrt[3]{(-a+x) (-b+x) (-c+x)} \left(a^2-b c d+(-2 a+b d+c d) x+(1-d) x^2\right)} \, dx","-\frac{i \left(\sqrt{3}-i\right) \log \left(\sqrt[3]{-1} \left(a^2-2 a x+x^2\right)-d^{2/3} \left(x^2 (-a-b-c)+x (a b+a c+b c)-a b c+x^3\right)^{2/3}+(-1)^{2/3} \sqrt[3]{d} (a-x) \sqrt[3]{x^2 (-a-b-c)+x (a b+a c+b c)-a b c+x^3}\right)}{4 d^{2/3}}+\frac{\left(1+i \sqrt{3}\right) \log \left(\sqrt[3]{d} \sqrt[3]{x^2 (-a-b-c)+x (a b+a c+b c)-a b c+x^3}+(-1)^{2/3} (a-x)\right)}{2 d^{2/3}}+\frac{\sqrt{\frac{1}{2} \left(-3+3 i \sqrt{3}\right)} \tan ^{-1}\left(\frac{3 \sqrt[3]{d} \sqrt[3]{x^2 (-a-b-c)+x (a b+a c+b c)-a b c+x^3}}{\sqrt{3} \sqrt[3]{d} \sqrt[3]{x^2 (-a-b-c)+x (a b+a c+b c)-a b c+x^3}+\sqrt{3} a-3 i a-\sqrt{3} x+3 i x}\right)}{d^{2/3}}",1,"Integrate[(a*b + a*c - 2*b*c + (-2*a + b + c)*x)/(((-a + x)*(-b + x)*(-c + x))^(1/3)*(a^2 - b*c*d + (-2*a + b*d + c*d)*x + (1 - d)*x^2)), x]","F",-1
2969,0,0,370,1.3924154,"\int \frac{(-2+x) \left(1-x+x^2\right)}{x^3 \left(-1+x+x^2\right) \sqrt[3]{\frac{1-x+2 x^2}{1-x+3 x^2}}} \, dx","Integrate[((-2 + x)*(1 - x + x^2))/(x^3*(-1 + x + x^2)*((1 - x + 2*x^2)/(1 - x + 3*x^2))^(1/3)),x]","\int \frac{(-2+x) \left(1-x+x^2\right)}{x^3 \left(-1+x+x^2\right) \sqrt[3]{\frac{1-x+2 x^2}{1-x+3 x^2}}} \, dx","\frac{\left(\frac{2 x^2-x+1}{3 x^2-x+1}\right)^{2/3} \left(-3 x^2+x-1\right)}{x^2}+\frac{7}{3} \log \left(\sqrt[3]{\frac{2 x^2-x+1}{3 x^2-x+1}}-1\right)-\frac{2\ 2^{2/3} \log \left(6^{2/3} \sqrt[3]{\frac{2 x^2-x+1}{3 x^2-x+1}}-3\right)}{\sqrt[3]{3}}-\frac{7}{6} \log \left(\left(\frac{2 x^2-x+1}{3 x^2-x+1}\right)^{2/3}+\sqrt[3]{\frac{2 x^2-x+1}{3 x^2-x+1}}+1\right)+\frac{2^{2/3} \log \left(2 \sqrt[3]{6} \left(\frac{2 x^2-x+1}{3 x^2-x+1}\right)^{2/3}+6^{2/3} \sqrt[3]{\frac{2 x^2-x+1}{3 x^2-x+1}}+3\right)}{\sqrt[3]{3}}-2\ 2^{2/3} \sqrt[6]{3} \tan ^{-1}\left(\frac{2\ 2^{2/3} \sqrt[3]{\frac{2 x^2-x+1}{3 x^2-x+1}}}{3^{5/6}}+\frac{1}{\sqrt{3}}\right)+\frac{7 \tan ^{-1}\left(\frac{2 \sqrt[3]{\frac{2 x^2-x+1}{3 x^2-x+1}}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3}}",1,"Integrate[((-2 + x)*(1 - x + x^2))/(x^3*(-1 + x + x^2)*((1 - x + 2*x^2)/(1 - x + 3*x^2))^(1/3)), x]","F",-1
2970,0,0,371,0.6177709,"\int \frac{x^3 \left(5 b+9 a x^4\right)}{\sqrt[4]{b x+a x^5} \left(1+b x^5+a x^9\right)} \, dx","Integrate[(x^3*(5*b + 9*a*x^4))/((b*x + a*x^5)^(1/4)*(1 + b*x^5 + a*x^9)),x]","\int \frac{x^3 \left(5 b+9 a x^4\right)}{\sqrt[4]{b x+a x^5} \left(1+b x^5+a x^9\right)} \, dx","-\sqrt{2} \tan ^{-1}\left(\frac{x^2 \sqrt[4]{a x^5+b x}-2^{2/3} x \sqrt[4]{a x^5+b x}}{2^{2/3} x \sqrt[4]{a x^5+b x}+x^2 \left(-\sqrt[4]{a x^5+b x}\right)-\sqrt{2} x+2 \sqrt[6]{2}}\right)+\sqrt{2} \tan ^{-1}\left(\frac{x^2 \sqrt[4]{a x^5+b x}-2^{2/3} x \sqrt[4]{a x^5+b x}}{2^{2/3} x \sqrt[4]{a x^5+b x}+x^2 \left(-\sqrt[4]{a x^5+b x}\right)+\sqrt{2} x-2 \sqrt[6]{2}}\right)-\sqrt{2} \tanh ^{-1}\left(\frac{-2\ 2^{5/6} x \sqrt[4]{a x^5+b x}-\sqrt{2} x^3 \sqrt[4]{a x^5+b x}+4 \sqrt[6]{2} x^2 \sqrt[4]{a x^5+b x}}{x^4 \left(-\sqrt{a x^5+b x}\right)+2\ 2^{2/3} x^3 \sqrt{a x^5+b x}-2 \sqrt[3]{2} x^2 \sqrt{a x^5+b x}-x^2+2\ 2^{2/3} x-2 \sqrt[3]{2}}\right)",1,"Integrate[(x^3*(5*b + 9*a*x^4))/((b*x + a*x^5)^(1/4)*(1 + b*x^5 + a*x^9)), x]","F",-1
2971,1,968,375,1.812479,"\int \frac{\sqrt{1+x^2} \left(1+x^4\right) \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{1-x^4} \, dx","Integrate[(Sqrt[1 + x^2]*(1 + x^4)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^4),x]","-\frac{\left(x^2+\sqrt{x^2+1} x+1\right) \left(71680 \sqrt{\sqrt{x+\sqrt{x^2+1}}+1} x^4+71680 \sqrt{x^2+1} \sqrt{\sqrt{x+\sqrt{x^2+1}}+1} x^3+5120 \sqrt{x+\sqrt{x^2+1}} \sqrt{\sqrt{x+\sqrt{x^2+1}}+1} x^3-6144 \sqrt{\sqrt{x+\sqrt{x^2+1}}+1} x^3+158130 \log \left(1-\sqrt{\sqrt{x+\sqrt{x^2+1}}+1}\right) x^2-158130 \log \left(\sqrt{\sqrt{x+\sqrt{x^2+1}}+1}+1\right) x^2-6144 \sqrt{x^2+1} \sqrt{\sqrt{x+\sqrt{x^2+1}}+1} x^2+5120 \sqrt{x^2+1} \sqrt{x+\sqrt{x^2+1}} \sqrt{\sqrt{x+\sqrt{x^2+1}}+1} x^2+4096 \sqrt{x+\sqrt{x^2+1}} \sqrt{\sqrt{x+\sqrt{x^2+1}}+1} x^2+386048 \sqrt{\sqrt{x+\sqrt{x^2+1}}+1} x^2+158130 \sqrt{x^2+1} \log \left(1-\sqrt{\sqrt{x+\sqrt{x^2+1}}+1}\right) x-158130 \sqrt{x^2+1} \log \left(\sqrt{\sqrt{x+\sqrt{x^2+1}}+1}+1\right) x+350208 \sqrt{x^2+1} \sqrt{\sqrt{x+\sqrt{x^2+1}}+1} x+4096 \sqrt{x^2+1} \sqrt{x+\sqrt{x^2+1}} \sqrt{\sqrt{x+\sqrt{x^2+1}}+1} x+690 \sqrt{x+\sqrt{x^2+1}} \sqrt{\sqrt{x+\sqrt{x^2+1}}+1} x-2508 \sqrt{\sqrt{x+\sqrt{x^2+1}}+1} x+79065 \log \left(1-\sqrt{\sqrt{x+\sqrt{x^2+1}}+1}\right)-79065 \log \left(\sqrt{\sqrt{x+\sqrt{x^2+1}}+1}+1\right)+80640 \left(2 x^2+2 \sqrt{x^2+1} x+1\right) \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\log \left(\sqrt{\sqrt{x+\sqrt{x^2+1}}+1}-\text{$\#$1}\right)}{\text{$\#$1}^3-2 \text{$\#$1}}\&\right]-80640 \left(2 x^2+2 \sqrt{x^2+1} x+1\right) \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\log \left(\sqrt{\sqrt{x+\sqrt{x^2+1}}+1}-\text{$\#$1}\right) \text{$\#$1}}{\text{$\#$1}^4-2 \text{$\#$1}^2+2}\&\right]+564 \sqrt{x^2+1} \sqrt{\sqrt{x+\sqrt{x^2+1}}+1}-1870 \sqrt{x^2+1} \sqrt{x+\sqrt{x^2+1}} \sqrt{\sqrt{x+\sqrt{x^2+1}}+1}+368 \sqrt{x+\sqrt{x^2+1}} \sqrt{\sqrt{x+\sqrt{x^2+1}}+1}+156064 \sqrt{\sqrt{x+\sqrt{x^2+1}}+1}\right)}{80640 \sqrt{x^2+1} \left(x+\sqrt{x^2+1}\right)^3}","-\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^3-2 \text{$\#$1}}\&\right]+\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^4-2 \text{$\#$1}^2+2}\&\right]+\frac{251}{128} \tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\frac{\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(-2560 x^3-2048 x^2-345 x-184\right)+\sqrt{x^2+1} \left(\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(-2560 x^2-2048 x+935\right)+\left(-35840 x^3+3072 x^2-175104 x-282\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\left(-35840 x^4+3072 x^3-193024 x^2+1254 x-78032\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{80640 \sqrt{x^2+1} x+40320 \left(2 x^2+1\right)}",1,"-1/80640*((1 + x^2 + x*Sqrt[1 + x^2])*(156064*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - 2508*x*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] + 386048*x^2*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - 6144*x^3*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] + 71680*x^4*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] + 564*Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] + 350208*x*Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - 6144*x^2*Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] + 71680*x^3*Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] + 368*Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] + 690*x*Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] + 4096*x^2*Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] + 5120*x^3*Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - 1870*Sqrt[1 + x^2]*Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] + 4096*x*Sqrt[1 + x^2]*Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] + 5120*x^2*Sqrt[1 + x^2]*Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] + 79065*Log[1 - Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]] + 158130*x^2*Log[1 - Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]] + 158130*x*Sqrt[1 + x^2]*Log[1 - Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]] - 79065*Log[1 + Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]] - 158130*x^2*Log[1 + Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]] - 158130*x*Sqrt[1 + x^2]*Log[1 + Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]] + 80640*(1 + 2*x^2 + 2*x*Sqrt[1 + x^2])*RootSum[-2 + 4*#1^4 - 4*#1^6 + #1^8 & , Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]/(-2*#1 + #1^3) & ] - 80640*(1 + 2*x^2 + 2*x*Sqrt[1 + x^2])*RootSum[2 - 8*#1^2 + 8*#1^4 - 4*#1^6 + #1^8 & , (Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1)/(2 - 2*#1^2 + #1^4) & ]))/(Sqrt[1 + x^2]*(x + Sqrt[1 + x^2])^3)","B",1
2972,1,968,375,0.5597593,"\int \frac{\sqrt{1+x^2} \left(1+x^4\right) \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{1-x^4} \, dx","Integrate[(Sqrt[1 + x^2]*(1 + x^4)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^4),x]","-\frac{\left(x^2+\sqrt{x^2+1} x+1\right) \left(71680 \sqrt{\sqrt{x+\sqrt{x^2+1}}+1} x^4+71680 \sqrt{x^2+1} \sqrt{\sqrt{x+\sqrt{x^2+1}}+1} x^3+5120 \sqrt{x+\sqrt{x^2+1}} \sqrt{\sqrt{x+\sqrt{x^2+1}}+1} x^3-6144 \sqrt{\sqrt{x+\sqrt{x^2+1}}+1} x^3+158130 \log \left(1-\sqrt{\sqrt{x+\sqrt{x^2+1}}+1}\right) x^2-158130 \log \left(\sqrt{\sqrt{x+\sqrt{x^2+1}}+1}+1\right) x^2-6144 \sqrt{x^2+1} \sqrt{\sqrt{x+\sqrt{x^2+1}}+1} x^2+5120 \sqrt{x^2+1} \sqrt{x+\sqrt{x^2+1}} \sqrt{\sqrt{x+\sqrt{x^2+1}}+1} x^2+4096 \sqrt{x+\sqrt{x^2+1}} \sqrt{\sqrt{x+\sqrt{x^2+1}}+1} x^2+386048 \sqrt{\sqrt{x+\sqrt{x^2+1}}+1} x^2+158130 \sqrt{x^2+1} \log \left(1-\sqrt{\sqrt{x+\sqrt{x^2+1}}+1}\right) x-158130 \sqrt{x^2+1} \log \left(\sqrt{\sqrt{x+\sqrt{x^2+1}}+1}+1\right) x+350208 \sqrt{x^2+1} \sqrt{\sqrt{x+\sqrt{x^2+1}}+1} x+4096 \sqrt{x^2+1} \sqrt{x+\sqrt{x^2+1}} \sqrt{\sqrt{x+\sqrt{x^2+1}}+1} x+690 \sqrt{x+\sqrt{x^2+1}} \sqrt{\sqrt{x+\sqrt{x^2+1}}+1} x-2508 \sqrt{\sqrt{x+\sqrt{x^2+1}}+1} x+79065 \log \left(1-\sqrt{\sqrt{x+\sqrt{x^2+1}}+1}\right)-79065 \log \left(\sqrt{\sqrt{x+\sqrt{x^2+1}}+1}+1\right)+80640 \left(2 x^2+2 \sqrt{x^2+1} x+1\right) \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\log \left(\sqrt{\sqrt{x+\sqrt{x^2+1}}+1}-\text{$\#$1}\right)}{\text{$\#$1}^3-2 \text{$\#$1}}\&\right]-80640 \left(2 x^2+2 \sqrt{x^2+1} x+1\right) \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\log \left(\sqrt{\sqrt{x+\sqrt{x^2+1}}+1}-\text{$\#$1}\right) \text{$\#$1}}{\text{$\#$1}^4-2 \text{$\#$1}^2+2}\&\right]+564 \sqrt{x^2+1} \sqrt{\sqrt{x+\sqrt{x^2+1}}+1}-1870 \sqrt{x^2+1} \sqrt{x+\sqrt{x^2+1}} \sqrt{\sqrt{x+\sqrt{x^2+1}}+1}+368 \sqrt{x+\sqrt{x^2+1}} \sqrt{\sqrt{x+\sqrt{x^2+1}}+1}+156064 \sqrt{\sqrt{x+\sqrt{x^2+1}}+1}\right)}{80640 \sqrt{x^2+1} \left(x+\sqrt{x^2+1}\right)^3}","-\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^3-2 \text{$\#$1}}\&\right]+\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^4-2 \text{$\#$1}^2+2}\&\right]+\frac{251}{128} \tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\frac{\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(-2560 x^3-2048 x^2-345 x-184\right)+\sqrt{x^2+1} \left(\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(-2560 x^2-2048 x+935\right)+\left(-35840 x^3+3072 x^2-175104 x-282\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\left(-35840 x^4+3072 x^3-193024 x^2+1254 x-78032\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{80640 \sqrt{x^2+1} x+40320 \left(2 x^2+1\right)}",1,"-1/80640*((1 + x^2 + x*Sqrt[1 + x^2])*(156064*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - 2508*x*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] + 386048*x^2*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - 6144*x^3*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] + 71680*x^4*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] + 564*Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] + 350208*x*Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - 6144*x^2*Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] + 71680*x^3*Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] + 368*Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] + 690*x*Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] + 4096*x^2*Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] + 5120*x^3*Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - 1870*Sqrt[1 + x^2]*Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] + 4096*x*Sqrt[1 + x^2]*Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] + 5120*x^2*Sqrt[1 + x^2]*Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] + 79065*Log[1 - Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]] + 158130*x^2*Log[1 - Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]] + 158130*x*Sqrt[1 + x^2]*Log[1 - Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]] - 79065*Log[1 + Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]] - 158130*x^2*Log[1 + Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]] - 158130*x*Sqrt[1 + x^2]*Log[1 + Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]] + 80640*(1 + 2*x^2 + 2*x*Sqrt[1 + x^2])*RootSum[-2 + 4*#1^4 - 4*#1^6 + #1^8 & , Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]/(-2*#1 + #1^3) & ] - 80640*(1 + 2*x^2 + 2*x*Sqrt[1 + x^2])*RootSum[2 - 8*#1^2 + 8*#1^4 - 4*#1^6 + #1^8 & , (Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1)/(2 - 2*#1^2 + #1^4) & ]))/(Sqrt[1 + x^2]*(x + Sqrt[1 + x^2])^3)","B",1
2973,1,319,376,2.0405615,"\int \frac{b^{12}+a^{12} x^{12}}{\sqrt{-b^4+a^4 x^4} \left(-b^{12}+a^{12} x^{12}\right)} \, dx","Integrate[(b^12 + a^12*x^12)/(Sqrt[-b^4 + a^4*x^4]*(-b^12 + a^12*x^12)),x]","\frac{x \left(-\sqrt{-\frac{a^2}{b^2}}\right)-2 i \sqrt{1-\frac{a^4 x^4}{b^4}} F\left(\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)+i \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(-\frac{2 i}{-i+\sqrt{3}};\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)+i \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(\frac{2 i}{-i+\sqrt{3}};\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)+i \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(-\frac{2 i}{i+\sqrt{3}};\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)+i \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(\frac{2 i}{i+\sqrt{3}};\left.i \sinh ^{-1}\left(\sqrt{-\frac{a^2}{b^2}} x\right)\right|-1\right)}{3 \sqrt{-\frac{a^2}{b^2}} \sqrt{a^4 x^4-b^4}}","-\frac{x}{3 \sqrt{a^4 x^4-b^4}}+\frac{1}{6} \text{RootSum}\left[\text{$\#$1}^8-8 i \text{$\#$1}^6 a^2 b^2+24 \text{$\#$1}^4 a^4 b^4+32 i \text{$\#$1}^2 a^6 b^6+16 a^8 b^8\&,\frac{-i \text{$\#$1}^6 \log \left(-\text{$\#$1} x+\sqrt{a^4 x^4-b^4}+a^2 x^2+i b^2\right)+i \text{$\#$1}^6 \log (x)+2 \text{$\#$1}^4 a^2 b^2 \log (x)-2 \text{$\#$1}^4 a^2 b^2 \log \left(-\text{$\#$1} x+\sqrt{a^4 x^4-b^4}+a^2 x^2+i b^2\right)+4 i \text{$\#$1}^2 a^4 b^4 \log (x)-4 i \text{$\#$1}^2 a^4 b^4 \log \left(-\text{$\#$1} x+\sqrt{a^4 x^4-b^4}+a^2 x^2+i b^2\right)-8 a^6 b^6 \log \left(-\text{$\#$1} x+\sqrt{a^4 x^4-b^4}+a^2 x^2+i b^2\right)+8 a^6 b^6 \log (x)}{-i \text{$\#$1}^7-6 \text{$\#$1}^5 a^2 b^2-12 i \text{$\#$1}^3 a^4 b^4+8 \text{$\#$1} a^6 b^6}\&\right]",1,"(-(Sqrt[-(a^2/b^2)]*x) - (2*I)*Sqrt[1 - (a^4*x^4)/b^4]*EllipticF[I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1] + I*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[(-2*I)/(-I + Sqrt[3]), I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1] + I*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[(2*I)/(-I + Sqrt[3]), I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1] + I*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[(-2*I)/(I + Sqrt[3]), I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1] + I*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[(2*I)/(I + Sqrt[3]), I*ArcSinh[Sqrt[-(a^2/b^2)]*x], -1])/(3*Sqrt[-(a^2/b^2)]*Sqrt[-b^4 + a^4*x^4])","A",1
2974,0,0,376,0.9416145,"\int \frac{\sqrt{a x^2+\sqrt{b+a^2 x^4}}}{\sqrt{b+a^2 x^4} \left(d+c x^4\right)} \, dx","Integrate[Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/(Sqrt[b + a^2*x^4]*(d + c*x^4)),x]","\int \frac{\sqrt{a x^2+\sqrt{b+a^2 x^4}}}{\sqrt{b+a^2 x^4} \left(d+c x^4\right)} \, dx","-\sqrt{2} a^{3/2} \text{RootSum}\left[\text{$\#$1}^8 c-16 \text{$\#$1}^6 a^2 d+4 \text{$\#$1}^6 b c+32 \text{$\#$1}^4 a^2 b d+6 \text{$\#$1}^4 b^2 c-16 \text{$\#$1}^2 a^2 b^2 d+4 \text{$\#$1}^2 b^3 c+b^4 c\&,\frac{\text{$\#$1}^4 \log \left(-\text{$\#$1}+i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)-2 \text{$\#$1}^2 b \log \left(-\text{$\#$1}+i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)+b^2 \log \left(-\text{$\#$1}+i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)}{\text{$\#$1}^6 c-12 \text{$\#$1}^4 a^2 d+3 \text{$\#$1}^4 b c+16 \text{$\#$1}^2 a^2 b d+3 \text{$\#$1}^2 b^2 c-4 a^2 b^2 d+b^3 c}\&\right]",1,"Integrate[Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/(Sqrt[b + a^2*x^4]*(d + c*x^4)), x]","F",-1
2975,0,0,376,0.4562463,"\int \frac{\sqrt{a x^2+\sqrt{b+a^2 x^4}}}{\sqrt{b+a^2 x^4} \left(d+c x^4\right)} \, dx","Integrate[Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/(Sqrt[b + a^2*x^4]*(d + c*x^4)),x]","\int \frac{\sqrt{a x^2+\sqrt{b+a^2 x^4}}}{\sqrt{b+a^2 x^4} \left(d+c x^4\right)} \, dx","-\sqrt{2} a^{3/2} \text{RootSum}\left[\text{$\#$1}^8 c-16 \text{$\#$1}^6 a^2 d+4 \text{$\#$1}^6 b c+32 \text{$\#$1}^4 a^2 b d+6 \text{$\#$1}^4 b^2 c-16 \text{$\#$1}^2 a^2 b^2 d+4 \text{$\#$1}^2 b^3 c+b^4 c\&,\frac{\text{$\#$1}^4 \log \left(-\text{$\#$1}+i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)-2 \text{$\#$1}^2 b \log \left(-\text{$\#$1}+i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)+b^2 \log \left(-\text{$\#$1}+i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)}{\text{$\#$1}^6 c-12 \text{$\#$1}^4 a^2 d+3 \text{$\#$1}^4 b c+16 \text{$\#$1}^2 a^2 b d+3 \text{$\#$1}^2 b^2 c-4 a^2 b^2 d+b^3 c}\&\right]",1,"Integrate[Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/(Sqrt[b + a^2*x^4]*(d + c*x^4)), x]","F",-1
2976,-1,0,380,180.0030862,"\int \frac{x}{x-\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","Integrate[x/(x - Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]]),x]","\text{\$Aborted}","-4 \text{RootSum}\left[-\text{$\#$1}^4+\text{$\#$1}^3 a+2 \text{$\#$1}^2 c-\text{$\#$1} a c+b-c^2\&,\frac{\text{$\#$1}^3 a^3 \left(-\log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)\right)-\text{$\#$1}^3 a c \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-\text{$\#$1}^2 a^2 c \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-\text{$\#$1}^2 b \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+\text{$\#$1} a^3 c \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+a^2 c^2 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-a^2 b \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+\text{$\#$1} a c^2 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-\text{$\#$1} a b \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)}{4 \text{$\#$1}^3-3 \text{$\#$1}^2 a-4 \text{$\#$1} c+a c}\&\right]+\frac{4}{3} \left(3 a^2+c\right) \sqrt{\sqrt{a x+b}+c}+\sqrt{a x+b} \left(\frac{4}{3} \sqrt{\sqrt{a x+b}+c}+2 a\right)+x",1,"$Aborted","F",-1
2977,0,0,380,4.8632789,"\int \frac{x}{x-\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","Integrate[x/(x - Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]]),x]","\int \frac{x}{x-\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","-4 \text{RootSum}\left[-\text{$\#$1}^4+\text{$\#$1}^3 a+2 \text{$\#$1}^2 c-\text{$\#$1} a c+b-c^2\&,\frac{\text{$\#$1}^3 a^3 \left(-\log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)\right)-\text{$\#$1}^3 a c \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-\text{$\#$1}^2 a^2 c \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-\text{$\#$1}^2 b \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+\text{$\#$1} a^3 c \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+a^2 c^2 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-a^2 b \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+\text{$\#$1} a c^2 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-\text{$\#$1} a b \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)}{4 \text{$\#$1}^3-3 \text{$\#$1}^2 a-4 \text{$\#$1} c+a c}\&\right]+\frac{4}{3} \left(3 a^2+c\right) \sqrt{\sqrt{a x+b}+c}+\sqrt{a x+b} \left(\frac{4}{3} \sqrt{\sqrt{a x+b}+c}+2 a\right)+x",1,"Integrate[x/(x - Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]]), x]","F",-1
2978,0,0,383,1.6685275,"\int \frac{\left(-2 x+(1+k) x^2\right) \left(1-(1+k) x+(a+k) x^2\right)}{((1-x) x (1-k x))^{2/3} \left(1-2 (1+k) x+\left(1+4 k+k^2\right) x^2-2 \left(k+k^2\right) x^3+\left(-b+k^2\right) x^4\right)} \, dx","Integrate[((-2*x + (1 + k)*x^2)*(1 - (1 + k)*x + (a + k)*x^2))/(((1 - x)*x*(1 - k*x))^(2/3)*(1 - 2*(1 + k)*x + (1 + 4*k + k^2)*x^2 - 2*(k + k^2)*x^3 + (-b + k^2)*x^4)),x]","\int \frac{\left(-2 x+(1+k) x^2\right) \left(1-(1+k) x+(a+k) x^2\right)}{((1-x) x (1-k x))^{2/3} \left(1-2 (1+k) x+\left(1+4 k+k^2\right) x^2-2 \left(k+k^2\right) x^3+\left(-b+k^2\right) x^4\right)} \, dx","\frac{\left(a+\sqrt{b}\right) \log \left(\sqrt[3]{k x^3+(-k-1) x^2+x}-\sqrt[6]{b} x\right)}{2 b^{5/6}}+\frac{\left(\sqrt{b}-a\right) \log \left(\sqrt[6]{b} x+\sqrt[3]{k x^3+(-k-1) x^2+x}\right)}{2 b^{5/6}}+\frac{\left(a-\sqrt{b}\right) \log \left(-\sqrt[6]{b} x \sqrt[3]{k x^3+(-k-1) x^2+x}+\sqrt[3]{b} x^2+\left(k x^3+(-k-1) x^2+x\right)^{2/3}\right)}{4 b^{5/6}}+\frac{\left(-a-\sqrt{b}\right) \log \left(\sqrt[6]{b} x \sqrt[3]{k x^3+(-k-1) x^2+x}+\sqrt[3]{b} x^2+\left(k x^3+(-k-1) x^2+x\right)^{2/3}\right)}{4 b^{5/6}}-\frac{\sqrt{3} \left(a-\sqrt{b}\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{b} x}{\sqrt[6]{b} x-2 \sqrt[3]{k x^3+(-k-1) x^2+x}}\right)}{2 b^{5/6}}+\frac{\sqrt{3} \left(a+\sqrt{b}\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{b} x}{\sqrt[6]{b} x+2 \sqrt[3]{k x^3+(-k-1) x^2+x}}\right)}{2 b^{5/6}}",1,"Integrate[((-2*x + (1 + k)*x^2)*(1 - (1 + k)*x + (a + k)*x^2))/(((1 - x)*x*(1 - k*x))^(2/3)*(1 - 2*(1 + k)*x + (1 + 4*k + k^2)*x^2 - 2*(k + k^2)*x^3 + (-b + k^2)*x^4)), x]","F",-1
2979,0,0,383,7.6184496,"\int \frac{(-2+(1+k) x) \left(1-(1+k) x+(a+k) x^2\right)}{\sqrt[3]{(1-x) x (1-k x)} \left(1-(2+2 k) x+\left(1+4 k+k^2\right) x^2-2 \left(k+k^2\right) x^3+\left(-b+k^2\right) x^4\right)} \, dx","Integrate[((-2 + (1 + k)*x)*(1 - (1 + k)*x + (a + k)*x^2))/(((1 - x)*x*(1 - k*x))^(1/3)*(1 - (2 + 2*k)*x + (1 + 4*k + k^2)*x^2 - 2*(k + k^2)*x^3 + (-b + k^2)*x^4)),x]","\int \frac{(-2+(1+k) x) \left(1-(1+k) x+(a+k) x^2\right)}{\sqrt[3]{(1-x) x (1-k x)} \left(1-(2+2 k) x+\left(1+4 k+k^2\right) x^2-2 \left(k+k^2\right) x^3+\left(-b+k^2\right) x^4\right)} \, dx","\frac{\left(a+\sqrt{b}\right) \log \left(\sqrt[3]{k x^3+(-k-1) x^2+x}-\sqrt[6]{b} x\right)}{2 b^{2/3}}+\frac{\left(a-\sqrt{b}\right) \log \left(\sqrt[6]{b} x+\sqrt[3]{k x^3+(-k-1) x^2+x}\right)}{2 b^{2/3}}+\frac{\left(\sqrt{b}-a\right) \log \left(-\sqrt[6]{b} x \sqrt[3]{k x^3+(-k-1) x^2+x}+\sqrt[3]{b} x^2+\left(k x^3+(-k-1) x^2+x\right)^{2/3}\right)}{4 b^{2/3}}+\frac{\left(-a-\sqrt{b}\right) \log \left(\sqrt[6]{b} x \sqrt[3]{k x^3+(-k-1) x^2+x}+\sqrt[3]{b} x^2+\left(k x^3+(-k-1) x^2+x\right)^{2/3}\right)}{4 b^{2/3}}-\frac{\sqrt{3} \left(a-\sqrt{b}\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{b} x}{\sqrt[6]{b} x-2 \sqrt[3]{k x^3+(-k-1) x^2+x}}\right)}{2 b^{2/3}}-\frac{\sqrt{3} \left(a+\sqrt{b}\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{b} x}{\sqrt[6]{b} x+2 \sqrt[3]{k x^3+(-k-1) x^2+x}}\right)}{2 b^{2/3}}",1,"Integrate[((-2 + (1 + k)*x)*(1 - (1 + k)*x + (a + k)*x^2))/(((1 - x)*x*(1 - k*x))^(1/3)*(1 - (2 + 2*k)*x + (1 + 4*k + k^2)*x^2 - 2*(k + k^2)*x^3 + (-b + k^2)*x^4)), x]","F",-1
2980,1,76,383,0.3595497,"\int \frac{1}{\sqrt{-b+a^2 x^2} \sqrt{a x+\sqrt{-b+a^2 x^2}} \sqrt[6]{c+\sqrt[4]{a x+\sqrt{-b+a^2 x^2}}}} \, dx","Integrate[1/(Sqrt[-b + a^2*x^2]*Sqrt[a*x + Sqrt[-b + a^2*x^2]]*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(1/6)),x]","-\frac{24 \left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{5/6} \, _2F_1\left(\frac{5}{6},3;\frac{11}{6};\frac{c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}{c}\right)}{5 a c^3}","-\frac{7 \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}}{\sqrt{3} \sqrt[6]{c}}\right)}{6 \sqrt{3} a c^{13/6}}+\frac{7 \tan ^{-1}\left(\frac{2 \sqrt[6]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}}{\sqrt{3} \sqrt[6]{c}}+\frac{1}{\sqrt{3}}\right)}{6 \sqrt{3} a c^{13/6}}-\frac{7 \tanh ^{-1}\left(\frac{\sqrt[6]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}}{\sqrt[6]{c}}\right)}{9 a c^{13/6}}-\frac{7 \tanh ^{-1}\left(\frac{\frac{\sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}}{\sqrt[6]{c}}+\sqrt[6]{c}}{\sqrt[6]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}}\right)}{18 a c^{13/6}}+\frac{7 \sqrt[4]{\sqrt{a^2 x^2-b}+a x} \left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{5/6}-6 c \left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{5/6}}{3 a c^2 \sqrt{\sqrt{a^2 x^2-b}+a x}}",1,"(-24*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(5/6)*Hypergeometric2F1[5/6, 3, 11/6, (c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))/c])/(5*a*c^3)","C",1
2981,1,444,383,2.142827,"\int \frac{x}{\sqrt{1+\sqrt{a x+\sqrt{-b+a^2 x^2}}}} \, dx","Integrate[x/Sqrt[1 + Sqrt[a*x + Sqrt[-b + a^2*x^2]]],x]","-\frac{-\frac{b^2 \left(\sqrt{\sqrt{a^2 x^2-b}+a x}+1\right)^{7/2}}{8 \left(\sqrt{a^2 x^2-b}+a x\right)^2}+\frac{25 b^2 \left(\sqrt{\sqrt{a^2 x^2-b}+a x}+1\right)^{5/2}}{48 \left(\sqrt{a^2 x^2-b}+a x\right)^{3/2}}-\frac{163 b^2 \left(\sqrt{\sqrt{a^2 x^2-b}+a x}+1\right)^{3/2}}{192 \left(\sqrt{a^2 x^2-b}+a x\right)}+\frac{93 b^2 \sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+1}}{128 \sqrt{\sqrt{a^2 x^2-b}+a x}}+\frac{35}{256} b^2 \log \left(1-\frac{1}{\sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+1}}\right)-\frac{35}{256} b^2 \log \left(\frac{1}{\sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+1}}+1\right)-\frac{1}{7} \left(\sqrt{\sqrt{a^2 x^2-b}+a x}+1\right)^{7/2}+\frac{3}{5} \left(\sqrt{\sqrt{a^2 x^2-b}+a x}+1\right)^{5/2}-\left(\sqrt{\sqrt{a^2 x^2-b}+a x}+1\right)^{3/2}+\sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+1}}{a^2}","\frac{35 b^2 \tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+1}\right)}{128 a^2}+\frac{\sqrt{a^2 x^2-b} \left(\sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+1} \left(-9216 a^2 x^2-12288 a x+2450 b^2+2304 b\right)+\left(7680 a^2 x^2+6144 a x-3675 b^2-1920 b\right) \sqrt{\sqrt{a^2 x^2-b}+a x} \sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+1}\right)+\sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+1} \left(-9216 a^3 x^3-12288 a^2 x^2+2450 a b^2 x+6912 a b x+1680 b^2+6144 b\right)+\left(7680 a^3 x^3+6144 a^2 x^2-3675 a b^2 x-5760 a b x-1960 b^2-3072 b\right) \sqrt{\sqrt{a^2 x^2-b}+a x} \sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+1}}{13440 a^2 \left(2 a^2 x^2-b\right)+26880 a^3 x \sqrt{a^2 x^2-b}}",1,"-((Sqrt[1 + Sqrt[a*x + Sqrt[-b + a^2*x^2]]] + (93*b^2*Sqrt[1 + Sqrt[a*x + Sqrt[-b + a^2*x^2]]])/(128*Sqrt[a*x + Sqrt[-b + a^2*x^2]]) - (1 + Sqrt[a*x + Sqrt[-b + a^2*x^2]])^(3/2) - (163*b^2*(1 + Sqrt[a*x + Sqrt[-b + a^2*x^2]])^(3/2))/(192*(a*x + Sqrt[-b + a^2*x^2])) + (3*(1 + Sqrt[a*x + Sqrt[-b + a^2*x^2]])^(5/2))/5 + (25*b^2*(1 + Sqrt[a*x + Sqrt[-b + a^2*x^2]])^(5/2))/(48*(a*x + Sqrt[-b + a^2*x^2])^(3/2)) - (1 + Sqrt[a*x + Sqrt[-b + a^2*x^2]])^(7/2)/7 - (b^2*(1 + Sqrt[a*x + Sqrt[-b + a^2*x^2]])^(7/2))/(8*(a*x + Sqrt[-b + a^2*x^2])^2) + (35*b^2*Log[1 - 1/Sqrt[1 + Sqrt[a*x + Sqrt[-b + a^2*x^2]]]])/256 - (35*b^2*Log[1 + 1/Sqrt[1 + Sqrt[a*x + Sqrt[-b + a^2*x^2]]]])/256)/a^2)","A",1
2982,0,0,384,0.6544089,"\int \frac{\left(d+c x^2\right) \left(a x+\sqrt{-b+a^2 x^2}\right)^{5/4}}{\left(-b+a^2 x^2\right)^{3/2}} \, dx","Integrate[((d + c*x^2)*(a*x + Sqrt[-b + a^2*x^2])^(5/4))/(-b + a^2*x^2)^(3/2),x]","\int \frac{\left(d+c x^2\right) \left(a x+\sqrt{-b+a^2 x^2}\right)^{5/4}}{\left(-b+a^2 x^2\right)^{3/2}} \, dx","\frac{4 \sqrt[8]{b} c x \sqrt[4]{\frac{\sqrt{a^2 x^2-b}}{\sqrt{b}}+\frac{a x}{\sqrt{b}}}}{5 a^2}+\frac{\sqrt{a^2 x^2-b} \sqrt[4]{\frac{\sqrt{a^2 x^2-b}+a x}{\sqrt{b}}} \left(4 a^2 \sqrt[8]{b} c x^2-5 a^2 \sqrt[8]{b} d-9 b^{9/8} c\right)}{5 a^3 \left(a x-\sqrt{b}\right) \left(a x+\sqrt{b}\right)}-\frac{5 \left(a^2 d+b c\right) \tan ^{-1}\left(\sqrt[4]{\frac{\sqrt{a^2 x^2-b}+a x}{\sqrt{b}}}\right)}{2 a^3 b^{3/8}}-\frac{5 \left(a^2 d+b c\right) \tanh ^{-1}\left(\sqrt[4]{\frac{\sqrt{a^2 x^2-b}+a x}{\sqrt{b}}}\right)}{2 a^3 b^{3/8}}-\frac{5 (-1)^{3/4} \left(a^2 d+b c\right) \tanh ^{-1}\left(\sqrt[4]{-1} \sqrt[4]{\frac{\sqrt{a^2 x^2-b}+a x}{\sqrt{b}}}\right)}{2 a^3 b^{3/8}}-\frac{5 \sqrt[4]{-1} \left(a^2 d+b c\right) \tanh ^{-1}\left((-1)^{3/4} \sqrt[4]{\frac{\sqrt{a^2 x^2-b}+a x}{\sqrt{b}}}\right)}{2 a^3 b^{3/8}}",1,"Integrate[((d + c*x^2)*(a*x + Sqrt[-b + a^2*x^2])^(5/4))/(-b + a^2*x^2)^(3/2), x]","F",-1
2983,1,183,385,0.6878858,"\int \frac{\left(-b+a x^2\right) \sqrt[3]{-x+x^3}}{-d+c x^2} \, dx","Integrate[((-b + a*x^2)*(-x + x^3)^(1/3))/(-d + c*x^2),x]","\frac{2 \left(1-x^2\right)^{2/3} x^4 \left(1-\frac{c x^2}{d}\right)^{2/3} (a (c-3 d)+3 b c) F_1\left(\frac{5}{3};\frac{2}{3},1;\frac{8}{3};x^2,\frac{c x^2}{d}\right)+5 x^2 \left(\left(1-x^2\right)^{2/3} (2 a d-3 b c) \, _2F_1\left(\frac{2}{3},\frac{2}{3};\frac{5}{3};\frac{(c-d) x^2}{c x^2-d}\right)+2 a d \left(x^2-1\right) \left(1-\frac{c x^2}{d}\right)^{2/3}\right)}{20 c d \left(x \left(x^2-1\right)\right)^{2/3} \left(1-\frac{c x^2}{d}\right)^{2/3}}","-\frac{\sqrt[3]{c-d} (b c-a d) \log \left(-\sqrt[3]{d} \sqrt[3]{x^3-x} x \sqrt[3]{c-d}+x^2 (c-d)^{2/3}+d^{2/3} \left(x^3-x\right)^{2/3}\right)}{4 c^2 \sqrt[3]{d}}+\frac{\log \left(\sqrt[3]{x^3-x}-x\right) (a c-3 a d+3 b c)}{6 c^2}+\frac{\sqrt[3]{c-d} (b c-a d) \log \left(x \sqrt[3]{c-d}+\sqrt[3]{d} \sqrt[3]{x^3-x}\right)}{2 c^2 \sqrt[3]{d}}+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-x}+x}\right) (a c-3 a d+3 b c)}{2 \sqrt{3} c^2}+\frac{\sqrt{3} \sqrt[3]{c-d} (b c-a d) \tan ^{-1}\left(\frac{\sqrt{3} x \sqrt[3]{c-d}}{x \sqrt[3]{c-d}-2 \sqrt[3]{d} \sqrt[3]{x^3-x}}\right)}{2 c^2 \sqrt[3]{d}}+\frac{\log \left(\sqrt[3]{x^3-x} x+\left(x^3-x\right)^{2/3}+x^2\right) (-a c+3 a d-3 b c)}{12 c^2}+\frac{a \sqrt[3]{x^3-x} x}{2 c}",1,"(2*(3*b*c + a*(c - 3*d))*x^4*(1 - x^2)^(2/3)*(1 - (c*x^2)/d)^(2/3)*AppellF1[5/3, 2/3, 1, 8/3, x^2, (c*x^2)/d] + 5*x^2*(2*a*d*(-1 + x^2)*(1 - (c*x^2)/d)^(2/3) + (-3*b*c + 2*a*d)*(1 - x^2)^(2/3)*Hypergeometric2F1[2/3, 2/3, 5/3, ((c - d)*x^2)/(-d + c*x^2)]))/(20*c*d*(x*(-1 + x^2))^(2/3)*(1 - (c*x^2)/d)^(2/3))","C",0
2984,0,0,387,6.9282028,"\int \frac{(-a b+(2 a-b) x) \left(a^2-2 a x+x^2\right)}{\sqrt[3]{x (-a+x) (-b+x)} \left(a^4 d-4 a^3 d x+\left(-b^2+6 a^2 d\right) x^2+2 (b-2 a d) x^3+(-1+d) x^4\right)} \, dx","Integrate[((-(a*b) + (2*a - b)*x)*(a^2 - 2*a*x + x^2))/((x*(-a + x)*(-b + x))^(1/3)*(a^4*d - 4*a^3*d*x + (-b^2 + 6*a^2*d)*x^2 + 2*(b - 2*a*d)*x^3 + (-1 + d)*x^4)),x]","\int \frac{(-a b+(2 a-b) x) \left(a^2-2 a x+x^2\right)}{\sqrt[3]{x (-a+x) (-b+x)} \left(a^4 d-4 a^3 d x+\left(-b^2+6 a^2 d\right) x^2+2 (b-2 a d) x^3+(-1+d) x^4\right)} \, dx","-\frac{\log \left(a^2 \sqrt[3]{d}+\sqrt[3]{x^2 (-a-b)+a b x+x^3} \left(a \sqrt[6]{d}-\sqrt[6]{d} x\right)+\left(x^2 (-a-b)+a b x+x^3\right)^{2/3}-2 a \sqrt[3]{d} x+\sqrt[3]{d} x^2\right)}{4 d^{2/3}}-\frac{\log \left(a^2 \sqrt[3]{d}+\sqrt[3]{x^2 (-a-b)+a b x+x^3} \left(\sqrt[6]{d} x-a \sqrt[6]{d}\right)+\left(x^2 (-a-b)+a b x+x^3\right)^{2/3}-2 a \sqrt[3]{d} x+\sqrt[3]{d} x^2\right)}{4 d^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{a^2}{\sqrt{3}}+\frac{2 \left(x^2 (-a-b)+a b x+x^3\right)^{2/3}}{\sqrt{3} \sqrt[3]{d}}-\frac{2 a x}{\sqrt{3}}+\frac{x^2}{\sqrt{3}}}{(a-x)^2}\right)}{2 d^{2/3}}+\frac{\log \left(\sqrt[3]{x^2 (-a-b)+a b x+x^3}+a \sqrt[6]{d}-\sqrt[6]{d} x\right)}{2 d^{2/3}}+\frac{\log \left(\sqrt[3]{x^2 (-a-b)+a b x+x^3}+a \left(-\sqrt[6]{d}\right)+\sqrt[6]{d} x\right)}{2 d^{2/3}}",1,"Integrate[((-(a*b) + (2*a - b)*x)*(a^2 - 2*a*x + x^2))/((x*(-a + x)*(-b + x))^(1/3)*(a^4*d - 4*a^3*d*x + (-b^2 + 6*a^2*d)*x^2 + 2*(b - 2*a*d)*x^3 + (-1 + d)*x^4)), x]","F",-1
2985,1,155,388,0.3383749,"\int \frac{b+d x}{x^4 \sqrt[4]{\frac{b+a x}{d+c x}}} \, dx","Integrate[(b + d*x)/(x^4*((b + a*x)/(d + c*x))^(1/4)),x]","\frac{\left(\frac{a x+b}{c x+d}\right)^{3/4} \left(x \left(4 b^2 (c x+d)^2 (3 d (3 a-4 d)+7 b c)-x \left(2 b c d (5 a-6 d)+5 a d^2 (3 a-4 d)+7 b^2 c^2\right) \left(x (b c-a d) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{d (b+a x)}{b (d+c x)}\right)+3 b (c x+d)\right)\right)-32 b^3 d (c x+d)^2\right)}{96 b^3 d^2 x^3}","\frac{\left(\frac{a x+b}{c x+d}\right)^{3/4} \left(-45 a^2 c d^2 x^3-45 a^2 d^3 x^2+6 a b c^2 d x^3+42 a b c d^2 x^2+36 a b d^3 x+60 a c d^3 x^3+60 a d^4 x^2+7 b^2 c^3 x^3+3 b^2 c^2 d x^2-36 b^2 c d^2 x-32 b^2 d^3-12 b c^2 d^2 x^3-60 b c d^3 x^2-48 b d^4 x\right)}{96 b^2 d^2 x^3}+\frac{\left(-15 a^3 d^3+5 a^2 b c d^2+20 a^2 d^4+3 a b^2 c^2 d-8 a b c d^3+7 b^3 c^3-12 b^2 c^2 d^2\right) \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{\frac{a x+b}{c x+d}}}{\sqrt[4]{b}}\right)}{64 b^{9/4} d^{11/4}}+\frac{\left(15 a^3 d^3-5 a^2 b c d^2-20 a^2 d^4-3 a b^2 c^2 d+8 a b c d^3-7 b^3 c^3+12 b^2 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{\frac{a x+b}{c x+d}}}{\sqrt[4]{b}}\right)}{64 b^{9/4} d^{11/4}}",1,"(((b + a*x)/(d + c*x))^(3/4)*(-32*b^3*d*(d + c*x)^2 + x*(4*b^2*(7*b*c + 3*(3*a - 4*d)*d)*(d + c*x)^2 - (7*b^2*c^2 + 2*b*c*(5*a - 6*d)*d + 5*a*(3*a - 4*d)*d^2)*x*(3*b*(d + c*x) + (b*c - a*d)*x*Hypergeometric2F1[3/4, 1, 7/4, (d*(b + a*x))/(b*(d + c*x))]))))/(96*b^3*d^2*x^3)","C",1
2986,-1,0,388,180.004431,"\int \frac{f+e x}{d+c x+\sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Integrate[(f + e*x)/(d + c*x + Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]),x]","\text{\$Aborted}","\frac{2 \text{RootSum}\left[\text{$\#$1}^4 (-c)-2 \text{$\#$1}^3 a-2 \text{$\#$1}^2 a d+b^2 c\&,\frac{\text{$\#$1}^3 c^2 f \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)-\text{$\#$1}^3 c d e \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)+\text{$\#$1}^3 a e \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)+\text{$\#$1}^2 a c f \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)+\text{$\#$1} a c d f \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)-b^2 c e \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)-\text{$\#$1} a d^2 e \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)}{2 \text{$\#$1}^3 c+3 \text{$\#$1}^2 a+2 \text{$\#$1} a d}\&\right]}{c^2}+\frac{\log \left(\sqrt{a^2 x^2+b^2}+a x\right) (d e-c f)}{c^2}-\frac{2 e \sqrt{\sqrt{a^2 x^2+b^2}+a x}}{c^2}+\frac{e x}{c}",1,"$Aborted","F",-1
2987,0,0,390,1.1494585,"\int \frac{1+x^6}{\sqrt[4]{-x^3+x^5} \left(1-x^6\right)} \, dx","Integrate[(1 + x^6)/((-x^3 + x^5)^(1/4)*(1 - x^6)),x]","\int \frac{1+x^6}{\sqrt[4]{-x^3+x^5} \left(1-x^6\right)} \, dx","\frac{4 \left(x^5-x^3\right)^{3/4}}{3 x^2 \left(x^2-1\right)}+\frac{\sqrt[4]{2} \tan ^{-1}\left(\frac{3^{7/8} \sqrt{2-\sqrt{2}} x \sqrt[4]{x^5-x^3}}{3^{3/4} \sqrt{x^5-x^3}-3 x^2}\right)}{3 \sqrt[8]{3 \left(17+12 \sqrt{2}\right)}}+\frac{1}{3} \sqrt[4]{2} \sqrt[8]{\frac{1}{3} \left(17+12 \sqrt{2}\right)} \tan ^{-1}\left(\frac{3^{7/8} \sqrt{2+\sqrt{2}} x \sqrt[4]{x^5-x^3}}{3^{3/4} \sqrt{x^5-x^3}-3 x^2}\right)+\frac{\sqrt[4]{2} \tanh ^{-1}\left(\frac{\frac{\sqrt[8]{3} x^2}{\sqrt{2-\sqrt{2}}}+\frac{\sqrt{x^5-x^3}}{\sqrt[8]{3} \sqrt{2-\sqrt{2}}}}{x \sqrt[4]{x^5-x^3}}\right)}{3 \sqrt[8]{3 \left(17+12 \sqrt{2}\right)}}+\frac{1}{3} \sqrt[4]{2} \sqrt[8]{\frac{1}{3} \left(17+12 \sqrt{2}\right)} \tanh ^{-1}\left(\frac{\frac{\sqrt[8]{3} x^2}{\sqrt{2+\sqrt{2}}}+\frac{\sqrt{x^5-x^3}}{\sqrt[8]{3} \sqrt{2+\sqrt{2}}}}{x \sqrt[4]{x^5-x^3}}\right)",1,"Integrate[(1 + x^6)/((-x^3 + x^5)^(1/4)*(1 - x^6)), x]","F",-1
2988,1,11755,390,23.4123443,"\int \frac{\sqrt{-b+a^2 x^2} \left(d+c x^4\right) \sqrt{a x+\sqrt{-b+a^2 x^2}}}{x^2} \, dx","Integrate[(Sqrt[-b + a^2*x^2]*(d + c*x^4)*Sqrt[a*x + Sqrt[-b + a^2*x^2]])/x^2,x]","\text{Result too large to show}","\frac{a \sqrt[4]{b} d \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{\sqrt{a^2 x^2-b}+a x}}{\sqrt{a^2 x^2-b}+a x-\sqrt{b}}\right)}{\sqrt{2}}-\frac{a \sqrt[4]{b} d \tanh ^{-1}\left(\frac{\frac{\sqrt{a^2 x^2-b}}{\sqrt{2} \sqrt[4]{b}}+\frac{a x}{\sqrt{2} \sqrt[4]{b}}+\frac{\sqrt[4]{b}}{\sqrt{2}}}{\sqrt{\sqrt{a^2 x^2-b}+a x}}\right)}{\sqrt{2}}+\frac{224 a^9 c x^{10}+2016 a^9 d x^6-504 a^7 b c x^8-2016 a^7 b d x^4+126 a^5 b^2 c x^6+126 a^5 b^2 d x^2+210 a^3 b^3 c x^4+63 a^3 b^3 d+\sqrt{a^2 x^2-b} \left(224 a^8 c x^9+2016 a^8 d x^5-392 a^6 b c x^7-1008 a^6 b d x^3-42 a^4 b^2 c x^5-126 a^4 b^2 d x+154 a^2 b^3 c x^3-16 b^4 c x\right)-72 a b^4 c x^2}{63 a^3 x \left(\sqrt{a^2 x^2-b}+a x\right)^{9/2}}",1,"Result too large to show","B",0
2989,1,440,392,1.367421,"\int \frac{\left(1+x^2\right)^{3/2} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","Integrate[((1 + x^2)^(3/2)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2)^2,x]","\frac{\left(x^2+\sqrt{x^2+1} x+1\right) \left(-\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{5 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-6 \text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+4 \text{$\#$1}^2-2}\&\right]+\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{5 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-6 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]+8 \left(2 \log \left(1-\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)-2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}+1\right)+\frac{\sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(8 x^4-7 x^2-11 \sqrt{x^2+1} x+8 \sqrt{x^2+1} x^3-5\right)}{\left(x^2-1\right) \left(2 x^2+2 \sqrt{x^2+1} x+1\right)}\right)\right)}{8 \sqrt{x^2+1} \left(\sqrt{x^2+1}+x\right)}","-\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{5 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-6 \text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+4 \text{$\#$1}^2-2}\&\right]+\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{5 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-6 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]-4 \tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\frac{\left(8 x^4-7 x^2-5\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}+\sqrt{x^2+1} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(8 x^3-11 x\right)}{\left(2 x^2+1\right) \left(x^2-1\right)+2 x \sqrt{x^2+1} \left(x^2-1\right)}",1,"((1 + x^2 + x*Sqrt[1 + x^2])*(8*(((-5 - 7*x^2 + 8*x^4 - 11*x*Sqrt[1 + x^2] + 8*x^3*Sqrt[1 + x^2])*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/((-1 + x^2)*(1 + 2*x^2 + 2*x*Sqrt[1 + x^2])) + 2*Log[1 - Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]] - 2*Log[1 + Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]]) + RootSum[-2 + 4*#1^4 - 4*#1^6 + #1^8 & , (2*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1] - 6*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^2 + 5*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^4)/(2*#1^3 - 3*#1^5 + #1^7) & ] - RootSum[2 - 8*#1^2 + 8*#1^4 - 4*#1^6 + #1^8 & , (-6*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1 + 5*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^3)/(-2 + 4*#1^2 - 3*#1^4 + #1^6) & ]))/(8*Sqrt[1 + x^2]*(x + Sqrt[1 + x^2]))","A",1
2990,1,440,392,0.333485,"\int \frac{\left(1+x^2\right)^{3/2} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","Integrate[((1 + x^2)^(3/2)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2)^2,x]","\frac{\left(x^2+\sqrt{x^2+1} x+1\right) \left(-\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{5 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-6 \text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+4 \text{$\#$1}^2-2}\&\right]+\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{5 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-6 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]+8 \left(2 \log \left(1-\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)-2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}+1\right)+\frac{\sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(8 x^4-7 x^2-11 \sqrt{x^2+1} x+8 \sqrt{x^2+1} x^3-5\right)}{\left(x^2-1\right) \left(2 x^2+2 \sqrt{x^2+1} x+1\right)}\right)\right)}{8 \sqrt{x^2+1} \left(\sqrt{x^2+1}+x\right)}","-\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{5 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-6 \text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+4 \text{$\#$1}^2-2}\&\right]+\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{5 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-6 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]-4 \tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\frac{\left(8 x^4-7 x^2-5\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}+\sqrt{x^2+1} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(8 x^3-11 x\right)}{\left(2 x^2+1\right) \left(x^2-1\right)+2 x \sqrt{x^2+1} \left(x^2-1\right)}",1,"((1 + x^2 + x*Sqrt[1 + x^2])*(8*(((-5 - 7*x^2 + 8*x^4 - 11*x*Sqrt[1 + x^2] + 8*x^3*Sqrt[1 + x^2])*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/((-1 + x^2)*(1 + 2*x^2 + 2*x*Sqrt[1 + x^2])) + 2*Log[1 - Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]] - 2*Log[1 + Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]]) + RootSum[-2 + 4*#1^4 - 4*#1^6 + #1^8 & , (2*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1] - 6*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^2 + 5*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^4)/(2*#1^3 - 3*#1^5 + #1^7) & ] - RootSum[2 - 8*#1^2 + 8*#1^4 - 4*#1^6 + #1^8 & , (-6*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1 + 5*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^3)/(-2 + 4*#1^2 - 3*#1^4 + #1^6) & ]))/(8*Sqrt[1 + x^2]*(x + Sqrt[1 + x^2]))","A",1
2991,1,440,392,0.2385964,"\int \frac{\left(1+x^2\right)^{3/2} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","Integrate[((1 + x^2)^(3/2)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2)^2,x]","\frac{\left(x^2+\sqrt{x^2+1} x+1\right) \left(-\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{5 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-6 \text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+4 \text{$\#$1}^2-2}\&\right]+\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{5 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-6 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]+8 \left(2 \log \left(1-\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)-2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}+1\right)+\frac{\sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(8 x^4-7 x^2-11 \sqrt{x^2+1} x+8 \sqrt{x^2+1} x^3-5\right)}{\left(x^2-1\right) \left(2 x^2+2 \sqrt{x^2+1} x+1\right)}\right)\right)}{8 \sqrt{x^2+1} \left(\sqrt{x^2+1}+x\right)}","-\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{5 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-6 \text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+4 \text{$\#$1}^2-2}\&\right]+\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{5 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-6 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]-4 \tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\frac{\left(8 x^4-7 x^2-5\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}+\sqrt{x^2+1} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(8 x^3-11 x\right)}{\left(2 x^2+1\right) \left(x^2-1\right)+2 x \sqrt{x^2+1} \left(x^2-1\right)}",1,"((1 + x^2 + x*Sqrt[1 + x^2])*(8*(((-5 - 7*x^2 + 8*x^4 - 11*x*Sqrt[1 + x^2] + 8*x^3*Sqrt[1 + x^2])*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/((-1 + x^2)*(1 + 2*x^2 + 2*x*Sqrt[1 + x^2])) + 2*Log[1 - Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]] - 2*Log[1 + Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]]) + RootSum[-2 + 4*#1^4 - 4*#1^6 + #1^8 & , (2*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1] - 6*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^2 + 5*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^4)/(2*#1^3 - 3*#1^5 + #1^7) & ] - RootSum[2 - 8*#1^2 + 8*#1^4 - 4*#1^6 + #1^8 & , (-6*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1 + 5*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^3)/(-2 + 4*#1^2 - 3*#1^4 + #1^6) & ]))/(8*Sqrt[1 + x^2]*(x + Sqrt[1 + x^2]))","A",1
2992,0,0,394,0.8452517,"\int \frac{\left(1+x^2+x^4\right) \sqrt{x^2+\sqrt{1+x^4}}}{\sqrt{1+x^4} \left(-1+x^2+x^4\right)} \, dx","Integrate[((1 + x^2 + x^4)*Sqrt[x^2 + Sqrt[1 + x^4]])/(Sqrt[1 + x^4]*(-1 + x^2 + x^4)),x]","\int \frac{\left(1+x^2+x^4\right) \sqrt{x^2+\sqrt{1+x^4}}}{\sqrt{1+x^4} \left(-1+x^2+x^4\right)} \, dx","\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)-\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^6-6 \text{$\#$1}^4+2 \text{$\#$1}^2+1\&,\frac{\text{$\#$1}^6 \left(-\log \left(\sqrt{x^4+1}+x^2-1\right)\right)+\text{$\#$1}^6 \log \left(\text{$\#$1} \sqrt{x^4+1}+\text{$\#$1} x^2-\text{$\#$1}+\sqrt{2} \sqrt{\sqrt{x^4+1}+x^2} x\right)-\text{$\#$1}^4 \log \left(\sqrt{x^4+1}+x^2-1\right)+\text{$\#$1}^4 \log \left(\text{$\#$1} \sqrt{x^4+1}+\text{$\#$1} x^2-\text{$\#$1}+\sqrt{2} \sqrt{\sqrt{x^4+1}+x^2} x\right)+\text{$\#$1}^2 \log \left(\sqrt{x^4+1}+x^2-1\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \sqrt{x^4+1}+\text{$\#$1} x^2-\text{$\#$1}+\sqrt{2} \sqrt{\sqrt{x^4+1}+x^2} x\right)-\log \left(\text{$\#$1} \sqrt{x^4+1}+\text{$\#$1} x^2-\text{$\#$1}+\sqrt{2} \sqrt{\sqrt{x^4+1}+x^2} x\right)+\log \left(\sqrt{x^4+1}+x^2-1\right)}{2 \text{$\#$1}^7-3 \text{$\#$1}^5-6 \text{$\#$1}^3+\text{$\#$1}}\&\right]}{\sqrt{2}}",1,"Integrate[((1 + x^2 + x^4)*Sqrt[x^2 + Sqrt[1 + x^4]])/(Sqrt[1 + x^4]*(-1 + x^2 + x^4)), x]","F",-1
2993,0,0,394,0.5002703,"\int \frac{\left(1+x^2+x^4\right) \sqrt{x^2+\sqrt{1+x^4}}}{\sqrt{1+x^4} \left(-1+x^2+x^4\right)} \, dx","Integrate[((1 + x^2 + x^4)*Sqrt[x^2 + Sqrt[1 + x^4]])/(Sqrt[1 + x^4]*(-1 + x^2 + x^4)),x]","\int \frac{\left(1+x^2+x^4\right) \sqrt{x^2+\sqrt{1+x^4}}}{\sqrt{1+x^4} \left(-1+x^2+x^4\right)} \, dx","\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)-\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^6-6 \text{$\#$1}^4+2 \text{$\#$1}^2+1\&,\frac{\text{$\#$1}^6 \left(-\log \left(\sqrt{x^4+1}+x^2-1\right)\right)+\text{$\#$1}^6 \log \left(\text{$\#$1} \sqrt{x^4+1}+\text{$\#$1} x^2-\text{$\#$1}+\sqrt{2} \sqrt{\sqrt{x^4+1}+x^2} x\right)-\text{$\#$1}^4 \log \left(\sqrt{x^4+1}+x^2-1\right)+\text{$\#$1}^4 \log \left(\text{$\#$1} \sqrt{x^4+1}+\text{$\#$1} x^2-\text{$\#$1}+\sqrt{2} \sqrt{\sqrt{x^4+1}+x^2} x\right)+\text{$\#$1}^2 \log \left(\sqrt{x^4+1}+x^2-1\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \sqrt{x^4+1}+\text{$\#$1} x^2-\text{$\#$1}+\sqrt{2} \sqrt{\sqrt{x^4+1}+x^2} x\right)-\log \left(\text{$\#$1} \sqrt{x^4+1}+\text{$\#$1} x^2-\text{$\#$1}+\sqrt{2} \sqrt{\sqrt{x^4+1}+x^2} x\right)+\log \left(\sqrt{x^4+1}+x^2-1\right)}{2 \text{$\#$1}^7-3 \text{$\#$1}^5-6 \text{$\#$1}^3+\text{$\#$1}}\&\right]}{\sqrt{2}}",1,"Integrate[((1 + x^2 + x^4)*Sqrt[x^2 + Sqrt[1 + x^4]])/(Sqrt[1 + x^4]*(-1 + x^2 + x^4)), x]","F",-1
2994,1,9604,397,24.2354574,"\int \frac{\sqrt{-b+a^2 x^2} \left(d+c x^4\right) \sqrt{a x+\sqrt{-b+a^2 x^2}}}{x} \, dx","Integrate[(Sqrt[-b + a^2*x^2]*(d + c*x^4)*Sqrt[a*x + Sqrt[-b + a^2*x^2]])/x,x]","\text{Result too large to show}","\sqrt{2} b^{3/4} d \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{\sqrt{a^2 x^2-b}+a x}}{\sqrt{a^2 x^2-b}+a x-\sqrt{b}}\right)+\sqrt{2} b^{3/4} d \tanh ^{-1}\left(\frac{\frac{\sqrt{a^2 x^2-b}}{\sqrt{2} \sqrt[4]{b}}+\frac{a x}{\sqrt{2} \sqrt[4]{b}}+\frac{\sqrt[4]{b}}{\sqrt{2}}}{\sqrt{\sqrt{a^2 x^2-b}+a x}}\right)+\frac{2 \left(5040 a^{10} c x^{10}+18480 a^{10} d x^6-10620 a^8 b c x^8-41580 a^8 b d x^4+4755 a^6 b^2 c x^6+24255 a^6 b^2 d x^2+3735 a^4 b^3 c x^4-2310 a^4 b^3 d-3078 a^2 b^4 c x^2+304 b^5 c\right)+2 \sqrt{a^2 x^2-b} \left(5040 a^9 c x^9+18480 a^9 d x^5-8100 a^7 b c x^7-32340 a^7 b d x^3+1335 a^5 b^2 c x^5+10395 a^5 b^2 d x+3705 a^3 b^3 c x^3-1368 a b^4 c x\right)}{3465 a^4 \left(\sqrt{a^2 x^2-b}+a x\right)^{9/2}}",1,"Result too large to show","B",0
2995,0,0,398,0.3235029,"\int \frac{\sqrt{a x^2+\sqrt{b+a^2 x^4}}}{d+c x^2} \, dx","Integrate[Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/(d + c*x^2),x]","\int \frac{\sqrt{a x^2+\sqrt{b+a^2 x^4}}}{d+c x^2} \, dx","\frac{\sqrt{a} \log \left(i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)}{\sqrt{2} c}-\frac{\sqrt{a} \text{RootSum}\left[\text{$\#$1}^4 c+4 i \text{$\#$1}^3 a d+2 \text{$\#$1}^2 b c-4 i \text{$\#$1} a b d+b^2 c\&,\frac{\text{$\#$1}^2 (-a) d \log \left(-\text{$\#$1}+i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)+2 i \text{$\#$1} b c \log \left(-\text{$\#$1}+i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)+a b d \log \left(-\text{$\#$1}+i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)}{i \text{$\#$1}^3 c-3 \text{$\#$1}^2 a d+i \text{$\#$1} b c+a b d}\&\right]}{\sqrt{2} c}",1,"Integrate[Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/(d + c*x^2), x]","F",-1
2996,0,0,398,0.0987466,"\int \frac{\sqrt{a x^2+\sqrt{b+a^2 x^4}}}{d+c x^2} \, dx","Integrate[Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/(d + c*x^2),x]","\int \frac{\sqrt{a x^2+\sqrt{b+a^2 x^4}}}{d+c x^2} \, dx","\frac{\sqrt{a} \log \left(i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)}{\sqrt{2} c}-\frac{\sqrt{a} \text{RootSum}\left[\text{$\#$1}^4 c+4 i \text{$\#$1}^3 a d+2 \text{$\#$1}^2 b c-4 i \text{$\#$1} a b d+b^2 c\&,\frac{\text{$\#$1}^2 (-a) d \log \left(-\text{$\#$1}+i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)+2 i \text{$\#$1} b c \log \left(-\text{$\#$1}+i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)+a b d \log \left(-\text{$\#$1}+i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)}{i \text{$\#$1}^3 c-3 \text{$\#$1}^2 a d+i \text{$\#$1} b c+a b d}\&\right]}{\sqrt{2} c}",1,"Integrate[Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/(d + c*x^2), x]","F",-1
2997,0,0,399,0.3862792,"\int \frac{x^5 \left(7 b+10 a x^3\right)}{\sqrt[4]{b x^3+a x^6} \left(1+b x^7+a x^{10}\right)} \, dx","Integrate[(x^5*(7*b + 10*a*x^3))/((b*x^3 + a*x^6)^(1/4)*(1 + b*x^7 + a*x^10)),x]","\int \frac{x^5 \left(7 b+10 a x^3\right)}{\sqrt[4]{b x^3+a x^6} \left(1+b x^7+a x^{10}\right)} \, dx","-\sqrt{2} \tan ^{-1}\left(\frac{x^2 \sqrt[4]{a x^6+b x^3}-2^{2/3} x \sqrt[4]{a x^6+b x^3}}{2^{2/3} x \sqrt[4]{a x^6+b x^3}+x^2 \left(-\sqrt[4]{a x^6+b x^3}\right)-\sqrt{2} x+2 \sqrt[6]{2}}\right)+\sqrt{2} \tan ^{-1}\left(\frac{x^2 \sqrt[4]{a x^6+b x^3}-2^{2/3} x \sqrt[4]{a x^6+b x^3}}{2^{2/3} x \sqrt[4]{a x^6+b x^3}+x^2 \left(-\sqrt[4]{a x^6+b x^3}\right)+\sqrt{2} x-2 \sqrt[6]{2}}\right)-\sqrt{2} \tanh ^{-1}\left(\frac{-\sqrt{2} x^3 \sqrt[4]{a x^6+b x^3}-2\ 2^{5/6} x \sqrt[4]{a x^6+b x^3}+4 \sqrt[6]{2} x^2 \sqrt[4]{a x^6+b x^3}}{2\ 2^{2/3} x^3 \sqrt{a x^6+b x^3}+x^4 \left(-\sqrt{a x^6+b x^3}\right)-2 \sqrt[3]{2} x^2 \sqrt{a x^6+b x^3}-x^2+2\ 2^{2/3} x-2 \sqrt[3]{2}}\right)",1,"Integrate[(x^5*(7*b + 10*a*x^3))/((b*x^3 + a*x^6)^(1/4)*(1 + b*x^7 + a*x^10)), x]","F",-1
2998,1,65821,399,7.8152704,"\int \frac{x^4 \left(-2 q+p x^3\right) \sqrt{q+p x^3}}{b x^8+a \left(q+p x^3\right)^4} \, dx","Integrate[(x^4*(-2*q + p*x^3)*Sqrt[q + p*x^3])/(b*x^8 + a*(q + p*x^3)^4),x]","\text{Result too large to show}","-\frac{\sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{x \left(\sqrt{\frac{2}{2-\sqrt{2}}} \sqrt[8]{a} \sqrt[8]{b}-\frac{2 \sqrt[8]{a} \sqrt[8]{b}}{\sqrt{2-\sqrt{2}}}\right) \sqrt{p x^3+q}}{-\sqrt[4]{a} p x^3-\sqrt[4]{a} q+\sqrt[4]{b} x^2}\right)}{4 a^{3/8} b^{5/8}}+\frac{\sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}} \sqrt[8]{a} \sqrt[8]{b} x \sqrt{p x^3+q}}{\sqrt[4]{a} p x^3+\sqrt[4]{a} q-\sqrt[4]{b} x^2}\right)}{4 a^{3/8} b^{5/8}}-\frac{\sqrt{2+\sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt{2-\sqrt{2}} \sqrt[8]{a} \sqrt[8]{b} x \sqrt{p x^3+q}}{\sqrt[4]{a} p x^3+\sqrt[4]{a} q+\sqrt[4]{b} x^2}\right)}{4 a^{3/8} b^{5/8}}+\frac{\sqrt{2-\sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt{2+\sqrt{2}} \sqrt[8]{a} \sqrt[8]{b} x \sqrt{p x^3+q}}{\sqrt[4]{a} p x^3+\sqrt[4]{a} q+\sqrt[4]{b} x^2}\right)}{4 a^{3/8} b^{5/8}}",1,"Result too large to show","C",0
2999,0,0,399,2.5860978,"\int \frac{\sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1+x^2\right)^2} \, dx","Integrate[(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 + x^2)^2,x]","\int \frac{\sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1+x^2\right)^2} \, dx","\frac{1}{64} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{13 \text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-16 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-6 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+8 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+3 \text{$\#$1}^3-\text{$\#$1}}\&\right]+\frac{\sqrt{x^2+1} \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(-2 x^2-x-1\right)+\left(26 x^2+x+5\right) \sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(-2 x^3-x^2-2 x-1\right)+\left(26 x^3+x^2+18 x+1\right) \sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{16 \left(2 x^4+3 x^2+1\right)+16 \sqrt{x^2+1} \left(2 x^3+2 x\right)}",1,"Integrate[(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 + x^2)^2, x]","F",-1
3000,0,0,399,0.2817503,"\int \frac{\sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1+x^2\right)^2} \, dx","Integrate[(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 + x^2)^2,x]","\int \frac{\sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1+x^2\right)^2} \, dx","\frac{1}{64} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{13 \text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-16 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-6 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+8 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+3 \text{$\#$1}^3-\text{$\#$1}}\&\right]+\frac{\sqrt{x^2+1} \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(-2 x^2-x-1\right)+\left(26 x^2+x+5\right) \sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(-2 x^3-x^2-2 x-1\right)+\left(26 x^3+x^2+18 x+1\right) \sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{16 \left(2 x^4+3 x^2+1\right)+16 \sqrt{x^2+1} \left(2 x^3+2 x\right)}",1,"Integrate[(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 + x^2)^2, x]","F",-1
3001,0,0,401,6.8187196,"\int \frac{\sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","Integrate[(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2)^2,x]","\int \frac{\sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","-\frac{1}{16} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-\text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+3 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]-\frac{1}{16} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-\text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-5 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+4 \text{$\#$1}^3-2 \text{$\#$1}}\&\right]-\frac{\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} x}{2 \left(x^2-1\right)}",1,"Integrate[(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2)^2, x]","F",-1
3002,0,0,401,0.3767589,"\int \frac{\sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","Integrate[(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2)^2,x]","\int \frac{\sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","-\frac{1}{16} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-\text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+3 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]-\frac{1}{16} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-\text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-5 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+4 \text{$\#$1}^3-2 \text{$\#$1}}\&\right]-\frac{\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} x}{2 \left(x^2-1\right)}",1,"Integrate[(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2)^2, x]","F",-1
3003,0,0,402,3.6607582,"\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1+x^2\right)^2 \sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 + x^2)^2*Sqrt[x + Sqrt[1 + x^2]]),x]","\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1+x^2\right)^2 \sqrt{x+\sqrt{1+x^2}}} \, dx","\frac{\sqrt{x^2+1} \left(\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(-2 x^2+5 x-1\right)+\left(2 x^2-x+1\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(-2 x^3+5 x^2-2 x-3\right)+\left(2 x^3-x^2+2 x-1\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{16 \left(2 x^4+3 x^2+1\right)+16 \sqrt{x^2+1} \left(2 x^3+2 x\right)}-\frac{1}{64} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{\text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-4 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-24 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+3 \text{$\#$1}^3-\text{$\#$1}}\&\right]",1,"Integrate[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 + x^2)^2*Sqrt[x + Sqrt[1 + x^2]]), x]","F",-1
3004,0,0,402,0.3168582,"\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1+x^2\right)^2 \sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 + x^2)^2*Sqrt[x + Sqrt[1 + x^2]]),x]","\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1+x^2\right)^2 \sqrt{x+\sqrt{1+x^2}}} \, dx","\frac{\sqrt{x^2+1} \left(\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(-2 x^2+5 x-1\right)+\left(2 x^2-x+1\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(-2 x^3+5 x^2-2 x-3\right)+\left(2 x^3-x^2+2 x-1\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{16 \left(2 x^4+3 x^2+1\right)+16 \sqrt{x^2+1} \left(2 x^3+2 x\right)}-\frac{1}{64} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{\text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-4 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-24 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+3 \text{$\#$1}^3-\text{$\#$1}}\&\right]",1,"Integrate[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 + x^2)^2*Sqrt[x + Sqrt[1 + x^2]]), x]","F",-1
3005,0,0,404,6.1990743,"\int \frac{(1+(-2+k) x) \left(1-2 k x+k^2 x^2\right)}{\sqrt[3]{(1-x) x (1-k x)} \left(b-4 b k x+\left(-1+6 b k^2\right) x^2+\left(2-4 b k^3\right) x^3+\left(-1+b k^4\right) x^4\right)} \, dx","Integrate[((1 + (-2 + k)*x)*(1 - 2*k*x + k^2*x^2))/(((1 - x)*x*(1 - k*x))^(1/3)*(b - 4*b*k*x + (-1 + 6*b*k^2)*x^2 + (2 - 4*b*k^3)*x^3 + (-1 + b*k^4)*x^4)),x]","\int \frac{(1+(-2+k) x) \left(1-2 k x+k^2 x^2\right)}{\sqrt[3]{(1-x) x (1-k x)} \left(b-4 b k x+\left(-1+6 b k^2\right) x^2+\left(2-4 b k^3\right) x^3+\left(-1+b k^4\right) x^4\right)} \, dx","-\frac{\log \left(\sqrt[6]{b} k^2 x-\sqrt[6]{b} k-k \sqrt[3]{k x^3+(-k-1) x^2+x}\right)}{2 b^{2/3}}-\frac{\log \left(\sqrt[6]{b} k^2 x-\sqrt[6]{b} k+k \sqrt[3]{k x^3+(-k-1) x^2+x}\right)}{2 b^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \left(k x^3+(-k-1) x^2+x\right)^{2/3}}{\sqrt{3} \sqrt[3]{b}}+\frac{k^2 x^2}{\sqrt{3}}-\frac{2 k x}{\sqrt{3}}+\frac{1}{\sqrt{3}}}{(k x-1)^2}\right)}{2 b^{2/3}}+\frac{\log \left(\sqrt[3]{b} k^4 x^2-2 \sqrt[3]{b} k^3 x+\sqrt[3]{b} k^2+\sqrt[3]{k x^3+(-k-1) x^2+x} \left(\sqrt[6]{b} k^2-\sqrt[6]{b} k^3 x\right)+k^2 \left(k x^3+(-k-1) x^2+x\right)^{2/3}\right)}{4 b^{2/3}}+\frac{\log \left(\sqrt[3]{b} k^4 x^2-2 \sqrt[3]{b} k^3 x+\sqrt[3]{b} k^2+\sqrt[3]{k x^3+(-k-1) x^2+x} \left(\sqrt[6]{b} k^3 x-\sqrt[6]{b} k^2\right)+k^2 \left(k x^3+(-k-1) x^2+x\right)^{2/3}\right)}{4 b^{2/3}}",1,"Integrate[((1 + (-2 + k)*x)*(1 - 2*k*x + k^2*x^2))/(((1 - x)*x*(1 - k*x))^(1/3)*(b - 4*b*k*x + (-1 + 6*b*k^2)*x^2 + (2 - 4*b*k^3)*x^3 + (-1 + b*k^4)*x^4)), x]","F",-1
3006,0,0,404,9.473373,"\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2 \sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x^2)^2*Sqrt[x + Sqrt[1 + x^2]]),x]","\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2 \sqrt{x+\sqrt{1+x^2}}} \, dx","-\frac{1}{16} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{4 \text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-8 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+\text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]+\frac{1}{16} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{4 \text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-8 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+7 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+4 \text{$\#$1}^3-2 \text{$\#$1}}\&\right]-\frac{\sqrt{\sqrt{\sqrt{x^2+1}+x}+1} x}{2 \left(x^2-1\right) \sqrt{\sqrt{x^2+1}+x}}",1,"Integrate[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x^2)^2*Sqrt[x + Sqrt[1 + x^2]]), x]","F",-1
3007,0,0,404,0.3925935,"\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2 \sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x^2)^2*Sqrt[x + Sqrt[1 + x^2]]),x]","\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2 \sqrt{x+\sqrt{1+x^2}}} \, dx","-\frac{1}{16} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{4 \text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-8 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+\text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]+\frac{1}{16} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{4 \text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-8 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+7 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+4 \text{$\#$1}^3-2 \text{$\#$1}}\&\right]-\frac{\sqrt{\sqrt{\sqrt{x^2+1}+x}+1} x}{2 \left(x^2-1\right) \sqrt{\sqrt{x^2+1}+x}}",1,"Integrate[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x^2)^2*Sqrt[x + Sqrt[1 + x^2]]), x]","F",-1
3008,0,0,405,4.6346079,"\int \frac{(a-2 b+x) \left(a^2-2 a x+x^2\right)}{\sqrt[3]{(-a+x) (-b+x)} \left(-b^2+a^4 d+2 \left(b-2 a^3 d\right) x+\left(-1+6 a^2 d\right) x^2-4 a d x^3+d x^4\right)} \, dx","Integrate[((a - 2*b + x)*(a^2 - 2*a*x + x^2))/(((-a + x)*(-b + x))^(1/3)*(-b^2 + a^4*d + 2*(b - 2*a^3*d)*x + (-1 + 6*a^2*d)*x^2 - 4*a*d*x^3 + d*x^4)),x]","\int \frac{(a-2 b+x) \left(a^2-2 a x+x^2\right)}{\sqrt[3]{(-a+x) (-b+x)} \left(-b^2+a^4 d+2 \left(b-2 a^3 d\right) x+\left(-1+6 a^2 d\right) x^2-4 a d x^3+d x^4\right)} \, dx","\frac{\log \left(a^2 \sqrt[6]{d}-a \sqrt[3]{x (-a-b)+a b+x^2}-a \sqrt[6]{d} x\right)}{2 d^{2/3}}+\frac{\log \left(a^2 \sqrt[6]{d}+a \sqrt[3]{x (-a-b)+a b+x^2}-a \sqrt[6]{d} x\right)}{2 d^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{a^2}{\sqrt{3}}+\frac{2 \left(x (-a-b)+a b+x^2\right)^{2/3}}{\sqrt{3} \sqrt[3]{d}}-\frac{2 a x}{\sqrt{3}}+\frac{x^2}{\sqrt{3}}}{(a-x)^2}\right)}{2 d^{2/3}}-\frac{\log \left(a^4 \sqrt[3]{d}-2 a^3 \sqrt[3]{d} x+a^2 \left(x (-a-b)+a b+x^2\right)^{2/3}+a^2 \sqrt[3]{d} x^2+\sqrt[3]{x (-a-b)+a b+x^2} \left(a^3 \sqrt[6]{d}-a^2 \sqrt[6]{d} x\right)\right)}{4 d^{2/3}}-\frac{\log \left(a^4 \sqrt[3]{d}-2 a^3 \sqrt[3]{d} x+a^2 \left(x (-a-b)+a b+x^2\right)^{2/3}+a^2 \sqrt[3]{d} x^2+\sqrt[3]{x (-a-b)+a b+x^2} \left(a^2 \sqrt[6]{d} x-a^3 \sqrt[6]{d}\right)\right)}{4 d^{2/3}}",1,"Integrate[((a - 2*b + x)*(a^2 - 2*a*x + x^2))/(((-a + x)*(-b + x))^(1/3)*(-b^2 + a^4*d + 2*(b - 2*a^3*d)*x + (-1 + 6*a^2*d)*x^2 - 4*a*d*x^3 + d*x^4)), x]","F",-1
3009,0,0,406,6.9588537,"\int \frac{\left(1+x^4\right) \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^4\right) \sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[((1 + x^4)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/((1 - x^4)*Sqrt[x + Sqrt[1 + x^2]]),x]","\int \frac{\left(1+x^4\right) \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^4\right) \sqrt{x+\sqrt{1+x^2}}} \, dx","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^2-1}\&\right]+\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+3 \text{$\#$1}^2-1}\&\right]+\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^2-1}\&\right]+\frac{\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} (2-16 x)+\sqrt{x^2+1} \left((-32 x-3) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-16 \sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\left(-32 x^2-3 x-8\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{24 \left(\sqrt{x^2+1}+x\right)^{3/2}}+\frac{1}{8} \tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)",1,"Integrate[((1 + x^4)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/((1 - x^4)*Sqrt[x + Sqrt[1 + x^2]]), x]","F",-1
3010,0,0,406,0.307688,"\int \frac{\left(1+x^4\right) \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^4\right) \sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[((1 + x^4)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/((1 - x^4)*Sqrt[x + Sqrt[1 + x^2]]),x]","\int \frac{\left(1+x^4\right) \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^4\right) \sqrt{x+\sqrt{1+x^2}}} \, dx","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^2-1}\&\right]+\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+3 \text{$\#$1}^2-1}\&\right]+\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^2-1}\&\right]+\frac{\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} (2-16 x)+\sqrt{x^2+1} \left((-32 x-3) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-16 \sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\left(-32 x^2-3 x-8\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{24 \left(\sqrt{x^2+1}+x\right)^{3/2}}+\frac{1}{8} \tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)",1,"Integrate[((1 + x^4)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/((1 - x^4)*Sqrt[x + Sqrt[1 + x^2]]), x]","F",-1
3011,1,328,407,4.4456092,"\int \frac{\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}}{x-\sqrt{b+a x}} \, dx","Integrate[(Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]])/(x - Sqrt[b + a*x]),x]","\frac{\sqrt{\sqrt{a x+b}+c} \left(-2 a \left(-3 \sqrt{a^2+4 b}+\sqrt{a x+b}+c\right)+2 a \left(3 \sqrt{a^2+4 b}+\sqrt{a x+b}+c\right)-\frac{3 \left(a \sqrt{a^2+4 b}-a^2-2 b\right) \tanh ^{-1}\left(\sqrt{2} \sqrt{\frac{\sqrt{a x+b}+c}{-\sqrt{a^2+4 b}+a+2 c}}\right)}{\sqrt{\frac{\sqrt{a x+b}+c}{-2 \sqrt{a^2+4 b}+2 a+4 c}}}-\frac{3 \sqrt{2} \left(a \sqrt{a^2+4 b}+a^2+2 b\right) \tanh ^{-1}\left(\sqrt{2} \sqrt{\frac{\sqrt{a x+b}+c}{\sqrt{a^2+4 b}+a+2 c}}\right)}{\sqrt{\frac{\sqrt{a x+b}+c}{\sqrt{a^2+4 b}+a+2 c}}}+4 c \sqrt{a^2+4 b}+4 \sqrt{a^2+4 b} \sqrt{a x+b}\right)}{3 \sqrt{a^2+4 b}}","\frac{2 \left(\sqrt{2} a^3+\sqrt{2} a c \sqrt{a^2+4 b}+\sqrt{2} a^2 \sqrt{a^2+4 b}+\sqrt{2} b \sqrt{a^2+4 b}+\sqrt{2} a^2 c+3 \sqrt{2} a b+2 \sqrt{2} b c\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{\sqrt{a x+b}+c}}{\sqrt{-\sqrt{a^2+4 b}-a-2 c}}\right)}{\sqrt{a^2+4 b} \sqrt{-\sqrt{a^2+4 b}-a-2 c}}+\frac{2 \left(-\sqrt{2} a^3+\sqrt{2} a c \sqrt{a^2+4 b}+\sqrt{2} a^2 \sqrt{a^2+4 b}+\sqrt{2} b \sqrt{a^2+4 b}-\sqrt{2} a^2 c-3 \sqrt{2} a b-2 \sqrt{2} b c\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{\sqrt{a x+b}+c}}{\sqrt{\sqrt{a^2+4 b}-a-2 c}}\right)}{\sqrt{a^2+4 b} \sqrt{\sqrt{a^2+4 b}-a-2 c}}+\frac{4}{3} (3 a+c) \sqrt{\sqrt{a x+b}+c}+\frac{4}{3} \sqrt{a x+b} \sqrt{\sqrt{a x+b}+c}",1,"(Sqrt[c + Sqrt[b + a*x]]*(4*Sqrt[a^2 + 4*b]*c + 4*Sqrt[a^2 + 4*b]*Sqrt[b + a*x] - 2*a*(-3*Sqrt[a^2 + 4*b] + c + Sqrt[b + a*x]) + 2*a*(3*Sqrt[a^2 + 4*b] + c + Sqrt[b + a*x]) - (3*(-a^2 - 2*b + a*Sqrt[a^2 + 4*b])*ArcTanh[Sqrt[2]*Sqrt[(c + Sqrt[b + a*x])/(a - Sqrt[a^2 + 4*b] + 2*c)]])/Sqrt[(c + Sqrt[b + a*x])/(2*a - 2*Sqrt[a^2 + 4*b] + 4*c)] - (3*Sqrt[2]*(a^2 + 2*b + a*Sqrt[a^2 + 4*b])*ArcTanh[Sqrt[2]*Sqrt[(c + Sqrt[b + a*x])/(a + Sqrt[a^2 + 4*b] + 2*c)]])/Sqrt[(c + Sqrt[b + a*x])/(a + Sqrt[a^2 + 4*b] + 2*c)]))/(3*Sqrt[a^2 + 4*b])","A",1
3012,1,151,411,0.1854161,"\int \frac{1+x}{(1-a x) \sqrt[4]{\frac{1-b x}{c+x}}} \, dx","Integrate[(1 + x)/((1 - a*x)*((1 - b*x)/(c + x))^(1/4)),x]","-\frac{4 \left(5 (a+1) \sqrt[4]{\frac{1-b x}{b c+1}} \, _2F_1\left(\frac{1}{4},\frac{1}{4};\frac{5}{4};\frac{b (c+x)}{b c+1}\right)-5 (a+1) \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{(a-b) (c+x)}{(a c+1) (1-b x)}\right)+a (c+x) \sqrt[4]{\frac{1-b x}{b c+1}} \, _2F_1\left(\frac{1}{4},\frac{5}{4};\frac{9}{4};\frac{b (c+x)}{b c+1}\right)\right)}{5 a^2 \sqrt[4]{\frac{1-b x}{c+x}}}","-\frac{(a b c+4 a b+a+4 b) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{\frac{1-b x}{c+x}}}{\sqrt{\frac{1-b x}{c+x}}-\sqrt{b}}\right)}{2 \sqrt{2} a^2 b^{5/4}}-\frac{(a b c+4 a b+a+4 b) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt[4]{\frac{1-b x}{c+x}}}{\sqrt{\frac{1-b x}{c+x}}+\sqrt{b}}\right)}{2 \sqrt{2} a^2 b^{5/4}}-\frac{\sqrt{2} (a+1) \sqrt[4]{a c+1} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b-a} \sqrt[4]{a c+1} \sqrt[4]{\frac{1-b x}{c+x}}}{\sqrt{b-a}-\sqrt{a c+1} \sqrt{\frac{1-b x}{c+x}}}\right)}{a^2 \sqrt[4]{b-a}}+\frac{\sqrt{2} (a+1) \sqrt[4]{a c+1} \tanh ^{-1}\left(\frac{\sqrt{a c+1} \sqrt{\frac{1-b x}{c+x}}+\sqrt{b-a}}{\sqrt{2} \sqrt[4]{b-a} \sqrt[4]{a c+1} \sqrt[4]{\frac{1-b x}{c+x}}}\right)}{a^2 \sqrt[4]{b-a}}+\frac{(c+x) \left(\frac{1-b x}{c+x}\right)^{3/4}}{a b}",1,"(-4*(5*(1 + a)*((1 - b*x)/(1 + b*c))^(1/4)*Hypergeometric2F1[1/4, 1/4, 5/4, (b*(c + x))/(1 + b*c)] - 5*(1 + a)*Hypergeometric2F1[1/4, 1, 5/4, ((a - b)*(c + x))/((1 + a*c)*(1 - b*x))] + a*(c + x)*((1 - b*x)/(1 + b*c))^(1/4)*Hypergeometric2F1[1/4, 5/4, 9/4, (b*(c + x))/(1 + b*c)]))/(5*a^2*((1 - b*x)/(c + x))^(1/4))","C",1
3013,0,0,413,0.4166231,"\int \frac{x^5 \left(-7 b+9 a x^2\right)}{\sqrt[4]{-b x^3+a x^5} \left(1-b x^7+a x^9\right)} \, dx","Integrate[(x^5*(-7*b + 9*a*x^2))/((-(b*x^3) + a*x^5)^(1/4)*(1 - b*x^7 + a*x^9)),x]","\int \frac{x^5 \left(-7 b+9 a x^2\right)}{\sqrt[4]{-b x^3+a x^5} \left(1-b x^7+a x^9\right)} \, dx","-\sqrt{2} \tan ^{-1}\left(\frac{x^2 \sqrt[4]{a x^5-b x^3}-2^{2/3} x \sqrt[4]{a x^5-b x^3}}{2^{2/3} x \sqrt[4]{a x^5-b x^3}+x^2 \left(-\sqrt[4]{a x^5-b x^3}\right)-\sqrt{2} x+2 \sqrt[6]{2}}\right)+\sqrt{2} \tan ^{-1}\left(\frac{x^2 \sqrt[4]{a x^5-b x^3}-2^{2/3} x \sqrt[4]{a x^5-b x^3}}{2^{2/3} x \sqrt[4]{a x^5-b x^3}+x^2 \left(-\sqrt[4]{a x^5-b x^3}\right)+\sqrt{2} x-2 \sqrt[6]{2}}\right)-\sqrt{2} \tanh ^{-1}\left(\frac{-\sqrt{2} x^3 \sqrt[4]{a x^5-b x^3}-2\ 2^{5/6} x \sqrt[4]{a x^5-b x^3}+4 \sqrt[6]{2} x^2 \sqrt[4]{a x^5-b x^3}}{2\ 2^{2/3} x^3 \sqrt{a x^5-b x^3}+x^4 \left(-\sqrt{a x^5-b x^3}\right)-2 \sqrt[3]{2} x^2 \sqrt{a x^5-b x^3}-x^2+2\ 2^{2/3} x-2 \sqrt[3]{2}}\right)",1,"Integrate[(x^5*(-7*b + 9*a*x^2))/((-(b*x^3) + a*x^5)^(1/4)*(1 - b*x^7 + a*x^9)), x]","F",-1
3014,1,190,415,1.0787713,"\int \frac{b+a x^4}{\sqrt{-b+a x^4} \left(-b+c^2 x^2+a x^4\right)} \, dx","Integrate[(b + a*x^4)/(Sqrt[-b + a*x^4]*(-b + c^2*x^2 + a*x^4)),x]","-\frac{i \sqrt{1-\frac{a x^4}{b}} \left(-\Pi \left(\frac{2 \sqrt{a} \sqrt{b}}{\sqrt{c^4+4 a b}-c^2};\left.i \sinh ^{-1}\left(\sqrt{-\frac{\sqrt{a}}{\sqrt{b}}} x\right)\right|-1\right)-\Pi \left(-\frac{2 \sqrt{a} \sqrt{b}}{c^2+\sqrt{c^4+4 a b}};\left.i \sinh ^{-1}\left(\sqrt{-\frac{\sqrt{a}}{\sqrt{b}}} x\right)\right|-1\right)+F\left(\left.i \sinh ^{-1}\left(\sqrt{-\frac{\sqrt{a}}{\sqrt{b}}} x\right)\right|-1\right)\right)}{\sqrt{-\frac{\sqrt{a}}{\sqrt{b}}} \sqrt{a x^4-b}}","\frac{i \left(\sqrt{2} c-(1-i) \sqrt{2 \sqrt{a} \sqrt{b}+i c^2}\right) \sqrt{-(-1)^{3/4} c \sqrt{2 \sqrt{a} \sqrt{b}+i c^2}-i \sqrt{a} \sqrt{b}+c^2} \tan ^{-1}\left(\frac{\sqrt{2} x \sqrt{-(-1)^{3/4} c \sqrt{2 \sqrt{a} \sqrt{b}+i c^2}-i \sqrt{a} \sqrt{b}+c^2}}{\sqrt{a x^4-b}+\sqrt{a} x^2+i \sqrt{b}}\right)}{2 \sqrt{a} \sqrt{b} c}-\frac{i \left(\sqrt{2} c+(1-i) \sqrt{2 \sqrt{a} \sqrt{b}+i c^2}\right) \sqrt{-(-1)^{3/4} c \sqrt{2 \sqrt{a} \sqrt{b}+i c^2}+i \sqrt{a} \sqrt{b}-c^2} \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt{-(-1)^{3/4} c \sqrt{2 \sqrt{a} \sqrt{b}+i c^2}+i \sqrt{a} \sqrt{b}-c^2}}{\sqrt{a x^4-b}+\sqrt{a} x^2+i \sqrt{b}}\right)}{2 \sqrt{a} \sqrt{b} c}",1,"((-I)*Sqrt[1 - (a*x^4)/b]*(EllipticF[I*ArcSinh[Sqrt[-(Sqrt[a]/Sqrt[b])]*x], -1] - EllipticPi[(2*Sqrt[a]*Sqrt[b])/(-c^2 + Sqrt[4*a*b + c^4]), I*ArcSinh[Sqrt[-(Sqrt[a]/Sqrt[b])]*x], -1] - EllipticPi[(-2*Sqrt[a]*Sqrt[b])/(c^2 + Sqrt[4*a*b + c^4]), I*ArcSinh[Sqrt[-(Sqrt[a]/Sqrt[b])]*x], -1]))/(Sqrt[-(Sqrt[a]/Sqrt[b])]*Sqrt[-b + a*x^4])","C",1
3015,0,0,415,1.6228354,"\int \frac{x (-a+x) \left(a b-2 b x+x^2\right)}{\sqrt[3]{x (-a+x) (-b+x)^2} \left(-b^2+2 b x+\left(-1+a^2 d\right) x^2-2 a d x^3+d x^4\right)} \, dx","Integrate[(x*(-a + x)*(a*b - 2*b*x + x^2))/((x*(-a + x)*(-b + x)^2)^(1/3)*(-b^2 + 2*b*x + (-1 + a^2*d)*x^2 - 2*a*d*x^3 + d*x^4)),x]","\int \frac{x (-a+x) \left(a b-2 b x+x^2\right)}{\sqrt[3]{x (-a+x) (-b+x)^2} \left(-b^2+2 b x+\left(-1+a^2 d\right) x^2-2 a d x^3+d x^4\right)} \, dx","-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{d} \sqrt[3]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}}{\sqrt[6]{d} \sqrt[3]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}+2 b-2 x}\right)}{2 d^{5/6}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{d} \sqrt[3]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}}{\sqrt[6]{d} \sqrt[3]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}-2 b+2 x}\right)}{2 d^{5/6}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{d} \sqrt[3]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4}}{b-x}\right)}{d^{5/6}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[3]{x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4} \left(b \sqrt[6]{d}-\sqrt[6]{d} x\right)}{\sqrt[3]{d} \left(x^2 \left(2 a b+b^2\right)-a b^2 x+x^3 (-a-2 b)+x^4\right)^{2/3}+b^2-2 b x+x^2}\right)}{2 d^{5/6}}",1,"Integrate[(x*(-a + x)*(a*b - 2*b*x + x^2))/((x*(-a + x)*(-b + x)^2)^(1/3)*(-b^2 + 2*b*x + (-1 + a^2*d)*x^2 - 2*a*d*x^3 + d*x^4)), x]","F",-1
3016,1,85,417,0.055948,"\int \frac{b+a x}{(-b+a x) \sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Integrate[(b + a*x)/((-b + a*x)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","\frac{3 x \sqrt[3]{\frac{a^3 x}{b^2}+1} \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};-\frac{a^3 x}{b^2}\right)-6 x \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2+b\right) x}{x a^3+b^2}\right)}{\sqrt[3]{x^2 \left(a^3 x+b^2\right)}}","-\frac{\log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-a x\right)}{a}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} a x}{2 \sqrt[3]{a^3 x^3+b^2 x^2}+a x}\right)}{a}-\frac{i \left(\sqrt{3}-i\right) \log \left(\sqrt[3]{-1} \sqrt[3]{a^3 x^3+b^2 x^2}+\sqrt[3]{a} x \sqrt[3]{a^2+b}\right)}{\sqrt[3]{a} \sqrt[3]{a^2+b}}+\frac{\log \left(a x \sqrt[3]{a^3 x^3+b^2 x^2}+\left(a^3 x^3+b^2 x^2\right)^{2/3}+a^2 x^2\right)}{2 a}+\frac{\sqrt{6 \left(-1+i \sqrt{3}\right)} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{a} x \sqrt[3]{a^2+b}}{\sqrt[3]{a} x \sqrt[3]{a^2+b}-2 \sqrt[3]{-1} \sqrt[3]{a^3 x^3+b^2 x^2}}\right)}{\sqrt[3]{a} \sqrt[3]{a^2+b}}+\frac{\left(1+i \sqrt{3}\right) \log \left((-1)^{2/3} \left(a^3 x^3+b^2 x^2\right)^{2/3}+a^{2/3} x^2 \left(a^2+b\right)^{2/3}-\sqrt[3]{-1} \sqrt[3]{a} x \sqrt[3]{a^2+b} \sqrt[3]{a^3 x^3+b^2 x^2}\right)}{2 \sqrt[3]{a} \sqrt[3]{a^2+b}}",1,"(3*x*(1 + (a^3*x)/b^2)^(1/3)*Hypergeometric2F1[1/3, 1/3, 4/3, -((a^3*x)/b^2)] - 6*x*Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 + b)*x)/(b^2 + a^3*x)])/(x^2*(b^2 + a^3*x))^(1/3)","C",1
3017,0,0,421,0.6054811,"\int \frac{\sqrt{b+a^2 x^4} \sqrt{a x^2+\sqrt{b+a^2 x^4}}}{-b+a^2 x^4} \, dx","Integrate[(Sqrt[b + a^2*x^4]*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]])/(-b + a^2*x^4),x]","\int \frac{\sqrt{b+a^2 x^4} \sqrt{a x^2+\sqrt{b+a^2 x^4}}}{-b+a^2 x^4} \, dx","\frac{\log \left(i a^{3/2} x^2+i \sqrt{a} \sqrt{a^2 x^4+b}+i \sqrt{2} a x \sqrt{\sqrt{a^2 x^4+b}+a x^2}\right)}{\sqrt{2} \sqrt{a}}-2 \sqrt{2} \sqrt{a} b \text{RootSum}\left[\text{$\#$1}^8+20 \text{$\#$1}^6 a b-26 \text{$\#$1}^4 a^2 b^2+20 \text{$\#$1}^2 a^3 b^3+a^4 b^4\&,\frac{\text{$\#$1}^4 \log \left(-\text{$\#$1}+i a^{3/2} x^2+i \sqrt{a} \sqrt{a^2 x^4+b}+i \sqrt{2} a x \sqrt{\sqrt{a^2 x^4+b}+a x^2}\right)-2 \text{$\#$1}^2 a b \log \left(-\text{$\#$1}+i a^{3/2} x^2+i \sqrt{a} \sqrt{a^2 x^4+b}+i \sqrt{2} a x \sqrt{\sqrt{a^2 x^4+b}+a x^2}\right)+a^2 b^2 \log \left(-\text{$\#$1}+i a^{3/2} x^2+i \sqrt{a} \sqrt{a^2 x^4+b}+i \sqrt{2} a x \sqrt{\sqrt{a^2 x^4+b}+a x^2}\right)}{\text{$\#$1}^6+15 \text{$\#$1}^4 a b-13 \text{$\#$1}^2 a^2 b^2+5 a^3 b^3}\&\right]",1,"Integrate[(Sqrt[b + a^2*x^4]*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]])/(-b + a^2*x^4), x]","F",-1
3018,0,0,421,0.2662676,"\int \frac{\sqrt{b+a^2 x^4} \sqrt{a x^2+\sqrt{b+a^2 x^4}}}{-b+a^2 x^4} \, dx","Integrate[(Sqrt[b + a^2*x^4]*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]])/(-b + a^2*x^4),x]","\int \frac{\sqrt{b+a^2 x^4} \sqrt{a x^2+\sqrt{b+a^2 x^4}}}{-b+a^2 x^4} \, dx","\frac{\log \left(i a^{3/2} x^2+i \sqrt{a} \sqrt{a^2 x^4+b}+i \sqrt{2} a x \sqrt{\sqrt{a^2 x^4+b}+a x^2}\right)}{\sqrt{2} \sqrt{a}}-2 \sqrt{2} \sqrt{a} b \text{RootSum}\left[\text{$\#$1}^8+20 \text{$\#$1}^6 a b-26 \text{$\#$1}^4 a^2 b^2+20 \text{$\#$1}^2 a^3 b^3+a^4 b^4\&,\frac{\text{$\#$1}^4 \log \left(-\text{$\#$1}+i a^{3/2} x^2+i \sqrt{a} \sqrt{a^2 x^4+b}+i \sqrt{2} a x \sqrt{\sqrt{a^2 x^4+b}+a x^2}\right)-2 \text{$\#$1}^2 a b \log \left(-\text{$\#$1}+i a^{3/2} x^2+i \sqrt{a} \sqrt{a^2 x^4+b}+i \sqrt{2} a x \sqrt{\sqrt{a^2 x^4+b}+a x^2}\right)+a^2 b^2 \log \left(-\text{$\#$1}+i a^{3/2} x^2+i \sqrt{a} \sqrt{a^2 x^4+b}+i \sqrt{2} a x \sqrt{\sqrt{a^2 x^4+b}+a x^2}\right)}{\text{$\#$1}^6+15 \text{$\#$1}^4 a b-13 \text{$\#$1}^2 a^2 b^2+5 a^3 b^3}\&\right]",1,"Integrate[(Sqrt[b + a^2*x^4]*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]])/(-b + a^2*x^4), x]","F",-1
3019,1,58,423,0.0640046,"\int \frac{1}{\sqrt[3]{(-a+x) (-b+x)^2} (b-a d+(-1+d) x)} \, dx","Integrate[1/(((-a + x)*(-b + x)^2)^(1/3)*(b - a*d + (-1 + d)*x)),x]","-\frac{3 (x-b) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{b-x}{a d-d x}\right)}{d (a-b) \sqrt[3]{(x-a) (b-x)^2}}","\frac{\log \left(\sqrt[3]{d} (a-b)^{2/3} \sqrt[3]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3}-x (a-b)^{2/3}+b (a-b)^{2/3}\right)}{d^{2/3} (a-b)}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} \sqrt[3]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3}}{\sqrt[3]{d} \sqrt[3]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3}-2 b+2 x}\right)}{d^{2/3} (a-b)}-\frac{\log \left(b^3 \left(-\sqrt[3]{a-b}\right)+d^{2/3} (a-b)^{4/3} \left(x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3\right)^{2/3}+\sqrt[3]{d} \sqrt[3]{a-b} \left(-a b+a x+b^2-b x\right) \sqrt[3]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3}+2 b^2 x \sqrt[3]{a-b}+a b^2 \sqrt[3]{a-b}-b x^2 \sqrt[3]{a-b}+a x^2 \sqrt[3]{a-b}-2 a b x \sqrt[3]{a-b}\right)}{2 d^{2/3} (a-b)}",1,"(-3*(-b + x)*Hypergeometric2F1[1/3, 1, 4/3, (b - x)/(a*d - d*x)])/((a - b)*d*((b - x)^2*(-a + x))^(1/3))","C",1
3020,0,0,423,1.1691044,"\int \frac{\left(-4-3 x+2 x^2\right) \left(1+x-x^2+x^4\right) \sqrt[3]{\frac{1+x-x^2+2 x^4}{1+x-x^2+3 x^4}}}{x^5 \left(-1-x+x^2+x^4\right)} \, dx","Integrate[((-4 - 3*x + 2*x^2)*(1 + x - x^2 + x^4)*((1 + x - x^2 + 2*x^4)/(1 + x - x^2 + 3*x^4))^(1/3))/(x^5*(-1 - x + x^2 + x^4)),x]","\int \frac{\left(-4-3 x+2 x^2\right) \left(1+x-x^2+x^4\right) \sqrt[3]{\frac{1+x-x^2+2 x^4}{1+x-x^2+3 x^4}}}{x^5 \left(-1-x+x^2+x^4\right)} \, dx","\frac{\sqrt[3]{\frac{2 x^4-x^2+x+1}{3 x^4-x^2+x+1}} \left(-3 x^4+x^2-x-1\right)}{x^4}+\frac{5}{3} \log \left(\sqrt[3]{\frac{2 x^4-x^2+x+1}{3 x^4-x^2+x+1}}-1\right)-\sqrt[3]{6} \log \left(6^{2/3} \sqrt[3]{\frac{2 x^4-x^2+x+1}{3 x^4-x^2+x+1}}-3\right)-\frac{5}{6} \log \left(\left(\frac{2 x^4-x^2+x+1}{3 x^4-x^2+x+1}\right)^{2/3}+\sqrt[3]{\frac{2 x^4-x^2+x+1}{3 x^4-x^2+x+1}}+1\right)+\frac{\sqrt[3]{3} \log \left(2 \sqrt[3]{6} \left(\frac{2 x^4-x^2+x+1}{3 x^4-x^2+x+1}\right)^{2/3}+6^{2/3} \sqrt[3]{\frac{2 x^4-x^2+x+1}{3 x^4-x^2+x+1}}+3\right)}{2^{2/3}}+\sqrt[3]{2} 3^{5/6} \tan ^{-1}\left(\frac{2\ 2^{2/3} \sqrt[3]{\frac{2 x^4-x^2+x+1}{3 x^4-x^2+x+1}}}{3^{5/6}}+\frac{1}{\sqrt{3}}\right)-\frac{5 \tan ^{-1}\left(\frac{2 \sqrt[3]{\frac{2 x^4-x^2+x+1}{3 x^4-x^2+x+1}}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3}}",1,"Integrate[((-4 - 3*x + 2*x^2)*(1 + x - x^2 + x^4)*((1 + x - x^2 + 2*x^4)/(1 + x - x^2 + 3*x^4))^(1/3))/(x^5*(-1 - x + x^2 + x^4)), x]","F",-1
3021,1,89,425,0.0618477,"\int \frac{-b+a x}{(b+a x) \sqrt[3]{-b^2 x^2+a^3 x^3}} \, dx","Integrate[(-b + a*x)/((b + a*x)*(-(b^2*x^2) + a^3*x^3)^(1/3)),x]","\frac{3 x \sqrt[3]{1-\frac{a^3 x}{b^2}} \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};\frac{a^3 x}{b^2}\right)-6 x \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{a \left(a^2+b\right) x}{a^3 x-b^2}\right)}{\sqrt[3]{x^2 \left(a^3 x-b^2\right)}}","-\frac{\log \left(\sqrt[3]{a^3 x^3-b^2 x^2}-a x\right)}{a}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} a x}{2 \sqrt[3]{a^3 x^3-b^2 x^2}+a x}\right)}{a}-\frac{i \left(\sqrt{3}-i\right) \log \left(\sqrt[3]{-1} \sqrt[3]{a^3 x^3-b^2 x^2}+\sqrt[3]{a} x \sqrt[3]{a^2+b}\right)}{\sqrt[3]{a} \sqrt[3]{a^2+b}}+\frac{\log \left(a x \sqrt[3]{a^3 x^3-b^2 x^2}+\left(a^3 x^3-b^2 x^2\right)^{2/3}+a^2 x^2\right)}{2 a}+\frac{\sqrt{6 \left(-1+i \sqrt{3}\right)} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{a} x \sqrt[3]{a^2+b}}{\sqrt[3]{a} x \sqrt[3]{a^2+b}-2 \sqrt[3]{-1} \sqrt[3]{a^3 x^3-b^2 x^2}}\right)}{\sqrt[3]{a} \sqrt[3]{a^2+b}}+\frac{\left(1+i \sqrt{3}\right) \log \left((-1)^{2/3} \left(a^3 x^3-b^2 x^2\right)^{2/3}+a^{2/3} x^2 \left(a^2+b\right)^{2/3}-\sqrt[3]{-1} \sqrt[3]{a} x \sqrt[3]{a^2+b} \sqrt[3]{a^3 x^3-b^2 x^2}\right)}{2 \sqrt[3]{a} \sqrt[3]{a^2+b}}",1,"(3*x*(1 - (a^3*x)/b^2)^(1/3)*Hypergeometric2F1[1/3, 1/3, 4/3, (a^3*x)/b^2] - 6*x*Hypergeometric2F1[1/3, 1, 4/3, (a*(a^2 + b)*x)/(-b^2 + a^3*x)])/(x^2*(-b^2 + a^3*x))^(1/3)","C",1
3022,1,3958,428,6.714916,"\int \frac{\left(-q+p x^4\right) \sqrt{q+p x^4}}{c x^4+b x^2 \left(q+p x^4\right)+a \left(q+p x^4\right)^2} \, dx","Integrate[((-q + p*x^4)*Sqrt[q + p*x^4])/(c*x^4 + b*x^2*(q + p*x^4) + a*(q + p*x^4)^2),x]","\text{Result too large to show}","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8 a-8 \text{$\#$1}^6 a \sqrt{p} \sqrt{q}+4 \text{$\#$1}^6 b+24 \text{$\#$1}^4 a p q-16 \text{$\#$1}^4 b \sqrt{p} \sqrt{q}+16 \text{$\#$1}^4 c-32 \text{$\#$1}^2 a p^{3/2} q^{3/2}+16 \text{$\#$1}^2 b p q+16 a p^2 q^2\&,\frac{-\text{$\#$1}^6 \log \left(-\text{$\#$1} x+\sqrt{p x^4+q}-\sqrt{p} x^2-\sqrt{q}\right)+\text{$\#$1}^6 \log (x)+2 \text{$\#$1}^4 \sqrt{p} \sqrt{q} \log \left(-\text{$\#$1} x+\sqrt{p x^4+q}-\sqrt{p} x^2-\sqrt{q}\right)-2 \text{$\#$1}^4 \sqrt{p} \sqrt{q} \log (x)+4 \text{$\#$1}^2 p q \log \left(-\text{$\#$1} x+\sqrt{p x^4+q}-\sqrt{p} x^2-\sqrt{q}\right)-4 \text{$\#$1}^2 p q \log (x)-8 p^{3/2} q^{3/2} \log \left(-\text{$\#$1} x+\sqrt{p x^4+q}-\sqrt{p} x^2-\sqrt{q}\right)+8 p^{3/2} q^{3/2} \log (x)}{\text{$\#$1}^7 (-a)+6 \text{$\#$1}^5 a \sqrt{p} \sqrt{q}-3 \text{$\#$1}^5 b-12 \text{$\#$1}^3 a p q+8 \text{$\#$1}^3 b \sqrt{p} \sqrt{q}-8 \text{$\#$1}^3 c+8 \text{$\#$1} a p^{3/2} q^{3/2}-4 \text{$\#$1} b p q}\&\right]",1,"((-I)*Sqrt[1 - (I*Sqrt[p]*x^2)/Sqrt[q]]*Sqrt[1 + (I*Sqrt[p]*x^2)/Sqrt[q]]*EllipticF[I*ArcSinh[Sqrt[(I*Sqrt[p])/Sqrt[q]]*x], -1])/(a*Sqrt[(I*Sqrt[p])/Sqrt[q]]*Sqrt[q + p*x^4]) - (I*q^2*Sqrt[1 - (I*Sqrt[p]*x^2)/Sqrt[q]]*Sqrt[1 + (I*Sqrt[p]*x^2)/Sqrt[q]]*EllipticPi[(I*Sqrt[q])/(Sqrt[p]*Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 1]), I*ArcSinh[Sqrt[(I*Sqrt[p])/Sqrt[q]]*x], -1])/(a*p^2*Sqrt[(I*Sqrt[p])/Sqrt[q]]*Sqrt[q + p*x^4]*Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 1]*(Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 1] - Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 2])*(Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 1] - Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 3])*(Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 1] - Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 4])) + (I*Sqrt[1 - (I*Sqrt[p]*x^2)/Sqrt[q]]*Sqrt[1 + (I*Sqrt[p]*x^2)/Sqrt[q]]*EllipticPi[(I*Sqrt[q])/(Sqrt[p]*Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 1]), I*ArcSinh[Sqrt[(I*Sqrt[p])/Sqrt[q]]*x], -1]*Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 1]^3)/(a*Sqrt[(I*Sqrt[p])/Sqrt[q]]*Sqrt[q + p*x^4]*(Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 1] - Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 2])*(Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 1] - Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 3])*(Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 1] - Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 4])) - (I*q^2*Sqrt[1 - (I*Sqrt[p]*x^2)/Sqrt[q]]*Sqrt[1 + (I*Sqrt[p]*x^2)/Sqrt[q]]*EllipticPi[(I*Sqrt[q])/(Sqrt[p]*Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 2]), I*ArcSinh[Sqrt[(I*Sqrt[p])/Sqrt[q]]*x], -1])/(a*p^2*Sqrt[(I*Sqrt[p])/Sqrt[q]]*Sqrt[q + p*x^4]*Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 2]*(-Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 1] + Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 2])*(Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 2] - Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 3])*(Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 2] - Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 4])) + (I*Sqrt[1 - (I*Sqrt[p]*x^2)/Sqrt[q]]*Sqrt[1 + (I*Sqrt[p]*x^2)/Sqrt[q]]*EllipticPi[(I*Sqrt[q])/(Sqrt[p]*Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 2]), I*ArcSinh[Sqrt[(I*Sqrt[p])/Sqrt[q]]*x], -1]*Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 2]^3)/(a*Sqrt[(I*Sqrt[p])/Sqrt[q]]*Sqrt[q + p*x^4]*(-Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 1] + Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 2])*(Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 2] - Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 3])*(Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 2] - Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 4])) - (I*q^2*Sqrt[1 - (I*Sqrt[p]*x^2)/Sqrt[q]]*Sqrt[1 + (I*Sqrt[p]*x^2)/Sqrt[q]]*EllipticPi[(I*Sqrt[q])/(Sqrt[p]*Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 3]), I*ArcSinh[Sqrt[(I*Sqrt[p])/Sqrt[q]]*x], -1])/(a*p^2*Sqrt[(I*Sqrt[p])/Sqrt[q]]*Sqrt[q + p*x^4]*Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 3]*(-Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 1] + Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 3])*(-Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 2] + Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 3])*(Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 3] - Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 4])) + (I*Sqrt[1 - (I*Sqrt[p]*x^2)/Sqrt[q]]*Sqrt[1 + (I*Sqrt[p]*x^2)/Sqrt[q]]*EllipticPi[(I*Sqrt[q])/(Sqrt[p]*Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 3]), I*ArcSinh[Sqrt[(I*Sqrt[p])/Sqrt[q]]*x], -1]*Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 3]^3)/(a*Sqrt[(I*Sqrt[p])/Sqrt[q]]*Sqrt[q + p*x^4]*(-Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 1] + Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 3])*(-Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 2] + Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 3])*(Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 3] - Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 4])) - (I*q^2*Sqrt[1 - (I*Sqrt[p]*x^2)/Sqrt[q]]*Sqrt[1 + (I*Sqrt[p]*x^2)/Sqrt[q]]*EllipticPi[(I*Sqrt[q])/(Sqrt[p]*Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 4]), I*ArcSinh[Sqrt[(I*Sqrt[p])/Sqrt[q]]*x], -1])/(a*p^2*Sqrt[(I*Sqrt[p])/Sqrt[q]]*Sqrt[q + p*x^4]*Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 4]*(-Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 1] + Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 4])*(-Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 2] + Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 4])*(-Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 3] + Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 4])) + (I*Sqrt[1 - (I*Sqrt[p]*x^2)/Sqrt[q]]*Sqrt[1 + (I*Sqrt[p]*x^2)/Sqrt[q]]*EllipticPi[(I*Sqrt[q])/(Sqrt[p]*Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 4]), I*ArcSinh[Sqrt[(I*Sqrt[p])/Sqrt[q]]*x], -1]*Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 4]^3)/(a*Sqrt[(I*Sqrt[p])/Sqrt[q]]*Sqrt[q + p*x^4]*(-Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 1] + Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 4])*(-Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 2] + Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 4])*(-Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 3] + Root[a*q^2 + b*q*#1 + (c + 2*a*p*q)*#1^2 + b*p*#1^3 + a*p^2*#1^4 & , 4]))","C",0
3023,1,556,428,0.8946936,"\int \frac{\left(1+x^4\right) \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\sqrt{1+x^2} \left(1-x^4\right)} \, dx","Integrate[((1 + x^4)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(Sqrt[1 + x^2]*(1 - x^4)),x]","-\frac{2 \left(x^2+\sqrt{x^2+1} x+1\right) \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^3-2 \text{$\#$1}}\&\right]-2 \left(x^2+\sqrt{x^2+1} x+1\right) \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^4-2 \text{$\#$1}^2+2}\&\right]-\left(x^2+\sqrt{x^2+1} x+1\right) \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+3 \text{$\#$1}^3-\text{$\#$1}}\&\right]+16 \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} x^2+16 \sqrt{x^2+1} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} x+20 \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}+8 x^2 \log \left(1-\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)-8 x^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}+1\right)+8 \sqrt{x^2+1} x \log \left(1-\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)-8 \sqrt{x^2+1} x \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}+1\right)+8 \log \left(1-\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)-8 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}+1\right)}{4 \left(x^2+\sqrt{x^2+1} x+1\right)}","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8+8 \text{$\#$1}^7+24 \text{$\#$1}^6+32 \text{$\#$1}^5+16 \text{$\#$1}^4+1\&,\frac{\log \left(-\text{$\#$1}+\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-1\right)}{\text{$\#$1}^7+7 \text{$\#$1}^6+18 \text{$\#$1}^5+20 \text{$\#$1}^4+8 \text{$\#$1}^3}\&\right]-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8+8 \text{$\#$1}^7+24 \text{$\#$1}^6+32 \text{$\#$1}^5+14 \text{$\#$1}^4-8 \text{$\#$1}^3-8 \text{$\#$1}^2-1\&,\frac{\log \left(-\text{$\#$1}+\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-1\right)}{\text{$\#$1}^3+3 \text{$\#$1}^2+\text{$\#$1}-1}\&\right]+\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8+8 \text{$\#$1}^7+24 \text{$\#$1}^6+32 \text{$\#$1}^5+18 \text{$\#$1}^4+8 \text{$\#$1}^3+8 \text{$\#$1}^2-1\&,\frac{\text{$\#$1} \log \left(-\text{$\#$1}+\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-1\right)+\log \left(-\text{$\#$1}+\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-1\right)}{\text{$\#$1}^4+4 \text{$\#$1}^3+4 \text{$\#$1}^2+1}\&\right]+\frac{\left(-4 x^2-5\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-4 x \sqrt{x^2+1} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{x^2+\sqrt{x^2+1} x+1}+4 \tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)",1,"-1/4*(20*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] + 16*x^2*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] + 16*x*Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] + 8*Log[1 - Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]] + 8*x^2*Log[1 - Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]] + 8*x*Sqrt[1 + x^2]*Log[1 - Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]] - 8*Log[1 + Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]] - 8*x^2*Log[1 + Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]] - 8*x*Sqrt[1 + x^2]*Log[1 + Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]] + 2*(1 + x^2 + x*Sqrt[1 + x^2])*RootSum[-2 + 4*#1^4 - 4*#1^6 + #1^8 & , Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]/(-2*#1 + #1^3) & ] - (1 + x^2 + x*Sqrt[1 + x^2])*RootSum[2 - 4*#1^2 + 6*#1^4 - 4*#1^6 + #1^8 & , Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]/(-#1 + 3*#1^3 - 3*#1^5 + #1^7) & ] - 2*(1 + x^2 + x*Sqrt[1 + x^2])*RootSum[2 - 8*#1^2 + 8*#1^4 - 4*#1^6 + #1^8 & , (Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1)/(2 - 2*#1^2 + #1^4) & ])/(1 + x^2 + x*Sqrt[1 + x^2])","A",1
3024,1,556,428,0.2931257,"\int \frac{\left(1+x^4\right) \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\sqrt{1+x^2} \left(1-x^4\right)} \, dx","Integrate[((1 + x^4)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(Sqrt[1 + x^2]*(1 - x^4)),x]","-\frac{2 \left(x^2+\sqrt{x^2+1} x+1\right) \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^3-2 \text{$\#$1}}\&\right]-2 \left(x^2+\sqrt{x^2+1} x+1\right) \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^4-2 \text{$\#$1}^2+2}\&\right]-\left(x^2+\sqrt{x^2+1} x+1\right) \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+3 \text{$\#$1}^3-\text{$\#$1}}\&\right]+16 \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} x^2+16 \sqrt{x^2+1} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} x+20 \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}+8 x^2 \log \left(1-\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)-8 x^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}+1\right)+8 \sqrt{x^2+1} x \log \left(1-\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)-8 \sqrt{x^2+1} x \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}+1\right)+8 \log \left(1-\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)-8 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}+1\right)}{4 \left(x^2+\sqrt{x^2+1} x+1\right)}","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8+8 \text{$\#$1}^7+24 \text{$\#$1}^6+32 \text{$\#$1}^5+16 \text{$\#$1}^4+1\&,\frac{\log \left(-\text{$\#$1}+\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-1\right)}{\text{$\#$1}^7+7 \text{$\#$1}^6+18 \text{$\#$1}^5+20 \text{$\#$1}^4+8 \text{$\#$1}^3}\&\right]-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8+8 \text{$\#$1}^7+24 \text{$\#$1}^6+32 \text{$\#$1}^5+14 \text{$\#$1}^4-8 \text{$\#$1}^3-8 \text{$\#$1}^2-1\&,\frac{\log \left(-\text{$\#$1}+\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-1\right)}{\text{$\#$1}^3+3 \text{$\#$1}^2+\text{$\#$1}-1}\&\right]+\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8+8 \text{$\#$1}^7+24 \text{$\#$1}^6+32 \text{$\#$1}^5+18 \text{$\#$1}^4+8 \text{$\#$1}^3+8 \text{$\#$1}^2-1\&,\frac{\text{$\#$1} \log \left(-\text{$\#$1}+\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-1\right)+\log \left(-\text{$\#$1}+\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-1\right)}{\text{$\#$1}^4+4 \text{$\#$1}^3+4 \text{$\#$1}^2+1}\&\right]+\frac{\left(-4 x^2-5\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-4 x \sqrt{x^2+1} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{x^2+\sqrt{x^2+1} x+1}+4 \tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)",1,"-1/4*(20*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] + 16*x^2*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] + 16*x*Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] + 8*Log[1 - Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]] + 8*x^2*Log[1 - Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]] + 8*x*Sqrt[1 + x^2]*Log[1 - Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]] - 8*Log[1 + Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]] - 8*x^2*Log[1 + Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]] - 8*x*Sqrt[1 + x^2]*Log[1 + Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]] + 2*(1 + x^2 + x*Sqrt[1 + x^2])*RootSum[-2 + 4*#1^4 - 4*#1^6 + #1^8 & , Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]/(-2*#1 + #1^3) & ] - (1 + x^2 + x*Sqrt[1 + x^2])*RootSum[2 - 4*#1^2 + 6*#1^4 - 4*#1^6 + #1^8 & , Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]/(-#1 + 3*#1^3 - 3*#1^5 + #1^7) & ] - 2*(1 + x^2 + x*Sqrt[1 + x^2])*RootSum[2 - 8*#1^2 + 8*#1^4 - 4*#1^6 + #1^8 & , (Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1)/(2 - 2*#1^2 + #1^4) & ])/(1 + x^2 + x*Sqrt[1 + x^2])","A",1
3025,0,0,429,0.583581,"\int \frac{1-x^3+x^6}{\sqrt[3]{x^2+x^4} \left(-1+x^6\right)} \, dx","Integrate[(1 - x^3 + x^6)/((x^2 + x^4)^(1/3)*(-1 + x^6)),x]","\int \frac{1-x^3+x^6}{\sqrt[3]{x^2+x^4} \left(-1+x^6\right)} \, dx","\frac{1}{2} \log \left(\sqrt[3]{x^4+x^2}-x\right)-\frac{1}{6} \log \left(\sqrt[3]{x^4+x^2}+x\right)+\frac{\log \left(2^{2/3} \sqrt[3]{x^4+x^2}-2 x\right)}{12 \sqrt[3]{2}}-\frac{\log \left(2^{2/3} \sqrt[3]{x^4+x^2}+2 x\right)}{4 \sqrt[3]{2}}+\frac{1}{12} \log \left(x^2-\sqrt[3]{x^4+x^2} x+\left(x^4+x^2\right)^{2/3}\right)-\frac{1}{4} \log \left(x^2+\sqrt[3]{x^4+x^2} x+\left(x^4+x^2\right)^{2/3}\right)+\frac{\log \left(-2 x^2+2^{2/3} \sqrt[3]{x^4+x^2} x-\sqrt[3]{2} \left(x^4+x^2\right)^{2/3}\right)}{8 \sqrt[3]{2}}-\frac{\log \left(2 x^2+2^{2/3} \sqrt[3]{x^4+x^2} x+\sqrt[3]{2} \left(x^4+x^2\right)^{2/3}\right)}{24 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^4+x^2}-x}\right)}{2 \sqrt{3}}-\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^4+x^2}+x}\right)-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^4+x^2}-x}\right)}{4 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^4+x^2}+x}\right)}{4 \sqrt[3]{2} \sqrt{3}}",1,"Integrate[(1 - x^3 + x^6)/((x^2 + x^4)^(1/3)*(-1 + x^6)), x]","F",-1
3026,0,0,429,0.377066,"\int \frac{1+x^3+x^6}{\sqrt[3]{x^2+x^4} \left(-1+x^6\right)} \, dx","Integrate[(1 + x^3 + x^6)/((x^2 + x^4)^(1/3)*(-1 + x^6)),x]","\int \frac{1+x^3+x^6}{\sqrt[3]{x^2+x^4} \left(-1+x^6\right)} \, dx","\frac{1}{6} \log \left(\sqrt[3]{x^4+x^2}-x\right)-\frac{1}{2} \log \left(\sqrt[3]{x^4+x^2}+x\right)+\frac{\log \left(2^{2/3} \sqrt[3]{x^4+x^2}-2 x\right)}{4 \sqrt[3]{2}}-\frac{\log \left(2^{2/3} \sqrt[3]{x^4+x^2}+2 x\right)}{12 \sqrt[3]{2}}+\frac{1}{4} \log \left(x^2-\sqrt[3]{x^4+x^2} x+\left(x^4+x^2\right)^{2/3}\right)-\frac{1}{12} \log \left(x^2+\sqrt[3]{x^4+x^2} x+\left(x^4+x^2\right)^{2/3}\right)+\frac{\log \left(-2 x^2+2^{2/3} \sqrt[3]{x^4+x^2} x-\sqrt[3]{2} \left(x^4+x^2\right)^{2/3}\right)}{24 \sqrt[3]{2}}-\frac{\log \left(2 x^2+2^{2/3} \sqrt[3]{x^4+x^2} x+\sqrt[3]{2} \left(x^4+x^2\right)^{2/3}\right)}{8 \sqrt[3]{2}}-\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^4+x^2}-x}\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^4+x^2}+x}\right)}{2 \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^4+x^2}-x}\right)}{4 \sqrt[3]{2} \sqrt{3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2^{2/3} \sqrt[3]{x^4+x^2}+x}\right)}{4 \sqrt[3]{2}}",1,"Integrate[(1 + x^3 + x^6)/((x^2 + x^4)^(1/3)*(-1 + x^6)), x]","F",-1
3027,0,0,431,10.9021207,"\int \frac{\sqrt{-b+a^2 x^2} \sqrt{a x+\sqrt{-b+a^2 x^2}}}{\sqrt{c+\sqrt{a x+\sqrt{-b+a^2 x^2}}}} \, dx","Integrate[(Sqrt[-b + a^2*x^2]*Sqrt[a*x + Sqrt[-b + a^2*x^2]])/Sqrt[c + Sqrt[a*x + Sqrt[-b + a^2*x^2]]],x]","\int \frac{\sqrt{-b+a^2 x^2} \sqrt{a x+\sqrt{-b+a^2 x^2}}}{\sqrt{c+\sqrt{a x+\sqrt{-b+a^2 x^2}}}} \, dx","\frac{5 b^2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+c}}{\sqrt{c}}\right)}{16 a c^{7/2}}+\frac{\sqrt{a^2 x^2-b} \left(\left(-2560 a^2 c^4 x^2-2048 a c^6 x-1575 b^2+640 b c^4\right) \sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+c}+\sqrt{\sqrt{a^2 x^2-b}+a x} \sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+c} \left(2240 a^2 c^3 x^2+1536 a c^5 x-10640 b c^3+2048 c^7\right)\right)+\sqrt{\sqrt{a^2 x^2-b}+a x} \sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+c} \left(2240 a^3 c^3 x^3+1536 a^2 c^5 x^2-11760 a b c^3 x+2048 a c^7 x+1050 b^2 c-768 b c^5\right)+\left(-2560 a^3 c^4 x^3-2048 a^2 c^6 x^2-1575 a b^2 x+1920 a b c^4 x-840 b^2 c^2+1024 b c^6\right) \sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+c}}{5040 a c^3 \left(\sqrt{a^2 x^2-b}+a x\right)^{3/2}}",1,"Integrate[(Sqrt[-b + a^2*x^2]*Sqrt[a*x + Sqrt[-b + a^2*x^2]])/Sqrt[c + Sqrt[a*x + Sqrt[-b + a^2*x^2]]], x]","F",-1
3028,0,0,432,0.236927,"\int \frac{\left(-1+a x^8\right) \left(1+a x^8\right)^{3/4}}{1+x^8+a^2 x^{16}} \, dx","Integrate[((-1 + a*x^8)*(1 + a*x^8)^(3/4))/(1 + x^8 + a^2*x^16),x]","\int \frac{\left(-1+a x^8\right) \left(1+a x^8\right)^{3/4}}{1+x^8+a^2 x^{16}} \, dx","\frac{\left(1+\sqrt[4]{-1}\right) \tan ^{-1}\left(\frac{(-1)^{7/8} \sqrt{2+\sqrt{2}} \sqrt[8]{2 a-1} x \sqrt[4]{a x^8+1}}{\sqrt{a x^8+1}+(-1)^{3/4} \sqrt[4]{2 a-1} x^2}\right)}{8 \sqrt[8]{2 a-1}}-\frac{i \left(\sqrt{2 \left(3-2 \sqrt{2}\right)}-i \sqrt{2}\right) \tan ^{-1}\left(\frac{(-1)^{7/8} \left(\sqrt{2}-2\right) \sqrt[8]{2 a-1} x \sqrt[4]{a x^8+1}}{\sqrt{2-\sqrt{2}} \sqrt{a x^8+1}+(-1)^{3/4} \sqrt{2-\sqrt{2}} \sqrt[4]{2 a-1} x^2}\right)}{16 \sqrt[8]{2 a-1}}+\frac{\left(\sqrt{2}+i \sqrt{2 \left(3-2 \sqrt{2}\right)}\right) \tanh ^{-1}\left(\frac{(-1)^{7/8} \sqrt[4]{2 a-1} x^2-\sqrt[8]{-1} \sqrt{a x^8+1}}{\sqrt{2-\sqrt{2}} \sqrt[8]{2 a-1} x \sqrt[4]{a x^8+1}}\right)}{16 \sqrt[8]{2 a-1}}+\frac{\left(1+\sqrt[4]{-1}\right) \tanh ^{-1}\left(\frac{(-1)^{7/8} \sqrt[4]{2 a-1} x^2-\sqrt[8]{-1} \sqrt{a x^8+1}}{\sqrt{2+\sqrt{2}} \sqrt[8]{2 a-1} x \sqrt[4]{a x^8+1}}\right)}{8 \sqrt[8]{2 a-1}}",1,"Integrate[((-1 + a*x^8)*(1 + a*x^8)^(3/4))/(1 + x^8 + a^2*x^16), x]","F",-1
3029,1,87,433,0.0458777,"\int \frac{-b+a x}{(b+a x) \sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Integrate[(-b + a*x)/((b + a*x)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","\frac{3 x \sqrt[3]{\frac{a^3 x}{b^2}+1} \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};-\frac{a^3 x}{b^2}\right)-6 x \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(a^3-a b\right) x}{x a^3+b^2}\right)}{\sqrt[3]{x^2 \left(a^3 x+b^2\right)}}","-\frac{\log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-a x\right)}{a}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} a x}{2 \sqrt[3]{a^3 x^3+b^2 x^2}+a x}\right)}{a}-\frac{i \left(\sqrt{3}-i\right) \log \left(\sqrt[3]{-1} \sqrt[3]{a^3 x^3+b^2 x^2}+\sqrt[3]{a} x \sqrt[3]{a^2-b}\right)}{\sqrt[3]{a} \sqrt[3]{a^2-b}}+\frac{\log \left(a x \sqrt[3]{a^3 x^3+b^2 x^2}+\left(a^3 x^3+b^2 x^2\right)^{2/3}+a^2 x^2\right)}{2 a}+\frac{\sqrt{6 \left(-1+i \sqrt{3}\right)} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{a} x \sqrt[3]{a^2-b}}{\sqrt[3]{a} x \sqrt[3]{a^2-b}-2 \sqrt[3]{-1} \sqrt[3]{a^3 x^3+b^2 x^2}}\right)}{\sqrt[3]{a} \sqrt[3]{a^2-b}}+\frac{\left(1+i \sqrt{3}\right) \log \left((-1)^{2/3} \left(a^3 x^3+b^2 x^2\right)^{2/3}+a^{2/3} x^2 \left(a^2-b\right)^{2/3}-\sqrt[3]{-1} \sqrt[3]{a} x \sqrt[3]{a^2-b} \sqrt[3]{a^3 x^3+b^2 x^2}\right)}{2 \sqrt[3]{a} \sqrt[3]{a^2-b}}",1,"(3*x*(1 + (a^3*x)/b^2)^(1/3)*Hypergeometric2F1[1/3, 1/3, 4/3, -((a^3*x)/b^2)] - 6*x*Hypergeometric2F1[1/3, 1, 4/3, ((a^3 - a*b)*x)/(b^2 + a^3*x)])/(x^2*(b^2 + a^3*x))^(1/3)","C",1
3030,1,249,434,0.8390541,"\int \frac{1}{\left(-1+x^2\right)^2 \sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[1/((-1 + x^2)^2*Sqrt[x + Sqrt[1 + x^2]]),x]","\frac{1}{8} \left(-\frac{4 x \left(\sqrt{x^2+1}+x\right)^{3/2}}{\left(x^2-1\right) \left(2 x^2+2 \sqrt{x^2+1} x+1\right)}+\left(\sqrt{2}-3\right) \sqrt{2 \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{1}{\sqrt{\sqrt{2}-1} \sqrt{\sqrt{x^2+1}+x}}\right)+\sqrt{2 \left(\sqrt{2}-1\right)} \left(3+\sqrt{2}\right) \tan ^{-1}\left(\frac{1}{\sqrt{1+\sqrt{2}} \sqrt{\sqrt{x^2+1}+x}}\right)-\left(\sqrt{2}-3\right) \sqrt{2 \left(1+\sqrt{2}\right)} \tanh ^{-1}\left(\frac{1}{\sqrt{\sqrt{2}-1} \sqrt{\sqrt{x^2+1}+x}}\right)-\sqrt{2 \left(\sqrt{2}-1\right)} \left(3+\sqrt{2}\right) \tanh ^{-1}\left(\frac{1}{\sqrt{1+\sqrt{2}} \sqrt{\sqrt{x^2+1}+x}}\right)\right)","\frac{\sqrt{\sqrt{x^2+1}+x} x^2}{2 \left(x^2-1\right)}-\frac{\sqrt{x^2+1} \sqrt{\sqrt{x^2+1}+x} x}{2 \left(x^2-1\right)}+\frac{\left(\sqrt{2 \left(1+\sqrt{2}\right)} x^2-4 \sqrt{1+\sqrt{2}} x^2+\sqrt{2 \left(1+5 \sqrt{2}\right)}\right) \tan ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{\sqrt{2}-1}}\right)}{8 (x-1) (x+1)}+\frac{\left(\sqrt{2 \left(\sqrt{2}-1\right)} x^2+4 \sqrt{\sqrt{2}-1} x^2-\sqrt{2 \left(5 \sqrt{2}-1\right)}\right) \tan ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{1+\sqrt{2}}}\right)}{8 (x-1) (x+1)}+\frac{\left(\sqrt{2 \left(1+\sqrt{2}\right)} x^2-4 \sqrt{1+\sqrt{2}} x^2+\sqrt{2 \left(1+5 \sqrt{2}\right)}\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{\sqrt{2}-1}}\right)}{8 (x-1) (x+1)}+\frac{\left(\sqrt{2 \left(\sqrt{2}-1\right)} x^2+4 \sqrt{\sqrt{2}-1} x^2-\sqrt{2 \left(5 \sqrt{2}-1\right)}\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{1+\sqrt{2}}}\right)}{8 (x-1) (x+1)}",1,"((-4*x*(x + Sqrt[1 + x^2])^(3/2))/((-1 + x^2)*(1 + 2*x^2 + 2*x*Sqrt[1 + x^2])) + (-3 + Sqrt[2])*Sqrt[2*(1 + Sqrt[2])]*ArcTan[1/(Sqrt[-1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]])] + Sqrt[2*(-1 + Sqrt[2])]*(3 + Sqrt[2])*ArcTan[1/(Sqrt[1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]])] - (-3 + Sqrt[2])*Sqrt[2*(1 + Sqrt[2])]*ArcTanh[1/(Sqrt[-1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]])] - Sqrt[2*(-1 + Sqrt[2])]*(3 + Sqrt[2])*ArcTanh[1/(Sqrt[1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]])])/8","A",0
3031,1,9145,437,5.6512795,"\int \frac{\left(c+b x+a x^2\right)^{3/2}}{1-x \sqrt{c+b x+a x^2}} \, dx","Integrate[(c + b*x + a*x^2)^(3/2)/(1 - x*Sqrt[c + b*x + a*x^2]),x]","\text{Result too large to show}","-2 \text{RootSum}\left[\text{$\#$1}^4 \sqrt{a}-\text{$\#$1}^3 b+4 \text{$\#$1}^2 a-4 \text{$\#$1} \sqrt{a} b+\text{$\#$1} b c-\sqrt{a} c^2+b^2\&,\frac{\text{$\#$1}^3 \sqrt{a} c \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)+\text{$\#$1}^2 \sqrt{a} b \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)-\text{$\#$1}^2 b c \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)+2 \text{$\#$1} a^{3/2} \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)-\text{$\#$1} b^2 \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)+\text{$\#$1} \sqrt{a} c^2 \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)+2 \text{$\#$1} a c \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)-a b \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)}{4 \text{$\#$1}^3 \sqrt{a}-3 \text{$\#$1}^2 b+8 \text{$\#$1} a-4 \sqrt{a} b+b c}\&\right]+\left(\sqrt{a}+c\right) \log \left(-2 \sqrt{a} \sqrt{a x^2+b x+c}+2 a x+b\right)-\frac{1}{2} x (a x+2 b)",1,"Result too large to show","B",0
3032,1,95,438,0.2791014,"\int \frac{(-b+x)^2}{\left((-a+x) (-b+x)^2\right)^{2/3} \left(-a^2+b^2 d+2 (a-b d) x+(-1+d) x^2\right)} \, dx","Integrate[(-b + x)^2/(((-a + x)*(-b + x)^2)^(2/3)*(-a^2 + b^2*d + 2*(a - b*d)*x + (-1 + d)*x^2)),x]","-\frac{3 (b-x)^2 \left(\, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{\sqrt{d} (b-x)}{x-a}\right)-\, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{\sqrt{d} (x-b)}{x-a}\right)\right)}{4 \sqrt{d} (a-b) \left((x-a) (b-x)^2\right)^{2/3}}","\frac{(x-a)^{2/3} (x-b) \left(-\sqrt[6]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+(x-a)^{2/3}+\sqrt[3]{d} (b-x)^{2/3}\right) \left(\sqrt[6]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+(x-a)^{2/3}+\sqrt[3]{d} (b-x)^{2/3}\right) \left((x-a)^{2/3} \sqrt[3]{b-x}+b \left(-\sqrt[3]{d}\right)+\sqrt[3]{d} x\right) \left(\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x-a}}{\sqrt[3]{x-a}-2 \sqrt[6]{d} \sqrt[3]{b-x}}\right)}{2 d^{5/6} (a-b)}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x-a}}{\sqrt[3]{x-a}+2 \sqrt[6]{d} \sqrt[3]{b-x}}\right)}{2 d^{5/6} (a-b)}+\frac{\tanh ^{-1}\left(\frac{\sqrt[3]{x-a} (b-x)^{2/3}}{\sqrt[6]{d} (x-b)}\right)}{d^{5/6} (a-b)}-\frac{\tanh ^{-1}\left(\frac{\frac{(x-a)^{2/3}}{\sqrt[6]{d}}+\sqrt[6]{d} (b-x)^{2/3}}{\sqrt[3]{x-a} \sqrt[3]{b-x}}\right)}{2 d^{5/6} (a-b)}\right)}{\left((x-a) (b-x)^2\right)^{2/3} \left(-a^2+2 a x+b^2 d-2 b d x+(d-1) x^2\right)}",1,"(-3*(b - x)^2*(Hypergeometric2F1[2/3, 1, 5/3, (Sqrt[d]*(b - x))/(-a + x)] - Hypergeometric2F1[2/3, 1, 5/3, (Sqrt[d]*(-b + x))/(-a + x)]))/(4*(a - b)*Sqrt[d]*((b - x)^2*(-a + x))^(2/3))","C",1
3033,1,91,441,0.0578549,"\int \frac{b+a x}{(-b+a x) \sqrt[3]{-b^2 x^2+a^3 x^3}} \, dx","Integrate[(b + a*x)/((-b + a*x)*(-(b^2*x^2) + a^3*x^3)^(1/3)),x]","\frac{3 x \sqrt[3]{1-\frac{a^3 x}{b^2}} \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};\frac{a^3 x}{b^2}\right)-6 x \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\left(a^3-a b\right) x}{a^3 x-b^2}\right)}{\sqrt[3]{x^2 \left(a^3 x-b^2\right)}}","-\frac{\log \left(\sqrt[3]{a^3 x^3-b^2 x^2}-a x\right)}{a}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} a x}{2 \sqrt[3]{a^3 x^3-b^2 x^2}+a x}\right)}{a}-\frac{i \left(\sqrt{3}-i\right) \log \left(\sqrt[3]{-1} \sqrt[3]{a^3 x^3-b^2 x^2}+\sqrt[3]{a} x \sqrt[3]{a^2-b}\right)}{\sqrt[3]{a} \sqrt[3]{a^2-b}}+\frac{\log \left(a x \sqrt[3]{a^3 x^3-b^2 x^2}+\left(a^3 x^3-b^2 x^2\right)^{2/3}+a^2 x^2\right)}{2 a}+\frac{\sqrt{6 \left(-1+i \sqrt{3}\right)} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{a} x \sqrt[3]{a^2-b}}{\sqrt[3]{a} x \sqrt[3]{a^2-b}-2 \sqrt[3]{-1} \sqrt[3]{a^3 x^3-b^2 x^2}}\right)}{\sqrt[3]{a} \sqrt[3]{a^2-b}}+\frac{\left(1+i \sqrt{3}\right) \log \left((-1)^{2/3} \left(a^3 x^3-b^2 x^2\right)^{2/3}+a^{2/3} x^2 \left(a^2-b\right)^{2/3}-\sqrt[3]{-1} \sqrt[3]{a} x \sqrt[3]{a^2-b} \sqrt[3]{a^3 x^3-b^2 x^2}\right)}{2 \sqrt[3]{a} \sqrt[3]{a^2-b}}",1,"(3*x*(1 - (a^3*x)/b^2)^(1/3)*Hypergeometric2F1[1/3, 1/3, 4/3, (a^3*x)/b^2] - 6*x*Hypergeometric2F1[1/3, 1, 4/3, ((a^3 - a*b)*x)/(-b^2 + a^3*x)])/(x^2*(-b^2 + a^3*x))^(1/3)","C",1
3034,-1,0,445,180.0007441,"\int \frac{1}{\sqrt[3]{a x+\sqrt{-b+a^2 x^2}} \sqrt[4]{c+\sqrt[3]{a x+\sqrt{-b+a^2 x^2}}}} \, dx","Integrate[1/((a*x + Sqrt[-b + a^2*x^2])^(1/3)*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^(1/4)),x]","\text{\$Aborted}","-\frac{585 b \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt[3]{\sqrt{a^2 x^2-b}+a x}+c}}{\sqrt[4]{c}}\right)}{2048 a c^{17/4}}+\frac{585 b \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt[3]{\sqrt{a^2 x^2-b}+a x}+c}}{\sqrt[4]{c}}\right)}{2048 a c^{17/4}}-\frac{585 b \left(\sqrt[3]{\sqrt{a^2 x^2-b}+a x}+c\right)^{3/4}}{1024 a c^4 \sqrt[3]{\sqrt{a^2 x^2-b}+a x}}+\frac{117 b \left(\sqrt[3]{\sqrt{a^2 x^2-b}+a x}+c\right)^{3/4}}{256 a c^3 \left(\sqrt{a^2 x^2-b}+a x\right)^{2/3}}-\frac{13 b \left(\sqrt[3]{\sqrt{a^2 x^2-b}+a x}+c\right)^{3/4}}{32 a c^2 \left(\sqrt{a^2 x^2-b}+a x\right)}+\frac{3 b \left(\sqrt[3]{\sqrt{a^2 x^2-b}+a x}+c\right)^{3/4}}{8 a c \left(\sqrt{a^2 x^2-b}+a x\right)^{4/3}}-\frac{8 c \left(\sqrt[3]{\sqrt{a^2 x^2-b}+a x}+c\right)^{3/4}}{7 a}+\frac{6 \sqrt[3]{\sqrt{a^2 x^2-b}+a x} \left(\sqrt[3]{\sqrt{a^2 x^2-b}+a x}+c\right)^{3/4}}{7 a}",1,"$Aborted","F",-1
3035,1,376,448,0.7151438,"\int \frac{x^4}{\sqrt[4]{-b+a x^4} \left(-b+2 a x^4+x^8\right)} \, dx","Integrate[x^4/((-b + a*x^4)^(1/4)*(-b + 2*a*x^4 + x^8)),x]","\frac{-\frac{\sqrt[4]{a-\sqrt{a^2+b}} \tan ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+b}+a^2+b}}{\sqrt[4]{a-\sqrt{a^2+b}} \sqrt[4]{a x^4-b}}\right)}{\sqrt[4]{-a \sqrt{a^2+b}+a^2+b}}+\frac{\sqrt[4]{\sqrt{a^2+b}+a} \tan ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+b}+a^2+b}}{\sqrt[4]{\sqrt{a^2+b}+a} \sqrt[4]{a x^4-b}}\right)}{\sqrt[4]{a \sqrt{a^2+b}+a^2+b}}-\frac{\sqrt[4]{a-\sqrt{a^2+b}} \tanh ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+b}+a^2+b}}{\sqrt[4]{a-\sqrt{a^2+b}} \sqrt[4]{a x^4-b}}\right)}{\sqrt[4]{-a \sqrt{a^2+b}+a^2+b}}+\frac{\sqrt[4]{\sqrt{a^2+b}+a} \tanh ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+b}+a^2+b}}{\sqrt[4]{\sqrt{a^2+b}+a} \sqrt[4]{a x^4-b}}\right)}{\sqrt[4]{a \sqrt{a^2+b}+a^2+b}}}{4 \sqrt{a^2+b}}","\frac{\left(\sqrt[4]{-1}-1\right) \tan ^{-1}\left(\frac{(-1)^{7/8} \sqrt{2+\sqrt{2}} x \sqrt[8]{a^2+b} \sqrt[4]{a x^4-b}}{(-1)^{3/4} x^2 \sqrt[4]{a^2+b}+\sqrt{a x^4-b}}\right)}{8 \left(a^2+b\right)^{5/8}}+\frac{i \left(\sqrt{2 \left(3+2 \sqrt{2}\right)}+i \sqrt{2}\right) \tan ^{-1}\left(\frac{(-1)^{7/8} \left(\sqrt{2}-2\right) x \sqrt[8]{a^2+b} \sqrt[4]{a x^4-b}}{(-1)^{3/4} \sqrt{2-\sqrt{2}} x^2 \sqrt[4]{a^2+b}+\sqrt{2-\sqrt{2}} \sqrt{a x^4-b}}\right)}{16 \left(a^2+b\right)^{5/8}}+\frac{\left(\sqrt{2}-i \sqrt{2 \left(3+2 \sqrt{2}\right)}\right) \tanh ^{-1}\left(\frac{(-1)^{7/8} x^2 \sqrt[4]{a^2+b}-\sqrt[8]{-1} \sqrt{a x^4-b}}{\sqrt{2-\sqrt{2}} x \sqrt[8]{a^2+b} \sqrt[4]{a x^4-b}}\right)}{16 \left(a^2+b\right)^{5/8}}+\frac{\left(\sqrt[4]{-1}-1\right) \tanh ^{-1}\left(\frac{(-1)^{7/8} x^2 \sqrt[4]{a^2+b}-\sqrt[8]{-1} \sqrt{a x^4-b}}{\sqrt{2+\sqrt{2}} x \sqrt[8]{a^2+b} \sqrt[4]{a x^4-b}}\right)}{8 \left(a^2+b\right)^{5/8}}",1,"(-(((a - Sqrt[a^2 + b])^(1/4)*ArcTan[((a^2 + b - a*Sqrt[a^2 + b])^(1/4)*x)/((a - Sqrt[a^2 + b])^(1/4)*(-b + a*x^4)^(1/4))])/(a^2 + b - a*Sqrt[a^2 + b])^(1/4)) + ((a + Sqrt[a^2 + b])^(1/4)*ArcTan[((a^2 + b + a*Sqrt[a^2 + b])^(1/4)*x)/((a + Sqrt[a^2 + b])^(1/4)*(-b + a*x^4)^(1/4))])/(a^2 + b + a*Sqrt[a^2 + b])^(1/4) - ((a - Sqrt[a^2 + b])^(1/4)*ArcTanh[((a^2 + b - a*Sqrt[a^2 + b])^(1/4)*x)/((a - Sqrt[a^2 + b])^(1/4)*(-b + a*x^4)^(1/4))])/(a^2 + b - a*Sqrt[a^2 + b])^(1/4) + ((a + Sqrt[a^2 + b])^(1/4)*ArcTanh[((a^2 + b + a*Sqrt[a^2 + b])^(1/4)*x)/((a + Sqrt[a^2 + b])^(1/4)*(-b + a*x^4)^(1/4))])/(a^2 + b + a*Sqrt[a^2 + b])^(1/4))/(4*Sqrt[a^2 + b])","A",1
3036,0,0,448,0.3755213,"\int \frac{\left(d+c x^2\right) \left(a x+\sqrt{-b+a^2 x^2}\right)^{3/4}}{\left(-b+a^2 x^2\right)^{5/2}} \, dx","Integrate[((d + c*x^2)*(a*x + Sqrt[-b + a^2*x^2])^(3/4))/(-b + a^2*x^2)^(5/2),x]","\int \frac{\left(d+c x^2\right) \left(a x+\sqrt{-b+a^2 x^2}\right)^{3/4}}{\left(-b+a^2 x^2\right)^{5/2}} \, dx","\frac{\sqrt{a^2 x^2-b} \left(\frac{\sqrt{a^2 x^2-b}+a x}{\sqrt{b}}\right)^{3/4} \left(55 a^4 d x^3-41 a^2 b c x^3-87 a^2 b d x+9 b^2 c x\right)}{96 a^2 b^{13/8} \left(a x-\sqrt{b}\right)^2 \left(a x+\sqrt{b}\right)^2}+\frac{\left(41 b c-55 a^2 d\right) \tan ^{-1}\left(\sqrt[4]{\frac{\sqrt{a^2 x^2-b}+a x}{\sqrt{b}}}\right)}{64 a^3 b^{13/8}}+\frac{\left(55 a^2 d-41 b c\right) \tanh ^{-1}\left(\sqrt[4]{\frac{\sqrt{a^2 x^2-b}+a x}{\sqrt{b}}}\right)}{64 a^3 b^{13/8}}-\frac{\sqrt[4]{-1} \left(55 a^2 d-41 b c\right) \tanh ^{-1}\left(\sqrt[4]{-1} \sqrt[4]{\frac{\sqrt{a^2 x^2-b}+a x}{\sqrt{b}}}\right)}{64 a^3 b^{13/8}}-\frac{(-1)^{3/4} \left(55 a^2 d-41 b c\right) \tanh ^{-1}\left((-1)^{3/4} \sqrt[4]{\frac{\sqrt{a^2 x^2-b}+a x}{\sqrt{b}}}\right)}{64 a^3 b^{13/8}}+\frac{\left(\frac{\sqrt{a^2 x^2-b}+a x}{\sqrt{b}}\right)^{3/4} \left(-55 a^4 d x^2+41 a^2 b c x^2+43 a^2 b d-53 b^2 c\right)}{96 a^3 b^{13/8} \left(a x-\sqrt{b}\right) \left(a x+\sqrt{b}\right)}",1,"Integrate[((d + c*x^2)*(a*x + Sqrt[-b + a^2*x^2])^(3/4))/(-b + a^2*x^2)^(5/2), x]","F",-1
3037,1,50,452,0.0290278,"\int \frac{x^2}{\left(1+x^4\right) \sqrt[4]{-x^2+x^6}} \, dx","Integrate[x^2/((1 + x^4)*(-x^2 + x^6)^(1/4)),x]","\frac{2 x^3 \sqrt[4]{1-x^4} F_1\left(\frac{5}{8};\frac{1}{4},1;\frac{13}{8};x^4,-x^4\right)}{5 \sqrt[4]{x^2 \left(x^4-1\right)}}","-\frac{1}{16} \sqrt{\sqrt{2}-1} \log \left(-2 x^2+2^{3/4} \sqrt{2+\sqrt{2}} \sqrt[4]{x^6-x^2} x-\sqrt{2} \sqrt{x^6-x^2}\right)+\frac{1}{16} \sqrt{\sqrt{2}-1} \log \left(2 \sqrt{2-\sqrt{2}} x^2+2 \sqrt[4]{2} \sqrt[4]{x^6-x^2} x+\sqrt{4-2 \sqrt{2}} \sqrt{x^6-x^2}\right)-\frac{1}{8} \sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}} x}{2^{3/4} \sqrt[4]{x^6-x^2}-\sqrt{2+\sqrt{2}} x}\right)-\frac{1}{8} \sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}} x}{2^{3/4} \sqrt[4]{x^6-x^2}+\sqrt{2+\sqrt{2}} x}\right)+\frac{1}{8} \sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{2^{3/4} \sqrt{2+\sqrt{2}} x \sqrt[4]{x^6-x^2}}{\sqrt{2} \sqrt{x^6-x^2}-2 x^2}\right)-\frac{1}{8} \sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{\frac{\sqrt[4]{2} x^2}{\sqrt{2-\sqrt{2}}}+\frac{\sqrt{x^6-x^2}}{\sqrt[4]{2} \sqrt{2-\sqrt{2}}}}{x \sqrt[4]{x^6-x^2}}\right)",1,"(2*x^3*(1 - x^4)^(1/4)*AppellF1[5/8, 1/4, 1, 13/8, x^4, -x^4])/(5*(x^2*(-1 + x^4))^(1/4))","C",0
3038,1,50,452,0.0185597,"\int \frac{x^2}{\left(1+x^4\right) \sqrt[4]{-x^2+x^6}} \, dx","Integrate[x^2/((1 + x^4)*(-x^2 + x^6)^(1/4)),x]","\frac{2 x^3 \sqrt[4]{1-x^4} F_1\left(\frac{5}{8};\frac{1}{4},1;\frac{13}{8};x^4,-x^4\right)}{5 \sqrt[4]{x^2 \left(x^4-1\right)}}","-\frac{1}{16} \sqrt{\sqrt{2}-1} \log \left(-2 x^2+2^{3/4} \sqrt{2+\sqrt{2}} \sqrt[4]{x^6-x^2} x-\sqrt{2} \sqrt{x^6-x^2}\right)+\frac{1}{16} \sqrt{\sqrt{2}-1} \log \left(2 \sqrt{2-\sqrt{2}} x^2+2 \sqrt[4]{2} \sqrt[4]{x^6-x^2} x+\sqrt{4-2 \sqrt{2}} \sqrt{x^6-x^2}\right)-\frac{1}{8} \sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}} x}{2^{3/4} \sqrt[4]{x^6-x^2}-\sqrt{2+\sqrt{2}} x}\right)-\frac{1}{8} \sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}} x}{2^{3/4} \sqrt[4]{x^6-x^2}+\sqrt{2+\sqrt{2}} x}\right)+\frac{1}{8} \sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{2^{3/4} \sqrt{2+\sqrt{2}} x \sqrt[4]{x^6-x^2}}{\sqrt{2} \sqrt{x^6-x^2}-2 x^2}\right)-\frac{1}{8} \sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{\frac{\sqrt[4]{2} x^2}{\sqrt{2-\sqrt{2}}}+\frac{\sqrt{x^6-x^2}}{\sqrt[4]{2} \sqrt{2-\sqrt{2}}}}{x \sqrt[4]{x^6-x^2}}\right)",1,"(2*x^3*(1 - x^4)^(1/4)*AppellF1[5/8, 1/4, 1, 13/8, x^4, -x^4])/(5*(x^2*(-1 + x^4))^(1/4))","C",0
3039,1,48,452,0.0259872,"\int \frac{-1+x^4}{\left(1+x^4\right) \sqrt[4]{-x^2+x^6}} \, dx","Integrate[(-1 + x^4)/((1 + x^4)*(-x^2 + x^6)^(1/4)),x]","\frac{2 \left(x^2 \left(x^4-1\right)\right)^{3/4} F_1\left(\frac{1}{8};-\frac{3}{4},1;\frac{9}{8};x^4,-x^4\right)}{x \left(1-x^4\right)^{3/4}}","\frac{1}{8} \sqrt{1+\sqrt{2}} \log \left(-2 x^2+2^{3/4} \sqrt{2+\sqrt{2}} \sqrt[4]{x^6-x^2} x-\sqrt{2} \sqrt{x^6-x^2}\right)-\frac{1}{8} \sqrt{1+\sqrt{2}} \log \left(2 \sqrt{2-\sqrt{2}} x^2+2 \sqrt[4]{2} \sqrt[4]{x^6-x^2} x+\sqrt{4-2 \sqrt{2}} \sqrt{x^6-x^2}\right)-\frac{1}{4} \sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}} x}{2^{3/4} \sqrt[4]{x^6-x^2}-\sqrt{2+\sqrt{2}} x}\right)-\frac{1}{4} \sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}} x}{2^{3/4} \sqrt[4]{x^6-x^2}+\sqrt{2+\sqrt{2}} x}\right)-\frac{1}{4} \sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{2^{3/4} \sqrt{2+\sqrt{2}} x \sqrt[4]{x^6-x^2}}{\sqrt{2} \sqrt{x^6-x^2}-2 x^2}\right)-\frac{1}{4} \sqrt{\sqrt{2}-1} \tanh ^{-1}\left(\frac{\frac{\sqrt[4]{2} x^2}{\sqrt{2-\sqrt{2}}}+\frac{\sqrt{x^6-x^2}}{\sqrt[4]{2} \sqrt{2-\sqrt{2}}}}{x \sqrt[4]{x^6-x^2}}\right)",1,"(2*(x^2*(-1 + x^4))^(3/4)*AppellF1[1/8, -3/4, 1, 9/8, x^4, -x^4])/(x*(1 - x^4)^(3/4))","C",0
3040,0,0,452,0.0736949,"\int \frac{\left(-b+a x^4\right)^{3/4}}{-b+2 a x^4+x^8} \, dx","Integrate[(-b + a*x^4)^(3/4)/(-b + 2*a*x^4 + x^8),x]","\int \frac{\left(-b+a x^4\right)^{3/4}}{-b+2 a x^4+x^8} \, dx","\frac{\left(-1-\sqrt[4]{-1}\right) \tan ^{-1}\left(\frac{(-1)^{7/8} \sqrt{2+\sqrt{2}} x \sqrt[8]{a^2+b} \sqrt[4]{a x^4-b}}{(-1)^{3/4} x^2 \sqrt[4]{a^2+b}+\sqrt{a x^4-b}}\right)}{8 \sqrt[8]{a^2+b}}+\frac{\left(\sqrt{2}+i \sqrt{2 \left(3-2 \sqrt{2}\right)}\right) \tan ^{-1}\left(\frac{(-1)^{7/8} \left(\sqrt{2}-2\right) x \sqrt[8]{a^2+b} \sqrt[4]{a x^4-b}}{(-1)^{3/4} \sqrt{2-\sqrt{2}} x^2 \sqrt[4]{a^2+b}+\sqrt{2-\sqrt{2}} \sqrt{a x^4-b}}\right)}{16 \sqrt[8]{a^2+b}}-\frac{i \left(\sqrt{2 \left(3-2 \sqrt{2}\right)}-i \sqrt{2}\right) \tanh ^{-1}\left(\frac{(-1)^{7/8} x^2 \sqrt[4]{a^2+b}-\sqrt[8]{-1} \sqrt{a x^4-b}}{\sqrt{2-\sqrt{2}} x \sqrt[8]{a^2+b} \sqrt[4]{a x^4-b}}\right)}{16 \sqrt[8]{a^2+b}}+\frac{\left(-1-\sqrt[4]{-1}\right) \tanh ^{-1}\left(\frac{(-1)^{7/8} x^2 \sqrt[4]{a^2+b}-\sqrt[8]{-1} \sqrt{a x^4-b}}{\sqrt{2+\sqrt{2}} x \sqrt[8]{a^2+b} \sqrt[4]{a x^4-b}}\right)}{8 \sqrt[8]{a^2+b}}",1,"Integrate[(-b + a*x^4)^(3/4)/(-b + 2*a*x^4 + x^8), x]","F",-1
3041,1,435,452,0.5189965,"\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1+x^2\right)^{5/2}} \, dx","Integrate[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/(1 + x^2)^(5/2),x]","\frac{3 \left(x^2+\sqrt{x^2+1} x+1\right)^3 \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{2 \text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-7 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+8 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+40 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+3 \text{$\#$1}^3-\text{$\#$1}}\&\right]-4 \left(\sqrt{\sqrt{x^2+1}+x}+1\right)^{3/2} \left(-6 \sqrt{x^2+1}+11 \sqrt{\sqrt{x^2+1}+x}-6 x-15\right) \left(x^2+\sqrt{x^2+1} x+1\right)^2-16 \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(x \left(\sqrt{\sqrt{x^2+1}+x}-1\right)-\sqrt{x^2+1}+\sqrt{x^2+1} \sqrt{\sqrt{x^2+1}+x}+\sqrt{\sqrt{x^2+1}+x}+49\right) \left(x^2+\sqrt{x^2+1} x+1\right)+256 \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{768 \left(x^2+1\right)^{3/2} \left(\sqrt{x^2+1}+x\right)^3}","\frac{1}{256} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{2 \text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-7 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+8 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+40 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+3 \text{$\#$1}^3-\text{$\#$1}}\&\right]+\frac{\sqrt{x^2+1} \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(-20 x^4+30 x^3-17 x^2-166 x-1\right)+\left(24 x^4+8 x^3+22 x^2+4 x+2\right) \sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(-20 x^5+30 x^4-27 x^3-151 x^2-7 x-117\right)+\left(24 x^5+8 x^4+34 x^3+8 x^2+10 x\right) \sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{192 \left(4 x^6+9 x^4+6 x^2+1\right)+192 \sqrt{x^2+1} \left(4 x^5+7 x^3+3 x\right)}",1,"(256*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - 4*(1 + x^2 + x*Sqrt[1 + x^2])^2*(1 + Sqrt[x + Sqrt[1 + x^2]])^(3/2)*(-15 - 6*x - 6*Sqrt[1 + x^2] + 11*Sqrt[x + Sqrt[1 + x^2]]) - 16*(1 + x^2 + x*Sqrt[1 + x^2])*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]*(49 - Sqrt[1 + x^2] + Sqrt[x + Sqrt[1 + x^2]] + Sqrt[1 + x^2]*Sqrt[x + Sqrt[1 + x^2]] + x*(-1 + Sqrt[x + Sqrt[1 + x^2]])) + 3*(1 + x^2 + x*Sqrt[1 + x^2])^3*RootSum[2 - 4*#1^2 + 6*#1^4 - 4*#1^6 + #1^8 & , (40*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1] + 8*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^2 - 7*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^4 + 2*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^6)/(-#1 + 3*#1^3 - 3*#1^5 + #1^7) & ])/(768*(1 + x^2)^(3/2)*(x + Sqrt[1 + x^2])^3)","A",1
3042,1,435,452,0.0546961,"\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1+x^2\right)^{5/2}} \, dx","Integrate[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/(1 + x^2)^(5/2),x]","\frac{3 \left(x^2+\sqrt{x^2+1} x+1\right)^3 \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{2 \text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-7 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+8 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+40 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+3 \text{$\#$1}^3-\text{$\#$1}}\&\right]-4 \left(\sqrt{\sqrt{x^2+1}+x}+1\right)^{3/2} \left(-6 \sqrt{x^2+1}+11 \sqrt{\sqrt{x^2+1}+x}-6 x-15\right) \left(x^2+\sqrt{x^2+1} x+1\right)^2-16 \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(x \left(\sqrt{\sqrt{x^2+1}+x}-1\right)-\sqrt{x^2+1}+\sqrt{x^2+1} \sqrt{\sqrt{x^2+1}+x}+\sqrt{\sqrt{x^2+1}+x}+49\right) \left(x^2+\sqrt{x^2+1} x+1\right)+256 \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{768 \left(x^2+1\right)^{3/2} \left(\sqrt{x^2+1}+x\right)^3}","\frac{1}{256} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{2 \text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-7 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+8 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+40 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+3 \text{$\#$1}^3-\text{$\#$1}}\&\right]+\frac{\sqrt{x^2+1} \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(-20 x^4+30 x^3-17 x^2-166 x-1\right)+\left(24 x^4+8 x^3+22 x^2+4 x+2\right) \sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(-20 x^5+30 x^4-27 x^3-151 x^2-7 x-117\right)+\left(24 x^5+8 x^4+34 x^3+8 x^2+10 x\right) \sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{192 \left(4 x^6+9 x^4+6 x^2+1\right)+192 \sqrt{x^2+1} \left(4 x^5+7 x^3+3 x\right)}",1,"(256*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - 4*(1 + x^2 + x*Sqrt[1 + x^2])^2*(1 + Sqrt[x + Sqrt[1 + x^2]])^(3/2)*(-15 - 6*x - 6*Sqrt[1 + x^2] + 11*Sqrt[x + Sqrt[1 + x^2]]) - 16*(1 + x^2 + x*Sqrt[1 + x^2])*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]*(49 - Sqrt[1 + x^2] + Sqrt[x + Sqrt[1 + x^2]] + Sqrt[1 + x^2]*Sqrt[x + Sqrt[1 + x^2]] + x*(-1 + Sqrt[x + Sqrt[1 + x^2]])) + 3*(1 + x^2 + x*Sqrt[1 + x^2])^3*RootSum[2 - 4*#1^2 + 6*#1^4 - 4*#1^6 + #1^8 & , (40*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1] + 8*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^2 - 7*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^4 + 2*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^6)/(-#1 + 3*#1^3 - 3*#1^5 + #1^7) & ])/(768*(1 + x^2)^(3/2)*(x + Sqrt[1 + x^2])^3)","A",1
3043,0,0,455,3.1765599,"\int \frac{x^2 \sqrt{b+a x}}{x^2-\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","Integrate[(x^2*Sqrt[b + a*x])/(x^2 - Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]]),x]","\int \frac{x^2 \sqrt{b+a x}}{x^2-\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","-4 a \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6 c-2 \text{$\#$1}^4 b+6 \text{$\#$1}^4 c^2-\text{$\#$1}^3 a^2+4 \text{$\#$1}^2 b c-4 \text{$\#$1}^2 c^3+\text{$\#$1} a^2 c+b^2-2 b c^2+c^4\&,\frac{\text{$\#$1}^6 (-c) \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+3 \text{$\#$1}^4 c^2 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-2 \text{$\#$1}^4 b \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-\text{$\#$1}^3 a^2 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-3 \text{$\#$1}^2 c^3 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+4 \text{$\#$1}^2 b c \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+\text{$\#$1} a^2 c \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+b^2 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+c^4 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-2 b c^2 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)}{8 \text{$\#$1}^7-24 \text{$\#$1}^5 c-8 \text{$\#$1}^3 b+24 \text{$\#$1}^3 c^2-3 \text{$\#$1}^2 a^2+8 \text{$\#$1} b c-8 \text{$\#$1} c^3+a^2 c}\&\right]+4 a \sqrt{\sqrt{a x+b}+c}+\frac{2 (a x+b)^{3/2}}{3 a}",1,"Integrate[(x^2*Sqrt[b + a*x])/(x^2 - Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]]), x]","F",-1
3044,0,0,455,2.8047014,"\int \frac{x^2 \sqrt{b+a x}}{x^2-\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","Integrate[(x^2*Sqrt[b + a*x])/(x^2 - Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]]),x]","\int \frac{x^2 \sqrt{b+a x}}{x^2-\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","-4 a \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6 c-2 \text{$\#$1}^4 b+6 \text{$\#$1}^4 c^2-\text{$\#$1}^3 a^2+4 \text{$\#$1}^2 b c-4 \text{$\#$1}^2 c^3+\text{$\#$1} a^2 c+b^2-2 b c^2+c^4\&,\frac{\text{$\#$1}^6 (-c) \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+3 \text{$\#$1}^4 c^2 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-2 \text{$\#$1}^4 b \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-\text{$\#$1}^3 a^2 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-3 \text{$\#$1}^2 c^3 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+4 \text{$\#$1}^2 b c \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+\text{$\#$1} a^2 c \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+b^2 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+c^4 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-2 b c^2 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)}{8 \text{$\#$1}^7-24 \text{$\#$1}^5 c-8 \text{$\#$1}^3 b+24 \text{$\#$1}^3 c^2-3 \text{$\#$1}^2 a^2+8 \text{$\#$1} b c-8 \text{$\#$1} c^3+a^2 c}\&\right]+4 a \sqrt{\sqrt{a x+b}+c}+\frac{2 (a x+b)^{3/2}}{3 a}",1,"Integrate[(x^2*Sqrt[b + a*x])/(x^2 - Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]]), x]","F",-1
3045,0,0,455,15.6542485,"\int \sqrt{b+a^2 x^2} \sqrt{a x+\sqrt{b+a^2 x^2}} \sqrt{c+\sqrt{a x+\sqrt{b+a^2 x^2}}} \, dx","Integrate[Sqrt[b + a^2*x^2]*Sqrt[a*x + Sqrt[b + a^2*x^2]]*Sqrt[c + Sqrt[a*x + Sqrt[b + a^2*x^2]]],x]","\int \sqrt{b+a^2 x^2} \sqrt{a x+\sqrt{b+a^2 x^2}} \sqrt{c+\sqrt{a x+\sqrt{b+a^2 x^2}}} \, dx","\frac{\sqrt{\sqrt{a^2 x^2+b}+a x} \sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c} \left(2240 a^3 c^3 x^3+1536 a^2 c^5 x^2+38640 a b c^3 x+2048 a c^7 x-2310 b^2 c+768 b c^5\right)+\sqrt{a^2 x^2+b} \left(\sqrt{\sqrt{a^2 x^2+b}+a x} \sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c} \left(2240 a^2 c^3 x^2+1536 a c^5 x+37520 b c^3+2048 c^7\right)+\left(40320 a^3 c^2 x^3-2560 a^2 c^4 x^2+94080 a b c^2 x-2048 a c^6 x+3465 b^2-640 b c^4\right) \sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}\right)+\left(40320 a^4 c^2 x^4-2560 a^3 c^4 x^3+114240 a^2 b c^2 x^2-2048 a^2 c^6 x^2+3465 a b^2 x-1920 a b c^4 x+32760 b^2 c^2-1024 b c^6\right) \sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}}{55440 a c^2 \left(\sqrt{a^2 x^2+b}+a x\right)^{3/2}}-\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}}{\sqrt{c}}\right)}{16 a c^{5/2}}",1,"Integrate[Sqrt[b + a^2*x^2]*Sqrt[a*x + Sqrt[b + a^2*x^2]]*Sqrt[c + Sqrt[a*x + Sqrt[b + a^2*x^2]]], x]","F",-1
3046,1,418,456,0.8597821,"\int \frac{x^4}{\sqrt[4]{b+a x^4} \left(b+2 a x^4+2 x^8\right)} \, dx","Integrate[x^4/((b + a*x^4)^(1/4)*(b + 2*a*x^4 + 2*x^8)),x]","\frac{-\frac{\sqrt[4]{a-\sqrt{a^2-2 b}} \tan ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2-2 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2-2 b}} \sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{-a \sqrt{a^2-2 b}+a^2-2 b}}+\frac{\sqrt[4]{\sqrt{a^2-2 b}+a} \tan ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2-2 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2-2 b}+a} \sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{a \sqrt{a^2-2 b}+a^2-2 b}}-\frac{\sqrt[4]{a-\sqrt{a^2-2 b}} \tanh ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2-2 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2-2 b}} \sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{-a \sqrt{a^2-2 b}+a^2-2 b}}+\frac{\sqrt[4]{\sqrt{a^2-2 b}+a} \tanh ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2-2 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2-2 b}+a} \sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{a \sqrt{a^2-2 b}+a^2-2 b}}}{4 \sqrt{a^2-2 b}}","\frac{\left(\sqrt[4]{-1}-1\right) \tan ^{-1}\left(\frac{(-1)^{7/8} \sqrt{2+\sqrt{2}} x \sqrt[8]{a^2-2 b} \sqrt[4]{a x^4+b}}{(-1)^{3/4} x^2 \sqrt[4]{a^2-2 b}+\sqrt{a x^4+b}}\right)}{8 \left(a^2-2 b\right)^{5/8}}+\frac{i \left(\sqrt{2 \left(3+2 \sqrt{2}\right)}+i \sqrt{2}\right) \tan ^{-1}\left(\frac{(-1)^{7/8} \left(\sqrt{2}-2\right) x \sqrt[8]{a^2-2 b} \sqrt[4]{a x^4+b}}{(-1)^{3/4} \sqrt{2-\sqrt{2}} x^2 \sqrt[4]{a^2-2 b}+\sqrt{2-\sqrt{2}} \sqrt{a x^4+b}}\right)}{16 \left(a^2-2 b\right)^{5/8}}+\frac{\left(\sqrt{2}-i \sqrt{2 \left(3+2 \sqrt{2}\right)}\right) \tanh ^{-1}\left(\frac{(-1)^{7/8} x^2 \sqrt[4]{a^2-2 b}-\sqrt[8]{-1} \sqrt{a x^4+b}}{\sqrt{2-\sqrt{2}} x \sqrt[8]{a^2-2 b} \sqrt[4]{a x^4+b}}\right)}{16 \left(a^2-2 b\right)^{5/8}}+\frac{\left(\sqrt[4]{-1}-1\right) \tanh ^{-1}\left(\frac{(-1)^{7/8} x^2 \sqrt[4]{a^2-2 b}-\sqrt[8]{-1} \sqrt{a x^4+b}}{\sqrt{2+\sqrt{2}} x \sqrt[8]{a^2-2 b} \sqrt[4]{a x^4+b}}\right)}{8 \left(a^2-2 b\right)^{5/8}}",1,"(-(((a - Sqrt[a^2 - 2*b])^(1/4)*ArcTan[((a^2 - a*Sqrt[a^2 - 2*b] - 2*b)^(1/4)*x)/((a - Sqrt[a^2 - 2*b])^(1/4)*(b + a*x^4)^(1/4))])/(a^2 - a*Sqrt[a^2 - 2*b] - 2*b)^(1/4)) + ((a + Sqrt[a^2 - 2*b])^(1/4)*ArcTan[((a^2 + a*Sqrt[a^2 - 2*b] - 2*b)^(1/4)*x)/((a + Sqrt[a^2 - 2*b])^(1/4)*(b + a*x^4)^(1/4))])/(a^2 + a*Sqrt[a^2 - 2*b] - 2*b)^(1/4) - ((a - Sqrt[a^2 - 2*b])^(1/4)*ArcTanh[((a^2 - a*Sqrt[a^2 - 2*b] - 2*b)^(1/4)*x)/((a - Sqrt[a^2 - 2*b])^(1/4)*(b + a*x^4)^(1/4))])/(a^2 - a*Sqrt[a^2 - 2*b] - 2*b)^(1/4) + ((a + Sqrt[a^2 - 2*b])^(1/4)*ArcTanh[((a^2 + a*Sqrt[a^2 - 2*b] - 2*b)^(1/4)*x)/((a + Sqrt[a^2 - 2*b])^(1/4)*(b + a*x^4)^(1/4))])/(a^2 + a*Sqrt[a^2 - 2*b] - 2*b)^(1/4))/(4*Sqrt[a^2 - 2*b])","A",1
3047,1,15065,457,7.8018123,"\int \frac{x^4 \left(-q+p x^4\right) \sqrt{q+p x^4}}{b x^8+a \left(q+p x^4\right)^4} \, dx","Integrate[(x^4*(-q + p*x^4)*Sqrt[q + p*x^4])/(b*x^8 + a*(q + p*x^4)^4),x]","\text{Result too large to show}","-\frac{\sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{x \left(\sqrt{\frac{2}{2-\sqrt{2}}} \sqrt[8]{a} \sqrt[8]{b}-\frac{2 \sqrt[8]{a} \sqrt[8]{b}}{\sqrt{2-\sqrt{2}}}\right) \sqrt{p x^4+q}}{-\sqrt[4]{a} p x^4-\sqrt[4]{a} q+\sqrt[4]{b} x^2}\right)}{8 a^{3/8} b^{5/8}}+\frac{\sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}} \sqrt[8]{a} \sqrt[8]{b} x \sqrt{p x^4+q}}{\sqrt[4]{a} p x^4+\sqrt[4]{a} q-\sqrt[4]{b} x^2}\right)}{8 a^{3/8} b^{5/8}}-\frac{\sqrt{2+\sqrt{2}} \tanh ^{-1}\left(\frac{\frac{\sqrt[8]{a} p x^4}{\sqrt{2-\sqrt{2}} \sqrt[8]{b}}+\frac{\sqrt[8]{a} q}{\sqrt{2-\sqrt{2}} \sqrt[8]{b}}+\frac{\sqrt[8]{b} x^2}{\sqrt{2-\sqrt{2}} \sqrt[8]{a}}}{x \sqrt{p x^4+q}}\right)}{8 a^{3/8} b^{5/8}}+\frac{\sqrt{2-\sqrt{2}} \tanh ^{-1}\left(\frac{\frac{\sqrt[8]{a} p x^4}{\sqrt{2+\sqrt{2}} \sqrt[8]{b}}+\frac{\sqrt[8]{a} q}{\sqrt{2+\sqrt{2}} \sqrt[8]{b}}+\frac{\sqrt[8]{b} x^2}{\sqrt{2+\sqrt{2}} \sqrt[8]{a}}}{x \sqrt{p x^4+q}}\right)}{8 a^{3/8} b^{5/8}}",1,"Result too large to show","C",0
3048,1,175,459,10.1322172,"\int \frac{1}{\sqrt[3]{1-3 x+3 x^3-9 x^4+3 x^6-9 x^7+x^9-3 x^{10}}} \, dx","Integrate[(1 - 3*x + 3*x^3 - 9*x^4 + 3*x^6 - 9*x^7 + x^9 - 3*x^10)^(-1/3),x]","\frac{\sqrt[3]{3 x-1} \left(x^3+1\right) \left(\sqrt[3]{2} \left(-2 \log \left(\sqrt[3]{6 x-2}+2\right)+\log \left((6 x-2)^{2/3}-2 \sqrt[3]{6 x-2}+4\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\sqrt[3]{6 x-2}-1}{\sqrt{3}}\right)\right)-4 \text{RootSum}\left[\text{$\#$1}^6-\text{$\#$1}^3+7\&,\frac{\text{$\#$1}^3 \log \left(\sqrt[3]{3 x-1}-\text{$\#$1}\right)-5 \log \left(\sqrt[3]{3 x-1}-\text{$\#$1}\right)}{2 \text{$\#$1}^4-\text{$\#$1}}\&\right]\right)}{12 \sqrt[3]{-\left((3 x-1) \left(x^3+1\right)^3\right)}}","\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^6+\text{$\#$1}^3+7\&,\frac{\text{$\#$1}^3 \log \left(x^3+1\right)-\text{$\#$1}^3 \log \left(-\text{$\#$1} x^3-\text{$\#$1}+\sqrt[3]{-3 x^{10}+x^9-9 x^7+3 x^6-9 x^4+3 x^3-3 x+1}\right)-5 \log \left(-\text{$\#$1} x^3-\text{$\#$1}+\sqrt[3]{-3 x^{10}+x^9-9 x^7+3 x^6-9 x^4+3 x^3-3 x+1}\right)+5 \log \left(x^3+1\right)}{2 \text{$\#$1}^4+\text{$\#$1}}\&\right]-\frac{\log \left(x^3+1\right)}{3\ 2^{2/3}}+\frac{\log \left(x^6+2 x^3+1\right)}{6\ 2^{2/3}}+\frac{\log \left(-2 x^3+\sqrt[3]{2} \sqrt[3]{-3 x^{10}+x^9-9 x^7+3 x^6-9 x^4+3 x^3-3 x+1}-2\right)}{3\ 2^{2/3}}-\frac{\log \left(4 x^6+8 x^3+2^{2/3} \left(-3 x^{10}+x^9-9 x^7+3 x^6-9 x^4+3 x^3-3 x+1\right)^{2/3}+\left(2 \sqrt[3]{2} x^3+2 \sqrt[3]{2}\right) \sqrt[3]{-3 x^{10}+x^9-9 x^7+3 x^6-9 x^4+3 x^3-3 x+1}+4\right)}{6\ 2^{2/3}}-\frac{\tan ^{-1}\left(\frac{\left(\sqrt{3} x+\sqrt{3}\right) \left(x^2-x+1\right)}{x^3+\sqrt[3]{2} \sqrt[3]{-3 x^{10}+x^9-9 x^7+3 x^6-9 x^4+3 x^3-3 x+1}+1}\right)}{2^{2/3} \sqrt{3}}",1,"((-1 + 3*x)^(1/3)*(1 + x^3)*(2^(1/3)*(2*Sqrt[3]*ArcTan[(-1 + (-2 + 6*x)^(1/3))/Sqrt[3]] - 2*Log[2 + (-2 + 6*x)^(1/3)] + Log[4 - 2*(-2 + 6*x)^(1/3) + (-2 + 6*x)^(2/3)]) - 4*RootSum[7 - #1^3 + #1^6 & , (-5*Log[(-1 + 3*x)^(1/3) - #1] + Log[(-1 + 3*x)^(1/3) - #1]*#1^3)/(-#1 + 2*#1^4) & ]))/(12*(-((-1 + 3*x)*(1 + x^3)^3))^(1/3))","A",1
3049,0,0,460,0.1088907,"\int \frac{\left(b+a x^4\right)^{3/4}}{b+2 a x^4+2 x^8} \, dx","Integrate[(b + a*x^4)^(3/4)/(b + 2*a*x^4 + 2*x^8),x]","\int \frac{\left(b+a x^4\right)^{3/4}}{b+2 a x^4+2 x^8} \, dx","\frac{\left(-1-\sqrt[4]{-1}\right) \tan ^{-1}\left(\frac{(-1)^{7/8} \sqrt{2+\sqrt{2}} x \sqrt[8]{a^2-2 b} \sqrt[4]{a x^4+b}}{(-1)^{3/4} x^2 \sqrt[4]{a^2-2 b}+\sqrt{a x^4+b}}\right)}{8 \sqrt[8]{a^2-2 b}}+\frac{\left(\sqrt{2}+i \sqrt{2 \left(3-2 \sqrt{2}\right)}\right) \tan ^{-1}\left(\frac{(-1)^{7/8} \left(\sqrt{2}-2\right) x \sqrt[8]{a^2-2 b} \sqrt[4]{a x^4+b}}{(-1)^{3/4} \sqrt{2-\sqrt{2}} x^2 \sqrt[4]{a^2-2 b}+\sqrt{2-\sqrt{2}} \sqrt{a x^4+b}}\right)}{16 \sqrt[8]{a^2-2 b}}-\frac{i \left(\sqrt{2 \left(3-2 \sqrt{2}\right)}-i \sqrt{2}\right) \tanh ^{-1}\left(\frac{(-1)^{7/8} x^2 \sqrt[4]{a^2-2 b}-\sqrt[8]{-1} \sqrt{a x^4+b}}{\sqrt{2-\sqrt{2}} x \sqrt[8]{a^2-2 b} \sqrt[4]{a x^4+b}}\right)}{16 \sqrt[8]{a^2-2 b}}+\frac{\left(-1-\sqrt[4]{-1}\right) \tanh ^{-1}\left(\frac{(-1)^{7/8} x^2 \sqrt[4]{a^2-2 b}-\sqrt[8]{-1} \sqrt{a x^4+b}}{\sqrt{2+\sqrt{2}} x \sqrt[8]{a^2-2 b} \sqrt[4]{a x^4+b}}\right)}{8 \sqrt[8]{a^2-2 b}}",1,"Integrate[(b + a*x^4)^(3/4)/(b + 2*a*x^4 + 2*x^8), x]","F",-1
3050,0,0,460,0.2451021,"\int \frac{\sqrt{a x^2+\sqrt{b+a^2 x^4}}}{(d+c x) \sqrt{b+a^2 x^4}} \, dx","Integrate[Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/((d + c*x)*Sqrt[b + a^2*x^4]),x]","\int \frac{\sqrt{a x^2+\sqrt{b+a^2 x^4}}}{(d+c x) \sqrt{b+a^2 x^4}} \, dx","\frac{i \sqrt{a} d \text{RootSum}\left[\text{$\#$1}^4 c^2-4 i \text{$\#$1}^3 a d^2+2 \text{$\#$1}^2 b c^2+4 i \text{$\#$1} a b d^2+b^2 c^2\&,\frac{b \log \left(-\text{$\#$1}+i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)-\text{$\#$1}^2 \log \left(-\text{$\#$1}+i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)}{\text{$\#$1}^3 c^2-3 i \text{$\#$1}^2 a d^2+\text{$\#$1} b c^2+i a b d^2}\&\right]}{\sqrt{2}}-\frac{\sqrt{-\sqrt{a^2 d^4+b c^4}-a d^2} \tan ^{-1}\left(\frac{c \sqrt{\sqrt{a^2 x^4+b}+a x^2}}{\sqrt{-\sqrt{a^2 d^4+b c^4}-a d^2}}\right)}{\sqrt{a^2 d^4+b c^4}}+\frac{\sqrt{\sqrt{a^2 d^4+b c^4}-a d^2} \tan ^{-1}\left(\frac{c \sqrt{\sqrt{a^2 x^4+b}+a x^2}}{\sqrt{\sqrt{a^2 d^4+b c^4}-a d^2}}\right)}{\sqrt{a^2 d^4+b c^4}}",1,"Integrate[Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/((d + c*x)*Sqrt[b + a^2*x^4]), x]","F",-1
3051,0,0,460,0.0934497,"\int \frac{\sqrt{a x^2+\sqrt{b+a^2 x^4}}}{(d+c x) \sqrt{b+a^2 x^4}} \, dx","Integrate[Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/((d + c*x)*Sqrt[b + a^2*x^4]),x]","\int \frac{\sqrt{a x^2+\sqrt{b+a^2 x^4}}}{(d+c x) \sqrt{b+a^2 x^4}} \, dx","\frac{i \sqrt{a} d \text{RootSum}\left[\text{$\#$1}^4 c^2-4 i \text{$\#$1}^3 a d^2+2 \text{$\#$1}^2 b c^2+4 i \text{$\#$1} a b d^2+b^2 c^2\&,\frac{b \log \left(-\text{$\#$1}+i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)-\text{$\#$1}^2 \log \left(-\text{$\#$1}+i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)}{\text{$\#$1}^3 c^2-3 i \text{$\#$1}^2 a d^2+\text{$\#$1} b c^2+i a b d^2}\&\right]}{\sqrt{2}}-\frac{\sqrt{-\sqrt{a^2 d^4+b c^4}-a d^2} \tan ^{-1}\left(\frac{c \sqrt{\sqrt{a^2 x^4+b}+a x^2}}{\sqrt{-\sqrt{a^2 d^4+b c^4}-a d^2}}\right)}{\sqrt{a^2 d^4+b c^4}}+\frac{\sqrt{\sqrt{a^2 d^4+b c^4}-a d^2} \tan ^{-1}\left(\frac{c \sqrt{\sqrt{a^2 x^4+b}+a x^2}}{\sqrt{\sqrt{a^2 d^4+b c^4}-a d^2}}\right)}{\sqrt{a^2 d^4+b c^4}}",1,"Integrate[Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/((d + c*x)*Sqrt[b + a^2*x^4]), x]","F",-1
3052,1,309,463,1.2495306,"\int \frac{1}{\sqrt{c+b x+a x^2} \left(c^3+a^3 b^3 x^3\right)} \, dx","Integrate[1/(Sqrt[c + b*x + a*x^2]*(c^3 + a^3*b^3*x^3)),x]","\frac{-\frac{\tan ^{-1}\left(\frac{-a b^2 x+b (c-2 a c)+2 a c x}{2 \sqrt{a} \sqrt{c} \sqrt{-\left((a-1) b^2\right)-c} \sqrt{x (a x+b)+c}}\right)}{\sqrt{-\left((a-1) b^2\right)-c}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[3]{-1} a b^2 x+b \left(2 \sqrt[3]{-1} a c+c\right)+2 a c x}{2 \sqrt{a} \sqrt{c} \sqrt{\left((-1)^{2/3} a+\sqrt[3]{-1}\right) b^2+c} \sqrt{x (a x+b)+c}}\right)}{\sqrt{\left((-1)^{2/3} a+\sqrt[3]{-1}\right) b^2+c}}+\frac{\tanh ^{-1}\left(\frac{-(-1)^{2/3} a b^2 x+b \left(c-2 (-1)^{2/3} a c\right)+2 a c x}{2 \sqrt{a} \sqrt{c} \sqrt{c-\sqrt[3]{-1} \left(a+\sqrt[3]{-1}\right) b^2} \sqrt{x (a x+b)+c}}\right)}{\sqrt{c-\sqrt[3]{-1} \left(a+\sqrt[3]{-1}\right) b^2}}}{3 \sqrt{a} c^{5/2}}","\frac{2 \tanh ^{-1}\left(-\frac{\sqrt{a} b \sqrt{a x^2+b x+c}}{\sqrt{c} \sqrt{a b^2-b^2+c}}+\frac{a b x}{\sqrt{c} \sqrt{a b^2-b^2+c}}+\frac{\sqrt{c}}{\sqrt{a b^2-b^2+c}}\right)}{3 \sqrt{a} c^{5/2} \sqrt{a b^2-b^2+c}}-\frac{\text{RootSum}\left[\text{$\#$1}^4 a^2 b^2+2 \text{$\#$1}^3 a^{3/2} b c-2 \text{$\#$1}^2 a^2 b^2 c-\text{$\#$1}^2 a b^2 c+4 \text{$\#$1}^2 a c^2-2 \text{$\#$1} a^{3/2} b c^2-4 \text{$\#$1} \sqrt{a} b c^2+a^2 b^2 c^2+a b^2 c^2+b^2 c^2\&,\frac{\text{$\#$1}^2 (-a) b \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)-4 \text{$\#$1} \sqrt{a} c \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)+a b c \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)+2 b c \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)}{-2 \text{$\#$1}^3 a^{3/2} b^2-3 \text{$\#$1}^2 a b c+2 \text{$\#$1} a^{3/2} b^2 c+\text{$\#$1} \sqrt{a} b^2 c-4 \text{$\#$1} \sqrt{a} c^2+a b c^2+2 b c^2}\&\right]}{3 \sqrt{a} c^2}",1,"(-(ArcTan[(b*(c - 2*a*c) - a*b^2*x + 2*a*c*x)/(2*Sqrt[a]*Sqrt[-((-1 + a)*b^2) - c]*Sqrt[c]*Sqrt[c + x*(b + a*x)])]/Sqrt[-((-1 + a)*b^2) - c]) + ArcTanh[(b*(c + 2*(-1)^(1/3)*a*c) + (-1)^(1/3)*a*b^2*x + 2*a*c*x)/(2*Sqrt[a]*Sqrt[c]*Sqrt[((-1)^(1/3) + (-1)^(2/3)*a)*b^2 + c]*Sqrt[c + x*(b + a*x)])]/Sqrt[((-1)^(1/3) + (-1)^(2/3)*a)*b^2 + c] + ArcTanh[(b*(c - 2*(-1)^(2/3)*a*c) - (-1)^(2/3)*a*b^2*x + 2*a*c*x)/(2*Sqrt[a]*Sqrt[c]*Sqrt[-((-1)^(1/3)*((-1)^(1/3) + a)*b^2) + c]*Sqrt[c + x*(b + a*x)])]/Sqrt[-((-1)^(1/3)*((-1)^(1/3) + a)*b^2) + c])/(3*Sqrt[a]*c^(5/2))","A",1
3053,0,0,463,0.409682,"\int \frac{\left(-d+c x^2\right) \sqrt{a x^2+\sqrt{b+a^2 x^4}}}{d+c x^2} \, dx","Integrate[((-d + c*x^2)*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]])/(d + c*x^2),x]","\int \frac{\left(-d+c x^2\right) \sqrt{a x^2+\sqrt{b+a^2 x^4}}}{d+c x^2} \, dx","\frac{\sqrt{2} \sqrt{a} d \text{RootSum}\left[\text{$\#$1}^4 c+4 \text{$\#$1}^3 a d-2 \text{$\#$1}^2 b c+4 \text{$\#$1} a b d+b^2 c\&,\frac{\text{$\#$1}^2 a d \log \left(-\text{$\#$1}+\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)-2 \text{$\#$1} b c \log \left(-\text{$\#$1}+\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)+a b d \log \left(-\text{$\#$1}+\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)}{\text{$\#$1}^3 c+3 \text{$\#$1}^2 a d-\text{$\#$1} b c+a b d}\&\right]}{c}-\frac{\sqrt{2} \sqrt{a} d \log \left(\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)}{c}+\frac{1}{2} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a^2 x^4+b}}{\sqrt{b}}+\frac{\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}}{\sqrt{b}}+\frac{a x^2}{\sqrt{b}}\right)}{\sqrt{2} \sqrt{a}}",1,"Integrate[((-d + c*x^2)*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]])/(d + c*x^2), x]","F",-1
3054,0,0,463,0.1629818,"\int \frac{\left(-d+c x^2\right) \sqrt{a x^2+\sqrt{b+a^2 x^4}}}{d+c x^2} \, dx","Integrate[((-d + c*x^2)*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]])/(d + c*x^2),x]","\int \frac{\left(-d+c x^2\right) \sqrt{a x^2+\sqrt{b+a^2 x^4}}}{d+c x^2} \, dx","\frac{\sqrt{2} \sqrt{a} d \text{RootSum}\left[\text{$\#$1}^4 c+4 \text{$\#$1}^3 a d-2 \text{$\#$1}^2 b c+4 \text{$\#$1} a b d+b^2 c\&,\frac{\text{$\#$1}^2 a d \log \left(-\text{$\#$1}+\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)-2 \text{$\#$1} b c \log \left(-\text{$\#$1}+\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)+a b d \log \left(-\text{$\#$1}+\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)}{\text{$\#$1}^3 c+3 \text{$\#$1}^2 a d-\text{$\#$1} b c+a b d}\&\right]}{c}-\frac{\sqrt{2} \sqrt{a} d \log \left(\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)}{c}+\frac{1}{2} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a^2 x^4+b}}{\sqrt{b}}+\frac{\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}}{\sqrt{b}}+\frac{a x^2}{\sqrt{b}}\right)}{\sqrt{2} \sqrt{a}}",1,"Integrate[((-d + c*x^2)*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]])/(d + c*x^2), x]","F",-1
3055,1,238,466,0.646824,"\int \sqrt{\frac{-1+a x-2 x^2+2 a x^3-x^4+a x^5}{1+a x-2 x^2-2 a x^3+x^4+a x^5}} \, dx","Integrate[Sqrt[(-1 + a*x - 2*x^2 + 2*a*x^3 - x^4 + a*x^5)/(1 + a*x - 2*x^2 - 2*a*x^3 + x^4 + a*x^5)],x]","\frac{\left(x^2-1\right) \sqrt{a x+1} \sqrt{\frac{\left(x^2+1\right)^2 (a x-1)}{\left(x^2-1\right)^2 (a x+1)}} \left((a+1) \left(\sqrt{\frac{a-1}{a+1}} \left(\sqrt{a x+1} (a x-1)^{3/2}+2 \sqrt{-(a x-1)^2} \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)+2 a (a x-1) \tanh ^{-1}\left(\sqrt{\frac{a-1}{a+1}} \sqrt{\frac{a x-1}{a x+1}}\right)\right)-2 (a-1) a (a x-1) \tanh ^{-1}\left(\frac{\sqrt{\frac{a x-1}{a x+1}}}{\sqrt{\frac{a-1}{a+1}}}\right)\right)}{a \sqrt{\frac{a-1}{a+1}} (a+1) \left(x^2+1\right) (a x-1)^{3/2}}","\frac{2 \sqrt{-(a+1)^2} \tan ^{-1}\left(\frac{\frac{(a+1)^2 x^2}{\sqrt{-a^2-2 a-1} \sqrt{a^2-1}}+\frac{(a+1)^2}{\sqrt{-a^2-2 a-1} \sqrt{a^2-1}}}{(x-1) (x+1) \sqrt{\frac{a x^5+2 a x^3+a x-x^4-2 x^2-1}{a x^5-2 a x^3+a x+x^4-2 x^2+1}}}\right)}{\sqrt{a^2-1}}-\frac{2 \sqrt{-(a-1)^2} \tan ^{-1}\left(\frac{\frac{(a-1)^2 x^2}{\sqrt{-a^2+2 a-1} \sqrt{a^2-1}}+\frac{(a-1)^2}{\sqrt{-a^2+2 a-1} \sqrt{a^2-1}}}{(x-1) (x+1) \sqrt{\frac{a x^5+2 a x^3+a x-x^4-2 x^2-1}{a x^5-2 a x^3+a x+x^4-2 x^2+1}}}\right)}{\sqrt{a^2-1}}+\frac{\sqrt{\frac{a x^5+2 a x^3+a x-x^4-2 x^2-1}{a x^5-2 a x^3+a x+x^4-2 x^2+1}} \left(a x^3-a x+x^2-1\right)}{a \left(x^2+1\right)}-\frac{2 \tanh ^{-1}\left(\frac{(x-1) (x+1) \sqrt{\frac{a x^5+2 a x^3+a x-x^4-2 x^2-1}{a x^5-2 a x^3+a x+x^4-2 x^2+1}}}{x^2+1}\right)}{a}",1,"(Sqrt[1 + a*x]*(-1 + x^2)*Sqrt[((-1 + a*x)*(1 + x^2)^2)/((1 + a*x)*(-1 + x^2)^2)]*(-2*(-1 + a)*a*(-1 + a*x)*ArcTanh[Sqrt[(-1 + a*x)/(1 + a*x)]/Sqrt[(-1 + a)/(1 + a)]] + (1 + a)*(Sqrt[(-1 + a)/(1 + a)]*((-1 + a*x)^(3/2)*Sqrt[1 + a*x] + 2*Sqrt[-(-1 + a*x)^2]*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]) + 2*a*(-1 + a*x)*ArcTanh[Sqrt[(-1 + a)/(1 + a)]*Sqrt[(-1 + a*x)/(1 + a*x)]])))/(a*Sqrt[(-1 + a)/(1 + a)]*(1 + a)*(-1 + a*x)^(3/2)*(1 + x^2))","A",0
3056,1,151,468,0.2653951,"\int \frac{1+x}{\left(-3+x^2\right) \sqrt[3]{1+x^2}} \, dx","Integrate[(1 + x)/((-3 + x^2)*(1 + x^2)^(1/3)),x]","\frac{9 x F_1\left(\frac{1}{2};\frac{1}{3},1;\frac{3}{2};-x^2,\frac{x^2}{3}\right)}{\left(x^2-3\right) \sqrt[3]{x^2+1} \left(2 x^2 \left(F_1\left(\frac{3}{2};\frac{1}{3},2;\frac{5}{2};-x^2,\frac{x^2}{3}\right)-F_1\left(\frac{3}{2};\frac{4}{3},1;\frac{5}{2};-x^2,\frac{x^2}{3}\right)\right)+9 F_1\left(\frac{1}{2};\frac{1}{3},1;\frac{3}{2};-x^2,\frac{x^2}{3}\right)\right)}-\frac{1}{6} x^2 F_1\left(1;\frac{1}{3},1;2;-x^2,\frac{x^2}{3}\right)","\frac{\sqrt[3]{\frac{1}{2} \left(9+5 \sqrt{3}\right)} \log \left(-6 \sqrt[3]{x^2+1}+2^{2/3} \sqrt{3} x+3\ 2^{2/3}\right)}{6\ 3^{2/3}}+\frac{\sqrt[3]{\frac{1}{2} \left(9-5 \sqrt{3}\right)} \log \left(6 \sqrt[3]{x^2+1}+2^{2/3} \sqrt{3} x-3\ 2^{2/3}\right)}{6\ 3^{2/3}}-\frac{\sqrt[3]{\frac{1}{2} \left(9-5 \sqrt{3}\right)} \log \left(-\sqrt[3]{2} x^2+2^{2/3} \sqrt{3} \sqrt[3]{x^2+1} x-6 \left(x^2+1\right)^{2/3}-3\ 2^{2/3} \sqrt[3]{x^2+1}+2 \sqrt[3]{2} \sqrt{3} x-3 \sqrt[3]{2}\right)}{12\ 3^{2/3}}-\frac{\sqrt[3]{\frac{1}{2} \left(9+5 \sqrt{3}\right)} \log \left(\sqrt[3]{2} x^2+2^{2/3} \sqrt{3} \sqrt[3]{x^2+1} x+6 \left(x^2+1\right)^{2/3}+3\ 2^{2/3} \sqrt[3]{x^2+1}+2 \sqrt[3]{2} \sqrt{3} x+3 \sqrt[3]{2}\right)}{12\ 3^{2/3}}+\frac{1}{6} \sqrt[3]{\frac{1}{2} \left(3 \sqrt{3}-5\right)} \tan ^{-1}\left(\frac{-\frac{\sqrt[3]{x^2+1}}{\sqrt{3}}+\frac{1}{3} 2^{2/3} x-\frac{2^{2/3}}{\sqrt{3}}}{\sqrt[3]{x^2+1}}\right)-\frac{1}{6} \sqrt[3]{\frac{1}{2} \left(5+3 \sqrt{3}\right)} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{x^2+1}}{\sqrt{3}}+\frac{1}{3} 2^{2/3} x+\frac{2^{2/3}}{\sqrt{3}}}{\sqrt[3]{x^2+1}}\right)",1,"-1/6*(x^2*AppellF1[1, 1/3, 1, 2, -x^2, x^2/3]) + (9*x*AppellF1[1/2, 1/3, 1, 3/2, -x^2, x^2/3])/((-3 + x^2)*(1 + x^2)^(1/3)*(9*AppellF1[1/2, 1/3, 1, 3/2, -x^2, x^2/3] + 2*x^2*(AppellF1[3/2, 1/3, 2, 5/2, -x^2, x^2/3] - AppellF1[3/2, 4/3, 1, 5/2, -x^2, x^2/3])))","C",0
3057,0,0,469,0.8289333,"\int \frac{1-x^4}{\left(1+x^4\right) \sqrt[4]{-x^3+x^5}} \, dx","Integrate[(1 - x^4)/((1 + x^4)*(-x^3 + x^5)^(1/4)),x]","\int \frac{1-x^4}{\left(1+x^4\right) \sqrt[4]{-x^3+x^5}} \, dx","\frac{1}{2} \sqrt[4]{3 \sqrt{2}-4} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}} x}{2^{7/8} \sqrt[4]{x^5-x^3}-\sqrt{2+\sqrt{2}} x}\right)+\frac{1}{2} \sqrt[4]{3 \sqrt{2}-4} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}} x}{2^{7/8} \sqrt[4]{x^5-x^3}+\sqrt{2+\sqrt{2}} x}\right)-\frac{1}{4} \sqrt[4]{4+3 \sqrt{2}} \log \left(-2 x^2+2^{7/8} \sqrt{2+\sqrt{2}} \sqrt[4]{x^5-x^3} x-2^{3/4} \sqrt{x^5-x^3}\right)+\frac{1}{4} \sqrt[4]{4+3 \sqrt{2}} \log \left(2 \sqrt{2-\sqrt{2}} x^2+2\ 2^{3/8} \sqrt[4]{x^5-x^3} x+2^{3/4} \sqrt{2-\sqrt{2}} \sqrt{x^5-x^3}\right)+\frac{1}{2} \sqrt[4]{4+3 \sqrt{2}} \tan ^{-1}\left(\frac{2^{7/8} \sqrt{2+\sqrt{2}} x \sqrt[4]{x^5-x^3}}{2^{3/4} \sqrt{x^5-x^3}-2 x^2}\right)+\frac{1}{2} \sqrt[4]{3 \sqrt{2}-4} \tanh ^{-1}\left(\frac{\frac{\sqrt[8]{2} x^2}{\sqrt{2-\sqrt{2}}}+\frac{\sqrt{x^5-x^3}}{\sqrt[8]{2} \sqrt{2-\sqrt{2}}}}{x \sqrt[4]{x^5-x^3}}\right)",1,"Integrate[(1 - x^4)/((1 + x^4)*(-x^3 + x^5)^(1/4)), x]","F",-1
3058,0,0,469,1.2872301,"\int \frac{-1+x^8}{\sqrt[4]{-x^2+x^6} \left(1+x^8\right)} \, dx","Integrate[(-1 + x^8)/((-x^2 + x^6)^(1/4)*(1 + x^8)),x]","\int \frac{-1+x^8}{\sqrt[4]{-x^2+x^6} \left(1+x^8\right)} \, dx","\frac{1}{8} \sqrt[4]{4+3 \sqrt{2}} \log \left(-2 x^2+2^{7/8} \sqrt{2+\sqrt{2}} \sqrt[4]{x^6-x^2} x-2^{3/4} \sqrt{x^6-x^2}\right)-\frac{1}{8} \sqrt[4]{4+3 \sqrt{2}} \log \left(2 \sqrt{2-\sqrt{2}} x^2+2\ 2^{3/8} \sqrt[4]{x^6-x^2} x+2^{3/4} \sqrt{2-\sqrt{2}} \sqrt{x^6-x^2}\right)-\frac{1}{4} \sqrt[4]{3 \sqrt{2}-4} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}} x}{2^{7/8} \sqrt[4]{x^6-x^2}-\sqrt{2+\sqrt{2}} x}\right)-\frac{1}{4} \sqrt[4]{3 \sqrt{2}-4} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}} x}{2^{7/8} \sqrt[4]{x^6-x^2}+\sqrt{2+\sqrt{2}} x}\right)-\frac{1}{4} \sqrt[4]{4+3 \sqrt{2}} \tan ^{-1}\left(\frac{2^{7/8} \sqrt{2+\sqrt{2}} x \sqrt[4]{x^6-x^2}}{2^{3/4} \sqrt{x^6-x^2}-2 x^2}\right)-\frac{1}{4} \sqrt[4]{3 \sqrt{2}-4} \tanh ^{-1}\left(\frac{\frac{\sqrt[8]{2} x^2}{\sqrt{2-\sqrt{2}}}+\frac{\sqrt{x^6-x^2}}{\sqrt[8]{2} \sqrt{2-\sqrt{2}}}}{x \sqrt[4]{x^6-x^2}}\right)",1,"Integrate[(-1 + x^8)/((-x^2 + x^6)^(1/4)*(1 + x^8)), x]","F",-1
3059,0,0,469,0.597681,"\int \frac{-1+x^8}{\sqrt[4]{-x^2+x^6} \left(1+x^8\right)} \, dx","Integrate[(-1 + x^8)/((-x^2 + x^6)^(1/4)*(1 + x^8)),x]","\int \frac{-1+x^8}{\sqrt[4]{-x^2+x^6} \left(1+x^8\right)} \, dx","\frac{1}{8} \sqrt[4]{4+3 \sqrt{2}} \log \left(-2 x^2+2^{7/8} \sqrt{2+\sqrt{2}} \sqrt[4]{x^6-x^2} x-2^{3/4} \sqrt{x^6-x^2}\right)-\frac{1}{8} \sqrt[4]{4+3 \sqrt{2}} \log \left(2 \sqrt{2-\sqrt{2}} x^2+2\ 2^{3/8} \sqrt[4]{x^6-x^2} x+2^{3/4} \sqrt{2-\sqrt{2}} \sqrt{x^6-x^2}\right)-\frac{1}{4} \sqrt[4]{3 \sqrt{2}-4} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}} x}{2^{7/8} \sqrt[4]{x^6-x^2}-\sqrt{2+\sqrt{2}} x}\right)-\frac{1}{4} \sqrt[4]{3 \sqrt{2}-4} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}} x}{2^{7/8} \sqrt[4]{x^6-x^2}+\sqrt{2+\sqrt{2}} x}\right)-\frac{1}{4} \sqrt[4]{4+3 \sqrt{2}} \tan ^{-1}\left(\frac{2^{7/8} \sqrt{2+\sqrt{2}} x \sqrt[4]{x^6-x^2}}{2^{3/4} \sqrt{x^6-x^2}-2 x^2}\right)-\frac{1}{4} \sqrt[4]{3 \sqrt{2}-4} \tanh ^{-1}\left(\frac{\frac{\sqrt[8]{2} x^2}{\sqrt{2-\sqrt{2}}}+\frac{\sqrt{x^6-x^2}}{\sqrt[8]{2} \sqrt{2-\sqrt{2}}}}{x \sqrt[4]{x^6-x^2}}\right)",1,"Integrate[(-1 + x^8)/((-x^2 + x^6)^(1/4)*(1 + x^8)), x]","F",-1
3060,0,0,470,174.9232307,"\int \frac{\sqrt[3]{a x+\sqrt{-b+a^2 x^2}}}{\sqrt[4]{c+\sqrt[3]{a x+\sqrt{-b+a^2 x^2}}}} \, dx","Integrate[(a*x + Sqrt[-b + a^2*x^2])^(1/3)/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^(1/4),x]","\int \frac{\sqrt[3]{a x+\sqrt{-b+a^2 x^2}}}{\sqrt[4]{c+\sqrt[3]{a x+\sqrt{-b+a^2 x^2}}}} \, dx","-\frac{15 b \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt[3]{\sqrt{a^2 x^2-b}+a x}+c}}{\sqrt[4]{c}}\right)}{32 a c^{9/4}}+\frac{15 b \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt[3]{\sqrt{a^2 x^2-b}+a x}+c}}{\sqrt[4]{c}}\right)}{32 a c^{9/4}}+\frac{\left(3072 a c^4 x+4620 b c\right) \left(\sqrt[3]{\sqrt{a^2 x^2-b}+a x}+c\right)^{3/4}+\sqrt[3]{\sqrt{a^2 x^2-b}+a x} \left(-2688 a c^3 x-5775 b\right) \left(\sqrt[3]{\sqrt{a^2 x^2-b}+a x}+c\right)^{3/4}+\left(\sqrt{a^2 x^2-b}+a x\right)^{2/3} \left(2464 a c^2 x-4096 c^5\right) \left(\sqrt[3]{\sqrt{a^2 x^2-b}+a x}+c\right)^{3/4}+\sqrt{a^2 x^2-b} \left(3072 c^4 \left(\sqrt[3]{\sqrt{a^2 x^2-b}+a x}+c\right)^{3/4}-2688 c^3 \sqrt[3]{\sqrt{a^2 x^2-b}+a x} \left(\sqrt[3]{\sqrt{a^2 x^2-b}+a x}+c\right)^{3/4}+2464 c^2 \left(\sqrt{a^2 x^2-b}+a x\right)^{2/3} \left(\sqrt[3]{\sqrt{a^2 x^2-b}+a x}+c\right)^{3/4}\right)}{6160 a c^2 \left(\sqrt{a^2 x^2-b}+a x\right)^{2/3}}",1,"Integrate[(a*x + Sqrt[-b + a^2*x^2])^(1/3)/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^(1/4), x]","F",-1
3061,0,0,471,0.3256815,"\int \frac{b^2+a x}{\left(-b^2+a x\right) \sqrt{b+\sqrt{b^2+a x^2}}} \, dx","Integrate[(b^2 + a*x)/((-b^2 + a*x)*Sqrt[b + Sqrt[b^2 + a*x^2]]),x]","\int \frac{b^2+a x}{\left(-b^2+a x\right) \sqrt{b+\sqrt{b^2+a x^2}}} \, dx","\frac{2 \left(\sqrt{2} \sqrt{a} \sqrt{b} \sqrt{\sqrt{a+b^2}+b}+\sqrt{2} \sqrt{b} \sqrt{a+b^2} \sqrt{\sqrt{a+b^2}+b}-\sqrt{2} b^{3/2} \sqrt{\sqrt{a+b^2}+b}\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{\sqrt{a x^2+b^2}-\sqrt{a} x}}{\sqrt{b} \sqrt{\sqrt{a+b^2}+b}}\right)}{a^{5/4}}-\frac{2 \left(-\sqrt{2} \sqrt{a} \sqrt{b} \sqrt{\sqrt{a+b^2}-b}+\sqrt{2} \sqrt{b} \sqrt{a+b^2} \sqrt{\sqrt{a+b^2}-b}+\sqrt{2} b^{3/2} \sqrt{\sqrt{a+b^2}-b}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{\sqrt{a x^2+b^2}-\sqrt{a} x}}{\sqrt{b} \sqrt{\sqrt{a+b^2}-b}}\right)}{a^{5/4}}+\frac{\sqrt{2} \sqrt{\sqrt{a x^2+b^2}-\sqrt{a} x} \left(\sqrt{a} x-b\right)}{\sqrt{a} b}+\frac{\sqrt{2} \sqrt{a x^2+b^2} \sqrt{\sqrt{a x^2+b^2}-\sqrt{a} x}}{\sqrt{a} b}-\frac{2 \sqrt{2} \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{\sqrt{a x^2+b^2}-\sqrt{a} x}}{\sqrt{b}}\right)}{\sqrt{a}}",1,"Integrate[(b^2 + a*x)/((-b^2 + a*x)*Sqrt[b + Sqrt[b^2 + a*x^2]]), x]","F",-1
3062,0,0,472,0.0928704,"\int \frac{\left(-b+a x^4\right)^{3/4}}{b-2 a x^4+2 x^8} \, dx","Integrate[(-b + a*x^4)^(3/4)/(b - 2*a*x^4 + 2*x^8),x]","\int \frac{\left(-b+a x^4\right)^{3/4}}{b-2 a x^4+2 x^8} \, dx","\frac{\left(1+\sqrt[4]{-1}\right) \tan ^{-1}\left(\frac{(-1)^{7/8} \sqrt{2+\sqrt{2}} x \sqrt[8]{a^2-2 b} \sqrt[4]{a x^4-b}}{(-1)^{3/4} x^2 \sqrt[4]{a^2-2 b}+\sqrt{a x^4-b}}\right)}{8 \sqrt[8]{a^2-2 b}}-\frac{i \left(\sqrt{2 \left(3-2 \sqrt{2}\right)}-i \sqrt{2}\right) \tan ^{-1}\left(\frac{(-1)^{7/8} \left(\sqrt{2}-2\right) x \sqrt[8]{a^2-2 b} \sqrt[4]{a x^4-b}}{(-1)^{3/4} \sqrt{2-\sqrt{2}} x^2 \sqrt[4]{a^2-2 b}+\sqrt{2-\sqrt{2}} \sqrt{a x^4-b}}\right)}{16 \sqrt[8]{a^2-2 b}}+\frac{\left(\sqrt{2}+i \sqrt{2 \left(3-2 \sqrt{2}\right)}\right) \tanh ^{-1}\left(\frac{(-1)^{7/8} x^2 \sqrt[4]{a^2-2 b}-\sqrt[8]{-1} \sqrt{a x^4-b}}{\sqrt{2-\sqrt{2}} x \sqrt[8]{a^2-2 b} \sqrt[4]{a x^4-b}}\right)}{16 \sqrt[8]{a^2-2 b}}+\frac{\left(1+\sqrt[4]{-1}\right) \tanh ^{-1}\left(\frac{(-1)^{7/8} x^2 \sqrt[4]{a^2-2 b}-\sqrt[8]{-1} \sqrt{a x^4-b}}{\sqrt{2+\sqrt{2}} x \sqrt[8]{a^2-2 b} \sqrt[4]{a x^4-b}}\right)}{8 \sqrt[8]{a^2-2 b}}",1,"Integrate[(-b + a*x^4)^(3/4)/(b - 2*a*x^4 + 2*x^8), x]","F",-1
3063,0,0,472,0.555647,"\int \frac{-d+c x^2}{\left(d+c x^2\right) \sqrt{a x^2+\sqrt{b+a^2 x^4}}} \, dx","Integrate[(-d + c*x^2)/((d + c*x^2)*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]),x]","\int \frac{-d+c x^2}{\left(d+c x^2\right) \sqrt{a x^2+\sqrt{b+a^2 x^4}}} \, dx","-\frac{\sqrt{2} \text{RootSum}\left[\text{$\#$1}^4 c+4 \text{$\#$1}^3 a d-2 \text{$\#$1}^2 b c+4 \text{$\#$1} a b d+b^2 c\&,\frac{\text{$\#$1}^2 a c d \log \left(-\text{$\#$1}+\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)+a b c d \log \left(-\text{$\#$1}+\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)+2 \text{$\#$1} a^2 d^2 \log \left(-\text{$\#$1}+\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)}{\text{$\#$1}^3 c+3 \text{$\#$1}^2 a d-\text{$\#$1} b c+a b d}\&\right]}{\sqrt{a} c}+\frac{2 \sqrt{2} \sqrt{a} d \tan ^{-1}\left(\frac{\sqrt{a^2 x^4+b}}{\sqrt{b}}+\frac{\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}}{\sqrt{b}}+\frac{a x^2}{\sqrt{b}}\right)}{\sqrt{b} c}+\frac{x}{2 \sqrt{\sqrt{a^2 x^4+b}+a x^2}}+\frac{\log \left(\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)}{2 \sqrt{2} \sqrt{a}}",1,"Integrate[(-d + c*x^2)/((d + c*x^2)*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]), x]","F",-1
3064,0,0,472,0.1604493,"\int \frac{-d+c x^2}{\left(d+c x^2\right) \sqrt{a x^2+\sqrt{b+a^2 x^4}}} \, dx","Integrate[(-d + c*x^2)/((d + c*x^2)*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]),x]","\int \frac{-d+c x^2}{\left(d+c x^2\right) \sqrt{a x^2+\sqrt{b+a^2 x^4}}} \, dx","-\frac{\sqrt{2} \text{RootSum}\left[\text{$\#$1}^4 c+4 \text{$\#$1}^3 a d-2 \text{$\#$1}^2 b c+4 \text{$\#$1} a b d+b^2 c\&,\frac{\text{$\#$1}^2 a c d \log \left(-\text{$\#$1}+\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)+a b c d \log \left(-\text{$\#$1}+\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)+2 \text{$\#$1} a^2 d^2 \log \left(-\text{$\#$1}+\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)}{\text{$\#$1}^3 c+3 \text{$\#$1}^2 a d-\text{$\#$1} b c+a b d}\&\right]}{\sqrt{a} c}+\frac{2 \sqrt{2} \sqrt{a} d \tan ^{-1}\left(\frac{\sqrt{a^2 x^4+b}}{\sqrt{b}}+\frac{\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}}{\sqrt{b}}+\frac{a x^2}{\sqrt{b}}\right)}{\sqrt{b} c}+\frac{x}{2 \sqrt{\sqrt{a^2 x^4+b}+a x^2}}+\frac{\log \left(\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)}{2 \sqrt{2} \sqrt{a}}",1,"Integrate[(-d + c*x^2)/((d + c*x^2)*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]), x]","F",-1
3065,1,426,476,0.7292535,"\int \frac{x^4}{\sqrt[4]{-b+a x^4} \left(b-2 a x^4+2 x^8\right)} \, dx","Integrate[x^4/((-b + a*x^4)^(1/4)*(b - 2*a*x^4 + 2*x^8)),x]","\frac{\frac{\sqrt[4]{a-\sqrt{a^2-2 b}} \tan ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2-2 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2-2 b}} \sqrt[4]{a x^4-b}}\right)}{\sqrt[4]{-a \sqrt{a^2-2 b}+a^2-2 b}}-\frac{\sqrt[4]{\sqrt{a^2-2 b}+a} \tan ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2-2 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2-2 b}+a} \sqrt[4]{a x^4-b}}\right)}{\sqrt[4]{a \sqrt{a^2-2 b}+a^2-2 b}}+\frac{\sqrt[4]{a-\sqrt{a^2-2 b}} \tanh ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2-2 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2-2 b}} \sqrt[4]{a x^4-b}}\right)}{\sqrt[4]{-a \sqrt{a^2-2 b}+a^2-2 b}}-\frac{\sqrt[4]{\sqrt{a^2-2 b}+a} \tanh ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2-2 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2-2 b}+a} \sqrt[4]{a x^4-b}}\right)}{\sqrt[4]{a \sqrt{a^2-2 b}+a^2-2 b}}}{4 \sqrt{a^2-2 b}}","\frac{\left(1-\sqrt[4]{-1}\right) \tan ^{-1}\left(\frac{(-1)^{7/8} \sqrt{2+\sqrt{2}} x \sqrt[8]{a^2-2 b} \sqrt[4]{a x^4-b}}{(-1)^{3/4} x^2 \sqrt[4]{a^2-2 b}+\sqrt{a x^4-b}}\right)}{8 \left(a^2-2 b\right)^{5/8}}+\frac{\left(\sqrt{2}-i \sqrt{2 \left(3+2 \sqrt{2}\right)}\right) \tan ^{-1}\left(\frac{(-1)^{7/8} \left(\sqrt{2}-2\right) x \sqrt[8]{a^2-2 b} \sqrt[4]{a x^4-b}}{(-1)^{3/4} \sqrt{2-\sqrt{2}} x^2 \sqrt[4]{a^2-2 b}+\sqrt{2-\sqrt{2}} \sqrt{a x^4-b}}\right)}{16 \left(a^2-2 b\right)^{5/8}}+\frac{i \left(\sqrt{2 \left(3+2 \sqrt{2}\right)}+i \sqrt{2}\right) \tanh ^{-1}\left(\frac{(-1)^{7/8} x^2 \sqrt[4]{a^2-2 b}-\sqrt[8]{-1} \sqrt{a x^4-b}}{\sqrt{2-\sqrt{2}} x \sqrt[8]{a^2-2 b} \sqrt[4]{a x^4-b}}\right)}{16 \left(a^2-2 b\right)^{5/8}}+\frac{\left(1-\sqrt[4]{-1}\right) \tanh ^{-1}\left(\frac{(-1)^{7/8} x^2 \sqrt[4]{a^2-2 b}-\sqrt[8]{-1} \sqrt{a x^4-b}}{\sqrt{2+\sqrt{2}} x \sqrt[8]{a^2-2 b} \sqrt[4]{a x^4-b}}\right)}{8 \left(a^2-2 b\right)^{5/8}}",1,"(((a - Sqrt[a^2 - 2*b])^(1/4)*ArcTan[((a^2 - a*Sqrt[a^2 - 2*b] - 2*b)^(1/4)*x)/((a - Sqrt[a^2 - 2*b])^(1/4)*(-b + a*x^4)^(1/4))])/(a^2 - a*Sqrt[a^2 - 2*b] - 2*b)^(1/4) - ((a + Sqrt[a^2 - 2*b])^(1/4)*ArcTan[((a^2 + a*Sqrt[a^2 - 2*b] - 2*b)^(1/4)*x)/((a + Sqrt[a^2 - 2*b])^(1/4)*(-b + a*x^4)^(1/4))])/(a^2 + a*Sqrt[a^2 - 2*b] - 2*b)^(1/4) + ((a - Sqrt[a^2 - 2*b])^(1/4)*ArcTanh[((a^2 - a*Sqrt[a^2 - 2*b] - 2*b)^(1/4)*x)/((a - Sqrt[a^2 - 2*b])^(1/4)*(-b + a*x^4)^(1/4))])/(a^2 - a*Sqrt[a^2 - 2*b] - 2*b)^(1/4) - ((a + Sqrt[a^2 - 2*b])^(1/4)*ArcTanh[((a^2 + a*Sqrt[a^2 - 2*b] - 2*b)^(1/4)*x)/((a + Sqrt[a^2 - 2*b])^(1/4)*(-b + a*x^4)^(1/4))])/(a^2 + a*Sqrt[a^2 - 2*b] - 2*b)^(1/4))/(4*Sqrt[a^2 - 2*b])","A",1
3066,0,0,477,2.0924592,"\int \frac{x^3 (-5 b+6 a x)}{\sqrt[4]{-b x+a x^2} \left(c-b x^5+a x^6\right)} \, dx","Integrate[(x^3*(-5*b + 6*a*x))/((-(b*x) + a*x^2)^(1/4)*(c - b*x^5 + a*x^6)),x]","\int \frac{x^3 (-5 b+6 a x)}{\sqrt[4]{-b x+a x^2} \left(c-b x^5+a x^6\right)} \, dx","-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt[3]{c} x^2 \sqrt[4]{a x^2-b x}-2^{2/3} x \sqrt[4]{a x^2-b x}}{-\sqrt[3]{c} x^2 \sqrt[4]{a x^2-b x}+2^{2/3} x \sqrt[4]{a x^2-b x}-\sqrt{2} c^{7/12} x+2 \sqrt[6]{2} \sqrt[4]{c}}\right)}{\sqrt[4]{c}}+\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt[3]{c} x^2 \sqrt[4]{a x^2-b x}-2^{2/3} x \sqrt[4]{a x^2-b x}}{-\sqrt[3]{c} x^2 \sqrt[4]{a x^2-b x}+2^{2/3} x \sqrt[4]{a x^2-b x}+\sqrt{2} c^{7/12} x-2 \sqrt[6]{2} \sqrt[4]{c}}\right)}{\sqrt[4]{c}}-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{-4 \sqrt[6]{2} c^{7/12} x^2 \sqrt[4]{a x^2-b x}+\sqrt{2} c^{11/12} x^3 \sqrt[4]{a x^2-b x}+2\ 2^{5/6} \sqrt[4]{c} x \sqrt[4]{a x^2-b x}}{c^{2/3} x^4 \sqrt{a x^2-b x}-2\ 2^{2/3} \sqrt[3]{c} x^3 \sqrt{a x^2-b x}+2 \sqrt[3]{2} x^2 \sqrt{a x^2-b x}+c^{7/6} x^2-2\ 2^{2/3} c^{5/6} x+2 \sqrt[3]{2} \sqrt{c}}\right)}{\sqrt[4]{c}}",1,"Integrate[(x^3*(-5*b + 6*a*x))/((-(b*x) + a*x^2)^(1/4)*(c - b*x^5 + a*x^6)), x]","F",-1
3067,1,89,481,0.278597,"\int \frac{-a+x}{\sqrt[3]{(-a+x) (-b+x)^2} \left(-b^2+a^2 d+2 (b-a d) x+(-1+d) x^2\right)} \, dx","Integrate[(-a + x)/(((-a + x)*(-b + x)^2)^(1/3)*(-b^2 + a^2*d + 2*(b - a*d)*x + (-1 + d)*x^2)),x]","-\frac{3 (x-b) \left(\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{b-x}{\sqrt{d} (x-a)}\right)+\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{x-b}{\sqrt{d} (x-a)}\right)\right)}{2 d (a-b) \sqrt[3]{(x-a) (b-x)^2}}","\frac{\left(1+i \sqrt{3}\right) (x-b)^{2/3} \left(-\sqrt[6]{d} \sqrt[3]{a-x} \sqrt[3]{x-b}+\sqrt[3]{d} (a-x)^{2/3}+(x-b)^{2/3}\right) \left(\sqrt[6]{d} \sqrt[3]{a-x} \sqrt[3]{x-b}+\sqrt[3]{d} (a-x)^{2/3}+(x-b)^{2/3}\right) \left(\sqrt[3]{a-x} (x-b)^{2/3}+a \left(-\sqrt[3]{d}\right)+\sqrt[3]{d} x\right) \left(\frac{\left(\sqrt{3}-3 i\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x-b}}{\sqrt[3]{x-b}-2 \sqrt[6]{d} \sqrt[3]{a-x}}\right)}{4 d^{5/6} (a-b)}+\frac{\left(-\sqrt{3}+3 i\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x-b}}{2 \sqrt[6]{d} \sqrt[3]{a-x}+\sqrt[3]{x-b}}\right)}{4 d^{5/6} (a-b)}+\frac{\left(1-i \sqrt{3}\right) \tanh ^{-1}\left(\frac{(a-x)^{2/3} \sqrt[3]{x-b}}{\sqrt[6]{d} (x-a)}\right)}{2 d^{5/6} (a-b)}+\frac{i \left(\sqrt{3}+i\right) \tanh ^{-1}\left(\frac{\sqrt[3]{d} (a-x)^{2/3}+(x-b)^{2/3}}{\sqrt[6]{d} \sqrt[3]{a-x} \sqrt[3]{x-b}}\right)}{4 d^{5/6} (a-b)}\right)}{2 \sqrt[3]{(x-a) (b-x)^2} \left(a^2 (-d)+2 a d x+b^2-2 b x-(d-1) x^2\right)}",1,"(-3*(-b + x)*(Hypergeometric2F1[1/3, 1, 4/3, (b - x)/(Sqrt[d]*(-a + x))] + Hypergeometric2F1[1/3, 1, 4/3, (-b + x)/(Sqrt[d]*(-a + x))]))/(2*(a - b)*d*((b - x)^2*(-a + x))^(1/3))","C",1
3068,0,0,482,0.2945238,"\int \frac{b-a x^4+2 x^8}{\sqrt[4]{b+a x^4} \left(-b-2 a x^4+x^8\right)} \, dx","Integrate[(b - a*x^4 + 2*x^8)/((b + a*x^4)^(1/4)*(-b - 2*a*x^4 + x^8)),x]","\int \frac{b-a x^4+2 x^8}{\sqrt[4]{b+a x^4} \left(-b-2 a x^4+x^8\right)} \, dx","\frac{3 \left(1+\sqrt[4]{-1}\right) \tan ^{-1}\left(\frac{(-1)^{7/8} \sqrt{2+\sqrt{2}} x \sqrt[8]{a^2+b} \sqrt[4]{a x^4+b}}{(-1)^{3/4} x^2 \sqrt[4]{a^2+b}+\sqrt{a x^4+b}}\right)}{8 \sqrt[8]{a^2+b}}-\frac{3 i \left(\sqrt{2 \left(3-2 \sqrt{2}\right)}-i \sqrt{2}\right) \tan ^{-1}\left(\frac{(-1)^{7/8} \left(\sqrt{2}-2\right) x \sqrt[8]{a^2+b} \sqrt[4]{a x^4+b}}{(-1)^{3/4} \sqrt{2-\sqrt{2}} x^2 \sqrt[4]{a^2+b}+\sqrt{2-\sqrt{2}} \sqrt{a x^4+b}}\right)}{16 \sqrt[8]{a^2+b}}+\frac{3 \left(\sqrt{2}+i \sqrt{2 \left(3-2 \sqrt{2}\right)}\right) \tanh ^{-1}\left(\frac{(-1)^{7/8} x^2 \sqrt[4]{a^2+b}-\sqrt[8]{-1} \sqrt{a x^4+b}}{\sqrt{2-\sqrt{2}} x \sqrt[8]{a^2+b} \sqrt[4]{a x^4+b}}\right)}{16 \sqrt[8]{a^2+b}}+\frac{3 \left(1+\sqrt[4]{-1}\right) \tanh ^{-1}\left(\frac{(-1)^{7/8} x^2 \sqrt[4]{a^2+b}-\sqrt[8]{-1} \sqrt{a x^4+b}}{\sqrt{2+\sqrt{2}} x \sqrt[8]{a^2+b} \sqrt[4]{a x^4+b}}\right)}{8 \sqrt[8]{a^2+b}}+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{a}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{\sqrt[4]{a}}",1,"Integrate[(b - a*x^4 + 2*x^8)/((b + a*x^4)^(1/4)*(-b - 2*a*x^4 + x^8)), x]","F",-1
3069,1,536,495,3.3243505,"\int \frac{\sqrt{-b+a^2 x^2}}{\sqrt{c+\sqrt{a x+\sqrt{-b+a^2 x^2}}}} \, dx","Integrate[Sqrt[-b + a^2*x^2]/Sqrt[c + Sqrt[a*x + Sqrt[-b + a^2*x^2]]],x]","\frac{\left(2 a x \left(\sqrt{a^2 x^2-b}+a x\right)-2 b\right) \left(\sqrt{\sqrt{a^2 x^2-b}+a x}+c\right)^{3/2} \left(\frac{\sqrt{c} \left(35 b^2 \left(56 c^2 \sqrt{\sqrt{a^2 x^2-b}+a x}-70 c \left(\sqrt{a^2 x^2-b}+a x\right)+105 \left(\sqrt{a^2 x^2-b}+a x\right)^{3/2}-48 c^3\right)+1536 a c^4 x \left(\sqrt{a^2 x^2-b}+a x\right) \left(4 c^2 \sqrt{\sqrt{a^2 x^2-b}+a x}+5 a x \sqrt{\sqrt{a^2 x^2-b}+a x}-6 a c x-8 c^3\right)-384 b c^4 \left(8 c^2 \sqrt{\sqrt{a^2 x^2-b}+a x}-6 c \left(\sqrt{a^2 x^2-b}+3 a x\right)+5 \sqrt{\sqrt{a^2 x^2-b}+a x} \left(\sqrt{a^2 x^2-b}+3 a x\right)-16 c^3\right)\right)}{\left(\sqrt{\sqrt{a^2 x^2-b}+a x}+c\right)^7}-\frac{105 b \left(35 b-256 c^4\right) \left(\sqrt{a^2 x^2-b}+a x\right)^2 \tanh ^{-1}\left(\frac{\sqrt{c}}{\sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+c}}\right)}{\left(\sqrt{\sqrt{a^2 x^2-b}+a x}+c\right)^{15/2}}\right)}{13440 a c^{9/2} \sqrt{4 a^2 x^2-4 b} \left(\frac{c}{\sqrt{\sqrt{a^2 x^2-b}+a x}+c}-1\right)^6}","-\frac{35 b^2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+c}}{\sqrt{c}}\right)}{128 a c^{9/2}}+\frac{2 b \tanh ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+c}}{\sqrt{c}}\right)}{a \sqrt{c}}+\frac{\sqrt{a^2 x^2-b} \left(\left(-9216 a^2 c^5 x^2-12288 a c^7 x-2450 b^2 c+2304 b c^5\right) \sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+c}+\sqrt{\sqrt{a^2 x^2-b}+a x} \sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+c} \left(7680 a^2 c^4 x^2+6144 a c^6 x+3675 b^2-1920 b c^4\right)\right)+\left(-9216 a^3 c^5 x^3-12288 a^2 c^7 x^2-2450 a b^2 c x+6912 a b c^5 x-1680 b^2 c^3+6144 b c^7\right) \sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+c}+\sqrt{\sqrt{a^2 x^2-b}+a x} \sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+c} \left(7680 a^3 c^4 x^3+6144 a^2 c^6 x^2+3675 a b^2 x-5760 a b c^4 x+1960 b^2 c^2-3072 b c^6\right)}{13440 a c^4 \left(2 a^2 x^2-b\right)+26880 a^2 c^4 x \sqrt{a^2 x^2-b}}",1,"((c + Sqrt[a*x + Sqrt[-b + a^2*x^2]])^(3/2)*(-2*b + 2*a*x*(a*x + Sqrt[-b + a^2*x^2]))*((Sqrt[c]*(1536*a*c^4*x*(a*x + Sqrt[-b + a^2*x^2])*(-8*c^3 - 6*a*c*x + 4*c^2*Sqrt[a*x + Sqrt[-b + a^2*x^2]] + 5*a*x*Sqrt[a*x + Sqrt[-b + a^2*x^2]]) + 35*b^2*(-48*c^3 + 56*c^2*Sqrt[a*x + Sqrt[-b + a^2*x^2]] - 70*c*(a*x + Sqrt[-b + a^2*x^2]) + 105*(a*x + Sqrt[-b + a^2*x^2])^(3/2)) - 384*b*c^4*(-16*c^3 + 8*c^2*Sqrt[a*x + Sqrt[-b + a^2*x^2]] - 6*c*(3*a*x + Sqrt[-b + a^2*x^2]) + 5*Sqrt[a*x + Sqrt[-b + a^2*x^2]]*(3*a*x + Sqrt[-b + a^2*x^2]))))/(c + Sqrt[a*x + Sqrt[-b + a^2*x^2]])^7 - (105*b*(35*b - 256*c^4)*(a*x + Sqrt[-b + a^2*x^2])^2*ArcTanh[Sqrt[c]/Sqrt[c + Sqrt[a*x + Sqrt[-b + a^2*x^2]]]])/(c + Sqrt[a*x + Sqrt[-b + a^2*x^2]])^(15/2)))/(13440*a*c^(9/2)*Sqrt[-4*b + 4*a^2*x^2]*(-1 + c/(c + Sqrt[a*x + Sqrt[-b + a^2*x^2]]))^6)","A",1
3070,0,0,496,0.7146401,"\int \frac{1+x}{\sqrt[3]{27+189 x+522 x^2+784 x^3+825 x^4+679 x^5+338 x^6+84 x^7+8 x^8}} \, dx","Integrate[(1 + x)/(27 + 189*x + 522*x^2 + 784*x^3 + 825*x^4 + 679*x^5 + 338*x^6 + 84*x^7 + 8*x^8)^(1/3),x]","\int \frac{1+x}{\sqrt[3]{27+189 x+522 x^2+784 x^3+825 x^4+679 x^5+338 x^6+84 x^7+8 x^8}} \, dx","-\frac{\log \left(2 x^2+7 x+3\right)}{5 \sqrt[3]{10}}+\frac{\log \left(4 x^4+28 x^3+61 x^2+42 x+9\right)}{10 \sqrt[3]{10}}+\frac{\log \left(2 \sqrt[3]{10} x^3+3 \sqrt[3]{10} x^2+5 \sqrt[3]{8 x^8+84 x^7+338 x^6+679 x^5+825 x^4+784 x^3+522 x^2+189 x+27}-11 \sqrt[3]{10} x-6 \sqrt[3]{10}\right)}{5 \sqrt[3]{10}}-\frac{\log \left(4\ 10^{2/3} x^6+12\ 10^{2/3} x^5-35\ 10^{2/3} x^4-90\ 10^{2/3} x^3+85\ 10^{2/3} x^2+25 \left(8 x^8+84 x^7+338 x^6+679 x^5+825 x^4+784 x^3+522 x^2+189 x+27\right)^{2/3}+\left(-10 \sqrt[3]{10} x^3-15 \sqrt[3]{10} x^2+55 \sqrt[3]{10} x+30 \sqrt[3]{10}\right) \sqrt[3]{8 x^8+84 x^7+338 x^6+679 x^5+825 x^4+784 x^3+522 x^2+189 x+27}+132\ 10^{2/3} x+36\ 10^{2/3}\right)}{10 \sqrt[3]{10}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{5 \sqrt{3} \sqrt[3]{8 x^8+84 x^7+338 x^6+679 x^5+825 x^4+784 x^3+522 x^2+189 x+27}}{-4 \sqrt[3]{10} x^3-6 \sqrt[3]{10} x^2+5 \sqrt[3]{8 x^8+84 x^7+338 x^6+679 x^5+825 x^4+784 x^3+522 x^2+189 x+27}+22 \sqrt[3]{10} x+12 \sqrt[3]{10}}\right)}{5 \sqrt[3]{10}}",1,"Integrate[(1 + x)/(27 + 189*x + 522*x^2 + 784*x^3 + 825*x^4 + 679*x^5 + 338*x^6 + 84*x^7 + 8*x^8)^(1/3), x]","F",-1
3071,1,78,497,0.4745463,"\int \frac{-1+k^2 x^4}{\sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)} \left(1+k^2 x^4\right)} \, dx","Integrate[(-1 + k^2*x^4)/(Sqrt[(1 - x^2)*(1 - k^2*x^2)]*(1 + k^2*x^4)),x]","\frac{\sqrt{1-x^2} \sqrt{1-k^2 x^2} \left(F\left(\sin ^{-1}(x)|k^2\right)-\Pi \left(-i k;\sin ^{-1}(x)|k^2\right)-\Pi \left(i k;\sin ^{-1}(x)|k^2\right)\right)}{\sqrt{\left(x^2-1\right) \left(k^2 x^2-1\right)}}","\frac{i \left(i \sqrt{k^2+2 i \sqrt{2} \sqrt{k^2+1} \sqrt{k}-2 k+1} k^2+\sqrt{2} \sqrt{k^2+1} \sqrt{k^2+2 i \sqrt{2} \sqrt{k^2+1} \sqrt{k}-2 k+1} \sqrt{k}+i \sqrt{k^2+2 i \sqrt{2} \sqrt{k^2+1} \sqrt{k}-2 k+1}\right) \tan ^{-1}\left(\frac{\sqrt{k^2+2 i \sqrt{2} \sqrt{k^2+1} \sqrt{k}-2 k+1} x}{\sqrt{k^2 x^4+\left(-k^2-1\right) x^2+1}+k x^2+1}\right)}{\left(\sqrt{k}-i\right)^2 \left(\sqrt{k}+i\right)^2 (k-i) (k+i)}-\frac{i \left(-i \sqrt{k^2-2 i \sqrt{2} \sqrt{k^2+1} \sqrt{k}-2 k+1} k^2+\sqrt{2} \sqrt{k^2+1} \sqrt{k^2-2 i \sqrt{2} \sqrt{k^2+1} \sqrt{k}-2 k+1} \sqrt{k}-i \sqrt{k^2-2 i \sqrt{2} \sqrt{k^2+1} \sqrt{k}-2 k+1}\right) \tan ^{-1}\left(\frac{\sqrt{k^2-2 i \sqrt{2} \sqrt{k^2+1} \sqrt{k}-2 k+1} x}{\sqrt{k^2 x^4+\left(-k^2-1\right) x^2+1}+k x^2+1}\right)}{\left(\sqrt{k}-i\right)^2 \left(\sqrt{k}+i\right)^2 (k-i) (k+i)}",1,"(Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*(EllipticF[ArcSin[x], k^2] - EllipticPi[(-I)*k, ArcSin[x], k^2] - EllipticPi[I*k, ArcSin[x], k^2]))/Sqrt[(-1 + x^2)*(-1 + k^2*x^2)]","C",1
3072,1,151,499,0.1748404,"\int \frac{1+2 x}{\sqrt[3]{-1+x^2} \left(3+x^2\right)} \, dx","Integrate[(1 + 2*x)/((-1 + x^2)^(1/3)*(3 + x^2)),x]","\frac{x \left(x \sqrt[3]{1-x^2} F_1\left(1;\frac{1}{3},1;2;x^2,-\frac{x^2}{3}\right)-\frac{27 F_1\left(\frac{1}{2};\frac{1}{3},1;\frac{3}{2};x^2,-\frac{x^2}{3}\right)}{\left(x^2+3\right) \left(2 x^2 \left(F_1\left(\frac{3}{2};\frac{1}{3},2;\frac{5}{2};x^2,-\frac{x^2}{3}\right)-F_1\left(\frac{3}{2};\frac{4}{3},1;\frac{5}{2};x^2,-\frac{x^2}{3}\right)\right)-9 F_1\left(\frac{1}{2};\frac{1}{3},1;\frac{3}{2};x^2,-\frac{x^2}{3}\right)\right)}\right)}{3 \sqrt[3]{x^2-1}}","\frac{(-1)^{2/3} \sqrt[3]{-54+35 i \sqrt{3}} \log \left(6 \sqrt[3]{x^2-1}-i 2^{2/3} \sqrt{3} x+3\ 2^{2/3}\right)}{6\ 6^{2/3}}-\frac{\sqrt[3]{-1} \sqrt[3]{-54-35 i \sqrt{3}} \log \left(6 \sqrt[3]{x^2-1}+i 2^{2/3} \sqrt{3} x+3\ 2^{2/3}\right)}{6\ 6^{2/3}}+\frac{\sqrt[3]{54+35 i \sqrt{3}} \log \left(-\sqrt[3]{2} x^2-i 2^{2/3} \sqrt{3} \sqrt[3]{x^2-1} x+6 \left(x^2-1\right)^{2/3}-3\ 2^{2/3} \sqrt[3]{x^2-1}+2 i \sqrt[3]{2} \sqrt{3} x+3 \sqrt[3]{2}\right)}{12\ 6^{2/3}}+\frac{\sqrt[3]{54-35 i \sqrt{3}} \log \left(-\sqrt[3]{2} x^2+i 2^{2/3} \sqrt{3} \sqrt[3]{x^2-1} x+6 \left(x^2-1\right)^{2/3}-3\ 2^{2/3} \sqrt[3]{x^2-1}-2 i \sqrt[3]{2} \sqrt{3} x+3 \sqrt[3]{2}\right)}{12\ 6^{2/3}}-\frac{\sqrt[6]{-253+1260 i \sqrt{3}} \tan ^{-1}\left(\frac{3 \sqrt[3]{x^2-1}}{\sqrt{3} \sqrt[3]{x^2-1}-i 2^{2/3} x-2^{2/3} \sqrt{3}}\right)}{6\ 2^{2/3}}-\frac{\sqrt[6]{-253-1260 i \sqrt{3}} \tan ^{-1}\left(\frac{3 \sqrt[3]{x^2-1}}{\sqrt{3} \sqrt[3]{x^2-1}+i 2^{2/3} x-2^{2/3} \sqrt{3}}\right)}{6\ 2^{2/3}}",1,"(x*(x*(1 - x^2)^(1/3)*AppellF1[1, 1/3, 1, 2, x^2, -1/3*x^2] - (27*AppellF1[1/2, 1/3, 1, 3/2, x^2, -1/3*x^2])/((3 + x^2)*(-9*AppellF1[1/2, 1/3, 1, 3/2, x^2, -1/3*x^2] + 2*x^2*(AppellF1[3/2, 1/3, 2, 5/2, x^2, -1/3*x^2] - AppellF1[3/2, 4/3, 1, 5/2, x^2, -1/3*x^2])))))/(3*(-1 + x^2)^(1/3))","C",0
3073,1,467,501,1.4045074,"\int \frac{x}{\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}} \, dx","Integrate[x/Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]],x]","\frac{32 \sqrt{1-\sqrt{\frac{x-1}{x}}} x^2+32 \sqrt{1-\sqrt{\frac{x-1}{x}}} \sqrt{\frac{x-1}{x}} x^2+384 x^2+114 \sqrt{1-\sqrt{\frac{x-1}{x}}} x+106 \sqrt{1-\sqrt{\frac{x-1}{x}}} \sqrt{\frac{x-1}{x}} x+4 \sqrt{\frac{x-1}{x}} x+52 x-177 \sqrt{1-\sqrt{1-\sqrt{\frac{x-1}{x}}}} \log \left(1-\frac{1}{\sqrt{1-\sqrt{1-\sqrt{\frac{x-1}{x}}}}}\right)+177 \sqrt{1-\sqrt{1-\sqrt{\frac{x-1}{x}}}} \log \left(\frac{1}{\sqrt{1-\sqrt{1-\sqrt{\frac{x-1}{x}}}}}+1\right)+6 \sqrt{\sqrt{2}-1} \left(41+30 \sqrt{2}\right) \sqrt{1-\sqrt{1-\sqrt{\frac{x-1}{x}}}} \tan ^{-1}\left(\frac{1}{\sqrt{1+\sqrt{2}} \sqrt{1-\sqrt{1-\sqrt{\frac{x-1}{x}}}}}\right)+6 \sqrt{1+\sqrt{2}} \left(30 \sqrt{2}-41\right) \sqrt{1-\sqrt{1-\sqrt{\frac{x-1}{x}}}} \tanh ^{-1}\left(\frac{1}{\sqrt{\sqrt{2}-1} \sqrt{1-\sqrt{1-\sqrt{\frac{x-1}{x}}}}}\right)-582}{768 \sqrt{1-\sqrt{1-\sqrt{\frac{x-1}{x}}}}}","\frac{-291 \left(1-\sqrt{1-\sqrt{1-\frac{1}{x}}}\right)^{15/2}+2275 \left(1-\sqrt{1-\sqrt{1-\frac{1}{x}}}\right)^{13/2}-6611 \left(1-\sqrt{1-\sqrt{1-\frac{1}{x}}}\right)^{11/2}+8403 \left(1-\sqrt{1-\sqrt{1-\frac{1}{x}}}\right)^{9/2}-3301 \left(1-\sqrt{1-\sqrt{1-\frac{1}{x}}}\right)^{7/2}-2139 \left(1-\sqrt{1-\sqrt{1-\frac{1}{x}}}\right)^{5/2}+1787 \left(1-\sqrt{1-\sqrt{1-\frac{1}{x}}}\right)^{3/2}+69 \sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}}{384 \left(\left(1-\sqrt{1-\sqrt{1-\frac{1}{x}}}\right)^2-2 \left(1-\sqrt{1-\sqrt{1-\frac{1}{x}}}\right)-1\right)^2 \left(1-\sqrt{1-\frac{1}{x}}\right)^2}+\left(-\frac{19}{64} \sqrt{\frac{1}{2} \left(\frac{1}{2}+\frac{1}{\sqrt{2}}\right)}-\frac{11}{64} \sqrt{\frac{1}{2}+\frac{1}{\sqrt{2}}}\right) \tan ^{-1}\left(\frac{\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}}{\sqrt{\sqrt{2}-1}}\right)+\frac{59}{128} \tanh ^{-1}\left(\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}\right)+\left(\frac{19}{64} \sqrt{\frac{1}{2} \left(\frac{1}{\sqrt{2}}-\frac{1}{2}\right)}-\frac{11}{64} \sqrt{\frac{1}{\sqrt{2}}-\frac{1}{2}}\right) \tanh ^{-1}\left(\frac{\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}}{\sqrt{1+\sqrt{2}}}\right)",1,"(-582 + 52*x + 114*Sqrt[1 - Sqrt[(-1 + x)/x]]*x + 4*Sqrt[(-1 + x)/x]*x + 106*Sqrt[1 - Sqrt[(-1 + x)/x]]*Sqrt[(-1 + x)/x]*x + 384*x^2 + 32*Sqrt[1 - Sqrt[(-1 + x)/x]]*x^2 + 32*Sqrt[1 - Sqrt[(-1 + x)/x]]*Sqrt[(-1 + x)/x]*x^2 + 6*Sqrt[-1 + Sqrt[2]]*(41 + 30*Sqrt[2])*Sqrt[1 - Sqrt[1 - Sqrt[(-1 + x)/x]]]*ArcTan[1/(Sqrt[1 + Sqrt[2]]*Sqrt[1 - Sqrt[1 - Sqrt[(-1 + x)/x]]])] + 6*Sqrt[1 + Sqrt[2]]*(-41 + 30*Sqrt[2])*Sqrt[1 - Sqrt[1 - Sqrt[(-1 + x)/x]]]*ArcTanh[1/(Sqrt[-1 + Sqrt[2]]*Sqrt[1 - Sqrt[1 - Sqrt[(-1 + x)/x]]])] - 177*Sqrt[1 - Sqrt[1 - Sqrt[(-1 + x)/x]]]*Log[1 - 1/Sqrt[1 - Sqrt[1 - Sqrt[(-1 + x)/x]]]] + 177*Sqrt[1 - Sqrt[1 - Sqrt[(-1 + x)/x]]]*Log[1 + 1/Sqrt[1 - Sqrt[1 - Sqrt[(-1 + x)/x]]]])/(768*Sqrt[1 - Sqrt[1 - Sqrt[(-1 + x)/x]]])","A",0
3074,1,69,501,0.1059652,"\int \frac{\sqrt[4]{-x^2+x^6} \left(1-x^4+x^8\right)}{x^4 \left(1+x^4\right)} \, dx","Integrate[((-x^2 + x^6)^(1/4)*(1 - x^4 + x^8))/(x^4*(1 + x^4)),x]","\frac{2 \sqrt[4]{x^2 \left(x^4-1\right)} \left(-5 x^4 F_1\left(\frac{3}{8};-\frac{1}{4},1;\frac{11}{8};x^4,-x^4\right)-\left(1-x^4\right)^{5/4}\right)}{5 x^3 \sqrt[4]{1-x^4}}","-\frac{3}{8} \sqrt{\frac{1}{2} \left(\sqrt{2}-1\right)} \log \left(-2 x^2+2^{3/4} \sqrt{2+\sqrt{2}} \sqrt[4]{x^6-x^2} x-\sqrt{2} \sqrt{x^6-x^2}\right)+\frac{3}{8} \sqrt{\frac{1}{2} \left(\sqrt{2}-1\right)} \log \left(2 \sqrt{2-\sqrt{2}} x^2+2 \sqrt[4]{2} \sqrt[4]{x^6-x^2} x+\sqrt{4-2 \sqrt{2}} \sqrt{x^6-x^2}\right)+\frac{3}{4} \sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}} x}{2^{3/4} \sqrt[4]{x^6-x^2}-\sqrt{2+\sqrt{2}} x}\right)+\frac{3}{4} \sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}} x}{2^{3/4} \sqrt[4]{x^6-x^2}+\sqrt{2+\sqrt{2}} x}\right)-\frac{3}{4} \sqrt{\frac{1}{2} \left(\sqrt{2}-1\right)} \tan ^{-1}\left(\frac{2^{3/4} \sqrt{2+\sqrt{2}} x \sqrt[4]{x^6-x^2}}{\sqrt{2} \sqrt{x^6-x^2}-2 x^2}\right)-\frac{3}{4} \sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tanh ^{-1}\left(\frac{\frac{\sqrt[4]{2} x^2}{\sqrt{2-\sqrt{2}}}+\frac{\sqrt{x^6-x^2}}{\sqrt[4]{2} \sqrt{2-\sqrt{2}}}}{x \sqrt[4]{x^6-x^2}}\right)+\frac{2 \sqrt[4]{x^6-x^2} \left(x^4-1\right)}{5 x^3}",1,"(2*(x^2*(-1 + x^4))^(1/4)*(-(1 - x^4)^(5/4) - 5*x^4*AppellF1[3/8, -1/4, 1, 11/8, x^4, -x^4]))/(5*x^3*(1 - x^4)^(1/4))","C",0
3075,1,69,501,0.0627838,"\int \frac{\sqrt[4]{-x^2+x^6} \left(1-x^4+x^8\right)}{x^4 \left(1+x^4\right)} \, dx","Integrate[((-x^2 + x^6)^(1/4)*(1 - x^4 + x^8))/(x^4*(1 + x^4)),x]","\frac{2 \sqrt[4]{x^2 \left(x^4-1\right)} \left(-5 x^4 F_1\left(\frac{3}{8};-\frac{1}{4},1;\frac{11}{8};x^4,-x^4\right)-\left(1-x^4\right)^{5/4}\right)}{5 x^3 \sqrt[4]{1-x^4}}","-\frac{3}{8} \sqrt{\frac{1}{2} \left(\sqrt{2}-1\right)} \log \left(-2 x^2+2^{3/4} \sqrt{2+\sqrt{2}} \sqrt[4]{x^6-x^2} x-\sqrt{2} \sqrt{x^6-x^2}\right)+\frac{3}{8} \sqrt{\frac{1}{2} \left(\sqrt{2}-1\right)} \log \left(2 \sqrt{2-\sqrt{2}} x^2+2 \sqrt[4]{2} \sqrt[4]{x^6-x^2} x+\sqrt{4-2 \sqrt{2}} \sqrt{x^6-x^2}\right)+\frac{3}{4} \sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}} x}{2^{3/4} \sqrt[4]{x^6-x^2}-\sqrt{2+\sqrt{2}} x}\right)+\frac{3}{4} \sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}} x}{2^{3/4} \sqrt[4]{x^6-x^2}+\sqrt{2+\sqrt{2}} x}\right)-\frac{3}{4} \sqrt{\frac{1}{2} \left(\sqrt{2}-1\right)} \tan ^{-1}\left(\frac{2^{3/4} \sqrt{2+\sqrt{2}} x \sqrt[4]{x^6-x^2}}{\sqrt{2} \sqrt{x^6-x^2}-2 x^2}\right)-\frac{3}{4} \sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tanh ^{-1}\left(\frac{\frac{\sqrt[4]{2} x^2}{\sqrt{2-\sqrt{2}}}+\frac{\sqrt{x^6-x^2}}{\sqrt[4]{2} \sqrt{2-\sqrt{2}}}}{x \sqrt[4]{x^6-x^2}}\right)+\frac{2 \sqrt[4]{x^6-x^2} \left(x^4-1\right)}{5 x^3}",1,"(2*(x^2*(-1 + x^4))^(1/4)*(-(1 - x^4)^(5/4) - 5*x^4*AppellF1[3/8, -1/4, 1, 11/8, x^4, -x^4]))/(5*x^3*(1 - x^4)^(1/4))","C",0
3076,1,69,501,0.0697533,"\int \frac{\sqrt[4]{-x^2+x^6} \left(1+x^4+x^8\right)}{x^4 \left(1+x^4\right)} \, dx","Integrate[((-x^2 + x^6)^(1/4)*(1 + x^4 + x^8))/(x^4*(1 + x^4)),x]","\frac{2 \sqrt[4]{x^2 \left(x^4-1\right)} \left(-5 x^4 F_1\left(\frac{3}{8};-\frac{1}{4},1;\frac{11}{8};x^4,-x^4\right)-3 \left(1-x^4\right)^{5/4}\right)}{15 x^3 \sqrt[4]{1-x^4}}","-\frac{1}{8} \sqrt{\frac{1}{2} \left(\sqrt{2}-1\right)} \log \left(-2 x^2+2^{3/4} \sqrt{2+\sqrt{2}} \sqrt[4]{x^6-x^2} x-\sqrt{2} \sqrt{x^6-x^2}\right)+\frac{1}{8} \sqrt{\frac{1}{2} \left(\sqrt{2}-1\right)} \log \left(2 \sqrt{2-\sqrt{2}} x^2+2 \sqrt[4]{2} \sqrt[4]{x^6-x^2} x+\sqrt{4-2 \sqrt{2}} \sqrt{x^6-x^2}\right)+\frac{1}{4} \sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}} x}{2^{3/4} \sqrt[4]{x^6-x^2}-\sqrt{2+\sqrt{2}} x}\right)+\frac{1}{4} \sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}} x}{2^{3/4} \sqrt[4]{x^6-x^2}+\sqrt{2+\sqrt{2}} x}\right)-\frac{1}{4} \sqrt{\frac{1}{2} \left(\sqrt{2}-1\right)} \tan ^{-1}\left(\frac{2^{3/4} \sqrt{2+\sqrt{2}} x \sqrt[4]{x^6-x^2}}{\sqrt{2} \sqrt{x^6-x^2}-2 x^2}\right)-\frac{1}{4} \sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tanh ^{-1}\left(\frac{\frac{\sqrt[4]{2} x^2}{\sqrt{2-\sqrt{2}}}+\frac{\sqrt{x^6-x^2}}{\sqrt[4]{2} \sqrt{2-\sqrt{2}}}}{x \sqrt[4]{x^6-x^2}}\right)+\frac{2 \sqrt[4]{x^6-x^2} \left(x^4-1\right)}{5 x^3}",1,"(2*(x^2*(-1 + x^4))^(1/4)*(-3*(1 - x^4)^(5/4) - 5*x^4*AppellF1[3/8, -1/4, 1, 11/8, x^4, -x^4]))/(15*x^3*(1 - x^4)^(1/4))","C",0
3077,1,69,501,0.0341617,"\int \frac{\sqrt[4]{-x^2+x^6} \left(1+x^4+x^8\right)}{x^4 \left(1+x^4\right)} \, dx","Integrate[((-x^2 + x^6)^(1/4)*(1 + x^4 + x^8))/(x^4*(1 + x^4)),x]","\frac{2 \sqrt[4]{x^2 \left(x^4-1\right)} \left(-5 x^4 F_1\left(\frac{3}{8};-\frac{1}{4},1;\frac{11}{8};x^4,-x^4\right)-3 \left(1-x^4\right)^{5/4}\right)}{15 x^3 \sqrt[4]{1-x^4}}","-\frac{1}{8} \sqrt{\frac{1}{2} \left(\sqrt{2}-1\right)} \log \left(-2 x^2+2^{3/4} \sqrt{2+\sqrt{2}} \sqrt[4]{x^6-x^2} x-\sqrt{2} \sqrt{x^6-x^2}\right)+\frac{1}{8} \sqrt{\frac{1}{2} \left(\sqrt{2}-1\right)} \log \left(2 \sqrt{2-\sqrt{2}} x^2+2 \sqrt[4]{2} \sqrt[4]{x^6-x^2} x+\sqrt{4-2 \sqrt{2}} \sqrt{x^6-x^2}\right)+\frac{1}{4} \sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}} x}{2^{3/4} \sqrt[4]{x^6-x^2}-\sqrt{2+\sqrt{2}} x}\right)+\frac{1}{4} \sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}} x}{2^{3/4} \sqrt[4]{x^6-x^2}+\sqrt{2+\sqrt{2}} x}\right)-\frac{1}{4} \sqrt{\frac{1}{2} \left(\sqrt{2}-1\right)} \tan ^{-1}\left(\frac{2^{3/4} \sqrt{2+\sqrt{2}} x \sqrt[4]{x^6-x^2}}{\sqrt{2} \sqrt{x^6-x^2}-2 x^2}\right)-\frac{1}{4} \sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tanh ^{-1}\left(\frac{\frac{\sqrt[4]{2} x^2}{\sqrt{2-\sqrt{2}}}+\frac{\sqrt{x^6-x^2}}{\sqrt[4]{2} \sqrt{2-\sqrt{2}}}}{x \sqrt[4]{x^6-x^2}}\right)+\frac{2 \sqrt[4]{x^6-x^2} \left(x^4-1\right)}{5 x^3}",1,"(2*(x^2*(-1 + x^4))^(1/4)*(-3*(1 - x^4)^(5/4) - 5*x^4*AppellF1[3/8, -1/4, 1, 11/8, x^4, -x^4]))/(15*x^3*(1 - x^4)^(1/4))","C",0
3078,1,158,506,0.1392038,"\int \frac{\sqrt[3]{b^2 x^2+a^3 x^3}}{-b+a x} \, dx","Integrate[(b^2*x^2 + a^3*x^3)^(1/3)/(-b + a*x),x]","\frac{3 x^2 \left(\left(a^3 b x+b^3\right) \, _2F_1\left(-\frac{1}{3},\frac{2}{3};\frac{5}{3};-\frac{a^3 x}{b^2}\right)+a^2 \left(a^3 x+b^2\right) \, _2F_1\left(\frac{2}{3},\frac{2}{3};\frac{5}{3};-\frac{a^3 x}{b^2}\right)-b^2 \left(a^2+b\right) \sqrt[3]{\frac{a^3 x}{b^2}+1} \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{a \left(a^2+b\right) x}{x a^3+b^2}\right)\right)}{2 a b \left(x^2 \left(a^3 x+b^2\right)\right)^{2/3} \sqrt[3]{\frac{a^3 x}{b^2}+1}}","\frac{\sqrt[3]{a^3 x^3+b^2 x^2}}{a}+\frac{\left(-3 a^2 b-b^2\right) \log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-a x\right)}{3 a^3}+\frac{\left(3 a^2 b+b^2\right) \log \left(a x \sqrt[3]{a^3 x^3+b^2 x^2}+\left(a^3 x^3+b^2 x^2\right)^{2/3}+a^2 x^2\right)}{6 a^3}-\frac{\left(3 a^2 b+b^2\right) \tan ^{-1}\left(\frac{\sqrt{3} a x}{2 \sqrt[3]{a^3 x^3+b^2 x^2}+a x}\right)}{\sqrt{3} a^3}+\frac{i \left(\sqrt{3} b \sqrt[3]{a^2+b}+i b \sqrt[3]{a^2+b}\right) \log \left(\sqrt[3]{-1} \sqrt[3]{a^3 x^3+b^2 x^2}+\sqrt[3]{a} x \sqrt[3]{a^2+b}\right)}{2 a^{5/3}}+\frac{\left(b \sqrt[3]{a^2+b}-i \sqrt{3} b \sqrt[3]{a^2+b}\right) \log \left((-1)^{2/3} \left(a^3 x^3+b^2 x^2\right)^{2/3}+a^{2/3} x^2 \left(a^2+b\right)^{2/3}-\sqrt[3]{-1} \sqrt[3]{a} x \sqrt[3]{a^2+b} \sqrt[3]{a^3 x^3+b^2 x^2}\right)}{4 a^{5/3}}-\frac{\sqrt{-3-3 i \sqrt{3}} b \sqrt[3]{a^2+b} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{a} x \sqrt[3]{a^2+b}}{\sqrt[3]{a} x \sqrt[3]{a^2+b}-2 \sqrt[3]{-1} \sqrt[3]{a^3 x^3+b^2 x^2}}\right)}{\sqrt{2} a^{5/3}}",1,"(3*x^2*((b^3 + a^3*b*x)*Hypergeometric2F1[-1/3, 2/3, 5/3, -((a^3*x)/b^2)] + a^2*(b^2 + a^3*x)*Hypergeometric2F1[2/3, 2/3, 5/3, -((a^3*x)/b^2)] - b^2*(a^2 + b)*(1 + (a^3*x)/b^2)^(1/3)*Hypergeometric2F1[2/3, 1, 5/3, (a*(a^2 + b)*x)/(b^2 + a^3*x)]))/(2*a*b*(x^2*(b^2 + a^3*x))^(2/3)*(1 + (a^3*x)/b^2)^(1/3))","C",1
3079,0,0,507,20.9004872,"\int \frac{\sqrt{-b+a^2 x^2}}{\sqrt{a x+\sqrt{-b+a^2 x^2}} \sqrt{c+\sqrt{a x+\sqrt{-b+a^2 x^2}}}} \, dx","Integrate[Sqrt[-b + a^2*x^2]/(Sqrt[a*x + Sqrt[-b + a^2*x^2]]*Sqrt[c + Sqrt[a*x + Sqrt[-b + a^2*x^2]]]),x]","\int \frac{\sqrt{-b+a^2 x^2}}{\sqrt{a x+\sqrt{-b+a^2 x^2}} \sqrt{c+\sqrt{a x+\sqrt{-b+a^2 x^2}}}} \, dx","\frac{63 b^2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+c}}{\sqrt{c}}\right)}{256 a c^{11/2}}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+c}}{\sqrt{c}}\right)}{a c^{3/2}}+\frac{\sqrt{a^2 x^2-b} \left(\sqrt{\sqrt{a^2 x^2-b}+a x} \sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+c} \left(3072 a^2 c^5 x^2+4096 a c^7 x+630 b^2 c-768 b c^5\right)+\left(-4096 a^2 c^6 x^2-1890 a b^2 x+7680 a b c^4 x-504 b^2 c^2+1024 b c^6\right) \sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+c}\right)+\sqrt{\sqrt{a^2 x^2-b}+a x} \sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+c} \left(3072 a^3 c^5 x^3+4096 a^2 c^7 x^2+630 a b^2 c x-2304 a b c^5 x+432 b^2 c^3-2048 b c^7\right)+\left(-4096 a^3 c^6 x^3-1890 a^2 b^2 x^2+7680 a^2 b c^4 x^2-504 a b^2 c^2 x+3072 a b c^6 x+945 b^3-4224 b^2 c^4\right) \sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+c}}{3840 a c^5 \left(\sqrt{a^2 x^2-b}+a x\right)^{5/2}}",1,"Integrate[Sqrt[-b + a^2*x^2]/(Sqrt[a*x + Sqrt[-b + a^2*x^2]]*Sqrt[c + Sqrt[a*x + Sqrt[-b + a^2*x^2]]]), x]","F",-1
3080,0,0,514,1.8221471,"\int \frac{\left(-3+x^2\right) \left(1-2 x^2+x^4+x^6\right)}{x^{10} \sqrt[4]{\frac{-a+a x^2+b x^3}{-c+c x^2+d x^3}}} \, dx","Integrate[((-3 + x^2)*(1 - 2*x^2 + x^4 + x^6))/(x^10*((-a + a*x^2 + b*x^3)/(-c + c*x^2 + d*x^3))^(1/4)),x]","\int \frac{\left(-3+x^2\right) \left(1-2 x^2+x^4+x^6\right)}{x^{10} \sqrt[4]{\frac{-a+a x^2+b x^3}{-c+c x^2+d x^3}}} \, dx","\frac{\left(\frac{a x^2-a+b x^3}{c x^2-c+d x^3}\right)^{3/4} \left(-96 a^2 c^3 x^8+64 a^2 c^3 x^6+96 a^2 c^3 x^4-96 a^2 c^3 x^2+32 a^2 c^3-96 a^2 c^2 d x^9-36 a^2 c^2 d x^7+72 a^2 c^2 d x^5-36 a^2 c^2 d x^3+3 a^2 c d^2 x^8-3 a^2 c d^2 x^6+7 a^2 d^3 x^9+36 a b c^3 x^7-72 a b c^3 x^5+36 a b c^3 x^3+42 a b c^2 d x^8-42 a b c^2 d x^6+6 a b c d^2 x^9-45 b^2 c^3 x^8+45 b^2 c^3 x^6-45 b^2 c^2 d x^9\right)}{96 a^3 c^2 x^9}+\frac{\left(32 a^3 c^2 d+7 a^3 d^3-32 a^2 b c^3+3 a^2 b c d^2+5 a b^2 c^2 d-15 b^3 c^3\right) \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt[4]{\frac{a x^2-a+b x^3}{c x^2-c+d x^3}}}{\sqrt[4]{a}}\right)}{64 a^{13/4} c^{11/4}}+\frac{\left(-32 a^3 c^2 d-7 a^3 d^3+32 a^2 b c^3-3 a^2 b c d^2-5 a b^2 c^2 d+15 b^3 c^3\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt[4]{\frac{a x^2-a+b x^3}{c x^2-c+d x^3}}}{\sqrt[4]{a}}\right)}{64 a^{13/4} c^{11/4}}",1,"Integrate[((-3 + x^2)*(1 - 2*x^2 + x^4 + x^6))/(x^10*((-a + a*x^2 + b*x^3)/(-c + c*x^2 + d*x^3))^(1/4)), x]","F",-1
3081,0,0,514,4.7535879,"\int \frac{\left(1+x^4\right) \sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{1-x^4} \, dx","Integrate[((1 + x^4)*Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^4),x]","\int \frac{\left(1+x^4\right) \sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{1-x^4} \, dx","\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^2-1}\&\right]-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^5-3 \text{$\#$1}^3+2 \text{$\#$1}}\&\right]-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\text{$\#$1}^5 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+4 \text{$\#$1}^2-2}\&\right]+\frac{\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} (-6 x-16)+\sqrt{x^2+1} \left((8-60 x) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-6 \sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\left(-60 x^2+8 x+75\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{105 \sqrt{\sqrt{x^2+1}+x}}+\tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)",1,"Integrate[((1 + x^4)*Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^4), x]","F",-1
3082,0,0,514,0.3083356,"\int \frac{\left(1+x^4\right) \sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{1-x^4} \, dx","Integrate[((1 + x^4)*Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^4),x]","\int \frac{\left(1+x^4\right) \sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{1-x^4} \, dx","\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^2-1}\&\right]-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^5-3 \text{$\#$1}^3+2 \text{$\#$1}}\&\right]-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\text{$\#$1}^5 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+4 \text{$\#$1}^2-2}\&\right]+\frac{\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} (-6 x-16)+\sqrt{x^2+1} \left((8-60 x) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-6 \sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\left(-60 x^2+8 x+75\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{105 \sqrt{\sqrt{x^2+1}+x}}+\tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)",1,"Integrate[((1 + x^4)*Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^4), x]","F",-1
3083,1,392,515,1.2627555,"\int \sqrt{b+a^2 x^2} \sqrt{c+\sqrt{a x+\sqrt{b+a^2 x^2}}} \, dx","Integrate[Sqrt[b + a^2*x^2]*Sqrt[c + Sqrt[a*x + Sqrt[b + a^2*x^2]]],x]","\frac{\left(\left(\sqrt{a^2 x^2+b}+a x\right)^2+b\right) \left(\sqrt{c} \sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c} \left(-105 b^2 \left(8 c^2 \sqrt{\sqrt{a^2 x^2+b}+a x}-10 c \left(\sqrt{a^2 x^2+b}+a x\right)+15 \left(\sqrt{a^2 x^2+b}+a x\right)^{3/2}+48 c^3\right)+80640 b c^3 \left(\sqrt{a^2 x^2+b}+a x\right)^2-128 c^3 \left(\sqrt{a^2 x^2+b}+a x\right)^2 \left(\sqrt{\sqrt{a^2 x^2+b}+a x}+c\right) \left(-24 c^2 \sqrt{\sqrt{a^2 x^2+b}+a x}+30 c \left(\sqrt{a^2 x^2+b}+a x\right)-35 \left(\sqrt{a^2 x^2+b}+a x\right)^{3/2}+16 c^3\right)\right)+315 b \left(5 b-256 c^4\right) \left(\sqrt{a^2 x^2+b}+a x\right)^2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}}{\sqrt{c}}\right)\right)}{80640 a c^{7/2} \sqrt{a^2 x^2+b} \left(\sqrt{a^2 x^2+b}+a x\right)^3}","\frac{5 b^2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}}{\sqrt{c}}\right)}{128 a c^{7/2}}-\frac{2 b \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}}{\sqrt{c}}\right)}{a}+\frac{\sqrt{\sqrt{a^2 x^2+b}+a x} \sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c} \left(2560 a^3 c^4 x^3+2048 a^2 c^6 x^2-1575 a b^2 x+1920 a b c^4 x-840 b^2 c^2+1024 b c^6\right)+\sqrt{a^2 x^2+b} \left(\sqrt{\sqrt{a^2 x^2+b}+a x} \sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c} \left(2560 a^2 c^4 x^2+2048 a c^6 x-1575 b^2+640 b c^4\right)+\left(35840 a^3 c^3 x^3-3072 a^2 c^5 x^2+179200 a b c^3 x-4096 a c^7 x+1050 b^2 c-768 b c^5\right) \sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}\right)+\left(35840 a^4 c^3 x^4-3072 a^3 c^5 x^3+197120 a^2 b c^3 x^2-4096 a^2 c^7 x^2+1050 a b^2 c x-2304 a b c^5 x+80080 b^2 c^3-2048 b c^7\right) \sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}}{40320 a c^3 \left(2 a^2 x^2+b\right)+80640 a^2 c^3 x \sqrt{a^2 x^2+b}}",1,"((b + (a*x + Sqrt[b + a^2*x^2])^2)*(Sqrt[c]*Sqrt[c + Sqrt[a*x + Sqrt[b + a^2*x^2]]]*(80640*b*c^3*(a*x + Sqrt[b + a^2*x^2])^2 - 128*c^3*(a*x + Sqrt[b + a^2*x^2])^2*(c + Sqrt[a*x + Sqrt[b + a^2*x^2]])*(16*c^3 - 24*c^2*Sqrt[a*x + Sqrt[b + a^2*x^2]] + 30*c*(a*x + Sqrt[b + a^2*x^2]) - 35*(a*x + Sqrt[b + a^2*x^2])^(3/2)) - 105*b^2*(48*c^3 + 8*c^2*Sqrt[a*x + Sqrt[b + a^2*x^2]] - 10*c*(a*x + Sqrt[b + a^2*x^2]) + 15*(a*x + Sqrt[b + a^2*x^2])^(3/2))) + 315*b*(5*b - 256*c^4)*(a*x + Sqrt[b + a^2*x^2])^2*ArcTanh[Sqrt[c + Sqrt[a*x + Sqrt[b + a^2*x^2]]]/Sqrt[c]]))/(80640*a*c^(7/2)*Sqrt[b + a^2*x^2]*(a*x + Sqrt[b + a^2*x^2])^3)","A",1
3084,1,144,518,0.3956736,"\int \frac{\sqrt{\left(-81+27 x+135 x^2-150 x^3+65 x^4-13 x^5+x^6\right)^3}}{-1+x} \, dx","Integrate[Sqrt[(-81 + 27*x + 135*x^2 - 150*x^3 + 65*x^4 - 13*x^5 + x^6)^3]/(-1 + x),x]","\frac{(x-3)^6 \left(x^2-x-1\right)^{3/2} \left(-1321205760 \tan ^{-1}\left(\frac{3-x}{2 \sqrt{x^2-x-1}}\right)+6127079805 \tanh ^{-1}\left(\frac{1-2 x}{2 \sqrt{x^2-x-1}}\right)+2 \sqrt{x^2-x-1} \left(1146880 x^8-23296000 x^7+199009280 x^6-910869760 x^5+2304529024 x^4-2700564848 x^3-508033624 x^2+4423205098 x-1245336401\right)\right)}{20643840 \sqrt{(x-3)^{12} \left(x^2-x-1\right)^3}}","-\frac{19451047 \log \left(x^8-19 x^7+152 x^6-657 x^5+1620 x^4-2133 x^3+972 x^2+729 x-729\right)}{65536}+\frac{\sqrt{x^{18}-39 x^{17}+702 x^{16}-7717 x^{15}+57735 x^{14}-309774 x^{13}+1221371 x^{12}-3554163 x^{11}+7498953 x^{10}-10819710 x^9+8764767 x^8+592677 x^7-10219851 x^6+9880866 x^5-885735 x^4-4704237 x^3+2480058 x^2+531441 x-531441} \left(1146880 x^8-23296000 x^7+199009280 x^6-910869760 x^5+2304529024 x^4-2700564848 x^3-508033624 x^2+4423205098 x-1245336401\right)}{10321920 (x-3)^6 \left(x^2-x-1\right)}+\frac{19451047 \log \left(-2 x^9+39 x^8-323 x^7+1466 x^6-3897 x^5+5886 x^4-4077 x^3-486 x^2+2187 x+2 \sqrt{x^{18}-39 x^{17}+702 x^{16}-7717 x^{15}+57735 x^{14}-309774 x^{13}+1221371 x^{12}-3554163 x^{11}+7498953 x^{10}-10819710 x^9+8764767 x^8+592677 x^7-10219851 x^6+9880866 x^5-885735 x^4-4704237 x^3+2480058 x^2+531441 x-531441}-729\right)}{65536}+128 \tan ^{-1}\left(\frac{\left(x^2-x-1\right) \left(x^6-18 x^5+135 x^4-540 x^3+1215 x^2-1458 x+729\right)}{x^9-20 x^8+171 x^7-809 x^6+2277 x^5-3753 x^4+3105 x^3-243 x^2-1458 x-\sqrt{x^{18}-39 x^{17}+702 x^{16}-7717 x^{15}+57735 x^{14}-309774 x^{13}+1221371 x^{12}-3554163 x^{11}+7498953 x^{10}-10819710 x^9+8764767 x^8+592677 x^7-10219851 x^6+9880866 x^5-885735 x^4-4704237 x^3+2480058 x^2+531441 x-531441}+729}\right)",1,"((-3 + x)^6*(-1 - x + x^2)^(3/2)*(2*Sqrt[-1 - x + x^2]*(-1245336401 + 4423205098*x - 508033624*x^2 - 2700564848*x^3 + 2304529024*x^4 - 910869760*x^5 + 199009280*x^6 - 23296000*x^7 + 1146880*x^8) - 1321205760*ArcTan[(3 - x)/(2*Sqrt[-1 - x + x^2])] + 6127079805*ArcTanh[(1 - 2*x)/(2*Sqrt[-1 - x + x^2])]))/(20643840*Sqrt[(-3 + x)^12*(-1 - x + x^2)^3])","A",1
3085,0,0,520,2.1534469,"\int \frac{\left(1+x^2+x^4\right)^2 \sqrt{x^2+\sqrt{1+x^4}}}{\sqrt{1+x^4} \left(-1+x^2+x^4\right)^2} \, dx","Integrate[((1 + x^2 + x^4)^2*Sqrt[x^2 + Sqrt[1 + x^4]])/(Sqrt[1 + x^4]*(-1 + x^2 + x^4)^2),x]","\int \frac{\left(1+x^2+x^4\right)^2 \sqrt{x^2+\sqrt{1+x^4}}}{\sqrt{1+x^4} \left(-1+x^2+x^4\right)^2} \, dx","-\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^6-6 \text{$\#$1}^4+2 \text{$\#$1}^2+1\&,\frac{-3 \text{$\#$1}^6 \log \left(\sqrt{x^4+1}+x^2-1\right)+3 \text{$\#$1}^6 \log \left(\text{$\#$1} \sqrt{x^4+1}+\text{$\#$1} x^2-\text{$\#$1}+\sqrt{2} \sqrt{\sqrt{x^4+1}+x^2} x\right)-\text{$\#$1}^4 \log \left(\sqrt{x^4+1}+x^2-1\right)+\text{$\#$1}^4 \log \left(\text{$\#$1} \sqrt{x^4+1}+\text{$\#$1} x^2-\text{$\#$1}+\sqrt{2} \sqrt{\sqrt{x^4+1}+x^2} x\right)+7 \text{$\#$1}^2 \log \left(\sqrt{x^4+1}+x^2-1\right)-7 \text{$\#$1}^2 \log \left(\text{$\#$1} \sqrt{x^4+1}+\text{$\#$1} x^2-\text{$\#$1}+\sqrt{2} \sqrt{\sqrt{x^4+1}+x^2} x\right)-\log \left(\text{$\#$1} \sqrt{x^4+1}+\text{$\#$1} x^2-\text{$\#$1}+\sqrt{2} \sqrt{\sqrt{x^4+1}+x^2} x\right)+\log \left(\sqrt{x^4+1}+x^2-1\right)}{2 \text{$\#$1}^7-3 \text{$\#$1}^5-6 \text{$\#$1}^3+\text{$\#$1}}\&\right]}{5 \sqrt{2}}+\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)+\frac{-2 x \sqrt{x^4+1} \sqrt{\sqrt{x^4+1}+x^2} \left(2 x^4+3 x^2+2\right)-2 x \left(2 x^6+3 x^4+3 x^2+1\right) \sqrt{\sqrt{x^4+1}+x^2}}{10 \sqrt{x^4+1} \left(x^4+x^2-1\right) x^2+5 \left(x^4+x^2-1\right) \left(2 x^4+1\right)}",1,"Integrate[((1 + x^2 + x^4)^2*Sqrt[x^2 + Sqrt[1 + x^4]])/(Sqrt[1 + x^4]*(-1 + x^2 + x^4)^2), x]","F",-1
3086,0,0,520,1.510444,"\int \frac{\left(1+x^2+x^4\right)^2 \sqrt{x^2+\sqrt{1+x^4}}}{\sqrt{1+x^4} \left(-1+x^2+x^4\right)^2} \, dx","Integrate[((1 + x^2 + x^4)^2*Sqrt[x^2 + Sqrt[1 + x^4]])/(Sqrt[1 + x^4]*(-1 + x^2 + x^4)^2),x]","\int \frac{\left(1+x^2+x^4\right)^2 \sqrt{x^2+\sqrt{1+x^4}}}{\sqrt{1+x^4} \left(-1+x^2+x^4\right)^2} \, dx","-\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^6-6 \text{$\#$1}^4+2 \text{$\#$1}^2+1\&,\frac{-3 \text{$\#$1}^6 \log \left(\sqrt{x^4+1}+x^2-1\right)+3 \text{$\#$1}^6 \log \left(\text{$\#$1} \sqrt{x^4+1}+\text{$\#$1} x^2-\text{$\#$1}+\sqrt{2} \sqrt{\sqrt{x^4+1}+x^2} x\right)-\text{$\#$1}^4 \log \left(\sqrt{x^4+1}+x^2-1\right)+\text{$\#$1}^4 \log \left(\text{$\#$1} \sqrt{x^4+1}+\text{$\#$1} x^2-\text{$\#$1}+\sqrt{2} \sqrt{\sqrt{x^4+1}+x^2} x\right)+7 \text{$\#$1}^2 \log \left(\sqrt{x^4+1}+x^2-1\right)-7 \text{$\#$1}^2 \log \left(\text{$\#$1} \sqrt{x^4+1}+\text{$\#$1} x^2-\text{$\#$1}+\sqrt{2} \sqrt{\sqrt{x^4+1}+x^2} x\right)-\log \left(\text{$\#$1} \sqrt{x^4+1}+\text{$\#$1} x^2-\text{$\#$1}+\sqrt{2} \sqrt{\sqrt{x^4+1}+x^2} x\right)+\log \left(\sqrt{x^4+1}+x^2-1\right)}{2 \text{$\#$1}^7-3 \text{$\#$1}^5-6 \text{$\#$1}^3+\text{$\#$1}}\&\right]}{5 \sqrt{2}}+\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)+\frac{-2 x \sqrt{x^4+1} \sqrt{\sqrt{x^4+1}+x^2} \left(2 x^4+3 x^2+2\right)-2 x \left(2 x^6+3 x^4+3 x^2+1\right) \sqrt{\sqrt{x^4+1}+x^2}}{10 \sqrt{x^4+1} \left(x^4+x^2-1\right) x^2+5 \left(x^4+x^2-1\right) \left(2 x^4+1\right)}",1,"Integrate[((1 + x^2 + x^4)^2*Sqrt[x^2 + Sqrt[1 + x^4]])/(Sqrt[1 + x^4]*(-1 + x^2 + x^4)^2), x]","F",-1
3087,1,293,524,1.5117434,"\int \frac{\left(-q+p x^4\right) \sqrt{q+p x^4}}{x^2 \left(a q+b x^2+a p x^4\right)} \, dx","Integrate[((-q + p*x^4)*Sqrt[q + p*x^4])/(x^2*(a*q + b*x^2 + a*p*x^4)),x]","\frac{-i b x \sqrt{\frac{p x^4}{q}+1} \Pi \left(\frac{2 i a \sqrt{p} \sqrt{q}}{\sqrt{b^2-4 a^2 p q}-b};\left.i \sinh ^{-1}\left(\sqrt{\frac{i \sqrt{p}}{\sqrt{q}}} x\right)\right|-1\right)-i b x \sqrt{\frac{p x^4}{q}+1} \Pi \left(-\frac{2 i a \sqrt{p} \sqrt{q}}{b+\sqrt{b^2-4 a^2 p q}};\left.i \sinh ^{-1}\left(\sqrt{\frac{i \sqrt{p}}{\sqrt{q}}} x\right)\right|-1\right)+a p x^4 \sqrt{\frac{i \sqrt{p}}{\sqrt{q}}}+a q \sqrt{\frac{i \sqrt{p}}{\sqrt{q}}}+i b x \sqrt{\frac{p x^4}{q}+1} F\left(\left.i \sinh ^{-1}\left(\sqrt{\frac{i \sqrt{p}}{\sqrt{q}}} x\right)\right|-1\right)}{a^2 x \sqrt{\frac{i \sqrt{p}}{\sqrt{q}}} \sqrt{p x^4+q}}","\frac{\left(\sqrt{2} b \sqrt{i \sqrt{b} \sqrt{2 a \sqrt{p} \sqrt{q}-b}+a \left(-\sqrt{p}\right) \sqrt{q}+b}-i \sqrt{2} \sqrt{b} \sqrt{i \sqrt{b} \sqrt{2 a \sqrt{p} \sqrt{q}-b}+a \left(-\sqrt{p}\right) \sqrt{q}+b} \sqrt{2 a \sqrt{p} \sqrt{q}-b}\right) \tan ^{-1}\left(\frac{\sqrt{2} x \sqrt{i \sqrt{b} \sqrt{2 a \sqrt{p} \sqrt{q}-b}+a \left(-\sqrt{p}\right) \sqrt{q}+b}}{\sqrt{a} \left(\sqrt{p x^4+q}+\sqrt{p} x^2+\sqrt{q}\right)}\right)}{2 a^{5/2} \sqrt{p} \sqrt{q}}-\frac{i \left(\sqrt{2} \sqrt{b} \sqrt{i \sqrt{b} \sqrt{2 a \sqrt{p} \sqrt{q}-b}+a \sqrt{p} \sqrt{q}-b} \sqrt{2 a \sqrt{p} \sqrt{q}-b}-i \sqrt{2} b \sqrt{i \sqrt{b} \sqrt{2 a \sqrt{p} \sqrt{q}-b}+a \sqrt{p} \sqrt{q}-b}\right) \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt{i \sqrt{b} \sqrt{2 a \sqrt{p} \sqrt{q}-b}+a \sqrt{p} \sqrt{q}-b}}{\sqrt{a} \left(\sqrt{p x^4+q}+\sqrt{p} x^2+\sqrt{q}\right)}\right)}{2 a^{5/2} \sqrt{p} \sqrt{q}}+\frac{\sqrt{p x^4+q}}{a x}",1,"(a*Sqrt[(I*Sqrt[p])/Sqrt[q]]*q + a*p*Sqrt[(I*Sqrt[p])/Sqrt[q]]*x^4 + I*b*x*Sqrt[1 + (p*x^4)/q]*EllipticF[I*ArcSinh[Sqrt[(I*Sqrt[p])/Sqrt[q]]*x], -1] - I*b*x*Sqrt[1 + (p*x^4)/q]*EllipticPi[((2*I)*a*Sqrt[p]*Sqrt[q])/(-b + Sqrt[b^2 - 4*a^2*p*q]), I*ArcSinh[Sqrt[(I*Sqrt[p])/Sqrt[q]]*x], -1] - I*b*x*Sqrt[1 + (p*x^4)/q]*EllipticPi[((-2*I)*a*Sqrt[p]*Sqrt[q])/(b + Sqrt[b^2 - 4*a^2*p*q]), I*ArcSinh[Sqrt[(I*Sqrt[p])/Sqrt[q]]*x], -1])/(a^2*Sqrt[(I*Sqrt[p])/Sqrt[q]]*x*Sqrt[q + p*x^4])","C",1
3088,1,162,526,0.1542667,"\int \frac{\sqrt[3]{b^2 x^2+a^3 x^3}}{b+a x} \, dx","Integrate[(b^2*x^2 + a^3*x^3)^(1/3)/(b + a*x),x]","\frac{3 x^2 \left(\left(a^3 b x+b^3\right) \, _2F_1\left(-\frac{1}{3},\frac{2}{3};\frac{5}{3};-\frac{a^3 x}{b^2}\right)-\left(a^2 \left(a^3 x+b^2\right) \, _2F_1\left(\frac{2}{3},\frac{2}{3};\frac{5}{3};-\frac{a^3 x}{b^2}\right)\right)+b^2 \left(a^2-b\right) \sqrt[3]{\frac{a^3 x}{b^2}+1} \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{\left(a^3-a b\right) x}{x a^3+b^2}\right)\right)}{2 a b \left(x^2 \left(a^3 x+b^2\right)\right)^{2/3} \sqrt[3]{\frac{a^3 x}{b^2}+1}}","\frac{\sqrt[3]{a^3 x^3+b^2 x^2}}{a}+\frac{\left(3 a^2 b-b^2\right) \log \left(\sqrt[3]{a^3 x^3+b^2 x^2}-a x\right)}{3 a^3}+\frac{\left(b^2-3 a^2 b\right) \log \left(a x \sqrt[3]{a^3 x^3+b^2 x^2}+\left(a^3 x^3+b^2 x^2\right)^{2/3}+a^2 x^2\right)}{6 a^3}+\frac{\left(3 a^2 b-b^2\right) \tan ^{-1}\left(\frac{\sqrt{3} a x}{2 \sqrt[3]{a^3 x^3+b^2 x^2}+a x}\right)}{\sqrt{3} a^3}+\frac{\left(b \sqrt[3]{a^2-b}-i \sqrt{3} b \sqrt[3]{a^2-b}\right) \log \left(\sqrt[3]{-1} \sqrt[3]{a^3 x^3+b^2 x^2}+\sqrt[3]{a} x \sqrt[3]{a^2-b}\right)}{2 a^{5/3}}+\frac{i \left(\sqrt{3} b \sqrt[3]{a^2-b}+i b \sqrt[3]{a^2-b}\right) \log \left((-1)^{2/3} \left(a^3 x^3+b^2 x^2\right)^{2/3}+a^{2/3} x^2 \left(a^2-b\right)^{2/3}-\sqrt[3]{-1} \sqrt[3]{a} x \sqrt[3]{a^2-b} \sqrt[3]{a^3 x^3+b^2 x^2}\right)}{4 a^{5/3}}+\frac{\sqrt{-3-3 i \sqrt{3}} b \sqrt[3]{a^2-b} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{a} x \sqrt[3]{a^2-b}}{\sqrt[3]{a} x \sqrt[3]{a^2-b}-2 \sqrt[3]{-1} \sqrt[3]{a^3 x^3+b^2 x^2}}\right)}{\sqrt{2} a^{5/3}}",1,"(3*x^2*((b^3 + a^3*b*x)*Hypergeometric2F1[-1/3, 2/3, 5/3, -((a^3*x)/b^2)] - a^2*(b^2 + a^3*x)*Hypergeometric2F1[2/3, 2/3, 5/3, -((a^3*x)/b^2)] + (a^2 - b)*b^2*(1 + (a^3*x)/b^2)^(1/3)*Hypergeometric2F1[2/3, 1, 5/3, ((a^3 - a*b)*x)/(b^2 + a^3*x)]))/(2*a*b*(x^2*(b^2 + a^3*x))^(2/3)*(1 + (a^3*x)/b^2)^(1/3))","C",1
3089,1,14841,526,23.4915417,"\int \frac{\left(-b+a^2 x^2\right)^{3/2} \sqrt[4]{a x+\sqrt{-b+a^2 x^2}}}{x} \, dx","Integrate[((-b + a^2*x^2)^(3/2)*(a*x + Sqrt[-b + a^2*x^2])^(1/4))/x,x]","\text{Result too large to show}","\sqrt{2+\sqrt{2}} b^{13/8} \tan ^{-1}\left(\frac{\left(\sqrt{\frac{2}{2-\sqrt{2}}} \sqrt[8]{b}-\frac{2 \sqrt[8]{b}}{\sqrt{2-\sqrt{2}}}\right) \sqrt[4]{\sqrt{a^2 x^2-b}+a x}}{\sqrt{\sqrt{a^2 x^2-b}+a x}-\sqrt[4]{b}}\right)+\sqrt{2-\sqrt{2}} b^{13/8} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}} \sqrt[8]{b} \sqrt[4]{\sqrt{a^2 x^2-b}+a x}}{\sqrt{\sqrt{a^2 x^2-b}+a x}-\sqrt[4]{b}}\right)+\sqrt{2+\sqrt{2}} b^{13/8} \tanh ^{-1}\left(\frac{\frac{\sqrt{\sqrt{a^2 x^2-b}+a x}}{\sqrt{2-\sqrt{2}} \sqrt[8]{b}}+\frac{\sqrt[8]{b}}{\sqrt{2-\sqrt{2}}}}{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}}\right)-\sqrt{2-\sqrt{2}} b^{13/8} \tanh ^{-1}\left(\frac{\frac{\sqrt{\sqrt{a^2 x^2-b}+a x}}{\sqrt{2+\sqrt{2}} \sqrt[8]{b}}+\frac{\sqrt[8]{b}}{\sqrt{2+\sqrt{2}}}}{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}}\right)+\frac{4 \left(132 a^6 x^6-627 a^4 b x^4+682 a^2 b^2 x^2-152 b^3\right)+4 \sqrt{a^2 x^2-b} \left(132 a^5 x^5-561 a^3 b x^3+418 a b^2 x\right)}{429 \left(\sqrt{a^2 x^2-b}+a x\right)^{11/4}}",1,"Result too large to show","B",0
3090,0,0,530,0.3029623,"\int \frac{\left(b^2+a x^2\right) \sqrt{b+\sqrt{b^2+a x^2}}}{-b^2+a x^2} \, dx","Integrate[((b^2 + a*x^2)*Sqrt[b + Sqrt[b^2 + a*x^2]])/(-b^2 + a*x^2),x]","\int \frac{\left(b^2+a x^2\right) \sqrt{b+\sqrt{b^2+a x^2}}}{-b^2+a x^2} \, dx","\frac{4 b x}{3 \sqrt{\sqrt{a x^2+b^2}+b}}+\frac{2 x \sqrt{a x^2+b^2}}{3 \sqrt{\sqrt{a x^2+b^2}+b}}+\frac{2 \sqrt{\sqrt{2}-1} b^{3/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{b} \sqrt{\sqrt{a x^2+b^2}+b}}-\frac{\sqrt{\sqrt{a x^2+b^2}+b}}{\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{b}}\right)}{\sqrt{a}}+\frac{2 i \left(\sqrt{2 \left(\sqrt{2}-1\right)} b^{3/2}+\sqrt{\sqrt{2}-1} b^{3/2}\right) \tan ^{-1}\left(\frac{\frac{i a x}{\sqrt{\sqrt{a x^2+b^2}+b}}-i \sqrt{a} \sqrt{\sqrt{a x^2+b^2}+b}}{\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{a} \sqrt{b}}\right)}{\sqrt{a}}+\frac{2 \sqrt{1+\sqrt{2}} b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{2 \left(\sqrt{2}-1\right)} \sqrt{b} \sqrt{\sqrt{a x^2+b^2}+b}}-\frac{\sqrt{\sqrt{a x^2+b^2}+b}}{\sqrt{2 \left(\sqrt{2}-1\right)} \sqrt{b}}\right)}{\sqrt{a}}-\frac{2 i \left(\sqrt{2 \left(1+\sqrt{2}\right)} b^{3/2}-\sqrt{1+\sqrt{2}} b^{3/2}\right) \tanh ^{-1}\left(\frac{\frac{i a x}{\sqrt{\sqrt{a x^2+b^2}+b}}-i \sqrt{a} \sqrt{\sqrt{a x^2+b^2}+b}}{\sqrt{2 \left(\sqrt{2}-1\right)} \sqrt{a} \sqrt{b}}\right)}{\sqrt{a}}",1,"Integrate[((b^2 + a*x^2)*Sqrt[b + Sqrt[b^2 + a*x^2]])/(-b^2 + a*x^2), x]","F",-1
3091,1,742,535,5.1757653,"\int \frac{d+c x^4}{x \sqrt{-b+a^2 x^2} \sqrt[4]{a x+\sqrt{-b+a^2 x^2}}} \, dx","Integrate[(d + c*x^4)/(x*Sqrt[-b + a^2*x^2]*(a*x + Sqrt[-b + a^2*x^2])^(1/4)),x]","\frac{4 \left(\frac{13585 a^5 d \sqrt{\text{sgn}(a)^2} \left(\sqrt{a^2 x^2-b}+a x\right)}{\sqrt{a^2} \text{sgn}(a)}+\frac{13585 a^4 d \sqrt{a^2 x^2-b} \left(\sqrt{a^2 x^2-b}+a x\right)^2 \left(2 \, _2F_1\left(\frac{3}{8},1;\frac{11}{8};-\frac{\left(a x+\sqrt{a^2 x^2-b}\right)^2}{b}\right)-1\right)}{a x \left(\sqrt{a^2 x^2-b}+a x\right)-b}-\frac{3 c \sqrt{a^2 x^2-b} \left(156 a b^3 x \left(8 \sqrt{a^2 x^2-b}+13 a x\right)+5720 a^7 x^7 \left(\sqrt{a^2 x^2-b}+a x\right)-260 a^5 b x^5 \left(14 \sqrt{a^2 x^2-b}+25 a x\right)-65 a^3 b^2 x^3 \left(21 \sqrt{a^2 x^2-b}+4 a x\right)-384 b^4\right)}{\left(\sqrt{a^2 x^2-b}+a x\right)^2 \left(a x \left(\sqrt{a^2 x^2-b}+a x\right)-b\right)}+\frac{3 c \sqrt{a^2 x^2-b} \left(b-2 a x \left(\sqrt{a^2 x^2-b}+a x\right)\right)^4 \left(-832 a b^3 x \left(8 \sqrt{a^2 x^2-b}+13 a x\right)+5720 a^7 x^7 \left(\sqrt{a^2 x^2-b}+a x\right)+260 a^5 b x^5 \left(5 \sqrt{a^2 x^2-b}-6 a x\right)+455 a^3 b^2 x^3 \left(16 \sqrt{a^2 x^2-b}+13 a x\right)+2048 b^4\right)}{-a b^5 x \left(11 \sqrt{a^2 x^2-b}+61 a x\right)+1024 a^{11} x^{11} \left(\sqrt{a^2 x^2-b}+a x\right)-256 a^9 b x^9 \left(11 \sqrt{a^2 x^2-b}+13 a x\right)+256 a^7 b^2 x^7 \left(11 \sqrt{a^2 x^2-b}+16 a x\right)-112 a^5 b^3 x^5 \left(11 \sqrt{a^2 x^2-b}+21 a x\right)+20 a^3 b^4 x^3 \left(11 \sqrt{a^2 x^2-b}+31 a x\right)+b^6}\right)}{40755 a^4 b \sqrt[4]{\sqrt{a^2 x^2-b}+a x}}","\frac{\sqrt{2+\sqrt{2}} d \tan ^{-1}\left(\frac{\left(\sqrt{\frac{2}{2-\sqrt{2}}} \sqrt[8]{b}-\frac{2 \sqrt[8]{b}}{\sqrt{2-\sqrt{2}}}\right) \sqrt[4]{\sqrt{a^2 x^2-b}+a x}}{\sqrt{\sqrt{a^2 x^2-b}+a x}-\sqrt[4]{b}}\right)}{b^{5/8}}+\frac{\sqrt{2-\sqrt{2}} d \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}} \sqrt[8]{b} \sqrt[4]{\sqrt{a^2 x^2-b}+a x}}{\sqrt{\sqrt{a^2 x^2-b}+a x}-\sqrt[4]{b}}\right)}{b^{5/8}}-\frac{\sqrt{2+\sqrt{2}} d \tanh ^{-1}\left(\frac{\frac{\sqrt{\sqrt{a^2 x^2-b}+a x}}{\sqrt{2-\sqrt{2}} \sqrt[8]{b}}+\frac{\sqrt[8]{b}}{\sqrt{2-\sqrt{2}}}}{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}}\right)}{b^{5/8}}+\frac{\sqrt{2-\sqrt{2}} d \tanh ^{-1}\left(\frac{\frac{\sqrt{\sqrt{a^2 x^2-b}+a x}}{\sqrt{2+\sqrt{2}} \sqrt[8]{b}}+\frac{\sqrt[8]{b}}{\sqrt{2+\sqrt{2}}}}{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}}\right)}{b^{5/8}}+\frac{4 c \left(260 a^6 x^6+325 a^4 b x^4-676 a^2 b^2 x^2+128 b^3\right)+4 c \sqrt{a^2 x^2-b} \left(260 a^5 x^5+455 a^3 b x^3-416 a b^2 x\right)}{715 a^4 \left(\sqrt{a^2 x^2-b}+a x\right)^{13/4}}",1,"(4*((3*c*Sqrt[-b + a^2*x^2]*(b - 2*a*x*(a*x + Sqrt[-b + a^2*x^2]))^4*(2048*b^4 + 5720*a^7*x^7*(a*x + Sqrt[-b + a^2*x^2]) + 260*a^5*b*x^5*(-6*a*x + 5*Sqrt[-b + a^2*x^2]) - 832*a*b^3*x*(13*a*x + 8*Sqrt[-b + a^2*x^2]) + 455*a^3*b^2*x^3*(13*a*x + 16*Sqrt[-b + a^2*x^2])))/(b^6 + 1024*a^11*x^11*(a*x + Sqrt[-b + a^2*x^2]) - 256*a^9*b*x^9*(13*a*x + 11*Sqrt[-b + a^2*x^2]) + 256*a^7*b^2*x^7*(16*a*x + 11*Sqrt[-b + a^2*x^2]) - 112*a^5*b^3*x^5*(21*a*x + 11*Sqrt[-b + a^2*x^2]) + 20*a^3*b^4*x^3*(31*a*x + 11*Sqrt[-b + a^2*x^2]) - a*b^5*x*(61*a*x + 11*Sqrt[-b + a^2*x^2])) - (3*c*Sqrt[-b + a^2*x^2]*(-384*b^4 + 5720*a^7*x^7*(a*x + Sqrt[-b + a^2*x^2]) + 156*a*b^3*x*(13*a*x + 8*Sqrt[-b + a^2*x^2]) - 260*a^5*b*x^5*(25*a*x + 14*Sqrt[-b + a^2*x^2]) - 65*a^3*b^2*x^3*(4*a*x + 21*Sqrt[-b + a^2*x^2])))/((a*x + Sqrt[-b + a^2*x^2])^2*(-b + a*x*(a*x + Sqrt[-b + a^2*x^2]))) + (13585*a^4*d*Sqrt[-b + a^2*x^2]*(a*x + Sqrt[-b + a^2*x^2])^2*(-1 + 2*Hypergeometric2F1[3/8, 1, 11/8, -((a*x + Sqrt[-b + a^2*x^2])^2/b)]))/(-b + a*x*(a*x + Sqrt[-b + a^2*x^2])) + (13585*a^5*d*(a*x + Sqrt[-b + a^2*x^2])*Sqrt[Sign[a]^2])/(Sqrt[a^2]*Sign[a])))/(40755*a^4*b*(a*x + Sqrt[-b + a^2*x^2])^(1/4))","C",0
3092,1,226,540,3.9049417,"\int \frac{\left(-b+a^2 x^2\right)^{3/2} \sqrt[4]{a x+\sqrt{-b+a^2 x^2}}}{x^2} \, dx","Integrate[((-b + a^2*x^2)^(3/2)*(a*x + Sqrt[-b + a^2*x^2])^(1/4))/x^2,x]","\frac{\left(a^2 x^2-b\right) \sqrt[4]{\sqrt{a^2 x^2-b}+a x} \left(56 a^5 x^5-812 a^3 b x^3-63 b^2 \sqrt{a^2 x^2-b}+126 a b x \left(2 a x \left(\sqrt{a^2 x^2-b}+a x\right)-b\right) \, _2F_1\left(\frac{1}{8},1;\frac{9}{8};-\frac{\left(a x+\sqrt{a^2 x^2-b}\right)^2}{b}\right)-784 a^2 b x^2 \sqrt{a^2 x^2-b}+56 a^4 x^4 \sqrt{a^2 x^2-b}+313 a b^2 x\right)}{63 x \left(b-a x \left(\sqrt{a^2 x^2-b}+a x\right)\right)^2}","\frac{1}{4} \sqrt{2-\sqrt{2}} a b^{9/8} \tan ^{-1}\left(\frac{\left(\sqrt{\frac{2}{2-\sqrt{2}}} \sqrt[8]{b}-\frac{2 \sqrt[8]{b}}{\sqrt{2-\sqrt{2}}}\right) \sqrt[4]{\sqrt{a^2 x^2-b}+a x}}{\sqrt{\sqrt{a^2 x^2-b}+a x}-\sqrt[4]{b}}\right)-\frac{1}{4} \sqrt{2+\sqrt{2}} a b^{9/8} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}} \sqrt[8]{b} \sqrt[4]{\sqrt{a^2 x^2-b}+a x}}{\sqrt{\sqrt{a^2 x^2-b}+a x}-\sqrt[4]{b}}\right)+\frac{1}{4} \sqrt{2-\sqrt{2}} a b^{9/8} \tanh ^{-1}\left(\frac{\frac{\sqrt{\sqrt{a^2 x^2-b}+a x}}{\sqrt{2-\sqrt{2}} \sqrt[8]{b}}+\frac{\sqrt[8]{b}}{\sqrt{2-\sqrt{2}}}}{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}}\right)+\frac{1}{4} \sqrt{2+\sqrt{2}} a b^{9/8} \tanh ^{-1}\left(\frac{\frac{\sqrt{\sqrt{a^2 x^2-b}+a x}}{\sqrt{2+\sqrt{2}} \sqrt[8]{b}}+\frac{\sqrt[8]{b}}{\sqrt{2+\sqrt{2}}}}{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}}\right)+\frac{112 a^6 x^6-1652 a^4 b x^4+1034 a^2 b^2 x^2+\sqrt{a^2 x^2-b} \left(112 a^5 x^5-1596 a^3 b x^3+250 a b^2 x\right)+63 b^3}{63 x \left(\sqrt{a^2 x^2-b}+a x\right)^{11/4}}",1,"((-b + a^2*x^2)*(a*x + Sqrt[-b + a^2*x^2])^(1/4)*(313*a*b^2*x - 812*a^3*b*x^3 + 56*a^5*x^5 - 63*b^2*Sqrt[-b + a^2*x^2] - 784*a^2*b*x^2*Sqrt[-b + a^2*x^2] + 56*a^4*x^4*Sqrt[-b + a^2*x^2] + 126*a*b*x*(-b + 2*a*x*(a*x + Sqrt[-b + a^2*x^2]))*Hypergeometric2F1[1/8, 1, 9/8, -((a*x + Sqrt[-b + a^2*x^2])^2/b)]))/(63*x*(b - a*x*(a*x + Sqrt[-b + a^2*x^2]))^2)","C",1
3093,1,93,541,0.2959891,"\int \frac{b-x}{\sqrt[3]{(-a+x) (-b+x)^2} \left(a^2-b^2 d-2 (a-b d) x+(1-d) x^2\right)} \, dx","Integrate[(b - x)/(((-a + x)*(-b + x)^2)^(1/3)*(a^2 - b^2*d - 2*(a - b*d)*x + (1 - d)*x^2)),x]","-\frac{3 (x-b) \left(\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\sqrt{d} (b-x)}{x-a}\right)-\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\sqrt{d} (x-b)}{x-a}\right)\right)}{2 \sqrt{d} (a-b) \sqrt[3]{(x-a) (b-x)^2}}","\frac{\log \left(a^3 \sqrt[3]{b-a}-2 a^2 x \sqrt[3]{b-a}-a^2 b \sqrt[3]{b-a}+\left(b d^{2/3} \sqrt[3]{a-b}-a d^{2/3} \sqrt[3]{a-b}\right) \left(x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3\right)^{2/3}+\sqrt[3]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3} \left(a \sqrt[3]{d} (a-b)^{2/3} (b-a)^{2/3}-\sqrt[3]{d} x (a-b)^{2/3} (b-a)^{2/3}\right)+a x^2 \sqrt[3]{b-a}-b x^2 \sqrt[3]{b-a}+2 a b x \sqrt[3]{b-a}\right)}{4 d^{2/3} \sqrt[3]{a-b} (b-a)^{2/3}}-\frac{\log \left(\sqrt[3]{d} (a-b)^{2/3} \sqrt[3]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3}-x (b-a)^{2/3}+a (b-a)^{2/3}\right)}{2 d^{2/3} \sqrt[3]{a-b} (b-a)^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} (a-b)^{2/3} \sqrt[3]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3}}{\sqrt[3]{d} (a-b)^{2/3} \sqrt[3]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3}+2 x (b-a)^{2/3}-2 a (b-a)^{2/3}}\right)}{2 d^{2/3} \sqrt[3]{a-b} (b-a)^{2/3}}",1,"(-3*(-b + x)*(Hypergeometric2F1[1/3, 1, 4/3, (Sqrt[d]*(b - x))/(-a + x)] - Hypergeometric2F1[1/3, 1, 4/3, (Sqrt[d]*(-b + x))/(-a + x)]))/(2*(a - b)*Sqrt[d]*((b - x)^2*(-a + x))^(1/3))","C",1
3094,1,93,541,0.1497539,"\int \frac{-b+x}{\sqrt[3]{(-a+x) (-b+x)^2} \left(-a^2+b^2 d+2 (a-b d) x+(-1+d) x^2\right)} \, dx","Integrate[(-b + x)/(((-a + x)*(-b + x)^2)^(1/3)*(-a^2 + b^2*d + 2*(a - b*d)*x + (-1 + d)*x^2)),x]","-\frac{3 (x-b) \left(\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\sqrt{d} (b-x)}{x-a}\right)-\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\sqrt{d} (x-b)}{x-a}\right)\right)}{2 \sqrt{d} (a-b) \sqrt[3]{(x-a) (b-x)^2}}","\frac{\log \left(a^3 \sqrt[3]{b-a}-2 a^2 x \sqrt[3]{b-a}-a^2 b \sqrt[3]{b-a}+\left(b d^{2/3} \sqrt[3]{a-b}-a d^{2/3} \sqrt[3]{a-b}\right) \left(x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3\right)^{2/3}+\sqrt[3]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3} \left(a \sqrt[3]{d} (a-b)^{2/3} (b-a)^{2/3}-\sqrt[3]{d} x (a-b)^{2/3} (b-a)^{2/3}\right)+a x^2 \sqrt[3]{b-a}-b x^2 \sqrt[3]{b-a}+2 a b x \sqrt[3]{b-a}\right)}{4 d^{2/3} \sqrt[3]{a-b} (b-a)^{2/3}}-\frac{\log \left(\sqrt[3]{d} (a-b)^{2/3} \sqrt[3]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3}-x (b-a)^{2/3}+a (b-a)^{2/3}\right)}{2 d^{2/3} \sqrt[3]{a-b} (b-a)^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} (a-b)^{2/3} \sqrt[3]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3}}{\sqrt[3]{d} (a-b)^{2/3} \sqrt[3]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3}+2 x (b-a)^{2/3}-2 a (b-a)^{2/3}}\right)}{2 d^{2/3} \sqrt[3]{a-b} (b-a)^{2/3}}",1,"(-3*(-b + x)*(Hypergeometric2F1[1/3, 1, 4/3, (Sqrt[d]*(b - x))/(-a + x)] - Hypergeometric2F1[1/3, 1, 4/3, (Sqrt[d]*(-b + x))/(-a + x)]))/(2*(a - b)*Sqrt[d]*((b - x)^2*(-a + x))^(1/3))","C",1
3095,0,0,541,0.3682845,"\int \frac{b^2+a x^2}{\left(-b^2+a x^2\right) \sqrt{b+\sqrt{b^2+a x^2}}} \, dx","Integrate[(b^2 + a*x^2)/((-b^2 + a*x^2)*Sqrt[b + Sqrt[b^2 + a*x^2]]),x]","\int \frac{b^2+a x^2}{\left(-b^2+a x^2\right) \sqrt{b+\sqrt{b^2+a x^2}}} \, dx","\frac{2 x}{\sqrt{\sqrt{a x^2+b^2}+b}}+\frac{2 \sqrt{2} \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{2} \sqrt{b} \sqrt{\sqrt{a x^2+b^2}+b}}-\frac{\sqrt{\sqrt{a x^2+b^2}+b}}{\sqrt{2} \sqrt{b}}\right)}{\sqrt{a}}-\frac{2 \sqrt{1+\sqrt{2}} \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{2 \left(\sqrt{2}-1\right)} \sqrt{b} \sqrt{\sqrt{a x^2+b^2}+b}}-\frac{\sqrt{\sqrt{a x^2+b^2}+b}}{\sqrt{2 \left(\sqrt{2}-1\right)} \sqrt{b}}\right)}{\sqrt{a}}-\frac{2 \sqrt{1+\sqrt{2}} \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{b} \sqrt{\sqrt{a x^2+b^2}+b}}-\frac{\sqrt{\sqrt{a x^2+b^2}+b}}{\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{b}}\right)}{\sqrt{a}}+\frac{2 \sqrt{\sqrt{2}-1} \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{2 \left(\sqrt{2}-1\right)} \sqrt{b} \sqrt{\sqrt{a x^2+b^2}+b}}-\frac{\sqrt{\sqrt{a x^2+b^2}+b}}{\sqrt{2 \left(\sqrt{2}-1\right)} \sqrt{b}}\right)}{\sqrt{a}}-\frac{2 \sqrt{\sqrt{2}-1} \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{b} \sqrt{\sqrt{a x^2+b^2}+b}}-\frac{\sqrt{\sqrt{a x^2+b^2}+b}}{\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{b}}\right)}{\sqrt{a}}",1,"Integrate[(b^2 + a*x^2)/((-b^2 + a*x^2)*Sqrt[b + Sqrt[b^2 + a*x^2]]), x]","F",-1
3096,1,53,543,0.0446861,"\int \frac{1}{\sqrt[3]{(-a+x) (-b+x)^2} (a-b d+(-1+d) x)} \, dx","Integrate[1/(((-a + x)*(-b + x)^2)^(1/3)*(a - b*d + (-1 + d)*x)),x]","\frac{3 (x-b) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{d (b-x)}{a-x}\right)}{(a-b) \sqrt[3]{(x-a) (b-x)^2}}","\frac{\left(\sqrt[3]{d}-i \sqrt{3} \sqrt[3]{d}\right) \log \left(\sqrt[3]{-1} (b-x) (b d-a d)^{2/3}-\sqrt[3]{d} (a-b)^{2/3} \sqrt[3]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3}\right)}{2 \sqrt[3]{a-b} (-(d (a-b)))^{2/3}}+\frac{\sqrt{-3-3 i \sqrt{3}} \sqrt[3]{d} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} (a-b)^{2/3} \sqrt[3]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3}}{\sqrt[3]{d} (a-b)^{2/3} \sqrt[3]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3}-2 \sqrt[3]{-1} x (b d-a d)^{2/3}+2 \sqrt[3]{-1} b (b d-a d)^{2/3}}\right)}{\sqrt{2} \sqrt[3]{a-b} (-(d (a-b)))^{2/3}}+\frac{i \left(\sqrt{3} \sqrt[3]{d}+i \sqrt[3]{d}\right) \log \left(-d^{2/3} (a-b)^{4/3} \left(x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3\right)^{2/3}+\sqrt[3]{-1} \sqrt[3]{d} (a-b)^{2/3} (x-b) (b d-a d)^{2/3} \sqrt[3]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3}+(-1)^{2/3} d \sqrt[3]{b d-a d} \left(a b^2-2 a b x+a x^2-b^3+2 b^2 x-b x^2\right)\right)}{4 \sqrt[3]{a-b} (-(d (a-b)))^{2/3}}",1,"(3*(-b + x)*Hypergeometric2F1[1/3, 1, 4/3, (d*(b - x))/(a - x)])/((a - b)*((b - x)^2*(-a + x))^(1/3))","C",1
3097,0,0,549,0.3337869,"\int \frac{\sqrt{b+a^2 x^4} \sqrt{a x^2+\sqrt{b+a^2 x^4}}}{d+c x^2} \, dx","Integrate[(Sqrt[b + a^2*x^4]*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]])/(d + c*x^2),x]","\int \frac{\sqrt{b+a^2 x^4} \sqrt{a x^2+\sqrt{b+a^2 x^4}}}{d+c x^2} \, dx","-\frac{\sqrt{a} \text{RootSum}\left[\text{$\#$1}^4 c+4 \text{$\#$1}^3 a d-2 \text{$\#$1}^2 b c+4 \text{$\#$1} a b d+b^2 c\&,\frac{\text{$\#$1}^2 b c^2 \log \left(-\text{$\#$1}+\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)+\text{$\#$1}^2 a^2 d^2 \log \left(-\text{$\#$1}+\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)+b^2 c^2 \log \left(-\text{$\#$1}+\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)+a^2 b d^2 \log \left(-\text{$\#$1}+\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)}{\text{$\#$1}^3 (-c)-3 \text{$\#$1}^2 a d+\text{$\#$1} b c-a b d}\&\right]}{\sqrt{2} c^2}+\frac{a x \sqrt{\sqrt{a^2 x^4+b}+a x^2}}{2 c}-\frac{\sqrt{a} \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a^2 x^4+b}}{\sqrt{b}}+\frac{\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}}{\sqrt{b}}+\frac{a x^2}{\sqrt{b}}\right)}{\sqrt{2} c}-\frac{a^{3/2} d \log \left(\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)}{\sqrt{2} c^2}",1,"Integrate[(Sqrt[b + a^2*x^4]*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]])/(d + c*x^2), x]","F",-1
3098,0,0,549,0.113669,"\int \frac{\sqrt{b+a^2 x^4} \sqrt{a x^2+\sqrt{b+a^2 x^4}}}{d+c x^2} \, dx","Integrate[(Sqrt[b + a^2*x^4]*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]])/(d + c*x^2),x]","\int \frac{\sqrt{b+a^2 x^4} \sqrt{a x^2+\sqrt{b+a^2 x^4}}}{d+c x^2} \, dx","-\frac{\sqrt{a} \text{RootSum}\left[\text{$\#$1}^4 c+4 \text{$\#$1}^3 a d-2 \text{$\#$1}^2 b c+4 \text{$\#$1} a b d+b^2 c\&,\frac{\text{$\#$1}^2 b c^2 \log \left(-\text{$\#$1}+\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)+\text{$\#$1}^2 a^2 d^2 \log \left(-\text{$\#$1}+\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)+b^2 c^2 \log \left(-\text{$\#$1}+\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)+a^2 b d^2 \log \left(-\text{$\#$1}+\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)}{\text{$\#$1}^3 (-c)-3 \text{$\#$1}^2 a d+\text{$\#$1} b c-a b d}\&\right]}{\sqrt{2} c^2}+\frac{a x \sqrt{\sqrt{a^2 x^4+b}+a x^2}}{2 c}-\frac{\sqrt{a} \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a^2 x^4+b}}{\sqrt{b}}+\frac{\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}}{\sqrt{b}}+\frac{a x^2}{\sqrt{b}}\right)}{\sqrt{2} c}-\frac{a^{3/2} d \log \left(\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)}{\sqrt{2} c^2}",1,"Integrate[(Sqrt[b + a^2*x^4]*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]])/(d + c*x^2), x]","F",-1
3099,0,0,553,0.0566787,"\int \frac{\sqrt{x^2+\sqrt{1+x^4}}}{1+a x} \, dx","Integrate[Sqrt[x^2 + Sqrt[1 + x^4]]/(1 + a*x),x]","\int \frac{\sqrt{x^2+\sqrt{1+x^4}}}{1+a x} \, dx","-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)}{a^2}+\frac{\left(a^4+\sqrt{a^4+1}+1\right) \tan ^{-1}\left(\frac{a \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{-\sqrt{a^4+1}-1}}\right)}{a^2 \sqrt{a^4+1} \sqrt{-\sqrt{a^4+1}-1}}+\frac{\left(-a^4+\sqrt{a^4+1}-1\right) \tan ^{-1}\left(\frac{a \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{\sqrt{a^4+1}-1}}\right)}{a^2 \sqrt{a^4+1} \sqrt{\sqrt{a^4+1}-1}}+\frac{\left(-\sqrt{2} \sqrt{-\sqrt{a^4+1}-a^2} a^2+\sqrt{2} \sqrt{a^4+1} \sqrt{-\sqrt{a^4+1}-a^2}+\sqrt{2} \sqrt{-\sqrt{a^4+1}-a^2}\right) \tan ^{-1}\left(\frac{\sqrt{2} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{-\sqrt{a^4+1}-a^2} \left(\sqrt{x^4+1}+x^2-1\right)}\right)}{2 a^2}+\frac{\left(\sqrt{2} \sqrt{\sqrt{a^4+1}-a^2} a^2+\sqrt{2} \sqrt{a^4+1} \sqrt{\sqrt{a^4+1}-a^2}-\sqrt{2} \sqrt{\sqrt{a^4+1}-a^2}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{\sqrt{a^4+1}-a^2} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)}{2 a^2}+\frac{\sqrt{\sqrt{x^4+1}+x^2}}{a}",1,"Integrate[Sqrt[x^2 + Sqrt[1 + x^4]]/(1 + a*x), x]","F",-1
3100,1,535,561,3.352514,"\int \frac{1}{\sqrt{c_4+\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5} (c_6+x c_7)} \, dx","Integrate[1/(Sqrt[C[4] + Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5]]*(C[6] + x*C[7])),x]","\frac{2 \left(\frac{\sqrt[4]{c_3} \tanh ^{-1}\left(\frac{\sqrt[4]{c_3} \sqrt{c_5 \sqrt{\frac{c_1 x+c_0}{c_3 x+c_2}}+c_4}}{\sqrt{\sqrt{c_3} c_4-\sqrt{c_1} c_5}}\right)}{\sqrt{\sqrt{c_3} c_4-\sqrt{c_1} c_5}}+\sqrt{c_3 c_6-c_2 c_7} \left(-\frac{\tanh ^{-1}\left(\frac{\sqrt{c_3 c_6-c_2 c_7} \sqrt{c_5 \sqrt{\frac{c_1 x+c_0}{c_3 x+c_2}}+c_4}}{\sqrt{-\sqrt{c_1 c_6-c_0 c_7} \sqrt{c_3 c_6-c_2 c_7} c_5+c_3 c_4 c_6-c_2 c_4 c_7}}\right)}{\sqrt{-\sqrt{c_1 c_6-c_0 c_7} \sqrt{c_3 c_6-c_2 c_7} c_5+c_3 c_4 c_6-c_2 c_4 c_7}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c_3 c_6-c_2 c_7} \sqrt{c_5 \sqrt{\frac{c_1 x+c_0}{c_3 x+c_2}}+c_4}}{\sqrt{\sqrt{c_1 c_6-c_0 c_7} \sqrt{c_3 c_6-c_2 c_7} c_5+c_3 c_4 c_6-c_2 c_4 c_7}}\right)}{\sqrt{\sqrt{c_1 c_6-c_0 c_7} \sqrt{c_3 c_6-c_2 c_7} c_5+c_3 c_4 c_6-c_2 c_4 c_7}}\right)+\frac{\sqrt[4]{c_3} \tanh ^{-1}\left(\frac{\sqrt[4]{c_3} \sqrt{c_5 \sqrt{\frac{c_1 x+c_0}{c_3 x+c_2}}+c_4}}{\sqrt{\sqrt{c_3} c_4+\sqrt{c_1} c_5}}\right)}{\sqrt{\sqrt{c_3} c_4+\sqrt{c_1} c_5}}\right)}{c_7}","\frac{2 \sqrt{c_3 c_6-c_2 c_7} \tan ^{-1}\left(\frac{\sqrt{c_3 c_6-c_2 c_7} \sqrt{c_5 \sqrt{\frac{c_1 x+c_0}{c_3 x+c_2}}+c_4}}{\sqrt{-\sqrt{c_1 c_6-c_0 c_7} \sqrt{c_3 c_6-c_2 c_7} c_5-c_3 c_4 c_6+c_2 c_4 c_7}}\right)}{c_7 \sqrt{-\sqrt{c_1 c_6-c_0 c_7} \sqrt{c_3 c_6-c_2 c_7} c_5-c_3 c_4 c_6+c_2 c_4 c_7}}+\frac{2 \sqrt{c_3 c_6-c_2 c_7} \tan ^{-1}\left(\frac{\sqrt{c_3 c_6-c_2 c_7} \sqrt{c_5 \sqrt{\frac{c_1 x+c_0}{c_3 x+c_2}}+c_4}}{\sqrt{\sqrt{c_1 c_6-c_0 c_7} \sqrt{c_3 c_6-c_2 c_7} c_5-c_3 c_4 c_6+c_2 c_4 c_7}}\right)}{c_7 \sqrt{\sqrt{c_1 c_6-c_0 c_7} \sqrt{c_3 c_6-c_2 c_7} c_5-c_3 c_4 c_6+c_2 c_4 c_7}}+\frac{2 \sqrt[4]{c_3} \tanh ^{-1}\left(\frac{\sqrt[4]{c_3} \sqrt{c_5 \sqrt{\frac{c_1 x+c_0}{c_3 x+c_2}}+c_4}}{\sqrt{\sqrt{c_3} c_4-\sqrt{c_1} c_5}}\right)}{\sqrt{\sqrt{c_3} c_4-\sqrt{c_1} c_5} c_7}+\frac{2 \sqrt[4]{c_3} \tanh ^{-1}\left(\frac{\sqrt[4]{c_3} \sqrt{c_5 \sqrt{\frac{c_1 x+c_0}{c_3 x+c_2}}+c_4}}{\sqrt{\sqrt{c_3} c_4+\sqrt{c_1} c_5}}\right)}{\sqrt{\sqrt{c_3} c_4+\sqrt{c_1} c_5} c_7}",1,"(2*((ArcTanh[(C[3]^(1/4)*Sqrt[C[4] + Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5]])/Sqrt[Sqrt[C[3]]*C[4] - Sqrt[C[1]]*C[5]]]*C[3]^(1/4))/Sqrt[Sqrt[C[3]]*C[4] - Sqrt[C[1]]*C[5]] + (ArcTanh[(C[3]^(1/4)*Sqrt[C[4] + Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5]])/Sqrt[Sqrt[C[3]]*C[4] + Sqrt[C[1]]*C[5]]]*C[3]^(1/4))/Sqrt[Sqrt[C[3]]*C[4] + Sqrt[C[1]]*C[5]] + Sqrt[C[3]*C[6] - C[2]*C[7]]*(-(ArcTanh[(Sqrt[C[4] + Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5]]*Sqrt[C[3]*C[6] - C[2]*C[7]])/Sqrt[C[3]*C[4]*C[6] - C[2]*C[4]*C[7] - C[5]*Sqrt[C[1]*C[6] - C[0]*C[7]]*Sqrt[C[3]*C[6] - C[2]*C[7]]]]/Sqrt[C[3]*C[4]*C[6] - C[2]*C[4]*C[7] - C[5]*Sqrt[C[1]*C[6] - C[0]*C[7]]*Sqrt[C[3]*C[6] - C[2]*C[7]]]) - ArcTanh[(Sqrt[C[4] + Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5]]*Sqrt[C[3]*C[6] - C[2]*C[7]])/Sqrt[C[3]*C[4]*C[6] - C[2]*C[4]*C[7] + C[5]*Sqrt[C[1]*C[6] - C[0]*C[7]]*Sqrt[C[3]*C[6] - C[2]*C[7]]]]/Sqrt[C[3]*C[4]*C[6] - C[2]*C[4]*C[7] + C[5]*Sqrt[C[1]*C[6] - C[0]*C[7]]*Sqrt[C[3]*C[6] - C[2]*C[7]]])))/C[7]","A",1
3101,1,93,569,0.2876279,"\int \frac{-b+x}{\sqrt[3]{(-a+x) (-b+x)^2} \left(-b^2+a^2 d+2 (b-a d) x+(-1+d) x^2\right)} \, dx","Integrate[(-b + x)/(((-a + x)*(-b + x)^2)^(1/3)*(-b^2 + a^2*d + 2*(b - a*d)*x + (-1 + d)*x^2)),x]","\frac{3 (x-b) \left(\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{b-x}{\sqrt{d} (x-a)}\right)-\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{x-b}{\sqrt{d} (x-a)}\right)\right)}{2 \sqrt{d} (a-b) \sqrt[3]{(x-a) (b-x)^2}}","-\frac{d^{4/3} (a-b)^{2/3} \log \left(a^3 d \sqrt[3]{a d-b d}-2 a^2 d x \sqrt[3]{a d-b d}-a^2 b d \sqrt[3]{a d-b d}+d^{2/3} (a-b)^{4/3} \left(x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3\right)^{2/3}+\sqrt[3]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3} \left(\sqrt[3]{d} x (a-b)^{2/3} (a d-b d)^{2/3}-a \sqrt[3]{d} (a-b)^{2/3} (a d-b d)^{2/3}\right)+a d x^2 \sqrt[3]{a d-b d}-b d x^2 \sqrt[3]{a d-b d}+2 a b d x \sqrt[3]{a d-b d}\right)}{4 (d (a-b))^{5/3}}+\frac{d^{4/3} (a-b)^{2/3} \log \left(\sqrt[3]{d} (a-b)^{2/3} \sqrt[3]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3}-x (a d-b d)^{2/3}+a (a d-b d)^{2/3}\right)}{2 (d (a-b))^{5/3}}+\frac{\sqrt{3} d^{4/3} (a-b)^{2/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{a d-b d} \sqrt[3]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3}}{\sqrt[3]{a d-b d} \sqrt[3]{x \left(2 a b+b^2\right)-a b^2+x^2 (-a-2 b)+x^3}+2 d^{2/3} x \sqrt[3]{a-b}-2 a d^{2/3} \sqrt[3]{a-b}}\right)}{2 (d (a-b))^{5/3}}",1,"(3*(-b + x)*(Hypergeometric2F1[1/3, 1, 4/3, (b - x)/(Sqrt[d]*(-a + x))] - Hypergeometric2F1[1/3, 1, 4/3, (-b + x)/(Sqrt[d]*(-a + x))]))/(2*(a - b)*Sqrt[d]*((b - x)^2*(-a + x))^(1/3))","C",1
3102,0,0,569,0.7170608,"\int \frac{\left(b^2+a x^2\right)^2}{\left(-b^2+a x^2\right)^2 \sqrt{b+\sqrt{b^2+a x^2}}} \, dx","Integrate[(b^2 + a*x^2)^2/((-b^2 + a*x^2)^2*Sqrt[b + Sqrt[b^2 + a*x^2]]),x]","\int \frac{\left(b^2+a x^2\right)^2}{\left(-b^2+a x^2\right)^2 \sqrt{b+\sqrt{b^2+a x^2}}} \, dx","\frac{2 x \left(a x^2-2 b^2\right)}{\left(a x^2-b^2\right) \sqrt{\sqrt{a x^2+b^2}+b}}-\frac{2 \sqrt{2} \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{2} \sqrt{b} \sqrt{\sqrt{a x^2+b^2}+b}}-\frac{\sqrt{\sqrt{a x^2+b^2}+b}}{\sqrt{2} \sqrt{b}}\right)}{\sqrt{a}}-\frac{\sqrt{\frac{1}{2} \left(\sqrt{2}-1\right)} \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{2 \left(\sqrt{2}-1\right)} \sqrt{b} \sqrt{\sqrt{a x^2+b^2}+b}}-\frac{\sqrt{\sqrt{a x^2+b^2}+b}}{\sqrt{2 \left(\sqrt{2}-1\right)} \sqrt{b}}\right)}{\sqrt{a}}-\frac{\sqrt{\frac{1}{2} \left(\sqrt{2}-1\right)} \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{b} \sqrt{\sqrt{a x^2+b^2}+b}}-\frac{\sqrt{\sqrt{a x^2+b^2}+b}}{\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{b}}\right)}{\sqrt{a}}-\frac{\sqrt{\sqrt{2}-1} \left(2+\sqrt{2}\right) \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{\sqrt{a x^2+b^2}+b}-\frac{a x}{\sqrt{\sqrt{a x^2+b^2}+b}}}{\sqrt{2 \left(\sqrt{2}-1\right)} \sqrt{a} \sqrt{b}}\right)}{2 \sqrt{a}}+\frac{\sqrt{\sqrt{2}-1} \left(2+\sqrt{2}\right) \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{\sqrt{a x^2+b^2}+b}-\frac{a x}{\sqrt{\sqrt{a x^2+b^2}+b}}}{\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{a} \sqrt{b}}\right)}{2 \sqrt{a}}",1,"Integrate[(b^2 + a*x^2)^2/((-b^2 + a*x^2)^2*Sqrt[b + Sqrt[b^2 + a*x^2]]), x]","F",-1
3103,1,475,586,0.8505619,"\int \frac{\sqrt{a x+\sqrt{-b+a x}}}{\sqrt{-b+a x} \left(1+a^2 x^2\right)} \, dx","Integrate[Sqrt[a*x + Sqrt[-b + a*x]]/(Sqrt[-b + a*x]*(1 + a^2*x^2)),x]","-\frac{i \left(\frac{\sqrt{\sqrt{-b-i}+i} \tan ^{-1}\left(\frac{\left(-1+2 \sqrt{-b-i}\right) \sqrt{a x-b}-2 b+\sqrt{-b-i}}{2 \sqrt{\sqrt{-b-i}+i} \sqrt{\sqrt{a x-b}+a x}}\right)+\sqrt{i-\sqrt{-b-i}} \tan ^{-1}\left(\frac{\left(1+2 \sqrt{-b-i}\right) \sqrt{a x-b}+2 b+\sqrt{-b-i}}{2 \sqrt{i-\sqrt{-b-i}} \sqrt{\sqrt{a x-b}+a x}}\right)}{\sqrt{-b-i}}-\frac{\sqrt{i-\sqrt{-b+i}} \tanh ^{-1}\left(\frac{\left(-1+2 \sqrt{-b+i}\right) \sqrt{a x-b}-2 b+\sqrt{-b+i}}{2 \sqrt{i-\sqrt{-b+i}} \sqrt{\sqrt{a x-b}+a x}}\right)}{\sqrt{-b+i}}-\frac{\sqrt{\sqrt{-b+i}+i} \tanh ^{-1}\left(\frac{\left(1+2 \sqrt{-b+i}\right) \sqrt{a x-b}+2 b+\sqrt{-b+i}}{2 \sqrt{\sqrt{-b+i}+i} \sqrt{\sqrt{a x-b}+a x}}\right)}{\sqrt{-b+i}}\right)}{2 a}","-\frac{\text{RootSum}\left[\text{$\#$1}^8+4 \text{$\#$1}^6 b-8 \text{$\#$1}^5 b+6 \text{$\#$1}^4 b^2+2 \text{$\#$1}^4 b+16 \text{$\#$1}^4-16 \text{$\#$1}^3 b^2-32 \text{$\#$1}^3+4 \text{$\#$1}^2 b^3+20 \text{$\#$1}^2 b^2+24 \text{$\#$1}^2-8 \text{$\#$1} b^3-8 \text{$\#$1} b^2-8 \text{$\#$1}+b^4+2 b^3+b^2+1\&,\frac{2 \text{$\#$1}^5 \log \left(\text{$\#$1}+\sqrt{a x-b}-\sqrt{\sqrt{a x-b}+a x}\right)-5 \text{$\#$1}^4 \log \left(\text{$\#$1}+\sqrt{a x-b}-\sqrt{\sqrt{a x-b}+a x}\right)+4 \text{$\#$1}^3 b \log \left(\text{$\#$1}+\sqrt{a x-b}-\sqrt{\sqrt{a x-b}+a x}\right)+4 \text{$\#$1}^3 \log \left(\text{$\#$1}+\sqrt{a x-b}-\sqrt{\sqrt{a x-b}+a x}\right)-6 \text{$\#$1}^2 b \log \left(\text{$\#$1}+\sqrt{a x-b}-\sqrt{\sqrt{a x-b}+a x}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1}+\sqrt{a x-b}-\sqrt{\sqrt{a x-b}+a x}\right)+2 \text{$\#$1} b^2 \log \left(\text{$\#$1}+\sqrt{a x-b}-\sqrt{\sqrt{a x-b}+a x}\right)-b^2 \log \left(\text{$\#$1}+\sqrt{a x-b}-\sqrt{\sqrt{a x-b}+a x}\right)+2 \text{$\#$1} b \log \left(\text{$\#$1}+\sqrt{a x-b}-\sqrt{\sqrt{a x-b}+a x}\right)}{\text{$\#$1}^7+3 \text{$\#$1}^5 b-5 \text{$\#$1}^4 b+3 \text{$\#$1}^3 b^2+\text{$\#$1}^3 b+8 \text{$\#$1}^3-6 \text{$\#$1}^2 b^2-12 \text{$\#$1}^2+\text{$\#$1} b^3+5 \text{$\#$1} b^2+6 \text{$\#$1}-b^3-b^2-1}\&\right]}{2 a}",1,"((-1/2*I)*((Sqrt[I + Sqrt[-I - b]]*ArcTan[(Sqrt[-I - b] - 2*b + (-1 + 2*Sqrt[-I - b])*Sqrt[-b + a*x])/(2*Sqrt[I + Sqrt[-I - b]]*Sqrt[a*x + Sqrt[-b + a*x]])] + Sqrt[I - Sqrt[-I - b]]*ArcTan[(Sqrt[-I - b] + 2*b + (1 + 2*Sqrt[-I - b])*Sqrt[-b + a*x])/(2*Sqrt[I - Sqrt[-I - b]]*Sqrt[a*x + Sqrt[-b + a*x]])])/Sqrt[-I - b] - (Sqrt[I - Sqrt[I - b]]*ArcTanh[(Sqrt[I - b] - 2*b + (-1 + 2*Sqrt[I - b])*Sqrt[-b + a*x])/(2*Sqrt[I - Sqrt[I - b]]*Sqrt[a*x + Sqrt[-b + a*x]])])/Sqrt[I - b] - (Sqrt[I + Sqrt[I - b]]*ArcTanh[(Sqrt[I - b] + 2*b + (1 + 2*Sqrt[I - b])*Sqrt[-b + a*x])/(2*Sqrt[I + Sqrt[I - b]]*Sqrt[a*x + Sqrt[-b + a*x]])])/Sqrt[I - b]))/a","C",1
3104,1,571,590,0.582807,"\int \frac{\left(1+x^4\right) \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{1-x^4} \, dx","Integrate[((1 + x^4)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^4),x]","\frac{1}{120} \left(120 \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^4-2 \text{$\#$1}^2+1}\&\right]-60 \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]+60 \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-4 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+6 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+4 \text{$\#$1}^3-2 \text{$\#$1}}\&\right]-48 \left(\sqrt{\sqrt{x^2+1}+x}+1\right)^{5/2}+80 \left(\sqrt{\sqrt{x^2+1}+x}+1\right)^{3/2}+\frac{30 \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{\sqrt{\sqrt{x^2+1}+x}}+\frac{60 \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{\sqrt{x^2+1}+x}+15 \log \left(1-\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)-15 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}+1\right)\right)","\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^4-2 \text{$\#$1}^2+1}\&\right]-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]+\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-4 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+6 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+4 \text{$\#$1}^3-2 \text{$\#$1}}\&\right]+\frac{\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} (15-8 x)+\sqrt{x^2+1} \left((16-48 x) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-8 \sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\left(-48 x^2+16 x+6\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{60 \sqrt{x^2+1}+60 x}-\frac{1}{4} \tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)",1,"((60*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(x + Sqrt[1 + x^2]) + (30*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/Sqrt[x + Sqrt[1 + x^2]] + 80*(1 + Sqrt[x + Sqrt[1 + x^2]])^(3/2) - 48*(1 + Sqrt[x + Sqrt[1 + x^2]])^(5/2) + 15*Log[1 - Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]] - 15*Log[1 + Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]] - 60*RootSum[-2 + 4*#1^4 - 4*#1^6 + #1^8 & , (2*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1] - 2*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^4 + Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^6)/(2*#1^3 - 3*#1^5 + #1^7) & ] + 120*RootSum[2 - 4*#1^2 + 6*#1^4 - 4*#1^6 + #1^8 & , (Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1)/(1 - 2*#1^2 + #1^4) & ] + 60*RootSum[2 - 8*#1^2 + 8*#1^4 - 4*#1^6 + #1^8 & , (-2*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1] + 6*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^2 - 4*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^4 + Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^6)/(-2*#1 + 4*#1^3 - 3*#1^5 + #1^7) & ])/120","A",1
3105,1,571,590,0.1863249,"\int \frac{\left(1+x^4\right) \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{1-x^4} \, dx","Integrate[((1 + x^4)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^4),x]","\frac{1}{120} \left(120 \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^4-2 \text{$\#$1}^2+1}\&\right]-60 \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]+60 \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-4 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+6 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+4 \text{$\#$1}^3-2 \text{$\#$1}}\&\right]-48 \left(\sqrt{\sqrt{x^2+1}+x}+1\right)^{5/2}+80 \left(\sqrt{\sqrt{x^2+1}+x}+1\right)^{3/2}+\frac{30 \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{\sqrt{\sqrt{x^2+1}+x}}+\frac{60 \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{\sqrt{x^2+1}+x}+15 \log \left(1-\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)-15 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}+1\right)\right)","\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^4-2 \text{$\#$1}^2+1}\&\right]-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]+\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-4 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+6 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+4 \text{$\#$1}^3-2 \text{$\#$1}}\&\right]+\frac{\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} (15-8 x)+\sqrt{x^2+1} \left((16-48 x) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-8 \sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\left(-48 x^2+16 x+6\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{60 \sqrt{x^2+1}+60 x}-\frac{1}{4} \tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)",1,"((60*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(x + Sqrt[1 + x^2]) + (30*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/Sqrt[x + Sqrt[1 + x^2]] + 80*(1 + Sqrt[x + Sqrt[1 + x^2]])^(3/2) - 48*(1 + Sqrt[x + Sqrt[1 + x^2]])^(5/2) + 15*Log[1 - Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]] - 15*Log[1 + Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]] - 60*RootSum[-2 + 4*#1^4 - 4*#1^6 + #1^8 & , (2*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1] - 2*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^4 + Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^6)/(2*#1^3 - 3*#1^5 + #1^7) & ] + 120*RootSum[2 - 4*#1^2 + 6*#1^4 - 4*#1^6 + #1^8 & , (Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1)/(1 - 2*#1^2 + #1^4) & ] + 60*RootSum[2 - 8*#1^2 + 8*#1^4 - 4*#1^6 + #1^8 & , (-2*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1] + 6*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^2 - 4*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^4 + Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^6)/(-2*#1 + 4*#1^3 - 3*#1^5 + #1^7) & ])/120","A",1
3106,1,765,603,1.0343859,"\int \frac{\left(1+x^2\right)^{5/2} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","Integrate[((1 + x^2)^(5/2)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2)^2,x]","\frac{\left(x^2+1\right)^{3/2} \left(\sqrt{x^2+1}+x\right) \left(-20160 \left(\sqrt{x^2+1}+x\right)^2 \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{13 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-14 \text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+4 \text{$\#$1}^2-2}\&\right]+20160 \left(\sqrt{x^2+1}+x\right)^2 \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{13 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-14 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]+8960 \left(\sqrt{x^2+1}+x\right)^2 \left(\sqrt{\sqrt{x^2+1}+x}+1\right)^{9/2}-34560 \left(\sqrt{x^2+1}+x\right)^2 \left(\sqrt{\sqrt{x^2+1}+x}+1\right)^{7/2}+48384 \left(\sqrt{x^2+1}+x\right)^2 \left(\sqrt{\sqrt{x^2+1}+x}+1\right)^{5/2}-26880 \left(\sqrt{x^2+1}+x\right)^2 \left(\sqrt{\sqrt{x^2+1}+x}+1\right)^{3/2}+1451520 \left(\sqrt{x^2+1}+x\right)^2 \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-3150 \left(\sqrt{x^2+1}+x\right)^{3/2} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}+2100 \left(\sqrt{x^2+1}+x\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\frac{161280 \left(3 x^2+3 \sqrt{x^2+1} x+1\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{x^2-1}-1680 \sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-10080 \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}+724185 \left(\sqrt{x^2+1}+x\right)^2 \log \left(1-\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)-724185 \left(\sqrt{x^2+1}+x\right)^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}+1\right)\right)}{80640 \left(x^2+\sqrt{x^2+1} x+1\right)^3}","-\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{13 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-14 \text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+4 \text{$\#$1}^2-2}\&\right]+\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{13 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-14 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]-\frac{2299}{128} \tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\frac{\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(10240 x^7+8192 x^6-3740 x^5-1680 x^4-8025 x^3-6328 x^2+1525 x-184\right)+\sqrt{x^2+1} \left(\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(10240 x^6+8192 x^5-8860 x^4-5776 x^3-2315 x^2-2416 x+935\right)+\left(143360 x^7-12288 x^6+5789696 x^5+7272 x^4-3989088 x^3+5298 x^2-3314848 x-282\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\left(143360 x^8-12288 x^7+5861376 x^6+1128 x^5-1112160 x^4+10470 x^3-6024144 x^2+690 x-803792\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{40320 \left(x^2-1\right) \left(8 x^4+8 x^2+1\right)+40320 \left(x^2-1\right) \sqrt{x^2+1} \left(8 x^3+4 x\right)}",1,"((1 + x^2)^(3/2)*(x + Sqrt[1 + x^2])*(-10080*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - 1680*Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] + 2100*(x + Sqrt[1 + x^2])*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - 3150*(x + Sqrt[1 + x^2])^(3/2)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] + 1451520*(x + Sqrt[1 + x^2])^2*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - (161280*(1 + 3*x^2 + 3*x*Sqrt[1 + x^2])*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(-1 + x^2) - 26880*(x + Sqrt[1 + x^2])^2*(1 + Sqrt[x + Sqrt[1 + x^2]])^(3/2) + 48384*(x + Sqrt[1 + x^2])^2*(1 + Sqrt[x + Sqrt[1 + x^2]])^(5/2) - 34560*(x + Sqrt[1 + x^2])^2*(1 + Sqrt[x + Sqrt[1 + x^2]])^(7/2) + 8960*(x + Sqrt[1 + x^2])^2*(1 + Sqrt[x + Sqrt[1 + x^2]])^(9/2) + 724185*(x + Sqrt[1 + x^2])^2*Log[1 - Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]] - 724185*(x + Sqrt[1 + x^2])^2*Log[1 + Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]] + 20160*(x + Sqrt[1 + x^2])^2*RootSum[-2 + 4*#1^4 - 4*#1^6 + #1^8 & , (2*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1] - 14*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^2 + 13*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^4)/(2*#1^3 - 3*#1^5 + #1^7) & ] - 20160*(x + Sqrt[1 + x^2])^2*RootSum[2 - 8*#1^2 + 8*#1^4 - 4*#1^6 + #1^8 & , (-14*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1 + 13*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^3)/(-2 + 4*#1^2 - 3*#1^4 + #1^6) & ]))/(80640*(1 + x^2 + x*Sqrt[1 + x^2])^3)","A",1
3107,1,765,603,0.594064,"\int \frac{\left(1+x^2\right)^{5/2} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","Integrate[((1 + x^2)^(5/2)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2)^2,x]","\frac{\left(x^2+1\right)^{3/2} \left(\sqrt{x^2+1}+x\right) \left(-20160 \left(\sqrt{x^2+1}+x\right)^2 \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{13 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-14 \text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+4 \text{$\#$1}^2-2}\&\right]+20160 \left(\sqrt{x^2+1}+x\right)^2 \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{13 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-14 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]+8960 \left(\sqrt{x^2+1}+x\right)^2 \left(\sqrt{\sqrt{x^2+1}+x}+1\right)^{9/2}-34560 \left(\sqrt{x^2+1}+x\right)^2 \left(\sqrt{\sqrt{x^2+1}+x}+1\right)^{7/2}+48384 \left(\sqrt{x^2+1}+x\right)^2 \left(\sqrt{\sqrt{x^2+1}+x}+1\right)^{5/2}-26880 \left(\sqrt{x^2+1}+x\right)^2 \left(\sqrt{\sqrt{x^2+1}+x}+1\right)^{3/2}+1451520 \left(\sqrt{x^2+1}+x\right)^2 \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-3150 \left(\sqrt{x^2+1}+x\right)^{3/2} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}+2100 \left(\sqrt{x^2+1}+x\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\frac{161280 \left(3 x^2+3 \sqrt{x^2+1} x+1\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{x^2-1}-1680 \sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-10080 \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}+724185 \left(\sqrt{x^2+1}+x\right)^2 \log \left(1-\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)-724185 \left(\sqrt{x^2+1}+x\right)^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}+1\right)\right)}{80640 \left(x^2+\sqrt{x^2+1} x+1\right)^3}","-\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{13 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-14 \text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+4 \text{$\#$1}^2-2}\&\right]+\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{13 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-14 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]-\frac{2299}{128} \tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\frac{\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(10240 x^7+8192 x^6-3740 x^5-1680 x^4-8025 x^3-6328 x^2+1525 x-184\right)+\sqrt{x^2+1} \left(\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(10240 x^6+8192 x^5-8860 x^4-5776 x^3-2315 x^2-2416 x+935\right)+\left(143360 x^7-12288 x^6+5789696 x^5+7272 x^4-3989088 x^3+5298 x^2-3314848 x-282\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\left(143360 x^8-12288 x^7+5861376 x^6+1128 x^5-1112160 x^4+10470 x^3-6024144 x^2+690 x-803792\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{40320 \left(x^2-1\right) \left(8 x^4+8 x^2+1\right)+40320 \left(x^2-1\right) \sqrt{x^2+1} \left(8 x^3+4 x\right)}",1,"((1 + x^2)^(3/2)*(x + Sqrt[1 + x^2])*(-10080*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - 1680*Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] + 2100*(x + Sqrt[1 + x^2])*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - 3150*(x + Sqrt[1 + x^2])^(3/2)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] + 1451520*(x + Sqrt[1 + x^2])^2*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - (161280*(1 + 3*x^2 + 3*x*Sqrt[1 + x^2])*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(-1 + x^2) - 26880*(x + Sqrt[1 + x^2])^2*(1 + Sqrt[x + Sqrt[1 + x^2]])^(3/2) + 48384*(x + Sqrt[1 + x^2])^2*(1 + Sqrt[x + Sqrt[1 + x^2]])^(5/2) - 34560*(x + Sqrt[1 + x^2])^2*(1 + Sqrt[x + Sqrt[1 + x^2]])^(7/2) + 8960*(x + Sqrt[1 + x^2])^2*(1 + Sqrt[x + Sqrt[1 + x^2]])^(9/2) + 724185*(x + Sqrt[1 + x^2])^2*Log[1 - Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]] - 724185*(x + Sqrt[1 + x^2])^2*Log[1 + Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]] + 20160*(x + Sqrt[1 + x^2])^2*RootSum[-2 + 4*#1^4 - 4*#1^6 + #1^8 & , (2*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1] - 14*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^2 + 13*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^4)/(2*#1^3 - 3*#1^5 + #1^7) & ] - 20160*(x + Sqrt[1 + x^2])^2*RootSum[2 - 8*#1^2 + 8*#1^4 - 4*#1^6 + #1^8 & , (-14*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1 + 13*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^3)/(-2 + 4*#1^2 - 3*#1^4 + #1^6) & ]))/(80640*(1 + x^2 + x*Sqrt[1 + x^2])^3)","A",1
3108,0,0,604,0.349181,"\int \frac{\sqrt{1+x^4}}{(1+x)^3 \sqrt{x^2+\sqrt{1+x^4}}} \, dx","Integrate[Sqrt[1 + x^4]/((1 + x)^3*Sqrt[x^2 + Sqrt[1 + x^4]]),x]","\int \frac{\sqrt{1+x^4}}{(1+x)^3 \sqrt{x^2+\sqrt{1+x^4}}} \, dx","-\frac{5 \tan ^{-1}\left(\frac{\sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{\sqrt{2}-1}}\right)}{2 \sqrt{2 \left(\sqrt{2}-1\right)}}-\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{\sqrt{2}-1}}\right)}{\sqrt{\sqrt{2}-1}}-3 \sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)+\frac{1}{2} \sqrt{\frac{1}{2} \left(73+53 \sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{2}-1\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)-\frac{5 \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{1+\sqrt{2}}}\right)}{2 \sqrt{2 \left(1+\sqrt{2}\right)}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{1+\sqrt{2}}}\right)}{\sqrt{1+\sqrt{2}}}+\frac{1}{2} \sqrt{\frac{1}{2} \left(53 \sqrt{2}-73\right)} \tanh ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)+\frac{x \sqrt{\sqrt{x^4+1}+x^2} \left(-48 x^{12}+72 x^{10}-96 x^8+72 x^6-52 x^4+9 x^2-5\right)+\sqrt{x^4+1} \left(x \sqrt{\sqrt{x^4+1}+x^2} \left(-48 x^{10}+72 x^8-72 x^6+36 x^4-22 x^2\right)+\left(16 x^{12}-16 x^{10}+28 x^8-4 x^6+9 x^4+x^2\right) \sqrt{\sqrt{x^4+1}+x^2}\right)+\left(16 x^{14}-16 x^{12}+36 x^{10}-12 x^8+21 x^6+x^4+2 x^2\right) \sqrt{\sqrt{x^4+1}+x^2}}{2 x \left(x^2-1\right)^2 \left(\sqrt{x^4+1}+x^2\right)^5}",1,"Integrate[Sqrt[1 + x^4]/((1 + x)^3*Sqrt[x^2 + Sqrt[1 + x^4]]), x]","F",-1
3109,1,547,617,1.9779401,"\int \frac{x^2}{\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}} \, dx","Integrate[x^2/Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]],x]","\frac{1024 \sqrt{1-\sqrt{\frac{x-1}{x}}} x^3+1024 \sqrt{1-\sqrt{\frac{x-1}{x}}} \sqrt{\frac{x-1}{x}} x^3+20480 x^3+1888 \sqrt{1-\sqrt{\frac{x-1}{x}}} x^2+1760 \sqrt{1-\sqrt{\frac{x-1}{x}}} \sqrt{\frac{x-1}{x}} x^2+64 \sqrt{\frac{x-1}{x}} x^2+1344 x^2+6702 \sqrt{1-\sqrt{\frac{x-1}{x}}} x+6030 \sqrt{1-\sqrt{\frac{x-1}{x}}} \sqrt{\frac{x-1}{x}} x+324 \sqrt{\frac{x-1}{x}} x+3092 x-10545 \sqrt{1-\sqrt{1-\sqrt{\frac{x-1}{x}}}} \log \left(1-\frac{1}{\sqrt{1-\sqrt{1-\sqrt{\frac{x-1}{x}}}}}\right)+10545 \sqrt{1-\sqrt{1-\sqrt{\frac{x-1}{x}}}} \log \left(\frac{1}{\sqrt{1-\sqrt{1-\sqrt{\frac{x-1}{x}}}}}+1\right)+30 \sqrt{\sqrt{2}-1} \left(498+361 \sqrt{2}\right) \sqrt{1-\sqrt{1-\sqrt{\frac{x-1}{x}}}} \tan ^{-1}\left(\frac{1}{\sqrt{1+\sqrt{2}} \sqrt{1-\sqrt{1-\sqrt{\frac{x-1}{x}}}}}\right)+30 \sqrt{1+\sqrt{2}} \left(361 \sqrt{2}-498\right) \sqrt{1-\sqrt{1-\sqrt{\frac{x-1}{x}}}} \tanh ^{-1}\left(\frac{1}{\sqrt{\sqrt{2}-1} \sqrt{1-\sqrt{1-\sqrt{\frac{x-1}{x}}}}}\right)-34530}{61440 \sqrt{1-\sqrt{1-\sqrt{\frac{x-1}{x}}}}}","\frac{-17265 \left(1-\sqrt{1-\sqrt{1-\frac{1}{x}}}\right)^{23/2}+204165 \left(1-\sqrt{1-\sqrt{1-\frac{1}{x}}}\right)^{21/2}-1002573 \left(1-\sqrt{1-\sqrt{1-\frac{1}{x}}}\right)^{19/2}+2613381 \left(1-\sqrt{1-\sqrt{1-\frac{1}{x}}}\right)^{17/2}-3755230 \left(1-\sqrt{1-\sqrt{1-\frac{1}{x}}}\right)^{15/2}+2531670 \left(1-\sqrt{1-\sqrt{1-\frac{1}{x}}}\right)^{13/2}+215274 \left(1-\sqrt{1-\sqrt{1-\frac{1}{x}}}\right)^{11/2}-1429914 \left(1-\sqrt{1-\sqrt{1-\frac{1}{x}}}\right)^{9/2}+598095 \left(1-\sqrt{1-\sqrt{1-\frac{1}{x}}}\right)^{7/2}+184677 \left(1-\sqrt{1-\sqrt{1-\frac{1}{x}}}\right)^{5/2}-148125 \left(1-\sqrt{1-\sqrt{1-\frac{1}{x}}}\right)^{3/2}-4395 \sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}}{30720 \left(\left(1-\sqrt{1-\sqrt{1-\frac{1}{x}}}\right)^2-2 \left(1-\sqrt{1-\sqrt{1-\frac{1}{x}}}\right)-1\right)^3 \left(1-\sqrt{1-\frac{1}{x}}\right)^3}+\left(-\frac{7}{32} \sqrt{\frac{1}{2} \left(\frac{1}{2}+\frac{1}{\sqrt{2}}\right)}-\frac{137 \sqrt{\frac{1}{2}+\frac{1}{\sqrt{2}}}}{1024}\right) \tan ^{-1}\left(\frac{\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}}{\sqrt{\sqrt{2}-1}}\right)+\frac{703 \tanh ^{-1}\left(\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}\right)}{2048}+\left(\frac{7}{32} \sqrt{\frac{1}{2} \left(\frac{1}{\sqrt{2}}-\frac{1}{2}\right)}-\frac{137 \sqrt{\frac{1}{\sqrt{2}}-\frac{1}{2}}}{1024}\right) \tanh ^{-1}\left(\frac{\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}}{\sqrt{1+\sqrt{2}}}\right)",1,"(-34530 + 3092*x + 6702*Sqrt[1 - Sqrt[(-1 + x)/x]]*x + 324*Sqrt[(-1 + x)/x]*x + 6030*Sqrt[1 - Sqrt[(-1 + x)/x]]*Sqrt[(-1 + x)/x]*x + 1344*x^2 + 1888*Sqrt[1 - Sqrt[(-1 + x)/x]]*x^2 + 64*Sqrt[(-1 + x)/x]*x^2 + 1760*Sqrt[1 - Sqrt[(-1 + x)/x]]*Sqrt[(-1 + x)/x]*x^2 + 20480*x^3 + 1024*Sqrt[1 - Sqrt[(-1 + x)/x]]*x^3 + 1024*Sqrt[1 - Sqrt[(-1 + x)/x]]*Sqrt[(-1 + x)/x]*x^3 + 30*Sqrt[-1 + Sqrt[2]]*(498 + 361*Sqrt[2])*Sqrt[1 - Sqrt[1 - Sqrt[(-1 + x)/x]]]*ArcTan[1/(Sqrt[1 + Sqrt[2]]*Sqrt[1 - Sqrt[1 - Sqrt[(-1 + x)/x]]])] + 30*Sqrt[1 + Sqrt[2]]*(-498 + 361*Sqrt[2])*Sqrt[1 - Sqrt[1 - Sqrt[(-1 + x)/x]]]*ArcTanh[1/(Sqrt[-1 + Sqrt[2]]*Sqrt[1 - Sqrt[1 - Sqrt[(-1 + x)/x]]])] - 10545*Sqrt[1 - Sqrt[1 - Sqrt[(-1 + x)/x]]]*Log[1 - 1/Sqrt[1 - Sqrt[1 - Sqrt[(-1 + x)/x]]]] + 10545*Sqrt[1 - Sqrt[1 - Sqrt[(-1 + x)/x]]]*Log[1 + 1/Sqrt[1 - Sqrt[1 - Sqrt[(-1 + x)/x]]]])/(61440*Sqrt[1 - Sqrt[1 - Sqrt[(-1 + x)/x]]])","A",0
3110,0,0,622,3.9035937,"\int \frac{\left(1+x^2\right) \left(-a-b x+a x^2\right)}{x^2 \left(-c+d x+c x^2\right) \sqrt[3]{\frac{-1+x^2-x c_0}{-1+x^2-x c_1}}} \, dx","Integrate[((1 + x^2)*(-a - b*x + a*x^2))/(x^2*(-c + d*x + c*x^2)*((-1 + x^2 - x*C[0])/(-1 + x^2 - x*C[1]))^(1/3)),x]","\int \frac{\left(1+x^2\right) \left(-a-b x+a x^2\right)}{x^2 \left(-c+d x+c x^2\right) \sqrt[3]{\frac{-1+x^2-x c_0}{-1+x^2-x c_1}}} \, dx","\frac{\log \left(-1+\sqrt[3]{\frac{x^2-c_0 x-1}{x^2-c_1 x-1}}\right) (-a c c_0+a c c_1+3 a d+3 b c)}{3 c^2}+\frac{\log \left(\left(\frac{x^2-c_0 x-1}{x^2-c_1 x-1}\right){}^{2/3}+\sqrt[3]{\frac{x^2-c_0 x-1}{x^2-c_1 x-1}}+1\right) (a c c_0-a c c_1-3 a d-3 b c)}{6 c^2}+\frac{\sqrt[3]{-d-c c_1} (a d+b c) \log \left(\sqrt[3]{\frac{-x^2+c_0 x+1}{-x^2+c_1 x+1}} \sqrt[3]{-d-c c_1}+\sqrt[3]{d+c c_0}\right)}{c^2 \sqrt[3]{d+c c_0}}-\frac{\sqrt[3]{-d-c c_1} (a d+b c) \log \left(-\sqrt[3]{\frac{-x^2+c_0 x+1}{-x^2+c_1 x+1}} \sqrt[3]{-d-c c_1} \sqrt[3]{d+c c_0}+\left(\frac{-x^2+c_0 x+1}{-x^2+c_1 x+1}\right){}^{2/3} (-d-c c_1){}^{2/3}+(d+c c_0){}^{2/3}\right)}{2 c^2 \sqrt[3]{d+c c_0}}+\frac{\sqrt{3} \sqrt[3]{-d-c c_1} (a d+b c) \tan ^{-1}\left(\frac{\sqrt[3]{d+c c_0}-2 \sqrt[3]{\frac{-x^2+c_0 x+1}{-x^2+c_1 x+1}} \sqrt[3]{-d-c c_1}}{\sqrt{3} \sqrt[3]{d+c c_0}}\right)}{c^2 \sqrt[3]{d+c c_0}}+\frac{\tan ^{-1}\left(\frac{1+2 \sqrt[3]{\frac{x^2-c_0 x-1}{x^2-c_1 x-1}}}{\sqrt{3}}\right) \left(-\sqrt{3} a c c_0+\sqrt{3} a c c_1+3 \sqrt{3} a d+3 \sqrt{3} b c\right)}{3 c^2}+\frac{\left(\frac{x^2-c_0 x-1}{x^2-c_1 x-1}\right){}^{2/3} \left(a x^2-a c_1 x-a\right)}{c x}",1,"Integrate[((1 + x^2)*(-a - b*x + a*x^2))/(x^2*(-c + d*x + c*x^2)*((-1 + x^2 - x*C[0])/(-1 + x^2 - x*C[1]))^(1/3)), x]","F",-1
3111,0,0,639,10.3095133,"\int \frac{\left(1+x^2\right)^2 \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2 \sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[((1 + x^2)^2*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/((1 - x^2)^2*Sqrt[x + Sqrt[1 + x^2]]),x]","\int \frac{\left(1+x^2\right)^2 \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2 \sqrt{x+\sqrt{1+x^2}}} \, dx","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{4 \text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-8 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-\text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]-\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{4 \text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-8 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+9 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+4 \text{$\#$1}^3-2 \text{$\#$1}}\&\right]-\frac{1}{8} \tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\frac{\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(64 x^5-4 x^4-16 x^3+2 x^2-48 x+2\right)+\sqrt{x^2+1} \left(\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(64 x^4-4 x^3-48 x^2+4 x-16\right)+\left(128 x^5+12 x^4-272 x^3-9 x^2-96 x-3\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\left(128 x^6+12 x^5-208 x^4-3 x^3-248 x^2-9 x-8\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{24 \left(x^2-1\right) \left(\sqrt{x^2+1}+x\right)^{7/2}}",1,"Integrate[((1 + x^2)^2*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/((1 - x^2)^2*Sqrt[x + Sqrt[1 + x^2]]), x]","F",-1
3112,0,0,639,0.3533747,"\int \frac{\left(1+x^2\right)^2 \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2 \sqrt{x+\sqrt{1+x^2}}} \, dx","Integrate[((1 + x^2)^2*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/((1 - x^2)^2*Sqrt[x + Sqrt[1 + x^2]]),x]","\int \frac{\left(1+x^2\right)^2 \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2 \sqrt{x+\sqrt{1+x^2}}} \, dx","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{4 \text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-8 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-\text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]-\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{4 \text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-8 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+9 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+4 \text{$\#$1}^3-2 \text{$\#$1}}\&\right]-\frac{1}{8} \tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\frac{\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(64 x^5-4 x^4-16 x^3+2 x^2-48 x+2\right)+\sqrt{x^2+1} \left(\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(64 x^4-4 x^3-48 x^2+4 x-16\right)+\left(128 x^5+12 x^4-272 x^3-9 x^2-96 x-3\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\left(128 x^6+12 x^5-208 x^4-3 x^3-248 x^2-9 x-8\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{24 \left(x^2-1\right) \left(\sqrt{x^2+1}+x\right)^{7/2}}",1,"Integrate[((1 + x^2)^2*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/((1 - x^2)^2*Sqrt[x + Sqrt[1 + x^2]]), x]","F",-1
3113,0,0,639,7.8767918,"\int \frac{\left(1+x^2\right)^2 \sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","Integrate[((1 + x^2)^2*Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2)^2,x]","\int \frac{\left(1+x^2\right)^2 \sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{7 \text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-15 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+13 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]+\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{7 \text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-15 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+5 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+4 \text{$\#$1}^3-2 \text{$\#$1}}\&\right]-\tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\frac{\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(24 x^5+32 x^4-6 x^3-16 x^2-18 x-16\right)+\sqrt{x^2+1} \left(\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(24 x^4+32 x^3-18 x^2-32 x-6\right)+\left(240 x^5-32 x^4-1170 x^3+24 x^2-120 x+8\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\left(240 x^6-32 x^5-1050 x^4+8 x^3-735 x^2+24 x+75\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{105 \left(x^2-1\right) \left(\sqrt{x^2+1}+x\right)^{5/2}}",1,"Integrate[((1 + x^2)^2*Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2)^2, x]","F",-1
3114,0,0,639,0.3252273,"\int \frac{\left(1+x^2\right)^2 \sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","Integrate[((1 + x^2)^2*Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2)^2,x]","\int \frac{\left(1+x^2\right)^2 \sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{7 \text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-15 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+13 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]+\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{7 \text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-15 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+5 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+4 \text{$\#$1}^3-2 \text{$\#$1}}\&\right]-\tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\frac{\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(24 x^5+32 x^4-6 x^3-16 x^2-18 x-16\right)+\sqrt{x^2+1} \left(\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(24 x^4+32 x^3-18 x^2-32 x-6\right)+\left(240 x^5-32 x^4-1170 x^3+24 x^2-120 x+8\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\left(240 x^6-32 x^5-1050 x^4+8 x^3-735 x^2+24 x+75\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{105 \left(x^2-1\right) \left(\sqrt{x^2+1}+x\right)^{5/2}}",1,"Integrate[((1 + x^2)^2*Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2)^2, x]","F",-1
3115,1,655,650,1.8296912,"\int \frac{x^2}{\sqrt{1+\sqrt{a x+\sqrt{-b+a^2 x^2}}}} \, dx","Integrate[x^2/Sqrt[1 + Sqrt[a*x + Sqrt[-b + a^2*x^2]]],x]","-\frac{-\frac{b^3 \left(\sqrt{\sqrt{a^2 x^2-b}+a x}+1\right)^{11/2}}{12 \left(\sqrt{a^2 x^2-b}+a x\right)^3}+\frac{61 b^3 \left(\sqrt{\sqrt{a^2 x^2-b}+a x}+1\right)^{9/2}}{120 \left(\sqrt{a^2 x^2-b}+a x\right)^{5/2}}-\frac{417 b^3 \left(\sqrt{\sqrt{a^2 x^2-b}+a x}+1\right)^{7/2}}{320 \left(\sqrt{a^2 x^2-b}+a x\right)^2}+\frac{3481 b^3 \left(\sqrt{\sqrt{a^2 x^2-b}+a x}+1\right)^{5/2}}{1920 \left(\sqrt{a^2 x^2-b}+a x\right)^{3/2}}-\frac{b^2 (2279 b+384) \left(\sqrt{\sqrt{a^2 x^2-b}+a x}+1\right)^{3/2}}{1536 \left(\sqrt{a^2 x^2-b}+a x\right)}+\frac{b^2 (793 b+640) \sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+1}}{1024 \sqrt{\sqrt{a^2 x^2-b}+a x}}+\frac{3 b^2 (77 b+128) \log \left(1-\frac{1}{\sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+1}}\right)}{2048}-\frac{3 b^2 (77 b+128) \log \left(\frac{1}{\sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+1}}+1\right)}{2048}-\frac{1}{11} \left(\sqrt{\sqrt{a^2 x^2-b}+a x}+1\right)^{11/2}+\frac{5}{9} \left(\sqrt{\sqrt{a^2 x^2-b}+a x}+1\right)^{9/2}-\frac{10}{7} \left(\sqrt{\sqrt{a^2 x^2-b}+a x}+1\right)^{7/2}+2 \left(\sqrt{\sqrt{a^2 x^2-b}+a x}+1\right)^{5/2}-\frac{1}{3} (b+5) \left(\sqrt{\sqrt{a^2 x^2-b}+a x}+1\right)^{3/2}+(b+1) \sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+1}}{2 a^3}","\frac{231 b^3 \tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+1}\right)}{2048 a^3}+\frac{3 b^2 \tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+1}\right)}{16 a^3}+\frac{\sqrt{a^2 x^2-b} \left(\sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+1} \left(-5734400 a^4 x^4-3932160 a^3 x^3-5160960 a^2 b x^2-5242880 a^2 x^2+1067220 a b^3 x+1774080 a b^2 x+1966080 a b x+365904 b^3+2007040 b^2+1310720 b\right)+\left(5160960 a^4 x^4+3276800 a^3 x^3+860160 a^2 b x^2+2621440 a^2 x^2-1600830 a b^3 x-2661120 a b^2 x-1638400 a b x-426888 b^3-860160 b^2-655360 b\right) \sqrt{\sqrt{a^2 x^2-b}+a x} \sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+1}\right)+\sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+1} \left(-5734400 a^5 x^5-3932160 a^4 x^4-2293760 a^3 b x^3-5242880 a^3 x^3+1067220 a^2 b^3 x^2+1774080 a^2 b^2 x^2+3932160 a^2 b x^2+365904 a b^3 x+5304320 a b^2 x+3932160 a b x-533610 b^4-591360 b^3-491520 b^2\right)+\left(5160960 a^5 x^5+3276800 a^4 x^4-1720320 a^3 b x^3+2621440 a^3 x^3-1600830 a^2 b^3 x^2-2661120 a^2 b^2 x^2-3276800 a^2 b x^2-426888 a b^3 x-1935360 a b^2 x-1966080 a b x+800415 b^4+1005312 b^3+409600 b^2\right) \sqrt{\sqrt{a^2 x^2-b}+a x} \sqrt{\sqrt{\sqrt{a^2 x^2-b}+a x}+1}}{7096320 a^3 \left(4 a^3 x^3-3 a b x\right)+7096320 a^3 \sqrt{a^2 x^2-b} \left(4 a^2 x^2-b\right)}",1,"-1/2*((1 + b)*Sqrt[1 + Sqrt[a*x + Sqrt[-b + a^2*x^2]]] + (b^2*(640 + 793*b)*Sqrt[1 + Sqrt[a*x + Sqrt[-b + a^2*x^2]]])/(1024*Sqrt[a*x + Sqrt[-b + a^2*x^2]]) - ((5 + b)*(1 + Sqrt[a*x + Sqrt[-b + a^2*x^2]])^(3/2))/3 - (b^2*(384 + 2279*b)*(1 + Sqrt[a*x + Sqrt[-b + a^2*x^2]])^(3/2))/(1536*(a*x + Sqrt[-b + a^2*x^2])) + 2*(1 + Sqrt[a*x + Sqrt[-b + a^2*x^2]])^(5/2) + (3481*b^3*(1 + Sqrt[a*x + Sqrt[-b + a^2*x^2]])^(5/2))/(1920*(a*x + Sqrt[-b + a^2*x^2])^(3/2)) - (10*(1 + Sqrt[a*x + Sqrt[-b + a^2*x^2]])^(7/2))/7 - (417*b^3*(1 + Sqrt[a*x + Sqrt[-b + a^2*x^2]])^(7/2))/(320*(a*x + Sqrt[-b + a^2*x^2])^2) + (5*(1 + Sqrt[a*x + Sqrt[-b + a^2*x^2]])^(9/2))/9 + (61*b^3*(1 + Sqrt[a*x + Sqrt[-b + a^2*x^2]])^(9/2))/(120*(a*x + Sqrt[-b + a^2*x^2])^(5/2)) - (1 + Sqrt[a*x + Sqrt[-b + a^2*x^2]])^(11/2)/11 - (b^3*(1 + Sqrt[a*x + Sqrt[-b + a^2*x^2]])^(11/2))/(12*(a*x + Sqrt[-b + a^2*x^2])^3) + (3*b^2*(128 + 77*b)*Log[1 - 1/Sqrt[1 + Sqrt[a*x + Sqrt[-b + a^2*x^2]]]])/2048 - (3*b^2*(128 + 77*b)*Log[1 + 1/Sqrt[1 + Sqrt[a*x + Sqrt[-b + a^2*x^2]]]])/2048)/a^3","A",1
3116,1,72,669,0.0481882,"\int \sqrt[3]{\frac{x}{-1-a x+3 x^2+3 a x^3-3 x^4-3 a x^5+x^6+a x^7}} \, dx","Integrate[(x/(-1 - a*x + 3*x^2 + 3*a*x^3 - 3*x^4 - 3*a*x^5 + x^6 + a*x^7))^(1/3),x]","\frac{3}{2} \left(x^2-1\right) \sqrt[3]{\frac{x}{\left(x^2-1\right)^3 (a x+1)}} \left(\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(a-1) x}{a x+1}\right)-\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(a+1) x}{a x+1}\right)\right)","\frac{\log \left(\sqrt[3]{\frac{x}{a x^7-3 a x^5+3 a x^3-a x+x^6-3 x^4+3 x^2-1}} \left(\sqrt[3]{1-a} x^2-\sqrt[3]{1-a}\right)+1\right)}{2 \sqrt[3]{1-a}}+\frac{\log \left(\left(\sqrt[3]{a+1} x^2-\sqrt[3]{a+1}\right) \sqrt[3]{\frac{x}{a x^7-3 a x^5+3 a x^3-a x+x^6-3 x^4+3 x^2-1}}-1\right)}{2 \sqrt[3]{a+1}}-\frac{\log \left(\sqrt[3]{\frac{x}{a x^7-3 a x^5+3 a x^3-a x+x^6-3 x^4+3 x^2-1}} \left(\sqrt[3]{1-a}-\sqrt[3]{1-a} x^2\right)+\left((1-a)^{2/3} x^4-2 (1-a)^{2/3} x^2+(1-a)^{2/3}\right) \left(\frac{x}{a x^7-3 a x^5+3 a x^3-a x+x^6-3 x^4+3 x^2-1}\right)^{2/3}+1\right)}{4 \sqrt[3]{1-a}}-\frac{\log \left(\sqrt[3]{\frac{x}{a x^7-3 a x^5+3 a x^3-a x+x^6-3 x^4+3 x^2-1}} \left(\sqrt[3]{a+1} x^2-\sqrt[3]{a+1}\right)+\left((a+1)^{2/3} x^4-2 (a+1)^{2/3} x^2+(a+1)^{2/3}\right) \left(\frac{x}{a x^7-3 a x^5+3 a x^3-a x+x^6-3 x^4+3 x^2-1}\right)^{2/3}+1\right)}{4 \sqrt[3]{a+1}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{\sqrt[3]{1-a} \left(2 x^2-2\right) \sqrt[3]{\frac{x}{a x^7-3 a x^5+3 a x^3-a x+x^6-3 x^4+3 x^2-1}}}{\sqrt{3}}\right)}{2 \sqrt[3]{1-a}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt[3]{a+1} \left(2 x^2-2\right) \sqrt[3]{\frac{x}{a x^7-3 a x^5+3 a x^3-a x+x^6-3 x^4+3 x^2-1}}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt[3]{a+1}}",1,"(3*(x/((1 + a*x)*(-1 + x^2)^3))^(1/3)*(-1 + x^2)*(Hypergeometric2F1[1/3, 1, 4/3, ((-1 + a)*x)/(1 + a*x)] - Hypergeometric2F1[1/3, 1, 4/3, ((1 + a)*x)/(1 + a*x)]))/2","C",1
3117,0,0,674,157.1250697,"\int \frac{\sqrt{-b+a^2 x^2} \sqrt[3]{a x+\sqrt{-b+a^2 x^2}}}{\sqrt[4]{c+\sqrt[3]{a x+\sqrt{-b+a^2 x^2}}}} \, dx","Integrate[(Sqrt[-b + a^2*x^2]*(a*x + Sqrt[-b + a^2*x^2])^(1/3))/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^(1/4),x]","\int \frac{\sqrt{-b+a^2 x^2} \sqrt[3]{a x+\sqrt{-b+a^2 x^2}}}{\sqrt[4]{c+\sqrt[3]{a x+\sqrt{-b+a^2 x^2}}}} \, dx","-\frac{1989 b^2 \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt[3]{\sqrt{a^2 x^2-b}+a x}+c}}{\sqrt[4]{c}}\right)}{16384 a c^{21/4}}+\frac{1989 b^2 \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt[3]{\sqrt{a^2 x^2-b}+a x}+c}}{\sqrt[4]{c}}\right)}{16384 a c^{21/4}}+\frac{\sqrt{a^2 x^2-b} \left(\left(6055526400 a^2 c^7 x^2-4026531840 a c^{10} x+2409402996 b^2 c-1513881600 b c^7\right) \left(\sqrt[3]{\sqrt{a^2 x^2-b}+a x}+c\right)^{3/4}+\sqrt[3]{\sqrt{a^2 x^2-b}+a x} \left(-5752750080 a^2 c^6 x^2+3523215360 a c^9 x-3011753745 b^2+1438187520 b c^6\right) \left(\sqrt[3]{\sqrt{a^2 x^2-b}+a x}+c\right)^{3/4}+\left(\sqrt{a^2 x^2-b}+a x\right)^{2/3} \left(\sqrt[3]{\sqrt{a^2 x^2-b}+a x}+c\right)^{3/4} \left(5513052160 a^2 c^5 x^2-3229614080 a c^8 x-26186997760 b c^5+2684354560 c^{11}\right)\right)+\left(6055526400 a^3 c^7 x^3-4026531840 a^2 c^{10} x^2+2409402996 a b^2 c x-4541644800 a b c^7 x-1860655104 b^2 c^4+2013265920 b c^{10}\right) \left(\sqrt[3]{\sqrt{a^2 x^2-b}+a x}+c\right)^{3/4}+\sqrt[3]{\sqrt{a^2 x^2-b}+a x} \left(-5752750080 a^3 c^6 x^3+3523215360 a^2 c^9 x^2-3011753745 a b^2 x+4314562560 a b c^6 x+1976946048 b^2 c^3-1761607680 b c^9\right) \left(\sqrt[3]{\sqrt{a^2 x^2-b}+a x}+c\right)^{3/4}+\left(\sqrt{a^2 x^2-b}+a x\right)^{2/3} \left(\sqrt[3]{\sqrt{a^2 x^2-b}+a x}+c\right)^{3/4} \left(5513052160 a^3 c^5 x^3-3229614080 a^2 c^8 x^2-28943523840 a b c^5 x+2684354560 a c^{11} x-2141691552 b^2 c^2+1614807040 b c^8\right)}{12404367360 a c^5 \left(\sqrt{a^2 x^2-b}+a x\right)^{5/3}}",1,"Integrate[(Sqrt[-b + a^2*x^2]*(a*x + Sqrt[-b + a^2*x^2])^(1/3))/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^(1/4), x]","F",-1
3118,1,317,678,2.3556935,"\int \frac{\sqrt[6]{a x+\sqrt{-b+a^2 x^2}}}{x^3 \sqrt{-b+a^2 x^2}} \, dx","Integrate[(a*x + Sqrt[-b + a^2*x^2])^(1/6)/(x^3*Sqrt[-b + a^2*x^2]),x]","\frac{12 \sqrt{a^2 x^2-b} \left(b-2 a x \left(\sqrt{a^2 x^2-b}+a x\right)\right)^4 \left(4 a^2 x^2 \left(2 a x \left(\sqrt{a^2 x^2-b}+a x\right)-b\right) \, _2F_1\left(\frac{7}{12},3;\frac{19}{12};-\frac{\left(a x+\sqrt{a^2 x^2-b}\right)^2}{b}\right)-b^2\right)}{17 b^2 x^2 \left(\sqrt{a^2 x^2-b}+a x\right)^{5/6} \left(128 a^9 x^9-320 a^7 b x^7+272 a^5 b^2 x^5-88 a^3 b^3 x^3+b^4 \sqrt{a^2 x^2-b}-32 a^2 b^3 x^2 \sqrt{a^2 x^2-b}+128 a^8 x^8 \sqrt{a^2 x^2-b}-256 a^6 b x^6 \sqrt{a^2 x^2-b}+160 a^4 b^2 x^4 \sqrt{a^2 x^2-b}+8 a b^4 x\right)}","-\frac{35 \sqrt{2+\sqrt{3}} a^2 \tan ^{-1}\left(\frac{\left(\sqrt{\frac{3}{2}} \sqrt[12]{b}-\frac{\sqrt[12]{b}}{\sqrt{2}}\right) \sqrt[6]{\sqrt{a^2 x^2-b}+a x}}{\sqrt[3]{\sqrt{a^2 x^2-b}+a x}-\sqrt[6]{b}}\right)}{72 b^{17/12}}-\frac{35 \sqrt{2-\sqrt{3}} a^2 \tan ^{-1}\left(\frac{\left(\frac{\sqrt[12]{b}}{\sqrt{2}}+\sqrt{\frac{3}{2}} \sqrt[12]{b}\right) \sqrt[6]{\sqrt{a^2 x^2-b}+a x}}{\sqrt[3]{\sqrt{a^2 x^2-b}+a x}-\sqrt[6]{b}}\right)}{72 b^{17/12}}+\frac{35 a^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[12]{b} \sqrt[6]{\sqrt{a^2 x^2-b}+a x}}{\sqrt[3]{\sqrt{a^2 x^2-b}+a x}-\sqrt[6]{b}}\right)}{36 \sqrt{2} b^{17/12}}+\frac{35 a^2 \tanh ^{-1}\left(\frac{\frac{\sqrt[3]{\sqrt{a^2 x^2-b}+a x}}{\sqrt{2} \sqrt[12]{b}}+\frac{\sqrt[12]{b}}{\sqrt{2}}}{\sqrt[6]{\sqrt{a^2 x^2-b}+a x}}\right)}{36 \sqrt{2} b^{17/12}}-\frac{35 \sqrt{2+\sqrt{3}} a^2 \tanh ^{-1}\left(\frac{\frac{\sqrt{2} \sqrt[3]{\sqrt{a^2 x^2-b}+a x}}{\left(\sqrt{3}-1\right) \sqrt[12]{b}}+\frac{\sqrt{2} \sqrt[12]{b}}{\sqrt{3}-1}}{\sqrt[6]{\sqrt{a^2 x^2-b}+a x}}\right)}{72 b^{17/12}}-\frac{35 \sqrt{2-\sqrt{3}} a^2 \tanh ^{-1}\left(\frac{\frac{\sqrt{2} \sqrt[3]{\sqrt{a^2 x^2-b}+a x}}{\left(1+\sqrt{3}\right) \sqrt[12]{b}}+\frac{\sqrt{2} \sqrt[12]{b}}{1+\sqrt{3}}}{\sqrt[6]{\sqrt{a^2 x^2-b}+a x}}\right)}{72 b^{17/12}}+\frac{7 \left(\sqrt{a^2 x^2-b}+a x\right)^{7/6}}{24 b x^2}-\frac{5}{24 x^2 \left(\sqrt{a^2 x^2-b}+a x\right)^{5/6}}",1,"(12*Sqrt[-b + a^2*x^2]*(b - 2*a*x*(a*x + Sqrt[-b + a^2*x^2]))^4*(-b^2 + 4*a^2*x^2*(-b + 2*a*x*(a*x + Sqrt[-b + a^2*x^2]))*Hypergeometric2F1[7/12, 3, 19/12, -((a*x + Sqrt[-b + a^2*x^2])^2/b)]))/(17*b^2*x^2*(a*x + Sqrt[-b + a^2*x^2])^(5/6)*(8*a*b^4*x - 88*a^3*b^3*x^3 + 272*a^5*b^2*x^5 - 320*a^7*b*x^7 + 128*a^9*x^9 + b^4*Sqrt[-b + a^2*x^2] - 32*a^2*b^3*x^2*Sqrt[-b + a^2*x^2] + 160*a^4*b^2*x^4*Sqrt[-b + a^2*x^2] - 256*a^6*b*x^6*Sqrt[-b + a^2*x^2] + 128*a^8*x^8*Sqrt[-b + a^2*x^2]))","C",1
3119,0,0,685,0.6427295,"\int \frac{x^2 \left(x^2 c_3-c_4\right) \sqrt[4]{\frac{x c_0+x^2 c_3+c_4}{x c_1+x^2 c_3+c_4}}}{\left(-x+x^2 c_3+c_4\right) \left(x+x^2 c_3+c_4\right) \left(x^2+x^4 c_3{}^2+2 x^2 c_3 c_4+c_4{}^2\right)} \, dx","Integrate[(x^2*(x^2*C[3] - C[4])*((x*C[0] + x^2*C[3] + C[4])/(x*C[1] + x^2*C[3] + C[4]))^(1/4))/((-x + x^2*C[3] + C[4])*(x + x^2*C[3] + C[4])*(x^2 + x^4*C[3]^2 + 2*x^2*C[3]*C[4] + C[4]^2)),x]","\int \frac{x^2 \left(x^2 c_3-c_4\right) \sqrt[4]{\frac{x c_0+x^2 c_3+c_4}{x c_1+x^2 c_3+c_4}}}{\left(-x+x^2 c_3+c_4\right) \left(x+x^2 c_3+c_4\right) \left(x^2+x^4 c_3{}^2+2 x^2 c_3 c_4+c_4{}^2\right)} \, dx","\frac{1}{4} (c_0-c_1) \text{RootSum}\left[\text{$\#$1}^8+\text{$\#$1}^8 c_1{}^2-2 \text{$\#$1}^4-2 \text{$\#$1}^4 c_0 c_1+1+c_0{}^2\&,\frac{\text{$\#$1} \log \left(-\text{$\#$1}+\sqrt[4]{\frac{c_3 x^2+c_0 x+c_4}{c_3 x^2+c_1 x+c_4}}\right)}{\text{$\#$1}^4+\text{$\#$1}^4 c_1{}^2-1-c_0 c_1}\&\right]+\frac{\sqrt[4]{1+c_0} \tan ^{-1}\left(\frac{\frac{\sqrt[4]{1+c_0}}{\sqrt{2} \sqrt[4]{-1-c_1}}-\frac{\sqrt[4]{-1-c_1} \sqrt{\frac{c_3 x^2+c_0 x+c_4}{c_3 x^2+c_1 x+c_4}}}{\sqrt{2} \sqrt[4]{1+c_0}}}{\sqrt[4]{\frac{c_3 x^2+c_0 x+c_4}{c_3 x^2+c_1 x+c_4}}}\right)}{2 \sqrt{2} \sqrt[4]{-1-c_1}}-\frac{\sqrt[4]{-1+c_0} \tan ^{-1}\left(\frac{\frac{\sqrt[4]{-1+c_0}}{\sqrt{2} \sqrt[4]{1-c_1}}-\frac{\sqrt[4]{1-c_1} \sqrt{\frac{c_3 x^2+c_0 x+c_4}{c_3 x^2+c_1 x+c_4}}}{\sqrt{2} \sqrt[4]{-1+c_0}}}{\sqrt[4]{\frac{c_3 x^2+c_0 x+c_4}{c_3 x^2+c_1 x+c_4}}}\right)}{2 \sqrt{2} \sqrt[4]{1-c_1}}-\frac{\sqrt[4]{1+c_0} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1+c_0} \sqrt[4]{-1-c_1} \sqrt[4]{\frac{c_3 x^2+c_0 x+c_4}{c_3 x^2+c_1 x+c_4}}}{\sqrt{-1-c_1} \sqrt{\frac{c_3 x^2+c_0 x+c_4}{c_3 x^2+c_1 x+c_4}}+\sqrt{1+c_0}}\right)}{2 \sqrt{2} \sqrt[4]{-1-c_1}}+\frac{\sqrt[4]{-1+c_0} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{-1+c_0} \sqrt[4]{1-c_1} \sqrt[4]{\frac{c_3 x^2+c_0 x+c_4}{c_3 x^2+c_1 x+c_4}}}{\sqrt{1-c_1} \sqrt{\frac{c_3 x^2+c_0 x+c_4}{c_3 x^2+c_1 x+c_4}}+\sqrt{-1+c_0}}\right)}{2 \sqrt{2} \sqrt[4]{1-c_1}}",1,"Integrate[(x^2*(x^2*C[3] - C[4])*((x*C[0] + x^2*C[3] + C[4])/(x*C[1] + x^2*C[3] + C[4]))^(1/4))/((-x + x^2*C[3] + C[4])*(x + x^2*C[3] + C[4])*(x^2 + x^4*C[3]^2 + 2*x^2*C[3]*C[4] + C[4]^2)), x]","F",-1
3120,-1,0,697,180.000723,"\int \frac{1}{\sqrt[4]{a x+\sqrt{-b+a^2 x^2}} \sqrt[3]{c+\sqrt[4]{a x+\sqrt{-b+a^2 x^2}}}} \, dx","Integrate[1/((a*x + Sqrt[-b + a^2*x^2])^(1/4)*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(1/3)),x]","\text{\$Aborted}","\frac{182 b \log \left(\sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}-\sqrt[3]{c}\right)}{729 a c^{16/3}}-\frac{91 b \log \left(\sqrt[3]{c} \sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}+\left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{2/3}+c^{2/3}\right)}{729 a c^{16/3}}+\frac{182 b \tan ^{-1}\left(\frac{2 \sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}}{\sqrt{3} \sqrt[3]{c}}+\frac{1}{\sqrt{3}}\right)}{243 \sqrt{3} a c^{16/3}}+\frac{\left(\sqrt{a^2 x^2-b}+a x\right)^{3/4} \left(3645 a c^5 x-2730 b c\right) \left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{2/3}+\left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{2/3} \left(3640 a b x+1944 b c^4\right)+\sqrt[4]{\sqrt{a^2 x^2-b}+a x} \left(6561 a c^7 x-2106 b c^3\right) \left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{2/3}+\sqrt{\sqrt{a^2 x^2-b}+a x} \left(2340 b c^2-4374 a c^6 x\right) \left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{2/3}+\sqrt{a^2 x^2-b} \left(6561 c^7 \sqrt[4]{\sqrt{a^2 x^2-b}+a x} \left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{2/3}-4374 c^6 \sqrt{\sqrt{a^2 x^2-b}+a x} \left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{2/3}+3645 c^5 \left(\sqrt{a^2 x^2-b}+a x\right)^{3/4} \left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{2/3}+3640 b \left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{2/3}\right)}{4860 a c^5 \left(\sqrt{a^2 x^2-b}+a x\right)^{5/4}}",1,"$Aborted","F",-1
3121,1,575,699,1.7572801,"\int \frac{1}{\sqrt[3]{c+\sqrt[4]{a x+\sqrt{-b+a^2 x^2}}}} \, dx","Integrate[(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(-1/3),x]","\frac{6 \left(-\frac{35 b \log \left(1-\frac{\sqrt[3]{c}}{\sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}}\right)}{729 c^{13/3}}+\frac{35 b \log \left(\frac{c^{2/3}}{\left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{2/3}}+\frac{\sqrt[3]{c}}{\sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}}+1\right)}{1458 c^{13/3}}+\frac{35 b \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{c}}{\sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}}+1}{\sqrt{3}}\right)}{243 \sqrt{3} c^{13/3}}+\frac{b \left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{11/3}}{12 c^4 \left(\sqrt{a^2 x^2-b}+a x\right)}-\frac{37 b \left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{8/3}}{108 c^4 \left(\sqrt{a^2 x^2-b}+a x\right)^{3/4}}+\frac{44 b \left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{5/3}}{81 c^4 \sqrt{\sqrt{a^2 x^2-b}+a x}}-\frac{104 b \left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{2/3}}{243 c^4 \sqrt[4]{\sqrt{a^2 x^2-b}+a x}}-\frac{1}{2} c^3 \left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{2/3}+\frac{3}{5} c^2 \left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{5/3}+\frac{1}{11} \left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{11/3}-\frac{3}{8} c \left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{8/3}\right)}{a}","-\frac{70 b \log \left(\sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}-\sqrt[3]{c}\right)}{243 a c^{13/3}}+\frac{35 b \log \left(\sqrt[3]{c} \sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}+\left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{2/3}+c^{2/3}\right)}{243 a c^{13/3}}-\frac{70 b \tan ^{-1}\left(\frac{2 \sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}}{\sqrt{3} \sqrt[3]{c}}+\frac{1}{\sqrt{3}}\right)}{81 \sqrt{3} a c^{13/3}}+\frac{\sqrt{\sqrt{a^2 x^2-b}+a x} \left(11550 b c-10935 a c^5 x\right) \left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{2/3}+\left(\sqrt{a^2 x^2-b}+a x\right)^{3/4} \left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{2/3} \left(9720 a c^4 x-15400 b\right)+\left(8910 b c^3-19683 a c^7 x\right) \left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{2/3}+\sqrt[4]{\sqrt{a^2 x^2-b}+a x} \left(13122 a c^6 x-9900 b c^2\right) \left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{2/3}+\sqrt{a^2 x^2-b} \left(-19683 c^7 \left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{2/3}+13122 c^6 \sqrt[4]{\sqrt{a^2 x^2-b}+a x} \left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{2/3}-10935 c^5 \sqrt{\sqrt{a^2 x^2-b}+a x} \left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{2/3}+9720 c^4 \left(\sqrt{a^2 x^2-b}+a x\right)^{3/4} \left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{2/3}\right)}{17820 a c^4 \sqrt{a^2 x^2-b}+17820 a^2 c^4 x}",1,"(6*(-1/2*(c^3*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(2/3)) - (104*b*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(2/3))/(243*c^4*(a*x + Sqrt[-b + a^2*x^2])^(1/4)) + (3*c^2*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(5/3))/5 + (44*b*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(5/3))/(81*c^4*Sqrt[a*x + Sqrt[-b + a^2*x^2]]) - (3*c*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(8/3))/8 - (37*b*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(8/3))/(108*c^4*(a*x + Sqrt[-b + a^2*x^2])^(3/4)) + (c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(11/3)/11 + (b*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(11/3))/(12*c^4*(a*x + Sqrt[-b + a^2*x^2])) + (35*b*ArcTan[(1 + (2*c^(1/3))/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(1/3))/Sqrt[3]])/(243*Sqrt[3]*c^(13/3)) - (35*b*Log[1 - c^(1/3)/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(1/3)])/(729*c^(13/3)) + (35*b*Log[1 + c^(2/3)/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(2/3) + c^(1/3)/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(1/3)])/(1458*c^(13/3))))/a","A",1
3122,1,171,708,0.2368097,"\int \sqrt[4]{\frac{1+a x-4 x^2-4 a x^3+6 x^4+6 a x^5-4 x^6-4 a x^7+x^8+a x^9}{-c+b x}} \, dx","Integrate[((1 + a*x - 4*x^2 - 4*a*x^3 + 6*x^4 + 6*a*x^5 - 4*x^6 - 4*a*x^7 + x^8 + a*x^9)/(-c + b*x))^(1/4),x]","\frac{4 (a x+1) \sqrt[4]{\frac{a (c-b x)}{a c+b}} \sqrt[4]{\frac{\left(x^2-1\right)^4 (a x+1)}{b x-c}} \left((a c+b)^2 \, _2F_1\left(-\frac{7}{4},\frac{5}{4};\frac{9}{4};\frac{a x b+b}{b+a c}\right)-a \left(a \left(b^2-c^2\right) \, _2F_1\left(\frac{1}{4},\frac{5}{4};\frac{9}{4};\frac{a x b+b}{b+a c}\right)+2 c (a c+b) \, _2F_1\left(-\frac{3}{4},\frac{5}{4};\frac{9}{4};\frac{a x b+b}{b+a c}\right)\right)\right)}{5 a^3 b^2 \left(x^2-1\right)}","\frac{32 a^3 b^2 x^9-192 a^3 b^2 x^7+384 a^3 b^2 x^5-320 a^3 b^2 x^3+96 a^3 b^2 x+36 a^3 b c x^8-108 a^3 b c x^6+108 a^3 b c x^4-36 a^3 b c x^2+45 a^3 c^2 x^7-135 a^3 c^2 x^5+135 a^3 c^2 x^3-45 a^3 c^2 x+36 a^2 b^2 x^8-204 a^2 b^2 x^6+396 a^2 b^2 x^4-324 a^2 b^2 x^2+96 a^2 b^2+42 a^2 b c x^7-126 a^2 b c x^5+126 a^2 b c x^3-42 a^2 b c x+45 a^2 c^2 x^6-135 a^2 c^2 x^4+135 a^2 c^2 x^2-45 a^2 c^2-3 a b^2 x^7+9 a b^2 x^5-9 a b^2 x^3+3 a b^2 x+6 a b c x^6-18 a b c x^4+18 a b c x^2-6 a b c-7 b^2 x^6+21 b^2 x^4-21 b^2 x^2+7 b^2}{96 a^2 b^3 \left(\frac{a x^9-4 a x^7+6 a x^5-4 a x^3+a x+x^8-4 x^6+6 x^4-4 x^2+1}{b x-c}\right)^{3/4}}+\frac{\left(32 a^3 b^2 c-15 a^3 c^3+32 a^2 b^3-5 a^2 b c^2+3 a b^2 c-7 b^3\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} (x-1) (x+1)}{\sqrt[4]{b} \sqrt[4]{\frac{a x^9-4 a x^7+6 a x^5-4 a x^3+a x+x^8-4 x^6+6 x^4-4 x^2+1}{b x-c}}}\right)}{64 a^{11/4} b^{13/4}}+\frac{\left(-32 a^3 b^2 c+15 a^3 c^3-32 a^2 b^3+5 a^2 b c^2-3 a b^2 c+7 b^3\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} (x-1) (x+1)}{\sqrt[4]{b} \sqrt[4]{\frac{a x^9-4 a x^7+6 a x^5-4 a x^3+a x+x^8-4 x^6+6 x^4-4 x^2+1}{b x-c}}}\right)}{64 a^{11/4} b^{13/4}}",1,"(4*(1 + a*x)*((a*(c - b*x))/(b + a*c))^(1/4)*(((1 + a*x)*(-1 + x^2)^4)/(-c + b*x))^(1/4)*((b + a*c)^2*Hypergeometric2F1[-7/4, 5/4, 9/4, (b + a*b*x)/(b + a*c)] - a*(2*c*(b + a*c)*Hypergeometric2F1[-3/4, 5/4, 9/4, (b + a*b*x)/(b + a*c)] + a*(b^2 - c^2)*Hypergeometric2F1[1/4, 5/4, 9/4, (b + a*b*x)/(b + a*c)])))/(5*a^3*b^2*(-1 + x^2))","C",1
3123,1,569,719,0.8600875,"\int \sqrt[3]{c+\sqrt[4]{a x+\sqrt{-b+a^2 x^2}}} \, dx","Integrate[(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(1/3),x]","-\frac{6 \left(-\frac{10 b \log \left(\sqrt[3]{c}-\sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}\right)}{729 c^{11/3}}+\frac{5 b \log \left(\sqrt[3]{c} \sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}+\left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{2/3}+c^{2/3}\right)}{729 c^{11/3}}+\frac{10 b \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}}{\sqrt[3]{c}}+1}{\sqrt{3}}\right)}{243 \sqrt{3} c^{11/3}}+\frac{1}{4} c^3 \left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{4/3}-\frac{5 b \sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}}{243 c^3 \sqrt[4]{\sqrt{a^2 x^2-b}+a x}}-\frac{3}{7} c^2 \left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{7/3}+\frac{b \sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}}{81 c^2 \sqrt{\sqrt{a^2 x^2-b}+a x}}-\frac{1}{13} \left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{13/3}+\frac{3}{10} c \left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{10/3}-\frac{b \sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}}{108 c \left(\sqrt{a^2 x^2-b}+a x\right)^{3/4}}-\frac{b \sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}}{12 \left(\sqrt{a^2 x^2-b}+a x\right)}\right)}{a}","\frac{20 b \log \left(\sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}-\sqrt[3]{c}\right)}{243 a c^{11/3}}-\frac{10 b \log \left(\sqrt[3]{c} \sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}+\left(\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c\right)^{2/3}+c^{2/3}\right)}{243 a c^{11/3}}-\frac{20 b \tan ^{-1}\left(\frac{2 \sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}}{\sqrt{3} \sqrt[3]{c}}+\frac{1}{\sqrt{3}}\right)}{81 \sqrt{3} a c^{11/3}}+\frac{\sqrt{\sqrt{a^2 x^2-b}+a x} \left(-4374 a c^5 x-5460 b c\right) \sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}+\left(\sqrt{a^2 x^2-b}+a x\right)^{3/4} \sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c} \left(3402 a c^4 x+9100 b\right)+\left(68040 a^2 c^3 x^2-19683 a c^7 x+2835 b c^3\right) \sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}+\sqrt[4]{\sqrt{a^2 x^2-b}+a x} \left(6561 a c^6 x+4095 b c^2\right) \sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}+\sqrt{a^2 x^2-b} \left(6561 c^6 \sqrt[4]{\sqrt{a^2 x^2-b}+a x} \sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}-4374 c^5 \sqrt{\sqrt{a^2 x^2-b}+a x} \sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}+3402 c^4 \left(\sqrt{a^2 x^2-b}+a x\right)^{3/4} \sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}+\left(68040 a c^3 x-19683 c^7\right) \sqrt[3]{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}+c}\right)}{73710 a c^3 \sqrt{a^2 x^2-b}+73710 a^2 c^3 x}",1,"(-6*(-1/12*(b*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(1/3))/(a*x + Sqrt[-b + a^2*x^2]) - (b*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(1/3))/(108*c*(a*x + Sqrt[-b + a^2*x^2])^(3/4)) + (b*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(1/3))/(81*c^2*Sqrt[a*x + Sqrt[-b + a^2*x^2]]) - (5*b*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(1/3))/(243*c^3*(a*x + Sqrt[-b + a^2*x^2])^(1/4)) + (c^3*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(4/3))/4 - (3*c^2*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(7/3))/7 + (3*c*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(10/3))/10 - (c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(13/3)/13 + (10*b*ArcTan[(1 + (2*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(1/3))/c^(1/3))/Sqrt[3]])/(243*Sqrt[3]*c^(11/3)) - (10*b*Log[c^(1/3) - (c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(1/3)])/(729*c^(11/3)) + (5*b*Log[c^(2/3) + c^(1/3)*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(1/3) + (c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(2/3)])/(729*c^(11/3))))/a","A",1
3124,1,2000,725,3.9454034,"\int \frac{\sqrt[4]{a x+\sqrt{-b+a^2 x^2}}}{x \left(-b+a^2 x^2\right)^{3/2}} \, dx","Integrate[(a*x + Sqrt[-b + a^2*x^2])^(1/4)/(x*(-b + a^2*x^2)^(3/2)),x]","\frac{2 \sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x+\sqrt{a^2 x^2-b}}}{\sqrt[8]{b}}+1\right) \left(a x+\sqrt{a^2 x^2-b}\right)^2+2 \log \left(\sqrt[8]{b}-\sqrt[4]{a x+\sqrt{a^2 x^2-b}}\right) \left(a x+\sqrt{a^2 x^2-b}\right)^2-2 \log \left(\sqrt[4]{a x+\sqrt{a^2 x^2-b}}+\sqrt[8]{b}\right) \left(a x+\sqrt{a^2 x^2-b}\right)^2-\sqrt{2} \log \left(\sqrt{a x+\sqrt{a^2 x^2-b}}-\sqrt{2} \sqrt[8]{b} \sqrt[4]{a x+\sqrt{a^2 x^2-b}}+\sqrt[4]{b}\right) \left(a x+\sqrt{a^2 x^2-b}\right)^2+\sqrt{2} \log \left(\sqrt{a x+\sqrt{a^2 x^2-b}}+\sqrt{2} \sqrt[8]{b} \sqrt[4]{a x+\sqrt{a^2 x^2-b}}+\sqrt[4]{b}\right) \left(a x+\sqrt{a^2 x^2-b}\right)^2+8 \cos \left(\frac{\pi }{8}\right) \log \left(\sqrt{a x+\sqrt{a^2 x^2-b}}-2 \sqrt[8]{b} \sin \left(\frac{\pi }{8}\right) \sqrt[4]{a x+\sqrt{a^2 x^2-b}}+\sqrt[4]{b}\right) \left(a x+\sqrt{a^2 x^2-b}\right)^2-8 \cos \left(\frac{\pi }{8}\right) \log \left(\sqrt{a x+\sqrt{a^2 x^2-b}}+2 \sqrt[8]{b} \sin \left(\frac{\pi }{8}\right) \sqrt[4]{a x+\sqrt{a^2 x^2-b}}+\sqrt[4]{b}\right) \left(a x+\sqrt{a^2 x^2-b}\right)^2+16 \tan ^{-1}\left(\frac{\sqrt[4]{a x+\sqrt{a^2 x^2-b}} \sec \left(\frac{\pi }{8}\right)}{\sqrt[8]{b}}-\tan \left(\frac{\pi }{8}\right)\right) \sin \left(\frac{\pi }{8}\right) \left(a x+\sqrt{a^2 x^2-b}\right)^2+16 \tan ^{-1}\left(\frac{\sec \left(\frac{\pi }{8}\right) \sqrt[4]{a x+\sqrt{a^2 x^2-b}}}{\sqrt[8]{b}}+\tan \left(\frac{\pi }{8}\right)\right) \sin \left(\frac{\pi }{8}\right) \left(a x+\sqrt{a^2 x^2-b}\right)^2-8 \log \left(\sqrt{a x+\sqrt{a^2 x^2-b}}-2 \sqrt[8]{b} \cos \left(\frac{\pi }{8}\right) \sqrt[4]{a x+\sqrt{a^2 x^2-b}}+\sqrt[4]{b}\right) \sin \left(\frac{\pi }{8}\right) \left(a x+\sqrt{a^2 x^2-b}\right)^2+8 \log \left(\sqrt{a x+\sqrt{a^2 x^2-b}}+2 \sqrt[8]{b} \cos \left(\frac{\pi }{8}\right) \sqrt[4]{a x+\sqrt{a^2 x^2-b}}+\sqrt[4]{b}\right) \sin \left(\frac{\pi }{8}\right) \left(a x+\sqrt{a^2 x^2-b}\right)^2+16 \tan ^{-1}\left(\cot \left(\frac{\pi }{8}\right)-\frac{\sqrt[4]{a x+\sqrt{a^2 x^2-b}} \csc \left(\frac{\pi }{8}\right)}{\sqrt[8]{b}}\right) \cos \left(\frac{\pi }{8}\right) \left(a x+\sqrt{a^2 x^2-b}\right)^2-16 \tan ^{-1}\left(\frac{\csc \left(\frac{\pi }{8}\right) \sqrt[4]{a x+\sqrt{a^2 x^2-b}}}{\sqrt[8]{b}}+\cot \left(\frac{\pi }{8}\right)\right) \cos \left(\frac{\pi }{8}\right) \left(a x+\sqrt{a^2 x^2-b}\right)^2-16 b^{3/8} \left(a x+\sqrt{a^2 x^2-b}\right)^{5/4}-4 \left(\left(a x+\sqrt{a^2 x^2-b}\right)^2-b\right) \tan ^{-1}\left(\frac{\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}{\sqrt[8]{b}}\right)-2 \sqrt{2} \left(\left(a x+\sqrt{a^2 x^2-b}\right)^2-b\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a x+\sqrt{a^2 x^2-b}}}{\sqrt[8]{b}}\right)-2 \sqrt{2} b \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x+\sqrt{a^2 x^2-b}}}{\sqrt[8]{b}}+1\right)-2 b \log \left(\sqrt[8]{b}-\sqrt[4]{a x+\sqrt{a^2 x^2-b}}\right)+2 b \log \left(\sqrt[4]{a x+\sqrt{a^2 x^2-b}}+\sqrt[8]{b}\right)+\sqrt{2} b \log \left(\sqrt{a x+\sqrt{a^2 x^2-b}}-\sqrt{2} \sqrt[8]{b} \sqrt[4]{a x+\sqrt{a^2 x^2-b}}+\sqrt[4]{b}\right)-\sqrt{2} b \log \left(\sqrt{a x+\sqrt{a^2 x^2-b}}+\sqrt{2} \sqrt[8]{b} \sqrt[4]{a x+\sqrt{a^2 x^2-b}}+\sqrt[4]{b}\right)-8 b \cos \left(\frac{\pi }{8}\right) \log \left(\sqrt{a x+\sqrt{a^2 x^2-b}}-2 \sqrt[8]{b} \sin \left(\frac{\pi }{8}\right) \sqrt[4]{a x+\sqrt{a^2 x^2-b}}+\sqrt[4]{b}\right)+8 b \cos \left(\frac{\pi }{8}\right) \log \left(\sqrt{a x+\sqrt{a^2 x^2-b}}+2 \sqrt[8]{b} \sin \left(\frac{\pi }{8}\right) \sqrt[4]{a x+\sqrt{a^2 x^2-b}}+\sqrt[4]{b}\right)-16 b \tan ^{-1}\left(\frac{\sqrt[4]{a x+\sqrt{a^2 x^2-b}} \sec \left(\frac{\pi }{8}\right)}{\sqrt[8]{b}}-\tan \left(\frac{\pi }{8}\right)\right) \sin \left(\frac{\pi }{8}\right)-16 b \tan ^{-1}\left(\frac{\sec \left(\frac{\pi }{8}\right) \sqrt[4]{a x+\sqrt{a^2 x^2-b}}}{\sqrt[8]{b}}+\tan \left(\frac{\pi }{8}\right)\right) \sin \left(\frac{\pi }{8}\right)+8 b \log \left(\sqrt{a x+\sqrt{a^2 x^2-b}}-2 \sqrt[8]{b} \cos \left(\frac{\pi }{8}\right) \sqrt[4]{a x+\sqrt{a^2 x^2-b}}+\sqrt[4]{b}\right) \sin \left(\frac{\pi }{8}\right)-8 b \log \left(\sqrt{a x+\sqrt{a^2 x^2-b}}+2 \sqrt[8]{b} \cos \left(\frac{\pi }{8}\right) \sqrt[4]{a x+\sqrt{a^2 x^2-b}}+\sqrt[4]{b}\right) \sin \left(\frac{\pi }{8}\right)-16 b \tan ^{-1}\left(\cot \left(\frac{\pi }{8}\right)-\frac{\sqrt[4]{a x+\sqrt{a^2 x^2-b}} \csc \left(\frac{\pi }{8}\right)}{\sqrt[8]{b}}\right) \cos \left(\frac{\pi }{8}\right)+16 b \tan ^{-1}\left(\frac{\csc \left(\frac{\pi }{8}\right) \sqrt[4]{a x+\sqrt{a^2 x^2-b}}}{\sqrt[8]{b}}+\cot \left(\frac{\pi }{8}\right)\right) \cos \left(\frac{\pi }{8}\right)}{8 b^{11/8} \sqrt{4 a^2 x^2-4 b} \left(a x+\sqrt{a^2 x^2-b}\right)}","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}}{\sqrt[8]{b}}\right)}{2 b^{11/8}}-\frac{\sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{\left(\sqrt{\frac{2}{2-\sqrt{2}}} \sqrt[8]{b}-\frac{2 \sqrt[8]{b}}{\sqrt{2-\sqrt{2}}}\right) \sqrt[4]{\sqrt{a^2 x^2-b}+a x}}{\sqrt{\sqrt{a^2 x^2-b}+a x}-\sqrt[4]{b}}\right)}{b^{11/8}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{b} \sqrt[4]{\sqrt{a^2 x^2-b}+a x}}{\sqrt{\sqrt{a^2 x^2-b}+a x}-\sqrt[4]{b}}\right)}{2 \sqrt{2} b^{11/8}}-\frac{\sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}} \sqrt[8]{b} \sqrt[4]{\sqrt{a^2 x^2-b}+a x}}{\sqrt{\sqrt{a^2 x^2-b}+a x}-\sqrt[4]{b}}\right)}{b^{11/8}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}}{\sqrt[8]{b}}\right)}{2 b^{11/8}}+\frac{\tanh ^{-1}\left(\frac{\frac{\sqrt{\sqrt{a^2 x^2-b}+a x}}{\sqrt{2} \sqrt[8]{b}}+\frac{\sqrt[8]{b}}{\sqrt{2}}}{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}}\right)}{2 \sqrt{2} b^{11/8}}-\frac{\sqrt{2+\sqrt{2}} \tanh ^{-1}\left(\frac{\frac{\sqrt{\sqrt{a^2 x^2-b}+a x}}{\sqrt{2-\sqrt{2}} \sqrt[8]{b}}+\frac{\sqrt[8]{b}}{\sqrt{2-\sqrt{2}}}}{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}}\right)}{b^{11/8}}+\frac{\sqrt{2-\sqrt{2}} \tanh ^{-1}\left(\frac{\frac{\sqrt{\sqrt{a^2 x^2-b}+a x}}{\sqrt{2+\sqrt{2}} \sqrt[8]{b}}+\frac{\sqrt[8]{b}}{\sqrt{2+\sqrt{2}}}}{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}}\right)}{b^{11/8}}+\frac{\left(\sqrt{a^2 x^2-b}+a x\right)^{5/4}}{b \left(-a x \sqrt{a^2 x^2-b}-a^2 x^2+b\right)}",1,"(-16*b^(3/8)*(a*x + Sqrt[-b + a^2*x^2])^(5/4) - 4*(-b + (a*x + Sqrt[-b + a^2*x^2])^2)*ArcTan[(a*x + Sqrt[-b + a^2*x^2])^(1/4)/b^(1/8)] - 2*Sqrt[2]*(-b + (a*x + Sqrt[-b + a^2*x^2])^2)*ArcTan[1 - (Sqrt[2]*(a*x + Sqrt[-b + a^2*x^2])^(1/4))/b^(1/8)] - 2*Sqrt[2]*b*ArcTan[1 + (Sqrt[2]*(a*x + Sqrt[-b + a^2*x^2])^(1/4))/b^(1/8)] + 2*Sqrt[2]*(a*x + Sqrt[-b + a^2*x^2])^2*ArcTan[1 + (Sqrt[2]*(a*x + Sqrt[-b + a^2*x^2])^(1/4))/b^(1/8)] - 16*b*ArcTan[Cot[Pi/8] - ((a*x + Sqrt[-b + a^2*x^2])^(1/4)*Csc[Pi/8])/b^(1/8)]*Cos[Pi/8] + 16*(a*x + Sqrt[-b + a^2*x^2])^2*ArcTan[Cot[Pi/8] - ((a*x + Sqrt[-b + a^2*x^2])^(1/4)*Csc[Pi/8])/b^(1/8)]*Cos[Pi/8] + 16*b*ArcTan[Cot[Pi/8] + ((a*x + Sqrt[-b + a^2*x^2])^(1/4)*Csc[Pi/8])/b^(1/8)]*Cos[Pi/8] - 16*(a*x + Sqrt[-b + a^2*x^2])^2*ArcTan[Cot[Pi/8] + ((a*x + Sqrt[-b + a^2*x^2])^(1/4)*Csc[Pi/8])/b^(1/8)]*Cos[Pi/8] - 2*b*Log[b^(1/8) - (a*x + Sqrt[-b + a^2*x^2])^(1/4)] + 2*(a*x + Sqrt[-b + a^2*x^2])^2*Log[b^(1/8) - (a*x + Sqrt[-b + a^2*x^2])^(1/4)] + 2*b*Log[b^(1/8) + (a*x + Sqrt[-b + a^2*x^2])^(1/4)] - 2*(a*x + Sqrt[-b + a^2*x^2])^2*Log[b^(1/8) + (a*x + Sqrt[-b + a^2*x^2])^(1/4)] + Sqrt[2]*b*Log[b^(1/4) - Sqrt[2]*b^(1/8)*(a*x + Sqrt[-b + a^2*x^2])^(1/4) + Sqrt[a*x + Sqrt[-b + a^2*x^2]]] - Sqrt[2]*(a*x + Sqrt[-b + a^2*x^2])^2*Log[b^(1/4) - Sqrt[2]*b^(1/8)*(a*x + Sqrt[-b + a^2*x^2])^(1/4) + Sqrt[a*x + Sqrt[-b + a^2*x^2]]] - Sqrt[2]*b*Log[b^(1/4) + Sqrt[2]*b^(1/8)*(a*x + Sqrt[-b + a^2*x^2])^(1/4) + Sqrt[a*x + Sqrt[-b + a^2*x^2]]] + Sqrt[2]*(a*x + Sqrt[-b + a^2*x^2])^2*Log[b^(1/4) + Sqrt[2]*b^(1/8)*(a*x + Sqrt[-b + a^2*x^2])^(1/4) + Sqrt[a*x + Sqrt[-b + a^2*x^2]]] - 8*b*Cos[Pi/8]*Log[b^(1/4) + Sqrt[a*x + Sqrt[-b + a^2*x^2]] - 2*b^(1/8)*(a*x + Sqrt[-b + a^2*x^2])^(1/4)*Sin[Pi/8]] + 8*(a*x + Sqrt[-b + a^2*x^2])^2*Cos[Pi/8]*Log[b^(1/4) + Sqrt[a*x + Sqrt[-b + a^2*x^2]] - 2*b^(1/8)*(a*x + Sqrt[-b + a^2*x^2])^(1/4)*Sin[Pi/8]] + 8*b*Cos[Pi/8]*Log[b^(1/4) + Sqrt[a*x + Sqrt[-b + a^2*x^2]] + 2*b^(1/8)*(a*x + Sqrt[-b + a^2*x^2])^(1/4)*Sin[Pi/8]] - 8*(a*x + Sqrt[-b + a^2*x^2])^2*Cos[Pi/8]*Log[b^(1/4) + Sqrt[a*x + Sqrt[-b + a^2*x^2]] + 2*b^(1/8)*(a*x + Sqrt[-b + a^2*x^2])^(1/4)*Sin[Pi/8]] - 16*b*ArcTan[((a*x + Sqrt[-b + a^2*x^2])^(1/4)*Sec[Pi/8])/b^(1/8) - Tan[Pi/8]]*Sin[Pi/8] + 16*(a*x + Sqrt[-b + a^2*x^2])^2*ArcTan[((a*x + Sqrt[-b + a^2*x^2])^(1/4)*Sec[Pi/8])/b^(1/8) - Tan[Pi/8]]*Sin[Pi/8] - 16*b*ArcTan[((a*x + Sqrt[-b + a^2*x^2])^(1/4)*Sec[Pi/8])/b^(1/8) + Tan[Pi/8]]*Sin[Pi/8] + 16*(a*x + Sqrt[-b + a^2*x^2])^2*ArcTan[((a*x + Sqrt[-b + a^2*x^2])^(1/4)*Sec[Pi/8])/b^(1/8) + Tan[Pi/8]]*Sin[Pi/8] + 8*b*Log[b^(1/4) + Sqrt[a*x + Sqrt[-b + a^2*x^2]] - 2*b^(1/8)*(a*x + Sqrt[-b + a^2*x^2])^(1/4)*Cos[Pi/8]]*Sin[Pi/8] - 8*(a*x + Sqrt[-b + a^2*x^2])^2*Log[b^(1/4) + Sqrt[a*x + Sqrt[-b + a^2*x^2]] - 2*b^(1/8)*(a*x + Sqrt[-b + a^2*x^2])^(1/4)*Cos[Pi/8]]*Sin[Pi/8] - 8*b*Log[b^(1/4) + Sqrt[a*x + Sqrt[-b + a^2*x^2]] + 2*b^(1/8)*(a*x + Sqrt[-b + a^2*x^2])^(1/4)*Cos[Pi/8]]*Sin[Pi/8] + 8*(a*x + Sqrt[-b + a^2*x^2])^2*Log[b^(1/4) + Sqrt[a*x + Sqrt[-b + a^2*x^2]] + 2*b^(1/8)*(a*x + Sqrt[-b + a^2*x^2])^(1/4)*Cos[Pi/8]]*Sin[Pi/8])/(8*b^(11/8)*Sqrt[-4*b + 4*a^2*x^2]*(a*x + Sqrt[-b + a^2*x^2]))","B",0
3125,0,0,723,0.4079679,"\int \frac{x \left(2 x^3 c_3-c_4\right)}{\left(-x+x^3 c_3+c_4\right) \sqrt[3]{\frac{x c_0+x^3 c_3+c_4}{x c_1+x^3 c_3+c_4}} \left(x^2+x^4 c_3+x^6 c_3{}^2+x c_4+2 x^3 c_3 c_4+c_4{}^2\right)} \, dx","Integrate[(x*(2*x^3*C[3] - C[4]))/((-x + x^3*C[3] + C[4])*((x*C[0] + x^3*C[3] + C[4])/(x*C[1] + x^3*C[3] + C[4]))^(1/3)*(x^2 + x^4*C[3] + x^6*C[3]^2 + x*C[4] + 2*x^3*C[3]*C[4] + C[4]^2)),x]","\int \frac{x \left(2 x^3 c_3-c_4\right)}{\left(-x+x^3 c_3+c_4\right) \sqrt[3]{\frac{x c_0+x^3 c_3+c_4}{x c_1+x^3 c_3+c_4}} \left(x^2+x^4 c_3+x^6 c_3{}^2+x c_4+2 x^3 c_3 c_4+c_4{}^2\right)} \, dx","\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^6+\text{$\#$1}^6 c_1{}^2-\text{$\#$1}^6 c_1-2 \text{$\#$1}^3+\text{$\#$1}^3 c_0-2 \text{$\#$1}^3 c_0 c_1+\text{$\#$1}^3 c_1+1+c_0{}^2-c_0\&,\frac{\text{$\#$1}^3 \left(-c_1{}^2\right) \log \left(-\text{$\#$1}+\sqrt[3]{\frac{c_3 x^3+c_0 x+c_4}{c_3 x^3+c_1 x+c_4}}\right)+\text{$\#$1}^3 c_1 \log \left(-\text{$\#$1}+\sqrt[3]{\frac{c_3 x^3+c_0 x+c_4}{c_3 x^3+c_1 x+c_4}}\right)-\text{$\#$1}^3 \log \left(-\text{$\#$1}+\sqrt[3]{\frac{c_3 x^3+c_0 x+c_4}{c_3 x^3+c_1 x+c_4}}\right)+c_0 \log \left(-\text{$\#$1}+\sqrt[3]{\frac{c_3 x^3+c_0 x+c_4}{c_3 x^3+c_1 x+c_4}}\right)+c_0 c_1 \log \left(-\text{$\#$1}+\sqrt[3]{\frac{c_3 x^3+c_0 x+c_4}{c_3 x^3+c_1 x+c_4}}\right)-2 c_1 \log \left(-\text{$\#$1}+\sqrt[3]{\frac{c_3 x^3+c_0 x+c_4}{c_3 x^3+c_1 x+c_4}}\right)+\log \left(-\text{$\#$1}+\sqrt[3]{\frac{c_3 x^3+c_0 x+c_4}{c_3 x^3+c_1 x+c_4}}\right)}{2 \text{$\#$1}^4+2 \text{$\#$1}^4 c_1{}^2-2 \text{$\#$1}^4 c_1-2 \text{$\#$1}+\text{$\#$1} c_0-2 \text{$\#$1} c_0 c_1+\text{$\#$1} c_1}\&\right]-\frac{\sqrt[3]{-1-c_1} \log \left(\sqrt[3]{-1-c_1} \sqrt[3]{\frac{c_3 x^3+c_0 x+c_4}{c_3 x^3+c_1 x+c_4}}+\sqrt[3]{1+c_0}\right)}{3 \sqrt[3]{1+c_0}}+\frac{\sqrt[3]{-1-c_1} \log \left(-\sqrt[3]{-1-c_1} \sqrt[3]{1+c_0} \sqrt[3]{\frac{c_3 x^3+c_0 x+c_4}{c_3 x^3+c_1 x+c_4}}+(-1-c_1){}^{2/3} \left(\frac{c_3 x^3+c_0 x+c_4}{c_3 x^3+c_1 x+c_4}\right){}^{2/3}+(1+c_0){}^{2/3}\right)}{6 \sqrt[3]{1+c_0}}-\frac{\sqrt[3]{-1-c_1} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{-1-c_1} \sqrt[3]{\frac{c_3 x^3+c_0 x+c_4}{c_3 x^3+c_1 x+c_4}}}{\sqrt{3} \sqrt[3]{1+c_0}}\right)}{\sqrt{3} \sqrt[3]{1+c_0}}",1,"Integrate[(x*(2*x^3*C[3] - C[4]))/((-x + x^3*C[3] + C[4])*((x*C[0] + x^3*C[3] + C[4])/(x*C[1] + x^3*C[3] + C[4]))^(1/3)*(x^2 + x^4*C[3] + x^6*C[3]^2 + x*C[4] + 2*x^3*C[3]*C[4] + C[4]^2)), x]","F",-1
3126,1,388,747,0.5494959,"\int \frac{(-d+c x) \sqrt{a x+\sqrt{b^2+a^2 x^2}}}{d+c x} \, dx","Integrate[((-d + c*x)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(d + c*x),x]","\frac{-\frac{4 a d \left(a d \left(a d-\sqrt{a^2 d^2+b^2 c^2}\right)+b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{\sqrt{a^2 x^2+b^2}+a x}}{\sqrt{a d-\sqrt{a^2 d^2+b^2 c^2}}}\right)}{c^{3/2} \sqrt{a^2 d^2+b^2 c^2} \sqrt{a d-\sqrt{a^2 d^2+b^2 c^2}}}+\frac{4 a d \left(a d \left(\sqrt{a^2 d^2+b^2 c^2}+a d\right)+b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{\sqrt{a^2 x^2+b^2}+a x}}{\sqrt{\sqrt{a^2 d^2+b^2 c^2}+a d}}\right)}{c^{3/2} \sqrt{a^2 d^2+b^2 c^2} \sqrt{\sqrt{a^2 d^2+b^2 c^2}+a d}}-\frac{4 a d \sqrt{\sqrt{a^2 x^2+b^2}+a x}}{c}-\frac{b^2}{\sqrt{\sqrt{a^2 x^2+b^2}+a x}}+\frac{1}{3} \left(\sqrt{a^2 x^2+b^2}+a x\right)^{3/2}}{a}","-\frac{4 b^2 \sqrt{c} d \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{\sqrt{a^2 x^2+b^2}+a x}}{\sqrt{a d-\sqrt{a^2 d^2+b^2 c^2}}}\right)}{\sqrt{a^2 d^2+b^2 c^2} \sqrt{a d-\sqrt{a^2 d^2+b^2 c^2}}}+\frac{4 b^2 \sqrt{c} d \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{\sqrt{a^2 x^2+b^2}+a x}}{\sqrt{\sqrt{a^2 d^2+b^2 c^2}+a d}}\right)}{\sqrt{a^2 d^2+b^2 c^2} \sqrt{\sqrt{a^2 d^2+b^2 c^2}+a d}}+\frac{4 a d^2 \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{\sqrt{a^2 x^2+b^2}+a x}}{\sqrt{a d-\sqrt{a^2 d^2+b^2 c^2}}}\right)}{c^{3/2} \sqrt{a d-\sqrt{a^2 d^2+b^2 c^2}}}+\frac{4 a d^2 \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{\sqrt{a^2 x^2+b^2}+a x}}{\sqrt{\sqrt{a^2 d^2+b^2 c^2}+a d}}\right)}{c^{3/2} \sqrt{\sqrt{a^2 d^2+b^2 c^2}+a d}}-\frac{4 a^2 d^3 \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{\sqrt{a^2 x^2+b^2}+a x}}{\sqrt{a d-\sqrt{a^2 d^2+b^2 c^2}}}\right)}{c^{3/2} \sqrt{a^2 d^2+b^2 c^2} \sqrt{a d-\sqrt{a^2 d^2+b^2 c^2}}}+\frac{4 a^2 d^3 \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{\sqrt{a^2 x^2+b^2}+a x}}{\sqrt{\sqrt{a^2 d^2+b^2 c^2}+a d}}\right)}{c^{3/2} \sqrt{a^2 d^2+b^2 c^2} \sqrt{\sqrt{a^2 d^2+b^2 c^2}+a d}}+\frac{2 \sqrt{a^2 x^2+b^2} (a c x-6 a d)+2 \left(a^2 c x^2-6 a^2 d x-b^2 c\right)}{3 a c \sqrt{\sqrt{a^2 x^2+b^2}+a x}}",1,"(-(b^2/Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]) - (4*a*d*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/c + (a*x + Sqrt[b^2 + a^2*x^2])^(3/2)/3 - (4*a*d*(b^2*c^2 + a*d*(a*d - Sqrt[b^2*c^2 + a^2*d^2]))*ArcTan[(Sqrt[c]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/Sqrt[a*d - Sqrt[b^2*c^2 + a^2*d^2]]])/(c^(3/2)*Sqrt[b^2*c^2 + a^2*d^2]*Sqrt[a*d - Sqrt[b^2*c^2 + a^2*d^2]]) + (4*a*d*(b^2*c^2 + a*d*(a*d + Sqrt[b^2*c^2 + a^2*d^2]))*ArcTan[(Sqrt[c]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/Sqrt[a*d + Sqrt[b^2*c^2 + a^2*d^2]]])/(c^(3/2)*Sqrt[b^2*c^2 + a^2*d^2]*Sqrt[a*d + Sqrt[b^2*c^2 + a^2*d^2]]))/a","A",1
3127,1,95,752,0.0694295,"\int \frac{\sqrt[3]{\frac{x}{-1-a x+3 x^2+3 a x^3-3 x^4-3 a x^5+x^6+a x^7}}}{x^3} \, dx","Integrate[(x/(-1 - a*x + 3*x^2 + 3*a*x^3 - 3*x^4 - 3*a*x^5 + x^6 + a*x^7))^(1/3)/x^3,x]","-\frac{3 \left(x^2-1\right) \sqrt[3]{\frac{x}{\left(x^2-1\right)^3 (a x+1)}} \left(3 a^2 x^2+5 x^2 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(a-1) x}{a x+1}\right)+5 x^2 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(a+1) x}{a x+1}\right)+a x-2\right)}{10 x^2}","-\frac{3 \sqrt[3]{\frac{x}{a x^7-3 a x^5+3 a x^3-a x+x^6-3 x^4+3 x^2-1}} \left(3 a^2 x^4-3 a^2 x^2+a x^3-a x-2 x^2+2\right)}{10 x^2}-\frac{\log \left(\sqrt[3]{\frac{x}{a x^7-3 a x^5+3 a x^3-a x+x^6-3 x^4+3 x^2-1}} \left(\sqrt[3]{1-a} x^2-\sqrt[3]{1-a}\right)+1\right)}{2 \sqrt[3]{1-a}}+\frac{\log \left(\left(\sqrt[3]{a+1} x^2-\sqrt[3]{a+1}\right) \sqrt[3]{\frac{x}{a x^7-3 a x^5+3 a x^3-a x+x^6-3 x^4+3 x^2-1}}-1\right)}{2 \sqrt[3]{a+1}}+\frac{\log \left(\sqrt[3]{\frac{x}{a x^7-3 a x^5+3 a x^3-a x+x^6-3 x^4+3 x^2-1}} \left(\sqrt[3]{1-a}-\sqrt[3]{1-a} x^2\right)+\left((1-a)^{2/3} x^4-2 (1-a)^{2/3} x^2+(1-a)^{2/3}\right) \left(\frac{x}{a x^7-3 a x^5+3 a x^3-a x+x^6-3 x^4+3 x^2-1}\right)^{2/3}+1\right)}{4 \sqrt[3]{1-a}}-\frac{\log \left(\sqrt[3]{\frac{x}{a x^7-3 a x^5+3 a x^3-a x+x^6-3 x^4+3 x^2-1}} \left(\sqrt[3]{a+1} x^2-\sqrt[3]{a+1}\right)+\left((a+1)^{2/3} x^4-2 (a+1)^{2/3} x^2+(a+1)^{2/3}\right) \left(\frac{x}{a x^7-3 a x^5+3 a x^3-a x+x^6-3 x^4+3 x^2-1}\right)^{2/3}+1\right)}{4 \sqrt[3]{a+1}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{\sqrt[3]{1-a} \left(2 x^2-2\right) \sqrt[3]{\frac{x}{a x^7-3 a x^5+3 a x^3-a x+x^6-3 x^4+3 x^2-1}}}{\sqrt{3}}\right)}{2 \sqrt[3]{1-a}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt[3]{a+1} \left(2 x^2-2\right) \sqrt[3]{\frac{x}{a x^7-3 a x^5+3 a x^3-a x+x^6-3 x^4+3 x^2-1}}}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt[3]{a+1}}",1,"(-3*(x/((1 + a*x)*(-1 + x^2)^3))^(1/3)*(-1 + x^2)*(-2 + a*x + 3*a^2*x^2 + 5*x^2*Hypergeometric2F1[1/3, 1, 4/3, ((-1 + a)*x)/(1 + a*x)] + 5*x^2*Hypergeometric2F1[1/3, 1, 4/3, ((1 + a)*x)/(1 + a*x)]))/(10*x^2)","C",1
3128,0,0,757,2.057897,"\int \frac{1}{a b c-(c+a b x)^2 \sqrt{c+b x+a x^2}} \, dx","Integrate[(a*b*c - (c + a*b*x)^2*Sqrt[c + b*x + a*x^2])^(-1),x]","\int \frac{1}{a b c-(c+a b x)^2 \sqrt{c+b x+a x^2}} \, dx","-2 \text{RootSum}\left[\text{$\#$1}^6 a^{5/2} b^2-\text{$\#$1}^5 a^2 b^3-4 \text{$\#$1}^5 a^2 b c-\text{$\#$1}^4 a^{5/2} b^2 c+6 \text{$\#$1}^4 a^{3/2} b^2 c+4 \text{$\#$1}^4 a^{3/2} c^2-8 \text{$\#$1}^3 a^{5/2} b c+2 \text{$\#$1}^3 a^2 b^3 c-2 \text{$\#$1}^3 a b^3 c-8 \text{$\#$1}^3 a b c^2-\text{$\#$1}^2 a^{5/2} b^2 c^2-4 \text{$\#$1}^2 a^{3/2} b^2 c^2+4 \text{$\#$1}^2 a^{3/2} c^3+12 \text{$\#$1}^2 a^2 b^2 c+5 \text{$\#$1}^2 \sqrt{a} b^2 c^2-6 \text{$\#$1} a^{3/2} b^3 c-\text{$\#$1} a^2 b^3 c^2+4 \text{$\#$1} a^2 b c^3+2 \text{$\#$1} a b^3 c^2-4 \text{$\#$1} a b c^3-\text{$\#$1} b^3 c^2+a^{5/2} b^2 c^3-2 a^{3/2} b^2 c^3+a b^4 c+\sqrt{a} b^2 c^3\&,\frac{2 \text{$\#$1}^3 a \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)-3 \text{$\#$1}^2 \sqrt{a} b \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)+\text{$\#$1} b^2 \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)+2 \text{$\#$1} a c \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)-\sqrt{a} b c \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)}{-6 \text{$\#$1}^5 a^{5/2} b^2+5 \text{$\#$1}^4 a^2 b^3+20 \text{$\#$1}^4 a^2 b c+4 \text{$\#$1}^3 a^{5/2} b^2 c-24 \text{$\#$1}^3 a^{3/2} b^2 c-16 \text{$\#$1}^3 a^{3/2} c^2+24 \text{$\#$1}^2 a^{5/2} b c-6 \text{$\#$1}^2 a^2 b^3 c+6 \text{$\#$1}^2 a b^3 c+24 \text{$\#$1}^2 a b c^2+2 \text{$\#$1} a^{5/2} b^2 c^2+8 \text{$\#$1} a^{3/2} b^2 c^2-8 \text{$\#$1} a^{3/2} c^3-24 \text{$\#$1} a^2 b^2 c-10 \text{$\#$1} \sqrt{a} b^2 c^2+6 a^{3/2} b^3 c+a^2 b^3 c^2-4 a^2 b c^3-2 a b^3 c^2+4 a b c^3+b^3 c^2}\&\right]",1,"Integrate[(a*b*c - (c + a*b*x)^2*Sqrt[c + b*x + a*x^2])^(-1), x]","F",-1
3129,1,2041,757,2.354193,"\int \frac{\sqrt[4]{a x+\sqrt{-b+a^2 x^2}}}{x^2 \left(-b+a^2 x^2\right)^{3/2}} \, dx","Integrate[(a*x + Sqrt[-b + a^2*x^2])^(1/4)/(x^2*(-b + a^2*x^2)^(3/2)),x]","\text{Result too large to show}","-\frac{a \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}}{\sqrt[8]{b}}\right)}{2 b^{15/8}}-\frac{\sqrt{2-\sqrt{2}} a \tan ^{-1}\left(\frac{\left(\sqrt{\frac{2}{2-\sqrt{2}}} \sqrt[8]{b}-\frac{2 \sqrt[8]{b}}{\sqrt{2-\sqrt{2}}}\right) \sqrt[4]{\sqrt{a^2 x^2-b}+a x}}{\sqrt{\sqrt{a^2 x^2-b}+a x}-\sqrt[4]{b}}\right)}{4 b^{15/8}}+\frac{a \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{b} \sqrt[4]{\sqrt{a^2 x^2-b}+a x}}{\sqrt{\sqrt{a^2 x^2-b}+a x}-\sqrt[4]{b}}\right)}{2 \sqrt{2} b^{15/8}}+\frac{\sqrt{2+\sqrt{2}} a \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}} \sqrt[8]{b} \sqrt[4]{\sqrt{a^2 x^2-b}+a x}}{\sqrt{\sqrt{a^2 x^2-b}+a x}-\sqrt[4]{b}}\right)}{4 b^{15/8}}-\frac{a \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}}{\sqrt[8]{b}}\right)}{2 b^{15/8}}-\frac{a \tanh ^{-1}\left(\frac{\frac{\sqrt{\sqrt{a^2 x^2-b}+a x}}{\sqrt{2} \sqrt[8]{b}}+\frac{\sqrt[8]{b}}{\sqrt{2}}}{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}}\right)}{2 \sqrt{2} b^{15/8}}-\frac{\sqrt{2-\sqrt{2}} a \tanh ^{-1}\left(\frac{\frac{\sqrt{\sqrt{a^2 x^2-b}+a x}}{\sqrt{2-\sqrt{2}} \sqrt[8]{b}}+\frac{\sqrt[8]{b}}{\sqrt{2-\sqrt{2}}}}{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}}\right)}{4 b^{15/8}}-\frac{\sqrt{2+\sqrt{2}} a \tanh ^{-1}\left(\frac{\frac{\sqrt{\sqrt{a^2 x^2-b}+a x}}{\sqrt{2+\sqrt{2}} \sqrt[8]{b}}+\frac{\sqrt[8]{b}}{\sqrt{2+\sqrt{2}}}}{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}}\right)}{4 b^{15/8}}-\frac{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}}{x \left(2 a^3 x^3-2 a b x\right)+x \sqrt{a^2 x^2-b} \left(2 a^2 x^2-b\right)}",1,"(-32*b^(15/8)*(a*x + Sqrt[-b + a^2*x^2])^(1/4) - 4*(-b^2 + (a*x + Sqrt[-b + a^2*x^2])^4)*ArcTan[(a*x + Sqrt[-b + a^2*x^2])^(1/4)/b^(1/8)] + 2*Sqrt[2]*(-b^2 + (a*x + Sqrt[-b + a^2*x^2])^4)*ArcTan[1 - (Sqrt[2]*(a*x + Sqrt[-b + a^2*x^2])^(1/4))/b^(1/8)] + 2*Sqrt[2]*b^2*ArcTan[1 + (Sqrt[2]*(a*x + Sqrt[-b + a^2*x^2])^(1/4))/b^(1/8)] - 2*Sqrt[2]*(a*x + Sqrt[-b + a^2*x^2])^4*ArcTan[1 + (Sqrt[2]*(a*x + Sqrt[-b + a^2*x^2])^(1/4))/b^(1/8)] + 4*b^2*ArcTan[((a*x + Sqrt[-b + a^2*x^2])^(1/4)*Sec[Pi/8])/b^(1/8) - Tan[Pi/8]]*Cos[Pi/8] - 4*(a*x + Sqrt[-b + a^2*x^2])^4*ArcTan[((a*x + Sqrt[-b + a^2*x^2])^(1/4)*Sec[Pi/8])/b^(1/8) - Tan[Pi/8]]*Cos[Pi/8] + 4*b^2*ArcTan[((a*x + Sqrt[-b + a^2*x^2])^(1/4)*Sec[Pi/8])/b^(1/8) + Tan[Pi/8]]*Cos[Pi/8] - 4*(a*x + Sqrt[-b + a^2*x^2])^4*ArcTan[((a*x + Sqrt[-b + a^2*x^2])^(1/4)*Sec[Pi/8])/b^(1/8) + Tan[Pi/8]]*Cos[Pi/8] - 2*b^2*Log[b^(1/8) - (a*x + Sqrt[-b + a^2*x^2])^(1/4)] + 2*(a*x + Sqrt[-b + a^2*x^2])^4*Log[b^(1/8) - (a*x + Sqrt[-b + a^2*x^2])^(1/4)] + 2*b^2*Log[b^(1/8) + (a*x + Sqrt[-b + a^2*x^2])^(1/4)] - 2*(a*x + Sqrt[-b + a^2*x^2])^4*Log[b^(1/8) + (a*x + Sqrt[-b + a^2*x^2])^(1/4)] - Sqrt[2]*b^2*Log[b^(1/4) - Sqrt[2]*b^(1/8)*(a*x + Sqrt[-b + a^2*x^2])^(1/4) + Sqrt[a*x + Sqrt[-b + a^2*x^2]]] + Sqrt[2]*(a*x + Sqrt[-b + a^2*x^2])^4*Log[b^(1/4) - Sqrt[2]*b^(1/8)*(a*x + Sqrt[-b + a^2*x^2])^(1/4) + Sqrt[a*x + Sqrt[-b + a^2*x^2]]] + Sqrt[2]*b^2*Log[b^(1/4) + Sqrt[2]*b^(1/8)*(a*x + Sqrt[-b + a^2*x^2])^(1/4) + Sqrt[a*x + Sqrt[-b + a^2*x^2]]] - Sqrt[2]*(a*x + Sqrt[-b + a^2*x^2])^4*Log[b^(1/4) + Sqrt[2]*b^(1/8)*(a*x + Sqrt[-b + a^2*x^2])^(1/4) + Sqrt[a*x + Sqrt[-b + a^2*x^2]]] - 2*b^2*Cos[Pi/8]*Log[b^(1/4) + Sqrt[a*x + Sqrt[-b + a^2*x^2]] - 2*b^(1/8)*(a*x + Sqrt[-b + a^2*x^2])^(1/4)*Cos[Pi/8]] + 2*(a*x + Sqrt[-b + a^2*x^2])^4*Cos[Pi/8]*Log[b^(1/4) + Sqrt[a*x + Sqrt[-b + a^2*x^2]] - 2*b^(1/8)*(a*x + Sqrt[-b + a^2*x^2])^(1/4)*Cos[Pi/8]] + 2*b^2*Cos[Pi/8]*Log[b^(1/4) + Sqrt[a*x + Sqrt[-b + a^2*x^2]] + 2*b^(1/8)*(a*x + Sqrt[-b + a^2*x^2])^(1/4)*Cos[Pi/8]] - 2*(a*x + Sqrt[-b + a^2*x^2])^4*Cos[Pi/8]*Log[b^(1/4) + Sqrt[a*x + Sqrt[-b + a^2*x^2]] + 2*b^(1/8)*(a*x + Sqrt[-b + a^2*x^2])^(1/4)*Cos[Pi/8]] - 4*b^2*ArcTan[Cot[Pi/8] - ((a*x + Sqrt[-b + a^2*x^2])^(1/4)*Csc[Pi/8])/b^(1/8)]*Sin[Pi/8] + 4*(a*x + Sqrt[-b + a^2*x^2])^4*ArcTan[Cot[Pi/8] - ((a*x + Sqrt[-b + a^2*x^2])^(1/4)*Csc[Pi/8])/b^(1/8)]*Sin[Pi/8] + 4*b^2*ArcTan[Cot[Pi/8] + ((a*x + Sqrt[-b + a^2*x^2])^(1/4)*Csc[Pi/8])/b^(1/8)]*Sin[Pi/8] - 4*(a*x + Sqrt[-b + a^2*x^2])^4*ArcTan[Cot[Pi/8] + ((a*x + Sqrt[-b + a^2*x^2])^(1/4)*Csc[Pi/8])/b^(1/8)]*Sin[Pi/8] - 2*b^2*Log[b^(1/4) + Sqrt[a*x + Sqrt[-b + a^2*x^2]] - 2*b^(1/8)*(a*x + Sqrt[-b + a^2*x^2])^(1/4)*Sin[Pi/8]]*Sin[Pi/8] + 2*(a*x + Sqrt[-b + a^2*x^2])^4*Log[b^(1/4) + Sqrt[a*x + Sqrt[-b + a^2*x^2]] - 2*b^(1/8)*(a*x + Sqrt[-b + a^2*x^2])^(1/4)*Sin[Pi/8]]*Sin[Pi/8] + 2*b^2*Log[b^(1/4) + Sqrt[a*x + Sqrt[-b + a^2*x^2]] + 2*b^(1/8)*(a*x + Sqrt[-b + a^2*x^2])^(1/4)*Sin[Pi/8]]*Sin[Pi/8] - 2*(a*x + Sqrt[-b + a^2*x^2])^4*Log[b^(1/4) + Sqrt[a*x + Sqrt[-b + a^2*x^2]] + 2*b^(1/8)*(a*x + Sqrt[-b + a^2*x^2])^(1/4)*Sin[Pi/8]]*Sin[Pi/8])/(16*b^(15/8)*x*Sqrt[-4*b + 4*a^2*x^2]*(-b + 2*a*x*(a*x + Sqrt[-b + a^2*x^2])))","B",0
3130,1,656,773,4.6826335,"\int \frac{\left(-1+x^2\right) \sqrt{c_4+\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5}}{1+x^2} \, dx","Integrate[((-1 + x^2)*Sqrt[C[4] + Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5]])/(1 + x^2),x]","4 (c_1 c_2-c_0 c_3) c_5{}^2 \left(-\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8 c_2{}^2+\text{$\#$1}^8 c_3{}^2-4 \text{$\#$1}^6 c_2{}^2 c_4-4 \text{$\#$1}^6 c_3{}^2 c_4+6 \text{$\#$1}^4 c_2{}^2 c_4{}^2+6 \text{$\#$1}^4 c_3{}^2 c_4{}^2-2 \text{$\#$1}^4 c_0 c_2 c_5{}^2-2 \text{$\#$1}^4 c_1 c_3 c_5{}^2-4 \text{$\#$1}^2 c_2{}^2 c_4{}^3-4 \text{$\#$1}^2 c_3{}^2 c_4{}^3+4 \text{$\#$1}^2 c_0 c_2 c_4 c_5{}^2+4 \text{$\#$1}^2 c_1 c_3 c_4 c_5{}^2+c_2{}^2 c_4{}^4+c_3{}^2 c_4{}^4+c_0{}^2 c_5{}^4+c_1{}^2 c_5{}^4-2 c_0 c_2 c_4{}^2 c_5{}^2-2 c_1 c_3 c_4{}^2 c_5{}^2\&,\frac{\text{$\#$1} \log \left(-\text{$\#$1}+\sqrt{c_5 \sqrt{\frac{c_1 x+c_0}{c_3 x+c_2}}+c_4}\right)}{\text{$\#$1}^4 c_2{}^2+\text{$\#$1}^4 c_3{}^2-2 \text{$\#$1}^2 c_2{}^2 c_4-2 \text{$\#$1}^2 c_3{}^2 c_4+c_2{}^2 c_4{}^2+c_3{}^2 c_4{}^2-c_0 c_2 c_5{}^2-c_1 c_3 c_5{}^2}\&\right]-\frac{(c_3 x+c_2) \sqrt{c_5 \sqrt{\frac{c_1 x+c_0}{c_3 x+c_2}}+c_4}}{4 c_3 (c_0 c_3-c_1 c_2) c_5{}^2}+\frac{\tan ^{-1}\left(\frac{\sqrt{c_3} \sqrt{c_5 \sqrt{\frac{c_1 x+c_0}{c_3 x+c_2}}+c_4}}{\sqrt{-c_3 c_4-\sqrt{c_1} \sqrt{c_3} c_5}}\right)}{8 \sqrt{c_1} c_3 c_5 \sqrt{-c_3 c_4-\sqrt{c_1} \sqrt{c_3} c_5}}-\frac{\tan ^{-1}\left(\frac{\sqrt{c_3} \sqrt{c_5 \sqrt{\frac{c_1 x+c_0}{c_3 x+c_2}}+c_4}}{\sqrt{\sqrt{c_1} \sqrt{c_3} c_5-c_3 c_4}}\right)}{8 \sqrt{c_1} c_3 c_5 \sqrt{\sqrt{c_1} \sqrt{c_3} c_5-c_3 c_4}}\right)","\left(c_0 c_3 c_5{}^2-c_1 c_2 c_5{}^2\right) \text{RootSum}\left[\text{$\#$1}^8 c_2{}^2+\text{$\#$1}^8 c_3{}^2-4 \text{$\#$1}^6 c_2{}^2 c_4-4 \text{$\#$1}^6 c_3{}^2 c_4+6 \text{$\#$1}^4 c_2{}^2 c_4{}^2+6 \text{$\#$1}^4 c_3{}^2 c_4{}^2-2 \text{$\#$1}^4 c_0 c_2 c_5{}^2-2 \text{$\#$1}^4 c_1 c_3 c_5{}^2-4 \text{$\#$1}^2 c_2{}^2 c_4{}^3-4 \text{$\#$1}^2 c_3{}^2 c_4{}^3+4 \text{$\#$1}^2 c_0 c_2 c_4 c_5{}^2+4 \text{$\#$1}^2 c_1 c_3 c_4 c_5{}^2+c_2{}^2 c_4{}^4+c_3{}^2 c_4{}^4+c_0{}^2 c_5{}^4+c_1{}^2 c_5{}^4-2 c_0 c_2 c_4{}^2 c_5{}^2-2 c_1 c_3 c_4{}^2 c_5{}^2\&,\frac{\text{$\#$1} \log \left(-\text{$\#$1}+\sqrt{c_5 \sqrt{\frac{c_1 x+c_0}{c_3 x+c_2}}+c_4}\right)}{\text{$\#$1}^4 c_2{}^2+\text{$\#$1}^4 c_3{}^2-2 \text{$\#$1}^2 c_2{}^2 c_4-2 \text{$\#$1}^2 c_3{}^2 c_4+c_2{}^2 c_4{}^2+c_3{}^2 c_4{}^2-c_0 c_2 c_5{}^2-c_1 c_3 c_5{}^2}\&\right]-\frac{(c_1 c_2-c_0 c_3) \sqrt{c_5 \sqrt{\frac{c_1 x+c_0}{c_3 x+c_2}}+c_4}}{c_3 \left(\frac{c_3 (c_1 x+c_0)}{c_3 x+c_2}-c_1\right)}-\frac{(c_0 c_3-c_1 c_2) c_5 \sqrt{\sqrt{c_3} \left(\sqrt{c_1} c_5-\sqrt{c_3} c_4\right)} \tan ^{-1}\left(\frac{\sqrt{\sqrt{c_1} \sqrt{c_3} c_5-c_3 c_4} \sqrt{c_5 \sqrt{\frac{c_1 x+c_0}{c_3 x+c_2}}+c_4}}{\sqrt{c_3} c_4-\sqrt{c_1} c_5}\right)}{2 \sqrt{c_1} c_3{}^{3/2} \left(\sqrt{c_1} c_5-\sqrt{c_3} c_4\right)}-\frac{(c_0 c_3-c_1 c_2) c_5 \sqrt{-\sqrt{c_3} \left(\sqrt{c_3} c_4+\sqrt{c_1} c_5\right)} \tan ^{-1}\left(\frac{\sqrt{-c_3 c_4-\sqrt{c_1} \sqrt{c_3} c_5} \sqrt{c_5 \sqrt{\frac{c_1 x+c_0}{c_3 x+c_2}}+c_4}}{\sqrt{c_3} c_4+\sqrt{c_1} c_5}\right)}{2 \sqrt{c_1} c_3{}^{3/2} \left(\sqrt{c_3} c_4+\sqrt{c_1} c_5\right)}",1,"4*(C[1]*C[2] - C[0]*C[3])*C[5]^2*(ArcTan[(Sqrt[C[3]]*Sqrt[C[4] + Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5]])/Sqrt[-(C[3]*C[4]) - Sqrt[C[1]]*Sqrt[C[3]]*C[5]]]/(8*Sqrt[C[1]]*C[3]*C[5]*Sqrt[-(C[3]*C[4]) - Sqrt[C[1]]*Sqrt[C[3]]*C[5]]) - ArcTan[(Sqrt[C[3]]*Sqrt[C[4] + Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5]])/Sqrt[-(C[3]*C[4]) + Sqrt[C[1]]*Sqrt[C[3]]*C[5]]]/(8*Sqrt[C[1]]*C[3]*C[5]*Sqrt[-(C[3]*C[4]) + Sqrt[C[1]]*Sqrt[C[3]]*C[5]]) - ((C[2] + x*C[3])*Sqrt[C[4] + Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5]])/(4*C[3]*(-(C[1]*C[2]) + C[0]*C[3])*C[5]^2) - RootSum[C[2]^2*C[4]^4 + C[3]^2*C[4]^4 - 2*C[0]*C[2]*C[4]^2*C[5]^2 - 2*C[1]*C[3]*C[4]^2*C[5]^2 + C[0]^2*C[5]^4 + C[1]^2*C[5]^4 - 4*C[2]^2*C[4]^3*#1^2 - 4*C[3]^2*C[4]^3*#1^2 + 4*C[0]*C[2]*C[4]*C[5]^2*#1^2 + 4*C[1]*C[3]*C[4]*C[5]^2*#1^2 + 6*C[2]^2*C[4]^2*#1^4 + 6*C[3]^2*C[4]^2*#1^4 - 2*C[0]*C[2]*C[5]^2*#1^4 - 2*C[1]*C[3]*C[5]^2*#1^4 - 4*C[2]^2*C[4]*#1^6 - 4*C[3]^2*C[4]*#1^6 + C[2]^2*#1^8 + C[3]^2*#1^8 & , (Log[Sqrt[C[4] + Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5]] - #1]*#1)/(C[2]^2*C[4]^2 + C[3]^2*C[4]^2 - C[0]*C[2]*C[5]^2 - C[1]*C[3]*C[5]^2 - 2*C[2]^2*C[4]*#1^2 - 2*C[3]^2*C[4]*#1^2 + C[2]^2*#1^4 + C[3]^2*#1^4) & ]/4)","A",1
3131,1,2441,787,7.3848547,"\int \frac{\sqrt{-b+a^2 x^2}}{\sqrt[4]{c+\sqrt[3]{a x+\sqrt{-b+a^2 x^2}}}} \, dx","Integrate[Sqrt[-b + a^2*x^2]/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^(1/4),x]","\text{Result too large to show}","\frac{13923 b^2 \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt[3]{\sqrt{a^2 x^2-b}+a x}+c}}{\sqrt[4]{c}}\right)}{131072 a c^{25/4}}-\frac{13923 b^2 \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt[3]{\sqrt{a^2 x^2-b}+a x}+c}}{\sqrt[4]{c}}\right)}{131072 a c^{25/4}}-\frac{3 b \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt[3]{\sqrt{a^2 x^2-b}+a x}+c}}{\sqrt[4]{c}}\right)}{a \sqrt[4]{c}}+\frac{3 b \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt[3]{\sqrt{a^2 x^2-b}+a x}+c}}{\sqrt[4]{c}}\right)}{a \sqrt[4]{c}}+\frac{\sqrt{a^2 x^2-b} \left(\sqrt[3]{\sqrt{a^2 x^2-b}+a x} \left(-6055526400 a^2 c^7 x^2+4026531840 a c^{10} x-1873980108 b^2 c+1513881600 b c^7\right) \left(\sqrt[3]{\sqrt{a^2 x^2-b}+a x}+c\right)^{3/4}+\left(\sqrt{a^2 x^2-b}+a x\right)^{2/3} \left(\sqrt[3]{\sqrt{a^2 x^2-b}+a x}+c\right)^{3/4} \left(5752750080 a^2 c^6 x^2-3523215360 a c^9 x+2342475135 b^2-1438187520 b c^6\right)+\left(6459228160 a^2 c^8 x^2-5368709120 a c^{11} x+1665760096 b^2 c^2-1614807040 b c^8\right) \left(\sqrt[3]{\sqrt{a^2 x^2-b}+a x}+c\right)^{3/4}\right)+\sqrt[3]{\sqrt{a^2 x^2-b}+a x} \left(-6055526400 a^3 c^7 x^3+4026531840 a^2 c^{10} x^2-1873980108 a b^2 c x+4541644800 a b c^7 x+1447176192 b^2 c^4-2013265920 b c^{10}\right) \left(\sqrt[3]{\sqrt{a^2 x^2-b}+a x}+c\right)^{3/4}+\left(\sqrt{a^2 x^2-b}+a x\right)^{2/3} \left(\sqrt[3]{\sqrt{a^2 x^2-b}+a x}+c\right)^{3/4} \left(5752750080 a^3 c^6 x^3-3523215360 a^2 c^9 x^2+2342475135 a b^2 x-4314562560 a b c^6 x-1537624704 b^2 c^3+1761607680 b c^9\right)+\left(6459228160 a^3 c^8 x^3-5368709120 a^2 c^{11} x^2+1665760096 a b^2 c^2 x-4844421120 a b c^8 x-1378263040 b^2 c^5+2684354560 b c^{11}\right) \left(\sqrt[3]{\sqrt{a^2 x^2-b}+a x}+c\right)^{3/4}}{11026104320 a c^6 \left(2 a^2 x^2-b\right)+22052208640 a^2 c^6 x \sqrt{a^2 x^2-b}}",1,"-1/44104417280*((c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^(35/4)*(1 - b/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^6 + c^6/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^6 - (6*c^5)/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^5 + (15*c^4)/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^4 - (20*c^3)/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^3 + (15*c^2)/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^2 - (6*c)/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3)))*(5752750080*c^(25/4) - (40981117100*b^2*c^(21/4))/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^11 - (44104417280*c^(69/4))/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^11 + (114912007980*b^2*c^(17/4))/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^10 + (359135969280*c^(65/4))/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^10 - (164814147960*b^2*c^(13/4))/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^9 - (1348907827200*c^(61/4))/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^9 + (130345727512*b^2*c^(9/4))/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^8 + (3109647810560*c^(57/4))/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^8 - (54345423132*b^2*c^(5/4))/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^7 - (4920099471360*c^(53/4))/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^7 + (9369900540*b^2*c^(1/4))/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^6 + (5625764904960*c^(49/4))/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^6 - (4736415170560*c^(45/4))/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^5 + (2922027417600*c^(41/4))/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^4 - (1286881935360*c^(37/4))/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^3 + (383415746560*c^(33/4))/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^2 - (69335777280*c^(29/4))/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3)) - (1009470*b*(4641*b - 131072*c^6)*(-1 + c/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3)))^6*ArcTan[c^(1/4)/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^(1/4)])/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^(23/4) + (504735*b*(4641*b - 131072*c^6)*(-1 + c/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3)))^6*Log[1 - c^(1/4)/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^(1/4)])/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^(23/4) - (2342475135*b^2*c^6*Log[1 + c^(1/4)/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^(1/4)])/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^(47/4) + (66156625920*b*c^12*Log[1 + c^(1/4)/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^(1/4)])/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^(47/4) + (14054850810*b^2*c^5*Log[1 + c^(1/4)/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^(1/4)])/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^(43/4) - (396939755520*b*c^11*Log[1 + c^(1/4)/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^(1/4)])/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^(43/4) - (35137127025*b^2*c^4*Log[1 + c^(1/4)/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^(1/4)])/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^(39/4) + (992349388800*b*c^10*Log[1 + c^(1/4)/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^(1/4)])/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^(39/4) + (46849502700*b^2*c^3*Log[1 + c^(1/4)/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^(1/4)])/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^(35/4) - (1323132518400*b*c^9*Log[1 + c^(1/4)/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^(1/4)])/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^(35/4) - (35137127025*b^2*c^2*Log[1 + c^(1/4)/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^(1/4)])/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^(31/4) + (992349388800*b*c^8*Log[1 + c^(1/4)/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^(1/4)])/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^(31/4) + (14054850810*b^2*c*Log[1 + c^(1/4)/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^(1/4)])/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^(27/4) - (396939755520*b*c^7*Log[1 + c^(1/4)/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^(1/4)])/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^(27/4) - (2342475135*b^2*Log[1 + c^(1/4)/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^(1/4)])/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^(23/4) + (66156625920*b*c^6*Log[1 + c^(1/4)/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^(1/4)])/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^(23/4)))/(a*c^(25/4)*Sqrt[((c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^6*(1 - b/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^6 + c^6/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^6 - (6*c^5)/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^5 + (15*c^4)/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^4 - (20*c^3)/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^3 + (15*c^2)/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^2 - (6*c)/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3)))^2)/(-1 + c/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3)))^6]*(-1 + c/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3)))^9)","B",0
3132,-1,0,803,180.0011885,"\int \frac{\sqrt{-b+a^2 x^2}}{\sqrt[3]{a x+\sqrt{-b+a^2 x^2}} \sqrt[4]{c+\sqrt[3]{a x+\sqrt{-b+a^2 x^2}}}} \, dx","Integrate[Sqrt[-b + a^2*x^2]/((a*x + Sqrt[-b + a^2*x^2])^(1/3)*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^(1/4)),x]","\text{\$Aborted}","-\frac{49725 \tan ^{-1}\left(\frac{\sqrt[4]{c+\sqrt[3]{a x+\sqrt{a^2 x^2-b}}}}{\sqrt[4]{c}}\right) b^2}{524288 a c^{29/4}}+\frac{49725 \tanh ^{-1}\left(\frac{\sqrt[4]{c+\sqrt[3]{a x+\sqrt{a^2 x^2-b}}}}{\sqrt[4]{c}}\right) b^2}{524288 a c^{29/4}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt[4]{c+\sqrt[3]{a x+\sqrt{a^2 x^2-b}}}}{\sqrt[4]{c}}\right) b}{4 a c^{5/4}}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt[4]{c+\sqrt[3]{a x+\sqrt{a^2 x^2-b}}}}{\sqrt[4]{c}}\right) b}{4 a c^{5/4}}+\frac{\left(a x+\sqrt{a^2 x^2-b}\right)^{2/3} \left(c+\sqrt[3]{a x+\sqrt{a^2 x^2-b}}\right)^{3/4} \left(-805306368 a^2 x^2 c^{10}+402653184 b c^{10}+1211105280 a^3 x^3 c^7-908328960 a b x c^7-224716800 b^2 c^4+290990700 a b^2 x c\right)+\sqrt{a^2 x^2-b} \left(\left(a x+\sqrt{a^2 x^2-b}\right)^{2/3} \left(c+\sqrt[3]{a x+\sqrt{a^2 x^2-b}}\right)^{3/4} \left(-805306368 a x c^{10}+1211105280 a^2 x^2 c^7-302776320 b c^7+290990700 b^2 c\right)+\left(1409286144 a^2 x^2 c^9-352321536 b c^9+5752750080 a b x c^6+238761600 b^2 c^3-727476750 a b^2 x\right) \left(c+\sqrt[3]{a x+\sqrt{a^2 x^2-b}}\right)^{3/4}+\left(1073741824 a x c^{11}-1291845632 a^2 x^2 c^8+322961408 b c^8-258658400 b^2 c^2\right) \sqrt[3]{a x+\sqrt{a^2 x^2-b}} \left(c+\sqrt[3]{a x+\sqrt{a^2 x^2-b}}\right)^{3/4}\right)+\left(1409286144 a^3 x^3 c^9-1056964608 a b x c^9-3081830400 b^2 c^6+5752750080 a^2 b x^2 c^6+238761600 a b^2 x c^3+363738375 b^3-727476750 a^2 b^2 x^2\right) \left(c+\sqrt[3]{a x+\sqrt{a^2 x^2-b}}\right)^{3/4}+\left(1073741824 a^2 x^2 c^{11}-536870912 b c^{11}-1291845632 a^3 x^3 c^8+968884224 a b x c^8+214016000 b^2 c^5-258658400 a b^2 x c^2\right) \sqrt[3]{a x+\sqrt{a^2 x^2-b}} \left(c+\sqrt[3]{a x+\sqrt{a^2 x^2-b}}\right)^{3/4}}{1917583360 a c^7 \left(a x+\sqrt{a^2 x^2-b}\right)^{7/3}}",1,"$Aborted","F",-1
3133,1,416,827,2.9555828,"\int \frac{\left(b+a x^4\right) \sqrt{-b-c x^2+a x^4}}{\left(-b+a x^4\right)^2} \, dx","Integrate[((b + a*x^4)*Sqrt[-b - c*x^2 + a*x^4])/(-b + a*x^4)^2,x]","\frac{1}{2} \sqrt{a x^4-b-c x^2} \left(\frac{x}{b-a x^4}-\frac{i \sqrt{\frac{4 a x^2}{\sqrt{4 a b+c^2}-c}+2} \sqrt{1-\frac{2 a x^2}{\sqrt{4 a b+c^2}+c}} \left(F\left(i \sinh ^{-1}\left(\sqrt{2} \sqrt{\frac{a}{\sqrt{c^2+4 a b}-c}} x\right)|\frac{c-\sqrt{c^2+4 a b}}{c+\sqrt{c^2+4 a b}}\right)-\Pi \left(\frac{c-\sqrt{c^2+4 a b}}{2 \sqrt{a} \sqrt{b}};i \sinh ^{-1}\left(\sqrt{2} \sqrt{\frac{a}{\sqrt{c^2+4 a b}-c}} x\right)|\frac{c-\sqrt{c^2+4 a b}}{c+\sqrt{c^2+4 a b}}\right)-\Pi \left(\frac{\sqrt{c^2+4 a b}-c}{2 \sqrt{a} \sqrt{b}};i \sinh ^{-1}\left(\sqrt{2} \sqrt{\frac{a}{\sqrt{c^2+4 a b}-c}} x\right)|\frac{c-\sqrt{c^2+4 a b}}{c+\sqrt{c^2+4 a b}}\right)\right)}{2 \sqrt{\frac{a}{\sqrt{4 a b+c^2}-c}} \left(a x^4-b-c x^2\right)}\right)","\frac{x \left(i a^{3/2} x^6-i \sqrt{a} c x^4-a \sqrt{b} x^4+i a \sqrt{a x^4-c x^2-b} x^4-i \sqrt{a} b x^2+\sqrt{b} c x^2-\frac{1}{2} i c \sqrt{a x^4-c x^2-b} x^2-\sqrt{a} \sqrt{b} \sqrt{a x^4-c x^2-b} x^2+b^{3/2}-i b \sqrt{a x^4-c x^2-b}\right)}{\left(a x^4-b\right) \left(-2 i a x^4+i c x^2+2 \sqrt{a} \sqrt{b} x^2-2 i \sqrt{a} \sqrt{a x^4-c x^2-b} x^2+2 i b+2 \sqrt{b} \sqrt{a x^4-c x^2-b}\right)}+\frac{\left(\frac{1}{2}-\frac{i}{2}\right) \sqrt[4]{a} \sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{c-(2-2 i) \sqrt[4]{a} \sqrt[4]{b} \sqrt{c}-2 i \sqrt{a} \sqrt{b}} x}{\sqrt{a} x^2+i \sqrt{b}+\sqrt{a x^4-c x^2-b}}\right)}{\sqrt{c} \sqrt{c-(2-2 i) \sqrt[4]{a} \sqrt[4]{b} \sqrt{c}-2 i \sqrt{a} \sqrt{b}}}-\frac{\tan ^{-1}\left(\frac{\sqrt{c-(2-2 i) \sqrt[4]{a} \sqrt[4]{b} \sqrt{c}-2 i \sqrt{a} \sqrt{b}} x}{\sqrt{a} x^2+i \sqrt{b}+\sqrt{a x^4-c x^2-b}}\right)}{2 \sqrt{c-(2-2 i) \sqrt[4]{a} \sqrt[4]{b} \sqrt{c}-2 i \sqrt{a} \sqrt{b}}}-\frac{\left(\frac{1}{2}-\frac{i}{2}\right) \sqrt[4]{a} \sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{c+(2-2 i) \sqrt[4]{a} \sqrt[4]{b} \sqrt{c}-2 i \sqrt{a} \sqrt{b}} x}{\sqrt{a} x^2+i \sqrt{b}+\sqrt{a x^4-c x^2-b}}\right)}{\sqrt{c} \sqrt{c+(2-2 i) \sqrt[4]{a} \sqrt[4]{b} \sqrt{c}-2 i \sqrt{a} \sqrt{b}}}-\frac{\tan ^{-1}\left(\frac{\sqrt{c+(2-2 i) \sqrt[4]{a} \sqrt[4]{b} \sqrt{c}-2 i \sqrt{a} \sqrt{b}} x}{\sqrt{a} x^2+i \sqrt{b}+\sqrt{a x^4-c x^2-b}}\right)}{2 \sqrt{c+(2-2 i) \sqrt[4]{a} \sqrt[4]{b} \sqrt{c}-2 i \sqrt{a} \sqrt{b}}}",1,"(Sqrt[-b - c*x^2 + a*x^4]*(x/(b - a*x^4) - ((I/2)*Sqrt[2 + (4*a*x^2)/(-c + Sqrt[4*a*b + c^2])]*Sqrt[1 - (2*a*x^2)/(c + Sqrt[4*a*b + c^2])]*(EllipticF[I*ArcSinh[Sqrt[2]*Sqrt[a/(-c + Sqrt[4*a*b + c^2])]*x], (c - Sqrt[4*a*b + c^2])/(c + Sqrt[4*a*b + c^2])] - EllipticPi[(c - Sqrt[4*a*b + c^2])/(2*Sqrt[a]*Sqrt[b]), I*ArcSinh[Sqrt[2]*Sqrt[a/(-c + Sqrt[4*a*b + c^2])]*x], (c - Sqrt[4*a*b + c^2])/(c + Sqrt[4*a*b + c^2])] - EllipticPi[(-c + Sqrt[4*a*b + c^2])/(2*Sqrt[a]*Sqrt[b]), I*ArcSinh[Sqrt[2]*Sqrt[a/(-c + Sqrt[4*a*b + c^2])]*x], (c - Sqrt[4*a*b + c^2])/(c + Sqrt[4*a*b + c^2])]))/(Sqrt[a/(-c + Sqrt[4*a*b + c^2])]*(-b - c*x^2 + a*x^4))))/2","C",1
3134,1,72,849,0.0733358,"\int \frac{-a-b c+(1+c) x}{\left((-a+x) (-b+x)^2\right)^{2/3} (a-b d+(-1+d) x)} \, dx","Integrate[(-a - b*c + (1 + c)*x)/(((-a + x)*(-b + x)^2)^(2/3)*(a - b*d + (-1 + d)*x)),x]","\frac{3 (x-b) \left((x-b) (c+d) \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{d (b-x)}{a-x}\right)+2 (a-x)\right)}{2 (a-b) \left((x-a) (b-x)^2\right)^{2/3}}","\frac{(b-x)^{4/3} (x-a)^{2/3} \left(\frac{\sqrt{3} (d-1) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x-a}}{\sqrt[3]{x-a}-2 \sqrt[3]{d} \sqrt[3]{b-x}}\right) a}{(a-b)^2 d^{2/3}}-\frac{(d-1) \log \left(\sqrt[3]{d} \sqrt[3]{b-x}+\sqrt[3]{x-a}\right) a}{(a-b)^2 d^{2/3}}+\frac{(d-1) \log \left(d^{2/3} (b-x)^{2/3}-\sqrt[3]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+(x-a)^{2/3}\right) a}{2 (a-b)^2 d^{2/3}}-\frac{3 (b-x)^{2/3} \sqrt[3]{x-a} a}{(a-b)^2 (x-b)}+\frac{\sqrt{3} c (a-b d) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x-a}}{\sqrt[3]{x-a}-2 \sqrt[3]{d} \sqrt[3]{b-x}}\right)}{(a-b)^2 d^{2/3}}+\frac{\sqrt{3} (a-b d) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x-a}}{\sqrt[3]{x-a}-2 \sqrt[3]{d} \sqrt[3]{b-x}}\right)}{(a-b)^2 d^{2/3}}+\frac{\sqrt{3} b c (d-1) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x-a}}{\sqrt[3]{x-a}-2 \sqrt[3]{d} \sqrt[3]{b-x}}\right)}{(a-b)^2 d^{2/3}}-\frac{c (a-b d) \log \left(\sqrt[3]{d} \sqrt[3]{b-x}+\sqrt[3]{x-a}\right)}{(a-b)^2 d^{2/3}}+\frac{(b d-a) \log \left(\sqrt[3]{d} \sqrt[3]{b-x}+\sqrt[3]{x-a}\right)}{(a-b)^2 d^{2/3}}-\frac{b c (d-1) \log \left(\sqrt[3]{d} \sqrt[3]{b-x}+\sqrt[3]{x-a}\right)}{(a-b)^2 d^{2/3}}+\frac{c (a-b d) \log \left(d^{2/3} (b-x)^{2/3}-\sqrt[3]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+(x-a)^{2/3}\right)}{2 (a-b)^2 d^{2/3}}+\frac{(a-b d) \log \left(d^{2/3} (b-x)^{2/3}-\sqrt[3]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+(x-a)^{2/3}\right)}{2 (a-b)^2 d^{2/3}}+\frac{b c (d-1) \log \left(d^{2/3} (b-x)^{2/3}-\sqrt[3]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+(x-a)^{2/3}\right)}{2 (a-b)^2 d^{2/3}}+\frac{3 b (b-x)^{2/3} \sqrt[3]{x-a}}{(a-b)^2 (x-b)}\right)}{\left((b-x)^2 (x-a)\right)^{2/3}}",1,"(3*(-b + x)*(2*(a - x) + (c + d)*(-b + x)*Hypergeometric2F1[2/3, 1, 5/3, (d*(b - x))/(a - x)]))/(2*(a - b)*((b - x)^2*(-a + x))^(2/3))","C",1
3135,1,65,857,0.0524903,"\int \frac{-a-b c+(1+c) x}{(-b+x) \sqrt[3]{(-a+x) (-b+x)^2} (a-b d+(-1+d) x)} \, dx","Integrate[(-a - b*c + (1 + c)*x)/((-b + x)*((-a + x)*(-b + x)^2)^(1/3)*(a - b*d + (-1 + d)*x)),x]","\frac{3 \left(2 (x-b) (c+d) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{d (b-x)}{a-x}\right)+a-x\right)}{2 (a-b) \sqrt[3]{(x-a) (b-x)^2}}","\frac{(b-x)^{2/3} \sqrt[3]{x-a} \left(-\frac{\sqrt{3} (d-1) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x-a}}{\sqrt[3]{x-a}-2 \sqrt[3]{d} \sqrt[3]{b-x}}\right) a}{(a-b)^2 \sqrt[3]{d}}-\frac{(d-1) \log \left(\sqrt[3]{d} \sqrt[3]{b-x}+\sqrt[3]{x-a}\right) a}{(a-b)^2 \sqrt[3]{d}}+\frac{(d-1) \log \left(d^{2/3} (b-x)^{2/3}-\sqrt[3]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+(x-a)^{2/3}\right) a}{2 (a-b)^2 \sqrt[3]{d}}+\frac{3 \sqrt[3]{b-x} (x-a)^{2/3} a}{2 (a-b)^2 (x-b)}-\frac{\sqrt{3} c (a-b d) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x-a}}{\sqrt[3]{x-a}-2 \sqrt[3]{d} \sqrt[3]{b-x}}\right)}{(a-b)^2 \sqrt[3]{d}}-\frac{\sqrt{3} (a-b d) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x-a}}{\sqrt[3]{x-a}-2 \sqrt[3]{d} \sqrt[3]{b-x}}\right)}{(a-b)^2 \sqrt[3]{d}}-\frac{\sqrt{3} b c (d-1) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x-a}}{\sqrt[3]{x-a}-2 \sqrt[3]{d} \sqrt[3]{b-x}}\right)}{(a-b)^2 \sqrt[3]{d}}-\frac{c (a-b d) \log \left(\sqrt[3]{d} \sqrt[3]{b-x}+\sqrt[3]{x-a}\right)}{(a-b)^2 \sqrt[3]{d}}+\frac{(b d-a) \log \left(\sqrt[3]{d} \sqrt[3]{b-x}+\sqrt[3]{x-a}\right)}{(a-b)^2 \sqrt[3]{d}}-\frac{b c (d-1) \log \left(\sqrt[3]{d} \sqrt[3]{b-x}+\sqrt[3]{x-a}\right)}{(a-b)^2 \sqrt[3]{d}}+\frac{c (a-b d) \log \left(d^{2/3} (b-x)^{2/3}-\sqrt[3]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+(x-a)^{2/3}\right)}{2 (a-b)^2 \sqrt[3]{d}}+\frac{(a-b d) \log \left(d^{2/3} (b-x)^{2/3}-\sqrt[3]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+(x-a)^{2/3}\right)}{2 (a-b)^2 \sqrt[3]{d}}+\frac{b c (d-1) \log \left(d^{2/3} (b-x)^{2/3}-\sqrt[3]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+(x-a)^{2/3}\right)}{2 (a-b)^2 \sqrt[3]{d}}-\frac{3 b \sqrt[3]{b-x} (x-a)^{2/3}}{2 (a-b)^2 (x-b)}\right)}{\sqrt[3]{(b-x)^2 (x-a)}}",1,"(3*(a - x + 2*(c + d)*(-b + x)*Hypergeometric2F1[1/3, 1, 4/3, (d*(b - x))/(a - x)]))/(2*(a - b)*((b - x)^2*(-a + x))^(1/3))","C",1
3136,0,0,876,0.586786,"\int \frac{\left(d+c x^2\right) \left(a x+\sqrt{-b+a^2 x^2}\right)^{5/4}}{x \left(-b+a^2 x^2\right)^{5/2}} \, dx","Integrate[((d + c*x^2)*(a*x + Sqrt[-b + a^2*x^2])^(5/4))/(x*(-b + a^2*x^2)^(5/2)),x]","\int \frac{\left(d+c x^2\right) \left(a x+\sqrt{-b+a^2 x^2}\right)^{5/4}}{x \left(-b+a^2 x^2\right)^{5/2}} \, dx","\frac{\sqrt[4]{\frac{a x+\sqrt{a^2 x^2-b}}{\sqrt{b}}} \left(-51 d x^2 a^4+45 b c x^2 a^2-b d a^2-97 b^2 c\right)}{96 a^2 b^{15/8} \left(a x-\sqrt{b}\right) \left(a x+\sqrt{b}\right)}+\frac{5 \left(29 a^2 d-3 b c\right) \tan ^{-1}\left(\sqrt[4]{\frac{a x+\sqrt{a^2 x^2-b}}{\sqrt{b}}}\right)}{64 a^2 b^{15/8}}-\frac{\sqrt{2-\sqrt{2}} d \tan ^{-1}\left(\frac{\frac{\sqrt{\frac{a x+\sqrt{a^2 x^2-b}}{\sqrt{b}}}}{\sqrt{2-\sqrt{2}}}-\frac{1}{\sqrt{2-\sqrt{2}}}}{\sqrt[4]{\frac{a x+\sqrt{a^2 x^2-b}}{\sqrt{b}}}}\right)}{b^{15/8}}-\frac{\sqrt{2+\sqrt{2}} d \tan ^{-1}\left(\frac{\frac{\sqrt{\frac{a x+\sqrt{a^2 x^2-b}}{\sqrt{b}}}}{\sqrt{2+\sqrt{2}}}-\frac{1}{\sqrt{2+\sqrt{2}}}}{\sqrt[4]{\frac{a x+\sqrt{a^2 x^2-b}}{\sqrt{b}}}}\right)}{b^{15/8}}+\frac{5 \left(29 a^2 d-3 b c\right) \tanh ^{-1}\left(\sqrt[4]{\frac{a x+\sqrt{a^2 x^2-b}}{\sqrt{b}}}\right)}{64 a^2 b^{15/8}}-\frac{5 (-1)^{3/4} \left(29 a^2 d-3 b c\right) \tanh ^{-1}\left(\sqrt[4]{-1} \sqrt[4]{\frac{a x+\sqrt{a^2 x^2-b}}{\sqrt{b}}}\right)}{64 a^2 b^{15/8}}-\frac{5 \sqrt[4]{-1} \left(29 a^2 d-3 b c\right) \tanh ^{-1}\left((-1)^{3/4} \sqrt[4]{\frac{a x+\sqrt{a^2 x^2-b}}{\sqrt{b}}}\right)}{64 a^2 b^{15/8}}-\frac{\sqrt{2-\sqrt{2}} d \tanh ^{-1}\left(\frac{\frac{\sqrt{\frac{a x+\sqrt{a^2 x^2-b}}{\sqrt{b}}}}{\sqrt{2-\sqrt{2}}}+\frac{1}{\sqrt{2-\sqrt{2}}}}{\sqrt[4]{\frac{a x+\sqrt{a^2 x^2-b}}{\sqrt{b}}}}\right)}{b^{15/8}}-\frac{\sqrt{2+\sqrt{2}} d \tanh ^{-1}\left(\frac{\frac{\sqrt{\frac{a x+\sqrt{a^2 x^2-b}}{\sqrt{b}}}}{\sqrt{2+\sqrt{2}}}+\frac{1}{\sqrt{2+\sqrt{2}}}}{\sqrt[4]{\frac{a x+\sqrt{a^2 x^2-b}}{\sqrt{b}}}}\right)}{b^{15/8}}+\frac{\sqrt{a^2 x^2-b} \left(51 d x^3 a^4-45 b c x^3 a^2-83 b d x a^2+13 b^2 c x\right) \sqrt[4]{\frac{a x+\sqrt{a^2 x^2-b}}{\sqrt{b}}}}{96 a b^{15/8} \left(a x-\sqrt{b}\right)^2 \left(a x+\sqrt{b}\right)^2}",1,"Integrate[((d + c*x^2)*(a*x + Sqrt[-b + a^2*x^2])^(5/4))/(x*(-b + a^2*x^2)^(5/2)), x]","F",-1
3137,1,821,884,2.5877769,"\int \frac{1}{\sqrt{c_4+\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5} (c_6+x c_7){}^2} \, dx","Integrate[1/(Sqrt[C[4] + Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5]]*(C[6] + x*C[7])^2),x]","\frac{(c_1 c_2-c_0 c_3) \left(\frac{(c_2+x c_3) \left(c_4-\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5\right) \sqrt{c_4+\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5} (c_1 c_6-c_0 c_7) (c_2 c_7-c_3 c_6)}{(c_1 c_2-c_0 c_3) (c_6+x c_7)}+c_4 c_5 \sqrt{c_1 c_6-c_0 c_7} (c_3 c_6-c_2 c_7){}^{3/4} \left(-\frac{\tan ^{-1}\left(\frac{\sqrt{c_4+\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5} \sqrt[4]{c_3 c_6-c_2 c_7}}{\sqrt{c_5 \sqrt{c_1 c_6-c_0 c_7}-c_4 \sqrt{c_3 c_6-c_2 c_7}}}\right)}{\sqrt{c_5 \sqrt{c_1 c_6-c_0 c_7}-c_4 \sqrt{c_3 c_6-c_2 c_7}}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c_4+\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5} \sqrt[4]{c_3 c_6-c_2 c_7}}{\sqrt{\sqrt{c_3 c_6-c_2 c_7} c_4+c_5 \sqrt{c_1 c_6-c_0 c_7}}}\right)}{\sqrt{\sqrt{c_3 c_6-c_2 c_7} c_4+c_5 \sqrt{c_1 c_6-c_0 c_7}}}\right)-\frac{1}{2} c_5 \sqrt{c_1 c_6-c_0 c_7} \sqrt[4]{c_3 c_6-c_2 c_7} \left(\tan ^{-1}\left(\frac{\sqrt{c_4+\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5} \sqrt[4]{c_3 c_6-c_2 c_7}}{\sqrt{c_5 \sqrt{c_1 c_6-c_0 c_7}-c_4 \sqrt{c_3 c_6-c_2 c_7}}}\right) \sqrt{c_5 \sqrt{c_1 c_6-c_0 c_7}-c_4 \sqrt{c_3 c_6-c_2 c_7}}-\tanh ^{-1}\left(\frac{\sqrt{c_4+\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5} \sqrt[4]{c_3 c_6-c_2 c_7}}{\sqrt{\sqrt{c_3 c_6-c_2 c_7} c_4+c_5 \sqrt{c_1 c_6-c_0 c_7}}}\right) \sqrt{\sqrt{c_3 c_6-c_2 c_7} c_4+c_5 \sqrt{c_1 c_6-c_0 c_7}}\right)\right)}{(c_0 c_7-c_1 c_6) (c_3 c_6-c_2 c_7) \left((c_3 c_6-c_2 c_7) c_4{}^2+c_5{}^2 (c_0 c_7-c_1 c_6)\right)}","\frac{\sqrt{c_4+\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5} \left(-c_1 c_2 c_4+c_0 c_3 c_4+c_1 c_2 \sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5-c_0 c_3 \sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5\right)}{\left(c_1 c_6-\frac{(c_0+x c_1) c_3 c_6}{c_2+x c_3}-c_0 c_7+\frac{(c_0+x c_1) c_2 c_7}{c_2+x c_3}\right) \left(-c_3 c_6 c_4{}^2+c_2 c_7 c_4{}^2+c_1 c_5{}^2 c_6-c_0 c_5{}^2 c_7\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{c_4+\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5} \sqrt{c_3 c_6-c_2 c_7}}{\sqrt{-\sqrt{c_1 c_6-c_0 c_7} \sqrt{c_3 c_6-c_2 c_7} c_5-c_3 c_4 c_6+c_2 c_4 c_7}}\right) \left(-c_1 c_2 \sqrt{c_1 c_6-c_0 c_7} c_5{}^2+c_0 c_3 \sqrt{c_1 c_6-c_0 c_7} c_5{}^2+c_1 c_2 c_4 \sqrt{c_3 c_6-c_2 c_7} c_5-c_0 c_3 c_4 \sqrt{c_3 c_6-c_2 c_7} c_5\right)}{2 \sqrt{c_1 c_6-c_0 c_7} \sqrt{c_3 c_6-c_2 c_7} \left(-c_3 c_6 c_4{}^2+c_2 c_7 c_4{}^2+c_1 c_5{}^2 c_6-c_0 c_5{}^2 c_7\right) \sqrt{-\sqrt{c_1 c_6-c_0 c_7} \sqrt{c_3 c_6-c_2 c_7} c_5-c_3 c_4 c_6+c_2 c_4 c_7}}+\frac{\tan ^{-1}\left(\frac{\sqrt{c_4+\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5} \sqrt{c_3 c_6-c_2 c_7}}{\sqrt{\sqrt{c_1 c_6-c_0 c_7} \sqrt{c_3 c_6-c_2 c_7} c_5-c_3 c_4 c_6+c_2 c_4 c_7}}\right) \left(-c_1 c_2 \sqrt{c_1 c_6-c_0 c_7} c_5{}^2+c_0 c_3 \sqrt{c_1 c_6-c_0 c_7} c_5{}^2-c_1 c_2 c_4 \sqrt{c_3 c_6-c_2 c_7} c_5+c_0 c_3 c_4 \sqrt{c_3 c_6-c_2 c_7} c_5\right)}{2 \sqrt{c_1 c_6-c_0 c_7} \sqrt{c_3 c_6-c_2 c_7} \left(-c_3 c_6 c_4{}^2+c_2 c_7 c_4{}^2+c_1 c_5{}^2 c_6-c_0 c_5{}^2 c_7\right) \sqrt{\sqrt{c_1 c_6-c_0 c_7} \sqrt{c_3 c_6-c_2 c_7} c_5-c_3 c_4 c_6+c_2 c_4 c_7}}",1,"((C[1]*C[2] - C[0]*C[3])*(((C[2] + x*C[3])*(C[4] - Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5])*Sqrt[C[4] + Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5]]*(C[1]*C[6] - C[0]*C[7])*(-(C[3]*C[6]) + C[2]*C[7]))/((C[1]*C[2] - C[0]*C[3])*(C[6] + x*C[7])) + C[4]*C[5]*Sqrt[C[1]*C[6] - C[0]*C[7]]*(C[3]*C[6] - C[2]*C[7])^(3/4)*(-(ArcTan[(Sqrt[C[4] + Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5]]*(C[3]*C[6] - C[2]*C[7])^(1/4))/Sqrt[C[5]*Sqrt[C[1]*C[6] - C[0]*C[7]] - C[4]*Sqrt[C[3]*C[6] - C[2]*C[7]]]]/Sqrt[C[5]*Sqrt[C[1]*C[6] - C[0]*C[7]] - C[4]*Sqrt[C[3]*C[6] - C[2]*C[7]]]) - ArcTanh[(Sqrt[C[4] + Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5]]*(C[3]*C[6] - C[2]*C[7])^(1/4))/Sqrt[C[5]*Sqrt[C[1]*C[6] - C[0]*C[7]] + C[4]*Sqrt[C[3]*C[6] - C[2]*C[7]]]]/Sqrt[C[5]*Sqrt[C[1]*C[6] - C[0]*C[7]] + C[4]*Sqrt[C[3]*C[6] - C[2]*C[7]]]) - (C[5]*Sqrt[C[1]*C[6] - C[0]*C[7]]*(C[3]*C[6] - C[2]*C[7])^(1/4)*(ArcTan[(Sqrt[C[4] + Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5]]*(C[3]*C[6] - C[2]*C[7])^(1/4))/Sqrt[C[5]*Sqrt[C[1]*C[6] - C[0]*C[7]] - C[4]*Sqrt[C[3]*C[6] - C[2]*C[7]]]]*Sqrt[C[5]*Sqrt[C[1]*C[6] - C[0]*C[7]] - C[4]*Sqrt[C[3]*C[6] - C[2]*C[7]]] - ArcTanh[(Sqrt[C[4] + Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5]]*(C[3]*C[6] - C[2]*C[7])^(1/4))/Sqrt[C[5]*Sqrt[C[1]*C[6] - C[0]*C[7]] + C[4]*Sqrt[C[3]*C[6] - C[2]*C[7]]]]*Sqrt[C[5]*Sqrt[C[1]*C[6] - C[0]*C[7]] + C[4]*Sqrt[C[3]*C[6] - C[2]*C[7]]]))/2))/((-(C[1]*C[6]) + C[0]*C[7])*(C[3]*C[6] - C[2]*C[7])*(C[5]^2*(-(C[1]*C[6]) + C[0]*C[7]) + C[4]^2*(C[3]*C[6] - C[2]*C[7])))","A",1
3138,1,322,887,0.4835187,"\int \frac{\sqrt[6]{\frac{1-b x}{c+x}} \left(1+d x^2\right)}{(1+b x) (1+c x)} \, dx","Integrate[(((1 - b*x)/(c + x))^(1/6)*(1 + d*x^2))/((1 + b*x)*(1 + c*x)),x]","\frac{6}{5} (c+x) \sqrt[6]{\frac{1-b x}{c+x}} \left(\frac{\left(b^2+d\right) \left(\frac{1-b x}{b c+1}\right)^{5/6} \, _2F_1\left(\frac{5}{6},\frac{5}{6};\frac{11}{6};\frac{b (c+x)}{b c+1}\right)}{b (b-c) (b x-1)}+\frac{2 \left(b^2+d\right) \, _2F_1\left(\frac{5}{6},1;\frac{11}{6};-\frac{2 b (c+x)}{(b c-1) (b x-1)}\right)}{b (b-c) (b c-1) (b x-1)}+\frac{b \left(c^2+d\right) \, _2F_1\left(\frac{5}{6},\frac{5}{6};\frac{11}{6};\frac{b (c+x)}{b c+1}\right)}{c^2 (b-c) (b c+1) \sqrt[6]{\frac{1-b x}{b c+1}}}-\frac{(b+c) \left(c^2+d\right) \, _2F_1\left(\frac{5}{6},1;\frac{11}{6};-\frac{(b+c) (c+x)}{\left(c^2-1\right) (b x-1)}\right)}{c^2 \left(c^2-1\right) (b-c) (b x-1)}+\frac{d \, _2F_1\left(-\frac{1}{6},\frac{5}{6};\frac{11}{6};\frac{b (c+x)}{b c+1}\right)}{b c \sqrt[6]{\frac{1-b x}{b c+1}}}\right)","\frac{d \sqrt[6]{\frac{1-b x}{c+x}} (c+x)}{b c}-\frac{\left(b c^2+7 c+6 b\right) d \tan ^{-1}\left(\frac{\sqrt[6]{\frac{1-b x}{c+x}}}{\sqrt[6]{b}}\right)}{3 b^{11/6} c^2}-\frac{2 \sqrt[6]{b+c} \left(c^2+d\right) \tan ^{-1}\left(\frac{\sqrt[6]{1-c^2} \sqrt[6]{\frac{1-b x}{c+x}}}{\sqrt[6]{b+c}}\right)}{c^2 (c-b) \sqrt[6]{1-c^2}}-\frac{\sqrt[6]{2} \sqrt{3} \left(b^2+d\right) \tan ^{-1}\left(\frac{2^{5/6} \sqrt[6]{b c-1} \sqrt[6]{\frac{1-b x}{c+x}}-\sqrt[6]{b}}{\sqrt{3} \sqrt[6]{b}}\right)}{b^{11/6} (b-c) \sqrt[6]{b c-1}}-\frac{\sqrt[6]{2} \sqrt{3} \left(b^2+d\right) \tan ^{-1}\left(\frac{\sqrt[6]{b}+2^{5/6} \sqrt[6]{b c-1} \sqrt[6]{\frac{1-b x}{c+x}}}{\sqrt{3} \sqrt[6]{b}}\right)}{b^{11/6} (b-c) \sqrt[6]{b c-1}}+\frac{\left(b c^2+7 c+6 b\right) d \tan ^{-1}\left(\frac{\sqrt[6]{b} \sqrt[6]{\frac{1-b x}{c+x}}}{\sqrt[3]{\frac{1-b x}{c+x}}-\sqrt[3]{b}}\right)}{6 b^{11/6} c^2}-\frac{\sqrt[6]{b+c} \left(c^2+d\right) \tan ^{-1}\left(\frac{\sqrt[6]{b+c} \sqrt[6]{1-c^2} \sqrt[6]{\frac{1-b x}{c+x}}}{\sqrt[3]{b+c}-\sqrt[3]{1-c^2} \sqrt[3]{\frac{1-b x}{c+x}}}\right)}{c^2 (c-b) \sqrt[6]{1-c^2}}-\frac{2 \sqrt[6]{2} \left(b^2+d\right) \tanh ^{-1}\left(\frac{\sqrt[6]{b c-1} \sqrt[6]{\frac{1-b x}{c+x}}}{\sqrt[6]{2} \sqrt[6]{b}}\right)}{b^{11/6} (b-c) \sqrt[6]{b c-1}}-\frac{\left(b c^2+7 c+6 b\right) d \tanh ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{b} \sqrt[6]{\frac{1-b x}{c+x}}}{\sqrt[3]{b}+\sqrt[3]{\frac{1-b x}{c+x}}}\right)}{2 \sqrt{3} b^{11/6} c^2}-\frac{\sqrt[6]{2} \left(b^2+d\right) \tanh ^{-1}\left(\frac{2^{5/6} \sqrt[6]{b} \sqrt[6]{b c-1} \sqrt[6]{\frac{1-b x}{c+x}}}{2 \sqrt[3]{b}+2^{2/3} \sqrt[3]{b c-1} \sqrt[3]{\frac{1-b x}{c+x}}}\right)}{b^{11/6} (b-c) \sqrt[6]{b c-1}}-\frac{\sqrt{3} \sqrt[6]{b+c} \left(c^2+d\right) \tanh ^{-1}\left(\frac{\sqrt[3]{b+c}+\sqrt[3]{1-c^2} \sqrt[3]{\frac{1-b x}{c+x}}}{\sqrt{3} \sqrt[6]{b+c} \sqrt[6]{1-c^2} \sqrt[6]{\frac{1-b x}{c+x}}}\right)}{c^2 (c-b) \sqrt[6]{1-c^2}}",1,"(6*(c + x)*((1 - b*x)/(c + x))^(1/6)*((d*Hypergeometric2F1[-1/6, 5/6, 11/6, (b*(c + x))/(1 + b*c)])/(b*c*((1 - b*x)/(1 + b*c))^(1/6)) + (b*(c^2 + d)*Hypergeometric2F1[5/6, 5/6, 11/6, (b*(c + x))/(1 + b*c)])/((b - c)*c^2*(1 + b*c)*((1 - b*x)/(1 + b*c))^(1/6)) + ((b^2 + d)*((1 - b*x)/(1 + b*c))^(5/6)*Hypergeometric2F1[5/6, 5/6, 11/6, (b*(c + x))/(1 + b*c)])/(b*(b - c)*(-1 + b*x)) + (2*(b^2 + d)*Hypergeometric2F1[5/6, 1, 11/6, (-2*b*(c + x))/((-1 + b*c)*(-1 + b*x))])/(b*(b - c)*(-1 + b*c)*(-1 + b*x)) - ((b + c)*(c^2 + d)*Hypergeometric2F1[5/6, 1, 11/6, -(((b + c)*(c + x))/((-1 + c^2)*(-1 + b*x)))])/((b - c)*c^2*(-1 + c^2)*(-1 + b*x))))/5","C",1
3139,0,0,963,0.9608907,"\int \frac{\sqrt{-b+a^2 x^2} \left(a x+\sqrt{-b+a^2 x^2}\right)^{3/4}}{\left(c+\sqrt[4]{a x+\sqrt{-b+a^2 x^2}}\right)^{2/3}} \, dx","Integrate[(Sqrt[-b + a^2*x^2]*(a*x + Sqrt[-b + a^2*x^2])^(3/4))/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(2/3),x]","\int \frac{\sqrt{-b+a^2 x^2} \left(a x+\sqrt{-b+a^2 x^2}\right)^{3/4}}{\left(c+\sqrt[4]{a x+\sqrt{-b+a^2 x^2}}\right)^{2/3}} \, dx","\frac{308 \tan ^{-1}\left(\frac{2 \sqrt[3]{c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}}{\sqrt{3} \sqrt[3]{c}}+\frac{1}{\sqrt{3}}\right) b^2}{243 \sqrt{3} a c^{17/3}}-\frac{308 \log \left(\sqrt[3]{c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}-\sqrt[3]{c}\right) b^2}{729 a c^{17/3}}+\frac{154 \log \left(c^{2/3}+\sqrt[3]{c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}} \sqrt[3]{c}+\left(c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}\right)^{2/3}\right) b^2}{729 a c^{17/3}}+\frac{\left(a x+\sqrt{a^2 x^2-b}\right)^{3/4} \sqrt[3]{c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}} \left(774840978 a x c^{13}+773778096 a^2 x^2 c^9-386889048 b c^9+1109188080 a^3 x^3 c^5-3287950380 a b x c^5+1089560472 b^2 c\right)+\sqrt{a^2 x^2-b} \left(\left(a x+\sqrt{a^2 x^2-b}\right)^{3/4} \sqrt[3]{c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}} \left(774840978 c^{13}+773778096 a x c^9+1109188080 a^2 x^2 c^5-2733356340 b c^5\right)+\left(-1205308188 a x c^{12}-1400169888 a^2 x^2 c^8+350042472 b c^8-1815934120 b^2\right) \sqrt[3]{c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}+\left(-1162261467 c^{14}-870500358 a x c^{10}-1188415800 a^2 x^2 c^6+3981192930 b c^6\right) \sqrt{a x+\sqrt{a^2 x^2-b}} \sqrt[3]{c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}+\left(3486784401 c^{15}+1004423490 a x c^{11}+1283489064 a^2 x^2 c^7-11373139206 b c^7\right) \sqrt[4]{a x+\sqrt{a^2 x^2-b}} \sqrt[3]{c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}\right)+\left(-1205308188 a^2 x^2 c^{12}+602654094 b c^{12}-1400169888 a^3 x^3 c^8+1050127416 a b x c^8-573080508 b^2 c^4-1815934120 a b^2 x\right) \sqrt[3]{c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}+\left(-1162261467 a x c^{14}-870500358 a^2 x^2 c^{10}+435250179 b c^{10}-1188415800 a^3 x^3 c^6+4575400830 a b x c^6-817170354 b^2 c^2\right) \sqrt{a x+\sqrt{a^2 x^2-b}} \sqrt[3]{c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}+\left(3486784401 a x c^{15}+1004423490 a^2 x^2 c^{11}-502211745 b c^{11}+1283489064 a^3 x^3 c^7-12014883738 a b x c^7+668593926 b^2 c^3\right) \sqrt[4]{a x+\sqrt{a^2 x^2-b}} \sqrt[3]{c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}}{2865402540 a c^5 \left(a x+\sqrt{a^2 x^2-b}\right)^{5/4}}",1,"Integrate[(Sqrt[-b + a^2*x^2]*(a*x + Sqrt[-b + a^2*x^2])^(3/4))/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(2/3), x]","F",-1
3140,1,1140,1178,9.9082858,"\int \frac{c_6+x c_7}{\sqrt{c_4+\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5}} \, dx","Integrate[(C[6] + x*C[7])/Sqrt[C[4] + Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5]],x]","-\frac{1}{16} (c_1 c_2-c_0 c_3) \left(\frac{8 (c_2+x c_3){}^2 \left(c_3 \left(c_4-3 \sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5\right) c_4{}^2+c_1 c_5{}^2 \left(3 c_4-\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5\right)\right) c_7 \left(c_4+\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5\right){}^{5/2}}{(c_1 c_2-c_0 c_3) \left(c_1 c_5{}^2-c_3 c_4{}^2\right){}^3}-\frac{2 (c_2+x c_3) \left(c_0 c_3{}^3 \sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5 c_7 c_4{}^4-c_1 c_3{}^2 \left(8 c_3 \left(c_4-\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5\right) c_6 c_4{}^2+\left(c_2 \left(9 \sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5-8 c_4\right) c_4{}^2+2 c_0 c_5{}^2 \left(13 c_4+4 \sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5\right)\right) c_7\right) c_4{}^2+c_1{}^3 c_5{}^4 \left(c_2 \left(\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5-2 c_4\right) c_7-8 c_3 \left(c_4-\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5\right) c_6\right)+c_1{}^2 c_3 c_5{}^2 \left(16 c_3 \left(c_4-\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5\right) c_6 c_4{}^2+\left(2 c_2 \left(5 c_4+12 \sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5\right) c_4{}^2+c_0 c_5{}^2 \left(10 c_4-9 \sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5\right)\right) c_7\right)\right) \sqrt{c_4+\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5}}{c_1 c_3 (c_1 c_2-c_0 c_3) \left(c_1 c_5{}^2-c_3 c_4{}^2\right){}^3}+\frac{\tan ^{-1}\left(\frac{\sqrt{c_3 c_4{}^2-c_1 c_5{}^2}}{\sqrt{\sqrt{c_1} \sqrt{c_3} c_5-c_3 c_4} \sqrt{c_4+\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5}}\right) c_5 \left(\sqrt{c_3} c_4-\sqrt{c_1} c_5\right) \left(c_5 (8 c_3 c_6-3 c_2 c_7) c_1{}^{3/2}+2 \sqrt{c_3} c_4 (4 c_3 c_6-3 c_2 c_7) c_1-5 c_0 c_3 c_5 c_7 \sqrt{c_1}-2 c_0 c_3{}^{3/2} c_4 c_7\right)}{c_1{}^{3/2} c_3{}^{3/2} \left(\sqrt{c_3} c_4+\sqrt{c_1} c_5\right){}^2 \sqrt{\sqrt{c_1} \sqrt{c_3} c_5-c_3 c_4} \sqrt{c_3 c_4{}^2-c_1 c_5{}^2}}+\frac{\tan ^{-1}\left(\frac{\sqrt{c_3 c_4{}^2-c_1 c_5{}^2}}{\sqrt{-c_3 c_4-\sqrt{c_1} \sqrt{c_3} c_5} \sqrt{c_4+\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5}}\right) c_5 \left(\sqrt{c_3} c_4+\sqrt{c_1} c_5\right) \left(c_5 (8 c_3 c_6-3 c_2 c_7) c_1{}^{3/2}+2 \sqrt{c_3} c_4 (3 c_2 c_7-4 c_3 c_6) c_1-5 c_0 c_3 c_5 c_7 \sqrt{c_1}+2 c_0 c_3{}^{3/2} c_4 c_7\right)}{c_1{}^{3/2} c_3{}^{3/2} \left(\sqrt{c_3} c_4-\sqrt{c_1} c_5\right){}^2 \sqrt{-c_3 c_4-\sqrt{c_1} \sqrt{c_3} c_5} \sqrt{c_3 c_4{}^2-c_1 c_5{}^2}}\right)","-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{c_3} \sqrt{c_4+\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5}}{\sqrt{\sqrt{c_3} c_4+\sqrt{c_1} c_5}}\right) \left(-8 c_2 c_3 c_5{}^2 c_6 c_1{}^{5/2}+3 c_2{}^2 c_5{}^2 c_7 c_1{}^{5/2}-8 c_2 c_3{}^{3/2} c_4 c_5 c_6 c_1{}^2+6 c_2{}^2 \sqrt{c_3} c_4 c_5 c_7 c_1{}^2+8 c_0 c_3{}^2 c_5{}^2 c_6 c_1{}^{3/2}+2 c_0 c_2 c_3 c_5{}^2 c_7 c_1{}^{3/2}+8 c_0 c_3{}^{5/2} c_4 c_5 c_6 c_1-4 c_0 c_2 c_3{}^{3/2} c_4 c_5 c_7 c_1-5 c_0{}^2 c_3{}^2 c_5{}^2 c_7 \sqrt{c_1}-2 c_0{}^2 c_3{}^{5/2} c_4 c_5 c_7\right)}{16 c_1{}^{3/2} c_3{}^{7/4} \left(\sqrt{c_3} c_4+\sqrt{c_1} c_5\right){}^{5/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{c_3} \sqrt{c_4+\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5}}{\sqrt{\sqrt{c_3} c_4-\sqrt{c_1} c_5}}\right) \sqrt{\sqrt{c_3} c_4-\sqrt{c_1} c_5} \left(8 c_2 c_3 c_5{}^2 c_6 c_1{}^{5/2}-3 c_2{}^2 c_5{}^2 c_7 c_1{}^{5/2}-8 c_2 c_3{}^{3/2} c_4 c_5 c_6 c_1{}^2+6 c_2{}^2 \sqrt{c_3} c_4 c_5 c_7 c_1{}^2-8 c_0 c_3{}^2 c_5{}^2 c_6 c_1{}^{3/2}-2 c_0 c_2 c_3 c_5{}^2 c_7 c_1{}^{3/2}+8 c_0 c_3{}^{5/2} c_4 c_5 c_6 c_1-4 c_0 c_2 c_3{}^{3/2} c_4 c_5 c_7 c_1+5 c_0{}^2 c_3{}^2 c_5{}^2 c_7 \sqrt{c_1}-2 c_0{}^2 c_3{}^{5/2} c_4 c_5 c_7\right)}{16 c_1{}^{3/2} c_3{}^{7/4} \left(\sqrt{c_1} c_5-\sqrt{c_3} c_4\right){}^3}+\frac{\sqrt{c_4+\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5} \left(4 x c_3{}^3 c_6 c_4{}^3+4 c_2 c_3{}^2 c_6 c_4{}^3+2 x^2 c_3{}^3 c_7 c_4{}^3-2 c_2{}^2 c_3 c_7 c_4{}^3-4 x c_1 c_3{}^2 c_5{}^2 c_6 c_4-4 c_1 c_2 c_3 c_5{}^2 c_6 c_4-c_1 c_2{}^2 c_5{}^2 c_7 c_4+3 x c_0 c_3{}^2 c_5{}^2 c_7 c_4-2 x^2 c_1 c_3{}^2 c_5{}^2 c_7 c_4+3 c_0 c_2 c_3 c_5{}^2 c_7 c_4-3 x c_1 c_2 c_3 c_5{}^2 c_7 c_4\right)}{4 c_3 \left(c_3 c_4{}^2-c_1 c_5{}^2\right){}^2}+\frac{\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} \sqrt{c_4+\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5} \left(-8 x c_1 c_4{}^2 c_5 c_6 c_3{}^3-x c_0 c_4{}^2 c_5 c_7 c_3{}^3-4 x^2 c_1 c_4{}^2 c_5 c_7 c_3{}^3+8 x c_1{}^2 c_5{}^3 c_6 c_3{}^2-8 c_1 c_2 c_4{}^2 c_5 c_6 c_3{}^2+4 x^2 c_1{}^2 c_5{}^3 c_7 c_3{}^2-5 x c_0 c_1 c_5{}^3 c_7 c_3{}^2-c_0 c_2 c_4{}^2 c_5 c_7 c_3{}^2+x c_1 c_2 c_4{}^2 c_5 c_7 c_3{}^2+8 c_1{}^2 c_2 c_5{}^3 c_6 c_3+5 x c_1{}^2 c_2 c_5{}^3 c_7 c_3-5 c_0 c_1 c_2 c_5{}^3 c_7 c_3+5 c_1 c_2{}^2 c_4{}^2 c_5 c_7 c_3+c_1{}^2 c_2{}^2 c_5{}^3 c_7\right)}{8 c_1 c_3 \left(c_3 c_4{}^2-c_1 c_5{}^2\right){}^2}",1,"-1/16*((C[1]*C[2] - C[0]*C[3])*((8*(C[2] + x*C[3])^2*(C[4] + Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5])^(5/2)*(C[3]*C[4]^2*(C[4] - 3*Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5]) + C[1]*C[5]^2*(3*C[4] - Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5]))*C[7])/((C[1]*C[2] - C[0]*C[3])*(-(C[3]*C[4]^2) + C[1]*C[5]^2)^3) + (ArcTan[Sqrt[C[3]*C[4]^2 - C[1]*C[5]^2]/(Sqrt[-(C[3]*C[4]) + Sqrt[C[1]]*Sqrt[C[3]]*C[5]]*Sqrt[C[4] + Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5]])]*C[5]*(Sqrt[C[3]]*C[4] - Sqrt[C[1]]*C[5])*(-2*C[0]*C[3]^(3/2)*C[4]*C[7] - 5*C[0]*Sqrt[C[1]]*C[3]*C[5]*C[7] + 2*C[1]*Sqrt[C[3]]*C[4]*(4*C[3]*C[6] - 3*C[2]*C[7]) + C[1]^(3/2)*C[5]*(8*C[3]*C[6] - 3*C[2]*C[7])))/(C[1]^(3/2)*C[3]^(3/2)*(Sqrt[C[3]]*C[4] + Sqrt[C[1]]*C[5])^2*Sqrt[-(C[3]*C[4]) + Sqrt[C[1]]*Sqrt[C[3]]*C[5]]*Sqrt[C[3]*C[4]^2 - C[1]*C[5]^2]) + (ArcTan[Sqrt[C[3]*C[4]^2 - C[1]*C[5]^2]/(Sqrt[-(C[3]*C[4]) - Sqrt[C[1]]*Sqrt[C[3]]*C[5]]*Sqrt[C[4] + Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5]])]*C[5]*(Sqrt[C[3]]*C[4] + Sqrt[C[1]]*C[5])*(2*C[0]*C[3]^(3/2)*C[4]*C[7] - 5*C[0]*Sqrt[C[1]]*C[3]*C[5]*C[7] + C[1]^(3/2)*C[5]*(8*C[3]*C[6] - 3*C[2]*C[7]) + 2*C[1]*Sqrt[C[3]]*C[4]*(-4*C[3]*C[6] + 3*C[2]*C[7])))/(C[1]^(3/2)*C[3]^(3/2)*(Sqrt[C[3]]*C[4] - Sqrt[C[1]]*C[5])^2*Sqrt[-(C[3]*C[4]) - Sqrt[C[1]]*Sqrt[C[3]]*C[5]]*Sqrt[C[3]*C[4]^2 - C[1]*C[5]^2]) - (2*(C[2] + x*C[3])*Sqrt[C[4] + Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5]]*(C[0]*C[3]^3*Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[4]^4*C[5]*C[7] + C[1]^3*C[5]^4*(-8*C[3]*(C[4] - Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5])*C[6] + C[2]*(-2*C[4] + Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5])*C[7]) - C[1]*C[3]^2*C[4]^2*(8*C[3]*C[4]^2*(C[4] - Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5])*C[6] + (2*C[0]*C[5]^2*(13*C[4] + 4*Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5]) + C[2]*C[4]^2*(-8*C[4] + 9*Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5]))*C[7]) + C[1]^2*C[3]*C[5]^2*(16*C[3]*C[4]^2*(C[4] - Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5])*C[6] + (C[0]*C[5]^2*(10*C[4] - 9*Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5]) + 2*C[2]*C[4]^2*(5*C[4] + 12*Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5]))*C[7])))/(C[1]*C[3]*(C[1]*C[2] - C[0]*C[3])*(-(C[3]*C[4]^2) + C[1]*C[5]^2)^3)))","A",1
3141,0,0,1186,0.7397059,"\int \frac{\sqrt{-b+a^2 x^2}}{\left(c+\sqrt[4]{a x+\sqrt{-b+a^2 x^2}}\right)^{2/3}} \, dx","Integrate[Sqrt[-b + a^2*x^2]/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(2/3),x]","\int \frac{\sqrt{-b+a^2 x^2}}{\left(c+\sqrt[4]{a x+\sqrt{-b+a^2 x^2}}\right)^{2/3}} \, dx","-\frac{21505 \tan ^{-1}\left(\frac{2 \sqrt[3]{c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}}{\sqrt{3} \sqrt[3]{c}}+\frac{1}{\sqrt{3}}\right) b^2}{19683 \sqrt{3} a c^{26/3}}+\frac{21505 \log \left(\sqrt[3]{c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}-\sqrt[3]{c}\right) b^2}{59049 a c^{26/3}}-\frac{21505 \log \left(c^{2/3}+\sqrt[3]{c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}} \sqrt[3]{c}+\left(c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}\right)^{2/3}\right) b^2}{118098 a c^{26/3}}+\frac{2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}}{\sqrt{3} \sqrt[3]{c}}+\frac{1}{\sqrt{3}}\right) b}{a c^{2/3}}-\frac{2 \log \left(\sqrt[3]{c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}-\sqrt[3]{c}\right) b}{a c^{2/3}}+\frac{\log \left(c^{2/3}+\sqrt[3]{c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}} \sqrt[3]{c}+\left(c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}\right)^{2/3}\right) b}{a c^{2/3}}+\frac{\left(a x+\sqrt{a^2 x^2-b}\right)^{3/4} \sqrt[3]{c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}} \left(2812385772 a^2 x^2 c^{12}-1406192886 b c^{12}+3267063072 a^3 x^3 c^8-2450297304 a b x c^8+1032601284 b^2 c^4+3272028760 a b^2 x\right)+\sqrt{a^2 x^2-b} \left(\left(a x+\sqrt{a^2 x^2-b}\right)^{3/4} \sqrt[3]{c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}} \left(2812385772 a x c^{12}+3267063072 a^2 x^2 c^8-816765768 b c^8+3272028760 b^2\right)+\left(-16271660538 a x c^{15}-4687309620 a^2 x^2 c^{11}+1171827405 b c^{11}-1204701498 b^2 c^3\right) \sqrt[3]{c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}+\left(-3615924564 a x c^{13}-3610964448 a^2 x^2 c^9+902741112 b c^9-1963217256 b^2 c\right) \sqrt{a x+\sqrt{a^2 x^2-b}} \sqrt[3]{c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}+\left(5423886846 a x c^{14}+4062335004 a^2 x^2 c^{10}-1015583751 b c^{10}+1472412942 b^2 c^2\right) \sqrt[4]{a x+\sqrt{a^2 x^2-b}} \sqrt[3]{c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}\right)+\left(-16271660538 a^2 x^2 c^{15}+8135830269 b c^{15}-4687309620 a^3 x^3 c^{11}+3515482215 a b x c^{11}-748701954 b^2 c^7-1204701498 a b^2 x c^3\right) \sqrt[3]{c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}+\left(-3615924564 a^2 x^2 c^{13}+1807962282 b c^{13}-3610964448 a^3 x^3 c^9+2708223336 a b x c^9-911118780 b^2 c^5-1963217256 a b^2 x c\right) \sqrt{a x+\sqrt{a^2 x^2-b}} \sqrt[3]{c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}+\left(5423886846 a^2 x^2 c^{14}-2711943423 b c^{14}+4062335004 a^3 x^3 c^{10}-3046751253 a b x c^{10}+820006902 b^2 c^6+1472412942 a b^2 x c^2\right) \sqrt[4]{a x+\sqrt{a^2 x^2-b}} \sqrt[3]{c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}}{5989615632 a \left(2 a^2 x^2-b\right) c^8+11979231264 a^2 x \sqrt{a^2 x^2-b} c^8}",1,"Integrate[Sqrt[-b + a^2*x^2]/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(2/3), x]","F",-1
3142,0,0,1202,22.2605784,"\int \left(b+a^2 x^2\right)^{3/2} \sqrt{a x+\sqrt{b+a^2 x^2}} \sqrt{c+\sqrt{a x+\sqrt{b+a^2 x^2}}} \, dx","Integrate[(b + a^2*x^2)^(3/2)*Sqrt[a*x + Sqrt[b + a^2*x^2]]*Sqrt[c + Sqrt[a*x + Sqrt[b + a^2*x^2]]],x]","\int \left(b+a^2 x^2\right)^{3/2} \sqrt{a x+\sqrt{b+a^2 x^2}} \sqrt{c+\sqrt{a x+\sqrt{b+a^2 x^2}}} \, dx","-\frac{33 \tanh ^{-1}\left(\frac{\sqrt{c+\sqrt{a x+\sqrt{a^2 x^2+b}}}}{\sqrt{c}}\right) b^4}{8192 a c^{13/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+\sqrt{a x+\sqrt{a^2 x^2+b}}}}{\sqrt{c}}\right) b^3}{16 a c^{5/2}}+\frac{\sqrt{a x+\sqrt{a^2 x^2+b}} \sqrt{c+\sqrt{a x+\sqrt{a^2 x^2+b}}} \left(1879048192 a^3 x^3 c^{15}+1409286144 a b x c^{15}+1409286144 a^4 x^4 c^{13}+176160768 b^2 c^{13}+1409286144 a^2 b x^2 c^{13}+2055208960 a^5 x^5 c^{11}+20180893696 a^3 b x^3 c^{11}+13851164672 a b^2 x c^{11}+3391094784 a^6 x^6 c^9+18295554048 a^4 b x^4 c^9+1757085696 b^3 c^9+15116402688 a^2 b^2 x^2 c^9+5904138240 a^7 x^7 c^7+29595238400 a^5 b x^5 c^7+267624448000 a^3 b^2 x^3 c^7+185450137600 a b^3 x c^7-5143607040 b^4 c^5-9932482560 a^2 b^3 x^2 c^5-219490128 a b^4 x c^3-320089770 b^5 c-640179540 a^2 b^4 x^2 c\right)+\sqrt{a^2 x^2+b} \left(\sqrt{a x+\sqrt{a^2 x^2+b}} \sqrt{c+\sqrt{a x+\sqrt{a^2 x^2+b}}} \left(1879048192 a^2 x^2 c^{15}+469762048 b c^{15}+1409286144 a^3 x^3 c^{13}+704643072 a b x c^{13}+2055208960 a^4 x^4 c^{11}+4531421184 b^2 c^{11}+19153289216 a^2 b x^2 c^{11}+3391094784 a^5 x^5 c^9+16600006656 a^3 b x^3 c^9+7240286208 a b^2 x c^9+5904138240 a^6 x^6 c^7+26643169280 a^4 b x^4 c^7+60891084800 b^3 c^7+255040880640 a^2 b^2 x^2 c^7-9932482560 a b^3 x c^5-219490128 b^4 c^3-640179540 a b^4 x c\right)+\left(-1879048192 a^3 x^3 c^{14}-939524096 a b x c^{14}-2348810240 a^4 x^4 c^{12}-146800640 b^2 c^{12}-1761607680 a^2 b x^2 c^{12}-3699376128 a^5 x^5 c^{10}-21311258624 a^3 b x^3 c^{10}-9499574272 a b^2 x c^{10}-6297747456 a^6 x^6 c^8-29887037440 a^4 b x^4 c^8-1474330624 b^3 c^8-18872795136 a^2 b^2 x^2 c^8+200740700160 a^7 x^7 c^6+647844986880 a^5 b x^5 c^6+948956037120 a^3 b^2 x^3 c^6+276208558080 a b^3 x c^6+7644464256 b^4 c^4+29797447680 a^2 b^3 x^2 c^4+512143632 a b^4 x c^2+480134655 b^5+1920538620 a^2 b^4 x^2\right) \sqrt{c+\sqrt{a x+\sqrt{a^2 x^2+b}}}\right)+\left(-1879048192 a^4 x^4 c^{14}-234881024 b^2 c^{14}-1879048192 a^2 b x^2 c^{14}-2348810240 a^5 x^5 c^{12}-2936012800 a^3 b x^3 c^{12}-734003200 a b^2 x c^{12}-3699376128 a^6 x^6 c^{10}-23160946688 a^4 b x^4 c^{10}-2317090816 b^3 c^{10}-19692781568 a^2 b^2 x^2 c^{10}-6297747456 a^7 x^7 c^8-33035911168 a^5 b x^5 c^8-33029095424 a^3 b^2 x^3 c^8-7568457728 a b^3 x c^8+200740700160 a^8 x^8 c^6+748215336960 a^6 b x^6 c^6+50005263360 b^4 c^6+1247785943040 a^4 b^2 x^4 c^6+682252247040 a^2 b^3 x^2 c^6+29797447680 a^3 b^3 x^3 c^4+22543188096 a b^4 x c^4+256071816 b^5 c^2+512143632 a^2 b^4 x^2 c^2+1920538620 a^3 b^4 x^3+1440403965 a b^5 x\right) \sqrt{c+\sqrt{a x+\sqrt{a^2 x^2+b}}}}{119189790720 a c^6 \left(a x+\sqrt{a^2 x^2+b}\right)^{7/2}}",1,"Integrate[(b + a^2*x^2)^(3/2)*Sqrt[a*x + Sqrt[b + a^2*x^2]]*Sqrt[c + Sqrt[a*x + Sqrt[b + a^2*x^2]]], x]","F",-1
3143,-1,0,1225,180.0023027,"\int \frac{\sqrt{-b+a^2 x^2} \sqrt[3]{c+\sqrt[4]{a x+\sqrt{-b+a^2 x^2}}}}{\sqrt[4]{a x+\sqrt{-b+a^2 x^2}}} \, dx","Integrate[(Sqrt[-b + a^2*x^2]*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(1/3))/(a*x + Sqrt[-b + a^2*x^2])^(1/4),x]","\text{\$Aborted}","-\frac{21505 \tan ^{-1}\left(\frac{2 \sqrt[3]{c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}}{\sqrt{3} \sqrt[3]{c}}+\frac{1}{\sqrt{3}}\right) b^2}{531441 \sqrt{3} a c^{26/3}}+\frac{21505 \log \left(\sqrt[3]{c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}-\sqrt[3]{c}\right) b^2}{1594323 a c^{26/3}}-\frac{21505 \log \left(c^{2/3}+\sqrt[3]{c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}} \sqrt[3]{c}+\left(c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}\right)^{2/3}\right) b^2}{3188646 a c^{26/3}}+\frac{2 \tan ^{-1}\left(\frac{2 \sqrt[3]{c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}}{\sqrt{3} \sqrt[3]{c}}+\frac{1}{\sqrt{3}}\right) b}{\sqrt{3} a c^{2/3}}-\frac{2 \log \left(\sqrt[3]{c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}-\sqrt[3]{c}\right) b}{3 a c^{2/3}}+\frac{\log \left(c^{2/3}+\sqrt[3]{c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}} \sqrt[3]{c}+\left(c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}\right)^{2/3}\right) b}{3 a c^{2/3}}+\frac{\left(a x+\sqrt{a^2 x^2-b}\right)^{3/4} \sqrt[3]{c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}} \left(4649045868 a^2 x^2 c^{13}-2324522934 b c^{13}+4642668576 a^3 x^3 c^9-3482001432 a b x c^9-911118780 b^2 c^5-1963217256 a b^2 x c\right)+\sqrt{a^2 x^2-b} \left(\left(a x+\sqrt{a^2 x^2-b}\right)^{3/4} \sqrt[3]{c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}} \left(4649045868 a x c^{13}+4642668576 a^2 x^2 c^9-1160667144 b c^9-1963217256 b^2 c\right)+\left(-7231849128 a^2 x^2 c^{12}+1807962282 b c^{12}+176421405888 a^3 x^3 c^8+558667785312 a b x c^8+1032601284 b^2 c^4+6544057520 a b^2 x\right) \sqrt[3]{c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}+\left(-6973568802 a x c^{14}-5223002148 a^2 x^2 c^{10}+1305750537 b c^{10}+1472412942 b^2 c^2\right) \sqrt{a x+\sqrt{a^2 x^2-b}} \sqrt[3]{c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}+\left(20920706406 a x c^{15}+6026540940 a^2 x^2 c^{11}-1506635235 b c^{11}-1204701498 b^2 c^3\right) \sqrt[4]{a x+\sqrt{a^2 x^2-b}} \sqrt[3]{c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}\right)+\left(-7231849128 a^3 x^3 c^{12}+5423886846 a b x c^{12}+176421405888 a^4 x^4 c^8-319355415288 b^2 c^8+470457082368 a^2 b x^2 c^8+1032601284 a b^2 x c^4-3272028760 b^3+6544057520 a^2 b^2 x^2\right) \sqrt[3]{c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}+\left(-6973568802 a^2 x^2 c^{14}+3486784401 b c^{14}-5223002148 a^3 x^3 c^{10}+3917251611 a b x c^{10}+820006902 b^2 c^6+1472412942 a b^2 x c^2\right) \sqrt{a x+\sqrt{a^2 x^2-b}} \sqrt[3]{c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}+\left(20920706406 a^2 x^2 c^{15}-10460353203 b c^{15}+6026540940 a^3 x^3 c^{11}-4519905705 a b x c^{11}-748701954 b^2 c^7-1204701498 a b^2 x c^3\right) \sqrt[4]{a x+\sqrt{a^2 x^2-b}} \sqrt[3]{c+\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}}{161719622064 a c^8 \left(a x+\sqrt{a^2 x^2-b}\right)^{9/4}}",1,"$Aborted","F",-1
3144,1,882,1293,8.5742855,"\int \frac{a b c-b^2 x+a^2 x^2}{\sqrt{c+b x+a x^2} \left(c+b x^2\right)^2} \, dx","Integrate[(a*b*c - b^2*x + a^2*x^2)/(Sqrt[c + b*x + a*x^2]*(c + b*x^2)^2),x]","\frac{\frac{4 \sqrt{c} \sqrt{c+x (b+a x)} \left(c x a^3-b c (b x+x+1) a^2+b^2 c (x b+b-1) a+b^3 (c-b x)\right)}{b x^2+c}+\frac{\left(\sqrt{c} b^{9/2}-i (3 a c+c) b^4-a c^{3/2} b^{7/2}-i a c (2 c+1) b^3-a (a+2) c^{3/2} b^{5/2}+i a^2 c (6 c-1) b^2+3 a^2 c^{3/2} b^{3/2}-2 i a^2 (2 a+1) c^2 b+a^3 c^{3/2} \sqrt{b}+2 i a^3 c^2\right) \log \left(-\frac{4 \left(-i b^{3/2}+\sqrt{c} b-a \sqrt{c}\right) c \left(x b^{3/2}-i \sqrt{c} b+2 c \sqrt{b}-2 i a \sqrt{c} x+2 \sqrt{-i \sqrt{c} b^{3/2}+c b-a c} \sqrt{c+x (b+a x)}\right)}{\sqrt{-i \sqrt{c} b^{3/2}+c b-a c} \left(b^3-3 i a \sqrt{c} b^{5/2}+2 a c b^2-2 i a \sqrt{c} b^{3/2}-4 a^2 c b-i a^2 \sqrt{c} \sqrt{b}+2 a^2 c\right) \left(\sqrt{c}-i \sqrt{b} x\right)}\right)}{\sqrt{-i \sqrt{c} b^{3/2}+c b-a c}}+\frac{\left(\sqrt{c} b^{9/2}+i (3 a c+c) b^4-a c^{3/2} b^{7/2}+i a c (2 c+1) b^3-a (a+2) c^{3/2} b^{5/2}-i a^2 c (6 c-1) b^2+3 a^2 c^{3/2} b^{3/2}+2 i a^2 (2 a+1) c^2 b+a^3 c^{3/2} \sqrt{b}-2 i a^3 c^2\right) \log \left(-\frac{4 \left(i b^{3/2}+\sqrt{c} b-a \sqrt{c}\right) c \left(x b^{3/2}+i \sqrt{c} b+2 c \sqrt{b}+2 i a \sqrt{c} x+2 \sqrt{i \sqrt{c} b^{3/2}+c b-a c} \sqrt{c+x (b+a x)}\right)}{\sqrt{i \sqrt{c} b^{3/2}+c b-a c} \left(b^3+3 i a \sqrt{c} b^{5/2}+2 a c b^2+2 i a \sqrt{c} b^{3/2}-4 a^2 c b+i a^2 \sqrt{c} \sqrt{b}+2 a^2 c\right) \left(i \sqrt{b} x+\sqrt{c}\right)}\right)}{\sqrt{i \sqrt{c} b^{3/2}+c b-a c}}}{8 c^{3/2} \left(b^3+c b^2-2 a c b+a^2 c\right)}","\frac{\left(-x b^4+a c b^3+c b^3+a c x b^3-a c b^2-a^2 c x b^2-a^2 c b-a^2 c x b+a^3 c x\right) \sqrt{a x^2+b x+c}}{2 c \left(b^3+c b^2-2 a c b+a^2 c\right) \left(b x^2+c\right)}-\frac{\text{RootSum}\left[b \text{$\#$1}^4+4 a c \text{$\#$1}^2-2 b c \text{$\#$1}^2-4 \sqrt{a} b c \text{$\#$1}+b c^2+b^2 c\&,\frac{\log \left(-\sqrt{a} x-\text{$\#$1}+\sqrt{a x^2+b x+c}\right) \text{$\#$1}^2 b^5-3 a c \log \left(-\sqrt{a} x-\text{$\#$1}+\sqrt{a x^2+b x+c}\right) b^5-2 c \log \left(-\sqrt{a} x-\text{$\#$1}+\sqrt{a x^2+b x+c}\right) b^5-a c \log \left(-\sqrt{a} x-\text{$\#$1}+\sqrt{a x^2+b x+c}\right) \text{$\#$1}^2 b^4-a c^2 \log \left(-\sqrt{a} x-\text{$\#$1}+\sqrt{a x^2+b x+c}\right) b^4-a c \log \left(-\sqrt{a} x-\text{$\#$1}+\sqrt{a x^2+b x+c}\right) b^4+6 a^{3/2} c \log \left(-\sqrt{a} x-\text{$\#$1}+\sqrt{a x^2+b x+c}\right) \text{$\#$1} b^4+2 \sqrt{a} c \log \left(-\sqrt{a} x-\text{$\#$1}+\sqrt{a x^2+b x+c}\right) \text{$\#$1} b^4-a^2 c \log \left(-\sqrt{a} x-\text{$\#$1}+\sqrt{a x^2+b x+c}\right) \text{$\#$1}^2 b^3-2 a c \log \left(-\sqrt{a} x-\text{$\#$1}+\sqrt{a x^2+b x+c}\right) \text{$\#$1}^2 b^3+7 a^2 c^2 \log \left(-\sqrt{a} x-\text{$\#$1}+\sqrt{a x^2+b x+c}\right) b^3+2 a c^2 \log \left(-\sqrt{a} x-\text{$\#$1}+\sqrt{a x^2+b x+c}\right) b^3-a^2 c \log \left(-\sqrt{a} x-\text{$\#$1}+\sqrt{a x^2+b x+c}\right) b^3+4 a^{3/2} c^2 \log \left(-\sqrt{a} x-\text{$\#$1}+\sqrt{a x^2+b x+c}\right) \text{$\#$1} b^3+2 a^{3/2} c \log \left(-\sqrt{a} x-\text{$\#$1}+\sqrt{a x^2+b x+c}\right) \text{$\#$1} b^3+3 a^2 c \log \left(-\sqrt{a} x-\text{$\#$1}+\sqrt{a x^2+b x+c}\right) \text{$\#$1}^2 b^2-4 a^3 c^2 \log \left(-\sqrt{a} x-\text{$\#$1}+\sqrt{a x^2+b x+c}\right) b^2-5 a^2 c^2 \log \left(-\sqrt{a} x-\text{$\#$1}+\sqrt{a x^2+b x+c}\right) b^2-12 a^{5/2} c^2 \log \left(-\sqrt{a} x-\text{$\#$1}+\sqrt{a x^2+b x+c}\right) \text{$\#$1} b^2+2 a^{5/2} c \log \left(-\sqrt{a} x-\text{$\#$1}+\sqrt{a x^2+b x+c}\right) \text{$\#$1} b^2+a^3 c \log \left(-\sqrt{a} x-\text{$\#$1}+\sqrt{a x^2+b x+c}\right) \text{$\#$1}^2 b+a^3 c^2 \log \left(-\sqrt{a} x-\text{$\#$1}+\sqrt{a x^2+b x+c}\right) b+8 a^{7/2} c^2 \log \left(-\sqrt{a} x-\text{$\#$1}+\sqrt{a x^2+b x+c}\right) \text{$\#$1} b+4 a^{5/2} c^2 \log \left(-\sqrt{a} x-\text{$\#$1}+\sqrt{a x^2+b x+c}\right) \text{$\#$1} b-4 a^{7/2} c^2 \log \left(-\sqrt{a} x-\text{$\#$1}+\sqrt{a x^2+b x+c}\right) \text{$\#$1}}{\text{$\#$1}^3 b^4-\sqrt{a} c b^4-c \text{$\#$1} b^4+c \text{$\#$1}^3 b^3-\sqrt{a} c^2 b^3-c^2 \text{$\#$1} b^3+2 a c \text{$\#$1} b^3-2 a c \text{$\#$1}^3 b^2+2 a^{3/2} c^2 b^2+4 a c^2 \text{$\#$1} b^2+a^2 c \text{$\#$1}^3 b-a^{5/2} c^2 b-5 a^2 c^2 \text{$\#$1} b+2 a^3 c^2 \text{$\#$1}}\&\right]}{8 c}",1,"((4*Sqrt[c]*Sqrt[c + x*(b + a*x)]*(a^3*c*x + b^3*(c - b*x) + a*b^2*c*(-1 + b + b*x) - a^2*b*c*(1 + x + b*x)))/(c + b*x^2) + ((b^(9/2)*Sqrt[c] + a^3*Sqrt[b]*c^(3/2) + 3*a^2*b^(3/2)*c^(3/2) - a*(2 + a)*b^(5/2)*c^(3/2) - a*b^(7/2)*c^(3/2) + (2*I)*a^3*c^2 - (2*I)*a^2*(1 + 2*a)*b*c^2 - I*a*b^3*c*(1 + 2*c) + I*a^2*b^2*c*(-1 + 6*c) - I*b^4*(c + 3*a*c))*Log[(-4*((-I)*b^(3/2) - a*Sqrt[c] + b*Sqrt[c])*c*((-I)*b*Sqrt[c] + 2*Sqrt[b]*c + b^(3/2)*x - (2*I)*a*Sqrt[c]*x + 2*Sqrt[(-I)*b^(3/2)*Sqrt[c] - a*c + b*c]*Sqrt[c + x*(b + a*x)]))/(Sqrt[(-I)*b^(3/2)*Sqrt[c] - a*c + b*c]*(b^3 - I*a^2*Sqrt[b]*Sqrt[c] - (2*I)*a*b^(3/2)*Sqrt[c] - (3*I)*a*b^(5/2)*Sqrt[c] + 2*a^2*c - 4*a^2*b*c + 2*a*b^2*c)*(Sqrt[c] - I*Sqrt[b]*x))])/Sqrt[(-I)*b^(3/2)*Sqrt[c] - a*c + b*c] + ((b^(9/2)*Sqrt[c] + a^3*Sqrt[b]*c^(3/2) + 3*a^2*b^(3/2)*c^(3/2) - a*(2 + a)*b^(5/2)*c^(3/2) - a*b^(7/2)*c^(3/2) - (2*I)*a^3*c^2 + (2*I)*a^2*(1 + 2*a)*b*c^2 + I*a*b^3*c*(1 + 2*c) - I*a^2*b^2*c*(-1 + 6*c) + I*b^4*(c + 3*a*c))*Log[(-4*(I*b^(3/2) - a*Sqrt[c] + b*Sqrt[c])*c*(I*b*Sqrt[c] + 2*Sqrt[b]*c + b^(3/2)*x + (2*I)*a*Sqrt[c]*x + 2*Sqrt[I*b^(3/2)*Sqrt[c] - a*c + b*c]*Sqrt[c + x*(b + a*x)]))/(Sqrt[I*b^(3/2)*Sqrt[c] - a*c + b*c]*(b^3 + I*a^2*Sqrt[b]*Sqrt[c] + (2*I)*a*b^(3/2)*Sqrt[c] + (3*I)*a*b^(5/2)*Sqrt[c] + 2*a^2*c - 4*a^2*b*c + 2*a*b^2*c)*(Sqrt[c] + I*Sqrt[b]*x))])/Sqrt[I*b^(3/2)*Sqrt[c] - a*c + b*c])/(8*c^(3/2)*(b^3 + a^2*c - 2*a*b*c + b^2*c))","C",1
3145,0,0,1310,0.6243209,"\int \frac{\left(b^2+a x^2\right)^2 \sqrt{b+\sqrt{b^2+a x^2}}}{\left(-b^2+a x^2\right)^2} \, dx","Integrate[((b^2 + a*x^2)^2*Sqrt[b + Sqrt[b^2 + a*x^2]])/(-b^2 + a*x^2)^2,x]","\int \frac{\left(b^2+a x^2\right)^2 \sqrt{b+\sqrt{b^2+a x^2}}}{\left(-b^2+a x^2\right)^2} \, dx","\frac{5 \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{2 \left(-1+\sqrt{2}\right)} \sqrt{b} \sqrt{b+\sqrt{b^2+a x^2}}}-\frac{\sqrt{b+\sqrt{b^2+a x^2}}}{\sqrt{2 \left(-1+\sqrt{2}\right)} \sqrt{b}}\right) b^{3/2}}{\sqrt{2 \left(-1+\sqrt{2}\right)} \sqrt{a}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{2 \left(-1+\sqrt{2}\right)} \sqrt{b} \sqrt{b+\sqrt{b^2+a x^2}}}-\frac{\sqrt{b+\sqrt{b^2+a x^2}}}{\sqrt{2 \left(-1+\sqrt{2}\right)} \sqrt{b}}\right) b^{3/2}}{\sqrt{-1+\sqrt{2}} \sqrt{a}}+\frac{\tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{b} \sqrt{b+\sqrt{b^2+a x^2}}}-\frac{\sqrt{b+\sqrt{b^2+a x^2}}}{\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{b}}\right) b^{3/2}}{\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{a}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{b} \sqrt{b+\sqrt{b^2+a x^2}}}-\frac{\sqrt{b+\sqrt{b^2+a x^2}}}{\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{b}}\right) b^{3/2}}{\sqrt{1+\sqrt{2}} \sqrt{a}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{2 \left(-1+\sqrt{2}\right)} \sqrt{b} \sqrt{b+\sqrt{b^2+a x^2}}}-\frac{\sqrt{b+\sqrt{b^2+a x^2}}}{\sqrt{2 \left(-1+\sqrt{2}\right)} \sqrt{b}}\right) b^{3/2}}{\sqrt{2 \left(-1+\sqrt{2}\right)} \sqrt{a}}+\frac{3 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{2 \left(-1+\sqrt{2}\right)} \sqrt{b} \sqrt{b+\sqrt{b^2+a x^2}}}-\frac{\sqrt{b+\sqrt{b^2+a x^2}}}{\sqrt{2 \left(-1+\sqrt{2}\right)} \sqrt{b}}\right) b^{3/2}}{\sqrt{-1+\sqrt{2}} \sqrt{a}}-\frac{5 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{b} \sqrt{b+\sqrt{b^2+a x^2}}}-\frac{\sqrt{b+\sqrt{b^2+a x^2}}}{\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{b}}\right) b^{3/2}}{\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{a}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{b} \sqrt{b+\sqrt{b^2+a x^2}}}-\frac{\sqrt{b+\sqrt{b^2+a x^2}}}{\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{b}}\right) b^{3/2}}{\sqrt{1+\sqrt{2}} \sqrt{a}}+\frac{-2 i x \left(-9 b^7-46 a x^2 b^5-20 a^2 x^4 b^3+24 a^3 x^6 b\right) a^{3/2}+2 i \left(a b^8-13 a^2 x^2 b^6-75 a^3 x^4 b^4-52 a^4 x^6 b^2+16 a^5 x^8\right)+\sqrt{b^2+a x^2} \left(2 i \left(-a b^7-27 a^2 x^2 b^5-32 a^3 x^4 b^3+24 a^4 x^6 b\right)-2 i a^{3/2} x \left(16 a^3 x^6-60 a^2 b^2 x^4-43 a b^4 x^2\right)\right)}{\frac{3 i x \left(a x^2-b^2\right) \left(5 b^4+20 a x^2 b^2+16 a^2 x^4\right) a^2}{\sqrt{b+\sqrt{b^2+a x^2}}}+3 i \left(a x^2-b^2\right) \left(-5 b^4-20 a x^2 b^2-16 a^2 x^4\right) \sqrt{b+\sqrt{b^2+a x^2}} a^{3/2}+\sqrt{b^2+a x^2} \left(\frac{3 i x \left(a x^2-b^2\right) \left(4 b^3+8 a x^2 b\right) a^2}{\sqrt{b+\sqrt{b^2+a x^2}}}+3 i \left(a x^2-b^2\right) \left(4 b^3+8 a x^2 b\right) \sqrt{b+\sqrt{b^2+a x^2}} a^{3/2}\right)}",1,"Integrate[((b^2 + a*x^2)^2*Sqrt[b + Sqrt[b^2 + a*x^2]])/(-b^2 + a*x^2)^2, x]","F",-1
3146,0,0,1356,0.1928175,"\int \frac{\sqrt{a x^2+\sqrt{b+a^2 x^4}}}{(d+c x)^2 \sqrt{b+a^2 x^4}} \, dx","Integrate[Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/((d + c*x)^2*Sqrt[b + a^2*x^4]),x]","\int \frac{\sqrt{a x^2+\sqrt{b+a^2 x^4}}}{(d+c x)^2 \sqrt{b+a^2 x^4}} \, dx","\frac{a^3 \tan ^{-1}\left(\frac{c \sqrt{a x^2+\sqrt{a^2 x^4+b}}}{\sqrt{-a d^2-\sqrt{b c^4+a^2 d^4}}}\right) d^5}{\left(b c^4+a^2 d^4\right)^{3/2} \sqrt{-a d^2-\sqrt{b c^4+a^2 d^4}}}-\frac{a^3 \tan ^{-1}\left(\frac{c \sqrt{a x^2+\sqrt{a^2 x^4+b}}}{\sqrt{\sqrt{b c^4+a^2 d^4}-a d^2}}\right) d^5}{\left(b c^4+a^2 d^4\right)^{3/2} \sqrt{\sqrt{b c^4+a^2 d^4}-a d^2}}+\frac{a^2 \tan ^{-1}\left(\frac{c \sqrt{a x^2+\sqrt{a^2 x^4+b}}}{\sqrt{-a d^2-\sqrt{b c^4+a^2 d^4}}}\right) d^3}{\left(b c^4+a^2 d^4\right) \sqrt{-a d^2-\sqrt{b c^4+a^2 d^4}}}+\frac{a^2 \tan ^{-1}\left(\frac{c \sqrt{a x^2+\sqrt{a^2 x^4+b}}}{\sqrt{\sqrt{b c^4+a^2 d^4}-a d^2}}\right) d^3}{\left(b c^4+a^2 d^4\right) \sqrt{\sqrt{b c^4+a^2 d^4}-a d^2}}+\frac{a c \sqrt{a x^2+\sqrt{a^2 x^4+b}} d^3}{\left(b c^4+a^2 d^4\right) \left(c^2 x^2-d^2\right)}+\frac{a^{3/2} \text{RootSum}\left[c^2 \text{$\#$1}^4-4 i a d^2 \text{$\#$1}^3+2 b c^2 \text{$\#$1}^2+4 i a b d^2 \text{$\#$1}+b^2 c^2\&,\frac{2 i b \log \left(i a x^2+i \sqrt{2} \sqrt{a} \sqrt{a x^2+\sqrt{a^2 x^4+b}} x-\text{$\#$1}+i \sqrt{a^2 x^4+b}\right) \text{$\#$1} c^2-a d^2 \log \left(i a x^2+i \sqrt{2} \sqrt{a} \sqrt{a x^2+\sqrt{a^2 x^4+b}} x-\text{$\#$1}+i \sqrt{a^2 x^4+b}\right) \text{$\#$1}^2+a b d^2 \log \left(i a x^2+i \sqrt{2} \sqrt{a} \sqrt{a x^2+\sqrt{a^2 x^4+b}} x-\text{$\#$1}+i \sqrt{a^2 x^4+b}\right)}{-i b \text{$\#$1}^3 c^6-i b^2 \text{$\#$1} c^6+a b^2 d^2 c^4-3 a b d^2 \text{$\#$1}^2 c^4-i a^2 d^4 \text{$\#$1}^3 c^2-i a^2 b d^4 \text{$\#$1} c^2+a^3 b d^6-3 a^3 d^6 \text{$\#$1}^2}\&\right] d^2}{\sqrt{2}}-\frac{a b c^4 \tan ^{-1}\left(\frac{c \sqrt{a x^2+\sqrt{a^2 x^4+b}}}{\sqrt{-a d^2-\sqrt{b c^4+a^2 d^4}}}\right) d}{\left(b c^4+a^2 d^4\right)^{3/2} \sqrt{-a d^2-\sqrt{b c^4+a^2 d^4}}}+\frac{a b c^4 \tan ^{-1}\left(\frac{c \sqrt{a x^2+\sqrt{a^2 x^4+b}}}{\sqrt{\sqrt{b c^4+a^2 d^4}-a d^2}}\right) d}{\left(b c^4+a^2 d^4\right)^{3/2} \sqrt{\sqrt{b c^4+a^2 d^4}-a d^2}}+\frac{b c^3 d}{\left(b c^4+a^2 d^4\right) \left(c^2 x^2-d^2\right) \sqrt{a x^2+\sqrt{a^2 x^4+b}}}+\frac{i \sqrt{a} x \left(\frac{i a^{3/2} c^2 x^2 d^2}{b c^4+a^2 d^4}+\frac{i \sqrt{a} c^2 \sqrt{a^2 x^4+b} d^2}{b c^4+a^2 d^4}\right)}{\left(c^2 x^2-d^2\right) \sqrt{a x^2+\sqrt{a^2 x^4+b}}}-\frac{b c^4 x}{\left(b c^4+a^2 d^4\right) \left(c^2 x^2-d^2\right) \sqrt{a x^2+\sqrt{a^2 x^4+b}}}",1,"Integrate[Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/((d + c*x)^2*Sqrt[b + a^2*x^4]), x]","F",-1
3147,1,66,1387,0.078499,"\int \frac{-b-a c+(1+c) x}{(-a+x) \sqrt[3]{(-a+x) (-b+x)^2} (b-a d+(-1+d) x)} \, dx","Integrate[(-b - a*c + (1 + c)*x)/((-a + x)*((-a + x)*(-b + x)^2)^(1/3)*(b - a*d + (-1 + d)*x)),x]","-\frac{3 (x-b) \left((c+d) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{b-x}{a d-d x}\right)-d\right)}{d (a-b) \sqrt[3]{(x-a) (b-x)^2}}","\frac{\left(1+i \sqrt{3}\right) \sqrt[3]{a-x} (x-b)^{2/3} \left(\sqrt[3]{d} \sqrt[3]{a-x}+\sqrt[3]{x-b}\right) \left(d^{2/3} (a-x)^{2/3}-\sqrt[3]{d} \sqrt[3]{x-b} \sqrt[3]{a-x}+(x-b)^{2/3}\right) \left(\frac{3 \left(a \sqrt[3]{x-b}-i \sqrt{3} a \sqrt[3]{x-b}\right)}{2 (a-b)^2 \sqrt[3]{a-x}}+\frac{3 i \left(\sqrt{3} \sqrt[3]{x-b} b+i \sqrt[3]{x-b} b\right)}{2 (a-b)^2 \sqrt[3]{a-x}}+\frac{3 \left(a c \sqrt[3]{x-b}-i \sqrt{3} a c \sqrt[3]{x-b}\right)}{2 (a-b)^2 \sqrt[3]{a-x}}+\frac{3 i \left(\sqrt{3} a \sqrt[3]{x-b} c+i a \sqrt[3]{x-b} c\right)}{2 (a-b)^2 \sqrt[3]{a-x}}+\frac{\left(-\sqrt{3} b+3 i b+\sqrt{3} a d-3 i a d\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x-b}}{\sqrt[3]{x-b}-2 \sqrt[3]{d} \sqrt[3]{a-x}}\right)}{2 (a-b)^2 d^{2/3}}+\frac{\left(-\sqrt{3} d b+3 i d b+\sqrt{3} b-3 i b\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x-b}}{\sqrt[3]{x-b}-2 \sqrt[3]{d} \sqrt[3]{a-x}}\right)}{2 (a-b)^2 d^{2/3}}+\frac{\left(\sqrt{3} a c-3 i a c-\sqrt{3} a d c+3 i a d c\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x-b}}{\sqrt[3]{x-b}-2 \sqrt[3]{d} \sqrt[3]{a-x}}\right)}{2 (a-b)^2 d^{2/3}}+\frac{\left(-\sqrt{3} b c+3 i b c+\sqrt{3} a d c-3 i a d c\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x-b}}{\sqrt[3]{x-b}-2 \sqrt[3]{d} \sqrt[3]{a-x}}\right)}{2 (a-b)^2 d^{2/3}}+\frac{\left(-i \sqrt{3} b+b+i \sqrt{3} a d-a d\right) \log \left(\sqrt[3]{d} \sqrt[3]{a-x}+\sqrt[3]{x-b}\right)}{2 (a-b)^2 d^{2/3}}+\frac{\left(-i \sqrt{3} d b+d b+i \sqrt{3} b-b\right) \log \left(\sqrt[3]{d} \sqrt[3]{a-x}+\sqrt[3]{x-b}\right)}{2 (a-b)^2 d^{2/3}}+\frac{\left(i \sqrt{3} a c-a c-i \sqrt{3} a d c+a d c\right) \log \left(\sqrt[3]{d} \sqrt[3]{a-x}+\sqrt[3]{x-b}\right)}{2 (a-b)^2 d^{2/3}}+\frac{\left(-i \sqrt{3} b c+b c+i \sqrt{3} a d c-a d c\right) \log \left(\sqrt[3]{d} \sqrt[3]{a-x}+\sqrt[3]{x-b}\right)}{2 (a-b)^2 d^{2/3}}+\frac{\left(i \sqrt{3} b-b-i \sqrt{3} a d+a d\right) \log \left(d^{2/3} (a-x)^{2/3}-\sqrt[3]{d} \sqrt[3]{x-b} \sqrt[3]{a-x}+(x-b)^{2/3}\right)}{4 (a-b)^2 d^{2/3}}+\frac{\left(i \sqrt{3} d b-d b-i \sqrt{3} b+b\right) \log \left(d^{2/3} (a-x)^{2/3}-\sqrt[3]{d} \sqrt[3]{x-b} \sqrt[3]{a-x}+(x-b)^{2/3}\right)}{4 (a-b)^2 d^{2/3}}+\frac{\left(i \sqrt{3} b c-b c-i \sqrt{3} a d c+a d c\right) \log \left(d^{2/3} (a-x)^{2/3}-\sqrt[3]{d} \sqrt[3]{x-b} \sqrt[3]{a-x}+(x-b)^{2/3}\right)}{4 (a-b)^2 d^{2/3}}+\frac{\left(-i \sqrt{3} a c+a c+i \sqrt{3} a d c-a d c\right) \log \left(d^{2/3} (a-x)^{2/3}-\sqrt[3]{d} \sqrt[3]{x-b} \sqrt[3]{a-x}+(x-b)^{2/3}\right)}{4 (a-b)^2 d^{2/3}}\right)}{2 \sqrt[3]{-\left((a-x) (b-x)^2\right)} (-b+a d-d x+x)}",1,"(-3*(-b + x)*(-d + (c + d)*Hypergeometric2F1[1/3, 1, 4/3, (b - x)/(a*d - d*x)]))/((a - b)*d*((b - x)^2*(-a + x))^(1/3))","C",1
3148,1,109,1655,0.3608575,"\int \frac{-a-b c+(1+c) x}{\sqrt[3]{(-a+x) (-b+x)^2} \left(-a^2+b^2 d+2 (a-b d) x+(-1+d) x^2\right)} \, dx","Integrate[(-a - b*c + (1 + c)*x)/(((-a + x)*(-b + x)^2)^(1/3)*(-a^2 + b^2*d + 2*(a - b*d)*x + (-1 + d)*x^2)),x]","\frac{3 (x-b) \left(\left(\sqrt{d}-c\right) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\sqrt{d} (b-x)}{x-a}\right)+\left(c+\sqrt{d}\right) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{\sqrt{d} (x-b)}{x-a}\right)\right)}{2 \sqrt{d} (a-b) \sqrt[3]{(x-a) (b-x)^2}}","\frac{(b-x)^{2/3} \sqrt[3]{x-a} \left(-\frac{\sqrt{3} b c \left(\sqrt{d}-1\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x-a}}{\sqrt[3]{x-a}-2 \sqrt[6]{d} \sqrt[3]{b-x}}\right)}{2 (a-b)^2 d^{2/3}}-\frac{\sqrt{3} a \left(\sqrt{d}-1\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x-a}}{\sqrt[3]{x-a}-2 \sqrt[6]{d} \sqrt[3]{b-x}}\right)}{2 (a-b)^2 d^{2/3}}-\frac{\sqrt{3} c \left(a-b \sqrt{d}\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x-a}}{\sqrt[3]{x-a}-2 \sqrt[6]{d} \sqrt[3]{b-x}}\right)}{2 (a-b)^2 d^{2/3}}-\frac{\sqrt{3} \left(a-b \sqrt{d}\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x-a}}{\sqrt[3]{x-a}-2 \sqrt[6]{d} \sqrt[3]{b-x}}\right)}{2 (a-b)^2 d^{2/3}}+\frac{\sqrt{3} b c \left(\sqrt{d}+1\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x-a}}{2 \sqrt[6]{d} \sqrt[3]{b-x}+\sqrt[3]{x-a}}\right)}{2 (a-b)^2 d^{2/3}}+\frac{\sqrt{3} a \left(\sqrt{d}+1\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x-a}}{2 \sqrt[6]{d} \sqrt[3]{b-x}+\sqrt[3]{x-a}}\right)}{2 (a-b)^2 d^{2/3}}-\frac{\sqrt{3} c \left(a+b \sqrt{d}\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x-a}}{2 \sqrt[6]{d} \sqrt[3]{b-x}+\sqrt[3]{x-a}}\right)}{2 (a-b)^2 d^{2/3}}-\frac{\sqrt{3} \left(a+b \sqrt{d}\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x-a}}{2 \sqrt[6]{d} \sqrt[3]{b-x}+\sqrt[3]{x-a}}\right)}{2 (a-b)^2 d^{2/3}}+\frac{b c \left(\sqrt{d}+1\right) \log \left(\sqrt[3]{x-a}-\sqrt[6]{d} \sqrt[3]{b-x}\right)}{2 (a-b)^2 d^{2/3}}+\frac{a \left(\sqrt{d}+1\right) \log \left(\sqrt[3]{x-a}-\sqrt[6]{d} \sqrt[3]{b-x}\right)}{2 (a-b)^2 d^{2/3}}+\frac{\left(-a-b \sqrt{d}\right) \log \left(\sqrt[3]{x-a}-\sqrt[6]{d} \sqrt[3]{b-x}\right)}{2 (a-b)^2 d^{2/3}}-\frac{c \left(a+b \sqrt{d}\right) \log \left(\sqrt[3]{x-a}-\sqrt[6]{d} \sqrt[3]{b-x}\right)}{2 (a-b)^2 d^{2/3}}-\frac{b c \left(\sqrt{d}-1\right) \log \left(\sqrt[6]{d} \sqrt[3]{b-x}+\sqrt[3]{x-a}\right)}{2 (a-b)^2 d^{2/3}}-\frac{a \left(\sqrt{d}-1\right) \log \left(\sqrt[6]{d} \sqrt[3]{b-x}+\sqrt[3]{x-a}\right)}{2 (a-b)^2 d^{2/3}}-\frac{c \left(a-b \sqrt{d}\right) \log \left(\sqrt[6]{d} \sqrt[3]{b-x}+\sqrt[3]{x-a}\right)}{2 (a-b)^2 d^{2/3}}+\frac{\left(b \sqrt{d}-a\right) \log \left(\sqrt[6]{d} \sqrt[3]{b-x}+\sqrt[3]{x-a}\right)}{2 (a-b)^2 d^{2/3}}+\frac{b c \left(\sqrt{d}-1\right) \log \left(\sqrt[3]{d} (b-x)^{2/3}-\sqrt[6]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+(x-a)^{2/3}\right)}{4 (a-b)^2 d^{2/3}}+\frac{a \left(\sqrt{d}-1\right) \log \left(\sqrt[3]{d} (b-x)^{2/3}-\sqrt[6]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+(x-a)^{2/3}\right)}{4 (a-b)^2 d^{2/3}}+\frac{c \left(a-b \sqrt{d}\right) \log \left(\sqrt[3]{d} (b-x)^{2/3}-\sqrt[6]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+(x-a)^{2/3}\right)}{4 (a-b)^2 d^{2/3}}+\frac{\left(a-b \sqrt{d}\right) \log \left(\sqrt[3]{d} (b-x)^{2/3}-\sqrt[6]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+(x-a)^{2/3}\right)}{4 (a-b)^2 d^{2/3}}-\frac{b c \left(\sqrt{d}+1\right) \log \left(\sqrt[3]{d} (b-x)^{2/3}+\sqrt[6]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+(x-a)^{2/3}\right)}{4 (a-b)^2 d^{2/3}}-\frac{a \left(\sqrt{d}+1\right) \log \left(\sqrt[3]{d} (b-x)^{2/3}+\sqrt[6]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+(x-a)^{2/3}\right)}{4 (a-b)^2 d^{2/3}}+\frac{c \left(a+b \sqrt{d}\right) \log \left(\sqrt[3]{d} (b-x)^{2/3}+\sqrt[6]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+(x-a)^{2/3}\right)}{4 (a-b)^2 d^{2/3}}+\frac{\left(a+b \sqrt{d}\right) \log \left(\sqrt[3]{d} (b-x)^{2/3}+\sqrt[6]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+(x-a)^{2/3}\right)}{4 (a-b)^2 d^{2/3}}\right)}{\sqrt[3]{(b-x)^2 (x-a)}}",1,"(3*(-b + x)*((-c + Sqrt[d])*Hypergeometric2F1[1/3, 1, 4/3, (Sqrt[d]*(b - x))/(-a + x)] + (c + Sqrt[d])*Hypergeometric2F1[1/3, 1, 4/3, (Sqrt[d]*(-b + x))/(-a + x)]))/(2*(a - b)*Sqrt[d]*((b - x)^2*(-a + x))^(1/3))","C",1
3149,1,107,1707,0.3592278,"\int \frac{-b-a c+(1+c) x}{\sqrt[3]{(-a+x) (-b+x)^2} \left(-b^2+a^2 d+2 (b-a d) x+(-1+d) x^2\right)} \, dx","Integrate[(-b - a*c + (1 + c)*x)/(((-a + x)*(-b + x)^2)^(1/3)*(-b^2 + a^2*d + 2*(b - a*d)*x + (-1 + d)*x^2)),x]","-\frac{3 (x-b) \left(\left(c-\sqrt{d}\right) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{b-x}{\sqrt{d} (x-a)}\right)+\left(c+\sqrt{d}\right) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{x-b}{\sqrt{d} (x-a)}\right)\right)}{2 d (a-b) \sqrt[3]{(x-a) (b-x)^2}}","\frac{(b-x)^{2/3} \sqrt[3]{x-a} \left(-\frac{\sqrt{3} b \left(\sqrt{d}-1\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{d} \sqrt[3]{x-a}}{\sqrt[6]{d} \sqrt[3]{x-a}-2 \sqrt[3]{b-x}}\right)}{2 (a-b)^2 d^{5/6}}-\frac{\sqrt{3} a c \left(\sqrt{d}-1\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{d} \sqrt[3]{x-a}}{\sqrt[6]{d} \sqrt[3]{x-a}-2 \sqrt[3]{b-x}}\right)}{2 (a-b)^2 d^{5/6}}+\frac{\sqrt{3} c \left(a \sqrt{d}-b\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{d} \sqrt[3]{x-a}}{\sqrt[6]{d} \sqrt[3]{x-a}-2 \sqrt[3]{b-x}}\right)}{2 (a-b)^2 d^{5/6}}+\frac{\sqrt{3} \left(a \sqrt{d}-b\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{d} \sqrt[3]{x-a}}{\sqrt[6]{d} \sqrt[3]{x-a}-2 \sqrt[3]{b-x}}\right)}{2 (a-b)^2 d^{5/6}}-\frac{\sqrt{3} b \left(\sqrt{d}+1\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{d} \sqrt[3]{x-a}}{2 \sqrt[3]{b-x}+\sqrt[6]{d} \sqrt[3]{x-a}}\right)}{2 (a-b)^2 d^{5/6}}-\frac{\sqrt{3} a c \left(\sqrt{d}+1\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{d} \sqrt[3]{x-a}}{2 \sqrt[3]{b-x}+\sqrt[6]{d} \sqrt[3]{x-a}}\right)}{2 (a-b)^2 d^{5/6}}+\frac{\sqrt{3} c \left(\sqrt{d} a+b\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{d} \sqrt[3]{x-a}}{2 \sqrt[3]{b-x}+\sqrt[6]{d} \sqrt[3]{x-a}}\right)}{2 (a-b)^2 d^{5/6}}+\frac{\sqrt{3} \left(\sqrt{d} a+b\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{d} \sqrt[3]{x-a}}{2 \sqrt[3]{b-x}+\sqrt[6]{d} \sqrt[3]{x-a}}\right)}{2 (a-b)^2 d^{5/6}}-\frac{b \left(\sqrt{d}+1\right) \log \left(\sqrt[3]{b-x}-\sqrt[6]{d} \sqrt[3]{x-a}\right)}{2 (a-b)^2 d^{5/6}}-\frac{a c \left(\sqrt{d}+1\right) \log \left(\sqrt[3]{b-x}-\sqrt[6]{d} \sqrt[3]{x-a}\right)}{2 (a-b)^2 d^{5/6}}+\frac{c \left(\sqrt{d} a+b\right) \log \left(\sqrt[3]{b-x}-\sqrt[6]{d} \sqrt[3]{x-a}\right)}{2 (a-b)^2 d^{5/6}}+\frac{\left(\sqrt{d} a+b\right) \log \left(\sqrt[3]{b-x}-\sqrt[6]{d} \sqrt[3]{x-a}\right)}{2 (a-b)^2 d^{5/6}}-\frac{b \left(\sqrt{d}-1\right) \log \left(\sqrt[3]{b-x}+\sqrt[6]{d} \sqrt[3]{x-a}\right)}{2 (a-b)^2 d^{5/6}}-\frac{a c \left(\sqrt{d}-1\right) \log \left(\sqrt[3]{b-x}+\sqrt[6]{d} \sqrt[3]{x-a}\right)}{2 (a-b)^2 d^{5/6}}+\frac{c \left(a \sqrt{d}-b\right) \log \left(\sqrt[3]{b-x}+\sqrt[6]{d} \sqrt[3]{x-a}\right)}{2 (a-b)^2 d^{5/6}}+\frac{\left(a \sqrt{d}-b\right) \log \left(\sqrt[3]{b-x}+\sqrt[6]{d} \sqrt[3]{x-a}\right)}{2 (a-b)^2 d^{5/6}}+\frac{b \left(\sqrt{d}-1\right) \log \left((b-x)^{2/3}-\sqrt[6]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+\sqrt[3]{d} (x-a)^{2/3}\right)}{4 (a-b)^2 d^{5/6}}+\frac{a c \left(\sqrt{d}-1\right) \log \left((b-x)^{2/3}-\sqrt[6]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+\sqrt[3]{d} (x-a)^{2/3}\right)}{4 (a-b)^2 d^{5/6}}+\frac{\left(b-a \sqrt{d}\right) \log \left((b-x)^{2/3}-\sqrt[6]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+\sqrt[3]{d} (x-a)^{2/3}\right)}{4 (a-b)^2 d^{5/6}}-\frac{c \left(a \sqrt{d}-b\right) \log \left((b-x)^{2/3}-\sqrt[6]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+\sqrt[3]{d} (x-a)^{2/3}\right)}{4 (a-b)^2 d^{5/6}}+\frac{b \left(\sqrt{d}+1\right) \log \left((b-x)^{2/3}+\sqrt[6]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+\sqrt[3]{d} (x-a)^{2/3}\right)}{4 (a-b)^2 d^{5/6}}+\frac{a c \left(\sqrt{d}+1\right) \log \left((b-x)^{2/3}+\sqrt[6]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+\sqrt[3]{d} (x-a)^{2/3}\right)}{4 (a-b)^2 d^{5/6}}+\frac{\left(-\sqrt{d} a-b\right) \log \left((b-x)^{2/3}+\sqrt[6]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+\sqrt[3]{d} (x-a)^{2/3}\right)}{4 (a-b)^2 d^{5/6}}-\frac{c \left(\sqrt{d} a+b\right) \log \left((b-x)^{2/3}+\sqrt[6]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+\sqrt[3]{d} (x-a)^{2/3}\right)}{4 (a-b)^2 d^{5/6}}\right)}{\sqrt[3]{(b-x)^2 (x-a)}}",1,"(-3*(-b + x)*((c - Sqrt[d])*Hypergeometric2F1[1/3, 1, 4/3, (b - x)/(Sqrt[d]*(-a + x))] + (c + Sqrt[d])*Hypergeometric2F1[1/3, 1, 4/3, (-b + x)/(Sqrt[d]*(-a + x))]))/(2*(a - b)*d*((b - x)^2*(-a + x))^(1/3))","C",1
3150,1,2281,1716,16.1288745,"\int \frac{c_8+x c_9}{\sqrt{c_4+\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5} (c_6+x c_7)} \, dx","Integrate[(C[8] + x*C[9])/(Sqrt[C[4] + Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5]]*(C[6] + x*C[7])),x]","\text{Result too large to show}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{c_4+\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5} \sqrt{c_3 c_6-c_2 c_7}}{\sqrt{-\sqrt{c_1 c_6-c_0 c_7} \sqrt{c_3 c_6-c_2 c_7} c_5-c_3 c_4 c_6+c_2 c_4 c_7}}\right) \sqrt{c_3 c_6-c_2 c_7} c_8}{c_7 \sqrt{-\sqrt{c_1 c_6-c_0 c_7} \sqrt{c_3 c_6-c_2 c_7} c_5-c_3 c_4 c_6+c_2 c_4 c_7}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt{c_4+\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5} \sqrt{c_3 c_6-c_2 c_7}}{\sqrt{\sqrt{c_1 c_6-c_0 c_7} \sqrt{c_3 c_6-c_2 c_7} c_5-c_3 c_4 c_6+c_2 c_4 c_7}}\right) \sqrt{c_3 c_6-c_2 c_7} c_8}{c_7 \sqrt{\sqrt{c_1 c_6-c_0 c_7} \sqrt{c_3 c_6-c_2 c_7} c_5-c_3 c_4 c_6+c_2 c_4 c_7}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{c_3} \sqrt{c_4+\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5}}{\sqrt{\sqrt{c_3} c_4-\sqrt{c_1} c_5}}\right) \sqrt[4]{c_3} c_8}{\sqrt{\sqrt{c_3} c_4-\sqrt{c_1} c_5} c_7}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{c_3} \sqrt{c_4+\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5}}{\sqrt{\sqrt{c_3} c_4+\sqrt{c_1} c_5}}\right) \sqrt[4]{c_3} c_8}{\sqrt{\sqrt{c_3} c_4+\sqrt{c_1} c_5} c_7}-\frac{2 \tan ^{-1}\left(\frac{\sqrt{c_4+\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5} \sqrt{c_2 c_7-c_3 c_6}}{\sqrt{-i \sqrt{c_1 c_6-c_0 c_7} \sqrt{c_2 c_7-c_3 c_6} c_5+c_3 c_4 c_6-c_2 c_4 c_7}}\right) c_6 \sqrt{c_2 c_7-c_3 c_6} c_9}{c_7{}^2 \sqrt{-i \sqrt{c_1 c_6-c_0 c_7} \sqrt{c_2 c_7-c_3 c_6} c_5+c_3 c_4 c_6-c_2 c_4 c_7}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt{c_4+\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5} \sqrt{c_2 c_7-c_3 c_6}}{\sqrt{i \sqrt{c_1 c_6-c_0 c_7} \sqrt{c_2 c_7-c_3 c_6} c_5+c_3 c_4 c_6-c_2 c_4 c_7}}\right) c_6 \sqrt{c_2 c_7-c_3 c_6} c_9}{c_7{}^2 \sqrt{i \sqrt{c_1 c_6-c_0 c_7} \sqrt{c_2 c_7-c_3 c_6} c_5+c_3 c_4 c_6-c_2 c_4 c_7}}+\frac{\sqrt{c_4+\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5} \left(-c_1 c_2 c_4 c_9+c_0 c_3 c_4 c_9+c_1 c_2 \sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5 c_9-c_0 c_3 \sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5 c_9\right)}{\left(c_1-\frac{(c_0+x c_1) c_3}{c_2+x c_3}\right) \left(c_1 c_5{}^2-c_3 c_4{}^2\right) c_7}+\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt{c_1} \sqrt{c_3} c_5-c_3 c_4} \sqrt{c_4+\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5}}{\sqrt{c_3} c_4-\sqrt{c_1} c_5}\right) \left(4 \sqrt{c_1} c_4 \sqrt{-\sqrt{c_3} \left(\sqrt{c_3} c_4-\sqrt{c_1} c_5\right)} c_6 c_9 c_3{}^{3/2}-4 c_1 c_5 \sqrt{-\sqrt{c_3} \left(\sqrt{c_3} c_4-\sqrt{c_1} c_5\right)} c_6 c_9 c_3-c_0 c_5 \sqrt{-\sqrt{c_3} \left(\sqrt{c_3} c_4-\sqrt{c_1} c_5\right)} c_7 c_9 c_3+c_1 c_2 c_5 \sqrt{-\sqrt{c_3} \left(\sqrt{c_3} c_4-\sqrt{c_1} c_5\right)} c_7 c_9\right)}{2 \sqrt{c_1} c_3 \left(\sqrt{c_3} c_4-\sqrt{c_1} c_5\right){}^2 c_7{}^2}+\frac{\tan ^{-1}\left(\frac{\sqrt{-c_3 c_4-\sqrt{c_1} \sqrt{c_3} c_5} \sqrt{c_4+\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5}}{\sqrt{c_3} c_4+\sqrt{c_1} c_5}\right) \left(4 \sqrt{c_1} c_4 \sqrt{-\sqrt{c_3} \left(\sqrt{c_3} c_4+\sqrt{c_1} c_5\right)} c_6 c_9 c_3{}^{3/2}+4 c_1 c_5 \sqrt{-\sqrt{c_3} \left(\sqrt{c_3} c_4+\sqrt{c_1} c_5\right)} c_6 c_9 c_3+c_0 c_5 \sqrt{-\sqrt{c_3} \left(\sqrt{c_3} c_4+\sqrt{c_1} c_5\right)} c_7 c_9 c_3-c_1 c_2 c_5 \sqrt{-\sqrt{c_3} \left(\sqrt{c_3} c_4+\sqrt{c_1} c_5\right)} c_7 c_9\right)}{2 \sqrt{c_1} c_3 \left(\sqrt{c_3} c_4+\sqrt{c_1} c_5\right){}^2 c_7{}^2}",1,"-4*(C[1]*C[2] - C[0]*C[3])*C[5]^2*((((2*C[4])/(C[4] + Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5])^(3/2) - 1/Sqrt[C[4] + Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5]])*C[9])/(4*(C[3]*C[4]^2 - C[1]*C[5]^2)*(C[3] + (C[3]*C[4]^2)/(C[4] + Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5])^2 - (C[1]*C[5]^2)/(C[4] + Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5])^2 - (2*C[3]*C[4])/(C[4] + Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5]))*C[7]) - (ArcTan[Sqrt[C[3]*C[4]^2 - C[1]*C[5]^2]/(Sqrt[-(C[3]*C[4]) + Sqrt[C[1]]*Sqrt[C[3]]*C[5]]*Sqrt[C[4] + Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5]])]*(4*Sqrt[C[1]]*C[3]^(5/2)*C[4]^3*C[7]*C[8] - 4*C[1]*C[3]^2*C[4]^2*C[5]*C[7]*C[8] - 4*C[1]^(3/2)*C[3]^(3/2)*C[4]*C[5]^2*C[7]*C[8] + 4*C[1]^2*C[3]*C[5]^3*C[7]*C[8] - 4*Sqrt[C[1]]*C[3]^(5/2)*C[4]^3*C[6]*C[9] + 4*C[1]*C[3]^2*C[4]^2*C[5]*C[6]*C[9] + 4*C[1]^(3/2)*C[3]^(3/2)*C[4]*C[5]^2*C[6]*C[9] - 4*C[1]^2*C[3]*C[5]^3*C[6]*C[9] + C[1]*C[2]*C[3]*C[4]^2*C[5]*C[7]*C[9] - C[0]*C[3]^2*C[4]^2*C[5]*C[7]*C[9] - 2*C[1]^(3/2)*C[2]*Sqrt[C[3]]*C[4]*C[5]^2*C[7]*C[9] + 2*C[0]*Sqrt[C[1]]*C[3]^(3/2)*C[4]*C[5]^2*C[7]*C[9] + C[1]^2*C[2]*C[5]^3*C[7]*C[9] - C[0]*C[1]*C[3]*C[5]^3*C[7]*C[9]))/(8*Sqrt[C[1]]*Sqrt[C[3]]*(-(C[1]*C[2]) + C[0]*C[3])*C[5]^2*Sqrt[-(C[3]*C[4]) + Sqrt[C[1]]*Sqrt[C[3]]*C[5]]*(C[3]*C[4]^2 - C[1]*C[5]^2)^(3/2)*C[7]^2) - (ArcTan[Sqrt[C[3]*C[4]^2 - C[1]*C[5]^2]/(Sqrt[-(C[3]*C[4]) - Sqrt[C[1]]*Sqrt[C[3]]*C[5]]*Sqrt[C[4] + Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5]])]*(4*Sqrt[C[1]]*C[3]^(5/2)*C[4]^3*C[7]*C[8] + 4*C[1]*C[3]^2*C[4]^2*C[5]*C[7]*C[8] - 4*C[1]^(3/2)*C[3]^(3/2)*C[4]*C[5]^2*C[7]*C[8] - 4*C[1]^2*C[3]*C[5]^3*C[7]*C[8] - 4*Sqrt[C[1]]*C[3]^(5/2)*C[4]^3*C[6]*C[9] - 4*C[1]*C[3]^2*C[4]^2*C[5]*C[6]*C[9] + 4*C[1]^(3/2)*C[3]^(3/2)*C[4]*C[5]^2*C[6]*C[9] + 4*C[1]^2*C[3]*C[5]^3*C[6]*C[9] - C[1]*C[2]*C[3]*C[4]^2*C[5]*C[7]*C[9] + C[0]*C[3]^2*C[4]^2*C[5]*C[7]*C[9] - 2*C[1]^(3/2)*C[2]*Sqrt[C[3]]*C[4]*C[5]^2*C[7]*C[9] + 2*C[0]*Sqrt[C[1]]*C[3]^(3/2)*C[4]*C[5]^2*C[7]*C[9] - C[1]^2*C[2]*C[5]^3*C[7]*C[9] + C[0]*C[1]*C[3]*C[5]^3*C[7]*C[9]))/(8*Sqrt[C[1]]*Sqrt[C[3]]*(-(C[1]*C[2]) + C[0]*C[3])*C[5]^2*Sqrt[-(C[3]*C[4]) - Sqrt[C[1]]*Sqrt[C[3]]*C[5]]*(C[3]*C[4]^2 - C[1]*C[5]^2)^(3/2)*C[7]^2) - (ArcTan[Sqrt[C[3]*C[4]^2*C[6] - C[1]*C[5]^2*C[6] - C[2]*C[4]^2*C[7] + C[0]*C[5]^2*C[7]]/(Sqrt[C[4] + Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5]]*Sqrt[-(C[3]*C[4]*C[6]) + C[2]*C[4]*C[7] + C[5]*Sqrt[C[1]*C[6] - C[0]*C[7]]*Sqrt[C[3]*C[6] - C[2]*C[7]]])]*(C[1]*C[3]*C[5]*C[6]^2*C[7]*C[8] - C[1]*C[2]*C[5]*C[6]*C[7]^2*C[8] - C[0]*C[3]*C[5]*C[6]*C[7]^2*C[8] + C[0]*C[2]*C[5]*C[7]^3*C[8] - C[3]*C[4]*C[6]*C[7]*Sqrt[C[1]*C[6] - C[0]*C[7]]*Sqrt[C[3]*C[6] - C[2]*C[7]]*C[8] + C[2]*C[4]*C[7]^2*Sqrt[C[1]*C[6] - C[0]*C[7]]*Sqrt[C[3]*C[6] - C[2]*C[7]]*C[8] - C[1]*C[3]*C[5]*C[6]^3*C[9] + C[1]*C[2]*C[5]*C[6]^2*C[7]*C[9] + C[0]*C[3]*C[5]*C[6]^2*C[7]*C[9] - C[0]*C[2]*C[5]*C[6]*C[7]^2*C[9] + C[3]*C[4]*C[6]^2*Sqrt[C[1]*C[6] - C[0]*C[7]]*Sqrt[C[3]*C[6] - C[2]*C[7]]*C[9] - C[2]*C[4]*C[6]*C[7]*Sqrt[C[1]*C[6] - C[0]*C[7]]*Sqrt[C[3]*C[6] - C[2]*C[7]]*C[9]))/(2*(-(C[1]*C[2]) + C[0]*C[3])*C[5]^2*C[7]^2*Sqrt[C[1]*C[6] - C[0]*C[7]]*Sqrt[C[3]*C[6] - C[2]*C[7]]*Sqrt[C[3]*C[4]^2*C[6] - C[1]*C[5]^2*C[6] - C[2]*C[4]^2*C[7] + C[0]*C[5]^2*C[7]]*Sqrt[-(C[3]*C[4]*C[6]) + C[2]*C[4]*C[7] + C[5]*Sqrt[C[1]*C[6] - C[0]*C[7]]*Sqrt[C[3]*C[6] - C[2]*C[7]]]) - (ArcTan[Sqrt[C[3]*C[4]^2*C[6] - C[1]*C[5]^2*C[6] - C[2]*C[4]^2*C[7] + C[0]*C[5]^2*C[7]]/(Sqrt[C[4] + Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5]]*Sqrt[-(C[3]*C[4]*C[6]) + C[2]*C[4]*C[7] - C[5]*Sqrt[C[1]*C[6] - C[0]*C[7]]*Sqrt[C[3]*C[6] - C[2]*C[7]]])]*(-(C[1]*C[3]*C[5]*C[6]^2*C[7]*C[8]) + C[1]*C[2]*C[5]*C[6]*C[7]^2*C[8] + C[0]*C[3]*C[5]*C[6]*C[7]^2*C[8] - C[0]*C[2]*C[5]*C[7]^3*C[8] - C[3]*C[4]*C[6]*C[7]*Sqrt[C[1]*C[6] - C[0]*C[7]]*Sqrt[C[3]*C[6] - C[2]*C[7]]*C[8] + C[2]*C[4]*C[7]^2*Sqrt[C[1]*C[6] - C[0]*C[7]]*Sqrt[C[3]*C[6] - C[2]*C[7]]*C[8] + C[1]*C[3]*C[5]*C[6]^3*C[9] - C[1]*C[2]*C[5]*C[6]^2*C[7]*C[9] - C[0]*C[3]*C[5]*C[6]^2*C[7]*C[9] + C[0]*C[2]*C[5]*C[6]*C[7]^2*C[9] + C[3]*C[4]*C[6]^2*Sqrt[C[1]*C[6] - C[0]*C[7]]*Sqrt[C[3]*C[6] - C[2]*C[7]]*C[9] - C[2]*C[4]*C[6]*C[7]*Sqrt[C[1]*C[6] - C[0]*C[7]]*Sqrt[C[3]*C[6] - C[2]*C[7]]*C[9]))/(2*(-(C[1]*C[2]) + C[0]*C[3])*C[5]^2*C[7]^2*Sqrt[C[1]*C[6] - C[0]*C[7]]*Sqrt[C[3]*C[6] - C[2]*C[7]]*Sqrt[C[3]*C[4]^2*C[6] - C[1]*C[5]^2*C[6] - C[2]*C[4]^2*C[7] + C[0]*C[5]^2*C[7]]*Sqrt[-(C[3]*C[4]*C[6]) + C[2]*C[4]*C[7] - C[5]*Sqrt[C[1]*C[6] - C[0]*C[7]]*Sqrt[C[3]*C[6] - C[2]*C[7]]]))","A",1
3151,1,111,1835,0.3367003,"\int \frac{(-b+x) (-a-b c+(1+c) x)}{\left((-a+x) (-b+x)^2\right)^{2/3} \left(-a^2+b^2 d+2 (a-b d) x+(-1+d) x^2\right)} \, dx","Integrate[((-b + x)*(-a - b*c + (1 + c)*x))/(((-a + x)*(-b + x)^2)^(2/3)*(-a^2 + b^2*d + 2*(a - b*d)*x + (-1 + d)*x^2)),x]","\frac{3 (b-x)^2 \left(\left(\sqrt{d}-c\right) \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{\sqrt{d} (b-x)}{x-a}\right)+\left(c+\sqrt{d}\right) \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{\sqrt{d} (x-b)}{x-a}\right)\right)}{4 \sqrt{d} (a-b) \left((x-a) (b-x)^2\right)^{2/3}}","\frac{(b-x)^{4/3} (x-a)^{2/3} \left(\sqrt[6]{d} \sqrt[3]{b-x}-\sqrt[3]{x-a}\right) \left(\sqrt[6]{d} \sqrt[3]{b-x}+\sqrt[3]{x-a}\right) \left(\sqrt[3]{d} (b-x)^{2/3}-\sqrt[6]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+(x-a)^{2/3}\right) \left(\sqrt[3]{d} (b-x)^{2/3}+\sqrt[6]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+(x-a)^{2/3}\right) \left(\frac{\sqrt{3} b c \left(\sqrt{d}-1\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x-a}}{\sqrt[3]{x-a}-2 \sqrt[6]{d} \sqrt[3]{b-x}}\right)}{2 (a-b)^2 d^{5/6}}+\frac{\sqrt{3} a \left(\sqrt{d}-1\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x-a}}{\sqrt[3]{x-a}-2 \sqrt[6]{d} \sqrt[3]{b-x}}\right)}{2 (a-b)^2 d^{5/6}}+\frac{\sqrt{3} c \left(a-b \sqrt{d}\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x-a}}{\sqrt[3]{x-a}-2 \sqrt[6]{d} \sqrt[3]{b-x}}\right)}{2 (a-b)^2 d^{5/6}}+\frac{\sqrt{3} \left(a-b \sqrt{d}\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x-a}}{\sqrt[3]{x-a}-2 \sqrt[6]{d} \sqrt[3]{b-x}}\right)}{2 (a-b)^2 d^{5/6}}+\frac{\sqrt{3} b c \left(\sqrt{d}+1\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x-a}}{2 \sqrt[6]{d} \sqrt[3]{b-x}+\sqrt[3]{x-a}}\right)}{2 (a-b)^2 d^{5/6}}+\frac{\sqrt{3} a \left(\sqrt{d}+1\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x-a}}{2 \sqrt[6]{d} \sqrt[3]{b-x}+\sqrt[3]{x-a}}\right)}{2 (a-b)^2 d^{5/6}}-\frac{\sqrt{3} c \left(a+b \sqrt{d}\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x-a}}{2 \sqrt[6]{d} \sqrt[3]{b-x}+\sqrt[3]{x-a}}\right)}{2 (a-b)^2 d^{5/6}}-\frac{\sqrt{3} \left(a+b \sqrt{d}\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x-a}}{2 \sqrt[6]{d} \sqrt[3]{b-x}+\sqrt[3]{x-a}}\right)}{2 (a-b)^2 d^{5/6}}-\frac{b c \left(\sqrt{d}+1\right) \log \left(\sqrt[3]{x-a}-\sqrt[6]{d} \sqrt[3]{b-x}\right)}{2 (a-b)^2 d^{5/6}}-\frac{a \left(\sqrt{d}+1\right) \log \left(\sqrt[3]{x-a}-\sqrt[6]{d} \sqrt[3]{b-x}\right)}{2 (a-b)^2 d^{5/6}}+\frac{c \left(a+b \sqrt{d}\right) \log \left(\sqrt[3]{x-a}-\sqrt[6]{d} \sqrt[3]{b-x}\right)}{2 (a-b)^2 d^{5/6}}+\frac{\left(a+b \sqrt{d}\right) \log \left(\sqrt[3]{x-a}-\sqrt[6]{d} \sqrt[3]{b-x}\right)}{2 (a-b)^2 d^{5/6}}-\frac{b c \left(\sqrt{d}-1\right) \log \left(\sqrt[6]{d} \sqrt[3]{b-x}+\sqrt[3]{x-a}\right)}{2 (a-b)^2 d^{5/6}}-\frac{a \left(\sqrt{d}-1\right) \log \left(\sqrt[6]{d} \sqrt[3]{b-x}+\sqrt[3]{x-a}\right)}{2 (a-b)^2 d^{5/6}}-\frac{c \left(a-b \sqrt{d}\right) \log \left(\sqrt[6]{d} \sqrt[3]{b-x}+\sqrt[3]{x-a}\right)}{2 (a-b)^2 d^{5/6}}+\frac{\left(b \sqrt{d}-a\right) \log \left(\sqrt[6]{d} \sqrt[3]{b-x}+\sqrt[3]{x-a}\right)}{2 (a-b)^2 d^{5/6}}+\frac{b c \left(\sqrt{d}-1\right) \log \left(\sqrt[3]{d} (b-x)^{2/3}-\sqrt[6]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+(x-a)^{2/3}\right)}{4 (a-b)^2 d^{5/6}}+\frac{a \left(\sqrt{d}-1\right) \log \left(\sqrt[3]{d} (b-x)^{2/3}-\sqrt[6]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+(x-a)^{2/3}\right)}{4 (a-b)^2 d^{5/6}}+\frac{c \left(a-b \sqrt{d}\right) \log \left(\sqrt[3]{d} (b-x)^{2/3}-\sqrt[6]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+(x-a)^{2/3}\right)}{4 (a-b)^2 d^{5/6}}+\frac{\left(a-b \sqrt{d}\right) \log \left(\sqrt[3]{d} (b-x)^{2/3}-\sqrt[6]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+(x-a)^{2/3}\right)}{4 (a-b)^2 d^{5/6}}+\frac{b c \left(\sqrt{d}+1\right) \log \left(\sqrt[3]{d} (b-x)^{2/3}+\sqrt[6]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+(x-a)^{2/3}\right)}{4 (a-b)^2 d^{5/6}}+\frac{a \left(\sqrt{d}+1\right) \log \left(\sqrt[3]{d} (b-x)^{2/3}+\sqrt[6]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+(x-a)^{2/3}\right)}{4 (a-b)^2 d^{5/6}}+\frac{\left(-a-b \sqrt{d}\right) \log \left(\sqrt[3]{d} (b-x)^{2/3}+\sqrt[6]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+(x-a)^{2/3}\right)}{4 (a-b)^2 d^{5/6}}-\frac{c \left(a+b \sqrt{d}\right) \log \left(\sqrt[3]{d} (b-x)^{2/3}+\sqrt[6]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+(x-a)^{2/3}\right)}{4 (a-b)^2 d^{5/6}}\right)}{\left((b-x)^2 (x-a)\right)^{2/3} \left(-a^2+2 x a+(d-1) x^2+b^2 d-2 b d x\right)}",1,"(3*(b - x)^2*((-c + Sqrt[d])*Hypergeometric2F1[2/3, 1, 5/3, (Sqrt[d]*(b - x))/(-a + x)] + (c + Sqrt[d])*Hypergeometric2F1[2/3, 1, 5/3, (Sqrt[d]*(-b + x))/(-a + x)]))/(4*(a - b)*Sqrt[d]*((b - x)^2*(-a + x))^(2/3))","C",1
3152,1,109,1886,0.8330544,"\int \frac{(-b+x) (-b-a c+(1+c) x)}{\left((-a+x) (-b+x)^2\right)^{2/3} \left(-b^2+a^2 d+2 (b-a d) x+(-1+d) x^2\right)} \, dx","Integrate[((-b + x)*(-b - a*c + (1 + c)*x))/(((-a + x)*(-b + x)^2)^(2/3)*(-b^2 + a^2*d + 2*(b - a*d)*x + (-1 + d)*x^2)),x]","-\frac{3 (b-x)^2 \left(\left(c-\sqrt{d}\right) \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{b-x}{\sqrt{d} (x-a)}\right)+\left(c+\sqrt{d}\right) \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{x-b}{\sqrt{d} (x-a)}\right)\right)}{4 d (a-b) \left((x-a) (b-x)^2\right)^{2/3}}","\frac{(b-x)^{4/3} (x-a)^{2/3} \left(\sqrt[3]{b-x}-\sqrt[6]{d} \sqrt[3]{x-a}\right) \left(\sqrt[3]{b-x}+\sqrt[6]{d} \sqrt[3]{x-a}\right) \left((b-x)^{2/3}-\sqrt[6]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+\sqrt[3]{d} (x-a)^{2/3}\right) \left((b-x)^{2/3}+\sqrt[6]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+\sqrt[3]{d} (x-a)^{2/3}\right) \left(\frac{\sqrt{3} b \left(\sqrt{d}-1\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{d} \sqrt[3]{x-a}}{\sqrt[6]{d} \sqrt[3]{x-a}-2 \sqrt[3]{b-x}}\right)}{2 (a-b)^2 d^{2/3}}+\frac{\sqrt{3} a c \left(\sqrt{d}-1\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{d} \sqrt[3]{x-a}}{\sqrt[6]{d} \sqrt[3]{x-a}-2 \sqrt[3]{b-x}}\right)}{2 (a-b)^2 d^{2/3}}-\frac{\sqrt{3} c \left(a \sqrt{d}-b\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{d} \sqrt[3]{x-a}}{\sqrt[6]{d} \sqrt[3]{x-a}-2 \sqrt[3]{b-x}}\right)}{2 (a-b)^2 d^{2/3}}-\frac{\sqrt{3} \left(a \sqrt{d}-b\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{d} \sqrt[3]{x-a}}{\sqrt[6]{d} \sqrt[3]{x-a}-2 \sqrt[3]{b-x}}\right)}{2 (a-b)^2 d^{2/3}}-\frac{\sqrt{3} b \left(\sqrt{d}+1\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{d} \sqrt[3]{x-a}}{2 \sqrt[3]{b-x}+\sqrt[6]{d} \sqrt[3]{x-a}}\right)}{2 (a-b)^2 d^{2/3}}-\frac{\sqrt{3} a c \left(\sqrt{d}+1\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{d} \sqrt[3]{x-a}}{2 \sqrt[3]{b-x}+\sqrt[6]{d} \sqrt[3]{x-a}}\right)}{2 (a-b)^2 d^{2/3}}+\frac{\sqrt{3} c \left(\sqrt{d} a+b\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{d} \sqrt[3]{x-a}}{2 \sqrt[3]{b-x}+\sqrt[6]{d} \sqrt[3]{x-a}}\right)}{2 (a-b)^2 d^{2/3}}+\frac{\sqrt{3} \left(\sqrt{d} a+b\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{d} \sqrt[3]{x-a}}{2 \sqrt[3]{b-x}+\sqrt[6]{d} \sqrt[3]{x-a}}\right)}{2 (a-b)^2 d^{2/3}}+\frac{b \left(\sqrt{d}+1\right) \log \left(\sqrt[3]{b-x}-\sqrt[6]{d} \sqrt[3]{x-a}\right)}{2 (a-b)^2 d^{2/3}}+\frac{a c \left(\sqrt{d}+1\right) \log \left(\sqrt[3]{b-x}-\sqrt[6]{d} \sqrt[3]{x-a}\right)}{2 (a-b)^2 d^{2/3}}+\frac{\left(-\sqrt{d} a-b\right) \log \left(\sqrt[3]{b-x}-\sqrt[6]{d} \sqrt[3]{x-a}\right)}{2 (a-b)^2 d^{2/3}}-\frac{c \left(\sqrt{d} a+b\right) \log \left(\sqrt[3]{b-x}-\sqrt[6]{d} \sqrt[3]{x-a}\right)}{2 (a-b)^2 d^{2/3}}-\frac{b \left(\sqrt{d}-1\right) \log \left(\sqrt[3]{b-x}+\sqrt[6]{d} \sqrt[3]{x-a}\right)}{2 (a-b)^2 d^{2/3}}-\frac{a c \left(\sqrt{d}-1\right) \log \left(\sqrt[3]{b-x}+\sqrt[6]{d} \sqrt[3]{x-a}\right)}{2 (a-b)^2 d^{2/3}}+\frac{c \left(a \sqrt{d}-b\right) \log \left(\sqrt[3]{b-x}+\sqrt[6]{d} \sqrt[3]{x-a}\right)}{2 (a-b)^2 d^{2/3}}+\frac{\left(a \sqrt{d}-b\right) \log \left(\sqrt[3]{b-x}+\sqrt[6]{d} \sqrt[3]{x-a}\right)}{2 (a-b)^2 d^{2/3}}+\frac{b \left(\sqrt{d}-1\right) \log \left((b-x)^{2/3}-\sqrt[6]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+\sqrt[3]{d} (x-a)^{2/3}\right)}{4 (a-b)^2 d^{2/3}}+\frac{a c \left(\sqrt{d}-1\right) \log \left((b-x)^{2/3}-\sqrt[6]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+\sqrt[3]{d} (x-a)^{2/3}\right)}{4 (a-b)^2 d^{2/3}}+\frac{\left(b-a \sqrt{d}\right) \log \left((b-x)^{2/3}-\sqrt[6]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+\sqrt[3]{d} (x-a)^{2/3}\right)}{4 (a-b)^2 d^{2/3}}-\frac{c \left(a \sqrt{d}-b\right) \log \left((b-x)^{2/3}-\sqrt[6]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+\sqrt[3]{d} (x-a)^{2/3}\right)}{4 (a-b)^2 d^{2/3}}-\frac{b \left(\sqrt{d}+1\right) \log \left((b-x)^{2/3}+\sqrt[6]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+\sqrt[3]{d} (x-a)^{2/3}\right)}{4 (a-b)^2 d^{2/3}}-\frac{a c \left(\sqrt{d}+1\right) \log \left((b-x)^{2/3}+\sqrt[6]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+\sqrt[3]{d} (x-a)^{2/3}\right)}{4 (a-b)^2 d^{2/3}}+\frac{c \left(\sqrt{d} a+b\right) \log \left((b-x)^{2/3}+\sqrt[6]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+\sqrt[3]{d} (x-a)^{2/3}\right)}{4 (a-b)^2 d^{2/3}}+\frac{\left(\sqrt{d} a+b\right) \log \left((b-x)^{2/3}+\sqrt[6]{d} \sqrt[3]{x-a} \sqrt[3]{b-x}+\sqrt[3]{d} (x-a)^{2/3}\right)}{4 (a-b)^2 d^{2/3}}\right)}{\left((b-x)^2 (x-a)\right)^{2/3} \left(-d a^2+2 d x a+b^2-(d-1) x^2-2 b x\right)}",1,"(-3*(b - x)^2*((c - Sqrt[d])*Hypergeometric2F1[2/3, 1, 5/3, (b - x)/(Sqrt[d]*(-a + x))] + (c + Sqrt[d])*Hypergeometric2F1[2/3, 1, 5/3, (-b + x)/(Sqrt[d]*(-a + x))]))/(4*(a - b)*d*((b - x)^2*(-a + x))^(2/3))","C",1
3153,1,1379,1916,5.3278159,"\int \frac{x^2-c x^2 \left(\frac{b+a x}{d+c x}\right)^{3/2}}{a-b \sqrt{\frac{b+a x}{d+c x}}} \, dx","Integrate[(x^2 - c*x^2*((b + a*x)/(d + c*x))^(3/2))/(a - b*Sqrt[(b + a*x)/(d + c*x)]),x]","\frac{1}{24} (a d-b c) \left(-\frac{8 \left(a^2-b\right) \sqrt{\frac{b+a x}{d+c x}} (d+c x)^3}{a c^2 \left(a c-b^2\right) (a d-b c)}+\frac{8 (a b-c) (d+c x)^3}{c^3 \left(a c-b^2\right) (b c-a d)}+\frac{12 \left(4 b c d a^3-\left(3 d b^3+2 c^2 b^2+2 c^2 d\right) a^2+b^2 c \left(b^2+d\right) a+b^3 c^2\right) (d+c x)^2}{a c^3 \left(b^2-a c\right)^2 (a d-b c)}+\frac{12 \left(4 c d a^3-b \left(2 c^2+3 b d\right) a^2+b c \left(b^2-3 d\right) a+b^2 \left(c^2+2 b d\right)\right) \sqrt{\frac{b+a x}{d+c x}} (d+c x)^2}{a c^2 \left(b^2-a c\right)^2 (a d-b c)}+\frac{24 \left(\left(c^3+2 a^2 d c\right) b^6-3 a^3 d^2 b^5-6 a^3 c^2 d b^4+a^2 c \left(-a c^3-2 d c^2+8 a^2 d^2\right) b^3+6 a^4 c^3 d b^2-6 a^5 c^2 d^2 b+a^4 c^3 d^2\right) (d+c x)}{a^2 c^3 \left(a c-b^2\right)^3 (a d-b c)}+\frac{24 \left(-6 c^2 d^2 a^5-3 b^4 d^2 a^3+3 b c^2 d (2 a c+d) a^3-3 b^3 c d (2 a c+d) a^2+b^2 c \left(-a c^3-2 d c^2+8 a^2 d^2\right) a^2+b^5 \left(c^3+2 a^2 d c+a d^2\right)\right) \sqrt{\frac{b+a x}{d+c x}} (d+c x)}{a^2 c^2 \left(a c-b^2\right)^3 (a d-b c)}+\frac{24 \left(6 c^2 d^2 a^5+3 b^4 d^2 a^3-3 b c^2 d (2 a c+d) a^3+3 b^3 c d (2 a c+d) a^2+b^2 c \left(a c^3+2 d c^2-8 a^2 d^2\right) a^2-b^5 \left(c^3+2 a^2 d c+a d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{b+a x}{d+c x}}}{\sqrt{a}}\right)}{a^{5/2} c^{5/2} \left(b^2-a c\right)^3}-\frac{5 \left(a^2-b\right) \left(3 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{b+a x}{d+c x}}}{\sqrt{a}}\right) (b c-a d)^2+\sqrt{a} \sqrt{c} \sqrt{\frac{b+a x}{d+c x}} (d+c x) (-3 b c+2 a x c+5 a d)\right)}{a^{7/2} c^{5/2} \left(a c-b^2\right)}+\frac{18 \left(4 c d a^3-b \left(2 c^2+3 b d\right) a^2+b c \left(b^2-3 d\right) a+b^2 \left(c^2+2 b d\right)\right) \left(\sqrt{a} \sqrt{c} \sqrt{\frac{b+a x}{d+c x}} (d+c x)+(a d-b c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{b+a x}{d+c x}}}{\sqrt{a}}\right)\right)}{a^{5/2} c^{5/2} \left(b^2-a c\right)^2}-\frac{48 \left(b^3-a^3 c\right) \left(b^3-a^2 d\right)^2 \log \left(a-b \sqrt{\frac{b+a x}{d+c x}}\right)}{a^3 b \left(b^2-a c\right)^4}+\frac{24 \left(c^3 b^7+a^3 d^2 b^6-a^2 c \left(a c^3+2 d c^2+4 a^2 d^2\right) b^4+6 a^5 c^2 d^2 b^2+a^4 c^3 d (2 a c+d) b-4 a^6 c^3 d^2\right) \log \left(\sqrt{a}-\sqrt{c} \sqrt{\frac{b+a x}{d+c x}}\right)}{a^3 \left(b-\sqrt{a} \sqrt{c}\right)^4 \left(b+\sqrt{a} \sqrt{c}\right)^3 c^3}-\frac{24 \left(c^3 b^7+a^3 d^2 b^6-a^2 c \left(a c^3+2 d c^2+4 a^2 d^2\right) b^4+6 a^5 c^2 d^2 b^2+a^4 c^3 d (2 a c+d) b-4 a^6 c^3 d^2\right) \log \left(\sqrt{a}+\sqrt{c} \sqrt{\frac{b+a x}{d+c x}}\right)}{\left(b+\sqrt{a} \sqrt{c}\right)^4 \left(a^{3/2} c^{3/2}-a b c\right)^3}\right)","\frac{-3 a^2 c^2 x^2 b^6+6 c^3 x b^6+6 a^2 c d x b^6-2 a^3 c^2 x^3 b^5-3 a c^3 x^2 b^5+3 a^3 c d x^2 b^5-6 a^3 d^2 x b^5-6 a c^2 d x b^5+2 a^2 c^3 x^3 b^4+9 a^3 c^3 x^2 b^4+3 a^2 c^2 d x^2 b^4-18 a^3 c^2 d x b^4+4 a^4 c^3 x^3 b^3+3 a^2 c^4 x^2 b^3-9 a^4 c^2 d x^2 b^3-6 a^3 c^4 x b^3+18 a^4 c d^2 x b^3-6 a^2 c^3 d x b^3-4 a^3 c^4 x^3 b^2-6 a^4 c^4 x^2 b^2-3 a^3 c^3 d x^2 b^2+6 a^3 c^2 d^2 x b^2+24 a^4 c^3 d x b^2-2 a^5 c^4 x^3 b+6 a^5 c^3 d x^2 b-18 a^5 c^2 d^2 x b+2 a^4 c^5 x^3}{6 a^2 c^2 \left(a c-b^2\right)^3}+\frac{\sqrt{\frac{b+a x}{d+c x}} \left(15 c^2 d b^7+15 c^3 x b^7-4 a c d^2 b^6-10 a c^3 x^2 b^6+3 a^2 c^2 d b^6+3 a^2 c^3 x b^6-14 a c^2 d x b^6-3 a^2 d^3 b^5+8 a^2 c^3 x^3 b^5+4 a^3 c d^2 b^5-2 a^3 c^3 x^2 b^5+10 a^2 c^2 d x^2 b^5+12 a c^3 d b^5+12 a c^4 x b^5-a^2 c d^2 x b^5+2 a^3 c^2 d x b^5-15 a^4 d^3 b^4-8 a^4 c^3 x^3 b^4-40 a^2 c^2 d^2 b^4+8 a^2 c^4 x^2 b^4+2 a^4 c^2 d x^2 b^4-24 a^3 c^3 d b^4-24 a^3 c^4 x b^4-5 a^4 c d^2 x b^4-32 a^2 c^3 d x b^4+12 a^3 c d^3 b^3-16 a^3 c^4 x^3 b^3-8 a^4 c^2 d^2 b^3+16 a^4 c^4 x^2 b^3-8 a^3 c^3 d x^2 b^3-3 a^2 c^4 d b^3-3 a^2 c^5 x b^3+20 a^3 c^2 d^2 x b^3+8 a^4 c^3 d x b^3+48 a^5 c d^3 b^2+16 a^5 c^4 x^3 b^2-4 a^3 c^3 d^2 b^2+2 a^3 c^5 x^2 b^2-16 a^5 c^3 d x^2 b^2-3 a^4 c^4 d b^2-3 a^4 c^5 x b^2+16 a^5 c^2 d^2 x b^2-2 a^3 c^4 d x b^2+15 a^4 c^2 d^3 b+8 a^4 c^5 x^3 b+52 a^5 c^3 d^2 b-14 a^5 c^5 x^2 b-2 a^4 c^4 d x^2 b+5 a^4 c^3 d^2 x b+38 a^5 c^4 d x b-57 a^6 c^2 d^3-8 a^6 c^5 x^3+14 a^6 c^4 d x^2-35 a^6 c^3 d^2 x\right)}{24 a^3 c^2 \left(a c-b^2\right)^3}+\frac{\left(5 c^3 b^{10}+a^2 c^3 b^9-3 a c^2 d b^9+15 a c^4 b^8-a^2 c d^2 b^8+a^3 c^2 d b^8-9 a^3 c^4 b^7-a^3 d^3 b^7+3 a^4 c d^2 b^7-33 a^2 c^3 d b^7-5 a^2 c^5 b^6-5 a^5 d^3 b^6+13 a^3 c^2 d^2 b^6-a^4 c^3 d b^6-9 a^4 c^5 b^5+5 a^4 c d^3 b^5-11 a^5 c^2 d^2 b^5-13 a^3 c^4 d b^5+a^3 c^6 b^4+21 a^6 c d^3 b^4+33 a^4 c^3 d^2 b^4+39 a^5 c^4 d b^4+a^5 c^6 b^3-15 a^5 c^2 d^3 b^3+5 a^6 c^3 d^2 b^3+a^4 c^5 d b^3-35 a^7 c^2 d^3 b^2+3 a^5 c^4 d^2 b^2+9 a^6 c^5 d b^2-5 a^6 c^3 d^3 b-45 a^7 c^4 d^2 b+35 a^8 c^3 d^3\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{b+a x}{d+c x}}}{\sqrt{a}}\right)}{8 a^{7/2} c^{5/2} \left(a c-b^2\right)^4}+\frac{\left(c^4 b^9+a^3 c d^2 b^8-a c^3 d b^8-a^4 d^3 b^7-a^3 c^5 b^6-4 a^4 c^2 d^2 b^6-2 a^2 c^4 d b^6+4 a^5 c d^3 b^5+2 a^3 c^3 d^2 b^5+a^4 c^4 d b^5+6 a^5 c^3 d^2 b^4-6 a^6 c^2 d^3 b^3+a^4 c^4 d^2 b^3+2 a^5 c^5 d b^3-a^5 c^3 d^3 b^2-6 a^6 c^4 d^2 b^2+4 a^7 c^3 d^3 b\right) \log (d+c x)}{a^3 c^3 \left(a c-b^2\right)^4}+\frac{2 \left(c b^{10}-a d b^9-a^3 c^2 b^7-2 a^2 c d b^7+2 a^3 d^2 b^6+a^4 c d b^6+a^4 c d^2 b^4+2 a^5 c^2 d b^4-a^5 d^3 b^3-2 a^6 c d^2 b^3-a^7 c^2 d^2 b+a^8 c d^3\right) \log \left(a-b \sqrt{\frac{b+a x}{d+c x}}\right)}{a^3 b \left(a c-b^2\right)^4}",1,"((-(b*c) + a*d)*((24*(-6*a^3*b^4*c^2*d + 6*a^4*b^2*c^3*d - 3*a^3*b^5*d^2 - 6*a^5*b*c^2*d^2 + a^4*c^3*d^2 + b^6*(c^3 + 2*a^2*c*d) + a^2*b^3*c*(-(a*c^3) - 2*c^2*d + 8*a^2*d^2))*(d + c*x))/(a^2*c^3*(-b^2 + a*c)^3*(-(b*c) + a*d)) + (24*(-3*a^3*b^4*d^2 - 6*a^5*c^2*d^2 - 3*a^2*b^3*c*d*(2*a*c + d) + 3*a^3*b*c^2*d*(2*a*c + d) + b^5*(c^3 + 2*a^2*c*d + a*d^2) + a^2*b^2*c*(-(a*c^3) - 2*c^2*d + 8*a^2*d^2))*Sqrt[(b + a*x)/(d + c*x)]*(d + c*x))/(a^2*c^2*(-b^2 + a*c)^3*(-(b*c) + a*d)) + (12*(b^3*c^2 + 4*a^3*b*c*d + a*b^2*c*(b^2 + d) - a^2*(2*b^2*c^2 + 3*b^3*d + 2*c^2*d))*(d + c*x)^2)/(a*c^3*(b^2 - a*c)^2*(-(b*c) + a*d)) + (12*(a*b*c*(b^2 - 3*d) + 4*a^3*c*d + b^2*(c^2 + 2*b*d) - a^2*b*(2*c^2 + 3*b*d))*Sqrt[(b + a*x)/(d + c*x)]*(d + c*x)^2)/(a*c^2*(b^2 - a*c)^2*(-(b*c) + a*d)) + (8*(a*b - c)*(d + c*x)^3)/(c^3*(-b^2 + a*c)*(b*c - a*d)) - (8*(a^2 - b)*Sqrt[(b + a*x)/(d + c*x)]*(d + c*x)^3)/(a*c^2*(-b^2 + a*c)*(-(b*c) + a*d)) + (24*(3*a^3*b^4*d^2 + 6*a^5*c^2*d^2 + 3*a^2*b^3*c*d*(2*a*c + d) - 3*a^3*b*c^2*d*(2*a*c + d) - b^5*(c^3 + 2*a^2*c*d + a*d^2) + a^2*b^2*c*(a*c^3 + 2*c^2*d - 8*a^2*d^2))*ArcTanh[(Sqrt[c]*Sqrt[(b + a*x)/(d + c*x)])/Sqrt[a]])/(a^(5/2)*c^(5/2)*(b^2 - a*c)^3) - (5*(a^2 - b)*(Sqrt[a]*Sqrt[c]*Sqrt[(b + a*x)/(d + c*x)]*(d + c*x)*(-3*b*c + 5*a*d + 2*a*c*x) + 3*(b*c - a*d)^2*ArcTanh[(Sqrt[c]*Sqrt[(b + a*x)/(d + c*x)])/Sqrt[a]]))/(a^(7/2)*c^(5/2)*(-b^2 + a*c)) + (18*(a*b*c*(b^2 - 3*d) + 4*a^3*c*d + b^2*(c^2 + 2*b*d) - a^2*b*(2*c^2 + 3*b*d))*(Sqrt[a]*Sqrt[c]*Sqrt[(b + a*x)/(d + c*x)]*(d + c*x) + (-(b*c) + a*d)*ArcTanh[(Sqrt[c]*Sqrt[(b + a*x)/(d + c*x)])/Sqrt[a]]))/(a^(5/2)*c^(5/2)*(b^2 - a*c)^2) - (48*(b^3 - a^3*c)*(b^3 - a^2*d)^2*Log[a - b*Sqrt[(b + a*x)/(d + c*x)]])/(a^3*b*(b^2 - a*c)^4) + (24*(b^7*c^3 + a^3*b^6*d^2 + 6*a^5*b^2*c^2*d^2 - 4*a^6*c^3*d^2 + a^4*b*c^3*d*(2*a*c + d) - a^2*b^4*c*(a*c^3 + 2*c^2*d + 4*a^2*d^2))*Log[Sqrt[a] - Sqrt[c]*Sqrt[(b + a*x)/(d + c*x)]])/(a^3*(b - Sqrt[a]*Sqrt[c])^4*(b + Sqrt[a]*Sqrt[c])^3*c^3) - (24*(b^7*c^3 + a^3*b^6*d^2 + 6*a^5*b^2*c^2*d^2 - 4*a^6*c^3*d^2 + a^4*b*c^3*d*(2*a*c + d) - a^2*b^4*c*(a*c^3 + 2*c^2*d + 4*a^2*d^2))*Log[Sqrt[a] + Sqrt[c]*Sqrt[(b + a*x)/(d + c*x)]])/((b + Sqrt[a]*Sqrt[c])^4*(-(a*b*c) + a^(3/2)*c^(3/2))^3)))/24","A",1
3154,1,8468,3329,18.3784783,"\int \frac{(c_6+x c_7){}^2}{\sqrt{c_4+\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5}} \, dx","Integrate[(C[6] + x*C[7])^2/Sqrt[C[4] + Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5]],x]","\text{Result too large to show}","-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{c_3} \sqrt{c_4+\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5}}{\sqrt{\sqrt{c_3} c_4+\sqrt{c_1} c_5}}\right) (c_0 c_3-c_1 c_2) c_5 c_6{}^2}{2 \sqrt{c_1} c_3{}^{3/4} \left(\sqrt{c_3} c_4+\sqrt{c_1} c_5\right){}^{3/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{c_3} \sqrt{c_4+\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5}}{\sqrt{\sqrt{c_3} c_4-\sqrt{c_1} c_5}}\right) (c_0 c_3-c_1 c_2) c_5 \sqrt{\sqrt{c_3} c_4-\sqrt{c_1} c_5} c_6{}^2}{2 \sqrt{c_1} c_3{}^{3/4} \left(\sqrt{c_1} c_5-\sqrt{c_3} c_4\right){}^2}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{c_3} \sqrt{c_4+\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5}}{\sqrt{\sqrt{c_3} c_4-\sqrt{c_1} c_5}}\right) \sqrt{\sqrt{c_3} c_4-\sqrt{c_1} c_5} \left(3 c_2{}^2 c_5{}^2 c_1{}^{5/2}-6 c_2{}^2 \sqrt{c_3} c_4 c_5 c_1{}^2+2 c_0 c_2 c_3 c_5{}^2 c_1{}^{3/2}+4 c_0 c_2 c_3{}^{3/2} c_4 c_5 c_1-5 c_0{}^2 c_3{}^2 c_5{}^2 \sqrt{c_1}+2 c_0{}^2 c_3{}^{5/2} c_4 c_5\right) c_7 c_6}{8 c_1{}^{3/2} c_3{}^{7/4} \left(\sqrt{c_1} c_5-\sqrt{c_3} c_4\right){}^3}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{c_3} \sqrt{c_4+\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5}}{\sqrt{\sqrt{c_3} c_4+\sqrt{c_1} c_5}}\right) \left(-3 c_2{}^2 c_5{}^2 c_1{}^{5/2}-6 c_2{}^2 \sqrt{c_3} c_4 c_5 c_1{}^2-2 c_0 c_2 c_3 c_5{}^2 c_1{}^{3/2}+4 c_0 c_2 c_3{}^{3/2} c_4 c_5 c_1+5 c_0{}^2 c_3{}^2 c_5{}^2 \sqrt{c_1}+2 c_0{}^2 c_3{}^{5/2} c_4 c_5\right) c_7 c_6}{8 c_1{}^{3/2} c_3{}^{7/4} \left(\sqrt{c_3} c_4+\sqrt{c_1} c_5\right){}^{5/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{c_3} \sqrt{c_4+\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5}}{\sqrt{\sqrt{c_3} c_4-\sqrt{c_1} c_5}}\right) \sqrt{\sqrt{c_3} c_4-\sqrt{c_1} c_5} \left(-7 c_2{}^3 c_5{}^3 c_1{}^4+22 c_2{}^3 \sqrt{c_3} c_4 c_5{}^2 c_1{}^{7/2}-3 c_0 c_2{}^2 c_3 c_5{}^3 c_1{}^3-20 c_2{}^3 c_3 c_4{}^2 c_5 c_1{}^3+6 c_0 c_2{}^2 c_3{}^{3/2} c_4 c_5{}^2 c_1{}^{5/2}-5 c_0{}^2 c_2 c_3{}^2 c_5{}^3 c_1{}^2+12 c_0 c_2{}^2 c_3{}^2 c_4{}^2 c_5 c_1{}^2-14 c_0{}^2 c_2 c_3{}^{5/2} c_4 c_5{}^2 c_1{}^{3/2}+15 c_0{}^3 c_3{}^3 c_5{}^3 c_1+4 c_0{}^2 c_2 c_3{}^3 c_4{}^2 c_5 c_1-14 c_0{}^3 c_3{}^{7/2} c_4 c_5{}^2 \sqrt{c_1}+4 c_0{}^3 c_3{}^4 c_4{}^2 c_5\right) c_7{}^2}{64 c_1{}^{5/2} c_3{}^{11/4} \left(\sqrt{c_1} c_5-\sqrt{c_3} c_4\right){}^4}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{c_3} \sqrt{c_4+\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5}}{\sqrt{\sqrt{c_3} c_4+\sqrt{c_1} c_5}}\right) \left(-7 c_2{}^3 c_5{}^3 c_1{}^4-22 c_2{}^3 \sqrt{c_3} c_4 c_5{}^2 c_1{}^{7/2}-3 c_0 c_2{}^2 c_3 c_5{}^3 c_1{}^3-20 c_2{}^3 c_3 c_4{}^2 c_5 c_1{}^3-6 c_0 c_2{}^2 c_3{}^{3/2} c_4 c_5{}^2 c_1{}^{5/2}-5 c_0{}^2 c_2 c_3{}^2 c_5{}^3 c_1{}^2+12 c_0 c_2{}^2 c_3{}^2 c_4{}^2 c_5 c_1{}^2+14 c_0{}^2 c_2 c_3{}^{5/2} c_4 c_5{}^2 c_1{}^{3/2}+15 c_0{}^3 c_3{}^3 c_5{}^3 c_1+4 c_0{}^2 c_2 c_3{}^3 c_4{}^2 c_5 c_1+14 c_0{}^3 c_3{}^{7/2} c_4 c_5{}^2 \sqrt{c_1}+4 c_0{}^3 c_3{}^4 c_4{}^2 c_5\right) c_7{}^2}{64 c_1{}^{5/2} c_3{}^{11/4} \left(\sqrt{c_3} c_4+\sqrt{c_1} c_5\right){}^{7/2}}+\frac{\sqrt{c_4+\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5} \left(c_2 c_4 c_6{}^2+x c_3 c_4 c_6{}^2\right)}{c_3 c_4{}^2-c_1 c_5{}^2}+\frac{\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} \sqrt{c_4+\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5} \left(c_2 c_5 c_6{}^2+x c_3 c_5 c_6{}^2\right)}{c_1 c_5{}^2-c_3 c_4{}^2}+\frac{\sqrt{c_4+\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5} \left(2 x^2 c_3{}^3 c_6 c_7 c_4{}^3-2 c_2{}^2 c_3 c_6 c_7 c_4{}^3-c_1 c_2{}^2 c_5{}^2 c_6 c_7 c_4+3 x c_0 c_3{}^2 c_5{}^2 c_6 c_7 c_4-2 x^2 c_1 c_3{}^2 c_5{}^2 c_6 c_7 c_4+3 c_0 c_2 c_3 c_5{}^2 c_6 c_7 c_4-3 x c_1 c_2 c_3 c_5{}^2 c_6 c_7 c_4\right)}{2 c_3 \left(c_3 c_4{}^2-c_1 c_5{}^2\right){}^2}+\frac{\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} \sqrt{c_4+\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5} \left(-x c_0 c_4{}^2 c_5 c_6 c_7 c_3{}^3-4 x^2 c_1 c_4{}^2 c_5 c_6 c_7 c_3{}^3+4 x^2 c_1{}^2 c_5{}^3 c_6 c_7 c_3{}^2-5 x c_0 c_1 c_5{}^3 c_6 c_7 c_3{}^2-c_0 c_2 c_4{}^2 c_5 c_6 c_7 c_3{}^2+x c_1 c_2 c_4{}^2 c_5 c_6 c_7 c_3{}^2+5 x c_1{}^2 c_2 c_5{}^3 c_6 c_7 c_3-5 c_0 c_1 c_2 c_5{}^3 c_6 c_7 c_3+5 c_1 c_2{}^2 c_4{}^2 c_5 c_6 c_7 c_3+c_1{}^2 c_2{}^2 c_5{}^3 c_6 c_7\right)}{4 c_1 c_3 \left(c_3 c_4{}^2-c_1 c_5{}^2\right){}^2}+\frac{\sqrt{c_4+\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5} \left(32 x^3 c_1 c_3{}^5 c_7{}^2 c_4{}^5+32 c_1 c_2{}^3 c_3{}^2 c_7{}^2 c_4{}^5-x c_0{}^2 c_3{}^4 c_5{}^2 c_7{}^2 c_4{}^3-64 x^3 c_1{}^2 c_3{}^4 c_5{}^2 c_7{}^2 c_4{}^3+40 x^2 c_0 c_1 c_3{}^4 c_5{}^2 c_7{}^2 c_4{}^3-c_0{}^2 c_2 c_3{}^3 c_5{}^2 c_7{}^2 c_4{}^3-40 x^2 c_1{}^2 c_2 c_3{}^3 c_5{}^2 c_7{}^2 c_4{}^3-62 x c_0 c_1 c_2 c_3{}^3 c_5{}^2 c_7{}^2 c_4{}^3+63 x c_1{}^2 c_2{}^2 c_3{}^2 c_5{}^2 c_7{}^2 c_4{}^3-102 c_0 c_1 c_2{}^2 c_3{}^2 c_5{}^2 c_7{}^2 c_4{}^3+39 c_1{}^2 c_2{}^3 c_3 c_5{}^2 c_7{}^2 c_4{}^3-11 c_1{}^3 c_2{}^3 c_5{}^4 c_7{}^2 c_4+32 x^3 c_1{}^3 c_3{}^3 c_5{}^4 c_7{}^2 c_4-40 x^2 c_0 c_1{}^2 c_3{}^3 c_5{}^4 c_7{}^2 c_4+61 x c_0{}^2 c_1 c_3{}^3 c_5{}^4 c_7{}^2 c_4+40 x^2 c_1{}^3 c_2 c_3{}^2 c_5{}^4 c_7{}^2 c_4-58 x c_0 c_1{}^2 c_2 c_3{}^2 c_5{}^4 c_7{}^2 c_4+61 c_0{}^2 c_1 c_2 c_3{}^2 c_5{}^4 c_7{}^2 c_4-3 x c_1{}^3 c_2{}^2 c_3 c_5{}^4 c_7{}^2 c_4-18 c_0 c_1{}^2 c_2{}^2 c_3 c_5{}^4 c_7{}^2 c_4\right)}{96 c_1 c_3{}^2 \left(c_3 c_4{}^2-c_1 c_5{}^2\right){}^3}+\frac{\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} \sqrt{c_4+\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5} \left(6 x c_0{}^2 c_4{}^4 c_5 c_7{}^2 c_3{}^5-32 x^3 c_1{}^2 c_4{}^4 c_5 c_7{}^2 c_3{}^5-4 x^2 c_0 c_1 c_4{}^4 c_5 c_7{}^2 c_3{}^5+64 x^3 c_1{}^3 c_4{}^2 c_5{}^3 c_7{}^2 c_3{}^4-32 x^2 c_0 c_1{}^2 c_4{}^2 c_5{}^3 c_7{}^2 c_3{}^4-21 x c_0{}^2 c_1 c_4{}^2 c_5{}^3 c_7{}^2 c_3{}^4+6 c_0{}^2 c_2 c_4{}^4 c_5 c_7{}^2 c_3{}^4+4 x^2 c_1{}^2 c_2 c_4{}^4 c_5 c_7{}^2 c_3{}^4+4 x c_0 c_1 c_2 c_4{}^4 c_5 c_7{}^2 c_3{}^4-32 x^3 c_1{}^4 c_5{}^5 c_7{}^2 c_3{}^3+36 x^2 c_0 c_1{}^3 c_5{}^5 c_7{}^2 c_3{}^3-45 x c_0{}^2 c_1{}^2 c_5{}^5 c_7{}^2 c_3{}^3+32 x^2 c_1{}^3 c_2 c_4{}^2 c_5{}^3 c_7{}^2 c_3{}^3+74 x c_0 c_1{}^2 c_2 c_4{}^2 c_5{}^3 c_7{}^2 c_3{}^3-21 c_0{}^2 c_1 c_2 c_4{}^2 c_5{}^3 c_7{}^2 c_3{}^3-10 x c_1{}^2 c_2{}^2 c_4{}^4 c_5 c_7{}^2 c_3{}^3+8 c_0 c_1 c_2{}^2 c_4{}^4 c_5 c_7{}^2 c_3{}^3-36 x^2 c_1{}^4 c_2 c_5{}^5 c_7{}^2 c_3{}^2+42 x c_0 c_1{}^3 c_2 c_5{}^5 c_7{}^2 c_3{}^2-45 c_0{}^2 c_1{}^2 c_2 c_5{}^5 c_7{}^2 c_3{}^2-53 x c_1{}^3 c_2{}^2 c_4{}^2 c_5{}^3 c_7{}^2 c_3{}^2+106 c_0 c_1{}^2 c_2{}^2 c_4{}^2 c_5{}^3 c_7{}^2 c_3{}^2-46 c_1{}^2 c_2{}^3 c_4{}^4 c_5 c_7{}^2 c_3{}^2+3 x c_1{}^4 c_2{}^2 c_5{}^5 c_7{}^2 c_3+6 c_0 c_1{}^3 c_2{}^2 c_5{}^5 c_7{}^2 c_3-21 c_1{}^3 c_2{}^3 c_4{}^2 c_5{}^3 c_7{}^2 c_3+7 c_1{}^4 c_2{}^3 c_5{}^5 c_7{}^2\right)}{96 c_1{}^2 c_3{}^2 \left(c_3 c_4{}^2-c_1 c_5{}^2\right){}^3}",1,"Result too large to show","B",0